%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN444-1 : TPTP v9.0.0. Released v2.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n012.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 05:39:08 AM UTC 2025
% Result : Unsatisfiable 0.70s 0.90s
% Output : Proof 0.91s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SYN444-1 : TPTP v9.0.0. Released v2.1.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n012.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Fri Jun 20 12:34:40 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.70/0.90 % SZS status Unsatisfiable
% 0.70/0.90 % SZS output start Proof
% 0.70/0.90 tff(c3_1_type, type, (
% 0.70/0.90 c3_1: $i > $o)).
% 0.70/0.90 tff(c2_1_type, type, (
% 0.70/0.90 c2_1: $i > $o)).
% 0.70/0.90 tff(c0_1_type, type, (
% 0.70/0.90 c0_1: $i > $o)).
% 0.70/0.90 tff(c1_1_type, type, (
% 0.70/0.90 c1_1: $i > $o)).
% 0.70/0.90 tff(ndr1_0_type, type, (
% 0.70/0.90 ndr1_0: $o)).
% 0.70/0.90 tff(a216_type, type, (
% 0.70/0.90 a216: $i)).
% 0.70/0.90 tff(hskp3_type, type, (
% 0.70/0.90 hskp3: $o)).
% 0.70/0.90 tff(a213_type, type, (
% 0.70/0.90 a213: $i)).
% 0.70/0.90 tff(hskp10_type, type, (
% 0.70/0.90 hskp10: $o)).
% 0.70/0.90 tff(a229_type, type, (
% 0.70/0.90 a229: $i)).
% 0.70/0.90 tff(a236_type, type, (
% 0.70/0.90 a236: $i)).
% 0.70/0.90 tff(a230_type, type, (
% 0.70/0.90 a230: $i)).
% 0.70/0.90 tff(hskp11_type, type, (
% 0.70/0.90 hskp11: $o)).
% 0.70/0.90 tff(hskp0_type, type, (
% 0.70/0.90 hskp0: $o)).
% 0.70/0.90 tff(a235_type, type, (
% 0.70/0.90 a235: $i)).
% 0.70/0.90 tff(a225_type, type, (
% 0.70/0.90 a225: $i)).
% 0.70/0.90 tff(hskp8_type, type, (
% 0.70/0.90 hskp8: $o)).
% 0.70/0.90 tff(a238_type, type, (
% 0.70/0.90 a238: $i)).
% 0.70/0.90 tff(hskp12_type, type, (
% 0.70/0.90 hskp12: $o)).
% 0.70/0.90 tff(a259_type, type, (
% 0.70/0.90 a259: $i)).
% 0.70/0.90 tff(hskp20_type, type, (
% 0.70/0.90 hskp20: $o)).
% 0.70/0.90 tff(a247_type, type, (
% 0.70/0.90 a247: $i)).
% 0.70/0.90 tff(hskp13_type, type, (
% 0.70/0.90 hskp13: $o)).
% 0.70/0.90 tff(hskp18_type, type, (
% 0.70/0.90 hskp18: $o)).
% 0.70/0.90 tff(hskp23_type, type, (
% 0.70/0.90 hskp23: $o)).
% 0.70/0.90 tff(a278_type, type, (
% 0.70/0.90 a278: $i)).
% 0.70/0.90 tff(hskp24_type, type, (
% 0.70/0.90 hskp24: $o)).
% 0.70/0.90 tff(a232_type, type, (
% 0.70/0.90 a232: $i)).
% 0.70/0.90 tff(hskp27_type, type, (
% 0.70/0.90 hskp27: $o)).
% 0.70/0.90 tff(hskp6_type, type, (
% 0.70/0.90 hskp6: $o)).
% 0.70/0.90 tff(a252_type, type, (
% 0.70/0.90 a252: $i)).
% 0.70/0.90 tff(hskp19_type, type, (
% 0.70/0.90 hskp19: $o)).
% 0.70/0.90 tff(a282_type, type, (
% 0.70/0.90 a282: $i)).
% 0.70/0.90 tff(hskp15_type, type, (
% 0.70/0.90 hskp15: $o)).
% 0.70/0.90 tff(a215_type, type, (
% 0.70/0.90 a215: $i)).
% 0.70/0.90 tff(hskp2_type, type, (
% 0.70/0.90 hskp2: $o)).
% 0.70/0.90 tff(a243_type, type, (
% 0.70/0.90 a243: $i)).
% 0.70/0.90 tff(a260_type, type, (
% 0.70/0.90 a260: $i)).
% 0.70/0.90 tff(hskp21_type, type, (
% 0.70/0.90 hskp21: $o)).
% 0.70/0.90 tff(hskp17_type, type, (
% 0.70/0.90 hskp17: $o)).
% 0.70/0.90 tff(a246_type, type, (
% 0.70/0.90 a246: $i)).
% 0.70/0.90 tff(hskp28_type, type, (
% 0.70/0.90 hskp28: $o)).
% 0.70/0.90 tff(a237_type, type, (
% 0.70/0.90 a237: $i)).
% 0.70/0.90 tff(hskp14_type, type, (
% 0.70/0.90 hskp14: $o)).
% 0.70/0.90 tff(a221_type, type, (
% 0.70/0.90 a221: $i)).
% 0.70/0.90 tff(a228_type, type, (
% 0.70/0.90 a228: $i)).
% 0.70/0.90 tff(hskp9_type, type, (
% 0.70/0.90 hskp9: $o)).
% 0.70/0.90 tff(a220_type, type, (
% 0.70/0.90 a220: $i)).
% 0.70/0.90 tff(hskp5_type, type, (
% 0.70/0.90 hskp5: $o)).
% 0.70/0.90 tff(a218_type, type, (
% 0.70/0.90 a218: $i)).
% 0.70/0.90 tff(hskp4_type, type, (
% 0.70/0.90 hskp4: $o)).
% 0.70/0.90 tff(a223_type, type, (
% 0.70/0.90 a223: $i)).
% 0.70/0.90 tff(hskp26_type, type, (
% 0.70/0.90 hskp26: $o)).
% 0.70/0.90 tff(a224_type, type, (
% 0.70/0.90 a224: $i)).
% 0.70/0.90 tff(hskp7_type, type, (
% 0.70/0.90 hskp7: $o)).
% 0.70/0.90 tff(1,plain,
% 0.70/0.90 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W))) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W))))),
% 0.70/0.90 inference(bind,[status(th)],[])).
% 0.70/0.90 tff(2,plain,
% 0.70/0.90 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))),
% 0.70/0.90 inference(quant_intro,[status(thm)],[1])).
% 0.70/0.90 tff(3,plain,
% 0.70/0.90 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))),
% 0.70/0.90 inference(rewrite,[status(thm)],[])).
% 0.70/0.90 tff(4,plain,
% 0.70/0.90 (^[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)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c0_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(V)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(V))))), (((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c2_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)))), (((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c3_1(W))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))) | (~c3_1(W))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c3_1(W)))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c3_1(W))))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c2_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c3_1(W))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c3_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c3_1(W)))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c3_1(W))))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c3_1(W))) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c3_1(W))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c3_1(W)))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c3_1(W))))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c2_1(U)) | c3_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c3_1(W))) | c1_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c3_1(W))) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | (~c3_1(W)))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c2_1(U)) | c3_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | (~c3_1(W))))), ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | (~c3_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | (~c3_1(W))) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)))), ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | (~c3_1(W))))), (((((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c0_1(W)) | c2_1(W)) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | (~c3_1(W))) | c2_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | (~c3_1(W))) | c2_1(W)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))), (((((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))))),
% 0.70/0.90 inference(bind,[status(th)],[])).
% 0.70/0.90 tff(5,plain,
% 0.70/0.90 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c0_1(W)) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))),
% 0.70/0.90 inference(quant_intro,[status(thm)],[4])).
% 0.70/0.90 tff(6,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c0_1(W)) | c2_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause172')).
% 0.70/0.90 tff(7,plain,
% 0.70/0.90 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))),
% 0.70/0.90 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.70/0.90 tff(8,plain,
% 0.70/0.90 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))),
% 0.70/0.90 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.70/0.90 tff(9,plain,(
% 0.70/0.90 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))),
% 0.70/0.90 inference(skolemize,[status(sab)],[8])).
% 0.70/0.90 tff(10,plain,
% 0.70/0.90 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))),
% 0.70/0.90 inference(modus_ponens,[status(thm)],[9, 2])).
% 0.70/0.90 tff(11,assumption,(~c0_1(a229)), introduced(assumption)).
% 0.70/0.90 tff(12,assumption,(~c3_1(a229)), introduced(assumption)).
% 0.70/0.90 tff(13,plain,
% 0.70/0.90 (((~hskp10) | c3_1(a229)) <=> ((~hskp10) | c3_1(a229))),
% 0.70/0.90 inference(rewrite,[status(thm)],[])).
% 0.70/0.90 tff(14,axiom,((~hskp10) | c3_1(a229)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause64')).
% 0.70/0.90 tff(15,plain,
% 0.70/0.90 ((~hskp10) | c3_1(a229)),
% 0.70/0.90 inference(modus_ponens,[status(thm)],[14, 13])).
% 0.70/0.90 tff(16,plain,
% 0.70/0.90 ((~hskp10) | c3_1(a229)),
% 0.70/0.90 inference(modus_ponens,[status(thm)],[15, 13])).
% 0.70/0.90 tff(17,plain,
% 0.70/0.90 ((~hskp10) | c3_1(a229)),
% 0.70/0.90 inference(modus_ponens,[status(thm)],[16, 13])).
% 0.70/0.90 tff(18,plain,
% 0.70/0.90 ((~hskp10) | c3_1(a229)),
% 0.70/0.90 inference(modus_ponens,[status(thm)],[17, 13])).
% 0.70/0.90 tff(19,plain,
% 0.70/0.90 ((~hskp10) | c3_1(a229)),
% 0.70/0.90 inference(modus_ponens,[status(thm)],[18, 13])).
% 0.70/0.90 tff(20,plain,
% 0.70/0.90 (~hskp10),
% 0.70/0.90 inference(unit_resolution,[status(thm)],[19, 12])).
% 0.70/0.90 tff(21,assumption,(~hskp10), introduced(assumption)).
% 0.70/0.90 tff(22,assumption,(~c0_1(a213)), introduced(assumption)).
% 0.70/0.90 tff(23,plain,
% 0.70/0.90 (^[U: $i] : refl((hskp11 | hskp10 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U))) <=> (hskp11 | hskp10 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U))))),
% 0.70/0.90 inference(bind,[status(th)],[])).
% 0.70/0.90 tff(24,plain,
% 0.70/0.90 (![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U))) <=> ![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))),
% 0.70/0.90 inference(quant_intro,[status(thm)],[23])).
% 0.70/0.90 tff(25,plain,
% 0.70/0.90 (![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U))) <=> ![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))),
% 0.70/0.90 inference(rewrite,[status(thm)],[])).
% 0.70/0.90 tff(26,plain,
% 0.70/0.90 (^[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)) | c0_1(U)) <=> (((~ndr1_0) | (~c1_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U))))), (((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c1_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c1_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))), (((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U))))), ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp10) <=> (((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U))) | hskp10))), rewrite((((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U))) | hskp10) <=> (hskp10 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))), ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp10) <=> (hskp10 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U))))), (((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp10) | hskp11) <=> ((hskp10 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U))) | hskp11))), rewrite(((hskp10 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U))) | hskp11) <=> (hskp11 | hskp10 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))), (((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp10) | hskp11) <=> (hskp11 | hskp10 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))))),
% 0.70/0.90 inference(bind,[status(th)],[])).
% 0.70/0.90 tff(27,plain,
% 0.70/0.90 (![U: $i] : ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp10) | hskp11) <=> ![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))),
% 0.70/0.90 inference(quant_intro,[status(thm)],[26])).
% 0.70/0.90 tff(28,axiom,(![U: $i] : ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp10) | hskp11)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause127')).
% 0.70/0.90 tff(29,plain,
% 0.70/0.90 (![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))),
% 0.70/0.90 inference(modus_ponens,[status(thm)],[28, 27])).
% 0.70/0.90 tff(30,plain,
% 0.70/0.90 (![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))),
% 0.70/0.90 inference(modus_ponens,[status(thm)],[29, 25])).
% 0.70/0.90 tff(31,plain,(
% 0.70/0.90 ![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))),
% 0.70/0.90 inference(skolemize,[status(sab)],[30])).
% 0.70/0.90 tff(32,plain,
% 0.70/0.90 (![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))),
% 0.70/0.90 inference(modus_ponens,[status(thm)],[31, 24])).
% 0.70/0.90 tff(33,plain,
% 0.70/0.90 (^[V: $i, U: $i] : refl((hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V)) <=> (hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V)))),
% 0.70/0.90 inference(bind,[status(th)],[])).
% 0.70/0.90 tff(34,plain,
% 0.70/0.90 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V)) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))),
% 0.70/0.90 inference(quant_intro,[status(thm)],[33])).
% 0.70/0.90 tff(35,plain,
% 0.70/0.90 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V)) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))),
% 0.70/0.90 inference(rewrite,[status(thm)],[])).
% 0.70/0.90 tff(36,plain,
% 0.70/0.90 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c1_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U))) | c1_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U))) | c1_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c1_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c1_1(V)) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c1_1(V)) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | hskp0) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V)) | hskp0))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V)) | hskp0) <=> (hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | hskp0) <=> (hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))))),
% 0.70/0.90 inference(bind,[status(th)],[])).
% 0.70/0.90 tff(37,plain,
% 0.70/0.90 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | hskp0) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))),
% 0.70/0.90 inference(quant_intro,[status(thm)],[36])).
% 0.70/0.90 tff(38,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | hskp0)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause155')).
% 0.70/0.90 tff(39,plain,
% 0.70/0.90 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))),
% 0.70/0.90 inference(modus_ponens,[status(thm)],[38, 37])).
% 0.70/0.90 tff(40,plain,
% 0.70/0.90 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))),
% 0.70/0.90 inference(modus_ponens,[status(thm)],[39, 35])).
% 0.70/0.90 tff(41,plain,(
% 0.70/0.90 ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))),
% 0.70/0.90 inference(skolemize,[status(sab)],[40])).
% 0.70/0.90 tff(42,plain,
% 0.70/0.90 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))),
% 0.70/0.90 inference(modus_ponens,[status(thm)],[41, 34])).
% 0.70/0.90 tff(43,assumption,(~hskp8), introduced(assumption)).
% 0.70/0.90 tff(44,plain,
% 0.70/0.90 (^[U: $i] : refl((hskp8 | hskp0 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U)) <=> (hskp8 | hskp0 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U)))),
% 0.70/0.90 inference(bind,[status(th)],[])).
% 0.70/0.90 tff(45,plain,
% 0.70/0.90 (![U: $i] : (hskp8 | hskp0 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U)) <=> ![U: $i] : (hskp8 | hskp0 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))),
% 0.70/0.90 inference(quant_intro,[status(thm)],[44])).
% 0.70/0.90 tff(46,plain,
% 0.70/0.90 (![U: $i] : (hskp8 | hskp0 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U)) <=> ![U: $i] : (hskp8 | hskp0 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))),
% 0.70/0.90 inference(rewrite,[status(thm)],[])).
% 0.70/0.90 tff(47,plain,
% 0.70/0.90 (^[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) | c0_1(U) | c2_1(U))), ((((~ndr1_0) | c0_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c0_1(U) | c2_1(U)))), (((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c0_1(U) | c2_1(U)) | c3_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))), (((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U)))), ((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp8) <=> (((~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U)) | hskp8))), rewrite((((~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U)) | hskp8) <=> (hskp8 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))), ((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp8) <=> (hskp8 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U)))), (((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp8) | hskp0) <=> ((hskp8 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U)) | hskp0))), rewrite(((hskp8 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U)) | hskp0) <=> (hskp8 | hskp0 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))), (((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp8) | hskp0) <=> (hskp8 | hskp0 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))))),
% 0.70/0.90 inference(bind,[status(th)],[])).
% 0.70/0.90 tff(48,plain,
% 0.70/0.90 (![U: $i] : ((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp8) | hskp0) <=> ![U: $i] : (hskp8 | hskp0 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))),
% 0.70/0.90 inference(quant_intro,[status(thm)],[47])).
% 0.70/0.90 tff(49,axiom,(![U: $i] : ((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp8) | hskp0)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause124')).
% 0.70/0.91 tff(50,plain,
% 0.70/0.91 (![U: $i] : (hskp8 | hskp0 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))),
% 0.70/0.91 inference(modus_ponens,[status(thm)],[49, 48])).
% 0.70/0.91 tff(51,plain,
% 0.70/0.91 (![U: $i] : (hskp8 | hskp0 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))),
% 0.70/0.91 inference(modus_ponens,[status(thm)],[50, 46])).
% 0.70/0.91 tff(52,plain,(
% 0.70/0.91 ![U: $i] : (hskp8 | hskp0 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))),
% 0.70/0.91 inference(skolemize,[status(sab)],[51])).
% 0.70/0.91 tff(53,plain,
% 0.70/0.91 (![U: $i] : (hskp8 | hskp0 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))),
% 0.70/0.91 inference(modus_ponens,[status(thm)],[52, 45])).
% 0.70/0.91 tff(54,plain,
% 0.70/0.91 (^[U: $i] : refl((hskp12 | hskp0 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U))) <=> (hskp12 | hskp0 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U))))),
% 0.70/0.91 inference(bind,[status(th)],[])).
% 0.70/0.91 tff(55,plain,
% 0.70/0.91 (![U: $i] : (hskp12 | hskp0 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp12 | hskp0 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 0.70/0.91 inference(quant_intro,[status(thm)],[54])).
% 0.70/0.91 tff(56,plain,
% 0.70/0.91 (![U: $i] : (hskp12 | hskp0 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp12 | hskp0 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 0.70/0.91 inference(rewrite,[status(thm)],[])).
% 0.70/0.91 tff(57,plain,
% 0.70/0.91 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp0) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U))) | hskp0))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U))) | hskp0) <=> (hskp0 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp0) <=> (hskp0 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp0) | hskp12) <=> ((hskp0 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U))) | hskp12))), rewrite(((hskp0 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U))) | hskp12) <=> (hskp12 | hskp0 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp0) | hskp12) <=> (hskp12 | hskp0 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))))),
% 0.70/0.91 inference(bind,[status(th)],[])).
% 0.70/0.91 tff(58,plain,
% 0.70/0.91 (![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp0) | hskp12) <=> ![U: $i] : (hskp12 | hskp0 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 0.70/0.91 inference(quant_intro,[status(thm)],[57])).
% 0.70/0.91 tff(59,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp0) | hskp12)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause140')).
% 0.70/0.91 tff(60,plain,
% 0.70/0.91 (![U: $i] : (hskp12 | hskp0 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 0.70/0.91 inference(modus_ponens,[status(thm)],[59, 58])).
% 0.70/0.91 tff(61,plain,
% 0.70/0.91 (![U: $i] : (hskp12 | hskp0 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 0.70/0.91 inference(modus_ponens,[status(thm)],[60, 56])).
% 0.70/0.91 tff(62,plain,(
% 0.70/0.91 ![U: $i] : (hskp12 | hskp0 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 0.70/0.91 inference(skolemize,[status(sab)],[61])).
% 0.70/0.91 tff(63,plain,
% 0.70/0.91 (![U: $i] : (hskp12 | hskp0 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 0.70/0.91 inference(modus_ponens,[status(thm)],[62, 55])).
% 0.70/0.91 tff(64,assumption,(~hskp0), introduced(assumption)).
% 0.70/0.91 tff(65,plain,
% 0.70/0.91 (^[U: $i] : refl((hskp20 | hskp13 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U))) <=> (hskp20 | hskp13 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U))))),
% 0.70/0.91 inference(bind,[status(th)],[])).
% 0.70/0.91 tff(66,plain,
% 0.70/0.91 (![U: $i] : (hskp20 | hskp13 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U))) <=> ![U: $i] : (hskp20 | hskp13 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))),
% 0.70/0.91 inference(quant_intro,[status(thm)],[65])).
% 0.70/0.91 tff(67,plain,
% 0.70/0.91 (![U: $i] : (hskp20 | hskp13 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U))) <=> ![U: $i] : (hskp20 | hskp13 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))),
% 0.70/0.91 inference(rewrite,[status(thm)],[])).
% 0.70/0.91 tff(68,plain,
% 0.70/0.91 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U))))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp20) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U))) | hskp20))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U))) | hskp20) <=> (hskp20 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp20) <=> (hskp20 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U))))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp20) | hskp13) <=> ((hskp20 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U))) | hskp13))), rewrite(((hskp20 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U))) | hskp13) <=> (hskp20 | hskp13 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp20) | hskp13) <=> (hskp20 | hskp13 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))))),
% 0.70/0.91 inference(bind,[status(th)],[])).
% 0.70/0.91 tff(69,plain,
% 0.70/0.91 (![U: $i] : ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp20) | hskp13) <=> ![U: $i] : (hskp20 | hskp13 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))),
% 0.70/0.91 inference(quant_intro,[status(thm)],[68])).
% 0.70/0.91 tff(70,axiom,(![U: $i] : ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp20) | hskp13)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause137')).
% 0.70/0.91 tff(71,plain,
% 0.70/0.91 (![U: $i] : (hskp20 | hskp13 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))),
% 0.70/0.91 inference(modus_ponens,[status(thm)],[70, 69])).
% 0.70/0.91 tff(72,plain,
% 0.70/0.91 (![U: $i] : (hskp20 | hskp13 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))),
% 0.70/0.91 inference(modus_ponens,[status(thm)],[71, 67])).
% 0.70/0.91 tff(73,plain,(
% 0.70/0.91 ![U: $i] : (hskp20 | hskp13 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))),
% 0.70/0.91 inference(skolemize,[status(sab)],[72])).
% 0.70/0.91 tff(74,plain,
% 0.70/0.91 (![U: $i] : (hskp20 | hskp13 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))),
% 0.70/0.91 inference(modus_ponens,[status(thm)],[73, 66])).
% 0.70/0.91 tff(75,assumption,(hskp23), introduced(assumption)).
% 0.70/0.91 tff(76,plain,
% 0.70/0.91 (((~hskp23) | (~c3_1(a278))) <=> ((~hskp23) | (~c3_1(a278)))),
% 0.70/0.91 inference(rewrite,[status(thm)],[])).
% 0.70/0.91 tff(77,plain,
% 0.70/0.91 (((~c3_1(a278)) | (~hskp23)) <=> ((~hskp23) | (~c3_1(a278)))),
% 0.70/0.91 inference(rewrite,[status(thm)],[])).
% 0.70/0.91 tff(78,axiom,((~c3_1(a278)) | (~hskp23)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause85')).
% 0.70/0.91 tff(79,plain,
% 0.70/0.91 ((~hskp23) | (~c3_1(a278))),
% 0.70/0.91 inference(modus_ponens,[status(thm)],[78, 77])).
% 0.70/0.91 tff(80,plain,
% 0.70/0.91 ((~hskp23) | (~c3_1(a278))),
% 0.70/0.91 inference(modus_ponens,[status(thm)],[79, 76])).
% 0.70/0.91 tff(81,plain,
% 0.70/0.91 (~c3_1(a278)),
% 0.70/0.91 inference(unit_resolution,[status(thm)],[80, 75])).
% 0.70/0.91 tff(82,plain,
% 0.70/0.91 (((~hskp23) | (~c2_1(a278))) <=> ((~hskp23) | (~c2_1(a278)))),
% 0.70/0.91 inference(rewrite,[status(thm)],[])).
% 0.70/0.91 tff(83,plain,
% 0.70/0.91 (((~c2_1(a278)) | (~hskp23)) <=> ((~hskp23) | (~c2_1(a278)))),
% 0.70/0.91 inference(rewrite,[status(thm)],[])).
% 0.70/0.91 tff(84,axiom,((~c2_1(a278)) | (~hskp23)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause84')).
% 0.70/0.91 tff(85,plain,
% 0.70/0.91 ((~hskp23) | (~c2_1(a278))),
% 0.70/0.91 inference(modus_ponens,[status(thm)],[84, 83])).
% 0.70/0.91 tff(86,plain,
% 0.70/0.91 ((~hskp23) | (~c2_1(a278))),
% 0.70/0.91 inference(modus_ponens,[status(thm)],[85, 82])).
% 0.70/0.91 tff(87,plain,
% 0.70/0.91 (~c2_1(a278)),
% 0.70/0.91 inference(unit_resolution,[status(thm)],[86, 75])).
% 0.70/0.91 tff(88,plain,
% 0.70/0.91 (((~hskp23) | (~c0_1(a278))) <=> ((~hskp23) | (~c0_1(a278)))),
% 0.70/0.91 inference(rewrite,[status(thm)],[])).
% 0.70/0.91 tff(89,plain,
% 0.70/0.91 (((~c0_1(a278)) | (~hskp23)) <=> ((~hskp23) | (~c0_1(a278)))),
% 0.70/0.91 inference(rewrite,[status(thm)],[])).
% 0.70/0.91 tff(90,axiom,((~c0_1(a278)) | (~hskp23)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause83')).
% 0.70/0.91 tff(91,plain,
% 0.70/0.91 ((~hskp23) | (~c0_1(a278))),
% 0.70/0.91 inference(modus_ponens,[status(thm)],[90, 89])).
% 0.70/0.91 tff(92,plain,
% 0.70/0.91 ((~hskp23) | (~c0_1(a278))),
% 0.70/0.91 inference(modus_ponens,[status(thm)],[91, 88])).
% 0.70/0.91 tff(93,plain,
% 0.70/0.91 (~c0_1(a278)),
% 0.70/0.91 inference(unit_resolution,[status(thm)],[92, 75])).
% 0.70/0.91 tff(94,assumption,(~ndr1_0), introduced(assumption)).
% 0.70/0.91 tff(95,plain,
% 0.70/0.91 ((ndr1_0 | (~hskp8)) <=> (ndr1_0 | (~hskp8))),
% 0.70/0.91 inference(rewrite,[status(thm)],[])).
% 0.70/0.91 tff(96,plain,
% 0.70/0.91 (((~hskp8) | ndr1_0) <=> (ndr1_0 | (~hskp8))),
% 0.70/0.91 inference(rewrite,[status(thm)],[])).
% 0.70/0.91 tff(97,axiom,((~hskp8) | ndr1_0), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause21')).
% 0.70/0.91 tff(98,plain,
% 0.70/0.91 (ndr1_0 | (~hskp8)),
% 0.70/0.91 inference(modus_ponens,[status(thm)],[97, 96])).
% 0.70/0.91 tff(99,plain,
% 0.70/0.91 (ndr1_0 | (~hskp8)),
% 0.70/0.91 inference(modus_ponens,[status(thm)],[98, 95])).
% 0.70/0.91 tff(100,plain,
% 0.70/0.91 (~hskp8),
% 0.70/0.91 inference(unit_resolution,[status(thm)],[99, 94])).
% 0.70/0.91 tff(101,plain,
% 0.70/0.91 ((ndr1_0 | (~hskp24)) <=> (ndr1_0 | (~hskp24))),
% 0.70/0.91 inference(rewrite,[status(thm)],[])).
% 0.70/0.91 tff(102,plain,
% 0.70/0.91 (((~hskp24) | ndr1_0) <=> (ndr1_0 | (~hskp24))),
% 0.70/0.91 inference(rewrite,[status(thm)],[])).
% 0.70/0.91 tff(103,axiom,((~hskp24) | ndr1_0), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause5')).
% 0.70/0.91 tff(104,plain,
% 0.70/0.91 (ndr1_0 | (~hskp24)),
% 0.70/0.91 inference(modus_ponens,[status(thm)],[103, 102])).
% 0.70/0.91 tff(105,plain,
% 0.70/0.91 (ndr1_0 | (~hskp24)),
% 0.70/0.91 inference(modus_ponens,[status(thm)],[104, 101])).
% 0.70/0.91 tff(106,plain,
% 0.70/0.91 (~hskp24),
% 0.70/0.91 inference(unit_resolution,[status(thm)],[105, 94])).
% 0.70/0.91 tff(107,plain,
% 0.70/0.91 ((ndr1_0 | (~hskp10)) <=> (ndr1_0 | (~hskp10))),
% 0.70/0.91 inference(rewrite,[status(thm)],[])).
% 0.70/0.91 tff(108,plain,
% 0.70/0.91 (((~hskp10) | ndr1_0) <=> (ndr1_0 | (~hskp10))),
% 0.70/0.91 inference(rewrite,[status(thm)],[])).
% 0.70/0.91 tff(109,axiom,((~hskp10) | ndr1_0), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause19')).
% 0.70/0.91 tff(110,plain,
% 0.70/0.91 (ndr1_0 | (~hskp10)),
% 0.70/0.91 inference(modus_ponens,[status(thm)],[109, 108])).
% 0.70/0.91 tff(111,plain,
% 0.70/0.91 (ndr1_0 | (~hskp10)),
% 0.70/0.91 inference(modus_ponens,[status(thm)],[110, 107])).
% 0.70/0.91 tff(112,plain,
% 0.70/0.91 (~hskp10),
% 0.70/0.91 inference(unit_resolution,[status(thm)],[111, 94])).
% 0.70/0.91 tff(113,plain,
% 0.70/0.91 ((hskp24 | hskp10 | hskp8) <=> (hskp24 | hskp10 | hskp8)),
% 0.70/0.91 inference(rewrite,[status(thm)],[])).
% 0.70/0.91 tff(114,plain,
% 0.70/0.91 (((hskp24 | hskp8) | hskp10) <=> (hskp24 | hskp10 | hskp8)),
% 0.70/0.91 inference(rewrite,[status(thm)],[])).
% 0.70/0.91 tff(115,axiom,((hskp24 | hskp8) | hskp10), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause32')).
% 0.70/0.91 tff(116,plain,
% 0.70/0.91 (hskp24 | hskp10 | hskp8),
% 0.70/0.91 inference(modus_ponens,[status(thm)],[115, 114])).
% 0.70/0.91 tff(117,plain,
% 0.70/0.91 (hskp24 | hskp10 | hskp8),
% 0.70/0.91 inference(modus_ponens,[status(thm)],[116, 113])).
% 0.70/0.91 tff(118,plain,
% 0.70/0.91 (hskp24 | hskp10 | hskp8),
% 0.70/0.91 inference(modus_ponens,[status(thm)],[117, 113])).
% 0.70/0.91 tff(119,plain,
% 0.70/0.91 (hskp24 | hskp10 | hskp8),
% 0.70/0.91 inference(modus_ponens,[status(thm)],[118, 113])).
% 0.70/0.91 tff(120,plain,
% 0.70/0.91 (hskp24 | hskp10 | hskp8),
% 0.70/0.91 inference(modus_ponens,[status(thm)],[119, 113])).
% 0.70/0.91 tff(121,plain,
% 0.70/0.91 ($false),
% 0.70/0.91 inference(unit_resolution,[status(thm)],[120, 112, 106, 100])).
% 0.70/0.91 tff(122,plain,(ndr1_0), inference(lemma,lemma(discharge,[]))).
% 0.70/0.91 tff(123,plain,
% 0.70/0.91 (((~![U: $i] : (hskp8 | hskp0 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp8 | hskp0 | c0_1(a278) | c2_1(a278) | c3_1(a278) | (~ndr1_0))) <=> ((~![U: $i] : (hskp8 | hskp0 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | hskp8 | hskp0 | c0_1(a278) | c2_1(a278) | c3_1(a278) | (~ndr1_0))),
% 0.70/0.91 inference(rewrite,[status(thm)],[])).
% 0.70/0.91 tff(124,plain,
% 0.70/0.91 ((hskp8 | hskp0 | (~ndr1_0) | c3_1(a278) | c0_1(a278) | c2_1(a278)) <=> (hskp8 | hskp0 | c0_1(a278) | c2_1(a278) | c3_1(a278) | (~ndr1_0))),
% 0.70/0.91 inference(rewrite,[status(thm)],[])).
% 0.70/0.91 tff(125,plain,
% 0.70/0.91 (((~![U: $i] : (hskp8 | hskp0 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp8 | hskp0 | (~ndr1_0) | c3_1(a278) | c0_1(a278) | c2_1(a278))) <=> ((~![U: $i] : (hskp8 | hskp0 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp8 | hskp0 | c0_1(a278) | c2_1(a278) | c3_1(a278) | (~ndr1_0)))),
% 0.70/0.91 inference(monotonicity,[status(thm)],[124])).
% 0.70/0.91 tff(126,plain,
% 0.70/0.91 (((~![U: $i] : (hskp8 | hskp0 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp8 | hskp0 | (~ndr1_0) | c3_1(a278) | c0_1(a278) | c2_1(a278))) <=> ((~![U: $i] : (hskp8 | hskp0 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | hskp8 | hskp0 | c0_1(a278) | c2_1(a278) | c3_1(a278) | (~ndr1_0))),
% 0.70/0.91 inference(transitivity,[status(thm)],[125, 123])).
% 0.70/0.91 tff(127,plain,
% 0.70/0.91 ((~![U: $i] : (hskp8 | hskp0 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp8 | hskp0 | (~ndr1_0) | c3_1(a278) | c0_1(a278) | c2_1(a278))),
% 0.70/0.91 inference(quant_inst,[status(thm)],[])).
% 0.70/0.91 tff(128,plain,
% 0.70/0.91 ((~![U: $i] : (hskp8 | hskp0 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | hskp8 | hskp0 | c0_1(a278) | c2_1(a278) | c3_1(a278) | (~ndr1_0)),
% 0.70/0.91 inference(modus_ponens,[status(thm)],[127, 126])).
% 0.70/0.91 tff(129,plain,
% 0.70/0.91 ($false),
% 0.70/0.91 inference(unit_resolution,[status(thm)],[128, 122, 43, 64, 93, 87, 81, 53])).
% 0.70/0.91 tff(130,plain,((~hskp23) | hskp8 | hskp0), inference(lemma,lemma(discharge,[]))).
% 0.70/0.91 tff(131,plain,
% 0.70/0.91 (~hskp23),
% 0.70/0.91 inference(unit_resolution,[status(thm)],[130, 64, 43])).
% 0.70/0.91 tff(132,assumption,(~hskp20), introduced(assumption)).
% 0.70/0.91 tff(133,plain,
% 0.70/0.91 ((hskp23 | hskp20 | hskp18) <=> (hskp23 | hskp20 | hskp18)),
% 0.70/0.91 inference(rewrite,[status(thm)],[])).
% 0.70/0.91 tff(134,plain,
% 0.70/0.91 (((hskp20 | hskp18) | hskp23) <=> (hskp23 | hskp20 | hskp18)),
% 0.70/0.91 inference(rewrite,[status(thm)],[])).
% 0.70/0.91 tff(135,plain,
% 0.70/0.91 ((hskp20 | hskp18) <=> (hskp20 | hskp18)),
% 0.70/0.91 inference(rewrite,[status(thm)],[])).
% 0.70/0.91 tff(136,plain,
% 0.70/0.91 (((hskp20 | hskp18) | hskp23) <=> ((hskp20 | hskp18) | hskp23)),
% 0.70/0.91 inference(monotonicity,[status(thm)],[135])).
% 0.70/0.91 tff(137,plain,
% 0.70/0.91 (((hskp20 | hskp18) | hskp23) <=> (hskp23 | hskp20 | hskp18)),
% 0.70/0.91 inference(transitivity,[status(thm)],[136, 134])).
% 0.70/0.91 tff(138,axiom,((hskp20 | hskp18) | hskp23), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause30')).
% 0.70/0.91 tff(139,plain,
% 0.70/0.91 (hskp23 | hskp20 | hskp18),
% 0.70/0.91 inference(modus_ponens,[status(thm)],[138, 137])).
% 0.70/0.91 tff(140,plain,
% 0.70/0.91 (hskp23 | hskp20 | hskp18),
% 0.70/0.91 inference(modus_ponens,[status(thm)],[139, 133])).
% 0.70/0.91 tff(141,plain,
% 0.70/0.91 (hskp23 | hskp20 | hskp18),
% 0.70/0.91 inference(modus_ponens,[status(thm)],[140, 133])).
% 0.70/0.91 tff(142,plain,
% 0.70/0.91 (hskp23 | hskp20 | hskp18),
% 0.70/0.91 inference(modus_ponens,[status(thm)],[141, 133])).
% 0.70/0.91 tff(143,plain,
% 0.70/0.91 (hskp23 | hskp20 | hskp18),
% 0.70/0.91 inference(modus_ponens,[status(thm)],[142, 133])).
% 0.70/0.91 tff(144,plain,
% 0.70/0.91 (hskp18),
% 0.70/0.91 inference(unit_resolution,[status(thm)],[143, 132, 131])).
% 0.70/0.91 tff(145,plain,
% 0.70/0.91 (((~hskp18) | (~c2_1(a247))) <=> ((~hskp18) | (~c2_1(a247)))),
% 0.70/0.91 inference(rewrite,[status(thm)],[])).
% 0.70/0.91 tff(146,plain,
% 0.70/0.91 (((~c2_1(a247)) | (~hskp18)) <=> ((~hskp18) | (~c2_1(a247)))),
% 0.70/0.91 inference(rewrite,[status(thm)],[])).
% 0.70/0.91 tff(147,axiom,((~c2_1(a247)) | (~hskp18)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause92')).
% 0.70/0.91 tff(148,plain,
% 0.70/0.91 ((~hskp18) | (~c2_1(a247))),
% 0.70/0.91 inference(modus_ponens,[status(thm)],[147, 146])).
% 0.70/0.91 tff(149,plain,
% 0.70/0.91 ((~hskp18) | (~c2_1(a247))),
% 0.70/0.91 inference(modus_ponens,[status(thm)],[148, 145])).
% 0.70/0.91 tff(150,plain,
% 0.70/0.91 (~c2_1(a247)),
% 0.70/0.91 inference(unit_resolution,[status(thm)],[149, 144])).
% 0.70/0.91 tff(151,plain,
% 0.70/0.91 (((~hskp18) | c3_1(a247)) <=> ((~hskp18) | c3_1(a247))),
% 0.70/0.91 inference(rewrite,[status(thm)],[])).
% 0.70/0.91 tff(152,axiom,((~hskp18) | c3_1(a247)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause54')).
% 0.70/0.91 tff(153,plain,
% 0.70/0.91 ((~hskp18) | c3_1(a247)),
% 0.70/0.91 inference(modus_ponens,[status(thm)],[152, 151])).
% 0.70/0.91 tff(154,plain,
% 0.70/0.91 ((~hskp18) | c3_1(a247)),
% 0.70/0.91 inference(modus_ponens,[status(thm)],[153, 151])).
% 0.70/0.91 tff(155,plain,
% 0.70/0.91 ((~hskp18) | c3_1(a247)),
% 0.70/0.91 inference(modus_ponens,[status(thm)],[154, 151])).
% 0.70/0.91 tff(156,plain,
% 0.70/0.91 ((~hskp18) | c3_1(a247)),
% 0.70/0.91 inference(modus_ponens,[status(thm)],[155, 151])).
% 0.70/0.91 tff(157,plain,
% 0.70/0.91 ((~hskp18) | c3_1(a247)),
% 0.70/0.91 inference(modus_ponens,[status(thm)],[156, 151])).
% 0.70/0.91 tff(158,plain,
% 0.70/0.91 (c3_1(a247)),
% 0.70/0.91 inference(unit_resolution,[status(thm)],[157, 144])).
% 0.70/0.91 tff(159,plain,
% 0.70/0.91 (hskp24),
% 0.70/0.91 inference(unit_resolution,[status(thm)],[120, 21, 43])).
% 0.70/0.91 tff(160,plain,
% 0.70/0.91 (((~hskp24) | c0_1(a282)) <=> ((~hskp24) | c0_1(a282))),
% 0.70/0.91 inference(rewrite,[status(thm)],[])).
% 0.70/0.91 tff(161,axiom,((~hskp24) | c0_1(a282)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause46')).
% 0.70/0.91 tff(162,plain,
% 0.70/0.91 ((~hskp24) | c0_1(a282)),
% 0.70/0.91 inference(modus_ponens,[status(thm)],[161, 160])).
% 0.70/0.91 tff(163,plain,
% 0.70/0.91 ((~hskp24) | c0_1(a282)),
% 0.70/0.91 inference(modus_ponens,[status(thm)],[162, 160])).
% 0.70/0.91 tff(164,plain,
% 0.70/0.91 ((~hskp24) | c0_1(a282)),
% 0.70/0.91 inference(modus_ponens,[status(thm)],[163, 160])).
% 0.70/0.91 tff(165,plain,
% 0.70/0.91 ((~hskp24) | c0_1(a282)),
% 0.70/0.91 inference(modus_ponens,[status(thm)],[164, 160])).
% 0.70/0.91 tff(166,plain,
% 0.70/0.91 ((~hskp24) | c0_1(a282)),
% 0.70/0.91 inference(modus_ponens,[status(thm)],[165, 160])).
% 0.70/0.91 tff(167,plain,
% 0.70/0.91 (c0_1(a282)),
% 0.70/0.91 inference(unit_resolution,[status(thm)],[166, 159])).
% 0.70/0.91 tff(168,plain,
% 0.70/0.91 (((~hskp24) | (~c3_1(a282))) <=> ((~hskp24) | (~c3_1(a282)))),
% 0.70/0.91 inference(rewrite,[status(thm)],[])).
% 0.70/0.91 tff(169,plain,
% 0.70/0.91 (((~c3_1(a282)) | (~hskp24)) <=> ((~hskp24) | (~c3_1(a282)))),
% 0.70/0.91 inference(rewrite,[status(thm)],[])).
% 0.70/0.91 tff(170,axiom,((~c3_1(a282)) | (~hskp24)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause82')).
% 0.70/0.91 tff(171,plain,
% 0.70/0.91 ((~hskp24) | (~c3_1(a282))),
% 0.70/0.91 inference(modus_ponens,[status(thm)],[170, 169])).
% 0.70/0.91 tff(172,plain,
% 0.70/0.91 ((~hskp24) | (~c3_1(a282))),
% 0.70/0.91 inference(modus_ponens,[status(thm)],[171, 168])).
% 0.70/0.91 tff(173,plain,
% 0.70/0.91 (~c3_1(a282)),
% 0.70/0.91 inference(unit_resolution,[status(thm)],[172, 159])).
% 0.70/0.91 tff(174,plain,
% 0.70/0.91 (((~hskp24) | (~c1_1(a282))) <=> ((~hskp24) | (~c1_1(a282)))),
% 0.70/0.91 inference(rewrite,[status(thm)],[])).
% 0.70/0.91 tff(175,plain,
% 0.70/0.91 (((~c1_1(a282)) | (~hskp24)) <=> ((~hskp24) | (~c1_1(a282)))),
% 0.70/0.91 inference(rewrite,[status(thm)],[])).
% 0.70/0.91 tff(176,axiom,((~c1_1(a282)) | (~hskp24)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause81')).
% 0.70/0.91 tff(177,plain,
% 0.70/0.91 ((~hskp24) | (~c1_1(a282))),
% 0.70/0.91 inference(modus_ponens,[status(thm)],[176, 175])).
% 0.70/0.91 tff(178,plain,
% 0.70/0.91 ((~hskp24) | (~c1_1(a282))),
% 0.70/0.91 inference(modus_ponens,[status(thm)],[177, 174])).
% 0.70/0.91 tff(179,plain,
% 0.70/0.91 (~c1_1(a282)),
% 0.70/0.91 inference(unit_resolution,[status(thm)],[178, 159])).
% 0.70/0.91 tff(180,assumption,(~c2_1(a282)), introduced(assumption)).
% 0.70/0.91 tff(181,assumption,(~c3_1(a282)), introduced(assumption)).
% 0.70/0.91 tff(182,assumption,(~c1_1(a282)), introduced(assumption)).
% 0.70/0.91 tff(183,plain,
% 0.70/0.91 (^[U: $i] : refl((hskp27 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) <=> (hskp27 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))))),
% 0.70/0.91 inference(bind,[status(th)],[])).
% 0.70/0.91 tff(184,plain,
% 0.70/0.91 (![U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 0.70/0.91 inference(quant_intro,[status(thm)],[183])).
% 0.70/0.91 tff(185,plain,
% 0.70/0.91 (![U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 0.70/0.91 inference(rewrite,[status(thm)],[])).
% 0.70/0.91 tff(186,plain,
% 0.70/0.91 (^[U: $i] : 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)) | hskp27) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) | hskp27))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) | hskp27) <=> (hskp27 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp27) <=> (hskp27 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))))),
% 0.70/0.91 inference(bind,[status(th)],[])).
% 0.70/0.91 tff(187,plain,
% 0.70/0.91 (![U: $i] : (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp27) <=> ![U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 0.70/0.91 inference(quant_intro,[status(thm)],[186])).
% 0.70/0.91 tff(188,axiom,(![U: $i] : (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp27)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause129')).
% 0.70/0.91 tff(189,plain,
% 0.70/0.91 (![U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 0.70/0.91 inference(modus_ponens,[status(thm)],[188, 187])).
% 0.70/0.91 tff(190,plain,
% 0.70/0.91 (![U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 0.70/0.91 inference(modus_ponens,[status(thm)],[189, 185])).
% 0.70/0.91 tff(191,plain,(
% 0.70/0.91 ![U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 0.70/0.91 inference(skolemize,[status(sab)],[190])).
% 0.70/0.91 tff(192,plain,
% 0.70/0.91 (![U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 0.70/0.91 inference(modus_ponens,[status(thm)],[191, 184])).
% 0.70/0.91 tff(193,plain,
% 0.70/0.91 (^[U: $i] : refl((hskp15 | hskp0 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U))) <=> (hskp15 | hskp0 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U))))),
% 0.70/0.91 inference(bind,[status(th)],[])).
% 0.70/0.91 tff(194,plain,
% 0.70/0.91 (![U: $i] : (hskp15 | hskp0 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp15 | hskp0 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))),
% 0.70/0.91 inference(quant_intro,[status(thm)],[193])).
% 0.70/0.91 tff(195,plain,
% 0.70/0.91 (![U: $i] : (hskp15 | hskp0 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp15 | hskp0 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))),
% 0.70/0.91 inference(rewrite,[status(thm)],[])).
% 0.70/0.91 tff(196,plain,
% 0.70/0.91 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c0_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) <=> (((~ndr1_0) | (~c0_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U))))), (((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))), (((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U))))), ((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp15) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U))) | hskp15))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U))) | hskp15) <=> (hskp15 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))), ((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp15) <=> (hskp15 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U))))), (((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp15) | hskp0) <=> ((hskp15 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U))) | hskp0))), rewrite(((hskp15 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U))) | hskp0) <=> (hskp15 | hskp0 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))), (((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp15) | hskp0) <=> (hskp15 | hskp0 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))))),
% 0.70/0.91 inference(bind,[status(th)],[])).
% 0.70/0.91 tff(197,plain,
% 0.70/0.91 (![U: $i] : ((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp15) | hskp0) <=> ![U: $i] : (hskp15 | hskp0 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))),
% 0.70/0.91 inference(quant_intro,[status(thm)],[196])).
% 0.70/0.91 tff(198,axiom,(![U: $i] : ((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp15) | hskp0)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause128')).
% 0.70/0.91 tff(199,plain,
% 0.70/0.91 (![U: $i] : (hskp15 | hskp0 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))),
% 0.70/0.91 inference(modus_ponens,[status(thm)],[198, 197])).
% 0.70/0.91 tff(200,plain,
% 0.70/0.91 (![U: $i] : (hskp15 | hskp0 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))),
% 0.70/0.91 inference(modus_ponens,[status(thm)],[199, 195])).
% 0.70/0.91 tff(201,plain,(
% 0.70/0.91 ![U: $i] : (hskp15 | hskp0 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))),
% 0.70/0.91 inference(skolemize,[status(sab)],[200])).
% 0.70/0.91 tff(202,plain,
% 0.70/0.91 (![U: $i] : (hskp15 | hskp0 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))),
% 0.70/0.91 inference(modus_ponens,[status(thm)],[201, 194])).
% 0.70/0.91 tff(203,assumption,(c0_1(a282)), introduced(assumption)).
% 0.70/0.91 tff(204,plain,
% 0.70/0.91 (((~![U: $i] : (hskp15 | hskp0 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp15 | hskp0 | c3_1(a282) | (~ndr1_0) | c2_1(a282) | (~c0_1(a282)))) <=> ((~![U: $i] : (hskp15 | hskp0 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | hskp15 | hskp0 | c3_1(a282) | (~ndr1_0) | c2_1(a282) | (~c0_1(a282)))),
% 0.70/0.91 inference(rewrite,[status(thm)],[])).
% 0.70/0.91 tff(205,plain,
% 0.70/0.91 ((hskp15 | hskp0 | (~ndr1_0) | c3_1(a282) | c2_1(a282) | (~c0_1(a282))) <=> (hskp15 | hskp0 | c3_1(a282) | (~ndr1_0) | c2_1(a282) | (~c0_1(a282)))),
% 0.70/0.91 inference(rewrite,[status(thm)],[])).
% 0.70/0.91 tff(206,plain,
% 0.70/0.91 (((~![U: $i] : (hskp15 | hskp0 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp15 | hskp0 | (~ndr1_0) | c3_1(a282) | c2_1(a282) | (~c0_1(a282)))) <=> ((~![U: $i] : (hskp15 | hskp0 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp15 | hskp0 | c3_1(a282) | (~ndr1_0) | c2_1(a282) | (~c0_1(a282))))),
% 0.70/0.91 inference(monotonicity,[status(thm)],[205])).
% 0.70/0.91 tff(207,plain,
% 0.70/0.91 (((~![U: $i] : (hskp15 | hskp0 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp15 | hskp0 | (~ndr1_0) | c3_1(a282) | c2_1(a282) | (~c0_1(a282)))) <=> ((~![U: $i] : (hskp15 | hskp0 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | hskp15 | hskp0 | c3_1(a282) | (~ndr1_0) | c2_1(a282) | (~c0_1(a282)))),
% 0.70/0.91 inference(transitivity,[status(thm)],[206, 204])).
% 0.70/0.91 tff(208,plain,
% 0.70/0.91 ((~![U: $i] : (hskp15 | hskp0 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp15 | hskp0 | (~ndr1_0) | c3_1(a282) | c2_1(a282) | (~c0_1(a282)))),
% 0.70/0.91 inference(quant_inst,[status(thm)],[])).
% 0.70/0.91 tff(209,plain,
% 0.70/0.91 ((~![U: $i] : (hskp15 | hskp0 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | hskp15 | hskp0 | c3_1(a282) | (~ndr1_0) | c2_1(a282) | (~c0_1(a282))),
% 0.70/0.91 inference(modus_ponens,[status(thm)],[208, 207])).
% 0.70/0.91 tff(210,plain,
% 0.70/0.91 (hskp15 | hskp0 | c2_1(a282)),
% 0.70/0.91 inference(unit_resolution,[status(thm)],[209, 122, 203, 181, 202])).
% 0.70/0.91 tff(211,plain,
% 0.70/0.91 (hskp15),
% 0.70/0.91 inference(unit_resolution,[status(thm)],[210, 180, 64])).
% 0.70/0.91 tff(212,plain,
% 0.70/0.91 (((~hskp15) | (~c3_1(a238))) <=> ((~hskp15) | (~c3_1(a238)))),
% 0.70/0.91 inference(rewrite,[status(thm)],[])).
% 0.70/0.91 tff(213,plain,
% 0.70/0.91 (((~c3_1(a238)) | (~hskp15)) <=> ((~hskp15) | (~c3_1(a238)))),
% 0.70/0.91 inference(rewrite,[status(thm)],[])).
% 0.70/0.91 tff(214,axiom,((~c3_1(a238)) | (~hskp15)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause97')).
% 0.70/0.91 tff(215,plain,
% 0.70/0.91 ((~hskp15) | (~c3_1(a238))),
% 0.70/0.91 inference(modus_ponens,[status(thm)],[214, 213])).
% 0.70/0.91 tff(216,plain,
% 0.70/0.91 ((~hskp15) | (~c3_1(a238))),
% 0.70/0.91 inference(modus_ponens,[status(thm)],[215, 212])).
% 0.70/0.91 tff(217,plain,
% 0.70/0.91 (~c3_1(a238)),
% 0.70/0.91 inference(unit_resolution,[status(thm)],[216, 211])).
% 0.70/0.91 tff(218,plain,
% 0.70/0.91 (((~hskp15) | c2_1(a238)) <=> ((~hskp15) | c2_1(a238))),
% 0.70/0.91 inference(rewrite,[status(thm)],[])).
% 0.70/0.91 tff(219,axiom,((~hskp15) | c2_1(a238)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause58')).
% 0.70/0.91 tff(220,plain,
% 0.70/0.91 ((~hskp15) | c2_1(a238)),
% 0.70/0.91 inference(modus_ponens,[status(thm)],[219, 218])).
% 0.70/0.91 tff(221,plain,
% 0.70/0.91 ((~hskp15) | c2_1(a238)),
% 0.70/0.91 inference(modus_ponens,[status(thm)],[220, 218])).
% 0.70/0.91 tff(222,plain,
% 0.70/0.91 ((~hskp15) | c2_1(a238)),
% 0.70/0.91 inference(modus_ponens,[status(thm)],[221, 218])).
% 0.70/0.91 tff(223,plain,
% 0.70/0.91 ((~hskp15) | c2_1(a238)),
% 0.70/0.91 inference(modus_ponens,[status(thm)],[222, 218])).
% 0.70/0.91 tff(224,plain,
% 0.70/0.91 ((~hskp15) | c2_1(a238)),
% 0.70/0.91 inference(modus_ponens,[status(thm)],[223, 218])).
% 0.70/0.91 tff(225,plain,
% 0.70/0.91 (c2_1(a238)),
% 0.70/0.91 inference(unit_resolution,[status(thm)],[224, 211])).
% 0.70/0.91 tff(226,plain,
% 0.70/0.91 (((~hskp15) | c0_1(a238)) <=> ((~hskp15) | c0_1(a238))),
% 0.70/0.91 inference(rewrite,[status(thm)],[])).
% 0.70/0.91 tff(227,axiom,((~hskp15) | c0_1(a238)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause57')).
% 0.70/0.91 tff(228,plain,
% 0.70/0.91 ((~hskp15) | c0_1(a238)),
% 0.70/0.91 inference(modus_ponens,[status(thm)],[227, 226])).
% 0.70/0.91 tff(229,plain,
% 0.70/0.91 ((~hskp15) | c0_1(a238)),
% 0.70/0.91 inference(modus_ponens,[status(thm)],[228, 226])).
% 0.70/0.91 tff(230,plain,
% 0.70/0.91 ((~hskp15) | c0_1(a238)),
% 0.70/0.91 inference(modus_ponens,[status(thm)],[229, 226])).
% 0.70/0.91 tff(231,plain,
% 0.70/0.91 ((~hskp15) | c0_1(a238)),
% 0.70/0.91 inference(modus_ponens,[status(thm)],[230, 226])).
% 0.70/0.91 tff(232,plain,
% 0.70/0.91 ((~hskp15) | c0_1(a238)),
% 0.70/0.91 inference(modus_ponens,[status(thm)],[231, 226])).
% 0.70/0.91 tff(233,plain,
% 0.70/0.91 (c0_1(a238)),
% 0.70/0.91 inference(unit_resolution,[status(thm)],[232, 211])).
% 0.70/0.91 tff(234,plain,
% 0.70/0.91 (((~![U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp27 | c3_1(a238) | (~ndr1_0) | (~c2_1(a238)) | (~c0_1(a238)))) <=> ((~![U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp27 | c3_1(a238) | (~ndr1_0) | (~c2_1(a238)) | (~c0_1(a238)))),
% 0.70/0.91 inference(rewrite,[status(thm)],[])).
% 0.70/0.91 tff(235,plain,
% 0.70/0.91 ((hskp27 | (~ndr1_0) | c3_1(a238) | (~c2_1(a238)) | (~c0_1(a238))) <=> (hskp27 | c3_1(a238) | (~ndr1_0) | (~c2_1(a238)) | (~c0_1(a238)))),
% 0.70/0.91 inference(rewrite,[status(thm)],[])).
% 0.70/0.91 tff(236,plain,
% 0.70/0.91 (((~![U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp27 | (~ndr1_0) | c3_1(a238) | (~c2_1(a238)) | (~c0_1(a238)))) <=> ((~![U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp27 | c3_1(a238) | (~ndr1_0) | (~c2_1(a238)) | (~c0_1(a238))))),
% 0.70/0.91 inference(monotonicity,[status(thm)],[235])).
% 0.70/0.91 tff(237,plain,
% 0.70/0.91 (((~![U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp27 | (~ndr1_0) | c3_1(a238) | (~c2_1(a238)) | (~c0_1(a238)))) <=> ((~![U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp27 | c3_1(a238) | (~ndr1_0) | (~c2_1(a238)) | (~c0_1(a238)))),
% 0.70/0.91 inference(transitivity,[status(thm)],[236, 234])).
% 0.70/0.91 tff(238,plain,
% 0.70/0.91 ((~![U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp27 | (~ndr1_0) | c3_1(a238) | (~c2_1(a238)) | (~c0_1(a238)))),
% 0.70/0.91 inference(quant_inst,[status(thm)],[])).
% 0.70/0.91 tff(239,plain,
% 0.70/0.91 ((~![U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp27 | c3_1(a238) | (~ndr1_0) | (~c2_1(a238)) | (~c0_1(a238))),
% 0.70/0.91 inference(modus_ponens,[status(thm)],[238, 237])).
% 0.70/0.91 tff(240,plain,
% 0.70/0.91 (hskp27),
% 0.70/0.91 inference(unit_resolution,[status(thm)],[239, 122, 233, 225, 217, 192])).
% 0.70/0.91 tff(241,plain,
% 0.70/0.91 (((~hskp27) | c3_1(a232)) <=> ((~hskp27) | c3_1(a232))),
% 0.70/0.91 inference(rewrite,[status(thm)],[])).
% 0.70/0.91 tff(242,axiom,((~hskp27) | c3_1(a232)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause41')).
% 0.70/0.91 tff(243,plain,
% 0.70/0.91 ((~hskp27) | c3_1(a232)),
% 0.70/0.91 inference(modus_ponens,[status(thm)],[242, 241])).
% 0.70/0.91 tff(244,plain,
% 0.70/0.91 ((~hskp27) | c3_1(a232)),
% 0.70/0.91 inference(modus_ponens,[status(thm)],[243, 241])).
% 0.70/0.91 tff(245,plain,
% 0.70/0.91 ((~hskp27) | c3_1(a232)),
% 0.70/0.91 inference(modus_ponens,[status(thm)],[244, 241])).
% 0.70/0.91 tff(246,plain,
% 0.70/0.91 ((~hskp27) | c3_1(a232)),
% 0.70/0.91 inference(modus_ponens,[status(thm)],[245, 241])).
% 0.70/0.91 tff(247,plain,
% 0.70/0.91 ((~hskp27) | c3_1(a232)),
% 0.70/0.91 inference(modus_ponens,[status(thm)],[246, 241])).
% 0.70/0.91 tff(248,plain,
% 0.70/0.91 (c3_1(a232)),
% 0.70/0.91 inference(unit_resolution,[status(thm)],[247, 240])).
% 0.70/0.91 tff(249,plain,
% 0.70/0.91 (((~hskp27) | c2_1(a232)) <=> ((~hskp27) | c2_1(a232))),
% 0.70/0.91 inference(rewrite,[status(thm)],[])).
% 0.70/0.91 tff(250,axiom,((~hskp27) | c2_1(a232)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause40')).
% 0.70/0.91 tff(251,plain,
% 0.70/0.91 ((~hskp27) | c2_1(a232)),
% 0.70/0.91 inference(modus_ponens,[status(thm)],[250, 249])).
% 0.70/0.91 tff(252,plain,
% 0.70/0.91 ((~hskp27) | c2_1(a232)),
% 0.70/0.91 inference(modus_ponens,[status(thm)],[251, 249])).
% 0.70/0.91 tff(253,plain,
% 0.70/0.91 ((~hskp27) | c2_1(a232)),
% 0.70/0.91 inference(modus_ponens,[status(thm)],[252, 249])).
% 0.70/0.91 tff(254,plain,
% 0.70/0.91 ((~hskp27) | c2_1(a232)),
% 0.70/0.91 inference(modus_ponens,[status(thm)],[253, 249])).
% 0.70/0.91 tff(255,plain,
% 0.70/0.91 ((~hskp27) | c2_1(a232)),
% 0.70/0.91 inference(modus_ponens,[status(thm)],[254, 249])).
% 0.70/0.91 tff(256,plain,
% 0.70/0.91 (c2_1(a232)),
% 0.70/0.91 inference(unit_resolution,[status(thm)],[255, 240])).
% 0.70/0.91 tff(257,plain,
% 0.70/0.91 (((~hskp27) | c0_1(a232)) <=> ((~hskp27) | c0_1(a232))),
% 0.70/0.91 inference(rewrite,[status(thm)],[])).
% 0.70/0.91 tff(258,axiom,((~hskp27) | c0_1(a232)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause39')).
% 0.70/0.91 tff(259,plain,
% 0.70/0.91 ((~hskp27) | c0_1(a232)),
% 0.70/0.91 inference(modus_ponens,[status(thm)],[258, 257])).
% 0.70/0.91 tff(260,plain,
% 0.70/0.91 ((~hskp27) | c0_1(a232)),
% 0.70/0.91 inference(modus_ponens,[status(thm)],[259, 257])).
% 0.70/0.91 tff(261,plain,
% 0.70/0.91 ((~hskp27) | c0_1(a232)),
% 0.70/0.91 inference(modus_ponens,[status(thm)],[260, 257])).
% 0.70/0.91 tff(262,plain,
% 0.70/0.91 ((~hskp27) | c0_1(a232)),
% 0.70/0.91 inference(modus_ponens,[status(thm)],[261, 257])).
% 0.70/0.91 tff(263,plain,
% 0.70/0.91 ((~hskp27) | c0_1(a232)),
% 0.70/0.91 inference(modus_ponens,[status(thm)],[262, 257])).
% 0.70/0.91 tff(264,plain,
% 0.70/0.91 (c0_1(a232)),
% 0.70/0.91 inference(unit_resolution,[status(thm)],[263, 240])).
% 0.70/0.91 tff(265,plain,
% 0.70/0.91 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp0 | c1_1(a282) | c3_1(a282) | (~ndr1_0) | (~c2_1(a232)) | (~c3_1(a232)) | (~c0_1(a232)) | c2_1(a282))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp0 | c1_1(a282) | c3_1(a282) | (~ndr1_0) | (~c2_1(a232)) | (~c3_1(a232)) | (~c0_1(a232)) | c2_1(a282))),
% 0.70/0.91 inference(rewrite,[status(thm)],[])).
% 0.70/0.91 tff(266,plain,
% 0.70/0.91 ((hskp0 | (~ndr1_0) | (~c2_1(a232)) | (~c0_1(a232)) | (~c3_1(a232)) | c3_1(a282) | c2_1(a282) | c1_1(a282)) <=> (hskp0 | c1_1(a282) | c3_1(a282) | (~ndr1_0) | (~c2_1(a232)) | (~c3_1(a232)) | (~c0_1(a232)) | c2_1(a282))),
% 0.70/0.91 inference(rewrite,[status(thm)],[])).
% 0.70/0.91 tff(267,plain,
% 0.70/0.91 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp0 | (~ndr1_0) | (~c2_1(a232)) | (~c0_1(a232)) | (~c3_1(a232)) | c3_1(a282) | c2_1(a282) | c1_1(a282))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp0 | c1_1(a282) | c3_1(a282) | (~ndr1_0) | (~c2_1(a232)) | (~c3_1(a232)) | (~c0_1(a232)) | c2_1(a282)))),
% 0.70/0.91 inference(monotonicity,[status(thm)],[266])).
% 0.70/0.91 tff(268,plain,
% 0.70/0.91 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp0 | (~ndr1_0) | (~c2_1(a232)) | (~c0_1(a232)) | (~c3_1(a232)) | c3_1(a282) | c2_1(a282) | c1_1(a282))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp0 | c1_1(a282) | c3_1(a282) | (~ndr1_0) | (~c2_1(a232)) | (~c3_1(a232)) | (~c0_1(a232)) | c2_1(a282))),
% 0.70/0.91 inference(transitivity,[status(thm)],[267, 265])).
% 0.70/0.91 tff(269,plain,
% 0.70/0.91 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp0 | (~ndr1_0) | (~c2_1(a232)) | (~c0_1(a232)) | (~c3_1(a232)) | c3_1(a282) | c2_1(a282) | c1_1(a282))),
% 0.70/0.91 inference(quant_inst,[status(thm)],[])).
% 0.70/0.91 tff(270,plain,
% 0.70/0.91 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp0 | c1_1(a282) | c3_1(a282) | (~ndr1_0) | (~c2_1(a232)) | (~c3_1(a232)) | (~c0_1(a232)) | c2_1(a282)),
% 0.70/0.91 inference(modus_ponens,[status(thm)],[269, 268])).
% 0.70/0.91 tff(271,plain,
% 0.70/0.91 ($false),
% 0.70/0.91 inference(unit_resolution,[status(thm)],[270, 122, 64, 264, 256, 248, 182, 181, 42, 180])).
% 0.70/0.91 tff(272,plain,(c2_1(a282) | hskp0 | c1_1(a282) | c3_1(a282) | (~c0_1(a282))), inference(lemma,lemma(discharge,[]))).
% 0.70/0.91 tff(273,plain,
% 0.70/0.91 (hskp0),
% 0.70/0.91 inference(unit_resolution,[status(thm)],[272, 180, 179, 173, 167])).
% 0.70/0.91 tff(274,plain,
% 0.70/0.91 (((~hskp0) | (~c2_1(a213))) <=> ((~hskp0) | (~c2_1(a213)))),
% 0.70/0.91 inference(rewrite,[status(thm)],[])).
% 0.70/0.91 tff(275,plain,
% 0.70/0.91 (((~c2_1(a213)) | (~hskp0)) <=> ((~hskp0) | (~c2_1(a213)))),
% 0.70/0.91 inference(rewrite,[status(thm)],[])).
% 0.70/0.91 tff(276,axiom,((~c2_1(a213)) | (~hskp0)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause122')).
% 0.70/0.91 tff(277,plain,
% 0.70/0.91 ((~hskp0) | (~c2_1(a213))),
% 0.70/0.91 inference(modus_ponens,[status(thm)],[276, 275])).
% 0.70/0.91 tff(278,plain,
% 0.70/0.91 ((~hskp0) | (~c2_1(a213))),
% 0.70/0.91 inference(modus_ponens,[status(thm)],[277, 274])).
% 0.70/0.91 tff(279,plain,
% 0.70/0.91 (~c2_1(a213)),
% 0.70/0.91 inference(unit_resolution,[status(thm)],[278, 273])).
% 0.70/0.91 tff(280,plain,
% 0.70/0.91 (((~hskp0) | c3_1(a213)) <=> ((~hskp0) | c3_1(a213))),
% 0.70/0.91 inference(rewrite,[status(thm)],[])).
% 0.70/0.91 tff(281,axiom,((~hskp0) | c3_1(a213)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause78')).
% 0.70/0.91 tff(282,plain,
% 0.70/0.91 ((~hskp0) | c3_1(a213)),
% 0.70/0.91 inference(modus_ponens,[status(thm)],[281, 280])).
% 0.70/0.91 tff(283,plain,
% 0.70/0.91 ((~hskp0) | c3_1(a213)),
% 0.70/0.91 inference(modus_ponens,[status(thm)],[282, 280])).
% 0.70/0.91 tff(284,plain,
% 0.70/0.91 ((~hskp0) | c3_1(a213)),
% 0.70/0.91 inference(modus_ponens,[status(thm)],[283, 280])).
