%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN448-1 : TPTP v9.0.0. Released v2.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n001.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 05:39:09 AM UTC 2025
% Result : Unsatisfiable 0.53s 0.69s
% Output : Proof 0.69s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SYN448-1 : TPTP v9.0.0. Released v2.1.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n001.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 20 12:39:50 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.53/0.69 % SZS status Unsatisfiable
% 0.53/0.69 % SZS output start Proof
% 0.53/0.69 tff(hskp0_type, type, (
% 0.53/0.69 hskp0: $o)).
% 0.53/0.69 tff(c2_1_type, type, (
% 0.53/0.69 c2_1: $i > $o)).
% 0.53/0.69 tff(a460_type, type, (
% 0.53/0.69 a460: $i)).
% 0.53/0.69 tff(c1_1_type, type, (
% 0.53/0.69 c1_1: $i > $o)).
% 0.53/0.69 tff(a494_type, type, (
% 0.53/0.69 a494: $i)).
% 0.53/0.69 tff(hskp17_type, type, (
% 0.53/0.69 hskp17: $o)).
% 0.53/0.69 tff(c3_1_type, type, (
% 0.53/0.69 c3_1: $i > $o)).
% 0.53/0.69 tff(a476_type, type, (
% 0.53/0.69 a476: $i)).
% 0.53/0.69 tff(c0_1_type, type, (
% 0.53/0.69 c0_1: $i > $o)).
% 0.53/0.69 tff(ndr1_0_type, type, (
% 0.53/0.69 ndr1_0: $o)).
% 0.53/0.69 tff(hskp9_type, type, (
% 0.53/0.69 hskp9: $o)).
% 0.53/0.69 tff(a480_type, type, (
% 0.53/0.69 a480: $i)).
% 0.53/0.69 tff(a493_type, type, (
% 0.53/0.69 a493: $i)).
% 0.53/0.69 tff(a524_type, type, (
% 0.53/0.69 a524: $i)).
% 0.53/0.69 tff(hskp3_type, type, (
% 0.53/0.69 hskp3: $o)).
% 0.53/0.69 tff(hskp12_type, type, (
% 0.53/0.69 hskp12: $o)).
% 0.53/0.69 tff(a474_type, type, (
% 0.53/0.69 a474: $i)).
% 0.53/0.69 tff(a466_type, type, (
% 0.53/0.69 a466: $i)).
% 0.53/0.69 tff(a503_type, type, (
% 0.53/0.69 a503: $i)).
% 0.53/0.69 tff(hskp20_type, type, (
% 0.53/0.69 hskp20: $o)).
% 0.53/0.69 tff(hskp6_type, type, (
% 0.53/0.69 hskp6: $o)).
% 0.53/0.69 tff(hskp14_type, type, (
% 0.53/0.69 hskp14: $o)).
% 0.53/0.69 tff(a488_type, type, (
% 0.53/0.69 a488: $i)).
% 0.53/0.69 tff(a463_type, type, (
% 0.53/0.69 a463: $i)).
% 0.53/0.69 tff(hskp1_type, type, (
% 0.53/0.69 hskp1: $o)).
% 0.53/0.69 tff(hskp5_type, type, (
% 0.53/0.69 hskp5: $o)).
% 0.53/0.69 tff(a478_type, type, (
% 0.53/0.69 a478: $i)).
% 0.53/0.69 tff(hskp11_type, type, (
% 0.53/0.69 hskp11: $o)).
% 0.53/0.69 tff(a461_type, type, (
% 0.53/0.69 a461: $i)).
% 0.53/0.69 tff(hskp25_type, type, (
% 0.53/0.69 hskp25: $o)).
% 0.53/0.69 tff(hskp27_type, type, (
% 0.53/0.69 hskp27: $o)).
% 0.53/0.69 tff(a473_type, type, (
% 0.53/0.69 a473: $i)).
% 0.53/0.69 tff(hskp22_type, type, (
% 0.53/0.69 hskp22: $o)).
% 0.53/0.69 tff(a470_type, type, (
% 0.53/0.69 a470: $i)).
% 0.53/0.69 tff(hskp26_type, type, (
% 0.53/0.69 hskp26: $o)).
% 0.53/0.69 tff(a467_type, type, (
% 0.53/0.69 a467: $i)).
% 0.53/0.69 tff(hskp4_type, type, (
% 0.53/0.69 hskp4: $o)).
% 0.53/0.69 tff(hskp15_type, type, (
% 0.53/0.69 hskp15: $o)).
% 0.53/0.69 tff(a492_type, type, (
% 0.53/0.69 a492: $i)).
% 0.53/0.69 tff(a465_type, type, (
% 0.53/0.69 a465: $i)).
% 0.53/0.69 tff(hskp2_type, type, (
% 0.53/0.69 hskp2: $o)).
% 0.53/0.69 tff(hskp16_type, type, (
% 0.53/0.69 hskp16: $o)).
% 0.53/0.69 tff(a471_type, type, (
% 0.53/0.69 a471: $i)).
% 0.53/0.69 tff(a512_type, type, (
% 0.53/0.69 a512: $i)).
% 0.53/0.69 tff(hskp21_type, type, (
% 0.53/0.69 hskp21: $o)).
% 0.53/0.69 tff(a468_type, type, (
% 0.53/0.69 a468: $i)).
% 0.53/0.69 tff(hskp7_type, type, (
% 0.53/0.69 hskp7: $o)).
% 0.53/0.69 tff(a500_type, type, (
% 0.53/0.69 a500: $i)).
% 0.53/0.69 tff(hskp18_type, type, (
% 0.53/0.69 hskp18: $o)).
% 0.53/0.69 tff(a502_type, type, (
% 0.53/0.69 a502: $i)).
% 0.53/0.69 tff(hskp19_type, type, (
% 0.53/0.69 hskp19: $o)).
% 0.53/0.69 tff(hskp28_type, type, (
% 0.53/0.69 hskp28: $o)).
% 0.53/0.69 tff(a490_type, type, (
% 0.53/0.69 a490: $i)).
% 0.53/0.69 tff(1,assumption,(~c2_1(a460)), introduced(assumption)).
% 0.53/0.69 tff(2,plain,
% 0.53/0.69 (^[V: $i, U: $i] : refl((hskp17 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V))) <=> (hskp17 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V))))),
% 0.53/0.69 inference(bind,[status(th)],[])).
% 0.53/0.69 tff(3,plain,
% 0.53/0.69 (![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))),
% 0.53/0.69 inference(quant_intro,[status(thm)],[2])).
% 0.53/0.69 tff(4,plain,
% 0.53/0.69 (![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))),
% 0.53/0.69 inference(rewrite,[status(thm)],[])).
% 0.53/0.69 tff(5,plain,
% 0.53/0.69 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | (~c0_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | (~c0_1(V)) | (~c2_1(V)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | (~c0_1(V)) | (~c2_1(V))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c1_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | (~c0_1(V)) | (~c2_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | (~c0_1(V)) | (~c2_1(V))) | c1_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_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))) | (~c2_1(V))) | c1_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_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))) | (~c2_1(V))) | c1_1(V)) | hskp17) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V))) | hskp17))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V))) | hskp17) <=> (hskp17 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_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))) | (~c2_1(V))) | c1_1(V)) | hskp17) <=> (hskp17 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))))),
% 0.53/0.69 inference(bind,[status(th)],[])).
% 0.53/0.69 tff(6,plain,
% 0.53/0.69 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c1_1(V)) | hskp17) <=> ![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))),
% 0.53/0.69 inference(quant_intro,[status(thm)],[5])).
% 0.53/0.69 tff(7,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c1_1(V)) | hskp17)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause170')).
% 0.53/0.69 tff(8,plain,
% 0.53/0.69 (![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))),
% 0.53/0.69 inference(modus_ponens,[status(thm)],[7, 6])).
% 0.53/0.69 tff(9,plain,
% 0.53/0.69 (![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))),
% 0.53/0.69 inference(modus_ponens,[status(thm)],[8, 4])).
% 0.53/0.69 tff(10,plain,(
% 0.53/0.69 ![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))),
% 0.53/0.69 inference(skolemize,[status(sab)],[9])).
% 0.53/0.69 tff(11,plain,
% 0.53/0.69 (![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))),
% 0.53/0.69 inference(modus_ponens,[status(thm)],[10, 3])).
% 0.53/0.69 tff(12,plain,
% 0.53/0.69 (^[V: $i, U: $i] : refl((hskp3 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V))) <=> (hskp3 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V))))),
% 0.53/0.69 inference(bind,[status(th)],[])).
% 0.53/0.69 tff(13,plain,
% 0.53/0.69 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))),
% 0.53/0.69 inference(quant_intro,[status(thm)],[12])).
% 0.53/0.69 tff(14,plain,
% 0.53/0.69 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))),
% 0.53/0.69 inference(rewrite,[status(thm)],[])).
% 0.53/0.69 tff(15,plain,
% 0.53/0.69 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) <=> ((~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c0_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)))), rewrite((((~c0_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(V)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V))) | c2_1(V)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_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) | (~c0_1(U)) | (~c3_1(U)) | (~c1_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) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V))) | c3_1(V)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_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) | (~c0_1(U)) | (~c3_1(U)) | (~c1_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)) | hskp3) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V))) | hskp3))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V))) | hskp3) <=> (hskp3 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_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)) | hskp3) <=> (hskp3 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))))),
% 0.53/0.69 inference(bind,[status(th)],[])).
% 0.53/0.69 tff(16,plain,
% 0.53/0.69 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(V)) | c3_1(V)) | hskp3) <=> ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))),
% 0.53/0.69 inference(quant_intro,[status(thm)],[15])).
% 0.53/0.69 tff(17,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)) | hskp3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause166')).
% 0.53/0.69 tff(18,plain,
% 0.53/0.69 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))),
% 0.53/0.69 inference(modus_ponens,[status(thm)],[17, 16])).
% 0.53/0.69 tff(19,plain,
% 0.53/0.69 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))),
% 0.53/0.69 inference(modus_ponens,[status(thm)],[18, 14])).
% 0.53/0.69 tff(20,plain,(
% 0.53/0.69 ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))),
% 0.53/0.69 inference(skolemize,[status(sab)],[19])).
% 0.53/0.69 tff(21,plain,
% 0.53/0.69 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))),
% 0.53/0.69 inference(modus_ponens,[status(thm)],[20, 13])).
% 0.53/0.69 tff(22,assumption,(~hskp12), introduced(assumption)).
% 0.53/0.69 tff(23,plain,
% 0.53/0.69 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c2_1(W)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c2_1(W)))),
% 0.53/0.69 inference(bind,[status(th)],[])).
% 0.53/0.69 tff(24,plain,
% 0.53/0.69 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))),
% 0.53/0.69 inference(quant_intro,[status(thm)],[23])).
% 0.53/0.69 tff(25,plain,
% 0.53/0.69 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))),
% 0.53/0.69 inference(rewrite,[status(thm)],[])).
% 0.53/0.69 tff(26,plain,
% 0.53/0.69 (^[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)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c0_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(V)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(V))))), (((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)))), (((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V))))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V))))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V))))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V))))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V))) | c0_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V))) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W)))), ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c0_1(W)) | c1_1(W)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W)) | c1_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W))), ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W)))), (((((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W)) | c2_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))), (((((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))))),
% 0.53/0.69 inference(bind,[status(th)],[])).
% 0.53/0.69 tff(27,plain,
% 0.53/0.69 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))),
% 0.53/0.69 inference(quant_intro,[status(thm)],[26])).
% 0.53/0.69 tff(28,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause172')).
% 0.53/0.69 tff(29,plain,
% 0.53/0.69 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))),
% 0.53/0.69 inference(modus_ponens,[status(thm)],[28, 27])).
% 0.53/0.69 tff(30,plain,
% 0.53/0.69 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))),
% 0.53/0.69 inference(modus_ponens,[status(thm)],[29, 25])).
% 0.53/0.69 tff(31,plain,(
% 0.53/0.69 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))),
% 0.53/0.69 inference(skolemize,[status(sab)],[30])).
% 0.53/0.69 tff(32,plain,
% 0.53/0.69 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))),
% 0.53/0.69 inference(modus_ponens,[status(thm)],[31, 24])).
% 0.53/0.69 tff(33,assumption,(~hskp17), introduced(assumption)).
% 0.53/0.69 tff(34,assumption,(~hskp0), introduced(assumption)).
% 0.53/0.69 tff(35,plain,
% 0.53/0.69 (^[V: $i, U: $i] : refl((hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V))) <=> (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V))))),
% 0.53/0.69 inference(bind,[status(th)],[])).
% 0.53/0.69 tff(36,plain,
% 0.53/0.69 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))),
% 0.53/0.69 inference(quant_intro,[status(thm)],[35])).
% 0.53/0.69 tff(37,plain,
% 0.53/0.69 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))),
% 0.53/0.69 inference(rewrite,[status(thm)],[])).
% 0.53/0.69 tff(38,plain,
% 0.53/0.69 (^[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) | c2_1(U) | c3_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) | c3_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) | c2_1(U) | c3_1(U) | (~c0_1(U)) | (~c0_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | (~c0_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_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) | c2_1(U) | c3_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) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V))) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_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) | c2_1(U) | c3_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)) | hskp12) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V))) | hskp12))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V))) | hskp12) <=> (hskp12 | (~ndr1_0) | c2_1(U) | c3_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)) | hskp12) <=> (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))))),
% 0.53/0.69 inference(bind,[status(th)],[])).
% 0.53/0.69 tff(39,plain,
% 0.53/0.69 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c3_1(V)) | hskp12) <=> ![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))),
% 0.53/0.69 inference(quant_intro,[status(thm)],[38])).
% 0.53/0.69 tff(40,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)) | hskp12)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause151')).
% 0.53/0.69 tff(41,plain,
% 0.53/0.69 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))),
% 0.53/0.69 inference(modus_ponens,[status(thm)],[40, 39])).
% 0.53/0.69 tff(42,plain,
% 0.53/0.69 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))),
% 0.53/0.69 inference(modus_ponens,[status(thm)],[41, 37])).
% 0.53/0.69 tff(43,plain,(
% 0.53/0.69 ![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))),
% 0.53/0.69 inference(skolemize,[status(sab)],[42])).
% 0.53/0.69 tff(44,plain,
% 0.53/0.69 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))),
% 0.53/0.69 inference(modus_ponens,[status(thm)],[43, 36])).
% 0.53/0.69 tff(45,assumption,(hskp14), introduced(assumption)).
% 0.53/0.69 tff(46,plain,
% 0.53/0.69 (((~hskp14) | (~c3_1(a488))) <=> ((~hskp14) | (~c3_1(a488)))),
% 0.53/0.69 inference(rewrite,[status(thm)],[])).
% 0.53/0.69 tff(47,plain,
% 0.53/0.69 (((~c3_1(a488)) | (~hskp14)) <=> ((~hskp14) | (~c3_1(a488)))),
% 0.53/0.69 inference(rewrite,[status(thm)],[])).
% 0.53/0.69 tff(48,axiom,((~c3_1(a488)) | (~hskp14)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause100')).
% 0.53/0.69 tff(49,plain,
% 0.53/0.69 ((~hskp14) | (~c3_1(a488))),
% 0.53/0.69 inference(modus_ponens,[status(thm)],[48, 47])).
% 0.53/0.69 tff(50,plain,
% 0.53/0.69 ((~hskp14) | (~c3_1(a488))),
% 0.53/0.69 inference(modus_ponens,[status(thm)],[49, 46])).
% 0.53/0.69 tff(51,plain,
% 0.53/0.69 (~c3_1(a488)),
% 0.53/0.69 inference(unit_resolution,[status(thm)],[50, 45])).
% 0.53/0.69 tff(52,plain,
% 0.53/0.69 (((~hskp14) | (~c2_1(a488))) <=> ((~hskp14) | (~c2_1(a488)))),
% 0.53/0.69 inference(rewrite,[status(thm)],[])).
% 0.53/0.69 tff(53,plain,
% 0.53/0.69 (((~c2_1(a488)) | (~hskp14)) <=> ((~hskp14) | (~c2_1(a488)))),
% 0.53/0.69 inference(rewrite,[status(thm)],[])).
% 0.53/0.69 tff(54,axiom,((~c2_1(a488)) | (~hskp14)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause99')).
% 0.53/0.69 tff(55,plain,
% 0.53/0.69 ((~hskp14) | (~c2_1(a488))),
% 0.53/0.69 inference(modus_ponens,[status(thm)],[54, 53])).
% 0.53/0.69 tff(56,plain,
% 0.53/0.69 ((~hskp14) | (~c2_1(a488))),
% 0.53/0.69 inference(modus_ponens,[status(thm)],[55, 52])).
% 0.53/0.69 tff(57,plain,
% 0.53/0.69 (~c2_1(a488)),
% 0.53/0.69 inference(unit_resolution,[status(thm)],[56, 45])).
% 0.53/0.69 tff(58,plain,
% 0.53/0.69 (((~hskp14) | (~c1_1(a488))) <=> ((~hskp14) | (~c1_1(a488)))),
% 0.53/0.69 inference(rewrite,[status(thm)],[])).
% 0.53/0.69 tff(59,plain,
% 0.53/0.69 (((~c1_1(a488)) | (~hskp14)) <=> ((~hskp14) | (~c1_1(a488)))),
% 0.53/0.69 inference(rewrite,[status(thm)],[])).
% 0.53/0.69 tff(60,axiom,((~c1_1(a488)) | (~hskp14)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause98')).
% 0.53/0.69 tff(61,plain,
% 0.53/0.69 ((~hskp14) | (~c1_1(a488))),
% 0.53/0.69 inference(modus_ponens,[status(thm)],[60, 59])).
% 0.53/0.69 tff(62,plain,
% 0.53/0.69 ((~hskp14) | (~c1_1(a488))),
% 0.53/0.69 inference(modus_ponens,[status(thm)],[61, 58])).
% 0.53/0.69 tff(63,plain,
% 0.53/0.69 (~c1_1(a488)),
% 0.53/0.69 inference(unit_resolution,[status(thm)],[62, 45])).
% 0.53/0.69 tff(64,plain,
% 0.53/0.69 (^[V: $i, U: $i] : refl((hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c2_1(V)) <=> (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c2_1(V)))),
% 0.53/0.69 inference(bind,[status(th)],[])).
% 0.53/0.69 tff(65,plain,
% 0.53/0.69 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c2_1(V)) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))),
% 0.53/0.69 inference(quant_intro,[status(thm)],[64])).
% 0.53/0.69 tff(66,plain,
% 0.53/0.69 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c2_1(V)) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))),
% 0.53/0.69 inference(rewrite,[status(thm)],[])).
% 0.53/0.69 tff(67,plain,
% 0.53/0.69 (^[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)) | c2_1(V)) <=> (((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))), ((((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c2_1(V)))), (((((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp0) <=> (((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c2_1(V)) | hskp0))), rewrite((((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c2_1(V)) | hskp0) <=> (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))), (((((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp0) <=> (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))))),
% 0.53/0.70 inference(bind,[status(th)],[])).
% 0.53/0.70 tff(68,plain,
% 0.53/0.70 (![V: $i, U: $i] : ((((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp0) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))),
% 0.53/0.70 inference(quant_intro,[status(thm)],[67])).
% 0.53/0.70 tff(69,axiom,(![V: $i, U: $i] : ((((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp0)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause144')).
% 0.53/0.70 tff(70,plain,
% 0.53/0.70 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))),
% 0.53/0.70 inference(modus_ponens,[status(thm)],[69, 68])).
% 0.53/0.70 tff(71,plain,
% 0.53/0.70 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))),
% 0.53/0.70 inference(modus_ponens,[status(thm)],[70, 66])).
% 0.53/0.70 tff(72,plain,(
% 0.53/0.70 ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))),
% 0.53/0.70 inference(skolemize,[status(sab)],[71])).
% 0.53/0.70 tff(73,plain,
% 0.53/0.70 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))),
% 0.53/0.70 inference(modus_ponens,[status(thm)],[72, 65])).
% 0.53/0.70 tff(74,plain,
% 0.53/0.70 (^[U: $i] : refl((hskp1 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) <=> (hskp1 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)))),
% 0.53/0.70 inference(bind,[status(th)],[])).
% 0.53/0.70 tff(75,plain,
% 0.53/0.70 (![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) <=> ![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 0.53/0.70 inference(quant_intro,[status(thm)],[74])).
% 0.53/0.70 tff(76,plain,
% 0.53/0.70 (![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) <=> ![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 0.53/0.70 inference(rewrite,[status(thm)],[])).
% 0.53/0.70 tff(77,plain,
% 0.53/0.70 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ndr1_0) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U))), ((((~ndr1_0) | c0_1(U)) | 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))), ((((~ndr1_0) | c0_1(U)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U)))), (((((~ndr1_0) | c0_1(U)) | 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))), (((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)))), ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) | hskp0) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) | hskp0))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) | hskp0) <=> (hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))), ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) | hskp0) <=> (hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)))), (((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) | hskp0) | hskp1) <=> ((hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) | hskp1))), rewrite(((hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) | hskp1) <=> (hskp1 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))), (((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) | hskp0) | hskp1) <=> (hskp1 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))))),
% 0.53/0.70 inference(bind,[status(th)],[])).
% 0.53/0.70 tff(78,plain,
% 0.53/0.70 (![U: $i] : ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) | hskp0) | hskp1) <=> ![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 0.53/0.70 inference(quant_intro,[status(thm)],[77])).
% 0.53/0.70 tff(79,axiom,(![U: $i] : ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) | hskp0) | hskp1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause125')).
% 0.53/0.70 tff(80,plain,
% 0.53/0.70 (![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 0.53/0.70 inference(modus_ponens,[status(thm)],[79, 78])).
% 0.53/0.70 tff(81,plain,
% 0.53/0.70 (![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 0.53/0.70 inference(modus_ponens,[status(thm)],[80, 76])).
% 0.53/0.70 tff(82,plain,(
% 0.53/0.70 ![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 0.53/0.70 inference(skolemize,[status(sab)],[81])).
% 0.53/0.70 tff(83,plain,
% 0.53/0.70 (![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 0.53/0.70 inference(modus_ponens,[status(thm)],[82, 75])).
% 0.53/0.70 tff(84,assumption,(hskp12), introduced(assumption)).
% 0.53/0.70 tff(85,plain,
% 0.53/0.70 (((~hskp12) | (~c2_1(a480))) <=> ((~hskp12) | (~c2_1(a480)))),
% 0.53/0.70 inference(rewrite,[status(thm)],[])).
% 0.53/0.70 tff(86,plain,
% 0.53/0.70 (((~c2_1(a480)) | (~hskp12)) <=> ((~hskp12) | (~c2_1(a480)))),
% 0.53/0.70 inference(rewrite,[status(thm)],[])).
% 0.53/0.70 tff(87,axiom,((~c2_1(a480)) | (~hskp12)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause104')).
% 0.53/0.70 tff(88,plain,
% 0.53/0.70 ((~hskp12) | (~c2_1(a480))),
% 0.53/0.70 inference(modus_ponens,[status(thm)],[87, 86])).
% 0.53/0.70 tff(89,plain,
% 0.53/0.70 ((~hskp12) | (~c2_1(a480))),
% 0.53/0.70 inference(modus_ponens,[status(thm)],[88, 85])).
% 0.53/0.70 tff(90,plain,
% 0.53/0.70 (~c2_1(a480)),
% 0.53/0.70 inference(unit_resolution,[status(thm)],[89, 84])).
% 0.53/0.70 tff(91,plain,
% 0.53/0.70 (((~hskp12) | (~c1_1(a480))) <=> ((~hskp12) | (~c1_1(a480)))),
% 0.53/0.70 inference(rewrite,[status(thm)],[])).
% 0.53/0.70 tff(92,plain,
% 0.53/0.70 (((~c1_1(a480)) | (~hskp12)) <=> ((~hskp12) | (~c1_1(a480)))),
% 0.53/0.70 inference(rewrite,[status(thm)],[])).
% 0.53/0.70 tff(93,axiom,((~c1_1(a480)) | (~hskp12)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause103')).
% 0.53/0.70 tff(94,plain,
% 0.53/0.70 ((~hskp12) | (~c1_1(a480))),
% 0.53/0.70 inference(modus_ponens,[status(thm)],[93, 92])).
% 0.53/0.70 tff(95,plain,
% 0.53/0.70 ((~hskp12) | (~c1_1(a480))),
% 0.53/0.70 inference(modus_ponens,[status(thm)],[94, 91])).
% 0.53/0.70 tff(96,plain,
% 0.53/0.70 (~c1_1(a480)),
% 0.53/0.70 inference(unit_resolution,[status(thm)],[95, 84])).
% 0.53/0.70 tff(97,plain,
% 0.53/0.70 (((~hskp12) | (~c0_1(a480))) <=> ((~hskp12) | (~c0_1(a480)))),
% 0.53/0.70 inference(rewrite,[status(thm)],[])).
% 0.53/0.70 tff(98,plain,
% 0.53/0.70 (((~c0_1(a480)) | (~hskp12)) <=> ((~hskp12) | (~c0_1(a480)))),
% 0.53/0.70 inference(rewrite,[status(thm)],[])).
% 0.53/0.70 tff(99,axiom,((~c0_1(a480)) | (~hskp12)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause102')).
% 0.53/0.70 tff(100,plain,
% 0.53/0.70 ((~hskp12) | (~c0_1(a480))),
% 0.53/0.70 inference(modus_ponens,[status(thm)],[99, 98])).
% 0.53/0.70 tff(101,plain,
% 0.53/0.70 ((~hskp12) | (~c0_1(a480))),
% 0.53/0.70 inference(modus_ponens,[status(thm)],[100, 97])).
% 0.53/0.70 tff(102,plain,
% 0.53/0.70 (~c0_1(a480)),
% 0.53/0.70 inference(unit_resolution,[status(thm)],[101, 84])).
% 0.53/0.70 tff(103,assumption,(~hskp5), introduced(assumption)).
% 0.53/0.70 tff(104,plain,
% 0.53/0.70 ((hskp5 | hskp11) <=> (hskp5 | hskp11)),
% 0.53/0.70 inference(rewrite,[status(thm)],[])).
% 0.53/0.70 tff(105,axiom,(hskp5 | hskp11), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause1')).
% 0.53/0.70 tff(106,plain,
% 0.53/0.70 (hskp5 | hskp11),
% 0.53/0.70 inference(modus_ponens,[status(thm)],[105, 104])).
% 0.53/0.70 tff(107,plain,
% 0.53/0.70 (hskp5 | hskp11),
% 0.53/0.70 inference(modus_ponens,[status(thm)],[106, 104])).
% 0.53/0.70 tff(108,plain,
% 0.53/0.70 (hskp5 | hskp11),
% 0.53/0.70 inference(modus_ponens,[status(thm)],[107, 104])).
% 0.53/0.70 tff(109,plain,
% 0.53/0.70 (hskp5 | hskp11),
% 0.53/0.70 inference(modus_ponens,[status(thm)],[108, 104])).
% 0.53/0.70 tff(110,plain,
% 0.53/0.70 (hskp5 | hskp11),
% 0.53/0.70 inference(modus_ponens,[status(thm)],[109, 104])).
% 0.53/0.70 tff(111,plain,
% 0.53/0.70 (hskp11),
% 0.53/0.70 inference(unit_resolution,[status(thm)],[110, 103])).
% 0.53/0.70 tff(112,plain,
% 0.53/0.70 (((~hskp11) | (~c3_1(a478))) <=> ((~hskp11) | (~c3_1(a478)))),
% 0.53/0.70 inference(rewrite,[status(thm)],[])).
% 0.53/0.70 tff(113,plain,
% 0.53/0.70 (((~c3_1(a478)) | (~hskp11)) <=> ((~hskp11) | (~c3_1(a478)))),
% 0.53/0.70 inference(rewrite,[status(thm)],[])).
% 0.53/0.70 tff(114,axiom,((~c3_1(a478)) | (~hskp11)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause106')).
% 0.53/0.70 tff(115,plain,
% 0.53/0.70 ((~hskp11) | (~c3_1(a478))),
% 0.53/0.70 inference(modus_ponens,[status(thm)],[114, 113])).
% 0.53/0.70 tff(116,plain,
% 0.53/0.70 ((~hskp11) | (~c3_1(a478))),
% 0.53/0.70 inference(modus_ponens,[status(thm)],[115, 112])).
% 0.53/0.70 tff(117,plain,
% 0.53/0.70 (~c3_1(a478)),
% 0.53/0.70 inference(unit_resolution,[status(thm)],[116, 111])).
% 0.53/0.70 tff(118,plain,
% 0.53/0.70 (((~hskp11) | (~c0_1(a478))) <=> ((~hskp11) | (~c0_1(a478)))),
% 0.53/0.70 inference(rewrite,[status(thm)],[])).
% 0.53/0.70 tff(119,plain,
% 0.53/0.70 (((~c0_1(a478)) | (~hskp11)) <=> ((~hskp11) | (~c0_1(a478)))),
% 0.53/0.70 inference(rewrite,[status(thm)],[])).
% 0.53/0.70 tff(120,axiom,((~c0_1(a478)) | (~hskp11)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause105')).
% 0.53/0.70 tff(121,plain,
% 0.53/0.70 ((~hskp11) | (~c0_1(a478))),
% 0.53/0.70 inference(modus_ponens,[status(thm)],[120, 119])).
% 0.53/0.70 tff(122,plain,
% 0.53/0.70 ((~hskp11) | (~c0_1(a478))),
% 0.53/0.70 inference(modus_ponens,[status(thm)],[121, 118])).
% 0.53/0.70 tff(123,plain,
% 0.53/0.70 (~c0_1(a478)),
% 0.53/0.70 inference(unit_resolution,[status(thm)],[122, 111])).
% 0.53/0.70 tff(124,plain,
% 0.53/0.70 (((~hskp11) | c2_1(a478)) <=> ((~hskp11) | c2_1(a478))),
% 0.53/0.70 inference(rewrite,[status(thm)],[])).
% 0.53/0.70 tff(125,axiom,((~hskp11) | c2_1(a478)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause67')).
% 0.53/0.70 tff(126,plain,
% 0.53/0.70 ((~hskp11) | c2_1(a478)),
% 0.53/0.70 inference(modus_ponens,[status(thm)],[125, 124])).
% 0.53/0.70 tff(127,plain,
% 0.53/0.70 ((~hskp11) | c2_1(a478)),
% 0.53/0.70 inference(modus_ponens,[status(thm)],[126, 124])).
% 0.53/0.70 tff(128,plain,
% 0.53/0.70 ((~hskp11) | c2_1(a478)),
% 0.53/0.70 inference(modus_ponens,[status(thm)],[127, 124])).
% 0.53/0.70 tff(129,plain,
% 0.53/0.70 ((~hskp11) | c2_1(a478)),
% 0.53/0.70 inference(modus_ponens,[status(thm)],[128, 124])).
% 0.53/0.70 tff(130,plain,
% 0.53/0.70 ((~hskp11) | c2_1(a478)),
% 0.53/0.70 inference(modus_ponens,[status(thm)],[129, 124])).
% 0.53/0.70 tff(131,plain,
% 0.53/0.70 (c2_1(a478)),
% 0.53/0.70 inference(unit_resolution,[status(thm)],[130, 111])).
% 0.53/0.70 tff(132,plain,
% 0.53/0.70 ((ndr1_0 | (~hskp11)) <=> (ndr1_0 | (~hskp11))),
% 0.53/0.70 inference(rewrite,[status(thm)],[])).
% 0.53/0.70 tff(133,plain,
% 0.53/0.70 (((~hskp11) | ndr1_0) <=> (ndr1_0 | (~hskp11))),
% 0.53/0.70 inference(rewrite,[status(thm)],[])).
% 0.53/0.70 tff(134,axiom,((~hskp11) | ndr1_0), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause19')).
% 0.53/0.70 tff(135,plain,
% 0.53/0.70 (ndr1_0 | (~hskp11)),
% 0.53/0.70 inference(modus_ponens,[status(thm)],[134, 133])).
% 0.53/0.70 tff(136,plain,
% 0.53/0.70 (ndr1_0 | (~hskp11)),
% 0.53/0.70 inference(modus_ponens,[status(thm)],[135, 132])).
% 0.53/0.70 tff(137,plain,
% 0.53/0.70 (ndr1_0),
% 0.53/0.70 inference(unit_resolution,[status(thm)],[136, 111])).
% 0.53/0.70 tff(138,assumption,(~c3_1(a478)), introduced(assumption)).
% 0.53/0.70 tff(139,assumption,(~c0_1(a478)), introduced(assumption)).
% 0.53/0.70 tff(140,assumption,(c2_1(a478)), introduced(assumption)).
% 0.53/0.70 tff(141,assumption,(ndr1_0), introduced(assumption)).
% 0.53/0.70 tff(142,plain,
% 0.53/0.70 (^[U: $i] : refl((hskp12 | hskp0 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))) <=> (hskp12 | hskp0 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))))),
% 0.53/0.70 inference(bind,[status(th)],[])).
% 0.53/0.70 tff(143,plain,
% 0.53/0.70 (![U: $i] : (hskp12 | hskp0 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))) <=> ![U: $i] : (hskp12 | hskp0 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))),
% 0.53/0.70 inference(quant_intro,[status(thm)],[142])).
% 0.53/0.70 tff(144,plain,
% 0.53/0.70 (![U: $i] : (hskp12 | hskp0 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))) <=> ![U: $i] : (hskp12 | hskp0 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))),
% 0.53/0.70 inference(rewrite,[status(thm)],[])).
% 0.53/0.70 tff(145,plain,
% 0.53/0.70 (^[U: $i] : 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)) | c3_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))), (((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))))), ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp0) <=> (((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))) | hskp0))), rewrite((((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))) | hskp0) <=> (hskp0 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))), ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp0) <=> (hskp0 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))))), (((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp0) | hskp12) <=> ((hskp0 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))) | hskp12))), rewrite(((hskp0 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))) | hskp12) <=> (hskp12 | hskp0 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))), (((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp0) | hskp12) <=> (hskp12 | hskp0 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))))),
% 0.53/0.70 inference(bind,[status(th)],[])).
% 0.53/0.70 tff(146,plain,
% 0.53/0.70 (![U: $i] : ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp0) | hskp12) <=> ![U: $i] : (hskp12 | hskp0 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))),
% 0.53/0.70 inference(quant_intro,[status(thm)],[145])).
% 0.53/0.70 tff(147,axiom,(![U: $i] : ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp0) | hskp12)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause128')).
% 0.53/0.70 tff(148,plain,
% 0.53/0.70 (![U: $i] : (hskp12 | hskp0 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))),
% 0.53/0.70 inference(modus_ponens,[status(thm)],[147, 146])).
% 0.53/0.70 tff(149,plain,
% 0.53/0.70 (![U: $i] : (hskp12 | hskp0 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))),
% 0.53/0.70 inference(modus_ponens,[status(thm)],[148, 144])).
% 0.53/0.70 tff(150,plain,(
% 0.53/0.70 ![U: $i] : (hskp12 | hskp0 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))),
% 0.53/0.70 inference(skolemize,[status(sab)],[149])).
% 0.53/0.70 tff(151,plain,
% 0.53/0.70 (![U: $i] : (hskp12 | hskp0 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))),
% 0.53/0.70 inference(modus_ponens,[status(thm)],[150, 143])).
% 0.53/0.70 tff(152,plain,
% 0.53/0.70 (((~![U: $i] : (hskp12 | hskp0 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp12 | hskp0 | c0_1(a478) | c3_1(a478) | (~ndr1_0) | (~c2_1(a478)))) <=> ((~![U: $i] : (hskp12 | hskp0 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | hskp12 | hskp0 | c0_1(a478) | c3_1(a478) | (~ndr1_0) | (~c2_1(a478)))),
% 0.53/0.70 inference(rewrite,[status(thm)],[])).
% 0.53/0.70 tff(153,plain,
% 0.53/0.70 ((hskp12 | hskp0 | (~ndr1_0) | c0_1(a478) | c3_1(a478) | (~c2_1(a478))) <=> (hskp12 | hskp0 | c0_1(a478) | c3_1(a478) | (~ndr1_0) | (~c2_1(a478)))),
% 0.53/0.70 inference(rewrite,[status(thm)],[])).
% 0.53/0.70 tff(154,plain,
% 0.53/0.70 (((~![U: $i] : (hskp12 | hskp0 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp12 | hskp0 | (~ndr1_0) | c0_1(a478) | c3_1(a478) | (~c2_1(a478)))) <=> ((~![U: $i] : (hskp12 | hskp0 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp12 | hskp0 | c0_1(a478) | c3_1(a478) | (~ndr1_0) | (~c2_1(a478))))),
% 0.53/0.70 inference(monotonicity,[status(thm)],[153])).
% 0.53/0.70 tff(155,plain,
% 0.53/0.70 (((~![U: $i] : (hskp12 | hskp0 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp12 | hskp0 | (~ndr1_0) | c0_1(a478) | c3_1(a478) | (~c2_1(a478)))) <=> ((~![U: $i] : (hskp12 | hskp0 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | hskp12 | hskp0 | c0_1(a478) | c3_1(a478) | (~ndr1_0) | (~c2_1(a478)))),
% 0.53/0.70 inference(transitivity,[status(thm)],[154, 152])).
% 0.53/0.70 tff(156,plain,
% 0.53/0.70 ((~![U: $i] : (hskp12 | hskp0 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp12 | hskp0 | (~ndr1_0) | c0_1(a478) | c3_1(a478) | (~c2_1(a478)))),
% 0.53/0.70 inference(quant_inst,[status(thm)],[])).
% 0.53/0.70 tff(157,plain,
% 0.53/0.70 ((~![U: $i] : (hskp12 | hskp0 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | hskp12 | hskp0 | c0_1(a478) | c3_1(a478) | (~ndr1_0) | (~c2_1(a478))),
% 0.53/0.70 inference(modus_ponens,[status(thm)],[156, 155])).
% 0.53/0.70 tff(158,plain,
% 0.53/0.70 (hskp12 | hskp0),
% 0.53/0.70 inference(unit_resolution,[status(thm)],[157, 141, 140, 139, 138, 151])).
% 0.53/0.70 tff(159,plain,
% 0.53/0.70 (hskp12),
% 0.53/0.70 inference(unit_resolution,[status(thm)],[158, 34])).
% 0.53/0.70 tff(160,plain,
% 0.53/0.70 (~c2_1(a480)),
% 0.53/0.70 inference(unit_resolution,[status(thm)],[89, 159])).
% 0.53/0.70 tff(161,plain,
% 0.53/0.70 (~c1_1(a480)),
% 0.53/0.70 inference(unit_resolution,[status(thm)],[95, 159])).
% 0.53/0.70 tff(162,plain,
% 0.53/0.70 (~c0_1(a480)),
% 0.53/0.70 inference(unit_resolution,[status(thm)],[101, 159])).
% 0.53/0.70 tff(163,plain,
% 0.53/0.70 (((~![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp1 | hskp0 | c0_1(a480) | c1_1(a480) | c2_1(a480) | (~ndr1_0))) <=> ((~![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp1 | hskp0 | c0_1(a480) | c1_1(a480) | c2_1(a480) | (~ndr1_0))),
% 0.53/0.70 inference(rewrite,[status(thm)],[])).
% 0.53/0.70 tff(164,plain,
% 0.53/0.70 ((hskp1 | hskp0 | (~ndr1_0) | c2_1(a480) | c1_1(a480) | c0_1(a480)) <=> (hskp1 | hskp0 | c0_1(a480) | c1_1(a480) | c2_1(a480) | (~ndr1_0))),
% 0.53/0.70 inference(rewrite,[status(thm)],[])).
% 0.53/0.70 tff(165,plain,
% 0.53/0.70 (((~![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp1 | hskp0 | (~ndr1_0) | c2_1(a480) | c1_1(a480) | c0_1(a480))) <=> ((~![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp1 | hskp0 | c0_1(a480) | c1_1(a480) | c2_1(a480) | (~ndr1_0)))),
% 0.53/0.70 inference(monotonicity,[status(thm)],[164])).
% 0.53/0.70 tff(166,plain,
% 0.53/0.70 (((~![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp1 | hskp0 | (~ndr1_0) | c2_1(a480) | c1_1(a480) | c0_1(a480))) <=> ((~![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp1 | hskp0 | c0_1(a480) | c1_1(a480) | c2_1(a480) | (~ndr1_0))),
% 0.53/0.70 inference(transitivity,[status(thm)],[165, 163])).
% 0.53/0.70 tff(167,plain,
% 0.53/0.70 ((~![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp1 | hskp0 | (~ndr1_0) | c2_1(a480) | c1_1(a480) | c0_1(a480))),
% 0.53/0.70 inference(quant_inst,[status(thm)],[])).
% 0.53/0.70 tff(168,plain,
% 0.53/0.70 ((~![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp1 | hskp0 | c0_1(a480) | c1_1(a480) | c2_1(a480) | (~ndr1_0)),
% 0.53/0.70 inference(modus_ponens,[status(thm)],[167, 166])).
% 0.53/0.70 tff(169,plain,
% 0.53/0.70 (hskp1),
% 0.53/0.70 inference(unit_resolution,[status(thm)],[168, 141, 34, 162, 161, 160, 83])).
% 0.53/0.70 tff(170,plain,
% 0.53/0.70 (((~hskp1) | (~c0_1(a463))) <=> ((~hskp1) | (~c0_1(a463)))),
% 0.53/0.70 inference(rewrite,[status(thm)],[])).
% 0.53/0.70 tff(171,plain,
% 0.53/0.70 (((~c0_1(a463)) | (~hskp1)) <=> ((~hskp1) | (~c0_1(a463)))),
% 0.53/0.70 inference(rewrite,[status(thm)],[])).
% 0.53/0.70 tff(172,axiom,((~c0_1(a463)) | (~hskp1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause121')).
% 0.53/0.70 tff(173,plain,
% 0.53/0.70 ((~hskp1) | (~c0_1(a463))),
% 0.53/0.70 inference(modus_ponens,[status(thm)],[172, 171])).
% 0.53/0.70 tff(174,plain,
% 0.53/0.70 ((~hskp1) | (~c0_1(a463))),
% 0.53/0.70 inference(modus_ponens,[status(thm)],[173, 170])).
% 0.53/0.70 tff(175,plain,
% 0.53/0.70 (~c0_1(a463)),
% 0.53/0.70 inference(unit_resolution,[status(thm)],[174, 169])).
% 0.53/0.70 tff(176,plain,
% 0.53/0.70 (((~hskp1) | (~c1_1(a463))) <=> ((~hskp1) | (~c1_1(a463)))),
% 0.53/0.70 inference(rewrite,[status(thm)],[])).
% 0.53/0.70 tff(177,plain,
% 0.53/0.70 (((~c1_1(a463)) | (~hskp1)) <=> ((~hskp1) | (~c1_1(a463)))),
% 0.53/0.70 inference(rewrite,[status(thm)],[])).
% 0.53/0.70 tff(178,axiom,((~c1_1(a463)) | (~hskp1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause122')).
% 0.53/0.70 tff(179,plain,
% 0.53/0.70 ((~hskp1) | (~c1_1(a463))),
% 0.53/0.70 inference(modus_ponens,[status(thm)],[178, 177])).
% 0.53/0.70 tff(180,plain,
% 0.53/0.70 ((~hskp1) | (~c1_1(a463))),
% 0.53/0.70 inference(modus_ponens,[status(thm)],[179, 176])).
% 0.53/0.70 tff(181,plain,
% 0.53/0.70 (~c1_1(a463)),
% 0.53/0.70 inference(unit_resolution,[status(thm)],[180, 169])).
% 0.53/0.70 tff(182,assumption,(~c1_1(a463)), introduced(assumption)).
% 0.53/0.70 tff(183,assumption,(~c0_1(a463)), introduced(assumption)).
% 0.53/0.70 tff(184,plain,
% 0.53/0.70 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | (hskp0 | c0_1(a480) | c1_1(a480) | c2_1(a480) | c0_1(a463) | c1_1(a463) | (~ndr1_0) | (~c2_1(a463)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | hskp0 | c0_1(a480) | c1_1(a480) | c2_1(a480) | c0_1(a463) | c1_1(a463) | (~ndr1_0) | (~c2_1(a463)))),
% 0.53/0.70 inference(rewrite,[status(thm)],[])).
% 0.53/0.70 tff(185,plain,
% 0.53/0.70 ((hskp0 | (~ndr1_0) | c1_1(a463) | c0_1(a463) | (~c2_1(a463)) | c1_1(a480) | c0_1(a480) | c2_1(a480)) <=> (hskp0 | c0_1(a480) | c1_1(a480) | c2_1(a480) | c0_1(a463) | c1_1(a463) | (~ndr1_0) | (~c2_1(a463)))),
% 0.53/0.70 inference(rewrite,[status(thm)],[])).
% 0.53/0.70 tff(186,plain,
% 0.53/0.70 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | (hskp0 | (~ndr1_0) | c1_1(a463) | c0_1(a463) | (~c2_1(a463)) | c1_1(a480) | c0_1(a480) | c2_1(a480))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | (hskp0 | c0_1(a480) | c1_1(a480) | c2_1(a480) | c0_1(a463) | c1_1(a463) | (~ndr1_0) | (~c2_1(a463))))),
% 0.53/0.70 inference(monotonicity,[status(thm)],[185])).
% 0.53/0.70 tff(187,plain,
% 0.53/0.70 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | (hskp0 | (~ndr1_0) | c1_1(a463) | c0_1(a463) | (~c2_1(a463)) | c1_1(a480) | c0_1(a480) | c2_1(a480))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | hskp0 | c0_1(a480) | c1_1(a480) | c2_1(a480) | c0_1(a463) | c1_1(a463) | (~ndr1_0) | (~c2_1(a463)))),
% 0.53/0.70 inference(transitivity,[status(thm)],[186, 184])).
% 0.53/0.70 tff(188,plain,
% 0.53/0.70 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | (hskp0 | (~ndr1_0) | c1_1(a463) | c0_1(a463) | (~c2_1(a463)) | c1_1(a480) | c0_1(a480) | c2_1(a480))),
% 0.53/0.70 inference(quant_inst,[status(thm)],[])).
% 0.53/0.70 tff(189,plain,
% 0.53/0.70 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | hskp0 | c0_1(a480) | c1_1(a480) | c2_1(a480) | c0_1(a463) | c1_1(a463) | (~ndr1_0) | (~c2_1(a463))),
% 0.53/0.70 inference(modus_ponens,[status(thm)],[188, 187])).
% 0.53/0.70 tff(190,plain,
% 0.53/0.70 (~c2_1(a463)),
% 0.53/0.70 inference(unit_resolution,[status(thm)],[189, 141, 34, 162, 161, 160, 183, 182, 73])).
% 0.53/0.70 tff(191,plain,
% 0.53/0.70 (((~hskp1) | c2_1(a463)) <=> ((~hskp1) | c2_1(a463))),
% 0.53/0.70 inference(rewrite,[status(thm)],[])).
% 0.53/0.70 tff(192,axiom,((~hskp1) | c2_1(a463)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause81')).
% 0.53/0.70 tff(193,plain,
% 0.53/0.70 ((~hskp1) | c2_1(a463)),
% 0.53/0.70 inference(modus_ponens,[status(thm)],[192, 191])).
% 0.53/0.70 tff(194,plain,
% 0.53/0.70 ((~hskp1) | c2_1(a463)),
% 0.53/0.70 inference(modus_ponens,[status(thm)],[193, 191])).
% 0.53/0.70 tff(195,plain,
% 0.53/0.70 ((~hskp1) | c2_1(a463)),
% 0.53/0.70 inference(modus_ponens,[status(thm)],[194, 191])).
% 0.53/0.70 tff(196,plain,
% 0.53/0.70 ((~hskp1) | c2_1(a463)),
% 0.53/0.70 inference(modus_ponens,[status(thm)],[195, 191])).
% 0.53/0.70 tff(197,plain,
% 0.53/0.70 ((~hskp1) | c2_1(a463)),
% 0.53/0.70 inference(modus_ponens,[status(thm)],[196, 191])).
% 0.53/0.70 tff(198,plain,
% 0.53/0.70 ($false),
% 0.53/0.70 inference(unit_resolution,[status(thm)],[197, 169, 190])).
% 0.53/0.70 tff(199,plain,(hskp0 | (~ndr1_0) | c0_1(a463) | c1_1(a463) | (~c2_1(a478)) | c0_1(a478) | c3_1(a478)), inference(lemma,lemma(discharge,[]))).
% 0.53/0.70 tff(200,plain,
% 0.53/0.70 ($false),
% 0.53/0.70 inference(unit_resolution,[status(thm)],[199, 181, 175, 141, 34, 140, 139, 138])).
% 0.53/0.70 tff(201,plain,(hskp0 | (~ndr1_0) | (~c2_1(a478)) | c0_1(a478) | c3_1(a478)), inference(lemma,lemma(discharge,[]))).
% 0.53/0.70 tff(202,plain,
% 0.53/0.70 (hskp0),
% 0.53/0.70 inference(unit_resolution,[status(thm)],[201, 137, 131, 123, 117])).
% 0.53/0.70 tff(203,plain,
% 0.53/0.70 (((~hskp0) | (~c3_1(a460))) <=> ((~hskp0) | (~c3_1(a460)))),
% 0.53/0.70 inference(rewrite,[status(thm)],[])).
% 0.53/0.70 tff(204,plain,
% 0.53/0.70 (((~c3_1(a460)) | (~hskp0)) <=> ((~hskp0) | (~c3_1(a460)))),
% 0.53/0.70 inference(rewrite,[status(thm)],[])).
% 0.53/0.70 tff(205,axiom,((~c3_1(a460)) | (~hskp0)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause124')).
% 0.53/0.70 tff(206,plain,
% 0.53/0.70 ((~hskp0) | (~c3_1(a460))),
% 0.53/0.70 inference(modus_ponens,[status(thm)],[205, 204])).
% 0.53/0.70 tff(207,plain,
% 0.53/0.70 ((~hskp0) | (~c3_1(a460))),
% 0.53/0.70 inference(modus_ponens,[status(thm)],[206, 203])).
% 0.53/0.70 tff(208,plain,
% 0.53/0.70 (~c3_1(a460)),
% 0.53/0.70 inference(unit_resolution,[status(thm)],[207, 202])).
% 0.53/0.70 tff(209,plain,
% 0.53/0.70 (((~hskp0) | c0_1(a460)) <=> ((~hskp0) | c0_1(a460))),
% 0.53/0.70 inference(rewrite,[status(thm)],[])).
% 0.53/0.70 tff(210,axiom,((~hskp0) | c0_1(a460)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause82')).
% 0.53/0.70 tff(211,plain,
% 0.53/0.70 ((~hskp0) | c0_1(a460)),
% 0.53/0.70 inference(modus_ponens,[status(thm)],[210, 209])).
% 0.53/0.70 tff(212,plain,
% 0.53/0.70 ((~hskp0) | c0_1(a460)),
% 0.53/0.70 inference(modus_ponens,[status(thm)],[211, 209])).
% 0.53/0.70 tff(213,plain,
% 0.53/0.70 ((~hskp0) | c0_1(a460)),
% 0.53/0.70 inference(modus_ponens,[status(thm)],[212, 209])).
% 0.53/0.70 tff(214,plain,
% 0.53/0.70 ((~hskp0) | c0_1(a460)),
% 0.53/0.70 inference(modus_ponens,[status(thm)],[213, 209])).
% 0.53/0.70 tff(215,plain,
% 0.53/0.70 ((~hskp0) | c0_1(a460)),
% 0.53/0.70 inference(modus_ponens,[status(thm)],[214, 209])).
% 0.53/0.70 tff(216,plain,
% 0.53/0.70 (c0_1(a460)),
% 0.53/0.70 inference(unit_resolution,[status(thm)],[215, 202])).
% 0.53/0.70 tff(217,plain,
% 0.53/0.70 (((~hskp0) | (~c2_1(a460))) <=> ((~hskp0) | (~c2_1(a460)))),
% 0.53/0.70 inference(rewrite,[status(thm)],[])).
% 0.53/0.70 tff(218,plain,
% 0.53/0.70 (((~c2_1(a460)) | (~hskp0)) <=> ((~hskp0) | (~c2_1(a460)))),
% 0.53/0.70 inference(rewrite,[status(thm)],[])).
% 0.53/0.70 tff(219,axiom,((~c2_1(a460)) | (~hskp0)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause123')).
% 0.53/0.70 tff(220,plain,
% 0.53/0.70 ((~hskp0) | (~c2_1(a460))),
% 0.53/0.70 inference(modus_ponens,[status(thm)],[219, 218])).
% 0.53/0.70 tff(221,plain,
% 0.53/0.70 ((~hskp0) | (~c2_1(a460))),
% 0.53/0.70 inference(modus_ponens,[status(thm)],[220, 217])).
% 0.53/0.70 tff(222,plain,
% 0.53/0.70 (~c2_1(a460)),
% 0.53/0.70 inference(unit_resolution,[status(thm)],[221, 202])).
% 0.53/0.70 tff(223,assumption,(~c3_1(a460)), introduced(assumption)).
% 0.53/0.70 tff(224,assumption,(c0_1(a460)), introduced(assumption)).
% 0.53/0.70 tff(225,plain,
% 0.53/0.70 (^[V: $i, U: $i] : refl((hskp14 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V))) <=> (hskp14 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V))))),
% 0.53/0.70 inference(bind,[status(th)],[])).
% 0.53/0.70 tff(226,plain,
% 0.53/0.70 (![V: $i, U: $i] : (hskp14 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp14 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))),
% 0.53/0.71 inference(quant_intro,[status(thm)],[225])).
% 0.53/0.71 tff(227,plain,
% 0.53/0.71 (![V: $i, U: $i] : (hskp14 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp14 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))),
% 0.53/0.71 inference(rewrite,[status(thm)],[])).
% 0.53/0.71 tff(228,plain,
% 0.53/0.71 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(V)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(V))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c0_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c0_1(V)) | hskp14) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V))) | hskp14))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V))) | hskp14) <=> (hskp14 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c0_1(V)) | hskp14) <=> (hskp14 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))))),
% 0.53/0.71 inference(bind,[status(th)],[])).
% 0.53/0.71 tff(229,plain,
% 0.53/0.71 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c0_1(V)) | hskp14) <=> ![V: $i, U: $i] : (hskp14 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))),
% 0.53/0.71 inference(quant_intro,[status(thm)],[228])).
% 0.53/0.71 tff(230,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c0_1(V)) | hskp14)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause168')).
% 0.53/0.71 tff(231,plain,
% 0.53/0.71 (![V: $i, U: $i] : (hskp14 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))),
% 0.53/0.71 inference(modus_ponens,[status(thm)],[230, 229])).
% 0.53/0.71 tff(232,plain,
% 0.53/0.71 (![V: $i, U: $i] : (hskp14 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))),
% 0.53/0.71 inference(modus_ponens,[status(thm)],[231, 227])).
% 0.53/0.71 tff(233,plain,(
% 0.53/0.71 ![V: $i, U: $i] : (hskp14 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))),
% 0.53/0.71 inference(skolemize,[status(sab)],[232])).
% 0.53/0.71 tff(234,plain,
% 0.53/0.71 (![V: $i, U: $i] : (hskp14 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))),
% 0.53/0.71 inference(modus_ponens,[status(thm)],[233, 226])).
% 0.53/0.71 tff(235,assumption,(hskp3), introduced(assumption)).
% 0.53/0.71 tff(236,plain,
% 0.53/0.71 (((~hskp3) | (~c0_1(a466))) <=> ((~hskp3) | (~c0_1(a466)))),
% 0.53/0.71 inference(rewrite,[status(thm)],[])).
% 0.53/0.71 tff(237,plain,
% 0.53/0.71 (((~c0_1(a466)) | (~hskp3)) <=> ((~hskp3) | (~c0_1(a466)))),
% 0.53/0.71 inference(rewrite,[status(thm)],[])).
% 0.53/0.71 tff(238,axiom,((~c0_1(a466)) | (~hskp3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause117')).
% 0.53/0.71 tff(239,plain,
% 0.53/0.71 ((~hskp3) | (~c0_1(a466))),
% 0.53/0.71 inference(modus_ponens,[status(thm)],[238, 237])).
% 0.53/0.71 tff(240,plain,
% 0.53/0.71 ((~hskp3) | (~c0_1(a466))),
% 0.53/0.71 inference(modus_ponens,[status(thm)],[239, 236])).
% 0.53/0.71 tff(241,plain,
% 0.53/0.71 (~c0_1(a466)),
% 0.53/0.71 inference(unit_resolution,[status(thm)],[240, 235])).
% 0.53/0.71 tff(242,plain,
% 0.53/0.71 (((~hskp3) | c3_1(a466)) <=> ((~hskp3) | c3_1(a466))),
% 0.53/0.71 inference(rewrite,[status(thm)],[])).
% 0.53/0.71 tff(243,axiom,((~hskp3) | c3_1(a466)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause80')).
% 0.53/0.71 tff(244,plain,
% 0.53/0.71 ((~hskp3) | c3_1(a466)),
% 0.53/0.71 inference(modus_ponens,[status(thm)],[243, 242])).
% 0.53/0.71 tff(245,plain,
% 0.53/0.71 ((~hskp3) | c3_1(a466)),
% 0.53/0.71 inference(modus_ponens,[status(thm)],[244, 242])).
% 0.53/0.71 tff(246,plain,
% 0.53/0.71 ((~hskp3) | c3_1(a466)),
% 0.53/0.71 inference(modus_ponens,[status(thm)],[245, 242])).
% 0.53/0.71 tff(247,plain,
% 0.53/0.71 ((~hskp3) | c3_1(a466)),
% 0.53/0.71 inference(modus_ponens,[status(thm)],[246, 242])).
% 0.53/0.71 tff(248,plain,
% 0.53/0.71 ((~hskp3) | c3_1(a466)),
% 0.53/0.71 inference(modus_ponens,[status(thm)],[247, 242])).
% 0.53/0.71 tff(249,plain,
% 0.53/0.71 (c3_1(a466)),
% 0.53/0.71 inference(unit_resolution,[status(thm)],[248, 235])).
% 0.53/0.71 tff(250,plain,
% 0.53/0.71 (((~hskp3) | c1_1(a466)) <=> ((~hskp3) | c1_1(a466))),
% 0.53/0.71 inference(rewrite,[status(thm)],[])).
% 0.53/0.71 tff(251,axiom,((~hskp3) | c1_1(a466)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause79')).
% 0.53/0.71 tff(252,plain,
% 0.53/0.71 ((~hskp3) | c1_1(a466)),
% 0.53/0.71 inference(modus_ponens,[status(thm)],[251, 250])).
% 0.53/0.71 tff(253,plain,
% 0.53/0.71 ((~hskp3) | c1_1(a466)),
% 0.53/0.71 inference(modus_ponens,[status(thm)],[252, 250])).
% 0.53/0.71 tff(254,plain,
% 0.53/0.71 ((~hskp3) | c1_1(a466)),
% 0.53/0.71 inference(modus_ponens,[status(thm)],[253, 250])).
% 0.53/0.71 tff(255,plain,
% 0.53/0.71 ((~hskp3) | c1_1(a466)),
% 0.53/0.71 inference(modus_ponens,[status(thm)],[254, 250])).
% 0.53/0.71 tff(256,plain,
% 0.53/0.71 ((~hskp3) | c1_1(a466)),
% 0.53/0.71 inference(modus_ponens,[status(thm)],[255, 250])).
% 0.53/0.71 tff(257,plain,
% 0.53/0.71 (c1_1(a466)),
% 0.53/0.71 inference(unit_resolution,[status(thm)],[256, 235])).
% 0.53/0.71 tff(258,assumption,(~c0_1(a466)), introduced(assumption)).
% 0.53/0.71 tff(259,assumption,(c3_1(a466)), introduced(assumption)).
% 0.53/0.71 tff(260,assumption,(c1_1(a466)), introduced(assumption)).
% 0.53/0.71 tff(261,plain,
% 0.53/0.71 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c1_1(a488) | c2_1(a488) | c0_1(a466) | c2_1(a460) | c3_1(a460) | (~ndr1_0) | (~c0_1(a460)) | (~c3_1(a466)) | (~c1_1(a466)) | c0_1(a488))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c1_1(a488) | c2_1(a488) | c0_1(a466) | c2_1(a460) | c3_1(a460) | (~ndr1_0) | (~c0_1(a460)) | (~c3_1(a466)) | (~c1_1(a466)) | c0_1(a488))),
% 0.53/0.71 inference(rewrite,[status(thm)],[])).
% 0.53/0.71 tff(262,plain,
% 0.53/0.71 (((~ndr1_0) | c2_1(a460) | c3_1(a460) | (~c0_1(a460)) | c0_1(a466) | (~c1_1(a466)) | (~c3_1(a466)) | c1_1(a488) | c0_1(a488) | c2_1(a488)) <=> (c1_1(a488) | c2_1(a488) | c0_1(a466) | c2_1(a460) | c3_1(a460) | (~ndr1_0) | (~c0_1(a460)) | (~c3_1(a466)) | (~c1_1(a466)) | c0_1(a488))),
% 0.53/0.71 inference(rewrite,[status(thm)],[])).
% 0.53/0.71 tff(263,plain,
% 0.53/0.71 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c2_1(a460) | c3_1(a460) | (~c0_1(a460)) | c0_1(a466) | (~c1_1(a466)) | (~c3_1(a466)) | c1_1(a488) | c0_1(a488) | c2_1(a488))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c1_1(a488) | c2_1(a488) | c0_1(a466) | c2_1(a460) | c3_1(a460) | (~ndr1_0) | (~c0_1(a460)) | (~c3_1(a466)) | (~c1_1(a466)) | c0_1(a488)))),
% 0.53/0.71 inference(monotonicity,[status(thm)],[262])).
% 0.53/0.71 tff(264,plain,
% 0.53/0.71 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c2_1(a460) | c3_1(a460) | (~c0_1(a460)) | c0_1(a466) | (~c1_1(a466)) | (~c3_1(a466)) | c1_1(a488) | c0_1(a488) | c2_1(a488))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c1_1(a488) | c2_1(a488) | c0_1(a466) | c2_1(a460) | c3_1(a460) | (~ndr1_0) | (~c0_1(a460)) | (~c3_1(a466)) | (~c1_1(a466)) | c0_1(a488))),
% 0.53/0.71 inference(transitivity,[status(thm)],[263, 261])).
% 0.53/0.71 tff(265,plain,
% 0.53/0.71 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c2_1(a460) | c3_1(a460) | (~c0_1(a460)) | c0_1(a466) | (~c1_1(a466)) | (~c3_1(a466)) | c1_1(a488) | c0_1(a488) | c2_1(a488))),
% 0.53/0.71 inference(quant_inst,[status(thm)],[])).
% 0.53/0.71 tff(266,plain,
% 0.53/0.71 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c1_1(a488) | c2_1(a488) | c0_1(a466) | c2_1(a460) | c3_1(a460) | (~ndr1_0) | (~c0_1(a460)) | (~c3_1(a466)) | (~c1_1(a466)) | c0_1(a488)),
% 0.53/0.71 inference(modus_ponens,[status(thm)],[265, 264])).
% 0.53/0.71 tff(267,plain,
% 0.53/0.71 (c0_1(a488)),
% 0.53/0.71 inference(unit_resolution,[status(thm)],[266, 141, 260, 259, 224, 63, 57, 258, 1, 223, 32])).
% 0.53/0.71 tff(268,plain,
% 0.53/0.71 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp12 | c1_1(a488) | c2_1(a488) | c3_1(a488) | (~ndr1_0) | (~c0_1(a488)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | hskp12 | c1_1(a488) | c2_1(a488) | c3_1(a488) | (~ndr1_0) | (~c0_1(a488)))),
% 0.53/0.71 inference(rewrite,[status(thm)],[])).
% 0.53/0.71 tff(269,plain,
% 0.53/0.71 ((hskp12 | (~ndr1_0) | c2_1(a488) | c3_1(a488) | (~c0_1(a488)) | c3_1(a488) | c1_1(a488) | (~c0_1(a488))) <=> (hskp12 | c1_1(a488) | c2_1(a488) | c3_1(a488) | (~ndr1_0) | (~c0_1(a488)))),
% 0.53/0.71 inference(rewrite,[status(thm)],[])).
% 0.53/0.71 tff(270,plain,
% 0.53/0.71 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp12 | (~ndr1_0) | c2_1(a488) | c3_1(a488) | (~c0_1(a488)) | c3_1(a488) | c1_1(a488) | (~c0_1(a488)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp12 | c1_1(a488) | c2_1(a488) | c3_1(a488) | (~ndr1_0) | (~c0_1(a488))))),
% 0.53/0.71 inference(monotonicity,[status(thm)],[269])).
% 0.53/0.71 tff(271,plain,
% 0.53/0.71 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp12 | (~ndr1_0) | c2_1(a488) | c3_1(a488) | (~c0_1(a488)) | c3_1(a488) | c1_1(a488) | (~c0_1(a488)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | hskp12 | c1_1(a488) | c2_1(a488) | c3_1(a488) | (~ndr1_0) | (~c0_1(a488)))),
% 0.53/0.71 inference(transitivity,[status(thm)],[270, 268])).
% 0.53/0.71 tff(272,plain,
% 0.53/0.71 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp12 | (~ndr1_0) | c2_1(a488) | c3_1(a488) | (~c0_1(a488)) | c3_1(a488) | c1_1(a488) | (~c0_1(a488)))),
% 0.53/0.71 inference(quant_inst,[status(thm)],[])).
% 0.53/0.71 tff(273,plain,
% 0.53/0.71 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | hskp12 | c1_1(a488) | c2_1(a488) | c3_1(a488) | (~ndr1_0) | (~c0_1(a488))),
% 0.53/0.71 inference(modus_ponens,[status(thm)],[272, 271])).
% 0.53/0.71 tff(274,plain,
% 0.53/0.71 (hskp12),
% 0.53/0.71 inference(unit_resolution,[status(thm)],[273, 141, 63, 57, 51, 44, 267])).
