%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN489-1 : TPTP v9.0.0. Released v2.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n011.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:39:19 AM UTC 2025
% Result : Unsatisfiable 0.84s 1.02s
% Output : Proof 1.07s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SYN489-1 : TPTP v9.0.0. Released v2.1.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.13/0.34 % Computer : n011.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Fri Jun 20 12:37:12 EDT 2025
% 0.13/0.34 % CPUTime :
% 0.84/1.02 % SZS status Unsatisfiable
% 0.84/1.02 % SZS output start Proof
% 0.84/1.02 tff(c1_1_type, type, (
% 0.84/1.02 c1_1: $i > $o)).
% 0.84/1.02 tff(a2553_type, type, (
% 0.84/1.02 a2553: $i)).
% 0.84/1.02 tff(hskp23_type, type, (
% 0.84/1.02 hskp23: $o)).
% 0.84/1.02 tff(c0_1_type, type, (
% 0.84/1.02 c0_1: $i > $o)).
% 0.84/1.02 tff(a2614_type, type, (
% 0.84/1.02 a2614: $i)).
% 0.84/1.02 tff(hskp27_type, type, (
% 0.84/1.02 hskp27: $o)).
% 0.84/1.02 tff(a2526_type, type, (
% 0.84/1.02 a2526: $i)).
% 0.84/1.02 tff(hskp9_type, type, (
% 0.84/1.02 hskp9: $o)).
% 0.84/1.02 tff(a2517_type, type, (
% 0.84/1.02 a2517: $i)).
% 0.84/1.02 tff(a2522_type, type, (
% 0.84/1.02 a2522: $i)).
% 0.84/1.02 tff(a2521_type, type, (
% 0.84/1.02 a2521: $i)).
% 0.84/1.02 tff(hskp3_type, type, (
% 0.84/1.02 hskp3: $o)).
% 0.84/1.02 tff(c3_1_type, type, (
% 0.84/1.02 c3_1: $i > $o)).
% 0.84/1.02 tff(c2_1_type, type, (
% 0.84/1.02 c2_1: $i > $o)).
% 0.84/1.02 tff(ndr1_0_type, type, (
% 0.84/1.02 ndr1_0: $o)).
% 0.84/1.02 tff(a2519_type, type, (
% 0.84/1.02 a2519: $i)).
% 0.84/1.02 tff(hskp21_type, type, (
% 0.84/1.02 hskp21: $o)).
% 0.84/1.02 tff(hskp30_type, type, (
% 0.84/1.02 hskp30: $o)).
% 0.84/1.02 tff(hskp26_type, type, (
% 0.84/1.02 hskp26: $o)).
% 0.84/1.02 tff(hskp4_type, type, (
% 0.84/1.02 hskp4: $o)).
% 0.84/1.02 tff(a2558_type, type, (
% 0.84/1.02 a2558: $i)).
% 0.84/1.02 tff(a2601_type, type, (
% 0.84/1.02 a2601: $i)).
% 0.84/1.02 tff(a2556_type, type, (
% 0.84/1.02 a2556: $i)).
% 0.84/1.02 tff(a2551_type, type, (
% 0.84/1.02 a2551: $i)).
% 0.84/1.02 tff(hskp25_type, type, (
% 0.84/1.02 hskp25: $o)).
% 0.84/1.02 tff(a2541_type, type, (
% 0.84/1.02 a2541: $i)).
% 0.84/1.02 tff(hskp17_type, type, (
% 0.84/1.02 hskp17: $o)).
% 0.84/1.02 tff(hskp29_type, type, (
% 0.84/1.02 hskp29: $o)).
% 0.84/1.02 tff(a2531_type, type, (
% 0.84/1.02 a2531: $i)).
% 0.84/1.02 tff(hskp11_type, type, (
% 0.84/1.02 hskp11: $o)).
% 0.84/1.02 tff(hskp8_type, type, (
% 0.84/1.02 hskp8: $o)).
% 0.84/1.02 tff(hskp1_type, type, (
% 0.84/1.02 hskp1: $o)).
% 0.84/1.02 tff(a2545_type, type, (
% 0.84/1.02 a2545: $i)).
% 0.84/1.02 tff(hskp18_type, type, (
% 0.84/1.02 hskp18: $o)).
% 0.84/1.02 tff(a2597_type, type, (
% 0.84/1.02 a2597: $i)).
% 0.84/1.02 tff(a2536_type, type, (
% 0.84/1.02 a2536: $i)).
% 0.84/1.02 tff(hskp14_type, type, (
% 0.84/1.02 hskp14: $o)).
% 0.84/1.02 tff(hskp31_type, type, (
% 0.84/1.02 hskp31: $o)).
% 0.84/1.02 tff(a2525_type, type, (
% 0.84/1.02 a2525: $i)).
% 0.84/1.02 tff(a2564_type, type, (
% 0.84/1.02 a2564: $i)).
% 0.84/1.02 tff(hskp24_type, type, (
% 0.84/1.02 hskp24: $o)).
% 0.84/1.02 tff(a2555_type, type, (
% 0.84/1.02 a2555: $i)).
% 0.84/1.02 tff(a2552_type, type, (
% 0.84/1.02 a2552: $i)).
% 0.84/1.02 tff(hskp22_type, type, (
% 0.84/1.02 hskp22: $o)).
% 0.84/1.02 tff(hskp10_type, type, (
% 0.84/1.02 hskp10: $o)).
% 0.84/1.02 tff(a2518_type, type, (
% 0.84/1.02 a2518: $i)).
% 0.84/1.02 tff(hskp2_type, type, (
% 0.84/1.02 hskp2: $o)).
% 0.84/1.02 tff(hskp19_type, type, (
% 0.84/1.02 hskp19: $o)).
% 0.84/1.02 tff(a2516_type, type, (
% 0.84/1.02 a2516: $i)).
% 0.84/1.02 tff(hskp0_type, type, (
% 0.84/1.02 hskp0: $o)).
% 0.84/1.02 tff(a2540_type, type, (
% 0.84/1.02 a2540: $i)).
% 0.84/1.02 tff(hskp16_type, type, (
% 0.84/1.02 hskp16: $o)).
% 0.84/1.02 tff(a2528_type, type, (
% 0.84/1.02 a2528: $i)).
% 0.84/1.02 tff(a2549_type, type, (
% 0.84/1.02 a2549: $i)).
% 0.84/1.02 tff(hskp20_type, type, (
% 0.84/1.02 hskp20: $o)).
% 0.84/1.02 tff(a2548_type, type, (
% 0.84/1.02 a2548: $i)).
% 0.84/1.02 tff(a2533_type, type, (
% 0.84/1.02 a2533: $i)).
% 0.84/1.02 tff(hskp12_type, type, (
% 0.84/1.02 hskp12: $o)).
% 0.84/1.02 tff(hskp5_type, type, (
% 0.84/1.02 hskp5: $o)).
% 0.84/1.02 tff(1,assumption,(~hskp23), introduced(assumption)).
% 0.84/1.02 tff(2,plain,
% 0.84/1.02 ((hskp23 | hskp27) <=> (hskp23 | hskp27)),
% 0.84/1.02 inference(rewrite,[status(thm)],[])).
% 0.84/1.02 tff(3,axiom,(hskp23 | hskp27), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause2')).
% 0.84/1.02 tff(4,plain,
% 0.84/1.02 (hskp23 | hskp27),
% 0.84/1.02 inference(modus_ponens,[status(thm)],[3, 2])).
% 0.84/1.02 tff(5,plain,
% 0.84/1.02 (hskp27),
% 0.84/1.02 inference(unit_resolution,[status(thm)],[4, 1])).
% 0.84/1.02 tff(6,plain,
% 0.84/1.02 (((~hskp27) | c1_1(a2614)) <=> ((~hskp27) | c1_1(a2614))),
% 0.84/1.02 inference(rewrite,[status(thm)],[])).
% 0.84/1.02 tff(7,axiom,((~hskp27) | c1_1(a2614)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause53')).
% 0.84/1.02 tff(8,plain,
% 0.84/1.02 ((~hskp27) | c1_1(a2614)),
% 0.84/1.02 inference(modus_ponens,[status(thm)],[7, 6])).
% 0.84/1.02 tff(9,plain,
% 0.84/1.02 ((~hskp27) | c1_1(a2614)),
% 0.84/1.02 inference(modus_ponens,[status(thm)],[8, 6])).
% 0.84/1.02 tff(10,plain,
% 0.84/1.02 ((~hskp27) | c1_1(a2614)),
% 0.84/1.02 inference(modus_ponens,[status(thm)],[9, 6])).
% 0.84/1.02 tff(11,plain,
% 0.84/1.02 ((~hskp27) | c1_1(a2614)),
% 0.84/1.02 inference(modus_ponens,[status(thm)],[10, 6])).
% 0.84/1.02 tff(12,plain,
% 0.84/1.02 ((~hskp27) | c1_1(a2614)),
% 0.84/1.02 inference(modus_ponens,[status(thm)],[11, 6])).
% 0.84/1.02 tff(13,plain,
% 0.84/1.02 (c1_1(a2614)),
% 0.84/1.02 inference(unit_resolution,[status(thm)],[12, 5])).
% 0.84/1.02 tff(14,assumption,(~hskp9), introduced(assumption)).
% 0.84/1.02 tff(15,plain,
% 0.84/1.02 (((~hskp27) | (~c3_1(a2614))) <=> ((~hskp27) | (~c3_1(a2614)))),
% 0.84/1.02 inference(rewrite,[status(thm)],[])).
% 0.84/1.02 tff(16,plain,
% 0.84/1.02 (((~c3_1(a2614)) | (~hskp27)) <=> ((~hskp27) | (~c3_1(a2614)))),
% 0.84/1.02 inference(rewrite,[status(thm)],[])).
% 0.84/1.02 tff(17,axiom,((~c3_1(a2614)) | (~hskp27)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause90')).
% 0.84/1.02 tff(18,plain,
% 0.84/1.02 ((~hskp27) | (~c3_1(a2614))),
% 0.84/1.02 inference(modus_ponens,[status(thm)],[17, 16])).
% 0.84/1.02 tff(19,plain,
% 0.84/1.02 ((~hskp27) | (~c3_1(a2614))),
% 0.84/1.02 inference(modus_ponens,[status(thm)],[18, 15])).
% 0.84/1.02 tff(20,plain,
% 0.84/1.02 (~c3_1(a2614)),
% 0.84/1.02 inference(unit_resolution,[status(thm)],[19, 5])).
% 0.84/1.02 tff(21,plain,
% 0.84/1.02 (((~hskp27) | (~c2_1(a2614))) <=> ((~hskp27) | (~c2_1(a2614)))),
% 0.84/1.02 inference(rewrite,[status(thm)],[])).
% 0.84/1.02 tff(22,plain,
% 0.84/1.02 (((~c2_1(a2614)) | (~hskp27)) <=> ((~hskp27) | (~c2_1(a2614)))),
% 0.84/1.02 inference(rewrite,[status(thm)],[])).
% 0.84/1.02 tff(23,axiom,((~c2_1(a2614)) | (~hskp27)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause89')).
% 0.84/1.02 tff(24,plain,
% 0.84/1.02 ((~hskp27) | (~c2_1(a2614))),
% 0.84/1.02 inference(modus_ponens,[status(thm)],[23, 22])).
% 0.84/1.02 tff(25,plain,
% 0.84/1.02 ((~hskp27) | (~c2_1(a2614))),
% 0.84/1.02 inference(modus_ponens,[status(thm)],[24, 21])).
% 0.84/1.02 tff(26,plain,
% 0.84/1.02 (~c2_1(a2614)),
% 0.84/1.02 inference(unit_resolution,[status(thm)],[25, 5])).
% 0.84/1.02 tff(27,plain,
% 0.84/1.02 (^[V: $i, U: $i] : refl((hskp9 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V)) <=> (hskp9 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V)))),
% 0.84/1.02 inference(bind,[status(th)],[])).
% 0.84/1.02 tff(28,plain,
% 0.84/1.02 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V)) <=> ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))),
% 0.84/1.02 inference(quant_intro,[status(thm)],[27])).
% 0.84/1.02 tff(29,plain,
% 0.84/1.02 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V)) <=> ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))),
% 0.84/1.02 inference(rewrite,[status(thm)],[])).
% 0.84/1.02 tff(30,plain,
% 0.84/1.02 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c1_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U))))), (((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))), (((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U))))), ((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U))) | c0_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U))) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V))), ((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V)))), (((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V))), (((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V)))), ((((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))), ((((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V)))), (((((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp9) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V)) | hskp9))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V)) | hskp9) <=> (hskp9 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))), (((((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp9) <=> (hskp9 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))))),
% 0.84/1.02 inference(bind,[status(th)],[])).
% 0.84/1.02 tff(31,plain,
% 0.84/1.02 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp9) <=> ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))),
% 0.84/1.02 inference(quant_intro,[status(thm)],[30])).
% 0.84/1.02 tff(32,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp9)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause164')).
% 0.84/1.02 tff(33,plain,
% 0.84/1.02 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))),
% 0.84/1.02 inference(modus_ponens,[status(thm)],[32, 31])).
% 0.84/1.02 tff(34,plain,
% 0.84/1.02 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))),
% 0.84/1.02 inference(modus_ponens,[status(thm)],[33, 29])).
% 0.84/1.02 tff(35,plain,(
% 0.84/1.02 ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))),
% 0.84/1.02 inference(skolemize,[status(sab)],[34])).
% 0.84/1.02 tff(36,plain,
% 0.84/1.02 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))),
% 0.84/1.02 inference(modus_ponens,[status(thm)],[35, 28])).
% 0.84/1.02 tff(37,assumption,(hskp3), introduced(assumption)).
% 0.84/1.02 tff(38,plain,
% 0.84/1.02 (((~hskp3) | (~c3_1(a2519))) <=> ((~hskp3) | (~c3_1(a2519)))),
% 0.84/1.02 inference(rewrite,[status(thm)],[])).
% 0.84/1.02 tff(39,plain,
% 0.84/1.02 (((~c3_1(a2519)) | (~hskp3)) <=> ((~hskp3) | (~c3_1(a2519)))),
% 0.84/1.02 inference(rewrite,[status(thm)],[])).
% 0.84/1.02 tff(40,axiom,((~c3_1(a2519)) | (~hskp3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause129')).
% 0.84/1.02 tff(41,plain,
% 0.84/1.02 ((~hskp3) | (~c3_1(a2519))),
% 0.84/1.02 inference(modus_ponens,[status(thm)],[40, 39])).
% 0.84/1.02 tff(42,plain,
% 0.84/1.02 ((~hskp3) | (~c3_1(a2519))),
% 0.84/1.02 inference(modus_ponens,[status(thm)],[41, 38])).
% 0.84/1.02 tff(43,plain,
% 0.84/1.02 (~c3_1(a2519)),
% 0.84/1.02 inference(unit_resolution,[status(thm)],[42, 37])).
% 0.84/1.02 tff(44,plain,
% 0.84/1.02 (((~hskp3) | (~c2_1(a2519))) <=> ((~hskp3) | (~c2_1(a2519)))),
% 0.84/1.02 inference(rewrite,[status(thm)],[])).
% 0.84/1.02 tff(45,plain,
% 0.84/1.02 (((~c2_1(a2519)) | (~hskp3)) <=> ((~hskp3) | (~c2_1(a2519)))),
% 0.84/1.02 inference(rewrite,[status(thm)],[])).
% 0.84/1.02 tff(46,axiom,((~c2_1(a2519)) | (~hskp3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause128')).
% 0.84/1.02 tff(47,plain,
% 0.84/1.02 ((~hskp3) | (~c2_1(a2519))),
% 0.84/1.02 inference(modus_ponens,[status(thm)],[46, 45])).
% 0.84/1.02 tff(48,plain,
% 0.84/1.02 ((~hskp3) | (~c2_1(a2519))),
% 0.84/1.02 inference(modus_ponens,[status(thm)],[47, 44])).
% 0.84/1.02 tff(49,plain,
% 0.84/1.02 (~c2_1(a2519)),
% 0.84/1.02 inference(unit_resolution,[status(thm)],[48, 37])).
% 0.84/1.02 tff(50,plain,
% 0.84/1.02 (((~hskp3) | (~c0_1(a2519))) <=> ((~hskp3) | (~c0_1(a2519)))),
% 0.84/1.02 inference(rewrite,[status(thm)],[])).
% 0.84/1.02 tff(51,plain,
% 0.84/1.02 (((~c0_1(a2519)) | (~hskp3)) <=> ((~hskp3) | (~c0_1(a2519)))),
% 0.84/1.02 inference(rewrite,[status(thm)],[])).
% 0.84/1.02 tff(52,axiom,((~c0_1(a2519)) | (~hskp3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause127')).
% 0.84/1.02 tff(53,plain,
% 0.84/1.02 ((~hskp3) | (~c0_1(a2519))),
% 0.84/1.02 inference(modus_ponens,[status(thm)],[52, 51])).
% 0.84/1.02 tff(54,plain,
% 0.84/1.02 ((~hskp3) | (~c0_1(a2519))),
% 0.84/1.02 inference(modus_ponens,[status(thm)],[53, 50])).
% 0.84/1.02 tff(55,plain,
% 0.84/1.02 (~c0_1(a2519)),
% 0.84/1.02 inference(unit_resolution,[status(thm)],[54, 37])).
% 0.84/1.02 tff(56,assumption,(~c3_1(a2614)), introduced(assumption)).
% 0.84/1.02 tff(57,assumption,(~c2_1(a2614)), introduced(assumption)).
% 0.84/1.02 tff(58,assumption,(c1_1(a2614)), introduced(assumption)).
% 0.84/1.02 tff(59,assumption,(~ndr1_0), introduced(assumption)).
% 0.84/1.02 tff(60,plain,
% 0.84/1.02 ((ndr1_0 | (~hskp21)) <=> (ndr1_0 | (~hskp21))),
% 0.84/1.02 inference(rewrite,[status(thm)],[])).
% 0.84/1.02 tff(61,plain,
% 0.84/1.02 (((~hskp21) | ndr1_0) <=> (ndr1_0 | (~hskp21))),
% 0.84/1.02 inference(rewrite,[status(thm)],[])).
% 0.84/1.02 tff(62,axiom,((~hskp21) | ndr1_0), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause13')).
% 0.84/1.02 tff(63,plain,
% 0.84/1.02 (ndr1_0 | (~hskp21)),
% 0.84/1.02 inference(modus_ponens,[status(thm)],[62, 61])).
% 0.84/1.02 tff(64,plain,
% 0.84/1.02 (ndr1_0 | (~hskp21)),
% 0.84/1.02 inference(modus_ponens,[status(thm)],[63, 60])).
% 0.84/1.02 tff(65,plain,
% 0.84/1.02 (~hskp21),
% 0.84/1.02 inference(unit_resolution,[status(thm)],[64, 59])).
% 0.84/1.02 tff(66,plain,
% 0.84/1.02 ((ndr1_0 | (~hskp30)) <=> (ndr1_0 | (~hskp30))),
% 0.84/1.02 inference(rewrite,[status(thm)],[])).
% 0.84/1.02 tff(67,plain,
% 0.84/1.02 (((~hskp30) | ndr1_0) <=> (ndr1_0 | (~hskp30))),
% 0.84/1.02 inference(rewrite,[status(thm)],[])).
% 0.84/1.02 tff(68,axiom,((~hskp30) | ndr1_0), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause4')).
% 0.84/1.02 tff(69,plain,
% 0.84/1.02 (ndr1_0 | (~hskp30)),
% 0.84/1.02 inference(modus_ponens,[status(thm)],[68, 67])).
% 0.84/1.02 tff(70,plain,
% 0.84/1.02 (ndr1_0 | (~hskp30)),
% 0.84/1.02 inference(modus_ponens,[status(thm)],[69, 66])).
% 0.84/1.02 tff(71,plain,
% 0.84/1.02 (~hskp30),
% 0.84/1.02 inference(unit_resolution,[status(thm)],[70, 59])).
% 0.84/1.02 tff(72,plain,
% 0.84/1.02 ((ndr1_0 | (~hskp26)) <=> (ndr1_0 | (~hskp26))),
% 0.84/1.02 inference(rewrite,[status(thm)],[])).
% 0.84/1.02 tff(73,plain,
% 0.84/1.02 (((~hskp26) | ndr1_0) <=> (ndr1_0 | (~hskp26))),
% 0.84/1.02 inference(rewrite,[status(thm)],[])).
% 0.84/1.02 tff(74,axiom,((~hskp26) | ndr1_0), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause8')).
% 0.84/1.02 tff(75,plain,
% 0.84/1.02 (ndr1_0 | (~hskp26)),
% 0.84/1.02 inference(modus_ponens,[status(thm)],[74, 73])).
% 0.84/1.02 tff(76,plain,
% 0.84/1.02 (ndr1_0 | (~hskp26)),
% 0.84/1.02 inference(modus_ponens,[status(thm)],[75, 72])).
% 0.84/1.02 tff(77,plain,
% 0.84/1.02 (~hskp26),
% 0.84/1.02 inference(unit_resolution,[status(thm)],[76, 59])).
% 0.84/1.02 tff(78,plain,
% 0.84/1.02 ((hskp30 | hskp26 | hskp21) <=> (hskp30 | hskp26 | hskp21)),
% 0.84/1.02 inference(rewrite,[status(thm)],[])).
% 0.84/1.02 tff(79,plain,
% 0.84/1.02 (((hskp30 | hskp21) | hskp26) <=> (hskp30 | hskp26 | hskp21)),
% 0.84/1.02 inference(rewrite,[status(thm)],[])).
% 0.84/1.02 tff(80,plain,
% 0.84/1.02 ((hskp30 | hskp21) <=> (hskp30 | hskp21)),
% 0.84/1.02 inference(rewrite,[status(thm)],[])).
% 0.84/1.02 tff(81,plain,
% 0.84/1.02 (((hskp30 | hskp21) | hskp26) <=> ((hskp30 | hskp21) | hskp26)),
% 0.84/1.02 inference(monotonicity,[status(thm)],[80])).
% 0.84/1.02 tff(82,plain,
% 0.84/1.02 (((hskp30 | hskp21) | hskp26) <=> (hskp30 | hskp26 | hskp21)),
% 0.84/1.02 inference(transitivity,[status(thm)],[81, 79])).
% 0.84/1.02 tff(83,axiom,((hskp30 | hskp21) | hskp26), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause35')).
% 0.84/1.02 tff(84,plain,
% 0.84/1.02 (hskp30 | hskp26 | hskp21),
% 0.84/1.02 inference(modus_ponens,[status(thm)],[83, 82])).
% 0.84/1.02 tff(85,plain,
% 0.84/1.02 (hskp30 | hskp26 | hskp21),
% 0.84/1.02 inference(modus_ponens,[status(thm)],[84, 78])).
% 0.84/1.02 tff(86,plain,
% 0.84/1.02 (hskp30 | hskp26 | hskp21),
% 0.84/1.02 inference(modus_ponens,[status(thm)],[85, 78])).
% 0.84/1.02 tff(87,plain,
% 0.84/1.02 (hskp30 | hskp26 | hskp21),
% 0.84/1.02 inference(modus_ponens,[status(thm)],[86, 78])).
% 0.84/1.02 tff(88,plain,
% 0.84/1.02 (hskp30 | hskp26 | hskp21),
% 0.84/1.02 inference(modus_ponens,[status(thm)],[87, 78])).
% 0.84/1.02 tff(89,plain,
% 0.84/1.02 ($false),
% 0.84/1.02 inference(unit_resolution,[status(thm)],[88, 77, 71, 65])).
% 0.84/1.02 tff(90,plain,(ndr1_0), inference(lemma,lemma(discharge,[]))).
% 0.84/1.02 tff(91,plain,
% 0.84/1.02 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp9 | c2_1(a2614) | c3_1(a2614) | c0_1(a2519) | c2_1(a2519) | c3_1(a2519) | (~ndr1_0) | (~c1_1(a2614)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp9 | c2_1(a2614) | c3_1(a2614) | c0_1(a2519) | c2_1(a2519) | c3_1(a2519) | (~ndr1_0) | (~c1_1(a2614)))),
% 0.84/1.02 inference(rewrite,[status(thm)],[])).
% 0.84/1.02 tff(92,plain,
% 0.84/1.02 ((hskp9 | (~ndr1_0) | c3_1(a2614) | c2_1(a2614) | (~c1_1(a2614)) | c3_1(a2519) | c0_1(a2519) | c2_1(a2519)) <=> (hskp9 | c2_1(a2614) | c3_1(a2614) | c0_1(a2519) | c2_1(a2519) | c3_1(a2519) | (~ndr1_0) | (~c1_1(a2614)))),
% 0.84/1.02 inference(rewrite,[status(thm)],[])).
% 0.84/1.02 tff(93,plain,
% 0.84/1.02 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp9 | (~ndr1_0) | c3_1(a2614) | c2_1(a2614) | (~c1_1(a2614)) | c3_1(a2519) | c0_1(a2519) | c2_1(a2519))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp9 | c2_1(a2614) | c3_1(a2614) | c0_1(a2519) | c2_1(a2519) | c3_1(a2519) | (~ndr1_0) | (~c1_1(a2614))))),
% 0.84/1.02 inference(monotonicity,[status(thm)],[92])).
% 0.84/1.02 tff(94,plain,
% 0.84/1.02 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp9 | (~ndr1_0) | c3_1(a2614) | c2_1(a2614) | (~c1_1(a2614)) | c3_1(a2519) | c0_1(a2519) | c2_1(a2519))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp9 | c2_1(a2614) | c3_1(a2614) | c0_1(a2519) | c2_1(a2519) | c3_1(a2519) | (~ndr1_0) | (~c1_1(a2614)))),
% 0.84/1.02 inference(transitivity,[status(thm)],[93, 91])).
% 0.84/1.02 tff(95,plain,
% 0.84/1.02 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp9 | (~ndr1_0) | c3_1(a2614) | c2_1(a2614) | (~c1_1(a2614)) | c3_1(a2519) | c0_1(a2519) | c2_1(a2519))),
% 0.84/1.02 inference(quant_inst,[status(thm)],[])).
% 0.84/1.02 tff(96,plain,
% 0.84/1.02 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp9 | c2_1(a2614) | c3_1(a2614) | c0_1(a2519) | c2_1(a2519) | c3_1(a2519) | (~ndr1_0) | (~c1_1(a2614))),
% 0.84/1.02 inference(modus_ponens,[status(thm)],[95, 94])).
% 0.84/1.02 tff(97,plain,
% 0.84/1.02 ($false),
% 0.84/1.02 inference(unit_resolution,[status(thm)],[96, 90, 14, 58, 57, 56, 55, 49, 43, 36])).
% 0.84/1.02 tff(98,plain,((~hskp3) | hskp9 | (~c1_1(a2614)) | c2_1(a2614) | c3_1(a2614)), inference(lemma,lemma(discharge,[]))).
% 0.84/1.02 tff(99,plain,
% 0.84/1.02 (~hskp3),
% 0.84/1.02 inference(unit_resolution,[status(thm)],[98, 13, 14, 26, 20])).
% 0.84/1.02 tff(100,plain,
% 0.84/1.02 (^[V: $i, U: $i] : refl((hskp3 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V))) <=> (hskp3 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V))))),
% 0.84/1.02 inference(bind,[status(th)],[])).
% 0.84/1.02 tff(101,plain,
% 0.84/1.02 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)))),
% 0.84/1.02 inference(quant_intro,[status(thm)],[100])).
% 0.84/1.02 tff(102,plain,
% 0.84/1.02 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)))),
% 0.84/1.02 inference(rewrite,[status(thm)],[])).
% 0.84/1.02 tff(103,plain,
% 0.84/1.02 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c3_1(U)) | (~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)))), rewrite((((~c3_1(U)) | (~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c0_1(V))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c0_1(V)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c0_1(V))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c0_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c2_1(V))) | hskp3) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V))) | hskp3))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V))) | hskp3) <=> (hskp3 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c2_1(V))) | hskp3) <=> (hskp3 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)))))),
% 0.84/1.02 inference(bind,[status(th)],[])).
% 0.84/1.02 tff(104,plain,
% 0.84/1.02 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c2_1(V))) | hskp3) <=> ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)))),
% 0.84/1.02 inference(quant_intro,[status(thm)],[103])).
% 0.84/1.02 tff(105,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c2_1(V))) | hskp3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause194')).
% 0.84/1.02 tff(106,plain,
% 0.84/1.02 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)))),
% 0.84/1.02 inference(modus_ponens,[status(thm)],[105, 104])).
% 0.84/1.02 tff(107,plain,
% 0.84/1.02 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)))),
% 0.84/1.02 inference(modus_ponens,[status(thm)],[106, 102])).
% 0.84/1.02 tff(108,plain,(
% 0.84/1.02 ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)))),
% 0.84/1.02 inference(skolemize,[status(sab)],[107])).
% 0.84/1.02 tff(109,plain,
% 0.84/1.02 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)))),
% 0.84/1.02 inference(modus_ponens,[status(thm)],[108, 101])).
% 0.84/1.02 tff(110,plain,
% 0.84/1.02 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp9 | c2_1(a2614) | c3_1(a2614) | (~ndr1_0) | c0_1(a2614) | (~c1_1(a2614)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp9 | c2_1(a2614) | c3_1(a2614) | (~ndr1_0) | c0_1(a2614) | (~c1_1(a2614)))),
% 0.84/1.02 inference(rewrite,[status(thm)],[])).
% 0.84/1.02 tff(111,plain,
% 0.84/1.02 ((hskp9 | (~ndr1_0) | c3_1(a2614) | c2_1(a2614) | (~c1_1(a2614)) | c3_1(a2614) | c0_1(a2614) | c2_1(a2614)) <=> (hskp9 | c2_1(a2614) | c3_1(a2614) | (~ndr1_0) | c0_1(a2614) | (~c1_1(a2614)))),
% 0.84/1.02 inference(rewrite,[status(thm)],[])).
% 0.84/1.02 tff(112,plain,
% 0.84/1.02 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp9 | (~ndr1_0) | c3_1(a2614) | c2_1(a2614) | (~c1_1(a2614)) | c3_1(a2614) | c0_1(a2614) | c2_1(a2614))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp9 | c2_1(a2614) | c3_1(a2614) | (~ndr1_0) | c0_1(a2614) | (~c1_1(a2614))))),
% 0.84/1.02 inference(monotonicity,[status(thm)],[111])).
% 0.84/1.02 tff(113,plain,
% 0.84/1.02 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp9 | (~ndr1_0) | c3_1(a2614) | c2_1(a2614) | (~c1_1(a2614)) | c3_1(a2614) | c0_1(a2614) | c2_1(a2614))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp9 | c2_1(a2614) | c3_1(a2614) | (~ndr1_0) | c0_1(a2614) | (~c1_1(a2614)))),
% 0.84/1.02 inference(transitivity,[status(thm)],[112, 110])).
% 0.84/1.02 tff(114,plain,
% 0.84/1.02 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp9 | (~ndr1_0) | c3_1(a2614) | c2_1(a2614) | (~c1_1(a2614)) | c3_1(a2614) | c0_1(a2614) | c2_1(a2614))),
% 0.84/1.02 inference(quant_inst,[status(thm)],[])).
% 0.84/1.02 tff(115,plain,
% 0.84/1.02 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp9 | c2_1(a2614) | c3_1(a2614) | (~ndr1_0) | c0_1(a2614) | (~c1_1(a2614))),
% 0.84/1.02 inference(modus_ponens,[status(thm)],[114, 113])).
% 0.84/1.02 tff(116,plain,
% 0.84/1.02 (c0_1(a2614)),
% 0.84/1.02 inference(unit_resolution,[status(thm)],[115, 90, 14, 13, 26, 20, 36])).
% 0.84/1.02 tff(117,plain,
% 0.84/1.02 (^[U: $i] : refl((hskp9 | hskp4 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U))) <=> (hskp9 | hskp4 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U))))),
% 0.84/1.02 inference(bind,[status(th)],[])).
% 0.84/1.02 tff(118,plain,
% 0.84/1.02 (![U: $i] : (hskp9 | hskp4 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp9 | hskp4 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))),
% 0.84/1.02 inference(quant_intro,[status(thm)],[117])).
% 0.84/1.02 tff(119,plain,
% 0.84/1.02 (![U: $i] : (hskp9 | hskp4 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp9 | hskp4 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))),
% 0.84/1.02 inference(rewrite,[status(thm)],[])).
% 0.84/1.02 tff(120,plain,
% 0.84/1.02 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c0_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) <=> (((~ndr1_0) | (~c0_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U))))), (((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))), (((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U))))), ((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp9) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U))) | hskp9))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U))) | hskp9) <=> (hskp9 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))), ((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp9) <=> (hskp9 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U))))), (((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp9) | hskp4) <=> ((hskp9 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U))) | hskp4))), rewrite(((hskp9 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U))) | hskp4) <=> (hskp9 | hskp4 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))), (((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp9) | hskp4) <=> (hskp9 | hskp4 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))))),
% 0.84/1.02 inference(bind,[status(th)],[])).
% 0.84/1.02 tff(121,plain,
% 0.84/1.02 (![U: $i] : ((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp9) | hskp4) <=> ![U: $i] : (hskp9 | hskp4 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))),
% 0.84/1.02 inference(quant_intro,[status(thm)],[120])).
% 0.84/1.02 tff(122,axiom,(![U: $i] : ((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp9) | hskp4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause147')).
% 0.84/1.02 tff(123,plain,
% 0.84/1.02 (![U: $i] : (hskp9 | hskp4 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))),
% 0.84/1.02 inference(modus_ponens,[status(thm)],[122, 121])).
% 0.84/1.02 tff(124,plain,
% 0.84/1.02 (![U: $i] : (hskp9 | hskp4 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))),
% 0.84/1.02 inference(modus_ponens,[status(thm)],[123, 119])).
% 0.84/1.02 tff(125,plain,(
% 0.84/1.02 ![U: $i] : (hskp9 | hskp4 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))),
% 0.84/1.02 inference(skolemize,[status(sab)],[124])).
% 0.84/1.02 tff(126,plain,
% 0.84/1.02 (![U: $i] : (hskp9 | hskp4 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))),
% 0.84/1.02 inference(modus_ponens,[status(thm)],[125, 118])).
% 0.84/1.02 tff(127,plain,
% 0.84/1.02 (((~![U: $i] : (hskp9 | hskp4 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp9 | hskp4 | c2_1(a2614) | c3_1(a2614) | (~ndr1_0) | (~c0_1(a2614)))) <=> ((~![U: $i] : (hskp9 | hskp4 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | hskp9 | hskp4 | c2_1(a2614) | c3_1(a2614) | (~ndr1_0) | (~c0_1(a2614)))),
% 0.84/1.02 inference(rewrite,[status(thm)],[])).
% 0.84/1.02 tff(128,plain,
% 0.84/1.02 ((hskp9 | hskp4 | (~ndr1_0) | c3_1(a2614) | c2_1(a2614) | (~c0_1(a2614))) <=> (hskp9 | hskp4 | c2_1(a2614) | c3_1(a2614) | (~ndr1_0) | (~c0_1(a2614)))),
% 0.84/1.02 inference(rewrite,[status(thm)],[])).
% 0.84/1.02 tff(129,plain,
% 0.84/1.02 (((~![U: $i] : (hskp9 | hskp4 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp9 | hskp4 | (~ndr1_0) | c3_1(a2614) | c2_1(a2614) | (~c0_1(a2614)))) <=> ((~![U: $i] : (hskp9 | hskp4 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp9 | hskp4 | c2_1(a2614) | c3_1(a2614) | (~ndr1_0) | (~c0_1(a2614))))),
% 0.84/1.02 inference(monotonicity,[status(thm)],[128])).
% 0.84/1.02 tff(130,plain,
% 0.84/1.02 (((~![U: $i] : (hskp9 | hskp4 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp9 | hskp4 | (~ndr1_0) | c3_1(a2614) | c2_1(a2614) | (~c0_1(a2614)))) <=> ((~![U: $i] : (hskp9 | hskp4 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | hskp9 | hskp4 | c2_1(a2614) | c3_1(a2614) | (~ndr1_0) | (~c0_1(a2614)))),
% 0.84/1.02 inference(transitivity,[status(thm)],[129, 127])).
% 0.84/1.02 tff(131,plain,
% 0.84/1.02 ((~![U: $i] : (hskp9 | hskp4 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp9 | hskp4 | (~ndr1_0) | c3_1(a2614) | c2_1(a2614) | (~c0_1(a2614)))),
% 0.84/1.02 inference(quant_inst,[status(thm)],[])).
% 0.84/1.02 tff(132,plain,
% 0.84/1.02 ((~![U: $i] : (hskp9 | hskp4 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | hskp9 | hskp4 | c2_1(a2614) | c3_1(a2614) | (~ndr1_0) | (~c0_1(a2614))),
% 0.84/1.02 inference(modus_ponens,[status(thm)],[131, 130])).
% 0.84/1.02 tff(133,plain,
% 0.84/1.02 (hskp4 | (~c0_1(a2614))),
% 0.84/1.02 inference(unit_resolution,[status(thm)],[132, 90, 14, 26, 20, 126])).
% 0.84/1.02 tff(134,plain,
% 0.84/1.02 (hskp4),
% 0.84/1.02 inference(unit_resolution,[status(thm)],[133, 116])).
% 0.84/1.02 tff(135,plain,
% 0.84/1.02 (((~hskp4) | c3_1(a2521)) <=> ((~hskp4) | c3_1(a2521))),
% 0.84/1.02 inference(rewrite,[status(thm)],[])).
% 0.84/1.02 tff(136,axiom,((~hskp4) | c3_1(a2521)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause86')).
% 0.84/1.02 tff(137,plain,
% 0.84/1.02 ((~hskp4) | c3_1(a2521)),
% 0.84/1.02 inference(modus_ponens,[status(thm)],[136, 135])).
% 0.84/1.02 tff(138,plain,
% 0.84/1.02 ((~hskp4) | c3_1(a2521)),
% 0.84/1.02 inference(modus_ponens,[status(thm)],[137, 135])).
% 0.84/1.02 tff(139,plain,
% 0.84/1.02 ((~hskp4) | c3_1(a2521)),
% 0.84/1.02 inference(modus_ponens,[status(thm)],[138, 135])).
% 0.84/1.02 tff(140,plain,
% 0.84/1.02 ((~hskp4) | c3_1(a2521)),
% 0.84/1.02 inference(modus_ponens,[status(thm)],[139, 135])).
% 0.84/1.02 tff(141,plain,
% 0.84/1.02 ((~hskp4) | c3_1(a2521)),
% 0.84/1.02 inference(modus_ponens,[status(thm)],[140, 135])).
% 0.84/1.02 tff(142,plain,
% 0.84/1.02 (c3_1(a2521)),
% 0.84/1.02 inference(unit_resolution,[status(thm)],[141, 134])).
% 0.84/1.02 tff(143,plain,
% 0.84/1.02 (((~hskp4) | c2_1(a2521)) <=> ((~hskp4) | c2_1(a2521))),
% 0.84/1.02 inference(rewrite,[status(thm)],[])).
% 0.84/1.02 tff(144,axiom,((~hskp4) | c2_1(a2521)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause85')).
% 0.84/1.02 tff(145,plain,
% 0.84/1.02 ((~hskp4) | c2_1(a2521)),
% 0.84/1.02 inference(modus_ponens,[status(thm)],[144, 143])).
% 0.84/1.02 tff(146,plain,
% 0.84/1.02 ((~hskp4) | c2_1(a2521)),
% 0.84/1.02 inference(modus_ponens,[status(thm)],[145, 143])).
% 0.84/1.02 tff(147,plain,
% 0.84/1.02 ((~hskp4) | c2_1(a2521)),
% 0.84/1.02 inference(modus_ponens,[status(thm)],[146, 143])).
% 0.84/1.02 tff(148,plain,
% 0.84/1.02 ((~hskp4) | c2_1(a2521)),
% 0.84/1.02 inference(modus_ponens,[status(thm)],[147, 143])).
% 0.84/1.02 tff(149,plain,
% 0.84/1.02 ((~hskp4) | c2_1(a2521)),
% 0.84/1.02 inference(modus_ponens,[status(thm)],[148, 143])).
% 0.84/1.02 tff(150,plain,
% 0.84/1.02 (c2_1(a2521)),
% 0.84/1.02 inference(unit_resolution,[status(thm)],[149, 134])).
% 0.84/1.02 tff(151,assumption,(~hskp30), introduced(assumption)).
% 0.84/1.02 tff(152,assumption,(~c0_1(a2526)), introduced(assumption)).
% 0.84/1.02 tff(153,plain,
% 0.84/1.02 (^[U: $i] : refl((hskp30 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) <=> (hskp30 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))))),
% 0.84/1.02 inference(bind,[status(th)],[])).
% 0.84/1.02 tff(154,plain,
% 0.84/1.02 (![U: $i] : (hskp30 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp30 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 0.84/1.02 inference(quant_intro,[status(thm)],[153])).
% 0.84/1.02 tff(155,plain,
% 0.84/1.02 (![U: $i] : (hskp30 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp30 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 0.84/1.02 inference(rewrite,[status(thm)],[])).
% 0.84/1.02 tff(156,plain,
% 0.84/1.02 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp30) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) | hskp30))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) | hskp30) <=> (hskp30 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp30) <=> (hskp30 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp30) | hskp9) <=> ((hskp30 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) | hskp9))), rewrite(((hskp30 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) | hskp9) <=> (hskp30 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp30) | hskp9) <=> (hskp30 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))))),
% 0.84/1.02 inference(bind,[status(th)],[])).
% 0.84/1.02 tff(157,plain,
% 0.84/1.02 (![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp30) | hskp9) <=> ![U: $i] : (hskp30 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 0.84/1.02 inference(quant_intro,[status(thm)],[156])).
% 0.84/1.02 tff(158,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp30) | hskp9)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause155')).
% 0.84/1.02 tff(159,plain,
% 0.84/1.02 (![U: $i] : (hskp30 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 0.84/1.02 inference(modus_ponens,[status(thm)],[158, 157])).
% 0.84/1.02 tff(160,plain,
% 0.84/1.02 (![U: $i] : (hskp30 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 0.84/1.02 inference(modus_ponens,[status(thm)],[159, 155])).
% 0.84/1.02 tff(161,plain,(
% 0.84/1.02 ![U: $i] : (hskp30 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 0.84/1.02 inference(skolemize,[status(sab)],[160])).
% 0.84/1.02 tff(162,plain,
% 0.84/1.02 (![U: $i] : (hskp30 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 0.84/1.02 inference(modus_ponens,[status(thm)],[161, 154])).
% 0.84/1.02 tff(163,assumption,(hskp21), introduced(assumption)).
% 0.84/1.02 tff(164,plain,
% 0.84/1.02 (((~hskp21) | (~c2_1(a2551))) <=> ((~hskp21) | (~c2_1(a2551)))),
% 0.84/1.02 inference(rewrite,[status(thm)],[])).
% 0.84/1.02 tff(165,plain,
% 0.84/1.02 (((~c2_1(a2551)) | (~hskp21)) <=> ((~hskp21) | (~c2_1(a2551)))),
% 0.84/1.02 inference(rewrite,[status(thm)],[])).
% 0.84/1.02 tff(166,axiom,((~c2_1(a2551)) | (~hskp21)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause99')).
% 0.84/1.02 tff(167,plain,
% 0.84/1.02 ((~hskp21) | (~c2_1(a2551))),
% 0.84/1.02 inference(modus_ponens,[status(thm)],[166, 165])).
% 0.84/1.02 tff(168,plain,
% 0.84/1.02 ((~hskp21) | (~c2_1(a2551))),
% 0.84/1.02 inference(modus_ponens,[status(thm)],[167, 164])).
% 0.84/1.02 tff(169,plain,
% 0.84/1.02 (~c2_1(a2551)),
% 0.84/1.02 inference(unit_resolution,[status(thm)],[168, 163])).
% 0.84/1.02 tff(170,plain,
% 0.84/1.02 (((~hskp21) | c1_1(a2551)) <=> ((~hskp21) | c1_1(a2551))),
% 0.84/1.02 inference(rewrite,[status(thm)],[])).
% 0.84/1.02 tff(171,axiom,((~hskp21) | c1_1(a2551)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause62')).
% 0.84/1.02 tff(172,plain,
% 0.84/1.02 ((~hskp21) | c1_1(a2551)),
% 0.84/1.02 inference(modus_ponens,[status(thm)],[171, 170])).
% 0.84/1.02 tff(173,plain,
% 0.84/1.02 ((~hskp21) | c1_1(a2551)),
% 0.84/1.02 inference(modus_ponens,[status(thm)],[172, 170])).
% 0.84/1.02 tff(174,plain,
% 0.84/1.02 ((~hskp21) | c1_1(a2551)),
% 0.84/1.02 inference(modus_ponens,[status(thm)],[173, 170])).
% 0.84/1.02 tff(175,plain,
% 0.84/1.02 ((~hskp21) | c1_1(a2551)),
% 0.84/1.02 inference(modus_ponens,[status(thm)],[174, 170])).
% 0.84/1.02 tff(176,plain,
% 0.84/1.02 ((~hskp21) | c1_1(a2551)),
% 0.84/1.02 inference(modus_ponens,[status(thm)],[175, 170])).
% 0.84/1.02 tff(177,plain,
% 0.84/1.02 (c1_1(a2551)),
% 0.84/1.02 inference(unit_resolution,[status(thm)],[176, 163])).
% 0.84/1.02 tff(178,plain,
% 0.84/1.02 (((~hskp21) | c0_1(a2551)) <=> ((~hskp21) | c0_1(a2551))),
% 0.84/1.02 inference(rewrite,[status(thm)],[])).
% 0.84/1.02 tff(179,axiom,((~hskp21) | c0_1(a2551)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause61')).
% 0.84/1.02 tff(180,plain,
% 0.84/1.02 ((~hskp21) | c0_1(a2551)),
% 0.84/1.03 inference(modus_ponens,[status(thm)],[179, 178])).
% 0.84/1.03 tff(181,plain,
% 0.84/1.03 ((~hskp21) | c0_1(a2551)),
% 0.84/1.03 inference(modus_ponens,[status(thm)],[180, 178])).
% 0.84/1.03 tff(182,plain,
% 0.84/1.03 ((~hskp21) | c0_1(a2551)),
% 0.84/1.03 inference(modus_ponens,[status(thm)],[181, 178])).
% 0.84/1.03 tff(183,plain,
% 0.84/1.03 ((~hskp21) | c0_1(a2551)),
% 0.84/1.03 inference(modus_ponens,[status(thm)],[182, 178])).
% 0.84/1.03 tff(184,plain,
% 0.84/1.03 ((~hskp21) | c0_1(a2551)),
% 0.84/1.03 inference(modus_ponens,[status(thm)],[183, 178])).
% 0.84/1.03 tff(185,plain,
% 0.84/1.03 (c0_1(a2551)),
% 0.84/1.03 inference(unit_resolution,[status(thm)],[184, 163])).
% 0.84/1.03 tff(186,plain,
% 0.84/1.03 (((~![U: $i] : (hskp30 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp30 | hskp9 | c2_1(a2551) | (~ndr1_0) | (~c0_1(a2551)) | (~c1_1(a2551)))) <=> ((~![U: $i] : (hskp30 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp30 | hskp9 | c2_1(a2551) | (~ndr1_0) | (~c0_1(a2551)) | (~c1_1(a2551)))),
% 0.84/1.03 inference(rewrite,[status(thm)],[])).
% 0.84/1.03 tff(187,plain,
% 0.84/1.03 ((hskp30 | hskp9 | (~ndr1_0) | c2_1(a2551) | (~c1_1(a2551)) | (~c0_1(a2551))) <=> (hskp30 | hskp9 | c2_1(a2551) | (~ndr1_0) | (~c0_1(a2551)) | (~c1_1(a2551)))),
% 0.84/1.03 inference(rewrite,[status(thm)],[])).
% 0.84/1.03 tff(188,plain,
% 0.84/1.03 (((~![U: $i] : (hskp30 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp30 | hskp9 | (~ndr1_0) | c2_1(a2551) | (~c1_1(a2551)) | (~c0_1(a2551)))) <=> ((~![U: $i] : (hskp30 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp30 | hskp9 | c2_1(a2551) | (~ndr1_0) | (~c0_1(a2551)) | (~c1_1(a2551))))),
% 0.84/1.03 inference(monotonicity,[status(thm)],[187])).
% 0.84/1.03 tff(189,plain,
% 0.84/1.03 (((~![U: $i] : (hskp30 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp30 | hskp9 | (~ndr1_0) | c2_1(a2551) | (~c1_1(a2551)) | (~c0_1(a2551)))) <=> ((~![U: $i] : (hskp30 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp30 | hskp9 | c2_1(a2551) | (~ndr1_0) | (~c0_1(a2551)) | (~c1_1(a2551)))),
% 0.84/1.03 inference(transitivity,[status(thm)],[188, 186])).
% 0.84/1.03 tff(190,plain,
% 0.84/1.03 ((~![U: $i] : (hskp30 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp30 | hskp9 | (~ndr1_0) | c2_1(a2551) | (~c1_1(a2551)) | (~c0_1(a2551)))),
% 0.84/1.03 inference(quant_inst,[status(thm)],[])).
% 0.84/1.03 tff(191,plain,
% 0.84/1.03 ((~![U: $i] : (hskp30 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp30 | hskp9 | c2_1(a2551) | (~ndr1_0) | (~c0_1(a2551)) | (~c1_1(a2551))),
% 0.84/1.03 inference(modus_ponens,[status(thm)],[190, 189])).
% 0.84/1.03 tff(192,plain,
% 0.84/1.03 (hskp9),
% 0.84/1.03 inference(unit_resolution,[status(thm)],[191, 90, 151, 185, 177, 169, 162])).
% 0.84/1.03 tff(193,plain,
% 0.84/1.03 (((~hskp9) | c1_1(a2526)) <=> ((~hskp9) | c1_1(a2526))),
% 0.84/1.03 inference(rewrite,[status(thm)],[])).
% 0.84/1.03 tff(194,axiom,((~hskp9) | c1_1(a2526)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause75')).
% 0.84/1.03 tff(195,plain,
% 0.84/1.03 ((~hskp9) | c1_1(a2526)),
% 0.84/1.03 inference(modus_ponens,[status(thm)],[194, 193])).
% 0.84/1.03 tff(196,plain,
% 0.84/1.03 ((~hskp9) | c1_1(a2526)),
% 0.84/1.03 inference(modus_ponens,[status(thm)],[195, 193])).
% 0.84/1.03 tff(197,plain,
% 0.84/1.03 ((~hskp9) | c1_1(a2526)),
% 0.84/1.03 inference(modus_ponens,[status(thm)],[196, 193])).
% 0.84/1.03 tff(198,plain,
% 0.84/1.03 ((~hskp9) | c1_1(a2526)),
% 0.84/1.03 inference(modus_ponens,[status(thm)],[197, 193])).
% 0.84/1.03 tff(199,plain,
% 0.84/1.03 ((~hskp9) | c1_1(a2526)),
% 0.84/1.03 inference(modus_ponens,[status(thm)],[198, 193])).
% 0.84/1.03 tff(200,plain,
% 0.84/1.03 (c1_1(a2526)),
% 0.84/1.03 inference(unit_resolution,[status(thm)],[199, 192])).
% 0.84/1.03 tff(201,plain,
% 0.84/1.03 (((~hskp9) | (~c0_1(a2526))) <=> ((~hskp9) | (~c0_1(a2526)))),
% 0.84/1.03 inference(rewrite,[status(thm)],[])).
% 0.84/1.03 tff(202,plain,
% 0.84/1.03 (((~c0_1(a2526)) | (~hskp9)) <=> ((~hskp9) | (~c0_1(a2526)))),
% 0.84/1.03 inference(rewrite,[status(thm)],[])).
% 0.84/1.03 tff(203,axiom,((~c0_1(a2526)) | (~hskp9)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause121')).
% 0.84/1.03 tff(204,plain,
% 0.84/1.03 ((~hskp9) | (~c0_1(a2526))),
% 0.84/1.03 inference(modus_ponens,[status(thm)],[203, 202])).
% 0.84/1.03 tff(205,plain,
% 0.84/1.03 ((~hskp9) | (~c0_1(a2526))),
% 0.84/1.03 inference(modus_ponens,[status(thm)],[204, 201])).
% 0.84/1.03 tff(206,plain,
% 0.84/1.03 (~c0_1(a2526)),
% 0.84/1.03 inference(unit_resolution,[status(thm)],[205, 192])).
% 0.84/1.03 tff(207,plain,
% 0.84/1.03 (((~hskp9) | c3_1(a2526)) <=> ((~hskp9) | c3_1(a2526))),
% 0.84/1.03 inference(rewrite,[status(thm)],[])).
% 0.84/1.03 tff(208,axiom,((~hskp9) | c3_1(a2526)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause76')).
% 0.84/1.03 tff(209,plain,
% 0.84/1.03 ((~hskp9) | c3_1(a2526)),
% 0.84/1.03 inference(modus_ponens,[status(thm)],[208, 207])).
% 0.84/1.03 tff(210,plain,
% 0.84/1.03 ((~hskp9) | c3_1(a2526)),
% 0.84/1.03 inference(modus_ponens,[status(thm)],[209, 207])).
% 0.84/1.03 tff(211,plain,
% 0.84/1.03 ((~hskp9) | c3_1(a2526)),
% 0.84/1.03 inference(modus_ponens,[status(thm)],[210, 207])).
% 0.84/1.03 tff(212,plain,
% 0.84/1.03 ((~hskp9) | c3_1(a2526)),
% 0.84/1.03 inference(modus_ponens,[status(thm)],[211, 207])).
% 0.84/1.03 tff(213,plain,
% 0.84/1.03 ((~hskp9) | c3_1(a2526)),
% 0.84/1.03 inference(modus_ponens,[status(thm)],[212, 207])).
% 0.84/1.03 tff(214,plain,
% 0.84/1.03 (c3_1(a2526)),
% 0.84/1.03 inference(unit_resolution,[status(thm)],[213, 192])).
% 0.84/1.03 tff(215,assumption,(c1_1(a2526)), introduced(assumption)).
% 0.84/1.03 tff(216,assumption,(c3_1(a2526)), introduced(assumption)).
% 0.84/1.03 tff(217,plain,
% 0.84/1.03 (^[V: $i, U: $i] : refl((hskp17 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))) <=> (hskp17 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))))),
% 0.84/1.03 inference(bind,[status(th)],[])).
% 0.84/1.03 tff(218,plain,
% 0.84/1.03 (![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 0.84/1.03 inference(quant_intro,[status(thm)],[217])).
% 0.84/1.03 tff(219,plain,
% 0.84/1.03 (![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 0.84/1.03 inference(rewrite,[status(thm)],[])).
% 0.84/1.03 tff(220,plain,
% 0.84/1.03 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c1_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c1_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c1_1(V)))), ((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c1_1(V))))), (((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c1_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V)))), (((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V))))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V)))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V))))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V)))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V))))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | hskp17) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))) | hskp17))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))) | hskp17) <=> (hskp17 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | hskp17) <=> (hskp17 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))))),
% 0.84/1.03 inference(bind,[status(th)],[])).
% 0.84/1.03 tff(221,plain,
% 0.84/1.03 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | hskp17) <=> ![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 0.84/1.03 inference(quant_intro,[status(thm)],[220])).
% 0.84/1.03 tff(222,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | hskp17)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause181')).
% 0.84/1.03 tff(223,plain,
% 0.84/1.03 (![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 0.84/1.03 inference(modus_ponens,[status(thm)],[222, 221])).
% 0.84/1.03 tff(224,plain,
% 0.84/1.03 (![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 0.84/1.03 inference(modus_ponens,[status(thm)],[223, 219])).
% 0.84/1.03 tff(225,plain,(
% 0.84/1.03 ![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 0.84/1.03 inference(skolemize,[status(sab)],[224])).
% 0.84/1.03 tff(226,plain,
% 0.84/1.03 (![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 0.84/1.03 inference(modus_ponens,[status(thm)],[225, 218])).
% 0.84/1.03 tff(227,plain,
% 0.84/1.03 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp17 | c2_1(a2614) | c3_1(a2614) | c0_1(a2526) | (~ndr1_0) | (~c3_1(a2526)) | (~c1_1(a2526)) | (~c1_1(a2614)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp17 | c2_1(a2614) | c3_1(a2614) | c0_1(a2526) | (~ndr1_0) | (~c3_1(a2526)) | (~c1_1(a2526)) | (~c1_1(a2614)))),
% 0.84/1.03 inference(rewrite,[status(thm)],[])).
% 0.84/1.03 tff(228,plain,
% 0.84/1.03 ((hskp17 | (~ndr1_0) | c3_1(a2614) | c2_1(a2614) | (~c1_1(a2614)) | c0_1(a2526) | (~c3_1(a2526)) | (~c1_1(a2526))) <=> (hskp17 | c2_1(a2614) | c3_1(a2614) | c0_1(a2526) | (~ndr1_0) | (~c3_1(a2526)) | (~c1_1(a2526)) | (~c1_1(a2614)))),
% 0.84/1.03 inference(rewrite,[status(thm)],[])).
% 0.84/1.03 tff(229,plain,
% 0.84/1.03 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | c3_1(a2614) | c2_1(a2614) | (~c1_1(a2614)) | c0_1(a2526) | (~c3_1(a2526)) | (~c1_1(a2526)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp17 | c2_1(a2614) | c3_1(a2614) | c0_1(a2526) | (~ndr1_0) | (~c3_1(a2526)) | (~c1_1(a2526)) | (~c1_1(a2614))))),
% 0.84/1.03 inference(monotonicity,[status(thm)],[228])).
% 0.84/1.03 tff(230,plain,
% 0.84/1.03 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | c3_1(a2614) | c2_1(a2614) | (~c1_1(a2614)) | c0_1(a2526) | (~c3_1(a2526)) | (~c1_1(a2526)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp17 | c2_1(a2614) | c3_1(a2614) | c0_1(a2526) | (~ndr1_0) | (~c3_1(a2526)) | (~c1_1(a2526)) | (~c1_1(a2614)))),
% 0.84/1.03 inference(transitivity,[status(thm)],[229, 227])).
% 0.84/1.03 tff(231,plain,
% 0.84/1.03 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | c3_1(a2614) | c2_1(a2614) | (~c1_1(a2614)) | c0_1(a2526) | (~c3_1(a2526)) | (~c1_1(a2526)))),
% 0.84/1.03 inference(quant_inst,[status(thm)],[])).
% 0.84/1.03 tff(232,plain,
% 0.84/1.03 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp17 | c2_1(a2614) | c3_1(a2614) | c0_1(a2526) | (~ndr1_0) | (~c3_1(a2526)) | (~c1_1(a2526)) | (~c1_1(a2614))),
% 0.84/1.03 inference(modus_ponens,[status(thm)],[231, 230])).
% 0.84/1.03 tff(233,plain,
% 0.84/1.03 (hskp17),
% 0.84/1.03 inference(unit_resolution,[status(thm)],[232, 90, 13, 215, 216, 26, 20, 152, 226])).
% 0.84/1.03 tff(234,plain,
% 0.84/1.03 (((~hskp17) | (~c2_1(a2541))) <=> ((~hskp17) | (~c2_1(a2541)))),
% 0.84/1.03 inference(rewrite,[status(thm)],[])).
% 0.84/1.03 tff(235,plain,
% 0.84/1.03 (((~c2_1(a2541)) | (~hskp17)) <=> ((~hskp17) | (~c2_1(a2541)))),
% 0.84/1.03 inference(rewrite,[status(thm)],[])).
% 0.84/1.03 tff(236,axiom,((~c2_1(a2541)) | (~hskp17)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause105')).
% 0.84/1.03 tff(237,plain,
% 0.84/1.03 ((~hskp17) | (~c2_1(a2541))),
% 0.84/1.03 inference(modus_ponens,[status(thm)],[236, 235])).
% 0.84/1.03 tff(238,plain,
% 0.84/1.03 ((~hskp17) | (~c2_1(a2541))),
% 0.84/1.03 inference(modus_ponens,[status(thm)],[237, 234])).
% 0.84/1.03 tff(239,plain,
% 0.84/1.03 (~c2_1(a2541)),
% 0.84/1.03 inference(unit_resolution,[status(thm)],[238, 233])).
% 0.84/1.03 tff(240,plain,
% 0.84/1.03 (((~hskp17) | (~c1_1(a2541))) <=> ((~hskp17) | (~c1_1(a2541)))),
% 0.84/1.03 inference(rewrite,[status(thm)],[])).
% 0.84/1.03 tff(241,plain,
% 0.84/1.03 (((~c1_1(a2541)) | (~hskp17)) <=> ((~hskp17) | (~c1_1(a2541)))),
% 0.84/1.03 inference(rewrite,[status(thm)],[])).
% 0.84/1.03 tff(242,axiom,((~c1_1(a2541)) | (~hskp17)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause104')).
% 0.84/1.03 tff(243,plain,
% 0.84/1.03 ((~hskp17) | (~c1_1(a2541))),
% 0.84/1.03 inference(modus_ponens,[status(thm)],[242, 241])).
% 0.84/1.03 tff(244,plain,
% 0.84/1.03 ((~hskp17) | (~c1_1(a2541))),
% 0.84/1.03 inference(modus_ponens,[status(thm)],[243, 240])).
% 0.84/1.03 tff(245,plain,
% 0.84/1.03 (~c1_1(a2541)),
% 0.84/1.03 inference(unit_resolution,[status(thm)],[244, 233])).
% 0.84/1.03 tff(246,plain,
% 0.84/1.03 (((~hskp17) | c3_1(a2541)) <=> ((~hskp17) | c3_1(a2541))),
% 0.84/1.03 inference(rewrite,[status(thm)],[])).
% 0.84/1.03 tff(247,axiom,((~hskp17) | c3_1(a2541)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause68')).
% 0.84/1.03 tff(248,plain,
% 0.84/1.03 ((~hskp17) | c3_1(a2541)),
% 0.84/1.03 inference(modus_ponens,[status(thm)],[247, 246])).
% 0.84/1.03 tff(249,plain,
% 0.84/1.03 ((~hskp17) | c3_1(a2541)),
% 0.84/1.03 inference(modus_ponens,[status(thm)],[248, 246])).
% 0.84/1.03 tff(250,plain,
% 0.84/1.03 ((~hskp17) | c3_1(a2541)),
% 0.84/1.03 inference(modus_ponens,[status(thm)],[249, 246])).
% 0.84/1.03 tff(251,plain,
% 0.84/1.03 ((~hskp17) | c3_1(a2541)),
% 0.84/1.03 inference(modus_ponens,[status(thm)],[250, 246])).
% 0.84/1.03 tff(252,plain,
% 0.84/1.03 ((~hskp17) | c3_1(a2541)),
% 0.84/1.03 inference(modus_ponens,[status(thm)],[251, 246])).
% 0.84/1.03 tff(253,plain,
% 0.84/1.03 (c3_1(a2541)),
% 0.84/1.03 inference(unit_resolution,[status(thm)],[252, 233])).
% 0.84/1.03 tff(254,assumption,(c0_1(a2614)), introduced(assumption)).
% 0.84/1.03 tff(255,plain,
% 0.84/1.03 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W))))),
% 0.84/1.03 inference(bind,[status(th)],[])).
% 0.84/1.03 tff(256,plain,
% 0.84/1.03 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))),
% 0.84/1.03 inference(quant_intro,[status(thm)],[255])).
% 0.84/1.03 tff(257,plain,
% 0.84/1.03 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))),
% 0.84/1.03 inference(rewrite,[status(thm)],[])).
% 0.84/1.03 tff(258,plain,
% 0.84/1.03 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c3_1(U)) | (~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)))), rewrite((((~c3_1(U)) | (~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(V)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(V))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(V))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c0_1(V)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c0_1(V))))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(W))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c0_1(V))) | (~c3_1(W))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c0_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c3_1(W)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c3_1(W))))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(W))) | c3_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c3_1(W))) | c3_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c3_1(W))) | c3_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | (~c3_1(W)))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(W))) | c3_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | (~c3_1(W))))), ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(W))) | c3_1(V)) | c1_1(W)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | (~c3_1(W))) | c1_1(W)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | (~c3_1(W))) | c1_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c3_1(W)))), ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(W))) | c3_1(V)) | c1_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c3_1(W))))), (((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(W))) | c3_1(V)) | c1_1(W)) | c2_1(W)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c3_1(W))) | c2_1(W)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c3_1(W))) | c2_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))), (((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(W))) | c3_1(V)) | c1_1(W)) | c2_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))))),
% 0.84/1.03 inference(bind,[status(th)],[])).
% 0.84/1.03 tff(259,plain,
% 0.84/1.03 (![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(W))) | c3_1(V)) | c1_1(W)) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))),
% 0.84/1.03 inference(quant_intro,[status(thm)],[258])).
% 0.84/1.03 tff(260,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(W))) | c3_1(V)) | c1_1(W)) | c2_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause203')).
% 0.84/1.03 tff(261,plain,
% 0.84/1.03 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))),
% 0.84/1.03 inference(modus_ponens,[status(thm)],[260, 259])).
% 0.84/1.03 tff(262,plain,
% 0.84/1.03 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))),
% 0.84/1.03 inference(modus_ponens,[status(thm)],[261, 257])).
% 0.84/1.03 tff(263,plain,(
% 0.84/1.03 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))),
% 0.84/1.03 inference(skolemize,[status(sab)],[262])).
% 0.84/1.03 tff(264,plain,
% 0.84/1.03 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))),
% 0.84/1.03 inference(modus_ponens,[status(thm)],[263, 256])).
% 0.84/1.03 tff(265,assumption,(~c2_1(a2541)), introduced(assumption)).
% 0.84/1.03 tff(266,assumption,(~c1_1(a2541)), introduced(assumption)).
% 0.84/1.03 tff(267,assumption,(c3_1(a2541)), introduced(assumption)).
% 0.84/1.03 tff(268,plain,
% 0.84/1.03 (^[V: $i, U: $i] : refl((hskp29 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V))) <=> (hskp29 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V))))),
% 0.84/1.03 inference(bind,[status(th)],[])).
% 0.84/1.03 tff(269,plain,
% 0.84/1.03 (![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))),
% 0.84/1.03 inference(quant_intro,[status(thm)],[268])).
% 0.84/1.03 tff(270,plain,
% 0.84/1.03 (![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))),
% 0.84/1.03 inference(rewrite,[status(thm)],[])).
% 0.84/1.03 tff(271,plain,
% 0.84/1.03 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c3_1(V))))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c3_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c3_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V))))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c1_1(V)) | c2_1(V)) | hskp29) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V))) | hskp29))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V))) | hskp29) <=> (hskp29 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c1_1(V)) | c2_1(V)) | hskp29) <=> (hskp29 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))))),
% 0.84/1.03 inference(bind,[status(th)],[])).
% 0.84/1.03 tff(272,plain,
% 0.84/1.03 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c1_1(V)) | c2_1(V)) | hskp29) <=> ![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))),
% 0.84/1.03 inference(quant_intro,[status(thm)],[271])).
% 0.84/1.03 tff(273,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c1_1(V)) | c2_1(V)) | hskp29)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause182')).
% 0.84/1.03 tff(274,plain,
% 0.84/1.03 (![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))),
% 0.84/1.03 inference(modus_ponens,[status(thm)],[273, 272])).
% 0.84/1.03 tff(275,plain,
% 0.84/1.03 (![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))),
% 0.84/1.03 inference(modus_ponens,[status(thm)],[274, 270])).
% 0.84/1.03 tff(276,plain,(
% 0.84/1.03 ![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))),
% 0.84/1.03 inference(skolemize,[status(sab)],[275])).
% 0.84/1.03 tff(277,plain,
% 0.84/1.03 (![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))),
% 0.84/1.03 inference(modus_ponens,[status(thm)],[276, 269])).
% 0.84/1.03 tff(278,plain,
% 0.84/1.03 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (c3_1(a2614) | c1_1(a2541) | c2_1(a2541) | (~ndr1_0) | (~c3_1(a2526)) | (~c2_1(a2526)) | (~c1_1(a2526)) | (~c3_1(a2541)) | (~c0_1(a2614)) | (~c1_1(a2614)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c3_1(a2614) | c1_1(a2541) | c2_1(a2541) | (~ndr1_0) | (~c3_1(a2526)) | (~c2_1(a2526)) | (~c1_1(a2526)) | (~c3_1(a2541)) | (~c0_1(a2614)) | (~c1_1(a2614)))),
% 0.84/1.03 inference(rewrite,[status(thm)],[])).
% 0.84/1.03 tff(279,plain,
% 0.84/1.03 (((~ndr1_0) | (~c3_1(a2526)) | (~c1_1(a2526)) | (~c2_1(a2526)) | c3_1(a2614) | (~c1_1(a2614)) | (~c0_1(a2614)) | c1_1(a2541) | c2_1(a2541) | (~c3_1(a2541))) <=> (c3_1(a2614) | c1_1(a2541) | c2_1(a2541) | (~ndr1_0) | (~c3_1(a2526)) | (~c2_1(a2526)) | (~c1_1(a2526)) | (~c3_1(a2541)) | (~c0_1(a2614)) | (~c1_1(a2614)))),
% 0.84/1.03 inference(rewrite,[status(thm)],[])).
% 0.84/1.03 tff(280,plain,
% 0.84/1.03 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a2526)) | (~c1_1(a2526)) | (~c2_1(a2526)) | c3_1(a2614) | (~c1_1(a2614)) | (~c0_1(a2614)) | c1_1(a2541) | c2_1(a2541) | (~c3_1(a2541)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (c3_1(a2614) | c1_1(a2541) | c2_1(a2541) | (~ndr1_0) | (~c3_1(a2526)) | (~c2_1(a2526)) | (~c1_1(a2526)) | (~c3_1(a2541)) | (~c0_1(a2614)) | (~c1_1(a2614))))),
% 0.84/1.03 inference(monotonicity,[status(thm)],[279])).
% 0.84/1.03 tff(281,plain,
% 0.84/1.03 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a2526)) | (~c1_1(a2526)) | (~c2_1(a2526)) | c3_1(a2614) | (~c1_1(a2614)) | (~c0_1(a2614)) | c1_1(a2541) | c2_1(a2541) | (~c3_1(a2541)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c3_1(a2614) | c1_1(a2541) | c2_1(a2541) | (~ndr1_0) | (~c3_1(a2526)) | (~c2_1(a2526)) | (~c1_1(a2526)) | (~c3_1(a2541)) | (~c0_1(a2614)) | (~c1_1(a2614)))),
% 0.84/1.03 inference(transitivity,[status(thm)],[280, 278])).
% 0.84/1.03 tff(282,plain,
% 0.84/1.03 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a2526)) | (~c1_1(a2526)) | (~c2_1(a2526)) | c3_1(a2614) | (~c1_1(a2614)) | (~c0_1(a2614)) | c1_1(a2541) | c2_1(a2541) | (~c3_1(a2541)))),
% 0.84/1.03 inference(quant_inst,[status(thm)],[])).
% 0.84/1.03 tff(283,plain,
% 0.84/1.03 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c3_1(a2614) | c1_1(a2541) | c2_1(a2541) | (~ndr1_0) | (~c3_1(a2526)) | (~c2_1(a2526)) | (~c1_1(a2526)) | (~c3_1(a2541)) | (~c0_1(a2614)) | (~c1_1(a2614))),
% 0.84/1.03 inference(modus_ponens,[status(thm)],[282, 281])).
% 0.84/1.03 tff(284,plain,
% 0.84/1.03 ((~c2_1(a2526)) | (~c0_1(a2614))),
% 0.84/1.03 inference(unit_resolution,[status(thm)],[283, 90, 58, 267, 215, 216, 56, 266, 265, 264])).
% 0.84/1.03 tff(285,plain,
% 0.84/1.03 (~c2_1(a2526)),
% 0.84/1.03 inference(unit_resolution,[status(thm)],[284, 254])).
% 0.84/1.03 tff(286,plain,
% 0.84/1.03 (^[V: $i, U: $i] : refl((hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V))) <=> (hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V))))),
% 0.84/1.03 inference(bind,[status(th)],[])).
% 0.84/1.03 tff(287,plain,
% 0.84/1.03 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))),
% 0.84/1.03 inference(quant_intro,[status(thm)],[286])).
% 0.84/1.03 tff(288,plain,
% 0.84/1.03 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))),
% 0.84/1.03 inference(rewrite,[status(thm)],[])).
% 0.84/1.03 tff(289,plain,
% 0.84/1.03 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c3_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)))), ((((~c3_1(U)) | (~ndr1_0)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c3_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c3_1(V)))), ((((~c3_1(U)) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c3_1(V))))), (((((~c3_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c3_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c3_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c3_1(V)))), (((((~c3_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c3_1(V))))), ((((((~c3_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c3_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c3_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | (~c3_1(V)))), ((((((~c3_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | (~c3_1(V))))), (((((((~c3_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | (~c3_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)))), (((((((~c3_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c3_1(V))))), ((((((((~c3_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c3_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c3_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))), ((((((((~c3_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V))))), (((((((((~c3_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | hskp11) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V))) | hskp11))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V))) | hskp11) <=> (hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))), (((((((((~c3_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | hskp11) <=> (hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))))),
% 0.84/1.03 inference(bind,[status(th)],[])).
% 0.84/1.03 tff(290,plain,
% 0.84/1.03 (![V: $i, U: $i] : ((((((((~c3_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | hskp11) <=> ![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))),
% 0.84/1.03 inference(quant_intro,[status(thm)],[289])).
% 0.84/1.03 tff(291,axiom,(![V: $i, U: $i] : ((((((((~c3_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | hskp11)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause170')).
% 0.84/1.03 tff(292,plain,
% 0.84/1.03 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))),
% 0.84/1.03 inference(modus_ponens,[status(thm)],[291, 290])).
% 0.84/1.03 tff(293,plain,
% 0.84/1.03 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))),
% 0.84/1.03 inference(modus_ponens,[status(thm)],[292, 288])).
% 0.84/1.03 tff(294,plain,(
% 0.84/1.03 ![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))),
% 0.84/1.03 inference(skolemize,[status(sab)],[293])).
% 0.84/1.03 tff(295,plain,
% 0.84/1.03 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))),
% 0.84/1.03 inference(modus_ponens,[status(thm)],[294, 287])).
% 0.84/1.03 tff(296,plain,
% 0.84/1.03 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp11 | c1_1(a2541) | c2_1(a2541) | c0_1(a2526) | (~ndr1_0) | (~c3_1(a2526)) | c2_1(a2526) | (~c3_1(a2541)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp11 | c1_1(a2541) | c2_1(a2541) | c0_1(a2526) | (~ndr1_0) | (~c3_1(a2526)) | c2_1(a2526) | (~c3_1(a2541)))),
% 0.84/1.03 inference(rewrite,[status(thm)],[])).
% 0.84/1.03 tff(297,plain,
% 0.84/1.03 ((hskp11 | (~ndr1_0) | c2_1(a2541) | c1_1(a2541) | (~c3_1(a2541)) | c0_1(a2526) | c2_1(a2526) | (~c3_1(a2526))) <=> (hskp11 | c1_1(a2541) | c2_1(a2541) | c0_1(a2526) | (~ndr1_0) | (~c3_1(a2526)) | c2_1(a2526) | (~c3_1(a2541)))),
% 0.84/1.03 inference(rewrite,[status(thm)],[])).
% 0.84/1.03 tff(298,plain,
% 0.84/1.03 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp11 | (~ndr1_0) | c2_1(a2541) | c1_1(a2541) | (~c3_1(a2541)) | c0_1(a2526) | c2_1(a2526) | (~c3_1(a2526)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp11 | c1_1(a2541) | c2_1(a2541) | c0_1(a2526) | (~ndr1_0) | (~c3_1(a2526)) | c2_1(a2526) | (~c3_1(a2541))))),
% 0.84/1.03 inference(monotonicity,[status(thm)],[297])).
% 0.84/1.03 tff(299,plain,
% 0.84/1.03 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp11 | (~ndr1_0) | c2_1(a2541) | c1_1(a2541) | (~c3_1(a2541)) | c0_1(a2526) | c2_1(a2526) | (~c3_1(a2526)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp11 | c1_1(a2541) | c2_1(a2541) | c0_1(a2526) | (~ndr1_0) | (~c3_1(a2526)) | c2_1(a2526) | (~c3_1(a2541)))),
% 0.84/1.03 inference(transitivity,[status(thm)],[298, 296])).
% 0.84/1.03 tff(300,plain,
% 0.84/1.03 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp11 | (~ndr1_0) | c2_1(a2541) | c1_1(a2541) | (~c3_1(a2541)) | c0_1(a2526) | c2_1(a2526) | (~c3_1(a2526)))),
% 0.84/1.04 inference(quant_inst,[status(thm)],[])).
% 0.84/1.04 tff(301,plain,
% 0.84/1.04 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp11 | c1_1(a2541) | c2_1(a2541) | c0_1(a2526) | (~ndr1_0) | (~c3_1(a2526)) | c2_1(a2526) | (~c3_1(a2541))),
% 0.84/1.04 inference(modus_ponens,[status(thm)],[300, 299])).
% 0.84/1.04 tff(302,plain,
% 0.84/1.04 (hskp11 | c2_1(a2526)),
% 0.84/1.04 inference(unit_resolution,[status(thm)],[301, 90, 267, 216, 266, 265, 152, 295])).
% 0.84/1.04 tff(303,plain,
% 0.84/1.04 (hskp11),
% 0.84/1.04 inference(unit_resolution,[status(thm)],[302, 285])).
% 0.84/1.04 tff(304,plain,
% 0.84/1.04 (((~hskp11) | (~c3_1(a2531))) <=> ((~hskp11) | (~c3_1(a2531)))),
% 0.84/1.04 inference(rewrite,[status(thm)],[])).
% 0.84/1.04 tff(305,plain,
% 0.84/1.04 (((~c3_1(a2531)) | (~hskp11)) <=> ((~hskp11) | (~c3_1(a2531)))),
% 0.84/1.04 inference(rewrite,[status(thm)],[])).
% 0.84/1.04 tff(306,axiom,((~c3_1(a2531)) | (~hskp11)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause118')).
% 0.84/1.04 tff(307,plain,
% 0.84/1.04 ((~hskp11) | (~c3_1(a2531))),
% 0.84/1.04 inference(modus_ponens,[status(thm)],[306, 305])).
% 0.84/1.04 tff(308,plain,
% 0.84/1.04 ((~hskp11) | (~c3_1(a2531))),
% 0.84/1.04 inference(modus_ponens,[status(thm)],[307, 304])).
% 0.84/1.04 tff(309,plain,
% 0.84/1.04 (~c3_1(a2531)),
% 0.84/1.04 inference(unit_resolution,[status(thm)],[308, 303])).
% 0.84/1.04 tff(310,plain,
% 0.84/1.04 (((~hskp11) | c2_1(a2531)) <=> ((~hskp11) | c2_1(a2531))),
% 0.84/1.04 inference(rewrite,[status(thm)],[])).
% 0.84/1.04 tff(311,axiom,((~hskp11) | c2_1(a2531)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause73')).
% 0.84/1.04 tff(312,plain,
% 0.84/1.04 ((~hskp11) | c2_1(a2531)),
% 0.84/1.04 inference(modus_ponens,[status(thm)],[311, 310])).
% 0.84/1.04 tff(313,plain,
% 0.84/1.04 ((~hskp11) | c2_1(a2531)),
% 0.84/1.04 inference(modus_ponens,[status(thm)],[312, 310])).
% 0.84/1.04 tff(314,plain,
% 0.84/1.04 ((~hskp11) | c2_1(a2531)),
% 0.84/1.04 inference(modus_ponens,[status(thm)],[313, 310])).
% 0.84/1.04 tff(315,plain,
% 0.84/1.04 ((~hskp11) | c2_1(a2531)),
% 0.84/1.04 inference(modus_ponens,[status(thm)],[314, 310])).
% 0.84/1.04 tff(316,plain,
% 0.84/1.04 ((~hskp11) | c2_1(a2531)),
% 0.84/1.04 inference(modus_ponens,[status(thm)],[315, 310])).
% 0.84/1.04 tff(317,plain,
% 0.84/1.04 (c2_1(a2531)),
% 0.84/1.04 inference(unit_resolution,[status(thm)],[316, 303])).
% 0.84/1.04 tff(318,plain,
% 0.84/1.04 (((~hskp11) | c1_1(a2531)) <=> ((~hskp11) | c1_1(a2531))),
% 0.84/1.04 inference(rewrite,[status(thm)],[])).
% 0.84/1.04 tff(319,axiom,((~hskp11) | c1_1(a2531)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause72')).
% 0.84/1.04 tff(320,plain,
% 0.84/1.04 ((~hskp11) | c1_1(a2531)),
% 0.84/1.04 inference(modus_ponens,[status(thm)],[319, 318])).
% 0.84/1.04 tff(321,plain,
% 0.84/1.04 ((~hskp11) | c1_1(a2531)),
% 0.84/1.04 inference(modus_ponens,[status(thm)],[320, 318])).
% 0.84/1.04 tff(322,plain,
% 0.84/1.04 ((~hskp11) | c1_1(a2531)),
% 0.84/1.04 inference(modus_ponens,[status(thm)],[321, 318])).
% 0.84/1.04 tff(323,plain,
% 0.84/1.04 ((~hskp11) | c1_1(a2531)),
% 0.84/1.04 inference(modus_ponens,[status(thm)],[322, 318])).
% 0.84/1.04 tff(324,plain,
% 0.84/1.04 ((~hskp11) | c1_1(a2531)),
% 0.84/1.04 inference(modus_ponens,[status(thm)],[323, 318])).
% 0.84/1.04 tff(325,plain,
% 0.84/1.04 (c1_1(a2531)),
% 0.84/1.04 inference(unit_resolution,[status(thm)],[324, 303])).
% 0.84/1.04 tff(326,plain,
% 0.84/1.04 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp29 | c1_1(a2541) | c2_1(a2541) | c3_1(a2531) | (~ndr1_0) | (~c2_1(a2531)) | (~c1_1(a2531)) | (~c3_1(a2541)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | hskp29 | c1_1(a2541) | c2_1(a2541) | c3_1(a2531) | (~ndr1_0) | (~c2_1(a2531)) | (~c1_1(a2531)) | (~c3_1(a2541)))),
% 0.84/1.04 inference(rewrite,[status(thm)],[])).
% 0.84/1.04 tff(327,plain,
% 0.84/1.04 ((hskp29 | (~ndr1_0) | c3_1(a2531) | (~c1_1(a2531)) | (~c2_1(a2531)) | c1_1(a2541) | c2_1(a2541) | (~c3_1(a2541))) <=> (hskp29 | c1_1(a2541) | c2_1(a2541) | c3_1(a2531) | (~ndr1_0) | (~c2_1(a2531)) | (~c1_1(a2531)) | (~c3_1(a2541)))),
% 0.84/1.04 inference(rewrite,[status(thm)],[])).
% 0.84/1.04 tff(328,plain,
% 0.84/1.04 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp29 | (~ndr1_0) | c3_1(a2531) | (~c1_1(a2531)) | (~c2_1(a2531)) | c1_1(a2541) | c2_1(a2541) | (~c3_1(a2541)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp29 | c1_1(a2541) | c2_1(a2541) | c3_1(a2531) | (~ndr1_0) | (~c2_1(a2531)) | (~c1_1(a2531)) | (~c3_1(a2541))))),
% 0.84/1.04 inference(monotonicity,[status(thm)],[327])).
% 0.84/1.04 tff(329,plain,
% 0.84/1.04 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp29 | (~ndr1_0) | c3_1(a2531) | (~c1_1(a2531)) | (~c2_1(a2531)) | c1_1(a2541) | c2_1(a2541) | (~c3_1(a2541)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | hskp29 | c1_1(a2541) | c2_1(a2541) | c3_1(a2531) | (~ndr1_0) | (~c2_1(a2531)) | (~c1_1(a2531)) | (~c3_1(a2541)))),
% 0.84/1.04 inference(transitivity,[status(thm)],[328, 326])).
% 0.84/1.04 tff(330,plain,
% 0.84/1.04 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp29 | (~ndr1_0) | c3_1(a2531) | (~c1_1(a2531)) | (~c2_1(a2531)) | c1_1(a2541) | c2_1(a2541) | (~c3_1(a2541)))),
% 0.84/1.04 inference(quant_inst,[status(thm)],[])).
% 0.84/1.04 tff(331,plain,
% 0.84/1.04 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | hskp29 | c1_1(a2541) | c2_1(a2541) | c3_1(a2531) | (~ndr1_0) | (~c2_1(a2531)) | (~c1_1(a2531)) | (~c3_1(a2541))),
% 0.84/1.04 inference(modus_ponens,[status(thm)],[330, 329])).
% 0.84/1.04 tff(332,plain,
% 0.84/1.04 (hskp29),
% 0.84/1.04 inference(unit_resolution,[status(thm)],[331, 90, 267, 325, 317, 266, 265, 309, 277])).
% 0.84/1.04 tff(333,plain,
% 0.84/1.04 (((~hskp29) | c3_1(a2556)) <=> ((~hskp29) | c3_1(a2556))),
% 0.84/1.04 inference(rewrite,[status(thm)],[])).
% 0.84/1.04 tff(334,axiom,((~hskp29) | c3_1(a2556)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause49')).
% 0.84/1.04 tff(335,plain,
% 0.84/1.04 ((~hskp29) | c3_1(a2556)),
% 0.84/1.04 inference(modus_ponens,[status(thm)],[334, 333])).
% 0.84/1.04 tff(336,plain,
% 0.84/1.04 ((~hskp29) | c3_1(a2556)),
% 0.84/1.04 inference(modus_ponens,[status(thm)],[335, 333])).
% 0.84/1.04 tff(337,plain,
% 0.84/1.04 ((~hskp29) | c3_1(a2556)),
% 0.84/1.04 inference(modus_ponens,[status(thm)],[336, 333])).
% 0.84/1.04 tff(338,plain,
% 0.84/1.04 ((~hskp29) | c3_1(a2556)),
% 0.84/1.04 inference(modus_ponens,[status(thm)],[337, 333])).
% 0.84/1.04 tff(339,plain,
% 0.84/1.04 ((~hskp29) | c3_1(a2556)),
% 0.84/1.04 inference(modus_ponens,[status(thm)],[338, 333])).
% 0.84/1.04 tff(340,plain,
% 0.84/1.04 (c3_1(a2556)),
% 0.84/1.04 inference(unit_resolution,[status(thm)],[339, 332])).
% 0.84/1.04 tff(341,plain,
% 0.84/1.04 (((~hskp29) | c2_1(a2556)) <=> ((~hskp29) | c2_1(a2556))),
% 0.84/1.04 inference(rewrite,[status(thm)],[])).
% 0.84/1.04 tff(342,axiom,((~hskp29) | c2_1(a2556)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause48')).
% 0.84/1.04 tff(343,plain,
% 0.84/1.04 ((~hskp29) | c2_1(a2556)),
% 0.84/1.04 inference(modus_ponens,[status(thm)],[342, 341])).
% 0.84/1.04 tff(344,plain,
% 0.84/1.04 ((~hskp29) | c2_1(a2556)),
% 0.84/1.04 inference(modus_ponens,[status(thm)],[343, 341])).
% 0.84/1.04 tff(345,plain,
% 0.84/1.04 ((~hskp29) | c2_1(a2556)),
% 0.84/1.04 inference(modus_ponens,[status(thm)],[344, 341])).
% 0.84/1.04 tff(346,plain,
% 0.84/1.04 ((~hskp29) | c2_1(a2556)),
% 0.84/1.04 inference(modus_ponens,[status(thm)],[345, 341])).
% 0.84/1.04 tff(347,plain,
% 0.84/1.04 ((~hskp29) | c2_1(a2556)),
% 0.84/1.04 inference(modus_ponens,[status(thm)],[346, 341])).
% 0.84/1.04 tff(348,plain,
% 0.84/1.04 (c2_1(a2556)),
% 0.84/1.04 inference(unit_resolution,[status(thm)],[347, 332])).
% 0.84/1.04 tff(349,plain,
% 0.84/1.04 (((~hskp29) | c1_1(a2556)) <=> ((~hskp29) | c1_1(a2556))),
% 0.84/1.04 inference(rewrite,[status(thm)],[])).
% 0.84/1.04 tff(350,axiom,((~hskp29) | c1_1(a2556)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause47')).
% 0.84/1.04 tff(351,plain,
% 0.84/1.04 ((~hskp29) | c1_1(a2556)),
% 0.84/1.04 inference(modus_ponens,[status(thm)],[350, 349])).
% 0.84/1.04 tff(352,plain,
% 0.84/1.04 ((~hskp29) | c1_1(a2556)),
% 0.84/1.04 inference(modus_ponens,[status(thm)],[351, 349])).
% 0.84/1.04 tff(353,plain,
% 0.84/1.04 ((~hskp29) | c1_1(a2556)),
% 0.84/1.04 inference(modus_ponens,[status(thm)],[352, 349])).
% 0.84/1.04 tff(354,plain,
% 0.84/1.04 ((~hskp29) | c1_1(a2556)),
% 0.84/1.04 inference(modus_ponens,[status(thm)],[353, 349])).
% 0.84/1.04 tff(355,plain,
% 0.84/1.04 ((~hskp29) | c1_1(a2556)),
% 0.84/1.04 inference(modus_ponens,[status(thm)],[354, 349])).
% 0.84/1.04 tff(356,plain,
% 0.84/1.04 (c1_1(a2556)),
% 0.84/1.04 inference(unit_resolution,[status(thm)],[355, 332])).
% 0.84/1.04 tff(357,plain,
% 0.84/1.04 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (c3_1(a2614) | c1_1(a2541) | c2_1(a2541) | (~ndr1_0) | (~c2_1(a2556)) | (~c3_1(a2556)) | (~c1_1(a2556)) | (~c3_1(a2541)) | (~c0_1(a2614)) | (~c1_1(a2614)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c3_1(a2614) | c1_1(a2541) | c2_1(a2541) | (~ndr1_0) | (~c2_1(a2556)) | (~c3_1(a2556)) | (~c1_1(a2556)) | (~c3_1(a2541)) | (~c0_1(a2614)) | (~c1_1(a2614)))),
% 0.84/1.04 inference(rewrite,[status(thm)],[])).
% 0.84/1.04 tff(358,plain,
% 0.84/1.04 (((~ndr1_0) | (~c3_1(a2556)) | (~c1_1(a2556)) | (~c2_1(a2556)) | c3_1(a2614) | (~c1_1(a2614)) | (~c0_1(a2614)) | c1_1(a2541) | c2_1(a2541) | (~c3_1(a2541))) <=> (c3_1(a2614) | c1_1(a2541) | c2_1(a2541) | (~ndr1_0) | (~c2_1(a2556)) | (~c3_1(a2556)) | (~c1_1(a2556)) | (~c3_1(a2541)) | (~c0_1(a2614)) | (~c1_1(a2614)))),
% 0.84/1.04 inference(rewrite,[status(thm)],[])).
% 0.84/1.04 tff(359,plain,
% 0.84/1.04 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a2556)) | (~c1_1(a2556)) | (~c2_1(a2556)) | c3_1(a2614) | (~c1_1(a2614)) | (~c0_1(a2614)) | c1_1(a2541) | c2_1(a2541) | (~c3_1(a2541)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (c3_1(a2614) | c1_1(a2541) | c2_1(a2541) | (~ndr1_0) | (~c2_1(a2556)) | (~c3_1(a2556)) | (~c1_1(a2556)) | (~c3_1(a2541)) | (~c0_1(a2614)) | (~c1_1(a2614))))),
% 0.84/1.04 inference(monotonicity,[status(thm)],[358])).
% 0.84/1.04 tff(360,plain,
% 0.84/1.04 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a2556)) | (~c1_1(a2556)) | (~c2_1(a2556)) | c3_1(a2614) | (~c1_1(a2614)) | (~c0_1(a2614)) | c1_1(a2541) | c2_1(a2541) | (~c3_1(a2541)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c3_1(a2614) | c1_1(a2541) | c2_1(a2541) | (~ndr1_0) | (~c2_1(a2556)) | (~c3_1(a2556)) | (~c1_1(a2556)) | (~c3_1(a2541)) | (~c0_1(a2614)) | (~c1_1(a2614)))),
% 0.84/1.04 inference(transitivity,[status(thm)],[359, 357])).
% 0.84/1.04 tff(361,plain,
% 0.84/1.04 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a2556)) | (~c1_1(a2556)) | (~c2_1(a2556)) | c3_1(a2614) | (~c1_1(a2614)) | (~c0_1(a2614)) | c1_1(a2541) | c2_1(a2541) | (~c3_1(a2541)))),
% 0.84/1.04 inference(quant_inst,[status(thm)],[])).
% 0.84/1.04 tff(362,plain,
% 0.84/1.04 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c3_1(a2614) | c1_1(a2541) | c2_1(a2541) | (~ndr1_0) | (~c2_1(a2556)) | (~c3_1(a2556)) | (~c1_1(a2556)) | (~c3_1(a2541)) | (~c0_1(a2614)) | (~c1_1(a2614))),
% 0.84/1.04 inference(modus_ponens,[status(thm)],[361, 360])).
% 0.84/1.04 tff(363,plain,
% 0.84/1.04 ($false),
% 0.84/1.04 inference(unit_resolution,[status(thm)],[362, 90, 356, 348, 340, 58, 267, 56, 266, 265, 264, 254])).
% 0.84/1.04 tff(364,plain,((~c0_1(a2614)) | (~c1_1(a2614)) | (~c3_1(a2541)) | c3_1(a2614) | c1_1(a2541) | c2_1(a2541) | (~c3_1(a2526)) | c0_1(a2526) | (~c1_1(a2526))), inference(lemma,lemma(discharge,[]))).
% 0.84/1.04 tff(365,plain,
% 0.84/1.04 (~c0_1(a2614)),
% 0.84/1.04 inference(unit_resolution,[status(thm)],[364, 13, 253, 20, 245, 239, 216, 152, 215])).
% 0.84/1.04 tff(366,plain,
% 0.84/1.04 (^[V: $i, U: $i] : refl((hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V)) <=> (hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V)))),
% 0.84/1.04 inference(bind,[status(th)],[])).
% 0.84/1.04 tff(367,plain,
% 0.84/1.04 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V)) <=> ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))),
% 0.84/1.04 inference(quant_intro,[status(thm)],[366])).
% 0.84/1.04 tff(368,plain,
% 0.84/1.04 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V)) <=> ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))),
% 0.84/1.04 inference(rewrite,[status(thm)],[])).
% 0.84/1.04 tff(369,plain,
% 0.84/1.04 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c1_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U))))), (((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))), (((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U))))), ((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U))) | c0_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U))) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V))), ((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V)))), (((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V))), (((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V)))), ((((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))), ((((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V)))), (((((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp1) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V)) | hskp1))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V)) | hskp1) <=> (hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))), (((((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp1) <=> (hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))))),
% 0.84/1.04 inference(bind,[status(th)],[])).
% 0.84/1.04 tff(370,plain,
% 0.84/1.04 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp1) <=> ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))),
% 0.84/1.04 inference(quant_intro,[status(thm)],[369])).
% 0.84/1.04 tff(371,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause165')).
% 0.84/1.04 tff(372,plain,
% 0.84/1.04 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))),
% 0.84/1.04 inference(modus_ponens,[status(thm)],[371, 370])).
% 0.84/1.04 tff(373,plain,
% 0.84/1.04 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))),
% 0.84/1.04 inference(modus_ponens,[status(thm)],[372, 368])).
% 0.84/1.04 tff(374,plain,(
% 0.84/1.04 ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))),
% 0.84/1.04 inference(skolemize,[status(sab)],[373])).
% 0.84/1.04 tff(375,plain,
% 0.84/1.04 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))),
% 0.84/1.04 inference(modus_ponens,[status(thm)],[374, 367])).
% 0.84/1.04 tff(376,plain,
% 0.84/1.04 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp1 | c2_1(a2614) | c3_1(a2614) | (~ndr1_0) | c0_1(a2614) | (~c1_1(a2614)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp1 | c2_1(a2614) | c3_1(a2614) | (~ndr1_0) | c0_1(a2614) | (~c1_1(a2614)))),
% 0.84/1.04 inference(rewrite,[status(thm)],[])).
% 0.84/1.04 tff(377,plain,
% 0.84/1.04 ((hskp1 | (~ndr1_0) | c3_1(a2614) | c2_1(a2614) | (~c1_1(a2614)) | c3_1(a2614) | c0_1(a2614) | c2_1(a2614)) <=> (hskp1 | c2_1(a2614) | c3_1(a2614) | (~ndr1_0) | c0_1(a2614) | (~c1_1(a2614)))),
% 0.84/1.04 inference(rewrite,[status(thm)],[])).
% 0.84/1.04 tff(378,plain,
% 0.84/1.04 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp1 | (~ndr1_0) | c3_1(a2614) | c2_1(a2614) | (~c1_1(a2614)) | c3_1(a2614) | c0_1(a2614) | c2_1(a2614))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp1 | c2_1(a2614) | c3_1(a2614) | (~ndr1_0) | c0_1(a2614) | (~c1_1(a2614))))),
% 0.84/1.04 inference(monotonicity,[status(thm)],[377])).
% 0.84/1.04 tff(379,plain,
% 0.84/1.04 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp1 | (~ndr1_0) | c3_1(a2614) | c2_1(a2614) | (~c1_1(a2614)) | c3_1(a2614) | c0_1(a2614) | c2_1(a2614))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp1 | c2_1(a2614) | c3_1(a2614) | (~ndr1_0) | c0_1(a2614) | (~c1_1(a2614)))),
% 0.84/1.04 inference(transitivity,[status(thm)],[378, 376])).
% 0.84/1.04 tff(380,plain,
% 0.84/1.04 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp1 | (~ndr1_0) | c3_1(a2614) | c2_1(a2614) | (~c1_1(a2614)) | c3_1(a2614) | c0_1(a2614) | c2_1(a2614))),
% 0.84/1.04 inference(quant_inst,[status(thm)],[])).
% 0.84/1.04 tff(381,plain,
% 0.84/1.04 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp1 | c2_1(a2614) | c3_1(a2614) | (~ndr1_0) | c0_1(a2614) | (~c1_1(a2614))),
% 0.84/1.04 inference(modus_ponens,[status(thm)],[380, 379])).
% 0.84/1.04 tff(382,plain,
% 0.84/1.04 (hskp1 | c0_1(a2614)),
% 0.84/1.04 inference(unit_resolution,[status(thm)],[381, 90, 13, 26, 20, 375])).
% 0.84/1.04 tff(383,plain,
% 0.84/1.04 (hskp1),
% 0.84/1.04 inference(unit_resolution,[status(thm)],[382, 365])).
% 0.84/1.04 tff(384,plain,
% 0.84/1.04 (((~hskp1) | (~c3_1(a2517))) <=> ((~hskp1) | (~c3_1(a2517)))),
% 0.84/1.04 inference(rewrite,[status(thm)],[])).
% 0.84/1.04 tff(385,plain,
% 0.84/1.04 (((~c3_1(a2517)) | (~hskp1)) <=> ((~hskp1) | (~c3_1(a2517)))),
% 0.84/1.04 inference(rewrite,[status(thm)],[])).
% 0.84/1.04 tff(386,axiom,((~c3_1(a2517)) | (~hskp1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause133')).
% 0.84/1.04 tff(387,plain,
% 0.84/1.04 ((~hskp1) | (~c3_1(a2517))),
% 0.84/1.04 inference(modus_ponens,[status(thm)],[386, 385])).
% 0.84/1.04 tff(388,plain,
% 0.84/1.04 ((~hskp1) | (~c3_1(a2517))),
% 0.84/1.04 inference(modus_ponens,[status(thm)],[387, 384])).
% 0.84/1.04 tff(389,plain,
% 0.84/1.04 (~c3_1(a2517)),
% 0.84/1.04 inference(unit_resolution,[status(thm)],[388, 383])).
% 0.84/1.04 tff(390,plain,
% 0.84/1.04 (((~hskp1) | (~c0_1(a2517))) <=> ((~hskp1) | (~c0_1(a2517)))),
% 0.84/1.04 inference(rewrite,[status(thm)],[])).
% 0.84/1.04 tff(391,plain,
% 0.84/1.04 (((~c0_1(a2517)) | (~hskp1)) <=> ((~hskp1) | (~c0_1(a2517)))),
% 0.84/1.04 inference(rewrite,[status(thm)],[])).
% 0.84/1.04 tff(392,axiom,((~c0_1(a2517)) | (~hskp1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause132')).
% 0.84/1.04 tff(393,plain,
% 0.84/1.04 ((~hskp1) | (~c0_1(a2517))),
% 0.84/1.04 inference(modus_ponens,[status(thm)],[392, 391])).
% 0.84/1.04 tff(394,plain,
% 0.84/1.04 ((~hskp1) | (~c0_1(a2517))),
% 0.84/1.04 inference(modus_ponens,[status(thm)],[393, 390])).
% 0.84/1.04 tff(395,plain,
% 0.84/1.04 (~c0_1(a2517)),
% 0.84/1.04 inference(unit_resolution,[status(thm)],[394, 383])).
% 0.84/1.04 tff(396,plain,
% 0.84/1.04 (((~hskp1) | c2_1(a2517)) <=> ((~hskp1) | c2_1(a2517))),
% 0.84/1.04 inference(rewrite,[status(thm)],[])).
% 0.84/1.04 tff(397,axiom,((~hskp1) | c2_1(a2517)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause88')).
% 0.84/1.04 tff(398,plain,
% 0.84/1.04 ((~hskp1) | c2_1(a2517)),
% 0.84/1.04 inference(modus_ponens,[status(thm)],[397, 396])).
% 0.84/1.04 tff(399,plain,
% 0.84/1.04 ((~hskp1) | c2_1(a2517)),
% 0.84/1.04 inference(modus_ponens,[status(thm)],[398, 396])).
% 0.84/1.04 tff(400,plain,
% 0.84/1.04 ((~hskp1) | c2_1(a2517)),
% 0.84/1.04 inference(modus_ponens,[status(thm)],[399, 396])).
% 0.84/1.04 tff(401,plain,
% 0.84/1.04 ((~hskp1) | c2_1(a2517)),
% 0.84/1.04 inference(modus_ponens,[status(thm)],[400, 396])).
% 0.84/1.04 tff(402,plain,
% 0.84/1.04 ((~hskp1) | c2_1(a2517)),
% 0.84/1.04 inference(modus_ponens,[status(thm)],[401, 396])).
% 0.84/1.04 tff(403,plain,
% 0.84/1.04 (c2_1(a2517)),
% 0.84/1.04 inference(unit_resolution,[status(thm)],[402, 383])).
% 0.84/1.04 tff(404,assumption,(~hskp29), introduced(assumption)).
% 0.84/1.04 tff(405,assumption,(~c3_1(a2517)), introduced(assumption)).
% 0.84/1.04 tff(406,assumption,(c2_1(a2517)), introduced(assumption)).
% 0.84/1.04 tff(407,plain,
% 0.84/1.04 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp29 | c1_1(a2541) | c2_1(a2541) | c3_1(a2517) | (~ndr1_0) | (~c1_1(a2517)) | (~c2_1(a2517)) | (~c3_1(a2541)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | hskp29 | c1_1(a2541) | c2_1(a2541) | c3_1(a2517) | (~ndr1_0) | (~c1_1(a2517)) | (~c2_1(a2517)) | (~c3_1(a2541)))),
% 0.84/1.04 inference(rewrite,[status(thm)],[])).
% 0.84/1.04 tff(408,plain,
% 0.84/1.04 ((hskp29 | (~ndr1_0) | c3_1(a2517) | (~c1_1(a2517)) | (~c2_1(a2517)) | c1_1(a2541) | c2_1(a2541) | (~c3_1(a2541))) <=> (hskp29 | c1_1(a2541) | c2_1(a2541) | c3_1(a2517) | (~ndr1_0) | (~c1_1(a2517)) | (~c2_1(a2517)) | (~c3_1(a2541)))),
% 0.84/1.04 inference(rewrite,[status(thm)],[])).
% 0.84/1.04 tff(409,plain,
% 0.84/1.04 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp29 | (~ndr1_0) | c3_1(a2517) | (~c1_1(a2517)) | (~c2_1(a2517)) | c1_1(a2541) | c2_1(a2541) | (~c3_1(a2541)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp29 | c1_1(a2541) | c2_1(a2541) | c3_1(a2517) | (~ndr1_0) | (~c1_1(a2517)) | (~c2_1(a2517)) | (~c3_1(a2541))))),
% 0.84/1.04 inference(monotonicity,[status(thm)],[408])).
% 0.84/1.04 tff(410,plain,
% 0.84/1.04 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp29 | (~ndr1_0) | c3_1(a2517) | (~c1_1(a2517)) | (~c2_1(a2517)) | c1_1(a2541) | c2_1(a2541) | (~c3_1(a2541)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | hskp29 | c1_1(a2541) | c2_1(a2541) | c3_1(a2517) | (~ndr1_0) | (~c1_1(a2517)) | (~c2_1(a2517)) | (~c3_1(a2541)))),
% 0.84/1.04 inference(transitivity,[status(thm)],[409, 407])).
% 0.84/1.04 tff(411,plain,
% 0.84/1.04 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp29 | (~ndr1_0) | c3_1(a2517) | (~c1_1(a2517)) | (~c2_1(a2517)) | c1_1(a2541) | c2_1(a2541) | (~c3_1(a2541)))),
% 0.84/1.04 inference(quant_inst,[status(thm)],[])).
% 0.84/1.04 tff(412,plain,
% 0.84/1.04 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | hskp29 | c1_1(a2541) | c2_1(a2541) | c3_1(a2517) | (~ndr1_0) | (~c1_1(a2517)) | (~c2_1(a2517)) | (~c3_1(a2541))),
% 0.84/1.04 inference(modus_ponens,[status(thm)],[411, 410])).
% 0.84/1.04 tff(413,plain,
% 0.84/1.04 (hskp29 | (~c1_1(a2517))),
% 0.84/1.04 inference(unit_resolution,[status(thm)],[412, 90, 267, 406, 266, 265, 405, 277])).
% 0.84/1.04 tff(414,plain,
% 0.84/1.04 (~c1_1(a2517)),
% 0.84/1.04 inference(unit_resolution,[status(thm)],[413, 404])).
% 0.84/1.04 tff(415,plain,
% 0.84/1.04 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W))) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W))))),
% 0.84/1.04 inference(bind,[status(th)],[])).
% 0.84/1.04 tff(416,plain,
% 0.84/1.04 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))),
% 0.84/1.04 inference(quant_intro,[status(thm)],[415])).
% 0.84/1.04 tff(417,plain,
% 0.84/1.04 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))),
% 0.84/1.04 inference(rewrite,[status(thm)],[])).
% 0.84/1.04 tff(418,plain,
% 0.84/1.04 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V))))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c2_1(W))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V))) | (~c2_1(W))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c2_1(W)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c2_1(W))))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c2_1(W))) | c1_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c2_1(W))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c2_1(W))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c2_1(W)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c2_1(W))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c2_1(W))))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c2_1(W))) | c1_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c2_1(W))) | c1_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c2_1(W))) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c2_1(W)))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c2_1(W))) | c1_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c2_1(W))))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c2_1(W))) | c1_1(U)) | c1_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c2_1(W))) | c3_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c2_1(W))) | c3_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | (~c2_1(W)))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c2_1(W))) | c1_1(U)) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | (~c2_1(W))))), ((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c2_1(W))) | c1_1(U)) | c1_1(V)) | c3_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | (~c2_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | (~c2_1(W))) | c0_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)))), ((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c2_1(W))) | c1_1(U)) | c1_1(V)) | c3_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W))))), (((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c2_1(W))) | c1_1(U)) | c1_1(V)) | c3_1(V)) | c0_1(W)) | c3_1(W)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W))) | c3_1(W)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W))) | c3_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))), (((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c2_1(W))) | c1_1(U)) | c1_1(V)) | c3_1(V)) | c0_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))))),
% 0.84/1.04 inference(bind,[status(th)],[])).
% 0.84/1.04 tff(419,plain,
% 0.84/1.04 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c2_1(W))) | c1_1(U)) | c1_1(V)) | c3_1(V)) | c0_1(W)) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))),
% 0.84/1.04 inference(quant_intro,[status(thm)],[418])).
% 0.84/1.04 tff(420,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c2_1(W))) | c1_1(U)) | c1_1(V)) | c3_1(V)) | c0_1(W)) | c3_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause196')).
% 0.84/1.04 tff(421,plain,
% 0.84/1.04 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))),
% 0.84/1.04 inference(modus_ponens,[status(thm)],[420, 419])).
% 0.84/1.04 tff(422,plain,
% 0.84/1.04 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))),
% 0.84/1.04 inference(modus_ponens,[status(thm)],[421, 417])).
% 0.84/1.04 tff(423,plain,(
% 0.84/1.04 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))),
% 0.84/1.04 inference(skolemize,[status(sab)],[422])).
% 0.84/1.04 tff(424,plain,
% 0.84/1.04 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))),
% 0.84/1.04 inference(modus_ponens,[status(thm)],[423, 416])).
% 0.84/1.04 tff(425,assumption,(~c0_1(a2517)), introduced(assumption)).
% 0.84/1.04 tff(426,plain,
% 0.84/1.04 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a2541) | c0_1(a2517) | c3_1(a2517) | (~ndr1_0) | c1_1(a2517) | (~c2_1(a2517)) | (~c3_1(a2541)) | (~c0_1(a2541)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a2541) | c0_1(a2517) | c3_1(a2517) | (~ndr1_0) | c1_1(a2517) | (~c2_1(a2517)) | (~c3_1(a2541)) | (~c0_1(a2541)))),
% 0.84/1.04 inference(rewrite,[status(thm)],[])).
% 0.84/1.04 tff(427,plain,
% 0.84/1.04 (((~ndr1_0) | c1_1(a2541) | (~c3_1(a2541)) | (~c0_1(a2541)) | c3_1(a2517) | c1_1(a2517) | (~c2_1(a2517)) | c3_1(a2517) | c0_1(a2517) | (~c2_1(a2517))) <=> (c1_1(a2541) | c0_1(a2517) | c3_1(a2517) | (~ndr1_0) | c1_1(a2517) | (~c2_1(a2517)) | (~c3_1(a2541)) | (~c0_1(a2541)))),
% 0.84/1.04 inference(rewrite,[status(thm)],[])).
% 0.84/1.04 tff(428,plain,
% 0.84/1.04 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a2541) | (~c3_1(a2541)) | (~c0_1(a2541)) | c3_1(a2517) | c1_1(a2517) | (~c2_1(a2517)) | c3_1(a2517) | c0_1(a2517) | (~c2_1(a2517)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a2541) | c0_1(a2517) | c3_1(a2517) | (~ndr1_0) | c1_1(a2517) | (~c2_1(a2517)) | (~c3_1(a2541)) | (~c0_1(a2541))))),
% 0.84/1.04 inference(monotonicity,[status(thm)],[427])).