% 0.70/0.91 tff(285,plain,
% 0.70/0.91 ((~hskp0) | c3_1(a213)),
% 0.70/0.91 inference(modus_ponens,[status(thm)],[284, 280])).
% 0.70/0.91 tff(286,plain,
% 0.70/0.91 ((~hskp0) | c3_1(a213)),
% 0.70/0.91 inference(modus_ponens,[status(thm)],[285, 280])).
% 0.70/0.91 tff(287,plain,
% 0.70/0.91 (c3_1(a213)),
% 0.70/0.91 inference(unit_resolution,[status(thm)],[286, 273])).
% 0.70/0.91 tff(288,plain,
% 0.70/0.91 (((~hskp0) | c1_1(a213)) <=> ((~hskp0) | c1_1(a213))),
% 0.70/0.91 inference(rewrite,[status(thm)],[])).
% 0.70/0.91 tff(289,axiom,((~hskp0) | c1_1(a213)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause77')).
% 0.70/0.91 tff(290,plain,
% 0.70/0.91 ((~hskp0) | c1_1(a213)),
% 0.70/0.91 inference(modus_ponens,[status(thm)],[289, 288])).
% 0.70/0.91 tff(291,plain,
% 0.70/0.91 ((~hskp0) | c1_1(a213)),
% 0.70/0.91 inference(modus_ponens,[status(thm)],[290, 288])).
% 0.70/0.91 tff(292,plain,
% 0.70/0.91 ((~hskp0) | c1_1(a213)),
% 0.70/0.91 inference(modus_ponens,[status(thm)],[291, 288])).
% 0.70/0.91 tff(293,plain,
% 0.70/0.91 ((~hskp0) | c1_1(a213)),
% 0.70/0.91 inference(modus_ponens,[status(thm)],[292, 288])).
% 0.70/0.91 tff(294,plain,
% 0.70/0.91 ((~hskp0) | c1_1(a213)),
% 0.70/0.91 inference(modus_ponens,[status(thm)],[293, 288])).
% 0.70/0.91 tff(295,plain,
% 0.70/0.91 (c1_1(a213)),
% 0.70/0.91 inference(unit_resolution,[status(thm)],[294, 273])).
% 0.70/0.91 tff(296,plain,
% 0.70/0.91 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W))) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W))))),
% 0.70/0.91 inference(bind,[status(th)],[])).
% 0.70/0.91 tff(297,plain,
% 0.70/0.91 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))),
% 0.70/0.91 inference(quant_intro,[status(thm)],[296])).
% 0.70/0.91 tff(298,plain,
% 0.70/0.91 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))),
% 0.70/0.91 inference(rewrite,[status(thm)],[])).
% 0.70/0.91 tff(299,plain,
% 0.70/0.91 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V))))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(W))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V))) | (~c3_1(W))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V)) | (~c3_1(W)))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V)) | (~c3_1(W))))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(W))) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V)) | (~c3_1(W))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V)) | (~c3_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V)) | (~c3_1(W)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V)) | (~c3_1(W))))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(W))) | c2_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V)) | (~c3_1(W))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V)) | (~c3_1(W))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(W)))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(W))) | c2_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(W))))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(W))) | c2_1(U)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(W))) | c2_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(W))) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | (~c3_1(W)))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(W))) | c2_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | (~c3_1(W))))), ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(W))) | c2_1(U)) | c1_1(V)) | c2_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | (~c3_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | (~c3_1(W))) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)))), ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(W))) | c2_1(U)) | c1_1(V)) | c2_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c3_1(W))))), (((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(W))) | c2_1(U)) | c1_1(V)) | c2_1(V)) | c0_1(W)) | c2_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c3_1(W))) | c2_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c3_1(W))) | c2_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))), (((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(W))) | c2_1(U)) | c1_1(V)) | c2_1(V)) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))))),
% 0.70/0.92 inference(bind,[status(th)],[])).
% 0.70/0.92 tff(300,plain,
% 0.70/0.92 (![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(W))) | c2_1(U)) | c1_1(V)) | c2_1(V)) | c0_1(W)) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))),
% 0.70/0.92 inference(quant_intro,[status(thm)],[299])).
% 0.70/0.92 tff(301,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(W))) | c2_1(U)) | c1_1(V)) | c2_1(V)) | c0_1(W)) | c2_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause171')).
% 0.70/0.92 tff(302,plain,
% 0.70/0.92 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))),
% 0.70/0.92 inference(modus_ponens,[status(thm)],[301, 300])).
% 0.70/0.92 tff(303,plain,
% 0.70/0.92 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))),
% 0.70/0.92 inference(modus_ponens,[status(thm)],[302, 298])).
% 0.70/0.92 tff(304,plain,(
% 0.70/0.92 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))),
% 0.70/0.92 inference(skolemize,[status(sab)],[303])).
% 0.70/0.92 tff(305,plain,
% 0.70/0.92 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))),
% 0.70/0.92 inference(modus_ponens,[status(thm)],[304, 297])).
% 0.70/0.92 tff(306,assumption,(~c2_1(a213)), introduced(assumption)).
% 0.70/0.92 tff(307,assumption,(hskp3), introduced(assumption)).
% 0.70/0.92 tff(308,plain,
% 0.70/0.92 (((~hskp3) | (~c2_1(a216))) <=> ((~hskp3) | (~c2_1(a216)))),
% 0.70/0.92 inference(rewrite,[status(thm)],[])).
% 0.70/0.92 tff(309,plain,
% 0.70/0.92 (((~c2_1(a216)) | (~hskp3)) <=> ((~hskp3) | (~c2_1(a216)))),
% 0.70/0.92 inference(rewrite,[status(thm)],[])).
% 0.70/0.92 tff(310,axiom,((~c2_1(a216)) | (~hskp3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause118')).
% 0.70/0.92 tff(311,plain,
% 0.70/0.92 ((~hskp3) | (~c2_1(a216))),
% 0.70/0.92 inference(modus_ponens,[status(thm)],[310, 309])).
% 0.70/0.92 tff(312,plain,
% 0.70/0.92 ((~hskp3) | (~c2_1(a216))),
% 0.70/0.92 inference(modus_ponens,[status(thm)],[311, 308])).
% 0.70/0.92 tff(313,plain,
% 0.70/0.92 (~c2_1(a216)),
% 0.70/0.92 inference(unit_resolution,[status(thm)],[312, 307])).
% 0.70/0.92 tff(314,plain,
% 0.70/0.92 (((~hskp3) | (~c0_1(a216))) <=> ((~hskp3) | (~c0_1(a216)))),
% 0.70/0.92 inference(rewrite,[status(thm)],[])).
% 0.70/0.92 tff(315,plain,
% 0.70/0.92 (((~c0_1(a216)) | (~hskp3)) <=> ((~hskp3) | (~c0_1(a216)))),
% 0.70/0.92 inference(rewrite,[status(thm)],[])).
% 0.70/0.92 tff(316,axiom,((~c0_1(a216)) | (~hskp3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause117')).
% 0.70/0.92 tff(317,plain,
% 0.70/0.92 ((~hskp3) | (~c0_1(a216))),
% 0.70/0.92 inference(modus_ponens,[status(thm)],[316, 315])).
% 0.70/0.92 tff(318,plain,
% 0.70/0.92 ((~hskp3) | (~c0_1(a216))),
% 0.70/0.92 inference(modus_ponens,[status(thm)],[317, 314])).
% 0.70/0.92 tff(319,plain,
% 0.70/0.92 (~c0_1(a216)),
% 0.70/0.92 inference(unit_resolution,[status(thm)],[318, 307])).
% 0.70/0.92 tff(320,assumption,(c3_1(a213)), introduced(assumption)).
% 0.70/0.92 tff(321,assumption,(c1_1(a213)), introduced(assumption)).
% 0.70/0.92 tff(322,plain,
% 0.70/0.92 (((~hskp3) | c3_1(a216)) <=> ((~hskp3) | c3_1(a216))),
% 0.70/0.92 inference(rewrite,[status(thm)],[])).
% 0.70/0.92 tff(323,axiom,((~hskp3) | c3_1(a216)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause73')).
% 0.70/0.92 tff(324,plain,
% 0.70/0.92 ((~hskp3) | c3_1(a216)),
% 0.70/0.92 inference(modus_ponens,[status(thm)],[323, 322])).
% 0.70/0.92 tff(325,plain,
% 0.70/0.92 ((~hskp3) | c3_1(a216)),
% 0.70/0.92 inference(modus_ponens,[status(thm)],[324, 322])).
% 0.70/0.92 tff(326,plain,
% 0.70/0.92 ((~hskp3) | c3_1(a216)),
% 0.70/0.92 inference(modus_ponens,[status(thm)],[325, 322])).
% 0.70/0.92 tff(327,plain,
% 0.70/0.92 ((~hskp3) | c3_1(a216)),
% 0.70/0.92 inference(modus_ponens,[status(thm)],[326, 322])).
% 0.70/0.92 tff(328,plain,
% 0.70/0.92 ((~hskp3) | c3_1(a216)),
% 0.70/0.92 inference(modus_ponens,[status(thm)],[327, 322])).
% 0.70/0.92 tff(329,plain,
% 0.70/0.92 (c3_1(a216)),
% 0.70/0.92 inference(unit_resolution,[status(thm)],[328, 307])).
% 0.70/0.92 tff(330,plain,
% 0.70/0.92 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | (c1_1(a282) | c0_1(a216) | c2_1(a216) | c2_1(a213) | (~ndr1_0) | (~c1_1(a213)) | (~c3_1(a213)) | (~c3_1(a216)) | c2_1(a282) | (~c0_1(a282)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a282) | c0_1(a216) | c2_1(a216) | c2_1(a213) | (~ndr1_0) | (~c1_1(a213)) | (~c3_1(a213)) | (~c3_1(a216)) | c2_1(a282) | (~c0_1(a282)))),
% 0.70/0.92 inference(rewrite,[status(thm)],[])).
% 0.70/0.92 tff(331,plain,
% 0.70/0.92 (((~ndr1_0) | c2_1(a213) | (~c1_1(a213)) | (~c3_1(a213)) | c2_1(a282) | c1_1(a282) | (~c0_1(a282)) | c0_1(a216) | c2_1(a216) | (~c3_1(a216))) <=> (c1_1(a282) | c0_1(a216) | c2_1(a216) | c2_1(a213) | (~ndr1_0) | (~c1_1(a213)) | (~c3_1(a213)) | (~c3_1(a216)) | c2_1(a282) | (~c0_1(a282)))),
% 0.70/0.92 inference(rewrite,[status(thm)],[])).
% 0.70/0.92 tff(332,plain,
% 0.70/0.92 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a213) | (~c1_1(a213)) | (~c3_1(a213)) | c2_1(a282) | c1_1(a282) | (~c0_1(a282)) | c0_1(a216) | c2_1(a216) | (~c3_1(a216)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | (c1_1(a282) | c0_1(a216) | c2_1(a216) | c2_1(a213) | (~ndr1_0) | (~c1_1(a213)) | (~c3_1(a213)) | (~c3_1(a216)) | c2_1(a282) | (~c0_1(a282))))),
% 0.70/0.92 inference(monotonicity,[status(thm)],[331])).
% 0.70/0.92 tff(333,plain,
% 0.70/0.92 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a213) | (~c1_1(a213)) | (~c3_1(a213)) | c2_1(a282) | c1_1(a282) | (~c0_1(a282)) | c0_1(a216) | c2_1(a216) | (~c3_1(a216)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a282) | c0_1(a216) | c2_1(a216) | c2_1(a213) | (~ndr1_0) | (~c1_1(a213)) | (~c3_1(a213)) | (~c3_1(a216)) | c2_1(a282) | (~c0_1(a282)))),
% 0.70/0.92 inference(transitivity,[status(thm)],[332, 330])).
% 0.70/0.92 tff(334,plain,
% 0.70/0.92 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a213) | (~c1_1(a213)) | (~c3_1(a213)) | c2_1(a282) | c1_1(a282) | (~c0_1(a282)) | c0_1(a216) | c2_1(a216) | (~c3_1(a216)))),
% 0.70/0.92 inference(quant_inst,[status(thm)],[])).
% 0.70/0.92 tff(335,plain,
% 0.70/0.92 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a282) | c0_1(a216) | c2_1(a216) | c2_1(a213) | (~ndr1_0) | (~c1_1(a213)) | (~c3_1(a213)) | (~c3_1(a216)) | c2_1(a282) | (~c0_1(a282))),
% 0.70/0.92 inference(modus_ponens,[status(thm)],[334, 333])).
% 0.70/0.92 tff(336,plain,
% 0.70/0.92 ($false),
% 0.70/0.92 inference(unit_resolution,[status(thm)],[335, 122, 203, 329, 321, 320, 182, 319, 313, 306, 305, 180])).
% 0.70/0.92 tff(337,plain,((~hskp3) | (~c0_1(a282)) | (~c1_1(a213)) | (~c3_1(a213)) | c1_1(a282) | c2_1(a213) | c2_1(a282)), inference(lemma,lemma(discharge,[]))).
% 0.70/0.92 tff(338,plain,
% 0.70/0.92 (~hskp3),
% 0.70/0.92 inference(unit_resolution,[status(thm)],[337, 295, 180, 287, 179, 279, 167])).
% 0.70/0.92 tff(339,plain,
% 0.70/0.92 (^[U: $i] : refl((hskp8 | hskp3 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U))) <=> (hskp8 | hskp3 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U))))),
% 0.70/0.92 inference(bind,[status(th)],[])).
% 0.70/0.92 tff(340,plain,
% 0.70/0.92 (![U: $i] : (hskp8 | hskp3 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp8 | hskp3 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 0.70/0.92 inference(quant_intro,[status(thm)],[339])).
% 0.70/0.92 tff(341,plain,
% 0.70/0.92 (![U: $i] : (hskp8 | hskp3 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp8 | hskp3 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 0.70/0.92 inference(rewrite,[status(thm)],[])).
% 0.70/0.92 tff(342,plain,
% 0.70/0.92 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp8) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U))) | hskp8))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U))) | hskp8) <=> (hskp8 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp8) <=> (hskp8 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp8) | hskp3) <=> ((hskp8 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U))) | hskp3))), rewrite(((hskp8 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U))) | hskp3) <=> (hskp8 | hskp3 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp8) | hskp3) <=> (hskp8 | hskp3 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))))),
% 0.70/0.92 inference(bind,[status(th)],[])).
% 0.70/0.92 tff(343,plain,
% 0.70/0.92 (![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp8) | hskp3) <=> ![U: $i] : (hskp8 | hskp3 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 0.70/0.92 inference(quant_intro,[status(thm)],[342])).
% 0.70/0.92 tff(344,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp8) | hskp3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause139')).
% 0.70/0.92 tff(345,plain,
% 0.70/0.92 (![U: $i] : (hskp8 | hskp3 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 0.70/0.92 inference(modus_ponens,[status(thm)],[344, 343])).
% 0.70/0.92 tff(346,plain,
% 0.70/0.92 (![U: $i] : (hskp8 | hskp3 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 0.70/0.92 inference(modus_ponens,[status(thm)],[345, 341])).
% 0.70/0.92 tff(347,plain,(
% 0.70/0.92 ![U: $i] : (hskp8 | hskp3 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 0.70/0.92 inference(skolemize,[status(sab)],[346])).
% 0.70/0.92 tff(348,plain,
% 0.70/0.92 (![U: $i] : (hskp8 | hskp3 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 0.70/0.92 inference(modus_ponens,[status(thm)],[347, 340])).
% 0.70/0.92 tff(349,assumption,(hskp20), introduced(assumption)).
% 0.70/0.92 tff(350,plain,
% 0.70/0.92 (((~hskp20) | (~c3_1(a259))) <=> ((~hskp20) | (~c3_1(a259)))),
% 0.70/0.92 inference(rewrite,[status(thm)],[])).
% 0.70/0.92 tff(351,plain,
% 0.70/0.92 (((~c3_1(a259)) | (~hskp20)) <=> ((~hskp20) | (~c3_1(a259)))),
% 0.70/0.92 inference(rewrite,[status(thm)],[])).
% 0.70/0.92 tff(352,axiom,((~c3_1(a259)) | (~hskp20)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause89')).
% 0.70/0.92 tff(353,plain,
% 0.70/0.92 ((~hskp20) | (~c3_1(a259))),
% 0.70/0.92 inference(modus_ponens,[status(thm)],[352, 351])).
% 0.70/0.92 tff(354,plain,
% 0.70/0.92 ((~hskp20) | (~c3_1(a259))),
% 0.70/0.92 inference(modus_ponens,[status(thm)],[353, 350])).
% 0.70/0.92 tff(355,plain,
% 0.70/0.92 (~c3_1(a259)),
% 0.70/0.92 inference(unit_resolution,[status(thm)],[354, 349])).
% 0.70/0.92 tff(356,plain,
% 0.70/0.92 (((~hskp20) | c1_1(a259)) <=> ((~hskp20) | c1_1(a259))),
% 0.70/0.92 inference(rewrite,[status(thm)],[])).
% 0.70/0.92 tff(357,axiom,((~hskp20) | c1_1(a259)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause51')).
% 0.70/0.92 tff(358,plain,
% 0.70/0.92 ((~hskp20) | c1_1(a259)),
% 0.70/0.92 inference(modus_ponens,[status(thm)],[357, 356])).
% 0.70/0.92 tff(359,plain,
% 0.70/0.92 ((~hskp20) | c1_1(a259)),
% 0.70/0.92 inference(modus_ponens,[status(thm)],[358, 356])).
% 0.70/0.92 tff(360,plain,
% 0.70/0.92 ((~hskp20) | c1_1(a259)),
% 0.70/0.92 inference(modus_ponens,[status(thm)],[359, 356])).
% 0.70/0.92 tff(361,plain,
% 0.70/0.92 ((~hskp20) | c1_1(a259)),
% 0.70/0.92 inference(modus_ponens,[status(thm)],[360, 356])).
% 0.70/0.92 tff(362,plain,
% 0.70/0.92 ((~hskp20) | c1_1(a259)),
% 0.70/0.92 inference(modus_ponens,[status(thm)],[361, 356])).
% 0.70/0.92 tff(363,plain,
% 0.70/0.92 (c1_1(a259)),
% 0.70/0.92 inference(unit_resolution,[status(thm)],[362, 349])).
% 0.70/0.92 tff(364,plain,
% 0.70/0.92 (((~hskp20) | c0_1(a259)) <=> ((~hskp20) | c0_1(a259))),
% 0.70/0.92 inference(rewrite,[status(thm)],[])).
% 0.70/0.92 tff(365,axiom,((~hskp20) | c0_1(a259)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause50')).
% 0.70/0.92 tff(366,plain,
% 0.70/0.92 ((~hskp20) | c0_1(a259)),
% 0.70/0.92 inference(modus_ponens,[status(thm)],[365, 364])).
% 0.70/0.92 tff(367,plain,
% 0.70/0.92 ((~hskp20) | c0_1(a259)),
% 0.70/0.92 inference(modus_ponens,[status(thm)],[366, 364])).
% 0.70/0.92 tff(368,plain,
% 0.70/0.92 ((~hskp20) | c0_1(a259)),
% 0.70/0.92 inference(modus_ponens,[status(thm)],[367, 364])).
% 0.70/0.92 tff(369,plain,
% 0.70/0.92 ((~hskp20) | c0_1(a259)),
% 0.70/0.92 inference(modus_ponens,[status(thm)],[368, 364])).
% 0.70/0.92 tff(370,plain,
% 0.70/0.92 ((~hskp20) | c0_1(a259)),
% 0.70/0.92 inference(modus_ponens,[status(thm)],[369, 364])).
% 0.70/0.92 tff(371,plain,
% 0.70/0.92 (c0_1(a259)),
% 0.70/0.92 inference(unit_resolution,[status(thm)],[370, 349])).
% 0.70/0.92 tff(372,assumption,(~hskp3), introduced(assumption)).
% 0.70/0.92 tff(373,plain,
% 0.70/0.92 (((~![U: $i] : (hskp8 | hskp3 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp8 | hskp3 | c3_1(a259) | (~ndr1_0) | (~c0_1(a259)) | (~c1_1(a259)))) <=> ((~![U: $i] : (hskp8 | hskp3 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp8 | hskp3 | c3_1(a259) | (~ndr1_0) | (~c0_1(a259)) | (~c1_1(a259)))),
% 0.70/0.92 inference(rewrite,[status(thm)],[])).
% 0.70/0.92 tff(374,plain,
% 0.70/0.92 ((hskp8 | hskp3 | (~ndr1_0) | c3_1(a259) | (~c1_1(a259)) | (~c0_1(a259))) <=> (hskp8 | hskp3 | c3_1(a259) | (~ndr1_0) | (~c0_1(a259)) | (~c1_1(a259)))),
% 0.70/0.92 inference(rewrite,[status(thm)],[])).
% 0.70/0.92 tff(375,plain,
% 0.70/0.92 (((~![U: $i] : (hskp8 | hskp3 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp8 | hskp3 | (~ndr1_0) | c3_1(a259) | (~c1_1(a259)) | (~c0_1(a259)))) <=> ((~![U: $i] : (hskp8 | hskp3 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp8 | hskp3 | c3_1(a259) | (~ndr1_0) | (~c0_1(a259)) | (~c1_1(a259))))),
% 0.70/0.92 inference(monotonicity,[status(thm)],[374])).
% 0.70/0.92 tff(376,plain,
% 0.70/0.92 (((~![U: $i] : (hskp8 | hskp3 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp8 | hskp3 | (~ndr1_0) | c3_1(a259) | (~c1_1(a259)) | (~c0_1(a259)))) <=> ((~![U: $i] : (hskp8 | hskp3 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp8 | hskp3 | c3_1(a259) | (~ndr1_0) | (~c0_1(a259)) | (~c1_1(a259)))),
% 0.70/0.92 inference(transitivity,[status(thm)],[375, 373])).
% 0.70/0.92 tff(377,plain,
% 0.70/0.92 ((~![U: $i] : (hskp8 | hskp3 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp8 | hskp3 | (~ndr1_0) | c3_1(a259) | (~c1_1(a259)) | (~c0_1(a259)))),
% 0.70/0.92 inference(quant_inst,[status(thm)],[])).
% 0.70/0.92 tff(378,plain,
% 0.70/0.92 ((~![U: $i] : (hskp8 | hskp3 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp8 | hskp3 | c3_1(a259) | (~ndr1_0) | (~c0_1(a259)) | (~c1_1(a259))),
% 0.70/0.92 inference(modus_ponens,[status(thm)],[377, 376])).
% 0.70/0.92 tff(379,plain,
% 0.70/0.92 ($false),
% 0.70/0.92 inference(unit_resolution,[status(thm)],[378, 122, 43, 372, 371, 363, 355, 348])).
% 0.70/0.92 tff(380,plain,((~hskp20) | hskp8 | hskp3), inference(lemma,lemma(discharge,[]))).
% 0.70/0.92 tff(381,plain,
% 0.70/0.92 (~hskp20),
% 0.70/0.92 inference(unit_resolution,[status(thm)],[380, 338, 43])).
% 0.70/0.92 tff(382,assumption,(~hskp11), introduced(assumption)).
% 0.70/0.92 tff(383,plain,
% 0.70/0.92 (((~![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp11 | hskp10 | c2_1(a213) | (~ndr1_0) | (~c1_1(a213)) | c0_1(a213))) <=> ((~![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | hskp11 | hskp10 | c2_1(a213) | (~ndr1_0) | (~c1_1(a213)) | c0_1(a213))),
% 0.70/0.92 inference(rewrite,[status(thm)],[])).
% 0.70/0.92 tff(384,plain,
% 0.70/0.92 ((hskp11 | hskp10 | (~ndr1_0) | c0_1(a213) | c2_1(a213) | (~c1_1(a213))) <=> (hskp11 | hskp10 | c2_1(a213) | (~ndr1_0) | (~c1_1(a213)) | c0_1(a213))),
% 0.70/0.92 inference(rewrite,[status(thm)],[])).
% 0.70/0.92 tff(385,plain,
% 0.70/0.92 (((~![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp11 | hskp10 | (~ndr1_0) | c0_1(a213) | c2_1(a213) | (~c1_1(a213)))) <=> ((~![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp11 | hskp10 | c2_1(a213) | (~ndr1_0) | (~c1_1(a213)) | c0_1(a213)))),
% 0.70/0.92 inference(monotonicity,[status(thm)],[384])).
% 0.70/0.92 tff(386,plain,
% 0.70/0.92 (((~![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp11 | hskp10 | (~ndr1_0) | c0_1(a213) | c2_1(a213) | (~c1_1(a213)))) <=> ((~![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | hskp11 | hskp10 | c2_1(a213) | (~ndr1_0) | (~c1_1(a213)) | c0_1(a213))),
% 0.70/0.92 inference(transitivity,[status(thm)],[385, 383])).
% 0.70/0.92 tff(387,plain,
% 0.70/0.92 ((~![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp11 | hskp10 | (~ndr1_0) | c0_1(a213) | c2_1(a213) | (~c1_1(a213)))),
% 0.70/0.92 inference(quant_inst,[status(thm)],[])).
% 0.70/0.92 tff(388,plain,
% 0.70/0.92 ((~![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | hskp11 | hskp10 | c2_1(a213) | (~ndr1_0) | (~c1_1(a213)) | c0_1(a213)),
% 0.70/0.92 inference(modus_ponens,[status(thm)],[387, 386])).
% 0.70/0.92 tff(389,plain,
% 0.70/0.92 (hskp11 | c0_1(a213)),
% 0.70/0.92 inference(unit_resolution,[status(thm)],[388, 122, 21, 321, 306, 32])).
% 0.70/0.92 tff(390,plain,
% 0.70/0.92 (c0_1(a213)),
% 0.70/0.92 inference(unit_resolution,[status(thm)],[389, 382])).
% 0.70/0.92 tff(391,plain,
% 0.70/0.92 (^[U: $i] : refl((hskp21 | hskp20 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) <=> (hskp21 | hskp20 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))))),
% 0.70/0.92 inference(bind,[status(th)],[])).
% 0.70/0.92 tff(392,plain,
% 0.70/0.92 (![U: $i] : (hskp21 | hskp20 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp21 | hskp20 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 0.70/0.92 inference(quant_intro,[status(thm)],[391])).
% 0.70/0.92 tff(393,plain,
% 0.70/0.92 (![U: $i] : (hskp21 | hskp20 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp21 | hskp20 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 0.70/0.92 inference(rewrite,[status(thm)],[])).
% 0.70/0.92 tff(394,plain,
% 0.70/0.92 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp20) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) | hskp20))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) | hskp20) <=> (hskp20 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp20) <=> (hskp20 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp20) | hskp21) <=> ((hskp20 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) | hskp21))), rewrite(((hskp20 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) | hskp21) <=> (hskp21 | hskp20 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp20) | hskp21) <=> (hskp21 | hskp20 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))))),
% 0.70/0.92 inference(bind,[status(th)],[])).
% 0.70/0.92 tff(395,plain,
% 0.70/0.92 (![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp20) | hskp21) <=> ![U: $i] : (hskp21 | hskp20 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 0.70/0.92 inference(quant_intro,[status(thm)],[394])).
% 0.70/0.92 tff(396,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp20) | hskp21)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause136')).
% 0.70/0.92 tff(397,plain,
% 0.70/0.92 (![U: $i] : (hskp21 | hskp20 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 0.70/0.92 inference(modus_ponens,[status(thm)],[396, 395])).
% 0.70/0.92 tff(398,plain,
% 0.70/0.92 (![U: $i] : (hskp21 | hskp20 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 0.70/0.92 inference(modus_ponens,[status(thm)],[397, 393])).
% 0.70/0.92 tff(399,plain,(
% 0.70/0.92 ![U: $i] : (hskp21 | hskp20 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 0.70/0.92 inference(skolemize,[status(sab)],[398])).
% 0.70/0.92 tff(400,plain,
% 0.70/0.92 (![U: $i] : (hskp21 | hskp20 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 0.70/0.92 inference(modus_ponens,[status(thm)],[399, 392])).
% 0.70/0.92 tff(401,plain,
% 0.70/0.92 (((~![U: $i] : (hskp21 | hskp20 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp21 | hskp20 | c2_1(a213) | (~ndr1_0) | (~c1_1(a213)) | (~c0_1(a213)))) <=> ((~![U: $i] : (hskp21 | hskp20 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp21 | hskp20 | c2_1(a213) | (~ndr1_0) | (~c1_1(a213)) | (~c0_1(a213)))),
% 0.70/0.92 inference(rewrite,[status(thm)],[])).
% 0.70/0.92 tff(402,plain,
% 0.70/0.92 ((hskp21 | hskp20 | (~ndr1_0) | c2_1(a213) | (~c1_1(a213)) | (~c0_1(a213))) <=> (hskp21 | hskp20 | c2_1(a213) | (~ndr1_0) | (~c1_1(a213)) | (~c0_1(a213)))),
% 0.70/0.92 inference(rewrite,[status(thm)],[])).
% 0.70/0.92 tff(403,plain,
% 0.70/0.92 (((~![U: $i] : (hskp21 | hskp20 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp21 | hskp20 | (~ndr1_0) | c2_1(a213) | (~c1_1(a213)) | (~c0_1(a213)))) <=> ((~![U: $i] : (hskp21 | hskp20 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp21 | hskp20 | c2_1(a213) | (~ndr1_0) | (~c1_1(a213)) | (~c0_1(a213))))),
% 0.70/0.92 inference(monotonicity,[status(thm)],[402])).
% 0.70/0.92 tff(404,plain,
% 0.70/0.92 (((~![U: $i] : (hskp21 | hskp20 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp21 | hskp20 | (~ndr1_0) | c2_1(a213) | (~c1_1(a213)) | (~c0_1(a213)))) <=> ((~![U: $i] : (hskp21 | hskp20 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp21 | hskp20 | c2_1(a213) | (~ndr1_0) | (~c1_1(a213)) | (~c0_1(a213)))),
% 0.70/0.92 inference(transitivity,[status(thm)],[403, 401])).
% 0.70/0.92 tff(405,plain,
% 0.70/0.92 ((~![U: $i] : (hskp21 | hskp20 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp21 | hskp20 | (~ndr1_0) | c2_1(a213) | (~c1_1(a213)) | (~c0_1(a213)))),
% 0.70/0.92 inference(quant_inst,[status(thm)],[])).
% 0.70/0.92 tff(406,plain,
% 0.70/0.92 ((~![U: $i] : (hskp21 | hskp20 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp21 | hskp20 | c2_1(a213) | (~ndr1_0) | (~c1_1(a213)) | (~c0_1(a213))),
% 0.70/0.92 inference(modus_ponens,[status(thm)],[405, 404])).
% 0.70/0.92 tff(407,plain,
% 0.70/0.92 (hskp21 | hskp20 | (~c0_1(a213))),
% 0.70/0.92 inference(unit_resolution,[status(thm)],[406, 122, 321, 306, 400])).
% 0.70/0.92 tff(408,plain,
% 0.70/0.92 (hskp21),
% 0.70/0.92 inference(unit_resolution,[status(thm)],[407, 390, 132])).
% 0.70/0.92 tff(409,plain,
% 0.70/0.92 (((~hskp21) | (~c2_1(a260))) <=> ((~hskp21) | (~c2_1(a260)))),
% 0.70/0.92 inference(rewrite,[status(thm)],[])).
% 0.70/0.92 tff(410,plain,
% 0.70/0.92 (((~c2_1(a260)) | (~hskp21)) <=> ((~hskp21) | (~c2_1(a260)))),
% 0.70/0.92 inference(rewrite,[status(thm)],[])).
% 0.70/0.92 tff(411,axiom,((~c2_1(a260)) | (~hskp21)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause88')).
% 0.70/0.92 tff(412,plain,
% 0.70/0.92 ((~hskp21) | (~c2_1(a260))),
% 0.70/0.92 inference(modus_ponens,[status(thm)],[411, 410])).
% 0.70/0.92 tff(413,plain,
% 0.70/0.92 ((~hskp21) | (~c2_1(a260))),
% 0.70/0.92 inference(modus_ponens,[status(thm)],[412, 409])).
% 0.70/0.92 tff(414,plain,
% 0.70/0.92 (~c2_1(a260)),
% 0.70/0.92 inference(unit_resolution,[status(thm)],[413, 408])).
% 0.70/0.92 tff(415,plain,
% 0.70/0.92 (((~hskp21) | (~c0_1(a260))) <=> ((~hskp21) | (~c0_1(a260)))),
% 0.70/0.92 inference(rewrite,[status(thm)],[])).
% 0.70/0.92 tff(416,plain,
% 0.70/0.92 (((~c0_1(a260)) | (~hskp21)) <=> ((~hskp21) | (~c0_1(a260)))),
% 0.70/0.92 inference(rewrite,[status(thm)],[])).
% 0.70/0.92 tff(417,axiom,((~c0_1(a260)) | (~hskp21)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause87')).
% 0.70/0.92 tff(418,plain,
% 0.70/0.92 ((~hskp21) | (~c0_1(a260))),
% 0.70/0.92 inference(modus_ponens,[status(thm)],[417, 416])).
% 0.70/0.92 tff(419,plain,
% 0.70/0.92 ((~hskp21) | (~c0_1(a260))),
% 0.70/0.92 inference(modus_ponens,[status(thm)],[418, 415])).
% 0.70/0.92 tff(420,plain,
% 0.70/0.92 (~c0_1(a260)),
% 0.70/0.92 inference(unit_resolution,[status(thm)],[419, 408])).
% 0.70/0.92 tff(421,plain,
% 0.70/0.92 (((~hskp21) | c1_1(a260)) <=> ((~hskp21) | c1_1(a260))),
% 0.70/0.92 inference(rewrite,[status(thm)],[])).
% 0.70/0.92 tff(422,axiom,((~hskp21) | c1_1(a260)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause49')).
% 0.70/0.92 tff(423,plain,
% 0.70/0.92 ((~hskp21) | c1_1(a260)),
% 0.70/0.92 inference(modus_ponens,[status(thm)],[422, 421])).
% 0.70/0.92 tff(424,plain,
% 0.70/0.92 ((~hskp21) | c1_1(a260)),
% 0.70/0.92 inference(modus_ponens,[status(thm)],[423, 421])).
% 0.70/0.92 tff(425,plain,
% 0.70/0.92 ((~hskp21) | c1_1(a260)),
% 0.70/0.92 inference(modus_ponens,[status(thm)],[424, 421])).
% 0.70/0.92 tff(426,plain,
% 0.70/0.92 ((~hskp21) | c1_1(a260)),
% 0.70/0.92 inference(modus_ponens,[status(thm)],[425, 421])).
% 0.70/0.92 tff(427,plain,
% 0.70/0.92 ((~hskp21) | c1_1(a260)),
% 0.70/0.92 inference(modus_ponens,[status(thm)],[426, 421])).
% 0.70/0.92 tff(428,plain,
% 0.70/0.92 (c1_1(a260)),
% 0.70/0.92 inference(unit_resolution,[status(thm)],[427, 408])).
% 0.70/0.92 tff(429,plain,
% 0.70/0.92 (((~![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp11 | hskp10 | c0_1(a260) | c2_1(a260) | (~ndr1_0) | (~c1_1(a260)))) <=> ((~![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | hskp11 | hskp10 | c0_1(a260) | c2_1(a260) | (~ndr1_0) | (~c1_1(a260)))),
% 0.70/0.92 inference(rewrite,[status(thm)],[])).
% 0.70/0.92 tff(430,plain,
% 0.70/0.92 ((hskp11 | hskp10 | (~ndr1_0) | c0_1(a260) | c2_1(a260) | (~c1_1(a260))) <=> (hskp11 | hskp10 | c0_1(a260) | c2_1(a260) | (~ndr1_0) | (~c1_1(a260)))),
% 0.70/0.92 inference(rewrite,[status(thm)],[])).
% 0.70/0.92 tff(431,plain,
% 0.70/0.92 (((~![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp11 | hskp10 | (~ndr1_0) | c0_1(a260) | c2_1(a260) | (~c1_1(a260)))) <=> ((~![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp11 | hskp10 | c0_1(a260) | c2_1(a260) | (~ndr1_0) | (~c1_1(a260))))),
% 0.70/0.92 inference(monotonicity,[status(thm)],[430])).
% 0.70/0.92 tff(432,plain,
% 0.70/0.92 (((~![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp11 | hskp10 | (~ndr1_0) | c0_1(a260) | c2_1(a260) | (~c1_1(a260)))) <=> ((~![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | hskp11 | hskp10 | c0_1(a260) | c2_1(a260) | (~ndr1_0) | (~c1_1(a260)))),
% 0.70/0.92 inference(transitivity,[status(thm)],[431, 429])).
% 0.70/0.92 tff(433,plain,
% 0.70/0.92 ((~![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp11 | hskp10 | (~ndr1_0) | c0_1(a260) | c2_1(a260) | (~c1_1(a260)))),
% 0.70/0.92 inference(quant_inst,[status(thm)],[])).
% 0.70/0.92 tff(434,plain,
% 0.70/0.92 ((~![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | hskp11 | hskp10 | c0_1(a260) | c2_1(a260) | (~ndr1_0) | (~c1_1(a260))),
% 0.70/0.92 inference(modus_ponens,[status(thm)],[433, 432])).
% 0.70/0.92 tff(435,plain,
% 0.70/0.92 ($false),
% 0.70/0.92 inference(unit_resolution,[status(thm)],[434, 122, 382, 21, 428, 420, 414, 32])).
% 0.70/0.92 tff(436,plain,(hskp11 | hskp10 | hskp20 | (~c1_1(a213)) | c2_1(a213)), inference(lemma,lemma(discharge,[]))).
% 0.70/0.92 tff(437,plain,
% 0.70/0.92 (hskp11),
% 0.70/0.92 inference(unit_resolution,[status(thm)],[436, 381, 21, 295, 279])).
% 0.70/0.92 tff(438,plain,
% 0.70/0.92 (((~hskp11) | (~c1_1(a230))) <=> ((~hskp11) | (~c1_1(a230)))),
% 0.70/0.92 inference(rewrite,[status(thm)],[])).
% 0.70/0.92 tff(439,plain,
% 0.70/0.92 (((~c1_1(a230)) | (~hskp11)) <=> ((~hskp11) | (~c1_1(a230)))),
% 0.70/0.92 inference(rewrite,[status(thm)],[])).
% 0.70/0.92 tff(440,axiom,((~c1_1(a230)) | (~hskp11)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause105')).
% 0.70/0.92 tff(441,plain,
% 0.70/0.92 ((~hskp11) | (~c1_1(a230))),
% 0.70/0.92 inference(modus_ponens,[status(thm)],[440, 439])).
% 0.70/0.92 tff(442,plain,
% 0.70/0.92 ((~hskp11) | (~c1_1(a230))),
% 0.70/0.92 inference(modus_ponens,[status(thm)],[441, 438])).
% 0.70/0.92 tff(443,plain,
% 0.70/0.92 (~c1_1(a230)),
% 0.70/0.92 inference(unit_resolution,[status(thm)],[442, 437])).
% 0.70/0.92 tff(444,plain,
% 0.70/0.92 (^[V: $i, U: $i] : refl((hskp17 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V)) <=> (hskp17 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V)))),
% 0.70/0.92 inference(bind,[status(th)],[])).
% 0.70/0.92 tff(445,plain,
% 0.70/0.92 (![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V)) <=> ![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))),
% 0.70/0.92 inference(quant_intro,[status(thm)],[444])).
% 0.70/0.92 tff(446,plain,
% 0.70/0.92 (![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V)) <=> ![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))),
% 0.70/0.92 inference(rewrite,[status(thm)],[])).
% 0.70/0.92 tff(447,plain,
% 0.70/0.92 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c1_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U))) | c1_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U))) | c1_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c1_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c1_1(V)) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c1_1(V)) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | hskp17) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V)) | hskp17))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V)) | hskp17) <=> (hskp17 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | hskp17) <=> (hskp17 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))))),
% 0.70/0.92 inference(bind,[status(th)],[])).
% 0.70/0.92 tff(448,plain,
% 0.70/0.92 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | hskp17) <=> ![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))),
% 0.70/0.92 inference(quant_intro,[status(thm)],[447])).
% 0.70/0.92 tff(449,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | hskp17)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause156')).
% 0.70/0.92 tff(450,plain,
% 0.70/0.92 (![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))),
% 0.70/0.92 inference(modus_ponens,[status(thm)],[449, 448])).
% 0.70/0.92 tff(451,plain,
% 0.70/0.92 (![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))),
% 0.70/0.92 inference(modus_ponens,[status(thm)],[450, 446])).
% 0.70/0.92 tff(452,plain,(
% 0.70/0.92 ![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))),
% 0.70/0.92 inference(skolemize,[status(sab)],[451])).
% 0.70/0.92 tff(453,plain,
% 0.70/0.92 (![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))),
% 0.70/0.92 inference(modus_ponens,[status(thm)],[452, 445])).
% 0.70/0.92 tff(454,plain,
% 0.70/0.92 (^[V: $i, U: $i] : refl((hskp27 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V))) <=> (hskp27 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V))))),
% 0.70/0.92 inference(bind,[status(th)],[])).
% 0.70/0.92 tff(455,plain,
% 0.70/0.92 (![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 0.70/0.92 inference(quant_intro,[status(thm)],[454])).
% 0.70/0.92 tff(456,plain,
% 0.70/0.92 (![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 0.70/0.92 inference(rewrite,[status(thm)],[])).
% 0.70/0.92 tff(457,plain,
% 0.70/0.92 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c0_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c0_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(V)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(V))))), (((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c2_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)))), (((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V))))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | hskp27) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V))) | hskp27))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V))) | hskp27) <=> (hskp27 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | hskp27) <=> (hskp27 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))))),
% 0.70/0.93 inference(bind,[status(th)],[])).
% 0.70/0.93 tff(458,plain,
% 0.70/0.93 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | hskp27) <=> ![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 0.70/0.93 inference(quant_intro,[status(thm)],[457])).
% 0.70/0.93 tff(459,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | hskp27)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause160')).
% 0.70/0.93 tff(460,plain,
% 0.70/0.93 (![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 0.70/0.93 inference(modus_ponens,[status(thm)],[459, 458])).
% 0.70/0.93 tff(461,plain,
% 0.70/0.93 (![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 0.70/0.93 inference(modus_ponens,[status(thm)],[460, 456])).
% 0.70/0.93 tff(462,plain,(
% 0.70/0.93 ![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 0.70/0.93 inference(skolemize,[status(sab)],[461])).
% 0.70/0.93 tff(463,plain,
% 0.70/0.93 (![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 0.70/0.93 inference(modus_ponens,[status(thm)],[462, 455])).
% 0.70/0.93 tff(464,plain,
% 0.70/0.93 (((~hskp11) | c3_1(a230)) <=> ((~hskp11) | c3_1(a230))),
% 0.70/0.93 inference(rewrite,[status(thm)],[])).
% 0.70/0.93 tff(465,axiom,((~hskp11) | c3_1(a230)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause62')).
% 0.70/0.93 tff(466,plain,
% 0.70/0.93 ((~hskp11) | c3_1(a230)),
% 0.70/0.93 inference(modus_ponens,[status(thm)],[465, 464])).
% 0.70/0.93 tff(467,plain,
% 0.70/0.93 ((~hskp11) | c3_1(a230)),
% 0.70/0.93 inference(modus_ponens,[status(thm)],[466, 464])).
% 0.70/0.93 tff(468,plain,
% 0.70/0.93 ((~hskp11) | c3_1(a230)),
% 0.70/0.93 inference(modus_ponens,[status(thm)],[467, 464])).
% 0.70/0.93 tff(469,plain,
% 0.70/0.93 ((~hskp11) | c3_1(a230)),
% 0.70/0.93 inference(modus_ponens,[status(thm)],[468, 464])).
% 0.70/0.93 tff(470,plain,
% 0.70/0.93 ((~hskp11) | c3_1(a230)),
% 0.70/0.93 inference(modus_ponens,[status(thm)],[469, 464])).
% 0.70/0.93 tff(471,plain,
% 0.70/0.93 (c3_1(a230)),
% 0.70/0.93 inference(unit_resolution,[status(thm)],[470, 437])).
% 0.70/0.93 tff(472,plain,
% 0.70/0.93 (((~hskp11) | c2_1(a230)) <=> ((~hskp11) | c2_1(a230))),
% 0.70/0.93 inference(rewrite,[status(thm)],[])).
% 0.70/0.93 tff(473,axiom,((~hskp11) | c2_1(a230)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause61')).
% 0.70/0.93 tff(474,plain,
% 0.70/0.93 ((~hskp11) | c2_1(a230)),
% 0.70/0.93 inference(modus_ponens,[status(thm)],[473, 472])).
% 0.70/0.93 tff(475,plain,
% 0.70/0.93 ((~hskp11) | c2_1(a230)),
% 0.70/0.93 inference(modus_ponens,[status(thm)],[474, 472])).
% 0.70/0.93 tff(476,plain,
% 0.70/0.93 ((~hskp11) | c2_1(a230)),
% 0.70/0.93 inference(modus_ponens,[status(thm)],[475, 472])).
% 0.70/0.93 tff(477,plain,
% 0.70/0.93 ((~hskp11) | c2_1(a230)),
% 0.70/0.93 inference(modus_ponens,[status(thm)],[476, 472])).
% 0.70/0.93 tff(478,plain,
% 0.70/0.93 ((~hskp11) | c2_1(a230)),
% 0.70/0.93 inference(modus_ponens,[status(thm)],[477, 472])).
% 0.70/0.93 tff(479,plain,
% 0.70/0.93 (c2_1(a230)),
% 0.70/0.93 inference(unit_resolution,[status(thm)],[478, 437])).
% 0.70/0.93 tff(480,plain,
% 0.70/0.93 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp27 | c3_1(a282) | c1_1(a230) | (~ndr1_0) | (~c3_1(a230)) | (~c2_1(a230)) | c2_1(a282) | (~c0_1(a282)))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp27 | c3_1(a282) | c1_1(a230) | (~ndr1_0) | (~c3_1(a230)) | (~c2_1(a230)) | c2_1(a282) | (~c0_1(a282)))),
% 0.70/0.93 inference(rewrite,[status(thm)],[])).
% 0.70/0.93 tff(481,plain,
% 0.70/0.93 ((hskp27 | (~ndr1_0) | c3_1(a282) | c2_1(a282) | (~c0_1(a282)) | c1_1(a230) | (~c3_1(a230)) | (~c2_1(a230))) <=> (hskp27 | c3_1(a282) | c1_1(a230) | (~ndr1_0) | (~c3_1(a230)) | (~c2_1(a230)) | c2_1(a282) | (~c0_1(a282)))),
% 0.70/0.93 inference(rewrite,[status(thm)],[])).
% 0.70/0.93 tff(482,plain,
% 0.70/0.93 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp27 | (~ndr1_0) | c3_1(a282) | c2_1(a282) | (~c0_1(a282)) | c1_1(a230) | (~c3_1(a230)) | (~c2_1(a230)))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp27 | c3_1(a282) | c1_1(a230) | (~ndr1_0) | (~c3_1(a230)) | (~c2_1(a230)) | c2_1(a282) | (~c0_1(a282))))),
% 0.70/0.93 inference(monotonicity,[status(thm)],[481])).
% 0.70/0.93 tff(483,plain,
% 0.70/0.93 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp27 | (~ndr1_0) | c3_1(a282) | c2_1(a282) | (~c0_1(a282)) | c1_1(a230) | (~c3_1(a230)) | (~c2_1(a230)))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp27 | c3_1(a282) | c1_1(a230) | (~ndr1_0) | (~c3_1(a230)) | (~c2_1(a230)) | c2_1(a282) | (~c0_1(a282)))),
% 0.70/0.93 inference(transitivity,[status(thm)],[482, 480])).
% 0.70/0.93 tff(484,plain,
% 0.70/0.93 ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp27 | (~ndr1_0) | c3_1(a282) | c2_1(a282) | (~c0_1(a282)) | c1_1(a230) | (~c3_1(a230)) | (~c2_1(a230)))),
% 0.70/0.93 inference(quant_inst,[status(thm)],[])).
% 0.70/0.93 tff(485,plain,
% 0.70/0.93 ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp27 | c3_1(a282) | c1_1(a230) | (~ndr1_0) | (~c3_1(a230)) | (~c2_1(a230)) | c2_1(a282) | (~c0_1(a282))),
% 0.70/0.93 inference(modus_ponens,[status(thm)],[484, 483])).
% 0.70/0.93 tff(486,plain,
% 0.70/0.93 (hskp27),
% 0.70/0.93 inference(unit_resolution,[status(thm)],[485, 122, 167, 479, 471, 173, 443, 463, 180])).
% 0.70/0.93 tff(487,plain,
% 0.70/0.93 (c3_1(a232)),
% 0.70/0.93 inference(unit_resolution,[status(thm)],[247, 486])).
% 0.70/0.93 tff(488,plain,
% 0.70/0.93 (c2_1(a232)),
% 0.70/0.93 inference(unit_resolution,[status(thm)],[255, 486])).
% 0.70/0.93 tff(489,plain,
% 0.70/0.93 (c0_1(a232)),
% 0.70/0.93 inference(unit_resolution,[status(thm)],[263, 486])).
% 0.70/0.93 tff(490,plain,
% 0.70/0.93 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp17 | c1_1(a282) | c3_1(a282) | (~ndr1_0) | (~c2_1(a232)) | (~c3_1(a232)) | (~c0_1(a232)) | c2_1(a282))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp17 | c1_1(a282) | c3_1(a282) | (~ndr1_0) | (~c2_1(a232)) | (~c3_1(a232)) | (~c0_1(a232)) | c2_1(a282))),
% 0.70/0.93 inference(rewrite,[status(thm)],[])).
% 0.70/0.93 tff(491,plain,
% 0.70/0.93 ((hskp17 | (~ndr1_0) | (~c2_1(a232)) | (~c0_1(a232)) | (~c3_1(a232)) | c3_1(a282) | c2_1(a282) | c1_1(a282)) <=> (hskp17 | c1_1(a282) | c3_1(a282) | (~ndr1_0) | (~c2_1(a232)) | (~c3_1(a232)) | (~c0_1(a232)) | c2_1(a282))),
% 0.70/0.93 inference(rewrite,[status(thm)],[])).
% 0.70/0.93 tff(492,plain,
% 0.70/0.93 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp17 | (~ndr1_0) | (~c2_1(a232)) | (~c0_1(a232)) | (~c3_1(a232)) | c3_1(a282) | c2_1(a282) | c1_1(a282))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp17 | c1_1(a282) | c3_1(a282) | (~ndr1_0) | (~c2_1(a232)) | (~c3_1(a232)) | (~c0_1(a232)) | c2_1(a282)))),
% 0.70/0.93 inference(monotonicity,[status(thm)],[491])).
% 0.70/0.93 tff(493,plain,
% 0.70/0.93 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp17 | (~ndr1_0) | (~c2_1(a232)) | (~c0_1(a232)) | (~c3_1(a232)) | c3_1(a282) | c2_1(a282) | c1_1(a282))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp17 | c1_1(a282) | c3_1(a282) | (~ndr1_0) | (~c2_1(a232)) | (~c3_1(a232)) | (~c0_1(a232)) | c2_1(a282))),
% 0.70/0.93 inference(transitivity,[status(thm)],[492, 490])).
% 0.70/0.93 tff(494,plain,
% 0.70/0.93 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp17 | (~ndr1_0) | (~c2_1(a232)) | (~c0_1(a232)) | (~c3_1(a232)) | c3_1(a282) | c2_1(a282) | c1_1(a282))),
% 0.70/0.93 inference(quant_inst,[status(thm)],[])).
% 0.70/0.93 tff(495,plain,
% 0.70/0.93 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp17 | c1_1(a282) | c3_1(a282) | (~ndr1_0) | (~c2_1(a232)) | (~c3_1(a232)) | (~c0_1(a232)) | c2_1(a282)),
% 0.70/0.93 inference(modus_ponens,[status(thm)],[494, 493])).
% 0.70/0.93 tff(496,plain,
% 0.70/0.93 (hskp17),
% 0.70/0.93 inference(unit_resolution,[status(thm)],[495, 122, 489, 488, 487, 179, 173, 453, 180])).
% 0.70/0.93 tff(497,plain,
% 0.70/0.93 (((~hskp17) | (~c2_1(a243))) <=> ((~hskp17) | (~c2_1(a243)))),
% 0.70/0.93 inference(rewrite,[status(thm)],[])).
% 0.70/0.93 tff(498,plain,
% 0.70/0.93 (((~c2_1(a243)) | (~hskp17)) <=> ((~hskp17) | (~c2_1(a243)))),
% 0.70/0.93 inference(rewrite,[status(thm)],[])).
% 0.70/0.93 tff(499,axiom,((~c2_1(a243)) | (~hskp17)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause95')).
% 0.70/0.93 tff(500,plain,
% 0.70/0.93 ((~hskp17) | (~c2_1(a243))),
% 0.70/0.93 inference(modus_ponens,[status(thm)],[499, 498])).
% 0.70/0.93 tff(501,plain,
% 0.70/0.93 ((~hskp17) | (~c2_1(a243))),
% 0.70/0.93 inference(modus_ponens,[status(thm)],[500, 497])).
% 0.70/0.93 tff(502,plain,
% 0.70/0.93 (~c2_1(a243)),
% 0.70/0.93 inference(unit_resolution,[status(thm)],[501, 496])).
% 0.70/0.93 tff(503,plain,
% 0.70/0.93 (((~hskp17) | (~c0_1(a243))) <=> ((~hskp17) | (~c0_1(a243)))),
% 0.70/0.93 inference(rewrite,[status(thm)],[])).
% 0.70/0.93 tff(504,plain,
% 0.70/0.93 (((~c0_1(a243)) | (~hskp17)) <=> ((~hskp17) | (~c0_1(a243)))),
% 0.70/0.93 inference(rewrite,[status(thm)],[])).
% 0.70/0.93 tff(505,axiom,((~c0_1(a243)) | (~hskp17)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause93')).
% 0.70/0.93 tff(506,plain,
% 0.70/0.93 ((~hskp17) | (~c0_1(a243))),
% 0.70/0.93 inference(modus_ponens,[status(thm)],[505, 504])).
% 0.70/0.93 tff(507,plain,
% 0.70/0.93 ((~hskp17) | (~c0_1(a243))),
% 0.70/0.93 inference(modus_ponens,[status(thm)],[506, 503])).
% 0.70/0.93 tff(508,plain,
% 0.70/0.93 (~c0_1(a243)),
% 0.70/0.93 inference(unit_resolution,[status(thm)],[507, 496])).
% 0.70/0.93 tff(509,plain,
% 0.70/0.93 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | (c3_1(a282) | c0_1(a243) | c2_1(a243) | c1_1(a230) | (~ndr1_0) | (~c3_1(a230)) | (~c2_1(a230)) | (~c3_1(a243)) | c2_1(a282) | (~c0_1(a282)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c3_1(a282) | c0_1(a243) | c2_1(a243) | c1_1(a230) | (~ndr1_0) | (~c3_1(a230)) | (~c2_1(a230)) | (~c3_1(a243)) | c2_1(a282) | (~c0_1(a282)))),
% 0.70/0.93 inference(rewrite,[status(thm)],[])).
% 0.70/0.93 tff(510,plain,
% 0.70/0.93 (((~ndr1_0) | c3_1(a282) | c2_1(a282) | (~c0_1(a282)) | c1_1(a230) | (~c3_1(a230)) | (~c2_1(a230)) | c0_1(a243) | c2_1(a243) | (~c3_1(a243))) <=> (c3_1(a282) | c0_1(a243) | c2_1(a243) | c1_1(a230) | (~ndr1_0) | (~c3_1(a230)) | (~c2_1(a230)) | (~c3_1(a243)) | c2_1(a282) | (~c0_1(a282)))),
% 0.70/0.93 inference(rewrite,[status(thm)],[])).
% 0.70/0.93 tff(511,plain,
% 0.70/0.93 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a282) | c2_1(a282) | (~c0_1(a282)) | c1_1(a230) | (~c3_1(a230)) | (~c2_1(a230)) | c0_1(a243) | c2_1(a243) | (~c3_1(a243)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | (c3_1(a282) | c0_1(a243) | c2_1(a243) | c1_1(a230) | (~ndr1_0) | (~c3_1(a230)) | (~c2_1(a230)) | (~c3_1(a243)) | c2_1(a282) | (~c0_1(a282))))),
% 0.70/0.93 inference(monotonicity,[status(thm)],[510])).
% 0.70/0.93 tff(512,plain,
% 0.70/0.93 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a282) | c2_1(a282) | (~c0_1(a282)) | c1_1(a230) | (~c3_1(a230)) | (~c2_1(a230)) | c0_1(a243) | c2_1(a243) | (~c3_1(a243)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c3_1(a282) | c0_1(a243) | c2_1(a243) | c1_1(a230) | (~ndr1_0) | (~c3_1(a230)) | (~c2_1(a230)) | (~c3_1(a243)) | c2_1(a282) | (~c0_1(a282)))),
% 0.70/0.93 inference(transitivity,[status(thm)],[511, 509])).
% 0.70/0.93 tff(513,plain,
% 0.70/0.93 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a282) | c2_1(a282) | (~c0_1(a282)) | c1_1(a230) | (~c3_1(a230)) | (~c2_1(a230)) | c0_1(a243) | c2_1(a243) | (~c3_1(a243)))),
% 0.70/0.93 inference(quant_inst,[status(thm)],[])).
% 0.70/0.93 tff(514,plain,
% 0.70/0.93 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c3_1(a282) | c0_1(a243) | c2_1(a243) | c1_1(a230) | (~ndr1_0) | (~c3_1(a230)) | (~c2_1(a230)) | (~c3_1(a243)) | c2_1(a282) | (~c0_1(a282))),
% 0.70/0.93 inference(modus_ponens,[status(thm)],[513, 512])).
% 0.70/0.93 tff(515,plain,
% 0.70/0.93 (~c3_1(a243)),
% 0.70/0.93 inference(unit_resolution,[status(thm)],[514, 122, 167, 479, 471, 173, 508, 502, 443, 10, 180])).
% 0.70/0.93 tff(516,plain,
% 0.70/0.93 (^[U: $i] : refl((hskp3 | hskp2 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)) <=> (hskp3 | hskp2 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)))),
% 0.70/0.93 inference(bind,[status(th)],[])).
% 0.70/0.93 tff(517,plain,
% 0.70/0.93 (![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)) <=> ![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))),
% 0.70/0.93 inference(quant_intro,[status(thm)],[516])).
% 0.70/0.93 tff(518,plain,
% 0.70/0.93 (![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)) <=> ![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))),
% 0.70/0.93 inference(rewrite,[status(thm)],[])).
% 0.70/0.93 tff(519,plain,
% 0.70/0.93 (^[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) | c3_1(U) | c1_1(U) | c0_1(U))), (((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)))), ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) | hskp2) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)) | hskp2))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)) | hskp2) <=> (hskp2 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))), ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) | hskp2) <=> (hskp2 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)))), (((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) | hskp2) | hskp3) <=> ((hskp2 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)) | hskp3))), rewrite(((hskp2 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)) | hskp3) <=> (hskp3 | hskp2 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))), (((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) | hskp2) | hskp3) <=> (hskp3 | hskp2 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))))),
% 0.70/0.93 inference(bind,[status(th)],[])).
% 0.70/0.93 tff(520,plain,
% 0.70/0.93 (![U: $i] : ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) | hskp2) | hskp3) <=> ![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))),
% 0.70/0.93 inference(quant_intro,[status(thm)],[519])).
% 0.70/0.93 tff(521,axiom,(![U: $i] : ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) | hskp2) | hskp3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause123')).
% 0.70/0.93 tff(522,plain,
% 0.70/0.93 (![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))),
% 0.70/0.93 inference(modus_ponens,[status(thm)],[521, 520])).
% 0.70/0.93 tff(523,plain,
% 0.70/0.93 (![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))),
% 0.70/0.93 inference(modus_ponens,[status(thm)],[522, 518])).
% 0.70/0.93 tff(524,plain,(
% 0.70/0.93 ![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))),
% 0.70/0.93 inference(skolemize,[status(sab)],[523])).
% 0.70/0.93 tff(525,plain,
% 0.70/0.93 (![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))),
% 0.70/0.93 inference(modus_ponens,[status(thm)],[524, 517])).
% 0.70/0.93 tff(526,plain,
% 0.70/0.93 (((~hskp17) | (~c1_1(a243))) <=> ((~hskp17) | (~c1_1(a243)))),
% 0.70/0.93 inference(rewrite,[status(thm)],[])).
% 0.70/0.93 tff(527,plain,
% 0.70/0.93 (((~c1_1(a243)) | (~hskp17)) <=> ((~hskp17) | (~c1_1(a243)))),
% 0.70/0.93 inference(rewrite,[status(thm)],[])).
% 0.70/0.93 tff(528,axiom,((~c1_1(a243)) | (~hskp17)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause94')).
% 0.70/0.93 tff(529,plain,
% 0.70/0.93 ((~hskp17) | (~c1_1(a243))),
% 0.70/0.93 inference(modus_ponens,[status(thm)],[528, 527])).
% 0.70/0.93 tff(530,plain,
% 0.70/0.93 ((~hskp17) | (~c1_1(a243))),
% 0.70/0.93 inference(modus_ponens,[status(thm)],[529, 526])).
% 0.70/0.93 tff(531,plain,
% 0.70/0.93 (~c1_1(a243)),
% 0.70/0.93 inference(unit_resolution,[status(thm)],[530, 496])).
% 0.70/0.93 tff(532,plain,
% 0.70/0.93 (((~![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp3 | hskp2 | c0_1(a243) | c1_1(a243) | (~ndr1_0) | c3_1(a243))) <=> ((~![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | hskp3 | hskp2 | c0_1(a243) | c1_1(a243) | (~ndr1_0) | c3_1(a243))),
% 0.70/0.93 inference(rewrite,[status(thm)],[])).
% 0.70/0.93 tff(533,plain,
% 0.70/0.93 ((hskp3 | hskp2 | (~ndr1_0) | c3_1(a243) | c1_1(a243) | c0_1(a243)) <=> (hskp3 | hskp2 | c0_1(a243) | c1_1(a243) | (~ndr1_0) | c3_1(a243))),
% 0.70/0.93 inference(rewrite,[status(thm)],[])).
% 0.70/0.93 tff(534,plain,
% 0.70/0.93 (((~![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp3 | hskp2 | (~ndr1_0) | c3_1(a243) | c1_1(a243) | c0_1(a243))) <=> ((~![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp3 | hskp2 | c0_1(a243) | c1_1(a243) | (~ndr1_0) | c3_1(a243)))),
% 0.70/0.93 inference(monotonicity,[status(thm)],[533])).
% 0.70/0.93 tff(535,plain,
% 0.70/0.93 (((~![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp3 | hskp2 | (~ndr1_0) | c3_1(a243) | c1_1(a243) | c0_1(a243))) <=> ((~![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | hskp3 | hskp2 | c0_1(a243) | c1_1(a243) | (~ndr1_0) | c3_1(a243))),
% 0.70/0.93 inference(transitivity,[status(thm)],[534, 532])).
% 0.70/0.93 tff(536,plain,
% 0.70/0.93 ((~![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp3 | hskp2 | (~ndr1_0) | c3_1(a243) | c1_1(a243) | c0_1(a243))),
% 0.70/0.93 inference(quant_inst,[status(thm)],[])).
% 0.70/0.93 tff(537,plain,
% 0.70/0.93 ((~![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | hskp3 | hskp2 | c0_1(a243) | c1_1(a243) | (~ndr1_0) | c3_1(a243)),
% 0.70/0.93 inference(modus_ponens,[status(thm)],[536, 535])).
% 0.70/0.93 tff(538,plain,
% 0.70/0.93 (hskp2),
% 0.70/0.93 inference(unit_resolution,[status(thm)],[537, 122, 338, 508, 531, 525, 515])).
% 0.70/0.93 tff(539,plain,
% 0.70/0.93 (((~hskp2) | (~c1_1(a215))) <=> ((~hskp2) | (~c1_1(a215)))),
% 0.70/0.93 inference(rewrite,[status(thm)],[])).
% 0.70/0.93 tff(540,plain,
% 0.70/0.93 (((~c1_1(a215)) | (~hskp2)) <=> ((~hskp2) | (~c1_1(a215)))),
% 0.70/0.93 inference(rewrite,[status(thm)],[])).
% 0.70/0.93 tff(541,axiom,((~c1_1(a215)) | (~hskp2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause120')).
% 0.70/0.93 tff(542,plain,
% 0.70/0.93 ((~hskp2) | (~c1_1(a215))),
% 0.70/0.93 inference(modus_ponens,[status(thm)],[541, 540])).
% 0.70/0.93 tff(543,plain,
% 0.70/0.93 ((~hskp2) | (~c1_1(a215))),
% 0.70/0.93 inference(modus_ponens,[status(thm)],[542, 539])).
% 0.70/0.93 tff(544,plain,
% 0.70/0.93 (~c1_1(a215)),
% 0.70/0.93 inference(unit_resolution,[status(thm)],[543, 538])).
% 0.70/0.93 tff(545,plain,
% 0.70/0.93 (((~hskp2) | (~c0_1(a215))) <=> ((~hskp2) | (~c0_1(a215)))),
% 0.70/0.93 inference(rewrite,[status(thm)],[])).
% 0.70/0.93 tff(546,plain,
% 0.70/0.93 (((~c0_1(a215)) | (~hskp2)) <=> ((~hskp2) | (~c0_1(a215)))),
% 0.70/0.93 inference(rewrite,[status(thm)],[])).
% 0.70/0.93 tff(547,axiom,((~c0_1(a215)) | (~hskp2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause119')).
% 0.70/0.93 tff(548,plain,
% 0.70/0.93 ((~hskp2) | (~c0_1(a215))),
% 0.70/0.93 inference(modus_ponens,[status(thm)],[547, 546])).
% 0.70/0.93 tff(549,plain,
% 0.70/0.93 ((~hskp2) | (~c0_1(a215))),
% 0.70/0.93 inference(modus_ponens,[status(thm)],[548, 545])).
% 0.70/0.93 tff(550,plain,
% 0.70/0.93 (~c0_1(a215)),
% 0.70/0.93 inference(unit_resolution,[status(thm)],[549, 538])).
% 0.70/0.93 tff(551,plain,
% 0.70/0.93 (((~hskp2) | c2_1(a215)) <=> ((~hskp2) | c2_1(a215))),
% 0.70/0.93 inference(rewrite,[status(thm)],[])).
% 0.70/0.93 tff(552,axiom,((~hskp2) | c2_1(a215)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause74')).
% 0.70/0.93 tff(553,plain,
% 0.70/0.93 ((~hskp2) | c2_1(a215)),
% 0.70/0.93 inference(modus_ponens,[status(thm)],[552, 551])).
% 0.70/0.93 tff(554,plain,
% 0.70/0.93 ((~hskp2) | c2_1(a215)),
% 0.70/0.93 inference(modus_ponens,[status(thm)],[553, 551])).
% 0.70/0.93 tff(555,plain,
% 0.70/0.93 ((~hskp2) | c2_1(a215)),
% 0.70/0.93 inference(modus_ponens,[status(thm)],[554, 551])).
% 0.70/0.93 tff(556,plain,
% 0.70/0.93 ((~hskp2) | c2_1(a215)),
% 0.70/0.93 inference(modus_ponens,[status(thm)],[555, 551])).
% 0.70/0.93 tff(557,plain,
% 0.70/0.93 ((~hskp2) | c2_1(a215)),
% 0.70/0.93 inference(modus_ponens,[status(thm)],[556, 551])).
% 0.70/0.93 tff(558,plain,
% 0.70/0.93 (c2_1(a215)),
% 0.70/0.93 inference(unit_resolution,[status(thm)],[557, 538])).