% 0.53/0.71 tff(275,plain,
% 0.53/0.71 (~c2_1(a480)),
% 0.53/0.71 inference(unit_resolution,[status(thm)],[89, 274])).
% 0.53/0.71 tff(276,plain,
% 0.53/0.71 (~c1_1(a480)),
% 0.53/0.71 inference(unit_resolution,[status(thm)],[95, 274])).
% 0.53/0.71 tff(277,plain,
% 0.53/0.71 (~c0_1(a480)),
% 0.53/0.71 inference(unit_resolution,[status(thm)],[101, 274])).
% 0.53/0.71 tff(278,plain,
% 0.53/0.71 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c2_1(a488) | c3_1(a488) | c0_1(a480) | c1_1(a480) | c2_1(a480) | c0_1(a466) | (~ndr1_0) | (~c3_1(a466)) | (~c1_1(a466)) | (~c0_1(a488)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c2_1(a488) | c3_1(a488) | c0_1(a480) | c1_1(a480) | c2_1(a480) | c0_1(a466) | (~ndr1_0) | (~c3_1(a466)) | (~c1_1(a466)) | (~c0_1(a488)))),
% 0.53/0.71 inference(rewrite,[status(thm)],[])).
% 0.53/0.71 tff(279,plain,
% 0.53/0.71 (((~ndr1_0) | c2_1(a488) | c3_1(a488) | (~c0_1(a488)) | c0_1(a466) | (~c1_1(a466)) | (~c3_1(a466)) | c1_1(a480) | c0_1(a480) | c2_1(a480)) <=> (c2_1(a488) | c3_1(a488) | c0_1(a480) | c1_1(a480) | c2_1(a480) | c0_1(a466) | (~ndr1_0) | (~c3_1(a466)) | (~c1_1(a466)) | (~c0_1(a488)))),
% 0.53/0.71 inference(rewrite,[status(thm)],[])).
% 0.53/0.71 tff(280,plain,
% 0.53/0.71 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c2_1(a488) | c3_1(a488) | (~c0_1(a488)) | c0_1(a466) | (~c1_1(a466)) | (~c3_1(a466)) | c1_1(a480) | c0_1(a480) | c2_1(a480))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c2_1(a488) | c3_1(a488) | c0_1(a480) | c1_1(a480) | c2_1(a480) | c0_1(a466) | (~ndr1_0) | (~c3_1(a466)) | (~c1_1(a466)) | (~c0_1(a488))))),
% 0.53/0.71 inference(monotonicity,[status(thm)],[279])).
% 0.53/0.71 tff(281,plain,
% 0.53/0.71 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c2_1(a488) | c3_1(a488) | (~c0_1(a488)) | c0_1(a466) | (~c1_1(a466)) | (~c3_1(a466)) | c1_1(a480) | c0_1(a480) | c2_1(a480))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c2_1(a488) | c3_1(a488) | c0_1(a480) | c1_1(a480) | c2_1(a480) | c0_1(a466) | (~ndr1_0) | (~c3_1(a466)) | (~c1_1(a466)) | (~c0_1(a488)))),
% 0.53/0.71 inference(transitivity,[status(thm)],[280, 278])).
% 0.53/0.71 tff(282,plain,
% 0.53/0.71 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c2_1(a488) | c3_1(a488) | (~c0_1(a488)) | c0_1(a466) | (~c1_1(a466)) | (~c3_1(a466)) | c1_1(a480) | c0_1(a480) | c2_1(a480))),
% 0.53/0.71 inference(quant_inst,[status(thm)],[])).
% 0.53/0.71 tff(283,plain,
% 0.53/0.71 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c2_1(a488) | c3_1(a488) | c0_1(a480) | c1_1(a480) | c2_1(a480) | c0_1(a466) | (~ndr1_0) | (~c3_1(a466)) | (~c1_1(a466)) | (~c0_1(a488))),
% 0.53/0.71 inference(modus_ponens,[status(thm)],[282, 281])).
% 0.53/0.71 tff(284,plain,
% 0.53/0.71 ($false),
% 0.53/0.71 inference(unit_resolution,[status(thm)],[283, 141, 260, 259, 57, 51, 277, 276, 275, 258, 32, 267])).
% 0.53/0.71 tff(285,plain,((~hskp14) | (~ndr1_0) | (~c1_1(a466)) | (~c3_1(a466)) | c0_1(a466) | (~c0_1(a460)) | c2_1(a460) | c3_1(a460)), inference(lemma,lemma(discharge,[]))).
% 0.53/0.71 tff(286,plain,
% 0.53/0.71 (~hskp14),
% 0.53/0.71 inference(unit_resolution,[status(thm)],[285, 257, 137, 249, 241, 224, 1, 223])).
% 0.53/0.71 tff(287,plain,
% 0.53/0.71 ((hskp5 | hskp25 | hskp14) <=> (hskp5 | hskp25 | hskp14)),
% 0.53/0.71 inference(rewrite,[status(thm)],[])).
% 0.53/0.71 tff(288,plain,
% 0.53/0.71 (((hskp25 | hskp5) | hskp14) <=> (hskp5 | hskp25 | hskp14)),
% 0.53/0.71 inference(rewrite,[status(thm)],[])).
% 0.53/0.71 tff(289,axiom,((hskp25 | hskp5) | hskp14), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause33')).
% 0.53/0.71 tff(290,plain,
% 0.53/0.71 (hskp5 | hskp25 | hskp14),
% 0.53/0.71 inference(modus_ponens,[status(thm)],[289, 288])).
% 0.53/0.71 tff(291,plain,
% 0.53/0.71 (hskp5 | hskp25 | hskp14),
% 0.53/0.71 inference(modus_ponens,[status(thm)],[290, 287])).
% 0.53/0.71 tff(292,plain,
% 0.53/0.71 (hskp5 | hskp25 | hskp14),
% 0.53/0.71 inference(modus_ponens,[status(thm)],[291, 287])).
% 0.53/0.71 tff(293,plain,
% 0.53/0.71 (hskp5 | hskp25 | hskp14),
% 0.53/0.71 inference(modus_ponens,[status(thm)],[292, 287])).
% 0.53/0.71 tff(294,plain,
% 0.53/0.71 (hskp5 | hskp25 | hskp14),
% 0.53/0.71 inference(modus_ponens,[status(thm)],[293, 287])).
% 0.53/0.71 tff(295,plain,
% 0.53/0.71 (hskp25),
% 0.53/0.71 inference(unit_resolution,[status(thm)],[294, 286, 103])).
% 0.53/0.71 tff(296,plain,
% 0.53/0.71 (((~hskp25) | c3_1(a461)) <=> ((~hskp25) | c3_1(a461))),
% 0.53/0.71 inference(rewrite,[status(thm)],[])).
% 0.53/0.71 tff(297,axiom,((~hskp25) | c3_1(a461)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause49')).
% 0.53/0.71 tff(298,plain,
% 0.53/0.71 ((~hskp25) | c3_1(a461)),
% 0.53/0.71 inference(modus_ponens,[status(thm)],[297, 296])).
% 0.53/0.71 tff(299,plain,
% 0.53/0.71 ((~hskp25) | c3_1(a461)),
% 0.53/0.71 inference(modus_ponens,[status(thm)],[298, 296])).
% 0.53/0.71 tff(300,plain,
% 0.53/0.71 ((~hskp25) | c3_1(a461)),
% 0.53/0.71 inference(modus_ponens,[status(thm)],[299, 296])).
% 0.53/0.71 tff(301,plain,
% 0.53/0.71 ((~hskp25) | c3_1(a461)),
% 0.53/0.71 inference(modus_ponens,[status(thm)],[300, 296])).
% 0.53/0.71 tff(302,plain,
% 0.53/0.71 ((~hskp25) | c3_1(a461)),
% 0.53/0.71 inference(modus_ponens,[status(thm)],[301, 296])).
% 0.53/0.71 tff(303,plain,
% 0.53/0.71 (c3_1(a461)),
% 0.53/0.71 inference(unit_resolution,[status(thm)],[302, 295])).
% 0.53/0.71 tff(304,plain,
% 0.53/0.71 (((~hskp25) | c2_1(a461)) <=> ((~hskp25) | c2_1(a461))),
% 0.53/0.71 inference(rewrite,[status(thm)],[])).
% 0.53/0.71 tff(305,axiom,((~hskp25) | c2_1(a461)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause48')).
% 0.53/0.71 tff(306,plain,
% 0.53/0.71 ((~hskp25) | c2_1(a461)),
% 0.53/0.71 inference(modus_ponens,[status(thm)],[305, 304])).
% 0.53/0.71 tff(307,plain,
% 0.53/0.71 ((~hskp25) | c2_1(a461)),
% 0.53/0.71 inference(modus_ponens,[status(thm)],[306, 304])).
% 0.53/0.71 tff(308,plain,
% 0.53/0.71 ((~hskp25) | c2_1(a461)),
% 0.53/0.71 inference(modus_ponens,[status(thm)],[307, 304])).
% 0.53/0.71 tff(309,plain,
% 0.53/0.71 ((~hskp25) | c2_1(a461)),
% 0.53/0.71 inference(modus_ponens,[status(thm)],[308, 304])).
% 0.53/0.71 tff(310,plain,
% 0.53/0.71 ((~hskp25) | c2_1(a461)),
% 0.53/0.71 inference(modus_ponens,[status(thm)],[309, 304])).
% 0.53/0.71 tff(311,plain,
% 0.53/0.71 (c2_1(a461)),
% 0.53/0.71 inference(unit_resolution,[status(thm)],[310, 295])).
% 0.53/0.71 tff(312,plain,
% 0.53/0.71 (((~hskp25) | c0_1(a461)) <=> ((~hskp25) | c0_1(a461))),
% 0.53/0.71 inference(rewrite,[status(thm)],[])).
% 0.53/0.71 tff(313,axiom,((~hskp25) | c0_1(a461)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause47')).
% 0.53/0.71 tff(314,plain,
% 0.53/0.71 ((~hskp25) | c0_1(a461)),
% 0.53/0.71 inference(modus_ponens,[status(thm)],[313, 312])).
% 0.53/0.71 tff(315,plain,
% 0.53/0.71 ((~hskp25) | c0_1(a461)),
% 0.53/0.71 inference(modus_ponens,[status(thm)],[314, 312])).
% 0.53/0.71 tff(316,plain,
% 0.53/0.71 ((~hskp25) | c0_1(a461)),
% 0.53/0.71 inference(modus_ponens,[status(thm)],[315, 312])).
% 0.53/0.71 tff(317,plain,
% 0.53/0.71 ((~hskp25) | c0_1(a461)),
% 0.53/0.71 inference(modus_ponens,[status(thm)],[316, 312])).
% 0.53/0.71 tff(318,plain,
% 0.53/0.71 ((~hskp25) | c0_1(a461)),
% 0.53/0.71 inference(modus_ponens,[status(thm)],[317, 312])).
% 0.53/0.71 tff(319,plain,
% 0.53/0.71 (c0_1(a461)),
% 0.53/0.71 inference(unit_resolution,[status(thm)],[318, 295])).
% 0.53/0.71 tff(320,plain,
% 0.53/0.71 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp14 | c0_1(a466) | (~ndr1_0) | (~c3_1(a466)) | (~c1_1(a466)) | (~c0_1(a461)) | (~c3_1(a461)) | (~c2_1(a461)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp14 | c0_1(a466) | (~ndr1_0) | (~c3_1(a466)) | (~c1_1(a466)) | (~c0_1(a461)) | (~c3_1(a461)) | (~c2_1(a461)))),
% 0.53/0.71 inference(rewrite,[status(thm)],[])).
% 0.53/0.71 tff(321,plain,
% 0.53/0.71 ((hskp14 | (~ndr1_0) | (~c2_1(a461)) | (~c0_1(a461)) | (~c3_1(a461)) | c0_1(a466) | (~c1_1(a466)) | (~c3_1(a466))) <=> (hskp14 | c0_1(a466) | (~ndr1_0) | (~c3_1(a466)) | (~c1_1(a466)) | (~c0_1(a461)) | (~c3_1(a461)) | (~c2_1(a461)))),
% 0.53/0.71 inference(rewrite,[status(thm)],[])).
% 0.53/0.71 tff(322,plain,
% 0.53/0.71 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp14 | (~ndr1_0) | (~c2_1(a461)) | (~c0_1(a461)) | (~c3_1(a461)) | c0_1(a466) | (~c1_1(a466)) | (~c3_1(a466)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp14 | c0_1(a466) | (~ndr1_0) | (~c3_1(a466)) | (~c1_1(a466)) | (~c0_1(a461)) | (~c3_1(a461)) | (~c2_1(a461))))),
% 0.53/0.71 inference(monotonicity,[status(thm)],[321])).
% 0.53/0.71 tff(323,plain,
% 0.53/0.71 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp14 | (~ndr1_0) | (~c2_1(a461)) | (~c0_1(a461)) | (~c3_1(a461)) | c0_1(a466) | (~c1_1(a466)) | (~c3_1(a466)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp14 | c0_1(a466) | (~ndr1_0) | (~c3_1(a466)) | (~c1_1(a466)) | (~c0_1(a461)) | (~c3_1(a461)) | (~c2_1(a461)))),
% 0.53/0.71 inference(transitivity,[status(thm)],[322, 320])).
% 0.53/0.71 tff(324,plain,
% 0.53/0.71 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp14 | (~ndr1_0) | (~c2_1(a461)) | (~c0_1(a461)) | (~c3_1(a461)) | c0_1(a466) | (~c1_1(a466)) | (~c3_1(a466)))),
% 0.53/0.71 inference(quant_inst,[status(thm)],[])).
% 0.53/0.71 tff(325,plain,
% 0.53/0.71 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp14 | c0_1(a466) | (~ndr1_0) | (~c3_1(a466)) | (~c1_1(a466)) | (~c0_1(a461)) | (~c3_1(a461)) | (~c2_1(a461))),
% 0.53/0.71 inference(modus_ponens,[status(thm)],[324, 323])).
% 0.53/0.71 tff(326,plain,
% 0.53/0.71 ($false),
% 0.53/0.71 inference(unit_resolution,[status(thm)],[325, 137, 286, 319, 311, 303, 257, 249, 241, 234])).
% 0.53/0.71 tff(327,plain,((~hskp3) | hskp5 | (~c0_1(a460)) | c2_1(a460) | c3_1(a460)), inference(lemma,lemma(discharge,[]))).
% 0.53/0.71 tff(328,plain,
% 0.53/0.71 (~hskp3),
% 0.53/0.71 inference(unit_resolution,[status(thm)],[327, 224, 103, 1, 223])).
% 0.53/0.71 tff(329,assumption,(~hskp3), introduced(assumption)).
% 0.53/0.71 tff(330,assumption,(hskp27), introduced(assumption)).
% 0.53/0.71 tff(331,plain,
% 0.53/0.71 (((~hskp27) | c3_1(a473)) <=> ((~hskp27) | c3_1(a473))),
% 0.53/0.71 inference(rewrite,[status(thm)],[])).
% 0.53/0.71 tff(332,axiom,((~hskp27) | c3_1(a473)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause43')).
% 0.53/0.71 tff(333,plain,
% 0.53/0.71 ((~hskp27) | c3_1(a473)),
% 0.53/0.71 inference(modus_ponens,[status(thm)],[332, 331])).
% 0.53/0.71 tff(334,plain,
% 0.53/0.71 ((~hskp27) | c3_1(a473)),
% 0.53/0.71 inference(modus_ponens,[status(thm)],[333, 331])).
% 0.53/0.71 tff(335,plain,
% 0.53/0.71 ((~hskp27) | c3_1(a473)),
% 0.53/0.71 inference(modus_ponens,[status(thm)],[334, 331])).
% 0.53/0.71 tff(336,plain,
% 0.53/0.71 ((~hskp27) | c3_1(a473)),
% 0.53/0.71 inference(modus_ponens,[status(thm)],[335, 331])).
% 0.53/0.71 tff(337,plain,
% 0.53/0.71 ((~hskp27) | c3_1(a473)),
% 0.53/0.71 inference(modus_ponens,[status(thm)],[336, 331])).
% 0.53/0.71 tff(338,plain,
% 0.53/0.71 (c3_1(a473)),
% 0.53/0.71 inference(unit_resolution,[status(thm)],[337, 330])).
% 0.53/0.71 tff(339,plain,
% 0.53/0.71 (((~hskp27) | c1_1(a473)) <=> ((~hskp27) | c1_1(a473))),
% 0.53/0.71 inference(rewrite,[status(thm)],[])).
% 0.53/0.71 tff(340,axiom,((~hskp27) | c1_1(a473)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause42')).
% 0.53/0.71 tff(341,plain,
% 0.53/0.71 ((~hskp27) | c1_1(a473)),
% 0.53/0.71 inference(modus_ponens,[status(thm)],[340, 339])).
% 0.53/0.72 tff(342,plain,
% 0.53/0.72 ((~hskp27) | c1_1(a473)),
% 0.53/0.72 inference(modus_ponens,[status(thm)],[341, 339])).
% 0.53/0.72 tff(343,plain,
% 0.53/0.72 ((~hskp27) | c1_1(a473)),
% 0.53/0.72 inference(modus_ponens,[status(thm)],[342, 339])).
% 0.53/0.72 tff(344,plain,
% 0.53/0.72 ((~hskp27) | c1_1(a473)),
% 0.53/0.72 inference(modus_ponens,[status(thm)],[343, 339])).
% 0.53/0.72 tff(345,plain,
% 0.53/0.72 ((~hskp27) | c1_1(a473)),
% 0.53/0.72 inference(modus_ponens,[status(thm)],[344, 339])).
% 0.53/0.72 tff(346,plain,
% 0.53/0.72 (c1_1(a473)),
% 0.53/0.72 inference(unit_resolution,[status(thm)],[345, 330])).
% 0.53/0.72 tff(347,plain,
% 0.53/0.72 (((~hskp27) | c0_1(a473)) <=> ((~hskp27) | c0_1(a473))),
% 0.53/0.72 inference(rewrite,[status(thm)],[])).
% 0.53/0.72 tff(348,axiom,((~hskp27) | c0_1(a473)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause41')).
% 0.53/0.72 tff(349,plain,
% 0.53/0.72 ((~hskp27) | c0_1(a473)),
% 0.53/0.72 inference(modus_ponens,[status(thm)],[348, 347])).
% 0.53/0.72 tff(350,plain,
% 0.53/0.72 ((~hskp27) | c0_1(a473)),
% 0.53/0.72 inference(modus_ponens,[status(thm)],[349, 347])).
% 0.53/0.72 tff(351,plain,
% 0.53/0.72 ((~hskp27) | c0_1(a473)),
% 0.53/0.72 inference(modus_ponens,[status(thm)],[350, 347])).
% 0.53/0.72 tff(352,plain,
% 0.53/0.72 ((~hskp27) | c0_1(a473)),
% 0.53/0.72 inference(modus_ponens,[status(thm)],[351, 347])).
% 0.53/0.72 tff(353,plain,
% 0.53/0.72 ((~hskp27) | c0_1(a473)),
% 0.53/0.72 inference(modus_ponens,[status(thm)],[352, 347])).
% 0.53/0.72 tff(354,plain,
% 0.53/0.72 (c0_1(a473)),
% 0.53/0.72 inference(unit_resolution,[status(thm)],[353, 330])).
% 0.53/0.72 tff(355,plain,
% 0.53/0.72 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp3 | c2_1(a460) | c3_1(a460) | (~ndr1_0) | (~c0_1(a460)) | (~c0_1(a473)) | (~c3_1(a473)) | (~c1_1(a473)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | hskp3 | c2_1(a460) | c3_1(a460) | (~ndr1_0) | (~c0_1(a460)) | (~c0_1(a473)) | (~c3_1(a473)) | (~c1_1(a473)))),
% 0.53/0.72 inference(rewrite,[status(thm)],[])).
% 0.53/0.72 tff(356,plain,
% 0.53/0.72 ((hskp3 | (~ndr1_0) | (~c0_1(a473)) | (~c3_1(a473)) | (~c1_1(a473)) | c3_1(a460) | c2_1(a460) | (~c0_1(a460))) <=> (hskp3 | c2_1(a460) | c3_1(a460) | (~ndr1_0) | (~c0_1(a460)) | (~c0_1(a473)) | (~c3_1(a473)) | (~c1_1(a473)))),
% 0.53/0.72 inference(rewrite,[status(thm)],[])).
% 0.53/0.72 tff(357,plain,
% 0.53/0.72 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp3 | (~ndr1_0) | (~c0_1(a473)) | (~c3_1(a473)) | (~c1_1(a473)) | c3_1(a460) | c2_1(a460) | (~c0_1(a460)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp3 | c2_1(a460) | c3_1(a460) | (~ndr1_0) | (~c0_1(a460)) | (~c0_1(a473)) | (~c3_1(a473)) | (~c1_1(a473))))),
% 0.53/0.72 inference(monotonicity,[status(thm)],[356])).
% 0.53/0.72 tff(358,plain,
% 0.53/0.72 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp3 | (~ndr1_0) | (~c0_1(a473)) | (~c3_1(a473)) | (~c1_1(a473)) | c3_1(a460) | c2_1(a460) | (~c0_1(a460)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | hskp3 | c2_1(a460) | c3_1(a460) | (~ndr1_0) | (~c0_1(a460)) | (~c0_1(a473)) | (~c3_1(a473)) | (~c1_1(a473)))),
% 0.53/0.72 inference(transitivity,[status(thm)],[357, 355])).
% 0.53/0.72 tff(359,plain,
% 0.53/0.72 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp3 | (~ndr1_0) | (~c0_1(a473)) | (~c3_1(a473)) | (~c1_1(a473)) | c3_1(a460) | c2_1(a460) | (~c0_1(a460)))),
% 0.53/0.72 inference(quant_inst,[status(thm)],[])).
% 0.53/0.72 tff(360,plain,
% 0.53/0.72 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | hskp3 | c2_1(a460) | c3_1(a460) | (~ndr1_0) | (~c0_1(a460)) | (~c0_1(a473)) | (~c3_1(a473)) | (~c1_1(a473))),
% 0.53/0.72 inference(modus_ponens,[status(thm)],[359, 358])).
% 0.53/0.72 tff(361,plain,
% 0.53/0.72 ($false),
% 0.53/0.72 inference(unit_resolution,[status(thm)],[360, 141, 329, 354, 346, 338, 224, 1, 223, 21])).
% 0.53/0.72 tff(362,plain,((~hskp27) | (~ndr1_0) | hskp3 | (~c0_1(a460)) | c2_1(a460) | c3_1(a460)), inference(lemma,lemma(discharge,[]))).
% 0.53/0.72 tff(363,plain,
% 0.53/0.72 (~hskp27),
% 0.53/0.72 inference(unit_resolution,[status(thm)],[362, 329, 137, 224, 1, 223])).
% 0.53/0.72 tff(364,plain,
% 0.53/0.72 ((hskp27 | hskp22 | hskp17) <=> (hskp27 | hskp22 | hskp17)),
% 0.53/0.72 inference(rewrite,[status(thm)],[])).
% 0.53/0.72 tff(365,plain,
% 0.53/0.72 (((hskp27 | hskp22) | hskp17) <=> (hskp27 | hskp22 | hskp17)),
% 0.53/0.72 inference(rewrite,[status(thm)],[])).
% 0.53/0.72 tff(366,plain,
% 0.53/0.72 ((hskp27 | hskp22) <=> (hskp27 | hskp22)),
% 0.53/0.72 inference(rewrite,[status(thm)],[])).
% 0.53/0.72 tff(367,plain,
% 0.53/0.72 (((hskp27 | hskp22) | hskp17) <=> ((hskp27 | hskp22) | hskp17)),
% 0.53/0.72 inference(monotonicity,[status(thm)],[366])).
% 0.53/0.72 tff(368,plain,
% 0.53/0.72 (((hskp27 | hskp22) | hskp17) <=> (hskp27 | hskp22 | hskp17)),
% 0.53/0.72 inference(transitivity,[status(thm)],[367, 365])).
% 0.53/0.72 tff(369,axiom,((hskp27 | hskp22) | hskp17), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause31')).
% 0.53/0.72 tff(370,plain,
% 0.53/0.72 (hskp27 | hskp22 | hskp17),
% 0.53/0.72 inference(modus_ponens,[status(thm)],[369, 368])).
% 0.53/0.72 tff(371,plain,
% 0.53/0.72 (hskp27 | hskp22 | hskp17),
% 0.53/0.72 inference(modus_ponens,[status(thm)],[370, 364])).
% 0.53/0.72 tff(372,plain,
% 0.53/0.72 (hskp27 | hskp22 | hskp17),
% 0.53/0.72 inference(modus_ponens,[status(thm)],[371, 364])).
% 0.53/0.72 tff(373,plain,
% 0.53/0.72 (hskp27 | hskp22 | hskp17),
% 0.53/0.72 inference(modus_ponens,[status(thm)],[372, 364])).
% 0.53/0.72 tff(374,plain,
% 0.53/0.72 (hskp27 | hskp22 | hskp17),
% 0.53/0.72 inference(modus_ponens,[status(thm)],[373, 364])).
% 0.53/0.72 tff(375,plain,
% 0.53/0.72 (hskp22),
% 0.53/0.72 inference(unit_resolution,[status(thm)],[374, 33, 363])).
% 0.53/0.72 tff(376,plain,
% 0.53/0.72 (((~hskp22) | c1_1(a524)) <=> ((~hskp22) | c1_1(a524))),
% 0.53/0.72 inference(rewrite,[status(thm)],[])).
% 0.53/0.72 tff(377,axiom,((~hskp22) | c1_1(a524)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause53')).
% 0.53/0.72 tff(378,plain,
% 0.53/0.72 ((~hskp22) | c1_1(a524)),
% 0.53/0.72 inference(modus_ponens,[status(thm)],[377, 376])).
% 0.53/0.72 tff(379,plain,
% 0.53/0.72 ((~hskp22) | c1_1(a524)),
% 0.53/0.72 inference(modus_ponens,[status(thm)],[378, 376])).
% 0.53/0.72 tff(380,plain,
% 0.53/0.72 ((~hskp22) | c1_1(a524)),
% 0.53/0.72 inference(modus_ponens,[status(thm)],[379, 376])).
% 0.53/0.72 tff(381,plain,
% 0.53/0.72 ((~hskp22) | c1_1(a524)),
% 0.53/0.72 inference(modus_ponens,[status(thm)],[380, 376])).
% 0.53/0.72 tff(382,plain,
% 0.53/0.72 ((~hskp22) | c1_1(a524)),
% 0.53/0.72 inference(modus_ponens,[status(thm)],[381, 376])).
% 0.53/0.72 tff(383,plain,
% 0.53/0.72 (c1_1(a524)),
% 0.53/0.72 inference(unit_resolution,[status(thm)],[382, 375])).
% 0.53/0.72 tff(384,plain,
% 0.53/0.72 (((~hskp22) | c0_1(a524)) <=> ((~hskp22) | c0_1(a524))),
% 0.53/0.72 inference(rewrite,[status(thm)],[])).
% 0.53/0.72 tff(385,axiom,((~hskp22) | c0_1(a524)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause52')).
% 0.53/0.72 tff(386,plain,
% 0.53/0.72 ((~hskp22) | c0_1(a524)),
% 0.53/0.72 inference(modus_ponens,[status(thm)],[385, 384])).
% 0.53/0.72 tff(387,plain,
% 0.53/0.72 ((~hskp22) | c0_1(a524)),
% 0.53/0.72 inference(modus_ponens,[status(thm)],[386, 384])).
% 0.53/0.72 tff(388,plain,
% 0.53/0.72 ((~hskp22) | c0_1(a524)),
% 0.53/0.72 inference(modus_ponens,[status(thm)],[387, 384])).
% 0.53/0.72 tff(389,plain,
% 0.53/0.72 ((~hskp22) | c0_1(a524)),
% 0.53/0.72 inference(modus_ponens,[status(thm)],[388, 384])).
% 0.53/0.72 tff(390,plain,
% 0.53/0.72 ((~hskp22) | c0_1(a524)),
% 0.53/0.72 inference(modus_ponens,[status(thm)],[389, 384])).
% 0.53/0.72 tff(391,plain,
% 0.53/0.72 (c0_1(a524)),
% 0.53/0.72 inference(unit_resolution,[status(thm)],[390, 375])).
% 0.53/0.72 tff(392,plain,
% 0.53/0.72 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp3 | c2_1(a460) | c3_1(a460) | (~ndr1_0) | (~c0_1(a460)) | (~c0_1(a524)) | (~c1_1(a524)) | (~c3_1(a524)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | hskp3 | c2_1(a460) | c3_1(a460) | (~ndr1_0) | (~c0_1(a460)) | (~c0_1(a524)) | (~c1_1(a524)) | (~c3_1(a524)))),
% 0.53/0.72 inference(rewrite,[status(thm)],[])).
% 0.53/0.72 tff(393,plain,
% 0.53/0.72 ((hskp3 | (~ndr1_0) | (~c0_1(a524)) | (~c3_1(a524)) | (~c1_1(a524)) | c3_1(a460) | c2_1(a460) | (~c0_1(a460))) <=> (hskp3 | c2_1(a460) | c3_1(a460) | (~ndr1_0) | (~c0_1(a460)) | (~c0_1(a524)) | (~c1_1(a524)) | (~c3_1(a524)))),
% 0.53/0.72 inference(rewrite,[status(thm)],[])).
% 0.53/0.72 tff(394,plain,
% 0.53/0.72 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp3 | (~ndr1_0) | (~c0_1(a524)) | (~c3_1(a524)) | (~c1_1(a524)) | c3_1(a460) | c2_1(a460) | (~c0_1(a460)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp3 | c2_1(a460) | c3_1(a460) | (~ndr1_0) | (~c0_1(a460)) | (~c0_1(a524)) | (~c1_1(a524)) | (~c3_1(a524))))),
% 0.53/0.72 inference(monotonicity,[status(thm)],[393])).
% 0.53/0.72 tff(395,plain,
% 0.53/0.72 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp3 | (~ndr1_0) | (~c0_1(a524)) | (~c3_1(a524)) | (~c1_1(a524)) | c3_1(a460) | c2_1(a460) | (~c0_1(a460)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | hskp3 | c2_1(a460) | c3_1(a460) | (~ndr1_0) | (~c0_1(a460)) | (~c0_1(a524)) | (~c1_1(a524)) | (~c3_1(a524)))),
% 0.53/0.72 inference(transitivity,[status(thm)],[394, 392])).
% 0.53/0.72 tff(396,plain,
% 0.53/0.72 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp3 | (~ndr1_0) | (~c0_1(a524)) | (~c3_1(a524)) | (~c1_1(a524)) | c3_1(a460) | c2_1(a460) | (~c0_1(a460)))),
% 0.53/0.72 inference(quant_inst,[status(thm)],[])).
% 0.53/0.72 tff(397,plain,
% 0.53/0.72 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | hskp3 | c2_1(a460) | c3_1(a460) | (~ndr1_0) | (~c0_1(a460)) | (~c0_1(a524)) | (~c1_1(a524)) | (~c3_1(a524))),
% 0.53/0.72 inference(modus_ponens,[status(thm)],[396, 395])).
% 0.53/0.72 tff(398,plain,
% 0.53/0.72 (~c3_1(a524)),
% 0.53/0.72 inference(unit_resolution,[status(thm)],[397, 137, 329, 391, 383, 224, 1, 223, 21])).
% 0.53/0.72 tff(399,plain,
% 0.53/0.72 (((~hskp22) | (~c2_1(a524))) <=> ((~hskp22) | (~c2_1(a524)))),
% 0.53/0.72 inference(rewrite,[status(thm)],[])).
% 0.53/0.72 tff(400,plain,
% 0.53/0.72 (((~c2_1(a524)) | (~hskp22)) <=> ((~hskp22) | (~c2_1(a524)))),
% 0.53/0.72 inference(rewrite,[status(thm)],[])).
% 0.53/0.72 tff(401,axiom,((~c2_1(a524)) | (~hskp22)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause87')).
% 0.53/0.72 tff(402,plain,
% 0.53/0.72 ((~hskp22) | (~c2_1(a524))),
% 0.53/0.72 inference(modus_ponens,[status(thm)],[401, 400])).
% 0.53/0.72 tff(403,plain,
% 0.53/0.72 ((~hskp22) | (~c2_1(a524))),
% 0.53/0.72 inference(modus_ponens,[status(thm)],[402, 399])).
% 0.53/0.72 tff(404,plain,
% 0.53/0.72 (~c2_1(a524)),
% 0.53/0.72 inference(unit_resolution,[status(thm)],[403, 375])).
% 0.53/0.72 tff(405,plain,
% 0.53/0.72 (^[V: $i, U: $i] : refl((hskp27 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c0_1(V) | c2_1(V)) <=> (hskp27 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c0_1(V) | c2_1(V)))),
% 0.53/0.72 inference(bind,[status(th)],[])).
% 0.53/0.72 tff(406,plain,
% 0.53/0.72 (![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c0_1(V) | c2_1(V)) <=> ![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c0_1(V) | c2_1(V))),
% 0.53/0.72 inference(quant_intro,[status(thm)],[405])).
% 0.53/0.72 tff(407,plain,
% 0.53/0.72 (![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c0_1(V) | c2_1(V)) <=> ![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c0_1(V) | c2_1(V))),
% 0.53/0.72 inference(rewrite,[status(thm)],[])).
% 0.53/0.72 tff(408,plain,
% 0.53/0.72 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(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) | c2_1(U) | c1_1(U) | c3_1(U))), (((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U)))), ((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U)) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c0_1(V))), ((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c0_1(V)))), (((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_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)))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | c3_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))), (((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_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)))), ((((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c0_1(V) | c2_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c0_1(V) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c0_1(V) | c2_1(V))), ((((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c0_1(V) | c2_1(V)))), (((((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp27) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c0_1(V) | c2_1(V)) | hskp27))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c0_1(V) | c2_1(V)) | hskp27) <=> (hskp27 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c0_1(V) | c2_1(V))), (((((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp27) <=> (hskp27 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c0_1(V) | c2_1(V))))),
% 0.53/0.72 inference(bind,[status(th)],[])).
% 0.53/0.72 tff(409,plain,
% 0.53/0.72 (![V: $i, U: $i] : ((((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp27) <=> ![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c0_1(V) | c2_1(V))),
% 0.53/0.72 inference(quant_intro,[status(thm)],[408])).
% 0.53/0.72 tff(410,axiom,(![V: $i, U: $i] : ((((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp27)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause143')).
% 0.53/0.72 tff(411,plain,
% 0.53/0.72 (![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c0_1(V) | c2_1(V))),
% 0.53/0.72 inference(modus_ponens,[status(thm)],[410, 409])).
% 0.53/0.72 tff(412,plain,
% 0.53/0.72 (![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c0_1(V) | c2_1(V))),
% 0.53/0.72 inference(modus_ponens,[status(thm)],[411, 407])).
% 0.53/0.72 tff(413,plain,(
% 0.53/0.72 ![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c0_1(V) | c2_1(V))),
% 0.53/0.72 inference(skolemize,[status(sab)],[412])).
% 0.53/0.72 tff(414,plain,
% 0.53/0.72 (![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c0_1(V) | c2_1(V))),
% 0.53/0.72 inference(modus_ponens,[status(thm)],[413, 406])).
% 0.53/0.72 tff(415,assumption,(~hskp25), introduced(assumption)).
% 0.53/0.72 tff(416,plain,
% 0.53/0.72 (hskp14),
% 0.53/0.72 inference(unit_resolution,[status(thm)],[294, 415, 103])).
% 0.53/0.72 tff(417,plain,
% 0.53/0.72 (~c3_1(a488)),
% 0.53/0.72 inference(unit_resolution,[status(thm)],[50, 416])).
% 0.53/0.72 tff(418,plain,
% 0.53/0.72 (~c2_1(a488)),
% 0.53/0.72 inference(unit_resolution,[status(thm)],[56, 416])).
% 0.53/0.72 tff(419,plain,
% 0.53/0.72 (~c1_1(a488)),
% 0.53/0.72 inference(unit_resolution,[status(thm)],[62, 416])).
% 0.53/0.72 tff(420,assumption,(~hskp27), introduced(assumption)).
% 0.53/0.72 tff(421,plain,
% 0.53/0.72 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp27 | c1_1(a488) | c2_1(a488) | c3_1(a488) | (~ndr1_0) | c0_1(a488))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp27 | c1_1(a488) | c2_1(a488) | c3_1(a488) | (~ndr1_0) | c0_1(a488))),
% 0.53/0.72 inference(rewrite,[status(thm)],[])).
% 0.53/0.72 tff(422,plain,
% 0.53/0.72 ((hskp27 | (~ndr1_0) | c2_1(a488) | c1_1(a488) | c3_1(a488) | c3_1(a488) | c0_1(a488) | c2_1(a488)) <=> (hskp27 | c1_1(a488) | c2_1(a488) | c3_1(a488) | (~ndr1_0) | c0_1(a488))),
% 0.53/0.72 inference(rewrite,[status(thm)],[])).
% 0.53/0.72 tff(423,plain,
% 0.53/0.72 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp27 | (~ndr1_0) | c2_1(a488) | c1_1(a488) | c3_1(a488) | c3_1(a488) | c0_1(a488) | c2_1(a488))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp27 | c1_1(a488) | c2_1(a488) | c3_1(a488) | (~ndr1_0) | c0_1(a488)))),
% 0.53/0.72 inference(monotonicity,[status(thm)],[422])).
% 0.53/0.72 tff(424,plain,
% 0.53/0.72 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp27 | (~ndr1_0) | c2_1(a488) | c1_1(a488) | c3_1(a488) | c3_1(a488) | c0_1(a488) | c2_1(a488))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp27 | c1_1(a488) | c2_1(a488) | c3_1(a488) | (~ndr1_0) | c0_1(a488))),
% 0.53/0.72 inference(transitivity,[status(thm)],[423, 421])).
% 0.53/0.72 tff(425,plain,
% 0.53/0.72 ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp27 | (~ndr1_0) | c2_1(a488) | c1_1(a488) | c3_1(a488) | c3_1(a488) | c0_1(a488) | c2_1(a488))),
% 0.53/0.72 inference(quant_inst,[status(thm)],[])).
% 0.53/0.72 tff(426,plain,
% 0.53/0.72 ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp27 | c1_1(a488) | c2_1(a488) | c3_1(a488) | (~ndr1_0) | c0_1(a488)),
% 0.53/0.72 inference(modus_ponens,[status(thm)],[425, 424])).
% 0.53/0.72 tff(427,plain,
% 0.53/0.72 (c0_1(a488)),
% 0.53/0.72 inference(unit_resolution,[status(thm)],[426, 137, 420, 419, 418, 417, 414])).
% 0.53/0.72 tff(428,plain,
% 0.53/0.72 (^[V: $i, U: $i] : refl((hskp25 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V)) <=> (hskp25 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V)))),
% 0.53/0.72 inference(bind,[status(th)],[])).
% 0.53/0.72 tff(429,plain,
% 0.53/0.72 (![V: $i, U: $i] : (hskp25 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V)) <=> ![V: $i, U: $i] : (hskp25 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))),
% 0.53/0.72 inference(quant_intro,[status(thm)],[428])).
% 0.53/0.72 tff(430,plain,
% 0.53/0.72 (![V: $i, U: $i] : (hskp25 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V)) <=> ![V: $i, U: $i] : (hskp25 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))),
% 0.53/0.72 inference(rewrite,[status(thm)],[])).
% 0.53/0.72 tff(431,plain,
% 0.53/0.72 (^[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)) | 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) | c1_1(U) | c3_1(U) | (~c0_1(U)))), (((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U))))), ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U))) | c0_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U))) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V))), ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V)))), (((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V)) | c1_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V))), (((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V)))), ((((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))), ((((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V)))), (((((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp25) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V)) | hskp25))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V)) | hskp25) <=> (hskp25 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))), (((((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp25) <=> (hskp25 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))))),
% 0.53/0.72 inference(bind,[status(th)],[])).
% 0.53/0.72 tff(432,plain,
% 0.53/0.72 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp25) <=> ![V: $i, U: $i] : (hskp25 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))),
% 0.53/0.72 inference(quant_intro,[status(thm)],[431])).
% 0.53/0.72 tff(433,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp25)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause145')).
% 0.53/0.72 tff(434,plain,
% 0.53/0.72 (![V: $i, U: $i] : (hskp25 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))),
% 0.53/0.72 inference(modus_ponens,[status(thm)],[433, 432])).
% 0.53/0.72 tff(435,plain,
% 0.53/0.72 (![V: $i, U: $i] : (hskp25 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))),
% 0.53/0.72 inference(modus_ponens,[status(thm)],[434, 430])).
% 0.53/0.72 tff(436,plain,(
% 0.53/0.72 ![V: $i, U: $i] : (hskp25 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))),
% 0.53/0.72 inference(skolemize,[status(sab)],[435])).
% 0.53/0.72 tff(437,plain,
% 0.53/0.72 (![V: $i, U: $i] : (hskp25 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))),
% 0.53/0.72 inference(modus_ponens,[status(thm)],[436, 429])).
% 0.53/0.72 tff(438,assumption,(~c3_1(a524)), introduced(assumption)).
% 0.53/0.72 tff(439,assumption,(~c2_1(a524)), introduced(assumption)).
% 0.53/0.72 tff(440,assumption,(c0_1(a524)), introduced(assumption)).
% 0.53/0.72 tff(441,plain,
% 0.53/0.72 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp12 | c2_1(a524) | c1_1(a488) | c3_1(a488) | (~ndr1_0) | (~c0_1(a488)) | (~c0_1(a524)) | c3_1(a524))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | hskp12 | c2_1(a524) | c1_1(a488) | c3_1(a488) | (~ndr1_0) | (~c0_1(a488)) | (~c0_1(a524)) | c3_1(a524))),
% 0.53/0.72 inference(rewrite,[status(thm)],[])).
% 0.53/0.72 tff(442,plain,
% 0.53/0.72 ((hskp12 | (~ndr1_0) | c2_1(a524) | c3_1(a524) | (~c0_1(a524)) | c3_1(a488) | c1_1(a488) | (~c0_1(a488))) <=> (hskp12 | c2_1(a524) | c1_1(a488) | c3_1(a488) | (~ndr1_0) | (~c0_1(a488)) | (~c0_1(a524)) | c3_1(a524))),
% 0.53/0.72 inference(rewrite,[status(thm)],[])).
% 0.53/0.72 tff(443,plain,
% 0.53/0.72 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp12 | (~ndr1_0) | c2_1(a524) | c3_1(a524) | (~c0_1(a524)) | c3_1(a488) | c1_1(a488) | (~c0_1(a488)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp12 | c2_1(a524) | c1_1(a488) | c3_1(a488) | (~ndr1_0) | (~c0_1(a488)) | (~c0_1(a524)) | c3_1(a524)))),
% 0.53/0.72 inference(monotonicity,[status(thm)],[442])).
% 0.53/0.72 tff(444,plain,
% 0.53/0.72 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp12 | (~ndr1_0) | c2_1(a524) | c3_1(a524) | (~c0_1(a524)) | c3_1(a488) | c1_1(a488) | (~c0_1(a488)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | hskp12 | c2_1(a524) | c1_1(a488) | c3_1(a488) | (~ndr1_0) | (~c0_1(a488)) | (~c0_1(a524)) | c3_1(a524))),
% 0.53/0.72 inference(transitivity,[status(thm)],[443, 441])).
% 0.53/0.72 tff(445,plain,
% 0.53/0.72 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp12 | (~ndr1_0) | c2_1(a524) | c3_1(a524) | (~c0_1(a524)) | c3_1(a488) | c1_1(a488) | (~c0_1(a488)))),
% 0.53/0.72 inference(quant_inst,[status(thm)],[])).
% 0.53/0.72 tff(446,plain,
% 0.53/0.72 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | hskp12 | c2_1(a524) | c1_1(a488) | c3_1(a488) | (~ndr1_0) | (~c0_1(a488)) | (~c0_1(a524)) | c3_1(a524)),
% 0.53/0.72 inference(modus_ponens,[status(thm)],[445, 444])).
% 0.53/0.72 tff(447,plain,
% 0.53/0.72 (hskp12),
% 0.53/0.72 inference(unit_resolution,[status(thm)],[446, 137, 440, 439, 419, 417, 44, 438, 427])).
% 0.53/0.72 tff(448,plain,
% 0.53/0.72 (~c2_1(a480)),
% 0.53/0.72 inference(unit_resolution,[status(thm)],[89, 447])).
% 0.53/0.72 tff(449,plain,
% 0.53/0.72 (~c1_1(a480)),
% 0.53/0.72 inference(unit_resolution,[status(thm)],[95, 447])).
% 0.53/0.72 tff(450,plain,
% 0.53/0.72 (~c0_1(a480)),
% 0.53/0.72 inference(unit_resolution,[status(thm)],[101, 447])).
% 0.53/0.72 tff(451,plain,
% 0.53/0.72 (((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | (hskp25 | c1_1(a488) | c3_1(a488) | c0_1(a480) | c1_1(a480) | c2_1(a480) | (~ndr1_0) | (~c0_1(a488)))) <=> ((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | hskp25 | c1_1(a488) | c3_1(a488) | c0_1(a480) | c1_1(a480) | c2_1(a480) | (~ndr1_0) | (~c0_1(a488)))),
% 0.53/0.72 inference(rewrite,[status(thm)],[])).
% 0.53/0.72 tff(452,plain,
% 0.53/0.72 ((hskp25 | (~ndr1_0) | c1_1(a488) | c3_1(a488) | (~c0_1(a488)) | c1_1(a480) | c0_1(a480) | c2_1(a480)) <=> (hskp25 | c1_1(a488) | c3_1(a488) | c0_1(a480) | c1_1(a480) | c2_1(a480) | (~ndr1_0) | (~c0_1(a488)))),
% 0.53/0.72 inference(rewrite,[status(thm)],[])).
% 0.53/0.72 tff(453,plain,
% 0.53/0.72 (((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | (hskp25 | (~ndr1_0) | c1_1(a488) | c3_1(a488) | (~c0_1(a488)) | c1_1(a480) | c0_1(a480) | c2_1(a480))) <=> ((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | (hskp25 | c1_1(a488) | c3_1(a488) | c0_1(a480) | c1_1(a480) | c2_1(a480) | (~ndr1_0) | (~c0_1(a488))))),
% 0.53/0.72 inference(monotonicity,[status(thm)],[452])).
% 0.53/0.72 tff(454,plain,
% 0.53/0.72 (((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | (hskp25 | (~ndr1_0) | c1_1(a488) | c3_1(a488) | (~c0_1(a488)) | c1_1(a480) | c0_1(a480) | c2_1(a480))) <=> ((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | hskp25 | c1_1(a488) | c3_1(a488) | c0_1(a480) | c1_1(a480) | c2_1(a480) | (~ndr1_0) | (~c0_1(a488)))),
% 0.53/0.73 inference(transitivity,[status(thm)],[453, 451])).
% 0.53/0.73 tff(455,plain,
% 0.53/0.73 ((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | (hskp25 | (~ndr1_0) | c1_1(a488) | c3_1(a488) | (~c0_1(a488)) | c1_1(a480) | c0_1(a480) | c2_1(a480))),
% 0.53/0.73 inference(quant_inst,[status(thm)],[])).
% 0.53/0.73 tff(456,plain,
% 0.53/0.73 ((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | hskp25 | c1_1(a488) | c3_1(a488) | c0_1(a480) | c1_1(a480) | c2_1(a480) | (~ndr1_0) | (~c0_1(a488))),
% 0.53/0.73 inference(modus_ponens,[status(thm)],[455, 454])).
% 0.53/0.73 tff(457,plain,
% 0.53/0.73 ($false),
% 0.53/0.73 inference(unit_resolution,[status(thm)],[456, 137, 415, 419, 417, 450, 449, 448, 437, 427])).
% 0.53/0.73 tff(458,plain,(hskp25 | (~c0_1(a524)) | c2_1(a524) | c3_1(a524) | hskp27 | hskp5), inference(lemma,lemma(discharge,[]))).
% 0.53/0.73 tff(459,plain,
% 0.53/0.73 (hskp25),
% 0.53/0.73 inference(unit_resolution,[status(thm)],[458, 391, 404, 398, 363, 103])).
% 0.53/0.73 tff(460,plain,
% 0.53/0.73 (c2_1(a461)),
% 0.53/0.73 inference(unit_resolution,[status(thm)],[310, 459])).
% 0.53/0.73 tff(461,plain,
% 0.53/0.73 (c0_1(a461)),
% 0.53/0.73 inference(unit_resolution,[status(thm)],[318, 459])).
% 0.53/0.73 tff(462,plain,
% 0.53/0.73 (c3_1(a461)),
% 0.53/0.73 inference(unit_resolution,[status(thm)],[302, 459])).
% 0.53/0.73 tff(463,assumption,(~c1_1(a461)), introduced(assumption)).
% 0.53/0.73 tff(464,assumption,(c3_1(a461)), introduced(assumption)).
% 0.53/0.73 tff(465,assumption,(c2_1(a461)), introduced(assumption)).
% 0.53/0.73 tff(466,assumption,(c0_1(a461)), introduced(assumption)).
% 0.53/0.73 tff(467,plain,
% 0.53/0.73 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp17 | (~ndr1_0) | (~c0_1(a461)) | (~c3_1(a461)) | c1_1(a461) | (~c2_1(a461)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))) | hskp17 | (~ndr1_0) | (~c0_1(a461)) | (~c3_1(a461)) | c1_1(a461) | (~c2_1(a461)))),
% 0.53/0.73 inference(rewrite,[status(thm)],[])).
% 0.53/0.73 tff(468,plain,
% 0.53/0.73 ((hskp17 | (~ndr1_0) | (~c2_1(a461)) | (~c0_1(a461)) | (~c3_1(a461)) | c1_1(a461) | (~c0_1(a461)) | (~c2_1(a461))) <=> (hskp17 | (~ndr1_0) | (~c0_1(a461)) | (~c3_1(a461)) | c1_1(a461) | (~c2_1(a461)))),
% 0.53/0.73 inference(rewrite,[status(thm)],[])).
% 0.53/0.73 tff(469,plain,
% 0.53/0.73 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp17 | (~ndr1_0) | (~c2_1(a461)) | (~c0_1(a461)) | (~c3_1(a461)) | c1_1(a461) | (~c0_1(a461)) | (~c2_1(a461)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp17 | (~ndr1_0) | (~c0_1(a461)) | (~c3_1(a461)) | c1_1(a461) | (~c2_1(a461))))),
% 0.53/0.73 inference(monotonicity,[status(thm)],[468])).
% 0.53/0.73 tff(470,plain,
% 0.53/0.73 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp17 | (~ndr1_0) | (~c2_1(a461)) | (~c0_1(a461)) | (~c3_1(a461)) | c1_1(a461) | (~c0_1(a461)) | (~c2_1(a461)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))) | hskp17 | (~ndr1_0) | (~c0_1(a461)) | (~c3_1(a461)) | c1_1(a461) | (~c2_1(a461)))),
% 0.53/0.73 inference(transitivity,[status(thm)],[469, 467])).
% 0.53/0.73 tff(471,plain,
% 0.53/0.73 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp17 | (~ndr1_0) | (~c2_1(a461)) | (~c0_1(a461)) | (~c3_1(a461)) | c1_1(a461) | (~c0_1(a461)) | (~c2_1(a461)))),
% 0.53/0.73 inference(quant_inst,[status(thm)],[])).
% 0.53/0.73 tff(472,plain,
% 0.53/0.73 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))) | hskp17 | (~ndr1_0) | (~c0_1(a461)) | (~c3_1(a461)) | c1_1(a461) | (~c2_1(a461))),
% 0.53/0.73 inference(modus_ponens,[status(thm)],[471, 470])).
% 0.53/0.73 tff(473,plain,
% 0.53/0.73 ($false),
% 0.53/0.73 inference(unit_resolution,[status(thm)],[472, 141, 33, 466, 465, 464, 11, 463])).
% 0.53/0.73 tff(474,plain,(c1_1(a461) | (~ndr1_0) | hskp17 | (~c0_1(a461)) | (~c2_1(a461)) | (~c3_1(a461))), inference(lemma,lemma(discharge,[]))).
% 0.53/0.73 tff(475,plain,
% 0.53/0.73 (c1_1(a461)),
% 0.53/0.73 inference(unit_resolution,[status(thm)],[474, 462, 33, 461, 460, 137])).
% 0.53/0.73 tff(476,plain,
% 0.53/0.73 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp3 | c2_1(a460) | c3_1(a460) | (~ndr1_0) | (~c0_1(a460)) | (~c0_1(a461)) | (~c3_1(a461)) | (~c1_1(a461)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | hskp3 | c2_1(a460) | c3_1(a460) | (~ndr1_0) | (~c0_1(a460)) | (~c0_1(a461)) | (~c3_1(a461)) | (~c1_1(a461)))),
% 0.53/0.73 inference(rewrite,[status(thm)],[])).
% 0.53/0.73 tff(477,plain,
% 0.53/0.73 ((hskp3 | (~ndr1_0) | (~c0_1(a461)) | (~c3_1(a461)) | (~c1_1(a461)) | c3_1(a460) | c2_1(a460) | (~c0_1(a460))) <=> (hskp3 | c2_1(a460) | c3_1(a460) | (~ndr1_0) | (~c0_1(a460)) | (~c0_1(a461)) | (~c3_1(a461)) | (~c1_1(a461)))),
% 0.53/0.73 inference(rewrite,[status(thm)],[])).
% 0.53/0.73 tff(478,plain,
% 0.53/0.73 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp3 | (~ndr1_0) | (~c0_1(a461)) | (~c3_1(a461)) | (~c1_1(a461)) | c3_1(a460) | c2_1(a460) | (~c0_1(a460)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp3 | c2_1(a460) | c3_1(a460) | (~ndr1_0) | (~c0_1(a460)) | (~c0_1(a461)) | (~c3_1(a461)) | (~c1_1(a461))))),
% 0.53/0.73 inference(monotonicity,[status(thm)],[477])).
% 0.53/0.73 tff(479,plain,
% 0.53/0.73 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp3 | (~ndr1_0) | (~c0_1(a461)) | (~c3_1(a461)) | (~c1_1(a461)) | c3_1(a460) | c2_1(a460) | (~c0_1(a460)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | hskp3 | c2_1(a460) | c3_1(a460) | (~ndr1_0) | (~c0_1(a460)) | (~c0_1(a461)) | (~c3_1(a461)) | (~c1_1(a461)))),
% 0.53/0.73 inference(transitivity,[status(thm)],[478, 476])).
% 0.53/0.73 tff(480,plain,
% 0.53/0.73 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp3 | (~ndr1_0) | (~c0_1(a461)) | (~c3_1(a461)) | (~c1_1(a461)) | c3_1(a460) | c2_1(a460) | (~c0_1(a460)))),
% 0.53/0.73 inference(quant_inst,[status(thm)],[])).
% 0.53/0.73 tff(481,plain,
% 0.53/0.73 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | hskp3 | c2_1(a460) | c3_1(a460) | (~ndr1_0) | (~c0_1(a460)) | (~c0_1(a461)) | (~c3_1(a461)) | (~c1_1(a461))),
% 0.53/0.73 inference(modus_ponens,[status(thm)],[480, 479])).
% 0.53/0.73 tff(482,plain,
% 0.53/0.73 ($false),
% 0.53/0.73 inference(unit_resolution,[status(thm)],[481, 137, 329, 461, 462, 224, 1, 223, 21, 475])).
% 0.53/0.73 tff(483,plain,(hskp17 | hskp3 | (~c0_1(a460)) | c2_1(a460) | c3_1(a460) | hskp5), inference(lemma,lemma(discharge,[]))).
% 0.53/0.73 tff(484,plain,
% 0.53/0.73 (hskp17),
% 0.53/0.73 inference(unit_resolution,[status(thm)],[483, 328, 224, 1, 223, 103])).
% 0.53/0.73 tff(485,plain,
% 0.53/0.73 (^[V: $i, U: $i] : refl((hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)) <=> (hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)))),
% 0.53/0.73 inference(bind,[status(th)],[])).
% 0.53/0.73 tff(486,plain,
% 0.53/0.73 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 0.53/0.73 inference(quant_intro,[status(thm)],[485])).
% 0.53/0.73 tff(487,plain,
% 0.53/0.73 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 0.53/0.73 inference(rewrite,[status(thm)],[])).
% 0.53/0.73 tff(488,plain,
% 0.53/0.73 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) <=> ((~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | c0_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U))) | c0_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U))) | c0_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | c0_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V)) | c1_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | c0_1(V)) | c1_1(V)) | c3_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | c0_1(V)) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp5) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)) | hskp5))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)) | hskp5) <=> (hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp5) <=> (hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))))),
% 0.53/0.73 inference(bind,[status(th)],[])).
% 0.53/0.73 tff(489,plain,
% 0.53/0.73 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp5) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 0.53/0.73 inference(quant_intro,[status(thm)],[488])).
% 0.53/0.73 tff(490,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause152')).
% 0.53/0.73 tff(491,plain,
% 0.53/0.73 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 0.53/0.73 inference(modus_ponens,[status(thm)],[490, 489])).
% 0.53/0.73 tff(492,plain,
% 0.53/0.73 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 0.53/0.73 inference(modus_ponens,[status(thm)],[491, 487])).
% 0.53/0.73 tff(493,plain,(
% 0.53/0.73 ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 0.53/0.73 inference(skolemize,[status(sab)],[492])).
% 0.53/0.73 tff(494,plain,
% 0.53/0.73 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 0.53/0.73 inference(modus_ponens,[status(thm)],[493, 486])).
% 0.53/0.73 tff(495,assumption,(~c3_1(a494)), introduced(assumption)).
% 0.53/0.73 tff(496,plain,
% 0.53/0.73 (hskp17),
% 0.53/0.73 inference(unit_resolution,[status(thm)],[483, 329, 224, 1, 223, 103])).
% 0.53/0.73 tff(497,plain,
% 0.53/0.73 (((~hskp17) | (~c1_1(a494))) <=> ((~hskp17) | (~c1_1(a494)))),
% 0.53/0.73 inference(rewrite,[status(thm)],[])).
% 0.53/0.73 tff(498,plain,
% 0.53/0.73 (((~c1_1(a494)) | (~hskp17)) <=> ((~hskp17) | (~c1_1(a494)))),
% 0.53/0.73 inference(rewrite,[status(thm)],[])).
% 0.53/0.73 tff(499,axiom,((~c1_1(a494)) | (~hskp17)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause93')).
% 0.53/0.73 tff(500,plain,
% 0.53/0.73 ((~hskp17) | (~c1_1(a494))),
% 0.53/0.73 inference(modus_ponens,[status(thm)],[499, 498])).
% 0.53/0.73 tff(501,plain,
% 0.53/0.73 ((~hskp17) | (~c1_1(a494))),
% 0.53/0.73 inference(modus_ponens,[status(thm)],[500, 497])).
% 0.53/0.73 tff(502,plain,
% 0.53/0.73 (~c1_1(a494)),
% 0.53/0.73 inference(unit_resolution,[status(thm)],[501, 496])).
% 0.53/0.73 tff(503,plain,
% 0.53/0.73 (((~hskp17) | (~c0_1(a494))) <=> ((~hskp17) | (~c0_1(a494)))),
% 0.53/0.73 inference(rewrite,[status(thm)],[])).
% 0.53/0.73 tff(504,plain,
% 0.53/0.73 (((~c0_1(a494)) | (~hskp17)) <=> ((~hskp17) | (~c0_1(a494)))),
% 0.53/0.73 inference(rewrite,[status(thm)],[])).
% 0.53/0.73 tff(505,axiom,((~c0_1(a494)) | (~hskp17)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause92')).
% 0.53/0.73 tff(506,plain,
% 0.53/0.73 ((~hskp17) | (~c0_1(a494))),
% 0.53/0.73 inference(modus_ponens,[status(thm)],[505, 504])).
% 0.53/0.73 tff(507,plain,
% 0.53/0.73 ((~hskp17) | (~c0_1(a494))),
% 0.53/0.73 inference(modus_ponens,[status(thm)],[506, 503])).
% 0.53/0.73 tff(508,plain,
% 0.53/0.73 (~c0_1(a494)),
% 0.53/0.73 inference(unit_resolution,[status(thm)],[507, 496])).
% 0.53/0.73 tff(509,assumption,(~c2_1(a494)), introduced(assumption)).
% 0.53/0.73 tff(510,assumption,(~c1_1(a494)), introduced(assumption)).
% 0.53/0.73 tff(511,assumption,(~c0_1(a494)), introduced(assumption)).
% 0.53/0.73 tff(512,plain,
% 0.53/0.73 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp27 | c0_1(a494) | c1_1(a494) | c3_1(a494) | (~ndr1_0) | c2_1(a494))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp27 | c0_1(a494) | c1_1(a494) | c3_1(a494) | (~ndr1_0) | c2_1(a494))),
% 0.53/0.73 inference(rewrite,[status(thm)],[])).
% 0.53/0.73 tff(513,plain,
% 0.53/0.73 ((hskp27 | (~ndr1_0) | c2_1(a494) | c1_1(a494) | c3_1(a494) | c3_1(a494) | c0_1(a494) | c2_1(a494)) <=> (hskp27 | c0_1(a494) | c1_1(a494) | c3_1(a494) | (~ndr1_0) | c2_1(a494))),
% 0.53/0.73 inference(rewrite,[status(thm)],[])).
% 0.53/0.73 tff(514,plain,
% 0.53/0.73 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp27 | (~ndr1_0) | c2_1(a494) | c1_1(a494) | c3_1(a494) | c3_1(a494) | c0_1(a494) | c2_1(a494))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp27 | c0_1(a494) | c1_1(a494) | c3_1(a494) | (~ndr1_0) | c2_1(a494)))),
% 0.53/0.73 inference(monotonicity,[status(thm)],[513])).
% 0.53/0.73 tff(515,plain,
% 0.53/0.73 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp27 | (~ndr1_0) | c2_1(a494) | c1_1(a494) | c3_1(a494) | c3_1(a494) | c0_1(a494) | c2_1(a494))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp27 | c0_1(a494) | c1_1(a494) | c3_1(a494) | (~ndr1_0) | c2_1(a494))),
% 0.53/0.73 inference(transitivity,[status(thm)],[514, 512])).
% 0.53/0.73 tff(516,plain,
% 0.53/0.73 ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp27 | (~ndr1_0) | c2_1(a494) | c1_1(a494) | c3_1(a494) | c3_1(a494) | c0_1(a494) | c2_1(a494))),
% 0.53/0.73 inference(quant_inst,[status(thm)],[])).
% 0.53/0.73 tff(517,plain,
% 0.53/0.73 ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp27 | c0_1(a494) | c1_1(a494) | c3_1(a494) | (~ndr1_0) | c2_1(a494)),
% 0.53/0.73 inference(modus_ponens,[status(thm)],[516, 515])).
% 0.53/0.73 tff(518,plain,
% 0.53/0.73 ($false),
% 0.53/0.73 inference(unit_resolution,[status(thm)],[517, 141, 420, 511, 510, 495, 414, 509])).
% 0.53/0.73 tff(519,plain,(c2_1(a494) | (~ndr1_0) | hskp27 | c0_1(a494) | c1_1(a494) | c3_1(a494)), inference(lemma,lemma(discharge,[]))).
% 0.53/0.73 tff(520,plain,
% 0.53/0.73 (c2_1(a494)),
% 0.53/0.73 inference(unit_resolution,[status(thm)],[519, 363, 137, 508, 502, 495])).
% 0.53/0.73 tff(521,plain,
% 0.53/0.73 (^[V: $i, U: $i] : refl((hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) <=> (hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))))),
% 0.53/0.73 inference(bind,[status(th)],[])).
% 0.53/0.73 tff(522,plain,
% 0.53/0.73 (![V: $i, U: $i] : (hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.53/0.73 inference(quant_intro,[status(thm)],[521])).
% 0.53/0.73 tff(523,plain,
% 0.53/0.73 (![V: $i, U: $i] : (hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.53/0.73 inference(rewrite,[status(thm)],[])).
% 0.53/0.73 tff(524,plain,
% 0.53/0.73 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V))) | c1_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(V)) | c1_1(V)) | hskp26) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) | hskp26))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) | hskp26) <=> (hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(V)) | c1_1(V)) | hskp26) <=> (hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))))),
% 0.53/0.73 inference(bind,[status(th)],[])).
% 0.53/0.73 tff(525,plain,
% 0.53/0.73 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(V)) | c1_1(V)) | hskp26) <=> ![V: $i, U: $i] : (hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.53/0.73 inference(quant_intro,[status(thm)],[524])).
% 0.53/0.73 tff(526,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(V)) | c1_1(V)) | hskp26)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause160')).
% 0.53/0.73 tff(527,plain,
% 0.53/0.73 (![V: $i, U: $i] : (hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.53/0.73 inference(modus_ponens,[status(thm)],[526, 525])).
% 0.53/0.73 tff(528,plain,
% 0.53/0.73 (![V: $i, U: $i] : (hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.53/0.73 inference(modus_ponens,[status(thm)],[527, 523])).
% 0.53/0.73 tff(529,plain,(
% 0.53/0.73 ![V: $i, U: $i] : (hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.53/0.73 inference(skolemize,[status(sab)],[528])).
% 0.53/0.73 tff(530,plain,
% 0.53/0.73 (![V: $i, U: $i] : (hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.53/0.73 inference(modus_ponens,[status(thm)],[529, 522])).
% 0.53/0.73 tff(531,plain,
% 0.53/0.73 (^[V: $i, U: $i] : refl((hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)) <=> (hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)))),
% 0.53/0.73 inference(bind,[status(th)],[])).
% 0.53/0.73 tff(532,plain,
% 0.53/0.73 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 0.53/0.73 inference(quant_intro,[status(thm)],[531])).
% 0.53/0.73 tff(533,plain,
% 0.53/0.73 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 0.53/0.73 inference(rewrite,[status(thm)],[])).