% 0.84/1.04 tff(429,plain,
% 0.84/1.04 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a2541) | (~c3_1(a2541)) | (~c0_1(a2541)) | c3_1(a2517) | c1_1(a2517) | (~c2_1(a2517)) | c3_1(a2517) | c0_1(a2517) | (~c2_1(a2517)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a2541) | c0_1(a2517) | c3_1(a2517) | (~ndr1_0) | c1_1(a2517) | (~c2_1(a2517)) | (~c3_1(a2541)) | (~c0_1(a2541)))),
% 0.84/1.04 inference(transitivity,[status(thm)],[428, 426])).
% 0.84/1.04 tff(430,plain,
% 0.84/1.04 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a2541) | (~c3_1(a2541)) | (~c0_1(a2541)) | c3_1(a2517) | c1_1(a2517) | (~c2_1(a2517)) | c3_1(a2517) | c0_1(a2517) | (~c2_1(a2517)))),
% 0.84/1.04 inference(quant_inst,[status(thm)],[])).
% 0.84/1.04 tff(431,plain,
% 0.84/1.04 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a2541) | c0_1(a2517) | c3_1(a2517) | (~ndr1_0) | c1_1(a2517) | (~c2_1(a2517)) | (~c3_1(a2541)) | (~c0_1(a2541))),
% 0.84/1.04 inference(modus_ponens,[status(thm)],[430, 429])).
% 0.84/1.04 tff(432,plain,
% 0.84/1.04 (c1_1(a2517) | (~c0_1(a2541))),
% 0.84/1.04 inference(unit_resolution,[status(thm)],[431, 90, 267, 406, 266, 425, 405, 424])).
% 0.84/1.04 tff(433,plain,
% 0.84/1.04 (~c0_1(a2541)),
% 0.84/1.04 inference(unit_resolution,[status(thm)],[432, 414])).
% 0.84/1.04 tff(434,plain,
% 0.84/1.04 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp11 | c1_1(a2541) | c2_1(a2541) | (~ndr1_0) | (~c3_1(a2541)) | c0_1(a2541))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp11 | c1_1(a2541) | c2_1(a2541) | (~ndr1_0) | (~c3_1(a2541)) | c0_1(a2541))),
% 0.84/1.04 inference(rewrite,[status(thm)],[])).
% 0.84/1.04 tff(435,plain,
% 0.84/1.04 ((hskp11 | (~ndr1_0) | c2_1(a2541) | c1_1(a2541) | (~c3_1(a2541)) | c0_1(a2541) | c2_1(a2541) | (~c3_1(a2541))) <=> (hskp11 | c1_1(a2541) | c2_1(a2541) | (~ndr1_0) | (~c3_1(a2541)) | c0_1(a2541))),
% 0.84/1.04 inference(rewrite,[status(thm)],[])).
% 0.84/1.04 tff(436,plain,
% 0.84/1.04 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp11 | (~ndr1_0) | c2_1(a2541) | c1_1(a2541) | (~c3_1(a2541)) | c0_1(a2541) | c2_1(a2541) | (~c3_1(a2541)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp11 | c1_1(a2541) | c2_1(a2541) | (~ndr1_0) | (~c3_1(a2541)) | c0_1(a2541)))),
% 0.84/1.04 inference(monotonicity,[status(thm)],[435])).
% 0.84/1.04 tff(437,plain,
% 0.84/1.04 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp11 | (~ndr1_0) | c2_1(a2541) | c1_1(a2541) | (~c3_1(a2541)) | c0_1(a2541) | c2_1(a2541) | (~c3_1(a2541)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp11 | c1_1(a2541) | c2_1(a2541) | (~ndr1_0) | (~c3_1(a2541)) | c0_1(a2541))),
% 0.84/1.04 inference(transitivity,[status(thm)],[436, 434])).
% 0.84/1.04 tff(438,plain,
% 0.84/1.04 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp11 | (~ndr1_0) | c2_1(a2541) | c1_1(a2541) | (~c3_1(a2541)) | c0_1(a2541) | c2_1(a2541) | (~c3_1(a2541)))),
% 0.84/1.04 inference(quant_inst,[status(thm)],[])).
% 0.84/1.04 tff(439,plain,
% 0.84/1.04 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp11 | c1_1(a2541) | c2_1(a2541) | (~ndr1_0) | (~c3_1(a2541)) | c0_1(a2541)),
% 0.84/1.04 inference(modus_ponens,[status(thm)],[438, 437])).
% 0.84/1.04 tff(440,plain,
% 0.84/1.04 (hskp11),
% 0.84/1.04 inference(unit_resolution,[status(thm)],[439, 90, 267, 266, 265, 295, 433])).
% 0.84/1.04 tff(441,plain,
% 0.84/1.04 (~c3_1(a2531)),
% 0.84/1.04 inference(unit_resolution,[status(thm)],[308, 440])).
% 0.84/1.04 tff(442,plain,
% 0.84/1.04 (c2_1(a2531)),
% 0.84/1.04 inference(unit_resolution,[status(thm)],[316, 440])).
% 0.84/1.04 tff(443,plain,
% 0.84/1.04 (c1_1(a2531)),
% 0.84/1.04 inference(unit_resolution,[status(thm)],[324, 440])).
% 0.84/1.04 tff(444,plain,
% 0.84/1.04 ($false),
% 0.84/1.04 inference(unit_resolution,[status(thm)],[331, 90, 404, 267, 443, 442, 266, 265, 441, 277])).
% 0.84/1.04 tff(445,plain,(hskp29 | (~c3_1(a2541)) | c1_1(a2541) | c2_1(a2541) | (~c2_1(a2517)) | c0_1(a2517) | c3_1(a2517)), inference(lemma,lemma(discharge,[]))).
% 0.84/1.04 tff(446,plain,
% 0.84/1.04 (hskp29),
% 0.84/1.04 inference(unit_resolution,[status(thm)],[445, 253, 245, 239, 403, 395, 389])).
% 0.84/1.04 tff(447,plain,
% 0.84/1.04 (c3_1(a2556)),
% 0.84/1.04 inference(unit_resolution,[status(thm)],[339, 446])).
% 0.84/1.05 tff(448,plain,
% 0.84/1.05 (c2_1(a2556)),
% 0.84/1.05 inference(unit_resolution,[status(thm)],[347, 446])).
% 0.84/1.05 tff(449,plain,
% 0.84/1.05 (c1_1(a2556)),
% 0.84/1.05 inference(unit_resolution,[status(thm)],[355, 446])).
% 0.84/1.05 tff(450,plain,
% 0.84/1.05 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W)))),
% 0.84/1.05 inference(bind,[status(th)],[])).
% 0.84/1.05 tff(451,plain,
% 0.84/1.05 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))),
% 0.84/1.05 inference(quant_intro,[status(thm)],[450])).
% 0.84/1.05 tff(452,plain,
% 0.84/1.05 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))),
% 0.84/1.05 inference(rewrite,[status(thm)],[])).
% 0.84/1.05 tff(453,plain,
% 0.84/1.05 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) <=> ((~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> (((~c1_1(U)) | (~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)))), rewrite((((~c1_1(U)) | (~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c1_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c1_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(V)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c1_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c1_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(V)) | c3_1(V)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c1_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c1_1(V))) | c3_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(V)) | c3_1(V)) | c0_1(W)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V))) | c0_1(W)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V))) | c0_1(W)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c0_1(W))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(V)) | c3_1(V)) | c0_1(W)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c0_1(W)))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c0_1(W)) | c1_1(W)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W)))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) | c3_1(W)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W)) | c3_1(W)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W)) | c3_1(W)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) | c3_1(W)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))))),
% 0.84/1.05 inference(bind,[status(th)],[])).
% 0.84/1.05 tff(454,plain,
% 0.84/1.05 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))),
% 0.84/1.05 inference(quant_intro,[status(thm)],[453])).
% 0.84/1.05 tff(455,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) | c3_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause195')).
% 0.84/1.05 tff(456,plain,
% 0.84/1.05 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))),
% 0.84/1.05 inference(modus_ponens,[status(thm)],[455, 454])).
% 0.84/1.05 tff(457,plain,
% 0.84/1.05 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))),
% 0.84/1.05 inference(modus_ponens,[status(thm)],[456, 452])).
% 0.84/1.05 tff(458,plain,(
% 0.84/1.05 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))),
% 0.84/1.05 inference(skolemize,[status(sab)],[457])).
% 0.84/1.05 tff(459,plain,
% 0.84/1.05 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))),
% 0.84/1.05 inference(modus_ponens,[status(thm)],[458, 451])).
% 0.84/1.05 tff(460,plain,
% 0.84/1.05 (^[V: $i, U: $i] : refl((hskp14 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))) <=> (hskp14 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))))),
% 0.84/1.05 inference(bind,[status(th)],[])).
% 0.84/1.05 tff(461,plain,
% 0.84/1.05 (![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.84/1.05 inference(quant_intro,[status(thm)],[460])).
% 0.84/1.05 tff(462,plain,
% 0.84/1.05 (![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.84/1.05 inference(rewrite,[status(thm)],[])).
% 0.84/1.05 tff(463,plain,
% 0.84/1.05 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c0_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V))) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c0_1(V)) | c3_1(V)) | hskp14) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))) | hskp14))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))) | hskp14) <=> (hskp14 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c0_1(V)) | c3_1(V)) | hskp14) <=> (hskp14 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))))),
% 0.84/1.05 inference(bind,[status(th)],[])).
% 0.84/1.05 tff(464,plain,
% 0.84/1.05 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c0_1(V)) | c3_1(V)) | hskp14) <=> ![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.84/1.05 inference(quant_intro,[status(thm)],[463])).
% 0.84/1.05 tff(465,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c0_1(V)) | c3_1(V)) | hskp14)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause179')).
% 0.84/1.05 tff(466,plain,
% 0.84/1.05 (![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.84/1.05 inference(modus_ponens,[status(thm)],[465, 464])).
% 0.84/1.05 tff(467,plain,
% 0.84/1.05 (![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.84/1.05 inference(modus_ponens,[status(thm)],[466, 462])).
% 0.84/1.05 tff(468,plain,(
% 0.84/1.05 ![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.84/1.05 inference(skolemize,[status(sab)],[467])).
% 0.84/1.05 tff(469,plain,
% 0.84/1.05 (![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.84/1.05 inference(modus_ponens,[status(thm)],[468, 461])).
% 0.84/1.05 tff(470,assumption,(~c2_1(a2551)), introduced(assumption)).
% 0.84/1.05 tff(471,assumption,(c1_1(a2551)), introduced(assumption)).
% 0.84/1.05 tff(472,assumption,(c0_1(a2551)), introduced(assumption)).
% 0.84/1.05 tff(473,plain,
% 0.84/1.05 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp14 | c2_1(a2551) | c0_1(a2517) | c3_1(a2517) | (~ndr1_0) | (~c2_1(a2517)) | (~c0_1(a2551)) | (~c1_1(a2551)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp14 | c2_1(a2551) | c0_1(a2517) | c3_1(a2517) | (~ndr1_0) | (~c2_1(a2517)) | (~c0_1(a2551)) | (~c1_1(a2551)))),
% 0.84/1.05 inference(rewrite,[status(thm)],[])).
% 0.84/1.05 tff(474,plain,
% 0.84/1.05 ((hskp14 | (~ndr1_0) | c2_1(a2551) | (~c1_1(a2551)) | (~c0_1(a2551)) | c3_1(a2517) | c0_1(a2517) | (~c2_1(a2517))) <=> (hskp14 | c2_1(a2551) | c0_1(a2517) | c3_1(a2517) | (~ndr1_0) | (~c2_1(a2517)) | (~c0_1(a2551)) | (~c1_1(a2551)))),
% 0.84/1.05 inference(rewrite,[status(thm)],[])).
% 0.84/1.05 tff(475,plain,
% 0.84/1.05 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp14 | (~ndr1_0) | c2_1(a2551) | (~c1_1(a2551)) | (~c0_1(a2551)) | c3_1(a2517) | c0_1(a2517) | (~c2_1(a2517)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp14 | c2_1(a2551) | c0_1(a2517) | c3_1(a2517) | (~ndr1_0) | (~c2_1(a2517)) | (~c0_1(a2551)) | (~c1_1(a2551))))),
% 0.84/1.05 inference(monotonicity,[status(thm)],[474])).
% 0.84/1.05 tff(476,plain,
% 0.84/1.05 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp14 | (~ndr1_0) | c2_1(a2551) | (~c1_1(a2551)) | (~c0_1(a2551)) | c3_1(a2517) | c0_1(a2517) | (~c2_1(a2517)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp14 | c2_1(a2551) | c0_1(a2517) | c3_1(a2517) | (~ndr1_0) | (~c2_1(a2517)) | (~c0_1(a2551)) | (~c1_1(a2551)))),
% 0.84/1.05 inference(transitivity,[status(thm)],[475, 473])).
% 0.84/1.05 tff(477,plain,
% 0.84/1.05 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp14 | (~ndr1_0) | c2_1(a2551) | (~c1_1(a2551)) | (~c0_1(a2551)) | c3_1(a2517) | c0_1(a2517) | (~c2_1(a2517)))),
% 0.84/1.05 inference(quant_inst,[status(thm)],[])).
% 0.84/1.05 tff(478,plain,
% 0.84/1.05 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp14 | c2_1(a2551) | c0_1(a2517) | c3_1(a2517) | (~ndr1_0) | (~c2_1(a2517)) | (~c0_1(a2551)) | (~c1_1(a2551))),
% 0.84/1.05 inference(modus_ponens,[status(thm)],[477, 476])).
% 0.84/1.05 tff(479,plain,
% 0.84/1.05 (hskp14),
% 0.84/1.05 inference(unit_resolution,[status(thm)],[478, 90, 472, 471, 403, 470, 395, 389, 469])).
% 0.84/1.05 tff(480,plain,
% 0.84/1.05 (((~hskp14) | (~c3_1(a2536))) <=> ((~hskp14) | (~c3_1(a2536)))),
% 0.84/1.05 inference(rewrite,[status(thm)],[])).
% 0.84/1.05 tff(481,plain,
% 0.84/1.05 (((~c3_1(a2536)) | (~hskp14)) <=> ((~hskp14) | (~c3_1(a2536)))),
% 0.84/1.05 inference(rewrite,[status(thm)],[])).
% 0.84/1.05 tff(482,axiom,((~c3_1(a2536)) | (~hskp14)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause112')).
% 0.84/1.05 tff(483,plain,
% 0.84/1.05 ((~hskp14) | (~c3_1(a2536))),
% 0.84/1.05 inference(modus_ponens,[status(thm)],[482, 481])).
% 0.84/1.05 tff(484,plain,
% 0.84/1.05 ((~hskp14) | (~c3_1(a2536))),
% 0.84/1.05 inference(modus_ponens,[status(thm)],[483, 480])).
% 0.84/1.05 tff(485,plain,
% 0.84/1.05 (~c3_1(a2536)),
% 0.84/1.05 inference(unit_resolution,[status(thm)],[484, 479])).
% 0.84/1.05 tff(486,plain,
% 0.84/1.05 (((~hskp14) | (~c1_1(a2536))) <=> ((~hskp14) | (~c1_1(a2536)))),
% 0.84/1.05 inference(rewrite,[status(thm)],[])).
% 0.84/1.05 tff(487,plain,
% 0.84/1.05 (((~c1_1(a2536)) | (~hskp14)) <=> ((~hskp14) | (~c1_1(a2536)))),
% 0.84/1.05 inference(rewrite,[status(thm)],[])).
% 0.84/1.05 tff(488,axiom,((~c1_1(a2536)) | (~hskp14)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause111')).
% 0.84/1.05 tff(489,plain,
% 0.84/1.05 ((~hskp14) | (~c1_1(a2536))),
% 0.84/1.05 inference(modus_ponens,[status(thm)],[488, 487])).
% 0.84/1.05 tff(490,plain,
% 0.84/1.05 ((~hskp14) | (~c1_1(a2536))),
% 0.84/1.05 inference(modus_ponens,[status(thm)],[489, 486])).
% 0.84/1.05 tff(491,plain,
% 0.84/1.05 (~c1_1(a2536)),
% 0.84/1.05 inference(unit_resolution,[status(thm)],[490, 479])).
% 0.84/1.05 tff(492,plain,
% 0.84/1.05 (((~hskp14) | (~c0_1(a2536))) <=> ((~hskp14) | (~c0_1(a2536)))),
% 0.84/1.05 inference(rewrite,[status(thm)],[])).
% 0.84/1.05 tff(493,plain,
% 0.84/1.05 (((~c0_1(a2536)) | (~hskp14)) <=> ((~hskp14) | (~c0_1(a2536)))),
% 0.84/1.05 inference(rewrite,[status(thm)],[])).
% 0.84/1.05 tff(494,axiom,((~c0_1(a2536)) | (~hskp14)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause110')).
% 0.84/1.05 tff(495,plain,
% 0.84/1.05 ((~hskp14) | (~c0_1(a2536))),
% 0.84/1.05 inference(modus_ponens,[status(thm)],[494, 493])).
% 0.84/1.05 tff(496,plain,
% 0.84/1.05 ((~hskp14) | (~c0_1(a2536))),
% 0.84/1.05 inference(modus_ponens,[status(thm)],[495, 492])).
% 0.84/1.05 tff(497,plain,
% 0.84/1.05 (~c0_1(a2536)),
% 0.84/1.05 inference(unit_resolution,[status(thm)],[496, 479])).
% 0.84/1.05 tff(498,plain,
% 0.84/1.05 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (c3_1(a2614) | c0_1(a2536) | c1_1(a2536) | c3_1(a2536) | (~ndr1_0) | (~c2_1(a2556)) | (~c1_1(a2556)) | (~c0_1(a2556)) | c0_1(a2614) | (~c1_1(a2614)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c3_1(a2614) | c0_1(a2536) | c1_1(a2536) | c3_1(a2536) | (~ndr1_0) | (~c2_1(a2556)) | (~c1_1(a2556)) | (~c0_1(a2556)) | c0_1(a2614) | (~c1_1(a2614)))),
% 0.84/1.05 inference(rewrite,[status(thm)],[])).
% 0.84/1.05 tff(499,plain,
% 0.84/1.05 (((~ndr1_0) | (~c1_1(a2556)) | (~c0_1(a2556)) | (~c2_1(a2556)) | c3_1(a2614) | c0_1(a2614) | (~c1_1(a2614)) | c3_1(a2536) | c1_1(a2536) | c0_1(a2536)) <=> (c3_1(a2614) | c0_1(a2536) | c1_1(a2536) | c3_1(a2536) | (~ndr1_0) | (~c2_1(a2556)) | (~c1_1(a2556)) | (~c0_1(a2556)) | c0_1(a2614) | (~c1_1(a2614)))),
% 0.84/1.05 inference(rewrite,[status(thm)],[])).
% 0.84/1.05 tff(500,plain,
% 0.84/1.05 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c1_1(a2556)) | (~c0_1(a2556)) | (~c2_1(a2556)) | c3_1(a2614) | c0_1(a2614) | (~c1_1(a2614)) | c3_1(a2536) | c1_1(a2536) | c0_1(a2536))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (c3_1(a2614) | c0_1(a2536) | c1_1(a2536) | c3_1(a2536) | (~ndr1_0) | (~c2_1(a2556)) | (~c1_1(a2556)) | (~c0_1(a2556)) | c0_1(a2614) | (~c1_1(a2614))))),
% 0.84/1.05 inference(monotonicity,[status(thm)],[499])).
% 0.84/1.05 tff(501,plain,
% 0.84/1.05 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c1_1(a2556)) | (~c0_1(a2556)) | (~c2_1(a2556)) | c3_1(a2614) | c0_1(a2614) | (~c1_1(a2614)) | c3_1(a2536) | c1_1(a2536) | c0_1(a2536))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c3_1(a2614) | c0_1(a2536) | c1_1(a2536) | c3_1(a2536) | (~ndr1_0) | (~c2_1(a2556)) | (~c1_1(a2556)) | (~c0_1(a2556)) | c0_1(a2614) | (~c1_1(a2614)))),
% 0.84/1.05 inference(transitivity,[status(thm)],[500, 498])).
% 0.84/1.05 tff(502,plain,
% 0.84/1.05 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c1_1(a2556)) | (~c0_1(a2556)) | (~c2_1(a2556)) | c3_1(a2614) | c0_1(a2614) | (~c1_1(a2614)) | c3_1(a2536) | c1_1(a2536) | c0_1(a2536))),
% 0.84/1.05 inference(quant_inst,[status(thm)],[])).
% 0.84/1.05 tff(503,plain,
% 0.84/1.05 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c3_1(a2614) | c0_1(a2536) | c1_1(a2536) | c3_1(a2536) | (~ndr1_0) | (~c2_1(a2556)) | (~c1_1(a2556)) | (~c0_1(a2556)) | c0_1(a2614) | (~c1_1(a2614))),
% 0.84/1.05 inference(modus_ponens,[status(thm)],[502, 501])).
% 0.84/1.05 tff(504,plain,
% 0.84/1.05 (~c0_1(a2556)),
% 0.84/1.05 inference(unit_resolution,[status(thm)],[503, 90, 449, 448, 13, 20, 497, 491, 485, 459, 365])).
% 0.84/1.05 tff(505,plain,
% 0.84/1.05 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W))))),
% 0.84/1.05 inference(bind,[status(th)],[])).
% 0.84/1.05 tff(506,plain,
% 0.84/1.05 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))),
% 0.84/1.05 inference(quant_intro,[status(thm)],[505])).
% 0.84/1.05 tff(507,plain,
% 0.84/1.05 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))),
% 0.84/1.05 inference(rewrite,[status(thm)],[])).
% 0.84/1.05 tff(508,plain,
% 0.84/1.05 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c3_1(U)) | (~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)))), rewrite((((~c3_1(U)) | (~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c0_1(V))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c0_1(V)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c0_1(V))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c0_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(V))) | (~c2_1(W))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V))) | (~c2_1(W))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(W)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(W))))), ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(V))) | (~c2_1(W))) | (~c3_1(W))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(W))) | (~c3_1(W))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(W))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(W)) | (~c3_1(W)))), ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(V))) | (~c2_1(W))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(W)) | (~c3_1(W))))), (((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c0_1(W)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(W)) | (~c3_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(W)) | (~c3_1(W))) | c0_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))), (((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c0_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))))),
% 0.84/1.05 inference(bind,[status(th)],[])).
% 0.84/1.05 tff(509,plain,
% 0.84/1.05 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))),
% 0.84/1.05 inference(quant_intro,[status(thm)],[508])).
% 0.84/1.05 tff(510,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c0_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause204')).
% 0.84/1.05 tff(511,plain,
% 0.84/1.05 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))),
% 0.84/1.05 inference(modus_ponens,[status(thm)],[510, 509])).
% 0.84/1.05 tff(512,plain,
% 0.84/1.05 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))),
% 0.84/1.05 inference(modus_ponens,[status(thm)],[511, 507])).
% 0.84/1.05 tff(513,plain,(
% 0.84/1.05 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))),
% 0.84/1.05 inference(skolemize,[status(sab)],[512])).
% 0.84/1.05 tff(514,plain,
% 0.84/1.05 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))),
% 0.84/1.05 inference(modus_ponens,[status(thm)],[513, 506])).
% 0.84/1.05 tff(515,plain,
% 0.84/1.05 (^[U: $i] : refl((hskp23 | hskp31 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U))) <=> (hskp23 | hskp31 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U))))),
% 0.84/1.05 inference(bind,[status(th)],[])).
% 0.84/1.05 tff(516,plain,
% 0.84/1.05 (![U: $i] : (hskp23 | hskp31 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U))) <=> ![U: $i] : (hskp23 | hskp31 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))),
% 0.84/1.05 inference(quant_intro,[status(thm)],[515])).
% 0.84/1.05 tff(517,plain,
% 0.84/1.05 (![U: $i] : (hskp23 | hskp31 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U))) <=> ![U: $i] : (hskp23 | hskp31 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))),
% 0.84/1.05 inference(rewrite,[status(thm)],[])).
% 0.84/1.05 tff(518,plain,
% 0.84/1.05 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c3_1(U)) | (~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)))), rewrite((((~c3_1(U)) | (~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp31) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U))) | hskp31))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U))) | hskp31) <=> (hskp31 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp31) <=> (hskp31 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp31) | hskp23) <=> ((hskp31 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U))) | hskp23))), rewrite(((hskp31 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U))) | hskp23) <=> (hskp23 | hskp31 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp31) | hskp23) <=> (hskp23 | hskp31 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))))),
% 0.84/1.05 inference(bind,[status(th)],[])).
% 0.84/1.05 tff(519,plain,
% 0.84/1.05 (![U: $i] : ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp31) | hskp23) <=> ![U: $i] : (hskp23 | hskp31 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))),
% 0.84/1.05 inference(quant_intro,[status(thm)],[518])).
% 0.84/1.05 tff(520,axiom,(![U: $i] : ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp31) | hskp23)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause161')).
% 0.84/1.05 tff(521,plain,
% 0.84/1.05 (![U: $i] : (hskp23 | hskp31 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))),
% 0.84/1.05 inference(modus_ponens,[status(thm)],[520, 519])).
% 0.84/1.05 tff(522,plain,
% 0.84/1.05 (![U: $i] : (hskp23 | hskp31 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))),
% 0.84/1.05 inference(modus_ponens,[status(thm)],[521, 517])).
% 0.84/1.05 tff(523,plain,(
% 0.84/1.05 ![U: $i] : (hskp23 | hskp31 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))),
% 0.84/1.05 inference(skolemize,[status(sab)],[522])).
% 0.84/1.05 tff(524,plain,
% 0.84/1.05 (![U: $i] : (hskp23 | hskp31 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))),
% 0.84/1.05 inference(modus_ponens,[status(thm)],[523, 516])).
% 0.84/1.05 tff(525,plain,
% 0.84/1.05 (((~![U: $i] : (hskp23 | hskp31 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))) | (hskp23 | hskp31 | (~ndr1_0) | (~c2_1(a2556)) | (~c3_1(a2556)) | (~c1_1(a2556)))) <=> ((~![U: $i] : (hskp23 | hskp31 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))) | hskp23 | hskp31 | (~ndr1_0) | (~c2_1(a2556)) | (~c3_1(a2556)) | (~c1_1(a2556)))),
% 0.84/1.05 inference(rewrite,[status(thm)],[])).
% 0.84/1.05 tff(526,plain,
% 0.84/1.05 ((hskp23 | hskp31 | (~ndr1_0) | (~c3_1(a2556)) | (~c1_1(a2556)) | (~c2_1(a2556))) <=> (hskp23 | hskp31 | (~ndr1_0) | (~c2_1(a2556)) | (~c3_1(a2556)) | (~c1_1(a2556)))),
% 0.84/1.05 inference(rewrite,[status(thm)],[])).
% 0.84/1.05 tff(527,plain,
% 0.84/1.05 (((~![U: $i] : (hskp23 | hskp31 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))) | (hskp23 | hskp31 | (~ndr1_0) | (~c3_1(a2556)) | (~c1_1(a2556)) | (~c2_1(a2556)))) <=> ((~![U: $i] : (hskp23 | hskp31 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))) | (hskp23 | hskp31 | (~ndr1_0) | (~c2_1(a2556)) | (~c3_1(a2556)) | (~c1_1(a2556))))),
% 0.84/1.05 inference(monotonicity,[status(thm)],[526])).
% 0.84/1.05 tff(528,plain,
% 0.84/1.05 (((~![U: $i] : (hskp23 | hskp31 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))) | (hskp23 | hskp31 | (~ndr1_0) | (~c3_1(a2556)) | (~c1_1(a2556)) | (~c2_1(a2556)))) <=> ((~![U: $i] : (hskp23 | hskp31 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))) | hskp23 | hskp31 | (~ndr1_0) | (~c2_1(a2556)) | (~c3_1(a2556)) | (~c1_1(a2556)))),
% 0.84/1.05 inference(transitivity,[status(thm)],[527, 525])).
% 0.84/1.05 tff(529,plain,
% 0.84/1.05 ((~![U: $i] : (hskp23 | hskp31 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))) | (hskp23 | hskp31 | (~ndr1_0) | (~c3_1(a2556)) | (~c1_1(a2556)) | (~c2_1(a2556)))),
% 0.84/1.05 inference(quant_inst,[status(thm)],[])).
% 0.84/1.05 tff(530,plain,
% 0.84/1.05 ((~![U: $i] : (hskp23 | hskp31 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))) | hskp23 | hskp31 | (~ndr1_0) | (~c2_1(a2556)) | (~c3_1(a2556)) | (~c1_1(a2556))),
% 0.84/1.05 inference(modus_ponens,[status(thm)],[529, 528])).
% 0.84/1.05 tff(531,plain,
% 0.84/1.05 (hskp31),
% 0.84/1.05 inference(unit_resolution,[status(thm)],[530, 1, 90, 449, 448, 447, 524])).
% 0.84/1.05 tff(532,plain,
% 0.84/1.05 (((~hskp31) | c3_1(a2597)) <=> ((~hskp31) | c3_1(a2597))),
% 0.84/1.05 inference(rewrite,[status(thm)],[])).
% 0.84/1.05 tff(533,axiom,((~hskp31) | c3_1(a2597)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause43')).
% 0.84/1.05 tff(534,plain,
% 0.84/1.05 ((~hskp31) | c3_1(a2597)),
% 0.84/1.05 inference(modus_ponens,[status(thm)],[533, 532])).
% 0.84/1.05 tff(535,plain,
% 0.84/1.05 ((~hskp31) | c3_1(a2597)),
% 0.84/1.05 inference(modus_ponens,[status(thm)],[534, 532])).
% 0.84/1.05 tff(536,plain,
% 0.84/1.05 ((~hskp31) | c3_1(a2597)),
% 0.84/1.05 inference(modus_ponens,[status(thm)],[535, 532])).
% 0.84/1.05 tff(537,plain,
% 0.84/1.05 ((~hskp31) | c3_1(a2597)),
% 0.84/1.05 inference(modus_ponens,[status(thm)],[536, 532])).
% 0.84/1.05 tff(538,plain,
% 0.84/1.05 ((~hskp31) | c3_1(a2597)),
% 0.84/1.05 inference(modus_ponens,[status(thm)],[537, 532])).
% 0.84/1.05 tff(539,plain,
% 0.84/1.05 (c3_1(a2597)),
% 0.84/1.05 inference(unit_resolution,[status(thm)],[538, 531])).
% 0.84/1.05 tff(540,plain,
% 0.84/1.05 (((~hskp31) | c1_1(a2597)) <=> ((~hskp31) | c1_1(a2597))),
% 0.84/1.05 inference(rewrite,[status(thm)],[])).
% 0.84/1.05 tff(541,axiom,((~hskp31) | c1_1(a2597)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause42')).
% 0.84/1.05 tff(542,plain,
% 0.84/1.05 ((~hskp31) | c1_1(a2597)),
% 0.84/1.05 inference(modus_ponens,[status(thm)],[541, 540])).
% 0.84/1.05 tff(543,plain,
% 0.84/1.05 ((~hskp31) | c1_1(a2597)),
% 0.84/1.05 inference(modus_ponens,[status(thm)],[542, 540])).
% 0.84/1.05 tff(544,plain,
% 0.84/1.05 ((~hskp31) | c1_1(a2597)),
% 0.84/1.05 inference(modus_ponens,[status(thm)],[543, 540])).
% 0.84/1.05 tff(545,plain,
% 0.84/1.05 ((~hskp31) | c1_1(a2597)),
% 0.84/1.05 inference(modus_ponens,[status(thm)],[544, 540])).
% 0.84/1.05 tff(546,plain,
% 0.84/1.05 ((~hskp31) | c1_1(a2597)),
% 0.84/1.05 inference(modus_ponens,[status(thm)],[545, 540])).
% 0.84/1.05 tff(547,plain,
% 0.84/1.05 (c1_1(a2597)),
% 0.84/1.05 inference(unit_resolution,[status(thm)],[546, 531])).
% 0.84/1.05 tff(548,plain,
% 0.84/1.05 (((~hskp31) | c0_1(a2597)) <=> ((~hskp31) | c0_1(a2597))),
% 0.84/1.05 inference(rewrite,[status(thm)],[])).
% 0.84/1.05 tff(549,axiom,((~hskp31) | c0_1(a2597)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause41')).
% 0.84/1.05 tff(550,plain,
% 0.84/1.05 ((~hskp31) | c0_1(a2597)),
% 0.84/1.05 inference(modus_ponens,[status(thm)],[549, 548])).
% 0.84/1.05 tff(551,plain,
% 0.84/1.05 ((~hskp31) | c0_1(a2597)),
% 0.84/1.05 inference(modus_ponens,[status(thm)],[550, 548])).
% 0.84/1.05 tff(552,plain,
% 0.84/1.05 ((~hskp31) | c0_1(a2597)),
% 0.84/1.05 inference(modus_ponens,[status(thm)],[551, 548])).
% 0.84/1.05 tff(553,plain,
% 0.84/1.05 ((~hskp31) | c0_1(a2597)),
% 0.84/1.05 inference(modus_ponens,[status(thm)],[552, 548])).
% 0.84/1.05 tff(554,plain,
% 0.84/1.05 ((~hskp31) | c0_1(a2597)),
% 0.84/1.05 inference(modus_ponens,[status(thm)],[553, 548])).
% 0.84/1.05 tff(555,plain,
% 0.84/1.05 (c0_1(a2597)),
% 0.84/1.05 inference(unit_resolution,[status(thm)],[554, 531])).
% 0.84/1.05 tff(556,plain,
% 0.84/1.05 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | (~c0_1(a2597)) | (~c3_1(a2597)) | (~c2_1(a2597)) | (~c1_1(a2597)) | (~c2_1(a2556)) | (~c3_1(a2556)) | c0_1(a2556))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | (~ndr1_0) | (~c0_1(a2597)) | (~c3_1(a2597)) | (~c2_1(a2597)) | (~c1_1(a2597)) | (~c2_1(a2556)) | (~c3_1(a2556)) | c0_1(a2556))),
% 0.84/1.05 inference(rewrite,[status(thm)],[])).
% 0.84/1.05 tff(557,plain,
% 0.84/1.05 (((~ndr1_0) | (~c3_1(a2597)) | (~c0_1(a2597)) | (~c2_1(a2597)) | (~c3_1(a2597)) | (~c1_1(a2597)) | (~c0_1(a2597)) | c0_1(a2556) | (~c2_1(a2556)) | (~c3_1(a2556))) <=> ((~ndr1_0) | (~c0_1(a2597)) | (~c3_1(a2597)) | (~c2_1(a2597)) | (~c1_1(a2597)) | (~c2_1(a2556)) | (~c3_1(a2556)) | c0_1(a2556))),
% 0.84/1.05 inference(rewrite,[status(thm)],[])).
% 0.84/1.05 tff(558,plain,
% 0.84/1.05 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a2597)) | (~c0_1(a2597)) | (~c2_1(a2597)) | (~c3_1(a2597)) | (~c1_1(a2597)) | (~c0_1(a2597)) | c0_1(a2556) | (~c2_1(a2556)) | (~c3_1(a2556)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | (~c0_1(a2597)) | (~c3_1(a2597)) | (~c2_1(a2597)) | (~c1_1(a2597)) | (~c2_1(a2556)) | (~c3_1(a2556)) | c0_1(a2556)))),
% 0.84/1.05 inference(monotonicity,[status(thm)],[557])).
% 0.84/1.05 tff(559,plain,
% 0.84/1.05 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a2597)) | (~c0_1(a2597)) | (~c2_1(a2597)) | (~c3_1(a2597)) | (~c1_1(a2597)) | (~c0_1(a2597)) | c0_1(a2556) | (~c2_1(a2556)) | (~c3_1(a2556)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | (~ndr1_0) | (~c0_1(a2597)) | (~c3_1(a2597)) | (~c2_1(a2597)) | (~c1_1(a2597)) | (~c2_1(a2556)) | (~c3_1(a2556)) | c0_1(a2556))),
% 0.84/1.05 inference(transitivity,[status(thm)],[558, 556])).
% 0.84/1.05 tff(560,plain,
% 0.84/1.05 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a2597)) | (~c0_1(a2597)) | (~c2_1(a2597)) | (~c3_1(a2597)) | (~c1_1(a2597)) | (~c0_1(a2597)) | c0_1(a2556) | (~c2_1(a2556)) | (~c3_1(a2556)))),
% 0.84/1.06 inference(quant_inst,[status(thm)],[])).
% 0.84/1.06 tff(561,plain,
% 0.84/1.06 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | (~ndr1_0) | (~c0_1(a2597)) | (~c3_1(a2597)) | (~c2_1(a2597)) | (~c1_1(a2597)) | (~c2_1(a2556)) | (~c3_1(a2556)) | c0_1(a2556)),
% 0.84/1.06 inference(modus_ponens,[status(thm)],[560, 559])).
% 0.84/1.06 tff(562,plain,
% 0.84/1.06 (~c2_1(a2597)),
% 0.84/1.06 inference(unit_resolution,[status(thm)],[561, 90, 555, 547, 539, 448, 447, 514, 504])).
% 0.84/1.06 tff(563,plain,
% 0.84/1.06 (^[V: $i, U: $i] : refl((hskp18 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V))) <=> (hskp18 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V))))),
% 0.84/1.06 inference(bind,[status(th)],[])).
% 0.84/1.06 tff(564,plain,
% 0.84/1.06 (![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 0.84/1.06 inference(quant_intro,[status(thm)],[563])).
% 0.84/1.06 tff(565,plain,
% 0.84/1.06 (![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 0.84/1.06 inference(rewrite,[status(thm)],[])).
% 0.84/1.06 tff(566,plain,
% 0.84/1.06 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c3_1(U)) | (~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)))), rewrite((((~c3_1(U)) | (~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | (~c1_1(V)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | (~c1_1(V))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | (~c1_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c1_1(V)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c1_1(V))))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c2_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V))))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(V)) | hskp18) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V))) | hskp18))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V))) | hskp18) <=> (hskp18 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(V)) | hskp18) <=> (hskp18 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))))),
% 0.84/1.06 inference(bind,[status(th)],[])).
% 0.84/1.06 tff(567,plain,
% 0.84/1.06 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(V)) | hskp18) <=> ![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 0.84/1.06 inference(quant_intro,[status(thm)],[566])).
% 0.84/1.06 tff(568,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(V)) | hskp18)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause193')).
% 0.84/1.06 tff(569,plain,
% 0.84/1.06 (![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 0.84/1.06 inference(modus_ponens,[status(thm)],[568, 567])).
% 0.84/1.06 tff(570,plain,
% 0.84/1.06 (![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 0.84/1.06 inference(modus_ponens,[status(thm)],[569, 565])).
% 0.84/1.06 tff(571,plain,(
% 0.84/1.06 ![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 0.84/1.06 inference(skolemize,[status(sab)],[570])).
% 0.84/1.06 tff(572,plain,
% 0.84/1.06 (![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 0.84/1.06 inference(modus_ponens,[status(thm)],[571, 564])).
% 0.84/1.06 tff(573,plain,
% 0.84/1.06 (((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp18 | (~ndr1_0) | (~c3_1(a2597)) | c2_1(a2597) | (~c1_1(a2597)) | (~c2_1(a2556)) | (~c3_1(a2556)) | (~c1_1(a2556)))) <=> ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp18 | (~ndr1_0) | (~c3_1(a2597)) | c2_1(a2597) | (~c1_1(a2597)) | (~c2_1(a2556)) | (~c3_1(a2556)) | (~c1_1(a2556)))),
% 0.84/1.06 inference(rewrite,[status(thm)],[])).
% 0.84/1.06 tff(574,plain,
% 0.84/1.06 ((hskp18 | (~ndr1_0) | (~c3_1(a2556)) | (~c1_1(a2556)) | (~c2_1(a2556)) | c2_1(a2597) | (~c3_1(a2597)) | (~c1_1(a2597))) <=> (hskp18 | (~ndr1_0) | (~c3_1(a2597)) | c2_1(a2597) | (~c1_1(a2597)) | (~c2_1(a2556)) | (~c3_1(a2556)) | (~c1_1(a2556)))),
% 0.84/1.06 inference(rewrite,[status(thm)],[])).
% 0.84/1.06 tff(575,plain,
% 0.84/1.06 (((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp18 | (~ndr1_0) | (~c3_1(a2556)) | (~c1_1(a2556)) | (~c2_1(a2556)) | c2_1(a2597) | (~c3_1(a2597)) | (~c1_1(a2597)))) <=> ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp18 | (~ndr1_0) | (~c3_1(a2597)) | c2_1(a2597) | (~c1_1(a2597)) | (~c2_1(a2556)) | (~c3_1(a2556)) | (~c1_1(a2556))))),
% 0.84/1.06 inference(monotonicity,[status(thm)],[574])).
% 0.84/1.06 tff(576,plain,
% 0.84/1.06 (((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp18 | (~ndr1_0) | (~c3_1(a2556)) | (~c1_1(a2556)) | (~c2_1(a2556)) | c2_1(a2597) | (~c3_1(a2597)) | (~c1_1(a2597)))) <=> ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp18 | (~ndr1_0) | (~c3_1(a2597)) | c2_1(a2597) | (~c1_1(a2597)) | (~c2_1(a2556)) | (~c3_1(a2556)) | (~c1_1(a2556)))),
% 0.84/1.06 inference(transitivity,[status(thm)],[575, 573])).
% 0.84/1.06 tff(577,plain,
% 0.84/1.06 ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp18 | (~ndr1_0) | (~c3_1(a2556)) | (~c1_1(a2556)) | (~c2_1(a2556)) | c2_1(a2597) | (~c3_1(a2597)) | (~c1_1(a2597)))),
% 0.84/1.06 inference(quant_inst,[status(thm)],[])).
% 0.84/1.06 tff(578,plain,
% 0.84/1.06 ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp18 | (~ndr1_0) | (~c3_1(a2597)) | c2_1(a2597) | (~c1_1(a2597)) | (~c2_1(a2556)) | (~c3_1(a2556)) | (~c1_1(a2556))),
% 0.84/1.06 inference(modus_ponens,[status(thm)],[577, 576])).
% 0.84/1.06 tff(579,plain,
% 0.84/1.06 (hskp18),
% 0.84/1.06 inference(unit_resolution,[status(thm)],[578, 90, 547, 539, 449, 448, 447, 572, 562])).
% 0.84/1.06 tff(580,plain,
% 0.84/1.06 (((~hskp18) | (~c0_1(a2545))) <=> ((~hskp18) | (~c0_1(a2545)))),
% 0.84/1.06 inference(rewrite,[status(thm)],[])).
% 0.84/1.06 tff(581,plain,
% 0.84/1.06 (((~c0_1(a2545)) | (~hskp18)) <=> ((~hskp18) | (~c0_1(a2545)))),
% 0.84/1.06 inference(rewrite,[status(thm)],[])).
% 0.84/1.06 tff(582,axiom,((~c0_1(a2545)) | (~hskp18)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause103')).
% 0.84/1.06 tff(583,plain,
% 0.84/1.06 ((~hskp18) | (~c0_1(a2545))),
% 0.84/1.06 inference(modus_ponens,[status(thm)],[582, 581])).
% 0.84/1.06 tff(584,plain,
% 0.84/1.06 ((~hskp18) | (~c0_1(a2545))),
% 0.84/1.06 inference(modus_ponens,[status(thm)],[583, 580])).
% 0.84/1.06 tff(585,plain,
% 0.84/1.06 (~c0_1(a2545)),
% 0.84/1.06 inference(unit_resolution,[status(thm)],[584, 579])).
% 0.84/1.06 tff(586,plain,
% 0.84/1.06 (((~hskp18) | c2_1(a2545)) <=> ((~hskp18) | c2_1(a2545))),
% 0.84/1.06 inference(rewrite,[status(thm)],[])).
% 0.84/1.06 tff(587,axiom,((~hskp18) | c2_1(a2545)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause67')).
% 0.84/1.06 tff(588,plain,
% 0.84/1.06 ((~hskp18) | c2_1(a2545)),
% 0.84/1.06 inference(modus_ponens,[status(thm)],[587, 586])).
% 0.84/1.06 tff(589,plain,
% 0.84/1.06 ((~hskp18) | c2_1(a2545)),
% 0.84/1.06 inference(modus_ponens,[status(thm)],[588, 586])).
% 0.84/1.06 tff(590,plain,
% 0.84/1.06 ((~hskp18) | c2_1(a2545)),
% 0.84/1.06 inference(modus_ponens,[status(thm)],[589, 586])).
% 0.84/1.06 tff(591,plain,
% 0.84/1.06 ((~hskp18) | c2_1(a2545)),
% 0.84/1.06 inference(modus_ponens,[status(thm)],[590, 586])).
% 0.84/1.06 tff(592,plain,
% 0.84/1.06 ((~hskp18) | c2_1(a2545)),
% 0.84/1.06 inference(modus_ponens,[status(thm)],[591, 586])).
% 0.84/1.06 tff(593,plain,
% 0.84/1.06 (c2_1(a2545)),
% 0.84/1.06 inference(unit_resolution,[status(thm)],[592, 579])).
% 0.84/1.06 tff(594,plain,
% 0.84/1.06 (((~hskp18) | c1_1(a2545)) <=> ((~hskp18) | c1_1(a2545))),
% 0.84/1.06 inference(rewrite,[status(thm)],[])).
% 0.84/1.06 tff(595,axiom,((~hskp18) | c1_1(a2545)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause66')).
% 0.84/1.06 tff(596,plain,
% 0.84/1.06 ((~hskp18) | c1_1(a2545)),
% 0.84/1.06 inference(modus_ponens,[status(thm)],[595, 594])).
% 0.84/1.06 tff(597,plain,
% 0.84/1.06 ((~hskp18) | c1_1(a2545)),
% 0.84/1.06 inference(modus_ponens,[status(thm)],[596, 594])).
% 0.84/1.06 tff(598,plain,
% 0.84/1.06 ((~hskp18) | c1_1(a2545)),
% 0.84/1.06 inference(modus_ponens,[status(thm)],[597, 594])).
% 0.84/1.06 tff(599,plain,
% 0.84/1.06 ((~hskp18) | c1_1(a2545)),
% 0.84/1.06 inference(modus_ponens,[status(thm)],[598, 594])).
% 0.84/1.06 tff(600,plain,
% 0.84/1.06 ((~hskp18) | c1_1(a2545)),
% 0.84/1.06 inference(modus_ponens,[status(thm)],[599, 594])).
% 0.84/1.06 tff(601,plain,
% 0.84/1.06 (c1_1(a2545)),
% 0.84/1.06 inference(unit_resolution,[status(thm)],[600, 579])).
% 0.84/1.06 tff(602,assumption,(hskp8), introduced(assumption)).
% 0.84/1.06 tff(603,plain,
% 0.84/1.06 (((~hskp8) | (~c3_1(a2525))) <=> ((~hskp8) | (~c3_1(a2525)))),
% 0.84/1.06 inference(rewrite,[status(thm)],[])).
% 0.84/1.06 tff(604,plain,
% 0.84/1.06 (((~c3_1(a2525)) | (~hskp8)) <=> ((~hskp8) | (~c3_1(a2525)))),
% 0.84/1.06 inference(rewrite,[status(thm)],[])).
% 0.84/1.06 tff(605,axiom,((~c3_1(a2525)) | (~hskp8)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause122')).
% 0.84/1.06 tff(606,plain,
% 0.84/1.06 ((~hskp8) | (~c3_1(a2525))),
% 0.84/1.06 inference(modus_ponens,[status(thm)],[605, 604])).
% 0.84/1.06 tff(607,plain,
% 0.84/1.06 ((~hskp8) | (~c3_1(a2525))),
% 0.84/1.06 inference(modus_ponens,[status(thm)],[606, 603])).
% 0.84/1.06 tff(608,plain,
% 0.84/1.06 (~c3_1(a2525)),
% 0.84/1.06 inference(unit_resolution,[status(thm)],[607, 602])).
% 0.84/1.06 tff(609,plain,
% 0.84/1.06 (((~hskp8) | c0_1(a2525)) <=> ((~hskp8) | c0_1(a2525))),
% 0.84/1.06 inference(rewrite,[status(thm)],[])).
% 0.84/1.06 tff(610,axiom,((~hskp8) | c0_1(a2525)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause77')).
% 0.84/1.06 tff(611,plain,
% 0.84/1.06 ((~hskp8) | c0_1(a2525)),
% 0.84/1.06 inference(modus_ponens,[status(thm)],[610, 609])).
% 0.84/1.06 tff(612,plain,
% 0.84/1.06 ((~hskp8) | c0_1(a2525)),
% 0.84/1.06 inference(modus_ponens,[status(thm)],[611, 609])).
% 0.84/1.06 tff(613,plain,
% 0.84/1.06 ((~hskp8) | c0_1(a2525)),
% 0.84/1.06 inference(modus_ponens,[status(thm)],[612, 609])).
% 0.84/1.06 tff(614,plain,
% 0.84/1.06 ((~hskp8) | c0_1(a2525)),
% 0.84/1.06 inference(modus_ponens,[status(thm)],[613, 609])).
% 0.84/1.06 tff(615,plain,
% 0.84/1.06 ((~hskp8) | c0_1(a2525)),
% 0.84/1.06 inference(modus_ponens,[status(thm)],[614, 609])).
% 0.84/1.06 tff(616,plain,
% 0.84/1.06 (c0_1(a2525)),
% 0.84/1.06 inference(unit_resolution,[status(thm)],[615, 602])).
% 0.84/1.06 tff(617,assumption,(c3_1(a2556)), introduced(assumption)).
% 0.84/1.06 tff(618,assumption,(c2_1(a2556)), introduced(assumption)).
% 0.84/1.06 tff(619,assumption,(c1_1(a2556)), introduced(assumption)).
% 0.84/1.06 tff(620,plain,
% 0.84/1.06 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (c1_1(a2541) | c2_1(a2541) | c3_1(a2525) | (~ndr1_0) | (~c2_1(a2556)) | (~c3_1(a2556)) | (~c1_1(a2556)) | (~c0_1(a2525)) | (~c1_1(a2525)) | (~c3_1(a2541)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a2541) | c2_1(a2541) | c3_1(a2525) | (~ndr1_0) | (~c2_1(a2556)) | (~c3_1(a2556)) | (~c1_1(a2556)) | (~c0_1(a2525)) | (~c1_1(a2525)) | (~c3_1(a2541)))),
% 0.84/1.06 inference(rewrite,[status(thm)],[])).
% 0.84/1.06 tff(621,plain,
% 0.84/1.06 (((~ndr1_0) | (~c3_1(a2556)) | (~c1_1(a2556)) | (~c2_1(a2556)) | c3_1(a2525) | (~c1_1(a2525)) | (~c0_1(a2525)) | c1_1(a2541) | c2_1(a2541) | (~c3_1(a2541))) <=> (c1_1(a2541) | c2_1(a2541) | c3_1(a2525) | (~ndr1_0) | (~c2_1(a2556)) | (~c3_1(a2556)) | (~c1_1(a2556)) | (~c0_1(a2525)) | (~c1_1(a2525)) | (~c3_1(a2541)))),
% 0.84/1.06 inference(rewrite,[status(thm)],[])).
% 0.84/1.06 tff(622,plain,
% 0.84/1.06 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a2556)) | (~c1_1(a2556)) | (~c2_1(a2556)) | c3_1(a2525) | (~c1_1(a2525)) | (~c0_1(a2525)) | c1_1(a2541) | c2_1(a2541) | (~c3_1(a2541)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (c1_1(a2541) | c2_1(a2541) | c3_1(a2525) | (~ndr1_0) | (~c2_1(a2556)) | (~c3_1(a2556)) | (~c1_1(a2556)) | (~c0_1(a2525)) | (~c1_1(a2525)) | (~c3_1(a2541))))),
% 0.84/1.06 inference(monotonicity,[status(thm)],[621])).
% 0.84/1.06 tff(623,plain,
% 0.84/1.06 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a2556)) | (~c1_1(a2556)) | (~c2_1(a2556)) | c3_1(a2525) | (~c1_1(a2525)) | (~c0_1(a2525)) | c1_1(a2541) | c2_1(a2541) | (~c3_1(a2541)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a2541) | c2_1(a2541) | c3_1(a2525) | (~ndr1_0) | (~c2_1(a2556)) | (~c3_1(a2556)) | (~c1_1(a2556)) | (~c0_1(a2525)) | (~c1_1(a2525)) | (~c3_1(a2541)))),
% 0.84/1.06 inference(transitivity,[status(thm)],[622, 620])).
% 0.84/1.06 tff(624,plain,
% 0.84/1.06 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a2556)) | (~c1_1(a2556)) | (~c2_1(a2556)) | c3_1(a2525) | (~c1_1(a2525)) | (~c0_1(a2525)) | c1_1(a2541) | c2_1(a2541) | (~c3_1(a2541)))),
% 0.84/1.06 inference(quant_inst,[status(thm)],[])).
% 0.84/1.06 tff(625,plain,
% 0.84/1.06 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a2541) | c2_1(a2541) | c3_1(a2525) | (~ndr1_0) | (~c2_1(a2556)) | (~c3_1(a2556)) | (~c1_1(a2556)) | (~c0_1(a2525)) | (~c1_1(a2525)) | (~c3_1(a2541))),
% 0.84/1.06 inference(modus_ponens,[status(thm)],[624, 623])).
% 0.84/1.06 tff(626,plain,
% 0.84/1.06 (~c1_1(a2525)),
% 0.84/1.06 inference(unit_resolution,[status(thm)],[625, 90, 619, 618, 617, 267, 616, 266, 265, 608, 264])).
% 0.84/1.06 tff(627,plain,
% 0.84/1.06 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W))) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W))))),
% 0.84/1.06 inference(bind,[status(th)],[])).
% 0.84/1.06 tff(628,plain,
% 0.84/1.06 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))),
% 0.84/1.06 inference(quant_intro,[status(thm)],[627])).
% 0.84/1.06 tff(629,plain,
% 0.84/1.06 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))),
% 0.84/1.06 inference(rewrite,[status(thm)],[])).
% 0.84/1.06 tff(630,plain,
% 0.84/1.06 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c0_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c0_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(V)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(V))))), (((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c1_1(W))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(V))) | (~c1_1(W))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(W)))), (((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(W))))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c1_1(W))) | (~c2_1(W))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(W))) | (~c2_1(W))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(W))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(W)) | (~c1_1(W)))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c1_1(W))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(W)) | (~c1_1(W))))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c1_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(W)) | (~c1_1(W))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(W)) | (~c1_1(W))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(W)) | (~c1_1(W)))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(W)) | (~c1_1(W))))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c1_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(W)) | (~c1_1(W))) | c3_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(W)) | (~c1_1(W))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(W)) | (~c1_1(W)))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(W)) | (~c1_1(W))))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c1_1(U)) | c3_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(W)) | (~c1_1(W))) | c1_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(W)) | (~c1_1(W))) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(W)) | (~c1_1(W)))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c1_1(U)) | c3_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(W)) | (~c1_1(W))))), ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c1_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(W)) | (~c1_1(W))) | c2_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(W)) | (~c1_1(W))) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | (~c2_1(W)) | (~c1_1(W)))), ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c1_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | (~c2_1(W)) | (~c1_1(W))))), (((((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c1_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | (~c2_1(W)) | (~c1_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | (~c2_1(W)) | (~c1_1(W))) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))), (((((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c1_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))))),
% 0.84/1.06 inference(bind,[status(th)],[])).
% 0.84/1.06 tff(631,plain,
% 0.84/1.06 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c1_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))),
% 0.84/1.06 inference(quant_intro,[status(thm)],[630])).
% 0.84/1.06 tff(632,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c1_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c0_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause197')).
% 0.84/1.06 tff(633,plain,
% 0.84/1.06 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))),
% 0.84/1.06 inference(modus_ponens,[status(thm)],[632, 631])).
% 0.84/1.06 tff(634,plain,
% 0.84/1.06 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))),
% 0.84/1.06 inference(modus_ponens,[status(thm)],[633, 629])).
% 0.84/1.06 tff(635,plain,(
% 0.84/1.06 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))),
% 0.84/1.06 inference(skolemize,[status(sab)],[634])).
% 0.84/1.06 tff(636,plain,
% 0.84/1.06 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))),
% 0.84/1.06 inference(modus_ponens,[status(thm)],[635, 628])).
% 0.84/1.06 tff(637,assumption,(~c0_1(a2545)), introduced(assumption)).
% 0.84/1.06 tff(638,assumption,(c2_1(a2545)), introduced(assumption)).
% 0.84/1.06 tff(639,assumption,(c1_1(a2545)), introduced(assumption)).
% 0.84/1.06 tff(640,plain,
% 0.84/1.06 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c0_1(a2545) | c1_1(a2541) | c2_1(a2541) | c3_1(a2525) | (~ndr1_0) | (~c0_1(a2525)) | c1_1(a2525) | (~c3_1(a2541)) | (~c2_1(a2545)) | (~c1_1(a2545)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c0_1(a2545) | c1_1(a2541) | c2_1(a2541) | c3_1(a2525) | (~ndr1_0) | (~c0_1(a2525)) | c1_1(a2525) | (~c3_1(a2541)) | (~c2_1(a2545)) | (~c1_1(a2545)))),
% 0.84/1.06 inference(rewrite,[status(thm)],[])).
% 0.84/1.06 tff(641,plain,
% 0.84/1.06 (((~ndr1_0) | c3_1(a2525) | c1_1(a2525) | (~c0_1(a2525)) | c1_1(a2541) | c2_1(a2541) | (~c3_1(a2541)) | c0_1(a2545) | (~c2_1(a2545)) | (~c1_1(a2545))) <=> (c0_1(a2545) | c1_1(a2541) | c2_1(a2541) | c3_1(a2525) | (~ndr1_0) | (~c0_1(a2525)) | c1_1(a2525) | (~c3_1(a2541)) | (~c2_1(a2545)) | (~c1_1(a2545)))),
% 0.84/1.06 inference(rewrite,[status(thm)],[])).
% 0.84/1.06 tff(642,plain,
% 0.84/1.06 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a2525) | c1_1(a2525) | (~c0_1(a2525)) | c1_1(a2541) | c2_1(a2541) | (~c3_1(a2541)) | c0_1(a2545) | (~c2_1(a2545)) | (~c1_1(a2545)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c0_1(a2545) | c1_1(a2541) | c2_1(a2541) | c3_1(a2525) | (~ndr1_0) | (~c0_1(a2525)) | c1_1(a2525) | (~c3_1(a2541)) | (~c2_1(a2545)) | (~c1_1(a2545))))),
% 0.84/1.06 inference(monotonicity,[status(thm)],[641])).
% 0.84/1.06 tff(643,plain,
% 0.84/1.06 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a2525) | c1_1(a2525) | (~c0_1(a2525)) | c1_1(a2541) | c2_1(a2541) | (~c3_1(a2541)) | c0_1(a2545) | (~c2_1(a2545)) | (~c1_1(a2545)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c0_1(a2545) | c1_1(a2541) | c2_1(a2541) | c3_1(a2525) | (~ndr1_0) | (~c0_1(a2525)) | c1_1(a2525) | (~c3_1(a2541)) | (~c2_1(a2545)) | (~c1_1(a2545)))),
% 0.84/1.06 inference(transitivity,[status(thm)],[642, 640])).
% 0.84/1.06 tff(644,plain,
% 0.84/1.06 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a2525) | c1_1(a2525) | (~c0_1(a2525)) | c1_1(a2541) | c2_1(a2541) | (~c3_1(a2541)) | c0_1(a2545) | (~c2_1(a2545)) | (~c1_1(a2545)))),
% 0.84/1.06 inference(quant_inst,[status(thm)],[])).
% 0.84/1.06 tff(645,plain,
% 0.84/1.06 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c0_1(a2545) | c1_1(a2541) | c2_1(a2541) | c3_1(a2525) | (~ndr1_0) | (~c0_1(a2525)) | c1_1(a2525) | (~c3_1(a2541)) | (~c2_1(a2545)) | (~c1_1(a2545))),
% 0.84/1.06 inference(modus_ponens,[status(thm)],[644, 643])).
% 0.84/1.06 tff(646,plain,
% 0.84/1.06 ($false),
% 0.84/1.06 inference(unit_resolution,[status(thm)],[645, 90, 639, 638, 267, 616, 637, 266, 265, 608, 636, 626])).
% 0.84/1.06 tff(647,plain,((~hskp8) | (~c1_1(a2545)) | (~c2_1(a2545)) | (~c3_1(a2541)) | c0_1(a2545) | c1_1(a2541) | c2_1(a2541) | (~c1_1(a2556)) | (~c2_1(a2556)) | (~c3_1(a2556))), inference(lemma,lemma(discharge,[]))).
% 0.84/1.06 tff(648,plain,
% 0.84/1.06 (~hskp8),
% 0.84/1.06 inference(unit_resolution,[status(thm)],[647, 601, 593, 253, 585, 245, 239, 449, 448, 447])).
% 0.84/1.06 tff(649,assumption,(~c0_1(a2614)), introduced(assumption)).
% 0.84/1.06 tff(650,plain,
% 0.84/1.06 (^[V: $i, U: $i] : refl((hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V)) <=> (hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V)))),
% 0.84/1.06 inference(bind,[status(th)],[])).
% 0.84/1.06 tff(651,plain,
% 0.84/1.06 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V)) <=> ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))),
% 0.84/1.06 inference(quant_intro,[status(thm)],[650])).
% 0.84/1.06 tff(652,plain,
% 0.84/1.06 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V)) <=> ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))),
% 0.84/1.06 inference(rewrite,[status(thm)],[])).
% 0.84/1.06 tff(653,plain,
% 0.84/1.06 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c0_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) <=> (((~ndr1_0) | (~c0_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U))))), (((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))), (((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))))), ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V))), ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V)))), (((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V))), (((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V)))), ((((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))), ((((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V)))), (((((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp8) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V)) | hskp8))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V)) | hskp8) <=> (hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))), (((((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp8) <=> (hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))))),
% 0.84/1.06 inference(bind,[status(th)],[])).
% 0.84/1.06 tff(654,plain,
% 0.84/1.06 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp8) <=> ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))),
% 0.84/1.06 inference(quant_intro,[status(thm)],[653])).
% 0.84/1.06 tff(655,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp8)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause163')).
% 0.84/1.06 tff(656,plain,
% 0.84/1.06 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))),
% 0.84/1.06 inference(modus_ponens,[status(thm)],[655, 654])).
% 0.84/1.06 tff(657,plain,
% 0.84/1.06 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))),
% 0.84/1.06 inference(modus_ponens,[status(thm)],[656, 652])).
% 0.84/1.06 tff(658,plain,(
% 0.84/1.06 ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))),
% 0.84/1.06 inference(skolemize,[status(sab)],[657])).
% 0.84/1.06 tff(659,plain,
% 0.84/1.06 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))),
% 0.84/1.06 inference(modus_ponens,[status(thm)],[658, 651])).
% 0.84/1.06 tff(660,assumption,(hskp25), introduced(assumption)).
% 0.84/1.06 tff(661,plain,
% 0.84/1.06 (((~hskp25) | (~c2_1(a2564))) <=> ((~hskp25) | (~c2_1(a2564)))),
% 0.84/1.06 inference(rewrite,[status(thm)],[])).
% 0.84/1.06 tff(662,plain,
% 0.84/1.06 (((~c2_1(a2564)) | (~hskp25)) <=> ((~hskp25) | (~c2_1(a2564)))),
% 0.84/1.06 inference(rewrite,[status(thm)],[])).
% 0.84/1.06 tff(663,axiom,((~c2_1(a2564)) | (~hskp25)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause93')).
% 0.84/1.06 tff(664,plain,
% 0.84/1.06 ((~hskp25) | (~c2_1(a2564))),
% 0.84/1.06 inference(modus_ponens,[status(thm)],[663, 662])).
% 0.84/1.06 tff(665,plain,
% 0.84/1.06 ((~hskp25) | (~c2_1(a2564))),
% 0.84/1.06 inference(modus_ponens,[status(thm)],[664, 661])).
% 0.84/1.06 tff(666,plain,
% 0.84/1.06 (~c2_1(a2564)),
% 0.84/1.06 inference(unit_resolution,[status(thm)],[665, 660])).
% 0.84/1.06 tff(667,plain,
% 0.84/1.06 (((~hskp25) | (~c1_1(a2564))) <=> ((~hskp25) | (~c1_1(a2564)))),
% 0.84/1.06 inference(rewrite,[status(thm)],[])).
% 0.84/1.06 tff(668,plain,
% 0.84/1.06 (((~c1_1(a2564)) | (~hskp25)) <=> ((~hskp25) | (~c1_1(a2564)))),
% 0.84/1.06 inference(rewrite,[status(thm)],[])).
% 0.84/1.06 tff(669,axiom,((~c1_1(a2564)) | (~hskp25)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause92')).
% 0.84/1.06 tff(670,plain,
% 0.84/1.06 ((~hskp25) | (~c1_1(a2564))),
% 0.84/1.06 inference(modus_ponens,[status(thm)],[669, 668])).
% 0.84/1.06 tff(671,plain,
% 0.84/1.06 ((~hskp25) | (~c1_1(a2564))),
% 0.84/1.06 inference(modus_ponens,[status(thm)],[670, 667])).
% 0.84/1.06 tff(672,plain,
% 0.84/1.06 (~c1_1(a2564)),
% 0.84/1.06 inference(unit_resolution,[status(thm)],[671, 660])).
% 0.84/1.06 tff(673,plain,
% 0.84/1.06 (((~hskp25) | c0_1(a2564)) <=> ((~hskp25) | c0_1(a2564))),
% 0.84/1.06 inference(rewrite,[status(thm)],[])).
% 0.84/1.06 tff(674,axiom,((~hskp25) | c0_1(a2564)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause56')).
% 0.84/1.06 tff(675,plain,
% 0.84/1.06 ((~hskp25) | c0_1(a2564)),
% 0.84/1.06 inference(modus_ponens,[status(thm)],[674, 673])).
% 0.84/1.06 tff(676,plain,
% 0.84/1.06 ((~hskp25) | c0_1(a2564)),
% 0.84/1.06 inference(modus_ponens,[status(thm)],[675, 673])).
% 0.84/1.06 tff(677,plain,
% 0.84/1.06 ((~hskp25) | c0_1(a2564)),
% 0.84/1.06 inference(modus_ponens,[status(thm)],[676, 673])).
% 0.84/1.06 tff(678,plain,
% 0.84/1.06 ((~hskp25) | c0_1(a2564)),
% 0.84/1.06 inference(modus_ponens,[status(thm)],[677, 673])).
% 0.84/1.06 tff(679,plain,
% 0.84/1.06 ((~hskp25) | c0_1(a2564)),
% 0.84/1.06 inference(modus_ponens,[status(thm)],[678, 673])).
% 0.84/1.06 tff(680,plain,
% 0.84/1.06 (c0_1(a2564)),
% 0.84/1.06 inference(unit_resolution,[status(thm)],[679, 660])).
% 0.84/1.06 tff(681,assumption,(~hskp8), introduced(assumption)).
% 0.84/1.06 tff(682,plain,
% 0.84/1.06 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp8 | c2_1(a2614) | c3_1(a2614) | c1_1(a2564) | c2_1(a2564) | (~ndr1_0) | (~c0_1(a2564)) | c0_1(a2614))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp8 | c2_1(a2614) | c3_1(a2614) | c1_1(a2564) | c2_1(a2564) | (~ndr1_0) | (~c0_1(a2564)) | c0_1(a2614))),
% 0.84/1.06 inference(rewrite,[status(thm)],[])).
% 0.84/1.06 tff(683,plain,
% 0.84/1.06 ((hskp8 | (~ndr1_0) | c2_1(a2564) | c1_1(a2564) | (~c0_1(a2564)) | c3_1(a2614) | c0_1(a2614) | c2_1(a2614)) <=> (hskp8 | c2_1(a2614) | c3_1(a2614) | c1_1(a2564) | c2_1(a2564) | (~ndr1_0) | (~c0_1(a2564)) | c0_1(a2614))),
% 0.84/1.06 inference(rewrite,[status(thm)],[])).
% 0.84/1.06 tff(684,plain,
% 0.84/1.06 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp8 | (~ndr1_0) | c2_1(a2564) | c1_1(a2564) | (~c0_1(a2564)) | c3_1(a2614) | c0_1(a2614) | c2_1(a2614))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp8 | c2_1(a2614) | c3_1(a2614) | c1_1(a2564) | c2_1(a2564) | (~ndr1_0) | (~c0_1(a2564)) | c0_1(a2614)))),
% 0.84/1.06 inference(monotonicity,[status(thm)],[683])).
% 0.84/1.06 tff(685,plain,
% 0.84/1.06 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp8 | (~ndr1_0) | c2_1(a2564) | c1_1(a2564) | (~c0_1(a2564)) | c3_1(a2614) | c0_1(a2614) | c2_1(a2614))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp8 | c2_1(a2614) | c3_1(a2614) | c1_1(a2564) | c2_1(a2564) | (~ndr1_0) | (~c0_1(a2564)) | c0_1(a2614))),
% 0.84/1.06 inference(transitivity,[status(thm)],[684, 682])).
% 0.84/1.06 tff(686,plain,
% 0.84/1.06 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp8 | (~ndr1_0) | c2_1(a2564) | c1_1(a2564) | (~c0_1(a2564)) | c3_1(a2614) | c0_1(a2614) | c2_1(a2614))),
% 0.84/1.06 inference(quant_inst,[status(thm)],[])).
% 0.84/1.06 tff(687,plain,
% 0.84/1.06 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp8 | c2_1(a2614) | c3_1(a2614) | c1_1(a2564) | c2_1(a2564) | (~ndr1_0) | (~c0_1(a2564)) | c0_1(a2614)),
% 0.84/1.06 inference(modus_ponens,[status(thm)],[686, 685])).
% 0.84/1.06 tff(688,plain,
% 0.84/1.06 ($false),
% 0.84/1.06 inference(unit_resolution,[status(thm)],[687, 90, 681, 680, 57, 56, 672, 666, 659, 649])).
% 0.84/1.06 tff(689,plain,((~hskp25) | hskp8 | c2_1(a2614) | c3_1(a2614) | c0_1(a2614)), inference(lemma,lemma(discharge,[]))).
% 0.84/1.06 tff(690,plain,
% 0.84/1.06 (~hskp25),
% 0.84/1.06 inference(unit_resolution,[status(thm)],[689, 648, 26, 20, 365])).
% 0.84/1.06 tff(691,plain,
% 0.84/1.06 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp8 | c2_1(a2614) | c3_1(a2614) | c1_1(a2541) | c2_1(a2541) | (~ndr1_0) | (~c0_1(a2541)) | c0_1(a2614))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp8 | c2_1(a2614) | c3_1(a2614) | c1_1(a2541) | c2_1(a2541) | (~ndr1_0) | (~c0_1(a2541)) | c0_1(a2614))),
% 0.84/1.06 inference(rewrite,[status(thm)],[])).
% 0.84/1.06 tff(692,plain,
% 0.84/1.06 ((hskp8 | (~ndr1_0) | c2_1(a2541) | c1_1(a2541) | (~c0_1(a2541)) | c3_1(a2614) | c0_1(a2614) | c2_1(a2614)) <=> (hskp8 | c2_1(a2614) | c3_1(a2614) | c1_1(a2541) | c2_1(a2541) | (~ndr1_0) | (~c0_1(a2541)) | c0_1(a2614))),
% 0.84/1.07 inference(rewrite,[status(thm)],[])).
% 0.84/1.07 tff(693,plain,
% 0.84/1.07 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp8 | (~ndr1_0) | c2_1(a2541) | c1_1(a2541) | (~c0_1(a2541)) | c3_1(a2614) | c0_1(a2614) | c2_1(a2614))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp8 | c2_1(a2614) | c3_1(a2614) | c1_1(a2541) | c2_1(a2541) | (~ndr1_0) | (~c0_1(a2541)) | c0_1(a2614)))),
% 0.84/1.07 inference(monotonicity,[status(thm)],[692])).
% 0.84/1.07 tff(694,plain,
% 0.84/1.07 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp8 | (~ndr1_0) | c2_1(a2541) | c1_1(a2541) | (~c0_1(a2541)) | c3_1(a2614) | c0_1(a2614) | c2_1(a2614))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp8 | c2_1(a2614) | c3_1(a2614) | c1_1(a2541) | c2_1(a2541) | (~ndr1_0) | (~c0_1(a2541)) | c0_1(a2614))),
% 0.84/1.07 inference(transitivity,[status(thm)],[693, 691])).
% 0.84/1.07 tff(695,plain,
% 0.84/1.07 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp8 | (~ndr1_0) | c2_1(a2541) | c1_1(a2541) | (~c0_1(a2541)) | c3_1(a2614) | c0_1(a2614) | c2_1(a2614))),
% 0.84/1.07 inference(quant_inst,[status(thm)],[])).
% 0.84/1.07 tff(696,plain,
% 0.84/1.07 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp8 | c2_1(a2614) | c3_1(a2614) | c1_1(a2541) | c2_1(a2541) | (~ndr1_0) | (~c0_1(a2541)) | c0_1(a2614)),
% 0.84/1.07 inference(modus_ponens,[status(thm)],[695, 694])).
% 0.84/1.07 tff(697,plain,
% 0.84/1.07 (hskp8 | (~c0_1(a2541)) | c0_1(a2614)),
% 0.84/1.07 inference(unit_resolution,[status(thm)],[696, 90, 26, 20, 245, 239, 659])).
% 0.84/1.07 tff(698,plain,
% 0.84/1.07 (~c0_1(a2541)),
% 0.84/1.07 inference(unit_resolution,[status(thm)],[697, 648, 365])).
% 0.84/1.07 tff(699,assumption,(~c0_1(a2541)), introduced(assumption)).
% 0.84/1.07 tff(700,plain,
% 0.84/1.07 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W))))),
% 0.84/1.07 inference(bind,[status(th)],[])).
% 0.84/1.07 tff(701,plain,
% 0.84/1.07 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))),
% 0.84/1.07 inference(quant_intro,[status(thm)],[700])).
% 0.84/1.07 tff(702,plain,
% 0.84/1.07 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))),
% 0.84/1.07 inference(rewrite,[status(thm)],[])).
% 0.84/1.07 tff(703,plain,
% 0.84/1.07 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) <=> ((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c3_1(W))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(V))) | (~c3_1(W))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c3_1(W)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c3_1(W))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c3_1(W))) | c1_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c3_1(W))) | c1_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c3_1(W))) | c1_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | (~c3_1(W)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c3_1(W))) | c1_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | (~c3_1(W))))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c3_1(W))) | c1_1(V)) | c0_1(W)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | (~c3_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | (~c3_1(W))) | c0_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c3_1(W))) | c1_1(V)) | c0_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c3_1(W))))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c3_1(W))) | c1_1(V)) | c0_1(W)) | c2_1(W)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c3_1(W))) | c2_1(W)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c3_1(W))) | c2_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c3_1(W))) | c1_1(V)) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))))),
% 0.84/1.07 inference(bind,[status(th)],[])).
% 0.84/1.07 tff(704,plain,
% 0.84/1.07 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c3_1(W))) | c1_1(V)) | c0_1(W)) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))),
% 0.84/1.07 inference(quant_intro,[status(thm)],[703])).
% 0.84/1.07 tff(705,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c3_1(W))) | c1_1(V)) | c0_1(W)) | c2_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause202')).
% 0.84/1.07 tff(706,plain,
% 0.84/1.07 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))),
% 0.84/1.07 inference(modus_ponens,[status(thm)],[705, 704])).
% 0.84/1.07 tff(707,plain,
% 0.84/1.07 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))),
% 0.84/1.07 inference(modus_ponens,[status(thm)],[706, 702])).
% 0.84/1.07 tff(708,plain,(
% 0.84/1.07 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))),
% 0.84/1.07 inference(skolemize,[status(sab)],[707])).
% 0.84/1.07 tff(709,plain,
% 0.84/1.07 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))),
% 0.84/1.07 inference(modus_ponens,[status(thm)],[708, 701])).
% 0.84/1.07 tff(710,assumption,(hskp24), introduced(assumption)).
% 0.84/1.07 tff(711,plain,
% 0.84/1.07 (((~hskp24) | (~c1_1(a2555))) <=> ((~hskp24) | (~c1_1(a2555)))),
% 0.84/1.07 inference(rewrite,[status(thm)],[])).
% 0.84/1.07 tff(712,plain,
% 0.84/1.07 (((~c1_1(a2555)) | (~hskp24)) <=> ((~hskp24) | (~c1_1(a2555)))),
% 0.84/1.07 inference(rewrite,[status(thm)],[])).
% 0.84/1.07 tff(713,axiom,((~c1_1(a2555)) | (~hskp24)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause94')).
% 0.84/1.07 tff(714,plain,
% 0.84/1.07 ((~hskp24) | (~c1_1(a2555))),
% 0.84/1.07 inference(modus_ponens,[status(thm)],[713, 712])).
% 0.84/1.07 tff(715,plain,
% 0.84/1.07 ((~hskp24) | (~c1_1(a2555))),
% 0.84/1.07 inference(modus_ponens,[status(thm)],[714, 711])).
% 0.84/1.07 tff(716,plain,
% 0.84/1.07 (~c1_1(a2555)),
% 0.84/1.07 inference(unit_resolution,[status(thm)],[715, 710])).
% 0.84/1.07 tff(717,plain,
% 0.84/1.07 (((~hskp24) | c2_1(a2555)) <=> ((~hskp24) | c2_1(a2555))),
% 0.84/1.07 inference(rewrite,[status(thm)],[])).
% 0.84/1.07 tff(718,axiom,((~hskp24) | c2_1(a2555)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause58')).
% 0.84/1.07 tff(719,plain,
% 0.84/1.07 ((~hskp24) | c2_1(a2555)),
% 0.84/1.07 inference(modus_ponens,[status(thm)],[718, 717])).
% 0.84/1.07 tff(720,plain,
% 0.84/1.07 ((~hskp24) | c2_1(a2555)),
% 0.84/1.07 inference(modus_ponens,[status(thm)],[719, 717])).
% 0.84/1.07 tff(721,plain,
% 0.84/1.07 ((~hskp24) | c2_1(a2555)),
% 0.84/1.07 inference(modus_ponens,[status(thm)],[720, 717])).
% 0.84/1.07 tff(722,plain,
% 0.84/1.07 ((~hskp24) | c2_1(a2555)),
% 0.84/1.07 inference(modus_ponens,[status(thm)],[721, 717])).
% 0.84/1.07 tff(723,plain,
% 0.84/1.07 ((~hskp24) | c2_1(a2555)),
% 0.84/1.07 inference(modus_ponens,[status(thm)],[722, 717])).
% 0.84/1.07 tff(724,plain,
% 0.84/1.07 (c2_1(a2555)),
% 0.84/1.07 inference(unit_resolution,[status(thm)],[723, 710])).
% 0.84/1.07 tff(725,plain,
% 0.84/1.07 (((~hskp24) | c0_1(a2555)) <=> ((~hskp24) | c0_1(a2555))),
% 0.84/1.07 inference(rewrite,[status(thm)],[])).
% 0.84/1.07 tff(726,axiom,((~hskp24) | c0_1(a2555)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause57')).
% 0.84/1.07 tff(727,plain,
% 0.84/1.07 ((~hskp24) | c0_1(a2555)),
% 0.84/1.07 inference(modus_ponens,[status(thm)],[726, 725])).
% 0.84/1.07 tff(728,plain,
% 0.84/1.07 ((~hskp24) | c0_1(a2555)),
% 0.84/1.07 inference(modus_ponens,[status(thm)],[727, 725])).
% 0.84/1.07 tff(729,plain,
% 0.84/1.07 ((~hskp24) | c0_1(a2555)),
% 0.84/1.07 inference(modus_ponens,[status(thm)],[728, 725])).
% 0.84/1.07 tff(730,plain,
% 0.84/1.07 ((~hskp24) | c0_1(a2555)),
% 0.84/1.07 inference(modus_ponens,[status(thm)],[729, 725])).
% 0.84/1.07 tff(731,plain,
% 0.84/1.07 ((~hskp24) | c0_1(a2555)),
% 0.84/1.07 inference(modus_ponens,[status(thm)],[730, 725])).
% 0.84/1.07 tff(732,plain,
% 0.84/1.07 (c0_1(a2555)),
% 0.84/1.07 inference(unit_resolution,[status(thm)],[731, 710])).
% 0.84/1.07 tff(733,assumption,(c3_1(a2597)), introduced(assumption)).
% 0.84/1.07 tff(734,assumption,(c1_1(a2597)), introduced(assumption)).
% 0.84/1.07 tff(735,assumption,(c0_1(a2597)), introduced(assumption)).
% 0.84/1.07 tff(736,plain,
% 0.84/1.07 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | (c1_1(a2555) | c2_1(a2541) | (~ndr1_0) | (~c0_1(a2597)) | (~c3_1(a2597)) | (~c1_1(a2597)) | (~c3_1(a2541)) | c0_1(a2541) | (~c2_1(a2555)) | (~c0_1(a2555)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a2555) | c2_1(a2541) | (~ndr1_0) | (~c0_1(a2597)) | (~c3_1(a2597)) | (~c1_1(a2597)) | (~c3_1(a2541)) | c0_1(a2541) | (~c2_1(a2555)) | (~c0_1(a2555)))),
% 0.84/1.07 inference(rewrite,[status(thm)],[])).
% 0.84/1.07 tff(737,plain,
% 0.84/1.07 (((~ndr1_0) | (~c3_1(a2597)) | (~c1_1(a2597)) | (~c0_1(a2597)) | c1_1(a2555) | (~c0_1(a2555)) | (~c2_1(a2555)) | c0_1(a2541) | c2_1(a2541) | (~c3_1(a2541))) <=> (c1_1(a2555) | c2_1(a2541) | (~ndr1_0) | (~c0_1(a2597)) | (~c3_1(a2597)) | (~c1_1(a2597)) | (~c3_1(a2541)) | c0_1(a2541) | (~c2_1(a2555)) | (~c0_1(a2555)))),
% 0.84/1.07 inference(rewrite,[status(thm)],[])).
% 0.84/1.07 tff(738,plain,
% 0.84/1.07 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a2597)) | (~c1_1(a2597)) | (~c0_1(a2597)) | c1_1(a2555) | (~c0_1(a2555)) | (~c2_1(a2555)) | c0_1(a2541) | c2_1(a2541) | (~c3_1(a2541)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | (c1_1(a2555) | c2_1(a2541) | (~ndr1_0) | (~c0_1(a2597)) | (~c3_1(a2597)) | (~c1_1(a2597)) | (~c3_1(a2541)) | c0_1(a2541) | (~c2_1(a2555)) | (~c0_1(a2555))))),
% 0.84/1.07 inference(monotonicity,[status(thm)],[737])).
% 0.84/1.07 tff(739,plain,
% 0.84/1.07 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a2597)) | (~c1_1(a2597)) | (~c0_1(a2597)) | c1_1(a2555) | (~c0_1(a2555)) | (~c2_1(a2555)) | c0_1(a2541) | c2_1(a2541) | (~c3_1(a2541)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a2555) | c2_1(a2541) | (~ndr1_0) | (~c0_1(a2597)) | (~c3_1(a2597)) | (~c1_1(a2597)) | (~c3_1(a2541)) | c0_1(a2541) | (~c2_1(a2555)) | (~c0_1(a2555)))),
% 0.84/1.07 inference(transitivity,[status(thm)],[738, 736])).
% 0.84/1.07 tff(740,plain,
% 0.84/1.07 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a2597)) | (~c1_1(a2597)) | (~c0_1(a2597)) | c1_1(a2555) | (~c0_1(a2555)) | (~c2_1(a2555)) | c0_1(a2541) | c2_1(a2541) | (~c3_1(a2541)))),
% 0.84/1.07 inference(quant_inst,[status(thm)],[])).
% 0.84/1.07 tff(741,plain,
% 0.84/1.07 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a2555) | c2_1(a2541) | (~ndr1_0) | (~c0_1(a2597)) | (~c3_1(a2597)) | (~c1_1(a2597)) | (~c3_1(a2541)) | c0_1(a2541) | (~c2_1(a2555)) | (~c0_1(a2555))),
% 0.84/1.07 inference(modus_ponens,[status(thm)],[740, 739])).
% 0.84/1.07 tff(742,plain,
% 0.84/1.07 ($false),
% 0.84/1.07 inference(unit_resolution,[status(thm)],[741, 90, 735, 734, 733, 732, 724, 267, 716, 265, 709, 699])).
% 0.84/1.07 tff(743,plain,((~hskp24) | (~c0_1(a2597)) | (~c1_1(a2597)) | (~c3_1(a2597)) | (~c3_1(a2541)) | c2_1(a2541) | c0_1(a2541)), inference(lemma,lemma(discharge,[]))).
% 0.84/1.07 tff(744,plain,
% 0.84/1.07 (~hskp24),
% 0.84/1.07 inference(unit_resolution,[status(thm)],[743, 698, 547, 539, 253, 239, 555])).
% 0.84/1.07 tff(745,plain,
% 0.84/1.07 (^[U: $i] : refl((hskp24 | hskp25 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) <=> (hskp24 | hskp25 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))))),
% 0.84/1.07 inference(bind,[status(th)],[])).
% 0.84/1.07 tff(746,plain,
% 0.84/1.07 (![U: $i] : (hskp24 | hskp25 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp24 | hskp25 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 0.84/1.07 inference(quant_intro,[status(thm)],[745])).
% 0.84/1.07 tff(747,plain,
% 0.84/1.07 (![U: $i] : (hskp24 | hskp25 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp24 | hskp25 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 0.84/1.07 inference(rewrite,[status(thm)],[])).
% 0.84/1.07 tff(748,plain,
% 0.84/1.07 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp24) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) | hskp24))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) | hskp24) <=> (hskp24 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp24) <=> (hskp24 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp24) | hskp25) <=> ((hskp24 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) | hskp25))), rewrite(((hskp24 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) | hskp25) <=> (hskp24 | hskp25 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp24) | hskp25) <=> (hskp24 | hskp25 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))))),
% 0.90/1.07 inference(bind,[status(th)],[])).
% 0.90/1.07 tff(749,plain,
% 0.90/1.07 (![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp24) | hskp25) <=> ![U: $i] : (hskp24 | hskp25 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 0.90/1.07 inference(quant_intro,[status(thm)],[748])).
% 0.90/1.07 tff(750,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp24) | hskp25)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause156')).
% 0.90/1.07 tff(751,plain,
% 0.90/1.07 (![U: $i] : (hskp24 | hskp25 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 0.90/1.07 inference(modus_ponens,[status(thm)],[750, 749])).
% 0.90/1.07 tff(752,plain,
% 0.90/1.07 (![U: $i] : (hskp24 | hskp25 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 0.90/1.07 inference(modus_ponens,[status(thm)],[751, 747])).
% 0.90/1.07 tff(753,plain,(
% 0.90/1.07 ![U: $i] : (hskp24 | hskp25 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 0.90/1.07 inference(skolemize,[status(sab)],[752])).
% 0.90/1.07 tff(754,plain,
% 0.90/1.07 (![U: $i] : (hskp24 | hskp25 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 0.90/1.07 inference(modus_ponens,[status(thm)],[753, 746])).
% 0.90/1.07 tff(755,plain,
% 0.90/1.07 (((~![U: $i] : (hskp24 | hskp25 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp24 | hskp25 | c2_1(a2551) | (~ndr1_0) | (~c0_1(a2551)) | (~c1_1(a2551)))) <=> ((~![U: $i] : (hskp24 | hskp25 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp24 | hskp25 | c2_1(a2551) | (~ndr1_0) | (~c0_1(a2551)) | (~c1_1(a2551)))),
% 0.90/1.07 inference(rewrite,[status(thm)],[])).
% 0.90/1.07 tff(756,plain,
% 0.90/1.07 ((hskp24 | hskp25 | (~ndr1_0) | c2_1(a2551) | (~c1_1(a2551)) | (~c0_1(a2551))) <=> (hskp24 | hskp25 | c2_1(a2551) | (~ndr1_0) | (~c0_1(a2551)) | (~c1_1(a2551)))),
% 0.90/1.07 inference(rewrite,[status(thm)],[])).
% 0.90/1.07 tff(757,plain,
% 0.90/1.07 (((~![U: $i] : (hskp24 | hskp25 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp24 | hskp25 | (~ndr1_0) | c2_1(a2551) | (~c1_1(a2551)) | (~c0_1(a2551)))) <=> ((~![U: $i] : (hskp24 | hskp25 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp24 | hskp25 | c2_1(a2551) | (~ndr1_0) | (~c0_1(a2551)) | (~c1_1(a2551))))),
% 0.90/1.07 inference(monotonicity,[status(thm)],[756])).
% 0.90/1.07 tff(758,plain,
% 0.90/1.07 (((~![U: $i] : (hskp24 | hskp25 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp24 | hskp25 | (~ndr1_0) | c2_1(a2551) | (~c1_1(a2551)) | (~c0_1(a2551)))) <=> ((~![U: $i] : (hskp24 | hskp25 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp24 | hskp25 | c2_1(a2551) | (~ndr1_0) | (~c0_1(a2551)) | (~c1_1(a2551)))),
% 0.90/1.07 inference(transitivity,[status(thm)],[757, 755])).
% 0.90/1.07 tff(759,plain,
% 0.90/1.07 ((~![U: $i] : (hskp24 | hskp25 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp24 | hskp25 | (~ndr1_0) | c2_1(a2551) | (~c1_1(a2551)) | (~c0_1(a2551)))),
% 0.90/1.07 inference(quant_inst,[status(thm)],[])).
% 0.90/1.07 tff(760,plain,
% 0.90/1.07 ((~![U: $i] : (hskp24 | hskp25 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp24 | hskp25 | c2_1(a2551) | (~ndr1_0) | (~c0_1(a2551)) | (~c1_1(a2551))),
% 0.90/1.07 inference(modus_ponens,[status(thm)],[759, 758])).
% 0.90/1.07 tff(761,plain,
% 0.90/1.07 (hskp24 | hskp25),
% 0.90/1.07 inference(unit_resolution,[status(thm)],[760, 90, 472, 471, 470, 754])).
% 0.90/1.07 tff(762,plain,
% 0.90/1.07 ($false),
% 0.90/1.07 inference(unit_resolution,[status(thm)],[761, 744, 690])).
% 0.90/1.07 tff(763,plain,(hskp23 | (~c0_1(a2551)) | (~c1_1(a2551)) | c2_1(a2551) | (~c3_1(a2526)) | c0_1(a2526) | (~c1_1(a2526))), inference(lemma,lemma(discharge,[]))).
% 0.90/1.07 tff(764,plain,
% 0.90/1.07 (hskp23),
% 0.90/1.07 inference(unit_resolution,[status(thm)],[763, 185, 177, 169, 214, 206, 200])).
% 0.90/1.07 tff(765,plain,
% 0.90/1.07 (((~hskp23) | (~c3_1(a2553))) <=> ((~hskp23) | (~c3_1(a2553)))),
% 0.90/1.07 inference(rewrite,[status(thm)],[])).
% 0.90/1.07 tff(766,plain,
% 0.90/1.07 (((~c3_1(a2553)) | (~hskp23)) <=> ((~hskp23) | (~c3_1(a2553)))),
% 0.90/1.07 inference(rewrite,[status(thm)],[])).
% 0.90/1.07 tff(767,axiom,((~c3_1(a2553)) | (~hskp23)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause96')).
% 0.90/1.07 tff(768,plain,
% 0.90/1.07 ((~hskp23) | (~c3_1(a2553))),
% 0.90/1.07 inference(modus_ponens,[status(thm)],[767, 766])).
% 0.90/1.07 tff(769,plain,
% 0.90/1.07 ((~hskp23) | (~c3_1(a2553))),
% 0.90/1.07 inference(modus_ponens,[status(thm)],[768, 765])).
% 0.90/1.07 tff(770,plain,
% 0.90/1.07 (~c3_1(a2553)),
% 0.90/1.07 inference(unit_resolution,[status(thm)],[769, 764])).
% 0.90/1.07 tff(771,plain,
% 0.90/1.07 (^[U: $i] : refl((hskp30 | hskp22 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U))) <=> (hskp30 | hskp22 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U))))),
% 0.90/1.07 inference(bind,[status(th)],[])).
% 0.90/1.07 tff(772,plain,
% 0.90/1.07 (![U: $i] : (hskp30 | hskp22 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp30 | hskp22 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))),
% 0.90/1.07 inference(quant_intro,[status(thm)],[771])).
% 0.90/1.07 tff(773,plain,
% 0.90/1.07 (![U: $i] : (hskp30 | hskp22 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp30 | hskp22 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))),
% 0.90/1.07 inference(rewrite,[status(thm)],[])).
% 0.90/1.07 tff(774,plain,
% 0.90/1.07 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c0_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) <=> (((~ndr1_0) | (~c0_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U))))), (((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))), (((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U))))), ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp30) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U))) | hskp30))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U))) | hskp30) <=> (hskp30 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))), ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp30) <=> (hskp30 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U))))), (((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp30) | hskp22) <=> ((hskp30 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U))) | hskp22))), rewrite(((hskp30 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U))) | hskp22) <=> (hskp30 | hskp22 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))), (((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp30) | hskp22) <=> (hskp30 | hskp22 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))))),
% 0.90/1.07 inference(bind,[status(th)],[])).
% 0.90/1.07 tff(775,plain,
% 0.90/1.07 (![U: $i] : ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp30) | hskp22) <=> ![U: $i] : (hskp30 | hskp22 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))),
% 0.90/1.07 inference(quant_intro,[status(thm)],[774])).
% 0.90/1.07 tff(776,axiom,(![U: $i] : ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp30) | hskp22)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause143')).
% 0.90/1.07 tff(777,plain,
% 0.90/1.07 (![U: $i] : (hskp30 | hskp22 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))),
% 0.90/1.07 inference(modus_ponens,[status(thm)],[776, 775])).
% 0.90/1.07 tff(778,plain,
% 0.90/1.07 (![U: $i] : (hskp30 | hskp22 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))),
% 0.90/1.07 inference(modus_ponens,[status(thm)],[777, 773])).
% 0.90/1.07 tff(779,plain,(
% 0.90/1.07 ![U: $i] : (hskp30 | hskp22 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))),
% 0.90/1.07 inference(skolemize,[status(sab)],[778])).
% 0.90/1.07 tff(780,plain,
% 0.90/1.07 (![U: $i] : (hskp30 | hskp22 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))),
% 0.90/1.07 inference(modus_ponens,[status(thm)],[779, 772])).
% 0.90/1.07 tff(781,plain,
% 0.90/1.07 (((~hskp23) | (~c1_1(a2553))) <=> ((~hskp23) | (~c1_1(a2553)))),
% 0.90/1.07 inference(rewrite,[status(thm)],[])).
% 0.90/1.07 tff(782,plain,
% 0.90/1.07 (((~c1_1(a2553)) | (~hskp23)) <=> ((~hskp23) | (~c1_1(a2553)))),
% 0.90/1.07 inference(rewrite,[status(thm)],[])).
% 0.90/1.07 tff(783,axiom,((~c1_1(a2553)) | (~hskp23)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause95')).
% 0.90/1.07 tff(784,plain,
% 0.90/1.07 ((~hskp23) | (~c1_1(a2553))),
% 0.90/1.07 inference(modus_ponens,[status(thm)],[783, 782])).
% 0.90/1.07 tff(785,plain,
% 0.90/1.07 ((~hskp23) | (~c1_1(a2553))),
% 0.90/1.07 inference(modus_ponens,[status(thm)],[784, 781])).
% 0.90/1.07 tff(786,plain,
% 0.90/1.07 (~c1_1(a2553)),
% 0.90/1.07 inference(unit_resolution,[status(thm)],[785, 764])).
% 0.90/1.07 tff(787,plain,
% 0.90/1.07 (((~hskp23) | c0_1(a2553)) <=> ((~hskp23) | c0_1(a2553))),
% 0.90/1.07 inference(rewrite,[status(thm)],[])).
% 0.90/1.07 tff(788,axiom,((~hskp23) | c0_1(a2553)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause59')).
% 0.90/1.07 tff(789,plain,
% 0.90/1.07 ((~hskp23) | c0_1(a2553)),
% 0.90/1.07 inference(modus_ponens,[status(thm)],[788, 787])).
% 0.90/1.07 tff(790,plain,
% 0.90/1.07 ((~hskp23) | c0_1(a2553)),
% 0.90/1.07 inference(modus_ponens,[status(thm)],[789, 787])).
% 0.90/1.07 tff(791,plain,
% 0.90/1.07 ((~hskp23) | c0_1(a2553)),
% 0.90/1.07 inference(modus_ponens,[status(thm)],[790, 787])).
% 0.90/1.07 tff(792,plain,
% 0.90/1.07 ((~hskp23) | c0_1(a2553)),
% 0.90/1.07 inference(modus_ponens,[status(thm)],[791, 787])).
% 0.90/1.07 tff(793,plain,
% 0.90/1.07 ((~hskp23) | c0_1(a2553)),
% 0.90/1.07 inference(modus_ponens,[status(thm)],[792, 787])).
% 0.90/1.07 tff(794,plain,
% 0.90/1.07 (c0_1(a2553)),
% 0.90/1.07 inference(unit_resolution,[status(thm)],[793, 764])).
% 0.90/1.07 tff(795,plain,
% 0.90/1.07 (((~![U: $i] : (hskp30 | hskp22 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp30 | hskp22 | c1_1(a2553) | c3_1(a2553) | (~ndr1_0) | (~c0_1(a2553)))) <=> ((~![U: $i] : (hskp30 | hskp22 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))) | hskp30 | hskp22 | c1_1(a2553) | c3_1(a2553) | (~ndr1_0) | (~c0_1(a2553)))),
% 0.90/1.07 inference(rewrite,[status(thm)],[])).
% 0.90/1.07 tff(796,plain,
% 0.90/1.07 ((hskp30 | hskp22 | (~ndr1_0) | c3_1(a2553) | c1_1(a2553) | (~c0_1(a2553))) <=> (hskp30 | hskp22 | c1_1(a2553) | c3_1(a2553) | (~ndr1_0) | (~c0_1(a2553)))),
% 0.90/1.07 inference(rewrite,[status(thm)],[])).
% 0.90/1.07 tff(797,plain,
% 0.90/1.07 (((~![U: $i] : (hskp30 | hskp22 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp30 | hskp22 | (~ndr1_0) | c3_1(a2553) | c1_1(a2553) | (~c0_1(a2553)))) <=> ((~![U: $i] : (hskp30 | hskp22 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp30 | hskp22 | c1_1(a2553) | c3_1(a2553) | (~ndr1_0) | (~c0_1(a2553))))),
% 0.90/1.07 inference(monotonicity,[status(thm)],[796])).
% 0.90/1.07 tff(798,plain,
% 0.90/1.07 (((~![U: $i] : (hskp30 | hskp22 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp30 | hskp22 | (~ndr1_0) | c3_1(a2553) | c1_1(a2553) | (~c0_1(a2553)))) <=> ((~![U: $i] : (hskp30 | hskp22 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))) | hskp30 | hskp22 | c1_1(a2553) | c3_1(a2553) | (~ndr1_0) | (~c0_1(a2553)))),
% 0.90/1.07 inference(transitivity,[status(thm)],[797, 795])).
% 0.90/1.07 tff(799,plain,
% 0.90/1.07 ((~![U: $i] : (hskp30 | hskp22 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp30 | hskp22 | (~ndr1_0) | c3_1(a2553) | c1_1(a2553) | (~c0_1(a2553)))),
% 0.90/1.07 inference(quant_inst,[status(thm)],[])).
% 0.90/1.07 tff(800,plain,
% 0.90/1.07 ((~![U: $i] : (hskp30 | hskp22 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))) | hskp30 | hskp22 | c1_1(a2553) | c3_1(a2553) | (~ndr1_0) | (~c0_1(a2553))),
% 0.90/1.07 inference(modus_ponens,[status(thm)],[799, 798])).
% 0.90/1.07 tff(801,plain,
% 0.90/1.07 (hskp22),
% 0.90/1.07 inference(unit_resolution,[status(thm)],[800, 90, 151, 794, 786, 770, 780])).
% 0.90/1.07 tff(802,plain,
% 0.90/1.07 (((~hskp22) | (~c3_1(a2552))) <=> ((~hskp22) | (~c3_1(a2552)))),
% 0.90/1.07 inference(rewrite,[status(thm)],[])).
% 0.90/1.07 tff(803,plain,
% 0.90/1.07 (((~c3_1(a2552)) | (~hskp22)) <=> ((~hskp22) | (~c3_1(a2552)))),
% 0.90/1.07 inference(rewrite,[status(thm)],[])).
% 0.90/1.07 tff(804,axiom,((~c3_1(a2552)) | (~hskp22)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause98')).
% 0.90/1.07 tff(805,plain,
% 0.90/1.07 ((~hskp22) | (~c3_1(a2552))),
% 0.90/1.07 inference(modus_ponens,[status(thm)],[804, 803])).
% 0.90/1.07 tff(806,plain,
% 0.90/1.07 ((~hskp22) | (~c3_1(a2552))),
% 0.90/1.07 inference(modus_ponens,[status(thm)],[805, 802])).
% 0.90/1.07 tff(807,plain,
% 0.90/1.07 (~c3_1(a2552)),
% 0.90/1.07 inference(unit_resolution,[status(thm)],[806, 801])).
% 0.90/1.07 tff(808,plain,
% 0.90/1.07 (((~hskp22) | c2_1(a2552)) <=> ((~hskp22) | c2_1(a2552))),
% 0.90/1.07 inference(rewrite,[status(thm)],[])).
% 0.90/1.07 tff(809,axiom,((~hskp22) | c2_1(a2552)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause60')).
% 0.90/1.07 tff(810,plain,
% 0.90/1.07 ((~hskp22) | c2_1(a2552)),
% 0.90/1.07 inference(modus_ponens,[status(thm)],[809, 808])).
% 0.90/1.07 tff(811,plain,
% 0.90/1.07 ((~hskp22) | c2_1(a2552)),
% 0.90/1.07 inference(modus_ponens,[status(thm)],[810, 808])).
% 0.90/1.07 tff(812,plain,
% 0.90/1.07 ((~hskp22) | c2_1(a2552)),
% 0.90/1.07 inference(modus_ponens,[status(thm)],[811, 808])).
% 0.90/1.07 tff(813,plain,
% 0.90/1.07 ((~hskp22) | c2_1(a2552)),
% 0.90/1.07 inference(modus_ponens,[status(thm)],[812, 808])).
% 0.90/1.07 tff(814,plain,
% 0.90/1.07 ((~hskp22) | c2_1(a2552)),
% 0.90/1.07 inference(modus_ponens,[status(thm)],[813, 808])).
% 0.90/1.07 tff(815,plain,
% 0.90/1.07 (c2_1(a2552)),
% 0.90/1.07 inference(unit_resolution,[status(thm)],[814, 801])).
% 0.90/1.07 tff(816,plain,
% 0.90/1.07 (((~hskp22) | (~c1_1(a2552))) <=> ((~hskp22) | (~c1_1(a2552)))),
% 0.90/1.07 inference(rewrite,[status(thm)],[])).
% 0.90/1.07 tff(817,plain,
% 0.90/1.07 (((~c1_1(a2552)) | (~hskp22)) <=> ((~hskp22) | (~c1_1(a2552)))),
% 0.90/1.07 inference(rewrite,[status(thm)],[])).
% 0.90/1.07 tff(818,axiom,((~c1_1(a2552)) | (~hskp22)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause97')).
% 0.90/1.07 tff(819,plain,
% 0.90/1.07 ((~hskp22) | (~c1_1(a2552))),
% 0.90/1.07 inference(modus_ponens,[status(thm)],[818, 817])).
% 0.90/1.07 tff(820,plain,
% 0.90/1.07 ((~hskp22) | (~c1_1(a2552))),
% 0.90/1.07 inference(modus_ponens,[status(thm)],[819, 816])).
% 0.90/1.07 tff(821,plain,
% 0.90/1.07 (~c1_1(a2552)),
% 0.90/1.07 inference(unit_resolution,[status(thm)],[820, 801])).
% 0.90/1.07 tff(822,assumption,(c2_1(a2552)), introduced(assumption)).
% 0.90/1.07 tff(823,assumption,(~c3_1(a2552)), introduced(assumption)).
% 0.90/1.07 tff(824,assumption,(~c1_1(a2552)), introduced(assumption)).
% 0.90/1.07 tff(825,plain,
% 0.90/1.07 (hskp23),
% 0.90/1.07 inference(unit_resolution,[status(thm)],[763, 472, 471, 470, 216, 152, 215])).
% 0.90/1.07 tff(826,plain,
% 0.90/1.07 (~c3_1(a2553)),
% 0.90/1.07 inference(unit_resolution,[status(thm)],[769, 825])).
% 0.90/1.07 tff(827,plain,
% 0.90/1.07 (~c1_1(a2553)),
% 0.90/1.07 inference(unit_resolution,[status(thm)],[785, 825])).
% 0.90/1.07 tff(828,plain,
% 0.90/1.07 (c0_1(a2553)),
% 0.90/1.07 inference(unit_resolution,[status(thm)],[793, 825])).
% 0.90/1.07 tff(829,assumption,(~c3_1(a2541)), introduced(assumption)).
% 0.90/1.07 tff(830,plain,
% 0.90/1.07 (~hskp17),
% 0.90/1.07 inference(unit_resolution,[status(thm)],[252, 829])).
% 0.90/1.07 tff(831,plain,
% 0.90/1.07 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp17 | c3_1(a2541) | (~c1_1(a2541)) | c2_1(a2541) | c0_1(a2526) | (~ndr1_0) | (~c3_1(a2526)) | (~c1_1(a2526)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp17 | c3_1(a2541) | (~c1_1(a2541)) | c2_1(a2541) | c0_1(a2526) | (~ndr1_0) | (~c3_1(a2526)) | (~c1_1(a2526)))),
% 0.90/1.07 inference(rewrite,[status(thm)],[])).
% 0.90/1.07 tff(832,plain,
% 0.90/1.07 ((hskp17 | (~ndr1_0) | c3_1(a2541) | c2_1(a2541) | (~c1_1(a2541)) | c0_1(a2526) | (~c3_1(a2526)) | (~c1_1(a2526))) <=> (hskp17 | c3_1(a2541) | (~c1_1(a2541)) | c2_1(a2541) | c0_1(a2526) | (~ndr1_0) | (~c3_1(a2526)) | (~c1_1(a2526)))),
% 0.90/1.07 inference(rewrite,[status(thm)],[])).
% 0.90/1.07 tff(833,plain,
% 0.90/1.07 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | c3_1(a2541) | c2_1(a2541) | (~c1_1(a2541)) | c0_1(a2526) | (~c3_1(a2526)) | (~c1_1(a2526)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp17 | c3_1(a2541) | (~c1_1(a2541)) | c2_1(a2541) | c0_1(a2526) | (~ndr1_0) | (~c3_1(a2526)) | (~c1_1(a2526))))),
% 0.90/1.07 inference(monotonicity,[status(thm)],[832])).
% 0.90/1.07 tff(834,plain,
% 0.90/1.07 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | c3_1(a2541) | c2_1(a2541) | (~c1_1(a2541)) | c0_1(a2526) | (~c3_1(a2526)) | (~c1_1(a2526)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp17 | c3_1(a2541) | (~c1_1(a2541)) | c2_1(a2541) | c0_1(a2526) | (~ndr1_0) | (~c3_1(a2526)) | (~c1_1(a2526)))),
% 0.90/1.07 inference(transitivity,[status(thm)],[833, 831])).
% 0.90/1.07 tff(835,plain,
% 0.90/1.07 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | c3_1(a2541) | c2_1(a2541) | (~c1_1(a2541)) | c0_1(a2526) | (~c3_1(a2526)) | (~c1_1(a2526)))),
% 0.90/1.07 inference(quant_inst,[status(thm)],[])).
% 0.90/1.07 tff(836,plain,
% 0.90/1.07 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp17 | c3_1(a2541) | (~c1_1(a2541)) | c2_1(a2541) | c0_1(a2526) | (~ndr1_0) | (~c3_1(a2526)) | (~c1_1(a2526))),
% 0.90/1.07 inference(modus_ponens,[status(thm)],[835, 834])).
% 0.90/1.07 tff(837,plain,
% 0.90/1.07 (~c1_1(a2541)),
% 0.90/1.07 inference(unit_resolution,[status(thm)],[836, 90, 830, 829, 215, 216, 265, 152, 226])).
% 0.90/1.07 tff(838,assumption,(~hskp2), introduced(assumption)).
% 0.90/1.07 tff(839,plain,
% 0.90/1.07 (^[V: $i, U: $i] : refl((hskp2 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V))) <=> (hskp2 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V))))),
% 0.90/1.07 inference(bind,[status(th)],[])).
% 0.90/1.07 tff(840,plain,
% 0.90/1.07 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))),
% 0.90/1.07 inference(quant_intro,[status(thm)],[839])).
% 0.90/1.07 tff(841,plain,
% 0.90/1.07 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))),
% 0.90/1.07 inference(rewrite,[status(thm)],[])).
% 0.90/1.07 tff(842,plain,
% 0.90/1.07 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c0_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c0_1(V)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c0_1(V))))), (((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c0_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c0_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c0_1(V)))), (((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c0_1(V))))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c0_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c0_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | (~c0_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | (~c0_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V))))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V))) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V))))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c3_1(V)) | hskp2) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V))) | hskp2))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V))) | hskp2) <=> (hskp2 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c3_1(V)) | hskp2) <=> (hskp2 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))))),
% 0.90/1.08 inference(bind,[status(th)],[])).
% 0.90/1.08 tff(843,plain,
% 0.90/1.08 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c3_1(V)) | hskp2) <=> ![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))),
% 0.90/1.08 inference(quant_intro,[status(thm)],[842])).
% 0.90/1.08 tff(844,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c3_1(V)) | hskp2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause174')).
% 0.90/1.08 tff(845,plain,
% 0.90/1.08 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))),
% 0.90/1.08 inference(modus_ponens,[status(thm)],[844, 843])).
% 0.90/1.08 tff(846,plain,
% 0.90/1.08 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))),
% 0.90/1.08 inference(modus_ponens,[status(thm)],[845, 841])).
% 0.90/1.08 tff(847,plain,(
% 0.90/1.08 ![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))),
% 0.90/1.08 inference(skolemize,[status(sab)],[846])).
% 0.90/1.08 tff(848,plain,
% 0.90/1.08 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))),
% 0.90/1.08 inference(modus_ponens,[status(thm)],[847, 840])).
% 0.90/1.08 tff(849,assumption,(~c3_1(a2553)), introduced(assumption)).
% 0.90/1.08 tff(850,assumption,(~c1_1(a2553)), introduced(assumption)).
% 0.90/1.08 tff(851,assumption,(c0_1(a2553)), introduced(assumption)).
% 0.90/1.08 tff(852,plain,
% 0.90/1.08 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp2 | c1_1(a2553) | c3_1(a2553) | (~ndr1_0) | (~c0_1(a2553)) | c2_1(a2553))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | hskp2 | c1_1(a2553) | c3_1(a2553) | (~ndr1_0) | (~c0_1(a2553)) | c2_1(a2553))),
% 0.90/1.08 inference(rewrite,[status(thm)],[])).
