%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN503-1 : TPTP v9.0.0. Released v2.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n002.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 05:39:22 AM UTC 2025
% Result : Unsatisfiable 0.74s 0.91s
% Output : Proof 0.92s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13 % Problem : SYN503-1 : TPTP v9.0.0. Released v2.1.0.
% 0.11/0.13 % Command : run_E %s %d THM
% 0.13/0.34 % Computer : n002.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Fri Jun 20 12:38:46 EDT 2025
% 0.13/0.34 % CPUTime :
% 0.74/0.91 % SZS status Unsatisfiable
% 0.74/0.91 % SZS output start Proof
% 0.74/0.91 tff(c2_1_type, type, (
% 0.74/0.91 c2_1: $i > $o)).
% 0.74/0.91 tff(a234_type, type, (
% 0.74/0.91 a234: $i)).
% 0.74/0.91 tff(c0_1_type, type, (
% 0.74/0.91 c0_1: $i > $o)).
% 0.74/0.91 tff(hskp26_type, type, (
% 0.74/0.91 hskp26: $o)).
% 0.74/0.91 tff(c3_1_type, type, (
% 0.74/0.91 c3_1: $i > $o)).
% 0.74/0.91 tff(a252_type, type, (
% 0.74/0.91 a252: $i)).
% 0.74/0.91 tff(c1_1_type, type, (
% 0.74/0.91 c1_1: $i > $o)).
% 0.74/0.91 tff(ndr1_0_type, type, (
% 0.74/0.91 ndr1_0: $o)).
% 0.74/0.91 tff(hskp10_type, type, (
% 0.74/0.91 hskp10: $o)).
% 0.74/0.91 tff(a214_type, type, (
% 0.74/0.91 a214: $i)).
% 0.74/0.91 tff(hskp1_type, type, (
% 0.74/0.91 hskp1: $o)).
% 0.74/0.91 tff(a226_type, type, (
% 0.74/0.91 a226: $i)).
% 0.74/0.91 tff(hskp9_type, type, (
% 0.74/0.91 hskp9: $o)).
% 0.74/0.91 tff(a255_type, type, (
% 0.74/0.91 a255: $i)).
% 0.74/0.91 tff(a261_type, type, (
% 0.74/0.91 a261: $i)).
% 0.74/0.91 tff(hskp27_type, type, (
% 0.74/0.91 hskp27: $o)).
% 0.74/0.91 tff(a274_type, type, (
% 0.74/0.91 a274: $i)).
% 0.74/0.91 tff(a218_type, type, (
% 0.74/0.91 a218: $i)).
% 0.74/0.91 tff(hskp5_type, type, (
% 0.74/0.91 hskp5: $o)).
% 0.74/0.91 tff(hskp12_type, type, (
% 0.74/0.91 hskp12: $o)).
% 0.74/0.91 tff(hskp23_type, type, (
% 0.74/0.91 hskp23: $o)).
% 0.74/0.91 tff(a215_type, type, (
% 0.74/0.91 a215: $i)).
% 0.74/0.91 tff(hskp2_type, type, (
% 0.74/0.91 hskp2: $o)).
% 0.74/0.91 tff(hskp17_type, type, (
% 0.74/0.91 hskp17: $o)).
% 0.74/0.91 tff(hskp18_type, type, (
% 0.74/0.91 hskp18: $o)).
% 0.74/0.91 tff(a237_type, type, (
% 0.74/0.91 a237: $i)).
% 0.74/0.91 tff(a241_type, type, (
% 0.74/0.91 a241: $i)).
% 0.74/0.91 tff(a220_type, type, (
% 0.74/0.91 a220: $i)).
% 0.74/0.91 tff(hskp6_type, type, (
% 0.74/0.91 hskp6: $o)).
% 0.74/0.91 tff(a320_type, type, (
% 0.74/0.91 a320: $i)).
% 0.74/0.91 tff(hskp19_type, type, (
% 0.74/0.91 hskp19: $o)).
% 0.74/0.91 tff(hskp4_type, type, (
% 0.74/0.91 hskp4: $o)).
% 0.74/0.91 tff(a217_type, type, (
% 0.74/0.91 a217: $i)).
% 0.74/0.91 tff(hskp3_type, type, (
% 0.74/0.91 hskp3: $o)).
% 0.74/0.91 tff(a216_type, type, (
% 0.74/0.91 a216: $i)).
% 0.74/0.91 tff(a242_type, type, (
% 0.74/0.91 a242: $i)).
% 0.74/0.91 tff(hskp15_type, type, (
% 0.74/0.91 hskp15: $o)).
% 0.74/0.91 tff(hskp24_type, type, (
% 0.74/0.91 hskp24: $o)).
% 0.74/0.91 tff(hskp25_type, type, (
% 0.74/0.91 hskp25: $o)).
% 0.74/0.91 tff(a280_type, type, (
% 0.74/0.91 a280: $i)).
% 0.74/0.91 tff(a245_type, type, (
% 0.74/0.91 a245: $i)).
% 0.74/0.91 tff(hskp16_type, type, (
% 0.74/0.91 hskp16: $o)).
% 0.74/0.91 tff(a259_type, type, (
% 0.74/0.91 a259: $i)).
% 0.74/0.91 tff(hskp21_type, type, (
% 0.74/0.91 hskp21: $o)).
% 0.74/0.91 tff(a248_type, type, (
% 0.74/0.91 a248: $i)).
% 0.74/0.91 tff(a271_type, type, (
% 0.74/0.91 a271: $i)).
% 0.74/0.91 tff(a231_type, type, (
% 0.74/0.91 a231: $i)).
% 0.74/0.91 tff(a213_type, type, (
% 0.74/0.91 a213: $i)).
% 0.74/0.91 tff(hskp0_type, type, (
% 0.74/0.91 hskp0: $o)).
% 0.74/0.91 tff(hskp13_type, type, (
% 0.74/0.91 hskp13: $o)).
% 0.74/0.91 tff(a239_type, type, (
% 0.74/0.91 a239: $i)).
% 0.74/0.91 tff(a225_type, type, (
% 0.74/0.91 a225: $i)).
% 0.74/0.91 tff(hskp8_type, type, (
% 0.74/0.91 hskp8: $o)).
% 0.74/0.91 tff(hskp22_type, type, (
% 0.74/0.91 hskp22: $o)).
% 0.74/0.91 tff(a296_type, type, (
% 0.74/0.91 a296: $i)).
% 0.74/0.91 tff(hskp29_type, type, (
% 0.74/0.91 hskp29: $o)).
% 0.74/0.91 tff(a223_type, type, (
% 0.74/0.91 a223: $i)).
% 0.74/0.91 tff(hskp7_type, type, (
% 0.74/0.91 hskp7: $o)).
% 0.74/0.91 tff(hskp14_type, type, (
% 0.74/0.91 hskp14: $o)).
% 0.74/0.91 tff(a236_type, type, (
% 0.74/0.91 a236: $i)).
% 0.74/0.91 tff(hskp11_type, type, (
% 0.74/0.91 hskp11: $o)).
% 0.74/0.91 tff(1,assumption,(~hskp26), introduced(assumption)).
% 0.74/0.91 tff(2,plain,
% 0.74/0.91 (^[V: $i, U: $i] : refl((hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))) <=> (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))))),
% 0.74/0.91 inference(bind,[status(th)],[])).
% 0.74/0.91 tff(3,plain,
% 0.74/0.91 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.74/0.91 inference(quant_intro,[status(thm)],[2])).
% 0.74/0.91 tff(4,plain,
% 0.74/0.91 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.74/0.91 inference(rewrite,[status(thm)],[])).
% 0.74/0.91 tff(5,plain,
% 0.74/0.91 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~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))) | c1_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c0_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V))) | c3_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c0_1(V)) | c3_1(V)) | hskp10) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))) | hskp10))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))) | hskp10) <=> (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c0_1(V)) | c3_1(V)) | hskp10) <=> (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))))),
% 0.74/0.91 inference(bind,[status(th)],[])).
% 0.74/0.91 tff(6,plain,
% 0.74/0.91 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c0_1(V)) | c3_1(V)) | hskp10) <=> ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.74/0.91 inference(quant_intro,[status(thm)],[5])).
% 0.74/0.91 tff(7,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c0_1(V)) | c3_1(V)) | hskp10)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause169')).
% 0.74/0.91 tff(8,plain,
% 0.74/0.91 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.74/0.91 inference(modus_ponens,[status(thm)],[7, 6])).
% 0.74/0.91 tff(9,plain,
% 0.74/0.91 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.74/0.91 inference(modus_ponens,[status(thm)],[8, 4])).
% 0.74/0.91 tff(10,plain,(
% 0.74/0.91 ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.74/0.91 inference(skolemize,[status(sab)],[9])).
% 0.74/0.91 tff(11,plain,
% 0.74/0.91 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.74/0.91 inference(modus_ponens,[status(thm)],[10, 3])).
% 0.74/0.91 tff(12,assumption,(~c3_1(a252)), introduced(assumption)).
% 0.74/0.91 tff(13,plain,
% 0.74/0.91 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W))) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W))))),
% 0.74/0.91 inference(bind,[status(th)],[])).
% 0.74/0.91 tff(14,plain,
% 0.74/0.91 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_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) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))),
% 0.74/0.91 inference(quant_intro,[status(thm)],[13])).
% 0.74/0.91 tff(15,plain,
% 0.74/0.91 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_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) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))),
% 0.74/0.91 inference(rewrite,[status(thm)],[])).
% 0.74/0.91 tff(16,plain,
% 0.74/0.91 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V))))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c0_1(W))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V))) | (~c0_1(W))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V))) | (~c0_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(W)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c0_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(W))))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c0_1(W))) | c2_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(W))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(W)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c0_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(W))))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c0_1(W))) | c2_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(W))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(W))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(W)))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c0_1(W))) | c2_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(W))))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c0_1(W))) | c2_1(U)) | c1_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(W))) | c3_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(W))) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | (~c0_1(W)))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c0_1(W))) | c2_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) | (~c2_1(V)) | (~c0_1(W))))), ((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c0_1(W))) | c2_1(U)) | c1_1(V)) | c3_1(V)) | c1_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | (~c0_1(W))) | c1_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | (~c0_1(W))) | c1_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c1_1(W) | (~c0_1(W)))), ((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c0_1(W))) | c2_1(U)) | c1_1(V)) | c3_1(V)) | c1_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c1_1(W) | (~c0_1(W))))), (((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c0_1(W))) | c2_1(U)) | c1_1(V)) | c3_1(V)) | c1_1(W)) | c3_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c1_1(W) | (~c0_1(W))) | c3_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c1_1(W) | (~c0_1(W))) | c3_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))), (((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c0_1(W))) | c2_1(U)) | c1_1(V)) | c3_1(V)) | c1_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))))),
% 0.74/0.91 inference(bind,[status(th)],[])).
% 0.74/0.91 tff(17,plain,
% 0.74/0.91 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c0_1(W))) | c2_1(U)) | c1_1(V)) | c3_1(V)) | c1_1(W)) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))),
% 0.74/0.91 inference(quant_intro,[status(thm)],[16])).
% 0.74/0.91 tff(18,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c0_1(W))) | c2_1(U)) | c1_1(V)) | c3_1(V)) | c1_1(W)) | c3_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause191')).
% 0.74/0.91 tff(19,plain,
% 0.74/0.91 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))),
% 0.74/0.91 inference(modus_ponens,[status(thm)],[18, 17])).
% 0.74/0.91 tff(20,plain,
% 0.74/0.91 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))),
% 0.74/0.91 inference(modus_ponens,[status(thm)],[19, 15])).
% 0.74/0.91 tff(21,plain,(
% 0.74/0.91 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))),
% 0.74/0.91 inference(skolemize,[status(sab)],[20])).
% 0.74/0.91 tff(22,plain,
% 0.74/0.91 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))),
% 0.74/0.91 inference(modus_ponens,[status(thm)],[21, 14])).
% 0.74/0.91 tff(23,assumption,(~hskp9), introduced(assumption)).
% 0.74/0.91 tff(24,plain,
% 0.74/0.91 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)) | (~c2_1(W)) | (~c0_1(W)) | (~c1_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)) | (~c2_1(W)) | (~c0_1(W)) | (~c1_1(W))))),
% 0.74/0.91 inference(bind,[status(th)],[])).
% 0.74/0.91 tff(25,plain,
% 0.74/0.91 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)) | (~c2_1(W)) | (~c0_1(W)) | (~c1_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)) | (~c2_1(W)) | (~c0_1(W)) | (~c1_1(W)))),
% 0.74/0.91 inference(quant_intro,[status(thm)],[24])).
% 0.74/0.91 tff(26,plain,
% 0.74/0.91 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)) | (~c2_1(W)) | (~c0_1(W)) | (~c1_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)) | (~c2_1(W)) | (~c0_1(W)) | (~c1_1(W)))),
% 0.74/0.91 inference(rewrite,[status(thm)],[])).
% 0.74/0.91 tff(27,plain,
% 0.74/0.91 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~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))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c0_1(V)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c0_1(V))))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c0_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V))))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c3_1(V))) | (~c0_1(W))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V))) | (~c0_1(W))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V))) | (~c0_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)) | (~c0_1(W)))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c3_1(V))) | (~c0_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)) | (~c0_1(W))))), ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c3_1(V))) | (~c0_1(W))) | (~c1_1(W))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)) | (~c0_1(W))) | (~c1_1(W))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)) | (~c0_1(W))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)) | (~c0_1(W)) | (~c1_1(W)))), ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c3_1(V))) | (~c0_1(W))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)) | (~c0_1(W)) | (~c1_1(W))))), (((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c3_1(V))) | (~c0_1(W))) | (~c1_1(W))) | (~c2_1(W))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)) | (~c0_1(W)) | (~c1_1(W))) | (~c2_1(W))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)) | (~c0_1(W)) | (~c1_1(W))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)) | (~c2_1(W)) | (~c0_1(W)) | (~c1_1(W)))), (((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c3_1(V))) | (~c0_1(W))) | (~c1_1(W))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)) | (~c2_1(W)) | (~c0_1(W)) | (~c1_1(W)))))),
% 0.74/0.91 inference(bind,[status(th)],[])).
% 0.74/0.91 tff(28,plain,
% 0.74/0.91 (![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c3_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)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)) | (~c2_1(W)) | (~c0_1(W)) | (~c1_1(W)))),
% 0.74/0.91 inference(quant_intro,[status(thm)],[27])).
% 0.74/0.91 tff(29,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c3_1(V))) | (~c0_1(W))) | (~c1_1(W))) | (~c2_1(W)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause200')).
% 0.74/0.91 tff(30,plain,
% 0.74/0.91 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)) | (~c2_1(W)) | (~c0_1(W)) | (~c1_1(W)))),
% 0.74/0.91 inference(modus_ponens,[status(thm)],[29, 28])).
% 0.74/0.91 tff(31,plain,
% 0.74/0.91 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)) | (~c2_1(W)) | (~c0_1(W)) | (~c1_1(W)))),
% 0.74/0.91 inference(modus_ponens,[status(thm)],[30, 26])).
% 0.74/0.91 tff(32,plain,(
% 0.74/0.91 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)) | (~c2_1(W)) | (~c0_1(W)) | (~c1_1(W)))),
% 0.74/0.91 inference(skolemize,[status(sab)],[31])).
% 0.74/0.91 tff(33,plain,
% 0.74/0.91 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)) | (~c2_1(W)) | (~c0_1(W)) | (~c1_1(W)))),
% 0.74/0.91 inference(modus_ponens,[status(thm)],[32, 25])).
% 0.74/0.91 tff(34,assumption,(~hskp27), introduced(assumption)).
% 0.74/0.91 tff(35,plain,
% 0.74/0.91 (^[V: $i, U: $i] : refl((hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V))) <=> (hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V))))),
% 0.74/0.91 inference(bind,[status(th)],[])).
% 0.74/0.91 tff(36,plain,
% 0.74/0.91 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.74/0.91 inference(quant_intro,[status(thm)],[35])).
% 0.74/0.91 tff(37,plain,
% 0.74/0.91 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.74/0.91 inference(rewrite,[status(thm)],[])).
% 0.74/0.91 tff(38,plain,
% 0.74/0.91 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V))))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) | c0_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V))) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V))))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) | c0_1(V)) | c3_1(V)) | hskp12) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V))) | hskp12))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V))) | hskp12) <=> (hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) | c0_1(V)) | c3_1(V)) | hskp12) <=> (hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))))),
% 0.74/0.91 inference(bind,[status(th)],[])).
% 0.74/0.91 tff(39,plain,
% 0.74/0.91 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) | c0_1(V)) | c3_1(V)) | hskp12) <=> ![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.74/0.91 inference(quant_intro,[status(thm)],[38])).
% 0.74/0.91 tff(40,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) | c0_1(V)) | c3_1(V)) | hskp12)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause168')).
% 0.74/0.91 tff(41,plain,
% 0.74/0.91 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.74/0.91 inference(modus_ponens,[status(thm)],[40, 39])).
% 0.74/0.91 tff(42,plain,
% 0.74/0.91 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.74/0.91 inference(modus_ponens,[status(thm)],[41, 37])).
% 0.74/0.91 tff(43,plain,(
% 0.74/0.91 ![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.74/0.91 inference(skolemize,[status(sab)],[42])).
% 0.74/0.91 tff(44,plain,
% 0.74/0.91 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.74/0.91 inference(modus_ponens,[status(thm)],[43, 36])).
% 0.74/0.91 tff(45,assumption,(~hskp5), introduced(assumption)).
% 0.74/0.91 tff(46,assumption,(hskp26), introduced(assumption)).
% 0.74/0.91 tff(47,plain,
% 0.74/0.91 (^[U: $i] : refl((hskp27 | hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) <=> (hskp27 | hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))))),
% 0.74/0.91 inference(bind,[status(th)],[])).
% 0.74/0.91 tff(48,plain,
% 0.74/0.91 (![U: $i] : (hskp27 | hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp27 | hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 0.74/0.91 inference(quant_intro,[status(thm)],[47])).
% 0.74/0.91 tff(49,plain,
% 0.74/0.91 (![U: $i] : (hskp27 | hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp27 | hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 0.74/0.91 inference(rewrite,[status(thm)],[])).
% 0.74/0.91 tff(50,plain,
% 0.74/0.91 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) <=> ((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp27) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | hskp27))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | hskp27) <=> (hskp27 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp27) <=> (hskp27 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp27) | hskp2) <=> ((hskp27 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | hskp2))), rewrite(((hskp27 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | hskp2) <=> (hskp27 | hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp27) | hskp2) <=> (hskp27 | hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))))),
% 0.74/0.91 inference(bind,[status(th)],[])).
% 0.74/0.91 tff(51,plain,
% 0.74/0.91 (![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp27) | hskp2) <=> ![U: $i] : (hskp27 | hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 0.74/0.91 inference(quant_intro,[status(thm)],[50])).
% 0.74/0.91 tff(52,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp27) | hskp2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause154')).
% 0.74/0.91 tff(53,plain,
% 0.74/0.91 (![U: $i] : (hskp27 | hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 0.74/0.91 inference(modus_ponens,[status(thm)],[52, 51])).
% 0.74/0.91 tff(54,plain,
% 0.74/0.91 (![U: $i] : (hskp27 | hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 0.74/0.91 inference(modus_ponens,[status(thm)],[53, 49])).
% 0.74/0.91 tff(55,plain,(
% 0.74/0.91 ![U: $i] : (hskp27 | hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 0.74/0.91 inference(skolemize,[status(sab)],[54])).
% 0.74/0.91 tff(56,plain,
% 0.74/0.91 (![U: $i] : (hskp27 | hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 0.74/0.91 inference(modus_ponens,[status(thm)],[55, 48])).
% 0.74/0.91 tff(57,plain,
% 0.74/0.91 (((~hskp26) | c3_1(a234)) <=> ((~hskp26) | c3_1(a234))),
% 0.74/0.91 inference(rewrite,[status(thm)],[])).
% 0.74/0.91 tff(58,axiom,((~hskp26) | c3_1(a234)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause51')).
% 0.74/0.91 tff(59,plain,
% 0.74/0.91 ((~hskp26) | c3_1(a234)),
% 0.74/0.91 inference(modus_ponens,[status(thm)],[58, 57])).
% 0.74/0.91 tff(60,plain,
% 0.74/0.91 ((~hskp26) | c3_1(a234)),
% 0.74/0.91 inference(modus_ponens,[status(thm)],[59, 57])).
% 0.74/0.91 tff(61,plain,
% 0.74/0.91 ((~hskp26) | c3_1(a234)),
% 0.74/0.91 inference(modus_ponens,[status(thm)],[60, 57])).
% 0.74/0.91 tff(62,plain,
% 0.74/0.91 ((~hskp26) | c3_1(a234)),
% 0.74/0.91 inference(modus_ponens,[status(thm)],[61, 57])).
% 0.74/0.91 tff(63,plain,
% 0.74/0.91 ((~hskp26) | c3_1(a234)),
% 0.74/0.91 inference(modus_ponens,[status(thm)],[62, 57])).
% 0.74/0.91 tff(64,plain,
% 0.74/0.91 (c3_1(a234)),
% 0.74/0.91 inference(unit_resolution,[status(thm)],[63, 46])).
% 0.74/0.91 tff(65,plain,
% 0.74/0.91 (((~hskp26) | c1_1(a234)) <=> ((~hskp26) | c1_1(a234))),
% 0.74/0.91 inference(rewrite,[status(thm)],[])).
% 0.74/0.91 tff(66,axiom,((~hskp26) | c1_1(a234)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause50')).
% 0.74/0.91 tff(67,plain,
% 0.74/0.91 ((~hskp26) | c1_1(a234)),
% 0.74/0.91 inference(modus_ponens,[status(thm)],[66, 65])).
% 0.74/0.91 tff(68,plain,
% 0.74/0.91 ((~hskp26) | c1_1(a234)),
% 0.74/0.91 inference(modus_ponens,[status(thm)],[67, 65])).
% 0.74/0.91 tff(69,plain,
% 0.74/0.91 ((~hskp26) | c1_1(a234)),
% 0.74/0.91 inference(modus_ponens,[status(thm)],[68, 65])).
% 0.74/0.91 tff(70,plain,
% 0.74/0.91 ((~hskp26) | c1_1(a234)),
% 0.74/0.91 inference(modus_ponens,[status(thm)],[69, 65])).
% 0.74/0.91 tff(71,plain,
% 0.74/0.91 ((~hskp26) | c1_1(a234)),
% 0.74/0.91 inference(modus_ponens,[status(thm)],[70, 65])).
% 0.74/0.91 tff(72,plain,
% 0.74/0.91 (c1_1(a234)),
% 0.74/0.91 inference(unit_resolution,[status(thm)],[71, 46])).
% 0.74/0.91 tff(73,plain,
% 0.74/0.91 (((~hskp26) | c0_1(a234)) <=> ((~hskp26) | c0_1(a234))),
% 0.74/0.91 inference(rewrite,[status(thm)],[])).
% 0.74/0.91 tff(74,axiom,((~hskp26) | c0_1(a234)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause49')).
% 0.74/0.91 tff(75,plain,
% 0.74/0.91 ((~hskp26) | c0_1(a234)),
% 0.74/0.91 inference(modus_ponens,[status(thm)],[74, 73])).
% 0.74/0.91 tff(76,plain,
% 0.74/0.91 ((~hskp26) | c0_1(a234)),
% 0.74/0.91 inference(modus_ponens,[status(thm)],[75, 73])).
% 0.74/0.91 tff(77,plain,
% 0.74/0.91 ((~hskp26) | c0_1(a234)),
% 0.74/0.91 inference(modus_ponens,[status(thm)],[76, 73])).
% 0.74/0.91 tff(78,plain,
% 0.74/0.91 ((~hskp26) | c0_1(a234)),
% 0.74/0.91 inference(modus_ponens,[status(thm)],[77, 73])).
% 0.74/0.91 tff(79,plain,
% 0.74/0.91 ((~hskp26) | c0_1(a234)),
% 0.74/0.91 inference(modus_ponens,[status(thm)],[78, 73])).
% 0.74/0.91 tff(80,plain,
% 0.74/0.91 (c0_1(a234)),
% 0.74/0.91 inference(unit_resolution,[status(thm)],[79, 46])).
% 0.74/0.91 tff(81,assumption,(~hskp2), introduced(assumption)).
% 0.74/0.91 tff(82,assumption,(~ndr1_0), introduced(assumption)).
% 0.74/0.91 tff(83,plain,
% 0.74/0.91 ((ndr1_0 | (~hskp17)) <=> (ndr1_0 | (~hskp17))),
% 0.74/0.91 inference(rewrite,[status(thm)],[])).
% 0.74/0.91 tff(84,plain,
% 0.74/0.91 (((~hskp17) | ndr1_0) <=> (ndr1_0 | (~hskp17))),
% 0.74/0.91 inference(rewrite,[status(thm)],[])).
% 0.74/0.91 tff(85,axiom,((~hskp17) | ndr1_0), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause15')).
% 0.74/0.91 tff(86,plain,
% 0.74/0.91 (ndr1_0 | (~hskp17)),
% 0.74/0.91 inference(modus_ponens,[status(thm)],[85, 84])).
% 0.74/0.91 tff(87,plain,
% 0.74/0.91 (ndr1_0 | (~hskp17)),
% 0.74/0.91 inference(modus_ponens,[status(thm)],[86, 83])).
% 0.74/0.91 tff(88,plain,
% 0.74/0.91 (~hskp17),
% 0.74/0.91 inference(unit_resolution,[status(thm)],[87, 82])).
% 0.74/0.91 tff(89,plain,
% 0.74/0.91 ((ndr1_0 | (~hskp27)) <=> (ndr1_0 | (~hskp27))),
% 0.74/0.91 inference(rewrite,[status(thm)],[])).
% 0.74/0.91 tff(90,plain,
% 0.74/0.91 (((~hskp27) | ndr1_0) <=> (ndr1_0 | (~hskp27))),
% 0.74/0.91 inference(rewrite,[status(thm)],[])).
% 0.74/0.91 tff(91,axiom,((~hskp27) | ndr1_0), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause5')).
% 0.74/0.91 tff(92,plain,
% 0.74/0.91 (ndr1_0 | (~hskp27)),
% 0.74/0.91 inference(modus_ponens,[status(thm)],[91, 90])).
% 0.74/0.91 tff(93,plain,
% 0.74/0.91 (ndr1_0 | (~hskp27)),
% 0.74/0.91 inference(modus_ponens,[status(thm)],[92, 89])).
% 0.74/0.91 tff(94,plain,
% 0.74/0.91 (~hskp27),
% 0.74/0.91 inference(unit_resolution,[status(thm)],[93, 82])).
% 0.74/0.91 tff(95,plain,
% 0.74/0.91 ((ndr1_0 | (~hskp18)) <=> (ndr1_0 | (~hskp18))),
% 0.74/0.91 inference(rewrite,[status(thm)],[])).
% 0.74/0.91 tff(96,plain,
% 0.74/0.91 (((~hskp18) | ndr1_0) <=> (ndr1_0 | (~hskp18))),
% 0.74/0.91 inference(rewrite,[status(thm)],[])).
% 0.74/0.91 tff(97,axiom,((~hskp18) | ndr1_0), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause14')).
% 0.74/0.91 tff(98,plain,
% 0.74/0.91 (ndr1_0 | (~hskp18)),
% 0.74/0.91 inference(modus_ponens,[status(thm)],[97, 96])).
% 0.74/0.91 tff(99,plain,
% 0.74/0.91 (ndr1_0 | (~hskp18)),
% 0.74/0.91 inference(modus_ponens,[status(thm)],[98, 95])).
% 0.74/0.91 tff(100,plain,
% 0.74/0.91 (~hskp18),
% 0.74/0.91 inference(unit_resolution,[status(thm)],[99, 82])).
% 0.74/0.91 tff(101,plain,
% 0.74/0.91 ((hskp27 | hskp18 | hskp17) <=> (hskp27 | hskp18 | hskp17)),
% 0.74/0.91 inference(rewrite,[status(thm)],[])).
% 0.74/0.91 tff(102,plain,
% 0.74/0.91 (((hskp18 | hskp27) | hskp17) <=> (hskp27 | hskp18 | hskp17)),
% 0.74/0.91 inference(rewrite,[status(thm)],[])).
% 0.74/0.91 tff(103,axiom,((hskp18 | hskp27) | hskp17), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause37')).
% 0.74/0.91 tff(104,plain,
% 0.74/0.91 (hskp27 | hskp18 | hskp17),
% 0.74/0.91 inference(modus_ponens,[status(thm)],[103, 102])).
% 0.74/0.91 tff(105,plain,
% 0.74/0.91 (hskp27 | hskp18 | hskp17),
% 0.74/0.91 inference(modus_ponens,[status(thm)],[104, 101])).
% 0.74/0.91 tff(106,plain,
% 0.74/0.91 (hskp27 | hskp18 | hskp17),
% 0.74/0.91 inference(modus_ponens,[status(thm)],[105, 101])).
% 0.74/0.91 tff(107,plain,
% 0.74/0.91 (hskp27 | hskp18 | hskp17),
% 0.74/0.91 inference(modus_ponens,[status(thm)],[106, 101])).
% 0.74/0.91 tff(108,plain,
% 0.74/0.91 (hskp27 | hskp18 | hskp17),
% 0.74/0.91 inference(modus_ponens,[status(thm)],[107, 101])).
% 0.74/0.91 tff(109,plain,
% 0.74/0.91 ($false),
% 0.74/0.91 inference(unit_resolution,[status(thm)],[108, 100, 94, 88])).
% 0.74/0.91 tff(110,plain,(ndr1_0), inference(lemma,lemma(discharge,[]))).
% 0.74/0.91 tff(111,plain,
% 0.74/0.91 (((~![U: $i] : (hskp27 | hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp27 | hskp2 | (~ndr1_0) | (~c0_1(a234)) | (~c3_1(a234)) | (~c1_1(a234)))) <=> ((~![U: $i] : (hskp27 | hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp27 | hskp2 | (~ndr1_0) | (~c0_1(a234)) | (~c3_1(a234)) | (~c1_1(a234)))),
% 0.74/0.91 inference(rewrite,[status(thm)],[])).
% 0.74/0.91 tff(112,plain,
% 0.74/0.91 ((hskp27 | hskp2 | (~ndr1_0) | (~c3_1(a234)) | (~c1_1(a234)) | (~c0_1(a234))) <=> (hskp27 | hskp2 | (~ndr1_0) | (~c0_1(a234)) | (~c3_1(a234)) | (~c1_1(a234)))),
% 0.74/0.91 inference(rewrite,[status(thm)],[])).
% 0.74/0.91 tff(113,plain,
% 0.74/0.91 (((~![U: $i] : (hskp27 | hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp27 | hskp2 | (~ndr1_0) | (~c3_1(a234)) | (~c1_1(a234)) | (~c0_1(a234)))) <=> ((~![U: $i] : (hskp27 | hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp27 | hskp2 | (~ndr1_0) | (~c0_1(a234)) | (~c3_1(a234)) | (~c1_1(a234))))),
% 0.74/0.91 inference(monotonicity,[status(thm)],[112])).
% 0.74/0.91 tff(114,plain,
% 0.74/0.91 (((~![U: $i] : (hskp27 | hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp27 | hskp2 | (~ndr1_0) | (~c3_1(a234)) | (~c1_1(a234)) | (~c0_1(a234)))) <=> ((~![U: $i] : (hskp27 | hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp27 | hskp2 | (~ndr1_0) | (~c0_1(a234)) | (~c3_1(a234)) | (~c1_1(a234)))),
% 0.74/0.91 inference(transitivity,[status(thm)],[113, 111])).
% 0.74/0.91 tff(115,plain,
% 0.74/0.91 ((~![U: $i] : (hskp27 | hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp27 | hskp2 | (~ndr1_0) | (~c3_1(a234)) | (~c1_1(a234)) | (~c0_1(a234)))),
% 0.74/0.91 inference(quant_inst,[status(thm)],[])).
% 0.74/0.91 tff(116,plain,
% 0.74/0.91 ((~![U: $i] : (hskp27 | hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp27 | hskp2 | (~ndr1_0) | (~c0_1(a234)) | (~c3_1(a234)) | (~c1_1(a234))),
% 0.74/0.91 inference(modus_ponens,[status(thm)],[115, 114])).
% 0.74/0.91 tff(117,plain,
% 0.74/0.91 ($false),
% 0.74/0.91 inference(unit_resolution,[status(thm)],[116, 110, 34, 81, 80, 72, 64, 56])).
% 0.74/0.91 tff(118,plain,((~hskp26) | hskp27 | hskp2), inference(lemma,lemma(discharge,[]))).
% 0.74/0.91 tff(119,plain,
% 0.74/0.91 (hskp2),
% 0.74/0.91 inference(unit_resolution,[status(thm)],[118, 46, 34])).
% 0.74/0.91 tff(120,plain,
% 0.74/0.91 (((~hskp2) | (~c1_1(a215))) <=> ((~hskp2) | (~c1_1(a215)))),
% 0.74/0.91 inference(rewrite,[status(thm)],[])).
% 0.74/0.91 tff(121,plain,
% 0.74/0.91 (((~c1_1(a215)) | (~hskp2)) <=> ((~hskp2) | (~c1_1(a215)))),
% 0.74/0.91 inference(rewrite,[status(thm)],[])).
% 0.74/0.91 tff(122,axiom,((~c1_1(a215)) | (~hskp2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause125')).
% 0.74/0.91 tff(123,plain,
% 0.74/0.91 ((~hskp2) | (~c1_1(a215))),
% 0.74/0.91 inference(modus_ponens,[status(thm)],[122, 121])).
% 0.74/0.91 tff(124,plain,
% 0.74/0.91 ((~hskp2) | (~c1_1(a215))),
% 0.74/0.91 inference(modus_ponens,[status(thm)],[123, 120])).
% 0.74/0.91 tff(125,plain,
% 0.74/0.91 (~c1_1(a215)),
% 0.74/0.91 inference(unit_resolution,[status(thm)],[124, 119])).
% 0.74/0.91 tff(126,plain,
% 0.74/0.91 (((~hskp2) | c2_1(a215)) <=> ((~hskp2) | c2_1(a215))),
% 0.74/0.91 inference(rewrite,[status(thm)],[])).
% 0.74/0.91 tff(127,axiom,((~hskp2) | c2_1(a215)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause83')).
% 0.74/0.91 tff(128,plain,
% 0.74/0.91 ((~hskp2) | c2_1(a215)),
% 0.74/0.91 inference(modus_ponens,[status(thm)],[127, 126])).
% 0.74/0.91 tff(129,plain,
% 0.74/0.91 ((~hskp2) | c2_1(a215)),
% 0.74/0.91 inference(modus_ponens,[status(thm)],[128, 126])).
% 0.74/0.91 tff(130,plain,
% 0.74/0.91 ((~hskp2) | c2_1(a215)),
% 0.74/0.91 inference(modus_ponens,[status(thm)],[129, 126])).
% 0.74/0.91 tff(131,plain,
% 0.74/0.91 ((~hskp2) | c2_1(a215)),
% 0.74/0.91 inference(modus_ponens,[status(thm)],[130, 126])).
% 0.74/0.91 tff(132,plain,
% 0.74/0.91 ((~hskp2) | c2_1(a215)),
% 0.74/0.91 inference(modus_ponens,[status(thm)],[131, 126])).
% 0.74/0.91 tff(133,plain,
% 0.74/0.91 (c2_1(a215)),
% 0.74/0.91 inference(unit_resolution,[status(thm)],[132, 119])).
% 0.74/0.91 tff(134,plain,
% 0.74/0.91 (((~hskp2) | (~c0_1(a215))) <=> ((~hskp2) | (~c0_1(a215)))),
% 0.74/0.91 inference(rewrite,[status(thm)],[])).
% 0.74/0.91 tff(135,plain,
% 0.74/0.91 (((~c0_1(a215)) | (~hskp2)) <=> ((~hskp2) | (~c0_1(a215)))),
% 0.74/0.91 inference(rewrite,[status(thm)],[])).
% 0.74/0.91 tff(136,axiom,((~c0_1(a215)) | (~hskp2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause124')).
% 0.74/0.91 tff(137,plain,
% 0.74/0.91 ((~hskp2) | (~c0_1(a215))),
% 0.74/0.91 inference(modus_ponens,[status(thm)],[136, 135])).
% 0.74/0.91 tff(138,plain,
% 0.74/0.91 ((~hskp2) | (~c0_1(a215))),
% 0.74/0.91 inference(modus_ponens,[status(thm)],[137, 134])).
% 0.74/0.91 tff(139,plain,
% 0.74/0.91 (~c0_1(a215)),
% 0.74/0.91 inference(unit_resolution,[status(thm)],[138, 119])).
% 0.74/0.91 tff(140,plain,
% 0.74/0.91 (^[V: $i, U: $i] : refl((hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) <=> (hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))))),
% 0.74/0.91 inference(bind,[status(th)],[])).
% 0.74/0.91 tff(141,plain,
% 0.74/0.91 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.74/0.91 inference(quant_intro,[status(thm)],[140])).
% 0.74/0.91 tff(142,plain,
% 0.74/0.91 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.74/0.91 inference(rewrite,[status(thm)],[])).
% 0.74/0.91 tff(143,plain,
% 0.74/0.91 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) <=> ((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V))) | c1_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(V)) | c1_1(V)) | hskp5) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) | hskp5))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) | hskp5) <=> (hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(V)) | c1_1(V)) | hskp5) <=> (hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))))),
% 0.74/0.92 inference(bind,[status(th)],[])).
% 0.74/0.92 tff(144,plain,
% 0.74/0.92 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(V)) | c1_1(V)) | hskp5) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.74/0.92 inference(quant_intro,[status(thm)],[143])).
% 0.74/0.92 tff(145,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(V)) | c1_1(V)) | hskp5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause178')).
% 0.74/0.92 tff(146,plain,
% 0.74/0.92 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.74/0.92 inference(modus_ponens,[status(thm)],[145, 144])).
% 0.74/0.92 tff(147,plain,
% 0.74/0.92 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.74/0.92 inference(modus_ponens,[status(thm)],[146, 142])).
% 0.74/0.92 tff(148,plain,(
% 0.74/0.92 ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.74/0.92 inference(skolemize,[status(sab)],[147])).
% 0.74/0.92 tff(149,plain,
% 0.74/0.92 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.74/0.92 inference(modus_ponens,[status(thm)],[148, 141])).
% 0.74/0.92 tff(150,assumption,(~c1_1(a215)), introduced(assumption)).
% 0.74/0.92 tff(151,assumption,(~c0_1(a215)), introduced(assumption)).
% 0.74/0.92 tff(152,assumption,(c2_1(a215)), introduced(assumption)).
% 0.74/0.92 tff(153,plain,
% 0.74/0.92 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp5 | c0_1(a215) | c1_1(a215) | (~ndr1_0) | (~c2_1(a215)) | (~c0_1(a234)) | (~c3_1(a234)) | (~c1_1(a234)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp5 | c0_1(a215) | c1_1(a215) | (~ndr1_0) | (~c2_1(a215)) | (~c0_1(a234)) | (~c3_1(a234)) | (~c1_1(a234)))),
% 0.74/0.92 inference(rewrite,[status(thm)],[])).
% 0.74/0.92 tff(154,plain,
% 0.74/0.92 ((hskp5 | (~ndr1_0) | (~c3_1(a234)) | (~c1_1(a234)) | (~c0_1(a234)) | c1_1(a215) | c0_1(a215) | (~c2_1(a215))) <=> (hskp5 | c0_1(a215) | c1_1(a215) | (~ndr1_0) | (~c2_1(a215)) | (~c0_1(a234)) | (~c3_1(a234)) | (~c1_1(a234)))),
% 0.74/0.92 inference(rewrite,[status(thm)],[])).
% 0.74/0.92 tff(155,plain,
% 0.74/0.92 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp5 | (~ndr1_0) | (~c3_1(a234)) | (~c1_1(a234)) | (~c0_1(a234)) | c1_1(a215) | c0_1(a215) | (~c2_1(a215)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp5 | c0_1(a215) | c1_1(a215) | (~ndr1_0) | (~c2_1(a215)) | (~c0_1(a234)) | (~c3_1(a234)) | (~c1_1(a234))))),
% 0.74/0.92 inference(monotonicity,[status(thm)],[154])).
% 0.74/0.92 tff(156,plain,
% 0.74/0.92 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp5 | (~ndr1_0) | (~c3_1(a234)) | (~c1_1(a234)) | (~c0_1(a234)) | c1_1(a215) | c0_1(a215) | (~c2_1(a215)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp5 | c0_1(a215) | c1_1(a215) | (~ndr1_0) | (~c2_1(a215)) | (~c0_1(a234)) | (~c3_1(a234)) | (~c1_1(a234)))),
% 0.74/0.92 inference(transitivity,[status(thm)],[155, 153])).
% 0.74/0.92 tff(157,plain,
% 0.74/0.92 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp5 | (~ndr1_0) | (~c3_1(a234)) | (~c1_1(a234)) | (~c0_1(a234)) | c1_1(a215) | c0_1(a215) | (~c2_1(a215)))),
% 0.74/0.92 inference(quant_inst,[status(thm)],[])).
% 0.74/0.92 tff(158,plain,
% 0.74/0.92 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp5 | c0_1(a215) | c1_1(a215) | (~ndr1_0) | (~c2_1(a215)) | (~c0_1(a234)) | (~c3_1(a234)) | (~c1_1(a234))),
% 0.74/0.92 inference(modus_ponens,[status(thm)],[157, 156])).
% 0.74/0.92 tff(159,plain,
% 0.74/0.92 ($false),
% 0.74/0.92 inference(unit_resolution,[status(thm)],[158, 110, 45, 80, 72, 64, 152, 151, 150, 149])).
% 0.74/0.92 tff(160,plain,((~hskp26) | hskp5 | (~c2_1(a215)) | c0_1(a215) | c1_1(a215)), inference(lemma,lemma(discharge,[]))).
% 0.74/0.92 tff(161,plain,
% 0.74/0.92 ($false),
% 0.74/0.92 inference(unit_resolution,[status(thm)],[160, 139, 133, 45, 46, 125])).
% 0.74/0.92 tff(162,plain,((~hskp26) | hskp5 | hskp27), inference(lemma,lemma(discharge,[]))).
% 0.74/0.92 tff(163,plain,
% 0.74/0.92 (~hskp26),
% 0.74/0.92 inference(unit_resolution,[status(thm)],[162, 45, 34])).
% 0.74/0.92 tff(164,assumption,(~c3_1(a237)), introduced(assumption)).
% 0.74/0.92 tff(165,plain,
% 0.74/0.92 (^[U: $i] : refl((hskp27 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U)) <=> (hskp27 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U)))),
% 0.74/0.92 inference(bind,[status(th)],[])).
% 0.74/0.92 tff(166,plain,
% 0.74/0.92 (![U: $i] : (hskp27 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U)) <=> ![U: $i] : (hskp27 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))),
% 0.74/0.92 inference(quant_intro,[status(thm)],[165])).
% 0.74/0.92 tff(167,plain,
% 0.74/0.92 (![U: $i] : (hskp27 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U)) <=> ![U: $i] : (hskp27 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))),
% 0.74/0.92 inference(rewrite,[status(thm)],[])).
% 0.74/0.92 tff(168,plain,
% 0.74/0.92 (^[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)) | hskp27) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U)) | hskp27))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U)) | hskp27) <=> (hskp27 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))), ((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | hskp27) <=> (hskp27 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U)))), (((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | hskp27) | hskp2) <=> ((hskp27 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U)) | hskp2))), rewrite(((hskp27 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U)) | hskp2) <=> (hskp27 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))), (((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | hskp27) | hskp2) <=> (hskp27 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))))),
% 0.74/0.92 inference(bind,[status(th)],[])).
% 0.74/0.92 tff(169,plain,
% 0.74/0.92 (![U: $i] : ((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | hskp27) | hskp2) <=> ![U: $i] : (hskp27 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))),
% 0.74/0.92 inference(quant_intro,[status(thm)],[168])).
% 0.74/0.92 tff(170,axiom,(![U: $i] : ((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | hskp27) | hskp2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause136')).
% 0.74/0.92 tff(171,plain,
% 0.74/0.92 (![U: $i] : (hskp27 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))),
% 0.74/0.92 inference(modus_ponens,[status(thm)],[170, 169])).
% 0.74/0.92 tff(172,plain,
% 0.74/0.92 (![U: $i] : (hskp27 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))),
% 0.74/0.92 inference(modus_ponens,[status(thm)],[171, 167])).
% 0.74/0.92 tff(173,plain,(
% 0.74/0.92 ![U: $i] : (hskp27 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))),
% 0.74/0.92 inference(skolemize,[status(sab)],[172])).
% 0.74/0.92 tff(174,plain,
% 0.74/0.92 (![U: $i] : (hskp27 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))),
% 0.74/0.92 inference(modus_ponens,[status(thm)],[173, 166])).
% 0.74/0.92 tff(175,assumption,(hskp4), introduced(assumption)).
% 0.74/0.92 tff(176,plain,
% 0.74/0.92 (((~hskp4) | (~c3_1(a217))) <=> ((~hskp4) | (~c3_1(a217)))),
% 0.74/0.92 inference(rewrite,[status(thm)],[])).
% 0.74/0.92 tff(177,plain,
% 0.74/0.92 (((~c3_1(a217)) | (~hskp4)) <=> ((~hskp4) | (~c3_1(a217)))),
% 0.74/0.92 inference(rewrite,[status(thm)],[])).
% 0.74/0.92 tff(178,axiom,((~c3_1(a217)) | (~hskp4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause122')).
% 0.74/0.92 tff(179,plain,
% 0.74/0.92 ((~hskp4) | (~c3_1(a217))),
% 0.74/0.92 inference(modus_ponens,[status(thm)],[178, 177])).
% 0.74/0.92 tff(180,plain,
% 0.74/0.92 ((~hskp4) | (~c3_1(a217))),
% 0.74/0.92 inference(modus_ponens,[status(thm)],[179, 176])).
% 0.74/0.92 tff(181,plain,
% 0.74/0.92 (~c3_1(a217)),
% 0.74/0.92 inference(unit_resolution,[status(thm)],[180, 175])).
% 0.74/0.92 tff(182,plain,
% 0.74/0.92 (((~hskp4) | (~c2_1(a217))) <=> ((~hskp4) | (~c2_1(a217)))),
% 0.74/0.92 inference(rewrite,[status(thm)],[])).
% 0.74/0.92 tff(183,plain,
% 0.74/0.92 (((~c2_1(a217)) | (~hskp4)) <=> ((~hskp4) | (~c2_1(a217)))),
% 0.74/0.92 inference(rewrite,[status(thm)],[])).
% 0.74/0.92 tff(184,axiom,((~c2_1(a217)) | (~hskp4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause121')).
% 0.74/0.92 tff(185,plain,
% 0.74/0.92 ((~hskp4) | (~c2_1(a217))),
% 0.74/0.92 inference(modus_ponens,[status(thm)],[184, 183])).
% 0.74/0.92 tff(186,plain,
% 0.74/0.92 ((~hskp4) | (~c2_1(a217))),
% 0.74/0.92 inference(modus_ponens,[status(thm)],[185, 182])).
% 0.74/0.92 tff(187,plain,
% 0.74/0.92 (~c2_1(a217)),
% 0.74/0.92 inference(unit_resolution,[status(thm)],[186, 175])).
% 0.74/0.92 tff(188,plain,
% 0.74/0.92 (((~hskp4) | (~c1_1(a217))) <=> ((~hskp4) | (~c1_1(a217)))),
% 0.74/0.92 inference(rewrite,[status(thm)],[])).
% 0.74/0.92 tff(189,plain,
% 0.74/0.92 (((~c1_1(a217)) | (~hskp4)) <=> ((~hskp4) | (~c1_1(a217)))),
% 0.74/0.92 inference(rewrite,[status(thm)],[])).
% 0.74/0.92 tff(190,axiom,((~c1_1(a217)) | (~hskp4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause120')).
% 0.74/0.92 tff(191,plain,
% 0.74/0.92 ((~hskp4) | (~c1_1(a217))),
% 0.74/0.92 inference(modus_ponens,[status(thm)],[190, 189])).
% 0.74/0.92 tff(192,plain,
% 0.74/0.92 ((~hskp4) | (~c1_1(a217))),
% 0.74/0.92 inference(modus_ponens,[status(thm)],[191, 188])).
% 0.74/0.92 tff(193,plain,
% 0.74/0.92 (~c1_1(a217)),
% 0.74/0.92 inference(unit_resolution,[status(thm)],[192, 175])).
% 0.74/0.92 tff(194,plain,
% 0.74/0.92 (((~![U: $i] : (hskp27 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | (hskp27 | hskp2 | c1_1(a217) | c2_1(a217) | c3_1(a217) | (~ndr1_0))) <=> ((~![U: $i] : (hskp27 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | hskp27 | hskp2 | c1_1(a217) | c2_1(a217) | c3_1(a217) | (~ndr1_0))),
% 0.74/0.92 inference(rewrite,[status(thm)],[])).
% 0.74/0.92 tff(195,plain,
% 0.74/0.92 ((hskp27 | hskp2 | (~ndr1_0) | c2_1(a217) | c1_1(a217) | c3_1(a217)) <=> (hskp27 | hskp2 | c1_1(a217) | c2_1(a217) | c3_1(a217) | (~ndr1_0))),
% 0.74/0.92 inference(rewrite,[status(thm)],[])).
% 0.74/0.92 tff(196,plain,
% 0.74/0.92 (((~![U: $i] : (hskp27 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | (hskp27 | hskp2 | (~ndr1_0) | c2_1(a217) | c1_1(a217) | c3_1(a217))) <=> ((~![U: $i] : (hskp27 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | (hskp27 | hskp2 | c1_1(a217) | c2_1(a217) | c3_1(a217) | (~ndr1_0)))),
% 0.74/0.92 inference(monotonicity,[status(thm)],[195])).
% 0.74/0.92 tff(197,plain,
% 0.74/0.92 (((~![U: $i] : (hskp27 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | (hskp27 | hskp2 | (~ndr1_0) | c2_1(a217) | c1_1(a217) | c3_1(a217))) <=> ((~![U: $i] : (hskp27 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | hskp27 | hskp2 | c1_1(a217) | c2_1(a217) | c3_1(a217) | (~ndr1_0))),
% 0.74/0.92 inference(transitivity,[status(thm)],[196, 194])).
% 0.74/0.92 tff(198,plain,
% 0.74/0.92 ((~![U: $i] : (hskp27 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | (hskp27 | hskp2 | (~ndr1_0) | c2_1(a217) | c1_1(a217) | c3_1(a217))),
% 0.74/0.92 inference(quant_inst,[status(thm)],[])).
% 0.74/0.92 tff(199,plain,
% 0.74/0.92 ((~![U: $i] : (hskp27 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | hskp27 | hskp2 | c1_1(a217) | c2_1(a217) | c3_1(a217) | (~ndr1_0)),
% 0.74/0.92 inference(modus_ponens,[status(thm)],[198, 197])).
% 0.74/0.92 tff(200,plain,
% 0.74/0.92 ($false),
% 0.74/0.92 inference(unit_resolution,[status(thm)],[199, 110, 34, 81, 193, 187, 181, 174])).
% 0.74/0.92 tff(201,plain,((~hskp4) | hskp27 | hskp2), inference(lemma,lemma(discharge,[]))).
% 0.74/0.92 tff(202,plain,
% 0.74/0.92 (~hskp4),
% 0.74/0.92 inference(unit_resolution,[status(thm)],[201, 81, 34])).
% 0.74/0.92 tff(203,assumption,(hskp3), introduced(assumption)).
% 0.74/0.92 tff(204,plain,
% 0.74/0.92 (((~hskp3) | c1_1(a216)) <=> ((~hskp3) | c1_1(a216))),
% 0.74/0.92 inference(rewrite,[status(thm)],[])).
% 0.74/0.92 tff(205,axiom,((~hskp3) | c1_1(a216)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause82')).
% 0.74/0.92 tff(206,plain,
% 0.74/0.92 ((~hskp3) | c1_1(a216)),
% 0.74/0.92 inference(modus_ponens,[status(thm)],[205, 204])).
% 0.74/0.92 tff(207,plain,
% 0.74/0.92 ((~hskp3) | c1_1(a216)),
% 0.74/0.92 inference(modus_ponens,[status(thm)],[206, 204])).
% 0.74/0.92 tff(208,plain,
% 0.74/0.92 ((~hskp3) | c1_1(a216)),
% 0.74/0.92 inference(modus_ponens,[status(thm)],[207, 204])).
% 0.74/0.92 tff(209,plain,
% 0.74/0.92 ((~hskp3) | c1_1(a216)),
% 0.74/0.92 inference(modus_ponens,[status(thm)],[208, 204])).
% 0.74/0.92 tff(210,plain,
% 0.74/0.92 ((~hskp3) | c1_1(a216)),
% 0.74/0.92 inference(modus_ponens,[status(thm)],[209, 204])).
% 0.74/0.92 tff(211,plain,
% 0.74/0.92 (c1_1(a216)),
% 0.74/0.92 inference(unit_resolution,[status(thm)],[210, 203])).
% 0.74/0.92 tff(212,plain,
% 0.74/0.92 (((~hskp3) | c0_1(a216)) <=> ((~hskp3) | c0_1(a216))),
% 0.74/0.92 inference(rewrite,[status(thm)],[])).
% 0.74/0.92 tff(213,axiom,((~hskp3) | c0_1(a216)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause81')).
% 0.74/0.92 tff(214,plain,
% 0.74/0.92 ((~hskp3) | c0_1(a216)),
% 0.74/0.92 inference(modus_ponens,[status(thm)],[213, 212])).
% 0.74/0.92 tff(215,plain,
% 0.74/0.92 ((~hskp3) | c0_1(a216)),
% 0.74/0.92 inference(modus_ponens,[status(thm)],[214, 212])).
% 0.74/0.92 tff(216,plain,
% 0.74/0.92 ((~hskp3) | c0_1(a216)),
% 0.74/0.92 inference(modus_ponens,[status(thm)],[215, 212])).
% 0.74/0.92 tff(217,plain,
% 0.74/0.92 ((~hskp3) | c0_1(a216)),
% 0.74/0.92 inference(modus_ponens,[status(thm)],[216, 212])).
% 0.74/0.92 tff(218,plain,
% 0.74/0.92 ((~hskp3) | c0_1(a216)),
% 0.74/0.92 inference(modus_ponens,[status(thm)],[217, 212])).
% 0.74/0.92 tff(219,plain,
% 0.74/0.92 (c0_1(a216)),
% 0.74/0.92 inference(unit_resolution,[status(thm)],[218, 203])).
% 0.74/0.92 tff(220,plain,
% 0.74/0.92 (((~![U: $i] : (hskp27 | hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp27 | hskp2 | (~ndr1_0) | (~c3_1(a216)) | (~c0_1(a216)) | (~c1_1(a216)))) <=> ((~![U: $i] : (hskp27 | hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp27 | hskp2 | (~ndr1_0) | (~c3_1(a216)) | (~c0_1(a216)) | (~c1_1(a216)))),
% 0.74/0.92 inference(rewrite,[status(thm)],[])).
% 0.74/0.92 tff(221,plain,
% 0.74/0.92 ((hskp27 | hskp2 | (~ndr1_0) | (~c3_1(a216)) | (~c1_1(a216)) | (~c0_1(a216))) <=> (hskp27 | hskp2 | (~ndr1_0) | (~c3_1(a216)) | (~c0_1(a216)) | (~c1_1(a216)))),
% 0.74/0.92 inference(rewrite,[status(thm)],[])).
% 0.74/0.92 tff(222,plain,
% 0.74/0.92 (((~![U: $i] : (hskp27 | hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp27 | hskp2 | (~ndr1_0) | (~c3_1(a216)) | (~c1_1(a216)) | (~c0_1(a216)))) <=> ((~![U: $i] : (hskp27 | hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp27 | hskp2 | (~ndr1_0) | (~c3_1(a216)) | (~c0_1(a216)) | (~c1_1(a216))))),
% 0.74/0.92 inference(monotonicity,[status(thm)],[221])).
% 0.74/0.92 tff(223,plain,
% 0.74/0.92 (((~![U: $i] : (hskp27 | hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp27 | hskp2 | (~ndr1_0) | (~c3_1(a216)) | (~c1_1(a216)) | (~c0_1(a216)))) <=> ((~![U: $i] : (hskp27 | hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp27 | hskp2 | (~ndr1_0) | (~c3_1(a216)) | (~c0_1(a216)) | (~c1_1(a216)))),
% 0.74/0.92 inference(transitivity,[status(thm)],[222, 220])).
% 0.74/0.92 tff(224,plain,
% 0.74/0.92 ((~![U: $i] : (hskp27 | hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp27 | hskp2 | (~ndr1_0) | (~c3_1(a216)) | (~c1_1(a216)) | (~c0_1(a216)))),
% 0.74/0.92 inference(quant_inst,[status(thm)],[])).
% 0.74/0.92 tff(225,plain,
% 0.74/0.92 ((~![U: $i] : (hskp27 | hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp27 | hskp2 | (~ndr1_0) | (~c3_1(a216)) | (~c0_1(a216)) | (~c1_1(a216))),
% 0.74/0.92 inference(modus_ponens,[status(thm)],[224, 223])).
% 0.74/0.92 tff(226,plain,
% 0.74/0.92 (~c3_1(a216)),
% 0.74/0.92 inference(unit_resolution,[status(thm)],[225, 110, 34, 81, 219, 211, 56])).
% 0.74/0.92 tff(227,plain,
% 0.74/0.92 (^[U: $i] : refl((hskp26 | hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))) <=> (hskp26 | hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))))),
% 0.74/0.92 inference(bind,[status(th)],[])).
% 0.74/0.92 tff(228,plain,
% 0.74/0.92 (![U: $i] : (hskp26 | hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))) <=> ![U: $i] : (hskp26 | hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))),
% 0.74/0.92 inference(quant_intro,[status(thm)],[227])).
% 0.74/0.92 tff(229,plain,
% 0.74/0.92 (![U: $i] : (hskp26 | hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))) <=> ![U: $i] : (hskp26 | hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))),
% 0.74/0.92 inference(rewrite,[status(thm)],[])).
% 0.74/0.92 tff(230,plain,
% 0.74/0.92 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c1_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U))))), (((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))), (((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))))), ((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp26) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))) | hskp26))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))) | hskp26) <=> (hskp26 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))), ((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp26) <=> (hskp26 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))))), (((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp26) | hskp9) <=> ((hskp26 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))) | hskp9))), rewrite(((hskp26 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))) | hskp9) <=> (hskp26 | hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))), (((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp26) | hskp9) <=> (hskp26 | hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))))),
% 0.74/0.92 inference(bind,[status(th)],[])).
% 0.74/0.92 tff(231,plain,
% 0.74/0.92 (![U: $i] : ((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp26) | hskp9) <=> ![U: $i] : (hskp26 | hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))),
% 0.74/0.92 inference(quant_intro,[status(thm)],[230])).
% 0.74/0.92 tff(232,axiom,(![U: $i] : ((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp26) | hskp9)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause144')).
% 0.74/0.92 tff(233,plain,
% 0.74/0.92 (![U: $i] : (hskp26 | hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))),
% 0.74/0.92 inference(modus_ponens,[status(thm)],[232, 231])).
% 0.74/0.92 tff(234,plain,
% 0.74/0.92 (![U: $i] : (hskp26 | hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))),
% 0.74/0.92 inference(modus_ponens,[status(thm)],[233, 229])).
% 0.74/0.92 tff(235,plain,(
% 0.74/0.92 ![U: $i] : (hskp26 | hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))),
% 0.74/0.92 inference(skolemize,[status(sab)],[234])).
% 0.74/0.92 tff(236,plain,
% 0.74/0.92 (![U: $i] : (hskp26 | hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))),
% 0.74/0.92 inference(modus_ponens,[status(thm)],[235, 228])).
% 0.74/0.92 tff(237,plain,
% 0.74/0.92 (((~hskp3) | (~c2_1(a216))) <=> ((~hskp3) | (~c2_1(a216)))),
% 0.74/0.92 inference(rewrite,[status(thm)],[])).
% 0.74/0.92 tff(238,plain,
% 0.74/0.92 (((~c2_1(a216)) | (~hskp3)) <=> ((~hskp3) | (~c2_1(a216)))),
% 0.74/0.92 inference(rewrite,[status(thm)],[])).
% 0.74/0.92 tff(239,axiom,((~c2_1(a216)) | (~hskp3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause123')).
% 0.74/0.92 tff(240,plain,
% 0.74/0.92 ((~hskp3) | (~c2_1(a216))),
% 0.74/0.92 inference(modus_ponens,[status(thm)],[239, 238])).
% 0.74/0.92 tff(241,plain,
% 0.74/0.92 ((~hskp3) | (~c2_1(a216))),
% 0.74/0.92 inference(modus_ponens,[status(thm)],[240, 237])).
% 0.74/0.92 tff(242,plain,
% 0.74/0.92 (~c2_1(a216)),
% 0.74/0.92 inference(unit_resolution,[status(thm)],[241, 203])).
% 0.74/0.92 tff(243,plain,
% 0.74/0.92 (((~![U: $i] : (hskp26 | hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp26 | hskp9 | c2_1(a216) | (~ndr1_0) | c3_1(a216) | (~c1_1(a216)))) <=> ((~![U: $i] : (hskp26 | hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | hskp26 | hskp9 | c2_1(a216) | (~ndr1_0) | c3_1(a216) | (~c1_1(a216)))),
% 0.74/0.92 inference(rewrite,[status(thm)],[])).
% 0.74/0.92 tff(244,plain,
% 0.74/0.92 ((hskp26 | hskp9 | (~ndr1_0) | c2_1(a216) | c3_1(a216) | (~c1_1(a216))) <=> (hskp26 | hskp9 | c2_1(a216) | (~ndr1_0) | c3_1(a216) | (~c1_1(a216)))),
% 0.74/0.92 inference(rewrite,[status(thm)],[])).
% 0.74/0.92 tff(245,plain,
% 0.74/0.92 (((~![U: $i] : (hskp26 | hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp26 | hskp9 | (~ndr1_0) | c2_1(a216) | c3_1(a216) | (~c1_1(a216)))) <=> ((~![U: $i] : (hskp26 | hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp26 | hskp9 | c2_1(a216) | (~ndr1_0) | c3_1(a216) | (~c1_1(a216))))),
% 0.74/0.92 inference(monotonicity,[status(thm)],[244])).
% 0.74/0.92 tff(246,plain,
% 0.74/0.92 (((~![U: $i] : (hskp26 | hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp26 | hskp9 | (~ndr1_0) | c2_1(a216) | c3_1(a216) | (~c1_1(a216)))) <=> ((~![U: $i] : (hskp26 | hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | hskp26 | hskp9 | c2_1(a216) | (~ndr1_0) | c3_1(a216) | (~c1_1(a216)))),
% 0.74/0.92 inference(transitivity,[status(thm)],[245, 243])).
% 0.74/0.92 tff(247,plain,
% 0.74/0.92 ((~![U: $i] : (hskp26 | hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp26 | hskp9 | (~ndr1_0) | c2_1(a216) | c3_1(a216) | (~c1_1(a216)))),
% 0.74/0.92 inference(quant_inst,[status(thm)],[])).
% 0.74/0.92 tff(248,plain,
% 0.74/0.92 ((~![U: $i] : (hskp26 | hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | hskp26 | hskp9 | c2_1(a216) | (~ndr1_0) | c3_1(a216) | (~c1_1(a216))),
% 0.74/0.92 inference(modus_ponens,[status(thm)],[247, 246])).
% 0.74/0.92 tff(249,plain,
% 0.74/0.92 ($false),
% 0.74/0.92 inference(unit_resolution,[status(thm)],[248, 110, 1, 23, 211, 242, 236, 226])).
% 0.74/0.92 tff(250,plain,((~hskp3) | hskp26 | hskp9 | hskp27 | hskp2), inference(lemma,lemma(discharge,[]))).
% 0.74/0.92 tff(251,plain,
% 0.74/0.92 (~hskp3),
% 0.74/0.92 inference(unit_resolution,[status(thm)],[250, 81, 23, 34, 1])).
% 0.74/0.92 tff(252,plain,
% 0.74/0.92 (^[U: $i] : refl((hskp3 | hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U)) <=> (hskp3 | hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U)))),
% 0.74/0.92 inference(bind,[status(th)],[])).
% 0.74/0.92 tff(253,plain,
% 0.74/0.92 (![U: $i] : (hskp3 | hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U)) <=> ![U: $i] : (hskp3 | hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))),
% 0.74/0.92 inference(quant_intro,[status(thm)],[252])).
% 0.74/0.92 tff(254,plain,
% 0.74/0.92 (![U: $i] : (hskp3 | hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U)) <=> ![U: $i] : (hskp3 | hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))),
% 0.74/0.92 inference(rewrite,[status(thm)],[])).
% 0.74/0.92 tff(255,plain,
% 0.74/0.92 (^[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)) | 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) | c0_1(U) | c3_1(U))), (((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U)))), ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_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))), ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) | hskp3) <=> (hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U)))), (((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) | hskp3) | hskp4) <=> ((hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U)) | hskp4))), rewrite(((hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U)) | hskp4) <=> (hskp3 | hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))), (((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) | hskp3) | hskp4) <=> (hskp3 | hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))))),
% 0.74/0.92 inference(bind,[status(th)],[])).
% 0.74/0.92 tff(256,plain,
% 0.74/0.92 (![U: $i] : ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) | hskp3) | hskp4) <=> ![U: $i] : (hskp3 | hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))),
% 0.74/0.92 inference(quant_intro,[status(thm)],[255])).
% 0.74/0.92 tff(257,axiom,(![U: $i] : ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) | hskp3) | hskp4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause131')).
% 0.74/0.92 tff(258,plain,
% 0.74/0.92 (![U: $i] : (hskp3 | hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))),
% 0.74/0.92 inference(modus_ponens,[status(thm)],[257, 256])).
% 0.74/0.92 tff(259,plain,
% 0.74/0.92 (![U: $i] : (hskp3 | hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))),
% 0.74/0.92 inference(modus_ponens,[status(thm)],[258, 254])).
% 0.74/0.92 tff(260,plain,(
% 0.74/0.92 ![U: $i] : (hskp3 | hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))),
% 0.74/0.92 inference(skolemize,[status(sab)],[259])).
% 0.74/0.92 tff(261,plain,
% 0.74/0.92 (![U: $i] : (hskp3 | hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))),
% 0.74/0.92 inference(modus_ponens,[status(thm)],[260, 253])).
% 0.74/0.92 tff(262,assumption,(hskp19), introduced(assumption)).
% 0.74/0.92 tff(263,plain,
% 0.74/0.92 (((~hskp19) | (~c3_1(a255))) <=> ((~hskp19) | (~c3_1(a255)))),
% 0.74/0.92 inference(rewrite,[status(thm)],[])).
% 0.74/0.92 tff(264,plain,
% 0.74/0.92 (((~c3_1(a255)) | (~hskp19)) <=> ((~hskp19) | (~c3_1(a255)))),
% 0.74/0.92 inference(rewrite,[status(thm)],[])).
% 0.74/0.92 tff(265,axiom,((~c3_1(a255)) | (~hskp19)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause98')).
% 0.74/0.92 tff(266,plain,
% 0.74/0.92 ((~hskp19) | (~c3_1(a255))),
% 0.74/0.92 inference(modus_ponens,[status(thm)],[265, 264])).
% 0.74/0.92 tff(267,plain,
% 0.74/0.92 ((~hskp19) | (~c3_1(a255))),
% 0.74/0.92 inference(modus_ponens,[status(thm)],[266, 263])).
% 0.74/0.92 tff(268,plain,
% 0.74/0.92 (~c3_1(a255)),
% 0.74/0.92 inference(unit_resolution,[status(thm)],[267, 262])).
% 0.74/0.92 tff(269,plain,
% 0.74/0.92 (((~hskp19) | (~c1_1(a255))) <=> ((~hskp19) | (~c1_1(a255)))),
% 0.74/0.92 inference(rewrite,[status(thm)],[])).
% 0.74/0.92 tff(270,plain,
% 0.74/0.92 (((~c1_1(a255)) | (~hskp19)) <=> ((~hskp19) | (~c1_1(a255)))),
% 0.74/0.92 inference(rewrite,[status(thm)],[])).
% 0.74/0.92 tff(271,axiom,((~c1_1(a255)) | (~hskp19)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause97')).
% 0.74/0.92 tff(272,plain,
% 0.74/0.92 ((~hskp19) | (~c1_1(a255))),
% 0.74/0.92 inference(modus_ponens,[status(thm)],[271, 270])).
% 0.74/0.92 tff(273,plain,
% 0.74/0.92 ((~hskp19) | (~c1_1(a255))),
% 0.74/0.92 inference(modus_ponens,[status(thm)],[272, 269])).
% 0.74/0.92 tff(274,plain,
% 0.74/0.92 (~c1_1(a255)),
% 0.74/0.92 inference(unit_resolution,[status(thm)],[273, 262])).
% 0.74/0.92 tff(275,plain,
% 0.74/0.92 (((~hskp19) | (~c0_1(a255))) <=> ((~hskp19) | (~c0_1(a255)))),
% 0.74/0.92 inference(rewrite,[status(thm)],[])).
% 0.74/0.92 tff(276,plain,
% 0.74/0.92 (((~c0_1(a255)) | (~hskp19)) <=> ((~hskp19) | (~c0_1(a255)))),
% 0.74/0.92 inference(rewrite,[status(thm)],[])).
% 0.74/0.92 tff(277,axiom,((~c0_1(a255)) | (~hskp19)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause96')).
% 0.74/0.92 tff(278,plain,
% 0.74/0.92 ((~hskp19) | (~c0_1(a255))),
% 0.74/0.92 inference(modus_ponens,[status(thm)],[277, 276])).
% 0.74/0.92 tff(279,plain,
% 0.74/0.92 ((~hskp19) | (~c0_1(a255))),
% 0.74/0.92 inference(modus_ponens,[status(thm)],[278, 275])).
% 0.74/0.92 tff(280,plain,
% 0.74/0.92 (~c0_1(a255)),
% 0.74/0.92 inference(unit_resolution,[status(thm)],[279, 262])).
% 0.74/0.92 tff(281,assumption,(~hskp4), introduced(assumption)).
% 0.74/0.92 tff(282,assumption,(~hskp3), introduced(assumption)).
% 0.74/0.92 tff(283,plain,
% 0.74/0.92 (((~![U: $i] : (hskp3 | hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))) | (hskp3 | hskp4 | c0_1(a255) | c1_1(a255) | c3_1(a255) | (~ndr1_0))) <=> ((~![U: $i] : (hskp3 | hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))) | hskp3 | hskp4 | c0_1(a255) | c1_1(a255) | c3_1(a255) | (~ndr1_0))),
% 0.74/0.92 inference(rewrite,[status(thm)],[])).
% 0.74/0.92 tff(284,plain,
% 0.74/0.92 ((hskp3 | hskp4 | (~ndr1_0) | c1_1(a255) | c0_1(a255) | c3_1(a255)) <=> (hskp3 | hskp4 | c0_1(a255) | c1_1(a255) | c3_1(a255) | (~ndr1_0))),
% 0.74/0.92 inference(rewrite,[status(thm)],[])).
% 0.74/0.92 tff(285,plain,
% 0.74/0.92 (((~![U: $i] : (hskp3 | hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))) | (hskp3 | hskp4 | (~ndr1_0) | c1_1(a255) | c0_1(a255) | c3_1(a255))) <=> ((~![U: $i] : (hskp3 | hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))) | (hskp3 | hskp4 | c0_1(a255) | c1_1(a255) | c3_1(a255) | (~ndr1_0)))),
% 0.74/0.92 inference(monotonicity,[status(thm)],[284])).
% 0.74/0.92 tff(286,plain,
% 0.74/0.92 (((~![U: $i] : (hskp3 | hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))) | (hskp3 | hskp4 | (~ndr1_0) | c1_1(a255) | c0_1(a255) | c3_1(a255))) <=> ((~![U: $i] : (hskp3 | hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))) | hskp3 | hskp4 | c0_1(a255) | c1_1(a255) | c3_1(a255) | (~ndr1_0))),
% 0.74/0.92 inference(transitivity,[status(thm)],[285, 283])).
% 0.74/0.92 tff(287,plain,
% 0.74/0.92 ((~![U: $i] : (hskp3 | hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))) | (hskp3 | hskp4 | (~ndr1_0) | c1_1(a255) | c0_1(a255) | c3_1(a255))),
% 0.74/0.92 inference(quant_inst,[status(thm)],[])).
% 0.74/0.92 tff(288,plain,
% 0.74/0.92 ((~![U: $i] : (hskp3 | hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))) | hskp3 | hskp4 | c0_1(a255) | c1_1(a255) | c3_1(a255) | (~ndr1_0)),
% 0.74/0.92 inference(modus_ponens,[status(thm)],[287, 286])).
% 0.74/0.92 tff(289,plain,
% 0.74/0.92 ($false),
% 0.74/0.92 inference(unit_resolution,[status(thm)],[288, 282, 110, 281, 280, 274, 268, 261])).
% 0.74/0.92 tff(290,plain,((~hskp19) | hskp3 | hskp4), inference(lemma,lemma(discharge,[]))).
% 0.74/0.92 tff(291,plain,
% 0.74/0.92 (~hskp19),
% 0.74/0.92 inference(unit_resolution,[status(thm)],[290, 251, 202])).
% 0.74/0.92 tff(292,plain,
% 0.74/0.92 (^[V: $i, U: $i] : refl((hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))) <=> (hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))))),
% 0.74/0.92 inference(bind,[status(th)],[])).
% 0.74/0.92 tff(293,plain,
% 0.74/0.92 (![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 0.74/0.92 inference(quant_intro,[status(thm)],[292])).
% 0.74/0.92 tff(294,plain,
% 0.74/0.92 (![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 0.74/0.92 inference(rewrite,[status(thm)],[])).
% 0.74/0.92 tff(295,plain,
% 0.74/0.92 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c1_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c1_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(V)))), ((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(V))))), (((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)))), (((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V))))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V))))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V))))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | hskp19) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))) | hskp19))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))) | hskp19) <=> (hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | hskp19) <=> (hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))))),
% 0.74/0.92 inference(bind,[status(th)],[])).
% 0.74/0.92 tff(296,plain,
% 0.74/0.92 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | hskp19) <=> ![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 0.74/0.92 inference(quant_intro,[status(thm)],[295])).
% 0.74/0.92 tff(297,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | hskp19)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause175')).
% 0.74/0.93 tff(298,plain,
% 0.74/0.93 (![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 0.74/0.93 inference(modus_ponens,[status(thm)],[297, 296])).
% 0.74/0.93 tff(299,plain,
% 0.74/0.93 (![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 0.74/0.93 inference(modus_ponens,[status(thm)],[298, 294])).
% 0.74/0.93 tff(300,plain,(
% 0.74/0.93 ![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 0.74/0.93 inference(skolemize,[status(sab)],[299])).
% 0.74/0.93 tff(301,plain,
% 0.74/0.93 (![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 0.74/0.93 inference(modus_ponens,[status(thm)],[300, 293])).
% 0.74/0.93 tff(302,assumption,(~c1_1(a320)), introduced(assumption)).
% 0.74/0.93 tff(303,plain,
% 0.74/0.93 (^[U: $i] : refl((hskp24 | hskp15 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U))) <=> (hskp24 | hskp15 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U))))),
% 0.74/0.93 inference(bind,[status(th)],[])).
% 0.74/0.93 tff(304,plain,
% 0.74/0.93 (![U: $i] : (hskp24 | hskp15 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U))) <=> ![U: $i] : (hskp24 | hskp15 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 0.74/0.93 inference(quant_intro,[status(thm)],[303])).
% 0.74/0.93 tff(305,plain,
% 0.74/0.93 (![U: $i] : (hskp24 | hskp15 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U))) <=> ![U: $i] : (hskp24 | hskp15 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 0.74/0.93 inference(rewrite,[status(thm)],[])).
% 0.74/0.93 tff(306,plain,
% 0.74/0.93 (^[U: $i] : 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(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U))))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp15) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U))) | hskp15))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U))) | hskp15) <=> (hskp15 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp15) <=> (hskp15 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U))))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp15) | hskp24) <=> ((hskp15 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U))) | hskp24))), rewrite(((hskp15 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U))) | hskp24) <=> (hskp24 | hskp15 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp15) | hskp24) <=> (hskp24 | hskp15 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))))),
% 0.74/0.93 inference(bind,[status(th)],[])).
% 0.74/0.93 tff(307,plain,
% 0.74/0.93 (![U: $i] : ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp15) | hskp24) <=> ![U: $i] : (hskp24 | hskp15 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 0.74/0.93 inference(quant_intro,[status(thm)],[306])).
% 0.74/0.93 tff(308,axiom,(![U: $i] : ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp15) | hskp24)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause151')).
% 0.74/0.93 tff(309,plain,
% 0.74/0.93 (![U: $i] : (hskp24 | hskp15 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 0.74/0.93 inference(modus_ponens,[status(thm)],[308, 307])).
% 0.74/0.93 tff(310,plain,
% 0.74/0.93 (![U: $i] : (hskp24 | hskp15 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 0.74/0.93 inference(modus_ponens,[status(thm)],[309, 305])).
% 0.74/0.93 tff(311,plain,(
% 0.74/0.93 ![U: $i] : (hskp24 | hskp15 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 0.74/0.93 inference(skolemize,[status(sab)],[310])).
% 0.74/0.93 tff(312,plain,
% 0.74/0.93 (![U: $i] : (hskp24 | hskp15 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 0.74/0.93 inference(modus_ponens,[status(thm)],[311, 304])).
% 0.74/0.93 tff(313,assumption,(~hskp19), introduced(assumption)).
% 0.74/0.93 tff(314,plain,
% 0.74/0.93 ((hskp25 | hskp19) <=> (hskp25 | hskp19)),
% 0.74/0.93 inference(rewrite,[status(thm)],[])).
% 0.74/0.93 tff(315,axiom,(hskp25 | hskp19), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause2')).
% 0.74/0.93 tff(316,plain,
% 0.74/0.93 (hskp25 | hskp19),
% 0.74/0.93 inference(modus_ponens,[status(thm)],[315, 314])).
% 0.74/0.93 tff(317,plain,
% 0.74/0.93 (hskp25 | hskp19),
% 0.74/0.93 inference(modus_ponens,[status(thm)],[316, 314])).
% 0.74/0.93 tff(318,plain,
% 0.74/0.93 (hskp25 | hskp19),
% 0.74/0.93 inference(modus_ponens,[status(thm)],[317, 314])).
% 0.74/0.93 tff(319,plain,
% 0.74/0.93 (hskp25 | hskp19),
% 0.74/0.93 inference(modus_ponens,[status(thm)],[318, 314])).
% 0.74/0.93 tff(320,plain,
% 0.74/0.93 (hskp25 | hskp19),
% 0.74/0.93 inference(modus_ponens,[status(thm)],[319, 314])).
% 0.74/0.93 tff(321,plain,
% 0.74/0.93 (hskp25),
% 0.74/0.93 inference(unit_resolution,[status(thm)],[320, 313])).
% 0.74/0.93 tff(322,plain,
% 0.74/0.93 (((~hskp25) | c3_1(a320)) <=> ((~hskp25) | c3_1(a320))),
% 0.74/0.93 inference(rewrite,[status(thm)],[])).
% 0.74/0.93 tff(323,axiom,((~hskp25) | c3_1(a320)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause53')).
% 0.74/0.93 tff(324,plain,
% 0.74/0.93 ((~hskp25) | c3_1(a320)),
% 0.74/0.93 inference(modus_ponens,[status(thm)],[323, 322])).
% 0.74/0.93 tff(325,plain,
% 0.74/0.93 ((~hskp25) | c3_1(a320)),
% 0.74/0.93 inference(modus_ponens,[status(thm)],[324, 322])).
% 0.74/0.93 tff(326,plain,
% 0.74/0.93 ((~hskp25) | c3_1(a320)),
% 0.74/0.93 inference(modus_ponens,[status(thm)],[325, 322])).
% 0.74/0.93 tff(327,plain,
% 0.74/0.93 ((~hskp25) | c3_1(a320)),
% 0.74/0.93 inference(modus_ponens,[status(thm)],[326, 322])).
% 0.74/0.93 tff(328,plain,
% 0.74/0.93 ((~hskp25) | c3_1(a320)),
% 0.74/0.93 inference(modus_ponens,[status(thm)],[327, 322])).
% 0.74/0.93 tff(329,plain,
% 0.74/0.93 (c3_1(a320)),
% 0.74/0.93 inference(unit_resolution,[status(thm)],[328, 321])).
% 0.74/0.93 tff(330,plain,
% 0.74/0.93 (((~hskp25) | c2_1(a320)) <=> ((~hskp25) | c2_1(a320))),
% 0.74/0.93 inference(rewrite,[status(thm)],[])).
% 0.74/0.93 tff(331,axiom,((~hskp25) | c2_1(a320)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause52')).
% 0.74/0.93 tff(332,plain,
% 0.74/0.93 ((~hskp25) | c2_1(a320)),
% 0.74/0.93 inference(modus_ponens,[status(thm)],[331, 330])).
% 0.74/0.93 tff(333,plain,
% 0.74/0.93 ((~hskp25) | c2_1(a320)),
% 0.74/0.93 inference(modus_ponens,[status(thm)],[332, 330])).
% 0.74/0.93 tff(334,plain,
% 0.74/0.93 ((~hskp25) | c2_1(a320)),
% 0.74/0.93 inference(modus_ponens,[status(thm)],[333, 330])).
% 0.74/0.93 tff(335,plain,
% 0.74/0.93 ((~hskp25) | c2_1(a320)),
% 0.74/0.93 inference(modus_ponens,[status(thm)],[334, 330])).
% 0.74/0.93 tff(336,plain,
% 0.74/0.93 ((~hskp25) | c2_1(a320)),
% 0.74/0.93 inference(modus_ponens,[status(thm)],[335, 330])).
% 0.74/0.93 tff(337,plain,
% 0.74/0.93 (c2_1(a320)),
% 0.74/0.93 inference(unit_resolution,[status(thm)],[336, 321])).
% 0.74/0.93 tff(338,assumption,(hskp24), introduced(assumption)).
% 0.74/0.93 tff(339,plain,
% 0.74/0.93 (((~hskp24) | (~c3_1(a280))) <=> ((~hskp24) | (~c3_1(a280)))),
% 0.74/0.93 inference(rewrite,[status(thm)],[])).
% 0.74/0.93 tff(340,plain,
% 0.74/0.93 (((~c3_1(a280)) | (~hskp24)) <=> ((~hskp24) | (~c3_1(a280)))),
% 0.74/0.93 inference(rewrite,[status(thm)],[])).
% 0.74/0.93 tff(341,axiom,((~c3_1(a280)) | (~hskp24)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause88')).
% 0.74/0.93 tff(342,plain,
% 0.74/0.93 ((~hskp24) | (~c3_1(a280))),
% 0.74/0.93 inference(modus_ponens,[status(thm)],[341, 340])).
% 0.74/0.93 tff(343,plain,
% 0.74/0.93 ((~hskp24) | (~c3_1(a280))),
% 0.74/0.93 inference(modus_ponens,[status(thm)],[342, 339])).
% 0.74/0.93 tff(344,plain,
% 0.74/0.93 (~c3_1(a280)),
% 0.74/0.93 inference(unit_resolution,[status(thm)],[343, 338])).
% 0.74/0.93 tff(345,plain,
% 0.74/0.93 (((~hskp24) | (~c2_1(a280))) <=> ((~hskp24) | (~c2_1(a280)))),
% 0.74/0.93 inference(rewrite,[status(thm)],[])).
% 0.74/0.93 tff(346,plain,
% 0.74/0.93 (((~c2_1(a280)) | (~hskp24)) <=> ((~hskp24) | (~c2_1(a280)))),
% 0.74/0.93 inference(rewrite,[status(thm)],[])).
% 0.74/0.93 tff(347,axiom,((~c2_1(a280)) | (~hskp24)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause87')).
% 0.74/0.93 tff(348,plain,
% 0.74/0.93 ((~hskp24) | (~c2_1(a280))),
% 0.74/0.93 inference(modus_ponens,[status(thm)],[347, 346])).
% 0.74/0.93 tff(349,plain,
% 0.74/0.93 ((~hskp24) | (~c2_1(a280))),
% 0.74/0.93 inference(modus_ponens,[status(thm)],[348, 345])).
% 0.74/0.93 tff(350,plain,
% 0.74/0.93 (~c2_1(a280)),
% 0.74/0.93 inference(unit_resolution,[status(thm)],[349, 338])).
% 0.74/0.93 tff(351,plain,
% 0.74/0.93 (((~hskp25) | (~c0_1(a320))) <=> ((~hskp25) | (~c0_1(a320)))),
% 0.74/0.93 inference(rewrite,[status(thm)],[])).
% 0.74/0.93 tff(352,plain,
% 0.74/0.93 (((~c0_1(a320)) | (~hskp25)) <=> ((~hskp25) | (~c0_1(a320)))),
% 0.74/0.93 inference(rewrite,[status(thm)],[])).
% 0.74/0.93 tff(353,axiom,((~c0_1(a320)) | (~hskp25)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause86')).
% 0.74/0.93 tff(354,plain,
% 0.74/0.93 ((~hskp25) | (~c0_1(a320))),
% 0.74/0.93 inference(modus_ponens,[status(thm)],[353, 352])).
% 0.74/0.93 tff(355,plain,
% 0.74/0.93 ((~hskp25) | (~c0_1(a320))),
% 0.74/0.93 inference(modus_ponens,[status(thm)],[354, 351])).
% 0.74/0.93 tff(356,plain,
% 0.74/0.93 (~c0_1(a320)),
% 0.74/0.93 inference(unit_resolution,[status(thm)],[355, 321])).
% 0.74/0.93 tff(357,plain,
% 0.74/0.93 (((~hskp24) | c1_1(a280)) <=> ((~hskp24) | c1_1(a280))),
% 0.74/0.93 inference(rewrite,[status(thm)],[])).
% 0.74/0.93 tff(358,axiom,((~hskp24) | c1_1(a280)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause54')).
% 0.74/0.93 tff(359,plain,
% 0.74/0.93 ((~hskp24) | c1_1(a280)),
% 0.74/0.93 inference(modus_ponens,[status(thm)],[358, 357])).
% 0.74/0.93 tff(360,plain,
% 0.74/0.93 ((~hskp24) | c1_1(a280)),
% 0.74/0.93 inference(modus_ponens,[status(thm)],[359, 357])).
% 0.74/0.93 tff(361,plain,
% 0.74/0.93 ((~hskp24) | c1_1(a280)),
% 0.74/0.93 inference(modus_ponens,[status(thm)],[360, 357])).
% 0.74/0.93 tff(362,plain,
% 0.74/0.93 ((~hskp24) | c1_1(a280)),
% 0.74/0.93 inference(modus_ponens,[status(thm)],[361, 357])).
% 0.74/0.93 tff(363,plain,
% 0.74/0.93 ((~hskp24) | c1_1(a280)),
% 0.74/0.93 inference(modus_ponens,[status(thm)],[362, 357])).
% 0.74/0.93 tff(364,plain,
% 0.74/0.93 (c1_1(a280)),
% 0.74/0.93 inference(unit_resolution,[status(thm)],[363, 338])).
% 0.74/0.93 tff(365,plain,
% 0.74/0.93 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp19 | c0_1(a320) | c2_1(a280) | c3_1(a280) | (~ndr1_0) | (~c1_1(a280)) | (~c2_1(a320)) | (~c3_1(a320)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp19 | c0_1(a320) | c2_1(a280) | c3_1(a280) | (~ndr1_0) | (~c1_1(a280)) | (~c2_1(a320)) | (~c3_1(a320)))),
% 0.74/0.93 inference(rewrite,[status(thm)],[])).
% 0.74/0.93 tff(366,plain,
% 0.74/0.93 ((hskp19 | (~ndr1_0) | c2_1(a280) | c3_1(a280) | (~c1_1(a280)) | c0_1(a320) | (~c3_1(a320)) | (~c2_1(a320))) <=> (hskp19 | c0_1(a320) | c2_1(a280) | c3_1(a280) | (~ndr1_0) | (~c1_1(a280)) | (~c2_1(a320)) | (~c3_1(a320)))),
% 0.74/0.93 inference(rewrite,[status(thm)],[])).
% 0.74/0.93 tff(367,plain,
% 0.74/0.93 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp19 | (~ndr1_0) | c2_1(a280) | c3_1(a280) | (~c1_1(a280)) | c0_1(a320) | (~c3_1(a320)) | (~c2_1(a320)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp19 | c0_1(a320) | c2_1(a280) | c3_1(a280) | (~ndr1_0) | (~c1_1(a280)) | (~c2_1(a320)) | (~c3_1(a320))))),
% 0.74/0.93 inference(monotonicity,[status(thm)],[366])).
% 0.74/0.93 tff(368,plain,
% 0.74/0.93 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp19 | (~ndr1_0) | c2_1(a280) | c3_1(a280) | (~c1_1(a280)) | c0_1(a320) | (~c3_1(a320)) | (~c2_1(a320)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp19 | c0_1(a320) | c2_1(a280) | c3_1(a280) | (~ndr1_0) | (~c1_1(a280)) | (~c2_1(a320)) | (~c3_1(a320)))),
% 0.74/0.93 inference(transitivity,[status(thm)],[367, 365])).
% 0.74/0.93 tff(369,plain,
% 0.74/0.93 ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp19 | (~ndr1_0) | c2_1(a280) | c3_1(a280) | (~c1_1(a280)) | c0_1(a320) | (~c3_1(a320)) | (~c2_1(a320)))),
% 0.74/0.93 inference(quant_inst,[status(thm)],[])).
% 0.74/0.93 tff(370,plain,
% 0.74/0.93 ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp19 | c0_1(a320) | c2_1(a280) | c3_1(a280) | (~ndr1_0) | (~c1_1(a280)) | (~c2_1(a320)) | (~c3_1(a320))),
% 0.74/0.93 inference(modus_ponens,[status(thm)],[369, 368])).
% 0.74/0.93 tff(371,plain,
% 0.74/0.93 ($false),
% 0.74/0.93 inference(unit_resolution,[status(thm)],[370, 313, 110, 337, 329, 364, 356, 350, 344, 301])).
% 0.74/0.93 tff(372,plain,((~hskp24) | hskp19), inference(lemma,lemma(discharge,[]))).
% 0.74/0.93 tff(373,plain,
% 0.74/0.93 (~hskp24),
% 0.74/0.93 inference(unit_resolution,[status(thm)],[372, 313])).
% 0.74/0.93 tff(374,plain,
% 0.74/0.93 (((~![U: $i] : (hskp24 | hskp15 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp24 | hskp15 | (~ndr1_0) | c1_1(a320) | (~c2_1(a320)) | (~c3_1(a320)))) <=> ((~![U: $i] : (hskp24 | hskp15 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | hskp24 | hskp15 | (~ndr1_0) | c1_1(a320) | (~c2_1(a320)) | (~c3_1(a320)))),
% 0.74/0.93 inference(rewrite,[status(thm)],[])).
% 0.74/0.93 tff(375,plain,
% 0.74/0.93 ((~![U: $i] : (hskp24 | hskp15 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp24 | hskp15 | (~ndr1_0) | c1_1(a320) | (~c2_1(a320)) | (~c3_1(a320)))),
% 0.74/0.93 inference(quant_inst,[status(thm)],[])).
% 0.74/0.93 tff(376,plain,
% 0.74/0.93 ((~![U: $i] : (hskp24 | hskp15 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | hskp24 | hskp15 | (~ndr1_0) | c1_1(a320) | (~c2_1(a320)) | (~c3_1(a320))),
% 0.74/0.93 inference(modus_ponens,[status(thm)],[375, 374])).
% 0.74/0.93 tff(377,plain,
% 0.74/0.93 (hskp15 | c1_1(a320)),
% 0.74/0.93 inference(unit_resolution,[status(thm)],[376, 110, 373, 337, 329, 312])).
% 0.74/0.93 tff(378,plain,
% 0.74/0.93 (hskp15),
% 0.74/0.93 inference(unit_resolution,[status(thm)],[377, 302])).
% 0.74/0.93 tff(379,plain,
% 0.74/0.93 (((~hskp15) | (~c2_1(a242))) <=> ((~hskp15) | (~c2_1(a242)))),
% 0.74/0.93 inference(rewrite,[status(thm)],[])).
% 0.74/0.93 tff(380,plain,
% 0.74/0.93 (((~c2_1(a242)) | (~hskp15)) <=> ((~hskp15) | (~c2_1(a242)))),
% 0.74/0.93 inference(rewrite,[status(thm)],[])).
% 0.74/0.93 tff(381,axiom,((~c2_1(a242)) | (~hskp15)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause104')).
% 0.74/0.93 tff(382,plain,
% 0.74/0.93 ((~hskp15) | (~c2_1(a242))),
% 0.74/0.93 inference(modus_ponens,[status(thm)],[381, 380])).
% 0.74/0.93 tff(383,plain,
% 0.74/0.93 ((~hskp15) | (~c2_1(a242))),
% 0.74/0.93 inference(modus_ponens,[status(thm)],[382, 379])).
% 0.74/0.93 tff(384,plain,
% 0.74/0.93 (~c2_1(a242)),
% 0.74/0.93 inference(unit_resolution,[status(thm)],[383, 378])).
% 0.74/0.93 tff(385,plain,
% 0.74/0.93 (((~hskp15) | c1_1(a242)) <=> ((~hskp15) | c1_1(a242))),
% 0.74/0.93 inference(rewrite,[status(thm)],[])).
% 0.74/0.93 tff(386,axiom,((~hskp15) | c1_1(a242)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause65')).
% 0.74/0.93 tff(387,plain,
% 0.74/0.93 ((~hskp15) | c1_1(a242)),
% 0.74/0.93 inference(modus_ponens,[status(thm)],[386, 385])).
% 0.74/0.93 tff(388,plain,
% 0.74/0.93 ((~hskp15) | c1_1(a242)),
% 0.74/0.93 inference(modus_ponens,[status(thm)],[387, 385])).
% 0.74/0.93 tff(389,plain,
% 0.74/0.93 ((~hskp15) | c1_1(a242)),
% 0.74/0.93 inference(modus_ponens,[status(thm)],[388, 385])).
% 0.74/0.93 tff(390,plain,
% 0.74/0.93 ((~hskp15) | c1_1(a242)),
% 0.74/0.93 inference(modus_ponens,[status(thm)],[389, 385])).
% 0.74/0.93 tff(391,plain,
% 0.74/0.93 ((~hskp15) | c1_1(a242)),
% 0.74/0.93 inference(modus_ponens,[status(thm)],[390, 385])).
% 0.74/0.93 tff(392,plain,
% 0.74/0.93 (c1_1(a242)),
% 0.74/0.93 inference(unit_resolution,[status(thm)],[391, 378])).
% 0.74/0.93 tff(393,plain,
% 0.74/0.93 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp19 | c0_1(a320) | c2_1(a242) | (~ndr1_0) | c3_1(a242) | (~c1_1(a242)) | (~c2_1(a320)) | (~c3_1(a320)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp19 | c0_1(a320) | c2_1(a242) | (~ndr1_0) | c3_1(a242) | (~c1_1(a242)) | (~c2_1(a320)) | (~c3_1(a320)))),
% 0.74/0.93 inference(rewrite,[status(thm)],[])).
% 0.74/0.93 tff(394,plain,
% 0.74/0.93 ((hskp19 | (~ndr1_0) | c2_1(a242) | c3_1(a242) | (~c1_1(a242)) | c0_1(a320) | (~c3_1(a320)) | (~c2_1(a320))) <=> (hskp19 | c0_1(a320) | c2_1(a242) | (~ndr1_0) | c3_1(a242) | (~c1_1(a242)) | (~c2_1(a320)) | (~c3_1(a320)))),
% 0.74/0.93 inference(rewrite,[status(thm)],[])).
% 0.74/0.93 tff(395,plain,
% 0.74/0.93 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp19 | (~ndr1_0) | c2_1(a242) | c3_1(a242) | (~c1_1(a242)) | c0_1(a320) | (~c3_1(a320)) | (~c2_1(a320)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp19 | c0_1(a320) | c2_1(a242) | (~ndr1_0) | c3_1(a242) | (~c1_1(a242)) | (~c2_1(a320)) | (~c3_1(a320))))),
% 0.74/0.93 inference(monotonicity,[status(thm)],[394])).
% 0.74/0.93 tff(396,plain,
% 0.74/0.93 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp19 | (~ndr1_0) | c2_1(a242) | c3_1(a242) | (~c1_1(a242)) | c0_1(a320) | (~c3_1(a320)) | (~c2_1(a320)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp19 | c0_1(a320) | c2_1(a242) | (~ndr1_0) | c3_1(a242) | (~c1_1(a242)) | (~c2_1(a320)) | (~c3_1(a320)))),
% 0.74/0.93 inference(transitivity,[status(thm)],[395, 393])).
% 0.74/0.93 tff(397,plain,
% 0.74/0.93 ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp19 | (~ndr1_0) | c2_1(a242) | c3_1(a242) | (~c1_1(a242)) | c0_1(a320) | (~c3_1(a320)) | (~c2_1(a320)))),
% 0.74/0.93 inference(quant_inst,[status(thm)],[])).
% 0.74/0.93 tff(398,plain,
% 0.74/0.93 ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp19 | c0_1(a320) | c2_1(a242) | (~ndr1_0) | c3_1(a242) | (~c1_1(a242)) | (~c2_1(a320)) | (~c3_1(a320))),
% 0.74/0.93 inference(modus_ponens,[status(thm)],[397, 396])).
% 0.74/0.93 tff(399,plain,
% 0.74/0.93 (c3_1(a242)),
% 0.74/0.93 inference(unit_resolution,[status(thm)],[398, 313, 110, 337, 329, 392, 356, 384, 301])).
% 0.74/0.93 tff(400,plain,
% 0.74/0.93 (^[V: $i, U: $i] : refl((hskp9 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V))) <=> (hskp9 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V))))),
% 0.74/0.93 inference(bind,[status(th)],[])).
% 0.77/0.93 tff(401,plain,
% 0.77/0.93 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))),
% 0.77/0.93 inference(quant_intro,[status(thm)],[400])).
% 0.77/0.93 tff(402,plain,
% 0.77/0.93 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))),
% 0.77/0.93 inference(rewrite,[status(thm)],[])).
% 0.77/0.93 tff(403,plain,
% 0.77/0.93 (^[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)) | (~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(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~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(U)) <=> ((~ndr1_0) | c1_1(U) | (~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(U)) | c0_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))), ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V))))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) | hskp9) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V))) | hskp9))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V))) | hskp9) <=> (hskp9 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) | hskp9) <=> (hskp9 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))))),
% 0.77/0.93 inference(bind,[status(th)],[])).
% 0.77/0.93 tff(404,plain,
% 0.77/0.93 (![V: $i, U: $i] : ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) | hskp9) <=> ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))),
% 0.77/0.93 inference(quant_intro,[status(thm)],[403])).
% 0.77/0.93 tff(405,axiom,(![V: $i, U: $i] : ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) | hskp9)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause181')).
% 0.77/0.93 tff(406,plain,
% 0.77/0.93 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))),
% 0.77/0.93 inference(modus_ponens,[status(thm)],[405, 404])).
% 0.77/0.93 tff(407,plain,
% 0.77/0.93 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))),
% 0.77/0.93 inference(modus_ponens,[status(thm)],[406, 402])).
% 0.77/0.93 tff(408,plain,(
% 0.77/0.93 ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))),
% 0.77/0.93 inference(skolemize,[status(sab)],[407])).
% 0.77/0.93 tff(409,plain,
% 0.77/0.93 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))),
% 0.77/0.93 inference(modus_ponens,[status(thm)],[408, 401])).
% 0.77/0.93 tff(410,plain,
% 0.77/0.93 (((~hskp15) | (~c0_1(a242))) <=> ((~hskp15) | (~c0_1(a242)))),
% 0.77/0.93 inference(rewrite,[status(thm)],[])).
% 0.77/0.93 tff(411,plain,
% 0.77/0.93 (((~c0_1(a242)) | (~hskp15)) <=> ((~hskp15) | (~c0_1(a242)))),
% 0.77/0.93 inference(rewrite,[status(thm)],[])).
% 0.77/0.93 tff(412,axiom,((~c0_1(a242)) | (~hskp15)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause103')).
% 0.77/0.93 tff(413,plain,
% 0.77/0.93 ((~hskp15) | (~c0_1(a242))),
% 0.77/0.93 inference(modus_ponens,[status(thm)],[412, 411])).
% 0.77/0.93 tff(414,plain,
% 0.77/0.93 ((~hskp15) | (~c0_1(a242))),
% 0.77/0.93 inference(modus_ponens,[status(thm)],[413, 410])).
% 0.77/0.93 tff(415,plain,
% 0.77/0.93 (~c0_1(a242)),
% 0.77/0.93 inference(unit_resolution,[status(thm)],[414, 378])).
% 0.77/0.93 tff(416,plain,
% 0.77/0.93 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp9 | c0_1(a242) | (~ndr1_0) | (~c3_1(a242)) | (~c1_1(a242)) | c1_1(a320) | (~c2_1(a320)) | (~c3_1(a320)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp9 | c0_1(a242) | (~ndr1_0) | (~c3_1(a242)) | (~c1_1(a242)) | c1_1(a320) | (~c2_1(a320)) | (~c3_1(a320)))),
% 0.77/0.93 inference(rewrite,[status(thm)],[])).
% 0.77/0.93 tff(417,plain,
% 0.77/0.93 ((hskp9 | (~ndr1_0) | c1_1(a320) | (~c2_1(a320)) | (~c3_1(a320)) | c0_1(a242) | (~c1_1(a242)) | (~c3_1(a242))) <=> (hskp9 | c0_1(a242) | (~ndr1_0) | (~c3_1(a242)) | (~c1_1(a242)) | c1_1(a320) | (~c2_1(a320)) | (~c3_1(a320)))),
% 0.77/0.93 inference(rewrite,[status(thm)],[])).
% 0.77/0.93 tff(418,plain,
% 0.77/0.93 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp9 | (~ndr1_0) | c1_1(a320) | (~c2_1(a320)) | (~c3_1(a320)) | c0_1(a242) | (~c1_1(a242)) | (~c3_1(a242)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp9 | c0_1(a242) | (~ndr1_0) | (~c3_1(a242)) | (~c1_1(a242)) | c1_1(a320) | (~c2_1(a320)) | (~c3_1(a320))))),
% 0.77/0.93 inference(monotonicity,[status(thm)],[417])).
% 0.77/0.93 tff(419,plain,
% 0.77/0.93 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp9 | (~ndr1_0) | c1_1(a320) | (~c2_1(a320)) | (~c3_1(a320)) | c0_1(a242) | (~c1_1(a242)) | (~c3_1(a242)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp9 | c0_1(a242) | (~ndr1_0) | (~c3_1(a242)) | (~c1_1(a242)) | c1_1(a320) | (~c2_1(a320)) | (~c3_1(a320)))),
% 0.77/0.93 inference(transitivity,[status(thm)],[418, 416])).
% 0.77/0.93 tff(420,plain,
% 0.77/0.93 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp9 | (~ndr1_0) | c1_1(a320) | (~c2_1(a320)) | (~c3_1(a320)) | c0_1(a242) | (~c1_1(a242)) | (~c3_1(a242)))),
% 0.77/0.93 inference(quant_inst,[status(thm)],[])).
% 0.77/0.93 tff(421,plain,
% 0.77/0.93 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp9 | c0_1(a242) | (~ndr1_0) | (~c3_1(a242)) | (~c1_1(a242)) | c1_1(a320) | (~c2_1(a320)) | (~c3_1(a320))),
% 0.77/0.93 inference(modus_ponens,[status(thm)],[420, 419])).
% 0.77/0.93 tff(422,plain,
% 0.77/0.93 ($false),
% 0.77/0.93 inference(unit_resolution,[status(thm)],[421, 110, 23, 337, 329, 392, 415, 409, 302, 399])).
% 0.77/0.93 tff(423,plain,(c1_1(a320) | hskp9 | hskp19), inference(lemma,lemma(discharge,[]))).
% 0.77/0.93 tff(424,plain,
% 0.77/0.93 (c1_1(a320)),
% 0.77/0.93 inference(unit_resolution,[status(thm)],[423, 291, 23])).
% 0.77/0.93 tff(425,plain,
% 0.77/0.93 (^[U: $i] : refl((hskp3 | hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))) <=> (hskp3 | hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))))),
% 0.77/0.93 inference(bind,[status(th)],[])).