% 0.53/0.73 tff(534,plain,
% 0.53/0.73 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | c0_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | c0_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V)) | c1_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_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) | (~c2_1(U)) | (~c3_1(U)) | (~c1_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(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | 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(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | 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(V)) | hskp4) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)) | hskp4))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)) | hskp4) <=> (hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | 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(V)) | hskp4) <=> (hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))))),
% 0.53/0.73 inference(bind,[status(th)],[])).
% 0.53/0.73 tff(535,plain,
% 0.53/0.73 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp4) <=> ![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 0.53/0.73 inference(quant_intro,[status(thm)],[534])).
% 0.53/0.73 tff(536,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause153')).
% 0.53/0.73 tff(537,plain,
% 0.53/0.73 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 0.53/0.73 inference(modus_ponens,[status(thm)],[536, 535])).
% 0.53/0.73 tff(538,plain,
% 0.53/0.73 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 0.53/0.73 inference(modus_ponens,[status(thm)],[537, 533])).
% 0.53/0.73 tff(539,plain,(
% 0.53/0.73 ![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 0.53/0.73 inference(skolemize,[status(sab)],[538])).
% 0.53/0.73 tff(540,plain,
% 0.53/0.73 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 0.53/0.73 inference(modus_ponens,[status(thm)],[539, 532])).
% 0.53/0.73 tff(541,assumption,(~hskp4), introduced(assumption)).
% 0.53/0.73 tff(542,assumption,(~c2_1(a492)), introduced(assumption)).
% 0.53/0.73 tff(543,assumption,(hskp15), introduced(assumption)).
% 0.53/0.73 tff(544,plain,
% 0.53/0.73 (((~hskp15) | c1_1(a492)) <=> ((~hskp15) | c1_1(a492))),
% 0.53/0.73 inference(rewrite,[status(thm)],[])).
% 0.53/0.73 tff(545,axiom,((~hskp15) | c1_1(a492)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause63')).
% 0.53/0.73 tff(546,plain,
% 0.53/0.73 ((~hskp15) | c1_1(a492)),
% 0.53/0.73 inference(modus_ponens,[status(thm)],[545, 544])).
% 0.53/0.73 tff(547,plain,
% 0.53/0.73 ((~hskp15) | c1_1(a492)),
% 0.53/0.73 inference(modus_ponens,[status(thm)],[546, 544])).
% 0.53/0.73 tff(548,plain,
% 0.53/0.73 ((~hskp15) | c1_1(a492)),
% 0.53/0.73 inference(modus_ponens,[status(thm)],[547, 544])).
% 0.53/0.73 tff(549,plain,
% 0.53/0.73 ((~hskp15) | c1_1(a492)),
% 0.53/0.73 inference(modus_ponens,[status(thm)],[548, 544])).
% 0.53/0.73 tff(550,plain,
% 0.53/0.73 ((~hskp15) | c1_1(a492)),
% 0.53/0.73 inference(modus_ponens,[status(thm)],[549, 544])).
% 0.53/0.74 tff(551,plain,
% 0.53/0.74 (c1_1(a492)),
% 0.53/0.74 inference(unit_resolution,[status(thm)],[550, 543])).
% 0.53/0.74 tff(552,plain,
% 0.53/0.74 (((~hskp15) | c3_1(a492)) <=> ((~hskp15) | c3_1(a492))),
% 0.53/0.74 inference(rewrite,[status(thm)],[])).
% 0.53/0.74 tff(553,axiom,((~hskp15) | c3_1(a492)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause64')).
% 0.53/0.74 tff(554,plain,
% 0.53/0.74 ((~hskp15) | c3_1(a492)),
% 0.53/0.74 inference(modus_ponens,[status(thm)],[553, 552])).
% 0.53/0.74 tff(555,plain,
% 0.53/0.74 ((~hskp15) | c3_1(a492)),
% 0.53/0.74 inference(modus_ponens,[status(thm)],[554, 552])).
% 0.53/0.74 tff(556,plain,
% 0.53/0.74 ((~hskp15) | c3_1(a492)),
% 0.53/0.74 inference(modus_ponens,[status(thm)],[555, 552])).
% 0.53/0.74 tff(557,plain,
% 0.53/0.74 ((~hskp15) | c3_1(a492)),
% 0.53/0.74 inference(modus_ponens,[status(thm)],[556, 552])).
% 0.53/0.74 tff(558,plain,
% 0.53/0.74 ((~hskp15) | c3_1(a492)),
% 0.53/0.74 inference(modus_ponens,[status(thm)],[557, 552])).
% 0.53/0.74 tff(559,plain,
% 0.53/0.74 (c3_1(a492)),
% 0.53/0.74 inference(unit_resolution,[status(thm)],[558, 543])).
% 0.53/0.74 tff(560,plain,
% 0.53/0.74 (^[V: $i, U: $i] : refl((hskp4 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)) <=> (hskp4 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)))),
% 0.53/0.74 inference(bind,[status(th)],[])).
% 0.53/0.74 tff(561,plain,
% 0.53/0.74 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 0.53/0.74 inference(quant_intro,[status(thm)],[560])).
% 0.53/0.74 tff(562,plain,
% 0.53/0.74 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 0.53/0.74 inference(rewrite,[status(thm)],[])).
% 0.53/0.74 tff(563,plain,
% 0.53/0.74 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V)) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V)))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp4) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)) | hskp4))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)) | hskp4) <=> (hskp4 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp4) <=> (hskp4 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))))),
% 0.53/0.74 inference(bind,[status(th)],[])).
% 0.53/0.74 tff(564,plain,
% 0.53/0.74 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp4) <=> ![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 0.53/0.74 inference(quant_intro,[status(thm)],[563])).
% 0.53/0.74 tff(565,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause149')).
% 0.53/0.74 tff(566,plain,
% 0.53/0.74 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 0.53/0.74 inference(modus_ponens,[status(thm)],[565, 564])).
% 0.53/0.74 tff(567,plain,
% 0.53/0.74 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 0.53/0.74 inference(modus_ponens,[status(thm)],[566, 562])).
% 0.53/0.74 tff(568,plain,(
% 0.53/0.74 ![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 0.53/0.74 inference(skolemize,[status(sab)],[567])).
% 0.53/0.74 tff(569,plain,
% 0.53/0.74 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 0.53/0.74 inference(modus_ponens,[status(thm)],[568, 561])).
% 0.53/0.74 tff(570,plain,
% 0.53/0.74 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp4 | c0_1(a494) | c1_1(a494) | c3_1(a494) | c2_1(a492) | (~ndr1_0) | (~c1_1(a492)) | (~c3_1(a492)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp4 | c0_1(a494) | c1_1(a494) | c3_1(a494) | c2_1(a492) | (~ndr1_0) | (~c1_1(a492)) | (~c3_1(a492)))),
% 0.53/0.74 inference(rewrite,[status(thm)],[])).
% 0.53/0.74 tff(571,plain,
% 0.53/0.74 ((hskp4 | (~ndr1_0) | c2_1(a492) | (~c3_1(a492)) | (~c1_1(a492)) | c3_1(a494) | c1_1(a494) | c0_1(a494)) <=> (hskp4 | c0_1(a494) | c1_1(a494) | c3_1(a494) | c2_1(a492) | (~ndr1_0) | (~c1_1(a492)) | (~c3_1(a492)))),
% 0.53/0.74 inference(rewrite,[status(thm)],[])).
% 0.53/0.74 tff(572,plain,
% 0.53/0.74 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp4 | (~ndr1_0) | c2_1(a492) | (~c3_1(a492)) | (~c1_1(a492)) | c3_1(a494) | c1_1(a494) | c0_1(a494))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp4 | c0_1(a494) | c1_1(a494) | c3_1(a494) | c2_1(a492) | (~ndr1_0) | (~c1_1(a492)) | (~c3_1(a492))))),
% 0.53/0.74 inference(monotonicity,[status(thm)],[571])).
% 0.53/0.74 tff(573,plain,
% 0.53/0.74 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp4 | (~ndr1_0) | c2_1(a492) | (~c3_1(a492)) | (~c1_1(a492)) | c3_1(a494) | c1_1(a494) | c0_1(a494))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp4 | c0_1(a494) | c1_1(a494) | c3_1(a494) | c2_1(a492) | (~ndr1_0) | (~c1_1(a492)) | (~c3_1(a492)))),
% 0.53/0.74 inference(transitivity,[status(thm)],[572, 570])).
% 0.53/0.74 tff(574,plain,
% 0.53/0.74 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp4 | (~ndr1_0) | c2_1(a492) | (~c3_1(a492)) | (~c1_1(a492)) | c3_1(a494) | c1_1(a494) | c0_1(a494))),
% 0.53/0.74 inference(quant_inst,[status(thm)],[])).
% 0.53/0.74 tff(575,plain,
% 0.53/0.74 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp4 | c0_1(a494) | c1_1(a494) | c3_1(a494) | c2_1(a492) | (~ndr1_0) | (~c1_1(a492)) | (~c3_1(a492))),
% 0.53/0.74 inference(modus_ponens,[status(thm)],[574, 573])).
% 0.53/0.74 tff(576,plain,
% 0.53/0.74 (hskp4 | c0_1(a494) | c1_1(a494) | (~c1_1(a492)) | (~c3_1(a492))),
% 0.53/0.74 inference(unit_resolution,[status(thm)],[575, 141, 495, 542, 569])).
% 0.53/0.74 tff(577,plain,
% 0.53/0.74 ($false),
% 0.53/0.74 inference(unit_resolution,[status(thm)],[576, 559, 551, 541, 511, 510])).
% 0.53/0.74 tff(578,plain,((~hskp15) | hskp4 | c0_1(a494) | c1_1(a494) | (~ndr1_0) | c3_1(a494) | c2_1(a492)), inference(lemma,lemma(discharge,[]))).
% 0.53/0.74 tff(579,plain,
% 0.53/0.74 (~hskp15),
% 0.53/0.74 inference(unit_resolution,[status(thm)],[578, 542, 541, 510, 137, 495, 511])).
% 0.53/0.74 tff(580,plain,
% 0.53/0.74 (^[U: $i] : refl((hskp15 | hskp3 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U)) <=> (hskp15 | hskp3 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U)))),
% 0.53/0.74 inference(bind,[status(th)],[])).
% 0.53/0.74 tff(581,plain,
% 0.53/0.74 (![U: $i] : (hskp15 | hskp3 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U)) <=> ![U: $i] : (hskp15 | hskp3 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))),
% 0.53/0.74 inference(quant_intro,[status(thm)],[580])).
% 0.53/0.74 tff(582,plain,
% 0.53/0.74 (![U: $i] : (hskp15 | hskp3 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U)) <=> ![U: $i] : (hskp15 | hskp3 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))),
% 0.53/0.74 inference(rewrite,[status(thm)],[])).
% 0.53/0.74 tff(583,plain,
% 0.53/0.74 (^[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) | c2_1(U) | c1_1(U) | c3_1(U))), (((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U)))), ((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | hskp3) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U)) | hskp3))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U)) | hskp3) <=> (hskp3 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))), ((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | hskp3) <=> (hskp3 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U)))), (((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | hskp3) | hskp15) <=> ((hskp3 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U)) | hskp15))), rewrite(((hskp3 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U)) | hskp15) <=> (hskp15 | hskp3 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))), (((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | hskp3) | hskp15) <=> (hskp15 | hskp3 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))))),
% 0.53/0.74 inference(bind,[status(th)],[])).
% 0.53/0.74 tff(584,plain,
% 0.53/0.74 (![U: $i] : ((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | hskp3) | hskp15) <=> ![U: $i] : (hskp15 | hskp3 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))),
% 0.53/0.74 inference(quant_intro,[status(thm)],[583])).
% 0.53/0.74 tff(585,axiom,(![U: $i] : ((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | hskp3) | hskp15)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause126')).
% 0.53/0.74 tff(586,plain,
% 0.53/0.74 (![U: $i] : (hskp15 | hskp3 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))),
% 0.53/0.74 inference(modus_ponens,[status(thm)],[585, 584])).
% 0.53/0.74 tff(587,plain,
% 0.53/0.74 (![U: $i] : (hskp15 | hskp3 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))),
% 0.53/0.74 inference(modus_ponens,[status(thm)],[586, 582])).
% 0.53/0.74 tff(588,plain,(
% 0.53/0.74 ![U: $i] : (hskp15 | hskp3 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))),
% 0.53/0.74 inference(skolemize,[status(sab)],[587])).
% 0.53/0.74 tff(589,plain,
% 0.53/0.74 (![U: $i] : (hskp15 | hskp3 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))),
% 0.53/0.74 inference(modus_ponens,[status(thm)],[588, 581])).
% 0.53/0.74 tff(590,plain,
% 0.53/0.74 (((~![U: $i] : (hskp15 | hskp3 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | (hskp15 | hskp3 | c2_1(a460) | c3_1(a460) | (~ndr1_0) | c1_1(a460))) <=> ((~![U: $i] : (hskp15 | hskp3 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | hskp15 | hskp3 | c2_1(a460) | c3_1(a460) | (~ndr1_0) | c1_1(a460))),
% 0.53/0.74 inference(rewrite,[status(thm)],[])).
% 0.53/0.74 tff(591,plain,
% 0.53/0.74 ((hskp15 | hskp3 | (~ndr1_0) | c2_1(a460) | c1_1(a460) | c3_1(a460)) <=> (hskp15 | hskp3 | c2_1(a460) | c3_1(a460) | (~ndr1_0) | c1_1(a460))),
% 0.53/0.74 inference(rewrite,[status(thm)],[])).
% 0.53/0.74 tff(592,plain,
% 0.53/0.74 (((~![U: $i] : (hskp15 | hskp3 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | (hskp15 | hskp3 | (~ndr1_0) | c2_1(a460) | c1_1(a460) | c3_1(a460))) <=> ((~![U: $i] : (hskp15 | hskp3 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | (hskp15 | hskp3 | c2_1(a460) | c3_1(a460) | (~ndr1_0) | c1_1(a460)))),
% 0.53/0.74 inference(monotonicity,[status(thm)],[591])).
% 0.53/0.74 tff(593,plain,
% 0.53/0.74 (((~![U: $i] : (hskp15 | hskp3 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | (hskp15 | hskp3 | (~ndr1_0) | c2_1(a460) | c1_1(a460) | c3_1(a460))) <=> ((~![U: $i] : (hskp15 | hskp3 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | hskp15 | hskp3 | c2_1(a460) | c3_1(a460) | (~ndr1_0) | c1_1(a460))),
% 0.53/0.74 inference(transitivity,[status(thm)],[592, 590])).
% 0.53/0.74 tff(594,plain,
% 0.53/0.74 ((~![U: $i] : (hskp15 | hskp3 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | (hskp15 | hskp3 | (~ndr1_0) | c2_1(a460) | c1_1(a460) | c3_1(a460))),
% 0.53/0.74 inference(quant_inst,[status(thm)],[])).
% 0.53/0.74 tff(595,plain,
% 0.53/0.74 ((~![U: $i] : (hskp15 | hskp3 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | hskp15 | hskp3 | c2_1(a460) | c3_1(a460) | (~ndr1_0) | c1_1(a460)),
% 0.53/0.74 inference(modus_ponens,[status(thm)],[594, 593])).
% 0.53/0.74 tff(596,plain,
% 0.53/0.74 (hskp15 | hskp3 | c2_1(a460) | c1_1(a460)),
% 0.53/0.74 inference(unit_resolution,[status(thm)],[595, 137, 223, 589])).
% 0.53/0.74 tff(597,plain,
% 0.53/0.74 (c1_1(a460)),
% 0.53/0.74 inference(unit_resolution,[status(thm)],[596, 579, 1, 329])).
% 0.53/0.74 tff(598,plain,
% 0.53/0.74 (^[U: $i] : refl((hskp15 | hskp2 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U))) <=> (hskp15 | hskp2 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U))))),
% 0.53/0.74 inference(bind,[status(th)],[])).
% 0.53/0.74 tff(599,plain,
% 0.53/0.74 (![U: $i] : (hskp15 | hskp2 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp15 | hskp2 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))),
% 0.53/0.74 inference(quant_intro,[status(thm)],[598])).
% 0.53/0.74 tff(600,plain,
% 0.53/0.74 (![U: $i] : (hskp15 | hskp2 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp15 | hskp2 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))),
% 0.53/0.74 inference(rewrite,[status(thm)],[])).
% 0.53/0.74 tff(601,plain,
% 0.53/0.74 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp15) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U))) | hskp15))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U))) | hskp15) <=> (hskp15 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp15) <=> (hskp15 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp15) | hskp2) <=> ((hskp15 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U))) | hskp2))), rewrite(((hskp15 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U))) | hskp2) <=> (hskp15 | hskp2 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp15) | hskp2) <=> (hskp15 | hskp2 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))))),
% 0.53/0.74 inference(bind,[status(th)],[])).
% 0.53/0.74 tff(602,plain,
% 0.53/0.74 (![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp15) | hskp2) <=> ![U: $i] : (hskp15 | hskp2 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))),
% 0.53/0.74 inference(quant_intro,[status(thm)],[601])).
% 0.53/0.74 tff(603,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp15) | hskp2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause139')).
% 0.53/0.74 tff(604,plain,
% 0.53/0.74 (![U: $i] : (hskp15 | hskp2 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))),
% 0.53/0.74 inference(modus_ponens,[status(thm)],[603, 602])).
% 0.53/0.74 tff(605,plain,
% 0.53/0.74 (![U: $i] : (hskp15 | hskp2 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))),
% 0.53/0.74 inference(modus_ponens,[status(thm)],[604, 600])).
% 0.53/0.74 tff(606,plain,(
% 0.53/0.74 ![U: $i] : (hskp15 | hskp2 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))),
% 0.53/0.74 inference(skolemize,[status(sab)],[605])).
% 0.53/0.74 tff(607,plain,
% 0.53/0.74 (![U: $i] : (hskp15 | hskp2 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))),
% 0.53/0.74 inference(modus_ponens,[status(thm)],[606, 599])).
% 0.53/0.74 tff(608,plain,
% 0.53/0.74 (((~![U: $i] : (hskp15 | hskp2 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))) | (hskp15 | hskp2 | c2_1(a460) | (~ndr1_0) | (~c1_1(a460)) | (~c0_1(a460)))) <=> ((~![U: $i] : (hskp15 | hskp2 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))) | hskp15 | hskp2 | c2_1(a460) | (~ndr1_0) | (~c1_1(a460)) | (~c0_1(a460)))),
% 0.53/0.74 inference(rewrite,[status(thm)],[])).
% 0.53/0.74 tff(609,plain,
% 0.53/0.74 ((hskp15 | hskp2 | (~ndr1_0) | c2_1(a460) | (~c0_1(a460)) | (~c1_1(a460))) <=> (hskp15 | hskp2 | c2_1(a460) | (~ndr1_0) | (~c1_1(a460)) | (~c0_1(a460)))),
% 0.53/0.74 inference(rewrite,[status(thm)],[])).
% 0.53/0.74 tff(610,plain,
% 0.53/0.74 (((~![U: $i] : (hskp15 | hskp2 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))) | (hskp15 | hskp2 | (~ndr1_0) | c2_1(a460) | (~c0_1(a460)) | (~c1_1(a460)))) <=> ((~![U: $i] : (hskp15 | hskp2 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))) | (hskp15 | hskp2 | c2_1(a460) | (~ndr1_0) | (~c1_1(a460)) | (~c0_1(a460))))),
% 0.53/0.74 inference(monotonicity,[status(thm)],[609])).
% 0.53/0.74 tff(611,plain,
% 0.53/0.74 (((~![U: $i] : (hskp15 | hskp2 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))) | (hskp15 | hskp2 | (~ndr1_0) | c2_1(a460) | (~c0_1(a460)) | (~c1_1(a460)))) <=> ((~![U: $i] : (hskp15 | hskp2 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))) | hskp15 | hskp2 | c2_1(a460) | (~ndr1_0) | (~c1_1(a460)) | (~c0_1(a460)))),
% 0.53/0.74 inference(transitivity,[status(thm)],[610, 608])).
% 0.53/0.74 tff(612,plain,
% 0.53/0.74 ((~![U: $i] : (hskp15 | hskp2 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))) | (hskp15 | hskp2 | (~ndr1_0) | c2_1(a460) | (~c0_1(a460)) | (~c1_1(a460)))),
% 0.53/0.74 inference(quant_inst,[status(thm)],[])).
% 0.53/0.74 tff(613,plain,
% 0.53/0.74 ((~![U: $i] : (hskp15 | hskp2 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))) | hskp15 | hskp2 | c2_1(a460) | (~ndr1_0) | (~c1_1(a460)) | (~c0_1(a460))),
% 0.53/0.74 inference(modus_ponens,[status(thm)],[612, 611])).
% 0.53/0.74 tff(614,plain,
% 0.53/0.74 (hskp15 | hskp2 | (~c1_1(a460)) | (~c0_1(a460))),
% 0.53/0.74 inference(unit_resolution,[status(thm)],[613, 137, 1, 607])).
% 0.53/0.74 tff(615,plain,
% 0.53/0.74 (hskp2),
% 0.53/0.74 inference(unit_resolution,[status(thm)],[614, 579, 224, 597])).
% 0.53/0.74 tff(616,plain,
% 0.53/0.74 (((~hskp2) | (~c3_1(a465))) <=> ((~hskp2) | (~c3_1(a465)))),
% 0.53/0.74 inference(rewrite,[status(thm)],[])).
% 0.53/0.74 tff(617,plain,
% 0.53/0.74 (((~c3_1(a465)) | (~hskp2)) <=> ((~hskp2) | (~c3_1(a465)))),
% 0.53/0.74 inference(rewrite,[status(thm)],[])).
% 0.53/0.74 tff(618,axiom,((~c3_1(a465)) | (~hskp2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause120')).
% 0.53/0.74 tff(619,plain,
% 0.53/0.74 ((~hskp2) | (~c3_1(a465))),
% 0.53/0.74 inference(modus_ponens,[status(thm)],[618, 617])).
% 0.53/0.74 tff(620,plain,
% 0.53/0.74 ((~hskp2) | (~c3_1(a465))),
% 0.53/0.74 inference(modus_ponens,[status(thm)],[619, 616])).
% 0.53/0.74 tff(621,plain,
% 0.53/0.74 (~c3_1(a465)),
% 0.53/0.74 inference(unit_resolution,[status(thm)],[620, 615])).
% 0.53/0.74 tff(622,plain,
% 0.53/0.74 (((~hskp2) | (~c2_1(a465))) <=> ((~hskp2) | (~c2_1(a465)))),
% 0.53/0.74 inference(rewrite,[status(thm)],[])).
% 0.53/0.74 tff(623,plain,
% 0.53/0.74 (((~c2_1(a465)) | (~hskp2)) <=> ((~hskp2) | (~c2_1(a465)))),
% 0.53/0.74 inference(rewrite,[status(thm)],[])).
% 0.53/0.74 tff(624,axiom,((~c2_1(a465)) | (~hskp2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause119')).
% 0.53/0.74 tff(625,plain,
% 0.53/0.74 ((~hskp2) | (~c2_1(a465))),
% 0.53/0.74 inference(modus_ponens,[status(thm)],[624, 623])).
% 0.53/0.74 tff(626,plain,
% 0.53/0.74 ((~hskp2) | (~c2_1(a465))),
% 0.53/0.74 inference(modus_ponens,[status(thm)],[625, 622])).
% 0.53/0.74 tff(627,plain,
% 0.53/0.74 (~c2_1(a465)),
% 0.53/0.74 inference(unit_resolution,[status(thm)],[626, 615])).
% 0.53/0.74 tff(628,plain,
% 0.53/0.74 (((~hskp2) | (~c0_1(a465))) <=> ((~hskp2) | (~c0_1(a465)))),
% 0.53/0.74 inference(rewrite,[status(thm)],[])).
% 0.53/0.74 tff(629,plain,
% 0.53/0.74 (((~c0_1(a465)) | (~hskp2)) <=> ((~hskp2) | (~c0_1(a465)))),
% 0.53/0.74 inference(rewrite,[status(thm)],[])).
% 0.53/0.74 tff(630,axiom,((~c0_1(a465)) | (~hskp2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause118')).
% 0.53/0.74 tff(631,plain,
% 0.53/0.74 ((~hskp2) | (~c0_1(a465))),
% 0.53/0.74 inference(modus_ponens,[status(thm)],[630, 629])).
% 0.53/0.74 tff(632,plain,
% 0.53/0.74 ((~hskp2) | (~c0_1(a465))),
% 0.53/0.74 inference(modus_ponens,[status(thm)],[631, 628])).
% 0.53/0.74 tff(633,plain,
% 0.53/0.74 (~c0_1(a465)),
% 0.53/0.74 inference(unit_resolution,[status(thm)],[632, 615])).
% 0.53/0.74 tff(634,assumption,(~c3_1(a465)), introduced(assumption)).
% 0.53/0.74 tff(635,assumption,(~c2_1(a465)), introduced(assumption)).
% 0.53/0.74 tff(636,assumption,(~c0_1(a465)), introduced(assumption)).
% 0.53/0.74 tff(637,plain,
% 0.53/0.74 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp27 | c1_1(a488) | c2_1(a488) | c3_1(a488) | c0_1(a465) | c2_1(a465) | c3_1(a465) | (~ndr1_0))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp27 | c1_1(a488) | c2_1(a488) | c3_1(a488) | c0_1(a465) | c2_1(a465) | c3_1(a465) | (~ndr1_0))),
% 0.53/0.74 inference(rewrite,[status(thm)],[])).
% 0.53/0.74 tff(638,plain,
% 0.53/0.74 ((hskp27 | (~ndr1_0) | c2_1(a488) | c1_1(a488) | c3_1(a488) | c3_1(a465) | c0_1(a465) | c2_1(a465)) <=> (hskp27 | c1_1(a488) | c2_1(a488) | c3_1(a488) | c0_1(a465) | c2_1(a465) | c3_1(a465) | (~ndr1_0))),
% 0.53/0.74 inference(rewrite,[status(thm)],[])).
% 0.53/0.74 tff(639,plain,
% 0.53/0.74 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp27 | (~ndr1_0) | c2_1(a488) | c1_1(a488) | c3_1(a488) | c3_1(a465) | c0_1(a465) | c2_1(a465))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp27 | c1_1(a488) | c2_1(a488) | c3_1(a488) | c0_1(a465) | c2_1(a465) | c3_1(a465) | (~ndr1_0)))),
% 0.53/0.74 inference(monotonicity,[status(thm)],[638])).
% 0.53/0.74 tff(640,plain,
% 0.53/0.74 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp27 | (~ndr1_0) | c2_1(a488) | c1_1(a488) | c3_1(a488) | c3_1(a465) | c0_1(a465) | c2_1(a465))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp27 | c1_1(a488) | c2_1(a488) | c3_1(a488) | c0_1(a465) | c2_1(a465) | c3_1(a465) | (~ndr1_0))),
% 0.53/0.74 inference(transitivity,[status(thm)],[639, 637])).
% 0.53/0.74 tff(641,plain,
% 0.53/0.74 ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp27 | (~ndr1_0) | c2_1(a488) | c1_1(a488) | c3_1(a488) | c3_1(a465) | c0_1(a465) | c2_1(a465))),
% 0.53/0.74 inference(quant_inst,[status(thm)],[])).
% 0.53/0.74 tff(642,plain,
% 0.53/0.74 ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp27 | c1_1(a488) | c2_1(a488) | c3_1(a488) | c0_1(a465) | c2_1(a465) | c3_1(a465) | (~ndr1_0)),
% 0.53/0.74 inference(modus_ponens,[status(thm)],[641, 640])).
% 0.53/0.74 tff(643,plain,
% 0.53/0.74 ($false),
% 0.53/0.74 inference(unit_resolution,[status(thm)],[642, 141, 420, 63, 57, 51, 636, 635, 634, 414])).
% 0.53/0.74 tff(644,plain,((~hskp14) | (~ndr1_0) | hskp27 | c0_1(a465) | c2_1(a465) | c3_1(a465)), inference(lemma,lemma(discharge,[]))).
% 0.53/0.74 tff(645,plain,
% 0.53/0.74 (~hskp14),
% 0.53/0.74 inference(unit_resolution,[status(thm)],[644, 633, 137, 363, 627, 621])).
% 0.53/0.74 tff(646,plain,
% 0.53/0.74 (hskp25),
% 0.53/0.74 inference(unit_resolution,[status(thm)],[294, 645, 103])).
% 0.53/0.74 tff(647,plain,
% 0.53/0.74 (c3_1(a461)),
% 0.53/0.74 inference(unit_resolution,[status(thm)],[302, 646])).
% 0.53/0.74 tff(648,plain,
% 0.53/0.74 (c0_1(a461)),
% 0.53/0.74 inference(unit_resolution,[status(thm)],[318, 646])).
% 0.53/0.74 tff(649,plain,
% 0.53/0.74 (c2_1(a461)),
% 0.53/0.74 inference(unit_resolution,[status(thm)],[310, 646])).
% 0.53/0.74 tff(650,plain,
% 0.53/0.74 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c3_1(W) | c1_1(W) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c3_1(W) | c1_1(W) | c0_1(W)))),
% 0.53/0.74 inference(bind,[status(th)],[])).
% 0.53/0.74 tff(651,plain,
% 0.53/0.74 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c3_1(W) | c1_1(W) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c3_1(W) | c1_1(W) | c0_1(W))),
% 0.53/0.74 inference(quant_intro,[status(thm)],[650])).
% 0.53/0.74 tff(652,plain,
% 0.53/0.74 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c3_1(W) | c1_1(W) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c3_1(W) | c1_1(W) | c0_1(W))),
% 0.53/0.75 inference(rewrite,[status(thm)],[])).
% 0.53/0.75 tff(653,plain,
% 0.53/0.75 (^[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))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | 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)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U))) | c1_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U))) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V)))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V)) | c0_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c0_1(W))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c0_1(W)))), ((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c0_1(W)) | c1_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c1_1(W) | c0_1(W))), ((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c1_1(W) | c0_1(W)))), (((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) | c3_1(W)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c1_1(W) | c0_1(W)) | c3_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c1_1(W) | c0_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c3_1(W) | c1_1(W) | c0_1(W))), (((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c3_1(W) | c1_1(W) | c0_1(W))))),
% 0.53/0.75 inference(bind,[status(th)],[])).
% 0.53/0.75 tff(654,plain,
% 0.53/0.75 (![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c3_1(W) | c1_1(W) | c0_1(W))),
% 0.53/0.75 inference(quant_intro,[status(thm)],[653])).
% 0.53/0.75 tff(655,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) | c3_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause171')).
% 0.53/0.75 tff(656,plain,
% 0.53/0.75 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c3_1(W) | c1_1(W) | c0_1(W))),
% 0.53/0.75 inference(modus_ponens,[status(thm)],[655, 654])).
% 0.53/0.75 tff(657,plain,
% 0.53/0.75 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c3_1(W) | c1_1(W) | c0_1(W))),
% 0.53/0.75 inference(modus_ponens,[status(thm)],[656, 652])).
% 0.53/0.75 tff(658,plain,(
% 0.53/0.75 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c3_1(W) | c1_1(W) | c0_1(W))),
% 0.53/0.75 inference(skolemize,[status(sab)],[657])).
% 0.53/0.75 tff(659,plain,
% 0.53/0.75 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c3_1(W) | c1_1(W) | c0_1(W))),
% 0.53/0.75 inference(modus_ponens,[status(thm)],[658, 651])).
% 0.53/0.75 tff(660,plain,
% 0.53/0.75 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a494) | c1_1(a494) | c3_1(a494) | c3_1(a478) | (~ndr1_0) | (~c2_1(a478)) | (~c1_1(a478)) | c2_1(a494))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a494) | c1_1(a494) | c3_1(a494) | c3_1(a478) | (~ndr1_0) | (~c2_1(a478)) | (~c1_1(a478)) | c2_1(a494))),
% 0.53/0.75 inference(rewrite,[status(thm)],[])).
% 0.53/0.75 tff(661,plain,
% 0.53/0.75 (((~ndr1_0) | c3_1(a478) | (~c2_1(a478)) | (~c1_1(a478)) | c3_1(a494) | c1_1(a494) | c2_1(a494) | c3_1(a494) | c1_1(a494) | c0_1(a494)) <=> (c0_1(a494) | c1_1(a494) | c3_1(a494) | c3_1(a478) | (~ndr1_0) | (~c2_1(a478)) | (~c1_1(a478)) | c2_1(a494))),
% 0.53/0.75 inference(rewrite,[status(thm)],[])).
% 0.53/0.75 tff(662,plain,
% 0.53/0.75 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a478) | (~c2_1(a478)) | (~c1_1(a478)) | c3_1(a494) | c1_1(a494) | c2_1(a494) | c3_1(a494) | c1_1(a494) | c0_1(a494))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a494) | c1_1(a494) | c3_1(a494) | c3_1(a478) | (~ndr1_0) | (~c2_1(a478)) | (~c1_1(a478)) | c2_1(a494)))),
% 0.53/0.75 inference(monotonicity,[status(thm)],[661])).
% 0.53/0.75 tff(663,plain,
% 0.53/0.75 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a478) | (~c2_1(a478)) | (~c1_1(a478)) | c3_1(a494) | c1_1(a494) | c2_1(a494) | c3_1(a494) | c1_1(a494) | c0_1(a494))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a494) | c1_1(a494) | c3_1(a494) | c3_1(a478) | (~ndr1_0) | (~c2_1(a478)) | (~c1_1(a478)) | c2_1(a494))),
% 0.53/0.75 inference(transitivity,[status(thm)],[662, 660])).
% 0.53/0.75 tff(664,plain,
% 0.53/0.75 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a478) | (~c2_1(a478)) | (~c1_1(a478)) | c3_1(a494) | c1_1(a494) | c2_1(a494) | c3_1(a494) | c1_1(a494) | c0_1(a494))),
% 0.53/0.75 inference(quant_inst,[status(thm)],[])).
% 0.53/0.75 tff(665,plain,
% 0.53/0.75 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a494) | c1_1(a494) | c3_1(a494) | c3_1(a478) | (~ndr1_0) | (~c2_1(a478)) | (~c1_1(a478)) | c2_1(a494)),
% 0.53/0.75 inference(modus_ponens,[status(thm)],[664, 663])).
% 0.59/0.75 tff(666,plain,
% 0.59/0.75 ((~c1_1(a478)) | c2_1(a494)),
% 0.59/0.75 inference(unit_resolution,[status(thm)],[665, 141, 140, 511, 510, 495, 138, 659])).
% 0.59/0.75 tff(667,plain,
% 0.59/0.75 (~c1_1(a478)),
% 0.59/0.75 inference(unit_resolution,[status(thm)],[666, 509])).
% 0.59/0.75 tff(668,plain,
% 0.59/0.75 (((~![U: $i] : (hskp15 | hskp3 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | (hskp15 | hskp3 | c1_1(a494) | c3_1(a494) | (~ndr1_0) | c2_1(a494))) <=> ((~![U: $i] : (hskp15 | hskp3 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | hskp15 | hskp3 | c1_1(a494) | c3_1(a494) | (~ndr1_0) | c2_1(a494))),
% 0.59/0.75 inference(rewrite,[status(thm)],[])).
% 0.59/0.75 tff(669,plain,
% 0.59/0.75 ((hskp15 | hskp3 | (~ndr1_0) | c2_1(a494) | c1_1(a494) | c3_1(a494)) <=> (hskp15 | hskp3 | c1_1(a494) | c3_1(a494) | (~ndr1_0) | c2_1(a494))),
% 0.59/0.75 inference(rewrite,[status(thm)],[])).
% 0.59/0.75 tff(670,plain,
% 0.59/0.75 (((~![U: $i] : (hskp15 | hskp3 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | (hskp15 | hskp3 | (~ndr1_0) | c2_1(a494) | c1_1(a494) | c3_1(a494))) <=> ((~![U: $i] : (hskp15 | hskp3 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | (hskp15 | hskp3 | c1_1(a494) | c3_1(a494) | (~ndr1_0) | c2_1(a494)))),
% 0.59/0.75 inference(monotonicity,[status(thm)],[669])).
% 0.59/0.75 tff(671,plain,
% 0.59/0.75 (((~![U: $i] : (hskp15 | hskp3 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | (hskp15 | hskp3 | (~ndr1_0) | c2_1(a494) | c1_1(a494) | c3_1(a494))) <=> ((~![U: $i] : (hskp15 | hskp3 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | hskp15 | hskp3 | c1_1(a494) | c3_1(a494) | (~ndr1_0) | c2_1(a494))),
% 0.59/0.75 inference(transitivity,[status(thm)],[670, 668])).
% 0.59/0.75 tff(672,plain,
% 0.59/0.75 ((~![U: $i] : (hskp15 | hskp3 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | (hskp15 | hskp3 | (~ndr1_0) | c2_1(a494) | c1_1(a494) | c3_1(a494))),
% 0.59/0.75 inference(quant_inst,[status(thm)],[])).
% 0.59/0.75 tff(673,plain,
% 0.59/0.75 ((~![U: $i] : (hskp15 | hskp3 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | hskp15 | hskp3 | c1_1(a494) | c3_1(a494) | (~ndr1_0) | c2_1(a494)),
% 0.59/0.75 inference(modus_ponens,[status(thm)],[672, 671])).
% 0.59/0.75 tff(674,plain,
% 0.59/0.75 (hskp15 | hskp3 | c3_1(a494) | c2_1(a494)),
% 0.59/0.75 inference(unit_resolution,[status(thm)],[673, 141, 510, 589])).
% 0.59/0.75 tff(675,plain,
% 0.59/0.75 (hskp15),
% 0.59/0.75 inference(unit_resolution,[status(thm)],[674, 509, 329, 495])).
% 0.59/0.75 tff(676,plain,
% 0.59/0.75 (c1_1(a492)),
% 0.59/0.75 inference(unit_resolution,[status(thm)],[550, 675])).
% 0.59/0.75 tff(677,plain,
% 0.59/0.75 (c3_1(a492)),
% 0.59/0.75 inference(unit_resolution,[status(thm)],[558, 675])).
% 0.59/0.75 tff(678,plain,
% 0.59/0.75 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp4 | c2_1(a492) | c0_1(a478) | c3_1(a478) | (~ndr1_0) | c1_1(a478) | (~c1_1(a492)) | (~c3_1(a492)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp4 | c2_1(a492) | c0_1(a478) | c3_1(a478) | (~ndr1_0) | c1_1(a478) | (~c1_1(a492)) | (~c3_1(a492)))),
% 0.59/0.75 inference(rewrite,[status(thm)],[])).
% 0.59/0.75 tff(679,plain,
% 0.59/0.75 ((hskp4 | (~ndr1_0) | c2_1(a492) | (~c3_1(a492)) | (~c1_1(a492)) | c3_1(a478) | c1_1(a478) | c0_1(a478)) <=> (hskp4 | c2_1(a492) | c0_1(a478) | c3_1(a478) | (~ndr1_0) | c1_1(a478) | (~c1_1(a492)) | (~c3_1(a492)))),
% 0.59/0.75 inference(rewrite,[status(thm)],[])).
% 0.59/0.75 tff(680,plain,
% 0.59/0.75 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp4 | (~ndr1_0) | c2_1(a492) | (~c3_1(a492)) | (~c1_1(a492)) | c3_1(a478) | c1_1(a478) | c0_1(a478))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp4 | c2_1(a492) | c0_1(a478) | c3_1(a478) | (~ndr1_0) | c1_1(a478) | (~c1_1(a492)) | (~c3_1(a492))))),
% 0.59/0.75 inference(monotonicity,[status(thm)],[679])).
% 0.59/0.75 tff(681,plain,
% 0.59/0.75 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp4 | (~ndr1_0) | c2_1(a492) | (~c3_1(a492)) | (~c1_1(a492)) | c3_1(a478) | c1_1(a478) | c0_1(a478))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp4 | c2_1(a492) | c0_1(a478) | c3_1(a478) | (~ndr1_0) | c1_1(a478) | (~c1_1(a492)) | (~c3_1(a492)))),
% 0.59/0.75 inference(transitivity,[status(thm)],[680, 678])).
% 0.59/0.75 tff(682,plain,
% 0.59/0.75 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp4 | (~ndr1_0) | c2_1(a492) | (~c3_1(a492)) | (~c1_1(a492)) | c3_1(a478) | c1_1(a478) | c0_1(a478))),
% 0.59/0.75 inference(quant_inst,[status(thm)],[])).
% 0.59/0.75 tff(683,plain,
% 0.59/0.75 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp4 | c2_1(a492) | c0_1(a478) | c3_1(a478) | (~ndr1_0) | c1_1(a478) | (~c1_1(a492)) | (~c3_1(a492))),
% 0.59/0.75 inference(modus_ponens,[status(thm)],[682, 681])).
% 0.59/0.75 tff(684,plain,
% 0.59/0.75 (c1_1(a478) | (~c1_1(a492)) | (~c3_1(a492))),
% 0.59/0.75 inference(unit_resolution,[status(thm)],[683, 141, 541, 542, 139, 138, 569])).
% 0.59/0.75 tff(685,plain,
% 0.59/0.75 ($false),
% 0.59/0.75 inference(unit_resolution,[status(thm)],[684, 677, 676, 667])).
% 0.59/0.75 tff(686,plain,(c2_1(a494) | (~ndr1_0) | hskp4 | c2_1(a492) | c0_1(a478) | c3_1(a478) | (~c2_1(a478)) | c0_1(a494) | c1_1(a494) | c3_1(a494) | hskp3), inference(lemma,lemma(discharge,[]))).
% 0.59/0.75 tff(687,plain,
% 0.59/0.75 (c2_1(a494)),
% 0.59/0.75 inference(unit_resolution,[status(thm)],[686, 495, 541, 542, 139, 138, 140, 511, 510, 141, 329])).
% 0.59/0.75 tff(688,plain,
% 0.59/0.75 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp26 | c0_1(a494) | c1_1(a494) | (~ndr1_0) | (~c0_1(a461)) | (~c3_1(a461)) | (~c2_1(a461)) | (~c2_1(a494)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp26 | c0_1(a494) | c1_1(a494) | (~ndr1_0) | (~c0_1(a461)) | (~c3_1(a461)) | (~c2_1(a461)) | (~c2_1(a494)))),
% 0.59/0.75 inference(rewrite,[status(thm)],[])).
% 0.59/0.75 tff(689,plain,
% 0.59/0.75 ((hskp26 | (~ndr1_0) | (~c2_1(a461)) | (~c0_1(a461)) | (~c3_1(a461)) | c1_1(a494) | c0_1(a494) | (~c2_1(a494))) <=> (hskp26 | c0_1(a494) | c1_1(a494) | (~ndr1_0) | (~c0_1(a461)) | (~c3_1(a461)) | (~c2_1(a461)) | (~c2_1(a494)))),
% 0.59/0.75 inference(rewrite,[status(thm)],[])).
% 0.59/0.75 tff(690,plain,
% 0.59/0.75 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp26 | (~ndr1_0) | (~c2_1(a461)) | (~c0_1(a461)) | (~c3_1(a461)) | c1_1(a494) | c0_1(a494) | (~c2_1(a494)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp26 | c0_1(a494) | c1_1(a494) | (~ndr1_0) | (~c0_1(a461)) | (~c3_1(a461)) | (~c2_1(a461)) | (~c2_1(a494))))),
% 0.59/0.75 inference(monotonicity,[status(thm)],[689])).
% 0.59/0.75 tff(691,plain,
% 0.59/0.75 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp26 | (~ndr1_0) | (~c2_1(a461)) | (~c0_1(a461)) | (~c3_1(a461)) | c1_1(a494) | c0_1(a494) | (~c2_1(a494)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp26 | c0_1(a494) | c1_1(a494) | (~ndr1_0) | (~c0_1(a461)) | (~c3_1(a461)) | (~c2_1(a461)) | (~c2_1(a494)))),
% 0.59/0.75 inference(transitivity,[status(thm)],[690, 688])).
% 0.59/0.75 tff(692,plain,
% 0.59/0.75 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp26 | (~ndr1_0) | (~c2_1(a461)) | (~c0_1(a461)) | (~c3_1(a461)) | c1_1(a494) | c0_1(a494) | (~c2_1(a494)))),
% 0.59/0.75 inference(quant_inst,[status(thm)],[])).
% 0.59/0.75 tff(693,plain,
% 0.59/0.75 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp26 | c0_1(a494) | c1_1(a494) | (~ndr1_0) | (~c0_1(a461)) | (~c3_1(a461)) | (~c2_1(a461)) | (~c2_1(a494))),
% 0.59/0.75 inference(modus_ponens,[status(thm)],[692, 691])).
% 0.59/0.75 tff(694,plain,
% 0.59/0.75 (hskp26 | c0_1(a494) | (~c2_1(a494))),
% 0.59/0.75 inference(unit_resolution,[status(thm)],[693, 141, 466, 465, 464, 510, 530])).
% 0.59/0.75 tff(695,plain,
% 0.59/0.75 (hskp26),
% 0.59/0.75 inference(unit_resolution,[status(thm)],[694, 687, 511])).
% 0.59/0.75 tff(696,plain,
% 0.59/0.75 (((~hskp26) | c3_1(a470)) <=> ((~hskp26) | c3_1(a470))),
% 0.59/0.75 inference(rewrite,[status(thm)],[])).
% 0.59/0.75 tff(697,axiom,((~hskp26) | c3_1(a470)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause46')).
% 0.59/0.75 tff(698,plain,
% 0.59/0.75 ((~hskp26) | c3_1(a470)),
% 0.59/0.75 inference(modus_ponens,[status(thm)],[697, 696])).
% 0.59/0.75 tff(699,plain,
% 0.59/0.75 ((~hskp26) | c3_1(a470)),
% 0.59/0.75 inference(modus_ponens,[status(thm)],[698, 696])).
% 0.59/0.75 tff(700,plain,
% 0.59/0.75 ((~hskp26) | c3_1(a470)),
% 0.59/0.75 inference(modus_ponens,[status(thm)],[699, 696])).
% 0.59/0.75 tff(701,plain,
% 0.59/0.75 ((~hskp26) | c3_1(a470)),
% 0.59/0.75 inference(modus_ponens,[status(thm)],[700, 696])).
% 0.59/0.75 tff(702,plain,
% 0.59/0.75 ((~hskp26) | c3_1(a470)),
% 0.59/0.75 inference(modus_ponens,[status(thm)],[701, 696])).
% 0.59/0.75 tff(703,plain,
% 0.59/0.75 (c3_1(a470)),
% 0.59/0.75 inference(unit_resolution,[status(thm)],[702, 695])).
% 0.59/0.75 tff(704,plain,
% 0.59/0.75 (((~hskp26) | c2_1(a470)) <=> ((~hskp26) | c2_1(a470))),
% 0.59/0.75 inference(rewrite,[status(thm)],[])).
% 0.59/0.75 tff(705,axiom,((~hskp26) | c2_1(a470)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause45')).
% 0.59/0.75 tff(706,plain,
% 0.59/0.75 ((~hskp26) | c2_1(a470)),
% 0.59/0.75 inference(modus_ponens,[status(thm)],[705, 704])).
% 0.59/0.75 tff(707,plain,
% 0.59/0.75 ((~hskp26) | c2_1(a470)),
% 0.59/0.75 inference(modus_ponens,[status(thm)],[706, 704])).
% 0.59/0.75 tff(708,plain,
% 0.59/0.75 ((~hskp26) | c2_1(a470)),
% 0.59/0.75 inference(modus_ponens,[status(thm)],[707, 704])).
% 0.59/0.75 tff(709,plain,
% 0.59/0.75 ((~hskp26) | c2_1(a470)),
% 0.59/0.75 inference(modus_ponens,[status(thm)],[708, 704])).
% 0.59/0.75 tff(710,plain,
% 0.59/0.75 ((~hskp26) | c2_1(a470)),
% 0.59/0.75 inference(modus_ponens,[status(thm)],[709, 704])).
% 0.59/0.75 tff(711,plain,
% 0.59/0.75 (c2_1(a470)),
% 0.59/0.75 inference(unit_resolution,[status(thm)],[710, 695])).
% 0.59/0.75 tff(712,plain,
% 0.59/0.75 (((~hskp26) | c1_1(a470)) <=> ((~hskp26) | c1_1(a470))),
% 0.59/0.75 inference(rewrite,[status(thm)],[])).
% 0.59/0.75 tff(713,axiom,((~hskp26) | c1_1(a470)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause44')).
% 0.59/0.75 tff(714,plain,
% 0.59/0.75 ((~hskp26) | c1_1(a470)),
% 0.59/0.75 inference(modus_ponens,[status(thm)],[713, 712])).
% 0.59/0.75 tff(715,plain,
% 0.59/0.75 ((~hskp26) | c1_1(a470)),
% 0.59/0.75 inference(modus_ponens,[status(thm)],[714, 712])).
% 0.59/0.75 tff(716,plain,
% 0.59/0.75 ((~hskp26) | c1_1(a470)),
% 0.59/0.75 inference(modus_ponens,[status(thm)],[715, 712])).
% 0.59/0.75 tff(717,plain,
% 0.59/0.75 ((~hskp26) | c1_1(a470)),
% 0.59/0.75 inference(modus_ponens,[status(thm)],[716, 712])).
% 0.59/0.75 tff(718,plain,
% 0.59/0.75 ((~hskp26) | c1_1(a470)),
% 0.59/0.75 inference(modus_ponens,[status(thm)],[717, 712])).
% 0.59/0.75 tff(719,plain,
% 0.59/0.75 (c1_1(a470)),
% 0.59/0.75 inference(unit_resolution,[status(thm)],[718, 695])).
% 0.59/0.75 tff(720,plain,
% 0.59/0.75 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp4 | c0_1(a494) | c1_1(a494) | c3_1(a494) | (~ndr1_0) | (~c2_1(a470)) | (~c1_1(a470)) | (~c3_1(a470)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp4 | c0_1(a494) | c1_1(a494) | c3_1(a494) | (~ndr1_0) | (~c2_1(a470)) | (~c1_1(a470)) | (~c3_1(a470)))),
% 0.59/0.75 inference(rewrite,[status(thm)],[])).
% 0.59/0.75 tff(721,plain,
% 0.59/0.75 ((hskp4 | (~ndr1_0) | (~c2_1(a470)) | (~c3_1(a470)) | (~c1_1(a470)) | c3_1(a494) | c1_1(a494) | c0_1(a494)) <=> (hskp4 | c0_1(a494) | c1_1(a494) | c3_1(a494) | (~ndr1_0) | (~c2_1(a470)) | (~c1_1(a470)) | (~c3_1(a470)))),
% 0.59/0.75 inference(rewrite,[status(thm)],[])).
% 0.59/0.75 tff(722,plain,
% 0.59/0.75 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp4 | (~ndr1_0) | (~c2_1(a470)) | (~c3_1(a470)) | (~c1_1(a470)) | c3_1(a494) | c1_1(a494) | c0_1(a494))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp4 | c0_1(a494) | c1_1(a494) | c3_1(a494) | (~ndr1_0) | (~c2_1(a470)) | (~c1_1(a470)) | (~c3_1(a470))))),
% 0.59/0.75 inference(monotonicity,[status(thm)],[721])).
% 0.59/0.75 tff(723,plain,
% 0.59/0.75 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp4 | (~ndr1_0) | (~c2_1(a470)) | (~c3_1(a470)) | (~c1_1(a470)) | c3_1(a494) | c1_1(a494) | c0_1(a494))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp4 | c0_1(a494) | c1_1(a494) | c3_1(a494) | (~ndr1_0) | (~c2_1(a470)) | (~c1_1(a470)) | (~c3_1(a470)))),
% 0.59/0.75 inference(transitivity,[status(thm)],[722, 720])).
% 0.59/0.75 tff(724,plain,
% 0.59/0.75 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp4 | (~ndr1_0) | (~c2_1(a470)) | (~c3_1(a470)) | (~c1_1(a470)) | c3_1(a494) | c1_1(a494) | c0_1(a494))),
% 0.59/0.75 inference(quant_inst,[status(thm)],[])).
% 0.59/0.75 tff(725,plain,
% 0.59/0.75 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp4 | c0_1(a494) | c1_1(a494) | c3_1(a494) | (~ndr1_0) | (~c2_1(a470)) | (~c1_1(a470)) | (~c3_1(a470))),
% 0.59/0.75 inference(modus_ponens,[status(thm)],[724, 723])).
% 0.59/0.75 tff(726,plain,
% 0.59/0.75 ($false),
% 0.59/0.75 inference(unit_resolution,[status(thm)],[725, 141, 541, 719, 711, 703, 511, 510, 495, 540])).
% 0.59/0.75 tff(727,plain,(c3_1(a494) | (~ndr1_0) | hskp4 | c0_1(a494) | c1_1(a494) | (~c0_1(a461)) | (~c2_1(a461)) | (~c3_1(a461)) | c2_1(a492) | c0_1(a478) | c3_1(a478) | (~c2_1(a478)) | hskp3), inference(lemma,lemma(discharge,[]))).
% 0.59/0.75 tff(728,plain,
% 0.59/0.75 ($false),
% 0.59/0.75 inference(unit_resolution,[status(thm)],[727, 649, 648, 495, 329, 511, 510, 541, 647, 542, 123, 117, 131, 137])).
% 0.59/0.75 tff(729,plain,(c2_1(a492) | c3_1(a494) | hskp3 | c0_1(a494) | c1_1(a494) | hskp4 | hskp5 | (~c0_1(a460)) | c2_1(a460) | c3_1(a460)), inference(lemma,lemma(discharge,[]))).
% 0.59/0.75 tff(730,plain,
% 0.59/0.75 (c2_1(a492)),
% 0.59/0.75 inference(unit_resolution,[status(thm)],[729, 511, 329, 495, 510, 541, 103, 224, 1, 223])).
% 0.59/0.75 tff(731,plain,
% 0.59/0.75 (((~hskp15) | (~c2_1(a492))) <=> ((~hskp15) | (~c2_1(a492)))),
% 0.59/0.75 inference(rewrite,[status(thm)],[])).
% 0.59/0.75 tff(732,plain,
% 0.59/0.75 (((~c2_1(a492)) | (~hskp15)) <=> ((~hskp15) | (~c2_1(a492)))),
% 0.59/0.75 inference(rewrite,[status(thm)],[])).
% 0.59/0.75 tff(733,axiom,((~c2_1(a492)) | (~hskp15)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause97')).
% 0.59/0.75 tff(734,plain,
% 0.59/0.75 ((~hskp15) | (~c2_1(a492))),
% 0.59/0.75 inference(modus_ponens,[status(thm)],[733, 732])).
% 0.59/0.75 tff(735,plain,
% 0.59/0.75 ((~hskp15) | (~c2_1(a492))),
% 0.59/0.75 inference(modus_ponens,[status(thm)],[734, 731])).
% 0.59/0.75 tff(736,plain,
% 0.59/0.75 (~hskp15),
% 0.59/0.75 inference(unit_resolution,[status(thm)],[735, 730])).
% 0.59/0.75 tff(737,plain,
% 0.59/0.75 (hskp15 | hskp3 | c1_1(a494) | c2_1(a494)),
% 0.59/0.75 inference(unit_resolution,[status(thm)],[673, 137, 495, 589])).
% 0.59/0.75 tff(738,plain,
% 0.59/0.75 (c2_1(a494)),
% 0.59/0.75 inference(unit_resolution,[status(thm)],[737, 736, 329, 510])).
% 0.59/0.75 tff(739,plain,
% 0.59/0.75 (c1_1(a460)),
% 0.59/0.75 inference(unit_resolution,[status(thm)],[596, 736, 1, 329])).
% 0.59/0.75 tff(740,plain,
% 0.59/0.75 (hskp2),
% 0.59/0.75 inference(unit_resolution,[status(thm)],[614, 736, 224, 739])).
% 0.59/0.75 tff(741,plain,
% 0.59/0.75 (~c3_1(a465)),
% 0.59/0.75 inference(unit_resolution,[status(thm)],[620, 740])).
% 0.59/0.75 tff(742,plain,
% 0.59/0.75 (~c2_1(a465)),
% 0.59/0.75 inference(unit_resolution,[status(thm)],[626, 740])).
% 0.59/0.75 tff(743,plain,
% 0.59/0.75 (~c0_1(a465)),
% 0.59/0.75 inference(unit_resolution,[status(thm)],[632, 740])).
% 0.59/0.75 tff(744,plain,
% 0.59/0.75 (~hskp14),
% 0.59/0.75 inference(unit_resolution,[status(thm)],[644, 743, 137, 363, 742, 741])).
% 0.59/0.75 tff(745,plain,
% 0.59/0.75 (hskp25),
% 0.59/0.75 inference(unit_resolution,[status(thm)],[294, 744, 103])).
% 0.59/0.75 tff(746,plain,
% 0.59/0.75 (c3_1(a461)),
% 0.59/0.75 inference(unit_resolution,[status(thm)],[302, 745])).
% 0.59/0.75 tff(747,plain,
% 0.59/0.75 (c2_1(a461)),
% 0.59/0.75 inference(unit_resolution,[status(thm)],[310, 745])).
% 0.59/0.75 tff(748,plain,
% 0.59/0.75 (c0_1(a461)),
% 0.59/0.75 inference(unit_resolution,[status(thm)],[318, 745])).
% 0.59/0.75 tff(749,plain,
% 0.59/0.75 (hskp26),
% 0.59/0.75 inference(unit_resolution,[status(thm)],[693, 137, 748, 747, 746, 511, 510, 530, 738])).
% 0.59/0.75 tff(750,plain,
% 0.59/0.75 (c3_1(a470)),
% 0.59/0.75 inference(unit_resolution,[status(thm)],[702, 749])).
% 0.59/0.75 tff(751,plain,
% 0.59/0.75 (c2_1(a470)),
% 0.59/0.75 inference(unit_resolution,[status(thm)],[710, 749])).
% 0.59/0.75 tff(752,plain,
% 0.59/0.75 (c1_1(a470)),
% 0.59/0.75 inference(unit_resolution,[status(thm)],[718, 749])).
% 0.59/0.75 tff(753,plain,
% 0.59/0.75 ($false),
% 0.59/0.75 inference(unit_resolution,[status(thm)],[725, 137, 541, 752, 751, 750, 511, 510, 495, 540])).
% 0.59/0.75 tff(754,plain,(c0_1(a494) | hskp4 | c1_1(a494) | c3_1(a494) | hskp5 | hskp3 | (~c0_1(a460)) | c2_1(a460) | c3_1(a460)), inference(lemma,lemma(discharge,[]))).
% 0.59/0.75 tff(755,plain,
% 0.59/0.75 (hskp4),
% 0.59/0.75 inference(unit_resolution,[status(thm)],[754, 502, 508, 495, 103, 329, 224, 1, 223])).
% 0.59/0.75 tff(756,plain,
% 0.59/0.75 (((~hskp4) | (~c1_1(a467))) <=> ((~hskp4) | (~c1_1(a467)))),
% 0.59/0.76 inference(rewrite,[status(thm)],[])).
% 0.59/0.76 tff(757,plain,
% 0.59/0.76 (((~c1_1(a467)) | (~hskp4)) <=> ((~hskp4) | (~c1_1(a467)))),
% 0.59/0.76 inference(rewrite,[status(thm)],[])).
% 0.59/0.76 tff(758,axiom,((~c1_1(a467)) | (~hskp4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause116')).
% 0.59/0.76 tff(759,plain,
% 0.59/0.76 ((~hskp4) | (~c1_1(a467))),
% 0.59/0.76 inference(modus_ponens,[status(thm)],[758, 757])).
% 0.59/0.76 tff(760,plain,
% 0.59/0.76 ((~hskp4) | (~c1_1(a467))),
% 0.59/0.76 inference(modus_ponens,[status(thm)],[759, 756])).
% 0.59/0.76 tff(761,plain,
% 0.59/0.76 (~c1_1(a467)),
% 0.59/0.76 inference(unit_resolution,[status(thm)],[760, 755])).
% 0.59/0.76 tff(762,plain,
% 0.59/0.76 (((~hskp4) | (~c0_1(a467))) <=> ((~hskp4) | (~c0_1(a467)))),
% 0.59/0.76 inference(rewrite,[status(thm)],[])).
% 0.59/0.76 tff(763,plain,
% 0.59/0.76 (((~c0_1(a467)) | (~hskp4)) <=> ((~hskp4) | (~c0_1(a467)))),
% 0.59/0.76 inference(rewrite,[status(thm)],[])).
% 0.59/0.76 tff(764,axiom,((~c0_1(a467)) | (~hskp4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause115')).
% 0.59/0.76 tff(765,plain,
% 0.59/0.76 ((~hskp4) | (~c0_1(a467))),
% 0.59/0.76 inference(modus_ponens,[status(thm)],[764, 763])).
% 0.59/0.76 tff(766,plain,
% 0.59/0.76 ((~hskp4) | (~c0_1(a467))),
% 0.59/0.76 inference(modus_ponens,[status(thm)],[765, 762])).
% 0.59/0.76 tff(767,plain,
% 0.59/0.76 (~c0_1(a467)),
% 0.59/0.76 inference(unit_resolution,[status(thm)],[766, 755])).
% 0.59/0.76 tff(768,plain,
% 0.59/0.76 (((~hskp4) | c3_1(a467)) <=> ((~hskp4) | c3_1(a467))),
% 0.59/0.76 inference(rewrite,[status(thm)],[])).
% 0.59/0.76 tff(769,axiom,((~hskp4) | c3_1(a467)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause78')).
% 0.59/0.76 tff(770,plain,
% 0.59/0.76 ((~hskp4) | c3_1(a467)),
% 0.59/0.76 inference(modus_ponens,[status(thm)],[769, 768])).
% 0.59/0.76 tff(771,plain,
% 0.59/0.76 ((~hskp4) | c3_1(a467)),
% 0.59/0.76 inference(modus_ponens,[status(thm)],[770, 768])).
% 0.59/0.76 tff(772,plain,
% 0.59/0.76 ((~hskp4) | c3_1(a467)),
% 0.59/0.76 inference(modus_ponens,[status(thm)],[771, 768])).
% 0.59/0.76 tff(773,plain,
% 0.59/0.76 ((~hskp4) | c3_1(a467)),
% 0.59/0.76 inference(modus_ponens,[status(thm)],[772, 768])).
% 0.59/0.76 tff(774,plain,
% 0.59/0.76 ((~hskp4) | c3_1(a467)),
% 0.59/0.76 inference(modus_ponens,[status(thm)],[773, 768])).
% 0.59/0.76 tff(775,plain,
% 0.59/0.76 (c3_1(a467)),
% 0.59/0.76 inference(unit_resolution,[status(thm)],[774, 755])).
% 0.59/0.76 tff(776,assumption,(~c1_1(a467)), introduced(assumption)).
% 0.59/0.76 tff(777,assumption,(~c0_1(a467)), introduced(assumption)).
% 0.59/0.76 tff(778,plain,
% 0.59/0.76 (((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | (hskp25 | c1_1(a488) | c3_1(a488) | c0_1(a467) | c1_1(a467) | (~ndr1_0) | c2_1(a467) | (~c0_1(a488)))) <=> ((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | hskp25 | c1_1(a488) | c3_1(a488) | c0_1(a467) | c1_1(a467) | (~ndr1_0) | c2_1(a467) | (~c0_1(a488)))),
% 0.59/0.76 inference(rewrite,[status(thm)],[])).
% 0.59/0.76 tff(779,plain,
% 0.59/0.76 ((hskp25 | (~ndr1_0) | c1_1(a488) | c3_1(a488) | (~c0_1(a488)) | c1_1(a467) | c0_1(a467) | c2_1(a467)) <=> (hskp25 | c1_1(a488) | c3_1(a488) | c0_1(a467) | c1_1(a467) | (~ndr1_0) | c2_1(a467) | (~c0_1(a488)))),
% 0.59/0.76 inference(rewrite,[status(thm)],[])).
% 0.59/0.76 tff(780,plain,
% 0.59/0.76 (((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | (hskp25 | (~ndr1_0) | c1_1(a488) | c3_1(a488) | (~c0_1(a488)) | c1_1(a467) | c0_1(a467) | c2_1(a467))) <=> ((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | (hskp25 | c1_1(a488) | c3_1(a488) | c0_1(a467) | c1_1(a467) | (~ndr1_0) | c2_1(a467) | (~c0_1(a488))))),
% 0.59/0.76 inference(monotonicity,[status(thm)],[779])).
% 0.59/0.76 tff(781,plain,
% 0.59/0.76 (((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | (hskp25 | (~ndr1_0) | c1_1(a488) | c3_1(a488) | (~c0_1(a488)) | c1_1(a467) | c0_1(a467) | c2_1(a467))) <=> ((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | hskp25 | c1_1(a488) | c3_1(a488) | c0_1(a467) | c1_1(a467) | (~ndr1_0) | c2_1(a467) | (~c0_1(a488)))),
% 0.59/0.76 inference(transitivity,[status(thm)],[780, 778])).
% 0.59/0.76 tff(782,plain,
% 0.59/0.76 ((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | (hskp25 | (~ndr1_0) | c1_1(a488) | c3_1(a488) | (~c0_1(a488)) | c1_1(a467) | c0_1(a467) | c2_1(a467))),
% 0.59/0.76 inference(quant_inst,[status(thm)],[])).
% 0.59/0.76 tff(783,plain,
% 0.59/0.76 ((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | hskp25 | c1_1(a488) | c3_1(a488) | c0_1(a467) | c1_1(a467) | (~ndr1_0) | c2_1(a467) | (~c0_1(a488))),
% 0.59/0.76 inference(modus_ponens,[status(thm)],[782, 781])).
% 0.59/0.76 tff(784,plain,
% 0.59/0.76 (c2_1(a467) | (~c0_1(a488))),
% 0.59/0.76 inference(unit_resolution,[status(thm)],[783, 137, 415, 419, 417, 777, 776, 437])).