% 0.90/1.08 tff(853,plain,
% 0.90/1.08 ((hskp2 | (~ndr1_0) | c3_1(a2553) | c2_1(a2553) | (~c0_1(a2553)) | c3_1(a2553) | c1_1(a2553) | (~c0_1(a2553))) <=> (hskp2 | c1_1(a2553) | c3_1(a2553) | (~ndr1_0) | (~c0_1(a2553)) | c2_1(a2553))),
% 0.90/1.08 inference(rewrite,[status(thm)],[])).
% 0.90/1.08 tff(854,plain,
% 0.90/1.08 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp2 | (~ndr1_0) | c3_1(a2553) | c2_1(a2553) | (~c0_1(a2553)) | c3_1(a2553) | c1_1(a2553) | (~c0_1(a2553)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp2 | c1_1(a2553) | c3_1(a2553) | (~ndr1_0) | (~c0_1(a2553)) | c2_1(a2553)))),
% 0.90/1.08 inference(monotonicity,[status(thm)],[853])).
% 0.90/1.08 tff(855,plain,
% 0.90/1.08 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp2 | (~ndr1_0) | c3_1(a2553) | c2_1(a2553) | (~c0_1(a2553)) | c3_1(a2553) | c1_1(a2553) | (~c0_1(a2553)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | hskp2 | c1_1(a2553) | c3_1(a2553) | (~ndr1_0) | (~c0_1(a2553)) | c2_1(a2553))),
% 0.90/1.08 inference(transitivity,[status(thm)],[854, 852])).
% 0.90/1.08 tff(856,plain,
% 0.90/1.08 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp2 | (~ndr1_0) | c3_1(a2553) | c2_1(a2553) | (~c0_1(a2553)) | c3_1(a2553) | c1_1(a2553) | (~c0_1(a2553)))),
% 0.90/1.08 inference(quant_inst,[status(thm)],[])).
% 0.90/1.08 tff(857,plain,
% 0.90/1.08 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | hskp2 | c1_1(a2553) | c3_1(a2553) | (~ndr1_0) | (~c0_1(a2553)) | c2_1(a2553)),
% 0.90/1.08 inference(modus_ponens,[status(thm)],[856, 855])).
% 0.90/1.08 tff(858,plain,
% 0.90/1.08 (hskp2 | c2_1(a2553)),
% 0.90/1.08 inference(unit_resolution,[status(thm)],[857, 90, 851, 850, 849, 848])).
% 0.90/1.08 tff(859,plain,
% 0.90/1.08 (c2_1(a2553)),
% 0.90/1.08 inference(unit_resolution,[status(thm)],[858, 838])).
% 0.90/1.08 tff(860,plain,
% 0.90/1.08 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp2 | c3_1(a2541) | c1_1(a2541) | c2_1(a2541) | (~ndr1_0) | (~c0_1(a2541)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | hskp2 | c3_1(a2541) | c1_1(a2541) | c2_1(a2541) | (~ndr1_0) | (~c0_1(a2541)))),
% 0.90/1.08 inference(rewrite,[status(thm)],[])).
% 0.90/1.08 tff(861,plain,
% 0.90/1.08 ((hskp2 | (~ndr1_0) | c3_1(a2541) | c2_1(a2541) | (~c0_1(a2541)) | c3_1(a2541) | c1_1(a2541) | (~c0_1(a2541))) <=> (hskp2 | c3_1(a2541) | c1_1(a2541) | c2_1(a2541) | (~ndr1_0) | (~c0_1(a2541)))),
% 0.90/1.08 inference(rewrite,[status(thm)],[])).
% 0.90/1.08 tff(862,plain,
% 0.90/1.08 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp2 | (~ndr1_0) | c3_1(a2541) | c2_1(a2541) | (~c0_1(a2541)) | c3_1(a2541) | c1_1(a2541) | (~c0_1(a2541)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp2 | c3_1(a2541) | c1_1(a2541) | c2_1(a2541) | (~ndr1_0) | (~c0_1(a2541))))),
% 0.90/1.08 inference(monotonicity,[status(thm)],[861])).
% 0.90/1.08 tff(863,plain,
% 0.90/1.08 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp2 | (~ndr1_0) | c3_1(a2541) | c2_1(a2541) | (~c0_1(a2541)) | c3_1(a2541) | c1_1(a2541) | (~c0_1(a2541)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | hskp2 | c3_1(a2541) | c1_1(a2541) | c2_1(a2541) | (~ndr1_0) | (~c0_1(a2541)))),
% 0.90/1.08 inference(transitivity,[status(thm)],[862, 860])).
% 0.90/1.08 tff(864,plain,
% 0.90/1.08 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp2 | (~ndr1_0) | c3_1(a2541) | c2_1(a2541) | (~c0_1(a2541)) | c3_1(a2541) | c1_1(a2541) | (~c0_1(a2541)))),
% 0.90/1.08 inference(quant_inst,[status(thm)],[])).
% 0.90/1.08 tff(865,plain,
% 0.90/1.08 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | hskp2 | c3_1(a2541) | c1_1(a2541) | c2_1(a2541) | (~ndr1_0) | (~c0_1(a2541))),
% 0.90/1.08 inference(modus_ponens,[status(thm)],[864, 863])).
% 0.90/1.08 tff(866,plain,
% 0.90/1.08 (hskp2 | (~c0_1(a2541))),
% 0.90/1.08 inference(unit_resolution,[status(thm)],[865, 90, 829, 266, 265, 848])).
% 0.90/1.08 tff(867,plain,
% 0.90/1.08 (~c0_1(a2541)),
% 0.90/1.08 inference(unit_resolution,[status(thm)],[866, 838])).
% 0.90/1.08 tff(868,plain,
% 0.90/1.08 (^[V: $i, U: $i] : refl((hskp2 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)) <=> (hskp2 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)))),
% 0.90/1.08 inference(bind,[status(th)],[])).
% 0.90/1.08 tff(869,plain,
% 0.90/1.08 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 0.90/1.08 inference(quant_intro,[status(thm)],[868])).
% 0.90/1.08 tff(870,plain,
% 0.90/1.08 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 0.90/1.08 inference(rewrite,[status(thm)],[])).
% 0.90/1.08 tff(871,plain,
% 0.90/1.08 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c2_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c2_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U))) | c0_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U))) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V)) | c1_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp2) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)) | hskp2))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)) | hskp2) <=> (hskp2 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp2) <=> (hskp2 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))))),
% 0.90/1.08 inference(bind,[status(th)],[])).
% 0.90/1.08 tff(872,plain,
% 0.90/1.08 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp2) <=> ![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 0.90/1.08 inference(quant_intro,[status(thm)],[871])).
% 0.90/1.08 tff(873,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause167')).
% 0.90/1.08 tff(874,plain,
% 0.90/1.08 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 0.90/1.08 inference(modus_ponens,[status(thm)],[873, 872])).
% 0.90/1.08 tff(875,plain,
% 0.90/1.08 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 0.90/1.08 inference(modus_ponens,[status(thm)],[874, 870])).
% 0.90/1.08 tff(876,plain,(
% 0.90/1.08 ![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 0.90/1.08 inference(skolemize,[status(sab)],[875])).
% 0.90/1.08 tff(877,plain,
% 0.90/1.08 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 0.90/1.08 inference(modus_ponens,[status(thm)],[876, 869])).
% 0.90/1.08 tff(878,plain,
% 0.90/1.08 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | c3_1(a2541) | c1_1(a2553) | c1_1(a2541) | (~ndr1_0) | c0_1(a2541) | (~c0_1(a2553)) | (~c2_1(a2553)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp2 | c3_1(a2541) | c1_1(a2553) | c1_1(a2541) | (~ndr1_0) | c0_1(a2541) | (~c0_1(a2553)) | (~c2_1(a2553)))),
% 0.90/1.08 inference(rewrite,[status(thm)],[])).
% 0.90/1.08 tff(879,plain,
% 0.90/1.08 ((hskp2 | (~ndr1_0) | c1_1(a2553) | (~c0_1(a2553)) | (~c2_1(a2553)) | c3_1(a2541) | c1_1(a2541) | c0_1(a2541)) <=> (hskp2 | c3_1(a2541) | c1_1(a2553) | c1_1(a2541) | (~ndr1_0) | c0_1(a2541) | (~c0_1(a2553)) | (~c2_1(a2553)))),
% 0.90/1.08 inference(rewrite,[status(thm)],[])).
% 0.90/1.08 tff(880,plain,
% 0.90/1.08 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | c1_1(a2553) | (~c0_1(a2553)) | (~c2_1(a2553)) | c3_1(a2541) | c1_1(a2541) | c0_1(a2541))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | c3_1(a2541) | c1_1(a2553) | c1_1(a2541) | (~ndr1_0) | c0_1(a2541) | (~c0_1(a2553)) | (~c2_1(a2553))))),
% 0.90/1.08 inference(monotonicity,[status(thm)],[879])).
% 0.90/1.08 tff(881,plain,
% 0.90/1.08 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | c1_1(a2553) | (~c0_1(a2553)) | (~c2_1(a2553)) | c3_1(a2541) | c1_1(a2541) | c0_1(a2541))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp2 | c3_1(a2541) | c1_1(a2553) | c1_1(a2541) | (~ndr1_0) | c0_1(a2541) | (~c0_1(a2553)) | (~c2_1(a2553)))),
% 0.90/1.08 inference(transitivity,[status(thm)],[880, 878])).
% 0.90/1.08 tff(882,plain,
% 0.90/1.08 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | c1_1(a2553) | (~c0_1(a2553)) | (~c2_1(a2553)) | c3_1(a2541) | c1_1(a2541) | c0_1(a2541))),
% 0.90/1.08 inference(quant_inst,[status(thm)],[])).
% 0.90/1.08 tff(883,plain,
% 0.90/1.08 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp2 | c3_1(a2541) | c1_1(a2553) | c1_1(a2541) | (~ndr1_0) | c0_1(a2541) | (~c0_1(a2553)) | (~c2_1(a2553))),
% 0.90/1.08 inference(modus_ponens,[status(thm)],[882, 881])).
% 0.90/1.08 tff(884,plain,
% 0.90/1.08 (hskp2 | c0_1(a2541) | (~c2_1(a2553))),
% 0.90/1.08 inference(unit_resolution,[status(thm)],[883, 90, 851, 829, 850, 266, 877])).
% 0.90/1.08 tff(885,plain,
% 0.90/1.08 ($false),
% 0.90/1.08 inference(unit_resolution,[status(thm)],[884, 867, 838, 859])).
% 0.90/1.08 tff(886,plain,(hskp2 | (~c0_1(a2553)) | c3_1(a2541) | c1_1(a2553) | c1_1(a2541) | c2_1(a2541) | c3_1(a2553)), inference(lemma,lemma(discharge,[]))).
% 0.90/1.08 tff(887,plain,
% 0.90/1.08 (hskp2),
% 0.90/1.08 inference(unit_resolution,[status(thm)],[886, 829, 828, 827, 837, 265, 826])).
% 0.90/1.08 tff(888,plain,
% 0.90/1.08 (((~hskp2) | (~c3_1(a2518))) <=> ((~hskp2) | (~c3_1(a2518)))),
% 0.90/1.08 inference(rewrite,[status(thm)],[])).
% 0.90/1.08 tff(889,plain,
% 0.90/1.08 (((~c3_1(a2518)) | (~hskp2)) <=> ((~hskp2) | (~c3_1(a2518)))),
% 0.90/1.08 inference(rewrite,[status(thm)],[])).
% 0.90/1.08 tff(890,axiom,((~c3_1(a2518)) | (~hskp2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause131')).
% 0.90/1.08 tff(891,plain,
% 0.90/1.08 ((~hskp2) | (~c3_1(a2518))),
% 0.90/1.08 inference(modus_ponens,[status(thm)],[890, 889])).
% 0.90/1.08 tff(892,plain,
% 0.90/1.08 ((~hskp2) | (~c3_1(a2518))),
% 0.90/1.08 inference(modus_ponens,[status(thm)],[891, 888])).
% 0.90/1.08 tff(893,plain,
% 0.90/1.08 (~c3_1(a2518)),
% 0.90/1.08 inference(unit_resolution,[status(thm)],[892, 887])).
% 0.90/1.08 tff(894,plain,
% 0.90/1.08 (((~hskp2) | (~c0_1(a2518))) <=> ((~hskp2) | (~c0_1(a2518)))),
% 0.90/1.08 inference(rewrite,[status(thm)],[])).
% 0.90/1.08 tff(895,plain,
% 0.90/1.08 (((~c0_1(a2518)) | (~hskp2)) <=> ((~hskp2) | (~c0_1(a2518)))),
% 0.90/1.08 inference(rewrite,[status(thm)],[])).
% 0.90/1.08 tff(896,axiom,((~c0_1(a2518)) | (~hskp2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause130')).
% 0.90/1.08 tff(897,plain,
% 0.90/1.08 ((~hskp2) | (~c0_1(a2518))),
% 0.90/1.08 inference(modus_ponens,[status(thm)],[896, 895])).
% 0.90/1.08 tff(898,plain,
% 0.90/1.08 ((~hskp2) | (~c0_1(a2518))),
% 0.90/1.08 inference(modus_ponens,[status(thm)],[897, 894])).
% 0.90/1.08 tff(899,plain,
% 0.90/1.08 (~c0_1(a2518)),
% 0.90/1.08 inference(unit_resolution,[status(thm)],[898, 887])).
% 0.90/1.08 tff(900,plain,
% 0.90/1.08 (((~hskp2) | c1_1(a2518)) <=> ((~hskp2) | c1_1(a2518))),
% 0.90/1.08 inference(rewrite,[status(thm)],[])).
% 0.90/1.08 tff(901,axiom,((~hskp2) | c1_1(a2518)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause87')).
% 0.90/1.08 tff(902,plain,
% 0.90/1.08 ((~hskp2) | c1_1(a2518)),
% 0.90/1.08 inference(modus_ponens,[status(thm)],[901, 900])).
% 0.90/1.08 tff(903,plain,
% 0.90/1.08 ((~hskp2) | c1_1(a2518)),
% 0.90/1.08 inference(modus_ponens,[status(thm)],[902, 900])).
% 0.90/1.08 tff(904,plain,
% 0.90/1.08 ((~hskp2) | c1_1(a2518)),
% 0.90/1.08 inference(modus_ponens,[status(thm)],[903, 900])).
% 0.90/1.08 tff(905,plain,
% 0.90/1.08 ((~hskp2) | c1_1(a2518)),
% 0.90/1.08 inference(modus_ponens,[status(thm)],[904, 900])).
% 0.90/1.08 tff(906,plain,
% 0.90/1.08 ((~hskp2) | c1_1(a2518)),
% 0.90/1.08 inference(modus_ponens,[status(thm)],[905, 900])).
% 0.90/1.08 tff(907,plain,
% 0.90/1.08 (c1_1(a2518)),
% 0.90/1.08 inference(unit_resolution,[status(thm)],[906, 887])).
% 0.90/1.08 tff(908,plain,
% 0.90/1.08 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp17 | c0_1(a2526) | c3_1(a2518) | (~ndr1_0) | (~c1_1(a2518)) | c2_1(a2518) | (~c3_1(a2526)) | (~c1_1(a2526)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp17 | c0_1(a2526) | c3_1(a2518) | (~ndr1_0) | (~c1_1(a2518)) | c2_1(a2518) | (~c3_1(a2526)) | (~c1_1(a2526)))),
% 0.90/1.08 inference(rewrite,[status(thm)],[])).
% 0.90/1.08 tff(909,plain,
% 0.90/1.08 ((hskp17 | (~ndr1_0) | c3_1(a2518) | c2_1(a2518) | (~c1_1(a2518)) | c0_1(a2526) | (~c3_1(a2526)) | (~c1_1(a2526))) <=> (hskp17 | c0_1(a2526) | c3_1(a2518) | (~ndr1_0) | (~c1_1(a2518)) | c2_1(a2518) | (~c3_1(a2526)) | (~c1_1(a2526)))),
% 0.90/1.08 inference(rewrite,[status(thm)],[])).
% 0.90/1.08 tff(910,plain,
% 0.90/1.08 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | c3_1(a2518) | c2_1(a2518) | (~c1_1(a2518)) | c0_1(a2526) | (~c3_1(a2526)) | (~c1_1(a2526)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp17 | c0_1(a2526) | c3_1(a2518) | (~ndr1_0) | (~c1_1(a2518)) | c2_1(a2518) | (~c3_1(a2526)) | (~c1_1(a2526))))),
% 0.90/1.08 inference(monotonicity,[status(thm)],[909])).
% 0.90/1.08 tff(911,plain,
% 0.90/1.08 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | c3_1(a2518) | c2_1(a2518) | (~c1_1(a2518)) | c0_1(a2526) | (~c3_1(a2526)) | (~c1_1(a2526)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp17 | c0_1(a2526) | c3_1(a2518) | (~ndr1_0) | (~c1_1(a2518)) | c2_1(a2518) | (~c3_1(a2526)) | (~c1_1(a2526)))),
% 0.90/1.08 inference(transitivity,[status(thm)],[910, 908])).
% 0.90/1.08 tff(912,plain,
% 0.90/1.08 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | c3_1(a2518) | c2_1(a2518) | (~c1_1(a2518)) | c0_1(a2526) | (~c3_1(a2526)) | (~c1_1(a2526)))),
% 0.90/1.08 inference(quant_inst,[status(thm)],[])).
% 0.90/1.08 tff(913,plain,
% 0.90/1.08 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp17 | c0_1(a2526) | c3_1(a2518) | (~ndr1_0) | (~c1_1(a2518)) | c2_1(a2518) | (~c3_1(a2526)) | (~c1_1(a2526))),
% 0.90/1.08 inference(modus_ponens,[status(thm)],[912, 911])).
% 0.90/1.08 tff(914,plain,
% 0.90/1.08 (c2_1(a2518)),
% 0.90/1.08 inference(unit_resolution,[status(thm)],[913, 90, 830, 215, 216, 907, 152, 893, 226])).
% 0.90/1.08 tff(915,plain,
% 0.90/1.08 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp14 | c2_1(a2551) | c0_1(a2518) | c3_1(a2518) | (~ndr1_0) | (~c2_1(a2518)) | (~c0_1(a2551)) | (~c1_1(a2551)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp14 | c2_1(a2551) | c0_1(a2518) | c3_1(a2518) | (~ndr1_0) | (~c2_1(a2518)) | (~c0_1(a2551)) | (~c1_1(a2551)))),
% 0.90/1.08 inference(rewrite,[status(thm)],[])).
% 0.90/1.08 tff(916,plain,
% 0.90/1.08 ((hskp14 | (~ndr1_0) | c2_1(a2551) | (~c1_1(a2551)) | (~c0_1(a2551)) | c3_1(a2518) | c0_1(a2518) | (~c2_1(a2518))) <=> (hskp14 | c2_1(a2551) | c0_1(a2518) | c3_1(a2518) | (~ndr1_0) | (~c2_1(a2518)) | (~c0_1(a2551)) | (~c1_1(a2551)))),
% 0.90/1.08 inference(rewrite,[status(thm)],[])).
% 0.90/1.08 tff(917,plain,
% 0.90/1.08 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp14 | (~ndr1_0) | c2_1(a2551) | (~c1_1(a2551)) | (~c0_1(a2551)) | c3_1(a2518) | c0_1(a2518) | (~c2_1(a2518)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp14 | c2_1(a2551) | c0_1(a2518) | c3_1(a2518) | (~ndr1_0) | (~c2_1(a2518)) | (~c0_1(a2551)) | (~c1_1(a2551))))),
% 0.90/1.08 inference(monotonicity,[status(thm)],[916])).
% 0.90/1.08 tff(918,plain,
% 0.90/1.08 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp14 | (~ndr1_0) | c2_1(a2551) | (~c1_1(a2551)) | (~c0_1(a2551)) | c3_1(a2518) | c0_1(a2518) | (~c2_1(a2518)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp14 | c2_1(a2551) | c0_1(a2518) | c3_1(a2518) | (~ndr1_0) | (~c2_1(a2518)) | (~c0_1(a2551)) | (~c1_1(a2551)))),
% 0.90/1.08 inference(transitivity,[status(thm)],[917, 915])).
% 0.90/1.08 tff(919,plain,
% 0.90/1.08 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp14 | (~ndr1_0) | c2_1(a2551) | (~c1_1(a2551)) | (~c0_1(a2551)) | c3_1(a2518) | c0_1(a2518) | (~c2_1(a2518)))),
% 0.90/1.08 inference(quant_inst,[status(thm)],[])).
% 0.90/1.08 tff(920,plain,
% 0.90/1.08 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp14 | c2_1(a2551) | c0_1(a2518) | c3_1(a2518) | (~ndr1_0) | (~c2_1(a2518)) | (~c0_1(a2551)) | (~c1_1(a2551))),
% 0.90/1.08 inference(modus_ponens,[status(thm)],[919, 918])).
% 0.90/1.08 tff(921,plain,
% 0.90/1.08 (hskp14),
% 0.90/1.08 inference(unit_resolution,[status(thm)],[920, 90, 472, 471, 470, 899, 893, 469, 914])).
% 0.90/1.08 tff(922,plain,
% 0.90/1.08 (~c3_1(a2536)),
% 0.90/1.08 inference(unit_resolution,[status(thm)],[484, 921])).
% 0.90/1.08 tff(923,plain,
% 0.90/1.08 (~c1_1(a2536)),
% 0.90/1.08 inference(unit_resolution,[status(thm)],[490, 921])).
% 0.90/1.08 tff(924,plain,
% 0.90/1.08 (~c0_1(a2536)),
% 0.90/1.08 inference(unit_resolution,[status(thm)],[496, 921])).
% 0.90/1.08 tff(925,assumption,(hskp2), introduced(assumption)).
% 0.90/1.08 tff(926,plain,
% 0.90/1.08 (~c3_1(a2518)),
% 0.90/1.08 inference(unit_resolution,[status(thm)],[892, 925])).
% 0.90/1.08 tff(927,plain,
% 0.90/1.08 (c1_1(a2518)),
% 0.90/1.08 inference(unit_resolution,[status(thm)],[906, 925])).
% 0.90/1.08 tff(928,plain,
% 0.90/1.08 (c2_1(a2518)),
% 0.90/1.08 inference(unit_resolution,[status(thm)],[913, 90, 830, 215, 216, 927, 152, 926, 226])).
% 0.90/1.08 tff(929,plain,
% 0.90/1.08 (~c0_1(a2518)),
% 0.90/1.08 inference(unit_resolution,[status(thm)],[898, 925])).
% 0.90/1.08 tff(930,plain,
% 0.90/1.08 (hskp14),
% 0.90/1.08 inference(unit_resolution,[status(thm)],[920, 90, 472, 471, 470, 929, 926, 469, 928])).
% 0.90/1.08 tff(931,plain,
% 0.90/1.08 (~c1_1(a2536)),
% 0.90/1.08 inference(unit_resolution,[status(thm)],[490, 930])).
% 0.90/1.08 tff(932,plain,
% 0.90/1.08 (~c3_1(a2536)),
% 0.90/1.08 inference(unit_resolution,[status(thm)],[484, 930])).
% 0.90/1.08 tff(933,plain,
% 0.90/1.08 (~c0_1(a2536)),
% 0.90/1.08 inference(unit_resolution,[status(thm)],[496, 930])).
% 0.90/1.08 tff(934,assumption,(c2_1(a2518)), introduced(assumption)).
% 0.90/1.08 tff(935,plain,
% 0.90/1.08 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W))) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W))))),
% 0.90/1.08 inference(bind,[status(th)],[])).
% 0.90/1.08 tff(936,plain,
% 0.90/1.08 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 0.90/1.08 inference(quant_intro,[status(thm)],[935])).
% 0.90/1.08 tff(937,plain,
% 0.90/1.08 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 0.90/1.08 inference(rewrite,[status(thm)],[])).
% 0.90/1.08 tff(938,plain,
% 0.90/1.08 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c2_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c2_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c1_1(V)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c1_1(V))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c1_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c2_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c2_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c2_1(W))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c2_1(V))) | (~c2_1(W))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c2_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c2_1(W)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c2_1(W))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c2_1(W))) | c1_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c2_1(W))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c2_1(W))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c2_1(W)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c2_1(W))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c2_1(W))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c2_1(W))) | c1_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c2_1(W))) | c0_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c2_1(W))) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | (~c2_1(W)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c2_1(W))) | c1_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | (~c2_1(W))))), ((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c2_1(W))) | c1_1(U)) | c0_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | (~c2_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | (~c2_1(W))) | c0_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)))), ((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c2_1(W))) | c1_1(U)) | c0_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W))))), (((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c2_1(W))) | c1_1(U)) | c0_1(V)) | c0_1(W)) | c1_1(W)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W))) | c1_1(W)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W))) | c1_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))), (((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c2_1(W))) | c1_1(U)) | c0_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))))),
% 0.90/1.08 inference(bind,[status(th)],[])).
% 0.90/1.08 tff(939,plain,
% 0.90/1.08 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c2_1(W))) | c1_1(U)) | c0_1(V)) | c0_1(W)) | c1_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 0.90/1.08 inference(quant_intro,[status(thm)],[938])).
% 0.90/1.08 tff(940,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c2_1(W))) | c1_1(U)) | c0_1(V)) | c0_1(W)) | c1_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause198')).
% 0.90/1.08 tff(941,plain,
% 0.90/1.08 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 0.90/1.08 inference(modus_ponens,[status(thm)],[940, 939])).
% 0.90/1.08 tff(942,plain,
% 0.90/1.08 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 0.90/1.08 inference(modus_ponens,[status(thm)],[941, 937])).
% 0.90/1.08 tff(943,plain,(
% 0.90/1.08 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 0.90/1.08 inference(skolemize,[status(sab)],[942])).
% 0.90/1.08 tff(944,plain,
% 0.90/1.08 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 0.90/1.08 inference(modus_ponens,[status(thm)],[943, 936])).
% 0.90/1.08 tff(945,assumption,(~c0_1(a2518)), introduced(assumption)).
% 0.90/1.08 tff(946,assumption,(~c1_1(a2536)), introduced(assumption)).
% 0.90/1.08 tff(947,assumption,(~c0_1(a2536)), introduced(assumption)).
% 0.90/1.08 tff(948,assumption,(c1_1(a2518)), introduced(assumption)).
% 0.90/1.08 tff(949,plain,
% 0.90/1.08 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a2555) | c0_1(a2536) | c1_1(a2536) | c0_1(a2518) | (~ndr1_0) | (~c1_1(a2518)) | (~c2_1(a2518)) | (~c2_1(a2536)) | (~c2_1(a2555)) | (~c0_1(a2555)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a2555) | c0_1(a2536) | c1_1(a2536) | c0_1(a2518) | (~ndr1_0) | (~c1_1(a2518)) | (~c2_1(a2518)) | (~c2_1(a2536)) | (~c2_1(a2555)) | (~c0_1(a2555)))),
% 0.90/1.08 inference(rewrite,[status(thm)],[])).
% 0.90/1.08 tff(950,plain,
% 0.90/1.08 (((~ndr1_0) | c1_1(a2555) | (~c0_1(a2555)) | (~c2_1(a2555)) | c0_1(a2518) | (~c1_1(a2518)) | (~c2_1(a2518)) | c1_1(a2536) | c0_1(a2536) | (~c2_1(a2536))) <=> (c1_1(a2555) | c0_1(a2536) | c1_1(a2536) | c0_1(a2518) | (~ndr1_0) | (~c1_1(a2518)) | (~c2_1(a2518)) | (~c2_1(a2536)) | (~c2_1(a2555)) | (~c0_1(a2555)))),
% 0.90/1.08 inference(rewrite,[status(thm)],[])).
% 0.90/1.08 tff(951,plain,
% 0.90/1.08 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a2555) | (~c0_1(a2555)) | (~c2_1(a2555)) | c0_1(a2518) | (~c1_1(a2518)) | (~c2_1(a2518)) | c1_1(a2536) | c0_1(a2536) | (~c2_1(a2536)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a2555) | c0_1(a2536) | c1_1(a2536) | c0_1(a2518) | (~ndr1_0) | (~c1_1(a2518)) | (~c2_1(a2518)) | (~c2_1(a2536)) | (~c2_1(a2555)) | (~c0_1(a2555))))),
% 0.90/1.08 inference(monotonicity,[status(thm)],[950])).
% 0.90/1.08 tff(952,plain,
% 0.90/1.08 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a2555) | (~c0_1(a2555)) | (~c2_1(a2555)) | c0_1(a2518) | (~c1_1(a2518)) | (~c2_1(a2518)) | c1_1(a2536) | c0_1(a2536) | (~c2_1(a2536)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a2555) | c0_1(a2536) | c1_1(a2536) | c0_1(a2518) | (~ndr1_0) | (~c1_1(a2518)) | (~c2_1(a2518)) | (~c2_1(a2536)) | (~c2_1(a2555)) | (~c0_1(a2555)))),
% 0.90/1.08 inference(transitivity,[status(thm)],[951, 949])).
% 0.90/1.08 tff(953,plain,
% 0.90/1.08 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a2555) | (~c0_1(a2555)) | (~c2_1(a2555)) | c0_1(a2518) | (~c1_1(a2518)) | (~c2_1(a2518)) | c1_1(a2536) | c0_1(a2536) | (~c2_1(a2536)))),
% 0.90/1.08 inference(quant_inst,[status(thm)],[])).
% 0.90/1.08 tff(954,plain,
% 0.90/1.08 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a2555) | c0_1(a2536) | c1_1(a2536) | c0_1(a2518) | (~ndr1_0) | (~c1_1(a2518)) | (~c2_1(a2518)) | (~c2_1(a2536)) | (~c2_1(a2555)) | (~c0_1(a2555))),
% 0.90/1.08 inference(modus_ponens,[status(thm)],[953, 952])).
% 0.90/1.08 tff(955,plain,
% 0.90/1.08 (~c2_1(a2536)),
% 0.90/1.08 inference(unit_resolution,[status(thm)],[954, 90, 732, 724, 948, 716, 947, 946, 945, 944, 934])).
% 0.90/1.09 tff(956,assumption,(~c3_1(a2536)), introduced(assumption)).
% 0.90/1.09 tff(957,plain,
% 0.90/1.09 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp8 | c1_1(a2541) | c2_1(a2541) | c0_1(a2536) | c3_1(a2536) | (~ndr1_0) | c2_1(a2536) | (~c0_1(a2541)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp8 | c1_1(a2541) | c2_1(a2541) | c0_1(a2536) | c3_1(a2536) | (~ndr1_0) | c2_1(a2536) | (~c0_1(a2541)))),
% 0.90/1.09 inference(rewrite,[status(thm)],[])).
% 0.90/1.09 tff(958,plain,
% 0.90/1.09 ((hskp8 | (~ndr1_0) | c2_1(a2541) | c1_1(a2541) | (~c0_1(a2541)) | c3_1(a2536) | c0_1(a2536) | c2_1(a2536)) <=> (hskp8 | c1_1(a2541) | c2_1(a2541) | c0_1(a2536) | c3_1(a2536) | (~ndr1_0) | c2_1(a2536) | (~c0_1(a2541)))),
% 0.90/1.09 inference(rewrite,[status(thm)],[])).
% 0.90/1.09 tff(959,plain,
% 0.90/1.09 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp8 | (~ndr1_0) | c2_1(a2541) | c1_1(a2541) | (~c0_1(a2541)) | c3_1(a2536) | c0_1(a2536) | c2_1(a2536))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp8 | c1_1(a2541) | c2_1(a2541) | c0_1(a2536) | c3_1(a2536) | (~ndr1_0) | c2_1(a2536) | (~c0_1(a2541))))),
% 0.90/1.09 inference(monotonicity,[status(thm)],[958])).
% 0.90/1.09 tff(960,plain,
% 0.90/1.09 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp8 | (~ndr1_0) | c2_1(a2541) | c1_1(a2541) | (~c0_1(a2541)) | c3_1(a2536) | c0_1(a2536) | c2_1(a2536))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp8 | c1_1(a2541) | c2_1(a2541) | c0_1(a2536) | c3_1(a2536) | (~ndr1_0) | c2_1(a2536) | (~c0_1(a2541)))),
% 0.90/1.09 inference(transitivity,[status(thm)],[959, 957])).
% 0.90/1.09 tff(961,plain,
% 0.90/1.09 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp8 | (~ndr1_0) | c2_1(a2541) | c1_1(a2541) | (~c0_1(a2541)) | c3_1(a2536) | c0_1(a2536) | c2_1(a2536))),
% 0.90/1.09 inference(quant_inst,[status(thm)],[])).
% 0.90/1.09 tff(962,plain,
% 0.90/1.09 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp8 | c1_1(a2541) | c2_1(a2541) | c0_1(a2536) | c3_1(a2536) | (~ndr1_0) | c2_1(a2536) | (~c0_1(a2541))),
% 0.90/1.09 inference(modus_ponens,[status(thm)],[961, 960])).
% 0.90/1.09 tff(963,plain,
% 0.90/1.09 (c2_1(a2536) | (~c0_1(a2541))),
% 0.90/1.09 inference(unit_resolution,[status(thm)],[962, 90, 681, 837, 265, 947, 956, 659])).
% 0.90/1.09 tff(964,plain,
% 0.90/1.09 (~c0_1(a2541)),
% 0.90/1.09 inference(unit_resolution,[status(thm)],[963, 955])).
% 0.90/1.09 tff(965,plain,
% 0.90/1.09 (^[V: $i, U: $i] : refl((hskp16 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))) <=> (hskp16 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))))),
% 0.90/1.09 inference(bind,[status(th)],[])).
% 0.90/1.09 tff(966,plain,
% 0.90/1.09 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 0.90/1.09 inference(quant_intro,[status(thm)],[965])).
% 0.90/1.09 tff(967,plain,
% 0.90/1.09 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 0.90/1.09 inference(rewrite,[status(thm)],[])).
% 0.90/1.09 tff(968,plain,
% 0.90/1.09 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c2_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c2_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c1_1(V)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c1_1(V))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c1_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c1_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c1_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c1_1(V)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c1_1(V))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) | hskp16) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))) | hskp16))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))) | hskp16) <=> (hskp16 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) | hskp16) <=> (hskp16 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))))),
% 0.90/1.09 inference(bind,[status(th)],[])).
% 0.90/1.09 tff(969,plain,
% 0.90/1.09 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) | hskp16) <=> ![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 0.90/1.09 inference(quant_intro,[status(thm)],[968])).
% 0.90/1.09 tff(970,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) | hskp16)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause186')).
% 0.90/1.09 tff(971,plain,
% 0.90/1.09 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 0.90/1.09 inference(modus_ponens,[status(thm)],[970, 969])).
% 0.90/1.09 tff(972,plain,
% 0.90/1.09 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 0.90/1.09 inference(modus_ponens,[status(thm)],[971, 967])).
% 0.90/1.09 tff(973,plain,(
% 0.90/1.09 ![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 0.90/1.09 inference(skolemize,[status(sab)],[972])).
% 0.90/1.09 tff(974,plain,
% 0.90/1.09 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 0.90/1.09 inference(modus_ponens,[status(thm)],[973, 966])).
% 0.90/1.09 tff(975,plain,
% 0.90/1.09 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp16 | c1_1(a2555) | c0_1(a2526) | (~ndr1_0) | (~c3_1(a2526)) | (~c1_1(a2526)) | (~c2_1(a2555)) | (~c0_1(a2555)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp16 | c1_1(a2555) | c0_1(a2526) | (~ndr1_0) | (~c3_1(a2526)) | (~c1_1(a2526)) | (~c2_1(a2555)) | (~c0_1(a2555)))),
% 0.90/1.09 inference(rewrite,[status(thm)],[])).
% 0.90/1.09 tff(976,plain,
% 0.90/1.09 ((hskp16 | (~ndr1_0) | c1_1(a2555) | (~c0_1(a2555)) | (~c2_1(a2555)) | c0_1(a2526) | (~c3_1(a2526)) | (~c1_1(a2526))) <=> (hskp16 | c1_1(a2555) | c0_1(a2526) | (~ndr1_0) | (~c3_1(a2526)) | (~c1_1(a2526)) | (~c2_1(a2555)) | (~c0_1(a2555)))),
% 0.90/1.09 inference(rewrite,[status(thm)],[])).
% 0.90/1.09 tff(977,plain,
% 0.90/1.09 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp16 | (~ndr1_0) | c1_1(a2555) | (~c0_1(a2555)) | (~c2_1(a2555)) | c0_1(a2526) | (~c3_1(a2526)) | (~c1_1(a2526)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp16 | c1_1(a2555) | c0_1(a2526) | (~ndr1_0) | (~c3_1(a2526)) | (~c1_1(a2526)) | (~c2_1(a2555)) | (~c0_1(a2555))))),
% 0.90/1.09 inference(monotonicity,[status(thm)],[976])).
% 0.90/1.09 tff(978,plain,
% 0.90/1.09 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp16 | (~ndr1_0) | c1_1(a2555) | (~c0_1(a2555)) | (~c2_1(a2555)) | c0_1(a2526) | (~c3_1(a2526)) | (~c1_1(a2526)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp16 | c1_1(a2555) | c0_1(a2526) | (~ndr1_0) | (~c3_1(a2526)) | (~c1_1(a2526)) | (~c2_1(a2555)) | (~c0_1(a2555)))),
% 0.90/1.09 inference(transitivity,[status(thm)],[977, 975])).
% 0.90/1.09 tff(979,plain,
% 0.90/1.09 ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp16 | (~ndr1_0) | c1_1(a2555) | (~c0_1(a2555)) | (~c2_1(a2555)) | c0_1(a2526) | (~c3_1(a2526)) | (~c1_1(a2526)))),
% 0.90/1.09 inference(quant_inst,[status(thm)],[])).
% 0.90/1.09 tff(980,plain,
% 0.90/1.09 ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp16 | c1_1(a2555) | c0_1(a2526) | (~ndr1_0) | (~c3_1(a2526)) | (~c1_1(a2526)) | (~c2_1(a2555)) | (~c0_1(a2555))),
% 0.90/1.09 inference(modus_ponens,[status(thm)],[979, 978])).
% 0.90/1.09 tff(981,plain,
% 0.90/1.09 (hskp16),
% 0.90/1.09 inference(unit_resolution,[status(thm)],[980, 90, 732, 724, 215, 216, 716, 152, 974])).
% 0.90/1.09 tff(982,plain,
% 0.90/1.09 (((~hskp16) | (~c2_1(a2540))) <=> ((~hskp16) | (~c2_1(a2540)))),
% 0.90/1.09 inference(rewrite,[status(thm)],[])).
% 0.90/1.09 tff(983,plain,
% 0.90/1.09 (((~c2_1(a2540)) | (~hskp16)) <=> ((~hskp16) | (~c2_1(a2540)))),
% 0.90/1.09 inference(rewrite,[status(thm)],[])).
% 0.90/1.09 tff(984,axiom,((~c2_1(a2540)) | (~hskp16)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause106')).
% 0.90/1.09 tff(985,plain,
% 0.90/1.09 ((~hskp16) | (~c2_1(a2540))),
% 0.90/1.09 inference(modus_ponens,[status(thm)],[984, 983])).
% 0.90/1.09 tff(986,plain,
% 0.90/1.09 ((~hskp16) | (~c2_1(a2540))),
% 0.90/1.09 inference(modus_ponens,[status(thm)],[985, 982])).
% 0.90/1.09 tff(987,plain,
% 0.90/1.09 (~c2_1(a2540)),
% 0.90/1.09 inference(unit_resolution,[status(thm)],[986, 981])).
% 0.90/1.09 tff(988,plain,
% 0.90/1.09 (((~hskp16) | c0_1(a2540)) <=> ((~hskp16) | c0_1(a2540))),
% 0.90/1.09 inference(rewrite,[status(thm)],[])).
% 0.90/1.09 tff(989,axiom,((~hskp16) | c0_1(a2540)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause69')).
% 0.90/1.09 tff(990,plain,
% 0.90/1.09 ((~hskp16) | c0_1(a2540)),
% 0.90/1.09 inference(modus_ponens,[status(thm)],[989, 988])).
% 0.90/1.09 tff(991,plain,
% 0.90/1.09 ((~hskp16) | c0_1(a2540)),
% 0.90/1.09 inference(modus_ponens,[status(thm)],[990, 988])).
% 0.90/1.09 tff(992,plain,
% 0.90/1.09 ((~hskp16) | c0_1(a2540)),
% 0.90/1.09 inference(modus_ponens,[status(thm)],[991, 988])).
% 0.90/1.09 tff(993,plain,
% 0.90/1.09 ((~hskp16) | c0_1(a2540)),
% 0.90/1.09 inference(modus_ponens,[status(thm)],[992, 988])).
% 0.90/1.09 tff(994,plain,
% 0.90/1.09 ((~hskp16) | c0_1(a2540)),
% 0.90/1.09 inference(modus_ponens,[status(thm)],[993, 988])).
% 0.90/1.09 tff(995,plain,
% 0.90/1.09 (c0_1(a2540)),
% 0.90/1.09 inference(unit_resolution,[status(thm)],[994, 981])).
% 0.90/1.09 tff(996,plain,
% 0.90/1.09 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp8 | c3_1(a2541) | c2_1(a2541) | c2_1(a2540) | (~ndr1_0) | (~c0_1(a2540)) | c1_1(a2540) | c0_1(a2541))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp8 | c3_1(a2541) | c2_1(a2541) | c2_1(a2540) | (~ndr1_0) | (~c0_1(a2540)) | c1_1(a2540) | c0_1(a2541))),
% 0.90/1.09 inference(rewrite,[status(thm)],[])).
% 0.90/1.09 tff(997,plain,
% 0.90/1.09 ((hskp8 | (~ndr1_0) | c2_1(a2540) | c1_1(a2540) | (~c0_1(a2540)) | c3_1(a2541) | c0_1(a2541) | c2_1(a2541)) <=> (hskp8 | c3_1(a2541) | c2_1(a2541) | c2_1(a2540) | (~ndr1_0) | (~c0_1(a2540)) | c1_1(a2540) | c0_1(a2541))),
% 0.90/1.09 inference(rewrite,[status(thm)],[])).
% 0.90/1.09 tff(998,plain,
% 0.90/1.09 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp8 | (~ndr1_0) | c2_1(a2540) | c1_1(a2540) | (~c0_1(a2540)) | c3_1(a2541) | c0_1(a2541) | c2_1(a2541))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp8 | c3_1(a2541) | c2_1(a2541) | c2_1(a2540) | (~ndr1_0) | (~c0_1(a2540)) | c1_1(a2540) | c0_1(a2541)))),
% 0.90/1.09 inference(monotonicity,[status(thm)],[997])).
% 0.90/1.09 tff(999,plain,
% 0.90/1.09 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp8 | (~ndr1_0) | c2_1(a2540) | c1_1(a2540) | (~c0_1(a2540)) | c3_1(a2541) | c0_1(a2541) | c2_1(a2541))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp8 | c3_1(a2541) | c2_1(a2541) | c2_1(a2540) | (~ndr1_0) | (~c0_1(a2540)) | c1_1(a2540) | c0_1(a2541))),
% 0.90/1.09 inference(transitivity,[status(thm)],[998, 996])).
% 0.90/1.09 tff(1000,plain,
% 0.90/1.09 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp8 | (~ndr1_0) | c2_1(a2540) | c1_1(a2540) | (~c0_1(a2540)) | c3_1(a2541) | c0_1(a2541) | c2_1(a2541))),
% 0.90/1.09 inference(quant_inst,[status(thm)],[])).
% 0.90/1.09 tff(1001,plain,
% 0.90/1.09 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp8 | c3_1(a2541) | c2_1(a2541) | c2_1(a2540) | (~ndr1_0) | (~c0_1(a2540)) | c1_1(a2540) | c0_1(a2541)),
% 0.90/1.09 inference(modus_ponens,[status(thm)],[1000, 999])).
% 0.90/1.09 tff(1002,plain,
% 0.90/1.09 (c1_1(a2540)),
% 0.90/1.09 inference(unit_resolution,[status(thm)],[1001, 90, 681, 829, 995, 265, 987, 659, 964])).
% 0.90/1.09 tff(1003,plain,
% 0.90/1.09 (((~hskp16) | (~c3_1(a2540))) <=> ((~hskp16) | (~c3_1(a2540)))),
% 0.90/1.09 inference(rewrite,[status(thm)],[])).
% 0.90/1.09 tff(1004,plain,
% 0.90/1.09 (((~c3_1(a2540)) | (~hskp16)) <=> ((~hskp16) | (~c3_1(a2540)))),
% 0.90/1.09 inference(rewrite,[status(thm)],[])).
% 0.90/1.09 tff(1005,axiom,((~c3_1(a2540)) | (~hskp16)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause107')).
% 0.90/1.09 tff(1006,plain,
% 0.90/1.09 ((~hskp16) | (~c3_1(a2540))),
% 0.90/1.09 inference(modus_ponens,[status(thm)],[1005, 1004])).
% 0.90/1.09 tff(1007,plain,
% 0.90/1.09 ((~hskp16) | (~c3_1(a2540))),
% 0.90/1.09 inference(modus_ponens,[status(thm)],[1006, 1003])).
% 0.90/1.09 tff(1008,plain,
% 0.90/1.09 (~c3_1(a2540)),
% 0.90/1.09 inference(unit_resolution,[status(thm)],[1007, 981])).
% 0.90/1.09 tff(1009,plain,
% 0.90/1.09 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp17 | c2_1(a2540) | c3_1(a2540) | c0_1(a2526) | (~ndr1_0) | (~c3_1(a2526)) | (~c1_1(a2526)) | (~c1_1(a2540)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp17 | c2_1(a2540) | c3_1(a2540) | c0_1(a2526) | (~ndr1_0) | (~c3_1(a2526)) | (~c1_1(a2526)) | (~c1_1(a2540)))),
% 0.90/1.09 inference(rewrite,[status(thm)],[])).
% 0.90/1.09 tff(1010,plain,
% 0.90/1.09 ((hskp17 | (~ndr1_0) | c3_1(a2540) | c2_1(a2540) | (~c1_1(a2540)) | c0_1(a2526) | (~c3_1(a2526)) | (~c1_1(a2526))) <=> (hskp17 | c2_1(a2540) | c3_1(a2540) | c0_1(a2526) | (~ndr1_0) | (~c3_1(a2526)) | (~c1_1(a2526)) | (~c1_1(a2540)))),
% 0.90/1.09 inference(rewrite,[status(thm)],[])).
% 0.90/1.09 tff(1011,plain,
% 0.90/1.09 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | c3_1(a2540) | c2_1(a2540) | (~c1_1(a2540)) | c0_1(a2526) | (~c3_1(a2526)) | (~c1_1(a2526)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp17 | c2_1(a2540) | c3_1(a2540) | c0_1(a2526) | (~ndr1_0) | (~c3_1(a2526)) | (~c1_1(a2526)) | (~c1_1(a2540))))),
% 0.90/1.09 inference(monotonicity,[status(thm)],[1010])).
% 0.90/1.09 tff(1012,plain,
% 0.90/1.09 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | c3_1(a2540) | c2_1(a2540) | (~c1_1(a2540)) | c0_1(a2526) | (~c3_1(a2526)) | (~c1_1(a2526)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp17 | c2_1(a2540) | c3_1(a2540) | c0_1(a2526) | (~ndr1_0) | (~c3_1(a2526)) | (~c1_1(a2526)) | (~c1_1(a2540)))),
% 0.90/1.09 inference(transitivity,[status(thm)],[1011, 1009])).
% 0.90/1.09 tff(1013,plain,
% 0.90/1.09 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | c3_1(a2540) | c2_1(a2540) | (~c1_1(a2540)) | c0_1(a2526) | (~c3_1(a2526)) | (~c1_1(a2526)))),
% 0.90/1.09 inference(quant_inst,[status(thm)],[])).
% 0.90/1.09 tff(1014,plain,
% 0.90/1.09 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp17 | c2_1(a2540) | c3_1(a2540) | c0_1(a2526) | (~ndr1_0) | (~c3_1(a2526)) | (~c1_1(a2526)) | (~c1_1(a2540))),
% 0.90/1.09 inference(modus_ponens,[status(thm)],[1013, 1012])).
% 0.90/1.09 tff(1015,plain,
% 0.90/1.09 ($false),
% 0.90/1.09 inference(unit_resolution,[status(thm)],[1014, 90, 830, 215, 216, 987, 1008, 152, 226, 1002])).
% 0.90/1.09 tff(1016,plain,((~hskp24) | (~c1_1(a2526)) | (~c3_1(a2526)) | c0_1(a2526) | hskp8 | c3_1(a2541) | c2_1(a2541) | c0_1(a2536) | c3_1(a2536) | (~c1_1(a2518)) | c1_1(a2536) | c0_1(a2518) | (~c2_1(a2518))), inference(lemma,lemma(discharge,[]))).
% 0.90/1.09 tff(1017,plain,
% 0.90/1.09 (~hskp24),
% 0.90/1.09 inference(unit_resolution,[status(thm)],[1016, 933, 216, 152, 681, 829, 265, 215, 932, 927, 931, 929, 928])).
% 0.90/1.09 tff(1018,plain,
% 0.90/1.09 ((hskp24 | hskp0) <=> (hskp24 | hskp0)),
% 0.90/1.09 inference(rewrite,[status(thm)],[])).
% 0.90/1.09 tff(1019,axiom,(hskp24 | hskp0), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause1')).
% 0.90/1.09 tff(1020,plain,
% 0.90/1.09 (hskp24 | hskp0),
% 0.90/1.09 inference(modus_ponens,[status(thm)],[1019, 1018])).
% 0.90/1.09 tff(1021,plain,
% 0.90/1.09 (hskp24 | hskp0),
% 0.90/1.09 inference(modus_ponens,[status(thm)],[1020, 1018])).
% 0.90/1.09 tff(1022,plain,
% 0.90/1.09 (hskp24 | hskp0),
% 0.90/1.09 inference(modus_ponens,[status(thm)],[1021, 1018])).
% 0.90/1.09 tff(1023,plain,
% 0.90/1.09 (hskp24 | hskp0),
% 0.90/1.09 inference(modus_ponens,[status(thm)],[1022, 1018])).
% 0.90/1.09 tff(1024,plain,
% 0.90/1.09 (hskp24 | hskp0),
% 0.90/1.09 inference(modus_ponens,[status(thm)],[1023, 1018])).
% 0.90/1.09 tff(1025,plain,
% 0.90/1.09 (hskp0),
% 0.90/1.09 inference(unit_resolution,[status(thm)],[1024, 1017])).
% 0.90/1.09 tff(1026,plain,
% 0.90/1.09 (((~hskp0) | (~c2_1(a2516))) <=> ((~hskp0) | (~c2_1(a2516)))),
% 0.90/1.09 inference(rewrite,[status(thm)],[])).
% 0.90/1.09 tff(1027,plain,
% 0.90/1.09 (((~c2_1(a2516)) | (~hskp0)) <=> ((~hskp0) | (~c2_1(a2516)))),
% 0.90/1.09 inference(rewrite,[status(thm)],[])).
% 0.90/1.09 tff(1028,axiom,((~c2_1(a2516)) | (~hskp0)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause136')).
% 0.90/1.09 tff(1029,plain,
% 0.90/1.09 ((~hskp0) | (~c2_1(a2516))),
% 0.90/1.09 inference(modus_ponens,[status(thm)],[1028, 1027])).
% 0.90/1.09 tff(1030,plain,
% 0.90/1.09 ((~hskp0) | (~c2_1(a2516))),
% 0.90/1.09 inference(modus_ponens,[status(thm)],[1029, 1026])).
% 0.90/1.09 tff(1031,plain,
% 0.90/1.09 (~c2_1(a2516)),
% 0.90/1.09 inference(unit_resolution,[status(thm)],[1030, 1025])).
% 0.90/1.09 tff(1032,plain,
% 0.90/1.09 (((~hskp0) | (~c1_1(a2516))) <=> ((~hskp0) | (~c1_1(a2516)))),
% 0.90/1.09 inference(rewrite,[status(thm)],[])).
% 0.90/1.09 tff(1033,plain,
% 0.90/1.09 (((~c1_1(a2516)) | (~hskp0)) <=> ((~hskp0) | (~c1_1(a2516)))),
% 0.90/1.09 inference(rewrite,[status(thm)],[])).
% 0.90/1.09 tff(1034,axiom,((~c1_1(a2516)) | (~hskp0)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause135')).
% 0.90/1.09 tff(1035,plain,
% 0.90/1.09 ((~hskp0) | (~c1_1(a2516))),
% 0.90/1.09 inference(modus_ponens,[status(thm)],[1034, 1033])).
% 0.90/1.09 tff(1036,plain,
% 0.90/1.09 ((~hskp0) | (~c1_1(a2516))),
% 0.90/1.09 inference(modus_ponens,[status(thm)],[1035, 1032])).
% 0.90/1.09 tff(1037,plain,
% 0.90/1.09 (~c1_1(a2516)),
% 0.90/1.09 inference(unit_resolution,[status(thm)],[1036, 1025])).
% 0.90/1.09 tff(1038,plain,
% 0.90/1.09 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c1_1(a2553) | c3_1(a2553) | c0_1(a2518) | c1_1(a2516) | c2_1(a2516) | (~ndr1_0) | (~c3_1(a2516)) | (~c1_1(a2518)) | (~c2_1(a2518)) | (~c0_1(a2553)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c1_1(a2553) | c3_1(a2553) | c0_1(a2518) | c1_1(a2516) | c2_1(a2516) | (~ndr1_0) | (~c3_1(a2516)) | (~c1_1(a2518)) | (~c2_1(a2518)) | (~c0_1(a2553)))),
% 0.90/1.09 inference(rewrite,[status(thm)],[])).
% 0.90/1.09 tff(1039,plain,
% 0.90/1.09 (((~ndr1_0) | c3_1(a2553) | c1_1(a2553) | (~c0_1(a2553)) | c1_1(a2516) | c2_1(a2516) | (~c3_1(a2516)) | c0_1(a2518) | (~c2_1(a2518)) | (~c1_1(a2518))) <=> (c1_1(a2553) | c3_1(a2553) | c0_1(a2518) | c1_1(a2516) | c2_1(a2516) | (~ndr1_0) | (~c3_1(a2516)) | (~c1_1(a2518)) | (~c2_1(a2518)) | (~c0_1(a2553)))),
% 0.90/1.09 inference(rewrite,[status(thm)],[])).
% 0.90/1.09 tff(1040,plain,
% 0.90/1.09 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a2553) | c1_1(a2553) | (~c0_1(a2553)) | c1_1(a2516) | c2_1(a2516) | (~c3_1(a2516)) | c0_1(a2518) | (~c2_1(a2518)) | (~c1_1(a2518)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c1_1(a2553) | c3_1(a2553) | c0_1(a2518) | c1_1(a2516) | c2_1(a2516) | (~ndr1_0) | (~c3_1(a2516)) | (~c1_1(a2518)) | (~c2_1(a2518)) | (~c0_1(a2553))))),
% 0.90/1.09 inference(monotonicity,[status(thm)],[1039])).
% 0.90/1.09 tff(1041,plain,
% 0.90/1.09 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a2553) | c1_1(a2553) | (~c0_1(a2553)) | c1_1(a2516) | c2_1(a2516) | (~c3_1(a2516)) | c0_1(a2518) | (~c2_1(a2518)) | (~c1_1(a2518)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c1_1(a2553) | c3_1(a2553) | c0_1(a2518) | c1_1(a2516) | c2_1(a2516) | (~ndr1_0) | (~c3_1(a2516)) | (~c1_1(a2518)) | (~c2_1(a2518)) | (~c0_1(a2553)))),
% 0.90/1.09 inference(transitivity,[status(thm)],[1040, 1038])).
% 0.90/1.09 tff(1042,plain,
% 0.90/1.09 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a2553) | c1_1(a2553) | (~c0_1(a2553)) | c1_1(a2516) | c2_1(a2516) | (~c3_1(a2516)) | c0_1(a2518) | (~c2_1(a2518)) | (~c1_1(a2518)))),
% 0.90/1.09 inference(quant_inst,[status(thm)],[])).
% 0.90/1.09 tff(1043,plain,
% 0.90/1.09 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c1_1(a2553) | c3_1(a2553) | c0_1(a2518) | c1_1(a2516) | c2_1(a2516) | (~ndr1_0) | (~c3_1(a2516)) | (~c1_1(a2518)) | (~c2_1(a2518)) | (~c0_1(a2553))),
% 0.90/1.09 inference(modus_ponens,[status(thm)],[1042, 1041])).
% 0.90/1.09 tff(1044,plain,
% 0.90/1.09 (~c3_1(a2516)),
% 0.90/1.09 inference(unit_resolution,[status(thm)],[1043, 90, 828, 927, 827, 826, 929, 1037, 1031, 636, 928])).
% 0.90/1.09 tff(1045,plain,
% 0.90/1.09 (((~hskp0) | (~c0_1(a2516))) <=> ((~hskp0) | (~c0_1(a2516)))),
% 0.90/1.09 inference(rewrite,[status(thm)],[])).
% 0.90/1.09 tff(1046,plain,
% 0.90/1.09 (((~c0_1(a2516)) | (~hskp0)) <=> ((~hskp0) | (~c0_1(a2516)))),
% 0.90/1.09 inference(rewrite,[status(thm)],[])).
% 0.90/1.09 tff(1047,axiom,((~c0_1(a2516)) | (~hskp0)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause134')).
% 0.90/1.09 tff(1048,plain,
% 0.90/1.09 ((~hskp0) | (~c0_1(a2516))),
% 0.90/1.09 inference(modus_ponens,[status(thm)],[1047, 1046])).
% 0.90/1.09 tff(1049,plain,
% 0.90/1.09 ((~hskp0) | (~c0_1(a2516))),
% 0.90/1.09 inference(modus_ponens,[status(thm)],[1048, 1045])).
% 0.90/1.09 tff(1050,plain,
% 0.90/1.09 (~c0_1(a2516)),
% 0.90/1.09 inference(unit_resolution,[status(thm)],[1049, 1025])).
% 0.90/1.09 tff(1051,plain,
% 0.90/1.09 (hskp25),
% 0.90/1.09 inference(unit_resolution,[status(thm)],[761, 1017])).
% 0.90/1.09 tff(1052,plain,
% 0.90/1.09 (~c2_1(a2564)),
% 0.90/1.09 inference(unit_resolution,[status(thm)],[665, 1051])).
% 0.90/1.09 tff(1053,plain,
% 0.90/1.09 (~c1_1(a2564)),
% 0.90/1.09 inference(unit_resolution,[status(thm)],[671, 1051])).
% 0.90/1.09 tff(1054,plain,
% 0.90/1.09 (c0_1(a2564)),
% 0.90/1.09 inference(unit_resolution,[status(thm)],[679, 1051])).
% 0.90/1.09 tff(1055,plain,
% 0.90/1.09 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp8 | c1_1(a2564) | c2_1(a2564) | c0_1(a2516) | c2_1(a2516) | (~ndr1_0) | c3_1(a2516) | (~c0_1(a2564)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp8 | c1_1(a2564) | c2_1(a2564) | c0_1(a2516) | c2_1(a2516) | (~ndr1_0) | c3_1(a2516) | (~c0_1(a2564)))),
% 0.90/1.09 inference(rewrite,[status(thm)],[])).
% 0.90/1.09 tff(1056,plain,
% 0.90/1.09 ((hskp8 | (~ndr1_0) | c2_1(a2564) | c1_1(a2564) | (~c0_1(a2564)) | c3_1(a2516) | c0_1(a2516) | c2_1(a2516)) <=> (hskp8 | c1_1(a2564) | c2_1(a2564) | c0_1(a2516) | c2_1(a2516) | (~ndr1_0) | c3_1(a2516) | (~c0_1(a2564)))),
% 0.90/1.09 inference(rewrite,[status(thm)],[])).
% 0.90/1.09 tff(1057,plain,
% 0.90/1.09 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp8 | (~ndr1_0) | c2_1(a2564) | c1_1(a2564) | (~c0_1(a2564)) | c3_1(a2516) | c0_1(a2516) | c2_1(a2516))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp8 | c1_1(a2564) | c2_1(a2564) | c0_1(a2516) | c2_1(a2516) | (~ndr1_0) | c3_1(a2516) | (~c0_1(a2564))))),
% 0.90/1.09 inference(monotonicity,[status(thm)],[1056])).
% 0.90/1.09 tff(1058,plain,
% 0.90/1.09 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp8 | (~ndr1_0) | c2_1(a2564) | c1_1(a2564) | (~c0_1(a2564)) | c3_1(a2516) | c0_1(a2516) | c2_1(a2516))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp8 | c1_1(a2564) | c2_1(a2564) | c0_1(a2516) | c2_1(a2516) | (~ndr1_0) | c3_1(a2516) | (~c0_1(a2564)))),
% 0.90/1.09 inference(transitivity,[status(thm)],[1057, 1055])).
% 0.90/1.09 tff(1059,plain,
% 0.90/1.09 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp8 | (~ndr1_0) | c2_1(a2564) | c1_1(a2564) | (~c0_1(a2564)) | c3_1(a2516) | c0_1(a2516) | c2_1(a2516))),
% 0.90/1.09 inference(quant_inst,[status(thm)],[])).
% 0.90/1.09 tff(1060,plain,
% 0.90/1.09 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp8 | c1_1(a2564) | c2_1(a2564) | c0_1(a2516) | c2_1(a2516) | (~ndr1_0) | c3_1(a2516) | (~c0_1(a2564))),
% 0.90/1.09 inference(modus_ponens,[status(thm)],[1059, 1058])).
% 0.90/1.09 tff(1061,plain,
% 0.90/1.09 ($false),
% 0.90/1.09 inference(unit_resolution,[status(thm)],[1060, 90, 681, 1054, 1053, 1052, 1050, 1031, 659, 1044])).
% 0.90/1.09 tff(1062,plain,((~hskp2) | hskp8 | (~c0_1(a2551)) | (~c1_1(a2551)) | c2_1(a2551) | (~c3_1(a2526)) | c0_1(a2526) | c3_1(a2541) | c2_1(a2541) | (~c1_1(a2526))), inference(lemma,lemma(discharge,[]))).
% 0.90/1.09 tff(1063,plain,
% 0.90/1.09 (hskp8),
% 0.90/1.09 inference(unit_resolution,[status(thm)],[1062, 887, 472, 471, 470, 216, 152, 829, 265, 215])).
% 0.90/1.09 tff(1064,plain,
% 0.90/1.09 (~c3_1(a2525)),
% 0.90/1.09 inference(unit_resolution,[status(thm)],[607, 1063])).
% 0.90/1.09 tff(1065,plain,
% 0.90/1.09 (((~hskp8) | c2_1(a2525)) <=> ((~hskp8) | c2_1(a2525))),
% 0.90/1.09 inference(rewrite,[status(thm)],[])).
% 0.90/1.09 tff(1066,axiom,((~hskp8) | c2_1(a2525)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause78')).
% 0.90/1.09 tff(1067,plain,
% 0.90/1.09 ((~hskp8) | c2_1(a2525)),
% 0.90/1.09 inference(modus_ponens,[status(thm)],[1066, 1065])).
% 0.90/1.09 tff(1068,plain,
% 0.90/1.09 ((~hskp8) | c2_1(a2525)),
% 0.90/1.09 inference(modus_ponens,[status(thm)],[1067, 1065])).
% 0.90/1.09 tff(1069,plain,
% 0.90/1.09 ((~hskp8) | c2_1(a2525)),
% 0.90/1.09 inference(modus_ponens,[status(thm)],[1068, 1065])).
% 0.90/1.09 tff(1070,plain,
% 0.90/1.09 ((~hskp8) | c2_1(a2525)),
% 0.90/1.09 inference(modus_ponens,[status(thm)],[1069, 1065])).
% 0.90/1.09 tff(1071,plain,
% 0.90/1.09 ((~hskp8) | c2_1(a2525)),
% 0.90/1.09 inference(modus_ponens,[status(thm)],[1070, 1065])).
% 0.90/1.09 tff(1072,plain,
% 0.90/1.09 (c2_1(a2525)),
% 0.90/1.09 inference(unit_resolution,[status(thm)],[1071, 1063])).
% 0.90/1.09 tff(1073,plain,
% 0.90/1.09 (c0_1(a2525)),
% 0.90/1.09 inference(unit_resolution,[status(thm)],[615, 1063])).
% 0.90/1.09 tff(1074,assumption,(~c3_1(a2525)), introduced(assumption)).
% 0.90/1.09 tff(1075,assumption,(c2_1(a2525)), introduced(assumption)).
% 0.90/1.09 tff(1076,assumption,(c0_1(a2525)), introduced(assumption)).
% 0.90/1.09 tff(1077,assumption,(~c0_1(a2552)), introduced(assumption)).
% 0.90/1.09 tff(1078,plain,
% 0.90/1.09 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W))) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W))))),
% 0.90/1.09 inference(bind,[status(th)],[])).
% 0.90/1.09 tff(1079,plain,
% 0.90/1.09 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 0.90/1.09 inference(quant_intro,[status(thm)],[1078])).
% 0.90/1.09 tff(1080,plain,
% 0.90/1.09 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 0.90/1.09 inference(rewrite,[status(thm)],[])).
% 0.90/1.09 tff(1081,plain,
% 0.90/1.09 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c2_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c2_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c2_1(V)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c2_1(V))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c2_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V))) | (~c2_1(W))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c2_1(W)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c2_1(W))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c3_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c2_1(W))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c2_1(W))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c2_1(W)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c2_1(W))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c2_1(W))) | c0_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c2_1(W))) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | (~c2_1(W)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | (~c2_1(W))))), ((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c3_1(U)) | c0_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | (~c2_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | (~c2_1(W))) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)))), ((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c3_1(U)) | c0_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W))))), (((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c3_1(U)) | c0_1(V)) | c0_1(W)) | c1_1(W)) <=> (((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W))) | c1_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W))) | c1_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))), (((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c3_1(U)) | c0_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))))),
% 0.90/1.10 inference(bind,[status(th)],[])).
% 0.90/1.10 tff(1082,plain,
% 0.90/1.10 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c3_1(U)) | c0_1(V)) | c0_1(W)) | c1_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 0.90/1.10 inference(quant_intro,[status(thm)],[1081])).
% 0.90/1.10 tff(1083,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c3_1(U)) | c0_1(V)) | c0_1(W)) | c1_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause199')).
% 0.90/1.10 tff(1084,plain,
% 0.90/1.10 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 0.90/1.10 inference(modus_ponens,[status(thm)],[1083, 1082])).
% 0.90/1.10 tff(1085,plain,
% 0.90/1.10 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 0.90/1.10 inference(modus_ponens,[status(thm)],[1084, 1080])).
% 0.90/1.10 tff(1086,plain,(
% 0.90/1.10 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 0.90/1.10 inference(skolemize,[status(sab)],[1085])).
% 0.90/1.10 tff(1087,plain,
% 0.90/1.10 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 0.90/1.10 inference(modus_ponens,[status(thm)],[1086, 1079])).
% 0.90/1.10 tff(1088,plain,
% 0.90/1.10 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a2552) | c0_1(a2526) | c3_1(a2525) | (~ndr1_0) | (~c0_1(a2525)) | (~c2_1(a2525)) | (~c3_1(a2526)) | (~c2_1(a2526)) | c0_1(a2552) | (~c2_1(a2552)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a2552) | c0_1(a2526) | c3_1(a2525) | (~ndr1_0) | (~c0_1(a2525)) | (~c2_1(a2525)) | (~c3_1(a2526)) | (~c2_1(a2526)) | c0_1(a2552) | (~c2_1(a2552)))),
% 0.90/1.10 inference(rewrite,[status(thm)],[])).
% 0.90/1.10 tff(1089,plain,
% 0.90/1.10 (((~ndr1_0) | c3_1(a2525) | (~c0_1(a2525)) | (~c2_1(a2525)) | c0_1(a2526) | (~c3_1(a2526)) | (~c2_1(a2526)) | c1_1(a2552) | c0_1(a2552) | (~c2_1(a2552))) <=> (c1_1(a2552) | c0_1(a2526) | c3_1(a2525) | (~ndr1_0) | (~c0_1(a2525)) | (~c2_1(a2525)) | (~c3_1(a2526)) | (~c2_1(a2526)) | c0_1(a2552) | (~c2_1(a2552)))),
% 0.90/1.10 inference(rewrite,[status(thm)],[])).
% 0.90/1.10 tff(1090,plain,
% 0.90/1.10 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a2525) | (~c0_1(a2525)) | (~c2_1(a2525)) | c0_1(a2526) | (~c3_1(a2526)) | (~c2_1(a2526)) | c1_1(a2552) | c0_1(a2552) | (~c2_1(a2552)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a2552) | c0_1(a2526) | c3_1(a2525) | (~ndr1_0) | (~c0_1(a2525)) | (~c2_1(a2525)) | (~c3_1(a2526)) | (~c2_1(a2526)) | c0_1(a2552) | (~c2_1(a2552))))),
% 0.90/1.10 inference(monotonicity,[status(thm)],[1089])).
% 0.90/1.10 tff(1091,plain,
% 0.90/1.10 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a2525) | (~c0_1(a2525)) | (~c2_1(a2525)) | c0_1(a2526) | (~c3_1(a2526)) | (~c2_1(a2526)) | c1_1(a2552) | c0_1(a2552) | (~c2_1(a2552)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a2552) | c0_1(a2526) | c3_1(a2525) | (~ndr1_0) | (~c0_1(a2525)) | (~c2_1(a2525)) | (~c3_1(a2526)) | (~c2_1(a2526)) | c0_1(a2552) | (~c2_1(a2552)))),
% 0.90/1.10 inference(transitivity,[status(thm)],[1090, 1088])).
% 0.90/1.10 tff(1092,plain,
% 0.90/1.10 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a2525) | (~c0_1(a2525)) | (~c2_1(a2525)) | c0_1(a2526) | (~c3_1(a2526)) | (~c2_1(a2526)) | c1_1(a2552) | c0_1(a2552) | (~c2_1(a2552)))),
% 0.90/1.10 inference(quant_inst,[status(thm)],[])).
% 0.90/1.10 tff(1093,plain,
% 0.90/1.10 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a2552) | c0_1(a2526) | c3_1(a2525) | (~ndr1_0) | (~c0_1(a2525)) | (~c2_1(a2525)) | (~c3_1(a2526)) | (~c2_1(a2526)) | c0_1(a2552) | (~c2_1(a2552))),
% 0.90/1.10 inference(modus_ponens,[status(thm)],[1092, 1091])).
% 0.90/1.10 tff(1094,plain,
% 0.90/1.10 ((~c2_1(a2526)) | c0_1(a2552)),
% 0.90/1.10 inference(unit_resolution,[status(thm)],[1093, 90, 822, 216, 1076, 1075, 824, 152, 1074, 1087])).
% 0.90/1.10 tff(1095,plain,
% 0.90/1.10 (~c2_1(a2526)),
% 0.90/1.10 inference(unit_resolution,[status(thm)],[1094, 1077])).
% 0.90/1.10 tff(1096,assumption,(~hskp10), introduced(assumption)).
% 0.90/1.10 tff(1097,plain,
% 0.90/1.10 (^[U: $i] : refl((hskp29 | hskp10 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U))) <=> (hskp29 | hskp10 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U))))),
% 0.90/1.10 inference(bind,[status(th)],[])).
% 0.90/1.10 tff(1098,plain,
% 0.90/1.10 (![U: $i] : (hskp29 | hskp10 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp29 | hskp10 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 0.90/1.10 inference(quant_intro,[status(thm)],[1097])).
% 0.90/1.10 tff(1099,plain,
% 0.90/1.10 (![U: $i] : (hskp29 | hskp10 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp29 | hskp10 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 0.90/1.10 inference(rewrite,[status(thm)],[])).
% 0.90/1.10 tff(1100,plain,
% 0.90/1.10 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp29) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U))) | hskp29))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U))) | hskp29) <=> (hskp29 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp29) <=> (hskp29 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp29) | hskp10) <=> ((hskp29 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U))) | hskp10))), rewrite(((hskp29 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U))) | hskp10) <=> (hskp29 | hskp10 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp29) | hskp10) <=> (hskp29 | hskp10 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))))),
% 0.90/1.10 inference(bind,[status(th)],[])).
% 0.90/1.10 tff(1101,plain,
% 0.90/1.10 (![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp29) | hskp10) <=> ![U: $i] : (hskp29 | hskp10 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 0.90/1.10 inference(quant_intro,[status(thm)],[1100])).
% 0.90/1.10 tff(1102,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp29) | hskp10)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause157')).
% 0.90/1.10 tff(1103,plain,
% 0.90/1.10 (![U: $i] : (hskp29 | hskp10 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 0.90/1.10 inference(modus_ponens,[status(thm)],[1102, 1101])).
% 0.90/1.10 tff(1104,plain,
% 0.90/1.10 (![U: $i] : (hskp29 | hskp10 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 0.90/1.10 inference(modus_ponens,[status(thm)],[1103, 1099])).
% 0.90/1.10 tff(1105,plain,(
% 0.90/1.10 ![U: $i] : (hskp29 | hskp10 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 0.90/1.10 inference(skolemize,[status(sab)],[1104])).
% 0.90/1.10 tff(1106,plain,
% 0.90/1.10 (![U: $i] : (hskp29 | hskp10 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 0.90/1.10 inference(modus_ponens,[status(thm)],[1105, 1098])).
% 0.90/1.10 tff(1107,plain,
% 0.90/1.10 (((~![U: $i] : (hskp29 | hskp10 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp29 | hskp10 | c3_1(a2525) | (~ndr1_0) | (~c0_1(a2525)) | (~c1_1(a2525)))) <=> ((~![U: $i] : (hskp29 | hskp10 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp29 | hskp10 | c3_1(a2525) | (~ndr1_0) | (~c0_1(a2525)) | (~c1_1(a2525)))),
% 0.90/1.10 inference(rewrite,[status(thm)],[])).
% 0.90/1.10 tff(1108,plain,
% 0.90/1.10 ((hskp29 | hskp10 | (~ndr1_0) | c3_1(a2525) | (~c1_1(a2525)) | (~c0_1(a2525))) <=> (hskp29 | hskp10 | c3_1(a2525) | (~ndr1_0) | (~c0_1(a2525)) | (~c1_1(a2525)))),
% 0.90/1.10 inference(rewrite,[status(thm)],[])).
% 0.90/1.10 tff(1109,plain,
% 0.90/1.10 (((~![U: $i] : (hskp29 | hskp10 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp29 | hskp10 | (~ndr1_0) | c3_1(a2525) | (~c1_1(a2525)) | (~c0_1(a2525)))) <=> ((~![U: $i] : (hskp29 | hskp10 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp29 | hskp10 | c3_1(a2525) | (~ndr1_0) | (~c0_1(a2525)) | (~c1_1(a2525))))),
% 0.90/1.10 inference(monotonicity,[status(thm)],[1108])).
% 0.90/1.10 tff(1110,plain,
% 0.90/1.10 (((~![U: $i] : (hskp29 | hskp10 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp29 | hskp10 | (~ndr1_0) | c3_1(a2525) | (~c1_1(a2525)) | (~c0_1(a2525)))) <=> ((~![U: $i] : (hskp29 | hskp10 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp29 | hskp10 | c3_1(a2525) | (~ndr1_0) | (~c0_1(a2525)) | (~c1_1(a2525)))),
% 0.90/1.10 inference(transitivity,[status(thm)],[1109, 1107])).
% 0.90/1.10 tff(1111,plain,
% 0.90/1.10 ((~![U: $i] : (hskp29 | hskp10 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp29 | hskp10 | (~ndr1_0) | c3_1(a2525) | (~c1_1(a2525)) | (~c0_1(a2525)))),
% 0.90/1.10 inference(quant_inst,[status(thm)],[])).
% 0.90/1.10 tff(1112,plain,
% 0.90/1.10 ((~![U: $i] : (hskp29 | hskp10 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp29 | hskp10 | c3_1(a2525) | (~ndr1_0) | (~c0_1(a2525)) | (~c1_1(a2525))),
% 0.90/1.10 inference(modus_ponens,[status(thm)],[1111, 1110])).
% 0.90/1.10 tff(1113,plain,
% 0.90/1.10 (hskp29 | hskp10 | (~c1_1(a2525))),
% 0.90/1.10 inference(unit_resolution,[status(thm)],[1112, 90, 1076, 1074, 1106])).
% 0.90/1.10 tff(1114,plain,
% 0.90/1.10 (~c1_1(a2525)),
% 0.90/1.10 inference(unit_resolution,[status(thm)],[1113, 1096, 404])).
% 0.90/1.10 tff(1115,assumption,(~c2_1(a2526)), introduced(assumption)).
% 0.90/1.10 tff(1116,plain,
% 0.90/1.10 (((~![U: $i] : (hskp29 | hskp10 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp29 | hskp10 | (~ndr1_0) | c3_1(a2551) | (~c0_1(a2551)) | (~c1_1(a2551)))) <=> ((~![U: $i] : (hskp29 | hskp10 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp29 | hskp10 | (~ndr1_0) | c3_1(a2551) | (~c0_1(a2551)) | (~c1_1(a2551)))),
% 0.90/1.10 inference(rewrite,[status(thm)],[])).
% 0.90/1.10 tff(1117,plain,
% 0.90/1.10 ((hskp29 | hskp10 | (~ndr1_0) | c3_1(a2551) | (~c1_1(a2551)) | (~c0_1(a2551))) <=> (hskp29 | hskp10 | (~ndr1_0) | c3_1(a2551) | (~c0_1(a2551)) | (~c1_1(a2551)))),
% 0.90/1.10 inference(rewrite,[status(thm)],[])).
% 0.90/1.10 tff(1118,plain,
% 0.90/1.10 (((~![U: $i] : (hskp29 | hskp10 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp29 | hskp10 | (~ndr1_0) | c3_1(a2551) | (~c1_1(a2551)) | (~c0_1(a2551)))) <=> ((~![U: $i] : (hskp29 | hskp10 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp29 | hskp10 | (~ndr1_0) | c3_1(a2551) | (~c0_1(a2551)) | (~c1_1(a2551))))),
% 0.90/1.10 inference(monotonicity,[status(thm)],[1117])).
% 0.90/1.10 tff(1119,plain,
% 0.90/1.10 (((~![U: $i] : (hskp29 | hskp10 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp29 | hskp10 | (~ndr1_0) | c3_1(a2551) | (~c1_1(a2551)) | (~c0_1(a2551)))) <=> ((~![U: $i] : (hskp29 | hskp10 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp29 | hskp10 | (~ndr1_0) | c3_1(a2551) | (~c0_1(a2551)) | (~c1_1(a2551)))),
% 0.90/1.10 inference(transitivity,[status(thm)],[1118, 1116])).
% 0.90/1.10 tff(1120,plain,
% 0.90/1.10 ((~![U: $i] : (hskp29 | hskp10 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp29 | hskp10 | (~ndr1_0) | c3_1(a2551) | (~c1_1(a2551)) | (~c0_1(a2551)))),
% 0.90/1.10 inference(quant_inst,[status(thm)],[])).
% 0.90/1.10 tff(1121,plain,
% 0.90/1.10 ((~![U: $i] : (hskp29 | hskp10 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp29 | hskp10 | (~ndr1_0) | c3_1(a2551) | (~c0_1(a2551)) | (~c1_1(a2551))),
% 0.90/1.10 inference(modus_ponens,[status(thm)],[1120, 1119])).
% 0.90/1.10 tff(1122,plain,
% 0.90/1.10 (hskp29 | hskp10 | c3_1(a2551)),
% 0.90/1.10 inference(unit_resolution,[status(thm)],[1121, 90, 472, 471, 1106])).
% 0.90/1.10 tff(1123,plain,
% 0.90/1.10 (c3_1(a2551)),
% 0.90/1.10 inference(unit_resolution,[status(thm)],[1122, 1096, 404])).
% 0.90/1.10 tff(1124,plain,
% 0.90/1.10 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | (c0_1(a2526) | (~ndr1_0) | (~c0_1(a2525)) | (~c2_1(a2525)) | c1_1(a2525) | (~c3_1(a2526)) | c2_1(a2526) | (~c3_1(a2551)) | (~c0_1(a2551)) | (~c1_1(a2551)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c0_1(a2526) | (~ndr1_0) | (~c0_1(a2525)) | (~c2_1(a2525)) | c1_1(a2525) | (~c3_1(a2526)) | c2_1(a2526) | (~c3_1(a2551)) | (~c0_1(a2551)) | (~c1_1(a2551)))),
% 0.90/1.10 inference(rewrite,[status(thm)],[])).
% 0.90/1.10 tff(1125,plain,
% 0.90/1.10 (((~ndr1_0) | (~c3_1(a2551)) | (~c1_1(a2551)) | (~c0_1(a2551)) | c1_1(a2525) | (~c0_1(a2525)) | (~c2_1(a2525)) | c0_1(a2526) | c2_1(a2526) | (~c3_1(a2526))) <=> (c0_1(a2526) | (~ndr1_0) | (~c0_1(a2525)) | (~c2_1(a2525)) | c1_1(a2525) | (~c3_1(a2526)) | c2_1(a2526) | (~c3_1(a2551)) | (~c0_1(a2551)) | (~c1_1(a2551)))),
% 0.90/1.10 inference(rewrite,[status(thm)],[])).
% 0.90/1.10 tff(1126,plain,
% 0.90/1.10 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a2551)) | (~c1_1(a2551)) | (~c0_1(a2551)) | c1_1(a2525) | (~c0_1(a2525)) | (~c2_1(a2525)) | c0_1(a2526) | c2_1(a2526) | (~c3_1(a2526)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | (c0_1(a2526) | (~ndr1_0) | (~c0_1(a2525)) | (~c2_1(a2525)) | c1_1(a2525) | (~c3_1(a2526)) | c2_1(a2526) | (~c3_1(a2551)) | (~c0_1(a2551)) | (~c1_1(a2551))))),
% 0.90/1.10 inference(monotonicity,[status(thm)],[1125])).
% 0.90/1.10 tff(1127,plain,
% 0.90/1.10 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a2551)) | (~c1_1(a2551)) | (~c0_1(a2551)) | c1_1(a2525) | (~c0_1(a2525)) | (~c2_1(a2525)) | c0_1(a2526) | c2_1(a2526) | (~c3_1(a2526)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c0_1(a2526) | (~ndr1_0) | (~c0_1(a2525)) | (~c2_1(a2525)) | c1_1(a2525) | (~c3_1(a2526)) | c2_1(a2526) | (~c3_1(a2551)) | (~c0_1(a2551)) | (~c1_1(a2551)))),
% 0.90/1.10 inference(transitivity,[status(thm)],[1126, 1124])).
% 0.90/1.10 tff(1128,plain,
% 0.90/1.10 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a2551)) | (~c1_1(a2551)) | (~c0_1(a2551)) | c1_1(a2525) | (~c0_1(a2525)) | (~c2_1(a2525)) | c0_1(a2526) | c2_1(a2526) | (~c3_1(a2526)))),
% 0.90/1.10 inference(quant_inst,[status(thm)],[])).
% 0.90/1.10 tff(1129,plain,
% 0.90/1.10 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c0_1(a2526) | (~ndr1_0) | (~c0_1(a2525)) | (~c2_1(a2525)) | c1_1(a2525) | (~c3_1(a2526)) | c2_1(a2526) | (~c3_1(a2551)) | (~c0_1(a2551)) | (~c1_1(a2551))),
% 0.90/1.10 inference(modus_ponens,[status(thm)],[1128, 1127])).
% 0.90/1.10 tff(1130,plain,
% 0.90/1.10 ($false),
% 0.90/1.10 inference(unit_resolution,[status(thm)],[1129, 90, 472, 471, 216, 1076, 1075, 152, 709, 1123, 1115, 1114])).
% 0.90/1.10 tff(1131,plain,(hskp10 | (~c0_1(a2551)) | (~c1_1(a2551)) | (~c3_1(a2526)) | (~c0_1(a2525)) | (~c2_1(a2525)) | c0_1(a2526) | c2_1(a2526) | hskp29 | c3_1(a2525)), inference(lemma,lemma(discharge,[]))).
% 0.90/1.10 tff(1132,plain,
% 0.90/1.10 (hskp10),
% 0.90/1.10 inference(unit_resolution,[status(thm)],[1131, 1095, 471, 216, 1076, 1075, 152, 472, 404, 1074])).
% 0.90/1.10 tff(1133,plain,
% 0.90/1.10 (((~hskp10) | (~c0_1(a2528))) <=> ((~hskp10) | (~c0_1(a2528)))),
% 0.90/1.10 inference(rewrite,[status(thm)],[])).
% 0.90/1.10 tff(1134,plain,
% 0.90/1.10 (((~c0_1(a2528)) | (~hskp10)) <=> ((~hskp10) | (~c0_1(a2528)))),
% 0.90/1.10 inference(rewrite,[status(thm)],[])).
% 0.90/1.10 tff(1135,axiom,((~c0_1(a2528)) | (~hskp10)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause119')).
% 0.90/1.10 tff(1136,plain,
% 0.90/1.10 ((~hskp10) | (~c0_1(a2528))),
% 0.90/1.10 inference(modus_ponens,[status(thm)],[1135, 1134])).
% 0.90/1.10 tff(1137,plain,
% 0.90/1.10 ((~hskp10) | (~c0_1(a2528))),
% 0.90/1.10 inference(modus_ponens,[status(thm)],[1136, 1133])).
% 0.90/1.10 tff(1138,plain,
% 0.90/1.10 (~c0_1(a2528)),
% 0.90/1.10 inference(unit_resolution,[status(thm)],[1137, 1132])).
% 0.90/1.10 tff(1139,plain,
% 0.90/1.10 (((~hskp10) | c3_1(a2528)) <=> ((~hskp10) | c3_1(a2528))),
% 0.90/1.10 inference(rewrite,[status(thm)],[])).
% 0.90/1.10 tff(1140,axiom,((~hskp10) | c3_1(a2528)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause74')).
% 0.90/1.10 tff(1141,plain,
% 0.90/1.10 ((~hskp10) | c3_1(a2528)),
% 0.90/1.10 inference(modus_ponens,[status(thm)],[1140, 1139])).
% 0.90/1.10 tff(1142,plain,
% 0.90/1.10 ((~hskp10) | c3_1(a2528)),
% 0.90/1.10 inference(modus_ponens,[status(thm)],[1141, 1139])).
% 0.90/1.10 tff(1143,plain,
% 0.90/1.10 ((~hskp10) | c3_1(a2528)),
% 0.90/1.10 inference(modus_ponens,[status(thm)],[1142, 1139])).
% 0.90/1.10 tff(1144,plain,
% 0.90/1.10 ((~hskp10) | c3_1(a2528)),
% 0.90/1.10 inference(modus_ponens,[status(thm)],[1143, 1139])).
% 0.90/1.10 tff(1145,plain,
% 0.90/1.10 ((~hskp10) | c3_1(a2528)),
% 0.90/1.10 inference(modus_ponens,[status(thm)],[1144, 1139])).
% 0.90/1.10 tff(1146,plain,
% 0.90/1.10 (c3_1(a2528)),
% 0.90/1.10 inference(unit_resolution,[status(thm)],[1145, 1132])).
% 0.90/1.10 tff(1147,plain,
% 0.90/1.10 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a2552) | c0_1(a2528) | c3_1(a2525) | (~ndr1_0) | (~c0_1(a2525)) | (~c2_1(a2525)) | (~c3_1(a2528)) | (~c2_1(a2528)) | c0_1(a2552) | (~c2_1(a2552)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a2552) | c0_1(a2528) | c3_1(a2525) | (~ndr1_0) | (~c0_1(a2525)) | (~c2_1(a2525)) | (~c3_1(a2528)) | (~c2_1(a2528)) | c0_1(a2552) | (~c2_1(a2552)))),
% 0.90/1.10 inference(rewrite,[status(thm)],[])).
% 0.90/1.10 tff(1148,plain,
% 0.90/1.10 (((~ndr1_0) | c3_1(a2525) | (~c0_1(a2525)) | (~c2_1(a2525)) | c0_1(a2528) | (~c3_1(a2528)) | (~c2_1(a2528)) | c1_1(a2552) | c0_1(a2552) | (~c2_1(a2552))) <=> (c1_1(a2552) | c0_1(a2528) | c3_1(a2525) | (~ndr1_0) | (~c0_1(a2525)) | (~c2_1(a2525)) | (~c3_1(a2528)) | (~c2_1(a2528)) | c0_1(a2552) | (~c2_1(a2552)))),
% 0.90/1.10 inference(rewrite,[status(thm)],[])).
% 0.90/1.10 tff(1149,plain,
% 0.90/1.10 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a2525) | (~c0_1(a2525)) | (~c2_1(a2525)) | c0_1(a2528) | (~c3_1(a2528)) | (~c2_1(a2528)) | c1_1(a2552) | c0_1(a2552) | (~c2_1(a2552)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a2552) | c0_1(a2528) | c3_1(a2525) | (~ndr1_0) | (~c0_1(a2525)) | (~c2_1(a2525)) | (~c3_1(a2528)) | (~c2_1(a2528)) | c0_1(a2552) | (~c2_1(a2552))))),
% 0.90/1.10 inference(monotonicity,[status(thm)],[1148])).
% 0.90/1.10 tff(1150,plain,
% 0.90/1.10 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a2525) | (~c0_1(a2525)) | (~c2_1(a2525)) | c0_1(a2528) | (~c3_1(a2528)) | (~c2_1(a2528)) | c1_1(a2552) | c0_1(a2552) | (~c2_1(a2552)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a2552) | c0_1(a2528) | c3_1(a2525) | (~ndr1_0) | (~c0_1(a2525)) | (~c2_1(a2525)) | (~c3_1(a2528)) | (~c2_1(a2528)) | c0_1(a2552) | (~c2_1(a2552)))),
% 0.90/1.10 inference(transitivity,[status(thm)],[1149, 1147])).
% 0.90/1.10 tff(1151,plain,
% 0.90/1.10 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a2525) | (~c0_1(a2525)) | (~c2_1(a2525)) | c0_1(a2528) | (~c3_1(a2528)) | (~c2_1(a2528)) | c1_1(a2552) | c0_1(a2552) | (~c2_1(a2552)))),
% 0.90/1.10 inference(quant_inst,[status(thm)],[])).
% 0.90/1.10 tff(1152,plain,
% 0.90/1.10 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a2552) | c0_1(a2528) | c3_1(a2525) | (~ndr1_0) | (~c0_1(a2525)) | (~c2_1(a2525)) | (~c3_1(a2528)) | (~c2_1(a2528)) | c0_1(a2552) | (~c2_1(a2552))),
% 0.90/1.10 inference(modus_ponens,[status(thm)],[1151, 1150])).
% 0.90/1.10 tff(1153,plain,
% 0.90/1.10 (~c2_1(a2528)),
% 0.90/1.10 inference(unit_resolution,[status(thm)],[1152, 90, 822, 1146, 1076, 1075, 824, 1138, 1074, 1087, 1077])).
% 0.90/1.10 tff(1154,plain,
% 0.90/1.10 (((~hskp10) | (~c1_1(a2528))) <=> ((~hskp10) | (~c1_1(a2528)))),
% 0.90/1.10 inference(rewrite,[status(thm)],[])).
% 0.90/1.10 tff(1155,plain,
% 0.90/1.10 (((~c1_1(a2528)) | (~hskp10)) <=> ((~hskp10) | (~c1_1(a2528)))),
% 0.90/1.10 inference(rewrite,[status(thm)],[])).
% 0.90/1.10 tff(1156,axiom,((~c1_1(a2528)) | (~hskp10)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause120')).
% 0.90/1.10 tff(1157,plain,
% 0.90/1.10 ((~hskp10) | (~c1_1(a2528))),
% 0.90/1.10 inference(modus_ponens,[status(thm)],[1156, 1155])).
% 0.90/1.10 tff(1158,plain,
% 0.90/1.10 ((~hskp10) | (~c1_1(a2528))),
% 0.90/1.10 inference(modus_ponens,[status(thm)],[1157, 1154])).
% 0.90/1.10 tff(1159,plain,
% 0.90/1.10 (~c1_1(a2528)),
% 0.90/1.10 inference(unit_resolution,[status(thm)],[1158, 1132])).
% 0.90/1.10 tff(1160,plain,
% 0.90/1.10 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c1_1(a2553) | c3_1(a2553) | c1_1(a2528) | c0_1(a2518) | (~ndr1_0) | (~c1_1(a2518)) | (~c2_1(a2518)) | (~c3_1(a2528)) | c2_1(a2528) | (~c0_1(a2553)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c1_1(a2553) | c3_1(a2553) | c1_1(a2528) | c0_1(a2518) | (~ndr1_0) | (~c1_1(a2518)) | (~c2_1(a2518)) | (~c3_1(a2528)) | c2_1(a2528) | (~c0_1(a2553)))),
% 0.90/1.10 inference(rewrite,[status(thm)],[])).
% 0.90/1.10 tff(1161,plain,
% 0.90/1.10 (((~ndr1_0) | c3_1(a2553) | c1_1(a2553) | (~c0_1(a2553)) | c1_1(a2528) | c2_1(a2528) | (~c3_1(a2528)) | c0_1(a2518) | (~c2_1(a2518)) | (~c1_1(a2518))) <=> (c1_1(a2553) | c3_1(a2553) | c1_1(a2528) | c0_1(a2518) | (~ndr1_0) | (~c1_1(a2518)) | (~c2_1(a2518)) | (~c3_1(a2528)) | c2_1(a2528) | (~c0_1(a2553)))),
% 0.90/1.10 inference(rewrite,[status(thm)],[])).
% 0.90/1.10 tff(1162,plain,
% 0.90/1.10 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a2553) | c1_1(a2553) | (~c0_1(a2553)) | c1_1(a2528) | c2_1(a2528) | (~c3_1(a2528)) | c0_1(a2518) | (~c2_1(a2518)) | (~c1_1(a2518)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c1_1(a2553) | c3_1(a2553) | c1_1(a2528) | c0_1(a2518) | (~ndr1_0) | (~c1_1(a2518)) | (~c2_1(a2518)) | (~c3_1(a2528)) | c2_1(a2528) | (~c0_1(a2553))))),
% 0.90/1.10 inference(monotonicity,[status(thm)],[1161])).
% 0.90/1.10 tff(1163,plain,
% 0.90/1.10 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a2553) | c1_1(a2553) | (~c0_1(a2553)) | c1_1(a2528) | c2_1(a2528) | (~c3_1(a2528)) | c0_1(a2518) | (~c2_1(a2518)) | (~c1_1(a2518)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c1_1(a2553) | c3_1(a2553) | c1_1(a2528) | c0_1(a2518) | (~ndr1_0) | (~c1_1(a2518)) | (~c2_1(a2518)) | (~c3_1(a2528)) | c2_1(a2528) | (~c0_1(a2553)))),
% 0.90/1.10 inference(transitivity,[status(thm)],[1162, 1160])).
% 0.90/1.10 tff(1164,plain,
% 0.90/1.10 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a2553) | c1_1(a2553) | (~c0_1(a2553)) | c1_1(a2528) | c2_1(a2528) | (~c3_1(a2528)) | c0_1(a2518) | (~c2_1(a2518)) | (~c1_1(a2518)))),
% 0.90/1.10 inference(quant_inst,[status(thm)],[])).
% 0.90/1.10 tff(1165,plain,
% 0.90/1.10 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c1_1(a2553) | c3_1(a2553) | c1_1(a2528) | c0_1(a2518) | (~ndr1_0) | (~c1_1(a2518)) | (~c2_1(a2518)) | (~c3_1(a2528)) | c2_1(a2528) | (~c0_1(a2553))),
% 0.90/1.10 inference(modus_ponens,[status(thm)],[1164, 1163])).
% 0.90/1.10 tff(1166,plain,
% 0.90/1.10 ($false),
% 0.90/1.10 inference(unit_resolution,[status(thm)],[1165, 90, 851, 1146, 948, 850, 849, 1159, 945, 636, 934, 1153])).
% 0.90/1.10 tff(1167,plain,(c0_1(a2552) | (~c0_1(a2553)) | (~c1_1(a2518)) | c1_1(a2553) | c3_1(a2553) | c0_1(a2518) | (~c2_1(a2518)) | (~c2_1(a2552)) | (~c0_1(a2525)) | (~c2_1(a2525)) | c1_1(a2552) | c3_1(a2525) | (~c1_1(a2551)) | (~c3_1(a2526)) | c0_1(a2526) | (~c0_1(a2551)) | hskp29), inference(lemma,lemma(discharge,[]))).
% 0.90/1.10 tff(1168,plain,
% 0.90/1.10 (c0_1(a2552)),
% 0.90/1.10 inference(unit_resolution,[status(thm)],[1167, 404, 948, 850, 849, 945, 934, 822, 1076, 1075, 824, 1074, 471, 216, 152, 472, 851])).
% 0.90/1.10 tff(1169,plain,
% 0.90/1.10 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp16 | c1_1(a2552) | c0_1(a2526) | (~ndr1_0) | (~c3_1(a2526)) | (~c1_1(a2526)) | (~c0_1(a2552)) | (~c2_1(a2552)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp16 | c1_1(a2552) | c0_1(a2526) | (~ndr1_0) | (~c3_1(a2526)) | (~c1_1(a2526)) | (~c0_1(a2552)) | (~c2_1(a2552)))),
% 0.90/1.10 inference(rewrite,[status(thm)],[])).
% 0.90/1.10 tff(1170,plain,
% 0.90/1.10 ((hskp16 | (~ndr1_0) | c1_1(a2552) | (~c0_1(a2552)) | (~c2_1(a2552)) | c0_1(a2526) | (~c3_1(a2526)) | (~c1_1(a2526))) <=> (hskp16 | c1_1(a2552) | c0_1(a2526) | (~ndr1_0) | (~c3_1(a2526)) | (~c1_1(a2526)) | (~c0_1(a2552)) | (~c2_1(a2552)))),
% 0.90/1.10 inference(rewrite,[status(thm)],[])).
% 0.90/1.10 tff(1171,plain,
% 0.90/1.10 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp16 | (~ndr1_0) | c1_1(a2552) | (~c0_1(a2552)) | (~c2_1(a2552)) | c0_1(a2526) | (~c3_1(a2526)) | (~c1_1(a2526)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp16 | c1_1(a2552) | c0_1(a2526) | (~ndr1_0) | (~c3_1(a2526)) | (~c1_1(a2526)) | (~c0_1(a2552)) | (~c2_1(a2552))))),
% 0.90/1.10 inference(monotonicity,[status(thm)],[1170])).
% 0.90/1.10 tff(1172,plain,
% 0.90/1.10 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp16 | (~ndr1_0) | c1_1(a2552) | (~c0_1(a2552)) | (~c2_1(a2552)) | c0_1(a2526) | (~c3_1(a2526)) | (~c1_1(a2526)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp16 | c1_1(a2552) | c0_1(a2526) | (~ndr1_0) | (~c3_1(a2526)) | (~c1_1(a2526)) | (~c0_1(a2552)) | (~c2_1(a2552)))),
% 0.90/1.10 inference(transitivity,[status(thm)],[1171, 1169])).
% 0.90/1.10 tff(1173,plain,
% 0.90/1.10 ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp16 | (~ndr1_0) | c1_1(a2552) | (~c0_1(a2552)) | (~c2_1(a2552)) | c0_1(a2526) | (~c3_1(a2526)) | (~c1_1(a2526)))),
% 0.90/1.10 inference(quant_inst,[status(thm)],[])).
% 0.90/1.10 tff(1174,plain,
% 0.90/1.10 ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp16 | c1_1(a2552) | c0_1(a2526) | (~ndr1_0) | (~c3_1(a2526)) | (~c1_1(a2526)) | (~c0_1(a2552)) | (~c2_1(a2552))),
% 0.90/1.10 inference(modus_ponens,[status(thm)],[1173, 1172])).
% 0.90/1.10 tff(1175,plain,
% 0.90/1.10 (hskp16 | (~c0_1(a2552))),
% 0.90/1.10 inference(unit_resolution,[status(thm)],[1174, 90, 822, 215, 216, 824, 152, 974])).
% 0.90/1.10 tff(1176,plain,
% 0.90/1.10 (hskp16),
% 0.90/1.10 inference(unit_resolution,[status(thm)],[1175, 1168])).
% 0.90/1.10 tff(1177,plain,
% 0.90/1.10 (~c3_1(a2540)),
% 0.90/1.10 inference(unit_resolution,[status(thm)],[1007, 1176])).
% 0.90/1.10 tff(1178,plain,
% 0.90/1.10 (~c2_1(a2540)),
% 0.90/1.10 inference(unit_resolution,[status(thm)],[986, 1176])).
% 0.90/1.10 tff(1179,plain,
% 0.90/1.10 (c0_1(a2540)),
% 0.90/1.10 inference(unit_resolution,[status(thm)],[994, 1176])).
% 0.90/1.10 tff(1180,plain,
% 0.90/1.10 (^[V: $i, U: $i] : refl((hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V))) <=> (hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V))))),
% 0.90/1.10 inference(bind,[status(th)],[])).
% 0.90/1.10 tff(1181,plain,
% 0.90/1.10 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))),
% 0.90/1.10 inference(quant_intro,[status(thm)],[1180])).
% 0.90/1.10 tff(1182,plain,
% 0.90/1.10 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))),
% 0.90/1.10 inference(rewrite,[status(thm)],[])).
% 0.90/1.10 tff(1183,plain,
% 0.90/1.10 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) <=> ((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c2_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V))) | c3_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(V)) | c3_1(V)) | hskp10) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V))) | hskp10))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V))) | hskp10) <=> (hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(V)) | c3_1(V)) | hskp10) <=> (hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))))),
% 0.90/1.11 inference(bind,[status(th)],[])).
% 0.90/1.11 tff(1184,plain,
% 0.90/1.11 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(V)) | c3_1(V)) | hskp10) <=> ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))),
% 0.90/1.11 inference(quant_intro,[status(thm)],[1183])).
% 0.90/1.11 tff(1185,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(V)) | c3_1(V)) | hskp10)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause189')).
% 0.90/1.11 tff(1186,plain,
% 0.90/1.11 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))),
% 0.90/1.11 inference(modus_ponens,[status(thm)],[1185, 1184])).
% 0.90/1.11 tff(1187,plain,
% 0.90/1.11 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))),
% 0.90/1.11 inference(modus_ponens,[status(thm)],[1186, 1182])).
% 0.90/1.11 tff(1188,plain,(
% 0.90/1.11 ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))),
% 0.90/1.11 inference(skolemize,[status(sab)],[1187])).
% 0.90/1.11 tff(1189,plain,
% 0.90/1.11 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))),
% 0.90/1.11 inference(modus_ponens,[status(thm)],[1188, 1181])).
% 0.90/1.11 tff(1190,assumption,(~c3_1(a2540)), introduced(assumption)).
% 0.90/1.11 tff(1191,assumption,(~c2_1(a2540)), introduced(assumption)).
% 0.90/1.11 tff(1192,assumption,(c0_1(a2540)), introduced(assumption)).
% 0.90/1.11 tff(1193,plain,
% 0.90/1.11 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp10 | c2_1(a2540) | c3_1(a2540) | (~ndr1_0) | (~c0_1(a2540)) | (~c3_1(a2551)) | (~c0_1(a2551)) | (~c1_1(a2551)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | hskp10 | c2_1(a2540) | c3_1(a2540) | (~ndr1_0) | (~c0_1(a2540)) | (~c3_1(a2551)) | (~c0_1(a2551)) | (~c1_1(a2551)))),
% 0.90/1.11 inference(rewrite,[status(thm)],[])).
% 0.90/1.11 tff(1194,plain,
% 0.90/1.11 ((hskp10 | (~ndr1_0) | (~c3_1(a2551)) | (~c1_1(a2551)) | (~c0_1(a2551)) | c3_1(a2540) | c2_1(a2540) | (~c0_1(a2540))) <=> (hskp10 | c2_1(a2540) | c3_1(a2540) | (~ndr1_0) | (~c0_1(a2540)) | (~c3_1(a2551)) | (~c0_1(a2551)) | (~c1_1(a2551)))),
% 0.90/1.11 inference(rewrite,[status(thm)],[])).
% 0.90/1.11 tff(1195,plain,
% 0.90/1.11 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp10 | (~ndr1_0) | (~c3_1(a2551)) | (~c1_1(a2551)) | (~c0_1(a2551)) | c3_1(a2540) | c2_1(a2540) | (~c0_1(a2540)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp10 | c2_1(a2540) | c3_1(a2540) | (~ndr1_0) | (~c0_1(a2540)) | (~c3_1(a2551)) | (~c0_1(a2551)) | (~c1_1(a2551))))),
% 0.90/1.11 inference(monotonicity,[status(thm)],[1194])).
% 0.90/1.11 tff(1196,plain,
% 0.90/1.11 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp10 | (~ndr1_0) | (~c3_1(a2551)) | (~c1_1(a2551)) | (~c0_1(a2551)) | c3_1(a2540) | c2_1(a2540) | (~c0_1(a2540)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | hskp10 | c2_1(a2540) | c3_1(a2540) | (~ndr1_0) | (~c0_1(a2540)) | (~c3_1(a2551)) | (~c0_1(a2551)) | (~c1_1(a2551)))),
% 0.90/1.11 inference(transitivity,[status(thm)],[1195, 1193])).
% 0.90/1.11 tff(1197,plain,
% 0.90/1.11 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp10 | (~ndr1_0) | (~c3_1(a2551)) | (~c1_1(a2551)) | (~c0_1(a2551)) | c3_1(a2540) | c2_1(a2540) | (~c0_1(a2540)))),
% 0.90/1.11 inference(quant_inst,[status(thm)],[])).
% 0.90/1.11 tff(1198,plain,
% 0.90/1.11 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | hskp10 | c2_1(a2540) | c3_1(a2540) | (~ndr1_0) | (~c0_1(a2540)) | (~c3_1(a2551)) | (~c0_1(a2551)) | (~c1_1(a2551))),
% 0.90/1.11 inference(modus_ponens,[status(thm)],[1197, 1196])).
% 0.90/1.11 tff(1199,plain,
% 0.90/1.11 ($false),
% 0.90/1.11 inference(unit_resolution,[status(thm)],[1198, 90, 1096, 472, 471, 1192, 1191, 1190, 1189, 1123])).
% 0.90/1.11 tff(1200,plain,(hskp10 | (~c0_1(a2551)) | (~c1_1(a2551)) | (~c0_1(a2540)) | c2_1(a2540) | c3_1(a2540) | hskp29), inference(lemma,lemma(discharge,[]))).
% 0.90/1.11 tff(1201,plain,
% 0.90/1.11 (hskp10),
% 0.90/1.11 inference(unit_resolution,[status(thm)],[1200, 1179, 471, 472, 1178, 1177, 404])).
% 0.90/1.11 tff(1202,plain,
% 0.90/1.11 (~c1_1(a2528)),
% 0.90/1.11 inference(unit_resolution,[status(thm)],[1158, 1201])).
% 0.90/1.11 tff(1203,plain,
% 0.90/1.11 (~c0_1(a2528)),
% 0.90/1.11 inference(unit_resolution,[status(thm)],[1137, 1201])).
% 0.90/1.11 tff(1204,plain,
% 0.90/1.11 (c3_1(a2528)),
% 0.90/1.11 inference(unit_resolution,[status(thm)],[1145, 1201])).
% 0.90/1.11 tff(1205,plain,
% 0.90/1.11 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c3_1(a2552) | c0_1(a2528) | c1_1(a2528) | (~ndr1_0) | (~c3_1(a2528)) | (~c2_1(a2528)) | (~c0_1(a2552)) | (~c2_1(a2552)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c3_1(a2552) | c0_1(a2528) | c1_1(a2528) | (~ndr1_0) | (~c3_1(a2528)) | (~c2_1(a2528)) | (~c0_1(a2552)) | (~c2_1(a2552)))),
% 0.90/1.11 inference(rewrite,[status(thm)],[])).
% 0.90/1.11 tff(1206,plain,
% 0.90/1.11 (((~ndr1_0) | c3_1(a2552) | (~c0_1(a2552)) | (~c2_1(a2552)) | c0_1(a2528) | (~c3_1(a2528)) | (~c2_1(a2528)) | c1_1(a2528) | c0_1(a2528) | (~c2_1(a2528))) <=> (c3_1(a2552) | c0_1(a2528) | c1_1(a2528) | (~ndr1_0) | (~c3_1(a2528)) | (~c2_1(a2528)) | (~c0_1(a2552)) | (~c2_1(a2552)))),
% 0.90/1.11 inference(rewrite,[status(thm)],[])).
% 0.90/1.11 tff(1207,plain,
% 0.90/1.11 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a2552) | (~c0_1(a2552)) | (~c2_1(a2552)) | c0_1(a2528) | (~c3_1(a2528)) | (~c2_1(a2528)) | c1_1(a2528) | c0_1(a2528) | (~c2_1(a2528)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c3_1(a2552) | c0_1(a2528) | c1_1(a2528) | (~ndr1_0) | (~c3_1(a2528)) | (~c2_1(a2528)) | (~c0_1(a2552)) | (~c2_1(a2552))))),
% 0.90/1.11 inference(monotonicity,[status(thm)],[1206])).
% 0.90/1.11 tff(1208,plain,
% 0.90/1.11 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a2552) | (~c0_1(a2552)) | (~c2_1(a2552)) | c0_1(a2528) | (~c3_1(a2528)) | (~c2_1(a2528)) | c1_1(a2528) | c0_1(a2528) | (~c2_1(a2528)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c3_1(a2552) | c0_1(a2528) | c1_1(a2528) | (~ndr1_0) | (~c3_1(a2528)) | (~c2_1(a2528)) | (~c0_1(a2552)) | (~c2_1(a2552)))),
% 0.90/1.11 inference(transitivity,[status(thm)],[1207, 1205])).
% 0.90/1.11 tff(1209,plain,
% 0.90/1.11 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a2552) | (~c0_1(a2552)) | (~c2_1(a2552)) | c0_1(a2528) | (~c3_1(a2528)) | (~c2_1(a2528)) | c1_1(a2528) | c0_1(a2528) | (~c2_1(a2528)))),
% 0.90/1.11 inference(quant_inst,[status(thm)],[])).
% 0.90/1.11 tff(1210,plain,
% 0.90/1.11 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c3_1(a2552) | c0_1(a2528) | c1_1(a2528) | (~ndr1_0) | (~c3_1(a2528)) | (~c2_1(a2528)) | (~c0_1(a2552)) | (~c2_1(a2552))),
% 0.90/1.11 inference(modus_ponens,[status(thm)],[1209, 1208])).
% 0.90/1.11 tff(1211,plain,
% 0.90/1.11 (~c2_1(a2528)),
% 0.90/1.11 inference(unit_resolution,[status(thm)],[1210, 90, 822, 1204, 823, 1203, 1202, 1087, 1168])).
% 0.90/1.11 tff(1212,assumption,(c0_1(a2552)), introduced(assumption)).
% 0.90/1.11 tff(1213,assumption,(~hskp18), introduced(assumption)).