% 0.77/0.93 tff(426,plain,
% 0.77/0.93 (![U: $i] : (hskp3 | hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp3 | hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 0.77/0.93 inference(quant_intro,[status(thm)],[425])).
% 0.77/0.93 tff(427,plain,
% 0.77/0.93 (![U: $i] : (hskp3 | hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp3 | hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 0.77/0.93 inference(rewrite,[status(thm)],[])).
% 0.77/0.93 tff(428,plain,
% 0.77/0.93 (^[U: $i] : 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)) | c0_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp3) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))) | hskp3))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))) | hskp3) <=> (hskp3 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp3) <=> (hskp3 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp3) | hskp6) <=> ((hskp3 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))) | hskp6))), rewrite(((hskp3 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))) | hskp6) <=> (hskp3 | hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp3) | hskp6) <=> (hskp3 | hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))))),
% 0.77/0.93 inference(bind,[status(th)],[])).
% 0.77/0.93 tff(429,plain,
% 0.77/0.93 (![U: $i] : ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp3) | hskp6) <=> ![U: $i] : (hskp3 | hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 0.77/0.93 inference(quant_intro,[status(thm)],[428])).
% 0.77/0.93 tff(430,axiom,(![U: $i] : ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp3) | hskp6)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause147')).
% 0.77/0.93 tff(431,plain,
% 0.77/0.93 (![U: $i] : (hskp3 | hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 0.77/0.93 inference(modus_ponens,[status(thm)],[430, 429])).
% 0.77/0.93 tff(432,plain,
% 0.77/0.93 (![U: $i] : (hskp3 | hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 0.77/0.93 inference(modus_ponens,[status(thm)],[431, 427])).
% 0.77/0.93 tff(433,plain,(
% 0.77/0.93 ![U: $i] : (hskp3 | hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 0.77/0.93 inference(skolemize,[status(sab)],[432])).
% 0.77/0.93 tff(434,plain,
% 0.77/0.93 (![U: $i] : (hskp3 | hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 0.77/0.93 inference(modus_ponens,[status(thm)],[433, 426])).
% 0.77/0.93 tff(435,plain,
% 0.77/0.93 (hskp25),
% 0.77/0.93 inference(unit_resolution,[status(thm)],[320, 291])).
% 0.77/0.93 tff(436,plain,
% 0.77/0.93 (~c0_1(a320)),
% 0.77/0.93 inference(unit_resolution,[status(thm)],[355, 435])).
% 0.77/0.93 tff(437,plain,
% 0.77/0.93 (c3_1(a320)),
% 0.77/0.93 inference(unit_resolution,[status(thm)],[328, 435])).
% 0.77/0.93 tff(438,plain,
% 0.77/0.93 (((~![U: $i] : (hskp3 | hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp3 | hskp6 | c0_1(a320) | (~ndr1_0) | (~c1_1(a320)) | (~c3_1(a320)))) <=> ((~![U: $i] : (hskp3 | hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp3 | hskp6 | c0_1(a320) | (~ndr1_0) | (~c1_1(a320)) | (~c3_1(a320)))),
% 0.77/0.93 inference(rewrite,[status(thm)],[])).
% 0.77/0.93 tff(439,plain,
% 0.77/0.93 ((hskp3 | hskp6 | (~ndr1_0) | c0_1(a320) | (~c3_1(a320)) | (~c1_1(a320))) <=> (hskp3 | hskp6 | c0_1(a320) | (~ndr1_0) | (~c1_1(a320)) | (~c3_1(a320)))),
% 0.77/0.93 inference(rewrite,[status(thm)],[])).
% 0.77/0.93 tff(440,plain,
% 0.77/0.93 (((~![U: $i] : (hskp3 | hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp3 | hskp6 | (~ndr1_0) | c0_1(a320) | (~c3_1(a320)) | (~c1_1(a320)))) <=> ((~![U: $i] : (hskp3 | hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp3 | hskp6 | c0_1(a320) | (~ndr1_0) | (~c1_1(a320)) | (~c3_1(a320))))),
% 0.77/0.93 inference(monotonicity,[status(thm)],[439])).
% 0.77/0.93 tff(441,plain,
% 0.77/0.93 (((~![U: $i] : (hskp3 | hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp3 | hskp6 | (~ndr1_0) | c0_1(a320) | (~c3_1(a320)) | (~c1_1(a320)))) <=> ((~![U: $i] : (hskp3 | hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp3 | hskp6 | c0_1(a320) | (~ndr1_0) | (~c1_1(a320)) | (~c3_1(a320)))),
% 0.77/0.93 inference(transitivity,[status(thm)],[440, 438])).
% 0.77/0.93 tff(442,plain,
% 0.77/0.93 ((~![U: $i] : (hskp3 | hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp3 | hskp6 | (~ndr1_0) | c0_1(a320) | (~c3_1(a320)) | (~c1_1(a320)))),
% 0.77/0.93 inference(quant_inst,[status(thm)],[])).
% 0.77/0.93 tff(443,plain,
% 0.77/0.93 ((~![U: $i] : (hskp3 | hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp3 | hskp6 | c0_1(a320) | (~ndr1_0) | (~c1_1(a320)) | (~c3_1(a320))),
% 0.77/0.93 inference(modus_ponens,[status(thm)],[442, 441])).
% 0.77/0.93 tff(444,plain,
% 0.77/0.93 (hskp6),
% 0.77/0.93 inference(unit_resolution,[status(thm)],[443, 251, 110, 437, 436, 434, 424])).
% 0.77/0.93 tff(445,plain,
% 0.77/0.93 (((~hskp6) | (~c3_1(a220))) <=> ((~hskp6) | (~c3_1(a220)))),
% 0.77/0.93 inference(rewrite,[status(thm)],[])).
% 0.77/0.93 tff(446,plain,
% 0.77/0.93 (((~c3_1(a220)) | (~hskp6)) <=> ((~hskp6) | (~c3_1(a220)))),
% 0.77/0.93 inference(rewrite,[status(thm)],[])).
% 0.77/0.93 tff(447,axiom,((~c3_1(a220)) | (~hskp6)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause117')).
% 0.77/0.93 tff(448,plain,
% 0.77/0.93 ((~hskp6) | (~c3_1(a220))),
% 0.77/0.93 inference(modus_ponens,[status(thm)],[447, 446])).
% 0.77/0.93 tff(449,plain,
% 0.77/0.93 ((~hskp6) | (~c3_1(a220))),
% 0.77/0.93 inference(modus_ponens,[status(thm)],[448, 445])).
% 0.77/0.93 tff(450,plain,
% 0.77/0.93 (~c3_1(a220)),
% 0.77/0.93 inference(unit_resolution,[status(thm)],[449, 444])).
% 0.77/0.93 tff(451,plain,
% 0.77/0.93 ((hskp3 | hskp16) <=> (hskp3 | hskp16)),
% 0.77/0.93 inference(rewrite,[status(thm)],[])).
% 0.77/0.93 tff(452,axiom,(hskp3 | hskp16), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause1')).
% 0.77/0.93 tff(453,plain,
% 0.77/0.93 (hskp3 | hskp16),
% 0.77/0.93 inference(modus_ponens,[status(thm)],[452, 451])).
% 0.77/0.93 tff(454,plain,
% 0.77/0.93 (hskp3 | hskp16),
% 0.77/0.93 inference(modus_ponens,[status(thm)],[453, 451])).
% 0.77/0.93 tff(455,plain,
% 0.77/0.93 (hskp3 | hskp16),
% 0.77/0.93 inference(modus_ponens,[status(thm)],[454, 451])).
% 0.77/0.93 tff(456,plain,
% 0.77/0.93 (hskp3 | hskp16),
% 0.77/0.93 inference(modus_ponens,[status(thm)],[455, 451])).
% 0.77/0.93 tff(457,plain,
% 0.77/0.93 (hskp3 | hskp16),
% 0.77/0.93 inference(modus_ponens,[status(thm)],[456, 451])).
% 0.77/0.93 tff(458,plain,
% 0.77/0.93 (hskp16),
% 0.77/0.93 inference(unit_resolution,[status(thm)],[457, 251])).
% 0.77/0.93 tff(459,plain,
% 0.77/0.93 (((~hskp16) | (~c3_1(a245))) <=> ((~hskp16) | (~c3_1(a245)))),
% 0.77/0.93 inference(rewrite,[status(thm)],[])).
% 0.77/0.93 tff(460,plain,
% 0.77/0.93 (((~c3_1(a245)) | (~hskp16)) <=> ((~hskp16) | (~c3_1(a245)))),
% 0.77/0.93 inference(rewrite,[status(thm)],[])).
% 0.77/0.93 tff(461,axiom,((~c3_1(a245)) | (~hskp16)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause102')).
% 0.77/0.93 tff(462,plain,
% 0.77/0.93 ((~hskp16) | (~c3_1(a245))),
% 0.77/0.93 inference(modus_ponens,[status(thm)],[461, 460])).
% 0.77/0.93 tff(463,plain,
% 0.77/0.93 ((~hskp16) | (~c3_1(a245))),
% 0.77/0.93 inference(modus_ponens,[status(thm)],[462, 459])).
% 0.77/0.93 tff(464,plain,
% 0.77/0.93 (~c3_1(a245)),
% 0.77/0.93 inference(unit_resolution,[status(thm)],[463, 458])).
% 0.77/0.93 tff(465,plain,
% 0.77/0.93 (((~hskp16) | (~c1_1(a245))) <=> ((~hskp16) | (~c1_1(a245)))),
% 0.77/0.93 inference(rewrite,[status(thm)],[])).
% 0.77/0.93 tff(466,plain,
% 0.77/0.93 (((~c1_1(a245)) | (~hskp16)) <=> ((~hskp16) | (~c1_1(a245)))),
% 0.77/0.93 inference(rewrite,[status(thm)],[])).
% 0.77/0.93 tff(467,axiom,((~c1_1(a245)) | (~hskp16)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause101')).
% 0.77/0.93 tff(468,plain,
% 0.77/0.93 ((~hskp16) | (~c1_1(a245))),
% 0.77/0.93 inference(modus_ponens,[status(thm)],[467, 466])).
% 0.77/0.93 tff(469,plain,
% 0.77/0.93 ((~hskp16) | (~c1_1(a245))),
% 0.77/0.93 inference(modus_ponens,[status(thm)],[468, 465])).
% 0.77/0.93 tff(470,plain,
% 0.77/0.93 (~c1_1(a245)),
% 0.77/0.93 inference(unit_resolution,[status(thm)],[469, 458])).
% 0.77/0.93 tff(471,plain,
% 0.77/0.93 (((~hskp16) | c0_1(a245)) <=> ((~hskp16) | c0_1(a245))),
% 0.77/0.93 inference(rewrite,[status(thm)],[])).
% 0.77/0.93 tff(472,axiom,((~hskp16) | c0_1(a245)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause64')).
% 0.77/0.93 tff(473,plain,
% 0.77/0.93 ((~hskp16) | c0_1(a245)),
% 0.77/0.93 inference(modus_ponens,[status(thm)],[472, 471])).
% 0.77/0.93 tff(474,plain,
% 0.77/0.93 ((~hskp16) | c0_1(a245)),
% 0.77/0.93 inference(modus_ponens,[status(thm)],[473, 471])).
% 0.77/0.93 tff(475,plain,
% 0.77/0.93 ((~hskp16) | c0_1(a245)),
% 0.77/0.93 inference(modus_ponens,[status(thm)],[474, 471])).
% 0.77/0.93 tff(476,plain,
% 0.77/0.93 ((~hskp16) | c0_1(a245)),
% 0.77/0.93 inference(modus_ponens,[status(thm)],[475, 471])).
% 0.77/0.93 tff(477,plain,
% 0.77/0.93 ((~hskp16) | c0_1(a245)),
% 0.77/0.93 inference(modus_ponens,[status(thm)],[476, 471])).
% 0.77/0.93 tff(478,plain,
% 0.77/0.93 (c0_1(a245)),
% 0.77/0.93 inference(unit_resolution,[status(thm)],[477, 458])).
% 0.77/0.93 tff(479,plain,
% 0.77/0.93 (((~hskp6) | c1_1(a220)) <=> ((~hskp6) | c1_1(a220))),
% 0.77/0.93 inference(rewrite,[status(thm)],[])).
% 0.77/0.93 tff(480,axiom,((~hskp6) | c1_1(a220)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause78')).
% 0.77/0.93 tff(481,plain,
% 0.77/0.93 ((~hskp6) | c1_1(a220)),
% 0.77/0.93 inference(modus_ponens,[status(thm)],[480, 479])).
% 0.77/0.93 tff(482,plain,
% 0.77/0.93 ((~hskp6) | c1_1(a220)),
% 0.77/0.93 inference(modus_ponens,[status(thm)],[481, 479])).
% 0.77/0.93 tff(483,plain,
% 0.77/0.93 ((~hskp6) | c1_1(a220)),
% 0.77/0.93 inference(modus_ponens,[status(thm)],[482, 479])).
% 0.77/0.93 tff(484,plain,
% 0.77/0.93 ((~hskp6) | c1_1(a220)),
% 0.77/0.93 inference(modus_ponens,[status(thm)],[483, 479])).
% 0.77/0.93 tff(485,plain,
% 0.77/0.93 ((~hskp6) | c1_1(a220)),
% 0.77/0.93 inference(modus_ponens,[status(thm)],[484, 479])).
% 0.77/0.93 tff(486,plain,
% 0.77/0.93 (c1_1(a220)),
% 0.77/0.93 inference(unit_resolution,[status(thm)],[485, 444])).
% 0.77/0.93 tff(487,plain,
% 0.77/0.93 (((~hskp6) | c2_1(a220)) <=> ((~hskp6) | c2_1(a220))),
% 0.77/0.93 inference(rewrite,[status(thm)],[])).
% 0.77/0.93 tff(488,axiom,((~hskp6) | c2_1(a220)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause79')).
% 0.77/0.93 tff(489,plain,
% 0.77/0.93 ((~hskp6) | c2_1(a220)),
% 0.77/0.93 inference(modus_ponens,[status(thm)],[488, 487])).
% 0.77/0.93 tff(490,plain,
% 0.77/0.93 ((~hskp6) | c2_1(a220)),
% 0.77/0.93 inference(modus_ponens,[status(thm)],[489, 487])).
% 0.77/0.93 tff(491,plain,
% 0.77/0.93 ((~hskp6) | c2_1(a220)),
% 0.77/0.93 inference(modus_ponens,[status(thm)],[490, 487])).
% 0.77/0.93 tff(492,plain,
% 0.77/0.93 ((~hskp6) | c2_1(a220)),
% 0.77/0.93 inference(modus_ponens,[status(thm)],[491, 487])).
% 0.77/0.93 tff(493,plain,
% 0.77/0.93 ((~hskp6) | c2_1(a220)),
% 0.77/0.93 inference(modus_ponens,[status(thm)],[492, 487])).
% 0.77/0.93 tff(494,plain,
% 0.77/0.93 (c2_1(a220)),
% 0.77/0.93 inference(unit_resolution,[status(thm)],[493, 444])).
% 0.77/0.93 tff(495,plain,
% 0.77/0.93 (c1_1(a320)),
% 0.77/0.93 inference(unit_resolution,[status(thm)],[423, 313, 23])).
% 0.77/0.94 tff(496,plain,
% 0.77/0.94 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c2_1(U)) | (~c3_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) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W))))),
% 0.77/0.94 inference(bind,[status(th)],[])).
% 0.77/0.94 tff(497,plain,
% 0.77/0.94 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_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) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))),
% 0.77/0.94 inference(quant_intro,[status(thm)],[496])).
% 0.77/0.94 tff(498,plain,
% 0.77/0.94 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_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) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))),
% 0.77/0.94 inference(rewrite,[status(thm)],[])).
% 0.77/0.94 tff(499,plain,
% 0.77/0.94 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~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)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V))))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c0_1(W))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V))) | (~c0_1(W))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V))) | (~c0_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(W)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c0_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(W))))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c0_1(W))) | c3_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(W))) | c3_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(W))) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(W)))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c0_1(W))) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(W))))), ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c0_1(W))) | c3_1(V)) | c1_1(W)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(W))) | c1_1(W)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(W))) | c1_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_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))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c0_1(W))) | c3_1(V)) | c1_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_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))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c0_1(W))) | c3_1(V)) | c1_1(W)) | c3_1(W)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_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) | (~c2_1(U)) | (~c3_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) | (~c2_1(U)) | (~c3_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))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c0_1(W))) | c3_1(V)) | c1_1(W)) | c3_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))))),
% 0.77/0.94 inference(bind,[status(th)],[])).
% 0.77/0.94 tff(500,plain,
% 0.77/0.94 (![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c0_1(W))) | c3_1(V)) | c1_1(W)) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))),
% 0.77/0.94 inference(quant_intro,[status(thm)],[499])).
% 0.77/0.94 tff(501,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c0_1(W))) | c3_1(V)) | c1_1(W)) | c3_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause196')).
% 0.77/0.94 tff(502,plain,
% 0.77/0.94 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))),
% 0.77/0.94 inference(modus_ponens,[status(thm)],[501, 500])).
% 0.77/0.94 tff(503,plain,
% 0.77/0.94 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))),
% 0.77/0.94 inference(modus_ponens,[status(thm)],[502, 498])).
% 0.77/0.94 tff(504,plain,(
% 0.77/0.94 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))),
% 0.77/0.94 inference(skolemize,[status(sab)],[503])).
% 0.77/0.94 tff(505,plain,
% 0.77/0.94 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))),
% 0.77/0.94 inference(modus_ponens,[status(thm)],[504, 497])).
% 0.77/0.94 tff(506,assumption,(~c3_1(a220)), introduced(assumption)).
% 0.77/0.94 tff(507,assumption,(~c3_1(a245)), introduced(assumption)).
% 0.77/0.94 tff(508,assumption,(~c1_1(a245)), introduced(assumption)).
% 0.77/0.94 tff(509,assumption,(c2_1(a220)), introduced(assumption)).
% 0.77/0.94 tff(510,assumption,(c1_1(a220)), introduced(assumption)).
% 0.77/0.94 tff(511,assumption,(c0_1(a245)), introduced(assumption)).
% 0.77/0.94 tff(512,plain,
% 0.77/0.94 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_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(a245) | c3_1(a245) | c3_1(a220) | (~ndr1_0) | (~c2_1(a220)) | (~c1_1(a220)) | (~c0_1(a245)) | (~c2_1(a320)) | (~c1_1(a320)) | (~c3_1(a320)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_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(a245) | c3_1(a245) | c3_1(a220) | (~ndr1_0) | (~c2_1(a220)) | (~c1_1(a220)) | (~c0_1(a245)) | (~c2_1(a320)) | (~c1_1(a320)) | (~c3_1(a320)))),
% 0.77/0.94 inference(rewrite,[status(thm)],[])).
% 0.77/0.94 tff(513,plain,
% 0.77/0.94 (((~ndr1_0) | (~c2_1(a320)) | (~c3_1(a320)) | (~c1_1(a320)) | c3_1(a220) | (~c1_1(a220)) | (~c2_1(a220)) | c3_1(a245) | c1_1(a245) | (~c0_1(a245))) <=> (c1_1(a245) | c3_1(a245) | c3_1(a220) | (~ndr1_0) | (~c2_1(a220)) | (~c1_1(a220)) | (~c0_1(a245)) | (~c2_1(a320)) | (~c1_1(a320)) | (~c3_1(a320)))),
% 0.77/0.94 inference(rewrite,[status(thm)],[])).
% 0.77/0.94 tff(514,plain,
% 0.77/0.94 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_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) | (~c2_1(a320)) | (~c3_1(a320)) | (~c1_1(a320)) | c3_1(a220) | (~c1_1(a220)) | (~c2_1(a220)) | c3_1(a245) | c1_1(a245) | (~c0_1(a245)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_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(a245) | c3_1(a245) | c3_1(a220) | (~ndr1_0) | (~c2_1(a220)) | (~c1_1(a220)) | (~c0_1(a245)) | (~c2_1(a320)) | (~c1_1(a320)) | (~c3_1(a320))))),
% 0.77/0.94 inference(monotonicity,[status(thm)],[513])).
% 0.77/0.94 tff(515,plain,
% 0.77/0.94 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_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) | (~c2_1(a320)) | (~c3_1(a320)) | (~c1_1(a320)) | c3_1(a220) | (~c1_1(a220)) | (~c2_1(a220)) | c3_1(a245) | c1_1(a245) | (~c0_1(a245)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_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(a245) | c3_1(a245) | c3_1(a220) | (~ndr1_0) | (~c2_1(a220)) | (~c1_1(a220)) | (~c0_1(a245)) | (~c2_1(a320)) | (~c1_1(a320)) | (~c3_1(a320)))),
% 0.77/0.94 inference(transitivity,[status(thm)],[514, 512])).
% 0.77/0.94 tff(516,plain,
% 0.77/0.94 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_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) | (~c2_1(a320)) | (~c3_1(a320)) | (~c1_1(a320)) | c3_1(a220) | (~c1_1(a220)) | (~c2_1(a220)) | c3_1(a245) | c1_1(a245) | (~c0_1(a245)))),
% 0.77/0.94 inference(quant_inst,[status(thm)],[])).
% 0.77/0.94 tff(517,plain,
% 0.77/0.94 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | c1_1(a245) | c3_1(a245) | c3_1(a220) | (~ndr1_0) | (~c2_1(a220)) | (~c1_1(a220)) | (~c0_1(a245)) | (~c2_1(a320)) | (~c1_1(a320)) | (~c3_1(a320))),
% 0.77/0.94 inference(modus_ponens,[status(thm)],[516, 515])).
% 0.77/0.94 tff(518,plain,
% 0.77/0.94 ($false),
% 0.77/0.94 inference(unit_resolution,[status(thm)],[517, 110, 337, 329, 511, 510, 509, 508, 507, 506, 505, 495])).
% 0.77/0.94 tff(519,plain,(hskp19 | (~c0_1(a245)) | (~c1_1(a220)) | (~c2_1(a220)) | c1_1(a245) | c3_1(a245) | c3_1(a220) | hskp9), inference(lemma,lemma(discharge,[]))).
% 0.77/0.94 tff(520,plain,
% 0.77/0.94 ($false),
% 0.77/0.94 inference(unit_resolution,[status(thm)],[519, 494, 486, 478, 291, 470, 464, 450, 23])).
% 0.77/0.94 tff(521,plain,(hskp2 | hskp9 | hskp27 | hskp26), inference(lemma,lemma(discharge,[]))).
% 0.77/0.94 tff(522,plain,
% 0.77/0.94 (hskp2),
% 0.77/0.94 inference(unit_resolution,[status(thm)],[521, 163, 34, 23])).
% 0.77/0.94 tff(523,plain,
% 0.77/0.94 (~c1_1(a215)),
% 0.77/0.94 inference(unit_resolution,[status(thm)],[124, 522])).
% 0.77/0.94 tff(524,plain,
% 0.77/0.94 (~c0_1(a215)),
% 0.77/0.94 inference(unit_resolution,[status(thm)],[138, 522])).
% 0.77/0.94 tff(525,plain,
% 0.77/0.94 (c2_1(a215)),
% 0.77/0.94 inference(unit_resolution,[status(thm)],[132, 522])).
% 0.77/0.94 tff(526,assumption,(~hskp12), introduced(assumption)).
% 0.77/0.94 tff(527,assumption,(~c2_1(a237)), introduced(assumption)).
% 0.77/0.94 tff(528,plain,
% 0.77/0.94 (~hskp26),
% 0.77/0.94 inference(unit_resolution,[status(thm)],[118, 81, 34])).
% 0.77/0.94 tff(529,plain,
% 0.77/0.94 (((~![U: $i] : (hskp27 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | (hskp27 | hskp2 | c2_1(a237) | c3_1(a237) | (~ndr1_0) | c1_1(a237))) <=> ((~![U: $i] : (hskp27 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | hskp27 | hskp2 | c2_1(a237) | c3_1(a237) | (~ndr1_0) | c1_1(a237))),
% 0.77/0.94 inference(rewrite,[status(thm)],[])).
% 0.77/0.94 tff(530,plain,
% 0.77/0.94 ((hskp27 | hskp2 | (~ndr1_0) | c2_1(a237) | c1_1(a237) | c3_1(a237)) <=> (hskp27 | hskp2 | c2_1(a237) | c3_1(a237) | (~ndr1_0) | c1_1(a237))),
% 0.77/0.94 inference(rewrite,[status(thm)],[])).
% 0.77/0.94 tff(531,plain,
% 0.77/0.94 (((~![U: $i] : (hskp27 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | (hskp27 | hskp2 | (~ndr1_0) | c2_1(a237) | c1_1(a237) | c3_1(a237))) <=> ((~![U: $i] : (hskp27 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | (hskp27 | hskp2 | c2_1(a237) | c3_1(a237) | (~ndr1_0) | c1_1(a237)))),
% 0.77/0.94 inference(monotonicity,[status(thm)],[530])).
% 0.77/0.94 tff(532,plain,
% 0.77/0.94 (((~![U: $i] : (hskp27 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | (hskp27 | hskp2 | (~ndr1_0) | c2_1(a237) | c1_1(a237) | c3_1(a237))) <=> ((~![U: $i] : (hskp27 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | hskp27 | hskp2 | c2_1(a237) | c3_1(a237) | (~ndr1_0) | c1_1(a237))),
% 0.77/0.94 inference(transitivity,[status(thm)],[531, 529])).
% 0.77/0.94 tff(533,plain,
% 0.77/0.94 ((~![U: $i] : (hskp27 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | (hskp27 | hskp2 | (~ndr1_0) | c2_1(a237) | c1_1(a237) | c3_1(a237))),
% 0.77/0.94 inference(quant_inst,[status(thm)],[])).
% 0.77/0.94 tff(534,plain,
% 0.77/0.94 ((~![U: $i] : (hskp27 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | hskp27 | hskp2 | c2_1(a237) | c3_1(a237) | (~ndr1_0) | c1_1(a237)),
% 0.77/0.94 inference(modus_ponens,[status(thm)],[533, 532])).
% 0.77/0.94 tff(535,plain,
% 0.77/0.94 (hskp2 | c2_1(a237) | c1_1(a237)),
% 0.77/0.94 inference(unit_resolution,[status(thm)],[534, 110, 34, 164, 174])).
% 0.77/0.94 tff(536,plain,
% 0.77/0.94 (c1_1(a237)),
% 0.77/0.94 inference(unit_resolution,[status(thm)],[535, 527, 81])).
% 0.77/0.94 tff(537,plain,
% 0.77/0.94 (((~![U: $i] : (hskp26 | hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp26 | hskp9 | c2_1(a237) | c3_1(a237) | (~ndr1_0) | (~c1_1(a237)))) <=> ((~![U: $i] : (hskp26 | hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | hskp26 | hskp9 | c2_1(a237) | c3_1(a237) | (~ndr1_0) | (~c1_1(a237)))),
% 0.77/0.94 inference(rewrite,[status(thm)],[])).
% 0.77/0.94 tff(538,plain,
% 0.77/0.94 ((hskp26 | hskp9 | (~ndr1_0) | c2_1(a237) | c3_1(a237) | (~c1_1(a237))) <=> (hskp26 | hskp9 | c2_1(a237) | c3_1(a237) | (~ndr1_0) | (~c1_1(a237)))),
% 0.77/0.94 inference(rewrite,[status(thm)],[])).
% 0.77/0.94 tff(539,plain,
% 0.77/0.94 (((~![U: $i] : (hskp26 | hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp26 | hskp9 | (~ndr1_0) | c2_1(a237) | c3_1(a237) | (~c1_1(a237)))) <=> ((~![U: $i] : (hskp26 | hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp26 | hskp9 | c2_1(a237) | c3_1(a237) | (~ndr1_0) | (~c1_1(a237))))),
% 0.77/0.94 inference(monotonicity,[status(thm)],[538])).
% 0.77/0.94 tff(540,plain,
% 0.77/0.94 (((~![U: $i] : (hskp26 | hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp26 | hskp9 | (~ndr1_0) | c2_1(a237) | c3_1(a237) | (~c1_1(a237)))) <=> ((~![U: $i] : (hskp26 | hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | hskp26 | hskp9 | c2_1(a237) | c3_1(a237) | (~ndr1_0) | (~c1_1(a237)))),
% 0.77/0.94 inference(transitivity,[status(thm)],[539, 537])).
% 0.77/0.94 tff(541,plain,
% 0.77/0.94 ((~![U: $i] : (hskp26 | hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp26 | hskp9 | (~ndr1_0) | c2_1(a237) | c3_1(a237) | (~c1_1(a237)))),
% 0.77/0.94 inference(quant_inst,[status(thm)],[])).
% 0.77/0.94 tff(542,plain,
% 0.77/0.94 ((~![U: $i] : (hskp26 | hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | hskp26 | hskp9 | c2_1(a237) | c3_1(a237) | (~ndr1_0) | (~c1_1(a237))),
% 0.77/0.94 inference(modus_ponens,[status(thm)],[541, 540])).
% 0.77/0.94 tff(543,plain,
% 0.77/0.94 (hskp26 | c2_1(a237) | (~c1_1(a237))),
% 0.77/0.94 inference(unit_resolution,[status(thm)],[542, 110, 23, 164, 236])).
% 0.77/0.94 tff(544,plain,
% 0.77/0.94 ($false),
% 0.77/0.94 inference(unit_resolution,[status(thm)],[543, 536, 527, 528])).
% 0.77/0.94 tff(545,plain,(c2_1(a237) | hskp9 | c3_1(a237) | hskp2 | hskp27), inference(lemma,lemma(discharge,[]))).
% 0.77/0.94 tff(546,plain,
% 0.77/0.94 (hskp2),
% 0.77/0.94 inference(unit_resolution,[status(thm)],[545, 527, 164, 23, 34])).
% 0.77/0.94 tff(547,plain,
% 0.77/0.94 (~c1_1(a215)),
% 0.77/0.94 inference(unit_resolution,[status(thm)],[124, 546])).
% 0.77/0.94 tff(548,plain,
% 0.77/0.94 (~c0_1(a215)),
% 0.77/0.94 inference(unit_resolution,[status(thm)],[138, 546])).
% 0.77/0.94 tff(549,plain,
% 0.77/0.94 (c2_1(a215)),
% 0.77/0.94 inference(unit_resolution,[status(thm)],[132, 546])).
% 0.77/0.94 tff(550,plain,
% 0.77/0.94 (((~hskp12) | c2_1(a237)) <=> ((~hskp12) | c2_1(a237))),
% 0.77/0.94 inference(rewrite,[status(thm)],[])).
% 0.77/0.94 tff(551,axiom,((~hskp12) | c2_1(a237)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause70')).
% 0.77/0.94 tff(552,plain,
% 0.77/0.94 ((~hskp12) | c2_1(a237)),
% 0.77/0.94 inference(modus_ponens,[status(thm)],[551, 550])).
% 0.77/0.94 tff(553,plain,
% 0.77/0.94 ((~hskp12) | c2_1(a237)),
% 0.77/0.94 inference(modus_ponens,[status(thm)],[552, 550])).
% 0.77/0.94 tff(554,plain,
% 0.77/0.94 ((~hskp12) | c2_1(a237)),
% 0.77/0.94 inference(modus_ponens,[status(thm)],[553, 550])).
% 0.77/0.94 tff(555,plain,
% 0.77/0.94 ((~hskp12) | c2_1(a237)),
% 0.77/0.94 inference(modus_ponens,[status(thm)],[554, 550])).
% 0.77/0.94 tff(556,plain,
% 0.77/0.94 ((~hskp12) | c2_1(a237)),
% 0.77/0.94 inference(modus_ponens,[status(thm)],[555, 550])).
% 0.77/0.94 tff(557,plain,
% 0.77/0.94 (~hskp12),
% 0.77/0.94 inference(unit_resolution,[status(thm)],[556, 527])).
% 0.77/0.94 tff(558,plain,
% 0.77/0.94 (^[V: $i, U: $i] : refl((hskp5 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V))) <=> (hskp5 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V))))),
% 0.77/0.94 inference(bind,[status(th)],[])).
% 0.77/0.94 tff(559,plain,
% 0.77/0.94 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))),
% 0.77/0.94 inference(quant_intro,[status(thm)],[558])).
% 0.77/0.94 tff(560,plain,
% 0.77/0.94 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))),
% 0.77/0.94 inference(rewrite,[status(thm)],[])).
% 0.77/0.94 tff(561,plain,
% 0.77/0.94 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c2_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V))) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c2_1(V)) | c3_1(V)) | hskp5) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V))) | hskp5))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V))) | hskp5) <=> (hskp5 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c2_1(V)) | c3_1(V)) | hskp5) <=> (hskp5 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))))),
% 0.77/0.94 inference(bind,[status(th)],[])).
% 0.77/0.94 tff(562,plain,
% 0.77/0.94 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c2_1(V)) | c3_1(V)) | hskp5) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))),
% 0.77/0.94 inference(quant_intro,[status(thm)],[561])).
% 0.77/0.94 tff(563,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c2_1(V)) | c3_1(V)) | hskp5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause177')).
% 0.77/0.94 tff(564,plain,
% 0.77/0.94 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))),
% 0.77/0.94 inference(modus_ponens,[status(thm)],[563, 562])).
% 0.77/0.94 tff(565,plain,
% 0.77/0.94 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))),
% 0.77/0.94 inference(modus_ponens,[status(thm)],[564, 560])).
% 0.77/0.94 tff(566,plain,(
% 0.77/0.94 ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))),
% 0.77/0.94 inference(skolemize,[status(sab)],[565])).
% 0.77/0.94 tff(567,plain,
% 0.77/0.94 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))),
% 0.77/0.94 inference(modus_ponens,[status(thm)],[566, 559])).
% 0.77/0.94 tff(568,assumption,(~c0_1(a237)), introduced(assumption)).
% 0.77/0.94 tff(569,plain,
% 0.77/0.94 (((~hskp12) | c0_1(a237)) <=> ((~hskp12) | c0_1(a237))),
% 0.77/0.94 inference(rewrite,[status(thm)],[])).
% 0.77/0.94 tff(570,axiom,((~hskp12) | c0_1(a237)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause69')).
% 0.77/0.94 tff(571,plain,
% 0.77/0.94 ((~hskp12) | c0_1(a237)),
% 0.77/0.94 inference(modus_ponens,[status(thm)],[570, 569])).
% 0.77/0.94 tff(572,plain,
% 0.77/0.94 ((~hskp12) | c0_1(a237)),
% 0.77/0.94 inference(modus_ponens,[status(thm)],[571, 569])).
% 0.77/0.94 tff(573,plain,
% 0.77/0.94 ((~hskp12) | c0_1(a237)),
% 0.77/0.94 inference(modus_ponens,[status(thm)],[572, 569])).
% 0.77/0.94 tff(574,plain,
% 0.77/0.94 ((~hskp12) | c0_1(a237)),
% 0.77/0.94 inference(modus_ponens,[status(thm)],[573, 569])).
% 0.77/0.94 tff(575,plain,
% 0.77/0.94 ((~hskp12) | c0_1(a237)),
% 0.77/0.94 inference(modus_ponens,[status(thm)],[574, 569])).
% 0.77/0.94 tff(576,plain,
% 0.77/0.94 (~hskp12),
% 0.77/0.94 inference(unit_resolution,[status(thm)],[575, 568])).
% 0.77/0.94 tff(577,plain,
% 0.77/0.94 (c2_1(a237)),
% 0.77/0.94 inference(unit_resolution,[status(thm)],[545, 81, 164, 23, 34])).
% 0.77/0.94 tff(578,plain,
% 0.77/0.94 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp12 | c0_1(a237) | c3_1(a237) | (~ndr1_0) | (~c2_1(a237)) | (~c1_1(a237)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp12 | c0_1(a237) | c3_1(a237) | (~ndr1_0) | (~c2_1(a237)) | (~c1_1(a237)))),
% 0.77/0.94 inference(rewrite,[status(thm)],[])).
% 0.77/0.94 tff(579,plain,
% 0.77/0.94 ((hskp12 | (~ndr1_0) | c3_1(a237) | (~c2_1(a237)) | (~c1_1(a237)) | c3_1(a237) | c0_1(a237) | (~c1_1(a237))) <=> (hskp12 | c0_1(a237) | c3_1(a237) | (~ndr1_0) | (~c2_1(a237)) | (~c1_1(a237)))),
% 0.77/0.94 inference(rewrite,[status(thm)],[])).
% 0.77/0.94 tff(580,plain,
% 0.77/0.94 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp12 | (~ndr1_0) | c3_1(a237) | (~c2_1(a237)) | (~c1_1(a237)) | c3_1(a237) | c0_1(a237) | (~c1_1(a237)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp12 | c0_1(a237) | c3_1(a237) | (~ndr1_0) | (~c2_1(a237)) | (~c1_1(a237))))),
% 0.77/0.94 inference(monotonicity,[status(thm)],[579])).
% 0.77/0.94 tff(581,plain,
% 0.77/0.94 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp12 | (~ndr1_0) | c3_1(a237) | (~c2_1(a237)) | (~c1_1(a237)) | c3_1(a237) | c0_1(a237) | (~c1_1(a237)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp12 | c0_1(a237) | c3_1(a237) | (~ndr1_0) | (~c2_1(a237)) | (~c1_1(a237)))),
% 0.77/0.94 inference(transitivity,[status(thm)],[580, 578])).
% 0.77/0.94 tff(582,plain,
% 0.77/0.94 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp12 | (~ndr1_0) | c3_1(a237) | (~c2_1(a237)) | (~c1_1(a237)) | c3_1(a237) | c0_1(a237) | (~c1_1(a237)))),
% 0.77/0.94 inference(quant_inst,[status(thm)],[])).
% 0.77/0.94 tff(583,plain,
% 0.77/0.94 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp12 | c0_1(a237) | c3_1(a237) | (~ndr1_0) | (~c2_1(a237)) | (~c1_1(a237))),
% 0.77/0.94 inference(modus_ponens,[status(thm)],[582, 581])).
% 0.77/0.94 tff(584,plain,
% 0.77/0.94 (hskp12 | c0_1(a237) | (~c2_1(a237)) | (~c1_1(a237))),
% 0.77/0.94 inference(unit_resolution,[status(thm)],[583, 110, 164, 44])).
% 0.77/0.94 tff(585,plain,
% 0.77/0.94 (~c1_1(a237)),
% 0.77/0.94 inference(unit_resolution,[status(thm)],[584, 577, 568, 576])).
% 0.77/0.94 tff(586,plain,
% 0.77/0.94 (^[V: $i, U: $i] : refl((hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)) <=> (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)))),
% 0.77/0.94 inference(bind,[status(th)],[])).
% 0.77/0.94 tff(587,plain,
% 0.77/0.94 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 0.77/0.94 inference(quant_intro,[status(thm)],[586])).
% 0.77/0.94 tff(588,plain,
% 0.77/0.94 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 0.77/0.94 inference(rewrite,[status(thm)],[])).
% 0.77/0.94 tff(589,plain,
% 0.77/0.94 (^[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)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | 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)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) | 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)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | 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)) | (~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)) | (~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)) | (~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)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp2) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)) | hskp2))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)) | hskp2) <=> (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp2) <=> (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))))),
% 0.77/0.94 inference(bind,[status(th)],[])).
% 0.77/0.94 tff(590,plain,
% 0.77/0.94 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp2) <=> ![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 0.77/0.94 inference(quant_intro,[status(thm)],[589])).
% 0.77/0.94 tff(591,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause163')).
% 0.77/0.94 tff(592,plain,
% 0.77/0.94 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 0.77/0.94 inference(modus_ponens,[status(thm)],[591, 590])).
% 0.77/0.94 tff(593,plain,
% 0.77/0.94 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 0.77/0.94 inference(modus_ponens,[status(thm)],[592, 588])).
% 0.77/0.94 tff(594,plain,(
% 0.77/0.94 ![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 0.77/0.94 inference(skolemize,[status(sab)],[593])).
% 0.77/0.94 tff(595,plain,
% 0.77/0.94 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 0.77/0.94 inference(modus_ponens,[status(thm)],[594, 587])).
% 0.77/0.94 tff(596,assumption,(~hskp18), introduced(assumption)).
% 0.77/0.94 tff(597,assumption,(hskp10), introduced(assumption)).
% 0.77/0.94 tff(598,plain,
% 0.77/0.94 (((~hskp10) | c1_1(a231)) <=> ((~hskp10) | c1_1(a231))),
% 0.77/0.94 inference(rewrite,[status(thm)],[])).
% 0.77/0.94 tff(599,axiom,((~hskp10) | c1_1(a231)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause72')).
% 0.77/0.94 tff(600,plain,
% 0.77/0.94 ((~hskp10) | c1_1(a231)),
% 0.77/0.94 inference(modus_ponens,[status(thm)],[599, 598])).
% 0.77/0.94 tff(601,plain,
% 0.77/0.94 ((~hskp10) | c1_1(a231)),
% 0.77/0.94 inference(modus_ponens,[status(thm)],[600, 598])).
% 0.77/0.94 tff(602,plain,
% 0.77/0.94 ((~hskp10) | c1_1(a231)),
% 0.77/0.94 inference(modus_ponens,[status(thm)],[601, 598])).
% 0.77/0.94 tff(603,plain,
% 0.77/0.94 ((~hskp10) | c1_1(a231)),
% 0.77/0.94 inference(modus_ponens,[status(thm)],[602, 598])).
% 0.77/0.94 tff(604,plain,
% 0.77/0.94 ((~hskp10) | c1_1(a231)),
% 0.77/0.94 inference(modus_ponens,[status(thm)],[603, 598])).
% 0.77/0.94 tff(605,plain,
% 0.77/0.94 (c1_1(a231)),
% 0.77/0.94 inference(unit_resolution,[status(thm)],[604, 597])).
% 0.77/0.94 tff(606,plain,
% 0.77/0.94 (^[V: $i, U: $i] : refl((hskp18 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V))) <=> (hskp18 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V))))),
% 0.77/0.94 inference(bind,[status(th)],[])).
% 0.77/0.94 tff(607,plain,
% 0.77/0.94 (![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))),
% 0.77/0.94 inference(quant_intro,[status(thm)],[606])).
% 0.77/0.94 tff(608,plain,
% 0.77/0.94 (![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))),
% 0.77/0.94 inference(rewrite,[status(thm)],[])).
% 0.77/0.94 tff(609,plain,
% 0.77/0.94 (^[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)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V))))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(V)))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(V))))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(V)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(V))))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V))))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) | hskp18) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V))) | hskp18))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V))) | hskp18) <=> (hskp18 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) | hskp18) <=> (hskp18 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))))),
% 0.77/0.94 inference(bind,[status(th)],[])).
% 0.77/0.94 tff(610,plain,
% 0.77/0.94 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) | hskp18) <=> ![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))),
% 0.77/0.94 inference(quant_intro,[status(thm)],[609])).
% 0.77/0.94 tff(611,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) | hskp18)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause182')).
% 0.77/0.94 tff(612,plain,
% 0.77/0.94 (![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))),
% 0.77/0.94 inference(modus_ponens,[status(thm)],[611, 610])).
% 0.77/0.94 tff(613,plain,
% 0.77/0.94 (![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))),
% 0.77/0.94 inference(modus_ponens,[status(thm)],[612, 608])).
% 0.77/0.94 tff(614,plain,(
% 0.77/0.94 ![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))),
% 0.77/0.94 inference(skolemize,[status(sab)],[613])).
% 0.77/0.94 tff(615,plain,
% 0.77/0.94 (![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))),
% 0.77/0.94 inference(modus_ponens,[status(thm)],[614, 607])).
% 0.77/0.94 tff(616,plain,
% 0.77/0.94 (hskp17),
% 0.77/0.94 inference(unit_resolution,[status(thm)],[108, 34, 596])).
% 0.77/0.94 tff(617,plain,
% 0.77/0.94 (((~hskp17) | c1_1(a248)) <=> ((~hskp17) | c1_1(a248))),
% 0.77/0.94 inference(rewrite,[status(thm)],[])).
% 0.77/0.94 tff(618,axiom,((~hskp17) | c1_1(a248)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause62')).
% 0.77/0.94 tff(619,plain,
% 0.77/0.94 ((~hskp17) | c1_1(a248)),
% 0.77/0.94 inference(modus_ponens,[status(thm)],[618, 617])).
% 0.77/0.94 tff(620,plain,
% 0.77/0.94 ((~hskp17) | c1_1(a248)),
% 0.77/0.94 inference(modus_ponens,[status(thm)],[619, 617])).
% 0.77/0.94 tff(621,plain,
% 0.77/0.94 ((~hskp17) | c1_1(a248)),
% 0.77/0.94 inference(modus_ponens,[status(thm)],[620, 617])).
% 0.77/0.94 tff(622,plain,
% 0.77/0.94 ((~hskp17) | c1_1(a248)),
% 0.77/0.94 inference(modus_ponens,[status(thm)],[621, 617])).
% 0.77/0.94 tff(623,plain,
% 0.77/0.94 ((~hskp17) | c1_1(a248)),
% 0.77/0.94 inference(modus_ponens,[status(thm)],[622, 617])).
% 0.77/0.94 tff(624,plain,
% 0.77/0.94 (c1_1(a248)),
% 0.77/0.94 inference(unit_resolution,[status(thm)],[623, 616])).
% 0.77/0.94 tff(625,plain,
% 0.77/0.94 (((~hskp17) | (~c2_1(a248))) <=> ((~hskp17) | (~c2_1(a248)))),
% 0.77/0.94 inference(rewrite,[status(thm)],[])).
% 0.77/0.94 tff(626,plain,
% 0.77/0.94 (((~c2_1(a248)) | (~hskp17)) <=> ((~hskp17) | (~c2_1(a248)))),
% 0.77/0.94 inference(rewrite,[status(thm)],[])).
% 0.77/0.94 tff(627,axiom,((~c2_1(a248)) | (~hskp17)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause100')).
% 0.77/0.94 tff(628,plain,
% 0.77/0.94 ((~hskp17) | (~c2_1(a248))),
% 0.77/0.94 inference(modus_ponens,[status(thm)],[627, 626])).
% 0.77/0.94 tff(629,plain,
% 0.77/0.94 ((~hskp17) | (~c2_1(a248))),
% 0.77/0.94 inference(modus_ponens,[status(thm)],[628, 625])).
% 0.77/0.95 tff(630,plain,
% 0.77/0.95 (~c2_1(a248)),
% 0.77/0.95 inference(unit_resolution,[status(thm)],[629, 616])).
% 0.77/0.95 tff(631,plain,
% 0.77/0.95 (((~hskp17) | c3_1(a248)) <=> ((~hskp17) | c3_1(a248))),
% 0.77/0.95 inference(rewrite,[status(thm)],[])).
% 0.77/0.95 tff(632,axiom,((~hskp17) | c3_1(a248)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause63')).
% 0.77/0.95 tff(633,plain,
% 0.77/0.95 ((~hskp17) | c3_1(a248)),
% 0.77/0.95 inference(modus_ponens,[status(thm)],[632, 631])).
% 0.77/0.95 tff(634,plain,
% 0.77/0.95 ((~hskp17) | c3_1(a248)),
% 0.77/0.95 inference(modus_ponens,[status(thm)],[633, 631])).
% 0.77/0.95 tff(635,plain,
% 0.77/0.95 ((~hskp17) | c3_1(a248)),
% 0.77/0.95 inference(modus_ponens,[status(thm)],[634, 631])).
% 0.77/0.95 tff(636,plain,
% 0.77/0.95 ((~hskp17) | c3_1(a248)),
% 0.77/0.95 inference(modus_ponens,[status(thm)],[635, 631])).
% 0.77/0.95 tff(637,plain,
% 0.77/0.95 ((~hskp17) | c3_1(a248)),
% 0.77/0.95 inference(modus_ponens,[status(thm)],[636, 631])).
% 0.77/0.95 tff(638,plain,
% 0.77/0.95 (c3_1(a248)),
% 0.77/0.95 inference(unit_resolution,[status(thm)],[637, 616])).
% 0.77/0.95 tff(639,assumption,(~c0_1(a248)), introduced(assumption)).
% 0.77/0.95 tff(640,assumption,(~c2_1(a248)), introduced(assumption)).
% 0.77/0.95 tff(641,assumption,(c3_1(a248)), introduced(assumption)).
% 0.77/0.95 tff(642,assumption,(c1_1(a248)), introduced(assumption)).
% 0.77/0.95 tff(643,plain,
% 0.77/0.95 (((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp18 | c2_1(a248) | (~ndr1_0) | (~c3_1(a248)) | c0_1(a248) | (~c1_1(a248)))) <=> ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp18 | c2_1(a248) | (~ndr1_0) | (~c3_1(a248)) | c0_1(a248) | (~c1_1(a248)))),
% 0.77/0.95 inference(rewrite,[status(thm)],[])).
% 0.77/0.95 tff(644,plain,
% 0.77/0.95 ((hskp18 | (~ndr1_0) | c2_1(a248) | (~c3_1(a248)) | (~c1_1(a248)) | c0_1(a248) | (~c1_1(a248)) | (~c3_1(a248))) <=> (hskp18 | c2_1(a248) | (~ndr1_0) | (~c3_1(a248)) | c0_1(a248) | (~c1_1(a248)))),
% 0.77/0.95 inference(rewrite,[status(thm)],[])).
% 0.77/0.95 tff(645,plain,
% 0.77/0.95 (((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp18 | (~ndr1_0) | c2_1(a248) | (~c3_1(a248)) | (~c1_1(a248)) | c0_1(a248) | (~c1_1(a248)) | (~c3_1(a248)))) <=> ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp18 | c2_1(a248) | (~ndr1_0) | (~c3_1(a248)) | c0_1(a248) | (~c1_1(a248))))),
% 0.77/0.95 inference(monotonicity,[status(thm)],[644])).
% 0.77/0.95 tff(646,plain,
% 0.77/0.95 (((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp18 | (~ndr1_0) | c2_1(a248) | (~c3_1(a248)) | (~c1_1(a248)) | c0_1(a248) | (~c1_1(a248)) | (~c3_1(a248)))) <=> ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp18 | c2_1(a248) | (~ndr1_0) | (~c3_1(a248)) | c0_1(a248) | (~c1_1(a248)))),
% 0.77/0.95 inference(transitivity,[status(thm)],[645, 643])).
% 0.77/0.95 tff(647,plain,
% 0.77/0.95 ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp18 | (~ndr1_0) | c2_1(a248) | (~c3_1(a248)) | (~c1_1(a248)) | c0_1(a248) | (~c1_1(a248)) | (~c3_1(a248)))),
% 0.77/0.95 inference(quant_inst,[status(thm)],[])).
% 0.77/0.95 tff(648,plain,
% 0.77/0.95 ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp18 | c2_1(a248) | (~ndr1_0) | (~c3_1(a248)) | c0_1(a248) | (~c1_1(a248))),
% 0.77/0.95 inference(modus_ponens,[status(thm)],[647, 646])).
% 0.77/0.95 tff(649,plain,
% 0.77/0.95 ($false),
% 0.77/0.95 inference(unit_resolution,[status(thm)],[648, 110, 596, 642, 641, 640, 615, 639])).
% 0.77/0.95 tff(650,plain,(c0_1(a248) | hskp18 | (~c1_1(a248)) | (~c3_1(a248)) | c2_1(a248)), inference(lemma,lemma(discharge,[]))).
% 0.77/0.95 tff(651,plain,
% 0.77/0.95 (c0_1(a248)),
% 0.77/0.95 inference(unit_resolution,[status(thm)],[650, 624, 596, 638, 630])).
% 0.77/0.95 tff(652,plain,
% 0.77/0.95 (((~![U: $i] : (hskp27 | hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp27 | hskp2 | (~ndr1_0) | (~c3_1(a248)) | (~c0_1(a248)) | (~c1_1(a248)))) <=> ((~![U: $i] : (hskp27 | hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp27 | hskp2 | (~ndr1_0) | (~c3_1(a248)) | (~c0_1(a248)) | (~c1_1(a248)))),
% 0.77/0.95 inference(rewrite,[status(thm)],[])).
% 0.77/0.95 tff(653,plain,
% 0.77/0.95 ((hskp27 | hskp2 | (~ndr1_0) | (~c3_1(a248)) | (~c1_1(a248)) | (~c0_1(a248))) <=> (hskp27 | hskp2 | (~ndr1_0) | (~c3_1(a248)) | (~c0_1(a248)) | (~c1_1(a248)))),
% 0.77/0.95 inference(rewrite,[status(thm)],[])).
% 0.77/0.95 tff(654,plain,
% 0.77/0.95 (((~![U: $i] : (hskp27 | hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp27 | hskp2 | (~ndr1_0) | (~c3_1(a248)) | (~c1_1(a248)) | (~c0_1(a248)))) <=> ((~![U: $i] : (hskp27 | hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp27 | hskp2 | (~ndr1_0) | (~c3_1(a248)) | (~c0_1(a248)) | (~c1_1(a248))))),
% 0.77/0.95 inference(monotonicity,[status(thm)],[653])).
% 0.77/0.95 tff(655,plain,
% 0.77/0.95 (((~![U: $i] : (hskp27 | hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp27 | hskp2 | (~ndr1_0) | (~c3_1(a248)) | (~c1_1(a248)) | (~c0_1(a248)))) <=> ((~![U: $i] : (hskp27 | hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp27 | hskp2 | (~ndr1_0) | (~c3_1(a248)) | (~c0_1(a248)) | (~c1_1(a248)))),
% 0.77/0.95 inference(transitivity,[status(thm)],[654, 652])).
% 0.77/0.95 tff(656,plain,
% 0.77/0.95 ((~![U: $i] : (hskp27 | hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp27 | hskp2 | (~ndr1_0) | (~c3_1(a248)) | (~c1_1(a248)) | (~c0_1(a248)))),
% 0.77/0.95 inference(quant_inst,[status(thm)],[])).
% 0.77/0.95 tff(657,plain,
% 0.77/0.95 ((~![U: $i] : (hskp27 | hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp27 | hskp2 | (~ndr1_0) | (~c3_1(a248)) | (~c0_1(a248)) | (~c1_1(a248))),
% 0.77/0.95 inference(modus_ponens,[status(thm)],[656, 655])).
% 0.77/0.95 tff(658,plain,
% 0.77/0.95 (hskp2 | (~c0_1(a248))),
% 0.77/0.95 inference(unit_resolution,[status(thm)],[657, 110, 34, 624, 638, 56])).
% 0.77/0.95 tff(659,plain,
% 0.77/0.95 (hskp2),
% 0.77/0.95 inference(unit_resolution,[status(thm)],[658, 651])).
% 0.77/0.95 tff(660,plain,
% 0.77/0.95 (~c1_1(a215)),
% 0.77/0.95 inference(unit_resolution,[status(thm)],[124, 659])).
% 0.77/0.95 tff(661,plain,
% 0.77/0.95 (~c0_1(a215)),
% 0.77/0.95 inference(unit_resolution,[status(thm)],[138, 659])).
% 0.77/0.95 tff(662,plain,
% 0.77/0.95 (c2_1(a215)),
% 0.77/0.95 inference(unit_resolution,[status(thm)],[132, 659])).
% 0.77/0.95 tff(663,plain,
% 0.77/0.95 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp5 | c0_1(a215) | c1_1(a215) | (~ndr1_0) | (~c2_1(a215)) | (~c3_1(a248)) | (~c0_1(a248)) | (~c1_1(a248)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp5 | c0_1(a215) | c1_1(a215) | (~ndr1_0) | (~c2_1(a215)) | (~c3_1(a248)) | (~c0_1(a248)) | (~c1_1(a248)))),
% 0.77/0.95 inference(rewrite,[status(thm)],[])).
% 0.77/0.95 tff(664,plain,
% 0.77/0.95 ((hskp5 | (~ndr1_0) | (~c3_1(a248)) | (~c1_1(a248)) | (~c0_1(a248)) | c1_1(a215) | c0_1(a215) | (~c2_1(a215))) <=> (hskp5 | c0_1(a215) | c1_1(a215) | (~ndr1_0) | (~c2_1(a215)) | (~c3_1(a248)) | (~c0_1(a248)) | (~c1_1(a248)))),
% 0.77/0.95 inference(rewrite,[status(thm)],[])).
% 0.77/0.95 tff(665,plain,
% 0.77/0.95 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp5 | (~ndr1_0) | (~c3_1(a248)) | (~c1_1(a248)) | (~c0_1(a248)) | c1_1(a215) | c0_1(a215) | (~c2_1(a215)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp5 | c0_1(a215) | c1_1(a215) | (~ndr1_0) | (~c2_1(a215)) | (~c3_1(a248)) | (~c0_1(a248)) | (~c1_1(a248))))),
% 0.77/0.95 inference(monotonicity,[status(thm)],[664])).
% 0.77/0.95 tff(666,plain,
% 0.77/0.95 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp5 | (~ndr1_0) | (~c3_1(a248)) | (~c1_1(a248)) | (~c0_1(a248)) | c1_1(a215) | c0_1(a215) | (~c2_1(a215)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp5 | c0_1(a215) | c1_1(a215) | (~ndr1_0) | (~c2_1(a215)) | (~c3_1(a248)) | (~c0_1(a248)) | (~c1_1(a248)))),
% 0.77/0.95 inference(transitivity,[status(thm)],[665, 663])).
% 0.77/0.95 tff(667,plain,
% 0.77/0.95 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp5 | (~ndr1_0) | (~c3_1(a248)) | (~c1_1(a248)) | (~c0_1(a248)) | c1_1(a215) | c0_1(a215) | (~c2_1(a215)))),
% 0.77/0.95 inference(quant_inst,[status(thm)],[])).
% 0.77/0.95 tff(668,plain,
% 0.77/0.95 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp5 | c0_1(a215) | c1_1(a215) | (~ndr1_0) | (~c2_1(a215)) | (~c3_1(a248)) | (~c0_1(a248)) | (~c1_1(a248))),
% 0.77/0.95 inference(modus_ponens,[status(thm)],[667, 666])).
% 0.77/0.95 tff(669,plain,
% 0.77/0.95 (hskp5),
% 0.77/0.95 inference(unit_resolution,[status(thm)],[668, 110, 624, 638, 662, 661, 660, 149, 651])).
% 0.77/0.95 tff(670,plain,
% 0.77/0.95 (((~hskp5) | (~c2_1(a218))) <=> ((~hskp5) | (~c2_1(a218)))),
% 0.77/0.95 inference(rewrite,[status(thm)],[])).
% 0.77/0.95 tff(671,plain,
% 0.77/0.95 (((~c2_1(a218)) | (~hskp5)) <=> ((~hskp5) | (~c2_1(a218)))),
% 0.77/0.95 inference(rewrite,[status(thm)],[])).
% 0.77/0.95 tff(672,axiom,((~c2_1(a218)) | (~hskp5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause119')).
% 0.77/0.95 tff(673,plain,
% 0.77/0.95 ((~hskp5) | (~c2_1(a218))),
% 0.77/0.95 inference(modus_ponens,[status(thm)],[672, 671])).
% 0.77/0.95 tff(674,plain,
% 0.77/0.95 ((~hskp5) | (~c2_1(a218))),
% 0.77/0.95 inference(modus_ponens,[status(thm)],[673, 670])).
% 0.77/0.95 tff(675,plain,
% 0.77/0.95 (~c2_1(a218)),
% 0.77/0.95 inference(unit_resolution,[status(thm)],[674, 669])).
% 0.77/0.95 tff(676,plain,
% 0.77/0.95 (((~hskp5) | (~c1_1(a218))) <=> ((~hskp5) | (~c1_1(a218)))),
% 0.77/0.95 inference(rewrite,[status(thm)],[])).
% 0.77/0.95 tff(677,plain,
% 0.77/0.95 (((~c1_1(a218)) | (~hskp5)) <=> ((~hskp5) | (~c1_1(a218)))),
% 0.77/0.95 inference(rewrite,[status(thm)],[])).
% 0.77/0.95 tff(678,axiom,((~c1_1(a218)) | (~hskp5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause118')).
% 0.77/0.95 tff(679,plain,
% 0.77/0.95 ((~hskp5) | (~c1_1(a218))),
% 0.77/0.95 inference(modus_ponens,[status(thm)],[678, 677])).
% 0.77/0.95 tff(680,plain,
% 0.77/0.95 ((~hskp5) | (~c1_1(a218))),
% 0.77/0.95 inference(modus_ponens,[status(thm)],[679, 676])).
% 0.77/0.95 tff(681,plain,
% 0.77/0.95 (~c1_1(a218)),
% 0.77/0.95 inference(unit_resolution,[status(thm)],[680, 669])).
% 0.77/0.95 tff(682,plain,
% 0.77/0.95 (((~hskp5) | c3_1(a218)) <=> ((~hskp5) | c3_1(a218))),
% 0.77/0.95 inference(rewrite,[status(thm)],[])).
% 0.77/0.95 tff(683,axiom,((~hskp5) | c3_1(a218)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause80')).
% 0.77/0.95 tff(684,plain,
% 0.77/0.95 ((~hskp5) | c3_1(a218)),
% 0.77/0.95 inference(modus_ponens,[status(thm)],[683, 682])).
% 0.77/0.95 tff(685,plain,
% 0.77/0.95 ((~hskp5) | c3_1(a218)),
% 0.77/0.95 inference(modus_ponens,[status(thm)],[684, 682])).
% 0.77/0.95 tff(686,plain,
% 0.77/0.95 ((~hskp5) | c3_1(a218)),
% 0.77/0.95 inference(modus_ponens,[status(thm)],[685, 682])).
% 0.77/0.95 tff(687,plain,
% 0.77/0.95 ((~hskp5) | c3_1(a218)),
% 0.77/0.95 inference(modus_ponens,[status(thm)],[686, 682])).
% 0.77/0.95 tff(688,plain,
% 0.77/0.95 ((~hskp5) | c3_1(a218)),
% 0.77/0.95 inference(modus_ponens,[status(thm)],[687, 682])).
% 0.77/0.95 tff(689,plain,
% 0.77/0.95 (c3_1(a218)),
% 0.77/0.95 inference(unit_resolution,[status(thm)],[688, 669])).
% 0.77/0.95 tff(690,assumption,(c0_1(a248)), introduced(assumption)).
% 0.77/0.95 tff(691,assumption,(hskp12), introduced(assumption)).
% 0.77/0.95 tff(692,plain,
% 0.77/0.95 (((~hskp12) | (~c3_1(a237))) <=> ((~hskp12) | (~c3_1(a237)))),
% 0.77/0.95 inference(rewrite,[status(thm)],[])).
% 0.77/0.95 tff(693,plain,
% 0.77/0.95 (((~c3_1(a237)) | (~hskp12)) <=> ((~hskp12) | (~c3_1(a237)))),
% 0.77/0.95 inference(rewrite,[status(thm)],[])).
% 0.77/0.95 tff(694,axiom,((~c3_1(a237)) | (~hskp12)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause108')).
% 0.77/0.95 tff(695,plain,
% 0.77/0.95 ((~hskp12) | (~c3_1(a237))),
% 0.77/0.95 inference(modus_ponens,[status(thm)],[694, 693])).
% 0.77/0.95 tff(696,plain,
% 0.77/0.95 ((~hskp12) | (~c3_1(a237))),
% 0.77/0.95 inference(modus_ponens,[status(thm)],[695, 692])).
% 0.77/0.95 tff(697,plain,
% 0.77/0.95 (~c3_1(a237)),
% 0.77/0.95 inference(unit_resolution,[status(thm)],[696, 691])).
% 0.77/0.95 tff(698,plain,
% 0.77/0.95 (c2_1(a237)),
% 0.77/0.95 inference(unit_resolution,[status(thm)],[556, 691])).
% 0.77/0.95 tff(699,plain,
% 0.77/0.95 (c0_1(a237)),
% 0.77/0.95 inference(unit_resolution,[status(thm)],[575, 691])).
% 0.77/0.95 tff(700,plain,
% 0.77/0.95 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | (c2_1(a248) | c3_1(a237) | (~ndr1_0) | c1_1(a237) | (~c2_1(a237)) | (~c0_1(a237)) | (~c3_1(a248)) | (~c0_1(a248)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | c2_1(a248) | c3_1(a237) | (~ndr1_0) | c1_1(a237) | (~c2_1(a237)) | (~c0_1(a237)) | (~c3_1(a248)) | (~c0_1(a248)))),
% 0.77/0.95 inference(rewrite,[status(thm)],[])).
% 0.77/0.95 tff(701,plain,
% 0.77/0.95 (((~ndr1_0) | c2_1(a248) | (~c3_1(a248)) | (~c0_1(a248)) | c3_1(a237) | c1_1(a237) | (~c2_1(a237)) | c3_1(a237) | c1_1(a237) | (~c0_1(a237))) <=> (c2_1(a248) | c3_1(a237) | (~ndr1_0) | c1_1(a237) | (~c2_1(a237)) | (~c0_1(a237)) | (~c3_1(a248)) | (~c0_1(a248)))),
% 0.77/0.95 inference(rewrite,[status(thm)],[])).
% 0.77/0.95 tff(702,plain,
% 0.77/0.95 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a248) | (~c3_1(a248)) | (~c0_1(a248)) | c3_1(a237) | c1_1(a237) | (~c2_1(a237)) | c3_1(a237) | c1_1(a237) | (~c0_1(a237)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | (c2_1(a248) | c3_1(a237) | (~ndr1_0) | c1_1(a237) | (~c2_1(a237)) | (~c0_1(a237)) | (~c3_1(a248)) | (~c0_1(a248))))),
% 0.77/0.95 inference(monotonicity,[status(thm)],[701])).
% 0.77/0.95 tff(703,plain,
% 0.77/0.95 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a248) | (~c3_1(a248)) | (~c0_1(a248)) | c3_1(a237) | c1_1(a237) | (~c2_1(a237)) | c3_1(a237) | c1_1(a237) | (~c0_1(a237)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | c2_1(a248) | c3_1(a237) | (~ndr1_0) | c1_1(a237) | (~c2_1(a237)) | (~c0_1(a237)) | (~c3_1(a248)) | (~c0_1(a248)))),
% 0.77/0.95 inference(transitivity,[status(thm)],[702, 700])).
% 0.77/0.95 tff(704,plain,
% 0.77/0.95 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a248) | (~c3_1(a248)) | (~c0_1(a248)) | c3_1(a237) | c1_1(a237) | (~c2_1(a237)) | c3_1(a237) | c1_1(a237) | (~c0_1(a237)))),
% 0.77/0.95 inference(quant_inst,[status(thm)],[])).
% 0.77/0.95 tff(705,plain,
% 0.77/0.95 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | c2_1(a248) | c3_1(a237) | (~ndr1_0) | c1_1(a237) | (~c2_1(a237)) | (~c0_1(a237)) | (~c3_1(a248)) | (~c0_1(a248))),
% 0.77/0.95 inference(modus_ponens,[status(thm)],[704, 703])).
% 0.77/0.95 tff(706,plain,
% 0.77/0.95 (c1_1(a237)),
% 0.77/0.95 inference(unit_resolution,[status(thm)],[705, 110, 641, 699, 698, 640, 697, 22, 690])).
% 0.77/0.95 tff(707,plain,
% 0.77/0.95 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W))) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W))))),
% 0.77/0.95 inference(bind,[status(th)],[])).
% 0.77/0.95 tff(708,plain,
% 0.77/0.95 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))),
% 0.77/0.95 inference(quant_intro,[status(thm)],[707])).
% 0.77/0.95 tff(709,plain,
% 0.77/0.95 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))),
% 0.77/0.95 inference(rewrite,[status(thm)],[])).
% 0.77/0.95 tff(710,plain,
% 0.77/0.95 (^[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) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(W))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V))) | (~c2_1(W))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(W)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(W))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(W))) | c3_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(W))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(W))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(W)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(W))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(W))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(W))) | c3_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(W))) | c1_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(W))) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(W)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(W))) | c3_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(W))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(W))) | c3_1(U)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(W))) | c2_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(W))) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | (~c2_1(W)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(W))) | c3_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | (~c2_1(W))))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(W))) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | (~c2_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | (~c2_1(W))) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(W))) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W))))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(W))) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c0_1(W)) | c1_1(W)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W))) | c1_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W))) | c1_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(W))) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))))),
% 0.77/0.95 inference(bind,[status(th)],[])).
% 0.77/0.95 tff(711,plain,
% 0.77/0.95 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(W))) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c0_1(W)) | c1_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))),
% 0.77/0.95 inference(quant_intro,[status(thm)],[710])).
% 0.77/0.95 tff(712,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(W))) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c0_1(W)) | c1_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause189')).
% 0.77/0.95 tff(713,plain,
% 0.77/0.95 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))),
% 0.77/0.95 inference(modus_ponens,[status(thm)],[712, 711])).
% 0.77/0.95 tff(714,plain,
% 0.77/0.95 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))),
% 0.77/0.95 inference(modus_ponens,[status(thm)],[713, 709])).
% 0.77/0.95 tff(715,plain,(
% 0.77/0.95 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))),
% 0.77/0.95 inference(skolemize,[status(sab)],[714])).
% 0.77/0.95 tff(716,plain,
% 0.77/0.95 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))),
% 0.77/0.95 inference(modus_ponens,[status(thm)],[715, 708])).
% 0.77/0.95 tff(717,assumption,(~c2_1(a218)), introduced(assumption)).
% 0.77/0.95 tff(718,assumption,(~c1_1(a218)), introduced(assumption)).
% 0.77/0.95 tff(719,assumption,(c3_1(a218)), introduced(assumption)).
% 0.77/0.95 tff(720,plain,
% 0.77/0.95 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | (c3_1(a237) | c1_1(a218) | c2_1(a218) | c0_1(a215) | c1_1(a215) | (~ndr1_0) | (~c2_1(a215)) | (~c3_1(a218)) | (~c0_1(a237)) | (~c1_1(a237)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | c3_1(a237) | c1_1(a218) | c2_1(a218) | c0_1(a215) | c1_1(a215) | (~ndr1_0) | (~c2_1(a215)) | (~c3_1(a218)) | (~c0_1(a237)) | (~c1_1(a237)))),
% 0.77/0.95 inference(rewrite,[status(thm)],[])).
% 0.77/0.95 tff(721,plain,
% 0.77/0.95 (((~ndr1_0) | c3_1(a237) | (~c1_1(a237)) | (~c0_1(a237)) | c1_1(a218) | c2_1(a218) | (~c3_1(a218)) | c0_1(a215) | c1_1(a215) | (~c2_1(a215))) <=> (c3_1(a237) | c1_1(a218) | c2_1(a218) | c0_1(a215) | c1_1(a215) | (~ndr1_0) | (~c2_1(a215)) | (~c3_1(a218)) | (~c0_1(a237)) | (~c1_1(a237)))),
% 0.77/0.95 inference(rewrite,[status(thm)],[])).
% 0.77/0.95 tff(722,plain,
% 0.77/0.95 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a237) | (~c1_1(a237)) | (~c0_1(a237)) | c1_1(a218) | c2_1(a218) | (~c3_1(a218)) | c0_1(a215) | c1_1(a215) | (~c2_1(a215)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | (c3_1(a237) | c1_1(a218) | c2_1(a218) | c0_1(a215) | c1_1(a215) | (~ndr1_0) | (~c2_1(a215)) | (~c3_1(a218)) | (~c0_1(a237)) | (~c1_1(a237))))),
% 0.77/0.95 inference(monotonicity,[status(thm)],[721])).
% 0.77/0.95 tff(723,plain,
% 0.77/0.95 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a237) | (~c1_1(a237)) | (~c0_1(a237)) | c1_1(a218) | c2_1(a218) | (~c3_1(a218)) | c0_1(a215) | c1_1(a215) | (~c2_1(a215)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | c3_1(a237) | c1_1(a218) | c2_1(a218) | c0_1(a215) | c1_1(a215) | (~ndr1_0) | (~c2_1(a215)) | (~c3_1(a218)) | (~c0_1(a237)) | (~c1_1(a237)))),
% 0.77/0.95 inference(transitivity,[status(thm)],[722, 720])).
% 0.77/0.95 tff(724,plain,
% 0.77/0.95 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a237) | (~c1_1(a237)) | (~c0_1(a237)) | c1_1(a218) | c2_1(a218) | (~c3_1(a218)) | c0_1(a215) | c1_1(a215) | (~c2_1(a215)))),
% 0.77/0.95 inference(quant_inst,[status(thm)],[])).
% 0.77/0.95 tff(725,plain,
% 0.77/0.95 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | c3_1(a237) | c1_1(a218) | c2_1(a218) | c0_1(a215) | c1_1(a215) | (~ndr1_0) | (~c2_1(a215)) | (~c3_1(a218)) | (~c0_1(a237)) | (~c1_1(a237))),
% 0.77/0.95 inference(modus_ponens,[status(thm)],[724, 723])).
% 0.77/0.95 tff(726,plain,
% 0.77/0.95 ($false),
% 0.77/0.95 inference(unit_resolution,[status(thm)],[725, 110, 699, 719, 152, 697, 718, 717, 151, 150, 716, 706])).
% 0.77/0.95 tff(727,plain,((~hskp12) | (~c3_1(a218)) | (~c2_1(a215)) | c1_1(a218) | c2_1(a218) | c0_1(a215) | c1_1(a215) | (~c3_1(a248)) | c2_1(a248) | (~c0_1(a248))), inference(lemma,lemma(discharge,[]))).
% 0.77/0.95 tff(728,plain,
% 0.77/0.95 (~hskp12),
% 0.77/0.95 inference(unit_resolution,[status(thm)],[727, 689, 662, 681, 675, 661, 660, 638, 630, 651])).
% 0.77/0.95 tff(729,plain,
% 0.77/0.95 (^[U: $i] : refl((hskp21 | hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U))) <=> (hskp21 | hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U))))),
% 0.77/0.95 inference(bind,[status(th)],[])).
% 0.77/0.95 tff(730,plain,
% 0.77/0.95 (![U: $i] : (hskp21 | hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U))) <=> ![U: $i] : (hskp21 | hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))),
% 0.77/0.95 inference(quant_intro,[status(thm)],[729])).
% 0.77/0.95 tff(731,plain,
% 0.77/0.95 (![U: $i] : (hskp21 | hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U))) <=> ![U: $i] : (hskp21 | hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))),
% 0.77/0.95 inference(rewrite,[status(thm)],[])).
% 0.77/0.95 tff(732,plain,
% 0.77/0.95 (^[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) | hskp21) <=> ((hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U))) | hskp21))), rewrite(((hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U))) | hskp21) <=> (hskp21 | hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))), (((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp12) | hskp21) <=> (hskp21 | hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))))),
% 0.77/0.95 inference(bind,[status(th)],[])).
% 0.77/0.95 tff(733,plain,
% 0.77/0.95 (![U: $i] : ((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp12) | hskp21) <=> ![U: $i] : (hskp21 | hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))),
% 0.77/0.95 inference(quant_intro,[status(thm)],[732])).
% 0.77/0.95 tff(734,axiom,(![U: $i] : ((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp12) | hskp21)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause143')).
% 0.77/0.95 tff(735,plain,
% 0.77/0.95 (![U: $i] : (hskp21 | hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))),
% 0.77/0.95 inference(modus_ponens,[status(thm)],[734, 733])).
% 0.77/0.95 tff(736,plain,
% 0.77/0.95 (![U: $i] : (hskp21 | hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))),
% 0.77/0.95 inference(modus_ponens,[status(thm)],[735, 731])).
% 0.77/0.95 tff(737,plain,(
% 0.77/0.95 ![U: $i] : (hskp21 | hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))),
% 0.77/0.95 inference(skolemize,[status(sab)],[736])).
% 0.77/0.95 tff(738,plain,
% 0.77/0.95 (![U: $i] : (hskp21 | hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))),
% 0.77/0.95 inference(modus_ponens,[status(thm)],[737, 730])).
% 0.77/0.95 tff(739,assumption,(hskp0), introduced(assumption)).
% 0.77/0.95 tff(740,plain,
% 0.77/0.95 (((~hskp0) | (~c3_1(a213))) <=> ((~hskp0) | (~c3_1(a213)))),
% 0.77/0.95 inference(rewrite,[status(thm)],[])).
% 0.77/0.95 tff(741,plain,
% 0.77/0.95 (((~c3_1(a213)) | (~hskp0)) <=> ((~hskp0) | (~c3_1(a213)))),
% 0.77/0.95 inference(rewrite,[status(thm)],[])).
% 0.77/0.95 tff(742,axiom,((~c3_1(a213)) | (~hskp0)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause129')).
% 0.77/0.95 tff(743,plain,
% 0.77/0.95 ((~hskp0) | (~c3_1(a213))),
% 0.77/0.95 inference(modus_ponens,[status(thm)],[742, 741])).
% 0.77/0.95 tff(744,plain,
% 0.77/0.95 ((~hskp0) | (~c3_1(a213))),
% 0.77/0.95 inference(modus_ponens,[status(thm)],[743, 740])).
% 0.77/0.95 tff(745,plain,
% 0.77/0.95 (~c3_1(a213)),
% 0.77/0.95 inference(unit_resolution,[status(thm)],[744, 739])).
% 0.77/0.95 tff(746,plain,
% 0.77/0.95 (((~hskp0) | (~c1_1(a213))) <=> ((~hskp0) | (~c1_1(a213)))),
% 0.77/0.95 inference(rewrite,[status(thm)],[])).
% 0.77/0.95 tff(747,plain,
% 0.77/0.95 (((~c1_1(a213)) | (~hskp0)) <=> ((~hskp0) | (~c1_1(a213)))),
% 0.77/0.95 inference(rewrite,[status(thm)],[])).
% 0.77/0.95 tff(748,axiom,((~c1_1(a213)) | (~hskp0)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause128')).
% 0.77/0.95 tff(749,plain,
% 0.77/0.95 ((~hskp0) | (~c1_1(a213))),
% 0.77/0.95 inference(modus_ponens,[status(thm)],[748, 747])).
% 0.77/0.95 tff(750,plain,
% 0.77/0.95 ((~hskp0) | (~c1_1(a213))),
% 0.77/0.95 inference(modus_ponens,[status(thm)],[749, 746])).
% 0.77/0.95 tff(751,plain,
% 0.77/0.95 (~c1_1(a213)),
% 0.77/0.95 inference(unit_resolution,[status(thm)],[750, 739])).
% 0.77/0.95 tff(752,plain,
% 0.77/0.95 (((~hskp0) | c2_1(a213)) <=> ((~hskp0) | c2_1(a213))),
% 0.77/0.95 inference(rewrite,[status(thm)],[])).
% 0.77/0.95 tff(753,axiom,((~hskp0) | c2_1(a213)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause85')).
% 0.77/0.95 tff(754,plain,
% 0.77/0.95 ((~hskp0) | c2_1(a213)),
% 0.77/0.95 inference(modus_ponens,[status(thm)],[753, 752])).
% 0.77/0.95 tff(755,plain,
% 0.77/0.95 ((~hskp0) | c2_1(a213)),
% 0.77/0.95 inference(modus_ponens,[status(thm)],[754, 752])).
% 0.77/0.95 tff(756,plain,
% 0.77/0.95 ((~hskp0) | c2_1(a213)),
% 0.77/0.95 inference(modus_ponens,[status(thm)],[755, 752])).
% 0.77/0.95 tff(757,plain,
% 0.77/0.95 ((~hskp0) | c2_1(a213)),
% 0.77/0.95 inference(modus_ponens,[status(thm)],[756, 752])).
% 0.77/0.95 tff(758,plain,
% 0.77/0.95 ((~hskp0) | c2_1(a213)),
% 0.77/0.95 inference(modus_ponens,[status(thm)],[757, 752])).
% 0.77/0.95 tff(759,plain,
% 0.77/0.95 (c2_1(a213)),
% 0.77/0.95 inference(unit_resolution,[status(thm)],[758, 739])).
% 0.77/0.95 tff(760,plain,
% 0.77/0.95 (c0_1(a248)),
% 0.77/0.95 inference(unit_resolution,[status(thm)],[650, 642, 596, 641, 640])).
% 0.77/0.95 tff(761,plain,
% 0.77/0.95 (hskp5),
% 0.77/0.95 inference(unit_resolution,[status(thm)],[668, 110, 642, 641, 152, 151, 150, 149, 760])).
% 0.77/0.95 tff(762,plain,
% 0.77/0.95 (~c2_1(a218)),
% 0.77/0.95 inference(unit_resolution,[status(thm)],[674, 761])).
% 0.77/0.95 tff(763,plain,
% 0.77/0.95 (~c1_1(a218)),
% 0.77/0.95 inference(unit_resolution,[status(thm)],[680, 761])).
% 0.77/0.95 tff(764,plain,
% 0.77/0.95 (c3_1(a218)),
% 0.77/0.95 inference(unit_resolution,[status(thm)],[688, 761])).
% 0.77/0.95 tff(765,plain,
% 0.77/0.95 (~hskp12),
% 0.77/0.95 inference(unit_resolution,[status(thm)],[727, 764, 152, 763, 762, 151, 150, 641, 640, 760])).
% 0.77/0.95 tff(766,assumption,(~c3_1(a213)), introduced(assumption)).
% 0.77/0.95 tff(767,assumption,(~c1_1(a213)), introduced(assumption)).
% 0.77/0.95 tff(768,assumption,(c2_1(a213)), introduced(assumption)).
% 0.77/0.95 tff(769,plain,
% 0.77/0.95 (((~![U: $i] : (hskp21 | hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp21 | hskp12 | c1_1(a213) | c3_1(a213) | (~ndr1_0) | (~c2_1(a213)))) <=> ((~![U: $i] : (hskp21 | hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | hskp21 | hskp12 | c1_1(a213) | c3_1(a213) | (~ndr1_0) | (~c2_1(a213)))),
% 0.77/0.95 inference(rewrite,[status(thm)],[])).
% 0.77/0.95 tff(770,plain,
% 0.77/0.95 ((hskp21 | hskp12 | (~ndr1_0) | c1_1(a213) | c3_1(a213) | (~c2_1(a213))) <=> (hskp21 | hskp12 | c1_1(a213) | c3_1(a213) | (~ndr1_0) | (~c2_1(a213)))),
% 0.77/0.96 inference(rewrite,[status(thm)],[])).
% 0.77/0.96 tff(771,plain,
% 0.77/0.96 (((~![U: $i] : (hskp21 | hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp21 | hskp12 | (~ndr1_0) | c1_1(a213) | c3_1(a213) | (~c2_1(a213)))) <=> ((~![U: $i] : (hskp21 | hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp21 | hskp12 | c1_1(a213) | c3_1(a213) | (~ndr1_0) | (~c2_1(a213))))),
% 0.77/0.96 inference(monotonicity,[status(thm)],[770])).
% 0.77/0.96 tff(772,plain,
% 0.77/0.96 (((~![U: $i] : (hskp21 | hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp21 | hskp12 | (~ndr1_0) | c1_1(a213) | c3_1(a213) | (~c2_1(a213)))) <=> ((~![U: $i] : (hskp21 | hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | hskp21 | hskp12 | c1_1(a213) | c3_1(a213) | (~ndr1_0) | (~c2_1(a213)))),
% 0.77/0.96 inference(transitivity,[status(thm)],[771, 769])).
% 0.77/0.96 tff(773,plain,
% 0.77/0.96 ((~![U: $i] : (hskp21 | hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp21 | hskp12 | (~ndr1_0) | c1_1(a213) | c3_1(a213) | (~c2_1(a213)))),
% 0.77/0.96 inference(quant_inst,[status(thm)],[])).
% 0.77/0.96 tff(774,plain,
% 0.77/0.96 ((~![U: $i] : (hskp21 | hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | hskp21 | hskp12 | c1_1(a213) | c3_1(a213) | (~ndr1_0) | (~c2_1(a213))),
% 0.77/0.96 inference(modus_ponens,[status(thm)],[773, 772])).
% 0.77/0.96 tff(775,plain,
% 0.77/0.96 (hskp21 | c1_1(a213) | (~c2_1(a213))),
% 0.77/0.96 inference(unit_resolution,[status(thm)],[774, 110, 765, 766, 738])).
% 0.77/0.96 tff(776,plain,
% 0.77/0.96 (hskp21),
% 0.77/0.96 inference(unit_resolution,[status(thm)],[775, 767, 768])).
% 0.77/0.96 tff(777,plain,
% 0.77/0.96 (((~hskp21) | c0_1(a259)) <=> ((~hskp21) | c0_1(a259))),
% 0.77/0.96 inference(rewrite,[status(thm)],[])).
% 0.77/0.96 tff(778,axiom,((~hskp21) | c0_1(a259)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause56')).
% 0.77/0.96 tff(779,plain,
% 0.77/0.96 ((~hskp21) | c0_1(a259)),
% 0.77/0.96 inference(modus_ponens,[status(thm)],[778, 777])).
% 0.77/0.96 tff(780,plain,
% 0.77/0.96 ((~hskp21) | c0_1(a259)),
% 0.77/0.96 inference(modus_ponens,[status(thm)],[779, 777])).
% 0.77/0.96 tff(781,plain,
% 0.77/0.96 ((~hskp21) | c0_1(a259)),
% 0.77/0.96 inference(modus_ponens,[status(thm)],[780, 777])).
% 0.77/0.96 tff(782,plain,
% 0.77/0.96 ((~hskp21) | c0_1(a259)),
% 0.77/0.96 inference(modus_ponens,[status(thm)],[781, 777])).
% 0.77/0.96 tff(783,plain,
% 0.77/0.96 ((~hskp21) | c0_1(a259)),
% 0.77/0.96 inference(modus_ponens,[status(thm)],[782, 777])).
% 0.77/0.96 tff(784,plain,
% 0.77/0.96 (c0_1(a259)),
% 0.77/0.96 inference(unit_resolution,[status(thm)],[783, 776])).
% 0.77/0.96 tff(785,assumption,(~c2_1(a259)), introduced(assumption)).
% 0.77/0.96 tff(786,plain,
% 0.77/0.96 (((~hskp21) | c3_1(a259)) <=> ((~hskp21) | c3_1(a259))),
% 0.77/0.96 inference(rewrite,[status(thm)],[])).
% 0.77/0.96 tff(787,axiom,((~hskp21) | c3_1(a259)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause57')).
% 0.77/0.96 tff(788,plain,
% 0.77/0.96 ((~hskp21) | c3_1(a259)),
% 0.77/0.96 inference(modus_ponens,[status(thm)],[787, 786])).
% 0.77/0.96 tff(789,plain,
% 0.77/0.96 ((~hskp21) | c3_1(a259)),
% 0.77/0.96 inference(modus_ponens,[status(thm)],[788, 786])).
% 0.77/0.96 tff(790,plain,
% 0.77/0.96 ((~hskp21) | c3_1(a259)),
% 0.77/0.96 inference(modus_ponens,[status(thm)],[789, 786])).
% 0.77/0.96 tff(791,plain,
% 0.77/0.96 ((~hskp21) | c3_1(a259)),
% 0.77/0.96 inference(modus_ponens,[status(thm)],[790, 786])).
% 0.77/0.96 tff(792,plain,
% 0.77/0.96 ((~hskp21) | c3_1(a259)),
% 0.77/0.96 inference(modus_ponens,[status(thm)],[791, 786])).
% 0.77/0.96 tff(793,plain,
% 0.77/0.96 (c3_1(a259)),
% 0.77/0.96 inference(unit_resolution,[status(thm)],[792, 776])).
% 0.77/0.96 tff(794,plain,
% 0.77/0.96 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W))) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W))))),
% 0.77/0.96 inference(bind,[status(th)],[])).
% 0.77/0.96 tff(795,plain,
% 0.77/0.96 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))),
% 0.77/0.96 inference(quant_intro,[status(thm)],[794])).
% 0.77/0.96 tff(796,plain,
% 0.77/0.96 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))),
% 0.77/0.96 inference(rewrite,[status(thm)],[])).
% 0.77/0.96 tff(797,plain,
% 0.77/0.96 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(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(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V))))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c0_1(W))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V))) | (~c0_1(W))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V))) | (~c0_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c0_1(W)))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c0_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c0_1(W))))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c0_1(W))) | c2_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c0_1(W))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c0_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c0_1(W)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c0_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c0_1(W))))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c0_1(W))) | c2_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c0_1(W))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c0_1(W))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(W)))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c0_1(W))) | c2_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(W))))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c0_1(W))) | c2_1(U)) | c1_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(W))) | c3_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(W))) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | (~c0_1(W)))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c0_1(W))) | c2_1(U)) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | (~c0_1(W))))), ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c0_1(W))) | c2_1(U)) | c1_1(V)) | c3_1(V)) | c1_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | (~c0_1(W))) | c1_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | (~c0_1(W))) | c1_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c1_1(W) | (~c0_1(W)))), ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c0_1(W))) | c2_1(U)) | c1_1(V)) | c3_1(V)) | c1_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c1_1(W) | (~c0_1(W))))), (((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c0_1(W))) | c2_1(U)) | c1_1(V)) | c3_1(V)) | c1_1(W)) | c2_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c1_1(W) | (~c0_1(W))) | c2_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c1_1(W) | (~c0_1(W))) | c2_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))), (((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c0_1(W))) | c2_1(U)) | c1_1(V)) | c3_1(V)) | c1_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))))),
% 0.77/0.96 inference(bind,[status(th)],[])).
% 0.77/0.96 tff(798,plain,
% 0.77/0.96 (![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c0_1(W))) | c2_1(U)) | c1_1(V)) | c3_1(V)) | c1_1(W)) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))),
% 0.77/0.96 inference(quant_intro,[status(thm)],[797])).
% 0.77/0.96 tff(799,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c0_1(W))) | c2_1(U)) | c1_1(V)) | c3_1(V)) | c1_1(W)) | c2_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause190')).
% 0.77/0.96 tff(800,plain,
% 0.77/0.96 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))),
% 0.77/0.96 inference(modus_ponens,[status(thm)],[799, 798])).
% 0.77/0.96 tff(801,plain,
% 0.77/0.96 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))),
% 0.77/0.96 inference(modus_ponens,[status(thm)],[800, 796])).
% 0.77/0.96 tff(802,plain,(
% 0.77/0.96 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))),
% 0.77/0.96 inference(skolemize,[status(sab)],[801])).
% 0.77/0.96 tff(803,plain,
% 0.77/0.96 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))),
% 0.77/0.96 inference(modus_ponens,[status(thm)],[802, 795])).
% 0.77/0.96 tff(804,plain,
% 0.77/0.96 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | (c2_1(a259) | c2_1(a248) | c1_1(a213) | c3_1(a213) | (~ndr1_0) | (~c2_1(a213)) | (~c3_1(a248)) | (~c1_1(a248)) | (~c0_1(a259)) | c1_1(a259))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | c2_1(a259) | c2_1(a248) | c1_1(a213) | c3_1(a213) | (~ndr1_0) | (~c2_1(a213)) | (~c3_1(a248)) | (~c1_1(a248)) | (~c0_1(a259)) | c1_1(a259))),
% 0.77/0.96 inference(rewrite,[status(thm)],[])).
% 0.77/0.96 tff(805,plain,
% 0.77/0.96 (((~ndr1_0) | c2_1(a248) | (~c3_1(a248)) | (~c1_1(a248)) | c3_1(a213) | c1_1(a213) | (~c2_1(a213)) | c2_1(a259) | c1_1(a259) | (~c0_1(a259))) <=> (c2_1(a259) | c2_1(a248) | c1_1(a213) | c3_1(a213) | (~ndr1_0) | (~c2_1(a213)) | (~c3_1(a248)) | (~c1_1(a248)) | (~c0_1(a259)) | c1_1(a259))),
% 0.77/0.96 inference(rewrite,[status(thm)],[])).
% 0.77/0.96 tff(806,plain,
% 0.77/0.96 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a248) | (~c3_1(a248)) | (~c1_1(a248)) | c3_1(a213) | c1_1(a213) | (~c2_1(a213)) | c2_1(a259) | c1_1(a259) | (~c0_1(a259)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | (c2_1(a259) | c2_1(a248) | c1_1(a213) | c3_1(a213) | (~ndr1_0) | (~c2_1(a213)) | (~c3_1(a248)) | (~c1_1(a248)) | (~c0_1(a259)) | c1_1(a259)))),
% 0.77/0.96 inference(monotonicity,[status(thm)],[805])).
% 0.77/0.96 tff(807,plain,
% 0.77/0.96 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a248) | (~c3_1(a248)) | (~c1_1(a248)) | c3_1(a213) | c1_1(a213) | (~c2_1(a213)) | c2_1(a259) | c1_1(a259) | (~c0_1(a259)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | c2_1(a259) | c2_1(a248) | c1_1(a213) | c3_1(a213) | (~ndr1_0) | (~c2_1(a213)) | (~c3_1(a248)) | (~c1_1(a248)) | (~c0_1(a259)) | c1_1(a259))),
% 0.77/0.96 inference(transitivity,[status(thm)],[806, 804])).
% 0.77/0.96 tff(808,plain,
% 0.77/0.96 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a248) | (~c3_1(a248)) | (~c1_1(a248)) | c3_1(a213) | c1_1(a213) | (~c2_1(a213)) | c2_1(a259) | c1_1(a259) | (~c0_1(a259)))),
% 0.77/0.96 inference(quant_inst,[status(thm)],[])).
% 0.77/0.96 tff(809,plain,
% 0.77/0.96 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | c2_1(a259) | c2_1(a248) | c1_1(a213) | c3_1(a213) | (~ndr1_0) | (~c2_1(a213)) | (~c3_1(a248)) | (~c1_1(a248)) | (~c0_1(a259)) | c1_1(a259)),
% 0.77/0.96 inference(modus_ponens,[status(thm)],[808, 807])).
% 0.77/0.96 tff(810,plain,
% 0.77/0.96 (c1_1(a213) | (~c2_1(a213)) | (~c0_1(a259)) | c1_1(a259)),
% 0.77/0.96 inference(unit_resolution,[status(thm)],[809, 110, 642, 641, 785, 640, 766, 803])).
% 0.77/0.96 tff(811,plain,
% 0.77/0.96 (c1_1(a259)),
% 0.77/0.96 inference(unit_resolution,[status(thm)],[810, 784, 768, 767])).
% 0.77/0.96 tff(812,assumption,(c1_1(a259)), introduced(assumption)).
% 0.77/0.96 tff(813,assumption,(hskp9), introduced(assumption)).
% 0.77/0.96 tff(814,plain,
% 0.77/0.96 (((~hskp9) | (~c2_1(a226))) <=> ((~hskp9) | (~c2_1(a226)))),
% 0.77/0.96 inference(rewrite,[status(thm)],[])).
% 0.77/0.96 tff(815,plain,
% 0.77/0.96 (((~c2_1(a226)) | (~hskp9)) <=> ((~hskp9) | (~c2_1(a226)))),
% 0.77/0.96 inference(rewrite,[status(thm)],[])).
% 0.77/0.96 tff(816,axiom,((~c2_1(a226)) | (~hskp9)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause113')).
% 0.77/0.96 tff(817,plain,
% 0.77/0.96 ((~hskp9) | (~c2_1(a226))),
% 0.77/0.96 inference(modus_ponens,[status(thm)],[816, 815])).
% 0.77/0.96 tff(818,plain,
% 0.77/0.96 ((~hskp9) | (~c2_1(a226))),
% 0.77/0.96 inference(modus_ponens,[status(thm)],[817, 814])).
% 0.77/0.96 tff(819,plain,
% 0.77/0.96 (~c2_1(a226)),
% 0.77/0.96 inference(unit_resolution,[status(thm)],[818, 813])).
% 0.77/0.96 tff(820,plain,
% 0.77/0.96 (((~hskp9) | (~c1_1(a226))) <=> ((~hskp9) | (~c1_1(a226)))),
% 0.77/0.96 inference(rewrite,[status(thm)],[])).
% 0.77/0.96 tff(821,plain,
% 0.77/0.96 (((~c1_1(a226)) | (~hskp9)) <=> ((~hskp9) | (~c1_1(a226)))),
% 0.77/0.96 inference(rewrite,[status(thm)],[])).
% 0.77/0.96 tff(822,axiom,((~c1_1(a226)) | (~hskp9)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause112')).
% 0.77/0.96 tff(823,plain,
% 0.77/0.96 ((~hskp9) | (~c1_1(a226))),
% 0.77/0.96 inference(modus_ponens,[status(thm)],[822, 821])).
% 0.77/0.96 tff(824,plain,
% 0.77/0.96 ((~hskp9) | (~c1_1(a226))),
% 0.77/0.96 inference(modus_ponens,[status(thm)],[823, 820])).
% 0.77/0.96 tff(825,plain,
% 0.77/0.96 (~c1_1(a226)),
% 0.77/0.96 inference(unit_resolution,[status(thm)],[824, 813])).
% 0.77/0.96 tff(826,plain,
% 0.77/0.96 (((~hskp9) | c0_1(a226)) <=> ((~hskp9) | c0_1(a226))),
% 0.77/0.96 inference(rewrite,[status(thm)],[])).
% 0.77/0.96 tff(827,axiom,((~hskp9) | c0_1(a226)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause74')).
% 0.77/0.96 tff(828,plain,
% 0.77/0.96 ((~hskp9) | c0_1(a226)),
% 0.77/0.96 inference(modus_ponens,[status(thm)],[827, 826])).
% 0.77/0.96 tff(829,plain,
% 0.77/0.96 ((~hskp9) | c0_1(a226)),
% 0.77/0.96 inference(modus_ponens,[status(thm)],[828, 826])).
% 0.77/0.96 tff(830,plain,
% 0.77/0.96 ((~hskp9) | c0_1(a226)),
% 0.77/0.96 inference(modus_ponens,[status(thm)],[829, 826])).
% 0.77/0.96 tff(831,plain,
% 0.77/0.96 ((~hskp9) | c0_1(a226)),
% 0.77/0.96 inference(modus_ponens,[status(thm)],[830, 826])).
% 0.77/0.96 tff(832,plain,
% 0.77/0.96 ((~hskp9) | c0_1(a226)),
% 0.77/0.96 inference(modus_ponens,[status(thm)],[831, 826])).
% 0.77/0.96 tff(833,plain,
% 0.77/0.96 (c0_1(a226)),
% 0.77/0.96 inference(unit_resolution,[status(thm)],[832, 813])).
% 0.77/0.96 tff(834,assumption,(c3_1(a259)), introduced(assumption)).
% 0.77/0.96 tff(835,plain,
% 0.77/0.96 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | (c2_1(a259) | c1_1(a226) | c2_1(a226) | c1_1(a213) | c3_1(a213) | (~ndr1_0) | (~c2_1(a213)) | (~c0_1(a226)) | (~c3_1(a259)) | (~c1_1(a259)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | c2_1(a259) | c1_1(a226) | c2_1(a226) | c1_1(a213) | c3_1(a213) | (~ndr1_0) | (~c2_1(a213)) | (~c0_1(a226)) | (~c3_1(a259)) | (~c1_1(a259)))),
% 0.77/0.96 inference(rewrite,[status(thm)],[])).
% 0.77/0.96 tff(836,plain,
% 0.77/0.96 (((~ndr1_0) | c2_1(a259) | (~c3_1(a259)) | (~c1_1(a259)) | c3_1(a213) | c1_1(a213) | (~c2_1(a213)) | c2_1(a226) | c1_1(a226) | (~c0_1(a226))) <=> (c2_1(a259) | c1_1(a226) | c2_1(a226) | c1_1(a213) | c3_1(a213) | (~ndr1_0) | (~c2_1(a213)) | (~c0_1(a226)) | (~c3_1(a259)) | (~c1_1(a259)))),
% 0.77/0.96 inference(rewrite,[status(thm)],[])).
% 0.77/0.96 tff(837,plain,
% 0.77/0.96 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a259) | (~c3_1(a259)) | (~c1_1(a259)) | c3_1(a213) | c1_1(a213) | (~c2_1(a213)) | c2_1(a226) | c1_1(a226) | (~c0_1(a226)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | (c2_1(a259) | c1_1(a226) | c2_1(a226) | c1_1(a213) | c3_1(a213) | (~ndr1_0) | (~c2_1(a213)) | (~c0_1(a226)) | (~c3_1(a259)) | (~c1_1(a259))))),
% 0.77/0.96 inference(monotonicity,[status(thm)],[836])).
% 0.77/0.96 tff(838,plain,
% 0.77/0.96 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a259) | (~c3_1(a259)) | (~c1_1(a259)) | c3_1(a213) | c1_1(a213) | (~c2_1(a213)) | c2_1(a226) | c1_1(a226) | (~c0_1(a226)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | c2_1(a259) | c1_1(a226) | c2_1(a226) | c1_1(a213) | c3_1(a213) | (~ndr1_0) | (~c2_1(a213)) | (~c0_1(a226)) | (~c3_1(a259)) | (~c1_1(a259)))),
% 0.77/0.96 inference(transitivity,[status(thm)],[837, 835])).
% 0.77/0.96 tff(839,plain,
% 0.77/0.96 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a259) | (~c3_1(a259)) | (~c1_1(a259)) | c3_1(a213) | c1_1(a213) | (~c2_1(a213)) | c2_1(a226) | c1_1(a226) | (~c0_1(a226)))),
% 0.77/0.96 inference(quant_inst,[status(thm)],[])).
% 0.77/0.96 tff(840,plain,
% 0.77/0.96 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | c2_1(a259) | c1_1(a226) | c2_1(a226) | c1_1(a213) | c3_1(a213) | (~ndr1_0) | (~c2_1(a213)) | (~c0_1(a226)) | (~c3_1(a259)) | (~c1_1(a259))),
% 0.77/0.96 inference(modus_ponens,[status(thm)],[839, 838])).
% 0.77/0.96 tff(841,plain,
% 0.77/0.96 ($false),
% 0.77/0.96 inference(unit_resolution,[status(thm)],[840, 110, 834, 833, 768, 785, 825, 819, 767, 766, 803, 812])).
% 0.77/0.96 tff(842,plain,((~hskp9) | (~c3_1(a259)) | (~c2_1(a213)) | c2_1(a259) | c1_1(a213) | c3_1(a213) | (~c1_1(a259))), inference(lemma,lemma(discharge,[]))).
% 0.77/0.96 tff(843,plain,
% 0.77/0.96 (~hskp9),
% 0.77/0.96 inference(unit_resolution,[status(thm)],[842, 811, 768, 785, 767, 766, 793])).
% 0.77/0.96 tff(844,plain,
% 0.77/0.96 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W))))),
% 0.77/0.96 inference(bind,[status(th)],[])).
% 0.77/0.96 tff(845,plain,
% 0.77/0.96 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~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)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))),
% 0.77/0.96 inference(quant_intro,[status(thm)],[844])).
% 0.77/0.96 tff(846,plain,
% 0.77/0.96 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~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)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))),
% 0.77/0.96 inference(rewrite,[status(thm)],[])).
% 0.77/0.96 tff(847,plain,
% 0.77/0.96 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~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)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c2_1(W))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V))) | (~c2_1(W))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(W)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(W))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c2_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(W))) | c2_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(W))) | c2_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(W)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c2_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(W))))), ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c2_1(V)) | c0_1(W)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(W))) | c0_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)))), ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c2_1(V)) | c0_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W))))), (((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c2_1(V)) | c0_1(W)) | c1_1(W)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W))) | c1_1(W)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W))) | c1_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))), (((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c2_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))))),
% 0.77/0.96 inference(bind,[status(th)],[])).
% 0.77/0.96 tff(848,plain,
% 0.77/0.96 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c2_1(V)) | c0_1(W)) | c1_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))),
% 0.77/0.96 inference(quant_intro,[status(thm)],[847])).
% 0.77/0.96 tff(849,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c2_1(V)) | c0_1(W)) | c1_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause194')).
% 0.77/0.96 tff(850,plain,
% 0.77/0.96 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))),
% 0.77/0.96 inference(modus_ponens,[status(thm)],[849, 848])).
% 0.77/0.96 tff(851,plain,
% 0.77/0.96 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))),
% 0.77/0.96 inference(modus_ponens,[status(thm)],[850, 846])).
% 0.77/0.96 tff(852,plain,(
% 0.77/0.96 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))),
% 0.77/0.96 inference(skolemize,[status(sab)],[851])).
% 0.77/0.96 tff(853,plain,
% 0.77/0.96 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))),
% 0.77/0.96 inference(modus_ponens,[status(thm)],[852, 845])).
% 0.77/0.96 tff(854,assumption,(hskp13), introduced(assumption)).
% 0.77/0.96 tff(855,plain,
% 0.77/0.96 (((~hskp13) | c3_1(a239)) <=> ((~hskp13) | c3_1(a239))),
% 0.77/0.96 inference(rewrite,[status(thm)],[])).
% 0.77/0.96 tff(856,axiom,((~hskp13) | c3_1(a239)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause68')).
% 0.77/0.96 tff(857,plain,
% 0.77/0.96 ((~hskp13) | c3_1(a239)),
% 0.77/0.96 inference(modus_ponens,[status(thm)],[856, 855])).