% 0.59/0.76 tff(785,plain,
% 0.59/0.76 (c2_1(a467)),
% 0.59/0.76 inference(unit_resolution,[status(thm)],[784, 427])).
% 0.59/0.76 tff(786,plain,
% 0.59/0.76 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a494) | c1_1(a494) | c3_1(a494) | c1_1(a488) | c2_1(a488) | c3_1(a488) | c3_1(a478) | (~ndr1_0) | (~c2_1(a478)) | (~c1_1(a478)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a494) | c1_1(a494) | c3_1(a494) | c1_1(a488) | c2_1(a488) | c3_1(a488) | c3_1(a478) | (~ndr1_0) | (~c2_1(a478)) | (~c1_1(a478)))),
% 0.59/0.76 inference(rewrite,[status(thm)],[])).
% 0.59/0.76 tff(787,plain,
% 0.59/0.76 (((~ndr1_0) | c3_1(a478) | (~c2_1(a478)) | (~c1_1(a478)) | c3_1(a488) | c1_1(a488) | c2_1(a488) | c3_1(a494) | c1_1(a494) | c0_1(a494)) <=> (c0_1(a494) | c1_1(a494) | c3_1(a494) | c1_1(a488) | c2_1(a488) | c3_1(a488) | c3_1(a478) | (~ndr1_0) | (~c2_1(a478)) | (~c1_1(a478)))),
% 0.59/0.76 inference(rewrite,[status(thm)],[])).
% 0.59/0.76 tff(788,plain,
% 0.59/0.76 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a478) | (~c2_1(a478)) | (~c1_1(a478)) | c3_1(a488) | c1_1(a488) | c2_1(a488) | c3_1(a494) | c1_1(a494) | c0_1(a494))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a494) | c1_1(a494) | c3_1(a494) | c1_1(a488) | c2_1(a488) | c3_1(a488) | c3_1(a478) | (~ndr1_0) | (~c2_1(a478)) | (~c1_1(a478))))),
% 0.59/0.76 inference(monotonicity,[status(thm)],[787])).
% 0.59/0.76 tff(789,plain,
% 0.59/0.76 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a478) | (~c2_1(a478)) | (~c1_1(a478)) | c3_1(a488) | c1_1(a488) | c2_1(a488) | c3_1(a494) | c1_1(a494) | c0_1(a494))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a494) | c1_1(a494) | c3_1(a494) | c1_1(a488) | c2_1(a488) | c3_1(a488) | c3_1(a478) | (~ndr1_0) | (~c2_1(a478)) | (~c1_1(a478)))),
% 0.59/0.76 inference(transitivity,[status(thm)],[788, 786])).
% 0.59/0.76 tff(790,plain,
% 0.59/0.76 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a478) | (~c2_1(a478)) | (~c1_1(a478)) | c3_1(a488) | c1_1(a488) | c2_1(a488) | c3_1(a494) | c1_1(a494) | c0_1(a494))),
% 0.59/0.76 inference(quant_inst,[status(thm)],[])).
% 0.59/0.76 tff(791,plain,
% 0.59/0.76 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a494) | c1_1(a494) | c3_1(a494) | c1_1(a488) | c2_1(a488) | c3_1(a488) | c3_1(a478) | (~ndr1_0) | (~c2_1(a478)) | (~c1_1(a478))),
% 0.59/0.76 inference(modus_ponens,[status(thm)],[790, 789])).
% 0.59/0.76 tff(792,plain,
% 0.59/0.76 (~c1_1(a478)),
% 0.59/0.76 inference(unit_resolution,[status(thm)],[791, 137, 131, 511, 510, 495, 419, 418, 417, 117, 659])).
% 0.59/0.76 tff(793,plain,
% 0.59/0.76 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W))) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W))))),
% 0.59/0.76 inference(bind,[status(th)],[])).
% 0.59/0.76 tff(794,plain,
% 0.59/0.76 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))),
% 0.59/0.76 inference(quant_intro,[status(thm)],[793])).
% 0.59/0.76 tff(795,plain,
% 0.59/0.76 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))),
% 0.59/0.76 inference(rewrite,[status(thm)],[])).
% 0.59/0.76 tff(796,plain,
% 0.59/0.76 (^[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))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(V)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(V))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c2_1(W))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(V))) | (~c2_1(W))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c2_1(W)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c2_1(W))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c2_1(W))) | (~c3_1(W))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c2_1(W))) | (~c3_1(W))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c2_1(W))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(W)) | (~c2_1(W)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c2_1(W))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(W)) | (~c2_1(W))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c2_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(W)) | (~c2_1(W))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(W)) | (~c2_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(W)) | (~c2_1(W)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(W)) | (~c2_1(W))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c2_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(W)) | (~c2_1(W))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(W)) | (~c2_1(W))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(W)) | (~c2_1(W)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c2_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(W)) | (~c2_1(W))))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c2_1(U)) | c1_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(W)) | (~c2_1(W))) | c3_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(W)) | (~c2_1(W))) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | (~c3_1(W)) | (~c2_1(W)))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c2_1(U)) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | (~c3_1(W)) | (~c2_1(W))))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c2_1(U)) | c1_1(V)) | c3_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | (~c3_1(W)) | (~c2_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | (~c3_1(W)) | (~c2_1(W))) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c2_1(U)) | c1_1(V)) | c3_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))))),
% 0.59/0.76 inference(bind,[status(th)],[])).
% 0.59/0.76 tff(797,plain,
% 0.59/0.76 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c2_1(U)) | c1_1(V)) | c3_1(V)) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))),
% 0.59/0.76 inference(quant_intro,[status(thm)],[796])).
% 0.59/0.76 tff(798,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c2_1(U)) | c1_1(V)) | c3_1(V)) | c0_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause176')).
% 0.59/0.76 tff(799,plain,
% 0.59/0.76 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))),
% 0.59/0.76 inference(modus_ponens,[status(thm)],[798, 797])).
% 0.59/0.76 tff(800,plain,
% 0.59/0.76 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))),
% 0.59/0.76 inference(modus_ponens,[status(thm)],[799, 795])).
% 0.59/0.76 tff(801,plain,(
% 0.59/0.76 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))),
% 0.59/0.76 inference(skolemize,[status(sab)],[800])).
% 0.59/0.76 tff(802,plain,
% 0.59/0.76 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))),
% 0.59/0.76 inference(modus_ponens,[status(thm)],[801, 794])).
% 0.59/0.76 tff(803,assumption,(c3_1(a467)), introduced(assumption)).
% 0.59/0.76 tff(804,plain,
% 0.59/0.76 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c3_1(a478) | c0_1(a467) | c2_1(a460) | (~ndr1_0) | (~c2_1(a478)) | c1_1(a478) | (~c1_1(a460)) | (~c0_1(a460)) | (~c3_1(a467)) | (~c2_1(a467)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c3_1(a478) | c0_1(a467) | c2_1(a460) | (~ndr1_0) | (~c2_1(a478)) | c1_1(a478) | (~c1_1(a460)) | (~c0_1(a460)) | (~c3_1(a467)) | (~c2_1(a467)))),
% 0.59/0.76 inference(rewrite,[status(thm)],[])).
% 0.59/0.76 tff(805,plain,
% 0.59/0.76 (((~ndr1_0) | c2_1(a460) | (~c0_1(a460)) | (~c1_1(a460)) | c3_1(a478) | c1_1(a478) | (~c2_1(a478)) | c0_1(a467) | (~c3_1(a467)) | (~c2_1(a467))) <=> (c3_1(a478) | c0_1(a467) | c2_1(a460) | (~ndr1_0) | (~c2_1(a478)) | c1_1(a478) | (~c1_1(a460)) | (~c0_1(a460)) | (~c3_1(a467)) | (~c2_1(a467)))),
% 0.59/0.76 inference(rewrite,[status(thm)],[])).
% 0.59/0.76 tff(806,plain,
% 0.59/0.76 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a460) | (~c0_1(a460)) | (~c1_1(a460)) | c3_1(a478) | c1_1(a478) | (~c2_1(a478)) | c0_1(a467) | (~c3_1(a467)) | (~c2_1(a467)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c3_1(a478) | c0_1(a467) | c2_1(a460) | (~ndr1_0) | (~c2_1(a478)) | c1_1(a478) | (~c1_1(a460)) | (~c0_1(a460)) | (~c3_1(a467)) | (~c2_1(a467))))),
% 0.59/0.76 inference(monotonicity,[status(thm)],[805])).
% 0.59/0.76 tff(807,plain,
% 0.59/0.76 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a460) | (~c0_1(a460)) | (~c1_1(a460)) | c3_1(a478) | c1_1(a478) | (~c2_1(a478)) | c0_1(a467) | (~c3_1(a467)) | (~c2_1(a467)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c3_1(a478) | c0_1(a467) | c2_1(a460) | (~ndr1_0) | (~c2_1(a478)) | c1_1(a478) | (~c1_1(a460)) | (~c0_1(a460)) | (~c3_1(a467)) | (~c2_1(a467)))),
% 0.60/0.76 inference(transitivity,[status(thm)],[806, 804])).
% 0.60/0.76 tff(808,plain,
% 0.60/0.76 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a460) | (~c0_1(a460)) | (~c1_1(a460)) | c3_1(a478) | c1_1(a478) | (~c2_1(a478)) | c0_1(a467) | (~c3_1(a467)) | (~c2_1(a467)))),
% 0.60/0.76 inference(quant_inst,[status(thm)],[])).
% 0.60/0.76 tff(809,plain,
% 0.60/0.76 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c3_1(a478) | c0_1(a467) | c2_1(a460) | (~ndr1_0) | (~c2_1(a478)) | c1_1(a478) | (~c1_1(a460)) | (~c0_1(a460)) | (~c3_1(a467)) | (~c2_1(a467))),
% 0.60/0.76 inference(modus_ponens,[status(thm)],[808, 807])).
% 0.60/0.76 tff(810,plain,
% 0.60/0.76 (c1_1(a478) | (~c1_1(a460)) | (~c2_1(a467))),
% 0.60/0.76 inference(unit_resolution,[status(thm)],[809, 137, 131, 803, 224, 117, 777, 1, 802])).
% 0.60/0.76 tff(811,plain,
% 0.60/0.76 (~c1_1(a460)),
% 0.60/0.76 inference(unit_resolution,[status(thm)],[810, 792, 785])).
% 0.60/0.76 tff(812,plain,
% 0.60/0.76 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp12 | c1_1(a488) | c3_1(a488) | c2_1(a460) | c3_1(a460) | (~ndr1_0) | (~c0_1(a460)) | (~c0_1(a488)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | hskp12 | c1_1(a488) | c3_1(a488) | c2_1(a460) | c3_1(a460) | (~ndr1_0) | (~c0_1(a460)) | (~c0_1(a488)))),
% 0.60/0.76 inference(rewrite,[status(thm)],[])).
% 0.60/0.76 tff(813,plain,
% 0.60/0.76 ((hskp12 | (~ndr1_0) | c2_1(a460) | c3_1(a460) | (~c0_1(a460)) | c3_1(a488) | c1_1(a488) | (~c0_1(a488))) <=> (hskp12 | c1_1(a488) | c3_1(a488) | c2_1(a460) | c3_1(a460) | (~ndr1_0) | (~c0_1(a460)) | (~c0_1(a488)))),
% 0.60/0.76 inference(rewrite,[status(thm)],[])).
% 0.60/0.76 tff(814,plain,
% 0.60/0.76 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp12 | (~ndr1_0) | c2_1(a460) | c3_1(a460) | (~c0_1(a460)) | c3_1(a488) | c1_1(a488) | (~c0_1(a488)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp12 | c1_1(a488) | c3_1(a488) | c2_1(a460) | c3_1(a460) | (~ndr1_0) | (~c0_1(a460)) | (~c0_1(a488))))),
% 0.60/0.76 inference(monotonicity,[status(thm)],[813])).
% 0.60/0.76 tff(815,plain,
% 0.60/0.76 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp12 | (~ndr1_0) | c2_1(a460) | c3_1(a460) | (~c0_1(a460)) | c3_1(a488) | c1_1(a488) | (~c0_1(a488)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | hskp12 | c1_1(a488) | c3_1(a488) | c2_1(a460) | c3_1(a460) | (~ndr1_0) | (~c0_1(a460)) | (~c0_1(a488)))),
% 0.60/0.76 inference(transitivity,[status(thm)],[814, 812])).
% 0.60/0.76 tff(816,plain,
% 0.60/0.76 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp12 | (~ndr1_0) | c2_1(a460) | c3_1(a460) | (~c0_1(a460)) | c3_1(a488) | c1_1(a488) | (~c0_1(a488)))),
% 0.60/0.76 inference(quant_inst,[status(thm)],[])).
% 0.60/0.76 tff(817,plain,
% 0.60/0.76 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | hskp12 | c1_1(a488) | c3_1(a488) | c2_1(a460) | c3_1(a460) | (~ndr1_0) | (~c0_1(a460)) | (~c0_1(a488))),
% 0.60/0.76 inference(modus_ponens,[status(thm)],[816, 815])).
% 0.60/0.76 tff(818,plain,
% 0.60/0.76 (hskp12),
% 0.60/0.76 inference(unit_resolution,[status(thm)],[817, 137, 224, 419, 417, 1, 223, 44, 427])).
% 0.60/0.76 tff(819,plain,
% 0.60/0.76 (~c2_1(a480)),
% 0.60/0.76 inference(unit_resolution,[status(thm)],[89, 818])).
% 0.60/0.76 tff(820,plain,
% 0.60/0.76 (~c1_1(a480)),
% 0.60/0.76 inference(unit_resolution,[status(thm)],[95, 818])).
% 0.60/0.76 tff(821,plain,
% 0.60/0.76 (~c0_1(a480)),
% 0.60/0.76 inference(unit_resolution,[status(thm)],[101, 818])).
% 0.60/0.76 tff(822,plain,
% 0.60/0.76 (((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | (hskp25 | c0_1(a480) | c1_1(a480) | c2_1(a480) | c3_1(a460) | (~ndr1_0) | c1_1(a460) | (~c0_1(a460)))) <=> ((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | hskp25 | c0_1(a480) | c1_1(a480) | c2_1(a480) | c3_1(a460) | (~ndr1_0) | c1_1(a460) | (~c0_1(a460)))),
% 0.60/0.76 inference(rewrite,[status(thm)],[])).
% 0.60/0.76 tff(823,plain,
% 0.60/0.76 ((hskp25 | (~ndr1_0) | c1_1(a460) | c3_1(a460) | (~c0_1(a460)) | c1_1(a480) | c0_1(a480) | c2_1(a480)) <=> (hskp25 | c0_1(a480) | c1_1(a480) | c2_1(a480) | c3_1(a460) | (~ndr1_0) | c1_1(a460) | (~c0_1(a460)))),
% 0.60/0.76 inference(rewrite,[status(thm)],[])).
% 0.60/0.76 tff(824,plain,
% 0.60/0.76 (((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | (hskp25 | (~ndr1_0) | c1_1(a460) | c3_1(a460) | (~c0_1(a460)) | c1_1(a480) | c0_1(a480) | c2_1(a480))) <=> ((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | (hskp25 | c0_1(a480) | c1_1(a480) | c2_1(a480) | c3_1(a460) | (~ndr1_0) | c1_1(a460) | (~c0_1(a460))))),
% 0.60/0.76 inference(monotonicity,[status(thm)],[823])).
% 0.60/0.76 tff(825,plain,
% 0.60/0.76 (((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | (hskp25 | (~ndr1_0) | c1_1(a460) | c3_1(a460) | (~c0_1(a460)) | c1_1(a480) | c0_1(a480) | c2_1(a480))) <=> ((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | hskp25 | c0_1(a480) | c1_1(a480) | c2_1(a480) | c3_1(a460) | (~ndr1_0) | c1_1(a460) | (~c0_1(a460)))),
% 0.60/0.76 inference(transitivity,[status(thm)],[824, 822])).
% 0.60/0.76 tff(826,plain,
% 0.60/0.76 ((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | (hskp25 | (~ndr1_0) | c1_1(a460) | c3_1(a460) | (~c0_1(a460)) | c1_1(a480) | c0_1(a480) | c2_1(a480))),
% 0.60/0.76 inference(quant_inst,[status(thm)],[])).
% 0.60/0.76 tff(827,plain,
% 0.60/0.76 ((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | hskp25 | c0_1(a480) | c1_1(a480) | c2_1(a480) | c3_1(a460) | (~ndr1_0) | c1_1(a460) | (~c0_1(a460))),
% 0.60/0.76 inference(modus_ponens,[status(thm)],[826, 825])).
% 0.60/0.76 tff(828,plain,
% 0.60/0.76 ($false),
% 0.60/0.76 inference(unit_resolution,[status(thm)],[827, 137, 415, 224, 821, 820, 819, 223, 437, 811])).
% 0.60/0.76 tff(829,plain,(hskp25 | (~c0_1(a460)) | c3_1(a460) | (~c3_1(a467)) | c0_1(a467) | c2_1(a460) | c1_1(a467) | c0_1(a494) | c1_1(a494) | c3_1(a494) | hskp27 | hskp5), inference(lemma,lemma(discharge,[]))).
% 0.60/0.76 tff(830,plain,
% 0.60/0.76 (hskp25),
% 0.60/0.76 inference(unit_resolution,[status(thm)],[829, 775, 223, 224, 767, 1, 761, 508, 502, 495, 363, 103])).
% 0.60/0.76 tff(831,plain,
% 0.60/0.76 (c3_1(a461)),
% 0.60/0.76 inference(unit_resolution,[status(thm)],[302, 830])).
% 0.60/0.76 tff(832,plain,
% 0.60/0.76 (c2_1(a461)),
% 0.60/0.76 inference(unit_resolution,[status(thm)],[310, 830])).
% 0.60/0.76 tff(833,plain,
% 0.60/0.76 (c0_1(a461)),
% 0.60/0.76 inference(unit_resolution,[status(thm)],[318, 830])).
% 0.60/0.76 tff(834,plain,
% 0.60/0.76 (hskp26 | (~c2_1(a494))),
% 0.60/0.76 inference(unit_resolution,[status(thm)],[693, 137, 833, 832, 831, 508, 502, 530])).
% 0.60/0.76 tff(835,plain,
% 0.60/0.76 (hskp26),
% 0.60/0.76 inference(unit_resolution,[status(thm)],[834, 520])).
% 0.60/0.76 tff(836,plain,
% 0.60/0.76 (c2_1(a470)),
% 0.60/0.76 inference(unit_resolution,[status(thm)],[710, 835])).
% 0.60/0.76 tff(837,plain,
% 0.60/0.76 (c1_1(a470)),
% 0.60/0.76 inference(unit_resolution,[status(thm)],[718, 835])).
% 0.60/0.76 tff(838,plain,
% 0.60/0.76 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp5 | c0_1(a494) | c1_1(a494) | c3_1(a494) | (~ndr1_0) | (~c2_1(a470)) | (~c0_1(a470)) | (~c1_1(a470)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp5 | c0_1(a494) | c1_1(a494) | c3_1(a494) | (~ndr1_0) | (~c2_1(a470)) | (~c0_1(a470)) | (~c1_1(a470)))),
% 0.60/0.77 inference(rewrite,[status(thm)],[])).
% 0.60/0.77 tff(839,plain,
% 0.60/0.77 ((hskp5 | (~ndr1_0) | (~c2_1(a470)) | (~c0_1(a470)) | (~c1_1(a470)) | c3_1(a494) | c1_1(a494) | c0_1(a494)) <=> (hskp5 | c0_1(a494) | c1_1(a494) | c3_1(a494) | (~ndr1_0) | (~c2_1(a470)) | (~c0_1(a470)) | (~c1_1(a470)))),
% 0.60/0.77 inference(rewrite,[status(thm)],[])).
% 0.60/0.77 tff(840,plain,
% 0.60/0.77 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp5 | (~ndr1_0) | (~c2_1(a470)) | (~c0_1(a470)) | (~c1_1(a470)) | c3_1(a494) | c1_1(a494) | c0_1(a494))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp5 | c0_1(a494) | c1_1(a494) | c3_1(a494) | (~ndr1_0) | (~c2_1(a470)) | (~c0_1(a470)) | (~c1_1(a470))))),
% 0.60/0.77 inference(monotonicity,[status(thm)],[839])).
% 0.60/0.77 tff(841,plain,
% 0.60/0.77 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp5 | (~ndr1_0) | (~c2_1(a470)) | (~c0_1(a470)) | (~c1_1(a470)) | c3_1(a494) | c1_1(a494) | c0_1(a494))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp5 | c0_1(a494) | c1_1(a494) | c3_1(a494) | (~ndr1_0) | (~c2_1(a470)) | (~c0_1(a470)) | (~c1_1(a470)))),
% 0.60/0.77 inference(transitivity,[status(thm)],[840, 838])).
% 0.60/0.77 tff(842,plain,
% 0.60/0.77 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp5 | (~ndr1_0) | (~c2_1(a470)) | (~c0_1(a470)) | (~c1_1(a470)) | c3_1(a494) | c1_1(a494) | c0_1(a494))),
% 0.60/0.77 inference(quant_inst,[status(thm)],[])).
% 0.60/0.77 tff(843,plain,
% 0.60/0.77 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp5 | c0_1(a494) | c1_1(a494) | c3_1(a494) | (~ndr1_0) | (~c2_1(a470)) | (~c0_1(a470)) | (~c1_1(a470))),
% 0.60/0.77 inference(modus_ponens,[status(thm)],[842, 841])).
% 0.60/0.77 tff(844,plain,
% 0.60/0.77 (~c0_1(a470)),
% 0.60/0.77 inference(unit_resolution,[status(thm)],[843, 103, 137, 837, 836, 508, 502, 495, 494])).
% 0.60/0.77 tff(845,assumption,(~c1_1(a460)), introduced(assumption)).
% 0.60/0.77 tff(846,plain,
% 0.60/0.77 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp27 | c0_1(a494) | c3_1(a494) | c2_1(a460) | c3_1(a460) | (~ndr1_0) | c1_1(a460) | c2_1(a494))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp27 | c0_1(a494) | c3_1(a494) | c2_1(a460) | c3_1(a460) | (~ndr1_0) | c1_1(a460) | c2_1(a494))),
% 0.60/0.77 inference(rewrite,[status(thm)],[])).
% 0.60/0.77 tff(847,plain,
% 0.60/0.77 ((hskp27 | (~ndr1_0) | c2_1(a460) | c1_1(a460) | c3_1(a460) | c3_1(a494) | c0_1(a494) | c2_1(a494)) <=> (hskp27 | c0_1(a494) | c3_1(a494) | c2_1(a460) | c3_1(a460) | (~ndr1_0) | c1_1(a460) | c2_1(a494))),
% 0.60/0.77 inference(rewrite,[status(thm)],[])).
% 0.60/0.77 tff(848,plain,
% 0.60/0.77 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp27 | (~ndr1_0) | c2_1(a460) | c1_1(a460) | c3_1(a460) | c3_1(a494) | c0_1(a494) | c2_1(a494))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp27 | c0_1(a494) | c3_1(a494) | c2_1(a460) | c3_1(a460) | (~ndr1_0) | c1_1(a460) | c2_1(a494)))),
% 0.60/0.77 inference(monotonicity,[status(thm)],[847])).
% 0.60/0.77 tff(849,plain,
% 0.60/0.77 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp27 | (~ndr1_0) | c2_1(a460) | c1_1(a460) | c3_1(a460) | c3_1(a494) | c0_1(a494) | c2_1(a494))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp27 | c0_1(a494) | c3_1(a494) | c2_1(a460) | c3_1(a460) | (~ndr1_0) | c1_1(a460) | c2_1(a494))),
% 0.60/0.77 inference(transitivity,[status(thm)],[848, 846])).
% 0.60/0.77 tff(850,plain,
% 0.60/0.77 ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp27 | (~ndr1_0) | c2_1(a460) | c1_1(a460) | c3_1(a460) | c3_1(a494) | c0_1(a494) | c2_1(a494))),
% 0.60/0.77 inference(quant_inst,[status(thm)],[])).
% 0.60/0.77 tff(851,plain,
% 0.60/0.77 ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp27 | c0_1(a494) | c3_1(a494) | c2_1(a460) | c3_1(a460) | (~ndr1_0) | c1_1(a460) | c2_1(a494)),
% 0.60/0.77 inference(modus_ponens,[status(thm)],[850, 849])).
% 0.60/0.77 tff(852,plain,
% 0.60/0.77 (hskp27 | c0_1(a494) | c1_1(a460) | c2_1(a494)),
% 0.60/0.77 inference(unit_resolution,[status(thm)],[851, 137, 495, 1, 223, 414])).
% 0.60/0.77 tff(853,plain,
% 0.60/0.77 (c2_1(a494)),
% 0.60/0.77 inference(unit_resolution,[status(thm)],[852, 845, 420, 511])).
% 0.60/0.77 tff(854,plain,
% 0.60/0.77 (hskp26 | (~c2_1(a494))),
% 0.60/0.77 inference(unit_resolution,[status(thm)],[693, 137, 466, 465, 464, 511, 510, 530])).
% 0.60/0.77 tff(855,plain,
% 0.60/0.77 (hskp26),
% 0.60/0.77 inference(unit_resolution,[status(thm)],[854, 853])).
% 0.60/0.77 tff(856,plain,
% 0.60/0.77 (c2_1(a470)),
% 0.60/0.77 inference(unit_resolution,[status(thm)],[710, 855])).
% 0.60/0.77 tff(857,plain,
% 0.60/0.77 (c1_1(a470)),
% 0.60/0.77 inference(unit_resolution,[status(thm)],[718, 855])).
% 0.60/0.77 tff(858,plain,
% 0.60/0.77 (~c0_1(a470)),
% 0.60/0.77 inference(unit_resolution,[status(thm)],[843, 103, 137, 857, 856, 511, 510, 495, 494])).
% 0.60/0.77 tff(859,plain,
% 0.60/0.77 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W))) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W))))),
% 0.60/0.77 inference(bind,[status(th)],[])).
% 0.60/0.77 tff(860,plain,
% 0.60/0.77 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))),
% 0.60/0.77 inference(quant_intro,[status(thm)],[859])).
% 0.60/0.77 tff(861,plain,
% 0.60/0.77 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))),
% 0.60/0.77 inference(rewrite,[status(thm)],[])).
% 0.60/0.77 tff(862,plain,
% 0.60/0.77 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V))))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(V)))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(V))))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c1_1(W))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(V))) | (~c1_1(W))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c1_1(W)))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c1_1(W))))), ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c1_1(W))) | c0_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c1_1(W))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c1_1(W))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c1_1(W)))), ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c1_1(W))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c1_1(W))))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c1_1(W))) | c0_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c1_1(W))) | c0_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c1_1(W))) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | (~c1_1(W)))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c1_1(W))) | c0_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | (~c1_1(W))))), ((((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c1_1(W))) | c0_1(U)) | c0_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | (~c1_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | (~c1_1(W))) | c0_1(W)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)))), ((((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c1_1(W))) | c0_1(U)) | c0_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W))))), (((((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c1_1(W))) | c0_1(U)) | c0_1(V)) | c0_1(W)) | c2_1(W)) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W))) | c2_1(W)))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W))) | c2_1(W)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))), (((((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c1_1(W))) | c0_1(U)) | c0_1(V)) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))))),
% 0.60/0.77 inference(bind,[status(th)],[])).
% 0.60/0.77 tff(863,plain,
% 0.60/0.77 (![W: $i, V: $i, U: $i] : ((((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c1_1(W))) | c0_1(U)) | c0_1(V)) | c0_1(W)) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))),
% 0.60/0.77 inference(quant_intro,[status(thm)],[862])).
% 0.60/0.77 tff(864,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c1_1(W))) | c0_1(U)) | c0_1(V)) | c0_1(W)) | c2_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause174')).
% 0.60/0.77 tff(865,plain,
% 0.60/0.77 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))),
% 0.60/0.77 inference(modus_ponens,[status(thm)],[864, 863])).
% 0.60/0.77 tff(866,plain,
% 0.60/0.77 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))),
% 0.60/0.77 inference(modus_ponens,[status(thm)],[865, 861])).
% 0.60/0.77 tff(867,plain,(
% 0.60/0.77 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))),
% 0.60/0.77 inference(skolemize,[status(sab)],[866])).
% 0.60/0.77 tff(868,plain,
% 0.60/0.77 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))),
% 0.60/0.77 inference(modus_ponens,[status(thm)],[867, 860])).
% 0.60/0.77 tff(869,plain,
% 0.60/0.77 (^[U: $i] : refl((hskp27 | hskp16 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U))) <=> (hskp27 | hskp16 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U))))),
% 0.60/0.77 inference(bind,[status(th)],[])).
% 0.60/0.77 tff(870,plain,
% 0.60/0.77 (![U: $i] : (hskp27 | hskp16 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp27 | hskp16 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))),
% 0.60/0.77 inference(quant_intro,[status(thm)],[869])).
% 0.60/0.77 tff(871,plain,
% 0.60/0.77 (![U: $i] : (hskp27 | hskp16 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp27 | hskp16 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))),
% 0.60/0.77 inference(rewrite,[status(thm)],[])).
% 0.60/0.77 tff(872,plain,
% 0.60/0.77 (^[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) | c1_1(U) | c3_1(U) | (~c0_1(U)))), (((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U))))), ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp27) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U))) | hskp27))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U))) | hskp27) <=> (hskp27 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))), ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp27) <=> (hskp27 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U))))), (((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp27) | hskp16) <=> ((hskp27 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U))) | hskp16))), rewrite(((hskp27 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U))) | hskp16) <=> (hskp27 | hskp16 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))), (((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp27) | hskp16) <=> (hskp27 | hskp16 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))))),
% 0.60/0.77 inference(bind,[status(th)],[])).
% 0.60/0.77 tff(873,plain,
% 0.60/0.77 (![U: $i] : ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp27) | hskp16) <=> ![U: $i] : (hskp27 | hskp16 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))),
% 0.60/0.77 inference(quant_intro,[status(thm)],[872])).
% 0.60/0.77 tff(874,axiom,(![U: $i] : ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp27) | hskp16)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause131')).
% 0.60/0.77 tff(875,plain,
% 0.60/0.77 (![U: $i] : (hskp27 | hskp16 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))),
% 0.60/0.77 inference(modus_ponens,[status(thm)],[874, 873])).
% 0.60/0.77 tff(876,plain,
% 0.60/0.77 (![U: $i] : (hskp27 | hskp16 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))),
% 0.60/0.77 inference(modus_ponens,[status(thm)],[875, 871])).
% 0.60/0.77 tff(877,plain,(
% 0.60/0.77 ![U: $i] : (hskp27 | hskp16 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))),
% 0.60/0.77 inference(skolemize,[status(sab)],[876])).
% 0.60/0.77 tff(878,plain,
% 0.60/0.77 (![U: $i] : (hskp27 | hskp16 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))),
% 0.60/0.77 inference(modus_ponens,[status(thm)],[877, 870])).
% 0.60/0.77 tff(879,plain,
% 0.60/0.77 (((~![U: $i] : (hskp27 | hskp16 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp27 | hskp16 | c3_1(a460) | (~ndr1_0) | c1_1(a460) | (~c0_1(a460)))) <=> ((~![U: $i] : (hskp27 | hskp16 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))) | hskp27 | hskp16 | c3_1(a460) | (~ndr1_0) | c1_1(a460) | (~c0_1(a460)))),
% 0.60/0.77 inference(rewrite,[status(thm)],[])).
% 0.60/0.77 tff(880,plain,
% 0.60/0.77 ((hskp27 | hskp16 | (~ndr1_0) | c1_1(a460) | c3_1(a460) | (~c0_1(a460))) <=> (hskp27 | hskp16 | c3_1(a460) | (~ndr1_0) | c1_1(a460) | (~c0_1(a460)))),
% 0.60/0.77 inference(rewrite,[status(thm)],[])).
% 0.60/0.77 tff(881,plain,
% 0.60/0.77 (((~![U: $i] : (hskp27 | hskp16 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp27 | hskp16 | (~ndr1_0) | c1_1(a460) | c3_1(a460) | (~c0_1(a460)))) <=> ((~![U: $i] : (hskp27 | hskp16 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp27 | hskp16 | c3_1(a460) | (~ndr1_0) | c1_1(a460) | (~c0_1(a460))))),
% 0.60/0.77 inference(monotonicity,[status(thm)],[880])).
% 0.60/0.77 tff(882,plain,
% 0.60/0.77 (((~![U: $i] : (hskp27 | hskp16 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp27 | hskp16 | (~ndr1_0) | c1_1(a460) | c3_1(a460) | (~c0_1(a460)))) <=> ((~![U: $i] : (hskp27 | hskp16 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))) | hskp27 | hskp16 | c3_1(a460) | (~ndr1_0) | c1_1(a460) | (~c0_1(a460)))),
% 0.60/0.77 inference(transitivity,[status(thm)],[881, 879])).
% 0.60/0.77 tff(883,plain,
% 0.60/0.77 ((~![U: $i] : (hskp27 | hskp16 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp27 | hskp16 | (~ndr1_0) | c1_1(a460) | c3_1(a460) | (~c0_1(a460)))),
% 0.60/0.77 inference(quant_inst,[status(thm)],[])).
% 0.60/0.77 tff(884,plain,
% 0.60/0.77 ((~![U: $i] : (hskp27 | hskp16 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))) | hskp27 | hskp16 | c3_1(a460) | (~ndr1_0) | c1_1(a460) | (~c0_1(a460))),
% 0.60/0.77 inference(modus_ponens,[status(thm)],[883, 882])).
% 0.60/0.77 tff(885,plain,
% 0.60/0.77 (hskp27 | hskp16 | c1_1(a460) | (~c0_1(a460))),
% 0.60/0.77 inference(unit_resolution,[status(thm)],[884, 137, 223, 878])).
% 0.60/0.77 tff(886,plain,
% 0.60/0.77 (hskp16),
% 0.60/0.77 inference(unit_resolution,[status(thm)],[885, 845, 420, 224])).
% 0.60/0.77 tff(887,plain,
% 0.60/0.77 (((~hskp16) | (~c2_1(a493))) <=> ((~hskp16) | (~c2_1(a493)))),
% 0.60/0.77 inference(rewrite,[status(thm)],[])).
% 0.60/0.77 tff(888,plain,
% 0.60/0.77 (((~c2_1(a493)) | (~hskp16)) <=> ((~hskp16) | (~c2_1(a493)))),
% 0.60/0.77 inference(rewrite,[status(thm)],[])).
% 0.60/0.77 tff(889,axiom,((~c2_1(a493)) | (~hskp16)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause96')).
% 0.60/0.77 tff(890,plain,
% 0.60/0.77 ((~hskp16) | (~c2_1(a493))),
% 0.60/0.77 inference(modus_ponens,[status(thm)],[889, 888])).
% 0.60/0.77 tff(891,plain,
% 0.60/0.77 ((~hskp16) | (~c2_1(a493))),
% 0.60/0.77 inference(modus_ponens,[status(thm)],[890, 887])).
% 0.60/0.77 tff(892,plain,
% 0.60/0.77 (~c2_1(a493)),
% 0.60/0.77 inference(unit_resolution,[status(thm)],[891, 886])).
% 0.60/0.77 tff(893,plain,
% 0.60/0.77 (((~hskp16) | (~c0_1(a493))) <=> ((~hskp16) | (~c0_1(a493)))),
% 0.60/0.77 inference(rewrite,[status(thm)],[])).
% 0.60/0.77 tff(894,plain,
% 0.60/0.77 (((~c0_1(a493)) | (~hskp16)) <=> ((~hskp16) | (~c0_1(a493)))),
% 0.60/0.77 inference(rewrite,[status(thm)],[])).
% 0.60/0.77 tff(895,axiom,((~c0_1(a493)) | (~hskp16)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause95')).
% 0.60/0.77 tff(896,plain,
% 0.60/0.77 ((~hskp16) | (~c0_1(a493))),
% 0.60/0.77 inference(modus_ponens,[status(thm)],[895, 894])).
% 0.60/0.77 tff(897,plain,
% 0.60/0.77 ((~hskp16) | (~c0_1(a493))),
% 0.60/0.77 inference(modus_ponens,[status(thm)],[896, 893])).
% 0.60/0.77 tff(898,plain,
% 0.60/0.77 (~c0_1(a493)),
% 0.60/0.77 inference(unit_resolution,[status(thm)],[897, 886])).
% 0.60/0.77 tff(899,plain,
% 0.60/0.77 (((~hskp16) | c1_1(a493)) <=> ((~hskp16) | c1_1(a493))),
% 0.60/0.77 inference(rewrite,[status(thm)],[])).
% 0.60/0.77 tff(900,axiom,((~hskp16) | c1_1(a493)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause62')).
% 0.60/0.77 tff(901,plain,
% 0.60/0.77 ((~hskp16) | c1_1(a493)),
% 0.60/0.77 inference(modus_ponens,[status(thm)],[900, 899])).
% 0.60/0.77 tff(902,plain,
% 0.60/0.77 ((~hskp16) | c1_1(a493)),
% 0.60/0.77 inference(modus_ponens,[status(thm)],[901, 899])).
% 0.60/0.77 tff(903,plain,
% 0.60/0.77 ((~hskp16) | c1_1(a493)),
% 0.60/0.77 inference(modus_ponens,[status(thm)],[902, 899])).
% 0.60/0.77 tff(904,plain,
% 0.60/0.77 ((~hskp16) | c1_1(a493)),
% 0.60/0.77 inference(modus_ponens,[status(thm)],[903, 899])).
% 0.60/0.77 tff(905,plain,
% 0.60/0.77 ((~hskp16) | c1_1(a493)),
% 0.60/0.77 inference(modus_ponens,[status(thm)],[904, 899])).
% 0.60/0.77 tff(906,plain,
% 0.60/0.77 (c1_1(a493)),
% 0.60/0.77 inference(unit_resolution,[status(thm)],[905, 886])).
% 0.60/0.77 tff(907,plain,
% 0.60/0.77 (c3_1(a470)),
% 0.60/0.77 inference(unit_resolution,[status(thm)],[702, 855])).
% 0.60/0.77 tff(908,plain,
% 0.60/0.77 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | (c0_1(a493) | c2_1(a493) | (~ndr1_0) | (~c1_1(a493)) | (~c2_1(a470)) | c0_1(a470) | (~c1_1(a470)) | (~c3_1(a470)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | c0_1(a493) | c2_1(a493) | (~ndr1_0) | (~c1_1(a493)) | (~c2_1(a470)) | c0_1(a470) | (~c1_1(a470)) | (~c3_1(a470)))),
% 0.60/0.77 inference(rewrite,[status(thm)],[])).
% 0.60/0.77 tff(909,plain,
% 0.60/0.77 (((~ndr1_0) | c0_1(a470) | (~c2_1(a470)) | (~c3_1(a470)) | c0_1(a470) | (~c1_1(a470)) | (~c3_1(a470)) | c0_1(a493) | c2_1(a493) | (~c1_1(a493))) <=> (c0_1(a493) | c2_1(a493) | (~ndr1_0) | (~c1_1(a493)) | (~c2_1(a470)) | c0_1(a470) | (~c1_1(a470)) | (~c3_1(a470)))),
% 0.60/0.77 inference(rewrite,[status(thm)],[])).
% 0.60/0.77 tff(910,plain,
% 0.60/0.77 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c0_1(a470) | (~c2_1(a470)) | (~c3_1(a470)) | c0_1(a470) | (~c1_1(a470)) | (~c3_1(a470)) | c0_1(a493) | c2_1(a493) | (~c1_1(a493)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | (c0_1(a493) | c2_1(a493) | (~ndr1_0) | (~c1_1(a493)) | (~c2_1(a470)) | c0_1(a470) | (~c1_1(a470)) | (~c3_1(a470))))),
% 0.60/0.77 inference(monotonicity,[status(thm)],[909])).
% 0.60/0.77 tff(911,plain,
% 0.60/0.77 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c0_1(a470) | (~c2_1(a470)) | (~c3_1(a470)) | c0_1(a470) | (~c1_1(a470)) | (~c3_1(a470)) | c0_1(a493) | c2_1(a493) | (~c1_1(a493)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | c0_1(a493) | c2_1(a493) | (~ndr1_0) | (~c1_1(a493)) | (~c2_1(a470)) | c0_1(a470) | (~c1_1(a470)) | (~c3_1(a470)))),
% 0.60/0.77 inference(transitivity,[status(thm)],[910, 908])).
% 0.60/0.77 tff(912,plain,
% 0.60/0.77 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c0_1(a470) | (~c2_1(a470)) | (~c3_1(a470)) | c0_1(a470) | (~c1_1(a470)) | (~c3_1(a470)) | c0_1(a493) | c2_1(a493) | (~c1_1(a493)))),
% 0.60/0.77 inference(quant_inst,[status(thm)],[])).
% 0.60/0.77 tff(913,plain,
% 0.60/0.77 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | c0_1(a493) | c2_1(a493) | (~ndr1_0) | (~c1_1(a493)) | (~c2_1(a470)) | c0_1(a470) | (~c1_1(a470)) | (~c3_1(a470))),
% 0.60/0.77 inference(modus_ponens,[status(thm)],[912, 911])).
% 0.60/0.77 tff(914,plain,
% 0.60/0.77 ($false),
% 0.60/0.77 inference(unit_resolution,[status(thm)],[913, 137, 857, 856, 907, 906, 898, 892, 868, 858])).
% 0.60/0.77 tff(915,plain,(c1_1(a460) | hskp5 | c0_1(a494) | c1_1(a494) | c3_1(a494) | (~c0_1(a461)) | (~c2_1(a461)) | (~c3_1(a461)) | hskp27 | c2_1(a460) | c3_1(a460) | (~c0_1(a460))), inference(lemma,lemma(discharge,[]))).
% 0.60/0.77 tff(916,plain,
% 0.60/0.77 (c1_1(a460)),
% 0.60/0.77 inference(unit_resolution,[status(thm)],[915, 508, 103, 502, 495, 833, 832, 831, 363, 1, 223, 224])).
% 0.60/0.77 tff(917,plain,
% 0.60/0.77 (c3_1(a470)),
% 0.60/0.77 inference(unit_resolution,[status(thm)],[702, 835])).
% 0.60/0.77 tff(918,plain,
% 0.60/0.77 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c1_1(a494) | c3_1(a494) | c2_1(a460) | (~ndr1_0) | (~c1_1(a460)) | (~c0_1(a460)) | (~c2_1(a494)) | (~c2_1(a470)) | c0_1(a470) | (~c3_1(a470)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c1_1(a494) | c3_1(a494) | c2_1(a460) | (~ndr1_0) | (~c1_1(a460)) | (~c0_1(a460)) | (~c2_1(a494)) | (~c2_1(a470)) | c0_1(a470) | (~c3_1(a470)))),
% 0.60/0.77 inference(rewrite,[status(thm)],[])).
% 0.60/0.77 tff(919,plain,
% 0.60/0.77 (((~ndr1_0) | c2_1(a460) | (~c0_1(a460)) | (~c1_1(a460)) | c3_1(a494) | c1_1(a494) | (~c2_1(a494)) | c0_1(a470) | (~c3_1(a470)) | (~c2_1(a470))) <=> (c1_1(a494) | c3_1(a494) | c2_1(a460) | (~ndr1_0) | (~c1_1(a460)) | (~c0_1(a460)) | (~c2_1(a494)) | (~c2_1(a470)) | c0_1(a470) | (~c3_1(a470)))),
% 0.60/0.77 inference(rewrite,[status(thm)],[])).
% 0.60/0.77 tff(920,plain,
% 0.60/0.77 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a460) | (~c0_1(a460)) | (~c1_1(a460)) | c3_1(a494) | c1_1(a494) | (~c2_1(a494)) | c0_1(a470) | (~c3_1(a470)) | (~c2_1(a470)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c1_1(a494) | c3_1(a494) | c2_1(a460) | (~ndr1_0) | (~c1_1(a460)) | (~c0_1(a460)) | (~c2_1(a494)) | (~c2_1(a470)) | c0_1(a470) | (~c3_1(a470))))),
% 0.60/0.78 inference(monotonicity,[status(thm)],[919])).
% 0.60/0.78 tff(921,plain,
% 0.60/0.78 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a460) | (~c0_1(a460)) | (~c1_1(a460)) | c3_1(a494) | c1_1(a494) | (~c2_1(a494)) | c0_1(a470) | (~c3_1(a470)) | (~c2_1(a470)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c1_1(a494) | c3_1(a494) | c2_1(a460) | (~ndr1_0) | (~c1_1(a460)) | (~c0_1(a460)) | (~c2_1(a494)) | (~c2_1(a470)) | c0_1(a470) | (~c3_1(a470)))),
% 0.60/0.78 inference(transitivity,[status(thm)],[920, 918])).
% 0.60/0.78 tff(922,plain,
% 0.60/0.78 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a460) | (~c0_1(a460)) | (~c1_1(a460)) | c3_1(a494) | c1_1(a494) | (~c2_1(a494)) | c0_1(a470) | (~c3_1(a470)) | (~c2_1(a470)))),
% 0.60/0.78 inference(quant_inst,[status(thm)],[])).
% 0.60/0.78 tff(923,plain,
% 0.60/0.78 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c1_1(a494) | c3_1(a494) | c2_1(a460) | (~ndr1_0) | (~c1_1(a460)) | (~c0_1(a460)) | (~c2_1(a494)) | (~c2_1(a470)) | c0_1(a470) | (~c3_1(a470))),
% 0.60/0.78 inference(modus_ponens,[status(thm)],[922, 921])).
% 0.60/0.78 tff(924,plain,
% 0.60/0.78 ($false),
% 0.60/0.78 inference(unit_resolution,[status(thm)],[923, 137, 836, 917, 224, 502, 495, 1, 802, 916, 520, 844])).
% 0.60/0.78 tff(925,plain,(hskp3 | (~c0_1(a460)) | c3_1(a494) | c2_1(a460) | hskp5 | c3_1(a460)), inference(lemma,lemma(discharge,[]))).
% 0.60/0.78 tff(926,plain,
% 0.60/0.78 (c3_1(a494)),
% 0.60/0.78 inference(unit_resolution,[status(thm)],[925, 328, 224, 1, 103, 223])).
% 0.60/0.78 tff(927,plain,
% 0.60/0.78 (((~hskp17) | (~c3_1(a494))) <=> ((~hskp17) | (~c3_1(a494)))),
% 0.60/0.78 inference(rewrite,[status(thm)],[])).
% 0.60/0.78 tff(928,plain,
% 0.60/0.78 (((~c3_1(a494)) | (~hskp17)) <=> ((~hskp17) | (~c3_1(a494)))),
% 0.60/0.78 inference(rewrite,[status(thm)],[])).
% 0.60/0.78 tff(929,axiom,((~c3_1(a494)) | (~hskp17)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause94')).
% 0.60/0.78 tff(930,plain,
% 0.60/0.78 ((~hskp17) | (~c3_1(a494))),
% 0.60/0.78 inference(modus_ponens,[status(thm)],[929, 928])).
% 0.60/0.78 tff(931,plain,
% 0.60/0.78 ((~hskp17) | (~c3_1(a494))),
% 0.60/0.78 inference(modus_ponens,[status(thm)],[930, 927])).
% 0.60/0.78 tff(932,plain,
% 0.60/0.78 ($false),
% 0.60/0.78 inference(unit_resolution,[status(thm)],[931, 926, 484])).
% 0.60/0.78 tff(933,plain,((~c0_1(a460)) | c2_1(a460) | hskp5 | c3_1(a460)), inference(lemma,lemma(discharge,[]))).
% 0.60/0.78 tff(934,plain,
% 0.60/0.78 ($false),
% 0.60/0.78 inference(unit_resolution,[status(thm)],[933, 222, 216, 103, 208])).
% 0.60/0.78 tff(935,plain,(hskp5), inference(lemma,lemma(discharge,[]))).
% 0.60/0.78 tff(936,plain,
% 0.60/0.78 ((ndr1_0 | (~hskp5)) <=> (ndr1_0 | (~hskp5))),
% 0.60/0.78 inference(rewrite,[status(thm)],[])).
% 0.60/0.78 tff(937,plain,
% 0.60/0.78 (((~hskp5) | ndr1_0) <=> (ndr1_0 | (~hskp5))),
% 0.60/0.78 inference(rewrite,[status(thm)],[])).
% 0.60/0.78 tff(938,axiom,((~hskp5) | ndr1_0), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause25')).
% 0.60/0.78 tff(939,plain,
% 0.60/0.78 (ndr1_0 | (~hskp5)),
% 0.60/0.78 inference(modus_ponens,[status(thm)],[938, 937])).
% 0.60/0.78 tff(940,plain,
% 0.60/0.78 (ndr1_0 | (~hskp5)),
% 0.60/0.78 inference(modus_ponens,[status(thm)],[939, 936])).
% 0.60/0.78 tff(941,plain,
% 0.60/0.78 (ndr1_0),
% 0.60/0.78 inference(unit_resolution,[status(thm)],[940, 935])).
% 0.60/0.78 tff(942,plain,
% 0.60/0.78 (hskp1),
% 0.60/0.78 inference(unit_resolution,[status(thm)],[168, 941, 34, 102, 96, 90, 83])).
% 0.60/0.78 tff(943,plain,
% 0.60/0.78 (~c1_1(a463)),
% 0.60/0.78 inference(unit_resolution,[status(thm)],[180, 942])).
% 0.60/0.78 tff(944,plain,
% 0.60/0.78 (~c0_1(a463)),
% 0.60/0.78 inference(unit_resolution,[status(thm)],[174, 942])).
% 0.60/0.78 tff(945,plain,
% 0.60/0.78 (c2_1(a463)),
% 0.60/0.78 inference(unit_resolution,[status(thm)],[197, 942])).
% 0.60/0.78 tff(946,plain,
% 0.60/0.78 ($false),
% 0.60/0.78 inference(unit_resolution,[status(thm)],[189, 941, 34, 945, 102, 96, 90, 944, 943, 73])).
% 0.60/0.78 tff(947,plain,((~hskp12) | hskp0), inference(lemma,lemma(discharge,[]))).
% 0.60/0.78 tff(948,plain,
% 0.60/0.78 (~hskp12),
% 0.60/0.78 inference(unit_resolution,[status(thm)],[947, 34])).
% 0.60/0.78 tff(949,plain,
% 0.60/0.78 (~c0_1(a488)),
% 0.60/0.78 inference(unit_resolution,[status(thm)],[273, 941, 948, 63, 57, 51, 44])).
% 0.60/0.78 tff(950,plain,
% 0.60/0.78 (^[V: $i, U: $i] : refl((hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U) | c3_1(V) | c1_1(V) | c0_1(V)) <=> (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U) | c3_1(V) | c1_1(V) | c0_1(V)))),
% 0.60/0.78 inference(bind,[status(th)],[])).
% 0.60/0.78 tff(951,plain,
% 0.60/0.78 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U) | c3_1(V) | c1_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U) | c3_1(V) | c1_1(V) | c0_1(V))),
% 0.60/0.78 inference(quant_intro,[status(thm)],[950])).
% 0.60/0.78 tff(952,plain,
% 0.60/0.78 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U) | c3_1(V) | c1_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U) | c3_1(V) | c1_1(V) | c0_1(V))),
% 0.60/0.78 inference(rewrite,[status(thm)],[])).
% 0.60/0.78 tff(953,plain,
% 0.60/0.78 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ndr1_0) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U))), ((((~ndr1_0) | c0_1(U)) | 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))), ((((~ndr1_0) | c0_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U)))), (((((~ndr1_0) | c0_1(U)) | 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) | c2_1(U) | c0_1(U) | c3_1(U))), (((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)))), ((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U) | c0_1(V))), ((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U) | c0_1(V)))), (((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U) | c0_1(V)) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U) | c1_1(V) | c0_1(V))), (((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U) | c1_1(V) | c0_1(V)))), ((((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U) | c1_1(V) | c0_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U) | c1_1(V) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U) | c3_1(V) | c1_1(V) | c0_1(V))), ((((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U) | c3_1(V) | c1_1(V) | c0_1(V)))), (((((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp0) <=> (((~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U) | c3_1(V) | c1_1(V) | c0_1(V)) | hskp0))), rewrite((((~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U) | c3_1(V) | c1_1(V) | c0_1(V)) | hskp0) <=> (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U) | c3_1(V) | c1_1(V) | c0_1(V))), (((((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp0) <=> (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U) | c3_1(V) | c1_1(V) | c0_1(V))))),
% 0.60/0.78 inference(bind,[status(th)],[])).
% 0.60/0.78 tff(954,plain,
% 0.60/0.78 (![V: $i, U: $i] : ((((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp0) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U) | c3_1(V) | c1_1(V) | c0_1(V))),
% 0.60/0.78 inference(quant_intro,[status(thm)],[953])).
% 0.60/0.78 tff(955,axiom,(![V: $i, U: $i] : ((((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp0)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause142')).
% 0.60/0.78 tff(956,plain,
% 0.60/0.78 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U) | c3_1(V) | c1_1(V) | c0_1(V))),
% 0.60/0.78 inference(modus_ponens,[status(thm)],[955, 954])).
% 0.60/0.78 tff(957,plain,
% 0.60/0.78 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U) | c3_1(V) | c1_1(V) | c0_1(V))),
% 0.60/0.78 inference(modus_ponens,[status(thm)],[956, 952])).
% 0.60/0.78 tff(958,plain,(
% 0.60/0.78 ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U) | c3_1(V) | c1_1(V) | c0_1(V))),
% 0.60/0.78 inference(skolemize,[status(sab)],[957])).
% 0.60/0.78 tff(959,plain,
% 0.60/0.78 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U) | c3_1(V) | c1_1(V) | c0_1(V))),
% 0.60/0.78 inference(modus_ponens,[status(thm)],[958, 951])).
% 0.60/0.78 tff(960,plain,
% 0.60/0.78 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | c1_1(a488) | c2_1(a488) | c3_1(a488) | (~ndr1_0) | c0_1(a488))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c1_1(a488) | c2_1(a488) | c3_1(a488) | (~ndr1_0) | c0_1(a488))),
% 0.60/0.78 inference(rewrite,[status(thm)],[])).
% 0.60/0.78 tff(961,plain,
% 0.60/0.78 ((hskp0 | (~ndr1_0) | c2_1(a488) | c0_1(a488) | c3_1(a488) | c3_1(a488) | c1_1(a488) | c0_1(a488)) <=> (hskp0 | c1_1(a488) | c2_1(a488) | c3_1(a488) | (~ndr1_0) | c0_1(a488))),
% 0.60/0.78 inference(rewrite,[status(thm)],[])).
% 0.60/0.78 tff(962,plain,
% 0.60/0.78 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c2_1(a488) | c0_1(a488) | c3_1(a488) | c3_1(a488) | c1_1(a488) | c0_1(a488))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | c1_1(a488) | c2_1(a488) | c3_1(a488) | (~ndr1_0) | c0_1(a488)))),
% 0.60/0.78 inference(monotonicity,[status(thm)],[961])).
% 0.60/0.78 tff(963,plain,
% 0.60/0.78 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c2_1(a488) | c0_1(a488) | c3_1(a488) | c3_1(a488) | c1_1(a488) | c0_1(a488))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c1_1(a488) | c2_1(a488) | c3_1(a488) | (~ndr1_0) | c0_1(a488))),
% 0.60/0.78 inference(transitivity,[status(thm)],[962, 960])).
% 0.60/0.78 tff(964,plain,
% 0.60/0.78 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c2_1(a488) | c0_1(a488) | c3_1(a488) | c3_1(a488) | c1_1(a488) | c0_1(a488))),
% 0.60/0.78 inference(quant_inst,[status(thm)],[])).
% 0.60/0.78 tff(965,plain,
% 0.60/0.78 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c1_1(a488) | c2_1(a488) | c3_1(a488) | (~ndr1_0) | c0_1(a488)),
% 0.60/0.78 inference(modus_ponens,[status(thm)],[964, 963])).
% 0.60/0.78 tff(966,plain,
% 0.60/0.78 ($false),
% 0.60/0.78 inference(unit_resolution,[status(thm)],[965, 941, 34, 63, 57, 51, 959, 949])).
% 0.60/0.78 tff(967,plain,((~hskp14) | hskp0), inference(lemma,lemma(discharge,[]))).
% 0.60/0.78 tff(968,plain,
% 0.60/0.78 (~hskp14),
% 0.60/0.78 inference(unit_resolution,[status(thm)],[967, 34])).
% 0.60/0.78 tff(969,plain,
% 0.60/0.78 (^[U: $i] : refl((hskp14 | hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U))) <=> (hskp14 | hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U))))),
% 0.60/0.78 inference(bind,[status(th)],[])).
% 0.60/0.78 tff(970,plain,
% 0.60/0.78 (![U: $i] : (hskp14 | hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U))) <=> ![U: $i] : (hskp14 | hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))),
% 0.60/0.78 inference(quant_intro,[status(thm)],[969])).
% 0.60/0.78 tff(971,plain,
% 0.60/0.78 (![U: $i] : (hskp14 | hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U))) <=> ![U: $i] : (hskp14 | hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))),
% 0.60/0.78 inference(rewrite,[status(thm)],[])).
% 0.60/0.78 tff(972,plain,
% 0.60/0.78 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c2_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) <=> (((~ndr1_0) | (~c2_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U))))), (((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))), (((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U))))), ((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp12) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U))) | hskp12))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U))) | hskp12) <=> (hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))), ((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp12) <=> (hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U))))), (((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp12) | hskp14) <=> ((hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U))) | hskp14))), rewrite(((hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U))) | hskp14) <=> (hskp14 | hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))), (((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp12) | hskp14) <=> (hskp14 | hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))))),
% 0.60/0.78 inference(bind,[status(th)],[])).
% 0.60/0.78 tff(973,plain,
% 0.60/0.78 (![U: $i] : ((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp12) | hskp14) <=> ![U: $i] : (hskp14 | hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))),
% 0.60/0.78 inference(quant_intro,[status(thm)],[972])).
% 0.60/0.78 tff(974,axiom,(![U: $i] : ((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp12) | hskp14)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause134')).
% 0.60/0.78 tff(975,plain,
% 0.60/0.78 (![U: $i] : (hskp14 | hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))),
% 0.60/0.78 inference(modus_ponens,[status(thm)],[974, 973])).
% 0.60/0.78 tff(976,plain,
% 0.60/0.78 (![U: $i] : (hskp14 | hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))),
% 0.60/0.78 inference(modus_ponens,[status(thm)],[975, 971])).
% 0.60/0.78 tff(977,plain,(
% 0.60/0.78 ![U: $i] : (hskp14 | hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))),
% 0.60/0.78 inference(skolemize,[status(sab)],[976])).
% 0.60/0.78 tff(978,plain,
% 0.60/0.78 (![U: $i] : (hskp14 | hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))),
% 0.60/0.78 inference(modus_ponens,[status(thm)],[977, 970])).
% 0.60/0.78 tff(979,assumption,(hskp6), introduced(assumption)).
% 0.60/0.78 tff(980,plain,
% 0.60/0.78 (((~hskp6) | (~c3_1(a471))) <=> ((~hskp6) | (~c3_1(a471)))),
% 0.60/0.78 inference(rewrite,[status(thm)],[])).
% 0.60/0.78 tff(981,plain,
% 0.60/0.78 (((~c3_1(a471)) | (~hskp6)) <=> ((~hskp6) | (~c3_1(a471)))),
% 0.60/0.78 inference(rewrite,[status(thm)],[])).
% 0.60/0.78 tff(982,axiom,((~c3_1(a471)) | (~hskp6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause113')).
% 0.60/0.78 tff(983,plain,
% 0.60/0.78 ((~hskp6) | (~c3_1(a471))),
% 0.60/0.78 inference(modus_ponens,[status(thm)],[982, 981])).
% 0.60/0.78 tff(984,plain,
% 0.60/0.78 ((~hskp6) | (~c3_1(a471))),
% 0.60/0.78 inference(modus_ponens,[status(thm)],[983, 980])).
% 0.60/0.78 tff(985,plain,
% 0.60/0.78 (~c3_1(a471)),
% 0.60/0.78 inference(unit_resolution,[status(thm)],[984, 979])).
% 0.60/0.78 tff(986,plain,
% 0.60/0.78 (((~hskp6) | (~c1_1(a471))) <=> ((~hskp6) | (~c1_1(a471)))),
% 0.60/0.78 inference(rewrite,[status(thm)],[])).
% 0.60/0.78 tff(987,plain,
% 0.60/0.78 (((~c1_1(a471)) | (~hskp6)) <=> ((~hskp6) | (~c1_1(a471)))),
% 0.60/0.78 inference(rewrite,[status(thm)],[])).
% 0.60/0.78 tff(988,axiom,((~c1_1(a471)) | (~hskp6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause112')).
% 0.60/0.78 tff(989,plain,
% 0.60/0.78 ((~hskp6) | (~c1_1(a471))),
% 0.60/0.78 inference(modus_ponens,[status(thm)],[988, 987])).
% 0.60/0.78 tff(990,plain,
% 0.60/0.78 ((~hskp6) | (~c1_1(a471))),
% 0.60/0.78 inference(modus_ponens,[status(thm)],[989, 986])).
% 0.60/0.78 tff(991,plain,
% 0.60/0.78 (~c1_1(a471)),
% 0.60/0.78 inference(unit_resolution,[status(thm)],[990, 979])).
% 0.60/0.78 tff(992,plain,
% 0.60/0.78 (((~hskp6) | c2_1(a471)) <=> ((~hskp6) | c2_1(a471))),
% 0.60/0.78 inference(rewrite,[status(thm)],[])).
% 0.60/0.78 tff(993,axiom,((~hskp6) | c2_1(a471)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause75')).
% 0.60/0.78 tff(994,plain,
% 0.60/0.78 ((~hskp6) | c2_1(a471)),
% 0.60/0.78 inference(modus_ponens,[status(thm)],[993, 992])).
% 0.60/0.78 tff(995,plain,
% 0.60/0.78 ((~hskp6) | c2_1(a471)),
% 0.60/0.78 inference(modus_ponens,[status(thm)],[994, 992])).
% 0.60/0.78 tff(996,plain,
% 0.60/0.78 ((~hskp6) | c2_1(a471)),
% 0.60/0.78 inference(modus_ponens,[status(thm)],[995, 992])).
% 0.60/0.78 tff(997,plain,
% 0.60/0.78 ((~hskp6) | c2_1(a471)),
% 0.60/0.78 inference(modus_ponens,[status(thm)],[996, 992])).
% 0.60/0.78 tff(998,plain,
% 0.60/0.78 ((~hskp6) | c2_1(a471)),
% 0.60/0.78 inference(modus_ponens,[status(thm)],[997, 992])).
% 0.60/0.78 tff(999,plain,
% 0.60/0.78 (c2_1(a471)),
% 0.60/0.78 inference(unit_resolution,[status(thm)],[998, 979])).
% 0.60/0.78 tff(1000,assumption,(~hskp14), introduced(assumption)).
% 0.60/0.78 tff(1001,plain,
% 0.60/0.78 (((~![U: $i] : (hskp14 | hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp14 | hskp12 | c1_1(a471) | c3_1(a471) | (~ndr1_0) | (~c2_1(a471)))) <=> ((~![U: $i] : (hskp14 | hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | hskp14 | hskp12 | c1_1(a471) | c3_1(a471) | (~ndr1_0) | (~c2_1(a471)))),
% 0.60/0.78 inference(rewrite,[status(thm)],[])).
% 0.60/0.78 tff(1002,plain,
% 0.60/0.78 ((hskp14 | hskp12 | (~ndr1_0) | c1_1(a471) | c3_1(a471) | (~c2_1(a471))) <=> (hskp14 | hskp12 | c1_1(a471) | c3_1(a471) | (~ndr1_0) | (~c2_1(a471)))),
% 0.60/0.78 inference(rewrite,[status(thm)],[])).
% 0.60/0.78 tff(1003,plain,
% 0.60/0.78 (((~![U: $i] : (hskp14 | hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp14 | hskp12 | (~ndr1_0) | c1_1(a471) | c3_1(a471) | (~c2_1(a471)))) <=> ((~![U: $i] : (hskp14 | hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp14 | hskp12 | c1_1(a471) | c3_1(a471) | (~ndr1_0) | (~c2_1(a471))))),
% 0.60/0.78 inference(monotonicity,[status(thm)],[1002])).
% 0.60/0.78 tff(1004,plain,
% 0.60/0.78 (((~![U: $i] : (hskp14 | hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp14 | hskp12 | (~ndr1_0) | c1_1(a471) | c3_1(a471) | (~c2_1(a471)))) <=> ((~![U: $i] : (hskp14 | hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | hskp14 | hskp12 | c1_1(a471) | c3_1(a471) | (~ndr1_0) | (~c2_1(a471)))),
% 0.60/0.78 inference(transitivity,[status(thm)],[1003, 1001])).
% 0.60/0.78 tff(1005,plain,
% 0.60/0.78 ((~![U: $i] : (hskp14 | hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp14 | hskp12 | (~ndr1_0) | c1_1(a471) | c3_1(a471) | (~c2_1(a471)))),
% 0.60/0.78 inference(quant_inst,[status(thm)],[])).
% 0.60/0.78 tff(1006,plain,
% 0.60/0.78 ((~![U: $i] : (hskp14 | hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | hskp14 | hskp12 | c1_1(a471) | c3_1(a471) | (~ndr1_0) | (~c2_1(a471))),
% 0.60/0.78 inference(modus_ponens,[status(thm)],[1005, 1004])).
% 0.60/0.78 tff(1007,plain,
% 0.60/0.78 ($false),
% 0.60/0.78 inference(unit_resolution,[status(thm)],[1006, 941, 1000, 22, 999, 991, 985, 978])).
% 0.60/0.78 tff(1008,plain,((~hskp6) | hskp14 | hskp12), inference(lemma,lemma(discharge,[]))).
% 0.60/0.78 tff(1009,plain,
% 0.60/0.78 (~hskp6),
% 0.60/0.78 inference(unit_resolution,[status(thm)],[1008, 968, 22])).