% 0.90/1.11 tff(1214,plain,
% 0.90/1.11 (^[U: $i] : refl((hskp18 | hskp10 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U))) <=> (hskp18 | hskp10 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U))))),
% 0.90/1.11 inference(bind,[status(th)],[])).
% 0.90/1.11 tff(1215,plain,
% 0.90/1.11 (![U: $i] : (hskp18 | hskp10 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U))) <=> ![U: $i] : (hskp18 | hskp10 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 0.90/1.11 inference(quant_intro,[status(thm)],[1214])).
% 0.90/1.11 tff(1216,plain,
% 0.90/1.11 (![U: $i] : (hskp18 | hskp10 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U))) <=> ![U: $i] : (hskp18 | hskp10 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 0.90/1.11 inference(rewrite,[status(thm)],[])).
% 0.90/1.11 tff(1217,plain,
% 0.90/1.11 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U))))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp18) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U))) | hskp18))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U))) | hskp18) <=> (hskp18 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp18) <=> (hskp18 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U))))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp18) | hskp10) <=> ((hskp18 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U))) | hskp10))), rewrite(((hskp18 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U))) | hskp10) <=> (hskp18 | hskp10 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp18) | hskp10) <=> (hskp18 | hskp10 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))))),
% 0.90/1.11 inference(bind,[status(th)],[])).
% 0.90/1.11 tff(1218,plain,
% 0.90/1.11 (![U: $i] : ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp18) | hskp10) <=> ![U: $i] : (hskp18 | hskp10 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 0.90/1.11 inference(quant_intro,[status(thm)],[1217])).
% 0.90/1.11 tff(1219,axiom,(![U: $i] : ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp18) | hskp10)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause150')).
% 0.90/1.11 tff(1220,plain,
% 0.90/1.11 (![U: $i] : (hskp18 | hskp10 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 0.90/1.11 inference(modus_ponens,[status(thm)],[1219, 1218])).
% 0.90/1.11 tff(1221,plain,
% 0.90/1.11 (![U: $i] : (hskp18 | hskp10 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 0.90/1.11 inference(modus_ponens,[status(thm)],[1220, 1216])).
% 0.90/1.11 tff(1222,plain,(
% 0.90/1.11 ![U: $i] : (hskp18 | hskp10 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 0.90/1.11 inference(skolemize,[status(sab)],[1221])).
% 0.90/1.11 tff(1223,plain,
% 0.90/1.11 (![U: $i] : (hskp18 | hskp10 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 0.90/1.11 inference(modus_ponens,[status(thm)],[1222, 1215])).
% 0.90/1.11 tff(1224,plain,
% 0.90/1.11 (((~![U: $i] : (hskp18 | hskp10 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp18 | hskp10 | c0_1(a2526) | (~ndr1_0) | (~c3_1(a2526)) | (~c2_1(a2526)))) <=> ((~![U: $i] : (hskp18 | hskp10 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | hskp18 | hskp10 | c0_1(a2526) | (~ndr1_0) | (~c3_1(a2526)) | (~c2_1(a2526)))),
% 0.90/1.11 inference(rewrite,[status(thm)],[])).
% 0.90/1.11 tff(1225,plain,
% 0.90/1.11 ((hskp18 | hskp10 | (~ndr1_0) | c0_1(a2526) | (~c3_1(a2526)) | (~c2_1(a2526))) <=> (hskp18 | hskp10 | c0_1(a2526) | (~ndr1_0) | (~c3_1(a2526)) | (~c2_1(a2526)))),
% 0.90/1.11 inference(rewrite,[status(thm)],[])).
% 0.90/1.11 tff(1226,plain,
% 0.90/1.11 (((~![U: $i] : (hskp18 | hskp10 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp18 | hskp10 | (~ndr1_0) | c0_1(a2526) | (~c3_1(a2526)) | (~c2_1(a2526)))) <=> ((~![U: $i] : (hskp18 | hskp10 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp18 | hskp10 | c0_1(a2526) | (~ndr1_0) | (~c3_1(a2526)) | (~c2_1(a2526))))),
% 0.90/1.11 inference(monotonicity,[status(thm)],[1225])).
% 0.90/1.11 tff(1227,plain,
% 0.90/1.11 (((~![U: $i] : (hskp18 | hskp10 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp18 | hskp10 | (~ndr1_0) | c0_1(a2526) | (~c3_1(a2526)) | (~c2_1(a2526)))) <=> ((~![U: $i] : (hskp18 | hskp10 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | hskp18 | hskp10 | c0_1(a2526) | (~ndr1_0) | (~c3_1(a2526)) | (~c2_1(a2526)))),
% 0.90/1.11 inference(transitivity,[status(thm)],[1226, 1224])).
% 0.90/1.11 tff(1228,plain,
% 0.90/1.11 ((~![U: $i] : (hskp18 | hskp10 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp18 | hskp10 | (~ndr1_0) | c0_1(a2526) | (~c3_1(a2526)) | (~c2_1(a2526)))),
% 0.90/1.11 inference(quant_inst,[status(thm)],[])).
% 0.90/1.11 tff(1229,plain,
% 0.90/1.11 ((~![U: $i] : (hskp18 | hskp10 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | hskp18 | hskp10 | c0_1(a2526) | (~ndr1_0) | (~c3_1(a2526)) | (~c2_1(a2526))),
% 0.90/1.11 inference(modus_ponens,[status(thm)],[1228, 1227])).
% 0.90/1.11 tff(1230,plain,
% 0.90/1.11 (hskp18 | hskp10 | (~c2_1(a2526))),
% 0.90/1.11 inference(unit_resolution,[status(thm)],[1229, 90, 216, 152, 1223])).
% 0.90/1.11 tff(1231,plain,
% 0.90/1.11 (~c2_1(a2526)),
% 0.90/1.11 inference(unit_resolution,[status(thm)],[1230, 1096, 1213])).
% 0.90/1.11 tff(1232,plain,
% 0.90/1.11 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | (c1_1(a2552) | c0_1(a2526) | (~ndr1_0) | (~c3_1(a2526)) | c2_1(a2526) | (~c3_1(a2551)) | (~c0_1(a2551)) | (~c1_1(a2551)) | (~c0_1(a2552)) | (~c2_1(a2552)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a2552) | c0_1(a2526) | (~ndr1_0) | (~c3_1(a2526)) | c2_1(a2526) | (~c3_1(a2551)) | (~c0_1(a2551)) | (~c1_1(a2551)) | (~c0_1(a2552)) | (~c2_1(a2552)))),
% 0.90/1.11 inference(rewrite,[status(thm)],[])).
% 0.90/1.11 tff(1233,plain,
% 0.90/1.11 (((~ndr1_0) | (~c3_1(a2551)) | (~c1_1(a2551)) | (~c0_1(a2551)) | c1_1(a2552) | (~c0_1(a2552)) | (~c2_1(a2552)) | c0_1(a2526) | c2_1(a2526) | (~c3_1(a2526))) <=> (c1_1(a2552) | c0_1(a2526) | (~ndr1_0) | (~c3_1(a2526)) | c2_1(a2526) | (~c3_1(a2551)) | (~c0_1(a2551)) | (~c1_1(a2551)) | (~c0_1(a2552)) | (~c2_1(a2552)))),
% 0.90/1.11 inference(rewrite,[status(thm)],[])).
% 0.90/1.11 tff(1234,plain,
% 0.90/1.11 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a2551)) | (~c1_1(a2551)) | (~c0_1(a2551)) | c1_1(a2552) | (~c0_1(a2552)) | (~c2_1(a2552)) | c0_1(a2526) | c2_1(a2526) | (~c3_1(a2526)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | (c1_1(a2552) | c0_1(a2526) | (~ndr1_0) | (~c3_1(a2526)) | c2_1(a2526) | (~c3_1(a2551)) | (~c0_1(a2551)) | (~c1_1(a2551)) | (~c0_1(a2552)) | (~c2_1(a2552))))),
% 0.90/1.11 inference(monotonicity,[status(thm)],[1233])).
% 0.90/1.11 tff(1235,plain,
% 0.90/1.11 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a2551)) | (~c1_1(a2551)) | (~c0_1(a2551)) | c1_1(a2552) | (~c0_1(a2552)) | (~c2_1(a2552)) | c0_1(a2526) | c2_1(a2526) | (~c3_1(a2526)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a2552) | c0_1(a2526) | (~ndr1_0) | (~c3_1(a2526)) | c2_1(a2526) | (~c3_1(a2551)) | (~c0_1(a2551)) | (~c1_1(a2551)) | (~c0_1(a2552)) | (~c2_1(a2552)))),
% 0.90/1.11 inference(transitivity,[status(thm)],[1234, 1232])).
% 0.90/1.11 tff(1236,plain,
% 0.90/1.11 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a2551)) | (~c1_1(a2551)) | (~c0_1(a2551)) | c1_1(a2552) | (~c0_1(a2552)) | (~c2_1(a2552)) | c0_1(a2526) | c2_1(a2526) | (~c3_1(a2526)))),
% 0.90/1.11 inference(quant_inst,[status(thm)],[])).
% 0.90/1.11 tff(1237,plain,
% 0.90/1.11 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a2552) | c0_1(a2526) | (~ndr1_0) | (~c3_1(a2526)) | c2_1(a2526) | (~c3_1(a2551)) | (~c0_1(a2551)) | (~c1_1(a2551)) | (~c0_1(a2552)) | (~c2_1(a2552))),
% 0.90/1.11 inference(modus_ponens,[status(thm)],[1236, 1235])).
% 0.90/1.11 tff(1238,plain,
% 0.90/1.11 ($false),
% 0.90/1.11 inference(unit_resolution,[status(thm)],[1237, 90, 822, 472, 471, 216, 824, 152, 709, 1123, 1231, 1212])).
% 0.90/1.11 tff(1239,plain,(hskp10 | (~c2_1(a2552)) | (~c0_1(a2551)) | (~c1_1(a2551)) | (~c3_1(a2526)) | c1_1(a2552) | c0_1(a2526) | (~c0_1(a2552)) | hskp18 | hskp29), inference(lemma,lemma(discharge,[]))).
% 0.90/1.11 tff(1240,plain,
% 0.90/1.11 (hskp10),
% 0.90/1.11 inference(unit_resolution,[status(thm)],[1239, 1212, 472, 471, 216, 824, 152, 822, 1213, 404])).
% 0.90/1.11 tff(1241,plain,
% 0.90/1.11 (~c1_1(a2528)),
% 0.90/1.11 inference(unit_resolution,[status(thm)],[1158, 1240])).
% 0.90/1.11 tff(1242,plain,
% 0.90/1.11 (~c0_1(a2528)),
% 0.90/1.11 inference(unit_resolution,[status(thm)],[1137, 1240])).
% 0.90/1.11 tff(1243,plain,
% 0.90/1.11 (c3_1(a2528)),
% 0.90/1.11 inference(unit_resolution,[status(thm)],[1145, 1240])).
% 0.90/1.11 tff(1244,plain,
% 0.90/1.11 (~c2_1(a2528)),
% 0.90/1.11 inference(unit_resolution,[status(thm)],[1210, 90, 822, 1243, 823, 1242, 1241, 1087, 1212])).
% 0.90/1.11 tff(1245,plain,
% 0.90/1.11 ($false),
% 0.90/1.11 inference(unit_resolution,[status(thm)],[1165, 90, 851, 1243, 948, 850, 849, 1241, 945, 636, 934, 1244])).
% 0.90/1.11 tff(1246,plain,((~c0_1(a2552)) | (~c0_1(a2553)) | (~c1_1(a2518)) | c1_1(a2553) | c3_1(a2553) | c0_1(a2518) | (~c2_1(a2518)) | (~c2_1(a2552)) | c3_1(a2552) | (~c0_1(a2551)) | (~c1_1(a2551)) | (~c3_1(a2526)) | c1_1(a2552) | c0_1(a2526) | hskp18 | hskp29), inference(lemma,lemma(discharge,[]))).
% 0.90/1.11 tff(1247,plain,
% 0.90/1.11 (hskp18),
% 0.90/1.11 inference(unit_resolution,[status(thm)],[1246, 1168, 948, 850, 849, 945, 934, 822, 823, 472, 471, 216, 824, 152, 851, 404])).
% 0.90/1.11 tff(1248,plain,
% 0.90/1.11 (~c0_1(a2545)),
% 0.90/1.11 inference(unit_resolution,[status(thm)],[584, 1247])).
% 0.90/1.11 tff(1249,plain,
% 0.90/1.11 (c2_1(a2545)),
% 0.90/1.11 inference(unit_resolution,[status(thm)],[592, 1247])).
% 0.90/1.11 tff(1250,plain,
% 0.90/1.11 (c1_1(a2545)),
% 0.90/1.11 inference(unit_resolution,[status(thm)],[600, 1247])).
% 0.90/1.11 tff(1251,plain,
% 0.90/1.11 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c1_1(a2553) | c3_1(a2553) | c0_1(a2545) | c1_1(a2528) | (~ndr1_0) | (~c3_1(a2528)) | c2_1(a2528) | (~c2_1(a2545)) | (~c1_1(a2545)) | (~c0_1(a2553)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c1_1(a2553) | c3_1(a2553) | c0_1(a2545) | c1_1(a2528) | (~ndr1_0) | (~c3_1(a2528)) | c2_1(a2528) | (~c2_1(a2545)) | (~c1_1(a2545)) | (~c0_1(a2553)))),
% 0.90/1.11 inference(rewrite,[status(thm)],[])).
% 0.90/1.11 tff(1252,plain,
% 0.90/1.11 (((~ndr1_0) | c3_1(a2553) | c1_1(a2553) | (~c0_1(a2553)) | c1_1(a2528) | c2_1(a2528) | (~c3_1(a2528)) | c0_1(a2545) | (~c2_1(a2545)) | (~c1_1(a2545))) <=> (c1_1(a2553) | c3_1(a2553) | c0_1(a2545) | c1_1(a2528) | (~ndr1_0) | (~c3_1(a2528)) | c2_1(a2528) | (~c2_1(a2545)) | (~c1_1(a2545)) | (~c0_1(a2553)))),
% 0.90/1.11 inference(rewrite,[status(thm)],[])).
% 0.90/1.11 tff(1253,plain,
% 0.90/1.11 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a2553) | c1_1(a2553) | (~c0_1(a2553)) | c1_1(a2528) | c2_1(a2528) | (~c3_1(a2528)) | c0_1(a2545) | (~c2_1(a2545)) | (~c1_1(a2545)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c1_1(a2553) | c3_1(a2553) | c0_1(a2545) | c1_1(a2528) | (~ndr1_0) | (~c3_1(a2528)) | c2_1(a2528) | (~c2_1(a2545)) | (~c1_1(a2545)) | (~c0_1(a2553))))),
% 0.90/1.11 inference(monotonicity,[status(thm)],[1252])).
% 0.90/1.11 tff(1254,plain,
% 0.90/1.11 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a2553) | c1_1(a2553) | (~c0_1(a2553)) | c1_1(a2528) | c2_1(a2528) | (~c3_1(a2528)) | c0_1(a2545) | (~c2_1(a2545)) | (~c1_1(a2545)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c1_1(a2553) | c3_1(a2553) | c0_1(a2545) | c1_1(a2528) | (~ndr1_0) | (~c3_1(a2528)) | c2_1(a2528) | (~c2_1(a2545)) | (~c1_1(a2545)) | (~c0_1(a2553)))),
% 0.90/1.11 inference(transitivity,[status(thm)],[1253, 1251])).
% 0.90/1.11 tff(1255,plain,
% 0.90/1.11 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a2553) | c1_1(a2553) | (~c0_1(a2553)) | c1_1(a2528) | c2_1(a2528) | (~c3_1(a2528)) | c0_1(a2545) | (~c2_1(a2545)) | (~c1_1(a2545)))),
% 0.90/1.11 inference(quant_inst,[status(thm)],[])).
% 0.90/1.11 tff(1256,plain,
% 0.90/1.11 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c1_1(a2553) | c3_1(a2553) | c0_1(a2545) | c1_1(a2528) | (~ndr1_0) | (~c3_1(a2528)) | c2_1(a2528) | (~c2_1(a2545)) | (~c1_1(a2545)) | (~c0_1(a2553))),
% 0.90/1.11 inference(modus_ponens,[status(thm)],[1255, 1254])).
% 0.90/1.11 tff(1257,plain,
% 0.90/1.11 ($false),
% 0.90/1.11 inference(unit_resolution,[status(thm)],[1256, 90, 851, 1250, 1249, 1204, 850, 849, 1248, 1202, 636, 1211])).
% 0.90/1.11 tff(1258,plain,(hskp29 | (~c0_1(a2553)) | c1_1(a2553) | c3_1(a2553) | (~c2_1(a2552)) | c3_1(a2552) | (~c1_1(a2551)) | (~c0_1(a2551)) | (~c1_1(a2518)) | c0_1(a2518) | (~c2_1(a2518)) | (~c3_1(a2526)) | c1_1(a2552) | c0_1(a2526) | (~c1_1(a2526)) | (~c0_1(a2525)) | (~c2_1(a2525)) | c3_1(a2525)), inference(lemma,lemma(discharge,[]))).
% 0.90/1.11 tff(1259,plain,
% 0.90/1.11 (hskp29),
% 0.90/1.11 inference(unit_resolution,[status(thm)],[1258, 907, 827, 826, 822, 823, 471, 472, 828, 899, 914, 216, 824, 152, 215, 1073, 1072, 1064])).
% 0.90/1.11 tff(1260,plain,
% 0.90/1.11 (c2_1(a2556)),
% 0.90/1.11 inference(unit_resolution,[status(thm)],[347, 1259])).
% 0.90/1.11 tff(1261,plain,
% 0.90/1.11 (c1_1(a2556)),
% 0.90/1.11 inference(unit_resolution,[status(thm)],[355, 1259])).
% 0.90/1.11 tff(1262,plain,
% 0.90/1.11 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a2536) | c1_1(a2536) | c3_1(a2536) | c0_1(a2518) | c3_1(a2518) | (~ndr1_0) | (~c1_1(a2518)) | (~c2_1(a2556)) | (~c1_1(a2556)) | (~c0_1(a2556)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a2536) | c1_1(a2536) | c3_1(a2536) | c0_1(a2518) | c3_1(a2518) | (~ndr1_0) | (~c1_1(a2518)) | (~c2_1(a2556)) | (~c1_1(a2556)) | (~c0_1(a2556)))),
% 0.90/1.11 inference(rewrite,[status(thm)],[])).
% 0.90/1.11 tff(1263,plain,
% 0.90/1.11 (((~ndr1_0) | (~c1_1(a2556)) | (~c0_1(a2556)) | (~c2_1(a2556)) | c3_1(a2518) | c0_1(a2518) | (~c1_1(a2518)) | c3_1(a2536) | c1_1(a2536) | c0_1(a2536)) <=> (c0_1(a2536) | c1_1(a2536) | c3_1(a2536) | c0_1(a2518) | c3_1(a2518) | (~ndr1_0) | (~c1_1(a2518)) | (~c2_1(a2556)) | (~c1_1(a2556)) | (~c0_1(a2556)))),
% 0.90/1.11 inference(rewrite,[status(thm)],[])).
% 0.90/1.11 tff(1264,plain,
% 0.90/1.11 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c1_1(a2556)) | (~c0_1(a2556)) | (~c2_1(a2556)) | c3_1(a2518) | c0_1(a2518) | (~c1_1(a2518)) | c3_1(a2536) | c1_1(a2536) | c0_1(a2536))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a2536) | c1_1(a2536) | c3_1(a2536) | c0_1(a2518) | c3_1(a2518) | (~ndr1_0) | (~c1_1(a2518)) | (~c2_1(a2556)) | (~c1_1(a2556)) | (~c0_1(a2556))))),
% 0.90/1.11 inference(monotonicity,[status(thm)],[1263])).
% 0.90/1.11 tff(1265,plain,
% 0.90/1.11 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c1_1(a2556)) | (~c0_1(a2556)) | (~c2_1(a2556)) | c3_1(a2518) | c0_1(a2518) | (~c1_1(a2518)) | c3_1(a2536) | c1_1(a2536) | c0_1(a2536))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a2536) | c1_1(a2536) | c3_1(a2536) | c0_1(a2518) | c3_1(a2518) | (~ndr1_0) | (~c1_1(a2518)) | (~c2_1(a2556)) | (~c1_1(a2556)) | (~c0_1(a2556)))),
% 0.90/1.11 inference(transitivity,[status(thm)],[1264, 1262])).
% 0.90/1.11 tff(1266,plain,
% 0.90/1.11 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c1_1(a2556)) | (~c0_1(a2556)) | (~c2_1(a2556)) | c3_1(a2518) | c0_1(a2518) | (~c1_1(a2518)) | c3_1(a2536) | c1_1(a2536) | c0_1(a2536))),
% 0.90/1.11 inference(quant_inst,[status(thm)],[])).
% 0.90/1.11 tff(1267,plain,
% 0.90/1.11 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a2536) | c1_1(a2536) | c3_1(a2536) | c0_1(a2518) | c3_1(a2518) | (~ndr1_0) | (~c1_1(a2518)) | (~c2_1(a2556)) | (~c1_1(a2556)) | (~c0_1(a2556))),
% 0.90/1.11 inference(modus_ponens,[status(thm)],[1266, 1265])).
% 0.90/1.11 tff(1268,plain,
% 0.90/1.11 (~c0_1(a2556)),
% 0.90/1.11 inference(unit_resolution,[status(thm)],[1267, 90, 1261, 1260, 907, 924, 923, 922, 899, 893, 459])).
% 0.90/1.11 tff(1269,plain,
% 0.90/1.11 (c3_1(a2556)),
% 0.90/1.11 inference(unit_resolution,[status(thm)],[339, 1259])).
% 0.90/1.11 tff(1270,plain,
% 0.90/1.11 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a2552) | c3_1(a2525) | (~ndr1_0) | (~c2_1(a2556)) | (~c3_1(a2556)) | c0_1(a2556) | (~c0_1(a2525)) | (~c2_1(a2525)) | c0_1(a2552) | (~c2_1(a2552)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a2552) | c3_1(a2525) | (~ndr1_0) | (~c2_1(a2556)) | (~c3_1(a2556)) | c0_1(a2556) | (~c0_1(a2525)) | (~c2_1(a2525)) | c0_1(a2552) | (~c2_1(a2552)))),
% 0.90/1.11 inference(rewrite,[status(thm)],[])).
% 0.90/1.11 tff(1271,plain,
% 0.90/1.11 (((~ndr1_0) | c3_1(a2525) | (~c0_1(a2525)) | (~c2_1(a2525)) | c0_1(a2556) | (~c3_1(a2556)) | (~c2_1(a2556)) | c1_1(a2552) | c0_1(a2552) | (~c2_1(a2552))) <=> (c1_1(a2552) | c3_1(a2525) | (~ndr1_0) | (~c2_1(a2556)) | (~c3_1(a2556)) | c0_1(a2556) | (~c0_1(a2525)) | (~c2_1(a2525)) | c0_1(a2552) | (~c2_1(a2552)))),
% 0.90/1.11 inference(rewrite,[status(thm)],[])).
% 0.90/1.11 tff(1272,plain,
% 0.90/1.11 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a2525) | (~c0_1(a2525)) | (~c2_1(a2525)) | c0_1(a2556) | (~c3_1(a2556)) | (~c2_1(a2556)) | c1_1(a2552) | c0_1(a2552) | (~c2_1(a2552)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a2552) | c3_1(a2525) | (~ndr1_0) | (~c2_1(a2556)) | (~c3_1(a2556)) | c0_1(a2556) | (~c0_1(a2525)) | (~c2_1(a2525)) | c0_1(a2552) | (~c2_1(a2552))))),
% 0.90/1.11 inference(monotonicity,[status(thm)],[1271])).
% 0.90/1.11 tff(1273,plain,
% 0.90/1.11 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a2525) | (~c0_1(a2525)) | (~c2_1(a2525)) | c0_1(a2556) | (~c3_1(a2556)) | (~c2_1(a2556)) | c1_1(a2552) | c0_1(a2552) | (~c2_1(a2552)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a2552) | c3_1(a2525) | (~ndr1_0) | (~c2_1(a2556)) | (~c3_1(a2556)) | c0_1(a2556) | (~c0_1(a2525)) | (~c2_1(a2525)) | c0_1(a2552) | (~c2_1(a2552)))),
% 0.90/1.11 inference(transitivity,[status(thm)],[1272, 1270])).
% 0.90/1.11 tff(1274,plain,
% 0.90/1.11 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a2525) | (~c0_1(a2525)) | (~c2_1(a2525)) | c0_1(a2556) | (~c3_1(a2556)) | (~c2_1(a2556)) | c1_1(a2552) | c0_1(a2552) | (~c2_1(a2552)))),
% 0.90/1.11 inference(quant_inst,[status(thm)],[])).
% 0.90/1.11 tff(1275,plain,
% 0.90/1.11 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a2552) | c3_1(a2525) | (~ndr1_0) | (~c2_1(a2556)) | (~c3_1(a2556)) | c0_1(a2556) | (~c0_1(a2525)) | (~c2_1(a2525)) | c0_1(a2552) | (~c2_1(a2552))),
% 0.90/1.11 inference(modus_ponens,[status(thm)],[1274, 1273])).
% 0.90/1.12 tff(1276,plain,
% 0.90/1.12 (c0_1(a2552)),
% 0.90/1.12 inference(unit_resolution,[status(thm)],[1275, 90, 1260, 1269, 822, 1073, 1072, 824, 1064, 1087, 1268])).
% 0.90/1.12 tff(1277,assumption,(~c3_1(a2518)), introduced(assumption)).
% 0.90/1.12 tff(1278,assumption,(hskp19), introduced(assumption)).
% 0.90/1.12 tff(1279,plain,
% 0.90/1.12 (((~hskp19) | (~c1_1(a2548))) <=> ((~hskp19) | (~c1_1(a2548)))),
% 0.90/1.12 inference(rewrite,[status(thm)],[])).
% 0.90/1.12 tff(1280,plain,
% 0.90/1.12 (((~c1_1(a2548)) | (~hskp19)) <=> ((~hskp19) | (~c1_1(a2548)))),
% 0.90/1.12 inference(rewrite,[status(thm)],[])).
% 0.90/1.12 tff(1281,axiom,((~c1_1(a2548)) | (~hskp19)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause102')).
% 0.90/1.12 tff(1282,plain,
% 0.90/1.12 ((~hskp19) | (~c1_1(a2548))),
% 0.90/1.12 inference(modus_ponens,[status(thm)],[1281, 1280])).
% 0.90/1.12 tff(1283,plain,
% 0.90/1.12 ((~hskp19) | (~c1_1(a2548))),
% 0.90/1.12 inference(modus_ponens,[status(thm)],[1282, 1279])).
% 0.90/1.12 tff(1284,plain,
% 0.90/1.12 (~c1_1(a2548)),
% 0.90/1.12 inference(unit_resolution,[status(thm)],[1283, 1278])).
% 0.90/1.12 tff(1285,plain,
% 0.90/1.12 (((~hskp19) | c3_1(a2548)) <=> ((~hskp19) | c3_1(a2548))),
% 0.90/1.12 inference(rewrite,[status(thm)],[])).
% 0.90/1.12 tff(1286,axiom,((~hskp19) | c3_1(a2548)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause65')).
% 0.90/1.12 tff(1287,plain,
% 0.90/1.12 ((~hskp19) | c3_1(a2548)),
% 0.90/1.12 inference(modus_ponens,[status(thm)],[1286, 1285])).
% 0.90/1.12 tff(1288,plain,
% 0.90/1.12 ((~hskp19) | c3_1(a2548)),
% 0.90/1.12 inference(modus_ponens,[status(thm)],[1287, 1285])).
% 0.90/1.12 tff(1289,plain,
% 0.90/1.12 ((~hskp19) | c3_1(a2548)),
% 0.90/1.12 inference(modus_ponens,[status(thm)],[1288, 1285])).
% 0.90/1.12 tff(1290,plain,
% 0.90/1.12 ((~hskp19) | c3_1(a2548)),
% 0.90/1.12 inference(modus_ponens,[status(thm)],[1289, 1285])).
% 0.90/1.12 tff(1291,plain,
% 0.90/1.12 ((~hskp19) | c3_1(a2548)),
% 0.90/1.12 inference(modus_ponens,[status(thm)],[1290, 1285])).
% 0.90/1.12 tff(1292,plain,
% 0.90/1.12 (c3_1(a2548)),
% 0.90/1.12 inference(unit_resolution,[status(thm)],[1291, 1278])).
% 0.90/1.12 tff(1293,plain,
% 0.90/1.12 (((~hskp19) | c0_1(a2548)) <=> ((~hskp19) | c0_1(a2548))),
% 0.90/1.12 inference(rewrite,[status(thm)],[])).
% 0.90/1.12 tff(1294,axiom,((~hskp19) | c0_1(a2548)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause64')).
% 0.90/1.12 tff(1295,plain,
% 0.90/1.12 ((~hskp19) | c0_1(a2548)),
% 0.90/1.12 inference(modus_ponens,[status(thm)],[1294, 1293])).
% 0.90/1.12 tff(1296,plain,
% 0.90/1.12 ((~hskp19) | c0_1(a2548)),
% 0.90/1.12 inference(modus_ponens,[status(thm)],[1295, 1293])).
% 0.90/1.12 tff(1297,plain,
% 0.90/1.12 ((~hskp19) | c0_1(a2548)),
% 0.90/1.12 inference(modus_ponens,[status(thm)],[1296, 1293])).
% 0.90/1.12 tff(1298,plain,
% 0.90/1.12 ((~hskp19) | c0_1(a2548)),
% 0.90/1.12 inference(modus_ponens,[status(thm)],[1297, 1293])).
% 0.90/1.12 tff(1299,plain,
% 0.90/1.12 ((~hskp19) | c0_1(a2548)),
% 0.90/1.12 inference(modus_ponens,[status(thm)],[1298, 1293])).
% 0.90/1.12 tff(1300,plain,
% 0.90/1.12 (c0_1(a2548)),
% 0.90/1.12 inference(unit_resolution,[status(thm)],[1299, 1278])).
% 0.90/1.12 tff(1301,plain,
% 0.90/1.12 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a2552) | c3_1(a2552) | c1_1(a2548) | c0_1(a2518) | c3_1(a2518) | (~ndr1_0) | (~c2_1(a2518)) | (~c3_1(a2548)) | (~c0_1(a2548)) | (~c2_1(a2552)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a2552) | c3_1(a2552) | c1_1(a2548) | c0_1(a2518) | c3_1(a2518) | (~ndr1_0) | (~c2_1(a2518)) | (~c3_1(a2548)) | (~c0_1(a2548)) | (~c2_1(a2552)))),
% 0.90/1.12 inference(rewrite,[status(thm)],[])).
% 0.90/1.12 tff(1302,plain,
% 0.90/1.12 (((~ndr1_0) | c1_1(a2548) | (~c3_1(a2548)) | (~c0_1(a2548)) | c3_1(a2552) | c1_1(a2552) | (~c2_1(a2552)) | c3_1(a2518) | c0_1(a2518) | (~c2_1(a2518))) <=> (c1_1(a2552) | c3_1(a2552) | c1_1(a2548) | c0_1(a2518) | c3_1(a2518) | (~ndr1_0) | (~c2_1(a2518)) | (~c3_1(a2548)) | (~c0_1(a2548)) | (~c2_1(a2552)))),
% 0.90/1.12 inference(rewrite,[status(thm)],[])).
% 0.90/1.12 tff(1303,plain,
% 0.90/1.12 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a2548) | (~c3_1(a2548)) | (~c0_1(a2548)) | c3_1(a2552) | c1_1(a2552) | (~c2_1(a2552)) | c3_1(a2518) | c0_1(a2518) | (~c2_1(a2518)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a2552) | c3_1(a2552) | c1_1(a2548) | c0_1(a2518) | c3_1(a2518) | (~ndr1_0) | (~c2_1(a2518)) | (~c3_1(a2548)) | (~c0_1(a2548)) | (~c2_1(a2552))))),
% 0.90/1.12 inference(monotonicity,[status(thm)],[1302])).
% 0.90/1.12 tff(1304,plain,
% 0.90/1.12 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a2548) | (~c3_1(a2548)) | (~c0_1(a2548)) | c3_1(a2552) | c1_1(a2552) | (~c2_1(a2552)) | c3_1(a2518) | c0_1(a2518) | (~c2_1(a2518)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a2552) | c3_1(a2552) | c1_1(a2548) | c0_1(a2518) | c3_1(a2518) | (~ndr1_0) | (~c2_1(a2518)) | (~c3_1(a2548)) | (~c0_1(a2548)) | (~c2_1(a2552)))),
% 0.90/1.12 inference(transitivity,[status(thm)],[1303, 1301])).
% 0.90/1.12 tff(1305,plain,
% 0.90/1.12 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a2548) | (~c3_1(a2548)) | (~c0_1(a2548)) | c3_1(a2552) | c1_1(a2552) | (~c2_1(a2552)) | c3_1(a2518) | c0_1(a2518) | (~c2_1(a2518)))),
% 0.90/1.12 inference(quant_inst,[status(thm)],[])).
% 0.90/1.12 tff(1306,plain,
% 0.90/1.12 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a2552) | c3_1(a2552) | c1_1(a2548) | c0_1(a2518) | c3_1(a2518) | (~ndr1_0) | (~c2_1(a2518)) | (~c3_1(a2548)) | (~c0_1(a2548)) | (~c2_1(a2552))),
% 0.90/1.12 inference(modus_ponens,[status(thm)],[1305, 1304])).
% 0.90/1.12 tff(1307,plain,
% 0.90/1.12 ($false),
% 0.90/1.12 inference(unit_resolution,[status(thm)],[1306, 90, 822, 1300, 1292, 824, 823, 1284, 945, 1277, 424, 934])).
% 0.90/1.12 tff(1308,plain,((~hskp19) | (~c2_1(a2552)) | c1_1(a2552) | c3_1(a2552) | c0_1(a2518) | c3_1(a2518) | (~c2_1(a2518))), inference(lemma,lemma(discharge,[]))).
% 0.90/1.12 tff(1309,plain,
% 0.90/1.12 (~hskp19),
% 0.90/1.12 inference(unit_resolution,[status(thm)],[1308, 899, 824, 823, 822, 893, 914])).
% 0.90/1.12 tff(1310,plain,
% 0.90/1.12 (^[U: $i] : refl((hskp20 | hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U)) <=> (hskp20 | hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U)))),
% 0.90/1.12 inference(bind,[status(th)],[])).
% 0.90/1.12 tff(1311,plain,
% 0.90/1.12 (![U: $i] : (hskp20 | hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U)) <=> ![U: $i] : (hskp20 | hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))),
% 0.90/1.12 inference(quant_intro,[status(thm)],[1310])).
% 0.90/1.12 tff(1312,plain,
% 0.90/1.12 (![U: $i] : (hskp20 | hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U)) <=> ![U: $i] : (hskp20 | hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))),
% 0.90/1.12 inference(rewrite,[status(thm)],[])).
% 0.90/1.12 tff(1313,plain,
% 0.90/1.12 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ndr1_0) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U))), ((((~ndr1_0) | c1_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c1_1(U)) | c2_1(U)))), rewrite((((~ndr1_0) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U))), ((((~ndr1_0) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U)))), (((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | c1_1(U)) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))), (((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U)))), ((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | hskp19) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U)) | hskp19))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U)) | hskp19) <=> (hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))), ((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | hskp19) <=> (hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U)))), (((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | hskp19) | hskp20) <=> ((hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U)) | hskp20))), rewrite(((hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U)) | hskp20) <=> (hskp20 | hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))), (((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | hskp19) | hskp20) <=> (hskp20 | hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))))),
% 0.90/1.12 inference(bind,[status(th)],[])).
% 0.90/1.12 tff(1314,plain,
% 0.90/1.12 (![U: $i] : ((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | hskp19) | hskp20) <=> ![U: $i] : (hskp20 | hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))),
% 0.90/1.12 inference(quant_intro,[status(thm)],[1313])).
% 0.90/1.12 tff(1315,axiom,(![U: $i] : ((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | hskp19) | hskp20)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause137')).
% 0.90/1.12 tff(1316,plain,
% 0.90/1.12 (![U: $i] : (hskp20 | hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))),
% 0.90/1.12 inference(modus_ponens,[status(thm)],[1315, 1314])).
% 0.90/1.12 tff(1317,plain,
% 0.90/1.12 (![U: $i] : (hskp20 | hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))),
% 0.90/1.12 inference(modus_ponens,[status(thm)],[1316, 1312])).
% 0.90/1.12 tff(1318,plain,(
% 0.90/1.12 ![U: $i] : (hskp20 | hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))),
% 0.90/1.12 inference(skolemize,[status(sab)],[1317])).
% 0.90/1.12 tff(1319,plain,
% 0.90/1.12 (![U: $i] : (hskp20 | hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))),
% 0.90/1.12 inference(modus_ponens,[status(thm)],[1318, 1311])).
% 0.90/1.12 tff(1320,plain,
% 0.90/1.12 (((~![U: $i] : (hskp20 | hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | (hskp20 | hskp19 | c3_1(a2541) | c1_1(a2541) | c2_1(a2541) | (~ndr1_0))) <=> ((~![U: $i] : (hskp20 | hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | hskp20 | hskp19 | c3_1(a2541) | c1_1(a2541) | c2_1(a2541) | (~ndr1_0))),
% 0.90/1.12 inference(rewrite,[status(thm)],[])).
% 0.90/1.12 tff(1321,plain,
% 0.90/1.12 ((hskp20 | hskp19 | (~ndr1_0) | c3_1(a2541) | c2_1(a2541) | c1_1(a2541)) <=> (hskp20 | hskp19 | c3_1(a2541) | c1_1(a2541) | c2_1(a2541) | (~ndr1_0))),
% 0.90/1.12 inference(rewrite,[status(thm)],[])).
% 0.90/1.12 tff(1322,plain,
% 0.90/1.12 (((~![U: $i] : (hskp20 | hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | (hskp20 | hskp19 | (~ndr1_0) | c3_1(a2541) | c2_1(a2541) | c1_1(a2541))) <=> ((~![U: $i] : (hskp20 | hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | (hskp20 | hskp19 | c3_1(a2541) | c1_1(a2541) | c2_1(a2541) | (~ndr1_0)))),
% 0.90/1.12 inference(monotonicity,[status(thm)],[1321])).
% 0.90/1.12 tff(1323,plain,
% 0.90/1.12 (((~![U: $i] : (hskp20 | hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | (hskp20 | hskp19 | (~ndr1_0) | c3_1(a2541) | c2_1(a2541) | c1_1(a2541))) <=> ((~![U: $i] : (hskp20 | hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | hskp20 | hskp19 | c3_1(a2541) | c1_1(a2541) | c2_1(a2541) | (~ndr1_0))),
% 0.90/1.12 inference(transitivity,[status(thm)],[1322, 1320])).
% 0.90/1.12 tff(1324,plain,
% 0.90/1.12 ((~![U: $i] : (hskp20 | hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | (hskp20 | hskp19 | (~ndr1_0) | c3_1(a2541) | c2_1(a2541) | c1_1(a2541))),
% 0.90/1.12 inference(quant_inst,[status(thm)],[])).
% 0.90/1.12 tff(1325,plain,
% 0.90/1.12 ((~![U: $i] : (hskp20 | hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | hskp20 | hskp19 | c3_1(a2541) | c1_1(a2541) | c2_1(a2541) | (~ndr1_0)),
% 0.90/1.12 inference(modus_ponens,[status(thm)],[1324, 1323])).
% 0.90/1.12 tff(1326,plain,
% 0.90/1.12 (hskp20 | hskp19 | c3_1(a2541) | c1_1(a2541)),
% 0.90/1.12 inference(unit_resolution,[status(thm)],[1325, 90, 265, 1319])).
% 0.90/1.12 tff(1327,plain,
% 0.90/1.12 (hskp20),
% 0.90/1.12 inference(unit_resolution,[status(thm)],[1326, 1309, 829, 837])).
% 0.90/1.12 tff(1328,plain,
% 0.90/1.12 (((~hskp20) | (~c1_1(a2549))) <=> ((~hskp20) | (~c1_1(a2549)))),
% 0.90/1.12 inference(rewrite,[status(thm)],[])).
% 0.90/1.12 tff(1329,plain,
% 0.90/1.12 (((~c1_1(a2549)) | (~hskp20)) <=> ((~hskp20) | (~c1_1(a2549)))),
% 0.90/1.12 inference(rewrite,[status(thm)],[])).
% 0.90/1.12 tff(1330,axiom,((~c1_1(a2549)) | (~hskp20)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause101')).
% 0.90/1.12 tff(1331,plain,
% 0.90/1.12 ((~hskp20) | (~c1_1(a2549))),
% 0.90/1.12 inference(modus_ponens,[status(thm)],[1330, 1329])).
% 0.90/1.12 tff(1332,plain,
% 0.90/1.12 ((~hskp20) | (~c1_1(a2549))),
% 0.90/1.12 inference(modus_ponens,[status(thm)],[1331, 1328])).
% 0.90/1.12 tff(1333,plain,
% 0.90/1.12 (~c1_1(a2549)),
% 0.90/1.12 inference(unit_resolution,[status(thm)],[1332, 1327])).
% 0.90/1.12 tff(1334,plain,
% 0.90/1.12 (((~hskp20) | (~c0_1(a2549))) <=> ((~hskp20) | (~c0_1(a2549)))),
% 0.90/1.12 inference(rewrite,[status(thm)],[])).
% 0.90/1.12 tff(1335,plain,
% 0.90/1.12 (((~c0_1(a2549)) | (~hskp20)) <=> ((~hskp20) | (~c0_1(a2549)))),
% 0.90/1.12 inference(rewrite,[status(thm)],[])).
% 0.90/1.12 tff(1336,axiom,((~c0_1(a2549)) | (~hskp20)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause100')).
% 0.90/1.12 tff(1337,plain,
% 0.90/1.12 ((~hskp20) | (~c0_1(a2549))),
% 0.90/1.12 inference(modus_ponens,[status(thm)],[1336, 1335])).
% 0.90/1.12 tff(1338,plain,
% 0.90/1.12 ((~hskp20) | (~c0_1(a2549))),
% 0.90/1.12 inference(modus_ponens,[status(thm)],[1337, 1334])).
% 0.90/1.12 tff(1339,plain,
% 0.90/1.12 (~c0_1(a2549)),
% 0.90/1.12 inference(unit_resolution,[status(thm)],[1338, 1327])).
% 0.90/1.12 tff(1340,plain,
% 0.90/1.12 (((~hskp20) | c2_1(a2549)) <=> ((~hskp20) | c2_1(a2549))),
% 0.90/1.12 inference(rewrite,[status(thm)],[])).
% 0.90/1.12 tff(1341,axiom,((~hskp20) | c2_1(a2549)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause63')).
% 0.90/1.12 tff(1342,plain,
% 0.90/1.12 ((~hskp20) | c2_1(a2549)),
% 0.90/1.12 inference(modus_ponens,[status(thm)],[1341, 1340])).
% 0.90/1.12 tff(1343,plain,
% 0.90/1.12 ((~hskp20) | c2_1(a2549)),
% 0.90/1.12 inference(modus_ponens,[status(thm)],[1342, 1340])).
% 0.90/1.12 tff(1344,plain,
% 0.90/1.12 ((~hskp20) | c2_1(a2549)),
% 0.90/1.12 inference(modus_ponens,[status(thm)],[1343, 1340])).
% 0.90/1.12 tff(1345,plain,
% 0.90/1.12 ((~hskp20) | c2_1(a2549)),
% 0.90/1.12 inference(modus_ponens,[status(thm)],[1344, 1340])).
% 0.90/1.12 tff(1346,plain,
% 0.90/1.12 ((~hskp20) | c2_1(a2549)),
% 0.90/1.12 inference(modus_ponens,[status(thm)],[1345, 1340])).
% 0.90/1.12 tff(1347,plain,
% 0.90/1.12 (c2_1(a2549)),
% 0.90/1.12 inference(unit_resolution,[status(thm)],[1346, 1327])).
% 0.90/1.12 tff(1348,plain,
% 0.90/1.12 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c3_1(a2552) | c0_1(a2549) | c1_1(a2549) | (~ndr1_0) | (~c2_1(a2556)) | (~c3_1(a2556)) | c0_1(a2556) | (~c2_1(a2549)) | (~c0_1(a2552)) | (~c2_1(a2552)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c3_1(a2552) | c0_1(a2549) | c1_1(a2549) | (~ndr1_0) | (~c2_1(a2556)) | (~c3_1(a2556)) | c0_1(a2556) | (~c2_1(a2549)) | (~c0_1(a2552)) | (~c2_1(a2552)))),
% 0.90/1.12 inference(rewrite,[status(thm)],[])).
% 0.90/1.12 tff(1349,plain,
% 0.90/1.12 (((~ndr1_0) | c3_1(a2552) | (~c0_1(a2552)) | (~c2_1(a2552)) | c0_1(a2556) | (~c3_1(a2556)) | (~c2_1(a2556)) | c1_1(a2549) | c0_1(a2549) | (~c2_1(a2549))) <=> (c3_1(a2552) | c0_1(a2549) | c1_1(a2549) | (~ndr1_0) | (~c2_1(a2556)) | (~c3_1(a2556)) | c0_1(a2556) | (~c2_1(a2549)) | (~c0_1(a2552)) | (~c2_1(a2552)))),
% 0.90/1.12 inference(rewrite,[status(thm)],[])).
% 0.90/1.12 tff(1350,plain,
% 0.90/1.12 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a2552) | (~c0_1(a2552)) | (~c2_1(a2552)) | c0_1(a2556) | (~c3_1(a2556)) | (~c2_1(a2556)) | c1_1(a2549) | c0_1(a2549) | (~c2_1(a2549)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c3_1(a2552) | c0_1(a2549) | c1_1(a2549) | (~ndr1_0) | (~c2_1(a2556)) | (~c3_1(a2556)) | c0_1(a2556) | (~c2_1(a2549)) | (~c0_1(a2552)) | (~c2_1(a2552))))),
% 0.90/1.12 inference(monotonicity,[status(thm)],[1349])).
% 0.90/1.12 tff(1351,plain,
% 0.90/1.12 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a2552) | (~c0_1(a2552)) | (~c2_1(a2552)) | c0_1(a2556) | (~c3_1(a2556)) | (~c2_1(a2556)) | c1_1(a2549) | c0_1(a2549) | (~c2_1(a2549)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c3_1(a2552) | c0_1(a2549) | c1_1(a2549) | (~ndr1_0) | (~c2_1(a2556)) | (~c3_1(a2556)) | c0_1(a2556) | (~c2_1(a2549)) | (~c0_1(a2552)) | (~c2_1(a2552)))),
% 0.90/1.12 inference(transitivity,[status(thm)],[1350, 1348])).
% 0.90/1.12 tff(1352,plain,
% 0.90/1.12 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a2552) | (~c0_1(a2552)) | (~c2_1(a2552)) | c0_1(a2556) | (~c3_1(a2556)) | (~c2_1(a2556)) | c1_1(a2549) | c0_1(a2549) | (~c2_1(a2549)))),
% 0.90/1.12 inference(quant_inst,[status(thm)],[])).
% 0.90/1.12 tff(1353,plain,
% 0.90/1.12 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c3_1(a2552) | c0_1(a2549) | c1_1(a2549) | (~ndr1_0) | (~c2_1(a2556)) | (~c3_1(a2556)) | c0_1(a2556) | (~c2_1(a2549)) | (~c0_1(a2552)) | (~c2_1(a2552))),
% 0.90/1.12 inference(modus_ponens,[status(thm)],[1352, 1351])).
% 0.90/1.12 tff(1354,plain,
% 0.90/1.12 ($false),
% 0.90/1.12 inference(unit_resolution,[status(thm)],[1353, 90, 1260, 1269, 822, 1347, 823, 1339, 1333, 1087, 1276, 1268])).
% 0.90/1.12 tff(1355,plain,(c3_1(a2541) | (~c2_1(a2552)) | c3_1(a2552) | c2_1(a2541) | c1_1(a2552) | (~c1_1(a2551)) | (~c0_1(a2551)) | (~c3_1(a2526)) | c0_1(a2526) | (~c1_1(a2526)) | c2_1(a2551)), inference(lemma,lemma(discharge,[]))).
% 0.90/1.12 tff(1356,plain,
% 0.90/1.12 (c3_1(a2541)),
% 0.90/1.12 inference(unit_resolution,[status(thm)],[1355, 265, 823, 822, 824, 471, 472, 216, 152, 215, 470])).
% 0.90/1.12 tff(1357,plain,
% 0.90/1.12 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp10 | c3_1(a2553) | (~ndr1_0) | (~c3_1(a2551)) | (~c0_1(a2551)) | (~c1_1(a2551)) | (~c0_1(a2553)) | c2_1(a2553))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | hskp10 | c3_1(a2553) | (~ndr1_0) | (~c3_1(a2551)) | (~c0_1(a2551)) | (~c1_1(a2551)) | (~c0_1(a2553)) | c2_1(a2553))),
% 0.90/1.12 inference(rewrite,[status(thm)],[])).
% 0.90/1.12 tff(1358,plain,
% 0.90/1.12 ((hskp10 | (~ndr1_0) | (~c3_1(a2551)) | (~c1_1(a2551)) | (~c0_1(a2551)) | c3_1(a2553) | c2_1(a2553) | (~c0_1(a2553))) <=> (hskp10 | c3_1(a2553) | (~ndr1_0) | (~c3_1(a2551)) | (~c0_1(a2551)) | (~c1_1(a2551)) | (~c0_1(a2553)) | c2_1(a2553))),
% 0.90/1.12 inference(rewrite,[status(thm)],[])).
% 0.90/1.12 tff(1359,plain,
% 0.90/1.12 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp10 | (~ndr1_0) | (~c3_1(a2551)) | (~c1_1(a2551)) | (~c0_1(a2551)) | c3_1(a2553) | c2_1(a2553) | (~c0_1(a2553)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp10 | c3_1(a2553) | (~ndr1_0) | (~c3_1(a2551)) | (~c0_1(a2551)) | (~c1_1(a2551)) | (~c0_1(a2553)) | c2_1(a2553)))),
% 0.90/1.12 inference(monotonicity,[status(thm)],[1358])).
% 0.90/1.12 tff(1360,plain,
% 0.90/1.12 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp10 | (~ndr1_0) | (~c3_1(a2551)) | (~c1_1(a2551)) | (~c0_1(a2551)) | c3_1(a2553) | c2_1(a2553) | (~c0_1(a2553)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | hskp10 | c3_1(a2553) | (~ndr1_0) | (~c3_1(a2551)) | (~c0_1(a2551)) | (~c1_1(a2551)) | (~c0_1(a2553)) | c2_1(a2553))),
% 0.90/1.12 inference(transitivity,[status(thm)],[1359, 1357])).
% 0.90/1.12 tff(1361,plain,
% 0.90/1.12 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp10 | (~ndr1_0) | (~c3_1(a2551)) | (~c1_1(a2551)) | (~c0_1(a2551)) | c3_1(a2553) | c2_1(a2553) | (~c0_1(a2553)))),
% 0.90/1.12 inference(quant_inst,[status(thm)],[])).
% 0.90/1.12 tff(1362,plain,
% 0.90/1.12 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | hskp10 | c3_1(a2553) | (~ndr1_0) | (~c3_1(a2551)) | (~c0_1(a2551)) | (~c1_1(a2551)) | (~c0_1(a2553)) | c2_1(a2553)),
% 0.90/1.12 inference(modus_ponens,[status(thm)],[1361, 1360])).
% 0.90/1.12 tff(1363,plain,
% 0.90/1.12 (c2_1(a2553)),
% 0.90/1.12 inference(unit_resolution,[status(thm)],[1362, 90, 1096, 851, 472, 471, 849, 1189, 1123])).
% 0.90/1.12 tff(1364,plain,
% 0.90/1.12 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp16 | c1_1(a2553) | c0_1(a2526) | (~ndr1_0) | (~c3_1(a2526)) | (~c1_1(a2526)) | (~c0_1(a2553)) | (~c2_1(a2553)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp16 | c1_1(a2553) | c0_1(a2526) | (~ndr1_0) | (~c3_1(a2526)) | (~c1_1(a2526)) | (~c0_1(a2553)) | (~c2_1(a2553)))),
% 0.90/1.12 inference(rewrite,[status(thm)],[])).
% 0.90/1.12 tff(1365,plain,
% 0.90/1.12 ((hskp16 | (~ndr1_0) | c1_1(a2553) | (~c0_1(a2553)) | (~c2_1(a2553)) | c0_1(a2526) | (~c3_1(a2526)) | (~c1_1(a2526))) <=> (hskp16 | c1_1(a2553) | c0_1(a2526) | (~ndr1_0) | (~c3_1(a2526)) | (~c1_1(a2526)) | (~c0_1(a2553)) | (~c2_1(a2553)))),
% 0.90/1.12 inference(rewrite,[status(thm)],[])).
% 0.90/1.12 tff(1366,plain,
% 0.90/1.12 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp16 | (~ndr1_0) | c1_1(a2553) | (~c0_1(a2553)) | (~c2_1(a2553)) | c0_1(a2526) | (~c3_1(a2526)) | (~c1_1(a2526)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp16 | c1_1(a2553) | c0_1(a2526) | (~ndr1_0) | (~c3_1(a2526)) | (~c1_1(a2526)) | (~c0_1(a2553)) | (~c2_1(a2553))))),
% 0.90/1.12 inference(monotonicity,[status(thm)],[1365])).
% 0.90/1.12 tff(1367,plain,
% 0.90/1.12 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp16 | (~ndr1_0) | c1_1(a2553) | (~c0_1(a2553)) | (~c2_1(a2553)) | c0_1(a2526) | (~c3_1(a2526)) | (~c1_1(a2526)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp16 | c1_1(a2553) | c0_1(a2526) | (~ndr1_0) | (~c3_1(a2526)) | (~c1_1(a2526)) | (~c0_1(a2553)) | (~c2_1(a2553)))),
% 0.90/1.12 inference(transitivity,[status(thm)],[1366, 1364])).
% 0.90/1.12 tff(1368,plain,
% 0.90/1.12 ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp16 | (~ndr1_0) | c1_1(a2553) | (~c0_1(a2553)) | (~c2_1(a2553)) | c0_1(a2526) | (~c3_1(a2526)) | (~c1_1(a2526)))),
% 0.90/1.12 inference(quant_inst,[status(thm)],[])).
% 0.90/1.12 tff(1369,plain,
% 0.90/1.12 ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp16 | c1_1(a2553) | c0_1(a2526) | (~ndr1_0) | (~c3_1(a2526)) | (~c1_1(a2526)) | (~c0_1(a2553)) | (~c2_1(a2553))),
% 0.90/1.12 inference(modus_ponens,[status(thm)],[1368, 1367])).
% 0.90/1.12 tff(1370,plain,
% 0.90/1.12 (hskp16 | (~c2_1(a2553))),
% 0.90/1.12 inference(unit_resolution,[status(thm)],[1369, 90, 851, 215, 216, 850, 152, 974])).
% 0.90/1.12 tff(1371,plain,
% 0.90/1.12 (hskp16),
% 0.90/1.12 inference(unit_resolution,[status(thm)],[1370, 1363])).
% 0.90/1.12 tff(1372,plain,
% 0.90/1.12 (c0_1(a2540)),
% 0.90/1.12 inference(unit_resolution,[status(thm)],[994, 1371])).
% 0.90/1.12 tff(1373,plain,
% 0.90/1.12 (~c2_1(a2540)),
% 0.90/1.12 inference(unit_resolution,[status(thm)],[986, 1371])).
% 0.90/1.12 tff(1374,plain,
% 0.90/1.12 (~c3_1(a2540)),
% 0.90/1.12 inference(unit_resolution,[status(thm)],[1007, 1371])).
% 0.90/1.12 tff(1375,plain,
% 0.90/1.12 ($false),
% 0.90/1.12 inference(unit_resolution,[status(thm)],[1200, 1374, 1373, 471, 472, 404, 1096, 1372])).
% 0.90/1.12 tff(1376,plain,(hskp10 | (~c1_1(a2551)) | (~c0_1(a2551)) | hskp29 | (~c0_1(a2553)) | (~c1_1(a2526)) | (~c3_1(a2526)) | c1_1(a2553) | c0_1(a2526) | c3_1(a2553)), inference(lemma,lemma(discharge,[]))).
% 0.90/1.12 tff(1377,plain,
% 0.90/1.12 (hskp10),
% 0.90/1.12 inference(unit_resolution,[status(thm)],[1376, 404, 472, 471, 851, 215, 216, 850, 152, 849])).
% 0.90/1.12 tff(1378,plain,
% 0.90/1.12 (~c0_1(a2528)),
% 0.90/1.12 inference(unit_resolution,[status(thm)],[1137, 1377])).
% 0.90/1.12 tff(1379,plain,
% 0.90/1.12 (~c1_1(a2528)),
% 0.90/1.12 inference(unit_resolution,[status(thm)],[1158, 1377])).
% 0.90/1.12 tff(1380,plain,
% 0.90/1.12 (c3_1(a2528)),
% 0.90/1.12 inference(unit_resolution,[status(thm)],[1145, 1377])).
% 0.90/1.12 tff(1381,assumption,(~c0_1(a2528)), introduced(assumption)).
% 0.90/1.12 tff(1382,assumption,(~c1_1(a2528)), introduced(assumption)).
% 0.90/1.12 tff(1383,assumption,(c3_1(a2528)), introduced(assumption)).
% 0.90/1.12 tff(1384,assumption,(~hskp11), introduced(assumption)).
% 0.90/1.12 tff(1385,plain,
% 0.90/1.12 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp11 | c1_1(a2541) | c2_1(a2541) | c0_1(a2528) | (~ndr1_0) | (~c3_1(a2528)) | c2_1(a2528) | (~c3_1(a2541)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp11 | c1_1(a2541) | c2_1(a2541) | c0_1(a2528) | (~ndr1_0) | (~c3_1(a2528)) | c2_1(a2528) | (~c3_1(a2541)))),
% 0.90/1.12 inference(rewrite,[status(thm)],[])).
% 0.90/1.12 tff(1386,plain,
% 0.90/1.12 ((hskp11 | (~ndr1_0) | c2_1(a2541) | c1_1(a2541) | (~c3_1(a2541)) | c0_1(a2528) | c2_1(a2528) | (~c3_1(a2528))) <=> (hskp11 | c1_1(a2541) | c2_1(a2541) | c0_1(a2528) | (~ndr1_0) | (~c3_1(a2528)) | c2_1(a2528) | (~c3_1(a2541)))),
% 0.90/1.12 inference(rewrite,[status(thm)],[])).
% 0.90/1.12 tff(1387,plain,
% 0.90/1.12 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp11 | (~ndr1_0) | c2_1(a2541) | c1_1(a2541) | (~c3_1(a2541)) | c0_1(a2528) | c2_1(a2528) | (~c3_1(a2528)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp11 | c1_1(a2541) | c2_1(a2541) | c0_1(a2528) | (~ndr1_0) | (~c3_1(a2528)) | c2_1(a2528) | (~c3_1(a2541))))),
% 0.90/1.12 inference(monotonicity,[status(thm)],[1386])).
% 0.90/1.12 tff(1388,plain,
% 0.90/1.12 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp11 | (~ndr1_0) | c2_1(a2541) | c1_1(a2541) | (~c3_1(a2541)) | c0_1(a2528) | c2_1(a2528) | (~c3_1(a2528)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp11 | c1_1(a2541) | c2_1(a2541) | c0_1(a2528) | (~ndr1_0) | (~c3_1(a2528)) | c2_1(a2528) | (~c3_1(a2541)))),
% 0.90/1.12 inference(transitivity,[status(thm)],[1387, 1385])).
% 0.90/1.12 tff(1389,plain,
% 0.90/1.12 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp11 | (~ndr1_0) | c2_1(a2541) | c1_1(a2541) | (~c3_1(a2541)) | c0_1(a2528) | c2_1(a2528) | (~c3_1(a2528)))),
% 0.90/1.12 inference(quant_inst,[status(thm)],[])).
% 0.90/1.12 tff(1390,plain,
% 0.90/1.12 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp11 | c1_1(a2541) | c2_1(a2541) | c0_1(a2528) | (~ndr1_0) | (~c3_1(a2528)) | c2_1(a2528) | (~c3_1(a2541))),
% 0.90/1.12 inference(modus_ponens,[status(thm)],[1389, 1388])).
% 0.90/1.12 tff(1391,plain,
% 0.90/1.12 (hskp11 | c2_1(a2528)),
% 0.90/1.12 inference(unit_resolution,[status(thm)],[1390, 90, 267, 1383, 266, 265, 1381, 295])).
% 0.90/1.12 tff(1392,plain,
% 0.90/1.12 (c2_1(a2528)),
% 0.90/1.12 inference(unit_resolution,[status(thm)],[1391, 1384])).
% 0.90/1.12 tff(1393,plain,
% 0.90/1.12 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c2_1(W) | (~c0_1(W))) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c2_1(W) | (~c0_1(W))))),
% 0.90/1.12 inference(bind,[status(th)],[])).
% 0.90/1.12 tff(1394,plain,
% 0.90/1.12 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c2_1(W) | (~c0_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c2_1(W) | (~c0_1(W)))),
% 0.90/1.12 inference(quant_intro,[status(thm)],[1393])).
% 0.90/1.12 tff(1395,plain,
% 0.90/1.12 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c2_1(W) | (~c0_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c2_1(W) | (~c0_1(W)))),
% 0.90/1.12 inference(rewrite,[status(thm)],[])).
% 0.90/1.12 tff(1396,plain,
% 0.90/1.12 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V))))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c0_1(W))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))) | (~c0_1(W))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))) | (~c0_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(W)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c0_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(W))))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c0_1(W))) | c2_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(W))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(W)))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c0_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(W))))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c0_1(W))) | c2_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(W))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(W))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(W)))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c0_1(W))) | c2_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(W))))), ((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c0_1(W))) | c2_1(U)) | c1_1(V)) | c1_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(W))) | c1_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(W))) | c1_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | (~c0_1(W)))), ((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c0_1(W))) | c2_1(U)) | c1_1(V)) | c1_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | (~c0_1(W))))), (((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c0_1(W))) | c2_1(U)) | c1_1(V)) | c1_1(W)) | c2_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | (~c0_1(W))) | c2_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | (~c0_1(W))) | c2_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c2_1(W) | (~c0_1(W)))), (((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c0_1(W))) | c2_1(U)) | c1_1(V)) | c1_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c2_1(W) | (~c0_1(W)))))),
% 0.90/1.12 inference(bind,[status(th)],[])).
% 0.90/1.12 tff(1397,plain,
% 0.90/1.12 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c0_1(W))) | c2_1(U)) | c1_1(V)) | c1_1(W)) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c2_1(W) | (~c0_1(W)))),
% 0.90/1.12 inference(quant_intro,[status(thm)],[1396])).
% 0.90/1.12 tff(1398,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c0_1(W))) | c2_1(U)) | c1_1(V)) | c1_1(W)) | c2_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause201')).
% 0.90/1.12 tff(1399,plain,
% 0.90/1.12 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c2_1(W) | (~c0_1(W)))),
% 0.90/1.12 inference(modus_ponens,[status(thm)],[1398, 1397])).
% 0.90/1.13 tff(1400,plain,
% 0.90/1.13 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c2_1(W) | (~c0_1(W)))),
% 0.90/1.13 inference(modus_ponens,[status(thm)],[1399, 1395])).
% 0.90/1.13 tff(1401,plain,(
% 0.90/1.13 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c2_1(W) | (~c0_1(W)))),
% 0.90/1.13 inference(skolemize,[status(sab)],[1400])).
% 0.90/1.13 tff(1402,plain,
% 0.90/1.13 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c2_1(W) | (~c0_1(W)))),
% 0.90/1.13 inference(modus_ponens,[status(thm)],[1401, 1394])).
% 0.90/1.13 tff(1403,plain,
% 0.90/1.13 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c2_1(W) | (~c0_1(W)))) | (c1_1(a2541) | c2_1(a2541) | c1_1(a2528) | (~ndr1_0) | (~c3_1(a2528)) | (~c2_1(a2528)) | (~c3_1(a2541)) | (~c0_1(a2541)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c2_1(W) | (~c0_1(W)))) | c1_1(a2541) | c2_1(a2541) | c1_1(a2528) | (~ndr1_0) | (~c3_1(a2528)) | (~c2_1(a2528)) | (~c3_1(a2541)) | (~c0_1(a2541)))),
% 0.90/1.13 inference(rewrite,[status(thm)],[])).
% 0.90/1.13 tff(1404,plain,
% 0.90/1.13 (((~ndr1_0) | c2_1(a2541) | (~c3_1(a2541)) | (~c0_1(a2541)) | c1_1(a2528) | (~c3_1(a2528)) | (~c2_1(a2528)) | c1_1(a2541) | c2_1(a2541) | (~c0_1(a2541))) <=> (c1_1(a2541) | c2_1(a2541) | c1_1(a2528) | (~ndr1_0) | (~c3_1(a2528)) | (~c2_1(a2528)) | (~c3_1(a2541)) | (~c0_1(a2541)))),
% 0.90/1.13 inference(rewrite,[status(thm)],[])).
% 0.90/1.13 tff(1405,plain,
% 0.90/1.13 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c2_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a2541) | (~c3_1(a2541)) | (~c0_1(a2541)) | c1_1(a2528) | (~c3_1(a2528)) | (~c2_1(a2528)) | c1_1(a2541) | c2_1(a2541) | (~c0_1(a2541)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c2_1(W) | (~c0_1(W)))) | (c1_1(a2541) | c2_1(a2541) | c1_1(a2528) | (~ndr1_0) | (~c3_1(a2528)) | (~c2_1(a2528)) | (~c3_1(a2541)) | (~c0_1(a2541))))),
% 0.90/1.13 inference(monotonicity,[status(thm)],[1404])).
% 0.90/1.13 tff(1406,plain,
% 0.90/1.13 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c2_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a2541) | (~c3_1(a2541)) | (~c0_1(a2541)) | c1_1(a2528) | (~c3_1(a2528)) | (~c2_1(a2528)) | c1_1(a2541) | c2_1(a2541) | (~c0_1(a2541)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c2_1(W) | (~c0_1(W)))) | c1_1(a2541) | c2_1(a2541) | c1_1(a2528) | (~ndr1_0) | (~c3_1(a2528)) | (~c2_1(a2528)) | (~c3_1(a2541)) | (~c0_1(a2541)))),
% 0.90/1.13 inference(transitivity,[status(thm)],[1405, 1403])).
% 0.90/1.13 tff(1407,plain,
% 0.90/1.13 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c2_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a2541) | (~c3_1(a2541)) | (~c0_1(a2541)) | c1_1(a2528) | (~c3_1(a2528)) | (~c2_1(a2528)) | c1_1(a2541) | c2_1(a2541) | (~c0_1(a2541)))),
% 0.90/1.13 inference(quant_inst,[status(thm)],[])).
% 0.90/1.13 tff(1408,plain,
% 0.90/1.13 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c2_1(W) | (~c0_1(W)))) | c1_1(a2541) | c2_1(a2541) | c1_1(a2528) | (~ndr1_0) | (~c3_1(a2528)) | (~c2_1(a2528)) | (~c3_1(a2541)) | (~c0_1(a2541))),
% 0.90/1.13 inference(modus_ponens,[status(thm)],[1407, 1406])).
% 0.90/1.13 tff(1409,plain,
% 0.90/1.13 ((~c2_1(a2528)) | (~c0_1(a2541))),
% 0.90/1.13 inference(unit_resolution,[status(thm)],[1408, 90, 267, 1383, 266, 265, 1382, 1402])).
% 0.90/1.13 tff(1410,plain,
% 0.90/1.13 (~c0_1(a2541)),
% 0.90/1.13 inference(unit_resolution,[status(thm)],[1409, 1392])).
% 0.90/1.13 tff(1411,plain,
% 0.90/1.13 ($false),
% 0.90/1.13 inference(unit_resolution,[status(thm)],[439, 90, 1384, 267, 266, 265, 295, 1410])).
% 0.90/1.13 tff(1412,plain,(hskp11 | (~c3_1(a2541)) | c1_1(a2541) | c2_1(a2541) | (~c3_1(a2528)) | c1_1(a2528) | c0_1(a2528)), inference(lemma,lemma(discharge,[]))).
% 0.90/1.13 tff(1413,plain,
% 0.90/1.13 (hskp11),
% 0.90/1.13 inference(unit_resolution,[status(thm)],[1412, 266, 267, 265, 1383, 1382, 1381])).
% 0.90/1.13 tff(1414,plain,
% 0.90/1.13 (~c3_1(a2531)),
% 0.90/1.13 inference(unit_resolution,[status(thm)],[308, 1413])).
% 0.90/1.13 tff(1415,plain,
% 0.90/1.13 (c2_1(a2531)),
% 0.90/1.13 inference(unit_resolution,[status(thm)],[316, 1413])).
% 0.90/1.13 tff(1416,plain,
% 0.90/1.13 (c1_1(a2531)),
% 0.90/1.13 inference(unit_resolution,[status(thm)],[324, 1413])).
% 0.90/1.13 tff(1417,plain,
% 0.90/1.13 ($false),
% 0.90/1.13 inference(unit_resolution,[status(thm)],[331, 90, 404, 267, 1416, 1415, 266, 265, 1414, 277])).
% 0.90/1.13 tff(1418,plain,(c1_1(a2541) | hskp29 | (~c3_1(a2541)) | c2_1(a2541) | (~c3_1(a2528)) | c1_1(a2528) | c0_1(a2528)), inference(lemma,lemma(discharge,[]))).
% 0.90/1.13 tff(1419,plain,
% 0.90/1.13 (c1_1(a2541)),
% 0.90/1.13 inference(unit_resolution,[status(thm)],[1418, 404, 267, 265, 1380, 1379, 1378])).
% 0.90/1.13 tff(1420,plain,
% 0.90/1.13 (~hskp17),
% 0.90/1.13 inference(unit_resolution,[status(thm)],[244, 1419])).
% 0.90/1.13 tff(1421,plain,
% 0.90/1.13 (^[U: $i] : refl((hskp29 | hskp2 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U))) <=> (hskp29 | hskp2 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U))))),
% 0.90/1.13 inference(bind,[status(th)],[])).
% 0.90/1.13 tff(1422,plain,
% 0.90/1.13 (![U: $i] : (hskp29 | hskp2 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp29 | hskp2 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))),
% 0.90/1.13 inference(quant_intro,[status(thm)],[1421])).
% 0.90/1.13 tff(1423,plain,
% 0.90/1.13 (![U: $i] : (hskp29 | hskp2 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp29 | hskp2 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))),
% 0.90/1.13 inference(rewrite,[status(thm)],[])).
% 0.90/1.13 tff(1424,plain,
% 0.90/1.13 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c0_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) <=> (((~ndr1_0) | (~c0_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U))))), (((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))), (((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U))))), ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp29) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U))) | hskp29))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U))) | hskp29) <=> (hskp29 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))), ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp29) <=> (hskp29 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U))))), (((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp29) | hskp2) <=> ((hskp29 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U))) | hskp2))), rewrite(((hskp29 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U))) | hskp2) <=> (hskp29 | hskp2 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))), (((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp29) | hskp2) <=> (hskp29 | hskp2 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))))),
% 0.90/1.13 inference(bind,[status(th)],[])).
% 0.90/1.13 tff(1425,plain,
% 0.90/1.13 (![U: $i] : ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp29) | hskp2) <=> ![U: $i] : (hskp29 | hskp2 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))),
% 0.90/1.13 inference(quant_intro,[status(thm)],[1424])).
% 0.90/1.13 tff(1426,axiom,(![U: $i] : ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp29) | hskp2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause144')).
% 0.90/1.13 tff(1427,plain,
% 0.90/1.13 (![U: $i] : (hskp29 | hskp2 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))),
% 0.90/1.13 inference(modus_ponens,[status(thm)],[1426, 1425])).
% 0.90/1.13 tff(1428,plain,
% 0.90/1.13 (![U: $i] : (hskp29 | hskp2 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))),
% 0.90/1.13 inference(modus_ponens,[status(thm)],[1427, 1423])).
% 0.90/1.13 tff(1429,plain,(
% 0.90/1.13 ![U: $i] : (hskp29 | hskp2 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))),
% 0.90/1.13 inference(skolemize,[status(sab)],[1428])).
% 0.90/1.13 tff(1430,plain,
% 0.90/1.13 (![U: $i] : (hskp29 | hskp2 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))),
% 0.90/1.13 inference(modus_ponens,[status(thm)],[1429, 1422])).
% 0.90/1.13 tff(1431,plain,
% 0.90/1.13 (((~![U: $i] : (hskp29 | hskp2 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp29 | hskp2 | c1_1(a2553) | c3_1(a2553) | (~ndr1_0) | (~c0_1(a2553)))) <=> ((~![U: $i] : (hskp29 | hskp2 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))) | hskp29 | hskp2 | c1_1(a2553) | c3_1(a2553) | (~ndr1_0) | (~c0_1(a2553)))),
% 0.90/1.13 inference(rewrite,[status(thm)],[])).
% 0.90/1.13 tff(1432,plain,
% 0.90/1.13 ((hskp29 | hskp2 | (~ndr1_0) | c3_1(a2553) | c1_1(a2553) | (~c0_1(a2553))) <=> (hskp29 | hskp2 | c1_1(a2553) | c3_1(a2553) | (~ndr1_0) | (~c0_1(a2553)))),
% 0.90/1.13 inference(rewrite,[status(thm)],[])).
% 0.90/1.13 tff(1433,plain,
% 0.90/1.13 (((~![U: $i] : (hskp29 | hskp2 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp29 | hskp2 | (~ndr1_0) | c3_1(a2553) | c1_1(a2553) | (~c0_1(a2553)))) <=> ((~![U: $i] : (hskp29 | hskp2 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp29 | hskp2 | c1_1(a2553) | c3_1(a2553) | (~ndr1_0) | (~c0_1(a2553))))),
% 0.90/1.13 inference(monotonicity,[status(thm)],[1432])).
% 0.90/1.13 tff(1434,plain,
% 0.90/1.13 (((~![U: $i] : (hskp29 | hskp2 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp29 | hskp2 | (~ndr1_0) | c3_1(a2553) | c1_1(a2553) | (~c0_1(a2553)))) <=> ((~![U: $i] : (hskp29 | hskp2 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))) | hskp29 | hskp2 | c1_1(a2553) | c3_1(a2553) | (~ndr1_0) | (~c0_1(a2553)))),
% 0.90/1.13 inference(transitivity,[status(thm)],[1433, 1431])).
% 0.90/1.13 tff(1435,plain,
% 0.90/1.13 ((~![U: $i] : (hskp29 | hskp2 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp29 | hskp2 | (~ndr1_0) | c3_1(a2553) | c1_1(a2553) | (~c0_1(a2553)))),
% 0.90/1.13 inference(quant_inst,[status(thm)],[])).
% 0.90/1.13 tff(1436,plain,
% 0.90/1.13 ((~![U: $i] : (hskp29 | hskp2 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))) | hskp29 | hskp2 | c1_1(a2553) | c3_1(a2553) | (~ndr1_0) | (~c0_1(a2553))),
% 0.90/1.13 inference(modus_ponens,[status(thm)],[1435, 1434])).
% 0.90/1.13 tff(1437,plain,
% 0.90/1.13 (hskp29 | hskp2),
% 0.90/1.13 inference(unit_resolution,[status(thm)],[1436, 90, 851, 850, 849, 1430])).
% 0.90/1.13 tff(1438,plain,
% 0.90/1.13 (hskp2),
% 0.90/1.13 inference(unit_resolution,[status(thm)],[1437, 404])).
% 0.90/1.13 tff(1439,plain,
% 0.90/1.13 (~c3_1(a2518)),
% 0.90/1.13 inference(unit_resolution,[status(thm)],[892, 1438])).
% 0.90/1.13 tff(1440,plain,
% 0.90/1.13 (c1_1(a2518)),
% 0.90/1.13 inference(unit_resolution,[status(thm)],[906, 1438])).
% 0.90/1.13 tff(1441,plain,
% 0.90/1.13 (hskp17 | c2_1(a2518)),
% 0.90/1.13 inference(unit_resolution,[status(thm)],[913, 90, 215, 216, 1440, 152, 1439, 226])).
% 0.90/1.13 tff(1442,plain,
% 0.90/1.13 (c2_1(a2518)),
% 0.90/1.13 inference(unit_resolution,[status(thm)],[1441, 1420])).
% 0.90/1.13 tff(1443,plain,
% 0.90/1.13 (~hskp19),
% 0.90/1.13 inference(unit_resolution,[status(thm)],[1308, 1442, 824, 823, 945, 1439, 822])).
% 0.90/1.13 tff(1444,plain,
% 0.90/1.13 ((~c2_1(a2518)) | c2_1(a2528)),
% 0.90/1.13 inference(unit_resolution,[status(thm)],[1165, 90, 851, 1380, 1440, 850, 849, 1379, 945, 636])).
% 0.90/1.13 tff(1445,plain,
% 0.90/1.13 (c2_1(a2528)),
% 0.90/1.13 inference(unit_resolution,[status(thm)],[1444, 1442])).
% 0.90/1.13 tff(1446,plain,
% 0.90/1.13 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c3_1(a2553) | c0_1(a2528) | c1_1(a2528) | (~ndr1_0) | (~c3_1(a2528)) | (~c2_1(a2528)) | (~c0_1(a2553)) | (~c2_1(a2553)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c3_1(a2553) | c0_1(a2528) | c1_1(a2528) | (~ndr1_0) | (~c3_1(a2528)) | (~c2_1(a2528)) | (~c0_1(a2553)) | (~c2_1(a2553)))),
% 0.90/1.13 inference(rewrite,[status(thm)],[])).
% 0.90/1.13 tff(1447,plain,
% 0.90/1.13 (((~ndr1_0) | c3_1(a2553) | (~c0_1(a2553)) | (~c2_1(a2553)) | c0_1(a2528) | (~c3_1(a2528)) | (~c2_1(a2528)) | c1_1(a2528) | c0_1(a2528) | (~c2_1(a2528))) <=> (c3_1(a2553) | c0_1(a2528) | c1_1(a2528) | (~ndr1_0) | (~c3_1(a2528)) | (~c2_1(a2528)) | (~c0_1(a2553)) | (~c2_1(a2553)))),
% 0.90/1.13 inference(rewrite,[status(thm)],[])).
% 0.90/1.13 tff(1448,plain,
% 0.90/1.13 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a2553) | (~c0_1(a2553)) | (~c2_1(a2553)) | c0_1(a2528) | (~c3_1(a2528)) | (~c2_1(a2528)) | c1_1(a2528) | c0_1(a2528) | (~c2_1(a2528)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c3_1(a2553) | c0_1(a2528) | c1_1(a2528) | (~ndr1_0) | (~c3_1(a2528)) | (~c2_1(a2528)) | (~c0_1(a2553)) | (~c2_1(a2553))))),
% 0.90/1.13 inference(monotonicity,[status(thm)],[1447])).
% 0.90/1.13 tff(1449,plain,
% 0.90/1.13 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a2553) | (~c0_1(a2553)) | (~c2_1(a2553)) | c0_1(a2528) | (~c3_1(a2528)) | (~c2_1(a2528)) | c1_1(a2528) | c0_1(a2528) | (~c2_1(a2528)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c3_1(a2553) | c0_1(a2528) | c1_1(a2528) | (~ndr1_0) | (~c3_1(a2528)) | (~c2_1(a2528)) | (~c0_1(a2553)) | (~c2_1(a2553)))),
% 0.90/1.13 inference(transitivity,[status(thm)],[1448, 1446])).
% 0.90/1.13 tff(1450,plain,
% 0.90/1.13 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a2553) | (~c0_1(a2553)) | (~c2_1(a2553)) | c0_1(a2528) | (~c3_1(a2528)) | (~c2_1(a2528)) | c1_1(a2528) | c0_1(a2528) | (~c2_1(a2528)))),
% 0.90/1.13 inference(quant_inst,[status(thm)],[])).
% 0.90/1.13 tff(1451,plain,
% 0.90/1.13 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c3_1(a2553) | c0_1(a2528) | c1_1(a2528) | (~ndr1_0) | (~c3_1(a2528)) | (~c2_1(a2528)) | (~c0_1(a2553)) | (~c2_1(a2553))),
% 0.90/1.13 inference(modus_ponens,[status(thm)],[1450, 1449])).
% 0.90/1.13 tff(1452,plain,
% 0.90/1.13 ((~c2_1(a2528)) | (~c2_1(a2553))),
% 0.90/1.13 inference(unit_resolution,[status(thm)],[1451, 90, 851, 1380, 849, 1378, 1379, 1087])).
% 0.90/1.13 tff(1453,plain,
% 0.90/1.13 (~c2_1(a2553)),
% 0.90/1.13 inference(unit_resolution,[status(thm)],[1452, 1445])).
% 0.90/1.13 tff(1454,plain,
% 0.90/1.13 (((~![U: $i] : (hskp20 | hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | (hskp20 | hskp19 | c1_1(a2553) | c3_1(a2553) | (~ndr1_0) | c2_1(a2553))) <=> ((~![U: $i] : (hskp20 | hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | hskp20 | hskp19 | c1_1(a2553) | c3_1(a2553) | (~ndr1_0) | c2_1(a2553))),
% 0.90/1.13 inference(rewrite,[status(thm)],[])).
% 0.90/1.13 tff(1455,plain,
% 0.90/1.13 ((hskp20 | hskp19 | (~ndr1_0) | c3_1(a2553) | c2_1(a2553) | c1_1(a2553)) <=> (hskp20 | hskp19 | c1_1(a2553) | c3_1(a2553) | (~ndr1_0) | c2_1(a2553))),
% 0.90/1.13 inference(rewrite,[status(thm)],[])).
% 0.90/1.13 tff(1456,plain,
% 0.90/1.13 (((~![U: $i] : (hskp20 | hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | (hskp20 | hskp19 | (~ndr1_0) | c3_1(a2553) | c2_1(a2553) | c1_1(a2553))) <=> ((~![U: $i] : (hskp20 | hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | (hskp20 | hskp19 | c1_1(a2553) | c3_1(a2553) | (~ndr1_0) | c2_1(a2553)))),
% 0.90/1.13 inference(monotonicity,[status(thm)],[1455])).
% 0.90/1.13 tff(1457,plain,
% 0.90/1.13 (((~![U: $i] : (hskp20 | hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | (hskp20 | hskp19 | (~ndr1_0) | c3_1(a2553) | c2_1(a2553) | c1_1(a2553))) <=> ((~![U: $i] : (hskp20 | hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | hskp20 | hskp19 | c1_1(a2553) | c3_1(a2553) | (~ndr1_0) | c2_1(a2553))),
% 0.90/1.13 inference(transitivity,[status(thm)],[1456, 1454])).
% 0.90/1.13 tff(1458,plain,
% 0.90/1.13 ((~![U: $i] : (hskp20 | hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | (hskp20 | hskp19 | (~ndr1_0) | c3_1(a2553) | c2_1(a2553) | c1_1(a2553))),
% 0.90/1.13 inference(quant_inst,[status(thm)],[])).
% 0.90/1.13 tff(1459,plain,
% 0.90/1.13 ((~![U: $i] : (hskp20 | hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | hskp20 | hskp19 | c1_1(a2553) | c3_1(a2553) | (~ndr1_0) | c2_1(a2553)),
% 0.90/1.13 inference(modus_ponens,[status(thm)],[1458, 1457])).
% 0.90/1.13 tff(1460,plain,
% 0.90/1.13 (hskp20 | hskp19 | c2_1(a2553)),
% 0.90/1.13 inference(unit_resolution,[status(thm)],[1459, 90, 850, 849, 1319])).
% 0.90/1.13 tff(1461,plain,
% 0.90/1.13 (hskp20),
% 0.90/1.13 inference(unit_resolution,[status(thm)],[1460, 1453, 1443])).
% 0.90/1.13 tff(1462,plain,
% 0.90/1.13 (~c1_1(a2549)),
% 0.90/1.13 inference(unit_resolution,[status(thm)],[1332, 1461])).
% 0.90/1.13 tff(1463,plain,
% 0.90/1.13 (~c0_1(a2549)),
% 0.90/1.13 inference(unit_resolution,[status(thm)],[1338, 1461])).
% 0.90/1.13 tff(1464,plain,
% 0.90/1.13 (^[V: $i, U: $i] : refl((hskp24 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V))) <=> (hskp24 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V))))),
% 0.90/1.13 inference(bind,[status(th)],[])).
% 0.90/1.13 tff(1465,plain,
% 0.90/1.13 (![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 0.90/1.13 inference(quant_intro,[status(thm)],[1464])).
% 0.90/1.13 tff(1466,plain,
% 0.90/1.13 (![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 0.90/1.13 inference(rewrite,[status(thm)],[])).
% 0.90/1.13 tff(1467,plain,
% 0.90/1.13 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c0_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c0_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(V)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(V))))), (((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c2_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)))), (((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V))))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | hskp24) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V))) | hskp24))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V))) | hskp24) <=> (hskp24 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | hskp24) <=> (hskp24 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))))),
% 0.90/1.13 inference(bind,[status(th)],[])).
% 0.90/1.13 tff(1468,plain,
% 0.90/1.13 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | hskp24) <=> ![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 0.90/1.13 inference(quant_intro,[status(thm)],[1467])).
% 0.90/1.13 tff(1469,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | hskp24)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause183')).
% 0.90/1.13 tff(1470,plain,
% 0.90/1.13 (![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 0.90/1.13 inference(modus_ponens,[status(thm)],[1469, 1468])).
% 0.90/1.13 tff(1471,plain,
% 0.90/1.13 (![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 0.90/1.13 inference(modus_ponens,[status(thm)],[1470, 1466])).
% 0.90/1.13 tff(1472,plain,(
% 0.90/1.13 ![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 0.90/1.13 inference(skolemize,[status(sab)],[1471])).
% 0.90/1.13 tff(1473,plain,
% 0.90/1.13 (![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 0.90/1.13 inference(modus_ponens,[status(thm)],[1472, 1465])).
% 0.90/1.13 tff(1474,plain,
% 0.90/1.13 (((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp24 | c3_1(a2553) | c1_1(a2528) | (~ndr1_0) | (~c3_1(a2528)) | (~c2_1(a2528)) | (~c0_1(a2553)) | c2_1(a2553))) <=> ((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp24 | c3_1(a2553) | c1_1(a2528) | (~ndr1_0) | (~c3_1(a2528)) | (~c2_1(a2528)) | (~c0_1(a2553)) | c2_1(a2553))),
% 0.90/1.13 inference(rewrite,[status(thm)],[])).
% 0.90/1.13 tff(1475,plain,
% 0.90/1.13 ((hskp24 | (~ndr1_0) | c3_1(a2553) | c2_1(a2553) | (~c0_1(a2553)) | c1_1(a2528) | (~c3_1(a2528)) | (~c2_1(a2528))) <=> (hskp24 | c3_1(a2553) | c1_1(a2528) | (~ndr1_0) | (~c3_1(a2528)) | (~c2_1(a2528)) | (~c0_1(a2553)) | c2_1(a2553))),
% 0.90/1.13 inference(rewrite,[status(thm)],[])).
% 0.90/1.13 tff(1476,plain,
% 0.90/1.13 (((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp24 | (~ndr1_0) | c3_1(a2553) | c2_1(a2553) | (~c0_1(a2553)) | c1_1(a2528) | (~c3_1(a2528)) | (~c2_1(a2528)))) <=> ((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp24 | c3_1(a2553) | c1_1(a2528) | (~ndr1_0) | (~c3_1(a2528)) | (~c2_1(a2528)) | (~c0_1(a2553)) | c2_1(a2553)))),
% 0.90/1.13 inference(monotonicity,[status(thm)],[1475])).
% 0.90/1.13 tff(1477,plain,
% 0.90/1.13 (((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp24 | (~ndr1_0) | c3_1(a2553) | c2_1(a2553) | (~c0_1(a2553)) | c1_1(a2528) | (~c3_1(a2528)) | (~c2_1(a2528)))) <=> ((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp24 | c3_1(a2553) | c1_1(a2528) | (~ndr1_0) | (~c3_1(a2528)) | (~c2_1(a2528)) | (~c0_1(a2553)) | c2_1(a2553))),
% 0.90/1.13 inference(transitivity,[status(thm)],[1476, 1474])).
% 0.90/1.13 tff(1478,plain,
% 0.90/1.13 ((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp24 | (~ndr1_0) | c3_1(a2553) | c2_1(a2553) | (~c0_1(a2553)) | c1_1(a2528) | (~c3_1(a2528)) | (~c2_1(a2528)))),
% 0.90/1.13 inference(quant_inst,[status(thm)],[])).
% 0.90/1.13 tff(1479,plain,
% 0.90/1.13 ((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp24 | c3_1(a2553) | c1_1(a2528) | (~ndr1_0) | (~c3_1(a2528)) | (~c2_1(a2528)) | (~c0_1(a2553)) | c2_1(a2553)),
% 0.90/1.13 inference(modus_ponens,[status(thm)],[1478, 1477])).
% 0.90/1.13 tff(1480,plain,
% 0.90/1.13 (hskp24 | (~c2_1(a2528)) | c2_1(a2553)),
% 0.90/1.13 inference(unit_resolution,[status(thm)],[1479, 90, 851, 1380, 849, 1379, 1473])).
% 0.90/1.13 tff(1481,plain,
% 0.90/1.13 (hskp24),
% 0.90/1.13 inference(unit_resolution,[status(thm)],[1480, 1453, 1445])).
% 0.90/1.13 tff(1482,plain,
% 0.90/1.13 (~c1_1(a2555)),
% 0.90/1.13 inference(unit_resolution,[status(thm)],[715, 1481])).
% 0.90/1.13 tff(1483,plain,
% 0.90/1.13 (c2_1(a2549)),
% 0.90/1.13 inference(unit_resolution,[status(thm)],[1346, 1461])).
% 0.90/1.13 tff(1484,plain,
% 0.90/1.13 (c2_1(a2555)),
% 0.90/1.13 inference(unit_resolution,[status(thm)],[723, 1481])).
% 0.90/1.13 tff(1485,plain,
% 0.90/1.13 (c0_1(a2555)),
% 0.90/1.13 inference(unit_resolution,[status(thm)],[731, 1481])).
% 0.90/1.13 tff(1486,plain,
% 0.90/1.13 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a2555) | c0_1(a2549) | c1_1(a2549) | c0_1(a2518) | (~ndr1_0) | (~c1_1(a2518)) | (~c2_1(a2518)) | (~c2_1(a2549)) | (~c2_1(a2555)) | (~c0_1(a2555)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a2555) | c0_1(a2549) | c1_1(a2549) | c0_1(a2518) | (~ndr1_0) | (~c1_1(a2518)) | (~c2_1(a2518)) | (~c2_1(a2549)) | (~c2_1(a2555)) | (~c0_1(a2555)))),
% 0.90/1.13 inference(rewrite,[status(thm)],[])).
% 0.90/1.13 tff(1487,plain,
% 0.90/1.13 (((~ndr1_0) | c1_1(a2555) | (~c0_1(a2555)) | (~c2_1(a2555)) | c0_1(a2518) | (~c1_1(a2518)) | (~c2_1(a2518)) | c1_1(a2549) | c0_1(a2549) | (~c2_1(a2549))) <=> (c1_1(a2555) | c0_1(a2549) | c1_1(a2549) | c0_1(a2518) | (~ndr1_0) | (~c1_1(a2518)) | (~c2_1(a2518)) | (~c2_1(a2549)) | (~c2_1(a2555)) | (~c0_1(a2555)))),
% 0.90/1.13 inference(rewrite,[status(thm)],[])).
% 0.90/1.13 tff(1488,plain,
% 0.90/1.13 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a2555) | (~c0_1(a2555)) | (~c2_1(a2555)) | c0_1(a2518) | (~c1_1(a2518)) | (~c2_1(a2518)) | c1_1(a2549) | c0_1(a2549) | (~c2_1(a2549)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a2555) | c0_1(a2549) | c1_1(a2549) | c0_1(a2518) | (~ndr1_0) | (~c1_1(a2518)) | (~c2_1(a2518)) | (~c2_1(a2549)) | (~c2_1(a2555)) | (~c0_1(a2555))))),
% 0.90/1.13 inference(monotonicity,[status(thm)],[1487])).
% 0.90/1.13 tff(1489,plain,
% 0.90/1.13 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a2555) | (~c0_1(a2555)) | (~c2_1(a2555)) | c0_1(a2518) | (~c1_1(a2518)) | (~c2_1(a2518)) | c1_1(a2549) | c0_1(a2549) | (~c2_1(a2549)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a2555) | c0_1(a2549) | c1_1(a2549) | c0_1(a2518) | (~ndr1_0) | (~c1_1(a2518)) | (~c2_1(a2518)) | (~c2_1(a2549)) | (~c2_1(a2555)) | (~c0_1(a2555)))),
% 0.90/1.13 inference(transitivity,[status(thm)],[1488, 1486])).
% 0.90/1.13 tff(1490,plain,
% 0.90/1.13 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a2555) | (~c0_1(a2555)) | (~c2_1(a2555)) | c0_1(a2518) | (~c1_1(a2518)) | (~c2_1(a2518)) | c1_1(a2549) | c0_1(a2549) | (~c2_1(a2549)))),
% 0.90/1.13 inference(quant_inst,[status(thm)],[])).
% 0.90/1.13 tff(1491,plain,
% 0.90/1.13 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a2555) | c0_1(a2549) | c1_1(a2549) | c0_1(a2518) | (~ndr1_0) | (~c1_1(a2518)) | (~c2_1(a2518)) | (~c2_1(a2549)) | (~c2_1(a2555)) | (~c0_1(a2555))),
% 0.90/1.13 inference(modus_ponens,[status(thm)],[1490, 1489])).
% 0.90/1.13 tff(1492,plain,
% 0.90/1.13 ($false),
% 0.90/1.13 inference(unit_resolution,[status(thm)],[1491, 90, 1485, 1484, 1483, 1440, 1482, 1463, 1462, 945, 944, 1442])).
% 0.90/1.13 tff(1493,plain,(hskp29 | c0_1(a2518) | (~c0_1(a2553)) | c3_1(a2553) | c1_1(a2553) | c1_1(a2552) | c3_1(a2552) | (~c2_1(a2552)) | (~c1_1(a2526)) | (~c3_1(a2526)) | c0_1(a2526) | (~c3_1(a2541)) | c2_1(a2541) | (~c0_1(a2551)) | (~c1_1(a2551))), inference(lemma,lemma(discharge,[]))).
% 0.90/1.13 tff(1494,plain,
% 0.90/1.13 (hskp29),
% 0.90/1.13 inference(unit_resolution,[status(thm)],[1493, 945, 828, 826, 827, 824, 823, 822, 215, 216, 152, 1356, 265, 472, 471])).
% 0.90/1.13 tff(1495,plain,
% 0.90/1.13 (c3_1(a2556)),
% 0.90/1.13 inference(unit_resolution,[status(thm)],[339, 1494])).
% 0.90/1.13 tff(1496,plain,
% 0.90/1.13 (c2_1(a2556)),
% 0.90/1.13 inference(unit_resolution,[status(thm)],[347, 1494])).
% 0.90/1.13 tff(1497,plain,
% 0.90/1.13 (c1_1(a2556)),
% 0.90/1.13 inference(unit_resolution,[status(thm)],[355, 1494])).
% 0.90/1.13 tff(1498,plain,
% 0.90/1.13 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c1_1(a2553) | c3_1(a2553) | c1_1(a2541) | c2_1(a2541) | c0_1(a2526) | (~ndr1_0) | (~c2_1(a2526)) | (~c1_1(a2526)) | (~c3_1(a2541)) | (~c0_1(a2553)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c1_1(a2553) | c3_1(a2553) | c1_1(a2541) | c2_1(a2541) | c0_1(a2526) | (~ndr1_0) | (~c2_1(a2526)) | (~c1_1(a2526)) | (~c3_1(a2541)) | (~c0_1(a2553)))),
% 0.90/1.13 inference(rewrite,[status(thm)],[])).
% 0.90/1.13 tff(1499,plain,
% 0.90/1.13 (((~ndr1_0) | c3_1(a2553) | c1_1(a2553) | (~c0_1(a2553)) | c1_1(a2541) | c2_1(a2541) | (~c3_1(a2541)) | c0_1(a2526) | (~c2_1(a2526)) | (~c1_1(a2526))) <=> (c1_1(a2553) | c3_1(a2553) | c1_1(a2541) | c2_1(a2541) | c0_1(a2526) | (~ndr1_0) | (~c2_1(a2526)) | (~c1_1(a2526)) | (~c3_1(a2541)) | (~c0_1(a2553)))),
% 0.90/1.13 inference(rewrite,[status(thm)],[])).
% 0.90/1.13 tff(1500,plain,
% 0.90/1.13 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a2553) | c1_1(a2553) | (~c0_1(a2553)) | c1_1(a2541) | c2_1(a2541) | (~c3_1(a2541)) | c0_1(a2526) | (~c2_1(a2526)) | (~c1_1(a2526)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c1_1(a2553) | c3_1(a2553) | c1_1(a2541) | c2_1(a2541) | c0_1(a2526) | (~ndr1_0) | (~c2_1(a2526)) | (~c1_1(a2526)) | (~c3_1(a2541)) | (~c0_1(a2553))))),
% 0.90/1.13 inference(monotonicity,[status(thm)],[1499])).
% 0.90/1.13 tff(1501,plain,
% 0.90/1.13 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a2553) | c1_1(a2553) | (~c0_1(a2553)) | c1_1(a2541) | c2_1(a2541) | (~c3_1(a2541)) | c0_1(a2526) | (~c2_1(a2526)) | (~c1_1(a2526)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c1_1(a2553) | c3_1(a2553) | c1_1(a2541) | c2_1(a2541) | c0_1(a2526) | (~ndr1_0) | (~c2_1(a2526)) | (~c1_1(a2526)) | (~c3_1(a2541)) | (~c0_1(a2553)))),
% 0.90/1.13 inference(transitivity,[status(thm)],[1500, 1498])).
% 0.90/1.13 tff(1502,plain,
% 0.90/1.13 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a2553) | c1_1(a2553) | (~c0_1(a2553)) | c1_1(a2541) | c2_1(a2541) | (~c3_1(a2541)) | c0_1(a2526) | (~c2_1(a2526)) | (~c1_1(a2526)))),
% 0.90/1.13 inference(quant_inst,[status(thm)],[])).
% 0.90/1.13 tff(1503,plain,
% 0.90/1.13 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c1_1(a2553) | c3_1(a2553) | c1_1(a2541) | c2_1(a2541) | c0_1(a2526) | (~ndr1_0) | (~c2_1(a2526)) | (~c1_1(a2526)) | (~c3_1(a2541)) | (~c0_1(a2553))),
% 0.90/1.13 inference(modus_ponens,[status(thm)],[1502, 1501])).
% 0.90/1.13 tff(1504,plain,
% 0.90/1.13 (~c2_1(a2526)),
% 0.90/1.13 inference(unit_resolution,[status(thm)],[1503, 90, 851, 267, 215, 850, 849, 266, 265, 152, 636])).
% 0.90/1.13 tff(1505,plain,
% 0.90/1.13 (hskp11 | c1_1(a2541) | c2_1(a2526) | (~c3_1(a2541))),
% 0.90/1.13 inference(unit_resolution,[status(thm)],[301, 90, 216, 265, 152, 295])).
% 0.90/1.13 tff(1506,plain,
% 0.90/1.13 (hskp11),
% 0.90/1.13 inference(unit_resolution,[status(thm)],[1505, 1504, 267, 266])).
% 0.90/1.13 tff(1507,plain,
% 0.90/1.13 (~c3_1(a2531)),
% 0.90/1.13 inference(unit_resolution,[status(thm)],[308, 1506])).
% 0.90/1.13 tff(1508,plain,
% 0.90/1.13 (c1_1(a2531)),
% 0.90/1.13 inference(unit_resolution,[status(thm)],[324, 1506])).
% 0.90/1.13 tff(1509,plain,
% 0.90/1.13 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (c1_1(a2541) | c2_1(a2541) | c3_1(a2531) | (~ndr1_0) | (~c2_1(a2556)) | (~c3_1(a2556)) | (~c1_1(a2556)) | (~c0_1(a2531)) | (~c1_1(a2531)) | (~c3_1(a2541)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a2541) | c2_1(a2541) | c3_1(a2531) | (~ndr1_0) | (~c2_1(a2556)) | (~c3_1(a2556)) | (~c1_1(a2556)) | (~c0_1(a2531)) | (~c1_1(a2531)) | (~c3_1(a2541)))),
% 0.90/1.14 inference(rewrite,[status(thm)],[])).
% 0.90/1.14 tff(1510,plain,
% 0.90/1.14 (((~ndr1_0) | (~c3_1(a2556)) | (~c1_1(a2556)) | (~c2_1(a2556)) | c3_1(a2531) | (~c1_1(a2531)) | (~c0_1(a2531)) | c1_1(a2541) | c2_1(a2541) | (~c3_1(a2541))) <=> (c1_1(a2541) | c2_1(a2541) | c3_1(a2531) | (~ndr1_0) | (~c2_1(a2556)) | (~c3_1(a2556)) | (~c1_1(a2556)) | (~c0_1(a2531)) | (~c1_1(a2531)) | (~c3_1(a2541)))),
% 0.90/1.14 inference(rewrite,[status(thm)],[])).
% 0.90/1.14 tff(1511,plain,
% 0.90/1.14 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a2556)) | (~c1_1(a2556)) | (~c2_1(a2556)) | c3_1(a2531) | (~c1_1(a2531)) | (~c0_1(a2531)) | c1_1(a2541) | c2_1(a2541) | (~c3_1(a2541)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (c1_1(a2541) | c2_1(a2541) | c3_1(a2531) | (~ndr1_0) | (~c2_1(a2556)) | (~c3_1(a2556)) | (~c1_1(a2556)) | (~c0_1(a2531)) | (~c1_1(a2531)) | (~c3_1(a2541))))),
% 0.90/1.14 inference(monotonicity,[status(thm)],[1510])).
% 0.90/1.14 tff(1512,plain,
% 0.90/1.14 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a2556)) | (~c1_1(a2556)) | (~c2_1(a2556)) | c3_1(a2531) | (~c1_1(a2531)) | (~c0_1(a2531)) | c1_1(a2541) | c2_1(a2541) | (~c3_1(a2541)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a2541) | c2_1(a2541) | c3_1(a2531) | (~ndr1_0) | (~c2_1(a2556)) | (~c3_1(a2556)) | (~c1_1(a2556)) | (~c0_1(a2531)) | (~c1_1(a2531)) | (~c3_1(a2541)))),
% 0.90/1.14 inference(transitivity,[status(thm)],[1511, 1509])).
% 0.90/1.14 tff(1513,plain,
% 0.90/1.14 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a2556)) | (~c1_1(a2556)) | (~c2_1(a2556)) | c3_1(a2531) | (~c1_1(a2531)) | (~c0_1(a2531)) | c1_1(a2541) | c2_1(a2541) | (~c3_1(a2541)))),
% 0.90/1.14 inference(quant_inst,[status(thm)],[])).
% 0.90/1.14 tff(1514,plain,
% 0.90/1.14 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a2541) | c2_1(a2541) | c3_1(a2531) | (~ndr1_0) | (~c2_1(a2556)) | (~c3_1(a2556)) | (~c1_1(a2556)) | (~c0_1(a2531)) | (~c1_1(a2531)) | (~c3_1(a2541))),
% 0.90/1.14 inference(modus_ponens,[status(thm)],[1513, 1512])).
% 0.90/1.14 tff(1515,plain,
% 0.90/1.14 (~c0_1(a2531)),
% 0.90/1.14 inference(unit_resolution,[status(thm)],[1514, 90, 619, 618, 617, 267, 1508, 266, 265, 1507, 264])).
% 0.90/1.14 tff(1516,plain,
% 0.90/1.14 (c2_1(a2531)),
% 0.90/1.14 inference(unit_resolution,[status(thm)],[316, 1506])).
% 0.90/1.14 tff(1517,plain,
% 0.90/1.14 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c1_1(a2553) | c3_1(a2553) | c1_1(a2541) | c2_1(a2541) | (~ndr1_0) | c0_1(a2531) | (~c2_1(a2531)) | (~c1_1(a2531)) | (~c3_1(a2541)) | (~c0_1(a2553)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c1_1(a2553) | c3_1(a2553) | c1_1(a2541) | c2_1(a2541) | (~ndr1_0) | c0_1(a2531) | (~c2_1(a2531)) | (~c1_1(a2531)) | (~c3_1(a2541)) | (~c0_1(a2553)))),
% 0.90/1.14 inference(rewrite,[status(thm)],[])).
% 0.90/1.14 tff(1518,plain,
% 0.90/1.14 (((~ndr1_0) | c3_1(a2553) | c1_1(a2553) | (~c0_1(a2553)) | c1_1(a2541) | c2_1(a2541) | (~c3_1(a2541)) | c0_1(a2531) | (~c2_1(a2531)) | (~c1_1(a2531))) <=> (c1_1(a2553) | c3_1(a2553) | c1_1(a2541) | c2_1(a2541) | (~ndr1_0) | c0_1(a2531) | (~c2_1(a2531)) | (~c1_1(a2531)) | (~c3_1(a2541)) | (~c0_1(a2553)))),
% 0.90/1.14 inference(rewrite,[status(thm)],[])).
% 0.90/1.14 tff(1519,plain,
% 0.90/1.14 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a2553) | c1_1(a2553) | (~c0_1(a2553)) | c1_1(a2541) | c2_1(a2541) | (~c3_1(a2541)) | c0_1(a2531) | (~c2_1(a2531)) | (~c1_1(a2531)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c1_1(a2553) | c3_1(a2553) | c1_1(a2541) | c2_1(a2541) | (~ndr1_0) | c0_1(a2531) | (~c2_1(a2531)) | (~c1_1(a2531)) | (~c3_1(a2541)) | (~c0_1(a2553))))),
% 0.90/1.14 inference(monotonicity,[status(thm)],[1518])).
% 0.90/1.14 tff(1520,plain,
% 0.90/1.14 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a2553) | c1_1(a2553) | (~c0_1(a2553)) | c1_1(a2541) | c2_1(a2541) | (~c3_1(a2541)) | c0_1(a2531) | (~c2_1(a2531)) | (~c1_1(a2531)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c1_1(a2553) | c3_1(a2553) | c1_1(a2541) | c2_1(a2541) | (~ndr1_0) | c0_1(a2531) | (~c2_1(a2531)) | (~c1_1(a2531)) | (~c3_1(a2541)) | (~c0_1(a2553)))),
% 0.90/1.14 inference(transitivity,[status(thm)],[1519, 1517])).
% 0.90/1.14 tff(1521,plain,
% 0.90/1.14 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a2553) | c1_1(a2553) | (~c0_1(a2553)) | c1_1(a2541) | c2_1(a2541) | (~c3_1(a2541)) | c0_1(a2531) | (~c2_1(a2531)) | (~c1_1(a2531)))),
% 0.90/1.14 inference(quant_inst,[status(thm)],[])).
% 0.90/1.14 tff(1522,plain,
% 0.90/1.14 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c1_1(a2553) | c3_1(a2553) | c1_1(a2541) | c2_1(a2541) | (~ndr1_0) | c0_1(a2531) | (~c2_1(a2531)) | (~c1_1(a2531)) | (~c3_1(a2541)) | (~c0_1(a2553))),
% 0.90/1.14 inference(modus_ponens,[status(thm)],[1521, 1520])).
% 0.90/1.14 tff(1523,plain,
% 0.90/1.14 ($false),
% 0.90/1.14 inference(unit_resolution,[status(thm)],[1522, 90, 851, 267, 1508, 1516, 850, 849, 266, 265, 636, 1515])).
% 0.90/1.14 tff(1524,plain,(c1_1(a2541) | (~c0_1(a2553)) | (~c3_1(a2541)) | c1_1(a2553) | c3_1(a2553) | c2_1(a2541) | (~c1_1(a2556)) | (~c2_1(a2556)) | (~c3_1(a2556)) | (~c3_1(a2526)) | c0_1(a2526) | (~c1_1(a2526))), inference(lemma,lemma(discharge,[]))).
% 0.90/1.14 tff(1525,plain,
% 0.90/1.14 (c1_1(a2541)),
% 0.90/1.14 inference(unit_resolution,[status(thm)],[1524, 1497, 1356, 827, 826, 265, 828, 1496, 1495, 216, 152, 215])).
% 0.90/1.14 tff(1526,plain,
% 0.90/1.14 (~hskp17),
% 0.90/1.14 inference(unit_resolution,[status(thm)],[244, 1525])).
% 0.90/1.14 tff(1527,plain,
% 0.90/1.14 (hskp16),
% 0.90/1.14 inference(unit_resolution,[status(thm)],[1370, 859])).
% 0.90/1.14 tff(1528,plain,
% 0.90/1.14 (~c3_1(a2540)),
% 0.90/1.14 inference(unit_resolution,[status(thm)],[1007, 1527])).
% 0.90/1.14 tff(1529,plain,
% 0.90/1.14 (~c2_1(a2540)),
% 0.90/1.14 inference(unit_resolution,[status(thm)],[986, 1527])).
% 0.90/1.14 tff(1530,assumption,(~hskp17), introduced(assumption)).
% 0.90/1.14 tff(1531,plain,
% 0.90/1.14 (~c1_1(a2540)),
% 0.90/1.14 inference(unit_resolution,[status(thm)],[1014, 90, 1530, 215, 216, 1529, 1528, 152, 226])).
% 0.90/1.14 tff(1532,plain,
% 0.90/1.14 (c0_1(a2540)),
% 0.90/1.14 inference(unit_resolution,[status(thm)],[994, 1527])).
% 0.90/1.14 tff(1533,plain,
% 0.90/1.14 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp2 | c2_1(a2540) | c3_1(a2540) | (~ndr1_0) | (~c0_1(a2540)) | c1_1(a2540))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | hskp2 | c2_1(a2540) | c3_1(a2540) | (~ndr1_0) | (~c0_1(a2540)) | c1_1(a2540))),
% 0.90/1.14 inference(rewrite,[status(thm)],[])).
% 0.90/1.14 tff(1534,plain,
% 0.90/1.14 ((hskp2 | (~ndr1_0) | c3_1(a2540) | c2_1(a2540) | (~c0_1(a2540)) | c3_1(a2540) | c1_1(a2540) | (~c0_1(a2540))) <=> (hskp2 | c2_1(a2540) | c3_1(a2540) | (~ndr1_0) | (~c0_1(a2540)) | c1_1(a2540))),
% 0.90/1.14 inference(rewrite,[status(thm)],[])).