% 0.77/0.96 tff(858,plain,
% 0.77/0.96 ((~hskp13) | c3_1(a239)),
% 0.77/0.96 inference(modus_ponens,[status(thm)],[857, 855])).
% 0.77/0.96 tff(859,plain,
% 0.77/0.96 ((~hskp13) | c3_1(a239)),
% 0.77/0.96 inference(modus_ponens,[status(thm)],[858, 855])).
% 0.77/0.96 tff(860,plain,
% 0.77/0.96 ((~hskp13) | c3_1(a239)),
% 0.77/0.96 inference(modus_ponens,[status(thm)],[859, 855])).
% 0.77/0.96 tff(861,plain,
% 0.77/0.96 ((~hskp13) | c3_1(a239)),
% 0.77/0.96 inference(modus_ponens,[status(thm)],[860, 855])).
% 0.77/0.96 tff(862,plain,
% 0.77/0.96 (c3_1(a239)),
% 0.77/0.96 inference(unit_resolution,[status(thm)],[861, 854])).
% 0.77/0.96 tff(863,plain,
% 0.77/0.96 (((~hskp13) | c2_1(a239)) <=> ((~hskp13) | c2_1(a239))),
% 0.77/0.96 inference(rewrite,[status(thm)],[])).
% 0.77/0.96 tff(864,axiom,((~hskp13) | c2_1(a239)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause67')).
% 0.77/0.96 tff(865,plain,
% 0.77/0.96 ((~hskp13) | c2_1(a239)),
% 0.77/0.96 inference(modus_ponens,[status(thm)],[864, 863])).
% 0.77/0.96 tff(866,plain,
% 0.77/0.96 ((~hskp13) | c2_1(a239)),
% 0.77/0.96 inference(modus_ponens,[status(thm)],[865, 863])).
% 0.77/0.96 tff(867,plain,
% 0.77/0.96 ((~hskp13) | c2_1(a239)),
% 0.77/0.96 inference(modus_ponens,[status(thm)],[866, 863])).
% 0.77/0.96 tff(868,plain,
% 0.77/0.96 ((~hskp13) | c2_1(a239)),
% 0.77/0.96 inference(modus_ponens,[status(thm)],[867, 863])).
% 0.77/0.96 tff(869,plain,
% 0.77/0.96 ((~hskp13) | c2_1(a239)),
% 0.77/0.96 inference(modus_ponens,[status(thm)],[868, 863])).
% 0.77/0.96 tff(870,plain,
% 0.77/0.96 (c2_1(a239)),
% 0.77/0.96 inference(unit_resolution,[status(thm)],[869, 854])).
% 0.77/0.96 tff(871,assumption,(c0_1(a259)), introduced(assumption)).
% 0.77/0.96 tff(872,plain,
% 0.77/0.96 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | (c2_1(a259) | c0_1(a215) | c1_1(a215) | (~ndr1_0) | (~c2_1(a215)) | (~c3_1(a239)) | (~c0_1(a239)) | (~c2_1(a239)) | (~c3_1(a259)) | (~c0_1(a259)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | c2_1(a259) | c0_1(a215) | c1_1(a215) | (~ndr1_0) | (~c2_1(a215)) | (~c3_1(a239)) | (~c0_1(a239)) | (~c2_1(a239)) | (~c3_1(a259)) | (~c0_1(a259)))),
% 0.77/0.96 inference(rewrite,[status(thm)],[])).
% 0.77/0.96 tff(873,plain,
% 0.77/0.96 (((~ndr1_0) | (~c2_1(a239)) | (~c3_1(a239)) | (~c0_1(a239)) | c2_1(a259) | (~c3_1(a259)) | (~c0_1(a259)) | c0_1(a215) | c1_1(a215) | (~c2_1(a215))) <=> (c2_1(a259) | c0_1(a215) | c1_1(a215) | (~ndr1_0) | (~c2_1(a215)) | (~c3_1(a239)) | (~c0_1(a239)) | (~c2_1(a239)) | (~c3_1(a259)) | (~c0_1(a259)))),
% 0.77/0.96 inference(rewrite,[status(thm)],[])).
% 0.77/0.96 tff(874,plain,
% 0.77/0.96 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a239)) | (~c3_1(a239)) | (~c0_1(a239)) | c2_1(a259) | (~c3_1(a259)) | (~c0_1(a259)) | c0_1(a215) | c1_1(a215) | (~c2_1(a215)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | (c2_1(a259) | c0_1(a215) | c1_1(a215) | (~ndr1_0) | (~c2_1(a215)) | (~c3_1(a239)) | (~c0_1(a239)) | (~c2_1(a239)) | (~c3_1(a259)) | (~c0_1(a259))))),
% 0.77/0.96 inference(monotonicity,[status(thm)],[873])).
% 0.77/0.96 tff(875,plain,
% 0.77/0.96 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a239)) | (~c3_1(a239)) | (~c0_1(a239)) | c2_1(a259) | (~c3_1(a259)) | (~c0_1(a259)) | c0_1(a215) | c1_1(a215) | (~c2_1(a215)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | c2_1(a259) | c0_1(a215) | c1_1(a215) | (~ndr1_0) | (~c2_1(a215)) | (~c3_1(a239)) | (~c0_1(a239)) | (~c2_1(a239)) | (~c3_1(a259)) | (~c0_1(a259)))),
% 0.77/0.96 inference(transitivity,[status(thm)],[874, 872])).
% 0.77/0.96 tff(876,plain,
% 0.77/0.96 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a239)) | (~c3_1(a239)) | (~c0_1(a239)) | c2_1(a259) | (~c3_1(a259)) | (~c0_1(a259)) | c0_1(a215) | c1_1(a215) | (~c2_1(a215)))),
% 0.77/0.96 inference(quant_inst,[status(thm)],[])).
% 0.77/0.96 tff(877,plain,
% 0.77/0.96 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | c2_1(a259) | c0_1(a215) | c1_1(a215) | (~ndr1_0) | (~c2_1(a215)) | (~c3_1(a239)) | (~c0_1(a239)) | (~c2_1(a239)) | (~c3_1(a259)) | (~c0_1(a259))),
% 0.77/0.96 inference(modus_ponens,[status(thm)],[876, 875])).
% 0.77/0.96 tff(878,plain,
% 0.77/0.96 (~c0_1(a239)),
% 0.77/0.96 inference(unit_resolution,[status(thm)],[877, 110, 871, 834, 870, 862, 152, 785, 151, 150, 853])).
% 0.77/0.96 tff(879,plain,
% 0.77/0.96 (((~hskp13) | (~c1_1(a239))) <=> ((~hskp13) | (~c1_1(a239)))),
% 0.77/0.96 inference(rewrite,[status(thm)],[])).
% 0.77/0.96 tff(880,plain,
% 0.77/0.96 (((~c1_1(a239)) | (~hskp13)) <=> ((~hskp13) | (~c1_1(a239)))),
% 0.77/0.96 inference(rewrite,[status(thm)],[])).
% 0.77/0.96 tff(881,axiom,((~c1_1(a239)) | (~hskp13)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause107')).
% 0.77/0.96 tff(882,plain,
% 0.77/0.96 ((~hskp13) | (~c1_1(a239))),
% 0.77/0.96 inference(modus_ponens,[status(thm)],[881, 880])).
% 0.77/0.96 tff(883,plain,
% 0.77/0.96 ((~hskp13) | (~c1_1(a239))),
% 0.77/0.96 inference(modus_ponens,[status(thm)],[882, 879])).
% 0.77/0.96 tff(884,plain,
% 0.77/0.96 (~c1_1(a239)),
% 0.77/0.96 inference(unit_resolution,[status(thm)],[883, 854])).
% 0.77/0.96 tff(885,assumption,(hskp15), introduced(assumption)).
% 0.77/0.96 tff(886,plain,
% 0.77/0.96 (~c0_1(a242)),
% 0.77/0.96 inference(unit_resolution,[status(thm)],[414, 885])).
% 0.77/0.96 tff(887,plain,
% 0.77/0.96 (c1_1(a242)),
% 0.77/0.96 inference(unit_resolution,[status(thm)],[391, 885])).
% 0.77/0.96 tff(888,plain,
% 0.77/0.96 (((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp18 | c2_1(a259) | c0_1(a242) | (~ndr1_0) | (~c3_1(a242)) | (~c1_1(a242)) | (~c3_1(a259)) | (~c1_1(a259)))) <=> ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp18 | c2_1(a259) | c0_1(a242) | (~ndr1_0) | (~c3_1(a242)) | (~c1_1(a242)) | (~c3_1(a259)) | (~c1_1(a259)))),
% 0.77/0.96 inference(rewrite,[status(thm)],[])).
% 0.77/0.96 tff(889,plain,
% 0.77/0.96 ((hskp18 | (~ndr1_0) | c2_1(a259) | (~c3_1(a259)) | (~c1_1(a259)) | c0_1(a242) | (~c1_1(a242)) | (~c3_1(a242))) <=> (hskp18 | c2_1(a259) | c0_1(a242) | (~ndr1_0) | (~c3_1(a242)) | (~c1_1(a242)) | (~c3_1(a259)) | (~c1_1(a259)))),
% 0.77/0.96 inference(rewrite,[status(thm)],[])).
% 0.77/0.96 tff(890,plain,
% 0.77/0.96 (((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp18 | (~ndr1_0) | c2_1(a259) | (~c3_1(a259)) | (~c1_1(a259)) | c0_1(a242) | (~c1_1(a242)) | (~c3_1(a242)))) <=> ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp18 | c2_1(a259) | c0_1(a242) | (~ndr1_0) | (~c3_1(a242)) | (~c1_1(a242)) | (~c3_1(a259)) | (~c1_1(a259))))),
% 0.77/0.96 inference(monotonicity,[status(thm)],[889])).
% 0.77/0.96 tff(891,plain,
% 0.77/0.96 (((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp18 | (~ndr1_0) | c2_1(a259) | (~c3_1(a259)) | (~c1_1(a259)) | c0_1(a242) | (~c1_1(a242)) | (~c3_1(a242)))) <=> ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp18 | c2_1(a259) | c0_1(a242) | (~ndr1_0) | (~c3_1(a242)) | (~c1_1(a242)) | (~c3_1(a259)) | (~c1_1(a259)))),
% 0.77/0.96 inference(transitivity,[status(thm)],[890, 888])).
% 0.77/0.96 tff(892,plain,
% 0.77/0.96 ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp18 | (~ndr1_0) | c2_1(a259) | (~c3_1(a259)) | (~c1_1(a259)) | c0_1(a242) | (~c1_1(a242)) | (~c3_1(a242)))),
% 0.77/0.97 inference(quant_inst,[status(thm)],[])).
% 0.77/0.97 tff(893,plain,
% 0.77/0.97 ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp18 | c2_1(a259) | c0_1(a242) | (~ndr1_0) | (~c3_1(a242)) | (~c1_1(a242)) | (~c3_1(a259)) | (~c1_1(a259))),
% 0.77/0.97 inference(modus_ponens,[status(thm)],[892, 891])).
% 0.77/0.97 tff(894,plain,
% 0.77/0.97 (~c3_1(a242)),
% 0.77/0.97 inference(unit_resolution,[status(thm)],[893, 110, 596, 834, 887, 785, 886, 615, 812])).
% 0.77/0.97 tff(895,assumption,(~c0_1(a239)), introduced(assumption)).
% 0.77/0.97 tff(896,plain,
% 0.77/0.97 (^[V: $i, U: $i] : refl((hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V)) <=> (hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V)))),
% 0.77/0.97 inference(bind,[status(th)],[])).
% 0.77/0.97 tff(897,plain,
% 0.77/0.97 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V)) <=> ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))),
% 0.77/0.97 inference(quant_intro,[status(thm)],[896])).
% 0.77/0.97 tff(898,plain,
% 0.77/0.97 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V)) <=> ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))),
% 0.77/0.97 inference(rewrite,[status(thm)],[])).
% 0.77/0.97 tff(899,plain,
% 0.77/0.97 (^[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)) | c0_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U))))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U))) | c0_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U))) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V)))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | 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)))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_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))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | 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)))), ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))), ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V)))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp9) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V)) | hskp9))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V)) | hskp9) <=> (hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp9) <=> (hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))))),
% 0.77/0.97 inference(bind,[status(th)],[])).
% 0.77/0.97 tff(900,plain,
% 0.77/0.97 (![V: $i, U: $i] : ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp9) <=> ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))),
% 0.77/0.97 inference(quant_intro,[status(thm)],[899])).
% 0.77/0.97 tff(901,axiom,(![V: $i, U: $i] : ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp9)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause159')).
% 0.77/0.97 tff(902,plain,
% 0.77/0.97 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))),
% 0.77/0.97 inference(modus_ponens,[status(thm)],[901, 900])).
% 0.77/0.97 tff(903,plain,
% 0.77/0.97 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))),
% 0.77/0.97 inference(modus_ponens,[status(thm)],[902, 898])).
% 0.77/0.97 tff(904,plain,(
% 0.77/0.97 ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))),
% 0.77/0.97 inference(skolemize,[status(sab)],[903])).
% 0.77/0.97 tff(905,plain,
% 0.77/0.97 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))),
% 0.77/0.97 inference(modus_ponens,[status(thm)],[904, 897])).
% 0.77/0.97 tff(906,plain,
% 0.77/0.97 (~c2_1(a242)),
% 0.77/0.97 inference(unit_resolution,[status(thm)],[383, 885])).
% 0.77/0.97 tff(907,assumption,(c3_1(a239)), introduced(assumption)).
% 0.77/0.97 tff(908,assumption,(c2_1(a239)), introduced(assumption)).
% 0.77/0.97 tff(909,plain,
% 0.77/0.97 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp9 | c0_1(a242) | c2_1(a242) | (~ndr1_0) | (~c3_1(a239)) | c0_1(a239) | (~c2_1(a239)) | c3_1(a242))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp9 | c0_1(a242) | c2_1(a242) | (~ndr1_0) | (~c3_1(a239)) | c0_1(a239) | (~c2_1(a239)) | c3_1(a242))),
% 0.77/0.97 inference(rewrite,[status(thm)],[])).
% 0.77/0.97 tff(910,plain,
% 0.77/0.97 ((hskp9 | (~ndr1_0) | c0_1(a239) | (~c2_1(a239)) | (~c3_1(a239)) | c3_1(a242) | c0_1(a242) | c2_1(a242)) <=> (hskp9 | c0_1(a242) | c2_1(a242) | (~ndr1_0) | (~c3_1(a239)) | c0_1(a239) | (~c2_1(a239)) | c3_1(a242))),
% 0.77/0.97 inference(rewrite,[status(thm)],[])).
% 0.77/0.97 tff(911,plain,
% 0.77/0.97 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp9 | (~ndr1_0) | c0_1(a239) | (~c2_1(a239)) | (~c3_1(a239)) | c3_1(a242) | c0_1(a242) | c2_1(a242))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp9 | c0_1(a242) | c2_1(a242) | (~ndr1_0) | (~c3_1(a239)) | c0_1(a239) | (~c2_1(a239)) | c3_1(a242)))),
% 0.77/0.97 inference(monotonicity,[status(thm)],[910])).
% 0.77/0.97 tff(912,plain,
% 0.77/0.97 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp9 | (~ndr1_0) | c0_1(a239) | (~c2_1(a239)) | (~c3_1(a239)) | c3_1(a242) | c0_1(a242) | c2_1(a242))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp9 | c0_1(a242) | c2_1(a242) | (~ndr1_0) | (~c3_1(a239)) | c0_1(a239) | (~c2_1(a239)) | c3_1(a242))),
% 0.77/0.97 inference(transitivity,[status(thm)],[911, 909])).
% 0.77/0.97 tff(913,plain,
% 0.77/0.97 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp9 | (~ndr1_0) | c0_1(a239) | (~c2_1(a239)) | (~c3_1(a239)) | c3_1(a242) | c0_1(a242) | c2_1(a242))),
% 0.77/0.97 inference(quant_inst,[status(thm)],[])).
% 0.77/0.97 tff(914,plain,
% 0.77/0.97 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp9 | c0_1(a242) | c2_1(a242) | (~ndr1_0) | (~c3_1(a239)) | c0_1(a239) | (~c2_1(a239)) | c3_1(a242)),
% 0.77/0.97 inference(modus_ponens,[status(thm)],[913, 912])).
% 0.77/0.97 tff(915,plain,
% 0.77/0.97 ($false),
% 0.77/0.97 inference(unit_resolution,[status(thm)],[914, 110, 23, 908, 907, 886, 906, 905, 895, 894])).
% 0.77/0.97 tff(916,plain,((~hskp15) | hskp9 | (~c2_1(a239)) | (~c3_1(a239)) | c0_1(a239) | hskp18 | (~c3_1(a259)) | c2_1(a259) | (~c1_1(a259))), inference(lemma,lemma(discharge,[]))).
% 0.77/0.97 tff(917,plain,
% 0.77/0.97 (~hskp15),
% 0.77/0.97 inference(unit_resolution,[status(thm)],[916, 878, 812, 862, 870, 596, 834, 785, 23])).
% 0.77/0.97 tff(918,assumption,(~hskp15), introduced(assumption)).
% 0.77/0.97 tff(919,assumption,(~hskp24), introduced(assumption)).
% 0.77/0.97 tff(920,assumption,(~c1_1(a239)), introduced(assumption)).
% 0.77/0.97 tff(921,plain,
% 0.77/0.97 (((~![U: $i] : (hskp24 | hskp15 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp24 | hskp15 | c1_1(a239) | (~ndr1_0) | (~c3_1(a239)) | (~c2_1(a239)))) <=> ((~![U: $i] : (hskp24 | hskp15 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | hskp24 | hskp15 | c1_1(a239) | (~ndr1_0) | (~c3_1(a239)) | (~c2_1(a239)))),
% 0.77/0.97 inference(rewrite,[status(thm)],[])).
% 0.77/0.97 tff(922,plain,
% 0.77/0.97 ((hskp24 | hskp15 | (~ndr1_0) | c1_1(a239) | (~c2_1(a239)) | (~c3_1(a239))) <=> (hskp24 | hskp15 | c1_1(a239) | (~ndr1_0) | (~c3_1(a239)) | (~c2_1(a239)))),
% 0.77/0.97 inference(rewrite,[status(thm)],[])).
% 0.77/0.97 tff(923,plain,
% 0.77/0.97 (((~![U: $i] : (hskp24 | hskp15 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp24 | hskp15 | (~ndr1_0) | c1_1(a239) | (~c2_1(a239)) | (~c3_1(a239)))) <=> ((~![U: $i] : (hskp24 | hskp15 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp24 | hskp15 | c1_1(a239) | (~ndr1_0) | (~c3_1(a239)) | (~c2_1(a239))))),
% 0.77/0.97 inference(monotonicity,[status(thm)],[922])).
% 0.77/0.97 tff(924,plain,
% 0.77/0.97 (((~![U: $i] : (hskp24 | hskp15 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp24 | hskp15 | (~ndr1_0) | c1_1(a239) | (~c2_1(a239)) | (~c3_1(a239)))) <=> ((~![U: $i] : (hskp24 | hskp15 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | hskp24 | hskp15 | c1_1(a239) | (~ndr1_0) | (~c3_1(a239)) | (~c2_1(a239)))),
% 0.77/0.97 inference(transitivity,[status(thm)],[923, 921])).
% 0.77/0.97 tff(925,plain,
% 0.77/0.97 ((~![U: $i] : (hskp24 | hskp15 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp24 | hskp15 | (~ndr1_0) | c1_1(a239) | (~c2_1(a239)) | (~c3_1(a239)))),
% 0.77/0.97 inference(quant_inst,[status(thm)],[])).
% 0.77/0.97 tff(926,plain,
% 0.77/0.97 ((~![U: $i] : (hskp24 | hskp15 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | hskp24 | hskp15 | c1_1(a239) | (~ndr1_0) | (~c3_1(a239)) | (~c2_1(a239))),
% 0.77/0.97 inference(modus_ponens,[status(thm)],[925, 924])).
% 0.77/0.97 tff(927,plain,
% 0.77/0.97 (hskp24 | hskp15 | (~c3_1(a239)) | (~c2_1(a239))),
% 0.77/0.97 inference(unit_resolution,[status(thm)],[926, 110, 920, 312])).
% 0.77/0.97 tff(928,plain,
% 0.77/0.97 ($false),
% 0.77/0.97 inference(unit_resolution,[status(thm)],[927, 862, 870, 919, 918])).
% 0.77/0.97 tff(929,plain,((~hskp13) | hskp24 | hskp15 | c1_1(a239)), inference(lemma,lemma(discharge,[]))).
% 0.77/0.97 tff(930,plain,
% 0.77/0.97 (hskp24),
% 0.77/0.97 inference(unit_resolution,[status(thm)],[929, 917, 854, 884])).
% 0.77/0.97 tff(931,plain,
% 0.77/0.97 (~c3_1(a280)),
% 0.77/0.97 inference(unit_resolution,[status(thm)],[343, 930])).
% 0.77/0.97 tff(932,plain,
% 0.77/0.97 (c1_1(a280)),
% 0.77/0.97 inference(unit_resolution,[status(thm)],[363, 930])).
% 0.77/0.97 tff(933,plain,
% 0.77/0.97 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | (c3_1(a280) | c1_1(a239) | c1_1(a218) | c2_1(a218) | (~ndr1_0) | (~c3_1(a218)) | c0_1(a239) | (~c2_1(a239)) | (~c0_1(a280)) | (~c1_1(a280)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | c3_1(a280) | c1_1(a239) | c1_1(a218) | c2_1(a218) | (~ndr1_0) | (~c3_1(a218)) | c0_1(a239) | (~c2_1(a239)) | (~c0_1(a280)) | (~c1_1(a280)))),
% 0.77/0.97 inference(rewrite,[status(thm)],[])).
% 0.77/0.97 tff(934,plain,
% 0.77/0.97 (((~ndr1_0) | c3_1(a280) | (~c1_1(a280)) | (~c0_1(a280)) | c1_1(a218) | c2_1(a218) | (~c3_1(a218)) | c0_1(a239) | c1_1(a239) | (~c2_1(a239))) <=> (c3_1(a280) | c1_1(a239) | c1_1(a218) | c2_1(a218) | (~ndr1_0) | (~c3_1(a218)) | c0_1(a239) | (~c2_1(a239)) | (~c0_1(a280)) | (~c1_1(a280)))),
% 0.77/0.97 inference(rewrite,[status(thm)],[])).
% 0.77/0.97 tff(935,plain,
% 0.77/0.97 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a280) | (~c1_1(a280)) | (~c0_1(a280)) | c1_1(a218) | c2_1(a218) | (~c3_1(a218)) | c0_1(a239) | c1_1(a239) | (~c2_1(a239)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | (c3_1(a280) | c1_1(a239) | c1_1(a218) | c2_1(a218) | (~ndr1_0) | (~c3_1(a218)) | c0_1(a239) | (~c2_1(a239)) | (~c0_1(a280)) | (~c1_1(a280))))),
% 0.77/0.97 inference(monotonicity,[status(thm)],[934])).
% 0.77/0.97 tff(936,plain,
% 0.77/0.97 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a280) | (~c1_1(a280)) | (~c0_1(a280)) | c1_1(a218) | c2_1(a218) | (~c3_1(a218)) | c0_1(a239) | c1_1(a239) | (~c2_1(a239)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | c3_1(a280) | c1_1(a239) | c1_1(a218) | c2_1(a218) | (~ndr1_0) | (~c3_1(a218)) | c0_1(a239) | (~c2_1(a239)) | (~c0_1(a280)) | (~c1_1(a280)))),
% 0.77/0.97 inference(transitivity,[status(thm)],[935, 933])).
% 0.77/0.97 tff(937,plain,
% 0.77/0.97 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a280) | (~c1_1(a280)) | (~c0_1(a280)) | c1_1(a218) | c2_1(a218) | (~c3_1(a218)) | c0_1(a239) | c1_1(a239) | (~c2_1(a239)))),
% 0.77/0.97 inference(quant_inst,[status(thm)],[])).
% 0.77/0.97 tff(938,plain,
% 0.77/0.97 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | c3_1(a280) | c1_1(a239) | c1_1(a218) | c2_1(a218) | (~ndr1_0) | (~c3_1(a218)) | c0_1(a239) | (~c2_1(a239)) | (~c0_1(a280)) | (~c1_1(a280))),
% 0.77/0.97 inference(modus_ponens,[status(thm)],[937, 936])).
% 0.77/0.97 tff(939,plain,
% 0.77/0.97 (~c0_1(a280)),
% 0.77/0.97 inference(unit_resolution,[status(thm)],[938, 110, 932, 870, 719, 931, 884, 718, 717, 716, 878])).
% 0.77/0.97 tff(940,plain,
% 0.77/0.97 (~c2_1(a280)),
% 0.77/0.97 inference(unit_resolution,[status(thm)],[349, 930])).
% 0.77/0.97 tff(941,plain,
% 0.77/0.97 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp9 | c2_1(a280) | c3_1(a280) | (~ndr1_0) | (~c3_1(a239)) | c0_1(a239) | (~c2_1(a239)) | c0_1(a280))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp9 | c2_1(a280) | c3_1(a280) | (~ndr1_0) | (~c3_1(a239)) | c0_1(a239) | (~c2_1(a239)) | c0_1(a280))),
% 0.77/0.97 inference(rewrite,[status(thm)],[])).
% 0.77/0.97 tff(942,plain,
% 0.77/0.97 ((hskp9 | (~ndr1_0) | c0_1(a239) | (~c2_1(a239)) | (~c3_1(a239)) | c3_1(a280) | c0_1(a280) | c2_1(a280)) <=> (hskp9 | c2_1(a280) | c3_1(a280) | (~ndr1_0) | (~c3_1(a239)) | c0_1(a239) | (~c2_1(a239)) | c0_1(a280))),
% 0.77/0.97 inference(rewrite,[status(thm)],[])).
% 0.77/0.97 tff(943,plain,
% 0.77/0.97 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp9 | (~ndr1_0) | c0_1(a239) | (~c2_1(a239)) | (~c3_1(a239)) | c3_1(a280) | c0_1(a280) | c2_1(a280))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp9 | c2_1(a280) | c3_1(a280) | (~ndr1_0) | (~c3_1(a239)) | c0_1(a239) | (~c2_1(a239)) | c0_1(a280)))),
% 0.77/0.97 inference(monotonicity,[status(thm)],[942])).
% 0.77/0.97 tff(944,plain,
% 0.77/0.97 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp9 | (~ndr1_0) | c0_1(a239) | (~c2_1(a239)) | (~c3_1(a239)) | c3_1(a280) | c0_1(a280) | c2_1(a280))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp9 | c2_1(a280) | c3_1(a280) | (~ndr1_0) | (~c3_1(a239)) | c0_1(a239) | (~c2_1(a239)) | c0_1(a280))),
% 0.77/0.97 inference(transitivity,[status(thm)],[943, 941])).
% 0.77/0.97 tff(945,plain,
% 0.77/0.97 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp9 | (~ndr1_0) | c0_1(a239) | (~c2_1(a239)) | (~c3_1(a239)) | c3_1(a280) | c0_1(a280) | c2_1(a280))),
% 0.77/0.97 inference(quant_inst,[status(thm)],[])).
% 0.77/0.97 tff(946,plain,
% 0.77/0.97 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp9 | c2_1(a280) | c3_1(a280) | (~ndr1_0) | (~c3_1(a239)) | c0_1(a239) | (~c2_1(a239)) | c0_1(a280)),
% 0.77/0.97 inference(modus_ponens,[status(thm)],[945, 944])).
% 0.77/0.97 tff(947,plain,
% 0.77/0.97 ($false),
% 0.77/0.97 inference(unit_resolution,[status(thm)],[946, 110, 23, 870, 862, 940, 931, 905, 878, 939])).
% 0.77/0.97 tff(948,plain,((~hskp13) | hskp9 | (~c3_1(a218)) | c1_1(a218) | c2_1(a218) | (~c1_1(a259)) | hskp18 | (~c3_1(a259)) | c2_1(a259) | (~c0_1(a259)) | (~c2_1(a215)) | c0_1(a215) | c1_1(a215)), inference(lemma,lemma(discharge,[]))).
% 0.77/0.97 tff(949,plain,
% 0.77/0.97 (~hskp13),
% 0.77/0.97 inference(unit_resolution,[status(thm)],[948, 843, 764, 763, 762, 811, 596, 793, 785, 784, 152, 151, 150])).
% 0.77/0.97 tff(950,plain,
% 0.77/0.97 ((hskp16 | hskp13 | hskp12) <=> (hskp16 | hskp13 | hskp12)),
% 0.77/0.97 inference(rewrite,[status(thm)],[])).
% 0.77/0.97 tff(951,plain,
% 0.77/0.97 (((hskp12 | hskp16) | hskp13) <=> (hskp16 | hskp13 | hskp12)),
% 0.77/0.97 inference(rewrite,[status(thm)],[])).
% 0.77/0.97 tff(952,axiom,((hskp12 | hskp16) | hskp13), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause38')).
% 0.77/0.97 tff(953,plain,
% 0.77/0.97 (hskp16 | hskp13 | hskp12),
% 0.77/0.97 inference(modus_ponens,[status(thm)],[952, 951])).
% 0.77/0.97 tff(954,plain,
% 0.77/0.97 (hskp16 | hskp13 | hskp12),
% 0.77/0.97 inference(modus_ponens,[status(thm)],[953, 950])).
% 0.77/0.97 tff(955,plain,
% 0.77/0.97 (hskp16 | hskp13 | hskp12),
% 0.77/0.97 inference(modus_ponens,[status(thm)],[954, 950])).
% 0.77/0.97 tff(956,plain,
% 0.77/0.97 (hskp16 | hskp13 | hskp12),
% 0.77/0.97 inference(modus_ponens,[status(thm)],[955, 950])).
% 0.77/0.97 tff(957,plain,
% 0.77/0.97 (hskp16 | hskp13 | hskp12),
% 0.77/0.97 inference(modus_ponens,[status(thm)],[956, 950])).
% 0.77/0.97 tff(958,plain,
% 0.77/0.97 (hskp16),
% 0.77/0.97 inference(unit_resolution,[status(thm)],[957, 949, 765])).
% 0.77/0.97 tff(959,plain,
% 0.77/0.97 (~c3_1(a245)),
% 0.77/0.97 inference(unit_resolution,[status(thm)],[463, 958])).
% 0.77/0.97 tff(960,plain,
% 0.77/0.97 (~c1_1(a245)),
% 0.77/0.97 inference(unit_resolution,[status(thm)],[469, 958])).
% 0.77/0.97 tff(961,plain,
% 0.77/0.97 (c0_1(a245)),
% 0.77/0.97 inference(unit_resolution,[status(thm)],[477, 958])).
% 0.77/0.97 tff(962,plain,
% 0.77/0.97 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | (c2_1(a259) | c1_1(a245) | c3_1(a245) | c1_1(a213) | c3_1(a213) | (~ndr1_0) | (~c2_1(a213)) | (~c0_1(a245)) | (~c3_1(a259)) | (~c0_1(a259)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | c2_1(a259) | c1_1(a245) | c3_1(a245) | c1_1(a213) | c3_1(a213) | (~ndr1_0) | (~c2_1(a213)) | (~c0_1(a245)) | (~c3_1(a259)) | (~c0_1(a259)))),
% 0.77/0.97 inference(rewrite,[status(thm)],[])).
% 0.77/0.97 tff(963,plain,
% 0.77/0.97 (((~ndr1_0) | c2_1(a259) | (~c3_1(a259)) | (~c0_1(a259)) | c3_1(a213) | c1_1(a213) | (~c2_1(a213)) | c3_1(a245) | c1_1(a245) | (~c0_1(a245))) <=> (c2_1(a259) | c1_1(a245) | c3_1(a245) | c1_1(a213) | c3_1(a213) | (~ndr1_0) | (~c2_1(a213)) | (~c0_1(a245)) | (~c3_1(a259)) | (~c0_1(a259)))),
% 0.77/0.97 inference(rewrite,[status(thm)],[])).
% 0.77/0.97 tff(964,plain,
% 0.77/0.97 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a259) | (~c3_1(a259)) | (~c0_1(a259)) | c3_1(a213) | c1_1(a213) | (~c2_1(a213)) | c3_1(a245) | c1_1(a245) | (~c0_1(a245)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | (c2_1(a259) | c1_1(a245) | c3_1(a245) | c1_1(a213) | c3_1(a213) | (~ndr1_0) | (~c2_1(a213)) | (~c0_1(a245)) | (~c3_1(a259)) | (~c0_1(a259))))),
% 0.77/0.97 inference(monotonicity,[status(thm)],[963])).
% 0.77/0.97 tff(965,plain,
% 0.77/0.97 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a259) | (~c3_1(a259)) | (~c0_1(a259)) | c3_1(a213) | c1_1(a213) | (~c2_1(a213)) | c3_1(a245) | c1_1(a245) | (~c0_1(a245)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | c2_1(a259) | c1_1(a245) | c3_1(a245) | c1_1(a213) | c3_1(a213) | (~ndr1_0) | (~c2_1(a213)) | (~c0_1(a245)) | (~c3_1(a259)) | (~c0_1(a259)))),
% 0.77/0.97 inference(transitivity,[status(thm)],[964, 962])).
% 0.77/0.97 tff(966,plain,
% 0.77/0.97 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a259) | (~c3_1(a259)) | (~c0_1(a259)) | c3_1(a213) | c1_1(a213) | (~c2_1(a213)) | c3_1(a245) | c1_1(a245) | (~c0_1(a245)))),
% 0.77/0.97 inference(quant_inst,[status(thm)],[])).
% 0.77/0.97 tff(967,plain,
% 0.77/0.97 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | c2_1(a259) | c1_1(a245) | c3_1(a245) | c1_1(a213) | c3_1(a213) | (~ndr1_0) | (~c2_1(a213)) | (~c0_1(a245)) | (~c3_1(a259)) | (~c0_1(a259))),
% 0.77/0.97 inference(modus_ponens,[status(thm)],[966, 965])).
% 0.77/0.97 tff(968,plain,
% 0.77/0.97 ($false),
% 0.77/0.97 inference(unit_resolution,[status(thm)],[967, 110, 784, 793, 961, 768, 785, 960, 959, 767, 766, 22])).
% 0.77/0.97 tff(969,plain,(c1_1(a213) | (~c2_1(a213)) | c2_1(a259) | c3_1(a213) | hskp18 | (~c2_1(a215)) | c0_1(a215) | c1_1(a215) | (~c1_1(a248)) | (~c3_1(a248)) | c2_1(a248)), inference(lemma,lemma(discharge,[]))).
% 0.77/0.97 tff(970,plain,
% 0.77/0.97 (c2_1(a259)),
% 0.77/0.97 inference(unit_resolution,[status(thm)],[969, 751, 759, 745, 596, 152, 151, 150, 642, 641, 640])).
% 0.77/0.97 tff(971,plain,
% 0.77/0.97 (((~hskp21) | (~c2_1(a259))) <=> ((~hskp21) | (~c2_1(a259)))),
% 0.77/0.97 inference(rewrite,[status(thm)],[])).
% 0.77/0.97 tff(972,plain,
% 0.77/0.97 (((~c2_1(a259)) | (~hskp21)) <=> ((~hskp21) | (~c2_1(a259)))),
% 0.77/0.97 inference(rewrite,[status(thm)],[])).
% 0.77/0.97 tff(973,axiom,((~c2_1(a259)) | (~hskp21)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause94')).
% 0.77/0.97 tff(974,plain,
% 0.77/0.97 ((~hskp21) | (~c2_1(a259))),
% 0.77/0.97 inference(modus_ponens,[status(thm)],[973, 972])).
% 0.77/0.97 tff(975,plain,
% 0.77/0.97 ((~hskp21) | (~c2_1(a259))),
% 0.77/0.97 inference(modus_ponens,[status(thm)],[974, 971])).
% 0.77/0.97 tff(976,plain,
% 0.77/0.97 (~hskp21),
% 0.77/0.97 inference(unit_resolution,[status(thm)],[975, 970])).
% 0.77/0.97 tff(977,plain,
% 0.77/0.97 ($false),
% 0.77/0.97 inference(unit_resolution,[status(thm)],[774, 110, 976, 765, 759, 751, 745, 738])).
% 0.77/0.97 tff(978,plain,((~hskp0) | hskp18 | (~c2_1(a215)) | c0_1(a215) | c1_1(a215) | (~c1_1(a248)) | (~c3_1(a248)) | c2_1(a248)), inference(lemma,lemma(discharge,[]))).
% 0.77/0.97 tff(979,plain,
% 0.77/0.97 (~hskp0),
% 0.77/0.97 inference(unit_resolution,[status(thm)],[978, 662, 596, 661, 660, 624, 638, 630])).
% 0.77/0.97 tff(980,assumption,(~hskp0), introduced(assumption)).
% 0.77/0.97 tff(981,plain,
% 0.77/0.97 ((hskp12 | hskp1 | hskp0) <=> (hskp12 | hskp1 | hskp0)),
% 0.77/0.97 inference(rewrite,[status(thm)],[])).
% 0.77/0.97 tff(982,plain,
% 0.77/0.97 (((hskp12 | hskp1) | hskp0) <=> (hskp12 | hskp1 | hskp0)),
% 0.77/0.97 inference(rewrite,[status(thm)],[])).
% 0.77/0.97 tff(983,plain,
% 0.77/0.97 ((hskp12 | hskp1) <=> (hskp12 | hskp1)),
% 0.77/0.97 inference(rewrite,[status(thm)],[])).
% 0.77/0.97 tff(984,plain,
% 0.77/0.97 (((hskp12 | hskp1) | hskp0) <=> ((hskp12 | hskp1) | hskp0)),
% 0.77/0.97 inference(monotonicity,[status(thm)],[983])).
% 0.77/0.97 tff(985,plain,
% 0.77/0.97 (((hskp12 | hskp1) | hskp0) <=> (hskp12 | hskp1 | hskp0)),
% 0.77/0.97 inference(transitivity,[status(thm)],[984, 982])).
% 0.77/0.97 tff(986,axiom,((hskp12 | hskp1) | hskp0), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause39')).
% 0.77/0.97 tff(987,plain,
% 0.77/0.97 (hskp12 | hskp1 | hskp0),
% 0.77/0.97 inference(modus_ponens,[status(thm)],[986, 985])).
% 0.77/0.97 tff(988,plain,
% 0.77/0.97 (hskp12 | hskp1 | hskp0),
% 0.77/0.97 inference(modus_ponens,[status(thm)],[987, 981])).
% 0.77/0.97 tff(989,plain,
% 0.77/0.97 (hskp12 | hskp1 | hskp0),
% 0.77/0.97 inference(modus_ponens,[status(thm)],[988, 981])).
% 0.77/0.97 tff(990,plain,
% 0.77/0.97 (hskp12 | hskp1 | hskp0),
% 0.77/0.97 inference(modus_ponens,[status(thm)],[989, 981])).
% 0.77/0.97 tff(991,plain,
% 0.77/0.97 (hskp12 | hskp1 | hskp0),
% 0.77/0.97 inference(modus_ponens,[status(thm)],[990, 981])).
% 0.77/0.97 tff(992,plain,
% 0.77/0.97 (hskp1),
% 0.77/0.97 inference(unit_resolution,[status(thm)],[991, 980, 526])).
% 0.77/0.97 tff(993,plain,
% 0.77/0.97 (((~hskp1) | (~c3_1(a214))) <=> ((~hskp1) | (~c3_1(a214)))),
% 0.77/0.97 inference(rewrite,[status(thm)],[])).
% 0.77/0.97 tff(994,plain,
% 0.77/0.97 (((~c3_1(a214)) | (~hskp1)) <=> ((~hskp1) | (~c3_1(a214)))),
% 0.77/0.97 inference(rewrite,[status(thm)],[])).
% 0.77/0.97 tff(995,axiom,((~c3_1(a214)) | (~hskp1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause127')).
% 0.77/0.97 tff(996,plain,
% 0.77/0.97 ((~hskp1) | (~c3_1(a214))),
% 0.77/0.97 inference(modus_ponens,[status(thm)],[995, 994])).
% 0.77/0.97 tff(997,plain,
% 0.77/0.97 ((~hskp1) | (~c3_1(a214))),
% 0.77/0.97 inference(modus_ponens,[status(thm)],[996, 993])).
% 0.77/0.97 tff(998,plain,
% 0.77/0.97 (~c3_1(a214)),
% 0.77/0.97 inference(unit_resolution,[status(thm)],[997, 992])).
% 0.77/0.97 tff(999,plain,
% 0.77/0.97 (^[U: $i] : refl((hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) <=> (hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)))),
% 0.77/0.97 inference(bind,[status(th)],[])).
% 0.77/0.97 tff(1000,plain,
% 0.77/0.97 (![U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) <=> ![U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 0.77/0.97 inference(quant_intro,[status(thm)],[999])).
% 0.77/0.97 tff(1001,plain,
% 0.77/0.97 (![U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) <=> ![U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 0.77/0.97 inference(rewrite,[status(thm)],[])).
% 0.77/0.97 tff(1002,plain,
% 0.77/0.97 (^[U: $i] : 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))))),
% 0.77/0.97 inference(bind,[status(th)],[])).
% 0.77/0.97 tff(1003,plain,
% 0.77/0.97 (![U: $i] : (((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) | hskp0) <=> ![U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 0.77/0.97 inference(quant_intro,[status(thm)],[1002])).
% 0.77/0.97 tff(1004,axiom,(![U: $i] : (((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) | hskp0)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause130')).
% 0.77/0.97 tff(1005,plain,
% 0.77/0.97 (![U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 0.77/0.97 inference(modus_ponens,[status(thm)],[1004, 1003])).
% 0.77/0.97 tff(1006,plain,
% 0.77/0.97 (![U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 0.77/0.97 inference(modus_ponens,[status(thm)],[1005, 1001])).
% 0.77/0.97 tff(1007,plain,(
% 0.77/0.97 ![U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 0.77/0.97 inference(skolemize,[status(sab)],[1006])).
% 0.77/0.97 tff(1008,plain,
% 0.77/0.97 (![U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 0.77/0.97 inference(modus_ponens,[status(thm)],[1007, 1000])).
% 0.77/0.97 tff(1009,plain,
% 0.77/0.97 (((~![U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp0 | c1_1(a218) | c2_1(a218) | (~ndr1_0) | c0_1(a218))) <=> ((~![U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp0 | c1_1(a218) | c2_1(a218) | (~ndr1_0) | c0_1(a218))),
% 0.77/0.97 inference(rewrite,[status(thm)],[])).
% 0.77/0.97 tff(1010,plain,
% 0.77/0.97 ((hskp0 | (~ndr1_0) | c2_1(a218) | c1_1(a218) | c0_1(a218)) <=> (hskp0 | c1_1(a218) | c2_1(a218) | (~ndr1_0) | c0_1(a218))),
% 0.77/0.97 inference(rewrite,[status(thm)],[])).
% 0.77/0.97 tff(1011,plain,
% 0.77/0.97 (((~![U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp0 | (~ndr1_0) | c2_1(a218) | c1_1(a218) | c0_1(a218))) <=> ((~![U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp0 | c1_1(a218) | c2_1(a218) | (~ndr1_0) | c0_1(a218)))),
% 0.77/0.97 inference(monotonicity,[status(thm)],[1010])).
% 0.77/0.97 tff(1012,plain,
% 0.77/0.97 (((~![U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp0 | (~ndr1_0) | c2_1(a218) | c1_1(a218) | c0_1(a218))) <=> ((~![U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp0 | c1_1(a218) | c2_1(a218) | (~ndr1_0) | c0_1(a218))),
% 0.77/0.97 inference(transitivity,[status(thm)],[1011, 1009])).
% 0.77/0.97 tff(1013,plain,
% 0.77/0.97 ((~![U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp0 | (~ndr1_0) | c2_1(a218) | c1_1(a218) | c0_1(a218))),
% 0.77/0.97 inference(quant_inst,[status(thm)],[])).
% 0.77/0.97 tff(1014,plain,
% 0.77/0.97 ((~![U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp0 | c1_1(a218) | c2_1(a218) | (~ndr1_0) | c0_1(a218)),
% 0.77/0.97 inference(modus_ponens,[status(thm)],[1013, 1012])).
% 0.77/0.97 tff(1015,plain,
% 0.77/0.97 (hskp0 | c0_1(a218)),
% 0.77/0.97 inference(unit_resolution,[status(thm)],[1014, 110, 718, 717, 1008])).
% 0.77/0.97 tff(1016,plain,
% 0.77/0.97 (c0_1(a218)),
% 0.77/0.97 inference(unit_resolution,[status(thm)],[1015, 980])).
% 0.77/0.97 tff(1017,plain,
% 0.77/0.97 (^[U: $i] : refl((hskp16 | hskp4 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> (hskp16 | hskp4 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))))),
% 0.77/0.97 inference(bind,[status(th)],[])).
% 0.77/0.97 tff(1018,plain,
% 0.77/0.97 (![U: $i] : (hskp16 | hskp4 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp16 | hskp4 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.77/0.97 inference(quant_intro,[status(thm)],[1017])).
% 0.77/0.97 tff(1019,plain,
% 0.77/0.97 (![U: $i] : (hskp16 | hskp4 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp16 | hskp4 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.77/0.97 inference(rewrite,[status(thm)],[])).
% 0.77/0.97 tff(1020,plain,
% 0.77/0.97 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp16) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp16))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp16) <=> (hskp16 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp16) <=> (hskp16 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp16) | hskp4) <=> ((hskp16 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp4))), rewrite(((hskp16 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp4) <=> (hskp16 | hskp4 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp16) | hskp4) <=> (hskp16 | hskp4 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))))),
% 0.77/0.97 inference(bind,[status(th)],[])).
% 0.77/0.97 tff(1021,plain,
% 0.77/0.97 (![U: $i] : ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp16) | hskp4) <=> ![U: $i] : (hskp16 | hskp4 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.77/0.97 inference(quant_intro,[status(thm)],[1020])).
% 0.77/0.97 tff(1022,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp16) | hskp4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause149')).
% 0.77/0.97 tff(1023,plain,
% 0.77/0.97 (![U: $i] : (hskp16 | hskp4 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.77/0.97 inference(modus_ponens,[status(thm)],[1022, 1021])).
% 0.77/0.97 tff(1024,plain,
% 0.77/0.97 (![U: $i] : (hskp16 | hskp4 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.77/0.97 inference(modus_ponens,[status(thm)],[1023, 1019])).
% 0.77/0.97 tff(1025,plain,(
% 0.77/0.97 ![U: $i] : (hskp16 | hskp4 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.77/0.97 inference(skolemize,[status(sab)],[1024])).
% 0.77/0.97 tff(1026,plain,
% 0.77/0.97 (![U: $i] : (hskp16 | hskp4 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.77/0.97 inference(modus_ponens,[status(thm)],[1025, 1018])).
% 0.77/0.97 tff(1027,plain,
% 0.77/0.97 (((~![U: $i] : (hskp16 | hskp4 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp16 | hskp4 | c1_1(a218) | (~ndr1_0) | (~c3_1(a218)) | (~c0_1(a218)))) <=> ((~![U: $i] : (hskp16 | hskp4 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp16 | hskp4 | c1_1(a218) | (~ndr1_0) | (~c3_1(a218)) | (~c0_1(a218)))),
% 0.77/0.97 inference(rewrite,[status(thm)],[])).
% 0.77/0.97 tff(1028,plain,
% 0.77/0.97 ((hskp16 | hskp4 | (~ndr1_0) | c1_1(a218) | (~c3_1(a218)) | (~c0_1(a218))) <=> (hskp16 | hskp4 | c1_1(a218) | (~ndr1_0) | (~c3_1(a218)) | (~c0_1(a218)))),
% 0.77/0.97 inference(rewrite,[status(thm)],[])).
% 0.77/0.97 tff(1029,plain,
% 0.77/0.97 (((~![U: $i] : (hskp16 | hskp4 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp16 | hskp4 | (~ndr1_0) | c1_1(a218) | (~c3_1(a218)) | (~c0_1(a218)))) <=> ((~![U: $i] : (hskp16 | hskp4 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp16 | hskp4 | c1_1(a218) | (~ndr1_0) | (~c3_1(a218)) | (~c0_1(a218))))),
% 0.77/0.98 inference(monotonicity,[status(thm)],[1028])).
% 0.77/0.98 tff(1030,plain,
% 0.77/0.98 (((~![U: $i] : (hskp16 | hskp4 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp16 | hskp4 | (~ndr1_0) | c1_1(a218) | (~c3_1(a218)) | (~c0_1(a218)))) <=> ((~![U: $i] : (hskp16 | hskp4 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp16 | hskp4 | c1_1(a218) | (~ndr1_0) | (~c3_1(a218)) | (~c0_1(a218)))),
% 0.77/0.98 inference(transitivity,[status(thm)],[1029, 1027])).
% 0.77/0.98 tff(1031,plain,
% 0.77/0.98 ((~![U: $i] : (hskp16 | hskp4 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp16 | hskp4 | (~ndr1_0) | c1_1(a218) | (~c3_1(a218)) | (~c0_1(a218)))),
% 0.77/0.98 inference(quant_inst,[status(thm)],[])).
% 0.77/0.98 tff(1032,plain,
% 0.77/0.98 ((~![U: $i] : (hskp16 | hskp4 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp16 | hskp4 | c1_1(a218) | (~ndr1_0) | (~c3_1(a218)) | (~c0_1(a218))),
% 0.77/0.98 inference(modus_ponens,[status(thm)],[1031, 1030])).
% 0.77/0.98 tff(1033,plain,
% 0.77/0.98 (hskp16 | hskp4 | (~c0_1(a218))),
% 0.77/0.98 inference(unit_resolution,[status(thm)],[1032, 110, 719, 718, 1026])).
% 0.77/0.98 tff(1034,plain,
% 0.77/0.98 (hskp16),
% 0.77/0.98 inference(unit_resolution,[status(thm)],[1033, 1016, 281])).
% 0.77/0.98 tff(1035,plain,
% 0.77/0.98 (~c3_1(a245)),
% 0.77/0.98 inference(unit_resolution,[status(thm)],[463, 1034])).
% 0.77/0.98 tff(1036,plain,
% 0.77/0.98 (~c1_1(a245)),
% 0.77/0.98 inference(unit_resolution,[status(thm)],[469, 1034])).
% 0.77/0.98 tff(1037,plain,
% 0.77/0.98 (((~hskp1) | c2_1(a214)) <=> ((~hskp1) | c2_1(a214))),
% 0.77/0.98 inference(rewrite,[status(thm)],[])).
% 0.77/0.98 tff(1038,axiom,((~hskp1) | c2_1(a214)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause84')).
% 0.77/0.98 tff(1039,plain,
% 0.77/0.98 ((~hskp1) | c2_1(a214)),
% 0.77/0.98 inference(modus_ponens,[status(thm)],[1038, 1037])).
% 0.77/0.98 tff(1040,plain,
% 0.77/0.98 ((~hskp1) | c2_1(a214)),
% 0.77/0.98 inference(modus_ponens,[status(thm)],[1039, 1037])).
% 0.77/0.98 tff(1041,plain,
% 0.77/0.98 ((~hskp1) | c2_1(a214)),
% 0.77/0.98 inference(modus_ponens,[status(thm)],[1040, 1037])).
% 0.77/0.98 tff(1042,plain,
% 0.77/0.98 ((~hskp1) | c2_1(a214)),
% 0.77/0.98 inference(modus_ponens,[status(thm)],[1041, 1037])).
% 0.77/0.98 tff(1043,plain,
% 0.77/0.98 ((~hskp1) | c2_1(a214)),
% 0.77/0.98 inference(modus_ponens,[status(thm)],[1042, 1037])).
% 0.77/0.98 tff(1044,plain,
% 0.77/0.98 (c2_1(a214)),
% 0.77/0.98 inference(unit_resolution,[status(thm)],[1043, 992])).
% 0.77/0.98 tff(1045,plain,
% 0.77/0.98 (c0_1(a245)),
% 0.77/0.98 inference(unit_resolution,[status(thm)],[477, 1034])).
% 0.77/0.98 tff(1046,plain,
% 0.77/0.98 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | (c2_1(a248) | c1_1(a245) | c3_1(a245) | c3_1(a214) | (~ndr1_0) | c1_1(a214) | (~c2_1(a214)) | (~c0_1(a245)) | (~c3_1(a248)) | (~c0_1(a248)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | c2_1(a248) | c1_1(a245) | c3_1(a245) | c3_1(a214) | (~ndr1_0) | c1_1(a214) | (~c2_1(a214)) | (~c0_1(a245)) | (~c3_1(a248)) | (~c0_1(a248)))),
% 0.77/0.98 inference(rewrite,[status(thm)],[])).
% 0.77/0.98 tff(1047,plain,
% 0.77/0.98 (((~ndr1_0) | c2_1(a248) | (~c3_1(a248)) | (~c0_1(a248)) | c3_1(a214) | c1_1(a214) | (~c2_1(a214)) | c3_1(a245) | c1_1(a245) | (~c0_1(a245))) <=> (c2_1(a248) | c1_1(a245) | c3_1(a245) | c3_1(a214) | (~ndr1_0) | c1_1(a214) | (~c2_1(a214)) | (~c0_1(a245)) | (~c3_1(a248)) | (~c0_1(a248)))),
% 0.77/0.98 inference(rewrite,[status(thm)],[])).
% 0.77/0.98 tff(1048,plain,
% 0.77/0.98 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a248) | (~c3_1(a248)) | (~c0_1(a248)) | c3_1(a214) | c1_1(a214) | (~c2_1(a214)) | c3_1(a245) | c1_1(a245) | (~c0_1(a245)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | (c2_1(a248) | c1_1(a245) | c3_1(a245) | c3_1(a214) | (~ndr1_0) | c1_1(a214) | (~c2_1(a214)) | (~c0_1(a245)) | (~c3_1(a248)) | (~c0_1(a248))))),
% 0.77/0.98 inference(monotonicity,[status(thm)],[1047])).
% 0.77/0.98 tff(1049,plain,
% 0.77/0.98 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a248) | (~c3_1(a248)) | (~c0_1(a248)) | c3_1(a214) | c1_1(a214) | (~c2_1(a214)) | c3_1(a245) | c1_1(a245) | (~c0_1(a245)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | c2_1(a248) | c1_1(a245) | c3_1(a245) | c3_1(a214) | (~ndr1_0) | c1_1(a214) | (~c2_1(a214)) | (~c0_1(a245)) | (~c3_1(a248)) | (~c0_1(a248)))),
% 0.77/0.98 inference(transitivity,[status(thm)],[1048, 1046])).
% 0.77/0.98 tff(1050,plain,
% 0.77/0.98 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a248) | (~c3_1(a248)) | (~c0_1(a248)) | c3_1(a214) | c1_1(a214) | (~c2_1(a214)) | c3_1(a245) | c1_1(a245) | (~c0_1(a245)))),
% 0.77/0.98 inference(quant_inst,[status(thm)],[])).
% 0.77/0.98 tff(1051,plain,
% 0.77/0.98 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | c2_1(a248) | c1_1(a245) | c3_1(a245) | c3_1(a214) | (~ndr1_0) | c1_1(a214) | (~c2_1(a214)) | (~c0_1(a245)) | (~c3_1(a248)) | (~c0_1(a248))),
% 0.77/0.98 inference(modus_ponens,[status(thm)],[1050, 1049])).
% 0.77/0.98 tff(1052,plain,
% 0.77/0.98 (c1_1(a214)),
% 0.77/0.98 inference(unit_resolution,[status(thm)],[1051, 110, 641, 1045, 1044, 640, 1036, 1035, 998, 22, 690])).
% 0.77/0.98 tff(1053,plain,
% 0.77/0.98 (((~hskp1) | (~c0_1(a214))) <=> ((~hskp1) | (~c0_1(a214)))),
% 0.77/0.98 inference(rewrite,[status(thm)],[])).
% 0.77/0.98 tff(1054,plain,
% 0.77/0.98 (((~c0_1(a214)) | (~hskp1)) <=> ((~hskp1) | (~c0_1(a214)))),
% 0.77/0.98 inference(rewrite,[status(thm)],[])).
% 0.77/0.98 tff(1055,axiom,((~c0_1(a214)) | (~hskp1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause126')).
% 0.77/0.98 tff(1056,plain,
% 0.77/0.98 ((~hskp1) | (~c0_1(a214))),
% 0.77/0.98 inference(modus_ponens,[status(thm)],[1055, 1054])).
% 0.77/0.98 tff(1057,plain,
% 0.77/0.98 ((~hskp1) | (~c0_1(a214))),
% 0.77/0.98 inference(modus_ponens,[status(thm)],[1056, 1053])).
% 0.77/0.98 tff(1058,plain,
% 0.77/0.98 (~c0_1(a214)),
% 0.77/0.98 inference(unit_resolution,[status(thm)],[1057, 992])).
% 0.77/0.98 tff(1059,plain,
% 0.77/0.98 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp12 | c0_1(a214) | c3_1(a214) | (~ndr1_0) | (~c1_1(a214)) | (~c2_1(a214)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp12 | c0_1(a214) | c3_1(a214) | (~ndr1_0) | (~c1_1(a214)) | (~c2_1(a214)))),
% 0.77/0.98 inference(rewrite,[status(thm)],[])).
% 0.77/0.98 tff(1060,plain,
% 0.77/0.98 ((hskp12 | (~ndr1_0) | c3_1(a214) | (~c2_1(a214)) | (~c1_1(a214)) | c3_1(a214) | c0_1(a214) | (~c1_1(a214))) <=> (hskp12 | c0_1(a214) | c3_1(a214) | (~ndr1_0) | (~c1_1(a214)) | (~c2_1(a214)))),
% 0.77/0.98 inference(rewrite,[status(thm)],[])).
% 0.77/0.98 tff(1061,plain,
% 0.77/0.98 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp12 | (~ndr1_0) | c3_1(a214) | (~c2_1(a214)) | (~c1_1(a214)) | c3_1(a214) | c0_1(a214) | (~c1_1(a214)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp12 | c0_1(a214) | c3_1(a214) | (~ndr1_0) | (~c1_1(a214)) | (~c2_1(a214))))),
% 0.77/0.98 inference(monotonicity,[status(thm)],[1060])).
% 0.77/0.98 tff(1062,plain,
% 0.77/0.98 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp12 | (~ndr1_0) | c3_1(a214) | (~c2_1(a214)) | (~c1_1(a214)) | c3_1(a214) | c0_1(a214) | (~c1_1(a214)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp12 | c0_1(a214) | c3_1(a214) | (~ndr1_0) | (~c1_1(a214)) | (~c2_1(a214)))),
% 0.77/0.98 inference(transitivity,[status(thm)],[1061, 1059])).
% 0.77/0.98 tff(1063,plain,
% 0.77/0.98 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp12 | (~ndr1_0) | c3_1(a214) | (~c2_1(a214)) | (~c1_1(a214)) | c3_1(a214) | c0_1(a214) | (~c1_1(a214)))),
% 0.77/0.98 inference(quant_inst,[status(thm)],[])).
% 0.77/0.98 tff(1064,plain,
% 0.77/0.98 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp12 | c0_1(a214) | c3_1(a214) | (~ndr1_0) | (~c1_1(a214)) | (~c2_1(a214))),
% 0.77/0.98 inference(modus_ponens,[status(thm)],[1063, 1062])).
% 0.77/0.98 tff(1065,plain,
% 0.77/0.98 ($false),
% 0.77/0.98 inference(unit_resolution,[status(thm)],[1064, 110, 526, 1044, 1058, 998, 44, 1052])).
% 0.77/0.98 tff(1066,plain,(hskp0 | hskp12 | (~c3_1(a248)) | c2_1(a248) | (~c0_1(a248)) | hskp4 | (~c3_1(a218)) | c1_1(a218) | c2_1(a218)), inference(lemma,lemma(discharge,[]))).
% 0.77/0.98 tff(1067,plain,
% 0.77/0.98 (hskp4),
% 0.77/0.98 inference(unit_resolution,[status(thm)],[1066, 979, 638, 630, 651, 728, 689, 681, 675])).
% 0.77/0.98 tff(1068,plain,
% 0.77/0.98 (~c2_1(a217)),
% 0.77/0.98 inference(unit_resolution,[status(thm)],[186, 1067])).
% 0.77/0.98 tff(1069,plain,
% 0.77/0.98 (~c1_1(a217)),
% 0.77/0.98 inference(unit_resolution,[status(thm)],[192, 1067])).
% 0.77/0.98 tff(1070,plain,
% 0.77/0.98 (~c3_1(a217)),
% 0.77/0.98 inference(unit_resolution,[status(thm)],[180, 1067])).
% 0.77/0.98 tff(1071,assumption,(~c1_1(a217)), introduced(assumption)).
% 0.77/0.98 tff(1072,assumption,(~c2_1(a217)), introduced(assumption)).
% 0.77/0.98 tff(1073,assumption,(~c3_1(a217)), introduced(assumption)).
% 0.77/0.98 tff(1074,assumption,(c0_1(a217)), introduced(assumption)).
% 0.77/0.98 tff(1075,plain,
% 0.77/0.98 (^[U: $i] : refl((hskp19 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) <=> (hskp19 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))))),
% 0.77/0.98 inference(bind,[status(th)],[])).
% 0.77/0.98 tff(1076,plain,
% 0.77/0.98 (![U: $i] : (hskp19 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp19 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 0.77/0.98 inference(quant_intro,[status(thm)],[1075])).
% 0.77/0.98 tff(1077,plain,
% 0.77/0.98 (![U: $i] : (hskp19 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp19 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 0.77/0.98 inference(rewrite,[status(thm)],[])).
% 0.77/0.98 tff(1078,plain,
% 0.77/0.98 (^[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)) | hskp18) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) | hskp18))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) | hskp18) <=> (hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))), ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp18) <=> (hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))))), (((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp18) | hskp19) <=> ((hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) | hskp19))), rewrite(((hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) | hskp19) <=> (hskp19 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))), (((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp18) | hskp19) <=> (hskp19 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))))),
% 0.77/0.98 inference(bind,[status(th)],[])).
% 0.77/0.98 tff(1079,plain,
% 0.77/0.98 (![U: $i] : ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp18) | hskp19) <=> ![U: $i] : (hskp19 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 0.77/0.98 inference(quant_intro,[status(thm)],[1078])).
% 0.77/0.98 tff(1080,axiom,(![U: $i] : ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp18) | hskp19)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause141')).
% 0.77/0.98 tff(1081,plain,
% 0.77/0.98 (![U: $i] : (hskp19 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 0.77/0.98 inference(modus_ponens,[status(thm)],[1080, 1079])).
% 0.77/0.98 tff(1082,plain,
% 0.77/0.98 (![U: $i] : (hskp19 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 0.77/0.98 inference(modus_ponens,[status(thm)],[1081, 1077])).
% 0.77/0.98 tff(1083,plain,(
% 0.77/0.98 ![U: $i] : (hskp19 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 0.77/0.98 inference(skolemize,[status(sab)],[1082])).
% 0.77/0.98 tff(1084,plain,
% 0.77/0.98 (![U: $i] : (hskp19 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 0.77/0.98 inference(modus_ponens,[status(thm)],[1083, 1076])).
% 0.77/0.98 tff(1085,plain,
% 0.77/0.98 (((~![U: $i] : (hskp19 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp19 | hskp18 | c1_1(a217) | c2_1(a217) | (~ndr1_0) | (~c0_1(a217)))) <=> ((~![U: $i] : (hskp19 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp19 | hskp18 | c1_1(a217) | c2_1(a217) | (~ndr1_0) | (~c0_1(a217)))),
% 0.77/0.98 inference(rewrite,[status(thm)],[])).
% 0.77/0.98 tff(1086,plain,
% 0.77/0.98 ((hskp19 | hskp18 | (~ndr1_0) | c2_1(a217) | c1_1(a217) | (~c0_1(a217))) <=> (hskp19 | hskp18 | c1_1(a217) | c2_1(a217) | (~ndr1_0) | (~c0_1(a217)))),
% 0.77/0.98 inference(rewrite,[status(thm)],[])).
% 0.77/0.98 tff(1087,plain,
% 0.77/0.98 (((~![U: $i] : (hskp19 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp19 | hskp18 | (~ndr1_0) | c2_1(a217) | c1_1(a217) | (~c0_1(a217)))) <=> ((~![U: $i] : (hskp19 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp19 | hskp18 | c1_1(a217) | c2_1(a217) | (~ndr1_0) | (~c0_1(a217))))),
% 0.77/0.98 inference(monotonicity,[status(thm)],[1086])).
% 0.77/0.98 tff(1088,plain,
% 0.77/0.98 (((~![U: $i] : (hskp19 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp19 | hskp18 | (~ndr1_0) | c2_1(a217) | c1_1(a217) | (~c0_1(a217)))) <=> ((~![U: $i] : (hskp19 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp19 | hskp18 | c1_1(a217) | c2_1(a217) | (~ndr1_0) | (~c0_1(a217)))),
% 0.77/0.98 inference(transitivity,[status(thm)],[1087, 1085])).
% 0.77/0.98 tff(1089,plain,
% 0.77/0.98 ((~![U: $i] : (hskp19 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp19 | hskp18 | (~ndr1_0) | c2_1(a217) | c1_1(a217) | (~c0_1(a217)))),
% 0.77/0.98 inference(quant_inst,[status(thm)],[])).
% 0.77/0.98 tff(1090,plain,
% 0.77/0.98 ((~![U: $i] : (hskp19 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp19 | hskp18 | c1_1(a217) | c2_1(a217) | (~ndr1_0) | (~c0_1(a217))),
% 0.77/0.98 inference(modus_ponens,[status(thm)],[1089, 1088])).
% 0.77/0.98 tff(1091,plain,
% 0.77/0.98 (hskp19 | c1_1(a217) | (~c0_1(a217))),
% 0.77/0.98 inference(unit_resolution,[status(thm)],[1090, 110, 596, 1072, 1084])).
% 0.77/0.98 tff(1092,plain,
% 0.77/0.98 (hskp19),
% 0.77/0.98 inference(unit_resolution,[status(thm)],[1091, 1074, 1071])).
% 0.77/0.98 tff(1093,plain,
% 0.77/0.98 (~c0_1(a255)),
% 0.77/0.98 inference(unit_resolution,[status(thm)],[279, 1092])).
% 0.77/0.98 tff(1094,plain,
% 0.77/0.98 (~c1_1(a255)),
% 0.77/0.98 inference(unit_resolution,[status(thm)],[273, 1092])).
% 0.77/0.98 tff(1095,plain,
% 0.77/0.98 (~c3_1(a255)),
% 0.77/0.98 inference(unit_resolution,[status(thm)],[267, 1092])).
% 0.77/0.98 tff(1096,assumption,(~c1_1(a255)), introduced(assumption)).
% 0.77/0.98 tff(1097,assumption,(~c0_1(a255)), introduced(assumption)).
% 0.77/0.98 tff(1098,plain,
% 0.77/0.98 (((~![U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp0 | c0_1(a255) | c1_1(a255) | (~ndr1_0) | c2_1(a255))) <=> ((~![U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp0 | c0_1(a255) | c1_1(a255) | (~ndr1_0) | c2_1(a255))),
% 0.77/0.98 inference(rewrite,[status(thm)],[])).
% 0.77/0.98 tff(1099,plain,
% 0.77/0.98 ((hskp0 | (~ndr1_0) | c2_1(a255) | c1_1(a255) | c0_1(a255)) <=> (hskp0 | c0_1(a255) | c1_1(a255) | (~ndr1_0) | c2_1(a255))),
% 0.77/0.98 inference(rewrite,[status(thm)],[])).
% 0.77/0.98 tff(1100,plain,
% 0.77/0.98 (((~![U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp0 | (~ndr1_0) | c2_1(a255) | c1_1(a255) | c0_1(a255))) <=> ((~![U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp0 | c0_1(a255) | c1_1(a255) | (~ndr1_0) | c2_1(a255)))),
% 0.77/0.98 inference(monotonicity,[status(thm)],[1099])).
% 0.77/0.98 tff(1101,plain,
% 0.77/0.98 (((~![U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp0 | (~ndr1_0) | c2_1(a255) | c1_1(a255) | c0_1(a255))) <=> ((~![U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp0 | c0_1(a255) | c1_1(a255) | (~ndr1_0) | c2_1(a255))),
% 0.77/0.98 inference(transitivity,[status(thm)],[1100, 1098])).
% 0.77/0.98 tff(1102,plain,
% 0.77/0.98 ((~![U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp0 | (~ndr1_0) | c2_1(a255) | c1_1(a255) | c0_1(a255))),
% 0.77/0.98 inference(quant_inst,[status(thm)],[])).
% 0.77/0.98 tff(1103,plain,
% 0.77/0.98 ((~![U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp0 | c0_1(a255) | c1_1(a255) | (~ndr1_0) | c2_1(a255)),
% 0.77/0.98 inference(modus_ponens,[status(thm)],[1102, 1101])).
% 0.77/0.98 tff(1104,plain,
% 0.77/0.98 (hskp0 | c2_1(a255)),
% 0.77/0.98 inference(unit_resolution,[status(thm)],[1103, 110, 1097, 1096, 1008])).
% 0.77/0.98 tff(1105,plain,
% 0.77/0.98 (c2_1(a255)),
% 0.77/0.98 inference(unit_resolution,[status(thm)],[1104, 980])).
% 0.77/0.98 tff(1106,plain,
% 0.77/0.98 (((~![U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp0 | c1_1(a217) | c2_1(a217) | (~ndr1_0) | c0_1(a217))) <=> ((~![U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp0 | c1_1(a217) | c2_1(a217) | (~ndr1_0) | c0_1(a217))),
% 0.77/0.98 inference(rewrite,[status(thm)],[])).
% 0.77/0.98 tff(1107,plain,
% 0.77/0.98 ((hskp0 | (~ndr1_0) | c2_1(a217) | c1_1(a217) | c0_1(a217)) <=> (hskp0 | c1_1(a217) | c2_1(a217) | (~ndr1_0) | c0_1(a217))),
% 0.77/0.98 inference(rewrite,[status(thm)],[])).
% 0.77/0.98 tff(1108,plain,
% 0.77/0.98 (((~![U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp0 | (~ndr1_0) | c2_1(a217) | c1_1(a217) | c0_1(a217))) <=> ((~![U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp0 | c1_1(a217) | c2_1(a217) | (~ndr1_0) | c0_1(a217)))),
% 0.77/0.98 inference(monotonicity,[status(thm)],[1107])).
% 0.77/0.98 tff(1109,plain,
% 0.77/0.98 (((~![U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp0 | (~ndr1_0) | c2_1(a217) | c1_1(a217) | c0_1(a217))) <=> ((~![U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp0 | c1_1(a217) | c2_1(a217) | (~ndr1_0) | c0_1(a217))),
% 0.77/0.98 inference(transitivity,[status(thm)],[1108, 1106])).
% 0.77/0.98 tff(1110,plain,
% 0.77/0.98 ((~![U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp0 | (~ndr1_0) | c2_1(a217) | c1_1(a217) | c0_1(a217))),
% 0.77/0.98 inference(quant_inst,[status(thm)],[])).
% 0.77/0.98 tff(1111,plain,
% 0.77/0.98 ((~![U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp0 | c1_1(a217) | c2_1(a217) | (~ndr1_0) | c0_1(a217)),
% 0.77/0.98 inference(modus_ponens,[status(thm)],[1110, 1109])).
% 0.77/0.98 tff(1112,plain,
% 0.77/0.98 (hskp0 | c1_1(a217) | c0_1(a217)),
% 0.77/0.98 inference(unit_resolution,[status(thm)],[1111, 110, 1072, 1008])).
% 0.77/0.98 tff(1113,plain,
% 0.77/0.98 (c0_1(a217)),
% 0.77/0.98 inference(unit_resolution,[status(thm)],[1112, 980, 1071])).
% 0.77/0.98 tff(1114,assumption,(~c3_1(a255)), introduced(assumption)).
% 0.77/0.98 tff(1115,plain,
% 0.77/0.98 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | (c1_1(a255) | c3_1(a255) | c2_1(a218) | c1_1(a217) | c3_1(a217) | (~ndr1_0) | (~c0_1(a217)) | (~c3_1(a218)) | (~c0_1(a218)) | (~c2_1(a255)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | c1_1(a255) | c3_1(a255) | c2_1(a218) | c1_1(a217) | c3_1(a217) | (~ndr1_0) | (~c0_1(a217)) | (~c3_1(a218)) | (~c0_1(a218)) | (~c2_1(a255)))),
% 0.77/0.98 inference(rewrite,[status(thm)],[])).
% 0.77/0.98 tff(1116,plain,
% 0.77/0.98 (((~ndr1_0) | c2_1(a218) | (~c3_1(a218)) | (~c0_1(a218)) | c3_1(a255) | c1_1(a255) | (~c2_1(a255)) | c3_1(a217) | c1_1(a217) | (~c0_1(a217))) <=> (c1_1(a255) | c3_1(a255) | c2_1(a218) | c1_1(a217) | c3_1(a217) | (~ndr1_0) | (~c0_1(a217)) | (~c3_1(a218)) | (~c0_1(a218)) | (~c2_1(a255)))),
% 0.77/0.98 inference(rewrite,[status(thm)],[])).
% 0.77/0.98 tff(1117,plain,
% 0.77/0.98 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a218) | (~c3_1(a218)) | (~c0_1(a218)) | c3_1(a255) | c1_1(a255) | (~c2_1(a255)) | c3_1(a217) | c1_1(a217) | (~c0_1(a217)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | (c1_1(a255) | c3_1(a255) | c2_1(a218) | c1_1(a217) | c3_1(a217) | (~ndr1_0) | (~c0_1(a217)) | (~c3_1(a218)) | (~c0_1(a218)) | (~c2_1(a255))))),
% 0.77/0.98 inference(monotonicity,[status(thm)],[1116])).
% 0.77/0.98 tff(1118,plain,
% 0.77/0.98 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a218) | (~c3_1(a218)) | (~c0_1(a218)) | c3_1(a255) | c1_1(a255) | (~c2_1(a255)) | c3_1(a217) | c1_1(a217) | (~c0_1(a217)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | c1_1(a255) | c3_1(a255) | c2_1(a218) | c1_1(a217) | c3_1(a217) | (~ndr1_0) | (~c0_1(a217)) | (~c3_1(a218)) | (~c0_1(a218)) | (~c2_1(a255)))),
% 0.77/0.98 inference(transitivity,[status(thm)],[1117, 1115])).
% 0.77/0.98 tff(1119,plain,
% 0.77/0.98 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a218) | (~c3_1(a218)) | (~c0_1(a218)) | c3_1(a255) | c1_1(a255) | (~c2_1(a255)) | c3_1(a217) | c1_1(a217) | (~c0_1(a217)))),
% 0.77/0.98 inference(quant_inst,[status(thm)],[])).
% 0.77/0.98 tff(1120,plain,
% 0.77/0.98 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | c1_1(a255) | c3_1(a255) | c2_1(a218) | c1_1(a217) | c3_1(a217) | (~ndr1_0) | (~c0_1(a217)) | (~c3_1(a218)) | (~c0_1(a218)) | (~c2_1(a255))),
% 0.77/0.98 inference(modus_ponens,[status(thm)],[1119, 1118])).
% 0.77/0.98 tff(1121,plain,
% 0.77/0.98 ((~c0_1(a217)) | (~c0_1(a218)) | (~c2_1(a255))),
% 0.77/0.98 inference(unit_resolution,[status(thm)],[1120, 110, 719, 1096, 1114, 717, 1071, 1073, 22])).
% 0.77/0.98 tff(1122,plain,
% 0.77/0.98 ($false),
% 0.77/0.98 inference(unit_resolution,[status(thm)],[1121, 1113, 1016, 1105])).
% 0.77/0.98 tff(1123,plain,(hskp0 | (~c3_1(a218)) | c1_1(a255) | c3_1(a255) | c2_1(a218) | c1_1(a217) | c3_1(a217) | c0_1(a255) | c2_1(a217) | c1_1(a218)), inference(lemma,lemma(discharge,[]))).
% 0.77/0.98 tff(1124,plain,
% 0.77/0.98 (hskp0),
% 0.77/0.98 inference(unit_resolution,[status(thm)],[1123, 1095, 719, 1094, 717, 1071, 1073, 1093, 1072, 718])).
% 0.77/0.98 tff(1125,plain,
% 0.77/0.98 (~c3_1(a213)),
% 0.77/0.98 inference(unit_resolution,[status(thm)],[744, 1124])).
% 0.77/0.98 tff(1126,plain,
% 0.77/0.98 (~c1_1(a213)),
% 0.77/0.98 inference(unit_resolution,[status(thm)],[750, 1124])).
% 0.77/0.98 tff(1127,plain,
% 0.77/0.98 (c2_1(a213)),
% 0.77/0.98 inference(unit_resolution,[status(thm)],[758, 1124])).
% 0.77/0.98 tff(1128,plain,
% 0.77/0.98 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | (c2_1(a248) | c1_1(a217) | c3_1(a217) | c1_1(a213) | c3_1(a213) | (~ndr1_0) | (~c2_1(a213)) | (~c0_1(a217)) | (~c3_1(a248)) | (~c0_1(a248)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | c2_1(a248) | c1_1(a217) | c3_1(a217) | c1_1(a213) | c3_1(a213) | (~ndr1_0) | (~c2_1(a213)) | (~c0_1(a217)) | (~c3_1(a248)) | (~c0_1(a248)))),
% 0.77/0.98 inference(rewrite,[status(thm)],[])).
% 0.77/0.98 tff(1129,plain,
% 0.77/0.98 (((~ndr1_0) | c2_1(a248) | (~c3_1(a248)) | (~c0_1(a248)) | c3_1(a213) | c1_1(a213) | (~c2_1(a213)) | c3_1(a217) | c1_1(a217) | (~c0_1(a217))) <=> (c2_1(a248) | c1_1(a217) | c3_1(a217) | c1_1(a213) | c3_1(a213) | (~ndr1_0) | (~c2_1(a213)) | (~c0_1(a217)) | (~c3_1(a248)) | (~c0_1(a248)))),
% 0.77/0.98 inference(rewrite,[status(thm)],[])).
% 0.77/0.98 tff(1130,plain,
% 0.77/0.98 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a248) | (~c3_1(a248)) | (~c0_1(a248)) | c3_1(a213) | c1_1(a213) | (~c2_1(a213)) | c3_1(a217) | c1_1(a217) | (~c0_1(a217)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | (c2_1(a248) | c1_1(a217) | c3_1(a217) | c1_1(a213) | c3_1(a213) | (~ndr1_0) | (~c2_1(a213)) | (~c0_1(a217)) | (~c3_1(a248)) | (~c0_1(a248))))),
% 0.77/0.98 inference(monotonicity,[status(thm)],[1129])).
% 0.77/0.98 tff(1131,plain,
% 0.77/0.98 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a248) | (~c3_1(a248)) | (~c0_1(a248)) | c3_1(a213) | c1_1(a213) | (~c2_1(a213)) | c3_1(a217) | c1_1(a217) | (~c0_1(a217)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | c2_1(a248) | c1_1(a217) | c3_1(a217) | c1_1(a213) | c3_1(a213) | (~ndr1_0) | (~c2_1(a213)) | (~c0_1(a217)) | (~c3_1(a248)) | (~c0_1(a248)))),
% 0.77/0.98 inference(transitivity,[status(thm)],[1130, 1128])).
% 0.77/0.98 tff(1132,plain,
% 0.77/0.98 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a248) | (~c3_1(a248)) | (~c0_1(a248)) | c3_1(a213) | c1_1(a213) | (~c2_1(a213)) | c3_1(a217) | c1_1(a217) | (~c0_1(a217)))),
% 0.77/0.98 inference(quant_inst,[status(thm)],[])).
% 0.77/0.98 tff(1133,plain,
% 0.77/0.98 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | c2_1(a248) | c1_1(a217) | c3_1(a217) | c1_1(a213) | c3_1(a213) | (~ndr1_0) | (~c2_1(a213)) | (~c0_1(a217)) | (~c3_1(a248)) | (~c0_1(a248))),
% 0.77/0.98 inference(modus_ponens,[status(thm)],[1132, 1131])).
% 0.77/0.98 tff(1134,plain,
% 0.77/0.98 ($false),
% 0.77/0.98 inference(unit_resolution,[status(thm)],[1133, 110, 641, 1127, 640, 1071, 1073, 1126, 1125, 22, 690, 1074])).
% 0.77/0.98 tff(1135,plain,((~c0_1(a217)) | (~c3_1(a248)) | c2_1(a248) | c1_1(a217) | c3_1(a217) | (~c0_1(a248)) | (~c3_1(a218)) | c2_1(a218) | c2_1(a217) | c1_1(a218) | hskp18), inference(lemma,lemma(discharge,[]))).
% 0.77/0.98 tff(1136,plain,
% 0.77/0.98 (~c0_1(a217)),
% 0.77/0.98 inference(unit_resolution,[status(thm)],[1135, 1071, 640, 641, 1073, 760, 764, 762, 1072, 763, 596])).
% 0.77/0.98 tff(1137,plain,
% 0.77/0.98 (hskp0),
% 0.77/0.98 inference(unit_resolution,[status(thm)],[1112, 1136, 1071])).
% 0.77/0.98 tff(1138,plain,
% 0.77/0.98 (~c3_1(a213)),
% 0.77/0.98 inference(unit_resolution,[status(thm)],[744, 1137])).
% 0.77/0.98 tff(1139,plain,
% 0.77/0.98 (~c1_1(a213)),
% 0.77/0.98 inference(unit_resolution,[status(thm)],[750, 1137])).
% 0.77/0.98 tff(1140,assumption,(~c0_1(a217)), introduced(assumption)).
% 0.77/0.98 tff(1141,plain,
% 0.77/0.98 (hskp0),
% 0.77/0.98 inference(unit_resolution,[status(thm)],[1112, 1140, 1071])).
% 0.77/0.98 tff(1142,plain,
% 0.77/0.98 (~c3_1(a213)),
% 0.77/0.98 inference(unit_resolution,[status(thm)],[744, 1141])).
% 0.77/0.98 tff(1143,plain,
% 0.77/0.98 (c2_1(a213)),
% 0.77/0.98 inference(unit_resolution,[status(thm)],[758, 1141])).
% 0.77/0.98 tff(1144,plain,
% 0.77/0.98 (~c1_1(a213)),
% 0.77/0.98 inference(unit_resolution,[status(thm)],[750, 1141])).
% 0.77/0.98 tff(1145,plain,
% 0.77/0.98 (hskp21 | hskp12),
% 0.77/0.98 inference(unit_resolution,[status(thm)],[774, 110, 768, 767, 766, 738])).
% 0.77/0.98 tff(1146,plain,
% 0.77/0.98 (hskp21),
% 0.77/0.98 inference(unit_resolution,[status(thm)],[1145, 526])).
% 0.77/0.98 tff(1147,plain,
% 0.77/0.98 (~c2_1(a259)),
% 0.77/0.98 inference(unit_resolution,[status(thm)],[975, 1146])).
% 0.77/0.98 tff(1148,plain,
% 0.77/0.98 (c0_1(a259)),
% 0.77/0.98 inference(unit_resolution,[status(thm)],[783, 1146])).
% 0.77/0.98 tff(1149,plain,
% 0.77/0.98 (c1_1(a259)),
% 0.77/0.98 inference(unit_resolution,[status(thm)],[809, 110, 1148, 642, 641, 768, 1147, 640, 767, 766, 803])).
% 0.77/0.98 tff(1150,plain,
% 0.77/0.98 (c3_1(a259)),
% 0.77/0.98 inference(unit_resolution,[status(thm)],[792, 1146])).
% 0.77/0.98 tff(1151,plain,
% 0.77/0.98 (~hskp9),
% 0.77/0.98 inference(unit_resolution,[status(thm)],[842, 1150, 768, 1147, 767, 766, 1149])).
% 0.77/0.98 tff(1152,plain,
% 0.77/0.98 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp9 | c2_1(a217) | c3_1(a217) | c0_1(a215) | (~ndr1_0) | (~c3_1(a215)) | (~c2_1(a215)) | c0_1(a217))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp9 | c2_1(a217) | c3_1(a217) | c0_1(a215) | (~ndr1_0) | (~c3_1(a215)) | (~c2_1(a215)) | c0_1(a217))),
% 0.77/0.98 inference(rewrite,[status(thm)],[])).
% 0.77/0.98 tff(1153,plain,
% 0.77/0.98 ((hskp9 | (~ndr1_0) | c0_1(a215) | (~c2_1(a215)) | (~c3_1(a215)) | c3_1(a217) | c0_1(a217) | c2_1(a217)) <=> (hskp9 | c2_1(a217) | c3_1(a217) | c0_1(a215) | (~ndr1_0) | (~c3_1(a215)) | (~c2_1(a215)) | c0_1(a217))),
% 0.77/0.98 inference(rewrite,[status(thm)],[])).
% 0.77/0.98 tff(1154,plain,
% 0.77/0.98 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp9 | (~ndr1_0) | c0_1(a215) | (~c2_1(a215)) | (~c3_1(a215)) | c3_1(a217) | c0_1(a217) | c2_1(a217))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp9 | c2_1(a217) | c3_1(a217) | c0_1(a215) | (~ndr1_0) | (~c3_1(a215)) | (~c2_1(a215)) | c0_1(a217)))),
% 0.77/0.99 inference(monotonicity,[status(thm)],[1153])).
% 0.77/0.99 tff(1155,plain,
% 0.77/0.99 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp9 | (~ndr1_0) | c0_1(a215) | (~c2_1(a215)) | (~c3_1(a215)) | c3_1(a217) | c0_1(a217) | c2_1(a217))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp9 | c2_1(a217) | c3_1(a217) | c0_1(a215) | (~ndr1_0) | (~c3_1(a215)) | (~c2_1(a215)) | c0_1(a217))),
% 0.77/0.99 inference(transitivity,[status(thm)],[1154, 1152])).
% 0.77/0.99 tff(1156,plain,
% 0.77/0.99 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp9 | (~ndr1_0) | c0_1(a215) | (~c2_1(a215)) | (~c3_1(a215)) | c3_1(a217) | c0_1(a217) | c2_1(a217))),
% 0.77/0.99 inference(quant_inst,[status(thm)],[])).
% 0.77/0.99 tff(1157,plain,
% 0.77/0.99 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp9 | c2_1(a217) | c3_1(a217) | c0_1(a215) | (~ndr1_0) | (~c3_1(a215)) | (~c2_1(a215)) | c0_1(a217)),
% 0.77/0.99 inference(modus_ponens,[status(thm)],[1156, 1155])).
% 0.77/0.99 tff(1158,plain,
% 0.77/0.99 (hskp9 | c2_1(a217) | (~c3_1(a215)) | c0_1(a217)),
% 0.77/0.99 inference(unit_resolution,[status(thm)],[1157, 110, 152, 1073, 151, 905])).
% 0.77/0.99 tff(1159,plain,
% 0.77/0.99 (~c3_1(a215)),
% 0.77/0.99 inference(unit_resolution,[status(thm)],[1158, 1151, 1072, 1140])).
% 0.77/0.99 tff(1160,assumption,(~hskp16), introduced(assumption)).
% 0.77/0.99 tff(1161,plain,
% 0.77/0.99 (hskp13),
% 0.77/0.99 inference(unit_resolution,[status(thm)],[957, 526, 1160])).
% 0.77/0.99 tff(1162,plain,
% 0.77/0.99 (c3_1(a239)),
% 0.77/0.99 inference(unit_resolution,[status(thm)],[861, 1161])).
% 0.77/0.99 tff(1163,plain,
% 0.77/0.99 (c2_1(a239)),
% 0.77/0.99 inference(unit_resolution,[status(thm)],[869, 1161])).
% 0.77/0.99 tff(1164,plain,
% 0.77/0.99 (~c3_1(a215)),
% 0.77/0.99 inference(unit_resolution,[status(thm)],[1158, 23, 1072, 1140])).
% 0.77/0.99 tff(1165,plain,
% 0.77/0.99 (((~![U: $i] : (hskp21 | hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp21 | hskp12 | c1_1(a215) | (~ndr1_0) | c3_1(a215) | (~c2_1(a215)))) <=> ((~![U: $i] : (hskp21 | hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | hskp21 | hskp12 | c1_1(a215) | (~ndr1_0) | c3_1(a215) | (~c2_1(a215)))),
% 0.77/0.99 inference(rewrite,[status(thm)],[])).
% 0.77/0.99 tff(1166,plain,
% 0.77/0.99 ((hskp21 | hskp12 | (~ndr1_0) | c1_1(a215) | c3_1(a215) | (~c2_1(a215))) <=> (hskp21 | hskp12 | c1_1(a215) | (~ndr1_0) | c3_1(a215) | (~c2_1(a215)))),
% 0.77/0.99 inference(rewrite,[status(thm)],[])).
% 0.77/0.99 tff(1167,plain,
% 0.77/0.99 (((~![U: $i] : (hskp21 | hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp21 | hskp12 | (~ndr1_0) | c1_1(a215) | c3_1(a215) | (~c2_1(a215)))) <=> ((~![U: $i] : (hskp21 | hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp21 | hskp12 | c1_1(a215) | (~ndr1_0) | c3_1(a215) | (~c2_1(a215))))),
% 0.77/0.99 inference(monotonicity,[status(thm)],[1166])).
% 0.77/0.99 tff(1168,plain,
% 0.77/0.99 (((~![U: $i] : (hskp21 | hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp21 | hskp12 | (~ndr1_0) | c1_1(a215) | c3_1(a215) | (~c2_1(a215)))) <=> ((~![U: $i] : (hskp21 | hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | hskp21 | hskp12 | c1_1(a215) | (~ndr1_0) | c3_1(a215) | (~c2_1(a215)))),
% 0.77/0.99 inference(transitivity,[status(thm)],[1167, 1165])).
% 0.77/0.99 tff(1169,plain,
% 0.77/0.99 ((~![U: $i] : (hskp21 | hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp21 | hskp12 | (~ndr1_0) | c1_1(a215) | c3_1(a215) | (~c2_1(a215)))),
% 0.77/0.99 inference(quant_inst,[status(thm)],[])).
% 0.77/0.99 tff(1170,plain,
% 0.77/0.99 ((~![U: $i] : (hskp21 | hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | hskp21 | hskp12 | c1_1(a215) | (~ndr1_0) | c3_1(a215) | (~c2_1(a215))),
% 0.77/0.99 inference(modus_ponens,[status(thm)],[1169, 1168])).
% 0.77/0.99 tff(1171,plain,
% 0.77/0.99 (hskp21 | hskp12 | c3_1(a215)),
% 0.77/0.99 inference(unit_resolution,[status(thm)],[1170, 110, 152, 150, 738])).
% 0.77/0.99 tff(1172,plain,
% 0.77/0.99 (hskp21),
% 0.77/0.99 inference(unit_resolution,[status(thm)],[1171, 526, 1164])).
% 0.77/0.99 tff(1173,plain,
% 0.77/0.99 (c3_1(a259)),
% 0.77/0.99 inference(unit_resolution,[status(thm)],[792, 1172])).
% 0.77/0.99 tff(1174,plain,
% 0.77/0.99 (c0_1(a259)),
% 0.77/0.99 inference(unit_resolution,[status(thm)],[783, 1172])).
% 0.77/0.99 tff(1175,plain,
% 0.77/0.99 (~c0_1(a239)),
% 0.77/0.99 inference(unit_resolution,[status(thm)],[877, 110, 1174, 1173, 1163, 1162, 152, 785, 151, 150, 853])).
% 0.77/0.99 tff(1176,plain,
% 0.77/0.99 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp9 | c2_1(a217) | c3_1(a217) | (~ndr1_0) | c0_1(a217) | (~c3_1(a239)) | c0_1(a239) | (~c2_1(a239)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp9 | c2_1(a217) | c3_1(a217) | (~ndr1_0) | c0_1(a217) | (~c3_1(a239)) | c0_1(a239) | (~c2_1(a239)))),
% 0.77/0.99 inference(rewrite,[status(thm)],[])).
% 0.77/0.99 tff(1177,plain,
% 0.77/0.99 ((hskp9 | (~ndr1_0) | c0_1(a239) | (~c2_1(a239)) | (~c3_1(a239)) | c3_1(a217) | c0_1(a217) | c2_1(a217)) <=> (hskp9 | c2_1(a217) | c3_1(a217) | (~ndr1_0) | c0_1(a217) | (~c3_1(a239)) | c0_1(a239) | (~c2_1(a239)))),
% 0.77/0.99 inference(rewrite,[status(thm)],[])).
% 0.77/0.99 tff(1178,plain,
% 0.77/0.99 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp9 | (~ndr1_0) | c0_1(a239) | (~c2_1(a239)) | (~c3_1(a239)) | c3_1(a217) | c0_1(a217) | c2_1(a217))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp9 | c2_1(a217) | c3_1(a217) | (~ndr1_0) | c0_1(a217) | (~c3_1(a239)) | c0_1(a239) | (~c2_1(a239))))),
% 0.77/0.99 inference(monotonicity,[status(thm)],[1177])).
% 0.77/0.99 tff(1179,plain,
% 0.77/0.99 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp9 | (~ndr1_0) | c0_1(a239) | (~c2_1(a239)) | (~c3_1(a239)) | c3_1(a217) | c0_1(a217) | c2_1(a217))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp9 | c2_1(a217) | c3_1(a217) | (~ndr1_0) | c0_1(a217) | (~c3_1(a239)) | c0_1(a239) | (~c2_1(a239)))),
% 0.77/0.99 inference(transitivity,[status(thm)],[1178, 1176])).
% 0.77/0.99 tff(1180,plain,
% 0.77/0.99 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp9 | (~ndr1_0) | c0_1(a239) | (~c2_1(a239)) | (~c3_1(a239)) | c3_1(a217) | c0_1(a217) | c2_1(a217))),
% 0.77/0.99 inference(quant_inst,[status(thm)],[])).
% 0.77/0.99 tff(1181,plain,
% 0.77/0.99 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp9 | c2_1(a217) | c3_1(a217) | (~ndr1_0) | c0_1(a217) | (~c3_1(a239)) | c0_1(a239) | (~c2_1(a239))),
% 0.77/0.99 inference(modus_ponens,[status(thm)],[1180, 1179])).
% 0.77/0.99 tff(1182,plain,
% 0.77/0.99 ($false),
% 0.77/0.99 inference(unit_resolution,[status(thm)],[1181, 110, 23, 1163, 1162, 1072, 1073, 905, 1140, 1175])).
% 0.77/0.99 tff(1183,plain,(hskp12 | hskp9 | c2_1(a217) | c3_1(a217) | c0_1(a217) | (~c2_1(a215)) | c2_1(a259) | c0_1(a215) | c1_1(a215) | hskp16), inference(lemma,lemma(discharge,[]))).
% 0.77/0.99 tff(1184,plain,
% 0.77/0.99 (hskp16),
% 0.77/0.99 inference(unit_resolution,[status(thm)],[1183, 1151, 1072, 1073, 1140, 152, 526, 151, 150, 1147])).
% 0.77/0.99 tff(1185,plain,
% 0.77/0.99 (~c3_1(a245)),
% 0.77/0.99 inference(unit_resolution,[status(thm)],[463, 1184])).
% 0.77/0.99 tff(1186,plain,
% 0.77/0.99 (~c1_1(a245)),
% 0.77/0.99 inference(unit_resolution,[status(thm)],[469, 1184])).
% 0.77/0.99 tff(1187,plain,
% 0.77/0.99 (c0_1(a245)),
% 0.77/0.99 inference(unit_resolution,[status(thm)],[477, 1184])).
% 0.77/0.99 tff(1188,plain,
% 0.77/0.99 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | (c2_1(a259) | c1_1(a245) | c3_1(a245) | c1_1(a215) | (~ndr1_0) | c3_1(a215) | (~c2_1(a215)) | (~c0_1(a245)) | (~c3_1(a259)) | (~c0_1(a259)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | c2_1(a259) | c1_1(a245) | c3_1(a245) | c1_1(a215) | (~ndr1_0) | c3_1(a215) | (~c2_1(a215)) | (~c0_1(a245)) | (~c3_1(a259)) | (~c0_1(a259)))),
% 0.77/0.99 inference(rewrite,[status(thm)],[])).
% 0.77/0.99 tff(1189,plain,
% 0.77/0.99 (((~ndr1_0) | c2_1(a259) | (~c3_1(a259)) | (~c0_1(a259)) | c3_1(a215) | c1_1(a215) | (~c2_1(a215)) | c3_1(a245) | c1_1(a245) | (~c0_1(a245))) <=> (c2_1(a259) | c1_1(a245) | c3_1(a245) | c1_1(a215) | (~ndr1_0) | c3_1(a215) | (~c2_1(a215)) | (~c0_1(a245)) | (~c3_1(a259)) | (~c0_1(a259)))),
% 0.77/0.99 inference(rewrite,[status(thm)],[])).
% 0.77/0.99 tff(1190,plain,
% 0.77/0.99 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a259) | (~c3_1(a259)) | (~c0_1(a259)) | c3_1(a215) | c1_1(a215) | (~c2_1(a215)) | c3_1(a245) | c1_1(a245) | (~c0_1(a245)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | (c2_1(a259) | c1_1(a245) | c3_1(a245) | c1_1(a215) | (~ndr1_0) | c3_1(a215) | (~c2_1(a215)) | (~c0_1(a245)) | (~c3_1(a259)) | (~c0_1(a259))))),
% 0.77/0.99 inference(monotonicity,[status(thm)],[1189])).
% 0.77/0.99 tff(1191,plain,
% 0.77/0.99 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a259) | (~c3_1(a259)) | (~c0_1(a259)) | c3_1(a215) | c1_1(a215) | (~c2_1(a215)) | c3_1(a245) | c1_1(a245) | (~c0_1(a245)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | c2_1(a259) | c1_1(a245) | c3_1(a245) | c1_1(a215) | (~ndr1_0) | c3_1(a215) | (~c2_1(a215)) | (~c0_1(a245)) | (~c3_1(a259)) | (~c0_1(a259)))),
% 0.77/0.99 inference(transitivity,[status(thm)],[1190, 1188])).
% 0.77/0.99 tff(1192,plain,
% 0.77/0.99 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a259) | (~c3_1(a259)) | (~c0_1(a259)) | c3_1(a215) | c1_1(a215) | (~c2_1(a215)) | c3_1(a245) | c1_1(a245) | (~c0_1(a245)))),
% 0.77/0.99 inference(quant_inst,[status(thm)],[])).
% 0.77/0.99 tff(1193,plain,
% 0.77/0.99 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | c2_1(a259) | c1_1(a245) | c3_1(a245) | c1_1(a215) | (~ndr1_0) | c3_1(a215) | (~c2_1(a215)) | (~c0_1(a245)) | (~c3_1(a259)) | (~c0_1(a259))),
% 0.77/0.99 inference(modus_ponens,[status(thm)],[1192, 1191])).
% 0.77/0.99 tff(1194,plain,
% 0.77/0.99 ($false),
% 0.77/0.99 inference(unit_resolution,[status(thm)],[1193, 110, 1148, 1150, 1187, 152, 1147, 1186, 1185, 150, 22, 1159])).
% 0.77/0.99 tff(1195,plain,(hskp12 | (~c2_1(a215)) | c1_1(a215) | c2_1(a217) | c3_1(a217) | c0_1(a217) | c0_1(a215) | (~c2_1(a213)) | c1_1(a213) | c3_1(a213) | (~c1_1(a248)) | (~c3_1(a248)) | c2_1(a248)), inference(lemma,lemma(discharge,[]))).
% 0.77/0.99 tff(1196,plain,
% 0.77/0.99 ($false),
% 0.77/0.99 inference(unit_resolution,[status(thm)],[1195, 1144, 1143, 150, 1072, 1073, 152, 151, 526, 1140, 1142, 642, 641, 640])).
% 0.77/0.99 tff(1197,plain,(c0_1(a217) | c1_1(a215) | c2_1(a217) | c3_1(a217) | (~c2_1(a215)) | c0_1(a215) | hskp12 | (~c1_1(a248)) | (~c3_1(a248)) | c2_1(a248) | c1_1(a217)), inference(lemma,lemma(discharge,[]))).
% 0.77/0.99 tff(1198,plain,
% 0.77/0.99 (hskp12),
% 0.77/0.99 inference(unit_resolution,[status(thm)],[1197, 1136, 1072, 1073, 152, 151, 150, 642, 641, 640, 1071])).
% 0.77/0.99 tff(1199,plain,
% 0.77/0.99 (~c3_1(a237)),
% 0.77/0.99 inference(unit_resolution,[status(thm)],[696, 1198])).
% 0.77/0.99 tff(1200,plain,
% 0.77/0.99 (c2_1(a213)),
% 0.77/0.99 inference(unit_resolution,[status(thm)],[758, 1137])).
% 0.77/0.99 tff(1201,plain,
% 0.77/0.99 (c0_1(a237)),
% 0.77/0.99 inference(unit_resolution,[status(thm)],[575, 1198])).
% 0.77/0.99 tff(1202,plain,
% 0.77/0.99 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | (c2_1(a248) | c3_1(a237) | c1_1(a213) | c3_1(a213) | (~ndr1_0) | (~c2_1(a213)) | c1_1(a237) | (~c0_1(a237)) | (~c3_1(a248)) | (~c0_1(a248)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | c2_1(a248) | c3_1(a237) | c1_1(a213) | c3_1(a213) | (~ndr1_0) | (~c2_1(a213)) | c1_1(a237) | (~c0_1(a237)) | (~c3_1(a248)) | (~c0_1(a248)))),
% 0.77/0.99 inference(rewrite,[status(thm)],[])).
% 0.77/0.99 tff(1203,plain,
% 0.77/0.99 (((~ndr1_0) | c2_1(a248) | (~c3_1(a248)) | (~c0_1(a248)) | c3_1(a213) | c1_1(a213) | (~c2_1(a213)) | c3_1(a237) | c1_1(a237) | (~c0_1(a237))) <=> (c2_1(a248) | c3_1(a237) | c1_1(a213) | c3_1(a213) | (~ndr1_0) | (~c2_1(a213)) | c1_1(a237) | (~c0_1(a237)) | (~c3_1(a248)) | (~c0_1(a248)))),
% 0.77/0.99 inference(rewrite,[status(thm)],[])).
% 0.77/0.99 tff(1204,plain,
% 0.77/0.99 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a248) | (~c3_1(a248)) | (~c0_1(a248)) | c3_1(a213) | c1_1(a213) | (~c2_1(a213)) | c3_1(a237) | c1_1(a237) | (~c0_1(a237)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | (c2_1(a248) | c3_1(a237) | c1_1(a213) | c3_1(a213) | (~ndr1_0) | (~c2_1(a213)) | c1_1(a237) | (~c0_1(a237)) | (~c3_1(a248)) | (~c0_1(a248))))),
% 0.77/0.99 inference(monotonicity,[status(thm)],[1203])).
% 0.77/0.99 tff(1205,plain,
% 0.77/0.99 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a248) | (~c3_1(a248)) | (~c0_1(a248)) | c3_1(a213) | c1_1(a213) | (~c2_1(a213)) | c3_1(a237) | c1_1(a237) | (~c0_1(a237)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | c2_1(a248) | c3_1(a237) | c1_1(a213) | c3_1(a213) | (~ndr1_0) | (~c2_1(a213)) | c1_1(a237) | (~c0_1(a237)) | (~c3_1(a248)) | (~c0_1(a248)))),
% 0.77/0.99 inference(transitivity,[status(thm)],[1204, 1202])).
% 0.77/0.99 tff(1206,plain,
% 0.77/0.99 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a248) | (~c3_1(a248)) | (~c0_1(a248)) | c3_1(a213) | c1_1(a213) | (~c2_1(a213)) | c3_1(a237) | c1_1(a237) | (~c0_1(a237)))),
% 0.77/0.99 inference(quant_inst,[status(thm)],[])).
% 0.77/0.99 tff(1207,plain,
% 0.77/0.99 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | c2_1(a248) | c3_1(a237) | c1_1(a213) | c3_1(a213) | (~ndr1_0) | (~c2_1(a213)) | c1_1(a237) | (~c0_1(a237)) | (~c3_1(a248)) | (~c0_1(a248))),
% 0.77/0.99 inference(modus_ponens,[status(thm)],[1206, 1205])).
% 0.77/0.99 tff(1208,plain,
% 0.77/0.99 (c1_1(a237)),
% 0.77/0.99 inference(unit_resolution,[status(thm)],[1207, 110, 641, 1201, 1200, 640, 1199, 1139, 1138, 22, 760])).
% 0.77/0.99 tff(1209,plain,
% 0.77/0.99 ($false),
% 0.77/0.99 inference(unit_resolution,[status(thm)],[725, 110, 1201, 764, 152, 1199, 763, 762, 151, 150, 716, 1208])).