% 0.70/0.93 tff(559,assumption,(~c1_1(a230)), introduced(assumption)).
% 0.70/0.93 tff(560,assumption,(c0_1(a213)), introduced(assumption)).
% 0.70/0.93 tff(561,plain,
% 0.70/0.93 (hskp21 | (~c0_1(a213))),
% 0.70/0.93 inference(unit_resolution,[status(thm)],[406, 122, 132, 321, 306, 400])).
% 0.70/0.93 tff(562,plain,
% 0.70/0.93 (hskp21),
% 0.70/0.93 inference(unit_resolution,[status(thm)],[561, 560])).
% 0.70/0.93 tff(563,plain,
% 0.70/0.93 (~c2_1(a260)),
% 0.70/0.93 inference(unit_resolution,[status(thm)],[413, 562])).
% 0.70/0.93 tff(564,plain,
% 0.70/0.93 (~c0_1(a260)),
% 0.70/0.93 inference(unit_resolution,[status(thm)],[419, 562])).
% 0.70/0.93 tff(565,assumption,(c3_1(a230)), introduced(assumption)).
% 0.70/0.93 tff(566,assumption,(c2_1(a230)), introduced(assumption)).
% 0.70/0.93 tff(567,plain,
% 0.70/0.93 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | (c3_1(a282) | c0_1(a260) | c2_1(a260) | c1_1(a230) | (~ndr1_0) | (~c3_1(a230)) | (~c2_1(a230)) | (~c3_1(a260)) | c2_1(a282) | (~c0_1(a282)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c3_1(a282) | c0_1(a260) | c2_1(a260) | c1_1(a230) | (~ndr1_0) | (~c3_1(a230)) | (~c2_1(a230)) | (~c3_1(a260)) | c2_1(a282) | (~c0_1(a282)))),
% 0.70/0.93 inference(rewrite,[status(thm)],[])).
% 0.70/0.93 tff(568,plain,
% 0.70/0.93 (((~ndr1_0) | c3_1(a282) | c2_1(a282) | (~c0_1(a282)) | c1_1(a230) | (~c3_1(a230)) | (~c2_1(a230)) | c0_1(a260) | c2_1(a260) | (~c3_1(a260))) <=> (c3_1(a282) | c0_1(a260) | c2_1(a260) | c1_1(a230) | (~ndr1_0) | (~c3_1(a230)) | (~c2_1(a230)) | (~c3_1(a260)) | c2_1(a282) | (~c0_1(a282)))),
% 0.70/0.93 inference(rewrite,[status(thm)],[])).
% 0.70/0.93 tff(569,plain,
% 0.70/0.93 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a282) | c2_1(a282) | (~c0_1(a282)) | c1_1(a230) | (~c3_1(a230)) | (~c2_1(a230)) | c0_1(a260) | c2_1(a260) | (~c3_1(a260)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | (c3_1(a282) | c0_1(a260) | c2_1(a260) | c1_1(a230) | (~ndr1_0) | (~c3_1(a230)) | (~c2_1(a230)) | (~c3_1(a260)) | c2_1(a282) | (~c0_1(a282))))),
% 0.70/0.93 inference(monotonicity,[status(thm)],[568])).
% 0.70/0.93 tff(570,plain,
% 0.70/0.93 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a282) | c2_1(a282) | (~c0_1(a282)) | c1_1(a230) | (~c3_1(a230)) | (~c2_1(a230)) | c0_1(a260) | c2_1(a260) | (~c3_1(a260)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c3_1(a282) | c0_1(a260) | c2_1(a260) | c1_1(a230) | (~ndr1_0) | (~c3_1(a230)) | (~c2_1(a230)) | (~c3_1(a260)) | c2_1(a282) | (~c0_1(a282)))),
% 0.70/0.93 inference(transitivity,[status(thm)],[569, 567])).
% 0.70/0.93 tff(571,plain,
% 0.70/0.93 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a282) | c2_1(a282) | (~c0_1(a282)) | c1_1(a230) | (~c3_1(a230)) | (~c2_1(a230)) | c0_1(a260) | c2_1(a260) | (~c3_1(a260)))),
% 0.70/0.93 inference(quant_inst,[status(thm)],[])).
% 0.70/0.93 tff(572,plain,
% 0.70/0.93 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c3_1(a282) | c0_1(a260) | c2_1(a260) | c1_1(a230) | (~ndr1_0) | (~c3_1(a230)) | (~c2_1(a230)) | (~c3_1(a260)) | c2_1(a282) | (~c0_1(a282))),
% 0.70/0.93 inference(modus_ponens,[status(thm)],[571, 570])).
% 0.70/0.93 tff(573,plain,
% 0.70/0.93 (~c3_1(a260)),
% 0.70/0.93 inference(unit_resolution,[status(thm)],[572, 122, 203, 566, 565, 181, 564, 563, 559, 10, 180])).
% 0.70/0.93 tff(574,plain,
% 0.70/0.93 (^[V: $i, U: $i] : refl(((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V))))),
% 0.70/0.93 inference(bind,[status(th)],[])).
% 0.70/0.93 tff(575,plain,
% 0.70/0.93 (![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))),
% 0.70/0.93 inference(quant_intro,[status(thm)],[574])).
% 0.70/0.93 tff(576,plain,
% 0.70/0.93 (![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))),
% 0.70/0.93 inference(rewrite,[status(thm)],[])).
% 0.70/0.93 tff(577,plain,
% 0.70/0.93 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) <=> ((~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c1_1(U)) | (~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)))), rewrite((((~c1_1(U)) | (~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | (~c3_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | (~c3_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | (~c3_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V))) | c1_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))))),
% 0.70/0.93 inference(bind,[status(th)],[])).
% 0.70/0.93 tff(578,plain,
% 0.70/0.93 (![V: $i, U: $i] : (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) | c1_1(V)) <=> ![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))),
% 0.70/0.93 inference(quant_intro,[status(thm)],[577])).
% 0.70/0.93 tff(579,axiom,(![V: $i, U: $i] : (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) | c1_1(V))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause150')).
% 0.70/0.93 tff(580,plain,
% 0.70/0.93 (![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))),
% 0.70/0.93 inference(modus_ponens,[status(thm)],[579, 578])).
% 0.70/0.93 tff(581,plain,
% 0.70/0.93 (![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))),
% 0.77/0.93 inference(modus_ponens,[status(thm)],[580, 576])).
% 0.77/0.93 tff(582,plain,(
% 0.77/0.93 ![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))),
% 0.77/0.93 inference(skolemize,[status(sab)],[581])).
% 0.77/0.93 tff(583,plain,
% 0.77/0.93 (![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))),
% 0.77/0.93 inference(modus_ponens,[status(thm)],[582, 575])).
% 0.77/0.93 tff(584,assumption,(~c1_1(a215)), introduced(assumption)).
% 0.77/0.93 tff(585,assumption,(~c0_1(a215)), introduced(assumption)).
% 0.77/0.93 tff(586,plain,
% 0.77/0.93 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (c0_1(a215) | c1_1(a215) | (~ndr1_0) | (~c1_1(a213)) | (~c3_1(a213)) | (~c0_1(a213)) | (~c3_1(a215)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | c0_1(a215) | c1_1(a215) | (~ndr1_0) | (~c1_1(a213)) | (~c3_1(a213)) | (~c0_1(a213)) | (~c3_1(a215)))),
% 0.77/0.93 inference(rewrite,[status(thm)],[])).
% 0.77/0.93 tff(587,plain,
% 0.77/0.93 (((~ndr1_0) | (~c1_1(a213)) | (~c0_1(a213)) | (~c3_1(a213)) | c0_1(a215) | c1_1(a215) | (~c3_1(a215))) <=> (c0_1(a215) | c1_1(a215) | (~ndr1_0) | (~c1_1(a213)) | (~c3_1(a213)) | (~c0_1(a213)) | (~c3_1(a215)))),
% 0.77/0.93 inference(rewrite,[status(thm)],[])).
% 0.77/0.93 tff(588,plain,
% 0.77/0.93 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | ((~ndr1_0) | (~c1_1(a213)) | (~c0_1(a213)) | (~c3_1(a213)) | c0_1(a215) | c1_1(a215) | (~c3_1(a215)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (c0_1(a215) | c1_1(a215) | (~ndr1_0) | (~c1_1(a213)) | (~c3_1(a213)) | (~c0_1(a213)) | (~c3_1(a215))))),
% 0.77/0.93 inference(monotonicity,[status(thm)],[587])).
% 0.77/0.93 tff(589,plain,
% 0.77/0.93 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | ((~ndr1_0) | (~c1_1(a213)) | (~c0_1(a213)) | (~c3_1(a213)) | c0_1(a215) | c1_1(a215) | (~c3_1(a215)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | c0_1(a215) | c1_1(a215) | (~ndr1_0) | (~c1_1(a213)) | (~c3_1(a213)) | (~c0_1(a213)) | (~c3_1(a215)))),
% 0.77/0.93 inference(transitivity,[status(thm)],[588, 586])).
% 0.77/0.93 tff(590,plain,
% 0.77/0.93 ((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | ((~ndr1_0) | (~c1_1(a213)) | (~c0_1(a213)) | (~c3_1(a213)) | c0_1(a215) | c1_1(a215) | (~c3_1(a215)))),
% 0.77/0.93 inference(quant_inst,[status(thm)],[])).
% 0.77/0.93 tff(591,plain,
% 0.77/0.93 ((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | c0_1(a215) | c1_1(a215) | (~ndr1_0) | (~c1_1(a213)) | (~c3_1(a213)) | (~c0_1(a213)) | (~c3_1(a215))),
% 0.77/0.93 inference(modus_ponens,[status(thm)],[590, 589])).
% 0.77/0.93 tff(592,plain,
% 0.77/0.93 ((~c0_1(a213)) | (~c3_1(a215))),
% 0.77/0.93 inference(unit_resolution,[status(thm)],[591, 122, 321, 320, 585, 584, 583])).
% 0.77/0.93 tff(593,plain,
% 0.77/0.93 (~c3_1(a215)),
% 0.77/0.93 inference(unit_resolution,[status(thm)],[592, 560])).
% 0.77/0.93 tff(594,plain,
% 0.77/0.93 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c0_1(W) | c2_1(W) | c3_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c0_1(W) | c2_1(W) | c3_1(W)))),
% 0.77/0.93 inference(bind,[status(th)],[])).
% 0.77/0.93 tff(595,plain,
% 0.77/0.93 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c0_1(W) | c2_1(W) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c0_1(W) | c2_1(W) | c3_1(W))),
% 0.77/0.93 inference(quant_intro,[status(thm)],[594])).
% 0.77/0.93 tff(596,plain,
% 0.77/0.93 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c0_1(W) | c2_1(W) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c0_1(W) | c2_1(W) | c3_1(W))),
% 0.77/0.93 inference(rewrite,[status(thm)],[])).
% 0.77/0.93 tff(597,plain,
% 0.77/0.93 (^[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)) | (~c0_1(U)) | (~c3_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(V)) | c3_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V))) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(V)) | c3_1(V)) | c0_1(W)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))) | c0_1(W)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))) | c0_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c0_1(W))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(V)) | c3_1(V)) | c0_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c0_1(W)))), ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(V)) | c3_1(V)) | c0_1(W)) | c2_1(W)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c0_1(W)) | c2_1(W)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c0_1(W) | c2_1(W))), ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(V)) | c3_1(V)) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c0_1(W) | c2_1(W)))), (((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(V)) | c3_1(V)) | c0_1(W)) | c2_1(W)) | c3_1(W)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c0_1(W) | c2_1(W)) | c3_1(W)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c0_1(W) | c2_1(W)) | c3_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c0_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))) | c0_1(V)) | c3_1(V)) | c0_1(W)) | c2_1(W)) | c3_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c0_1(W) | c2_1(W) | c3_1(W))))),
% 0.77/0.94 inference(bind,[status(th)],[])).
% 0.77/0.94 tff(598,plain,
% 0.77/0.94 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(V)) | c3_1(V)) | c0_1(W)) | c2_1(W)) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c0_1(W) | c2_1(W) | c3_1(W))),
% 0.77/0.94 inference(quant_intro,[status(thm)],[597])).
% 0.77/0.94 tff(599,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(V)) | c3_1(V)) | c0_1(W)) | c2_1(W)) | c3_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause170')).
% 0.77/0.94 tff(600,plain,
% 0.77/0.94 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c0_1(W) | c2_1(W) | c3_1(W))),
% 0.77/0.94 inference(modus_ponens,[status(thm)],[599, 598])).
% 0.77/0.94 tff(601,plain,
% 0.77/0.94 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c0_1(W) | c2_1(W) | c3_1(W))),
% 0.77/0.94 inference(modus_ponens,[status(thm)],[600, 596])).
% 0.77/0.94 tff(602,plain,(
% 0.77/0.94 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c0_1(W) | c2_1(W) | c3_1(W))),
% 0.77/0.94 inference(skolemize,[status(sab)],[601])).
% 0.77/0.94 tff(603,plain,
% 0.77/0.94 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c0_1(W) | c2_1(W) | c3_1(W))),
% 0.77/0.94 inference(modus_ponens,[status(thm)],[602, 595])).
% 0.77/0.94 tff(604,assumption,(c2_1(a215)), introduced(assumption)).
% 0.77/0.94 tff(605,plain,
% 0.77/0.94 (hskp27),
% 0.77/0.94 inference(unit_resolution,[status(thm)],[485, 122, 203, 566, 565, 181, 559, 463, 180])).
% 0.77/0.94 tff(606,plain,
% 0.77/0.94 (c3_1(a232)),
% 0.77/0.94 inference(unit_resolution,[status(thm)],[247, 605])).
% 0.77/0.94 tff(607,plain,
% 0.77/0.94 (c2_1(a232)),
% 0.77/0.94 inference(unit_resolution,[status(thm)],[255, 605])).
% 0.77/0.94 tff(608,plain,
% 0.77/0.94 (c0_1(a232)),
% 0.77/0.94 inference(unit_resolution,[status(thm)],[263, 605])).
% 0.77/0.94 tff(609,plain,
% 0.77/0.94 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c0_1(W) | c2_1(W) | c3_1(W))) | (c0_1(a260) | c2_1(a260) | c0_1(a215) | (~ndr1_0) | (~c2_1(a215)) | c3_1(a215) | (~c2_1(a232)) | (~c3_1(a232)) | (~c0_1(a232)) | c3_1(a260))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c0_1(W) | c2_1(W) | c3_1(W))) | c0_1(a260) | c2_1(a260) | c0_1(a215) | (~ndr1_0) | (~c2_1(a215)) | c3_1(a215) | (~c2_1(a232)) | (~c3_1(a232)) | (~c0_1(a232)) | c3_1(a260))),
% 0.77/0.94 inference(rewrite,[status(thm)],[])).
% 0.77/0.94 tff(610,plain,
% 0.77/0.94 (((~ndr1_0) | (~c2_1(a232)) | (~c0_1(a232)) | (~c3_1(a232)) | c3_1(a215) | c0_1(a215) | (~c2_1(a215)) | c0_1(a260) | c2_1(a260) | c3_1(a260)) <=> (c0_1(a260) | c2_1(a260) | c0_1(a215) | (~ndr1_0) | (~c2_1(a215)) | c3_1(a215) | (~c2_1(a232)) | (~c3_1(a232)) | (~c0_1(a232)) | c3_1(a260))),
% 0.77/0.94 inference(rewrite,[status(thm)],[])).
% 0.77/0.94 tff(611,plain,
% 0.77/0.94 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c0_1(W) | c2_1(W) | c3_1(W))) | ((~ndr1_0) | (~c2_1(a232)) | (~c0_1(a232)) | (~c3_1(a232)) | c3_1(a215) | c0_1(a215) | (~c2_1(a215)) | c0_1(a260) | c2_1(a260) | c3_1(a260))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c0_1(W) | c2_1(W) | c3_1(W))) | (c0_1(a260) | c2_1(a260) | c0_1(a215) | (~ndr1_0) | (~c2_1(a215)) | c3_1(a215) | (~c2_1(a232)) | (~c3_1(a232)) | (~c0_1(a232)) | c3_1(a260)))),
% 0.77/0.94 inference(monotonicity,[status(thm)],[610])).
% 0.77/0.94 tff(612,plain,
% 0.77/0.94 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c0_1(W) | c2_1(W) | c3_1(W))) | ((~ndr1_0) | (~c2_1(a232)) | (~c0_1(a232)) | (~c3_1(a232)) | c3_1(a215) | c0_1(a215) | (~c2_1(a215)) | c0_1(a260) | c2_1(a260) | c3_1(a260))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c0_1(W) | c2_1(W) | c3_1(W))) | c0_1(a260) | c2_1(a260) | c0_1(a215) | (~ndr1_0) | (~c2_1(a215)) | c3_1(a215) | (~c2_1(a232)) | (~c3_1(a232)) | (~c0_1(a232)) | c3_1(a260))),
% 0.77/0.94 inference(transitivity,[status(thm)],[611, 609])).
% 0.77/0.94 tff(613,plain,
% 0.77/0.94 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c0_1(W) | c2_1(W) | c3_1(W))) | ((~ndr1_0) | (~c2_1(a232)) | (~c0_1(a232)) | (~c3_1(a232)) | c3_1(a215) | c0_1(a215) | (~c2_1(a215)) | c0_1(a260) | c2_1(a260) | c3_1(a260))),
% 0.77/0.94 inference(quant_inst,[status(thm)],[])).
% 0.77/0.94 tff(614,plain,
% 0.77/0.94 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c0_1(W) | c2_1(W) | c3_1(W))) | c0_1(a260) | c2_1(a260) | c0_1(a215) | (~ndr1_0) | (~c2_1(a215)) | c3_1(a215) | (~c2_1(a232)) | (~c3_1(a232)) | (~c0_1(a232)) | c3_1(a260)),
% 0.77/0.94 inference(modus_ponens,[status(thm)],[613, 612])).
% 0.77/0.94 tff(615,plain,
% 0.77/0.94 ($false),
% 0.77/0.94 inference(unit_resolution,[status(thm)],[614, 122, 608, 607, 606, 604, 564, 563, 585, 603, 593, 573])).
% 0.77/0.94 tff(616,plain,((~c0_1(a213)) | (~c2_1(a215)) | c0_1(a215) | (~c0_1(a282)) | (~c2_1(a230)) | (~c3_1(a230)) | c3_1(a282) | c1_1(a230) | c2_1(a282) | (~c1_1(a213)) | (~c3_1(a213)) | c1_1(a215) | hskp20 | c2_1(a213)), inference(lemma,lemma(discharge,[]))).
% 0.77/0.94 tff(617,plain,
% 0.77/0.94 (~c0_1(a213)),
% 0.77/0.94 inference(unit_resolution,[status(thm)],[616, 558, 550, 167, 479, 471, 173, 443, 180, 295, 287, 544, 381, 279])).
% 0.77/0.94 tff(618,plain,
% 0.77/0.94 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c2_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c2_1(W)))),
% 0.77/0.94 inference(bind,[status(th)],[])).
% 0.77/0.94 tff(619,plain,
% 0.77/0.94 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))),
% 0.77/0.94 inference(quant_intro,[status(thm)],[618])).
% 0.77/0.94 tff(620,plain,
% 0.77/0.94 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))),
% 0.77/0.94 inference(rewrite,[status(thm)],[])).
% 0.77/0.94 tff(621,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((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) <=> ((~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c0_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c0_1(V)) | c0_1(W)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))) | c0_1(W)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))) | c0_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c0_1(V)) | c0_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W)))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c0_1(V)) | c0_1(W)) | c1_1(W)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W)) | c1_1(W)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c0_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W)))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c0_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W)) | c2_1(W)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c0_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))))),
% 0.77/0.94 inference(bind,[status(th)],[])).
% 0.77/0.94 tff(622,plain,
% 0.77/0.94 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_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)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))),
% 0.77/0.94 inference(quant_intro,[status(thm)],[621])).
% 0.77/0.94 tff(623,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c0_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause174')).
% 0.77/0.94 tff(624,plain,
% 0.77/0.94 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))),
% 0.77/0.94 inference(modus_ponens,[status(thm)],[623, 622])).
% 0.77/0.94 tff(625,plain,
% 0.77/0.94 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))),
% 0.77/0.94 inference(modus_ponens,[status(thm)],[624, 620])).
% 0.77/0.94 tff(626,plain,(
% 0.77/0.94 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))),
% 0.77/0.94 inference(skolemize,[status(sab)],[625])).
% 0.77/0.94 tff(627,plain,
% 0.77/0.94 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))),
% 0.77/0.94 inference(modus_ponens,[status(thm)],[626, 619])).
% 0.77/0.94 tff(628,plain,
% 0.77/0.94 (hskp11),
% 0.77/0.94 inference(unit_resolution,[status(thm)],[389, 22])).
% 0.77/0.94 tff(629,plain,
% 0.77/0.94 (~c1_1(a230)),
% 0.77/0.94 inference(unit_resolution,[status(thm)],[442, 628])).
% 0.77/0.94 tff(630,plain,
% 0.77/0.94 (c3_1(a230)),
% 0.77/0.94 inference(unit_resolution,[status(thm)],[470, 628])).
% 0.77/0.94 tff(631,plain,
% 0.77/0.94 (c2_1(a230)),
% 0.77/0.94 inference(unit_resolution,[status(thm)],[478, 628])).
% 0.77/0.94 tff(632,plain,
% 0.77/0.94 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | (c3_1(a282) | c1_1(a230) | c2_1(a213) | (~ndr1_0) | (~c3_1(a213)) | c0_1(a213) | (~c3_1(a230)) | (~c2_1(a230)) | c2_1(a282) | (~c0_1(a282)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c3_1(a282) | c1_1(a230) | c2_1(a213) | (~ndr1_0) | (~c3_1(a213)) | c0_1(a213) | (~c3_1(a230)) | (~c2_1(a230)) | c2_1(a282) | (~c0_1(a282)))),
% 0.77/0.94 inference(rewrite,[status(thm)],[])).
% 0.77/0.94 tff(633,plain,
% 0.77/0.94 (((~ndr1_0) | c3_1(a282) | c2_1(a282) | (~c0_1(a282)) | c1_1(a230) | (~c3_1(a230)) | (~c2_1(a230)) | c0_1(a213) | c2_1(a213) | (~c3_1(a213))) <=> (c3_1(a282) | c1_1(a230) | c2_1(a213) | (~ndr1_0) | (~c3_1(a213)) | c0_1(a213) | (~c3_1(a230)) | (~c2_1(a230)) | c2_1(a282) | (~c0_1(a282)))),
% 0.77/0.94 inference(rewrite,[status(thm)],[])).
% 0.77/0.94 tff(634,plain,
% 0.77/0.94 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a282) | c2_1(a282) | (~c0_1(a282)) | c1_1(a230) | (~c3_1(a230)) | (~c2_1(a230)) | c0_1(a213) | c2_1(a213) | (~c3_1(a213)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | (c3_1(a282) | c1_1(a230) | c2_1(a213) | (~ndr1_0) | (~c3_1(a213)) | c0_1(a213) | (~c3_1(a230)) | (~c2_1(a230)) | c2_1(a282) | (~c0_1(a282))))),
% 0.77/0.94 inference(monotonicity,[status(thm)],[633])).
% 0.77/0.94 tff(635,plain,
% 0.77/0.94 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a282) | c2_1(a282) | (~c0_1(a282)) | c1_1(a230) | (~c3_1(a230)) | (~c2_1(a230)) | c0_1(a213) | c2_1(a213) | (~c3_1(a213)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c3_1(a282) | c1_1(a230) | c2_1(a213) | (~ndr1_0) | (~c3_1(a213)) | c0_1(a213) | (~c3_1(a230)) | (~c2_1(a230)) | c2_1(a282) | (~c0_1(a282)))),
% 0.77/0.94 inference(transitivity,[status(thm)],[634, 632])).
% 0.77/0.94 tff(636,plain,
% 0.77/0.94 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a282) | c2_1(a282) | (~c0_1(a282)) | c1_1(a230) | (~c3_1(a230)) | (~c2_1(a230)) | c0_1(a213) | c2_1(a213) | (~c3_1(a213)))),
% 0.77/0.94 inference(quant_inst,[status(thm)],[])).
% 0.77/0.94 tff(637,plain,
% 0.77/0.94 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c3_1(a282) | c1_1(a230) | c2_1(a213) | (~ndr1_0) | (~c3_1(a213)) | c0_1(a213) | (~c3_1(a230)) | (~c2_1(a230)) | c2_1(a282) | (~c0_1(a282))),
% 0.77/0.94 inference(modus_ponens,[status(thm)],[636, 635])).
% 0.77/0.94 tff(638,plain,
% 0.77/0.94 (c2_1(a282)),
% 0.77/0.94 inference(unit_resolution,[status(thm)],[637, 122, 203, 631, 630, 320, 181, 629, 306, 10, 22])).
% 0.77/0.94 tff(639,plain,
% 0.77/0.94 (^[V: $i, U: $i] : refl((hskp18 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V))) <=> (hskp18 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V))))),
% 0.77/0.94 inference(bind,[status(th)],[])).
% 0.77/0.94 tff(640,plain,
% 0.77/0.94 (![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))),
% 0.77/0.94 inference(quant_intro,[status(thm)],[639])).
% 0.77/0.94 tff(641,plain,
% 0.77/0.94 (![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))),
% 0.77/0.94 inference(rewrite,[status(thm)],[])).
% 0.77/0.94 tff(642,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) | (~c1_1(U)) | (~c3_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V))))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V))))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V))))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c1_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V))) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V))))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c1_1(V)) | c3_1(V)) | hskp18) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V))) | hskp18))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V))) | hskp18) <=> (hskp18 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c1_1(V)) | c3_1(V)) | hskp18) <=> (hskp18 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))))),
% 0.77/0.94 inference(bind,[status(th)],[])).
% 0.77/0.94 tff(643,plain,
% 0.77/0.94 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c1_1(V)) | c3_1(V)) | hskp18) <=> ![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))),
% 0.77/0.94 inference(quant_intro,[status(thm)],[642])).
% 0.77/0.94 tff(644,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c1_1(V)) | c3_1(V)) | hskp18)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause159')).
% 0.77/0.94 tff(645,plain,
% 0.77/0.94 (![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))),
% 0.77/0.94 inference(modus_ponens,[status(thm)],[644, 643])).
% 0.77/0.94 tff(646,plain,
% 0.77/0.94 (![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))),
% 0.77/0.94 inference(modus_ponens,[status(thm)],[645, 641])).
% 0.77/0.94 tff(647,plain,(
% 0.77/0.94 ![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))),
% 0.77/0.94 inference(skolemize,[status(sab)],[646])).
% 0.77/0.94 tff(648,plain,
% 0.77/0.94 (![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))),
% 0.77/0.94 inference(modus_ponens,[status(thm)],[647, 640])).
% 0.77/0.94 tff(649,plain,
% 0.77/0.94 (((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp18 | c1_1(a282) | c3_1(a282) | c2_1(a213) | (~ndr1_0) | (~c1_1(a213)) | (~c3_1(a213)) | (~c2_1(a282)))) <=> ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp18 | c1_1(a282) | c3_1(a282) | c2_1(a213) | (~ndr1_0) | (~c1_1(a213)) | (~c3_1(a213)) | (~c2_1(a282)))),
% 0.77/0.94 inference(rewrite,[status(thm)],[])).
% 0.77/0.94 tff(650,plain,
% 0.77/0.94 ((hskp18 | (~ndr1_0) | c2_1(a213) | (~c1_1(a213)) | (~c3_1(a213)) | c3_1(a282) | c1_1(a282) | (~c2_1(a282))) <=> (hskp18 | c1_1(a282) | c3_1(a282) | c2_1(a213) | (~ndr1_0) | (~c1_1(a213)) | (~c3_1(a213)) | (~c2_1(a282)))),
% 0.77/0.94 inference(rewrite,[status(thm)],[])).
% 0.77/0.94 tff(651,plain,
% 0.77/0.94 (((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp18 | (~ndr1_0) | c2_1(a213) | (~c1_1(a213)) | (~c3_1(a213)) | c3_1(a282) | c1_1(a282) | (~c2_1(a282)))) <=> ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp18 | c1_1(a282) | c3_1(a282) | c2_1(a213) | (~ndr1_0) | (~c1_1(a213)) | (~c3_1(a213)) | (~c2_1(a282))))),
% 0.77/0.94 inference(monotonicity,[status(thm)],[650])).
% 0.77/0.94 tff(652,plain,
% 0.77/0.94 (((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp18 | (~ndr1_0) | c2_1(a213) | (~c1_1(a213)) | (~c3_1(a213)) | c3_1(a282) | c1_1(a282) | (~c2_1(a282)))) <=> ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp18 | c1_1(a282) | c3_1(a282) | c2_1(a213) | (~ndr1_0) | (~c1_1(a213)) | (~c3_1(a213)) | (~c2_1(a282)))),
% 0.77/0.94 inference(transitivity,[status(thm)],[651, 649])).
% 0.77/0.94 tff(653,plain,
% 0.77/0.94 ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp18 | (~ndr1_0) | c2_1(a213) | (~c1_1(a213)) | (~c3_1(a213)) | c3_1(a282) | c1_1(a282) | (~c2_1(a282)))),
% 0.77/0.94 inference(quant_inst,[status(thm)],[])).
% 0.77/0.94 tff(654,plain,
% 0.77/0.94 ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp18 | c1_1(a282) | c3_1(a282) | c2_1(a213) | (~ndr1_0) | (~c1_1(a213)) | (~c3_1(a213)) | (~c2_1(a282))),
% 0.77/0.94 inference(modus_ponens,[status(thm)],[653, 652])).
% 0.77/0.94 tff(655,plain,
% 0.77/0.94 (hskp18 | (~c2_1(a282))),
% 0.77/0.94 inference(unit_resolution,[status(thm)],[654, 122, 321, 320, 182, 181, 306, 648])).
% 0.77/0.94 tff(656,plain,
% 0.77/0.94 (hskp18),
% 0.77/0.94 inference(unit_resolution,[status(thm)],[655, 638])).
% 0.77/0.94 tff(657,plain,
% 0.77/0.94 (~c2_1(a247)),
% 0.77/0.94 inference(unit_resolution,[status(thm)],[149, 656])).
% 0.77/0.94 tff(658,plain,
% 0.77/0.94 (((~hskp18) | c0_1(a247)) <=> ((~hskp18) | c0_1(a247))),
% 0.77/0.94 inference(rewrite,[status(thm)],[])).
% 0.77/0.94 tff(659,axiom,((~hskp18) | c0_1(a247)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause53')).
% 0.77/0.94 tff(660,plain,
% 0.77/0.94 ((~hskp18) | c0_1(a247)),
% 0.77/0.94 inference(modus_ponens,[status(thm)],[659, 658])).
% 0.77/0.94 tff(661,plain,
% 0.77/0.94 ((~hskp18) | c0_1(a247)),
% 0.77/0.94 inference(modus_ponens,[status(thm)],[660, 658])).
% 0.77/0.94 tff(662,plain,
% 0.77/0.94 ((~hskp18) | c0_1(a247)),
% 0.77/0.94 inference(modus_ponens,[status(thm)],[661, 658])).
% 0.77/0.94 tff(663,plain,
% 0.77/0.94 ((~hskp18) | c0_1(a247)),
% 0.77/0.94 inference(modus_ponens,[status(thm)],[662, 658])).
% 0.77/0.94 tff(664,plain,
% 0.77/0.94 ((~hskp18) | c0_1(a247)),
% 0.77/0.94 inference(modus_ponens,[status(thm)],[663, 658])).
% 0.77/0.94 tff(665,plain,
% 0.77/0.94 (c0_1(a247)),
% 0.77/0.94 inference(unit_resolution,[status(thm)],[664, 656])).
% 0.77/0.94 tff(666,plain,
% 0.77/0.94 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | (c2_1(a247) | c2_1(a213) | (~ndr1_0) | (~c1_1(a213)) | (~c3_1(a213)) | c0_1(a213) | c1_1(a247) | (~c0_1(a247)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c2_1(a247) | c2_1(a213) | (~ndr1_0) | (~c1_1(a213)) | (~c3_1(a213)) | c0_1(a213) | c1_1(a247) | (~c0_1(a247)))),
% 0.77/0.94 inference(rewrite,[status(thm)],[])).
% 0.77/0.94 tff(667,plain,
% 0.77/0.94 (((~ndr1_0) | c2_1(a213) | (~c1_1(a213)) | (~c3_1(a213)) | c2_1(a247) | c1_1(a247) | (~c0_1(a247)) | c0_1(a213) | c2_1(a213) | (~c3_1(a213))) <=> (c2_1(a247) | c2_1(a213) | (~ndr1_0) | (~c1_1(a213)) | (~c3_1(a213)) | c0_1(a213) | c1_1(a247) | (~c0_1(a247)))),
% 0.77/0.94 inference(rewrite,[status(thm)],[])).
% 0.77/0.94 tff(668,plain,
% 0.77/0.94 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a213) | (~c1_1(a213)) | (~c3_1(a213)) | c2_1(a247) | c1_1(a247) | (~c0_1(a247)) | c0_1(a213) | c2_1(a213) | (~c3_1(a213)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | (c2_1(a247) | c2_1(a213) | (~ndr1_0) | (~c1_1(a213)) | (~c3_1(a213)) | c0_1(a213) | c1_1(a247) | (~c0_1(a247))))),
% 0.77/0.94 inference(monotonicity,[status(thm)],[667])).
% 0.77/0.94 tff(669,plain,
% 0.77/0.94 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a213) | (~c1_1(a213)) | (~c3_1(a213)) | c2_1(a247) | c1_1(a247) | (~c0_1(a247)) | c0_1(a213) | c2_1(a213) | (~c3_1(a213)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c2_1(a247) | c2_1(a213) | (~ndr1_0) | (~c1_1(a213)) | (~c3_1(a213)) | c0_1(a213) | c1_1(a247) | (~c0_1(a247)))),
% 0.77/0.94 inference(transitivity,[status(thm)],[668, 666])).
% 0.77/0.94 tff(670,plain,
% 0.77/0.94 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a213) | (~c1_1(a213)) | (~c3_1(a213)) | c2_1(a247) | c1_1(a247) | (~c0_1(a247)) | c0_1(a213) | c2_1(a213) | (~c3_1(a213)))),
% 0.77/0.94 inference(quant_inst,[status(thm)],[])).
% 0.77/0.94 tff(671,plain,
% 0.77/0.94 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c2_1(a247) | c2_1(a213) | (~ndr1_0) | (~c1_1(a213)) | (~c3_1(a213)) | c0_1(a213) | c1_1(a247) | (~c0_1(a247))),
% 0.77/0.94 inference(modus_ponens,[status(thm)],[670, 669])).
% 0.77/0.94 tff(672,plain,
% 0.77/0.94 (c1_1(a247)),
% 0.77/0.94 inference(unit_resolution,[status(thm)],[671, 122, 665, 321, 320, 657, 306, 305, 22])).
% 0.77/0.94 tff(673,plain,
% 0.77/0.94 (^[V: $i, U: $i] : refl((hskp28 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V))) <=> (hskp28 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V))))),
% 0.77/0.94 inference(bind,[status(th)],[])).
% 0.77/0.94 tff(674,plain,
% 0.77/0.94 (![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))),
% 0.77/0.94 inference(quant_intro,[status(thm)],[673])).
% 0.77/0.94 tff(675,plain,
% 0.77/0.94 (![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))),
% 0.77/0.94 inference(rewrite,[status(thm)],[])).
% 0.77/0.94 tff(676,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)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~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(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c1_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V))) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c1_1(V)) | c3_1(V)) | hskp28) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V))) | hskp28))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V))) | hskp28) <=> (hskp28 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c1_1(V)) | c3_1(V)) | hskp28) <=> (hskp28 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))))),
% 0.77/0.94 inference(bind,[status(th)],[])).
% 0.77/0.94 tff(677,plain,
% 0.77/0.94 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c1_1(V)) | c3_1(V)) | hskp28) <=> ![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))),
% 0.77/0.94 inference(quant_intro,[status(thm)],[676])).
% 0.77/0.94 tff(678,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c1_1(V)) | c3_1(V)) | hskp28)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause158')).
% 0.77/0.94 tff(679,plain,
% 0.77/0.94 (![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))),
% 0.77/0.94 inference(modus_ponens,[status(thm)],[678, 677])).
% 0.77/0.94 tff(680,plain,
% 0.77/0.94 (![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))),
% 0.77/0.94 inference(modus_ponens,[status(thm)],[679, 675])).
% 0.77/0.94 tff(681,plain,(
% 0.77/0.94 ![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))),
% 0.77/0.94 inference(skolemize,[status(sab)],[680])).
% 0.77/0.94 tff(682,plain,
% 0.77/0.94 (![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))),
% 0.77/0.94 inference(modus_ponens,[status(thm)],[681, 674])).
% 0.77/0.94 tff(683,assumption,(~hskp28), introduced(assumption)).
% 0.77/0.94 tff(684,plain,
% 0.77/0.94 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp28 | c1_1(a282) | c3_1(a282) | c2_1(a247) | (~ndr1_0) | (~c1_1(a247)) | (~c0_1(a247)) | (~c2_1(a282)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp28 | c1_1(a282) | c3_1(a282) | c2_1(a247) | (~ndr1_0) | (~c1_1(a247)) | (~c0_1(a247)) | (~c2_1(a282)))),
% 0.77/0.94 inference(rewrite,[status(thm)],[])).
% 0.77/0.94 tff(685,plain,
% 0.77/0.94 ((hskp28 | (~ndr1_0) | c2_1(a247) | (~c1_1(a247)) | (~c0_1(a247)) | c3_1(a282) | c1_1(a282) | (~c2_1(a282))) <=> (hskp28 | c1_1(a282) | c3_1(a282) | c2_1(a247) | (~ndr1_0) | (~c1_1(a247)) | (~c0_1(a247)) | (~c2_1(a282)))),
% 0.77/0.94 inference(rewrite,[status(thm)],[])).
% 0.77/0.95 tff(686,plain,
% 0.77/0.95 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp28 | (~ndr1_0) | c2_1(a247) | (~c1_1(a247)) | (~c0_1(a247)) | c3_1(a282) | c1_1(a282) | (~c2_1(a282)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp28 | c1_1(a282) | c3_1(a282) | c2_1(a247) | (~ndr1_0) | (~c1_1(a247)) | (~c0_1(a247)) | (~c2_1(a282))))),
% 0.77/0.95 inference(monotonicity,[status(thm)],[685])).
% 0.77/0.95 tff(687,plain,
% 0.77/0.95 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp28 | (~ndr1_0) | c2_1(a247) | (~c1_1(a247)) | (~c0_1(a247)) | c3_1(a282) | c1_1(a282) | (~c2_1(a282)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp28 | c1_1(a282) | c3_1(a282) | c2_1(a247) | (~ndr1_0) | (~c1_1(a247)) | (~c0_1(a247)) | (~c2_1(a282)))),
% 0.77/0.95 inference(transitivity,[status(thm)],[686, 684])).
% 0.77/0.95 tff(688,plain,
% 0.77/0.95 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp28 | (~ndr1_0) | c2_1(a247) | (~c1_1(a247)) | (~c0_1(a247)) | c3_1(a282) | c1_1(a282) | (~c2_1(a282)))),
% 0.77/0.95 inference(quant_inst,[status(thm)],[])).
% 0.77/0.95 tff(689,plain,
% 0.77/0.95 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp28 | c1_1(a282) | c3_1(a282) | c2_1(a247) | (~ndr1_0) | (~c1_1(a247)) | (~c0_1(a247)) | (~c2_1(a282))),
% 0.77/0.95 inference(modus_ponens,[status(thm)],[688, 687])).
% 0.77/0.95 tff(690,plain,
% 0.77/0.95 ($false),
% 0.77/0.95 inference(unit_resolution,[status(thm)],[689, 683, 122, 665, 182, 181, 657, 682, 638, 672])).
% 0.77/0.95 tff(691,plain,(c0_1(a213) | hskp28 | c1_1(a282) | c3_1(a282) | (~c1_1(a213)) | (~c3_1(a213)) | c2_1(a213) | (~c0_1(a282)) | hskp10), inference(lemma,lemma(discharge,[]))).
% 0.77/0.95 tff(692,plain,
% 0.77/0.95 (hskp28),
% 0.77/0.95 inference(unit_resolution,[status(thm)],[691, 617, 179, 173, 295, 287, 279, 167, 21])).
% 0.77/0.95 tff(693,plain,
% 0.77/0.95 (((~hskp28) | c2_1(a246)) <=> ((~hskp28) | c2_1(a246))),
% 0.77/0.95 inference(rewrite,[status(thm)],[])).
% 0.77/0.95 tff(694,axiom,((~hskp28) | c2_1(a246)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause38')).
% 0.77/0.95 tff(695,plain,
% 0.77/0.95 ((~hskp28) | c2_1(a246)),
% 0.77/0.95 inference(modus_ponens,[status(thm)],[694, 693])).
% 0.77/0.95 tff(696,plain,
% 0.77/0.95 ((~hskp28) | c2_1(a246)),
% 0.77/0.95 inference(modus_ponens,[status(thm)],[695, 693])).
% 0.77/0.95 tff(697,plain,
% 0.77/0.95 ((~hskp28) | c2_1(a246)),
% 0.77/0.95 inference(modus_ponens,[status(thm)],[696, 693])).
% 0.77/0.95 tff(698,plain,
% 0.77/0.95 ((~hskp28) | c2_1(a246)),
% 0.77/0.95 inference(modus_ponens,[status(thm)],[697, 693])).
% 0.77/0.95 tff(699,plain,
% 0.77/0.95 ((~hskp28) | c2_1(a246)),
% 0.77/0.95 inference(modus_ponens,[status(thm)],[698, 693])).
% 0.77/0.95 tff(700,plain,
% 0.77/0.95 (c2_1(a246)),
% 0.77/0.95 inference(unit_resolution,[status(thm)],[699, 692])).
% 0.77/0.95 tff(701,plain,
% 0.77/0.95 (((~hskp28) | c1_1(a246)) <=> ((~hskp28) | c1_1(a246))),
% 0.77/0.95 inference(rewrite,[status(thm)],[])).
% 0.77/0.95 tff(702,axiom,((~hskp28) | c1_1(a246)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause37')).
% 0.77/0.95 tff(703,plain,
% 0.77/0.95 ((~hskp28) | c1_1(a246)),
% 0.77/0.95 inference(modus_ponens,[status(thm)],[702, 701])).
% 0.77/0.95 tff(704,plain,
% 0.77/0.95 ((~hskp28) | c1_1(a246)),
% 0.77/0.95 inference(modus_ponens,[status(thm)],[703, 701])).
% 0.77/0.95 tff(705,plain,
% 0.77/0.95 ((~hskp28) | c1_1(a246)),
% 0.77/0.95 inference(modus_ponens,[status(thm)],[704, 701])).
% 0.77/0.95 tff(706,plain,
% 0.77/0.95 ((~hskp28) | c1_1(a246)),
% 0.77/0.95 inference(modus_ponens,[status(thm)],[705, 701])).
% 0.77/0.95 tff(707,plain,
% 0.77/0.95 ((~hskp28) | c1_1(a246)),
% 0.77/0.95 inference(modus_ponens,[status(thm)],[706, 701])).
% 0.77/0.95 tff(708,plain,
% 0.77/0.95 (c1_1(a246)),
% 0.77/0.95 inference(unit_resolution,[status(thm)],[707, 692])).
% 0.77/0.95 tff(709,plain,
% 0.77/0.95 (((~hskp28) | c0_1(a246)) <=> ((~hskp28) | c0_1(a246))),
% 0.77/0.95 inference(rewrite,[status(thm)],[])).
% 0.77/0.95 tff(710,axiom,((~hskp28) | c0_1(a246)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause36')).
% 0.77/0.95 tff(711,plain,
% 0.77/0.95 ((~hskp28) | c0_1(a246)),
% 0.77/0.95 inference(modus_ponens,[status(thm)],[710, 709])).
% 0.77/0.95 tff(712,plain,
% 0.77/0.95 ((~hskp28) | c0_1(a246)),
% 0.77/0.95 inference(modus_ponens,[status(thm)],[711, 709])).
% 0.77/0.95 tff(713,plain,
% 0.77/0.95 ((~hskp28) | c0_1(a246)),
% 0.77/0.95 inference(modus_ponens,[status(thm)],[712, 709])).
% 0.77/0.95 tff(714,plain,
% 0.77/0.95 ((~hskp28) | c0_1(a246)),
% 0.77/0.95 inference(modus_ponens,[status(thm)],[713, 709])).
% 0.77/0.95 tff(715,plain,
% 0.77/0.95 ((~hskp28) | c0_1(a246)),
% 0.77/0.95 inference(modus_ponens,[status(thm)],[714, 709])).
% 0.77/0.95 tff(716,plain,
% 0.77/0.95 (c0_1(a246)),
% 0.77/0.95 inference(unit_resolution,[status(thm)],[715, 692])).
% 0.77/0.95 tff(717,plain,
% 0.77/0.95 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a243) | c1_1(a243) | c2_1(a243) | (~ndr1_0) | (~c1_1(a213)) | (~c3_1(a213)) | c0_1(a213) | (~c0_1(a246)) | (~c1_1(a246)) | (~c2_1(a246)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c0_1(a243) | c1_1(a243) | c2_1(a243) | (~ndr1_0) | (~c1_1(a213)) | (~c3_1(a213)) | c0_1(a213) | (~c0_1(a246)) | (~c1_1(a246)) | (~c2_1(a246)))),
% 0.77/0.95 inference(rewrite,[status(thm)],[])).
% 0.77/0.95 tff(718,plain,
% 0.77/0.95 (((~ndr1_0) | (~c2_1(a246)) | (~c1_1(a246)) | (~c0_1(a246)) | c0_1(a213) | (~c3_1(a213)) | (~c1_1(a213)) | c1_1(a243) | c0_1(a243) | c2_1(a243)) <=> (c0_1(a243) | c1_1(a243) | c2_1(a243) | (~ndr1_0) | (~c1_1(a213)) | (~c3_1(a213)) | c0_1(a213) | (~c0_1(a246)) | (~c1_1(a246)) | (~c2_1(a246)))),
% 0.77/0.95 inference(rewrite,[status(thm)],[])).
% 0.77/0.95 tff(719,plain,
% 0.77/0.95 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | (~c2_1(a246)) | (~c1_1(a246)) | (~c0_1(a246)) | c0_1(a213) | (~c3_1(a213)) | (~c1_1(a213)) | c1_1(a243) | c0_1(a243) | c2_1(a243))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a243) | c1_1(a243) | c2_1(a243) | (~ndr1_0) | (~c1_1(a213)) | (~c3_1(a213)) | c0_1(a213) | (~c0_1(a246)) | (~c1_1(a246)) | (~c2_1(a246))))),
% 0.77/0.95 inference(monotonicity,[status(thm)],[718])).
% 0.77/0.95 tff(720,plain,
% 0.77/0.95 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | (~c2_1(a246)) | (~c1_1(a246)) | (~c0_1(a246)) | c0_1(a213) | (~c3_1(a213)) | (~c1_1(a213)) | c1_1(a243) | c0_1(a243) | c2_1(a243))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c0_1(a243) | c1_1(a243) | c2_1(a243) | (~ndr1_0) | (~c1_1(a213)) | (~c3_1(a213)) | c0_1(a213) | (~c0_1(a246)) | (~c1_1(a246)) | (~c2_1(a246)))),
% 0.77/0.95 inference(transitivity,[status(thm)],[719, 717])).
% 0.77/0.95 tff(721,plain,
% 0.77/0.95 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | (~c2_1(a246)) | (~c1_1(a246)) | (~c0_1(a246)) | c0_1(a213) | (~c3_1(a213)) | (~c1_1(a213)) | c1_1(a243) | c0_1(a243) | c2_1(a243))),
% 0.77/0.95 inference(quant_inst,[status(thm)],[])).
% 0.77/0.95 tff(722,plain,
% 0.77/0.95 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c0_1(a243) | c1_1(a243) | c2_1(a243) | (~ndr1_0) | (~c1_1(a213)) | (~c3_1(a213)) | c0_1(a213) | (~c0_1(a246)) | (~c1_1(a246)) | (~c2_1(a246))),
% 0.77/0.95 inference(modus_ponens,[status(thm)],[721, 720])).
% 0.77/0.95 tff(723,plain,
% 0.77/0.95 ($false),
% 0.77/0.95 inference(unit_resolution,[status(thm)],[722, 122, 716, 708, 700, 295, 287, 508, 531, 502, 627, 617])).
% 0.77/0.95 tff(724,plain,(c2_1(a282) | hskp10 | hskp8), inference(lemma,lemma(discharge,[]))).
% 0.77/0.95 tff(725,plain,
% 0.77/0.95 (c2_1(a282)),
% 0.77/0.95 inference(unit_resolution,[status(thm)],[724, 21, 43])).
% 0.77/0.95 tff(726,plain,
% 0.77/0.95 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_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) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W))))),
% 0.77/0.95 inference(bind,[status(th)],[])).
% 0.77/0.95 tff(727,plain,
% 0.77/0.95 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 0.77/0.95 inference(quant_intro,[status(thm)],[726])).
% 0.77/0.95 tff(728,plain,
% 0.77/0.95 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 0.77/0.95 inference(rewrite,[status(thm)],[])).
% 0.77/0.95 tff(729,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((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V))))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(W))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V))) | (~c3_1(W))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c3_1(W)))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c3_1(W))))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(W))) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c3_1(W))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c3_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c3_1(W)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c3_1(W))))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(W))) | c2_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c3_1(W))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c3_1(W))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(W)))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(W))) | c2_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(W))))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(W))) | c2_1(U)) | c1_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(W))) | c3_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(W))) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | (~c3_1(W)))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(W))) | c2_1(U)) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | (~c3_1(W))))), ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(W))) | c2_1(U)) | c1_1(V)) | c3_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | (~c3_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | (~c3_1(W))) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)))), ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(W))) | c2_1(U)) | c1_1(V)) | c3_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c3_1(W))))), (((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(W))) | c2_1(U)) | c1_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c3_1(W))) | c1_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c3_1(W))) | c1_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))), (((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(W))) | c2_1(U)) | c1_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))))),
% 0.77/0.95 inference(bind,[status(th)],[])).
% 0.77/0.95 tff(730,plain,
% 0.77/0.95 (![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(W))) | c2_1(U)) | c1_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 0.77/0.95 inference(quant_intro,[status(thm)],[729])).
% 0.77/0.95 tff(731,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(W))) | c2_1(U)) | c1_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause169')).
% 0.77/0.95 tff(732,plain,
% 0.77/0.95 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 0.77/0.95 inference(modus_ponens,[status(thm)],[731, 730])).
% 0.77/0.95 tff(733,plain,
% 0.77/0.95 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 0.77/0.95 inference(modus_ponens,[status(thm)],[732, 728])).
% 0.77/0.95 tff(734,plain,(
% 0.77/0.95 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 0.77/0.95 inference(skolemize,[status(sab)],[733])).
% 0.77/0.95 tff(735,plain,
% 0.77/0.95 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 0.77/0.95 inference(modus_ponens,[status(thm)],[734, 727])).
% 0.77/0.95 tff(736,plain,
% 0.77/0.95 (((~![U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp27 | c3_1(a282) | (~ndr1_0) | (~c2_1(a282)) | (~c0_1(a282)))) <=> ((~![U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp27 | c3_1(a282) | (~ndr1_0) | (~c2_1(a282)) | (~c0_1(a282)))),
% 0.77/0.95 inference(rewrite,[status(thm)],[])).
% 0.77/0.95 tff(737,plain,
% 0.77/0.95 ((hskp27 | (~ndr1_0) | c3_1(a282) | (~c2_1(a282)) | (~c0_1(a282))) <=> (hskp27 | c3_1(a282) | (~ndr1_0) | (~c2_1(a282)) | (~c0_1(a282)))),
% 0.77/0.95 inference(rewrite,[status(thm)],[])).
% 0.77/0.95 tff(738,plain,
% 0.77/0.95 (((~![U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp27 | (~ndr1_0) | c3_1(a282) | (~c2_1(a282)) | (~c0_1(a282)))) <=> ((~![U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp27 | c3_1(a282) | (~ndr1_0) | (~c2_1(a282)) | (~c0_1(a282))))),
% 0.77/0.95 inference(monotonicity,[status(thm)],[737])).
% 0.77/0.95 tff(739,plain,
% 0.77/0.95 (((~![U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp27 | (~ndr1_0) | c3_1(a282) | (~c2_1(a282)) | (~c0_1(a282)))) <=> ((~![U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp27 | c3_1(a282) | (~ndr1_0) | (~c2_1(a282)) | (~c0_1(a282)))),
% 0.77/0.95 inference(transitivity,[status(thm)],[738, 736])).
% 0.77/0.95 tff(740,plain,
% 0.77/0.95 ((~![U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp27 | (~ndr1_0) | c3_1(a282) | (~c2_1(a282)) | (~c0_1(a282)))),
% 0.77/0.95 inference(quant_inst,[status(thm)],[])).
% 0.77/0.95 tff(741,plain,
% 0.77/0.95 ((~![U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp27 | c3_1(a282) | (~ndr1_0) | (~c2_1(a282)) | (~c0_1(a282))),
% 0.77/0.95 inference(modus_ponens,[status(thm)],[740, 739])).
% 0.77/0.95 tff(742,plain,
% 0.77/0.95 (hskp27 | (~c2_1(a282))),
% 0.77/0.95 inference(unit_resolution,[status(thm)],[741, 122, 167, 173, 192])).
% 0.77/0.95 tff(743,plain,
% 0.77/0.95 (hskp27),
% 0.77/0.95 inference(unit_resolution,[status(thm)],[742, 725])).
% 0.77/0.95 tff(744,plain,
% 0.77/0.95 (c3_1(a232)),
% 0.77/0.95 inference(unit_resolution,[status(thm)],[247, 743])).
% 0.77/0.95 tff(745,plain,
% 0.77/0.95 (c2_1(a232)),
% 0.77/0.95 inference(unit_resolution,[status(thm)],[255, 743])).
% 0.77/0.95 tff(746,plain,
% 0.77/0.95 (c0_1(a232)),
% 0.77/0.95 inference(unit_resolution,[status(thm)],[263, 743])).
% 0.77/0.95 tff(747,assumption,(hskp13), introduced(assumption)).
% 0.77/0.95 tff(748,plain,
% 0.77/0.95 (((~hskp13) | (~c3_1(a236))) <=> ((~hskp13) | (~c3_1(a236)))),
% 0.77/0.95 inference(rewrite,[status(thm)],[])).
% 0.77/0.95 tff(749,plain,
% 0.77/0.95 (((~c3_1(a236)) | (~hskp13)) <=> ((~hskp13) | (~c3_1(a236)))),
% 0.77/0.95 inference(rewrite,[status(thm)],[])).
% 0.77/0.95 tff(750,axiom,((~c3_1(a236)) | (~hskp13)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause101')).
% 0.77/0.95 tff(751,plain,
% 0.77/0.95 ((~hskp13) | (~c3_1(a236))),
% 0.77/0.95 inference(modus_ponens,[status(thm)],[750, 749])).
% 0.77/0.95 tff(752,plain,
% 0.77/0.95 ((~hskp13) | (~c3_1(a236))),
% 0.77/0.95 inference(modus_ponens,[status(thm)],[751, 748])).
% 0.77/0.95 tff(753,plain,
% 0.77/0.95 (~c3_1(a236)),
% 0.77/0.95 inference(unit_resolution,[status(thm)],[752, 747])).
% 0.77/0.95 tff(754,plain,
% 0.77/0.95 (((~hskp13) | (~c2_1(a236))) <=> ((~hskp13) | (~c2_1(a236)))),
% 0.77/0.95 inference(rewrite,[status(thm)],[])).
% 0.77/0.95 tff(755,plain,
% 0.77/0.95 (((~c2_1(a236)) | (~hskp13)) <=> ((~hskp13) | (~c2_1(a236)))),
% 0.77/0.95 inference(rewrite,[status(thm)],[])).
% 0.77/0.95 tff(756,axiom,((~c2_1(a236)) | (~hskp13)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause100')).
% 0.77/0.95 tff(757,plain,
% 0.77/0.95 ((~hskp13) | (~c2_1(a236))),
% 0.77/0.95 inference(modus_ponens,[status(thm)],[756, 755])).
% 0.77/0.95 tff(758,plain,
% 0.77/0.95 ((~hskp13) | (~c2_1(a236))),
% 0.77/0.95 inference(modus_ponens,[status(thm)],[757, 754])).
% 0.77/0.95 tff(759,plain,
% 0.77/0.95 (~c2_1(a236)),
% 0.77/0.95 inference(unit_resolution,[status(thm)],[758, 747])).
% 0.77/0.95 tff(760,plain,
% 0.77/0.95 (((~hskp13) | (~c1_1(a236))) <=> ((~hskp13) | (~c1_1(a236)))),
% 0.77/0.95 inference(rewrite,[status(thm)],[])).
% 0.77/0.95 tff(761,plain,
% 0.77/0.95 (((~c1_1(a236)) | (~hskp13)) <=> ((~hskp13) | (~c1_1(a236)))),
% 0.77/0.95 inference(rewrite,[status(thm)],[])).
% 0.77/0.95 tff(762,axiom,((~c1_1(a236)) | (~hskp13)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause99')).
% 0.77/0.95 tff(763,plain,
% 0.77/0.95 ((~hskp13) | (~c1_1(a236))),
% 0.77/0.95 inference(modus_ponens,[status(thm)],[762, 761])).
% 0.77/0.95 tff(764,plain,
% 0.77/0.95 ((~hskp13) | (~c1_1(a236))),
% 0.77/0.95 inference(modus_ponens,[status(thm)],[763, 760])).
% 0.77/0.95 tff(765,plain,
% 0.77/0.95 (~c1_1(a236)),
% 0.77/0.95 inference(unit_resolution,[status(thm)],[764, 747])).
% 0.77/0.95 tff(766,assumption,(c3_1(a232)), introduced(assumption)).
% 0.77/0.95 tff(767,assumption,(c2_1(a232)), introduced(assumption)).
% 0.77/0.95 tff(768,assumption,(c0_1(a232)), introduced(assumption)).
% 0.77/0.95 tff(769,plain,
% 0.77/0.95 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp0 | c1_1(a236) | c2_1(a236) | c3_1(a236) | (~ndr1_0) | (~c2_1(a232)) | (~c3_1(a232)) | (~c0_1(a232)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp0 | c1_1(a236) | c2_1(a236) | c3_1(a236) | (~ndr1_0) | (~c2_1(a232)) | (~c3_1(a232)) | (~c0_1(a232)))),
% 0.77/0.95 inference(rewrite,[status(thm)],[])).
% 0.77/0.95 tff(770,plain,
% 0.77/0.95 ((hskp0 | (~ndr1_0) | (~c2_1(a232)) | (~c0_1(a232)) | (~c3_1(a232)) | c3_1(a236) | c2_1(a236) | c1_1(a236)) <=> (hskp0 | c1_1(a236) | c2_1(a236) | c3_1(a236) | (~ndr1_0) | (~c2_1(a232)) | (~c3_1(a232)) | (~c0_1(a232)))),
% 0.77/0.95 inference(rewrite,[status(thm)],[])).
% 0.77/0.95 tff(771,plain,
% 0.77/0.95 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp0 | (~ndr1_0) | (~c2_1(a232)) | (~c0_1(a232)) | (~c3_1(a232)) | c3_1(a236) | c2_1(a236) | c1_1(a236))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp0 | c1_1(a236) | c2_1(a236) | c3_1(a236) | (~ndr1_0) | (~c2_1(a232)) | (~c3_1(a232)) | (~c0_1(a232))))),
% 0.77/0.95 inference(monotonicity,[status(thm)],[770])).
% 0.77/0.95 tff(772,plain,
% 0.77/0.95 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp0 | (~ndr1_0) | (~c2_1(a232)) | (~c0_1(a232)) | (~c3_1(a232)) | c3_1(a236) | c2_1(a236) | c1_1(a236))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp0 | c1_1(a236) | c2_1(a236) | c3_1(a236) | (~ndr1_0) | (~c2_1(a232)) | (~c3_1(a232)) | (~c0_1(a232)))),
% 0.77/0.95 inference(transitivity,[status(thm)],[771, 769])).
% 0.77/0.95 tff(773,plain,
% 0.77/0.95 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp0 | (~ndr1_0) | (~c2_1(a232)) | (~c0_1(a232)) | (~c3_1(a232)) | c3_1(a236) | c2_1(a236) | c1_1(a236))),
% 0.77/0.95 inference(quant_inst,[status(thm)],[])).
% 0.77/0.95 tff(774,plain,
% 0.77/0.95 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp0 | c1_1(a236) | c2_1(a236) | c3_1(a236) | (~ndr1_0) | (~c2_1(a232)) | (~c3_1(a232)) | (~c0_1(a232))),
% 0.77/0.95 inference(modus_ponens,[status(thm)],[773, 772])).
% 0.77/0.95 tff(775,plain,
% 0.77/0.95 ($false),
% 0.77/0.95 inference(unit_resolution,[status(thm)],[774, 122, 64, 768, 767, 766, 765, 759, 753, 42])).
% 0.77/0.95 tff(776,plain,((~hskp13) | hskp0 | (~c0_1(a232)) | (~c2_1(a232)) | (~c3_1(a232))), inference(lemma,lemma(discharge,[]))).
% 0.77/0.95 tff(777,plain,
% 0.77/0.95 (~hskp13),
% 0.77/0.95 inference(unit_resolution,[status(thm)],[776, 64, 746, 745, 744])).
% 0.77/0.95 tff(778,plain,
% 0.77/0.95 ((hskp13 | hskp11 | hskp10) <=> (hskp13 | hskp11 | hskp10)),
% 0.77/0.95 inference(rewrite,[status(thm)],[])).
% 0.77/0.95 tff(779,plain,
% 0.77/0.95 (((hskp10 | hskp11) | hskp13) <=> (hskp13 | hskp11 | hskp10)),
% 0.77/0.95 inference(rewrite,[status(thm)],[])).
% 0.77/0.95 tff(780,axiom,((hskp10 | hskp11) | hskp13), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause35')).
% 0.77/0.95 tff(781,plain,
% 0.77/0.95 (hskp13 | hskp11 | hskp10),
% 0.77/0.95 inference(modus_ponens,[status(thm)],[780, 779])).
% 0.77/0.95 tff(782,plain,
% 0.77/0.95 (hskp13 | hskp11 | hskp10),
% 0.77/0.95 inference(modus_ponens,[status(thm)],[781, 778])).
% 0.77/0.95 tff(783,plain,
% 0.77/0.95 (hskp13 | hskp11 | hskp10),
% 0.77/0.95 inference(modus_ponens,[status(thm)],[782, 778])).
% 0.77/0.95 tff(784,plain,
% 0.77/0.95 (hskp13 | hskp11 | hskp10),
% 0.77/0.95 inference(modus_ponens,[status(thm)],[783, 778])).
% 0.77/0.95 tff(785,plain,
% 0.77/0.95 (hskp13 | hskp11 | hskp10),
% 0.77/0.95 inference(modus_ponens,[status(thm)],[784, 778])).
% 0.77/0.95 tff(786,plain,
% 0.77/0.95 (hskp11),
% 0.77/0.95 inference(unit_resolution,[status(thm)],[785, 777, 21])).
% 0.77/0.95 tff(787,plain,
% 0.77/0.95 (~c1_1(a230)),
% 0.77/0.95 inference(unit_resolution,[status(thm)],[442, 786])).
% 0.77/0.95 tff(788,plain,
% 0.77/0.95 (c3_1(a230)),
% 0.77/0.95 inference(unit_resolution,[status(thm)],[470, 786])).
% 0.77/0.95 tff(789,plain,
% 0.77/0.95 (c2_1(a230)),
% 0.77/0.95 inference(unit_resolution,[status(thm)],[478, 786])).
% 0.77/0.95 tff(790,assumption,(hskp19), introduced(assumption)).
% 0.77/0.95 tff(791,plain,
% 0.77/0.95 (((~hskp19) | (~c3_1(a252))) <=> ((~hskp19) | (~c3_1(a252)))),
% 0.77/0.95 inference(rewrite,[status(thm)],[])).
% 0.77/0.95 tff(792,plain,
% 0.77/0.95 (((~c3_1(a252)) | (~hskp19)) <=> ((~hskp19) | (~c3_1(a252)))),
% 0.77/0.95 inference(rewrite,[status(thm)],[])).
% 0.77/0.95 tff(793,axiom,((~c3_1(a252)) | (~hskp19)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause91')).
% 0.77/0.95 tff(794,plain,
% 0.77/0.95 ((~hskp19) | (~c3_1(a252))),
% 0.77/0.95 inference(modus_ponens,[status(thm)],[793, 792])).
% 0.77/0.95 tff(795,plain,
% 0.77/0.95 ((~hskp19) | (~c3_1(a252))),
% 0.77/0.95 inference(modus_ponens,[status(thm)],[794, 791])).
% 0.77/0.95 tff(796,plain,
% 0.77/0.95 (~c3_1(a252)),
% 0.77/0.95 inference(unit_resolution,[status(thm)],[795, 790])).
% 0.77/0.95 tff(797,plain,
% 0.77/0.95 (((~hskp19) | (~c2_1(a252))) <=> ((~hskp19) | (~c2_1(a252)))),
% 0.77/0.95 inference(rewrite,[status(thm)],[])).
% 0.77/0.95 tff(798,plain,
% 0.77/0.95 (((~c2_1(a252)) | (~hskp19)) <=> ((~hskp19) | (~c2_1(a252)))),
% 0.77/0.95 inference(rewrite,[status(thm)],[])).
% 0.77/0.95 tff(799,axiom,((~c2_1(a252)) | (~hskp19)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause90')).
% 0.77/0.95 tff(800,plain,
% 0.77/0.95 ((~hskp19) | (~c2_1(a252))),
% 0.77/0.95 inference(modus_ponens,[status(thm)],[799, 798])).
% 0.77/0.95 tff(801,plain,
% 0.77/0.95 ((~hskp19) | (~c2_1(a252))),
% 0.77/0.95 inference(modus_ponens,[status(thm)],[800, 797])).
% 0.77/0.95 tff(802,plain,
% 0.77/0.95 (~c2_1(a252)),
% 0.77/0.95 inference(unit_resolution,[status(thm)],[801, 790])).
% 0.77/0.95 tff(803,plain,
% 0.77/0.95 (((~![U: $i] : (hskp8 | hskp0 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp8 | hskp0 | c2_1(a252) | c3_1(a252) | (~ndr1_0) | c0_1(a252))) <=> ((~![U: $i] : (hskp8 | hskp0 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | hskp8 | hskp0 | c2_1(a252) | c3_1(a252) | (~ndr1_0) | c0_1(a252))),
% 0.77/0.95 inference(rewrite,[status(thm)],[])).
% 0.77/0.95 tff(804,plain,
% 0.77/0.95 ((hskp8 | hskp0 | (~ndr1_0) | c3_1(a252) | c0_1(a252) | c2_1(a252)) <=> (hskp8 | hskp0 | c2_1(a252) | c3_1(a252) | (~ndr1_0) | c0_1(a252))),
% 0.77/0.95 inference(rewrite,[status(thm)],[])).
% 0.77/0.95 tff(805,plain,
% 0.77/0.95 (((~![U: $i] : (hskp8 | hskp0 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp8 | hskp0 | (~ndr1_0) | c3_1(a252) | c0_1(a252) | c2_1(a252))) <=> ((~![U: $i] : (hskp8 | hskp0 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp8 | hskp0 | c2_1(a252) | c3_1(a252) | (~ndr1_0) | c0_1(a252)))),
% 0.77/0.95 inference(monotonicity,[status(thm)],[804])).