% 0.90/1.14 tff(1535,plain,
% 0.90/1.14 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp2 | (~ndr1_0) | c3_1(a2540) | c2_1(a2540) | (~c0_1(a2540)) | c3_1(a2540) | c1_1(a2540) | (~c0_1(a2540)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp2 | c2_1(a2540) | c3_1(a2540) | (~ndr1_0) | (~c0_1(a2540)) | c1_1(a2540)))),
% 0.90/1.14 inference(monotonicity,[status(thm)],[1534])).
% 0.90/1.14 tff(1536,plain,
% 0.90/1.14 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp2 | (~ndr1_0) | c3_1(a2540) | c2_1(a2540) | (~c0_1(a2540)) | c3_1(a2540) | c1_1(a2540) | (~c0_1(a2540)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | hskp2 | c2_1(a2540) | c3_1(a2540) | (~ndr1_0) | (~c0_1(a2540)) | c1_1(a2540))),
% 0.90/1.14 inference(transitivity,[status(thm)],[1535, 1533])).
% 0.90/1.14 tff(1537,plain,
% 0.90/1.14 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp2 | (~ndr1_0) | c3_1(a2540) | c2_1(a2540) | (~c0_1(a2540)) | c3_1(a2540) | c1_1(a2540) | (~c0_1(a2540)))),
% 0.90/1.14 inference(quant_inst,[status(thm)],[])).
% 0.90/1.14 tff(1538,plain,
% 0.90/1.14 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | hskp2 | c2_1(a2540) | c3_1(a2540) | (~ndr1_0) | (~c0_1(a2540)) | c1_1(a2540)),
% 0.90/1.14 inference(modus_ponens,[status(thm)],[1537, 1536])).
% 0.90/1.14 tff(1539,plain,
% 0.90/1.14 ($false),
% 0.90/1.14 inference(unit_resolution,[status(thm)],[1538, 90, 838, 1532, 1529, 1528, 848, 1531])).
% 0.90/1.14 tff(1540,plain,(hskp2 | hskp17 | (~c1_1(a2526)) | (~c3_1(a2526)) | c0_1(a2526) | (~c0_1(a2553)) | c1_1(a2553) | c3_1(a2553)), inference(lemma,lemma(discharge,[]))).
% 0.90/1.14 tff(1541,plain,
% 0.90/1.14 (hskp2),
% 0.90/1.14 inference(unit_resolution,[status(thm)],[1540, 1526, 215, 216, 152, 828, 827, 826])).
% 0.90/1.14 tff(1542,plain,
% 0.90/1.14 (~c3_1(a2518)),
% 0.90/1.14 inference(unit_resolution,[status(thm)],[892, 1541])).
% 0.90/1.14 tff(1543,plain,
% 0.90/1.14 (c1_1(a2518)),
% 0.90/1.14 inference(unit_resolution,[status(thm)],[906, 1541])).
% 0.90/1.14 tff(1544,plain,
% 0.90/1.14 (c2_1(a2518)),
% 0.90/1.14 inference(unit_resolution,[status(thm)],[913, 90, 1526, 215, 216, 1543, 152, 1542, 226])).
% 0.90/1.14 tff(1545,plain,
% 0.90/1.14 (~hskp19),
% 0.90/1.14 inference(unit_resolution,[status(thm)],[1308, 1544, 824, 823, 945, 1542, 822])).
% 0.90/1.14 tff(1546,plain,
% 0.90/1.14 (((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp18 | (~c1_1(a2541)) | c2_1(a2541) | (~ndr1_0) | (~c2_1(a2556)) | (~c3_1(a2556)) | (~c1_1(a2556)) | (~c3_1(a2541)))) <=> ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp18 | (~c1_1(a2541)) | c2_1(a2541) | (~ndr1_0) | (~c2_1(a2556)) | (~c3_1(a2556)) | (~c1_1(a2556)) | (~c3_1(a2541)))),
% 0.90/1.14 inference(rewrite,[status(thm)],[])).
% 0.90/1.14 tff(1547,plain,
% 0.90/1.14 ((hskp18 | (~ndr1_0) | (~c3_1(a2556)) | (~c1_1(a2556)) | (~c2_1(a2556)) | c2_1(a2541) | (~c3_1(a2541)) | (~c1_1(a2541))) <=> (hskp18 | (~c1_1(a2541)) | c2_1(a2541) | (~ndr1_0) | (~c2_1(a2556)) | (~c3_1(a2556)) | (~c1_1(a2556)) | (~c3_1(a2541)))),
% 0.90/1.14 inference(rewrite,[status(thm)],[])).
% 0.90/1.14 tff(1548,plain,
% 0.90/1.14 (((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp18 | (~ndr1_0) | (~c3_1(a2556)) | (~c1_1(a2556)) | (~c2_1(a2556)) | c2_1(a2541) | (~c3_1(a2541)) | (~c1_1(a2541)))) <=> ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp18 | (~c1_1(a2541)) | c2_1(a2541) | (~ndr1_0) | (~c2_1(a2556)) | (~c3_1(a2556)) | (~c1_1(a2556)) | (~c3_1(a2541))))),
% 0.90/1.14 inference(monotonicity,[status(thm)],[1547])).
% 0.90/1.14 tff(1549,plain,
% 0.90/1.14 (((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp18 | (~ndr1_0) | (~c3_1(a2556)) | (~c1_1(a2556)) | (~c2_1(a2556)) | c2_1(a2541) | (~c3_1(a2541)) | (~c1_1(a2541)))) <=> ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp18 | (~c1_1(a2541)) | c2_1(a2541) | (~ndr1_0) | (~c2_1(a2556)) | (~c3_1(a2556)) | (~c1_1(a2556)) | (~c3_1(a2541)))),
% 0.90/1.14 inference(transitivity,[status(thm)],[1548, 1546])).
% 0.90/1.14 tff(1550,plain,
% 0.90/1.14 ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp18 | (~ndr1_0) | (~c3_1(a2556)) | (~c1_1(a2556)) | (~c2_1(a2556)) | c2_1(a2541) | (~c3_1(a2541)) | (~c1_1(a2541)))),
% 0.90/1.14 inference(quant_inst,[status(thm)],[])).
% 0.90/1.14 tff(1551,plain,
% 0.90/1.14 ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp18 | (~c1_1(a2541)) | c2_1(a2541) | (~ndr1_0) | (~c2_1(a2556)) | (~c3_1(a2556)) | (~c1_1(a2556)) | (~c3_1(a2541))),
% 0.90/1.14 inference(modus_ponens,[status(thm)],[1550, 1549])).
% 0.90/1.14 tff(1552,plain,
% 0.90/1.14 (hskp18 | (~c1_1(a2541))),
% 0.90/1.14 inference(unit_resolution,[status(thm)],[1551, 90, 1497, 1496, 1495, 1356, 265, 572])).
% 0.90/1.14 tff(1553,plain,
% 0.90/1.14 (hskp18),
% 0.90/1.14 inference(unit_resolution,[status(thm)],[1552, 1525])).
% 0.90/1.14 tff(1554,plain,
% 0.90/1.14 (~c0_1(a2545)),
% 0.90/1.14 inference(unit_resolution,[status(thm)],[584, 1553])).
% 0.90/1.14 tff(1555,plain,
% 0.90/1.14 (c2_1(a2545)),
% 0.90/1.14 inference(unit_resolution,[status(thm)],[592, 1553])).
% 0.90/1.14 tff(1556,plain,
% 0.90/1.14 (c1_1(a2545)),
% 0.90/1.14 inference(unit_resolution,[status(thm)],[600, 1553])).
% 0.90/1.14 tff(1557,plain,
% 0.90/1.14 (hskp14),
% 0.90/1.14 inference(unit_resolution,[status(thm)],[920, 90, 472, 471, 470, 945, 1542, 469, 1544])).
% 0.90/1.14 tff(1558,plain,
% 0.90/1.14 (~c3_1(a2536)),
% 0.90/1.14 inference(unit_resolution,[status(thm)],[484, 1557])).
% 0.90/1.14 tff(1559,plain,
% 0.90/1.14 (~c1_1(a2536)),
% 0.90/1.14 inference(unit_resolution,[status(thm)],[490, 1557])).
% 0.90/1.14 tff(1560,plain,
% 0.90/1.14 (~c0_1(a2536)),
% 0.90/1.14 inference(unit_resolution,[status(thm)],[496, 1557])).
% 0.90/1.14 tff(1561,plain,
% 0.90/1.14 (~c0_1(a2556)),
% 0.90/1.14 inference(unit_resolution,[status(thm)],[1267, 90, 1497, 1496, 1543, 1560, 1559, 1558, 945, 1542, 459])).
% 0.90/1.14 tff(1562,assumption,(~c0_1(a2556)), introduced(assumption)).
% 0.90/1.14 tff(1563,assumption,(hskp20), introduced(assumption)).
% 0.90/1.14 tff(1564,plain,
% 0.90/1.14 (~c1_1(a2549)),
% 0.90/1.14 inference(unit_resolution,[status(thm)],[1332, 1563])).
% 0.90/1.14 tff(1565,plain,
% 0.90/1.14 (~c0_1(a2549)),
% 0.90/1.14 inference(unit_resolution,[status(thm)],[1338, 1563])).
% 0.90/1.14 tff(1566,plain,
% 0.90/1.14 (c2_1(a2549)),
% 0.90/1.14 inference(unit_resolution,[status(thm)],[1346, 1563])).
% 0.90/1.14 tff(1567,plain,
% 0.90/1.14 (~c0_1(a2552)),
% 0.90/1.14 inference(unit_resolution,[status(thm)],[1353, 90, 618, 617, 822, 1566, 823, 1565, 1564, 1087, 1562])).
% 0.90/1.14 tff(1568,plain,
% 0.90/1.14 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c3_1(a2553) | c0_1(a2549) | c1_1(a2549) | (~ndr1_0) | (~c2_1(a2556)) | (~c3_1(a2556)) | c0_1(a2556) | (~c2_1(a2549)) | (~c0_1(a2553)) | (~c2_1(a2553)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c3_1(a2553) | c0_1(a2549) | c1_1(a2549) | (~ndr1_0) | (~c2_1(a2556)) | (~c3_1(a2556)) | c0_1(a2556) | (~c2_1(a2549)) | (~c0_1(a2553)) | (~c2_1(a2553)))),
% 0.90/1.14 inference(rewrite,[status(thm)],[])).
% 0.90/1.14 tff(1569,plain,
% 0.90/1.14 (((~ndr1_0) | c3_1(a2553) | (~c0_1(a2553)) | (~c2_1(a2553)) | c0_1(a2556) | (~c3_1(a2556)) | (~c2_1(a2556)) | c1_1(a2549) | c0_1(a2549) | (~c2_1(a2549))) <=> (c3_1(a2553) | c0_1(a2549) | c1_1(a2549) | (~ndr1_0) | (~c2_1(a2556)) | (~c3_1(a2556)) | c0_1(a2556) | (~c2_1(a2549)) | (~c0_1(a2553)) | (~c2_1(a2553)))),
% 0.90/1.14 inference(rewrite,[status(thm)],[])).
% 0.90/1.14 tff(1570,plain,
% 0.90/1.14 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a2553) | (~c0_1(a2553)) | (~c2_1(a2553)) | c0_1(a2556) | (~c3_1(a2556)) | (~c2_1(a2556)) | c1_1(a2549) | c0_1(a2549) | (~c2_1(a2549)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c3_1(a2553) | c0_1(a2549) | c1_1(a2549) | (~ndr1_0) | (~c2_1(a2556)) | (~c3_1(a2556)) | c0_1(a2556) | (~c2_1(a2549)) | (~c0_1(a2553)) | (~c2_1(a2553))))),
% 0.90/1.14 inference(monotonicity,[status(thm)],[1569])).
% 0.90/1.14 tff(1571,plain,
% 0.90/1.14 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a2553) | (~c0_1(a2553)) | (~c2_1(a2553)) | c0_1(a2556) | (~c3_1(a2556)) | (~c2_1(a2556)) | c1_1(a2549) | c0_1(a2549) | (~c2_1(a2549)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c3_1(a2553) | c0_1(a2549) | c1_1(a2549) | (~ndr1_0) | (~c2_1(a2556)) | (~c3_1(a2556)) | c0_1(a2556) | (~c2_1(a2549)) | (~c0_1(a2553)) | (~c2_1(a2553)))),
% 0.90/1.14 inference(transitivity,[status(thm)],[1570, 1568])).
% 0.90/1.14 tff(1572,plain,
% 0.90/1.14 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a2553) | (~c0_1(a2553)) | (~c2_1(a2553)) | c0_1(a2556) | (~c3_1(a2556)) | (~c2_1(a2556)) | c1_1(a2549) | c0_1(a2549) | (~c2_1(a2549)))),
% 0.90/1.14 inference(quant_inst,[status(thm)],[])).
% 0.90/1.14 tff(1573,plain,
% 0.90/1.14 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c3_1(a2553) | c0_1(a2549) | c1_1(a2549) | (~ndr1_0) | (~c2_1(a2556)) | (~c3_1(a2556)) | c0_1(a2556) | (~c2_1(a2549)) | (~c0_1(a2553)) | (~c2_1(a2553))),
% 0.90/1.14 inference(modus_ponens,[status(thm)],[1572, 1571])).
% 0.90/1.14 tff(1574,plain,
% 0.90/1.14 (~c2_1(a2553)),
% 0.90/1.14 inference(unit_resolution,[status(thm)],[1573, 90, 618, 617, 851, 1566, 849, 1565, 1564, 1087, 1562])).
% 0.90/1.14 tff(1575,plain,
% 0.90/1.14 (^[V: $i, U: $i] : refl((hskp3 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) <=> (hskp3 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))))),
% 0.90/1.14 inference(bind,[status(th)],[])).
% 0.90/1.14 tff(1576,plain,
% 0.90/1.14 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.90/1.14 inference(quant_intro,[status(thm)],[1575])).
% 0.90/1.14 tff(1577,plain,
% 0.90/1.14 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.90/1.14 inference(rewrite,[status(thm)],[])).
% 0.90/1.14 tff(1578,plain,
% 0.90/1.14 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c2_1(V)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c2_1(V))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c2_1(V))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c2_1(V))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c2_1(V)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c2_1(V))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c2_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V))))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) | c1_1(V)) | hskp3) <=> (((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) | hskp3))), rewrite((((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) | hskp3) <=> (hskp3 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) | c1_1(V)) | hskp3) <=> (hskp3 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))))),
% 0.90/1.14 inference(bind,[status(th)],[])).
% 0.90/1.14 tff(1579,plain,
% 0.90/1.14 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) | c1_1(V)) | hskp3) <=> ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.90/1.14 inference(quant_intro,[status(thm)],[1578])).
% 0.90/1.14 tff(1580,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) | c1_1(V)) | hskp3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause175')).
% 0.90/1.14 tff(1581,plain,
% 0.90/1.14 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.90/1.14 inference(modus_ponens,[status(thm)],[1580, 1579])).
% 0.90/1.14 tff(1582,plain,
% 0.90/1.14 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.90/1.14 inference(modus_ponens,[status(thm)],[1581, 1577])).
% 0.90/1.14 tff(1583,plain,(
% 0.90/1.14 ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.90/1.14 inference(skolemize,[status(sab)],[1582])).
% 0.90/1.14 tff(1584,plain,
% 0.90/1.14 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.90/1.14 inference(modus_ponens,[status(thm)],[1583, 1576])).
% 0.90/1.14 tff(1585,plain,
% 0.90/1.14 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp3 | c0_1(a2549) | c1_1(a2549) | c0_1(a2545) | (~ndr1_0) | (~c2_1(a2545)) | (~c1_1(a2545)) | (~c2_1(a2549)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp3 | c0_1(a2549) | c1_1(a2549) | c0_1(a2545) | (~ndr1_0) | (~c2_1(a2545)) | (~c1_1(a2545)) | (~c2_1(a2549)))),
% 0.90/1.14 inference(rewrite,[status(thm)],[])).
% 0.90/1.14 tff(1586,plain,
% 0.90/1.14 ((hskp3 | (~ndr1_0) | c0_1(a2545) | (~c1_1(a2545)) | (~c2_1(a2545)) | c1_1(a2549) | c0_1(a2549) | (~c2_1(a2549))) <=> (hskp3 | c0_1(a2549) | c1_1(a2549) | c0_1(a2545) | (~ndr1_0) | (~c2_1(a2545)) | (~c1_1(a2545)) | (~c2_1(a2549)))),
% 0.90/1.14 inference(rewrite,[status(thm)],[])).
% 0.90/1.14 tff(1587,plain,
% 0.90/1.14 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp3 | (~ndr1_0) | c0_1(a2545) | (~c1_1(a2545)) | (~c2_1(a2545)) | c1_1(a2549) | c0_1(a2549) | (~c2_1(a2549)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp3 | c0_1(a2549) | c1_1(a2549) | c0_1(a2545) | (~ndr1_0) | (~c2_1(a2545)) | (~c1_1(a2545)) | (~c2_1(a2549))))),
% 0.90/1.14 inference(monotonicity,[status(thm)],[1586])).
% 0.90/1.14 tff(1588,plain,
% 0.90/1.14 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp3 | (~ndr1_0) | c0_1(a2545) | (~c1_1(a2545)) | (~c2_1(a2545)) | c1_1(a2549) | c0_1(a2549) | (~c2_1(a2549)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp3 | c0_1(a2549) | c1_1(a2549) | c0_1(a2545) | (~ndr1_0) | (~c2_1(a2545)) | (~c1_1(a2545)) | (~c2_1(a2549)))),
% 0.90/1.14 inference(transitivity,[status(thm)],[1587, 1585])).
% 0.90/1.14 tff(1589,plain,
% 0.90/1.14 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp3 | (~ndr1_0) | c0_1(a2545) | (~c1_1(a2545)) | (~c2_1(a2545)) | c1_1(a2549) | c0_1(a2549) | (~c2_1(a2549)))),
% 0.90/1.14 inference(quant_inst,[status(thm)],[])).
% 0.90/1.14 tff(1590,plain,
% 0.90/1.14 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp3 | c0_1(a2549) | c1_1(a2549) | c0_1(a2545) | (~ndr1_0) | (~c2_1(a2545)) | (~c1_1(a2545)) | (~c2_1(a2549))),
% 0.90/1.14 inference(modus_ponens,[status(thm)],[1589, 1588])).
% 0.90/1.14 tff(1591,plain,
% 0.90/1.14 (hskp3),
% 0.90/1.14 inference(unit_resolution,[status(thm)],[1590, 90, 1566, 639, 638, 1565, 1564, 637, 1584])).
% 0.90/1.14 tff(1592,plain,
% 0.90/1.14 (~c3_1(a2519)),
% 0.90/1.14 inference(unit_resolution,[status(thm)],[42, 1591])).
% 0.90/1.14 tff(1593,plain,
% 0.90/1.14 (~c2_1(a2519)),
% 0.90/1.14 inference(unit_resolution,[status(thm)],[48, 1591])).
% 0.90/1.14 tff(1594,plain,
% 0.90/1.14 (~c0_1(a2519)),
% 0.90/1.14 inference(unit_resolution,[status(thm)],[54, 1591])).
% 0.90/1.14 tff(1595,plain,
% 0.90/1.14 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp8 | c1_1(a2553) | c0_1(a2519) | c2_1(a2519) | c3_1(a2519) | (~ndr1_0) | (~c0_1(a2553)) | c2_1(a2553))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp8 | c1_1(a2553) | c0_1(a2519) | c2_1(a2519) | c3_1(a2519) | (~ndr1_0) | (~c0_1(a2553)) | c2_1(a2553))),
% 0.90/1.14 inference(rewrite,[status(thm)],[])).
% 0.90/1.14 tff(1596,plain,
% 0.90/1.14 ((hskp8 | (~ndr1_0) | c2_1(a2553) | c1_1(a2553) | (~c0_1(a2553)) | c3_1(a2519) | c0_1(a2519) | c2_1(a2519)) <=> (hskp8 | c1_1(a2553) | c0_1(a2519) | c2_1(a2519) | c3_1(a2519) | (~ndr1_0) | (~c0_1(a2553)) | c2_1(a2553))),
% 0.90/1.14 inference(rewrite,[status(thm)],[])).
% 0.90/1.14 tff(1597,plain,
% 0.90/1.14 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp8 | (~ndr1_0) | c2_1(a2553) | c1_1(a2553) | (~c0_1(a2553)) | c3_1(a2519) | c0_1(a2519) | c2_1(a2519))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp8 | c1_1(a2553) | c0_1(a2519) | c2_1(a2519) | c3_1(a2519) | (~ndr1_0) | (~c0_1(a2553)) | c2_1(a2553)))),
% 0.90/1.14 inference(monotonicity,[status(thm)],[1596])).
% 0.90/1.14 tff(1598,plain,
% 0.90/1.14 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp8 | (~ndr1_0) | c2_1(a2553) | c1_1(a2553) | (~c0_1(a2553)) | c3_1(a2519) | c0_1(a2519) | c2_1(a2519))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp8 | c1_1(a2553) | c0_1(a2519) | c2_1(a2519) | c3_1(a2519) | (~ndr1_0) | (~c0_1(a2553)) | c2_1(a2553))),
% 0.90/1.14 inference(transitivity,[status(thm)],[1597, 1595])).
% 0.90/1.14 tff(1599,plain,
% 0.90/1.14 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp8 | (~ndr1_0) | c2_1(a2553) | c1_1(a2553) | (~c0_1(a2553)) | c3_1(a2519) | c0_1(a2519) | c2_1(a2519))),
% 0.90/1.14 inference(quant_inst,[status(thm)],[])).
% 0.90/1.14 tff(1600,plain,
% 0.90/1.14 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp8 | c1_1(a2553) | c0_1(a2519) | c2_1(a2519) | c3_1(a2519) | (~ndr1_0) | (~c0_1(a2553)) | c2_1(a2553)),
% 0.90/1.14 inference(modus_ponens,[status(thm)],[1599, 1598])).
% 0.90/1.14 tff(1601,plain,
% 0.90/1.14 (hskp8),
% 0.90/1.14 inference(unit_resolution,[status(thm)],[1600, 90, 851, 850, 1594, 1593, 1592, 659, 1574])).
% 0.90/1.14 tff(1602,plain,
% 0.90/1.14 (~c3_1(a2525)),
% 0.90/1.14 inference(unit_resolution,[status(thm)],[607, 1601])).
% 0.90/1.14 tff(1603,plain,
% 0.90/1.14 (c2_1(a2525)),
% 0.90/1.14 inference(unit_resolution,[status(thm)],[1071, 1601])).
% 0.90/1.14 tff(1604,plain,
% 0.90/1.14 (c0_1(a2525)),
% 0.90/1.14 inference(unit_resolution,[status(thm)],[615, 1601])).
% 0.90/1.14 tff(1605,plain,
% 0.90/1.14 ($false),
% 0.90/1.14 inference(unit_resolution,[status(thm)],[1275, 90, 618, 617, 822, 1604, 1603, 824, 1602, 1087, 1567, 1562])).
% 0.90/1.14 tff(1606,plain,((~hskp20) | (~c2_1(a2556)) | (~c3_1(a2556)) | (~c2_1(a2552)) | c1_1(a2552) | c0_1(a2556) | (~c0_1(a2553)) | c1_1(a2553) | (~c1_1(a2545)) | (~c2_1(a2545)) | c0_1(a2545) | c3_1(a2552) | c3_1(a2553)), inference(lemma,lemma(discharge,[]))).
% 0.90/1.14 tff(1607,plain,
% 0.90/1.14 (~hskp20),
% 0.90/1.14 inference(unit_resolution,[status(thm)],[1606, 1496, 1495, 822, 824, 1561, 828, 827, 1556, 1555, 1554, 823, 826])).
% 0.90/1.14 tff(1608,plain,
% 0.90/1.14 (hskp20 | hskp19 | c2_1(a2553)),
% 0.90/1.14 inference(unit_resolution,[status(thm)],[1459, 90, 827, 826, 1319])).
% 0.90/1.14 tff(1609,plain,
% 0.90/1.14 (c2_1(a2553)),
% 0.90/1.14 inference(unit_resolution,[status(thm)],[1608, 1607, 1545])).
% 0.90/1.14 tff(1610,plain,
% 0.90/1.14 (((~![U: $i] : (hskp20 | hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | (hskp20 | hskp19 | c1_1(a2536) | c3_1(a2536) | (~ndr1_0) | c2_1(a2536))) <=> ((~![U: $i] : (hskp20 | hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | hskp20 | hskp19 | c1_1(a2536) | c3_1(a2536) | (~ndr1_0) | c2_1(a2536))),
% 0.90/1.14 inference(rewrite,[status(thm)],[])).
% 0.90/1.14 tff(1611,plain,
% 0.90/1.14 ((hskp20 | hskp19 | (~ndr1_0) | c3_1(a2536) | c2_1(a2536) | c1_1(a2536)) <=> (hskp20 | hskp19 | c1_1(a2536) | c3_1(a2536) | (~ndr1_0) | c2_1(a2536))),
% 0.90/1.14 inference(rewrite,[status(thm)],[])).
% 0.90/1.14 tff(1612,plain,
% 0.90/1.14 (((~![U: $i] : (hskp20 | hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | (hskp20 | hskp19 | (~ndr1_0) | c3_1(a2536) | c2_1(a2536) | c1_1(a2536))) <=> ((~![U: $i] : (hskp20 | hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | (hskp20 | hskp19 | c1_1(a2536) | c3_1(a2536) | (~ndr1_0) | c2_1(a2536)))),
% 0.90/1.14 inference(monotonicity,[status(thm)],[1611])).
% 0.90/1.14 tff(1613,plain,
% 0.90/1.14 (((~![U: $i] : (hskp20 | hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | (hskp20 | hskp19 | (~ndr1_0) | c3_1(a2536) | c2_1(a2536) | c1_1(a2536))) <=> ((~![U: $i] : (hskp20 | hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | hskp20 | hskp19 | c1_1(a2536) | c3_1(a2536) | (~ndr1_0) | c2_1(a2536))),
% 0.90/1.14 inference(transitivity,[status(thm)],[1612, 1610])).
% 0.90/1.14 tff(1614,plain,
% 0.90/1.14 ((~![U: $i] : (hskp20 | hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | (hskp20 | hskp19 | (~ndr1_0) | c3_1(a2536) | c2_1(a2536) | c1_1(a2536))),
% 0.90/1.14 inference(quant_inst,[status(thm)],[])).
% 0.90/1.14 tff(1615,plain,
% 0.90/1.14 ((~![U: $i] : (hskp20 | hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | hskp20 | hskp19 | c1_1(a2536) | c3_1(a2536) | (~ndr1_0) | c2_1(a2536)),
% 0.90/1.14 inference(modus_ponens,[status(thm)],[1614, 1613])).
% 0.90/1.14 tff(1616,plain,
% 0.90/1.14 (hskp20 | c2_1(a2536)),
% 0.90/1.14 inference(unit_resolution,[status(thm)],[1615, 90, 1545, 1559, 1558, 1319])).
% 0.90/1.14 tff(1617,plain,
% 0.90/1.14 (c2_1(a2536)),
% 0.90/1.14 inference(unit_resolution,[status(thm)],[1616, 1607])).
% 0.90/1.14 tff(1618,plain,
% 0.90/1.14 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a2553) | c0_1(a2545) | c0_1(a2536) | c1_1(a2536) | (~ndr1_0) | (~c2_1(a2536)) | (~c2_1(a2545)) | (~c1_1(a2545)) | (~c0_1(a2553)) | (~c2_1(a2553)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a2553) | c0_1(a2545) | c0_1(a2536) | c1_1(a2536) | (~ndr1_0) | (~c2_1(a2536)) | (~c2_1(a2545)) | (~c1_1(a2545)) | (~c0_1(a2553)) | (~c2_1(a2553)))),
% 0.90/1.14 inference(rewrite,[status(thm)],[])).
% 0.90/1.14 tff(1619,plain,
% 0.90/1.14 (((~ndr1_0) | c1_1(a2553) | (~c0_1(a2553)) | (~c2_1(a2553)) | c0_1(a2545) | (~c1_1(a2545)) | (~c2_1(a2545)) | c1_1(a2536) | c0_1(a2536) | (~c2_1(a2536))) <=> (c1_1(a2553) | c0_1(a2545) | c0_1(a2536) | c1_1(a2536) | (~ndr1_0) | (~c2_1(a2536)) | (~c2_1(a2545)) | (~c1_1(a2545)) | (~c0_1(a2553)) | (~c2_1(a2553)))),
% 0.90/1.14 inference(rewrite,[status(thm)],[])).
% 0.90/1.14 tff(1620,plain,
% 0.90/1.14 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a2553) | (~c0_1(a2553)) | (~c2_1(a2553)) | c0_1(a2545) | (~c1_1(a2545)) | (~c2_1(a2545)) | c1_1(a2536) | c0_1(a2536) | (~c2_1(a2536)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a2553) | c0_1(a2545) | c0_1(a2536) | c1_1(a2536) | (~ndr1_0) | (~c2_1(a2536)) | (~c2_1(a2545)) | (~c1_1(a2545)) | (~c0_1(a2553)) | (~c2_1(a2553))))),
% 0.90/1.14 inference(monotonicity,[status(thm)],[1619])).
% 0.90/1.15 tff(1621,plain,
% 0.90/1.15 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a2553) | (~c0_1(a2553)) | (~c2_1(a2553)) | c0_1(a2545) | (~c1_1(a2545)) | (~c2_1(a2545)) | c1_1(a2536) | c0_1(a2536) | (~c2_1(a2536)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a2553) | c0_1(a2545) | c0_1(a2536) | c1_1(a2536) | (~ndr1_0) | (~c2_1(a2536)) | (~c2_1(a2545)) | (~c1_1(a2545)) | (~c0_1(a2553)) | (~c2_1(a2553)))),
% 0.90/1.15 inference(transitivity,[status(thm)],[1620, 1618])).
% 0.90/1.15 tff(1622,plain,
% 0.90/1.15 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a2553) | (~c0_1(a2553)) | (~c2_1(a2553)) | c0_1(a2545) | (~c1_1(a2545)) | (~c2_1(a2545)) | c1_1(a2536) | c0_1(a2536) | (~c2_1(a2536)))),
% 0.90/1.15 inference(quant_inst,[status(thm)],[])).
% 0.90/1.15 tff(1623,plain,
% 0.90/1.15 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a2553) | c0_1(a2545) | c0_1(a2536) | c1_1(a2536) | (~ndr1_0) | (~c2_1(a2536)) | (~c2_1(a2545)) | (~c1_1(a2545)) | (~c0_1(a2553)) | (~c2_1(a2553))),
% 0.90/1.15 inference(modus_ponens,[status(thm)],[1622, 1621])).
% 0.90/1.15 tff(1624,plain,
% 0.90/1.15 ((~c2_1(a2536)) | (~c2_1(a2553))),
% 0.90/1.15 inference(unit_resolution,[status(thm)],[1623, 90, 828, 1556, 1555, 827, 1554, 1560, 1559, 944])).
% 0.90/1.15 tff(1625,plain,
% 0.90/1.15 ($false),
% 0.90/1.15 inference(unit_resolution,[status(thm)],[1624, 1617, 1609])).
% 0.90/1.15 tff(1626,plain,(c0_1(a2518) | (~c2_1(a2552)) | c1_1(a2552) | c3_1(a2552) | (~c0_1(a2551)) | (~c1_1(a2551)) | c2_1(a2551) | (~c1_1(a2526)) | (~c3_1(a2526)) | c0_1(a2526) | c2_1(a2541)), inference(lemma,lemma(discharge,[]))).
% 0.90/1.15 tff(1627,plain,
% 0.90/1.15 (c0_1(a2518)),
% 0.90/1.15 inference(unit_resolution,[status(thm)],[1626, 265, 824, 823, 472, 471, 470, 215, 216, 152, 822])).
% 0.90/1.15 tff(1628,plain,
% 0.90/1.15 (~hskp2),
% 0.90/1.15 inference(unit_resolution,[status(thm)],[898, 1627])).
% 0.90/1.15 tff(1629,plain,
% 0.90/1.15 (hskp29 | hskp2),
% 0.90/1.15 inference(unit_resolution,[status(thm)],[1436, 90, 828, 827, 826, 1430])).
% 0.90/1.15 tff(1630,plain,
% 0.90/1.15 (hskp29),
% 0.90/1.15 inference(unit_resolution,[status(thm)],[1629, 1628])).
% 0.90/1.15 tff(1631,plain,
% 0.90/1.15 (c3_1(a2556)),
% 0.90/1.15 inference(unit_resolution,[status(thm)],[339, 1630])).
% 0.90/1.15 tff(1632,plain,
% 0.90/1.15 (c2_1(a2556)),
% 0.90/1.15 inference(unit_resolution,[status(thm)],[347, 1630])).
% 0.90/1.15 tff(1633,plain,
% 0.90/1.15 (c1_1(a2556)),
% 0.90/1.15 inference(unit_resolution,[status(thm)],[355, 1630])).
% 0.90/1.15 tff(1634,plain,
% 0.90/1.15 (hskp17),
% 0.90/1.15 inference(unit_resolution,[status(thm)],[1540, 1628, 215, 216, 152, 828, 827, 826])).
% 0.90/1.15 tff(1635,plain,
% 0.90/1.15 (~c1_1(a2541)),
% 0.90/1.15 inference(unit_resolution,[status(thm)],[244, 1634])).
% 0.90/1.15 tff(1636,plain,
% 0.90/1.15 ($false),
% 0.90/1.15 inference(unit_resolution,[status(thm)],[1524, 1635, 1633, 1356, 827, 826, 265, 828, 1632, 1631, 216, 152, 215])).
% 0.90/1.15 tff(1637,plain,(c2_1(a2541) | (~c3_1(a2526)) | c0_1(a2526) | (~c1_1(a2526)) | c1_1(a2552) | c3_1(a2552) | (~c0_1(a2551)) | (~c1_1(a2551)) | c2_1(a2551) | (~c2_1(a2552))), inference(lemma,lemma(discharge,[]))).
% 0.90/1.15 tff(1638,plain,
% 0.90/1.15 (c2_1(a2541)),
% 0.90/1.15 inference(unit_resolution,[status(thm)],[1637, 214, 206, 200, 821, 807, 185, 177, 169, 815])).
% 0.90/1.15 tff(1639,plain,
% 0.90/1.15 (~hskp17),
% 0.90/1.15 inference(unit_resolution,[status(thm)],[238, 1638])).
% 0.90/1.15 tff(1640,plain,
% 0.90/1.15 (hskp2),
% 0.90/1.15 inference(unit_resolution,[status(thm)],[1540, 1639, 200, 214, 206, 794, 786, 770])).
% 0.90/1.15 tff(1641,plain,
% 0.90/1.15 (~c3_1(a2518)),
% 0.90/1.15 inference(unit_resolution,[status(thm)],[892, 1640])).
% 0.90/1.15 tff(1642,plain,
% 0.90/1.15 (c1_1(a2518)),
% 0.90/1.15 inference(unit_resolution,[status(thm)],[906, 1640])).
% 0.90/1.15 tff(1643,plain,
% 0.90/1.15 (c2_1(a2518)),
% 0.90/1.15 inference(unit_resolution,[status(thm)],[913, 90, 1639, 200, 214, 1642, 206, 1641, 226])).
% 0.90/1.15 tff(1644,plain,
% 0.90/1.15 (~c0_1(a2518)),
% 0.90/1.15 inference(unit_resolution,[status(thm)],[898, 1640])).
% 0.90/1.15 tff(1645,assumption,(~c3_1(a2551)), introduced(assumption)).
% 0.90/1.15 tff(1646,plain,
% 0.90/1.15 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp17 | c2_1(a2551) | c0_1(a2526) | (~ndr1_0) | (~c3_1(a2526)) | (~c1_1(a2526)) | c3_1(a2551) | (~c1_1(a2551)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp17 | c2_1(a2551) | c0_1(a2526) | (~ndr1_0) | (~c3_1(a2526)) | (~c1_1(a2526)) | c3_1(a2551) | (~c1_1(a2551)))),
% 0.90/1.15 inference(rewrite,[status(thm)],[])).
% 0.90/1.15 tff(1647,plain,
% 0.90/1.15 ((hskp17 | (~ndr1_0) | c3_1(a2551) | c2_1(a2551) | (~c1_1(a2551)) | c0_1(a2526) | (~c3_1(a2526)) | (~c1_1(a2526))) <=> (hskp17 | c2_1(a2551) | c0_1(a2526) | (~ndr1_0) | (~c3_1(a2526)) | (~c1_1(a2526)) | c3_1(a2551) | (~c1_1(a2551)))),
% 0.90/1.15 inference(rewrite,[status(thm)],[])).
% 0.90/1.15 tff(1648,plain,
% 0.90/1.15 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | c3_1(a2551) | c2_1(a2551) | (~c1_1(a2551)) | c0_1(a2526) | (~c3_1(a2526)) | (~c1_1(a2526)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp17 | c2_1(a2551) | c0_1(a2526) | (~ndr1_0) | (~c3_1(a2526)) | (~c1_1(a2526)) | c3_1(a2551) | (~c1_1(a2551))))),
% 0.90/1.15 inference(monotonicity,[status(thm)],[1647])).
% 0.90/1.15 tff(1649,plain,
% 0.90/1.15 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | c3_1(a2551) | c2_1(a2551) | (~c1_1(a2551)) | c0_1(a2526) | (~c3_1(a2526)) | (~c1_1(a2526)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp17 | c2_1(a2551) | c0_1(a2526) | (~ndr1_0) | (~c3_1(a2526)) | (~c1_1(a2526)) | c3_1(a2551) | (~c1_1(a2551)))),
% 0.90/1.15 inference(transitivity,[status(thm)],[1648, 1646])).
% 0.90/1.15 tff(1650,plain,
% 0.90/1.15 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | c3_1(a2551) | c2_1(a2551) | (~c1_1(a2551)) | c0_1(a2526) | (~c3_1(a2526)) | (~c1_1(a2526)))),
% 0.90/1.15 inference(quant_inst,[status(thm)],[])).
% 0.90/1.15 tff(1651,plain,
% 0.90/1.15 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp17 | c2_1(a2551) | c0_1(a2526) | (~ndr1_0) | (~c3_1(a2526)) | (~c1_1(a2526)) | c3_1(a2551) | (~c1_1(a2551))),
% 0.90/1.15 inference(modus_ponens,[status(thm)],[1650, 1649])).
% 0.90/1.15 tff(1652,plain,
% 0.90/1.15 ($false),
% 0.90/1.15 inference(unit_resolution,[status(thm)],[1651, 90, 1530, 471, 215, 216, 470, 152, 226, 1645])).
% 0.90/1.15 tff(1653,plain,(c3_1(a2551) | hskp17 | (~c1_1(a2551)) | (~c1_1(a2526)) | (~c3_1(a2526)) | c2_1(a2551) | c0_1(a2526)), inference(lemma,lemma(discharge,[]))).
% 0.90/1.15 tff(1654,plain,
% 0.90/1.15 (c3_1(a2551)),
% 0.90/1.15 inference(unit_resolution,[status(thm)],[1653, 1639, 177, 200, 214, 169, 206])).
% 0.90/1.15 tff(1655,assumption,(hskp10), introduced(assumption)).
% 0.90/1.15 tff(1656,plain,
% 0.90/1.15 (~c1_1(a2528)),
% 0.90/1.15 inference(unit_resolution,[status(thm)],[1158, 1655])).
% 0.90/1.15 tff(1657,plain,
% 0.90/1.15 (c3_1(a2528)),
% 0.90/1.15 inference(unit_resolution,[status(thm)],[1145, 1655])).
% 0.90/1.15 tff(1658,plain,
% 0.90/1.15 (c2_1(a2528)),
% 0.90/1.15 inference(unit_resolution,[status(thm)],[1165, 90, 851, 1657, 948, 850, 849, 1656, 945, 636, 934])).
% 0.90/1.15 tff(1659,plain,
% 0.90/1.15 (~c0_1(a2528)),
% 0.90/1.15 inference(unit_resolution,[status(thm)],[1137, 1655])).
% 0.90/1.15 tff(1660,plain,
% 0.90/1.15 ((~c2_1(a2528)) | (~c2_1(a2553))),
% 0.90/1.15 inference(unit_resolution,[status(thm)],[1451, 90, 851, 1657, 849, 1659, 1656, 1087])).
% 0.90/1.15 tff(1661,plain,
% 0.90/1.15 (~c2_1(a2553)),
% 0.90/1.15 inference(unit_resolution,[status(thm)],[1660, 1658])).
% 0.90/1.15 tff(1662,assumption,(c3_1(a2551)), introduced(assumption)).
% 0.90/1.15 tff(1663,plain,
% 0.90/1.15 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c2_1(W) | (~c0_1(W)))) | (c1_1(a2553) | c2_1(a2551) | c1_1(a2528) | (~ndr1_0) | (~c3_1(a2528)) | (~c2_1(a2528)) | (~c3_1(a2551)) | (~c0_1(a2551)) | (~c0_1(a2553)) | c2_1(a2553))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c2_1(W) | (~c0_1(W)))) | c1_1(a2553) | c2_1(a2551) | c1_1(a2528) | (~ndr1_0) | (~c3_1(a2528)) | (~c2_1(a2528)) | (~c3_1(a2551)) | (~c0_1(a2551)) | (~c0_1(a2553)) | c2_1(a2553))),
% 0.90/1.15 inference(rewrite,[status(thm)],[])).
% 0.90/1.15 tff(1664,plain,
% 0.90/1.15 (((~ndr1_0) | c2_1(a2551) | (~c3_1(a2551)) | (~c0_1(a2551)) | c1_1(a2528) | (~c3_1(a2528)) | (~c2_1(a2528)) | c1_1(a2553) | c2_1(a2553) | (~c0_1(a2553))) <=> (c1_1(a2553) | c2_1(a2551) | c1_1(a2528) | (~ndr1_0) | (~c3_1(a2528)) | (~c2_1(a2528)) | (~c3_1(a2551)) | (~c0_1(a2551)) | (~c0_1(a2553)) | c2_1(a2553))),
% 0.90/1.15 inference(rewrite,[status(thm)],[])).
% 0.90/1.15 tff(1665,plain,
% 0.90/1.15 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c2_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a2551) | (~c3_1(a2551)) | (~c0_1(a2551)) | c1_1(a2528) | (~c3_1(a2528)) | (~c2_1(a2528)) | c1_1(a2553) | c2_1(a2553) | (~c0_1(a2553)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c2_1(W) | (~c0_1(W)))) | (c1_1(a2553) | c2_1(a2551) | c1_1(a2528) | (~ndr1_0) | (~c3_1(a2528)) | (~c2_1(a2528)) | (~c3_1(a2551)) | (~c0_1(a2551)) | (~c0_1(a2553)) | c2_1(a2553)))),
% 0.90/1.15 inference(monotonicity,[status(thm)],[1664])).
% 0.90/1.15 tff(1666,plain,
% 0.90/1.15 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c2_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a2551) | (~c3_1(a2551)) | (~c0_1(a2551)) | c1_1(a2528) | (~c3_1(a2528)) | (~c2_1(a2528)) | c1_1(a2553) | c2_1(a2553) | (~c0_1(a2553)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c2_1(W) | (~c0_1(W)))) | c1_1(a2553) | c2_1(a2551) | c1_1(a2528) | (~ndr1_0) | (~c3_1(a2528)) | (~c2_1(a2528)) | (~c3_1(a2551)) | (~c0_1(a2551)) | (~c0_1(a2553)) | c2_1(a2553))),
% 0.90/1.15 inference(transitivity,[status(thm)],[1665, 1663])).
% 0.90/1.15 tff(1667,plain,
% 0.90/1.15 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c2_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a2551) | (~c3_1(a2551)) | (~c0_1(a2551)) | c1_1(a2528) | (~c3_1(a2528)) | (~c2_1(a2528)) | c1_1(a2553) | c2_1(a2553) | (~c0_1(a2553)))),
% 0.90/1.15 inference(quant_inst,[status(thm)],[])).
% 0.90/1.15 tff(1668,plain,
% 0.90/1.15 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c2_1(W) | (~c0_1(W)))) | c1_1(a2553) | c2_1(a2551) | c1_1(a2528) | (~ndr1_0) | (~c3_1(a2528)) | (~c2_1(a2528)) | (~c3_1(a2551)) | (~c0_1(a2551)) | (~c0_1(a2553)) | c2_1(a2553)),
% 0.90/1.15 inference(modus_ponens,[status(thm)],[1667, 1666])).
% 0.90/1.15 tff(1669,plain,
% 0.90/1.15 ((~c2_1(a2528)) | c2_1(a2553)),
% 0.90/1.15 inference(unit_resolution,[status(thm)],[1668, 90, 851, 472, 1657, 850, 470, 1656, 1402, 1662])).
% 0.90/1.15 tff(1670,plain,
% 0.90/1.15 ($false),
% 0.90/1.15 inference(unit_resolution,[status(thm)],[1669, 1661, 1658])).
% 0.90/1.15 tff(1671,plain,((~hskp10) | (~c0_1(a2553)) | (~c0_1(a2551)) | c1_1(a2553) | c2_1(a2551) | (~c3_1(a2551)) | c3_1(a2553) | (~c1_1(a2518)) | c0_1(a2518) | (~c2_1(a2518))), inference(lemma,lemma(discharge,[]))).
% 0.90/1.15 tff(1672,plain,
% 0.90/1.15 (~hskp10),
% 0.90/1.15 inference(unit_resolution,[status(thm)],[1671, 794, 185, 786, 169, 1654, 770, 1642, 1644, 1643])).
% 0.90/1.15 tff(1673,plain,
% 0.90/1.15 (hskp29),
% 0.90/1.15 inference(unit_resolution,[status(thm)],[1376, 1672, 185, 177, 794, 200, 214, 786, 206, 770])).
% 0.90/1.15 tff(1674,plain,
% 0.90/1.15 (c2_1(a2556)),
% 0.90/1.15 inference(unit_resolution,[status(thm)],[347, 1673])).
% 0.90/1.15 tff(1675,plain,
% 0.90/1.15 (hskp10 | c2_1(a2553)),
% 0.90/1.15 inference(unit_resolution,[status(thm)],[1362, 90, 794, 185, 177, 770, 1189, 1654])).
% 0.90/1.15 tff(1676,plain,
% 0.90/1.15 (c2_1(a2553)),
% 0.90/1.15 inference(unit_resolution,[status(thm)],[1675, 1672])).
% 0.90/1.15 tff(1677,plain,
% 0.90/1.15 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | (c1_1(a2553) | c0_1(a2526) | (~ndr1_0) | (~c3_1(a2526)) | c2_1(a2526) | (~c3_1(a2551)) | (~c0_1(a2551)) | (~c1_1(a2551)) | (~c0_1(a2553)) | (~c2_1(a2553)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a2553) | c0_1(a2526) | (~ndr1_0) | (~c3_1(a2526)) | c2_1(a2526) | (~c3_1(a2551)) | (~c0_1(a2551)) | (~c1_1(a2551)) | (~c0_1(a2553)) | (~c2_1(a2553)))),
% 0.90/1.15 inference(rewrite,[status(thm)],[])).
% 0.90/1.15 tff(1678,plain,
% 0.90/1.15 (((~ndr1_0) | (~c3_1(a2551)) | (~c1_1(a2551)) | (~c0_1(a2551)) | c1_1(a2553) | (~c0_1(a2553)) | (~c2_1(a2553)) | c0_1(a2526) | c2_1(a2526) | (~c3_1(a2526))) <=> (c1_1(a2553) | c0_1(a2526) | (~ndr1_0) | (~c3_1(a2526)) | c2_1(a2526) | (~c3_1(a2551)) | (~c0_1(a2551)) | (~c1_1(a2551)) | (~c0_1(a2553)) | (~c2_1(a2553)))),
% 0.90/1.15 inference(rewrite,[status(thm)],[])).
% 0.90/1.15 tff(1679,plain,
% 0.90/1.15 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a2551)) | (~c1_1(a2551)) | (~c0_1(a2551)) | c1_1(a2553) | (~c0_1(a2553)) | (~c2_1(a2553)) | c0_1(a2526) | c2_1(a2526) | (~c3_1(a2526)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | (c1_1(a2553) | c0_1(a2526) | (~ndr1_0) | (~c3_1(a2526)) | c2_1(a2526) | (~c3_1(a2551)) | (~c0_1(a2551)) | (~c1_1(a2551)) | (~c0_1(a2553)) | (~c2_1(a2553))))),
% 0.90/1.15 inference(monotonicity,[status(thm)],[1678])).
% 0.90/1.15 tff(1680,plain,
% 0.90/1.15 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a2551)) | (~c1_1(a2551)) | (~c0_1(a2551)) | c1_1(a2553) | (~c0_1(a2553)) | (~c2_1(a2553)) | c0_1(a2526) | c2_1(a2526) | (~c3_1(a2526)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a2553) | c0_1(a2526) | (~ndr1_0) | (~c3_1(a2526)) | c2_1(a2526) | (~c3_1(a2551)) | (~c0_1(a2551)) | (~c1_1(a2551)) | (~c0_1(a2553)) | (~c2_1(a2553)))),
% 0.90/1.15 inference(transitivity,[status(thm)],[1679, 1677])).
% 0.90/1.15 tff(1681,plain,
% 0.90/1.15 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a2551)) | (~c1_1(a2551)) | (~c0_1(a2551)) | c1_1(a2553) | (~c0_1(a2553)) | (~c2_1(a2553)) | c0_1(a2526) | c2_1(a2526) | (~c3_1(a2526)))),
% 0.90/1.15 inference(quant_inst,[status(thm)],[])).
% 0.90/1.15 tff(1682,plain,
% 0.90/1.15 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a2553) | c0_1(a2526) | (~ndr1_0) | (~c3_1(a2526)) | c2_1(a2526) | (~c3_1(a2551)) | (~c0_1(a2551)) | (~c1_1(a2551)) | (~c0_1(a2553)) | (~c2_1(a2553))),
% 0.90/1.15 inference(modus_ponens,[status(thm)],[1681, 1680])).
% 0.90/1.15 tff(1683,plain,
% 0.90/1.15 (c2_1(a2526) | (~c2_1(a2553))),
% 0.90/1.15 inference(unit_resolution,[status(thm)],[1682, 90, 794, 185, 177, 214, 786, 206, 709, 1654])).
% 0.90/1.15 tff(1684,plain,
% 0.90/1.15 (c2_1(a2526)),
% 0.90/1.15 inference(unit_resolution,[status(thm)],[1683, 1676])).
% 0.90/1.15 tff(1685,plain,
% 0.90/1.15 (((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp18 | c2_1(a2551) | (~ndr1_0) | (~c3_1(a2526)) | (~c2_1(a2526)) | (~c1_1(a2526)) | (~c3_1(a2551)) | (~c1_1(a2551)))) <=> ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp18 | c2_1(a2551) | (~ndr1_0) | (~c3_1(a2526)) | (~c2_1(a2526)) | (~c1_1(a2526)) | (~c3_1(a2551)) | (~c1_1(a2551)))),
% 0.90/1.15 inference(rewrite,[status(thm)],[])).
% 0.90/1.15 tff(1686,plain,
% 0.90/1.15 ((hskp18 | (~ndr1_0) | (~c3_1(a2526)) | (~c1_1(a2526)) | (~c2_1(a2526)) | c2_1(a2551) | (~c3_1(a2551)) | (~c1_1(a2551))) <=> (hskp18 | c2_1(a2551) | (~ndr1_0) | (~c3_1(a2526)) | (~c2_1(a2526)) | (~c1_1(a2526)) | (~c3_1(a2551)) | (~c1_1(a2551)))),
% 0.90/1.15 inference(rewrite,[status(thm)],[])).
% 0.90/1.15 tff(1687,plain,
% 0.90/1.15 (((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp18 | (~ndr1_0) | (~c3_1(a2526)) | (~c1_1(a2526)) | (~c2_1(a2526)) | c2_1(a2551) | (~c3_1(a2551)) | (~c1_1(a2551)))) <=> ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp18 | c2_1(a2551) | (~ndr1_0) | (~c3_1(a2526)) | (~c2_1(a2526)) | (~c1_1(a2526)) | (~c3_1(a2551)) | (~c1_1(a2551))))),
% 0.90/1.15 inference(monotonicity,[status(thm)],[1686])).
% 0.90/1.15 tff(1688,plain,
% 0.90/1.15 (((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp18 | (~ndr1_0) | (~c3_1(a2526)) | (~c1_1(a2526)) | (~c2_1(a2526)) | c2_1(a2551) | (~c3_1(a2551)) | (~c1_1(a2551)))) <=> ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp18 | c2_1(a2551) | (~ndr1_0) | (~c3_1(a2526)) | (~c2_1(a2526)) | (~c1_1(a2526)) | (~c3_1(a2551)) | (~c1_1(a2551)))),
% 0.90/1.15 inference(transitivity,[status(thm)],[1687, 1685])).
% 0.90/1.15 tff(1689,plain,
% 0.90/1.15 ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp18 | (~ndr1_0) | (~c3_1(a2526)) | (~c1_1(a2526)) | (~c2_1(a2526)) | c2_1(a2551) | (~c3_1(a2551)) | (~c1_1(a2551)))),
% 0.90/1.15 inference(quant_inst,[status(thm)],[])).
% 0.90/1.15 tff(1690,plain,
% 0.90/1.15 ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp18 | c2_1(a2551) | (~ndr1_0) | (~c3_1(a2526)) | (~c2_1(a2526)) | (~c1_1(a2526)) | (~c3_1(a2551)) | (~c1_1(a2551))),
% 0.90/1.15 inference(modus_ponens,[status(thm)],[1689, 1688])).
% 0.90/1.15 tff(1691,plain,
% 0.90/1.15 (hskp18 | (~c2_1(a2526)) | (~c3_1(a2551))),
% 0.90/1.15 inference(unit_resolution,[status(thm)],[1690, 90, 177, 200, 214, 169, 572])).
% 0.90/1.15 tff(1692,plain,
% 0.90/1.15 (hskp18),
% 0.90/1.15 inference(unit_resolution,[status(thm)],[1691, 1684, 1654])).
% 0.90/1.15 tff(1693,plain,
% 0.90/1.15 (c2_1(a2545)),
% 0.90/1.15 inference(unit_resolution,[status(thm)],[592, 1692])).
% 0.90/1.15 tff(1694,plain,
% 0.90/1.15 (c1_1(a2545)),
% 0.90/1.15 inference(unit_resolution,[status(thm)],[600, 1692])).
% 0.90/1.15 tff(1695,plain,
% 0.90/1.15 (hskp14),
% 0.90/1.15 inference(unit_resolution,[status(thm)],[920, 90, 185, 177, 169, 1644, 1641, 469, 1643])).
% 0.90/1.15 tff(1696,plain,
% 0.90/1.15 (~c1_1(a2536)),
% 0.90/1.15 inference(unit_resolution,[status(thm)],[490, 1695])).
% 0.90/1.15 tff(1697,plain,
% 0.90/1.15 (~c0_1(a2536)),
% 0.90/1.15 inference(unit_resolution,[status(thm)],[496, 1695])).
% 0.90/1.15 tff(1698,plain,
% 0.90/1.15 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a2553) | c0_1(a2536) | c1_1(a2536) | c0_1(a2518) | (~ndr1_0) | (~c1_1(a2518)) | (~c2_1(a2518)) | (~c2_1(a2536)) | (~c0_1(a2553)) | (~c2_1(a2553)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a2553) | c0_1(a2536) | c1_1(a2536) | c0_1(a2518) | (~ndr1_0) | (~c1_1(a2518)) | (~c2_1(a2518)) | (~c2_1(a2536)) | (~c0_1(a2553)) | (~c2_1(a2553)))),
% 0.90/1.15 inference(rewrite,[status(thm)],[])).
% 0.90/1.15 tff(1699,plain,
% 0.90/1.15 (((~ndr1_0) | c1_1(a2553) | (~c0_1(a2553)) | (~c2_1(a2553)) | c0_1(a2518) | (~c1_1(a2518)) | (~c2_1(a2518)) | c1_1(a2536) | c0_1(a2536) | (~c2_1(a2536))) <=> (c1_1(a2553) | c0_1(a2536) | c1_1(a2536) | c0_1(a2518) | (~ndr1_0) | (~c1_1(a2518)) | (~c2_1(a2518)) | (~c2_1(a2536)) | (~c0_1(a2553)) | (~c2_1(a2553)))),
% 0.90/1.15 inference(rewrite,[status(thm)],[])).
% 0.90/1.15 tff(1700,plain,
% 0.90/1.15 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a2553) | (~c0_1(a2553)) | (~c2_1(a2553)) | c0_1(a2518) | (~c1_1(a2518)) | (~c2_1(a2518)) | c1_1(a2536) | c0_1(a2536) | (~c2_1(a2536)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a2553) | c0_1(a2536) | c1_1(a2536) | c0_1(a2518) | (~ndr1_0) | (~c1_1(a2518)) | (~c2_1(a2518)) | (~c2_1(a2536)) | (~c0_1(a2553)) | (~c2_1(a2553))))),
% 0.90/1.15 inference(monotonicity,[status(thm)],[1699])).
% 0.90/1.15 tff(1701,plain,
% 0.90/1.15 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a2553) | (~c0_1(a2553)) | (~c2_1(a2553)) | c0_1(a2518) | (~c1_1(a2518)) | (~c2_1(a2518)) | c1_1(a2536) | c0_1(a2536) | (~c2_1(a2536)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a2553) | c0_1(a2536) | c1_1(a2536) | c0_1(a2518) | (~ndr1_0) | (~c1_1(a2518)) | (~c2_1(a2518)) | (~c2_1(a2536)) | (~c0_1(a2553)) | (~c2_1(a2553)))),
% 0.90/1.15 inference(transitivity,[status(thm)],[1700, 1698])).
% 0.90/1.15 tff(1702,plain,
% 0.90/1.15 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a2553) | (~c0_1(a2553)) | (~c2_1(a2553)) | c0_1(a2518) | (~c1_1(a2518)) | (~c2_1(a2518)) | c1_1(a2536) | c0_1(a2536) | (~c2_1(a2536)))),
% 0.90/1.15 inference(quant_inst,[status(thm)],[])).
% 0.90/1.15 tff(1703,plain,
% 0.90/1.15 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a2553) | c0_1(a2536) | c1_1(a2536) | c0_1(a2518) | (~ndr1_0) | (~c1_1(a2518)) | (~c2_1(a2518)) | (~c2_1(a2536)) | (~c0_1(a2553)) | (~c2_1(a2553))),
% 0.90/1.15 inference(modus_ponens,[status(thm)],[1702, 1701])).
% 0.90/1.15 tff(1704,plain,
% 0.90/1.15 ((~c2_1(a2536)) | (~c2_1(a2553))),
% 0.90/1.15 inference(unit_resolution,[status(thm)],[1703, 90, 794, 1642, 786, 1697, 1696, 1644, 944, 1643])).
% 0.90/1.15 tff(1705,plain,
% 0.90/1.15 (~c2_1(a2536)),
% 0.90/1.15 inference(unit_resolution,[status(thm)],[1704, 1676])).
% 0.90/1.15 tff(1706,plain,
% 0.90/1.15 (~c3_1(a2536)),
% 0.90/1.15 inference(unit_resolution,[status(thm)],[484, 1695])).
% 0.90/1.15 tff(1707,plain,
% 0.90/1.15 (~hskp19),
% 0.90/1.15 inference(unit_resolution,[status(thm)],[1308, 1643, 821, 807, 1644, 1641, 815])).
% 0.90/1.15 tff(1708,plain,
% 0.90/1.15 (hskp20 | c2_1(a2536)),
% 0.90/1.15 inference(unit_resolution,[status(thm)],[1615, 90, 1707, 1696, 1706, 1319])).
% 0.90/1.15 tff(1709,plain,
% 0.90/1.15 (hskp20),
% 0.90/1.15 inference(unit_resolution,[status(thm)],[1708, 1705])).
% 0.90/1.15 tff(1710,plain,
% 0.90/1.15 (c3_1(a2556)),
% 0.90/1.15 inference(unit_resolution,[status(thm)],[339, 1673])).
% 0.90/1.15 tff(1711,plain,
% 0.90/1.15 (~c0_1(a2545)),
% 0.90/1.15 inference(unit_resolution,[status(thm)],[584, 1692])).
% 0.90/1.15 tff(1712,plain,
% 0.90/1.15 (c0_1(a2556)),
% 0.90/1.15 inference(unit_resolution,[status(thm)],[1606, 1711, 1710, 815, 821, 1709, 794, 786, 1694, 1693, 1674, 807, 770])).
% 0.90/1.15 tff(1713,plain,
% 0.90/1.15 (c1_1(a2556)),
% 0.90/1.15 inference(unit_resolution,[status(thm)],[355, 1673])).
% 0.90/1.15 tff(1714,plain,
% 0.90/1.15 ($false),
% 0.90/1.15 inference(unit_resolution,[status(thm)],[1267, 90, 1713, 1674, 1642, 1697, 1696, 1706, 1644, 1641, 459, 1712])).
% 0.90/1.15 tff(1715,plain,((~hskp21) | hskp30), inference(lemma,lemma(discharge,[]))).
% 0.90/1.15 tff(1716,plain,
% 0.90/1.15 (~hskp21),
% 0.90/1.15 inference(unit_resolution,[status(thm)],[1715, 151])).
% 0.90/1.15 tff(1717,plain,
% 0.90/1.15 (hskp26),
% 0.90/1.15 inference(unit_resolution,[status(thm)],[88, 1716, 151])).
% 0.90/1.15 tff(1718,plain,
% 0.90/1.15 (((~hskp26) | c0_1(a2601)) <=> ((~hskp26) | c0_1(a2601))),
% 0.90/1.15 inference(rewrite,[status(thm)],[])).
% 0.90/1.15 tff(1719,axiom,((~hskp26) | c0_1(a2601)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause54')).
% 0.90/1.15 tff(1720,plain,
% 0.90/1.15 ((~hskp26) | c0_1(a2601)),
% 0.90/1.15 inference(modus_ponens,[status(thm)],[1719, 1718])).
% 0.90/1.15 tff(1721,plain,
% 0.90/1.15 ((~hskp26) | c0_1(a2601)),
% 0.90/1.15 inference(modus_ponens,[status(thm)],[1720, 1718])).
% 0.90/1.15 tff(1722,plain,
% 0.90/1.15 ((~hskp26) | c0_1(a2601)),
% 0.90/1.15 inference(modus_ponens,[status(thm)],[1721, 1718])).
% 0.90/1.15 tff(1723,plain,
% 0.90/1.15 ((~hskp26) | c0_1(a2601)),
% 0.90/1.15 inference(modus_ponens,[status(thm)],[1722, 1718])).
% 0.90/1.15 tff(1724,plain,
% 0.90/1.15 ((~hskp26) | c0_1(a2601)),
% 0.90/1.15 inference(modus_ponens,[status(thm)],[1723, 1718])).
% 0.90/1.15 tff(1725,plain,
% 0.90/1.15 (c0_1(a2601)),
% 0.90/1.15 inference(unit_resolution,[status(thm)],[1724, 1717])).
% 0.90/1.15 tff(1726,plain,
% 0.90/1.15 (((~hskp26) | c3_1(a2601)) <=> ((~hskp26) | c3_1(a2601))),
% 0.90/1.15 inference(rewrite,[status(thm)],[])).
% 0.90/1.15 tff(1727,axiom,((~hskp26) | c3_1(a2601)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause55')).
% 0.90/1.15 tff(1728,plain,
% 0.90/1.15 ((~hskp26) | c3_1(a2601)),
% 0.90/1.15 inference(modus_ponens,[status(thm)],[1727, 1726])).
% 0.90/1.15 tff(1729,plain,
% 0.90/1.15 ((~hskp26) | c3_1(a2601)),
% 0.90/1.15 inference(modus_ponens,[status(thm)],[1728, 1726])).
% 0.90/1.15 tff(1730,plain,
% 0.90/1.15 ((~hskp26) | c3_1(a2601)),
% 0.90/1.15 inference(modus_ponens,[status(thm)],[1729, 1726])).
% 0.90/1.15 tff(1731,plain,
% 0.90/1.15 ((~hskp26) | c3_1(a2601)),
% 0.90/1.15 inference(modus_ponens,[status(thm)],[1730, 1726])).
% 0.90/1.15 tff(1732,plain,
% 0.90/1.15 ((~hskp26) | c3_1(a2601)),
% 0.90/1.15 inference(modus_ponens,[status(thm)],[1731, 1726])).
% 0.90/1.15 tff(1733,plain,
% 0.90/1.15 (c3_1(a2601)),
% 0.90/1.15 inference(unit_resolution,[status(thm)],[1732, 1717])).
% 0.90/1.15 tff(1734,plain,
% 0.90/1.15 (((~hskp26) | (~c2_1(a2601))) <=> ((~hskp26) | (~c2_1(a2601)))),
% 0.90/1.15 inference(rewrite,[status(thm)],[])).
% 0.90/1.15 tff(1735,plain,
% 0.90/1.15 (((~c2_1(a2601)) | (~hskp26)) <=> ((~hskp26) | (~c2_1(a2601)))),
% 0.90/1.15 inference(rewrite,[status(thm)],[])).
% 0.90/1.15 tff(1736,axiom,((~c2_1(a2601)) | (~hskp26)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause91')).
% 0.90/1.15 tff(1737,plain,
% 0.90/1.15 ((~hskp26) | (~c2_1(a2601))),
% 0.90/1.15 inference(modus_ponens,[status(thm)],[1736, 1735])).
% 0.90/1.15 tff(1738,plain,
% 0.90/1.15 ((~hskp26) | (~c2_1(a2601))),
% 0.90/1.15 inference(modus_ponens,[status(thm)],[1737, 1734])).
% 0.90/1.15 tff(1739,plain,
% 0.90/1.15 (~c2_1(a2601)),
% 0.90/1.15 inference(unit_resolution,[status(thm)],[1738, 1717])).
% 0.90/1.15 tff(1740,assumption,(~c3_1(a2526)), introduced(assumption)).
% 0.90/1.15 tff(1741,plain,
% 0.90/1.15 (~hskp9),
% 0.90/1.15 inference(unit_resolution,[status(thm)],[213, 1740])).
% 0.90/1.15 tff(1742,plain,
% 0.90/1.15 (((~![U: $i] : (hskp30 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp30 | hskp9 | c2_1(a2601) | (~ndr1_0) | (~c0_1(a2601)) | (~c1_1(a2601)))) <=> ((~![U: $i] : (hskp30 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp30 | hskp9 | c2_1(a2601) | (~ndr1_0) | (~c0_1(a2601)) | (~c1_1(a2601)))),
% 0.90/1.15 inference(rewrite,[status(thm)],[])).
% 0.90/1.15 tff(1743,plain,
% 0.90/1.15 ((hskp30 | hskp9 | (~ndr1_0) | c2_1(a2601) | (~c1_1(a2601)) | (~c0_1(a2601))) <=> (hskp30 | hskp9 | c2_1(a2601) | (~ndr1_0) | (~c0_1(a2601)) | (~c1_1(a2601)))),
% 0.90/1.15 inference(rewrite,[status(thm)],[])).
% 0.90/1.15 tff(1744,plain,
% 0.90/1.15 (((~![U: $i] : (hskp30 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp30 | hskp9 | (~ndr1_0) | c2_1(a2601) | (~c1_1(a2601)) | (~c0_1(a2601)))) <=> ((~![U: $i] : (hskp30 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp30 | hskp9 | c2_1(a2601) | (~ndr1_0) | (~c0_1(a2601)) | (~c1_1(a2601))))),
% 0.90/1.15 inference(monotonicity,[status(thm)],[1743])).
% 0.90/1.15 tff(1745,plain,
% 0.90/1.15 (((~![U: $i] : (hskp30 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp30 | hskp9 | (~ndr1_0) | c2_1(a2601) | (~c1_1(a2601)) | (~c0_1(a2601)))) <=> ((~![U: $i] : (hskp30 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp30 | hskp9 | c2_1(a2601) | (~ndr1_0) | (~c0_1(a2601)) | (~c1_1(a2601)))),
% 0.90/1.15 inference(transitivity,[status(thm)],[1744, 1742])).
% 0.90/1.15 tff(1746,plain,
% 0.90/1.15 ((~![U: $i] : (hskp30 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp30 | hskp9 | (~ndr1_0) | c2_1(a2601) | (~c1_1(a2601)) | (~c0_1(a2601)))),
% 0.90/1.15 inference(quant_inst,[status(thm)],[])).
% 0.90/1.15 tff(1747,plain,
% 0.90/1.15 ((~![U: $i] : (hskp30 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp30 | hskp9 | c2_1(a2601) | (~ndr1_0) | (~c0_1(a2601)) | (~c1_1(a2601))),
% 0.90/1.15 inference(modus_ponens,[status(thm)],[1746, 1745])).
% 0.90/1.15 tff(1748,plain,
% 0.90/1.15 (hskp9 | (~c1_1(a2601))),
% 0.90/1.15 inference(unit_resolution,[status(thm)],[1747, 90, 151, 1725, 1739, 162])).
% 0.90/1.15 tff(1749,plain,
% 0.90/1.15 (~c1_1(a2601)),
% 0.90/1.15 inference(unit_resolution,[status(thm)],[1748, 1741])).
% 0.90/1.15 tff(1750,plain,
% 0.90/1.15 (^[U: $i] : refl((hskp22 | hskp21 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) <=> (hskp22 | hskp21 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))))),
% 0.90/1.15 inference(bind,[status(th)],[])).
% 0.90/1.15 tff(1751,plain,
% 0.90/1.15 (![U: $i] : (hskp22 | hskp21 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp22 | hskp21 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 0.90/1.15 inference(quant_intro,[status(thm)],[1750])).
% 0.90/1.15 tff(1752,plain,
% 0.90/1.15 (![U: $i] : (hskp22 | hskp21 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp22 | hskp21 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 0.90/1.15 inference(rewrite,[status(thm)],[])).
% 0.90/1.15 tff(1753,plain,
% 0.90/1.15 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c0_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) <=> (((~ndr1_0) | (~c0_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U))))), (((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))), (((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))))), ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp21) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) | hskp21))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) | hskp21) <=> (hskp21 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))), ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp21) <=> (hskp21 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))))), (((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp21) | hskp22) <=> ((hskp21 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) | hskp22))), rewrite(((hskp21 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) | hskp22) <=> (hskp22 | hskp21 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))), (((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp21) | hskp22) <=> (hskp22 | hskp21 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))))),
% 0.90/1.15 inference(bind,[status(th)],[])).
% 0.90/1.15 tff(1754,plain,
% 0.90/1.15 (![U: $i] : ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp21) | hskp22) <=> ![U: $i] : (hskp22 | hskp21 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 0.90/1.15 inference(quant_intro,[status(thm)],[1753])).
% 0.90/1.15 tff(1755,axiom,(![U: $i] : ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp21) | hskp22)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause141')).
% 0.90/1.15 tff(1756,plain,
% 0.90/1.15 (![U: $i] : (hskp22 | hskp21 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 0.90/1.15 inference(modus_ponens,[status(thm)],[1755, 1754])).
% 0.90/1.15 tff(1757,plain,
% 0.90/1.15 (![U: $i] : (hskp22 | hskp21 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 0.90/1.15 inference(modus_ponens,[status(thm)],[1756, 1752])).
% 0.90/1.15 tff(1758,plain,(
% 0.90/1.15 ![U: $i] : (hskp22 | hskp21 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 0.90/1.15 inference(skolemize,[status(sab)],[1757])).
% 0.90/1.15 tff(1759,plain,
% 0.90/1.15 (![U: $i] : (hskp22 | hskp21 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 0.90/1.15 inference(modus_ponens,[status(thm)],[1758, 1751])).
% 0.90/1.15 tff(1760,plain,
% 0.90/1.15 (((~![U: $i] : (hskp22 | hskp21 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp22 | hskp21 | c2_1(a2601) | (~ndr1_0) | (~c0_1(a2601)) | c1_1(a2601))) <=> ((~![U: $i] : (hskp22 | hskp21 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp22 | hskp21 | c2_1(a2601) | (~ndr1_0) | (~c0_1(a2601)) | c1_1(a2601))),
% 0.90/1.15 inference(rewrite,[status(thm)],[])).
% 0.90/1.15 tff(1761,plain,
% 0.90/1.15 ((hskp22 | hskp21 | (~ndr1_0) | c2_1(a2601) | c1_1(a2601) | (~c0_1(a2601))) <=> (hskp22 | hskp21 | c2_1(a2601) | (~ndr1_0) | (~c0_1(a2601)) | c1_1(a2601))),
% 0.90/1.15 inference(rewrite,[status(thm)],[])).
% 0.90/1.15 tff(1762,plain,
% 0.90/1.15 (((~![U: $i] : (hskp22 | hskp21 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp22 | hskp21 | (~ndr1_0) | c2_1(a2601) | c1_1(a2601) | (~c0_1(a2601)))) <=> ((~![U: $i] : (hskp22 | hskp21 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp22 | hskp21 | c2_1(a2601) | (~ndr1_0) | (~c0_1(a2601)) | c1_1(a2601)))),
% 0.90/1.15 inference(monotonicity,[status(thm)],[1761])).
% 0.90/1.15 tff(1763,plain,
% 0.90/1.15 (((~![U: $i] : (hskp22 | hskp21 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp22 | hskp21 | (~ndr1_0) | c2_1(a2601) | c1_1(a2601) | (~c0_1(a2601)))) <=> ((~![U: $i] : (hskp22 | hskp21 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp22 | hskp21 | c2_1(a2601) | (~ndr1_0) | (~c0_1(a2601)) | c1_1(a2601))),
% 0.90/1.15 inference(transitivity,[status(thm)],[1762, 1760])).
% 0.90/1.15 tff(1764,plain,
% 0.90/1.15 ((~![U: $i] : (hskp22 | hskp21 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp22 | hskp21 | (~ndr1_0) | c2_1(a2601) | c1_1(a2601) | (~c0_1(a2601)))),
% 0.90/1.16 inference(quant_inst,[status(thm)],[])).
% 0.90/1.16 tff(1765,plain,
% 0.90/1.16 ((~![U: $i] : (hskp22 | hskp21 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp22 | hskp21 | c2_1(a2601) | (~ndr1_0) | (~c0_1(a2601)) | c1_1(a2601)),
% 0.90/1.16 inference(modus_ponens,[status(thm)],[1764, 1763])).
% 0.90/1.16 tff(1766,plain,
% 0.90/1.16 (hskp22 | c1_1(a2601)),
% 0.90/1.16 inference(unit_resolution,[status(thm)],[1765, 90, 1716, 1725, 1739, 1759])).
% 0.90/1.16 tff(1767,plain,
% 0.90/1.16 (hskp22),
% 0.90/1.16 inference(unit_resolution,[status(thm)],[1766, 1749])).
% 0.90/1.16 tff(1768,plain,
% 0.90/1.16 (~c3_1(a2552)),
% 0.90/1.16 inference(unit_resolution,[status(thm)],[806, 1767])).
% 0.90/1.16 tff(1769,plain,
% 0.90/1.16 (~c1_1(a2552)),
% 0.90/1.16 inference(unit_resolution,[status(thm)],[820, 1767])).
% 0.90/1.16 tff(1770,plain,
% 0.90/1.16 (c2_1(a2552)),
% 0.90/1.16 inference(unit_resolution,[status(thm)],[814, 1767])).
% 0.90/1.16 tff(1771,plain,
% 0.90/1.16 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a2552) | c3_1(a2552) | (~ndr1_0) | c0_1(a2552) | (~c2_1(a2552)) | (~c3_1(a2601)) | (~c0_1(a2601)) | c1_1(a2601))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a2552) | c3_1(a2552) | (~ndr1_0) | c0_1(a2552) | (~c2_1(a2552)) | (~c3_1(a2601)) | (~c0_1(a2601)) | c1_1(a2601))),
% 0.90/1.16 inference(rewrite,[status(thm)],[])).
% 0.90/1.16 tff(1772,plain,
% 0.90/1.16 (((~ndr1_0) | c1_1(a2601) | (~c3_1(a2601)) | (~c0_1(a2601)) | c3_1(a2552) | c1_1(a2552) | (~c2_1(a2552)) | c3_1(a2552) | c0_1(a2552) | (~c2_1(a2552))) <=> (c1_1(a2552) | c3_1(a2552) | (~ndr1_0) | c0_1(a2552) | (~c2_1(a2552)) | (~c3_1(a2601)) | (~c0_1(a2601)) | c1_1(a2601))),
% 0.90/1.16 inference(rewrite,[status(thm)],[])).
% 0.90/1.16 tff(1773,plain,
% 0.90/1.16 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a2601) | (~c3_1(a2601)) | (~c0_1(a2601)) | c3_1(a2552) | c1_1(a2552) | (~c2_1(a2552)) | c3_1(a2552) | c0_1(a2552) | (~c2_1(a2552)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a2552) | c3_1(a2552) | (~ndr1_0) | c0_1(a2552) | (~c2_1(a2552)) | (~c3_1(a2601)) | (~c0_1(a2601)) | c1_1(a2601)))),
% 0.90/1.16 inference(monotonicity,[status(thm)],[1772])).
% 0.90/1.16 tff(1774,plain,
% 0.90/1.16 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a2601) | (~c3_1(a2601)) | (~c0_1(a2601)) | c3_1(a2552) | c1_1(a2552) | (~c2_1(a2552)) | c3_1(a2552) | c0_1(a2552) | (~c2_1(a2552)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a2552) | c3_1(a2552) | (~ndr1_0) | c0_1(a2552) | (~c2_1(a2552)) | (~c3_1(a2601)) | (~c0_1(a2601)) | c1_1(a2601))),
% 0.90/1.16 inference(transitivity,[status(thm)],[1773, 1771])).
% 0.90/1.16 tff(1775,plain,
% 0.90/1.16 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a2601) | (~c3_1(a2601)) | (~c0_1(a2601)) | c3_1(a2552) | c1_1(a2552) | (~c2_1(a2552)) | c3_1(a2552) | c0_1(a2552) | (~c2_1(a2552)))),
% 0.90/1.16 inference(quant_inst,[status(thm)],[])).
% 0.90/1.16 tff(1776,plain,
% 0.90/1.16 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a2552) | c3_1(a2552) | (~ndr1_0) | c0_1(a2552) | (~c2_1(a2552)) | (~c3_1(a2601)) | (~c0_1(a2601)) | c1_1(a2601)),
% 0.90/1.16 inference(modus_ponens,[status(thm)],[1775, 1774])).
% 0.90/1.16 tff(1777,plain,
% 0.90/1.16 (c0_1(a2552)),
% 0.90/1.16 inference(unit_resolution,[status(thm)],[1776, 90, 1725, 1733, 1770, 1769, 1768, 424, 1749])).
% 0.90/1.16 tff(1778,plain,
% 0.90/1.16 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c3_1(a2526) | c1_1(a2552) | c3_1(a2552) | c0_1(a2526) | (~ndr1_0) | (~c2_1(a2526)) | (~c2_1(a2552)) | (~c3_1(a2601)) | (~c0_1(a2601)) | c1_1(a2601))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c3_1(a2526) | c1_1(a2552) | c3_1(a2552) | c0_1(a2526) | (~ndr1_0) | (~c2_1(a2526)) | (~c2_1(a2552)) | (~c3_1(a2601)) | (~c0_1(a2601)) | c1_1(a2601))),
% 0.90/1.16 inference(rewrite,[status(thm)],[])).
% 0.90/1.16 tff(1779,plain,
% 0.90/1.16 (((~ndr1_0) | c1_1(a2601) | (~c3_1(a2601)) | (~c0_1(a2601)) | c3_1(a2552) | c1_1(a2552) | (~c2_1(a2552)) | c3_1(a2526) | c0_1(a2526) | (~c2_1(a2526))) <=> (c3_1(a2526) | c1_1(a2552) | c3_1(a2552) | c0_1(a2526) | (~ndr1_0) | (~c2_1(a2526)) | (~c2_1(a2552)) | (~c3_1(a2601)) | (~c0_1(a2601)) | c1_1(a2601))),
% 0.90/1.16 inference(rewrite,[status(thm)],[])).
% 0.90/1.16 tff(1780,plain,
% 0.90/1.16 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a2601) | (~c3_1(a2601)) | (~c0_1(a2601)) | c3_1(a2552) | c1_1(a2552) | (~c2_1(a2552)) | c3_1(a2526) | c0_1(a2526) | (~c2_1(a2526)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c3_1(a2526) | c1_1(a2552) | c3_1(a2552) | c0_1(a2526) | (~ndr1_0) | (~c2_1(a2526)) | (~c2_1(a2552)) | (~c3_1(a2601)) | (~c0_1(a2601)) | c1_1(a2601)))),
% 0.90/1.16 inference(monotonicity,[status(thm)],[1779])).
% 0.90/1.16 tff(1781,plain,
% 0.90/1.16 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a2601) | (~c3_1(a2601)) | (~c0_1(a2601)) | c3_1(a2552) | c1_1(a2552) | (~c2_1(a2552)) | c3_1(a2526) | c0_1(a2526) | (~c2_1(a2526)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c3_1(a2526) | c1_1(a2552) | c3_1(a2552) | c0_1(a2526) | (~ndr1_0) | (~c2_1(a2526)) | (~c2_1(a2552)) | (~c3_1(a2601)) | (~c0_1(a2601)) | c1_1(a2601))),
% 0.90/1.16 inference(transitivity,[status(thm)],[1780, 1778])).
% 0.90/1.16 tff(1782,plain,
% 0.90/1.16 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a2601) | (~c3_1(a2601)) | (~c0_1(a2601)) | c3_1(a2552) | c1_1(a2552) | (~c2_1(a2552)) | c3_1(a2526) | c0_1(a2526) | (~c2_1(a2526)))),
% 0.90/1.16 inference(quant_inst,[status(thm)],[])).
% 0.90/1.16 tff(1783,plain,
% 0.90/1.16 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c3_1(a2526) | c1_1(a2552) | c3_1(a2552) | c0_1(a2526) | (~ndr1_0) | (~c2_1(a2526)) | (~c2_1(a2552)) | (~c3_1(a2601)) | (~c0_1(a2601)) | c1_1(a2601)),
% 0.90/1.16 inference(modus_ponens,[status(thm)],[1782, 1781])).
% 0.90/1.16 tff(1784,plain,
% 0.90/1.16 (~c2_1(a2526)),
% 0.90/1.16 inference(unit_resolution,[status(thm)],[1783, 90, 1725, 1733, 1770, 1740, 1769, 1768, 152, 424, 1749])).
% 0.90/1.16 tff(1785,plain,
% 0.90/1.16 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp9 | c3_1(a2526) | c0_1(a2526) | (~ndr1_0) | c2_1(a2526) | (~c1_1(a2526)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp9 | c3_1(a2526) | c0_1(a2526) | (~ndr1_0) | c2_1(a2526) | (~c1_1(a2526)))),
% 0.90/1.16 inference(rewrite,[status(thm)],[])).
% 0.90/1.16 tff(1786,plain,
% 0.90/1.16 ((hskp9 | (~ndr1_0) | c3_1(a2526) | c2_1(a2526) | (~c1_1(a2526)) | c3_1(a2526) | c0_1(a2526) | c2_1(a2526)) <=> (hskp9 | c3_1(a2526) | c0_1(a2526) | (~ndr1_0) | c2_1(a2526) | (~c1_1(a2526)))),
% 0.90/1.16 inference(rewrite,[status(thm)],[])).
% 0.90/1.16 tff(1787,plain,
% 0.90/1.16 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp9 | (~ndr1_0) | c3_1(a2526) | c2_1(a2526) | (~c1_1(a2526)) | c3_1(a2526) | c0_1(a2526) | c2_1(a2526))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp9 | c3_1(a2526) | c0_1(a2526) | (~ndr1_0) | c2_1(a2526) | (~c1_1(a2526))))),
% 0.90/1.16 inference(monotonicity,[status(thm)],[1786])).
% 0.90/1.16 tff(1788,plain,
% 0.90/1.16 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp9 | (~ndr1_0) | c3_1(a2526) | c2_1(a2526) | (~c1_1(a2526)) | c3_1(a2526) | c0_1(a2526) | c2_1(a2526))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp9 | c3_1(a2526) | c0_1(a2526) | (~ndr1_0) | c2_1(a2526) | (~c1_1(a2526)))),
% 0.90/1.16 inference(transitivity,[status(thm)],[1787, 1785])).
% 0.90/1.16 tff(1789,plain,
% 0.90/1.16 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp9 | (~ndr1_0) | c3_1(a2526) | c2_1(a2526) | (~c1_1(a2526)) | c3_1(a2526) | c0_1(a2526) | c2_1(a2526))),
% 0.90/1.16 inference(quant_inst,[status(thm)],[])).
% 0.90/1.16 tff(1790,plain,
% 0.90/1.16 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp9 | c3_1(a2526) | c0_1(a2526) | (~ndr1_0) | c2_1(a2526) | (~c1_1(a2526))),
% 0.90/1.16 inference(modus_ponens,[status(thm)],[1789, 1788])).
% 0.90/1.16 tff(1791,plain,
% 0.90/1.16 (~c1_1(a2526)),
% 0.90/1.16 inference(unit_resolution,[status(thm)],[1790, 90, 1741, 1740, 152, 36, 1784])).
% 0.90/1.16 tff(1792,plain,
% 0.90/1.16 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | c1_1(a2526) | c3_1(a2526) | c1_1(a2552) | c0_1(a2526) | (~ndr1_0) | (~c0_1(a2552)) | (~c2_1(a2552)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp2 | c1_1(a2526) | c3_1(a2526) | c1_1(a2552) | c0_1(a2526) | (~ndr1_0) | (~c0_1(a2552)) | (~c2_1(a2552)))),
% 0.90/1.16 inference(rewrite,[status(thm)],[])).
% 0.90/1.16 tff(1793,plain,
% 0.90/1.16 ((hskp2 | (~ndr1_0) | c1_1(a2552) | (~c0_1(a2552)) | (~c2_1(a2552)) | c3_1(a2526) | c1_1(a2526) | c0_1(a2526)) <=> (hskp2 | c1_1(a2526) | c3_1(a2526) | c1_1(a2552) | c0_1(a2526) | (~ndr1_0) | (~c0_1(a2552)) | (~c2_1(a2552)))),
% 0.90/1.16 inference(rewrite,[status(thm)],[])).
% 0.90/1.16 tff(1794,plain,
% 0.90/1.16 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | c1_1(a2552) | (~c0_1(a2552)) | (~c2_1(a2552)) | c3_1(a2526) | c1_1(a2526) | c0_1(a2526))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | c1_1(a2526) | c3_1(a2526) | c1_1(a2552) | c0_1(a2526) | (~ndr1_0) | (~c0_1(a2552)) | (~c2_1(a2552))))),
% 0.90/1.16 inference(monotonicity,[status(thm)],[1793])).
% 0.90/1.16 tff(1795,plain,
% 0.90/1.16 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | c1_1(a2552) | (~c0_1(a2552)) | (~c2_1(a2552)) | c3_1(a2526) | c1_1(a2526) | c0_1(a2526))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp2 | c1_1(a2526) | c3_1(a2526) | c1_1(a2552) | c0_1(a2526) | (~ndr1_0) | (~c0_1(a2552)) | (~c2_1(a2552)))),
% 0.90/1.16 inference(transitivity,[status(thm)],[1794, 1792])).
% 0.90/1.16 tff(1796,plain,
% 0.90/1.16 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | c1_1(a2552) | (~c0_1(a2552)) | (~c2_1(a2552)) | c3_1(a2526) | c1_1(a2526) | c0_1(a2526))),
% 0.90/1.16 inference(quant_inst,[status(thm)],[])).
% 0.90/1.16 tff(1797,plain,
% 0.90/1.16 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp2 | c1_1(a2526) | c3_1(a2526) | c1_1(a2552) | c0_1(a2526) | (~ndr1_0) | (~c0_1(a2552)) | (~c2_1(a2552))),
% 0.90/1.16 inference(modus_ponens,[status(thm)],[1796, 1795])).
% 0.90/1.16 tff(1798,plain,
% 0.90/1.16 (hskp2 | c1_1(a2526) | (~c0_1(a2552))),
% 0.90/1.16 inference(unit_resolution,[status(thm)],[1797, 90, 1770, 1740, 1769, 152, 877])).
% 0.90/1.16 tff(1799,plain,
% 0.90/1.16 (hskp2),
% 0.90/1.16 inference(unit_resolution,[status(thm)],[1798, 1791, 1777])).
% 0.90/1.16 tff(1800,plain,
% 0.90/1.16 (~c0_1(a2518)),
% 0.90/1.16 inference(unit_resolution,[status(thm)],[898, 1799])).
% 0.90/1.16 tff(1801,plain,
% 0.90/1.16 (c1_1(a2518)),
% 0.90/1.16 inference(unit_resolution,[status(thm)],[906, 1799])).
% 0.90/1.16 tff(1802,plain,
% 0.90/1.16 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c2_1(a2601) | c1_1(a2552) | c3_1(a2552) | c0_1(a2518) | (~ndr1_0) | (~c1_1(a2518)) | (~c2_1(a2518)) | (~c0_1(a2552)) | (~c3_1(a2601)) | c1_1(a2601))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c2_1(a2601) | c1_1(a2552) | c3_1(a2552) | c0_1(a2518) | (~ndr1_0) | (~c1_1(a2518)) | (~c2_1(a2518)) | (~c0_1(a2552)) | (~c3_1(a2601)) | c1_1(a2601))),
% 0.90/1.16 inference(rewrite,[status(thm)],[])).
% 0.90/1.16 tff(1803,plain,
% 0.90/1.16 (((~ndr1_0) | c3_1(a2552) | c1_1(a2552) | (~c0_1(a2552)) | c1_1(a2601) | c2_1(a2601) | (~c3_1(a2601)) | c0_1(a2518) | (~c2_1(a2518)) | (~c1_1(a2518))) <=> (c2_1(a2601) | c1_1(a2552) | c3_1(a2552) | c0_1(a2518) | (~ndr1_0) | (~c1_1(a2518)) | (~c2_1(a2518)) | (~c0_1(a2552)) | (~c3_1(a2601)) | c1_1(a2601))),
% 0.90/1.16 inference(rewrite,[status(thm)],[])).
% 0.90/1.16 tff(1804,plain,
% 0.90/1.16 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a2552) | c1_1(a2552) | (~c0_1(a2552)) | c1_1(a2601) | c2_1(a2601) | (~c3_1(a2601)) | c0_1(a2518) | (~c2_1(a2518)) | (~c1_1(a2518)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c2_1(a2601) | c1_1(a2552) | c3_1(a2552) | c0_1(a2518) | (~ndr1_0) | (~c1_1(a2518)) | (~c2_1(a2518)) | (~c0_1(a2552)) | (~c3_1(a2601)) | c1_1(a2601)))),
% 0.90/1.16 inference(monotonicity,[status(thm)],[1803])).
% 0.90/1.16 tff(1805,plain,
% 0.90/1.16 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a2552) | c1_1(a2552) | (~c0_1(a2552)) | c1_1(a2601) | c2_1(a2601) | (~c3_1(a2601)) | c0_1(a2518) | (~c2_1(a2518)) | (~c1_1(a2518)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c2_1(a2601) | c1_1(a2552) | c3_1(a2552) | c0_1(a2518) | (~ndr1_0) | (~c1_1(a2518)) | (~c2_1(a2518)) | (~c0_1(a2552)) | (~c3_1(a2601)) | c1_1(a2601))),
% 0.90/1.16 inference(transitivity,[status(thm)],[1804, 1802])).
% 0.90/1.16 tff(1806,plain,
% 0.90/1.16 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a2552) | c1_1(a2552) | (~c0_1(a2552)) | c1_1(a2601) | c2_1(a2601) | (~c3_1(a2601)) | c0_1(a2518) | (~c2_1(a2518)) | (~c1_1(a2518)))),
% 0.90/1.16 inference(quant_inst,[status(thm)],[])).
% 0.90/1.16 tff(1807,plain,
% 0.90/1.16 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c2_1(a2601) | c1_1(a2552) | c3_1(a2552) | c0_1(a2518) | (~ndr1_0) | (~c1_1(a2518)) | (~c2_1(a2518)) | (~c0_1(a2552)) | (~c3_1(a2601)) | c1_1(a2601)),
% 0.90/1.16 inference(modus_ponens,[status(thm)],[1806, 1805])).
% 0.90/1.16 tff(1808,plain,
% 0.90/1.16 (~c2_1(a2518)),
% 0.90/1.16 inference(unit_resolution,[status(thm)],[1807, 90, 1733, 1801, 1739, 1769, 1768, 1800, 636, 1777, 1749])).
% 0.90/1.16 tff(1809,plain,
% 0.90/1.16 (~c3_1(a2518)),
% 0.90/1.16 inference(unit_resolution,[status(thm)],[892, 1799])).
% 0.90/1.16 tff(1810,plain,
% 0.90/1.16 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp9 | c0_1(a2518) | c3_1(a2518) | (~ndr1_0) | (~c1_1(a2518)) | c2_1(a2518))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp9 | c0_1(a2518) | c3_1(a2518) | (~ndr1_0) | (~c1_1(a2518)) | c2_1(a2518))),
% 0.90/1.16 inference(rewrite,[status(thm)],[])).
% 0.90/1.16 tff(1811,plain,
% 0.90/1.16 ((hskp9 | (~ndr1_0) | c3_1(a2518) | c2_1(a2518) | (~c1_1(a2518)) | c3_1(a2518) | c0_1(a2518) | c2_1(a2518)) <=> (hskp9 | c0_1(a2518) | c3_1(a2518) | (~ndr1_0) | (~c1_1(a2518)) | c2_1(a2518))),
% 0.90/1.16 inference(rewrite,[status(thm)],[])).
% 0.90/1.16 tff(1812,plain,
% 0.90/1.16 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp9 | (~ndr1_0) | c3_1(a2518) | c2_1(a2518) | (~c1_1(a2518)) | c3_1(a2518) | c0_1(a2518) | c2_1(a2518))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp9 | c0_1(a2518) | c3_1(a2518) | (~ndr1_0) | (~c1_1(a2518)) | c2_1(a2518)))),
% 0.90/1.16 inference(monotonicity,[status(thm)],[1811])).
% 0.90/1.16 tff(1813,plain,
% 0.90/1.16 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp9 | (~ndr1_0) | c3_1(a2518) | c2_1(a2518) | (~c1_1(a2518)) | c3_1(a2518) | c0_1(a2518) | c2_1(a2518))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp9 | c0_1(a2518) | c3_1(a2518) | (~ndr1_0) | (~c1_1(a2518)) | c2_1(a2518))),
% 0.90/1.16 inference(transitivity,[status(thm)],[1812, 1810])).
% 0.90/1.16 tff(1814,plain,
% 0.90/1.16 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp9 | (~ndr1_0) | c3_1(a2518) | c2_1(a2518) | (~c1_1(a2518)) | c3_1(a2518) | c0_1(a2518) | c2_1(a2518))),
% 0.90/1.16 inference(quant_inst,[status(thm)],[])).
% 0.90/1.16 tff(1815,plain,
% 0.90/1.16 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp9 | c0_1(a2518) | c3_1(a2518) | (~ndr1_0) | (~c1_1(a2518)) | c2_1(a2518)),
% 0.90/1.16 inference(modus_ponens,[status(thm)],[1814, 1813])).
% 0.90/1.16 tff(1816,plain,
% 0.90/1.16 ($false),
% 0.90/1.16 inference(unit_resolution,[status(thm)],[1815, 90, 1741, 1801, 1800, 1809, 36, 1808])).
% 0.90/1.16 tff(1817,plain,(c3_1(a2526) | c0_1(a2526) | hskp30), inference(lemma,lemma(discharge,[]))).
% 0.90/1.16 tff(1818,plain,
% 0.90/1.16 (c3_1(a2526)),
% 0.90/1.16 inference(unit_resolution,[status(thm)],[1817, 152, 151])).
% 0.90/1.16 tff(1819,plain,
% 0.90/1.16 (^[V: $i, U: $i] : refl((hskp21 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V))) <=> (hskp21 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V))))),
% 0.90/1.16 inference(bind,[status(th)],[])).
% 0.90/1.16 tff(1820,plain,
% 0.90/1.16 (![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))),
% 0.90/1.16 inference(quant_intro,[status(thm)],[1819])).
% 0.90/1.16 tff(1821,plain,
% 0.90/1.16 (![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))),
% 0.90/1.16 inference(rewrite,[status(thm)],[])).
% 0.90/1.16 tff(1822,plain,
% 0.90/1.16 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c3_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c3_1(U)) | c2_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c3_1(U)) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c3_1(U)) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V))) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c3_1(U)) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c3_1(U)) | c2_1(V)) | c3_1(V)) | hskp21) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V))) | hskp21))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V))) | hskp21) <=> (hskp21 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c3_1(U)) | c2_1(V)) | c3_1(V)) | hskp21) <=> (hskp21 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))))),
% 0.90/1.16 inference(bind,[status(th)],[])).
% 0.90/1.16 tff(1823,plain,
% 0.90/1.16 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c3_1(U)) | c2_1(V)) | c3_1(V)) | hskp21) <=> ![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))),
% 0.90/1.16 inference(quant_intro,[status(thm)],[1822])).
% 0.90/1.16 tff(1824,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c3_1(U)) | c2_1(V)) | c3_1(V)) | hskp21)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause184')).
% 0.90/1.16 tff(1825,plain,
% 0.90/1.16 (![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))),
% 0.90/1.16 inference(modus_ponens,[status(thm)],[1824, 1823])).
% 0.90/1.16 tff(1826,plain,
% 0.90/1.16 (![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))),
% 0.90/1.16 inference(modus_ponens,[status(thm)],[1825, 1821])).
% 0.90/1.16 tff(1827,plain,(
% 0.90/1.16 ![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))),
% 0.90/1.16 inference(skolemize,[status(sab)],[1826])).
% 0.90/1.16 tff(1828,plain,
% 0.90/1.16 (![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))),
% 0.90/1.16 inference(modus_ponens,[status(thm)],[1827, 1820])).
% 0.90/1.16 tff(1829,assumption,(~hskp21), introduced(assumption)).
% 0.90/1.16 tff(1830,plain,
% 0.90/1.16 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp21 | c2_1(a2614) | c3_1(a2614) | (~ndr1_0) | (~c0_1(a2614)) | (~c1_1(a2614)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | hskp21 | c2_1(a2614) | c3_1(a2614) | (~ndr1_0) | (~c0_1(a2614)) | (~c1_1(a2614)))),
% 0.90/1.16 inference(rewrite,[status(thm)],[])).
% 0.90/1.16 tff(1831,plain,
% 0.90/1.16 ((hskp21 | (~ndr1_0) | c3_1(a2614) | (~c1_1(a2614)) | (~c0_1(a2614)) | c3_1(a2614) | c2_1(a2614) | (~c0_1(a2614))) <=> (hskp21 | c2_1(a2614) | c3_1(a2614) | (~ndr1_0) | (~c0_1(a2614)) | (~c1_1(a2614)))),
% 0.90/1.16 inference(rewrite,[status(thm)],[])).
% 0.90/1.16 tff(1832,plain,
% 0.90/1.16 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp21 | (~ndr1_0) | c3_1(a2614) | (~c1_1(a2614)) | (~c0_1(a2614)) | c3_1(a2614) | c2_1(a2614) | (~c0_1(a2614)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp21 | c2_1(a2614) | c3_1(a2614) | (~ndr1_0) | (~c0_1(a2614)) | (~c1_1(a2614))))),
% 0.90/1.16 inference(monotonicity,[status(thm)],[1831])).
% 0.90/1.16 tff(1833,plain,
% 0.90/1.16 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp21 | (~ndr1_0) | c3_1(a2614) | (~c1_1(a2614)) | (~c0_1(a2614)) | c3_1(a2614) | c2_1(a2614) | (~c0_1(a2614)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | hskp21 | c2_1(a2614) | c3_1(a2614) | (~ndr1_0) | (~c0_1(a2614)) | (~c1_1(a2614)))),
% 0.90/1.16 inference(transitivity,[status(thm)],[1832, 1830])).
% 0.90/1.16 tff(1834,plain,
% 0.90/1.16 ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp21 | (~ndr1_0) | c3_1(a2614) | (~c1_1(a2614)) | (~c0_1(a2614)) | c3_1(a2614) | c2_1(a2614) | (~c0_1(a2614)))),
% 0.90/1.16 inference(quant_inst,[status(thm)],[])).
% 0.90/1.16 tff(1835,plain,
% 0.90/1.16 ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | hskp21 | c2_1(a2614) | c3_1(a2614) | (~ndr1_0) | (~c0_1(a2614)) | (~c1_1(a2614))),
% 0.90/1.16 inference(modus_ponens,[status(thm)],[1834, 1833])).
% 0.90/1.16 tff(1836,plain,
% 0.90/1.16 (~c0_1(a2614)),
% 0.90/1.16 inference(unit_resolution,[status(thm)],[1835, 90, 1829, 13, 26, 20, 1828])).
% 0.90/1.16 tff(1837,plain,
% 0.90/1.16 (^[V: $i, U: $i] : refl((hskp10 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V))) <=> (hskp10 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V))))),
% 0.90/1.16 inference(bind,[status(th)],[])).
% 0.90/1.16 tff(1838,plain,
% 0.90/1.16 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))),
% 0.90/1.16 inference(quant_intro,[status(thm)],[1837])).
% 0.90/1.16 tff(1839,plain,
% 0.90/1.16 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))),
% 0.90/1.16 inference(rewrite,[status(thm)],[])).
% 0.90/1.16 tff(1840,plain,
% 0.90/1.16 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c1_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c1_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c1_1(V)))), ((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c1_1(V))))), (((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c1_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c1_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c1_1(V)))), (((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c1_1(V))))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c1_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c1_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | (~c1_1(V)))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | (~c1_1(V))))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | (~c1_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V))))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V))))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp10) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V))) | hskp10))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V))) | hskp10) <=> (hskp10 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp10) <=> (hskp10 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))))),
% 0.90/1.17 inference(bind,[status(th)],[])).
% 0.90/1.17 tff(1841,plain,
% 0.90/1.17 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp10) <=> ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))),
% 0.90/1.17 inference(quant_intro,[status(thm)],[1840])).
% 0.90/1.17 tff(1842,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp10)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause169')).
% 0.90/1.17 tff(1843,plain,
% 0.90/1.17 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))),
% 0.90/1.17 inference(modus_ponens,[status(thm)],[1842, 1841])).
% 0.90/1.17 tff(1844,plain,
% 0.90/1.17 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))),
% 0.90/1.17 inference(modus_ponens,[status(thm)],[1843, 1839])).
% 0.90/1.17 tff(1845,plain,(
% 0.90/1.17 ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))),
% 0.90/1.17 inference(skolemize,[status(sab)],[1844])).
% 0.90/1.17 tff(1846,plain,
% 0.90/1.17 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))),
% 0.90/1.17 inference(modus_ponens,[status(thm)],[1845, 1838])).
% 0.90/1.17 tff(1847,plain,
% 0.90/1.17 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp10 | c2_1(a2614) | c3_1(a2614) | (~ndr1_0) | c0_1(a2614) | (~c1_1(a2614)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp10 | c2_1(a2614) | c3_1(a2614) | (~ndr1_0) | c0_1(a2614) | (~c1_1(a2614)))),
% 0.90/1.17 inference(rewrite,[status(thm)],[])).
% 0.90/1.17 tff(1848,plain,
% 0.90/1.17 ((hskp10 | (~ndr1_0) | c3_1(a2614) | c2_1(a2614) | (~c1_1(a2614)) | c0_1(a2614) | c2_1(a2614) | (~c1_1(a2614))) <=> (hskp10 | c2_1(a2614) | c3_1(a2614) | (~ndr1_0) | c0_1(a2614) | (~c1_1(a2614)))),
% 0.90/1.17 inference(rewrite,[status(thm)],[])).
% 0.90/1.17 tff(1849,plain,
% 0.90/1.17 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp10 | (~ndr1_0) | c3_1(a2614) | c2_1(a2614) | (~c1_1(a2614)) | c0_1(a2614) | c2_1(a2614) | (~c1_1(a2614)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp10 | c2_1(a2614) | c3_1(a2614) | (~ndr1_0) | c0_1(a2614) | (~c1_1(a2614))))),
% 0.90/1.17 inference(monotonicity,[status(thm)],[1848])).
% 0.90/1.17 tff(1850,plain,
% 0.90/1.17 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp10 | (~ndr1_0) | c3_1(a2614) | c2_1(a2614) | (~c1_1(a2614)) | c0_1(a2614) | c2_1(a2614) | (~c1_1(a2614)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp10 | c2_1(a2614) | c3_1(a2614) | (~ndr1_0) | c0_1(a2614) | (~c1_1(a2614)))),
% 0.90/1.17 inference(transitivity,[status(thm)],[1849, 1847])).
% 0.90/1.17 tff(1851,plain,
% 0.90/1.17 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp10 | (~ndr1_0) | c3_1(a2614) | c2_1(a2614) | (~c1_1(a2614)) | c0_1(a2614) | c2_1(a2614) | (~c1_1(a2614)))),
% 0.90/1.17 inference(quant_inst,[status(thm)],[])).
% 0.90/1.17 tff(1852,plain,
% 0.90/1.17 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp10 | c2_1(a2614) | c3_1(a2614) | (~ndr1_0) | c0_1(a2614) | (~c1_1(a2614))),
% 0.90/1.17 inference(modus_ponens,[status(thm)],[1851, 1850])).
% 0.90/1.17 tff(1853,plain,
% 0.90/1.17 (hskp10),
% 0.90/1.17 inference(unit_resolution,[status(thm)],[1852, 90, 13, 26, 20, 1846, 1836])).
% 0.90/1.17 tff(1854,plain,
% 0.90/1.17 (~c0_1(a2528)),
% 0.90/1.17 inference(unit_resolution,[status(thm)],[1137, 1853])).
% 0.90/1.17 tff(1855,plain,
% 0.90/1.17 (~c1_1(a2528)),
% 0.90/1.17 inference(unit_resolution,[status(thm)],[1158, 1853])).
% 0.90/1.17 tff(1856,plain,
% 0.90/1.17 (hskp9),
% 0.90/1.17 inference(unit_resolution,[status(thm)],[115, 90, 13, 26, 20, 36, 1836])).
% 0.90/1.17 tff(1857,plain,
% 0.90/1.17 (c1_1(a2526)),
% 0.90/1.17 inference(unit_resolution,[status(thm)],[199, 1856])).
% 0.90/1.17 tff(1858,plain,
% 0.90/1.17 (hskp17 | (~c1_1(a2526))),
% 0.90/1.17 inference(unit_resolution,[status(thm)],[232, 90, 13, 216, 26, 20, 152, 226])).
% 0.90/1.17 tff(1859,plain,
% 0.90/1.17 (hskp17),
% 0.90/1.17 inference(unit_resolution,[status(thm)],[1858, 1857])).
% 0.90/1.17 tff(1860,plain,
% 0.90/1.17 (~c1_1(a2541)),
% 0.90/1.17 inference(unit_resolution,[status(thm)],[244, 1859])).
% 0.90/1.17 tff(1861,plain,
% 0.90/1.17 (~c2_1(a2541)),
% 0.90/1.17 inference(unit_resolution,[status(thm)],[238, 1859])).
% 0.90/1.17 tff(1862,plain,
% 0.90/1.17 (c3_1(a2541)),
% 0.90/1.17 inference(unit_resolution,[status(thm)],[252, 1859])).
% 0.90/1.17 tff(1863,plain,
% 0.90/1.17 (c3_1(a2528)),
% 0.90/1.17 inference(unit_resolution,[status(thm)],[1145, 1853])).
% 0.90/1.17 tff(1864,plain,
% 0.90/1.17 (hskp11),
% 0.90/1.17 inference(unit_resolution,[status(thm)],[1412, 1863, 1862, 1861, 1860, 1855, 1854])).
% 0.90/1.17 tff(1865,plain,
% 0.90/1.17 (~c3_1(a2531)),
% 0.90/1.17 inference(unit_resolution,[status(thm)],[308, 1864])).
% 0.90/1.17 tff(1866,plain,
% 0.90/1.17 (c1_1(a2531)),
% 0.90/1.17 inference(unit_resolution,[status(thm)],[324, 1864])).
% 0.90/1.17 tff(1867,plain,
% 0.90/1.17 (hskp1),
% 0.90/1.17 inference(unit_resolution,[status(thm)],[381, 90, 13, 26, 20, 375, 1836])).
% 0.90/1.17 tff(1868,plain,
% 0.90/1.17 (~c3_1(a2517)),
% 0.90/1.17 inference(unit_resolution,[status(thm)],[388, 1867])).
% 0.90/1.17 tff(1869,plain,
% 0.90/1.17 (c2_1(a2517)),
% 0.90/1.17 inference(unit_resolution,[status(thm)],[402, 1867])).
% 0.90/1.17 tff(1870,plain,
% 0.90/1.17 (~c0_1(a2517)),
% 0.90/1.17 inference(unit_resolution,[status(thm)],[394, 1867])).
% 0.90/1.17 tff(1871,plain,
% 0.90/1.17 (hskp29),
% 0.90/1.17 inference(unit_resolution,[status(thm)],[445, 1860, 1870, 1861, 1862, 1869, 1868])).
% 0.90/1.17 tff(1872,plain,
% 0.90/1.17 (c3_1(a2556)),
% 0.90/1.17 inference(unit_resolution,[status(thm)],[339, 1871])).
% 0.90/1.17 tff(1873,plain,
% 0.90/1.17 (c2_1(a2556)),
% 0.90/1.17 inference(unit_resolution,[status(thm)],[347, 1871])).
% 0.90/1.17 tff(1874,plain,
% 0.90/1.17 (c1_1(a2556)),
% 0.90/1.17 inference(unit_resolution,[status(thm)],[355, 1871])).
% 0.90/1.17 tff(1875,plain,
% 0.90/1.17 (~c0_1(a2531)),
% 0.90/1.17 inference(unit_resolution,[status(thm)],[1514, 90, 1874, 1873, 1872, 1862, 1866, 1860, 1861, 1865, 264])).
% 0.90/1.17 tff(1876,assumption,(c3_1(a2601)), introduced(assumption)).
% 0.90/1.17 tff(1877,plain,
% 0.90/1.17 (hskp31),
% 0.90/1.17 inference(unit_resolution,[status(thm)],[530, 1, 90, 1874, 1873, 1872, 524])).
% 0.90/1.17 tff(1878,plain,
% 0.90/1.17 (c0_1(a2597)),
% 0.90/1.17 inference(unit_resolution,[status(thm)],[554, 1877])).
% 0.90/1.17 tff(1879,plain,
% 0.90/1.17 (c3_1(a2597)),
% 0.90/1.17 inference(unit_resolution,[status(thm)],[538, 1877])).
% 0.90/1.17 tff(1880,plain,
% 0.90/1.17 (c1_1(a2597)),
% 0.90/1.17 inference(unit_resolution,[status(thm)],[546, 1877])).
% 0.90/1.17 tff(1881,assumption,(~c2_1(a2601)), introduced(assumption)).
% 0.90/1.17 tff(1882,assumption,(c0_1(a2601)), introduced(assumption)).
% 0.90/1.17 tff(1883,assumption,(~hskp22), introduced(assumption)).