% 0.77/0.99 tff(1210,plain,(c1_1(a217) | (~c2_1(a215)) | c0_1(a215) | c1_1(a215) | (~c3_1(a248)) | c2_1(a248) | c2_1(a217) | c3_1(a217) | (~c1_1(a248)) | hskp18), inference(lemma,lemma(discharge,[]))).
% 0.77/0.99 tff(1211,plain,
% 0.77/0.99 ($false),
% 0.77/0.99 inference(unit_resolution,[status(thm)],[1210, 1070, 1069, 661, 660, 638, 630, 662, 1068, 624, 596])).
% 0.77/0.99 tff(1212,plain,(hskp27 | hskp18), inference(lemma,lemma(discharge,[]))).
% 0.77/0.99 tff(1213,plain,
% 0.77/0.99 (hskp27),
% 0.77/0.99 inference(unit_resolution,[status(thm)],[1212, 596])).
% 0.77/0.99 tff(1214,plain,
% 0.77/0.99 (((~hskp27) | c3_1(a261)) <=> ((~hskp27) | c3_1(a261))),
% 0.77/0.99 inference(rewrite,[status(thm)],[])).
% 0.77/0.99 tff(1215,axiom,((~hskp27) | c3_1(a261)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause48')).
% 0.77/0.99 tff(1216,plain,
% 0.77/0.99 ((~hskp27) | c3_1(a261)),
% 0.77/0.99 inference(modus_ponens,[status(thm)],[1215, 1214])).
% 0.77/0.99 tff(1217,plain,
% 0.77/0.99 ((~hskp27) | c3_1(a261)),
% 0.77/0.99 inference(modus_ponens,[status(thm)],[1216, 1214])).
% 0.77/0.99 tff(1218,plain,
% 0.77/0.99 ((~hskp27) | c3_1(a261)),
% 0.77/0.99 inference(modus_ponens,[status(thm)],[1217, 1214])).
% 0.77/0.99 tff(1219,plain,
% 0.77/0.99 ((~hskp27) | c3_1(a261)),
% 0.77/0.99 inference(modus_ponens,[status(thm)],[1218, 1214])).
% 0.77/0.99 tff(1220,plain,
% 0.77/0.99 ((~hskp27) | c3_1(a261)),
% 0.77/0.99 inference(modus_ponens,[status(thm)],[1219, 1214])).
% 0.77/0.99 tff(1221,plain,
% 0.77/0.99 (c3_1(a261)),
% 0.77/0.99 inference(unit_resolution,[status(thm)],[1220, 1213])).
% 0.77/0.99 tff(1222,plain,
% 0.77/0.99 (((~hskp27) | c2_1(a261)) <=> ((~hskp27) | c2_1(a261))),
% 0.77/0.99 inference(rewrite,[status(thm)],[])).
% 0.77/0.99 tff(1223,axiom,((~hskp27) | c2_1(a261)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause47')).
% 0.77/0.99 tff(1224,plain,
% 0.77/0.99 ((~hskp27) | c2_1(a261)),
% 0.77/0.99 inference(modus_ponens,[status(thm)],[1223, 1222])).
% 0.77/0.99 tff(1225,plain,
% 0.77/0.99 ((~hskp27) | c2_1(a261)),
% 0.77/0.99 inference(modus_ponens,[status(thm)],[1224, 1222])).
% 0.77/0.99 tff(1226,plain,
% 0.77/0.99 ((~hskp27) | c2_1(a261)),
% 0.77/0.99 inference(modus_ponens,[status(thm)],[1225, 1222])).
% 0.77/0.99 tff(1227,plain,
% 0.77/0.99 ((~hskp27) | c2_1(a261)),
% 0.77/0.99 inference(modus_ponens,[status(thm)],[1226, 1222])).
% 0.77/0.99 tff(1228,plain,
% 0.77/0.99 ((~hskp27) | c2_1(a261)),
% 0.77/0.99 inference(modus_ponens,[status(thm)],[1227, 1222])).
% 0.77/0.99 tff(1229,plain,
% 0.77/0.99 (c2_1(a261)),
% 0.77/0.99 inference(unit_resolution,[status(thm)],[1228, 1213])).
% 0.77/0.99 tff(1230,plain,
% 0.77/0.99 (((~hskp27) | c1_1(a261)) <=> ((~hskp27) | c1_1(a261))),
% 0.77/0.99 inference(rewrite,[status(thm)],[])).
% 0.77/0.99 tff(1231,axiom,((~hskp27) | c1_1(a261)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause46')).
% 0.77/0.99 tff(1232,plain,
% 0.77/0.99 ((~hskp27) | c1_1(a261)),
% 0.77/0.99 inference(modus_ponens,[status(thm)],[1231, 1230])).
% 0.77/0.99 tff(1233,plain,
% 0.77/0.99 ((~hskp27) | c1_1(a261)),
% 0.77/0.99 inference(modus_ponens,[status(thm)],[1232, 1230])).
% 0.77/0.99 tff(1234,plain,
% 0.77/0.99 ((~hskp27) | c1_1(a261)),
% 0.77/0.99 inference(modus_ponens,[status(thm)],[1233, 1230])).
% 0.77/0.99 tff(1235,plain,
% 0.77/0.99 ((~hskp27) | c1_1(a261)),
% 0.77/0.99 inference(modus_ponens,[status(thm)],[1234, 1230])).
% 0.77/0.99 tff(1236,plain,
% 0.77/0.99 ((~hskp27) | c1_1(a261)),
% 0.77/0.99 inference(modus_ponens,[status(thm)],[1235, 1230])).
% 0.77/0.99 tff(1237,plain,
% 0.77/0.99 (c1_1(a261)),
% 0.77/0.99 inference(unit_resolution,[status(thm)],[1236, 1213])).
% 0.77/0.99 tff(1238,plain,
% 0.77/0.99 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)) | (~c2_1(W)) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | (~c1_1(a261)) | (~c2_1(a261)) | (~c0_1(a261)) | (~c3_1(a261)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)) | (~c2_1(W)) | (~c0_1(W)) | (~c1_1(W)))) | (~ndr1_0) | (~c1_1(a261)) | (~c2_1(a261)) | (~c0_1(a261)) | (~c3_1(a261)))),
% 0.77/0.99 inference(rewrite,[status(thm)],[])).
% 0.77/0.99 tff(1239,plain,
% 0.77/0.99 (((~ndr1_0) | (~c2_1(a261)) | (~c3_1(a261)) | (~c1_1(a261)) | (~c3_1(a261)) | (~c2_1(a261)) | (~c0_1(a261)) | (~c2_1(a261)) | (~c0_1(a261)) | (~c1_1(a261))) <=> ((~ndr1_0) | (~c1_1(a261)) | (~c2_1(a261)) | (~c0_1(a261)) | (~c3_1(a261)))),
% 0.77/0.99 inference(rewrite,[status(thm)],[])).
% 0.77/0.99 tff(1240,plain,
% 0.77/0.99 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)) | (~c2_1(W)) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a261)) | (~c3_1(a261)) | (~c1_1(a261)) | (~c3_1(a261)) | (~c2_1(a261)) | (~c0_1(a261)) | (~c2_1(a261)) | (~c0_1(a261)) | (~c1_1(a261)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)) | (~c2_1(W)) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | (~c1_1(a261)) | (~c2_1(a261)) | (~c0_1(a261)) | (~c3_1(a261))))),
% 0.77/0.99 inference(monotonicity,[status(thm)],[1239])).
% 0.77/0.99 tff(1241,plain,
% 0.77/0.99 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)) | (~c2_1(W)) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a261)) | (~c3_1(a261)) | (~c1_1(a261)) | (~c3_1(a261)) | (~c2_1(a261)) | (~c0_1(a261)) | (~c2_1(a261)) | (~c0_1(a261)) | (~c1_1(a261)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)) | (~c2_1(W)) | (~c0_1(W)) | (~c1_1(W)))) | (~ndr1_0) | (~c1_1(a261)) | (~c2_1(a261)) | (~c0_1(a261)) | (~c3_1(a261)))),
% 0.77/0.99 inference(transitivity,[status(thm)],[1240, 1238])).
% 0.77/0.99 tff(1242,plain,
% 0.77/0.99 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)) | (~c2_1(W)) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a261)) | (~c3_1(a261)) | (~c1_1(a261)) | (~c3_1(a261)) | (~c2_1(a261)) | (~c0_1(a261)) | (~c2_1(a261)) | (~c0_1(a261)) | (~c1_1(a261)))),
% 0.77/0.99 inference(quant_inst,[status(thm)],[])).
% 0.77/0.99 tff(1243,plain,
% 0.77/0.99 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)) | (~c2_1(W)) | (~c0_1(W)) | (~c1_1(W)))) | (~ndr1_0) | (~c1_1(a261)) | (~c2_1(a261)) | (~c0_1(a261)) | (~c3_1(a261))),
% 0.77/0.99 inference(modus_ponens,[status(thm)],[1242, 1241])).
% 0.77/0.99 tff(1244,plain,
% 0.77/0.99 (~c0_1(a261)),
% 0.77/0.99 inference(unit_resolution,[status(thm)],[1243, 110, 1237, 1229, 1221, 33])).
% 0.77/0.99 tff(1245,plain,
% 0.77/0.99 (^[V: $i, U: $i] : refl((hskp15 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))) <=> (hskp15 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))))),
% 0.77/0.99 inference(bind,[status(th)],[])).
% 0.77/0.99 tff(1246,plain,
% 0.77/0.99 (![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 0.77/0.99 inference(quant_intro,[status(thm)],[1245])).
% 0.77/0.99 tff(1247,plain,
% 0.77/0.99 (![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 0.77/0.99 inference(rewrite,[status(thm)],[])).
% 0.77/0.99 tff(1248,plain,
% 0.77/0.99 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c3_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)))), ((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c3_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(V)))), ((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(V))))), (((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(V)) | (~c2_1(V)))), (((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(V)) | (~c2_1(V))))), ((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c1_1(V)) | (~c2_1(V)))), ((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c1_1(V)) | (~c2_1(V))))), (((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | (~c1_1(V)) | (~c2_1(V)))), (((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | (~c1_1(V)) | (~c2_1(V))))), ((((((((~c3_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) | (~c3_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))), ((((((((~c3_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) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))))), (((((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | hskp15) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))) | hskp15))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))) | hskp15) <=> (hskp15 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))), (((((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | hskp15) <=> (hskp15 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))))),
% 0.77/0.99 inference(bind,[status(th)],[])).
% 0.77/0.99 tff(1249,plain,
% 0.77/0.99 (![V: $i, U: $i] : ((((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | hskp15) <=> ![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 0.77/0.99 inference(quant_intro,[status(thm)],[1248])).
% 0.77/0.99 tff(1250,axiom,(![V: $i, U: $i] : ((((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | hskp15)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause171')).
% 0.77/0.99 tff(1251,plain,
% 0.77/0.99 (![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 0.77/0.99 inference(modus_ponens,[status(thm)],[1250, 1249])).
% 0.77/0.99 tff(1252,plain,
% 0.77/0.99 (![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 0.77/0.99 inference(modus_ponens,[status(thm)],[1251, 1247])).
% 0.77/0.99 tff(1253,plain,(
% 0.77/0.99 ![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 0.77/0.99 inference(skolemize,[status(sab)],[1252])).
% 0.77/0.99 tff(1254,plain,
% 0.77/0.99 (![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 0.77/0.99 inference(modus_ponens,[status(thm)],[1253, 1246])).
% 0.77/0.99 tff(1255,assumption,(hskp5), introduced(assumption)).
% 0.77/0.99 tff(1256,plain,
% 0.77/0.99 (~c2_1(a218)),
% 0.77/0.99 inference(unit_resolution,[status(thm)],[674, 1255])).
% 0.77/0.99 tff(1257,plain,
% 0.77/0.99 (~c1_1(a218)),
% 0.77/0.99 inference(unit_resolution,[status(thm)],[680, 1255])).
% 0.77/0.99 tff(1258,plain,
% 0.77/0.99 (c3_1(a218)),
% 0.77/0.99 inference(unit_resolution,[status(thm)],[688, 1255])).
% 0.77/0.99 tff(1259,plain,
% 0.77/0.99 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp15 | c1_1(a218) | c2_1(a218) | (~ndr1_0) | (~c1_1(a261)) | (~c2_1(a261)) | c0_1(a261) | (~c3_1(a218)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp15 | c1_1(a218) | c2_1(a218) | (~ndr1_0) | (~c1_1(a261)) | (~c2_1(a261)) | c0_1(a261) | (~c3_1(a218)))),
% 0.77/0.99 inference(rewrite,[status(thm)],[])).
% 0.77/0.99 tff(1260,plain,
% 0.77/0.99 ((hskp15 | (~ndr1_0) | c2_1(a218) | c1_1(a218) | (~c3_1(a218)) | c0_1(a261) | (~c1_1(a261)) | (~c2_1(a261))) <=> (hskp15 | c1_1(a218) | c2_1(a218) | (~ndr1_0) | (~c1_1(a261)) | (~c2_1(a261)) | c0_1(a261) | (~c3_1(a218)))),
% 0.77/0.99 inference(rewrite,[status(thm)],[])).
% 0.77/0.99 tff(1261,plain,
% 0.77/0.99 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp15 | (~ndr1_0) | c2_1(a218) | c1_1(a218) | (~c3_1(a218)) | c0_1(a261) | (~c1_1(a261)) | (~c2_1(a261)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp15 | c1_1(a218) | c2_1(a218) | (~ndr1_0) | (~c1_1(a261)) | (~c2_1(a261)) | c0_1(a261) | (~c3_1(a218))))),
% 0.77/0.99 inference(monotonicity,[status(thm)],[1260])).
% 0.77/0.99 tff(1262,plain,
% 0.77/0.99 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp15 | (~ndr1_0) | c2_1(a218) | c1_1(a218) | (~c3_1(a218)) | c0_1(a261) | (~c1_1(a261)) | (~c2_1(a261)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp15 | c1_1(a218) | c2_1(a218) | (~ndr1_0) | (~c1_1(a261)) | (~c2_1(a261)) | c0_1(a261) | (~c3_1(a218)))),
% 0.77/0.99 inference(transitivity,[status(thm)],[1261, 1259])).
% 0.77/0.99 tff(1263,plain,
% 0.77/0.99 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp15 | (~ndr1_0) | c2_1(a218) | c1_1(a218) | (~c3_1(a218)) | c0_1(a261) | (~c1_1(a261)) | (~c2_1(a261)))),
% 0.77/0.99 inference(quant_inst,[status(thm)],[])).
% 0.77/0.99 tff(1264,plain,
% 0.77/0.99 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp15 | c1_1(a218) | c2_1(a218) | (~ndr1_0) | (~c1_1(a261)) | (~c2_1(a261)) | c0_1(a261) | (~c3_1(a218))),
% 0.77/0.99 inference(modus_ponens,[status(thm)],[1263, 1262])).
% 0.77/0.99 tff(1265,plain,
% 0.77/0.99 (hskp15),
% 0.77/0.99 inference(unit_resolution,[status(thm)],[1264, 110, 1237, 1229, 1258, 1257, 1256, 1254, 1244])).
% 0.77/0.99 tff(1266,plain,
% 0.77/0.99 (~c2_1(a242)),
% 0.77/0.99 inference(unit_resolution,[status(thm)],[383, 1265])).
% 0.77/0.99 tff(1267,plain,
% 0.77/0.99 (~c0_1(a242)),
% 0.77/0.99 inference(unit_resolution,[status(thm)],[414, 1265])).
% 0.77/0.99 tff(1268,plain,
% 0.77/0.99 (c1_1(a242)),
% 0.77/0.99 inference(unit_resolution,[status(thm)],[391, 1265])).
% 0.77/0.99 tff(1269,plain,
% 0.77/0.99 (((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp18 | c0_1(a242) | c2_1(a242) | (~ndr1_0) | (~c3_1(a242)) | (~c1_1(a242)))) <=> ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp18 | c0_1(a242) | c2_1(a242) | (~ndr1_0) | (~c3_1(a242)) | (~c1_1(a242)))),
% 0.77/0.99 inference(rewrite,[status(thm)],[])).
% 0.77/0.99 tff(1270,plain,
% 0.77/0.99 ((hskp18 | (~ndr1_0) | c2_1(a242) | (~c3_1(a242)) | (~c1_1(a242)) | c0_1(a242) | (~c1_1(a242)) | (~c3_1(a242))) <=> (hskp18 | c0_1(a242) | c2_1(a242) | (~ndr1_0) | (~c3_1(a242)) | (~c1_1(a242)))),
% 0.77/0.99 inference(rewrite,[status(thm)],[])).
% 0.77/0.99 tff(1271,plain,
% 0.77/0.99 (((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp18 | (~ndr1_0) | c2_1(a242) | (~c3_1(a242)) | (~c1_1(a242)) | c0_1(a242) | (~c1_1(a242)) | (~c3_1(a242)))) <=> ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp18 | c0_1(a242) | c2_1(a242) | (~ndr1_0) | (~c3_1(a242)) | (~c1_1(a242))))),
% 0.77/0.99 inference(monotonicity,[status(thm)],[1270])).
% 0.77/0.99 tff(1272,plain,
% 0.77/0.99 (((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp18 | (~ndr1_0) | c2_1(a242) | (~c3_1(a242)) | (~c1_1(a242)) | c0_1(a242) | (~c1_1(a242)) | (~c3_1(a242)))) <=> ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp18 | c0_1(a242) | c2_1(a242) | (~ndr1_0) | (~c3_1(a242)) | (~c1_1(a242)))),
% 0.77/0.99 inference(transitivity,[status(thm)],[1271, 1269])).
% 0.77/0.99 tff(1273,plain,
% 0.77/0.99 ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp18 | (~ndr1_0) | c2_1(a242) | (~c3_1(a242)) | (~c1_1(a242)) | c0_1(a242) | (~c1_1(a242)) | (~c3_1(a242)))),
% 0.77/0.99 inference(quant_inst,[status(thm)],[])).
% 0.77/0.99 tff(1274,plain,
% 0.77/0.99 ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp18 | c0_1(a242) | c2_1(a242) | (~ndr1_0) | (~c3_1(a242)) | (~c1_1(a242))),
% 0.77/0.99 inference(modus_ponens,[status(thm)],[1273, 1272])).
% 0.77/0.99 tff(1275,plain,
% 0.77/0.99 (~c3_1(a242)),
% 0.77/0.99 inference(unit_resolution,[status(thm)],[1274, 110, 596, 1268, 1267, 1266, 615])).
% 0.77/0.99 tff(1276,plain,
% 0.77/0.99 (^[V: $i, U: $i] : refl((hskp18 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))) <=> (hskp18 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))))),
% 0.77/0.99 inference(bind,[status(th)],[])).
% 0.77/0.99 tff(1277,plain,
% 0.77/0.99 (![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 0.77/0.99 inference(quant_intro,[status(thm)],[1276])).
% 0.77/0.99 tff(1278,plain,
% 0.77/0.99 (![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 0.77/0.99 inference(rewrite,[status(thm)],[])).
% 0.77/0.99 tff(1279,plain,
% 0.77/0.99 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c3_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_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)) | (~c0_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_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)) | (~c0_1(V))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c3_1(U)) | c1_1(V)) | hskp18) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))) | hskp18))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))) | hskp18) <=> (hskp18 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c3_1(U)) | c1_1(V)) | hskp18) <=> (hskp18 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))))),
% 0.77/1.00 inference(bind,[status(th)],[])).
% 0.77/1.00 tff(1280,plain,
% 0.77/1.00 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c3_1(U)) | c1_1(V)) | hskp18) <=> ![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 0.77/1.00 inference(quant_intro,[status(thm)],[1279])).
% 0.77/1.00 tff(1281,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c3_1(U)) | c1_1(V)) | hskp18)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause184')).
% 0.77/1.00 tff(1282,plain,
% 0.77/1.00 (![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 0.77/1.00 inference(modus_ponens,[status(thm)],[1281, 1280])).
% 0.77/1.00 tff(1283,plain,
% 0.77/1.00 (![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 0.77/1.00 inference(modus_ponens,[status(thm)],[1282, 1278])).
% 0.77/1.00 tff(1284,plain,(
% 0.77/1.00 ![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 0.77/1.00 inference(skolemize,[status(sab)],[1283])).
% 0.77/1.00 tff(1285,plain,
% 0.77/1.00 (![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 0.77/1.00 inference(modus_ponens,[status(thm)],[1284, 1277])).
% 0.77/1.00 tff(1286,plain,
% 0.77/1.00 (((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp18 | c2_1(a259) | (~ndr1_0) | (~c1_1(a261)) | (~c3_1(a261)) | c0_1(a261) | (~c3_1(a259)) | (~c1_1(a259)))) <=> ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp18 | c2_1(a259) | (~ndr1_0) | (~c1_1(a261)) | (~c3_1(a261)) | c0_1(a261) | (~c3_1(a259)) | (~c1_1(a259)))),
% 0.84/1.00 inference(rewrite,[status(thm)],[])).
% 0.84/1.00 tff(1287,plain,
% 0.84/1.00 ((hskp18 | (~ndr1_0) | c2_1(a259) | (~c3_1(a259)) | (~c1_1(a259)) | c0_1(a261) | (~c1_1(a261)) | (~c3_1(a261))) <=> (hskp18 | c2_1(a259) | (~ndr1_0) | (~c1_1(a261)) | (~c3_1(a261)) | c0_1(a261) | (~c3_1(a259)) | (~c1_1(a259)))),
% 0.84/1.00 inference(rewrite,[status(thm)],[])).
% 0.84/1.00 tff(1288,plain,
% 0.84/1.00 (((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp18 | (~ndr1_0) | c2_1(a259) | (~c3_1(a259)) | (~c1_1(a259)) | c0_1(a261) | (~c1_1(a261)) | (~c3_1(a261)))) <=> ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp18 | c2_1(a259) | (~ndr1_0) | (~c1_1(a261)) | (~c3_1(a261)) | c0_1(a261) | (~c3_1(a259)) | (~c1_1(a259))))),
% 0.84/1.00 inference(monotonicity,[status(thm)],[1287])).
% 0.84/1.00 tff(1289,plain,
% 0.84/1.00 (((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp18 | (~ndr1_0) | c2_1(a259) | (~c3_1(a259)) | (~c1_1(a259)) | c0_1(a261) | (~c1_1(a261)) | (~c3_1(a261)))) <=> ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp18 | c2_1(a259) | (~ndr1_0) | (~c1_1(a261)) | (~c3_1(a261)) | c0_1(a261) | (~c3_1(a259)) | (~c1_1(a259)))),
% 0.84/1.00 inference(transitivity,[status(thm)],[1288, 1286])).
% 0.84/1.00 tff(1290,plain,
% 0.84/1.00 ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp18 | (~ndr1_0) | c2_1(a259) | (~c3_1(a259)) | (~c1_1(a259)) | c0_1(a261) | (~c1_1(a261)) | (~c3_1(a261)))),
% 0.84/1.00 inference(quant_inst,[status(thm)],[])).
% 0.84/1.00 tff(1291,plain,
% 0.84/1.00 ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp18 | c2_1(a259) | (~ndr1_0) | (~c1_1(a261)) | (~c3_1(a261)) | c0_1(a261) | (~c3_1(a259)) | (~c1_1(a259))),
% 0.84/1.00 inference(modus_ponens,[status(thm)],[1290, 1289])).
% 0.84/1.00 tff(1292,plain,
% 0.84/1.00 (~c1_1(a259)),
% 0.84/1.00 inference(unit_resolution,[status(thm)],[1291, 110, 596, 1237, 1221, 1150, 1147, 615, 1244])).
% 0.84/1.00 tff(1293,plain,
% 0.84/1.00 (^[V: $i, U: $i] : refl((hskp10 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V))) <=> (hskp10 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V))))),
% 0.84/1.00 inference(bind,[status(th)],[])).
% 0.84/1.00 tff(1294,plain,
% 0.84/1.00 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))),
% 0.84/1.00 inference(quant_intro,[status(thm)],[1293])).
% 0.84/1.00 tff(1295,plain,
% 0.84/1.00 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))),
% 0.84/1.00 inference(rewrite,[status(thm)],[])).
% 0.84/1.00 tff(1296,plain,
% 0.84/1.00 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c3_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)))), ((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c3_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(V)))), ((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(V))))), (((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(V)))), (((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(V))))), ((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(V)))), ((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(V))))), (((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(V)))), (((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(V))))), ((((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))), ((((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V))))), (((((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | hskp10) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V))) | hskp10))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V))) | hskp10) <=> (hskp10 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))), (((((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | hskp10) <=> (hskp10 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))))),
% 0.84/1.00 inference(bind,[status(th)],[])).
% 0.84/1.00 tff(1297,plain,
% 0.84/1.00 (![V: $i, U: $i] : ((((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | hskp10) <=> ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))),
% 0.84/1.00 inference(quant_intro,[status(thm)],[1296])).
% 0.84/1.00 tff(1298,axiom,(![V: $i, U: $i] : ((((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | hskp10)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause173')).
% 0.84/1.00 tff(1299,plain,
% 0.84/1.00 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))),
% 0.84/1.00 inference(modus_ponens,[status(thm)],[1298, 1297])).
% 0.84/1.00 tff(1300,plain,
% 0.84/1.00 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))),
% 0.84/1.00 inference(modus_ponens,[status(thm)],[1299, 1295])).
% 0.84/1.00 tff(1301,plain,(
% 0.84/1.00 ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))),
% 0.84/1.00 inference(skolemize,[status(sab)],[1300])).
% 0.84/1.00 tff(1302,plain,
% 0.84/1.00 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))),
% 0.84/1.00 inference(modus_ponens,[status(thm)],[1301, 1294])).
% 0.84/1.00 tff(1303,plain,
% 0.84/1.00 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp10 | c2_1(a259) | (~ndr1_0) | (~c1_1(a261)) | (~c3_1(a261)) | c0_1(a261) | (~c3_1(a259)) | c1_1(a259))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp10 | c2_1(a259) | (~ndr1_0) | (~c1_1(a261)) | (~c3_1(a261)) | c0_1(a261) | (~c3_1(a259)) | c1_1(a259))),
% 0.84/1.00 inference(rewrite,[status(thm)],[])).
% 0.84/1.00 tff(1304,plain,
% 0.84/1.00 ((hskp10 | (~ndr1_0) | c2_1(a259) | c1_1(a259) | (~c3_1(a259)) | c0_1(a261) | (~c1_1(a261)) | (~c3_1(a261))) <=> (hskp10 | c2_1(a259) | (~ndr1_0) | (~c1_1(a261)) | (~c3_1(a261)) | c0_1(a261) | (~c3_1(a259)) | c1_1(a259))),
% 0.84/1.00 inference(rewrite,[status(thm)],[])).
% 0.84/1.00 tff(1305,plain,
% 0.84/1.00 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp10 | (~ndr1_0) | c2_1(a259) | c1_1(a259) | (~c3_1(a259)) | c0_1(a261) | (~c1_1(a261)) | (~c3_1(a261)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp10 | c2_1(a259) | (~ndr1_0) | (~c1_1(a261)) | (~c3_1(a261)) | c0_1(a261) | (~c3_1(a259)) | c1_1(a259)))),
% 0.84/1.00 inference(monotonicity,[status(thm)],[1304])).
% 0.84/1.00 tff(1306,plain,
% 0.84/1.00 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp10 | (~ndr1_0) | c2_1(a259) | c1_1(a259) | (~c3_1(a259)) | c0_1(a261) | (~c1_1(a261)) | (~c3_1(a261)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp10 | c2_1(a259) | (~ndr1_0) | (~c1_1(a261)) | (~c3_1(a261)) | c0_1(a261) | (~c3_1(a259)) | c1_1(a259))),
% 0.84/1.00 inference(transitivity,[status(thm)],[1305, 1303])).
% 0.84/1.00 tff(1307,plain,
% 0.84/1.00 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp10 | (~ndr1_0) | c2_1(a259) | c1_1(a259) | (~c3_1(a259)) | c0_1(a261) | (~c1_1(a261)) | (~c3_1(a261)))),
% 0.84/1.00 inference(quant_inst,[status(thm)],[])).
% 0.84/1.00 tff(1308,plain,
% 0.84/1.00 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp10 | c2_1(a259) | (~ndr1_0) | (~c1_1(a261)) | (~c3_1(a261)) | c0_1(a261) | (~c3_1(a259)) | c1_1(a259)),
% 0.84/1.00 inference(modus_ponens,[status(thm)],[1307, 1306])).
% 0.84/1.00 tff(1309,plain,
% 0.84/1.00 (hskp10),
% 0.84/1.00 inference(unit_resolution,[status(thm)],[1308, 110, 1237, 1221, 1150, 1147, 1302, 1292, 1244])).
% 0.84/1.00 tff(1310,plain,
% 0.84/1.00 (((~hskp10) | (~c0_1(a231))) <=> ((~hskp10) | (~c0_1(a231)))),
% 0.84/1.00 inference(rewrite,[status(thm)],[])).
% 0.84/1.00 tff(1311,plain,
% 0.84/1.00 (((~c0_1(a231)) | (~hskp10)) <=> ((~hskp10) | (~c0_1(a231)))),
% 0.84/1.00 inference(rewrite,[status(thm)],[])).
% 0.84/1.00 tff(1312,axiom,((~c0_1(a231)) | (~hskp10)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause111')).
% 0.84/1.00 tff(1313,plain,
% 0.84/1.00 ((~hskp10) | (~c0_1(a231))),
% 0.84/1.00 inference(modus_ponens,[status(thm)],[1312, 1311])).
% 0.84/1.00 tff(1314,plain,
% 0.84/1.00 ((~hskp10) | (~c0_1(a231))),
% 0.84/1.00 inference(modus_ponens,[status(thm)],[1313, 1310])).
% 0.84/1.00 tff(1315,plain,
% 0.84/1.00 (~c0_1(a231)),
% 0.84/1.00 inference(unit_resolution,[status(thm)],[1314, 1309])).
% 0.84/1.00 tff(1316,plain,
% 0.84/1.00 (^[U: $i] : refl((hskp17 | hskp12 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) <=> (hskp17 | hskp12 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))))),
% 0.84/1.00 inference(bind,[status(th)],[])).
% 0.84/1.00 tff(1317,plain,
% 0.84/1.00 (![U: $i] : (hskp17 | hskp12 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp17 | hskp12 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 0.84/1.00 inference(quant_intro,[status(thm)],[1316])).
% 0.84/1.00 tff(1318,plain,
% 0.84/1.00 (![U: $i] : (hskp17 | hskp12 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp17 | hskp12 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 0.84/1.00 inference(rewrite,[status(thm)],[])).
% 0.84/1.00 tff(1319,plain,
% 0.84/1.00 (^[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)) | hskp12) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) | hskp12))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) | hskp12) <=> (hskp12 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))), ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp12) <=> (hskp12 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))))), (((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp12) | hskp17) <=> ((hskp12 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) | hskp17))), rewrite(((hskp12 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) | hskp17) <=> (hskp17 | hskp12 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))), (((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp12) | hskp17) <=> (hskp17 | hskp12 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))))),
% 0.84/1.00 inference(bind,[status(th)],[])).
% 0.84/1.00 tff(1320,plain,
% 0.84/1.00 (![U: $i] : ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp12) | hskp17) <=> ![U: $i] : (hskp17 | hskp12 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 0.84/1.00 inference(quant_intro,[status(thm)],[1319])).
% 0.84/1.00 tff(1321,axiom,(![U: $i] : ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp12) | hskp17)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause142')).
% 0.84/1.00 tff(1322,plain,
% 0.84/1.00 (![U: $i] : (hskp17 | hskp12 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 0.84/1.00 inference(modus_ponens,[status(thm)],[1321, 1320])).
% 0.84/1.00 tff(1323,plain,
% 0.84/1.00 (![U: $i] : (hskp17 | hskp12 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 0.84/1.00 inference(modus_ponens,[status(thm)],[1322, 1318])).
% 0.84/1.00 tff(1324,plain,(
% 0.84/1.00 ![U: $i] : (hskp17 | hskp12 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 0.84/1.00 inference(skolemize,[status(sab)],[1323])).
% 0.84/1.00 tff(1325,plain,
% 0.84/1.00 (![U: $i] : (hskp17 | hskp12 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 0.84/1.00 inference(modus_ponens,[status(thm)],[1324, 1317])).
% 0.84/1.00 tff(1326,plain,
% 0.84/1.00 (((~![U: $i] : (hskp17 | hskp12 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp17 | hskp12 | c2_1(a259) | (~ndr1_0) | (~c0_1(a259)) | c1_1(a259))) <=> ((~![U: $i] : (hskp17 | hskp12 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp17 | hskp12 | c2_1(a259) | (~ndr1_0) | (~c0_1(a259)) | c1_1(a259))),
% 0.84/1.00 inference(rewrite,[status(thm)],[])).
% 0.84/1.00 tff(1327,plain,
% 0.84/1.00 ((hskp17 | hskp12 | (~ndr1_0) | c2_1(a259) | c1_1(a259) | (~c0_1(a259))) <=> (hskp17 | hskp12 | c2_1(a259) | (~ndr1_0) | (~c0_1(a259)) | c1_1(a259))),
% 0.84/1.00 inference(rewrite,[status(thm)],[])).
% 0.84/1.00 tff(1328,plain,
% 0.84/1.00 (((~![U: $i] : (hskp17 | hskp12 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp17 | hskp12 | (~ndr1_0) | c2_1(a259) | c1_1(a259) | (~c0_1(a259)))) <=> ((~![U: $i] : (hskp17 | hskp12 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp17 | hskp12 | c2_1(a259) | (~ndr1_0) | (~c0_1(a259)) | c1_1(a259)))),
% 0.84/1.00 inference(monotonicity,[status(thm)],[1327])).
% 0.84/1.00 tff(1329,plain,
% 0.84/1.00 (((~![U: $i] : (hskp17 | hskp12 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp17 | hskp12 | (~ndr1_0) | c2_1(a259) | c1_1(a259) | (~c0_1(a259)))) <=> ((~![U: $i] : (hskp17 | hskp12 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp17 | hskp12 | c2_1(a259) | (~ndr1_0) | (~c0_1(a259)) | c1_1(a259))),
% 0.84/1.00 inference(transitivity,[status(thm)],[1328, 1326])).
% 0.84/1.00 tff(1330,plain,
% 0.84/1.00 ((~![U: $i] : (hskp17 | hskp12 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp17 | hskp12 | (~ndr1_0) | c2_1(a259) | c1_1(a259) | (~c0_1(a259)))),
% 0.84/1.00 inference(quant_inst,[status(thm)],[])).
% 0.84/1.00 tff(1331,plain,
% 0.84/1.00 ((~![U: $i] : (hskp17 | hskp12 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp17 | hskp12 | c2_1(a259) | (~ndr1_0) | (~c0_1(a259)) | c1_1(a259)),
% 0.84/1.00 inference(modus_ponens,[status(thm)],[1330, 1329])).
% 0.84/1.00 tff(1332,plain,
% 0.84/1.00 (hskp17 | c1_1(a259)),
% 0.84/1.00 inference(unit_resolution,[status(thm)],[1331, 110, 526, 1148, 1147, 1325])).
% 0.84/1.00 tff(1333,plain,
% 0.84/1.00 (hskp17),
% 0.84/1.00 inference(unit_resolution,[status(thm)],[1332, 1292])).
% 0.84/1.00 tff(1334,plain,
% 0.84/1.00 (~c2_1(a248)),
% 0.84/1.00 inference(unit_resolution,[status(thm)],[629, 1333])).
% 0.84/1.00 tff(1335,plain,
% 0.84/1.00 (((~hskp10) | c3_1(a231)) <=> ((~hskp10) | c3_1(a231))),
% 0.84/1.00 inference(rewrite,[status(thm)],[])).
% 0.84/1.00 tff(1336,axiom,((~hskp10) | c3_1(a231)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause73')).
% 0.84/1.00 tff(1337,plain,
% 0.84/1.00 ((~hskp10) | c3_1(a231)),
% 0.84/1.00 inference(modus_ponens,[status(thm)],[1336, 1335])).
% 0.84/1.00 tff(1338,plain,
% 0.84/1.00 ((~hskp10) | c3_1(a231)),
% 0.84/1.00 inference(modus_ponens,[status(thm)],[1337, 1335])).
% 0.84/1.00 tff(1339,plain,
% 0.84/1.00 ((~hskp10) | c3_1(a231)),
% 0.84/1.00 inference(modus_ponens,[status(thm)],[1338, 1335])).
% 0.84/1.00 tff(1340,plain,
% 0.84/1.00 ((~hskp10) | c3_1(a231)),
% 0.84/1.00 inference(modus_ponens,[status(thm)],[1339, 1335])).
% 0.84/1.00 tff(1341,plain,
% 0.84/1.00 ((~hskp10) | c3_1(a231)),
% 0.84/1.00 inference(modus_ponens,[status(thm)],[1340, 1335])).
% 0.84/1.00 tff(1342,plain,
% 0.84/1.00 (c3_1(a231)),
% 0.84/1.00 inference(unit_resolution,[status(thm)],[1341, 1309])).
% 0.84/1.00 tff(1343,plain,
% 0.84/1.00 (c1_1(a231)),
% 0.84/1.00 inference(unit_resolution,[status(thm)],[604, 1309])).
% 0.84/1.00 tff(1344,plain,
% 0.84/1.00 (c3_1(a248)),
% 0.84/1.00 inference(unit_resolution,[status(thm)],[637, 1333])).
% 0.84/1.00 tff(1345,plain,
% 0.84/1.00 (c1_1(a248)),
% 0.84/1.00 inference(unit_resolution,[status(thm)],[623, 1333])).
% 0.84/1.00 tff(1346,plain,
% 0.84/1.00 (((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp18 | c2_1(a248) | c0_1(a231) | (~ndr1_0) | (~c1_1(a231)) | (~c3_1(a231)) | (~c3_1(a248)) | (~c1_1(a248)))) <=> ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp18 | c2_1(a248) | c0_1(a231) | (~ndr1_0) | (~c1_1(a231)) | (~c3_1(a231)) | (~c3_1(a248)) | (~c1_1(a248)))),
% 0.84/1.00 inference(rewrite,[status(thm)],[])).
% 0.84/1.00 tff(1347,plain,
% 0.84/1.00 ((hskp18 | (~ndr1_0) | c2_1(a248) | (~c3_1(a248)) | (~c1_1(a248)) | c0_1(a231) | (~c1_1(a231)) | (~c3_1(a231))) <=> (hskp18 | c2_1(a248) | c0_1(a231) | (~ndr1_0) | (~c1_1(a231)) | (~c3_1(a231)) | (~c3_1(a248)) | (~c1_1(a248)))),
% 0.84/1.00 inference(rewrite,[status(thm)],[])).
% 0.84/1.00 tff(1348,plain,
% 0.84/1.00 (((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp18 | (~ndr1_0) | c2_1(a248) | (~c3_1(a248)) | (~c1_1(a248)) | c0_1(a231) | (~c1_1(a231)) | (~c3_1(a231)))) <=> ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp18 | c2_1(a248) | c0_1(a231) | (~ndr1_0) | (~c1_1(a231)) | (~c3_1(a231)) | (~c3_1(a248)) | (~c1_1(a248))))),
% 0.84/1.00 inference(monotonicity,[status(thm)],[1347])).
% 0.84/1.00 tff(1349,plain,
% 0.84/1.00 (((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp18 | (~ndr1_0) | c2_1(a248) | (~c3_1(a248)) | (~c1_1(a248)) | c0_1(a231) | (~c1_1(a231)) | (~c3_1(a231)))) <=> ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp18 | c2_1(a248) | c0_1(a231) | (~ndr1_0) | (~c1_1(a231)) | (~c3_1(a231)) | (~c3_1(a248)) | (~c1_1(a248)))),
% 0.84/1.00 inference(transitivity,[status(thm)],[1348, 1346])).
% 0.84/1.00 tff(1350,plain,
% 0.84/1.00 ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp18 | (~ndr1_0) | c2_1(a248) | (~c3_1(a248)) | (~c1_1(a248)) | c0_1(a231) | (~c1_1(a231)) | (~c3_1(a231)))),
% 0.84/1.00 inference(quant_inst,[status(thm)],[])).
% 0.84/1.00 tff(1351,plain,
% 0.84/1.00 ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp18 | c2_1(a248) | c0_1(a231) | (~ndr1_0) | (~c1_1(a231)) | (~c3_1(a231)) | (~c3_1(a248)) | (~c1_1(a248))),
% 0.84/1.00 inference(modus_ponens,[status(thm)],[1350, 1349])).
% 0.84/1.00 tff(1352,plain,
% 0.84/1.00 ($false),
% 0.84/1.00 inference(unit_resolution,[status(thm)],[1351, 110, 596, 1345, 1344, 1343, 1342, 1334, 1315, 615])).
% 0.84/1.00 tff(1353,plain,(hskp12 | hskp18 | (~c2_1(a213)) | c1_1(a213) | c3_1(a213)), inference(lemma,lemma(discharge,[]))).
% 0.84/1.00 tff(1354,plain,
% 0.84/1.00 ($false),
% 0.84/1.00 inference(unit_resolution,[status(thm)],[1353, 751, 759, 596, 526, 745])).
% 0.84/1.00 tff(1355,plain,((~hskp0) | hskp18 | hskp12), inference(lemma,lemma(discharge,[]))).
% 0.84/1.00 tff(1356,plain,
% 0.84/1.00 (~hskp0),
% 0.84/1.00 inference(unit_resolution,[status(thm)],[1355, 526, 596])).
% 0.84/1.00 tff(1357,plain,
% 0.84/1.00 (hskp1),
% 0.84/1.00 inference(unit_resolution,[status(thm)],[991, 1356, 526])).
% 0.84/1.00 tff(1358,plain,
% 0.84/1.00 (~c3_1(a214)),
% 0.84/1.00 inference(unit_resolution,[status(thm)],[997, 1357])).
% 0.84/1.00 tff(1359,plain,
% 0.84/1.00 (~c0_1(a214)),
% 0.84/1.00 inference(unit_resolution,[status(thm)],[1057, 1357])).
% 0.84/1.00 tff(1360,plain,
% 0.84/1.00 (c2_1(a214)),
% 0.84/1.00 inference(unit_resolution,[status(thm)],[1043, 1357])).
% 0.84/1.00 tff(1361,plain,
% 0.84/1.00 (~c1_1(a214)),
% 0.84/1.00 inference(unit_resolution,[status(thm)],[1064, 110, 526, 1360, 1359, 1358, 44])).
% 0.84/1.00 tff(1362,plain,
% 0.84/1.00 (((~![U: $i] : (hskp21 | hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp21 | hskp12 | c3_1(a214) | (~ndr1_0) | c1_1(a214) | (~c2_1(a214)))) <=> ((~![U: $i] : (hskp21 | hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | hskp21 | hskp12 | c3_1(a214) | (~ndr1_0) | c1_1(a214) | (~c2_1(a214)))),
% 0.84/1.00 inference(rewrite,[status(thm)],[])).
% 0.84/1.00 tff(1363,plain,
% 0.84/1.00 ((hskp21 | hskp12 | (~ndr1_0) | c1_1(a214) | c3_1(a214) | (~c2_1(a214))) <=> (hskp21 | hskp12 | c3_1(a214) | (~ndr1_0) | c1_1(a214) | (~c2_1(a214)))),
% 0.84/1.00 inference(rewrite,[status(thm)],[])).
% 0.84/1.00 tff(1364,plain,
% 0.84/1.00 (((~![U: $i] : (hskp21 | hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp21 | hskp12 | (~ndr1_0) | c1_1(a214) | c3_1(a214) | (~c2_1(a214)))) <=> ((~![U: $i] : (hskp21 | hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp21 | hskp12 | c3_1(a214) | (~ndr1_0) | c1_1(a214) | (~c2_1(a214))))),
% 0.84/1.00 inference(monotonicity,[status(thm)],[1363])).
% 0.84/1.00 tff(1365,plain,
% 0.84/1.00 (((~![U: $i] : (hskp21 | hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp21 | hskp12 | (~ndr1_0) | c1_1(a214) | c3_1(a214) | (~c2_1(a214)))) <=> ((~![U: $i] : (hskp21 | hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | hskp21 | hskp12 | c3_1(a214) | (~ndr1_0) | c1_1(a214) | (~c2_1(a214)))),
% 0.84/1.00 inference(transitivity,[status(thm)],[1364, 1362])).
% 0.84/1.00 tff(1366,plain,
% 0.84/1.00 ((~![U: $i] : (hskp21 | hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp21 | hskp12 | (~ndr1_0) | c1_1(a214) | c3_1(a214) | (~c2_1(a214)))),
% 0.84/1.00 inference(quant_inst,[status(thm)],[])).
% 0.84/1.00 tff(1367,plain,
% 0.84/1.00 ((~![U: $i] : (hskp21 | hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | hskp21 | hskp12 | c3_1(a214) | (~ndr1_0) | c1_1(a214) | (~c2_1(a214))),
% 0.84/1.00 inference(modus_ponens,[status(thm)],[1366, 1365])).
% 0.84/1.00 tff(1368,plain,
% 0.84/1.00 (hskp21 | c1_1(a214)),
% 0.84/1.00 inference(unit_resolution,[status(thm)],[1367, 110, 526, 1360, 1358, 738])).
% 0.84/1.00 tff(1369,plain,
% 0.84/1.00 (hskp21),
% 0.84/1.00 inference(unit_resolution,[status(thm)],[1368, 1361])).
% 0.84/1.00 tff(1370,plain,
% 0.84/1.00 (~c2_1(a259)),
% 0.84/1.00 inference(unit_resolution,[status(thm)],[975, 1369])).
% 0.84/1.00 tff(1371,plain,
% 0.84/1.00 (c3_1(a259)),
% 0.84/1.00 inference(unit_resolution,[status(thm)],[792, 1369])).
% 0.84/1.00 tff(1372,plain,
% 0.84/1.00 (~c1_1(a259)),
% 0.84/1.00 inference(unit_resolution,[status(thm)],[1291, 110, 596, 1237, 1221, 1371, 1370, 615, 1244])).
% 0.84/1.00 tff(1373,plain,
% 0.84/1.00 (c0_1(a259)),
% 0.84/1.00 inference(unit_resolution,[status(thm)],[783, 1369])).
% 0.84/1.00 tff(1374,plain,
% 0.84/1.00 (((~![U: $i] : (hskp19 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp19 | hskp18 | c2_1(a259) | (~ndr1_0) | (~c0_1(a259)) | c1_1(a259))) <=> ((~![U: $i] : (hskp19 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp19 | hskp18 | c2_1(a259) | (~ndr1_0) | (~c0_1(a259)) | c1_1(a259))),
% 0.84/1.00 inference(rewrite,[status(thm)],[])).
% 0.84/1.00 tff(1375,plain,
% 0.84/1.00 ((hskp19 | hskp18 | (~ndr1_0) | c2_1(a259) | c1_1(a259) | (~c0_1(a259))) <=> (hskp19 | hskp18 | c2_1(a259) | (~ndr1_0) | (~c0_1(a259)) | c1_1(a259))),
% 0.84/1.00 inference(rewrite,[status(thm)],[])).
% 0.84/1.00 tff(1376,plain,
% 0.84/1.00 (((~![U: $i] : (hskp19 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp19 | hskp18 | (~ndr1_0) | c2_1(a259) | c1_1(a259) | (~c0_1(a259)))) <=> ((~![U: $i] : (hskp19 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp19 | hskp18 | c2_1(a259) | (~ndr1_0) | (~c0_1(a259)) | c1_1(a259)))),
% 0.84/1.00 inference(monotonicity,[status(thm)],[1375])).
% 0.84/1.00 tff(1377,plain,
% 0.84/1.00 (((~![U: $i] : (hskp19 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp19 | hskp18 | (~ndr1_0) | c2_1(a259) | c1_1(a259) | (~c0_1(a259)))) <=> ((~![U: $i] : (hskp19 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp19 | hskp18 | c2_1(a259) | (~ndr1_0) | (~c0_1(a259)) | c1_1(a259))),
% 0.84/1.00 inference(transitivity,[status(thm)],[1376, 1374])).
% 0.84/1.00 tff(1378,plain,
% 0.84/1.00 ((~![U: $i] : (hskp19 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp19 | hskp18 | (~ndr1_0) | c2_1(a259) | c1_1(a259) | (~c0_1(a259)))),
% 0.84/1.00 inference(quant_inst,[status(thm)],[])).
% 0.84/1.00 tff(1379,plain,
% 0.84/1.00 ((~![U: $i] : (hskp19 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp19 | hskp18 | c2_1(a259) | (~ndr1_0) | (~c0_1(a259)) | c1_1(a259)),
% 0.84/1.00 inference(modus_ponens,[status(thm)],[1378, 1377])).
% 0.84/1.01 tff(1380,plain,
% 0.84/1.01 (hskp19 | c1_1(a259)),
% 0.84/1.01 inference(unit_resolution,[status(thm)],[1379, 110, 596, 1373, 1370, 1084])).
% 0.84/1.01 tff(1381,plain,
% 0.84/1.01 (hskp19),
% 0.84/1.01 inference(unit_resolution,[status(thm)],[1380, 1372])).
% 0.84/1.01 tff(1382,plain,
% 0.84/1.01 (~c1_1(a255)),
% 0.84/1.01 inference(unit_resolution,[status(thm)],[273, 1381])).
% 0.84/1.01 tff(1383,plain,
% 0.84/1.01 (~c0_1(a255)),
% 0.84/1.01 inference(unit_resolution,[status(thm)],[279, 1381])).
% 0.84/1.01 tff(1384,plain,
% 0.84/1.01 (c2_1(a255)),
% 0.84/1.01 inference(unit_resolution,[status(thm)],[1103, 110, 1356, 1383, 1382, 1008])).
% 0.84/1.01 tff(1385,plain,
% 0.84/1.01 (hskp17 | c1_1(a259)),
% 0.84/1.01 inference(unit_resolution,[status(thm)],[1331, 110, 526, 1373, 1370, 1325])).
% 0.84/1.01 tff(1386,plain,
% 0.84/1.01 (hskp17),
% 0.84/1.01 inference(unit_resolution,[status(thm)],[1385, 1372])).
% 0.84/1.01 tff(1387,plain,
% 0.84/1.01 (~c2_1(a248)),
% 0.84/1.01 inference(unit_resolution,[status(thm)],[629, 1386])).
% 0.84/1.01 tff(1388,plain,
% 0.84/1.01 (~c3_1(a255)),
% 0.84/1.01 inference(unit_resolution,[status(thm)],[267, 1381])).
% 0.84/1.01 tff(1389,plain,
% 0.84/1.01 (c3_1(a248)),
% 0.84/1.01 inference(unit_resolution,[status(thm)],[637, 1386])).
% 0.84/1.01 tff(1390,plain,
% 0.84/1.01 (c1_1(a248)),
% 0.84/1.01 inference(unit_resolution,[status(thm)],[623, 1386])).
% 0.84/1.01 tff(1391,plain,
% 0.84/1.01 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | (c2_1(a259) | c1_1(a255) | c3_1(a255) | c2_1(a248) | (~ndr1_0) | (~c3_1(a248)) | (~c1_1(a248)) | (~c2_1(a255)) | (~c0_1(a259)) | c1_1(a259))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | c2_1(a259) | c1_1(a255) | c3_1(a255) | c2_1(a248) | (~ndr1_0) | (~c3_1(a248)) | (~c1_1(a248)) | (~c2_1(a255)) | (~c0_1(a259)) | c1_1(a259))),
% 0.84/1.01 inference(rewrite,[status(thm)],[])).
% 0.84/1.01 tff(1392,plain,
% 0.84/1.01 (((~ndr1_0) | c2_1(a248) | (~c3_1(a248)) | (~c1_1(a248)) | c3_1(a255) | c1_1(a255) | (~c2_1(a255)) | c2_1(a259) | c1_1(a259) | (~c0_1(a259))) <=> (c2_1(a259) | c1_1(a255) | c3_1(a255) | c2_1(a248) | (~ndr1_0) | (~c3_1(a248)) | (~c1_1(a248)) | (~c2_1(a255)) | (~c0_1(a259)) | c1_1(a259))),
% 0.84/1.01 inference(rewrite,[status(thm)],[])).
% 0.84/1.01 tff(1393,plain,
% 0.84/1.01 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a248) | (~c3_1(a248)) | (~c1_1(a248)) | c3_1(a255) | c1_1(a255) | (~c2_1(a255)) | c2_1(a259) | c1_1(a259) | (~c0_1(a259)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | (c2_1(a259) | c1_1(a255) | c3_1(a255) | c2_1(a248) | (~ndr1_0) | (~c3_1(a248)) | (~c1_1(a248)) | (~c2_1(a255)) | (~c0_1(a259)) | c1_1(a259)))),
% 0.84/1.01 inference(monotonicity,[status(thm)],[1392])).
% 0.84/1.01 tff(1394,plain,
% 0.84/1.01 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a248) | (~c3_1(a248)) | (~c1_1(a248)) | c3_1(a255) | c1_1(a255) | (~c2_1(a255)) | c2_1(a259) | c1_1(a259) | (~c0_1(a259)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | c2_1(a259) | c1_1(a255) | c3_1(a255) | c2_1(a248) | (~ndr1_0) | (~c3_1(a248)) | (~c1_1(a248)) | (~c2_1(a255)) | (~c0_1(a259)) | c1_1(a259))),
% 0.84/1.01 inference(transitivity,[status(thm)],[1393, 1391])).
% 0.84/1.01 tff(1395,plain,
% 0.84/1.01 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a248) | (~c3_1(a248)) | (~c1_1(a248)) | c3_1(a255) | c1_1(a255) | (~c2_1(a255)) | c2_1(a259) | c1_1(a259) | (~c0_1(a259)))),
% 0.84/1.01 inference(quant_inst,[status(thm)],[])).
% 0.84/1.01 tff(1396,plain,
% 0.84/1.01 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | c2_1(a259) | c1_1(a255) | c3_1(a255) | c2_1(a248) | (~ndr1_0) | (~c3_1(a248)) | (~c1_1(a248)) | (~c2_1(a255)) | (~c0_1(a259)) | c1_1(a259)),
% 0.84/1.01 inference(modus_ponens,[status(thm)],[1395, 1394])).
% 0.84/1.01 tff(1397,plain,
% 0.84/1.01 ($false),
% 0.84/1.01 inference(unit_resolution,[status(thm)],[1396, 110, 1373, 1390, 1389, 1370, 1382, 1388, 1387, 803, 1372, 1384])).
% 0.84/1.01 tff(1398,plain,(hskp12 | hskp18), inference(lemma,lemma(discharge,[]))).
% 0.84/1.01 tff(1399,plain,
% 0.84/1.01 (hskp12),
% 0.84/1.01 inference(unit_resolution,[status(thm)],[1398, 596])).
% 0.84/1.01 tff(1400,plain,
% 0.84/1.01 (~c3_1(a237)),
% 0.84/1.01 inference(unit_resolution,[status(thm)],[696, 1399])).
% 0.84/1.01 tff(1401,plain,
% 0.84/1.01 (c2_1(a237)),
% 0.84/1.01 inference(unit_resolution,[status(thm)],[556, 1399])).
% 0.84/1.01 tff(1402,plain,
% 0.84/1.01 (c0_1(a237)),
% 0.84/1.01 inference(unit_resolution,[status(thm)],[575, 1399])).
% 0.84/1.01 tff(1403,plain,
% 0.84/1.01 (((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp18 | c3_1(a237) | c1_1(a218) | (~ndr1_0) | (~c3_1(a218)) | (~c0_1(a218)) | (~c2_1(a237)) | (~c0_1(a237)))) <=> ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp18 | c3_1(a237) | c1_1(a218) | (~ndr1_0) | (~c3_1(a218)) | (~c0_1(a218)) | (~c2_1(a237)) | (~c0_1(a237)))),
% 0.84/1.01 inference(rewrite,[status(thm)],[])).
% 0.84/1.01 tff(1404,plain,
% 0.84/1.01 ((hskp18 | (~ndr1_0) | c3_1(a237) | (~c2_1(a237)) | (~c0_1(a237)) | c1_1(a218) | (~c3_1(a218)) | (~c0_1(a218))) <=> (hskp18 | c3_1(a237) | c1_1(a218) | (~ndr1_0) | (~c3_1(a218)) | (~c0_1(a218)) | (~c2_1(a237)) | (~c0_1(a237)))),
% 0.84/1.01 inference(rewrite,[status(thm)],[])).
% 0.84/1.01 tff(1405,plain,
% 0.84/1.01 (((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp18 | (~ndr1_0) | c3_1(a237) | (~c2_1(a237)) | (~c0_1(a237)) | c1_1(a218) | (~c3_1(a218)) | (~c0_1(a218)))) <=> ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp18 | c3_1(a237) | c1_1(a218) | (~ndr1_0) | (~c3_1(a218)) | (~c0_1(a218)) | (~c2_1(a237)) | (~c0_1(a237))))),
% 0.84/1.01 inference(monotonicity,[status(thm)],[1404])).
% 0.84/1.01 tff(1406,plain,
% 0.84/1.01 (((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp18 | (~ndr1_0) | c3_1(a237) | (~c2_1(a237)) | (~c0_1(a237)) | c1_1(a218) | (~c3_1(a218)) | (~c0_1(a218)))) <=> ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp18 | c3_1(a237) | c1_1(a218) | (~ndr1_0) | (~c3_1(a218)) | (~c0_1(a218)) | (~c2_1(a237)) | (~c0_1(a237)))),
% 0.84/1.01 inference(transitivity,[status(thm)],[1405, 1403])).
% 0.84/1.01 tff(1407,plain,
% 0.84/1.01 ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp18 | (~ndr1_0) | c3_1(a237) | (~c2_1(a237)) | (~c0_1(a237)) | c1_1(a218) | (~c3_1(a218)) | (~c0_1(a218)))),
% 0.84/1.01 inference(quant_inst,[status(thm)],[])).
% 0.84/1.01 tff(1408,plain,
% 0.84/1.01 ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp18 | c3_1(a237) | c1_1(a218) | (~ndr1_0) | (~c3_1(a218)) | (~c0_1(a218)) | (~c2_1(a237)) | (~c0_1(a237))),
% 0.84/1.01 inference(modus_ponens,[status(thm)],[1407, 1406])).
% 0.84/1.01 tff(1409,plain,
% 0.84/1.01 (~c0_1(a218)),
% 0.84/1.01 inference(unit_resolution,[status(thm)],[1408, 110, 596, 1402, 1401, 1258, 1400, 1257, 1285])).
% 0.84/1.01 tff(1410,plain,
% 0.84/1.01 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c0_1(W)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c0_1(W)))),
% 0.84/1.01 inference(bind,[status(th)],[])).
% 0.84/1.01 tff(1411,plain,
% 0.84/1.01 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))),
% 0.84/1.01 inference(quant_intro,[status(thm)],[1410])).
% 0.84/1.01 tff(1412,plain,
% 0.84/1.01 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))),
% 0.84/1.01 inference(rewrite,[status(thm)],[])).
% 0.84/1.01 tff(1413,plain,
% 0.84/1.01 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c0_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c0_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(V)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(V))))), (((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)))), (((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(V))))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | (~c3_1(V)))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | (~c3_1(V))))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(W)) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | (~c3_1(V))) | c0_1(W)))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | (~c3_1(V))) | c0_1(W)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | (~c3_1(V)) | c0_1(W))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(W)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | (~c3_1(V)) | c0_1(W)))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(W)) | c2_1(W)) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | (~c3_1(V)) | c0_1(W)) | c2_1(W)))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | (~c3_1(V)) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | (~c3_1(V)) | c2_1(W) | c0_1(W))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | (~c3_1(V)) | c2_1(W) | c0_1(W)))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(W)) | c2_1(W)) | c3_1(W)) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | (~c3_1(V)) | c2_1(W) | c0_1(W)) | c3_1(W)))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | (~c3_1(V)) | c2_1(W) | c0_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(W)) | c2_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c0_1(W)))), ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(W)) | c2_1(W)) | c3_1(W)) | c0_1(V)) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c0_1(W)) | c0_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c0_1(W)) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))), ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(W)) | c2_1(W)) | c3_1(W)) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c0_1(W)))), (((((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(W)) | c2_1(W)) | c3_1(W)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c0_1(W)) | c1_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c0_1(W)) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))), (((((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(W)) | c2_1(W)) | c3_1(W)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))))),
% 0.84/1.01 inference(bind,[status(th)],[])).
% 0.84/1.01 tff(1414,plain,
% 0.84/1.01 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(W)) | c2_1(W)) | c3_1(W)) | c0_1(V)) | c1_1(V)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))),
% 0.84/1.01 inference(quant_intro,[status(thm)],[1413])).
% 0.84/1.01 tff(1415,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(W)) | c2_1(W)) | c3_1(W)) | c0_1(V)) | c1_1(V))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause187')).
% 0.84/1.01 tff(1416,plain,
% 0.84/1.01 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))),
% 0.84/1.01 inference(modus_ponens,[status(thm)],[1415, 1414])).
% 0.84/1.01 tff(1417,plain,
% 0.84/1.01 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))),
% 0.84/1.01 inference(modus_ponens,[status(thm)],[1416, 1412])).
% 0.84/1.01 tff(1418,plain,(
% 0.84/1.01 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))),
% 0.84/1.01 inference(skolemize,[status(sab)],[1417])).
% 0.84/1.01 tff(1419,plain,
% 0.84/1.01 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))),
% 0.84/1.01 inference(modus_ponens,[status(thm)],[1418, 1411])).
% 0.84/1.01 tff(1420,plain,
% 0.84/1.01 (hskp0),
% 0.84/1.01 inference(unit_resolution,[status(thm)],[1014, 110, 1257, 1256, 1008, 1409])).
% 0.84/1.01 tff(1421,plain,
% 0.84/1.01 (~c3_1(a213)),
% 0.84/1.01 inference(unit_resolution,[status(thm)],[744, 1420])).
% 0.84/1.01 tff(1422,plain,
% 0.84/1.01 (~c1_1(a213)),
% 0.84/1.01 inference(unit_resolution,[status(thm)],[750, 1420])).
% 0.84/1.01 tff(1423,plain,
% 0.84/1.01 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | (c0_1(a242) | c2_1(a242) | c1_1(a218) | c1_1(a213) | c3_1(a213) | (~ndr1_0) | (~c0_1(a213)) | (~c3_1(a218)) | c0_1(a218) | c3_1(a242))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c0_1(a242) | c2_1(a242) | c1_1(a218) | c1_1(a213) | c3_1(a213) | (~ndr1_0) | (~c0_1(a213)) | (~c3_1(a218)) | c0_1(a218) | c3_1(a242))),
% 0.84/1.01 inference(rewrite,[status(thm)],[])).
% 0.84/1.01 tff(1424,plain,
% 0.84/1.01 (((~ndr1_0) | c1_1(a213) | c3_1(a213) | (~c0_1(a213)) | c1_1(a218) | c0_1(a218) | (~c3_1(a218)) | c3_1(a242) | c2_1(a242) | c0_1(a242)) <=> (c0_1(a242) | c2_1(a242) | c1_1(a218) | c1_1(a213) | c3_1(a213) | (~ndr1_0) | (~c0_1(a213)) | (~c3_1(a218)) | c0_1(a218) | c3_1(a242))),
% 0.84/1.01 inference(rewrite,[status(thm)],[])).
% 0.84/1.01 tff(1425,plain,
% 0.84/1.01 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a213) | c3_1(a213) | (~c0_1(a213)) | c1_1(a218) | c0_1(a218) | (~c3_1(a218)) | c3_1(a242) | c2_1(a242) | c0_1(a242))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | (c0_1(a242) | c2_1(a242) | c1_1(a218) | c1_1(a213) | c3_1(a213) | (~ndr1_0) | (~c0_1(a213)) | (~c3_1(a218)) | c0_1(a218) | c3_1(a242)))),
% 0.84/1.01 inference(monotonicity,[status(thm)],[1424])).
% 0.84/1.01 tff(1426,plain,
% 0.84/1.01 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a213) | c3_1(a213) | (~c0_1(a213)) | c1_1(a218) | c0_1(a218) | (~c3_1(a218)) | c3_1(a242) | c2_1(a242) | c0_1(a242))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c0_1(a242) | c2_1(a242) | c1_1(a218) | c1_1(a213) | c3_1(a213) | (~ndr1_0) | (~c0_1(a213)) | (~c3_1(a218)) | c0_1(a218) | c3_1(a242))),
% 0.84/1.01 inference(transitivity,[status(thm)],[1425, 1423])).
% 0.84/1.01 tff(1427,plain,
% 0.84/1.01 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a213) | c3_1(a213) | (~c0_1(a213)) | c1_1(a218) | c0_1(a218) | (~c3_1(a218)) | c3_1(a242) | c2_1(a242) | c0_1(a242))),
% 0.84/1.01 inference(quant_inst,[status(thm)],[])).
% 0.84/1.01 tff(1428,plain,
% 0.84/1.01 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c0_1(a242) | c2_1(a242) | c1_1(a218) | c1_1(a213) | c3_1(a213) | (~ndr1_0) | (~c0_1(a213)) | (~c3_1(a218)) | c0_1(a218) | c3_1(a242)),
% 0.84/1.01 inference(modus_ponens,[status(thm)],[1427, 1426])).
% 0.84/1.01 tff(1429,plain,
% 0.84/1.01 (~c0_1(a213)),
% 0.84/1.01 inference(unit_resolution,[status(thm)],[1428, 110, 1258, 1267, 1266, 1257, 1422, 1421, 1419, 1409, 1275])).
% 0.84/1.01 tff(1430,plain,
% 0.84/1.01 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W))))),
% 0.84/1.01 inference(bind,[status(th)],[])).
% 0.84/1.01 tff(1431,plain,
% 0.84/1.01 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_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)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))),
% 0.84/1.01 inference(quant_intro,[status(thm)],[1430])).
% 0.84/1.01 tff(1432,plain,
% 0.84/1.01 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_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)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))),
% 0.84/1.01 inference(rewrite,[status(thm)],[])).
% 0.84/1.01 tff(1433,plain,
% 0.84/1.01 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~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)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(W))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V))) | (~c2_1(W))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(W)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(W))))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(W))) | c0_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(W))) | c0_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(W))) | c0_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(W)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(W))) | c0_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(W))))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(W))) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(W))) | c2_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(W))) | c2_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | (~c2_1(W)))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(W))) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | (~c2_1(W))))), ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(W))) | c0_1(V)) | c2_1(V)) | c0_1(W)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | (~c2_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | (~c2_1(W))) | c0_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)))), ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(W))) | c0_1(V)) | c2_1(V)) | c0_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W))))), (((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(W))) | c0_1(V)) | c2_1(V)) | c0_1(W)) | c1_1(W)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W))) | c1_1(W)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W))) | c1_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))), (((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(W))) | c0_1(V)) | c2_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))))),
% 0.84/1.01 inference(bind,[status(th)],[])).
% 0.84/1.01 tff(1434,plain,
% 0.84/1.01 (![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(W))) | c0_1(V)) | c2_1(V)) | c0_1(W)) | c1_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))),
% 0.84/1.01 inference(quant_intro,[status(thm)],[1433])).
% 0.84/1.01 tff(1435,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(W))) | c0_1(V)) | c2_1(V)) | c0_1(W)) | c1_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause192')).
% 0.84/1.01 tff(1436,plain,
% 0.84/1.01 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))),
% 0.84/1.01 inference(modus_ponens,[status(thm)],[1435, 1434])).
% 0.84/1.01 tff(1437,plain,
% 0.84/1.01 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))),
% 0.84/1.01 inference(modus_ponens,[status(thm)],[1436, 1432])).
% 0.84/1.01 tff(1438,plain,(
% 0.84/1.01 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))),
% 0.84/1.01 inference(skolemize,[status(sab)],[1437])).
% 0.84/1.01 tff(1439,plain,
% 0.84/1.01 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))),
% 0.84/1.01 inference(modus_ponens,[status(thm)],[1438, 1431])).
% 0.84/1.01 tff(1440,plain,
% 0.84/1.01 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp19 | c2_1(a242) | (~ndr1_0) | (~c2_1(a261)) | (~c3_1(a261)) | c0_1(a261) | c3_1(a242) | (~c1_1(a242)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp19 | c2_1(a242) | (~ndr1_0) | (~c2_1(a261)) | (~c3_1(a261)) | c0_1(a261) | c3_1(a242) | (~c1_1(a242)))),
% 0.84/1.01 inference(rewrite,[status(thm)],[])).
% 0.84/1.01 tff(1441,plain,
% 0.84/1.01 ((hskp19 | (~ndr1_0) | c2_1(a242) | c3_1(a242) | (~c1_1(a242)) | c0_1(a261) | (~c3_1(a261)) | (~c2_1(a261))) <=> (hskp19 | c2_1(a242) | (~ndr1_0) | (~c2_1(a261)) | (~c3_1(a261)) | c0_1(a261) | c3_1(a242) | (~c1_1(a242)))),
% 0.84/1.01 inference(rewrite,[status(thm)],[])).
% 0.84/1.01 tff(1442,plain,
% 0.84/1.01 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp19 | (~ndr1_0) | c2_1(a242) | c3_1(a242) | (~c1_1(a242)) | c0_1(a261) | (~c3_1(a261)) | (~c2_1(a261)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp19 | c2_1(a242) | (~ndr1_0) | (~c2_1(a261)) | (~c3_1(a261)) | c0_1(a261) | c3_1(a242) | (~c1_1(a242))))),
% 0.84/1.01 inference(monotonicity,[status(thm)],[1441])).
% 0.84/1.01 tff(1443,plain,
% 0.84/1.01 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp19 | (~ndr1_0) | c2_1(a242) | c3_1(a242) | (~c1_1(a242)) | c0_1(a261) | (~c3_1(a261)) | (~c2_1(a261)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp19 | c2_1(a242) | (~ndr1_0) | (~c2_1(a261)) | (~c3_1(a261)) | c0_1(a261) | c3_1(a242) | (~c1_1(a242)))),
% 0.84/1.01 inference(transitivity,[status(thm)],[1442, 1440])).
% 0.84/1.01 tff(1444,plain,
% 0.84/1.01 ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp19 | (~ndr1_0) | c2_1(a242) | c3_1(a242) | (~c1_1(a242)) | c0_1(a261) | (~c3_1(a261)) | (~c2_1(a261)))),
% 0.84/1.01 inference(quant_inst,[status(thm)],[])).
% 0.84/1.01 tff(1445,plain,
% 0.84/1.01 ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp19 | c2_1(a242) | (~ndr1_0) | (~c2_1(a261)) | (~c3_1(a261)) | c0_1(a261) | c3_1(a242) | (~c1_1(a242))),
% 0.84/1.01 inference(modus_ponens,[status(thm)],[1444, 1443])).
% 0.84/1.01 tff(1446,plain,
% 0.84/1.01 (hskp19),
% 0.84/1.01 inference(unit_resolution,[status(thm)],[1445, 110, 1229, 1221, 1268, 1266, 301, 1244, 1275])).
% 0.84/1.01 tff(1447,plain,
% 0.84/1.01 (~c1_1(a255)),
% 0.84/1.01 inference(unit_resolution,[status(thm)],[273, 1446])).
% 0.84/1.01 tff(1448,plain,
% 0.84/1.01 (~c0_1(a255)),
% 0.84/1.01 inference(unit_resolution,[status(thm)],[279, 1446])).
% 0.84/1.01 tff(1449,plain,
% 0.84/1.01 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | (c0_1(a255) | c1_1(a255) | c2_1(a218) | (~ndr1_0) | (~c1_1(a261)) | (~c2_1(a261)) | (~c3_1(a261)) | (~c3_1(a218)) | c0_1(a218) | (~c2_1(a255)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | c0_1(a255) | c1_1(a255) | c2_1(a218) | (~ndr1_0) | (~c1_1(a261)) | (~c2_1(a261)) | (~c3_1(a261)) | (~c3_1(a218)) | c0_1(a218) | (~c2_1(a255)))),
% 0.84/1.01 inference(rewrite,[status(thm)],[])).
% 0.84/1.01 tff(1450,plain,
% 0.84/1.01 (((~ndr1_0) | (~c2_1(a261)) | (~c3_1(a261)) | (~c1_1(a261)) | c0_1(a218) | c2_1(a218) | (~c3_1(a218)) | c0_1(a255) | c1_1(a255) | (~c2_1(a255))) <=> (c0_1(a255) | c1_1(a255) | c2_1(a218) | (~ndr1_0) | (~c1_1(a261)) | (~c2_1(a261)) | (~c3_1(a261)) | (~c3_1(a218)) | c0_1(a218) | (~c2_1(a255)))),
% 0.84/1.01 inference(rewrite,[status(thm)],[])).
% 0.84/1.01 tff(1451,plain,
% 0.84/1.01 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a261)) | (~c3_1(a261)) | (~c1_1(a261)) | c0_1(a218) | c2_1(a218) | (~c3_1(a218)) | c0_1(a255) | c1_1(a255) | (~c2_1(a255)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | (c0_1(a255) | c1_1(a255) | c2_1(a218) | (~ndr1_0) | (~c1_1(a261)) | (~c2_1(a261)) | (~c3_1(a261)) | (~c3_1(a218)) | c0_1(a218) | (~c2_1(a255))))),
% 0.84/1.01 inference(monotonicity,[status(thm)],[1450])).
% 0.84/1.01 tff(1452,plain,
% 0.84/1.01 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a261)) | (~c3_1(a261)) | (~c1_1(a261)) | c0_1(a218) | c2_1(a218) | (~c3_1(a218)) | c0_1(a255) | c1_1(a255) | (~c2_1(a255)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | c0_1(a255) | c1_1(a255) | c2_1(a218) | (~ndr1_0) | (~c1_1(a261)) | (~c2_1(a261)) | (~c3_1(a261)) | (~c3_1(a218)) | c0_1(a218) | (~c2_1(a255)))),
% 0.84/1.01 inference(transitivity,[status(thm)],[1451, 1449])).
% 0.84/1.01 tff(1453,plain,
% 0.84/1.01 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a261)) | (~c3_1(a261)) | (~c1_1(a261)) | c0_1(a218) | c2_1(a218) | (~c3_1(a218)) | c0_1(a255) | c1_1(a255) | (~c2_1(a255)))),
% 0.84/1.01 inference(quant_inst,[status(thm)],[])).
% 0.84/1.01 tff(1454,plain,
% 0.84/1.01 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | c0_1(a255) | c1_1(a255) | c2_1(a218) | (~ndr1_0) | (~c1_1(a261)) | (~c2_1(a261)) | (~c3_1(a261)) | (~c3_1(a218)) | c0_1(a218) | (~c2_1(a255))),
% 0.84/1.01 inference(modus_ponens,[status(thm)],[1453, 1452])).
% 0.84/1.01 tff(1455,plain,
% 0.84/1.01 (~c2_1(a255)),
% 0.84/1.01 inference(unit_resolution,[status(thm)],[1454, 110, 1237, 1229, 1221, 1258, 1448, 1447, 1256, 1439, 1409])).
% 0.84/1.01 tff(1456,plain,
% 0.84/1.01 (^[V: $i, U: $i] : refl((hskp8 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V)) <=> (hskp8 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V)))),
% 0.84/1.01 inference(bind,[status(th)],[])).
% 0.84/1.01 tff(1457,plain,
% 0.84/1.01 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V)) <=> ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))),
% 0.84/1.01 inference(quant_intro,[status(thm)],[1456])).
% 0.84/1.01 tff(1458,plain,
% 0.84/1.01 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V)) <=> ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))),
% 0.84/1.01 inference(rewrite,[status(thm)],[])).
% 0.84/1.01 tff(1459,plain,
% 0.84/1.01 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c1_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U))))), (((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))), (((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))))), ((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V))), ((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V)))), (((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c2_1(V))), (((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c2_1(V)))), ((((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c2_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))), ((((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V)))), (((((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | hskp8) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V)) | hskp8))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V)) | hskp8) <=> (hskp8 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))), (((((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | hskp8) <=> (hskp8 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))))),
% 0.84/1.01 inference(bind,[status(th)],[])).
% 0.84/1.01 tff(1460,plain,
% 0.84/1.01 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | hskp8) <=> ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))),
% 0.84/1.01 inference(quant_intro,[status(thm)],[1459])).
% 0.84/1.01 tff(1461,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | hskp8)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause158')).
% 0.84/1.01 tff(1462,plain,
% 0.84/1.01 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))),
% 0.84/1.01 inference(modus_ponens,[status(thm)],[1461, 1460])).
% 0.84/1.01 tff(1463,plain,
% 0.84/1.01 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))),
% 0.84/1.01 inference(modus_ponens,[status(thm)],[1462, 1458])).
% 0.84/1.01 tff(1464,plain,(
% 0.84/1.01 ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))),
% 0.84/1.01 inference(skolemize,[status(sab)],[1463])).
% 0.84/1.01 tff(1465,plain,
% 0.84/1.01 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))),
% 0.84/1.02 inference(modus_ponens,[status(thm)],[1464, 1457])).
% 0.84/1.02 tff(1466,plain,
% 0.84/1.02 (~c3_1(a255)),
% 0.84/1.02 inference(unit_resolution,[status(thm)],[267, 1446])).
% 0.84/1.02 tff(1467,plain,
% 0.84/1.02 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp8 | c1_1(a255) | c3_1(a255) | c2_1(a242) | (~ndr1_0) | c3_1(a242) | (~c1_1(a242)) | c2_1(a255))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp8 | c1_1(a255) | c3_1(a255) | c2_1(a242) | (~ndr1_0) | c3_1(a242) | (~c1_1(a242)) | c2_1(a255))),
% 0.84/1.02 inference(rewrite,[status(thm)],[])).
% 0.84/1.02 tff(1468,plain,
% 0.84/1.02 ((hskp8 | (~ndr1_0) | c2_1(a242) | c3_1(a242) | (~c1_1(a242)) | c3_1(a255) | c1_1(a255) | c2_1(a255)) <=> (hskp8 | c1_1(a255) | c3_1(a255) | c2_1(a242) | (~ndr1_0) | c3_1(a242) | (~c1_1(a242)) | c2_1(a255))),
% 0.84/1.02 inference(rewrite,[status(thm)],[])).
% 0.84/1.02 tff(1469,plain,
% 0.84/1.02 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp8 | (~ndr1_0) | c2_1(a242) | c3_1(a242) | (~c1_1(a242)) | c3_1(a255) | c1_1(a255) | c2_1(a255))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp8 | c1_1(a255) | c3_1(a255) | c2_1(a242) | (~ndr1_0) | c3_1(a242) | (~c1_1(a242)) | c2_1(a255)))),
% 0.84/1.02 inference(monotonicity,[status(thm)],[1468])).
% 0.84/1.02 tff(1470,plain,
% 0.84/1.02 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp8 | (~ndr1_0) | c2_1(a242) | c3_1(a242) | (~c1_1(a242)) | c3_1(a255) | c1_1(a255) | c2_1(a255))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp8 | c1_1(a255) | c3_1(a255) | c2_1(a242) | (~ndr1_0) | c3_1(a242) | (~c1_1(a242)) | c2_1(a255))),
% 0.84/1.02 inference(transitivity,[status(thm)],[1469, 1467])).
% 0.84/1.02 tff(1471,plain,
% 0.84/1.02 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp8 | (~ndr1_0) | c2_1(a242) | c3_1(a242) | (~c1_1(a242)) | c3_1(a255) | c1_1(a255) | c2_1(a255))),
% 0.84/1.02 inference(quant_inst,[status(thm)],[])).
% 0.84/1.02 tff(1472,plain,
% 0.84/1.02 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp8 | c1_1(a255) | c3_1(a255) | c2_1(a242) | (~ndr1_0) | c3_1(a242) | (~c1_1(a242)) | c2_1(a255)),
% 0.84/1.02 inference(modus_ponens,[status(thm)],[1471, 1470])).
% 0.84/1.02 tff(1473,plain,
% 0.84/1.02 (hskp8 | c2_1(a255)),
% 0.84/1.02 inference(unit_resolution,[status(thm)],[1472, 110, 1268, 1447, 1466, 1266, 1465, 1275])).
% 0.84/1.02 tff(1474,plain,
% 0.84/1.02 (hskp8),
% 0.84/1.02 inference(unit_resolution,[status(thm)],[1473, 1455])).
% 0.84/1.02 tff(1475,plain,
% 0.84/1.02 (((~hskp8) | (~c2_1(a225))) <=> ((~hskp8) | (~c2_1(a225)))),
% 0.84/1.02 inference(rewrite,[status(thm)],[])).
% 0.84/1.02 tff(1476,plain,
% 0.84/1.02 (((~c2_1(a225)) | (~hskp8)) <=> ((~hskp8) | (~c2_1(a225)))),
% 0.84/1.02 inference(rewrite,[status(thm)],[])).
% 0.84/1.02 tff(1477,axiom,((~c2_1(a225)) | (~hskp8)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause115')).
% 0.84/1.02 tff(1478,plain,
% 0.84/1.02 ((~hskp8) | (~c2_1(a225))),
% 0.84/1.02 inference(modus_ponens,[status(thm)],[1477, 1476])).
% 0.84/1.02 tff(1479,plain,
% 0.84/1.02 ((~hskp8) | (~c2_1(a225))),
% 0.84/1.02 inference(modus_ponens,[status(thm)],[1478, 1475])).
% 0.84/1.02 tff(1480,plain,
% 0.84/1.02 (~c2_1(a225)),
% 0.84/1.02 inference(unit_resolution,[status(thm)],[1479, 1474])).
% 0.84/1.02 tff(1481,plain,
% 0.84/1.02 (((~hskp8) | (~c0_1(a225))) <=> ((~hskp8) | (~c0_1(a225)))),
% 0.84/1.02 inference(rewrite,[status(thm)],[])).
% 0.84/1.02 tff(1482,plain,
% 0.84/1.02 (((~c0_1(a225)) | (~hskp8)) <=> ((~hskp8) | (~c0_1(a225)))),
% 0.84/1.02 inference(rewrite,[status(thm)],[])).
% 0.84/1.02 tff(1483,axiom,((~c0_1(a225)) | (~hskp8)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause114')).
% 0.84/1.02 tff(1484,plain,
% 0.84/1.02 ((~hskp8) | (~c0_1(a225))),
% 0.84/1.02 inference(modus_ponens,[status(thm)],[1483, 1482])).
% 0.84/1.02 tff(1485,plain,
% 0.84/1.02 ((~hskp8) | (~c0_1(a225))),
% 0.84/1.02 inference(modus_ponens,[status(thm)],[1484, 1481])).
% 0.84/1.02 tff(1486,plain,
% 0.84/1.02 (~c0_1(a225)),
% 0.84/1.02 inference(unit_resolution,[status(thm)],[1485, 1474])).
% 0.84/1.02 tff(1487,plain,
% 0.84/1.02 (c2_1(a213)),
% 0.84/1.02 inference(unit_resolution,[status(thm)],[758, 1420])).
% 0.84/1.02 tff(1488,plain,
% 0.84/1.02 (((~hskp8) | c3_1(a225)) <=> ((~hskp8) | c3_1(a225))),
% 0.84/1.02 inference(rewrite,[status(thm)],[])).
% 0.84/1.02 tff(1489,axiom,((~hskp8) | c3_1(a225)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause75')).
% 0.84/1.02 tff(1490,plain,
% 0.84/1.02 ((~hskp8) | c3_1(a225)),
% 0.84/1.02 inference(modus_ponens,[status(thm)],[1489, 1488])).
% 0.84/1.02 tff(1491,plain,
% 0.84/1.02 ((~hskp8) | c3_1(a225)),
% 0.84/1.02 inference(modus_ponens,[status(thm)],[1490, 1488])).
% 0.84/1.02 tff(1492,plain,
% 0.84/1.02 ((~hskp8) | c3_1(a225)),
% 0.84/1.02 inference(modus_ponens,[status(thm)],[1491, 1488])).
% 0.84/1.02 tff(1493,plain,
% 0.84/1.02 ((~hskp8) | c3_1(a225)),
% 0.84/1.02 inference(modus_ponens,[status(thm)],[1492, 1488])).
% 0.84/1.02 tff(1494,plain,
% 0.84/1.02 ((~hskp8) | c3_1(a225)),
% 0.84/1.02 inference(modus_ponens,[status(thm)],[1493, 1488])).
% 0.84/1.02 tff(1495,plain,
% 0.84/1.02 (c3_1(a225)),
% 0.84/1.02 inference(unit_resolution,[status(thm)],[1494, 1474])).
% 0.84/1.02 tff(1496,plain,
% 0.84/1.02 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | (c0_1(a225) | c2_1(a225) | c1_1(a213) | (~ndr1_0) | c0_1(a213) | (~c2_1(a213)) | (~c1_1(a261)) | (~c2_1(a261)) | (~c3_1(a261)) | (~c3_1(a225)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | c0_1(a225) | c2_1(a225) | c1_1(a213) | (~ndr1_0) | c0_1(a213) | (~c2_1(a213)) | (~c1_1(a261)) | (~c2_1(a261)) | (~c3_1(a261)) | (~c3_1(a225)))),
% 0.84/1.02 inference(rewrite,[status(thm)],[])).
% 0.84/1.02 tff(1497,plain,
% 0.84/1.02 (((~ndr1_0) | (~c2_1(a261)) | (~c3_1(a261)) | (~c1_1(a261)) | c0_1(a225) | c2_1(a225) | (~c3_1(a225)) | c0_1(a213) | c1_1(a213) | (~c2_1(a213))) <=> (c0_1(a225) | c2_1(a225) | c1_1(a213) | (~ndr1_0) | c0_1(a213) | (~c2_1(a213)) | (~c1_1(a261)) | (~c2_1(a261)) | (~c3_1(a261)) | (~c3_1(a225)))),
% 0.84/1.02 inference(rewrite,[status(thm)],[])).
% 0.84/1.02 tff(1498,plain,
% 0.84/1.02 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a261)) | (~c3_1(a261)) | (~c1_1(a261)) | c0_1(a225) | c2_1(a225) | (~c3_1(a225)) | c0_1(a213) | c1_1(a213) | (~c2_1(a213)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | (c0_1(a225) | c2_1(a225) | c1_1(a213) | (~ndr1_0) | c0_1(a213) | (~c2_1(a213)) | (~c1_1(a261)) | (~c2_1(a261)) | (~c3_1(a261)) | (~c3_1(a225))))),
% 0.84/1.02 inference(monotonicity,[status(thm)],[1497])).
% 0.84/1.02 tff(1499,plain,
% 0.84/1.02 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a261)) | (~c3_1(a261)) | (~c1_1(a261)) | c0_1(a225) | c2_1(a225) | (~c3_1(a225)) | c0_1(a213) | c1_1(a213) | (~c2_1(a213)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | c0_1(a225) | c2_1(a225) | c1_1(a213) | (~ndr1_0) | c0_1(a213) | (~c2_1(a213)) | (~c1_1(a261)) | (~c2_1(a261)) | (~c3_1(a261)) | (~c3_1(a225)))),
% 0.84/1.02 inference(transitivity,[status(thm)],[1498, 1496])).
% 0.84/1.02 tff(1500,plain,
% 0.84/1.02 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a261)) | (~c3_1(a261)) | (~c1_1(a261)) | c0_1(a225) | c2_1(a225) | (~c3_1(a225)) | c0_1(a213) | c1_1(a213) | (~c2_1(a213)))),
% 0.84/1.02 inference(quant_inst,[status(thm)],[])).
% 0.84/1.02 tff(1501,plain,
% 0.84/1.02 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | c0_1(a225) | c2_1(a225) | c1_1(a213) | (~ndr1_0) | c0_1(a213) | (~c2_1(a213)) | (~c1_1(a261)) | (~c2_1(a261)) | (~c3_1(a261)) | (~c3_1(a225))),
% 0.84/1.02 inference(modus_ponens,[status(thm)],[1500, 1499])).
% 0.84/1.02 tff(1502,plain,
% 0.84/1.02 ($false),
% 0.84/1.02 inference(unit_resolution,[status(thm)],[1501, 110, 1237, 1229, 1221, 1495, 1487, 1486, 1480, 1422, 1439, 1429])).
% 0.84/1.02 tff(1503,plain,((~hskp5) | hskp18), inference(lemma,lemma(discharge,[]))).
% 0.84/1.02 tff(1504,plain,
% 0.84/1.02 (~hskp5),
% 0.84/1.02 inference(unit_resolution,[status(thm)],[1503, 596])).
% 0.84/1.02 tff(1505,plain,
% 0.84/1.02 (c3_1(a231)),
% 0.84/1.02 inference(unit_resolution,[status(thm)],[1341, 597])).
% 0.84/1.02 tff(1506,plain,
% 0.84/1.02 (~c0_1(a231)),
% 0.84/1.02 inference(unit_resolution,[status(thm)],[1314, 597])).
% 0.84/1.02 tff(1507,assumption,(~c0_1(a231)), introduced(assumption)).
% 0.84/1.02 tff(1508,assumption,(c3_1(a231)), introduced(assumption)).
% 0.84/1.02 tff(1509,assumption,(c1_1(a231)), introduced(assumption)).
% 0.84/1.02 tff(1510,plain,
% 0.84/1.02 (((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp18 | c3_1(a237) | c1_1(a226) | (~ndr1_0) | (~c3_1(a226)) | (~c0_1(a226)) | (~c2_1(a237)) | (~c0_1(a237)))) <=> ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp18 | c3_1(a237) | c1_1(a226) | (~ndr1_0) | (~c3_1(a226)) | (~c0_1(a226)) | (~c2_1(a237)) | (~c0_1(a237)))),
% 0.84/1.02 inference(rewrite,[status(thm)],[])).
% 0.84/1.02 tff(1511,plain,
% 0.84/1.02 ((hskp18 | (~ndr1_0) | c3_1(a237) | (~c2_1(a237)) | (~c0_1(a237)) | c1_1(a226) | (~c3_1(a226)) | (~c0_1(a226))) <=> (hskp18 | c3_1(a237) | c1_1(a226) | (~ndr1_0) | (~c3_1(a226)) | (~c0_1(a226)) | (~c2_1(a237)) | (~c0_1(a237)))),
% 0.84/1.02 inference(rewrite,[status(thm)],[])).
% 0.84/1.02 tff(1512,plain,
% 0.84/1.02 (((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp18 | (~ndr1_0) | c3_1(a237) | (~c2_1(a237)) | (~c0_1(a237)) | c1_1(a226) | (~c3_1(a226)) | (~c0_1(a226)))) <=> ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp18 | c3_1(a237) | c1_1(a226) | (~ndr1_0) | (~c3_1(a226)) | (~c0_1(a226)) | (~c2_1(a237)) | (~c0_1(a237))))),
% 0.84/1.02 inference(monotonicity,[status(thm)],[1511])).
% 0.84/1.02 tff(1513,plain,
% 0.84/1.02 (((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp18 | (~ndr1_0) | c3_1(a237) | (~c2_1(a237)) | (~c0_1(a237)) | c1_1(a226) | (~c3_1(a226)) | (~c0_1(a226)))) <=> ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp18 | c3_1(a237) | c1_1(a226) | (~ndr1_0) | (~c3_1(a226)) | (~c0_1(a226)) | (~c2_1(a237)) | (~c0_1(a237)))),
% 0.84/1.02 inference(transitivity,[status(thm)],[1512, 1510])).
% 0.84/1.02 tff(1514,plain,
% 0.84/1.02 ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp18 | (~ndr1_0) | c3_1(a237) | (~c2_1(a237)) | (~c0_1(a237)) | c1_1(a226) | (~c3_1(a226)) | (~c0_1(a226)))),
% 0.84/1.02 inference(quant_inst,[status(thm)],[])).
% 0.84/1.02 tff(1515,plain,
% 0.84/1.02 ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp18 | c3_1(a237) | c1_1(a226) | (~ndr1_0) | (~c3_1(a226)) | (~c0_1(a226)) | (~c2_1(a237)) | (~c0_1(a237))),
% 0.84/1.02 inference(modus_ponens,[status(thm)],[1514, 1513])).
% 0.84/1.02 tff(1516,plain,
% 0.84/1.02 (~c3_1(a226)),
% 0.84/1.02 inference(unit_resolution,[status(thm)],[1515, 110, 596, 1402, 1401, 833, 1400, 825, 1285])).
% 0.84/1.02 tff(1517,plain,
% 0.84/1.02 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | (c3_1(a237) | c1_1(a226) | (~ndr1_0) | (~c1_1(a261)) | (~c2_1(a261)) | (~c3_1(a261)) | c3_1(a226) | (~c0_1(a226)) | (~c2_1(a237)) | (~c1_1(a237)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | c3_1(a237) | c1_1(a226) | (~ndr1_0) | (~c1_1(a261)) | (~c2_1(a261)) | (~c3_1(a261)) | c3_1(a226) | (~c0_1(a226)) | (~c2_1(a237)) | (~c1_1(a237)))),
% 0.84/1.02 inference(rewrite,[status(thm)],[])).
% 0.84/1.02 tff(1518,plain,
% 0.84/1.02 (((~ndr1_0) | (~c2_1(a261)) | (~c3_1(a261)) | (~c1_1(a261)) | c3_1(a237) | (~c1_1(a237)) | (~c2_1(a237)) | c3_1(a226) | c1_1(a226) | (~c0_1(a226))) <=> (c3_1(a237) | c1_1(a226) | (~ndr1_0) | (~c1_1(a261)) | (~c2_1(a261)) | (~c3_1(a261)) | c3_1(a226) | (~c0_1(a226)) | (~c2_1(a237)) | (~c1_1(a237)))),
% 0.84/1.02 inference(rewrite,[status(thm)],[])).
% 0.84/1.02 tff(1519,plain,
% 0.84/1.02 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_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) | (~c2_1(a261)) | (~c3_1(a261)) | (~c1_1(a261)) | c3_1(a237) | (~c1_1(a237)) | (~c2_1(a237)) | c3_1(a226) | c1_1(a226) | (~c0_1(a226)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | (c3_1(a237) | c1_1(a226) | (~ndr1_0) | (~c1_1(a261)) | (~c2_1(a261)) | (~c3_1(a261)) | c3_1(a226) | (~c0_1(a226)) | (~c2_1(a237)) | (~c1_1(a237))))),
% 0.84/1.02 inference(monotonicity,[status(thm)],[1518])).
% 0.84/1.02 tff(1520,plain,
% 0.84/1.02 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_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) | (~c2_1(a261)) | (~c3_1(a261)) | (~c1_1(a261)) | c3_1(a237) | (~c1_1(a237)) | (~c2_1(a237)) | c3_1(a226) | c1_1(a226) | (~c0_1(a226)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | c3_1(a237) | c1_1(a226) | (~ndr1_0) | (~c1_1(a261)) | (~c2_1(a261)) | (~c3_1(a261)) | c3_1(a226) | (~c0_1(a226)) | (~c2_1(a237)) | (~c1_1(a237)))),
% 0.84/1.02 inference(transitivity,[status(thm)],[1519, 1517])).
% 0.84/1.02 tff(1521,plain,
% 0.84/1.02 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_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) | (~c2_1(a261)) | (~c3_1(a261)) | (~c1_1(a261)) | c3_1(a237) | (~c1_1(a237)) | (~c2_1(a237)) | c3_1(a226) | c1_1(a226) | (~c0_1(a226)))),
% 0.84/1.02 inference(quant_inst,[status(thm)],[])).
% 0.84/1.02 tff(1522,plain,
% 0.84/1.02 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | c3_1(a237) | c1_1(a226) | (~ndr1_0) | (~c1_1(a261)) | (~c2_1(a261)) | (~c3_1(a261)) | c3_1(a226) | (~c0_1(a226)) | (~c2_1(a237)) | (~c1_1(a237))),
% 0.84/1.02 inference(modus_ponens,[status(thm)],[1521, 1520])).
% 0.84/1.02 tff(1523,plain,
% 0.84/1.02 (~c1_1(a237)),
% 0.84/1.02 inference(unit_resolution,[status(thm)],[1522, 110, 1237, 1229, 1221, 1401, 833, 1400, 825, 505, 1516])).
% 0.84/1.02 tff(1524,plain,
% 0.84/1.02 (((~![U: $i] : (hskp19 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp19 | hskp18 | c1_1(a226) | c2_1(a226) | (~ndr1_0) | (~c0_1(a226)))) <=> ((~![U: $i] : (hskp19 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp19 | hskp18 | c1_1(a226) | c2_1(a226) | (~ndr1_0) | (~c0_1(a226)))),
% 0.84/1.02 inference(rewrite,[status(thm)],[])).
% 0.84/1.02 tff(1525,plain,
% 0.84/1.02 ((hskp19 | hskp18 | (~ndr1_0) | c2_1(a226) | c1_1(a226) | (~c0_1(a226))) <=> (hskp19 | hskp18 | c1_1(a226) | c2_1(a226) | (~ndr1_0) | (~c0_1(a226)))),
% 0.84/1.02 inference(rewrite,[status(thm)],[])).
% 0.84/1.02 tff(1526,plain,
% 0.84/1.02 (((~![U: $i] : (hskp19 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp19 | hskp18 | (~ndr1_0) | c2_1(a226) | c1_1(a226) | (~c0_1(a226)))) <=> ((~![U: $i] : (hskp19 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp19 | hskp18 | c1_1(a226) | c2_1(a226) | (~ndr1_0) | (~c0_1(a226))))),
% 0.84/1.02 inference(monotonicity,[status(thm)],[1525])).
% 0.84/1.02 tff(1527,plain,
% 0.84/1.02 (((~![U: $i] : (hskp19 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp19 | hskp18 | (~ndr1_0) | c2_1(a226) | c1_1(a226) | (~c0_1(a226)))) <=> ((~![U: $i] : (hskp19 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp19 | hskp18 | c1_1(a226) | c2_1(a226) | (~ndr1_0) | (~c0_1(a226)))),
% 0.84/1.02 inference(transitivity,[status(thm)],[1526, 1524])).
% 0.84/1.02 tff(1528,plain,
% 0.84/1.02 ((~![U: $i] : (hskp19 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp19 | hskp18 | (~ndr1_0) | c2_1(a226) | c1_1(a226) | (~c0_1(a226)))),
% 0.84/1.02 inference(quant_inst,[status(thm)],[])).
% 0.84/1.02 tff(1529,plain,
% 0.84/1.02 ((~![U: $i] : (hskp19 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp19 | hskp18 | c1_1(a226) | c2_1(a226) | (~ndr1_0) | (~c0_1(a226))),
% 0.84/1.02 inference(modus_ponens,[status(thm)],[1528, 1527])).
% 0.84/1.02 tff(1530,plain,
% 0.84/1.02 (hskp19),
% 0.84/1.02 inference(unit_resolution,[status(thm)],[1529, 110, 596, 833, 825, 819, 1084])).
% 0.84/1.02 tff(1531,plain,
% 0.84/1.02 (~c1_1(a255)),
% 0.84/1.02 inference(unit_resolution,[status(thm)],[273, 1530])).
% 0.84/1.02 tff(1532,plain,
% 0.84/1.02 (~c0_1(a255)),
% 0.84/1.02 inference(unit_resolution,[status(thm)],[279, 1530])).
% 0.84/1.02 tff(1533,plain,
% 0.84/1.02 (^[V: $i, U: $i] : refl((hskp26 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))) <=> (hskp26 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))))),
% 0.84/1.02 inference(bind,[status(th)],[])).
% 0.84/1.02 tff(1534,plain,
% 0.84/1.02 (![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 0.84/1.02 inference(quant_intro,[status(thm)],[1533])).
% 0.84/1.02 tff(1535,plain,
% 0.84/1.02 (![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 0.84/1.02 inference(rewrite,[status(thm)],[])).
% 0.84/1.02 tff(1536,plain,
% 0.84/1.02 (^[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))) | c2_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V))))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V))))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_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)) | (~c2_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_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))) | 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)) | (~c2_1(V))))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | hskp26) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))) | hskp26))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))) | hskp26) <=> (hskp26 | (~ndr1_0) | c2_1(U) | c3_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))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | hskp26) <=> (hskp26 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))))),
% 0.84/1.02 inference(bind,[status(th)],[])).
% 0.84/1.02 tff(1537,plain,
% 0.84/1.02 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | hskp26) <=> ![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 0.84/1.02 inference(quant_intro,[status(thm)],[1536])).
% 0.84/1.02 tff(1538,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | hskp26)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause172')).
% 0.84/1.02 tff(1539,plain,
% 0.84/1.02 (![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 0.84/1.02 inference(modus_ponens,[status(thm)],[1538, 1537])).
% 0.84/1.02 tff(1540,plain,
% 0.84/1.02 (![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 0.84/1.02 inference(modus_ponens,[status(thm)],[1539, 1535])).
% 0.84/1.02 tff(1541,plain,(
% 0.84/1.02 ![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 0.84/1.02 inference(skolemize,[status(sab)],[1540])).
% 0.84/1.02 tff(1542,plain,
% 0.84/1.02 (![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 0.84/1.02 inference(modus_ponens,[status(thm)],[1541, 1534])).
% 0.84/1.02 tff(1543,plain,
% 0.84/1.02 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp26 | c2_1(a226) | (~ndr1_0) | (~c1_1(a261)) | (~c2_1(a261)) | c0_1(a261) | c3_1(a226) | (~c0_1(a226)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp26 | c2_1(a226) | (~ndr1_0) | (~c1_1(a261)) | (~c2_1(a261)) | c0_1(a261) | c3_1(a226) | (~c0_1(a226)))),
% 0.84/1.02 inference(rewrite,[status(thm)],[])).
% 0.84/1.02 tff(1544,plain,
% 0.84/1.02 ((hskp26 | (~ndr1_0) | c2_1(a226) | c3_1(a226) | (~c0_1(a226)) | c0_1(a261) | (~c1_1(a261)) | (~c2_1(a261))) <=> (hskp26 | c2_1(a226) | (~ndr1_0) | (~c1_1(a261)) | (~c2_1(a261)) | c0_1(a261) | c3_1(a226) | (~c0_1(a226)))),
% 0.84/1.02 inference(rewrite,[status(thm)],[])).
% 0.84/1.02 tff(1545,plain,
% 0.84/1.02 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp26 | (~ndr1_0) | c2_1(a226) | c3_1(a226) | (~c0_1(a226)) | c0_1(a261) | (~c1_1(a261)) | (~c2_1(a261)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp26 | c2_1(a226) | (~ndr1_0) | (~c1_1(a261)) | (~c2_1(a261)) | c0_1(a261) | c3_1(a226) | (~c0_1(a226))))),
% 0.84/1.02 inference(monotonicity,[status(thm)],[1544])).
% 0.84/1.02 tff(1546,plain,
% 0.84/1.02 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp26 | (~ndr1_0) | c2_1(a226) | c3_1(a226) | (~c0_1(a226)) | c0_1(a261) | (~c1_1(a261)) | (~c2_1(a261)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp26 | c2_1(a226) | (~ndr1_0) | (~c1_1(a261)) | (~c2_1(a261)) | c0_1(a261) | c3_1(a226) | (~c0_1(a226)))),
% 0.84/1.02 inference(transitivity,[status(thm)],[1545, 1543])).
% 0.84/1.02 tff(1547,plain,
% 0.84/1.02 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp26 | (~ndr1_0) | c2_1(a226) | c3_1(a226) | (~c0_1(a226)) | c0_1(a261) | (~c1_1(a261)) | (~c2_1(a261)))),
% 0.84/1.02 inference(quant_inst,[status(thm)],[])).
% 0.84/1.02 tff(1548,plain,
% 0.84/1.02 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp26 | c2_1(a226) | (~ndr1_0) | (~c1_1(a261)) | (~c2_1(a261)) | c0_1(a261) | c3_1(a226) | (~c0_1(a226))),
% 0.84/1.02 inference(modus_ponens,[status(thm)],[1547, 1546])).
% 0.84/1.02 tff(1549,plain,
% 0.84/1.02 (hskp26),
% 0.84/1.02 inference(unit_resolution,[status(thm)],[1548, 110, 1237, 1229, 833, 819, 1542, 1244, 1516])).
% 0.84/1.02 tff(1550,plain,
% 0.84/1.02 (c3_1(a234)),
% 0.84/1.02 inference(unit_resolution,[status(thm)],[63, 1549])).
% 0.84/1.02 tff(1551,plain,
% 0.84/1.02 (c1_1(a234)),
% 0.84/1.02 inference(unit_resolution,[status(thm)],[71, 1549])).
% 0.84/1.02 tff(1552,plain,
% 0.84/1.02 (c0_1(a234)),
% 0.84/1.02 inference(unit_resolution,[status(thm)],[79, 1549])).
% 0.84/1.02 tff(1553,plain,
% 0.84/1.02 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp5 | c0_1(a255) | c1_1(a255) | (~ndr1_0) | (~c0_1(a234)) | (~c3_1(a234)) | (~c1_1(a234)) | (~c2_1(a255)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp5 | c0_1(a255) | c1_1(a255) | (~ndr1_0) | (~c0_1(a234)) | (~c3_1(a234)) | (~c1_1(a234)) | (~c2_1(a255)))),
% 0.84/1.02 inference(rewrite,[status(thm)],[])).