% 0.77/0.95 tff(806,plain,
% 0.77/0.95 (((~![U: $i] : (hskp8 | hskp0 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp8 | hskp0 | (~ndr1_0) | c3_1(a252) | c0_1(a252) | c2_1(a252))) <=> ((~![U: $i] : (hskp8 | hskp0 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | hskp8 | hskp0 | c2_1(a252) | c3_1(a252) | (~ndr1_0) | c0_1(a252))),
% 0.77/0.95 inference(transitivity,[status(thm)],[805, 803])).
% 0.77/0.95 tff(807,plain,
% 0.77/0.95 ((~![U: $i] : (hskp8 | hskp0 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp8 | hskp0 | (~ndr1_0) | c3_1(a252) | c0_1(a252) | c2_1(a252))),
% 0.77/0.95 inference(quant_inst,[status(thm)],[])).
% 0.77/0.95 tff(808,plain,
% 0.77/0.95 ((~![U: $i] : (hskp8 | hskp0 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | hskp8 | hskp0 | c2_1(a252) | c3_1(a252) | (~ndr1_0) | c0_1(a252)),
% 0.77/0.95 inference(modus_ponens,[status(thm)],[807, 806])).
% 0.77/0.95 tff(809,plain,
% 0.77/0.95 (c0_1(a252)),
% 0.77/0.95 inference(unit_resolution,[status(thm)],[808, 122, 43, 64, 802, 796, 53])).
% 0.77/0.95 tff(810,plain,
% 0.77/0.95 (((~hskp19) | c1_1(a252)) <=> ((~hskp19) | c1_1(a252))),
% 0.77/0.95 inference(rewrite,[status(thm)],[])).
% 0.77/0.95 tff(811,axiom,((~hskp19) | c1_1(a252)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause52')).
% 0.77/0.95 tff(812,plain,
% 0.77/0.95 ((~hskp19) | c1_1(a252)),
% 0.77/0.95 inference(modus_ponens,[status(thm)],[811, 810])).
% 0.77/0.95 tff(813,plain,
% 0.77/0.95 ((~hskp19) | c1_1(a252)),
% 0.77/0.95 inference(modus_ponens,[status(thm)],[812, 810])).
% 0.77/0.95 tff(814,plain,
% 0.77/0.95 ((~hskp19) | c1_1(a252)),
% 0.77/0.95 inference(modus_ponens,[status(thm)],[813, 810])).
% 0.77/0.95 tff(815,plain,
% 0.77/0.95 ((~hskp19) | c1_1(a252)),
% 0.77/0.95 inference(modus_ponens,[status(thm)],[814, 810])).
% 0.77/0.95 tff(816,plain,
% 0.77/0.95 ((~hskp19) | c1_1(a252)),
% 0.77/0.95 inference(modus_ponens,[status(thm)],[815, 810])).
% 0.77/0.95 tff(817,plain,
% 0.77/0.95 (c1_1(a252)),
% 0.77/0.95 inference(unit_resolution,[status(thm)],[816, 790])).
% 0.77/0.95 tff(818,plain,
% 0.77/0.95 (((~![U: $i] : (hskp8 | hskp3 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp8 | hskp3 | c3_1(a252) | (~ndr1_0) | (~c0_1(a252)) | (~c1_1(a252)))) <=> ((~![U: $i] : (hskp8 | hskp3 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp8 | hskp3 | c3_1(a252) | (~ndr1_0) | (~c0_1(a252)) | (~c1_1(a252)))),
% 0.77/0.95 inference(rewrite,[status(thm)],[])).
% 0.77/0.95 tff(819,plain,
% 0.77/0.95 ((hskp8 | hskp3 | (~ndr1_0) | c3_1(a252) | (~c1_1(a252)) | (~c0_1(a252))) <=> (hskp8 | hskp3 | c3_1(a252) | (~ndr1_0) | (~c0_1(a252)) | (~c1_1(a252)))),
% 0.77/0.95 inference(rewrite,[status(thm)],[])).
% 0.77/0.95 tff(820,plain,
% 0.77/0.95 (((~![U: $i] : (hskp8 | hskp3 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp8 | hskp3 | (~ndr1_0) | c3_1(a252) | (~c1_1(a252)) | (~c0_1(a252)))) <=> ((~![U: $i] : (hskp8 | hskp3 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp8 | hskp3 | c3_1(a252) | (~ndr1_0) | (~c0_1(a252)) | (~c1_1(a252))))),
% 0.77/0.95 inference(monotonicity,[status(thm)],[819])).
% 0.77/0.95 tff(821,plain,
% 0.77/0.95 (((~![U: $i] : (hskp8 | hskp3 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp8 | hskp3 | (~ndr1_0) | c3_1(a252) | (~c1_1(a252)) | (~c0_1(a252)))) <=> ((~![U: $i] : (hskp8 | hskp3 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp8 | hskp3 | c3_1(a252) | (~ndr1_0) | (~c0_1(a252)) | (~c1_1(a252)))),
% 0.77/0.95 inference(transitivity,[status(thm)],[820, 818])).
% 0.77/0.95 tff(822,plain,
% 0.77/0.95 ((~![U: $i] : (hskp8 | hskp3 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp8 | hskp3 | (~ndr1_0) | c3_1(a252) | (~c1_1(a252)) | (~c0_1(a252)))),
% 0.77/0.95 inference(quant_inst,[status(thm)],[])).
% 0.77/0.95 tff(823,plain,
% 0.77/0.95 ((~![U: $i] : (hskp8 | hskp3 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp8 | hskp3 | c3_1(a252) | (~ndr1_0) | (~c0_1(a252)) | (~c1_1(a252))),
% 0.77/0.95 inference(modus_ponens,[status(thm)],[822, 821])).
% 0.77/0.95 tff(824,plain,
% 0.77/0.95 (hskp3 | (~c0_1(a252))),
% 0.77/0.95 inference(unit_resolution,[status(thm)],[823, 122, 43, 817, 796, 348])).
% 0.77/0.95 tff(825,plain,
% 0.77/0.95 (hskp3),
% 0.77/0.95 inference(unit_resolution,[status(thm)],[824, 809])).
% 0.77/0.95 tff(826,plain,
% 0.77/0.95 (~c2_1(a216)),
% 0.77/0.95 inference(unit_resolution,[status(thm)],[312, 825])).
% 0.77/0.95 tff(827,plain,
% 0.77/0.95 (~c0_1(a216)),
% 0.77/0.95 inference(unit_resolution,[status(thm)],[318, 825])).
% 0.77/0.95 tff(828,plain,
% 0.77/0.95 (c3_1(a216)),
% 0.77/0.95 inference(unit_resolution,[status(thm)],[328, 825])).
% 0.77/0.95 tff(829,plain,
% 0.77/0.95 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | (c2_1(a252) | c3_1(a252) | c1_1(a230) | c0_1(a216) | c2_1(a216) | (~ndr1_0) | (~c3_1(a216)) | (~c3_1(a230)) | (~c2_1(a230)) | (~c0_1(a252)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c2_1(a252) | c3_1(a252) | c1_1(a230) | c0_1(a216) | c2_1(a216) | (~ndr1_0) | (~c3_1(a216)) | (~c3_1(a230)) | (~c2_1(a230)) | (~c0_1(a252)))),
% 0.77/0.95 inference(rewrite,[status(thm)],[])).
% 0.77/0.95 tff(830,plain,
% 0.77/0.95 (((~ndr1_0) | c3_1(a252) | c2_1(a252) | (~c0_1(a252)) | c1_1(a230) | (~c3_1(a230)) | (~c2_1(a230)) | c0_1(a216) | c2_1(a216) | (~c3_1(a216))) <=> (c2_1(a252) | c3_1(a252) | c1_1(a230) | c0_1(a216) | c2_1(a216) | (~ndr1_0) | (~c3_1(a216)) | (~c3_1(a230)) | (~c2_1(a230)) | (~c0_1(a252)))),
% 0.77/0.95 inference(rewrite,[status(thm)],[])).
% 0.77/0.95 tff(831,plain,
% 0.77/0.95 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a252) | c2_1(a252) | (~c0_1(a252)) | c1_1(a230) | (~c3_1(a230)) | (~c2_1(a230)) | c0_1(a216) | c2_1(a216) | (~c3_1(a216)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | (c2_1(a252) | c3_1(a252) | c1_1(a230) | c0_1(a216) | c2_1(a216) | (~ndr1_0) | (~c3_1(a216)) | (~c3_1(a230)) | (~c2_1(a230)) | (~c0_1(a252))))),
% 0.77/0.95 inference(monotonicity,[status(thm)],[830])).
% 0.77/0.95 tff(832,plain,
% 0.77/0.95 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a252) | c2_1(a252) | (~c0_1(a252)) | c1_1(a230) | (~c3_1(a230)) | (~c2_1(a230)) | c0_1(a216) | c2_1(a216) | (~c3_1(a216)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c2_1(a252) | c3_1(a252) | c1_1(a230) | c0_1(a216) | c2_1(a216) | (~ndr1_0) | (~c3_1(a216)) | (~c3_1(a230)) | (~c2_1(a230)) | (~c0_1(a252)))),
% 0.77/0.95 inference(transitivity,[status(thm)],[831, 829])).
% 0.77/0.95 tff(833,plain,
% 0.77/0.95 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a252) | c2_1(a252) | (~c0_1(a252)) | c1_1(a230) | (~c3_1(a230)) | (~c2_1(a230)) | c0_1(a216) | c2_1(a216) | (~c3_1(a216)))),
% 0.77/0.95 inference(quant_inst,[status(thm)],[])).
% 0.77/0.95 tff(834,plain,
% 0.77/0.95 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c2_1(a252) | c3_1(a252) | c1_1(a230) | c0_1(a216) | c2_1(a216) | (~ndr1_0) | (~c3_1(a216)) | (~c3_1(a230)) | (~c2_1(a230)) | (~c0_1(a252))),
% 0.77/0.95 inference(modus_ponens,[status(thm)],[833, 832])).
% 0.77/0.95 tff(835,plain,
% 0.77/0.95 ($false),
% 0.77/0.95 inference(unit_resolution,[status(thm)],[834, 122, 566, 565, 828, 802, 796, 559, 827, 826, 10, 809])).
% 0.77/0.95 tff(836,plain,((~hskp19) | (~c2_1(a230)) | (~c3_1(a230)) | c1_1(a230) | hskp8 | hskp0), inference(lemma,lemma(discharge,[]))).
% 0.77/0.95 tff(837,plain,
% 0.77/0.95 (~hskp19),
% 0.77/0.95 inference(unit_resolution,[status(thm)],[836, 789, 788, 787, 43, 64])).
% 0.77/0.95 tff(838,plain,
% 0.77/0.95 (^[V: $i, U: $i] : refl((hskp19 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))) <=> (hskp19 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))))),
% 0.77/0.95 inference(bind,[status(th)],[])).
% 0.77/0.95 tff(839,plain,
% 0.77/0.95 (![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 0.77/0.95 inference(quant_intro,[status(thm)],[838])).
% 0.77/0.95 tff(840,plain,
% 0.77/0.95 (![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 0.77/0.95 inference(rewrite,[status(thm)],[])).
% 0.77/0.95 tff(841,plain,
% 0.77/0.95 (^[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(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(V)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(V))))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c0_1(V)))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c0_1(V))))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c0_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c0_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c0_1(V)))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c0_1(V))))), ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c1_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c0_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c0_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))), ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c1_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c1_1(U)) | c1_1(V)) | hskp19) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))) | hskp19))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))) | hskp19) <=> (hskp19 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c1_1(U)) | c1_1(V)) | hskp19) <=> (hskp19 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))))),
% 0.77/0.95 inference(bind,[status(th)],[])).
% 0.77/0.95 tff(842,plain,
% 0.77/0.95 (![V: $i, U: $i] : ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c1_1(U)) | c1_1(V)) | hskp19) <=> ![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 0.77/0.95 inference(quant_intro,[status(thm)],[841])).
% 0.77/0.95 tff(843,axiom,(![V: $i, U: $i] : ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c1_1(U)) | c1_1(V)) | hskp19)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause164')).
% 0.77/0.95 tff(844,plain,
% 0.77/0.95 (![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 0.77/0.96 inference(modus_ponens,[status(thm)],[843, 842])).
% 0.77/0.96 tff(845,plain,
% 0.77/0.96 (![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 0.77/0.96 inference(modus_ponens,[status(thm)],[844, 840])).
% 0.77/0.96 tff(846,plain,(
% 0.77/0.96 ![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 0.77/0.96 inference(skolemize,[status(sab)],[845])).
% 0.77/0.96 tff(847,plain,
% 0.77/0.96 (![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 0.77/0.96 inference(modus_ponens,[status(thm)],[846, 839])).
% 0.77/0.96 tff(848,plain,
% 0.77/0.96 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp19 | c1_1(a230) | (~ndr1_0) | (~c3_1(a230)) | (~c2_1(a230)) | (~c0_1(a230)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp19 | c1_1(a230) | (~ndr1_0) | (~c3_1(a230)) | (~c2_1(a230)) | (~c0_1(a230)))),
% 0.77/0.96 inference(rewrite,[status(thm)],[])).
% 0.77/0.96 tff(849,plain,
% 0.77/0.96 ((hskp19 | (~ndr1_0) | c1_1(a230) | (~c2_1(a230)) | (~c3_1(a230)) | c1_1(a230) | (~c3_1(a230)) | (~c0_1(a230))) <=> (hskp19 | c1_1(a230) | (~ndr1_0) | (~c3_1(a230)) | (~c2_1(a230)) | (~c0_1(a230)))),
% 0.77/0.96 inference(rewrite,[status(thm)],[])).
% 0.77/0.96 tff(850,plain,
% 0.77/0.96 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp19 | (~ndr1_0) | c1_1(a230) | (~c2_1(a230)) | (~c3_1(a230)) | c1_1(a230) | (~c3_1(a230)) | (~c0_1(a230)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp19 | c1_1(a230) | (~ndr1_0) | (~c3_1(a230)) | (~c2_1(a230)) | (~c0_1(a230))))),
% 0.77/0.96 inference(monotonicity,[status(thm)],[849])).
% 0.77/0.96 tff(851,plain,
% 0.77/0.96 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp19 | (~ndr1_0) | c1_1(a230) | (~c2_1(a230)) | (~c3_1(a230)) | c1_1(a230) | (~c3_1(a230)) | (~c0_1(a230)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp19 | c1_1(a230) | (~ndr1_0) | (~c3_1(a230)) | (~c2_1(a230)) | (~c0_1(a230)))),
% 0.77/0.96 inference(transitivity,[status(thm)],[850, 848])).
% 0.77/0.96 tff(852,plain,
% 0.77/0.96 ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp19 | (~ndr1_0) | c1_1(a230) | (~c2_1(a230)) | (~c3_1(a230)) | c1_1(a230) | (~c3_1(a230)) | (~c0_1(a230)))),
% 0.77/0.96 inference(quant_inst,[status(thm)],[])).
% 0.77/0.96 tff(853,plain,
% 0.77/0.96 ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp19 | c1_1(a230) | (~ndr1_0) | (~c3_1(a230)) | (~c2_1(a230)) | (~c0_1(a230))),
% 0.77/0.96 inference(modus_ponens,[status(thm)],[852, 851])).
% 0.77/0.96 tff(854,plain,
% 0.77/0.96 (hskp19 | (~c0_1(a230))),
% 0.77/0.96 inference(unit_resolution,[status(thm)],[853, 122, 789, 788, 787, 847])).
% 0.77/0.96 tff(855,plain,
% 0.77/0.96 (~c0_1(a230)),
% 0.77/0.96 inference(unit_resolution,[status(thm)],[854, 837])).
% 0.77/0.96 tff(856,assumption,(~c1_1(a232)), introduced(assumption)).
% 0.77/0.96 tff(857,assumption,(~hskp19), introduced(assumption)).
% 0.77/0.96 tff(858,plain,
% 0.77/0.96 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp19 | c1_1(a230) | (~ndr1_0) | c1_1(a232) | (~c3_1(a232)) | (~c0_1(a232)) | (~c3_1(a230)) | (~c2_1(a230)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp19 | c1_1(a230) | (~ndr1_0) | c1_1(a232) | (~c3_1(a232)) | (~c0_1(a232)) | (~c3_1(a230)) | (~c2_1(a230)))),
% 0.77/0.96 inference(rewrite,[status(thm)],[])).
% 0.77/0.96 tff(859,plain,
% 0.77/0.96 ((hskp19 | (~ndr1_0) | c1_1(a230) | (~c2_1(a230)) | (~c3_1(a230)) | c1_1(a232) | (~c3_1(a232)) | (~c0_1(a232))) <=> (hskp19 | c1_1(a230) | (~ndr1_0) | c1_1(a232) | (~c3_1(a232)) | (~c0_1(a232)) | (~c3_1(a230)) | (~c2_1(a230)))),
% 0.77/0.96 inference(rewrite,[status(thm)],[])).
% 0.77/0.96 tff(860,plain,
% 0.77/0.96 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp19 | (~ndr1_0) | c1_1(a230) | (~c2_1(a230)) | (~c3_1(a230)) | c1_1(a232) | (~c3_1(a232)) | (~c0_1(a232)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp19 | c1_1(a230) | (~ndr1_0) | c1_1(a232) | (~c3_1(a232)) | (~c0_1(a232)) | (~c3_1(a230)) | (~c2_1(a230))))),
% 0.77/0.96 inference(monotonicity,[status(thm)],[859])).
% 0.77/0.96 tff(861,plain,
% 0.77/0.96 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp19 | (~ndr1_0) | c1_1(a230) | (~c2_1(a230)) | (~c3_1(a230)) | c1_1(a232) | (~c3_1(a232)) | (~c0_1(a232)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp19 | c1_1(a230) | (~ndr1_0) | c1_1(a232) | (~c3_1(a232)) | (~c0_1(a232)) | (~c3_1(a230)) | (~c2_1(a230)))),
% 0.77/0.96 inference(transitivity,[status(thm)],[860, 858])).
% 0.77/0.96 tff(862,plain,
% 0.77/0.96 ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp19 | (~ndr1_0) | c1_1(a230) | (~c2_1(a230)) | (~c3_1(a230)) | c1_1(a232) | (~c3_1(a232)) | (~c0_1(a232)))),
% 0.77/0.96 inference(quant_inst,[status(thm)],[])).
% 0.77/0.96 tff(863,plain,
% 0.77/0.96 ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp19 | c1_1(a230) | (~ndr1_0) | c1_1(a232) | (~c3_1(a232)) | (~c0_1(a232)) | (~c3_1(a230)) | (~c2_1(a230))),
% 0.77/0.96 inference(modus_ponens,[status(thm)],[862, 861])).
% 0.77/0.96 tff(864,plain,
% 0.77/0.96 ($false),
% 0.77/0.96 inference(unit_resolution,[status(thm)],[863, 122, 857, 768, 766, 566, 565, 559, 847, 856])).
% 0.77/0.96 tff(865,plain,(c1_1(a232) | hskp19 | (~c0_1(a232)) | (~c3_1(a232)) | (~c2_1(a230)) | (~c3_1(a230)) | c1_1(a230)), inference(lemma,lemma(discharge,[]))).
% 0.77/0.96 tff(866,plain,
% 0.77/0.96 (c1_1(a232)),
% 0.77/0.96 inference(unit_resolution,[status(thm)],[865, 837, 787, 744, 789, 788, 746])).
% 0.77/0.96 tff(867,plain,
% 0.77/0.96 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (c1_1(a230) | (~ndr1_0) | (~c1_1(a232)) | (~c3_1(a232)) | (~c0_1(a232)) | (~c3_1(a230)) | c0_1(a230))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | c1_1(a230) | (~ndr1_0) | (~c1_1(a232)) | (~c3_1(a232)) | (~c0_1(a232)) | (~c3_1(a230)) | c0_1(a230))),
% 0.77/0.96 inference(rewrite,[status(thm)],[])).
% 0.77/0.96 tff(868,plain,
% 0.77/0.96 (((~ndr1_0) | (~c1_1(a232)) | (~c0_1(a232)) | (~c3_1(a232)) | c0_1(a230) | c1_1(a230) | (~c3_1(a230))) <=> (c1_1(a230) | (~ndr1_0) | (~c1_1(a232)) | (~c3_1(a232)) | (~c0_1(a232)) | (~c3_1(a230)) | c0_1(a230))),
% 0.77/0.96 inference(rewrite,[status(thm)],[])).
% 0.77/0.96 tff(869,plain,
% 0.77/0.96 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | ((~ndr1_0) | (~c1_1(a232)) | (~c0_1(a232)) | (~c3_1(a232)) | c0_1(a230) | c1_1(a230) | (~c3_1(a230)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (c1_1(a230) | (~ndr1_0) | (~c1_1(a232)) | (~c3_1(a232)) | (~c0_1(a232)) | (~c3_1(a230)) | c0_1(a230)))),
% 0.77/0.96 inference(monotonicity,[status(thm)],[868])).
% 0.77/0.96 tff(870,plain,
% 0.77/0.96 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | ((~ndr1_0) | (~c1_1(a232)) | (~c0_1(a232)) | (~c3_1(a232)) | c0_1(a230) | c1_1(a230) | (~c3_1(a230)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | c1_1(a230) | (~ndr1_0) | (~c1_1(a232)) | (~c3_1(a232)) | (~c0_1(a232)) | (~c3_1(a230)) | c0_1(a230))),
% 0.77/0.96 inference(transitivity,[status(thm)],[869, 867])).
% 0.77/0.96 tff(871,plain,
% 0.77/0.96 ((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | ((~ndr1_0) | (~c1_1(a232)) | (~c0_1(a232)) | (~c3_1(a232)) | c0_1(a230) | c1_1(a230) | (~c3_1(a230)))),
% 0.77/0.96 inference(quant_inst,[status(thm)],[])).
% 0.77/0.96 tff(872,plain,
% 0.77/0.96 ((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | c1_1(a230) | (~ndr1_0) | (~c1_1(a232)) | (~c3_1(a232)) | (~c0_1(a232)) | (~c3_1(a230)) | c0_1(a230)),
% 0.77/0.96 inference(modus_ponens,[status(thm)],[871, 870])).
% 0.77/0.96 tff(873,plain,
% 0.77/0.96 ($false),
% 0.77/0.96 inference(unit_resolution,[status(thm)],[872, 122, 746, 744, 788, 787, 583, 866, 855])).
% 0.77/0.96 tff(874,plain,(hskp0 | hskp8 | hskp10), inference(lemma,lemma(discharge,[]))).
% 0.77/0.96 tff(875,plain,
% 0.77/0.96 (hskp0),
% 0.77/0.96 inference(unit_resolution,[status(thm)],[874, 21, 43])).
% 0.77/0.96 tff(876,plain,
% 0.77/0.96 (~c2_1(a213)),
% 0.77/0.96 inference(unit_resolution,[status(thm)],[278, 875])).
% 0.77/0.96 tff(877,plain,
% 0.77/0.96 (c1_1(a213)),
% 0.77/0.96 inference(unit_resolution,[status(thm)],[294, 875])).
% 0.77/0.96 tff(878,plain,
% 0.77/0.96 (hskp11 | c0_1(a213)),
% 0.77/0.96 inference(unit_resolution,[status(thm)],[388, 122, 21, 877, 876, 32])).
% 0.77/0.96 tff(879,plain,
% 0.77/0.96 (c0_1(a213)),
% 0.77/0.96 inference(unit_resolution,[status(thm)],[878, 382])).
% 0.77/0.96 tff(880,plain,
% 0.77/0.96 (hskp20),
% 0.77/0.96 inference(unit_resolution,[status(thm)],[436, 382, 21, 877, 876])).
% 0.77/0.96 tff(881,plain,
% 0.77/0.96 (hskp3),
% 0.77/0.96 inference(unit_resolution,[status(thm)],[380, 880, 43])).
% 0.77/0.96 tff(882,plain,
% 0.77/0.96 (~c0_1(a216)),
% 0.77/0.96 inference(unit_resolution,[status(thm)],[318, 881])).
% 0.77/0.96 tff(883,plain,
% 0.77/0.96 (c3_1(a213)),
% 0.77/0.96 inference(unit_resolution,[status(thm)],[286, 875])).
% 0.77/0.96 tff(884,plain,
% 0.77/0.96 (c3_1(a216)),
% 0.77/0.96 inference(unit_resolution,[status(thm)],[328, 881])).
% 0.77/0.96 tff(885,plain,
% 0.77/0.96 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (c0_1(a216) | (~ndr1_0) | (~c1_1(a213)) | (~c3_1(a213)) | (~c0_1(a213)) | c1_1(a216) | (~c3_1(a216)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | c0_1(a216) | (~ndr1_0) | (~c1_1(a213)) | (~c3_1(a213)) | (~c0_1(a213)) | c1_1(a216) | (~c3_1(a216)))),
% 0.77/0.96 inference(rewrite,[status(thm)],[])).
% 0.77/0.96 tff(886,plain,
% 0.77/0.96 (((~ndr1_0) | (~c1_1(a213)) | (~c0_1(a213)) | (~c3_1(a213)) | c0_1(a216) | c1_1(a216) | (~c3_1(a216))) <=> (c0_1(a216) | (~ndr1_0) | (~c1_1(a213)) | (~c3_1(a213)) | (~c0_1(a213)) | c1_1(a216) | (~c3_1(a216)))),
% 0.77/0.96 inference(rewrite,[status(thm)],[])).
% 0.77/0.96 tff(887,plain,
% 0.77/0.96 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | ((~ndr1_0) | (~c1_1(a213)) | (~c0_1(a213)) | (~c3_1(a213)) | c0_1(a216) | c1_1(a216) | (~c3_1(a216)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (c0_1(a216) | (~ndr1_0) | (~c1_1(a213)) | (~c3_1(a213)) | (~c0_1(a213)) | c1_1(a216) | (~c3_1(a216))))),
% 0.77/0.96 inference(monotonicity,[status(thm)],[886])).
% 0.77/0.96 tff(888,plain,
% 0.77/0.96 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | ((~ndr1_0) | (~c1_1(a213)) | (~c0_1(a213)) | (~c3_1(a213)) | c0_1(a216) | c1_1(a216) | (~c3_1(a216)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | c0_1(a216) | (~ndr1_0) | (~c1_1(a213)) | (~c3_1(a213)) | (~c0_1(a213)) | c1_1(a216) | (~c3_1(a216)))),
% 0.77/0.96 inference(transitivity,[status(thm)],[887, 885])).
% 0.77/0.96 tff(889,plain,
% 0.77/0.96 ((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | ((~ndr1_0) | (~c1_1(a213)) | (~c0_1(a213)) | (~c3_1(a213)) | c0_1(a216) | c1_1(a216) | (~c3_1(a216)))),
% 0.77/0.96 inference(quant_inst,[status(thm)],[])).
% 0.77/0.96 tff(890,plain,
% 0.77/0.96 ((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | c0_1(a216) | (~ndr1_0) | (~c1_1(a213)) | (~c3_1(a213)) | (~c0_1(a213)) | c1_1(a216) | (~c3_1(a216))),
% 0.77/0.96 inference(modus_ponens,[status(thm)],[889, 888])).
% 0.77/0.96 tff(891,plain,
% 0.77/0.96 (c1_1(a216)),
% 0.77/0.96 inference(unit_resolution,[status(thm)],[890, 122, 884, 877, 883, 882, 583, 879])).
% 0.77/0.96 tff(892,plain,
% 0.77/0.96 (~c2_1(a216)),
% 0.77/0.96 inference(unit_resolution,[status(thm)],[312, 881])).
% 0.77/0.96 tff(893,plain,
% 0.77/0.96 (((~![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp11 | hskp10 | c0_1(a216) | c2_1(a216) | (~ndr1_0) | (~c1_1(a216)))) <=> ((~![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | hskp11 | hskp10 | c0_1(a216) | c2_1(a216) | (~ndr1_0) | (~c1_1(a216)))),
% 0.77/0.96 inference(rewrite,[status(thm)],[])).
% 0.77/0.96 tff(894,plain,
% 0.77/0.96 ((hskp11 | hskp10 | (~ndr1_0) | c0_1(a216) | c2_1(a216) | (~c1_1(a216))) <=> (hskp11 | hskp10 | c0_1(a216) | c2_1(a216) | (~ndr1_0) | (~c1_1(a216)))),
% 0.77/0.96 inference(rewrite,[status(thm)],[])).
% 0.77/0.96 tff(895,plain,
% 0.77/0.96 (((~![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp11 | hskp10 | (~ndr1_0) | c0_1(a216) | c2_1(a216) | (~c1_1(a216)))) <=> ((~![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp11 | hskp10 | c0_1(a216) | c2_1(a216) | (~ndr1_0) | (~c1_1(a216))))),
% 0.77/0.96 inference(monotonicity,[status(thm)],[894])).
% 0.77/0.96 tff(896,plain,
% 0.77/0.96 (((~![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp11 | hskp10 | (~ndr1_0) | c0_1(a216) | c2_1(a216) | (~c1_1(a216)))) <=> ((~![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | hskp11 | hskp10 | c0_1(a216) | c2_1(a216) | (~ndr1_0) | (~c1_1(a216)))),
% 0.77/0.96 inference(transitivity,[status(thm)],[895, 893])).
% 0.77/0.96 tff(897,plain,
% 0.77/0.96 ((~![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp11 | hskp10 | (~ndr1_0) | c0_1(a216) | c2_1(a216) | (~c1_1(a216)))),
% 0.77/0.96 inference(quant_inst,[status(thm)],[])).
% 0.77/0.96 tff(898,plain,
% 0.77/0.96 ((~![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | hskp11 | hskp10 | c0_1(a216) | c2_1(a216) | (~ndr1_0) | (~c1_1(a216))),
% 0.77/0.96 inference(modus_ponens,[status(thm)],[897, 896])).
% 0.77/0.96 tff(899,plain,
% 0.77/0.96 ($false),
% 0.77/0.96 inference(unit_resolution,[status(thm)],[898, 122, 382, 21, 882, 892, 32, 891])).
% 0.77/0.96 tff(900,plain,(hskp11 | hskp10 | hskp8), inference(lemma,lemma(discharge,[]))).
% 0.77/0.96 tff(901,plain,
% 0.77/0.96 (hskp11),
% 0.77/0.96 inference(unit_resolution,[status(thm)],[900, 21, 43])).
% 0.77/0.96 tff(902,plain,
% 0.77/0.96 (~c1_1(a230)),
% 0.77/0.96 inference(unit_resolution,[status(thm)],[442, 901])).
% 0.77/0.96 tff(903,plain,
% 0.77/0.96 (c3_1(a230)),
% 0.77/0.96 inference(unit_resolution,[status(thm)],[470, 901])).
% 0.77/0.96 tff(904,plain,
% 0.77/0.96 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c1_1(a282) | c3_1(a282) | c1_1(a230) | c2_1(a213) | (~ndr1_0) | (~c1_1(a213)) | (~c3_1(a213)) | (~c3_1(a230)) | c0_1(a230) | (~c2_1(a282)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c1_1(a282) | c3_1(a282) | c1_1(a230) | c2_1(a213) | (~ndr1_0) | (~c1_1(a213)) | (~c3_1(a213)) | (~c3_1(a230)) | c0_1(a230) | (~c2_1(a282)))),
% 0.77/0.96 inference(rewrite,[status(thm)],[])).
% 0.77/0.96 tff(905,plain,
% 0.77/0.96 (((~ndr1_0) | c2_1(a213) | (~c1_1(a213)) | (~c3_1(a213)) | c3_1(a282) | c1_1(a282) | (~c2_1(a282)) | c1_1(a230) | c0_1(a230) | (~c3_1(a230))) <=> (c1_1(a282) | c3_1(a282) | c1_1(a230) | c2_1(a213) | (~ndr1_0) | (~c1_1(a213)) | (~c3_1(a213)) | (~c3_1(a230)) | c0_1(a230) | (~c2_1(a282)))),
% 0.77/0.96 inference(rewrite,[status(thm)],[])).
% 0.77/0.96 tff(906,plain,
% 0.77/0.96 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a213) | (~c1_1(a213)) | (~c3_1(a213)) | c3_1(a282) | c1_1(a282) | (~c2_1(a282)) | c1_1(a230) | c0_1(a230) | (~c3_1(a230)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c1_1(a282) | c3_1(a282) | c1_1(a230) | c2_1(a213) | (~ndr1_0) | (~c1_1(a213)) | (~c3_1(a213)) | (~c3_1(a230)) | c0_1(a230) | (~c2_1(a282))))),
% 0.77/0.96 inference(monotonicity,[status(thm)],[905])).
% 0.77/0.96 tff(907,plain,
% 0.77/0.96 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a213) | (~c1_1(a213)) | (~c3_1(a213)) | c3_1(a282) | c1_1(a282) | (~c2_1(a282)) | c1_1(a230) | c0_1(a230) | (~c3_1(a230)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c1_1(a282) | c3_1(a282) | c1_1(a230) | c2_1(a213) | (~ndr1_0) | (~c1_1(a213)) | (~c3_1(a213)) | (~c3_1(a230)) | c0_1(a230) | (~c2_1(a282)))),
% 0.77/0.96 inference(transitivity,[status(thm)],[906, 904])).
% 0.77/0.96 tff(908,plain,
% 0.77/0.96 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a213) | (~c1_1(a213)) | (~c3_1(a213)) | c3_1(a282) | c1_1(a282) | (~c2_1(a282)) | c1_1(a230) | c0_1(a230) | (~c3_1(a230)))),
% 0.77/0.96 inference(quant_inst,[status(thm)],[])).
% 0.77/0.96 tff(909,plain,
% 0.77/0.96 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c1_1(a282) | c3_1(a282) | c1_1(a230) | c2_1(a213) | (~ndr1_0) | (~c1_1(a213)) | (~c3_1(a213)) | (~c3_1(a230)) | c0_1(a230) | (~c2_1(a282))),
% 0.77/0.96 inference(modus_ponens,[status(thm)],[908, 907])).
% 0.77/0.96 tff(910,plain,
% 0.77/0.96 (c0_1(a230)),
% 0.77/0.96 inference(unit_resolution,[status(thm)],[909, 122, 903, 877, 883, 179, 173, 902, 876, 735, 725])).
% 0.77/0.96 tff(911,plain,
% 0.77/0.96 (c2_1(a230)),
% 0.77/0.96 inference(unit_resolution,[status(thm)],[478, 901])).
% 0.77/0.96 tff(912,plain,
% 0.77/0.96 (hskp19),
% 0.77/0.96 inference(unit_resolution,[status(thm)],[853, 122, 911, 903, 902, 847, 910])).
% 0.77/0.96 tff(913,plain,
% 0.77/0.96 (~c3_1(a252)),
% 0.77/0.96 inference(unit_resolution,[status(thm)],[795, 912])).
% 0.77/0.96 tff(914,plain,
% 0.77/0.96 (~c2_1(a252)),
% 0.77/0.96 inference(unit_resolution,[status(thm)],[801, 912])).
% 0.77/0.96 tff(915,plain,
% 0.77/0.96 (c1_1(a252)),
% 0.77/0.96 inference(unit_resolution,[status(thm)],[816, 912])).
% 0.77/0.96 tff(916,assumption,(~c3_1(a252)), introduced(assumption)).
% 0.77/0.96 tff(917,assumption,(c1_1(a252)), introduced(assumption)).
% 0.77/0.96 tff(918,plain,
% 0.77/0.96 (hskp3 | (~c0_1(a252))),
% 0.77/0.96 inference(unit_resolution,[status(thm)],[823, 122, 43, 917, 916, 348])).
% 0.77/0.96 tff(919,plain,
% 0.77/0.96 (~c0_1(a252)),
% 0.77/0.96 inference(unit_resolution,[status(thm)],[918, 372])).
% 0.77/0.96 tff(920,plain,
% 0.77/0.96 (^[V: $i, U: $i] : refl((hskp3 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V))) <=> (hskp3 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V))))),
% 0.77/0.96 inference(bind,[status(th)],[])).
% 0.77/0.96 tff(921,plain,
% 0.77/0.96 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))),
% 0.77/0.96 inference(quant_intro,[status(thm)],[920])).
% 0.77/0.96 tff(922,plain,
% 0.77/0.96 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))),
% 0.77/0.96 inference(rewrite,[status(thm)],[])).
% 0.77/0.96 tff(923,plain,
% 0.77/0.96 (^[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)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c1_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(V)))), ((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(V))))), (((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(V))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(V))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(V)))), (((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(V))))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | (~c3_1(V)))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | (~c3_1(V))))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c2_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | (~c3_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V))))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V))))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | hskp3) <=> (((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V))) | hskp3))), rewrite((((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V))) | hskp3) <=> (hskp3 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | hskp3) <=> (hskp3 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))))),
% 0.77/0.96 inference(bind,[status(th)],[])).
% 0.77/0.96 tff(924,plain,
% 0.77/0.96 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | hskp3) <=> ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))),
% 0.77/0.96 inference(quant_intro,[status(thm)],[923])).
% 0.77/0.96 tff(925,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | hskp3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause145')).
% 0.77/0.96 tff(926,plain,
% 0.77/0.96 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))),
% 0.77/0.96 inference(modus_ponens,[status(thm)],[925, 924])).
% 0.77/0.96 tff(927,plain,
% 0.77/0.96 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))),
% 0.77/0.96 inference(modus_ponens,[status(thm)],[926, 922])).
% 0.77/0.96 tff(928,plain,(
% 0.77/0.96 ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))),
% 0.77/0.96 inference(skolemize,[status(sab)],[927])).
% 0.77/0.96 tff(929,plain,
% 0.77/0.96 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))),
% 0.77/0.96 inference(modus_ponens,[status(thm)],[928, 921])).
% 0.77/0.96 tff(930,plain,
% 0.77/0.96 (~hskp20),
% 0.77/0.96 inference(unit_resolution,[status(thm)],[380, 372, 43])).
% 0.77/0.96 tff(931,plain,
% 0.77/0.96 (((~![U: $i] : (hskp20 | hskp13 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp20 | hskp13 | c2_1(a213) | (~ndr1_0) | (~c1_1(a213)) | (~c3_1(a213)))) <=> ((~![U: $i] : (hskp20 | hskp13 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | hskp20 | hskp13 | c2_1(a213) | (~ndr1_0) | (~c1_1(a213)) | (~c3_1(a213)))),
% 0.77/0.96 inference(rewrite,[status(thm)],[])).
% 0.77/0.96 tff(932,plain,
% 0.77/0.96 ((hskp20 | hskp13 | (~ndr1_0) | c2_1(a213) | (~c1_1(a213)) | (~c3_1(a213))) <=> (hskp20 | hskp13 | c2_1(a213) | (~ndr1_0) | (~c1_1(a213)) | (~c3_1(a213)))),
% 0.77/0.96 inference(rewrite,[status(thm)],[])).
% 0.77/0.96 tff(933,plain,
% 0.77/0.96 (((~![U: $i] : (hskp20 | hskp13 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp20 | hskp13 | (~ndr1_0) | c2_1(a213) | (~c1_1(a213)) | (~c3_1(a213)))) <=> ((~![U: $i] : (hskp20 | hskp13 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp20 | hskp13 | c2_1(a213) | (~ndr1_0) | (~c1_1(a213)) | (~c3_1(a213))))),
% 0.77/0.96 inference(monotonicity,[status(thm)],[932])).
% 0.77/0.96 tff(934,plain,
% 0.77/0.96 (((~![U: $i] : (hskp20 | hskp13 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp20 | hskp13 | (~ndr1_0) | c2_1(a213) | (~c1_1(a213)) | (~c3_1(a213)))) <=> ((~![U: $i] : (hskp20 | hskp13 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | hskp20 | hskp13 | c2_1(a213) | (~ndr1_0) | (~c1_1(a213)) | (~c3_1(a213)))),
% 0.77/0.96 inference(transitivity,[status(thm)],[933, 931])).
% 0.77/0.96 tff(935,plain,
% 0.77/0.96 ((~![U: $i] : (hskp20 | hskp13 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp20 | hskp13 | (~ndr1_0) | c2_1(a213) | (~c1_1(a213)) | (~c3_1(a213)))),
% 0.77/0.96 inference(quant_inst,[status(thm)],[])).
% 0.77/0.96 tff(936,plain,
% 0.77/0.96 ((~![U: $i] : (hskp20 | hskp13 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | hskp20 | hskp13 | c2_1(a213) | (~ndr1_0) | (~c1_1(a213)) | (~c3_1(a213))),
% 0.77/0.96 inference(modus_ponens,[status(thm)],[935, 934])).
% 0.77/0.96 tff(937,plain,
% 0.77/0.96 (hskp20 | hskp13),
% 0.77/0.96 inference(unit_resolution,[status(thm)],[936, 122, 321, 320, 306, 74])).
% 0.77/0.96 tff(938,plain,
% 0.77/0.96 (hskp13),
% 0.77/0.96 inference(unit_resolution,[status(thm)],[937, 930])).
% 0.77/0.96 tff(939,plain,
% 0.77/0.96 (~c3_1(a236)),
% 0.77/0.96 inference(unit_resolution,[status(thm)],[752, 938])).
% 0.77/0.96 tff(940,plain,
% 0.77/0.96 (~c2_1(a236)),
% 0.77/0.96 inference(unit_resolution,[status(thm)],[758, 938])).
% 0.77/0.96 tff(941,plain,
% 0.77/0.96 (~c1_1(a236)),
% 0.77/0.96 inference(unit_resolution,[status(thm)],[764, 938])).
% 0.77/0.96 tff(942,plain,
% 0.77/0.96 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp17 | c1_1(a236) | c2_1(a236) | c3_1(a236) | (~ndr1_0) | (~c2_1(a232)) | (~c3_1(a232)) | (~c0_1(a232)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp17 | c1_1(a236) | c2_1(a236) | c3_1(a236) | (~ndr1_0) | (~c2_1(a232)) | (~c3_1(a232)) | (~c0_1(a232)))),
% 0.77/0.96 inference(rewrite,[status(thm)],[])).
% 0.77/0.96 tff(943,plain,
% 0.77/0.96 ((hskp17 | (~ndr1_0) | (~c2_1(a232)) | (~c0_1(a232)) | (~c3_1(a232)) | c3_1(a236) | c2_1(a236) | c1_1(a236)) <=> (hskp17 | c1_1(a236) | c2_1(a236) | c3_1(a236) | (~ndr1_0) | (~c2_1(a232)) | (~c3_1(a232)) | (~c0_1(a232)))),
% 0.77/0.96 inference(rewrite,[status(thm)],[])).
% 0.77/0.96 tff(944,plain,
% 0.77/0.96 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp17 | (~ndr1_0) | (~c2_1(a232)) | (~c0_1(a232)) | (~c3_1(a232)) | c3_1(a236) | c2_1(a236) | c1_1(a236))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp17 | c1_1(a236) | c2_1(a236) | c3_1(a236) | (~ndr1_0) | (~c2_1(a232)) | (~c3_1(a232)) | (~c0_1(a232))))),
% 0.77/0.96 inference(monotonicity,[status(thm)],[943])).
% 0.77/0.96 tff(945,plain,
% 0.77/0.96 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp17 | (~ndr1_0) | (~c2_1(a232)) | (~c0_1(a232)) | (~c3_1(a232)) | c3_1(a236) | c2_1(a236) | c1_1(a236))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp17 | c1_1(a236) | c2_1(a236) | c3_1(a236) | (~ndr1_0) | (~c2_1(a232)) | (~c3_1(a232)) | (~c0_1(a232)))),
% 0.77/0.96 inference(transitivity,[status(thm)],[944, 942])).
% 0.77/0.96 tff(946,plain,
% 0.77/0.96 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp17 | (~ndr1_0) | (~c2_1(a232)) | (~c0_1(a232)) | (~c3_1(a232)) | c3_1(a236) | c2_1(a236) | c1_1(a236))),
% 0.77/0.96 inference(quant_inst,[status(thm)],[])).
% 0.77/0.96 tff(947,plain,
% 0.77/0.96 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp17 | c1_1(a236) | c2_1(a236) | c3_1(a236) | (~ndr1_0) | (~c2_1(a232)) | (~c3_1(a232)) | (~c0_1(a232))),
% 0.77/0.96 inference(modus_ponens,[status(thm)],[946, 945])).
% 0.77/0.96 tff(948,plain,
% 0.77/0.96 (hskp17),
% 0.77/0.96 inference(unit_resolution,[status(thm)],[947, 122, 768, 767, 766, 941, 940, 939, 453])).
% 0.77/0.96 tff(949,plain,
% 0.77/0.96 (~c1_1(a243)),
% 0.77/0.96 inference(unit_resolution,[status(thm)],[530, 948])).
% 0.77/0.96 tff(950,plain,
% 0.77/0.96 (~c0_1(a243)),
% 0.77/0.96 inference(unit_resolution,[status(thm)],[507, 948])).
% 0.77/0.96 tff(951,assumption,(~c2_1(a252)), introduced(assumption)).
% 0.77/0.96 tff(952,plain,
% 0.77/0.96 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp3 | c2_1(a252) | c0_1(a243) | c1_1(a243) | (~ndr1_0) | (~c3_1(a243)) | c0_1(a252) | (~c1_1(a252)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp3 | c2_1(a252) | c0_1(a243) | c1_1(a243) | (~ndr1_0) | (~c3_1(a243)) | c0_1(a252) | (~c1_1(a252)))),
% 0.77/0.96 inference(rewrite,[status(thm)],[])).
% 0.77/0.96 tff(953,plain,
% 0.77/0.96 ((hskp3 | (~ndr1_0) | c0_1(a252) | c2_1(a252) | (~c1_1(a252)) | c0_1(a243) | c1_1(a243) | (~c3_1(a243))) <=> (hskp3 | c2_1(a252) | c0_1(a243) | c1_1(a243) | (~ndr1_0) | (~c3_1(a243)) | c0_1(a252) | (~c1_1(a252)))),
% 0.77/0.96 inference(rewrite,[status(thm)],[])).
% 0.77/0.96 tff(954,plain,
% 0.77/0.96 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp3 | (~ndr1_0) | c0_1(a252) | c2_1(a252) | (~c1_1(a252)) | c0_1(a243) | c1_1(a243) | (~c3_1(a243)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp3 | c2_1(a252) | c0_1(a243) | c1_1(a243) | (~ndr1_0) | (~c3_1(a243)) | c0_1(a252) | (~c1_1(a252))))),
% 0.77/0.96 inference(monotonicity,[status(thm)],[953])).
% 0.77/0.96 tff(955,plain,
% 0.77/0.96 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp3 | (~ndr1_0) | c0_1(a252) | c2_1(a252) | (~c1_1(a252)) | c0_1(a243) | c1_1(a243) | (~c3_1(a243)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp3 | c2_1(a252) | c0_1(a243) | c1_1(a243) | (~ndr1_0) | (~c3_1(a243)) | c0_1(a252) | (~c1_1(a252)))),
% 0.77/0.96 inference(transitivity,[status(thm)],[954, 952])).
% 0.77/0.96 tff(956,plain,
% 0.77/0.96 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp3 | (~ndr1_0) | c0_1(a252) | c2_1(a252) | (~c1_1(a252)) | c0_1(a243) | c1_1(a243) | (~c3_1(a243)))),
% 0.77/0.96 inference(quant_inst,[status(thm)],[])).
% 0.77/0.96 tff(957,plain,
% 0.77/0.96 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp3 | c2_1(a252) | c0_1(a243) | c1_1(a243) | (~ndr1_0) | (~c3_1(a243)) | c0_1(a252) | (~c1_1(a252))),
% 0.77/0.96 inference(modus_ponens,[status(thm)],[956, 955])).
% 0.77/0.96 tff(958,plain,
% 0.77/0.96 (~c3_1(a243)),
% 0.77/0.96 inference(unit_resolution,[status(thm)],[957, 122, 372, 917, 951, 950, 949, 929, 919])).
% 0.77/0.96 tff(959,plain,
% 0.77/0.96 (hskp2),
% 0.77/0.96 inference(unit_resolution,[status(thm)],[537, 122, 372, 950, 949, 525, 958])).
% 0.77/0.96 tff(960,plain,
% 0.77/0.96 (~c1_1(a215)),
% 0.77/0.96 inference(unit_resolution,[status(thm)],[543, 959])).
% 0.77/0.96 tff(961,plain,
% 0.77/0.96 (~c0_1(a215)),
% 0.77/0.96 inference(unit_resolution,[status(thm)],[549, 959])).
% 0.77/0.96 tff(962,plain,
% 0.77/0.96 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp3 | c2_1(a252) | c0_1(a215) | c1_1(a215) | (~ndr1_0) | (~c3_1(a215)) | c0_1(a252) | (~c1_1(a252)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp3 | c2_1(a252) | c0_1(a215) | c1_1(a215) | (~ndr1_0) | (~c3_1(a215)) | c0_1(a252) | (~c1_1(a252)))),
% 0.77/0.96 inference(rewrite,[status(thm)],[])).
% 0.77/0.96 tff(963,plain,
% 0.77/0.96 ((hskp3 | (~ndr1_0) | c0_1(a252) | c2_1(a252) | (~c1_1(a252)) | c0_1(a215) | c1_1(a215) | (~c3_1(a215))) <=> (hskp3 | c2_1(a252) | c0_1(a215) | c1_1(a215) | (~ndr1_0) | (~c3_1(a215)) | c0_1(a252) | (~c1_1(a252)))),
% 0.77/0.96 inference(rewrite,[status(thm)],[])).
% 0.77/0.96 tff(964,plain,
% 0.77/0.96 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp3 | (~ndr1_0) | c0_1(a252) | c2_1(a252) | (~c1_1(a252)) | c0_1(a215) | c1_1(a215) | (~c3_1(a215)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp3 | c2_1(a252) | c0_1(a215) | c1_1(a215) | (~ndr1_0) | (~c3_1(a215)) | c0_1(a252) | (~c1_1(a252))))),
% 0.77/0.96 inference(monotonicity,[status(thm)],[963])).
% 0.77/0.96 tff(965,plain,
% 0.77/0.96 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp3 | (~ndr1_0) | c0_1(a252) | c2_1(a252) | (~c1_1(a252)) | c0_1(a215) | c1_1(a215) | (~c3_1(a215)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp3 | c2_1(a252) | c0_1(a215) | c1_1(a215) | (~ndr1_0) | (~c3_1(a215)) | c0_1(a252) | (~c1_1(a252)))),
% 0.77/0.97 inference(transitivity,[status(thm)],[964, 962])).
% 0.77/0.97 tff(966,plain,
% 0.77/0.97 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp3 | (~ndr1_0) | c0_1(a252) | c2_1(a252) | (~c1_1(a252)) | c0_1(a215) | c1_1(a215) | (~c3_1(a215)))),
% 0.77/0.97 inference(quant_inst,[status(thm)],[])).
% 0.77/0.97 tff(967,plain,
% 0.77/0.97 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp3 | c2_1(a252) | c0_1(a215) | c1_1(a215) | (~ndr1_0) | (~c3_1(a215)) | c0_1(a252) | (~c1_1(a252))),
% 0.77/0.97 inference(modus_ponens,[status(thm)],[966, 965])).
% 0.77/0.97 tff(968,plain,
% 0.77/0.97 (~c3_1(a215)),
% 0.77/0.97 inference(unit_resolution,[status(thm)],[967, 122, 372, 917, 951, 961, 960, 929, 919])).
% 0.77/0.97 tff(969,plain,
% 0.77/0.97 (~c2_1(a243)),
% 0.77/0.97 inference(unit_resolution,[status(thm)],[501, 948])).
% 0.77/0.97 tff(970,plain,
% 0.77/0.97 (c2_1(a215)),
% 0.77/0.97 inference(unit_resolution,[status(thm)],[557, 959])).
% 0.77/0.97 tff(971,plain,
% 0.77/0.97 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c0_1(W) | c2_1(W) | c3_1(W))) | (c0_1(a243) | c2_1(a243) | c0_1(a215) | (~ndr1_0) | (~c2_1(a215)) | c3_1(a215) | (~c2_1(a232)) | (~c3_1(a232)) | (~c0_1(a232)) | c3_1(a243))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c0_1(W) | c2_1(W) | c3_1(W))) | c0_1(a243) | c2_1(a243) | c0_1(a215) | (~ndr1_0) | (~c2_1(a215)) | c3_1(a215) | (~c2_1(a232)) | (~c3_1(a232)) | (~c0_1(a232)) | c3_1(a243))),
% 0.77/0.97 inference(rewrite,[status(thm)],[])).
% 0.77/0.97 tff(972,plain,
% 0.77/0.97 (((~ndr1_0) | (~c2_1(a232)) | (~c0_1(a232)) | (~c3_1(a232)) | c3_1(a215) | c0_1(a215) | (~c2_1(a215)) | c0_1(a243) | c2_1(a243) | c3_1(a243)) <=> (c0_1(a243) | c2_1(a243) | c0_1(a215) | (~ndr1_0) | (~c2_1(a215)) | c3_1(a215) | (~c2_1(a232)) | (~c3_1(a232)) | (~c0_1(a232)) | c3_1(a243))),
% 0.77/0.97 inference(rewrite,[status(thm)],[])).
% 0.77/0.97 tff(973,plain,
% 0.77/0.97 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c0_1(W) | c2_1(W) | c3_1(W))) | ((~ndr1_0) | (~c2_1(a232)) | (~c0_1(a232)) | (~c3_1(a232)) | c3_1(a215) | c0_1(a215) | (~c2_1(a215)) | c0_1(a243) | c2_1(a243) | c3_1(a243))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c0_1(W) | c2_1(W) | c3_1(W))) | (c0_1(a243) | c2_1(a243) | c0_1(a215) | (~ndr1_0) | (~c2_1(a215)) | c3_1(a215) | (~c2_1(a232)) | (~c3_1(a232)) | (~c0_1(a232)) | c3_1(a243)))),
% 0.77/0.97 inference(monotonicity,[status(thm)],[972])).
% 0.77/0.97 tff(974,plain,
% 0.77/0.97 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c0_1(W) | c2_1(W) | c3_1(W))) | ((~ndr1_0) | (~c2_1(a232)) | (~c0_1(a232)) | (~c3_1(a232)) | c3_1(a215) | c0_1(a215) | (~c2_1(a215)) | c0_1(a243) | c2_1(a243) | c3_1(a243))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c0_1(W) | c2_1(W) | c3_1(W))) | c0_1(a243) | c2_1(a243) | c0_1(a215) | (~ndr1_0) | (~c2_1(a215)) | c3_1(a215) | (~c2_1(a232)) | (~c3_1(a232)) | (~c0_1(a232)) | c3_1(a243))),
% 0.77/0.97 inference(transitivity,[status(thm)],[973, 971])).
% 0.77/0.97 tff(975,plain,
% 0.77/0.97 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c0_1(W) | c2_1(W) | c3_1(W))) | ((~ndr1_0) | (~c2_1(a232)) | (~c0_1(a232)) | (~c3_1(a232)) | c3_1(a215) | c0_1(a215) | (~c2_1(a215)) | c0_1(a243) | c2_1(a243) | c3_1(a243))),
% 0.77/0.97 inference(quant_inst,[status(thm)],[])).
% 0.77/0.97 tff(976,plain,
% 0.77/0.97 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c0_1(W) | c2_1(W) | c3_1(W))) | c0_1(a243) | c2_1(a243) | c0_1(a215) | (~ndr1_0) | (~c2_1(a215)) | c3_1(a215) | (~c2_1(a232)) | (~c3_1(a232)) | (~c0_1(a232)) | c3_1(a243)),
% 0.77/0.97 inference(modus_ponens,[status(thm)],[975, 974])).
% 0.77/0.97 tff(977,plain,
% 0.77/0.97 ($false),
% 0.81/0.97 inference(unit_resolution,[status(thm)],[976, 122, 768, 767, 766, 970, 950, 969, 961, 603, 958, 968])).
% 0.81/0.97 tff(978,plain,(hskp3 | (~c0_1(a232)) | (~c2_1(a232)) | (~c3_1(a232)) | (~c1_1(a252)) | c2_1(a252) | (~c1_1(a213)) | (~c3_1(a213)) | c2_1(a213) | hskp8 | c3_1(a252)), inference(lemma,lemma(discharge,[]))).
% 0.81/0.97 tff(979,plain,
% 0.81/0.97 (hskp3),
% 0.81/0.97 inference(unit_resolution,[status(thm)],[978, 746, 745, 744, 915, 914, 877, 883, 876, 43, 913])).
% 0.81/0.97 tff(980,plain,
% 0.81/0.97 (~c2_1(a216)),
% 0.81/0.97 inference(unit_resolution,[status(thm)],[312, 979])).
% 0.81/0.97 tff(981,plain,
% 0.81/0.97 (~c0_1(a216)),
% 0.81/0.97 inference(unit_resolution,[status(thm)],[318, 979])).
% 0.81/0.97 tff(982,plain,
% 0.81/0.97 (c3_1(a216)),
% 0.81/0.97 inference(unit_resolution,[status(thm)],[328, 979])).
% 0.81/0.97 tff(983,plain,
% 0.81/0.97 (~c0_1(a252)),
% 0.81/0.97 inference(unit_resolution,[status(thm)],[834, 122, 911, 903, 982, 914, 913, 902, 981, 980, 10])).
% 0.81/0.97 tff(984,plain,
% 0.81/0.97 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W))))),
% 0.81/0.97 inference(bind,[status(th)],[])).
% 0.81/0.97 tff(985,plain,
% 0.81/0.97 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))),
% 0.81/0.97 inference(quant_intro,[status(thm)],[984])).
% 0.81/0.97 tff(986,plain,
% 0.81/0.97 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))),
% 0.81/0.97 inference(rewrite,[status(thm)],[])).
% 0.81/0.97 tff(987,plain,
% 0.81/0.97 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) <=> ((~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c1_1(W))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V))) | (~c1_1(W))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c1_1(W)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c1_1(W))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c1_1(W))) | c3_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c1_1(W))) | c3_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c1_1(W))) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | (~c1_1(W)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c1_1(W))) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | (~c1_1(W))))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c1_1(W))) | c3_1(V)) | c0_1(W)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_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)) | (~c1_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)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c1_1(W))) | c3_1(V)) | c0_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W))))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c1_1(W))) | c3_1(V)) | c0_1(W)) | c3_1(W)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_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)) | (~c1_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)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c1_1(W))) | c3_1(V)) | c0_1(W)) | c3_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))))),
% 0.81/0.97 inference(bind,[status(th)],[])).
% 0.81/0.97 tff(988,plain,
% 0.81/0.97 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c1_1(W))) | c3_1(V)) | c0_1(W)) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))),
% 0.81/0.97 inference(quant_intro,[status(thm)],[987])).
% 0.81/0.97 tff(989,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c1_1(W))) | c3_1(V)) | c0_1(W)) | c3_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause175')).
% 0.81/0.97 tff(990,plain,
% 0.81/0.97 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))),
% 0.81/0.97 inference(modus_ponens,[status(thm)],[989, 988])).
% 0.81/0.97 tff(991,plain,
% 0.81/0.97 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))),
% 0.81/0.97 inference(modus_ponens,[status(thm)],[990, 986])).
% 0.81/0.97 tff(992,plain,(
% 0.81/0.97 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))),
% 0.81/0.97 inference(skolemize,[status(sab)],[991])).
% 0.81/0.97 tff(993,plain,
% 0.81/0.97 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))),
% 0.81/0.97 inference(modus_ponens,[status(thm)],[992, 985])).
% 0.81/0.97 tff(994,plain,
% 0.81/0.97 (hskp18),
% 0.81/0.97 inference(unit_resolution,[status(thm)],[654, 122, 877, 883, 179, 173, 876, 648, 725])).
% 0.81/0.97 tff(995,plain,
% 0.81/0.97 (~c2_1(a247)),
% 0.81/0.97 inference(unit_resolution,[status(thm)],[149, 994])).
% 0.81/0.97 tff(996,plain,
% 0.81/0.97 (c0_1(a247)),
% 0.81/0.97 inference(unit_resolution,[status(thm)],[664, 994])).
% 0.81/0.97 tff(997,plain,
% 0.81/0.97 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | (c2_1(a247) | c0_1(a216) | c2_1(a216) | c2_1(a213) | (~ndr1_0) | (~c1_1(a213)) | (~c3_1(a213)) | (~c3_1(a216)) | c1_1(a247) | (~c0_1(a247)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c2_1(a247) | c0_1(a216) | c2_1(a216) | c2_1(a213) | (~ndr1_0) | (~c1_1(a213)) | (~c3_1(a213)) | (~c3_1(a216)) | c1_1(a247) | (~c0_1(a247)))),
% 0.81/0.97 inference(rewrite,[status(thm)],[])).
% 0.81/0.97 tff(998,plain,
% 0.81/0.97 (((~ndr1_0) | c2_1(a213) | (~c1_1(a213)) | (~c3_1(a213)) | c2_1(a247) | c1_1(a247) | (~c0_1(a247)) | c0_1(a216) | c2_1(a216) | (~c3_1(a216))) <=> (c2_1(a247) | c0_1(a216) | c2_1(a216) | c2_1(a213) | (~ndr1_0) | (~c1_1(a213)) | (~c3_1(a213)) | (~c3_1(a216)) | c1_1(a247) | (~c0_1(a247)))),
% 0.81/0.97 inference(rewrite,[status(thm)],[])).
% 0.81/0.97 tff(999,plain,
% 0.81/0.97 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a213) | (~c1_1(a213)) | (~c3_1(a213)) | c2_1(a247) | c1_1(a247) | (~c0_1(a247)) | c0_1(a216) | c2_1(a216) | (~c3_1(a216)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | (c2_1(a247) | c0_1(a216) | c2_1(a216) | c2_1(a213) | (~ndr1_0) | (~c1_1(a213)) | (~c3_1(a213)) | (~c3_1(a216)) | c1_1(a247) | (~c0_1(a247))))),
% 0.81/0.97 inference(monotonicity,[status(thm)],[998])).
% 0.81/0.97 tff(1000,plain,
% 0.81/0.97 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a213) | (~c1_1(a213)) | (~c3_1(a213)) | c2_1(a247) | c1_1(a247) | (~c0_1(a247)) | c0_1(a216) | c2_1(a216) | (~c3_1(a216)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c2_1(a247) | c0_1(a216) | c2_1(a216) | c2_1(a213) | (~ndr1_0) | (~c1_1(a213)) | (~c3_1(a213)) | (~c3_1(a216)) | c1_1(a247) | (~c0_1(a247)))),
% 0.81/0.97 inference(transitivity,[status(thm)],[999, 997])).
% 0.81/0.97 tff(1001,plain,
% 0.81/0.97 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a213) | (~c1_1(a213)) | (~c3_1(a213)) | c2_1(a247) | c1_1(a247) | (~c0_1(a247)) | c0_1(a216) | c2_1(a216) | (~c3_1(a216)))),
% 0.81/0.97 inference(quant_inst,[status(thm)],[])).
% 0.81/0.97 tff(1002,plain,
% 0.81/0.97 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c2_1(a247) | c0_1(a216) | c2_1(a216) | c2_1(a213) | (~ndr1_0) | (~c1_1(a213)) | (~c3_1(a213)) | (~c3_1(a216)) | c1_1(a247) | (~c0_1(a247))),
% 0.81/0.97 inference(modus_ponens,[status(thm)],[1001, 1000])).
% 0.81/0.97 tff(1003,plain,
% 0.81/0.97 (c1_1(a247)),
% 0.81/0.97 inference(unit_resolution,[status(thm)],[1002, 122, 996, 982, 877, 883, 995, 981, 980, 876, 305])).
% 0.81/0.97 tff(1004,plain,
% 0.81/0.97 (^[V: $i, U: $i] : refl((hskp20 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V))) <=> (hskp20 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V))))),
% 0.81/0.97 inference(bind,[status(th)],[])).
% 0.81/0.97 tff(1005,plain,
% 0.81/0.97 (![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))),
% 0.81/0.97 inference(quant_intro,[status(thm)],[1004])).
% 0.81/0.97 tff(1006,plain,
% 0.81/0.97 (![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))),
% 0.81/0.97 inference(rewrite,[status(thm)],[])).
% 0.81/0.97 tff(1007,plain,
% 0.81/0.97 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) <=> ((~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c1_1(U)) | (~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)))), rewrite((((~c1_1(U)) | (~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | (~c0_1(V))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c0_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c0_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c0_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c2_1(V))) | hskp20) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V))) | hskp20))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V))) | hskp20) <=> (hskp20 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c2_1(V))) | hskp20) <=> (hskp20 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))))),
% 0.81/0.97 inference(bind,[status(th)],[])).
% 0.81/0.97 tff(1008,plain,
% 0.81/0.97 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c2_1(V))) | hskp20) <=> ![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))),
% 0.81/0.97 inference(quant_intro,[status(thm)],[1007])).
% 0.81/0.97 tff(1009,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c2_1(V))) | hskp20)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause167')).
% 0.81/0.97 tff(1010,plain,
% 0.81/0.97 (![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))),
% 0.81/0.97 inference(modus_ponens,[status(thm)],[1009, 1008])).
% 0.81/0.97 tff(1011,plain,
% 0.81/0.97 (![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))),
% 0.81/0.97 inference(modus_ponens,[status(thm)],[1010, 1006])).
% 0.81/0.97 tff(1012,plain,(
% 0.81/0.97 ![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))),
% 0.81/0.97 inference(skolemize,[status(sab)],[1011])).
% 0.81/0.97 tff(1013,plain,
% 0.81/0.97 (![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))),
% 0.81/0.97 inference(modus_ponens,[status(thm)],[1012, 1005])).
% 0.81/0.97 tff(1014,plain,
% 0.81/0.97 (c3_1(a247)),
% 0.81/0.97 inference(unit_resolution,[status(thm)],[157, 994])).
% 0.81/0.97 tff(1015,plain,
% 0.81/0.97 (hskp28 | (~c1_1(a247))),
% 0.81/0.97 inference(unit_resolution,[status(thm)],[689, 122, 996, 179, 173, 995, 682, 725])).
% 0.81/0.97 tff(1016,plain,
% 0.81/0.97 (hskp28),
% 0.81/0.97 inference(unit_resolution,[status(thm)],[1015, 1003])).
% 0.81/0.97 tff(1017,plain,
% 0.81/0.97 (c2_1(a246)),
% 0.81/0.97 inference(unit_resolution,[status(thm)],[699, 1016])).
% 0.81/0.97 tff(1018,plain,
% 0.81/0.97 (c1_1(a246)),
% 0.81/0.97 inference(unit_resolution,[status(thm)],[707, 1016])).
% 0.81/0.97 tff(1019,plain,
% 0.81/0.97 (c0_1(a246)),
% 0.81/0.97 inference(unit_resolution,[status(thm)],[715, 1016])).
% 0.81/0.97 tff(1020,plain,
% 0.81/0.97 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp20 | (~ndr1_0) | (~c0_1(a246)) | (~c1_1(a246)) | (~c2_1(a246)) | (~c1_1(a247)) | (~c3_1(a247)) | (~c0_1(a247)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | hskp20 | (~ndr1_0) | (~c0_1(a246)) | (~c1_1(a246)) | (~c2_1(a246)) | (~c1_1(a247)) | (~c3_1(a247)) | (~c0_1(a247)))),
% 0.81/0.97 inference(rewrite,[status(thm)],[])).
% 0.81/0.97 tff(1021,plain,
% 0.81/0.97 ((hskp20 | (~ndr1_0) | (~c1_1(a247)) | (~c0_1(a247)) | (~c3_1(a247)) | (~c1_1(a246)) | (~c2_1(a246)) | (~c0_1(a246))) <=> (hskp20 | (~ndr1_0) | (~c0_1(a246)) | (~c1_1(a246)) | (~c2_1(a246)) | (~c1_1(a247)) | (~c3_1(a247)) | (~c0_1(a247)))),
% 0.81/0.97 inference(rewrite,[status(thm)],[])).