% 0.60/0.78 tff(1010,plain,
% 0.60/0.78 ((hskp20 | hskp12 | hskp6) <=> (hskp20 | hskp12 | hskp6)),
% 0.60/0.78 inference(rewrite,[status(thm)],[])).
% 0.60/0.78 tff(1011,plain,
% 0.60/0.78 (((hskp20 | hskp6) | hskp12) <=> (hskp20 | hskp12 | hskp6)),
% 0.60/0.78 inference(rewrite,[status(thm)],[])).
% 0.60/0.78 tff(1012,axiom,((hskp20 | hskp6) | hskp12), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause37')).
% 0.60/0.78 tff(1013,plain,
% 0.60/0.78 (hskp20 | hskp12 | hskp6),
% 0.60/0.78 inference(modus_ponens,[status(thm)],[1012, 1011])).
% 0.60/0.78 tff(1014,plain,
% 0.60/0.78 (hskp20 | hskp12 | hskp6),
% 0.60/0.78 inference(modus_ponens,[status(thm)],[1013, 1010])).
% 0.60/0.78 tff(1015,plain,
% 0.60/0.78 (hskp20 | hskp12 | hskp6),
% 0.60/0.78 inference(modus_ponens,[status(thm)],[1014, 1010])).
% 0.60/0.78 tff(1016,plain,
% 0.60/0.78 (hskp20 | hskp12 | hskp6),
% 0.60/0.78 inference(modus_ponens,[status(thm)],[1015, 1010])).
% 0.60/0.78 tff(1017,plain,
% 0.60/0.78 (hskp20 | hskp12 | hskp6),
% 0.60/0.78 inference(modus_ponens,[status(thm)],[1016, 1010])).
% 0.60/0.78 tff(1018,plain,
% 0.60/0.78 (hskp20),
% 0.60/0.78 inference(unit_resolution,[status(thm)],[1017, 1009, 22])).
% 0.60/0.78 tff(1019,plain,
% 0.60/0.78 (((~hskp20) | (~c1_1(a503))) <=> ((~hskp20) | (~c1_1(a503)))),
% 0.60/0.78 inference(rewrite,[status(thm)],[])).
% 0.60/0.78 tff(1020,plain,
% 0.60/0.78 (((~c1_1(a503)) | (~hskp20)) <=> ((~hskp20) | (~c1_1(a503)))),
% 0.60/0.78 inference(rewrite,[status(thm)],[])).
% 0.60/0.78 tff(1021,axiom,((~c1_1(a503)) | (~hskp20)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause89')).
% 0.60/0.78 tff(1022,plain,
% 0.60/0.78 ((~hskp20) | (~c1_1(a503))),
% 0.60/0.78 inference(modus_ponens,[status(thm)],[1021, 1020])).
% 0.60/0.78 tff(1023,plain,
% 0.60/0.78 ((~hskp20) | (~c1_1(a503))),
% 0.60/0.78 inference(modus_ponens,[status(thm)],[1022, 1019])).
% 0.60/0.78 tff(1024,plain,
% 0.60/0.78 (~c1_1(a503)),
% 0.60/0.78 inference(unit_resolution,[status(thm)],[1023, 1018])).
% 0.60/0.78 tff(1025,plain,
% 0.60/0.78 (((~hskp20) | c3_1(a503)) <=> ((~hskp20) | c3_1(a503))),
% 0.60/0.78 inference(rewrite,[status(thm)],[])).
% 0.60/0.78 tff(1026,axiom,((~hskp20) | c3_1(a503)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause57')).
% 0.60/0.78 tff(1027,plain,
% 0.60/0.78 ((~hskp20) | c3_1(a503)),
% 0.60/0.78 inference(modus_ponens,[status(thm)],[1026, 1025])).
% 0.60/0.78 tff(1028,plain,
% 0.60/0.78 ((~hskp20) | c3_1(a503)),
% 0.60/0.78 inference(modus_ponens,[status(thm)],[1027, 1025])).
% 0.60/0.78 tff(1029,plain,
% 0.60/0.78 ((~hskp20) | c3_1(a503)),
% 0.60/0.78 inference(modus_ponens,[status(thm)],[1028, 1025])).
% 0.60/0.78 tff(1030,plain,
% 0.60/0.78 ((~hskp20) | c3_1(a503)),
% 0.60/0.78 inference(modus_ponens,[status(thm)],[1029, 1025])).
% 0.60/0.78 tff(1031,plain,
% 0.60/0.78 ((~hskp20) | c3_1(a503)),
% 0.60/0.78 inference(modus_ponens,[status(thm)],[1030, 1025])).
% 0.60/0.78 tff(1032,plain,
% 0.60/0.78 (c3_1(a503)),
% 0.60/0.78 inference(unit_resolution,[status(thm)],[1031, 1018])).
% 0.60/0.78 tff(1033,plain,
% 0.60/0.78 (((~hskp20) | c2_1(a503)) <=> ((~hskp20) | c2_1(a503))),
% 0.60/0.78 inference(rewrite,[status(thm)],[])).
% 0.60/0.78 tff(1034,axiom,((~hskp20) | c2_1(a503)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause56')).
% 0.60/0.78 tff(1035,plain,
% 0.60/0.78 ((~hskp20) | c2_1(a503)),
% 0.60/0.78 inference(modus_ponens,[status(thm)],[1034, 1033])).
% 0.60/0.78 tff(1036,plain,
% 0.60/0.78 ((~hskp20) | c2_1(a503)),
% 0.60/0.78 inference(modus_ponens,[status(thm)],[1035, 1033])).
% 0.60/0.78 tff(1037,plain,
% 0.60/0.78 ((~hskp20) | c2_1(a503)),
% 0.60/0.78 inference(modus_ponens,[status(thm)],[1036, 1033])).
% 0.60/0.78 tff(1038,plain,
% 0.60/0.78 ((~hskp20) | c2_1(a503)),
% 0.60/0.78 inference(modus_ponens,[status(thm)],[1037, 1033])).
% 0.60/0.78 tff(1039,plain,
% 0.60/0.78 ((~hskp20) | c2_1(a503)),
% 0.60/0.78 inference(modus_ponens,[status(thm)],[1038, 1033])).
% 0.60/0.78 tff(1040,plain,
% 0.60/0.78 (c2_1(a503)),
% 0.60/0.78 inference(unit_resolution,[status(thm)],[1039, 1018])).
% 0.60/0.78 tff(1041,plain,
% 0.60/0.78 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp17 | c1_1(a503) | (~ndr1_0) | (~c3_1(a503)) | (~c2_1(a503)) | (~c0_1(a503)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))) | hskp17 | c1_1(a503) | (~ndr1_0) | (~c3_1(a503)) | (~c2_1(a503)) | (~c0_1(a503)))),
% 0.60/0.78 inference(rewrite,[status(thm)],[])).
% 0.60/0.78 tff(1042,plain,
% 0.60/0.78 ((hskp17 | (~ndr1_0) | (~c2_1(a503)) | (~c0_1(a503)) | (~c3_1(a503)) | c1_1(a503) | (~c0_1(a503)) | (~c2_1(a503))) <=> (hskp17 | c1_1(a503) | (~ndr1_0) | (~c3_1(a503)) | (~c2_1(a503)) | (~c0_1(a503)))),
% 0.60/0.78 inference(rewrite,[status(thm)],[])).
% 0.60/0.78 tff(1043,plain,
% 0.60/0.78 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp17 | (~ndr1_0) | (~c2_1(a503)) | (~c0_1(a503)) | (~c3_1(a503)) | c1_1(a503) | (~c0_1(a503)) | (~c2_1(a503)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp17 | c1_1(a503) | (~ndr1_0) | (~c3_1(a503)) | (~c2_1(a503)) | (~c0_1(a503))))),
% 0.60/0.78 inference(monotonicity,[status(thm)],[1042])).
% 0.60/0.78 tff(1044,plain,
% 0.60/0.78 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp17 | (~ndr1_0) | (~c2_1(a503)) | (~c0_1(a503)) | (~c3_1(a503)) | c1_1(a503) | (~c0_1(a503)) | (~c2_1(a503)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))) | hskp17 | c1_1(a503) | (~ndr1_0) | (~c3_1(a503)) | (~c2_1(a503)) | (~c0_1(a503)))),
% 0.60/0.78 inference(transitivity,[status(thm)],[1043, 1041])).
% 0.60/0.78 tff(1045,plain,
% 0.60/0.78 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp17 | (~ndr1_0) | (~c2_1(a503)) | (~c0_1(a503)) | (~c3_1(a503)) | c1_1(a503) | (~c0_1(a503)) | (~c2_1(a503)))),
% 0.60/0.78 inference(quant_inst,[status(thm)],[])).
% 0.60/0.78 tff(1046,plain,
% 0.60/0.78 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))) | hskp17 | c1_1(a503) | (~ndr1_0) | (~c3_1(a503)) | (~c2_1(a503)) | (~c0_1(a503))),
% 0.60/0.78 inference(modus_ponens,[status(thm)],[1045, 1044])).
% 0.60/0.78 tff(1047,plain,
% 0.60/0.78 (~c0_1(a503)),
% 0.60/0.78 inference(unit_resolution,[status(thm)],[1046, 941, 33, 1040, 1032, 1024, 11])).
% 0.60/0.78 tff(1048,plain,
% 0.60/0.78 (^[U: $i] : refl((hskp12 | hskp3 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U))) <=> (hskp12 | hskp3 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U))))),
% 0.60/0.78 inference(bind,[status(th)],[])).
% 0.60/0.79 tff(1049,plain,
% 0.60/0.79 (![U: $i] : (hskp12 | hskp3 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U))) <=> ![U: $i] : (hskp12 | hskp3 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)))),
% 0.60/0.79 inference(quant_intro,[status(thm)],[1048])).
% 0.60/0.79 tff(1050,plain,
% 0.60/0.79 (![U: $i] : (hskp12 | hskp3 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U))) <=> ![U: $i] : (hskp12 | hskp3 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)))),
% 0.60/0.79 inference(rewrite,[status(thm)],[])).
% 0.60/0.79 tff(1051,plain,
% 0.60/0.79 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U))))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp3) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U))) | hskp3))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U))) | hskp3) <=> (hskp3 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp3) <=> (hskp3 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U))))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp3) | hskp12) <=> ((hskp3 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U))) | hskp12))), rewrite(((hskp3 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U))) | hskp12) <=> (hskp12 | hskp3 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp3) | hskp12) <=> (hskp12 | hskp3 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)))))),
% 0.60/0.79 inference(bind,[status(th)],[])).
% 0.60/0.79 tff(1052,plain,
% 0.60/0.79 (![U: $i] : ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp3) | hskp12) <=> ![U: $i] : (hskp12 | hskp3 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)))),
% 0.60/0.79 inference(quant_intro,[status(thm)],[1051])).
% 0.60/0.79 tff(1053,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp3) | hskp12)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause137')).
% 0.60/0.79 tff(1054,plain,
% 0.60/0.79 (![U: $i] : (hskp12 | hskp3 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)))),
% 0.60/0.79 inference(modus_ponens,[status(thm)],[1053, 1052])).
% 0.60/0.79 tff(1055,plain,
% 0.60/0.79 (![U: $i] : (hskp12 | hskp3 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)))),
% 0.60/0.79 inference(modus_ponens,[status(thm)],[1054, 1050])).
% 0.60/0.79 tff(1056,plain,(
% 0.60/0.79 ![U: $i] : (hskp12 | hskp3 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)))),
% 0.60/0.79 inference(skolemize,[status(sab)],[1055])).
% 0.60/0.79 tff(1057,plain,
% 0.60/0.79 (![U: $i] : (hskp12 | hskp3 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)))),
% 0.60/0.79 inference(modus_ponens,[status(thm)],[1056, 1049])).
% 0.60/0.79 tff(1058,assumption,(~hskp6), introduced(assumption)).
% 0.60/0.79 tff(1059,plain,
% 0.60/0.79 (hskp20),
% 0.60/0.79 inference(unit_resolution,[status(thm)],[1017, 1058, 22])).
% 0.60/0.79 tff(1060,plain,
% 0.60/0.79 (~c1_1(a503)),
% 0.60/0.79 inference(unit_resolution,[status(thm)],[1023, 1059])).
% 0.60/0.79 tff(1061,plain,
% 0.60/0.79 (c3_1(a503)),
% 0.60/0.79 inference(unit_resolution,[status(thm)],[1031, 1059])).
% 0.60/0.79 tff(1062,plain,
% 0.60/0.79 (c2_1(a503)),
% 0.60/0.79 inference(unit_resolution,[status(thm)],[1039, 1059])).
% 0.60/0.79 tff(1063,plain,
% 0.60/0.79 (~c0_1(a503)),
% 0.60/0.79 inference(unit_resolution,[status(thm)],[1046, 941, 33, 1062, 1061, 1060, 11])).
% 0.60/0.79 tff(1064,plain,
% 0.60/0.79 (^[U: $i] : refl((hskp6 | hskp2 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) <=> (hskp6 | hskp2 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))))),
% 0.60/0.79 inference(bind,[status(th)],[])).
% 0.60/0.79 tff(1065,plain,
% 0.60/0.79 (![U: $i] : (hskp6 | hskp2 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) <=> ![U: $i] : (hskp6 | hskp2 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 0.60/0.79 inference(quant_intro,[status(thm)],[1064])).
% 0.60/0.79 tff(1066,plain,
% 0.60/0.79 (![U: $i] : (hskp6 | hskp2 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) <=> ![U: $i] : (hskp6 | hskp2 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 0.60/0.79 inference(rewrite,[status(thm)],[])).
% 0.60/0.79 tff(1067,plain,
% 0.60/0.79 (^[U: $i] : 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)) | hskp6) <=> (((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) | hskp6))), rewrite((((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) | hskp6) <=> (hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))), ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp6) <=> (hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))))), (((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp6) | hskp2) <=> ((hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) | hskp2))), rewrite(((hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) | hskp2) <=> (hskp6 | hskp2 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))), (((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp6) | hskp2) <=> (hskp6 | hskp2 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))))),
% 0.60/0.79 inference(bind,[status(th)],[])).
% 0.60/0.79 tff(1068,plain,
% 0.60/0.79 (![U: $i] : ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp6) | hskp2) <=> ![U: $i] : (hskp6 | hskp2 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 0.60/0.79 inference(quant_intro,[status(thm)],[1067])).
% 0.60/0.79 tff(1069,axiom,(![U: $i] : ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp6) | hskp2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause127')).
% 0.60/0.79 tff(1070,plain,
% 0.60/0.79 (![U: $i] : (hskp6 | hskp2 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 0.60/0.79 inference(modus_ponens,[status(thm)],[1069, 1068])).
% 0.60/0.79 tff(1071,plain,
% 0.60/0.79 (![U: $i] : (hskp6 | hskp2 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 0.60/0.79 inference(modus_ponens,[status(thm)],[1070, 1066])).
% 0.60/0.79 tff(1072,plain,(
% 0.60/0.79 ![U: $i] : (hskp6 | hskp2 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 0.60/0.79 inference(skolemize,[status(sab)],[1071])).
% 0.60/0.79 tff(1073,plain,
% 0.60/0.79 (![U: $i] : (hskp6 | hskp2 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 0.60/0.79 inference(modus_ponens,[status(thm)],[1072, 1065])).
% 0.60/0.79 tff(1074,assumption,(~hskp2), introduced(assumption)).
% 0.60/0.79 tff(1075,plain,
% 0.60/0.79 (((~![U: $i] : (hskp6 | hskp2 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp6 | hskp2 | c1_1(a503) | (~ndr1_0) | (~c2_1(a503)) | c0_1(a503))) <=> ((~![U: $i] : (hskp6 | hskp2 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp6 | hskp2 | c1_1(a503) | (~ndr1_0) | (~c2_1(a503)) | c0_1(a503))),
% 0.60/0.79 inference(rewrite,[status(thm)],[])).
% 0.60/0.79 tff(1076,plain,
% 0.60/0.79 ((hskp6 | hskp2 | (~ndr1_0) | c1_1(a503) | c0_1(a503) | (~c2_1(a503))) <=> (hskp6 | hskp2 | c1_1(a503) | (~ndr1_0) | (~c2_1(a503)) | c0_1(a503))),
% 0.60/0.79 inference(rewrite,[status(thm)],[])).
% 0.60/0.79 tff(1077,plain,
% 0.60/0.79 (((~![U: $i] : (hskp6 | hskp2 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp6 | hskp2 | (~ndr1_0) | c1_1(a503) | c0_1(a503) | (~c2_1(a503)))) <=> ((~![U: $i] : (hskp6 | hskp2 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp6 | hskp2 | c1_1(a503) | (~ndr1_0) | (~c2_1(a503)) | c0_1(a503)))),
% 0.60/0.79 inference(monotonicity,[status(thm)],[1076])).
% 0.60/0.79 tff(1078,plain,
% 0.60/0.79 (((~![U: $i] : (hskp6 | hskp2 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp6 | hskp2 | (~ndr1_0) | c1_1(a503) | c0_1(a503) | (~c2_1(a503)))) <=> ((~![U: $i] : (hskp6 | hskp2 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp6 | hskp2 | c1_1(a503) | (~ndr1_0) | (~c2_1(a503)) | c0_1(a503))),
% 0.60/0.79 inference(transitivity,[status(thm)],[1077, 1075])).
% 0.60/0.79 tff(1079,plain,
% 0.60/0.79 ((~![U: $i] : (hskp6 | hskp2 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp6 | hskp2 | (~ndr1_0) | c1_1(a503) | c0_1(a503) | (~c2_1(a503)))),
% 0.60/0.79 inference(quant_inst,[status(thm)],[])).
% 0.60/0.79 tff(1080,plain,
% 0.60/0.79 ((~![U: $i] : (hskp6 | hskp2 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp6 | hskp2 | c1_1(a503) | (~ndr1_0) | (~c2_1(a503)) | c0_1(a503)),
% 0.60/0.79 inference(modus_ponens,[status(thm)],[1079, 1078])).
% 0.60/0.79 tff(1081,plain,
% 0.60/0.79 ($false),
% 0.60/0.79 inference(unit_resolution,[status(thm)],[1080, 941, 1058, 1074, 1062, 1060, 1073, 1063])).
% 0.60/0.79 tff(1082,plain,(hskp6 | hskp2 | hskp17 | hskp12), inference(lemma,lemma(discharge,[]))).
% 0.60/0.79 tff(1083,plain,
% 0.60/0.79 (hskp2),
% 0.60/0.79 inference(unit_resolution,[status(thm)],[1082, 1009, 33, 22])).
% 0.60/0.79 tff(1084,plain,
% 0.60/0.79 (~c3_1(a465)),
% 0.60/0.79 inference(unit_resolution,[status(thm)],[620, 1083])).
% 0.60/0.79 tff(1085,plain,
% 0.60/0.79 (~c2_1(a465)),
% 0.60/0.79 inference(unit_resolution,[status(thm)],[626, 1083])).
% 0.60/0.79 tff(1086,plain,
% 0.60/0.79 (~c0_1(a465)),
% 0.60/0.79 inference(unit_resolution,[status(thm)],[632, 1083])).
% 0.60/0.79 tff(1087,plain,
% 0.60/0.79 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | c0_1(a465) | c2_1(a465) | c3_1(a465) | (~ndr1_0) | c1_1(a465))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c0_1(a465) | c2_1(a465) | c3_1(a465) | (~ndr1_0) | c1_1(a465))),
% 0.60/0.79 inference(rewrite,[status(thm)],[])).
% 0.60/0.79 tff(1088,plain,
% 0.60/0.79 ((hskp0 | (~ndr1_0) | c2_1(a465) | c0_1(a465) | c3_1(a465) | c3_1(a465) | c1_1(a465) | c0_1(a465)) <=> (hskp0 | c0_1(a465) | c2_1(a465) | c3_1(a465) | (~ndr1_0) | c1_1(a465))),
% 0.60/0.79 inference(rewrite,[status(thm)],[])).
% 0.60/0.79 tff(1089,plain,
% 0.60/0.79 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c2_1(a465) | c0_1(a465) | c3_1(a465) | c3_1(a465) | c1_1(a465) | c0_1(a465))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | c0_1(a465) | c2_1(a465) | c3_1(a465) | (~ndr1_0) | c1_1(a465)))),
% 0.60/0.79 inference(monotonicity,[status(thm)],[1088])).
% 0.60/0.79 tff(1090,plain,
% 0.60/0.79 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c2_1(a465) | c0_1(a465) | c3_1(a465) | c3_1(a465) | c1_1(a465) | c0_1(a465))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c0_1(a465) | c2_1(a465) | c3_1(a465) | (~ndr1_0) | c1_1(a465))),
% 0.60/0.79 inference(transitivity,[status(thm)],[1089, 1087])).
% 0.60/0.79 tff(1091,plain,
% 0.60/0.79 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c2_1(a465) | c0_1(a465) | c3_1(a465) | c3_1(a465) | c1_1(a465) | c0_1(a465))),
% 0.60/0.79 inference(quant_inst,[status(thm)],[])).
% 0.60/0.79 tff(1092,plain,
% 0.60/0.79 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c0_1(a465) | c2_1(a465) | c3_1(a465) | (~ndr1_0) | c1_1(a465)),
% 0.60/0.79 inference(modus_ponens,[status(thm)],[1091, 1090])).
% 0.60/0.79 tff(1093,plain,
% 0.60/0.79 (c1_1(a465)),
% 0.60/0.79 inference(unit_resolution,[status(thm)],[1092, 941, 34, 1086, 1085, 1084, 959])).
% 0.60/0.79 tff(1094,plain,
% 0.60/0.79 (^[V: $i, U: $i] : refl((hskp21 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V))) <=> (hskp21 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V))))),
% 0.60/0.79 inference(bind,[status(th)],[])).
% 0.60/0.79 tff(1095,plain,
% 0.60/0.79 (![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))),
% 0.60/0.79 inference(quant_intro,[status(thm)],[1094])).
% 0.60/0.79 tff(1096,plain,
% 0.60/0.79 (![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))),
% 0.60/0.79 inference(rewrite,[status(thm)],[])).
% 0.60/0.79 tff(1097,plain,
% 0.60/0.79 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(V)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(V))))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(V)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(V))))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c2_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | (~c1_1(V))))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | (~c1_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | (~c1_1(V))) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V))))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c2_1(V)) | c3_1(V)) | hskp21) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V))) | hskp21))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V))) | hskp21) <=> (hskp21 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c2_1(V)) | c3_1(V)) | hskp21) <=> (hskp21 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))))),
% 0.60/0.79 inference(bind,[status(th)],[])).
% 0.60/0.79 tff(1098,plain,
% 0.60/0.79 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c2_1(V)) | c3_1(V)) | hskp21) <=> ![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))),
% 0.60/0.79 inference(quant_intro,[status(thm)],[1097])).
% 0.60/0.79 tff(1099,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c2_1(V)) | c3_1(V)) | hskp21)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause159')).
% 0.60/0.79 tff(1100,plain,
% 0.60/0.79 (![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))),
% 0.60/0.79 inference(modus_ponens,[status(thm)],[1099, 1098])).
% 0.60/0.79 tff(1101,plain,
% 0.60/0.79 (![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))),
% 0.60/0.79 inference(modus_ponens,[status(thm)],[1100, 1096])).
% 0.60/0.79 tff(1102,plain,(
% 0.60/0.79 ![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))),
% 0.60/0.79 inference(skolemize,[status(sab)],[1101])).
% 0.60/0.79 tff(1103,plain,
% 0.60/0.79 (![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))),
% 0.60/0.79 inference(modus_ponens,[status(thm)],[1102, 1095])).
% 0.60/0.79 tff(1104,plain,
% 0.60/0.79 (((~hskp5) | (~c2_1(a468))) <=> ((~hskp5) | (~c2_1(a468)))),
% 0.60/0.79 inference(rewrite,[status(thm)],[])).
% 0.60/0.79 tff(1105,plain,
% 0.60/0.79 (((~c2_1(a468)) | (~hskp5)) <=> ((~hskp5) | (~c2_1(a468)))),
% 0.60/0.79 inference(rewrite,[status(thm)],[])).
% 0.60/0.79 tff(1106,axiom,((~c2_1(a468)) | (~hskp5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause114')).
% 0.60/0.79 tff(1107,plain,
% 0.60/0.79 ((~hskp5) | (~c2_1(a468))),
% 0.60/0.79 inference(modus_ponens,[status(thm)],[1106, 1105])).
% 0.60/0.79 tff(1108,plain,
% 0.60/0.79 ((~hskp5) | (~c2_1(a468))),
% 0.60/0.79 inference(modus_ponens,[status(thm)],[1107, 1104])).
% 0.60/0.79 tff(1109,plain,
% 0.60/0.79 (~c2_1(a468)),
% 0.60/0.79 inference(unit_resolution,[status(thm)],[1108, 935])).
% 0.60/0.79 tff(1110,plain,
% 0.60/0.79 (((~hskp5) | c3_1(a468)) <=> ((~hskp5) | c3_1(a468))),
% 0.60/0.79 inference(rewrite,[status(thm)],[])).
% 0.60/0.79 tff(1111,axiom,((~hskp5) | c3_1(a468)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause77')).
% 0.60/0.79 tff(1112,plain,
% 0.60/0.79 ((~hskp5) | c3_1(a468)),
% 0.60/0.79 inference(modus_ponens,[status(thm)],[1111, 1110])).
% 0.60/0.79 tff(1113,plain,
% 0.60/0.79 ((~hskp5) | c3_1(a468)),
% 0.60/0.79 inference(modus_ponens,[status(thm)],[1112, 1110])).
% 0.60/0.79 tff(1114,plain,
% 0.60/0.79 ((~hskp5) | c3_1(a468)),
% 0.60/0.79 inference(modus_ponens,[status(thm)],[1113, 1110])).
% 0.60/0.79 tff(1115,plain,
% 0.60/0.79 ((~hskp5) | c3_1(a468)),
% 0.60/0.79 inference(modus_ponens,[status(thm)],[1114, 1110])).
% 0.60/0.79 tff(1116,plain,
% 0.60/0.79 ((~hskp5) | c3_1(a468)),
% 0.60/0.79 inference(modus_ponens,[status(thm)],[1115, 1110])).
% 0.60/0.79 tff(1117,plain,
% 0.60/0.79 (c3_1(a468)),
% 0.60/0.79 inference(unit_resolution,[status(thm)],[1116, 935])).
% 0.60/0.79 tff(1118,plain,
% 0.60/0.79 (((~hskp5) | c0_1(a468)) <=> ((~hskp5) | c0_1(a468))),
% 0.60/0.79 inference(rewrite,[status(thm)],[])).
% 0.60/0.79 tff(1119,axiom,((~hskp5) | c0_1(a468)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause76')).
% 0.60/0.79 tff(1120,plain,
% 0.60/0.79 ((~hskp5) | c0_1(a468)),
% 0.60/0.79 inference(modus_ponens,[status(thm)],[1119, 1118])).
% 0.60/0.79 tff(1121,plain,
% 0.60/0.79 ((~hskp5) | c0_1(a468)),
% 0.60/0.79 inference(modus_ponens,[status(thm)],[1120, 1118])).
% 0.60/0.79 tff(1122,plain,
% 0.60/0.79 ((~hskp5) | c0_1(a468)),
% 0.60/0.79 inference(modus_ponens,[status(thm)],[1121, 1118])).
% 0.60/0.79 tff(1123,plain,
% 0.60/0.79 ((~hskp5) | c0_1(a468)),
% 0.60/0.79 inference(modus_ponens,[status(thm)],[1122, 1118])).
% 0.60/0.79 tff(1124,plain,
% 0.60/0.79 ((~hskp5) | c0_1(a468)),
% 0.60/0.79 inference(modus_ponens,[status(thm)],[1123, 1118])).
% 0.60/0.79 tff(1125,plain,
% 0.60/0.79 (c0_1(a468)),
% 0.60/0.79 inference(unit_resolution,[status(thm)],[1124, 935])).
% 0.60/0.79 tff(1126,plain,
% 0.60/0.79 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp21 | c2_1(a468) | c2_1(a465) | c3_1(a465) | (~ndr1_0) | (~c0_1(a468)) | (~c3_1(a468)) | (~c1_1(a465)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | hskp21 | c2_1(a468) | c2_1(a465) | c3_1(a465) | (~ndr1_0) | (~c0_1(a468)) | (~c3_1(a468)) | (~c1_1(a465)))),
% 0.60/0.79 inference(rewrite,[status(thm)],[])).
% 0.60/0.79 tff(1127,plain,
% 0.60/0.79 ((hskp21 | (~ndr1_0) | c2_1(a468) | (~c0_1(a468)) | (~c3_1(a468)) | c3_1(a465) | c2_1(a465) | (~c1_1(a465))) <=> (hskp21 | c2_1(a468) | c2_1(a465) | c3_1(a465) | (~ndr1_0) | (~c0_1(a468)) | (~c3_1(a468)) | (~c1_1(a465)))),
% 0.60/0.79 inference(rewrite,[status(thm)],[])).
% 0.60/0.79 tff(1128,plain,
% 0.60/0.79 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp21 | (~ndr1_0) | c2_1(a468) | (~c0_1(a468)) | (~c3_1(a468)) | c3_1(a465) | c2_1(a465) | (~c1_1(a465)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp21 | c2_1(a468) | c2_1(a465) | c3_1(a465) | (~ndr1_0) | (~c0_1(a468)) | (~c3_1(a468)) | (~c1_1(a465))))),
% 0.60/0.79 inference(monotonicity,[status(thm)],[1127])).
% 0.60/0.79 tff(1129,plain,
% 0.60/0.79 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp21 | (~ndr1_0) | c2_1(a468) | (~c0_1(a468)) | (~c3_1(a468)) | c3_1(a465) | c2_1(a465) | (~c1_1(a465)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | hskp21 | c2_1(a468) | c2_1(a465) | c3_1(a465) | (~ndr1_0) | (~c0_1(a468)) | (~c3_1(a468)) | (~c1_1(a465)))),
% 0.60/0.79 inference(transitivity,[status(thm)],[1128, 1126])).
% 0.60/0.79 tff(1130,plain,
% 0.60/0.79 ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp21 | (~ndr1_0) | c2_1(a468) | (~c0_1(a468)) | (~c3_1(a468)) | c3_1(a465) | c2_1(a465) | (~c1_1(a465)))),
% 0.60/0.79 inference(quant_inst,[status(thm)],[])).
% 0.60/0.79 tff(1131,plain,
% 0.60/0.79 ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | hskp21 | c2_1(a468) | c2_1(a465) | c3_1(a465) | (~ndr1_0) | (~c0_1(a468)) | (~c3_1(a468)) | (~c1_1(a465))),
% 0.60/0.79 inference(modus_ponens,[status(thm)],[1130, 1129])).
% 0.60/0.79 tff(1132,plain,
% 0.60/0.79 (hskp21),
% 0.60/0.79 inference(unit_resolution,[status(thm)],[1131, 941, 1125, 1117, 1109, 1085, 1084, 1103, 1093])).
% 0.60/0.79 tff(1133,plain,
% 0.60/0.79 (((~hskp21) | (~c1_1(a512))) <=> ((~hskp21) | (~c1_1(a512)))),
% 0.60/0.79 inference(rewrite,[status(thm)],[])).
% 0.60/0.79 tff(1134,plain,
% 0.60/0.79 (((~c1_1(a512)) | (~hskp21)) <=> ((~hskp21) | (~c1_1(a512)))),
% 0.60/0.79 inference(rewrite,[status(thm)],[])).
% 0.60/0.79 tff(1135,axiom,((~c1_1(a512)) | (~hskp21)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause88')).
% 0.60/0.79 tff(1136,plain,
% 0.60/0.79 ((~hskp21) | (~c1_1(a512))),
% 0.60/0.79 inference(modus_ponens,[status(thm)],[1135, 1134])).
% 0.60/0.79 tff(1137,plain,
% 0.60/0.79 ((~hskp21) | (~c1_1(a512))),
% 0.60/0.79 inference(modus_ponens,[status(thm)],[1136, 1133])).
% 0.60/0.79 tff(1138,plain,
% 0.60/0.79 (~c1_1(a512)),
% 0.60/0.79 inference(unit_resolution,[status(thm)],[1137, 1132])).
% 0.60/0.79 tff(1139,plain,
% 0.60/0.79 (((~hskp21) | c3_1(a512)) <=> ((~hskp21) | c3_1(a512))),
% 0.60/0.79 inference(rewrite,[status(thm)],[])).
% 0.60/0.79 tff(1140,axiom,((~hskp21) | c3_1(a512)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause55')).
% 0.60/0.79 tff(1141,plain,
% 0.60/0.79 ((~hskp21) | c3_1(a512)),
% 0.60/0.79 inference(modus_ponens,[status(thm)],[1140, 1139])).
% 0.60/0.79 tff(1142,plain,
% 0.60/0.79 ((~hskp21) | c3_1(a512)),
% 0.60/0.79 inference(modus_ponens,[status(thm)],[1141, 1139])).
% 0.60/0.79 tff(1143,plain,
% 0.60/0.79 ((~hskp21) | c3_1(a512)),
% 0.60/0.79 inference(modus_ponens,[status(thm)],[1142, 1139])).
% 0.60/0.79 tff(1144,plain,
% 0.60/0.79 ((~hskp21) | c3_1(a512)),
% 0.60/0.79 inference(modus_ponens,[status(thm)],[1143, 1139])).
% 0.60/0.79 tff(1145,plain,
% 0.60/0.79 ((~hskp21) | c3_1(a512)),
% 0.60/0.79 inference(modus_ponens,[status(thm)],[1144, 1139])).
% 0.60/0.79 tff(1146,plain,
% 0.60/0.79 (c3_1(a512)),
% 0.60/0.79 inference(unit_resolution,[status(thm)],[1145, 1132])).
% 0.60/0.79 tff(1147,plain,
% 0.60/0.79 (((~hskp21) | c0_1(a512)) <=> ((~hskp21) | c0_1(a512))),
% 0.60/0.79 inference(rewrite,[status(thm)],[])).
% 0.60/0.79 tff(1148,axiom,((~hskp21) | c0_1(a512)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause54')).
% 0.60/0.79 tff(1149,plain,
% 0.60/0.79 ((~hskp21) | c0_1(a512)),
% 0.60/0.79 inference(modus_ponens,[status(thm)],[1148, 1147])).
% 0.60/0.79 tff(1150,plain,
% 0.60/0.79 ((~hskp21) | c0_1(a512)),
% 0.60/0.79 inference(modus_ponens,[status(thm)],[1149, 1147])).
% 0.60/0.79 tff(1151,plain,
% 0.60/0.79 ((~hskp21) | c0_1(a512)),
% 0.60/0.79 inference(modus_ponens,[status(thm)],[1150, 1147])).
% 0.60/0.79 tff(1152,plain,
% 0.60/0.79 ((~hskp21) | c0_1(a512)),
% 0.60/0.79 inference(modus_ponens,[status(thm)],[1151, 1147])).
% 0.60/0.79 tff(1153,plain,
% 0.60/0.79 ((~hskp21) | c0_1(a512)),
% 0.60/0.79 inference(modus_ponens,[status(thm)],[1152, 1147])).
% 0.60/0.79 tff(1154,plain,
% 0.60/0.79 (c0_1(a512)),
% 0.60/0.79 inference(unit_resolution,[status(thm)],[1153, 1132])).
% 0.60/0.79 tff(1155,plain,
% 0.60/0.79 (((~![U: $i] : (hskp12 | hskp3 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)))) | (hskp12 | hskp3 | c1_1(a512) | (~ndr1_0) | (~c3_1(a512)) | (~c0_1(a512)))) <=> ((~![U: $i] : (hskp12 | hskp3 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)))) | hskp12 | hskp3 | c1_1(a512) | (~ndr1_0) | (~c3_1(a512)) | (~c0_1(a512)))),
% 0.60/0.79 inference(rewrite,[status(thm)],[])).
% 0.60/0.79 tff(1156,plain,
% 0.60/0.79 ((hskp12 | hskp3 | (~ndr1_0) | c1_1(a512) | (~c0_1(a512)) | (~c3_1(a512))) <=> (hskp12 | hskp3 | c1_1(a512) | (~ndr1_0) | (~c3_1(a512)) | (~c0_1(a512)))),
% 0.60/0.79 inference(rewrite,[status(thm)],[])).
% 0.60/0.79 tff(1157,plain,
% 0.60/0.79 (((~![U: $i] : (hskp12 | hskp3 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)))) | (hskp12 | hskp3 | (~ndr1_0) | c1_1(a512) | (~c0_1(a512)) | (~c3_1(a512)))) <=> ((~![U: $i] : (hskp12 | hskp3 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)))) | (hskp12 | hskp3 | c1_1(a512) | (~ndr1_0) | (~c3_1(a512)) | (~c0_1(a512))))),
% 0.60/0.79 inference(monotonicity,[status(thm)],[1156])).
% 0.60/0.79 tff(1158,plain,
% 0.60/0.79 (((~![U: $i] : (hskp12 | hskp3 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)))) | (hskp12 | hskp3 | (~ndr1_0) | c1_1(a512) | (~c0_1(a512)) | (~c3_1(a512)))) <=> ((~![U: $i] : (hskp12 | hskp3 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)))) | hskp12 | hskp3 | c1_1(a512) | (~ndr1_0) | (~c3_1(a512)) | (~c0_1(a512)))),
% 0.60/0.79 inference(transitivity,[status(thm)],[1157, 1155])).
% 0.60/0.80 tff(1159,plain,
% 0.60/0.80 ((~![U: $i] : (hskp12 | hskp3 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)))) | (hskp12 | hskp3 | (~ndr1_0) | c1_1(a512) | (~c0_1(a512)) | (~c3_1(a512)))),
% 0.60/0.80 inference(quant_inst,[status(thm)],[])).
% 0.60/0.80 tff(1160,plain,
% 0.60/0.80 ((~![U: $i] : (hskp12 | hskp3 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)))) | hskp12 | hskp3 | c1_1(a512) | (~ndr1_0) | (~c3_1(a512)) | (~c0_1(a512))),
% 0.60/0.80 inference(modus_ponens,[status(thm)],[1159, 1158])).
% 0.60/0.80 tff(1161,plain,
% 0.60/0.80 (hskp3),
% 0.60/0.80 inference(unit_resolution,[status(thm)],[1160, 941, 22, 1154, 1146, 1138, 1057])).
% 0.60/0.80 tff(1162,plain,
% 0.60/0.80 (~c0_1(a466)),
% 0.60/0.80 inference(unit_resolution,[status(thm)],[240, 1161])).
% 0.60/0.80 tff(1163,plain,
% 0.60/0.80 (c3_1(a466)),
% 0.60/0.80 inference(unit_resolution,[status(thm)],[248, 1161])).
% 0.60/0.80 tff(1164,plain,
% 0.60/0.80 (c1_1(a466)),
% 0.60/0.80 inference(unit_resolution,[status(thm)],[256, 1161])).
% 0.60/0.80 tff(1165,plain,
% 0.60/0.80 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | (c0_1(a466) | (~ndr1_0) | (~c3_1(a466)) | c2_1(a466) | (~c1_1(a466)) | (~c3_1(a503)) | (~c2_1(a503)) | c0_1(a503))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | c0_1(a466) | (~ndr1_0) | (~c3_1(a466)) | c2_1(a466) | (~c1_1(a466)) | (~c3_1(a503)) | (~c2_1(a503)) | c0_1(a503))),
% 0.60/0.80 inference(rewrite,[status(thm)],[])).
% 0.60/0.80 tff(1166,plain,
% 0.60/0.80 (((~ndr1_0) | c0_1(a503) | (~c2_1(a503)) | (~c3_1(a503)) | c0_1(a466) | (~c1_1(a466)) | (~c3_1(a466)) | c0_1(a466) | c2_1(a466) | (~c1_1(a466))) <=> (c0_1(a466) | (~ndr1_0) | (~c3_1(a466)) | c2_1(a466) | (~c1_1(a466)) | (~c3_1(a503)) | (~c2_1(a503)) | c0_1(a503))),
% 0.60/0.80 inference(rewrite,[status(thm)],[])).
% 0.60/0.80 tff(1167,plain,
% 0.60/0.80 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c0_1(a503) | (~c2_1(a503)) | (~c3_1(a503)) | c0_1(a466) | (~c1_1(a466)) | (~c3_1(a466)) | c0_1(a466) | c2_1(a466) | (~c1_1(a466)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | (c0_1(a466) | (~ndr1_0) | (~c3_1(a466)) | c2_1(a466) | (~c1_1(a466)) | (~c3_1(a503)) | (~c2_1(a503)) | c0_1(a503)))),
% 0.60/0.80 inference(monotonicity,[status(thm)],[1166])).
% 0.60/0.80 tff(1168,plain,
% 0.60/0.80 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c0_1(a503) | (~c2_1(a503)) | (~c3_1(a503)) | c0_1(a466) | (~c1_1(a466)) | (~c3_1(a466)) | c0_1(a466) | c2_1(a466) | (~c1_1(a466)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | c0_1(a466) | (~ndr1_0) | (~c3_1(a466)) | c2_1(a466) | (~c1_1(a466)) | (~c3_1(a503)) | (~c2_1(a503)) | c0_1(a503))),
% 0.60/0.80 inference(transitivity,[status(thm)],[1167, 1165])).
% 0.60/0.80 tff(1169,plain,
% 0.60/0.80 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c0_1(a503) | (~c2_1(a503)) | (~c3_1(a503)) | c0_1(a466) | (~c1_1(a466)) | (~c3_1(a466)) | c0_1(a466) | c2_1(a466) | (~c1_1(a466)))),
% 0.60/0.80 inference(quant_inst,[status(thm)],[])).
% 0.60/0.80 tff(1170,plain,
% 0.60/0.80 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | c0_1(a466) | (~ndr1_0) | (~c3_1(a466)) | c2_1(a466) | (~c1_1(a466)) | (~c3_1(a503)) | (~c2_1(a503)) | c0_1(a503)),
% 0.60/0.80 inference(modus_ponens,[status(thm)],[1169, 1168])).
% 0.60/0.80 tff(1171,plain,
% 0.60/0.80 (c2_1(a466)),
% 0.60/0.80 inference(unit_resolution,[status(thm)],[1170, 941, 1040, 1032, 1164, 1163, 1162, 868, 1047])).
% 0.60/0.80 tff(1172,plain,
% 0.60/0.80 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | (c0_1(a466) | c0_1(a465) | c2_1(a465) | (~ndr1_0) | (~c1_1(a465)) | (~c3_1(a466)) | (~c2_1(a466)) | (~c1_1(a466)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | c0_1(a466) | c0_1(a465) | c2_1(a465) | (~ndr1_0) | (~c1_1(a465)) | (~c3_1(a466)) | (~c2_1(a466)) | (~c1_1(a466)))),
% 0.60/0.80 inference(rewrite,[status(thm)],[])).
% 0.60/0.80 tff(1173,plain,
% 0.60/0.80 (((~ndr1_0) | c0_1(a466) | (~c2_1(a466)) | (~c3_1(a466)) | c0_1(a466) | (~c1_1(a466)) | (~c3_1(a466)) | c0_1(a465) | c2_1(a465) | (~c1_1(a465))) <=> (c0_1(a466) | c0_1(a465) | c2_1(a465) | (~ndr1_0) | (~c1_1(a465)) | (~c3_1(a466)) | (~c2_1(a466)) | (~c1_1(a466)))),
% 0.60/0.80 inference(rewrite,[status(thm)],[])).
% 0.60/0.80 tff(1174,plain,
% 0.60/0.80 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c0_1(a466) | (~c2_1(a466)) | (~c3_1(a466)) | c0_1(a466) | (~c1_1(a466)) | (~c3_1(a466)) | c0_1(a465) | c2_1(a465) | (~c1_1(a465)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | (c0_1(a466) | c0_1(a465) | c2_1(a465) | (~ndr1_0) | (~c1_1(a465)) | (~c3_1(a466)) | (~c2_1(a466)) | (~c1_1(a466))))),
% 0.60/0.80 inference(monotonicity,[status(thm)],[1173])).
% 0.60/0.80 tff(1175,plain,
% 0.60/0.80 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c0_1(a466) | (~c2_1(a466)) | (~c3_1(a466)) | c0_1(a466) | (~c1_1(a466)) | (~c3_1(a466)) | c0_1(a465) | c2_1(a465) | (~c1_1(a465)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | c0_1(a466) | c0_1(a465) | c2_1(a465) | (~ndr1_0) | (~c1_1(a465)) | (~c3_1(a466)) | (~c2_1(a466)) | (~c1_1(a466)))),
% 0.60/0.80 inference(transitivity,[status(thm)],[1174, 1172])).
% 0.60/0.80 tff(1176,plain,
% 0.60/0.80 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c0_1(a466) | (~c2_1(a466)) | (~c3_1(a466)) | c0_1(a466) | (~c1_1(a466)) | (~c3_1(a466)) | c0_1(a465) | c2_1(a465) | (~c1_1(a465)))),
% 0.60/0.80 inference(quant_inst,[status(thm)],[])).
% 0.60/0.80 tff(1177,plain,
% 0.60/0.80 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | c0_1(a466) | c0_1(a465) | c2_1(a465) | (~ndr1_0) | (~c1_1(a465)) | (~c3_1(a466)) | (~c2_1(a466)) | (~c1_1(a466))),
% 0.60/0.80 inference(modus_ponens,[status(thm)],[1176, 1175])).
% 0.60/0.80 tff(1178,plain,
% 0.60/0.80 ($false),
% 0.60/0.80 inference(unit_resolution,[status(thm)],[1177, 941, 1164, 1163, 1162, 1086, 1085, 868, 1093, 1171])).
% 0.60/0.80 tff(1179,plain,(hskp0 | hskp12 | hskp17), inference(lemma,lemma(discharge,[]))).
% 0.60/0.80 tff(1180,plain,
% 0.60/0.80 (hskp0),
% 0.60/0.80 inference(unit_resolution,[status(thm)],[1179, 33, 22])).
% 0.60/0.80 tff(1181,plain,
% 0.60/0.80 (~c3_1(a460)),
% 0.60/0.80 inference(unit_resolution,[status(thm)],[207, 1180])).
% 0.60/0.80 tff(1182,assumption,(~c0_1(a460)), introduced(assumption)).
% 0.60/0.80 tff(1183,plain,
% 0.60/0.80 (~hskp0),
% 0.60/0.80 inference(unit_resolution,[status(thm)],[215, 1182])).
% 0.60/0.80 tff(1184,assumption,(~c0_1(a503)), introduced(assumption)).
% 0.60/0.80 tff(1185,plain,
% 0.60/0.80 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | c0_1(a460) | c2_1(a460) | c3_1(a460) | (~ndr1_0) | c1_1(a460))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c0_1(a460) | c2_1(a460) | c3_1(a460) | (~ndr1_0) | c1_1(a460))),
% 0.60/0.80 inference(rewrite,[status(thm)],[])).
% 0.60/0.80 tff(1186,plain,
% 0.60/0.80 ((hskp0 | (~ndr1_0) | c2_1(a460) | c0_1(a460) | c3_1(a460) | c3_1(a460) | c1_1(a460) | c0_1(a460)) <=> (hskp0 | c0_1(a460) | c2_1(a460) | c3_1(a460) | (~ndr1_0) | c1_1(a460))),
% 0.60/0.80 inference(rewrite,[status(thm)],[])).
% 0.60/0.80 tff(1187,plain,
% 0.60/0.80 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c2_1(a460) | c0_1(a460) | c3_1(a460) | c3_1(a460) | c1_1(a460) | c0_1(a460))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | c0_1(a460) | c2_1(a460) | c3_1(a460) | (~ndr1_0) | c1_1(a460)))),
% 0.60/0.80 inference(monotonicity,[status(thm)],[1186])).
% 0.60/0.80 tff(1188,plain,
% 0.60/0.80 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c2_1(a460) | c0_1(a460) | c3_1(a460) | c3_1(a460) | c1_1(a460) | c0_1(a460))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c0_1(a460) | c2_1(a460) | c3_1(a460) | (~ndr1_0) | c1_1(a460))),
% 0.60/0.80 inference(transitivity,[status(thm)],[1187, 1185])).
% 0.60/0.80 tff(1189,plain,
% 0.60/0.80 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c2_1(a460) | c0_1(a460) | c3_1(a460) | c3_1(a460) | c1_1(a460) | c0_1(a460))),
% 0.60/0.80 inference(quant_inst,[status(thm)],[])).
% 0.60/0.80 tff(1190,plain,
% 0.60/0.80 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c0_1(a460) | c2_1(a460) | c3_1(a460) | (~ndr1_0) | c1_1(a460)),
% 0.60/0.80 inference(modus_ponens,[status(thm)],[1189, 1188])).
% 0.60/0.80 tff(1191,plain,
% 0.60/0.80 (c1_1(a460)),
% 0.60/0.80 inference(unit_resolution,[status(thm)],[1190, 941, 1183, 1182, 1, 223, 959])).
% 0.60/0.80 tff(1192,plain,
% 0.60/0.80 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp21 | c2_1(a468) | c2_1(a460) | c3_1(a460) | (~ndr1_0) | (~c0_1(a468)) | (~c3_1(a468)) | (~c1_1(a460)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | hskp21 | c2_1(a468) | c2_1(a460) | c3_1(a460) | (~ndr1_0) | (~c0_1(a468)) | (~c3_1(a468)) | (~c1_1(a460)))),
% 0.60/0.80 inference(rewrite,[status(thm)],[])).
% 0.60/0.80 tff(1193,plain,
% 0.60/0.80 ((hskp21 | (~ndr1_0) | c2_1(a468) | (~c0_1(a468)) | (~c3_1(a468)) | c3_1(a460) | c2_1(a460) | (~c1_1(a460))) <=> (hskp21 | c2_1(a468) | c2_1(a460) | c3_1(a460) | (~ndr1_0) | (~c0_1(a468)) | (~c3_1(a468)) | (~c1_1(a460)))),
% 0.60/0.80 inference(rewrite,[status(thm)],[])).
% 0.60/0.80 tff(1194,plain,
% 0.60/0.80 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp21 | (~ndr1_0) | c2_1(a468) | (~c0_1(a468)) | (~c3_1(a468)) | c3_1(a460) | c2_1(a460) | (~c1_1(a460)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp21 | c2_1(a468) | c2_1(a460) | c3_1(a460) | (~ndr1_0) | (~c0_1(a468)) | (~c3_1(a468)) | (~c1_1(a460))))),
% 0.60/0.80 inference(monotonicity,[status(thm)],[1193])).
% 0.60/0.80 tff(1195,plain,
% 0.60/0.80 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp21 | (~ndr1_0) | c2_1(a468) | (~c0_1(a468)) | (~c3_1(a468)) | c3_1(a460) | c2_1(a460) | (~c1_1(a460)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | hskp21 | c2_1(a468) | c2_1(a460) | c3_1(a460) | (~ndr1_0) | (~c0_1(a468)) | (~c3_1(a468)) | (~c1_1(a460)))),
% 0.60/0.80 inference(transitivity,[status(thm)],[1194, 1192])).
% 0.60/0.80 tff(1196,plain,
% 0.60/0.80 ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp21 | (~ndr1_0) | c2_1(a468) | (~c0_1(a468)) | (~c3_1(a468)) | c3_1(a460) | c2_1(a460) | (~c1_1(a460)))),
% 0.60/0.80 inference(quant_inst,[status(thm)],[])).
% 0.60/0.80 tff(1197,plain,
% 0.60/0.80 ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | hskp21 | c2_1(a468) | c2_1(a460) | c3_1(a460) | (~ndr1_0) | (~c0_1(a468)) | (~c3_1(a468)) | (~c1_1(a460))),
% 0.60/0.80 inference(modus_ponens,[status(thm)],[1196, 1195])).
% 0.60/0.80 tff(1198,plain,
% 0.60/0.80 (hskp21 | (~c1_1(a460))),
% 0.60/0.80 inference(unit_resolution,[status(thm)],[1197, 941, 1125, 1117, 1109, 1, 223, 1103])).
% 0.60/0.80 tff(1199,plain,
% 0.60/0.80 (hskp21),
% 0.60/0.80 inference(unit_resolution,[status(thm)],[1198, 1191])).
% 0.60/0.80 tff(1200,plain,
% 0.60/0.80 (~c1_1(a512)),
% 0.60/0.80 inference(unit_resolution,[status(thm)],[1137, 1199])).
% 0.60/0.80 tff(1201,plain,
% 0.60/0.80 (c3_1(a512)),
% 0.60/0.80 inference(unit_resolution,[status(thm)],[1145, 1199])).
% 0.60/0.80 tff(1202,plain,
% 0.60/0.80 (c0_1(a512)),
% 0.60/0.80 inference(unit_resolution,[status(thm)],[1153, 1199])).
% 0.60/0.80 tff(1203,plain,
% 0.60/0.80 (~hskp12),
% 0.60/0.80 inference(unit_resolution,[status(thm)],[947, 1183])).
% 0.60/0.80 tff(1204,plain,
% 0.60/0.80 (hskp3),
% 0.60/0.80 inference(unit_resolution,[status(thm)],[1160, 941, 1203, 1202, 1201, 1200, 1057])).
% 0.60/0.80 tff(1205,plain,
% 0.60/0.80 (c1_1(a466)),
% 0.60/0.80 inference(unit_resolution,[status(thm)],[256, 1204])).
% 0.60/0.80 tff(1206,plain,
% 0.60/0.80 (~c0_1(a466)),
% 0.60/0.80 inference(unit_resolution,[status(thm)],[240, 1204])).
% 0.60/0.80 tff(1207,plain,
% 0.60/0.80 (~hskp14),
% 0.60/0.80 inference(unit_resolution,[status(thm)],[967, 1183])).
% 0.60/0.80 tff(1208,plain,
% 0.60/0.80 (~hskp6),
% 0.60/0.80 inference(unit_resolution,[status(thm)],[1008, 1207, 1203])).
% 0.60/0.80 tff(1209,plain,
% 0.60/0.80 (hskp20),
% 0.60/0.80 inference(unit_resolution,[status(thm)],[1017, 1208, 1203])).
% 0.60/0.80 tff(1210,plain,
% 0.60/0.80 (c3_1(a466)),
% 0.60/0.80 inference(unit_resolution,[status(thm)],[248, 1204])).
% 0.60/0.80 tff(1211,assumption,(hskp20), introduced(assumption)).
% 0.60/0.80 tff(1212,plain,
% 0.60/0.80 (~c1_1(a503)),
% 0.60/0.80 inference(unit_resolution,[status(thm)],[1023, 1211])).
% 0.60/0.80 tff(1213,plain,
% 0.60/0.80 (c3_1(a503)),
% 0.60/0.80 inference(unit_resolution,[status(thm)],[1031, 1211])).
% 0.60/0.80 tff(1214,plain,
% 0.60/0.80 (c2_1(a503)),
% 0.60/0.80 inference(unit_resolution,[status(thm)],[1039, 1211])).
% 0.60/0.80 tff(1215,plain,
% 0.60/0.80 (~c0_1(a503)),
% 0.60/0.80 inference(unit_resolution,[status(thm)],[1046, 941, 33, 1214, 1213, 1212, 11])).
% 0.60/0.80 tff(1216,assumption,(c1_1(a460)), introduced(assumption)).
% 0.60/0.80 tff(1217,plain,
% 0.60/0.80 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | (c0_1(a460) | c0_1(a466) | c2_1(a460) | (~ndr1_0) | (~c1_1(a460)) | (~c3_1(a466)) | (~c1_1(a466)) | (~c3_1(a503)) | (~c2_1(a503)) | c0_1(a503))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | c0_1(a460) | c0_1(a466) | c2_1(a460) | (~ndr1_0) | (~c1_1(a460)) | (~c3_1(a466)) | (~c1_1(a466)) | (~c3_1(a503)) | (~c2_1(a503)) | c0_1(a503))),
% 0.60/0.80 inference(rewrite,[status(thm)],[])).
% 0.60/0.80 tff(1218,plain,
% 0.60/0.80 (((~ndr1_0) | c0_1(a503) | (~c2_1(a503)) | (~c3_1(a503)) | c0_1(a466) | (~c1_1(a466)) | (~c3_1(a466)) | c0_1(a460) | c2_1(a460) | (~c1_1(a460))) <=> (c0_1(a460) | c0_1(a466) | c2_1(a460) | (~ndr1_0) | (~c1_1(a460)) | (~c3_1(a466)) | (~c1_1(a466)) | (~c3_1(a503)) | (~c2_1(a503)) | c0_1(a503))),
% 0.60/0.80 inference(rewrite,[status(thm)],[])).
% 0.60/0.80 tff(1219,plain,
% 0.60/0.80 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c0_1(a503) | (~c2_1(a503)) | (~c3_1(a503)) | c0_1(a466) | (~c1_1(a466)) | (~c3_1(a466)) | c0_1(a460) | c2_1(a460) | (~c1_1(a460)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | (c0_1(a460) | c0_1(a466) | c2_1(a460) | (~ndr1_0) | (~c1_1(a460)) | (~c3_1(a466)) | (~c1_1(a466)) | (~c3_1(a503)) | (~c2_1(a503)) | c0_1(a503)))),
% 0.60/0.80 inference(monotonicity,[status(thm)],[1218])).
% 0.60/0.80 tff(1220,plain,
% 0.60/0.80 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c0_1(a503) | (~c2_1(a503)) | (~c3_1(a503)) | c0_1(a466) | (~c1_1(a466)) | (~c3_1(a466)) | c0_1(a460) | c2_1(a460) | (~c1_1(a460)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | c0_1(a460) | c0_1(a466) | c2_1(a460) | (~ndr1_0) | (~c1_1(a460)) | (~c3_1(a466)) | (~c1_1(a466)) | (~c3_1(a503)) | (~c2_1(a503)) | c0_1(a503))),
% 0.60/0.80 inference(transitivity,[status(thm)],[1219, 1217])).
% 0.60/0.80 tff(1221,plain,
% 0.60/0.80 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c0_1(a503) | (~c2_1(a503)) | (~c3_1(a503)) | c0_1(a466) | (~c1_1(a466)) | (~c3_1(a466)) | c0_1(a460) | c2_1(a460) | (~c1_1(a460)))),
% 0.60/0.80 inference(quant_inst,[status(thm)],[])).
% 0.60/0.80 tff(1222,plain,
% 0.60/0.80 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | c0_1(a460) | c0_1(a466) | c2_1(a460) | (~ndr1_0) | (~c1_1(a460)) | (~c3_1(a466)) | (~c1_1(a466)) | (~c3_1(a503)) | (~c2_1(a503)) | c0_1(a503)),
% 0.60/0.80 inference(modus_ponens,[status(thm)],[1221, 1220])).
% 0.60/0.80 tff(1223,plain,
% 0.60/0.80 ($false),
% 0.60/0.80 inference(unit_resolution,[status(thm)],[1222, 941, 1214, 1213, 260, 259, 1182, 258, 1, 868, 1216, 1215])).
% 0.60/0.80 tff(1224,plain,((~hskp20) | (~c1_1(a466)) | (~c3_1(a466)) | c0_1(a460) | c0_1(a466) | c2_1(a460) | (~c1_1(a460)) | hskp17), inference(lemma,lemma(discharge,[]))).
% 0.60/0.80 tff(1225,plain,
% 0.60/0.80 (hskp17),
% 0.60/0.80 inference(unit_resolution,[status(thm)],[1224, 1210, 1209, 1182, 1206, 1, 1191, 1205])).
% 0.60/0.80 tff(1226,plain,
% 0.60/0.80 (~c1_1(a494)),
% 0.60/0.80 inference(unit_resolution,[status(thm)],[501, 1225])).
% 0.60/0.80 tff(1227,plain,
% 0.60/0.80 (~c3_1(a494)),
% 0.60/0.80 inference(unit_resolution,[status(thm)],[931, 1225])).
% 0.60/0.80 tff(1228,plain,
% 0.60/0.80 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | c0_1(a460) | c0_1(a494) | c1_1(a494) | c3_1(a494) | c2_1(a460) | c3_1(a460) | (~ndr1_0))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c0_1(a460) | c0_1(a494) | c1_1(a494) | c3_1(a494) | c2_1(a460) | c3_1(a460) | (~ndr1_0))),
% 0.60/0.80 inference(rewrite,[status(thm)],[])).
% 0.60/0.80 tff(1229,plain,
% 0.60/0.80 ((hskp0 | (~ndr1_0) | c2_1(a460) | c0_1(a460) | c3_1(a460) | c3_1(a494) | c1_1(a494) | c0_1(a494)) <=> (hskp0 | c0_1(a460) | c0_1(a494) | c1_1(a494) | c3_1(a494) | c2_1(a460) | c3_1(a460) | (~ndr1_0))),
% 0.60/0.80 inference(rewrite,[status(thm)],[])).
% 0.60/0.80 tff(1230,plain,
% 0.60/0.80 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c2_1(a460) | c0_1(a460) | c3_1(a460) | c3_1(a494) | c1_1(a494) | c0_1(a494))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | c0_1(a460) | c0_1(a494) | c1_1(a494) | c3_1(a494) | c2_1(a460) | c3_1(a460) | (~ndr1_0)))),
% 0.60/0.80 inference(monotonicity,[status(thm)],[1229])).
% 0.60/0.80 tff(1231,plain,
% 0.60/0.80 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c2_1(a460) | c0_1(a460) | c3_1(a460) | c3_1(a494) | c1_1(a494) | c0_1(a494))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c0_1(a460) | c0_1(a494) | c1_1(a494) | c3_1(a494) | c2_1(a460) | c3_1(a460) | (~ndr1_0))),
% 0.60/0.80 inference(transitivity,[status(thm)],[1230, 1228])).
% 0.60/0.80 tff(1232,plain,
% 0.60/0.80 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c2_1(a460) | c0_1(a460) | c3_1(a460) | c3_1(a494) | c1_1(a494) | c0_1(a494))),
% 0.60/0.80 inference(quant_inst,[status(thm)],[])).
% 0.60/0.80 tff(1233,plain,
% 0.60/0.80 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c0_1(a460) | c0_1(a494) | c1_1(a494) | c3_1(a494) | c2_1(a460) | c3_1(a460) | (~ndr1_0)),
% 0.60/0.80 inference(modus_ponens,[status(thm)],[1232, 1231])).
% 0.60/0.80 tff(1234,plain,
% 0.60/0.80 (c0_1(a494) | c1_1(a494)),
% 0.60/0.80 inference(unit_resolution,[status(thm)],[1233, 941, 1183, 1182, 495, 1, 223, 959])).
% 0.60/0.80 tff(1235,plain,
% 0.60/0.80 (c0_1(a494)),
% 0.60/0.80 inference(unit_resolution,[status(thm)],[1234, 510])).
% 0.60/0.80 tff(1236,assumption,(c0_1(a494)), introduced(assumption)).
% 0.60/0.80 tff(1237,plain,
% 0.60/0.80 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp12 | (~c0_1(a494)) | c1_1(a494) | c3_1(a494) | (~ndr1_0) | c2_1(a494))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | hskp12 | (~c0_1(a494)) | c1_1(a494) | c3_1(a494) | (~ndr1_0) | c2_1(a494))),
% 0.60/0.81 inference(rewrite,[status(thm)],[])).
% 0.60/0.81 tff(1238,plain,
% 0.60/0.81 ((hskp12 | (~ndr1_0) | c2_1(a494) | c3_1(a494) | (~c0_1(a494)) | c3_1(a494) | c1_1(a494) | (~c0_1(a494))) <=> (hskp12 | (~c0_1(a494)) | c1_1(a494) | c3_1(a494) | (~ndr1_0) | c2_1(a494))),
% 0.60/0.81 inference(rewrite,[status(thm)],[])).
% 0.60/0.81 tff(1239,plain,
% 0.60/0.81 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp12 | (~ndr1_0) | c2_1(a494) | c3_1(a494) | (~c0_1(a494)) | c3_1(a494) | c1_1(a494) | (~c0_1(a494)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp12 | (~c0_1(a494)) | c1_1(a494) | c3_1(a494) | (~ndr1_0) | c2_1(a494)))),
% 0.60/0.81 inference(monotonicity,[status(thm)],[1238])).
% 0.60/0.81 tff(1240,plain,
% 0.60/0.81 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp12 | (~ndr1_0) | c2_1(a494) | c3_1(a494) | (~c0_1(a494)) | c3_1(a494) | c1_1(a494) | (~c0_1(a494)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | hskp12 | (~c0_1(a494)) | c1_1(a494) | c3_1(a494) | (~ndr1_0) | c2_1(a494))),
% 0.60/0.81 inference(transitivity,[status(thm)],[1239, 1237])).
% 0.60/0.81 tff(1241,plain,
% 0.60/0.81 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp12 | (~ndr1_0) | c2_1(a494) | c3_1(a494) | (~c0_1(a494)) | c3_1(a494) | c1_1(a494) | (~c0_1(a494)))),
% 0.60/0.81 inference(quant_inst,[status(thm)],[])).
% 0.60/0.81 tff(1242,plain,
% 0.60/0.81 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | hskp12 | (~c0_1(a494)) | c1_1(a494) | c3_1(a494) | (~ndr1_0) | c2_1(a494)),
% 0.60/0.81 inference(modus_ponens,[status(thm)],[1241, 1240])).
% 0.60/0.81 tff(1243,plain,
% 0.60/0.81 ($false),
% 0.60/0.81 inference(unit_resolution,[status(thm)],[1242, 941, 22, 1236, 510, 495, 44, 509])).
% 0.60/0.81 tff(1244,plain,(c2_1(a494) | hskp12 | (~c0_1(a494)) | c1_1(a494) | c3_1(a494)), inference(lemma,lemma(discharge,[]))).
% 0.60/0.81 tff(1245,plain,
% 0.60/0.81 (c2_1(a494)),
% 0.60/0.81 inference(unit_resolution,[status(thm)],[1244, 1235, 1203, 510, 495])).