% 0.84/1.02 tff(1554,plain,
% 0.84/1.02 ((hskp5 | (~ndr1_0) | (~c3_1(a234)) | (~c1_1(a234)) | (~c0_1(a234)) | c1_1(a255) | c0_1(a255) | (~c2_1(a255))) <=> (hskp5 | c0_1(a255) | c1_1(a255) | (~ndr1_0) | (~c0_1(a234)) | (~c3_1(a234)) | (~c1_1(a234)) | (~c2_1(a255)))),
% 0.84/1.02 inference(rewrite,[status(thm)],[])).
% 0.84/1.02 tff(1555,plain,
% 0.84/1.02 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp5 | (~ndr1_0) | (~c3_1(a234)) | (~c1_1(a234)) | (~c0_1(a234)) | c1_1(a255) | c0_1(a255) | (~c2_1(a255)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp5 | c0_1(a255) | c1_1(a255) | (~ndr1_0) | (~c0_1(a234)) | (~c3_1(a234)) | (~c1_1(a234)) | (~c2_1(a255))))),
% 0.84/1.02 inference(monotonicity,[status(thm)],[1554])).
% 0.84/1.02 tff(1556,plain,
% 0.84/1.02 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp5 | (~ndr1_0) | (~c3_1(a234)) | (~c1_1(a234)) | (~c0_1(a234)) | c1_1(a255) | c0_1(a255) | (~c2_1(a255)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp5 | c0_1(a255) | c1_1(a255) | (~ndr1_0) | (~c0_1(a234)) | (~c3_1(a234)) | (~c1_1(a234)) | (~c2_1(a255)))),
% 0.84/1.02 inference(transitivity,[status(thm)],[1555, 1553])).
% 0.84/1.02 tff(1557,plain,
% 0.84/1.02 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp5 | (~ndr1_0) | (~c3_1(a234)) | (~c1_1(a234)) | (~c0_1(a234)) | c1_1(a255) | c0_1(a255) | (~c2_1(a255)))),
% 0.84/1.02 inference(quant_inst,[status(thm)],[])).
% 0.84/1.02 tff(1558,plain,
% 0.84/1.02 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp5 | c0_1(a255) | c1_1(a255) | (~ndr1_0) | (~c0_1(a234)) | (~c3_1(a234)) | (~c1_1(a234)) | (~c2_1(a255))),
% 0.84/1.02 inference(modus_ponens,[status(thm)],[1557, 1556])).
% 0.84/1.02 tff(1559,plain,
% 0.84/1.02 (~c2_1(a255)),
% 0.84/1.02 inference(unit_resolution,[status(thm)],[1558, 110, 45, 1552, 1551, 1550, 1532, 1531, 149])).
% 0.84/1.02 tff(1560,plain,
% 0.84/1.02 (^[U: $i] : refl((hskp6 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)) <=> (hskp6 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)))),
% 0.84/1.02 inference(bind,[status(th)],[])).
% 0.84/1.02 tff(1561,plain,
% 0.84/1.02 (![U: $i] : (hskp6 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)) <=> ![U: $i] : (hskp6 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))),
% 0.84/1.02 inference(quant_intro,[status(thm)],[1560])).
% 0.84/1.02 tff(1562,plain,
% 0.84/1.02 (![U: $i] : (hskp6 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)) <=> ![U: $i] : (hskp6 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))),
% 0.84/1.02 inference(rewrite,[status(thm)],[])).
% 0.84/1.02 tff(1563,plain,
% 0.84/1.02 (^[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)) | 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)) | hskp6) <=> (((~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)) | hskp6))), rewrite((((~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)) | hskp6) <=> (hskp6 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))), ((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp6) <=> (hskp6 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)))), (((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp6) | hskp5) <=> ((hskp6 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)) | hskp5))), rewrite(((hskp6 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)) | hskp5) <=> (hskp6 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))), (((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp6) | hskp5) <=> (hskp6 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))))),
% 0.84/1.02 inference(bind,[status(th)],[])).
% 0.84/1.02 tff(1564,plain,
% 0.84/1.02 (![U: $i] : ((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp6) | hskp5) <=> ![U: $i] : (hskp6 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))),
% 0.84/1.02 inference(quant_intro,[status(thm)],[1563])).
% 0.84/1.02 tff(1565,axiom,(![U: $i] : ((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp6) | hskp5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause132')).
% 0.84/1.02 tff(1566,plain,
% 0.84/1.02 (![U: $i] : (hskp6 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))),
% 0.84/1.02 inference(modus_ponens,[status(thm)],[1565, 1564])).
% 0.84/1.02 tff(1567,plain,
% 0.84/1.02 (![U: $i] : (hskp6 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))),
% 0.84/1.02 inference(modus_ponens,[status(thm)],[1566, 1562])).
% 0.84/1.02 tff(1568,plain,(
% 0.84/1.02 ![U: $i] : (hskp6 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))),
% 0.84/1.02 inference(skolemize,[status(sab)],[1567])).
% 0.84/1.02 tff(1569,plain,
% 0.84/1.02 (![U: $i] : (hskp6 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))),
% 0.84/1.02 inference(modus_ponens,[status(thm)],[1568, 1561])).
% 0.84/1.02 tff(1570,plain,
% 0.84/1.02 (~c3_1(a255)),
% 0.84/1.02 inference(unit_resolution,[status(thm)],[267, 1530])).
% 0.84/1.02 tff(1571,plain,
% 0.84/1.02 (((~![U: $i] : (hskp6 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp6 | hskp5 | c0_1(a255) | c3_1(a255) | (~ndr1_0) | c2_1(a255))) <=> ((~![U: $i] : (hskp6 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | hskp6 | hskp5 | c0_1(a255) | c3_1(a255) | (~ndr1_0) | c2_1(a255))),
% 0.84/1.02 inference(rewrite,[status(thm)],[])).
% 0.84/1.02 tff(1572,plain,
% 0.84/1.03 ((hskp6 | hskp5 | (~ndr1_0) | c2_1(a255) | c0_1(a255) | c3_1(a255)) <=> (hskp6 | hskp5 | c0_1(a255) | c3_1(a255) | (~ndr1_0) | c2_1(a255))),
% 0.84/1.03 inference(rewrite,[status(thm)],[])).
% 0.84/1.03 tff(1573,plain,
% 0.84/1.03 (((~![U: $i] : (hskp6 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp6 | hskp5 | (~ndr1_0) | c2_1(a255) | c0_1(a255) | c3_1(a255))) <=> ((~![U: $i] : (hskp6 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp6 | hskp5 | c0_1(a255) | c3_1(a255) | (~ndr1_0) | c2_1(a255)))),
% 0.84/1.03 inference(monotonicity,[status(thm)],[1572])).
% 0.84/1.03 tff(1574,plain,
% 0.84/1.03 (((~![U: $i] : (hskp6 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp6 | hskp5 | (~ndr1_0) | c2_1(a255) | c0_1(a255) | c3_1(a255))) <=> ((~![U: $i] : (hskp6 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | hskp6 | hskp5 | c0_1(a255) | c3_1(a255) | (~ndr1_0) | c2_1(a255))),
% 0.84/1.03 inference(transitivity,[status(thm)],[1573, 1571])).
% 0.84/1.03 tff(1575,plain,
% 0.84/1.03 ((~![U: $i] : (hskp6 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp6 | hskp5 | (~ndr1_0) | c2_1(a255) | c0_1(a255) | c3_1(a255))),
% 0.84/1.03 inference(quant_inst,[status(thm)],[])).
% 0.84/1.03 tff(1576,plain,
% 0.84/1.03 ((~![U: $i] : (hskp6 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | hskp6 | hskp5 | c0_1(a255) | c3_1(a255) | (~ndr1_0) | c2_1(a255)),
% 0.84/1.03 inference(modus_ponens,[status(thm)],[1575, 1574])).
% 0.84/1.03 tff(1577,plain,
% 0.84/1.03 (hskp6),
% 0.84/1.03 inference(unit_resolution,[status(thm)],[1576, 110, 45, 1532, 1570, 1569, 1559])).
% 0.84/1.03 tff(1578,plain,
% 0.84/1.03 (~c3_1(a220)),
% 0.84/1.03 inference(unit_resolution,[status(thm)],[449, 1577])).
% 0.84/1.03 tff(1579,plain,
% 0.84/1.03 (c2_1(a220)),
% 0.84/1.03 inference(unit_resolution,[status(thm)],[493, 1577])).
% 0.84/1.03 tff(1580,plain,
% 0.84/1.03 (c1_1(a220)),
% 0.84/1.03 inference(unit_resolution,[status(thm)],[485, 1577])).
% 0.84/1.03 tff(1581,plain,
% 0.84/1.03 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | (c3_1(a237) | c3_1(a220) | (~ndr1_0) | (~c1_1(a261)) | (~c2_1(a261)) | (~c3_1(a261)) | (~c2_1(a220)) | (~c1_1(a220)) | c1_1(a237) | (~c0_1(a237)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | c3_1(a237) | c3_1(a220) | (~ndr1_0) | (~c1_1(a261)) | (~c2_1(a261)) | (~c3_1(a261)) | (~c2_1(a220)) | (~c1_1(a220)) | c1_1(a237) | (~c0_1(a237)))),
% 0.84/1.03 inference(rewrite,[status(thm)],[])).
% 0.84/1.03 tff(1582,plain,
% 0.84/1.03 (((~ndr1_0) | (~c2_1(a261)) | (~c3_1(a261)) | (~c1_1(a261)) | c3_1(a220) | (~c1_1(a220)) | (~c2_1(a220)) | c3_1(a237) | c1_1(a237) | (~c0_1(a237))) <=> (c3_1(a237) | c3_1(a220) | (~ndr1_0) | (~c1_1(a261)) | (~c2_1(a261)) | (~c3_1(a261)) | (~c2_1(a220)) | (~c1_1(a220)) | c1_1(a237) | (~c0_1(a237)))),
% 0.84/1.03 inference(rewrite,[status(thm)],[])).
% 0.84/1.03 tff(1583,plain,
% 0.84/1.03 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_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) | (~c2_1(a261)) | (~c3_1(a261)) | (~c1_1(a261)) | c3_1(a220) | (~c1_1(a220)) | (~c2_1(a220)) | c3_1(a237) | c1_1(a237) | (~c0_1(a237)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | (c3_1(a237) | c3_1(a220) | (~ndr1_0) | (~c1_1(a261)) | (~c2_1(a261)) | (~c3_1(a261)) | (~c2_1(a220)) | (~c1_1(a220)) | c1_1(a237) | (~c0_1(a237))))),
% 0.84/1.03 inference(monotonicity,[status(thm)],[1582])).
% 0.84/1.03 tff(1584,plain,
% 0.84/1.03 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_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) | (~c2_1(a261)) | (~c3_1(a261)) | (~c1_1(a261)) | c3_1(a220) | (~c1_1(a220)) | (~c2_1(a220)) | c3_1(a237) | c1_1(a237) | (~c0_1(a237)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | c3_1(a237) | c3_1(a220) | (~ndr1_0) | (~c1_1(a261)) | (~c2_1(a261)) | (~c3_1(a261)) | (~c2_1(a220)) | (~c1_1(a220)) | c1_1(a237) | (~c0_1(a237)))),
% 0.84/1.03 inference(transitivity,[status(thm)],[1583, 1581])).
% 0.84/1.03 tff(1585,plain,
% 0.84/1.03 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_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) | (~c2_1(a261)) | (~c3_1(a261)) | (~c1_1(a261)) | c3_1(a220) | (~c1_1(a220)) | (~c2_1(a220)) | c3_1(a237) | c1_1(a237) | (~c0_1(a237)))),
% 0.84/1.03 inference(quant_inst,[status(thm)],[])).
% 0.84/1.03 tff(1586,plain,
% 0.84/1.03 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | c3_1(a237) | c3_1(a220) | (~ndr1_0) | (~c1_1(a261)) | (~c2_1(a261)) | (~c3_1(a261)) | (~c2_1(a220)) | (~c1_1(a220)) | c1_1(a237) | (~c0_1(a237))),
% 0.84/1.03 inference(modus_ponens,[status(thm)],[1585, 1584])).
% 0.84/1.03 tff(1587,plain,
% 0.84/1.03 ($false),
% 0.84/1.03 inference(unit_resolution,[status(thm)],[1586, 110, 1237, 1229, 1221, 1402, 1580, 1579, 1400, 1578, 505, 1523])).
% 0.84/1.03 tff(1588,plain,((~hskp9) | hskp5 | hskp18), inference(lemma,lemma(discharge,[]))).
% 0.84/1.03 tff(1589,plain,
% 0.84/1.03 (~hskp9),
% 0.84/1.03 inference(unit_resolution,[status(thm)],[1588, 45, 596])).
% 0.84/1.03 tff(1590,assumption,(~c3_1(a259)), introduced(assumption)).
% 0.84/1.03 tff(1591,plain,
% 0.84/1.03 (~hskp21),
% 0.84/1.03 inference(unit_resolution,[status(thm)],[792, 1590])).
% 0.84/1.03 tff(1592,assumption,(c3_1(a261)), introduced(assumption)).
% 0.84/1.03 tff(1593,assumption,(c2_1(a261)), introduced(assumption)).
% 0.84/1.03 tff(1594,assumption,(c1_1(a261)), introduced(assumption)).
% 0.84/1.03 tff(1595,plain,
% 0.84/1.03 (~c0_1(a261)),
% 0.84/1.03 inference(unit_resolution,[status(thm)],[1243, 110, 1594, 1593, 1592, 33])).
% 0.84/1.03 tff(1596,plain,
% 0.84/1.03 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp9 | c0_1(a259) | c3_1(a259) | c2_1(a259) | (~ndr1_0) | (~c2_1(a261)) | (~c3_1(a261)) | c0_1(a261))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp9 | c0_1(a259) | c3_1(a259) | c2_1(a259) | (~ndr1_0) | (~c2_1(a261)) | (~c3_1(a261)) | c0_1(a261))),
% 0.84/1.03 inference(rewrite,[status(thm)],[])).
% 0.84/1.03 tff(1597,plain,
% 0.84/1.03 ((hskp9 | (~ndr1_0) | c0_1(a261) | (~c2_1(a261)) | (~c3_1(a261)) | c3_1(a259) | c0_1(a259) | c2_1(a259)) <=> (hskp9 | c0_1(a259) | c3_1(a259) | c2_1(a259) | (~ndr1_0) | (~c2_1(a261)) | (~c3_1(a261)) | c0_1(a261))),
% 0.84/1.03 inference(rewrite,[status(thm)],[])).
% 0.84/1.03 tff(1598,plain,
% 0.84/1.03 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp9 | (~ndr1_0) | c0_1(a261) | (~c2_1(a261)) | (~c3_1(a261)) | c3_1(a259) | c0_1(a259) | c2_1(a259))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp9 | c0_1(a259) | c3_1(a259) | c2_1(a259) | (~ndr1_0) | (~c2_1(a261)) | (~c3_1(a261)) | c0_1(a261)))),
% 0.84/1.03 inference(monotonicity,[status(thm)],[1597])).
% 0.84/1.03 tff(1599,plain,
% 0.84/1.03 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp9 | (~ndr1_0) | c0_1(a261) | (~c2_1(a261)) | (~c3_1(a261)) | c3_1(a259) | c0_1(a259) | c2_1(a259))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp9 | c0_1(a259) | c3_1(a259) | c2_1(a259) | (~ndr1_0) | (~c2_1(a261)) | (~c3_1(a261)) | c0_1(a261))),
% 0.84/1.03 inference(transitivity,[status(thm)],[1598, 1596])).
% 0.84/1.03 tff(1600,plain,
% 0.84/1.03 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp9 | (~ndr1_0) | c0_1(a261) | (~c2_1(a261)) | (~c3_1(a261)) | c3_1(a259) | c0_1(a259) | c2_1(a259))),
% 0.84/1.03 inference(quant_inst,[status(thm)],[])).
% 0.84/1.03 tff(1601,plain,
% 0.84/1.03 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp9 | c0_1(a259) | c3_1(a259) | c2_1(a259) | (~ndr1_0) | (~c2_1(a261)) | (~c3_1(a261)) | c0_1(a261)),
% 0.84/1.03 inference(modus_ponens,[status(thm)],[1600, 1599])).
% 0.84/1.03 tff(1602,plain,
% 0.84/1.03 (c0_1(a259)),
% 0.84/1.03 inference(unit_resolution,[status(thm)],[1601, 110, 23, 1593, 1592, 1590, 785, 905, 1595])).
% 0.84/1.03 tff(1603,plain,
% 0.84/1.03 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W))))),
% 0.84/1.03 inference(bind,[status(th)],[])).
% 0.84/1.03 tff(1604,plain,
% 0.84/1.03 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))),
% 0.84/1.03 inference(quant_intro,[status(thm)],[1603])).
% 0.84/1.03 tff(1605,plain,
% 0.84/1.03 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))),
% 0.84/1.03 inference(rewrite,[status(thm)],[])).
% 0.84/1.03 tff(1606,plain,
% 0.84/1.03 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~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))) | (~c0_1(W))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V))) | (~c0_1(W))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V))) | (~c0_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c0_1(W)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c0_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c0_1(W))))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c0_1(W))) | (~c1_1(W))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c0_1(W))) | (~c1_1(W))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c0_1(W))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c0_1(W)) | (~c1_1(W)))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c0_1(W))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c0_1(W)) | (~c1_1(W))))), ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c0_1(W))) | (~c1_1(W))) | c3_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c0_1(W)) | (~c1_1(W))) | c3_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c0_1(W)) | (~c1_1(W))) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | (~c0_1(W)) | (~c1_1(W)))), ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c0_1(W))) | (~c1_1(W))) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | (~c0_1(W)) | (~c1_1(W))))), (((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c0_1(W))) | (~c1_1(W))) | c3_1(V)) | c2_1(W)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | (~c0_1(W)) | (~c1_1(W))) | c2_1(W)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | (~c0_1(W)) | (~c1_1(W))) | c2_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))), (((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c0_1(W))) | (~c1_1(W))) | c3_1(V)) | c2_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))))),
% 0.84/1.03 inference(bind,[status(th)],[])).
% 0.84/1.03 tff(1607,plain,
% 0.84/1.03 (![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c0_1(W))) | (~c1_1(W))) | c3_1(V)) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))),
% 0.84/1.03 inference(quant_intro,[status(thm)],[1606])).
% 0.84/1.03 tff(1608,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c0_1(W))) | (~c1_1(W))) | c3_1(V)) | c2_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause199')).
% 0.84/1.03 tff(1609,plain,
% 0.84/1.03 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))),
% 0.84/1.03 inference(modus_ponens,[status(thm)],[1608, 1607])).
% 0.84/1.03 tff(1610,plain,
% 0.84/1.03 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))),
% 0.84/1.03 inference(modus_ponens,[status(thm)],[1609, 1605])).
% 0.84/1.03 tff(1611,plain,(
% 0.84/1.03 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))),
% 0.84/1.03 inference(skolemize,[status(sab)],[1610])).
% 0.84/1.03 tff(1612,plain,
% 0.84/1.03 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))),
% 0.84/1.03 inference(modus_ponens,[status(thm)],[1611, 1604])).
% 0.84/1.03 tff(1613,plain,
% 0.84/1.03 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | (c3_1(a259) | c2_1(a259) | (~ndr1_0) | (~c1_1(a261)) | (~c2_1(a261)) | (~c3_1(a261)) | (~c0_1(a259)) | (~c1_1(a259)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | c3_1(a259) | c2_1(a259) | (~ndr1_0) | (~c1_1(a261)) | (~c2_1(a261)) | (~c3_1(a261)) | (~c0_1(a259)) | (~c1_1(a259)))),
% 0.84/1.03 inference(rewrite,[status(thm)],[])).
% 0.84/1.03 tff(1614,plain,
% 0.84/1.03 (((~ndr1_0) | (~c2_1(a261)) | (~c3_1(a261)) | (~c1_1(a261)) | c3_1(a259) | (~c1_1(a259)) | (~c0_1(a259)) | c2_1(a259) | (~c0_1(a259)) | (~c1_1(a259))) <=> (c3_1(a259) | c2_1(a259) | (~ndr1_0) | (~c1_1(a261)) | (~c2_1(a261)) | (~c3_1(a261)) | (~c0_1(a259)) | (~c1_1(a259)))),
% 0.84/1.03 inference(rewrite,[status(thm)],[])).
% 0.84/1.03 tff(1615,plain,
% 0.84/1.03 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a261)) | (~c3_1(a261)) | (~c1_1(a261)) | c3_1(a259) | (~c1_1(a259)) | (~c0_1(a259)) | c2_1(a259) | (~c0_1(a259)) | (~c1_1(a259)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | (c3_1(a259) | c2_1(a259) | (~ndr1_0) | (~c1_1(a261)) | (~c2_1(a261)) | (~c3_1(a261)) | (~c0_1(a259)) | (~c1_1(a259))))),
% 0.84/1.03 inference(monotonicity,[status(thm)],[1614])).
% 0.84/1.03 tff(1616,plain,
% 0.84/1.03 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a261)) | (~c3_1(a261)) | (~c1_1(a261)) | c3_1(a259) | (~c1_1(a259)) | (~c0_1(a259)) | c2_1(a259) | (~c0_1(a259)) | (~c1_1(a259)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | c3_1(a259) | c2_1(a259) | (~ndr1_0) | (~c1_1(a261)) | (~c2_1(a261)) | (~c3_1(a261)) | (~c0_1(a259)) | (~c1_1(a259)))),
% 0.84/1.03 inference(transitivity,[status(thm)],[1615, 1613])).
% 0.84/1.03 tff(1617,plain,
% 0.84/1.03 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a261)) | (~c3_1(a261)) | (~c1_1(a261)) | c3_1(a259) | (~c1_1(a259)) | (~c0_1(a259)) | c2_1(a259) | (~c0_1(a259)) | (~c1_1(a259)))),
% 0.84/1.03 inference(quant_inst,[status(thm)],[])).
% 0.84/1.03 tff(1618,plain,
% 0.84/1.03 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | c3_1(a259) | c2_1(a259) | (~ndr1_0) | (~c1_1(a261)) | (~c2_1(a261)) | (~c3_1(a261)) | (~c0_1(a259)) | (~c1_1(a259))),
% 0.84/1.03 inference(modus_ponens,[status(thm)],[1617, 1616])).
% 0.84/1.03 tff(1619,plain,
% 0.84/1.03 ((~c0_1(a259)) | (~c1_1(a259))),
% 0.84/1.03 inference(unit_resolution,[status(thm)],[1618, 110, 1594, 1593, 1592, 1590, 785, 1612])).
% 0.84/1.03 tff(1620,plain,
% 0.84/1.03 (~c1_1(a259)),
% 0.84/1.03 inference(unit_resolution,[status(thm)],[1619, 1602])).
% 0.84/1.03 tff(1621,plain,
% 0.84/1.03 (^[U: $i] : refl((hskp19 | hskp21 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U)) <=> (hskp19 | hskp21 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U)))),
% 0.84/1.03 inference(bind,[status(th)],[])).
% 0.84/1.03 tff(1622,plain,
% 0.84/1.03 (![U: $i] : (hskp19 | hskp21 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U)) <=> ![U: $i] : (hskp19 | hskp21 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))),
% 0.84/1.03 inference(quant_intro,[status(thm)],[1621])).
% 0.84/1.03 tff(1623,plain,
% 0.84/1.03 (![U: $i] : (hskp19 | hskp21 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U)) <=> ![U: $i] : (hskp19 | hskp21 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))),
% 0.84/1.03 inference(rewrite,[status(thm)],[])).
% 0.84/1.03 tff(1624,plain,
% 0.84/1.03 (^[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)) | hskp21) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U)) | hskp21))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U)) | hskp21) <=> (hskp21 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))), ((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | hskp21) <=> (hskp21 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U)))), (((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | hskp21) | hskp19) <=> ((hskp21 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U)) | hskp19))), rewrite(((hskp21 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U)) | hskp19) <=> (hskp19 | hskp21 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))), (((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | hskp21) | hskp19) <=> (hskp19 | hskp21 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))))),
% 0.84/1.03 inference(bind,[status(th)],[])).
% 0.84/1.03 tff(1625,plain,
% 0.84/1.03 (![U: $i] : ((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | hskp21) | hskp19) <=> ![U: $i] : (hskp19 | hskp21 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))),
% 0.84/1.03 inference(quant_intro,[status(thm)],[1624])).
% 0.84/1.03 tff(1626,axiom,(![U: $i] : ((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | hskp21) | hskp19)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause135')).
% 0.84/1.03 tff(1627,plain,
% 0.84/1.03 (![U: $i] : (hskp19 | hskp21 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))),
% 0.84/1.03 inference(modus_ponens,[status(thm)],[1626, 1625])).
% 0.84/1.03 tff(1628,plain,
% 0.84/1.03 (![U: $i] : (hskp19 | hskp21 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))),
% 0.84/1.03 inference(modus_ponens,[status(thm)],[1627, 1623])).
% 0.84/1.03 tff(1629,plain,(
% 0.84/1.03 ![U: $i] : (hskp19 | hskp21 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))),
% 0.84/1.03 inference(skolemize,[status(sab)],[1628])).
% 0.84/1.03 tff(1630,plain,
% 0.84/1.03 (![U: $i] : (hskp19 | hskp21 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))),
% 0.84/1.03 inference(modus_ponens,[status(thm)],[1629, 1622])).
% 0.84/1.03 tff(1631,plain,
% 0.84/1.03 (((~![U: $i] : (hskp19 | hskp21 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | (hskp19 | hskp21 | c3_1(a259) | c2_1(a259) | (~ndr1_0) | c1_1(a259))) <=> ((~![U: $i] : (hskp19 | hskp21 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | hskp19 | hskp21 | c3_1(a259) | c2_1(a259) | (~ndr1_0) | c1_1(a259))),
% 0.84/1.03 inference(rewrite,[status(thm)],[])).
% 0.84/1.03 tff(1632,plain,
% 0.84/1.03 ((hskp19 | hskp21 | (~ndr1_0) | c2_1(a259) | c1_1(a259) | c3_1(a259)) <=> (hskp19 | hskp21 | c3_1(a259) | c2_1(a259) | (~ndr1_0) | c1_1(a259))),
% 0.84/1.03 inference(rewrite,[status(thm)],[])).
% 0.84/1.03 tff(1633,plain,
% 0.84/1.03 (((~![U: $i] : (hskp19 | hskp21 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | (hskp19 | hskp21 | (~ndr1_0) | c2_1(a259) | c1_1(a259) | c3_1(a259))) <=> ((~![U: $i] : (hskp19 | hskp21 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | (hskp19 | hskp21 | c3_1(a259) | c2_1(a259) | (~ndr1_0) | c1_1(a259)))),
% 0.84/1.03 inference(monotonicity,[status(thm)],[1632])).
% 0.84/1.03 tff(1634,plain,
% 0.84/1.03 (((~![U: $i] : (hskp19 | hskp21 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | (hskp19 | hskp21 | (~ndr1_0) | c2_1(a259) | c1_1(a259) | c3_1(a259))) <=> ((~![U: $i] : (hskp19 | hskp21 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | hskp19 | hskp21 | c3_1(a259) | c2_1(a259) | (~ndr1_0) | c1_1(a259))),
% 0.84/1.03 inference(transitivity,[status(thm)],[1633, 1631])).
% 0.84/1.03 tff(1635,plain,
% 0.84/1.03 ((~![U: $i] : (hskp19 | hskp21 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | (hskp19 | hskp21 | (~ndr1_0) | c2_1(a259) | c1_1(a259) | c3_1(a259))),
% 0.84/1.03 inference(quant_inst,[status(thm)],[])).
% 0.84/1.03 tff(1636,plain,
% 0.84/1.03 ((~![U: $i] : (hskp19 | hskp21 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | hskp19 | hskp21 | c3_1(a259) | c2_1(a259) | (~ndr1_0) | c1_1(a259)),
% 0.84/1.03 inference(modus_ponens,[status(thm)],[1635, 1634])).
% 0.84/1.03 tff(1637,plain,
% 0.84/1.03 (hskp19 | hskp21 | c3_1(a259) | c1_1(a259)),
% 0.84/1.03 inference(unit_resolution,[status(thm)],[1636, 110, 785, 1630])).
% 0.84/1.03 tff(1638,plain,
% 0.84/1.03 (hskp19),
% 0.84/1.03 inference(unit_resolution,[status(thm)],[1637, 1620, 1590, 1591])).
% 0.84/1.03 tff(1639,plain,
% 0.84/1.03 (~c1_1(a255)),
% 0.84/1.03 inference(unit_resolution,[status(thm)],[273, 1638])).
% 0.84/1.03 tff(1640,plain,
% 0.84/1.03 (~c0_1(a255)),
% 0.84/1.03 inference(unit_resolution,[status(thm)],[279, 1638])).
% 0.84/1.03 tff(1641,plain,
% 0.84/1.03 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp26 | c3_1(a259) | c2_1(a259) | (~ndr1_0) | (~c1_1(a261)) | (~c2_1(a261)) | c0_1(a261) | (~c0_1(a259)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp26 | c3_1(a259) | c2_1(a259) | (~ndr1_0) | (~c1_1(a261)) | (~c2_1(a261)) | c0_1(a261) | (~c0_1(a259)))),
% 0.84/1.03 inference(rewrite,[status(thm)],[])).
% 0.84/1.03 tff(1642,plain,
% 0.84/1.03 ((hskp26 | (~ndr1_0) | c2_1(a259) | c3_1(a259) | (~c0_1(a259)) | c0_1(a261) | (~c1_1(a261)) | (~c2_1(a261))) <=> (hskp26 | c3_1(a259) | c2_1(a259) | (~ndr1_0) | (~c1_1(a261)) | (~c2_1(a261)) | c0_1(a261) | (~c0_1(a259)))),
% 0.84/1.03 inference(rewrite,[status(thm)],[])).
% 0.84/1.03 tff(1643,plain,
% 0.84/1.03 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp26 | (~ndr1_0) | c2_1(a259) | c3_1(a259) | (~c0_1(a259)) | c0_1(a261) | (~c1_1(a261)) | (~c2_1(a261)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp26 | c3_1(a259) | c2_1(a259) | (~ndr1_0) | (~c1_1(a261)) | (~c2_1(a261)) | c0_1(a261) | (~c0_1(a259))))),
% 0.84/1.03 inference(monotonicity,[status(thm)],[1642])).
% 0.84/1.03 tff(1644,plain,
% 0.84/1.03 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp26 | (~ndr1_0) | c2_1(a259) | c3_1(a259) | (~c0_1(a259)) | c0_1(a261) | (~c1_1(a261)) | (~c2_1(a261)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp26 | c3_1(a259) | c2_1(a259) | (~ndr1_0) | (~c1_1(a261)) | (~c2_1(a261)) | c0_1(a261) | (~c0_1(a259)))),
% 0.84/1.03 inference(transitivity,[status(thm)],[1643, 1641])).
% 0.84/1.03 tff(1645,plain,
% 0.84/1.03 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp26 | (~ndr1_0) | c2_1(a259) | c3_1(a259) | (~c0_1(a259)) | c0_1(a261) | (~c1_1(a261)) | (~c2_1(a261)))),
% 0.84/1.03 inference(quant_inst,[status(thm)],[])).
% 0.84/1.03 tff(1646,plain,
% 0.84/1.03 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp26 | c3_1(a259) | c2_1(a259) | (~ndr1_0) | (~c1_1(a261)) | (~c2_1(a261)) | c0_1(a261) | (~c0_1(a259))),
% 0.84/1.03 inference(modus_ponens,[status(thm)],[1645, 1644])).
% 0.84/1.03 tff(1647,plain,
% 0.84/1.03 (hskp26 | c3_1(a259) | (~c0_1(a259))),
% 0.84/1.03 inference(unit_resolution,[status(thm)],[1646, 110, 1594, 1593, 785, 1542, 1595])).
% 0.84/1.03 tff(1648,plain,
% 0.84/1.03 (hskp26),
% 0.84/1.03 inference(unit_resolution,[status(thm)],[1647, 1602, 1590])).
% 0.84/1.03 tff(1649,plain,
% 0.84/1.03 (c3_1(a234)),
% 0.84/1.03 inference(unit_resolution,[status(thm)],[63, 1648])).
% 0.84/1.03 tff(1650,plain,
% 0.84/1.03 (c1_1(a234)),
% 0.84/1.03 inference(unit_resolution,[status(thm)],[71, 1648])).
% 0.84/1.03 tff(1651,plain,
% 0.84/1.03 (c0_1(a234)),
% 0.84/1.03 inference(unit_resolution,[status(thm)],[79, 1648])).
% 0.84/1.03 tff(1652,plain,
% 0.84/1.03 (~c2_1(a255)),
% 0.84/1.03 inference(unit_resolution,[status(thm)],[1558, 110, 45, 1651, 1650, 1649, 1640, 1639, 149])).
% 0.84/1.03 tff(1653,plain,
% 0.84/1.03 (~c3_1(a255)),
% 0.84/1.03 inference(unit_resolution,[status(thm)],[267, 1638])).
% 0.84/1.03 tff(1654,plain,
% 0.84/1.03 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp9 | c0_1(a255) | c3_1(a255) | (~ndr1_0) | (~c2_1(a261)) | (~c3_1(a261)) | c0_1(a261) | c2_1(a255))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp9 | c0_1(a255) | c3_1(a255) | (~ndr1_0) | (~c2_1(a261)) | (~c3_1(a261)) | c0_1(a261) | c2_1(a255))),
% 0.84/1.03 inference(rewrite,[status(thm)],[])).
% 0.84/1.03 tff(1655,plain,
% 0.84/1.03 ((hskp9 | (~ndr1_0) | c0_1(a261) | (~c2_1(a261)) | (~c3_1(a261)) | c3_1(a255) | c0_1(a255) | c2_1(a255)) <=> (hskp9 | c0_1(a255) | c3_1(a255) | (~ndr1_0) | (~c2_1(a261)) | (~c3_1(a261)) | c0_1(a261) | c2_1(a255))),
% 0.84/1.03 inference(rewrite,[status(thm)],[])).
% 0.84/1.03 tff(1656,plain,
% 0.84/1.03 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp9 | (~ndr1_0) | c0_1(a261) | (~c2_1(a261)) | (~c3_1(a261)) | c3_1(a255) | c0_1(a255) | c2_1(a255))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp9 | c0_1(a255) | c3_1(a255) | (~ndr1_0) | (~c2_1(a261)) | (~c3_1(a261)) | c0_1(a261) | c2_1(a255)))),
% 0.84/1.03 inference(monotonicity,[status(thm)],[1655])).
% 0.84/1.03 tff(1657,plain,
% 0.84/1.03 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp9 | (~ndr1_0) | c0_1(a261) | (~c2_1(a261)) | (~c3_1(a261)) | c3_1(a255) | c0_1(a255) | c2_1(a255))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp9 | c0_1(a255) | c3_1(a255) | (~ndr1_0) | (~c2_1(a261)) | (~c3_1(a261)) | c0_1(a261) | c2_1(a255))),
% 0.84/1.03 inference(transitivity,[status(thm)],[1656, 1654])).
% 0.84/1.03 tff(1658,plain,
% 0.84/1.03 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp9 | (~ndr1_0) | c0_1(a261) | (~c2_1(a261)) | (~c3_1(a261)) | c3_1(a255) | c0_1(a255) | c2_1(a255))),
% 0.84/1.03 inference(quant_inst,[status(thm)],[])).
% 0.84/1.03 tff(1659,plain,
% 0.84/1.03 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp9 | c0_1(a255) | c3_1(a255) | (~ndr1_0) | (~c2_1(a261)) | (~c3_1(a261)) | c0_1(a261) | c2_1(a255)),
% 0.84/1.03 inference(modus_ponens,[status(thm)],[1658, 1657])).
% 0.84/1.03 tff(1660,plain,
% 0.84/1.03 ($false),
% 0.84/1.03 inference(unit_resolution,[status(thm)],[1659, 110, 23, 1593, 1592, 1640, 1653, 905, 1595, 1652])).
% 0.84/1.03 tff(1661,plain,(c3_1(a259) | hskp9 | (~c2_1(a261)) | (~c3_1(a261)) | hskp5 | c2_1(a259) | (~c1_1(a261))), inference(lemma,lemma(discharge,[]))).
% 0.84/1.03 tff(1662,plain,
% 0.84/1.03 (c3_1(a259)),
% 0.84/1.03 inference(unit_resolution,[status(thm)],[1661, 23, 1229, 1221, 45, 785, 1237])).
% 0.84/1.03 tff(1663,plain,
% 0.84/1.03 (((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp18 | c2_1(a259) | c0_1(a231) | (~ndr1_0) | (~c1_1(a231)) | (~c3_1(a231)) | (~c3_1(a259)) | (~c1_1(a259)))) <=> ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp18 | c2_1(a259) | c0_1(a231) | (~ndr1_0) | (~c1_1(a231)) | (~c3_1(a231)) | (~c3_1(a259)) | (~c1_1(a259)))),
% 0.84/1.04 inference(rewrite,[status(thm)],[])).
% 0.84/1.04 tff(1664,plain,
% 0.84/1.04 ((hskp18 | (~ndr1_0) | c2_1(a259) | (~c3_1(a259)) | (~c1_1(a259)) | c0_1(a231) | (~c1_1(a231)) | (~c3_1(a231))) <=> (hskp18 | c2_1(a259) | c0_1(a231) | (~ndr1_0) | (~c1_1(a231)) | (~c3_1(a231)) | (~c3_1(a259)) | (~c1_1(a259)))),
% 0.84/1.04 inference(rewrite,[status(thm)],[])).
% 0.84/1.04 tff(1665,plain,
% 0.84/1.04 (((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp18 | (~ndr1_0) | c2_1(a259) | (~c3_1(a259)) | (~c1_1(a259)) | c0_1(a231) | (~c1_1(a231)) | (~c3_1(a231)))) <=> ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp18 | c2_1(a259) | c0_1(a231) | (~ndr1_0) | (~c1_1(a231)) | (~c3_1(a231)) | (~c3_1(a259)) | (~c1_1(a259))))),
% 0.84/1.04 inference(monotonicity,[status(thm)],[1664])).
% 0.84/1.04 tff(1666,plain,
% 0.84/1.04 (((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp18 | (~ndr1_0) | c2_1(a259) | (~c3_1(a259)) | (~c1_1(a259)) | c0_1(a231) | (~c1_1(a231)) | (~c3_1(a231)))) <=> ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp18 | c2_1(a259) | c0_1(a231) | (~ndr1_0) | (~c1_1(a231)) | (~c3_1(a231)) | (~c3_1(a259)) | (~c1_1(a259)))),
% 0.84/1.04 inference(transitivity,[status(thm)],[1665, 1663])).
% 0.84/1.04 tff(1667,plain,
% 0.84/1.04 ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp18 | (~ndr1_0) | c2_1(a259) | (~c3_1(a259)) | (~c1_1(a259)) | c0_1(a231) | (~c1_1(a231)) | (~c3_1(a231)))),
% 0.84/1.04 inference(quant_inst,[status(thm)],[])).
% 0.84/1.04 tff(1668,plain,
% 0.84/1.04 ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp18 | c2_1(a259) | c0_1(a231) | (~ndr1_0) | (~c1_1(a231)) | (~c3_1(a231)) | (~c3_1(a259)) | (~c1_1(a259))),
% 0.84/1.04 inference(modus_ponens,[status(thm)],[1667, 1666])).
% 0.84/1.04 tff(1669,plain,
% 0.84/1.04 ((~c3_1(a259)) | (~c1_1(a259))),
% 0.84/1.04 inference(unit_resolution,[status(thm)],[1668, 110, 596, 1509, 1508, 785, 1507, 615])).
% 0.84/1.04 tff(1670,plain,
% 0.84/1.04 (~c1_1(a259)),
% 0.84/1.04 inference(unit_resolution,[status(thm)],[1669, 1662])).
% 0.84/1.04 tff(1671,plain,
% 0.84/1.04 (^[V: $i, U: $i] : refl((hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V))) <=> (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V))))),
% 0.84/1.04 inference(bind,[status(th)],[])).
% 0.84/1.04 tff(1672,plain,
% 0.84/1.04 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))),
% 0.84/1.04 inference(quant_intro,[status(thm)],[1671])).
% 0.84/1.04 tff(1673,plain,
% 0.84/1.04 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))),
% 0.84/1.04 inference(rewrite,[status(thm)],[])).
% 0.84/1.04 tff(1674,plain,
% 0.84/1.04 (^[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)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c0_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(V)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(V))))), (((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)))), (((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(V))))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | (~c3_1(V)))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | (~c3_1(V))))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | (~c3_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | (~c3_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V))))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V))))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | hskp5) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V))) | hskp5))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V))) | hskp5) <=> (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | hskp5) <=> (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))))),
% 0.84/1.04 inference(bind,[status(th)],[])).
% 0.84/1.04 tff(1675,plain,
% 0.84/1.04 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | hskp5) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))),
% 0.84/1.04 inference(quant_intro,[status(thm)],[1674])).
% 0.84/1.04 tff(1676,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | hskp5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause162')).
% 0.84/1.04 tff(1677,plain,
% 0.84/1.04 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))),
% 0.84/1.04 inference(modus_ponens,[status(thm)],[1676, 1675])).
% 0.84/1.04 tff(1678,plain,
% 0.84/1.04 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))),
% 0.84/1.04 inference(modus_ponens,[status(thm)],[1677, 1673])).
% 0.84/1.04 tff(1679,plain,(
% 0.84/1.04 ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))),
% 0.84/1.04 inference(skolemize,[status(sab)],[1678])).
% 0.84/1.04 tff(1680,plain,
% 0.84/1.04 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))),
% 0.84/1.04 inference(modus_ponens,[status(thm)],[1679, 1672])).
% 0.84/1.04 tff(1681,plain,
% 0.84/1.04 ((hskp22 | hskp18 | hskp9) <=> (hskp22 | hskp18 | hskp9)),
% 0.84/1.04 inference(rewrite,[status(thm)],[])).
% 0.84/1.04 tff(1682,plain,
% 0.84/1.04 (((hskp18 | hskp9) | hskp22) <=> (hskp22 | hskp18 | hskp9)),
% 0.84/1.04 inference(rewrite,[status(thm)],[])).
% 0.84/1.04 tff(1683,axiom,((hskp18 | hskp9) | hskp22), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause36')).
% 0.84/1.04 tff(1684,plain,
% 0.84/1.04 (hskp22 | hskp18 | hskp9),
% 0.84/1.04 inference(modus_ponens,[status(thm)],[1683, 1682])).
% 0.84/1.04 tff(1685,plain,
% 0.84/1.04 (hskp22 | hskp18 | hskp9),
% 0.84/1.04 inference(modus_ponens,[status(thm)],[1684, 1681])).
% 0.84/1.04 tff(1686,plain,
% 0.84/1.04 (hskp22 | hskp18 | hskp9),
% 0.84/1.04 inference(modus_ponens,[status(thm)],[1685, 1681])).
% 0.84/1.04 tff(1687,plain,
% 0.84/1.04 (hskp22 | hskp18 | hskp9),
% 0.84/1.04 inference(modus_ponens,[status(thm)],[1686, 1681])).
% 0.84/1.04 tff(1688,plain,
% 0.84/1.04 (hskp22 | hskp18 | hskp9),
% 0.84/1.04 inference(modus_ponens,[status(thm)],[1687, 1681])).
% 0.84/1.04 tff(1689,plain,
% 0.84/1.04 (hskp22),
% 0.84/1.04 inference(unit_resolution,[status(thm)],[1688, 23, 596])).
% 0.84/1.04 tff(1690,plain,
% 0.84/1.04 (((~hskp22) | (~c2_1(a271))) <=> ((~hskp22) | (~c2_1(a271)))),
% 0.84/1.04 inference(rewrite,[status(thm)],[])).
% 0.84/1.04 tff(1691,plain,
% 0.84/1.04 (((~c2_1(a271)) | (~hskp22)) <=> ((~hskp22) | (~c2_1(a271)))),
% 0.84/1.04 inference(rewrite,[status(thm)],[])).
% 0.84/1.04 tff(1692,axiom,((~c2_1(a271)) | (~hskp22)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause93')).
% 0.84/1.04 tff(1693,plain,
% 0.84/1.04 ((~hskp22) | (~c2_1(a271))),
% 0.84/1.04 inference(modus_ponens,[status(thm)],[1692, 1691])).
% 0.84/1.04 tff(1694,plain,
% 0.84/1.04 ((~hskp22) | (~c2_1(a271))),
% 0.84/1.04 inference(modus_ponens,[status(thm)],[1693, 1690])).
% 0.84/1.04 tff(1695,plain,
% 0.84/1.04 (~c2_1(a271)),
% 0.84/1.04 inference(unit_resolution,[status(thm)],[1694, 1689])).
% 0.84/1.04 tff(1696,plain,
% 0.84/1.04 (((~hskp22) | (~c1_1(a271))) <=> ((~hskp22) | (~c1_1(a271)))),
% 0.84/1.04 inference(rewrite,[status(thm)],[])).
% 0.84/1.04 tff(1697,plain,
% 0.84/1.04 (((~c1_1(a271)) | (~hskp22)) <=> ((~hskp22) | (~c1_1(a271)))),
% 0.84/1.04 inference(rewrite,[status(thm)],[])).
% 0.84/1.04 tff(1698,axiom,((~c1_1(a271)) | (~hskp22)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause92')).
% 0.84/1.04 tff(1699,plain,
% 0.84/1.04 ((~hskp22) | (~c1_1(a271))),
% 0.84/1.04 inference(modus_ponens,[status(thm)],[1698, 1697])).
% 0.84/1.04 tff(1700,plain,
% 0.84/1.04 ((~hskp22) | (~c1_1(a271))),
% 0.84/1.04 inference(modus_ponens,[status(thm)],[1699, 1696])).
% 0.84/1.04 tff(1701,plain,
% 0.84/1.04 (~c1_1(a271)),
% 0.84/1.04 inference(unit_resolution,[status(thm)],[1700, 1689])).
% 0.84/1.04 tff(1702,plain,
% 0.84/1.04 (((~hskp22) | (~c0_1(a271))) <=> ((~hskp22) | (~c0_1(a271)))),
% 0.84/1.04 inference(rewrite,[status(thm)],[])).
% 0.84/1.04 tff(1703,plain,
% 0.84/1.04 (((~c0_1(a271)) | (~hskp22)) <=> ((~hskp22) | (~c0_1(a271)))),
% 0.84/1.04 inference(rewrite,[status(thm)],[])).
% 0.84/1.04 tff(1704,axiom,((~c0_1(a271)) | (~hskp22)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause91')).
% 0.84/1.04 tff(1705,plain,
% 0.84/1.04 ((~hskp22) | (~c0_1(a271))),
% 0.84/1.04 inference(modus_ponens,[status(thm)],[1704, 1703])).
% 0.84/1.04 tff(1706,plain,
% 0.84/1.04 ((~hskp22) | (~c0_1(a271))),
% 0.84/1.04 inference(modus_ponens,[status(thm)],[1705, 1702])).
% 0.84/1.04 tff(1707,plain,
% 0.84/1.04 (~c0_1(a271)),
% 0.84/1.04 inference(unit_resolution,[status(thm)],[1706, 1689])).
% 0.84/1.04 tff(1708,plain,
% 0.84/1.04 (((~![U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp0 | c0_1(a271) | c1_1(a271) | c2_1(a271) | (~ndr1_0))) <=> ((~![U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp0 | c0_1(a271) | c1_1(a271) | c2_1(a271) | (~ndr1_0))),
% 0.84/1.04 inference(rewrite,[status(thm)],[])).
% 0.84/1.04 tff(1709,plain,
% 0.84/1.04 ((hskp0 | (~ndr1_0) | c2_1(a271) | c1_1(a271) | c0_1(a271)) <=> (hskp0 | c0_1(a271) | c1_1(a271) | c2_1(a271) | (~ndr1_0))),
% 0.84/1.04 inference(rewrite,[status(thm)],[])).
% 0.84/1.04 tff(1710,plain,
% 0.84/1.04 (((~![U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp0 | (~ndr1_0) | c2_1(a271) | c1_1(a271) | c0_1(a271))) <=> ((~![U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp0 | c0_1(a271) | c1_1(a271) | c2_1(a271) | (~ndr1_0)))),
% 0.84/1.04 inference(monotonicity,[status(thm)],[1709])).
% 0.84/1.04 tff(1711,plain,
% 0.84/1.04 (((~![U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp0 | (~ndr1_0) | c2_1(a271) | c1_1(a271) | c0_1(a271))) <=> ((~![U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp0 | c0_1(a271) | c1_1(a271) | c2_1(a271) | (~ndr1_0))),
% 0.84/1.04 inference(transitivity,[status(thm)],[1710, 1708])).
% 0.84/1.04 tff(1712,plain,
% 0.84/1.04 ((~![U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp0 | (~ndr1_0) | c2_1(a271) | c1_1(a271) | c0_1(a271))),
% 0.84/1.04 inference(quant_inst,[status(thm)],[])).
% 0.84/1.04 tff(1713,plain,
% 0.84/1.04 ((~![U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp0 | c0_1(a271) | c1_1(a271) | c2_1(a271) | (~ndr1_0)),
% 0.84/1.04 inference(modus_ponens,[status(thm)],[1712, 1711])).
% 0.84/1.04 tff(1714,plain,
% 0.84/1.04 (hskp0),
% 0.84/1.04 inference(unit_resolution,[status(thm)],[1713, 110, 1707, 1701, 1695, 1008])).
% 0.84/1.04 tff(1715,plain,
% 0.84/1.04 (~c3_1(a213)),
% 0.84/1.04 inference(unit_resolution,[status(thm)],[744, 1714])).
% 0.84/1.04 tff(1716,plain,
% 0.84/1.04 (~c1_1(a213)),
% 0.84/1.04 inference(unit_resolution,[status(thm)],[750, 1714])).
% 0.84/1.04 tff(1717,plain,
% 0.84/1.04 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp5 | c2_1(a259) | c1_1(a213) | c3_1(a213) | (~ndr1_0) | (~c0_1(a213)) | (~c3_1(a259)) | c1_1(a259))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | hskp5 | c2_1(a259) | c1_1(a213) | c3_1(a213) | (~ndr1_0) | (~c0_1(a213)) | (~c3_1(a259)) | c1_1(a259))),
% 0.84/1.04 inference(rewrite,[status(thm)],[])).
% 0.84/1.04 tff(1718,plain,
% 0.84/1.04 ((hskp5 | (~ndr1_0) | c1_1(a213) | c3_1(a213) | (~c0_1(a213)) | c1_1(a259) | c2_1(a259) | (~c3_1(a259))) <=> (hskp5 | c2_1(a259) | c1_1(a213) | c3_1(a213) | (~ndr1_0) | (~c0_1(a213)) | (~c3_1(a259)) | c1_1(a259))),
% 0.84/1.04 inference(rewrite,[status(thm)],[])).
% 0.84/1.04 tff(1719,plain,
% 0.84/1.04 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a213) | c3_1(a213) | (~c0_1(a213)) | c1_1(a259) | c2_1(a259) | (~c3_1(a259)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp5 | c2_1(a259) | c1_1(a213) | c3_1(a213) | (~ndr1_0) | (~c0_1(a213)) | (~c3_1(a259)) | c1_1(a259)))),
% 0.84/1.04 inference(monotonicity,[status(thm)],[1718])).
% 0.84/1.04 tff(1720,plain,
% 0.84/1.04 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a213) | c3_1(a213) | (~c0_1(a213)) | c1_1(a259) | c2_1(a259) | (~c3_1(a259)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | hskp5 | c2_1(a259) | c1_1(a213) | c3_1(a213) | (~ndr1_0) | (~c0_1(a213)) | (~c3_1(a259)) | c1_1(a259))),
% 0.84/1.04 inference(transitivity,[status(thm)],[1719, 1717])).
% 0.84/1.04 tff(1721,plain,
% 0.84/1.04 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a213) | c3_1(a213) | (~c0_1(a213)) | c1_1(a259) | c2_1(a259) | (~c3_1(a259)))),
% 0.84/1.04 inference(quant_inst,[status(thm)],[])).
% 0.84/1.04 tff(1722,plain,
% 0.84/1.04 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | hskp5 | c2_1(a259) | c1_1(a213) | c3_1(a213) | (~ndr1_0) | (~c0_1(a213)) | (~c3_1(a259)) | c1_1(a259)),
% 0.84/1.04 inference(modus_ponens,[status(thm)],[1721, 1720])).
% 0.84/1.04 tff(1723,plain,
% 0.84/1.04 (~c0_1(a213)),
% 0.84/1.04 inference(unit_resolution,[status(thm)],[1722, 110, 45, 1662, 785, 1716, 1715, 1680, 1670])).
% 0.84/1.04 tff(1724,plain,
% 0.84/1.04 (c2_1(a213)),
% 0.84/1.04 inference(unit_resolution,[status(thm)],[758, 1714])).
% 0.84/1.04 tff(1725,plain,
% 0.84/1.04 (((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp18 | c3_1(a237) | (~ndr1_0) | (~c2_1(a237)) | (~c0_1(a237)) | (~c3_1(a259)) | (~c0_1(a259)) | c1_1(a259))) <=> ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp18 | c3_1(a237) | (~ndr1_0) | (~c2_1(a237)) | (~c0_1(a237)) | (~c3_1(a259)) | (~c0_1(a259)) | c1_1(a259))),
% 0.84/1.04 inference(rewrite,[status(thm)],[])).
% 0.84/1.04 tff(1726,plain,
% 0.84/1.04 ((hskp18 | (~ndr1_0) | c3_1(a237) | (~c2_1(a237)) | (~c0_1(a237)) | c1_1(a259) | (~c3_1(a259)) | (~c0_1(a259))) <=> (hskp18 | c3_1(a237) | (~ndr1_0) | (~c2_1(a237)) | (~c0_1(a237)) | (~c3_1(a259)) | (~c0_1(a259)) | c1_1(a259))),
% 0.84/1.04 inference(rewrite,[status(thm)],[])).
% 0.84/1.04 tff(1727,plain,
% 0.84/1.04 (((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp18 | (~ndr1_0) | c3_1(a237) | (~c2_1(a237)) | (~c0_1(a237)) | c1_1(a259) | (~c3_1(a259)) | (~c0_1(a259)))) <=> ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp18 | c3_1(a237) | (~ndr1_0) | (~c2_1(a237)) | (~c0_1(a237)) | (~c3_1(a259)) | (~c0_1(a259)) | c1_1(a259)))),
% 0.84/1.04 inference(monotonicity,[status(thm)],[1726])).
% 0.84/1.04 tff(1728,plain,
% 0.84/1.04 (((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp18 | (~ndr1_0) | c3_1(a237) | (~c2_1(a237)) | (~c0_1(a237)) | c1_1(a259) | (~c3_1(a259)) | (~c0_1(a259)))) <=> ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp18 | c3_1(a237) | (~ndr1_0) | (~c2_1(a237)) | (~c0_1(a237)) | (~c3_1(a259)) | (~c0_1(a259)) | c1_1(a259))),
% 0.84/1.04 inference(transitivity,[status(thm)],[1727, 1725])).
% 0.84/1.04 tff(1729,plain,
% 0.84/1.04 ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp18 | (~ndr1_0) | c3_1(a237) | (~c2_1(a237)) | (~c0_1(a237)) | c1_1(a259) | (~c3_1(a259)) | (~c0_1(a259)))),
% 0.84/1.04 inference(quant_inst,[status(thm)],[])).
% 0.84/1.04 tff(1730,plain,
% 0.84/1.04 ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp18 | c3_1(a237) | (~ndr1_0) | (~c2_1(a237)) | (~c0_1(a237)) | (~c3_1(a259)) | (~c0_1(a259)) | c1_1(a259)),
% 0.84/1.04 inference(modus_ponens,[status(thm)],[1729, 1728])).
% 0.84/1.04 tff(1731,plain,
% 0.84/1.04 (~c0_1(a259)),
% 0.84/1.04 inference(unit_resolution,[status(thm)],[1730, 110, 596, 1662, 1402, 1401, 1400, 1285, 1670])).
% 0.84/1.04 tff(1732,plain,
% 0.84/1.04 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | (c0_1(a259) | c2_1(a259) | c1_1(a213) | (~ndr1_0) | c0_1(a213) | (~c2_1(a213)) | (~c1_1(a261)) | (~c2_1(a261)) | (~c3_1(a261)) | (~c3_1(a259)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | c0_1(a259) | c2_1(a259) | c1_1(a213) | (~ndr1_0) | c0_1(a213) | (~c2_1(a213)) | (~c1_1(a261)) | (~c2_1(a261)) | (~c3_1(a261)) | (~c3_1(a259)))),
% 0.84/1.04 inference(rewrite,[status(thm)],[])).
% 0.84/1.04 tff(1733,plain,
% 0.84/1.04 (((~ndr1_0) | (~c2_1(a261)) | (~c3_1(a261)) | (~c1_1(a261)) | c0_1(a259) | c2_1(a259) | (~c3_1(a259)) | c0_1(a213) | c1_1(a213) | (~c2_1(a213))) <=> (c0_1(a259) | c2_1(a259) | c1_1(a213) | (~ndr1_0) | c0_1(a213) | (~c2_1(a213)) | (~c1_1(a261)) | (~c2_1(a261)) | (~c3_1(a261)) | (~c3_1(a259)))),
% 0.84/1.04 inference(rewrite,[status(thm)],[])).
% 0.84/1.04 tff(1734,plain,
% 0.84/1.04 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a261)) | (~c3_1(a261)) | (~c1_1(a261)) | c0_1(a259) | c2_1(a259) | (~c3_1(a259)) | c0_1(a213) | c1_1(a213) | (~c2_1(a213)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | (c0_1(a259) | c2_1(a259) | c1_1(a213) | (~ndr1_0) | c0_1(a213) | (~c2_1(a213)) | (~c1_1(a261)) | (~c2_1(a261)) | (~c3_1(a261)) | (~c3_1(a259))))),
% 0.84/1.04 inference(monotonicity,[status(thm)],[1733])).
% 0.84/1.04 tff(1735,plain,
% 0.84/1.04 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a261)) | (~c3_1(a261)) | (~c1_1(a261)) | c0_1(a259) | c2_1(a259) | (~c3_1(a259)) | c0_1(a213) | c1_1(a213) | (~c2_1(a213)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | c0_1(a259) | c2_1(a259) | c1_1(a213) | (~ndr1_0) | c0_1(a213) | (~c2_1(a213)) | (~c1_1(a261)) | (~c2_1(a261)) | (~c3_1(a261)) | (~c3_1(a259)))),
% 0.84/1.04 inference(transitivity,[status(thm)],[1734, 1732])).
% 0.84/1.04 tff(1736,plain,
% 0.84/1.04 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a261)) | (~c3_1(a261)) | (~c1_1(a261)) | c0_1(a259) | c2_1(a259) | (~c3_1(a259)) | c0_1(a213) | c1_1(a213) | (~c2_1(a213)))),
% 0.84/1.04 inference(quant_inst,[status(thm)],[])).
% 0.84/1.04 tff(1737,plain,
% 0.84/1.04 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | c0_1(a259) | c2_1(a259) | c1_1(a213) | (~ndr1_0) | c0_1(a213) | (~c2_1(a213)) | (~c1_1(a261)) | (~c2_1(a261)) | (~c3_1(a261)) | (~c3_1(a259))),
% 0.84/1.04 inference(modus_ponens,[status(thm)],[1736, 1735])).
% 0.84/1.04 tff(1738,plain,
% 0.84/1.04 ($false),
% 0.84/1.04 inference(unit_resolution,[status(thm)],[1737, 110, 1237, 1229, 1221, 1731, 1662, 1724, 785, 1716, 1439, 1723])).
% 0.84/1.04 tff(1739,plain,(hskp9 | c2_1(a259) | hskp5 | hskp18 | (~c1_1(a231)) | (~c3_1(a231)) | c0_1(a231)), inference(lemma,lemma(discharge,[]))).
% 0.84/1.04 tff(1740,plain,
% 0.84/1.04 (c2_1(a259)),
% 0.84/1.04 inference(unit_resolution,[status(thm)],[1739, 1589, 45, 596, 1509, 1508, 1507])).
% 0.84/1.04 tff(1741,plain,
% 0.84/1.04 (~hskp21),
% 0.84/1.04 inference(unit_resolution,[status(thm)],[975, 1740])).
% 0.84/1.04 tff(1742,plain,
% 0.84/1.04 (hskp22),
% 0.84/1.04 inference(unit_resolution,[status(thm)],[1688, 1589, 596])).
% 0.84/1.04 tff(1743,plain,
% 0.84/1.04 (~c0_1(a271)),
% 0.84/1.04 inference(unit_resolution,[status(thm)],[1706, 1742])).
% 0.84/1.04 tff(1744,assumption,(~hskp21), introduced(assumption)).
% 0.84/1.04 tff(1745,plain,
% 0.84/1.04 (~c2_1(a271)),
% 0.84/1.04 inference(unit_resolution,[status(thm)],[1694, 1742])).
% 0.84/1.04 tff(1746,plain,
% 0.84/1.04 (~c1_1(a271)),
% 0.84/1.04 inference(unit_resolution,[status(thm)],[1700, 1742])).
% 0.84/1.04 tff(1747,assumption,(~c2_1(a271)), introduced(assumption)).
% 0.84/1.04 tff(1748,assumption,(~c0_1(a271)), introduced(assumption)).
% 0.84/1.04 tff(1749,assumption,(c2_1(a255)), introduced(assumption)).
% 0.84/1.04 tff(1750,plain,
% 0.84/1.04 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | (c0_1(a271) | c2_1(a271) | c0_1(a255) | c1_1(a255) | (~ndr1_0) | (~c1_1(a261)) | (~c2_1(a261)) | (~c3_1(a261)) | (~c2_1(a255)) | (~c3_1(a271)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | c0_1(a271) | c2_1(a271) | c0_1(a255) | c1_1(a255) | (~ndr1_0) | (~c1_1(a261)) | (~c2_1(a261)) | (~c3_1(a261)) | (~c2_1(a255)) | (~c3_1(a271)))),
% 0.84/1.04 inference(rewrite,[status(thm)],[])).
% 0.84/1.04 tff(1751,plain,
% 0.84/1.04 (((~ndr1_0) | (~c2_1(a261)) | (~c3_1(a261)) | (~c1_1(a261)) | c0_1(a271) | c2_1(a271) | (~c3_1(a271)) | c0_1(a255) | c1_1(a255) | (~c2_1(a255))) <=> (c0_1(a271) | c2_1(a271) | c0_1(a255) | c1_1(a255) | (~ndr1_0) | (~c1_1(a261)) | (~c2_1(a261)) | (~c3_1(a261)) | (~c2_1(a255)) | (~c3_1(a271)))),
% 0.84/1.04 inference(rewrite,[status(thm)],[])).
% 0.84/1.04 tff(1752,plain,
% 0.84/1.04 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a261)) | (~c3_1(a261)) | (~c1_1(a261)) | c0_1(a271) | c2_1(a271) | (~c3_1(a271)) | c0_1(a255) | c1_1(a255) | (~c2_1(a255)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | (c0_1(a271) | c2_1(a271) | c0_1(a255) | c1_1(a255) | (~ndr1_0) | (~c1_1(a261)) | (~c2_1(a261)) | (~c3_1(a261)) | (~c2_1(a255)) | (~c3_1(a271))))),
% 0.84/1.04 inference(monotonicity,[status(thm)],[1751])).
% 0.84/1.04 tff(1753,plain,
% 0.84/1.04 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a261)) | (~c3_1(a261)) | (~c1_1(a261)) | c0_1(a271) | c2_1(a271) | (~c3_1(a271)) | c0_1(a255) | c1_1(a255) | (~c2_1(a255)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | c0_1(a271) | c2_1(a271) | c0_1(a255) | c1_1(a255) | (~ndr1_0) | (~c1_1(a261)) | (~c2_1(a261)) | (~c3_1(a261)) | (~c2_1(a255)) | (~c3_1(a271)))),
% 0.84/1.04 inference(transitivity,[status(thm)],[1752, 1750])).
% 0.84/1.04 tff(1754,plain,
% 0.84/1.04 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a261)) | (~c3_1(a261)) | (~c1_1(a261)) | c0_1(a271) | c2_1(a271) | (~c3_1(a271)) | c0_1(a255) | c1_1(a255) | (~c2_1(a255)))),
% 0.84/1.04 inference(quant_inst,[status(thm)],[])).
% 0.84/1.04 tff(1755,plain,
% 0.84/1.04 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | c0_1(a271) | c2_1(a271) | c0_1(a255) | c1_1(a255) | (~ndr1_0) | (~c1_1(a261)) | (~c2_1(a261)) | (~c3_1(a261)) | (~c2_1(a255)) | (~c3_1(a271))),
% 0.84/1.04 inference(modus_ponens,[status(thm)],[1754, 1753])).
% 0.84/1.04 tff(1756,plain,
% 0.84/1.04 ((~c2_1(a255)) | (~c3_1(a271))),
% 0.84/1.04 inference(unit_resolution,[status(thm)],[1755, 110, 1594, 1593, 1592, 1748, 1747, 1097, 1096, 1439])).
% 0.84/1.04 tff(1757,plain,
% 0.84/1.04 (~c3_1(a271)),
% 0.84/1.04 inference(unit_resolution,[status(thm)],[1756, 1749])).
% 0.84/1.04 tff(1758,plain,
% 0.84/1.04 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | (c0_1(a255) | c1_1(a255) | c0_1(a231) | (~ndr1_0) | (~c1_1(a261)) | (~c2_1(a261)) | (~c3_1(a261)) | c2_1(a231) | (~c3_1(a231)) | (~c2_1(a255)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | c0_1(a255) | c1_1(a255) | c0_1(a231) | (~ndr1_0) | (~c1_1(a261)) | (~c2_1(a261)) | (~c3_1(a261)) | c2_1(a231) | (~c3_1(a231)) | (~c2_1(a255)))),
% 0.84/1.04 inference(rewrite,[status(thm)],[])).
% 0.84/1.04 tff(1759,plain,
% 0.84/1.04 (((~ndr1_0) | (~c2_1(a261)) | (~c3_1(a261)) | (~c1_1(a261)) | c0_1(a231) | c2_1(a231) | (~c3_1(a231)) | c0_1(a255) | c1_1(a255) | (~c2_1(a255))) <=> (c0_1(a255) | c1_1(a255) | c0_1(a231) | (~ndr1_0) | (~c1_1(a261)) | (~c2_1(a261)) | (~c3_1(a261)) | c2_1(a231) | (~c3_1(a231)) | (~c2_1(a255)))),
% 0.84/1.04 inference(rewrite,[status(thm)],[])).
% 0.84/1.04 tff(1760,plain,
% 0.84/1.04 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a261)) | (~c3_1(a261)) | (~c1_1(a261)) | c0_1(a231) | c2_1(a231) | (~c3_1(a231)) | c0_1(a255) | c1_1(a255) | (~c2_1(a255)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | (c0_1(a255) | c1_1(a255) | c0_1(a231) | (~ndr1_0) | (~c1_1(a261)) | (~c2_1(a261)) | (~c3_1(a261)) | c2_1(a231) | (~c3_1(a231)) | (~c2_1(a255))))),
% 0.84/1.04 inference(monotonicity,[status(thm)],[1759])).
% 0.84/1.04 tff(1761,plain,
% 0.84/1.04 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a261)) | (~c3_1(a261)) | (~c1_1(a261)) | c0_1(a231) | c2_1(a231) | (~c3_1(a231)) | c0_1(a255) | c1_1(a255) | (~c2_1(a255)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | c0_1(a255) | c1_1(a255) | c0_1(a231) | (~ndr1_0) | (~c1_1(a261)) | (~c2_1(a261)) | (~c3_1(a261)) | c2_1(a231) | (~c3_1(a231)) | (~c2_1(a255)))),
% 0.84/1.04 inference(transitivity,[status(thm)],[1760, 1758])).
% 0.84/1.04 tff(1762,plain,
% 0.84/1.04 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a261)) | (~c3_1(a261)) | (~c1_1(a261)) | c0_1(a231) | c2_1(a231) | (~c3_1(a231)) | c0_1(a255) | c1_1(a255) | (~c2_1(a255)))),
% 0.84/1.04 inference(quant_inst,[status(thm)],[])).
% 0.84/1.04 tff(1763,plain,
% 0.84/1.04 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | c0_1(a255) | c1_1(a255) | c0_1(a231) | (~ndr1_0) | (~c1_1(a261)) | (~c2_1(a261)) | (~c3_1(a261)) | c2_1(a231) | (~c3_1(a231)) | (~c2_1(a255))),
% 0.84/1.04 inference(modus_ponens,[status(thm)],[1762, 1761])).
% 0.84/1.04 tff(1764,plain,
% 0.84/1.04 (c2_1(a231) | (~c2_1(a255))),
% 0.84/1.04 inference(unit_resolution,[status(thm)],[1763, 110, 1594, 1593, 1592, 1508, 1097, 1096, 1507, 1439])).
% 0.84/1.04 tff(1765,plain,
% 0.84/1.04 (c2_1(a231)),
% 0.84/1.04 inference(unit_resolution,[status(thm)],[1764, 1749])).
% 0.84/1.04 tff(1766,plain,
% 0.84/1.04 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp9 | c0_1(a271) | c2_1(a271) | c0_1(a231) | (~ndr1_0) | (~c2_1(a231)) | (~c3_1(a231)) | c3_1(a271))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp9 | c0_1(a271) | c2_1(a271) | c0_1(a231) | (~ndr1_0) | (~c2_1(a231)) | (~c3_1(a231)) | c3_1(a271))),
% 0.84/1.04 inference(rewrite,[status(thm)],[])).
% 0.84/1.04 tff(1767,plain,
% 0.84/1.04 ((hskp9 | (~ndr1_0) | c0_1(a231) | (~c2_1(a231)) | (~c3_1(a231)) | c3_1(a271) | c0_1(a271) | c2_1(a271)) <=> (hskp9 | c0_1(a271) | c2_1(a271) | c0_1(a231) | (~ndr1_0) | (~c2_1(a231)) | (~c3_1(a231)) | c3_1(a271))),
% 0.84/1.04 inference(rewrite,[status(thm)],[])).
% 0.84/1.04 tff(1768,plain,
% 0.84/1.04 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp9 | (~ndr1_0) | c0_1(a231) | (~c2_1(a231)) | (~c3_1(a231)) | c3_1(a271) | c0_1(a271) | c2_1(a271))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp9 | c0_1(a271) | c2_1(a271) | c0_1(a231) | (~ndr1_0) | (~c2_1(a231)) | (~c3_1(a231)) | c3_1(a271)))),
% 0.84/1.04 inference(monotonicity,[status(thm)],[1767])).
% 0.84/1.04 tff(1769,plain,
% 0.84/1.04 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp9 | (~ndr1_0) | c0_1(a231) | (~c2_1(a231)) | (~c3_1(a231)) | c3_1(a271) | c0_1(a271) | c2_1(a271))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp9 | c0_1(a271) | c2_1(a271) | c0_1(a231) | (~ndr1_0) | (~c2_1(a231)) | (~c3_1(a231)) | c3_1(a271))),
% 0.84/1.04 inference(transitivity,[status(thm)],[1768, 1766])).
% 0.84/1.04 tff(1770,plain,
% 0.84/1.04 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp9 | (~ndr1_0) | c0_1(a231) | (~c2_1(a231)) | (~c3_1(a231)) | c3_1(a271) | c0_1(a271) | c2_1(a271))),
% 0.84/1.04 inference(quant_inst,[status(thm)],[])).
% 0.84/1.04 tff(1771,plain,
% 0.84/1.04 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp9 | c0_1(a271) | c2_1(a271) | c0_1(a231) | (~ndr1_0) | (~c2_1(a231)) | (~c3_1(a231)) | c3_1(a271)),
% 0.84/1.04 inference(modus_ponens,[status(thm)],[1770, 1769])).
% 0.84/1.04 tff(1772,plain,
% 0.84/1.04 ($false),
% 0.84/1.04 inference(unit_resolution,[status(thm)],[1771, 110, 23, 1508, 1748, 1747, 1507, 905, 1765, 1757])).
% 0.84/1.04 tff(1773,plain,((~c2_1(a255)) | hskp9 | (~c3_1(a231)) | c0_1(a271) | c2_1(a271) | c0_1(a231) | (~c1_1(a261)) | (~c2_1(a261)) | (~c3_1(a261)) | c0_1(a255) | c1_1(a255)), inference(lemma,lemma(discharge,[]))).
% 0.84/1.04 tff(1774,plain,
% 0.84/1.04 (~c2_1(a255)),
% 0.84/1.04 inference(unit_resolution,[status(thm)],[1773, 1097, 1508, 1748, 1747, 1507, 1594, 1593, 1592, 23, 1096])).
% 0.84/1.04 tff(1775,assumption,(~c2_1(a255)), introduced(assumption)).
% 0.84/1.04 tff(1776,assumption,(~c0_1(a261)), introduced(assumption)).
% 0.84/1.04 tff(1777,plain,
% 0.84/1.04 ($false),
% 0.84/1.04 inference(unit_resolution,[status(thm)],[1659, 110, 23, 1593, 1592, 1097, 1114, 905, 1776, 1775])).
% 0.84/1.04 tff(1778,plain,(c3_1(a255) | hskp9 | (~c2_1(a261)) | (~c3_1(a261)) | c0_1(a255) | c0_1(a261) | c2_1(a255)), inference(lemma,lemma(discharge,[]))).
% 0.84/1.04 tff(1779,plain,
% 0.84/1.04 (c3_1(a255)),
% 0.84/1.04 inference(unit_resolution,[status(thm)],[1778, 1097, 1593, 1592, 23, 1595, 1774])).
% 0.84/1.05 tff(1780,plain,
% 0.84/1.05 (~hskp19),
% 0.84/1.05 inference(unit_resolution,[status(thm)],[267, 1779])).
% 0.84/1.05 tff(1781,assumption,(~c1_1(a271)), introduced(assumption)).
% 0.84/1.05 tff(1782,plain,
% 0.84/1.05 (((~![U: $i] : (hskp19 | hskp21 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | (hskp19 | hskp21 | c1_1(a271) | c2_1(a271) | (~ndr1_0) | c3_1(a271))) <=> ((~![U: $i] : (hskp19 | hskp21 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | hskp19 | hskp21 | c1_1(a271) | c2_1(a271) | (~ndr1_0) | c3_1(a271))),
% 0.84/1.05 inference(rewrite,[status(thm)],[])).
% 0.84/1.05 tff(1783,plain,
% 0.84/1.05 ((hskp19 | hskp21 | (~ndr1_0) | c2_1(a271) | c1_1(a271) | c3_1(a271)) <=> (hskp19 | hskp21 | c1_1(a271) | c2_1(a271) | (~ndr1_0) | c3_1(a271))),
% 0.84/1.05 inference(rewrite,[status(thm)],[])).
% 0.84/1.05 tff(1784,plain,
% 0.84/1.05 (((~![U: $i] : (hskp19 | hskp21 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | (hskp19 | hskp21 | (~ndr1_0) | c2_1(a271) | c1_1(a271) | c3_1(a271))) <=> ((~![U: $i] : (hskp19 | hskp21 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | (hskp19 | hskp21 | c1_1(a271) | c2_1(a271) | (~ndr1_0) | c3_1(a271)))),
% 0.84/1.05 inference(monotonicity,[status(thm)],[1783])).
% 0.84/1.05 tff(1785,plain,
% 0.84/1.05 (((~![U: $i] : (hskp19 | hskp21 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | (hskp19 | hskp21 | (~ndr1_0) | c2_1(a271) | c1_1(a271) | c3_1(a271))) <=> ((~![U: $i] : (hskp19 | hskp21 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | hskp19 | hskp21 | c1_1(a271) | c2_1(a271) | (~ndr1_0) | c3_1(a271))),
% 0.84/1.05 inference(transitivity,[status(thm)],[1784, 1782])).
% 0.84/1.05 tff(1786,plain,
% 0.84/1.05 ((~![U: $i] : (hskp19 | hskp21 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | (hskp19 | hskp21 | (~ndr1_0) | c2_1(a271) | c1_1(a271) | c3_1(a271))),
% 0.84/1.05 inference(quant_inst,[status(thm)],[])).
% 0.84/1.05 tff(1787,plain,
% 0.84/1.05 ((~![U: $i] : (hskp19 | hskp21 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | hskp19 | hskp21 | c1_1(a271) | c2_1(a271) | (~ndr1_0) | c3_1(a271)),
% 0.84/1.05 inference(modus_ponens,[status(thm)],[1786, 1785])).
% 0.84/1.05 tff(1788,plain,
% 0.84/1.05 (hskp19 | c3_1(a271)),
% 0.84/1.05 inference(unit_resolution,[status(thm)],[1787, 110, 1744, 1781, 1747, 1630])).
% 0.84/1.05 tff(1789,plain,
% 0.84/1.05 (c3_1(a271)),
% 0.84/1.05 inference(unit_resolution,[status(thm)],[1788, 1780])).
% 0.84/1.05 tff(1790,plain,
% 0.84/1.05 (^[V: $i, U: $i] : refl((hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V))) <=> (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V))))),
% 0.84/1.05 inference(bind,[status(th)],[])).
% 0.84/1.05 tff(1791,plain,
% 0.84/1.05 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))),
% 0.84/1.05 inference(quant_intro,[status(thm)],[1790])).
% 0.84/1.05 tff(1792,plain,
% 0.84/1.05 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))),
% 0.84/1.05 inference(rewrite,[status(thm)],[])).
% 0.84/1.05 tff(1793,plain,
% 0.84/1.05 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V))))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V))))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp5) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V))) | hskp5))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V))) | hskp5) <=> (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp5) <=> (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))))),
% 0.84/1.05 inference(bind,[status(th)],[])).
% 0.84/1.05 tff(1794,plain,
% 0.84/1.05 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp5) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))),
% 0.84/1.05 inference(quant_intro,[status(thm)],[1793])).
% 0.84/1.05 tff(1795,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause166')).
% 0.84/1.05 tff(1796,plain,
% 0.84/1.05 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))),
% 0.84/1.05 inference(modus_ponens,[status(thm)],[1795, 1794])).
% 0.84/1.05 tff(1797,plain,
% 0.84/1.05 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))),
% 0.84/1.05 inference(modus_ponens,[status(thm)],[1796, 1792])).
% 0.84/1.05 tff(1798,plain,(
% 0.84/1.05 ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))),
% 0.84/1.05 inference(skolemize,[status(sab)],[1797])).
% 0.84/1.05 tff(1799,plain,
% 0.84/1.05 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))),
% 0.84/1.05 inference(modus_ponens,[status(thm)],[1798, 1791])).
% 0.84/1.05 tff(1800,assumption,(c2_1(a237)), introduced(assumption)).
% 0.84/1.05 tff(1801,plain,
% 0.84/1.05 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp5 | c0_1(a255) | (~c3_1(a255)) | c3_1(a237) | (~ndr1_0) | (~c2_1(a237)) | (~c1_1(a237)) | c2_1(a255))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp5 | c0_1(a255) | (~c3_1(a255)) | c3_1(a237) | (~ndr1_0) | (~c2_1(a237)) | (~c1_1(a237)) | c2_1(a255))),
% 0.84/1.05 inference(rewrite,[status(thm)],[])).
% 0.84/1.05 tff(1802,plain,
% 0.84/1.05 ((hskp5 | (~ndr1_0) | c3_1(a237) | (~c2_1(a237)) | (~c1_1(a237)) | c0_1(a255) | c2_1(a255) | (~c3_1(a255))) <=> (hskp5 | c0_1(a255) | (~c3_1(a255)) | c3_1(a237) | (~ndr1_0) | (~c2_1(a237)) | (~c1_1(a237)) | c2_1(a255))),
% 0.84/1.05 inference(rewrite,[status(thm)],[])).
% 0.84/1.05 tff(1803,plain,
% 0.84/1.05 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp5 | (~ndr1_0) | c3_1(a237) | (~c2_1(a237)) | (~c1_1(a237)) | c0_1(a255) | c2_1(a255) | (~c3_1(a255)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp5 | c0_1(a255) | (~c3_1(a255)) | c3_1(a237) | (~ndr1_0) | (~c2_1(a237)) | (~c1_1(a237)) | c2_1(a255)))),
% 0.84/1.05 inference(monotonicity,[status(thm)],[1802])).
% 0.84/1.05 tff(1804,plain,
% 0.84/1.05 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp5 | (~ndr1_0) | c3_1(a237) | (~c2_1(a237)) | (~c1_1(a237)) | c0_1(a255) | c2_1(a255) | (~c3_1(a255)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp5 | c0_1(a255) | (~c3_1(a255)) | c3_1(a237) | (~ndr1_0) | (~c2_1(a237)) | (~c1_1(a237)) | c2_1(a255))),
% 0.84/1.05 inference(transitivity,[status(thm)],[1803, 1801])).
% 0.84/1.05 tff(1805,plain,
% 0.84/1.05 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp5 | (~ndr1_0) | c3_1(a237) | (~c2_1(a237)) | (~c1_1(a237)) | c0_1(a255) | c2_1(a255) | (~c3_1(a255)))),
% 0.84/1.05 inference(quant_inst,[status(thm)],[])).
% 0.84/1.05 tff(1806,plain,
% 0.84/1.05 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp5 | c0_1(a255) | (~c3_1(a255)) | c3_1(a237) | (~ndr1_0) | (~c2_1(a237)) | (~c1_1(a237)) | c2_1(a255)),
% 0.84/1.05 inference(modus_ponens,[status(thm)],[1805, 1804])).
% 0.84/1.05 tff(1807,plain,
% 0.84/1.05 ((~c3_1(a255)) | (~c1_1(a237)) | c2_1(a255)),
% 0.84/1.05 inference(unit_resolution,[status(thm)],[1806, 110, 45, 1800, 1097, 164, 1799])).
% 0.84/1.05 tff(1808,plain,
% 0.84/1.05 (~c1_1(a237)),
% 0.84/1.05 inference(unit_resolution,[status(thm)],[1807, 1779, 1774])).
% 0.84/1.05 tff(1809,assumption,(c0_1(a237)), introduced(assumption)).
% 0.84/1.05 tff(1810,plain,
% 0.84/1.05 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp5 | c1_1(a271) | c2_1(a271) | c3_1(a237) | (~ndr1_0) | c1_1(a237) | (~c0_1(a237)) | (~c3_1(a271)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | hskp5 | c1_1(a271) | c2_1(a271) | c3_1(a237) | (~ndr1_0) | c1_1(a237) | (~c0_1(a237)) | (~c3_1(a271)))),
% 0.84/1.05 inference(rewrite,[status(thm)],[])).
% 0.84/1.05 tff(1811,plain,
% 0.84/1.05 ((hskp5 | (~ndr1_0) | c1_1(a237) | c3_1(a237) | (~c0_1(a237)) | c1_1(a271) | c2_1(a271) | (~c3_1(a271))) <=> (hskp5 | c1_1(a271) | c2_1(a271) | c3_1(a237) | (~ndr1_0) | c1_1(a237) | (~c0_1(a237)) | (~c3_1(a271)))),
% 0.84/1.05 inference(rewrite,[status(thm)],[])).
% 0.84/1.05 tff(1812,plain,
% 0.84/1.05 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a237) | c3_1(a237) | (~c0_1(a237)) | c1_1(a271) | c2_1(a271) | (~c3_1(a271)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp5 | c1_1(a271) | c2_1(a271) | c3_1(a237) | (~ndr1_0) | c1_1(a237) | (~c0_1(a237)) | (~c3_1(a271))))),
% 0.84/1.05 inference(monotonicity,[status(thm)],[1811])).
% 0.84/1.05 tff(1813,plain,
% 0.84/1.05 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a237) | c3_1(a237) | (~c0_1(a237)) | c1_1(a271) | c2_1(a271) | (~c3_1(a271)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | hskp5 | c1_1(a271) | c2_1(a271) | c3_1(a237) | (~ndr1_0) | c1_1(a237) | (~c0_1(a237)) | (~c3_1(a271)))),
% 0.84/1.05 inference(transitivity,[status(thm)],[1812, 1810])).
% 0.84/1.05 tff(1814,plain,
% 0.84/1.05 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a237) | c3_1(a237) | (~c0_1(a237)) | c1_1(a271) | c2_1(a271) | (~c3_1(a271)))),
% 0.84/1.05 inference(quant_inst,[status(thm)],[])).
% 0.84/1.05 tff(1815,plain,
% 0.84/1.05 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | hskp5 | c1_1(a271) | c2_1(a271) | c3_1(a237) | (~ndr1_0) | c1_1(a237) | (~c0_1(a237)) | (~c3_1(a271))),
% 0.84/1.05 inference(modus_ponens,[status(thm)],[1814, 1813])).
% 0.84/1.05 tff(1816,plain,
% 0.84/1.05 ($false),
% 0.84/1.05 inference(unit_resolution,[status(thm)],[1815, 110, 45, 1809, 1781, 1747, 164, 1680, 1808, 1789])).
% 0.84/1.05 tff(1817,plain,(c0_1(a255) | hskp5 | (~c0_1(a237)) | c1_1(a271) | c2_1(a271) | c3_1(a237) | hskp21 | (~c2_1(a237)) | (~c2_1(a261)) | (~c3_1(a261)) | hskp9 | (~c3_1(a231)) | c0_1(a271) | c0_1(a231) | (~c1_1(a261)) | c1_1(a255)), inference(lemma,lemma(discharge,[]))).
% 0.84/1.05 tff(1818,plain,
% 0.84/1.05 (c0_1(a255)),
% 0.84/1.05 inference(unit_resolution,[status(thm)],[1817, 1096, 1402, 1746, 1745, 1400, 1744, 1401, 1229, 1221, 1589, 1508, 1743, 1507, 1237, 45])).
% 0.84/1.05 tff(1819,plain,
% 0.84/1.05 (((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp18 | (~c0_1(a255)) | c1_1(a255) | (~c3_1(a255)) | c3_1(a237) | (~ndr1_0) | (~c2_1(a237)) | (~c0_1(a237)))) <=> ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp18 | (~c0_1(a255)) | c1_1(a255) | (~c3_1(a255)) | c3_1(a237) | (~ndr1_0) | (~c2_1(a237)) | (~c0_1(a237)))),
% 0.84/1.05 inference(rewrite,[status(thm)],[])).
% 0.84/1.05 tff(1820,plain,
% 0.84/1.05 ((hskp18 | (~ndr1_0) | c3_1(a237) | (~c2_1(a237)) | (~c0_1(a237)) | c1_1(a255) | (~c3_1(a255)) | (~c0_1(a255))) <=> (hskp18 | (~c0_1(a255)) | c1_1(a255) | (~c3_1(a255)) | c3_1(a237) | (~ndr1_0) | (~c2_1(a237)) | (~c0_1(a237)))),
% 0.84/1.05 inference(rewrite,[status(thm)],[])).
% 0.84/1.05 tff(1821,plain,
% 0.84/1.05 (((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp18 | (~ndr1_0) | c3_1(a237) | (~c2_1(a237)) | (~c0_1(a237)) | c1_1(a255) | (~c3_1(a255)) | (~c0_1(a255)))) <=> ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp18 | (~c0_1(a255)) | c1_1(a255) | (~c3_1(a255)) | c3_1(a237) | (~ndr1_0) | (~c2_1(a237)) | (~c0_1(a237))))),
% 0.84/1.05 inference(monotonicity,[status(thm)],[1820])).
% 0.84/1.05 tff(1822,plain,
% 0.84/1.05 (((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp18 | (~ndr1_0) | c3_1(a237) | (~c2_1(a237)) | (~c0_1(a237)) | c1_1(a255) | (~c3_1(a255)) | (~c0_1(a255)))) <=> ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp18 | (~c0_1(a255)) | c1_1(a255) | (~c3_1(a255)) | c3_1(a237) | (~ndr1_0) | (~c2_1(a237)) | (~c0_1(a237)))),
% 0.84/1.05 inference(transitivity,[status(thm)],[1821, 1819])).
% 0.84/1.05 tff(1823,plain,
% 0.84/1.05 ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp18 | (~ndr1_0) | c3_1(a237) | (~c2_1(a237)) | (~c0_1(a237)) | c1_1(a255) | (~c3_1(a255)) | (~c0_1(a255)))),
% 0.84/1.05 inference(quant_inst,[status(thm)],[])).
% 0.84/1.05 tff(1824,plain,
% 0.84/1.05 ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp18 | (~c0_1(a255)) | c1_1(a255) | (~c3_1(a255)) | c3_1(a237) | (~ndr1_0) | (~c2_1(a237)) | (~c0_1(a237))),
% 0.84/1.05 inference(modus_ponens,[status(thm)],[1823, 1822])).
% 0.84/1.05 tff(1825,plain,
% 0.84/1.05 ((~c0_1(a255)) | (~c3_1(a255))),
% 0.84/1.05 inference(unit_resolution,[status(thm)],[1824, 110, 596, 1402, 1401, 1096, 1400, 1285])).
% 0.84/1.05 tff(1826,plain,
% 0.84/1.05 (~c3_1(a255)),
% 0.84/1.05 inference(unit_resolution,[status(thm)],[1825, 1818])).
% 0.84/1.05 tff(1827,plain,
% 0.84/1.05 (~hskp19),
% 0.84/1.05 inference(unit_resolution,[status(thm)],[279, 1818])).
% 0.84/1.05 tff(1828,plain,
% 0.84/1.05 (hskp19 | c3_1(a271)),
% 0.84/1.05 inference(unit_resolution,[status(thm)],[1787, 110, 1744, 1746, 1745, 1630])).
% 0.84/1.05 tff(1829,plain,
% 0.84/1.05 (c3_1(a271)),
% 0.84/1.05 inference(unit_resolution,[status(thm)],[1828, 1827])).
% 0.84/1.05 tff(1830,plain,
% 0.84/1.05 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp5 | c1_1(a271) | c2_1(a271) | (~c0_1(a255)) | c1_1(a255) | c3_1(a255) | (~ndr1_0) | (~c3_1(a271)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | hskp5 | c1_1(a271) | c2_1(a271) | (~c0_1(a255)) | c1_1(a255) | c3_1(a255) | (~ndr1_0) | (~c3_1(a271)))),
% 0.84/1.05 inference(rewrite,[status(thm)],[])).
% 0.84/1.05 tff(1831,plain,
% 0.84/1.05 ((hskp5 | (~ndr1_0) | c1_1(a255) | c3_1(a255) | (~c0_1(a255)) | c1_1(a271) | c2_1(a271) | (~c3_1(a271))) <=> (hskp5 | c1_1(a271) | c2_1(a271) | (~c0_1(a255)) | c1_1(a255) | c3_1(a255) | (~ndr1_0) | (~c3_1(a271)))),
% 0.84/1.05 inference(rewrite,[status(thm)],[])).
% 0.84/1.05 tff(1832,plain,
% 0.84/1.05 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a255) | c3_1(a255) | (~c0_1(a255)) | c1_1(a271) | c2_1(a271) | (~c3_1(a271)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp5 | c1_1(a271) | c2_1(a271) | (~c0_1(a255)) | c1_1(a255) | c3_1(a255) | (~ndr1_0) | (~c3_1(a271))))),
% 0.84/1.05 inference(monotonicity,[status(thm)],[1831])).
% 0.84/1.05 tff(1833,plain,
% 0.84/1.05 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a255) | c3_1(a255) | (~c0_1(a255)) | c1_1(a271) | c2_1(a271) | (~c3_1(a271)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | hskp5 | c1_1(a271) | c2_1(a271) | (~c0_1(a255)) | c1_1(a255) | c3_1(a255) | (~ndr1_0) | (~c3_1(a271)))),
% 0.84/1.05 inference(transitivity,[status(thm)],[1832, 1830])).
% 0.84/1.05 tff(1834,plain,
% 0.84/1.05 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a255) | c3_1(a255) | (~c0_1(a255)) | c1_1(a271) | c2_1(a271) | (~c3_1(a271)))),
% 0.84/1.05 inference(quant_inst,[status(thm)],[])).
% 0.84/1.05 tff(1835,plain,
% 0.84/1.05 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | hskp5 | c1_1(a271) | c2_1(a271) | (~c0_1(a255)) | c1_1(a255) | c3_1(a255) | (~ndr1_0) | (~c3_1(a271))),
% 0.84/1.05 inference(modus_ponens,[status(thm)],[1834, 1833])).
% 0.84/1.05 tff(1836,plain,
% 0.84/1.05 ((~c0_1(a255)) | c3_1(a255) | (~c3_1(a271))),
% 0.84/1.05 inference(unit_resolution,[status(thm)],[1835, 110, 45, 1746, 1745, 1096, 1680])).
% 0.84/1.05 tff(1837,plain,
% 0.84/1.05 ($false),
% 0.84/1.05 inference(unit_resolution,[status(thm)],[1836, 1829, 1826, 1818])).
% 0.84/1.05 tff(1838,plain,(c1_1(a255) | hskp5 | hskp21 | hskp18 | (~c3_1(a231)) | c0_1(a231)), inference(lemma,lemma(discharge,[]))).
% 0.84/1.05 tff(1839,plain,
% 0.84/1.05 (c1_1(a255)),
% 0.84/1.05 inference(unit_resolution,[status(thm)],[1838, 45, 1741, 596, 1508, 1507])).
% 0.84/1.05 tff(1840,plain,
% 0.84/1.05 (~hskp19),
% 0.84/1.05 inference(unit_resolution,[status(thm)],[273, 1839])).
% 0.84/1.05 tff(1841,plain,
% 0.84/1.05 (hskp19 | c3_1(a271)),
% 0.84/1.05 inference(unit_resolution,[status(thm)],[1787, 110, 1741, 1746, 1745, 1630])).
% 0.84/1.05 tff(1842,plain,
% 0.84/1.05 (c3_1(a271)),
% 0.84/1.05 inference(unit_resolution,[status(thm)],[1841, 1840])).
% 0.84/1.05 tff(1843,plain,
% 0.84/1.05 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp5 | c0_1(a271) | c2_1(a271) | c3_1(a237) | (~ndr1_0) | (~c2_1(a237)) | (~c1_1(a237)) | (~c3_1(a271)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp5 | c0_1(a271) | c2_1(a271) | c3_1(a237) | (~ndr1_0) | (~c2_1(a237)) | (~c1_1(a237)) | (~c3_1(a271)))),
% 0.84/1.05 inference(rewrite,[status(thm)],[])).
% 0.84/1.05 tff(1844,plain,
% 0.84/1.05 ((hskp5 | (~ndr1_0) | c3_1(a237) | (~c2_1(a237)) | (~c1_1(a237)) | c0_1(a271) | c2_1(a271) | (~c3_1(a271))) <=> (hskp5 | c0_1(a271) | c2_1(a271) | c3_1(a237) | (~ndr1_0) | (~c2_1(a237)) | (~c1_1(a237)) | (~c3_1(a271)))),
% 0.84/1.05 inference(rewrite,[status(thm)],[])).
% 0.84/1.05 tff(1845,plain,
% 0.84/1.05 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp5 | (~ndr1_0) | c3_1(a237) | (~c2_1(a237)) | (~c1_1(a237)) | c0_1(a271) | c2_1(a271) | (~c3_1(a271)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp5 | c0_1(a271) | c2_1(a271) | c3_1(a237) | (~ndr1_0) | (~c2_1(a237)) | (~c1_1(a237)) | (~c3_1(a271))))),
% 0.84/1.05 inference(monotonicity,[status(thm)],[1844])).
% 0.84/1.05 tff(1846,plain,
% 0.84/1.05 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp5 | (~ndr1_0) | c3_1(a237) | (~c2_1(a237)) | (~c1_1(a237)) | c0_1(a271) | c2_1(a271) | (~c3_1(a271)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp5 | c0_1(a271) | c2_1(a271) | c3_1(a237) | (~ndr1_0) | (~c2_1(a237)) | (~c1_1(a237)) | (~c3_1(a271)))),
% 0.84/1.05 inference(transitivity,[status(thm)],[1845, 1843])).
% 0.84/1.05 tff(1847,plain,
% 0.84/1.05 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp5 | (~ndr1_0) | c3_1(a237) | (~c2_1(a237)) | (~c1_1(a237)) | c0_1(a271) | c2_1(a271) | (~c3_1(a271)))),
% 0.84/1.05 inference(quant_inst,[status(thm)],[])).
% 0.84/1.05 tff(1848,plain,
% 0.84/1.05 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp5 | c0_1(a271) | c2_1(a271) | c3_1(a237) | (~ndr1_0) | (~c2_1(a237)) | (~c1_1(a237)) | (~c3_1(a271))),
% 0.84/1.05 inference(modus_ponens,[status(thm)],[1847, 1846])).
% 0.84/1.05 tff(1849,plain,
% 0.84/1.05 ((~c1_1(a237)) | (~c3_1(a271))),
% 0.84/1.05 inference(unit_resolution,[status(thm)],[1848, 110, 45, 1401, 1743, 1745, 1400, 1799])).
% 0.84/1.05 tff(1850,plain,
% 0.84/1.05 (~c1_1(a237)),
% 0.84/1.05 inference(unit_resolution,[status(thm)],[1849, 1842])).
% 0.84/1.05 tff(1851,plain,
% 0.84/1.05 ($false),
% 0.84/1.05 inference(unit_resolution,[status(thm)],[1815, 110, 45, 1402, 1746, 1745, 1400, 1680, 1850, 1842])).
% 0.84/1.05 tff(1852,plain,(hskp5 | hskp18 | (~c3_1(a231)) | c0_1(a231) | (~c1_1(a231))), inference(lemma,lemma(discharge,[]))).
% 0.84/1.05 tff(1853,plain,
% 0.84/1.05 ($false),
% 0.84/1.05 inference(unit_resolution,[status(thm)],[1852, 1506, 1505, 596, 1504, 605])).
% 0.84/1.05 tff(1854,plain,((~hskp10) | hskp18), inference(lemma,lemma(discharge,[]))).
% 0.84/1.05 tff(1855,plain,
% 0.84/1.05 (~hskp10),
% 0.84/1.05 inference(unit_resolution,[status(thm)],[1854, 596])).
% 0.84/1.05 tff(1856,plain,
% 0.84/1.05 (~hskp9),
% 0.84/1.05 inference(unit_resolution,[status(thm)],[1588, 1504, 596])).
% 0.84/1.05 tff(1857,plain,
% 0.84/1.05 (hskp22),
% 0.84/1.05 inference(unit_resolution,[status(thm)],[1688, 1856, 596])).
% 0.84/1.05 tff(1858,plain,
% 0.84/1.05 (~c2_1(a271)),
% 0.84/1.05 inference(unit_resolution,[status(thm)],[1694, 1857])).
% 0.84/1.05 tff(1859,plain,
% 0.84/1.05 (~c1_1(a271)),
% 0.84/1.05 inference(unit_resolution,[status(thm)],[1700, 1857])).
% 0.84/1.05 tff(1860,plain,
% 0.84/1.05 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp10 | c1_1(a271) | c2_1(a271) | (~ndr1_0) | (~c1_1(a261)) | (~c3_1(a261)) | c0_1(a261) | (~c3_1(a271)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp10 | c1_1(a271) | c2_1(a271) | (~ndr1_0) | (~c1_1(a261)) | (~c3_1(a261)) | c0_1(a261) | (~c3_1(a271)))),
% 0.84/1.05 inference(rewrite,[status(thm)],[])).
% 0.84/1.05 tff(1861,plain,
% 0.84/1.05 ((hskp10 | (~ndr1_0) | c2_1(a271) | c1_1(a271) | (~c3_1(a271)) | c0_1(a261) | (~c1_1(a261)) | (~c3_1(a261))) <=> (hskp10 | c1_1(a271) | c2_1(a271) | (~ndr1_0) | (~c1_1(a261)) | (~c3_1(a261)) | c0_1(a261) | (~c3_1(a271)))),
% 0.84/1.05 inference(rewrite,[status(thm)],[])).
% 0.84/1.05 tff(1862,plain,
% 0.84/1.05 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp10 | (~ndr1_0) | c2_1(a271) | c1_1(a271) | (~c3_1(a271)) | c0_1(a261) | (~c1_1(a261)) | (~c3_1(a261)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp10 | c1_1(a271) | c2_1(a271) | (~ndr1_0) | (~c1_1(a261)) | (~c3_1(a261)) | c0_1(a261) | (~c3_1(a271))))),
% 0.84/1.05 inference(monotonicity,[status(thm)],[1861])).
% 0.84/1.05 tff(1863,plain,
% 0.84/1.05 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp10 | (~ndr1_0) | c2_1(a271) | c1_1(a271) | (~c3_1(a271)) | c0_1(a261) | (~c1_1(a261)) | (~c3_1(a261)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp10 | c1_1(a271) | c2_1(a271) | (~ndr1_0) | (~c1_1(a261)) | (~c3_1(a261)) | c0_1(a261) | (~c3_1(a271)))),
% 0.84/1.05 inference(transitivity,[status(thm)],[1862, 1860])).
% 0.84/1.05 tff(1864,plain,
% 0.84/1.05 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp10 | (~ndr1_0) | c2_1(a271) | c1_1(a271) | (~c3_1(a271)) | c0_1(a261) | (~c1_1(a261)) | (~c3_1(a261)))),
% 0.84/1.05 inference(quant_inst,[status(thm)],[])).
% 0.84/1.05 tff(1865,plain,
% 0.84/1.05 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp10 | c1_1(a271) | c2_1(a271) | (~ndr1_0) | (~c1_1(a261)) | (~c3_1(a261)) | c0_1(a261) | (~c3_1(a271))),
% 0.84/1.05 inference(modus_ponens,[status(thm)],[1864, 1863])).
% 0.84/1.05 tff(1866,plain,
% 0.84/1.05 (hskp10 | (~c3_1(a271))),
% 0.84/1.05 inference(unit_resolution,[status(thm)],[1865, 110, 1237, 1221, 1859, 1858, 1302, 1244])).
% 0.84/1.05 tff(1867,plain,
% 0.84/1.05 (~c3_1(a271)),
% 0.84/1.05 inference(unit_resolution,[status(thm)],[1866, 1855])).
% 0.84/1.05 tff(1868,plain,
% 0.84/1.05 (~c0_1(a271)),
% 0.84/1.05 inference(unit_resolution,[status(thm)],[1706, 1857])).
% 0.84/1.05 tff(1869,plain,
% 0.84/1.05 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp9 | c0_1(a271) | c2_1(a271) | (~ndr1_0) | (~c2_1(a261)) | (~c3_1(a261)) | c0_1(a261) | c3_1(a271))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp9 | c0_1(a271) | c2_1(a271) | (~ndr1_0) | (~c2_1(a261)) | (~c3_1(a261)) | c0_1(a261) | c3_1(a271))),
% 0.84/1.05 inference(rewrite,[status(thm)],[])).
% 0.84/1.05 tff(1870,plain,
% 0.84/1.05 ((hskp9 | (~ndr1_0) | c0_1(a261) | (~c2_1(a261)) | (~c3_1(a261)) | c3_1(a271) | c0_1(a271) | c2_1(a271)) <=> (hskp9 | c0_1(a271) | c2_1(a271) | (~ndr1_0) | (~c2_1(a261)) | (~c3_1(a261)) | c0_1(a261) | c3_1(a271))),
% 0.84/1.05 inference(rewrite,[status(thm)],[])).
% 0.84/1.05 tff(1871,plain,
% 0.84/1.05 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp9 | (~ndr1_0) | c0_1(a261) | (~c2_1(a261)) | (~c3_1(a261)) | c3_1(a271) | c0_1(a271) | c2_1(a271))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp9 | c0_1(a271) | c2_1(a271) | (~ndr1_0) | (~c2_1(a261)) | (~c3_1(a261)) | c0_1(a261) | c3_1(a271)))),
% 0.84/1.05 inference(monotonicity,[status(thm)],[1870])).
% 0.84/1.05 tff(1872,plain,
% 0.84/1.05 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp9 | (~ndr1_0) | c0_1(a261) | (~c2_1(a261)) | (~c3_1(a261)) | c3_1(a271) | c0_1(a271) | c2_1(a271))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp9 | c0_1(a271) | c2_1(a271) | (~ndr1_0) | (~c2_1(a261)) | (~c3_1(a261)) | c0_1(a261) | c3_1(a271))),
% 0.84/1.05 inference(transitivity,[status(thm)],[1871, 1869])).
% 0.84/1.05 tff(1873,plain,
% 0.84/1.05 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp9 | (~ndr1_0) | c0_1(a261) | (~c2_1(a261)) | (~c3_1(a261)) | c3_1(a271) | c0_1(a271) | c2_1(a271))),
% 0.84/1.05 inference(quant_inst,[status(thm)],[])).