% 0.81/0.97 tff(1022,plain,
% 0.81/0.97 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp20 | (~ndr1_0) | (~c1_1(a247)) | (~c0_1(a247)) | (~c3_1(a247)) | (~c1_1(a246)) | (~c2_1(a246)) | (~c0_1(a246)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp20 | (~ndr1_0) | (~c0_1(a246)) | (~c1_1(a246)) | (~c2_1(a246)) | (~c1_1(a247)) | (~c3_1(a247)) | (~c0_1(a247))))),
% 0.81/0.97 inference(monotonicity,[status(thm)],[1021])).
% 0.81/0.97 tff(1023,plain,
% 0.81/0.97 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp20 | (~ndr1_0) | (~c1_1(a247)) | (~c0_1(a247)) | (~c3_1(a247)) | (~c1_1(a246)) | (~c2_1(a246)) | (~c0_1(a246)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | hskp20 | (~ndr1_0) | (~c0_1(a246)) | (~c1_1(a246)) | (~c2_1(a246)) | (~c1_1(a247)) | (~c3_1(a247)) | (~c0_1(a247)))),
% 0.81/0.97 inference(transitivity,[status(thm)],[1022, 1020])).
% 0.81/0.97 tff(1024,plain,
% 0.81/0.97 ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp20 | (~ndr1_0) | (~c1_1(a247)) | (~c0_1(a247)) | (~c3_1(a247)) | (~c1_1(a246)) | (~c2_1(a246)) | (~c0_1(a246)))),
% 0.81/0.97 inference(quant_inst,[status(thm)],[])).
% 0.81/0.97 tff(1025,plain,
% 0.81/0.97 ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | hskp20 | (~ndr1_0) | (~c0_1(a246)) | (~c1_1(a246)) | (~c2_1(a246)) | (~c1_1(a247)) | (~c3_1(a247)) | (~c0_1(a247))),
% 0.81/0.97 inference(modus_ponens,[status(thm)],[1024, 1023])).
% 0.81/0.97 tff(1026,plain,
% 0.81/0.97 (hskp20),
% 0.81/0.97 inference(unit_resolution,[status(thm)],[1025, 122, 1019, 1018, 1017, 996, 1014, 1013, 1003])).
% 0.81/0.97 tff(1027,plain,
% 0.81/0.97 (~c3_1(a259)),
% 0.81/0.97 inference(unit_resolution,[status(thm)],[354, 1026])).
% 0.81/0.97 tff(1028,plain,
% 0.81/0.97 (c1_1(a259)),
% 0.81/0.97 inference(unit_resolution,[status(thm)],[362, 1026])).
% 0.81/0.97 tff(1029,plain,
% 0.81/0.97 (c0_1(a259)),
% 0.81/0.97 inference(unit_resolution,[status(thm)],[370, 1026])).
% 0.81/0.97 tff(1030,plain,
% 0.81/0.97 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | (c3_1(a259) | c3_1(a252) | (~ndr1_0) | (~c0_1(a246)) | (~c1_1(a246)) | (~c2_1(a246)) | c0_1(a252) | (~c1_1(a252)) | (~c0_1(a259)) | (~c1_1(a259)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c3_1(a259) | c3_1(a252) | (~ndr1_0) | (~c0_1(a246)) | (~c1_1(a246)) | (~c2_1(a246)) | c0_1(a252) | (~c1_1(a252)) | (~c0_1(a259)) | (~c1_1(a259)))),
% 0.81/0.97 inference(rewrite,[status(thm)],[])).
% 0.81/0.97 tff(1031,plain,
% 0.81/0.97 (((~ndr1_0) | (~c2_1(a246)) | (~c1_1(a246)) | (~c0_1(a246)) | c3_1(a259) | (~c1_1(a259)) | (~c0_1(a259)) | c0_1(a252) | c3_1(a252) | (~c1_1(a252))) <=> (c3_1(a259) | c3_1(a252) | (~ndr1_0) | (~c0_1(a246)) | (~c1_1(a246)) | (~c2_1(a246)) | c0_1(a252) | (~c1_1(a252)) | (~c0_1(a259)) | (~c1_1(a259)))),
% 0.81/0.97 inference(rewrite,[status(thm)],[])).
% 0.81/0.97 tff(1032,plain,
% 0.81/0.97 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a246)) | (~c1_1(a246)) | (~c0_1(a246)) | c3_1(a259) | (~c1_1(a259)) | (~c0_1(a259)) | c0_1(a252) | c3_1(a252) | (~c1_1(a252)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | (c3_1(a259) | c3_1(a252) | (~ndr1_0) | (~c0_1(a246)) | (~c1_1(a246)) | (~c2_1(a246)) | c0_1(a252) | (~c1_1(a252)) | (~c0_1(a259)) | (~c1_1(a259))))),
% 0.81/0.97 inference(monotonicity,[status(thm)],[1031])).
% 0.81/0.97 tff(1033,plain,
% 0.81/0.97 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a246)) | (~c1_1(a246)) | (~c0_1(a246)) | c3_1(a259) | (~c1_1(a259)) | (~c0_1(a259)) | c0_1(a252) | c3_1(a252) | (~c1_1(a252)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c3_1(a259) | c3_1(a252) | (~ndr1_0) | (~c0_1(a246)) | (~c1_1(a246)) | (~c2_1(a246)) | c0_1(a252) | (~c1_1(a252)) | (~c0_1(a259)) | (~c1_1(a259)))),
% 0.81/0.97 inference(transitivity,[status(thm)],[1032, 1030])).
% 0.81/0.97 tff(1034,plain,
% 0.81/0.97 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a246)) | (~c1_1(a246)) | (~c0_1(a246)) | c3_1(a259) | (~c1_1(a259)) | (~c0_1(a259)) | c0_1(a252) | c3_1(a252) | (~c1_1(a252)))),
% 0.81/0.97 inference(quant_inst,[status(thm)],[])).
% 0.81/0.97 tff(1035,plain,
% 0.81/0.97 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c3_1(a259) | c3_1(a252) | (~ndr1_0) | (~c0_1(a246)) | (~c1_1(a246)) | (~c2_1(a246)) | c0_1(a252) | (~c1_1(a252)) | (~c0_1(a259)) | (~c1_1(a259))),
% 0.81/0.97 inference(modus_ponens,[status(thm)],[1034, 1033])).
% 0.81/0.97 tff(1036,plain,
% 0.81/0.97 ($false),
% 0.81/0.97 inference(unit_resolution,[status(thm)],[1035, 122, 1019, 1018, 1017, 1029, 1028, 915, 1027, 913, 993, 983])).
% 0.81/0.97 tff(1037,plain,(hskp10 | hskp8), inference(lemma,lemma(discharge,[]))).
% 0.81/0.97 tff(1038,plain,
% 0.81/0.97 (hskp10),
% 0.81/0.97 inference(unit_resolution,[status(thm)],[1037, 43])).
% 0.81/0.97 tff(1039,plain,
% 0.81/0.97 (((~hskp10) | (~c0_1(a229))) <=> ((~hskp10) | (~c0_1(a229)))),
% 0.81/0.97 inference(rewrite,[status(thm)],[])).
% 0.81/0.97 tff(1040,plain,
% 0.81/0.97 (((~c0_1(a229)) | (~hskp10)) <=> ((~hskp10) | (~c0_1(a229)))),
% 0.81/0.97 inference(rewrite,[status(thm)],[])).
% 0.81/0.97 tff(1041,axiom,((~c0_1(a229)) | (~hskp10)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause106')).
% 0.81/0.97 tff(1042,plain,
% 0.81/0.97 ((~hskp10) | (~c0_1(a229))),
% 0.81/0.97 inference(modus_ponens,[status(thm)],[1041, 1040])).
% 0.81/0.97 tff(1043,plain,
% 0.81/0.97 ((~hskp10) | (~c0_1(a229))),
% 0.81/0.97 inference(modus_ponens,[status(thm)],[1042, 1039])).
% 0.81/0.97 tff(1044,plain,
% 0.81/0.97 (~c0_1(a229)),
% 0.81/0.97 inference(unit_resolution,[status(thm)],[1043, 1038])).
% 0.81/0.97 tff(1045,plain,
% 0.81/0.97 (c3_1(a229)),
% 0.81/0.97 inference(unit_resolution,[status(thm)],[19, 1038])).
% 0.81/0.97 tff(1046,plain,
% 0.81/0.97 (((~hskp10) | c2_1(a229)) <=> ((~hskp10) | c2_1(a229))),
% 0.81/0.97 inference(rewrite,[status(thm)],[])).
% 0.81/0.97 tff(1047,axiom,((~hskp10) | c2_1(a229)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause63')).
% 0.81/0.97 tff(1048,plain,
% 0.81/0.97 ((~hskp10) | c2_1(a229)),
% 0.81/0.97 inference(modus_ponens,[status(thm)],[1047, 1046])).
% 0.81/0.97 tff(1049,plain,
% 0.81/0.97 ((~hskp10) | c2_1(a229)),
% 0.81/0.97 inference(modus_ponens,[status(thm)],[1048, 1046])).
% 0.81/0.97 tff(1050,plain,
% 0.81/0.97 ((~hskp10) | c2_1(a229)),
% 0.81/0.97 inference(modus_ponens,[status(thm)],[1049, 1046])).
% 0.81/0.97 tff(1051,plain,
% 0.81/0.97 ((~hskp10) | c2_1(a229)),
% 0.81/0.97 inference(modus_ponens,[status(thm)],[1050, 1046])).
% 0.81/0.97 tff(1052,plain,
% 0.81/0.97 ((~hskp10) | c2_1(a229)),
% 0.81/0.97 inference(modus_ponens,[status(thm)],[1051, 1046])).
% 0.81/0.97 tff(1053,plain,
% 0.81/0.97 (c2_1(a229)),
% 0.81/0.97 inference(unit_resolution,[status(thm)],[1052, 1038])).
% 0.81/0.97 tff(1054,plain,
% 0.81/0.97 (^[V: $i, U: $i] : refl((hskp6 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))) <=> (hskp6 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))))),
% 0.81/0.97 inference(bind,[status(th)],[])).
% 0.81/0.97 tff(1055,plain,
% 0.81/0.97 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 0.81/0.97 inference(quant_intro,[status(thm)],[1054])).
% 0.81/0.97 tff(1056,plain,
% 0.81/0.97 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 0.81/0.97 inference(rewrite,[status(thm)],[])).
% 0.81/0.97 tff(1057,plain,
% 0.81/0.97 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(V)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(V))))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c2_1(V)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c2_1(V))))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c2_1(V)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c2_1(V))))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) | hskp6) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))) | hskp6))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))) | hskp6) <=> (hskp6 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) | hskp6) <=> (hskp6 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))))),
% 0.81/0.97 inference(bind,[status(th)],[])).
% 0.81/0.97 tff(1058,plain,
% 0.81/0.97 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) | hskp6) <=> ![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 0.81/0.97 inference(quant_intro,[status(thm)],[1057])).
% 0.81/0.97 tff(1059,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) | hskp6)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause162')).
% 0.81/0.97 tff(1060,plain,
% 0.81/0.97 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 0.81/0.97 inference(modus_ponens,[status(thm)],[1059, 1058])).
% 0.81/0.97 tff(1061,plain,
% 0.81/0.97 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 0.81/0.97 inference(modus_ponens,[status(thm)],[1060, 1056])).
% 0.81/0.97 tff(1062,plain,(
% 0.81/0.97 ![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 0.81/0.97 inference(skolemize,[status(sab)],[1061])).
% 0.81/0.97 tff(1063,plain,
% 0.81/0.97 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 0.81/0.97 inference(modus_ponens,[status(thm)],[1062, 1055])).
% 0.81/0.97 tff(1064,assumption,(hskp18), introduced(assumption)).
% 0.81/0.97 tff(1065,plain,
% 0.81/0.97 (~c2_1(a247)),
% 0.81/0.97 inference(unit_resolution,[status(thm)],[149, 1064])).
% 0.81/0.97 tff(1066,assumption,(c3_1(a229)), introduced(assumption)).
% 0.81/0.97 tff(1067,assumption,(c2_1(a229)), introduced(assumption)).
% 0.81/0.97 tff(1068,plain,
% 0.81/0.97 (c3_1(a247)),
% 0.81/0.97 inference(unit_resolution,[status(thm)],[157, 1064])).
% 0.81/0.97 tff(1069,plain,
% 0.81/0.97 (c0_1(a247)),
% 0.81/0.97 inference(unit_resolution,[status(thm)],[664, 1064])).
% 0.81/0.97 tff(1070,assumption,(~hskp6), introduced(assumption)).
% 0.81/0.97 tff(1071,plain,
% 0.81/0.97 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp6 | c2_1(a247) | c0_1(a229) | (~ndr1_0) | (~c2_1(a229)) | (~c3_1(a229)) | (~c3_1(a247)) | (~c0_1(a247)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp6 | c2_1(a247) | c0_1(a229) | (~ndr1_0) | (~c2_1(a229)) | (~c3_1(a229)) | (~c3_1(a247)) | (~c0_1(a247)))),
% 0.81/0.98 inference(rewrite,[status(thm)],[])).
% 0.81/0.98 tff(1072,plain,
% 0.81/0.98 ((hskp6 | (~ndr1_0) | c2_1(a247) | (~c0_1(a247)) | (~c3_1(a247)) | c0_1(a229) | (~c3_1(a229)) | (~c2_1(a229))) <=> (hskp6 | c2_1(a247) | c0_1(a229) | (~ndr1_0) | (~c2_1(a229)) | (~c3_1(a229)) | (~c3_1(a247)) | (~c0_1(a247)))),
% 0.81/0.98 inference(rewrite,[status(thm)],[])).
% 0.81/0.98 tff(1073,plain,
% 0.81/0.98 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp6 | (~ndr1_0) | c2_1(a247) | (~c0_1(a247)) | (~c3_1(a247)) | c0_1(a229) | (~c3_1(a229)) | (~c2_1(a229)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp6 | c2_1(a247) | c0_1(a229) | (~ndr1_0) | (~c2_1(a229)) | (~c3_1(a229)) | (~c3_1(a247)) | (~c0_1(a247))))),
% 0.81/0.98 inference(monotonicity,[status(thm)],[1072])).
% 0.81/0.98 tff(1074,plain,
% 0.81/0.98 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp6 | (~ndr1_0) | c2_1(a247) | (~c0_1(a247)) | (~c3_1(a247)) | c0_1(a229) | (~c3_1(a229)) | (~c2_1(a229)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp6 | c2_1(a247) | c0_1(a229) | (~ndr1_0) | (~c2_1(a229)) | (~c3_1(a229)) | (~c3_1(a247)) | (~c0_1(a247)))),
% 0.81/0.98 inference(transitivity,[status(thm)],[1073, 1071])).
% 0.81/0.98 tff(1075,plain,
% 0.81/0.98 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp6 | (~ndr1_0) | c2_1(a247) | (~c0_1(a247)) | (~c3_1(a247)) | c0_1(a229) | (~c3_1(a229)) | (~c2_1(a229)))),
% 0.81/0.98 inference(quant_inst,[status(thm)],[])).
% 0.81/0.98 tff(1076,plain,
% 0.81/0.98 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp6 | c2_1(a247) | c0_1(a229) | (~ndr1_0) | (~c2_1(a229)) | (~c3_1(a229)) | (~c3_1(a247)) | (~c0_1(a247))),
% 0.81/0.98 inference(modus_ponens,[status(thm)],[1075, 1074])).
% 0.81/0.98 tff(1077,plain,
% 0.81/0.98 ($false),
% 0.81/0.98 inference(unit_resolution,[status(thm)],[1076, 122, 1070, 1069, 1068, 1067, 1066, 1065, 11, 1063])).
% 0.81/0.98 tff(1078,plain,((~hskp18) | hskp6 | (~c2_1(a229)) | (~c3_1(a229)) | c0_1(a229)), inference(lemma,lemma(discharge,[]))).
% 0.81/0.98 tff(1079,plain,
% 0.81/0.98 (hskp6),
% 0.81/0.98 inference(unit_resolution,[status(thm)],[1078, 144, 1053, 1045, 1044])).
% 0.81/0.98 tff(1080,assumption,(~hskp27), introduced(assumption)).
% 0.81/0.98 tff(1081,assumption,(hskp15), introduced(assumption)).
% 0.81/0.98 tff(1082,plain,
% 0.81/0.98 (~c3_1(a238)),
% 0.81/0.98 inference(unit_resolution,[status(thm)],[216, 1081])).
% 0.81/0.98 tff(1083,plain,
% 0.81/0.98 (c2_1(a238)),
% 0.81/0.98 inference(unit_resolution,[status(thm)],[224, 1081])).
% 0.81/0.98 tff(1084,plain,
% 0.81/0.98 (c0_1(a238)),
% 0.81/0.98 inference(unit_resolution,[status(thm)],[232, 1081])).
% 0.81/0.98 tff(1085,plain,
% 0.81/0.98 ($false),
% 0.81/0.98 inference(unit_resolution,[status(thm)],[239, 122, 1080, 1084, 1083, 1082, 192])).
% 0.81/0.98 tff(1086,plain,((~hskp15) | hskp27), inference(lemma,lemma(discharge,[]))).
% 0.81/0.98 tff(1087,plain,
% 0.81/0.98 (~hskp15),
% 0.81/0.98 inference(unit_resolution,[status(thm)],[1086, 1080])).
% 0.81/0.98 tff(1088,assumption,(hskp6), introduced(assumption)).
% 0.81/0.98 tff(1089,plain,
% 0.81/0.98 (((~hskp6) | (~c2_1(a221))) <=> ((~hskp6) | (~c2_1(a221)))),
% 0.81/0.98 inference(rewrite,[status(thm)],[])).
% 0.81/0.98 tff(1090,plain,
% 0.81/0.98 (((~c2_1(a221)) | (~hskp6)) <=> ((~hskp6) | (~c2_1(a221)))),
% 0.81/0.98 inference(rewrite,[status(thm)],[])).
% 0.81/0.98 tff(1091,axiom,((~c2_1(a221)) | (~hskp6)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause112')).
% 0.81/0.98 tff(1092,plain,
% 0.81/0.98 ((~hskp6) | (~c2_1(a221))),
% 0.81/0.98 inference(modus_ponens,[status(thm)],[1091, 1090])).
% 0.81/0.98 tff(1093,plain,
% 0.81/0.98 ((~hskp6) | (~c2_1(a221))),
% 0.81/0.98 inference(modus_ponens,[status(thm)],[1092, 1089])).
% 0.81/0.98 tff(1094,plain,
% 0.81/0.98 (~c2_1(a221)),
% 0.81/0.98 inference(unit_resolution,[status(thm)],[1093, 1088])).
% 0.81/0.98 tff(1095,plain,
% 0.81/0.98 (((~hskp6) | c0_1(a221)) <=> ((~hskp6) | c0_1(a221))),
% 0.81/0.98 inference(rewrite,[status(thm)],[])).
% 0.81/0.98 tff(1096,axiom,((~hskp6) | c0_1(a221)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause69')).
% 0.81/0.98 tff(1097,plain,
% 0.81/0.98 ((~hskp6) | c0_1(a221)),
% 0.81/0.98 inference(modus_ponens,[status(thm)],[1096, 1095])).
% 0.81/0.98 tff(1098,plain,
% 0.81/0.98 ((~hskp6) | c0_1(a221)),
% 0.81/0.98 inference(modus_ponens,[status(thm)],[1097, 1095])).
% 0.81/0.98 tff(1099,plain,
% 0.81/0.98 ((~hskp6) | c0_1(a221)),
% 0.81/0.98 inference(modus_ponens,[status(thm)],[1098, 1095])).
% 0.81/0.98 tff(1100,plain,
% 0.81/0.98 ((~hskp6) | c0_1(a221)),
% 0.81/0.98 inference(modus_ponens,[status(thm)],[1099, 1095])).
% 0.81/0.98 tff(1101,plain,
% 0.81/0.98 ((~hskp6) | c0_1(a221)),
% 0.81/0.98 inference(modus_ponens,[status(thm)],[1100, 1095])).
% 0.81/0.98 tff(1102,plain,
% 0.81/0.98 (c0_1(a221)),
% 0.81/0.98 inference(unit_resolution,[status(thm)],[1101, 1088])).
% 0.81/0.98 tff(1103,plain,
% 0.81/0.98 (((~![U: $i] : (hskp15 | hskp0 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp15 | hskp0 | c2_1(a221) | (~ndr1_0) | c3_1(a221) | (~c0_1(a221)))) <=> ((~![U: $i] : (hskp15 | hskp0 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | hskp15 | hskp0 | c2_1(a221) | (~ndr1_0) | c3_1(a221) | (~c0_1(a221)))),
% 0.81/0.98 inference(rewrite,[status(thm)],[])).
% 0.81/0.98 tff(1104,plain,
% 0.81/0.98 ((hskp15 | hskp0 | (~ndr1_0) | c3_1(a221) | c2_1(a221) | (~c0_1(a221))) <=> (hskp15 | hskp0 | c2_1(a221) | (~ndr1_0) | c3_1(a221) | (~c0_1(a221)))),
% 0.81/0.98 inference(rewrite,[status(thm)],[])).
% 0.81/0.98 tff(1105,plain,
% 0.81/0.98 (((~![U: $i] : (hskp15 | hskp0 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp15 | hskp0 | (~ndr1_0) | c3_1(a221) | c2_1(a221) | (~c0_1(a221)))) <=> ((~![U: $i] : (hskp15 | hskp0 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp15 | hskp0 | c2_1(a221) | (~ndr1_0) | c3_1(a221) | (~c0_1(a221))))),
% 0.81/0.98 inference(monotonicity,[status(thm)],[1104])).
% 0.81/0.98 tff(1106,plain,
% 0.81/0.98 (((~![U: $i] : (hskp15 | hskp0 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp15 | hskp0 | (~ndr1_0) | c3_1(a221) | c2_1(a221) | (~c0_1(a221)))) <=> ((~![U: $i] : (hskp15 | hskp0 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | hskp15 | hskp0 | c2_1(a221) | (~ndr1_0) | c3_1(a221) | (~c0_1(a221)))),
% 0.81/0.98 inference(transitivity,[status(thm)],[1105, 1103])).
% 0.81/0.98 tff(1107,plain,
% 0.81/0.98 ((~![U: $i] : (hskp15 | hskp0 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp15 | hskp0 | (~ndr1_0) | c3_1(a221) | c2_1(a221) | (~c0_1(a221)))),
% 0.81/0.98 inference(quant_inst,[status(thm)],[])).
% 0.81/0.98 tff(1108,plain,
% 0.81/0.98 ((~![U: $i] : (hskp15 | hskp0 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | hskp15 | hskp0 | c2_1(a221) | (~ndr1_0) | c3_1(a221) | (~c0_1(a221))),
% 0.81/0.98 inference(modus_ponens,[status(thm)],[1107, 1106])).
% 0.81/0.98 tff(1109,plain,
% 0.81/0.98 (c3_1(a221)),
% 0.81/0.98 inference(unit_resolution,[status(thm)],[1108, 122, 1087, 64, 1102, 1094, 202])).
% 0.81/0.98 tff(1110,plain,
% 0.81/0.98 (((~hskp6) | c1_1(a221)) <=> ((~hskp6) | c1_1(a221))),
% 0.81/0.98 inference(rewrite,[status(thm)],[])).
% 0.81/0.98 tff(1111,axiom,((~hskp6) | c1_1(a221)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause70')).
% 0.81/0.98 tff(1112,plain,
% 0.81/0.98 ((~hskp6) | c1_1(a221)),
% 0.81/0.98 inference(modus_ponens,[status(thm)],[1111, 1110])).
% 0.81/0.98 tff(1113,plain,
% 0.81/0.98 ((~hskp6) | c1_1(a221)),
% 0.81/0.98 inference(modus_ponens,[status(thm)],[1112, 1110])).
% 0.81/0.98 tff(1114,plain,
% 0.81/0.98 ((~hskp6) | c1_1(a221)),
% 0.81/0.98 inference(modus_ponens,[status(thm)],[1113, 1110])).
% 0.81/0.98 tff(1115,plain,
% 0.81/0.98 ((~hskp6) | c1_1(a221)),
% 0.81/0.98 inference(modus_ponens,[status(thm)],[1114, 1110])).
% 0.81/0.98 tff(1116,plain,
% 0.81/0.98 ((~hskp6) | c1_1(a221)),
% 0.81/0.98 inference(modus_ponens,[status(thm)],[1115, 1110])).
% 0.81/0.98 tff(1117,plain,
% 0.81/0.98 (c1_1(a221)),
% 0.81/0.98 inference(unit_resolution,[status(thm)],[1116, 1088])).
% 0.81/0.98 tff(1118,plain,
% 0.81/0.98 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (c0_1(a229) | (~ndr1_0) | (~c1_1(a221)) | (~c3_1(a221)) | (~c0_1(a221)) | c1_1(a229) | (~c3_1(a229)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | c0_1(a229) | (~ndr1_0) | (~c1_1(a221)) | (~c3_1(a221)) | (~c0_1(a221)) | c1_1(a229) | (~c3_1(a229)))),
% 0.81/0.98 inference(rewrite,[status(thm)],[])).
% 0.81/0.98 tff(1119,plain,
% 0.81/0.98 (((~ndr1_0) | (~c1_1(a221)) | (~c0_1(a221)) | (~c3_1(a221)) | c0_1(a229) | c1_1(a229) | (~c3_1(a229))) <=> (c0_1(a229) | (~ndr1_0) | (~c1_1(a221)) | (~c3_1(a221)) | (~c0_1(a221)) | c1_1(a229) | (~c3_1(a229)))),
% 0.81/0.98 inference(rewrite,[status(thm)],[])).
% 0.81/0.98 tff(1120,plain,
% 0.81/0.98 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | ((~ndr1_0) | (~c1_1(a221)) | (~c0_1(a221)) | (~c3_1(a221)) | c0_1(a229) | c1_1(a229) | (~c3_1(a229)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (c0_1(a229) | (~ndr1_0) | (~c1_1(a221)) | (~c3_1(a221)) | (~c0_1(a221)) | c1_1(a229) | (~c3_1(a229))))),
% 0.81/0.98 inference(monotonicity,[status(thm)],[1119])).
% 0.81/0.98 tff(1121,plain,
% 0.81/0.98 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | ((~ndr1_0) | (~c1_1(a221)) | (~c0_1(a221)) | (~c3_1(a221)) | c0_1(a229) | c1_1(a229) | (~c3_1(a229)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | c0_1(a229) | (~ndr1_0) | (~c1_1(a221)) | (~c3_1(a221)) | (~c0_1(a221)) | c1_1(a229) | (~c3_1(a229)))),
% 0.81/0.98 inference(transitivity,[status(thm)],[1120, 1118])).
% 0.81/0.98 tff(1122,plain,
% 0.81/0.98 ((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | ((~ndr1_0) | (~c1_1(a221)) | (~c0_1(a221)) | (~c3_1(a221)) | c0_1(a229) | c1_1(a229) | (~c3_1(a229)))),
% 0.81/0.98 inference(quant_inst,[status(thm)],[])).
% 0.81/0.98 tff(1123,plain,
% 0.81/0.98 ((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | c0_1(a229) | (~ndr1_0) | (~c1_1(a221)) | (~c3_1(a221)) | (~c0_1(a221)) | c1_1(a229) | (~c3_1(a229))),
% 0.81/0.98 inference(modus_ponens,[status(thm)],[1122, 1121])).
% 0.81/0.98 tff(1124,plain,
% 0.81/0.98 (c1_1(a229)),
% 0.81/0.98 inference(unit_resolution,[status(thm)],[1123, 122, 1045, 1102, 1117, 1044, 583, 1109])).
% 0.81/0.98 tff(1125,plain,
% 0.81/0.98 (^[U: $i] : refl((hskp15 | hskp14 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U))) <=> (hskp15 | hskp14 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U))))),
% 0.81/0.98 inference(bind,[status(th)],[])).
% 0.81/0.98 tff(1126,plain,
% 0.81/0.98 (![U: $i] : (hskp15 | hskp14 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U))) <=> ![U: $i] : (hskp15 | hskp14 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))),
% 0.81/0.98 inference(quant_intro,[status(thm)],[1125])).
% 0.81/0.98 tff(1127,plain,
% 0.81/0.98 (![U: $i] : (hskp15 | hskp14 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U))) <=> ![U: $i] : (hskp15 | hskp14 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))),
% 0.81/0.98 inference(rewrite,[status(thm)],[])).
% 0.81/0.98 tff(1128,plain,
% 0.81/0.98 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U))))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp14) <=> (((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U))) | hskp14))), rewrite((((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U))) | hskp14) <=> (hskp14 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp14) <=> (hskp14 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U))))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp14) | hskp15) <=> ((hskp14 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U))) | hskp15))), rewrite(((hskp14 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U))) | hskp15) <=> (hskp15 | hskp14 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp14) | hskp15) <=> (hskp15 | hskp14 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))))),
% 0.81/0.98 inference(bind,[status(th)],[])).
% 0.81/0.98 tff(1129,plain,
% 0.81/0.98 (![U: $i] : ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp14) | hskp15) <=> ![U: $i] : (hskp15 | hskp14 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))),
% 0.81/0.98 inference(quant_intro,[status(thm)],[1128])).
% 0.81/0.98 tff(1130,axiom,(![U: $i] : ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp14) | hskp15)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause131')).
% 0.81/0.98 tff(1131,plain,
% 0.81/0.98 (![U: $i] : (hskp15 | hskp14 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))),
% 0.81/0.98 inference(modus_ponens,[status(thm)],[1130, 1129])).
% 0.81/0.98 tff(1132,plain,
% 0.81/0.98 (![U: $i] : (hskp15 | hskp14 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))),
% 0.81/0.98 inference(modus_ponens,[status(thm)],[1131, 1127])).
% 0.81/0.98 tff(1133,plain,(
% 0.81/0.98 ![U: $i] : (hskp15 | hskp14 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))),
% 0.81/0.98 inference(skolemize,[status(sab)],[1132])).
% 0.81/0.98 tff(1134,plain,
% 0.81/0.98 (![U: $i] : (hskp15 | hskp14 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))),
% 0.81/0.98 inference(modus_ponens,[status(thm)],[1133, 1126])).
% 0.81/0.98 tff(1135,plain,
% 0.81/0.98 (((~![U: $i] : (hskp15 | hskp14 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp15 | hskp14 | c0_1(a229) | (~ndr1_0) | (~c1_1(a229)) | (~c3_1(a229)))) <=> ((~![U: $i] : (hskp15 | hskp14 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))) | hskp15 | hskp14 | c0_1(a229) | (~ndr1_0) | (~c1_1(a229)) | (~c3_1(a229)))),
% 0.81/0.98 inference(rewrite,[status(thm)],[])).
% 0.81/0.98 tff(1136,plain,
% 0.81/0.98 ((hskp15 | hskp14 | (~ndr1_0) | c0_1(a229) | (~c1_1(a229)) | (~c3_1(a229))) <=> (hskp15 | hskp14 | c0_1(a229) | (~ndr1_0) | (~c1_1(a229)) | (~c3_1(a229)))),
% 0.81/0.98 inference(rewrite,[status(thm)],[])).
% 0.81/0.98 tff(1137,plain,
% 0.81/0.98 (((~![U: $i] : (hskp15 | hskp14 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp15 | hskp14 | (~ndr1_0) | c0_1(a229) | (~c1_1(a229)) | (~c3_1(a229)))) <=> ((~![U: $i] : (hskp15 | hskp14 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp15 | hskp14 | c0_1(a229) | (~ndr1_0) | (~c1_1(a229)) | (~c3_1(a229))))),
% 0.81/0.98 inference(monotonicity,[status(thm)],[1136])).
% 0.81/0.98 tff(1138,plain,
% 0.81/0.98 (((~![U: $i] : (hskp15 | hskp14 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp15 | hskp14 | (~ndr1_0) | c0_1(a229) | (~c1_1(a229)) | (~c3_1(a229)))) <=> ((~![U: $i] : (hskp15 | hskp14 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))) | hskp15 | hskp14 | c0_1(a229) | (~ndr1_0) | (~c1_1(a229)) | (~c3_1(a229)))),
% 0.81/0.98 inference(transitivity,[status(thm)],[1137, 1135])).
% 0.81/0.98 tff(1139,plain,
% 0.81/0.98 ((~![U: $i] : (hskp15 | hskp14 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp15 | hskp14 | (~ndr1_0) | c0_1(a229) | (~c1_1(a229)) | (~c3_1(a229)))),
% 0.81/0.98 inference(quant_inst,[status(thm)],[])).
% 0.81/0.98 tff(1140,plain,
% 0.81/0.98 ((~![U: $i] : (hskp15 | hskp14 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))) | hskp15 | hskp14 | c0_1(a229) | (~ndr1_0) | (~c1_1(a229)) | (~c3_1(a229))),
% 0.81/0.98 inference(modus_ponens,[status(thm)],[1139, 1138])).
% 0.81/0.98 tff(1141,plain,
% 0.81/0.98 (hskp15 | hskp14 | (~c1_1(a229))),
% 0.81/0.98 inference(unit_resolution,[status(thm)],[1140, 122, 1045, 1044, 1134])).
% 0.81/0.98 tff(1142,plain,
% 0.81/0.98 (hskp14),
% 0.81/0.98 inference(unit_resolution,[status(thm)],[1141, 1124, 1087])).
% 0.81/0.98 tff(1143,plain,
% 0.81/0.98 (((~hskp14) | c2_1(a237)) <=> ((~hskp14) | c2_1(a237))),
% 0.81/0.98 inference(rewrite,[status(thm)],[])).
% 0.81/0.98 tff(1144,axiom,((~hskp14) | c2_1(a237)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause60')).
% 0.81/0.98 tff(1145,plain,
% 0.81/0.98 ((~hskp14) | c2_1(a237)),
% 0.81/0.98 inference(modus_ponens,[status(thm)],[1144, 1143])).
% 0.81/0.98 tff(1146,plain,
% 0.81/0.98 ((~hskp14) | c2_1(a237)),
% 0.81/0.98 inference(modus_ponens,[status(thm)],[1145, 1143])).
% 0.81/0.98 tff(1147,plain,
% 0.81/0.98 ((~hskp14) | c2_1(a237)),
% 0.81/0.98 inference(modus_ponens,[status(thm)],[1146, 1143])).
% 0.81/0.98 tff(1148,plain,
% 0.81/0.98 ((~hskp14) | c2_1(a237)),
% 0.81/0.98 inference(modus_ponens,[status(thm)],[1147, 1143])).
% 0.81/0.98 tff(1149,plain,
% 0.81/0.98 ((~hskp14) | c2_1(a237)),
% 0.81/0.98 inference(modus_ponens,[status(thm)],[1148, 1143])).
% 0.81/0.98 tff(1150,plain,
% 0.81/0.98 (c2_1(a237)),
% 0.81/0.98 inference(unit_resolution,[status(thm)],[1149, 1142])).
% 0.81/0.98 tff(1151,plain,
% 0.81/0.98 (((~hskp14) | c0_1(a237)) <=> ((~hskp14) | c0_1(a237))),
% 0.81/0.98 inference(rewrite,[status(thm)],[])).
% 0.81/0.98 tff(1152,axiom,((~hskp14) | c0_1(a237)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause59')).
% 0.81/0.98 tff(1153,plain,
% 0.81/0.98 ((~hskp14) | c0_1(a237)),
% 0.81/0.98 inference(modus_ponens,[status(thm)],[1152, 1151])).
% 0.81/0.98 tff(1154,plain,
% 0.81/0.98 ((~hskp14) | c0_1(a237)),
% 0.81/0.98 inference(modus_ponens,[status(thm)],[1153, 1151])).
% 0.81/0.98 tff(1155,plain,
% 0.81/0.98 ((~hskp14) | c0_1(a237)),
% 0.81/0.98 inference(modus_ponens,[status(thm)],[1154, 1151])).
% 0.81/0.98 tff(1156,plain,
% 0.81/0.98 ((~hskp14) | c0_1(a237)),
% 0.81/0.98 inference(modus_ponens,[status(thm)],[1155, 1151])).
% 0.81/0.98 tff(1157,plain,
% 0.81/0.98 ((~hskp14) | c0_1(a237)),
% 0.81/0.98 inference(modus_ponens,[status(thm)],[1156, 1151])).
% 0.81/0.98 tff(1158,plain,
% 0.81/0.98 (c0_1(a237)),
% 0.81/0.98 inference(unit_resolution,[status(thm)],[1157, 1142])).
% 0.81/0.98 tff(1159,plain,
% 0.81/0.98 (((~![U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp27 | (~ndr1_0) | c3_1(a237) | (~c2_1(a237)) | (~c0_1(a237)))) <=> ((~![U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp27 | (~ndr1_0) | c3_1(a237) | (~c2_1(a237)) | (~c0_1(a237)))),
% 0.81/0.98 inference(rewrite,[status(thm)],[])).
% 0.81/0.98 tff(1160,plain,
% 0.81/0.98 ((~![U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp27 | (~ndr1_0) | c3_1(a237) | (~c2_1(a237)) | (~c0_1(a237)))),
% 0.81/0.98 inference(quant_inst,[status(thm)],[])).
% 0.81/0.98 tff(1161,plain,
% 0.81/0.98 ((~![U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp27 | (~ndr1_0) | c3_1(a237) | (~c2_1(a237)) | (~c0_1(a237))),
% 0.81/0.98 inference(modus_ponens,[status(thm)],[1160, 1159])).
% 0.81/0.98 tff(1162,plain,
% 0.81/0.98 (c3_1(a237)),
% 0.81/0.98 inference(unit_resolution,[status(thm)],[1161, 122, 1080, 1158, 1150, 192])).
% 0.81/0.98 tff(1163,assumption,(~hskp15), introduced(assumption)).
% 0.81/0.98 tff(1164,assumption,(hskp14), introduced(assumption)).
% 0.81/0.98 tff(1165,plain,
% 0.81/0.98 (((~hskp14) | (~c1_1(a237))) <=> ((~hskp14) | (~c1_1(a237)))),
% 0.81/0.98 inference(rewrite,[status(thm)],[])).
% 0.81/0.98 tff(1166,plain,
% 0.81/0.98 (((~c1_1(a237)) | (~hskp14)) <=> ((~hskp14) | (~c1_1(a237)))),
% 0.81/0.98 inference(rewrite,[status(thm)],[])).
% 0.81/0.98 tff(1167,axiom,((~c1_1(a237)) | (~hskp14)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause98')).
% 0.81/0.98 tff(1168,plain,
% 0.81/0.98 ((~hskp14) | (~c1_1(a237))),
% 0.81/0.98 inference(modus_ponens,[status(thm)],[1167, 1166])).
% 0.81/0.98 tff(1169,plain,
% 0.81/0.98 ((~hskp14) | (~c1_1(a237))),
% 0.81/0.98 inference(modus_ponens,[status(thm)],[1168, 1165])).
% 0.81/0.98 tff(1170,plain,
% 0.81/0.98 (~c1_1(a237)),
% 0.81/0.98 inference(unit_resolution,[status(thm)],[1169, 1164])).
% 0.81/0.98 tff(1171,plain,
% 0.81/0.98 (c0_1(a237)),
% 0.81/0.98 inference(unit_resolution,[status(thm)],[1157, 1164])).
% 0.81/0.98 tff(1172,plain,
% 0.81/0.98 (c2_1(a237)),
% 0.81/0.98 inference(unit_resolution,[status(thm)],[1149, 1164])).
% 0.81/0.98 tff(1173,plain,
% 0.81/0.98 (^[U: $i] : refl((hskp28 | hskp15 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U))) <=> (hskp28 | hskp15 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U))))),
% 0.81/0.98 inference(bind,[status(th)],[])).
% 0.81/0.98 tff(1174,plain,
% 0.81/0.98 (![U: $i] : (hskp28 | hskp15 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp28 | hskp15 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 0.81/0.98 inference(quant_intro,[status(thm)],[1173])).
% 0.81/0.98 tff(1175,plain,
% 0.81/0.98 (![U: $i] : (hskp28 | hskp15 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp28 | hskp15 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 0.81/0.98 inference(rewrite,[status(thm)],[])).
% 0.81/0.98 tff(1176,plain,
% 0.81/0.98 (^[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)) | c1_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp28) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U))) | hskp28))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U))) | hskp28) <=> (hskp28 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp28) <=> (hskp28 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp28) | hskp15) <=> ((hskp28 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U))) | hskp15))), rewrite(((hskp28 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U))) | hskp15) <=> (hskp28 | hskp15 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp28) | hskp15) <=> (hskp28 | hskp15 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))))),
% 0.81/0.98 inference(bind,[status(th)],[])).
% 0.81/0.98 tff(1177,plain,
% 0.81/0.98 (![U: $i] : ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp28) | hskp15) <=> ![U: $i] : (hskp28 | hskp15 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 0.81/0.98 inference(quant_intro,[status(thm)],[1176])).
% 0.81/0.98 tff(1178,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp28) | hskp15)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause133')).
% 0.81/0.98 tff(1179,plain,
% 0.81/0.98 (![U: $i] : (hskp28 | hskp15 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 0.81/0.98 inference(modus_ponens,[status(thm)],[1178, 1177])).
% 0.81/0.98 tff(1180,plain,
% 0.81/0.98 (![U: $i] : (hskp28 | hskp15 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 0.81/0.98 inference(modus_ponens,[status(thm)],[1179, 1175])).
% 0.81/0.98 tff(1181,plain,(
% 0.81/0.98 ![U: $i] : (hskp28 | hskp15 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 0.81/0.98 inference(skolemize,[status(sab)],[1180])).
% 0.81/0.98 tff(1182,plain,
% 0.81/0.98 (![U: $i] : (hskp28 | hskp15 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 0.81/0.98 inference(modus_ponens,[status(thm)],[1181, 1174])).
% 0.81/0.98 tff(1183,assumption,(~c1_1(a237)), introduced(assumption)).
% 0.81/0.98 tff(1184,plain,
% 0.81/0.98 (((~![U: $i] : (hskp28 | hskp15 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp28 | hskp15 | c1_1(a237) | (~ndr1_0) | (~c2_1(a237)) | (~c0_1(a237)))) <=> ((~![U: $i] : (hskp28 | hskp15 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp28 | hskp15 | c1_1(a237) | (~ndr1_0) | (~c2_1(a237)) | (~c0_1(a237)))),
% 0.81/0.98 inference(rewrite,[status(thm)],[])).
% 0.81/0.98 tff(1185,plain,
% 0.81/0.98 ((hskp28 | hskp15 | (~ndr1_0) | c1_1(a237) | (~c2_1(a237)) | (~c0_1(a237))) <=> (hskp28 | hskp15 | c1_1(a237) | (~ndr1_0) | (~c2_1(a237)) | (~c0_1(a237)))),
% 0.81/0.98 inference(rewrite,[status(thm)],[])).
% 0.81/0.98 tff(1186,plain,
% 0.81/0.98 (((~![U: $i] : (hskp28 | hskp15 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp28 | hskp15 | (~ndr1_0) | c1_1(a237) | (~c2_1(a237)) | (~c0_1(a237)))) <=> ((~![U: $i] : (hskp28 | hskp15 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp28 | hskp15 | c1_1(a237) | (~ndr1_0) | (~c2_1(a237)) | (~c0_1(a237))))),
% 0.81/0.98 inference(monotonicity,[status(thm)],[1185])).
% 0.81/0.98 tff(1187,plain,
% 0.81/0.98 (((~![U: $i] : (hskp28 | hskp15 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp28 | hskp15 | (~ndr1_0) | c1_1(a237) | (~c2_1(a237)) | (~c0_1(a237)))) <=> ((~![U: $i] : (hskp28 | hskp15 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp28 | hskp15 | c1_1(a237) | (~ndr1_0) | (~c2_1(a237)) | (~c0_1(a237)))),
% 0.81/0.98 inference(transitivity,[status(thm)],[1186, 1184])).
% 0.81/0.98 tff(1188,plain,
% 0.81/0.98 ((~![U: $i] : (hskp28 | hskp15 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp28 | hskp15 | (~ndr1_0) | c1_1(a237) | (~c2_1(a237)) | (~c0_1(a237)))),
% 0.81/0.98 inference(quant_inst,[status(thm)],[])).
% 0.81/0.98 tff(1189,plain,
% 0.81/0.98 ((~![U: $i] : (hskp28 | hskp15 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp28 | hskp15 | c1_1(a237) | (~ndr1_0) | (~c2_1(a237)) | (~c0_1(a237))),
% 0.81/0.98 inference(modus_ponens,[status(thm)],[1188, 1187])).
% 0.81/0.98 tff(1190,plain,
% 0.81/0.98 (hskp28 | (~c2_1(a237)) | (~c0_1(a237))),
% 0.81/0.98 inference(unit_resolution,[status(thm)],[1189, 122, 1163, 1183, 1182])).
% 0.81/0.98 tff(1191,plain,
% 0.81/0.98 ($false),
% 0.81/0.98 inference(unit_resolution,[status(thm)],[1190, 1172, 1171, 683])).
% 0.81/0.98 tff(1192,plain,((~hskp14) | hskp28 | hskp15 | c1_1(a237)), inference(lemma,lemma(discharge,[]))).
% 0.81/0.98 tff(1193,plain,
% 0.81/0.98 ($false),
% 0.81/0.98 inference(unit_resolution,[status(thm)],[1192, 1170, 1164, 1163, 683])).
% 0.81/0.98 tff(1194,plain,((~hskp14) | hskp15 | hskp28), inference(lemma,lemma(discharge,[]))).
% 0.81/0.98 tff(1195,plain,
% 0.81/0.98 (hskp28),
% 0.81/0.98 inference(unit_resolution,[status(thm)],[1194, 1142, 1087])).
% 0.81/0.98 tff(1196,plain,
% 0.81/0.98 (c2_1(a246)),
% 0.81/0.98 inference(unit_resolution,[status(thm)],[699, 1195])).
% 0.81/0.98 tff(1197,plain,
% 0.81/0.98 (c1_1(a246)),
% 0.81/0.98 inference(unit_resolution,[status(thm)],[707, 1195])).
% 0.81/0.98 tff(1198,plain,
% 0.81/0.98 (c0_1(a246)),
% 0.81/0.98 inference(unit_resolution,[status(thm)],[715, 1195])).
% 0.81/0.98 tff(1199,plain,
% 0.81/0.98 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp20 | (~ndr1_0) | (~c1_1(a221)) | (~c3_1(a221)) | (~c0_1(a221)) | (~c0_1(a246)) | (~c1_1(a246)) | (~c2_1(a246)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | hskp20 | (~ndr1_0) | (~c1_1(a221)) | (~c3_1(a221)) | (~c0_1(a221)) | (~c0_1(a246)) | (~c1_1(a246)) | (~c2_1(a246)))),
% 0.81/0.98 inference(rewrite,[status(thm)],[])).
% 0.81/0.98 tff(1200,plain,
% 0.81/0.98 ((hskp20 | (~ndr1_0) | (~c1_1(a221)) | (~c0_1(a221)) | (~c3_1(a221)) | (~c1_1(a246)) | (~c2_1(a246)) | (~c0_1(a246))) <=> (hskp20 | (~ndr1_0) | (~c1_1(a221)) | (~c3_1(a221)) | (~c0_1(a221)) | (~c0_1(a246)) | (~c1_1(a246)) | (~c2_1(a246)))),
% 0.81/0.98 inference(rewrite,[status(thm)],[])).
% 0.81/0.98 tff(1201,plain,
% 0.81/0.98 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp20 | (~ndr1_0) | (~c1_1(a221)) | (~c0_1(a221)) | (~c3_1(a221)) | (~c1_1(a246)) | (~c2_1(a246)) | (~c0_1(a246)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp20 | (~ndr1_0) | (~c1_1(a221)) | (~c3_1(a221)) | (~c0_1(a221)) | (~c0_1(a246)) | (~c1_1(a246)) | (~c2_1(a246))))),
% 0.81/0.98 inference(monotonicity,[status(thm)],[1200])).
% 0.81/0.98 tff(1202,plain,
% 0.81/0.98 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp20 | (~ndr1_0) | (~c1_1(a221)) | (~c0_1(a221)) | (~c3_1(a221)) | (~c1_1(a246)) | (~c2_1(a246)) | (~c0_1(a246)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | hskp20 | (~ndr1_0) | (~c1_1(a221)) | (~c3_1(a221)) | (~c0_1(a221)) | (~c0_1(a246)) | (~c1_1(a246)) | (~c2_1(a246)))),
% 0.81/0.98 inference(transitivity,[status(thm)],[1201, 1199])).
% 0.81/0.98 tff(1203,plain,
% 0.81/0.98 ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp20 | (~ndr1_0) | (~c1_1(a221)) | (~c0_1(a221)) | (~c3_1(a221)) | (~c1_1(a246)) | (~c2_1(a246)) | (~c0_1(a246)))),
% 0.81/0.98 inference(quant_inst,[status(thm)],[])).
% 0.81/0.98 tff(1204,plain,
% 0.81/0.98 ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | hskp20 | (~ndr1_0) | (~c1_1(a221)) | (~c3_1(a221)) | (~c0_1(a221)) | (~c0_1(a246)) | (~c1_1(a246)) | (~c2_1(a246))),
% 0.81/0.98 inference(modus_ponens,[status(thm)],[1203, 1202])).
% 0.81/0.98 tff(1205,plain,
% 0.81/0.98 (hskp20),
% 0.81/0.98 inference(unit_resolution,[status(thm)],[1204, 122, 1198, 1197, 1196, 1102, 1117, 1013, 1109])).
% 0.81/0.98 tff(1206,plain,
% 0.81/0.98 (hskp3),
% 0.81/0.98 inference(unit_resolution,[status(thm)],[380, 1205, 43])).
% 0.81/0.98 tff(1207,plain,
% 0.81/0.98 (~c2_1(a216)),
% 0.81/0.98 inference(unit_resolution,[status(thm)],[312, 1206])).
% 0.81/0.98 tff(1208,plain,
% 0.81/0.98 (~c0_1(a216)),
% 0.81/0.98 inference(unit_resolution,[status(thm)],[318, 1206])).
% 0.81/0.98 tff(1209,plain,
% 0.81/0.98 (~c1_1(a237)),
% 0.81/0.98 inference(unit_resolution,[status(thm)],[1169, 1142])).
% 0.81/0.98 tff(1210,plain,
% 0.81/0.98 (~c3_1(a259)),
% 0.81/0.98 inference(unit_resolution,[status(thm)],[354, 1205])).
% 0.81/0.98 tff(1211,plain,
% 0.81/0.98 (c3_1(a216)),
% 0.81/0.98 inference(unit_resolution,[status(thm)],[328, 1206])).
% 0.81/0.98 tff(1212,plain,
% 0.81/0.98 (c0_1(a259)),
% 0.81/0.98 inference(unit_resolution,[status(thm)],[370, 1205])).
% 0.81/0.98 tff(1213,plain,
% 0.81/0.98 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | (c3_1(a259) | c1_1(a237) | c0_1(a216) | c2_1(a216) | (~ndr1_0) | (~c3_1(a216)) | (~c3_1(a237)) | (~c2_1(a237)) | c2_1(a259) | (~c0_1(a259)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c3_1(a259) | c1_1(a237) | c0_1(a216) | c2_1(a216) | (~ndr1_0) | (~c3_1(a216)) | (~c3_1(a237)) | (~c2_1(a237)) | c2_1(a259) | (~c0_1(a259)))),
% 0.81/0.98 inference(rewrite,[status(thm)],[])).
% 0.81/0.98 tff(1214,plain,
% 0.81/0.98 (((~ndr1_0) | c3_1(a259) | c2_1(a259) | (~c0_1(a259)) | c1_1(a237) | (~c3_1(a237)) | (~c2_1(a237)) | c0_1(a216) | c2_1(a216) | (~c3_1(a216))) <=> (c3_1(a259) | c1_1(a237) | c0_1(a216) | c2_1(a216) | (~ndr1_0) | (~c3_1(a216)) | (~c3_1(a237)) | (~c2_1(a237)) | c2_1(a259) | (~c0_1(a259)))),
% 0.81/0.98 inference(rewrite,[status(thm)],[])).
% 0.81/0.98 tff(1215,plain,
% 0.81/0.98 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a259) | c2_1(a259) | (~c0_1(a259)) | c1_1(a237) | (~c3_1(a237)) | (~c2_1(a237)) | c0_1(a216) | c2_1(a216) | (~c3_1(a216)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | (c3_1(a259) | c1_1(a237) | c0_1(a216) | c2_1(a216) | (~ndr1_0) | (~c3_1(a216)) | (~c3_1(a237)) | (~c2_1(a237)) | c2_1(a259) | (~c0_1(a259))))),
% 0.81/0.98 inference(monotonicity,[status(thm)],[1214])).
% 0.81/0.98 tff(1216,plain,
% 0.81/0.98 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a259) | c2_1(a259) | (~c0_1(a259)) | c1_1(a237) | (~c3_1(a237)) | (~c2_1(a237)) | c0_1(a216) | c2_1(a216) | (~c3_1(a216)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c3_1(a259) | c1_1(a237) | c0_1(a216) | c2_1(a216) | (~ndr1_0) | (~c3_1(a216)) | (~c3_1(a237)) | (~c2_1(a237)) | c2_1(a259) | (~c0_1(a259)))),
% 0.81/0.98 inference(transitivity,[status(thm)],[1215, 1213])).
% 0.81/0.98 tff(1217,plain,
% 0.81/0.98 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a259) | c2_1(a259) | (~c0_1(a259)) | c1_1(a237) | (~c3_1(a237)) | (~c2_1(a237)) | c0_1(a216) | c2_1(a216) | (~c3_1(a216)))),
% 0.81/0.98 inference(quant_inst,[status(thm)],[])).
% 0.81/0.98 tff(1218,plain,
% 0.81/0.98 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c3_1(a259) | c1_1(a237) | c0_1(a216) | c2_1(a216) | (~ndr1_0) | (~c3_1(a216)) | (~c3_1(a237)) | (~c2_1(a237)) | c2_1(a259) | (~c0_1(a259))),
% 0.81/0.98 inference(modus_ponens,[status(thm)],[1217, 1216])).
% 0.81/0.98 tff(1219,plain,
% 0.81/0.98 (c2_1(a259)),
% 0.81/0.98 inference(unit_resolution,[status(thm)],[1218, 122, 1212, 1150, 1211, 1210, 1209, 1208, 1207, 10, 1162])).
% 0.81/0.98 tff(1220,plain,
% 0.81/0.98 (((~![U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp27 | c3_1(a259) | (~ndr1_0) | (~c2_1(a259)) | (~c0_1(a259)))) <=> ((~![U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp27 | c3_1(a259) | (~ndr1_0) | (~c2_1(a259)) | (~c0_1(a259)))),
% 0.81/0.98 inference(rewrite,[status(thm)],[])).
% 0.81/0.98 tff(1221,plain,
% 0.81/0.98 ((hskp27 | (~ndr1_0) | c3_1(a259) | (~c2_1(a259)) | (~c0_1(a259))) <=> (hskp27 | c3_1(a259) | (~ndr1_0) | (~c2_1(a259)) | (~c0_1(a259)))),
% 0.81/0.98 inference(rewrite,[status(thm)],[])).
% 0.81/0.98 tff(1222,plain,
% 0.81/0.98 (((~![U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp27 | (~ndr1_0) | c3_1(a259) | (~c2_1(a259)) | (~c0_1(a259)))) <=> ((~![U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp27 | c3_1(a259) | (~ndr1_0) | (~c2_1(a259)) | (~c0_1(a259))))),
% 0.81/0.98 inference(monotonicity,[status(thm)],[1221])).
% 0.81/0.98 tff(1223,plain,
% 0.81/0.98 (((~![U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp27 | (~ndr1_0) | c3_1(a259) | (~c2_1(a259)) | (~c0_1(a259)))) <=> ((~![U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp27 | c3_1(a259) | (~ndr1_0) | (~c2_1(a259)) | (~c0_1(a259)))),
% 0.81/0.98 inference(transitivity,[status(thm)],[1222, 1220])).
% 0.81/0.98 tff(1224,plain,
% 0.81/0.98 ((~![U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp27 | (~ndr1_0) | c3_1(a259) | (~c2_1(a259)) | (~c0_1(a259)))),
% 0.81/0.98 inference(quant_inst,[status(thm)],[])).
% 0.81/0.98 tff(1225,plain,
% 0.81/0.98 ((~![U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp27 | c3_1(a259) | (~ndr1_0) | (~c2_1(a259)) | (~c0_1(a259))),
% 0.81/0.98 inference(modus_ponens,[status(thm)],[1224, 1223])).
% 0.81/0.98 tff(1226,plain,
% 0.81/0.98 ($false),
% 0.81/0.98 inference(unit_resolution,[status(thm)],[1225, 122, 1080, 1212, 1210, 192, 1219])).
% 0.81/0.98 tff(1227,plain,((~hskp6) | hskp27 | hskp8 | hskp0), inference(lemma,lemma(discharge,[]))).
% 0.81/0.98 tff(1228,plain,
% 0.81/0.98 (hskp27),
% 0.81/0.98 inference(unit_resolution,[status(thm)],[1227, 1079, 43, 64])).
% 0.81/0.98 tff(1229,plain,
% 0.81/0.98 (c3_1(a232)),
% 0.81/0.98 inference(unit_resolution,[status(thm)],[247, 1228])).
% 0.81/0.98 tff(1230,plain,
% 0.81/0.98 (c2_1(a232)),
% 0.81/0.98 inference(unit_resolution,[status(thm)],[255, 1228])).
% 0.81/0.98 tff(1231,plain,
% 0.81/0.98 (c0_1(a232)),
% 0.81/0.98 inference(unit_resolution,[status(thm)],[263, 1228])).
% 0.81/0.98 tff(1232,plain,
% 0.81/0.98 (~hskp13),
% 0.81/0.98 inference(unit_resolution,[status(thm)],[776, 1231, 64, 1230, 1229])).
% 0.81/0.98 tff(1233,plain,
% 0.81/0.98 (((~![U: $i] : (hskp20 | hskp13 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp20 | hskp13 | c2_1(a247) | (~ndr1_0) | (~c1_1(a247)) | (~c3_1(a247)))) <=> ((~![U: $i] : (hskp20 | hskp13 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | hskp20 | hskp13 | c2_1(a247) | (~ndr1_0) | (~c1_1(a247)) | (~c3_1(a247)))),
% 0.81/0.98 inference(rewrite,[status(thm)],[])).
% 0.81/0.98 tff(1234,plain,
% 0.81/0.98 ((hskp20 | hskp13 | (~ndr1_0) | c2_1(a247) | (~c1_1(a247)) | (~c3_1(a247))) <=> (hskp20 | hskp13 | c2_1(a247) | (~ndr1_0) | (~c1_1(a247)) | (~c3_1(a247)))),
% 0.81/0.98 inference(rewrite,[status(thm)],[])).
% 0.81/0.98 tff(1235,plain,
% 0.81/0.98 (((~![U: $i] : (hskp20 | hskp13 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp20 | hskp13 | (~ndr1_0) | c2_1(a247) | (~c1_1(a247)) | (~c3_1(a247)))) <=> ((~![U: $i] : (hskp20 | hskp13 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp20 | hskp13 | c2_1(a247) | (~ndr1_0) | (~c1_1(a247)) | (~c3_1(a247))))),
% 0.81/0.98 inference(monotonicity,[status(thm)],[1234])).
% 0.81/0.98 tff(1236,plain,
% 0.81/0.98 (((~![U: $i] : (hskp20 | hskp13 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp20 | hskp13 | (~ndr1_0) | c2_1(a247) | (~c1_1(a247)) | (~c3_1(a247)))) <=> ((~![U: $i] : (hskp20 | hskp13 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | hskp20 | hskp13 | c2_1(a247) | (~ndr1_0) | (~c1_1(a247)) | (~c3_1(a247)))),
% 0.81/0.98 inference(transitivity,[status(thm)],[1235, 1233])).
% 0.81/0.98 tff(1237,plain,
% 0.81/0.98 ((~![U: $i] : (hskp20 | hskp13 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp20 | hskp13 | (~ndr1_0) | c2_1(a247) | (~c1_1(a247)) | (~c3_1(a247)))),
% 0.81/0.99 inference(quant_inst,[status(thm)],[])).
% 0.81/0.99 tff(1238,plain,
% 0.81/0.99 ((~![U: $i] : (hskp20 | hskp13 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | hskp20 | hskp13 | c2_1(a247) | (~ndr1_0) | (~c1_1(a247)) | (~c3_1(a247))),
% 0.81/0.99 inference(modus_ponens,[status(thm)],[1237, 1236])).
% 0.81/0.99 tff(1239,plain,
% 0.81/0.99 (~c1_1(a247)),
% 0.81/0.99 inference(unit_resolution,[status(thm)],[1238, 122, 132, 1232, 158, 150, 74])).
% 0.81/0.99 tff(1240,plain,
% 0.81/0.99 (^[V: $i, U: $i] : refl((hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))) <=> (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))))),
% 0.81/0.99 inference(bind,[status(th)],[])).
% 0.81/0.99 tff(1241,plain,
% 0.81/0.99 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 0.81/0.99 inference(quant_intro,[status(thm)],[1240])).
% 0.81/0.99 tff(1242,plain,
% 0.81/0.99 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 0.81/0.99 inference(rewrite,[status(thm)],[])).
% 0.81/0.99 tff(1243,plain,
% 0.81/0.99 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | (~c0_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | (~c0_1(V))) | c1_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c0_1(V)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c0_1(V))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c0_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c0_1(V))) | c2_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c2_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)) | c2_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c2_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)) | c2_1(V)) | hskp11) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))) | hskp11))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))) | hskp11) <=> (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c2_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)) | c2_1(V)) | hskp11) <=> (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))))),
% 0.81/0.99 inference(bind,[status(th)],[])).
% 0.81/0.99 tff(1244,plain,
% 0.81/0.99 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) | c2_1(V)) | hskp11) <=> ![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 0.81/0.99 inference(quant_intro,[status(thm)],[1243])).
% 0.81/0.99 tff(1245,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) | c2_1(V)) | hskp11)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause163')).
% 0.81/0.99 tff(1246,plain,
% 0.81/0.99 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 0.81/0.99 inference(modus_ponens,[status(thm)],[1245, 1244])).
% 0.81/0.99 tff(1247,plain,
% 0.81/0.99 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 0.81/0.99 inference(modus_ponens,[status(thm)],[1246, 1242])).
% 0.81/0.99 tff(1248,plain,(
% 0.81/0.99 ![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 0.81/0.99 inference(skolemize,[status(sab)],[1247])).
% 0.81/0.99 tff(1249,plain,
% 0.81/0.99 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 0.81/0.99 inference(modus_ponens,[status(thm)],[1248, 1241])).
% 0.81/0.99 tff(1250,plain,
% 0.81/0.99 (c0_1(a247)),
% 0.81/0.99 inference(unit_resolution,[status(thm)],[664, 144])).
% 0.81/0.99 tff(1251,plain,
% 0.81/0.99 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp11 | c2_1(a247) | (~ndr1_0) | (~c2_1(a232)) | (~c3_1(a232)) | (~c0_1(a232)) | c1_1(a247) | (~c0_1(a247)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp11 | c2_1(a247) | (~ndr1_0) | (~c2_1(a232)) | (~c3_1(a232)) | (~c0_1(a232)) | c1_1(a247) | (~c0_1(a247)))),
% 0.81/0.99 inference(rewrite,[status(thm)],[])).
% 0.81/0.99 tff(1252,plain,
% 0.81/0.99 ((hskp11 | (~ndr1_0) | (~c2_1(a232)) | (~c0_1(a232)) | (~c3_1(a232)) | c2_1(a247) | c1_1(a247) | (~c0_1(a247))) <=> (hskp11 | c2_1(a247) | (~ndr1_0) | (~c2_1(a232)) | (~c3_1(a232)) | (~c0_1(a232)) | c1_1(a247) | (~c0_1(a247)))),
% 0.81/0.99 inference(rewrite,[status(thm)],[])).
% 0.81/0.99 tff(1253,plain,
% 0.81/0.99 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp11 | (~ndr1_0) | (~c2_1(a232)) | (~c0_1(a232)) | (~c3_1(a232)) | c2_1(a247) | c1_1(a247) | (~c0_1(a247)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp11 | c2_1(a247) | (~ndr1_0) | (~c2_1(a232)) | (~c3_1(a232)) | (~c0_1(a232)) | c1_1(a247) | (~c0_1(a247))))),
% 0.81/0.99 inference(monotonicity,[status(thm)],[1252])).
% 0.81/0.99 tff(1254,plain,
% 0.81/0.99 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp11 | (~ndr1_0) | (~c2_1(a232)) | (~c0_1(a232)) | (~c3_1(a232)) | c2_1(a247) | c1_1(a247) | (~c0_1(a247)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp11 | c2_1(a247) | (~ndr1_0) | (~c2_1(a232)) | (~c3_1(a232)) | (~c0_1(a232)) | c1_1(a247) | (~c0_1(a247)))),
% 0.81/0.99 inference(transitivity,[status(thm)],[1253, 1251])).
% 0.81/0.99 tff(1255,plain,
% 0.81/0.99 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp11 | (~ndr1_0) | (~c2_1(a232)) | (~c0_1(a232)) | (~c3_1(a232)) | c2_1(a247) | c1_1(a247) | (~c0_1(a247)))),
% 0.81/0.99 inference(quant_inst,[status(thm)],[])).
% 0.81/0.99 tff(1256,plain,
% 0.81/0.99 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp11 | c2_1(a247) | (~ndr1_0) | (~c2_1(a232)) | (~c3_1(a232)) | (~c0_1(a232)) | c1_1(a247) | (~c0_1(a247))),
% 0.81/0.99 inference(modus_ponens,[status(thm)],[1255, 1254])).
% 0.81/0.99 tff(1257,plain,
% 0.81/0.99 (hskp11),
% 0.81/0.99 inference(unit_resolution,[status(thm)],[1256, 122, 1231, 1230, 1229, 1250, 150, 1249, 1239])).
% 0.81/0.99 tff(1258,plain,
% 0.81/0.99 (c2_1(a230)),
% 0.81/0.99 inference(unit_resolution,[status(thm)],[478, 1257])).
% 0.81/0.99 tff(1259,plain,
% 0.81/0.99 (c3_1(a230)),
% 0.81/0.99 inference(unit_resolution,[status(thm)],[470, 1257])).
% 0.81/0.99 tff(1260,plain,
% 0.81/0.99 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W))))),
% 0.81/0.99 inference(bind,[status(th)],[])).
% 0.81/0.99 tff(1261,plain,
% 0.81/0.99 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))),
% 0.81/0.99 inference(quant_intro,[status(thm)],[1260])).
% 0.81/0.99 tff(1262,plain,
% 0.81/0.99 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))),
% 0.81/0.99 inference(rewrite,[status(thm)],[])).
% 0.81/0.99 tff(1263,plain,
% 0.81/0.99 (^[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)) | (~c1_1(U)) | (~c3_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V))) | (~c2_1(W))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V)) | (~c2_1(W)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V)) | (~c2_1(W))))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | (~c3_1(W))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V)) | (~c2_1(W))) | (~c3_1(W))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V)) | (~c2_1(W))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V)) | (~c2_1(W)) | (~c3_1(W)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V)) | (~c2_1(W)) | (~c3_1(W))))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c1_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V)) | (~c2_1(W)) | (~c3_1(W))) | c1_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V)) | (~c2_1(W)) | (~c3_1(W))) | c1_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(W)) | (~c3_1(W)))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c1_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(W)) | (~c3_1(W))))), ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(W)) | (~c3_1(W))) | c2_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(W)) | (~c3_1(W))) | c2_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | (~c2_1(W)) | (~c3_1(W)))), ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | (~c2_1(W)) | (~c3_1(W))))), (((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c1_1(V)) | c2_1(V)) | c0_1(W)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | (~c2_1(W)) | (~c3_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | (~c2_1(W)) | (~c3_1(W))) | c0_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))), (((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c1_1(V)) | c2_1(V)) | c0_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))))),
% 0.81/0.99 inference(bind,[status(th)],[])).