% 0.60/0.81 tff(1246,plain,
% 0.60/0.81 (((~![U: $i] : (hskp14 | hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp14 | hskp12 | c1_1(a494) | c3_1(a494) | (~ndr1_0) | (~c2_1(a494)))) <=> ((~![U: $i] : (hskp14 | hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | hskp14 | hskp12 | c1_1(a494) | c3_1(a494) | (~ndr1_0) | (~c2_1(a494)))),
% 0.60/0.81 inference(rewrite,[status(thm)],[])).
% 0.60/0.81 tff(1247,plain,
% 0.60/0.81 ((hskp14 | hskp12 | (~ndr1_0) | c1_1(a494) | c3_1(a494) | (~c2_1(a494))) <=> (hskp14 | hskp12 | c1_1(a494) | c3_1(a494) | (~ndr1_0) | (~c2_1(a494)))),
% 0.60/0.81 inference(rewrite,[status(thm)],[])).
% 0.60/0.81 tff(1248,plain,
% 0.60/0.81 (((~![U: $i] : (hskp14 | hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp14 | hskp12 | (~ndr1_0) | c1_1(a494) | c3_1(a494) | (~c2_1(a494)))) <=> ((~![U: $i] : (hskp14 | hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp14 | hskp12 | c1_1(a494) | c3_1(a494) | (~ndr1_0) | (~c2_1(a494))))),
% 0.60/0.81 inference(monotonicity,[status(thm)],[1247])).
% 0.60/0.81 tff(1249,plain,
% 0.60/0.81 (((~![U: $i] : (hskp14 | hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp14 | hskp12 | (~ndr1_0) | c1_1(a494) | c3_1(a494) | (~c2_1(a494)))) <=> ((~![U: $i] : (hskp14 | hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | hskp14 | hskp12 | c1_1(a494) | c3_1(a494) | (~ndr1_0) | (~c2_1(a494)))),
% 0.60/0.81 inference(transitivity,[status(thm)],[1248, 1246])).
% 0.60/0.81 tff(1250,plain,
% 0.60/0.81 ((~![U: $i] : (hskp14 | hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp14 | hskp12 | (~ndr1_0) | c1_1(a494) | c3_1(a494) | (~c2_1(a494)))),
% 0.60/0.81 inference(quant_inst,[status(thm)],[])).
% 0.60/0.81 tff(1251,plain,
% 0.60/0.81 ((~![U: $i] : (hskp14 | hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | hskp14 | hskp12 | c1_1(a494) | c3_1(a494) | (~ndr1_0) | (~c2_1(a494))),
% 0.60/0.81 inference(modus_ponens,[status(thm)],[1250, 1249])).
% 0.60/0.81 tff(1252,plain,
% 0.60/0.81 (hskp14 | c1_1(a494) | (~c2_1(a494))),
% 0.60/0.81 inference(unit_resolution,[status(thm)],[1251, 941, 1203, 495, 978])).
% 0.60/0.81 tff(1253,plain,
% 0.60/0.81 (hskp14),
% 0.60/0.81 inference(unit_resolution,[status(thm)],[1252, 1245, 510])).
% 0.60/0.81 tff(1254,plain,
% 0.60/0.81 (~c3_1(a488)),
% 0.60/0.81 inference(unit_resolution,[status(thm)],[50, 1253])).
% 0.60/0.81 tff(1255,plain,
% 0.60/0.81 (~c2_1(a488)),
% 0.60/0.81 inference(unit_resolution,[status(thm)],[56, 1253])).
% 0.60/0.81 tff(1256,plain,
% 0.60/0.81 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp12 | (~c0_1(a494)) | c1_1(a494) | c3_1(a494) | c2_1(a488) | c3_1(a488) | (~ndr1_0) | (~c0_1(a488)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | hskp12 | (~c0_1(a494)) | c1_1(a494) | c3_1(a494) | c2_1(a488) | c3_1(a488) | (~ndr1_0) | (~c0_1(a488)))),
% 0.60/0.81 inference(rewrite,[status(thm)],[])).
% 0.60/0.81 tff(1257,plain,
% 0.60/0.81 ((hskp12 | (~ndr1_0) | c2_1(a488) | c3_1(a488) | (~c0_1(a488)) | c3_1(a494) | c1_1(a494) | (~c0_1(a494))) <=> (hskp12 | (~c0_1(a494)) | c1_1(a494) | c3_1(a494) | c2_1(a488) | c3_1(a488) | (~ndr1_0) | (~c0_1(a488)))),
% 0.60/0.81 inference(rewrite,[status(thm)],[])).
% 0.60/0.81 tff(1258,plain,
% 0.60/0.81 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp12 | (~ndr1_0) | c2_1(a488) | c3_1(a488) | (~c0_1(a488)) | c3_1(a494) | c1_1(a494) | (~c0_1(a494)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp12 | (~c0_1(a494)) | c1_1(a494) | c3_1(a494) | c2_1(a488) | c3_1(a488) | (~ndr1_0) | (~c0_1(a488))))),
% 0.60/0.81 inference(monotonicity,[status(thm)],[1257])).
% 0.60/0.81 tff(1259,plain,
% 0.60/0.81 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp12 | (~ndr1_0) | c2_1(a488) | c3_1(a488) | (~c0_1(a488)) | c3_1(a494) | c1_1(a494) | (~c0_1(a494)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | hskp12 | (~c0_1(a494)) | c1_1(a494) | c3_1(a494) | c2_1(a488) | c3_1(a488) | (~ndr1_0) | (~c0_1(a488)))),
% 0.60/0.81 inference(transitivity,[status(thm)],[1258, 1256])).
% 0.60/0.81 tff(1260,plain,
% 0.60/0.81 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp12 | (~ndr1_0) | c2_1(a488) | c3_1(a488) | (~c0_1(a488)) | c3_1(a494) | c1_1(a494) | (~c0_1(a494)))),
% 0.60/0.81 inference(quant_inst,[status(thm)],[])).
% 0.60/0.81 tff(1261,plain,
% 0.60/0.81 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | hskp12 | (~c0_1(a494)) | c1_1(a494) | c3_1(a494) | c2_1(a488) | c3_1(a488) | (~ndr1_0) | (~c0_1(a488))),
% 0.60/0.81 inference(modus_ponens,[status(thm)],[1260, 1259])).
% 0.60/0.81 tff(1262,plain,
% 0.60/0.81 (~c0_1(a488)),
% 0.60/0.81 inference(unit_resolution,[status(thm)],[1261, 941, 1203, 1235, 510, 495, 1255, 1254, 44])).
% 0.60/0.81 tff(1263,plain,
% 0.60/0.81 (~c1_1(a488)),
% 0.60/0.81 inference(unit_resolution,[status(thm)],[62, 1253])).
% 0.60/0.81 tff(1264,plain,
% 0.60/0.81 ($false),
% 0.60/0.81 inference(unit_resolution,[status(thm)],[965, 941, 1183, 1263, 1255, 1254, 959, 1262])).
% 0.60/0.81 tff(1265,plain,(c1_1(a494) | c3_1(a494) | c0_1(a460) | c2_1(a460) | c3_1(a460)), inference(lemma,lemma(discharge,[]))).
% 0.60/0.81 tff(1266,plain,
% 0.60/0.81 ($false),
% 0.60/0.81 inference(unit_resolution,[status(thm)],[1265, 1227, 1226, 1182, 1, 223])).
% 0.60/0.81 tff(1267,plain,(c3_1(a460) | c0_1(a460) | c2_1(a460)), inference(lemma,lemma(discharge,[]))).
% 0.60/0.81 tff(1268,plain,
% 0.60/0.81 (c3_1(a460)),
% 0.60/0.81 inference(unit_resolution,[status(thm)],[1267, 1182, 1])).
% 0.60/0.81 tff(1269,plain,
% 0.60/0.81 (c3_1(a503)),
% 0.60/0.81 inference(unit_resolution,[status(thm)],[1031, 1209])).
% 0.60/0.81 tff(1270,plain,
% 0.60/0.81 (c2_1(a503)),
% 0.60/0.81 inference(unit_resolution,[status(thm)],[1039, 1209])).
% 0.60/0.81 tff(1271,plain,
% 0.60/0.81 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | (c0_1(a460) | c2_1(a460) | (~c3_1(a460)) | (~ndr1_0) | (~c1_1(a460)) | (~c3_1(a503)) | (~c2_1(a503)) | c0_1(a503))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | c0_1(a460) | c2_1(a460) | (~c3_1(a460)) | (~ndr1_0) | (~c1_1(a460)) | (~c3_1(a503)) | (~c2_1(a503)) | c0_1(a503))),
% 0.65/0.81 inference(rewrite,[status(thm)],[])).
% 0.65/0.81 tff(1272,plain,
% 0.65/0.81 (((~ndr1_0) | c0_1(a503) | (~c2_1(a503)) | (~c3_1(a503)) | c0_1(a460) | (~c1_1(a460)) | (~c3_1(a460)) | c0_1(a460) | c2_1(a460) | (~c1_1(a460))) <=> (c0_1(a460) | c2_1(a460) | (~c3_1(a460)) | (~ndr1_0) | (~c1_1(a460)) | (~c3_1(a503)) | (~c2_1(a503)) | c0_1(a503))),
% 0.65/0.81 inference(rewrite,[status(thm)],[])).
% 0.65/0.81 tff(1273,plain,
% 0.65/0.81 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c0_1(a503) | (~c2_1(a503)) | (~c3_1(a503)) | c0_1(a460) | (~c1_1(a460)) | (~c3_1(a460)) | c0_1(a460) | c2_1(a460) | (~c1_1(a460)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | (c0_1(a460) | c2_1(a460) | (~c3_1(a460)) | (~ndr1_0) | (~c1_1(a460)) | (~c3_1(a503)) | (~c2_1(a503)) | c0_1(a503)))),
% 0.65/0.81 inference(monotonicity,[status(thm)],[1272])).
% 0.65/0.81 tff(1274,plain,
% 0.65/0.81 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c0_1(a503) | (~c2_1(a503)) | (~c3_1(a503)) | c0_1(a460) | (~c1_1(a460)) | (~c3_1(a460)) | c0_1(a460) | c2_1(a460) | (~c1_1(a460)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | c0_1(a460) | c2_1(a460) | (~c3_1(a460)) | (~ndr1_0) | (~c1_1(a460)) | (~c3_1(a503)) | (~c2_1(a503)) | c0_1(a503))),
% 0.65/0.81 inference(transitivity,[status(thm)],[1273, 1271])).
% 0.65/0.81 tff(1275,plain,
% 0.65/0.81 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c0_1(a503) | (~c2_1(a503)) | (~c3_1(a503)) | c0_1(a460) | (~c1_1(a460)) | (~c3_1(a460)) | c0_1(a460) | c2_1(a460) | (~c1_1(a460)))),
% 0.65/0.81 inference(quant_inst,[status(thm)],[])).
% 0.65/0.81 tff(1276,plain,
% 0.65/0.81 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | c0_1(a460) | c2_1(a460) | (~c3_1(a460)) | (~ndr1_0) | (~c1_1(a460)) | (~c3_1(a503)) | (~c2_1(a503)) | c0_1(a503)),
% 0.65/0.81 inference(modus_ponens,[status(thm)],[1275, 1274])).
% 0.65/0.81 tff(1277,plain,
% 0.65/0.81 (~c1_1(a460)),
% 0.65/0.81 inference(unit_resolution,[status(thm)],[1276, 941, 1270, 1269, 1182, 1, 1268, 868, 1184])).
% 0.65/0.81 tff(1278,plain,
% 0.65/0.81 (~c1_1(a503)),
% 0.65/0.81 inference(unit_resolution,[status(thm)],[1023, 1209])).
% 0.65/0.81 tff(1279,plain,
% 0.65/0.81 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | (hskp0 | c0_1(a460) | c1_1(a503) | c2_1(a460) | (~ndr1_0) | c1_1(a460) | (~c2_1(a503)) | c0_1(a503))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | hskp0 | c0_1(a460) | c1_1(a503) | c2_1(a460) | (~ndr1_0) | c1_1(a460) | (~c2_1(a503)) | c0_1(a503))),
% 0.65/0.81 inference(rewrite,[status(thm)],[])).
% 0.65/0.81 tff(1280,plain,
% 0.65/0.81 ((hskp0 | (~ndr1_0) | c1_1(a503) | c0_1(a503) | (~c2_1(a503)) | c1_1(a460) | c0_1(a460) | c2_1(a460)) <=> (hskp0 | c0_1(a460) | c1_1(a503) | c2_1(a460) | (~ndr1_0) | c1_1(a460) | (~c2_1(a503)) | c0_1(a503))),
% 0.65/0.81 inference(rewrite,[status(thm)],[])).
% 0.65/0.81 tff(1281,plain,
% 0.65/0.81 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | (hskp0 | (~ndr1_0) | c1_1(a503) | c0_1(a503) | (~c2_1(a503)) | c1_1(a460) | c0_1(a460) | c2_1(a460))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | (hskp0 | c0_1(a460) | c1_1(a503) | c2_1(a460) | (~ndr1_0) | c1_1(a460) | (~c2_1(a503)) | c0_1(a503)))),
% 0.65/0.81 inference(monotonicity,[status(thm)],[1280])).
% 0.65/0.81 tff(1282,plain,
% 0.65/0.81 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | (hskp0 | (~ndr1_0) | c1_1(a503) | c0_1(a503) | (~c2_1(a503)) | c1_1(a460) | c0_1(a460) | c2_1(a460))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | hskp0 | c0_1(a460) | c1_1(a503) | c2_1(a460) | (~ndr1_0) | c1_1(a460) | (~c2_1(a503)) | c0_1(a503))),
% 0.65/0.81 inference(transitivity,[status(thm)],[1281, 1279])).
% 0.65/0.81 tff(1283,plain,
% 0.65/0.81 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | (hskp0 | (~ndr1_0) | c1_1(a503) | c0_1(a503) | (~c2_1(a503)) | c1_1(a460) | c0_1(a460) | c2_1(a460))),
% 0.65/0.81 inference(quant_inst,[status(thm)],[])).
% 0.65/0.81 tff(1284,plain,
% 0.65/0.81 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | hskp0 | c0_1(a460) | c1_1(a503) | c2_1(a460) | (~ndr1_0) | c1_1(a460) | (~c2_1(a503)) | c0_1(a503)),
% 0.65/0.81 inference(modus_ponens,[status(thm)],[1283, 1282])).
% 0.65/0.81 tff(1285,plain,
% 0.65/0.81 ($false),
% 0.65/0.81 inference(unit_resolution,[status(thm)],[1284, 941, 1183, 1270, 1182, 1278, 1, 73, 1277, 1184])).
% 0.65/0.81 tff(1286,plain,(c0_1(a503) | c0_1(a460) | c2_1(a460)), inference(lemma,lemma(discharge,[]))).
% 0.65/0.81 tff(1287,plain,
% 0.65/0.81 (c0_1(a503)),
% 0.65/0.81 inference(unit_resolution,[status(thm)],[1286, 1182, 1])).
% 0.65/0.81 tff(1288,plain,
% 0.65/0.81 (hskp17 | (~c0_1(a503))),
% 0.65/0.81 inference(unit_resolution,[status(thm)],[1046, 941, 1270, 1269, 1278, 11])).
% 0.65/0.81 tff(1289,plain,
% 0.65/0.81 (hskp17),
% 0.65/0.81 inference(unit_resolution,[status(thm)],[1288, 1287])).
% 0.65/0.81 tff(1290,plain,
% 0.65/0.81 (~c1_1(a494)),
% 0.65/0.81 inference(unit_resolution,[status(thm)],[501, 1289])).
% 0.65/0.81 tff(1291,plain,
% 0.65/0.81 (~c3_1(a494)),
% 0.65/0.81 inference(unit_resolution,[status(thm)],[931, 1289])).
% 0.65/0.81 tff(1292,plain,
% 0.65/0.81 (c1_1(a494) | (~c2_1(a494))),
% 0.65/0.81 inference(unit_resolution,[status(thm)],[1251, 941, 968, 948, 495, 978])).
% 0.65/0.81 tff(1293,plain,
% 0.65/0.81 (~c2_1(a494)),
% 0.65/0.81 inference(unit_resolution,[status(thm)],[1292, 510])).
% 0.65/0.81 tff(1294,plain,
% 0.65/0.81 (~c0_1(a494)),
% 0.65/0.81 inference(unit_resolution,[status(thm)],[1244, 1293, 948, 510, 495])).
% 0.65/0.81 tff(1295,plain,
% 0.65/0.81 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | c0_1(a494) | c1_1(a494) | c3_1(a494) | (~ndr1_0) | c2_1(a494))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c0_1(a494) | c1_1(a494) | c3_1(a494) | (~ndr1_0) | c2_1(a494))),
% 0.65/0.81 inference(rewrite,[status(thm)],[])).
% 0.65/0.81 tff(1296,plain,
% 0.65/0.81 ((hskp0 | (~ndr1_0) | c2_1(a494) | c0_1(a494) | c3_1(a494) | c3_1(a494) | c1_1(a494) | c0_1(a494)) <=> (hskp0 | c0_1(a494) | c1_1(a494) | c3_1(a494) | (~ndr1_0) | c2_1(a494))),
% 0.65/0.81 inference(rewrite,[status(thm)],[])).
% 0.65/0.81 tff(1297,plain,
% 0.65/0.81 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c2_1(a494) | c0_1(a494) | c3_1(a494) | c3_1(a494) | c1_1(a494) | c0_1(a494))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | c0_1(a494) | c1_1(a494) | c3_1(a494) | (~ndr1_0) | c2_1(a494)))),
% 0.65/0.81 inference(monotonicity,[status(thm)],[1296])).
% 0.65/0.81 tff(1298,plain,
% 0.65/0.81 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c2_1(a494) | c0_1(a494) | c3_1(a494) | c3_1(a494) | c1_1(a494) | c0_1(a494))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c0_1(a494) | c1_1(a494) | c3_1(a494) | (~ndr1_0) | c2_1(a494))),
% 0.65/0.81 inference(transitivity,[status(thm)],[1297, 1295])).
% 0.65/0.81 tff(1299,plain,
% 0.65/0.81 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c2_1(a494) | c0_1(a494) | c3_1(a494) | c3_1(a494) | c1_1(a494) | c0_1(a494))),
% 0.65/0.81 inference(quant_inst,[status(thm)],[])).
% 0.65/0.81 tff(1300,plain,
% 0.65/0.81 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c0_1(a494) | c1_1(a494) | c3_1(a494) | (~ndr1_0) | c2_1(a494)),
% 0.65/0.81 inference(modus_ponens,[status(thm)],[1299, 1298])).
% 0.65/0.81 tff(1301,plain,
% 0.65/0.81 ($false),
% 0.65/0.81 inference(unit_resolution,[status(thm)],[1300, 941, 34, 1294, 510, 495, 959, 1293])).
% 0.65/0.81 tff(1302,plain,(c1_1(a494) | hskp0 | c3_1(a494)), inference(lemma,lemma(discharge,[]))).
% 0.65/0.81 tff(1303,plain,
% 0.65/0.81 ($false),
% 0.65/0.81 inference(unit_resolution,[status(thm)],[1302, 1291, 1290, 1183])).
% 0.65/0.81 tff(1304,plain,(c0_1(a460) | c2_1(a460)), inference(lemma,lemma(discharge,[]))).
% 0.65/0.81 tff(1305,plain,
% 0.65/0.81 (c0_1(a460)),
% 0.65/0.81 inference(unit_resolution,[status(thm)],[1304, 1])).
% 0.65/0.81 tff(1306,plain,
% 0.65/0.81 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp12 | c2_1(a460) | c3_1(a460) | (~ndr1_0) | c1_1(a460) | (~c0_1(a460)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | hskp12 | c2_1(a460) | c3_1(a460) | (~ndr1_0) | c1_1(a460) | (~c0_1(a460)))),
% 0.65/0.81 inference(rewrite,[status(thm)],[])).
% 0.65/0.81 tff(1307,plain,
% 0.65/0.81 ((hskp12 | (~ndr1_0) | c2_1(a460) | c3_1(a460) | (~c0_1(a460)) | c3_1(a460) | c1_1(a460) | (~c0_1(a460))) <=> (hskp12 | c2_1(a460) | c3_1(a460) | (~ndr1_0) | c1_1(a460) | (~c0_1(a460)))),
% 0.65/0.81 inference(rewrite,[status(thm)],[])).
% 0.65/0.81 tff(1308,plain,
% 0.65/0.81 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp12 | (~ndr1_0) | c2_1(a460) | c3_1(a460) | (~c0_1(a460)) | c3_1(a460) | c1_1(a460) | (~c0_1(a460)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp12 | c2_1(a460) | c3_1(a460) | (~ndr1_0) | c1_1(a460) | (~c0_1(a460))))),
% 0.65/0.81 inference(monotonicity,[status(thm)],[1307])).
% 0.65/0.81 tff(1309,plain,
% 0.65/0.81 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp12 | (~ndr1_0) | c2_1(a460) | c3_1(a460) | (~c0_1(a460)) | c3_1(a460) | c1_1(a460) | (~c0_1(a460)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | hskp12 | c2_1(a460) | c3_1(a460) | (~ndr1_0) | c1_1(a460) | (~c0_1(a460)))),
% 0.65/0.81 inference(transitivity,[status(thm)],[1308, 1306])).
% 0.65/0.81 tff(1310,plain,
% 0.65/0.81 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp12 | (~ndr1_0) | c2_1(a460) | c3_1(a460) | (~c0_1(a460)) | c3_1(a460) | c1_1(a460) | (~c0_1(a460)))),
% 0.65/0.81 inference(quant_inst,[status(thm)],[])).
% 0.65/0.81 tff(1311,plain,
% 0.65/0.81 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | hskp12 | c2_1(a460) | c3_1(a460) | (~ndr1_0) | c1_1(a460) | (~c0_1(a460))),
% 0.65/0.81 inference(modus_ponens,[status(thm)],[1310, 1309])).
% 0.65/0.81 tff(1312,plain,
% 0.65/0.81 (c1_1(a460)),
% 0.65/0.81 inference(unit_resolution,[status(thm)],[1311, 941, 22, 1305, 1, 1181, 44])).
% 0.65/0.81 tff(1313,plain,
% 0.65/0.81 (hskp21 | (~c1_1(a460))),
% 0.65/0.81 inference(unit_resolution,[status(thm)],[1197, 941, 1125, 1117, 1109, 1, 1181, 1103])).
% 0.65/0.81 tff(1314,plain,
% 0.65/0.81 (hskp21),
% 0.65/0.81 inference(unit_resolution,[status(thm)],[1313, 1312])).
% 0.65/0.81 tff(1315,plain,
% 0.65/0.81 (~c1_1(a512)),
% 0.65/0.81 inference(unit_resolution,[status(thm)],[1137, 1314])).
% 0.65/0.81 tff(1316,plain,
% 0.65/0.81 (c3_1(a512)),
% 0.65/0.81 inference(unit_resolution,[status(thm)],[1145, 1314])).
% 0.65/0.81 tff(1317,plain,
% 0.65/0.81 (c0_1(a512)),
% 0.65/0.81 inference(unit_resolution,[status(thm)],[1153, 1314])).
% 0.65/0.81 tff(1318,plain,
% 0.65/0.81 (hskp3),
% 0.65/0.81 inference(unit_resolution,[status(thm)],[1160, 941, 22, 1317, 1316, 1315, 1057])).
% 0.65/0.81 tff(1319,plain,
% 0.65/0.81 (~c0_1(a466)),
% 0.65/0.81 inference(unit_resolution,[status(thm)],[240, 1318])).
% 0.65/0.81 tff(1320,plain,
% 0.65/0.81 (^[V: $i, U: $i] : refl((hskp7 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V)) <=> (hskp7 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V)))),
% 0.65/0.81 inference(bind,[status(th)],[])).
% 0.65/0.81 tff(1321,plain,
% 0.65/0.81 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V)) <=> ![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))),
% 0.65/0.81 inference(quant_intro,[status(thm)],[1320])).
% 0.65/0.81 tff(1322,plain,
% 0.65/0.81 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V)) <=> ![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))),
% 0.65/0.81 inference(rewrite,[status(thm)],[])).
% 0.65/0.81 tff(1323,plain,
% 0.65/0.81 (^[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(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) | c2_1(U) | c3_1(U) | (~c0_1(U)))), (((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))))), ((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V))), ((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V)))), (((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V))), (((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V)))), ((((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))), ((((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V)))), (((((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp7) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V)) | hskp7))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V)) | hskp7) <=> (hskp7 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))), (((((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp7) <=> (hskp7 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))))),
% 0.65/0.81 inference(bind,[status(th)],[])).
% 0.65/0.81 tff(1324,plain,
% 0.65/0.81 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp7) <=> ![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))),
% 0.65/0.81 inference(quant_intro,[status(thm)],[1323])).
% 0.65/0.81 tff(1325,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause146')).
% 0.65/0.81 tff(1326,plain,
% 0.65/0.81 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))),
% 0.65/0.81 inference(modus_ponens,[status(thm)],[1325, 1324])).
% 0.65/0.81 tff(1327,plain,
% 0.65/0.81 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))),
% 0.65/0.81 inference(modus_ponens,[status(thm)],[1326, 1322])).
% 0.65/0.81 tff(1328,plain,(
% 0.65/0.81 ![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))),
% 0.65/0.81 inference(skolemize,[status(sab)],[1327])).
% 0.65/0.81 tff(1329,plain,
% 0.65/0.81 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))),
% 0.65/0.81 inference(modus_ponens,[status(thm)],[1328, 1321])).
% 0.65/0.82 tff(1330,plain,
% 0.65/0.82 (c1_1(a466)),
% 0.65/0.82 inference(unit_resolution,[status(thm)],[256, 1318])).
% 0.65/0.82 tff(1331,plain,
% 0.65/0.82 (c3_1(a466)),
% 0.65/0.82 inference(unit_resolution,[status(thm)],[248, 1318])).
% 0.65/0.82 tff(1332,plain,
% 0.65/0.82 ((~hskp14) | (~c1_1(a466)) | (~c3_1(a466)) | c0_1(a466) | (~c0_1(a460)) | c2_1(a460) | c3_1(a460)),
% 0.65/0.82 inference(unit_resolution,[status(thm)],[285, 941])).
% 0.65/0.82 tff(1333,plain,
% 0.65/0.82 (~hskp14),
% 0.65/0.82 inference(unit_resolution,[status(thm)],[1332, 1331, 1305, 1319, 1330, 1, 1181])).
% 0.65/0.82 tff(1334,plain,
% 0.65/0.82 (~hskp6),
% 0.65/0.82 inference(unit_resolution,[status(thm)],[1008, 1333, 22])).
% 0.65/0.82 tff(1335,plain,
% 0.65/0.82 (hskp2),
% 0.65/0.82 inference(unit_resolution,[status(thm)],[1082, 1334, 33, 22])).
% 0.65/0.82 tff(1336,plain,
% 0.65/0.82 (~c3_1(a465)),
% 0.65/0.82 inference(unit_resolution,[status(thm)],[620, 1335])).
% 0.65/0.82 tff(1337,plain,
% 0.65/0.82 (~c2_1(a465)),
% 0.65/0.82 inference(unit_resolution,[status(thm)],[626, 1335])).
% 0.65/0.82 tff(1338,plain,
% 0.65/0.82 (~c0_1(a465)),
% 0.65/0.82 inference(unit_resolution,[status(thm)],[632, 1335])).
% 0.65/0.82 tff(1339,plain,
% 0.65/0.82 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp7 | c0_1(a465) | c2_1(a465) | c3_1(a465) | c2_1(a460) | c3_1(a460) | (~ndr1_0) | (~c0_1(a460)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp7 | c0_1(a465) | c2_1(a465) | c3_1(a465) | c2_1(a460) | c3_1(a460) | (~ndr1_0) | (~c0_1(a460)))),
% 0.65/0.82 inference(rewrite,[status(thm)],[])).
% 0.65/0.82 tff(1340,plain,
% 0.65/0.82 ((hskp7 | (~ndr1_0) | c2_1(a460) | c3_1(a460) | (~c0_1(a460)) | c3_1(a465) | c0_1(a465) | c2_1(a465)) <=> (hskp7 | c0_1(a465) | c2_1(a465) | c3_1(a465) | c2_1(a460) | c3_1(a460) | (~ndr1_0) | (~c0_1(a460)))),
% 0.65/0.82 inference(rewrite,[status(thm)],[])).
% 0.65/0.82 tff(1341,plain,
% 0.65/0.82 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp7 | (~ndr1_0) | c2_1(a460) | c3_1(a460) | (~c0_1(a460)) | c3_1(a465) | c0_1(a465) | c2_1(a465))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp7 | c0_1(a465) | c2_1(a465) | c3_1(a465) | c2_1(a460) | c3_1(a460) | (~ndr1_0) | (~c0_1(a460))))),
% 0.65/0.82 inference(monotonicity,[status(thm)],[1340])).
% 0.65/0.82 tff(1342,plain,
% 0.65/0.82 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp7 | (~ndr1_0) | c2_1(a460) | c3_1(a460) | (~c0_1(a460)) | c3_1(a465) | c0_1(a465) | c2_1(a465))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp7 | c0_1(a465) | c2_1(a465) | c3_1(a465) | c2_1(a460) | c3_1(a460) | (~ndr1_0) | (~c0_1(a460)))),
% 0.65/0.82 inference(transitivity,[status(thm)],[1341, 1339])).
% 0.65/0.82 tff(1343,plain,
% 0.65/0.82 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp7 | (~ndr1_0) | c2_1(a460) | c3_1(a460) | (~c0_1(a460)) | c3_1(a465) | c0_1(a465) | c2_1(a465))),
% 0.65/0.82 inference(quant_inst,[status(thm)],[])).
% 0.65/0.82 tff(1344,plain,
% 0.65/0.82 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp7 | c0_1(a465) | c2_1(a465) | c3_1(a465) | c2_1(a460) | c3_1(a460) | (~ndr1_0) | (~c0_1(a460))),
% 0.65/0.82 inference(modus_ponens,[status(thm)],[1343, 1342])).
% 0.65/0.82 tff(1345,plain,
% 0.65/0.82 (hskp7),
% 0.65/0.82 inference(unit_resolution,[status(thm)],[1344, 941, 1305, 1338, 1337, 1336, 1, 1181, 1329])).
% 0.65/0.82 tff(1346,plain,
% 0.65/0.82 (((~hskp7) | (~c2_1(a474))) <=> ((~hskp7) | (~c2_1(a474)))),
% 0.65/0.82 inference(rewrite,[status(thm)],[])).
% 0.65/0.82 tff(1347,plain,
% 0.65/0.82 (((~c2_1(a474)) | (~hskp7)) <=> ((~hskp7) | (~c2_1(a474)))),
% 0.65/0.82 inference(rewrite,[status(thm)],[])).
% 0.65/0.82 tff(1348,axiom,((~c2_1(a474)) | (~hskp7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause111')).
% 0.65/0.82 tff(1349,plain,
% 0.65/0.82 ((~hskp7) | (~c2_1(a474))),
% 0.65/0.82 inference(modus_ponens,[status(thm)],[1348, 1347])).
% 0.65/0.82 tff(1350,plain,
% 0.65/0.82 ((~hskp7) | (~c2_1(a474))),
% 0.65/0.82 inference(modus_ponens,[status(thm)],[1349, 1346])).
% 0.65/0.82 tff(1351,plain,
% 0.65/0.82 (~c2_1(a474)),
% 0.65/0.82 inference(unit_resolution,[status(thm)],[1350, 1345])).
% 0.65/0.82 tff(1352,plain,
% 0.65/0.82 (((~hskp7) | (~c1_1(a474))) <=> ((~hskp7) | (~c1_1(a474)))),
% 0.65/0.82 inference(rewrite,[status(thm)],[])).
% 0.65/0.82 tff(1353,plain,
% 0.65/0.82 (((~c1_1(a474)) | (~hskp7)) <=> ((~hskp7) | (~c1_1(a474)))),
% 0.65/0.82 inference(rewrite,[status(thm)],[])).
% 0.65/0.82 tff(1354,axiom,((~c1_1(a474)) | (~hskp7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause110')).
% 0.65/0.82 tff(1355,plain,
% 0.65/0.82 ((~hskp7) | (~c1_1(a474))),
% 0.65/0.82 inference(modus_ponens,[status(thm)],[1354, 1353])).
% 0.65/0.82 tff(1356,plain,
% 0.65/0.82 ((~hskp7) | (~c1_1(a474))),
% 0.65/0.82 inference(modus_ponens,[status(thm)],[1355, 1352])).
% 0.65/0.82 tff(1357,plain,
% 0.65/0.82 (~c1_1(a474)),
% 0.65/0.82 inference(unit_resolution,[status(thm)],[1356, 1345])).
% 0.65/0.82 tff(1358,plain,
% 0.65/0.82 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c1_1(a474) | c2_1(a474) | c0_1(a466) | c2_1(a460) | c3_1(a460) | (~ndr1_0) | (~c0_1(a460)) | (~c3_1(a466)) | (~c1_1(a466)) | c0_1(a474))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c1_1(a474) | c2_1(a474) | c0_1(a466) | c2_1(a460) | c3_1(a460) | (~ndr1_0) | (~c0_1(a460)) | (~c3_1(a466)) | (~c1_1(a466)) | c0_1(a474))),
% 0.65/0.82 inference(rewrite,[status(thm)],[])).
% 0.65/0.82 tff(1359,plain,
% 0.65/0.82 (((~ndr1_0) | c2_1(a460) | c3_1(a460) | (~c0_1(a460)) | c0_1(a466) | (~c1_1(a466)) | (~c3_1(a466)) | c1_1(a474) | c0_1(a474) | c2_1(a474)) <=> (c1_1(a474) | c2_1(a474) | c0_1(a466) | c2_1(a460) | c3_1(a460) | (~ndr1_0) | (~c0_1(a460)) | (~c3_1(a466)) | (~c1_1(a466)) | c0_1(a474))),
% 0.65/0.82 inference(rewrite,[status(thm)],[])).
% 0.65/0.82 tff(1360,plain,
% 0.65/0.82 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c2_1(a460) | c3_1(a460) | (~c0_1(a460)) | c0_1(a466) | (~c1_1(a466)) | (~c3_1(a466)) | c1_1(a474) | c0_1(a474) | c2_1(a474))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c1_1(a474) | c2_1(a474) | c0_1(a466) | c2_1(a460) | c3_1(a460) | (~ndr1_0) | (~c0_1(a460)) | (~c3_1(a466)) | (~c1_1(a466)) | c0_1(a474)))),
% 0.65/0.82 inference(monotonicity,[status(thm)],[1359])).
% 0.65/0.82 tff(1361,plain,
% 0.65/0.82 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c2_1(a460) | c3_1(a460) | (~c0_1(a460)) | c0_1(a466) | (~c1_1(a466)) | (~c3_1(a466)) | c1_1(a474) | c0_1(a474) | c2_1(a474))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c1_1(a474) | c2_1(a474) | c0_1(a466) | c2_1(a460) | c3_1(a460) | (~ndr1_0) | (~c0_1(a460)) | (~c3_1(a466)) | (~c1_1(a466)) | c0_1(a474))),
% 0.65/0.82 inference(transitivity,[status(thm)],[1360, 1358])).
% 0.65/0.82 tff(1362,plain,
% 0.65/0.82 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c2_1(a460) | c3_1(a460) | (~c0_1(a460)) | c0_1(a466) | (~c1_1(a466)) | (~c3_1(a466)) | c1_1(a474) | c0_1(a474) | c2_1(a474))),
% 0.65/0.82 inference(quant_inst,[status(thm)],[])).
% 0.65/0.82 tff(1363,plain,
% 0.65/0.82 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c1_1(a474) | c2_1(a474) | c0_1(a466) | c2_1(a460) | c3_1(a460) | (~ndr1_0) | (~c0_1(a460)) | (~c3_1(a466)) | (~c1_1(a466)) | c0_1(a474)),
% 0.65/0.82 inference(modus_ponens,[status(thm)],[1362, 1361])).
% 0.65/0.82 tff(1364,plain,
% 0.65/0.82 (c0_1(a474)),
% 0.65/0.82 inference(unit_resolution,[status(thm)],[1363, 941, 1330, 1331, 1305, 1357, 1351, 1319, 1, 1181, 32])).
% 0.65/0.82 tff(1365,plain,
% 0.65/0.82 (hskp20),
% 0.65/0.82 inference(unit_resolution,[status(thm)],[1017, 1334, 22])).
% 0.65/0.82 tff(1366,plain,
% 0.65/0.82 (~c1_1(a503)),
% 0.65/0.82 inference(unit_resolution,[status(thm)],[1023, 1365])).
% 0.65/0.82 tff(1367,plain,
% 0.65/0.82 (c3_1(a503)),
% 0.65/0.82 inference(unit_resolution,[status(thm)],[1031, 1365])).
% 0.65/0.82 tff(1368,plain,
% 0.65/0.82 (c2_1(a503)),
% 0.65/0.82 inference(unit_resolution,[status(thm)],[1039, 1365])).
% 0.65/0.82 tff(1369,plain,
% 0.65/0.82 (~c0_1(a503)),
% 0.65/0.82 inference(unit_resolution,[status(thm)],[1046, 941, 33, 1368, 1367, 1366, 11])).
% 0.65/0.82 tff(1370,plain,
% 0.65/0.82 (c2_1(a466)),
% 0.65/0.82 inference(unit_resolution,[status(thm)],[1170, 941, 1368, 1367, 1330, 1331, 1319, 868, 1369])).
% 0.65/0.82 tff(1371,plain,
% 0.65/0.82 (^[V: $i, U: $i] : refl((hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))) <=> (hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))))),
% 0.65/0.82 inference(bind,[status(th)],[])).
% 0.65/0.82 tff(1372,plain,
% 0.65/0.82 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 0.65/0.82 inference(quant_intro,[status(thm)],[1371])).
% 0.65/0.82 tff(1373,plain,
% 0.65/0.82 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 0.65/0.82 inference(rewrite,[status(thm)],[])).
% 0.65/0.82 tff(1374,plain,
% 0.65/0.82 (^[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(V))) <=> (((~ndr1_0) | (~c0_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(V)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(V))))), (((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)))), (((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V))))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V))))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V))))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | hskp9) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))) | hskp9))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))) | hskp9) <=> (hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | hskp9) <=> (hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))))),
% 0.65/0.82 inference(bind,[status(th)],[])).
% 0.65/0.82 tff(1375,plain,
% 0.65/0.82 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | hskp9) <=> ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 0.65/0.82 inference(quant_intro,[status(thm)],[1374])).
% 0.65/0.82 tff(1376,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | hskp9)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause156')).
% 0.65/0.82 tff(1377,plain,
% 0.65/0.82 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 0.65/0.82 inference(modus_ponens,[status(thm)],[1376, 1375])).
% 0.65/0.82 tff(1378,plain,
% 0.65/0.82 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 0.65/0.82 inference(modus_ponens,[status(thm)],[1377, 1373])).
% 0.65/0.82 tff(1379,plain,(
% 0.65/0.82 ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 0.65/0.82 inference(skolemize,[status(sab)],[1378])).
% 0.65/0.82 tff(1380,plain,
% 0.65/0.82 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 0.65/0.82 inference(modus_ponens,[status(thm)],[1379, 1372])).
% 0.65/0.82 tff(1381,plain,
% 0.65/0.82 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp9 | c1_1(a474) | c2_1(a474) | c0_1(a466) | (~ndr1_0) | (~c2_1(a466)) | (~c1_1(a466)) | (~c0_1(a474)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp9 | c1_1(a474) | c2_1(a474) | c0_1(a466) | (~ndr1_0) | (~c2_1(a466)) | (~c1_1(a466)) | (~c0_1(a474)))),
% 0.65/0.82 inference(rewrite,[status(thm)],[])).
% 0.65/0.82 tff(1382,plain,
% 0.65/0.82 ((hskp9 | (~ndr1_0) | c2_1(a474) | c1_1(a474) | (~c0_1(a474)) | c0_1(a466) | (~c1_1(a466)) | (~c2_1(a466))) <=> (hskp9 | c1_1(a474) | c2_1(a474) | c0_1(a466) | (~ndr1_0) | (~c2_1(a466)) | (~c1_1(a466)) | (~c0_1(a474)))),
% 0.65/0.82 inference(rewrite,[status(thm)],[])).
% 0.65/0.82 tff(1383,plain,
% 0.65/0.82 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp9 | (~ndr1_0) | c2_1(a474) | c1_1(a474) | (~c0_1(a474)) | c0_1(a466) | (~c1_1(a466)) | (~c2_1(a466)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp9 | c1_1(a474) | c2_1(a474) | c0_1(a466) | (~ndr1_0) | (~c2_1(a466)) | (~c1_1(a466)) | (~c0_1(a474))))),
% 0.65/0.82 inference(monotonicity,[status(thm)],[1382])).
% 0.65/0.82 tff(1384,plain,
% 0.65/0.82 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp9 | (~ndr1_0) | c2_1(a474) | c1_1(a474) | (~c0_1(a474)) | c0_1(a466) | (~c1_1(a466)) | (~c2_1(a466)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp9 | c1_1(a474) | c2_1(a474) | c0_1(a466) | (~ndr1_0) | (~c2_1(a466)) | (~c1_1(a466)) | (~c0_1(a474)))),
% 0.65/0.82 inference(transitivity,[status(thm)],[1383, 1381])).
% 0.65/0.82 tff(1385,plain,
% 0.65/0.82 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp9 | (~ndr1_0) | c2_1(a474) | c1_1(a474) | (~c0_1(a474)) | c0_1(a466) | (~c1_1(a466)) | (~c2_1(a466)))),
% 0.65/0.82 inference(quant_inst,[status(thm)],[])).
% 0.65/0.82 tff(1386,plain,
% 0.65/0.82 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp9 | c1_1(a474) | c2_1(a474) | c0_1(a466) | (~ndr1_0) | (~c2_1(a466)) | (~c1_1(a466)) | (~c0_1(a474))),
% 0.65/0.82 inference(modus_ponens,[status(thm)],[1385, 1384])).
% 0.65/0.82 tff(1387,plain,
% 0.65/0.82 (hskp9),
% 0.65/0.82 inference(unit_resolution,[status(thm)],[1386, 941, 1330, 1357, 1351, 1319, 1380, 1370, 1364])).
% 0.65/0.82 tff(1388,plain,
% 0.65/0.82 (((~hskp9) | (~c1_1(a476))) <=> ((~hskp9) | (~c1_1(a476)))),
% 0.65/0.82 inference(rewrite,[status(thm)],[])).
% 0.65/0.82 tff(1389,plain,
% 0.65/0.82 (((~c1_1(a476)) | (~hskp9)) <=> ((~hskp9) | (~c1_1(a476)))),
% 0.65/0.82 inference(rewrite,[status(thm)],[])).
% 0.65/0.82 tff(1390,axiom,((~c1_1(a476)) | (~hskp9)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause108')).
% 0.65/0.82 tff(1391,plain,
% 0.65/0.82 ((~hskp9) | (~c1_1(a476))),
% 0.65/0.82 inference(modus_ponens,[status(thm)],[1390, 1389])).
% 0.65/0.82 tff(1392,plain,
% 0.65/0.82 ((~hskp9) | (~c1_1(a476))),
% 0.65/0.82 inference(modus_ponens,[status(thm)],[1391, 1388])).
% 0.65/0.82 tff(1393,plain,
% 0.65/0.82 (~c1_1(a476)),
% 0.65/0.82 inference(unit_resolution,[status(thm)],[1392, 1387])).
% 0.65/0.82 tff(1394,plain,
% 0.65/0.82 (((~hskp9) | c2_1(a476)) <=> ((~hskp9) | c2_1(a476))),
% 0.65/0.82 inference(rewrite,[status(thm)],[])).
% 0.65/0.82 tff(1395,axiom,((~hskp9) | c2_1(a476)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause71')).
% 0.65/0.82 tff(1396,plain,
% 0.65/0.82 ((~hskp9) | c2_1(a476)),
% 0.65/0.82 inference(modus_ponens,[status(thm)],[1395, 1394])).
% 0.65/0.82 tff(1397,plain,
% 0.65/0.82 ((~hskp9) | c2_1(a476)),
% 0.65/0.82 inference(modus_ponens,[status(thm)],[1396, 1394])).
% 0.65/0.82 tff(1398,plain,
% 0.65/0.82 ((~hskp9) | c2_1(a476)),
% 0.65/0.82 inference(modus_ponens,[status(thm)],[1397, 1394])).
% 0.65/0.82 tff(1399,plain,
% 0.65/0.82 ((~hskp9) | c2_1(a476)),
% 0.65/0.82 inference(modus_ponens,[status(thm)],[1398, 1394])).
% 0.65/0.82 tff(1400,plain,
% 0.65/0.82 ((~hskp9) | c2_1(a476)),
% 0.65/0.82 inference(modus_ponens,[status(thm)],[1399, 1394])).
% 0.65/0.82 tff(1401,plain,
% 0.65/0.82 (c2_1(a476)),
% 0.65/0.82 inference(unit_resolution,[status(thm)],[1400, 1387])).
% 0.65/0.82 tff(1402,plain,
% 0.65/0.82 (((~hskp9) | c0_1(a476)) <=> ((~hskp9) | c0_1(a476))),
% 0.65/0.82 inference(rewrite,[status(thm)],[])).
% 0.65/0.82 tff(1403,axiom,((~hskp9) | c0_1(a476)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause70')).
% 0.65/0.82 tff(1404,plain,
% 0.65/0.82 ((~hskp9) | c0_1(a476)),
% 0.65/0.82 inference(modus_ponens,[status(thm)],[1403, 1402])).
% 0.65/0.82 tff(1405,plain,
% 0.65/0.82 ((~hskp9) | c0_1(a476)),
% 0.65/0.82 inference(modus_ponens,[status(thm)],[1404, 1402])).
% 0.65/0.82 tff(1406,plain,
% 0.65/0.82 ((~hskp9) | c0_1(a476)),
% 0.65/0.82 inference(modus_ponens,[status(thm)],[1405, 1402])).
% 0.65/0.82 tff(1407,plain,
% 0.65/0.82 ((~hskp9) | c0_1(a476)),
% 0.65/0.82 inference(modus_ponens,[status(thm)],[1406, 1402])).
% 0.65/0.82 tff(1408,plain,
% 0.65/0.82 ((~hskp9) | c0_1(a476)),
% 0.65/0.82 inference(modus_ponens,[status(thm)],[1407, 1402])).
% 0.65/0.82 tff(1409,plain,
% 0.65/0.82 (c0_1(a476)),
% 0.65/0.82 inference(unit_resolution,[status(thm)],[1408, 1387])).
% 0.65/0.82 tff(1410,plain,
% 0.65/0.82 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp17 | c1_1(a476) | (~ndr1_0) | (~c3_1(a476)) | (~c2_1(a476)) | (~c0_1(a476)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))) | hskp17 | c1_1(a476) | (~ndr1_0) | (~c3_1(a476)) | (~c2_1(a476)) | (~c0_1(a476)))),
% 0.65/0.82 inference(rewrite,[status(thm)],[])).
% 0.65/0.82 tff(1411,plain,
% 0.65/0.82 ((hskp17 | (~ndr1_0) | (~c2_1(a476)) | (~c0_1(a476)) | (~c3_1(a476)) | c1_1(a476) | (~c0_1(a476)) | (~c2_1(a476))) <=> (hskp17 | c1_1(a476) | (~ndr1_0) | (~c3_1(a476)) | (~c2_1(a476)) | (~c0_1(a476)))),
% 0.65/0.82 inference(rewrite,[status(thm)],[])).
% 0.65/0.82 tff(1412,plain,
% 0.65/0.82 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp17 | (~ndr1_0) | (~c2_1(a476)) | (~c0_1(a476)) | (~c3_1(a476)) | c1_1(a476) | (~c0_1(a476)) | (~c2_1(a476)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp17 | c1_1(a476) | (~ndr1_0) | (~c3_1(a476)) | (~c2_1(a476)) | (~c0_1(a476))))),
% 0.65/0.82 inference(monotonicity,[status(thm)],[1411])).
% 0.65/0.82 tff(1413,plain,
% 0.65/0.82 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp17 | (~ndr1_0) | (~c2_1(a476)) | (~c0_1(a476)) | (~c3_1(a476)) | c1_1(a476) | (~c0_1(a476)) | (~c2_1(a476)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))) | hskp17 | c1_1(a476) | (~ndr1_0) | (~c3_1(a476)) | (~c2_1(a476)) | (~c0_1(a476)))),
% 0.65/0.82 inference(transitivity,[status(thm)],[1412, 1410])).
% 0.65/0.82 tff(1414,plain,
% 0.65/0.82 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp17 | (~ndr1_0) | (~c2_1(a476)) | (~c0_1(a476)) | (~c3_1(a476)) | c1_1(a476) | (~c0_1(a476)) | (~c2_1(a476)))),
% 0.65/0.82 inference(quant_inst,[status(thm)],[])).
% 0.65/0.82 tff(1415,plain,
% 0.65/0.82 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))) | hskp17 | c1_1(a476) | (~ndr1_0) | (~c3_1(a476)) | (~c2_1(a476)) | (~c0_1(a476))),
% 0.65/0.82 inference(modus_ponens,[status(thm)],[1414, 1413])).
% 0.65/0.82 tff(1416,plain,
% 0.65/0.82 (~c3_1(a476)),
% 0.65/0.82 inference(unit_resolution,[status(thm)],[1415, 941, 33, 1409, 1401, 1393, 11])).
% 0.65/0.82 tff(1417,plain,
% 0.65/0.82 (((~![U: $i] : (hskp14 | hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp14 | hskp12 | c1_1(a476) | (~ndr1_0) | c3_1(a476) | (~c2_1(a476)))) <=> ((~![U: $i] : (hskp14 | hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | hskp14 | hskp12 | c1_1(a476) | (~ndr1_0) | c3_1(a476) | (~c2_1(a476)))),
% 0.65/0.82 inference(rewrite,[status(thm)],[])).
% 0.65/0.82 tff(1418,plain,
% 0.65/0.82 ((hskp14 | hskp12 | (~ndr1_0) | c1_1(a476) | c3_1(a476) | (~c2_1(a476))) <=> (hskp14 | hskp12 | c1_1(a476) | (~ndr1_0) | c3_1(a476) | (~c2_1(a476)))),
% 0.65/0.82 inference(rewrite,[status(thm)],[])).
% 0.65/0.82 tff(1419,plain,
% 0.65/0.82 (((~![U: $i] : (hskp14 | hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp14 | hskp12 | (~ndr1_0) | c1_1(a476) | c3_1(a476) | (~c2_1(a476)))) <=> ((~![U: $i] : (hskp14 | hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp14 | hskp12 | c1_1(a476) | (~ndr1_0) | c3_1(a476) | (~c2_1(a476))))),
% 0.65/0.82 inference(monotonicity,[status(thm)],[1418])).
% 0.65/0.82 tff(1420,plain,
% 0.65/0.82 (((~![U: $i] : (hskp14 | hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp14 | hskp12 | (~ndr1_0) | c1_1(a476) | c3_1(a476) | (~c2_1(a476)))) <=> ((~![U: $i] : (hskp14 | hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | hskp14 | hskp12 | c1_1(a476) | (~ndr1_0) | c3_1(a476) | (~c2_1(a476)))),
% 0.65/0.82 inference(transitivity,[status(thm)],[1419, 1417])).
% 0.65/0.82 tff(1421,plain,
% 0.65/0.82 ((~![U: $i] : (hskp14 | hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp14 | hskp12 | (~ndr1_0) | c1_1(a476) | c3_1(a476) | (~c2_1(a476)))),
% 0.65/0.82 inference(quant_inst,[status(thm)],[])).
% 0.65/0.82 tff(1422,plain,
% 0.65/0.82 ((~![U: $i] : (hskp14 | hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | hskp14 | hskp12 | c1_1(a476) | (~ndr1_0) | c3_1(a476) | (~c2_1(a476))),
% 0.65/0.82 inference(modus_ponens,[status(thm)],[1421, 1420])).
% 0.65/0.82 tff(1423,plain,
% 0.65/0.82 ($false),
% 0.65/0.82 inference(unit_resolution,[status(thm)],[1422, 941, 1333, 22, 1401, 1393, 978, 1416])).
% 0.65/0.82 tff(1424,plain,(hskp17 | hskp12 | c2_1(a460)), inference(lemma,lemma(discharge,[]))).
% 0.65/0.82 tff(1425,plain,
% 0.65/0.82 (hskp17),
% 0.65/0.82 inference(unit_resolution,[status(thm)],[1424, 22, 1])).
% 0.65/0.82 tff(1426,plain,
% 0.65/0.82 (~c1_1(a494)),
% 0.65/0.82 inference(unit_resolution,[status(thm)],[501, 1425])).
% 0.65/0.82 tff(1427,plain,
% 0.65/0.82 (~c3_1(a494)),
% 0.65/0.82 inference(unit_resolution,[status(thm)],[931, 1425])).
% 0.65/0.82 tff(1428,plain,
% 0.65/0.82 (hskp0),
% 0.65/0.82 inference(unit_resolution,[status(thm)],[1302, 510, 495])).
% 0.65/0.82 tff(1429,plain,
% 0.65/0.82 (~c3_1(a460)),
% 0.65/0.82 inference(unit_resolution,[status(thm)],[207, 1428])).
% 0.65/0.82 tff(1430,plain,
% 0.65/0.82 (c1_1(a460)),
% 0.65/0.82 inference(unit_resolution,[status(thm)],[1311, 941, 22, 1305, 1, 1429, 44])).
% 0.65/0.82 tff(1431,plain,
% 0.65/0.82 (hskp21 | (~c1_1(a460))),
% 0.65/0.82 inference(unit_resolution,[status(thm)],[1197, 941, 1125, 1117, 1109, 1, 1429, 1103])).
% 0.65/0.82 tff(1432,plain,
% 0.65/0.82 (hskp21),
% 0.65/0.82 inference(unit_resolution,[status(thm)],[1431, 1430])).
% 0.65/0.82 tff(1433,plain,
% 0.65/0.82 (~c1_1(a512)),
% 0.65/0.82 inference(unit_resolution,[status(thm)],[1137, 1432])).
% 0.65/0.82 tff(1434,plain,
% 0.65/0.82 (c3_1(a512)),
% 0.65/0.82 inference(unit_resolution,[status(thm)],[1145, 1432])).
% 0.65/0.82 tff(1435,plain,
% 0.65/0.82 (c0_1(a512)),
% 0.65/0.82 inference(unit_resolution,[status(thm)],[1153, 1432])).
% 0.65/0.82 tff(1436,plain,
% 0.65/0.82 (hskp3),
% 0.65/0.82 inference(unit_resolution,[status(thm)],[1160, 941, 22, 1435, 1434, 1433, 1057])).
% 0.65/0.82 tff(1437,plain,
% 0.65/0.82 (c1_1(a466)),
% 0.65/0.82 inference(unit_resolution,[status(thm)],[256, 1436])).
% 0.65/0.82 tff(1438,plain,
% 0.65/0.82 (~c0_1(a466)),
% 0.65/0.82 inference(unit_resolution,[status(thm)],[240, 1436])).
% 0.65/0.82 tff(1439,plain,
% 0.65/0.82 (c3_1(a466)),
% 0.65/0.82 inference(unit_resolution,[status(thm)],[248, 1436])).
% 0.65/0.82 tff(1440,plain,
% 0.65/0.82 (~hskp14),
% 0.65/0.82 inference(unit_resolution,[status(thm)],[1332, 1439, 1305, 1438, 1437, 1, 1429])).
% 0.65/0.82 tff(1441,plain,
% 0.65/0.82 (hskp14 | c1_1(a494) | (~c2_1(a494))),
% 0.65/0.82 inference(unit_resolution,[status(thm)],[1251, 941, 22, 495, 978])).
% 0.65/0.83 tff(1442,plain,
% 0.65/0.83 (~c2_1(a494)),
% 0.65/0.83 inference(unit_resolution,[status(thm)],[1441, 1440, 510])).
% 0.65/0.83 tff(1443,plain,
% 0.65/0.83 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp12 | (~c0_1(a494)) | c1_1(a494) | c3_1(a494) | c2_1(a460) | c3_1(a460) | (~ndr1_0) | (~c0_1(a460)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | hskp12 | (~c0_1(a494)) | c1_1(a494) | c3_1(a494) | c2_1(a460) | c3_1(a460) | (~ndr1_0) | (~c0_1(a460)))),
% 0.65/0.83 inference(rewrite,[status(thm)],[])).
% 0.65/0.83 tff(1444,plain,
% 0.65/0.83 ((hskp12 | (~ndr1_0) | c2_1(a460) | c3_1(a460) | (~c0_1(a460)) | c3_1(a494) | c1_1(a494) | (~c0_1(a494))) <=> (hskp12 | (~c0_1(a494)) | c1_1(a494) | c3_1(a494) | c2_1(a460) | c3_1(a460) | (~ndr1_0) | (~c0_1(a460)))),
% 0.65/0.83 inference(rewrite,[status(thm)],[])).
% 0.65/0.83 tff(1445,plain,
% 0.65/0.83 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp12 | (~ndr1_0) | c2_1(a460) | c3_1(a460) | (~c0_1(a460)) | c3_1(a494) | c1_1(a494) | (~c0_1(a494)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp12 | (~c0_1(a494)) | c1_1(a494) | c3_1(a494) | c2_1(a460) | c3_1(a460) | (~ndr1_0) | (~c0_1(a460))))),
% 0.65/0.83 inference(monotonicity,[status(thm)],[1444])).
% 0.65/0.83 tff(1446,plain,
% 0.65/0.83 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp12 | (~ndr1_0) | c2_1(a460) | c3_1(a460) | (~c0_1(a460)) | c3_1(a494) | c1_1(a494) | (~c0_1(a494)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | hskp12 | (~c0_1(a494)) | c1_1(a494) | c3_1(a494) | c2_1(a460) | c3_1(a460) | (~ndr1_0) | (~c0_1(a460)))),
% 0.65/0.83 inference(transitivity,[status(thm)],[1445, 1443])).
% 0.65/0.83 tff(1447,plain,
% 0.65/0.83 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp12 | (~ndr1_0) | c2_1(a460) | c3_1(a460) | (~c0_1(a460)) | c3_1(a494) | c1_1(a494) | (~c0_1(a494)))),
% 0.65/0.83 inference(quant_inst,[status(thm)],[])).
% 0.65/0.83 tff(1448,plain,
% 0.65/0.83 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | hskp12 | (~c0_1(a494)) | c1_1(a494) | c3_1(a494) | c2_1(a460) | c3_1(a460) | (~ndr1_0) | (~c0_1(a460))),
% 0.65/0.83 inference(modus_ponens,[status(thm)],[1447, 1446])).
% 0.65/0.83 tff(1449,plain,
% 0.65/0.83 ((~c0_1(a494)) | c1_1(a494) | c3_1(a460)),
% 0.65/0.83 inference(unit_resolution,[status(thm)],[1448, 941, 22, 1305, 495, 1, 44])).
% 0.65/0.83 tff(1450,plain,
% 0.65/0.83 (~c0_1(a494)),
% 0.65/0.83 inference(unit_resolution,[status(thm)],[1449, 1429, 510])).
% 0.65/0.83 tff(1451,plain,
% 0.65/0.83 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a494) | c1_1(a494) | c0_1(a466) | c2_1(a460) | c3_1(a460) | (~ndr1_0) | (~c0_1(a460)) | (~c3_1(a466)) | (~c1_1(a466)) | c2_1(a494))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c0_1(a494) | c1_1(a494) | c0_1(a466) | c2_1(a460) | c3_1(a460) | (~ndr1_0) | (~c0_1(a460)) | (~c3_1(a466)) | (~c1_1(a466)) | c2_1(a494))),
% 0.65/0.83 inference(rewrite,[status(thm)],[])).
% 0.65/0.83 tff(1452,plain,
% 0.65/0.83 (((~ndr1_0) | c2_1(a460) | c3_1(a460) | (~c0_1(a460)) | c0_1(a466) | (~c1_1(a466)) | (~c3_1(a466)) | c1_1(a494) | c0_1(a494) | c2_1(a494)) <=> (c0_1(a494) | c1_1(a494) | c0_1(a466) | c2_1(a460) | c3_1(a460) | (~ndr1_0) | (~c0_1(a460)) | (~c3_1(a466)) | (~c1_1(a466)) | c2_1(a494))),
% 0.65/0.83 inference(rewrite,[status(thm)],[])).
% 0.65/0.83 tff(1453,plain,
% 0.65/0.83 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c2_1(a460) | c3_1(a460) | (~c0_1(a460)) | c0_1(a466) | (~c1_1(a466)) | (~c3_1(a466)) | c1_1(a494) | c0_1(a494) | c2_1(a494))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a494) | c1_1(a494) | c0_1(a466) | c2_1(a460) | c3_1(a460) | (~ndr1_0) | (~c0_1(a460)) | (~c3_1(a466)) | (~c1_1(a466)) | c2_1(a494)))),
% 0.65/0.83 inference(monotonicity,[status(thm)],[1452])).
% 0.65/0.83 tff(1454,plain,
% 0.65/0.83 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c2_1(a460) | c3_1(a460) | (~c0_1(a460)) | c0_1(a466) | (~c1_1(a466)) | (~c3_1(a466)) | c1_1(a494) | c0_1(a494) | c2_1(a494))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c0_1(a494) | c1_1(a494) | c0_1(a466) | c2_1(a460) | c3_1(a460) | (~ndr1_0) | (~c0_1(a460)) | (~c3_1(a466)) | (~c1_1(a466)) | c2_1(a494))),
% 0.65/0.83 inference(transitivity,[status(thm)],[1453, 1451])).
% 0.65/0.83 tff(1455,plain,
% 0.65/0.83 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c2_1(a460) | c3_1(a460) | (~c0_1(a460)) | c0_1(a466) | (~c1_1(a466)) | (~c3_1(a466)) | c1_1(a494) | c0_1(a494) | c2_1(a494))),
% 0.65/0.83 inference(quant_inst,[status(thm)],[])).
% 0.65/0.83 tff(1456,plain,
% 0.65/0.83 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c0_1(a494) | c1_1(a494) | c0_1(a466) | c2_1(a460) | c3_1(a460) | (~ndr1_0) | (~c0_1(a460)) | (~c3_1(a466)) | (~c1_1(a466)) | c2_1(a494)),
% 0.65/0.83 inference(modus_ponens,[status(thm)],[1455, 1454])).
% 0.65/0.83 tff(1457,plain,
% 0.65/0.83 ($false),
% 0.65/0.83 inference(unit_resolution,[status(thm)],[1456, 941, 1437, 1439, 1305, 1450, 510, 1438, 1, 1429, 32, 1442])).
% 0.65/0.83 tff(1458,plain,(c1_1(a494) | c2_1(a460) | hskp12 | c3_1(a494)), inference(lemma,lemma(discharge,[]))).
% 0.65/0.83 tff(1459,plain,
% 0.65/0.83 ($false),
% 0.65/0.83 inference(unit_resolution,[status(thm)],[1458, 1427, 1426, 22, 1])).
% 0.65/0.83 tff(1460,plain,(hskp12 | c2_1(a460)), inference(lemma,lemma(discharge,[]))).
% 0.65/0.83 tff(1461,plain,
% 0.65/0.83 (hskp12),
% 0.65/0.83 inference(unit_resolution,[status(thm)],[1460, 1])).
% 0.65/0.83 tff(1462,plain,
% 0.65/0.83 (hskp0),
% 0.65/0.83 inference(unit_resolution,[status(thm)],[947, 1461])).
% 0.65/0.83 tff(1463,plain,
% 0.65/0.83 (~c3_1(a460)),
% 0.65/0.83 inference(unit_resolution,[status(thm)],[207, 1462])).
% 0.65/0.83 tff(1464,plain,
% 0.65/0.83 (~c2_1(a480)),
% 0.65/0.83 inference(unit_resolution,[status(thm)],[89, 1461])).
% 0.65/0.83 tff(1465,plain,
% 0.65/0.83 (~c1_1(a480)),
% 0.65/0.83 inference(unit_resolution,[status(thm)],[95, 1461])).
% 0.65/0.83 tff(1466,plain,
% 0.65/0.83 (~c0_1(a480)),
% 0.65/0.83 inference(unit_resolution,[status(thm)],[101, 1461])).
% 0.65/0.83 tff(1467,plain,
% 0.65/0.83 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a480) | c1_1(a480) | c2_1(a480) | c0_1(a466) | c2_1(a460) | c3_1(a460) | (~ndr1_0) | (~c0_1(a460)) | (~c3_1(a466)) | (~c1_1(a466)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c0_1(a480) | c1_1(a480) | c2_1(a480) | c0_1(a466) | c2_1(a460) | c3_1(a460) | (~ndr1_0) | (~c0_1(a460)) | (~c3_1(a466)) | (~c1_1(a466)))),
% 0.65/0.83 inference(rewrite,[status(thm)],[])).
% 0.65/0.83 tff(1468,plain,
% 0.65/0.83 (((~ndr1_0) | c2_1(a460) | c3_1(a460) | (~c0_1(a460)) | c0_1(a466) | (~c1_1(a466)) | (~c3_1(a466)) | c1_1(a480) | c0_1(a480) | c2_1(a480)) <=> (c0_1(a480) | c1_1(a480) | c2_1(a480) | c0_1(a466) | c2_1(a460) | c3_1(a460) | (~ndr1_0) | (~c0_1(a460)) | (~c3_1(a466)) | (~c1_1(a466)))),
% 0.65/0.83 inference(rewrite,[status(thm)],[])).
% 0.65/0.83 tff(1469,plain,
% 0.65/0.83 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c2_1(a460) | c3_1(a460) | (~c0_1(a460)) | c0_1(a466) | (~c1_1(a466)) | (~c3_1(a466)) | c1_1(a480) | c0_1(a480) | c2_1(a480))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a480) | c1_1(a480) | c2_1(a480) | c0_1(a466) | c2_1(a460) | c3_1(a460) | (~ndr1_0) | (~c0_1(a460)) | (~c3_1(a466)) | (~c1_1(a466))))),
% 0.65/0.83 inference(monotonicity,[status(thm)],[1468])).