% 0.84/1.05 tff(1874,plain,
% 0.84/1.05 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp9 | c0_1(a271) | c2_1(a271) | (~ndr1_0) | (~c2_1(a261)) | (~c3_1(a261)) | c0_1(a261) | c3_1(a271)),
% 0.84/1.05 inference(modus_ponens,[status(thm)],[1873, 1872])).
% 0.84/1.05 tff(1875,plain,
% 0.84/1.05 ($false),
% 0.84/1.05 inference(unit_resolution,[status(thm)],[1874, 110, 1856, 1229, 1221, 1868, 1858, 905, 1244, 1867])).
% 0.84/1.05 tff(1876,plain,(hskp18), inference(lemma,lemma(discharge,[]))).
% 0.84/1.05 tff(1877,plain,
% 0.84/1.05 (((~hskp18) | c2_1(a252)) <=> ((~hskp18) | c2_1(a252))),
% 0.84/1.05 inference(rewrite,[status(thm)],[])).
% 0.84/1.05 tff(1878,axiom,((~hskp18) | c2_1(a252)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause61')).
% 0.84/1.05 tff(1879,plain,
% 0.84/1.05 ((~hskp18) | c2_1(a252)),
% 0.84/1.05 inference(modus_ponens,[status(thm)],[1878, 1877])).
% 0.84/1.05 tff(1880,plain,
% 0.84/1.05 ((~hskp18) | c2_1(a252)),
% 0.84/1.05 inference(modus_ponens,[status(thm)],[1879, 1877])).
% 0.84/1.05 tff(1881,plain,
% 0.84/1.05 ((~hskp18) | c2_1(a252)),
% 0.84/1.05 inference(modus_ponens,[status(thm)],[1880, 1877])).
% 0.84/1.05 tff(1882,plain,
% 0.84/1.05 ((~hskp18) | c2_1(a252)),
% 0.84/1.05 inference(modus_ponens,[status(thm)],[1881, 1877])).
% 0.84/1.05 tff(1883,plain,
% 0.84/1.05 ((~hskp18) | c2_1(a252)),
% 0.84/1.05 inference(modus_ponens,[status(thm)],[1882, 1877])).
% 0.84/1.05 tff(1884,plain,
% 0.84/1.05 (c2_1(a252)),
% 0.84/1.05 inference(unit_resolution,[status(thm)],[1883, 1876])).
% 0.84/1.05 tff(1885,plain,
% 0.84/1.05 (((~hskp18) | c0_1(a252)) <=> ((~hskp18) | c0_1(a252))),
% 0.84/1.06 inference(rewrite,[status(thm)],[])).
% 0.84/1.06 tff(1886,axiom,((~hskp18) | c0_1(a252)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause60')).
% 0.84/1.06 tff(1887,plain,
% 0.84/1.06 ((~hskp18) | c0_1(a252)),
% 0.84/1.06 inference(modus_ponens,[status(thm)],[1886, 1885])).
% 0.84/1.06 tff(1888,plain,
% 0.84/1.06 ((~hskp18) | c0_1(a252)),
% 0.84/1.06 inference(modus_ponens,[status(thm)],[1887, 1885])).
% 0.84/1.06 tff(1889,plain,
% 0.84/1.06 ((~hskp18) | c0_1(a252)),
% 0.84/1.06 inference(modus_ponens,[status(thm)],[1888, 1885])).
% 0.84/1.06 tff(1890,plain,
% 0.84/1.06 ((~hskp18) | c0_1(a252)),
% 0.84/1.06 inference(modus_ponens,[status(thm)],[1889, 1885])).
% 0.84/1.06 tff(1891,plain,
% 0.84/1.06 ((~hskp18) | c0_1(a252)),
% 0.84/1.06 inference(modus_ponens,[status(thm)],[1890, 1885])).
% 0.84/1.06 tff(1892,plain,
% 0.84/1.06 (c0_1(a252)),
% 0.84/1.06 inference(unit_resolution,[status(thm)],[1891, 1876])).
% 0.84/1.06 tff(1893,plain,
% 0.84/1.06 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | c0_1(a237) | c3_1(a237) | (~ndr1_0) | c1_1(a237) | (~c3_1(a252)) | (~c0_1(a252)) | (~c2_1(a252)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp2 | c0_1(a237) | c3_1(a237) | (~ndr1_0) | c1_1(a237) | (~c3_1(a252)) | (~c0_1(a252)) | (~c2_1(a252)))),
% 0.84/1.06 inference(rewrite,[status(thm)],[])).
% 0.84/1.06 tff(1894,plain,
% 0.84/1.06 ((hskp2 | (~ndr1_0) | (~c2_1(a252)) | (~c3_1(a252)) | (~c0_1(a252)) | c3_1(a237) | c1_1(a237) | c0_1(a237)) <=> (hskp2 | c0_1(a237) | c3_1(a237) | (~ndr1_0) | c1_1(a237) | (~c3_1(a252)) | (~c0_1(a252)) | (~c2_1(a252)))),
% 0.84/1.06 inference(rewrite,[status(thm)],[])).
% 0.84/1.06 tff(1895,plain,
% 0.84/1.06 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | (~c2_1(a252)) | (~c3_1(a252)) | (~c0_1(a252)) | c3_1(a237) | c1_1(a237) | c0_1(a237))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | c0_1(a237) | c3_1(a237) | (~ndr1_0) | c1_1(a237) | (~c3_1(a252)) | (~c0_1(a252)) | (~c2_1(a252))))),
% 0.84/1.06 inference(monotonicity,[status(thm)],[1894])).
% 0.84/1.06 tff(1896,plain,
% 0.84/1.06 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | (~c2_1(a252)) | (~c3_1(a252)) | (~c0_1(a252)) | c3_1(a237) | c1_1(a237) | c0_1(a237))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp2 | c0_1(a237) | c3_1(a237) | (~ndr1_0) | c1_1(a237) | (~c3_1(a252)) | (~c0_1(a252)) | (~c2_1(a252)))),
% 0.84/1.06 inference(transitivity,[status(thm)],[1895, 1893])).
% 0.84/1.06 tff(1897,plain,
% 0.84/1.06 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | (~c2_1(a252)) | (~c3_1(a252)) | (~c0_1(a252)) | c3_1(a237) | c1_1(a237) | c0_1(a237))),
% 0.84/1.06 inference(quant_inst,[status(thm)],[])).
% 0.84/1.06 tff(1898,plain,
% 0.84/1.06 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp2 | c0_1(a237) | c3_1(a237) | (~ndr1_0) | c1_1(a237) | (~c3_1(a252)) | (~c0_1(a252)) | (~c2_1(a252))),
% 0.84/1.06 inference(modus_ponens,[status(thm)],[1897, 1896])).
% 0.84/1.06 tff(1899,plain,
% 0.84/1.06 (hskp2 | c0_1(a237) | c1_1(a237) | (~c3_1(a252))),
% 0.84/1.06 inference(unit_resolution,[status(thm)],[1898, 110, 1892, 1884, 164, 595])).
% 0.84/1.06 tff(1900,plain,
% 0.84/1.06 (~c3_1(a252)),
% 0.84/1.06 inference(unit_resolution,[status(thm)],[1899, 585, 568, 81])).
% 0.84/1.06 tff(1901,plain,
% 0.84/1.06 (((~hskp18) | (~c1_1(a252))) <=> ((~hskp18) | (~c1_1(a252)))),
% 0.84/1.06 inference(rewrite,[status(thm)],[])).
% 0.84/1.06 tff(1902,plain,
% 0.84/1.06 (((~c1_1(a252)) | (~hskp18)) <=> ((~hskp18) | (~c1_1(a252)))),
% 0.84/1.06 inference(rewrite,[status(thm)],[])).
% 0.84/1.06 tff(1903,axiom,((~c1_1(a252)) | (~hskp18)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause99')).
% 0.84/1.06 tff(1904,plain,
% 0.84/1.06 ((~hskp18) | (~c1_1(a252))),
% 0.84/1.06 inference(modus_ponens,[status(thm)],[1903, 1902])).
% 0.84/1.06 tff(1905,plain,
% 0.84/1.06 ((~hskp18) | (~c1_1(a252))),
% 0.84/1.06 inference(modus_ponens,[status(thm)],[1904, 1901])).
% 0.84/1.06 tff(1906,plain,
% 0.84/1.06 (~c1_1(a252)),
% 0.84/1.06 inference(unit_resolution,[status(thm)],[1905, 1876])).
% 0.84/1.06 tff(1907,plain,
% 0.84/1.06 (((~![U: $i] : (hskp21 | hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp21 | hskp12 | c3_1(a237) | (~ndr1_0) | c1_1(a237) | (~c2_1(a237)))) <=> ((~![U: $i] : (hskp21 | hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | hskp21 | hskp12 | c3_1(a237) | (~ndr1_0) | c1_1(a237) | (~c2_1(a237)))),
% 0.84/1.06 inference(rewrite,[status(thm)],[])).
% 0.84/1.06 tff(1908,plain,
% 0.84/1.06 ((hskp21 | hskp12 | (~ndr1_0) | c1_1(a237) | c3_1(a237) | (~c2_1(a237))) <=> (hskp21 | hskp12 | c3_1(a237) | (~ndr1_0) | c1_1(a237) | (~c2_1(a237)))),
% 0.84/1.06 inference(rewrite,[status(thm)],[])).
% 0.84/1.06 tff(1909,plain,
% 0.84/1.06 (((~![U: $i] : (hskp21 | hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp21 | hskp12 | (~ndr1_0) | c1_1(a237) | c3_1(a237) | (~c2_1(a237)))) <=> ((~![U: $i] : (hskp21 | hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp21 | hskp12 | c3_1(a237) | (~ndr1_0) | c1_1(a237) | (~c2_1(a237))))),
% 0.84/1.06 inference(monotonicity,[status(thm)],[1908])).
% 0.84/1.06 tff(1910,plain,
% 0.84/1.06 (((~![U: $i] : (hskp21 | hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp21 | hskp12 | (~ndr1_0) | c1_1(a237) | c3_1(a237) | (~c2_1(a237)))) <=> ((~![U: $i] : (hskp21 | hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | hskp21 | hskp12 | c3_1(a237) | (~ndr1_0) | c1_1(a237) | (~c2_1(a237)))),
% 0.84/1.06 inference(transitivity,[status(thm)],[1909, 1907])).
% 0.84/1.06 tff(1911,plain,
% 0.84/1.06 ((~![U: $i] : (hskp21 | hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp21 | hskp12 | (~ndr1_0) | c1_1(a237) | c3_1(a237) | (~c2_1(a237)))),
% 0.84/1.06 inference(quant_inst,[status(thm)],[])).
% 0.84/1.06 tff(1912,plain,
% 0.84/1.06 ((~![U: $i] : (hskp21 | hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | hskp21 | hskp12 | c3_1(a237) | (~ndr1_0) | c1_1(a237) | (~c2_1(a237))),
% 0.84/1.06 inference(modus_ponens,[status(thm)],[1911, 1910])).
% 0.84/1.06 tff(1913,plain,
% 0.84/1.06 (hskp21 | hskp12 | c1_1(a237) | (~c2_1(a237))),
% 0.84/1.06 inference(unit_resolution,[status(thm)],[1912, 110, 164, 738])).
% 0.84/1.06 tff(1914,plain,
% 0.84/1.06 (hskp21),
% 0.84/1.06 inference(unit_resolution,[status(thm)],[1913, 577, 576, 585])).
% 0.84/1.06 tff(1915,plain,
% 0.84/1.06 (~c2_1(a259)),
% 0.84/1.06 inference(unit_resolution,[status(thm)],[975, 1914])).
% 0.84/1.06 tff(1916,plain,
% 0.84/1.06 (c3_1(a259)),
% 0.84/1.06 inference(unit_resolution,[status(thm)],[792, 1914])).
% 0.84/1.06 tff(1917,plain,
% 0.84/1.06 (c0_1(a259)),
% 0.84/1.06 inference(unit_resolution,[status(thm)],[783, 1914])).
% 0.84/1.06 tff(1918,plain,
% 0.84/1.06 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | (c2_1(a259) | c1_1(a252) | c3_1(a237) | (~ndr1_0) | c1_1(a237) | (~c2_1(a237)) | c3_1(a252) | (~c0_1(a252)) | (~c3_1(a259)) | (~c0_1(a259)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | c2_1(a259) | c1_1(a252) | c3_1(a237) | (~ndr1_0) | c1_1(a237) | (~c2_1(a237)) | c3_1(a252) | (~c0_1(a252)) | (~c3_1(a259)) | (~c0_1(a259)))),
% 0.84/1.06 inference(rewrite,[status(thm)],[])).
% 0.84/1.06 tff(1919,plain,
% 0.84/1.06 (((~ndr1_0) | c2_1(a259) | (~c3_1(a259)) | (~c0_1(a259)) | c3_1(a237) | c1_1(a237) | (~c2_1(a237)) | c3_1(a252) | c1_1(a252) | (~c0_1(a252))) <=> (c2_1(a259) | c1_1(a252) | c3_1(a237) | (~ndr1_0) | c1_1(a237) | (~c2_1(a237)) | c3_1(a252) | (~c0_1(a252)) | (~c3_1(a259)) | (~c0_1(a259)))),
% 0.84/1.06 inference(rewrite,[status(thm)],[])).
% 0.84/1.06 tff(1920,plain,
% 0.84/1.06 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a259) | (~c3_1(a259)) | (~c0_1(a259)) | c3_1(a237) | c1_1(a237) | (~c2_1(a237)) | c3_1(a252) | c1_1(a252) | (~c0_1(a252)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | (c2_1(a259) | c1_1(a252) | c3_1(a237) | (~ndr1_0) | c1_1(a237) | (~c2_1(a237)) | c3_1(a252) | (~c0_1(a252)) | (~c3_1(a259)) | (~c0_1(a259))))),
% 0.84/1.06 inference(monotonicity,[status(thm)],[1919])).
% 0.84/1.06 tff(1921,plain,
% 0.84/1.06 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a259) | (~c3_1(a259)) | (~c0_1(a259)) | c3_1(a237) | c1_1(a237) | (~c2_1(a237)) | c3_1(a252) | c1_1(a252) | (~c0_1(a252)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | c2_1(a259) | c1_1(a252) | c3_1(a237) | (~ndr1_0) | c1_1(a237) | (~c2_1(a237)) | c3_1(a252) | (~c0_1(a252)) | (~c3_1(a259)) | (~c0_1(a259)))),
% 0.84/1.06 inference(transitivity,[status(thm)],[1920, 1918])).
% 0.84/1.06 tff(1922,plain,
% 0.84/1.06 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a259) | (~c3_1(a259)) | (~c0_1(a259)) | c3_1(a237) | c1_1(a237) | (~c2_1(a237)) | c3_1(a252) | c1_1(a252) | (~c0_1(a252)))),
% 0.84/1.06 inference(quant_inst,[status(thm)],[])).
% 0.84/1.06 tff(1923,plain,
% 0.84/1.06 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | c2_1(a259) | c1_1(a252) | c3_1(a237) | (~ndr1_0) | c1_1(a237) | (~c2_1(a237)) | c3_1(a252) | (~c0_1(a252)) | (~c3_1(a259)) | (~c0_1(a259))),
% 0.84/1.06 inference(modus_ponens,[status(thm)],[1922, 1921])).
% 0.84/1.06 tff(1924,plain,
% 0.84/1.06 ($false),
% 0.84/1.06 inference(unit_resolution,[status(thm)],[1923, 110, 1917, 1916, 1892, 577, 1915, 1906, 164, 22, 1900, 585])).
% 0.84/1.06 tff(1925,plain,(hskp2 | c3_1(a237) | c0_1(a237) | hskp9 | hskp27), inference(lemma,lemma(discharge,[]))).
% 0.84/1.06 tff(1926,plain,
% 0.84/1.06 (hskp2),
% 0.84/1.06 inference(unit_resolution,[status(thm)],[1925, 568, 164, 23, 34])).
% 0.84/1.06 tff(1927,plain,
% 0.84/1.06 (~c1_1(a215)),
% 0.84/1.06 inference(unit_resolution,[status(thm)],[124, 1926])).
% 0.84/1.06 tff(1928,plain,
% 0.84/1.06 (~c0_1(a215)),
% 0.84/1.06 inference(unit_resolution,[status(thm)],[138, 1926])).
% 0.84/1.06 tff(1929,plain,
% 0.84/1.06 (c2_1(a215)),
% 0.84/1.06 inference(unit_resolution,[status(thm)],[132, 1926])).
% 0.84/1.06 tff(1930,plain,
% 0.84/1.06 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp9 | c0_1(a237) | c2_1(a237) | c3_1(a237) | c0_1(a215) | (~ndr1_0) | (~c3_1(a215)) | (~c2_1(a215)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp9 | c0_1(a237) | c2_1(a237) | c3_1(a237) | c0_1(a215) | (~ndr1_0) | (~c3_1(a215)) | (~c2_1(a215)))),
% 0.84/1.06 inference(rewrite,[status(thm)],[])).
% 0.84/1.06 tff(1931,plain,
% 0.84/1.06 ((hskp9 | (~ndr1_0) | c0_1(a215) | (~c2_1(a215)) | (~c3_1(a215)) | c3_1(a237) | c0_1(a237) | c2_1(a237)) <=> (hskp9 | c0_1(a237) | c2_1(a237) | c3_1(a237) | c0_1(a215) | (~ndr1_0) | (~c3_1(a215)) | (~c2_1(a215)))),
% 0.84/1.06 inference(rewrite,[status(thm)],[])).
% 0.84/1.06 tff(1932,plain,
% 0.84/1.06 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp9 | (~ndr1_0) | c0_1(a215) | (~c2_1(a215)) | (~c3_1(a215)) | c3_1(a237) | c0_1(a237) | c2_1(a237))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp9 | c0_1(a237) | c2_1(a237) | c3_1(a237) | c0_1(a215) | (~ndr1_0) | (~c3_1(a215)) | (~c2_1(a215))))),
% 0.84/1.06 inference(monotonicity,[status(thm)],[1931])).
% 0.84/1.06 tff(1933,plain,
% 0.84/1.06 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp9 | (~ndr1_0) | c0_1(a215) | (~c2_1(a215)) | (~c3_1(a215)) | c3_1(a237) | c0_1(a237) | c2_1(a237))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp9 | c0_1(a237) | c2_1(a237) | c3_1(a237) | c0_1(a215) | (~ndr1_0) | (~c3_1(a215)) | (~c2_1(a215)))),
% 0.84/1.06 inference(transitivity,[status(thm)],[1932, 1930])).
% 0.84/1.06 tff(1934,plain,
% 0.84/1.06 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp9 | (~ndr1_0) | c0_1(a215) | (~c2_1(a215)) | (~c3_1(a215)) | c3_1(a237) | c0_1(a237) | c2_1(a237))),
% 0.84/1.06 inference(quant_inst,[status(thm)],[])).
% 0.84/1.06 tff(1935,plain,
% 0.84/1.06 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp9 | c0_1(a237) | c2_1(a237) | c3_1(a237) | c0_1(a215) | (~ndr1_0) | (~c3_1(a215)) | (~c2_1(a215))),
% 0.84/1.06 inference(modus_ponens,[status(thm)],[1934, 1933])).
% 0.84/1.06 tff(1936,plain,
% 0.84/1.06 (c2_1(a237) | (~c3_1(a215))),
% 0.84/1.06 inference(unit_resolution,[status(thm)],[1935, 110, 23, 568, 152, 164, 151, 905])).
% 0.84/1.06 tff(1937,plain,
% 0.84/1.06 (~c3_1(a215)),
% 0.84/1.06 inference(unit_resolution,[status(thm)],[1936, 527])).
% 0.84/1.06 tff(1938,plain,
% 0.84/1.06 (hskp21 | c3_1(a215)),
% 0.84/1.06 inference(unit_resolution,[status(thm)],[1170, 110, 576, 152, 150, 738])).
% 0.84/1.06 tff(1939,plain,
% 0.84/1.06 (hskp21),
% 0.84/1.06 inference(unit_resolution,[status(thm)],[1938, 1937])).
% 0.84/1.06 tff(1940,plain,
% 0.84/1.06 (~c2_1(a259)),
% 0.84/1.06 inference(unit_resolution,[status(thm)],[975, 1939])).
% 0.84/1.06 tff(1941,plain,
% 0.84/1.06 (c3_1(a259)),
% 0.84/1.06 inference(unit_resolution,[status(thm)],[792, 1939])).
% 0.84/1.06 tff(1942,plain,
% 0.84/1.06 (c0_1(a259)),
% 0.84/1.06 inference(unit_resolution,[status(thm)],[783, 1939])).
% 0.84/1.06 tff(1943,plain,
% 0.84/1.06 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | (c2_1(a259) | c0_1(a215) | c1_1(a215) | (~ndr1_0) | (~c2_1(a215)) | (~c3_1(a252)) | (~c0_1(a252)) | (~c2_1(a252)) | (~c3_1(a259)) | (~c0_1(a259)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | c2_1(a259) | c0_1(a215) | c1_1(a215) | (~ndr1_0) | (~c2_1(a215)) | (~c3_1(a252)) | (~c0_1(a252)) | (~c2_1(a252)) | (~c3_1(a259)) | (~c0_1(a259)))),
% 0.84/1.06 inference(rewrite,[status(thm)],[])).
% 0.84/1.06 tff(1944,plain,
% 0.84/1.06 (((~ndr1_0) | (~c2_1(a252)) | (~c3_1(a252)) | (~c0_1(a252)) | c2_1(a259) | (~c3_1(a259)) | (~c0_1(a259)) | c0_1(a215) | c1_1(a215) | (~c2_1(a215))) <=> (c2_1(a259) | c0_1(a215) | c1_1(a215) | (~ndr1_0) | (~c2_1(a215)) | (~c3_1(a252)) | (~c0_1(a252)) | (~c2_1(a252)) | (~c3_1(a259)) | (~c0_1(a259)))),
% 0.84/1.06 inference(rewrite,[status(thm)],[])).
% 0.84/1.06 tff(1945,plain,
% 0.84/1.06 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a252)) | (~c3_1(a252)) | (~c0_1(a252)) | c2_1(a259) | (~c3_1(a259)) | (~c0_1(a259)) | c0_1(a215) | c1_1(a215) | (~c2_1(a215)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | (c2_1(a259) | c0_1(a215) | c1_1(a215) | (~ndr1_0) | (~c2_1(a215)) | (~c3_1(a252)) | (~c0_1(a252)) | (~c2_1(a252)) | (~c3_1(a259)) | (~c0_1(a259))))),
% 0.84/1.06 inference(monotonicity,[status(thm)],[1944])).
% 0.84/1.06 tff(1946,plain,
% 0.84/1.06 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a252)) | (~c3_1(a252)) | (~c0_1(a252)) | c2_1(a259) | (~c3_1(a259)) | (~c0_1(a259)) | c0_1(a215) | c1_1(a215) | (~c2_1(a215)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | c2_1(a259) | c0_1(a215) | c1_1(a215) | (~ndr1_0) | (~c2_1(a215)) | (~c3_1(a252)) | (~c0_1(a252)) | (~c2_1(a252)) | (~c3_1(a259)) | (~c0_1(a259)))),
% 0.84/1.06 inference(transitivity,[status(thm)],[1945, 1943])).
% 0.84/1.06 tff(1947,plain,
% 0.84/1.06 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a252)) | (~c3_1(a252)) | (~c0_1(a252)) | c2_1(a259) | (~c3_1(a259)) | (~c0_1(a259)) | c0_1(a215) | c1_1(a215) | (~c2_1(a215)))),
% 0.84/1.06 inference(quant_inst,[status(thm)],[])).
% 0.84/1.06 tff(1948,plain,
% 0.84/1.06 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | c2_1(a259) | c0_1(a215) | c1_1(a215) | (~ndr1_0) | (~c2_1(a215)) | (~c3_1(a252)) | (~c0_1(a252)) | (~c2_1(a252)) | (~c3_1(a259)) | (~c0_1(a259))),
% 0.84/1.06 inference(modus_ponens,[status(thm)],[1947, 1946])).
% 0.84/1.06 tff(1949,plain,
% 0.84/1.06 (~c3_1(a252)),
% 0.84/1.06 inference(unit_resolution,[status(thm)],[1948, 110, 1942, 1941, 1892, 1884, 152, 1940, 151, 150, 853])).
% 0.84/1.06 tff(1950,plain,
% 0.84/1.06 (((~![U: $i] : (hskp6 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp6 | hskp5 | c0_1(a237) | c2_1(a237) | c3_1(a237) | (~ndr1_0))) <=> ((~![U: $i] : (hskp6 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | hskp6 | hskp5 | c0_1(a237) | c2_1(a237) | c3_1(a237) | (~ndr1_0))),
% 0.84/1.06 inference(rewrite,[status(thm)],[])).
% 0.84/1.06 tff(1951,plain,
% 0.84/1.06 ((hskp6 | hskp5 | (~ndr1_0) | c2_1(a237) | c0_1(a237) | c3_1(a237)) <=> (hskp6 | hskp5 | c0_1(a237) | c2_1(a237) | c3_1(a237) | (~ndr1_0))),
% 0.84/1.06 inference(rewrite,[status(thm)],[])).
% 0.84/1.06 tff(1952,plain,
% 0.84/1.06 (((~![U: $i] : (hskp6 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp6 | hskp5 | (~ndr1_0) | c2_1(a237) | c0_1(a237) | c3_1(a237))) <=> ((~![U: $i] : (hskp6 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp6 | hskp5 | c0_1(a237) | c2_1(a237) | c3_1(a237) | (~ndr1_0)))),
% 0.84/1.06 inference(monotonicity,[status(thm)],[1951])).
% 0.84/1.06 tff(1953,plain,
% 0.84/1.06 (((~![U: $i] : (hskp6 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp6 | hskp5 | (~ndr1_0) | c2_1(a237) | c0_1(a237) | c3_1(a237))) <=> ((~![U: $i] : (hskp6 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | hskp6 | hskp5 | c0_1(a237) | c2_1(a237) | c3_1(a237) | (~ndr1_0))),
% 0.84/1.06 inference(transitivity,[status(thm)],[1952, 1950])).
% 0.84/1.06 tff(1954,plain,
% 0.84/1.06 ((~![U: $i] : (hskp6 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp6 | hskp5 | (~ndr1_0) | c2_1(a237) | c0_1(a237) | c3_1(a237))),
% 0.84/1.06 inference(quant_inst,[status(thm)],[])).
% 0.84/1.06 tff(1955,plain,
% 0.84/1.06 ((~![U: $i] : (hskp6 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | hskp6 | hskp5 | c0_1(a237) | c2_1(a237) | c3_1(a237) | (~ndr1_0)),
% 0.84/1.06 inference(modus_ponens,[status(thm)],[1954, 1953])).
% 0.84/1.06 tff(1956,plain,
% 0.84/1.06 (hskp6 | c0_1(a237) | c2_1(a237)),
% 0.84/1.06 inference(unit_resolution,[status(thm)],[1955, 110, 45, 164, 1569])).
% 0.84/1.06 tff(1957,plain,
% 0.84/1.06 (hskp6),
% 0.84/1.06 inference(unit_resolution,[status(thm)],[1956, 527, 568])).
% 0.84/1.06 tff(1958,plain,
% 0.84/1.06 (~c3_1(a220)),
% 0.84/1.06 inference(unit_resolution,[status(thm)],[449, 1957])).
% 0.84/1.06 tff(1959,plain,
% 0.84/1.06 (c2_1(a220)),
% 0.84/1.06 inference(unit_resolution,[status(thm)],[493, 1957])).
% 0.84/1.06 tff(1960,plain,
% 0.84/1.06 (c1_1(a220)),
% 0.84/1.06 inference(unit_resolution,[status(thm)],[485, 1957])).
% 0.84/1.06 tff(1961,plain,
% 0.84/1.06 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp12 | c0_1(a237) | c3_1(a237) | c3_1(a220) | (~ndr1_0) | (~c2_1(a220)) | (~c1_1(a220)) | (~c1_1(a237)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp12 | c0_1(a237) | c3_1(a237) | c3_1(a220) | (~ndr1_0) | (~c2_1(a220)) | (~c1_1(a220)) | (~c1_1(a237)))),
% 0.84/1.06 inference(rewrite,[status(thm)],[])).
% 0.84/1.06 tff(1962,plain,
% 0.84/1.06 ((hskp12 | (~ndr1_0) | c3_1(a220) | (~c2_1(a220)) | (~c1_1(a220)) | c3_1(a237) | c0_1(a237) | (~c1_1(a237))) <=> (hskp12 | c0_1(a237) | c3_1(a237) | c3_1(a220) | (~ndr1_0) | (~c2_1(a220)) | (~c1_1(a220)) | (~c1_1(a237)))),
% 0.84/1.06 inference(rewrite,[status(thm)],[])).
% 0.84/1.06 tff(1963,plain,
% 0.84/1.06 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp12 | (~ndr1_0) | c3_1(a220) | (~c2_1(a220)) | (~c1_1(a220)) | c3_1(a237) | c0_1(a237) | (~c1_1(a237)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp12 | c0_1(a237) | c3_1(a237) | c3_1(a220) | (~ndr1_0) | (~c2_1(a220)) | (~c1_1(a220)) | (~c1_1(a237))))),
% 0.84/1.06 inference(monotonicity,[status(thm)],[1962])).
% 0.84/1.06 tff(1964,plain,
% 0.84/1.06 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp12 | (~ndr1_0) | c3_1(a220) | (~c2_1(a220)) | (~c1_1(a220)) | c3_1(a237) | c0_1(a237) | (~c1_1(a237)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp12 | c0_1(a237) | c3_1(a237) | c3_1(a220) | (~ndr1_0) | (~c2_1(a220)) | (~c1_1(a220)) | (~c1_1(a237)))),
% 0.84/1.06 inference(transitivity,[status(thm)],[1963, 1961])).
% 0.84/1.06 tff(1965,plain,
% 0.84/1.06 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp12 | (~ndr1_0) | c3_1(a220) | (~c2_1(a220)) | (~c1_1(a220)) | c3_1(a237) | c0_1(a237) | (~c1_1(a237)))),
% 0.84/1.06 inference(quant_inst,[status(thm)],[])).
% 0.84/1.06 tff(1966,plain,
% 0.84/1.06 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp12 | c0_1(a237) | c3_1(a237) | c3_1(a220) | (~ndr1_0) | (~c2_1(a220)) | (~c1_1(a220)) | (~c1_1(a237))),
% 0.84/1.06 inference(modus_ponens,[status(thm)],[1965, 1964])).
% 0.84/1.06 tff(1967,plain,
% 0.84/1.06 (~c1_1(a237)),
% 0.84/1.06 inference(unit_resolution,[status(thm)],[1966, 110, 576, 568, 1960, 1959, 164, 1958, 44])).
% 0.84/1.06 tff(1968,plain,
% 0.84/1.06 (((~![U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp0 | c0_1(a237) | c2_1(a237) | (~ndr1_0) | c1_1(a237))) <=> ((~![U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp0 | c0_1(a237) | c2_1(a237) | (~ndr1_0) | c1_1(a237))),
% 0.84/1.06 inference(rewrite,[status(thm)],[])).
% 0.84/1.06 tff(1969,plain,
% 0.84/1.06 ((hskp0 | (~ndr1_0) | c2_1(a237) | c1_1(a237) | c0_1(a237)) <=> (hskp0 | c0_1(a237) | c2_1(a237) | (~ndr1_0) | c1_1(a237))),
% 0.84/1.06 inference(rewrite,[status(thm)],[])).
% 0.84/1.06 tff(1970,plain,
% 0.84/1.06 (((~![U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp0 | (~ndr1_0) | c2_1(a237) | c1_1(a237) | c0_1(a237))) <=> ((~![U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp0 | c0_1(a237) | c2_1(a237) | (~ndr1_0) | c1_1(a237)))),
% 0.84/1.06 inference(monotonicity,[status(thm)],[1969])).
% 0.84/1.06 tff(1971,plain,
% 0.84/1.06 (((~![U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp0 | (~ndr1_0) | c2_1(a237) | c1_1(a237) | c0_1(a237))) <=> ((~![U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp0 | c0_1(a237) | c2_1(a237) | (~ndr1_0) | c1_1(a237))),
% 0.84/1.06 inference(transitivity,[status(thm)],[1970, 1968])).
% 0.84/1.06 tff(1972,plain,
% 0.84/1.06 ((~![U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp0 | (~ndr1_0) | c2_1(a237) | c1_1(a237) | c0_1(a237))),
% 0.84/1.06 inference(quant_inst,[status(thm)],[])).
% 0.84/1.06 tff(1973,plain,
% 0.84/1.06 ((~![U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp0 | c0_1(a237) | c2_1(a237) | (~ndr1_0) | c1_1(a237)),
% 0.84/1.06 inference(modus_ponens,[status(thm)],[1972, 1971])).
% 0.84/1.06 tff(1974,plain,
% 0.84/1.06 (hskp0 | c2_1(a237) | c1_1(a237)),
% 0.84/1.06 inference(unit_resolution,[status(thm)],[1973, 110, 568, 1008])).
% 0.84/1.06 tff(1975,plain,
% 0.84/1.06 (hskp0),
% 0.84/1.06 inference(unit_resolution,[status(thm)],[1974, 1967, 527])).
% 0.84/1.06 tff(1976,plain,
% 0.84/1.06 (~c3_1(a213)),
% 0.84/1.06 inference(unit_resolution,[status(thm)],[744, 1975])).
% 0.84/1.06 tff(1977,plain,
% 0.84/1.06 (~c1_1(a213)),
% 0.84/1.06 inference(unit_resolution,[status(thm)],[750, 1975])).
% 0.84/1.06 tff(1978,plain,
% 0.84/1.06 (c2_1(a213)),
% 0.84/1.06 inference(unit_resolution,[status(thm)],[758, 1975])).
% 0.84/1.06 tff(1979,plain,
% 0.84/1.06 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | (c2_1(a259) | c1_1(a252) | c1_1(a213) | c3_1(a213) | (~ndr1_0) | (~c2_1(a213)) | c3_1(a252) | (~c0_1(a252)) | (~c3_1(a259)) | (~c0_1(a259)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | c2_1(a259) | c1_1(a252) | c1_1(a213) | c3_1(a213) | (~ndr1_0) | (~c2_1(a213)) | c3_1(a252) | (~c0_1(a252)) | (~c3_1(a259)) | (~c0_1(a259)))),
% 0.84/1.06 inference(rewrite,[status(thm)],[])).
% 0.84/1.06 tff(1980,plain,
% 0.84/1.06 (((~ndr1_0) | c2_1(a259) | (~c3_1(a259)) | (~c0_1(a259)) | c3_1(a213) | c1_1(a213) | (~c2_1(a213)) | c3_1(a252) | c1_1(a252) | (~c0_1(a252))) <=> (c2_1(a259) | c1_1(a252) | c1_1(a213) | c3_1(a213) | (~ndr1_0) | (~c2_1(a213)) | c3_1(a252) | (~c0_1(a252)) | (~c3_1(a259)) | (~c0_1(a259)))),
% 0.84/1.06 inference(rewrite,[status(thm)],[])).
% 0.84/1.06 tff(1981,plain,
% 0.84/1.06 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a259) | (~c3_1(a259)) | (~c0_1(a259)) | c3_1(a213) | c1_1(a213) | (~c2_1(a213)) | c3_1(a252) | c1_1(a252) | (~c0_1(a252)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | (c2_1(a259) | c1_1(a252) | c1_1(a213) | c3_1(a213) | (~ndr1_0) | (~c2_1(a213)) | c3_1(a252) | (~c0_1(a252)) | (~c3_1(a259)) | (~c0_1(a259))))),
% 0.84/1.06 inference(monotonicity,[status(thm)],[1980])).
% 0.84/1.06 tff(1982,plain,
% 0.84/1.06 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a259) | (~c3_1(a259)) | (~c0_1(a259)) | c3_1(a213) | c1_1(a213) | (~c2_1(a213)) | c3_1(a252) | c1_1(a252) | (~c0_1(a252)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | c2_1(a259) | c1_1(a252) | c1_1(a213) | c3_1(a213) | (~ndr1_0) | (~c2_1(a213)) | c3_1(a252) | (~c0_1(a252)) | (~c3_1(a259)) | (~c0_1(a259)))),
% 0.84/1.06 inference(transitivity,[status(thm)],[1981, 1979])).
% 0.84/1.06 tff(1983,plain,
% 0.84/1.06 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a259) | (~c3_1(a259)) | (~c0_1(a259)) | c3_1(a213) | c1_1(a213) | (~c2_1(a213)) | c3_1(a252) | c1_1(a252) | (~c0_1(a252)))),
% 0.84/1.06 inference(quant_inst,[status(thm)],[])).
% 0.84/1.06 tff(1984,plain,
% 0.84/1.06 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | c2_1(a259) | c1_1(a252) | c1_1(a213) | c3_1(a213) | (~ndr1_0) | (~c2_1(a213)) | c3_1(a252) | (~c0_1(a252)) | (~c3_1(a259)) | (~c0_1(a259))),
% 0.84/1.06 inference(modus_ponens,[status(thm)],[1983, 1982])).
% 0.84/1.06 tff(1985,plain,
% 0.84/1.06 ($false),
% 0.84/1.06 inference(unit_resolution,[status(thm)],[1984, 110, 1942, 1941, 1892, 1978, 1940, 1906, 1977, 1976, 22, 1949])).
% 0.84/1.06 tff(1986,plain,(c2_1(a237) | c0_1(a237) | c3_1(a237) | (~c2_1(a215)) | c0_1(a215) | c1_1(a215) | hskp9 | hskp5), inference(lemma,lemma(discharge,[]))).
% 0.84/1.06 tff(1987,plain,
% 0.84/1.06 (c2_1(a237)),
% 0.84/1.06 inference(unit_resolution,[status(thm)],[1986, 568, 164, 1929, 1928, 1927, 23, 45])).
% 0.84/1.06 tff(1988,plain,
% 0.84/1.06 (~c1_1(a237)),
% 0.84/1.06 inference(unit_resolution,[status(thm)],[584, 1987, 568, 576])).
% 0.84/1.06 tff(1989,plain,
% 0.84/1.06 (hskp21),
% 0.84/1.06 inference(unit_resolution,[status(thm)],[1913, 1987, 576, 1988])).
% 0.84/1.06 tff(1990,plain,
% 0.84/1.06 (~c2_1(a259)),
% 0.84/1.06 inference(unit_resolution,[status(thm)],[975, 1989])).
% 0.84/1.06 tff(1991,plain,
% 0.84/1.06 (c3_1(a259)),
% 0.84/1.06 inference(unit_resolution,[status(thm)],[792, 1989])).
% 0.84/1.06 tff(1992,plain,
% 0.84/1.06 (c0_1(a259)),
% 0.84/1.06 inference(unit_resolution,[status(thm)],[783, 1989])).
% 0.84/1.06 tff(1993,plain,
% 0.84/1.06 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | (c0_1(a237) | c2_1(a259) | (~ndr1_0) | c1_1(a237) | (~c2_1(a237)) | (~c3_1(a252)) | (~c0_1(a252)) | (~c2_1(a252)) | (~c3_1(a259)) | (~c0_1(a259)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | c0_1(a237) | c2_1(a259) | (~ndr1_0) | c1_1(a237) | (~c2_1(a237)) | (~c3_1(a252)) | (~c0_1(a252)) | (~c2_1(a252)) | (~c3_1(a259)) | (~c0_1(a259)))),
% 0.84/1.06 inference(rewrite,[status(thm)],[])).
% 0.84/1.06 tff(1994,plain,
% 0.84/1.06 (((~ndr1_0) | (~c2_1(a252)) | (~c3_1(a252)) | (~c0_1(a252)) | c2_1(a259) | (~c3_1(a259)) | (~c0_1(a259)) | c0_1(a237) | c1_1(a237) | (~c2_1(a237))) <=> (c0_1(a237) | c2_1(a259) | (~ndr1_0) | c1_1(a237) | (~c2_1(a237)) | (~c3_1(a252)) | (~c0_1(a252)) | (~c2_1(a252)) | (~c3_1(a259)) | (~c0_1(a259)))),
% 0.84/1.06 inference(rewrite,[status(thm)],[])).
% 0.84/1.06 tff(1995,plain,
% 0.84/1.06 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a252)) | (~c3_1(a252)) | (~c0_1(a252)) | c2_1(a259) | (~c3_1(a259)) | (~c0_1(a259)) | c0_1(a237) | c1_1(a237) | (~c2_1(a237)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | (c0_1(a237) | c2_1(a259) | (~ndr1_0) | c1_1(a237) | (~c2_1(a237)) | (~c3_1(a252)) | (~c0_1(a252)) | (~c2_1(a252)) | (~c3_1(a259)) | (~c0_1(a259))))),
% 0.84/1.07 inference(monotonicity,[status(thm)],[1994])).
% 0.84/1.07 tff(1996,plain,
% 0.84/1.07 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a252)) | (~c3_1(a252)) | (~c0_1(a252)) | c2_1(a259) | (~c3_1(a259)) | (~c0_1(a259)) | c0_1(a237) | c1_1(a237) | (~c2_1(a237)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | c0_1(a237) | c2_1(a259) | (~ndr1_0) | c1_1(a237) | (~c2_1(a237)) | (~c3_1(a252)) | (~c0_1(a252)) | (~c2_1(a252)) | (~c3_1(a259)) | (~c0_1(a259)))),
% 0.84/1.07 inference(transitivity,[status(thm)],[1995, 1993])).
% 0.84/1.07 tff(1997,plain,
% 0.84/1.07 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a252)) | (~c3_1(a252)) | (~c0_1(a252)) | c2_1(a259) | (~c3_1(a259)) | (~c0_1(a259)) | c0_1(a237) | c1_1(a237) | (~c2_1(a237)))),
% 0.84/1.07 inference(quant_inst,[status(thm)],[])).
% 0.84/1.07 tff(1998,plain,
% 0.84/1.07 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | c0_1(a237) | c2_1(a259) | (~ndr1_0) | c1_1(a237) | (~c2_1(a237)) | (~c3_1(a252)) | (~c0_1(a252)) | (~c2_1(a252)) | (~c3_1(a259)) | (~c0_1(a259))),
% 0.84/1.07 inference(modus_ponens,[status(thm)],[1997, 1996])).
% 0.84/1.07 tff(1999,plain,
% 0.84/1.07 (~c3_1(a252)),
% 0.84/1.07 inference(unit_resolution,[status(thm)],[1998, 110, 1992, 1991, 1892, 1884, 568, 1987, 1990, 853, 1988])).
% 0.84/1.07 tff(2000,plain,
% 0.84/1.07 ($false),
% 0.84/1.07 inference(unit_resolution,[status(thm)],[1923, 110, 1992, 1991, 1892, 1987, 1990, 1906, 164, 22, 1999, 1988])).
% 0.84/1.07 tff(2001,plain,(c0_1(a237) | c3_1(a237) | hskp9 | hskp5 | hskp27), inference(lemma,lemma(discharge,[]))).
% 0.84/1.07 tff(2002,plain,
% 0.84/1.07 (c0_1(a237)),
% 0.84/1.07 inference(unit_resolution,[status(thm)],[2001, 164, 23, 45, 34])).
% 0.84/1.07 tff(2003,plain,
% 0.84/1.07 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp5 | c2_1(a237) | c3_1(a237) | (~ndr1_0) | (~c0_1(a237)) | (~c1_1(a237)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | hskp5 | c2_1(a237) | c3_1(a237) | (~ndr1_0) | (~c0_1(a237)) | (~c1_1(a237)))),
% 0.84/1.07 inference(rewrite,[status(thm)],[])).
% 0.84/1.07 tff(2004,plain,
% 0.84/1.07 ((hskp5 | (~ndr1_0) | c2_1(a237) | (~c1_1(a237)) | (~c0_1(a237)) | c3_1(a237) | c2_1(a237) | (~c0_1(a237))) <=> (hskp5 | c2_1(a237) | c3_1(a237) | (~ndr1_0) | (~c0_1(a237)) | (~c1_1(a237)))),
% 0.84/1.07 inference(rewrite,[status(thm)],[])).
% 0.84/1.07 tff(2005,plain,
% 0.84/1.07 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp5 | (~ndr1_0) | c2_1(a237) | (~c1_1(a237)) | (~c0_1(a237)) | c3_1(a237) | c2_1(a237) | (~c0_1(a237)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp5 | c2_1(a237) | c3_1(a237) | (~ndr1_0) | (~c0_1(a237)) | (~c1_1(a237))))),
% 0.84/1.07 inference(monotonicity,[status(thm)],[2004])).
% 0.84/1.07 tff(2006,plain,
% 0.84/1.07 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp5 | (~ndr1_0) | c2_1(a237) | (~c1_1(a237)) | (~c0_1(a237)) | c3_1(a237) | c2_1(a237) | (~c0_1(a237)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | hskp5 | c2_1(a237) | c3_1(a237) | (~ndr1_0) | (~c0_1(a237)) | (~c1_1(a237)))),
% 0.84/1.07 inference(transitivity,[status(thm)],[2005, 2003])).
% 0.84/1.07 tff(2007,plain,
% 0.84/1.07 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp5 | (~ndr1_0) | c2_1(a237) | (~c1_1(a237)) | (~c0_1(a237)) | c3_1(a237) | c2_1(a237) | (~c0_1(a237)))),
% 0.84/1.07 inference(quant_inst,[status(thm)],[])).
% 0.84/1.07 tff(2008,plain,
% 0.84/1.07 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | hskp5 | c2_1(a237) | c3_1(a237) | (~ndr1_0) | (~c0_1(a237)) | (~c1_1(a237))),
% 0.84/1.07 inference(modus_ponens,[status(thm)],[2007, 2006])).
% 0.84/1.07 tff(2009,plain,
% 0.84/1.07 (~c1_1(a237)),
% 0.84/1.07 inference(unit_resolution,[status(thm)],[2008, 110, 45, 2002, 527, 164, 567])).
% 0.84/1.07 tff(2010,plain,
% 0.84/1.07 (((~![U: $i] : (hskp17 | hskp12 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp17 | hskp12 | c2_1(a237) | (~ndr1_0) | c1_1(a237) | (~c0_1(a237)))) <=> ((~![U: $i] : (hskp17 | hskp12 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp17 | hskp12 | c2_1(a237) | (~ndr1_0) | c1_1(a237) | (~c0_1(a237)))),
% 0.84/1.07 inference(rewrite,[status(thm)],[])).
% 0.84/1.07 tff(2011,plain,
% 0.84/1.07 ((hskp17 | hskp12 | (~ndr1_0) | c2_1(a237) | c1_1(a237) | (~c0_1(a237))) <=> (hskp17 | hskp12 | c2_1(a237) | (~ndr1_0) | c1_1(a237) | (~c0_1(a237)))),
% 0.84/1.07 inference(rewrite,[status(thm)],[])).
% 0.84/1.07 tff(2012,plain,
% 0.84/1.07 (((~![U: $i] : (hskp17 | hskp12 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp17 | hskp12 | (~ndr1_0) | c2_1(a237) | c1_1(a237) | (~c0_1(a237)))) <=> ((~![U: $i] : (hskp17 | hskp12 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp17 | hskp12 | c2_1(a237) | (~ndr1_0) | c1_1(a237) | (~c0_1(a237))))),
% 0.84/1.07 inference(monotonicity,[status(thm)],[2011])).
% 0.84/1.07 tff(2013,plain,
% 0.84/1.07 (((~![U: $i] : (hskp17 | hskp12 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp17 | hskp12 | (~ndr1_0) | c2_1(a237) | c1_1(a237) | (~c0_1(a237)))) <=> ((~![U: $i] : (hskp17 | hskp12 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp17 | hskp12 | c2_1(a237) | (~ndr1_0) | c1_1(a237) | (~c0_1(a237)))),
% 0.84/1.07 inference(transitivity,[status(thm)],[2012, 2010])).
% 0.84/1.07 tff(2014,plain,
% 0.84/1.07 ((~![U: $i] : (hskp17 | hskp12 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp17 | hskp12 | (~ndr1_0) | c2_1(a237) | c1_1(a237) | (~c0_1(a237)))),
% 0.84/1.07 inference(quant_inst,[status(thm)],[])).
% 0.84/1.07 tff(2015,plain,
% 0.84/1.07 ((~![U: $i] : (hskp17 | hskp12 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp17 | hskp12 | c2_1(a237) | (~ndr1_0) | c1_1(a237) | (~c0_1(a237))),
% 0.84/1.07 inference(modus_ponens,[status(thm)],[2014, 2013])).
% 0.84/1.07 tff(2016,plain,
% 0.84/1.07 (hskp17 | hskp12 | c2_1(a237) | c1_1(a237)),
% 0.84/1.07 inference(unit_resolution,[status(thm)],[2015, 110, 2002, 1325])).
% 0.84/1.07 tff(2017,plain,
% 0.84/1.07 (hskp17),
% 0.84/1.07 inference(unit_resolution,[status(thm)],[2016, 2009, 527, 557])).
% 0.84/1.07 tff(2018,plain,
% 0.84/1.07 (c3_1(a248)),
% 0.84/1.07 inference(unit_resolution,[status(thm)],[637, 2017])).
% 0.84/1.07 tff(2019,plain,
% 0.84/1.07 (c1_1(a248)),
% 0.84/1.07 inference(unit_resolution,[status(thm)],[623, 2017])).
% 0.84/1.07 tff(2020,plain,
% 0.84/1.07 (~c0_1(a248)),
% 0.84/1.07 inference(unit_resolution,[status(thm)],[668, 110, 45, 2019, 2018, 549, 548, 547, 149])).
% 0.84/1.07 tff(2021,plain,
% 0.84/1.07 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp9 | c1_1(a252) | (~ndr1_0) | (~c3_1(a248)) | c0_1(a248) | (~c1_1(a248)) | (~c3_1(a252)) | (~c2_1(a252)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp9 | c1_1(a252) | (~ndr1_0) | (~c3_1(a248)) | c0_1(a248) | (~c1_1(a248)) | (~c3_1(a252)) | (~c2_1(a252)))),
% 0.84/1.07 inference(rewrite,[status(thm)],[])).
% 0.84/1.07 tff(2022,plain,
% 0.84/1.07 ((hskp9 | (~ndr1_0) | c1_1(a252) | (~c2_1(a252)) | (~c3_1(a252)) | c0_1(a248) | (~c1_1(a248)) | (~c3_1(a248))) <=> (hskp9 | c1_1(a252) | (~ndr1_0) | (~c3_1(a248)) | c0_1(a248) | (~c1_1(a248)) | (~c3_1(a252)) | (~c2_1(a252)))),
% 0.84/1.07 inference(rewrite,[status(thm)],[])).
% 0.84/1.07 tff(2023,plain,
% 0.84/1.07 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp9 | (~ndr1_0) | c1_1(a252) | (~c2_1(a252)) | (~c3_1(a252)) | c0_1(a248) | (~c1_1(a248)) | (~c3_1(a248)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp9 | c1_1(a252) | (~ndr1_0) | (~c3_1(a248)) | c0_1(a248) | (~c1_1(a248)) | (~c3_1(a252)) | (~c2_1(a252))))),
% 0.84/1.07 inference(monotonicity,[status(thm)],[2022])).
% 0.84/1.07 tff(2024,plain,
% 0.84/1.07 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp9 | (~ndr1_0) | c1_1(a252) | (~c2_1(a252)) | (~c3_1(a252)) | c0_1(a248) | (~c1_1(a248)) | (~c3_1(a248)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp9 | c1_1(a252) | (~ndr1_0) | (~c3_1(a248)) | c0_1(a248) | (~c1_1(a248)) | (~c3_1(a252)) | (~c2_1(a252)))),
% 0.84/1.07 inference(transitivity,[status(thm)],[2023, 2021])).
% 0.84/1.07 tff(2025,plain,
% 0.84/1.07 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp9 | (~ndr1_0) | c1_1(a252) | (~c2_1(a252)) | (~c3_1(a252)) | c0_1(a248) | (~c1_1(a248)) | (~c3_1(a248)))),
% 0.84/1.07 inference(quant_inst,[status(thm)],[])).
% 0.84/1.07 tff(2026,plain,
% 0.84/1.07 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp9 | c1_1(a252) | (~ndr1_0) | (~c3_1(a248)) | c0_1(a248) | (~c1_1(a248)) | (~c3_1(a252)) | (~c2_1(a252))),
% 0.84/1.07 inference(modus_ponens,[status(thm)],[2025, 2024])).
% 0.84/1.07 tff(2027,plain,
% 0.84/1.07 (~c3_1(a252)),
% 0.84/1.07 inference(unit_resolution,[status(thm)],[2026, 110, 23, 1884, 2019, 2018, 1906, 409, 2020])).
% 0.84/1.07 tff(2028,plain,
% 0.84/1.07 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp9 | c1_1(a215) | (~ndr1_0) | (~c3_1(a215)) | (~c2_1(a215)) | (~c3_1(a248)) | c0_1(a248) | (~c1_1(a248)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp9 | c1_1(a215) | (~ndr1_0) | (~c3_1(a215)) | (~c2_1(a215)) | (~c3_1(a248)) | c0_1(a248) | (~c1_1(a248)))),
% 0.84/1.07 inference(rewrite,[status(thm)],[])).
% 0.84/1.07 tff(2029,plain,
% 0.84/1.07 ((hskp9 | (~ndr1_0) | c1_1(a215) | (~c2_1(a215)) | (~c3_1(a215)) | c0_1(a248) | (~c1_1(a248)) | (~c3_1(a248))) <=> (hskp9 | c1_1(a215) | (~ndr1_0) | (~c3_1(a215)) | (~c2_1(a215)) | (~c3_1(a248)) | c0_1(a248) | (~c1_1(a248)))),
% 0.84/1.07 inference(rewrite,[status(thm)],[])).
% 0.84/1.07 tff(2030,plain,
% 0.84/1.07 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp9 | (~ndr1_0) | c1_1(a215) | (~c2_1(a215)) | (~c3_1(a215)) | c0_1(a248) | (~c1_1(a248)) | (~c3_1(a248)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp9 | c1_1(a215) | (~ndr1_0) | (~c3_1(a215)) | (~c2_1(a215)) | (~c3_1(a248)) | c0_1(a248) | (~c1_1(a248))))),
% 0.84/1.07 inference(monotonicity,[status(thm)],[2029])).
% 0.84/1.07 tff(2031,plain,
% 0.84/1.07 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp9 | (~ndr1_0) | c1_1(a215) | (~c2_1(a215)) | (~c3_1(a215)) | c0_1(a248) | (~c1_1(a248)) | (~c3_1(a248)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp9 | c1_1(a215) | (~ndr1_0) | (~c3_1(a215)) | (~c2_1(a215)) | (~c3_1(a248)) | c0_1(a248) | (~c1_1(a248)))),
% 0.84/1.07 inference(transitivity,[status(thm)],[2030, 2028])).
% 0.84/1.07 tff(2032,plain,
% 0.84/1.07 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp9 | (~ndr1_0) | c1_1(a215) | (~c2_1(a215)) | (~c3_1(a215)) | c0_1(a248) | (~c1_1(a248)) | (~c3_1(a248)))),
% 0.84/1.07 inference(quant_inst,[status(thm)],[])).
% 0.84/1.07 tff(2033,plain,
% 0.84/1.07 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp9 | c1_1(a215) | (~ndr1_0) | (~c3_1(a215)) | (~c2_1(a215)) | (~c3_1(a248)) | c0_1(a248) | (~c1_1(a248))),
% 0.84/1.07 inference(modus_ponens,[status(thm)],[2032, 2031])).
% 0.84/1.07 tff(2034,plain,
% 0.84/1.07 (~c3_1(a215)),
% 0.84/1.07 inference(unit_resolution,[status(thm)],[2033, 110, 23, 2019, 2018, 549, 547, 409, 2020])).
% 0.84/1.07 tff(2035,plain,
% 0.84/1.07 (((~![U: $i] : (hskp21 | hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp21 | hskp12 | c1_1(a252) | (~ndr1_0) | c3_1(a252) | (~c2_1(a252)))) <=> ((~![U: $i] : (hskp21 | hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | hskp21 | hskp12 | c1_1(a252) | (~ndr1_0) | c3_1(a252) | (~c2_1(a252)))),
% 0.84/1.07 inference(rewrite,[status(thm)],[])).
% 0.84/1.07 tff(2036,plain,
% 0.84/1.07 ((hskp21 | hskp12 | (~ndr1_0) | c1_1(a252) | c3_1(a252) | (~c2_1(a252))) <=> (hskp21 | hskp12 | c1_1(a252) | (~ndr1_0) | c3_1(a252) | (~c2_1(a252)))),
% 0.84/1.07 inference(rewrite,[status(thm)],[])).
% 0.84/1.07 tff(2037,plain,
% 0.84/1.07 (((~![U: $i] : (hskp21 | hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp21 | hskp12 | (~ndr1_0) | c1_1(a252) | c3_1(a252) | (~c2_1(a252)))) <=> ((~![U: $i] : (hskp21 | hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp21 | hskp12 | c1_1(a252) | (~ndr1_0) | c3_1(a252) | (~c2_1(a252))))),
% 0.84/1.07 inference(monotonicity,[status(thm)],[2036])).
% 0.84/1.07 tff(2038,plain,
% 0.84/1.07 (((~![U: $i] : (hskp21 | hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp21 | hskp12 | (~ndr1_0) | c1_1(a252) | c3_1(a252) | (~c2_1(a252)))) <=> ((~![U: $i] : (hskp21 | hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | hskp21 | hskp12 | c1_1(a252) | (~ndr1_0) | c3_1(a252) | (~c2_1(a252)))),
% 0.84/1.07 inference(transitivity,[status(thm)],[2037, 2035])).
% 0.84/1.07 tff(2039,plain,
% 0.84/1.07 ((~![U: $i] : (hskp21 | hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp21 | hskp12 | (~ndr1_0) | c1_1(a252) | c3_1(a252) | (~c2_1(a252)))),
% 0.84/1.07 inference(quant_inst,[status(thm)],[])).
% 0.84/1.07 tff(2040,plain,
% 0.84/1.07 ((~![U: $i] : (hskp21 | hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | hskp21 | hskp12 | c1_1(a252) | (~ndr1_0) | c3_1(a252) | (~c2_1(a252))),
% 0.84/1.07 inference(modus_ponens,[status(thm)],[2039, 2038])).
% 0.84/1.07 tff(2041,plain,
% 0.84/1.07 (hskp21 | hskp12 | c3_1(a252)),
% 0.84/1.07 inference(unit_resolution,[status(thm)],[2040, 110, 1884, 1906, 738])).
% 0.84/1.07 tff(2042,plain,
% 0.84/1.07 (hskp21),
% 0.84/1.07 inference(unit_resolution,[status(thm)],[2041, 2027, 557])).
% 0.84/1.07 tff(2043,plain,
% 0.84/1.07 (~c2_1(a259)),
% 0.84/1.07 inference(unit_resolution,[status(thm)],[975, 2042])).
% 0.84/1.07 tff(2044,plain,
% 0.84/1.07 (c3_1(a259)),
% 0.84/1.07 inference(unit_resolution,[status(thm)],[792, 2042])).
% 0.84/1.07 tff(2045,plain,
% 0.84/1.07 (c0_1(a259)),
% 0.84/1.07 inference(unit_resolution,[status(thm)],[783, 2042])).
% 0.84/1.07 tff(2046,plain,
% 0.84/1.07 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | (c2_1(a259) | c1_1(a252) | c1_1(a215) | (~ndr1_0) | c3_1(a215) | (~c2_1(a215)) | c3_1(a252) | (~c0_1(a252)) | (~c3_1(a259)) | (~c0_1(a259)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | c2_1(a259) | c1_1(a252) | c1_1(a215) | (~ndr1_0) | c3_1(a215) | (~c2_1(a215)) | c3_1(a252) | (~c0_1(a252)) | (~c3_1(a259)) | (~c0_1(a259)))),
% 0.84/1.07 inference(rewrite,[status(thm)],[])).
% 0.84/1.07 tff(2047,plain,
% 0.84/1.07 (((~ndr1_0) | c2_1(a259) | (~c3_1(a259)) | (~c0_1(a259)) | c3_1(a215) | c1_1(a215) | (~c2_1(a215)) | c3_1(a252) | c1_1(a252) | (~c0_1(a252))) <=> (c2_1(a259) | c1_1(a252) | c1_1(a215) | (~ndr1_0) | c3_1(a215) | (~c2_1(a215)) | c3_1(a252) | (~c0_1(a252)) | (~c3_1(a259)) | (~c0_1(a259)))),
% 0.84/1.07 inference(rewrite,[status(thm)],[])).
% 0.84/1.07 tff(2048,plain,
% 0.84/1.07 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a259) | (~c3_1(a259)) | (~c0_1(a259)) | c3_1(a215) | c1_1(a215) | (~c2_1(a215)) | c3_1(a252) | c1_1(a252) | (~c0_1(a252)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | (c2_1(a259) | c1_1(a252) | c1_1(a215) | (~ndr1_0) | c3_1(a215) | (~c2_1(a215)) | c3_1(a252) | (~c0_1(a252)) | (~c3_1(a259)) | (~c0_1(a259))))),
% 0.84/1.07 inference(monotonicity,[status(thm)],[2047])).
% 0.84/1.07 tff(2049,plain,
% 0.84/1.07 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a259) | (~c3_1(a259)) | (~c0_1(a259)) | c3_1(a215) | c1_1(a215) | (~c2_1(a215)) | c3_1(a252) | c1_1(a252) | (~c0_1(a252)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | c2_1(a259) | c1_1(a252) | c1_1(a215) | (~ndr1_0) | c3_1(a215) | (~c2_1(a215)) | c3_1(a252) | (~c0_1(a252)) | (~c3_1(a259)) | (~c0_1(a259)))),
% 0.84/1.07 inference(transitivity,[status(thm)],[2048, 2046])).
% 0.84/1.07 tff(2050,plain,
% 0.84/1.07 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a259) | (~c3_1(a259)) | (~c0_1(a259)) | c3_1(a215) | c1_1(a215) | (~c2_1(a215)) | c3_1(a252) | c1_1(a252) | (~c0_1(a252)))),
% 0.84/1.07 inference(quant_inst,[status(thm)],[])).
% 0.84/1.07 tff(2051,plain,
% 0.84/1.07 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | c2_1(a259) | c1_1(a252) | c1_1(a215) | (~ndr1_0) | c3_1(a215) | (~c2_1(a215)) | c3_1(a252) | (~c0_1(a252)) | (~c3_1(a259)) | (~c0_1(a259))),
% 0.84/1.07 inference(modus_ponens,[status(thm)],[2050, 2049])).
% 0.84/1.07 tff(2052,plain,
% 0.84/1.07 ($false),
% 0.84/1.07 inference(unit_resolution,[status(thm)],[2051, 110, 2045, 2044, 1892, 549, 2043, 1906, 547, 22, 2034, 2027])).
% 0.84/1.07 tff(2053,plain,(c2_1(a237) | hskp9 | hskp5 | c3_1(a237) | hskp27), inference(lemma,lemma(discharge,[]))).
% 0.84/1.07 tff(2054,plain,
% 0.84/1.07 (c2_1(a237)),
% 0.84/1.07 inference(unit_resolution,[status(thm)],[2053, 164, 45, 23, 34])).
% 0.84/1.07 tff(2055,plain,
% 0.84/1.07 (c1_1(a237)),
% 0.84/1.07 inference(unit_resolution,[status(thm)],[1913, 1744, 1800, 526])).
% 0.84/1.07 tff(2056,plain,
% 0.84/1.07 (c3_1(a252)),
% 0.84/1.07 inference(unit_resolution,[status(thm)],[2041, 1744, 526])).
% 0.84/1.07 tff(2057,plain,
% 0.84/1.07 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W))))),
% 0.84/1.07 inference(bind,[status(th)],[])).
% 0.84/1.07 tff(2058,plain,
% 0.84/1.07 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))),
% 0.84/1.07 inference(quant_intro,[status(thm)],[2057])).
% 0.84/1.07 tff(2059,plain,
% 0.84/1.07 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))),
% 0.84/1.07 inference(rewrite,[status(thm)],[])).
% 0.84/1.07 tff(2060,plain,
% 0.84/1.07 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~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)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~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)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~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)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c1_1(W))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V))) | (~c1_1(W))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c1_1(W)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c1_1(W))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c1_1(W))) | c3_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c1_1(W))) | c3_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c1_1(W))) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | (~c1_1(W)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c1_1(W))) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | (~c1_1(W))))), ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c1_1(W))) | c3_1(V)) | c2_1(W)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | (~c1_1(W))) | c2_1(W)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | (~c1_1(W))) | c2_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | (~c1_1(W)))), ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c1_1(W))) | c3_1(V)) | c2_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | (~c1_1(W))))), (((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c1_1(W))) | c3_1(V)) | c2_1(W)) | c3_1(W)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | (~c1_1(W))) | c3_1(W)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | (~c1_1(W))) | c3_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))), (((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c1_1(W))) | c3_1(V)) | c2_1(W)) | c3_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))))),
% 0.84/1.07 inference(bind,[status(th)],[])).
% 0.84/1.07 tff(2061,plain,
% 0.84/1.07 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c1_1(W))) | c3_1(V)) | c2_1(W)) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))),
% 0.84/1.07 inference(quant_intro,[status(thm)],[2060])).
% 0.84/1.07 tff(2062,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c1_1(W))) | c3_1(V)) | c2_1(W)) | c3_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause197')).
% 0.84/1.07 tff(2063,plain,
% 0.84/1.07 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))),
% 0.84/1.07 inference(modus_ponens,[status(thm)],[2062, 2061])).
% 0.84/1.07 tff(2064,plain,
% 0.84/1.07 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))),
% 0.84/1.07 inference(modus_ponens,[status(thm)],[2063, 2059])).
% 0.84/1.07 tff(2065,plain,(
% 0.84/1.07 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))),
% 0.84/1.07 inference(skolemize,[status(sab)],[2064])).
% 0.84/1.07 tff(2066,plain,
% 0.84/1.07 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))),
% 0.84/1.07 inference(modus_ponens,[status(thm)],[2065, 2058])).
% 0.84/1.07 tff(2067,plain,
% 0.84/1.07 (^[U: $i] : refl((hskp26 | hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> (hskp26 | hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))))),
% 0.84/1.07 inference(bind,[status(th)],[])).
% 0.84/1.07 tff(2068,plain,
% 0.84/1.07 (![U: $i] : (hskp26 | hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp26 | hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.84/1.07 inference(quant_intro,[status(thm)],[2067])).
% 0.84/1.07 tff(2069,plain,
% 0.84/1.07 (![U: $i] : (hskp26 | hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp26 | hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.84/1.07 inference(rewrite,[status(thm)],[])).
% 0.84/1.07 tff(2070,plain,
% 0.84/1.07 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp26) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp26))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp26) <=> (hskp26 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp26) <=> (hskp26 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp26) | hskp23) <=> ((hskp26 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp23))), rewrite(((hskp26 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp23) <=> (hskp26 | hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp26) | hskp23) <=> (hskp26 | hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))))),
% 0.84/1.07 inference(bind,[status(th)],[])).
% 0.84/1.07 tff(2071,plain,
% 0.84/1.07 (![U: $i] : ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp26) | hskp23) <=> ![U: $i] : (hskp26 | hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.84/1.07 inference(quant_intro,[status(thm)],[2070])).
% 0.84/1.07 tff(2072,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp26) | hskp23)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause148')).
% 0.84/1.07 tff(2073,plain,
% 0.84/1.07 (![U: $i] : (hskp26 | hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.84/1.07 inference(modus_ponens,[status(thm)],[2072, 2071])).
% 0.84/1.07 tff(2074,plain,
% 0.84/1.07 (![U: $i] : (hskp26 | hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.84/1.07 inference(modus_ponens,[status(thm)],[2073, 2069])).
% 0.84/1.07 tff(2075,plain,(
% 0.84/1.07 ![U: $i] : (hskp26 | hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.84/1.07 inference(skolemize,[status(sab)],[2074])).
% 0.84/1.07 tff(2076,plain,
% 0.84/1.07 (![U: $i] : (hskp26 | hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.84/1.07 inference(modus_ponens,[status(thm)],[2075, 2068])).
% 0.84/1.07 tff(2077,plain,
% 0.84/1.07 (((~![U: $i] : (hskp26 | hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp26 | hskp23 | c1_1(a252) | (~ndr1_0) | (~c3_1(a252)) | (~c0_1(a252)))) <=> ((~![U: $i] : (hskp26 | hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp26 | hskp23 | c1_1(a252) | (~ndr1_0) | (~c3_1(a252)) | (~c0_1(a252)))),
% 0.84/1.07 inference(rewrite,[status(thm)],[])).
% 0.84/1.07 tff(2078,plain,
% 0.84/1.07 ((hskp26 | hskp23 | (~ndr1_0) | c1_1(a252) | (~c3_1(a252)) | (~c0_1(a252))) <=> (hskp26 | hskp23 | c1_1(a252) | (~ndr1_0) | (~c3_1(a252)) | (~c0_1(a252)))),
% 0.84/1.07 inference(rewrite,[status(thm)],[])).
% 0.84/1.07 tff(2079,plain,
% 0.84/1.08 (((~![U: $i] : (hskp26 | hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp26 | hskp23 | (~ndr1_0) | c1_1(a252) | (~c3_1(a252)) | (~c0_1(a252)))) <=> ((~![U: $i] : (hskp26 | hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp26 | hskp23 | c1_1(a252) | (~ndr1_0) | (~c3_1(a252)) | (~c0_1(a252))))),
% 0.84/1.08 inference(monotonicity,[status(thm)],[2078])).
% 0.84/1.08 tff(2080,plain,
% 0.84/1.08 (((~![U: $i] : (hskp26 | hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp26 | hskp23 | (~ndr1_0) | c1_1(a252) | (~c3_1(a252)) | (~c0_1(a252)))) <=> ((~![U: $i] : (hskp26 | hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp26 | hskp23 | c1_1(a252) | (~ndr1_0) | (~c3_1(a252)) | (~c0_1(a252)))),
% 0.84/1.08 inference(transitivity,[status(thm)],[2079, 2077])).
% 0.84/1.08 tff(2081,plain,
% 0.84/1.08 ((~![U: $i] : (hskp26 | hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp26 | hskp23 | (~ndr1_0) | c1_1(a252) | (~c3_1(a252)) | (~c0_1(a252)))),
% 0.84/1.08 inference(quant_inst,[status(thm)],[])).
% 0.84/1.08 tff(2082,plain,
% 0.84/1.08 ((~![U: $i] : (hskp26 | hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp26 | hskp23 | c1_1(a252) | (~ndr1_0) | (~c3_1(a252)) | (~c0_1(a252))),
% 0.84/1.08 inference(modus_ponens,[status(thm)],[2081, 2080])).
% 0.84/1.08 tff(2083,plain,
% 0.84/1.08 (hskp26 | hskp23 | (~c3_1(a252))),
% 0.84/1.08 inference(unit_resolution,[status(thm)],[2082, 110, 1892, 1906, 2076])).
% 0.84/1.08 tff(2084,plain,
% 0.84/1.08 (hskp23),
% 0.84/1.08 inference(unit_resolution,[status(thm)],[2083, 2056, 1])).
% 0.84/1.08 tff(2085,plain,
% 0.84/1.08 (((~hskp23) | (~c3_1(a274))) <=> ((~hskp23) | (~c3_1(a274)))),
% 0.84/1.08 inference(rewrite,[status(thm)],[])).
% 0.84/1.08 tff(2086,plain,
% 0.84/1.08 (((~c3_1(a274)) | (~hskp23)) <=> ((~hskp23) | (~c3_1(a274)))),
% 0.84/1.08 inference(rewrite,[status(thm)],[])).
% 0.84/1.08 tff(2087,axiom,((~c3_1(a274)) | (~hskp23)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause90')).
% 0.84/1.08 tff(2088,plain,
% 0.84/1.08 ((~hskp23) | (~c3_1(a274))),
% 0.84/1.08 inference(modus_ponens,[status(thm)],[2087, 2086])).
% 0.84/1.08 tff(2089,plain,
% 0.84/1.08 ((~hskp23) | (~c3_1(a274))),
% 0.84/1.08 inference(modus_ponens,[status(thm)],[2088, 2085])).
% 0.84/1.08 tff(2090,plain,
% 0.84/1.08 (~c3_1(a274)),
% 0.84/1.08 inference(unit_resolution,[status(thm)],[2089, 2084])).
% 0.84/1.08 tff(2091,plain,
% 0.84/1.08 (((~hskp23) | c1_1(a274)) <=> ((~hskp23) | c1_1(a274))),
% 0.84/1.08 inference(rewrite,[status(thm)],[])).
% 0.84/1.08 tff(2092,axiom,((~hskp23) | c1_1(a274)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause55')).
% 0.84/1.08 tff(2093,plain,
% 0.84/1.08 ((~hskp23) | c1_1(a274)),
% 0.84/1.08 inference(modus_ponens,[status(thm)],[2092, 2091])).
% 0.84/1.08 tff(2094,plain,
% 0.84/1.08 ((~hskp23) | c1_1(a274)),
% 0.84/1.08 inference(modus_ponens,[status(thm)],[2093, 2091])).
% 0.84/1.08 tff(2095,plain,
% 0.84/1.08 ((~hskp23) | c1_1(a274)),
% 0.84/1.08 inference(modus_ponens,[status(thm)],[2094, 2091])).
% 0.84/1.08 tff(2096,plain,
% 0.84/1.08 ((~hskp23) | c1_1(a274)),
% 0.84/1.08 inference(modus_ponens,[status(thm)],[2095, 2091])).
% 0.84/1.08 tff(2097,plain,
% 0.84/1.08 ((~hskp23) | c1_1(a274)),
% 0.84/1.08 inference(modus_ponens,[status(thm)],[2096, 2091])).
% 0.84/1.08 tff(2098,plain,
% 0.84/1.08 (c1_1(a274)),
% 0.84/1.08 inference(unit_resolution,[status(thm)],[2097, 2084])).
% 0.84/1.08 tff(2099,plain,
% 0.84/1.08 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))) | (c3_1(a274) | c3_1(a237) | (~ndr1_0) | (~c0_1(a237)) | (~c1_1(a237)) | (~c3_1(a252)) | (~c0_1(a252)) | (~c2_1(a252)) | c2_1(a274) | (~c1_1(a274)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))) | c3_1(a274) | c3_1(a237) | (~ndr1_0) | (~c0_1(a237)) | (~c1_1(a237)) | (~c3_1(a252)) | (~c0_1(a252)) | (~c2_1(a252)) | c2_1(a274) | (~c1_1(a274)))),
% 0.84/1.08 inference(rewrite,[status(thm)],[])).
% 0.84/1.08 tff(2100,plain,
% 0.84/1.08 (((~ndr1_0) | (~c2_1(a252)) | (~c3_1(a252)) | (~c0_1(a252)) | c3_1(a237) | (~c1_1(a237)) | (~c0_1(a237)) | c3_1(a274) | c2_1(a274) | (~c1_1(a274))) <=> (c3_1(a274) | c3_1(a237) | (~ndr1_0) | (~c0_1(a237)) | (~c1_1(a237)) | (~c3_1(a252)) | (~c0_1(a252)) | (~c2_1(a252)) | c2_1(a274) | (~c1_1(a274)))),
% 0.84/1.08 inference(rewrite,[status(thm)],[])).
% 0.84/1.08 tff(2101,plain,
% 0.84/1.08 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a252)) | (~c3_1(a252)) | (~c0_1(a252)) | c3_1(a237) | (~c1_1(a237)) | (~c0_1(a237)) | c3_1(a274) | c2_1(a274) | (~c1_1(a274)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))) | (c3_1(a274) | c3_1(a237) | (~ndr1_0) | (~c0_1(a237)) | (~c1_1(a237)) | (~c3_1(a252)) | (~c0_1(a252)) | (~c2_1(a252)) | c2_1(a274) | (~c1_1(a274))))),
% 0.84/1.08 inference(monotonicity,[status(thm)],[2100])).
% 0.84/1.08 tff(2102,plain,
% 0.84/1.08 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a252)) | (~c3_1(a252)) | (~c0_1(a252)) | c3_1(a237) | (~c1_1(a237)) | (~c0_1(a237)) | c3_1(a274) | c2_1(a274) | (~c1_1(a274)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))) | c3_1(a274) | c3_1(a237) | (~ndr1_0) | (~c0_1(a237)) | (~c1_1(a237)) | (~c3_1(a252)) | (~c0_1(a252)) | (~c2_1(a252)) | c2_1(a274) | (~c1_1(a274)))),
% 0.84/1.08 inference(transitivity,[status(thm)],[2101, 2099])).
% 0.84/1.08 tff(2103,plain,
% 0.84/1.08 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a252)) | (~c3_1(a252)) | (~c0_1(a252)) | c3_1(a237) | (~c1_1(a237)) | (~c0_1(a237)) | c3_1(a274) | c2_1(a274) | (~c1_1(a274)))),
% 0.84/1.08 inference(quant_inst,[status(thm)],[])).
% 0.84/1.08 tff(2104,plain,
% 0.84/1.08 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))) | c3_1(a274) | c3_1(a237) | (~ndr1_0) | (~c0_1(a237)) | (~c1_1(a237)) | (~c3_1(a252)) | (~c0_1(a252)) | (~c2_1(a252)) | c2_1(a274) | (~c1_1(a274))),
% 0.84/1.08 inference(modus_ponens,[status(thm)],[2103, 2102])).
% 0.84/1.08 tff(2105,plain,
% 0.84/1.08 (c2_1(a274)),
% 0.84/1.08 inference(unit_resolution,[status(thm)],[2104, 110, 2098, 1892, 1884, 1809, 2090, 164, 2066, 2056, 2055])).
% 0.84/1.08 tff(2106,plain,
% 0.84/1.08 (((~hskp23) | (~c0_1(a274))) <=> ((~hskp23) | (~c0_1(a274)))),
% 0.84/1.08 inference(rewrite,[status(thm)],[])).
% 0.84/1.08 tff(2107,plain,
% 0.84/1.08 (((~c0_1(a274)) | (~hskp23)) <=> ((~hskp23) | (~c0_1(a274)))),
% 0.84/1.08 inference(rewrite,[status(thm)],[])).
% 0.84/1.08 tff(2108,axiom,((~c0_1(a274)) | (~hskp23)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause89')).
% 0.84/1.08 tff(2109,plain,
% 0.84/1.08 ((~hskp23) | (~c0_1(a274))),
% 0.84/1.08 inference(modus_ponens,[status(thm)],[2108, 2107])).
% 0.84/1.08 tff(2110,plain,
% 0.84/1.08 ((~hskp23) | (~c0_1(a274))),
% 0.84/1.08 inference(modus_ponens,[status(thm)],[2109, 2106])).
% 0.84/1.08 tff(2111,plain,
% 0.84/1.08 (~c0_1(a274)),
% 0.84/1.08 inference(unit_resolution,[status(thm)],[2110, 2084])).
% 0.84/1.08 tff(2112,plain,
% 0.84/1.08 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp12 | c0_1(a274) | c3_1(a274) | (~ndr1_0) | (~c2_1(a274)) | (~c1_1(a274)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp12 | c0_1(a274) | c3_1(a274) | (~ndr1_0) | (~c2_1(a274)) | (~c1_1(a274)))),
% 0.84/1.08 inference(rewrite,[status(thm)],[])).
% 0.84/1.08 tff(2113,plain,
% 0.84/1.08 ((hskp12 | (~ndr1_0) | c3_1(a274) | (~c2_1(a274)) | (~c1_1(a274)) | c3_1(a274) | c0_1(a274) | (~c1_1(a274))) <=> (hskp12 | c0_1(a274) | c3_1(a274) | (~ndr1_0) | (~c2_1(a274)) | (~c1_1(a274)))),
% 0.84/1.08 inference(rewrite,[status(thm)],[])).
% 0.84/1.08 tff(2114,plain,
% 0.84/1.08 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp12 | (~ndr1_0) | c3_1(a274) | (~c2_1(a274)) | (~c1_1(a274)) | c3_1(a274) | c0_1(a274) | (~c1_1(a274)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp12 | c0_1(a274) | c3_1(a274) | (~ndr1_0) | (~c2_1(a274)) | (~c1_1(a274))))),
% 0.84/1.08 inference(monotonicity,[status(thm)],[2113])).
% 0.84/1.08 tff(2115,plain,
% 0.84/1.08 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp12 | (~ndr1_0) | c3_1(a274) | (~c2_1(a274)) | (~c1_1(a274)) | c3_1(a274) | c0_1(a274) | (~c1_1(a274)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp12 | c0_1(a274) | c3_1(a274) | (~ndr1_0) | (~c2_1(a274)) | (~c1_1(a274)))),
% 0.84/1.08 inference(transitivity,[status(thm)],[2114, 2112])).
% 0.84/1.08 tff(2116,plain,
% 0.84/1.08 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp12 | (~ndr1_0) | c3_1(a274) | (~c2_1(a274)) | (~c1_1(a274)) | c3_1(a274) | c0_1(a274) | (~c1_1(a274)))),
% 0.84/1.08 inference(quant_inst,[status(thm)],[])).
% 0.84/1.08 tff(2117,plain,
% 0.84/1.08 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp12 | c0_1(a274) | c3_1(a274) | (~ndr1_0) | (~c2_1(a274)) | (~c1_1(a274))),
% 0.84/1.08 inference(modus_ponens,[status(thm)],[2116, 2115])).
% 0.84/1.08 tff(2118,plain,
% 0.84/1.08 ($false),
% 0.84/1.08 inference(unit_resolution,[status(thm)],[2117, 110, 526, 2098, 2111, 2090, 44, 2105])).
% 0.84/1.08 tff(2119,plain,(hskp21 | hskp12 | (~c0_1(a237)) | c3_1(a237) | hskp26 | (~c2_1(a237))), inference(lemma,lemma(discharge,[]))).
% 0.84/1.08 tff(2120,plain,
% 0.84/1.08 (hskp21),
% 0.84/1.08 inference(unit_resolution,[status(thm)],[2119, 528, 1809, 164, 526, 1800])).
% 0.84/1.08 tff(2121,plain,
% 0.84/1.08 (c3_1(a259)),
% 0.84/1.08 inference(unit_resolution,[status(thm)],[792, 2120])).
% 0.84/1.08 tff(2122,plain,
% 0.84/1.08 (c0_1(a259)),
% 0.84/1.08 inference(unit_resolution,[status(thm)],[783, 2120])).
% 0.84/1.08 tff(2123,plain,
% 0.84/1.08 (^[U: $i] : refl((hskp3 | hskp27 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> (hskp3 | hskp27 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))))),
% 0.84/1.08 inference(bind,[status(th)],[])).
% 0.84/1.08 tff(2124,plain,
% 0.84/1.08 (![U: $i] : (hskp3 | hskp27 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp3 | hskp27 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.84/1.08 inference(quant_intro,[status(thm)],[2123])).
% 0.84/1.08 tff(2125,plain,
% 0.84/1.08 (![U: $i] : (hskp3 | hskp27 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp3 | hskp27 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.92/1.08 inference(rewrite,[status(thm)],[])).
% 0.92/1.08 tff(2126,plain,
% 0.92/1.08 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp3) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp3))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp3) <=> (hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp3) <=> (hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp3) | hskp27) <=> ((hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp27))), rewrite(((hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp27) <=> (hskp3 | hskp27 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp3) | hskp27) <=> (hskp3 | hskp27 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))))),
% 0.92/1.08 inference(bind,[status(th)],[])).
% 0.92/1.08 tff(2127,plain,
% 0.92/1.08 (![U: $i] : ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp3) | hskp27) <=> ![U: $i] : (hskp3 | hskp27 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.92/1.08 inference(quant_intro,[status(thm)],[2126])).
% 0.92/1.08 tff(2128,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp3) | hskp27)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause152')).
% 0.92/1.08 tff(2129,plain,
% 0.92/1.08 (![U: $i] : (hskp3 | hskp27 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.92/1.08 inference(modus_ponens,[status(thm)],[2128, 2127])).
% 0.92/1.08 tff(2130,plain,
% 0.92/1.08 (![U: $i] : (hskp3 | hskp27 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.92/1.08 inference(modus_ponens,[status(thm)],[2129, 2125])).
% 0.92/1.08 tff(2131,plain,(
% 0.92/1.08 ![U: $i] : (hskp3 | hskp27 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.92/1.08 inference(skolemize,[status(sab)],[2130])).
% 0.92/1.08 tff(2132,plain,
% 0.92/1.08 (![U: $i] : (hskp3 | hskp27 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.92/1.08 inference(modus_ponens,[status(thm)],[2131, 2124])).
% 0.92/1.08 tff(2133,plain,
% 0.92/1.08 (((~![U: $i] : (hskp3 | hskp27 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp3 | hskp27 | c2_1(a259) | (~ndr1_0) | (~c3_1(a259)) | (~c0_1(a259)))) <=> ((~![U: $i] : (hskp3 | hskp27 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp3 | hskp27 | c2_1(a259) | (~ndr1_0) | (~c3_1(a259)) | (~c0_1(a259)))),
% 0.92/1.08 inference(rewrite,[status(thm)],[])).
% 0.92/1.08 tff(2134,plain,
% 0.92/1.08 ((hskp3 | hskp27 | (~ndr1_0) | c2_1(a259) | (~c3_1(a259)) | (~c0_1(a259))) <=> (hskp3 | hskp27 | c2_1(a259) | (~ndr1_0) | (~c3_1(a259)) | (~c0_1(a259)))),
% 0.92/1.08 inference(rewrite,[status(thm)],[])).
% 0.92/1.08 tff(2135,plain,
% 0.92/1.08 (((~![U: $i] : (hskp3 | hskp27 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp3 | hskp27 | (~ndr1_0) | c2_1(a259) | (~c3_1(a259)) | (~c0_1(a259)))) <=> ((~![U: $i] : (hskp3 | hskp27 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp3 | hskp27 | c2_1(a259) | (~ndr1_0) | (~c3_1(a259)) | (~c0_1(a259))))),
% 0.92/1.08 inference(monotonicity,[status(thm)],[2134])).
% 0.92/1.08 tff(2136,plain,
% 0.92/1.08 (((~![U: $i] : (hskp3 | hskp27 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp3 | hskp27 | (~ndr1_0) | c2_1(a259) | (~c3_1(a259)) | (~c0_1(a259)))) <=> ((~![U: $i] : (hskp3 | hskp27 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp3 | hskp27 | c2_1(a259) | (~ndr1_0) | (~c3_1(a259)) | (~c0_1(a259)))),
% 0.92/1.08 inference(transitivity,[status(thm)],[2135, 2133])).
% 0.92/1.08 tff(2137,plain,
% 0.92/1.08 ((~![U: $i] : (hskp3 | hskp27 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp3 | hskp27 | (~ndr1_0) | c2_1(a259) | (~c3_1(a259)) | (~c0_1(a259)))),
% 0.92/1.08 inference(quant_inst,[status(thm)],[])).
% 0.92/1.08 tff(2138,plain,
% 0.92/1.08 ((~![U: $i] : (hskp3 | hskp27 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp3 | hskp27 | c2_1(a259) | (~ndr1_0) | (~c3_1(a259)) | (~c0_1(a259))),
% 0.92/1.08 inference(modus_ponens,[status(thm)],[2137, 2136])).
% 0.92/1.08 tff(2139,plain,
% 0.92/1.08 (hskp3 | (~c3_1(a259)) | (~c0_1(a259))),
% 0.92/1.08 inference(unit_resolution,[status(thm)],[2138, 110, 34, 785, 2132])).
% 0.92/1.08 tff(2140,plain,
% 0.92/1.08 (hskp3),
% 0.92/1.08 inference(unit_resolution,[status(thm)],[2139, 2122, 2121])).
% 0.92/1.08 tff(2141,plain,
% 0.92/1.08 (c1_1(a216)),
% 0.92/1.08 inference(unit_resolution,[status(thm)],[210, 2140])).
% 0.92/1.08 tff(2142,plain,
% 0.92/1.08 (c0_1(a216)),
% 0.92/1.08 inference(unit_resolution,[status(thm)],[218, 2140])).
% 0.92/1.08 tff(2143,plain,
% 0.92/1.08 (~c3_1(a216)),
% 0.92/1.08 inference(unit_resolution,[status(thm)],[225, 110, 34, 81, 2142, 2141, 56])).
% 0.92/1.08 tff(2144,plain,
% 0.92/1.08 (~c2_1(a216)),
% 0.92/1.08 inference(unit_resolution,[status(thm)],[241, 2140])).
% 0.92/1.08 tff(2145,plain,
% 0.92/1.08 ($false),
% 0.92/1.08 inference(unit_resolution,[status(thm)],[248, 110, 528, 23, 2141, 2144, 236, 2143])).
% 0.92/1.08 tff(2146,plain,(hskp2 | hskp9 | hskp27 | c2_1(a259) | (~c0_1(a237)) | c3_1(a237) | hskp12 | (~c2_1(a237))), inference(lemma,lemma(discharge,[]))).
% 0.92/1.08 tff(2147,plain,
% 0.92/1.08 (hskp2),
% 0.92/1.08 inference(unit_resolution,[status(thm)],[2146, 785, 34, 23, 2002, 164, 526, 2054])).
% 0.92/1.08 tff(2148,plain,
% 0.92/1.08 (~c1_1(a215)),
% 0.92/1.08 inference(unit_resolution,[status(thm)],[124, 2147])).
% 0.92/1.08 tff(2149,plain,
% 0.92/1.08 (~c0_1(a215)),
% 0.92/1.08 inference(unit_resolution,[status(thm)],[138, 2147])).
% 0.92/1.08 tff(2150,plain,
% 0.92/1.08 (c2_1(a215)),
% 0.92/1.08 inference(unit_resolution,[status(thm)],[132, 2147])).
% 0.92/1.08 tff(2151,plain,
% 0.92/1.08 (~hskp26),
% 0.92/1.08 inference(unit_resolution,[status(thm)],[160, 2150, 45, 2149, 2148])).
% 0.92/1.08 tff(2152,plain,
% 0.92/1.08 (hskp21),
% 0.92/1.08 inference(unit_resolution,[status(thm)],[2119, 2151, 2002, 164, 526, 2054])).
% 0.92/1.08 tff(2153,plain,
% 0.92/1.08 (c0_1(a259)),
% 0.92/1.08 inference(unit_resolution,[status(thm)],[783, 2152])).
% 0.92/1.08 tff(2154,plain,
% 0.92/1.08 (c3_1(a259)),
% 0.92/1.08 inference(unit_resolution,[status(thm)],[792, 2152])).
% 0.92/1.08 tff(2155,plain,
% 0.92/1.08 ((~c3_1(a252)) | (~c3_1(a259)) | (~c0_1(a259))),
% 0.92/1.08 inference(unit_resolution,[status(thm)],[1948, 110, 1892, 1884, 2150, 785, 2149, 2148, 853])).
% 0.92/1.08 tff(2156,plain,
% 0.92/1.08 (~c3_1(a252)),
% 0.92/1.08 inference(unit_resolution,[status(thm)],[2155, 2154, 2153])).
% 0.92/1.08 tff(2157,plain,
% 0.92/1.08 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | (c2_1(a259) | c1_1(a252) | (~ndr1_0) | c3_1(a252) | (~c0_1(a252)) | (~c2_1(a252)) | (~c3_1(a259)) | (~c0_1(a259)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | c2_1(a259) | c1_1(a252) | (~ndr1_0) | c3_1(a252) | (~c0_1(a252)) | (~c2_1(a252)) | (~c3_1(a259)) | (~c0_1(a259)))),
% 0.92/1.08 inference(rewrite,[status(thm)],[])).
% 0.92/1.08 tff(2158,plain,
% 0.92/1.08 (((~ndr1_0) | c2_1(a259) | (~c3_1(a259)) | (~c0_1(a259)) | c3_1(a252) | c1_1(a252) | (~c2_1(a252)) | c3_1(a252) | c1_1(a252) | (~c0_1(a252))) <=> (c2_1(a259) | c1_1(a252) | (~ndr1_0) | c3_1(a252) | (~c0_1(a252)) | (~c2_1(a252)) | (~c3_1(a259)) | (~c0_1(a259)))),
% 0.92/1.08 inference(rewrite,[status(thm)],[])).
% 0.92/1.08 tff(2159,plain,
% 0.92/1.08 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a259) | (~c3_1(a259)) | (~c0_1(a259)) | c3_1(a252) | c1_1(a252) | (~c2_1(a252)) | c3_1(a252) | c1_1(a252) | (~c0_1(a252)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | (c2_1(a259) | c1_1(a252) | (~ndr1_0) | c3_1(a252) | (~c0_1(a252)) | (~c2_1(a252)) | (~c3_1(a259)) | (~c0_1(a259))))),
% 0.92/1.08 inference(monotonicity,[status(thm)],[2158])).
% 0.92/1.08 tff(2160,plain,
% 0.92/1.08 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a259) | (~c3_1(a259)) | (~c0_1(a259)) | c3_1(a252) | c1_1(a252) | (~c2_1(a252)) | c3_1(a252) | c1_1(a252) | (~c0_1(a252)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | c2_1(a259) | c1_1(a252) | (~ndr1_0) | c3_1(a252) | (~c0_1(a252)) | (~c2_1(a252)) | (~c3_1(a259)) | (~c0_1(a259)))),
% 0.92/1.08 inference(transitivity,[status(thm)],[2159, 2157])).
% 0.92/1.08 tff(2161,plain,
% 0.92/1.08 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a259) | (~c3_1(a259)) | (~c0_1(a259)) | c3_1(a252) | c1_1(a252) | (~c2_1(a252)) | c3_1(a252) | c1_1(a252) | (~c0_1(a252)))),
% 0.92/1.08 inference(quant_inst,[status(thm)],[])).
% 0.92/1.08 tff(2162,plain,
% 0.92/1.08 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | c2_1(a259) | c1_1(a252) | (~ndr1_0) | c3_1(a252) | (~c0_1(a252)) | (~c2_1(a252)) | (~c3_1(a259)) | (~c0_1(a259))),
% 0.92/1.08 inference(modus_ponens,[status(thm)],[2161, 2160])).
% 0.92/1.08 tff(2163,plain,
% 0.92/1.08 ($false),
% 0.92/1.08 inference(unit_resolution,[status(thm)],[2162, 110, 2153, 2154, 1892, 1884, 785, 1906, 22, 2156])).
% 0.92/1.08 tff(2164,plain,(c2_1(a259) | c3_1(a237) | hskp12 | hskp5 | hskp27 | hskp9), inference(lemma,lemma(discharge,[]))).
% 0.92/1.08 tff(2165,plain,
% 0.92/1.08 (c2_1(a259)),
% 0.92/1.08 inference(unit_resolution,[status(thm)],[2164, 526, 164, 45, 34, 23])).
% 0.92/1.08 tff(2166,plain,
% 0.92/1.08 (hskp21),
% 0.92/1.08 inference(unit_resolution,[status(thm)],[2119, 526, 163, 164, 2002, 2054])).
% 0.92/1.08 tff(2167,plain,
% 0.92/1.08 ($false),
% 0.92/1.08 inference(unit_resolution,[status(thm)],[975, 2166, 2165])).
% 0.92/1.08 tff(2168,plain,(hskp12 | c3_1(a237) | hskp5 | hskp27 | hskp9), inference(lemma,lemma(discharge,[]))).
% 0.92/1.08 tff(2169,plain,
% 0.92/1.08 (hskp12),
% 0.92/1.08 inference(unit_resolution,[status(thm)],[2168, 164, 45, 34, 23])).
% 0.92/1.08 tff(2170,plain,
% 0.92/1.08 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp9 | c0_1(a320) | c1_1(a252) | (~ndr1_0) | (~c3_1(a252)) | (~c2_1(a252)) | (~c1_1(a320)) | (~c3_1(a320)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp9 | c0_1(a320) | c1_1(a252) | (~ndr1_0) | (~c3_1(a252)) | (~c2_1(a252)) | (~c1_1(a320)) | (~c3_1(a320)))),
% 0.92/1.08 inference(rewrite,[status(thm)],[])).
% 0.92/1.08 tff(2171,plain,
% 0.92/1.08 ((hskp9 | (~ndr1_0) | c1_1(a252) | (~c2_1(a252)) | (~c3_1(a252)) | c0_1(a320) | (~c1_1(a320)) | (~c3_1(a320))) <=> (hskp9 | c0_1(a320) | c1_1(a252) | (~ndr1_0) | (~c3_1(a252)) | (~c2_1(a252)) | (~c1_1(a320)) | (~c3_1(a320)))),
% 0.92/1.08 inference(rewrite,[status(thm)],[])).
% 0.92/1.08 tff(2172,plain,
% 0.92/1.08 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp9 | (~ndr1_0) | c1_1(a252) | (~c2_1(a252)) | (~c3_1(a252)) | c0_1(a320) | (~c1_1(a320)) | (~c3_1(a320)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp9 | c0_1(a320) | c1_1(a252) | (~ndr1_0) | (~c3_1(a252)) | (~c2_1(a252)) | (~c1_1(a320)) | (~c3_1(a320))))),
% 0.92/1.08 inference(monotonicity,[status(thm)],[2171])).
% 0.92/1.08 tff(2173,plain,
% 0.92/1.08 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp9 | (~ndr1_0) | c1_1(a252) | (~c2_1(a252)) | (~c3_1(a252)) | c0_1(a320) | (~c1_1(a320)) | (~c3_1(a320)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp9 | c0_1(a320) | c1_1(a252) | (~ndr1_0) | (~c3_1(a252)) | (~c2_1(a252)) | (~c1_1(a320)) | (~c3_1(a320)))),
% 0.92/1.08 inference(transitivity,[status(thm)],[2172, 2170])).
% 0.92/1.08 tff(2174,plain,
% 0.92/1.08 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp9 | (~ndr1_0) | c1_1(a252) | (~c2_1(a252)) | (~c3_1(a252)) | c0_1(a320) | (~c1_1(a320)) | (~c3_1(a320)))),
% 0.92/1.08 inference(quant_inst,[status(thm)],[])).
% 0.92/1.08 tff(2175,plain,
% 0.92/1.08 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp9 | c0_1(a320) | c1_1(a252) | (~ndr1_0) | (~c3_1(a252)) | (~c2_1(a252)) | (~c1_1(a320)) | (~c3_1(a320))),
% 0.92/1.08 inference(modus_ponens,[status(thm)],[2174, 2173])).
% 0.92/1.08 tff(2176,plain,
% 0.92/1.08 (~c3_1(a252)),
% 0.92/1.08 inference(unit_resolution,[status(thm)],[2175, 110, 23, 329, 1884, 356, 1906, 409, 495])).
% 0.92/1.08 tff(2177,plain,
% 0.92/1.08 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W))))),
% 0.92/1.08 inference(bind,[status(th)],[])).
% 0.92/1.08 tff(2178,plain,
% 0.92/1.08 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))),
% 0.92/1.08 inference(quant_intro,[status(thm)],[2177])).
% 0.92/1.08 tff(2179,plain,
% 0.92/1.08 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))),
% 0.92/1.08 inference(rewrite,[status(thm)],[])).
% 0.92/1.08 tff(2180,plain,
% 0.92/1.08 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c2_1(W))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V))) | (~c2_1(W))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c2_1(W)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c2_1(W))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c2_1(W))) | (~c3_1(W))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c2_1(W))) | (~c3_1(W))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c2_1(W))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c2_1(W)) | (~c3_1(W)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c2_1(W))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c2_1(W)) | (~c3_1(W))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c1_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c2_1(W)) | (~c3_1(W))) | c1_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c2_1(W)) | (~c3_1(W))) | c1_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c2_1(W)) | (~c3_1(W)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c1_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c2_1(W)) | (~c3_1(W))))), ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c1_1(V)) | c3_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c2_1(W)) | (~c3_1(W))) | c3_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c2_1(W)) | (~c3_1(W))) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | (~c2_1(W)) | (~c3_1(W)))), ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | (~c2_1(W)) | (~c3_1(W))))), (((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c1_1(V)) | c3_1(V)) | c0_1(W)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | (~c2_1(W)) | (~c3_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | (~c2_1(W)) | (~c3_1(W))) | c0_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))), (((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c1_1(V)) | c3_1(V)) | c0_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))))),
% 0.92/1.08 inference(bind,[status(th)],[])).
% 0.92/1.08 tff(2181,plain,
% 0.92/1.08 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c1_1(V)) | c3_1(V)) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))),
% 0.92/1.08 inference(quant_intro,[status(thm)],[2180])).
% 0.92/1.08 tff(2182,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c1_1(V)) | c3_1(V)) | c0_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause195')).
% 0.92/1.09 tff(2183,plain,
% 0.92/1.09 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))),
% 0.92/1.09 inference(modus_ponens,[status(thm)],[2182, 2181])).
% 0.92/1.09 tff(2184,plain,
% 0.92/1.09 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))),
% 0.92/1.09 inference(modus_ponens,[status(thm)],[2183, 2179])).
% 0.92/1.09 tff(2185,plain,(
% 0.92/1.09 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))),
% 0.92/1.09 inference(skolemize,[status(sab)],[2184])).
% 0.92/1.09 tff(2186,plain,
% 0.92/1.09 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))),
% 0.92/1.09 inference(modus_ponens,[status(thm)],[2185, 2178])).
% 0.92/1.09 tff(2187,plain,
% 0.92/1.09 (^[U: $i] : refl((hskp29 | hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) <=> (hskp29 | hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))))),
% 0.92/1.09 inference(bind,[status(th)],[])).
% 0.92/1.09 tff(2188,plain,
% 0.92/1.09 (![U: $i] : (hskp29 | hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp29 | hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))),
% 0.92/1.09 inference(quant_intro,[status(thm)],[2187])).
% 0.92/1.09 tff(2189,plain,
% 0.92/1.09 (![U: $i] : (hskp29 | hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp29 | hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))),
% 0.92/1.09 inference(rewrite,[status(thm)],[])).
% 0.92/1.09 tff(2190,plain,
% 0.92/1.09 (^[U: $i] : 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)) | hskp26) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | hskp26))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | hskp26) <=> (hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp26) <=> (hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp26) | hskp29) <=> ((hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | hskp29))), rewrite(((hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | hskp29) <=> (hskp29 | hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp26) | hskp29) <=> (hskp29 | hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))))),
% 0.92/1.09 inference(bind,[status(th)],[])).
% 0.92/1.09 tff(2191,plain,
% 0.92/1.09 (![U: $i] : ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp26) | hskp29) <=> ![U: $i] : (hskp29 | hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))),
% 0.92/1.09 inference(quant_intro,[status(thm)],[2190])).
% 0.92/1.09 tff(2192,axiom,(![U: $i] : ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp26) | hskp29)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause156')).
% 0.92/1.09 tff(2193,plain,
% 0.92/1.09 (![U: $i] : (hskp29 | hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))),
% 0.92/1.09 inference(modus_ponens,[status(thm)],[2192, 2191])).
% 0.92/1.09 tff(2194,plain,
% 0.92/1.09 (![U: $i] : (hskp29 | hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))),
% 0.92/1.09 inference(modus_ponens,[status(thm)],[2193, 2189])).
% 0.92/1.09 tff(2195,plain,(
% 0.92/1.09 ![U: $i] : (hskp29 | hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))),
% 0.92/1.09 inference(skolemize,[status(sab)],[2194])).
% 0.92/1.09 tff(2196,plain,
% 0.92/1.09 (![U: $i] : (hskp29 | hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))),
% 0.92/1.09 inference(modus_ponens,[status(thm)],[2195, 2188])).
% 0.92/1.09 tff(2197,plain,
% 0.92/1.09 (((~![U: $i] : (hskp29 | hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | (hskp29 | hskp26 | (~ndr1_0) | (~c2_1(a320)) | (~c1_1(a320)) | (~c3_1(a320)))) <=> ((~![U: $i] : (hskp29 | hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | hskp29 | hskp26 | (~ndr1_0) | (~c2_1(a320)) | (~c1_1(a320)) | (~c3_1(a320)))),
% 0.92/1.09 inference(rewrite,[status(thm)],[])).
% 0.92/1.09 tff(2198,plain,
% 0.92/1.09 ((hskp29 | hskp26 | (~ndr1_0) | (~c2_1(a320)) | (~c3_1(a320)) | (~c1_1(a320))) <=> (hskp29 | hskp26 | (~ndr1_0) | (~c2_1(a320)) | (~c1_1(a320)) | (~c3_1(a320)))),
% 0.92/1.09 inference(rewrite,[status(thm)],[])).
% 0.92/1.09 tff(2199,plain,
% 0.92/1.09 (((~![U: $i] : (hskp29 | hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | (hskp29 | hskp26 | (~ndr1_0) | (~c2_1(a320)) | (~c3_1(a320)) | (~c1_1(a320)))) <=> ((~![U: $i] : (hskp29 | hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | (hskp29 | hskp26 | (~ndr1_0) | (~c2_1(a320)) | (~c1_1(a320)) | (~c3_1(a320))))),
% 0.92/1.09 inference(monotonicity,[status(thm)],[2198])).