% 0.81/0.99 tff(1264,plain,
% 0.81/0.99 (![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c1_1(V)) | c2_1(V)) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))),
% 0.81/0.99 inference(quant_intro,[status(thm)],[1263])).
% 0.81/0.99 tff(1265,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c1_1(V)) | c2_1(V)) | c0_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause176')).
% 0.81/0.99 tff(1266,plain,
% 0.81/0.99 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))),
% 0.81/0.99 inference(modus_ponens,[status(thm)],[1265, 1264])).
% 0.81/0.99 tff(1267,plain,
% 0.81/0.99 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))),
% 0.81/0.99 inference(modus_ponens,[status(thm)],[1266, 1262])).
% 0.81/0.99 tff(1268,plain,(
% 0.81/0.99 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))),
% 0.81/0.99 inference(skolemize,[status(sab)],[1267])).
% 0.81/0.99 tff(1269,plain,
% 0.81/0.99 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))),
% 0.81/0.99 inference(modus_ponens,[status(thm)],[1268, 1261])).
% 0.81/0.99 tff(1270,plain,
% 0.81/0.99 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | (c2_1(a247) | c0_1(a229) | (~ndr1_0) | (~c2_1(a232)) | (~c1_1(a232)) | (~c3_1(a232)) | (~c2_1(a229)) | (~c3_1(a229)) | c1_1(a247) | (~c0_1(a247)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | c2_1(a247) | c0_1(a229) | (~ndr1_0) | (~c2_1(a232)) | (~c1_1(a232)) | (~c3_1(a232)) | (~c2_1(a229)) | (~c3_1(a229)) | c1_1(a247) | (~c0_1(a247)))),
% 0.81/0.99 inference(rewrite,[status(thm)],[])).
% 0.81/0.99 tff(1271,plain,
% 0.81/0.99 (((~ndr1_0) | (~c2_1(a232)) | (~c1_1(a232)) | (~c3_1(a232)) | c2_1(a247) | c1_1(a247) | (~c0_1(a247)) | c0_1(a229) | (~c2_1(a229)) | (~c3_1(a229))) <=> (c2_1(a247) | c0_1(a229) | (~ndr1_0) | (~c2_1(a232)) | (~c1_1(a232)) | (~c3_1(a232)) | (~c2_1(a229)) | (~c3_1(a229)) | c1_1(a247) | (~c0_1(a247)))),
% 0.81/0.99 inference(rewrite,[status(thm)],[])).
% 0.81/0.99 tff(1272,plain,
% 0.81/0.99 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a232)) | (~c1_1(a232)) | (~c3_1(a232)) | c2_1(a247) | c1_1(a247) | (~c0_1(a247)) | c0_1(a229) | (~c2_1(a229)) | (~c3_1(a229)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | (c2_1(a247) | c0_1(a229) | (~ndr1_0) | (~c2_1(a232)) | (~c1_1(a232)) | (~c3_1(a232)) | (~c2_1(a229)) | (~c3_1(a229)) | c1_1(a247) | (~c0_1(a247))))),
% 0.81/0.99 inference(monotonicity,[status(thm)],[1271])).
% 0.81/0.99 tff(1273,plain,
% 0.81/0.99 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a232)) | (~c1_1(a232)) | (~c3_1(a232)) | c2_1(a247) | c1_1(a247) | (~c0_1(a247)) | c0_1(a229) | (~c2_1(a229)) | (~c3_1(a229)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | c2_1(a247) | c0_1(a229) | (~ndr1_0) | (~c2_1(a232)) | (~c1_1(a232)) | (~c3_1(a232)) | (~c2_1(a229)) | (~c3_1(a229)) | c1_1(a247) | (~c0_1(a247)))),
% 0.81/0.99 inference(transitivity,[status(thm)],[1272, 1270])).
% 0.81/0.99 tff(1274,plain,
% 0.81/0.99 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a232)) | (~c1_1(a232)) | (~c3_1(a232)) | c2_1(a247) | c1_1(a247) | (~c0_1(a247)) | c0_1(a229) | (~c2_1(a229)) | (~c3_1(a229)))),
% 0.81/0.99 inference(quant_inst,[status(thm)],[])).
% 0.81/0.99 tff(1275,plain,
% 0.81/0.99 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | c2_1(a247) | c0_1(a229) | (~ndr1_0) | (~c2_1(a232)) | (~c1_1(a232)) | (~c3_1(a232)) | (~c2_1(a229)) | (~c3_1(a229)) | c1_1(a247) | (~c0_1(a247))),
% 0.81/0.99 inference(modus_ponens,[status(thm)],[1274, 1273])).
% 0.81/0.99 tff(1276,plain,
% 0.81/0.99 (~c1_1(a232)),
% 0.81/0.99 inference(unit_resolution,[status(thm)],[1275, 122, 1230, 1229, 1250, 1053, 1045, 150, 1044, 1269, 1239])).
% 0.81/0.99 tff(1277,plain,
% 0.81/0.99 (~c1_1(a230)),
% 0.81/0.99 inference(unit_resolution,[status(thm)],[442, 1257])).
% 0.81/0.99 tff(1278,plain,
% 0.81/0.99 (~hskp19),
% 0.81/0.99 inference(unit_resolution,[status(thm)],[836, 1277, 64, 1259, 43, 1258])).
% 0.81/0.99 tff(1279,plain,
% 0.81/0.99 ($false),
% 0.81/0.99 inference(unit_resolution,[status(thm)],[865, 1278, 1277, 1231, 1229, 1276, 1259, 1258])).
% 0.81/0.99 tff(1280,plain,(hskp20 | hskp0 | hskp8), inference(lemma,lemma(discharge,[]))).
% 0.81/0.99 tff(1281,plain,
% 0.81/0.99 (hskp20),
% 0.81/0.99 inference(unit_resolution,[status(thm)],[1280, 64, 43])).
% 0.81/0.99 tff(1282,plain,
% 0.81/0.99 (~c3_1(a259)),
% 0.81/0.99 inference(unit_resolution,[status(thm)],[354, 1281])).
% 0.81/0.99 tff(1283,plain,
% 0.81/0.99 (c1_1(a259)),
% 0.81/0.99 inference(unit_resolution,[status(thm)],[362, 1281])).
% 0.81/0.99 tff(1284,plain,
% 0.81/0.99 (c0_1(a259)),
% 0.81/0.99 inference(unit_resolution,[status(thm)],[370, 1281])).
% 0.81/0.99 tff(1285,plain,
% 0.81/0.99 (((~![U: $i] : (hskp12 | hskp0 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp12 | hskp0 | c3_1(a259) | (~ndr1_0) | (~c0_1(a259)) | (~c1_1(a259)))) <=> ((~![U: $i] : (hskp12 | hskp0 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp12 | hskp0 | c3_1(a259) | (~ndr1_0) | (~c0_1(a259)) | (~c1_1(a259)))),
% 0.81/0.99 inference(rewrite,[status(thm)],[])).
% 0.81/0.99 tff(1286,plain,
% 0.81/0.99 ((hskp12 | hskp0 | (~ndr1_0) | c3_1(a259) | (~c1_1(a259)) | (~c0_1(a259))) <=> (hskp12 | hskp0 | c3_1(a259) | (~ndr1_0) | (~c0_1(a259)) | (~c1_1(a259)))),
% 0.81/0.99 inference(rewrite,[status(thm)],[])).
% 0.81/0.99 tff(1287,plain,
% 0.81/0.99 (((~![U: $i] : (hskp12 | hskp0 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp12 | hskp0 | (~ndr1_0) | c3_1(a259) | (~c1_1(a259)) | (~c0_1(a259)))) <=> ((~![U: $i] : (hskp12 | hskp0 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp12 | hskp0 | c3_1(a259) | (~ndr1_0) | (~c0_1(a259)) | (~c1_1(a259))))),
% 0.81/0.99 inference(monotonicity,[status(thm)],[1286])).
% 0.81/0.99 tff(1288,plain,
% 0.81/0.99 (((~![U: $i] : (hskp12 | hskp0 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp12 | hskp0 | (~ndr1_0) | c3_1(a259) | (~c1_1(a259)) | (~c0_1(a259)))) <=> ((~![U: $i] : (hskp12 | hskp0 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp12 | hskp0 | c3_1(a259) | (~ndr1_0) | (~c0_1(a259)) | (~c1_1(a259)))),
% 0.81/0.99 inference(transitivity,[status(thm)],[1287, 1285])).
% 0.81/0.99 tff(1289,plain,
% 0.81/0.99 ((~![U: $i] : (hskp12 | hskp0 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp12 | hskp0 | (~ndr1_0) | c3_1(a259) | (~c1_1(a259)) | (~c0_1(a259)))),
% 0.81/0.99 inference(quant_inst,[status(thm)],[])).
% 0.81/0.99 tff(1290,plain,
% 0.81/0.99 ((~![U: $i] : (hskp12 | hskp0 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp12 | hskp0 | c3_1(a259) | (~ndr1_0) | (~c0_1(a259)) | (~c1_1(a259))),
% 0.81/0.99 inference(modus_ponens,[status(thm)],[1289, 1288])).
% 0.81/0.99 tff(1291,plain,
% 0.81/0.99 (hskp12),
% 0.81/0.99 inference(unit_resolution,[status(thm)],[1290, 122, 64, 1284, 1283, 1282, 63])).
% 0.81/0.99 tff(1292,plain,
% 0.81/0.99 (((~hskp12) | (~c3_1(a235))) <=> ((~hskp12) | (~c3_1(a235)))),
% 0.81/0.99 inference(rewrite,[status(thm)],[])).
% 0.81/0.99 tff(1293,plain,
% 0.81/0.99 (((~c3_1(a235)) | (~hskp12)) <=> ((~hskp12) | (~c3_1(a235)))),
% 0.81/0.99 inference(rewrite,[status(thm)],[])).
% 0.81/0.99 tff(1294,axiom,((~c3_1(a235)) | (~hskp12)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause104')).
% 0.81/0.99 tff(1295,plain,
% 0.81/0.99 ((~hskp12) | (~c3_1(a235))),
% 0.81/0.99 inference(modus_ponens,[status(thm)],[1294, 1293])).
% 0.81/0.99 tff(1296,plain,
% 0.81/0.99 ((~hskp12) | (~c3_1(a235))),
% 0.81/0.99 inference(modus_ponens,[status(thm)],[1295, 1292])).
% 0.81/0.99 tff(1297,plain,
% 0.81/0.99 (~c3_1(a235)),
% 0.81/0.99 inference(unit_resolution,[status(thm)],[1296, 1291])).
% 0.81/0.99 tff(1298,plain,
% 0.81/0.99 (((~hskp12) | (~c0_1(a235))) <=> ((~hskp12) | (~c0_1(a235)))),
% 0.81/0.99 inference(rewrite,[status(thm)],[])).
% 0.81/0.99 tff(1299,plain,
% 0.81/0.99 (((~c0_1(a235)) | (~hskp12)) <=> ((~hskp12) | (~c0_1(a235)))),
% 0.81/0.99 inference(rewrite,[status(thm)],[])).
% 0.81/0.99 tff(1300,axiom,((~c0_1(a235)) | (~hskp12)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause102')).
% 0.81/0.99 tff(1301,plain,
% 0.81/0.99 ((~hskp12) | (~c0_1(a235))),
% 0.81/0.99 inference(modus_ponens,[status(thm)],[1300, 1299])).
% 0.81/0.99 tff(1302,plain,
% 0.81/0.99 ((~hskp12) | (~c0_1(a235))),
% 0.81/0.99 inference(modus_ponens,[status(thm)],[1301, 1298])).
% 0.81/0.99 tff(1303,plain,
% 0.81/0.99 (~c0_1(a235)),
% 0.81/0.99 inference(unit_resolution,[status(thm)],[1302, 1291])).
% 0.81/0.99 tff(1304,plain,
% 0.81/0.99 (((~![U: $i] : (hskp8 | hskp0 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp8 | hskp0 | c0_1(a235) | c3_1(a235) | (~ndr1_0) | c2_1(a235))) <=> ((~![U: $i] : (hskp8 | hskp0 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | hskp8 | hskp0 | c0_1(a235) | c3_1(a235) | (~ndr1_0) | c2_1(a235))),
% 0.81/0.99 inference(rewrite,[status(thm)],[])).
% 0.81/0.99 tff(1305,plain,
% 0.81/0.99 ((hskp8 | hskp0 | (~ndr1_0) | c3_1(a235) | c0_1(a235) | c2_1(a235)) <=> (hskp8 | hskp0 | c0_1(a235) | c3_1(a235) | (~ndr1_0) | c2_1(a235))),
% 0.81/0.99 inference(rewrite,[status(thm)],[])).
% 0.81/0.99 tff(1306,plain,
% 0.81/0.99 (((~![U: $i] : (hskp8 | hskp0 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp8 | hskp0 | (~ndr1_0) | c3_1(a235) | c0_1(a235) | c2_1(a235))) <=> ((~![U: $i] : (hskp8 | hskp0 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp8 | hskp0 | c0_1(a235) | c3_1(a235) | (~ndr1_0) | c2_1(a235)))),
% 0.81/0.99 inference(monotonicity,[status(thm)],[1305])).
% 0.81/0.99 tff(1307,plain,
% 0.81/0.99 (((~![U: $i] : (hskp8 | hskp0 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp8 | hskp0 | (~ndr1_0) | c3_1(a235) | c0_1(a235) | c2_1(a235))) <=> ((~![U: $i] : (hskp8 | hskp0 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | hskp8 | hskp0 | c0_1(a235) | c3_1(a235) | (~ndr1_0) | c2_1(a235))),
% 0.81/0.99 inference(transitivity,[status(thm)],[1306, 1304])).
% 0.81/0.99 tff(1308,plain,
% 0.81/0.99 ((~![U: $i] : (hskp8 | hskp0 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp8 | hskp0 | (~ndr1_0) | c3_1(a235) | c0_1(a235) | c2_1(a235))),
% 0.81/0.99 inference(quant_inst,[status(thm)],[])).
% 0.81/0.99 tff(1309,plain,
% 0.81/0.99 ((~![U: $i] : (hskp8 | hskp0 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | hskp8 | hskp0 | c0_1(a235) | c3_1(a235) | (~ndr1_0) | c2_1(a235)),
% 0.81/0.99 inference(modus_ponens,[status(thm)],[1308, 1307])).
% 0.81/0.99 tff(1310,plain,
% 0.81/0.99 (c2_1(a235)),
% 0.81/0.99 inference(unit_resolution,[status(thm)],[1309, 122, 43, 64, 1303, 1297, 53])).
% 0.81/0.99 tff(1311,plain,
% 0.81/0.99 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_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) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W))))),
% 0.81/0.99 inference(bind,[status(th)],[])).
% 0.81/0.99 tff(1312,plain,
% 0.81/0.99 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 0.81/0.99 inference(quant_intro,[status(thm)],[1311])).
% 0.81/0.99 tff(1313,plain,
% 0.81/0.99 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 0.81/0.99 inference(rewrite,[status(thm)],[])).
% 0.81/0.99 tff(1314,plain,
% 0.81/0.99 (^[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)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c2_1(W))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V))) | (~c2_1(W))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c2_1(W)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c2_1(W))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c2_1(W))) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c2_1(W))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c2_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c2_1(W)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c2_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c2_1(W))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c2_1(W))) | c2_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c2_1(W))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c2_1(W))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c2_1(W)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c2_1(W))) | c2_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c2_1(W))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c2_1(W))) | c2_1(U)) | c1_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c2_1(W))) | c3_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c2_1(W))) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | (~c2_1(W)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c2_1(W))) | c2_1(U)) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | (~c2_1(W))))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c2_1(W))) | c2_1(U)) | c1_1(V)) | c3_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | (~c2_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | (~c2_1(W))) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c2_1(W))) | c2_1(U)) | c1_1(V)) | c3_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W))))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c2_1(W))) | c2_1(U)) | c1_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W))) | c1_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W))) | c1_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c2_1(W))) | c2_1(U)) | c1_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))))),
% 0.81/0.99 inference(bind,[status(th)],[])).
% 0.81/0.99 tff(1315,plain,
% 0.81/0.99 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c2_1(W))) | c2_1(U)) | c1_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 0.81/0.99 inference(quant_intro,[status(thm)],[1314])).
% 0.81/0.99 tff(1316,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c2_1(W))) | c2_1(U)) | c1_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause168')).
% 0.81/0.99 tff(1317,plain,
% 0.81/0.99 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 0.81/0.99 inference(modus_ponens,[status(thm)],[1316, 1315])).
% 0.81/0.99 tff(1318,plain,
% 0.81/0.99 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 0.81/0.99 inference(modus_ponens,[status(thm)],[1317, 1313])).
% 0.81/0.99 tff(1319,plain,(
% 0.81/0.99 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 0.81/0.99 inference(skolemize,[status(sab)],[1318])).
% 0.81/0.99 tff(1320,plain,
% 0.81/0.99 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 0.81/0.99 inference(modus_ponens,[status(thm)],[1319, 1312])).
% 0.81/0.99 tff(1321,plain,
% 0.81/0.99 (~hskp18),
% 0.81/0.99 inference(unit_resolution,[status(thm)],[1078, 1070, 1053, 1045, 1044])).
% 0.81/0.99 tff(1322,plain,
% 0.81/0.99 (^[U: $i] : refl((hskp18 | hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) <=> (hskp18 | hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))))),
% 0.81/0.99 inference(bind,[status(th)],[])).
% 0.81/0.99 tff(1323,plain,
% 0.81/0.99 (![U: $i] : (hskp18 | hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp18 | hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 0.81/0.99 inference(quant_intro,[status(thm)],[1322])).
% 0.81/0.99 tff(1324,plain,
% 0.81/0.99 (![U: $i] : (hskp18 | hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp18 | hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 0.81/0.99 inference(rewrite,[status(thm)],[])).
% 0.81/0.99 tff(1325,plain,
% 0.81/0.99 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp6) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) | hskp6))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) | hskp6) <=> (hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp6) <=> (hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp6) | hskp18) <=> ((hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) | hskp18))), rewrite(((hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) | hskp18) <=> (hskp18 | hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp6) | hskp18) <=> (hskp18 | hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))))),
% 0.81/0.99 inference(bind,[status(th)],[])).
% 0.81/0.99 tff(1326,plain,
% 0.81/0.99 (![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp6) | hskp18) <=> ![U: $i] : (hskp18 | hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 0.81/0.99 inference(quant_intro,[status(thm)],[1325])).
% 0.81/0.99 tff(1327,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp6) | hskp18)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause135')).
% 0.81/0.99 tff(1328,plain,
% 0.81/0.99 (![U: $i] : (hskp18 | hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 0.81/0.99 inference(modus_ponens,[status(thm)],[1327, 1326])).
% 0.81/0.99 tff(1329,plain,
% 0.81/0.99 (![U: $i] : (hskp18 | hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 0.81/0.99 inference(modus_ponens,[status(thm)],[1328, 1324])).
% 0.81/0.99 tff(1330,plain,(
% 0.81/0.99 ![U: $i] : (hskp18 | hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 0.81/0.99 inference(skolemize,[status(sab)],[1329])).
% 0.81/0.99 tff(1331,plain,
% 0.81/0.99 (![U: $i] : (hskp18 | hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 0.81/0.99 inference(modus_ponens,[status(thm)],[1330, 1323])).
% 0.81/0.99 tff(1332,plain,
% 0.81/0.99 (((~![U: $i] : (hskp18 | hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp18 | hskp6 | (~ndr1_0) | c2_1(a259) | (~c0_1(a259)) | (~c1_1(a259)))) <=> ((~![U: $i] : (hskp18 | hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp18 | hskp6 | (~ndr1_0) | c2_1(a259) | (~c0_1(a259)) | (~c1_1(a259)))),
% 0.81/0.99 inference(rewrite,[status(thm)],[])).
% 0.81/0.99 tff(1333,plain,
% 0.81/0.99 ((hskp18 | hskp6 | (~ndr1_0) | c2_1(a259) | (~c1_1(a259)) | (~c0_1(a259))) <=> (hskp18 | hskp6 | (~ndr1_0) | c2_1(a259) | (~c0_1(a259)) | (~c1_1(a259)))),
% 0.81/0.99 inference(rewrite,[status(thm)],[])).
% 0.81/0.99 tff(1334,plain,
% 0.81/0.99 (((~![U: $i] : (hskp18 | hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp18 | hskp6 | (~ndr1_0) | c2_1(a259) | (~c1_1(a259)) | (~c0_1(a259)))) <=> ((~![U: $i] : (hskp18 | hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp18 | hskp6 | (~ndr1_0) | c2_1(a259) | (~c0_1(a259)) | (~c1_1(a259))))),
% 0.81/0.99 inference(monotonicity,[status(thm)],[1333])).
% 0.81/0.99 tff(1335,plain,
% 0.81/0.99 (((~![U: $i] : (hskp18 | hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp18 | hskp6 | (~ndr1_0) | c2_1(a259) | (~c1_1(a259)) | (~c0_1(a259)))) <=> ((~![U: $i] : (hskp18 | hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp18 | hskp6 | (~ndr1_0) | c2_1(a259) | (~c0_1(a259)) | (~c1_1(a259)))),
% 0.81/0.99 inference(transitivity,[status(thm)],[1334, 1332])).
% 0.81/0.99 tff(1336,plain,
% 0.81/0.99 ((~![U: $i] : (hskp18 | hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp18 | hskp6 | (~ndr1_0) | c2_1(a259) | (~c1_1(a259)) | (~c0_1(a259)))),
% 0.81/0.99 inference(quant_inst,[status(thm)],[])).
% 0.81/0.99 tff(1337,plain,
% 0.81/0.99 ((~![U: $i] : (hskp18 | hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp18 | hskp6 | (~ndr1_0) | c2_1(a259) | (~c0_1(a259)) | (~c1_1(a259))),
% 0.81/0.99 inference(modus_ponens,[status(thm)],[1336, 1335])).
% 0.81/0.99 tff(1338,plain,
% 0.81/0.99 (hskp18 | hskp6 | c2_1(a259)),
% 0.81/0.99 inference(unit_resolution,[status(thm)],[1337, 122, 1284, 1283, 1331])).
% 0.81/0.99 tff(1339,plain,
% 0.81/0.99 (c2_1(a259)),
% 0.81/0.99 inference(unit_resolution,[status(thm)],[1338, 1321, 1070])).
% 0.81/0.99 tff(1340,plain,
% 0.81/0.99 (^[V: $i, U: $i] : refl((hskp0 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c1_1(V)) <=> (hskp0 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c1_1(V)))),
% 0.81/0.99 inference(bind,[status(th)],[])).
% 0.81/0.99 tff(1341,plain,
% 0.81/0.99 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c1_1(V)) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c1_1(V))),
% 0.81/0.99 inference(quant_intro,[status(thm)],[1340])).
% 0.81/1.00 tff(1342,plain,
% 0.81/1.00 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c1_1(V)) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c1_1(V))),
% 0.81/1.00 inference(rewrite,[status(thm)],[])).
% 0.81/1.00 tff(1343,plain,
% 0.81/1.00 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U))))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V)) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V)))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c1_1(V))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c1_1(V)))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp0) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c1_1(V)) | hskp0))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c1_1(V)) | hskp0) <=> (hskp0 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c1_1(V))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp0) <=> (hskp0 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c1_1(V))))),
% 0.81/1.00 inference(bind,[status(th)],[])).
% 0.81/1.00 tff(1344,plain,
% 0.81/1.00 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp0) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c1_1(V))),
% 0.81/1.00 inference(quant_intro,[status(thm)],[1343])).
% 0.81/1.00 tff(1345,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp0)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause144')).
% 0.81/1.00 tff(1346,plain,
% 0.81/1.00 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c1_1(V))),
% 0.81/1.00 inference(modus_ponens,[status(thm)],[1345, 1344])).
% 0.81/1.00 tff(1347,plain,
% 0.81/1.00 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c1_1(V))),
% 0.81/1.00 inference(modus_ponens,[status(thm)],[1346, 1342])).
% 0.81/1.00 tff(1348,plain,(
% 0.81/1.00 ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c1_1(V))),
% 0.81/1.00 inference(skolemize,[status(sab)],[1347])).
% 0.81/1.00 tff(1349,plain,
% 0.81/1.00 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c1_1(V))),
% 0.81/1.00 inference(modus_ponens,[status(thm)],[1348, 1341])).
% 0.81/1.00 tff(1350,plain,
% 0.81/1.00 (^[V: $i, U: $i] : refl((hskp9 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))) <=> (hskp9 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))))),
% 0.81/1.00 inference(bind,[status(th)],[])).
% 0.81/1.00 tff(1351,plain,
% 0.81/1.00 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.81/1.00 inference(quant_intro,[status(thm)],[1350])).
% 0.81/1.00 tff(1352,plain,
% 0.81/1.00 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.81/1.00 inference(rewrite,[status(thm)],[])).
% 0.81/1.00 tff(1353,plain,
% 0.81/1.00 (^[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)) | hskp9) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))) | hskp9))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))) | hskp9) <=> (hskp9 | (~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)) | hskp9) <=> (hskp9 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))))),
% 0.81/1.00 inference(bind,[status(th)],[])).
% 0.81/1.00 tff(1354,plain,
% 0.81/1.00 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c0_1(V)) | c3_1(V)) | hskp9) <=> ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.81/1.00 inference(quant_intro,[status(thm)],[1353])).
% 0.81/1.00 tff(1355,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)) | hskp9)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause154')).
% 0.81/1.00 tff(1356,plain,
% 0.81/1.00 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.81/1.00 inference(modus_ponens,[status(thm)],[1355, 1354])).
% 0.81/1.00 tff(1357,plain,
% 0.81/1.00 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.81/1.00 inference(modus_ponens,[status(thm)],[1356, 1352])).
% 0.81/1.00 tff(1358,plain,(
% 0.81/1.00 ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.81/1.00 inference(skolemize,[status(sab)],[1357])).
% 0.81/1.00 tff(1359,plain,
% 0.81/1.00 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.81/1.00 inference(modus_ponens,[status(thm)],[1358, 1351])).
% 0.81/1.00 tff(1360,plain,
% 0.81/1.00 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp9 | c3_1(a259) | c0_1(a235) | c3_1(a235) | (~ndr1_0) | (~c2_1(a235)) | (~c0_1(a259)) | (~c1_1(a259)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp9 | c3_1(a259) | c0_1(a235) | c3_1(a235) | (~ndr1_0) | (~c2_1(a235)) | (~c0_1(a259)) | (~c1_1(a259)))),
% 0.81/1.00 inference(rewrite,[status(thm)],[])).
% 0.81/1.00 tff(1361,plain,
% 0.81/1.00 ((hskp9 | (~ndr1_0) | c3_1(a259) | (~c1_1(a259)) | (~c0_1(a259)) | c3_1(a235) | c0_1(a235) | (~c2_1(a235))) <=> (hskp9 | c3_1(a259) | c0_1(a235) | c3_1(a235) | (~ndr1_0) | (~c2_1(a235)) | (~c0_1(a259)) | (~c1_1(a259)))),
% 0.81/1.00 inference(rewrite,[status(thm)],[])).
% 0.81/1.00 tff(1362,plain,
% 0.81/1.00 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp9 | (~ndr1_0) | c3_1(a259) | (~c1_1(a259)) | (~c0_1(a259)) | c3_1(a235) | c0_1(a235) | (~c2_1(a235)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp9 | c3_1(a259) | c0_1(a235) | c3_1(a235) | (~ndr1_0) | (~c2_1(a235)) | (~c0_1(a259)) | (~c1_1(a259))))),
% 0.81/1.00 inference(monotonicity,[status(thm)],[1361])).
% 0.81/1.00 tff(1363,plain,
% 0.81/1.00 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp9 | (~ndr1_0) | c3_1(a259) | (~c1_1(a259)) | (~c0_1(a259)) | c3_1(a235) | c0_1(a235) | (~c2_1(a235)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp9 | c3_1(a259) | c0_1(a235) | c3_1(a235) | (~ndr1_0) | (~c2_1(a235)) | (~c0_1(a259)) | (~c1_1(a259)))),
% 0.81/1.00 inference(transitivity,[status(thm)],[1362, 1360])).
% 0.81/1.00 tff(1364,plain,
% 0.81/1.00 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp9 | (~ndr1_0) | c3_1(a259) | (~c1_1(a259)) | (~c0_1(a259)) | c3_1(a235) | c0_1(a235) | (~c2_1(a235)))),
% 0.81/1.00 inference(quant_inst,[status(thm)],[])).
% 0.81/1.00 tff(1365,plain,
% 0.81/1.00 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp9 | c3_1(a259) | c0_1(a235) | c3_1(a235) | (~ndr1_0) | (~c2_1(a235)) | (~c0_1(a259)) | (~c1_1(a259))),
% 0.81/1.00 inference(modus_ponens,[status(thm)],[1364, 1363])).
% 0.81/1.00 tff(1366,plain,
% 0.81/1.00 (hskp9),
% 0.81/1.00 inference(unit_resolution,[status(thm)],[1365, 122, 1284, 1283, 1282, 1303, 1297, 1359, 1310])).
% 0.81/1.00 tff(1367,plain,
% 0.81/1.00 (((~hskp9) | (~c2_1(a228))) <=> ((~hskp9) | (~c2_1(a228)))),
% 0.81/1.00 inference(rewrite,[status(thm)],[])).
% 0.81/1.00 tff(1368,plain,
% 0.81/1.00 (((~c2_1(a228)) | (~hskp9)) <=> ((~hskp9) | (~c2_1(a228)))),
% 0.81/1.00 inference(rewrite,[status(thm)],[])).
% 0.81/1.00 tff(1369,axiom,((~c2_1(a228)) | (~hskp9)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause108')).
% 0.81/1.00 tff(1370,plain,
% 0.81/1.00 ((~hskp9) | (~c2_1(a228))),
% 0.81/1.00 inference(modus_ponens,[status(thm)],[1369, 1368])).
% 0.81/1.00 tff(1371,plain,
% 0.81/1.00 ((~hskp9) | (~c2_1(a228))),
% 0.81/1.00 inference(modus_ponens,[status(thm)],[1370, 1367])).
% 0.81/1.00 tff(1372,plain,
% 0.81/1.00 (~c2_1(a228)),
% 0.81/1.00 inference(unit_resolution,[status(thm)],[1371, 1366])).
% 0.81/1.00 tff(1373,plain,
% 0.81/1.00 (((~hskp12) | (~c1_1(a235))) <=> ((~hskp12) | (~c1_1(a235)))),
% 0.81/1.00 inference(rewrite,[status(thm)],[])).
% 0.81/1.00 tff(1374,plain,
% 0.81/1.00 (((~c1_1(a235)) | (~hskp12)) <=> ((~hskp12) | (~c1_1(a235)))),
% 0.81/1.00 inference(rewrite,[status(thm)],[])).
% 0.81/1.00 tff(1375,axiom,((~c1_1(a235)) | (~hskp12)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause103')).
% 0.81/1.00 tff(1376,plain,
% 0.81/1.00 ((~hskp12) | (~c1_1(a235))),
% 0.81/1.00 inference(modus_ponens,[status(thm)],[1375, 1374])).
% 0.81/1.00 tff(1377,plain,
% 0.81/1.00 ((~hskp12) | (~c1_1(a235))),
% 0.81/1.00 inference(modus_ponens,[status(thm)],[1376, 1373])).
% 0.81/1.00 tff(1378,plain,
% 0.81/1.00 (~c1_1(a235)),
% 0.81/1.00 inference(unit_resolution,[status(thm)],[1377, 1291])).
% 0.81/1.00 tff(1379,plain,
% 0.81/1.00 (((~hskp9) | c3_1(a228)) <=> ((~hskp9) | c3_1(a228))),
% 0.81/1.00 inference(rewrite,[status(thm)],[])).
% 0.81/1.00 tff(1380,axiom,((~hskp9) | c3_1(a228)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause65')).
% 0.81/1.00 tff(1381,plain,
% 0.81/1.00 ((~hskp9) | c3_1(a228)),
% 0.81/1.00 inference(modus_ponens,[status(thm)],[1380, 1379])).
% 0.81/1.00 tff(1382,plain,
% 0.81/1.00 ((~hskp9) | c3_1(a228)),
% 0.81/1.00 inference(modus_ponens,[status(thm)],[1381, 1379])).
% 0.81/1.00 tff(1383,plain,
% 0.81/1.00 ((~hskp9) | c3_1(a228)),
% 0.81/1.00 inference(modus_ponens,[status(thm)],[1382, 1379])).
% 0.81/1.00 tff(1384,plain,
% 0.81/1.00 ((~hskp9) | c3_1(a228)),
% 0.81/1.00 inference(modus_ponens,[status(thm)],[1383, 1379])).
% 0.81/1.00 tff(1385,plain,
% 0.81/1.00 ((~hskp9) | c3_1(a228)),
% 0.81/1.00 inference(modus_ponens,[status(thm)],[1384, 1379])).
% 0.81/1.00 tff(1386,plain,
% 0.81/1.00 (c3_1(a228)),
% 0.81/1.00 inference(unit_resolution,[status(thm)],[1385, 1366])).
% 0.81/1.00 tff(1387,plain,
% 0.81/1.00 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c1_1(V))) | (hskp0 | c0_1(a235) | c1_1(a235) | c3_1(a235) | c2_1(a228) | (~ndr1_0) | (~c3_1(a228)) | (~c0_1(a228)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c1_1(V))) | hskp0 | c0_1(a235) | c1_1(a235) | c3_1(a235) | c2_1(a228) | (~ndr1_0) | (~c3_1(a228)) | (~c0_1(a228)))),
% 0.81/1.00 inference(rewrite,[status(thm)],[])).
% 0.81/1.00 tff(1388,plain,
% 0.81/1.00 ((hskp0 | (~ndr1_0) | c2_1(a228) | (~c0_1(a228)) | (~c3_1(a228)) | c3_1(a235) | c0_1(a235) | c1_1(a235)) <=> (hskp0 | c0_1(a235) | c1_1(a235) | c3_1(a235) | c2_1(a228) | (~ndr1_0) | (~c3_1(a228)) | (~c0_1(a228)))),
% 0.81/1.00 inference(rewrite,[status(thm)],[])).
% 0.81/1.00 tff(1389,plain,
% 0.81/1.00 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c1_1(V))) | (hskp0 | (~ndr1_0) | c2_1(a228) | (~c0_1(a228)) | (~c3_1(a228)) | c3_1(a235) | c0_1(a235) | c1_1(a235))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c1_1(V))) | (hskp0 | c0_1(a235) | c1_1(a235) | c3_1(a235) | c2_1(a228) | (~ndr1_0) | (~c3_1(a228)) | (~c0_1(a228))))),
% 0.81/1.00 inference(monotonicity,[status(thm)],[1388])).
% 0.81/1.00 tff(1390,plain,
% 0.81/1.00 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c1_1(V))) | (hskp0 | (~ndr1_0) | c2_1(a228) | (~c0_1(a228)) | (~c3_1(a228)) | c3_1(a235) | c0_1(a235) | c1_1(a235))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c1_1(V))) | hskp0 | c0_1(a235) | c1_1(a235) | c3_1(a235) | c2_1(a228) | (~ndr1_0) | (~c3_1(a228)) | (~c0_1(a228)))),
% 0.81/1.00 inference(transitivity,[status(thm)],[1389, 1387])).
% 0.81/1.00 tff(1391,plain,
% 0.81/1.00 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c1_1(V))) | (hskp0 | (~ndr1_0) | c2_1(a228) | (~c0_1(a228)) | (~c3_1(a228)) | c3_1(a235) | c0_1(a235) | c1_1(a235))),
% 0.81/1.00 inference(quant_inst,[status(thm)],[])).
% 0.81/1.00 tff(1392,plain,
% 0.81/1.00 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c1_1(V))) | hskp0 | c0_1(a235) | c1_1(a235) | c3_1(a235) | c2_1(a228) | (~ndr1_0) | (~c3_1(a228)) | (~c0_1(a228))),
% 0.81/1.00 inference(modus_ponens,[status(thm)],[1391, 1390])).
% 0.81/1.00 tff(1393,plain,
% 0.81/1.00 (~c0_1(a228)),
% 0.81/1.00 inference(unit_resolution,[status(thm)],[1392, 122, 64, 1386, 1303, 1378, 1297, 1372, 1349])).
% 0.81/1.00 tff(1394,plain,
% 0.81/1.00 (((~hskp9) | (~c1_1(a228))) <=> ((~hskp9) | (~c1_1(a228)))),
% 0.81/1.00 inference(rewrite,[status(thm)],[])).
% 0.81/1.00 tff(1395,plain,
% 0.81/1.00 (((~c1_1(a228)) | (~hskp9)) <=> ((~hskp9) | (~c1_1(a228)))),
% 0.81/1.00 inference(rewrite,[status(thm)],[])).
% 0.81/1.00 tff(1396,axiom,((~c1_1(a228)) | (~hskp9)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause107')).
% 0.81/1.00 tff(1397,plain,
% 0.81/1.00 ((~hskp9) | (~c1_1(a228))),
% 0.81/1.00 inference(modus_ponens,[status(thm)],[1396, 1395])).
% 0.81/1.00 tff(1398,plain,
% 0.81/1.00 ((~hskp9) | (~c1_1(a228))),
% 0.81/1.00 inference(modus_ponens,[status(thm)],[1397, 1394])).
% 0.81/1.00 tff(1399,plain,
% 0.81/1.00 (~c1_1(a228)),
% 0.81/1.00 inference(unit_resolution,[status(thm)],[1398, 1366])).
% 0.81/1.00 tff(1400,plain,
% 0.81/1.00 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a229) | c1_1(a228) | c2_1(a228) | (~ndr1_0) | c0_1(a228) | (~c1_1(a229)) | (~c3_1(a229)) | (~c2_1(a259)) | (~c0_1(a259)) | (~c1_1(a259)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c0_1(a229) | c1_1(a228) | c2_1(a228) | (~ndr1_0) | c0_1(a228) | (~c1_1(a229)) | (~c3_1(a229)) | (~c2_1(a259)) | (~c0_1(a259)) | (~c1_1(a259)))),
% 0.81/1.00 inference(rewrite,[status(thm)],[])).
% 0.81/1.00 tff(1401,plain,
% 0.81/1.00 (((~ndr1_0) | (~c2_1(a259)) | (~c1_1(a259)) | (~c0_1(a259)) | c0_1(a229) | (~c3_1(a229)) | (~c1_1(a229)) | c1_1(a228) | c0_1(a228) | c2_1(a228)) <=> (c0_1(a229) | c1_1(a228) | c2_1(a228) | (~ndr1_0) | c0_1(a228) | (~c1_1(a229)) | (~c3_1(a229)) | (~c2_1(a259)) | (~c0_1(a259)) | (~c1_1(a259)))),
% 0.81/1.00 inference(rewrite,[status(thm)],[])).
% 0.81/1.00 tff(1402,plain,
% 0.81/1.00 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | (~c2_1(a259)) | (~c1_1(a259)) | (~c0_1(a259)) | c0_1(a229) | (~c3_1(a229)) | (~c1_1(a229)) | c1_1(a228) | c0_1(a228) | c2_1(a228))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a229) | c1_1(a228) | c2_1(a228) | (~ndr1_0) | c0_1(a228) | (~c1_1(a229)) | (~c3_1(a229)) | (~c2_1(a259)) | (~c0_1(a259)) | (~c1_1(a259))))),
% 0.81/1.00 inference(monotonicity,[status(thm)],[1401])).
% 0.81/1.00 tff(1403,plain,
% 0.81/1.00 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | (~c2_1(a259)) | (~c1_1(a259)) | (~c0_1(a259)) | c0_1(a229) | (~c3_1(a229)) | (~c1_1(a229)) | c1_1(a228) | c0_1(a228) | c2_1(a228))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c0_1(a229) | c1_1(a228) | c2_1(a228) | (~ndr1_0) | c0_1(a228) | (~c1_1(a229)) | (~c3_1(a229)) | (~c2_1(a259)) | (~c0_1(a259)) | (~c1_1(a259)))),
% 0.81/1.00 inference(transitivity,[status(thm)],[1402, 1400])).
% 0.81/1.00 tff(1404,plain,
% 0.81/1.00 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | (~c2_1(a259)) | (~c1_1(a259)) | (~c0_1(a259)) | c0_1(a229) | (~c3_1(a229)) | (~c1_1(a229)) | c1_1(a228) | c0_1(a228) | c2_1(a228))),
% 0.81/1.00 inference(quant_inst,[status(thm)],[])).
% 0.81/1.00 tff(1405,plain,
% 0.81/1.00 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c0_1(a229) | c1_1(a228) | c2_1(a228) | (~ndr1_0) | c0_1(a228) | (~c1_1(a229)) | (~c3_1(a229)) | (~c2_1(a259)) | (~c0_1(a259)) | (~c1_1(a259))),
% 0.81/1.00 inference(modus_ponens,[status(thm)],[1404, 1403])).
% 0.81/1.00 tff(1406,plain,
% 0.81/1.00 (~c1_1(a229)),
% 0.81/1.00 inference(unit_resolution,[status(thm)],[1405, 122, 1284, 1283, 1045, 1044, 1399, 1372, 627, 1393, 1339])).
% 0.81/1.00 tff(1407,plain,
% 0.81/1.00 (hskp27 | (~c2_1(a259))),
% 0.81/1.00 inference(unit_resolution,[status(thm)],[1225, 122, 1284, 1282, 192])).
% 0.81/1.00 tff(1408,plain,
% 0.81/1.00 (hskp27),
% 0.81/1.00 inference(unit_resolution,[status(thm)],[1407, 1339])).
% 0.81/1.00 tff(1409,plain,
% 0.81/1.00 (c3_1(a232)),
% 0.81/1.00 inference(unit_resolution,[status(thm)],[247, 1408])).
% 0.81/1.00 tff(1410,plain,
% 0.81/1.00 (c0_1(a232)),
% 0.81/1.00 inference(unit_resolution,[status(thm)],[263, 1408])).
% 0.81/1.00 tff(1411,assumption,(~c1_1(a229)), introduced(assumption)).
% 0.81/1.00 tff(1412,assumption,(c1_1(a232)), introduced(assumption)).
% 0.81/1.00 tff(1413,plain,
% 0.81/1.00 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (c0_1(a229) | (~ndr1_0) | (~c1_1(a232)) | (~c3_1(a232)) | (~c0_1(a232)) | c1_1(a229) | (~c3_1(a229)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | c0_1(a229) | (~ndr1_0) | (~c1_1(a232)) | (~c3_1(a232)) | (~c0_1(a232)) | c1_1(a229) | (~c3_1(a229)))),
% 0.81/1.00 inference(rewrite,[status(thm)],[])).
% 0.81/1.00 tff(1414,plain,
% 0.81/1.00 (((~ndr1_0) | (~c1_1(a232)) | (~c0_1(a232)) | (~c3_1(a232)) | c0_1(a229) | c1_1(a229) | (~c3_1(a229))) <=> (c0_1(a229) | (~ndr1_0) | (~c1_1(a232)) | (~c3_1(a232)) | (~c0_1(a232)) | c1_1(a229) | (~c3_1(a229)))),
% 0.81/1.00 inference(rewrite,[status(thm)],[])).
% 0.81/1.00 tff(1415,plain,
% 0.81/1.00 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | ((~ndr1_0) | (~c1_1(a232)) | (~c0_1(a232)) | (~c3_1(a232)) | c0_1(a229) | c1_1(a229) | (~c3_1(a229)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (c0_1(a229) | (~ndr1_0) | (~c1_1(a232)) | (~c3_1(a232)) | (~c0_1(a232)) | c1_1(a229) | (~c3_1(a229))))),
% 0.81/1.00 inference(monotonicity,[status(thm)],[1414])).
% 0.81/1.00 tff(1416,plain,
% 0.81/1.00 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | ((~ndr1_0) | (~c1_1(a232)) | (~c0_1(a232)) | (~c3_1(a232)) | c0_1(a229) | c1_1(a229) | (~c3_1(a229)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | c0_1(a229) | (~ndr1_0) | (~c1_1(a232)) | (~c3_1(a232)) | (~c0_1(a232)) | c1_1(a229) | (~c3_1(a229)))),
% 0.81/1.00 inference(transitivity,[status(thm)],[1415, 1413])).
% 0.81/1.00 tff(1417,plain,
% 0.81/1.00 ((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | ((~ndr1_0) | (~c1_1(a232)) | (~c0_1(a232)) | (~c3_1(a232)) | c0_1(a229) | c1_1(a229) | (~c3_1(a229)))),
% 0.81/1.00 inference(quant_inst,[status(thm)],[])).
% 0.81/1.00 tff(1418,plain,
% 0.81/1.00 ((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | c0_1(a229) | (~ndr1_0) | (~c1_1(a232)) | (~c3_1(a232)) | (~c0_1(a232)) | c1_1(a229) | (~c3_1(a229))),
% 0.81/1.00 inference(modus_ponens,[status(thm)],[1417, 1416])).
% 0.81/1.00 tff(1419,plain,
% 0.81/1.00 ($false),
% 0.81/1.00 inference(unit_resolution,[status(thm)],[1418, 122, 768, 766, 1066, 11, 583, 1412, 1411])).
% 0.81/1.00 tff(1420,plain,((~c1_1(a232)) | (~c0_1(a232)) | (~c3_1(a232)) | (~c3_1(a229)) | c0_1(a229) | c1_1(a229)), inference(lemma,lemma(discharge,[]))).
% 0.81/1.00 tff(1421,plain,
% 0.81/1.00 (~c1_1(a232)),
% 0.81/1.00 inference(unit_resolution,[status(thm)],[1420, 1410, 1409, 1045, 1044, 1406])).
% 0.81/1.00 tff(1422,plain,
% 0.81/1.00 (c2_1(a232)),
% 0.81/1.00 inference(unit_resolution,[status(thm)],[255, 1408])).
% 0.81/1.00 tff(1423,assumption,(~hskp18), introduced(assumption)).
% 0.81/1.00 tff(1424,plain,
% 0.81/1.00 (((~![U: $i] : (hskp18 | hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp18 | hskp6 | c2_1(a252) | (~ndr1_0) | (~c0_1(a252)) | (~c1_1(a252)))) <=> ((~![U: $i] : (hskp18 | hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp18 | hskp6 | c2_1(a252) | (~ndr1_0) | (~c0_1(a252)) | (~c1_1(a252)))),
% 0.81/1.00 inference(rewrite,[status(thm)],[])).
% 0.81/1.00 tff(1425,plain,
% 0.81/1.00 ((hskp18 | hskp6 | (~ndr1_0) | c2_1(a252) | (~c1_1(a252)) | (~c0_1(a252))) <=> (hskp18 | hskp6 | c2_1(a252) | (~ndr1_0) | (~c0_1(a252)) | (~c1_1(a252)))),
% 0.81/1.00 inference(rewrite,[status(thm)],[])).
% 0.81/1.00 tff(1426,plain,
% 0.81/1.00 (((~![U: $i] : (hskp18 | hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp18 | hskp6 | (~ndr1_0) | c2_1(a252) | (~c1_1(a252)) | (~c0_1(a252)))) <=> ((~![U: $i] : (hskp18 | hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp18 | hskp6 | c2_1(a252) | (~ndr1_0) | (~c0_1(a252)) | (~c1_1(a252))))),
% 0.81/1.00 inference(monotonicity,[status(thm)],[1425])).
% 0.81/1.00 tff(1427,plain,
% 0.81/1.00 (((~![U: $i] : (hskp18 | hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp18 | hskp6 | (~ndr1_0) | c2_1(a252) | (~c1_1(a252)) | (~c0_1(a252)))) <=> ((~![U: $i] : (hskp18 | hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp18 | hskp6 | c2_1(a252) | (~ndr1_0) | (~c0_1(a252)) | (~c1_1(a252)))),
% 0.81/1.00 inference(transitivity,[status(thm)],[1426, 1424])).
% 0.81/1.00 tff(1428,plain,
% 0.81/1.00 ((~![U: $i] : (hskp18 | hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp18 | hskp6 | (~ndr1_0) | c2_1(a252) | (~c1_1(a252)) | (~c0_1(a252)))),
% 0.81/1.00 inference(quant_inst,[status(thm)],[])).
% 0.81/1.00 tff(1429,plain,
% 0.81/1.00 ((~![U: $i] : (hskp18 | hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp18 | hskp6 | c2_1(a252) | (~ndr1_0) | (~c0_1(a252)) | (~c1_1(a252))),
% 0.81/1.00 inference(modus_ponens,[status(thm)],[1428, 1427])).
% 0.81/1.00 tff(1430,plain,
% 0.81/1.00 (~c0_1(a252)),
% 0.81/1.00 inference(unit_resolution,[status(thm)],[1429, 122, 1423, 1070, 817, 802, 1331])).
% 0.81/1.00 tff(1431,plain,
% 0.81/1.00 ($false),
% 0.81/1.00 inference(unit_resolution,[status(thm)],[808, 122, 43, 64, 802, 796, 53, 1430])).
% 0.81/1.00 tff(1432,plain,((~hskp19) | hskp8 | hskp0 | hskp18 | hskp6), inference(lemma,lemma(discharge,[]))).
% 0.81/1.00 tff(1433,plain,
% 0.81/1.00 (~hskp19),
% 0.81/1.00 inference(unit_resolution,[status(thm)],[1432, 1321, 64, 1070, 43])).
% 0.81/1.00 tff(1434,plain,
% 0.81/1.00 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp19 | (~ndr1_0) | (~c2_1(a232)) | c1_1(a232) | (~c3_1(a232)) | (~c0_1(a232)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp19 | (~ndr1_0) | (~c2_1(a232)) | c1_1(a232) | (~c3_1(a232)) | (~c0_1(a232)))),
% 0.81/1.00 inference(rewrite,[status(thm)],[])).
% 0.81/1.00 tff(1435,plain,
% 0.81/1.00 ((hskp19 | (~ndr1_0) | c1_1(a232) | (~c2_1(a232)) | (~c3_1(a232)) | c1_1(a232) | (~c3_1(a232)) | (~c0_1(a232))) <=> (hskp19 | (~ndr1_0) | (~c2_1(a232)) | c1_1(a232) | (~c3_1(a232)) | (~c0_1(a232)))),
% 0.81/1.00 inference(rewrite,[status(thm)],[])).
% 0.81/1.00 tff(1436,plain,
% 0.81/1.00 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp19 | (~ndr1_0) | c1_1(a232) | (~c2_1(a232)) | (~c3_1(a232)) | c1_1(a232) | (~c3_1(a232)) | (~c0_1(a232)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp19 | (~ndr1_0) | (~c2_1(a232)) | c1_1(a232) | (~c3_1(a232)) | (~c0_1(a232))))),
% 0.81/1.00 inference(monotonicity,[status(thm)],[1435])).
% 0.81/1.00 tff(1437,plain,
% 0.81/1.00 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp19 | (~ndr1_0) | c1_1(a232) | (~c2_1(a232)) | (~c3_1(a232)) | c1_1(a232) | (~c3_1(a232)) | (~c0_1(a232)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp19 | (~ndr1_0) | (~c2_1(a232)) | c1_1(a232) | (~c3_1(a232)) | (~c0_1(a232)))),
% 0.81/1.00 inference(transitivity,[status(thm)],[1436, 1434])).
% 0.81/1.00 tff(1438,plain,
% 0.81/1.00 ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp19 | (~ndr1_0) | c1_1(a232) | (~c2_1(a232)) | (~c3_1(a232)) | c1_1(a232) | (~c3_1(a232)) | (~c0_1(a232)))),
% 0.81/1.00 inference(quant_inst,[status(thm)],[])).
% 0.81/1.00 tff(1439,plain,
% 0.81/1.00 ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp19 | (~ndr1_0) | (~c2_1(a232)) | c1_1(a232) | (~c3_1(a232)) | (~c0_1(a232))),
% 0.81/1.00 inference(modus_ponens,[status(thm)],[1438, 1437])).
% 0.81/1.00 tff(1440,plain,
% 0.81/1.00 ($false),
% 0.81/1.00 inference(unit_resolution,[status(thm)],[1439, 122, 1433, 1410, 1422, 1409, 847, 1421])).
% 0.81/1.00 tff(1441,plain,(hskp6 | hskp0 | hskp8), inference(lemma,lemma(discharge,[]))).
% 0.81/1.00 tff(1442,plain,
% 0.81/1.00 (hskp6),
% 0.81/1.00 inference(unit_resolution,[status(thm)],[1441, 64, 43])).
% 0.81/1.00 tff(1443,plain,
% 0.81/1.00 (~c2_1(a221)),
% 0.81/1.00 inference(unit_resolution,[status(thm)],[1093, 1442])).
% 0.81/1.00 tff(1444,plain,
% 0.81/1.00 (c1_1(a221)),
% 0.81/1.00 inference(unit_resolution,[status(thm)],[1116, 1442])).
% 0.81/1.00 tff(1445,plain,
% 0.81/1.00 (c0_1(a221)),
% 0.81/1.00 inference(unit_resolution,[status(thm)],[1101, 1442])).
% 0.81/1.00 tff(1446,plain,
% 0.81/1.00 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a235) | c1_1(a235) | c3_1(a235) | c2_1(a221) | (~ndr1_0) | (~c1_1(a221)) | (~c0_1(a221)) | (~c2_1(a235)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a235) | c1_1(a235) | c3_1(a235) | c2_1(a221) | (~ndr1_0) | (~c1_1(a221)) | (~c0_1(a221)) | (~c2_1(a235)))),
% 0.81/1.00 inference(rewrite,[status(thm)],[])).
% 0.81/1.00 tff(1447,plain,
% 0.81/1.00 (((~ndr1_0) | c2_1(a221) | (~c1_1(a221)) | (~c0_1(a221)) | c3_1(a235) | c1_1(a235) | (~c2_1(a235)) | c1_1(a235) | c0_1(a235) | (~c2_1(a235))) <=> (c0_1(a235) | c1_1(a235) | c3_1(a235) | c2_1(a221) | (~ndr1_0) | (~c1_1(a221)) | (~c0_1(a221)) | (~c2_1(a235)))),
% 0.81/1.00 inference(rewrite,[status(thm)],[])).
% 0.81/1.00 tff(1448,plain,
% 0.81/1.00 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a221) | (~c1_1(a221)) | (~c0_1(a221)) | c3_1(a235) | c1_1(a235) | (~c2_1(a235)) | c1_1(a235) | c0_1(a235) | (~c2_1(a235)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a235) | c1_1(a235) | c3_1(a235) | c2_1(a221) | (~ndr1_0) | (~c1_1(a221)) | (~c0_1(a221)) | (~c2_1(a235))))),
% 0.81/1.00 inference(monotonicity,[status(thm)],[1447])).
% 0.81/1.00 tff(1449,plain,
% 0.81/1.00 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a221) | (~c1_1(a221)) | (~c0_1(a221)) | c3_1(a235) | c1_1(a235) | (~c2_1(a235)) | c1_1(a235) | c0_1(a235) | (~c2_1(a235)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a235) | c1_1(a235) | c3_1(a235) | c2_1(a221) | (~ndr1_0) | (~c1_1(a221)) | (~c0_1(a221)) | (~c2_1(a235)))),
% 0.81/1.00 inference(transitivity,[status(thm)],[1448, 1446])).
% 0.81/1.00 tff(1450,plain,
% 0.81/1.00 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a221) | (~c1_1(a221)) | (~c0_1(a221)) | c3_1(a235) | c1_1(a235) | (~c2_1(a235)) | c1_1(a235) | c0_1(a235) | (~c2_1(a235)))),
% 0.81/1.00 inference(quant_inst,[status(thm)],[])).
% 0.81/1.00 tff(1451,plain,
% 0.81/1.00 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a235) | c1_1(a235) | c3_1(a235) | c2_1(a221) | (~ndr1_0) | (~c1_1(a221)) | (~c0_1(a221)) | (~c2_1(a235))),
% 0.81/1.00 inference(modus_ponens,[status(thm)],[1450, 1449])).
% 0.81/1.00 tff(1452,plain,
% 0.81/1.00 ($false),
% 0.81/1.00 inference(unit_resolution,[status(thm)],[1451, 122, 1445, 1444, 1303, 1378, 1297, 1443, 1320, 1310])).
% 0.81/1.00 tff(1453,plain,(hskp0 | hskp8), inference(lemma,lemma(discharge,[]))).
% 0.81/1.00 tff(1454,plain,
% 0.81/1.00 (hskp0),
% 0.81/1.00 inference(unit_resolution,[status(thm)],[1453, 43])).
% 0.81/1.00 tff(1455,plain,
% 0.81/1.00 (c1_1(a213)),
% 0.81/1.00 inference(unit_resolution,[status(thm)],[294, 1454])).
% 0.81/1.00 tff(1456,plain,
% 0.81/1.00 (~c2_1(a213)),
% 0.81/1.00 inference(unit_resolution,[status(thm)],[278, 1454])).
% 0.81/1.00 tff(1457,plain,
% 0.81/1.00 (c3_1(a213)),
% 0.81/1.00 inference(unit_resolution,[status(thm)],[286, 1454])).
% 0.81/1.00 tff(1458,plain,
% 0.81/1.00 (hskp13),
% 0.81/1.00 inference(unit_resolution,[status(thm)],[937, 132])).
% 0.81/1.00 tff(1459,plain,
% 0.81/1.00 (~c1_1(a236)),
% 0.81/1.00 inference(unit_resolution,[status(thm)],[764, 1458])).
% 0.81/1.00 tff(1460,plain,
% 0.81/1.00 (~c3_1(a236)),
% 0.81/1.00 inference(unit_resolution,[status(thm)],[752, 1458])).
% 0.81/1.00 tff(1461,plain,
% 0.81/1.00 (~c2_1(a236)),
% 0.81/1.00 inference(unit_resolution,[status(thm)],[758, 1458])).
% 0.81/1.00 tff(1462,plain,
% 0.81/1.00 (^[V: $i, U: $i] : refl((hskp6 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V)) <=> (hskp6 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V)))),
% 0.81/1.00 inference(bind,[status(th)],[])).
% 0.81/1.00 tff(1463,plain,
% 0.81/1.00 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))),
% 0.81/1.00 inference(quant_intro,[status(thm)],[1462])).
% 0.81/1.00 tff(1464,plain,
% 0.81/1.00 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))),
% 0.81/1.00 inference(rewrite,[status(thm)],[])).
% 0.81/1.00 tff(1465,plain,
% 0.81/1.00 (^[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)) | c2_1(V) | 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)) | c2_1(V) | c0_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)) | c2_1(V) | c0_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_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) | c2_1(V) | c0_1(V)))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp6) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V)) | hskp6))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V)) | hskp6) <=> (hskp6 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp6) <=> (hskp6 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))))),
% 0.81/1.00 inference(bind,[status(th)],[])).
% 0.81/1.00 tff(1466,plain,
% 0.81/1.00 (![V: $i, U: $i] : ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp6) <=> ![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))),
% 0.81/1.00 inference(quant_intro,[status(thm)],[1465])).
% 0.81/1.00 tff(1467,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)) | hskp6)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause146')).
% 0.81/1.00 tff(1468,plain,
% 0.81/1.00 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))),
% 0.81/1.00 inference(modus_ponens,[status(thm)],[1467, 1466])).
% 0.81/1.00 tff(1469,plain,
% 0.81/1.00 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))),
% 0.81/1.00 inference(modus_ponens,[status(thm)],[1468, 1464])).
% 0.81/1.00 tff(1470,plain,(
% 0.81/1.00 ![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))),
% 0.81/1.00 inference(skolemize,[status(sab)],[1469])).
% 0.81/1.00 tff(1471,plain,
% 0.81/1.00 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))),
% 0.81/1.00 inference(modus_ponens,[status(thm)],[1470, 1463])).
% 0.81/1.01 tff(1472,assumption,(~c3_1(a236)), introduced(assumption)).
% 0.81/1.01 tff(1473,assumption,(~c2_1(a236)), introduced(assumption)).
% 0.81/1.01 tff(1474,plain,
% 0.81/1.01 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp6 | c2_1(a236) | c3_1(a236) | c0_1(a229) | (~ndr1_0) | (~c2_1(a229)) | (~c3_1(a229)) | c0_1(a236))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp6 | c2_1(a236) | c3_1(a236) | c0_1(a229) | (~ndr1_0) | (~c2_1(a229)) | (~c3_1(a229)) | c0_1(a236))),
% 0.81/1.01 inference(rewrite,[status(thm)],[])).
% 0.81/1.01 tff(1475,plain,
% 0.81/1.01 ((hskp6 | (~ndr1_0) | c0_1(a229) | (~c2_1(a229)) | (~c3_1(a229)) | c3_1(a236) | c2_1(a236) | c0_1(a236)) <=> (hskp6 | c2_1(a236) | c3_1(a236) | c0_1(a229) | (~ndr1_0) | (~c2_1(a229)) | (~c3_1(a229)) | c0_1(a236))),
% 0.81/1.01 inference(rewrite,[status(thm)],[])).
% 0.81/1.01 tff(1476,plain,
% 0.81/1.01 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp6 | (~ndr1_0) | c0_1(a229) | (~c2_1(a229)) | (~c3_1(a229)) | c3_1(a236) | c2_1(a236) | c0_1(a236))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp6 | c2_1(a236) | c3_1(a236) | c0_1(a229) | (~ndr1_0) | (~c2_1(a229)) | (~c3_1(a229)) | c0_1(a236)))),
% 0.81/1.01 inference(monotonicity,[status(thm)],[1475])).
% 0.81/1.01 tff(1477,plain,
% 0.81/1.01 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp6 | (~ndr1_0) | c0_1(a229) | (~c2_1(a229)) | (~c3_1(a229)) | c3_1(a236) | c2_1(a236) | c0_1(a236))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp6 | c2_1(a236) | c3_1(a236) | c0_1(a229) | (~ndr1_0) | (~c2_1(a229)) | (~c3_1(a229)) | c0_1(a236))),
% 0.81/1.01 inference(transitivity,[status(thm)],[1476, 1474])).
% 0.81/1.01 tff(1478,plain,
% 0.81/1.01 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp6 | (~ndr1_0) | c0_1(a229) | (~c2_1(a229)) | (~c3_1(a229)) | c3_1(a236) | c2_1(a236) | c0_1(a236))),
% 0.81/1.01 inference(quant_inst,[status(thm)],[])).
% 0.81/1.01 tff(1479,plain,
% 0.81/1.01 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp6 | c2_1(a236) | c3_1(a236) | c0_1(a229) | (~ndr1_0) | (~c2_1(a229)) | (~c3_1(a229)) | c0_1(a236)),
% 0.81/1.01 inference(modus_ponens,[status(thm)],[1478, 1477])).
% 0.81/1.01 tff(1480,plain,
% 0.81/1.01 (hskp6 | c0_1(a236)),
% 0.81/1.01 inference(unit_resolution,[status(thm)],[1479, 122, 1067, 1066, 1473, 1472, 11, 1471])).
% 0.81/1.01 tff(1481,plain,
% 0.81/1.01 (c0_1(a236)),
% 0.81/1.01 inference(unit_resolution,[status(thm)],[1480, 1070])).
% 0.81/1.01 tff(1482,assumption,(~c1_1(a236)), introduced(assumption)).
% 0.81/1.01 tff(1483,plain,
% 0.81/1.01 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | (c1_1(a236) | c2_1(a236) | c0_1(a229) | (~ndr1_0) | (~c2_1(a229)) | (~c1_1(a229)) | (~c3_1(a229)) | (~c0_1(a236)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | c1_1(a236) | c2_1(a236) | c0_1(a229) | (~ndr1_0) | (~c2_1(a229)) | (~c1_1(a229)) | (~c3_1(a229)) | (~c0_1(a236)))),
% 0.81/1.01 inference(rewrite,[status(thm)],[])).
% 0.81/1.01 tff(1484,plain,
% 0.81/1.01 (((~ndr1_0) | (~c2_1(a229)) | (~c1_1(a229)) | (~c3_1(a229)) | c2_1(a236) | c1_1(a236) | (~c0_1(a236)) | c0_1(a229) | (~c2_1(a229)) | (~c3_1(a229))) <=> (c1_1(a236) | c2_1(a236) | c0_1(a229) | (~ndr1_0) | (~c2_1(a229)) | (~c1_1(a229)) | (~c3_1(a229)) | (~c0_1(a236)))),
% 0.81/1.01 inference(rewrite,[status(thm)],[])).
% 0.81/1.01 tff(1485,plain,
% 0.81/1.01 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a229)) | (~c1_1(a229)) | (~c3_1(a229)) | c2_1(a236) | c1_1(a236) | (~c0_1(a236)) | c0_1(a229) | (~c2_1(a229)) | (~c3_1(a229)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | (c1_1(a236) | c2_1(a236) | c0_1(a229) | (~ndr1_0) | (~c2_1(a229)) | (~c1_1(a229)) | (~c3_1(a229)) | (~c0_1(a236))))),
% 0.81/1.01 inference(monotonicity,[status(thm)],[1484])).
% 0.81/1.01 tff(1486,plain,
% 0.81/1.01 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a229)) | (~c1_1(a229)) | (~c3_1(a229)) | c2_1(a236) | c1_1(a236) | (~c0_1(a236)) | c0_1(a229) | (~c2_1(a229)) | (~c3_1(a229)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | c1_1(a236) | c2_1(a236) | c0_1(a229) | (~ndr1_0) | (~c2_1(a229)) | (~c1_1(a229)) | (~c3_1(a229)) | (~c0_1(a236)))),
% 0.81/1.01 inference(transitivity,[status(thm)],[1485, 1483])).
% 0.81/1.01 tff(1487,plain,
% 0.81/1.01 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a229)) | (~c1_1(a229)) | (~c3_1(a229)) | c2_1(a236) | c1_1(a236) | (~c0_1(a236)) | c0_1(a229) | (~c2_1(a229)) | (~c3_1(a229)))),
% 0.81/1.01 inference(quant_inst,[status(thm)],[])).
% 0.81/1.01 tff(1488,plain,
% 0.81/1.01 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | c1_1(a236) | c2_1(a236) | c0_1(a229) | (~ndr1_0) | (~c2_1(a229)) | (~c1_1(a229)) | (~c3_1(a229)) | (~c0_1(a236))),
% 0.81/1.01 inference(modus_ponens,[status(thm)],[1487, 1486])).
% 0.81/1.01 tff(1489,plain,
% 0.81/1.01 ((~c1_1(a229)) | (~c0_1(a236))),
% 0.81/1.01 inference(unit_resolution,[status(thm)],[1488, 122, 1067, 1066, 1482, 1473, 11, 1269])).
% 0.81/1.01 tff(1490,plain,
% 0.81/1.01 (~c1_1(a229)),
% 0.81/1.01 inference(unit_resolution,[status(thm)],[1489, 1481])).
% 0.81/1.01 tff(1491,plain,
% 0.81/1.01 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp6 | c0_1(a229) | c2_1(a213) | (~ndr1_0) | (~c3_1(a213)) | (~c0_1(a213)) | (~c2_1(a229)) | (~c3_1(a229)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp6 | c0_1(a229) | c2_1(a213) | (~ndr1_0) | (~c3_1(a213)) | (~c0_1(a213)) | (~c2_1(a229)) | (~c3_1(a229)))),
% 0.81/1.01 inference(rewrite,[status(thm)],[])).