% 0.65/0.83 tff(1470,plain,
% 0.65/0.83 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c2_1(a460) | c3_1(a460) | (~c0_1(a460)) | c0_1(a466) | (~c1_1(a466)) | (~c3_1(a466)) | c1_1(a480) | c0_1(a480) | c2_1(a480))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c0_1(a480) | c1_1(a480) | c2_1(a480) | c0_1(a466) | c2_1(a460) | c3_1(a460) | (~ndr1_0) | (~c0_1(a460)) | (~c3_1(a466)) | (~c1_1(a466)))),
% 0.65/0.83 inference(transitivity,[status(thm)],[1469, 1467])).
% 0.65/0.83 tff(1471,plain,
% 0.65/0.83 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c2_1(a460) | c3_1(a460) | (~c0_1(a460)) | c0_1(a466) | (~c1_1(a466)) | (~c3_1(a466)) | c1_1(a480) | c0_1(a480) | c2_1(a480))),
% 0.65/0.83 inference(quant_inst,[status(thm)],[])).
% 0.65/0.83 tff(1472,plain,
% 0.65/0.83 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c0_1(a480) | c1_1(a480) | c2_1(a480) | c0_1(a466) | c2_1(a460) | c3_1(a460) | (~ndr1_0) | (~c0_1(a460)) | (~c3_1(a466)) | (~c1_1(a466))),
% 0.65/0.83 inference(modus_ponens,[status(thm)],[1471, 1470])).
% 0.65/0.83 tff(1473,plain,
% 0.65/0.83 ($false),
% 0.65/0.83 inference(unit_resolution,[status(thm)],[1472, 941, 257, 249, 1305, 1466, 1465, 1464, 241, 1, 1463, 32])).
% 0.65/0.83 tff(1474,plain,((~hskp3) | c2_1(a460)), inference(lemma,lemma(discharge,[]))).
% 0.65/0.83 tff(1475,plain,
% 0.65/0.83 (~hskp3),
% 0.65/0.83 inference(unit_resolution,[status(thm)],[1474, 1])).
% 0.65/0.83 tff(1476,plain,
% 0.65/0.83 ((~hskp27) | hskp3 | (~c0_1(a460)) | c2_1(a460) | c3_1(a460)),
% 0.65/0.83 inference(unit_resolution,[status(thm)],[362, 941])).
% 0.65/0.83 tff(1477,plain,
% 0.65/0.83 (~hskp27),
% 0.65/0.83 inference(unit_resolution,[status(thm)],[1476, 1475, 1305, 1, 1463])).
% 0.65/0.83 tff(1478,plain,
% 0.65/0.83 (hskp22),
% 0.65/0.83 inference(unit_resolution,[status(thm)],[374, 33, 1477])).
% 0.65/0.83 tff(1479,plain,
% 0.65/0.83 (c1_1(a524)),
% 0.65/0.83 inference(unit_resolution,[status(thm)],[382, 1478])).
% 0.65/0.83 tff(1480,plain,
% 0.65/0.83 (c0_1(a524)),
% 0.65/0.83 inference(unit_resolution,[status(thm)],[390, 1478])).
% 0.65/0.83 tff(1481,plain,
% 0.65/0.83 (~c3_1(a524)),
% 0.65/0.83 inference(unit_resolution,[status(thm)],[397, 941, 1475, 1480, 1479, 1305, 1, 1463, 21])).
% 0.65/0.83 tff(1482,plain,
% 0.65/0.83 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp3 | c2_1(a460) | c3_1(a460) | (~ndr1_0) | (~c0_1(a468)) | (~c1_1(a468)) | (~c3_1(a468)) | (~c0_1(a460)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | hskp3 | c2_1(a460) | c3_1(a460) | (~ndr1_0) | (~c0_1(a468)) | (~c1_1(a468)) | (~c3_1(a468)) | (~c0_1(a460)))),
% 0.65/0.83 inference(rewrite,[status(thm)],[])).
% 0.65/0.83 tff(1483,plain,
% 0.65/0.83 ((hskp3 | (~ndr1_0) | (~c0_1(a468)) | (~c3_1(a468)) | (~c1_1(a468)) | c3_1(a460) | c2_1(a460) | (~c0_1(a460))) <=> (hskp3 | c2_1(a460) | c3_1(a460) | (~ndr1_0) | (~c0_1(a468)) | (~c1_1(a468)) | (~c3_1(a468)) | (~c0_1(a460)))),
% 0.65/0.83 inference(rewrite,[status(thm)],[])).
% 0.65/0.83 tff(1484,plain,
% 0.65/0.83 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp3 | (~ndr1_0) | (~c0_1(a468)) | (~c3_1(a468)) | (~c1_1(a468)) | c3_1(a460) | c2_1(a460) | (~c0_1(a460)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp3 | c2_1(a460) | c3_1(a460) | (~ndr1_0) | (~c0_1(a468)) | (~c1_1(a468)) | (~c3_1(a468)) | (~c0_1(a460))))),
% 0.65/0.83 inference(monotonicity,[status(thm)],[1483])).
% 0.65/0.83 tff(1485,plain,
% 0.65/0.83 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp3 | (~ndr1_0) | (~c0_1(a468)) | (~c3_1(a468)) | (~c1_1(a468)) | c3_1(a460) | c2_1(a460) | (~c0_1(a460)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | hskp3 | c2_1(a460) | c3_1(a460) | (~ndr1_0) | (~c0_1(a468)) | (~c1_1(a468)) | (~c3_1(a468)) | (~c0_1(a460)))),
% 0.65/0.83 inference(transitivity,[status(thm)],[1484, 1482])).
% 0.65/0.83 tff(1486,plain,
% 0.65/0.83 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp3 | (~ndr1_0) | (~c0_1(a468)) | (~c3_1(a468)) | (~c1_1(a468)) | c3_1(a460) | c2_1(a460) | (~c0_1(a460)))),
% 0.65/0.83 inference(quant_inst,[status(thm)],[])).
% 0.65/0.83 tff(1487,plain,
% 0.65/0.83 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | hskp3 | c2_1(a460) | c3_1(a460) | (~ndr1_0) | (~c0_1(a468)) | (~c1_1(a468)) | (~c3_1(a468)) | (~c0_1(a460))),
% 0.65/0.83 inference(modus_ponens,[status(thm)],[1486, 1485])).
% 0.65/0.83 tff(1488,plain,
% 0.65/0.83 (hskp3 | (~c1_1(a468))),
% 0.65/0.83 inference(unit_resolution,[status(thm)],[1487, 941, 1125, 1117, 1305, 1, 1463, 21])).
% 0.65/0.83 tff(1489,plain,
% 0.65/0.83 (~c1_1(a468)),
% 0.65/0.83 inference(unit_resolution,[status(thm)],[1488, 1475])).
% 0.65/0.83 tff(1490,plain,
% 0.65/0.83 (^[U: $i] : refl((hskp17 | hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) <=> (hskp17 | hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))))),
% 0.65/0.83 inference(bind,[status(th)],[])).
% 0.65/0.83 tff(1491,plain,
% 0.65/0.83 (![U: $i] : (hskp17 | hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp17 | hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 0.65/0.83 inference(quant_intro,[status(thm)],[1490])).
% 0.65/0.83 tff(1492,plain,
% 0.65/0.83 (![U: $i] : (hskp17 | hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp17 | hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 0.65/0.83 inference(rewrite,[status(thm)],[])).
% 0.65/0.83 tff(1493,plain,
% 0.65/0.83 (^[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)) | hskp16) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) | hskp16))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) | hskp16) <=> (hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))), ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp16) <=> (hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))))), (((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp16) | hskp17) <=> ((hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) | hskp17))), rewrite(((hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) | hskp17) <=> (hskp17 | hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))), (((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp16) | hskp17) <=> (hskp17 | hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))))),
% 0.65/0.83 inference(bind,[status(th)],[])).
% 0.65/0.83 tff(1494,plain,
% 0.65/0.83 (![U: $i] : ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp16) | hskp17) <=> ![U: $i] : (hskp17 | hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 0.65/0.83 inference(quant_intro,[status(thm)],[1493])).
% 0.65/0.83 tff(1495,axiom,(![U: $i] : ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp16) | hskp17)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause129')).
% 0.65/0.83 tff(1496,plain,
% 0.65/0.83 (![U: $i] : (hskp17 | hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 0.65/0.83 inference(modus_ponens,[status(thm)],[1495, 1494])).
% 0.65/0.83 tff(1497,plain,
% 0.65/0.83 (![U: $i] : (hskp17 | hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 0.65/0.83 inference(modus_ponens,[status(thm)],[1496, 1492])).
% 0.65/0.83 tff(1498,plain,(
% 0.65/0.83 ![U: $i] : (hskp17 | hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 0.65/0.83 inference(skolemize,[status(sab)],[1497])).
% 0.65/0.83 tff(1499,plain,
% 0.65/0.83 (![U: $i] : (hskp17 | hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 0.65/0.83 inference(modus_ponens,[status(thm)],[1498, 1491])).
% 0.65/0.83 tff(1500,plain,
% 0.65/0.83 (((~![U: $i] : (hskp17 | hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp17 | hskp16 | c2_1(a468) | (~ndr1_0) | (~c0_1(a468)) | c1_1(a468))) <=> ((~![U: $i] : (hskp17 | hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp17 | hskp16 | c2_1(a468) | (~ndr1_0) | (~c0_1(a468)) | c1_1(a468))),
% 0.65/0.83 inference(rewrite,[status(thm)],[])).
% 0.65/0.83 tff(1501,plain,
% 0.65/0.83 ((hskp17 | hskp16 | (~ndr1_0) | c2_1(a468) | c1_1(a468) | (~c0_1(a468))) <=> (hskp17 | hskp16 | c2_1(a468) | (~ndr1_0) | (~c0_1(a468)) | c1_1(a468))),
% 0.65/0.83 inference(rewrite,[status(thm)],[])).
% 0.65/0.83 tff(1502,plain,
% 0.65/0.83 (((~![U: $i] : (hskp17 | hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp17 | hskp16 | (~ndr1_0) | c2_1(a468) | c1_1(a468) | (~c0_1(a468)))) <=> ((~![U: $i] : (hskp17 | hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp17 | hskp16 | c2_1(a468) | (~ndr1_0) | (~c0_1(a468)) | c1_1(a468)))),
% 0.65/0.83 inference(monotonicity,[status(thm)],[1501])).
% 0.65/0.83 tff(1503,plain,
% 0.65/0.83 (((~![U: $i] : (hskp17 | hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp17 | hskp16 | (~ndr1_0) | c2_1(a468) | c1_1(a468) | (~c0_1(a468)))) <=> ((~![U: $i] : (hskp17 | hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp17 | hskp16 | c2_1(a468) | (~ndr1_0) | (~c0_1(a468)) | c1_1(a468))),
% 0.65/0.83 inference(transitivity,[status(thm)],[1502, 1500])).
% 0.65/0.83 tff(1504,plain,
% 0.65/0.83 ((~![U: $i] : (hskp17 | hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp17 | hskp16 | (~ndr1_0) | c2_1(a468) | c1_1(a468) | (~c0_1(a468)))),
% 0.65/0.83 inference(quant_inst,[status(thm)],[])).
% 0.65/0.83 tff(1505,plain,
% 0.65/0.83 ((~![U: $i] : (hskp17 | hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp17 | hskp16 | c2_1(a468) | (~ndr1_0) | (~c0_1(a468)) | c1_1(a468)),
% 0.65/0.83 inference(modus_ponens,[status(thm)],[1504, 1503])).
% 0.65/0.83 tff(1506,plain,
% 0.65/0.83 (hskp17 | hskp16 | c1_1(a468)),
% 0.65/0.83 inference(unit_resolution,[status(thm)],[1505, 941, 1125, 1109, 1499])).
% 0.65/0.83 tff(1507,plain,
% 0.65/0.83 (hskp16),
% 0.65/0.83 inference(unit_resolution,[status(thm)],[1506, 33, 1489])).
% 0.65/0.83 tff(1508,plain,
% 0.65/0.83 (~c0_1(a493)),
% 0.65/0.83 inference(unit_resolution,[status(thm)],[897, 1507])).
% 0.65/0.83 tff(1509,plain,
% 0.65/0.83 (~c2_1(a524)),
% 0.65/0.83 inference(unit_resolution,[status(thm)],[403, 1478])).
% 0.65/0.83 tff(1510,plain,
% 0.65/0.83 (c1_1(a493)),
% 0.65/0.83 inference(unit_resolution,[status(thm)],[905, 1507])).
% 0.65/0.83 tff(1511,plain,
% 0.65/0.83 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c2_1(a524) | c0_1(a493) | c0_1(a480) | c1_1(a480) | c2_1(a480) | (~ndr1_0) | (~c1_1(a493)) | (~c3_1(a493)) | (~c0_1(a524)) | c3_1(a524))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c2_1(a524) | c0_1(a493) | c0_1(a480) | c1_1(a480) | c2_1(a480) | (~ndr1_0) | (~c1_1(a493)) | (~c3_1(a493)) | (~c0_1(a524)) | c3_1(a524))),
% 0.65/0.83 inference(rewrite,[status(thm)],[])).
% 0.65/0.83 tff(1512,plain,
% 0.65/0.83 (((~ndr1_0) | c2_1(a524) | c3_1(a524) | (~c0_1(a524)) | c0_1(a493) | (~c1_1(a493)) | (~c3_1(a493)) | c1_1(a480) | c0_1(a480) | c2_1(a480)) <=> (c2_1(a524) | c0_1(a493) | c0_1(a480) | c1_1(a480) | c2_1(a480) | (~ndr1_0) | (~c1_1(a493)) | (~c3_1(a493)) | (~c0_1(a524)) | c3_1(a524))),
% 0.65/0.83 inference(rewrite,[status(thm)],[])).
% 0.65/0.83 tff(1513,plain,
% 0.65/0.83 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c2_1(a524) | c3_1(a524) | (~c0_1(a524)) | c0_1(a493) | (~c1_1(a493)) | (~c3_1(a493)) | c1_1(a480) | c0_1(a480) | c2_1(a480))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c2_1(a524) | c0_1(a493) | c0_1(a480) | c1_1(a480) | c2_1(a480) | (~ndr1_0) | (~c1_1(a493)) | (~c3_1(a493)) | (~c0_1(a524)) | c3_1(a524)))),
% 0.65/0.83 inference(monotonicity,[status(thm)],[1512])).
% 0.65/0.83 tff(1514,plain,
% 0.65/0.83 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c2_1(a524) | c3_1(a524) | (~c0_1(a524)) | c0_1(a493) | (~c1_1(a493)) | (~c3_1(a493)) | c1_1(a480) | c0_1(a480) | c2_1(a480))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c2_1(a524) | c0_1(a493) | c0_1(a480) | c1_1(a480) | c2_1(a480) | (~ndr1_0) | (~c1_1(a493)) | (~c3_1(a493)) | (~c0_1(a524)) | c3_1(a524))),
% 0.65/0.83 inference(transitivity,[status(thm)],[1513, 1511])).
% 0.65/0.83 tff(1515,plain,
% 0.65/0.83 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c2_1(a524) | c3_1(a524) | (~c0_1(a524)) | c0_1(a493) | (~c1_1(a493)) | (~c3_1(a493)) | c1_1(a480) | c0_1(a480) | c2_1(a480))),
% 0.65/0.83 inference(quant_inst,[status(thm)],[])).
% 0.65/0.83 tff(1516,plain,
% 0.65/0.83 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c2_1(a524) | c0_1(a493) | c0_1(a480) | c1_1(a480) | c2_1(a480) | (~ndr1_0) | (~c1_1(a493)) | (~c3_1(a493)) | (~c0_1(a524)) | c3_1(a524)),
% 0.65/0.83 inference(modus_ponens,[status(thm)],[1515, 1514])).
% 0.65/0.83 tff(1517,plain,
% 0.65/0.83 (~c3_1(a493)),
% 0.65/0.83 inference(unit_resolution,[status(thm)],[1516, 941, 1480, 1510, 1509, 1508, 1466, 1465, 1464, 32, 1481])).
% 0.65/0.83 tff(1518,plain,
% 0.65/0.83 (~c2_1(a493)),
% 0.65/0.83 inference(unit_resolution,[status(thm)],[891, 1507])).
% 0.65/0.83 tff(1519,plain,
% 0.65/0.83 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp27 | c0_1(a493) | c2_1(a493) | c1_1(a480) | c2_1(a480) | (~ndr1_0) | c3_1(a480) | c3_1(a493))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp27 | c0_1(a493) | c2_1(a493) | c1_1(a480) | c2_1(a480) | (~ndr1_0) | c3_1(a480) | c3_1(a493))),
% 0.65/0.83 inference(rewrite,[status(thm)],[])).
% 0.65/0.83 tff(1520,plain,
% 0.65/0.83 ((hskp27 | (~ndr1_0) | c2_1(a480) | c1_1(a480) | c3_1(a480) | c3_1(a493) | c0_1(a493) | c2_1(a493)) <=> (hskp27 | c0_1(a493) | c2_1(a493) | c1_1(a480) | c2_1(a480) | (~ndr1_0) | c3_1(a480) | c3_1(a493))),
% 0.65/0.83 inference(rewrite,[status(thm)],[])).
% 0.65/0.83 tff(1521,plain,
% 0.65/0.83 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp27 | (~ndr1_0) | c2_1(a480) | c1_1(a480) | c3_1(a480) | c3_1(a493) | c0_1(a493) | c2_1(a493))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp27 | c0_1(a493) | c2_1(a493) | c1_1(a480) | c2_1(a480) | (~ndr1_0) | c3_1(a480) | c3_1(a493)))),
% 0.65/0.83 inference(monotonicity,[status(thm)],[1520])).
% 0.65/0.83 tff(1522,plain,
% 0.65/0.83 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp27 | (~ndr1_0) | c2_1(a480) | c1_1(a480) | c3_1(a480) | c3_1(a493) | c0_1(a493) | c2_1(a493))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp27 | c0_1(a493) | c2_1(a493) | c1_1(a480) | c2_1(a480) | (~ndr1_0) | c3_1(a480) | c3_1(a493))),
% 0.65/0.83 inference(transitivity,[status(thm)],[1521, 1519])).
% 0.65/0.83 tff(1523,plain,
% 0.65/0.83 ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp27 | (~ndr1_0) | c2_1(a480) | c1_1(a480) | c3_1(a480) | c3_1(a493) | c0_1(a493) | c2_1(a493))),
% 0.65/0.83 inference(quant_inst,[status(thm)],[])).
% 0.65/0.83 tff(1524,plain,
% 0.65/0.83 ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp27 | c0_1(a493) | c2_1(a493) | c1_1(a480) | c2_1(a480) | (~ndr1_0) | c3_1(a480) | c3_1(a493)),
% 0.65/0.83 inference(modus_ponens,[status(thm)],[1523, 1522])).
% 0.65/0.83 tff(1525,plain,
% 0.65/0.83 (c3_1(a480)),
% 0.65/0.83 inference(unit_resolution,[status(thm)],[1524, 941, 1477, 1508, 1518, 1465, 1464, 414, 1517])).
% 0.65/0.83 tff(1526,plain,
% 0.65/0.83 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp27 | c0_1(a493) | c2_1(a493) | c2_1(a460) | c3_1(a460) | (~ndr1_0) | c1_1(a460) | c3_1(a493))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp27 | c0_1(a493) | c2_1(a493) | c2_1(a460) | c3_1(a460) | (~ndr1_0) | c1_1(a460) | c3_1(a493))),
% 0.65/0.84 inference(rewrite,[status(thm)],[])).
% 0.65/0.84 tff(1527,plain,
% 0.65/0.84 ((hskp27 | (~ndr1_0) | c2_1(a460) | c1_1(a460) | c3_1(a460) | c3_1(a493) | c0_1(a493) | c2_1(a493)) <=> (hskp27 | c0_1(a493) | c2_1(a493) | c2_1(a460) | c3_1(a460) | (~ndr1_0) | c1_1(a460) | c3_1(a493))),
% 0.65/0.84 inference(rewrite,[status(thm)],[])).
% 0.65/0.84 tff(1528,plain,
% 0.65/0.84 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp27 | (~ndr1_0) | c2_1(a460) | c1_1(a460) | c3_1(a460) | c3_1(a493) | c0_1(a493) | c2_1(a493))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp27 | c0_1(a493) | c2_1(a493) | c2_1(a460) | c3_1(a460) | (~ndr1_0) | c1_1(a460) | c3_1(a493)))),
% 0.65/0.84 inference(monotonicity,[status(thm)],[1527])).
% 0.65/0.84 tff(1529,plain,
% 0.65/0.84 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp27 | (~ndr1_0) | c2_1(a460) | c1_1(a460) | c3_1(a460) | c3_1(a493) | c0_1(a493) | c2_1(a493))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp27 | c0_1(a493) | c2_1(a493) | c2_1(a460) | c3_1(a460) | (~ndr1_0) | c1_1(a460) | c3_1(a493))),
% 0.65/0.84 inference(transitivity,[status(thm)],[1528, 1526])).
% 0.65/0.84 tff(1530,plain,
% 0.65/0.84 ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp27 | (~ndr1_0) | c2_1(a460) | c1_1(a460) | c3_1(a460) | c3_1(a493) | c0_1(a493) | c2_1(a493))),
% 0.65/0.84 inference(quant_inst,[status(thm)],[])).
% 0.65/0.84 tff(1531,plain,
% 0.65/0.84 ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp27 | c0_1(a493) | c2_1(a493) | c2_1(a460) | c3_1(a460) | (~ndr1_0) | c1_1(a460) | c3_1(a493)),
% 0.65/0.84 inference(modus_ponens,[status(thm)],[1530, 1529])).
% 0.65/0.84 tff(1532,plain,
% 0.65/0.84 (c1_1(a460)),
% 0.65/0.84 inference(unit_resolution,[status(thm)],[1531, 941, 1477, 1508, 1518, 1, 1463, 414, 1517])).
% 0.65/0.84 tff(1533,assumption,(~hskp20), introduced(assumption)).
% 0.65/0.84 tff(1534,plain,
% 0.65/0.84 (^[U: $i] : refl((hskp20 | hskp18 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U))) <=> (hskp20 | hskp18 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U))))),
% 0.65/0.84 inference(bind,[status(th)],[])).
% 0.65/0.84 tff(1535,plain,
% 0.65/0.84 (![U: $i] : (hskp20 | hskp18 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp20 | hskp18 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))),
% 0.65/0.84 inference(quant_intro,[status(thm)],[1534])).
% 0.65/0.84 tff(1536,plain,
% 0.65/0.84 (![U: $i] : (hskp20 | hskp18 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp20 | hskp18 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))),
% 0.65/0.84 inference(rewrite,[status(thm)],[])).
% 0.65/0.84 tff(1537,plain,
% 0.65/0.84 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp18) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U))) | hskp18))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U))) | hskp18) <=> (hskp18 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp18) <=> (hskp18 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp18) | hskp20) <=> ((hskp18 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U))) | hskp20))), rewrite(((hskp18 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U))) | hskp20) <=> (hskp20 | hskp18 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp18) | hskp20) <=> (hskp20 | hskp18 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))))),
% 0.65/0.84 inference(bind,[status(th)],[])).
% 0.65/0.84 tff(1538,plain,
% 0.65/0.84 (![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp18) | hskp20) <=> ![U: $i] : (hskp20 | hskp18 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))),
% 0.65/0.84 inference(quant_intro,[status(thm)],[1537])).
% 0.65/0.84 tff(1539,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp18) | hskp20)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause138')).
% 0.65/0.84 tff(1540,plain,
% 0.65/0.84 (![U: $i] : (hskp20 | hskp18 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))),
% 0.65/0.84 inference(modus_ponens,[status(thm)],[1539, 1538])).
% 0.65/0.84 tff(1541,plain,
% 0.65/0.84 (![U: $i] : (hskp20 | hskp18 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))),
% 0.65/0.84 inference(modus_ponens,[status(thm)],[1540, 1536])).
% 0.65/0.84 tff(1542,plain,(
% 0.65/0.84 ![U: $i] : (hskp20 | hskp18 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))),
% 0.65/0.84 inference(skolemize,[status(sab)],[1541])).
% 0.65/0.84 tff(1543,plain,
% 0.65/0.84 (![U: $i] : (hskp20 | hskp18 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))),
% 0.65/0.84 inference(modus_ponens,[status(thm)],[1542, 1535])).
% 0.65/0.84 tff(1544,plain,
% 0.65/0.84 (((~![U: $i] : (hskp20 | hskp18 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))) | (hskp20 | hskp18 | c2_1(a460) | (~ndr1_0) | (~c1_1(a460)) | (~c0_1(a460)))) <=> ((~![U: $i] : (hskp20 | hskp18 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))) | hskp20 | hskp18 | c2_1(a460) | (~ndr1_0) | (~c1_1(a460)) | (~c0_1(a460)))),
% 0.65/0.84 inference(rewrite,[status(thm)],[])).
% 0.65/0.84 tff(1545,plain,
% 0.65/0.84 ((hskp20 | hskp18 | (~ndr1_0) | c2_1(a460) | (~c0_1(a460)) | (~c1_1(a460))) <=> (hskp20 | hskp18 | c2_1(a460) | (~ndr1_0) | (~c1_1(a460)) | (~c0_1(a460)))),
% 0.65/0.84 inference(rewrite,[status(thm)],[])).
% 0.65/0.84 tff(1546,plain,
% 0.65/0.84 (((~![U: $i] : (hskp20 | hskp18 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))) | (hskp20 | hskp18 | (~ndr1_0) | c2_1(a460) | (~c0_1(a460)) | (~c1_1(a460)))) <=> ((~![U: $i] : (hskp20 | hskp18 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))) | (hskp20 | hskp18 | c2_1(a460) | (~ndr1_0) | (~c1_1(a460)) | (~c0_1(a460))))),
% 0.65/0.84 inference(monotonicity,[status(thm)],[1545])).
% 0.65/0.84 tff(1547,plain,
% 0.65/0.84 (((~![U: $i] : (hskp20 | hskp18 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))) | (hskp20 | hskp18 | (~ndr1_0) | c2_1(a460) | (~c0_1(a460)) | (~c1_1(a460)))) <=> ((~![U: $i] : (hskp20 | hskp18 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))) | hskp20 | hskp18 | c2_1(a460) | (~ndr1_0) | (~c1_1(a460)) | (~c0_1(a460)))),
% 0.65/0.84 inference(transitivity,[status(thm)],[1546, 1544])).
% 0.65/0.84 tff(1548,plain,
% 0.65/0.84 ((~![U: $i] : (hskp20 | hskp18 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))) | (hskp20 | hskp18 | (~ndr1_0) | c2_1(a460) | (~c0_1(a460)) | (~c1_1(a460)))),
% 0.65/0.84 inference(quant_inst,[status(thm)],[])).
% 0.65/0.84 tff(1549,plain,
% 0.65/0.84 ((~![U: $i] : (hskp20 | hskp18 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))) | hskp20 | hskp18 | c2_1(a460) | (~ndr1_0) | (~c1_1(a460)) | (~c0_1(a460))),
% 0.65/0.84 inference(modus_ponens,[status(thm)],[1548, 1547])).
% 0.65/0.84 tff(1550,plain,
% 0.65/0.84 (hskp20 | hskp18 | (~c1_1(a460)) | (~c0_1(a460))),
% 0.65/0.84 inference(unit_resolution,[status(thm)],[1549, 941, 1, 1543])).
% 0.65/0.84 tff(1551,plain,
% 0.65/0.84 (hskp18),
% 0.65/0.84 inference(unit_resolution,[status(thm)],[1550, 1533, 1305, 1532])).
% 0.65/0.84 tff(1552,plain,
% 0.65/0.84 (((~hskp18) | (~c0_1(a500))) <=> ((~hskp18) | (~c0_1(a500)))),
% 0.65/0.84 inference(rewrite,[status(thm)],[])).
% 0.65/0.84 tff(1553,plain,
% 0.65/0.84 (((~c0_1(a500)) | (~hskp18)) <=> ((~hskp18) | (~c0_1(a500)))),
% 0.65/0.84 inference(rewrite,[status(thm)],[])).
% 0.65/0.84 tff(1554,axiom,((~c0_1(a500)) | (~hskp18)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause91')).
% 0.65/0.84 tff(1555,plain,
% 0.65/0.84 ((~hskp18) | (~c0_1(a500))),
% 0.65/0.84 inference(modus_ponens,[status(thm)],[1554, 1553])).
% 0.65/0.84 tff(1556,plain,
% 0.65/0.84 ((~hskp18) | (~c0_1(a500))),
% 0.65/0.84 inference(modus_ponens,[status(thm)],[1555, 1552])).
% 0.65/0.84 tff(1557,plain,
% 0.65/0.84 (~c0_1(a500)),
% 0.65/0.84 inference(unit_resolution,[status(thm)],[1556, 1551])).
% 0.65/0.84 tff(1558,plain,
% 0.65/0.84 (((~hskp18) | c2_1(a500)) <=> ((~hskp18) | c2_1(a500))),
% 0.65/0.84 inference(rewrite,[status(thm)],[])).
% 0.65/0.84 tff(1559,axiom,((~hskp18) | c2_1(a500)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause61')).
% 0.65/0.84 tff(1560,plain,
% 0.65/0.84 ((~hskp18) | c2_1(a500)),
% 0.65/0.84 inference(modus_ponens,[status(thm)],[1559, 1558])).
% 0.65/0.84 tff(1561,plain,
% 0.65/0.84 ((~hskp18) | c2_1(a500)),
% 0.65/0.84 inference(modus_ponens,[status(thm)],[1560, 1558])).
% 0.65/0.84 tff(1562,plain,
% 0.65/0.84 ((~hskp18) | c2_1(a500)),
% 0.65/0.84 inference(modus_ponens,[status(thm)],[1561, 1558])).
% 0.65/0.84 tff(1563,plain,
% 0.65/0.84 ((~hskp18) | c2_1(a500)),
% 0.65/0.84 inference(modus_ponens,[status(thm)],[1562, 1558])).
% 0.65/0.84 tff(1564,plain,
% 0.65/0.84 ((~hskp18) | c2_1(a500)),
% 0.65/0.84 inference(modus_ponens,[status(thm)],[1563, 1558])).
% 0.65/0.84 tff(1565,plain,
% 0.65/0.84 (c2_1(a500)),
% 0.65/0.84 inference(unit_resolution,[status(thm)],[1564, 1551])).
% 0.65/0.84 tff(1566,plain,
% 0.65/0.84 (((~hskp18) | c1_1(a500)) <=> ((~hskp18) | c1_1(a500))),
% 0.65/0.84 inference(rewrite,[status(thm)],[])).
% 0.65/0.84 tff(1567,axiom,((~hskp18) | c1_1(a500)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause60')).
% 0.65/0.84 tff(1568,plain,
% 0.65/0.84 ((~hskp18) | c1_1(a500)),
% 0.65/0.84 inference(modus_ponens,[status(thm)],[1567, 1566])).
% 0.65/0.84 tff(1569,plain,
% 0.65/0.84 ((~hskp18) | c1_1(a500)),
% 0.65/0.84 inference(modus_ponens,[status(thm)],[1568, 1566])).
% 0.65/0.84 tff(1570,plain,
% 0.65/0.84 ((~hskp18) | c1_1(a500)),
% 0.65/0.84 inference(modus_ponens,[status(thm)],[1569, 1566])).
% 0.65/0.84 tff(1571,plain,
% 0.65/0.84 ((~hskp18) | c1_1(a500)),
% 0.65/0.84 inference(modus_ponens,[status(thm)],[1570, 1566])).
% 0.65/0.84 tff(1572,plain,
% 0.65/0.84 ((~hskp18) | c1_1(a500)),
% 0.65/0.84 inference(modus_ponens,[status(thm)],[1571, 1566])).
% 0.65/0.84 tff(1573,plain,
% 0.65/0.84 (c1_1(a500)),
% 0.65/0.84 inference(unit_resolution,[status(thm)],[1572, 1551])).
% 0.65/0.84 tff(1574,plain,
% 0.65/0.84 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp9 | c0_1(a500) | c2_1(a468) | (~ndr1_0) | (~c0_1(a468)) | c1_1(a468) | (~c2_1(a500)) | (~c1_1(a500)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp9 | c0_1(a500) | c2_1(a468) | (~ndr1_0) | (~c0_1(a468)) | c1_1(a468) | (~c2_1(a500)) | (~c1_1(a500)))),
% 0.65/0.84 inference(rewrite,[status(thm)],[])).
% 0.65/0.84 tff(1575,plain,
% 0.65/0.84 ((hskp9 | (~ndr1_0) | c2_1(a468) | c1_1(a468) | (~c0_1(a468)) | c0_1(a500) | (~c1_1(a500)) | (~c2_1(a500))) <=> (hskp9 | c0_1(a500) | c2_1(a468) | (~ndr1_0) | (~c0_1(a468)) | c1_1(a468) | (~c2_1(a500)) | (~c1_1(a500)))),
% 0.65/0.84 inference(rewrite,[status(thm)],[])).
% 0.65/0.84 tff(1576,plain,
% 0.65/0.84 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp9 | (~ndr1_0) | c2_1(a468) | c1_1(a468) | (~c0_1(a468)) | c0_1(a500) | (~c1_1(a500)) | (~c2_1(a500)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp9 | c0_1(a500) | c2_1(a468) | (~ndr1_0) | (~c0_1(a468)) | c1_1(a468) | (~c2_1(a500)) | (~c1_1(a500))))),
% 0.65/0.84 inference(monotonicity,[status(thm)],[1575])).
% 0.65/0.84 tff(1577,plain,
% 0.65/0.84 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp9 | (~ndr1_0) | c2_1(a468) | c1_1(a468) | (~c0_1(a468)) | c0_1(a500) | (~c1_1(a500)) | (~c2_1(a500)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp9 | c0_1(a500) | c2_1(a468) | (~ndr1_0) | (~c0_1(a468)) | c1_1(a468) | (~c2_1(a500)) | (~c1_1(a500)))),
% 0.65/0.84 inference(transitivity,[status(thm)],[1576, 1574])).
% 0.65/0.84 tff(1578,plain,
% 0.65/0.84 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp9 | (~ndr1_0) | c2_1(a468) | c1_1(a468) | (~c0_1(a468)) | c0_1(a500) | (~c1_1(a500)) | (~c2_1(a500)))),
% 0.65/0.84 inference(quant_inst,[status(thm)],[])).
% 0.65/0.84 tff(1579,plain,
% 0.65/0.84 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp9 | c0_1(a500) | c2_1(a468) | (~ndr1_0) | (~c0_1(a468)) | c1_1(a468) | (~c2_1(a500)) | (~c1_1(a500))),
% 0.65/0.84 inference(modus_ponens,[status(thm)],[1578, 1577])).
% 0.65/0.84 tff(1580,plain,
% 0.65/0.84 (hskp9),
% 0.65/0.84 inference(unit_resolution,[status(thm)],[1579, 941, 1573, 1565, 1125, 1557, 1109, 1380, 1489])).
% 0.65/0.84 tff(1581,plain,
% 0.65/0.84 (~c1_1(a476)),
% 0.65/0.84 inference(unit_resolution,[status(thm)],[1392, 1580])).
% 0.65/0.84 tff(1582,plain,
% 0.65/0.84 (c2_1(a476)),
% 0.65/0.84 inference(unit_resolution,[status(thm)],[1400, 1580])).
% 0.65/0.84 tff(1583,plain,
% 0.65/0.84 (c0_1(a476)),
% 0.65/0.84 inference(unit_resolution,[status(thm)],[1408, 1580])).
% 0.65/0.84 tff(1584,plain,
% 0.65/0.84 (~c3_1(a476)),
% 0.65/0.84 inference(unit_resolution,[status(thm)],[1415, 941, 33, 1583, 1582, 1581, 11])).
% 0.65/0.84 tff(1585,plain,
% 0.65/0.84 (^[U: $i] : refl((hskp20 | hskp19 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U))) <=> (hskp20 | hskp19 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U))))),
% 0.65/0.84 inference(bind,[status(th)],[])).
% 0.65/0.84 tff(1586,plain,
% 0.65/0.84 (![U: $i] : (hskp20 | hskp19 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U))) <=> ![U: $i] : (hskp20 | hskp19 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))),
% 0.65/0.84 inference(quant_intro,[status(thm)],[1585])).
% 0.65/0.84 tff(1587,plain,
% 0.65/0.84 (![U: $i] : (hskp20 | hskp19 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U))) <=> ![U: $i] : (hskp20 | hskp19 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))),
% 0.65/0.84 inference(rewrite,[status(thm)],[])).
% 0.65/0.84 tff(1588,plain,
% 0.65/0.84 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c2_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) <=> (((~ndr1_0) | (~c2_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U))))), (((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))), (((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U))))), ((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp19) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U))) | hskp19))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U))) | hskp19) <=> (hskp19 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))), ((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp19) <=> (hskp19 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U))))), (((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp19) | hskp20) <=> ((hskp19 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U))) | hskp20))), rewrite(((hskp19 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U))) | hskp20) <=> (hskp20 | hskp19 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))), (((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp19) | hskp20) <=> (hskp20 | hskp19 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))))),
% 0.65/0.84 inference(bind,[status(th)],[])).
% 0.65/0.84 tff(1589,plain,
% 0.65/0.84 (![U: $i] : ((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp19) | hskp20) <=> ![U: $i] : (hskp20 | hskp19 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))),
% 0.65/0.84 inference(quant_intro,[status(thm)],[1588])).
% 0.65/0.84 tff(1590,axiom,(![U: $i] : ((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp19) | hskp20)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause133')).
% 0.65/0.84 tff(1591,plain,
% 0.65/0.84 (![U: $i] : (hskp20 | hskp19 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))),
% 0.65/0.84 inference(modus_ponens,[status(thm)],[1590, 1589])).
% 0.65/0.84 tff(1592,plain,
% 0.65/0.84 (![U: $i] : (hskp20 | hskp19 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))),
% 0.65/0.84 inference(modus_ponens,[status(thm)],[1591, 1587])).
% 0.65/0.84 tff(1593,plain,(
% 0.65/0.84 ![U: $i] : (hskp20 | hskp19 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))),
% 0.65/0.84 inference(skolemize,[status(sab)],[1592])).
% 0.65/0.84 tff(1594,plain,
% 0.65/0.84 (![U: $i] : (hskp20 | hskp19 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))),
% 0.65/0.84 inference(modus_ponens,[status(thm)],[1593, 1586])).
% 0.65/0.84 tff(1595,plain,
% 0.65/0.84 (((~![U: $i] : (hskp20 | hskp19 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp20 | hskp19 | c1_1(a476) | (~ndr1_0) | c3_1(a476) | (~c2_1(a476)))) <=> ((~![U: $i] : (hskp20 | hskp19 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | hskp20 | hskp19 | c1_1(a476) | (~ndr1_0) | c3_1(a476) | (~c2_1(a476)))),
% 0.65/0.84 inference(rewrite,[status(thm)],[])).
% 0.65/0.84 tff(1596,plain,
% 0.65/0.84 ((hskp20 | hskp19 | (~ndr1_0) | c1_1(a476) | c3_1(a476) | (~c2_1(a476))) <=> (hskp20 | hskp19 | c1_1(a476) | (~ndr1_0) | c3_1(a476) | (~c2_1(a476)))),
% 0.65/0.84 inference(rewrite,[status(thm)],[])).
% 0.65/0.84 tff(1597,plain,
% 0.65/0.84 (((~![U: $i] : (hskp20 | hskp19 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp20 | hskp19 | (~ndr1_0) | c1_1(a476) | c3_1(a476) | (~c2_1(a476)))) <=> ((~![U: $i] : (hskp20 | hskp19 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp20 | hskp19 | c1_1(a476) | (~ndr1_0) | c3_1(a476) | (~c2_1(a476))))),
% 0.65/0.84 inference(monotonicity,[status(thm)],[1596])).
% 0.65/0.84 tff(1598,plain,
% 0.65/0.84 (((~![U: $i] : (hskp20 | hskp19 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp20 | hskp19 | (~ndr1_0) | c1_1(a476) | c3_1(a476) | (~c2_1(a476)))) <=> ((~![U: $i] : (hskp20 | hskp19 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | hskp20 | hskp19 | c1_1(a476) | (~ndr1_0) | c3_1(a476) | (~c2_1(a476)))),
% 0.65/0.84 inference(transitivity,[status(thm)],[1597, 1595])).
% 0.65/0.84 tff(1599,plain,
% 0.65/0.84 ((~![U: $i] : (hskp20 | hskp19 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp20 | hskp19 | (~ndr1_0) | c1_1(a476) | c3_1(a476) | (~c2_1(a476)))),
% 0.65/0.84 inference(quant_inst,[status(thm)],[])).
% 0.65/0.84 tff(1600,plain,
% 0.65/0.84 ((~![U: $i] : (hskp20 | hskp19 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | hskp20 | hskp19 | c1_1(a476) | (~ndr1_0) | c3_1(a476) | (~c2_1(a476))),
% 0.65/0.84 inference(modus_ponens,[status(thm)],[1599, 1598])).
% 0.65/0.84 tff(1601,plain,
% 0.65/0.84 (hskp19),
% 0.65/0.84 inference(unit_resolution,[status(thm)],[1600, 941, 1533, 1582, 1581, 1594, 1584])).
% 0.65/0.84 tff(1602,plain,
% 0.65/0.84 (((~hskp19) | (~c0_1(a502))) <=> ((~hskp19) | (~c0_1(a502)))),
% 0.65/0.84 inference(rewrite,[status(thm)],[])).
% 0.65/0.84 tff(1603,plain,
% 0.65/0.84 (((~c0_1(a502)) | (~hskp19)) <=> ((~hskp19) | (~c0_1(a502)))),
% 0.65/0.84 inference(rewrite,[status(thm)],[])).
% 0.65/0.84 tff(1604,axiom,((~c0_1(a502)) | (~hskp19)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause90')).
% 0.65/0.84 tff(1605,plain,
% 0.65/0.84 ((~hskp19) | (~c0_1(a502))),
% 0.65/0.84 inference(modus_ponens,[status(thm)],[1604, 1603])).
% 0.65/0.84 tff(1606,plain,
% 0.65/0.84 ((~hskp19) | (~c0_1(a502))),
% 0.65/0.84 inference(modus_ponens,[status(thm)],[1605, 1602])).
% 0.65/0.84 tff(1607,plain,
% 0.65/0.84 (~c0_1(a502)),
% 0.65/0.84 inference(unit_resolution,[status(thm)],[1606, 1601])).
% 0.65/0.84 tff(1608,plain,
% 0.65/0.84 (((~hskp19) | c3_1(a502)) <=> ((~hskp19) | c3_1(a502))),
% 0.65/0.84 inference(rewrite,[status(thm)],[])).
% 0.65/0.84 tff(1609,axiom,((~hskp19) | c3_1(a502)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause59')).
% 0.65/0.84 tff(1610,plain,
% 0.65/0.84 ((~hskp19) | c3_1(a502)),
% 0.65/0.84 inference(modus_ponens,[status(thm)],[1609, 1608])).
% 0.65/0.84 tff(1611,plain,
% 0.65/0.84 ((~hskp19) | c3_1(a502)),
% 0.65/0.84 inference(modus_ponens,[status(thm)],[1610, 1608])).
% 0.65/0.84 tff(1612,plain,
% 0.65/0.84 ((~hskp19) | c3_1(a502)),
% 0.65/0.84 inference(modus_ponens,[status(thm)],[1611, 1608])).
% 0.65/0.84 tff(1613,plain,
% 0.65/0.84 ((~hskp19) | c3_1(a502)),
% 0.65/0.84 inference(modus_ponens,[status(thm)],[1612, 1608])).
% 0.65/0.84 tff(1614,plain,
% 0.65/0.84 ((~hskp19) | c3_1(a502)),
% 0.65/0.84 inference(modus_ponens,[status(thm)],[1613, 1608])).
% 0.65/0.84 tff(1615,plain,
% 0.65/0.84 (c3_1(a502)),
% 0.65/0.84 inference(unit_resolution,[status(thm)],[1614, 1601])).
% 0.65/0.84 tff(1616,plain,
% 0.65/0.84 (((~hskp19) | c2_1(a502)) <=> ((~hskp19) | c2_1(a502))),
% 0.65/0.84 inference(rewrite,[status(thm)],[])).
% 0.65/0.84 tff(1617,axiom,((~hskp19) | c2_1(a502)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause58')).
% 0.65/0.84 tff(1618,plain,
% 0.65/0.84 ((~hskp19) | c2_1(a502)),
% 0.65/0.84 inference(modus_ponens,[status(thm)],[1617, 1616])).
% 0.65/0.84 tff(1619,plain,
% 0.65/0.84 ((~hskp19) | c2_1(a502)),
% 0.65/0.84 inference(modus_ponens,[status(thm)],[1618, 1616])).
% 0.65/0.84 tff(1620,plain,
% 0.65/0.84 ((~hskp19) | c2_1(a502)),
% 0.65/0.84 inference(modus_ponens,[status(thm)],[1619, 1616])).
% 0.65/0.84 tff(1621,plain,
% 0.65/0.84 ((~hskp19) | c2_1(a502)),
% 0.65/0.84 inference(modus_ponens,[status(thm)],[1620, 1616])).
% 0.65/0.84 tff(1622,plain,
% 0.65/0.84 ((~hskp19) | c2_1(a502)),
% 0.65/0.84 inference(modus_ponens,[status(thm)],[1621, 1616])).
% 0.65/0.84 tff(1623,plain,
% 0.65/0.84 (c2_1(a502)),
% 0.65/0.84 inference(unit_resolution,[status(thm)],[1622, 1601])).
% 0.65/0.84 tff(1624,plain,
% 0.65/0.84 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c2_1(a524) | c0_1(a502) | c1_1(a476) | (~ndr1_0) | c3_1(a476) | (~c2_1(a476)) | (~c3_1(a502)) | (~c2_1(a502)) | (~c0_1(a524)) | (~c1_1(a524)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c2_1(a524) | c0_1(a502) | c1_1(a476) | (~ndr1_0) | c3_1(a476) | (~c2_1(a476)) | (~c3_1(a502)) | (~c2_1(a502)) | (~c0_1(a524)) | (~c1_1(a524)))),
% 0.69/0.84 inference(rewrite,[status(thm)],[])).
% 0.69/0.84 tff(1625,plain,
% 0.69/0.84 (((~ndr1_0) | c2_1(a524) | (~c0_1(a524)) | (~c1_1(a524)) | c3_1(a476) | c1_1(a476) | (~c2_1(a476)) | c0_1(a502) | (~c3_1(a502)) | (~c2_1(a502))) <=> (c2_1(a524) | c0_1(a502) | c1_1(a476) | (~ndr1_0) | c3_1(a476) | (~c2_1(a476)) | (~c3_1(a502)) | (~c2_1(a502)) | (~c0_1(a524)) | (~c1_1(a524)))),
% 0.69/0.84 inference(rewrite,[status(thm)],[])).
% 0.69/0.84 tff(1626,plain,
% 0.69/0.84 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a524) | (~c0_1(a524)) | (~c1_1(a524)) | c3_1(a476) | c1_1(a476) | (~c2_1(a476)) | c0_1(a502) | (~c3_1(a502)) | (~c2_1(a502)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c2_1(a524) | c0_1(a502) | c1_1(a476) | (~ndr1_0) | c3_1(a476) | (~c2_1(a476)) | (~c3_1(a502)) | (~c2_1(a502)) | (~c0_1(a524)) | (~c1_1(a524))))),
% 0.69/0.84 inference(monotonicity,[status(thm)],[1625])).
% 0.69/0.84 tff(1627,plain,
% 0.69/0.84 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a524) | (~c0_1(a524)) | (~c1_1(a524)) | c3_1(a476) | c1_1(a476) | (~c2_1(a476)) | c0_1(a502) | (~c3_1(a502)) | (~c2_1(a502)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c2_1(a524) | c0_1(a502) | c1_1(a476) | (~ndr1_0) | c3_1(a476) | (~c2_1(a476)) | (~c3_1(a502)) | (~c2_1(a502)) | (~c0_1(a524)) | (~c1_1(a524)))),
% 0.69/0.84 inference(transitivity,[status(thm)],[1626, 1624])).
% 0.69/0.84 tff(1628,plain,
% 0.69/0.84 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a524) | (~c0_1(a524)) | (~c1_1(a524)) | c3_1(a476) | c1_1(a476) | (~c2_1(a476)) | c0_1(a502) | (~c3_1(a502)) | (~c2_1(a502)))),
% 0.69/0.84 inference(quant_inst,[status(thm)],[])).
% 0.69/0.84 tff(1629,plain,
% 0.69/0.84 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c2_1(a524) | c0_1(a502) | c1_1(a476) | (~ndr1_0) | c3_1(a476) | (~c2_1(a476)) | (~c3_1(a502)) | (~c2_1(a502)) | (~c0_1(a524)) | (~c1_1(a524))),
% 0.69/0.84 inference(modus_ponens,[status(thm)],[1628, 1627])).
% 0.69/0.84 tff(1630,plain,
% 0.69/0.84 ($false),
% 0.69/0.84 inference(unit_resolution,[status(thm)],[1629, 941, 1480, 1479, 1623, 1615, 1582, 1509, 1607, 1581, 802, 1584])).
% 0.69/0.84 tff(1631,plain,(hskp20 | hskp17 | c2_1(a460)), inference(lemma,lemma(discharge,[]))).
% 0.69/0.84 tff(1632,plain,
% 0.69/0.84 (hskp20),
% 0.69/0.84 inference(unit_resolution,[status(thm)],[1631, 33, 1])).
% 0.69/0.84 tff(1633,plain,
% 0.69/0.84 (~c1_1(a503)),
% 0.69/0.84 inference(unit_resolution,[status(thm)],[1023, 1632])).
% 0.69/0.84 tff(1634,plain,
% 0.69/0.84 (c3_1(a503)),
% 0.69/0.84 inference(unit_resolution,[status(thm)],[1031, 1632])).
% 0.69/0.84 tff(1635,plain,
% 0.69/0.84 (c2_1(a503)),
% 0.69/0.84 inference(unit_resolution,[status(thm)],[1039, 1632])).
% 0.69/0.84 tff(1636,plain,
% 0.69/0.84 (~c0_1(a503)),
% 0.69/0.84 inference(unit_resolution,[status(thm)],[1046, 941, 33, 1635, 1634, 1633, 11])).
% 0.69/0.84 tff(1637,plain,
% 0.69/0.84 (^[V: $i, U: $i] : refl((hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V))) <=> (hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V))))),
% 0.69/0.84 inference(bind,[status(th)],[])).
% 0.69/0.84 tff(1638,plain,
% 0.69/0.84 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))),
% 0.69/0.84 inference(quant_intro,[status(thm)],[1637])).
% 0.69/0.84 tff(1639,plain,
% 0.69/0.84 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))),
% 0.69/0.84 inference(rewrite,[status(thm)],[])).
% 0.69/0.84 tff(1640,plain,
% 0.69/0.84 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c3_1(V)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c3_1(V))))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c3_1(V))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c3_1(V))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c3_1(V)))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c3_1(V))))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c3_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V))))), ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))), ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V))))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c0_1(V)) | c2_1(V)) | hskp9) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V))) | hskp9))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V))) | hskp9) <=> (hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c0_1(V)) | c2_1(V)) | hskp9) <=> (hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))))),
% 0.69/0.84 inference(bind,[status(th)],[])).
% 0.69/0.84 tff(1641,plain,
% 0.69/0.84 (![V: $i, U: $i] : ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c0_1(V)) | c2_1(V)) | hskp9) <=> ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))),
% 0.69/0.84 inference(quant_intro,[status(thm)],[1640])).
% 0.69/0.84 tff(1642,axiom,(![V: $i, U: $i] : ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c0_1(V)) | c2_1(V)) | hskp9)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause155')).
% 0.69/0.84 tff(1643,plain,
% 0.69/0.84 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))),
% 0.69/0.84 inference(modus_ponens,[status(thm)],[1642, 1641])).
% 0.69/0.84 tff(1644,plain,
% 0.69/0.84 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))),
% 0.69/0.84 inference(modus_ponens,[status(thm)],[1643, 1639])).
% 0.69/0.84 tff(1645,plain,(
% 0.69/0.84 ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))),
% 0.69/0.84 inference(skolemize,[status(sab)],[1644])).
% 0.69/0.85 tff(1646,plain,
% 0.69/0.85 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))),
% 0.69/0.85 inference(modus_ponens,[status(thm)],[1645, 1638])).
% 0.69/0.85 tff(1647,plain,
% 0.69/0.85 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp9 | c0_1(a480) | c2_1(a480) | (~ndr1_0) | (~c3_1(a480)) | (~c3_1(a503)) | (~c2_1(a503)) | c0_1(a503))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp9 | c0_1(a480) | c2_1(a480) | (~ndr1_0) | (~c3_1(a480)) | (~c3_1(a503)) | (~c2_1(a503)) | c0_1(a503))),
% 0.69/0.85 inference(rewrite,[status(thm)],[])).
% 0.69/0.85 tff(1648,plain,
% 0.69/0.85 ((hskp9 | (~ndr1_0) | c0_1(a503) | (~c2_1(a503)) | (~c3_1(a503)) | c0_1(a480) | c2_1(a480) | (~c3_1(a480))) <=> (hskp9 | c0_1(a480) | c2_1(a480) | (~ndr1_0) | (~c3_1(a480)) | (~c3_1(a503)) | (~c2_1(a503)) | c0_1(a503))),
% 0.69/0.85 inference(rewrite,[status(thm)],[])).
% 0.69/0.85 tff(1649,plain,
% 0.69/0.85 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp9 | (~ndr1_0) | c0_1(a503) | (~c2_1(a503)) | (~c3_1(a503)) | c0_1(a480) | c2_1(a480) | (~c3_1(a480)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp9 | c0_1(a480) | c2_1(a480) | (~ndr1_0) | (~c3_1(a480)) | (~c3_1(a503)) | (~c2_1(a503)) | c0_1(a503)))),
% 0.69/0.85 inference(monotonicity,[status(thm)],[1648])).
% 0.69/0.85 tff(1650,plain,
% 0.69/0.85 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp9 | (~ndr1_0) | c0_1(a503) | (~c2_1(a503)) | (~c3_1(a503)) | c0_1(a480) | c2_1(a480) | (~c3_1(a480)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp9 | c0_1(a480) | c2_1(a480) | (~ndr1_0) | (~c3_1(a480)) | (~c3_1(a503)) | (~c2_1(a503)) | c0_1(a503))),
% 0.69/0.85 inference(transitivity,[status(thm)],[1649, 1647])).
% 0.69/0.85 tff(1651,plain,
% 0.69/0.85 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp9 | (~ndr1_0) | c0_1(a503) | (~c2_1(a503)) | (~c3_1(a503)) | c0_1(a480) | c2_1(a480) | (~c3_1(a480)))),
% 0.69/0.85 inference(quant_inst,[status(thm)],[])).
% 0.69/0.85 tff(1652,plain,
% 0.69/0.85 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp9 | c0_1(a480) | c2_1(a480) | (~ndr1_0) | (~c3_1(a480)) | (~c3_1(a503)) | (~c2_1(a503)) | c0_1(a503)),
% 0.69/0.85 inference(modus_ponens,[status(thm)],[1651, 1650])).
% 0.69/0.85 tff(1653,plain,
% 0.69/0.85 (hskp9),
% 0.69/0.85 inference(unit_resolution,[status(thm)],[1652, 941, 1635, 1634, 1466, 1464, 1646, 1636, 1525])).
% 0.69/0.85 tff(1654,plain,
% 0.69/0.85 (~c1_1(a476)),
% 0.69/0.85 inference(unit_resolution,[status(thm)],[1392, 1653])).
% 0.69/0.85 tff(1655,plain,
% 0.69/0.85 (c2_1(a476)),
% 0.69/0.85 inference(unit_resolution,[status(thm)],[1400, 1653])).
% 0.69/0.85 tff(1656,plain,
% 0.69/0.85 (c0_1(a476)),
% 0.69/0.85 inference(unit_resolution,[status(thm)],[1408, 1653])).
% 0.69/0.85 tff(1657,plain,
% 0.69/0.85 (~c3_1(a476)),
% 0.69/0.85 inference(unit_resolution,[status(thm)],[1415, 941, 33, 1656, 1655, 1654, 11])).
% 0.69/0.85 tff(1658,plain,
% 0.69/0.85 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c2_1(a524) | c1_1(a476) | (~ndr1_0) | c3_1(a476) | (~c2_1(a476)) | (~c3_1(a503)) | (~c2_1(a503)) | c0_1(a503) | (~c0_1(a524)) | (~c1_1(a524)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c2_1(a524) | c1_1(a476) | (~ndr1_0) | c3_1(a476) | (~c2_1(a476)) | (~c3_1(a503)) | (~c2_1(a503)) | c0_1(a503) | (~c0_1(a524)) | (~c1_1(a524)))),
% 0.69/0.85 inference(rewrite,[status(thm)],[])).
% 0.69/0.85 tff(1659,plain,
% 0.69/0.85 (((~ndr1_0) | c2_1(a524) | (~c0_1(a524)) | (~c1_1(a524)) | c3_1(a476) | c1_1(a476) | (~c2_1(a476)) | c0_1(a503) | (~c3_1(a503)) | (~c2_1(a503))) <=> (c2_1(a524) | c1_1(a476) | (~ndr1_0) | c3_1(a476) | (~c2_1(a476)) | (~c3_1(a503)) | (~c2_1(a503)) | c0_1(a503) | (~c0_1(a524)) | (~c1_1(a524)))),
% 0.69/0.85 inference(rewrite,[status(thm)],[])).
% 0.69/0.85 tff(1660,plain,
% 0.69/0.85 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a524) | (~c0_1(a524)) | (~c1_1(a524)) | c3_1(a476) | c1_1(a476) | (~c2_1(a476)) | c0_1(a503) | (~c3_1(a503)) | (~c2_1(a503)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c2_1(a524) | c1_1(a476) | (~ndr1_0) | c3_1(a476) | (~c2_1(a476)) | (~c3_1(a503)) | (~c2_1(a503)) | c0_1(a503) | (~c0_1(a524)) | (~c1_1(a524))))),
% 0.69/0.85 inference(monotonicity,[status(thm)],[1659])).
% 0.69/0.85 tff(1661,plain,
% 0.69/0.85 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a524) | (~c0_1(a524)) | (~c1_1(a524)) | c3_1(a476) | c1_1(a476) | (~c2_1(a476)) | c0_1(a503) | (~c3_1(a503)) | (~c2_1(a503)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c2_1(a524) | c1_1(a476) | (~ndr1_0) | c3_1(a476) | (~c2_1(a476)) | (~c3_1(a503)) | (~c2_1(a503)) | c0_1(a503) | (~c0_1(a524)) | (~c1_1(a524)))),
% 0.69/0.85 inference(transitivity,[status(thm)],[1660, 1658])).
% 0.69/0.85 tff(1662,plain,
% 0.69/0.85 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a524) | (~c0_1(a524)) | (~c1_1(a524)) | c3_1(a476) | c1_1(a476) | (~c2_1(a476)) | c0_1(a503) | (~c3_1(a503)) | (~c2_1(a503)))),
% 0.69/0.85 inference(quant_inst,[status(thm)],[])).
% 0.69/0.85 tff(1663,plain,
% 0.69/0.85 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c2_1(a524) | c1_1(a476) | (~ndr1_0) | c3_1(a476) | (~c2_1(a476)) | (~c3_1(a503)) | (~c2_1(a503)) | c0_1(a503) | (~c0_1(a524)) | (~c1_1(a524))),
% 0.69/0.85 inference(modus_ponens,[status(thm)],[1662, 1661])).
% 0.69/0.85 tff(1664,plain,
% 0.69/0.85 ($false),
% 0.69/0.85 inference(unit_resolution,[status(thm)],[1663, 941, 1480, 1479, 1635, 1634, 1655, 1509, 1654, 802, 1636, 1657])).
% 0.69/0.85 tff(1665,plain,(hskp17 | c2_1(a460)), inference(lemma,lemma(discharge,[]))).
% 0.69/0.85 tff(1666,plain,
% 0.69/0.85 (hskp17),
% 0.69/0.85 inference(unit_resolution,[status(thm)],[1665, 1])).
% 0.69/0.85 tff(1667,plain,
% 0.69/0.85 (~c1_1(a494)),
% 0.69/0.85 inference(unit_resolution,[status(thm)],[501, 1666])).
% 0.69/0.85 tff(1668,plain,
% 0.69/0.85 (~c3_1(a494)),
% 0.69/0.85 inference(unit_resolution,[status(thm)],[931, 1666])).
% 0.69/0.85 tff(1669,assumption,(~c0_1(a470)), introduced(assumption)).
% 0.69/0.85 tff(1670,plain,
% 0.69/0.85 (~hskp27),
% 0.69/0.85 inference(unit_resolution,[status(thm)],[1476, 329, 1305, 1, 1463])).
% 0.69/0.85 tff(1671,plain,
% 0.69/0.85 (hskp22),
% 0.69/0.85 inference(unit_resolution,[status(thm)],[374, 1670, 33])).
% 0.69/0.85 tff(1672,plain,
% 0.69/0.85 (c1_1(a524)),
% 0.69/0.85 inference(unit_resolution,[status(thm)],[382, 1671])).
% 0.69/0.85 tff(1673,plain,
% 0.69/0.85 (c0_1(a524)),
% 0.69/0.85 inference(unit_resolution,[status(thm)],[390, 1671])).
% 0.69/0.85 tff(1674,plain,
% 0.69/0.85 (~c3_1(a524)),
% 0.69/0.85 inference(unit_resolution,[status(thm)],[397, 941, 329, 1673, 1672, 1305, 1, 1463, 21])).
% 0.69/0.85 tff(1675,plain,
% 0.69/0.85 (~c1_1(a468)),
% 0.69/0.85 inference(unit_resolution,[status(thm)],[1488, 329])).
% 0.69/0.85 tff(1676,plain,
% 0.69/0.85 (hskp16),
% 0.69/0.85 inference(unit_resolution,[status(thm)],[1506, 1675, 33])).
% 0.69/0.85 tff(1677,plain,
% 0.69/0.85 (~c0_1(a493)),
% 0.69/0.85 inference(unit_resolution,[status(thm)],[897, 1676])).
% 0.69/0.85 tff(1678,plain,
% 0.69/0.85 (~c2_1(a524)),
% 0.69/0.85 inference(unit_resolution,[status(thm)],[403, 1671])).
% 0.69/0.85 tff(1679,plain,
% 0.69/0.85 (c1_1(a493)),
% 0.69/0.85 inference(unit_resolution,[status(thm)],[905, 1676])).
% 0.69/0.85 tff(1680,plain,
% 0.69/0.85 (~c3_1(a493)),
% 0.69/0.85 inference(unit_resolution,[status(thm)],[1516, 941, 1673, 1679, 1678, 1677, 1466, 1465, 1464, 32, 1674])).
% 0.69/0.85 tff(1681,assumption,(c2_1(a494)), introduced(assumption)).
% 0.69/0.85 tff(1682,assumption,(c1_1(a524)), introduced(assumption)).
% 0.69/0.85 tff(1683,assumption,(hskp19), introduced(assumption)).
% 0.69/0.85 tff(1684,plain,
% 0.69/0.85 (~c0_1(a502)),
% 0.69/0.85 inference(unit_resolution,[status(thm)],[1606, 1683])).
% 0.69/0.85 tff(1685,plain,
% 0.69/0.85 (c3_1(a502)),
% 0.69/0.85 inference(unit_resolution,[status(thm)],[1614, 1683])).
% 0.69/0.85 tff(1686,plain,
% 0.69/0.85 (c2_1(a502)),
% 0.69/0.85 inference(unit_resolution,[status(thm)],[1622, 1683])).
% 0.69/0.85 tff(1687,plain,
% 0.69/0.85 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c2_1(a524) | c0_1(a502) | c1_1(a494) | c3_1(a494) | (~ndr1_0) | (~c2_1(a494)) | (~c3_1(a502)) | (~c2_1(a502)) | (~c0_1(a524)) | (~c1_1(a524)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c2_1(a524) | c0_1(a502) | c1_1(a494) | c3_1(a494) | (~ndr1_0) | (~c2_1(a494)) | (~c3_1(a502)) | (~c2_1(a502)) | (~c0_1(a524)) | (~c1_1(a524)))),
% 0.69/0.85 inference(rewrite,[status(thm)],[])).
% 0.69/0.85 tff(1688,plain,
% 0.69/0.85 (((~ndr1_0) | c2_1(a524) | (~c0_1(a524)) | (~c1_1(a524)) | c3_1(a494) | c1_1(a494) | (~c2_1(a494)) | c0_1(a502) | (~c3_1(a502)) | (~c2_1(a502))) <=> (c2_1(a524) | c0_1(a502) | c1_1(a494) | c3_1(a494) | (~ndr1_0) | (~c2_1(a494)) | (~c3_1(a502)) | (~c2_1(a502)) | (~c0_1(a524)) | (~c1_1(a524)))),
% 0.69/0.85 inference(rewrite,[status(thm)],[])).
% 0.69/0.85 tff(1689,plain,
% 0.69/0.85 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a524) | (~c0_1(a524)) | (~c1_1(a524)) | c3_1(a494) | c1_1(a494) | (~c2_1(a494)) | c0_1(a502) | (~c3_1(a502)) | (~c2_1(a502)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c2_1(a524) | c0_1(a502) | c1_1(a494) | c3_1(a494) | (~ndr1_0) | (~c2_1(a494)) | (~c3_1(a502)) | (~c2_1(a502)) | (~c0_1(a524)) | (~c1_1(a524))))),
% 0.69/0.85 inference(monotonicity,[status(thm)],[1688])).