% 0.90/1.17 tff(1884,plain,
% 0.90/1.17 (hskp22 | c1_1(a2601)),
% 0.90/1.17 inference(unit_resolution,[status(thm)],[1765, 90, 1829, 1882, 1881, 1759])).
% 0.90/1.17 tff(1885,plain,
% 0.90/1.17 (c1_1(a2601)),
% 0.90/1.17 inference(unit_resolution,[status(thm)],[1884, 1883])).
% 0.90/1.17 tff(1886,plain,
% 0.90/1.17 (((~![U: $i] : (hskp22 | hskp21 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp22 | hskp21 | c1_1(a2541) | c2_1(a2541) | (~ndr1_0) | (~c0_1(a2541)))) <=> ((~![U: $i] : (hskp22 | hskp21 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp22 | hskp21 | c1_1(a2541) | c2_1(a2541) | (~ndr1_0) | (~c0_1(a2541)))),
% 0.90/1.17 inference(rewrite,[status(thm)],[])).
% 0.90/1.17 tff(1887,plain,
% 0.90/1.17 ((hskp22 | hskp21 | (~ndr1_0) | c2_1(a2541) | c1_1(a2541) | (~c0_1(a2541))) <=> (hskp22 | hskp21 | c1_1(a2541) | c2_1(a2541) | (~ndr1_0) | (~c0_1(a2541)))),
% 0.90/1.17 inference(rewrite,[status(thm)],[])).
% 0.90/1.17 tff(1888,plain,
% 0.90/1.17 (((~![U: $i] : (hskp22 | hskp21 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp22 | hskp21 | (~ndr1_0) | c2_1(a2541) | c1_1(a2541) | (~c0_1(a2541)))) <=> ((~![U: $i] : (hskp22 | hskp21 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp22 | hskp21 | c1_1(a2541) | c2_1(a2541) | (~ndr1_0) | (~c0_1(a2541))))),
% 0.90/1.17 inference(monotonicity,[status(thm)],[1887])).
% 0.90/1.17 tff(1889,plain,
% 0.90/1.17 (((~![U: $i] : (hskp22 | hskp21 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp22 | hskp21 | (~ndr1_0) | c2_1(a2541) | c1_1(a2541) | (~c0_1(a2541)))) <=> ((~![U: $i] : (hskp22 | hskp21 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp22 | hskp21 | c1_1(a2541) | c2_1(a2541) | (~ndr1_0) | (~c0_1(a2541)))),
% 0.90/1.17 inference(transitivity,[status(thm)],[1888, 1886])).
% 0.90/1.17 tff(1890,plain,
% 0.90/1.17 ((~![U: $i] : (hskp22 | hskp21 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp22 | hskp21 | (~ndr1_0) | c2_1(a2541) | c1_1(a2541) | (~c0_1(a2541)))),
% 0.90/1.17 inference(quant_inst,[status(thm)],[])).
% 0.90/1.17 tff(1891,plain,
% 0.90/1.17 ((~![U: $i] : (hskp22 | hskp21 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp22 | hskp21 | c1_1(a2541) | c2_1(a2541) | (~ndr1_0) | (~c0_1(a2541))),
% 0.90/1.17 inference(modus_ponens,[status(thm)],[1890, 1889])).
% 0.90/1.17 tff(1892,plain,
% 0.90/1.17 (hskp22 | (~c0_1(a2541))),
% 0.90/1.17 inference(unit_resolution,[status(thm)],[1891, 90, 1829, 266, 265, 1759])).
% 0.90/1.17 tff(1893,plain,
% 0.90/1.17 (~c0_1(a2541)),
% 0.90/1.17 inference(unit_resolution,[status(thm)],[1892, 1883])).
% 0.90/1.17 tff(1894,plain,
% 0.90/1.17 (~hskp24),
% 0.90/1.17 inference(unit_resolution,[status(thm)],[743, 1893, 734, 733, 267, 265, 735])).
% 0.90/1.17 tff(1895,plain,
% 0.90/1.17 (((~![U: $i] : (hskp24 | hskp25 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp24 | hskp25 | c2_1(a2601) | (~ndr1_0) | (~c0_1(a2601)) | (~c1_1(a2601)))) <=> ((~![U: $i] : (hskp24 | hskp25 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp24 | hskp25 | c2_1(a2601) | (~ndr1_0) | (~c0_1(a2601)) | (~c1_1(a2601)))),
% 0.90/1.17 inference(rewrite,[status(thm)],[])).
% 0.90/1.17 tff(1896,plain,
% 0.90/1.17 ((hskp24 | hskp25 | (~ndr1_0) | c2_1(a2601) | (~c1_1(a2601)) | (~c0_1(a2601))) <=> (hskp24 | hskp25 | c2_1(a2601) | (~ndr1_0) | (~c0_1(a2601)) | (~c1_1(a2601)))),
% 0.90/1.17 inference(rewrite,[status(thm)],[])).
% 0.90/1.17 tff(1897,plain,
% 0.90/1.17 (((~![U: $i] : (hskp24 | hskp25 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp24 | hskp25 | (~ndr1_0) | c2_1(a2601) | (~c1_1(a2601)) | (~c0_1(a2601)))) <=> ((~![U: $i] : (hskp24 | hskp25 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp24 | hskp25 | c2_1(a2601) | (~ndr1_0) | (~c0_1(a2601)) | (~c1_1(a2601))))),
% 0.90/1.17 inference(monotonicity,[status(thm)],[1896])).
% 0.90/1.17 tff(1898,plain,
% 0.90/1.17 (((~![U: $i] : (hskp24 | hskp25 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp24 | hskp25 | (~ndr1_0) | c2_1(a2601) | (~c1_1(a2601)) | (~c0_1(a2601)))) <=> ((~![U: $i] : (hskp24 | hskp25 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp24 | hskp25 | c2_1(a2601) | (~ndr1_0) | (~c0_1(a2601)) | (~c1_1(a2601)))),
% 0.90/1.17 inference(transitivity,[status(thm)],[1897, 1895])).
% 0.90/1.17 tff(1899,plain,
% 0.90/1.17 ((~![U: $i] : (hskp24 | hskp25 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp24 | hskp25 | (~ndr1_0) | c2_1(a2601) | (~c1_1(a2601)) | (~c0_1(a2601)))),
% 0.90/1.17 inference(quant_inst,[status(thm)],[])).
% 0.90/1.17 tff(1900,plain,
% 0.90/1.17 ((~![U: $i] : (hskp24 | hskp25 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp24 | hskp25 | c2_1(a2601) | (~ndr1_0) | (~c0_1(a2601)) | (~c1_1(a2601))),
% 0.90/1.17 inference(modus_ponens,[status(thm)],[1899, 1898])).
% 0.90/1.17 tff(1901,plain,
% 0.90/1.17 (hskp24 | hskp25 | (~c1_1(a2601))),
% 0.90/1.17 inference(unit_resolution,[status(thm)],[1900, 90, 1882, 1881, 754])).
% 0.90/1.17 tff(1902,plain,
% 0.90/1.17 (hskp25),
% 0.90/1.17 inference(unit_resolution,[status(thm)],[1901, 1894, 1885])).
% 0.90/1.17 tff(1903,plain,
% 0.90/1.17 (((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp18 | c2_1(a2601) | (~ndr1_0) | (~c2_1(a2556)) | (~c3_1(a2556)) | (~c1_1(a2556)) | (~c3_1(a2601)) | (~c1_1(a2601)))) <=> ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp18 | c2_1(a2601) | (~ndr1_0) | (~c2_1(a2556)) | (~c3_1(a2556)) | (~c1_1(a2556)) | (~c3_1(a2601)) | (~c1_1(a2601)))),
% 0.90/1.17 inference(rewrite,[status(thm)],[])).
% 0.90/1.17 tff(1904,plain,
% 0.90/1.17 ((hskp18 | (~ndr1_0) | (~c3_1(a2556)) | (~c1_1(a2556)) | (~c2_1(a2556)) | c2_1(a2601) | (~c3_1(a2601)) | (~c1_1(a2601))) <=> (hskp18 | c2_1(a2601) | (~ndr1_0) | (~c2_1(a2556)) | (~c3_1(a2556)) | (~c1_1(a2556)) | (~c3_1(a2601)) | (~c1_1(a2601)))),
% 0.90/1.17 inference(rewrite,[status(thm)],[])).
% 0.90/1.17 tff(1905,plain,
% 0.90/1.17 (((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp18 | (~ndr1_0) | (~c3_1(a2556)) | (~c1_1(a2556)) | (~c2_1(a2556)) | c2_1(a2601) | (~c3_1(a2601)) | (~c1_1(a2601)))) <=> ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp18 | c2_1(a2601) | (~ndr1_0) | (~c2_1(a2556)) | (~c3_1(a2556)) | (~c1_1(a2556)) | (~c3_1(a2601)) | (~c1_1(a2601))))),
% 0.90/1.17 inference(monotonicity,[status(thm)],[1904])).
% 0.90/1.17 tff(1906,plain,
% 0.90/1.17 (((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp18 | (~ndr1_0) | (~c3_1(a2556)) | (~c1_1(a2556)) | (~c2_1(a2556)) | c2_1(a2601) | (~c3_1(a2601)) | (~c1_1(a2601)))) <=> ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp18 | c2_1(a2601) | (~ndr1_0) | (~c2_1(a2556)) | (~c3_1(a2556)) | (~c1_1(a2556)) | (~c3_1(a2601)) | (~c1_1(a2601)))),
% 0.90/1.17 inference(transitivity,[status(thm)],[1905, 1903])).
% 0.90/1.17 tff(1907,plain,
% 0.90/1.17 ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp18 | (~ndr1_0) | (~c3_1(a2556)) | (~c1_1(a2556)) | (~c2_1(a2556)) | c2_1(a2601) | (~c3_1(a2601)) | (~c1_1(a2601)))),
% 0.90/1.17 inference(quant_inst,[status(thm)],[])).
% 0.90/1.17 tff(1908,plain,
% 0.90/1.17 ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp18 | c2_1(a2601) | (~ndr1_0) | (~c2_1(a2556)) | (~c3_1(a2556)) | (~c1_1(a2556)) | (~c3_1(a2601)) | (~c1_1(a2601))),
% 0.90/1.17 inference(modus_ponens,[status(thm)],[1907, 1906])).
% 0.90/1.17 tff(1909,plain,
% 0.90/1.17 (hskp18 | (~c1_1(a2601))),
% 0.90/1.17 inference(unit_resolution,[status(thm)],[1908, 90, 619, 618, 617, 1876, 1881, 572])).
% 0.90/1.17 tff(1910,plain,
% 0.90/1.17 (hskp18),
% 0.90/1.17 inference(unit_resolution,[status(thm)],[1909, 1885])).
% 0.90/1.17 tff(1911,plain,
% 0.90/1.17 (c2_1(a2545)),
% 0.90/1.17 inference(unit_resolution,[status(thm)],[592, 1910])).
% 0.90/1.17 tff(1912,plain,
% 0.90/1.17 (~c0_1(a2545)),
% 0.90/1.17 inference(unit_resolution,[status(thm)],[584, 1910])).
% 0.90/1.17 tff(1913,plain,
% 0.90/1.17 (c1_1(a2545)),
% 0.90/1.17 inference(unit_resolution,[status(thm)],[600, 1910])).
% 0.90/1.17 tff(1914,plain,
% 0.90/1.17 (~hskp8),
% 0.90/1.17 inference(unit_resolution,[status(thm)],[647, 1913, 267, 266, 1912, 1911, 265, 619, 618, 617])).
% 0.90/1.17 tff(1915,plain,
% 0.90/1.17 ($false),
% 0.90/1.17 inference(unit_resolution,[status(thm)],[689, 1914, 1902, 57, 56, 649])).
% 0.90/1.17 tff(1916,plain,(hskp22 | c2_1(a2614) | c3_1(a2614) | c0_1(a2614) | (~c3_1(a2541)) | c1_1(a2541) | c2_1(a2541) | (~c1_1(a2556)) | (~c2_1(a2556)) | (~c3_1(a2556)) | (~c0_1(a2601)) | c2_1(a2601) | (~c1_1(a2597)) | (~c3_1(a2597)) | (~c0_1(a2597)) | (~c3_1(a2601)) | hskp21), inference(lemma,lemma(discharge,[]))).
% 0.90/1.17 tff(1917,plain,
% 0.90/1.17 (hskp22),
% 0.90/1.17 inference(unit_resolution,[status(thm)],[1916, 26, 20, 1836, 1862, 1860, 1861, 1874, 1873, 1872, 1882, 1881, 1880, 1879, 1878, 1876, 1829])).
% 0.90/1.17 tff(1918,plain,
% 0.90/1.17 (~c3_1(a2552)),
% 0.90/1.17 inference(unit_resolution,[status(thm)],[806, 1917])).
% 0.90/1.17 tff(1919,plain,
% 0.90/1.17 (~c1_1(a2552)),
% 0.90/1.17 inference(unit_resolution,[status(thm)],[820, 1917])).
% 0.90/1.17 tff(1920,plain,
% 0.90/1.17 (c2_1(a2531)),
% 0.90/1.17 inference(unit_resolution,[status(thm)],[316, 1864])).
% 0.90/1.17 tff(1921,plain,
% 0.90/1.17 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c1_1(a2552) | c3_1(a2552) | c1_1(a2541) | c2_1(a2541) | (~ndr1_0) | c0_1(a2531) | (~c2_1(a2531)) | (~c1_1(a2531)) | (~c3_1(a2541)) | (~c0_1(a2552)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c1_1(a2552) | c3_1(a2552) | c1_1(a2541) | c2_1(a2541) | (~ndr1_0) | c0_1(a2531) | (~c2_1(a2531)) | (~c1_1(a2531)) | (~c3_1(a2541)) | (~c0_1(a2552)))),
% 0.90/1.17 inference(rewrite,[status(thm)],[])).
% 0.90/1.17 tff(1922,plain,
% 0.90/1.17 (((~ndr1_0) | c3_1(a2552) | c1_1(a2552) | (~c0_1(a2552)) | c1_1(a2541) | c2_1(a2541) | (~c3_1(a2541)) | c0_1(a2531) | (~c2_1(a2531)) | (~c1_1(a2531))) <=> (c1_1(a2552) | c3_1(a2552) | c1_1(a2541) | c2_1(a2541) | (~ndr1_0) | c0_1(a2531) | (~c2_1(a2531)) | (~c1_1(a2531)) | (~c3_1(a2541)) | (~c0_1(a2552)))),
% 0.90/1.17 inference(rewrite,[status(thm)],[])).
% 0.90/1.17 tff(1923,plain,
% 0.90/1.17 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a2552) | c1_1(a2552) | (~c0_1(a2552)) | c1_1(a2541) | c2_1(a2541) | (~c3_1(a2541)) | c0_1(a2531) | (~c2_1(a2531)) | (~c1_1(a2531)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c1_1(a2552) | c3_1(a2552) | c1_1(a2541) | c2_1(a2541) | (~ndr1_0) | c0_1(a2531) | (~c2_1(a2531)) | (~c1_1(a2531)) | (~c3_1(a2541)) | (~c0_1(a2552))))),
% 0.90/1.17 inference(monotonicity,[status(thm)],[1922])).
% 0.90/1.17 tff(1924,plain,
% 0.90/1.17 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a2552) | c1_1(a2552) | (~c0_1(a2552)) | c1_1(a2541) | c2_1(a2541) | (~c3_1(a2541)) | c0_1(a2531) | (~c2_1(a2531)) | (~c1_1(a2531)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c1_1(a2552) | c3_1(a2552) | c1_1(a2541) | c2_1(a2541) | (~ndr1_0) | c0_1(a2531) | (~c2_1(a2531)) | (~c1_1(a2531)) | (~c3_1(a2541)) | (~c0_1(a2552)))),
% 0.90/1.17 inference(transitivity,[status(thm)],[1923, 1921])).
% 0.90/1.17 tff(1925,plain,
% 0.90/1.17 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a2552) | c1_1(a2552) | (~c0_1(a2552)) | c1_1(a2541) | c2_1(a2541) | (~c3_1(a2541)) | c0_1(a2531) | (~c2_1(a2531)) | (~c1_1(a2531)))),
% 0.90/1.17 inference(quant_inst,[status(thm)],[])).
% 0.90/1.17 tff(1926,plain,
% 0.90/1.17 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c1_1(a2552) | c3_1(a2552) | c1_1(a2541) | c2_1(a2541) | (~ndr1_0) | c0_1(a2531) | (~c2_1(a2531)) | (~c1_1(a2531)) | (~c3_1(a2541)) | (~c0_1(a2552))),
% 0.90/1.17 inference(modus_ponens,[status(thm)],[1925, 1924])).
% 0.90/1.17 tff(1927,plain,
% 0.90/1.17 (~c0_1(a2552)),
% 0.90/1.17 inference(unit_resolution,[status(thm)],[1926, 90, 1862, 1866, 1920, 1919, 1918, 1860, 1861, 636, 1875])).
% 0.90/1.17 tff(1928,plain,
% 0.90/1.17 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (c3_1(a2614) | c1_1(a2552) | c3_1(a2552) | (~ndr1_0) | (~c2_1(a2556)) | (~c1_1(a2556)) | (~c0_1(a2556)) | c0_1(a2552) | c0_1(a2614) | (~c1_1(a2614)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c3_1(a2614) | c1_1(a2552) | c3_1(a2552) | (~ndr1_0) | (~c2_1(a2556)) | (~c1_1(a2556)) | (~c0_1(a2556)) | c0_1(a2552) | c0_1(a2614) | (~c1_1(a2614)))),
% 0.90/1.17 inference(rewrite,[status(thm)],[])).
% 0.90/1.17 tff(1929,plain,
% 0.90/1.17 (((~ndr1_0) | (~c1_1(a2556)) | (~c0_1(a2556)) | (~c2_1(a2556)) | c3_1(a2614) | c0_1(a2614) | (~c1_1(a2614)) | c3_1(a2552) | c1_1(a2552) | c0_1(a2552)) <=> (c3_1(a2614) | c1_1(a2552) | c3_1(a2552) | (~ndr1_0) | (~c2_1(a2556)) | (~c1_1(a2556)) | (~c0_1(a2556)) | c0_1(a2552) | c0_1(a2614) | (~c1_1(a2614)))),
% 0.90/1.17 inference(rewrite,[status(thm)],[])).
% 0.90/1.17 tff(1930,plain,
% 0.90/1.17 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c1_1(a2556)) | (~c0_1(a2556)) | (~c2_1(a2556)) | c3_1(a2614) | c0_1(a2614) | (~c1_1(a2614)) | c3_1(a2552) | c1_1(a2552) | c0_1(a2552))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (c3_1(a2614) | c1_1(a2552) | c3_1(a2552) | (~ndr1_0) | (~c2_1(a2556)) | (~c1_1(a2556)) | (~c0_1(a2556)) | c0_1(a2552) | c0_1(a2614) | (~c1_1(a2614))))),
% 0.90/1.17 inference(monotonicity,[status(thm)],[1929])).
% 0.90/1.17 tff(1931,plain,
% 0.90/1.17 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c1_1(a2556)) | (~c0_1(a2556)) | (~c2_1(a2556)) | c3_1(a2614) | c0_1(a2614) | (~c1_1(a2614)) | c3_1(a2552) | c1_1(a2552) | c0_1(a2552))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c3_1(a2614) | c1_1(a2552) | c3_1(a2552) | (~ndr1_0) | (~c2_1(a2556)) | (~c1_1(a2556)) | (~c0_1(a2556)) | c0_1(a2552) | c0_1(a2614) | (~c1_1(a2614)))),
% 0.90/1.17 inference(transitivity,[status(thm)],[1930, 1928])).
% 0.90/1.17 tff(1932,plain,
% 0.90/1.17 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c1_1(a2556)) | (~c0_1(a2556)) | (~c2_1(a2556)) | c3_1(a2614) | c0_1(a2614) | (~c1_1(a2614)) | c3_1(a2552) | c1_1(a2552) | c0_1(a2552))),
% 0.90/1.17 inference(quant_inst,[status(thm)],[])).
% 0.90/1.17 tff(1933,plain,
% 0.90/1.17 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c3_1(a2614) | c1_1(a2552) | c3_1(a2552) | (~ndr1_0) | (~c2_1(a2556)) | (~c1_1(a2556)) | (~c0_1(a2556)) | c0_1(a2552) | c0_1(a2614) | (~c1_1(a2614))),
% 0.90/1.17 inference(modus_ponens,[status(thm)],[1932, 1931])).
% 0.90/1.17 tff(1934,plain,
% 0.90/1.17 (~c0_1(a2556)),
% 0.90/1.17 inference(unit_resolution,[status(thm)],[1933, 90, 1874, 1873, 13, 20, 1919, 1918, 459, 1836, 1927])).
% 0.90/1.17 tff(1935,plain,
% 0.90/1.17 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (c3_1(a2614) | c1_1(a2552) | c3_1(a2552) | (~ndr1_0) | (~c0_1(a2597)) | (~c2_1(a2597)) | (~c1_1(a2597)) | c0_1(a2552) | c0_1(a2614) | (~c1_1(a2614)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c3_1(a2614) | c1_1(a2552) | c3_1(a2552) | (~ndr1_0) | (~c0_1(a2597)) | (~c2_1(a2597)) | (~c1_1(a2597)) | c0_1(a2552) | c0_1(a2614) | (~c1_1(a2614)))),
% 0.90/1.17 inference(rewrite,[status(thm)],[])).
% 0.90/1.17 tff(1936,plain,
% 0.90/1.17 (((~ndr1_0) | (~c1_1(a2597)) | (~c0_1(a2597)) | (~c2_1(a2597)) | c3_1(a2614) | c0_1(a2614) | (~c1_1(a2614)) | c3_1(a2552) | c1_1(a2552) | c0_1(a2552)) <=> (c3_1(a2614) | c1_1(a2552) | c3_1(a2552) | (~ndr1_0) | (~c0_1(a2597)) | (~c2_1(a2597)) | (~c1_1(a2597)) | c0_1(a2552) | c0_1(a2614) | (~c1_1(a2614)))),
% 0.90/1.17 inference(rewrite,[status(thm)],[])).
% 0.90/1.17 tff(1937,plain,
% 0.90/1.17 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c1_1(a2597)) | (~c0_1(a2597)) | (~c2_1(a2597)) | c3_1(a2614) | c0_1(a2614) | (~c1_1(a2614)) | c3_1(a2552) | c1_1(a2552) | c0_1(a2552))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (c3_1(a2614) | c1_1(a2552) | c3_1(a2552) | (~ndr1_0) | (~c0_1(a2597)) | (~c2_1(a2597)) | (~c1_1(a2597)) | c0_1(a2552) | c0_1(a2614) | (~c1_1(a2614))))),
% 0.90/1.17 inference(monotonicity,[status(thm)],[1936])).
% 0.90/1.17 tff(1938,plain,
% 0.90/1.17 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c1_1(a2597)) | (~c0_1(a2597)) | (~c2_1(a2597)) | c3_1(a2614) | c0_1(a2614) | (~c1_1(a2614)) | c3_1(a2552) | c1_1(a2552) | c0_1(a2552))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c3_1(a2614) | c1_1(a2552) | c3_1(a2552) | (~ndr1_0) | (~c0_1(a2597)) | (~c2_1(a2597)) | (~c1_1(a2597)) | c0_1(a2552) | c0_1(a2614) | (~c1_1(a2614)))),
% 0.90/1.17 inference(transitivity,[status(thm)],[1937, 1935])).
% 0.90/1.17 tff(1939,plain,
% 0.90/1.17 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c1_1(a2597)) | (~c0_1(a2597)) | (~c2_1(a2597)) | c3_1(a2614) | c0_1(a2614) | (~c1_1(a2614)) | c3_1(a2552) | c1_1(a2552) | c0_1(a2552))),
% 0.90/1.17 inference(quant_inst,[status(thm)],[])).
% 0.90/1.17 tff(1940,plain,
% 0.90/1.17 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c3_1(a2614) | c1_1(a2552) | c3_1(a2552) | (~ndr1_0) | (~c0_1(a2597)) | (~c2_1(a2597)) | (~c1_1(a2597)) | c0_1(a2552) | c0_1(a2614) | (~c1_1(a2614))),
% 0.90/1.17 inference(modus_ponens,[status(thm)],[1939, 1938])).
% 0.90/1.17 tff(1941,plain,
% 0.90/1.17 (~c2_1(a2597)),
% 0.90/1.17 inference(unit_resolution,[status(thm)],[1940, 90, 1878, 1880, 13, 20, 1919, 1918, 459, 1836, 1927])).
% 0.90/1.17 tff(1942,plain,
% 0.90/1.17 (c2_1(a2552)),
% 0.90/1.17 inference(unit_resolution,[status(thm)],[814, 1917])).
% 0.90/1.17 tff(1943,plain,
% 0.90/1.17 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a2552) | c3_1(a2552) | c1_1(a2541) | (~ndr1_0) | (~c3_1(a2541)) | (~c0_1(a2541)) | c0_1(a2552) | (~c2_1(a2552)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a2552) | c3_1(a2552) | c1_1(a2541) | (~ndr1_0) | (~c3_1(a2541)) | (~c0_1(a2541)) | c0_1(a2552) | (~c2_1(a2552)))),
% 0.90/1.17 inference(rewrite,[status(thm)],[])).
% 0.90/1.17 tff(1944,plain,
% 0.90/1.17 (((~ndr1_0) | c1_1(a2541) | (~c3_1(a2541)) | (~c0_1(a2541)) | c3_1(a2552) | c1_1(a2552) | (~c2_1(a2552)) | c3_1(a2552) | c0_1(a2552) | (~c2_1(a2552))) <=> (c1_1(a2552) | c3_1(a2552) | c1_1(a2541) | (~ndr1_0) | (~c3_1(a2541)) | (~c0_1(a2541)) | c0_1(a2552) | (~c2_1(a2552)))),
% 0.90/1.17 inference(rewrite,[status(thm)],[])).
% 0.90/1.17 tff(1945,plain,
% 0.90/1.17 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a2541) | (~c3_1(a2541)) | (~c0_1(a2541)) | c3_1(a2552) | c1_1(a2552) | (~c2_1(a2552)) | c3_1(a2552) | c0_1(a2552) | (~c2_1(a2552)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a2552) | c3_1(a2552) | c1_1(a2541) | (~ndr1_0) | (~c3_1(a2541)) | (~c0_1(a2541)) | c0_1(a2552) | (~c2_1(a2552))))),
% 0.90/1.17 inference(monotonicity,[status(thm)],[1944])).
% 0.90/1.17 tff(1946,plain,
% 0.90/1.17 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a2541) | (~c3_1(a2541)) | (~c0_1(a2541)) | c3_1(a2552) | c1_1(a2552) | (~c2_1(a2552)) | c3_1(a2552) | c0_1(a2552) | (~c2_1(a2552)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a2552) | c3_1(a2552) | c1_1(a2541) | (~ndr1_0) | (~c3_1(a2541)) | (~c0_1(a2541)) | c0_1(a2552) | (~c2_1(a2552)))),
% 0.90/1.17 inference(transitivity,[status(thm)],[1945, 1943])).
% 0.90/1.17 tff(1947,plain,
% 0.90/1.17 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a2541) | (~c3_1(a2541)) | (~c0_1(a2541)) | c3_1(a2552) | c1_1(a2552) | (~c2_1(a2552)) | c3_1(a2552) | c0_1(a2552) | (~c2_1(a2552)))),
% 0.90/1.17 inference(quant_inst,[status(thm)],[])).
% 0.90/1.17 tff(1948,plain,
% 0.90/1.17 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a2552) | c3_1(a2552) | c1_1(a2541) | (~ndr1_0) | (~c3_1(a2541)) | (~c0_1(a2541)) | c0_1(a2552) | (~c2_1(a2552))),
% 0.90/1.17 inference(modus_ponens,[status(thm)],[1947, 1946])).
% 0.90/1.17 tff(1949,plain,
% 0.90/1.17 (~c0_1(a2541)),
% 0.90/1.17 inference(unit_resolution,[status(thm)],[1948, 90, 1942, 1862, 1919, 1918, 1860, 424, 1927])).
% 0.90/1.17 tff(1950,plain,
% 0.90/1.17 (~hskp24),
% 0.90/1.17 inference(unit_resolution,[status(thm)],[743, 1949, 1880, 1879, 1862, 1861, 1878])).
% 0.90/1.17 tff(1951,plain,
% 0.90/1.17 (((~![U: $i] : (hskp24 | hskp25 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp24 | hskp25 | (~ndr1_0) | (~c0_1(a2597)) | c2_1(a2597) | (~c1_1(a2597)))) <=> ((~![U: $i] : (hskp24 | hskp25 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp24 | hskp25 | (~ndr1_0) | (~c0_1(a2597)) | c2_1(a2597) | (~c1_1(a2597)))),
% 0.90/1.17 inference(rewrite,[status(thm)],[])).
% 0.90/1.17 tff(1952,plain,
% 0.90/1.17 ((hskp24 | hskp25 | (~ndr1_0) | c2_1(a2597) | (~c1_1(a2597)) | (~c0_1(a2597))) <=> (hskp24 | hskp25 | (~ndr1_0) | (~c0_1(a2597)) | c2_1(a2597) | (~c1_1(a2597)))),
% 0.90/1.17 inference(rewrite,[status(thm)],[])).
% 0.90/1.17 tff(1953,plain,
% 0.90/1.17 (((~![U: $i] : (hskp24 | hskp25 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp24 | hskp25 | (~ndr1_0) | c2_1(a2597) | (~c1_1(a2597)) | (~c0_1(a2597)))) <=> ((~![U: $i] : (hskp24 | hskp25 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp24 | hskp25 | (~ndr1_0) | (~c0_1(a2597)) | c2_1(a2597) | (~c1_1(a2597))))),
% 0.90/1.17 inference(monotonicity,[status(thm)],[1952])).
% 0.90/1.17 tff(1954,plain,
% 0.90/1.17 (((~![U: $i] : (hskp24 | hskp25 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp24 | hskp25 | (~ndr1_0) | c2_1(a2597) | (~c1_1(a2597)) | (~c0_1(a2597)))) <=> ((~![U: $i] : (hskp24 | hskp25 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp24 | hskp25 | (~ndr1_0) | (~c0_1(a2597)) | c2_1(a2597) | (~c1_1(a2597)))),
% 0.90/1.17 inference(transitivity,[status(thm)],[1953, 1951])).
% 0.90/1.17 tff(1955,plain,
% 0.90/1.17 ((~![U: $i] : (hskp24 | hskp25 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp24 | hskp25 | (~ndr1_0) | c2_1(a2597) | (~c1_1(a2597)) | (~c0_1(a2597)))),
% 0.90/1.17 inference(quant_inst,[status(thm)],[])).
% 0.90/1.17 tff(1956,plain,
% 0.90/1.17 ((~![U: $i] : (hskp24 | hskp25 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp24 | hskp25 | (~ndr1_0) | (~c0_1(a2597)) | c2_1(a2597) | (~c1_1(a2597))),
% 0.90/1.17 inference(modus_ponens,[status(thm)],[1955, 1954])).
% 0.90/1.17 tff(1957,plain,
% 0.90/1.17 (hskp24 | hskp25 | c2_1(a2597)),
% 0.90/1.17 inference(unit_resolution,[status(thm)],[1956, 90, 1878, 1880, 754])).
% 0.90/1.17 tff(1958,plain,
% 0.90/1.17 (hskp25),
% 0.90/1.17 inference(unit_resolution,[status(thm)],[1957, 1950, 1941])).
% 0.90/1.17 tff(1959,plain,
% 0.90/1.17 (hskp8),
% 0.90/1.17 inference(unit_resolution,[status(thm)],[689, 1958, 26, 20, 1836])).
% 0.90/1.17 tff(1960,plain,
% 0.90/1.17 (~c3_1(a2525)),
% 0.90/1.17 inference(unit_resolution,[status(thm)],[607, 1959])).
% 0.90/1.17 tff(1961,plain,
% 0.90/1.17 (c2_1(a2525)),
% 0.90/1.17 inference(unit_resolution,[status(thm)],[1071, 1959])).
% 0.90/1.17 tff(1962,plain,
% 0.90/1.17 (c0_1(a2525)),
% 0.90/1.17 inference(unit_resolution,[status(thm)],[615, 1959])).
% 0.90/1.17 tff(1963,plain,
% 0.90/1.17 ($false),
% 0.90/1.17 inference(unit_resolution,[status(thm)],[1275, 90, 1873, 1872, 1942, 1962, 1961, 1919, 1960, 1087, 1927, 1934])).
% 0.90/1.17 tff(1964,plain,(hskp23 | (~c0_1(a2601)) | c2_1(a2601) | (~c3_1(a2601)) | hskp21 | (~c3_1(a2526)) | c0_1(a2526)), inference(lemma,lemma(discharge,[]))).
% 0.90/1.17 tff(1965,plain,
% 0.90/1.17 (hskp23),
% 0.90/1.17 inference(unit_resolution,[status(thm)],[1964, 1818, 1739, 1733, 1716, 1725, 152])).
% 0.90/1.17 tff(1966,plain,
% 0.90/1.17 (~c1_1(a2553)),
% 0.90/1.17 inference(unit_resolution,[status(thm)],[785, 1965])).
% 0.90/1.17 tff(1967,plain,
% 0.90/1.17 (~c3_1(a2553)),
% 0.90/1.17 inference(unit_resolution,[status(thm)],[769, 1965])).
% 0.90/1.17 tff(1968,assumption,(~c0_1(a2553)), introduced(assumption)).
% 0.90/1.17 tff(1969,plain,
% 0.90/1.17 (~hskp23),
% 0.90/1.17 inference(unit_resolution,[status(thm)],[793, 1968])).
% 0.90/1.17 tff(1970,plain,
% 0.90/1.17 (hskp27),
% 0.90/1.17 inference(unit_resolution,[status(thm)],[4, 1969])).
% 0.90/1.17 tff(1971,plain,
% 0.90/1.17 (~c3_1(a2614)),
% 0.90/1.17 inference(unit_resolution,[status(thm)],[19, 1970])).
% 0.90/1.17 tff(1972,plain,
% 0.90/1.17 (~c2_1(a2614)),
% 0.90/1.17 inference(unit_resolution,[status(thm)],[25, 1970])).
% 0.90/1.17 tff(1973,plain,
% 0.90/1.17 (c1_1(a2614)),
% 0.90/1.17 inference(unit_resolution,[status(thm)],[12, 1970])).
% 0.90/1.17 tff(1974,plain,
% 0.90/1.17 (~c0_1(a2614)),
% 0.90/1.17 inference(unit_resolution,[status(thm)],[1835, 90, 1829, 1973, 1972, 1971, 1828])).
% 0.90/1.17 tff(1975,plain,
% 0.90/1.17 (hskp1),
% 0.90/1.17 inference(unit_resolution,[status(thm)],[381, 90, 1973, 1972, 1971, 375, 1974])).
% 0.90/1.17 tff(1976,plain,
% 0.90/1.17 (~c3_1(a2517)),
% 0.90/1.17 inference(unit_resolution,[status(thm)],[388, 1975])).
% 0.90/1.17 tff(1977,plain,
% 0.90/1.17 (c2_1(a2517)),
% 0.90/1.17 inference(unit_resolution,[status(thm)],[402, 1975])).
% 0.90/1.17 tff(1978,plain,
% 0.90/1.17 (hskp9),
% 0.90/1.17 inference(unit_resolution,[status(thm)],[115, 90, 1973, 1972, 1971, 36, 1974])).
% 0.90/1.17 tff(1979,plain,
% 0.90/1.17 (c1_1(a2526)),
% 0.90/1.17 inference(unit_resolution,[status(thm)],[199, 1978])).
% 0.90/1.18 tff(1980,plain,
% 0.90/1.18 (hskp17 | (~c1_1(a2526))),
% 0.90/1.18 inference(unit_resolution,[status(thm)],[232, 90, 1973, 216, 1972, 1971, 152, 226])).
% 0.90/1.18 tff(1981,plain,
% 0.90/1.18 (hskp17),
% 0.90/1.18 inference(unit_resolution,[status(thm)],[1980, 1979])).
% 0.90/1.18 tff(1982,plain,
% 0.90/1.18 (~c1_1(a2541)),
% 0.90/1.18 inference(unit_resolution,[status(thm)],[244, 1981])).
% 0.90/1.18 tff(1983,plain,
% 0.90/1.18 (~c0_1(a2517)),
% 0.90/1.18 inference(unit_resolution,[status(thm)],[394, 1975])).
% 0.90/1.18 tff(1984,plain,
% 0.90/1.18 (c3_1(a2541)),
% 0.90/1.18 inference(unit_resolution,[status(thm)],[252, 1981])).
% 0.90/1.18 tff(1985,plain,
% 0.90/1.18 (~c2_1(a2541)),
% 0.90/1.18 inference(unit_resolution,[status(thm)],[238, 1981])).
% 0.90/1.18 tff(1986,plain,
% 0.90/1.18 (hskp29),
% 0.90/1.18 inference(unit_resolution,[status(thm)],[445, 1985, 1984, 1983, 1982, 1977, 1976])).
% 0.90/1.18 tff(1987,plain,
% 0.90/1.18 (c3_1(a2556)),
% 0.90/1.18 inference(unit_resolution,[status(thm)],[339, 1986])).
% 0.90/1.18 tff(1988,plain,
% 0.90/1.18 (c2_1(a2556)),
% 0.90/1.18 inference(unit_resolution,[status(thm)],[347, 1986])).
% 0.90/1.18 tff(1989,plain,
% 0.90/1.18 (c1_1(a2556)),
% 0.90/1.18 inference(unit_resolution,[status(thm)],[355, 1986])).
% 0.90/1.18 tff(1990,plain,
% 0.90/1.18 (hskp31),
% 0.90/1.18 inference(unit_resolution,[status(thm)],[530, 1969, 90, 1989, 1988, 1987, 524])).
% 0.90/1.18 tff(1991,plain,
% 0.90/1.18 (c0_1(a2597)),
% 0.90/1.18 inference(unit_resolution,[status(thm)],[554, 1990])).
% 0.90/1.18 tff(1992,plain,
% 0.90/1.18 (c3_1(a2597)),
% 0.90/1.18 inference(unit_resolution,[status(thm)],[538, 1990])).
% 0.90/1.18 tff(1993,plain,
% 0.90/1.18 (c1_1(a2597)),
% 0.90/1.18 inference(unit_resolution,[status(thm)],[546, 1990])).
% 0.90/1.18 tff(1994,plain,
% 0.90/1.18 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a2553) | c3_1(a2614) | c1_1(a2553) | c3_1(a2553) | (~ndr1_0) | (~c2_1(a2556)) | (~c1_1(a2556)) | (~c0_1(a2556)) | c0_1(a2614) | (~c1_1(a2614)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a2553) | c3_1(a2614) | c1_1(a2553) | c3_1(a2553) | (~ndr1_0) | (~c2_1(a2556)) | (~c1_1(a2556)) | (~c0_1(a2556)) | c0_1(a2614) | (~c1_1(a2614)))),
% 0.90/1.18 inference(rewrite,[status(thm)],[])).
% 0.90/1.18 tff(1995,plain,
% 0.90/1.18 (((~ndr1_0) | (~c1_1(a2556)) | (~c0_1(a2556)) | (~c2_1(a2556)) | c3_1(a2614) | c0_1(a2614) | (~c1_1(a2614)) | c3_1(a2553) | c1_1(a2553) | c0_1(a2553)) <=> (c0_1(a2553) | c3_1(a2614) | c1_1(a2553) | c3_1(a2553) | (~ndr1_0) | (~c2_1(a2556)) | (~c1_1(a2556)) | (~c0_1(a2556)) | c0_1(a2614) | (~c1_1(a2614)))),
% 0.90/1.18 inference(rewrite,[status(thm)],[])).
% 0.90/1.18 tff(1996,plain,
% 0.90/1.18 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c1_1(a2556)) | (~c0_1(a2556)) | (~c2_1(a2556)) | c3_1(a2614) | c0_1(a2614) | (~c1_1(a2614)) | c3_1(a2553) | c1_1(a2553) | c0_1(a2553))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a2553) | c3_1(a2614) | c1_1(a2553) | c3_1(a2553) | (~ndr1_0) | (~c2_1(a2556)) | (~c1_1(a2556)) | (~c0_1(a2556)) | c0_1(a2614) | (~c1_1(a2614))))),
% 0.90/1.18 inference(monotonicity,[status(thm)],[1995])).
% 0.90/1.18 tff(1997,plain,
% 0.90/1.18 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c1_1(a2556)) | (~c0_1(a2556)) | (~c2_1(a2556)) | c3_1(a2614) | c0_1(a2614) | (~c1_1(a2614)) | c3_1(a2553) | c1_1(a2553) | c0_1(a2553))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a2553) | c3_1(a2614) | c1_1(a2553) | c3_1(a2553) | (~ndr1_0) | (~c2_1(a2556)) | (~c1_1(a2556)) | (~c0_1(a2556)) | c0_1(a2614) | (~c1_1(a2614)))),
% 0.90/1.18 inference(transitivity,[status(thm)],[1996, 1994])).
% 0.90/1.18 tff(1998,plain,
% 0.90/1.18 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c1_1(a2556)) | (~c0_1(a2556)) | (~c2_1(a2556)) | c3_1(a2614) | c0_1(a2614) | (~c1_1(a2614)) | c3_1(a2553) | c1_1(a2553) | c0_1(a2553))),
% 1.01/1.18 inference(quant_inst,[status(thm)],[])).
% 1.01/1.18 tff(1999,plain,
% 1.01/1.18 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a2553) | c3_1(a2614) | c1_1(a2553) | c3_1(a2553) | (~ndr1_0) | (~c2_1(a2556)) | (~c1_1(a2556)) | (~c0_1(a2556)) | c0_1(a2614) | (~c1_1(a2614))),
% 1.01/1.18 inference(modus_ponens,[status(thm)],[1998, 1997])).
% 1.01/1.18 tff(2000,plain,
% 1.01/1.18 (~c0_1(a2556)),
% 1.01/1.18 inference(unit_resolution,[status(thm)],[1999, 90, 1989, 1988, 1973, 1968, 1971, 850, 849, 459, 1974])).
% 1.01/1.18 tff(2001,plain,
% 1.01/1.18 (~c2_1(a2597)),
% 1.01/1.18 inference(unit_resolution,[status(thm)],[561, 90, 1991, 1993, 1992, 1988, 1987, 514, 2000])).
% 1.01/1.18 tff(2002,plain,
% 1.01/1.18 (hskp18),
% 1.01/1.18 inference(unit_resolution,[status(thm)],[578, 90, 1993, 1992, 1989, 1988, 1987, 572, 2001])).
% 1.01/1.18 tff(2003,plain,
% 1.01/1.18 (c2_1(a2545)),
% 1.01/1.18 inference(unit_resolution,[status(thm)],[592, 2002])).
% 1.01/1.18 tff(2004,plain,
% 1.01/1.18 (~c0_1(a2545)),
% 1.01/1.18 inference(unit_resolution,[status(thm)],[584, 2002])).
% 1.01/1.18 tff(2005,plain,
% 1.01/1.18 (c1_1(a2545)),
% 1.01/1.18 inference(unit_resolution,[status(thm)],[600, 2002])).
% 1.01/1.18 tff(2006,plain,
% 1.01/1.18 (~hskp8),
% 1.01/1.18 inference(unit_resolution,[status(thm)],[647, 2005, 1984, 1982, 2004, 2003, 1985, 1989, 1988, 1987])).
% 1.01/1.18 tff(2007,plain,
% 1.01/1.18 (hskp8 | (~c0_1(a2541))),
% 1.01/1.18 inference(unit_resolution,[status(thm)],[696, 90, 1972, 1971, 1982, 1985, 659, 1974])).
% 1.01/1.18 tff(2008,plain,
% 1.01/1.18 (~c0_1(a2541)),
% 1.01/1.18 inference(unit_resolution,[status(thm)],[2007, 2006])).
% 1.01/1.18 tff(2009,plain,
% 1.01/1.18 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp8 | c2_1(a2614) | c3_1(a2614) | c2_1(a2601) | (~ndr1_0) | (~c0_1(a2601)) | c1_1(a2601) | c0_1(a2614))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp8 | c2_1(a2614) | c3_1(a2614) | c2_1(a2601) | (~ndr1_0) | (~c0_1(a2601)) | c1_1(a2601) | c0_1(a2614))),
% 1.01/1.18 inference(rewrite,[status(thm)],[])).
% 1.01/1.18 tff(2010,plain,
% 1.01/1.18 ((hskp8 | (~ndr1_0) | c2_1(a2601) | c1_1(a2601) | (~c0_1(a2601)) | c3_1(a2614) | c0_1(a2614) | c2_1(a2614)) <=> (hskp8 | c2_1(a2614) | c3_1(a2614) | c2_1(a2601) | (~ndr1_0) | (~c0_1(a2601)) | c1_1(a2601) | c0_1(a2614))),
% 1.01/1.18 inference(rewrite,[status(thm)],[])).
% 1.01/1.18 tff(2011,plain,
% 1.01/1.18 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp8 | (~ndr1_0) | c2_1(a2601) | c1_1(a2601) | (~c0_1(a2601)) | c3_1(a2614) | c0_1(a2614) | c2_1(a2614))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp8 | c2_1(a2614) | c3_1(a2614) | c2_1(a2601) | (~ndr1_0) | (~c0_1(a2601)) | c1_1(a2601) | c0_1(a2614)))),
% 1.01/1.18 inference(monotonicity,[status(thm)],[2010])).
% 1.01/1.18 tff(2012,plain,
% 1.01/1.18 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp8 | (~ndr1_0) | c2_1(a2601) | c1_1(a2601) | (~c0_1(a2601)) | c3_1(a2614) | c0_1(a2614) | c2_1(a2614))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp8 | c2_1(a2614) | c3_1(a2614) | c2_1(a2601) | (~ndr1_0) | (~c0_1(a2601)) | c1_1(a2601) | c0_1(a2614))),
% 1.01/1.18 inference(transitivity,[status(thm)],[2011, 2009])).
% 1.01/1.18 tff(2013,plain,
% 1.01/1.18 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp8 | (~ndr1_0) | c2_1(a2601) | c1_1(a2601) | (~c0_1(a2601)) | c3_1(a2614) | c0_1(a2614) | c2_1(a2614))),
% 1.01/1.18 inference(quant_inst,[status(thm)],[])).
% 1.01/1.18 tff(2014,plain,
% 1.01/1.18 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp8 | c2_1(a2614) | c3_1(a2614) | c2_1(a2601) | (~ndr1_0) | (~c0_1(a2601)) | c1_1(a2601) | c0_1(a2614)),
% 1.01/1.18 inference(modus_ponens,[status(thm)],[2013, 2012])).
% 1.01/1.18 tff(2015,plain,
% 1.01/1.18 (hskp8 | c1_1(a2601)),
% 1.01/1.18 inference(unit_resolution,[status(thm)],[2014, 90, 1882, 1972, 1971, 1881, 659, 1974])).
% 1.01/1.18 tff(2016,plain,
% 1.01/1.18 (c1_1(a2601)),
% 1.01/1.18 inference(unit_resolution,[status(thm)],[2015, 2006])).
% 1.01/1.18 tff(2017,plain,
% 1.01/1.18 (~hskp25),
% 1.01/1.18 inference(unit_resolution,[status(thm)],[689, 2006, 1972, 1971, 1974])).
% 1.01/1.18 tff(2018,plain,
% 1.01/1.18 (hskp24),
% 1.01/1.18 inference(unit_resolution,[status(thm)],[1901, 2017, 2016])).
% 1.01/1.18 tff(2019,plain,
% 1.01/1.18 ($false),
% 1.01/1.18 inference(unit_resolution,[status(thm)],[743, 2018, 2008, 1993, 1992, 1984, 1985, 1991])).
% 1.01/1.18 tff(2020,plain,(c0_1(a2553) | (~c0_1(a2601)) | c2_1(a2601) | c1_1(a2553) | c3_1(a2553) | (~c3_1(a2526)) | c0_1(a2526) | hskp21), inference(lemma,lemma(discharge,[]))).
% 1.01/1.18 tff(2021,plain,
% 1.01/1.18 (c0_1(a2553)),
% 1.01/1.18 inference(unit_resolution,[status(thm)],[2020, 850, 1739, 1725, 849, 1818, 152, 1716])).
% 1.01/1.18 tff(2022,plain,
% 1.01/1.18 (hskp22 | c1_1(a2553) | (~c0_1(a2553))),
% 1.01/1.18 inference(unit_resolution,[status(thm)],[800, 90, 151, 849, 780])).
% 1.01/1.18 tff(2023,plain,
% 1.01/1.18 (hskp22),
% 1.01/1.18 inference(unit_resolution,[status(thm)],[2022, 2021, 850])).
% 1.01/1.18 tff(2024,plain,
% 1.01/1.18 (~c3_1(a2552)),
% 1.01/1.18 inference(unit_resolution,[status(thm)],[806, 2023])).
% 1.01/1.18 tff(2025,plain,
% 1.01/1.18 (~c1_1(a2552)),
% 1.01/1.18 inference(unit_resolution,[status(thm)],[820, 2023])).
% 1.01/1.18 tff(2026,plain,
% 1.01/1.18 (c2_1(a2552)),
% 1.01/1.18 inference(unit_resolution,[status(thm)],[814, 2023])).
% 1.01/1.18 tff(2027,assumption,(~c1_1(a2526)), introduced(assumption)).
% 1.01/1.18 tff(2028,plain,
% 1.01/1.18 (~hskp9),
% 1.01/1.18 inference(unit_resolution,[status(thm)],[199, 2027])).
% 1.01/1.18 tff(2029,plain,
% 1.01/1.18 (~c1_1(a2601)),
% 1.01/1.18 inference(unit_resolution,[status(thm)],[1748, 2028])).
% 1.01/1.18 tff(2030,plain,
% 1.01/1.18 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c2_1(W) | (~c0_1(W)))) | (c1_1(a2526) | c2_1(a2601) | (~ndr1_0) | (~c3_1(a2526)) | (~c2_1(a2526)) | (~c3_1(a2601)) | (~c0_1(a2601)) | c1_1(a2601))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c2_1(W) | (~c0_1(W)))) | c1_1(a2526) | c2_1(a2601) | (~ndr1_0) | (~c3_1(a2526)) | (~c2_1(a2526)) | (~c3_1(a2601)) | (~c0_1(a2601)) | c1_1(a2601))),
% 1.01/1.18 inference(rewrite,[status(thm)],[])).
% 1.01/1.18 tff(2031,plain,
% 1.01/1.18 (((~ndr1_0) | c2_1(a2601) | (~c3_1(a2601)) | (~c0_1(a2601)) | c1_1(a2526) | (~c3_1(a2526)) | (~c2_1(a2526)) | c1_1(a2601) | c2_1(a2601) | (~c0_1(a2601))) <=> (c1_1(a2526) | c2_1(a2601) | (~ndr1_0) | (~c3_1(a2526)) | (~c2_1(a2526)) | (~c3_1(a2601)) | (~c0_1(a2601)) | c1_1(a2601))),
% 1.01/1.18 inference(rewrite,[status(thm)],[])).
% 1.01/1.18 tff(2032,plain,
% 1.01/1.18 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c2_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a2601) | (~c3_1(a2601)) | (~c0_1(a2601)) | c1_1(a2526) | (~c3_1(a2526)) | (~c2_1(a2526)) | c1_1(a2601) | c2_1(a2601) | (~c0_1(a2601)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c2_1(W) | (~c0_1(W)))) | (c1_1(a2526) | c2_1(a2601) | (~ndr1_0) | (~c3_1(a2526)) | (~c2_1(a2526)) | (~c3_1(a2601)) | (~c0_1(a2601)) | c1_1(a2601)))),
% 1.01/1.18 inference(monotonicity,[status(thm)],[2031])).
% 1.01/1.18 tff(2033,plain,
% 1.01/1.18 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c2_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a2601) | (~c3_1(a2601)) | (~c0_1(a2601)) | c1_1(a2526) | (~c3_1(a2526)) | (~c2_1(a2526)) | c1_1(a2601) | c2_1(a2601) | (~c0_1(a2601)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c2_1(W) | (~c0_1(W)))) | c1_1(a2526) | c2_1(a2601) | (~ndr1_0) | (~c3_1(a2526)) | (~c2_1(a2526)) | (~c3_1(a2601)) | (~c0_1(a2601)) | c1_1(a2601))),
% 1.01/1.18 inference(transitivity,[status(thm)],[2032, 2030])).
% 1.01/1.18 tff(2034,plain,
% 1.01/1.18 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c2_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a2601) | (~c3_1(a2601)) | (~c0_1(a2601)) | c1_1(a2526) | (~c3_1(a2526)) | (~c2_1(a2526)) | c1_1(a2601) | c2_1(a2601) | (~c0_1(a2601)))),
% 1.01/1.18 inference(quant_inst,[status(thm)],[])).
% 1.01/1.18 tff(2035,plain,
% 1.01/1.18 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c2_1(W) | (~c0_1(W)))) | c1_1(a2526) | c2_1(a2601) | (~ndr1_0) | (~c3_1(a2526)) | (~c2_1(a2526)) | (~c3_1(a2601)) | (~c0_1(a2601)) | c1_1(a2601)),
% 1.01/1.18 inference(modus_ponens,[status(thm)],[2034, 2033])).
% 1.01/1.18 tff(2036,plain,
% 1.01/1.18 (~c2_1(a2526)),
% 1.01/1.18 inference(unit_resolution,[status(thm)],[2035, 90, 1725, 1733, 2027, 1818, 1739, 1402, 2029])).
% 1.01/1.18 tff(2037,plain,
% 1.01/1.18 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp11 | c2_1(a2601) | c0_1(a2526) | (~ndr1_0) | (~c3_1(a2526)) | c2_1(a2526) | (~c3_1(a2601)) | c1_1(a2601))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp11 | c2_1(a2601) | c0_1(a2526) | (~ndr1_0) | (~c3_1(a2526)) | c2_1(a2526) | (~c3_1(a2601)) | c1_1(a2601))),
% 1.01/1.18 inference(rewrite,[status(thm)],[])).
% 1.01/1.18 tff(2038,plain,
% 1.01/1.18 ((hskp11 | (~ndr1_0) | c2_1(a2601) | c1_1(a2601) | (~c3_1(a2601)) | c0_1(a2526) | c2_1(a2526) | (~c3_1(a2526))) <=> (hskp11 | c2_1(a2601) | c0_1(a2526) | (~ndr1_0) | (~c3_1(a2526)) | c2_1(a2526) | (~c3_1(a2601)) | c1_1(a2601))),
% 1.01/1.18 inference(rewrite,[status(thm)],[])).
% 1.01/1.18 tff(2039,plain,
% 1.01/1.18 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp11 | (~ndr1_0) | c2_1(a2601) | c1_1(a2601) | (~c3_1(a2601)) | c0_1(a2526) | c2_1(a2526) | (~c3_1(a2526)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp11 | c2_1(a2601) | c0_1(a2526) | (~ndr1_0) | (~c3_1(a2526)) | c2_1(a2526) | (~c3_1(a2601)) | c1_1(a2601)))),
% 1.01/1.18 inference(monotonicity,[status(thm)],[2038])).
% 1.01/1.18 tff(2040,plain,
% 1.01/1.18 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp11 | (~ndr1_0) | c2_1(a2601) | c1_1(a2601) | (~c3_1(a2601)) | c0_1(a2526) | c2_1(a2526) | (~c3_1(a2526)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp11 | c2_1(a2601) | c0_1(a2526) | (~ndr1_0) | (~c3_1(a2526)) | c2_1(a2526) | (~c3_1(a2601)) | c1_1(a2601))),
% 1.01/1.18 inference(transitivity,[status(thm)],[2039, 2037])).
% 1.01/1.18 tff(2041,plain,
% 1.01/1.18 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp11 | (~ndr1_0) | c2_1(a2601) | c1_1(a2601) | (~c3_1(a2601)) | c0_1(a2526) | c2_1(a2526) | (~c3_1(a2526)))),
% 1.01/1.18 inference(quant_inst,[status(thm)],[])).
% 1.01/1.18 tff(2042,plain,
% 1.01/1.18 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp11 | c2_1(a2601) | c0_1(a2526) | (~ndr1_0) | (~c3_1(a2526)) | c2_1(a2526) | (~c3_1(a2601)) | c1_1(a2601)),
% 1.01/1.18 inference(modus_ponens,[status(thm)],[2041, 2040])).
% 1.01/1.18 tff(2043,plain,
% 1.01/1.18 (hskp11 | (~c3_1(a2526)) | c2_1(a2526) | c1_1(a2601)),
% 1.01/1.18 inference(unit_resolution,[status(thm)],[2042, 90, 1733, 1739, 152, 295])).
% 1.01/1.18 tff(2044,plain,
% 1.01/1.18 (hskp11),
% 1.01/1.18 inference(unit_resolution,[status(thm)],[2043, 2036, 1818, 2029])).
% 1.01/1.18 tff(2045,plain,
% 1.01/1.18 (~c3_1(a2531)),
% 1.01/1.18 inference(unit_resolution,[status(thm)],[308, 2044])).
% 1.01/1.18 tff(2046,plain,
% 1.01/1.18 (c2_1(a2531)),
% 1.01/1.18 inference(unit_resolution,[status(thm)],[316, 2044])).
% 1.01/1.18 tff(2047,plain,
% 1.01/1.18 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a2552) | c3_1(a2552) | c3_1(a2531) | (~ndr1_0) | c0_1(a2531) | (~c2_1(a2531)) | (~c2_1(a2552)) | (~c3_1(a2601)) | (~c0_1(a2601)) | c1_1(a2601))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a2552) | c3_1(a2552) | c3_1(a2531) | (~ndr1_0) | c0_1(a2531) | (~c2_1(a2531)) | (~c2_1(a2552)) | (~c3_1(a2601)) | (~c0_1(a2601)) | c1_1(a2601))),
% 1.01/1.18 inference(rewrite,[status(thm)],[])).
% 1.01/1.18 tff(2048,plain,
% 1.01/1.18 (((~ndr1_0) | c1_1(a2601) | (~c3_1(a2601)) | (~c0_1(a2601)) | c3_1(a2552) | c1_1(a2552) | (~c2_1(a2552)) | c3_1(a2531) | c0_1(a2531) | (~c2_1(a2531))) <=> (c1_1(a2552) | c3_1(a2552) | c3_1(a2531) | (~ndr1_0) | c0_1(a2531) | (~c2_1(a2531)) | (~c2_1(a2552)) | (~c3_1(a2601)) | (~c0_1(a2601)) | c1_1(a2601))),
% 1.01/1.18 inference(rewrite,[status(thm)],[])).
% 1.01/1.18 tff(2049,plain,
% 1.01/1.18 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a2601) | (~c3_1(a2601)) | (~c0_1(a2601)) | c3_1(a2552) | c1_1(a2552) | (~c2_1(a2552)) | c3_1(a2531) | c0_1(a2531) | (~c2_1(a2531)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a2552) | c3_1(a2552) | c3_1(a2531) | (~ndr1_0) | c0_1(a2531) | (~c2_1(a2531)) | (~c2_1(a2552)) | (~c3_1(a2601)) | (~c0_1(a2601)) | c1_1(a2601)))),
% 1.01/1.18 inference(monotonicity,[status(thm)],[2048])).
% 1.01/1.18 tff(2050,plain,
% 1.01/1.18 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a2601) | (~c3_1(a2601)) | (~c0_1(a2601)) | c3_1(a2552) | c1_1(a2552) | (~c2_1(a2552)) | c3_1(a2531) | c0_1(a2531) | (~c2_1(a2531)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a2552) | c3_1(a2552) | c3_1(a2531) | (~ndr1_0) | c0_1(a2531) | (~c2_1(a2531)) | (~c2_1(a2552)) | (~c3_1(a2601)) | (~c0_1(a2601)) | c1_1(a2601))),
% 1.01/1.18 inference(transitivity,[status(thm)],[2049, 2047])).
% 1.01/1.18 tff(2051,plain,
% 1.01/1.18 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a2601) | (~c3_1(a2601)) | (~c0_1(a2601)) | c3_1(a2552) | c1_1(a2552) | (~c2_1(a2552)) | c3_1(a2531) | c0_1(a2531) | (~c2_1(a2531)))),
% 1.01/1.18 inference(quant_inst,[status(thm)],[])).
% 1.01/1.18 tff(2052,plain,
% 1.01/1.18 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a2552) | c3_1(a2552) | c3_1(a2531) | (~ndr1_0) | c0_1(a2531) | (~c2_1(a2531)) | (~c2_1(a2552)) | (~c3_1(a2601)) | (~c0_1(a2601)) | c1_1(a2601)),
% 1.01/1.18 inference(modus_ponens,[status(thm)],[2051, 2050])).
% 1.01/1.18 tff(2053,plain,
% 1.01/1.18 (c0_1(a2531)),
% 1.01/1.18 inference(unit_resolution,[status(thm)],[2052, 90, 1725, 1733, 822, 2046, 824, 823, 2045, 424, 2029])).
% 1.01/1.18 tff(2054,plain,
% 1.01/1.18 (^[V: $i, U: $i] : refl((hskp21 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))) <=> (hskp21 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))))),
% 1.01/1.18 inference(bind,[status(th)],[])).
% 1.01/1.18 tff(2055,plain,
% 1.01/1.18 (![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 1.01/1.18 inference(quant_intro,[status(thm)],[2054])).
% 1.01/1.18 tff(2056,plain,
% 1.01/1.18 (![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 1.01/1.18 inference(rewrite,[status(thm)],[])).
% 1.01/1.18 tff(2057,plain,
% 1.01/1.18 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c3_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c3_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c3_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c3_1(U)) | c1_1(V)) | hskp21) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))) | hskp21))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))) | hskp21) <=> (hskp21 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c3_1(U)) | c1_1(V)) | hskp21) <=> (hskp21 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))))),
% 1.01/1.18 inference(bind,[status(th)],[])).
% 1.01/1.18 tff(2058,plain,
% 1.01/1.18 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c3_1(U)) | c1_1(V)) | hskp21) <=> ![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 1.01/1.18 inference(quant_intro,[status(thm)],[2057])).
% 1.01/1.18 tff(2059,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c3_1(U)) | c1_1(V)) | hskp21)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause187')).
% 1.01/1.18 tff(2060,plain,
% 1.01/1.18 (![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 1.01/1.18 inference(modus_ponens,[status(thm)],[2059, 2058])).
% 1.01/1.18 tff(2061,plain,
% 1.01/1.18 (![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 1.01/1.18 inference(modus_ponens,[status(thm)],[2060, 2056])).
% 1.01/1.18 tff(2062,plain,(
% 1.01/1.18 ![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 1.01/1.18 inference(skolemize,[status(sab)],[2061])).
% 1.01/1.18 tff(2063,plain,
% 1.01/1.18 (![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 1.01/1.18 inference(modus_ponens,[status(thm)],[2062, 2055])).
% 1.01/1.18 tff(2064,plain,
% 1.01/1.18 (c1_1(a2531)),
% 1.01/1.18 inference(unit_resolution,[status(thm)],[324, 2044])).
% 1.01/1.18 tff(2065,plain,
% 1.01/1.18 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp21 | c3_1(a2531) | (~ndr1_0) | (~c0_1(a2531)) | (~c1_1(a2531)) | (~c3_1(a2601)) | (~c0_1(a2601)) | c1_1(a2601))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp21 | c3_1(a2531) | (~ndr1_0) | (~c0_1(a2531)) | (~c1_1(a2531)) | (~c3_1(a2601)) | (~c0_1(a2601)) | c1_1(a2601))),
% 1.01/1.18 inference(rewrite,[status(thm)],[])).
% 1.01/1.18 tff(2066,plain,
% 1.01/1.18 ((hskp21 | (~ndr1_0) | c3_1(a2531) | (~c1_1(a2531)) | (~c0_1(a2531)) | c1_1(a2601) | (~c3_1(a2601)) | (~c0_1(a2601))) <=> (hskp21 | c3_1(a2531) | (~ndr1_0) | (~c0_1(a2531)) | (~c1_1(a2531)) | (~c3_1(a2601)) | (~c0_1(a2601)) | c1_1(a2601))),
% 1.01/1.18 inference(rewrite,[status(thm)],[])).
% 1.01/1.18 tff(2067,plain,
% 1.01/1.18 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp21 | (~ndr1_0) | c3_1(a2531) | (~c1_1(a2531)) | (~c0_1(a2531)) | c1_1(a2601) | (~c3_1(a2601)) | (~c0_1(a2601)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp21 | c3_1(a2531) | (~ndr1_0) | (~c0_1(a2531)) | (~c1_1(a2531)) | (~c3_1(a2601)) | (~c0_1(a2601)) | c1_1(a2601)))),
% 1.01/1.18 inference(monotonicity,[status(thm)],[2066])).
% 1.01/1.18 tff(2068,plain,
% 1.01/1.18 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp21 | (~ndr1_0) | c3_1(a2531) | (~c1_1(a2531)) | (~c0_1(a2531)) | c1_1(a2601) | (~c3_1(a2601)) | (~c0_1(a2601)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp21 | c3_1(a2531) | (~ndr1_0) | (~c0_1(a2531)) | (~c1_1(a2531)) | (~c3_1(a2601)) | (~c0_1(a2601)) | c1_1(a2601))),
% 1.01/1.18 inference(transitivity,[status(thm)],[2067, 2065])).
% 1.01/1.18 tff(2069,plain,
% 1.01/1.18 ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp21 | (~ndr1_0) | c3_1(a2531) | (~c1_1(a2531)) | (~c0_1(a2531)) | c1_1(a2601) | (~c3_1(a2601)) | (~c0_1(a2601)))),
% 1.01/1.18 inference(quant_inst,[status(thm)],[])).
% 1.01/1.18 tff(2070,plain,
% 1.01/1.18 ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp21 | c3_1(a2531) | (~ndr1_0) | (~c0_1(a2531)) | (~c1_1(a2531)) | (~c3_1(a2601)) | (~c0_1(a2601)) | c1_1(a2601)),
% 1.01/1.18 inference(modus_ponens,[status(thm)],[2069, 2068])).
% 1.01/1.18 tff(2071,plain,
% 1.01/1.18 ($false),
% 1.01/1.18 inference(unit_resolution,[status(thm)],[2070, 90, 1716, 1725, 1733, 2064, 2045, 2063, 2029, 2053])).
% 1.01/1.18 tff(2072,plain,(c1_1(a2526) | (~c2_1(a2552)) | c1_1(a2552) | c3_1(a2552) | c0_1(a2526) | hskp30), inference(lemma,lemma(discharge,[]))).
% 1.01/1.18 tff(2073,plain,
% 1.01/1.18 (c1_1(a2526)),
% 1.01/1.18 inference(unit_resolution,[status(thm)],[2072, 2026, 2025, 2024, 152, 151])).
% 1.01/1.18 tff(2074,plain,
% 1.01/1.18 (hskp29 | hskp2 | c1_1(a2553) | (~c0_1(a2553))),
% 1.01/1.18 inference(unit_resolution,[status(thm)],[1436, 90, 849, 1430])).
% 1.01/1.18 tff(2075,plain,
% 1.01/1.18 (hskp2),
% 1.01/1.18 inference(unit_resolution,[status(thm)],[2074, 404, 851, 850])).
% 1.01/1.18 tff(2076,plain,
% 1.01/1.18 (~c3_1(a2518)),
% 1.01/1.18 inference(unit_resolution,[status(thm)],[892, 2075])).
% 1.01/1.18 tff(2077,plain,
% 1.01/1.18 (~c0_1(a2518)),
% 1.01/1.18 inference(unit_resolution,[status(thm)],[898, 2075])).
% 1.01/1.18 tff(2078,plain,
% 1.01/1.18 (c1_1(a2518)),
% 1.01/1.18 inference(unit_resolution,[status(thm)],[906, 2075])).
% 1.01/1.18 tff(2079,plain,
% 1.01/1.18 (~hskp19),
% 1.01/1.18 inference(unit_resolution,[status(thm)],[1308, 934, 824, 823, 945, 1277, 822])).
% 1.01/1.18 tff(2080,assumption,(~hskp19), introduced(assumption)).
% 1.01/1.18 tff(2081,assumption,(~hskp20), introduced(assumption)).
% 1.01/1.18 tff(2082,plain,
% 1.01/1.18 (hskp20 | hskp19 | c1_1(a2553) | c2_1(a2553)),
% 1.01/1.18 inference(unit_resolution,[status(thm)],[1459, 90, 849, 1319])).
% 1.01/1.18 tff(2083,plain,
% 1.01/1.18 (c2_1(a2553)),
% 1.01/1.18 inference(unit_resolution,[status(thm)],[2082, 2081, 850, 2080])).
% 1.01/1.18 tff(2084,plain,
% 1.01/1.18 (^[V: $i, U: $i] : refl((hskp12 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V))) <=> (hskp12 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V))))),
% 1.01/1.18 inference(bind,[status(th)],[])).
% 1.01/1.18 tff(2085,plain,
% 1.01/1.18 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.01/1.18 inference(quant_intro,[status(thm)],[2084])).
% 1.01/1.18 tff(2086,plain,
% 1.01/1.18 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.01/1.18 inference(rewrite,[status(thm)],[])).
% 1.01/1.18 tff(2087,plain,
% 1.01/1.18 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c2_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c2_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c1_1(V)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c1_1(V))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c1_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c1_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | (~c1_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | (~c1_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | (~c1_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c1_1(V))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) | c0_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c1_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c1_1(V))) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) | c0_1(V)) | c3_1(V)) | hskp12) <=> (((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V))) | hskp12))), rewrite((((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V))) | hskp12) <=> (hskp12 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) | c0_1(V)) | c3_1(V)) | hskp12) <=> (hskp12 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))))),
% 1.01/1.18 inference(bind,[status(th)],[])).
% 1.01/1.18 tff(2088,plain,
% 1.01/1.18 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) | c0_1(V)) | c3_1(V)) | hskp12) <=> ![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.01/1.18 inference(quant_intro,[status(thm)],[2087])).
% 1.01/1.18 tff(2089,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) | c0_1(V)) | c3_1(V)) | hskp12)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause178')).
% 1.01/1.18 tff(2090,plain,
% 1.01/1.18 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.01/1.18 inference(modus_ponens,[status(thm)],[2089, 2088])).
% 1.01/1.18 tff(2091,plain,
% 1.01/1.18 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.01/1.18 inference(modus_ponens,[status(thm)],[2090, 2086])).
% 1.01/1.18 tff(2092,plain,(
% 1.01/1.18 ![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.01/1.18 inference(skolemize,[status(sab)],[2091])).
% 1.01/1.18 tff(2093,plain,
% 1.01/1.18 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.01/1.18 inference(modus_ponens,[status(thm)],[2092, 2085])).
% 1.01/1.18 tff(2094,plain,
% 1.01/1.18 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp12 | c3_1(a2553) | c0_1(a2518) | c3_1(a2518) | (~ndr1_0) | (~c1_1(a2518)) | (~c0_1(a2553)) | (~c2_1(a2553)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp12 | c3_1(a2553) | c0_1(a2518) | c3_1(a2518) | (~ndr1_0) | (~c1_1(a2518)) | (~c0_1(a2553)) | (~c2_1(a2553)))),
% 1.01/1.19 inference(rewrite,[status(thm)],[])).
% 1.01/1.19 tff(2095,plain,
% 1.01/1.19 ((hskp12 | (~ndr1_0) | c3_1(a2553) | (~c0_1(a2553)) | (~c2_1(a2553)) | c3_1(a2518) | c0_1(a2518) | (~c1_1(a2518))) <=> (hskp12 | c3_1(a2553) | c0_1(a2518) | c3_1(a2518) | (~ndr1_0) | (~c1_1(a2518)) | (~c0_1(a2553)) | (~c2_1(a2553)))),
% 1.01/1.19 inference(rewrite,[status(thm)],[])).
% 1.01/1.19 tff(2096,plain,
% 1.01/1.19 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp12 | (~ndr1_0) | c3_1(a2553) | (~c0_1(a2553)) | (~c2_1(a2553)) | c3_1(a2518) | c0_1(a2518) | (~c1_1(a2518)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp12 | c3_1(a2553) | c0_1(a2518) | c3_1(a2518) | (~ndr1_0) | (~c1_1(a2518)) | (~c0_1(a2553)) | (~c2_1(a2553))))),
% 1.01/1.19 inference(monotonicity,[status(thm)],[2095])).
% 1.01/1.19 tff(2097,plain,
% 1.01/1.19 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp12 | (~ndr1_0) | c3_1(a2553) | (~c0_1(a2553)) | (~c2_1(a2553)) | c3_1(a2518) | c0_1(a2518) | (~c1_1(a2518)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp12 | c3_1(a2553) | c0_1(a2518) | c3_1(a2518) | (~ndr1_0) | (~c1_1(a2518)) | (~c0_1(a2553)) | (~c2_1(a2553)))),
% 1.01/1.19 inference(transitivity,[status(thm)],[2096, 2094])).
% 1.01/1.19 tff(2098,plain,
% 1.01/1.19 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp12 | (~ndr1_0) | c3_1(a2553) | (~c0_1(a2553)) | (~c2_1(a2553)) | c3_1(a2518) | c0_1(a2518) | (~c1_1(a2518)))),
% 1.01/1.19 inference(quant_inst,[status(thm)],[])).
% 1.01/1.19 tff(2099,plain,
% 1.01/1.19 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp12 | c3_1(a2553) | c0_1(a2518) | c3_1(a2518) | (~ndr1_0) | (~c1_1(a2518)) | (~c0_1(a2553)) | (~c2_1(a2553))),
% 1.01/1.19 inference(modus_ponens,[status(thm)],[2098, 2097])).
% 1.01/1.19 tff(2100,plain,
% 1.01/1.19 (hskp12 | (~c2_1(a2553))),
% 1.01/1.19 inference(unit_resolution,[status(thm)],[2099, 90, 851, 948, 849, 945, 1277, 2093])).
% 1.01/1.19 tff(2101,plain,
% 1.01/1.19 (hskp12),
% 1.01/1.19 inference(unit_resolution,[status(thm)],[2100, 2083])).
% 1.01/1.19 tff(2102,plain,
% 1.01/1.19 (((~hskp12) | (~c3_1(a2533))) <=> ((~hskp12) | (~c3_1(a2533)))),
% 1.01/1.19 inference(rewrite,[status(thm)],[])).
% 1.01/1.19 tff(2103,plain,
% 1.01/1.19 (((~c3_1(a2533)) | (~hskp12)) <=> ((~hskp12) | (~c3_1(a2533)))),
% 1.01/1.19 inference(rewrite,[status(thm)],[])).
% 1.01/1.19 tff(2104,axiom,((~c3_1(a2533)) | (~hskp12)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause117')).
% 1.01/1.19 tff(2105,plain,
% 1.01/1.19 ((~hskp12) | (~c3_1(a2533))),
% 1.01/1.19 inference(modus_ponens,[status(thm)],[2104, 2103])).
% 1.01/1.19 tff(2106,plain,
% 1.01/1.19 ((~hskp12) | (~c3_1(a2533))),
% 1.01/1.19 inference(modus_ponens,[status(thm)],[2105, 2102])).
% 1.01/1.19 tff(2107,plain,
% 1.01/1.19 (~c3_1(a2533)),
% 1.01/1.19 inference(unit_resolution,[status(thm)],[2106, 2101])).
% 1.01/1.19 tff(2108,plain,
% 1.01/1.19 (((~hskp12) | (~c2_1(a2533))) <=> ((~hskp12) | (~c2_1(a2533)))),
% 1.01/1.19 inference(rewrite,[status(thm)],[])).
% 1.01/1.19 tff(2109,plain,
% 1.01/1.19 (((~c2_1(a2533)) | (~hskp12)) <=> ((~hskp12) | (~c2_1(a2533)))),
% 1.01/1.19 inference(rewrite,[status(thm)],[])).
% 1.01/1.19 tff(2110,axiom,((~c2_1(a2533)) | (~hskp12)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause116')).
% 1.01/1.19 tff(2111,plain,
% 1.01/1.19 ((~hskp12) | (~c2_1(a2533))),
% 1.01/1.19 inference(modus_ponens,[status(thm)],[2110, 2109])).
% 1.01/1.19 tff(2112,plain,
% 1.01/1.19 ((~hskp12) | (~c2_1(a2533))),
% 1.01/1.19 inference(modus_ponens,[status(thm)],[2111, 2108])).
% 1.01/1.19 tff(2113,plain,
% 1.01/1.19 (~c2_1(a2533)),
% 1.01/1.19 inference(unit_resolution,[status(thm)],[2112, 2101])).
% 1.01/1.19 tff(2114,plain,
% 1.01/1.19 (((~hskp12) | (~c1_1(a2533))) <=> ((~hskp12) | (~c1_1(a2533)))),
% 1.01/1.19 inference(rewrite,[status(thm)],[])).
% 1.01/1.19 tff(2115,plain,
% 1.01/1.19 (((~c1_1(a2533)) | (~hskp12)) <=> ((~hskp12) | (~c1_1(a2533)))),
% 1.01/1.19 inference(rewrite,[status(thm)],[])).
% 1.01/1.19 tff(2116,axiom,((~c1_1(a2533)) | (~hskp12)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause115')).
% 1.01/1.19 tff(2117,plain,
% 1.01/1.19 ((~hskp12) | (~c1_1(a2533))),
% 1.01/1.19 inference(modus_ponens,[status(thm)],[2116, 2115])).
% 1.01/1.19 tff(2118,plain,
% 1.01/1.19 ((~hskp12) | (~c1_1(a2533))),
% 1.01/1.19 inference(modus_ponens,[status(thm)],[2117, 2114])).
% 1.01/1.19 tff(2119,plain,
% 1.01/1.19 (~c1_1(a2533)),
% 1.01/1.19 inference(unit_resolution,[status(thm)],[2118, 2101])).
% 1.01/1.19 tff(2120,plain,
% 1.01/1.19 (((~![U: $i] : (hskp20 | hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | (hskp20 | hskp19 | c1_1(a2533) | c2_1(a2533) | c3_1(a2533) | (~ndr1_0))) <=> ((~![U: $i] : (hskp20 | hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | hskp20 | hskp19 | c1_1(a2533) | c2_1(a2533) | c3_1(a2533) | (~ndr1_0))),
% 1.01/1.19 inference(rewrite,[status(thm)],[])).
% 1.01/1.19 tff(2121,plain,
% 1.01/1.19 ((hskp20 | hskp19 | (~ndr1_0) | c3_1(a2533) | c2_1(a2533) | c1_1(a2533)) <=> (hskp20 | hskp19 | c1_1(a2533) | c2_1(a2533) | c3_1(a2533) | (~ndr1_0))),
% 1.01/1.19 inference(rewrite,[status(thm)],[])).
% 1.01/1.19 tff(2122,plain,
% 1.01/1.19 (((~![U: $i] : (hskp20 | hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | (hskp20 | hskp19 | (~ndr1_0) | c3_1(a2533) | c2_1(a2533) | c1_1(a2533))) <=> ((~![U: $i] : (hskp20 | hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | (hskp20 | hskp19 | c1_1(a2533) | c2_1(a2533) | c3_1(a2533) | (~ndr1_0)))),
% 1.01/1.19 inference(monotonicity,[status(thm)],[2121])).
% 1.01/1.19 tff(2123,plain,
% 1.01/1.19 (((~![U: $i] : (hskp20 | hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | (hskp20 | hskp19 | (~ndr1_0) | c3_1(a2533) | c2_1(a2533) | c1_1(a2533))) <=> ((~![U: $i] : (hskp20 | hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | hskp20 | hskp19 | c1_1(a2533) | c2_1(a2533) | c3_1(a2533) | (~ndr1_0))),
% 1.01/1.19 inference(transitivity,[status(thm)],[2122, 2120])).
% 1.01/1.19 tff(2124,plain,
% 1.01/1.19 ((~![U: $i] : (hskp20 | hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | (hskp20 | hskp19 | (~ndr1_0) | c3_1(a2533) | c2_1(a2533) | c1_1(a2533))),
% 1.01/1.19 inference(quant_inst,[status(thm)],[])).
% 1.01/1.19 tff(2125,plain,
% 1.01/1.19 ((~![U: $i] : (hskp20 | hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | hskp20 | hskp19 | c1_1(a2533) | c2_1(a2533) | c3_1(a2533) | (~ndr1_0)),
% 1.01/1.19 inference(modus_ponens,[status(thm)],[2124, 2123])).
% 1.01/1.19 tff(2126,plain,
% 1.01/1.19 ($false),
% 1.01/1.19 inference(unit_resolution,[status(thm)],[2125, 90, 2081, 2080, 2119, 2113, 2107, 1319])).
% 1.01/1.19 tff(2127,plain,(hskp20 | hskp19 | (~c0_1(a2553)) | (~c1_1(a2518)) | c3_1(a2553) | c0_1(a2518) | c3_1(a2518) | c1_1(a2553)), inference(lemma,lemma(discharge,[]))).
% 1.01/1.19 tff(2128,plain,
% 1.01/1.19 (hskp20),
% 1.01/1.19 inference(unit_resolution,[status(thm)],[2127, 2079, 851, 948, 849, 945, 1277, 850])).
% 1.01/1.19 tff(2129,plain,
% 1.01/1.19 (~c1_1(a2549)),
% 1.01/1.19 inference(unit_resolution,[status(thm)],[1332, 2128])).
% 1.01/1.19 tff(2130,plain,
% 1.01/1.19 (~c0_1(a2549)),
% 1.01/1.19 inference(unit_resolution,[status(thm)],[1338, 2128])).
% 1.01/1.19 tff(2131,plain,
% 1.01/1.19 (c2_1(a2549)),
% 1.01/1.19 inference(unit_resolution,[status(thm)],[1346, 2128])).
% 1.01/1.19 tff(2132,plain,
% 1.01/1.19 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a2553) | c0_1(a2549) | c1_1(a2549) | c0_1(a2518) | (~ndr1_0) | (~c1_1(a2518)) | (~c2_1(a2518)) | (~c2_1(a2549)) | (~c0_1(a2553)) | (~c2_1(a2553)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a2553) | c0_1(a2549) | c1_1(a2549) | c0_1(a2518) | (~ndr1_0) | (~c1_1(a2518)) | (~c2_1(a2518)) | (~c2_1(a2549)) | (~c0_1(a2553)) | (~c2_1(a2553)))),
% 1.01/1.19 inference(rewrite,[status(thm)],[])).
% 1.01/1.19 tff(2133,plain,
% 1.01/1.19 (((~ndr1_0) | c1_1(a2553) | (~c0_1(a2553)) | (~c2_1(a2553)) | c0_1(a2518) | (~c1_1(a2518)) | (~c2_1(a2518)) | c1_1(a2549) | c0_1(a2549) | (~c2_1(a2549))) <=> (c1_1(a2553) | c0_1(a2549) | c1_1(a2549) | c0_1(a2518) | (~ndr1_0) | (~c1_1(a2518)) | (~c2_1(a2518)) | (~c2_1(a2549)) | (~c0_1(a2553)) | (~c2_1(a2553)))),
% 1.01/1.19 inference(rewrite,[status(thm)],[])).
% 1.01/1.19 tff(2134,plain,
% 1.01/1.19 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a2553) | (~c0_1(a2553)) | (~c2_1(a2553)) | c0_1(a2518) | (~c1_1(a2518)) | (~c2_1(a2518)) | c1_1(a2549) | c0_1(a2549) | (~c2_1(a2549)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a2553) | c0_1(a2549) | c1_1(a2549) | c0_1(a2518) | (~ndr1_0) | (~c1_1(a2518)) | (~c2_1(a2518)) | (~c2_1(a2549)) | (~c0_1(a2553)) | (~c2_1(a2553))))),
% 1.01/1.19 inference(monotonicity,[status(thm)],[2133])).
% 1.01/1.19 tff(2135,plain,
% 1.01/1.19 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a2553) | (~c0_1(a2553)) | (~c2_1(a2553)) | c0_1(a2518) | (~c1_1(a2518)) | (~c2_1(a2518)) | c1_1(a2549) | c0_1(a2549) | (~c2_1(a2549)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a2553) | c0_1(a2549) | c1_1(a2549) | c0_1(a2518) | (~ndr1_0) | (~c1_1(a2518)) | (~c2_1(a2518)) | (~c2_1(a2549)) | (~c0_1(a2553)) | (~c2_1(a2553)))),
% 1.01/1.19 inference(transitivity,[status(thm)],[2134, 2132])).
% 1.01/1.19 tff(2136,plain,
% 1.01/1.19 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a2553) | (~c0_1(a2553)) | (~c2_1(a2553)) | c0_1(a2518) | (~c1_1(a2518)) | (~c2_1(a2518)) | c1_1(a2549) | c0_1(a2549) | (~c2_1(a2549)))),
% 1.01/1.19 inference(quant_inst,[status(thm)],[])).
% 1.01/1.19 tff(2137,plain,
% 1.01/1.19 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a2553) | c0_1(a2549) | c1_1(a2549) | c0_1(a2518) | (~ndr1_0) | (~c1_1(a2518)) | (~c2_1(a2518)) | (~c2_1(a2549)) | (~c0_1(a2553)) | (~c2_1(a2553))),
% 1.01/1.19 inference(modus_ponens,[status(thm)],[2136, 2135])).
% 1.01/1.19 tff(2138,plain,
% 1.01/1.19 (~c2_1(a2553)),
% 1.01/1.19 inference(unit_resolution,[status(thm)],[2137, 90, 851, 2131, 948, 850, 2130, 2129, 945, 944, 934])).
% 1.01/1.19 tff(2139,plain,
% 1.01/1.19 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp3 | c0_1(a2549) | c1_1(a2549) | c0_1(a2518) | (~ndr1_0) | (~c1_1(a2518)) | (~c2_1(a2518)) | (~c2_1(a2549)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp3 | c0_1(a2549) | c1_1(a2549) | c0_1(a2518) | (~ndr1_0) | (~c1_1(a2518)) | (~c2_1(a2518)) | (~c2_1(a2549)))),
% 1.01/1.19 inference(rewrite,[status(thm)],[])).
% 1.01/1.19 tff(2140,plain,
% 1.01/1.19 ((hskp3 | (~ndr1_0) | c0_1(a2518) | (~c1_1(a2518)) | (~c2_1(a2518)) | c1_1(a2549) | c0_1(a2549) | (~c2_1(a2549))) <=> (hskp3 | c0_1(a2549) | c1_1(a2549) | c0_1(a2518) | (~ndr1_0) | (~c1_1(a2518)) | (~c2_1(a2518)) | (~c2_1(a2549)))),
% 1.01/1.19 inference(rewrite,[status(thm)],[])).
% 1.01/1.19 tff(2141,plain,
% 1.01/1.19 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp3 | (~ndr1_0) | c0_1(a2518) | (~c1_1(a2518)) | (~c2_1(a2518)) | c1_1(a2549) | c0_1(a2549) | (~c2_1(a2549)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp3 | c0_1(a2549) | c1_1(a2549) | c0_1(a2518) | (~ndr1_0) | (~c1_1(a2518)) | (~c2_1(a2518)) | (~c2_1(a2549))))),
% 1.01/1.19 inference(monotonicity,[status(thm)],[2140])).
% 1.01/1.19 tff(2142,plain,
% 1.01/1.19 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp3 | (~ndr1_0) | c0_1(a2518) | (~c1_1(a2518)) | (~c2_1(a2518)) | c1_1(a2549) | c0_1(a2549) | (~c2_1(a2549)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp3 | c0_1(a2549) | c1_1(a2549) | c0_1(a2518) | (~ndr1_0) | (~c1_1(a2518)) | (~c2_1(a2518)) | (~c2_1(a2549)))),
% 1.01/1.19 inference(transitivity,[status(thm)],[2141, 2139])).
% 1.01/1.19 tff(2143,plain,
% 1.01/1.19 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp3 | (~ndr1_0) | c0_1(a2518) | (~c1_1(a2518)) | (~c2_1(a2518)) | c1_1(a2549) | c0_1(a2549) | (~c2_1(a2549)))),
% 1.01/1.19 inference(quant_inst,[status(thm)],[])).
% 1.01/1.19 tff(2144,plain,
% 1.01/1.19 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp3 | c0_1(a2549) | c1_1(a2549) | c0_1(a2518) | (~ndr1_0) | (~c1_1(a2518)) | (~c2_1(a2518)) | (~c2_1(a2549))),
% 1.01/1.19 inference(modus_ponens,[status(thm)],[2143, 2142])).
% 1.01/1.19 tff(2145,plain,
% 1.01/1.19 (hskp3),
% 1.01/1.19 inference(unit_resolution,[status(thm)],[2144, 90, 2131, 948, 2130, 2129, 945, 1584, 934])).
% 1.01/1.19 tff(2146,plain,
% 1.01/1.19 (~c3_1(a2519)),
% 1.01/1.19 inference(unit_resolution,[status(thm)],[42, 2145])).
% 1.01/1.19 tff(2147,plain,
% 1.01/1.19 (~c2_1(a2519)),
% 1.01/1.19 inference(unit_resolution,[status(thm)],[48, 2145])).
% 1.01/1.19 tff(2148,plain,
% 1.01/1.19 (~c0_1(a2519)),
% 1.01/1.19 inference(unit_resolution,[status(thm)],[54, 2145])).
% 1.01/1.19 tff(2149,plain,
% 1.01/1.19 (hskp8),
% 1.01/1.19 inference(unit_resolution,[status(thm)],[1600, 90, 851, 850, 2148, 2147, 2146, 659, 2138])).
% 1.01/1.19 tff(2150,plain,
% 1.01/1.19 (~c3_1(a2525)),
% 1.01/1.19 inference(unit_resolution,[status(thm)],[607, 2149])).
% 1.01/1.19 tff(2151,plain,
% 1.01/1.19 (c0_1(a2525)),
% 1.01/1.19 inference(unit_resolution,[status(thm)],[615, 2149])).
% 1.01/1.19 tff(2152,plain,
% 1.01/1.19 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp21 | c3_1(a2553) | c3_1(a2525) | (~ndr1_0) | (~c0_1(a2525)) | (~c1_1(a2525)) | (~c0_1(a2553)) | c2_1(a2553))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | hskp21 | c3_1(a2553) | c3_1(a2525) | (~ndr1_0) | (~c0_1(a2525)) | (~c1_1(a2525)) | (~c0_1(a2553)) | c2_1(a2553))),
% 1.01/1.19 inference(rewrite,[status(thm)],[])).
% 1.01/1.19 tff(2153,plain,
% 1.01/1.19 ((hskp21 | (~ndr1_0) | c3_1(a2525) | (~c1_1(a2525)) | (~c0_1(a2525)) | c3_1(a2553) | c2_1(a2553) | (~c0_1(a2553))) <=> (hskp21 | c3_1(a2553) | c3_1(a2525) | (~ndr1_0) | (~c0_1(a2525)) | (~c1_1(a2525)) | (~c0_1(a2553)) | c2_1(a2553))),
% 1.01/1.19 inference(rewrite,[status(thm)],[])).
% 1.01/1.19 tff(2154,plain,
% 1.01/1.19 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp21 | (~ndr1_0) | c3_1(a2525) | (~c1_1(a2525)) | (~c0_1(a2525)) | c3_1(a2553) | c2_1(a2553) | (~c0_1(a2553)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp21 | c3_1(a2553) | c3_1(a2525) | (~ndr1_0) | (~c0_1(a2525)) | (~c1_1(a2525)) | (~c0_1(a2553)) | c2_1(a2553)))),
% 1.01/1.19 inference(monotonicity,[status(thm)],[2153])).
% 1.01/1.19 tff(2155,plain,
% 1.01/1.19 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp21 | (~ndr1_0) | c3_1(a2525) | (~c1_1(a2525)) | (~c0_1(a2525)) | c3_1(a2553) | c2_1(a2553) | (~c0_1(a2553)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | hskp21 | c3_1(a2553) | c3_1(a2525) | (~ndr1_0) | (~c0_1(a2525)) | (~c1_1(a2525)) | (~c0_1(a2553)) | c2_1(a2553))),
% 1.01/1.19 inference(transitivity,[status(thm)],[2154, 2152])).
% 1.01/1.19 tff(2156,plain,
% 1.01/1.19 ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp21 | (~ndr1_0) | c3_1(a2525) | (~c1_1(a2525)) | (~c0_1(a2525)) | c3_1(a2553) | c2_1(a2553) | (~c0_1(a2553)))),
% 1.01/1.19 inference(quant_inst,[status(thm)],[])).
% 1.01/1.19 tff(2157,plain,
% 1.01/1.19 ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | hskp21 | c3_1(a2553) | c3_1(a2525) | (~ndr1_0) | (~c0_1(a2525)) | (~c1_1(a2525)) | (~c0_1(a2553)) | c2_1(a2553)),
% 1.01/1.19 inference(modus_ponens,[status(thm)],[2156, 2155])).
% 1.01/1.19 tff(2158,plain,
% 1.01/1.19 (~c1_1(a2525)),
% 1.01/1.19 inference(unit_resolution,[status(thm)],[2157, 90, 1829, 851, 2151, 849, 2150, 1828, 2138])).
% 1.01/1.19 tff(2159,plain,
% 1.01/1.19 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a2552) | c0_1(a2549) | c1_1(a2549) | c0_1(a2518) | (~ndr1_0) | (~c1_1(a2518)) | (~c2_1(a2518)) | (~c2_1(a2549)) | (~c0_1(a2552)) | (~c2_1(a2552)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a2552) | c0_1(a2549) | c1_1(a2549) | c0_1(a2518) | (~ndr1_0) | (~c1_1(a2518)) | (~c2_1(a2518)) | (~c2_1(a2549)) | (~c0_1(a2552)) | (~c2_1(a2552)))),
% 1.01/1.19 inference(rewrite,[status(thm)],[])).
% 1.01/1.19 tff(2160,plain,
% 1.01/1.19 (((~ndr1_0) | c1_1(a2552) | (~c0_1(a2552)) | (~c2_1(a2552)) | c0_1(a2518) | (~c1_1(a2518)) | (~c2_1(a2518)) | c1_1(a2549) | c0_1(a2549) | (~c2_1(a2549))) <=> (c1_1(a2552) | c0_1(a2549) | c1_1(a2549) | c0_1(a2518) | (~ndr1_0) | (~c1_1(a2518)) | (~c2_1(a2518)) | (~c2_1(a2549)) | (~c0_1(a2552)) | (~c2_1(a2552)))),
% 1.01/1.19 inference(rewrite,[status(thm)],[])).
% 1.01/1.19 tff(2161,plain,
% 1.01/1.19 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a2552) | (~c0_1(a2552)) | (~c2_1(a2552)) | c0_1(a2518) | (~c1_1(a2518)) | (~c2_1(a2518)) | c1_1(a2549) | c0_1(a2549) | (~c2_1(a2549)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a2552) | c0_1(a2549) | c1_1(a2549) | c0_1(a2518) | (~ndr1_0) | (~c1_1(a2518)) | (~c2_1(a2518)) | (~c2_1(a2549)) | (~c0_1(a2552)) | (~c2_1(a2552))))),
% 1.01/1.19 inference(monotonicity,[status(thm)],[2160])).
% 1.01/1.19 tff(2162,plain,
% 1.01/1.19 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a2552) | (~c0_1(a2552)) | (~c2_1(a2552)) | c0_1(a2518) | (~c1_1(a2518)) | (~c2_1(a2518)) | c1_1(a2549) | c0_1(a2549) | (~c2_1(a2549)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a2552) | c0_1(a2549) | c1_1(a2549) | c0_1(a2518) | (~ndr1_0) | (~c1_1(a2518)) | (~c2_1(a2518)) | (~c2_1(a2549)) | (~c0_1(a2552)) | (~c2_1(a2552)))),
% 1.01/1.19 inference(transitivity,[status(thm)],[2161, 2159])).
% 1.01/1.19 tff(2163,plain,
% 1.01/1.19 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a2552) | (~c0_1(a2552)) | (~c2_1(a2552)) | c0_1(a2518) | (~c1_1(a2518)) | (~c2_1(a2518)) | c1_1(a2549) | c0_1(a2549) | (~c2_1(a2549)))),
% 1.01/1.19 inference(quant_inst,[status(thm)],[])).
% 1.01/1.19 tff(2164,plain,
% 1.01/1.19 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a2552) | c0_1(a2549) | c1_1(a2549) | c0_1(a2518) | (~ndr1_0) | (~c1_1(a2518)) | (~c2_1(a2518)) | (~c2_1(a2549)) | (~c0_1(a2552)) | (~c2_1(a2552))),
% 1.01/1.19 inference(modus_ponens,[status(thm)],[2163, 2162])).
% 1.01/1.19 tff(2165,plain,
% 1.01/1.19 (~c0_1(a2552)),
% 1.01/1.19 inference(unit_resolution,[status(thm)],[2164, 90, 822, 2131, 948, 824, 2130, 2129, 945, 944, 934])).
% 1.01/1.19 tff(2166,plain,
% 1.01/1.19 (c2_1(a2525)),
% 1.01/1.19 inference(unit_resolution,[status(thm)],[1071, 2149])).
% 1.01/1.19 tff(2167,plain,
% 1.01/1.19 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a2552) | c0_1(a2518) | (~ndr1_0) | (~c1_1(a2518)) | (~c2_1(a2518)) | (~c0_1(a2525)) | (~c2_1(a2525)) | c1_1(a2525) | c0_1(a2552) | (~c2_1(a2552)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a2552) | c0_1(a2518) | (~ndr1_0) | (~c1_1(a2518)) | (~c2_1(a2518)) | (~c0_1(a2525)) | (~c2_1(a2525)) | c1_1(a2525) | c0_1(a2552) | (~c2_1(a2552)))),
% 1.01/1.19 inference(rewrite,[status(thm)],[])).
% 1.01/1.19 tff(2168,plain,
% 1.01/1.19 (((~ndr1_0) | c1_1(a2525) | (~c0_1(a2525)) | (~c2_1(a2525)) | c0_1(a2518) | (~c1_1(a2518)) | (~c2_1(a2518)) | c1_1(a2552) | c0_1(a2552) | (~c2_1(a2552))) <=> (c1_1(a2552) | c0_1(a2518) | (~ndr1_0) | (~c1_1(a2518)) | (~c2_1(a2518)) | (~c0_1(a2525)) | (~c2_1(a2525)) | c1_1(a2525) | c0_1(a2552) | (~c2_1(a2552)))),
% 1.01/1.19 inference(rewrite,[status(thm)],[])).
% 1.01/1.19 tff(2169,plain,
% 1.01/1.19 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a2525) | (~c0_1(a2525)) | (~c2_1(a2525)) | c0_1(a2518) | (~c1_1(a2518)) | (~c2_1(a2518)) | c1_1(a2552) | c0_1(a2552) | (~c2_1(a2552)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a2552) | c0_1(a2518) | (~ndr1_0) | (~c1_1(a2518)) | (~c2_1(a2518)) | (~c0_1(a2525)) | (~c2_1(a2525)) | c1_1(a2525) | c0_1(a2552) | (~c2_1(a2552))))),
% 1.01/1.19 inference(monotonicity,[status(thm)],[2168])).
% 1.01/1.19 tff(2170,plain,
% 1.01/1.19 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a2525) | (~c0_1(a2525)) | (~c2_1(a2525)) | c0_1(a2518) | (~c1_1(a2518)) | (~c2_1(a2518)) | c1_1(a2552) | c0_1(a2552) | (~c2_1(a2552)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a2552) | c0_1(a2518) | (~ndr1_0) | (~c1_1(a2518)) | (~c2_1(a2518)) | (~c0_1(a2525)) | (~c2_1(a2525)) | c1_1(a2525) | c0_1(a2552) | (~c2_1(a2552)))),
% 1.01/1.19 inference(transitivity,[status(thm)],[2169, 2167])).
% 1.01/1.19 tff(2171,plain,
% 1.01/1.19 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a2525) | (~c0_1(a2525)) | (~c2_1(a2525)) | c0_1(a2518) | (~c1_1(a2518)) | (~c2_1(a2518)) | c1_1(a2552) | c0_1(a2552) | (~c2_1(a2552)))),
% 1.01/1.19 inference(quant_inst,[status(thm)],[])).
% 1.01/1.19 tff(2172,plain,
% 1.01/1.19 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a2552) | c0_1(a2518) | (~ndr1_0) | (~c1_1(a2518)) | (~c2_1(a2518)) | (~c0_1(a2525)) | (~c2_1(a2525)) | c1_1(a2525) | c0_1(a2552) | (~c2_1(a2552))),
% 1.01/1.19 inference(modus_ponens,[status(thm)],[2171, 2170])).
% 1.01/1.19 tff(2173,plain,
% 1.01/1.19 ($false),
% 1.01/1.19 inference(unit_resolution,[status(thm)],[2172, 90, 822, 2151, 2166, 948, 824, 945, 944, 2165, 934, 2158])).
% 1.01/1.19 tff(2174,plain,((~c2_1(a2518)) | (~c2_1(a2552)) | (~c1_1(a2518)) | c1_1(a2552) | c0_1(a2518) | hskp21 | (~c0_1(a2553)) | c3_1(a2553) | c1_1(a2553) | c3_1(a2518) | c3_1(a2552)), inference(lemma,lemma(discharge,[]))).
% 1.01/1.19 tff(2175,plain,
% 1.01/1.19 (~c2_1(a2518)),
% 1.01/1.19 inference(unit_resolution,[status(thm)],[2174, 2078, 822, 824, 2077, 1829, 851, 849, 850, 2076, 823])).
% 1.01/1.19 tff(2176,plain,
% 1.01/1.19 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp10 | c0_1(a2518) | c3_1(a2518) | (~ndr1_0) | (~c1_1(a2518)) | c2_1(a2518))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp10 | c0_1(a2518) | c3_1(a2518) | (~ndr1_0) | (~c1_1(a2518)) | c2_1(a2518))),
% 1.01/1.19 inference(rewrite,[status(thm)],[])).
% 1.01/1.19 tff(2177,plain,
% 1.01/1.19 ((hskp10 | (~ndr1_0) | c3_1(a2518) | c2_1(a2518) | (~c1_1(a2518)) | c0_1(a2518) | c2_1(a2518) | (~c1_1(a2518))) <=> (hskp10 | c0_1(a2518) | c3_1(a2518) | (~ndr1_0) | (~c1_1(a2518)) | c2_1(a2518))),
% 1.01/1.19 inference(rewrite,[status(thm)],[])).
% 1.01/1.19 tff(2178,plain,
% 1.01/1.19 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp10 | (~ndr1_0) | c3_1(a2518) | c2_1(a2518) | (~c1_1(a2518)) | c0_1(a2518) | c2_1(a2518) | (~c1_1(a2518)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp10 | c0_1(a2518) | c3_1(a2518) | (~ndr1_0) | (~c1_1(a2518)) | c2_1(a2518)))),
% 1.01/1.19 inference(monotonicity,[status(thm)],[2177])).
% 1.01/1.19 tff(2179,plain,
% 1.01/1.19 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp10 | (~ndr1_0) | c3_1(a2518) | c2_1(a2518) | (~c1_1(a2518)) | c0_1(a2518) | c2_1(a2518) | (~c1_1(a2518)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp10 | c0_1(a2518) | c3_1(a2518) | (~ndr1_0) | (~c1_1(a2518)) | c2_1(a2518))),
% 1.01/1.19 inference(transitivity,[status(thm)],[2178, 2176])).
% 1.01/1.19 tff(2180,plain,
% 1.01/1.19 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp10 | (~ndr1_0) | c3_1(a2518) | c2_1(a2518) | (~c1_1(a2518)) | c0_1(a2518) | c2_1(a2518) | (~c1_1(a2518)))),
% 1.01/1.19 inference(quant_inst,[status(thm)],[])).
% 1.01/1.19 tff(2181,plain,
% 1.01/1.19 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp10 | c0_1(a2518) | c3_1(a2518) | (~ndr1_0) | (~c1_1(a2518)) | c2_1(a2518)),
% 1.01/1.19 inference(modus_ponens,[status(thm)],[2180, 2179])).
% 1.01/1.19 tff(2182,plain,
% 1.01/1.19 (hskp10 | c2_1(a2518)),
% 1.01/1.19 inference(unit_resolution,[status(thm)],[2181, 90, 2078, 2077, 2076, 1846])).
% 1.01/1.19 tff(2183,plain,
% 1.01/1.19 (hskp10),
% 1.01/1.19 inference(unit_resolution,[status(thm)],[2182, 2175])).
% 1.01/1.19 tff(2184,plain,
% 1.01/1.19 (~c0_1(a2528)),
% 1.01/1.19 inference(unit_resolution,[status(thm)],[1137, 2183])).
% 1.01/1.19 tff(2185,plain,
% 1.01/1.19 (hskp17 | c2_1(a2518)),
% 1.01/1.19 inference(unit_resolution,[status(thm)],[913, 90, 215, 216, 2078, 152, 2076, 226])).
% 1.01/1.19 tff(2186,plain,
% 1.01/1.19 (hskp17),
% 1.01/1.19 inference(unit_resolution,[status(thm)],[2185, 2175])).
% 1.01/1.19 tff(2187,plain,
% 1.01/1.19 (~c1_1(a2541)),
% 1.01/1.19 inference(unit_resolution,[status(thm)],[244, 2186])).
% 1.01/1.19 tff(2188,plain,
% 1.01/1.19 (c3_1(a2541)),
% 1.01/1.19 inference(unit_resolution,[status(thm)],[252, 2186])).
% 1.01/1.19 tff(2189,plain,
% 1.01/1.19 (~c2_1(a2541)),
% 1.01/1.19 inference(unit_resolution,[status(thm)],[238, 2186])).
% 1.01/1.19 tff(2190,plain,
% 1.01/1.19 (c3_1(a2528)),
% 1.01/1.19 inference(unit_resolution,[status(thm)],[1145, 2183])).
% 1.01/1.19 tff(2191,plain,
% 1.01/1.19 (~c1_1(a2528)),
% 1.01/1.19 inference(unit_resolution,[status(thm)],[1158, 2183])).
% 1.01/1.19 tff(2192,plain,
% 1.01/1.19 ($false),
% 1.01/1.19 inference(unit_resolution,[status(thm)],[1418, 2191, 2190, 404, 2189, 2188, 2187, 2184])).
% 1.01/1.19 tff(2193,plain,(hskp29 | (~c1_1(a2526)) | (~c3_1(a2526)) | c0_1(a2526) | (~c2_1(a2552)) | c1_1(a2552) | hskp21 | (~c0_1(a2553)) | c3_1(a2553) | c1_1(a2553) | c3_1(a2552)), inference(lemma,lemma(discharge,[]))).
% 1.01/1.19 tff(2194,plain,
% 1.01/1.19 (hskp29),
% 1.01/1.19 inference(unit_resolution,[status(thm)],[2193, 2073, 1818, 152, 2026, 2025, 1716, 2021, 849, 850, 2024])).
% 1.01/1.19 tff(2195,plain,
% 1.01/1.19 (c3_1(a2556)),
% 1.01/1.19 inference(unit_resolution,[status(thm)],[339, 2194])).
% 1.01/1.19 tff(2196,plain,
% 1.01/1.19 (c2_1(a2556)),
% 1.01/1.19 inference(unit_resolution,[status(thm)],[347, 2194])).
% 1.01/1.19 tff(2197,plain,
% 1.01/1.19 (c1_1(a2556)),
% 1.01/1.19 inference(unit_resolution,[status(thm)],[355, 2194])).
% 1.01/1.19 tff(2198,assumption,(hskp17), introduced(assumption)).
% 1.01/1.19 tff(2199,plain,
% 1.01/1.19 (~c1_1(a2541)),
% 1.01/1.19 inference(unit_resolution,[status(thm)],[244, 2198])).
% 1.01/1.19 tff(2200,plain,
% 1.01/1.19 (c3_1(a2541)),
% 1.01/1.19 inference(unit_resolution,[status(thm)],[252, 2198])).
% 1.01/1.19 tff(2201,plain,
% 1.01/1.19 (~c2_1(a2541)),
% 1.01/1.19 inference(unit_resolution,[status(thm)],[238, 2198])).
% 1.01/1.19 tff(2202,plain,
% 1.01/1.19 ($false),
% 1.01/1.19 inference(unit_resolution,[status(thm)],[1524, 2201, 2200, 851, 850, 849, 619, 618, 2199, 617, 216, 152, 215])).
% 1.01/1.19 tff(2203,plain,((~hskp17) | (~c0_1(a2553)) | c1_1(a2553) | c3_1(a2553) | (~c1_1(a2556)) | (~c2_1(a2556)) | (~c3_1(a2556)) | (~c3_1(a2526)) | c0_1(a2526) | (~c1_1(a2526))), inference(lemma,lemma(discharge,[]))).
% 1.01/1.19 tff(2204,plain,
% 1.01/1.19 (~hskp17),
% 1.01/1.19 inference(unit_resolution,[status(thm)],[2203, 2021, 850, 849, 2197, 2196, 2195, 1818, 152, 2073])).
% 1.01/1.19 tff(2205,plain,
% 1.01/1.19 (hskp2),
% 1.01/1.19 inference(unit_resolution,[status(thm)],[1540, 2204, 2073, 1818, 152, 2021, 850, 849])).
% 1.01/1.19 tff(2206,plain,
% 1.01/1.19 (~c3_1(a2518)),
% 1.01/1.19 inference(unit_resolution,[status(thm)],[892, 2205])).
% 1.01/1.19 tff(2207,plain,
% 1.01/1.19 (~c0_1(a2518)),
% 1.01/1.19 inference(unit_resolution,[status(thm)],[898, 2205])).
% 1.01/1.19 tff(2208,plain,
% 1.01/1.19 (c1_1(a2518)),
% 1.01/1.19 inference(unit_resolution,[status(thm)],[906, 2205])).
% 1.01/1.19 tff(2209,plain,
% 1.01/1.19 (~c2_1(a2518)),
% 1.01/1.19 inference(unit_resolution,[status(thm)],[2174, 2208, 2026, 2025, 2207, 1716, 2021, 849, 850, 2206, 2024])).
% 1.01/1.19 tff(2210,plain,
% 1.01/1.19 ($false),
% 1.01/1.19 inference(unit_resolution,[status(thm)],[913, 90, 2204, 2073, 1818, 2208, 152, 2206, 226, 2209])).
% 1.01/1.20 tff(2211,plain,(c1_1(a2553) | c0_1(a2526) | c3_1(a2553) | hskp30), inference(lemma,lemma(discharge,[]))).
% 1.01/1.20 tff(2212,plain,
% 1.01/1.20 ($false),
% 1.01/1.20 inference(unit_resolution,[status(thm)],[2211, 1967, 1966, 152, 151])).
% 1.01/1.20 tff(2213,plain,(c0_1(a2526) | hskp30), inference(lemma,lemma(discharge,[]))).
% 1.01/1.20 tff(2214,plain,
% 1.01/1.20 (c0_1(a2526)),
% 1.01/1.20 inference(unit_resolution,[status(thm)],[2213, 151])).
% 1.01/1.20 tff(2215,plain,
% 1.01/1.20 (~hskp9),
% 1.01/1.20 inference(unit_resolution,[status(thm)],[205, 2214])).