% 0.92/1.09 tff(2200,plain,
% 0.92/1.09 (((~![U: $i] : (hskp29 | hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | (hskp29 | hskp26 | (~ndr1_0) | (~c2_1(a320)) | (~c3_1(a320)) | (~c1_1(a320)))) <=> ((~![U: $i] : (hskp29 | hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | hskp29 | hskp26 | (~ndr1_0) | (~c2_1(a320)) | (~c1_1(a320)) | (~c3_1(a320)))),
% 0.92/1.09 inference(transitivity,[status(thm)],[2199, 2197])).
% 0.92/1.09 tff(2201,plain,
% 0.92/1.09 ((~![U: $i] : (hskp29 | hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | (hskp29 | hskp26 | (~ndr1_0) | (~c2_1(a320)) | (~c3_1(a320)) | (~c1_1(a320)))),
% 0.92/1.09 inference(quant_inst,[status(thm)],[])).
% 0.92/1.09 tff(2202,plain,
% 0.92/1.09 ((~![U: $i] : (hskp29 | hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | hskp29 | hskp26 | (~ndr1_0) | (~c2_1(a320)) | (~c1_1(a320)) | (~c3_1(a320))),
% 0.92/1.09 inference(modus_ponens,[status(thm)],[2201, 2200])).
% 0.92/1.09 tff(2203,plain,
% 0.92/1.09 (hskp29),
% 0.92/1.09 inference(unit_resolution,[status(thm)],[2202, 110, 1, 337, 329, 2196, 495])).
% 0.92/1.09 tff(2204,plain,
% 0.92/1.09 (((~hskp29) | c3_1(a296)) <=> ((~hskp29) | c3_1(a296))),
% 0.92/1.09 inference(rewrite,[status(thm)],[])).
% 0.92/1.09 tff(2205,axiom,((~hskp29) | c3_1(a296)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause42')).
% 0.92/1.09 tff(2206,plain,
% 0.92/1.09 ((~hskp29) | c3_1(a296)),
% 0.92/1.09 inference(modus_ponens,[status(thm)],[2205, 2204])).
% 0.92/1.09 tff(2207,plain,
% 0.92/1.09 ((~hskp29) | c3_1(a296)),
% 0.92/1.09 inference(modus_ponens,[status(thm)],[2206, 2204])).
% 0.92/1.09 tff(2208,plain,
% 0.92/1.09 ((~hskp29) | c3_1(a296)),
% 0.92/1.09 inference(modus_ponens,[status(thm)],[2207, 2204])).
% 0.92/1.09 tff(2209,plain,
% 0.92/1.09 ((~hskp29) | c3_1(a296)),
% 0.92/1.09 inference(modus_ponens,[status(thm)],[2208, 2204])).
% 0.92/1.09 tff(2210,plain,
% 0.92/1.09 ((~hskp29) | c3_1(a296)),
% 0.92/1.09 inference(modus_ponens,[status(thm)],[2209, 2204])).
% 0.92/1.09 tff(2211,plain,
% 0.92/1.09 (c3_1(a296)),
% 0.92/1.09 inference(unit_resolution,[status(thm)],[2210, 2203])).
% 0.92/1.09 tff(2212,plain,
% 0.92/1.09 (((~hskp29) | c2_1(a296)) <=> ((~hskp29) | c2_1(a296))),
% 0.92/1.09 inference(rewrite,[status(thm)],[])).
% 0.92/1.09 tff(2213,axiom,((~hskp29) | c2_1(a296)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause41')).
% 0.92/1.09 tff(2214,plain,
% 0.92/1.09 ((~hskp29) | c2_1(a296)),
% 0.92/1.09 inference(modus_ponens,[status(thm)],[2213, 2212])).
% 0.92/1.09 tff(2215,plain,
% 0.92/1.09 ((~hskp29) | c2_1(a296)),
% 0.92/1.09 inference(modus_ponens,[status(thm)],[2214, 2212])).
% 0.92/1.09 tff(2216,plain,
% 0.92/1.09 ((~hskp29) | c2_1(a296)),
% 0.92/1.09 inference(modus_ponens,[status(thm)],[2215, 2212])).
% 0.92/1.09 tff(2217,plain,
% 0.92/1.09 ((~hskp29) | c2_1(a296)),
% 0.92/1.09 inference(modus_ponens,[status(thm)],[2216, 2212])).
% 0.92/1.09 tff(2218,plain,
% 0.92/1.09 ((~hskp29) | c2_1(a296)),
% 0.92/1.09 inference(modus_ponens,[status(thm)],[2217, 2212])).
% 0.92/1.09 tff(2219,plain,
% 0.92/1.09 (c2_1(a296)),
% 0.92/1.09 inference(unit_resolution,[status(thm)],[2218, 2203])).
% 0.92/1.09 tff(2220,plain,
% 0.92/1.09 (((~hskp29) | c0_1(a296)) <=> ((~hskp29) | c0_1(a296))),
% 0.92/1.09 inference(rewrite,[status(thm)],[])).
% 0.92/1.09 tff(2221,axiom,((~hskp29) | c0_1(a296)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause40')).
% 0.92/1.09 tff(2222,plain,
% 0.92/1.09 ((~hskp29) | c0_1(a296)),
% 0.92/1.09 inference(modus_ponens,[status(thm)],[2221, 2220])).
% 0.92/1.09 tff(2223,plain,
% 0.92/1.09 ((~hskp29) | c0_1(a296)),
% 0.92/1.09 inference(modus_ponens,[status(thm)],[2222, 2220])).
% 0.92/1.09 tff(2224,plain,
% 0.92/1.09 ((~hskp29) | c0_1(a296)),
% 0.92/1.09 inference(modus_ponens,[status(thm)],[2223, 2220])).
% 0.92/1.09 tff(2225,plain,
% 0.92/1.09 ((~hskp29) | c0_1(a296)),
% 0.92/1.09 inference(modus_ponens,[status(thm)],[2224, 2220])).
% 0.92/1.09 tff(2226,plain,
% 0.92/1.09 ((~hskp29) | c0_1(a296)),
% 0.92/1.09 inference(modus_ponens,[status(thm)],[2225, 2220])).
% 0.92/1.09 tff(2227,plain,
% 0.92/1.09 (c0_1(a296)),
% 0.92/1.09 inference(unit_resolution,[status(thm)],[2226, 2203])).
% 0.92/1.09 tff(2228,plain,
% 0.92/1.09 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | (c0_1(a320) | c1_1(a252) | (~ndr1_0) | (~c2_1(a296)) | (~c3_1(a296)) | (~c0_1(a296)) | c3_1(a252) | (~c2_1(a252)) | (~c2_1(a320)) | (~c3_1(a320)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | c0_1(a320) | c1_1(a252) | (~ndr1_0) | (~c2_1(a296)) | (~c3_1(a296)) | (~c0_1(a296)) | c3_1(a252) | (~c2_1(a252)) | (~c2_1(a320)) | (~c3_1(a320)))),
% 0.92/1.09 inference(rewrite,[status(thm)],[])).
% 0.92/1.09 tff(2229,plain,
% 0.92/1.09 (((~ndr1_0) | (~c2_1(a296)) | (~c3_1(a296)) | (~c0_1(a296)) | c3_1(a252) | c1_1(a252) | (~c2_1(a252)) | c0_1(a320) | (~c2_1(a320)) | (~c3_1(a320))) <=> (c0_1(a320) | c1_1(a252) | (~ndr1_0) | (~c2_1(a296)) | (~c3_1(a296)) | (~c0_1(a296)) | c3_1(a252) | (~c2_1(a252)) | (~c2_1(a320)) | (~c3_1(a320)))),
% 0.92/1.09 inference(rewrite,[status(thm)],[])).
% 0.92/1.09 tff(2230,plain,
% 0.92/1.09 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a296)) | (~c3_1(a296)) | (~c0_1(a296)) | c3_1(a252) | c1_1(a252) | (~c2_1(a252)) | c0_1(a320) | (~c2_1(a320)) | (~c3_1(a320)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | (c0_1(a320) | c1_1(a252) | (~ndr1_0) | (~c2_1(a296)) | (~c3_1(a296)) | (~c0_1(a296)) | c3_1(a252) | (~c2_1(a252)) | (~c2_1(a320)) | (~c3_1(a320))))),
% 0.92/1.09 inference(monotonicity,[status(thm)],[2229])).
% 0.92/1.09 tff(2231,plain,
% 0.92/1.09 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a296)) | (~c3_1(a296)) | (~c0_1(a296)) | c3_1(a252) | c1_1(a252) | (~c2_1(a252)) | c0_1(a320) | (~c2_1(a320)) | (~c3_1(a320)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | c0_1(a320) | c1_1(a252) | (~ndr1_0) | (~c2_1(a296)) | (~c3_1(a296)) | (~c0_1(a296)) | c3_1(a252) | (~c2_1(a252)) | (~c2_1(a320)) | (~c3_1(a320)))),
% 0.92/1.09 inference(transitivity,[status(thm)],[2230, 2228])).
% 0.92/1.09 tff(2232,plain,
% 0.92/1.09 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a296)) | (~c3_1(a296)) | (~c0_1(a296)) | c3_1(a252) | c1_1(a252) | (~c2_1(a252)) | c0_1(a320) | (~c2_1(a320)) | (~c3_1(a320)))),
% 0.92/1.09 inference(quant_inst,[status(thm)],[])).
% 0.92/1.09 tff(2233,plain,
% 0.92/1.09 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | c0_1(a320) | c1_1(a252) | (~ndr1_0) | (~c2_1(a296)) | (~c3_1(a296)) | (~c0_1(a296)) | c3_1(a252) | (~c2_1(a252)) | (~c2_1(a320)) | (~c3_1(a320))),
% 0.92/1.09 inference(modus_ponens,[status(thm)],[2232, 2231])).
% 0.92/1.09 tff(2234,plain,
% 0.92/1.09 ($false),
% 0.92/1.09 inference(unit_resolution,[status(thm)],[2233, 110, 2227, 2219, 2211, 337, 329, 1884, 356, 1906, 2186, 2176])).
% 0.92/1.09 tff(2235,plain,(hskp19 | hskp9 | hskp26), inference(lemma,lemma(discharge,[]))).
% 0.92/1.09 tff(2236,plain,
% 0.92/1.09 (hskp19),
% 0.92/1.09 inference(unit_resolution,[status(thm)],[2235, 1, 23])).
% 0.92/1.09 tff(2237,plain,
% 0.92/1.09 (~c0_1(a255)),
% 0.92/1.09 inference(unit_resolution,[status(thm)],[279, 2236])).
% 0.92/1.09 tff(2238,plain,
% 0.92/1.09 (~c3_1(a255)),
% 0.92/1.09 inference(unit_resolution,[status(thm)],[267, 2236])).
% 0.92/1.09 tff(2239,plain,
% 0.92/1.09 (~c1_1(a255)),
% 0.92/1.09 inference(unit_resolution,[status(thm)],[273, 2236])).
% 0.92/1.09 tff(2240,assumption,(~hskp6), introduced(assumption)).
% 0.92/1.09 tff(2241,plain,
% 0.92/1.09 (hskp6 | c2_1(a255)),
% 0.92/1.09 inference(unit_resolution,[status(thm)],[1576, 110, 45, 1097, 1114, 1569])).
% 0.92/1.09 tff(2242,plain,
% 0.92/1.09 (c2_1(a255)),
% 0.92/1.09 inference(unit_resolution,[status(thm)],[2241, 2240])).
% 0.92/1.09 tff(2243,plain,
% 0.92/1.09 (^[U: $i] : refl((hskp3 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) <=> (hskp3 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))))),
% 0.92/1.09 inference(bind,[status(th)],[])).
% 0.92/1.09 tff(2244,plain,
% 0.92/1.09 (![U: $i] : (hskp3 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) <=> ![U: $i] : (hskp3 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 0.92/1.09 inference(quant_intro,[status(thm)],[2243])).
% 0.92/1.09 tff(2245,plain,
% 0.92/1.09 (![U: $i] : (hskp3 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) <=> ![U: $i] : (hskp3 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 0.92/1.09 inference(rewrite,[status(thm)],[])).
% 0.92/1.09 tff(2246,plain,
% 0.92/1.09 (^[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)) | hskp3) <=> (((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) | hskp3))), rewrite((((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) | hskp3) <=> (hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))), ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp3) <=> (hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))))), (((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp3) | hskp6) <=> ((hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) | hskp6))), rewrite(((hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) | hskp6) <=> (hskp3 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))), (((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp3) | hskp6) <=> (hskp3 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))))),
% 0.92/1.09 inference(bind,[status(th)],[])).
% 0.92/1.09 tff(2247,plain,
% 0.92/1.09 (![U: $i] : ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp3) | hskp6) <=> ![U: $i] : (hskp3 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 0.92/1.09 inference(quant_intro,[status(thm)],[2246])).
% 0.92/1.09 tff(2248,axiom,(![U: $i] : ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp3) | hskp6)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause137')).
% 0.92/1.09 tff(2249,plain,
% 0.92/1.09 (![U: $i] : (hskp3 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 0.92/1.09 inference(modus_ponens,[status(thm)],[2248, 2247])).
% 0.92/1.09 tff(2250,plain,
% 0.92/1.09 (![U: $i] : (hskp3 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 0.92/1.09 inference(modus_ponens,[status(thm)],[2249, 2245])).
% 0.92/1.09 tff(2251,plain,(
% 0.92/1.09 ![U: $i] : (hskp3 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 0.92/1.09 inference(skolemize,[status(sab)],[2250])).
% 0.92/1.09 tff(2252,plain,
% 0.92/1.09 (![U: $i] : (hskp3 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 0.92/1.09 inference(modus_ponens,[status(thm)],[2251, 2244])).
% 0.92/1.09 tff(2253,plain,
% 0.92/1.09 (((~![U: $i] : (hskp3 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp3 | hskp6 | c0_1(a215) | c1_1(a215) | (~ndr1_0) | (~c2_1(a215)))) <=> ((~![U: $i] : (hskp3 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp3 | hskp6 | c0_1(a215) | c1_1(a215) | (~ndr1_0) | (~c2_1(a215)))),
% 0.92/1.09 inference(rewrite,[status(thm)],[])).
% 0.92/1.09 tff(2254,plain,
% 0.92/1.09 ((hskp3 | hskp6 | (~ndr1_0) | c1_1(a215) | c0_1(a215) | (~c2_1(a215))) <=> (hskp3 | hskp6 | c0_1(a215) | c1_1(a215) | (~ndr1_0) | (~c2_1(a215)))),
% 0.92/1.09 inference(rewrite,[status(thm)],[])).
% 0.92/1.09 tff(2255,plain,
% 0.92/1.09 (((~![U: $i] : (hskp3 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp3 | hskp6 | (~ndr1_0) | c1_1(a215) | c0_1(a215) | (~c2_1(a215)))) <=> ((~![U: $i] : (hskp3 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp3 | hskp6 | c0_1(a215) | c1_1(a215) | (~ndr1_0) | (~c2_1(a215))))),
% 0.92/1.09 inference(monotonicity,[status(thm)],[2254])).
% 0.92/1.09 tff(2256,plain,
% 0.92/1.09 (((~![U: $i] : (hskp3 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp3 | hskp6 | (~ndr1_0) | c1_1(a215) | c0_1(a215) | (~c2_1(a215)))) <=> ((~![U: $i] : (hskp3 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp3 | hskp6 | c0_1(a215) | c1_1(a215) | (~ndr1_0) | (~c2_1(a215)))),
% 0.92/1.09 inference(transitivity,[status(thm)],[2255, 2253])).
% 0.92/1.09 tff(2257,plain,
% 0.92/1.09 ((~![U: $i] : (hskp3 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp3 | hskp6 | (~ndr1_0) | c1_1(a215) | c0_1(a215) | (~c2_1(a215)))),
% 0.92/1.09 inference(quant_inst,[status(thm)],[])).
% 0.92/1.09 tff(2258,plain,
% 0.92/1.09 ((~![U: $i] : (hskp3 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp3 | hskp6 | c0_1(a215) | c1_1(a215) | (~ndr1_0) | (~c2_1(a215))),
% 0.92/1.09 inference(modus_ponens,[status(thm)],[2257, 2256])).
% 0.92/1.09 tff(2259,plain,
% 0.92/1.09 (hskp3 | hskp6),
% 0.92/1.09 inference(unit_resolution,[status(thm)],[2258, 110, 152, 151, 150, 2252])).
% 0.92/1.09 tff(2260,plain,
% 0.92/1.09 (hskp3),
% 0.92/1.09 inference(unit_resolution,[status(thm)],[2259, 2240])).
% 0.92/1.09 tff(2261,plain,
% 0.92/1.09 (~c2_1(a216)),
% 0.92/1.09 inference(unit_resolution,[status(thm)],[241, 2260])).
% 0.92/1.09 tff(2262,plain,
% 0.92/1.09 (c0_1(a216)),
% 0.92/1.09 inference(unit_resolution,[status(thm)],[218, 2260])).
% 0.92/1.09 tff(2263,plain,
% 0.92/1.09 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | (c1_1(a255) | c3_1(a255) | c1_1(a252) | c2_1(a216) | (~ndr1_0) | (~c3_1(a216)) | (~c0_1(a216)) | c3_1(a252) | (~c0_1(a252)) | (~c2_1(a255)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | c1_1(a255) | c3_1(a255) | c1_1(a252) | c2_1(a216) | (~ndr1_0) | (~c3_1(a216)) | (~c0_1(a216)) | c3_1(a252) | (~c0_1(a252)) | (~c2_1(a255)))),
% 0.92/1.09 inference(rewrite,[status(thm)],[])).
% 0.92/1.09 tff(2264,plain,
% 0.92/1.09 (((~ndr1_0) | c2_1(a216) | (~c3_1(a216)) | (~c0_1(a216)) | c3_1(a255) | c1_1(a255) | (~c2_1(a255)) | c3_1(a252) | c1_1(a252) | (~c0_1(a252))) <=> (c1_1(a255) | c3_1(a255) | c1_1(a252) | c2_1(a216) | (~ndr1_0) | (~c3_1(a216)) | (~c0_1(a216)) | c3_1(a252) | (~c0_1(a252)) | (~c2_1(a255)))),
% 0.92/1.09 inference(rewrite,[status(thm)],[])).
% 0.92/1.09 tff(2265,plain,
% 0.92/1.09 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a216) | (~c3_1(a216)) | (~c0_1(a216)) | c3_1(a255) | c1_1(a255) | (~c2_1(a255)) | c3_1(a252) | c1_1(a252) | (~c0_1(a252)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | (c1_1(a255) | c3_1(a255) | c1_1(a252) | c2_1(a216) | (~ndr1_0) | (~c3_1(a216)) | (~c0_1(a216)) | c3_1(a252) | (~c0_1(a252)) | (~c2_1(a255))))),
% 0.92/1.09 inference(monotonicity,[status(thm)],[2264])).
% 0.92/1.09 tff(2266,plain,
% 0.92/1.09 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a216) | (~c3_1(a216)) | (~c0_1(a216)) | c3_1(a255) | c1_1(a255) | (~c2_1(a255)) | c3_1(a252) | c1_1(a252) | (~c0_1(a252)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | c1_1(a255) | c3_1(a255) | c1_1(a252) | c2_1(a216) | (~ndr1_0) | (~c3_1(a216)) | (~c0_1(a216)) | c3_1(a252) | (~c0_1(a252)) | (~c2_1(a255)))),
% 0.92/1.09 inference(transitivity,[status(thm)],[2265, 2263])).
% 0.92/1.09 tff(2267,plain,
% 0.92/1.09 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a216) | (~c3_1(a216)) | (~c0_1(a216)) | c3_1(a255) | c1_1(a255) | (~c2_1(a255)) | c3_1(a252) | c1_1(a252) | (~c0_1(a252)))),
% 0.92/1.09 inference(quant_inst,[status(thm)],[])).
% 0.92/1.09 tff(2268,plain,
% 0.92/1.09 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | c1_1(a255) | c3_1(a255) | c1_1(a252) | c2_1(a216) | (~ndr1_0) | (~c3_1(a216)) | (~c0_1(a216)) | c3_1(a252) | (~c0_1(a252)) | (~c2_1(a255))),
% 0.92/1.09 inference(modus_ponens,[status(thm)],[2267, 2266])).
% 0.92/1.09 tff(2269,plain,
% 0.92/1.09 (~c3_1(a216)),
% 0.92/1.09 inference(unit_resolution,[status(thm)],[2268, 110, 1892, 2262, 1096, 1114, 1906, 2261, 22, 2242, 12])).
% 0.92/1.09 tff(2270,assumption,(~hskp7), introduced(assumption)).
% 0.92/1.09 tff(2271,plain,
% 0.92/1.09 (^[U: $i] : refl((hskp7 | hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) <=> (hskp7 | hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))))),
% 0.92/1.09 inference(bind,[status(th)],[])).
% 0.92/1.09 tff(2272,plain,
% 0.92/1.09 (![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 0.92/1.09 inference(quant_intro,[status(thm)],[2271])).
% 0.92/1.09 tff(2273,plain,
% 0.92/1.09 (![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 0.92/1.09 inference(rewrite,[status(thm)],[])).
% 0.92/1.09 tff(2274,plain,
% 0.92/1.09 (^[U: $i] : 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)) | c3_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp7) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) | hskp7))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) | hskp7) <=> (hskp7 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp7) <=> (hskp7 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp7) | hskp6) <=> ((hskp7 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) | hskp6))), rewrite(((hskp7 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) | hskp6) <=> (hskp7 | hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp7) | hskp6) <=> (hskp7 | hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))))),
% 0.92/1.09 inference(bind,[status(th)],[])).
% 0.92/1.09 tff(2275,plain,
% 0.92/1.09 (![U: $i] : ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp7) | hskp6) <=> ![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 0.92/1.09 inference(quant_intro,[status(thm)],[2274])).
% 0.92/1.09 tff(2276,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp7) | hskp6)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause153')).
% 0.92/1.09 tff(2277,plain,
% 0.92/1.09 (![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 0.92/1.09 inference(modus_ponens,[status(thm)],[2276, 2275])).
% 0.92/1.09 tff(2278,plain,
% 0.92/1.09 (![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 0.92/1.09 inference(modus_ponens,[status(thm)],[2277, 2273])).
% 0.92/1.09 tff(2279,plain,(
% 0.92/1.09 ![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 0.92/1.09 inference(skolemize,[status(sab)],[2278])).
% 0.92/1.09 tff(2280,plain,
% 0.92/1.09 (![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 0.92/1.09 inference(modus_ponens,[status(thm)],[2279, 2272])).
% 0.92/1.09 tff(2281,plain,
% 0.92/1.09 (((~![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp7 | hskp6 | c3_1(a237) | (~ndr1_0) | (~c2_1(a237)) | (~c0_1(a237)))) <=> ((~![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp7 | hskp6 | c3_1(a237) | (~ndr1_0) | (~c2_1(a237)) | (~c0_1(a237)))),
% 0.92/1.09 inference(rewrite,[status(thm)],[])).
% 0.92/1.09 tff(2282,plain,
% 0.92/1.09 ((hskp7 | hskp6 | (~ndr1_0) | c3_1(a237) | (~c2_1(a237)) | (~c0_1(a237))) <=> (hskp7 | hskp6 | c3_1(a237) | (~ndr1_0) | (~c2_1(a237)) | (~c0_1(a237)))),
% 0.92/1.09 inference(rewrite,[status(thm)],[])).
% 0.92/1.09 tff(2283,plain,
% 0.92/1.09 (((~![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp7 | hskp6 | (~ndr1_0) | c3_1(a237) | (~c2_1(a237)) | (~c0_1(a237)))) <=> ((~![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp7 | hskp6 | c3_1(a237) | (~ndr1_0) | (~c2_1(a237)) | (~c0_1(a237))))),
% 0.92/1.09 inference(monotonicity,[status(thm)],[2282])).
% 0.92/1.09 tff(2284,plain,
% 0.92/1.09 (((~![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp7 | hskp6 | (~ndr1_0) | c3_1(a237) | (~c2_1(a237)) | (~c0_1(a237)))) <=> ((~![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp7 | hskp6 | c3_1(a237) | (~ndr1_0) | (~c2_1(a237)) | (~c0_1(a237)))),
% 0.92/1.09 inference(transitivity,[status(thm)],[2283, 2281])).
% 0.92/1.09 tff(2285,plain,
% 0.92/1.09 ((~![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp7 | hskp6 | (~ndr1_0) | c3_1(a237) | (~c2_1(a237)) | (~c0_1(a237)))),
% 0.92/1.09 inference(quant_inst,[status(thm)],[])).
% 0.92/1.09 tff(2286,plain,
% 0.92/1.09 ((~![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp7 | hskp6 | c3_1(a237) | (~ndr1_0) | (~c2_1(a237)) | (~c0_1(a237))),
% 0.92/1.09 inference(modus_ponens,[status(thm)],[2285, 2284])).
% 0.92/1.09 tff(2287,plain,
% 0.92/1.09 (hskp7 | (~c2_1(a237)) | (~c0_1(a237))),
% 0.92/1.09 inference(unit_resolution,[status(thm)],[2286, 110, 2240, 164, 2280])).
% 0.92/1.09 tff(2288,plain,
% 0.92/1.09 ($false),
% 0.92/1.09 inference(unit_resolution,[status(thm)],[2287, 698, 699, 2270])).
% 0.92/1.09 tff(2289,plain,((~hskp12) | hskp7 | hskp6 | c3_1(a237)), inference(lemma,lemma(discharge,[]))).
% 0.92/1.09 tff(2290,plain,
% 0.92/1.09 (hskp7),
% 0.92/1.09 inference(unit_resolution,[status(thm)],[2289, 2240, 691, 164])).
% 0.92/1.09 tff(2291,plain,
% 0.92/1.09 (((~hskp7) | (~c0_1(a223))) <=> ((~hskp7) | (~c0_1(a223)))),
% 0.92/1.09 inference(rewrite,[status(thm)],[])).
% 0.92/1.09 tff(2292,plain,
% 0.92/1.09 (((~c0_1(a223)) | (~hskp7)) <=> ((~hskp7) | (~c0_1(a223)))),
% 0.92/1.09 inference(rewrite,[status(thm)],[])).
% 0.92/1.09 tff(2293,axiom,((~c0_1(a223)) | (~hskp7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause116')).
% 0.92/1.09 tff(2294,plain,
% 0.92/1.09 ((~hskp7) | (~c0_1(a223))),
% 0.92/1.09 inference(modus_ponens,[status(thm)],[2293, 2292])).
% 0.92/1.09 tff(2295,plain,
% 0.92/1.09 ((~hskp7) | (~c0_1(a223))),
% 0.92/1.09 inference(modus_ponens,[status(thm)],[2294, 2291])).
% 0.92/1.09 tff(2296,plain,
% 0.92/1.09 (~c0_1(a223)),
% 0.92/1.09 inference(unit_resolution,[status(thm)],[2295, 2290])).
% 0.92/1.09 tff(2297,plain,
% 0.92/1.09 (((~hskp7) | c2_1(a223)) <=> ((~hskp7) | c2_1(a223))),
% 0.92/1.09 inference(rewrite,[status(thm)],[])).
% 0.92/1.09 tff(2298,axiom,((~hskp7) | c2_1(a223)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause77')).
% 0.92/1.09 tff(2299,plain,
% 0.92/1.09 ((~hskp7) | c2_1(a223)),
% 0.92/1.09 inference(modus_ponens,[status(thm)],[2298, 2297])).
% 0.92/1.09 tff(2300,plain,
% 0.92/1.09 ((~hskp7) | c2_1(a223)),
% 0.92/1.09 inference(modus_ponens,[status(thm)],[2299, 2297])).
% 0.92/1.09 tff(2301,plain,
% 0.92/1.09 ((~hskp7) | c2_1(a223)),
% 0.92/1.09 inference(modus_ponens,[status(thm)],[2300, 2297])).
% 0.92/1.09 tff(2302,plain,
% 0.92/1.09 ((~hskp7) | c2_1(a223)),
% 0.92/1.09 inference(modus_ponens,[status(thm)],[2301, 2297])).
% 0.92/1.09 tff(2303,plain,
% 0.92/1.09 ((~hskp7) | c2_1(a223)),
% 0.92/1.09 inference(modus_ponens,[status(thm)],[2302, 2297])).
% 0.92/1.09 tff(2304,plain,
% 0.92/1.09 (c2_1(a223)),
% 0.92/1.09 inference(unit_resolution,[status(thm)],[2303, 2290])).
% 0.92/1.09 tff(2305,plain,
% 0.92/1.09 (((~hskp7) | c1_1(a223)) <=> ((~hskp7) | c1_1(a223))),
% 0.92/1.09 inference(rewrite,[status(thm)],[])).
% 0.92/1.09 tff(2306,axiom,((~hskp7) | c1_1(a223)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause76')).
% 0.92/1.09 tff(2307,plain,
% 0.92/1.09 ((~hskp7) | c1_1(a223)),
% 0.92/1.09 inference(modus_ponens,[status(thm)],[2306, 2305])).
% 0.92/1.09 tff(2308,plain,
% 0.92/1.09 ((~hskp7) | c1_1(a223)),
% 0.92/1.09 inference(modus_ponens,[status(thm)],[2307, 2305])).
% 0.92/1.09 tff(2309,plain,
% 0.92/1.09 ((~hskp7) | c1_1(a223)),
% 0.92/1.09 inference(modus_ponens,[status(thm)],[2308, 2305])).
% 0.92/1.09 tff(2310,plain,
% 0.92/1.09 ((~hskp7) | c1_1(a223)),
% 0.92/1.09 inference(modus_ponens,[status(thm)],[2309, 2305])).
% 0.92/1.09 tff(2311,plain,
% 0.92/1.09 ((~hskp7) | c1_1(a223)),
% 0.92/1.09 inference(modus_ponens,[status(thm)],[2310, 2305])).
% 0.92/1.09 tff(2312,plain,
% 0.92/1.09 (c1_1(a223)),
% 0.92/1.09 inference(unit_resolution,[status(thm)],[2311, 2290])).
% 0.92/1.09 tff(2313,plain,
% 0.92/1.09 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp26 | c0_1(a223) | c2_1(a216) | (~ndr1_0) | c3_1(a216) | (~c0_1(a216)) | (~c2_1(a223)) | (~c1_1(a223)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp26 | c0_1(a223) | c2_1(a216) | (~ndr1_0) | c3_1(a216) | (~c0_1(a216)) | (~c2_1(a223)) | (~c1_1(a223)))),
% 0.92/1.09 inference(rewrite,[status(thm)],[])).
% 0.92/1.09 tff(2314,plain,
% 0.92/1.09 ((hskp26 | (~ndr1_0) | c2_1(a216) | c3_1(a216) | (~c0_1(a216)) | c0_1(a223) | (~c1_1(a223)) | (~c2_1(a223))) <=> (hskp26 | c0_1(a223) | c2_1(a216) | (~ndr1_0) | c3_1(a216) | (~c0_1(a216)) | (~c2_1(a223)) | (~c1_1(a223)))),
% 0.92/1.09 inference(rewrite,[status(thm)],[])).
% 0.92/1.09 tff(2315,plain,
% 0.92/1.09 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp26 | (~ndr1_0) | c2_1(a216) | c3_1(a216) | (~c0_1(a216)) | c0_1(a223) | (~c1_1(a223)) | (~c2_1(a223)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp26 | c0_1(a223) | c2_1(a216) | (~ndr1_0) | c3_1(a216) | (~c0_1(a216)) | (~c2_1(a223)) | (~c1_1(a223))))),
% 0.92/1.09 inference(monotonicity,[status(thm)],[2314])).
% 0.92/1.09 tff(2316,plain,
% 0.92/1.09 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp26 | (~ndr1_0) | c2_1(a216) | c3_1(a216) | (~c0_1(a216)) | c0_1(a223) | (~c1_1(a223)) | (~c2_1(a223)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp26 | c0_1(a223) | c2_1(a216) | (~ndr1_0) | c3_1(a216) | (~c0_1(a216)) | (~c2_1(a223)) | (~c1_1(a223)))),
% 0.92/1.09 inference(transitivity,[status(thm)],[2315, 2313])).
% 0.92/1.09 tff(2317,plain,
% 0.92/1.09 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp26 | (~ndr1_0) | c2_1(a216) | c3_1(a216) | (~c0_1(a216)) | c0_1(a223) | (~c1_1(a223)) | (~c2_1(a223)))),
% 0.92/1.09 inference(quant_inst,[status(thm)],[])).
% 0.92/1.09 tff(2318,plain,
% 0.92/1.09 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp26 | c0_1(a223) | c2_1(a216) | (~ndr1_0) | c3_1(a216) | (~c0_1(a216)) | (~c2_1(a223)) | (~c1_1(a223))),
% 0.92/1.09 inference(modus_ponens,[status(thm)],[2317, 2316])).
% 0.92/1.09 tff(2319,plain,
% 0.92/1.09 ($false),
% 0.92/1.09 inference(unit_resolution,[status(thm)],[2318, 110, 1, 2312, 2304, 2262, 2296, 2261, 1542, 2269])).
% 0.92/1.09 tff(2320,plain,(hskp6 | hskp26 | c1_1(a255) | c3_1(a255) | c3_1(a252) | hskp5 | c0_1(a255) | (~c2_1(a215)) | c0_1(a215) | c1_1(a215) | (~hskp12) | c3_1(a237)), inference(lemma,lemma(discharge,[]))).
% 0.92/1.09 tff(2321,plain,
% 0.92/1.09 (hskp6),
% 0.92/1.09 inference(unit_resolution,[status(thm)],[2320, 12, 2239, 2238, 1, 45, 2237, 152, 151, 150, 691, 164])).
% 0.92/1.09 tff(2322,plain,
% 0.92/1.09 (~c3_1(a220)),
% 0.92/1.09 inference(unit_resolution,[status(thm)],[449, 2321])).
% 0.92/1.09 tff(2323,assumption,(~hskp10), introduced(assumption)).
% 0.92/1.09 tff(2324,plain,
% 0.92/1.09 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp10 | c0_1(a255) | c3_1(a255) | c1_1(a252) | (~ndr1_0) | (~c0_1(a252)) | (~c2_1(a252)) | (~c2_1(a255)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp10 | c0_1(a255) | c3_1(a255) | c1_1(a252) | (~ndr1_0) | (~c0_1(a252)) | (~c2_1(a252)) | (~c2_1(a255)))),
% 0.92/1.09 inference(rewrite,[status(thm)],[])).
% 0.92/1.09 tff(2325,plain,
% 0.92/1.09 ((hskp10 | (~ndr1_0) | c1_1(a252) | (~c2_1(a252)) | (~c0_1(a252)) | c3_1(a255) | c0_1(a255) | (~c2_1(a255))) <=> (hskp10 | c0_1(a255) | c3_1(a255) | c1_1(a252) | (~ndr1_0) | (~c0_1(a252)) | (~c2_1(a252)) | (~c2_1(a255)))),
% 0.92/1.10 inference(rewrite,[status(thm)],[])).
% 0.92/1.10 tff(2326,plain,
% 0.92/1.10 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp10 | (~ndr1_0) | c1_1(a252) | (~c2_1(a252)) | (~c0_1(a252)) | c3_1(a255) | c0_1(a255) | (~c2_1(a255)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp10 | c0_1(a255) | c3_1(a255) | c1_1(a252) | (~ndr1_0) | (~c0_1(a252)) | (~c2_1(a252)) | (~c2_1(a255))))),
% 0.92/1.10 inference(monotonicity,[status(thm)],[2325])).
% 0.92/1.10 tff(2327,plain,
% 0.92/1.10 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp10 | (~ndr1_0) | c1_1(a252) | (~c2_1(a252)) | (~c0_1(a252)) | c3_1(a255) | c0_1(a255) | (~c2_1(a255)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp10 | c0_1(a255) | c3_1(a255) | c1_1(a252) | (~ndr1_0) | (~c0_1(a252)) | (~c2_1(a252)) | (~c2_1(a255)))),
% 0.92/1.10 inference(transitivity,[status(thm)],[2326, 2324])).
% 0.92/1.10 tff(2328,plain,
% 0.92/1.10 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp10 | (~ndr1_0) | c1_1(a252) | (~c2_1(a252)) | (~c0_1(a252)) | c3_1(a255) | c0_1(a255) | (~c2_1(a255)))),
% 0.92/1.10 inference(quant_inst,[status(thm)],[])).
% 0.92/1.10 tff(2329,plain,
% 0.92/1.10 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp10 | c0_1(a255) | c3_1(a255) | c1_1(a252) | (~ndr1_0) | (~c0_1(a252)) | (~c2_1(a252)) | (~c2_1(a255))),
% 0.92/1.10 inference(modus_ponens,[status(thm)],[2328, 2327])).
% 0.92/1.10 tff(2330,plain,
% 0.92/1.10 (hskp10 | (~c2_1(a255))),
% 0.92/1.10 inference(unit_resolution,[status(thm)],[2329, 110, 1892, 1884, 1097, 1114, 1906, 11])).
% 0.92/1.10 tff(2331,plain,
% 0.92/1.10 (~c2_1(a255)),
% 0.92/1.10 inference(unit_resolution,[status(thm)],[2330, 2323])).
% 0.92/1.10 tff(2332,plain,
% 0.92/1.10 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | (c0_1(a255) | c3_1(a255) | c1_1(a252) | c0_1(a215) | c1_1(a215) | (~ndr1_0) | (~c3_1(a215)) | c3_1(a252) | (~c0_1(a252)) | c2_1(a255))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c0_1(a255) | c3_1(a255) | c1_1(a252) | c0_1(a215) | c1_1(a215) | (~ndr1_0) | (~c3_1(a215)) | c3_1(a252) | (~c0_1(a252)) | c2_1(a255))),
% 0.92/1.10 inference(rewrite,[status(thm)],[])).
% 0.92/1.10 tff(2333,plain,
% 0.92/1.10 (((~ndr1_0) | c1_1(a252) | c3_1(a252) | (~c0_1(a252)) | c1_1(a215) | c0_1(a215) | (~c3_1(a215)) | c3_1(a255) | c2_1(a255) | c0_1(a255)) <=> (c0_1(a255) | c3_1(a255) | c1_1(a252) | c0_1(a215) | c1_1(a215) | (~ndr1_0) | (~c3_1(a215)) | c3_1(a252) | (~c0_1(a252)) | c2_1(a255))),
% 0.92/1.10 inference(rewrite,[status(thm)],[])).
% 0.92/1.10 tff(2334,plain,
% 0.92/1.10 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a252) | c3_1(a252) | (~c0_1(a252)) | c1_1(a215) | c0_1(a215) | (~c3_1(a215)) | c3_1(a255) | c2_1(a255) | c0_1(a255))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | (c0_1(a255) | c3_1(a255) | c1_1(a252) | c0_1(a215) | c1_1(a215) | (~ndr1_0) | (~c3_1(a215)) | c3_1(a252) | (~c0_1(a252)) | c2_1(a255)))),
% 0.92/1.10 inference(monotonicity,[status(thm)],[2333])).
% 0.92/1.10 tff(2335,plain,
% 0.92/1.10 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a252) | c3_1(a252) | (~c0_1(a252)) | c1_1(a215) | c0_1(a215) | (~c3_1(a215)) | c3_1(a255) | c2_1(a255) | c0_1(a255))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c0_1(a255) | c3_1(a255) | c1_1(a252) | c0_1(a215) | c1_1(a215) | (~ndr1_0) | (~c3_1(a215)) | c3_1(a252) | (~c0_1(a252)) | c2_1(a255))),
% 0.92/1.10 inference(transitivity,[status(thm)],[2334, 2332])).
% 0.92/1.10 tff(2336,plain,
% 0.92/1.10 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a252) | c3_1(a252) | (~c0_1(a252)) | c1_1(a215) | c0_1(a215) | (~c3_1(a215)) | c3_1(a255) | c2_1(a255) | c0_1(a255))),
% 0.92/1.10 inference(quant_inst,[status(thm)],[])).
% 0.92/1.10 tff(2337,plain,
% 0.92/1.10 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c0_1(a255) | c3_1(a255) | c1_1(a252) | c0_1(a215) | c1_1(a215) | (~ndr1_0) | (~c3_1(a215)) | c3_1(a252) | (~c0_1(a252)) | c2_1(a255)),
% 0.92/1.10 inference(modus_ponens,[status(thm)],[2336, 2335])).
% 0.92/1.10 tff(2338,plain,
% 0.92/1.10 ((~c3_1(a215)) | c3_1(a252) | c2_1(a255)),
% 0.92/1.10 inference(unit_resolution,[status(thm)],[2337, 110, 1892, 1097, 1114, 1906, 151, 150, 1419])).
% 0.92/1.10 tff(2339,plain,
% 0.92/1.10 (~c3_1(a215)),
% 0.92/1.10 inference(unit_resolution,[status(thm)],[2338, 2331, 12])).
% 0.92/1.10 tff(2340,plain,
% 0.92/1.10 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp10 | c1_1(a252) | c0_1(a215) | (~ndr1_0) | c3_1(a215) | (~c2_1(a215)) | (~c0_1(a252)) | (~c2_1(a252)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp10 | c1_1(a252) | c0_1(a215) | (~ndr1_0) | c3_1(a215) | (~c2_1(a215)) | (~c0_1(a252)) | (~c2_1(a252)))),
% 0.92/1.10 inference(rewrite,[status(thm)],[])).
% 0.92/1.10 tff(2341,plain,
% 0.92/1.10 ((hskp10 | (~ndr1_0) | c1_1(a252) | (~c2_1(a252)) | (~c0_1(a252)) | c3_1(a215) | c0_1(a215) | (~c2_1(a215))) <=> (hskp10 | c1_1(a252) | c0_1(a215) | (~ndr1_0) | c3_1(a215) | (~c2_1(a215)) | (~c0_1(a252)) | (~c2_1(a252)))),
% 0.92/1.10 inference(rewrite,[status(thm)],[])).
% 0.92/1.10 tff(2342,plain,
% 0.92/1.10 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp10 | (~ndr1_0) | c1_1(a252) | (~c2_1(a252)) | (~c0_1(a252)) | c3_1(a215) | c0_1(a215) | (~c2_1(a215)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp10 | c1_1(a252) | c0_1(a215) | (~ndr1_0) | c3_1(a215) | (~c2_1(a215)) | (~c0_1(a252)) | (~c2_1(a252))))),
% 0.92/1.10 inference(monotonicity,[status(thm)],[2341])).
% 0.92/1.10 tff(2343,plain,
% 0.92/1.10 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp10 | (~ndr1_0) | c1_1(a252) | (~c2_1(a252)) | (~c0_1(a252)) | c3_1(a215) | c0_1(a215) | (~c2_1(a215)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp10 | c1_1(a252) | c0_1(a215) | (~ndr1_0) | c3_1(a215) | (~c2_1(a215)) | (~c0_1(a252)) | (~c2_1(a252)))),
% 0.92/1.10 inference(transitivity,[status(thm)],[2342, 2340])).
% 0.92/1.10 tff(2344,plain,
% 0.92/1.10 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp10 | (~ndr1_0) | c1_1(a252) | (~c2_1(a252)) | (~c0_1(a252)) | c3_1(a215) | c0_1(a215) | (~c2_1(a215)))),
% 0.92/1.10 inference(quant_inst,[status(thm)],[])).
% 0.92/1.10 tff(2345,plain,
% 0.92/1.10 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp10 | c1_1(a252) | c0_1(a215) | (~ndr1_0) | c3_1(a215) | (~c2_1(a215)) | (~c0_1(a252)) | (~c2_1(a252))),
% 0.92/1.10 inference(modus_ponens,[status(thm)],[2344, 2343])).
% 0.92/1.10 tff(2346,plain,
% 0.92/1.10 ($false),
% 0.92/1.10 inference(unit_resolution,[status(thm)],[2345, 110, 2323, 1892, 1884, 152, 1906, 151, 11, 2339])).
% 0.92/1.10 tff(2347,plain,(hskp10 | (~c2_1(a215)) | c0_1(a215) | c3_1(a252) | c0_1(a255) | c3_1(a255) | c1_1(a215)), inference(lemma,lemma(discharge,[]))).
% 0.92/1.10 tff(2348,plain,
% 0.92/1.10 (hskp10),
% 0.92/1.10 inference(unit_resolution,[status(thm)],[2347, 12, 151, 152, 2237, 2238, 150])).
% 0.92/1.10 tff(2349,plain,
% 0.92/1.10 (~c0_1(a231)),
% 0.92/1.10 inference(unit_resolution,[status(thm)],[1314, 2348])).
% 0.92/1.10 tff(2350,plain,
% 0.92/1.10 (c2_1(a220)),
% 0.92/1.10 inference(unit_resolution,[status(thm)],[493, 2321])).
% 0.92/1.10 tff(2351,plain,
% 0.92/1.10 (c1_1(a220)),
% 0.92/1.10 inference(unit_resolution,[status(thm)],[485, 2321])).
% 0.92/1.10 tff(2352,plain,
% 0.92/1.10 (c3_1(a231)),
% 0.92/1.10 inference(unit_resolution,[status(thm)],[1341, 2348])).
% 0.92/1.10 tff(2353,plain,
% 0.92/1.10 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp5 | c0_1(a231) | c3_1(a220) | (~ndr1_0) | (~c2_1(a220)) | (~c1_1(a220)) | c2_1(a231) | (~c3_1(a231)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp5 | c0_1(a231) | c3_1(a220) | (~ndr1_0) | (~c2_1(a220)) | (~c1_1(a220)) | c2_1(a231) | (~c3_1(a231)))),
% 0.92/1.10 inference(rewrite,[status(thm)],[])).
% 0.92/1.10 tff(2354,plain,
% 0.92/1.10 ((hskp5 | (~ndr1_0) | c3_1(a220) | (~c2_1(a220)) | (~c1_1(a220)) | c0_1(a231) | c2_1(a231) | (~c3_1(a231))) <=> (hskp5 | c0_1(a231) | c3_1(a220) | (~ndr1_0) | (~c2_1(a220)) | (~c1_1(a220)) | c2_1(a231) | (~c3_1(a231)))),
% 0.92/1.10 inference(rewrite,[status(thm)],[])).
% 0.92/1.10 tff(2355,plain,
% 0.92/1.10 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp5 | (~ndr1_0) | c3_1(a220) | (~c2_1(a220)) | (~c1_1(a220)) | c0_1(a231) | c2_1(a231) | (~c3_1(a231)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp5 | c0_1(a231) | c3_1(a220) | (~ndr1_0) | (~c2_1(a220)) | (~c1_1(a220)) | c2_1(a231) | (~c3_1(a231))))),
% 0.92/1.10 inference(monotonicity,[status(thm)],[2354])).
% 0.92/1.10 tff(2356,plain,
% 0.92/1.10 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp5 | (~ndr1_0) | c3_1(a220) | (~c2_1(a220)) | (~c1_1(a220)) | c0_1(a231) | c2_1(a231) | (~c3_1(a231)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp5 | c0_1(a231) | c3_1(a220) | (~ndr1_0) | (~c2_1(a220)) | (~c1_1(a220)) | c2_1(a231) | (~c3_1(a231)))),
% 0.92/1.10 inference(transitivity,[status(thm)],[2355, 2353])).
% 0.92/1.10 tff(2357,plain,
% 0.92/1.10 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp5 | (~ndr1_0) | c3_1(a220) | (~c2_1(a220)) | (~c1_1(a220)) | c0_1(a231) | c2_1(a231) | (~c3_1(a231)))),
% 0.92/1.10 inference(quant_inst,[status(thm)],[])).
% 0.92/1.10 tff(2358,plain,
% 0.92/1.10 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp5 | c0_1(a231) | c3_1(a220) | (~ndr1_0) | (~c2_1(a220)) | (~c1_1(a220)) | c2_1(a231) | (~c3_1(a231))),
% 0.92/1.10 inference(modus_ponens,[status(thm)],[2357, 2356])).
% 0.92/1.10 tff(2359,plain,
% 0.92/1.10 (c2_1(a231)),
% 0.92/1.10 inference(unit_resolution,[status(thm)],[2358, 110, 45, 2352, 2351, 2350, 2349, 2322, 1799])).
% 0.92/1.10 tff(2360,plain,
% 0.92/1.10 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp9 | c0_1(a255) | c3_1(a255) | c0_1(a231) | (~ndr1_0) | (~c2_1(a231)) | (~c3_1(a231)) | c2_1(a255))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp9 | c0_1(a255) | c3_1(a255) | c0_1(a231) | (~ndr1_0) | (~c2_1(a231)) | (~c3_1(a231)) | c2_1(a255))),
% 0.92/1.10 inference(rewrite,[status(thm)],[])).
% 0.92/1.10 tff(2361,plain,
% 0.92/1.10 ((hskp9 | (~ndr1_0) | c0_1(a231) | (~c2_1(a231)) | (~c3_1(a231)) | c3_1(a255) | c0_1(a255) | c2_1(a255)) <=> (hskp9 | c0_1(a255) | c3_1(a255) | c0_1(a231) | (~ndr1_0) | (~c2_1(a231)) | (~c3_1(a231)) | c2_1(a255))),
% 0.92/1.10 inference(rewrite,[status(thm)],[])).
% 0.92/1.10 tff(2362,plain,
% 0.92/1.10 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp9 | (~ndr1_0) | c0_1(a231) | (~c2_1(a231)) | (~c3_1(a231)) | c3_1(a255) | c0_1(a255) | c2_1(a255))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp9 | c0_1(a255) | c3_1(a255) | c0_1(a231) | (~ndr1_0) | (~c2_1(a231)) | (~c3_1(a231)) | c2_1(a255)))),
% 0.92/1.10 inference(monotonicity,[status(thm)],[2361])).
% 0.92/1.10 tff(2363,plain,
% 0.92/1.10 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp9 | (~ndr1_0) | c0_1(a231) | (~c2_1(a231)) | (~c3_1(a231)) | c3_1(a255) | c0_1(a255) | c2_1(a255))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp9 | c0_1(a255) | c3_1(a255) | c0_1(a231) | (~ndr1_0) | (~c2_1(a231)) | (~c3_1(a231)) | c2_1(a255))),
% 0.92/1.10 inference(transitivity,[status(thm)],[2362, 2360])).
% 0.92/1.10 tff(2364,plain,
% 0.92/1.10 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp9 | (~ndr1_0) | c0_1(a231) | (~c2_1(a231)) | (~c3_1(a231)) | c3_1(a255) | c0_1(a255) | c2_1(a255))),
% 0.92/1.10 inference(quant_inst,[status(thm)],[])).
% 0.92/1.10 tff(2365,plain,
% 0.92/1.10 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp9 | c0_1(a255) | c3_1(a255) | c0_1(a231) | (~ndr1_0) | (~c2_1(a231)) | (~c3_1(a231)) | c2_1(a255)),
% 0.92/1.10 inference(modus_ponens,[status(thm)],[2364, 2363])).
% 0.92/1.10 tff(2366,plain,
% 0.92/1.10 ((~c2_1(a231)) | c2_1(a255)),
% 0.92/1.10 inference(unit_resolution,[status(thm)],[2365, 110, 23, 2352, 2237, 2238, 2349, 905])).
% 0.92/1.10 tff(2367,plain,
% 0.92/1.10 (c2_1(a255)),
% 0.92/1.10 inference(unit_resolution,[status(thm)],[2366, 2359])).
% 0.92/1.10 tff(2368,plain,
% 0.92/1.10 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W))))),
% 0.92/1.10 inference(bind,[status(th)],[])).
% 0.92/1.10 tff(2369,plain,
% 0.92/1.10 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~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)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))),
% 0.92/1.10 inference(quant_intro,[status(thm)],[2368])).
% 0.92/1.10 tff(2370,plain,
% 0.92/1.10 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~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)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))),
% 0.92/1.10 inference(rewrite,[status(thm)],[])).
% 0.92/1.10 tff(2371,plain,
% 0.92/1.10 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~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))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c0_1(V)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c0_1(V))))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c0_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V))))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V))) | (~c2_1(W))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)) | (~c2_1(W)))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)) | (~c2_1(W))))), ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c0_1(W)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)) | (~c2_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)) | (~c2_1(W))) | c0_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)))), ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c0_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W))))), (((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c0_1(W)) | c1_1(W)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W))) | c1_1(W)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W))) | c1_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))), (((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))))),
% 0.92/1.10 inference(bind,[status(th)],[])).
% 0.92/1.10 tff(2372,plain,
% 0.92/1.10 (![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c0_1(W)) | c1_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))),
% 0.92/1.10 inference(quant_intro,[status(thm)],[2371])).
% 0.92/1.10 tff(2373,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c0_1(W)) | c1_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause198')).
% 0.92/1.10 tff(2374,plain,
% 0.92/1.10 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))),
% 0.92/1.10 inference(modus_ponens,[status(thm)],[2373, 2372])).
% 0.92/1.10 tff(2375,plain,
% 0.92/1.10 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))),
% 0.92/1.10 inference(modus_ponens,[status(thm)],[2374, 2370])).
% 0.92/1.10 tff(2376,plain,(
% 0.92/1.10 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))),
% 0.92/1.10 inference(skolemize,[status(sab)],[2375])).
% 0.92/1.10 tff(2377,plain,
% 0.92/1.10 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))),
% 0.92/1.10 inference(modus_ponens,[status(thm)],[2376, 2369])).
% 0.92/1.10 tff(2378,plain,
% 0.92/1.10 (c1_1(a231)),
% 0.92/1.10 inference(unit_resolution,[status(thm)],[604, 2348])).
% 0.92/1.10 tff(2379,plain,
% 0.92/1.10 (((~![U: $i] : (hskp29 | hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | (hskp29 | hskp26 | (~ndr1_0) | (~c2_1(a231)) | (~c1_1(a231)) | (~c3_1(a231)))) <=> ((~![U: $i] : (hskp29 | hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | hskp29 | hskp26 | (~ndr1_0) | (~c2_1(a231)) | (~c1_1(a231)) | (~c3_1(a231)))),
% 0.92/1.10 inference(rewrite,[status(thm)],[])).
% 0.92/1.10 tff(2380,plain,
% 0.92/1.10 ((hskp29 | hskp26 | (~ndr1_0) | (~c2_1(a231)) | (~c3_1(a231)) | (~c1_1(a231))) <=> (hskp29 | hskp26 | (~ndr1_0) | (~c2_1(a231)) | (~c1_1(a231)) | (~c3_1(a231)))),
% 0.92/1.10 inference(rewrite,[status(thm)],[])).
% 0.92/1.10 tff(2381,plain,
% 0.92/1.10 (((~![U: $i] : (hskp29 | hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | (hskp29 | hskp26 | (~ndr1_0) | (~c2_1(a231)) | (~c3_1(a231)) | (~c1_1(a231)))) <=> ((~![U: $i] : (hskp29 | hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | (hskp29 | hskp26 | (~ndr1_0) | (~c2_1(a231)) | (~c1_1(a231)) | (~c3_1(a231))))),
% 0.92/1.10 inference(monotonicity,[status(thm)],[2380])).
% 0.92/1.10 tff(2382,plain,
% 0.92/1.10 (((~![U: $i] : (hskp29 | hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | (hskp29 | hskp26 | (~ndr1_0) | (~c2_1(a231)) | (~c3_1(a231)) | (~c1_1(a231)))) <=> ((~![U: $i] : (hskp29 | hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | hskp29 | hskp26 | (~ndr1_0) | (~c2_1(a231)) | (~c1_1(a231)) | (~c3_1(a231)))),
% 0.92/1.10 inference(transitivity,[status(thm)],[2381, 2379])).
% 0.92/1.10 tff(2383,plain,
% 0.92/1.10 ((~![U: $i] : (hskp29 | hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | (hskp29 | hskp26 | (~ndr1_0) | (~c2_1(a231)) | (~c3_1(a231)) | (~c1_1(a231)))),
% 0.92/1.10 inference(quant_inst,[status(thm)],[])).
% 0.92/1.10 tff(2384,plain,
% 0.92/1.10 ((~![U: $i] : (hskp29 | hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | hskp29 | hskp26 | (~ndr1_0) | (~c2_1(a231)) | (~c1_1(a231)) | (~c3_1(a231))),
% 0.92/1.10 inference(modus_ponens,[status(thm)],[2383, 2382])).
% 0.92/1.10 tff(2385,plain,
% 0.92/1.10 (hskp29 | (~c2_1(a231))),
% 0.92/1.10 inference(unit_resolution,[status(thm)],[2384, 110, 1, 2378, 2352, 2196])).
% 0.92/1.10 tff(2386,plain,
% 0.92/1.10 (hskp29),
% 0.92/1.10 inference(unit_resolution,[status(thm)],[2385, 2359])).
% 0.92/1.10 tff(2387,plain,
% 0.92/1.10 (c3_1(a296)),
% 0.92/1.10 inference(unit_resolution,[status(thm)],[2210, 2386])).
% 0.92/1.10 tff(2388,plain,
% 0.92/1.10 (c2_1(a296)),
% 0.92/1.10 inference(unit_resolution,[status(thm)],[2218, 2386])).
% 0.92/1.10 tff(2389,plain,
% 0.92/1.10 (c0_1(a296)),
% 0.92/1.10 inference(unit_resolution,[status(thm)],[2226, 2386])).
% 0.92/1.10 tff(2390,plain,
% 0.92/1.10 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | (c0_1(a255) | c1_1(a255) | (~ndr1_0) | (~c2_1(a296)) | (~c3_1(a296)) | (~c0_1(a296)) | (~c2_1(a231)) | (~c1_1(a231)) | (~c3_1(a231)) | (~c2_1(a255)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | c0_1(a255) | c1_1(a255) | (~ndr1_0) | (~c2_1(a296)) | (~c3_1(a296)) | (~c0_1(a296)) | (~c2_1(a231)) | (~c1_1(a231)) | (~c3_1(a231)) | (~c2_1(a255)))),
% 0.92/1.10 inference(rewrite,[status(thm)],[])).
% 0.92/1.10 tff(2391,plain,
% 0.92/1.10 (((~ndr1_0) | (~c2_1(a231)) | (~c3_1(a231)) | (~c1_1(a231)) | (~c3_1(a296)) | (~c2_1(a296)) | (~c0_1(a296)) | c0_1(a255) | c1_1(a255) | (~c2_1(a255))) <=> (c0_1(a255) | c1_1(a255) | (~ndr1_0) | (~c2_1(a296)) | (~c3_1(a296)) | (~c0_1(a296)) | (~c2_1(a231)) | (~c1_1(a231)) | (~c3_1(a231)) | (~c2_1(a255)))),
% 0.92/1.10 inference(rewrite,[status(thm)],[])).
% 0.92/1.10 tff(2392,plain,
% 0.92/1.10 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a231)) | (~c3_1(a231)) | (~c1_1(a231)) | (~c3_1(a296)) | (~c2_1(a296)) | (~c0_1(a296)) | c0_1(a255) | c1_1(a255) | (~c2_1(a255)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | (c0_1(a255) | c1_1(a255) | (~ndr1_0) | (~c2_1(a296)) | (~c3_1(a296)) | (~c0_1(a296)) | (~c2_1(a231)) | (~c1_1(a231)) | (~c3_1(a231)) | (~c2_1(a255))))),
% 0.92/1.10 inference(monotonicity,[status(thm)],[2391])).
% 0.92/1.10 tff(2393,plain,
% 0.92/1.10 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a231)) | (~c3_1(a231)) | (~c1_1(a231)) | (~c3_1(a296)) | (~c2_1(a296)) | (~c0_1(a296)) | c0_1(a255) | c1_1(a255) | (~c2_1(a255)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | c0_1(a255) | c1_1(a255) | (~ndr1_0) | (~c2_1(a296)) | (~c3_1(a296)) | (~c0_1(a296)) | (~c2_1(a231)) | (~c1_1(a231)) | (~c3_1(a231)) | (~c2_1(a255)))),
% 0.92/1.10 inference(transitivity,[status(thm)],[2392, 2390])).
% 0.92/1.10 tff(2394,plain,
% 0.92/1.10 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a231)) | (~c3_1(a231)) | (~c1_1(a231)) | (~c3_1(a296)) | (~c2_1(a296)) | (~c0_1(a296)) | c0_1(a255) | c1_1(a255) | (~c2_1(a255)))),
% 0.92/1.10 inference(quant_inst,[status(thm)],[])).
% 0.92/1.10 tff(2395,plain,
% 0.92/1.10 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | c0_1(a255) | c1_1(a255) | (~ndr1_0) | (~c2_1(a296)) | (~c3_1(a296)) | (~c0_1(a296)) | (~c2_1(a231)) | (~c1_1(a231)) | (~c3_1(a231)) | (~c2_1(a255))),
% 0.92/1.10 inference(modus_ponens,[status(thm)],[2394, 2393])).
% 0.92/1.10 tff(2396,plain,
% 0.92/1.10 ($false),
% 0.92/1.10 inference(unit_resolution,[status(thm)],[2395, 110, 2389, 2388, 2387, 2378, 2352, 2237, 2239, 2377, 2367, 2359])).
% 0.92/1.10 tff(2397,plain,(c3_1(a252) | hskp9 | hskp26 | hskp5 | (~c2_1(a215)) | c0_1(a215) | c1_1(a215) | (~hskp12) | c3_1(a237)), inference(lemma,lemma(discharge,[]))).
% 0.92/1.10 tff(2398,plain,
% 0.92/1.10 (c3_1(a252)),
% 0.92/1.10 inference(unit_resolution,[status(thm)],[2397, 2169, 163, 45, 525, 524, 523, 23, 164])).
% 0.92/1.10 tff(2399,plain,
% 0.92/1.10 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W))))),
% 0.92/1.10 inference(bind,[status(th)],[])).
% 0.92/1.10 tff(2400,plain,
% 0.92/1.10 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))),
% 0.92/1.10 inference(quant_intro,[status(thm)],[2399])).
% 0.92/1.10 tff(2401,plain,
% 0.92/1.10 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))),
% 0.92/1.10 inference(rewrite,[status(thm)],[])).
% 0.92/1.10 tff(2402,plain,
% 0.92/1.10 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~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)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c1_1(W))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c1_1(W)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c1_1(W))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | c1_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c1_1(W))) | c1_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c1_1(W))) | c1_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c1_1(W)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | c1_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c1_1(W))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | c1_1(V)) | c3_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c1_1(W))) | c3_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c1_1(W))) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | (~c1_1(W)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | 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)) | (~c1_1(W))))), ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | c1_1(V)) | c3_1(V)) | c0_1(W)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | (~c1_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | (~c1_1(W))) | c0_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)))), ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | c1_1(V)) | c3_1(V)) | c0_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c1_1(W))))), (((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | c1_1(V)) | c3_1(V)) | c0_1(W)) | c3_1(W)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c1_1(W))) | c3_1(W)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c1_1(W))) | c3_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))), (((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | c1_1(V)) | c3_1(V)) | c0_1(W)) | c3_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))))),
% 0.92/1.11 inference(bind,[status(th)],[])).
% 0.92/1.11 tff(2403,plain,
% 0.92/1.11 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | c1_1(V)) | c3_1(V)) | c0_1(W)) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))),
% 0.92/1.11 inference(quant_intro,[status(thm)],[2402])).
% 0.92/1.11 tff(2404,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | c1_1(V)) | c3_1(V)) | c0_1(W)) | c3_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause193')).
% 0.92/1.11 tff(2405,plain,
% 0.92/1.11 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))),
% 0.92/1.11 inference(modus_ponens,[status(thm)],[2404, 2403])).
% 0.92/1.11 tff(2406,plain,
% 0.92/1.11 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))),
% 0.92/1.11 inference(modus_ponens,[status(thm)],[2405, 2401])).
% 0.92/1.11 tff(2407,plain,(
% 0.92/1.11 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))),
% 0.92/1.11 inference(skolemize,[status(sab)],[2406])).
% 0.92/1.11 tff(2408,plain,
% 0.92/1.11 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))),
% 0.92/1.11 inference(modus_ponens,[status(thm)],[2407, 2400])).
% 0.92/1.11 tff(2409,plain,
% 0.92/1.11 (hskp23),
% 0.92/1.11 inference(unit_resolution,[status(thm)],[2083, 2398, 163])).
% 0.92/1.11 tff(2410,plain,
% 0.92/1.11 (~c3_1(a274)),
% 0.92/1.11 inference(unit_resolution,[status(thm)],[2089, 2409])).
% 0.92/1.11 tff(2411,plain,
% 0.92/1.11 (~c0_1(a274)),
% 0.92/1.11 inference(unit_resolution,[status(thm)],[2110, 2409])).
% 0.92/1.11 tff(2412,plain,
% 0.92/1.11 (c1_1(a274)),
% 0.92/1.11 inference(unit_resolution,[status(thm)],[2097, 2409])).
% 0.92/1.11 tff(2413,plain,
% 0.92/1.11 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a274) | c3_1(a274) | c3_1(a237) | (~ndr1_0) | c1_1(a237) | (~c0_1(a237)) | (~c3_1(a252)) | (~c0_1(a252)) | (~c2_1(a252)) | (~c1_1(a274)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a274) | c3_1(a274) | c3_1(a237) | (~ndr1_0) | c1_1(a237) | (~c0_1(a237)) | (~c3_1(a252)) | (~c0_1(a252)) | (~c2_1(a252)) | (~c1_1(a274)))),
% 0.92/1.11 inference(rewrite,[status(thm)],[])).
% 0.92/1.11 tff(2414,plain,
% 0.92/1.11 (((~ndr1_0) | (~c2_1(a252)) | (~c3_1(a252)) | (~c0_1(a252)) | c3_1(a237) | c1_1(a237) | (~c0_1(a237)) | c3_1(a274) | c0_1(a274) | (~c1_1(a274))) <=> (c0_1(a274) | c3_1(a274) | c3_1(a237) | (~ndr1_0) | c1_1(a237) | (~c0_1(a237)) | (~c3_1(a252)) | (~c0_1(a252)) | (~c2_1(a252)) | (~c1_1(a274)))),
% 0.92/1.11 inference(rewrite,[status(thm)],[])).
% 0.92/1.11 tff(2415,plain,
% 0.92/1.11 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a252)) | (~c3_1(a252)) | (~c0_1(a252)) | c3_1(a237) | c1_1(a237) | (~c0_1(a237)) | c3_1(a274) | c0_1(a274) | (~c1_1(a274)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a274) | c3_1(a274) | c3_1(a237) | (~ndr1_0) | c1_1(a237) | (~c0_1(a237)) | (~c3_1(a252)) | (~c0_1(a252)) | (~c2_1(a252)) | (~c1_1(a274))))),
% 0.92/1.11 inference(monotonicity,[status(thm)],[2414])).
% 0.92/1.11 tff(2416,plain,
% 0.92/1.11 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a252)) | (~c3_1(a252)) | (~c0_1(a252)) | c3_1(a237) | c1_1(a237) | (~c0_1(a237)) | c3_1(a274) | c0_1(a274) | (~c1_1(a274)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a274) | c3_1(a274) | c3_1(a237) | (~ndr1_0) | c1_1(a237) | (~c0_1(a237)) | (~c3_1(a252)) | (~c0_1(a252)) | (~c2_1(a252)) | (~c1_1(a274)))),
% 0.92/1.11 inference(transitivity,[status(thm)],[2415, 2413])).
% 0.92/1.11 tff(2417,plain,
% 0.92/1.11 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a252)) | (~c3_1(a252)) | (~c0_1(a252)) | c3_1(a237) | c1_1(a237) | (~c0_1(a237)) | c3_1(a274) | c0_1(a274) | (~c1_1(a274)))),
% 0.92/1.11 inference(quant_inst,[status(thm)],[])).
% 0.92/1.11 tff(2418,plain,
% 0.92/1.11 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a274) | c3_1(a274) | c3_1(a237) | (~ndr1_0) | c1_1(a237) | (~c0_1(a237)) | (~c3_1(a252)) | (~c0_1(a252)) | (~c2_1(a252)) | (~c1_1(a274))),
% 0.92/1.11 inference(modus_ponens,[status(thm)],[2417, 2416])).
% 0.92/1.11 tff(2419,plain,
% 0.92/1.11 (c1_1(a237)),
% 0.92/1.11 inference(unit_resolution,[status(thm)],[2418, 110, 2412, 1892, 1884, 2002, 2411, 2410, 164, 2408, 2398])).
% 0.92/1.11 tff(2420,plain,
% 0.92/1.11 (((~![U: $i] : (hskp26 | hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp26 | hskp9 | c3_1(a274) | (~ndr1_0) | c2_1(a274) | (~c1_1(a274)))) <=> ((~![U: $i] : (hskp26 | hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | hskp26 | hskp9 | c3_1(a274) | (~ndr1_0) | c2_1(a274) | (~c1_1(a274)))),
% 0.92/1.11 inference(rewrite,[status(thm)],[])).
% 0.92/1.11 tff(2421,plain,
% 0.92/1.11 ((hskp26 | hskp9 | (~ndr1_0) | c2_1(a274) | c3_1(a274) | (~c1_1(a274))) <=> (hskp26 | hskp9 | c3_1(a274) | (~ndr1_0) | c2_1(a274) | (~c1_1(a274)))),
% 0.92/1.11 inference(rewrite,[status(thm)],[])).
% 0.92/1.11 tff(2422,plain,
% 0.92/1.11 (((~![U: $i] : (hskp26 | hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp26 | hskp9 | (~ndr1_0) | c2_1(a274) | c3_1(a274) | (~c1_1(a274)))) <=> ((~![U: $i] : (hskp26 | hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp26 | hskp9 | c3_1(a274) | (~ndr1_0) | c2_1(a274) | (~c1_1(a274))))),
% 0.92/1.11 inference(monotonicity,[status(thm)],[2421])).
% 0.92/1.11 tff(2423,plain,
% 0.92/1.11 (((~![U: $i] : (hskp26 | hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp26 | hskp9 | (~ndr1_0) | c2_1(a274) | c3_1(a274) | (~c1_1(a274)))) <=> ((~![U: $i] : (hskp26 | hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | hskp26 | hskp9 | c3_1(a274) | (~ndr1_0) | c2_1(a274) | (~c1_1(a274)))),
% 0.92/1.11 inference(transitivity,[status(thm)],[2422, 2420])).
% 0.92/1.11 tff(2424,plain,
% 0.92/1.11 ((~![U: $i] : (hskp26 | hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp26 | hskp9 | (~ndr1_0) | c2_1(a274) | c3_1(a274) | (~c1_1(a274)))),
% 0.92/1.11 inference(quant_inst,[status(thm)],[])).
% 0.92/1.11 tff(2425,plain,
% 0.92/1.11 ((~![U: $i] : (hskp26 | hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | hskp26 | hskp9 | c3_1(a274) | (~ndr1_0) | c2_1(a274) | (~c1_1(a274))),
% 0.92/1.11 inference(modus_ponens,[status(thm)],[2424, 2423])).
% 0.92/1.11 tff(2426,plain,
% 0.92/1.11 (c2_1(a274)),
% 0.92/1.11 inference(unit_resolution,[status(thm)],[2425, 110, 163, 23, 2412, 2410, 236])).
% 0.92/1.11 tff(2427,plain,
% 0.92/1.11 (^[V: $i, U: $i] : refl((hskp14 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))) <=> (hskp14 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))))),
% 0.92/1.11 inference(bind,[status(th)],[])).
% 0.92/1.11 tff(2428,plain,
% 0.92/1.11 (![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.92/1.11 inference(quant_intro,[status(thm)],[2427])).
% 0.92/1.11 tff(2429,plain,
% 0.92/1.11 (![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.92/1.11 inference(rewrite,[status(thm)],[])).
% 0.92/1.11 tff(2430,plain,
% 0.92/1.11 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c0_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V))) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c0_1(V)) | c3_1(V)) | hskp14) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))) | hskp14))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))) | hskp14) <=> (hskp14 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c0_1(V)) | c3_1(V)) | hskp14) <=> (hskp14 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))))),
% 0.92/1.11 inference(bind,[status(th)],[])).
% 0.92/1.11 tff(2431,plain,
% 0.92/1.11 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c0_1(V)) | c3_1(V)) | hskp14) <=> ![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.92/1.11 inference(quant_intro,[status(thm)],[2430])).
% 0.92/1.11 tff(2432,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c0_1(V)) | c3_1(V)) | hskp14)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause170')).
% 0.92/1.11 tff(2433,plain,
% 0.92/1.11 (![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.92/1.11 inference(modus_ponens,[status(thm)],[2432, 2431])).
% 0.92/1.11 tff(2434,plain,
% 0.92/1.11 (![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.92/1.11 inference(modus_ponens,[status(thm)],[2433, 2429])).
% 0.92/1.11 tff(2435,plain,(
% 0.92/1.11 ![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.92/1.11 inference(skolemize,[status(sab)],[2434])).
% 0.92/1.11 tff(2436,plain,
% 0.92/1.11 (![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.92/1.11 inference(modus_ponens,[status(thm)],[2435, 2428])).
% 0.92/1.11 tff(2437,plain,
% 0.92/1.11 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp14 | c0_1(a274) | c3_1(a274) | c3_1(a237) | (~ndr1_0) | (~c0_1(a237)) | (~c1_1(a237)) | (~c2_1(a274)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp14 | c0_1(a274) | c3_1(a274) | c3_1(a237) | (~ndr1_0) | (~c0_1(a237)) | (~c1_1(a237)) | (~c2_1(a274)))),
% 0.92/1.11 inference(rewrite,[status(thm)],[])).
% 0.92/1.11 tff(2438,plain,
% 0.92/1.11 ((hskp14 | (~ndr1_0) | c3_1(a237) | (~c1_1(a237)) | (~c0_1(a237)) | c3_1(a274) | c0_1(a274) | (~c2_1(a274))) <=> (hskp14 | c0_1(a274) | c3_1(a274) | c3_1(a237) | (~ndr1_0) | (~c0_1(a237)) | (~c1_1(a237)) | (~c2_1(a274)))),
% 0.92/1.11 inference(rewrite,[status(thm)],[])).
% 0.92/1.11 tff(2439,plain,
% 0.92/1.11 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp14 | (~ndr1_0) | c3_1(a237) | (~c1_1(a237)) | (~c0_1(a237)) | c3_1(a274) | c0_1(a274) | (~c2_1(a274)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp14 | c0_1(a274) | c3_1(a274) | c3_1(a237) | (~ndr1_0) | (~c0_1(a237)) | (~c1_1(a237)) | (~c2_1(a274))))),
% 0.92/1.11 inference(monotonicity,[status(thm)],[2438])).
% 0.92/1.11 tff(2440,plain,
% 0.92/1.11 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp14 | (~ndr1_0) | c3_1(a237) | (~c1_1(a237)) | (~c0_1(a237)) | c3_1(a274) | c0_1(a274) | (~c2_1(a274)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp14 | c0_1(a274) | c3_1(a274) | c3_1(a237) | (~ndr1_0) | (~c0_1(a237)) | (~c1_1(a237)) | (~c2_1(a274)))),
% 0.92/1.11 inference(transitivity,[status(thm)],[2439, 2437])).
% 0.92/1.11 tff(2441,plain,
% 0.92/1.11 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp14 | (~ndr1_0) | c3_1(a237) | (~c1_1(a237)) | (~c0_1(a237)) | c3_1(a274) | c0_1(a274) | (~c2_1(a274)))),
% 0.92/1.11 inference(quant_inst,[status(thm)],[])).
% 0.92/1.11 tff(2442,plain,
% 0.92/1.11 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp14 | c0_1(a274) | c3_1(a274) | c3_1(a237) | (~ndr1_0) | (~c0_1(a237)) | (~c1_1(a237)) | (~c2_1(a274))),
% 0.92/1.11 inference(modus_ponens,[status(thm)],[2441, 2440])).
% 0.92/1.11 tff(2443,plain,
% 0.92/1.11 (hskp14 | (~c2_1(a274))),
% 0.92/1.11 inference(unit_resolution,[status(thm)],[2442, 110, 2002, 2411, 2410, 164, 2436, 2419])).
% 0.92/1.11 tff(2444,plain,
% 0.92/1.11 (hskp14),
% 0.92/1.11 inference(unit_resolution,[status(thm)],[2443, 2426])).
% 0.92/1.11 tff(2445,plain,
% 0.92/1.11 (((~hskp14) | (~c1_1(a241))) <=> ((~hskp14) | (~c1_1(a241)))),
% 0.92/1.11 inference(rewrite,[status(thm)],[])).
% 0.92/1.11 tff(2446,plain,
% 0.92/1.11 (((~c1_1(a241)) | (~hskp14)) <=> ((~hskp14) | (~c1_1(a241)))),
% 0.92/1.11 inference(rewrite,[status(thm)],[])).
% 0.92/1.11 tff(2447,axiom,((~c1_1(a241)) | (~hskp14)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause106')).
% 0.92/1.11 tff(2448,plain,
% 0.92/1.11 ((~hskp14) | (~c1_1(a241))),
% 0.92/1.11 inference(modus_ponens,[status(thm)],[2447, 2446])).
% 0.92/1.11 tff(2449,plain,
% 0.92/1.11 ((~hskp14) | (~c1_1(a241))),
% 0.92/1.11 inference(modus_ponens,[status(thm)],[2448, 2445])).
% 0.92/1.11 tff(2450,plain,
% 0.92/1.11 (~c1_1(a241)),
% 0.92/1.11 inference(unit_resolution,[status(thm)],[2449, 2444])).
% 0.92/1.11 tff(2451,plain,
% 0.92/1.11 (((~hskp14) | c3_1(a241)) <=> ((~hskp14) | c3_1(a241))),
% 0.92/1.11 inference(rewrite,[status(thm)],[])).
% 0.92/1.11 tff(2452,axiom,((~hskp14) | c3_1(a241)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause66')).
% 0.92/1.11 tff(2453,plain,
% 0.92/1.11 ((~hskp14) | c3_1(a241)),
% 0.92/1.11 inference(modus_ponens,[status(thm)],[2452, 2451])).
% 0.92/1.11 tff(2454,plain,
% 0.92/1.11 ((~hskp14) | c3_1(a241)),
% 0.92/1.11 inference(modus_ponens,[status(thm)],[2453, 2451])).
% 0.92/1.11 tff(2455,plain,
% 0.92/1.11 ((~hskp14) | c3_1(a241)),
% 0.92/1.11 inference(modus_ponens,[status(thm)],[2454, 2451])).
% 0.92/1.11 tff(2456,plain,
% 0.92/1.11 ((~hskp14) | c3_1(a241)),
% 0.92/1.11 inference(modus_ponens,[status(thm)],[2455, 2451])).
% 0.92/1.11 tff(2457,plain,
% 0.92/1.11 ((~hskp14) | c3_1(a241)),
% 0.92/1.11 inference(modus_ponens,[status(thm)],[2456, 2451])).
% 0.92/1.11 tff(2458,plain,
% 0.92/1.11 (c3_1(a241)),
% 0.92/1.11 inference(unit_resolution,[status(thm)],[2457, 2444])).
% 0.92/1.11 tff(2459,plain,
% 0.92/1.11 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | (c1_1(a241) | c3_1(a237) | c0_1(a215) | c1_1(a215) | (~ndr1_0) | (~c2_1(a215)) | (~c0_1(a237)) | (~c1_1(a237)) | c2_1(a241) | (~c3_1(a241)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | c1_1(a241) | c3_1(a237) | c0_1(a215) | c1_1(a215) | (~ndr1_0) | (~c2_1(a215)) | (~c0_1(a237)) | (~c1_1(a237)) | c2_1(a241) | (~c3_1(a241)))),
% 0.92/1.11 inference(rewrite,[status(thm)],[])).
% 0.92/1.11 tff(2460,plain,
% 0.92/1.11 (((~ndr1_0) | c3_1(a237) | (~c1_1(a237)) | (~c0_1(a237)) | c1_1(a241) | c2_1(a241) | (~c3_1(a241)) | c0_1(a215) | c1_1(a215) | (~c2_1(a215))) <=> (c1_1(a241) | c3_1(a237) | c0_1(a215) | c1_1(a215) | (~ndr1_0) | (~c2_1(a215)) | (~c0_1(a237)) | (~c1_1(a237)) | c2_1(a241) | (~c3_1(a241)))),
% 0.92/1.11 inference(rewrite,[status(thm)],[])).
% 0.92/1.11 tff(2461,plain,
% 0.92/1.11 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a237) | (~c1_1(a237)) | (~c0_1(a237)) | c1_1(a241) | c2_1(a241) | (~c3_1(a241)) | c0_1(a215) | c1_1(a215) | (~c2_1(a215)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | (c1_1(a241) | c3_1(a237) | c0_1(a215) | c1_1(a215) | (~ndr1_0) | (~c2_1(a215)) | (~c0_1(a237)) | (~c1_1(a237)) | c2_1(a241) | (~c3_1(a241))))),
% 0.92/1.11 inference(monotonicity,[status(thm)],[2460])).
% 0.92/1.11 tff(2462,plain,
% 0.92/1.11 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a237) | (~c1_1(a237)) | (~c0_1(a237)) | c1_1(a241) | c2_1(a241) | (~c3_1(a241)) | c0_1(a215) | c1_1(a215) | (~c2_1(a215)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | c1_1(a241) | c3_1(a237) | c0_1(a215) | c1_1(a215) | (~ndr1_0) | (~c2_1(a215)) | (~c0_1(a237)) | (~c1_1(a237)) | c2_1(a241) | (~c3_1(a241)))),
% 0.92/1.11 inference(transitivity,[status(thm)],[2461, 2459])).
% 0.92/1.11 tff(2463,plain,
% 0.92/1.11 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a237) | (~c1_1(a237)) | (~c0_1(a237)) | c1_1(a241) | c2_1(a241) | (~c3_1(a241)) | c0_1(a215) | c1_1(a215) | (~c2_1(a215)))),
% 0.92/1.11 inference(quant_inst,[status(thm)],[])).
% 0.92/1.11 tff(2464,plain,
% 0.92/1.11 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | c1_1(a241) | c3_1(a237) | c0_1(a215) | c1_1(a215) | (~ndr1_0) | (~c2_1(a215)) | (~c0_1(a237)) | (~c1_1(a237)) | c2_1(a241) | (~c3_1(a241))),
% 0.92/1.11 inference(modus_ponens,[status(thm)],[2463, 2462])).
% 0.92/1.11 tff(2465,plain,
% 0.92/1.11 (c2_1(a241)),
% 0.92/1.11 inference(unit_resolution,[status(thm)],[2464, 110, 2458, 2002, 525, 2450, 164, 524, 523, 716, 2419])).
% 0.92/1.11 tff(2466,plain,
% 0.92/1.11 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp10 | c0_1(a274) | c3_1(a274) | c1_1(a252) | (~ndr1_0) | (~c0_1(a252)) | (~c2_1(a252)) | (~c2_1(a274)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp10 | c0_1(a274) | c3_1(a274) | c1_1(a252) | (~ndr1_0) | (~c0_1(a252)) | (~c2_1(a252)) | (~c2_1(a274)))),
% 0.92/1.11 inference(rewrite,[status(thm)],[])).
% 0.92/1.11 tff(2467,plain,
% 0.92/1.11 ((hskp10 | (~ndr1_0) | c1_1(a252) | (~c2_1(a252)) | (~c0_1(a252)) | c3_1(a274) | c0_1(a274) | (~c2_1(a274))) <=> (hskp10 | c0_1(a274) | c3_1(a274) | c1_1(a252) | (~ndr1_0) | (~c0_1(a252)) | (~c2_1(a252)) | (~c2_1(a274)))),
% 0.92/1.11 inference(rewrite,[status(thm)],[])).
% 0.92/1.11 tff(2468,plain,
% 0.92/1.11 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp10 | (~ndr1_0) | c1_1(a252) | (~c2_1(a252)) | (~c0_1(a252)) | c3_1(a274) | c0_1(a274) | (~c2_1(a274)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp10 | c0_1(a274) | c3_1(a274) | c1_1(a252) | (~ndr1_0) | (~c0_1(a252)) | (~c2_1(a252)) | (~c2_1(a274))))),
% 0.92/1.11 inference(monotonicity,[status(thm)],[2467])).
% 0.92/1.11 tff(2469,plain,
% 0.92/1.11 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp10 | (~ndr1_0) | c1_1(a252) | (~c2_1(a252)) | (~c0_1(a252)) | c3_1(a274) | c0_1(a274) | (~c2_1(a274)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp10 | c0_1(a274) | c3_1(a274) | c1_1(a252) | (~ndr1_0) | (~c0_1(a252)) | (~c2_1(a252)) | (~c2_1(a274)))),
% 0.92/1.11 inference(transitivity,[status(thm)],[2468, 2466])).
% 0.92/1.11 tff(2470,plain,
% 0.92/1.11 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp10 | (~ndr1_0) | c1_1(a252) | (~c2_1(a252)) | (~c0_1(a252)) | c3_1(a274) | c0_1(a274) | (~c2_1(a274)))),
% 0.92/1.11 inference(quant_inst,[status(thm)],[])).
% 0.92/1.11 tff(2471,plain,
% 0.92/1.11 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp10 | c0_1(a274) | c3_1(a274) | c1_1(a252) | (~ndr1_0) | (~c0_1(a252)) | (~c2_1(a252)) | (~c2_1(a274))),
% 0.92/1.11 inference(modus_ponens,[status(thm)],[2470, 2469])).
% 0.92/1.11 tff(2472,plain,
% 0.92/1.11 (hskp10 | (~c2_1(a274))),
% 0.92/1.11 inference(unit_resolution,[status(thm)],[2471, 110, 1892, 1884, 2411, 2410, 1906, 11])).
% 0.92/1.11 tff(2473,plain,
% 0.92/1.11 (hskp10),
% 0.92/1.11 inference(unit_resolution,[status(thm)],[2472, 2426])).
% 0.92/1.11 tff(2474,plain,
% 0.92/1.11 (~c0_1(a231)),
% 0.92/1.11 inference(unit_resolution,[status(thm)],[1314, 2473])).
% 0.92/1.11 tff(2475,plain,
% 0.92/1.11 (c3_1(a231)),
% 0.92/1.11 inference(unit_resolution,[status(thm)],[1341, 2473])).
% 0.92/1.11 tff(2476,plain,
% 0.92/1.11 (c1_1(a231)),
% 0.92/1.11 inference(unit_resolution,[status(thm)],[604, 2473])).
% 0.92/1.11 tff(2477,plain,
% 0.92/1.11 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp9 | c1_1(a241) | c0_1(a231) | (~ndr1_0) | (~c1_1(a231)) | (~c3_1(a231)) | (~c3_1(a241)) | (~c2_1(a241)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp9 | c1_1(a241) | c0_1(a231) | (~ndr1_0) | (~c1_1(a231)) | (~c3_1(a231)) | (~c3_1(a241)) | (~c2_1(a241)))),
% 0.92/1.11 inference(rewrite,[status(thm)],[])).
% 0.92/1.11 tff(2478,plain,
% 0.92/1.11 ((hskp9 | (~ndr1_0) | c1_1(a241) | (~c2_1(a241)) | (~c3_1(a241)) | c0_1(a231) | (~c1_1(a231)) | (~c3_1(a231))) <=> (hskp9 | c1_1(a241) | c0_1(a231) | (~ndr1_0) | (~c1_1(a231)) | (~c3_1(a231)) | (~c3_1(a241)) | (~c2_1(a241)))),
% 0.92/1.11 inference(rewrite,[status(thm)],[])).
% 0.92/1.11 tff(2479,plain,
% 0.92/1.11 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp9 | (~ndr1_0) | c1_1(a241) | (~c2_1(a241)) | (~c3_1(a241)) | c0_1(a231) | (~c1_1(a231)) | (~c3_1(a231)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp9 | c1_1(a241) | c0_1(a231) | (~ndr1_0) | (~c1_1(a231)) | (~c3_1(a231)) | (~c3_1(a241)) | (~c2_1(a241))))),
% 0.92/1.11 inference(monotonicity,[status(thm)],[2478])).
% 0.92/1.11 tff(2480,plain,
% 0.92/1.11 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp9 | (~ndr1_0) | c1_1(a241) | (~c2_1(a241)) | (~c3_1(a241)) | c0_1(a231) | (~c1_1(a231)) | (~c3_1(a231)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp9 | c1_1(a241) | c0_1(a231) | (~ndr1_0) | (~c1_1(a231)) | (~c3_1(a231)) | (~c3_1(a241)) | (~c2_1(a241)))),
% 0.92/1.11 inference(transitivity,[status(thm)],[2479, 2477])).
% 0.92/1.11 tff(2481,plain,
% 0.92/1.11 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp9 | (~ndr1_0) | c1_1(a241) | (~c2_1(a241)) | (~c3_1(a241)) | c0_1(a231) | (~c1_1(a231)) | (~c3_1(a231)))),
% 0.92/1.11 inference(quant_inst,[status(thm)],[])).
% 0.92/1.11 tff(2482,plain,
% 0.92/1.11 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp9 | c1_1(a241) | c0_1(a231) | (~ndr1_0) | (~c1_1(a231)) | (~c3_1(a231)) | (~c3_1(a241)) | (~c2_1(a241))),
% 0.92/1.11 inference(modus_ponens,[status(thm)],[2481, 2480])).
% 0.92/1.11 tff(2483,plain,
% 0.92/1.11 ($false),
% 0.92/1.11 inference(unit_resolution,[status(thm)],[2482, 110, 23, 2458, 2476, 2475, 2450, 2474, 409, 2465])).
% 0.92/1.11 tff(2484,plain,(c3_1(a237) | hskp9 | hskp5 | hskp27), inference(lemma,lemma(discharge,[]))).
% 0.92/1.11 tff(2485,plain,
% 0.92/1.11 (c3_1(a237)),
% 0.92/1.11 inference(unit_resolution,[status(thm)],[2484, 45, 23, 34])).
% 0.92/1.11 tff(2486,plain,
% 0.92/1.11 (~hskp12),
% 0.92/1.11 inference(unit_resolution,[status(thm)],[696, 2485])).
% 0.92/1.11 tff(2487,plain,
% 0.92/1.11 (hskp21),
% 0.92/1.11 inference(unit_resolution,[status(thm)],[2041, 12, 526])).
% 0.92/1.11 tff(2488,plain,
% 0.92/1.11 (~c2_1(a259)),
% 0.92/1.11 inference(unit_resolution,[status(thm)],[975, 2487])).
% 0.92/1.11 tff(2489,plain,
% 0.92/1.11 (c3_1(a259)),
% 0.92/1.11 inference(unit_resolution,[status(thm)],[792, 2487])).
% 0.92/1.11 tff(2490,plain,
% 0.92/1.11 (c0_1(a259)),
% 0.92/1.11 inference(unit_resolution,[status(thm)],[783, 2487])).
% 0.92/1.11 tff(2491,plain,
% 0.92/1.11 ($false),
% 0.92/1.11 inference(unit_resolution,[status(thm)],[2162, 110, 2490, 2489, 1892, 1884, 2488, 1906, 22, 12])).
% 0.92/1.11 tff(2492,plain,(c3_1(a252) | hskp12), inference(lemma,lemma(discharge,[]))).
% 0.92/1.11 tff(2493,plain,
% 0.92/1.11 (c3_1(a252)),
% 0.92/1.11 inference(unit_resolution,[status(thm)],[2492, 2486])).
% 0.92/1.11 tff(2494,plain,
% 0.92/1.11 (hskp23),
% 0.92/1.11 inference(unit_resolution,[status(thm)],[2083, 2493, 163])).
% 0.92/1.11 tff(2495,plain,
% 0.92/1.11 (~c3_1(a274)),
% 0.92/1.11 inference(unit_resolution,[status(thm)],[2089, 2494])).
% 0.92/1.11 tff(2496,plain,
% 0.92/1.11 (~c0_1(a274)),
% 0.92/1.11 inference(unit_resolution,[status(thm)],[2110, 2494])).
% 0.92/1.11 tff(2497,plain,
% 0.92/1.11 (c1_1(a274)),
% 0.92/1.11 inference(unit_resolution,[status(thm)],[2097, 2494])).
% 0.92/1.11 tff(2498,plain,
% 0.92/1.11 (~c2_1(a274)),
% 0.92/1.11 inference(unit_resolution,[status(thm)],[2117, 110, 2486, 2497, 2496, 2495, 44])).
% 0.92/1.11 tff(2499,plain,
% 0.92/1.11 ($false),
% 0.92/1.11 inference(unit_resolution,[status(thm)],[2425, 110, 163, 23, 2497, 2495, 236, 2498])).
% 0.92/1.11 tff(2500,plain,(hskp5 | hskp9 | hskp27), inference(lemma,lemma(discharge,[]))).
% 0.92/1.11 tff(2501,plain,
% 0.92/1.11 (hskp5),
% 0.92/1.11 inference(unit_resolution,[status(thm)],[2500, 34, 23])).
% 0.92/1.11 tff(2502,plain,
% 0.92/1.11 (~c1_1(a218)),
% 0.92/1.11 inference(unit_resolution,[status(thm)],[680, 2501])).
% 0.92/1.11 tff(2503,plain,
% 0.92/1.11 (hskp2),
% 0.92/1.11 inference(unit_resolution,[status(thm)],[521, 1, 34, 23])).
% 0.92/1.11 tff(2504,plain,
% 0.92/1.11 (~c1_1(a215)),
% 0.92/1.11 inference(unit_resolution,[status(thm)],[124, 2503])).
% 0.92/1.11 tff(2505,plain,
% 0.92/1.11 (~c0_1(a215)),
% 0.92/1.11 inference(unit_resolution,[status(thm)],[138, 2503])).
% 0.92/1.11 tff(2506,plain,
% 0.92/1.11 (c2_1(a215)),
% 0.92/1.11 inference(unit_resolution,[status(thm)],[132, 2503])).
% 0.92/1.11 tff(2507,plain,
% 0.92/1.11 (~c2_1(a218)),
% 0.92/1.11 inference(unit_resolution,[status(thm)],[674, 2501])).
% 0.92/1.11 tff(2508,plain,
% 0.92/1.11 (c3_1(a218)),
% 0.92/1.11 inference(unit_resolution,[status(thm)],[688, 2501])).
% 0.92/1.11 tff(2509,plain,
% 0.92/1.11 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | (c1_1(a252) | c2_1(a218) | (~ndr1_0) | (~c3_1(a218)) | (~c0_1(a218)) | c3_1(a252) | (~c0_1(a252)) | (~c2_1(a252)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | c1_1(a252) | c2_1(a218) | (~ndr1_0) | (~c3_1(a218)) | (~c0_1(a218)) | c3_1(a252) | (~c0_1(a252)) | (~c2_1(a252)))),
% 0.92/1.11 inference(rewrite,[status(thm)],[])).
% 0.92/1.11 tff(2510,plain,
% 0.92/1.11 (((~ndr1_0) | c2_1(a218) | (~c3_1(a218)) | (~c0_1(a218)) | c3_1(a252) | c1_1(a252) | (~c2_1(a252)) | c3_1(a252) | c1_1(a252) | (~c0_1(a252))) <=> (c1_1(a252) | c2_1(a218) | (~ndr1_0) | (~c3_1(a218)) | (~c0_1(a218)) | c3_1(a252) | (~c0_1(a252)) | (~c2_1(a252)))),
% 0.92/1.11 inference(rewrite,[status(thm)],[])).
% 0.92/1.11 tff(2511,plain,
% 0.92/1.11 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a218) | (~c3_1(a218)) | (~c0_1(a218)) | c3_1(a252) | c1_1(a252) | (~c2_1(a252)) | c3_1(a252) | c1_1(a252) | (~c0_1(a252)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | (c1_1(a252) | c2_1(a218) | (~ndr1_0) | (~c3_1(a218)) | (~c0_1(a218)) | c3_1(a252) | (~c0_1(a252)) | (~c2_1(a252))))),
% 0.92/1.11 inference(monotonicity,[status(thm)],[2510])).
% 0.92/1.11 tff(2512,plain,
% 0.92/1.11 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a218) | (~c3_1(a218)) | (~c0_1(a218)) | c3_1(a252) | c1_1(a252) | (~c2_1(a252)) | c3_1(a252) | c1_1(a252) | (~c0_1(a252)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | c1_1(a252) | c2_1(a218) | (~ndr1_0) | (~c3_1(a218)) | (~c0_1(a218)) | c3_1(a252) | (~c0_1(a252)) | (~c2_1(a252)))),
% 0.92/1.11 inference(transitivity,[status(thm)],[2511, 2509])).
% 0.92/1.11 tff(2513,plain,
% 0.92/1.11 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a218) | (~c3_1(a218)) | (~c0_1(a218)) | c3_1(a252) | c1_1(a252) | (~c2_1(a252)) | c3_1(a252) | c1_1(a252) | (~c0_1(a252)))),
% 0.92/1.12 inference(quant_inst,[status(thm)],[])).
% 0.92/1.12 tff(2514,plain,
% 0.92/1.12 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | c1_1(a252) | c2_1(a218) | (~ndr1_0) | (~c3_1(a218)) | (~c0_1(a218)) | c3_1(a252) | (~c0_1(a252)) | (~c2_1(a252))),
% 0.92/1.12 inference(modus_ponens,[status(thm)],[2513, 2512])).
% 0.92/1.12 tff(2515,plain,
% 0.92/1.12 (~c0_1(a218)),
% 0.92/1.12 inference(unit_resolution,[status(thm)],[2514, 110, 1892, 1884, 719, 1906, 717, 22, 12])).
% 0.92/1.12 tff(2516,plain,
% 0.92/1.12 (^[V: $i, U: $i] : refl((hskp26 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V))) <=> (hskp26 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V))))),
% 0.92/1.12 inference(bind,[status(th)],[])).
% 0.92/1.12 tff(2517,plain,
% 0.92/1.12 (![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))),
% 0.92/1.12 inference(quant_intro,[status(thm)],[2516])).
% 0.92/1.12 tff(2518,plain,
% 0.92/1.12 (![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))),
% 0.92/1.12 inference(rewrite,[status(thm)],[])).
% 0.92/1.12 tff(2519,plain,
% 0.92/1.12 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V))))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V))))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp26) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V))) | hskp26))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V))) | hskp26) <=> (hskp26 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp26) <=> (hskp26 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))))),
% 0.92/1.12 inference(bind,[status(th)],[])).
% 0.92/1.12 tff(2520,plain,
% 0.92/1.12 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp26) <=> ![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))),
% 0.92/1.12 inference(quant_intro,[status(thm)],[2519])).
% 0.92/1.12 tff(2521,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp26)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause165')).
% 0.92/1.12 tff(2522,plain,
% 0.92/1.12 (![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))),
% 0.92/1.12 inference(modus_ponens,[status(thm)],[2521, 2520])).
% 0.92/1.12 tff(2523,plain,
% 0.92/1.12 (![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))),
% 0.92/1.12 inference(modus_ponens,[status(thm)],[2522, 2518])).
% 0.92/1.12 tff(2524,plain,(
% 0.92/1.12 ![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))),
% 0.92/1.12 inference(skolemize,[status(sab)],[2523])).
% 0.92/1.12 tff(2525,plain,
% 0.92/1.12 (![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))),
% 0.92/1.12 inference(modus_ponens,[status(thm)],[2524, 2517])).
% 0.92/1.12 tff(2526,plain,
% 0.92/1.12 (hskp12),
% 0.92/1.12 inference(unit_resolution,[status(thm)],[2492, 12])).
% 0.92/1.12 tff(2527,plain,
% 0.92/1.12 (~c3_1(a237)),
% 0.92/1.12 inference(unit_resolution,[status(thm)],[696, 2526])).
% 0.92/1.12 tff(2528,plain,
% 0.92/1.12 (c0_1(a237)),
% 0.92/1.12 inference(unit_resolution,[status(thm)],[575, 2526])).
% 0.92/1.12 tff(2529,plain,
% 0.92/1.12 (~c1_1(a237)),
% 0.92/1.12 inference(unit_resolution,[status(thm)],[725, 110, 2528, 719, 152, 2527, 718, 717, 151, 150, 716])).
% 0.92/1.12 tff(2530,plain,
% 0.92/1.12 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | (c0_1(a255) | c3_1(a255) | c1_1(a252) | c1_1(a218) | (~ndr1_0) | (~c3_1(a218)) | c0_1(a218) | c3_1(a252) | (~c0_1(a252)) | c2_1(a255))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c0_1(a255) | c3_1(a255) | c1_1(a252) | c1_1(a218) | (~ndr1_0) | (~c3_1(a218)) | c0_1(a218) | c3_1(a252) | (~c0_1(a252)) | c2_1(a255))),
% 0.92/1.12 inference(rewrite,[status(thm)],[])).
% 0.92/1.12 tff(2531,plain,
% 0.92/1.12 (((~ndr1_0) | c1_1(a252) | c3_1(a252) | (~c0_1(a252)) | c1_1(a218) | c0_1(a218) | (~c3_1(a218)) | c3_1(a255) | c2_1(a255) | c0_1(a255)) <=> (c0_1(a255) | c3_1(a255) | c1_1(a252) | c1_1(a218) | (~ndr1_0) | (~c3_1(a218)) | c0_1(a218) | c3_1(a252) | (~c0_1(a252)) | c2_1(a255))),
% 0.92/1.12 inference(rewrite,[status(thm)],[])).
% 0.92/1.12 tff(2532,plain,
% 0.92/1.12 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a252) | c3_1(a252) | (~c0_1(a252)) | c1_1(a218) | c0_1(a218) | (~c3_1(a218)) | c3_1(a255) | c2_1(a255) | c0_1(a255))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | (c0_1(a255) | c3_1(a255) | c1_1(a252) | c1_1(a218) | (~ndr1_0) | (~c3_1(a218)) | c0_1(a218) | c3_1(a252) | (~c0_1(a252)) | c2_1(a255)))),
% 0.92/1.12 inference(monotonicity,[status(thm)],[2531])).
% 0.92/1.12 tff(2533,plain,
% 0.92/1.12 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a252) | c3_1(a252) | (~c0_1(a252)) | c1_1(a218) | c0_1(a218) | (~c3_1(a218)) | c3_1(a255) | c2_1(a255) | c0_1(a255))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c0_1(a255) | c3_1(a255) | c1_1(a252) | c1_1(a218) | (~ndr1_0) | (~c3_1(a218)) | c0_1(a218) | c3_1(a252) | (~c0_1(a252)) | c2_1(a255))),
% 0.92/1.12 inference(transitivity,[status(thm)],[2532, 2530])).
% 0.92/1.12 tff(2534,plain,
% 0.92/1.12 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a252) | c3_1(a252) | (~c0_1(a252)) | c1_1(a218) | c0_1(a218) | (~c3_1(a218)) | c3_1(a255) | c2_1(a255) | c0_1(a255))),
% 0.92/1.12 inference(quant_inst,[status(thm)],[])).
% 0.92/1.12 tff(2535,plain,
% 0.92/1.12 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c0_1(a255) | c3_1(a255) | c1_1(a252) | c1_1(a218) | (~ndr1_0) | (~c3_1(a218)) | c0_1(a218) | c3_1(a252) | (~c0_1(a252)) | c2_1(a255)),
% 0.92/1.12 inference(modus_ponens,[status(thm)],[2534, 2533])).
% 0.92/1.12 tff(2536,plain,
% 0.92/1.12 (c0_1(a218) | c3_1(a252) | c2_1(a255)),
% 0.92/1.12 inference(unit_resolution,[status(thm)],[2535, 110, 1892, 719, 1097, 1114, 1906, 718, 1419])).
% 0.92/1.12 tff(2537,plain,
% 0.92/1.12 (c2_1(a255)),
% 0.92/1.12 inference(unit_resolution,[status(thm)],[2536, 2515, 12])).
% 0.92/1.12 tff(2538,assumption,(~c1_1(a237)), introduced(assumption)).
% 0.92/1.12 tff(2539,plain,
% 0.92/1.12 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | (c1_1(a255) | c3_1(a255) | c3_1(a237) | c2_1(a216) | (~ndr1_0) | (~c3_1(a216)) | (~c0_1(a216)) | c1_1(a237) | (~c0_1(a237)) | (~c2_1(a255)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | c1_1(a255) | c3_1(a255) | c3_1(a237) | c2_1(a216) | (~ndr1_0) | (~c3_1(a216)) | (~c0_1(a216)) | c1_1(a237) | (~c0_1(a237)) | (~c2_1(a255)))),
% 0.92/1.12 inference(rewrite,[status(thm)],[])).
% 0.92/1.12 tff(2540,plain,
% 0.92/1.12 (((~ndr1_0) | c2_1(a216) | (~c3_1(a216)) | (~c0_1(a216)) | c3_1(a255) | c1_1(a255) | (~c2_1(a255)) | c3_1(a237) | c1_1(a237) | (~c0_1(a237))) <=> (c1_1(a255) | c3_1(a255) | c3_1(a237) | c2_1(a216) | (~ndr1_0) | (~c3_1(a216)) | (~c0_1(a216)) | c1_1(a237) | (~c0_1(a237)) | (~c2_1(a255)))),
% 0.92/1.12 inference(rewrite,[status(thm)],[])).