% 0.69/0.85 tff(1690,plain,
% 0.69/0.85 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a524) | (~c0_1(a524)) | (~c1_1(a524)) | c3_1(a494) | c1_1(a494) | (~c2_1(a494)) | c0_1(a502) | (~c3_1(a502)) | (~c2_1(a502)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c2_1(a524) | c0_1(a502) | c1_1(a494) | c3_1(a494) | (~ndr1_0) | (~c2_1(a494)) | (~c3_1(a502)) | (~c2_1(a502)) | (~c0_1(a524)) | (~c1_1(a524)))),
% 0.69/0.85 inference(transitivity,[status(thm)],[1689, 1687])).
% 0.69/0.85 tff(1691,plain,
% 0.69/0.85 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a524) | (~c0_1(a524)) | (~c1_1(a524)) | c3_1(a494) | c1_1(a494) | (~c2_1(a494)) | c0_1(a502) | (~c3_1(a502)) | (~c2_1(a502)))),
% 0.69/0.85 inference(quant_inst,[status(thm)],[])).
% 0.69/0.85 tff(1692,plain,
% 0.69/0.85 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c2_1(a524) | c0_1(a502) | c1_1(a494) | c3_1(a494) | (~ndr1_0) | (~c2_1(a494)) | (~c3_1(a502)) | (~c2_1(a502)) | (~c0_1(a524)) | (~c1_1(a524))),
% 0.69/0.85 inference(modus_ponens,[status(thm)],[1691, 1690])).
% 0.69/0.85 tff(1693,plain,
% 0.69/0.85 ($false),
% 0.69/0.85 inference(unit_resolution,[status(thm)],[1692, 941, 440, 1682, 1686, 1685, 439, 1684, 510, 495, 802, 1681])).
% 0.69/0.85 tff(1694,plain,((~hskp19) | (~c0_1(a524)) | (~c1_1(a524)) | c2_1(a524) | c1_1(a494) | c3_1(a494) | (~c2_1(a494))), inference(lemma,lemma(discharge,[]))).
% 0.69/0.85 tff(1695,plain,
% 0.69/0.85 (~hskp19),
% 0.69/0.85 inference(unit_resolution,[status(thm)],[1694, 1681, 1682, 439, 510, 495, 440])).
% 0.69/0.85 tff(1696,plain,
% 0.69/0.85 (((~![U: $i] : (hskp20 | hskp19 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp20 | hskp19 | c1_1(a494) | c3_1(a494) | (~ndr1_0) | (~c2_1(a494)))) <=> ((~![U: $i] : (hskp20 | hskp19 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | hskp20 | hskp19 | c1_1(a494) | c3_1(a494) | (~ndr1_0) | (~c2_1(a494)))),
% 0.69/0.85 inference(rewrite,[status(thm)],[])).
% 0.69/0.85 tff(1697,plain,
% 0.69/0.85 ((hskp20 | hskp19 | (~ndr1_0) | c1_1(a494) | c3_1(a494) | (~c2_1(a494))) <=> (hskp20 | hskp19 | c1_1(a494) | c3_1(a494) | (~ndr1_0) | (~c2_1(a494)))),
% 0.69/0.85 inference(rewrite,[status(thm)],[])).
% 0.69/0.85 tff(1698,plain,
% 0.69/0.85 (((~![U: $i] : (hskp20 | hskp19 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp20 | hskp19 | (~ndr1_0) | c1_1(a494) | c3_1(a494) | (~c2_1(a494)))) <=> ((~![U: $i] : (hskp20 | hskp19 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp20 | hskp19 | c1_1(a494) | c3_1(a494) | (~ndr1_0) | (~c2_1(a494))))),
% 0.69/0.85 inference(monotonicity,[status(thm)],[1697])).
% 0.69/0.85 tff(1699,plain,
% 0.69/0.85 (((~![U: $i] : (hskp20 | hskp19 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp20 | hskp19 | (~ndr1_0) | c1_1(a494) | c3_1(a494) | (~c2_1(a494)))) <=> ((~![U: $i] : (hskp20 | hskp19 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | hskp20 | hskp19 | c1_1(a494) | c3_1(a494) | (~ndr1_0) | (~c2_1(a494)))),
% 0.69/0.85 inference(transitivity,[status(thm)],[1698, 1696])).
% 0.69/0.85 tff(1700,plain,
% 0.69/0.85 ((~![U: $i] : (hskp20 | hskp19 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp20 | hskp19 | (~ndr1_0) | c1_1(a494) | c3_1(a494) | (~c2_1(a494)))),
% 0.69/0.85 inference(quant_inst,[status(thm)],[])).
% 0.69/0.85 tff(1701,plain,
% 0.69/0.85 ((~![U: $i] : (hskp20 | hskp19 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | hskp20 | hskp19 | c1_1(a494) | c3_1(a494) | (~ndr1_0) | (~c2_1(a494))),
% 0.69/0.85 inference(modus_ponens,[status(thm)],[1700, 1699])).
% 0.69/0.85 tff(1702,plain,
% 0.69/0.85 (hskp20 | hskp19 | c1_1(a494) | (~c2_1(a494))),
% 0.69/0.85 inference(unit_resolution,[status(thm)],[1701, 941, 495, 1594])).
% 0.69/0.85 tff(1703,plain,
% 0.69/0.85 (hskp20),
% 0.69/0.85 inference(unit_resolution,[status(thm)],[1702, 1695, 510, 1681])).
% 0.69/0.85 tff(1704,plain,
% 0.69/0.85 (~c1_1(a503)),
% 0.69/0.85 inference(unit_resolution,[status(thm)],[1023, 1703])).
% 0.69/0.85 tff(1705,plain,
% 0.69/0.85 (c3_1(a503)),
% 0.69/0.85 inference(unit_resolution,[status(thm)],[1031, 1703])).
% 0.69/0.85 tff(1706,plain,
% 0.69/0.85 (c2_1(a503)),
% 0.69/0.85 inference(unit_resolution,[status(thm)],[1039, 1703])).
% 0.69/0.85 tff(1707,plain,
% 0.69/0.85 (~c0_1(a503)),
% 0.69/0.85 inference(unit_resolution,[status(thm)],[1046, 941, 33, 1706, 1705, 1704, 11])).
% 0.69/0.85 tff(1708,plain,
% 0.69/0.85 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c2_1(a524) | c1_1(a494) | c3_1(a494) | (~ndr1_0) | (~c2_1(a494)) | (~c3_1(a503)) | (~c2_1(a503)) | c0_1(a503) | (~c0_1(a524)) | (~c1_1(a524)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c2_1(a524) | c1_1(a494) | c3_1(a494) | (~ndr1_0) | (~c2_1(a494)) | (~c3_1(a503)) | (~c2_1(a503)) | c0_1(a503) | (~c0_1(a524)) | (~c1_1(a524)))),
% 0.69/0.85 inference(rewrite,[status(thm)],[])).
% 0.69/0.85 tff(1709,plain,
% 0.69/0.85 (((~ndr1_0) | c2_1(a524) | (~c0_1(a524)) | (~c1_1(a524)) | c3_1(a494) | c1_1(a494) | (~c2_1(a494)) | c0_1(a503) | (~c3_1(a503)) | (~c2_1(a503))) <=> (c2_1(a524) | c1_1(a494) | c3_1(a494) | (~ndr1_0) | (~c2_1(a494)) | (~c3_1(a503)) | (~c2_1(a503)) | c0_1(a503) | (~c0_1(a524)) | (~c1_1(a524)))),
% 0.69/0.85 inference(rewrite,[status(thm)],[])).
% 0.69/0.85 tff(1710,plain,
% 0.69/0.85 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a524) | (~c0_1(a524)) | (~c1_1(a524)) | c3_1(a494) | c1_1(a494) | (~c2_1(a494)) | c0_1(a503) | (~c3_1(a503)) | (~c2_1(a503)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c2_1(a524) | c1_1(a494) | c3_1(a494) | (~ndr1_0) | (~c2_1(a494)) | (~c3_1(a503)) | (~c2_1(a503)) | c0_1(a503) | (~c0_1(a524)) | (~c1_1(a524))))),
% 0.69/0.85 inference(monotonicity,[status(thm)],[1709])).
% 0.69/0.85 tff(1711,plain,
% 0.69/0.85 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a524) | (~c0_1(a524)) | (~c1_1(a524)) | c3_1(a494) | c1_1(a494) | (~c2_1(a494)) | c0_1(a503) | (~c3_1(a503)) | (~c2_1(a503)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c2_1(a524) | c1_1(a494) | c3_1(a494) | (~ndr1_0) | (~c2_1(a494)) | (~c3_1(a503)) | (~c2_1(a503)) | c0_1(a503) | (~c0_1(a524)) | (~c1_1(a524)))),
% 0.69/0.85 inference(transitivity,[status(thm)],[1710, 1708])).
% 0.69/0.85 tff(1712,plain,
% 0.69/0.85 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a524) | (~c0_1(a524)) | (~c1_1(a524)) | c3_1(a494) | c1_1(a494) | (~c2_1(a494)) | c0_1(a503) | (~c3_1(a503)) | (~c2_1(a503)))),
% 0.69/0.85 inference(quant_inst,[status(thm)],[])).
% 0.69/0.85 tff(1713,plain,
% 0.69/0.85 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c2_1(a524) | c1_1(a494) | c3_1(a494) | (~ndr1_0) | (~c2_1(a494)) | (~c3_1(a503)) | (~c2_1(a503)) | c0_1(a503) | (~c0_1(a524)) | (~c1_1(a524))),
% 0.69/0.85 inference(modus_ponens,[status(thm)],[1712, 1711])).
% 0.69/0.85 tff(1714,plain,
% 0.69/0.85 ($false),
% 0.69/0.85 inference(unit_resolution,[status(thm)],[1713, 941, 440, 1682, 1706, 1705, 439, 510, 495, 802, 1681, 1707])).
% 0.69/0.85 tff(1715,plain,((~c2_1(a494)) | (~c0_1(a524)) | (~c1_1(a524)) | c2_1(a524) | c1_1(a494) | c3_1(a494) | hskp17), inference(lemma,lemma(discharge,[]))).
% 0.69/0.85 tff(1716,plain,
% 0.69/0.85 (~c2_1(a494)),
% 0.69/0.85 inference(unit_resolution,[status(thm)],[1715, 1673, 1672, 1678, 510, 495, 33])).
% 0.69/0.85 tff(1717,plain,
% 0.69/0.85 (~c2_1(a493)),
% 0.69/0.85 inference(unit_resolution,[status(thm)],[891, 1676])).
% 0.69/0.85 tff(1718,plain,
% 0.69/0.85 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp27 | c1_1(a494) | c3_1(a494) | c0_1(a493) | c2_1(a493) | (~ndr1_0) | c3_1(a493) | c2_1(a494))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp27 | c1_1(a494) | c3_1(a494) | c0_1(a493) | c2_1(a493) | (~ndr1_0) | c3_1(a493) | c2_1(a494))),
% 0.69/0.85 inference(rewrite,[status(thm)],[])).
% 0.69/0.85 tff(1719,plain,
% 0.69/0.85 ((hskp27 | (~ndr1_0) | c2_1(a494) | c1_1(a494) | c3_1(a494) | c3_1(a493) | c0_1(a493) | c2_1(a493)) <=> (hskp27 | c1_1(a494) | c3_1(a494) | c0_1(a493) | c2_1(a493) | (~ndr1_0) | c3_1(a493) | c2_1(a494))),
% 0.69/0.85 inference(rewrite,[status(thm)],[])).
% 0.69/0.85 tff(1720,plain,
% 0.69/0.85 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp27 | (~ndr1_0) | c2_1(a494) | c1_1(a494) | c3_1(a494) | c3_1(a493) | c0_1(a493) | c2_1(a493))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp27 | c1_1(a494) | c3_1(a494) | c0_1(a493) | c2_1(a493) | (~ndr1_0) | c3_1(a493) | c2_1(a494)))),
% 0.69/0.85 inference(monotonicity,[status(thm)],[1719])).
% 0.69/0.85 tff(1721,plain,
% 0.69/0.85 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp27 | (~ndr1_0) | c2_1(a494) | c1_1(a494) | c3_1(a494) | c3_1(a493) | c0_1(a493) | c2_1(a493))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp27 | c1_1(a494) | c3_1(a494) | c0_1(a493) | c2_1(a493) | (~ndr1_0) | c3_1(a493) | c2_1(a494))),
% 0.69/0.85 inference(transitivity,[status(thm)],[1720, 1718])).
% 0.69/0.85 tff(1722,plain,
% 0.69/0.85 ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp27 | (~ndr1_0) | c2_1(a494) | c1_1(a494) | c3_1(a494) | c3_1(a493) | c0_1(a493) | c2_1(a493))),
% 0.69/0.85 inference(quant_inst,[status(thm)],[])).
% 0.69/0.85 tff(1723,plain,
% 0.69/0.85 ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp27 | c1_1(a494) | c3_1(a494) | c0_1(a493) | c2_1(a493) | (~ndr1_0) | c3_1(a493) | c2_1(a494)),
% 0.69/0.85 inference(modus_ponens,[status(thm)],[1722, 1721])).
% 0.69/0.85 tff(1724,plain,
% 0.69/0.85 ($false),
% 0.69/0.85 inference(unit_resolution,[status(thm)],[1723, 941, 1670, 510, 495, 1677, 1717, 414, 1716, 1680])).
% 0.69/0.85 tff(1725,plain,(hskp3 | c1_1(a494) | c3_1(a494) | hskp17 | c2_1(a460)), inference(lemma,lemma(discharge,[]))).
% 0.69/0.85 tff(1726,plain,
% 0.69/0.85 (hskp17),
% 0.69/0.85 inference(unit_resolution,[status(thm)],[1725, 510, 1475, 495, 1])).
% 0.69/0.85 tff(1727,plain,
% 0.69/0.85 (~c0_1(a494)),
% 0.69/0.85 inference(unit_resolution,[status(thm)],[507, 1726])).
% 0.69/0.85 tff(1728,plain,
% 0.69/0.85 (c2_1(a494) | hskp27 | c0_1(a494) | c1_1(a494) | c3_1(a494)),
% 0.69/0.85 inference(unit_resolution,[status(thm)],[519, 941])).
% 0.69/0.85 tff(1729,plain,
% 0.69/0.85 (c2_1(a494)),
% 0.69/0.85 inference(unit_resolution,[status(thm)],[1728, 1727, 495, 510, 1477])).
% 0.69/0.85 tff(1730,plain,
% 0.69/0.85 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c0_1(a502) | c1_1(a494) | c3_1(a494) | c2_1(a460) | (~ndr1_0) | (~c1_1(a460)) | (~c0_1(a460)) | (~c2_1(a494)) | (~c3_1(a502)) | (~c2_1(a502)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c0_1(a502) | c1_1(a494) | c3_1(a494) | c2_1(a460) | (~ndr1_0) | (~c1_1(a460)) | (~c0_1(a460)) | (~c2_1(a494)) | (~c3_1(a502)) | (~c2_1(a502)))),
% 0.69/0.85 inference(rewrite,[status(thm)],[])).
% 0.69/0.85 tff(1731,plain,
% 0.69/0.85 (((~ndr1_0) | c2_1(a460) | (~c0_1(a460)) | (~c1_1(a460)) | c3_1(a494) | c1_1(a494) | (~c2_1(a494)) | c0_1(a502) | (~c3_1(a502)) | (~c2_1(a502))) <=> (c0_1(a502) | c1_1(a494) | c3_1(a494) | c2_1(a460) | (~ndr1_0) | (~c1_1(a460)) | (~c0_1(a460)) | (~c2_1(a494)) | (~c3_1(a502)) | (~c2_1(a502)))),
% 0.69/0.85 inference(rewrite,[status(thm)],[])).
% 0.69/0.85 tff(1732,plain,
% 0.69/0.85 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a460) | (~c0_1(a460)) | (~c1_1(a460)) | c3_1(a494) | c1_1(a494) | (~c2_1(a494)) | c0_1(a502) | (~c3_1(a502)) | (~c2_1(a502)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c0_1(a502) | c1_1(a494) | c3_1(a494) | c2_1(a460) | (~ndr1_0) | (~c1_1(a460)) | (~c0_1(a460)) | (~c2_1(a494)) | (~c3_1(a502)) | (~c2_1(a502))))),
% 0.69/0.85 inference(monotonicity,[status(thm)],[1731])).
% 0.69/0.85 tff(1733,plain,
% 0.69/0.85 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a460) | (~c0_1(a460)) | (~c1_1(a460)) | c3_1(a494) | c1_1(a494) | (~c2_1(a494)) | c0_1(a502) | (~c3_1(a502)) | (~c2_1(a502)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c0_1(a502) | c1_1(a494) | c3_1(a494) | c2_1(a460) | (~ndr1_0) | (~c1_1(a460)) | (~c0_1(a460)) | (~c2_1(a494)) | (~c3_1(a502)) | (~c2_1(a502)))),
% 0.69/0.85 inference(transitivity,[status(thm)],[1732, 1730])).
% 0.69/0.85 tff(1734,plain,
% 0.69/0.85 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a460) | (~c0_1(a460)) | (~c1_1(a460)) | c3_1(a494) | c1_1(a494) | (~c2_1(a494)) | c0_1(a502) | (~c3_1(a502)) | (~c2_1(a502)))),
% 0.69/0.85 inference(quant_inst,[status(thm)],[])).
% 0.69/0.85 tff(1735,plain,
% 0.69/0.85 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c0_1(a502) | c1_1(a494) | c3_1(a494) | c2_1(a460) | (~ndr1_0) | (~c1_1(a460)) | (~c0_1(a460)) | (~c2_1(a494)) | (~c3_1(a502)) | (~c2_1(a502))),
% 0.69/0.85 inference(modus_ponens,[status(thm)],[1734, 1733])).
% 0.69/0.85 tff(1736,plain,
% 0.69/0.85 (~c1_1(a460)),
% 0.69/0.85 inference(unit_resolution,[status(thm)],[1735, 941, 1686, 1685, 1305, 1684, 510, 495, 1, 802, 1729])).
% 0.69/0.85 tff(1737,plain,
% 0.69/0.85 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W)))),
% 0.69/0.85 inference(bind,[status(th)],[])).
% 0.69/0.85 tff(1738,plain,
% 0.69/0.85 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))),
% 0.69/0.85 inference(quant_intro,[status(thm)],[1737])).
% 0.69/0.85 tff(1739,plain,
% 0.69/0.85 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))),
% 0.69/0.85 inference(rewrite,[status(thm)],[])).
% 0.69/0.85 tff(1740,plain,
% 0.69/0.85 (^[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))) <=> ((~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c0_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)))), rewrite((((~c0_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_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) | (~c0_1(U)) | (~c3_1(U)) | (~c1_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))) | c1_1(W)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c1_1(W)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c1_1(W)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c1_1(W)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c1_1(W)) | c2_1(W)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W)) | c2_1(W)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W)) | c2_1(W)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c2_1(W))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c1_1(W)) | c2_1(W)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c2_1(W)))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c1_1(W)) | c2_1(W)) | c3_1(W)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c2_1(W)) | c3_1(W)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c2_1(W)) | c3_1(W)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c1_1(W)) | c2_1(W)) | c3_1(W)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W)))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c1_1(W)) | c2_1(W)) | c3_1(W)) | c0_1(V)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W)) | c0_1(V)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W)) | c0_1(V)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c1_1(W)) | c2_1(W)) | c3_1(W)) | c0_1(V)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))))),
% 0.69/0.85 inference(bind,[status(th)],[])).
% 0.69/0.85 tff(1741,plain,
% 0.69/0.85 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c1_1(W)) | c2_1(W)) | c3_1(W)) | c0_1(V)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))),
% 0.69/0.85 inference(quant_intro,[status(thm)],[1740])).
% 0.69/0.85 tff(1742,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c1_1(W)) | c2_1(W)) | c3_1(W)) | c0_1(V))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause175')).
% 0.69/0.85 tff(1743,plain,
% 0.69/0.85 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))),
% 0.69/0.85 inference(modus_ponens,[status(thm)],[1742, 1741])).
% 0.69/0.85 tff(1744,plain,
% 0.69/0.85 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))),
% 0.69/0.85 inference(modus_ponens,[status(thm)],[1743, 1739])).
% 0.69/0.85 tff(1745,plain,(
% 0.69/0.85 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))),
% 0.69/0.85 inference(skolemize,[status(sab)],[1744])).
% 0.69/0.85 tff(1746,plain,
% 0.69/0.85 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))),
% 0.69/0.85 inference(modus_ponens,[status(thm)],[1745, 1738])).
% 0.69/0.85 tff(1747,plain,
% 0.69/0.85 (^[V: $i, U: $i] : refl((hskp28 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c2_1(V)) <=> (hskp28 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c2_1(V)))),
% 0.69/0.85 inference(bind,[status(th)],[])).
% 0.69/0.85 tff(1748,plain,
% 0.69/0.85 (![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c2_1(V)) <=> ![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))),
% 0.69/0.85 inference(quant_intro,[status(thm)],[1747])).
% 0.69/0.85 tff(1749,plain,
% 0.69/0.85 (![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c2_1(V)) <=> ![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))),
% 0.69/0.85 inference(rewrite,[status(thm)],[])).
% 0.69/0.85 tff(1750,plain,
% 0.69/0.85 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U))))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V)))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c2_1(V)))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | hskp28) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c2_1(V)) | hskp28))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c2_1(V)) | hskp28) <=> (hskp28 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | hskp28) <=> (hskp28 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))))),
% 0.69/0.86 inference(bind,[status(th)],[])).
% 0.69/0.86 tff(1751,plain,
% 0.69/0.86 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | hskp28) <=> ![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))),
% 0.69/0.86 inference(quant_intro,[status(thm)],[1750])).
% 0.69/0.86 tff(1752,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | hskp28)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause150')).
% 0.69/0.86 tff(1753,plain,
% 0.69/0.86 (![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))),
% 0.69/0.86 inference(modus_ponens,[status(thm)],[1752, 1751])).
% 0.69/0.86 tff(1754,plain,
% 0.69/0.86 (![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))),
% 0.69/0.86 inference(modus_ponens,[status(thm)],[1753, 1749])).
% 0.69/0.86 tff(1755,plain,(
% 0.69/0.86 ![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))),
% 0.69/0.86 inference(skolemize,[status(sab)],[1754])).
% 0.69/0.86 tff(1756,plain,
% 0.69/0.86 (![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))),
% 0.69/0.86 inference(modus_ponens,[status(thm)],[1755, 1748])).
% 0.69/0.86 tff(1757,plain,
% 0.69/0.86 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp28 | c2_1(a468) | c2_1(a460) | c3_1(a460) | (~ndr1_0) | (~c0_1(a468)) | (~c3_1(a468)) | c1_1(a460))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp28 | c2_1(a468) | c2_1(a460) | c3_1(a460) | (~ndr1_0) | (~c0_1(a468)) | (~c3_1(a468)) | c1_1(a460))),
% 0.69/0.86 inference(rewrite,[status(thm)],[])).
% 0.69/0.86 tff(1758,plain,
% 0.69/0.86 ((hskp28 | (~ndr1_0) | c2_1(a468) | (~c0_1(a468)) | (~c3_1(a468)) | c3_1(a460) | c1_1(a460) | c2_1(a460)) <=> (hskp28 | c2_1(a468) | c2_1(a460) | c3_1(a460) | (~ndr1_0) | (~c0_1(a468)) | (~c3_1(a468)) | c1_1(a460))),
% 0.69/0.86 inference(rewrite,[status(thm)],[])).
% 0.69/0.86 tff(1759,plain,
% 0.69/0.86 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp28 | (~ndr1_0) | c2_1(a468) | (~c0_1(a468)) | (~c3_1(a468)) | c3_1(a460) | c1_1(a460) | c2_1(a460))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp28 | c2_1(a468) | c2_1(a460) | c3_1(a460) | (~ndr1_0) | (~c0_1(a468)) | (~c3_1(a468)) | c1_1(a460)))),
% 0.69/0.86 inference(monotonicity,[status(thm)],[1758])).
% 0.69/0.86 tff(1760,plain,
% 0.69/0.86 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp28 | (~ndr1_0) | c2_1(a468) | (~c0_1(a468)) | (~c3_1(a468)) | c3_1(a460) | c1_1(a460) | c2_1(a460))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp28 | c2_1(a468) | c2_1(a460) | c3_1(a460) | (~ndr1_0) | (~c0_1(a468)) | (~c3_1(a468)) | c1_1(a460))),
% 0.69/0.86 inference(transitivity,[status(thm)],[1759, 1757])).
% 0.69/0.86 tff(1761,plain,
% 0.69/0.86 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp28 | (~ndr1_0) | c2_1(a468) | (~c0_1(a468)) | (~c3_1(a468)) | c3_1(a460) | c1_1(a460) | c2_1(a460))),
% 0.69/0.86 inference(quant_inst,[status(thm)],[])).
% 0.69/0.86 tff(1762,plain,
% 0.69/0.86 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp28 | c2_1(a468) | c2_1(a460) | c3_1(a460) | (~ndr1_0) | (~c0_1(a468)) | (~c3_1(a468)) | c1_1(a460)),
% 0.69/0.86 inference(modus_ponens,[status(thm)],[1761, 1760])).
% 0.69/0.86 tff(1763,plain,
% 0.69/0.86 (hskp28 | c1_1(a460)),
% 0.69/0.86 inference(unit_resolution,[status(thm)],[1762, 941, 1125, 1117, 1109, 1, 1463, 1756])).
% 0.69/0.86 tff(1764,plain,
% 0.69/0.86 (hskp28),
% 0.69/0.86 inference(unit_resolution,[status(thm)],[1763, 1736])).
% 0.69/0.86 tff(1765,plain,
% 0.69/0.86 (((~hskp28) | c1_1(a490)) <=> ((~hskp28) | c1_1(a490))),
% 0.69/0.86 inference(rewrite,[status(thm)],[])).
% 0.69/0.86 tff(1766,axiom,((~hskp28) | c1_1(a490)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause39')).
% 0.69/0.86 tff(1767,plain,
% 0.69/0.86 ((~hskp28) | c1_1(a490)),
% 0.69/0.86 inference(modus_ponens,[status(thm)],[1766, 1765])).
% 0.69/0.86 tff(1768,plain,
% 0.69/0.86 ((~hskp28) | c1_1(a490)),
% 0.69/0.86 inference(modus_ponens,[status(thm)],[1767, 1765])).
% 0.69/0.86 tff(1769,plain,
% 0.69/0.86 ((~hskp28) | c1_1(a490)),
% 0.69/0.86 inference(modus_ponens,[status(thm)],[1768, 1765])).
% 0.69/0.86 tff(1770,plain,
% 0.69/0.86 ((~hskp28) | c1_1(a490)),
% 0.69/0.86 inference(modus_ponens,[status(thm)],[1769, 1765])).
% 0.69/0.86 tff(1771,plain,
% 0.69/0.86 ((~hskp28) | c1_1(a490)),
% 0.69/0.86 inference(modus_ponens,[status(thm)],[1770, 1765])).
% 0.69/0.86 tff(1772,plain,
% 0.69/0.86 (c1_1(a490)),
% 0.69/0.86 inference(unit_resolution,[status(thm)],[1771, 1764])).
% 0.69/0.86 tff(1773,plain,
% 0.69/0.86 (((~hskp28) | c0_1(a490)) <=> ((~hskp28) | c0_1(a490))),
% 0.69/0.86 inference(rewrite,[status(thm)],[])).
% 0.69/0.86 tff(1774,axiom,((~hskp28) | c0_1(a490)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause38')).
% 0.69/0.86 tff(1775,plain,
% 0.69/0.86 ((~hskp28) | c0_1(a490)),
% 0.69/0.86 inference(modus_ponens,[status(thm)],[1774, 1773])).
% 0.69/0.86 tff(1776,plain,
% 0.69/0.86 ((~hskp28) | c0_1(a490)),
% 0.69/0.86 inference(modus_ponens,[status(thm)],[1775, 1773])).
% 0.69/0.86 tff(1777,plain,
% 0.69/0.86 ((~hskp28) | c0_1(a490)),
% 0.69/0.86 inference(modus_ponens,[status(thm)],[1776, 1773])).
% 0.69/0.86 tff(1778,plain,
% 0.69/0.86 ((~hskp28) | c0_1(a490)),
% 0.69/0.86 inference(modus_ponens,[status(thm)],[1777, 1773])).
% 0.69/0.86 tff(1779,plain,
% 0.69/0.86 ((~hskp28) | c0_1(a490)),
% 0.69/0.86 inference(modus_ponens,[status(thm)],[1778, 1773])).
% 0.69/0.86 tff(1780,plain,
% 0.69/0.86 (c0_1(a490)),
% 0.69/0.86 inference(unit_resolution,[status(thm)],[1779, 1764])).
% 0.69/0.86 tff(1781,plain,
% 0.69/0.86 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | (c0_1(a502) | c2_1(a460) | c3_1(a460) | (~ndr1_0) | c1_1(a460) | (~c0_1(a490)) | (~c3_1(a490)) | (~c1_1(a490)) | (~c3_1(a502)) | (~c2_1(a502)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c0_1(a502) | c2_1(a460) | c3_1(a460) | (~ndr1_0) | c1_1(a460) | (~c0_1(a490)) | (~c3_1(a490)) | (~c1_1(a490)) | (~c3_1(a502)) | (~c2_1(a502)))),
% 0.69/0.86 inference(rewrite,[status(thm)],[])).
% 0.69/0.86 tff(1782,plain,
% 0.69/0.86 (((~ndr1_0) | (~c0_1(a490)) | (~c3_1(a490)) | (~c1_1(a490)) | c0_1(a502) | (~c3_1(a502)) | (~c2_1(a502)) | c3_1(a460) | c1_1(a460) | c2_1(a460)) <=> (c0_1(a502) | c2_1(a460) | c3_1(a460) | (~ndr1_0) | c1_1(a460) | (~c0_1(a490)) | (~c3_1(a490)) | (~c1_1(a490)) | (~c3_1(a502)) | (~c2_1(a502)))),
% 0.69/0.86 inference(rewrite,[status(thm)],[])).
% 0.69/0.86 tff(1783,plain,
% 0.69/0.86 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | (~c0_1(a490)) | (~c3_1(a490)) | (~c1_1(a490)) | c0_1(a502) | (~c3_1(a502)) | (~c2_1(a502)) | c3_1(a460) | c1_1(a460) | c2_1(a460))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | (c0_1(a502) | c2_1(a460) | c3_1(a460) | (~ndr1_0) | c1_1(a460) | (~c0_1(a490)) | (~c3_1(a490)) | (~c1_1(a490)) | (~c3_1(a502)) | (~c2_1(a502))))),
% 0.69/0.86 inference(monotonicity,[status(thm)],[1782])).
% 0.69/0.86 tff(1784,plain,
% 0.69/0.86 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | (~c0_1(a490)) | (~c3_1(a490)) | (~c1_1(a490)) | c0_1(a502) | (~c3_1(a502)) | (~c2_1(a502)) | c3_1(a460) | c1_1(a460) | c2_1(a460))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c0_1(a502) | c2_1(a460) | c3_1(a460) | (~ndr1_0) | c1_1(a460) | (~c0_1(a490)) | (~c3_1(a490)) | (~c1_1(a490)) | (~c3_1(a502)) | (~c2_1(a502)))),
% 0.69/0.86 inference(transitivity,[status(thm)],[1783, 1781])).
% 0.69/0.86 tff(1785,plain,
% 0.69/0.86 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | (~c0_1(a490)) | (~c3_1(a490)) | (~c1_1(a490)) | c0_1(a502) | (~c3_1(a502)) | (~c2_1(a502)) | c3_1(a460) | c1_1(a460) | c2_1(a460))),
% 0.69/0.86 inference(quant_inst,[status(thm)],[])).
% 0.69/0.86 tff(1786,plain,
% 0.69/0.86 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c0_1(a502) | c2_1(a460) | c3_1(a460) | (~ndr1_0) | c1_1(a460) | (~c0_1(a490)) | (~c3_1(a490)) | (~c1_1(a490)) | (~c3_1(a502)) | (~c2_1(a502))),
% 0.69/0.86 inference(modus_ponens,[status(thm)],[1785, 1784])).
% 0.69/0.86 tff(1787,plain,
% 0.69/0.86 (~c3_1(a490)),
% 0.69/0.86 inference(unit_resolution,[status(thm)],[1786, 941, 1780, 1772, 1686, 1685, 1684, 1, 1463, 1746, 1736])).
% 0.69/0.86 tff(1788,plain,
% 0.69/0.86 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a502) | c0_1(a480) | c1_1(a480) | c2_1(a480) | c2_1(a460) | c3_1(a460) | (~ndr1_0) | (~c0_1(a460)) | (~c3_1(a502)) | (~c1_1(a502)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c0_1(a502) | c0_1(a480) | c1_1(a480) | c2_1(a480) | c2_1(a460) | c3_1(a460) | (~ndr1_0) | (~c0_1(a460)) | (~c3_1(a502)) | (~c1_1(a502)))),
% 0.69/0.86 inference(rewrite,[status(thm)],[])).
% 0.69/0.86 tff(1789,plain,
% 0.69/0.86 (((~ndr1_0) | c2_1(a460) | c3_1(a460) | (~c0_1(a460)) | c0_1(a502) | (~c1_1(a502)) | (~c3_1(a502)) | c1_1(a480) | c0_1(a480) | c2_1(a480)) <=> (c0_1(a502) | c0_1(a480) | c1_1(a480) | c2_1(a480) | c2_1(a460) | c3_1(a460) | (~ndr1_0) | (~c0_1(a460)) | (~c3_1(a502)) | (~c1_1(a502)))),
% 0.69/0.86 inference(rewrite,[status(thm)],[])).
% 0.69/0.86 tff(1790,plain,
% 0.69/0.86 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c2_1(a460) | c3_1(a460) | (~c0_1(a460)) | c0_1(a502) | (~c1_1(a502)) | (~c3_1(a502)) | c1_1(a480) | c0_1(a480) | c2_1(a480))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a502) | c0_1(a480) | c1_1(a480) | c2_1(a480) | c2_1(a460) | c3_1(a460) | (~ndr1_0) | (~c0_1(a460)) | (~c3_1(a502)) | (~c1_1(a502))))),
% 0.69/0.86 inference(monotonicity,[status(thm)],[1789])).
% 0.69/0.86 tff(1791,plain,
% 0.69/0.86 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c2_1(a460) | c3_1(a460) | (~c0_1(a460)) | c0_1(a502) | (~c1_1(a502)) | (~c3_1(a502)) | c1_1(a480) | c0_1(a480) | c2_1(a480))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c0_1(a502) | c0_1(a480) | c1_1(a480) | c2_1(a480) | c2_1(a460) | c3_1(a460) | (~ndr1_0) | (~c0_1(a460)) | (~c3_1(a502)) | (~c1_1(a502)))),
% 0.69/0.86 inference(transitivity,[status(thm)],[1790, 1788])).
% 0.69/0.86 tff(1792,plain,
% 0.69/0.86 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c2_1(a460) | c3_1(a460) | (~c0_1(a460)) | c0_1(a502) | (~c1_1(a502)) | (~c3_1(a502)) | c1_1(a480) | c0_1(a480) | c2_1(a480))),
% 0.69/0.86 inference(quant_inst,[status(thm)],[])).
% 0.69/0.86 tff(1793,plain,
% 0.69/0.86 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c0_1(a502) | c0_1(a480) | c1_1(a480) | c2_1(a480) | c2_1(a460) | c3_1(a460) | (~ndr1_0) | (~c0_1(a460)) | (~c3_1(a502)) | (~c1_1(a502))),
% 0.69/0.86 inference(modus_ponens,[status(thm)],[1792, 1791])).
% 0.69/0.86 tff(1794,plain,
% 0.69/0.86 (~c1_1(a502)),
% 0.69/0.86 inference(unit_resolution,[status(thm)],[1793, 941, 1685, 1305, 1684, 1466, 1465, 1464, 1, 1463, 32])).
% 0.69/0.86 tff(1795,plain,
% 0.69/0.86 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c3_1(U) | (~c2_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) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W)))),
% 0.69/0.86 inference(bind,[status(th)],[])).
% 0.69/0.86 tff(1796,plain,
% 0.69/0.86 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_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) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))),
% 0.69/0.86 inference(quant_intro,[status(thm)],[1795])).
% 0.69/0.86 tff(1797,plain,
% 0.69/0.86 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_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) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))),
% 0.69/0.86 inference(rewrite,[status(thm)],[])).
% 0.69/0.86 tff(1798,plain,
% 0.69/0.86 (^[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) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | 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)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_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)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | 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)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | 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)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c3_1(U)) | c1_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V))) | c0_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V))) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c3_1(U)) | c1_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W)))), ((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c3_1(U)) | c1_1(V)) | c0_1(W)) | c1_1(W)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W)) | c1_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W))), ((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c3_1(U)) | c1_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W)))), (((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c3_1(U)) | c1_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> (((~ndr1_0) | c3_1(U) | (~c2_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) | c3_1(U) | (~c2_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) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_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))) | c3_1(U)) | c1_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))))),
% 0.69/0.86 inference(bind,[status(th)],[])).
% 0.69/0.86 tff(1799,plain,
% 0.69/0.86 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c3_1(U)) | c1_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))),
% 0.69/0.86 inference(quant_intro,[status(thm)],[1798])).
% 0.69/0.86 tff(1800,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c3_1(U)) | c1_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause173')).
% 0.69/0.86 tff(1801,plain,
% 0.69/0.86 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))),
% 0.69/0.86 inference(modus_ponens,[status(thm)],[1800, 1799])).
% 0.69/0.86 tff(1802,plain,
% 0.69/0.86 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))),
% 0.69/0.86 inference(modus_ponens,[status(thm)],[1801, 1797])).
% 0.69/0.86 tff(1803,plain,(
% 0.69/0.86 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))),
% 0.69/0.86 inference(skolemize,[status(sab)],[1802])).
% 0.69/0.86 tff(1804,plain,
% 0.69/0.86 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))),
% 0.69/0.86 inference(modus_ponens,[status(thm)],[1803, 1796])).
% 0.69/0.86 tff(1805,plain,
% 0.69/0.86 (((~hskp28) | c2_1(a490)) <=> ((~hskp28) | c2_1(a490))),
% 0.69/0.86 inference(rewrite,[status(thm)],[])).
% 0.69/0.86 tff(1806,axiom,((~hskp28) | c2_1(a490)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause40')).
% 0.69/0.86 tff(1807,plain,
% 0.69/0.86 ((~hskp28) | c2_1(a490)),
% 0.69/0.86 inference(modus_ponens,[status(thm)],[1806, 1805])).
% 0.69/0.86 tff(1808,plain,
% 0.69/0.86 ((~hskp28) | c2_1(a490)),
% 0.69/0.86 inference(modus_ponens,[status(thm)],[1807, 1805])).
% 0.69/0.86 tff(1809,plain,
% 0.69/0.86 ((~hskp28) | c2_1(a490)),
% 0.69/0.86 inference(modus_ponens,[status(thm)],[1808, 1805])).
% 0.69/0.86 tff(1810,plain,
% 0.69/0.86 ((~hskp28) | c2_1(a490)),
% 0.69/0.86 inference(modus_ponens,[status(thm)],[1809, 1805])).
% 0.69/0.86 tff(1811,plain,
% 0.69/0.86 ((~hskp28) | c2_1(a490)),
% 0.69/0.86 inference(modus_ponens,[status(thm)],[1810, 1805])).
% 0.69/0.86 tff(1812,plain,
% 0.69/0.86 (c2_1(a490)),
% 0.69/0.86 inference(unit_resolution,[status(thm)],[1811, 1764])).
% 0.69/0.86 tff(1813,plain,
% 0.69/0.86 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a480) | c1_1(a480) | c2_1(a480) | (~ndr1_0) | (~c2_1(a490)) | (~c0_1(a490)) | c3_1(a490) | (~c3_1(a502)) | (~c2_1(a502)) | c1_1(a502))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c0_1(a480) | c1_1(a480) | c2_1(a480) | (~ndr1_0) | (~c2_1(a490)) | (~c0_1(a490)) | c3_1(a490) | (~c3_1(a502)) | (~c2_1(a502)) | c1_1(a502))),
% 0.69/0.86 inference(rewrite,[status(thm)],[])).
% 0.69/0.86 tff(1814,plain,
% 0.69/0.86 (((~ndr1_0) | c3_1(a490) | (~c2_1(a490)) | (~c0_1(a490)) | c1_1(a502) | (~c3_1(a502)) | (~c2_1(a502)) | c1_1(a480) | c0_1(a480) | c2_1(a480)) <=> (c0_1(a480) | c1_1(a480) | c2_1(a480) | (~ndr1_0) | (~c2_1(a490)) | (~c0_1(a490)) | c3_1(a490) | (~c3_1(a502)) | (~c2_1(a502)) | c1_1(a502))),
% 0.69/0.86 inference(rewrite,[status(thm)],[])).
% 0.69/0.86 tff(1815,plain,
% 0.69/0.86 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_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) | c3_1(a490) | (~c2_1(a490)) | (~c0_1(a490)) | c1_1(a502) | (~c3_1(a502)) | (~c2_1(a502)) | c1_1(a480) | c0_1(a480) | c2_1(a480))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a480) | c1_1(a480) | c2_1(a480) | (~ndr1_0) | (~c2_1(a490)) | (~c0_1(a490)) | c3_1(a490) | (~c3_1(a502)) | (~c2_1(a502)) | c1_1(a502)))),
% 0.69/0.86 inference(monotonicity,[status(thm)],[1814])).
% 0.69/0.86 tff(1816,plain,
% 0.69/0.86 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_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) | c3_1(a490) | (~c2_1(a490)) | (~c0_1(a490)) | c1_1(a502) | (~c3_1(a502)) | (~c2_1(a502)) | c1_1(a480) | c0_1(a480) | c2_1(a480))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c0_1(a480) | c1_1(a480) | c2_1(a480) | (~ndr1_0) | (~c2_1(a490)) | (~c0_1(a490)) | c3_1(a490) | (~c3_1(a502)) | (~c2_1(a502)) | c1_1(a502))),
% 0.69/0.86 inference(transitivity,[status(thm)],[1815, 1813])).
% 0.69/0.86 tff(1817,plain,
% 0.69/0.86 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_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) | c3_1(a490) | (~c2_1(a490)) | (~c0_1(a490)) | c1_1(a502) | (~c3_1(a502)) | (~c2_1(a502)) | c1_1(a480) | c0_1(a480) | c2_1(a480))),
% 0.69/0.86 inference(quant_inst,[status(thm)],[])).
% 0.69/0.86 tff(1818,plain,
% 0.69/0.86 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c0_1(a480) | c1_1(a480) | c2_1(a480) | (~ndr1_0) | (~c2_1(a490)) | (~c0_1(a490)) | c3_1(a490) | (~c3_1(a502)) | (~c2_1(a502)) | c1_1(a502)),
% 0.69/0.86 inference(modus_ponens,[status(thm)],[1817, 1816])).
% 0.69/0.86 tff(1819,plain,
% 0.69/0.86 ($false),
% 0.69/0.86 inference(unit_resolution,[status(thm)],[1818, 941, 1780, 1812, 1686, 1685, 1466, 1465, 1464, 1804, 1794, 1787])).
% 0.69/0.86 tff(1820,plain,((~hskp19) | c2_1(a460) | c1_1(a494) | c3_1(a494)), inference(lemma,lemma(discharge,[]))).
% 0.69/0.86 tff(1821,plain,
% 0.69/0.86 (~hskp19),
% 0.69/0.86 inference(unit_resolution,[status(thm)],[1820, 510, 1, 495])).
% 0.69/0.86 tff(1822,plain,
% 0.69/0.86 (hskp20),
% 0.69/0.86 inference(unit_resolution,[status(thm)],[1702, 1821, 510, 1729])).
% 0.69/0.86 tff(1823,plain,
% 0.69/0.86 (~c1_1(a503)),
% 0.69/0.86 inference(unit_resolution,[status(thm)],[1023, 1822])).
% 0.69/0.86 tff(1824,plain,
% 0.69/0.86 (c3_1(a503)),
% 0.69/0.86 inference(unit_resolution,[status(thm)],[1031, 1822])).
% 0.69/0.86 tff(1825,plain,
% 0.69/0.86 (c2_1(a503)),
% 0.69/0.86 inference(unit_resolution,[status(thm)],[1039, 1822])).
% 0.69/0.86 tff(1826,assumption,(hskp28), introduced(assumption)).
% 0.69/0.86 tff(1827,plain,
% 0.69/0.86 (c1_1(a490)),
% 0.69/0.86 inference(unit_resolution,[status(thm)],[1771, 1826])).
% 0.69/0.86 tff(1828,plain,
% 0.69/0.86 (c0_1(a490)),
% 0.69/0.86 inference(unit_resolution,[status(thm)],[1779, 1826])).
% 0.69/0.86 tff(1829,plain,
% 0.69/0.86 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp3 | c2_1(a460) | c3_1(a460) | (~ndr1_0) | (~c0_1(a460)) | (~c0_1(a490)) | (~c3_1(a490)) | (~c1_1(a490)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | hskp3 | c2_1(a460) | c3_1(a460) | (~ndr1_0) | (~c0_1(a460)) | (~c0_1(a490)) | (~c3_1(a490)) | (~c1_1(a490)))),
% 0.69/0.86 inference(rewrite,[status(thm)],[])).
% 0.69/0.86 tff(1830,plain,
% 0.69/0.86 ((hskp3 | (~ndr1_0) | (~c0_1(a490)) | (~c3_1(a490)) | (~c1_1(a490)) | c3_1(a460) | c2_1(a460) | (~c0_1(a460))) <=> (hskp3 | c2_1(a460) | c3_1(a460) | (~ndr1_0) | (~c0_1(a460)) | (~c0_1(a490)) | (~c3_1(a490)) | (~c1_1(a490)))),
% 0.69/0.86 inference(rewrite,[status(thm)],[])).
% 0.69/0.86 tff(1831,plain,
% 0.69/0.86 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp3 | (~ndr1_0) | (~c0_1(a490)) | (~c3_1(a490)) | (~c1_1(a490)) | c3_1(a460) | c2_1(a460) | (~c0_1(a460)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp3 | c2_1(a460) | c3_1(a460) | (~ndr1_0) | (~c0_1(a460)) | (~c0_1(a490)) | (~c3_1(a490)) | (~c1_1(a490))))),
% 0.69/0.86 inference(monotonicity,[status(thm)],[1830])).
% 0.69/0.86 tff(1832,plain,
% 0.69/0.86 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp3 | (~ndr1_0) | (~c0_1(a490)) | (~c3_1(a490)) | (~c1_1(a490)) | c3_1(a460) | c2_1(a460) | (~c0_1(a460)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | hskp3 | c2_1(a460) | c3_1(a460) | (~ndr1_0) | (~c0_1(a460)) | (~c0_1(a490)) | (~c3_1(a490)) | (~c1_1(a490)))),
% 0.69/0.86 inference(transitivity,[status(thm)],[1831, 1829])).
% 0.69/0.86 tff(1833,plain,
% 0.69/0.86 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp3 | (~ndr1_0) | (~c0_1(a490)) | (~c3_1(a490)) | (~c1_1(a490)) | c3_1(a460) | c2_1(a460) | (~c0_1(a460)))),
% 0.69/0.86 inference(quant_inst,[status(thm)],[])).
% 0.69/0.86 tff(1834,plain,
% 0.69/0.86 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | hskp3 | c2_1(a460) | c3_1(a460) | (~ndr1_0) | (~c0_1(a460)) | (~c0_1(a490)) | (~c3_1(a490)) | (~c1_1(a490))),
% 0.69/0.86 inference(modus_ponens,[status(thm)],[1833, 1832])).
% 0.69/0.86 tff(1835,plain,
% 0.69/0.86 (~c3_1(a490)),
% 0.69/0.86 inference(unit_resolution,[status(thm)],[1834, 941, 1475, 1828, 1827, 1305, 1, 1463, 21])).
% 0.69/0.86 tff(1836,assumption,(~c1_1(a503)), introduced(assumption)).
% 0.69/0.86 tff(1837,assumption,(c3_1(a503)), introduced(assumption)).
% 0.69/0.86 tff(1838,assumption,(c2_1(a503)), introduced(assumption)).
% 0.69/0.86 tff(1839,plain,
% 0.69/0.86 (c2_1(a490)),
% 0.69/0.86 inference(unit_resolution,[status(thm)],[1811, 1826])).
% 0.69/0.86 tff(1840,plain,
% 0.69/0.86 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c1_1(a503) | c0_1(a480) | c1_1(a480) | c2_1(a480) | (~ndr1_0) | (~c2_1(a490)) | (~c0_1(a490)) | c3_1(a490) | (~c3_1(a503)) | (~c2_1(a503)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c1_1(a503) | c0_1(a480) | c1_1(a480) | c2_1(a480) | (~ndr1_0) | (~c2_1(a490)) | (~c0_1(a490)) | c3_1(a490) | (~c3_1(a503)) | (~c2_1(a503)))),
% 0.69/0.86 inference(rewrite,[status(thm)],[])).
% 0.69/0.86 tff(1841,plain,
% 0.69/0.86 (((~ndr1_0) | c3_1(a490) | (~c2_1(a490)) | (~c0_1(a490)) | c1_1(a503) | (~c3_1(a503)) | (~c2_1(a503)) | c1_1(a480) | c0_1(a480) | c2_1(a480)) <=> (c1_1(a503) | c0_1(a480) | c1_1(a480) | c2_1(a480) | (~ndr1_0) | (~c2_1(a490)) | (~c0_1(a490)) | c3_1(a490) | (~c3_1(a503)) | (~c2_1(a503)))),
% 0.69/0.87 inference(rewrite,[status(thm)],[])).
% 0.69/0.87 tff(1842,plain,
% 0.69/0.87 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_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) | c3_1(a490) | (~c2_1(a490)) | (~c0_1(a490)) | c1_1(a503) | (~c3_1(a503)) | (~c2_1(a503)) | c1_1(a480) | c0_1(a480) | c2_1(a480))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c1_1(a503) | c0_1(a480) | c1_1(a480) | c2_1(a480) | (~ndr1_0) | (~c2_1(a490)) | (~c0_1(a490)) | c3_1(a490) | (~c3_1(a503)) | (~c2_1(a503))))),
% 0.69/0.87 inference(monotonicity,[status(thm)],[1841])).
% 0.69/0.87 tff(1843,plain,
% 0.69/0.87 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_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) | c3_1(a490) | (~c2_1(a490)) | (~c0_1(a490)) | c1_1(a503) | (~c3_1(a503)) | (~c2_1(a503)) | c1_1(a480) | c0_1(a480) | c2_1(a480))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c1_1(a503) | c0_1(a480) | c1_1(a480) | c2_1(a480) | (~ndr1_0) | (~c2_1(a490)) | (~c0_1(a490)) | c3_1(a490) | (~c3_1(a503)) | (~c2_1(a503)))),
% 0.69/0.87 inference(transitivity,[status(thm)],[1842, 1840])).
% 0.69/0.87 tff(1844,plain,
% 0.69/0.87 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_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) | c3_1(a490) | (~c2_1(a490)) | (~c0_1(a490)) | c1_1(a503) | (~c3_1(a503)) | (~c2_1(a503)) | c1_1(a480) | c0_1(a480) | c2_1(a480))),
% 0.69/0.87 inference(quant_inst,[status(thm)],[])).
% 0.69/0.87 tff(1845,plain,
% 0.69/0.87 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c1_1(a503) | c0_1(a480) | c1_1(a480) | c2_1(a480) | (~ndr1_0) | (~c2_1(a490)) | (~c0_1(a490)) | c3_1(a490) | (~c3_1(a503)) | (~c2_1(a503))),
% 0.69/0.87 inference(modus_ponens,[status(thm)],[1844, 1843])).
% 0.69/0.87 tff(1846,plain,
% 0.69/0.87 ($false),
% 0.69/0.87 inference(unit_resolution,[status(thm)],[1845, 941, 1828, 1839, 1838, 1837, 1836, 1466, 1465, 1464, 1804, 1835])).
% 0.69/0.87 tff(1847,plain,((~hskp28) | (~c2_1(a503)) | (~c3_1(a503)) | c1_1(a503) | c2_1(a460)), inference(lemma,lemma(discharge,[]))).
% 0.69/0.87 tff(1848,plain,
% 0.69/0.87 (~hskp28),
% 0.69/0.87 inference(unit_resolution,[status(thm)],[1847, 1825, 1824, 1823, 1])).
% 0.69/0.87 tff(1849,plain,
% 0.69/0.87 (c1_1(a460)),
% 0.69/0.87 inference(unit_resolution,[status(thm)],[1763, 1848])).
% 0.69/0.87 tff(1850,plain,
% 0.69/0.87 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c1_1(a494) | c3_1(a494) | c2_1(a460) | (~ndr1_0) | (~c1_1(a460)) | (~c0_1(a460)) | (~c2_1(a494)) | (~c3_1(a503)) | (~c2_1(a503)) | c0_1(a503))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c1_1(a494) | c3_1(a494) | c2_1(a460) | (~ndr1_0) | (~c1_1(a460)) | (~c0_1(a460)) | (~c2_1(a494)) | (~c3_1(a503)) | (~c2_1(a503)) | c0_1(a503))),
% 0.69/0.87 inference(rewrite,[status(thm)],[])).
% 0.69/0.87 tff(1851,plain,
% 0.69/0.87 (((~ndr1_0) | c2_1(a460) | (~c0_1(a460)) | (~c1_1(a460)) | c3_1(a494) | c1_1(a494) | (~c2_1(a494)) | c0_1(a503) | (~c3_1(a503)) | (~c2_1(a503))) <=> (c1_1(a494) | c3_1(a494) | c2_1(a460) | (~ndr1_0) | (~c1_1(a460)) | (~c0_1(a460)) | (~c2_1(a494)) | (~c3_1(a503)) | (~c2_1(a503)) | c0_1(a503))),
% 0.69/0.87 inference(rewrite,[status(thm)],[])).
% 0.69/0.87 tff(1852,plain,
% 0.69/0.87 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a460) | (~c0_1(a460)) | (~c1_1(a460)) | c3_1(a494) | c1_1(a494) | (~c2_1(a494)) | c0_1(a503) | (~c3_1(a503)) | (~c2_1(a503)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c1_1(a494) | c3_1(a494) | c2_1(a460) | (~ndr1_0) | (~c1_1(a460)) | (~c0_1(a460)) | (~c2_1(a494)) | (~c3_1(a503)) | (~c2_1(a503)) | c0_1(a503)))),
% 0.69/0.87 inference(monotonicity,[status(thm)],[1851])).
% 0.69/0.87 tff(1853,plain,
% 0.69/0.87 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a460) | (~c0_1(a460)) | (~c1_1(a460)) | c3_1(a494) | c1_1(a494) | (~c2_1(a494)) | c0_1(a503) | (~c3_1(a503)) | (~c2_1(a503)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c1_1(a494) | c3_1(a494) | c2_1(a460) | (~ndr1_0) | (~c1_1(a460)) | (~c0_1(a460)) | (~c2_1(a494)) | (~c3_1(a503)) | (~c2_1(a503)) | c0_1(a503))),
% 0.69/0.87 inference(transitivity,[status(thm)],[1852, 1850])).
% 0.69/0.87 tff(1854,plain,
% 0.69/0.87 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a460) | (~c0_1(a460)) | (~c1_1(a460)) | c3_1(a494) | c1_1(a494) | (~c2_1(a494)) | c0_1(a503) | (~c3_1(a503)) | (~c2_1(a503)))),
% 0.69/0.87 inference(quant_inst,[status(thm)],[])).
% 0.69/0.87 tff(1855,plain,
% 0.69/0.87 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c1_1(a494) | c3_1(a494) | c2_1(a460) | (~ndr1_0) | (~c1_1(a460)) | (~c0_1(a460)) | (~c2_1(a494)) | (~c3_1(a503)) | (~c2_1(a503)) | c0_1(a503)),
% 0.69/0.87 inference(modus_ponens,[status(thm)],[1854, 1853])).
% 0.69/0.87 tff(1856,plain,
% 0.69/0.87 ($false),
% 0.69/0.87 inference(unit_resolution,[status(thm)],[1855, 941, 1825, 1824, 1305, 510, 495, 1, 802, 1849, 1729, 1184])).
% 0.69/0.87 tff(1857,plain,(c0_1(a503) | c1_1(a494) | c3_1(a494) | c2_1(a460)), inference(lemma,lemma(discharge,[]))).
% 0.69/0.87 tff(1858,plain,
% 0.69/0.87 (c0_1(a503)),
% 0.69/0.87 inference(unit_resolution,[status(thm)],[1857, 510, 495, 1])).
% 0.69/0.87 tff(1859,plain,
% 0.69/0.87 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp26 | c0_1(a494) | c1_1(a494) | (~ndr1_0) | (~c2_1(a494)) | (~c3_1(a503)) | (~c2_1(a503)) | (~c0_1(a503)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp26 | c0_1(a494) | c1_1(a494) | (~ndr1_0) | (~c2_1(a494)) | (~c3_1(a503)) | (~c2_1(a503)) | (~c0_1(a503)))),
% 0.69/0.87 inference(rewrite,[status(thm)],[])).
% 0.69/0.87 tff(1860,plain,
% 0.69/0.87 ((hskp26 | (~ndr1_0) | (~c2_1(a503)) | (~c0_1(a503)) | (~c3_1(a503)) | c1_1(a494) | c0_1(a494) | (~c2_1(a494))) <=> (hskp26 | c0_1(a494) | c1_1(a494) | (~ndr1_0) | (~c2_1(a494)) | (~c3_1(a503)) | (~c2_1(a503)) | (~c0_1(a503)))),
% 0.69/0.87 inference(rewrite,[status(thm)],[])).
% 0.69/0.87 tff(1861,plain,
% 0.69/0.87 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp26 | (~ndr1_0) | (~c2_1(a503)) | (~c0_1(a503)) | (~c3_1(a503)) | c1_1(a494) | c0_1(a494) | (~c2_1(a494)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp26 | c0_1(a494) | c1_1(a494) | (~ndr1_0) | (~c2_1(a494)) | (~c3_1(a503)) | (~c2_1(a503)) | (~c0_1(a503))))),
% 0.69/0.87 inference(monotonicity,[status(thm)],[1860])).
% 0.69/0.87 tff(1862,plain,
% 0.69/0.87 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp26 | (~ndr1_0) | (~c2_1(a503)) | (~c0_1(a503)) | (~c3_1(a503)) | c1_1(a494) | c0_1(a494) | (~c2_1(a494)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp26 | c0_1(a494) | c1_1(a494) | (~ndr1_0) | (~c2_1(a494)) | (~c3_1(a503)) | (~c2_1(a503)) | (~c0_1(a503)))),
% 0.69/0.87 inference(transitivity,[status(thm)],[1861, 1859])).
% 0.69/0.87 tff(1863,plain,
% 0.69/0.87 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp26 | (~ndr1_0) | (~c2_1(a503)) | (~c0_1(a503)) | (~c3_1(a503)) | c1_1(a494) | c0_1(a494) | (~c2_1(a494)))),
% 0.69/0.87 inference(quant_inst,[status(thm)],[])).
% 0.69/0.87 tff(1864,plain,
% 0.69/0.87 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp26 | c0_1(a494) | c1_1(a494) | (~ndr1_0) | (~c2_1(a494)) | (~c3_1(a503)) | (~c2_1(a503)) | (~c0_1(a503))),
% 0.69/0.87 inference(modus_ponens,[status(thm)],[1863, 1862])).
% 0.69/0.87 tff(1865,plain,
% 0.69/0.87 (hskp26 | (~c0_1(a503))),
% 0.69/0.87 inference(unit_resolution,[status(thm)],[1864, 941, 1825, 1824, 1727, 510, 530, 1729])).
% 0.69/0.87 tff(1866,plain,
% 0.69/0.87 (hskp26),
% 0.69/0.87 inference(unit_resolution,[status(thm)],[1865, 1858])).
% 0.69/0.87 tff(1867,plain,
% 0.69/0.87 (c3_1(a470)),
% 0.69/0.87 inference(unit_resolution,[status(thm)],[702, 1866])).
% 0.69/0.87 tff(1868,plain,
% 0.69/0.87 (c2_1(a470)),
% 0.69/0.87 inference(unit_resolution,[status(thm)],[710, 1866])).
% 0.69/0.87 tff(1869,plain,
% 0.69/0.87 ($false),
% 0.69/0.87 inference(unit_resolution,[status(thm)],[923, 941, 1868, 1867, 1305, 510, 495, 1, 802, 1849, 1729, 1669])).
% 0.69/0.87 tff(1870,plain,(c0_1(a470) | c1_1(a494) | c3_1(a494) | c2_1(a460)), inference(lemma,lemma(discharge,[]))).
% 0.69/0.87 tff(1871,plain,
% 0.69/0.87 (c0_1(a470)),
% 0.69/0.87 inference(unit_resolution,[status(thm)],[1870, 510, 495, 1])).
% 0.69/0.87 tff(1872,plain,
% 0.69/0.87 (c1_1(a470)),
% 0.69/0.87 inference(unit_resolution,[status(thm)],[718, 1866])).
% 0.69/0.87 tff(1873,plain,
% 0.69/0.87 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp3 | c2_1(a460) | c3_1(a460) | (~ndr1_0) | (~c0_1(a460)) | (~c0_1(a470)) | (~c1_1(a470)) | (~c3_1(a470)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | hskp3 | c2_1(a460) | c3_1(a460) | (~ndr1_0) | (~c0_1(a460)) | (~c0_1(a470)) | (~c1_1(a470)) | (~c3_1(a470)))),
% 0.69/0.87 inference(rewrite,[status(thm)],[])).
% 0.69/0.87 tff(1874,plain,
% 0.69/0.87 ((hskp3 | (~ndr1_0) | (~c0_1(a470)) | (~c3_1(a470)) | (~c1_1(a470)) | c3_1(a460) | c2_1(a460) | (~c0_1(a460))) <=> (hskp3 | c2_1(a460) | c3_1(a460) | (~ndr1_0) | (~c0_1(a460)) | (~c0_1(a470)) | (~c1_1(a470)) | (~c3_1(a470)))),
% 0.69/0.87 inference(rewrite,[status(thm)],[])).
% 0.69/0.87 tff(1875,plain,
% 0.69/0.87 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp3 | (~ndr1_0) | (~c0_1(a470)) | (~c3_1(a470)) | (~c1_1(a470)) | c3_1(a460) | c2_1(a460) | (~c0_1(a460)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp3 | c2_1(a460) | c3_1(a460) | (~ndr1_0) | (~c0_1(a460)) | (~c0_1(a470)) | (~c1_1(a470)) | (~c3_1(a470))))),
% 0.69/0.87 inference(monotonicity,[status(thm)],[1874])).
% 0.69/0.87 tff(1876,plain,
% 0.69/0.87 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp3 | (~ndr1_0) | (~c0_1(a470)) | (~c3_1(a470)) | (~c1_1(a470)) | c3_1(a460) | c2_1(a460) | (~c0_1(a460)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | hskp3 | c2_1(a460) | c3_1(a460) | (~ndr1_0) | (~c0_1(a460)) | (~c0_1(a470)) | (~c1_1(a470)) | (~c3_1(a470)))),
% 0.69/0.87 inference(transitivity,[status(thm)],[1875, 1873])).
% 0.69/0.87 tff(1877,plain,
% 0.69/0.87 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp3 | (~ndr1_0) | (~c0_1(a470)) | (~c3_1(a470)) | (~c1_1(a470)) | c3_1(a460) | c2_1(a460) | (~c0_1(a460)))),
% 0.69/0.87 inference(quant_inst,[status(thm)],[])).
% 0.69/0.87 tff(1878,plain,
% 0.69/0.87 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | hskp3 | c2_1(a460) | c3_1(a460) | (~ndr1_0) | (~c0_1(a460)) | (~c0_1(a470)) | (~c1_1(a470)) | (~c3_1(a470))),
% 0.69/0.87 inference(modus_ponens,[status(thm)],[1877, 1876])).
% 0.69/0.87 tff(1879,plain,
% 0.69/0.87 ($false),
% 0.69/0.87 inference(unit_resolution,[status(thm)],[1878, 941, 1475, 1872, 1867, 1305, 1, 1463, 21, 1871])).
% 0.69/0.87 tff(1880,plain,(c1_1(a494) | c2_1(a460) | c3_1(a494)), inference(lemma,lemma(discharge,[]))).
% 0.69/0.87 tff(1881,plain,
% 0.69/0.87 ($false),
% 0.69/0.87 inference(unit_resolution,[status(thm)],[1880, 1668, 1667, 1])).
% 0.69/0.87 tff(1882,plain,(c2_1(a460)), inference(lemma,lemma(discharge,[]))).
% 0.69/0.87 tff(1883,plain,
% 0.69/0.87 (~hskp0),
% 0.69/0.87 inference(unit_resolution,[status(thm)],[221, 1882])).
% 0.69/0.87 tff(1884,plain,
% 0.69/0.87 (~hskp12),
% 0.69/0.87 inference(unit_resolution,[status(thm)],[947, 1883])).
% 0.69/0.87 tff(1885,plain,
% 0.69/0.87 (hskp17),
% 0.69/0.87 inference(unit_resolution,[status(thm)],[1179, 1883, 1884])).
% 0.69/0.87 tff(1886,plain,
% 0.69/0.87 (~c1_1(a494)),
% 0.69/0.87 inference(unit_resolution,[status(thm)],[501, 1885])).
% 0.69/0.87 tff(1887,plain,
% 0.69/0.87 (~c3_1(a494)),
% 0.69/0.87 inference(unit_resolution,[status(thm)],[931, 1885])).
% 0.69/0.87 tff(1888,plain,
% 0.69/0.87 ($false),
% 0.69/0.87 inference(unit_resolution,[status(thm)],[1302, 1887, 1886, 1883])).
% 0.69/0.87 % SZS output end Proof
% 0.69/0.87 % E exiting
%------------------------------------------------------------------------------