% 1.01/1.20 tff(2216,plain,
% 1.01/1.20 (~c1_1(a2601)),
% 1.01/1.20 inference(unit_resolution,[status(thm)],[1748, 2215])).
% 1.01/1.20 tff(2217,assumption,(~c1_1(a2601)), introduced(assumption)).
% 1.01/1.20 tff(2218,assumption,(c0_1(a2526)), introduced(assumption)).
% 1.01/1.20 tff(2219,plain,
% 1.01/1.20 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp21 | c3_1(a2526) | (~c0_1(a2526)) | (~ndr1_0) | (~c1_1(a2526)) | (~c3_1(a2601)) | (~c0_1(a2601)) | c1_1(a2601))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp21 | c3_1(a2526) | (~c0_1(a2526)) | (~ndr1_0) | (~c1_1(a2526)) | (~c3_1(a2601)) | (~c0_1(a2601)) | c1_1(a2601))),
% 1.01/1.20 inference(rewrite,[status(thm)],[])).
% 1.01/1.20 tff(2220,plain,
% 1.01/1.20 ((hskp21 | (~ndr1_0) | c3_1(a2526) | (~c1_1(a2526)) | (~c0_1(a2526)) | c1_1(a2601) | (~c3_1(a2601)) | (~c0_1(a2601))) <=> (hskp21 | c3_1(a2526) | (~c0_1(a2526)) | (~ndr1_0) | (~c1_1(a2526)) | (~c3_1(a2601)) | (~c0_1(a2601)) | c1_1(a2601))),
% 1.01/1.20 inference(rewrite,[status(thm)],[])).
% 1.01/1.20 tff(2221,plain,
% 1.01/1.20 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp21 | (~ndr1_0) | c3_1(a2526) | (~c1_1(a2526)) | (~c0_1(a2526)) | c1_1(a2601) | (~c3_1(a2601)) | (~c0_1(a2601)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp21 | c3_1(a2526) | (~c0_1(a2526)) | (~ndr1_0) | (~c1_1(a2526)) | (~c3_1(a2601)) | (~c0_1(a2601)) | c1_1(a2601)))),
% 1.01/1.20 inference(monotonicity,[status(thm)],[2220])).
% 1.01/1.20 tff(2222,plain,
% 1.01/1.20 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp21 | (~ndr1_0) | c3_1(a2526) | (~c1_1(a2526)) | (~c0_1(a2526)) | c1_1(a2601) | (~c3_1(a2601)) | (~c0_1(a2601)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp21 | c3_1(a2526) | (~c0_1(a2526)) | (~ndr1_0) | (~c1_1(a2526)) | (~c3_1(a2601)) | (~c0_1(a2601)) | c1_1(a2601))),
% 1.01/1.20 inference(transitivity,[status(thm)],[2221, 2219])).
% 1.01/1.20 tff(2223,plain,
% 1.01/1.20 ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp21 | (~ndr1_0) | c3_1(a2526) | (~c1_1(a2526)) | (~c0_1(a2526)) | c1_1(a2601) | (~c3_1(a2601)) | (~c0_1(a2601)))),
% 1.01/1.20 inference(quant_inst,[status(thm)],[])).
% 1.01/1.20 tff(2224,plain,
% 1.01/1.20 ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp21 | c3_1(a2526) | (~c0_1(a2526)) | (~ndr1_0) | (~c1_1(a2526)) | (~c3_1(a2601)) | (~c0_1(a2601)) | c1_1(a2601)),
% 1.01/1.20 inference(modus_ponens,[status(thm)],[2223, 2222])).
% 1.01/1.20 tff(2225,plain,
% 1.01/1.20 (~c1_1(a2526)),
% 1.01/1.20 inference(unit_resolution,[status(thm)],[2224, 90, 1829, 1882, 1876, 1740, 2218, 2063, 2217])).
% 1.01/1.20 tff(2226,plain,
% 1.01/1.20 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp2 | c1_1(a2526) | c3_1(a2526) | (~c0_1(a2526)) | (~ndr1_0) | c2_1(a2526))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | hskp2 | c1_1(a2526) | c3_1(a2526) | (~c0_1(a2526)) | (~ndr1_0) | c2_1(a2526))),
% 1.01/1.20 inference(rewrite,[status(thm)],[])).
% 1.01/1.20 tff(2227,plain,
% 1.01/1.20 ((hskp2 | (~ndr1_0) | c3_1(a2526) | c2_1(a2526) | (~c0_1(a2526)) | c3_1(a2526) | c1_1(a2526) | (~c0_1(a2526))) <=> (hskp2 | c1_1(a2526) | c3_1(a2526) | (~c0_1(a2526)) | (~ndr1_0) | c2_1(a2526))),
% 1.01/1.20 inference(rewrite,[status(thm)],[])).
% 1.01/1.20 tff(2228,plain,
% 1.01/1.20 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp2 | (~ndr1_0) | c3_1(a2526) | c2_1(a2526) | (~c0_1(a2526)) | c3_1(a2526) | c1_1(a2526) | (~c0_1(a2526)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp2 | c1_1(a2526) | c3_1(a2526) | (~c0_1(a2526)) | (~ndr1_0) | c2_1(a2526)))),
% 1.01/1.20 inference(monotonicity,[status(thm)],[2227])).
% 1.01/1.20 tff(2229,plain,
% 1.01/1.20 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp2 | (~ndr1_0) | c3_1(a2526) | c2_1(a2526) | (~c0_1(a2526)) | c3_1(a2526) | c1_1(a2526) | (~c0_1(a2526)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | hskp2 | c1_1(a2526) | c3_1(a2526) | (~c0_1(a2526)) | (~ndr1_0) | c2_1(a2526))),
% 1.01/1.20 inference(transitivity,[status(thm)],[2228, 2226])).
% 1.01/1.20 tff(2230,plain,
% 1.01/1.20 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp2 | (~ndr1_0) | c3_1(a2526) | c2_1(a2526) | (~c0_1(a2526)) | c3_1(a2526) | c1_1(a2526) | (~c0_1(a2526)))),
% 1.01/1.20 inference(quant_inst,[status(thm)],[])).
% 1.01/1.20 tff(2231,plain,
% 1.01/1.20 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | hskp2 | c1_1(a2526) | c3_1(a2526) | (~c0_1(a2526)) | (~ndr1_0) | c2_1(a2526)),
% 1.01/1.20 inference(modus_ponens,[status(thm)],[2230, 2229])).
% 1.01/1.20 tff(2232,plain,
% 1.01/1.20 (hskp2 | c2_1(a2526)),
% 1.01/1.20 inference(unit_resolution,[status(thm)],[2231, 90, 2225, 1740, 2218, 848])).
% 1.01/1.20 tff(2233,plain,
% 1.01/1.20 (c2_1(a2526)),
% 1.01/1.20 inference(unit_resolution,[status(thm)],[2232, 838])).
% 1.01/1.20 tff(2234,plain,
% 1.01/1.20 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W))) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W))))),
% 1.01/1.20 inference(bind,[status(th)],[])).
% 1.01/1.20 tff(2235,plain,
% 1.01/1.20 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 1.01/1.20 inference(quant_intro,[status(thm)],[2234])).
% 1.01/1.20 tff(2236,plain,
% 1.01/1.20 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 1.01/1.20 inference(rewrite,[status(thm)],[])).
% 1.01/1.20 tff(2237,plain,
% 1.01/1.20 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c2_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c2_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c0_1(V)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c0_1(V))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c0_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c2_1(W))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V))) | (~c2_1(W))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(W)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(W))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c3_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(W))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(W))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(W)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(W))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c3_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(W))) | c1_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(W))) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(W)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c3_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(W))))), ((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c3_1(U)) | c1_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(W))) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)))), ((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c3_1(U)) | c1_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W))))), (((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c3_1(U)) | c1_1(V)) | c0_1(W)) | c1_1(W)) <=> (((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W))) | c1_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W))) | c1_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))), (((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c3_1(U)) | c1_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))))),
% 1.01/1.20 inference(bind,[status(th)],[])).
% 1.01/1.20 tff(2238,plain,
% 1.01/1.20 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c3_1(U)) | c1_1(V)) | c0_1(W)) | c1_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 1.01/1.20 inference(quant_intro,[status(thm)],[2237])).
% 1.01/1.20 tff(2239,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c3_1(U)) | c1_1(V)) | c0_1(W)) | c1_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause200')).
% 1.01/1.20 tff(2240,plain,
% 1.01/1.20 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 1.01/1.20 inference(modus_ponens,[status(thm)],[2239, 2238])).
% 1.01/1.20 tff(2241,plain,
% 1.01/1.20 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 1.01/1.20 inference(modus_ponens,[status(thm)],[2240, 2236])).
% 1.01/1.20 tff(2242,plain,(
% 1.01/1.20 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 1.01/1.20 inference(skolemize,[status(sab)],[2241])).
% 1.01/1.20 tff(2243,plain,
% 1.01/1.20 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 1.01/1.20 inference(modus_ponens,[status(thm)],[2242, 2235])).
% 1.01/1.20 tff(2244,plain,
% 1.01/1.20 ((hskp21 | hskp20 | hskp2) <=> (hskp21 | hskp20 | hskp2)),
% 1.01/1.20 inference(rewrite,[status(thm)],[])).
% 1.01/1.20 tff(2245,plain,
% 1.01/1.20 (((hskp21 | hskp2) | hskp20) <=> (hskp21 | hskp20 | hskp2)),
% 1.01/1.20 inference(rewrite,[status(thm)],[])).
% 1.01/1.20 tff(2246,plain,
% 1.01/1.20 ((hskp21 | hskp2) <=> (hskp21 | hskp2)),
% 1.01/1.20 inference(rewrite,[status(thm)],[])).
% 1.01/1.20 tff(2247,plain,
% 1.01/1.20 (((hskp21 | hskp2) | hskp20) <=> ((hskp21 | hskp2) | hskp20)),
% 1.01/1.20 inference(monotonicity,[status(thm)],[2246])).
% 1.01/1.20 tff(2248,plain,
% 1.01/1.20 (((hskp21 | hskp2) | hskp20) <=> (hskp21 | hskp20 | hskp2)),
% 1.01/1.20 inference(transitivity,[status(thm)],[2247, 2245])).
% 1.01/1.20 tff(2249,axiom,((hskp21 | hskp2) | hskp20), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause37')).
% 1.01/1.20 tff(2250,plain,
% 1.01/1.20 (hskp21 | hskp20 | hskp2),
% 1.01/1.20 inference(modus_ponens,[status(thm)],[2249, 2248])).
% 1.01/1.20 tff(2251,plain,
% 1.01/1.20 (hskp21 | hskp20 | hskp2),
% 1.01/1.20 inference(modus_ponens,[status(thm)],[2250, 2244])).
% 1.01/1.20 tff(2252,plain,
% 1.01/1.20 (hskp21 | hskp20 | hskp2),
% 1.01/1.20 inference(modus_ponens,[status(thm)],[2251, 2244])).
% 1.01/1.20 tff(2253,plain,
% 1.01/1.20 (hskp21 | hskp20 | hskp2),
% 1.01/1.20 inference(modus_ponens,[status(thm)],[2252, 2244])).
% 1.01/1.20 tff(2254,plain,
% 1.01/1.20 (hskp21 | hskp20 | hskp2),
% 1.01/1.20 inference(modus_ponens,[status(thm)],[2253, 2244])).
% 1.01/1.20 tff(2255,plain,
% 1.01/1.20 (hskp20),
% 1.01/1.20 inference(unit_resolution,[status(thm)],[2254, 838, 1829])).
% 1.01/1.20 tff(2256,plain,
% 1.01/1.20 (~c1_1(a2549)),
% 1.01/1.20 inference(unit_resolution,[status(thm)],[1332, 2255])).
% 1.01/1.20 tff(2257,plain,
% 1.01/1.20 (~c0_1(a2549)),
% 1.01/1.20 inference(unit_resolution,[status(thm)],[1338, 2255])).
% 1.01/1.20 tff(2258,plain,
% 1.01/1.20 (c2_1(a2549)),
% 1.01/1.20 inference(unit_resolution,[status(thm)],[1346, 2255])).
% 1.01/1.20 tff(2259,plain,
% 1.01/1.20 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c3_1(a2526) | c0_1(a2549) | c1_1(a2549) | (~c0_1(a2526)) | (~ndr1_0) | (~c2_1(a2526)) | (~c2_1(a2549)) | (~c3_1(a2601)) | (~c0_1(a2601)) | c1_1(a2601))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c3_1(a2526) | c0_1(a2549) | c1_1(a2549) | (~c0_1(a2526)) | (~ndr1_0) | (~c2_1(a2526)) | (~c2_1(a2549)) | (~c3_1(a2601)) | (~c0_1(a2601)) | c1_1(a2601))),
% 1.01/1.20 inference(rewrite,[status(thm)],[])).
% 1.01/1.20 tff(2260,plain,
% 1.01/1.20 (((~ndr1_0) | c3_1(a2526) | (~c0_1(a2526)) | (~c2_1(a2526)) | c1_1(a2601) | (~c3_1(a2601)) | (~c0_1(a2601)) | c1_1(a2549) | c0_1(a2549) | (~c2_1(a2549))) <=> (c3_1(a2526) | c0_1(a2549) | c1_1(a2549) | (~c0_1(a2526)) | (~ndr1_0) | (~c2_1(a2526)) | (~c2_1(a2549)) | (~c3_1(a2601)) | (~c0_1(a2601)) | c1_1(a2601))),
% 1.01/1.20 inference(rewrite,[status(thm)],[])).
% 1.01/1.20 tff(2261,plain,
% 1.01/1.20 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a2526) | (~c0_1(a2526)) | (~c2_1(a2526)) | c1_1(a2601) | (~c3_1(a2601)) | (~c0_1(a2601)) | c1_1(a2549) | c0_1(a2549) | (~c2_1(a2549)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c3_1(a2526) | c0_1(a2549) | c1_1(a2549) | (~c0_1(a2526)) | (~ndr1_0) | (~c2_1(a2526)) | (~c2_1(a2549)) | (~c3_1(a2601)) | (~c0_1(a2601)) | c1_1(a2601)))),
% 1.01/1.20 inference(monotonicity,[status(thm)],[2260])).
% 1.01/1.20 tff(2262,plain,
% 1.01/1.20 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a2526) | (~c0_1(a2526)) | (~c2_1(a2526)) | c1_1(a2601) | (~c3_1(a2601)) | (~c0_1(a2601)) | c1_1(a2549) | c0_1(a2549) | (~c2_1(a2549)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c3_1(a2526) | c0_1(a2549) | c1_1(a2549) | (~c0_1(a2526)) | (~ndr1_0) | (~c2_1(a2526)) | (~c2_1(a2549)) | (~c3_1(a2601)) | (~c0_1(a2601)) | c1_1(a2601))),
% 1.01/1.20 inference(transitivity,[status(thm)],[2261, 2259])).
% 1.01/1.20 tff(2263,plain,
% 1.01/1.20 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a2526) | (~c0_1(a2526)) | (~c2_1(a2526)) | c1_1(a2601) | (~c3_1(a2601)) | (~c0_1(a2601)) | c1_1(a2549) | c0_1(a2549) | (~c2_1(a2549)))),
% 1.01/1.20 inference(quant_inst,[status(thm)],[])).
% 1.01/1.20 tff(2264,plain,
% 1.01/1.20 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c3_1(a2526) | c0_1(a2549) | c1_1(a2549) | (~c0_1(a2526)) | (~ndr1_0) | (~c2_1(a2526)) | (~c2_1(a2549)) | (~c3_1(a2601)) | (~c0_1(a2601)) | c1_1(a2601)),
% 1.01/1.20 inference(modus_ponens,[status(thm)],[2263, 2262])).
% 1.01/1.20 tff(2265,plain,
% 1.01/1.20 ($false),
% 1.01/1.20 inference(unit_resolution,[status(thm)],[2264, 90, 1882, 1876, 2258, 1740, 2257, 2256, 2218, 2243, 2233, 2217])).
% 1.01/1.20 tff(2266,plain,(hskp2 | (~c0_1(a2601)) | (~c3_1(a2601)) | c3_1(a2526) | (~c0_1(a2526)) | c1_1(a2601) | hskp21), inference(lemma,lemma(discharge,[]))).
% 1.01/1.20 tff(2267,plain,
% 1.01/1.20 (hskp2),
% 1.01/1.20 inference(unit_resolution,[status(thm)],[2266, 1740, 1876, 1882, 2218, 2217, 1829])).
% 1.01/1.20 tff(2268,plain,
% 1.01/1.20 (~c0_1(a2518)),
% 1.01/1.20 inference(unit_resolution,[status(thm)],[898, 2267])).
% 1.01/1.20 tff(2269,plain,
% 1.01/1.20 (c1_1(a2518)),
% 1.01/1.20 inference(unit_resolution,[status(thm)],[906, 2267])).
% 1.01/1.20 tff(2270,plain,
% 1.01/1.20 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c1_1(a2526) | c3_1(a2526) | c2_1(a2601) | (~c0_1(a2526)) | c0_1(a2518) | (~ndr1_0) | (~c1_1(a2518)) | (~c2_1(a2518)) | (~c3_1(a2601)) | c1_1(a2601))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c1_1(a2526) | c3_1(a2526) | c2_1(a2601) | (~c0_1(a2526)) | c0_1(a2518) | (~ndr1_0) | (~c1_1(a2518)) | (~c2_1(a2518)) | (~c3_1(a2601)) | c1_1(a2601))),
% 1.01/1.20 inference(rewrite,[status(thm)],[])).
% 1.01/1.20 tff(2271,plain,
% 1.01/1.20 (((~ndr1_0) | c3_1(a2526) | c1_1(a2526) | (~c0_1(a2526)) | c1_1(a2601) | c2_1(a2601) | (~c3_1(a2601)) | c0_1(a2518) | (~c2_1(a2518)) | (~c1_1(a2518))) <=> (c1_1(a2526) | c3_1(a2526) | c2_1(a2601) | (~c0_1(a2526)) | c0_1(a2518) | (~ndr1_0) | (~c1_1(a2518)) | (~c2_1(a2518)) | (~c3_1(a2601)) | c1_1(a2601))),
% 1.01/1.20 inference(rewrite,[status(thm)],[])).
% 1.01/1.20 tff(2272,plain,
% 1.01/1.20 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a2526) | c1_1(a2526) | (~c0_1(a2526)) | c1_1(a2601) | c2_1(a2601) | (~c3_1(a2601)) | c0_1(a2518) | (~c2_1(a2518)) | (~c1_1(a2518)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c1_1(a2526) | c3_1(a2526) | c2_1(a2601) | (~c0_1(a2526)) | c0_1(a2518) | (~ndr1_0) | (~c1_1(a2518)) | (~c2_1(a2518)) | (~c3_1(a2601)) | c1_1(a2601)))),
% 1.01/1.20 inference(monotonicity,[status(thm)],[2271])).
% 1.01/1.20 tff(2273,plain,
% 1.01/1.20 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a2526) | c1_1(a2526) | (~c0_1(a2526)) | c1_1(a2601) | c2_1(a2601) | (~c3_1(a2601)) | c0_1(a2518) | (~c2_1(a2518)) | (~c1_1(a2518)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c1_1(a2526) | c3_1(a2526) | c2_1(a2601) | (~c0_1(a2526)) | c0_1(a2518) | (~ndr1_0) | (~c1_1(a2518)) | (~c2_1(a2518)) | (~c3_1(a2601)) | c1_1(a2601))),
% 1.01/1.20 inference(transitivity,[status(thm)],[2272, 2270])).
% 1.01/1.20 tff(2274,plain,
% 1.01/1.20 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a2526) | c1_1(a2526) | (~c0_1(a2526)) | c1_1(a2601) | c2_1(a2601) | (~c3_1(a2601)) | c0_1(a2518) | (~c2_1(a2518)) | (~c1_1(a2518)))),
% 1.01/1.20 inference(quant_inst,[status(thm)],[])).
% 1.01/1.20 tff(2275,plain,
% 1.01/1.20 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c1_1(a2526) | c3_1(a2526) | c2_1(a2601) | (~c0_1(a2526)) | c0_1(a2518) | (~ndr1_0) | (~c1_1(a2518)) | (~c2_1(a2518)) | (~c3_1(a2601)) | c1_1(a2601)),
% 1.01/1.20 inference(modus_ponens,[status(thm)],[2274, 2273])).
% 1.01/1.20 tff(2276,plain,
% 1.01/1.20 (~c2_1(a2518)),
% 1.01/1.20 inference(unit_resolution,[status(thm)],[2275, 90, 1876, 2225, 1740, 2269, 1881, 2218, 2268, 636, 2217])).
% 1.01/1.20 tff(2277,plain,
% 1.01/1.20 (~c3_1(a2518)),
% 1.01/1.20 inference(unit_resolution,[status(thm)],[892, 2267])).
% 1.01/1.20 tff(2278,plain,
% 1.01/1.20 (~hskp9),
% 1.01/1.20 inference(unit_resolution,[status(thm)],[205, 2218])).
% 1.01/1.20 tff(2279,plain,
% 1.01/1.20 ($false),
% 1.01/1.20 inference(unit_resolution,[status(thm)],[1815, 90, 2278, 2269, 2268, 2277, 36, 2276])).
% 1.01/1.20 tff(2280,plain,(c3_1(a2526) | (~c3_1(a2601)) | c2_1(a2601) | (~c0_1(a2526)) | c1_1(a2601) | (~c0_1(a2601)) | hskp21), inference(lemma,lemma(discharge,[]))).
% 1.01/1.20 tff(2281,plain,
% 1.01/1.20 (c3_1(a2526)),
% 1.01/1.20 inference(unit_resolution,[status(thm)],[2280, 1876, 1881, 2218, 2217, 1882, 1829])).
% 1.01/1.20 tff(2282,plain,
% 1.01/1.20 (~c2_1(a2526)),
% 1.01/1.20 inference(unit_resolution,[status(thm)],[2035, 90, 1882, 1876, 2027, 2281, 1881, 1402, 2217])).
% 1.01/1.20 tff(2283,plain,
% 1.01/1.20 (hskp22),
% 1.01/1.20 inference(unit_resolution,[status(thm)],[1884, 2217])).
% 1.01/1.20 tff(2284,plain,
% 1.01/1.20 (~c3_1(a2552)),
% 1.01/1.20 inference(unit_resolution,[status(thm)],[806, 2283])).
% 1.01/1.20 tff(2285,plain,
% 1.01/1.20 (~c1_1(a2552)),
% 1.01/1.20 inference(unit_resolution,[status(thm)],[820, 2283])).
% 1.01/1.20 tff(2286,plain,
% 1.01/1.20 (c2_1(a2552)),
% 1.01/1.20 inference(unit_resolution,[status(thm)],[814, 2283])).
% 1.01/1.20 tff(2287,plain,
% 1.01/1.20 (c0_1(a2552)),
% 1.01/1.20 inference(unit_resolution,[status(thm)],[1776, 90, 1882, 1876, 2286, 2285, 2284, 424, 2217])).
% 1.01/1.20 tff(2288,assumption,(hskp27), introduced(assumption)).
% 1.01/1.20 tff(2289,plain,
% 1.01/1.20 (~c3_1(a2614)),
% 1.01/1.20 inference(unit_resolution,[status(thm)],[19, 2288])).
% 1.01/1.20 tff(2290,plain,
% 1.01/1.20 (c1_1(a2614)),
% 1.01/1.20 inference(unit_resolution,[status(thm)],[12, 2288])).
% 1.01/1.20 tff(2291,plain,
% 1.01/1.20 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp21 | c1_1(a2526) | c3_1(a2614) | (~c0_1(a2526)) | (~ndr1_0) | (~c3_1(a2526)) | (~c0_1(a2614)) | (~c1_1(a2614)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp21 | c1_1(a2526) | c3_1(a2614) | (~c0_1(a2526)) | (~ndr1_0) | (~c3_1(a2526)) | (~c0_1(a2614)) | (~c1_1(a2614)))),
% 1.01/1.20 inference(rewrite,[status(thm)],[])).
% 1.01/1.20 tff(2292,plain,
% 1.01/1.20 ((hskp21 | (~ndr1_0) | c3_1(a2614) | (~c1_1(a2614)) | (~c0_1(a2614)) | c1_1(a2526) | (~c3_1(a2526)) | (~c0_1(a2526))) <=> (hskp21 | c1_1(a2526) | c3_1(a2614) | (~c0_1(a2526)) | (~ndr1_0) | (~c3_1(a2526)) | (~c0_1(a2614)) | (~c1_1(a2614)))),
% 1.01/1.20 inference(rewrite,[status(thm)],[])).
% 1.01/1.20 tff(2293,plain,
% 1.01/1.20 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp21 | (~ndr1_0) | c3_1(a2614) | (~c1_1(a2614)) | (~c0_1(a2614)) | c1_1(a2526) | (~c3_1(a2526)) | (~c0_1(a2526)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp21 | c1_1(a2526) | c3_1(a2614) | (~c0_1(a2526)) | (~ndr1_0) | (~c3_1(a2526)) | (~c0_1(a2614)) | (~c1_1(a2614))))),
% 1.01/1.20 inference(monotonicity,[status(thm)],[2292])).
% 1.01/1.20 tff(2294,plain,
% 1.01/1.20 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp21 | (~ndr1_0) | c3_1(a2614) | (~c1_1(a2614)) | (~c0_1(a2614)) | c1_1(a2526) | (~c3_1(a2526)) | (~c0_1(a2526)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp21 | c1_1(a2526) | c3_1(a2614) | (~c0_1(a2526)) | (~ndr1_0) | (~c3_1(a2526)) | (~c0_1(a2614)) | (~c1_1(a2614)))),
% 1.01/1.20 inference(transitivity,[status(thm)],[2293, 2291])).
% 1.01/1.20 tff(2295,plain,
% 1.01/1.20 ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp21 | (~ndr1_0) | c3_1(a2614) | (~c1_1(a2614)) | (~c0_1(a2614)) | c1_1(a2526) | (~c3_1(a2526)) | (~c0_1(a2526)))),
% 1.01/1.20 inference(quant_inst,[status(thm)],[])).
% 1.01/1.20 tff(2296,plain,
% 1.01/1.20 ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp21 | c1_1(a2526) | c3_1(a2614) | (~c0_1(a2526)) | (~ndr1_0) | (~c3_1(a2526)) | (~c0_1(a2614)) | (~c1_1(a2614))),
% 1.01/1.20 inference(modus_ponens,[status(thm)],[2295, 2294])).
% 1.01/1.20 tff(2297,plain,
% 1.01/1.20 (~c0_1(a2614)),
% 1.01/1.20 inference(unit_resolution,[status(thm)],[2296, 90, 1829, 2290, 2027, 216, 2289, 2218, 2063])).
% 1.01/1.20 tff(2298,plain,
% 1.01/1.20 (~c2_1(a2614)),
% 1.01/1.20 inference(unit_resolution,[status(thm)],[25, 2288])).
% 1.01/1.20 tff(2299,plain,
% 1.01/1.20 ($false),
% 1.01/1.20 inference(unit_resolution,[status(thm)],[115, 90, 2278, 2290, 2298, 2289, 36, 2297])).
% 1.01/1.20 tff(2300,plain,((~hskp27) | hskp21 | c1_1(a2526) | (~c3_1(a2526)) | (~c0_1(a2526))), inference(lemma,lemma(discharge,[]))).
% 1.01/1.20 tff(2301,plain,
% 1.01/1.20 (~hskp27),
% 1.01/1.20 inference(unit_resolution,[status(thm)],[2300, 2027, 1829, 2281, 2218])).
% 1.01/1.20 tff(2302,plain,
% 1.01/1.20 (hskp23),
% 1.01/1.20 inference(unit_resolution,[status(thm)],[4, 2301])).
% 1.01/1.20 tff(2303,plain,
% 1.01/1.20 (~c1_1(a2553)),
% 1.01/1.20 inference(unit_resolution,[status(thm)],[785, 2302])).
% 1.01/1.20 tff(2304,plain,
% 1.01/1.20 (~c3_1(a2553)),
% 1.01/1.20 inference(unit_resolution,[status(thm)],[769, 2302])).
% 1.01/1.20 tff(2305,plain,
% 1.01/1.20 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | c0_1(a2553) | c1_1(a2553) | c3_1(a2553) | c1_1(a2552) | (~ndr1_0) | (~c0_1(a2552)) | (~c2_1(a2552)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp2 | c0_1(a2553) | c1_1(a2553) | c3_1(a2553) | c1_1(a2552) | (~ndr1_0) | (~c0_1(a2552)) | (~c2_1(a2552)))),
% 1.01/1.20 inference(rewrite,[status(thm)],[])).
% 1.01/1.20 tff(2306,plain,
% 1.01/1.20 ((hskp2 | (~ndr1_0) | c1_1(a2552) | (~c0_1(a2552)) | (~c2_1(a2552)) | c3_1(a2553) | c1_1(a2553) | c0_1(a2553)) <=> (hskp2 | c0_1(a2553) | c1_1(a2553) | c3_1(a2553) | c1_1(a2552) | (~ndr1_0) | (~c0_1(a2552)) | (~c2_1(a2552)))),
% 1.01/1.20 inference(rewrite,[status(thm)],[])).
% 1.01/1.20 tff(2307,plain,
% 1.01/1.20 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | c1_1(a2552) | (~c0_1(a2552)) | (~c2_1(a2552)) | c3_1(a2553) | c1_1(a2553) | c0_1(a2553))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | c0_1(a2553) | c1_1(a2553) | c3_1(a2553) | c1_1(a2552) | (~ndr1_0) | (~c0_1(a2552)) | (~c2_1(a2552))))),
% 1.01/1.20 inference(monotonicity,[status(thm)],[2306])).
% 1.01/1.20 tff(2308,plain,
% 1.01/1.20 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | c1_1(a2552) | (~c0_1(a2552)) | (~c2_1(a2552)) | c3_1(a2553) | c1_1(a2553) | c0_1(a2553))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp2 | c0_1(a2553) | c1_1(a2553) | c3_1(a2553) | c1_1(a2552) | (~ndr1_0) | (~c0_1(a2552)) | (~c2_1(a2552)))),
% 1.01/1.20 inference(transitivity,[status(thm)],[2307, 2305])).
% 1.01/1.20 tff(2309,plain,
% 1.01/1.20 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | c1_1(a2552) | (~c0_1(a2552)) | (~c2_1(a2552)) | c3_1(a2553) | c1_1(a2553) | c0_1(a2553))),
% 1.01/1.20 inference(quant_inst,[status(thm)],[])).
% 1.01/1.20 tff(2310,plain,
% 1.01/1.20 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp2 | c0_1(a2553) | c1_1(a2553) | c3_1(a2553) | c1_1(a2552) | (~ndr1_0) | (~c0_1(a2552)) | (~c2_1(a2552))),
% 1.01/1.20 inference(modus_ponens,[status(thm)],[2309, 2308])).
% 1.01/1.20 tff(2311,plain,
% 1.04/1.20 (hskp2 | c0_1(a2553)),
% 1.04/1.20 inference(unit_resolution,[status(thm)],[2310, 90, 822, 850, 849, 824, 877, 1212])).
% 1.04/1.20 tff(2312,plain,
% 1.04/1.20 (hskp2),
% 1.04/1.20 inference(unit_resolution,[status(thm)],[2311, 1968])).
% 1.04/1.20 tff(2313,plain,
% 1.04/1.20 (~c0_1(a2518)),
% 1.04/1.20 inference(unit_resolution,[status(thm)],[898, 2312])).
% 1.04/1.20 tff(2314,plain,
% 1.04/1.20 (c1_1(a2518)),
% 1.04/1.20 inference(unit_resolution,[status(thm)],[906, 2312])).
% 1.04/1.20 tff(2315,plain,
% 1.04/1.20 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c1_1(a2526) | c1_1(a2552) | c3_1(a2552) | c0_1(a2518) | (~ndr1_0) | (~c1_1(a2518)) | (~c2_1(a2518)) | (~c3_1(a2526)) | c2_1(a2526) | (~c0_1(a2552)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c1_1(a2526) | c1_1(a2552) | c3_1(a2552) | c0_1(a2518) | (~ndr1_0) | (~c1_1(a2518)) | (~c2_1(a2518)) | (~c3_1(a2526)) | c2_1(a2526) | (~c0_1(a2552)))),
% 1.04/1.20 inference(rewrite,[status(thm)],[])).
% 1.04/1.20 tff(2316,plain,
% 1.04/1.20 (((~ndr1_0) | c3_1(a2552) | c1_1(a2552) | (~c0_1(a2552)) | c1_1(a2526) | c2_1(a2526) | (~c3_1(a2526)) | c0_1(a2518) | (~c2_1(a2518)) | (~c1_1(a2518))) <=> (c1_1(a2526) | c1_1(a2552) | c3_1(a2552) | c0_1(a2518) | (~ndr1_0) | (~c1_1(a2518)) | (~c2_1(a2518)) | (~c3_1(a2526)) | c2_1(a2526) | (~c0_1(a2552)))),
% 1.04/1.20 inference(rewrite,[status(thm)],[])).
% 1.04/1.20 tff(2317,plain,
% 1.04/1.20 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a2552) | c1_1(a2552) | (~c0_1(a2552)) | c1_1(a2526) | c2_1(a2526) | (~c3_1(a2526)) | c0_1(a2518) | (~c2_1(a2518)) | (~c1_1(a2518)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c1_1(a2526) | c1_1(a2552) | c3_1(a2552) | c0_1(a2518) | (~ndr1_0) | (~c1_1(a2518)) | (~c2_1(a2518)) | (~c3_1(a2526)) | c2_1(a2526) | (~c0_1(a2552))))),
% 1.04/1.20 inference(monotonicity,[status(thm)],[2316])).
% 1.04/1.20 tff(2318,plain,
% 1.04/1.20 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a2552) | c1_1(a2552) | (~c0_1(a2552)) | c1_1(a2526) | c2_1(a2526) | (~c3_1(a2526)) | c0_1(a2518) | (~c2_1(a2518)) | (~c1_1(a2518)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c1_1(a2526) | c1_1(a2552) | c3_1(a2552) | c0_1(a2518) | (~ndr1_0) | (~c1_1(a2518)) | (~c2_1(a2518)) | (~c3_1(a2526)) | c2_1(a2526) | (~c0_1(a2552)))),
% 1.04/1.20 inference(transitivity,[status(thm)],[2317, 2315])).
% 1.04/1.20 tff(2319,plain,
% 1.04/1.20 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a2552) | c1_1(a2552) | (~c0_1(a2552)) | c1_1(a2526) | c2_1(a2526) | (~c3_1(a2526)) | c0_1(a2518) | (~c2_1(a2518)) | (~c1_1(a2518)))),
% 1.04/1.20 inference(quant_inst,[status(thm)],[])).
% 1.04/1.20 tff(2320,plain,
% 1.04/1.20 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c1_1(a2526) | c1_1(a2552) | c3_1(a2552) | c0_1(a2518) | (~ndr1_0) | (~c1_1(a2518)) | (~c2_1(a2518)) | (~c3_1(a2526)) | c2_1(a2526) | (~c0_1(a2552))),
% 1.04/1.20 inference(modus_ponens,[status(thm)],[2319, 2318])).
% 1.04/1.20 tff(2321,plain,
% 1.04/1.20 (~c2_1(a2518)),
% 1.04/1.20 inference(unit_resolution,[status(thm)],[2320, 90, 2027, 216, 2314, 824, 823, 2313, 636, 1212, 1115])).
% 1.04/1.20 tff(2322,plain,
% 1.04/1.20 (~c3_1(a2518)),
% 1.04/1.20 inference(unit_resolution,[status(thm)],[892, 2312])).
% 1.04/1.20 tff(2323,plain,
% 1.04/1.20 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp9 | c2_1(a2614) | c3_1(a2614) | c0_1(a2518) | c3_1(a2518) | (~ndr1_0) | c2_1(a2518) | (~c1_1(a2614)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp9 | c2_1(a2614) | c3_1(a2614) | c0_1(a2518) | c3_1(a2518) | (~ndr1_0) | c2_1(a2518) | (~c1_1(a2614)))),
% 1.04/1.21 inference(rewrite,[status(thm)],[])).
% 1.04/1.21 tff(2324,plain,
% 1.04/1.21 ((hskp9 | (~ndr1_0) | c3_1(a2614) | c2_1(a2614) | (~c1_1(a2614)) | c3_1(a2518) | c0_1(a2518) | c2_1(a2518)) <=> (hskp9 | c2_1(a2614) | c3_1(a2614) | c0_1(a2518) | c3_1(a2518) | (~ndr1_0) | c2_1(a2518) | (~c1_1(a2614)))),
% 1.04/1.21 inference(rewrite,[status(thm)],[])).
% 1.04/1.21 tff(2325,plain,
% 1.04/1.21 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp9 | (~ndr1_0) | c3_1(a2614) | c2_1(a2614) | (~c1_1(a2614)) | c3_1(a2518) | c0_1(a2518) | c2_1(a2518))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp9 | c2_1(a2614) | c3_1(a2614) | c0_1(a2518) | c3_1(a2518) | (~ndr1_0) | c2_1(a2518) | (~c1_1(a2614))))),
% 1.04/1.21 inference(monotonicity,[status(thm)],[2324])).
% 1.04/1.21 tff(2326,plain,
% 1.04/1.21 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp9 | (~ndr1_0) | c3_1(a2614) | c2_1(a2614) | (~c1_1(a2614)) | c3_1(a2518) | c0_1(a2518) | c2_1(a2518))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp9 | c2_1(a2614) | c3_1(a2614) | c0_1(a2518) | c3_1(a2518) | (~ndr1_0) | c2_1(a2518) | (~c1_1(a2614)))),
% 1.04/1.21 inference(transitivity,[status(thm)],[2325, 2323])).
% 1.04/1.21 tff(2327,plain,
% 1.04/1.21 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp9 | (~ndr1_0) | c3_1(a2614) | c2_1(a2614) | (~c1_1(a2614)) | c3_1(a2518) | c0_1(a2518) | c2_1(a2518))),
% 1.04/1.21 inference(quant_inst,[status(thm)],[])).
% 1.04/1.21 tff(2328,plain,
% 1.04/1.21 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp9 | c2_1(a2614) | c3_1(a2614) | c0_1(a2518) | c3_1(a2518) | (~ndr1_0) | c2_1(a2518) | (~c1_1(a2614))),
% 1.04/1.21 inference(modus_ponens,[status(thm)],[2327, 2326])).
% 1.04/1.21 tff(2329,plain,
% 1.04/1.21 ($false),
% 1.04/1.21 inference(unit_resolution,[status(thm)],[2328, 90, 14, 1973, 1972, 1971, 2313, 2322, 36, 2321])).
% 1.04/1.21 tff(2330,plain,(c0_1(a2553) | hskp9 | c1_1(a2526) | (~c3_1(a2526)) | c1_1(a2552) | c3_1(a2552) | (~c0_1(a2552)) | c2_1(a2526) | (~c2_1(a2552)) | c1_1(a2553) | c3_1(a2553)), inference(lemma,lemma(discharge,[]))).
% 1.04/1.21 tff(2331,plain,
% 1.04/1.21 (c0_1(a2553)),
% 1.04/1.21 inference(unit_resolution,[status(thm)],[2330, 849, 2027, 216, 824, 823, 1212, 1115, 822, 850, 2278])).
% 1.04/1.21 tff(2332,plain,
% 1.04/1.21 (hskp2 | (~c0_1(a2553)) | c2_1(a2553)),
% 1.04/1.21 inference(unit_resolution,[status(thm)],[857, 90, 850, 849, 848])).
% 1.04/1.21 tff(2333,plain,
% 1.04/1.21 (c2_1(a2553)),
% 1.04/1.21 inference(unit_resolution,[status(thm)],[2332, 838, 851])).
% 1.04/1.21 tff(2334,plain,
% 1.04/1.21 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a2526) | c3_1(a2553) | c0_1(a2549) | c1_1(a2549) | (~c0_1(a2526)) | (~ndr1_0) | (~c3_1(a2526)) | (~c2_1(a2549)) | (~c0_1(a2553)) | (~c2_1(a2553)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a2526) | c3_1(a2553) | c0_1(a2549) | c1_1(a2549) | (~c0_1(a2526)) | (~ndr1_0) | (~c3_1(a2526)) | (~c2_1(a2549)) | (~c0_1(a2553)) | (~c2_1(a2553)))),
% 1.04/1.21 inference(rewrite,[status(thm)],[])).
% 1.04/1.21 tff(2335,plain,
% 1.04/1.21 (((~ndr1_0) | c3_1(a2553) | (~c0_1(a2553)) | (~c2_1(a2553)) | c1_1(a2526) | (~c3_1(a2526)) | (~c0_1(a2526)) | c1_1(a2549) | c0_1(a2549) | (~c2_1(a2549))) <=> (c1_1(a2526) | c3_1(a2553) | c0_1(a2549) | c1_1(a2549) | (~c0_1(a2526)) | (~ndr1_0) | (~c3_1(a2526)) | (~c2_1(a2549)) | (~c0_1(a2553)) | (~c2_1(a2553)))),
% 1.04/1.21 inference(rewrite,[status(thm)],[])).
% 1.04/1.21 tff(2336,plain,
% 1.04/1.21 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a2553) | (~c0_1(a2553)) | (~c2_1(a2553)) | c1_1(a2526) | (~c3_1(a2526)) | (~c0_1(a2526)) | c1_1(a2549) | c0_1(a2549) | (~c2_1(a2549)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a2526) | c3_1(a2553) | c0_1(a2549) | c1_1(a2549) | (~c0_1(a2526)) | (~ndr1_0) | (~c3_1(a2526)) | (~c2_1(a2549)) | (~c0_1(a2553)) | (~c2_1(a2553))))),
% 1.04/1.21 inference(monotonicity,[status(thm)],[2335])).
% 1.04/1.21 tff(2337,plain,
% 1.04/1.21 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a2553) | (~c0_1(a2553)) | (~c2_1(a2553)) | c1_1(a2526) | (~c3_1(a2526)) | (~c0_1(a2526)) | c1_1(a2549) | c0_1(a2549) | (~c2_1(a2549)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a2526) | c3_1(a2553) | c0_1(a2549) | c1_1(a2549) | (~c0_1(a2526)) | (~ndr1_0) | (~c3_1(a2526)) | (~c2_1(a2549)) | (~c0_1(a2553)) | (~c2_1(a2553)))),
% 1.04/1.21 inference(transitivity,[status(thm)],[2336, 2334])).
% 1.04/1.21 tff(2338,plain,
% 1.04/1.21 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a2553) | (~c0_1(a2553)) | (~c2_1(a2553)) | c1_1(a2526) | (~c3_1(a2526)) | (~c0_1(a2526)) | c1_1(a2549) | c0_1(a2549) | (~c2_1(a2549)))),
% 1.04/1.21 inference(quant_inst,[status(thm)],[])).
% 1.04/1.21 tff(2339,plain,
% 1.04/1.21 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a2526) | c3_1(a2553) | c0_1(a2549) | c1_1(a2549) | (~c0_1(a2526)) | (~ndr1_0) | (~c3_1(a2526)) | (~c2_1(a2549)) | (~c0_1(a2553)) | (~c2_1(a2553))),
% 1.04/1.21 inference(modus_ponens,[status(thm)],[2338, 2337])).
% 1.04/1.21 tff(2340,plain,
% 1.04/1.21 ($false),
% 1.04/1.21 inference(unit_resolution,[status(thm)],[2339, 90, 851, 2258, 2027, 216, 849, 2257, 2256, 2218, 2243, 2333])).
% 1.04/1.21 tff(2341,plain,(hskp2 | (~c0_1(a2553)) | c1_1(a2526) | (~c3_1(a2526)) | c3_1(a2553) | (~c0_1(a2526)) | c1_1(a2553) | hskp21), inference(lemma,lemma(discharge,[]))).
% 1.04/1.21 tff(2342,plain,
% 1.04/1.21 (hskp2),
% 1.04/1.21 inference(unit_resolution,[status(thm)],[2341, 2331, 2027, 216, 849, 2218, 850, 1829])).
% 1.04/1.21 tff(2343,plain,
% 1.04/1.21 (~c3_1(a2518)),
% 1.04/1.21 inference(unit_resolution,[status(thm)],[892, 2342])).
% 1.04/1.21 tff(2344,plain,
% 1.04/1.21 (~c0_1(a2518)),
% 1.04/1.21 inference(unit_resolution,[status(thm)],[898, 2342])).
% 1.04/1.21 tff(2345,plain,
% 1.04/1.21 (c1_1(a2518)),
% 1.04/1.21 inference(unit_resolution,[status(thm)],[906, 2342])).
% 1.04/1.21 tff(2346,plain,
% 1.04/1.21 (~c2_1(a2518)),
% 1.04/1.21 inference(unit_resolution,[status(thm)],[2174, 2345, 822, 824, 2331, 1829, 2344, 849, 850, 2343, 823])).
% 1.04/1.21 tff(2347,plain,
% 1.04/1.21 ($false),
% 1.04/1.21 inference(unit_resolution,[status(thm)],[1815, 90, 2278, 2345, 2344, 2343, 36, 2346])).
% 1.04/1.21 tff(2348,plain,(c3_1(a2553) | (~c2_1(a2552)) | c1_1(a2552) | hskp21 | c1_1(a2553) | c3_1(a2552) | c1_1(a2526) | (~c3_1(a2526)) | (~c0_1(a2526)) | (~c0_1(a2552)) | c2_1(a2526)), inference(lemma,lemma(discharge,[]))).
% 1.04/1.21 tff(2349,plain,
% 1.04/1.21 ($false),
% 1.04/1.21 inference(unit_resolution,[status(thm)],[2348, 2304, 2303, 2285, 1829, 2286, 2284, 2027, 2281, 2218, 2287, 2282])).
% 1.04/1.21 tff(2350,plain,(c1_1(a2526) | hskp21 | (~c0_1(a2526)) | (~c0_1(a2601)) | (~c3_1(a2601)) | c2_1(a2601) | c1_1(a2601)), inference(lemma,lemma(discharge,[]))).
% 1.04/1.21 tff(2351,plain,
% 1.04/1.21 (c1_1(a2526)),
% 1.04/1.21 inference(unit_resolution,[status(thm)],[2350, 1716, 2214, 1725, 1733, 1739, 2216])).
% 1.04/1.21 tff(2352,plain,
% 1.04/1.21 (((~![U: $i] : (hskp30 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp30 | hskp9 | (~c0_1(a2526)) | (~ndr1_0) | c2_1(a2526) | (~c1_1(a2526)))) <=> ((~![U: $i] : (hskp30 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp30 | hskp9 | (~c0_1(a2526)) | (~ndr1_0) | c2_1(a2526) | (~c1_1(a2526)))),
% 1.04/1.21 inference(rewrite,[status(thm)],[])).
% 1.04/1.21 tff(2353,plain,
% 1.04/1.21 ((hskp30 | hskp9 | (~ndr1_0) | c2_1(a2526) | (~c1_1(a2526)) | (~c0_1(a2526))) <=> (hskp30 | hskp9 | (~c0_1(a2526)) | (~ndr1_0) | c2_1(a2526) | (~c1_1(a2526)))),
% 1.04/1.21 inference(rewrite,[status(thm)],[])).
% 1.04/1.21 tff(2354,plain,
% 1.04/1.21 (((~![U: $i] : (hskp30 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp30 | hskp9 | (~ndr1_0) | c2_1(a2526) | (~c1_1(a2526)) | (~c0_1(a2526)))) <=> ((~![U: $i] : (hskp30 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp30 | hskp9 | (~c0_1(a2526)) | (~ndr1_0) | c2_1(a2526) | (~c1_1(a2526))))),
% 1.04/1.21 inference(monotonicity,[status(thm)],[2353])).
% 1.04/1.21 tff(2355,plain,
% 1.04/1.21 (((~![U: $i] : (hskp30 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp30 | hskp9 | (~ndr1_0) | c2_1(a2526) | (~c1_1(a2526)) | (~c0_1(a2526)))) <=> ((~![U: $i] : (hskp30 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp30 | hskp9 | (~c0_1(a2526)) | (~ndr1_0) | c2_1(a2526) | (~c1_1(a2526)))),
% 1.04/1.21 inference(transitivity,[status(thm)],[2354, 2352])).
% 1.04/1.21 tff(2356,plain,
% 1.04/1.21 ((~![U: $i] : (hskp30 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp30 | hskp9 | (~ndr1_0) | c2_1(a2526) | (~c1_1(a2526)) | (~c0_1(a2526)))),
% 1.04/1.21 inference(quant_inst,[status(thm)],[])).
% 1.04/1.21 tff(2357,plain,
% 1.04/1.21 ((~![U: $i] : (hskp30 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp30 | hskp9 | (~c0_1(a2526)) | (~ndr1_0) | c2_1(a2526) | (~c1_1(a2526))),
% 1.04/1.21 inference(modus_ponens,[status(thm)],[2356, 2355])).
% 1.04/1.21 tff(2358,plain,
% 1.04/1.21 (c2_1(a2526) | (~c1_1(a2526))),
% 1.04/1.21 inference(unit_resolution,[status(thm)],[2357, 90, 151, 2215, 2214, 162])).
% 1.04/1.21 tff(2359,plain,
% 1.04/1.21 (c2_1(a2526)),
% 1.04/1.21 inference(unit_resolution,[status(thm)],[2358, 2351])).
% 1.04/1.21 tff(2360,plain,
% 1.04/1.21 (c3_1(a2526)),
% 1.04/1.21 inference(unit_resolution,[status(thm)],[2280, 1733, 1739, 2214, 2216, 1725, 1716])).
% 1.04/1.21 tff(2361,plain,
% 1.04/1.21 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | (hskp3 | (~c0_1(a2526)) | (~ndr1_0) | (~c3_1(a2526)) | (~c2_1(a2526)) | (~c1_1(a2526)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | hskp3 | (~c0_1(a2526)) | (~ndr1_0) | (~c3_1(a2526)) | (~c2_1(a2526)) | (~c1_1(a2526)))),
% 1.04/1.21 inference(rewrite,[status(thm)],[])).
% 1.04/1.21 tff(2362,plain,
% 1.04/1.21 ((hskp3 | (~ndr1_0) | (~c3_1(a2526)) | (~c0_1(a2526)) | (~c2_1(a2526)) | (~c1_1(a2526)) | (~c0_1(a2526)) | (~c2_1(a2526))) <=> (hskp3 | (~c0_1(a2526)) | (~ndr1_0) | (~c3_1(a2526)) | (~c2_1(a2526)) | (~c1_1(a2526)))),
% 1.04/1.21 inference(rewrite,[status(thm)],[])).
% 1.04/1.21 tff(2363,plain,
% 1.04/1.21 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | (hskp3 | (~ndr1_0) | (~c3_1(a2526)) | (~c0_1(a2526)) | (~c2_1(a2526)) | (~c1_1(a2526)) | (~c0_1(a2526)) | (~c2_1(a2526)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | (hskp3 | (~c0_1(a2526)) | (~ndr1_0) | (~c3_1(a2526)) | (~c2_1(a2526)) | (~c1_1(a2526))))),
% 1.04/1.21 inference(monotonicity,[status(thm)],[2362])).
% 1.04/1.21 tff(2364,plain,
% 1.04/1.21 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | (hskp3 | (~ndr1_0) | (~c3_1(a2526)) | (~c0_1(a2526)) | (~c2_1(a2526)) | (~c1_1(a2526)) | (~c0_1(a2526)) | (~c2_1(a2526)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | hskp3 | (~c0_1(a2526)) | (~ndr1_0) | (~c3_1(a2526)) | (~c2_1(a2526)) | (~c1_1(a2526)))),
% 1.04/1.21 inference(transitivity,[status(thm)],[2363, 2361])).
% 1.04/1.21 tff(2365,plain,
% 1.04/1.21 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | (hskp3 | (~ndr1_0) | (~c3_1(a2526)) | (~c0_1(a2526)) | (~c2_1(a2526)) | (~c1_1(a2526)) | (~c0_1(a2526)) | (~c2_1(a2526)))),
% 1.04/1.21 inference(quant_inst,[status(thm)],[])).
% 1.04/1.21 tff(2366,plain,
% 1.04/1.21 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | hskp3 | (~c0_1(a2526)) | (~ndr1_0) | (~c3_1(a2526)) | (~c2_1(a2526)) | (~c1_1(a2526))),
% 1.04/1.21 inference(modus_ponens,[status(thm)],[2365, 2364])).
% 1.04/1.21 tff(2367,plain,
% 1.04/1.21 (hskp3),
% 1.04/1.21 inference(unit_resolution,[status(thm)],[2366, 90, 2351, 2360, 2214, 109, 2359])).
% 1.04/1.21 tff(2368,plain,
% 1.04/1.21 (~c3_1(a2519)),
% 1.04/1.21 inference(unit_resolution,[status(thm)],[42, 2367])).
% 1.04/1.21 tff(2369,plain,
% 1.04/1.21 (~c2_1(a2519)),
% 1.04/1.21 inference(unit_resolution,[status(thm)],[48, 2367])).
% 1.04/1.21 tff(2370,plain,
% 1.04/1.21 (~c0_1(a2519)),
% 1.04/1.21 inference(unit_resolution,[status(thm)],[54, 2367])).
% 1.04/1.21 tff(2371,plain,
% 1.04/1.21 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp9 | c0_1(a2519) | c2_1(a2519) | c3_1(a2519) | (~ndr1_0) | (~c1_1(a2519)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp9 | c0_1(a2519) | c2_1(a2519) | c3_1(a2519) | (~ndr1_0) | (~c1_1(a2519)))),
% 1.04/1.21 inference(rewrite,[status(thm)],[])).
% 1.04/1.21 tff(2372,plain,
% 1.04/1.21 ((hskp9 | (~ndr1_0) | c3_1(a2519) | c2_1(a2519) | (~c1_1(a2519)) | c3_1(a2519) | c0_1(a2519) | c2_1(a2519)) <=> (hskp9 | c0_1(a2519) | c2_1(a2519) | c3_1(a2519) | (~ndr1_0) | (~c1_1(a2519)))),
% 1.04/1.21 inference(rewrite,[status(thm)],[])).
% 1.04/1.21 tff(2373,plain,
% 1.04/1.21 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp9 | (~ndr1_0) | c3_1(a2519) | c2_1(a2519) | (~c1_1(a2519)) | c3_1(a2519) | c0_1(a2519) | c2_1(a2519))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp9 | c0_1(a2519) | c2_1(a2519) | c3_1(a2519) | (~ndr1_0) | (~c1_1(a2519))))),
% 1.04/1.21 inference(monotonicity,[status(thm)],[2372])).
% 1.04/1.21 tff(2374,plain,
% 1.04/1.21 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp9 | (~ndr1_0) | c3_1(a2519) | c2_1(a2519) | (~c1_1(a2519)) | c3_1(a2519) | c0_1(a2519) | c2_1(a2519))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp9 | c0_1(a2519) | c2_1(a2519) | c3_1(a2519) | (~ndr1_0) | (~c1_1(a2519)))),
% 1.04/1.21 inference(transitivity,[status(thm)],[2373, 2371])).
% 1.04/1.21 tff(2375,plain,
% 1.04/1.21 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp9 | (~ndr1_0) | c3_1(a2519) | c2_1(a2519) | (~c1_1(a2519)) | c3_1(a2519) | c0_1(a2519) | c2_1(a2519))),
% 1.04/1.21 inference(quant_inst,[status(thm)],[])).
% 1.04/1.21 tff(2376,plain,
% 1.04/1.21 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp9 | c0_1(a2519) | c2_1(a2519) | c3_1(a2519) | (~ndr1_0) | (~c1_1(a2519))),
% 1.04/1.21 inference(modus_ponens,[status(thm)],[2375, 2374])).
% 1.04/1.21 tff(2377,plain,
% 1.04/1.21 (~c1_1(a2519)),
% 1.04/1.21 inference(unit_resolution,[status(thm)],[2376, 90, 2215, 2370, 2369, 2368, 36])).
% 1.04/1.21 tff(2378,plain,
% 1.04/1.21 (hskp22),
% 1.04/1.21 inference(unit_resolution,[status(thm)],[1766, 2216])).
% 1.04/1.21 tff(2379,plain,
% 1.04/1.21 (~c3_1(a2552)),
% 1.04/1.21 inference(unit_resolution,[status(thm)],[806, 2378])).
% 1.04/1.21 tff(2380,plain,
% 1.04/1.21 (~c1_1(a2552)),
% 1.04/1.21 inference(unit_resolution,[status(thm)],[820, 2378])).
% 1.04/1.21 tff(2381,plain,
% 1.04/1.21 (c2_1(a2552)),
% 1.04/1.21 inference(unit_resolution,[status(thm)],[814, 2378])).
% 1.04/1.21 tff(2382,plain,
% 1.04/1.21 (c0_1(a2552)),
% 1.04/1.21 inference(unit_resolution,[status(thm)],[1776, 90, 1725, 1733, 2381, 2380, 2379, 424, 2216])).
% 1.04/1.21 tff(2383,plain,
% 1.04/1.21 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | c1_1(a2552) | c0_1(a2519) | c3_1(a2519) | (~ndr1_0) | c1_1(a2519) | (~c0_1(a2552)) | (~c2_1(a2552)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp2 | c1_1(a2552) | c0_1(a2519) | c3_1(a2519) | (~ndr1_0) | c1_1(a2519) | (~c0_1(a2552)) | (~c2_1(a2552)))),
% 1.04/1.21 inference(rewrite,[status(thm)],[])).
% 1.04/1.21 tff(2384,plain,
% 1.04/1.21 ((hskp2 | (~ndr1_0) | c1_1(a2552) | (~c0_1(a2552)) | (~c2_1(a2552)) | c3_1(a2519) | c1_1(a2519) | c0_1(a2519)) <=> (hskp2 | c1_1(a2552) | c0_1(a2519) | c3_1(a2519) | (~ndr1_0) | c1_1(a2519) | (~c0_1(a2552)) | (~c2_1(a2552)))),
% 1.04/1.21 inference(rewrite,[status(thm)],[])).
% 1.04/1.21 tff(2385,plain,
% 1.04/1.21 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | c1_1(a2552) | (~c0_1(a2552)) | (~c2_1(a2552)) | c3_1(a2519) | c1_1(a2519) | c0_1(a2519))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | c1_1(a2552) | c0_1(a2519) | c3_1(a2519) | (~ndr1_0) | c1_1(a2519) | (~c0_1(a2552)) | (~c2_1(a2552))))),
% 1.04/1.21 inference(monotonicity,[status(thm)],[2384])).
% 1.04/1.21 tff(2386,plain,
% 1.04/1.21 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | c1_1(a2552) | (~c0_1(a2552)) | (~c2_1(a2552)) | c3_1(a2519) | c1_1(a2519) | c0_1(a2519))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp2 | c1_1(a2552) | c0_1(a2519) | c3_1(a2519) | (~ndr1_0) | c1_1(a2519) | (~c0_1(a2552)) | (~c2_1(a2552)))),
% 1.04/1.21 inference(transitivity,[status(thm)],[2385, 2383])).
% 1.04/1.21 tff(2387,plain,
% 1.04/1.21 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | c1_1(a2552) | (~c0_1(a2552)) | (~c2_1(a2552)) | c3_1(a2519) | c1_1(a2519) | c0_1(a2519))),
% 1.04/1.21 inference(quant_inst,[status(thm)],[])).
% 1.04/1.21 tff(2388,plain,
% 1.04/1.21 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp2 | c1_1(a2552) | c0_1(a2519) | c3_1(a2519) | (~ndr1_0) | c1_1(a2519) | (~c0_1(a2552)) | (~c2_1(a2552))),
% 1.04/1.21 inference(modus_ponens,[status(thm)],[2387, 2386])).
% 1.04/1.21 tff(2389,plain,
% 1.04/1.21 (hskp2 | c1_1(a2519)),
% 1.04/1.21 inference(unit_resolution,[status(thm)],[2388, 90, 2381, 2380, 2370, 2368, 877, 2382])).
% 1.04/1.21 tff(2390,plain,
% 1.04/1.21 (hskp2),
% 1.04/1.21 inference(unit_resolution,[status(thm)],[2389, 2377])).
% 1.04/1.21 tff(2391,plain,
% 1.04/1.21 (~c3_1(a2518)),
% 1.04/1.21 inference(unit_resolution,[status(thm)],[892, 2390])).
% 1.04/1.21 tff(2392,plain,
% 1.04/1.21 (~c0_1(a2518)),
% 1.04/1.21 inference(unit_resolution,[status(thm)],[898, 2390])).
% 1.04/1.21 tff(2393,plain,
% 1.04/1.21 (c1_1(a2518)),
% 1.04/1.21 inference(unit_resolution,[status(thm)],[906, 2390])).
% 1.04/1.21 tff(2394,plain,
% 1.04/1.21 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~c0_1(a2526)) | c0_1(a2519) | c3_1(a2519) | c0_1(a2518) | c3_1(a2518) | (~ndr1_0) | (~c1_1(a2518)) | c1_1(a2519) | (~c2_1(a2526)) | (~c1_1(a2526)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (~c0_1(a2526)) | c0_1(a2519) | c3_1(a2519) | c0_1(a2518) | c3_1(a2518) | (~ndr1_0) | (~c1_1(a2518)) | c1_1(a2519) | (~c2_1(a2526)) | (~c1_1(a2526)))),
% 1.04/1.21 inference(rewrite,[status(thm)],[])).
% 1.04/1.21 tff(2395,plain,
% 1.04/1.21 (((~ndr1_0) | (~c1_1(a2526)) | (~c0_1(a2526)) | (~c2_1(a2526)) | c3_1(a2518) | c0_1(a2518) | (~c1_1(a2518)) | c3_1(a2519) | c1_1(a2519) | c0_1(a2519)) <=> ((~c0_1(a2526)) | c0_1(a2519) | c3_1(a2519) | c0_1(a2518) | c3_1(a2518) | (~ndr1_0) | (~c1_1(a2518)) | c1_1(a2519) | (~c2_1(a2526)) | (~c1_1(a2526)))),
% 1.04/1.21 inference(rewrite,[status(thm)],[])).
% 1.04/1.21 tff(2396,plain,
% 1.04/1.21 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c1_1(a2526)) | (~c0_1(a2526)) | (~c2_1(a2526)) | c3_1(a2518) | c0_1(a2518) | (~c1_1(a2518)) | c3_1(a2519) | c1_1(a2519) | c0_1(a2519))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~c0_1(a2526)) | c0_1(a2519) | c3_1(a2519) | c0_1(a2518) | c3_1(a2518) | (~ndr1_0) | (~c1_1(a2518)) | c1_1(a2519) | (~c2_1(a2526)) | (~c1_1(a2526))))),
% 1.04/1.21 inference(monotonicity,[status(thm)],[2395])).
% 1.04/1.21 tff(2397,plain,
% 1.04/1.21 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c1_1(a2526)) | (~c0_1(a2526)) | (~c2_1(a2526)) | c3_1(a2518) | c0_1(a2518) | (~c1_1(a2518)) | c3_1(a2519) | c1_1(a2519) | c0_1(a2519))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (~c0_1(a2526)) | c0_1(a2519) | c3_1(a2519) | c0_1(a2518) | c3_1(a2518) | (~ndr1_0) | (~c1_1(a2518)) | c1_1(a2519) | (~c2_1(a2526)) | (~c1_1(a2526)))),
% 1.04/1.21 inference(transitivity,[status(thm)],[2396, 2394])).
% 1.04/1.21 tff(2398,plain,
% 1.04/1.21 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c1_1(a2526)) | (~c0_1(a2526)) | (~c2_1(a2526)) | c3_1(a2518) | c0_1(a2518) | (~c1_1(a2518)) | c3_1(a2519) | c1_1(a2519) | c0_1(a2519))),
% 1.04/1.21 inference(quant_inst,[status(thm)],[])).
% 1.04/1.21 tff(2399,plain,
% 1.04/1.21 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (~c0_1(a2526)) | c0_1(a2519) | c3_1(a2519) | c0_1(a2518) | c3_1(a2518) | (~ndr1_0) | (~c1_1(a2518)) | c1_1(a2519) | (~c2_1(a2526)) | (~c1_1(a2526))),
% 1.04/1.21 inference(modus_ponens,[status(thm)],[2398, 2397])).
% 1.04/1.21 tff(2400,plain,
% 1.04/1.21 ($false),
% 1.04/1.21 inference(unit_resolution,[status(thm)],[2399, 90, 2351, 2393, 2214, 2370, 2368, 2392, 2391, 459, 2359, 2377])).
% 1.04/1.21 tff(2401,plain,(hskp30), inference(lemma,lemma(discharge,[]))).
% 1.04/1.21 tff(2402,plain,
% 1.04/1.21 (((~hskp30) | c2_1(a2558)) <=> ((~hskp30) | c2_1(a2558))),
% 1.04/1.21 inference(rewrite,[status(thm)],[])).
% 1.04/1.21 tff(2403,axiom,((~hskp30) | c2_1(a2558)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause46')).
% 1.04/1.21 tff(2404,plain,
% 1.04/1.21 ((~hskp30) | c2_1(a2558)),
% 1.04/1.21 inference(modus_ponens,[status(thm)],[2403, 2402])).
% 1.04/1.21 tff(2405,plain,
% 1.04/1.21 ((~hskp30) | c2_1(a2558)),
% 1.04/1.21 inference(modus_ponens,[status(thm)],[2404, 2402])).
% 1.04/1.21 tff(2406,plain,
% 1.04/1.21 ((~hskp30) | c2_1(a2558)),
% 1.04/1.21 inference(modus_ponens,[status(thm)],[2405, 2402])).
% 1.04/1.21 tff(2407,plain,
% 1.04/1.21 ((~hskp30) | c2_1(a2558)),
% 1.04/1.21 inference(modus_ponens,[status(thm)],[2406, 2402])).
% 1.04/1.21 tff(2408,plain,
% 1.04/1.21 ((~hskp30) | c2_1(a2558)),
% 1.04/1.21 inference(modus_ponens,[status(thm)],[2407, 2402])).
% 1.04/1.21 tff(2409,plain,
% 1.04/1.21 (c2_1(a2558)),
% 1.04/1.21 inference(unit_resolution,[status(thm)],[2408, 2401])).
% 1.04/1.21 tff(2410,plain,
% 1.04/1.21 (((~hskp30) | c1_1(a2558)) <=> ((~hskp30) | c1_1(a2558))),
% 1.04/1.21 inference(rewrite,[status(thm)],[])).
% 1.04/1.21 tff(2411,axiom,((~hskp30) | c1_1(a2558)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause45')).
% 1.04/1.21 tff(2412,plain,
% 1.04/1.21 ((~hskp30) | c1_1(a2558)),
% 1.04/1.21 inference(modus_ponens,[status(thm)],[2411, 2410])).
% 1.04/1.21 tff(2413,plain,
% 1.04/1.21 ((~hskp30) | c1_1(a2558)),
% 1.04/1.21 inference(modus_ponens,[status(thm)],[2412, 2410])).
% 1.04/1.21 tff(2414,plain,
% 1.04/1.21 ((~hskp30) | c1_1(a2558)),
% 1.04/1.21 inference(modus_ponens,[status(thm)],[2413, 2410])).
% 1.04/1.21 tff(2415,plain,
% 1.04/1.21 ((~hskp30) | c1_1(a2558)),
% 1.04/1.21 inference(modus_ponens,[status(thm)],[2414, 2410])).
% 1.04/1.21 tff(2416,plain,
% 1.04/1.21 ((~hskp30) | c1_1(a2558)),
% 1.04/1.21 inference(modus_ponens,[status(thm)],[2415, 2410])).
% 1.04/1.21 tff(2417,plain,
% 1.04/1.21 (c1_1(a2558)),
% 1.04/1.21 inference(unit_resolution,[status(thm)],[2416, 2401])).
% 1.04/1.21 tff(2418,plain,
% 1.04/1.21 (((~hskp30) | c0_1(a2558)) <=> ((~hskp30) | c0_1(a2558))),
% 1.04/1.21 inference(rewrite,[status(thm)],[])).
% 1.04/1.21 tff(2419,axiom,((~hskp30) | c0_1(a2558)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause44')).
% 1.04/1.21 tff(2420,plain,
% 1.04/1.21 ((~hskp30) | c0_1(a2558)),
% 1.04/1.21 inference(modus_ponens,[status(thm)],[2419, 2418])).
% 1.04/1.21 tff(2421,plain,
% 1.04/1.21 ((~hskp30) | c0_1(a2558)),
% 1.04/1.21 inference(modus_ponens,[status(thm)],[2420, 2418])).
% 1.04/1.21 tff(2422,plain,
% 1.04/1.21 ((~hskp30) | c0_1(a2558)),
% 1.04/1.21 inference(modus_ponens,[status(thm)],[2421, 2418])).
% 1.04/1.21 tff(2423,plain,
% 1.04/1.21 ((~hskp30) | c0_1(a2558)),
% 1.04/1.21 inference(modus_ponens,[status(thm)],[2422, 2418])).
% 1.04/1.21 tff(2424,plain,
% 1.04/1.21 ((~hskp30) | c0_1(a2558)),
% 1.04/1.21 inference(modus_ponens,[status(thm)],[2423, 2418])).
% 1.04/1.21 tff(2425,plain,
% 1.04/1.21 (c0_1(a2558)),
% 1.04/1.21 inference(unit_resolution,[status(thm)],[2424, 2401])).
% 1.04/1.21 tff(2426,plain,
% 1.04/1.21 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | (hskp3 | (~ndr1_0) | (~c2_1(a2558)) | (~c0_1(a2558)) | (~c1_1(a2558)) | (~c0_1(a2521)) | (~c2_1(a2521)) | (~c3_1(a2521)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | hskp3 | (~ndr1_0) | (~c2_1(a2558)) | (~c0_1(a2558)) | (~c1_1(a2558)) | (~c0_1(a2521)) | (~c2_1(a2521)) | (~c3_1(a2521)))),
% 1.04/1.21 inference(rewrite,[status(thm)],[])).
% 1.04/1.21 tff(2427,plain,
% 1.04/1.21 ((hskp3 | (~ndr1_0) | (~c3_1(a2521)) | (~c0_1(a2521)) | (~c2_1(a2521)) | (~c1_1(a2558)) | (~c0_1(a2558)) | (~c2_1(a2558))) <=> (hskp3 | (~ndr1_0) | (~c2_1(a2558)) | (~c0_1(a2558)) | (~c1_1(a2558)) | (~c0_1(a2521)) | (~c2_1(a2521)) | (~c3_1(a2521)))),
% 1.04/1.21 inference(rewrite,[status(thm)],[])).
% 1.04/1.21 tff(2428,plain,
% 1.04/1.21 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | (hskp3 | (~ndr1_0) | (~c3_1(a2521)) | (~c0_1(a2521)) | (~c2_1(a2521)) | (~c1_1(a2558)) | (~c0_1(a2558)) | (~c2_1(a2558)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | (hskp3 | (~ndr1_0) | (~c2_1(a2558)) | (~c0_1(a2558)) | (~c1_1(a2558)) | (~c0_1(a2521)) | (~c2_1(a2521)) | (~c3_1(a2521))))),
% 1.04/1.21 inference(monotonicity,[status(thm)],[2427])).
% 1.04/1.21 tff(2429,plain,
% 1.04/1.21 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | (hskp3 | (~ndr1_0) | (~c3_1(a2521)) | (~c0_1(a2521)) | (~c2_1(a2521)) | (~c1_1(a2558)) | (~c0_1(a2558)) | (~c2_1(a2558)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | hskp3 | (~ndr1_0) | (~c2_1(a2558)) | (~c0_1(a2558)) | (~c1_1(a2558)) | (~c0_1(a2521)) | (~c2_1(a2521)) | (~c3_1(a2521)))),
% 1.04/1.21 inference(transitivity,[status(thm)],[2428, 2426])).
% 1.04/1.21 tff(2430,plain,
% 1.04/1.21 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | (hskp3 | (~ndr1_0) | (~c3_1(a2521)) | (~c0_1(a2521)) | (~c2_1(a2521)) | (~c1_1(a2558)) | (~c0_1(a2558)) | (~c2_1(a2558)))),
% 1.04/1.21 inference(quant_inst,[status(thm)],[])).
% 1.04/1.21 tff(2431,plain,
% 1.04/1.21 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | hskp3 | (~ndr1_0) | (~c2_1(a2558)) | (~c0_1(a2558)) | (~c1_1(a2558)) | (~c0_1(a2521)) | (~c2_1(a2521)) | (~c3_1(a2521))),
% 1.04/1.21 inference(modus_ponens,[status(thm)],[2430, 2429])).
% 1.04/1.21 tff(2432,plain,
% 1.04/1.21 (hskp3 | (~c0_1(a2521))),
% 1.04/1.21 inference(unit_resolution,[status(thm)],[2431, 90, 2425, 2417, 2409, 150, 142, 109])).
% 1.04/1.21 tff(2433,plain,
% 1.04/1.21 (~c0_1(a2521)),
% 1.04/1.21 inference(unit_resolution,[status(thm)],[2432, 99])).
% 1.04/1.21 tff(2434,plain,
% 1.04/1.21 (((~hskp4) | (~c1_1(a2521))) <=> ((~hskp4) | (~c1_1(a2521)))),
% 1.04/1.21 inference(rewrite,[status(thm)],[])).
% 1.04/1.21 tff(2435,plain,
% 1.04/1.21 (((~c1_1(a2521)) | (~hskp4)) <=> ((~hskp4) | (~c1_1(a2521)))),
% 1.04/1.21 inference(rewrite,[status(thm)],[])).
% 1.04/1.21 tff(2436,axiom,((~c1_1(a2521)) | (~hskp4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause126')).
% 1.04/1.21 tff(2437,plain,
% 1.04/1.21 ((~hskp4) | (~c1_1(a2521))),
% 1.04/1.21 inference(modus_ponens,[status(thm)],[2436, 2435])).
% 1.04/1.21 tff(2438,plain,
% 1.04/1.21 ((~hskp4) | (~c1_1(a2521))),
% 1.04/1.21 inference(modus_ponens,[status(thm)],[2437, 2434])).
% 1.04/1.21 tff(2439,plain,
% 1.04/1.21 (~c1_1(a2521)),
% 1.04/1.21 inference(unit_resolution,[status(thm)],[2438, 134])).
% 1.04/1.21 tff(2440,plain,
% 1.04/1.21 (^[V: $i, U: $i] : refl((hskp5 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) <=> (hskp5 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))))),
% 1.04/1.21 inference(bind,[status(th)],[])).
% 1.04/1.21 tff(2441,plain,
% 1.04/1.21 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.04/1.21 inference(quant_intro,[status(thm)],[2440])).
% 1.04/1.21 tff(2442,plain,
% 1.04/1.21 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.04/1.21 inference(rewrite,[status(thm)],[])).
% 1.04/1.21 tff(2443,plain,
% 1.04/1.21 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) <=> ((~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> (((~c1_1(U)) | (~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)))), rewrite((((~c1_1(U)) | (~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V))) | c1_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) | c1_1(V)) | hskp5) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) | hskp5))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) | hskp5) <=> (hskp5 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) | c1_1(V)) | hskp5) <=> (hskp5 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))))),
% 1.04/1.21 inference(bind,[status(th)],[])).
% 1.04/1.21 tff(2444,plain,
% 1.04/1.21 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) | c1_1(V)) | hskp5) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.04/1.21 inference(quant_intro,[status(thm)],[2443])).
% 1.04/1.21 tff(2445,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) | c1_1(V)) | hskp5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause185')).
% 1.04/1.21 tff(2446,plain,
% 1.04/1.21 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.04/1.21 inference(modus_ponens,[status(thm)],[2445, 2444])).
% 1.04/1.21 tff(2447,plain,
% 1.04/1.21 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.04/1.21 inference(modus_ponens,[status(thm)],[2446, 2442])).
% 1.04/1.21 tff(2448,plain,(
% 1.04/1.21 ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.04/1.21 inference(skolemize,[status(sab)],[2447])).
% 1.04/1.21 tff(2449,plain,
% 1.04/1.21 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.04/1.21 inference(modus_ponens,[status(thm)],[2448, 2441])).
% 1.04/1.21 tff(2450,plain,
% 1.04/1.21 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp5 | c1_1(a2521) | (~ndr1_0) | (~c2_1(a2558)) | (~c0_1(a2558)) | (~c1_1(a2558)) | c0_1(a2521) | (~c3_1(a2521)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp5 | c1_1(a2521) | (~ndr1_0) | (~c2_1(a2558)) | (~c0_1(a2558)) | (~c1_1(a2558)) | c0_1(a2521) | (~c3_1(a2521)))),
% 1.04/1.22 inference(rewrite,[status(thm)],[])).
% 1.04/1.22 tff(2451,plain,
% 1.04/1.22 ((hskp5 | (~ndr1_0) | (~c1_1(a2558)) | (~c0_1(a2558)) | (~c2_1(a2558)) | c1_1(a2521) | c0_1(a2521) | (~c3_1(a2521))) <=> (hskp5 | c1_1(a2521) | (~ndr1_0) | (~c2_1(a2558)) | (~c0_1(a2558)) | (~c1_1(a2558)) | c0_1(a2521) | (~c3_1(a2521)))),
% 1.04/1.22 inference(rewrite,[status(thm)],[])).
% 1.04/1.22 tff(2452,plain,
% 1.04/1.22 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp5 | (~ndr1_0) | (~c1_1(a2558)) | (~c0_1(a2558)) | (~c2_1(a2558)) | c1_1(a2521) | c0_1(a2521) | (~c3_1(a2521)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp5 | c1_1(a2521) | (~ndr1_0) | (~c2_1(a2558)) | (~c0_1(a2558)) | (~c1_1(a2558)) | c0_1(a2521) | (~c3_1(a2521))))),
% 1.04/1.22 inference(monotonicity,[status(thm)],[2451])).
% 1.04/1.22 tff(2453,plain,
% 1.04/1.22 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp5 | (~ndr1_0) | (~c1_1(a2558)) | (~c0_1(a2558)) | (~c2_1(a2558)) | c1_1(a2521) | c0_1(a2521) | (~c3_1(a2521)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp5 | c1_1(a2521) | (~ndr1_0) | (~c2_1(a2558)) | (~c0_1(a2558)) | (~c1_1(a2558)) | c0_1(a2521) | (~c3_1(a2521)))),
% 1.04/1.22 inference(transitivity,[status(thm)],[2452, 2450])).
% 1.04/1.22 tff(2454,plain,
% 1.04/1.22 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp5 | (~ndr1_0) | (~c1_1(a2558)) | (~c0_1(a2558)) | (~c2_1(a2558)) | c1_1(a2521) | c0_1(a2521) | (~c3_1(a2521)))),
% 1.04/1.22 inference(quant_inst,[status(thm)],[])).
% 1.04/1.22 tff(2455,plain,
% 1.04/1.22 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp5 | c1_1(a2521) | (~ndr1_0) | (~c2_1(a2558)) | (~c0_1(a2558)) | (~c1_1(a2558)) | c0_1(a2521) | (~c3_1(a2521))),
% 1.04/1.22 inference(modus_ponens,[status(thm)],[2454, 2453])).
% 1.04/1.22 tff(2456,plain,
% 1.04/1.22 (hskp5 | c0_1(a2521)),
% 1.04/1.22 inference(unit_resolution,[status(thm)],[2455, 90, 2425, 2417, 2409, 142, 2439, 2449])).
% 1.04/1.22 tff(2457,plain,
% 1.04/1.22 (hskp5),
% 1.04/1.22 inference(unit_resolution,[status(thm)],[2456, 2433])).
% 1.04/1.22 tff(2458,plain,
% 1.04/1.22 (((~hskp5) | (~c0_1(a2522))) <=> ((~hskp5) | (~c0_1(a2522)))),
% 1.04/1.22 inference(rewrite,[status(thm)],[])).
% 1.04/1.22 tff(2459,plain,
% 1.04/1.22 (((~c0_1(a2522)) | (~hskp5)) <=> ((~hskp5) | (~c0_1(a2522)))),
% 1.04/1.22 inference(rewrite,[status(thm)],[])).
% 1.04/1.22 tff(2460,axiom,((~c0_1(a2522)) | (~hskp5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause125')).
% 1.04/1.22 tff(2461,plain,
% 1.04/1.22 ((~hskp5) | (~c0_1(a2522))),
% 1.04/1.22 inference(modus_ponens,[status(thm)],[2460, 2459])).
% 1.04/1.22 tff(2462,plain,
% 1.04/1.22 ((~hskp5) | (~c0_1(a2522))),
% 1.04/1.22 inference(modus_ponens,[status(thm)],[2461, 2458])).
% 1.04/1.22 tff(2463,plain,
% 1.04/1.22 (~c0_1(a2522)),
% 1.04/1.22 inference(unit_resolution,[status(thm)],[2462, 2457])).
% 1.04/1.22 tff(2464,plain,
% 1.04/1.22 (((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp24 | c2_1(a2614) | c3_1(a2614) | c1_1(a2521) | (~ndr1_0) | (~c2_1(a2521)) | (~c3_1(a2521)) | (~c0_1(a2614)))) <=> ((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp24 | c2_1(a2614) | c3_1(a2614) | c1_1(a2521) | (~ndr1_0) | (~c2_1(a2521)) | (~c3_1(a2521)) | (~c0_1(a2614)))),
% 1.04/1.22 inference(rewrite,[status(thm)],[])).
% 1.04/1.22 tff(2465,plain,
% 1.04/1.22 ((hskp24 | (~ndr1_0) | c3_1(a2614) | c2_1(a2614) | (~c0_1(a2614)) | c1_1(a2521) | (~c3_1(a2521)) | (~c2_1(a2521))) <=> (hskp24 | c2_1(a2614) | c3_1(a2614) | c1_1(a2521) | (~ndr1_0) | (~c2_1(a2521)) | (~c3_1(a2521)) | (~c0_1(a2614)))),
% 1.04/1.22 inference(rewrite,[status(thm)],[])).
% 1.04/1.22 tff(2466,plain,
% 1.04/1.22 (((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp24 | (~ndr1_0) | c3_1(a2614) | c2_1(a2614) | (~c0_1(a2614)) | c1_1(a2521) | (~c3_1(a2521)) | (~c2_1(a2521)))) <=> ((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp24 | c2_1(a2614) | c3_1(a2614) | c1_1(a2521) | (~ndr1_0) | (~c2_1(a2521)) | (~c3_1(a2521)) | (~c0_1(a2614))))),
% 1.04/1.22 inference(monotonicity,[status(thm)],[2465])).
% 1.04/1.22 tff(2467,plain,
% 1.04/1.22 (((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp24 | (~ndr1_0) | c3_1(a2614) | c2_1(a2614) | (~c0_1(a2614)) | c1_1(a2521) | (~c3_1(a2521)) | (~c2_1(a2521)))) <=> ((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp24 | c2_1(a2614) | c3_1(a2614) | c1_1(a2521) | (~ndr1_0) | (~c2_1(a2521)) | (~c3_1(a2521)) | (~c0_1(a2614)))),
% 1.04/1.22 inference(transitivity,[status(thm)],[2466, 2464])).
% 1.04/1.22 tff(2468,plain,
% 1.04/1.22 ((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp24 | (~ndr1_0) | c3_1(a2614) | c2_1(a2614) | (~c0_1(a2614)) | c1_1(a2521) | (~c3_1(a2521)) | (~c2_1(a2521)))),
% 1.04/1.22 inference(quant_inst,[status(thm)],[])).
% 1.04/1.22 tff(2469,plain,
% 1.04/1.22 ((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp24 | c2_1(a2614) | c3_1(a2614) | c1_1(a2521) | (~ndr1_0) | (~c2_1(a2521)) | (~c3_1(a2521)) | (~c0_1(a2614))),
% 1.04/1.22 inference(modus_ponens,[status(thm)],[2468, 2467])).
% 1.04/1.22 tff(2470,plain,
% 1.04/1.22 (hskp24),
% 1.04/1.22 inference(unit_resolution,[status(thm)],[2469, 90, 150, 142, 26, 20, 2439, 1473, 116])).
% 1.04/1.22 tff(2471,plain,
% 1.04/1.22 (~c1_1(a2555)),
% 1.04/1.22 inference(unit_resolution,[status(thm)],[715, 2470])).
% 1.04/1.22 tff(2472,plain,
% 1.04/1.22 (((~hskp5) | c2_1(a2522)) <=> ((~hskp5) | c2_1(a2522))),
% 1.04/1.22 inference(rewrite,[status(thm)],[])).
% 1.04/1.22 tff(2473,axiom,((~hskp5) | c2_1(a2522)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause83')).
% 1.04/1.22 tff(2474,plain,
% 1.04/1.22 ((~hskp5) | c2_1(a2522)),
% 1.04/1.22 inference(modus_ponens,[status(thm)],[2473, 2472])).
% 1.04/1.22 tff(2475,plain,
% 1.04/1.22 ((~hskp5) | c2_1(a2522)),
% 1.04/1.22 inference(modus_ponens,[status(thm)],[2474, 2472])).
% 1.04/1.22 tff(2476,plain,
% 1.04/1.22 ((~hskp5) | c2_1(a2522)),
% 1.04/1.22 inference(modus_ponens,[status(thm)],[2475, 2472])).
% 1.04/1.22 tff(2477,plain,
% 1.04/1.22 ((~hskp5) | c2_1(a2522)),
% 1.04/1.22 inference(modus_ponens,[status(thm)],[2476, 2472])).
% 1.04/1.22 tff(2478,plain,
% 1.04/1.22 ((~hskp5) | c2_1(a2522)),
% 1.04/1.22 inference(modus_ponens,[status(thm)],[2477, 2472])).
% 1.04/1.22 tff(2479,plain,
% 1.04/1.22 (c2_1(a2522)),
% 1.04/1.22 inference(unit_resolution,[status(thm)],[2478, 2457])).
% 1.04/1.22 tff(2480,plain,
% 1.04/1.22 (c2_1(a2555)),
% 1.04/1.22 inference(unit_resolution,[status(thm)],[723, 2470])).
% 1.04/1.22 tff(2481,plain,
% 1.04/1.22 (c0_1(a2555)),
% 1.04/1.22 inference(unit_resolution,[status(thm)],[731, 2470])).
% 1.04/1.22 tff(2482,plain,
% 1.04/1.22 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a2555) | c0_1(a2522) | c1_1(a2521) | (~ndr1_0) | c0_1(a2521) | (~c2_1(a2521)) | (~c1_1(a2522)) | (~c2_1(a2522)) | (~c2_1(a2555)) | (~c0_1(a2555)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a2555) | c0_1(a2522) | c1_1(a2521) | (~ndr1_0) | c0_1(a2521) | (~c2_1(a2521)) | (~c1_1(a2522)) | (~c2_1(a2522)) | (~c2_1(a2555)) | (~c0_1(a2555)))),
% 1.04/1.22 inference(rewrite,[status(thm)],[])).
% 1.04/1.22 tff(2483,plain,
% 1.04/1.22 (((~ndr1_0) | c1_1(a2555) | (~c0_1(a2555)) | (~c2_1(a2555)) | c0_1(a2522) | (~c1_1(a2522)) | (~c2_1(a2522)) | c1_1(a2521) | c0_1(a2521) | (~c2_1(a2521))) <=> (c1_1(a2555) | c0_1(a2522) | c1_1(a2521) | (~ndr1_0) | c0_1(a2521) | (~c2_1(a2521)) | (~c1_1(a2522)) | (~c2_1(a2522)) | (~c2_1(a2555)) | (~c0_1(a2555)))),
% 1.04/1.22 inference(rewrite,[status(thm)],[])).
% 1.04/1.22 tff(2484,plain,
% 1.04/1.22 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a2555) | (~c0_1(a2555)) | (~c2_1(a2555)) | c0_1(a2522) | (~c1_1(a2522)) | (~c2_1(a2522)) | c1_1(a2521) | c0_1(a2521) | (~c2_1(a2521)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a2555) | c0_1(a2522) | c1_1(a2521) | (~ndr1_0) | c0_1(a2521) | (~c2_1(a2521)) | (~c1_1(a2522)) | (~c2_1(a2522)) | (~c2_1(a2555)) | (~c0_1(a2555))))),
% 1.04/1.22 inference(monotonicity,[status(thm)],[2483])).
% 1.04/1.22 tff(2485,plain,
% 1.04/1.22 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a2555) | (~c0_1(a2555)) | (~c2_1(a2555)) | c0_1(a2522) | (~c1_1(a2522)) | (~c2_1(a2522)) | c1_1(a2521) | c0_1(a2521) | (~c2_1(a2521)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a2555) | c0_1(a2522) | c1_1(a2521) | (~ndr1_0) | c0_1(a2521) | (~c2_1(a2521)) | (~c1_1(a2522)) | (~c2_1(a2522)) | (~c2_1(a2555)) | (~c0_1(a2555)))),
% 1.04/1.22 inference(transitivity,[status(thm)],[2484, 2482])).
% 1.04/1.22 tff(2486,plain,
% 1.04/1.22 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a2555) | (~c0_1(a2555)) | (~c2_1(a2555)) | c0_1(a2522) | (~c1_1(a2522)) | (~c2_1(a2522)) | c1_1(a2521) | c0_1(a2521) | (~c2_1(a2521)))),
% 1.04/1.22 inference(quant_inst,[status(thm)],[])).
% 1.04/1.22 tff(2487,plain,
% 1.04/1.22 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a2555) | c0_1(a2522) | c1_1(a2521) | (~ndr1_0) | c0_1(a2521) | (~c2_1(a2521)) | (~c1_1(a2522)) | (~c2_1(a2522)) | (~c2_1(a2555)) | (~c0_1(a2555))),
% 1.04/1.22 inference(modus_ponens,[status(thm)],[2486, 2485])).
% 1.04/1.22 tff(2488,plain,
% 1.04/1.22 (~c1_1(a2522)),
% 1.04/1.22 inference(unit_resolution,[status(thm)],[2487, 90, 2481, 2480, 2479, 150, 2471, 2463, 2439, 944, 2433])).
% 1.04/1.22 tff(2489,plain,
% 1.04/1.22 (^[U: $i] : refl((hskp23 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) <=> (hskp23 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))))),
% 1.04/1.22 inference(bind,[status(th)],[])).
% 1.04/1.22 tff(2490,plain,
% 1.04/1.22 (![U: $i] : (hskp23 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp23 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 1.04/1.22 inference(quant_intro,[status(thm)],[2489])).
% 1.04/1.22 tff(2491,plain,
% 1.04/1.22 (![U: $i] : (hskp23 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp23 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 1.04/1.22 inference(rewrite,[status(thm)],[])).
% 1.04/1.22 tff(2492,plain,
% 1.04/1.22 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c0_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) <=> (((~ndr1_0) | (~c0_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U))))), (((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))), (((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))))), ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp23) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) | hskp23))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) | hskp23) <=> (hskp23 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))), ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp23) <=> (hskp23 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))))), (((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp23) | hskp1) <=> ((hskp23 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) | hskp1))), rewrite(((hskp23 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) | hskp1) <=> (hskp23 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))), (((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp23) | hskp1) <=> (hskp23 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))))),
% 1.04/1.22 inference(bind,[status(th)],[])).
% 1.04/1.22 tff(2493,plain,
% 1.04/1.22 (![U: $i] : ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp23) | hskp1) <=> ![U: $i] : (hskp23 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 1.04/1.22 inference(quant_intro,[status(thm)],[2492])).
% 1.04/1.22 tff(2494,axiom,(![U: $i] : ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp23) | hskp1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause142')).
% 1.04/1.22 tff(2495,plain,
% 1.04/1.22 (![U: $i] : (hskp23 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 1.04/1.22 inference(modus_ponens,[status(thm)],[2494, 2493])).
% 1.04/1.22 tff(2496,plain,
% 1.04/1.22 (![U: $i] : (hskp23 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 1.04/1.22 inference(modus_ponens,[status(thm)],[2495, 2491])).
% 1.04/1.22 tff(2497,plain,(
% 1.04/1.22 ![U: $i] : (hskp23 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 1.04/1.22 inference(skolemize,[status(sab)],[2496])).
% 1.04/1.22 tff(2498,plain,
% 1.04/1.22 (![U: $i] : (hskp23 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 1.04/1.22 inference(modus_ponens,[status(thm)],[2497, 2490])).
% 1.04/1.22 tff(2499,plain,
% 1.04/1.22 (^[U: $i] : refl((hskp25 | hskp3 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U))) <=> (hskp25 | hskp3 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U))))),
% 1.04/1.22 inference(bind,[status(th)],[])).
% 1.04/1.22 tff(2500,plain,
% 1.04/1.22 (![U: $i] : (hskp25 | hskp3 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U))) <=> ![U: $i] : (hskp25 | hskp3 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))),
% 1.04/1.22 inference(quant_intro,[status(thm)],[2499])).
% 1.04/1.22 tff(2501,plain,
% 1.04/1.22 (![U: $i] : (hskp25 | hskp3 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U))) <=> ![U: $i] : (hskp25 | hskp3 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))),
% 1.04/1.22 inference(rewrite,[status(thm)],[])).
% 1.04/1.22 tff(2502,plain,
% 1.04/1.22 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c2_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c2_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp25) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U))) | hskp25))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U))) | hskp25) <=> (hskp25 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp25) <=> (hskp25 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp25) | hskp3) <=> ((hskp25 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U))) | hskp3))), rewrite(((hskp25 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U))) | hskp3) <=> (hskp25 | hskp3 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp25) | hskp3) <=> (hskp25 | hskp3 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))))),
% 1.04/1.22 inference(bind,[status(th)],[])).
% 1.04/1.22 tff(2503,plain,
% 1.04/1.22 (![U: $i] : ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp25) | hskp3) <=> ![U: $i] : (hskp25 | hskp3 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))),
% 1.04/1.22 inference(quant_intro,[status(thm)],[2502])).
% 1.04/1.22 tff(2504,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp25) | hskp3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause151')).
% 1.04/1.22 tff(2505,plain,
% 1.04/1.22 (![U: $i] : (hskp25 | hskp3 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))),
% 1.04/1.22 inference(modus_ponens,[status(thm)],[2504, 2503])).
% 1.04/1.22 tff(2506,plain,
% 1.04/1.22 (![U: $i] : (hskp25 | hskp3 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))),
% 1.04/1.22 inference(modus_ponens,[status(thm)],[2505, 2501])).
% 1.04/1.22 tff(2507,plain,(
% 1.04/1.22 ![U: $i] : (hskp25 | hskp3 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))),
% 1.04/1.22 inference(skolemize,[status(sab)],[2506])).
% 1.04/1.22 tff(2508,plain,
% 1.04/1.22 (![U: $i] : (hskp25 | hskp3 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))),
% 1.04/1.22 inference(modus_ponens,[status(thm)],[2507, 2500])).
% 1.04/1.22 tff(2509,plain,
% 1.04/1.22 (((~![U: $i] : (hskp25 | hskp3 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))) | (hskp25 | hskp3 | c1_1(a2555) | (~ndr1_0) | (~c2_1(a2555)) | (~c0_1(a2555)))) <=> ((~![U: $i] : (hskp25 | hskp3 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))) | hskp25 | hskp3 | c1_1(a2555) | (~ndr1_0) | (~c2_1(a2555)) | (~c0_1(a2555)))),
% 1.04/1.22 inference(rewrite,[status(thm)],[])).
% 1.04/1.22 tff(2510,plain,
% 1.04/1.22 ((hskp25 | hskp3 | (~ndr1_0) | c1_1(a2555) | (~c0_1(a2555)) | (~c2_1(a2555))) <=> (hskp25 | hskp3 | c1_1(a2555) | (~ndr1_0) | (~c2_1(a2555)) | (~c0_1(a2555)))),
% 1.04/1.22 inference(rewrite,[status(thm)],[])).
% 1.04/1.22 tff(2511,plain,
% 1.04/1.22 (((~![U: $i] : (hskp25 | hskp3 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))) | (hskp25 | hskp3 | (~ndr1_0) | c1_1(a2555) | (~c0_1(a2555)) | (~c2_1(a2555)))) <=> ((~![U: $i] : (hskp25 | hskp3 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))) | (hskp25 | hskp3 | c1_1(a2555) | (~ndr1_0) | (~c2_1(a2555)) | (~c0_1(a2555))))),
% 1.04/1.22 inference(monotonicity,[status(thm)],[2510])).
% 1.04/1.22 tff(2512,plain,
% 1.04/1.22 (((~![U: $i] : (hskp25 | hskp3 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))) | (hskp25 | hskp3 | (~ndr1_0) | c1_1(a2555) | (~c0_1(a2555)) | (~c2_1(a2555)))) <=> ((~![U: $i] : (hskp25 | hskp3 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))) | hskp25 | hskp3 | c1_1(a2555) | (~ndr1_0) | (~c2_1(a2555)) | (~c0_1(a2555)))),
% 1.04/1.22 inference(transitivity,[status(thm)],[2511, 2509])).
% 1.04/1.22 tff(2513,plain,
% 1.04/1.22 ((~![U: $i] : (hskp25 | hskp3 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))) | (hskp25 | hskp3 | (~ndr1_0) | c1_1(a2555) | (~c0_1(a2555)) | (~c2_1(a2555)))),
% 1.04/1.22 inference(quant_inst,[status(thm)],[])).
% 1.04/1.22 tff(2514,plain,
% 1.04/1.22 ((~![U: $i] : (hskp25 | hskp3 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))) | hskp25 | hskp3 | c1_1(a2555) | (~ndr1_0) | (~c2_1(a2555)) | (~c0_1(a2555))),
% 1.04/1.22 inference(modus_ponens,[status(thm)],[2513, 2512])).
% 1.04/1.22 tff(2515,plain,
% 1.04/1.22 (hskp25 | hskp3),
% 1.04/1.22 inference(unit_resolution,[status(thm)],[2514, 90, 2481, 2480, 2471, 2508])).
% 1.04/1.22 tff(2516,plain,
% 1.04/1.22 (hskp25),
% 1.04/1.22 inference(unit_resolution,[status(thm)],[2515, 99])).
% 1.04/1.22 tff(2517,plain,
% 1.04/1.22 (~c2_1(a2564)),
% 1.04/1.22 inference(unit_resolution,[status(thm)],[665, 2516])).
% 1.04/1.22 tff(2518,plain,
% 1.04/1.22 (~c1_1(a2564)),
% 1.04/1.22 inference(unit_resolution,[status(thm)],[671, 2516])).
% 1.04/1.22 tff(2519,plain,
% 1.04/1.22 (c0_1(a2564)),
% 1.04/1.22 inference(unit_resolution,[status(thm)],[679, 2516])).
% 1.04/1.22 tff(2520,plain,
% 1.04/1.22 (((~![U: $i] : (hskp23 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp23 | hskp1 | c1_1(a2564) | c2_1(a2564) | (~ndr1_0) | (~c0_1(a2564)))) <=> ((~![U: $i] : (hskp23 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp23 | hskp1 | c1_1(a2564) | c2_1(a2564) | (~ndr1_0) | (~c0_1(a2564)))),
% 1.04/1.22 inference(rewrite,[status(thm)],[])).
% 1.04/1.22 tff(2521,plain,
% 1.04/1.22 ((hskp23 | hskp1 | (~ndr1_0) | c2_1(a2564) | c1_1(a2564) | (~c0_1(a2564))) <=> (hskp23 | hskp1 | c1_1(a2564) | c2_1(a2564) | (~ndr1_0) | (~c0_1(a2564)))),
% 1.04/1.22 inference(rewrite,[status(thm)],[])).
% 1.04/1.22 tff(2522,plain,
% 1.04/1.22 (((~![U: $i] : (hskp23 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp23 | hskp1 | (~ndr1_0) | c2_1(a2564) | c1_1(a2564) | (~c0_1(a2564)))) <=> ((~![U: $i] : (hskp23 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp23 | hskp1 | c1_1(a2564) | c2_1(a2564) | (~ndr1_0) | (~c0_1(a2564))))),
% 1.04/1.22 inference(monotonicity,[status(thm)],[2521])).
% 1.04/1.22 tff(2523,plain,
% 1.04/1.22 (((~![U: $i] : (hskp23 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp23 | hskp1 | (~ndr1_0) | c2_1(a2564) | c1_1(a2564) | (~c0_1(a2564)))) <=> ((~![U: $i] : (hskp23 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp23 | hskp1 | c1_1(a2564) | c2_1(a2564) | (~ndr1_0) | (~c0_1(a2564)))),
% 1.04/1.22 inference(transitivity,[status(thm)],[2522, 2520])).
% 1.04/1.22 tff(2524,plain,
% 1.04/1.22 ((~![U: $i] : (hskp23 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp23 | hskp1 | (~ndr1_0) | c2_1(a2564) | c1_1(a2564) | (~c0_1(a2564)))),
% 1.04/1.22 inference(quant_inst,[status(thm)],[])).
% 1.04/1.22 tff(2525,plain,
% 1.04/1.22 ((~![U: $i] : (hskp23 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp23 | hskp1 | c1_1(a2564) | c2_1(a2564) | (~ndr1_0) | (~c0_1(a2564))),
% 1.04/1.22 inference(modus_ponens,[status(thm)],[2524, 2523])).
% 1.04/1.22 tff(2526,plain,
% 1.04/1.22 (hskp1),
% 1.04/1.22 inference(unit_resolution,[status(thm)],[2525, 1, 90, 2519, 2518, 2517, 2498])).
% 1.04/1.22 tff(2527,plain,
% 1.04/1.22 (~c0_1(a2517)),
% 1.04/1.22 inference(unit_resolution,[status(thm)],[394, 2526])).
% 1.04/1.22 tff(2528,plain,
% 1.04/1.22 (c2_1(a2517)),
% 1.04/1.22 inference(unit_resolution,[status(thm)],[402, 2526])).
% 1.04/1.22 tff(2529,plain,
% 1.04/1.22 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a2555) | c0_1(a2522) | c0_1(a2517) | (~ndr1_0) | (~c1_1(a2517)) | (~c2_1(a2517)) | c1_1(a2522) | (~c2_1(a2522)) | (~c2_1(a2555)) | (~c0_1(a2555)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a2555) | c0_1(a2522) | c0_1(a2517) | (~ndr1_0) | (~c1_1(a2517)) | (~c2_1(a2517)) | c1_1(a2522) | (~c2_1(a2522)) | (~c2_1(a2555)) | (~c0_1(a2555)))),
% 1.04/1.22 inference(rewrite,[status(thm)],[])).
% 1.04/1.22 tff(2530,plain,
% 1.04/1.22 (((~ndr1_0) | c1_1(a2555) | (~c0_1(a2555)) | (~c2_1(a2555)) | c0_1(a2517) | (~c1_1(a2517)) | (~c2_1(a2517)) | c1_1(a2522) | c0_1(a2522) | (~c2_1(a2522))) <=> (c1_1(a2555) | c0_1(a2522) | c0_1(a2517) | (~ndr1_0) | (~c1_1(a2517)) | (~c2_1(a2517)) | c1_1(a2522) | (~c2_1(a2522)) | (~c2_1(a2555)) | (~c0_1(a2555)))),
% 1.04/1.22 inference(rewrite,[status(thm)],[])).
% 1.04/1.22 tff(2531,plain,
% 1.04/1.22 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a2555) | (~c0_1(a2555)) | (~c2_1(a2555)) | c0_1(a2517) | (~c1_1(a2517)) | (~c2_1(a2517)) | c1_1(a2522) | c0_1(a2522) | (~c2_1(a2522)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a2555) | c0_1(a2522) | c0_1(a2517) | (~ndr1_0) | (~c1_1(a2517)) | (~c2_1(a2517)) | c1_1(a2522) | (~c2_1(a2522)) | (~c2_1(a2555)) | (~c0_1(a2555))))),
% 1.04/1.22 inference(monotonicity,[status(thm)],[2530])).
% 1.04/1.22 tff(2532,plain,
% 1.04/1.22 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a2555) | (~c0_1(a2555)) | (~c2_1(a2555)) | c0_1(a2517) | (~c1_1(a2517)) | (~c2_1(a2517)) | c1_1(a2522) | c0_1(a2522) | (~c2_1(a2522)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a2555) | c0_1(a2522) | c0_1(a2517) | (~ndr1_0) | (~c1_1(a2517)) | (~c2_1(a2517)) | c1_1(a2522) | (~c2_1(a2522)) | (~c2_1(a2555)) | (~c0_1(a2555)))),
% 1.04/1.22 inference(transitivity,[status(thm)],[2531, 2529])).
% 1.04/1.22 tff(2533,plain,
% 1.04/1.22 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a2555) | (~c0_1(a2555)) | (~c2_1(a2555)) | c0_1(a2517) | (~c1_1(a2517)) | (~c2_1(a2517)) | c1_1(a2522) | c0_1(a2522) | (~c2_1(a2522)))),
% 1.04/1.22 inference(quant_inst,[status(thm)],[])).
% 1.04/1.22 tff(2534,plain,
% 1.04/1.22 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a2555) | c0_1(a2522) | c0_1(a2517) | (~ndr1_0) | (~c1_1(a2517)) | (~c2_1(a2517)) | c1_1(a2522) | (~c2_1(a2522)) | (~c2_1(a2555)) | (~c0_1(a2555))),
% 1.04/1.22 inference(modus_ponens,[status(thm)],[2533, 2532])).
% 1.04/1.22 tff(2535,plain,
% 1.04/1.22 (~c1_1(a2517)),
% 1.04/1.22 inference(unit_resolution,[status(thm)],[2534, 90, 2481, 2480, 2479, 2528, 2471, 2463, 2527, 944, 2488])).
% 1.04/1.22 tff(2536,plain,
% 1.04/1.22 (~c3_1(a2517)),
% 1.04/1.22 inference(unit_resolution,[status(thm)],[388, 2526])).
% 1.04/1.22 tff(2537,plain,
% 1.04/1.22 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a2555) | c0_1(a2517) | c3_1(a2517) | (~ndr1_0) | c1_1(a2517) | (~c2_1(a2517)) | (~c3_1(a2555)) | (~c0_1(a2555)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a2555) | c0_1(a2517) | c3_1(a2517) | (~ndr1_0) | c1_1(a2517) | (~c2_1(a2517)) | (~c3_1(a2555)) | (~c0_1(a2555)))),
% 1.04/1.22 inference(rewrite,[status(thm)],[])).
% 1.04/1.22 tff(2538,plain,
% 1.04/1.22 (((~ndr1_0) | c1_1(a2555) | (~c3_1(a2555)) | (~c0_1(a2555)) | c3_1(a2517) | c1_1(a2517) | (~c2_1(a2517)) | c3_1(a2517) | c0_1(a2517) | (~c2_1(a2517))) <=> (c1_1(a2555) | c0_1(a2517) | c3_1(a2517) | (~ndr1_0) | c1_1(a2517) | (~c2_1(a2517)) | (~c3_1(a2555)) | (~c0_1(a2555)))),
% 1.04/1.22 inference(rewrite,[status(thm)],[])).
% 1.04/1.22 tff(2539,plain,
% 1.04/1.22 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a2555) | (~c3_1(a2555)) | (~c0_1(a2555)) | c3_1(a2517) | c1_1(a2517) | (~c2_1(a2517)) | c3_1(a2517) | c0_1(a2517) | (~c2_1(a2517)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a2555) | c0_1(a2517) | c3_1(a2517) | (~ndr1_0) | c1_1(a2517) | (~c2_1(a2517)) | (~c3_1(a2555)) | (~c0_1(a2555))))),
% 1.04/1.22 inference(monotonicity,[status(thm)],[2538])).
% 1.04/1.22 tff(2540,plain,
% 1.04/1.22 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a2555) | (~c3_1(a2555)) | (~c0_1(a2555)) | c3_1(a2517) | c1_1(a2517) | (~c2_1(a2517)) | c3_1(a2517) | c0_1(a2517) | (~c2_1(a2517)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a2555) | c0_1(a2517) | c3_1(a2517) | (~ndr1_0) | c1_1(a2517) | (~c2_1(a2517)) | (~c3_1(a2555)) | (~c0_1(a2555)))),
% 1.04/1.22 inference(transitivity,[status(thm)],[2539, 2537])).
% 1.04/1.22 tff(2541,plain,
% 1.04/1.22 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a2555) | (~c3_1(a2555)) | (~c0_1(a2555)) | c3_1(a2517) | c1_1(a2517) | (~c2_1(a2517)) | c3_1(a2517) | c0_1(a2517) | (~c2_1(a2517)))),
% 1.04/1.22 inference(quant_inst,[status(thm)],[])).
% 1.04/1.22 tff(2542,plain,
% 1.04/1.22 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a2555) | c0_1(a2517) | c3_1(a2517) | (~ndr1_0) | c1_1(a2517) | (~c2_1(a2517)) | (~c3_1(a2555)) | (~c0_1(a2555))),
% 1.04/1.22 inference(modus_ponens,[status(thm)],[2541, 2540])).
% 1.04/1.22 tff(2543,plain,
% 1.04/1.22 (~c3_1(a2555)),
% 1.04/1.22 inference(unit_resolution,[status(thm)],[2542, 90, 2481, 2528, 2471, 2527, 2536, 424, 2535])).
% 1.04/1.22 tff(2544,plain,
% 1.04/1.22 (((~hskp5) | c3_1(a2522)) <=> ((~hskp5) | c3_1(a2522))),
% 1.04/1.22 inference(rewrite,[status(thm)],[])).
% 1.04/1.22 tff(2545,axiom,((~hskp5) | c3_1(a2522)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause84')).
% 1.04/1.22 tff(2546,plain,
% 1.04/1.22 ((~hskp5) | c3_1(a2522)),
% 1.04/1.22 inference(modus_ponens,[status(thm)],[2545, 2544])).
% 1.04/1.22 tff(2547,plain,
% 1.04/1.22 ((~hskp5) | c3_1(a2522)),
% 1.04/1.22 inference(modus_ponens,[status(thm)],[2546, 2544])).
% 1.04/1.22 tff(2548,plain,
% 1.04/1.22 ((~hskp5) | c3_1(a2522)),
% 1.04/1.22 inference(modus_ponens,[status(thm)],[2547, 2544])).
% 1.04/1.22 tff(2549,plain,
% 1.04/1.22 ((~hskp5) | c3_1(a2522)),
% 1.04/1.22 inference(modus_ponens,[status(thm)],[2548, 2544])).
% 1.04/1.22 tff(2550,plain,
% 1.04/1.22 ((~hskp5) | c3_1(a2522)),
% 1.04/1.22 inference(modus_ponens,[status(thm)],[2549, 2544])).
% 1.04/1.22 tff(2551,plain,
% 1.04/1.22 (c3_1(a2522)),
% 1.04/1.22 inference(unit_resolution,[status(thm)],[2550, 2457])).
% 1.04/1.22 tff(2552,plain,
% 1.04/1.22 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a2522) | c0_1(a2517) | (~ndr1_0) | c1_1(a2517) | (~c2_1(a2517)) | (~c2_1(a2522)) | (~c3_1(a2522)) | c3_1(a2555) | (~c2_1(a2555)) | (~c0_1(a2555)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a2522) | c0_1(a2517) | (~ndr1_0) | c1_1(a2517) | (~c2_1(a2517)) | (~c2_1(a2522)) | (~c3_1(a2522)) | c3_1(a2555) | (~c2_1(a2555)) | (~c0_1(a2555)))),
% 1.04/1.23 inference(rewrite,[status(thm)],[])).