% 0.81/1.01 tff(1492,plain,
% 0.81/1.01 ((hskp6 | (~ndr1_0) | c2_1(a213) | (~c0_1(a213)) | (~c3_1(a213)) | c0_1(a229) | (~c3_1(a229)) | (~c2_1(a229))) <=> (hskp6 | c0_1(a229) | c2_1(a213) | (~ndr1_0) | (~c3_1(a213)) | (~c0_1(a213)) | (~c2_1(a229)) | (~c3_1(a229)))),
% 0.81/1.01 inference(rewrite,[status(thm)],[])).
% 0.81/1.01 tff(1493,plain,
% 0.81/1.01 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp6 | (~ndr1_0) | c2_1(a213) | (~c0_1(a213)) | (~c3_1(a213)) | c0_1(a229) | (~c3_1(a229)) | (~c2_1(a229)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp6 | c0_1(a229) | c2_1(a213) | (~ndr1_0) | (~c3_1(a213)) | (~c0_1(a213)) | (~c2_1(a229)) | (~c3_1(a229))))),
% 0.81/1.01 inference(monotonicity,[status(thm)],[1492])).
% 0.81/1.01 tff(1494,plain,
% 0.81/1.01 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp6 | (~ndr1_0) | c2_1(a213) | (~c0_1(a213)) | (~c3_1(a213)) | c0_1(a229) | (~c3_1(a229)) | (~c2_1(a229)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp6 | c0_1(a229) | c2_1(a213) | (~ndr1_0) | (~c3_1(a213)) | (~c0_1(a213)) | (~c2_1(a229)) | (~c3_1(a229)))),
% 0.81/1.01 inference(transitivity,[status(thm)],[1493, 1491])).
% 0.81/1.01 tff(1495,plain,
% 0.81/1.01 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp6 | (~ndr1_0) | c2_1(a213) | (~c0_1(a213)) | (~c3_1(a213)) | c0_1(a229) | (~c3_1(a229)) | (~c2_1(a229)))),
% 0.81/1.01 inference(quant_inst,[status(thm)],[])).
% 0.81/1.01 tff(1496,plain,
% 0.81/1.01 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp6 | c0_1(a229) | c2_1(a213) | (~ndr1_0) | (~c3_1(a213)) | (~c0_1(a213)) | (~c2_1(a229)) | (~c3_1(a229))),
% 0.81/1.01 inference(modus_ponens,[status(thm)],[1495, 1494])).
% 0.81/1.01 tff(1497,plain,
% 0.81/1.01 (hskp6 | (~c0_1(a213))),
% 0.81/1.01 inference(unit_resolution,[status(thm)],[1496, 122, 1067, 1066, 320, 11, 306, 1063])).
% 0.81/1.01 tff(1498,plain,
% 0.81/1.01 (~c0_1(a213)),
% 0.81/1.01 inference(unit_resolution,[status(thm)],[1497, 1070])).
% 0.81/1.01 tff(1499,plain,
% 0.81/1.01 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | (c2_1(a236) | c3_1(a236) | c2_1(a213) | (~ndr1_0) | (~c3_1(a213)) | c0_1(a213) | (~c2_1(a229)) | c1_1(a229) | (~c3_1(a229)) | (~c0_1(a236)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c2_1(a236) | c3_1(a236) | c2_1(a213) | (~ndr1_0) | (~c3_1(a213)) | c0_1(a213) | (~c2_1(a229)) | c1_1(a229) | (~c3_1(a229)) | (~c0_1(a236)))),
% 0.81/1.01 inference(rewrite,[status(thm)],[])).
% 0.81/1.01 tff(1500,plain,
% 0.81/1.01 (((~ndr1_0) | c3_1(a236) | c2_1(a236) | (~c0_1(a236)) | c1_1(a229) | (~c3_1(a229)) | (~c2_1(a229)) | c0_1(a213) | c2_1(a213) | (~c3_1(a213))) <=> (c2_1(a236) | c3_1(a236) | c2_1(a213) | (~ndr1_0) | (~c3_1(a213)) | c0_1(a213) | (~c2_1(a229)) | c1_1(a229) | (~c3_1(a229)) | (~c0_1(a236)))),
% 0.81/1.01 inference(rewrite,[status(thm)],[])).
% 0.81/1.01 tff(1501,plain,
% 0.81/1.01 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a236) | c2_1(a236) | (~c0_1(a236)) | c1_1(a229) | (~c3_1(a229)) | (~c2_1(a229)) | c0_1(a213) | c2_1(a213) | (~c3_1(a213)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | (c2_1(a236) | c3_1(a236) | c2_1(a213) | (~ndr1_0) | (~c3_1(a213)) | c0_1(a213) | (~c2_1(a229)) | c1_1(a229) | (~c3_1(a229)) | (~c0_1(a236))))),
% 0.81/1.01 inference(monotonicity,[status(thm)],[1500])).
% 0.81/1.01 tff(1502,plain,
% 0.81/1.01 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a236) | c2_1(a236) | (~c0_1(a236)) | c1_1(a229) | (~c3_1(a229)) | (~c2_1(a229)) | c0_1(a213) | c2_1(a213) | (~c3_1(a213)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c2_1(a236) | c3_1(a236) | c2_1(a213) | (~ndr1_0) | (~c3_1(a213)) | c0_1(a213) | (~c2_1(a229)) | c1_1(a229) | (~c3_1(a229)) | (~c0_1(a236)))),
% 0.81/1.01 inference(transitivity,[status(thm)],[1501, 1499])).
% 0.81/1.01 tff(1503,plain,
% 0.81/1.01 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a236) | c2_1(a236) | (~c0_1(a236)) | c1_1(a229) | (~c3_1(a229)) | (~c2_1(a229)) | c0_1(a213) | c2_1(a213) | (~c3_1(a213)))),
% 0.81/1.01 inference(quant_inst,[status(thm)],[])).
% 0.81/1.01 tff(1504,plain,
% 0.81/1.01 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c2_1(a236) | c3_1(a236) | c2_1(a213) | (~ndr1_0) | (~c3_1(a213)) | c0_1(a213) | (~c2_1(a229)) | c1_1(a229) | (~c3_1(a229)) | (~c0_1(a236))),
% 0.81/1.01 inference(modus_ponens,[status(thm)],[1503, 1502])).
% 0.81/1.01 tff(1505,plain,
% 0.81/1.01 ($false),
% 0.81/1.01 inference(unit_resolution,[status(thm)],[1504, 122, 1067, 1066, 320, 1473, 1472, 306, 10, 1498, 1490, 1481])).
% 0.81/1.01 tff(1506,plain,(hskp6 | (~c2_1(a229)) | (~c3_1(a229)) | (~c3_1(a213)) | c2_1(a236) | c3_1(a236) | c2_1(a213) | c1_1(a236) | c0_1(a229)), inference(lemma,lemma(discharge,[]))).
% 0.81/1.01 tff(1507,plain,
% 0.81/1.01 (hskp6),
% 0.81/1.01 inference(unit_resolution,[status(thm)],[1506, 1461, 1066, 320, 1067, 1460, 306, 1459, 11])).
% 0.81/1.01 tff(1508,plain,
% 0.81/1.01 (~c2_1(a221)),
% 0.81/1.01 inference(unit_resolution,[status(thm)],[1093, 1507])).
% 0.81/1.01 tff(1509,assumption,(~hskp14), introduced(assumption)).
% 0.81/1.01 tff(1510,plain,
% 0.81/1.01 (hskp15 | hskp14 | (~c1_1(a229))),
% 0.81/1.01 inference(unit_resolution,[status(thm)],[1140, 122, 1066, 11, 1134])).
% 0.81/1.01 tff(1511,plain,
% 0.81/1.01 (~c1_1(a229)),
% 0.81/1.01 inference(unit_resolution,[status(thm)],[1510, 1509, 1163])).
% 0.81/1.01 tff(1512,plain,
% 0.81/1.01 (((~![U: $i] : (hskp15 | hskp14 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp15 | hskp14 | (~ndr1_0) | (~c1_1(a213)) | (~c3_1(a213)) | c0_1(a213))) <=> ((~![U: $i] : (hskp15 | hskp14 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))) | hskp15 | hskp14 | (~ndr1_0) | (~c1_1(a213)) | (~c3_1(a213)) | c0_1(a213))),
% 0.81/1.01 inference(rewrite,[status(thm)],[])).
% 0.81/1.01 tff(1513,plain,
% 0.81/1.01 ((hskp15 | hskp14 | (~ndr1_0) | c0_1(a213) | (~c1_1(a213)) | (~c3_1(a213))) <=> (hskp15 | hskp14 | (~ndr1_0) | (~c1_1(a213)) | (~c3_1(a213)) | c0_1(a213))),
% 0.81/1.01 inference(rewrite,[status(thm)],[])).
% 0.81/1.01 tff(1514,plain,
% 0.81/1.01 (((~![U: $i] : (hskp15 | hskp14 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp15 | hskp14 | (~ndr1_0) | c0_1(a213) | (~c1_1(a213)) | (~c3_1(a213)))) <=> ((~![U: $i] : (hskp15 | hskp14 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp15 | hskp14 | (~ndr1_0) | (~c1_1(a213)) | (~c3_1(a213)) | c0_1(a213)))),
% 0.81/1.01 inference(monotonicity,[status(thm)],[1513])).
% 0.81/1.01 tff(1515,plain,
% 0.81/1.01 (((~![U: $i] : (hskp15 | hskp14 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp15 | hskp14 | (~ndr1_0) | c0_1(a213) | (~c1_1(a213)) | (~c3_1(a213)))) <=> ((~![U: $i] : (hskp15 | hskp14 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))) | hskp15 | hskp14 | (~ndr1_0) | (~c1_1(a213)) | (~c3_1(a213)) | c0_1(a213))),
% 0.81/1.01 inference(transitivity,[status(thm)],[1514, 1512])).
% 0.81/1.01 tff(1516,plain,
% 0.81/1.01 ((~![U: $i] : (hskp15 | hskp14 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp15 | hskp14 | (~ndr1_0) | c0_1(a213) | (~c1_1(a213)) | (~c3_1(a213)))),
% 0.81/1.01 inference(quant_inst,[status(thm)],[])).
% 0.81/1.01 tff(1517,plain,
% 0.81/1.01 ((~![U: $i] : (hskp15 | hskp14 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))) | hskp15 | hskp14 | (~ndr1_0) | (~c1_1(a213)) | (~c3_1(a213)) | c0_1(a213)),
% 0.81/1.01 inference(modus_ponens,[status(thm)],[1516, 1515])).
% 0.81/1.01 tff(1518,plain,
% 0.81/1.01 (hskp15 | hskp14 | c0_1(a213)),
% 0.81/1.01 inference(unit_resolution,[status(thm)],[1517, 122, 321, 320, 1134])).
% 0.81/1.01 tff(1519,plain,
% 0.81/1.01 (c0_1(a213)),
% 0.81/1.01 inference(unit_resolution,[status(thm)],[1518, 1509, 1163])).
% 0.81/1.01 tff(1520,plain,
% 0.81/1.01 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (c0_1(a229) | (~ndr1_0) | (~c1_1(a213)) | (~c3_1(a213)) | (~c0_1(a213)) | c1_1(a229) | (~c3_1(a229)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | c0_1(a229) | (~ndr1_0) | (~c1_1(a213)) | (~c3_1(a213)) | (~c0_1(a213)) | c1_1(a229) | (~c3_1(a229)))),
% 0.81/1.01 inference(rewrite,[status(thm)],[])).
% 0.81/1.01 tff(1521,plain,
% 0.81/1.01 (((~ndr1_0) | (~c1_1(a213)) | (~c0_1(a213)) | (~c3_1(a213)) | c0_1(a229) | c1_1(a229) | (~c3_1(a229))) <=> (c0_1(a229) | (~ndr1_0) | (~c1_1(a213)) | (~c3_1(a213)) | (~c0_1(a213)) | c1_1(a229) | (~c3_1(a229)))),
% 0.81/1.01 inference(rewrite,[status(thm)],[])).
% 0.81/1.01 tff(1522,plain,
% 0.81/1.01 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | ((~ndr1_0) | (~c1_1(a213)) | (~c0_1(a213)) | (~c3_1(a213)) | c0_1(a229) | c1_1(a229) | (~c3_1(a229)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (c0_1(a229) | (~ndr1_0) | (~c1_1(a213)) | (~c3_1(a213)) | (~c0_1(a213)) | c1_1(a229) | (~c3_1(a229))))),
% 0.81/1.01 inference(monotonicity,[status(thm)],[1521])).
% 0.81/1.01 tff(1523,plain,
% 0.81/1.01 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | ((~ndr1_0) | (~c1_1(a213)) | (~c0_1(a213)) | (~c3_1(a213)) | c0_1(a229) | c1_1(a229) | (~c3_1(a229)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | c0_1(a229) | (~ndr1_0) | (~c1_1(a213)) | (~c3_1(a213)) | (~c0_1(a213)) | c1_1(a229) | (~c3_1(a229)))),
% 0.81/1.01 inference(transitivity,[status(thm)],[1522, 1520])).
% 0.81/1.01 tff(1524,plain,
% 0.81/1.01 ((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | ((~ndr1_0) | (~c1_1(a213)) | (~c0_1(a213)) | (~c3_1(a213)) | c0_1(a229) | c1_1(a229) | (~c3_1(a229)))),
% 0.81/1.01 inference(quant_inst,[status(thm)],[])).
% 0.81/1.01 tff(1525,plain,
% 0.81/1.01 ((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | c0_1(a229) | (~ndr1_0) | (~c1_1(a213)) | (~c3_1(a213)) | (~c0_1(a213)) | c1_1(a229) | (~c3_1(a229))),
% 0.81/1.01 inference(modus_ponens,[status(thm)],[1524, 1523])).
% 0.81/1.01 tff(1526,plain,
% 0.81/1.01 ((~c0_1(a213)) | c1_1(a229)),
% 0.81/1.01 inference(unit_resolution,[status(thm)],[1525, 122, 1066, 321, 320, 11, 583])).
% 0.81/1.01 tff(1527,plain,
% 0.81/1.01 ($false),
% 0.81/1.01 inference(unit_resolution,[status(thm)],[1526, 1519, 1511])).
% 0.81/1.01 tff(1528,plain,(hskp14 | (~c3_1(a229)) | (~c1_1(a213)) | (~c3_1(a213)) | c0_1(a229) | hskp15), inference(lemma,lemma(discharge,[]))).
% 0.81/1.01 tff(1529,plain,
% 0.81/1.01 (hskp14),
% 0.81/1.01 inference(unit_resolution,[status(thm)],[1528, 1087, 321, 320, 11, 1066])).
% 0.81/1.01 tff(1530,plain,
% 0.81/1.01 (hskp28),
% 0.81/1.01 inference(unit_resolution,[status(thm)],[1194, 1529, 1087])).
% 0.81/1.01 tff(1531,plain,
% 0.81/1.01 (c2_1(a246)),
% 0.81/1.01 inference(unit_resolution,[status(thm)],[699, 1530])).
% 0.81/1.01 tff(1532,plain,
% 0.81/1.01 (c0_1(a246)),
% 0.81/1.01 inference(unit_resolution,[status(thm)],[715, 1530])).
% 0.81/1.01 tff(1533,plain,
% 0.81/1.01 (((~![U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp27 | (~ndr1_0) | (~c0_1(a246)) | c3_1(a246) | (~c2_1(a246)))) <=> ((~![U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp27 | (~ndr1_0) | (~c0_1(a246)) | c3_1(a246) | (~c2_1(a246)))),
% 0.81/1.01 inference(rewrite,[status(thm)],[])).
% 0.81/1.01 tff(1534,plain,
% 0.81/1.01 ((hskp27 | (~ndr1_0) | c3_1(a246) | (~c2_1(a246)) | (~c0_1(a246))) <=> (hskp27 | (~ndr1_0) | (~c0_1(a246)) | c3_1(a246) | (~c2_1(a246)))),
% 0.81/1.01 inference(rewrite,[status(thm)],[])).
% 0.81/1.01 tff(1535,plain,
% 0.81/1.01 (((~![U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp27 | (~ndr1_0) | c3_1(a246) | (~c2_1(a246)) | (~c0_1(a246)))) <=> ((~![U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp27 | (~ndr1_0) | (~c0_1(a246)) | c3_1(a246) | (~c2_1(a246))))),
% 0.81/1.01 inference(monotonicity,[status(thm)],[1534])).
% 0.81/1.01 tff(1536,plain,
% 0.81/1.01 (((~![U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp27 | (~ndr1_0) | c3_1(a246) | (~c2_1(a246)) | (~c0_1(a246)))) <=> ((~![U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp27 | (~ndr1_0) | (~c0_1(a246)) | c3_1(a246) | (~c2_1(a246)))),
% 0.81/1.01 inference(transitivity,[status(thm)],[1535, 1533])).
% 0.81/1.01 tff(1537,plain,
% 0.81/1.01 ((~![U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp27 | (~ndr1_0) | c3_1(a246) | (~c2_1(a246)) | (~c0_1(a246)))),
% 0.81/1.01 inference(quant_inst,[status(thm)],[])).
% 0.81/1.01 tff(1538,plain,
% 0.81/1.01 ((~![U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp27 | (~ndr1_0) | (~c0_1(a246)) | c3_1(a246) | (~c2_1(a246))),
% 0.81/1.01 inference(modus_ponens,[status(thm)],[1537, 1536])).
% 0.81/1.01 tff(1539,plain,
% 0.81/1.01 (c3_1(a246)),
% 0.81/1.01 inference(unit_resolution,[status(thm)],[1538, 122, 1080, 1532, 1531, 192])).
% 0.81/1.01 tff(1540,plain,
% 0.81/1.01 (c1_1(a246)),
% 0.81/1.01 inference(unit_resolution,[status(thm)],[707, 1530])).
% 0.81/1.01 tff(1541,plain,
% 0.81/1.01 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp20 | (~ndr1_0) | (~c0_1(a246)) | (~c1_1(a246)) | (~c2_1(a246)) | (~c3_1(a246)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | hskp20 | (~ndr1_0) | (~c0_1(a246)) | (~c1_1(a246)) | (~c2_1(a246)) | (~c3_1(a246)))),
% 0.81/1.01 inference(rewrite,[status(thm)],[])).
% 0.81/1.01 tff(1542,plain,
% 0.81/1.01 ((hskp20 | (~ndr1_0) | (~c1_1(a246)) | (~c0_1(a246)) | (~c3_1(a246)) | (~c1_1(a246)) | (~c2_1(a246)) | (~c0_1(a246))) <=> (hskp20 | (~ndr1_0) | (~c0_1(a246)) | (~c1_1(a246)) | (~c2_1(a246)) | (~c3_1(a246)))),
% 0.81/1.01 inference(rewrite,[status(thm)],[])).
% 0.81/1.01 tff(1543,plain,
% 0.81/1.01 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp20 | (~ndr1_0) | (~c1_1(a246)) | (~c0_1(a246)) | (~c3_1(a246)) | (~c1_1(a246)) | (~c2_1(a246)) | (~c0_1(a246)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp20 | (~ndr1_0) | (~c0_1(a246)) | (~c1_1(a246)) | (~c2_1(a246)) | (~c3_1(a246))))),
% 0.81/1.01 inference(monotonicity,[status(thm)],[1542])).
% 0.81/1.01 tff(1544,plain,
% 0.81/1.01 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp20 | (~ndr1_0) | (~c1_1(a246)) | (~c0_1(a246)) | (~c3_1(a246)) | (~c1_1(a246)) | (~c2_1(a246)) | (~c0_1(a246)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | hskp20 | (~ndr1_0) | (~c0_1(a246)) | (~c1_1(a246)) | (~c2_1(a246)) | (~c3_1(a246)))),
% 0.81/1.01 inference(transitivity,[status(thm)],[1543, 1541])).
% 0.81/1.01 tff(1545,plain,
% 0.81/1.01 ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp20 | (~ndr1_0) | (~c1_1(a246)) | (~c0_1(a246)) | (~c3_1(a246)) | (~c1_1(a246)) | (~c2_1(a246)) | (~c0_1(a246)))),
% 0.81/1.01 inference(quant_inst,[status(thm)],[])).
% 0.81/1.01 tff(1546,plain,
% 0.81/1.01 ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | hskp20 | (~ndr1_0) | (~c0_1(a246)) | (~c1_1(a246)) | (~c2_1(a246)) | (~c3_1(a246))),
% 0.81/1.01 inference(modus_ponens,[status(thm)],[1545, 1544])).
% 0.81/1.01 tff(1547,plain,
% 0.81/1.01 ($false),
% 0.81/1.01 inference(unit_resolution,[status(thm)],[1546, 122, 132, 1532, 1540, 1531, 1013, 1539])).
% 0.81/1.01 tff(1548,plain,(hskp27 | hskp20 | (~c1_1(a213)) | (~c3_1(a213)) | c0_1(a229) | (~c3_1(a229))), inference(lemma,lemma(discharge,[]))).
% 0.81/1.01 tff(1549,plain,
% 0.81/1.01 (hskp27),
% 0.81/1.01 inference(unit_resolution,[status(thm)],[1548, 132, 321, 320, 11, 1066])).
% 0.81/1.01 tff(1550,plain,
% 0.81/1.01 (c3_1(a232)),
% 0.81/1.01 inference(unit_resolution,[status(thm)],[247, 1549])).
% 0.81/1.01 tff(1551,plain,
% 0.81/1.01 (c2_1(a232)),
% 0.81/1.01 inference(unit_resolution,[status(thm)],[255, 1549])).
% 0.81/1.01 tff(1552,plain,
% 0.81/1.01 (c0_1(a232)),
% 0.81/1.01 inference(unit_resolution,[status(thm)],[263, 1549])).
% 0.81/1.01 tff(1553,plain,
% 0.81/1.01 (hskp17),
% 0.81/1.01 inference(unit_resolution,[status(thm)],[947, 122, 1552, 1551, 1550, 1459, 1461, 1460, 453])).
% 0.81/1.01 tff(1554,plain,
% 0.81/1.01 (~c2_1(a243)),
% 0.81/1.01 inference(unit_resolution,[status(thm)],[501, 1553])).
% 0.81/1.01 tff(1555,plain,
% 0.81/1.01 (~c1_1(a243)),
% 0.81/1.01 inference(unit_resolution,[status(thm)],[530, 1553])).
% 0.81/1.01 tff(1556,plain,
% 0.81/1.01 (~c0_1(a243)),
% 0.81/1.01 inference(unit_resolution,[status(thm)],[507, 1553])).
% 0.81/1.01 tff(1557,plain,
% 0.81/1.01 (c1_1(a221)),
% 0.81/1.01 inference(unit_resolution,[status(thm)],[1116, 1507])).
% 0.81/1.01 tff(1558,plain,
% 0.81/1.01 (c0_1(a221)),
% 0.81/1.01 inference(unit_resolution,[status(thm)],[1101, 1507])).
% 0.81/1.01 tff(1559,plain,
% 0.81/1.01 (((~![U: $i] : (hskp21 | hskp20 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp21 | hskp20 | c2_1(a221) | (~ndr1_0) | (~c1_1(a221)) | (~c0_1(a221)))) <=> ((~![U: $i] : (hskp21 | hskp20 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp21 | hskp20 | c2_1(a221) | (~ndr1_0) | (~c1_1(a221)) | (~c0_1(a221)))),
% 0.81/1.01 inference(rewrite,[status(thm)],[])).
% 0.81/1.01 tff(1560,plain,
% 0.81/1.01 ((hskp21 | hskp20 | (~ndr1_0) | c2_1(a221) | (~c1_1(a221)) | (~c0_1(a221))) <=> (hskp21 | hskp20 | c2_1(a221) | (~ndr1_0) | (~c1_1(a221)) | (~c0_1(a221)))),
% 0.81/1.01 inference(rewrite,[status(thm)],[])).
% 0.81/1.01 tff(1561,plain,
% 0.81/1.01 (((~![U: $i] : (hskp21 | hskp20 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp21 | hskp20 | (~ndr1_0) | c2_1(a221) | (~c1_1(a221)) | (~c0_1(a221)))) <=> ((~![U: $i] : (hskp21 | hskp20 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp21 | hskp20 | c2_1(a221) | (~ndr1_0) | (~c1_1(a221)) | (~c0_1(a221))))),
% 0.81/1.01 inference(monotonicity,[status(thm)],[1560])).
% 0.81/1.01 tff(1562,plain,
% 0.81/1.01 (((~![U: $i] : (hskp21 | hskp20 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp21 | hskp20 | (~ndr1_0) | c2_1(a221) | (~c1_1(a221)) | (~c0_1(a221)))) <=> ((~![U: $i] : (hskp21 | hskp20 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp21 | hskp20 | c2_1(a221) | (~ndr1_0) | (~c1_1(a221)) | (~c0_1(a221)))),
% 0.81/1.01 inference(transitivity,[status(thm)],[1561, 1559])).
% 0.81/1.01 tff(1563,plain,
% 0.81/1.01 ((~![U: $i] : (hskp21 | hskp20 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp21 | hskp20 | (~ndr1_0) | c2_1(a221) | (~c1_1(a221)) | (~c0_1(a221)))),
% 0.81/1.01 inference(quant_inst,[status(thm)],[])).
% 0.81/1.01 tff(1564,plain,
% 0.81/1.01 ((~![U: $i] : (hskp21 | hskp20 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp21 | hskp20 | c2_1(a221) | (~ndr1_0) | (~c1_1(a221)) | (~c0_1(a221))),
% 0.81/1.01 inference(modus_ponens,[status(thm)],[1563, 1562])).
% 0.81/1.01 tff(1565,plain,
% 0.81/1.01 (hskp21),
% 0.81/1.01 inference(unit_resolution,[status(thm)],[1564, 122, 132, 1558, 1557, 1508, 400])).
% 0.81/1.01 tff(1566,plain,
% 0.81/1.01 (~c0_1(a260)),
% 0.81/1.01 inference(unit_resolution,[status(thm)],[419, 1565])).
% 0.81/1.01 tff(1567,plain,
% 0.81/1.01 (c1_1(a260)),
% 0.81/1.01 inference(unit_resolution,[status(thm)],[427, 1565])).
% 0.81/1.01 tff(1568,assumption,(hskp28), introduced(assumption)).
% 0.81/1.01 tff(1569,plain,
% 0.81/1.01 (c2_1(a246)),
% 0.81/1.01 inference(unit_resolution,[status(thm)],[699, 1568])).
% 0.81/1.01 tff(1570,plain,
% 0.81/1.01 (c1_1(a246)),
% 0.81/1.01 inference(unit_resolution,[status(thm)],[707, 1568])).
% 0.81/1.01 tff(1571,plain,
% 0.81/1.01 (c0_1(a246)),
% 0.81/1.01 inference(unit_resolution,[status(thm)],[715, 1568])).
% 0.81/1.01 tff(1572,plain,
% 0.81/1.01 (~c3_1(a246)),
% 0.81/1.01 inference(unit_resolution,[status(thm)],[1546, 122, 132, 1571, 1570, 1569, 1013])).
% 0.81/1.01 tff(1573,assumption,(~c2_1(a243)), introduced(assumption)).
% 0.81/1.01 tff(1574,assumption,(~c1_1(a243)), introduced(assumption)).
% 0.81/1.01 tff(1575,assumption,(~c0_1(a243)), introduced(assumption)).
% 0.81/1.01 tff(1576,assumption,(~c0_1(a260)), introduced(assumption)).
% 0.81/1.01 tff(1577,assumption,(c1_1(a260)), introduced(assumption)).
% 0.81/1.01 tff(1578,plain,
% 0.81/1.01 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a260) | c0_1(a243) | c1_1(a243) | c2_1(a243) | (~ndr1_0) | (~c0_1(a246)) | (~c1_1(a246)) | (~c2_1(a246)) | (~c1_1(a260)) | (~c3_1(a260)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c0_1(a260) | c0_1(a243) | c1_1(a243) | c2_1(a243) | (~ndr1_0) | (~c0_1(a246)) | (~c1_1(a246)) | (~c2_1(a246)) | (~c1_1(a260)) | (~c3_1(a260)))),
% 0.81/1.01 inference(rewrite,[status(thm)],[])).
% 0.81/1.01 tff(1579,plain,
% 0.81/1.01 (((~ndr1_0) | (~c2_1(a246)) | (~c1_1(a246)) | (~c0_1(a246)) | c0_1(a260) | (~c3_1(a260)) | (~c1_1(a260)) | c1_1(a243) | c0_1(a243) | c2_1(a243)) <=> (c0_1(a260) | c0_1(a243) | c1_1(a243) | c2_1(a243) | (~ndr1_0) | (~c0_1(a246)) | (~c1_1(a246)) | (~c2_1(a246)) | (~c1_1(a260)) | (~c3_1(a260)))),
% 0.81/1.01 inference(rewrite,[status(thm)],[])).
% 0.81/1.01 tff(1580,plain,
% 0.81/1.01 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | (~c2_1(a246)) | (~c1_1(a246)) | (~c0_1(a246)) | c0_1(a260) | (~c3_1(a260)) | (~c1_1(a260)) | c1_1(a243) | c0_1(a243) | c2_1(a243))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a260) | c0_1(a243) | c1_1(a243) | c2_1(a243) | (~ndr1_0) | (~c0_1(a246)) | (~c1_1(a246)) | (~c2_1(a246)) | (~c1_1(a260)) | (~c3_1(a260))))),
% 0.81/1.01 inference(monotonicity,[status(thm)],[1579])).
% 0.81/1.01 tff(1581,plain,
% 0.81/1.01 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | (~c2_1(a246)) | (~c1_1(a246)) | (~c0_1(a246)) | c0_1(a260) | (~c3_1(a260)) | (~c1_1(a260)) | c1_1(a243) | c0_1(a243) | c2_1(a243))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c0_1(a260) | c0_1(a243) | c1_1(a243) | c2_1(a243) | (~ndr1_0) | (~c0_1(a246)) | (~c1_1(a246)) | (~c2_1(a246)) | (~c1_1(a260)) | (~c3_1(a260)))),
% 0.81/1.01 inference(transitivity,[status(thm)],[1580, 1578])).
% 0.81/1.01 tff(1582,plain,
% 0.81/1.01 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | (~c2_1(a246)) | (~c1_1(a246)) | (~c0_1(a246)) | c0_1(a260) | (~c3_1(a260)) | (~c1_1(a260)) | c1_1(a243) | c0_1(a243) | c2_1(a243))),
% 0.81/1.02 inference(quant_inst,[status(thm)],[])).
% 0.81/1.02 tff(1583,plain,
% 0.81/1.02 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c0_1(a260) | c0_1(a243) | c1_1(a243) | c2_1(a243) | (~ndr1_0) | (~c0_1(a246)) | (~c1_1(a246)) | (~c2_1(a246)) | (~c1_1(a260)) | (~c3_1(a260))),
% 0.81/1.02 inference(modus_ponens,[status(thm)],[1582, 1581])).
% 0.81/1.02 tff(1584,plain,
% 0.81/1.02 (~c3_1(a260)),
% 0.81/1.02 inference(unit_resolution,[status(thm)],[1583, 122, 1571, 1570, 1569, 1577, 1576, 1575, 1574, 1573, 627])).
% 0.81/1.02 tff(1585,plain,
% 0.81/1.02 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | (c0_1(a260) | (~ndr1_0) | (~c0_1(a246)) | c3_1(a246) | (~c1_1(a246)) | (~c2_1(a246)) | (~c1_1(a260)) | c3_1(a260))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c0_1(a260) | (~ndr1_0) | (~c0_1(a246)) | c3_1(a246) | (~c1_1(a246)) | (~c2_1(a246)) | (~c1_1(a260)) | c3_1(a260))),
% 0.81/1.02 inference(rewrite,[status(thm)],[])).
% 0.81/1.02 tff(1586,plain,
% 0.81/1.02 (((~ndr1_0) | (~c2_1(a246)) | (~c1_1(a246)) | (~c0_1(a246)) | c3_1(a246) | (~c1_1(a246)) | (~c0_1(a246)) | c0_1(a260) | c3_1(a260) | (~c1_1(a260))) <=> (c0_1(a260) | (~ndr1_0) | (~c0_1(a246)) | c3_1(a246) | (~c1_1(a246)) | (~c2_1(a246)) | (~c1_1(a260)) | c3_1(a260))),
% 0.81/1.02 inference(rewrite,[status(thm)],[])).
% 0.81/1.02 tff(1587,plain,
% 0.81/1.02 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a246)) | (~c1_1(a246)) | (~c0_1(a246)) | c3_1(a246) | (~c1_1(a246)) | (~c0_1(a246)) | c0_1(a260) | c3_1(a260) | (~c1_1(a260)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | (c0_1(a260) | (~ndr1_0) | (~c0_1(a246)) | c3_1(a246) | (~c1_1(a246)) | (~c2_1(a246)) | (~c1_1(a260)) | c3_1(a260)))),
% 0.81/1.02 inference(monotonicity,[status(thm)],[1586])).
% 0.81/1.02 tff(1588,plain,
% 0.81/1.02 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a246)) | (~c1_1(a246)) | (~c0_1(a246)) | c3_1(a246) | (~c1_1(a246)) | (~c0_1(a246)) | c0_1(a260) | c3_1(a260) | (~c1_1(a260)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c0_1(a260) | (~ndr1_0) | (~c0_1(a246)) | c3_1(a246) | (~c1_1(a246)) | (~c2_1(a246)) | (~c1_1(a260)) | c3_1(a260))),
% 0.81/1.02 inference(transitivity,[status(thm)],[1587, 1585])).
% 0.81/1.02 tff(1589,plain,
% 0.81/1.02 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a246)) | (~c1_1(a246)) | (~c0_1(a246)) | c3_1(a246) | (~c1_1(a246)) | (~c0_1(a246)) | c0_1(a260) | c3_1(a260) | (~c1_1(a260)))),
% 0.81/1.02 inference(quant_inst,[status(thm)],[])).
% 0.81/1.02 tff(1590,plain,
% 0.81/1.02 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c0_1(a260) | (~ndr1_0) | (~c0_1(a246)) | c3_1(a246) | (~c1_1(a246)) | (~c2_1(a246)) | (~c1_1(a260)) | c3_1(a260)),
% 0.81/1.02 inference(modus_ponens,[status(thm)],[1589, 1588])).
% 0.81/1.02 tff(1591,plain,
% 0.81/1.02 ($false),
% 0.81/1.02 inference(unit_resolution,[status(thm)],[1590, 122, 1571, 1570, 1569, 1577, 1576, 993, 1584, 1572])).
% 0.81/1.02 tff(1592,plain,((~hskp28) | (~c1_1(a260)) | c0_1(a260) | hskp20 | c0_1(a243) | c1_1(a243) | c2_1(a243)), inference(lemma,lemma(discharge,[]))).
% 0.81/1.02 tff(1593,plain,
% 0.81/1.02 (~hskp28),
% 0.81/1.02 inference(unit_resolution,[status(thm)],[1592, 1567, 1566, 132, 1556, 1555, 1554])).
% 0.81/1.02 tff(1594,plain,
% 0.81/1.02 (hskp14),
% 0.81/1.02 inference(unit_resolution,[status(thm)],[1528, 1163, 321, 320, 11, 1066])).
% 0.81/1.02 tff(1595,plain,
% 0.81/1.02 ($false),
% 0.81/1.02 inference(unit_resolution,[status(thm)],[1194, 1594, 1163, 683])).
% 0.81/1.02 tff(1596,plain,(hskp15 | hskp28 | (~c1_1(a213)) | (~c3_1(a213)) | c0_1(a229) | (~c3_1(a229))), inference(lemma,lemma(discharge,[]))).
% 0.81/1.02 tff(1597,plain,
% 0.81/1.02 (hskp15),
% 0.81/1.02 inference(unit_resolution,[status(thm)],[1596, 1593, 321, 320, 11, 1066])).
% 0.81/1.02 tff(1598,plain,
% 0.81/1.02 (~c3_1(a238)),
% 0.81/1.02 inference(unit_resolution,[status(thm)],[216, 1597])).
% 0.81/1.02 tff(1599,plain,
% 0.81/1.02 (c2_1(a238)),
% 0.81/1.02 inference(unit_resolution,[status(thm)],[224, 1597])).
% 0.81/1.02 tff(1600,plain,
% 0.81/1.02 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp28 | c3_1(a238) | c2_1(a221) | (~ndr1_0) | (~c1_1(a221)) | (~c0_1(a221)) | c1_1(a238) | (~c2_1(a238)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp28 | c3_1(a238) | c2_1(a221) | (~ndr1_0) | (~c1_1(a221)) | (~c0_1(a221)) | c1_1(a238) | (~c2_1(a238)))),
% 0.81/1.02 inference(rewrite,[status(thm)],[])).
% 0.81/1.02 tff(1601,plain,
% 0.81/1.02 ((hskp28 | (~ndr1_0) | c2_1(a221) | (~c1_1(a221)) | (~c0_1(a221)) | c3_1(a238) | c1_1(a238) | (~c2_1(a238))) <=> (hskp28 | c3_1(a238) | c2_1(a221) | (~ndr1_0) | (~c1_1(a221)) | (~c0_1(a221)) | c1_1(a238) | (~c2_1(a238)))),
% 0.81/1.02 inference(rewrite,[status(thm)],[])).
% 0.81/1.02 tff(1602,plain,
% 0.81/1.02 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp28 | (~ndr1_0) | c2_1(a221) | (~c1_1(a221)) | (~c0_1(a221)) | c3_1(a238) | c1_1(a238) | (~c2_1(a238)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp28 | c3_1(a238) | c2_1(a221) | (~ndr1_0) | (~c1_1(a221)) | (~c0_1(a221)) | c1_1(a238) | (~c2_1(a238))))),
% 0.81/1.02 inference(monotonicity,[status(thm)],[1601])).
% 0.81/1.02 tff(1603,plain,
% 0.81/1.02 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp28 | (~ndr1_0) | c2_1(a221) | (~c1_1(a221)) | (~c0_1(a221)) | c3_1(a238) | c1_1(a238) | (~c2_1(a238)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp28 | c3_1(a238) | c2_1(a221) | (~ndr1_0) | (~c1_1(a221)) | (~c0_1(a221)) | c1_1(a238) | (~c2_1(a238)))),
% 0.81/1.02 inference(transitivity,[status(thm)],[1602, 1600])).
% 0.81/1.02 tff(1604,plain,
% 0.81/1.02 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp28 | (~ndr1_0) | c2_1(a221) | (~c1_1(a221)) | (~c0_1(a221)) | c3_1(a238) | c1_1(a238) | (~c2_1(a238)))),
% 0.81/1.02 inference(quant_inst,[status(thm)],[])).
% 0.81/1.02 tff(1605,plain,
% 0.81/1.02 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp28 | c3_1(a238) | c2_1(a221) | (~ndr1_0) | (~c1_1(a221)) | (~c0_1(a221)) | c1_1(a238) | (~c2_1(a238))),
% 0.81/1.02 inference(modus_ponens,[status(thm)],[1604, 1603])).
% 0.81/1.02 tff(1606,plain,
% 0.81/1.02 (c1_1(a238)),
% 0.81/1.02 inference(unit_resolution,[status(thm)],[1605, 1593, 122, 1599, 1558, 1557, 1598, 1508, 682])).
% 0.81/1.02 tff(1607,plain,
% 0.81/1.02 (c0_1(a238)),
% 0.81/1.02 inference(unit_resolution,[status(thm)],[232, 1597])).
% 0.81/1.02 tff(1608,plain,
% 0.81/1.02 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | (c0_1(a260) | c3_1(a238) | (~ndr1_0) | (~c2_1(a238)) | (~c0_1(a238)) | (~c1_1(a238)) | (~c1_1(a260)) | c3_1(a260))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c0_1(a260) | c3_1(a238) | (~ndr1_0) | (~c2_1(a238)) | (~c0_1(a238)) | (~c1_1(a238)) | (~c1_1(a260)) | c3_1(a260))),
% 0.81/1.02 inference(rewrite,[status(thm)],[])).
% 0.81/1.02 tff(1609,plain,
% 0.81/1.02 (((~ndr1_0) | (~c2_1(a238)) | (~c1_1(a238)) | (~c0_1(a238)) | c3_1(a238) | (~c1_1(a238)) | (~c0_1(a238)) | c0_1(a260) | c3_1(a260) | (~c1_1(a260))) <=> (c0_1(a260) | c3_1(a238) | (~ndr1_0) | (~c2_1(a238)) | (~c0_1(a238)) | (~c1_1(a238)) | (~c1_1(a260)) | c3_1(a260))),
% 0.81/1.02 inference(rewrite,[status(thm)],[])).
% 0.81/1.02 tff(1610,plain,
% 0.81/1.02 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a238)) | (~c1_1(a238)) | (~c0_1(a238)) | c3_1(a238) | (~c1_1(a238)) | (~c0_1(a238)) | c0_1(a260) | c3_1(a260) | (~c1_1(a260)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | (c0_1(a260) | c3_1(a238) | (~ndr1_0) | (~c2_1(a238)) | (~c0_1(a238)) | (~c1_1(a238)) | (~c1_1(a260)) | c3_1(a260)))),
% 0.81/1.02 inference(monotonicity,[status(thm)],[1609])).
% 0.81/1.02 tff(1611,plain,
% 0.81/1.02 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a238)) | (~c1_1(a238)) | (~c0_1(a238)) | c3_1(a238) | (~c1_1(a238)) | (~c0_1(a238)) | c0_1(a260) | c3_1(a260) | (~c1_1(a260)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c0_1(a260) | c3_1(a238) | (~ndr1_0) | (~c2_1(a238)) | (~c0_1(a238)) | (~c1_1(a238)) | (~c1_1(a260)) | c3_1(a260))),
% 0.81/1.02 inference(transitivity,[status(thm)],[1610, 1608])).
% 0.81/1.02 tff(1612,plain,
% 0.81/1.02 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a238)) | (~c1_1(a238)) | (~c0_1(a238)) | c3_1(a238) | (~c1_1(a238)) | (~c0_1(a238)) | c0_1(a260) | c3_1(a260) | (~c1_1(a260)))),
% 0.81/1.02 inference(quant_inst,[status(thm)],[])).
% 0.81/1.02 tff(1613,plain,
% 0.81/1.02 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c0_1(a260) | c3_1(a238) | (~ndr1_0) | (~c2_1(a238)) | (~c0_1(a238)) | (~c1_1(a238)) | (~c1_1(a260)) | c3_1(a260)),
% 0.81/1.02 inference(modus_ponens,[status(thm)],[1612, 1611])).
% 0.81/1.02 tff(1614,plain,
% 0.81/1.02 ((~c1_1(a238)) | c3_1(a260)),
% 0.81/1.02 inference(unit_resolution,[status(thm)],[1613, 122, 1567, 1607, 1599, 1566, 1598, 993])).
% 0.81/1.02 tff(1615,plain,
% 0.81/1.02 (c3_1(a260)),
% 0.81/1.02 inference(unit_resolution,[status(thm)],[1614, 1606])).
% 0.81/1.02 tff(1616,plain,
% 0.81/1.02 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a260) | c0_1(a243) | c1_1(a243) | c2_1(a243) | (~ndr1_0) | (~c2_1(a238)) | (~c0_1(a238)) | (~c1_1(a238)) | (~c1_1(a260)) | (~c3_1(a260)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c0_1(a260) | c0_1(a243) | c1_1(a243) | c2_1(a243) | (~ndr1_0) | (~c2_1(a238)) | (~c0_1(a238)) | (~c1_1(a238)) | (~c1_1(a260)) | (~c3_1(a260)))),
% 0.81/1.02 inference(rewrite,[status(thm)],[])).
% 0.81/1.02 tff(1617,plain,
% 0.81/1.02 (((~ndr1_0) | (~c2_1(a238)) | (~c1_1(a238)) | (~c0_1(a238)) | c0_1(a260) | (~c3_1(a260)) | (~c1_1(a260)) | c1_1(a243) | c0_1(a243) | c2_1(a243)) <=> (c0_1(a260) | c0_1(a243) | c1_1(a243) | c2_1(a243) | (~ndr1_0) | (~c2_1(a238)) | (~c0_1(a238)) | (~c1_1(a238)) | (~c1_1(a260)) | (~c3_1(a260)))),
% 0.81/1.02 inference(rewrite,[status(thm)],[])).
% 0.81/1.02 tff(1618,plain,
% 0.81/1.02 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | (~c2_1(a238)) | (~c1_1(a238)) | (~c0_1(a238)) | c0_1(a260) | (~c3_1(a260)) | (~c1_1(a260)) | c1_1(a243) | c0_1(a243) | c2_1(a243))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a260) | c0_1(a243) | c1_1(a243) | c2_1(a243) | (~ndr1_0) | (~c2_1(a238)) | (~c0_1(a238)) | (~c1_1(a238)) | (~c1_1(a260)) | (~c3_1(a260))))),
% 0.81/1.02 inference(monotonicity,[status(thm)],[1617])).
% 0.81/1.02 tff(1619,plain,
% 0.81/1.02 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | (~c2_1(a238)) | (~c1_1(a238)) | (~c0_1(a238)) | c0_1(a260) | (~c3_1(a260)) | (~c1_1(a260)) | c1_1(a243) | c0_1(a243) | c2_1(a243))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c0_1(a260) | c0_1(a243) | c1_1(a243) | c2_1(a243) | (~ndr1_0) | (~c2_1(a238)) | (~c0_1(a238)) | (~c1_1(a238)) | (~c1_1(a260)) | (~c3_1(a260)))),
% 0.81/1.02 inference(transitivity,[status(thm)],[1618, 1616])).
% 0.81/1.02 tff(1620,plain,
% 0.81/1.02 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | (~c2_1(a238)) | (~c1_1(a238)) | (~c0_1(a238)) | c0_1(a260) | (~c3_1(a260)) | (~c1_1(a260)) | c1_1(a243) | c0_1(a243) | c2_1(a243))),
% 0.81/1.02 inference(quant_inst,[status(thm)],[])).
% 0.81/1.02 tff(1621,plain,
% 0.81/1.02 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c0_1(a260) | c0_1(a243) | c1_1(a243) | c2_1(a243) | (~ndr1_0) | (~c2_1(a238)) | (~c0_1(a238)) | (~c1_1(a238)) | (~c1_1(a260)) | (~c3_1(a260))),
% 0.81/1.02 inference(modus_ponens,[status(thm)],[1620, 1619])).
% 0.81/1.02 tff(1622,plain,
% 0.81/1.02 ((~c1_1(a238)) | (~c3_1(a260))),
% 0.81/1.02 inference(unit_resolution,[status(thm)],[1621, 122, 1567, 1607, 1599, 1566, 1556, 1555, 1554, 627])).
% 0.81/1.02 tff(1623,plain,
% 0.81/1.02 ($false),
% 0.81/1.02 inference(unit_resolution,[status(thm)],[1622, 1615, 1606])).
% 0.81/1.02 tff(1624,plain,(hskp20 | (~c1_1(a213)) | (~c3_1(a213)) | c0_1(a229) | (~c3_1(a229)) | (~c2_1(a229)) | c2_1(a213)), inference(lemma,lemma(discharge,[]))).
% 0.81/1.02 tff(1625,plain,
% 0.81/1.02 (hskp20),
% 0.81/1.02 inference(unit_resolution,[status(thm)],[1624, 1455, 1457, 1044, 1045, 1053, 1456])).
% 0.81/1.02 tff(1626,plain,
% 0.81/1.02 (hskp3),
% 0.81/1.02 inference(unit_resolution,[status(thm)],[380, 1625, 43])).
% 0.81/1.02 tff(1627,plain,
% 0.81/1.02 (~c2_1(a216)),
% 0.81/1.02 inference(unit_resolution,[status(thm)],[312, 1626])).
% 0.81/1.02 tff(1628,plain,
% 0.81/1.02 (~c0_1(a216)),
% 0.81/1.02 inference(unit_resolution,[status(thm)],[318, 1626])).
% 0.81/1.02 tff(1629,plain,
% 0.81/1.02 (c3_1(a216)),
% 0.81/1.02 inference(unit_resolution,[status(thm)],[328, 1626])).
% 0.81/1.02 tff(1630,plain,
% 0.81/1.02 (~c1_1(a237)),
% 0.81/1.02 inference(unit_resolution,[status(thm)],[1169, 1594])).
% 0.81/1.02 tff(1631,plain,
% 0.81/1.02 (c2_1(a237)),
% 0.81/1.02 inference(unit_resolution,[status(thm)],[1149, 1594])).
% 0.81/1.02 tff(1632,plain,
% 0.81/1.02 (c0_1(a237)),
% 0.81/1.02 inference(unit_resolution,[status(thm)],[1157, 1594])).
% 0.81/1.02 tff(1633,plain,
% 0.81/1.02 (hskp28),
% 0.81/1.02 inference(unit_resolution,[status(thm)],[1596, 1163, 321, 320, 11, 1066])).
% 0.81/1.02 tff(1634,plain,
% 0.81/1.02 (c2_1(a246)),
% 0.81/1.02 inference(unit_resolution,[status(thm)],[699, 1633])).
% 0.81/1.02 tff(1635,plain,
% 0.81/1.02 (c1_1(a246)),
% 0.81/1.02 inference(unit_resolution,[status(thm)],[707, 1633])).
% 0.81/1.02 tff(1636,plain,
% 0.81/1.02 (c0_1(a246)),
% 0.81/1.02 inference(unit_resolution,[status(thm)],[715, 1633])).
% 0.81/1.02 tff(1637,plain,
% 0.81/1.02 (^[V: $i, U: $i] : refl((hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V))) <=> (hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V))))),
% 0.81/1.02 inference(bind,[status(th)],[])).
% 0.81/1.02 tff(1638,plain,
% 0.81/1.02 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))),
% 0.81/1.02 inference(quant_intro,[status(thm)],[1637])).
% 0.81/1.02 tff(1639,plain,
% 0.81/1.02 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))),
% 0.81/1.02 inference(rewrite,[status(thm)],[])).
% 0.81/1.02 tff(1640,plain,
% 0.81/1.02 (^[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)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) | c1_1(V)) | hskp5) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V))) | hskp5))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V))) | hskp5) <=> (hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) | c1_1(V)) | hskp5) <=> (hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))))),
% 0.81/1.02 inference(bind,[status(th)],[])).
% 0.81/1.02 tff(1641,plain,
% 0.81/1.02 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) | c1_1(V)) | hskp5) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))),
% 0.81/1.02 inference(quant_intro,[status(thm)],[1640])).
% 0.81/1.02 tff(1642,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) | c1_1(V)) | hskp5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause149')).
% 0.81/1.02 tff(1643,plain,
% 0.81/1.02 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))),
% 0.81/1.02 inference(modus_ponens,[status(thm)],[1642, 1641])).
% 0.81/1.02 tff(1644,plain,
% 0.81/1.02 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))),
% 0.81/1.02 inference(modus_ponens,[status(thm)],[1643, 1639])).
% 0.81/1.02 tff(1645,plain,(
% 0.81/1.02 ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))),
% 0.81/1.02 inference(skolemize,[status(sab)],[1644])).
% 0.81/1.02 tff(1646,plain,
% 0.81/1.02 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))),
% 0.81/1.02 inference(modus_ponens,[status(thm)],[1645, 1638])).
% 0.81/1.02 tff(1647,assumption,(c2_1(a237)), introduced(assumption)).
% 0.81/1.02 tff(1648,assumption,(c0_1(a237)), introduced(assumption)).
% 0.81/1.02 tff(1649,plain,
% 0.81/1.02 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp5 | c1_1(a237) | c0_1(a229) | (~ndr1_0) | c1_1(a229) | (~c3_1(a229)) | (~c2_1(a237)) | (~c0_1(a237)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp5 | c1_1(a237) | c0_1(a229) | (~ndr1_0) | c1_1(a229) | (~c3_1(a229)) | (~c2_1(a237)) | (~c0_1(a237)))),
% 0.81/1.02 inference(rewrite,[status(thm)],[])).
% 0.81/1.02 tff(1650,plain,
% 0.81/1.02 ((hskp5 | (~ndr1_0) | c1_1(a237) | (~c2_1(a237)) | (~c0_1(a237)) | c0_1(a229) | c1_1(a229) | (~c3_1(a229))) <=> (hskp5 | c1_1(a237) | c0_1(a229) | (~ndr1_0) | c1_1(a229) | (~c3_1(a229)) | (~c2_1(a237)) | (~c0_1(a237)))),
% 0.81/1.02 inference(rewrite,[status(thm)],[])).
% 0.81/1.02 tff(1651,plain,
% 0.81/1.02 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a237) | (~c2_1(a237)) | (~c0_1(a237)) | c0_1(a229) | c1_1(a229) | (~c3_1(a229)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp5 | c1_1(a237) | c0_1(a229) | (~ndr1_0) | c1_1(a229) | (~c3_1(a229)) | (~c2_1(a237)) | (~c0_1(a237))))),
% 0.81/1.02 inference(monotonicity,[status(thm)],[1650])).
% 0.81/1.02 tff(1652,plain,
% 0.81/1.02 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a237) | (~c2_1(a237)) | (~c0_1(a237)) | c0_1(a229) | c1_1(a229) | (~c3_1(a229)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp5 | c1_1(a237) | c0_1(a229) | (~ndr1_0) | c1_1(a229) | (~c3_1(a229)) | (~c2_1(a237)) | (~c0_1(a237)))),
% 0.81/1.02 inference(transitivity,[status(thm)],[1651, 1649])).
% 0.81/1.02 tff(1653,plain,
% 0.81/1.02 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a237) | (~c2_1(a237)) | (~c0_1(a237)) | c0_1(a229) | c1_1(a229) | (~c3_1(a229)))),
% 0.81/1.02 inference(quant_inst,[status(thm)],[])).
% 0.81/1.02 tff(1654,plain,
% 0.81/1.02 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp5 | c1_1(a237) | c0_1(a229) | (~ndr1_0) | c1_1(a229) | (~c3_1(a229)) | (~c2_1(a237)) | (~c0_1(a237))),
% 0.81/1.02 inference(modus_ponens,[status(thm)],[1653, 1652])).
% 0.81/1.02 tff(1655,plain,
% 0.81/1.02 (hskp5 | c1_1(a229)),
% 0.81/1.02 inference(unit_resolution,[status(thm)],[1654, 122, 1648, 1647, 1066, 1183, 11, 1646])).
% 0.81/1.02 tff(1656,plain,
% 0.81/1.02 (hskp5),
% 0.81/1.02 inference(unit_resolution,[status(thm)],[1655, 1411])).
% 0.81/1.02 tff(1657,plain,
% 0.81/1.02 (((~hskp5) | (~c3_1(a220))) <=> ((~hskp5) | (~c3_1(a220)))),
% 0.81/1.02 inference(rewrite,[status(thm)],[])).
% 0.81/1.02 tff(1658,plain,
% 0.81/1.02 (((~c3_1(a220)) | (~hskp5)) <=> ((~hskp5) | (~c3_1(a220)))),
% 0.81/1.02 inference(rewrite,[status(thm)],[])).
% 0.81/1.02 tff(1659,axiom,((~c3_1(a220)) | (~hskp5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause114')).
% 0.81/1.02 tff(1660,plain,
% 0.81/1.02 ((~hskp5) | (~c3_1(a220))),
% 0.81/1.02 inference(modus_ponens,[status(thm)],[1659, 1658])).
% 0.81/1.02 tff(1661,plain,
% 0.81/1.02 ((~hskp5) | (~c3_1(a220))),
% 0.81/1.02 inference(modus_ponens,[status(thm)],[1660, 1657])).
% 0.81/1.02 tff(1662,plain,
% 0.81/1.02 (~c3_1(a220)),
% 0.81/1.02 inference(unit_resolution,[status(thm)],[1661, 1656])).
% 0.81/1.02 tff(1663,plain,
% 0.81/1.02 (((~hskp5) | c2_1(a220)) <=> ((~hskp5) | c2_1(a220))),
% 0.81/1.02 inference(rewrite,[status(thm)],[])).
% 0.81/1.02 tff(1664,axiom,((~hskp5) | c2_1(a220)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause71')).
% 0.81/1.02 tff(1665,plain,
% 0.81/1.02 ((~hskp5) | c2_1(a220)),
% 0.81/1.02 inference(modus_ponens,[status(thm)],[1664, 1663])).
% 0.81/1.02 tff(1666,plain,
% 0.81/1.02 ((~hskp5) | c2_1(a220)),
% 0.81/1.02 inference(modus_ponens,[status(thm)],[1665, 1663])).
% 0.81/1.02 tff(1667,plain,
% 0.81/1.02 ((~hskp5) | c2_1(a220)),
% 0.81/1.02 inference(modus_ponens,[status(thm)],[1666, 1663])).
% 0.81/1.02 tff(1668,plain,
% 0.81/1.02 ((~hskp5) | c2_1(a220)),
% 0.81/1.02 inference(modus_ponens,[status(thm)],[1667, 1663])).
% 0.81/1.02 tff(1669,plain,
% 0.81/1.02 ((~hskp5) | c2_1(a220)),
% 0.81/1.02 inference(modus_ponens,[status(thm)],[1668, 1663])).
% 0.81/1.02 tff(1670,plain,
% 0.81/1.02 (c2_1(a220)),
% 0.81/1.02 inference(unit_resolution,[status(thm)],[1669, 1656])).
% 0.81/1.02 tff(1671,plain,
% 0.81/1.02 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a229) | c3_1(a220) | c2_1(a213) | (~ndr1_0) | (~c1_1(a213)) | (~c3_1(a213)) | c1_1(a220) | (~c2_1(a220)) | c1_1(a229) | (~c3_1(a229)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a229) | c3_1(a220) | c2_1(a213) | (~ndr1_0) | (~c1_1(a213)) | (~c3_1(a213)) | c1_1(a220) | (~c2_1(a220)) | c1_1(a229) | (~c3_1(a229)))),
% 0.81/1.02 inference(rewrite,[status(thm)],[])).
% 0.81/1.02 tff(1672,plain,
% 0.81/1.02 (((~ndr1_0) | c2_1(a213) | (~c1_1(a213)) | (~c3_1(a213)) | c3_1(a220) | c1_1(a220) | (~c2_1(a220)) | c1_1(a229) | c0_1(a229) | (~c3_1(a229))) <=> (c0_1(a229) | c3_1(a220) | c2_1(a213) | (~ndr1_0) | (~c1_1(a213)) | (~c3_1(a213)) | c1_1(a220) | (~c2_1(a220)) | c1_1(a229) | (~c3_1(a229)))),
% 0.81/1.02 inference(rewrite,[status(thm)],[])).
% 0.81/1.02 tff(1673,plain,
% 0.81/1.02 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a213) | (~c1_1(a213)) | (~c3_1(a213)) | c3_1(a220) | c1_1(a220) | (~c2_1(a220)) | c1_1(a229) | c0_1(a229) | (~c3_1(a229)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a229) | c3_1(a220) | c2_1(a213) | (~ndr1_0) | (~c1_1(a213)) | (~c3_1(a213)) | c1_1(a220) | (~c2_1(a220)) | c1_1(a229) | (~c3_1(a229))))),
% 0.81/1.02 inference(monotonicity,[status(thm)],[1672])).
% 0.81/1.02 tff(1674,plain,
% 0.81/1.02 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a213) | (~c1_1(a213)) | (~c3_1(a213)) | c3_1(a220) | c1_1(a220) | (~c2_1(a220)) | c1_1(a229) | c0_1(a229) | (~c3_1(a229)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a229) | c3_1(a220) | c2_1(a213) | (~ndr1_0) | (~c1_1(a213)) | (~c3_1(a213)) | c1_1(a220) | (~c2_1(a220)) | c1_1(a229) | (~c3_1(a229)))),
% 0.81/1.02 inference(transitivity,[status(thm)],[1673, 1671])).
% 0.81/1.02 tff(1675,plain,
% 0.81/1.02 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a213) | (~c1_1(a213)) | (~c3_1(a213)) | c3_1(a220) | c1_1(a220) | (~c2_1(a220)) | c1_1(a229) | c0_1(a229) | (~c3_1(a229)))),
% 0.81/1.02 inference(quant_inst,[status(thm)],[])).
% 0.81/1.02 tff(1676,plain,
% 0.81/1.02 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a229) | c3_1(a220) | c2_1(a213) | (~ndr1_0) | (~c1_1(a213)) | (~c3_1(a213)) | c1_1(a220) | (~c2_1(a220)) | c1_1(a229) | (~c3_1(a229))),
% 0.81/1.02 inference(modus_ponens,[status(thm)],[1675, 1674])).
% 0.81/1.02 tff(1677,plain,
% 0.81/1.02 (c1_1(a220)),
% 0.81/1.02 inference(unit_resolution,[status(thm)],[1676, 122, 1066, 1670, 321, 320, 11, 1662, 306, 735, 1411])).
% 0.81/1.02 tff(1678,assumption,(c1_1(a246)), introduced(assumption)).
% 0.81/1.02 tff(1679,assumption,(c0_1(a246)), introduced(assumption)).
% 0.81/1.02 tff(1680,plain,
% 0.81/1.02 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (c0_1(a229) | (~ndr1_0) | (~c0_1(a246)) | (~c1_1(a246)) | (~c3_1(a246)) | c1_1(a229) | (~c3_1(a229)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | c0_1(a229) | (~ndr1_0) | (~c0_1(a246)) | (~c1_1(a246)) | (~c3_1(a246)) | c1_1(a229) | (~c3_1(a229)))),
% 0.81/1.02 inference(rewrite,[status(thm)],[])).
% 0.81/1.02 tff(1681,plain,
% 0.81/1.02 (((~ndr1_0) | (~c1_1(a246)) | (~c0_1(a246)) | (~c3_1(a246)) | c0_1(a229) | c1_1(a229) | (~c3_1(a229))) <=> (c0_1(a229) | (~ndr1_0) | (~c0_1(a246)) | (~c1_1(a246)) | (~c3_1(a246)) | c1_1(a229) | (~c3_1(a229)))),
% 0.81/1.02 inference(rewrite,[status(thm)],[])).
% 0.81/1.02 tff(1682,plain,
% 0.81/1.02 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | ((~ndr1_0) | (~c1_1(a246)) | (~c0_1(a246)) | (~c3_1(a246)) | c0_1(a229) | c1_1(a229) | (~c3_1(a229)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (c0_1(a229) | (~ndr1_0) | (~c0_1(a246)) | (~c1_1(a246)) | (~c3_1(a246)) | c1_1(a229) | (~c3_1(a229))))),
% 0.81/1.02 inference(monotonicity,[status(thm)],[1681])).
% 0.81/1.02 tff(1683,plain,
% 0.81/1.02 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | ((~ndr1_0) | (~c1_1(a246)) | (~c0_1(a246)) | (~c3_1(a246)) | c0_1(a229) | c1_1(a229) | (~c3_1(a229)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | c0_1(a229) | (~ndr1_0) | (~c0_1(a246)) | (~c1_1(a246)) | (~c3_1(a246)) | c1_1(a229) | (~c3_1(a229)))),
% 0.81/1.02 inference(transitivity,[status(thm)],[1682, 1680])).
% 0.81/1.02 tff(1684,plain,
% 0.81/1.02 ((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | ((~ndr1_0) | (~c1_1(a246)) | (~c0_1(a246)) | (~c3_1(a246)) | c0_1(a229) | c1_1(a229) | (~c3_1(a229)))),
% 0.81/1.02 inference(quant_inst,[status(thm)],[])).
% 0.81/1.02 tff(1685,plain,
% 0.81/1.02 ((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | c0_1(a229) | (~ndr1_0) | (~c0_1(a246)) | (~c1_1(a246)) | (~c3_1(a246)) | c1_1(a229) | (~c3_1(a229))),
% 0.81/1.02 inference(modus_ponens,[status(thm)],[1684, 1683])).
% 0.81/1.02 tff(1686,plain,
% 0.81/1.02 ((~c3_1(a246)) | c1_1(a229)),
% 0.81/1.02 inference(unit_resolution,[status(thm)],[1685, 122, 1679, 1678, 1066, 11, 583])).
% 0.81/1.02 tff(1687,plain,
% 0.81/1.02 (~c3_1(a246)),
% 0.81/1.02 inference(unit_resolution,[status(thm)],[1686, 1411])).
% 0.81/1.02 tff(1688,plain,
% 0.81/1.02 (((~hskp5) | (~c0_1(a220))) <=> ((~hskp5) | (~c0_1(a220)))),
% 0.81/1.02 inference(rewrite,[status(thm)],[])).
% 0.81/1.02 tff(1689,plain,
% 0.81/1.02 (((~c0_1(a220)) | (~hskp5)) <=> ((~hskp5) | (~c0_1(a220)))),
% 0.81/1.02 inference(rewrite,[status(thm)],[])).
% 0.81/1.02 tff(1690,axiom,((~c0_1(a220)) | (~hskp5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause113')).
% 0.81/1.02 tff(1691,plain,
% 0.81/1.02 ((~hskp5) | (~c0_1(a220))),
% 0.81/1.02 inference(modus_ponens,[status(thm)],[1690, 1689])).
% 0.81/1.02 tff(1692,plain,
% 0.81/1.02 ((~hskp5) | (~c0_1(a220))),
% 0.81/1.02 inference(modus_ponens,[status(thm)],[1691, 1688])).
% 0.81/1.02 tff(1693,plain,
% 0.81/1.02 (~c0_1(a220)),
% 0.81/1.02 inference(unit_resolution,[status(thm)],[1692, 1656])).
% 0.81/1.02 tff(1694,assumption,(c2_1(a246)), introduced(assumption)).
% 0.81/1.02 tff(1695,plain,
% 0.81/1.02 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | (c0_1(a220) | c3_1(a220) | (~ndr1_0) | (~c1_1(a220)) | (~c0_1(a246)) | c3_1(a246) | (~c1_1(a246)) | (~c2_1(a246)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c0_1(a220) | c3_1(a220) | (~ndr1_0) | (~c1_1(a220)) | (~c0_1(a246)) | c3_1(a246) | (~c1_1(a246)) | (~c2_1(a246)))),
% 0.81/1.02 inference(rewrite,[status(thm)],[])).
% 0.81/1.02 tff(1696,plain,
% 0.81/1.02 (((~ndr1_0) | (~c2_1(a246)) | (~c1_1(a246)) | (~c0_1(a246)) | c3_1(a246) | (~c1_1(a246)) | (~c0_1(a246)) | c0_1(a220) | c3_1(a220) | (~c1_1(a220))) <=> (c0_1(a220) | c3_1(a220) | (~ndr1_0) | (~c1_1(a220)) | (~c0_1(a246)) | c3_1(a246) | (~c1_1(a246)) | (~c2_1(a246)))),
% 0.81/1.02 inference(rewrite,[status(thm)],[])).
% 0.81/1.02 tff(1697,plain,
% 0.81/1.02 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a246)) | (~c1_1(a246)) | (~c0_1(a246)) | c3_1(a246) | (~c1_1(a246)) | (~c0_1(a246)) | c0_1(a220) | c3_1(a220) | (~c1_1(a220)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | (c0_1(a220) | c3_1(a220) | (~ndr1_0) | (~c1_1(a220)) | (~c0_1(a246)) | c3_1(a246) | (~c1_1(a246)) | (~c2_1(a246))))),
% 0.81/1.02 inference(monotonicity,[status(thm)],[1696])).
% 0.81/1.02 tff(1698,plain,
% 0.81/1.02 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a246)) | (~c1_1(a246)) | (~c0_1(a246)) | c3_1(a246) | (~c1_1(a246)) | (~c0_1(a246)) | c0_1(a220) | c3_1(a220) | (~c1_1(a220)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c0_1(a220) | c3_1(a220) | (~ndr1_0) | (~c1_1(a220)) | (~c0_1(a246)) | c3_1(a246) | (~c1_1(a246)) | (~c2_1(a246)))),
% 0.81/1.03 inference(transitivity,[status(thm)],[1697, 1695])).