% 0.92/1.12 tff(2541,plain,
% 0.92/1.12 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a216) | (~c3_1(a216)) | (~c0_1(a216)) | c3_1(a255) | c1_1(a255) | (~c2_1(a255)) | c3_1(a237) | c1_1(a237) | (~c0_1(a237)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | (c1_1(a255) | c3_1(a255) | c3_1(a237) | c2_1(a216) | (~ndr1_0) | (~c3_1(a216)) | (~c0_1(a216)) | c1_1(a237) | (~c0_1(a237)) | (~c2_1(a255))))),
% 0.92/1.12 inference(monotonicity,[status(thm)],[2540])).
% 0.92/1.12 tff(2542,plain,
% 0.92/1.12 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a216) | (~c3_1(a216)) | (~c0_1(a216)) | c3_1(a255) | c1_1(a255) | (~c2_1(a255)) | c3_1(a237) | c1_1(a237) | (~c0_1(a237)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | c1_1(a255) | c3_1(a255) | c3_1(a237) | c2_1(a216) | (~ndr1_0) | (~c3_1(a216)) | (~c0_1(a216)) | c1_1(a237) | (~c0_1(a237)) | (~c2_1(a255)))),
% 0.92/1.12 inference(transitivity,[status(thm)],[2541, 2539])).
% 0.92/1.12 tff(2543,plain,
% 0.92/1.12 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a216) | (~c3_1(a216)) | (~c0_1(a216)) | c3_1(a255) | c1_1(a255) | (~c2_1(a255)) | c3_1(a237) | c1_1(a237) | (~c0_1(a237)))),
% 0.92/1.12 inference(quant_inst,[status(thm)],[])).
% 0.92/1.12 tff(2544,plain,
% 0.92/1.12 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | c1_1(a255) | c3_1(a255) | c3_1(a237) | c2_1(a216) | (~ndr1_0) | (~c3_1(a216)) | (~c0_1(a216)) | c1_1(a237) | (~c0_1(a237)) | (~c2_1(a255))),
% 0.92/1.12 inference(modus_ponens,[status(thm)],[2543, 2542])).
% 0.92/1.12 tff(2545,plain,
% 0.92/1.12 (~c3_1(a216)),
% 0.92/1.12 inference(unit_resolution,[status(thm)],[2544, 110, 699, 2262, 1096, 1114, 697, 2261, 22, 1749, 2538])).
% 0.92/1.12 tff(2546,plain,
% 0.92/1.12 (hskp7),
% 0.92/1.12 inference(unit_resolution,[status(thm)],[2289, 2240, 691, 697])).
% 0.92/1.12 tff(2547,plain,
% 0.92/1.12 (~c0_1(a223)),
% 0.92/1.12 inference(unit_resolution,[status(thm)],[2295, 2546])).
% 0.92/1.12 tff(2548,plain,
% 0.92/1.12 (c2_1(a223)),
% 0.92/1.12 inference(unit_resolution,[status(thm)],[2303, 2546])).
% 0.92/1.12 tff(2549,plain,
% 0.92/1.12 (c1_1(a223)),
% 0.92/1.12 inference(unit_resolution,[status(thm)],[2311, 2546])).
% 0.92/1.12 tff(2550,plain,
% 0.92/1.12 ($false),
% 0.92/1.12 inference(unit_resolution,[status(thm)],[2318, 110, 1, 2549, 2548, 2262, 2547, 2261, 1542, 2545])).
% 0.92/1.12 tff(2551,plain,(hskp6 | hskp26 | c1_1(a255) | c3_1(a255) | (~c2_1(a255)) | c1_1(a237) | (~c2_1(a215)) | c0_1(a215) | c1_1(a215) | (~hskp12)), inference(lemma,lemma(discharge,[]))).
% 0.92/1.12 tff(2552,plain,
% 0.92/1.12 (hskp6),
% 0.92/1.12 inference(unit_resolution,[status(thm)],[2551, 2537, 1096, 1114, 1, 2529, 152, 151, 150, 2526])).
% 0.92/1.12 tff(2553,plain,
% 0.92/1.12 (~c3_1(a220)),
% 0.92/1.12 inference(unit_resolution,[status(thm)],[449, 2552])).
% 0.92/1.12 tff(2554,plain,
% 0.92/1.12 (c2_1(a220)),
% 0.92/1.12 inference(unit_resolution,[status(thm)],[493, 2552])).
% 0.92/1.12 tff(2555,plain,
% 0.92/1.12 (c1_1(a220)),
% 0.92/1.12 inference(unit_resolution,[status(thm)],[485, 2552])).
% 0.92/1.12 tff(2556,plain,
% 0.92/1.12 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp26 | c3_1(a220) | c2_1(a218) | (~ndr1_0) | (~c3_1(a218)) | c0_1(a218) | (~c2_1(a220)) | (~c1_1(a220)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp26 | c3_1(a220) | c2_1(a218) | (~ndr1_0) | (~c3_1(a218)) | c0_1(a218) | (~c2_1(a220)) | (~c1_1(a220)))),
% 0.92/1.12 inference(rewrite,[status(thm)],[])).
% 0.92/1.12 tff(2557,plain,
% 0.92/1.12 ((hskp26 | (~ndr1_0) | c3_1(a220) | (~c2_1(a220)) | (~c1_1(a220)) | c0_1(a218) | c2_1(a218) | (~c3_1(a218))) <=> (hskp26 | c3_1(a220) | c2_1(a218) | (~ndr1_0) | (~c3_1(a218)) | c0_1(a218) | (~c2_1(a220)) | (~c1_1(a220)))),
% 0.92/1.12 inference(rewrite,[status(thm)],[])).
% 0.92/1.12 tff(2558,plain,
% 0.92/1.12 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp26 | (~ndr1_0) | c3_1(a220) | (~c2_1(a220)) | (~c1_1(a220)) | c0_1(a218) | c2_1(a218) | (~c3_1(a218)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp26 | c3_1(a220) | c2_1(a218) | (~ndr1_0) | (~c3_1(a218)) | c0_1(a218) | (~c2_1(a220)) | (~c1_1(a220))))),
% 0.92/1.12 inference(monotonicity,[status(thm)],[2557])).
% 0.92/1.12 tff(2559,plain,
% 0.92/1.12 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp26 | (~ndr1_0) | c3_1(a220) | (~c2_1(a220)) | (~c1_1(a220)) | c0_1(a218) | c2_1(a218) | (~c3_1(a218)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp26 | c3_1(a220) | c2_1(a218) | (~ndr1_0) | (~c3_1(a218)) | c0_1(a218) | (~c2_1(a220)) | (~c1_1(a220)))),
% 0.92/1.12 inference(transitivity,[status(thm)],[2558, 2556])).
% 0.92/1.12 tff(2560,plain,
% 0.92/1.12 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp26 | (~ndr1_0) | c3_1(a220) | (~c2_1(a220)) | (~c1_1(a220)) | c0_1(a218) | c2_1(a218) | (~c3_1(a218)))),
% 0.92/1.12 inference(quant_inst,[status(thm)],[])).
% 0.92/1.12 tff(2561,plain,
% 0.92/1.12 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp26 | c3_1(a220) | c2_1(a218) | (~ndr1_0) | (~c3_1(a218)) | c0_1(a218) | (~c2_1(a220)) | (~c1_1(a220))),
% 0.92/1.12 inference(modus_ponens,[status(thm)],[2560, 2559])).
% 0.92/1.12 tff(2562,plain,
% 0.92/1.12 ($false),
% 0.92/1.12 inference(unit_resolution,[status(thm)],[2561, 110, 1, 2555, 2554, 719, 2553, 717, 2525, 2515])).
% 0.92/1.12 tff(2563,plain,(c3_1(a252) | hskp26 | (~c3_1(a218)) | c2_1(a218) | c1_1(a255) | c3_1(a255) | (~c2_1(a215)) | c0_1(a215) | c1_1(a215) | c0_1(a255) | c1_1(a218)), inference(lemma,lemma(discharge,[]))).
% 0.92/1.12 tff(2564,plain,
% 0.92/1.12 (c3_1(a252)),
% 0.92/1.12 inference(unit_resolution,[status(thm)],[2563, 1, 2508, 2507, 2239, 2238, 2506, 2505, 2504, 2237, 2502])).
% 0.92/1.12 tff(2565,plain,
% 0.92/1.12 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | (c2_1(a218) | c0_1(a215) | c1_1(a215) | (~ndr1_0) | (~c2_1(a215)) | (~c3_1(a218)) | (~c0_1(a218)) | (~c3_1(a252)) | (~c0_1(a252)) | (~c2_1(a252)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | c2_1(a218) | c0_1(a215) | c1_1(a215) | (~ndr1_0) | (~c2_1(a215)) | (~c3_1(a218)) | (~c0_1(a218)) | (~c3_1(a252)) | (~c0_1(a252)) | (~c2_1(a252)))),
% 0.92/1.12 inference(rewrite,[status(thm)],[])).
% 0.92/1.12 tff(2566,plain,
% 0.92/1.12 (((~ndr1_0) | (~c2_1(a252)) | (~c3_1(a252)) | (~c0_1(a252)) | c2_1(a218) | (~c3_1(a218)) | (~c0_1(a218)) | c0_1(a215) | c1_1(a215) | (~c2_1(a215))) <=> (c2_1(a218) | c0_1(a215) | c1_1(a215) | (~ndr1_0) | (~c2_1(a215)) | (~c3_1(a218)) | (~c0_1(a218)) | (~c3_1(a252)) | (~c0_1(a252)) | (~c2_1(a252)))),
% 0.92/1.12 inference(rewrite,[status(thm)],[])).
% 0.92/1.12 tff(2567,plain,
% 0.92/1.12 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a252)) | (~c3_1(a252)) | (~c0_1(a252)) | c2_1(a218) | (~c3_1(a218)) | (~c0_1(a218)) | c0_1(a215) | c1_1(a215) | (~c2_1(a215)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | (c2_1(a218) | c0_1(a215) | c1_1(a215) | (~ndr1_0) | (~c2_1(a215)) | (~c3_1(a218)) | (~c0_1(a218)) | (~c3_1(a252)) | (~c0_1(a252)) | (~c2_1(a252))))),
% 0.92/1.12 inference(monotonicity,[status(thm)],[2566])).
% 0.92/1.12 tff(2568,plain,
% 0.92/1.12 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a252)) | (~c3_1(a252)) | (~c0_1(a252)) | c2_1(a218) | (~c3_1(a218)) | (~c0_1(a218)) | c0_1(a215) | c1_1(a215) | (~c2_1(a215)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | c2_1(a218) | c0_1(a215) | c1_1(a215) | (~ndr1_0) | (~c2_1(a215)) | (~c3_1(a218)) | (~c0_1(a218)) | (~c3_1(a252)) | (~c0_1(a252)) | (~c2_1(a252)))),
% 0.92/1.12 inference(transitivity,[status(thm)],[2567, 2565])).
% 0.92/1.12 tff(2569,plain,
% 0.92/1.12 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a252)) | (~c3_1(a252)) | (~c0_1(a252)) | c2_1(a218) | (~c3_1(a218)) | (~c0_1(a218)) | c0_1(a215) | c1_1(a215) | (~c2_1(a215)))),
% 0.92/1.12 inference(quant_inst,[status(thm)],[])).
% 0.92/1.12 tff(2570,plain,
% 0.92/1.12 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | c2_1(a218) | c0_1(a215) | c1_1(a215) | (~ndr1_0) | (~c2_1(a215)) | (~c3_1(a218)) | (~c0_1(a218)) | (~c3_1(a252)) | (~c0_1(a252)) | (~c2_1(a252))),
% 0.92/1.12 inference(modus_ponens,[status(thm)],[2569, 2568])).
% 0.92/1.12 tff(2571,plain,
% 0.92/1.12 ((~c0_1(a218)) | (~c3_1(a252))),
% 0.92/1.12 inference(unit_resolution,[status(thm)],[2570, 110, 1892, 1884, 2508, 2506, 2507, 2505, 2504, 853])).
% 0.92/1.12 tff(2572,plain,
% 0.92/1.12 (~c0_1(a218)),
% 0.92/1.12 inference(unit_resolution,[status(thm)],[2571, 2564])).
% 0.92/1.12 tff(2573,plain,
% 0.92/1.12 (hskp23),
% 0.92/1.12 inference(unit_resolution,[status(thm)],[2083, 2564, 1])).
% 0.92/1.12 tff(2574,plain,
% 0.92/1.12 (~c3_1(a274)),
% 0.92/1.12 inference(unit_resolution,[status(thm)],[2089, 2573])).
% 0.92/1.12 tff(2575,plain,
% 0.92/1.12 (c1_1(a274)),
% 0.92/1.12 inference(unit_resolution,[status(thm)],[2097, 2573])).
% 0.92/1.12 tff(2576,plain,
% 0.92/1.12 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp26 | c3_1(a274) | c2_1(a218) | (~ndr1_0) | (~c3_1(a218)) | c0_1(a218) | (~c2_1(a274)) | (~c1_1(a274)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp26 | c3_1(a274) | c2_1(a218) | (~ndr1_0) | (~c3_1(a218)) | c0_1(a218) | (~c2_1(a274)) | (~c1_1(a274)))),
% 0.92/1.12 inference(rewrite,[status(thm)],[])).
% 0.92/1.12 tff(2577,plain,
% 0.92/1.12 ((hskp26 | (~ndr1_0) | c3_1(a274) | (~c2_1(a274)) | (~c1_1(a274)) | c0_1(a218) | c2_1(a218) | (~c3_1(a218))) <=> (hskp26 | c3_1(a274) | c2_1(a218) | (~ndr1_0) | (~c3_1(a218)) | c0_1(a218) | (~c2_1(a274)) | (~c1_1(a274)))),
% 0.92/1.12 inference(rewrite,[status(thm)],[])).
% 0.92/1.12 tff(2578,plain,
% 0.92/1.12 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp26 | (~ndr1_0) | c3_1(a274) | (~c2_1(a274)) | (~c1_1(a274)) | c0_1(a218) | c2_1(a218) | (~c3_1(a218)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp26 | c3_1(a274) | c2_1(a218) | (~ndr1_0) | (~c3_1(a218)) | c0_1(a218) | (~c2_1(a274)) | (~c1_1(a274))))),
% 0.92/1.12 inference(monotonicity,[status(thm)],[2577])).
% 0.92/1.12 tff(2579,plain,
% 0.92/1.12 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp26 | (~ndr1_0) | c3_1(a274) | (~c2_1(a274)) | (~c1_1(a274)) | c0_1(a218) | c2_1(a218) | (~c3_1(a218)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp26 | c3_1(a274) | c2_1(a218) | (~ndr1_0) | (~c3_1(a218)) | c0_1(a218) | (~c2_1(a274)) | (~c1_1(a274)))),
% 0.92/1.12 inference(transitivity,[status(thm)],[2578, 2576])).
% 0.92/1.12 tff(2580,plain,
% 0.92/1.12 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp26 | (~ndr1_0) | c3_1(a274) | (~c2_1(a274)) | (~c1_1(a274)) | c0_1(a218) | c2_1(a218) | (~c3_1(a218)))),
% 0.92/1.12 inference(quant_inst,[status(thm)],[])).
% 0.92/1.12 tff(2581,plain,
% 0.92/1.12 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp26 | c3_1(a274) | c2_1(a218) | (~ndr1_0) | (~c3_1(a218)) | c0_1(a218) | (~c2_1(a274)) | (~c1_1(a274))),
% 0.92/1.12 inference(modus_ponens,[status(thm)],[2580, 2579])).
% 0.92/1.12 tff(2582,plain,
% 0.92/1.12 (~c2_1(a274)),
% 0.92/1.12 inference(unit_resolution,[status(thm)],[2581, 110, 1, 2575, 2508, 2574, 2507, 2525, 2572])).
% 0.92/1.12 tff(2583,plain,
% 0.92/1.12 ($false),
% 0.92/1.12 inference(unit_resolution,[status(thm)],[2425, 110, 1, 23, 2575, 2574, 236, 2582])).
% 0.92/1.12 tff(2584,plain,(hskp26 | hskp9 | hskp27), inference(lemma,lemma(discharge,[]))).
% 0.92/1.12 tff(2585,plain,
% 0.92/1.12 (hskp26),
% 0.92/1.12 inference(unit_resolution,[status(thm)],[2584, 34, 23])).
% 0.92/1.12 tff(2586,plain,
% 0.92/1.12 (c3_1(a234)),
% 0.92/1.12 inference(unit_resolution,[status(thm)],[63, 2585])).
% 0.92/1.12 tff(2587,plain,
% 0.92/1.12 (c1_1(a234)),
% 0.92/1.12 inference(unit_resolution,[status(thm)],[71, 2585])).
% 0.92/1.12 tff(2588,plain,
% 0.92/1.12 (c0_1(a234)),
% 0.92/1.12 inference(unit_resolution,[status(thm)],[79, 2585])).
% 0.92/1.12 tff(2589,assumption,(c2_1(a234)), introduced(assumption)).
% 0.92/1.12 tff(2590,assumption,(c3_1(a234)), introduced(assumption)).
% 0.92/1.12 tff(2591,assumption,(c1_1(a234)), introduced(assumption)).
% 0.92/1.12 tff(2592,assumption,(c0_1(a234)), introduced(assumption)).
% 0.92/1.12 tff(2593,plain,
% 0.92/1.12 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)) | (~c2_1(W)) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | (~c0_1(a234)) | (~c3_1(a234)) | (~c1_1(a234)) | (~c2_1(a234)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)) | (~c2_1(W)) | (~c0_1(W)) | (~c1_1(W)))) | (~ndr1_0) | (~c0_1(a234)) | (~c3_1(a234)) | (~c1_1(a234)) | (~c2_1(a234)))),
% 0.92/1.12 inference(rewrite,[status(thm)],[])).
% 0.92/1.12 tff(2594,plain,
% 0.92/1.12 (((~ndr1_0) | (~c2_1(a234)) | (~c3_1(a234)) | (~c1_1(a234)) | (~c3_1(a234)) | (~c2_1(a234)) | (~c0_1(a234)) | (~c2_1(a234)) | (~c0_1(a234)) | (~c1_1(a234))) <=> ((~ndr1_0) | (~c0_1(a234)) | (~c3_1(a234)) | (~c1_1(a234)) | (~c2_1(a234)))),
% 0.92/1.12 inference(rewrite,[status(thm)],[])).
% 0.92/1.12 tff(2595,plain,
% 0.92/1.12 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)) | (~c2_1(W)) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a234)) | (~c3_1(a234)) | (~c1_1(a234)) | (~c3_1(a234)) | (~c2_1(a234)) | (~c0_1(a234)) | (~c2_1(a234)) | (~c0_1(a234)) | (~c1_1(a234)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)) | (~c2_1(W)) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | (~c0_1(a234)) | (~c3_1(a234)) | (~c1_1(a234)) | (~c2_1(a234))))),
% 0.92/1.12 inference(monotonicity,[status(thm)],[2594])).
% 0.92/1.12 tff(2596,plain,
% 0.92/1.12 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)) | (~c2_1(W)) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a234)) | (~c3_1(a234)) | (~c1_1(a234)) | (~c3_1(a234)) | (~c2_1(a234)) | (~c0_1(a234)) | (~c2_1(a234)) | (~c0_1(a234)) | (~c1_1(a234)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)) | (~c2_1(W)) | (~c0_1(W)) | (~c1_1(W)))) | (~ndr1_0) | (~c0_1(a234)) | (~c3_1(a234)) | (~c1_1(a234)) | (~c2_1(a234)))),
% 0.92/1.12 inference(transitivity,[status(thm)],[2595, 2593])).
% 0.92/1.12 tff(2597,plain,
% 0.92/1.12 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)) | (~c2_1(W)) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a234)) | (~c3_1(a234)) | (~c1_1(a234)) | (~c3_1(a234)) | (~c2_1(a234)) | (~c0_1(a234)) | (~c2_1(a234)) | (~c0_1(a234)) | (~c1_1(a234)))),
% 0.92/1.12 inference(quant_inst,[status(thm)],[])).
% 0.92/1.12 tff(2598,plain,
% 0.92/1.12 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)) | (~c2_1(W)) | (~c0_1(W)) | (~c1_1(W)))) | (~ndr1_0) | (~c0_1(a234)) | (~c3_1(a234)) | (~c1_1(a234)) | (~c2_1(a234))),
% 0.92/1.12 inference(modus_ponens,[status(thm)],[2597, 2596])).
% 0.92/1.12 tff(2599,plain,
% 0.92/1.12 ($false),
% 0.92/1.12 inference(unit_resolution,[status(thm)],[2598, 110, 2592, 2591, 2590, 33, 2589])).
% 0.92/1.12 tff(2600,plain,((~c2_1(a234)) | (~c0_1(a234)) | (~c1_1(a234)) | (~c3_1(a234))), inference(lemma,lemma(discharge,[]))).
% 0.92/1.12 tff(2601,plain,
% 0.92/1.12 (~c2_1(a234)),
% 0.92/1.12 inference(unit_resolution,[status(thm)],[2600, 2588, 2587, 2586])).
% 0.92/1.12 tff(2602,plain,
% 0.92/1.12 (hskp2),
% 0.92/1.12 inference(unit_resolution,[status(thm)],[118, 2585, 34])).
% 0.92/1.12 tff(2603,plain,
% 0.92/1.12 (~c1_1(a215)),
% 0.92/1.12 inference(unit_resolution,[status(thm)],[124, 2602])).
% 0.92/1.12 tff(2604,plain,
% 0.92/1.12 (~c0_1(a215)),
% 0.92/1.12 inference(unit_resolution,[status(thm)],[138, 2602])).
% 0.92/1.12 tff(2605,plain,
% 0.92/1.12 (c2_1(a215)),
% 0.92/1.12 inference(unit_resolution,[status(thm)],[132, 2602])).
% 0.92/1.12 tff(2606,plain,
% 0.92/1.12 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | (c0_1(a215) | c1_1(a215) | (~ndr1_0) | (~c2_1(a215)) | (~c0_1(a234)) | (~c3_1(a234)) | c2_1(a234) | (~c3_1(a252)) | (~c0_1(a252)) | (~c2_1(a252)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | c0_1(a215) | c1_1(a215) | (~ndr1_0) | (~c2_1(a215)) | (~c0_1(a234)) | (~c3_1(a234)) | c2_1(a234) | (~c3_1(a252)) | (~c0_1(a252)) | (~c2_1(a252)))),
% 0.92/1.12 inference(rewrite,[status(thm)],[])).
% 0.92/1.12 tff(2607,plain,
% 0.92/1.12 (((~ndr1_0) | (~c2_1(a252)) | (~c3_1(a252)) | (~c0_1(a252)) | c2_1(a234) | (~c3_1(a234)) | (~c0_1(a234)) | c0_1(a215) | c1_1(a215) | (~c2_1(a215))) <=> (c0_1(a215) | c1_1(a215) | (~ndr1_0) | (~c2_1(a215)) | (~c0_1(a234)) | (~c3_1(a234)) | c2_1(a234) | (~c3_1(a252)) | (~c0_1(a252)) | (~c2_1(a252)))),
% 0.92/1.12 inference(rewrite,[status(thm)],[])).
% 0.92/1.12 tff(2608,plain,
% 0.92/1.12 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a252)) | (~c3_1(a252)) | (~c0_1(a252)) | c2_1(a234) | (~c3_1(a234)) | (~c0_1(a234)) | c0_1(a215) | c1_1(a215) | (~c2_1(a215)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | (c0_1(a215) | c1_1(a215) | (~ndr1_0) | (~c2_1(a215)) | (~c0_1(a234)) | (~c3_1(a234)) | c2_1(a234) | (~c3_1(a252)) | (~c0_1(a252)) | (~c2_1(a252))))),
% 0.92/1.12 inference(monotonicity,[status(thm)],[2607])).
% 0.92/1.12 tff(2609,plain,
% 0.92/1.12 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a252)) | (~c3_1(a252)) | (~c0_1(a252)) | c2_1(a234) | (~c3_1(a234)) | (~c0_1(a234)) | c0_1(a215) | c1_1(a215) | (~c2_1(a215)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | c0_1(a215) | c1_1(a215) | (~ndr1_0) | (~c2_1(a215)) | (~c0_1(a234)) | (~c3_1(a234)) | c2_1(a234) | (~c3_1(a252)) | (~c0_1(a252)) | (~c2_1(a252)))),
% 0.92/1.13 inference(transitivity,[status(thm)],[2608, 2606])).
% 0.92/1.13 tff(2610,plain,
% 0.92/1.13 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a252)) | (~c3_1(a252)) | (~c0_1(a252)) | c2_1(a234) | (~c3_1(a234)) | (~c0_1(a234)) | c0_1(a215) | c1_1(a215) | (~c2_1(a215)))),
% 0.92/1.13 inference(quant_inst,[status(thm)],[])).
% 0.92/1.13 tff(2611,plain,
% 0.92/1.13 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | c0_1(a215) | c1_1(a215) | (~ndr1_0) | (~c2_1(a215)) | (~c0_1(a234)) | (~c3_1(a234)) | c2_1(a234) | (~c3_1(a252)) | (~c0_1(a252)) | (~c2_1(a252))),
% 0.92/1.13 inference(modus_ponens,[status(thm)],[2610, 2609])).
% 0.92/1.13 tff(2612,plain,
% 0.92/1.13 (~c3_1(a252)),
% 0.92/1.13 inference(unit_resolution,[status(thm)],[2611, 110, 2588, 2586, 1892, 1884, 2605, 2604, 2603, 853, 2601])).
% 0.92/1.13 tff(2613,plain,
% 0.92/1.13 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | (c1_1(a252) | (~ndr1_0) | (~c0_1(a234)) | (~c3_1(a234)) | c2_1(a234) | c3_1(a252) | (~c0_1(a252)) | (~c2_1(a252)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | c1_1(a252) | (~ndr1_0) | (~c0_1(a234)) | (~c3_1(a234)) | c2_1(a234) | c3_1(a252) | (~c0_1(a252)) | (~c2_1(a252)))),
% 0.92/1.13 inference(rewrite,[status(thm)],[])).
% 0.92/1.13 tff(2614,plain,
% 0.92/1.13 (((~ndr1_0) | c2_1(a234) | (~c3_1(a234)) | (~c0_1(a234)) | c3_1(a252) | c1_1(a252) | (~c2_1(a252)) | c3_1(a252) | c1_1(a252) | (~c0_1(a252))) <=> (c1_1(a252) | (~ndr1_0) | (~c0_1(a234)) | (~c3_1(a234)) | c2_1(a234) | c3_1(a252) | (~c0_1(a252)) | (~c2_1(a252)))),
% 0.92/1.13 inference(rewrite,[status(thm)],[])).
% 0.92/1.13 tff(2615,plain,
% 0.92/1.13 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a234) | (~c3_1(a234)) | (~c0_1(a234)) | c3_1(a252) | c1_1(a252) | (~c2_1(a252)) | c3_1(a252) | c1_1(a252) | (~c0_1(a252)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | (c1_1(a252) | (~ndr1_0) | (~c0_1(a234)) | (~c3_1(a234)) | c2_1(a234) | c3_1(a252) | (~c0_1(a252)) | (~c2_1(a252))))),
% 0.92/1.13 inference(monotonicity,[status(thm)],[2614])).
% 0.92/1.13 tff(2616,plain,
% 0.92/1.13 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a234) | (~c3_1(a234)) | (~c0_1(a234)) | c3_1(a252) | c1_1(a252) | (~c2_1(a252)) | c3_1(a252) | c1_1(a252) | (~c0_1(a252)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | c1_1(a252) | (~ndr1_0) | (~c0_1(a234)) | (~c3_1(a234)) | c2_1(a234) | c3_1(a252) | (~c0_1(a252)) | (~c2_1(a252)))),
% 0.92/1.13 inference(transitivity,[status(thm)],[2615, 2613])).
% 0.92/1.13 tff(2617,plain,
% 0.92/1.13 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a234) | (~c3_1(a234)) | (~c0_1(a234)) | c3_1(a252) | c1_1(a252) | (~c2_1(a252)) | c3_1(a252) | c1_1(a252) | (~c0_1(a252)))),
% 0.92/1.13 inference(quant_inst,[status(thm)],[])).
% 0.92/1.13 tff(2618,plain,
% 0.92/1.13 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | c1_1(a252) | (~ndr1_0) | (~c0_1(a234)) | (~c3_1(a234)) | c2_1(a234) | c3_1(a252) | (~c0_1(a252)) | (~c2_1(a252))),
% 0.92/1.13 inference(modus_ponens,[status(thm)],[2617, 2616])).
% 0.92/1.13 tff(2619,plain,
% 0.92/1.13 ($false),
% 0.92/1.13 inference(unit_resolution,[status(thm)],[2618, 110, 2588, 2586, 1892, 1884, 1906, 22, 2612, 2601])).
% 0.92/1.13 tff(2620,plain,(hskp27 | hskp9), inference(lemma,lemma(discharge,[]))).
% 0.92/1.13 tff(2621,plain,
% 0.92/1.13 (hskp27),
% 0.92/1.13 inference(unit_resolution,[status(thm)],[2620, 23])).
% 0.92/1.13 tff(2622,plain,
% 0.92/1.13 (c3_1(a261)),
% 0.92/1.13 inference(unit_resolution,[status(thm)],[1220, 2621])).
% 0.92/1.13 tff(2623,plain,
% 0.92/1.13 (c2_1(a261)),
% 0.92/1.13 inference(unit_resolution,[status(thm)],[1228, 2621])).
% 0.92/1.13 tff(2624,plain,
% 0.92/1.13 (c1_1(a261)),
% 0.92/1.13 inference(unit_resolution,[status(thm)],[1236, 2621])).
% 0.92/1.13 tff(2625,plain,
% 0.92/1.13 (~c0_1(a261)),
% 0.92/1.13 inference(unit_resolution,[status(thm)],[1243, 110, 2624, 2623, 2622, 33])).
% 0.92/1.13 tff(2626,plain,
% 0.92/1.13 (c2_1(a255)),
% 0.92/1.13 inference(unit_resolution,[status(thm)],[1778, 2238, 2623, 2622, 2237, 2625, 23])).
% 0.92/1.13 tff(2627,plain,
% 0.92/1.13 (((~![U: $i] : (hskp29 | hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | (hskp29 | hskp26 | (~ndr1_0) | (~c1_1(a261)) | (~c2_1(a261)) | (~c3_1(a261)))) <=> ((~![U: $i] : (hskp29 | hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | hskp29 | hskp26 | (~ndr1_0) | (~c1_1(a261)) | (~c2_1(a261)) | (~c3_1(a261)))),
% 0.92/1.13 inference(rewrite,[status(thm)],[])).
% 0.92/1.13 tff(2628,plain,
% 0.92/1.13 ((hskp29 | hskp26 | (~ndr1_0) | (~c2_1(a261)) | (~c3_1(a261)) | (~c1_1(a261))) <=> (hskp29 | hskp26 | (~ndr1_0) | (~c1_1(a261)) | (~c2_1(a261)) | (~c3_1(a261)))),
% 0.92/1.13 inference(rewrite,[status(thm)],[])).
% 0.92/1.13 tff(2629,plain,
% 0.92/1.13 (((~![U: $i] : (hskp29 | hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | (hskp29 | hskp26 | (~ndr1_0) | (~c2_1(a261)) | (~c3_1(a261)) | (~c1_1(a261)))) <=> ((~![U: $i] : (hskp29 | hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | (hskp29 | hskp26 | (~ndr1_0) | (~c1_1(a261)) | (~c2_1(a261)) | (~c3_1(a261))))),
% 0.92/1.13 inference(monotonicity,[status(thm)],[2628])).
% 0.92/1.13 tff(2630,plain,
% 0.92/1.13 (((~![U: $i] : (hskp29 | hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | (hskp29 | hskp26 | (~ndr1_0) | (~c2_1(a261)) | (~c3_1(a261)) | (~c1_1(a261)))) <=> ((~![U: $i] : (hskp29 | hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | hskp29 | hskp26 | (~ndr1_0) | (~c1_1(a261)) | (~c2_1(a261)) | (~c3_1(a261)))),
% 0.92/1.13 inference(transitivity,[status(thm)],[2629, 2627])).
% 0.92/1.13 tff(2631,plain,
% 0.92/1.13 ((~![U: $i] : (hskp29 | hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | (hskp29 | hskp26 | (~ndr1_0) | (~c2_1(a261)) | (~c3_1(a261)) | (~c1_1(a261)))),
% 0.92/1.13 inference(quant_inst,[status(thm)],[])).
% 0.92/1.13 tff(2632,plain,
% 0.92/1.13 ((~![U: $i] : (hskp29 | hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | hskp29 | hskp26 | (~ndr1_0) | (~c1_1(a261)) | (~c2_1(a261)) | (~c3_1(a261))),
% 0.92/1.13 inference(modus_ponens,[status(thm)],[2631, 2630])).
% 0.92/1.13 tff(2633,plain,
% 0.92/1.13 (hskp29 | hskp26),
% 0.92/1.13 inference(unit_resolution,[status(thm)],[2632, 110, 2624, 2623, 2622, 2196])).
% 0.92/1.13 tff(2634,plain,
% 0.92/1.13 (hskp29),
% 0.92/1.13 inference(unit_resolution,[status(thm)],[2633, 1])).
% 0.92/1.13 tff(2635,plain,
% 0.92/1.13 (c3_1(a296)),
% 0.92/1.13 inference(unit_resolution,[status(thm)],[2210, 2634])).
% 0.92/1.13 tff(2636,plain,
% 0.92/1.13 (c2_1(a296)),
% 0.92/1.13 inference(unit_resolution,[status(thm)],[2218, 2634])).
% 0.92/1.13 tff(2637,plain,
% 0.92/1.13 (c0_1(a296)),
% 0.92/1.13 inference(unit_resolution,[status(thm)],[2226, 2634])).
% 0.92/1.13 tff(2638,plain,
% 0.92/1.13 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | (c0_1(a255) | c1_1(a255) | (~ndr1_0) | (~c1_1(a261)) | (~c2_1(a261)) | (~c3_1(a261)) | (~c2_1(a296)) | (~c3_1(a296)) | (~c0_1(a296)) | (~c2_1(a255)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | c0_1(a255) | c1_1(a255) | (~ndr1_0) | (~c1_1(a261)) | (~c2_1(a261)) | (~c3_1(a261)) | (~c2_1(a296)) | (~c3_1(a296)) | (~c0_1(a296)) | (~c2_1(a255)))),
% 0.92/1.13 inference(rewrite,[status(thm)],[])).
% 0.92/1.13 tff(2639,plain,
% 0.92/1.13 (((~ndr1_0) | (~c2_1(a261)) | (~c3_1(a261)) | (~c1_1(a261)) | (~c3_1(a296)) | (~c2_1(a296)) | (~c0_1(a296)) | c0_1(a255) | c1_1(a255) | (~c2_1(a255))) <=> (c0_1(a255) | c1_1(a255) | (~ndr1_0) | (~c1_1(a261)) | (~c2_1(a261)) | (~c3_1(a261)) | (~c2_1(a296)) | (~c3_1(a296)) | (~c0_1(a296)) | (~c2_1(a255)))),
% 0.92/1.13 inference(rewrite,[status(thm)],[])).
% 0.92/1.13 tff(2640,plain,
% 0.92/1.13 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a261)) | (~c3_1(a261)) | (~c1_1(a261)) | (~c3_1(a296)) | (~c2_1(a296)) | (~c0_1(a296)) | c0_1(a255) | c1_1(a255) | (~c2_1(a255)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | (c0_1(a255) | c1_1(a255) | (~ndr1_0) | (~c1_1(a261)) | (~c2_1(a261)) | (~c3_1(a261)) | (~c2_1(a296)) | (~c3_1(a296)) | (~c0_1(a296)) | (~c2_1(a255))))),
% 0.92/1.13 inference(monotonicity,[status(thm)],[2639])).
% 0.92/1.13 tff(2641,plain,
% 0.92/1.13 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a261)) | (~c3_1(a261)) | (~c1_1(a261)) | (~c3_1(a296)) | (~c2_1(a296)) | (~c0_1(a296)) | c0_1(a255) | c1_1(a255) | (~c2_1(a255)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | c0_1(a255) | c1_1(a255) | (~ndr1_0) | (~c1_1(a261)) | (~c2_1(a261)) | (~c3_1(a261)) | (~c2_1(a296)) | (~c3_1(a296)) | (~c0_1(a296)) | (~c2_1(a255)))),
% 0.92/1.13 inference(transitivity,[status(thm)],[2640, 2638])).
% 0.92/1.13 tff(2642,plain,
% 0.92/1.13 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a261)) | (~c3_1(a261)) | (~c1_1(a261)) | (~c3_1(a296)) | (~c2_1(a296)) | (~c0_1(a296)) | c0_1(a255) | c1_1(a255) | (~c2_1(a255)))),
% 0.92/1.13 inference(quant_inst,[status(thm)],[])).
% 0.92/1.13 tff(2643,plain,
% 0.92/1.13 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | c0_1(a255) | c1_1(a255) | (~ndr1_0) | (~c1_1(a261)) | (~c2_1(a261)) | (~c3_1(a261)) | (~c2_1(a296)) | (~c3_1(a296)) | (~c0_1(a296)) | (~c2_1(a255))),
% 0.92/1.13 inference(modus_ponens,[status(thm)],[2642, 2641])).
% 0.92/1.13 tff(2644,plain,
% 0.92/1.13 ($false),
% 0.92/1.13 inference(unit_resolution,[status(thm)],[2643, 110, 2637, 2636, 2635, 2624, 2623, 2622, 2237, 2239, 2377, 2626])).
% 0.92/1.13 tff(2645,plain,(hskp26 | hskp9), inference(lemma,lemma(discharge,[]))).
% 0.92/1.13 tff(2646,plain,
% 0.92/1.13 (hskp26),
% 0.92/1.13 inference(unit_resolution,[status(thm)],[2645, 23])).
% 0.92/1.13 tff(2647,plain,
% 0.92/1.13 (c0_1(a234)),
% 0.92/1.13 inference(unit_resolution,[status(thm)],[79, 2646])).
% 0.92/1.13 tff(2648,plain,
% 0.92/1.13 (c1_1(a234)),
% 0.92/1.13 inference(unit_resolution,[status(thm)],[71, 2646])).
% 0.92/1.13 tff(2649,plain,
% 0.92/1.13 (c3_1(a234)),
% 0.92/1.13 inference(unit_resolution,[status(thm)],[63, 2646])).
% 0.92/1.13 tff(2650,plain,
% 0.92/1.13 (~c2_1(a234)),
% 0.92/1.13 inference(unit_resolution,[status(thm)],[2600, 2649, 2648, 2647])).
% 0.92/1.13 tff(2651,plain,
% 0.92/1.13 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp9 | c1_1(a252) | (~ndr1_0) | (~c1_1(a261)) | (~c3_1(a261)) | c0_1(a261) | (~c3_1(a252)) | (~c2_1(a252)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp9 | c1_1(a252) | (~ndr1_0) | (~c1_1(a261)) | (~c3_1(a261)) | c0_1(a261) | (~c3_1(a252)) | (~c2_1(a252)))),
% 0.92/1.13 inference(rewrite,[status(thm)],[])).
% 0.92/1.13 tff(2652,plain,
% 0.92/1.13 ((hskp9 | (~ndr1_0) | c1_1(a252) | (~c2_1(a252)) | (~c3_1(a252)) | c0_1(a261) | (~c1_1(a261)) | (~c3_1(a261))) <=> (hskp9 | c1_1(a252) | (~ndr1_0) | (~c1_1(a261)) | (~c3_1(a261)) | c0_1(a261) | (~c3_1(a252)) | (~c2_1(a252)))),
% 0.92/1.13 inference(rewrite,[status(thm)],[])).
% 0.92/1.13 tff(2653,plain,
% 0.92/1.13 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp9 | (~ndr1_0) | c1_1(a252) | (~c2_1(a252)) | (~c3_1(a252)) | c0_1(a261) | (~c1_1(a261)) | (~c3_1(a261)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp9 | c1_1(a252) | (~ndr1_0) | (~c1_1(a261)) | (~c3_1(a261)) | c0_1(a261) | (~c3_1(a252)) | (~c2_1(a252))))),
% 0.92/1.13 inference(monotonicity,[status(thm)],[2652])).
% 0.92/1.13 tff(2654,plain,
% 0.92/1.13 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp9 | (~ndr1_0) | c1_1(a252) | (~c2_1(a252)) | (~c3_1(a252)) | c0_1(a261) | (~c1_1(a261)) | (~c3_1(a261)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp9 | c1_1(a252) | (~ndr1_0) | (~c1_1(a261)) | (~c3_1(a261)) | c0_1(a261) | (~c3_1(a252)) | (~c2_1(a252)))),
% 0.92/1.13 inference(transitivity,[status(thm)],[2653, 2651])).
% 0.92/1.13 tff(2655,plain,
% 0.92/1.13 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp9 | (~ndr1_0) | c1_1(a252) | (~c2_1(a252)) | (~c3_1(a252)) | c0_1(a261) | (~c1_1(a261)) | (~c3_1(a261)))),
% 0.92/1.13 inference(quant_inst,[status(thm)],[])).
% 0.92/1.13 tff(2656,plain,
% 0.92/1.13 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp9 | c1_1(a252) | (~ndr1_0) | (~c1_1(a261)) | (~c3_1(a261)) | c0_1(a261) | (~c3_1(a252)) | (~c2_1(a252))),
% 0.92/1.13 inference(modus_ponens,[status(thm)],[2655, 2654])).
% 0.92/1.13 tff(2657,plain,
% 0.92/1.13 (~c3_1(a252)),
% 0.92/1.13 inference(unit_resolution,[status(thm)],[2656, 110, 23, 2624, 2622, 1884, 1906, 409, 2625])).
% 0.92/1.13 tff(2658,plain,
% 0.92/1.13 (hskp12),
% 0.92/1.13 inference(unit_resolution,[status(thm)],[2492, 2657])).
% 0.92/1.13 tff(2659,plain,
% 0.92/1.13 (~c3_1(a237)),
% 0.92/1.13 inference(unit_resolution,[status(thm)],[696, 2658])).
% 0.92/1.13 tff(2660,plain,
% 0.92/1.13 (c2_1(a237)),
% 0.92/1.13 inference(unit_resolution,[status(thm)],[556, 2658])).
% 0.92/1.13 tff(2661,plain,
% 0.92/1.13 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_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(a252) | c3_1(a237) | (~ndr1_0) | (~c1_1(a261)) | (~c2_1(a261)) | (~c3_1(a261)) | (~c2_1(a237)) | (~c1_1(a237)) | c3_1(a252) | (~c0_1(a252)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_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(a252) | c3_1(a237) | (~ndr1_0) | (~c1_1(a261)) | (~c2_1(a261)) | (~c3_1(a261)) | (~c2_1(a237)) | (~c1_1(a237)) | c3_1(a252) | (~c0_1(a252)))),
% 0.92/1.13 inference(rewrite,[status(thm)],[])).
% 0.92/1.13 tff(2662,plain,
% 0.92/1.13 (((~ndr1_0) | (~c2_1(a261)) | (~c3_1(a261)) | (~c1_1(a261)) | c3_1(a237) | (~c1_1(a237)) | (~c2_1(a237)) | c3_1(a252) | c1_1(a252) | (~c0_1(a252))) <=> (c1_1(a252) | c3_1(a237) | (~ndr1_0) | (~c1_1(a261)) | (~c2_1(a261)) | (~c3_1(a261)) | (~c2_1(a237)) | (~c1_1(a237)) | c3_1(a252) | (~c0_1(a252)))),
% 0.92/1.13 inference(rewrite,[status(thm)],[])).
% 0.92/1.13 tff(2663,plain,
% 0.92/1.13 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_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) | (~c2_1(a261)) | (~c3_1(a261)) | (~c1_1(a261)) | c3_1(a237) | (~c1_1(a237)) | (~c2_1(a237)) | c3_1(a252) | c1_1(a252) | (~c0_1(a252)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_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(a252) | c3_1(a237) | (~ndr1_0) | (~c1_1(a261)) | (~c2_1(a261)) | (~c3_1(a261)) | (~c2_1(a237)) | (~c1_1(a237)) | c3_1(a252) | (~c0_1(a252))))),
% 0.92/1.13 inference(monotonicity,[status(thm)],[2662])).
% 0.92/1.13 tff(2664,plain,
% 0.92/1.13 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_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) | (~c2_1(a261)) | (~c3_1(a261)) | (~c1_1(a261)) | c3_1(a237) | (~c1_1(a237)) | (~c2_1(a237)) | c3_1(a252) | c1_1(a252) | (~c0_1(a252)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_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(a252) | c3_1(a237) | (~ndr1_0) | (~c1_1(a261)) | (~c2_1(a261)) | (~c3_1(a261)) | (~c2_1(a237)) | (~c1_1(a237)) | c3_1(a252) | (~c0_1(a252)))),
% 0.92/1.13 inference(transitivity,[status(thm)],[2663, 2661])).
% 0.92/1.13 tff(2665,plain,
% 0.92/1.13 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_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) | (~c2_1(a261)) | (~c3_1(a261)) | (~c1_1(a261)) | c3_1(a237) | (~c1_1(a237)) | (~c2_1(a237)) | c3_1(a252) | c1_1(a252) | (~c0_1(a252)))),
% 0.92/1.13 inference(quant_inst,[status(thm)],[])).
% 0.92/1.13 tff(2666,plain,
% 0.92/1.13 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_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(a252) | c3_1(a237) | (~ndr1_0) | (~c1_1(a261)) | (~c2_1(a261)) | (~c3_1(a261)) | (~c2_1(a237)) | (~c1_1(a237)) | c3_1(a252) | (~c0_1(a252))),
% 0.92/1.13 inference(modus_ponens,[status(thm)],[2665, 2664])).
% 0.92/1.13 tff(2667,plain,
% 0.92/1.13 (~c1_1(a237)),
% 0.92/1.13 inference(unit_resolution,[status(thm)],[2666, 110, 2624, 2623, 2622, 1892, 2660, 1906, 2659, 505, 2657])).
% 0.92/1.13 tff(2668,plain,
% 0.92/1.13 (c0_1(a237)),
% 0.92/1.13 inference(unit_resolution,[status(thm)],[575, 2658])).
% 0.92/1.13 tff(2669,plain,
% 0.92/1.13 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | (c3_1(a237) | (~ndr1_0) | (~c0_1(a234)) | (~c3_1(a234)) | c2_1(a234) | c1_1(a237) | (~c2_1(a237)) | (~c0_1(a237)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | c3_1(a237) | (~ndr1_0) | (~c0_1(a234)) | (~c3_1(a234)) | c2_1(a234) | c1_1(a237) | (~c2_1(a237)) | (~c0_1(a237)))),
% 0.92/1.13 inference(rewrite,[status(thm)],[])).
% 0.92/1.13 tff(2670,plain,
% 0.92/1.13 (((~ndr1_0) | c2_1(a234) | (~c3_1(a234)) | (~c0_1(a234)) | c3_1(a237) | c1_1(a237) | (~c2_1(a237)) | c3_1(a237) | c1_1(a237) | (~c0_1(a237))) <=> (c3_1(a237) | (~ndr1_0) | (~c0_1(a234)) | (~c3_1(a234)) | c2_1(a234) | c1_1(a237) | (~c2_1(a237)) | (~c0_1(a237)))),
% 0.92/1.13 inference(rewrite,[status(thm)],[])).
% 0.92/1.13 tff(2671,plain,
% 0.92/1.13 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a234) | (~c3_1(a234)) | (~c0_1(a234)) | c3_1(a237) | c1_1(a237) | (~c2_1(a237)) | c3_1(a237) | c1_1(a237) | (~c0_1(a237)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | (c3_1(a237) | (~ndr1_0) | (~c0_1(a234)) | (~c3_1(a234)) | c2_1(a234) | c1_1(a237) | (~c2_1(a237)) | (~c0_1(a237))))),
% 0.92/1.13 inference(monotonicity,[status(thm)],[2670])).
% 0.92/1.13 tff(2672,plain,
% 0.92/1.13 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a234) | (~c3_1(a234)) | (~c0_1(a234)) | c3_1(a237) | c1_1(a237) | (~c2_1(a237)) | c3_1(a237) | c1_1(a237) | (~c0_1(a237)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | c3_1(a237) | (~ndr1_0) | (~c0_1(a234)) | (~c3_1(a234)) | c2_1(a234) | c1_1(a237) | (~c2_1(a237)) | (~c0_1(a237)))),
% 0.92/1.13 inference(transitivity,[status(thm)],[2671, 2669])).
% 0.92/1.13 tff(2673,plain,
% 0.92/1.13 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a234) | (~c3_1(a234)) | (~c0_1(a234)) | c3_1(a237) | c1_1(a237) | (~c2_1(a237)) | c3_1(a237) | c1_1(a237) | (~c0_1(a237)))),
% 0.92/1.13 inference(quant_inst,[status(thm)],[])).
% 0.92/1.13 tff(2674,plain,
% 0.92/1.13 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | c3_1(a237) | (~ndr1_0) | (~c0_1(a234)) | (~c3_1(a234)) | c2_1(a234) | c1_1(a237) | (~c2_1(a237)) | (~c0_1(a237))),
% 0.92/1.13 inference(modus_ponens,[status(thm)],[2673, 2672])).
% 0.92/1.13 tff(2675,plain,
% 0.92/1.13 ($false),
% 0.92/1.13 inference(unit_resolution,[status(thm)],[2674, 110, 2647, 2649, 2668, 2660, 2659, 22, 2667, 2650])).
% 0.92/1.13 tff(2676,plain,(hskp9), inference(lemma,lemma(discharge,[]))).
% 0.92/1.13 tff(2677,plain,
% 0.92/1.13 (~c2_1(a226)),
% 0.92/1.13 inference(unit_resolution,[status(thm)],[818, 2676])).
% 0.92/1.13 tff(2678,plain,
% 0.92/1.13 (c0_1(a226)),
% 0.92/1.13 inference(unit_resolution,[status(thm)],[832, 2676])).
% 0.92/1.13 tff(2679,plain,
% 0.92/1.13 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | (c1_1(a252) | c2_1(a226) | (~ndr1_0) | (~c3_1(a226)) | (~c0_1(a226)) | c3_1(a252) | (~c0_1(a252)) | (~c2_1(a252)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | c1_1(a252) | c2_1(a226) | (~ndr1_0) | (~c3_1(a226)) | (~c0_1(a226)) | c3_1(a252) | (~c0_1(a252)) | (~c2_1(a252)))),
% 0.92/1.13 inference(rewrite,[status(thm)],[])).
% 0.92/1.13 tff(2680,plain,
% 0.92/1.13 (((~ndr1_0) | c2_1(a226) | (~c3_1(a226)) | (~c0_1(a226)) | c3_1(a252) | c1_1(a252) | (~c2_1(a252)) | c3_1(a252) | c1_1(a252) | (~c0_1(a252))) <=> (c1_1(a252) | c2_1(a226) | (~ndr1_0) | (~c3_1(a226)) | (~c0_1(a226)) | c3_1(a252) | (~c0_1(a252)) | (~c2_1(a252)))),
% 0.92/1.13 inference(rewrite,[status(thm)],[])).
% 0.92/1.13 tff(2681,plain,
% 0.92/1.13 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a226) | (~c3_1(a226)) | (~c0_1(a226)) | c3_1(a252) | c1_1(a252) | (~c2_1(a252)) | c3_1(a252) | c1_1(a252) | (~c0_1(a252)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | (c1_1(a252) | c2_1(a226) | (~ndr1_0) | (~c3_1(a226)) | (~c0_1(a226)) | c3_1(a252) | (~c0_1(a252)) | (~c2_1(a252))))),
% 0.92/1.13 inference(monotonicity,[status(thm)],[2680])).
% 0.92/1.13 tff(2682,plain,
% 0.92/1.13 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a226) | (~c3_1(a226)) | (~c0_1(a226)) | c3_1(a252) | c1_1(a252) | (~c2_1(a252)) | c3_1(a252) | c1_1(a252) | (~c0_1(a252)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | c1_1(a252) | c2_1(a226) | (~ndr1_0) | (~c3_1(a226)) | (~c0_1(a226)) | c3_1(a252) | (~c0_1(a252)) | (~c2_1(a252)))),
% 0.92/1.13 inference(transitivity,[status(thm)],[2681, 2679])).
% 0.92/1.13 tff(2683,plain,
% 0.92/1.13 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a226) | (~c3_1(a226)) | (~c0_1(a226)) | c3_1(a252) | c1_1(a252) | (~c2_1(a252)) | c3_1(a252) | c1_1(a252) | (~c0_1(a252)))),
% 0.92/1.13 inference(quant_inst,[status(thm)],[])).
% 0.92/1.13 tff(2684,plain,
% 0.92/1.13 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | c1_1(a252) | c2_1(a226) | (~ndr1_0) | (~c3_1(a226)) | (~c0_1(a226)) | c3_1(a252) | (~c0_1(a252)) | (~c2_1(a252))),
% 0.92/1.13 inference(modus_ponens,[status(thm)],[2683, 2682])).
% 0.92/1.13 tff(2685,plain,
% 0.92/1.13 (~c3_1(a226)),
% 0.92/1.13 inference(unit_resolution,[status(thm)],[2684, 110, 1892, 1884, 2678, 1906, 2677, 22, 12])).
% 0.92/1.13 tff(2686,plain,
% 0.92/1.13 (^[V: $i, U: $i] : refl((hskp1 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)) <=> (hskp1 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)))),
% 0.92/1.13 inference(bind,[status(th)],[])).
% 0.92/1.13 tff(2687,plain,
% 0.92/1.13 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 0.92/1.13 inference(quant_intro,[status(thm)],[2686])).
% 0.92/1.13 tff(2688,plain,
% 0.92/1.13 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 0.92/1.13 inference(rewrite,[status(thm)],[])).
% 0.92/1.13 tff(2689,plain,
% 0.92/1.13 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c0_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | c2_1(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)) | 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)) | c2_1(U)) | c3_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)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | 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)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | 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)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp1) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)) | hskp1))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)) | hskp1) <=> (hskp1 | (~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)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp1) <=> (hskp1 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))))),
% 0.92/1.13 inference(bind,[status(th)],[])).
% 0.92/1.13 tff(2690,plain,
% 0.92/1.13 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp1) <=> ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 0.92/1.13 inference(quant_intro,[status(thm)],[2689])).
% 0.92/1.13 tff(2691,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause157')).
% 0.92/1.13 tff(2692,plain,
% 0.92/1.13 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 0.92/1.13 inference(modus_ponens,[status(thm)],[2691, 2690])).
% 0.92/1.13 tff(2693,plain,
% 0.92/1.13 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 0.92/1.13 inference(modus_ponens,[status(thm)],[2692, 2688])).
% 0.92/1.13 tff(2694,plain,(
% 0.92/1.13 ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 0.92/1.13 inference(skolemize,[status(sab)],[2693])).
% 0.92/1.13 tff(2695,plain,
% 0.92/1.13 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 0.92/1.13 inference(modus_ponens,[status(thm)],[2694, 2687])).
% 0.92/1.13 tff(2696,assumption,(hskp21), introduced(assumption)).
% 0.92/1.13 tff(2697,plain,
% 0.92/1.13 (~c2_1(a259)),
% 0.92/1.13 inference(unit_resolution,[status(thm)],[975, 2696])).
% 0.92/1.13 tff(2698,plain,
% 0.92/1.13 (c3_1(a259)),
% 0.92/1.13 inference(unit_resolution,[status(thm)],[792, 2696])).
% 0.92/1.13 tff(2699,plain,
% 0.92/1.13 (c0_1(a259)),
% 0.92/1.13 inference(unit_resolution,[status(thm)],[783, 2696])).
% 0.92/1.13 tff(2700,plain,
% 0.92/1.13 ($false),
% 0.92/1.13 inference(unit_resolution,[status(thm)],[2162, 110, 2699, 2698, 1892, 1884, 2697, 1906, 22, 12])).
% 0.92/1.13 tff(2701,plain,((~hskp21) | c3_1(a252)), inference(lemma,lemma(discharge,[]))).
% 0.92/1.13 tff(2702,plain,
% 0.92/1.13 (~hskp21),
% 0.92/1.13 inference(unit_resolution,[status(thm)],[2701, 12])).
% 0.92/1.13 tff(2703,plain,
% 0.92/1.13 (~c1_1(a226)),
% 0.92/1.13 inference(unit_resolution,[status(thm)],[824, 2676])).
% 0.92/1.13 tff(2704,plain,
% 0.92/1.13 (((~![U: $i] : (hskp19 | hskp21 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | (hskp19 | hskp21 | c1_1(a226) | c2_1(a226) | (~ndr1_0) | c3_1(a226))) <=> ((~![U: $i] : (hskp19 | hskp21 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | hskp19 | hskp21 | c1_1(a226) | c2_1(a226) | (~ndr1_0) | c3_1(a226))),
% 0.92/1.13 inference(rewrite,[status(thm)],[])).
% 0.92/1.13 tff(2705,plain,
% 0.92/1.13 ((hskp19 | hskp21 | (~ndr1_0) | c2_1(a226) | c1_1(a226) | c3_1(a226)) <=> (hskp19 | hskp21 | c1_1(a226) | c2_1(a226) | (~ndr1_0) | c3_1(a226))),
% 0.92/1.13 inference(rewrite,[status(thm)],[])).
% 0.92/1.13 tff(2706,plain,
% 0.92/1.13 (((~![U: $i] : (hskp19 | hskp21 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | (hskp19 | hskp21 | (~ndr1_0) | c2_1(a226) | c1_1(a226) | c3_1(a226))) <=> ((~![U: $i] : (hskp19 | hskp21 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | (hskp19 | hskp21 | c1_1(a226) | c2_1(a226) | (~ndr1_0) | c3_1(a226)))),
% 0.92/1.13 inference(monotonicity,[status(thm)],[2705])).
% 0.92/1.13 tff(2707,plain,
% 0.92/1.13 (((~![U: $i] : (hskp19 | hskp21 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | (hskp19 | hskp21 | (~ndr1_0) | c2_1(a226) | c1_1(a226) | c3_1(a226))) <=> ((~![U: $i] : (hskp19 | hskp21 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | hskp19 | hskp21 | c1_1(a226) | c2_1(a226) | (~ndr1_0) | c3_1(a226))),
% 0.92/1.13 inference(transitivity,[status(thm)],[2706, 2704])).
% 0.92/1.13 tff(2708,plain,
% 0.92/1.13 ((~![U: $i] : (hskp19 | hskp21 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | (hskp19 | hskp21 | (~ndr1_0) | c2_1(a226) | c1_1(a226) | c3_1(a226))),
% 0.92/1.13 inference(quant_inst,[status(thm)],[])).
% 0.92/1.13 tff(2709,plain,
% 0.92/1.13 ((~![U: $i] : (hskp19 | hskp21 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | hskp19 | hskp21 | c1_1(a226) | c2_1(a226) | (~ndr1_0) | c3_1(a226)),
% 0.92/1.13 inference(modus_ponens,[status(thm)],[2708, 2707])).
% 0.92/1.13 tff(2710,plain,
% 0.92/1.13 (hskp19 | hskp21 | c3_1(a226)),
% 0.92/1.13 inference(unit_resolution,[status(thm)],[2709, 110, 2703, 2677, 1630])).
% 0.92/1.13 tff(2711,plain,
% 0.92/1.13 (hskp19),
% 0.92/1.13 inference(unit_resolution,[status(thm)],[2710, 2702, 2685])).
% 0.92/1.13 tff(2712,plain,
% 0.92/1.13 (~c3_1(a255)),
% 0.92/1.13 inference(unit_resolution,[status(thm)],[267, 2711])).
% 0.92/1.13 tff(2713,plain,
% 0.92/1.13 (~c1_1(a255)),
% 0.92/1.13 inference(unit_resolution,[status(thm)],[273, 2711])).
% 0.92/1.13 tff(2714,plain,
% 0.92/1.13 (~c0_1(a255)),
% 0.92/1.13 inference(unit_resolution,[status(thm)],[279, 2711])).
% 0.92/1.13 tff(2715,plain,
% 0.92/1.13 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | c0_1(a255) | c1_1(a255) | c3_1(a255) | c2_1(a226) | (~ndr1_0) | c3_1(a226) | (~c0_1(a226)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp1 | c0_1(a255) | c1_1(a255) | c3_1(a255) | c2_1(a226) | (~ndr1_0) | c3_1(a226) | (~c0_1(a226)))),
% 0.92/1.13 inference(rewrite,[status(thm)],[])).
% 0.92/1.13 tff(2716,plain,
% 0.92/1.13 ((hskp1 | (~ndr1_0) | c2_1(a226) | c3_1(a226) | (~c0_1(a226)) | c3_1(a255) | c1_1(a255) | c0_1(a255)) <=> (hskp1 | c0_1(a255) | c1_1(a255) | c3_1(a255) | c2_1(a226) | (~ndr1_0) | c3_1(a226) | (~c0_1(a226)))),
% 0.92/1.13 inference(rewrite,[status(thm)],[])).
% 0.92/1.13 tff(2717,plain,
% 0.92/1.13 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | (~ndr1_0) | c2_1(a226) | c3_1(a226) | (~c0_1(a226)) | c3_1(a255) | c1_1(a255) | c0_1(a255))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | c0_1(a255) | c1_1(a255) | c3_1(a255) | c2_1(a226) | (~ndr1_0) | c3_1(a226) | (~c0_1(a226))))),
% 0.92/1.13 inference(monotonicity,[status(thm)],[2716])).
% 0.92/1.13 tff(2718,plain,
% 0.92/1.13 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | (~ndr1_0) | c2_1(a226) | c3_1(a226) | (~c0_1(a226)) | c3_1(a255) | c1_1(a255) | c0_1(a255))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp1 | c0_1(a255) | c1_1(a255) | c3_1(a255) | c2_1(a226) | (~ndr1_0) | c3_1(a226) | (~c0_1(a226)))),
% 0.92/1.14 inference(transitivity,[status(thm)],[2717, 2715])).
% 0.92/1.14 tff(2719,plain,
% 0.92/1.14 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | (~ndr1_0) | c2_1(a226) | c3_1(a226) | (~c0_1(a226)) | c3_1(a255) | c1_1(a255) | c0_1(a255))),
% 0.92/1.14 inference(quant_inst,[status(thm)],[])).
% 0.92/1.14 tff(2720,plain,
% 0.92/1.14 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp1 | c0_1(a255) | c1_1(a255) | c3_1(a255) | c2_1(a226) | (~ndr1_0) | c3_1(a226) | (~c0_1(a226))),
% 0.92/1.14 inference(modus_ponens,[status(thm)],[2719, 2718])).
% 0.92/1.14 tff(2721,plain,
% 0.92/1.14 (hskp1),
% 0.92/1.14 inference(unit_resolution,[status(thm)],[2720, 110, 2678, 2714, 2713, 2712, 2677, 2695, 2685])).
% 0.92/1.14 tff(2722,plain,
% 0.92/1.14 (~c3_1(a214)),
% 0.92/1.14 inference(unit_resolution,[status(thm)],[997, 2721])).
% 0.92/1.14 tff(2723,plain,
% 0.92/1.14 (~c0_1(a214)),
% 0.92/1.14 inference(unit_resolution,[status(thm)],[1057, 2721])).
% 0.92/1.14 tff(2724,plain,
% 0.92/1.14 (c2_1(a214)),
% 0.92/1.14 inference(unit_resolution,[status(thm)],[1043, 2721])).
% 0.92/1.14 tff(2725,plain,
% 0.92/1.14 (c2_1(a237)),
% 0.92/1.14 inference(unit_resolution,[status(thm)],[556, 2526])).
% 0.92/1.14 tff(2726,assumption,(~c3_1(a226)), introduced(assumption)).
% 0.92/1.14 tff(2727,plain,
% 0.92/1.14 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp26 | c0_1(a231) | c2_1(a226) | (~ndr1_0) | c3_1(a226) | (~c0_1(a226)) | (~c2_1(a231)) | (~c1_1(a231)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp26 | c0_1(a231) | c2_1(a226) | (~ndr1_0) | c3_1(a226) | (~c0_1(a226)) | (~c2_1(a231)) | (~c1_1(a231)))),
% 0.92/1.14 inference(rewrite,[status(thm)],[])).
% 0.92/1.14 tff(2728,plain,
% 0.92/1.14 ((hskp26 | (~ndr1_0) | c2_1(a226) | c3_1(a226) | (~c0_1(a226)) | c0_1(a231) | (~c1_1(a231)) | (~c2_1(a231))) <=> (hskp26 | c0_1(a231) | c2_1(a226) | (~ndr1_0) | c3_1(a226) | (~c0_1(a226)) | (~c2_1(a231)) | (~c1_1(a231)))),
% 0.92/1.14 inference(rewrite,[status(thm)],[])).
% 0.92/1.14 tff(2729,plain,
% 0.92/1.14 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp26 | (~ndr1_0) | c2_1(a226) | c3_1(a226) | (~c0_1(a226)) | c0_1(a231) | (~c1_1(a231)) | (~c2_1(a231)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp26 | c0_1(a231) | c2_1(a226) | (~ndr1_0) | c3_1(a226) | (~c0_1(a226)) | (~c2_1(a231)) | (~c1_1(a231))))),
% 0.92/1.14 inference(monotonicity,[status(thm)],[2728])).
% 0.92/1.14 tff(2730,plain,
% 0.92/1.14 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp26 | (~ndr1_0) | c2_1(a226) | c3_1(a226) | (~c0_1(a226)) | c0_1(a231) | (~c1_1(a231)) | (~c2_1(a231)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp26 | c0_1(a231) | c2_1(a226) | (~ndr1_0) | c3_1(a226) | (~c0_1(a226)) | (~c2_1(a231)) | (~c1_1(a231)))),
% 0.92/1.14 inference(transitivity,[status(thm)],[2729, 2727])).
% 0.92/1.14 tff(2731,plain,
% 0.92/1.14 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp26 | (~ndr1_0) | c2_1(a226) | c3_1(a226) | (~c0_1(a226)) | c0_1(a231) | (~c1_1(a231)) | (~c2_1(a231)))),
% 0.92/1.14 inference(quant_inst,[status(thm)],[])).
% 0.92/1.14 tff(2732,plain,
% 0.92/1.14 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp26 | c0_1(a231) | c2_1(a226) | (~ndr1_0) | c3_1(a226) | (~c0_1(a226)) | (~c2_1(a231)) | (~c1_1(a231))),
% 0.92/1.14 inference(modus_ponens,[status(thm)],[2731, 2730])).
% 0.92/1.14 tff(2733,plain,
% 0.92/1.14 (~c2_1(a231)),
% 0.92/1.14 inference(unit_resolution,[status(thm)],[2732, 110, 1, 605, 2678, 1506, 2677, 1542, 2726])).
% 0.92/1.14 tff(2734,plain,
% 0.92/1.14 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp26 | c3_1(a237) | c0_1(a231) | (~ndr1_0) | c2_1(a231) | (~c3_1(a231)) | (~c2_1(a237)) | (~c1_1(a237)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp26 | c3_1(a237) | c0_1(a231) | (~ndr1_0) | c2_1(a231) | (~c3_1(a231)) | (~c2_1(a237)) | (~c1_1(a237)))),
% 0.92/1.14 inference(rewrite,[status(thm)],[])).
% 0.92/1.14 tff(2735,plain,
% 0.92/1.14 ((hskp26 | (~ndr1_0) | c3_1(a237) | (~c2_1(a237)) | (~c1_1(a237)) | c0_1(a231) | c2_1(a231) | (~c3_1(a231))) <=> (hskp26 | c3_1(a237) | c0_1(a231) | (~ndr1_0) | c2_1(a231) | (~c3_1(a231)) | (~c2_1(a237)) | (~c1_1(a237)))),
% 0.92/1.14 inference(rewrite,[status(thm)],[])).
% 0.92/1.14 tff(2736,plain,
% 0.92/1.14 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp26 | (~ndr1_0) | c3_1(a237) | (~c2_1(a237)) | (~c1_1(a237)) | c0_1(a231) | c2_1(a231) | (~c3_1(a231)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp26 | c3_1(a237) | c0_1(a231) | (~ndr1_0) | c2_1(a231) | (~c3_1(a231)) | (~c2_1(a237)) | (~c1_1(a237))))),
% 0.92/1.14 inference(monotonicity,[status(thm)],[2735])).
% 0.92/1.14 tff(2737,plain,
% 0.92/1.14 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp26 | (~ndr1_0) | c3_1(a237) | (~c2_1(a237)) | (~c1_1(a237)) | c0_1(a231) | c2_1(a231) | (~c3_1(a231)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp26 | c3_1(a237) | c0_1(a231) | (~ndr1_0) | c2_1(a231) | (~c3_1(a231)) | (~c2_1(a237)) | (~c1_1(a237)))),
% 0.92/1.14 inference(transitivity,[status(thm)],[2736, 2734])).
% 0.92/1.14 tff(2738,plain,
% 0.92/1.14 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp26 | (~ndr1_0) | c3_1(a237) | (~c2_1(a237)) | (~c1_1(a237)) | c0_1(a231) | c2_1(a231) | (~c3_1(a231)))),
% 0.92/1.14 inference(quant_inst,[status(thm)],[])).
% 0.92/1.14 tff(2739,plain,
% 0.92/1.14 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp26 | c3_1(a237) | c0_1(a231) | (~ndr1_0) | c2_1(a231) | (~c3_1(a231)) | (~c2_1(a237)) | (~c1_1(a237))),
% 0.92/1.14 inference(modus_ponens,[status(thm)],[2738, 2737])).
% 0.92/1.14 tff(2740,plain,
% 0.92/1.14 (~c1_1(a237)),
% 0.92/1.14 inference(unit_resolution,[status(thm)],[2739, 110, 1, 1800, 1505, 164, 1506, 2525, 2733])).
% 0.92/1.14 tff(2741,plain,
% 0.92/1.14 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | (c3_1(a237) | c1_1(a226) | c2_1(a226) | (~ndr1_0) | (~c0_1(a226)) | c2_1(a231) | (~c1_1(a231)) | (~c3_1(a231)) | c1_1(a237) | (~c2_1(a237)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | c3_1(a237) | c1_1(a226) | c2_1(a226) | (~ndr1_0) | (~c0_1(a226)) | c2_1(a231) | (~c1_1(a231)) | (~c3_1(a231)) | c1_1(a237) | (~c2_1(a237)))),
% 0.92/1.14 inference(rewrite,[status(thm)],[])).
% 0.92/1.14 tff(2742,plain,
% 0.92/1.14 (((~ndr1_0) | c2_1(a231) | (~c3_1(a231)) | (~c1_1(a231)) | c3_1(a237) | c1_1(a237) | (~c2_1(a237)) | c2_1(a226) | c1_1(a226) | (~c0_1(a226))) <=> (c3_1(a237) | c1_1(a226) | c2_1(a226) | (~ndr1_0) | (~c0_1(a226)) | c2_1(a231) | (~c1_1(a231)) | (~c3_1(a231)) | c1_1(a237) | (~c2_1(a237)))),
% 0.92/1.14 inference(rewrite,[status(thm)],[])).
% 0.92/1.14 tff(2743,plain,
% 0.92/1.14 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a231) | (~c3_1(a231)) | (~c1_1(a231)) | c3_1(a237) | c1_1(a237) | (~c2_1(a237)) | c2_1(a226) | c1_1(a226) | (~c0_1(a226)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | (c3_1(a237) | c1_1(a226) | c2_1(a226) | (~ndr1_0) | (~c0_1(a226)) | c2_1(a231) | (~c1_1(a231)) | (~c3_1(a231)) | c1_1(a237) | (~c2_1(a237))))),
% 0.92/1.14 inference(monotonicity,[status(thm)],[2742])).
% 0.92/1.14 tff(2744,plain,
% 0.92/1.14 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a231) | (~c3_1(a231)) | (~c1_1(a231)) | c3_1(a237) | c1_1(a237) | (~c2_1(a237)) | c2_1(a226) | c1_1(a226) | (~c0_1(a226)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | c3_1(a237) | c1_1(a226) | c2_1(a226) | (~ndr1_0) | (~c0_1(a226)) | c2_1(a231) | (~c1_1(a231)) | (~c3_1(a231)) | c1_1(a237) | (~c2_1(a237)))),
% 0.92/1.14 inference(transitivity,[status(thm)],[2743, 2741])).
% 0.92/1.14 tff(2745,plain,
% 0.92/1.14 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a231) | (~c3_1(a231)) | (~c1_1(a231)) | c3_1(a237) | c1_1(a237) | (~c2_1(a237)) | c2_1(a226) | c1_1(a226) | (~c0_1(a226)))),
% 0.92/1.14 inference(quant_inst,[status(thm)],[])).
% 0.92/1.14 tff(2746,plain,
% 0.92/1.14 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | c3_1(a237) | c1_1(a226) | c2_1(a226) | (~ndr1_0) | (~c0_1(a226)) | c2_1(a231) | (~c1_1(a231)) | (~c3_1(a231)) | c1_1(a237) | (~c2_1(a237))),
% 0.92/1.14 inference(modus_ponens,[status(thm)],[2745, 2744])).
% 0.92/1.14 tff(2747,plain,
% 0.92/1.14 ($false),
% 0.92/1.14 inference(unit_resolution,[status(thm)],[2746, 110, 1800, 605, 1505, 2678, 164, 2703, 2677, 803, 2740, 2733])).
% 0.92/1.14 tff(2748,plain,((~hskp10) | (~c2_1(a237)) | c3_1(a237) | hskp26 | c3_1(a226)), inference(lemma,lemma(discharge,[]))).
% 0.92/1.14 tff(2749,plain,
% 0.92/1.14 (~hskp10),
% 0.92/1.14 inference(unit_resolution,[status(thm)],[2748, 2725, 2527, 1, 2685])).
% 0.92/1.14 tff(2750,plain,
% 0.92/1.14 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp10 | c1_1(a252) | c0_1(a214) | c3_1(a214) | (~ndr1_0) | (~c2_1(a214)) | (~c0_1(a252)) | (~c2_1(a252)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp10 | c1_1(a252) | c0_1(a214) | c3_1(a214) | (~ndr1_0) | (~c2_1(a214)) | (~c0_1(a252)) | (~c2_1(a252)))),
% 0.92/1.14 inference(rewrite,[status(thm)],[])).
% 0.92/1.14 tff(2751,plain,
% 0.92/1.14 ((hskp10 | (~ndr1_0) | c1_1(a252) | (~c2_1(a252)) | (~c0_1(a252)) | c3_1(a214) | c0_1(a214) | (~c2_1(a214))) <=> (hskp10 | c1_1(a252) | c0_1(a214) | c3_1(a214) | (~ndr1_0) | (~c2_1(a214)) | (~c0_1(a252)) | (~c2_1(a252)))),
% 0.92/1.14 inference(rewrite,[status(thm)],[])).
% 0.92/1.14 tff(2752,plain,
% 0.92/1.14 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp10 | (~ndr1_0) | c1_1(a252) | (~c2_1(a252)) | (~c0_1(a252)) | c3_1(a214) | c0_1(a214) | (~c2_1(a214)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp10 | c1_1(a252) | c0_1(a214) | c3_1(a214) | (~ndr1_0) | (~c2_1(a214)) | (~c0_1(a252)) | (~c2_1(a252))))),
% 0.92/1.14 inference(monotonicity,[status(thm)],[2751])).
% 0.92/1.14 tff(2753,plain,
% 0.92/1.14 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp10 | (~ndr1_0) | c1_1(a252) | (~c2_1(a252)) | (~c0_1(a252)) | c3_1(a214) | c0_1(a214) | (~c2_1(a214)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp10 | c1_1(a252) | c0_1(a214) | c3_1(a214) | (~ndr1_0) | (~c2_1(a214)) | (~c0_1(a252)) | (~c2_1(a252)))),
% 0.92/1.14 inference(transitivity,[status(thm)],[2752, 2750])).
% 0.92/1.14 tff(2754,plain,
% 0.92/1.14 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp10 | (~ndr1_0) | c1_1(a252) | (~c2_1(a252)) | (~c0_1(a252)) | c3_1(a214) | c0_1(a214) | (~c2_1(a214)))),
% 0.92/1.14 inference(quant_inst,[status(thm)],[])).
% 0.92/1.14 tff(2755,plain,
% 0.92/1.14 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp10 | c1_1(a252) | c0_1(a214) | c3_1(a214) | (~ndr1_0) | (~c2_1(a214)) | (~c0_1(a252)) | (~c2_1(a252))),
% 0.92/1.14 inference(modus_ponens,[status(thm)],[2754, 2753])).
% 0.92/1.14 tff(2756,plain,
% 0.92/1.14 ($false),
% 0.92/1.14 inference(unit_resolution,[status(thm)],[2755, 110, 2749, 1892, 1884, 2724, 1906, 2723, 2722, 11])).
% 0.92/1.14 tff(2757,plain,(c3_1(a252) | hskp26), inference(lemma,lemma(discharge,[]))).
% 0.92/1.14 tff(2758,plain,
% 0.92/1.14 (c3_1(a252)),
% 0.92/1.14 inference(unit_resolution,[status(thm)],[2757, 1])).
% 0.92/1.14 tff(2759,plain,
% 0.92/1.14 (^[V: $i, U: $i] : refl((hskp11 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V))) <=> (hskp11 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V))))),
% 0.92/1.14 inference(bind,[status(th)],[])).
% 0.92/1.14 tff(2760,plain,
% 0.92/1.14 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.92/1.14 inference(quant_intro,[status(thm)],[2759])).
% 0.92/1.14 tff(2761,plain,
% 0.92/1.14 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.92/1.14 inference(rewrite,[status(thm)],[])).
% 0.92/1.14 tff(2762,plain,
% 0.92/1.14 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c0_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V))) | c3_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c0_1(V)) | c3_1(V)) | hskp11) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V))) | hskp11))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V))) | hskp11) <=> (hskp11 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c0_1(V)) | c3_1(V)) | hskp11) <=> (hskp11 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))))),
% 0.92/1.14 inference(bind,[status(th)],[])).
% 0.92/1.14 tff(2763,plain,
% 0.92/1.14 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c0_1(V)) | c3_1(V)) | hskp11) <=> ![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.92/1.14 inference(quant_intro,[status(thm)],[2762])).
% 0.92/1.14 tff(2764,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c0_1(V)) | c3_1(V)) | hskp11)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause167')).
% 0.92/1.14 tff(2765,plain,
% 0.92/1.14 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.92/1.14 inference(modus_ponens,[status(thm)],[2764, 2763])).
% 0.92/1.14 tff(2766,plain,
% 0.92/1.14 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.92/1.14 inference(modus_ponens,[status(thm)],[2765, 2761])).
% 0.92/1.14 tff(2767,plain,(
% 0.92/1.14 ![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.92/1.14 inference(skolemize,[status(sab)],[2766])).
% 0.92/1.14 tff(2768,plain,
% 0.92/1.14 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.92/1.14 inference(modus_ponens,[status(thm)],[2767, 2760])).
% 0.92/1.14 tff(2769,plain,
% 0.92/1.14 (hskp23),
% 0.92/1.14 inference(unit_resolution,[status(thm)],[2083, 2758, 1])).
% 0.92/1.14 tff(2770,plain,
% 0.92/1.14 (~c3_1(a274)),
% 0.92/1.14 inference(unit_resolution,[status(thm)],[2089, 2769])).
% 0.92/1.14 tff(2771,plain,
% 0.92/1.14 (~c0_1(a274)),
% 0.92/1.14 inference(unit_resolution,[status(thm)],[2110, 2769])).
% 0.92/1.14 tff(2772,plain,
% 0.92/1.14 (c1_1(a274)),
% 0.92/1.14 inference(unit_resolution,[status(thm)],[2097, 2769])).
% 0.92/1.14 tff(2773,plain,
% 0.92/1.14 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp11 | c0_1(a274) | c3_1(a274) | c1_1(a252) | (~ndr1_0) | (~c0_1(a252)) | (~c2_1(a252)) | (~c1_1(a274)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp11 | c0_1(a274) | c3_1(a274) | c1_1(a252) | (~ndr1_0) | (~c0_1(a252)) | (~c2_1(a252)) | (~c1_1(a274)))),
% 0.92/1.14 inference(rewrite,[status(thm)],[])).
% 0.92/1.14 tff(2774,plain,
% 0.92/1.14 ((hskp11 | (~ndr1_0) | c1_1(a252) | (~c2_1(a252)) | (~c0_1(a252)) | c3_1(a274) | c0_1(a274) | (~c1_1(a274))) <=> (hskp11 | c0_1(a274) | c3_1(a274) | c1_1(a252) | (~ndr1_0) | (~c0_1(a252)) | (~c2_1(a252)) | (~c1_1(a274)))),
% 0.92/1.14 inference(rewrite,[status(thm)],[])).
% 0.92/1.14 tff(2775,plain,
% 0.92/1.14 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp11 | (~ndr1_0) | c1_1(a252) | (~c2_1(a252)) | (~c0_1(a252)) | c3_1(a274) | c0_1(a274) | (~c1_1(a274)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp11 | c0_1(a274) | c3_1(a274) | c1_1(a252) | (~ndr1_0) | (~c0_1(a252)) | (~c2_1(a252)) | (~c1_1(a274))))),
% 0.92/1.14 inference(monotonicity,[status(thm)],[2774])).
% 0.92/1.14 tff(2776,plain,
% 0.92/1.14 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp11 | (~ndr1_0) | c1_1(a252) | (~c2_1(a252)) | (~c0_1(a252)) | c3_1(a274) | c0_1(a274) | (~c1_1(a274)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp11 | c0_1(a274) | c3_1(a274) | c1_1(a252) | (~ndr1_0) | (~c0_1(a252)) | (~c2_1(a252)) | (~c1_1(a274)))),
% 0.92/1.14 inference(transitivity,[status(thm)],[2775, 2773])).
% 0.92/1.14 tff(2777,plain,
% 0.92/1.14 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp11 | (~ndr1_0) | c1_1(a252) | (~c2_1(a252)) | (~c0_1(a252)) | c3_1(a274) | c0_1(a274) | (~c1_1(a274)))),
% 0.92/1.14 inference(quant_inst,[status(thm)],[])).
% 0.92/1.14 tff(2778,plain,
% 0.92/1.14 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp11 | c0_1(a274) | c3_1(a274) | c1_1(a252) | (~ndr1_0) | (~c0_1(a252)) | (~c2_1(a252)) | (~c1_1(a274))),
% 0.92/1.14 inference(modus_ponens,[status(thm)],[2777, 2776])).
% 0.92/1.14 tff(2779,plain,
% 0.92/1.14 (hskp11),
% 0.92/1.14 inference(unit_resolution,[status(thm)],[2778, 110, 2772, 1892, 1884, 2771, 2770, 1906, 2768])).
% 0.92/1.14 tff(2780,plain,
% 0.92/1.14 (((~hskp11) | (~c3_1(a236))) <=> ((~hskp11) | (~c3_1(a236)))),
% 0.92/1.14 inference(rewrite,[status(thm)],[])).
% 0.92/1.14 tff(2781,plain,
% 0.92/1.14 (((~c3_1(a236)) | (~hskp11)) <=> ((~hskp11) | (~c3_1(a236)))),
% 0.92/1.14 inference(rewrite,[status(thm)],[])).
% 0.92/1.14 tff(2782,axiom,((~c3_1(a236)) | (~hskp11)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause110')).
% 0.92/1.14 tff(2783,plain,
% 0.92/1.14 ((~hskp11) | (~c3_1(a236))),
% 0.92/1.14 inference(modus_ponens,[status(thm)],[2782, 2781])).
% 0.92/1.14 tff(2784,plain,
% 0.92/1.14 ((~hskp11) | (~c3_1(a236))),
% 0.92/1.14 inference(modus_ponens,[status(thm)],[2783, 2780])).
% 0.92/1.14 tff(2785,plain,
% 0.92/1.14 (~c3_1(a236)),
% 0.92/1.14 inference(unit_resolution,[status(thm)],[2784, 2779])).
% 0.92/1.14 tff(2786,plain,
% 0.92/1.14 (((~hskp11) | (~c2_1(a236))) <=> ((~hskp11) | (~c2_1(a236)))),
% 0.92/1.14 inference(rewrite,[status(thm)],[])).
% 0.92/1.14 tff(2787,plain,
% 0.92/1.14 (((~c2_1(a236)) | (~hskp11)) <=> ((~hskp11) | (~c2_1(a236)))),
% 0.92/1.14 inference(rewrite,[status(thm)],[])).
% 0.92/1.14 tff(2788,axiom,((~c2_1(a236)) | (~hskp11)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause109')).
% 0.92/1.14 tff(2789,plain,
% 0.92/1.14 ((~hskp11) | (~c2_1(a236))),
% 0.92/1.14 inference(modus_ponens,[status(thm)],[2788, 2787])).
% 0.92/1.14 tff(2790,plain,
% 0.92/1.14 ((~hskp11) | (~c2_1(a236))),
% 0.92/1.14 inference(modus_ponens,[status(thm)],[2789, 2786])).
% 0.92/1.14 tff(2791,plain,
% 0.92/1.14 (~c2_1(a236)),
% 0.92/1.14 inference(unit_resolution,[status(thm)],[2790, 2779])).
% 0.92/1.14 tff(2792,plain,
% 0.92/1.14 (((~hskp11) | c0_1(a236)) <=> ((~hskp11) | c0_1(a236))),
% 0.92/1.14 inference(rewrite,[status(thm)],[])).
% 0.92/1.14 tff(2793,axiom,((~hskp11) | c0_1(a236)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause71')).
% 0.92/1.14 tff(2794,plain,
% 0.92/1.14 ((~hskp11) | c0_1(a236)),
% 0.92/1.14 inference(modus_ponens,[status(thm)],[2793, 2792])).
% 0.92/1.14 tff(2795,plain,
% 0.92/1.14 ((~hskp11) | c0_1(a236)),
% 0.92/1.14 inference(modus_ponens,[status(thm)],[2794, 2792])).
% 0.92/1.14 tff(2796,plain,
% 0.92/1.14 ((~hskp11) | c0_1(a236)),
% 0.92/1.14 inference(modus_ponens,[status(thm)],[2795, 2792])).
% 0.92/1.14 tff(2797,plain,
% 0.92/1.14 ((~hskp11) | c0_1(a236)),
% 0.92/1.14 inference(modus_ponens,[status(thm)],[2796, 2792])).
% 0.92/1.14 tff(2798,plain,
% 0.92/1.14 ((~hskp11) | c0_1(a236)),
% 0.92/1.14 inference(modus_ponens,[status(thm)],[2797, 2792])).
% 0.92/1.14 tff(2799,plain,
% 0.92/1.14 (c0_1(a236)),
% 0.92/1.14 inference(unit_resolution,[status(thm)],[2798, 2779])).
% 0.92/1.14 tff(2800,plain,
% 0.92/1.14 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))) | (c2_1(a236) | c3_1(a236) | (~ndr1_0) | (~c0_1(a236)) | (~c1_1(a236)) | (~c3_1(a252)) | (~c0_1(a252)) | (~c2_1(a252)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))) | c2_1(a236) | c3_1(a236) | (~ndr1_0) | (~c0_1(a236)) | (~c1_1(a236)) | (~c3_1(a252)) | (~c0_1(a252)) | (~c2_1(a252)))),
% 0.92/1.14 inference(rewrite,[status(thm)],[])).
% 0.92/1.14 tff(2801,plain,
% 0.92/1.14 (((~ndr1_0) | (~c2_1(a252)) | (~c3_1(a252)) | (~c0_1(a252)) | c3_1(a236) | (~c1_1(a236)) | (~c0_1(a236)) | c3_1(a236) | c2_1(a236) | (~c1_1(a236))) <=> (c2_1(a236) | c3_1(a236) | (~ndr1_0) | (~c0_1(a236)) | (~c1_1(a236)) | (~c3_1(a252)) | (~c0_1(a252)) | (~c2_1(a252)))),
% 0.92/1.14 inference(rewrite,[status(thm)],[])).
% 0.92/1.14 tff(2802,plain,
% 0.92/1.14 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a252)) | (~c3_1(a252)) | (~c0_1(a252)) | c3_1(a236) | (~c1_1(a236)) | (~c0_1(a236)) | c3_1(a236) | c2_1(a236) | (~c1_1(a236)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))) | (c2_1(a236) | c3_1(a236) | (~ndr1_0) | (~c0_1(a236)) | (~c1_1(a236)) | (~c3_1(a252)) | (~c0_1(a252)) | (~c2_1(a252))))),
% 0.92/1.14 inference(monotonicity,[status(thm)],[2801])).
% 0.92/1.14 tff(2803,plain,
% 0.92/1.14 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a252)) | (~c3_1(a252)) | (~c0_1(a252)) | c3_1(a236) | (~c1_1(a236)) | (~c0_1(a236)) | c3_1(a236) | c2_1(a236) | (~c1_1(a236)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))) | c2_1(a236) | c3_1(a236) | (~ndr1_0) | (~c0_1(a236)) | (~c1_1(a236)) | (~c3_1(a252)) | (~c0_1(a252)) | (~c2_1(a252)))),
% 0.92/1.14 inference(transitivity,[status(thm)],[2802, 2800])).
% 0.92/1.14 tff(2804,plain,
% 0.92/1.14 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a252)) | (~c3_1(a252)) | (~c0_1(a252)) | c3_1(a236) | (~c1_1(a236)) | (~c0_1(a236)) | c3_1(a236) | c2_1(a236) | (~c1_1(a236)))),
% 0.92/1.14 inference(quant_inst,[status(thm)],[])).
% 0.92/1.14 tff(2805,plain,
% 0.92/1.14 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))) | c2_1(a236) | c3_1(a236) | (~ndr1_0) | (~c0_1(a236)) | (~c1_1(a236)) | (~c3_1(a252)) | (~c0_1(a252)) | (~c2_1(a252))),
% 0.92/1.14 inference(modus_ponens,[status(thm)],[2804, 2803])).
% 0.92/1.14 tff(2806,plain,
% 0.92/1.14 (~c1_1(a236)),
% 0.92/1.14 inference(unit_resolution,[status(thm)],[2805, 110, 1892, 1884, 2799, 2791, 2785, 2066, 2758])).
% 0.92/1.14 tff(2807,plain,
% 0.92/1.14 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a274) | c3_1(a274) | c3_1(a236) | (~ndr1_0) | c1_1(a236) | (~c0_1(a236)) | (~c3_1(a252)) | (~c0_1(a252)) | (~c2_1(a252)) | (~c1_1(a274)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a274) | c3_1(a274) | c3_1(a236) | (~ndr1_0) | c1_1(a236) | (~c0_1(a236)) | (~c3_1(a252)) | (~c0_1(a252)) | (~c2_1(a252)) | (~c1_1(a274)))),
% 0.92/1.14 inference(rewrite,[status(thm)],[])).
% 0.92/1.14 tff(2808,plain,
% 0.92/1.14 (((~ndr1_0) | (~c2_1(a252)) | (~c3_1(a252)) | (~c0_1(a252)) | c3_1(a236) | c1_1(a236) | (~c0_1(a236)) | c3_1(a274) | c0_1(a274) | (~c1_1(a274))) <=> (c0_1(a274) | c3_1(a274) | c3_1(a236) | (~ndr1_0) | c1_1(a236) | (~c0_1(a236)) | (~c3_1(a252)) | (~c0_1(a252)) | (~c2_1(a252)) | (~c1_1(a274)))),
% 0.92/1.14 inference(rewrite,[status(thm)],[])).
% 0.92/1.14 tff(2809,plain,
% 0.92/1.14 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a252)) | (~c3_1(a252)) | (~c0_1(a252)) | c3_1(a236) | c1_1(a236) | (~c0_1(a236)) | c3_1(a274) | c0_1(a274) | (~c1_1(a274)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a274) | c3_1(a274) | c3_1(a236) | (~ndr1_0) | c1_1(a236) | (~c0_1(a236)) | (~c3_1(a252)) | (~c0_1(a252)) | (~c2_1(a252)) | (~c1_1(a274))))),
% 0.92/1.14 inference(monotonicity,[status(thm)],[2808])).
% 0.92/1.14 tff(2810,plain,
% 0.92/1.14 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a252)) | (~c3_1(a252)) | (~c0_1(a252)) | c3_1(a236) | c1_1(a236) | (~c0_1(a236)) | c3_1(a274) | c0_1(a274) | (~c1_1(a274)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a274) | c3_1(a274) | c3_1(a236) | (~ndr1_0) | c1_1(a236) | (~c0_1(a236)) | (~c3_1(a252)) | (~c0_1(a252)) | (~c2_1(a252)) | (~c1_1(a274)))),
% 0.92/1.14 inference(transitivity,[status(thm)],[2809, 2807])).
% 0.92/1.14 tff(2811,plain,
% 0.92/1.14 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a252)) | (~c3_1(a252)) | (~c0_1(a252)) | c3_1(a236) | c1_1(a236) | (~c0_1(a236)) | c3_1(a274) | c0_1(a274) | (~c1_1(a274)))),
% 0.92/1.14 inference(quant_inst,[status(thm)],[])).
% 0.92/1.14 tff(2812,plain,
% 0.92/1.14 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a274) | c3_1(a274) | c3_1(a236) | (~ndr1_0) | c1_1(a236) | (~c0_1(a236)) | (~c3_1(a252)) | (~c0_1(a252)) | (~c2_1(a252)) | (~c1_1(a274))),
% 0.92/1.15 inference(modus_ponens,[status(thm)],[2811, 2810])).
% 0.92/1.15 tff(2813,plain,
% 0.92/1.15 ($false),
% 0.92/1.15 inference(unit_resolution,[status(thm)],[2812, 110, 2772, 1892, 1884, 2799, 2771, 2770, 2785, 2408, 2806, 2758])).
% 0.92/1.15 tff(2814,plain,(hskp26), inference(lemma,lemma(discharge,[]))).
% 0.92/1.15 tff(2815,plain,
% 0.92/1.15 (c0_1(a234)),
% 0.92/1.15 inference(unit_resolution,[status(thm)],[79, 2814])).
% 0.92/1.15 tff(2816,plain,
% 0.92/1.15 (c1_1(a234)),
% 0.92/1.15 inference(unit_resolution,[status(thm)],[71, 2814])).
% 0.92/1.15 tff(2817,plain,
% 0.92/1.15 (c3_1(a234)),
% 0.92/1.15 inference(unit_resolution,[status(thm)],[63, 2814])).
% 0.92/1.15 tff(2818,plain,
% 0.92/1.15 (~c2_1(a234)),
% 0.92/1.15 inference(unit_resolution,[status(thm)],[2600, 2817, 2816, 2815])).
% 0.92/1.15 tff(2819,plain,
% 0.92/1.15 (^[V: $i, U: $i] : refl((hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))) <=> (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))))),
% 0.92/1.15 inference(bind,[status(th)],[])).
% 0.92/1.15 tff(2820,plain,
% 0.92/1.15 (![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 0.92/1.15 inference(quant_intro,[status(thm)],[2819])).
% 0.92/1.15 tff(2821,plain,
% 0.92/1.15 (![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 0.92/1.15 inference(rewrite,[status(thm)],[])).
% 0.92/1.15 tff(2822,plain,
% 0.92/1.15 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c2_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c2_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c2_1(U)) | c1_1(V)) | hskp22) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))) | hskp22))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))) | hskp22) <=> (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c2_1(U)) | c1_1(V)) | hskp22) <=> (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))))),
% 0.92/1.15 inference(bind,[status(th)],[])).
% 0.92/1.15 tff(2823,plain,
% 0.92/1.15 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c2_1(U)) | c1_1(V)) | hskp22) <=> ![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 0.92/1.15 inference(quant_intro,[status(thm)],[2822])).
% 0.92/1.15 tff(2824,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c2_1(U)) | c1_1(V)) | hskp22)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause183')).
% 0.92/1.15 tff(2825,plain,
% 0.92/1.15 (![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 0.92/1.15 inference(modus_ponens,[status(thm)],[2824, 2823])).
% 0.92/1.15 tff(2826,plain,
% 0.92/1.15 (![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 0.92/1.15 inference(modus_ponens,[status(thm)],[2825, 2821])).
% 0.92/1.15 tff(2827,plain,(
% 0.92/1.15 ![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 0.92/1.15 inference(skolemize,[status(sab)],[2826])).
% 0.92/1.15 tff(2828,plain,
% 0.92/1.15 (![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 0.92/1.15 inference(modus_ponens,[status(thm)],[2827, 2820])).
% 0.92/1.15 tff(2829,plain,
% 0.92/1.15 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp22 | c1_1(a252) | (~ndr1_0) | (~c0_1(a234)) | (~c1_1(a234)) | c2_1(a234) | (~c0_1(a252)) | (~c2_1(a252)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp22 | c1_1(a252) | (~ndr1_0) | (~c0_1(a234)) | (~c1_1(a234)) | c2_1(a234) | (~c0_1(a252)) | (~c2_1(a252)))),
% 0.92/1.15 inference(rewrite,[status(thm)],[])).
% 0.92/1.15 tff(2830,plain,
% 0.92/1.15 ((hskp22 | (~ndr1_0) | c2_1(a234) | (~c1_1(a234)) | (~c0_1(a234)) | c1_1(a252) | (~c2_1(a252)) | (~c0_1(a252))) <=> (hskp22 | c1_1(a252) | (~ndr1_0) | (~c0_1(a234)) | (~c1_1(a234)) | c2_1(a234) | (~c0_1(a252)) | (~c2_1(a252)))),
% 0.92/1.15 inference(rewrite,[status(thm)],[])).
% 0.92/1.15 tff(2831,plain,
% 0.92/1.15 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp22 | (~ndr1_0) | c2_1(a234) | (~c1_1(a234)) | (~c0_1(a234)) | c1_1(a252) | (~c2_1(a252)) | (~c0_1(a252)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp22 | c1_1(a252) | (~ndr1_0) | (~c0_1(a234)) | (~c1_1(a234)) | c2_1(a234) | (~c0_1(a252)) | (~c2_1(a252))))),
% 0.92/1.15 inference(monotonicity,[status(thm)],[2830])).
% 0.92/1.15 tff(2832,plain,
% 0.92/1.15 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp22 | (~ndr1_0) | c2_1(a234) | (~c1_1(a234)) | (~c0_1(a234)) | c1_1(a252) | (~c2_1(a252)) | (~c0_1(a252)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp22 | c1_1(a252) | (~ndr1_0) | (~c0_1(a234)) | (~c1_1(a234)) | c2_1(a234) | (~c0_1(a252)) | (~c2_1(a252)))),
% 0.92/1.15 inference(transitivity,[status(thm)],[2831, 2829])).
% 0.92/1.15 tff(2833,plain,
% 0.92/1.15 ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp22 | (~ndr1_0) | c2_1(a234) | (~c1_1(a234)) | (~c0_1(a234)) | c1_1(a252) | (~c2_1(a252)) | (~c0_1(a252)))),
% 0.92/1.15 inference(quant_inst,[status(thm)],[])).
% 0.92/1.15 tff(2834,plain,
% 0.92/1.15 ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp22 | c1_1(a252) | (~ndr1_0) | (~c0_1(a234)) | (~c1_1(a234)) | c2_1(a234) | (~c0_1(a252)) | (~c2_1(a252))),
% 0.92/1.15 inference(modus_ponens,[status(thm)],[2833, 2832])).
% 0.92/1.15 tff(2835,plain,
% 0.92/1.15 (hskp22),
% 0.92/1.15 inference(unit_resolution,[status(thm)],[2834, 110, 2815, 2816, 1892, 1884, 1906, 2828, 2818])).
% 0.92/1.15 tff(2836,plain,
% 0.92/1.15 (~c2_1(a271)),
% 0.92/1.15 inference(unit_resolution,[status(thm)],[1694, 2835])).
% 0.92/1.15 tff(2837,plain,
% 0.92/1.15 (~c1_1(a271)),
% 0.92/1.15 inference(unit_resolution,[status(thm)],[1700, 2835])).
% 0.92/1.15 tff(2838,plain,
% 0.92/1.15 (~c0_1(a271)),
% 0.92/1.15 inference(unit_resolution,[status(thm)],[1706, 2835])).
% 0.92/1.15 tff(2839,plain,
% 0.92/1.15 (hskp0),
% 0.92/1.15 inference(unit_resolution,[status(thm)],[1713, 110, 2838, 2837, 2836, 1008])).
% 0.92/1.15 tff(2840,plain,
% 0.92/1.15 (~c3_1(a213)),
% 0.92/1.15 inference(unit_resolution,[status(thm)],[744, 2839])).
% 0.92/1.15 tff(2841,plain,
% 0.92/1.15 (~c1_1(a213)),
% 0.92/1.15 inference(unit_resolution,[status(thm)],[750, 2839])).
% 0.92/1.15 tff(2842,plain,
% 0.92/1.15 (c2_1(a213)),
% 0.92/1.15 inference(unit_resolution,[status(thm)],[758, 2839])).
% 0.92/1.15 tff(2843,plain,
% 0.92/1.15 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | (c1_1(a226) | c2_1(a226) | c1_1(a213) | c3_1(a213) | (~ndr1_0) | (~c2_1(a213)) | (~c3_1(a234)) | (~c1_1(a234)) | c2_1(a234) | (~c0_1(a226)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | c1_1(a226) | c2_1(a226) | c1_1(a213) | c3_1(a213) | (~ndr1_0) | (~c2_1(a213)) | (~c3_1(a234)) | (~c1_1(a234)) | c2_1(a234) | (~c0_1(a226)))),
% 0.92/1.15 inference(rewrite,[status(thm)],[])).
% 0.92/1.15 tff(2844,plain,
% 0.92/1.15 (((~ndr1_0) | c2_1(a234) | (~c3_1(a234)) | (~c1_1(a234)) | c3_1(a213) | c1_1(a213) | (~c2_1(a213)) | c2_1(a226) | c1_1(a226) | (~c0_1(a226))) <=> (c1_1(a226) | c2_1(a226) | c1_1(a213) | c3_1(a213) | (~ndr1_0) | (~c2_1(a213)) | (~c3_1(a234)) | (~c1_1(a234)) | c2_1(a234) | (~c0_1(a226)))),
% 0.92/1.15 inference(rewrite,[status(thm)],[])).
% 0.92/1.15 tff(2845,plain,
% 0.92/1.15 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a234) | (~c3_1(a234)) | (~c1_1(a234)) | c3_1(a213) | c1_1(a213) | (~c2_1(a213)) | c2_1(a226) | c1_1(a226) | (~c0_1(a226)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | (c1_1(a226) | c2_1(a226) | c1_1(a213) | c3_1(a213) | (~ndr1_0) | (~c2_1(a213)) | (~c3_1(a234)) | (~c1_1(a234)) | c2_1(a234) | (~c0_1(a226))))),
% 0.92/1.15 inference(monotonicity,[status(thm)],[2844])).
% 0.92/1.15 tff(2846,plain,
% 0.92/1.15 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a234) | (~c3_1(a234)) | (~c1_1(a234)) | c3_1(a213) | c1_1(a213) | (~c2_1(a213)) | c2_1(a226) | c1_1(a226) | (~c0_1(a226)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | c1_1(a226) | c2_1(a226) | c1_1(a213) | c3_1(a213) | (~ndr1_0) | (~c2_1(a213)) | (~c3_1(a234)) | (~c1_1(a234)) | c2_1(a234) | (~c0_1(a226)))),
% 0.92/1.15 inference(transitivity,[status(thm)],[2845, 2843])).
% 0.92/1.15 tff(2847,plain,
% 0.92/1.15 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a234) | (~c3_1(a234)) | (~c1_1(a234)) | c3_1(a213) | c1_1(a213) | (~c2_1(a213)) | c2_1(a226) | c1_1(a226) | (~c0_1(a226)))),
% 0.92/1.15 inference(quant_inst,[status(thm)],[])).
% 0.92/1.15 tff(2848,plain,
% 0.92/1.15 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | c1_1(a226) | c2_1(a226) | c1_1(a213) | c3_1(a213) | (~ndr1_0) | (~c2_1(a213)) | (~c3_1(a234)) | (~c1_1(a234)) | c2_1(a234) | (~c0_1(a226))),
% 0.92/1.15 inference(modus_ponens,[status(thm)],[2847, 2846])).
% 0.92/1.15 tff(2849,plain,
% 0.92/1.15 ($false),
% 0.92/1.15 inference(unit_resolution,[status(thm)],[2848, 110, 2816, 2817, 2678, 2842, 2703, 2677, 2841, 2840, 803, 2818])).
% 0.92/1.15 % SZS output end Proof
% 0.92/1.16 % E exiting
%------------------------------------------------------------------------------