% 1.04/1.23 tff(2553,plain,
% 1.04/1.23 (((~ndr1_0) | c3_1(a2555) | (~c0_1(a2555)) | (~c2_1(a2555)) | c0_1(a2522) | (~c3_1(a2522)) | (~c2_1(a2522)) | c1_1(a2517) | c0_1(a2517) | (~c2_1(a2517))) <=> (c0_1(a2522) | c0_1(a2517) | (~ndr1_0) | c1_1(a2517) | (~c2_1(a2517)) | (~c2_1(a2522)) | (~c3_1(a2522)) | c3_1(a2555) | (~c2_1(a2555)) | (~c0_1(a2555)))),
% 1.04/1.23 inference(rewrite,[status(thm)],[])).
% 1.04/1.23 tff(2554,plain,
% 1.04/1.23 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a2555) | (~c0_1(a2555)) | (~c2_1(a2555)) | c0_1(a2522) | (~c3_1(a2522)) | (~c2_1(a2522)) | c1_1(a2517) | c0_1(a2517) | (~c2_1(a2517)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a2522) | c0_1(a2517) | (~ndr1_0) | c1_1(a2517) | (~c2_1(a2517)) | (~c2_1(a2522)) | (~c3_1(a2522)) | c3_1(a2555) | (~c2_1(a2555)) | (~c0_1(a2555))))),
% 1.04/1.23 inference(monotonicity,[status(thm)],[2553])).
% 1.04/1.23 tff(2555,plain,
% 1.04/1.23 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a2555) | (~c0_1(a2555)) | (~c2_1(a2555)) | c0_1(a2522) | (~c3_1(a2522)) | (~c2_1(a2522)) | c1_1(a2517) | c0_1(a2517) | (~c2_1(a2517)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a2522) | c0_1(a2517) | (~ndr1_0) | c1_1(a2517) | (~c2_1(a2517)) | (~c2_1(a2522)) | (~c3_1(a2522)) | c3_1(a2555) | (~c2_1(a2555)) | (~c0_1(a2555)))),
% 1.04/1.23 inference(transitivity,[status(thm)],[2554, 2552])).
% 1.04/1.23 tff(2556,plain,
% 1.04/1.23 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a2555) | (~c0_1(a2555)) | (~c2_1(a2555)) | c0_1(a2522) | (~c3_1(a2522)) | (~c2_1(a2522)) | c1_1(a2517) | c0_1(a2517) | (~c2_1(a2517)))),
% 1.04/1.23 inference(quant_inst,[status(thm)],[])).
% 1.04/1.23 tff(2557,plain,
% 1.04/1.23 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a2522) | c0_1(a2517) | (~ndr1_0) | c1_1(a2517) | (~c2_1(a2517)) | (~c2_1(a2522)) | (~c3_1(a2522)) | c3_1(a2555) | (~c2_1(a2555)) | (~c0_1(a2555))),
% 1.04/1.23 inference(modus_ponens,[status(thm)],[2556, 2555])).
% 1.04/1.23 tff(2558,plain,
% 1.04/1.23 ($false),
% 1.04/1.23 inference(unit_resolution,[status(thm)],[2557, 90, 2481, 2480, 2479, 2551, 2528, 2463, 2527, 1087, 2543, 2535])).
% 1.04/1.23 tff(2559,plain,(hskp23 | hskp9), inference(lemma,lemma(discharge,[]))).
% 1.04/1.23 tff(2560,plain,
% 1.04/1.23 (hskp23),
% 1.04/1.23 inference(unit_resolution,[status(thm)],[2559, 14])).
% 1.04/1.23 tff(2561,plain,
% 1.04/1.23 (~c1_1(a2553)),
% 1.04/1.23 inference(unit_resolution,[status(thm)],[785, 2560])).
% 1.04/1.23 tff(2562,plain,
% 1.04/1.23 (~c3_1(a2553)),
% 1.04/1.23 inference(unit_resolution,[status(thm)],[769, 2560])).
% 1.04/1.23 tff(2563,plain,
% 1.04/1.23 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp9 | c0_1(a2553) | c2_1(a2614) | c3_1(a2614) | c3_1(a2553) | (~ndr1_0) | c2_1(a2553) | (~c1_1(a2614)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp9 | c0_1(a2553) | c2_1(a2614) | c3_1(a2614) | c3_1(a2553) | (~ndr1_0) | c2_1(a2553) | (~c1_1(a2614)))),
% 1.04/1.23 inference(rewrite,[status(thm)],[])).
% 1.04/1.23 tff(2564,plain,
% 1.04/1.23 ((hskp9 | (~ndr1_0) | c3_1(a2614) | c2_1(a2614) | (~c1_1(a2614)) | c3_1(a2553) | c0_1(a2553) | c2_1(a2553)) <=> (hskp9 | c0_1(a2553) | c2_1(a2614) | c3_1(a2614) | c3_1(a2553) | (~ndr1_0) | c2_1(a2553) | (~c1_1(a2614)))),
% 1.04/1.23 inference(rewrite,[status(thm)],[])).
% 1.04/1.23 tff(2565,plain,
% 1.04/1.23 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp9 | (~ndr1_0) | c3_1(a2614) | c2_1(a2614) | (~c1_1(a2614)) | c3_1(a2553) | c0_1(a2553) | c2_1(a2553))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp9 | c0_1(a2553) | c2_1(a2614) | c3_1(a2614) | c3_1(a2553) | (~ndr1_0) | c2_1(a2553) | (~c1_1(a2614))))),
% 1.04/1.23 inference(monotonicity,[status(thm)],[2564])).
% 1.04/1.23 tff(2566,plain,
% 1.04/1.23 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp9 | (~ndr1_0) | c3_1(a2614) | c2_1(a2614) | (~c1_1(a2614)) | c3_1(a2553) | c0_1(a2553) | c2_1(a2553))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp9 | c0_1(a2553) | c2_1(a2614) | c3_1(a2614) | c3_1(a2553) | (~ndr1_0) | c2_1(a2553) | (~c1_1(a2614)))),
% 1.04/1.23 inference(transitivity,[status(thm)],[2565, 2563])).
% 1.04/1.23 tff(2567,plain,
% 1.04/1.23 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp9 | (~ndr1_0) | c3_1(a2614) | c2_1(a2614) | (~c1_1(a2614)) | c3_1(a2553) | c0_1(a2553) | c2_1(a2553))),
% 1.04/1.23 inference(quant_inst,[status(thm)],[])).
% 1.04/1.23 tff(2568,plain,
% 1.04/1.23 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp9 | c0_1(a2553) | c2_1(a2614) | c3_1(a2614) | c3_1(a2553) | (~ndr1_0) | c2_1(a2553) | (~c1_1(a2614))),
% 1.04/1.23 inference(modus_ponens,[status(thm)],[2567, 2566])).
% 1.04/1.23 tff(2569,plain,
% 1.04/1.23 (c2_1(a2553)),
% 1.04/1.23 inference(unit_resolution,[status(thm)],[2568, 90, 14, 1973, 1968, 1972, 1971, 849, 36])).
% 1.04/1.23 tff(2570,plain,
% 1.04/1.23 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a2553) | c3_1(a2614) | c1_1(a2553) | c3_1(a2553) | (~ndr1_0) | (~c2_1(a2558)) | (~c0_1(a2558)) | (~c1_1(a2558)) | c0_1(a2614) | (~c1_1(a2614)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a2553) | c3_1(a2614) | c1_1(a2553) | c3_1(a2553) | (~ndr1_0) | (~c2_1(a2558)) | (~c0_1(a2558)) | (~c1_1(a2558)) | c0_1(a2614) | (~c1_1(a2614)))),
% 1.04/1.23 inference(rewrite,[status(thm)],[])).
% 1.04/1.23 tff(2571,plain,
% 1.04/1.23 (((~ndr1_0) | (~c1_1(a2558)) | (~c0_1(a2558)) | (~c2_1(a2558)) | c3_1(a2614) | c0_1(a2614) | (~c1_1(a2614)) | c3_1(a2553) | c1_1(a2553) | c0_1(a2553)) <=> (c0_1(a2553) | c3_1(a2614) | c1_1(a2553) | c3_1(a2553) | (~ndr1_0) | (~c2_1(a2558)) | (~c0_1(a2558)) | (~c1_1(a2558)) | c0_1(a2614) | (~c1_1(a2614)))),
% 1.04/1.23 inference(rewrite,[status(thm)],[])).
% 1.04/1.23 tff(2572,plain,
% 1.04/1.23 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c1_1(a2558)) | (~c0_1(a2558)) | (~c2_1(a2558)) | c3_1(a2614) | c0_1(a2614) | (~c1_1(a2614)) | c3_1(a2553) | c1_1(a2553) | c0_1(a2553))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a2553) | c3_1(a2614) | c1_1(a2553) | c3_1(a2553) | (~ndr1_0) | (~c2_1(a2558)) | (~c0_1(a2558)) | (~c1_1(a2558)) | c0_1(a2614) | (~c1_1(a2614))))),
% 1.04/1.23 inference(monotonicity,[status(thm)],[2571])).
% 1.04/1.23 tff(2573,plain,
% 1.04/1.23 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c1_1(a2558)) | (~c0_1(a2558)) | (~c2_1(a2558)) | c3_1(a2614) | c0_1(a2614) | (~c1_1(a2614)) | c3_1(a2553) | c1_1(a2553) | c0_1(a2553))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a2553) | c3_1(a2614) | c1_1(a2553) | c3_1(a2553) | (~ndr1_0) | (~c2_1(a2558)) | (~c0_1(a2558)) | (~c1_1(a2558)) | c0_1(a2614) | (~c1_1(a2614)))),
% 1.04/1.23 inference(transitivity,[status(thm)],[2572, 2570])).
% 1.04/1.23 tff(2574,plain,
% 1.04/1.23 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c1_1(a2558)) | (~c0_1(a2558)) | (~c2_1(a2558)) | c3_1(a2614) | c0_1(a2614) | (~c1_1(a2614)) | c3_1(a2553) | c1_1(a2553) | c0_1(a2553))),
% 1.04/1.23 inference(quant_inst,[status(thm)],[])).
% 1.04/1.23 tff(2575,plain,
% 1.04/1.23 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a2553) | c3_1(a2614) | c1_1(a2553) | c3_1(a2553) | (~ndr1_0) | (~c2_1(a2558)) | (~c0_1(a2558)) | (~c1_1(a2558)) | c0_1(a2614) | (~c1_1(a2614))),
% 1.04/1.23 inference(modus_ponens,[status(thm)],[2574, 2573])).
% 1.04/1.23 tff(2576,plain,
% 1.04/1.23 (c0_1(a2614)),
% 1.04/1.23 inference(unit_resolution,[status(thm)],[2575, 90, 2425, 2417, 2409, 1973, 1968, 1971, 850, 849, 459])).
% 1.04/1.23 tff(2577,plain,
% 1.04/1.23 (hskp4 | (~c0_1(a2614))),
% 1.04/1.23 inference(unit_resolution,[status(thm)],[132, 90, 14, 1972, 1971, 126])).
% 1.04/1.23 tff(2578,plain,
% 1.04/1.23 (hskp4),
% 1.04/1.23 inference(unit_resolution,[status(thm)],[2577, 2576])).
% 1.04/1.23 tff(2579,plain,
% 1.04/1.23 (~c1_1(a2521)),
% 1.04/1.23 inference(unit_resolution,[status(thm)],[2438, 2578])).
% 1.04/1.23 tff(2580,plain,
% 1.04/1.23 (c3_1(a2521)),
% 1.04/1.23 inference(unit_resolution,[status(thm)],[141, 2578])).
% 1.04/1.23 tff(2581,plain,
% 1.04/1.23 (c2_1(a2521)),
% 1.04/1.23 inference(unit_resolution,[status(thm)],[149, 2578])).
% 1.04/1.23 tff(2582,plain,
% 1.04/1.23 (hskp24),
% 1.04/1.23 inference(unit_resolution,[status(thm)],[2469, 90, 2581, 2580, 1972, 1971, 2579, 1473, 2576])).
% 1.04/1.23 tff(2583,plain,
% 1.04/1.23 (~c1_1(a2555)),
% 1.04/1.23 inference(unit_resolution,[status(thm)],[715, 2582])).
% 1.04/1.23 tff(2584,plain,
% 1.04/1.23 (c0_1(a2555)),
% 1.04/1.23 inference(unit_resolution,[status(thm)],[731, 2582])).
% 1.04/1.23 tff(2585,plain,
% 1.04/1.23 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a2553) | c1_1(a2555) | c1_1(a2553) | c3_1(a2553) | (~ndr1_0) | (~c2_1(a2553)) | (~c3_1(a2555)) | (~c0_1(a2555)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a2553) | c1_1(a2555) | c1_1(a2553) | c3_1(a2553) | (~ndr1_0) | (~c2_1(a2553)) | (~c3_1(a2555)) | (~c0_1(a2555)))),
% 1.04/1.23 inference(rewrite,[status(thm)],[])).
% 1.04/1.23 tff(2586,plain,
% 1.04/1.23 (((~ndr1_0) | c1_1(a2555) | (~c3_1(a2555)) | (~c0_1(a2555)) | c3_1(a2553) | c1_1(a2553) | (~c2_1(a2553)) | c3_1(a2553) | c0_1(a2553) | (~c2_1(a2553))) <=> (c0_1(a2553) | c1_1(a2555) | c1_1(a2553) | c3_1(a2553) | (~ndr1_0) | (~c2_1(a2553)) | (~c3_1(a2555)) | (~c0_1(a2555)))),
% 1.04/1.23 inference(rewrite,[status(thm)],[])).
% 1.04/1.23 tff(2587,plain,
% 1.04/1.23 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a2555) | (~c3_1(a2555)) | (~c0_1(a2555)) | c3_1(a2553) | c1_1(a2553) | (~c2_1(a2553)) | c3_1(a2553) | c0_1(a2553) | (~c2_1(a2553)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a2553) | c1_1(a2555) | c1_1(a2553) | c3_1(a2553) | (~ndr1_0) | (~c2_1(a2553)) | (~c3_1(a2555)) | (~c0_1(a2555))))),
% 1.04/1.23 inference(monotonicity,[status(thm)],[2586])).
% 1.04/1.23 tff(2588,plain,
% 1.04/1.23 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a2555) | (~c3_1(a2555)) | (~c0_1(a2555)) | c3_1(a2553) | c1_1(a2553) | (~c2_1(a2553)) | c3_1(a2553) | c0_1(a2553) | (~c2_1(a2553)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a2553) | c1_1(a2555) | c1_1(a2553) | c3_1(a2553) | (~ndr1_0) | (~c2_1(a2553)) | (~c3_1(a2555)) | (~c0_1(a2555)))),
% 1.04/1.23 inference(transitivity,[status(thm)],[2587, 2585])).
% 1.04/1.23 tff(2589,plain,
% 1.04/1.23 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a2555) | (~c3_1(a2555)) | (~c0_1(a2555)) | c3_1(a2553) | c1_1(a2553) | (~c2_1(a2553)) | c3_1(a2553) | c0_1(a2553) | (~c2_1(a2553)))),
% 1.04/1.23 inference(quant_inst,[status(thm)],[])).
% 1.04/1.23 tff(2590,plain,
% 1.04/1.23 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a2553) | c1_1(a2555) | c1_1(a2553) | c3_1(a2553) | (~ndr1_0) | (~c2_1(a2553)) | (~c3_1(a2555)) | (~c0_1(a2555))),
% 1.04/1.23 inference(modus_ponens,[status(thm)],[2589, 2588])).
% 1.04/1.23 tff(2591,plain,
% 1.04/1.23 (~c3_1(a2555)),
% 1.04/1.23 inference(unit_resolution,[status(thm)],[2590, 90, 2584, 1968, 2583, 850, 849, 424, 2569])).
% 1.04/1.23 tff(2592,plain,
% 1.04/1.23 (^[V: $i, U: $i] : refl((hskp1 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)) <=> (hskp1 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)))),
% 1.04/1.23 inference(bind,[status(th)],[])).
% 1.04/1.23 tff(2593,plain,
% 1.04/1.23 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 1.04/1.23 inference(quant_intro,[status(thm)],[2592])).
% 1.04/1.23 tff(2594,plain,
% 1.04/1.23 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 1.04/1.23 inference(rewrite,[status(thm)],[])).
% 1.04/1.23 tff(2595,plain,
% 1.04/1.23 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c2_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c2_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U))))), (((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))), (((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))))), ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) | c0_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c0_1(V))), ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c0_1(V)))), (((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c0_1(V)) | c1_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V))), (((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V)))), ((((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))), ((((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)))), (((((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp1) <=> (((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)) | hskp1))), rewrite((((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)) | hskp1) <=> (hskp1 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))), (((((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp1) <=> (hskp1 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))))),
% 1.04/1.23 inference(bind,[status(th)],[])).
% 1.04/1.23 tff(2596,plain,
% 1.04/1.23 (![V: $i, U: $i] : ((((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp1) <=> ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 1.04/1.23 inference(quant_intro,[status(thm)],[2595])).
% 1.04/1.23 tff(2597,axiom,(![V: $i, U: $i] : ((((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause162')).
% 1.04/1.23 tff(2598,plain,
% 1.04/1.23 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 1.04/1.23 inference(modus_ponens,[status(thm)],[2597, 2596])).
% 1.04/1.23 tff(2599,plain,
% 1.04/1.23 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 1.04/1.23 inference(modus_ponens,[status(thm)],[2598, 2594])).
% 1.04/1.23 tff(2600,plain,(
% 1.04/1.23 ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 1.04/1.23 inference(skolemize,[status(sab)],[2599])).
% 1.04/1.23 tff(2601,plain,
% 1.04/1.23 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 1.04/1.23 inference(modus_ponens,[status(thm)],[2600, 2593])).
% 1.04/1.23 tff(2602,plain,
% 1.04/1.23 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | c0_1(a2553) | c1_1(a2553) | c3_1(a2553) | (~ndr1_0) | (~c2_1(a2553)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp1 | c0_1(a2553) | c1_1(a2553) | c3_1(a2553) | (~ndr1_0) | (~c2_1(a2553)))),
% 1.04/1.23 inference(rewrite,[status(thm)],[])).
% 1.04/1.23 tff(2603,plain,
% 1.04/1.23 ((hskp1 | (~ndr1_0) | c1_1(a2553) | c0_1(a2553) | (~c2_1(a2553)) | c3_1(a2553) | c1_1(a2553) | c0_1(a2553)) <=> (hskp1 | c0_1(a2553) | c1_1(a2553) | c3_1(a2553) | (~ndr1_0) | (~c2_1(a2553)))),
% 1.04/1.23 inference(rewrite,[status(thm)],[])).
% 1.04/1.23 tff(2604,plain,
% 1.04/1.23 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | (~ndr1_0) | c1_1(a2553) | c0_1(a2553) | (~c2_1(a2553)) | c3_1(a2553) | c1_1(a2553) | c0_1(a2553))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | c0_1(a2553) | c1_1(a2553) | c3_1(a2553) | (~ndr1_0) | (~c2_1(a2553))))),
% 1.04/1.23 inference(monotonicity,[status(thm)],[2603])).
% 1.04/1.23 tff(2605,plain,
% 1.04/1.23 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | (~ndr1_0) | c1_1(a2553) | c0_1(a2553) | (~c2_1(a2553)) | c3_1(a2553) | c1_1(a2553) | c0_1(a2553))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp1 | c0_1(a2553) | c1_1(a2553) | c3_1(a2553) | (~ndr1_0) | (~c2_1(a2553)))),
% 1.04/1.23 inference(transitivity,[status(thm)],[2604, 2602])).
% 1.04/1.23 tff(2606,plain,
% 1.04/1.23 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | (~ndr1_0) | c1_1(a2553) | c0_1(a2553) | (~c2_1(a2553)) | c3_1(a2553) | c1_1(a2553) | c0_1(a2553))),
% 1.04/1.23 inference(quant_inst,[status(thm)],[])).
% 1.04/1.23 tff(2607,plain,
% 1.04/1.23 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp1 | c0_1(a2553) | c1_1(a2553) | c3_1(a2553) | (~ndr1_0) | (~c2_1(a2553))),
% 1.04/1.23 inference(modus_ponens,[status(thm)],[2606, 2605])).
% 1.04/1.23 tff(2608,plain,
% 1.04/1.23 (hskp1 | c0_1(a2553) | (~c2_1(a2553))),
% 1.04/1.23 inference(unit_resolution,[status(thm)],[2607, 90, 850, 849, 2601])).
% 1.04/1.23 tff(2609,plain,
% 1.04/1.23 (hskp1),
% 1.04/1.23 inference(unit_resolution,[status(thm)],[2608, 2569, 1968])).
% 1.04/1.23 tff(2610,plain,
% 1.04/1.23 (~c3_1(a2517)),
% 1.04/1.23 inference(unit_resolution,[status(thm)],[388, 2609])).
% 1.04/1.23 tff(2611,plain,
% 1.04/1.23 (~c0_1(a2517)),
% 1.04/1.23 inference(unit_resolution,[status(thm)],[394, 2609])).
% 1.04/1.23 tff(2612,plain,
% 1.04/1.23 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp14 | c0_1(a2553) | c2_1(a2614) | c3_1(a2553) | (~ndr1_0) | (~c2_1(a2553)) | (~c0_1(a2614)) | (~c1_1(a2614)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp14 | c0_1(a2553) | c2_1(a2614) | c3_1(a2553) | (~ndr1_0) | (~c2_1(a2553)) | (~c0_1(a2614)) | (~c1_1(a2614)))),
% 1.04/1.23 inference(rewrite,[status(thm)],[])).
% 1.04/1.23 tff(2613,plain,
% 1.04/1.23 ((hskp14 | (~ndr1_0) | c2_1(a2614) | (~c1_1(a2614)) | (~c0_1(a2614)) | c3_1(a2553) | c0_1(a2553) | (~c2_1(a2553))) <=> (hskp14 | c0_1(a2553) | c2_1(a2614) | c3_1(a2553) | (~ndr1_0) | (~c2_1(a2553)) | (~c0_1(a2614)) | (~c1_1(a2614)))),
% 1.04/1.23 inference(rewrite,[status(thm)],[])).
% 1.04/1.23 tff(2614,plain,
% 1.04/1.23 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp14 | (~ndr1_0) | c2_1(a2614) | (~c1_1(a2614)) | (~c0_1(a2614)) | c3_1(a2553) | c0_1(a2553) | (~c2_1(a2553)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp14 | c0_1(a2553) | c2_1(a2614) | c3_1(a2553) | (~ndr1_0) | (~c2_1(a2553)) | (~c0_1(a2614)) | (~c1_1(a2614))))),
% 1.04/1.23 inference(monotonicity,[status(thm)],[2613])).
% 1.04/1.23 tff(2615,plain,
% 1.04/1.23 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp14 | (~ndr1_0) | c2_1(a2614) | (~c1_1(a2614)) | (~c0_1(a2614)) | c3_1(a2553) | c0_1(a2553) | (~c2_1(a2553)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp14 | c0_1(a2553) | c2_1(a2614) | c3_1(a2553) | (~ndr1_0) | (~c2_1(a2553)) | (~c0_1(a2614)) | (~c1_1(a2614)))),
% 1.04/1.23 inference(transitivity,[status(thm)],[2614, 2612])).
% 1.04/1.23 tff(2616,plain,
% 1.04/1.23 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp14 | (~ndr1_0) | c2_1(a2614) | (~c1_1(a2614)) | (~c0_1(a2614)) | c3_1(a2553) | c0_1(a2553) | (~c2_1(a2553)))),
% 1.04/1.23 inference(quant_inst,[status(thm)],[])).
% 1.04/1.23 tff(2617,plain,
% 1.04/1.23 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp14 | c0_1(a2553) | c2_1(a2614) | c3_1(a2553) | (~ndr1_0) | (~c2_1(a2553)) | (~c0_1(a2614)) | (~c1_1(a2614))),
% 1.04/1.23 inference(modus_ponens,[status(thm)],[2616, 2615])).
% 1.04/1.23 tff(2618,plain,
% 1.04/1.23 (hskp14 | (~c2_1(a2553)) | (~c0_1(a2614))),
% 1.04/1.23 inference(unit_resolution,[status(thm)],[2617, 90, 1973, 1968, 1972, 849, 469])).
% 1.04/1.23 tff(2619,plain,
% 1.04/1.23 (hskp14),
% 1.04/1.23 inference(unit_resolution,[status(thm)],[2618, 2576, 2569])).
% 1.04/1.23 tff(2620,plain,
% 1.04/1.23 (~c3_1(a2536)),
% 1.04/1.23 inference(unit_resolution,[status(thm)],[484, 2619])).
% 1.04/1.23 tff(2621,plain,
% 1.04/1.23 (~c1_1(a2536)),
% 1.04/1.23 inference(unit_resolution,[status(thm)],[490, 2619])).
% 1.04/1.23 tff(2622,plain,
% 1.04/1.23 (~c0_1(a2536)),
% 1.04/1.23 inference(unit_resolution,[status(thm)],[496, 2619])).
% 1.04/1.23 tff(2623,plain,
% 1.04/1.23 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a2536) | c1_1(a2536) | c3_1(a2536) | c0_1(a2517) | c3_1(a2517) | (~ndr1_0) | (~c2_1(a2558)) | (~c0_1(a2558)) | (~c1_1(a2558)) | (~c1_1(a2517)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a2536) | c1_1(a2536) | c3_1(a2536) | c0_1(a2517) | c3_1(a2517) | (~ndr1_0) | (~c2_1(a2558)) | (~c0_1(a2558)) | (~c1_1(a2558)) | (~c1_1(a2517)))),
% 1.04/1.23 inference(rewrite,[status(thm)],[])).
% 1.04/1.23 tff(2624,plain,
% 1.04/1.23 (((~ndr1_0) | (~c1_1(a2558)) | (~c0_1(a2558)) | (~c2_1(a2558)) | c3_1(a2517) | c0_1(a2517) | (~c1_1(a2517)) | c3_1(a2536) | c1_1(a2536) | c0_1(a2536)) <=> (c0_1(a2536) | c1_1(a2536) | c3_1(a2536) | c0_1(a2517) | c3_1(a2517) | (~ndr1_0) | (~c2_1(a2558)) | (~c0_1(a2558)) | (~c1_1(a2558)) | (~c1_1(a2517)))),
% 1.04/1.23 inference(rewrite,[status(thm)],[])).
% 1.04/1.23 tff(2625,plain,
% 1.04/1.23 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c1_1(a2558)) | (~c0_1(a2558)) | (~c2_1(a2558)) | c3_1(a2517) | c0_1(a2517) | (~c1_1(a2517)) | c3_1(a2536) | c1_1(a2536) | c0_1(a2536))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a2536) | c1_1(a2536) | c3_1(a2536) | c0_1(a2517) | c3_1(a2517) | (~ndr1_0) | (~c2_1(a2558)) | (~c0_1(a2558)) | (~c1_1(a2558)) | (~c1_1(a2517))))),
% 1.04/1.23 inference(monotonicity,[status(thm)],[2624])).
% 1.04/1.23 tff(2626,plain,
% 1.04/1.23 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c1_1(a2558)) | (~c0_1(a2558)) | (~c2_1(a2558)) | c3_1(a2517) | c0_1(a2517) | (~c1_1(a2517)) | c3_1(a2536) | c1_1(a2536) | c0_1(a2536))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a2536) | c1_1(a2536) | c3_1(a2536) | c0_1(a2517) | c3_1(a2517) | (~ndr1_0) | (~c2_1(a2558)) | (~c0_1(a2558)) | (~c1_1(a2558)) | (~c1_1(a2517)))),
% 1.04/1.23 inference(transitivity,[status(thm)],[2625, 2623])).
% 1.04/1.23 tff(2627,plain,
% 1.04/1.23 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c1_1(a2558)) | (~c0_1(a2558)) | (~c2_1(a2558)) | c3_1(a2517) | c0_1(a2517) | (~c1_1(a2517)) | c3_1(a2536) | c1_1(a2536) | c0_1(a2536))),
% 1.04/1.23 inference(quant_inst,[status(thm)],[])).
% 1.04/1.23 tff(2628,plain,
% 1.04/1.23 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a2536) | c1_1(a2536) | c3_1(a2536) | c0_1(a2517) | c3_1(a2517) | (~ndr1_0) | (~c2_1(a2558)) | (~c0_1(a2558)) | (~c1_1(a2558)) | (~c1_1(a2517))),
% 1.04/1.23 inference(modus_ponens,[status(thm)],[2627, 2626])).
% 1.04/1.23 tff(2629,plain,
% 1.04/1.23 (~c1_1(a2517)),
% 1.04/1.23 inference(unit_resolution,[status(thm)],[2628, 90, 2425, 2417, 2409, 2622, 2621, 2620, 2611, 2610, 459])).
% 1.04/1.23 tff(2630,plain,
% 1.04/1.23 (c2_1(a2517)),
% 1.04/1.23 inference(unit_resolution,[status(thm)],[402, 2609])).
% 1.04/1.23 tff(2631,plain,
% 1.04/1.23 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a2553) | c3_1(a2553) | c1_1(a2521) | c0_1(a2517) | c3_1(a2517) | (~ndr1_0) | (~c2_1(a2517)) | (~c0_1(a2521)) | (~c3_1(a2521)) | (~c2_1(a2553)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a2553) | c3_1(a2553) | c1_1(a2521) | c0_1(a2517) | c3_1(a2517) | (~ndr1_0) | (~c2_1(a2517)) | (~c0_1(a2521)) | (~c3_1(a2521)) | (~c2_1(a2553)))),
% 1.04/1.23 inference(rewrite,[status(thm)],[])).
% 1.04/1.23 tff(2632,plain,
% 1.04/1.23 (((~ndr1_0) | c1_1(a2521) | (~c3_1(a2521)) | (~c0_1(a2521)) | c3_1(a2553) | c1_1(a2553) | (~c2_1(a2553)) | c3_1(a2517) | c0_1(a2517) | (~c2_1(a2517))) <=> (c1_1(a2553) | c3_1(a2553) | c1_1(a2521) | c0_1(a2517) | c3_1(a2517) | (~ndr1_0) | (~c2_1(a2517)) | (~c0_1(a2521)) | (~c3_1(a2521)) | (~c2_1(a2553)))),
% 1.04/1.23 inference(rewrite,[status(thm)],[])).
% 1.04/1.23 tff(2633,plain,
% 1.04/1.23 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a2521) | (~c3_1(a2521)) | (~c0_1(a2521)) | c3_1(a2553) | c1_1(a2553) | (~c2_1(a2553)) | c3_1(a2517) | c0_1(a2517) | (~c2_1(a2517)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a2553) | c3_1(a2553) | c1_1(a2521) | c0_1(a2517) | c3_1(a2517) | (~ndr1_0) | (~c2_1(a2517)) | (~c0_1(a2521)) | (~c3_1(a2521)) | (~c2_1(a2553))))),
% 1.04/1.23 inference(monotonicity,[status(thm)],[2632])).
% 1.04/1.23 tff(2634,plain,
% 1.04/1.23 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a2521) | (~c3_1(a2521)) | (~c0_1(a2521)) | c3_1(a2553) | c1_1(a2553) | (~c2_1(a2553)) | c3_1(a2517) | c0_1(a2517) | (~c2_1(a2517)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a2553) | c3_1(a2553) | c1_1(a2521) | c0_1(a2517) | c3_1(a2517) | (~ndr1_0) | (~c2_1(a2517)) | (~c0_1(a2521)) | (~c3_1(a2521)) | (~c2_1(a2553)))),
% 1.04/1.23 inference(transitivity,[status(thm)],[2633, 2631])).
% 1.04/1.23 tff(2635,plain,
% 1.04/1.23 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a2521) | (~c3_1(a2521)) | (~c0_1(a2521)) | c3_1(a2553) | c1_1(a2553) | (~c2_1(a2553)) | c3_1(a2517) | c0_1(a2517) | (~c2_1(a2517)))),
% 1.04/1.23 inference(quant_inst,[status(thm)],[])).
% 1.04/1.23 tff(2636,plain,
% 1.04/1.23 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a2553) | c3_1(a2553) | c1_1(a2521) | c0_1(a2517) | c3_1(a2517) | (~ndr1_0) | (~c2_1(a2517)) | (~c0_1(a2521)) | (~c3_1(a2521)) | (~c2_1(a2553))),
% 1.04/1.23 inference(modus_ponens,[status(thm)],[2635, 2634])).
% 1.04/1.23 tff(2637,plain,
% 1.04/1.23 (~c0_1(a2521)),
% 1.04/1.23 inference(unit_resolution,[status(thm)],[2636, 90, 2580, 2630, 850, 849, 2579, 2611, 2610, 424, 2569])).
% 1.04/1.23 tff(2638,plain,
% 1.04/1.23 (hskp5),
% 1.04/1.23 inference(unit_resolution,[status(thm)],[2455, 90, 2425, 2417, 2409, 2580, 2579, 2449, 2637])).
% 1.04/1.23 tff(2639,plain,
% 1.04/1.23 (~c0_1(a2522)),
% 1.04/1.23 inference(unit_resolution,[status(thm)],[2462, 2638])).
% 1.04/1.23 tff(2640,plain,
% 1.04/1.23 (c2_1(a2522)),
% 1.04/1.23 inference(unit_resolution,[status(thm)],[2478, 2638])).
% 1.04/1.23 tff(2641,plain,
% 1.04/1.23 (c2_1(a2555)),
% 1.04/1.23 inference(unit_resolution,[status(thm)],[723, 2582])).
% 1.04/1.23 tff(2642,plain,
% 1.04/1.23 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a2555) | c0_1(a2522) | c0_1(a2517) | (~ndr1_0) | c1_1(a2517) | (~c2_1(a2517)) | (~c1_1(a2522)) | (~c2_1(a2522)) | (~c2_1(a2555)) | (~c0_1(a2555)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a2555) | c0_1(a2522) | c0_1(a2517) | (~ndr1_0) | c1_1(a2517) | (~c2_1(a2517)) | (~c1_1(a2522)) | (~c2_1(a2522)) | (~c2_1(a2555)) | (~c0_1(a2555)))),
% 1.04/1.23 inference(rewrite,[status(thm)],[])).
% 1.04/1.23 tff(2643,plain,
% 1.04/1.23 (((~ndr1_0) | c1_1(a2555) | (~c0_1(a2555)) | (~c2_1(a2555)) | c0_1(a2522) | (~c1_1(a2522)) | (~c2_1(a2522)) | c1_1(a2517) | c0_1(a2517) | (~c2_1(a2517))) <=> (c1_1(a2555) | c0_1(a2522) | c0_1(a2517) | (~ndr1_0) | c1_1(a2517) | (~c2_1(a2517)) | (~c1_1(a2522)) | (~c2_1(a2522)) | (~c2_1(a2555)) | (~c0_1(a2555)))),
% 1.04/1.23 inference(rewrite,[status(thm)],[])).
% 1.04/1.23 tff(2644,plain,
% 1.04/1.23 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a2555) | (~c0_1(a2555)) | (~c2_1(a2555)) | c0_1(a2522) | (~c1_1(a2522)) | (~c2_1(a2522)) | c1_1(a2517) | c0_1(a2517) | (~c2_1(a2517)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a2555) | c0_1(a2522) | c0_1(a2517) | (~ndr1_0) | c1_1(a2517) | (~c2_1(a2517)) | (~c1_1(a2522)) | (~c2_1(a2522)) | (~c2_1(a2555)) | (~c0_1(a2555))))),
% 1.04/1.23 inference(monotonicity,[status(thm)],[2643])).
% 1.04/1.23 tff(2645,plain,
% 1.04/1.23 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a2555) | (~c0_1(a2555)) | (~c2_1(a2555)) | c0_1(a2522) | (~c1_1(a2522)) | (~c2_1(a2522)) | c1_1(a2517) | c0_1(a2517) | (~c2_1(a2517)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a2555) | c0_1(a2522) | c0_1(a2517) | (~ndr1_0) | c1_1(a2517) | (~c2_1(a2517)) | (~c1_1(a2522)) | (~c2_1(a2522)) | (~c2_1(a2555)) | (~c0_1(a2555)))),
% 1.04/1.23 inference(transitivity,[status(thm)],[2644, 2642])).
% 1.04/1.24 tff(2646,plain,
% 1.04/1.24 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a2555) | (~c0_1(a2555)) | (~c2_1(a2555)) | c0_1(a2522) | (~c1_1(a2522)) | (~c2_1(a2522)) | c1_1(a2517) | c0_1(a2517) | (~c2_1(a2517)))),
% 1.04/1.24 inference(quant_inst,[status(thm)],[])).
% 1.04/1.24 tff(2647,plain,
% 1.04/1.24 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a2555) | c0_1(a2522) | c0_1(a2517) | (~ndr1_0) | c1_1(a2517) | (~c2_1(a2517)) | (~c1_1(a2522)) | (~c2_1(a2522)) | (~c2_1(a2555)) | (~c0_1(a2555))),
% 1.04/1.24 inference(modus_ponens,[status(thm)],[2646, 2645])).
% 1.04/1.24 tff(2648,plain,
% 1.04/1.24 (~c1_1(a2522)),
% 1.04/1.24 inference(unit_resolution,[status(thm)],[2647, 90, 2584, 2641, 2640, 2630, 2583, 2639, 2611, 944, 2629])).
% 1.04/1.24 tff(2649,plain,
% 1.04/1.24 (c3_1(a2522)),
% 1.04/1.24 inference(unit_resolution,[status(thm)],[2550, 2638])).
% 1.04/1.24 tff(2650,plain,
% 1.04/1.24 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a2522) | (~ndr1_0) | c1_1(a2522) | (~c2_1(a2522)) | (~c3_1(a2522)) | c3_1(a2555) | (~c2_1(a2555)) | (~c0_1(a2555)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a2522) | (~ndr1_0) | c1_1(a2522) | (~c2_1(a2522)) | (~c3_1(a2522)) | c3_1(a2555) | (~c2_1(a2555)) | (~c0_1(a2555)))),
% 1.04/1.24 inference(rewrite,[status(thm)],[])).
% 1.04/1.24 tff(2651,plain,
% 1.04/1.24 (((~ndr1_0) | c3_1(a2555) | (~c0_1(a2555)) | (~c2_1(a2555)) | c0_1(a2522) | (~c3_1(a2522)) | (~c2_1(a2522)) | c1_1(a2522) | c0_1(a2522) | (~c2_1(a2522))) <=> (c0_1(a2522) | (~ndr1_0) | c1_1(a2522) | (~c2_1(a2522)) | (~c3_1(a2522)) | c3_1(a2555) | (~c2_1(a2555)) | (~c0_1(a2555)))),
% 1.04/1.24 inference(rewrite,[status(thm)],[])).
% 1.04/1.24 tff(2652,plain,
% 1.04/1.24 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a2555) | (~c0_1(a2555)) | (~c2_1(a2555)) | c0_1(a2522) | (~c3_1(a2522)) | (~c2_1(a2522)) | c1_1(a2522) | c0_1(a2522) | (~c2_1(a2522)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a2522) | (~ndr1_0) | c1_1(a2522) | (~c2_1(a2522)) | (~c3_1(a2522)) | c3_1(a2555) | (~c2_1(a2555)) | (~c0_1(a2555))))),
% 1.04/1.24 inference(monotonicity,[status(thm)],[2651])).
% 1.04/1.24 tff(2653,plain,
% 1.04/1.24 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a2555) | (~c0_1(a2555)) | (~c2_1(a2555)) | c0_1(a2522) | (~c3_1(a2522)) | (~c2_1(a2522)) | c1_1(a2522) | c0_1(a2522) | (~c2_1(a2522)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a2522) | (~ndr1_0) | c1_1(a2522) | (~c2_1(a2522)) | (~c3_1(a2522)) | c3_1(a2555) | (~c2_1(a2555)) | (~c0_1(a2555)))),
% 1.04/1.24 inference(transitivity,[status(thm)],[2652, 2650])).
% 1.04/1.24 tff(2654,plain,
% 1.04/1.24 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a2555) | (~c0_1(a2555)) | (~c2_1(a2555)) | c0_1(a2522) | (~c3_1(a2522)) | (~c2_1(a2522)) | c1_1(a2522) | c0_1(a2522) | (~c2_1(a2522)))),
% 1.04/1.24 inference(quant_inst,[status(thm)],[])).
% 1.04/1.24 tff(2655,plain,
% 1.04/1.24 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a2522) | (~ndr1_0) | c1_1(a2522) | (~c2_1(a2522)) | (~c3_1(a2522)) | c3_1(a2555) | (~c2_1(a2555)) | (~c0_1(a2555))),
% 1.04/1.24 inference(modus_ponens,[status(thm)],[2654, 2653])).
% 1.04/1.24 tff(2656,plain,
% 1.04/1.24 ($false),
% 1.04/1.24 inference(unit_resolution,[status(thm)],[2655, 90, 2584, 2641, 2640, 2649, 2639, 1087, 2648, 2591])).
% 1.04/1.24 tff(2657,plain,(c0_1(a2553) | c1_1(a2553) | c3_1(a2553) | hskp9), inference(lemma,lemma(discharge,[]))).
% 1.04/1.24 tff(2658,plain,
% 1.04/1.24 (c0_1(a2553)),
% 1.04/1.24 inference(unit_resolution,[status(thm)],[2657, 850, 849, 14])).
% 1.04/1.24 tff(2659,plain,
% 1.04/1.24 (hskp2 | c1_1(a2553) | (~c0_1(a2553)) | c2_1(a2553)),
% 1.04/1.24 inference(unit_resolution,[status(thm)],[857, 90, 849, 848])).
% 1.04/1.24 tff(2660,plain,
% 1.04/1.24 (c2_1(a2553)),
% 1.04/1.24 inference(unit_resolution,[status(thm)],[2659, 838, 850, 2658])).
% 1.04/1.24 tff(2661,assumption,(c2_1(a2553)), introduced(assumption)).
% 1.04/1.24 tff(2662,plain,
% 1.04/1.24 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | c1_1(a2553) | c0_1(a2519) | c3_1(a2519) | (~ndr1_0) | c1_1(a2519) | (~c0_1(a2553)) | (~c2_1(a2553)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp2 | c1_1(a2553) | c0_1(a2519) | c3_1(a2519) | (~ndr1_0) | c1_1(a2519) | (~c0_1(a2553)) | (~c2_1(a2553)))),
% 1.04/1.24 inference(rewrite,[status(thm)],[])).
% 1.04/1.24 tff(2663,plain,
% 1.04/1.24 ((hskp2 | (~ndr1_0) | c1_1(a2553) | (~c0_1(a2553)) | (~c2_1(a2553)) | c3_1(a2519) | c1_1(a2519) | c0_1(a2519)) <=> (hskp2 | c1_1(a2553) | c0_1(a2519) | c3_1(a2519) | (~ndr1_0) | c1_1(a2519) | (~c0_1(a2553)) | (~c2_1(a2553)))),
% 1.04/1.24 inference(rewrite,[status(thm)],[])).
% 1.04/1.24 tff(2664,plain,
% 1.04/1.24 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | c1_1(a2553) | (~c0_1(a2553)) | (~c2_1(a2553)) | c3_1(a2519) | c1_1(a2519) | c0_1(a2519))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | c1_1(a2553) | c0_1(a2519) | c3_1(a2519) | (~ndr1_0) | c1_1(a2519) | (~c0_1(a2553)) | (~c2_1(a2553))))),
% 1.04/1.24 inference(monotonicity,[status(thm)],[2663])).
% 1.04/1.24 tff(2665,plain,
% 1.04/1.24 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | c1_1(a2553) | (~c0_1(a2553)) | (~c2_1(a2553)) | c3_1(a2519) | c1_1(a2519) | c0_1(a2519))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp2 | c1_1(a2553) | c0_1(a2519) | c3_1(a2519) | (~ndr1_0) | c1_1(a2519) | (~c0_1(a2553)) | (~c2_1(a2553)))),
% 1.04/1.24 inference(transitivity,[status(thm)],[2664, 2662])).
% 1.04/1.24 tff(2666,plain,
% 1.04/1.24 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | c1_1(a2553) | (~c0_1(a2553)) | (~c2_1(a2553)) | c3_1(a2519) | c1_1(a2519) | c0_1(a2519))),
% 1.04/1.24 inference(quant_inst,[status(thm)],[])).
% 1.04/1.24 tff(2667,plain,
% 1.04/1.24 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp2 | c1_1(a2553) | c0_1(a2519) | c3_1(a2519) | (~ndr1_0) | c1_1(a2519) | (~c0_1(a2553)) | (~c2_1(a2553))),
% 1.04/1.24 inference(modus_ponens,[status(thm)],[2666, 2665])).
% 1.04/1.24 tff(2668,plain,
% 1.04/1.24 (c1_1(a2519)),
% 1.04/1.24 inference(unit_resolution,[status(thm)],[2667, 90, 838, 851, 850, 55, 43, 877, 2661])).
% 1.04/1.24 tff(2669,plain,
% 1.04/1.24 ($false),
% 1.04/1.24 inference(unit_resolution,[status(thm)],[2376, 90, 14, 55, 49, 43, 36, 2668])).
% 1.04/1.24 tff(2670,plain,((~hskp3) | hskp9 | hskp2 | (~c0_1(a2553)) | c1_1(a2553) | (~c2_1(a2553))), inference(lemma,lemma(discharge,[]))).
% 1.04/1.24 tff(2671,plain,
% 1.04/1.24 (~hskp3),
% 1.04/1.24 inference(unit_resolution,[status(thm)],[2670, 838, 14, 2658, 850, 2660])).
% 1.04/1.24 tff(2672,plain,
% 1.04/1.24 ((hskp27 | hskp3 | hskp2) <=> (hskp27 | hskp3 | hskp2)),
% 1.04/1.24 inference(rewrite,[status(thm)],[])).
% 1.04/1.24 tff(2673,plain,
% 1.04/1.24 (((hskp2 | hskp27) | hskp3) <=> (hskp27 | hskp3 | hskp2)),
% 1.04/1.24 inference(rewrite,[status(thm)],[])).
% 1.04/1.24 tff(2674,axiom,((hskp2 | hskp27) | hskp3), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause40')).
% 1.04/1.24 tff(2675,plain,
% 1.04/1.24 (hskp27 | hskp3 | hskp2),
% 1.04/1.24 inference(modus_ponens,[status(thm)],[2674, 2673])).
% 1.04/1.24 tff(2676,plain,
% 1.04/1.24 (hskp27 | hskp3 | hskp2),
% 1.04/1.24 inference(modus_ponens,[status(thm)],[2675, 2672])).
% 1.04/1.24 tff(2677,plain,
% 1.04/1.24 (hskp27 | hskp3 | hskp2),
% 1.04/1.24 inference(modus_ponens,[status(thm)],[2676, 2672])).
% 1.04/1.24 tff(2678,plain,
% 1.04/1.24 (hskp27 | hskp3 | hskp2),
% 1.04/1.24 inference(modus_ponens,[status(thm)],[2677, 2672])).
% 1.04/1.24 tff(2679,plain,
% 1.04/1.24 (hskp27 | hskp3 | hskp2),
% 1.04/1.24 inference(modus_ponens,[status(thm)],[2678, 2672])).
% 1.04/1.24 tff(2680,plain,
% 1.04/1.24 (hskp27),
% 1.04/1.24 inference(unit_resolution,[status(thm)],[2679, 2671, 838])).
% 1.04/1.24 tff(2681,plain,
% 1.04/1.24 (~c3_1(a2614)),
% 1.04/1.24 inference(unit_resolution,[status(thm)],[19, 2680])).
% 1.04/1.24 tff(2682,plain,
% 1.04/1.24 (~c2_1(a2614)),
% 1.04/1.24 inference(unit_resolution,[status(thm)],[25, 2680])).
% 1.04/1.24 tff(2683,plain,
% 1.04/1.24 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp2 | c2_1(a2614) | c3_1(a2614) | c1_1(a2553) | c3_1(a2553) | (~ndr1_0) | (~c0_1(a2553)) | (~c0_1(a2614)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | hskp2 | c2_1(a2614) | c3_1(a2614) | c1_1(a2553) | c3_1(a2553) | (~ndr1_0) | (~c0_1(a2553)) | (~c0_1(a2614)))),
% 1.04/1.24 inference(rewrite,[status(thm)],[])).
% 1.04/1.24 tff(2684,plain,
% 1.04/1.24 ((hskp2 | (~ndr1_0) | c3_1(a2614) | c2_1(a2614) | (~c0_1(a2614)) | c3_1(a2553) | c1_1(a2553) | (~c0_1(a2553))) <=> (hskp2 | c2_1(a2614) | c3_1(a2614) | c1_1(a2553) | c3_1(a2553) | (~ndr1_0) | (~c0_1(a2553)) | (~c0_1(a2614)))),
% 1.04/1.24 inference(rewrite,[status(thm)],[])).
% 1.04/1.24 tff(2685,plain,
% 1.04/1.24 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp2 | (~ndr1_0) | c3_1(a2614) | c2_1(a2614) | (~c0_1(a2614)) | c3_1(a2553) | c1_1(a2553) | (~c0_1(a2553)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp2 | c2_1(a2614) | c3_1(a2614) | c1_1(a2553) | c3_1(a2553) | (~ndr1_0) | (~c0_1(a2553)) | (~c0_1(a2614))))),
% 1.04/1.24 inference(monotonicity,[status(thm)],[2684])).
% 1.04/1.24 tff(2686,plain,
% 1.04/1.24 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp2 | (~ndr1_0) | c3_1(a2614) | c2_1(a2614) | (~c0_1(a2614)) | c3_1(a2553) | c1_1(a2553) | (~c0_1(a2553)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | hskp2 | c2_1(a2614) | c3_1(a2614) | c1_1(a2553) | c3_1(a2553) | (~ndr1_0) | (~c0_1(a2553)) | (~c0_1(a2614)))),
% 1.04/1.24 inference(transitivity,[status(thm)],[2685, 2683])).
% 1.04/1.24 tff(2687,plain,
% 1.04/1.24 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp2 | (~ndr1_0) | c3_1(a2614) | c2_1(a2614) | (~c0_1(a2614)) | c3_1(a2553) | c1_1(a2553) | (~c0_1(a2553)))),
% 1.04/1.24 inference(quant_inst,[status(thm)],[])).
% 1.04/1.24 tff(2688,plain,
% 1.04/1.24 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | hskp2 | c2_1(a2614) | c3_1(a2614) | c1_1(a2553) | c3_1(a2553) | (~ndr1_0) | (~c0_1(a2553)) | (~c0_1(a2614))),
% 1.04/1.24 inference(modus_ponens,[status(thm)],[2687, 2686])).
% 1.04/1.24 tff(2689,plain,
% 1.04/1.24 (~c0_1(a2614)),
% 1.04/1.24 inference(unit_resolution,[status(thm)],[2688, 90, 838, 2658, 2682, 2681, 850, 849, 848])).
% 1.04/1.24 tff(2690,plain,
% 1.04/1.24 (c1_1(a2614)),
% 1.04/1.24 inference(unit_resolution,[status(thm)],[12, 2680])).
% 1.04/1.24 tff(2691,plain,
% 1.04/1.24 ($false),
% 1.04/1.24 inference(unit_resolution,[status(thm)],[115, 90, 14, 2690, 2682, 2681, 36, 2689])).
% 1.04/1.24 tff(2692,plain,(hskp2 | hskp9 | c1_1(a2553) | c3_1(a2553)), inference(lemma,lemma(discharge,[]))).
% 1.04/1.24 tff(2693,plain,
% 1.04/1.24 (hskp2),
% 1.04/1.24 inference(unit_resolution,[status(thm)],[2692, 850, 14, 849])).
% 1.04/1.24 tff(2694,plain,
% 1.04/1.24 (~c3_1(a2518)),
% 1.04/1.24 inference(unit_resolution,[status(thm)],[892, 2693])).
% 1.04/1.24 tff(2695,plain,
% 1.04/1.24 (~c0_1(a2518)),
% 1.04/1.24 inference(unit_resolution,[status(thm)],[898, 2693])).
% 1.04/1.24 tff(2696,plain,
% 1.04/1.24 (c1_1(a2518)),
% 1.04/1.24 inference(unit_resolution,[status(thm)],[906, 2693])).
% 1.04/1.24 tff(2697,plain,
% 1.04/1.24 (c2_1(a2518)),
% 1.04/1.24 inference(unit_resolution,[status(thm)],[1815, 90, 14, 2696, 2695, 2694, 36])).
% 1.04/1.24 tff(2698,plain,
% 1.04/1.24 ($false),
% 1.04/1.24 inference(unit_resolution,[status(thm)],[1835, 90, 1829, 1973, 1972, 1971, 1828, 2576])).
% 1.04/1.24 tff(2699,plain,(c0_1(a2553) | hskp21 | c1_1(a2553) | c3_1(a2553)), inference(lemma,lemma(discharge,[]))).
% 1.04/1.24 tff(2700,plain,
% 1.07/1.24 (c0_1(a2553)),
% 1.07/1.24 inference(unit_resolution,[status(thm)],[2699, 1829, 850, 849])).
% 1.07/1.24 tff(2701,plain,
% 1.07/1.24 (c2_1(a2553)),
% 1.07/1.24 inference(unit_resolution,[status(thm)],[2659, 838, 850, 2700])).
% 1.07/1.24 tff(2702,plain,
% 1.07/1.24 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c3_1(a2553) | c0_1(a2549) | c1_1(a2549) | (~ndr1_0) | (~c3_1(a2549)) | (~c2_1(a2549)) | (~c0_1(a2553)) | (~c2_1(a2553)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c3_1(a2553) | c0_1(a2549) | c1_1(a2549) | (~ndr1_0) | (~c3_1(a2549)) | (~c2_1(a2549)) | (~c0_1(a2553)) | (~c2_1(a2553)))),
% 1.07/1.24 inference(rewrite,[status(thm)],[])).
% 1.07/1.24 tff(2703,plain,
% 1.07/1.24 (((~ndr1_0) | c3_1(a2553) | (~c0_1(a2553)) | (~c2_1(a2553)) | c0_1(a2549) | (~c3_1(a2549)) | (~c2_1(a2549)) | c1_1(a2549) | c0_1(a2549) | (~c2_1(a2549))) <=> (c3_1(a2553) | c0_1(a2549) | c1_1(a2549) | (~ndr1_0) | (~c3_1(a2549)) | (~c2_1(a2549)) | (~c0_1(a2553)) | (~c2_1(a2553)))),
% 1.07/1.24 inference(rewrite,[status(thm)],[])).
% 1.07/1.24 tff(2704,plain,
% 1.07/1.24 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a2553) | (~c0_1(a2553)) | (~c2_1(a2553)) | c0_1(a2549) | (~c3_1(a2549)) | (~c2_1(a2549)) | c1_1(a2549) | c0_1(a2549) | (~c2_1(a2549)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c3_1(a2553) | c0_1(a2549) | c1_1(a2549) | (~ndr1_0) | (~c3_1(a2549)) | (~c2_1(a2549)) | (~c0_1(a2553)) | (~c2_1(a2553))))),
% 1.07/1.24 inference(monotonicity,[status(thm)],[2703])).
% 1.07/1.24 tff(2705,plain,
% 1.07/1.24 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a2553) | (~c0_1(a2553)) | (~c2_1(a2553)) | c0_1(a2549) | (~c3_1(a2549)) | (~c2_1(a2549)) | c1_1(a2549) | c0_1(a2549) | (~c2_1(a2549)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c3_1(a2553) | c0_1(a2549) | c1_1(a2549) | (~ndr1_0) | (~c3_1(a2549)) | (~c2_1(a2549)) | (~c0_1(a2553)) | (~c2_1(a2553)))),
% 1.07/1.24 inference(transitivity,[status(thm)],[2704, 2702])).
% 1.07/1.24 tff(2706,plain,
% 1.07/1.24 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a2553) | (~c0_1(a2553)) | (~c2_1(a2553)) | c0_1(a2549) | (~c3_1(a2549)) | (~c2_1(a2549)) | c1_1(a2549) | c0_1(a2549) | (~c2_1(a2549)))),
% 1.07/1.24 inference(quant_inst,[status(thm)],[])).
% 1.07/1.24 tff(2707,plain,
% 1.07/1.24 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c3_1(a2553) | c0_1(a2549) | c1_1(a2549) | (~ndr1_0) | (~c3_1(a2549)) | (~c2_1(a2549)) | (~c0_1(a2553)) | (~c2_1(a2553))),
% 1.07/1.24 inference(modus_ponens,[status(thm)],[2706, 2705])).
% 1.07/1.24 tff(2708,plain,
% 1.07/1.24 (~c3_1(a2549)),
% 1.07/1.24 inference(unit_resolution,[status(thm)],[2707, 90, 2700, 2258, 849, 2257, 2256, 1087, 2661])).
% 1.07/1.24 tff(2709,plain,
% 1.07/1.24 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | c1_1(a2553) | c0_1(a2549) | c1_1(a2549) | (~ndr1_0) | c3_1(a2549) | (~c0_1(a2553)) | (~c2_1(a2553)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp2 | c1_1(a2553) | c0_1(a2549) | c1_1(a2549) | (~ndr1_0) | c3_1(a2549) | (~c0_1(a2553)) | (~c2_1(a2553)))),
% 1.07/1.24 inference(rewrite,[status(thm)],[])).
% 1.07/1.24 tff(2710,plain,
% 1.07/1.24 ((hskp2 | (~ndr1_0) | c1_1(a2553) | (~c0_1(a2553)) | (~c2_1(a2553)) | c3_1(a2549) | c1_1(a2549) | c0_1(a2549)) <=> (hskp2 | c1_1(a2553) | c0_1(a2549) | c1_1(a2549) | (~ndr1_0) | c3_1(a2549) | (~c0_1(a2553)) | (~c2_1(a2553)))),
% 1.07/1.24 inference(rewrite,[status(thm)],[])).
% 1.07/1.24 tff(2711,plain,
% 1.07/1.24 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | c1_1(a2553) | (~c0_1(a2553)) | (~c2_1(a2553)) | c3_1(a2549) | c1_1(a2549) | c0_1(a2549))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | c1_1(a2553) | c0_1(a2549) | c1_1(a2549) | (~ndr1_0) | c3_1(a2549) | (~c0_1(a2553)) | (~c2_1(a2553))))),
% 1.07/1.24 inference(monotonicity,[status(thm)],[2710])).
% 1.07/1.24 tff(2712,plain,
% 1.07/1.24 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | c1_1(a2553) | (~c0_1(a2553)) | (~c2_1(a2553)) | c3_1(a2549) | c1_1(a2549) | c0_1(a2549))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp2 | c1_1(a2553) | c0_1(a2549) | c1_1(a2549) | (~ndr1_0) | c3_1(a2549) | (~c0_1(a2553)) | (~c2_1(a2553)))),
% 1.07/1.24 inference(transitivity,[status(thm)],[2711, 2709])).
% 1.07/1.24 tff(2713,plain,
% 1.07/1.24 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | c1_1(a2553) | (~c0_1(a2553)) | (~c2_1(a2553)) | c3_1(a2549) | c1_1(a2549) | c0_1(a2549))),
% 1.07/1.24 inference(quant_inst,[status(thm)],[])).
% 1.07/1.24 tff(2714,plain,
% 1.07/1.24 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp2 | c1_1(a2553) | c0_1(a2549) | c1_1(a2549) | (~ndr1_0) | c3_1(a2549) | (~c0_1(a2553)) | (~c2_1(a2553))),
% 1.07/1.24 inference(modus_ponens,[status(thm)],[2713, 2712])).
% 1.07/1.24 tff(2715,plain,
% 1.07/1.24 ($false),
% 1.07/1.24 inference(unit_resolution,[status(thm)],[2714, 90, 838, 2700, 850, 2257, 2256, 877, 2661, 2708])).
% 1.07/1.24 tff(2716,plain,(hskp2 | c1_1(a2553) | (~c2_1(a2553)) | c3_1(a2553) | hskp21), inference(lemma,lemma(discharge,[]))).
% 1.07/1.24 tff(2717,plain,
% 1.07/1.24 ($false),
% 1.07/1.24 inference(unit_resolution,[status(thm)],[2716, 2701, 838, 850, 849, 1829])).
% 1.07/1.24 tff(2718,plain,(hskp2 | c1_1(a2553) | c3_1(a2553) | hskp21), inference(lemma,lemma(discharge,[]))).
% 1.07/1.24 tff(2719,plain,
% 1.07/1.24 (hskp2),
% 1.07/1.24 inference(unit_resolution,[status(thm)],[2718, 1829, 849, 850])).
% 1.07/1.24 tff(2720,plain,
% 1.07/1.24 (c1_1(a2518)),
% 1.07/1.24 inference(unit_resolution,[status(thm)],[906, 2719])).
% 1.07/1.24 tff(2721,plain,
% 1.07/1.24 (~c3_1(a2518)),
% 1.07/1.24 inference(unit_resolution,[status(thm)],[892, 2719])).
% 1.07/1.24 tff(2722,plain,
% 1.07/1.24 (((~![U: $i] : (hskp22 | hskp21 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp22 | hskp21 | c1_1(a2553) | (~ndr1_0) | (~c0_1(a2553)) | c2_1(a2553))) <=> ((~![U: $i] : (hskp22 | hskp21 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp22 | hskp21 | c1_1(a2553) | (~ndr1_0) | (~c0_1(a2553)) | c2_1(a2553))),
% 1.07/1.24 inference(rewrite,[status(thm)],[])).
% 1.07/1.24 tff(2723,plain,
% 1.07/1.24 ((hskp22 | hskp21 | (~ndr1_0) | c2_1(a2553) | c1_1(a2553) | (~c0_1(a2553))) <=> (hskp22 | hskp21 | c1_1(a2553) | (~ndr1_0) | (~c0_1(a2553)) | c2_1(a2553))),
% 1.07/1.24 inference(rewrite,[status(thm)],[])).
% 1.07/1.24 tff(2724,plain,
% 1.07/1.24 (((~![U: $i] : (hskp22 | hskp21 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp22 | hskp21 | (~ndr1_0) | c2_1(a2553) | c1_1(a2553) | (~c0_1(a2553)))) <=> ((~![U: $i] : (hskp22 | hskp21 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp22 | hskp21 | c1_1(a2553) | (~ndr1_0) | (~c0_1(a2553)) | c2_1(a2553)))),
% 1.07/1.24 inference(monotonicity,[status(thm)],[2723])).
% 1.07/1.24 tff(2725,plain,
% 1.07/1.24 (((~![U: $i] : (hskp22 | hskp21 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp22 | hskp21 | (~ndr1_0) | c2_1(a2553) | c1_1(a2553) | (~c0_1(a2553)))) <=> ((~![U: $i] : (hskp22 | hskp21 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp22 | hskp21 | c1_1(a2553) | (~ndr1_0) | (~c0_1(a2553)) | c2_1(a2553))),
% 1.07/1.24 inference(transitivity,[status(thm)],[2724, 2722])).
% 1.07/1.24 tff(2726,plain,
% 1.07/1.24 ((~![U: $i] : (hskp22 | hskp21 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp22 | hskp21 | (~ndr1_0) | c2_1(a2553) | c1_1(a2553) | (~c0_1(a2553)))),
% 1.07/1.24 inference(quant_inst,[status(thm)],[])).
% 1.07/1.24 tff(2727,plain,
% 1.07/1.24 ((~![U: $i] : (hskp22 | hskp21 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp22 | hskp21 | c1_1(a2553) | (~ndr1_0) | (~c0_1(a2553)) | c2_1(a2553)),
% 1.07/1.24 inference(modus_ponens,[status(thm)],[2726, 2725])).
% 1.07/1.24 tff(2728,plain,
% 1.07/1.24 (hskp22 | hskp21 | (~c0_1(a2553)) | c2_1(a2553)),
% 1.07/1.24 inference(unit_resolution,[status(thm)],[2727, 90, 850, 1759])).
% 1.07/1.24 tff(2729,plain,
% 1.07/1.24 (c2_1(a2553)),
% 1.07/1.24 inference(unit_resolution,[status(thm)],[2728, 1883, 1829, 2700])).
% 1.07/1.24 tff(2730,plain,
% 1.07/1.24 (hskp2),
% 1.07/1.24 inference(unit_resolution,[status(thm)],[2716, 2729, 850, 849, 1829])).
% 1.07/1.24 tff(2731,plain,
% 1.07/1.24 (~c3_1(a2518)),
% 1.07/1.24 inference(unit_resolution,[status(thm)],[892, 2730])).
% 1.07/1.24 tff(2732,plain,
% 1.07/1.24 (~c0_1(a2518)),
% 1.07/1.24 inference(unit_resolution,[status(thm)],[898, 2730])).
% 1.07/1.24 tff(2733,plain,
% 1.07/1.24 (c1_1(a2518)),
% 1.07/1.24 inference(unit_resolution,[status(thm)],[906, 2730])).
% 1.07/1.24 tff(2734,plain,
% 1.07/1.24 (hskp12),
% 1.07/1.24 inference(unit_resolution,[status(thm)],[2099, 90, 2700, 2733, 849, 2732, 2731, 2093, 2729])).
% 1.07/1.24 tff(2735,plain,
% 1.07/1.24 (~c2_1(a2533)),
% 1.07/1.24 inference(unit_resolution,[status(thm)],[2112, 2734])).
% 1.07/1.24 tff(2736,plain,
% 1.07/1.24 (~c1_1(a2533)),
% 1.07/1.24 inference(unit_resolution,[status(thm)],[2118, 2734])).
% 1.07/1.24 tff(2737,plain,
% 1.07/1.24 (((~![U: $i] : (hskp22 | hskp21 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp22 | hskp21 | c1_1(a2533) | c2_1(a2533) | (~ndr1_0) | (~c0_1(a2533)))) <=> ((~![U: $i] : (hskp22 | hskp21 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp22 | hskp21 | c1_1(a2533) | c2_1(a2533) | (~ndr1_0) | (~c0_1(a2533)))),
% 1.07/1.24 inference(rewrite,[status(thm)],[])).
% 1.07/1.24 tff(2738,plain,
% 1.07/1.24 ((hskp22 | hskp21 | (~ndr1_0) | c2_1(a2533) | c1_1(a2533) | (~c0_1(a2533))) <=> (hskp22 | hskp21 | c1_1(a2533) | c2_1(a2533) | (~ndr1_0) | (~c0_1(a2533)))),
% 1.07/1.24 inference(rewrite,[status(thm)],[])).
% 1.07/1.24 tff(2739,plain,
% 1.07/1.24 (((~![U: $i] : (hskp22 | hskp21 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp22 | hskp21 | (~ndr1_0) | c2_1(a2533) | c1_1(a2533) | (~c0_1(a2533)))) <=> ((~![U: $i] : (hskp22 | hskp21 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp22 | hskp21 | c1_1(a2533) | c2_1(a2533) | (~ndr1_0) | (~c0_1(a2533))))),
% 1.07/1.24 inference(monotonicity,[status(thm)],[2738])).
% 1.07/1.24 tff(2740,plain,
% 1.07/1.24 (((~![U: $i] : (hskp22 | hskp21 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp22 | hskp21 | (~ndr1_0) | c2_1(a2533) | c1_1(a2533) | (~c0_1(a2533)))) <=> ((~![U: $i] : (hskp22 | hskp21 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp22 | hskp21 | c1_1(a2533) | c2_1(a2533) | (~ndr1_0) | (~c0_1(a2533)))),
% 1.07/1.24 inference(transitivity,[status(thm)],[2739, 2737])).
% 1.07/1.24 tff(2741,plain,
% 1.07/1.24 ((~![U: $i] : (hskp22 | hskp21 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp22 | hskp21 | (~ndr1_0) | c2_1(a2533) | c1_1(a2533) | (~c0_1(a2533)))),
% 1.07/1.24 inference(quant_inst,[status(thm)],[])).
% 1.07/1.24 tff(2742,plain,
% 1.07/1.24 ((~![U: $i] : (hskp22 | hskp21 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp22 | hskp21 | c1_1(a2533) | c2_1(a2533) | (~ndr1_0) | (~c0_1(a2533))),
% 1.07/1.24 inference(modus_ponens,[status(thm)],[2741, 2740])).
% 1.07/1.24 tff(2743,plain,
% 1.07/1.24 (~c0_1(a2533)),
% 1.07/1.24 inference(unit_resolution,[status(thm)],[2742, 90, 1883, 1829, 2736, 2735, 1759])).
% 1.07/1.24 tff(2744,plain,
% 1.07/1.24 (~c3_1(a2533)),
% 1.07/1.24 inference(unit_resolution,[status(thm)],[2106, 2734])).
% 1.07/1.24 tff(2745,plain,
% 1.07/1.24 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a2533) | c3_1(a2533) | c0_1(a2518) | c3_1(a2518) | (~ndr1_0) | (~c2_1(a2558)) | (~c0_1(a2558)) | (~c1_1(a2558)) | (~c1_1(a2518)) | c0_1(a2533))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c1_1(a2533) | c3_1(a2533) | c0_1(a2518) | c3_1(a2518) | (~ndr1_0) | (~c2_1(a2558)) | (~c0_1(a2558)) | (~c1_1(a2558)) | (~c1_1(a2518)) | c0_1(a2533))),
% 1.07/1.24 inference(rewrite,[status(thm)],[])).
% 1.07/1.24 tff(2746,plain,
% 1.07/1.24 (((~ndr1_0) | (~c1_1(a2558)) | (~c0_1(a2558)) | (~c2_1(a2558)) | c3_1(a2518) | c0_1(a2518) | (~c1_1(a2518)) | c3_1(a2533) | c1_1(a2533) | c0_1(a2533)) <=> (c1_1(a2533) | c3_1(a2533) | c0_1(a2518) | c3_1(a2518) | (~ndr1_0) | (~c2_1(a2558)) | (~c0_1(a2558)) | (~c1_1(a2558)) | (~c1_1(a2518)) | c0_1(a2533))),
% 1.07/1.24 inference(rewrite,[status(thm)],[])).
% 1.07/1.24 tff(2747,plain,
% 1.07/1.24 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c1_1(a2558)) | (~c0_1(a2558)) | (~c2_1(a2558)) | c3_1(a2518) | c0_1(a2518) | (~c1_1(a2518)) | c3_1(a2533) | c1_1(a2533) | c0_1(a2533))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a2533) | c3_1(a2533) | c0_1(a2518) | c3_1(a2518) | (~ndr1_0) | (~c2_1(a2558)) | (~c0_1(a2558)) | (~c1_1(a2558)) | (~c1_1(a2518)) | c0_1(a2533)))),
% 1.07/1.24 inference(monotonicity,[status(thm)],[2746])).
% 1.07/1.24 tff(2748,plain,
% 1.07/1.24 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c1_1(a2558)) | (~c0_1(a2558)) | (~c2_1(a2558)) | c3_1(a2518) | c0_1(a2518) | (~c1_1(a2518)) | c3_1(a2533) | c1_1(a2533) | c0_1(a2533))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c1_1(a2533) | c3_1(a2533) | c0_1(a2518) | c3_1(a2518) | (~ndr1_0) | (~c2_1(a2558)) | (~c0_1(a2558)) | (~c1_1(a2558)) | (~c1_1(a2518)) | c0_1(a2533))),
% 1.07/1.24 inference(transitivity,[status(thm)],[2747, 2745])).
% 1.07/1.24 tff(2749,plain,
% 1.07/1.24 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c1_1(a2558)) | (~c0_1(a2558)) | (~c2_1(a2558)) | c3_1(a2518) | c0_1(a2518) | (~c1_1(a2518)) | c3_1(a2533) | c1_1(a2533) | c0_1(a2533))),
% 1.07/1.24 inference(quant_inst,[status(thm)],[])).
% 1.07/1.24 tff(2750,plain,
% 1.07/1.24 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c1_1(a2533) | c3_1(a2533) | c0_1(a2518) | c3_1(a2518) | (~ndr1_0) | (~c2_1(a2558)) | (~c0_1(a2558)) | (~c1_1(a2558)) | (~c1_1(a2518)) | c0_1(a2533)),
% 1.07/1.24 inference(modus_ponens,[status(thm)],[2749, 2748])).
% 1.07/1.24 tff(2751,plain,
% 1.07/1.24 ($false),
% 1.07/1.24 inference(unit_resolution,[status(thm)],[2750, 90, 2425, 2417, 2409, 2733, 2736, 2744, 2732, 2731, 459, 2743])).
% 1.07/1.24 tff(2752,plain,(hskp22 | hskp21 | c3_1(a2553) | c1_1(a2553)), inference(lemma,lemma(discharge,[]))).
% 1.07/1.24 tff(2753,plain,
% 1.07/1.24 (hskp22),
% 1.07/1.24 inference(unit_resolution,[status(thm)],[2752, 1829, 849, 850])).
% 1.07/1.24 tff(2754,plain,
% 1.07/1.24 (~c3_1(a2552)),
% 1.07/1.24 inference(unit_resolution,[status(thm)],[806, 2753])).
% 1.07/1.24 tff(2755,plain,
% 1.07/1.24 (~c1_1(a2552)),
% 1.07/1.24 inference(unit_resolution,[status(thm)],[820, 2753])).
% 1.07/1.24 tff(2756,plain,
% 1.07/1.24 (c2_1(a2552)),
% 1.07/1.24 inference(unit_resolution,[status(thm)],[814, 2753])).
% 1.07/1.24 tff(2757,plain,
% 1.07/1.24 (~c0_1(a2518)),
% 1.07/1.24 inference(unit_resolution,[status(thm)],[898, 2719])).
% 1.07/1.24 tff(2758,plain,
% 1.07/1.24 (~c2_1(a2518)),
% 1.07/1.24 inference(unit_resolution,[status(thm)],[2174, 2757, 2756, 2755, 2754, 1829, 2700, 849, 850, 2721, 2720])).
% 1.07/1.24 tff(2759,plain,
% 1.07/1.24 ($false),
% 1.07/1.24 inference(unit_resolution,[status(thm)],[1815, 90, 14, 2720, 2757, 2721, 36, 2758])).
% 1.07/1.24 tff(2760,plain,(hskp21 | hskp9 | c3_1(a2553) | c1_1(a2553)), inference(lemma,lemma(discharge,[]))).
% 1.07/1.24 tff(2761,plain,
% 1.07/1.24 (hskp21),
% 1.07/1.24 inference(unit_resolution,[status(thm)],[2760, 850, 849, 14])).
% 1.07/1.24 tff(2762,plain,
% 1.07/1.24 (~c2_1(a2551)),
% 1.07/1.24 inference(unit_resolution,[status(thm)],[168, 2761])).
% 1.07/1.24 tff(2763,plain,
% 1.07/1.24 (c1_1(a2551)),
% 1.07/1.24 inference(unit_resolution,[status(thm)],[176, 2761])).
% 1.07/1.24 tff(2764,plain,
% 1.07/1.24 (c0_1(a2551)),
% 1.07/1.24 inference(unit_resolution,[status(thm)],[184, 2761])).
% 1.07/1.24 tff(2765,plain,
% 1.07/1.24 (hskp14 | (~c2_1(a2518))),
% 1.07/1.24 inference(unit_resolution,[status(thm)],[920, 90, 2764, 2763, 2762, 2695, 2694, 469])).
% 1.07/1.24 tff(2766,plain,
% 1.07/1.24 (hskp14),
% 1.07/1.24 inference(unit_resolution,[status(thm)],[2765, 2697])).
% 1.07/1.24 tff(2767,plain,
% 1.07/1.24 (~c3_1(a2536)),
% 1.07/1.24 inference(unit_resolution,[status(thm)],[484, 2766])).
% 1.07/1.24 tff(2768,plain,
% 1.07/1.24 (~c1_1(a2536)),
% 1.07/1.24 inference(unit_resolution,[status(thm)],[490, 2766])).
% 1.07/1.24 tff(2769,plain,
% 1.07/1.24 (~c0_1(a2536)),
% 1.07/1.24 inference(unit_resolution,[status(thm)],[496, 2766])).
% 1.07/1.25 tff(2770,plain,
% 1.07/1.25 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a2536) | c1_1(a2536) | c3_1(a2536) | c0_1(a2518) | c3_1(a2518) | (~ndr1_0) | (~c2_1(a2558)) | (~c0_1(a2558)) | (~c1_1(a2558)) | (~c1_1(a2518)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a2536) | c1_1(a2536) | c3_1(a2536) | c0_1(a2518) | c3_1(a2518) | (~ndr1_0) | (~c2_1(a2558)) | (~c0_1(a2558)) | (~c1_1(a2558)) | (~c1_1(a2518)))),
% 1.07/1.25 inference(rewrite,[status(thm)],[])).
% 1.07/1.25 tff(2771,plain,
% 1.07/1.25 (((~ndr1_0) | (~c1_1(a2558)) | (~c0_1(a2558)) | (~c2_1(a2558)) | c3_1(a2518) | c0_1(a2518) | (~c1_1(a2518)) | c3_1(a2536) | c1_1(a2536) | c0_1(a2536)) <=> (c0_1(a2536) | c1_1(a2536) | c3_1(a2536) | c0_1(a2518) | c3_1(a2518) | (~ndr1_0) | (~c2_1(a2558)) | (~c0_1(a2558)) | (~c1_1(a2558)) | (~c1_1(a2518)))),
% 1.07/1.25 inference(rewrite,[status(thm)],[])).
% 1.07/1.25 tff(2772,plain,
% 1.07/1.25 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c1_1(a2558)) | (~c0_1(a2558)) | (~c2_1(a2558)) | c3_1(a2518) | c0_1(a2518) | (~c1_1(a2518)) | c3_1(a2536) | c1_1(a2536) | c0_1(a2536))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a2536) | c1_1(a2536) | c3_1(a2536) | c0_1(a2518) | c3_1(a2518) | (~ndr1_0) | (~c2_1(a2558)) | (~c0_1(a2558)) | (~c1_1(a2558)) | (~c1_1(a2518))))),
% 1.07/1.25 inference(monotonicity,[status(thm)],[2771])).
% 1.07/1.25 tff(2773,plain,
% 1.07/1.25 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c1_1(a2558)) | (~c0_1(a2558)) | (~c2_1(a2558)) | c3_1(a2518) | c0_1(a2518) | (~c1_1(a2518)) | c3_1(a2536) | c1_1(a2536) | c0_1(a2536))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a2536) | c1_1(a2536) | c3_1(a2536) | c0_1(a2518) | c3_1(a2518) | (~ndr1_0) | (~c2_1(a2558)) | (~c0_1(a2558)) | (~c1_1(a2558)) | (~c1_1(a2518)))),
% 1.07/1.25 inference(transitivity,[status(thm)],[2772, 2770])).
% 1.07/1.25 tff(2774,plain,
% 1.07/1.25 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c1_1(a2558)) | (~c0_1(a2558)) | (~c2_1(a2558)) | c3_1(a2518) | c0_1(a2518) | (~c1_1(a2518)) | c3_1(a2536) | c1_1(a2536) | c0_1(a2536))),
% 1.07/1.25 inference(quant_inst,[status(thm)],[])).
% 1.07/1.25 tff(2775,plain,
% 1.07/1.25 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a2536) | c1_1(a2536) | c3_1(a2536) | c0_1(a2518) | c3_1(a2518) | (~ndr1_0) | (~c2_1(a2558)) | (~c0_1(a2558)) | (~c1_1(a2558)) | (~c1_1(a2518))),
% 1.07/1.25 inference(modus_ponens,[status(thm)],[2774, 2773])).
% 1.07/1.25 tff(2776,plain,
% 1.07/1.25 ($false),
% 1.07/1.25 inference(unit_resolution,[status(thm)],[2775, 90, 2425, 2417, 2409, 2696, 2769, 2768, 2767, 2695, 2694, 459])).
% 1.07/1.25 tff(2777,plain,(c1_1(a2553) | hskp9 | c3_1(a2553)), inference(lemma,lemma(discharge,[]))).
% 1.07/1.25 tff(2778,plain,
% 1.07/1.25 ($false),
% 1.07/1.25 inference(unit_resolution,[status(thm)],[2777, 2562, 2561, 14])).
% 1.07/1.25 tff(2779,plain,(hskp9), inference(lemma,lemma(discharge,[]))).
% 1.07/1.25 tff(2780,plain,
% 1.07/1.25 (~c0_1(a2526)),
% 1.07/1.25 inference(unit_resolution,[status(thm)],[205, 2779])).
% 1.07/1.25 tff(2781,plain,
% 1.07/1.25 (c3_1(a2526)),
% 1.07/1.25 inference(unit_resolution,[status(thm)],[213, 2779])).
% 1.07/1.25 tff(2782,plain,
% 1.07/1.25 (c1_1(a2526)),
% 1.07/1.25 inference(unit_resolution,[status(thm)],[199, 2779])).
% 1.07/1.25 tff(2783,plain,
% 1.07/1.25 (hskp17),
% 1.07/1.25 inference(unit_resolution,[status(thm)],[232, 90, 13, 2782, 2781, 26, 20, 2780, 226])).
% 1.07/1.25 tff(2784,plain,
% 1.07/1.25 (~c2_1(a2541)),
% 1.07/1.25 inference(unit_resolution,[status(thm)],[238, 2783])).
% 1.07/1.25 tff(2785,plain,
% 1.07/1.25 (c3_1(a2541)),
% 1.07/1.25 inference(unit_resolution,[status(thm)],[252, 2783])).
% 1.07/1.25 tff(2786,plain,
% 1.07/1.25 (~c1_1(a2541)),
% 1.07/1.25 inference(unit_resolution,[status(thm)],[244, 2783])).
% 1.07/1.25 tff(2787,plain,
% 1.07/1.25 (~c0_1(a2614)),
% 1.07/1.25 inference(unit_resolution,[status(thm)],[364, 2786, 2782, 20, 2785, 2784, 2781, 2780, 13])).
% 1.07/1.25 tff(2788,plain,
% 1.07/1.25 (^[V: $i, U: $i] : refl((hskp14 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))) <=> (hskp14 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))))),
% 1.07/1.25 inference(bind,[status(th)],[])).
% 1.07/1.25 tff(2789,plain,
% 1.07/1.25 (![V: $i, U: $i] : (hskp14 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp14 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 1.07/1.25 inference(quant_intro,[status(thm)],[2788])).
% 1.07/1.25 tff(2790,plain,
% 1.07/1.25 (![V: $i, U: $i] : (hskp14 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp14 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 1.07/1.25 inference(rewrite,[status(thm)],[])).
% 1.07/1.25 tff(2791,plain,
% 1.07/1.25 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) <=> ((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c0_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c0_1(V)) | hskp14) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))) | hskp14))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))) | hskp14) <=> (hskp14 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c0_1(V)) | hskp14) <=> (hskp14 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))))),
% 1.07/1.25 inference(bind,[status(th)],[])).
% 1.07/1.25 tff(2792,plain,
% 1.07/1.25 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c0_1(V)) | hskp14) <=> ![V: $i, U: $i] : (hskp14 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 1.07/1.25 inference(quant_intro,[status(thm)],[2791])).
% 1.07/1.25 tff(2793,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c0_1(V)) | hskp14)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause190')).
% 1.07/1.25 tff(2794,plain,
% 1.07/1.25 (![V: $i, U: $i] : (hskp14 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 1.07/1.25 inference(modus_ponens,[status(thm)],[2793, 2792])).
% 1.07/1.25 tff(2795,plain,
% 1.07/1.25 (![V: $i, U: $i] : (hskp14 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 1.07/1.25 inference(modus_ponens,[status(thm)],[2794, 2790])).
% 1.07/1.25 tff(2796,plain,(
% 1.07/1.25 ![V: $i, U: $i] : (hskp14 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 1.07/1.25 inference(skolemize,[status(sab)],[2795])).
% 1.07/1.25 tff(2797,plain,
% 1.07/1.25 (![V: $i, U: $i] : (hskp14 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 1.07/1.25 inference(modus_ponens,[status(thm)],[2796, 2789])).
% 1.07/1.25 tff(2798,plain,
% 1.07/1.25 (hskp10),
% 1.07/1.25 inference(unit_resolution,[status(thm)],[1852, 90, 13, 26, 20, 1846, 2787])).
% 1.07/1.25 tff(2799,plain,
% 1.07/1.25 (~c1_1(a2528)),
% 1.07/1.25 inference(unit_resolution,[status(thm)],[1158, 2798])).
% 1.07/1.25 tff(2800,plain,
% 1.07/1.25 (~c0_1(a2528)),
% 1.07/1.25 inference(unit_resolution,[status(thm)],[1137, 2798])).
% 1.07/1.25 tff(2801,plain,
% 1.07/1.25 (c3_1(a2528)),
% 1.07/1.25 inference(unit_resolution,[status(thm)],[1145, 2798])).
% 1.07/1.25 tff(2802,plain,
% 1.07/1.25 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp5 | c0_1(a2528) | c1_1(a2528) | (~ndr1_0) | (~c2_1(a2558)) | (~c0_1(a2558)) | (~c1_1(a2558)) | (~c3_1(a2528)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp5 | c0_1(a2528) | c1_1(a2528) | (~ndr1_0) | (~c2_1(a2558)) | (~c0_1(a2558)) | (~c1_1(a2558)) | (~c3_1(a2528)))),
% 1.07/1.25 inference(rewrite,[status(thm)],[])).
% 1.07/1.25 tff(2803,plain,
% 1.07/1.25 ((hskp5 | (~ndr1_0) | (~c1_1(a2558)) | (~c0_1(a2558)) | (~c2_1(a2558)) | c1_1(a2528) | c0_1(a2528) | (~c3_1(a2528))) <=> (hskp5 | c0_1(a2528) | c1_1(a2528) | (~ndr1_0) | (~c2_1(a2558)) | (~c0_1(a2558)) | (~c1_1(a2558)) | (~c3_1(a2528)))),
% 1.07/1.25 inference(rewrite,[status(thm)],[])).
% 1.07/1.25 tff(2804,plain,
% 1.07/1.25 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp5 | (~ndr1_0) | (~c1_1(a2558)) | (~c0_1(a2558)) | (~c2_1(a2558)) | c1_1(a2528) | c0_1(a2528) | (~c3_1(a2528)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp5 | c0_1(a2528) | c1_1(a2528) | (~ndr1_0) | (~c2_1(a2558)) | (~c0_1(a2558)) | (~c1_1(a2558)) | (~c3_1(a2528))))),
% 1.07/1.25 inference(monotonicity,[status(thm)],[2803])).
% 1.07/1.25 tff(2805,plain,
% 1.07/1.25 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp5 | (~ndr1_0) | (~c1_1(a2558)) | (~c0_1(a2558)) | (~c2_1(a2558)) | c1_1(a2528) | c0_1(a2528) | (~c3_1(a2528)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp5 | c0_1(a2528) | c1_1(a2528) | (~ndr1_0) | (~c2_1(a2558)) | (~c0_1(a2558)) | (~c1_1(a2558)) | (~c3_1(a2528)))),
% 1.07/1.25 inference(transitivity,[status(thm)],[2804, 2802])).
% 1.07/1.25 tff(2806,plain,
% 1.07/1.25 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp5 | (~ndr1_0) | (~c1_1(a2558)) | (~c0_1(a2558)) | (~c2_1(a2558)) | c1_1(a2528) | c0_1(a2528) | (~c3_1(a2528)))),
% 1.07/1.25 inference(quant_inst,[status(thm)],[])).
% 1.07/1.25 tff(2807,plain,
% 1.07/1.25 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp5 | c0_1(a2528) | c1_1(a2528) | (~ndr1_0) | (~c2_1(a2558)) | (~c0_1(a2558)) | (~c1_1(a2558)) | (~c3_1(a2528))),
% 1.07/1.25 inference(modus_ponens,[status(thm)],[2806, 2805])).
% 1.07/1.25 tff(2808,plain,
% 1.07/1.25 (hskp5),
% 1.07/1.25 inference(unit_resolution,[status(thm)],[2807, 90, 2425, 2417, 2409, 2801, 2800, 2799, 2449])).
% 1.07/1.25 tff(2809,plain,
% 1.07/1.25 (~c0_1(a2522)),
% 1.07/1.25 inference(unit_resolution,[status(thm)],[2462, 2808])).
% 1.07/1.25 tff(2810,plain,
% 1.07/1.25 (c3_1(a2522)),
% 1.07/1.25 inference(unit_resolution,[status(thm)],[2550, 2808])).
% 1.07/1.25 tff(2811,plain,
% 1.07/1.25 (c2_1(a2522)),
% 1.07/1.25 inference(unit_resolution,[status(thm)],[2478, 2808])).
% 1.07/1.25 tff(2812,plain,
% 1.07/1.25 (hskp1),
% 1.07/1.25 inference(unit_resolution,[status(thm)],[382, 2787])).
% 1.07/1.25 tff(2813,plain,
% 1.07/1.25 (~c3_1(a2517)),
% 1.07/1.25 inference(unit_resolution,[status(thm)],[388, 2812])).
% 1.07/1.25 tff(2814,plain,
% 1.07/1.25 (c2_1(a2517)),
% 1.07/1.25 inference(unit_resolution,[status(thm)],[402, 2812])).
% 1.07/1.25 tff(2815,plain,
% 1.07/1.25 (~c0_1(a2517)),
% 1.07/1.25 inference(unit_resolution,[status(thm)],[394, 2812])).
% 1.07/1.25 tff(2816,plain,
% 1.07/1.25 (hskp29),
% 1.07/1.25 inference(unit_resolution,[status(thm)],[445, 2815, 2786, 2784, 2785, 2814, 2813])).
% 1.07/1.25 tff(2817,plain,
% 1.07/1.25 (c3_1(a2556)),
% 1.07/1.25 inference(unit_resolution,[status(thm)],[339, 2816])).
% 1.07/1.25 tff(2818,plain,
% 1.07/1.25 (c2_1(a2556)),
% 1.07/1.25 inference(unit_resolution,[status(thm)],[347, 2816])).
% 1.07/1.25 tff(2819,plain,
% 1.07/1.25 (c1_1(a2556)),
% 1.07/1.25 inference(unit_resolution,[status(thm)],[355, 2816])).
% 1.07/1.25 tff(2820,plain,
% 1.07/1.25 (hskp31),
% 1.07/1.25 inference(unit_resolution,[status(thm)],[530, 1, 90, 2819, 2818, 2817, 524])).
% 1.07/1.25 tff(2821,plain,
% 1.07/1.25 (c3_1(a2597)),
% 1.07/1.25 inference(unit_resolution,[status(thm)],[538, 2820])).
% 1.07/1.25 tff(2822,plain,
% 1.07/1.25 (c1_1(a2597)),
% 1.07/1.25 inference(unit_resolution,[status(thm)],[546, 2820])).
% 1.07/1.25 tff(2823,plain,
% 1.07/1.25 (c0_1(a2597)),
% 1.07/1.25 inference(unit_resolution,[status(thm)],[554, 2820])).
% 1.07/1.25 tff(2824,plain,
% 1.07/1.25 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp14 | c0_1(a2522) | (~ndr1_0) | (~c0_1(a2597)) | (~c3_1(a2597)) | (~c1_1(a2597)) | (~c2_1(a2522)) | (~c3_1(a2522)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp14 | c0_1(a2522) | (~ndr1_0) | (~c0_1(a2597)) | (~c3_1(a2597)) | (~c1_1(a2597)) | (~c2_1(a2522)) | (~c3_1(a2522)))),
% 1.07/1.25 inference(rewrite,[status(thm)],[])).
% 1.07/1.25 tff(2825,plain,
% 1.07/1.25 ((hskp14 | (~ndr1_0) | (~c3_1(a2597)) | (~c1_1(a2597)) | (~c0_1(a2597)) | c0_1(a2522) | (~c3_1(a2522)) | (~c2_1(a2522))) <=> (hskp14 | c0_1(a2522) | (~ndr1_0) | (~c0_1(a2597)) | (~c3_1(a2597)) | (~c1_1(a2597)) | (~c2_1(a2522)) | (~c3_1(a2522)))),
% 1.07/1.25 inference(rewrite,[status(thm)],[])).
% 1.07/1.25 tff(2826,plain,
% 1.07/1.25 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp14 | (~ndr1_0) | (~c3_1(a2597)) | (~c1_1(a2597)) | (~c0_1(a2597)) | c0_1(a2522) | (~c3_1(a2522)) | (~c2_1(a2522)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp14 | c0_1(a2522) | (~ndr1_0) | (~c0_1(a2597)) | (~c3_1(a2597)) | (~c1_1(a2597)) | (~c2_1(a2522)) | (~c3_1(a2522))))),
% 1.07/1.25 inference(monotonicity,[status(thm)],[2825])).
% 1.07/1.25 tff(2827,plain,
% 1.07/1.25 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp14 | (~ndr1_0) | (~c3_1(a2597)) | (~c1_1(a2597)) | (~c0_1(a2597)) | c0_1(a2522) | (~c3_1(a2522)) | (~c2_1(a2522)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp14 | c0_1(a2522) | (~ndr1_0) | (~c0_1(a2597)) | (~c3_1(a2597)) | (~c1_1(a2597)) | (~c2_1(a2522)) | (~c3_1(a2522)))),
% 1.07/1.25 inference(transitivity,[status(thm)],[2826, 2824])).
% 1.07/1.25 tff(2828,plain,
% 1.07/1.25 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp14 | (~ndr1_0) | (~c3_1(a2597)) | (~c1_1(a2597)) | (~c0_1(a2597)) | c0_1(a2522) | (~c3_1(a2522)) | (~c2_1(a2522)))),
% 1.07/1.25 inference(quant_inst,[status(thm)],[])).
% 1.07/1.25 tff(2829,plain,
% 1.07/1.25 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp14 | c0_1(a2522) | (~ndr1_0) | (~c0_1(a2597)) | (~c3_1(a2597)) | (~c1_1(a2597)) | (~c2_1(a2522)) | (~c3_1(a2522))),
% 1.07/1.25 inference(modus_ponens,[status(thm)],[2828, 2827])).
% 1.07/1.25 tff(2830,plain,
% 1.07/1.25 (hskp14),
% 1.07/1.25 inference(unit_resolution,[status(thm)],[2829, 90, 2823, 2822, 2821, 2811, 2810, 2809, 2797])).
% 1.07/1.25 tff(2831,plain,
% 1.07/1.25 (~c3_1(a2536)),
% 1.07/1.25 inference(unit_resolution,[status(thm)],[484, 2830])).
% 1.07/1.25 tff(2832,plain,
% 1.07/1.25 (~c1_1(a2536)),
% 1.07/1.25 inference(unit_resolution,[status(thm)],[490, 2830])).
% 1.07/1.25 tff(2833,plain,
% 1.07/1.25 (~c0_1(a2536)),
% 1.07/1.25 inference(unit_resolution,[status(thm)],[496, 2830])).
% 1.07/1.25 tff(2834,plain,
% 1.07/1.25 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (c3_1(a2614) | c0_1(a2536) | c1_1(a2536) | c3_1(a2536) | (~ndr1_0) | (~c2_1(a2558)) | (~c0_1(a2558)) | (~c1_1(a2558)) | c0_1(a2614) | (~c1_1(a2614)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c3_1(a2614) | c0_1(a2536) | c1_1(a2536) | c3_1(a2536) | (~ndr1_0) | (~c2_1(a2558)) | (~c0_1(a2558)) | (~c1_1(a2558)) | c0_1(a2614) | (~c1_1(a2614)))),
% 1.07/1.25 inference(rewrite,[status(thm)],[])).
% 1.07/1.25 tff(2835,plain,
% 1.07/1.25 (((~ndr1_0) | (~c1_1(a2558)) | (~c0_1(a2558)) | (~c2_1(a2558)) | c3_1(a2614) | c0_1(a2614) | (~c1_1(a2614)) | c3_1(a2536) | c1_1(a2536) | c0_1(a2536)) <=> (c3_1(a2614) | c0_1(a2536) | c1_1(a2536) | c3_1(a2536) | (~ndr1_0) | (~c2_1(a2558)) | (~c0_1(a2558)) | (~c1_1(a2558)) | c0_1(a2614) | (~c1_1(a2614)))),
% 1.07/1.25 inference(rewrite,[status(thm)],[])).
% 1.07/1.25 tff(2836,plain,
% 1.07/1.25 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c1_1(a2558)) | (~c0_1(a2558)) | (~c2_1(a2558)) | c3_1(a2614) | c0_1(a2614) | (~c1_1(a2614)) | c3_1(a2536) | c1_1(a2536) | c0_1(a2536))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (c3_1(a2614) | c0_1(a2536) | c1_1(a2536) | c3_1(a2536) | (~ndr1_0) | (~c2_1(a2558)) | (~c0_1(a2558)) | (~c1_1(a2558)) | c0_1(a2614) | (~c1_1(a2614))))),
% 1.07/1.25 inference(monotonicity,[status(thm)],[2835])).
% 1.07/1.25 tff(2837,plain,
% 1.07/1.25 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c1_1(a2558)) | (~c0_1(a2558)) | (~c2_1(a2558)) | c3_1(a2614) | c0_1(a2614) | (~c1_1(a2614)) | c3_1(a2536) | c1_1(a2536) | c0_1(a2536))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c3_1(a2614) | c0_1(a2536) | c1_1(a2536) | c3_1(a2536) | (~ndr1_0) | (~c2_1(a2558)) | (~c0_1(a2558)) | (~c1_1(a2558)) | c0_1(a2614) | (~c1_1(a2614)))),
% 1.07/1.25 inference(transitivity,[status(thm)],[2836, 2834])).
% 1.07/1.25 tff(2838,plain,
% 1.07/1.25 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c1_1(a2558)) | (~c0_1(a2558)) | (~c2_1(a2558)) | c3_1(a2614) | c0_1(a2614) | (~c1_1(a2614)) | c3_1(a2536) | c1_1(a2536) | c0_1(a2536))),
% 1.07/1.25 inference(quant_inst,[status(thm)],[])).
% 1.07/1.25 tff(2839,plain,
% 1.07/1.25 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c3_1(a2614) | c0_1(a2536) | c1_1(a2536) | c3_1(a2536) | (~ndr1_0) | (~c2_1(a2558)) | (~c0_1(a2558)) | (~c1_1(a2558)) | c0_1(a2614) | (~c1_1(a2614))),
% 1.07/1.25 inference(modus_ponens,[status(thm)],[2838, 2837])).
% 1.07/1.25 tff(2840,plain,
% 1.07/1.25 ($false),
% 1.07/1.25 inference(unit_resolution,[status(thm)],[2839, 90, 2425, 2417, 2409, 13, 20, 2833, 2832, 2831, 459, 2787])).
% 1.07/1.25 tff(2841,plain,(hskp23), inference(lemma,lemma(discharge,[]))).
% 1.07/1.25 tff(2842,plain,
% 1.07/1.25 (~c1_1(a2553)),
% 1.07/1.25 inference(unit_resolution,[status(thm)],[785, 2841])).
% 1.07/1.25 tff(2843,plain,
% 1.07/1.25 (~c3_1(a2553)),
% 1.07/1.25 inference(unit_resolution,[status(thm)],[769, 2841])).
% 1.07/1.25 tff(2844,plain,
% 1.07/1.25 (hskp21),
% 1.07/1.25 inference(unit_resolution,[status(thm)],[2699, 1968, 850, 849])).
% 1.07/1.25 tff(2845,plain,
% 1.07/1.25 (c1_1(a2551)),
% 1.07/1.25 inference(unit_resolution,[status(thm)],[176, 2844])).
% 1.07/1.25 tff(2846,plain,
% 1.07/1.25 (c0_1(a2551)),
% 1.07/1.25 inference(unit_resolution,[status(thm)],[184, 2844])).
% 1.07/1.25 tff(2847,plain,
% 1.07/1.25 (~c2_1(a2551)),
% 1.07/1.25 inference(unit_resolution,[status(thm)],[168, 2844])).
% 1.07/1.25 tff(2848,plain,
% 1.07/1.25 ($false),
% 1.07/1.25 inference(unit_resolution,[status(thm)],[763, 2847, 2846, 2781, 1969, 2845, 2780, 2782])).
% 1.07/1.25 tff(2849,plain,(c0_1(a2553) | c1_1(a2553) | c3_1(a2553)), inference(lemma,lemma(discharge,[]))).
% 1.07/1.25 tff(2850,plain,
% 1.07/1.25 (c0_1(a2553)),
% 1.07/1.25 inference(unit_resolution,[status(thm)],[2849, 849, 850])).
% 1.07/1.25 tff(2851,plain,
% 1.07/1.25 (hskp29 | hskp2 | c3_1(a2553) | (~c0_1(a2553))),
% 1.07/1.25 inference(unit_resolution,[status(thm)],[1436, 90, 850, 1430])).
% 1.07/1.25 tff(2852,plain,
% 1.07/1.25 (hskp29),
% 1.07/1.25 inference(unit_resolution,[status(thm)],[2851, 838, 2850, 849])).
% 1.07/1.25 tff(2853,plain,
% 1.07/1.25 (c3_1(a2556)),
% 1.07/1.25 inference(unit_resolution,[status(thm)],[339, 2852])).
% 1.07/1.25 tff(2854,plain,
% 1.07/1.25 (c1_1(a2556)),
% 1.07/1.25 inference(unit_resolution,[status(thm)],[355, 2852])).
% 1.07/1.25 tff(2855,plain,
% 1.07/1.25 (c2_1(a2556)),
% 1.07/1.25 inference(unit_resolution,[status(thm)],[347, 2852])).
% 1.07/1.25 tff(2856,plain,
% 1.07/1.25 (hskp17),
% 1.07/1.25 inference(unit_resolution,[status(thm)],[1540, 838, 2782, 2781, 2780, 2850, 850, 849])).
% 1.07/1.25 tff(2857,plain,
% 1.07/1.25 (~c2_1(a2541)),
% 1.07/1.25 inference(unit_resolution,[status(thm)],[238, 2856])).
% 1.07/1.25 tff(2858,plain,
% 1.07/1.25 (c3_1(a2541)),
% 1.07/1.25 inference(unit_resolution,[status(thm)],[252, 2856])).
% 1.07/1.25 tff(2859,plain,
% 1.07/1.25 (~c1_1(a2541)),
% 1.07/1.25 inference(unit_resolution,[status(thm)],[244, 2856])).
% 1.07/1.25 tff(2860,plain,
% 1.07/1.25 ($false),
% 1.07/1.25 inference(unit_resolution,[status(thm)],[1524, 2859, 2858, 850, 2850, 849, 2857, 2855, 2854, 2853, 2781, 2780, 2782])).
% 1.07/1.25 tff(2861,plain,(hskp2 | c1_1(a2553) | c3_1(a2553)), inference(lemma,lemma(discharge,[]))).
% 1.07/1.25 tff(2862,plain,
% 1.07/1.25 (hskp2),
% 1.07/1.25 inference(unit_resolution,[status(thm)],[2861, 849, 850])).
% 1.07/1.25 tff(2863,plain,
% 1.07/1.25 (~c3_1(a2518)),
% 1.07/1.25 inference(unit_resolution,[status(thm)],[892, 2862])).
% 1.07/1.25 tff(2864,plain,
% 1.07/1.25 (~c0_1(a2518)),
% 1.07/1.25 inference(unit_resolution,[status(thm)],[898, 2862])).
% 1.07/1.25 tff(2865,assumption,(~c2_1(a2518)), introduced(assumption)).
% 1.07/1.25 tff(2866,plain,
% 1.07/1.25 (c1_1(a2518)),
% 1.07/1.25 inference(unit_resolution,[status(thm)],[906, 2862])).
% 1.07/1.25 tff(2867,plain,
% 1.07/1.25 (hskp10 | c2_1(a2518)),
% 1.07/1.25 inference(unit_resolution,[status(thm)],[2181, 90, 2866, 2864, 2863, 1846])).
% 1.07/1.25 tff(2868,plain,
% 1.07/1.25 (hskp10),
% 1.07/1.25 inference(unit_resolution,[status(thm)],[2867, 2865])).
% 1.07/1.25 tff(2869,plain,
% 1.07/1.25 (~c0_1(a2528)),
% 1.07/1.25 inference(unit_resolution,[status(thm)],[1137, 2868])).
% 1.07/1.25 tff(2870,plain,
% 1.07/1.25 (hskp17 | c2_1(a2518)),
% 1.07/1.25 inference(unit_resolution,[status(thm)],[913, 90, 2782, 2781, 2866, 2780, 2863, 226])).
% 1.07/1.25 tff(2871,plain,
% 1.07/1.25 (hskp17),
% 1.07/1.25 inference(unit_resolution,[status(thm)],[2870, 2865])).
% 1.07/1.25 tff(2872,plain,
% 1.07/1.25 (~c1_1(a2541)),
% 1.07/1.25 inference(unit_resolution,[status(thm)],[244, 2871])).
% 1.07/1.25 tff(2873,plain,
% 1.07/1.25 (~c1_1(a2528)),
% 1.07/1.25 inference(unit_resolution,[status(thm)],[1158, 2868])).
% 1.07/1.25 tff(2874,plain,
% 1.07/1.25 (c3_1(a2528)),
% 1.07/1.25 inference(unit_resolution,[status(thm)],[1145, 2868])).
% 1.07/1.25 tff(2875,plain,
% 1.07/1.25 (c3_1(a2541)),
% 1.07/1.25 inference(unit_resolution,[status(thm)],[252, 2871])).
% 1.07/1.25 tff(2876,plain,
% 1.07/1.25 (~c2_1(a2541)),
% 1.07/1.25 inference(unit_resolution,[status(thm)],[238, 2871])).
% 1.07/1.25 tff(2877,plain,
% 1.07/1.25 (hskp29),
% 1.07/1.25 inference(unit_resolution,[status(thm)],[1418, 2876, 2875, 2874, 2873, 2872, 2869])).
% 1.07/1.25 tff(2878,plain,
% 1.07/1.25 (c2_1(a2556)),
% 1.07/1.25 inference(unit_resolution,[status(thm)],[347, 2877])).
% 1.07/1.25 tff(2879,plain,
% 1.07/1.25 (c1_1(a2556)),
% 1.07/1.25 inference(unit_resolution,[status(thm)],[355, 2877])).
% 1.07/1.25 tff(2880,plain,
% 1.07/1.25 (c3_1(a2556)),
% 1.07/1.25 inference(unit_resolution,[status(thm)],[339, 2877])).
% 1.07/1.25 tff(2881,plain,
% 1.07/1.25 ($false),
% 1.07/1.25 inference(unit_resolution,[status(thm)],[2203, 2880, 2879, 2780, 2781, 850, 849, 2850, 2871, 2878, 2782])).
% 1.07/1.25 tff(2882,plain,(c2_1(a2518) | c1_1(a2553) | c3_1(a2553)), inference(lemma,lemma(discharge,[]))).
% 1.07/1.25 tff(2883,plain,
% 1.07/1.25 (c2_1(a2518)),
% 1.07/1.25 inference(unit_resolution,[status(thm)],[2882, 849, 850])).
% 1.07/1.25 tff(2884,plain,
% 1.07/1.25 (hskp29),
% 1.07/1.25 inference(unit_resolution,[status(thm)],[2193, 2756, 2780, 2781, 2782, 2755, 1829, 2850, 849, 850, 2754])).
% 1.07/1.26 tff(2885,plain,
% 1.07/1.26 (c2_1(a2556)),
% 1.07/1.26 inference(unit_resolution,[status(thm)],[347, 2884])).
% 1.07/1.26 tff(2886,plain,
% 1.07/1.26 (~c2_1(a2518)),
% 1.07/1.26 inference(unit_resolution,[status(thm)],[2174, 2755, 2864, 2756, 2754, 1829, 2850, 849, 850, 2863, 2866])).
% 1.07/1.26 tff(2887,plain,
% 1.07/1.26 (hskp17),
% 1.07/1.26 inference(unit_resolution,[status(thm)],[2870, 2886])).
% 1.07/1.26 tff(2888,plain,
% 1.07/1.26 (c1_1(a2556)),
% 1.07/1.26 inference(unit_resolution,[status(thm)],[355, 2884])).
% 1.07/1.26 tff(2889,plain,
% 1.07/1.26 (c3_1(a2556)),
% 1.07/1.26 inference(unit_resolution,[status(thm)],[339, 2884])).
% 1.07/1.26 tff(2890,plain,
% 1.07/1.26 ($false),
% 1.07/1.26 inference(unit_resolution,[status(thm)],[2203, 2889, 2888, 2780, 2781, 850, 849, 2850, 2887, 2885, 2782])).
% 1.07/1.26 tff(2891,plain,(hskp21 | c1_1(a2553) | c3_1(a2553)), inference(lemma,lemma(discharge,[]))).
% 1.07/1.26 tff(2892,plain,
% 1.07/1.26 (hskp21),
% 1.07/1.26 inference(unit_resolution,[status(thm)],[2891, 849, 850])).
% 1.07/1.26 tff(2893,plain,
% 1.07/1.26 (~c2_1(a2551)),
% 1.07/1.26 inference(unit_resolution,[status(thm)],[168, 2892])).
% 1.07/1.26 tff(2894,plain,
% 1.07/1.26 (c1_1(a2551)),
% 1.07/1.26 inference(unit_resolution,[status(thm)],[176, 2892])).
% 1.07/1.26 tff(2895,plain,
% 1.07/1.26 (c0_1(a2551)),
% 1.07/1.26 inference(unit_resolution,[status(thm)],[184, 2892])).
% 1.07/1.26 tff(2896,plain,
% 1.07/1.26 (hskp14 | (~c2_1(a2518))),
% 1.07/1.26 inference(unit_resolution,[status(thm)],[920, 90, 2895, 2894, 2893, 2864, 2863, 469])).
% 1.07/1.26 tff(2897,plain,
% 1.07/1.26 (hskp14),
% 1.07/1.26 inference(unit_resolution,[status(thm)],[2896, 2883])).
% 1.07/1.26 tff(2898,plain,
% 1.07/1.26 (~c3_1(a2536)),
% 1.07/1.26 inference(unit_resolution,[status(thm)],[484, 2897])).
% 1.07/1.26 tff(2899,plain,
% 1.07/1.26 (~c1_1(a2536)),
% 1.07/1.26 inference(unit_resolution,[status(thm)],[490, 2897])).
% 1.07/1.26 tff(2900,plain,
% 1.07/1.26 (~c0_1(a2536)),
% 1.07/1.26 inference(unit_resolution,[status(thm)],[496, 2897])).
% 1.07/1.26 tff(2901,plain,
% 1.07/1.26 ($false),
% 1.07/1.26 inference(unit_resolution,[status(thm)],[2775, 90, 2425, 2417, 2409, 2866, 2900, 2899, 2898, 2864, 2863, 459])).
% 1.07/1.26 tff(2902,plain,(c3_1(a2553) | c1_1(a2553)), inference(lemma,lemma(discharge,[]))).
% 1.07/1.26 tff(2903,plain,
% 1.07/1.26 ($false),
% 1.07/1.26 inference(unit_resolution,[status(thm)],[2902, 2843, 2842])).
% 1.07/1.26 % SZS output end Proof
% 1.07/1.26 % E exiting
%------------------------------------------------------------------------------