% 0.81/1.03 tff(1699,plain,
% 0.81/1.03 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a246)) | (~c1_1(a246)) | (~c0_1(a246)) | c3_1(a246) | (~c1_1(a246)) | (~c0_1(a246)) | c0_1(a220) | c3_1(a220) | (~c1_1(a220)))),
% 0.81/1.03 inference(quant_inst,[status(thm)],[])).
% 0.81/1.03 tff(1700,plain,
% 0.81/1.03 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c0_1(a220) | c3_1(a220) | (~ndr1_0) | (~c1_1(a220)) | (~c0_1(a246)) | c3_1(a246) | (~c1_1(a246)) | (~c2_1(a246))),
% 0.81/1.03 inference(modus_ponens,[status(thm)],[1699, 1698])).
% 0.81/1.03 tff(1701,plain,
% 0.81/1.03 ($false),
% 0.81/1.03 inference(unit_resolution,[status(thm)],[1700, 122, 1679, 1678, 1694, 1693, 1662, 993, 1687, 1677])).
% 0.81/1.03 tff(1702,plain,(c1_1(a229) | (~c0_1(a246)) | (~c1_1(a246)) | (~c2_1(a246)) | (~c3_1(a229)) | (~c1_1(a213)) | (~c3_1(a213)) | c0_1(a229) | c2_1(a213) | (~c0_1(a237)) | (~c2_1(a237)) | c1_1(a237)), inference(lemma,lemma(discharge,[]))).
% 0.81/1.03 tff(1703,plain,
% 0.81/1.03 (c1_1(a229)),
% 0.81/1.03 inference(unit_resolution,[status(thm)],[1702, 1636, 1635, 1634, 1066, 321, 320, 11, 306, 1632, 1631, 1630])).
% 0.81/1.03 tff(1704,assumption,(~c3_1(a237)), introduced(assumption)).
% 0.81/1.03 tff(1705,assumption,(c1_1(a229)), introduced(assumption)).
% 0.81/1.03 tff(1706,plain,
% 0.81/1.03 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W))) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W))))),
% 0.81/1.03 inference(bind,[status(th)],[])).
% 0.81/1.03 tff(1707,plain,
% 0.81/1.03 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))),
% 0.81/1.03 inference(quant_intro,[status(thm)],[1706])).
% 0.81/1.03 tff(1708,plain,
% 0.81/1.03 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))),
% 0.81/1.03 inference(rewrite,[status(thm)],[])).
% 0.81/1.03 tff(1709,plain,
% 0.81/1.03 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c2_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c2_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(V)))), ((((~c2_1(U)) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(V))))), (((((~c2_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(V))) | (~c1_1(W))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(V)) | (~c1_1(W)))), (((((~c2_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(V)) | (~c1_1(W))))), ((((((~c2_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | (~c2_1(W))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(V)) | (~c1_1(W))) | (~c2_1(W))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(V)) | (~c1_1(W))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(V)) | (~c2_1(W)) | (~c1_1(W)))), ((((((~c2_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(V)) | (~c2_1(W)) | (~c1_1(W))))), (((((((~c2_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c1_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(V)) | (~c2_1(W)) | (~c1_1(W))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(V)) | (~c2_1(W)) | (~c1_1(W))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(V)) | (~c2_1(W)) | (~c1_1(W)))), (((((((~c2_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(V)) | (~c2_1(W)) | (~c1_1(W))))), ((((((((~c2_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c1_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(V)) | (~c2_1(W)) | (~c1_1(W))) | c3_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(V)) | (~c2_1(W)) | (~c1_1(W))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | (~c0_1(V)) | (~c2_1(W)) | (~c1_1(W)))), ((((((((~c2_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | (~c0_1(V)) | (~c2_1(W)) | (~c1_1(W))))), (((((((((~c2_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c1_1(U)) | c3_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | (~c0_1(V)) | (~c2_1(W)) | (~c1_1(W))) | c1_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | (~c0_1(V)) | (~c2_1(W)) | (~c1_1(W))) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(W)) | (~c1_1(W)))), (((((((((~c2_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c1_1(U)) | c3_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(W)) | (~c1_1(W))))), ((((((((((~c2_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c1_1(U)) | c3_1(U)) | c1_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(W)) | (~c1_1(W))) | c3_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(W)) | (~c1_1(W))) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | (~c2_1(W)) | (~c1_1(W)))), ((((((((((~c2_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c1_1(U)) | c3_1(U)) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | (~c2_1(W)) | (~c1_1(W))))), (((((((((((~c2_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c1_1(U)) | c3_1(U)) | c1_1(V)) | c3_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | (~c2_1(W)) | (~c1_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | (~c2_1(W)) | (~c1_1(W))) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))), (((((((((((~c2_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c1_1(U)) | c3_1(U)) | c1_1(V)) | c3_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))))),
% 0.81/1.03 inference(bind,[status(th)],[])).
% 0.81/1.03 tff(1710,plain,
% 0.81/1.03 (![W: $i, V: $i, U: $i] : ((((((((((~c2_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c1_1(U)) | c3_1(U)) | c1_1(V)) | c3_1(V)) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))),
% 0.81/1.03 inference(quant_intro,[status(thm)],[1709])).
% 0.81/1.03 tff(1711,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c2_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c1_1(U)) | c3_1(U)) | c1_1(V)) | c3_1(V)) | c0_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause173')).
% 0.81/1.03 tff(1712,plain,
% 0.81/1.03 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))),
% 0.81/1.03 inference(modus_ponens,[status(thm)],[1711, 1710])).
% 0.81/1.03 tff(1713,plain,
% 0.81/1.03 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))),
% 0.81/1.03 inference(modus_ponens,[status(thm)],[1712, 1708])).
% 0.81/1.03 tff(1714,plain,(
% 0.81/1.03 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))),
% 0.81/1.03 inference(skolemize,[status(sab)],[1713])).
% 0.81/1.03 tff(1715,plain,
% 0.81/1.03 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))),
% 0.81/1.03 inference(modus_ponens,[status(thm)],[1714, 1707])).
% 0.81/1.03 tff(1716,plain,
% 0.81/1.03 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c1_1(a237) | c0_1(a229) | (~ndr1_0) | (~c2_1(a229)) | (~c1_1(a229)) | c3_1(a237) | (~c2_1(a237)) | (~c0_1(a237)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c1_1(a237) | c0_1(a229) | (~ndr1_0) | (~c2_1(a229)) | (~c1_1(a229)) | c3_1(a237) | (~c2_1(a237)) | (~c0_1(a237)))),
% 0.81/1.03 inference(rewrite,[status(thm)],[])).
% 0.81/1.03 tff(1717,plain,
% 0.81/1.03 (((~ndr1_0) | c3_1(a237) | c1_1(a237) | (~c2_1(a237)) | c3_1(a237) | c1_1(a237) | (~c0_1(a237)) | c0_1(a229) | (~c2_1(a229)) | (~c1_1(a229))) <=> (c1_1(a237) | c0_1(a229) | (~ndr1_0) | (~c2_1(a229)) | (~c1_1(a229)) | c3_1(a237) | (~c2_1(a237)) | (~c0_1(a237)))),
% 0.81/1.03 inference(rewrite,[status(thm)],[])).
% 0.81/1.03 tff(1718,plain,
% 0.81/1.03 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a237) | c1_1(a237) | (~c2_1(a237)) | c3_1(a237) | c1_1(a237) | (~c0_1(a237)) | c0_1(a229) | (~c2_1(a229)) | (~c1_1(a229)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c1_1(a237) | c0_1(a229) | (~ndr1_0) | (~c2_1(a229)) | (~c1_1(a229)) | c3_1(a237) | (~c2_1(a237)) | (~c0_1(a237))))),
% 0.81/1.03 inference(monotonicity,[status(thm)],[1717])).
% 0.81/1.03 tff(1719,plain,
% 0.81/1.03 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a237) | c1_1(a237) | (~c2_1(a237)) | c3_1(a237) | c1_1(a237) | (~c0_1(a237)) | c0_1(a229) | (~c2_1(a229)) | (~c1_1(a229)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c1_1(a237) | c0_1(a229) | (~ndr1_0) | (~c2_1(a229)) | (~c1_1(a229)) | c3_1(a237) | (~c2_1(a237)) | (~c0_1(a237)))),
% 0.81/1.03 inference(transitivity,[status(thm)],[1718, 1716])).
% 0.81/1.03 tff(1720,plain,
% 0.81/1.03 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a237) | c1_1(a237) | (~c2_1(a237)) | c3_1(a237) | c1_1(a237) | (~c0_1(a237)) | c0_1(a229) | (~c2_1(a229)) | (~c1_1(a229)))),
% 0.81/1.03 inference(quant_inst,[status(thm)],[])).
% 0.81/1.03 tff(1721,plain,
% 0.81/1.03 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c1_1(a237) | c0_1(a229) | (~ndr1_0) | (~c2_1(a229)) | (~c1_1(a229)) | c3_1(a237) | (~c2_1(a237)) | (~c0_1(a237))),
% 0.81/1.03 inference(modus_ponens,[status(thm)],[1720, 1719])).
% 0.81/1.03 tff(1722,plain,
% 0.81/1.03 ($false),
% 0.81/1.03 inference(unit_resolution,[status(thm)],[1721, 122, 1648, 1647, 1067, 1183, 11, 1715, 1705, 1704])).
% 0.81/1.03 tff(1723,plain,(c3_1(a237) | (~c0_1(a237)) | (~c2_1(a237)) | (~c2_1(a229)) | c1_1(a237) | c0_1(a229) | (~c1_1(a229))), inference(lemma,lemma(discharge,[]))).
% 0.81/1.03 tff(1724,plain,
% 0.81/1.03 (c3_1(a237)),
% 0.81/1.03 inference(unit_resolution,[status(thm)],[1723, 1632, 1631, 1067, 1630, 11, 1703])).
% 0.81/1.03 tff(1725,assumption,(~c2_1(a216)), introduced(assumption)).
% 0.81/1.03 tff(1726,assumption,(~c0_1(a216)), introduced(assumption)).
% 0.81/1.03 tff(1727,plain,
% 0.81/1.03 (^[V: $i, U: $i] : refl((hskp13 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))) <=> (hskp13 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))))),
% 0.81/1.03 inference(bind,[status(th)],[])).
% 0.81/1.03 tff(1728,plain,
% 0.81/1.03 (![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 0.81/1.03 inference(quant_intro,[status(thm)],[1727])).
% 0.81/1.03 tff(1729,plain,
% 0.81/1.03 (![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 0.81/1.03 inference(rewrite,[status(thm)],[])).
% 0.81/1.03 tff(1730,plain,
% 0.81/1.03 (^[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)) | (~c3_1(V)) | (~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)) | (~c3_1(V)) | (~c1_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)) | (~c3_1(V)) | (~c1_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c1_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)) | (~c3_1(V)) | (~c1_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)) | (~c3_1(V)) | (~c1_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_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) | (~c3_1(V)) | (~c1_1(V))))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) | hskp13) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))) | hskp13))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))) | hskp13) <=> (hskp13 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) | hskp13) <=> (hskp13 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))))),
% 0.81/1.03 inference(bind,[status(th)],[])).
% 0.81/1.03 tff(1731,plain,
% 0.81/1.03 (![V: $i, U: $i] : ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) | hskp13) <=> ![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 0.81/1.03 inference(quant_intro,[status(thm)],[1730])).
% 0.81/1.03 tff(1732,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)) | hskp13)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause161')).
% 0.81/1.03 tff(1733,plain,
% 0.81/1.03 (![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 0.81/1.03 inference(modus_ponens,[status(thm)],[1732, 1731])).
% 0.81/1.03 tff(1734,plain,
% 0.81/1.03 (![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 0.81/1.03 inference(modus_ponens,[status(thm)],[1733, 1729])).
% 0.81/1.03 tff(1735,plain,(
% 0.81/1.03 ![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 0.87/1.03 inference(skolemize,[status(sab)],[1734])).
% 0.87/1.03 tff(1736,plain,
% 0.87/1.03 (![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 0.87/1.03 inference(modus_ponens,[status(thm)],[1735, 1728])).
% 0.87/1.03 tff(1737,plain,
% 0.87/1.03 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp13 | c1_1(a237) | c0_1(a229) | (~ndr1_0) | (~c1_1(a229)) | (~c3_1(a229)) | (~c3_1(a237)) | (~c2_1(a237)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp13 | c1_1(a237) | c0_1(a229) | (~ndr1_0) | (~c1_1(a229)) | (~c3_1(a229)) | (~c3_1(a237)) | (~c2_1(a237)))),
% 0.87/1.03 inference(rewrite,[status(thm)],[])).
% 0.87/1.03 tff(1738,plain,
% 0.87/1.03 ((hskp13 | (~ndr1_0) | c1_1(a237) | (~c2_1(a237)) | (~c3_1(a237)) | c0_1(a229) | (~c3_1(a229)) | (~c1_1(a229))) <=> (hskp13 | c1_1(a237) | c0_1(a229) | (~ndr1_0) | (~c1_1(a229)) | (~c3_1(a229)) | (~c3_1(a237)) | (~c2_1(a237)))),
% 0.87/1.03 inference(rewrite,[status(thm)],[])).
% 0.87/1.03 tff(1739,plain,
% 0.87/1.03 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp13 | (~ndr1_0) | c1_1(a237) | (~c2_1(a237)) | (~c3_1(a237)) | c0_1(a229) | (~c3_1(a229)) | (~c1_1(a229)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp13 | c1_1(a237) | c0_1(a229) | (~ndr1_0) | (~c1_1(a229)) | (~c3_1(a229)) | (~c3_1(a237)) | (~c2_1(a237))))),
% 0.87/1.03 inference(monotonicity,[status(thm)],[1738])).
% 0.87/1.03 tff(1740,plain,
% 0.87/1.03 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp13 | (~ndr1_0) | c1_1(a237) | (~c2_1(a237)) | (~c3_1(a237)) | c0_1(a229) | (~c3_1(a229)) | (~c1_1(a229)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp13 | c1_1(a237) | c0_1(a229) | (~ndr1_0) | (~c1_1(a229)) | (~c3_1(a229)) | (~c3_1(a237)) | (~c2_1(a237)))),
% 0.87/1.03 inference(transitivity,[status(thm)],[1739, 1737])).
% 0.87/1.03 tff(1741,plain,
% 0.87/1.03 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp13 | (~ndr1_0) | c1_1(a237) | (~c2_1(a237)) | (~c3_1(a237)) | c0_1(a229) | (~c3_1(a229)) | (~c1_1(a229)))),
% 0.87/1.03 inference(quant_inst,[status(thm)],[])).
% 0.87/1.03 tff(1742,plain,
% 0.87/1.03 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp13 | c1_1(a237) | c0_1(a229) | (~ndr1_0) | (~c1_1(a229)) | (~c3_1(a229)) | (~c3_1(a237)) | (~c2_1(a237))),
% 0.87/1.03 inference(modus_ponens,[status(thm)],[1741, 1740])).
% 0.87/1.03 tff(1743,plain,
% 0.87/1.03 (hskp13 | (~c1_1(a229)) | (~c3_1(a237))),
% 0.87/1.03 inference(unit_resolution,[status(thm)],[1742, 122, 1631, 1066, 1630, 11, 1736])).
% 0.87/1.03 tff(1744,plain,
% 0.87/1.03 (hskp13),
% 0.87/1.03 inference(unit_resolution,[status(thm)],[1743, 1724, 1703])).
% 0.87/1.03 tff(1745,plain,
% 0.87/1.03 (~c3_1(a236)),
% 0.87/1.03 inference(unit_resolution,[status(thm)],[752, 1744])).
% 0.87/1.03 tff(1746,plain,
% 0.87/1.03 (~c2_1(a236)),
% 0.87/1.03 inference(unit_resolution,[status(thm)],[758, 1744])).
% 0.87/1.03 tff(1747,assumption,(c3_1(a216)), introduced(assumption)).
% 0.87/1.03 tff(1748,plain,
% 0.87/1.03 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | (c1_1(a237) | c2_1(a236) | c3_1(a236) | c0_1(a216) | c2_1(a216) | (~ndr1_0) | (~c3_1(a216)) | (~c0_1(a236)) | (~c3_1(a237)) | (~c2_1(a237)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a237) | c2_1(a236) | c3_1(a236) | c0_1(a216) | c2_1(a216) | (~ndr1_0) | (~c3_1(a216)) | (~c0_1(a236)) | (~c3_1(a237)) | (~c2_1(a237)))),
% 0.87/1.03 inference(rewrite,[status(thm)],[])).
% 0.87/1.03 tff(1749,plain,
% 0.87/1.03 (((~ndr1_0) | c3_1(a236) | c2_1(a236) | (~c0_1(a236)) | c1_1(a237) | (~c3_1(a237)) | (~c2_1(a237)) | c0_1(a216) | c2_1(a216) | (~c3_1(a216))) <=> (c1_1(a237) | c2_1(a236) | c3_1(a236) | c0_1(a216) | c2_1(a216) | (~ndr1_0) | (~c3_1(a216)) | (~c0_1(a236)) | (~c3_1(a237)) | (~c2_1(a237)))),
% 0.87/1.03 inference(rewrite,[status(thm)],[])).
% 0.87/1.03 tff(1750,plain,
% 0.87/1.03 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a236) | c2_1(a236) | (~c0_1(a236)) | c1_1(a237) | (~c3_1(a237)) | (~c2_1(a237)) | c0_1(a216) | c2_1(a216) | (~c3_1(a216)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | (c1_1(a237) | c2_1(a236) | c3_1(a236) | c0_1(a216) | c2_1(a216) | (~ndr1_0) | (~c3_1(a216)) | (~c0_1(a236)) | (~c3_1(a237)) | (~c2_1(a237))))),
% 0.87/1.03 inference(monotonicity,[status(thm)],[1749])).
% 0.87/1.03 tff(1751,plain,
% 0.87/1.03 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a236) | c2_1(a236) | (~c0_1(a236)) | c1_1(a237) | (~c3_1(a237)) | (~c2_1(a237)) | c0_1(a216) | c2_1(a216) | (~c3_1(a216)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a237) | c2_1(a236) | c3_1(a236) | c0_1(a216) | c2_1(a216) | (~ndr1_0) | (~c3_1(a216)) | (~c0_1(a236)) | (~c3_1(a237)) | (~c2_1(a237)))),
% 0.87/1.03 inference(transitivity,[status(thm)],[1750, 1748])).
% 0.87/1.03 tff(1752,plain,
% 0.87/1.03 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a236) | c2_1(a236) | (~c0_1(a236)) | c1_1(a237) | (~c3_1(a237)) | (~c2_1(a237)) | c0_1(a216) | c2_1(a216) | (~c3_1(a216)))),
% 0.87/1.03 inference(quant_inst,[status(thm)],[])).
% 0.87/1.03 tff(1753,plain,
% 0.87/1.03 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a237) | c2_1(a236) | c3_1(a236) | c0_1(a216) | c2_1(a216) | (~ndr1_0) | (~c3_1(a216)) | (~c0_1(a236)) | (~c3_1(a237)) | (~c2_1(a237))),
% 0.87/1.03 inference(modus_ponens,[status(thm)],[1752, 1751])).
% 0.87/1.03 tff(1754,plain,
% 0.87/1.03 (~c0_1(a236)),
% 0.87/1.03 inference(unit_resolution,[status(thm)],[1753, 122, 1631, 1747, 1630, 1746, 1745, 1726, 1725, 10, 1724])).
% 0.87/1.03 tff(1755,plain,
% 0.87/1.03 (hskp20),
% 0.87/1.03 inference(unit_resolution,[status(thm)],[1624, 321, 320, 11, 1066, 1067, 306])).
% 0.87/1.03 tff(1756,plain,
% 0.87/1.03 (~c3_1(a259)),
% 0.87/1.03 inference(unit_resolution,[status(thm)],[354, 1755])).
% 0.87/1.03 tff(1757,plain,
% 0.87/1.03 (c0_1(a259)),
% 0.87/1.03 inference(unit_resolution,[status(thm)],[370, 1755])).
% 0.87/1.03 tff(1758,plain,
% 0.87/1.03 ((~c3_1(a237)) | c2_1(a259)),
% 0.87/1.03 inference(unit_resolution,[status(thm)],[1218, 122, 1757, 1631, 1747, 1756, 1630, 1726, 1725, 10])).
% 0.87/1.03 tff(1759,plain,
% 0.87/1.03 (c2_1(a259)),
% 0.87/1.03 inference(unit_resolution,[status(thm)],[1758, 1724])).
% 0.87/1.03 tff(1760,plain,
% 0.87/1.03 (~c1_1(a236)),
% 0.87/1.03 inference(unit_resolution,[status(thm)],[764, 1744])).
% 0.87/1.03 tff(1761,plain,
% 0.87/1.03 (c1_1(a259)),
% 0.87/1.03 inference(unit_resolution,[status(thm)],[362, 1755])).
% 0.87/1.03 tff(1762,plain,
% 0.87/1.03 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c1_1(a236) | c2_1(a236) | c0_1(a229) | (~ndr1_0) | (~c1_1(a229)) | (~c3_1(a229)) | c0_1(a236) | (~c2_1(a259)) | (~c0_1(a259)) | (~c1_1(a259)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c1_1(a236) | c2_1(a236) | c0_1(a229) | (~ndr1_0) | (~c1_1(a229)) | (~c3_1(a229)) | c0_1(a236) | (~c2_1(a259)) | (~c0_1(a259)) | (~c1_1(a259)))),
% 0.87/1.03 inference(rewrite,[status(thm)],[])).
% 0.87/1.03 tff(1763,plain,
% 0.87/1.03 (((~ndr1_0) | (~c2_1(a259)) | (~c1_1(a259)) | (~c0_1(a259)) | c0_1(a229) | (~c3_1(a229)) | (~c1_1(a229)) | c1_1(a236) | c0_1(a236) | c2_1(a236)) <=> (c1_1(a236) | c2_1(a236) | c0_1(a229) | (~ndr1_0) | (~c1_1(a229)) | (~c3_1(a229)) | c0_1(a236) | (~c2_1(a259)) | (~c0_1(a259)) | (~c1_1(a259)))),
% 0.87/1.03 inference(rewrite,[status(thm)],[])).
% 0.87/1.03 tff(1764,plain,
% 0.87/1.03 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | (~c2_1(a259)) | (~c1_1(a259)) | (~c0_1(a259)) | c0_1(a229) | (~c3_1(a229)) | (~c1_1(a229)) | c1_1(a236) | c0_1(a236) | c2_1(a236))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c1_1(a236) | c2_1(a236) | c0_1(a229) | (~ndr1_0) | (~c1_1(a229)) | (~c3_1(a229)) | c0_1(a236) | (~c2_1(a259)) | (~c0_1(a259)) | (~c1_1(a259))))),
% 0.87/1.03 inference(monotonicity,[status(thm)],[1763])).
% 0.87/1.03 tff(1765,plain,
% 0.87/1.03 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | (~c2_1(a259)) | (~c1_1(a259)) | (~c0_1(a259)) | c0_1(a229) | (~c3_1(a229)) | (~c1_1(a229)) | c1_1(a236) | c0_1(a236) | c2_1(a236))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c1_1(a236) | c2_1(a236) | c0_1(a229) | (~ndr1_0) | (~c1_1(a229)) | (~c3_1(a229)) | c0_1(a236) | (~c2_1(a259)) | (~c0_1(a259)) | (~c1_1(a259)))),
% 0.87/1.03 inference(transitivity,[status(thm)],[1764, 1762])).
% 0.87/1.03 tff(1766,plain,
% 0.87/1.03 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | (~c2_1(a259)) | (~c1_1(a259)) | (~c0_1(a259)) | c0_1(a229) | (~c3_1(a229)) | (~c1_1(a229)) | c1_1(a236) | c0_1(a236) | c2_1(a236))),
% 0.87/1.03 inference(quant_inst,[status(thm)],[])).
% 0.87/1.03 tff(1767,plain,
% 0.87/1.03 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c1_1(a236) | c2_1(a236) | c0_1(a229) | (~ndr1_0) | (~c1_1(a229)) | (~c3_1(a229)) | c0_1(a236) | (~c2_1(a259)) | (~c0_1(a259)) | (~c1_1(a259))),
% 0.87/1.03 inference(modus_ponens,[status(thm)],[1766, 1765])).
% 0.87/1.03 tff(1768,plain,
% 0.87/1.03 ($false),
% 0.87/1.03 inference(unit_resolution,[status(thm)],[1767, 122, 1757, 1761, 1066, 1760, 1746, 11, 627, 1703, 1759, 1754])).
% 0.87/1.03 tff(1769,plain,(hskp15 | (~c3_1(a229)) | c0_1(a229) | (~c3_1(a216)) | c0_1(a216) | c2_1(a216) | (~c2_1(a229)) | (~c1_1(a213)) | (~c3_1(a213)) | c2_1(a213)), inference(lemma,lemma(discharge,[]))).
% 0.87/1.03 tff(1770,plain,
% 0.87/1.03 (hskp15),
% 0.87/1.03 inference(unit_resolution,[status(thm)],[1769, 1045, 1044, 1629, 1628, 1627, 1053, 1455, 1457, 1456])).
% 0.87/1.03 tff(1771,plain,
% 0.87/1.03 (hskp27),
% 0.87/1.03 inference(unit_resolution,[status(thm)],[1086, 1770])).
% 0.87/1.03 tff(1772,plain,
% 0.87/1.03 (c0_1(a232)),
% 0.87/1.03 inference(unit_resolution,[status(thm)],[263, 1771])).
% 0.87/1.03 tff(1773,plain,
% 0.87/1.03 (~hskp18),
% 0.87/1.03 inference(unit_resolution,[status(thm)],[1078, 1070, 1067, 1066, 11])).
% 0.87/1.03 tff(1774,plain,
% 0.87/1.03 (hskp18 | hskp6 | c2_1(a259)),
% 0.87/1.03 inference(unit_resolution,[status(thm)],[1337, 122, 1757, 1761, 1331])).
% 0.87/1.03 tff(1775,plain,
% 0.87/1.03 (c2_1(a259)),
% 0.87/1.03 inference(unit_resolution,[status(thm)],[1774, 1773, 1070])).
% 0.87/1.03 tff(1776,plain,
% 0.87/1.03 ($false),
% 0.87/1.03 inference(unit_resolution,[status(thm)],[1506, 753, 759, 1066, 320, 1067, 1070, 306, 765, 11])).
% 0.87/1.03 tff(1777,plain,((~hskp13) | (~c3_1(a229)) | (~c3_1(a213)) | (~c2_1(a229)) | hskp6 | c2_1(a213) | c0_1(a229)), inference(lemma,lemma(discharge,[]))).
% 0.87/1.03 tff(1778,plain,
% 0.87/1.03 (~hskp13),
% 0.87/1.03 inference(unit_resolution,[status(thm)],[1777, 1070, 320, 1067, 1066, 306, 11])).
% 0.87/1.03 tff(1779,plain,
% 0.87/1.03 (^[U: $i] : refl((hskp13 | hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U))) <=> (hskp13 | hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U))))),
% 0.87/1.03 inference(bind,[status(th)],[])).
% 0.87/1.03 tff(1780,plain,
% 0.87/1.03 (![U: $i] : (hskp13 | hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp13 | hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 0.87/1.03 inference(quant_intro,[status(thm)],[1779])).
% 0.87/1.03 tff(1781,plain,
% 0.87/1.03 (![U: $i] : (hskp13 | hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp13 | hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 0.87/1.03 inference(rewrite,[status(thm)],[])).
% 0.87/1.03 tff(1782,plain,
% 0.87/1.03 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp4) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U))) | hskp4))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U))) | hskp4) <=> (hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp4) <=> (hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp4) | hskp13) <=> ((hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U))) | hskp13))), rewrite(((hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U))) | hskp13) <=> (hskp13 | hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp4) | hskp13) <=> (hskp13 | hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))))),
% 0.87/1.03 inference(bind,[status(th)],[])).
% 0.87/1.03 tff(1783,plain,
% 0.87/1.03 (![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp4) | hskp13) <=> ![U: $i] : (hskp13 | hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 0.87/1.03 inference(quant_intro,[status(thm)],[1782])).
% 0.87/1.03 tff(1784,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp4) | hskp13)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause141')).
% 0.87/1.03 tff(1785,plain,
% 0.87/1.03 (![U: $i] : (hskp13 | hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 0.87/1.03 inference(modus_ponens,[status(thm)],[1784, 1783])).
% 0.87/1.03 tff(1786,plain,
% 0.87/1.03 (![U: $i] : (hskp13 | hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 0.87/1.03 inference(modus_ponens,[status(thm)],[1785, 1781])).
% 0.87/1.03 tff(1787,plain,(
% 0.87/1.03 ![U: $i] : (hskp13 | hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 0.87/1.03 inference(skolemize,[status(sab)],[1786])).
% 0.87/1.03 tff(1788,plain,
% 0.87/1.03 (![U: $i] : (hskp13 | hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 0.87/1.03 inference(modus_ponens,[status(thm)],[1787, 1780])).
% 0.87/1.03 tff(1789,plain,
% 0.87/1.03 (((~![U: $i] : (hskp13 | hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp13 | hskp4 | c3_1(a259) | (~ndr1_0) | (~c0_1(a259)) | (~c1_1(a259)))) <=> ((~![U: $i] : (hskp13 | hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp13 | hskp4 | c3_1(a259) | (~ndr1_0) | (~c0_1(a259)) | (~c1_1(a259)))),
% 0.87/1.03 inference(rewrite,[status(thm)],[])).
% 0.87/1.03 tff(1790,plain,
% 0.87/1.03 ((hskp13 | hskp4 | (~ndr1_0) | c3_1(a259) | (~c1_1(a259)) | (~c0_1(a259))) <=> (hskp13 | hskp4 | c3_1(a259) | (~ndr1_0) | (~c0_1(a259)) | (~c1_1(a259)))),
% 0.87/1.03 inference(rewrite,[status(thm)],[])).
% 0.87/1.03 tff(1791,plain,
% 0.87/1.03 (((~![U: $i] : (hskp13 | hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp13 | hskp4 | (~ndr1_0) | c3_1(a259) | (~c1_1(a259)) | (~c0_1(a259)))) <=> ((~![U: $i] : (hskp13 | hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp13 | hskp4 | c3_1(a259) | (~ndr1_0) | (~c0_1(a259)) | (~c1_1(a259))))),
% 0.87/1.03 inference(monotonicity,[status(thm)],[1790])).
% 0.87/1.03 tff(1792,plain,
% 0.87/1.03 (((~![U: $i] : (hskp13 | hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp13 | hskp4 | (~ndr1_0) | c3_1(a259) | (~c1_1(a259)) | (~c0_1(a259)))) <=> ((~![U: $i] : (hskp13 | hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp13 | hskp4 | c3_1(a259) | (~ndr1_0) | (~c0_1(a259)) | (~c1_1(a259)))),
% 0.87/1.03 inference(transitivity,[status(thm)],[1791, 1789])).
% 0.87/1.03 tff(1793,plain,
% 0.87/1.03 ((~![U: $i] : (hskp13 | hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp13 | hskp4 | (~ndr1_0) | c3_1(a259) | (~c1_1(a259)) | (~c0_1(a259)))),
% 0.87/1.03 inference(quant_inst,[status(thm)],[])).
% 0.87/1.03 tff(1794,plain,
% 0.87/1.03 ((~![U: $i] : (hskp13 | hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp13 | hskp4 | c3_1(a259) | (~ndr1_0) | (~c0_1(a259)) | (~c1_1(a259))),
% 0.87/1.03 inference(modus_ponens,[status(thm)],[1793, 1792])).
% 0.87/1.03 tff(1795,plain,
% 0.87/1.03 (hskp13 | hskp4),
% 0.87/1.03 inference(unit_resolution,[status(thm)],[1794, 122, 1757, 1761, 1756, 1788])).
% 0.87/1.03 tff(1796,plain,
% 0.87/1.03 (hskp4),
% 0.87/1.03 inference(unit_resolution,[status(thm)],[1795, 1778])).
% 0.87/1.03 tff(1797,plain,
% 0.87/1.03 (((~hskp4) | (~c1_1(a218))) <=> ((~hskp4) | (~c1_1(a218)))),
% 0.87/1.03 inference(rewrite,[status(thm)],[])).
% 0.87/1.03 tff(1798,plain,
% 0.87/1.03 (((~c1_1(a218)) | (~hskp4)) <=> ((~hskp4) | (~c1_1(a218)))),
% 0.87/1.03 inference(rewrite,[status(thm)],[])).
% 0.87/1.03 tff(1799,axiom,((~c1_1(a218)) | (~hskp4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause116')).
% 0.87/1.03 tff(1800,plain,
% 0.87/1.03 ((~hskp4) | (~c1_1(a218))),
% 0.87/1.03 inference(modus_ponens,[status(thm)],[1799, 1798])).
% 0.87/1.03 tff(1801,plain,
% 0.87/1.03 ((~hskp4) | (~c1_1(a218))),
% 0.87/1.03 inference(modus_ponens,[status(thm)],[1800, 1797])).
% 0.87/1.03 tff(1802,plain,
% 0.87/1.03 (~c1_1(a218)),
% 0.87/1.03 inference(unit_resolution,[status(thm)],[1801, 1796])).
% 0.87/1.03 tff(1803,plain,
% 0.87/1.03 (((~hskp4) | (~c0_1(a218))) <=> ((~hskp4) | (~c0_1(a218)))),
% 0.87/1.03 inference(rewrite,[status(thm)],[])).
% 0.87/1.03 tff(1804,plain,
% 0.87/1.03 (((~c0_1(a218)) | (~hskp4)) <=> ((~hskp4) | (~c0_1(a218)))),
% 0.87/1.03 inference(rewrite,[status(thm)],[])).
% 0.87/1.03 tff(1805,axiom,((~c0_1(a218)) | (~hskp4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause115')).
% 0.87/1.03 tff(1806,plain,
% 0.87/1.03 ((~hskp4) | (~c0_1(a218))),
% 0.87/1.03 inference(modus_ponens,[status(thm)],[1805, 1804])).
% 0.87/1.03 tff(1807,plain,
% 0.87/1.03 ((~hskp4) | (~c0_1(a218))),
% 0.87/1.03 inference(modus_ponens,[status(thm)],[1806, 1803])).
% 0.87/1.03 tff(1808,plain,
% 0.87/1.03 (~c0_1(a218)),
% 0.87/1.03 inference(unit_resolution,[status(thm)],[1807, 1796])).
% 0.87/1.03 tff(1809,plain,
% 0.87/1.03 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a218) | c1_1(a218) | (~ndr1_0) | (~c1_1(a213)) | (~c3_1(a213)) | c0_1(a213) | c2_1(a218) | (~c2_1(a259)) | (~c0_1(a259)) | (~c1_1(a259)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c0_1(a218) | c1_1(a218) | (~ndr1_0) | (~c1_1(a213)) | (~c3_1(a213)) | c0_1(a213) | c2_1(a218) | (~c2_1(a259)) | (~c0_1(a259)) | (~c1_1(a259)))),
% 0.87/1.03 inference(rewrite,[status(thm)],[])).
% 0.87/1.03 tff(1810,plain,
% 0.87/1.03 (((~ndr1_0) | (~c2_1(a259)) | (~c1_1(a259)) | (~c0_1(a259)) | c0_1(a213) | (~c3_1(a213)) | (~c1_1(a213)) | c1_1(a218) | c0_1(a218) | c2_1(a218)) <=> (c0_1(a218) | c1_1(a218) | (~ndr1_0) | (~c1_1(a213)) | (~c3_1(a213)) | c0_1(a213) | c2_1(a218) | (~c2_1(a259)) | (~c0_1(a259)) | (~c1_1(a259)))),
% 0.87/1.03 inference(rewrite,[status(thm)],[])).
% 0.87/1.03 tff(1811,plain,
% 0.87/1.03 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | (~c2_1(a259)) | (~c1_1(a259)) | (~c0_1(a259)) | c0_1(a213) | (~c3_1(a213)) | (~c1_1(a213)) | c1_1(a218) | c0_1(a218) | c2_1(a218))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a218) | c1_1(a218) | (~ndr1_0) | (~c1_1(a213)) | (~c3_1(a213)) | c0_1(a213) | c2_1(a218) | (~c2_1(a259)) | (~c0_1(a259)) | (~c1_1(a259))))),
% 0.87/1.03 inference(monotonicity,[status(thm)],[1810])).
% 0.87/1.03 tff(1812,plain,
% 0.87/1.03 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | (~c2_1(a259)) | (~c1_1(a259)) | (~c0_1(a259)) | c0_1(a213) | (~c3_1(a213)) | (~c1_1(a213)) | c1_1(a218) | c0_1(a218) | c2_1(a218))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c0_1(a218) | c1_1(a218) | (~ndr1_0) | (~c1_1(a213)) | (~c3_1(a213)) | c0_1(a213) | c2_1(a218) | (~c2_1(a259)) | (~c0_1(a259)) | (~c1_1(a259)))),
% 0.87/1.03 inference(transitivity,[status(thm)],[1811, 1809])).
% 0.87/1.03 tff(1813,plain,
% 0.87/1.04 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | (~c2_1(a259)) | (~c1_1(a259)) | (~c0_1(a259)) | c0_1(a213) | (~c3_1(a213)) | (~c1_1(a213)) | c1_1(a218) | c0_1(a218) | c2_1(a218))),
% 0.87/1.04 inference(quant_inst,[status(thm)],[])).
% 0.87/1.04 tff(1814,plain,
% 0.87/1.04 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c0_1(a218) | c1_1(a218) | (~ndr1_0) | (~c1_1(a213)) | (~c3_1(a213)) | c0_1(a213) | c2_1(a218) | (~c2_1(a259)) | (~c0_1(a259)) | (~c1_1(a259))),
% 0.87/1.04 inference(modus_ponens,[status(thm)],[1813, 1812])).
% 0.87/1.04 tff(1815,plain,
% 0.87/1.04 (c2_1(a218)),
% 0.87/1.04 inference(unit_resolution,[status(thm)],[1814, 122, 1757, 1761, 321, 320, 1808, 1802, 627, 1498, 1775])).
% 0.87/1.04 tff(1816,plain,
% 0.87/1.04 (((~hskp4) | c3_1(a218)) <=> ((~hskp4) | c3_1(a218))),
% 0.87/1.04 inference(rewrite,[status(thm)],[])).
% 0.87/1.04 tff(1817,axiom,((~hskp4) | c3_1(a218)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause72')).
% 0.87/1.04 tff(1818,plain,
% 0.87/1.04 ((~hskp4) | c3_1(a218)),
% 0.87/1.04 inference(modus_ponens,[status(thm)],[1817, 1816])).
% 0.87/1.04 tff(1819,plain,
% 0.87/1.04 ((~hskp4) | c3_1(a218)),
% 0.87/1.04 inference(modus_ponens,[status(thm)],[1818, 1816])).
% 0.87/1.04 tff(1820,plain,
% 0.87/1.04 ((~hskp4) | c3_1(a218)),
% 0.87/1.04 inference(modus_ponens,[status(thm)],[1819, 1816])).
% 0.87/1.04 tff(1821,plain,
% 0.87/1.04 ((~hskp4) | c3_1(a218)),
% 0.87/1.04 inference(modus_ponens,[status(thm)],[1820, 1816])).
% 0.87/1.04 tff(1822,plain,
% 0.87/1.04 ((~hskp4) | c3_1(a218)),
% 0.87/1.04 inference(modus_ponens,[status(thm)],[1821, 1816])).
% 0.87/1.04 tff(1823,plain,
% 0.87/1.04 (c3_1(a218)),
% 0.87/1.04 inference(unit_resolution,[status(thm)],[1822, 1796])).
% 0.87/1.04 tff(1824,plain,
% 0.87/1.04 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp13 | c1_1(a218) | (~ndr1_0) | (~c1_1(a213)) | (~c3_1(a213)) | c0_1(a213) | (~c2_1(a218)) | (~c3_1(a218)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp13 | c1_1(a218) | (~ndr1_0) | (~c1_1(a213)) | (~c3_1(a213)) | c0_1(a213) | (~c2_1(a218)) | (~c3_1(a218)))),
% 0.87/1.04 inference(rewrite,[status(thm)],[])).
% 0.87/1.04 tff(1825,plain,
% 0.87/1.04 ((hskp13 | (~ndr1_0) | c1_1(a218) | (~c2_1(a218)) | (~c3_1(a218)) | c0_1(a213) | (~c3_1(a213)) | (~c1_1(a213))) <=> (hskp13 | c1_1(a218) | (~ndr1_0) | (~c1_1(a213)) | (~c3_1(a213)) | c0_1(a213) | (~c2_1(a218)) | (~c3_1(a218)))),
% 0.87/1.04 inference(rewrite,[status(thm)],[])).
% 0.87/1.04 tff(1826,plain,
% 0.87/1.04 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp13 | (~ndr1_0) | c1_1(a218) | (~c2_1(a218)) | (~c3_1(a218)) | c0_1(a213) | (~c3_1(a213)) | (~c1_1(a213)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp13 | c1_1(a218) | (~ndr1_0) | (~c1_1(a213)) | (~c3_1(a213)) | c0_1(a213) | (~c2_1(a218)) | (~c3_1(a218))))),
% 0.87/1.04 inference(monotonicity,[status(thm)],[1825])).
% 0.87/1.04 tff(1827,plain,
% 0.87/1.04 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp13 | (~ndr1_0) | c1_1(a218) | (~c2_1(a218)) | (~c3_1(a218)) | c0_1(a213) | (~c3_1(a213)) | (~c1_1(a213)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp13 | c1_1(a218) | (~ndr1_0) | (~c1_1(a213)) | (~c3_1(a213)) | c0_1(a213) | (~c2_1(a218)) | (~c3_1(a218)))),
% 0.87/1.04 inference(transitivity,[status(thm)],[1826, 1824])).
% 0.87/1.04 tff(1828,plain,
% 0.87/1.04 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp13 | (~ndr1_0) | c1_1(a218) | (~c2_1(a218)) | (~c3_1(a218)) | c0_1(a213) | (~c3_1(a213)) | (~c1_1(a213)))),
% 0.87/1.04 inference(quant_inst,[status(thm)],[])).
% 0.87/1.04 tff(1829,plain,
% 0.87/1.04 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp13 | c1_1(a218) | (~ndr1_0) | (~c1_1(a213)) | (~c3_1(a213)) | c0_1(a213) | (~c2_1(a218)) | (~c3_1(a218))),
% 0.87/1.04 inference(modus_ponens,[status(thm)],[1828, 1827])).
% 0.87/1.04 tff(1830,plain,
% 0.87/1.04 ($false),
% 0.87/1.04 inference(unit_resolution,[status(thm)],[1829, 122, 1778, 1823, 321, 320, 1802, 1736, 1498, 1815])).
% 0.87/1.04 tff(1831,plain,(hskp6 | (~c1_1(a213)) | (~c3_1(a213)) | (~c2_1(a229)) | (~c3_1(a229)) | c2_1(a213) | c0_1(a229)), inference(lemma,lemma(discharge,[]))).
% 0.87/1.04 tff(1832,plain,
% 0.87/1.04 (hskp6),
% 0.87/1.04 inference(unit_resolution,[status(thm)],[1831, 1455, 1457, 1053, 1045, 1456, 1044])).
% 0.87/1.04 tff(1833,plain,
% 0.87/1.04 (c1_1(a221)),
% 0.87/1.04 inference(unit_resolution,[status(thm)],[1116, 1832])).
% 0.87/1.04 tff(1834,plain,
% 0.87/1.04 (~c2_1(a221)),
% 0.87/1.04 inference(unit_resolution,[status(thm)],[1093, 1832])).
% 0.87/1.04 tff(1835,plain,
% 0.87/1.04 (c0_1(a221)),
% 0.87/1.04 inference(unit_resolution,[status(thm)],[1101, 1832])).
% 0.87/1.04 tff(1836,plain,
% 0.87/1.04 (c3_1(a232)),
% 0.87/1.04 inference(unit_resolution,[status(thm)],[247, 1771])).
% 0.87/1.04 tff(1837,plain,
% 0.87/1.04 (c2_1(a232)),
% 0.87/1.04 inference(unit_resolution,[status(thm)],[255, 1771])).
% 0.87/1.04 tff(1838,assumption,(c1_1(a221)), introduced(assumption)).
% 0.87/1.04 tff(1839,assumption,(c0_1(a221)), introduced(assumption)).
% 0.87/1.04 tff(1840,plain,
% 0.87/1.04 ((~c3_1(a221)) | c1_1(a229)),
% 0.87/1.04 inference(unit_resolution,[status(thm)],[1123, 122, 1066, 1839, 1838, 11, 583])).
% 0.87/1.04 tff(1841,plain,
% 0.87/1.04 (~c3_1(a221)),
% 0.87/1.04 inference(unit_resolution,[status(thm)],[1840, 1411])).
% 0.87/1.04 tff(1842,plain,
% 0.87/1.04 (~c1_1(a232)),
% 0.87/1.04 inference(unit_resolution,[status(thm)],[1420, 1411, 766, 1066, 11, 768])).
% 0.87/1.04 tff(1843,plain,
% 0.87/1.04 (~c0_1(a213)),
% 0.87/1.04 inference(unit_resolution,[status(thm)],[1526, 1411])).
% 0.87/1.04 tff(1844,assumption,(~c2_1(a221)), introduced(assumption)).
% 0.87/1.04 tff(1845,plain,
% 0.87/1.04 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | (c2_1(a221) | c2_1(a213) | (~ndr1_0) | (~c3_1(a213)) | c0_1(a213) | c3_1(a221) | (~c0_1(a221)) | (~c2_1(a232)) | c1_1(a232) | (~c3_1(a232)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c2_1(a221) | c2_1(a213) | (~ndr1_0) | (~c3_1(a213)) | c0_1(a213) | c3_1(a221) | (~c0_1(a221)) | (~c2_1(a232)) | c1_1(a232) | (~c3_1(a232)))),
% 0.87/1.04 inference(rewrite,[status(thm)],[])).
% 0.87/1.04 tff(1846,plain,
% 0.87/1.04 (((~ndr1_0) | c3_1(a221) | c2_1(a221) | (~c0_1(a221)) | c1_1(a232) | (~c3_1(a232)) | (~c2_1(a232)) | c0_1(a213) | c2_1(a213) | (~c3_1(a213))) <=> (c2_1(a221) | c2_1(a213) | (~ndr1_0) | (~c3_1(a213)) | c0_1(a213) | c3_1(a221) | (~c0_1(a221)) | (~c2_1(a232)) | c1_1(a232) | (~c3_1(a232)))),
% 0.87/1.04 inference(rewrite,[status(thm)],[])).
% 0.87/1.04 tff(1847,plain,
% 0.87/1.04 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a221) | c2_1(a221) | (~c0_1(a221)) | c1_1(a232) | (~c3_1(a232)) | (~c2_1(a232)) | c0_1(a213) | c2_1(a213) | (~c3_1(a213)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | (c2_1(a221) | c2_1(a213) | (~ndr1_0) | (~c3_1(a213)) | c0_1(a213) | c3_1(a221) | (~c0_1(a221)) | (~c2_1(a232)) | c1_1(a232) | (~c3_1(a232))))),
% 0.87/1.04 inference(monotonicity,[status(thm)],[1846])).
% 0.87/1.04 tff(1848,plain,
% 0.87/1.04 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a221) | c2_1(a221) | (~c0_1(a221)) | c1_1(a232) | (~c3_1(a232)) | (~c2_1(a232)) | c0_1(a213) | c2_1(a213) | (~c3_1(a213)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c2_1(a221) | c2_1(a213) | (~ndr1_0) | (~c3_1(a213)) | c0_1(a213) | c3_1(a221) | (~c0_1(a221)) | (~c2_1(a232)) | c1_1(a232) | (~c3_1(a232)))),
% 0.87/1.04 inference(transitivity,[status(thm)],[1847, 1845])).
% 0.87/1.04 tff(1849,plain,
% 0.87/1.04 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a221) | c2_1(a221) | (~c0_1(a221)) | c1_1(a232) | (~c3_1(a232)) | (~c2_1(a232)) | c0_1(a213) | c2_1(a213) | (~c3_1(a213)))),
% 0.87/1.04 inference(quant_inst,[status(thm)],[])).
% 0.87/1.04 tff(1850,plain,
% 0.87/1.04 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c2_1(a221) | c2_1(a213) | (~ndr1_0) | (~c3_1(a213)) | c0_1(a213) | c3_1(a221) | (~c0_1(a221)) | (~c2_1(a232)) | c1_1(a232) | (~c3_1(a232))),
% 0.87/1.04 inference(modus_ponens,[status(thm)],[1849, 1848])).
% 0.87/1.04 tff(1851,plain,
% 0.87/1.04 ($false),
% 0.87/1.04 inference(unit_resolution,[status(thm)],[1850, 122, 767, 766, 1839, 320, 1844, 306, 10, 1843, 1842, 1841])).
% 0.87/1.04 tff(1852,plain,(c1_1(a229) | (~c2_1(a232)) | (~c3_1(a232)) | (~c0_1(a221)) | (~c3_1(a213)) | c2_1(a221) | c2_1(a213) | (~c3_1(a229)) | (~c1_1(a221)) | c0_1(a229) | (~c0_1(a232)) | (~c1_1(a213))), inference(lemma,lemma(discharge,[]))).
% 0.87/1.04 tff(1853,plain,
% 0.87/1.04 (c1_1(a229)),
% 0.87/1.04 inference(unit_resolution,[status(thm)],[1852, 1837, 1836, 1835, 1457, 1834, 1456, 1045, 1833, 1044, 1772, 1455])).
% 0.87/1.04 tff(1854,plain,
% 0.87/1.04 (~c3_1(a238)),
% 0.87/1.04 inference(unit_resolution,[status(thm)],[216, 1770])).
% 0.87/1.04 tff(1855,plain,
% 0.87/1.04 (c2_1(a238)),
% 0.87/1.04 inference(unit_resolution,[status(thm)],[224, 1770])).
% 0.87/1.04 tff(1856,plain,
% 0.87/1.04 (c0_1(a238)),
% 0.87/1.04 inference(unit_resolution,[status(thm)],[232, 1770])).
% 0.87/1.04 tff(1857,plain,
% 0.87/1.04 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c3_1(a238) | c0_1(a229) | (~ndr1_0) | (~c2_1(a229)) | (~c1_1(a229)) | c1_1(a238) | (~c2_1(a238)) | (~c0_1(a238)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c3_1(a238) | c0_1(a229) | (~ndr1_0) | (~c2_1(a229)) | (~c1_1(a229)) | c1_1(a238) | (~c2_1(a238)) | (~c0_1(a238)))),
% 0.87/1.04 inference(rewrite,[status(thm)],[])).
% 0.87/1.04 tff(1858,plain,
% 0.87/1.04 (((~ndr1_0) | c3_1(a238) | c1_1(a238) | (~c2_1(a238)) | c3_1(a238) | c1_1(a238) | (~c0_1(a238)) | c0_1(a229) | (~c2_1(a229)) | (~c1_1(a229))) <=> (c3_1(a238) | c0_1(a229) | (~ndr1_0) | (~c2_1(a229)) | (~c1_1(a229)) | c1_1(a238) | (~c2_1(a238)) | (~c0_1(a238)))),
% 0.87/1.04 inference(rewrite,[status(thm)],[])).
% 0.87/1.04 tff(1859,plain,
% 0.87/1.04 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a238) | c1_1(a238) | (~c2_1(a238)) | c3_1(a238) | c1_1(a238) | (~c0_1(a238)) | c0_1(a229) | (~c2_1(a229)) | (~c1_1(a229)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c3_1(a238) | c0_1(a229) | (~ndr1_0) | (~c2_1(a229)) | (~c1_1(a229)) | c1_1(a238) | (~c2_1(a238)) | (~c0_1(a238))))),
% 0.87/1.04 inference(monotonicity,[status(thm)],[1858])).
% 0.87/1.04 tff(1860,plain,
% 0.87/1.04 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a238) | c1_1(a238) | (~c2_1(a238)) | c3_1(a238) | c1_1(a238) | (~c0_1(a238)) | c0_1(a229) | (~c2_1(a229)) | (~c1_1(a229)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c3_1(a238) | c0_1(a229) | (~ndr1_0) | (~c2_1(a229)) | (~c1_1(a229)) | c1_1(a238) | (~c2_1(a238)) | (~c0_1(a238)))),
% 0.87/1.04 inference(transitivity,[status(thm)],[1859, 1857])).
% 0.87/1.04 tff(1861,plain,
% 0.87/1.04 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a238) | c1_1(a238) | (~c2_1(a238)) | c3_1(a238) | c1_1(a238) | (~c0_1(a238)) | c0_1(a229) | (~c2_1(a229)) | (~c1_1(a229)))),
% 0.87/1.04 inference(quant_inst,[status(thm)],[])).
% 0.87/1.04 tff(1862,plain,
% 0.87/1.04 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c3_1(a238) | c0_1(a229) | (~ndr1_0) | (~c2_1(a229)) | (~c1_1(a229)) | c1_1(a238) | (~c2_1(a238)) | (~c0_1(a238))),
% 0.87/1.04 inference(modus_ponens,[status(thm)],[1861, 1860])).
% 0.87/1.04 tff(1863,plain,
% 0.87/1.04 ((~c1_1(a229)) | c1_1(a238)),
% 0.87/1.04 inference(unit_resolution,[status(thm)],[1862, 122, 1856, 1855, 1053, 1854, 1044, 1715])).
% 0.87/1.04 tff(1864,plain,
% 0.87/1.04 (c1_1(a238)),
% 0.87/1.04 inference(unit_resolution,[status(thm)],[1863, 1853])).
% 0.87/1.04 tff(1865,plain,
% 0.87/1.04 (~c3_1(a259)),
% 0.87/1.04 inference(unit_resolution,[status(thm)],[354, 1625])).
% 0.87/1.04 tff(1866,plain,
% 0.87/1.04 (c1_1(a259)),
% 0.87/1.04 inference(unit_resolution,[status(thm)],[362, 1625])).
% 0.87/1.04 tff(1867,plain,
% 0.87/1.04 (c0_1(a259)),
% 0.87/1.04 inference(unit_resolution,[status(thm)],[370, 1625])).
% 0.87/1.04 tff(1868,assumption,(c1_1(a238)), introduced(assumption)).
% 0.87/1.04 tff(1869,assumption,(~hskp13), introduced(assumption)).
% 0.87/1.04 tff(1870,assumption,(~c3_1(a259)), introduced(assumption)).
% 0.87/1.04 tff(1871,assumption,(c1_1(a259)), introduced(assumption)).
% 0.87/1.04 tff(1872,assumption,(c0_1(a259)), introduced(assumption)).
% 0.87/1.04 tff(1873,plain,
% 0.87/1.04 (hskp13 | hskp4),
% 0.87/1.04 inference(unit_resolution,[status(thm)],[1794, 122, 1872, 1871, 1870, 1788])).
% 0.87/1.04 tff(1874,plain,
% 0.87/1.04 (hskp4),
% 0.87/1.04 inference(unit_resolution,[status(thm)],[1873, 1869])).
% 0.87/1.04 tff(1875,plain,
% 0.87/1.04 (~c1_1(a218)),
% 0.87/1.04 inference(unit_resolution,[status(thm)],[1801, 1874])).
% 0.87/1.04 tff(1876,plain,
% 0.87/1.04 (~c0_1(a218)),
% 0.87/1.04 inference(unit_resolution,[status(thm)],[1807, 1874])).
% 0.87/1.04 tff(1877,assumption,(c2_1(a238)), introduced(assumption)).
% 0.87/1.04 tff(1878,assumption,(c0_1(a238)), introduced(assumption)).
% 0.87/1.04 tff(1879,plain,
% 0.87/1.04 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a229) | c0_1(a218) | c1_1(a218) | (~ndr1_0) | c2_1(a218) | (~c1_1(a229)) | (~c3_1(a229)) | (~c2_1(a238)) | (~c0_1(a238)) | (~c1_1(a238)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c0_1(a229) | c0_1(a218) | c1_1(a218) | (~ndr1_0) | c2_1(a218) | (~c1_1(a229)) | (~c3_1(a229)) | (~c2_1(a238)) | (~c0_1(a238)) | (~c1_1(a238)))),
% 0.87/1.04 inference(rewrite,[status(thm)],[])).
% 0.87/1.04 tff(1880,plain,
% 0.87/1.04 (((~ndr1_0) | (~c2_1(a238)) | (~c1_1(a238)) | (~c0_1(a238)) | c0_1(a229) | (~c3_1(a229)) | (~c1_1(a229)) | c1_1(a218) | c0_1(a218) | c2_1(a218)) <=> (c0_1(a229) | c0_1(a218) | c1_1(a218) | (~ndr1_0) | c2_1(a218) | (~c1_1(a229)) | (~c3_1(a229)) | (~c2_1(a238)) | (~c0_1(a238)) | (~c1_1(a238)))),
% 0.87/1.04 inference(rewrite,[status(thm)],[])).
% 0.87/1.04 tff(1881,plain,
% 0.87/1.04 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | (~c2_1(a238)) | (~c1_1(a238)) | (~c0_1(a238)) | c0_1(a229) | (~c3_1(a229)) | (~c1_1(a229)) | c1_1(a218) | c0_1(a218) | c2_1(a218))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a229) | c0_1(a218) | c1_1(a218) | (~ndr1_0) | c2_1(a218) | (~c1_1(a229)) | (~c3_1(a229)) | (~c2_1(a238)) | (~c0_1(a238)) | (~c1_1(a238))))),
% 0.87/1.04 inference(monotonicity,[status(thm)],[1880])).
% 0.87/1.04 tff(1882,plain,
% 0.87/1.04 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | (~c2_1(a238)) | (~c1_1(a238)) | (~c0_1(a238)) | c0_1(a229) | (~c3_1(a229)) | (~c1_1(a229)) | c1_1(a218) | c0_1(a218) | c2_1(a218))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c0_1(a229) | c0_1(a218) | c1_1(a218) | (~ndr1_0) | c2_1(a218) | (~c1_1(a229)) | (~c3_1(a229)) | (~c2_1(a238)) | (~c0_1(a238)) | (~c1_1(a238)))),
% 0.87/1.04 inference(transitivity,[status(thm)],[1881, 1879])).
% 0.87/1.04 tff(1883,plain,
% 0.87/1.04 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | (~c2_1(a238)) | (~c1_1(a238)) | (~c0_1(a238)) | c0_1(a229) | (~c3_1(a229)) | (~c1_1(a229)) | c1_1(a218) | c0_1(a218) | c2_1(a218))),
% 0.87/1.04 inference(quant_inst,[status(thm)],[])).
% 0.87/1.04 tff(1884,plain,
% 0.87/1.04 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c0_1(a229) | c0_1(a218) | c1_1(a218) | (~ndr1_0) | c2_1(a218) | (~c1_1(a229)) | (~c3_1(a229)) | (~c2_1(a238)) | (~c0_1(a238)) | (~c1_1(a238))),
% 0.87/1.04 inference(modus_ponens,[status(thm)],[1883, 1882])).
% 0.87/1.04 tff(1885,plain,
% 0.87/1.04 (c2_1(a218)),
% 0.87/1.04 inference(unit_resolution,[status(thm)],[1884, 122, 1878, 1877, 1066, 11, 1876, 1875, 627, 1705, 1868])).
% 0.87/1.04 tff(1886,plain,
% 0.87/1.04 (c3_1(a218)),
% 0.87/1.04 inference(unit_resolution,[status(thm)],[1822, 1874])).
% 0.87/1.04 tff(1887,plain,
% 0.87/1.04 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp13 | c0_1(a229) | c1_1(a218) | (~ndr1_0) | (~c2_1(a218)) | (~c3_1(a218)) | (~c1_1(a229)) | (~c3_1(a229)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp13 | c0_1(a229) | c1_1(a218) | (~ndr1_0) | (~c2_1(a218)) | (~c3_1(a218)) | (~c1_1(a229)) | (~c3_1(a229)))),
% 0.87/1.04 inference(rewrite,[status(thm)],[])).
% 0.87/1.04 tff(1888,plain,
% 0.87/1.04 ((hskp13 | (~ndr1_0) | c1_1(a218) | (~c2_1(a218)) | (~c3_1(a218)) | c0_1(a229) | (~c3_1(a229)) | (~c1_1(a229))) <=> (hskp13 | c0_1(a229) | c1_1(a218) | (~ndr1_0) | (~c2_1(a218)) | (~c3_1(a218)) | (~c1_1(a229)) | (~c3_1(a229)))),
% 0.87/1.04 inference(rewrite,[status(thm)],[])).
% 0.87/1.04 tff(1889,plain,
% 0.87/1.04 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp13 | (~ndr1_0) | c1_1(a218) | (~c2_1(a218)) | (~c3_1(a218)) | c0_1(a229) | (~c3_1(a229)) | (~c1_1(a229)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp13 | c0_1(a229) | c1_1(a218) | (~ndr1_0) | (~c2_1(a218)) | (~c3_1(a218)) | (~c1_1(a229)) | (~c3_1(a229))))),
% 0.87/1.04 inference(monotonicity,[status(thm)],[1888])).
% 0.87/1.04 tff(1890,plain,
% 0.87/1.04 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp13 | (~ndr1_0) | c1_1(a218) | (~c2_1(a218)) | (~c3_1(a218)) | c0_1(a229) | (~c3_1(a229)) | (~c1_1(a229)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp13 | c0_1(a229) | c1_1(a218) | (~ndr1_0) | (~c2_1(a218)) | (~c3_1(a218)) | (~c1_1(a229)) | (~c3_1(a229)))),
% 0.87/1.04 inference(transitivity,[status(thm)],[1889, 1887])).
% 0.87/1.04 tff(1891,plain,
% 0.87/1.04 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp13 | (~ndr1_0) | c1_1(a218) | (~c2_1(a218)) | (~c3_1(a218)) | c0_1(a229) | (~c3_1(a229)) | (~c1_1(a229)))),
% 0.87/1.04 inference(quant_inst,[status(thm)],[])).
% 0.87/1.04 tff(1892,plain,
% 0.87/1.04 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp13 | c0_1(a229) | c1_1(a218) | (~ndr1_0) | (~c2_1(a218)) | (~c3_1(a218)) | (~c1_1(a229)) | (~c3_1(a229))),
% 0.87/1.04 inference(modus_ponens,[status(thm)],[1891, 1890])).
% 0.87/1.04 tff(1893,plain,
% 0.87/1.04 ($false),
% 0.87/1.04 inference(unit_resolution,[status(thm)],[1892, 122, 1869, 1066, 1886, 11, 1875, 1736, 1705, 1885])).
% 0.87/1.04 tff(1894,plain,(hskp13 | (~c3_1(a229)) | c0_1(a229) | (~c1_1(a229)) | (~c0_1(a238)) | (~c2_1(a238)) | (~c1_1(a238)) | (~c0_1(a259)) | (~c1_1(a259)) | c3_1(a259)), inference(lemma,lemma(discharge,[]))).
% 0.87/1.04 tff(1895,plain,
% 0.87/1.04 (hskp13),
% 0.87/1.04 inference(unit_resolution,[status(thm)],[1894, 1045, 1044, 1853, 1856, 1855, 1864, 1867, 1866, 1865])).
% 0.87/1.04 tff(1896,plain,
% 0.87/1.04 (~c2_1(a236)),
% 0.87/1.04 inference(unit_resolution,[status(thm)],[758, 1895])).
% 0.87/1.04 tff(1897,plain,
% 0.87/1.04 (~c1_1(a236)),
% 0.87/1.04 inference(unit_resolution,[status(thm)],[764, 1895])).
% 0.87/1.04 tff(1898,plain,
% 0.87/1.04 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c1_1(a236) | c2_1(a236) | c0_1(a229) | (~ndr1_0) | (~c1_1(a229)) | (~c3_1(a229)) | c0_1(a236) | (~c2_1(a238)) | (~c0_1(a238)) | (~c1_1(a238)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c1_1(a236) | c2_1(a236) | c0_1(a229) | (~ndr1_0) | (~c1_1(a229)) | (~c3_1(a229)) | c0_1(a236) | (~c2_1(a238)) | (~c0_1(a238)) | (~c1_1(a238)))),
% 0.87/1.04 inference(rewrite,[status(thm)],[])).
% 0.87/1.04 tff(1899,plain,
% 0.87/1.04 (((~ndr1_0) | (~c2_1(a238)) | (~c1_1(a238)) | (~c0_1(a238)) | c0_1(a229) | (~c3_1(a229)) | (~c1_1(a229)) | c1_1(a236) | c0_1(a236) | c2_1(a236)) <=> (c1_1(a236) | c2_1(a236) | c0_1(a229) | (~ndr1_0) | (~c1_1(a229)) | (~c3_1(a229)) | c0_1(a236) | (~c2_1(a238)) | (~c0_1(a238)) | (~c1_1(a238)))),
% 0.87/1.04 inference(rewrite,[status(thm)],[])).
% 0.87/1.04 tff(1900,plain,
% 0.87/1.04 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | (~c2_1(a238)) | (~c1_1(a238)) | (~c0_1(a238)) | c0_1(a229) | (~c3_1(a229)) | (~c1_1(a229)) | c1_1(a236) | c0_1(a236) | c2_1(a236))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c1_1(a236) | c2_1(a236) | c0_1(a229) | (~ndr1_0) | (~c1_1(a229)) | (~c3_1(a229)) | c0_1(a236) | (~c2_1(a238)) | (~c0_1(a238)) | (~c1_1(a238))))),
% 0.87/1.04 inference(monotonicity,[status(thm)],[1899])).
% 0.87/1.04 tff(1901,plain,
% 0.87/1.04 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | (~c2_1(a238)) | (~c1_1(a238)) | (~c0_1(a238)) | c0_1(a229) | (~c3_1(a229)) | (~c1_1(a229)) | c1_1(a236) | c0_1(a236) | c2_1(a236))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c1_1(a236) | c2_1(a236) | c0_1(a229) | (~ndr1_0) | (~c1_1(a229)) | (~c3_1(a229)) | c0_1(a236) | (~c2_1(a238)) | (~c0_1(a238)) | (~c1_1(a238)))),
% 0.87/1.04 inference(transitivity,[status(thm)],[1900, 1898])).
% 0.87/1.04 tff(1902,plain,
% 0.87/1.04 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | (~c2_1(a238)) | (~c1_1(a238)) | (~c0_1(a238)) | c0_1(a229) | (~c3_1(a229)) | (~c1_1(a229)) | c1_1(a236) | c0_1(a236) | c2_1(a236))),
% 0.87/1.04 inference(quant_inst,[status(thm)],[])).
% 0.87/1.04 tff(1903,plain,
% 0.87/1.04 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c1_1(a236) | c2_1(a236) | c0_1(a229) | (~ndr1_0) | (~c1_1(a229)) | (~c3_1(a229)) | c0_1(a236) | (~c2_1(a238)) | (~c0_1(a238)) | (~c1_1(a238))),
% 0.87/1.04 inference(modus_ponens,[status(thm)],[1902, 1901])).
% 0.87/1.04 tff(1904,plain,
% 0.87/1.04 (c0_1(a236)),
% 0.87/1.04 inference(unit_resolution,[status(thm)],[1903, 122, 1856, 1855, 1045, 1897, 1896, 1044, 627, 1853, 1864])).
% 0.87/1.04 tff(1905,plain,
% 0.87/1.04 (^[V: $i, U: $i] : refl((hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V))) <=> (hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V))))),
% 0.87/1.04 inference(bind,[status(th)],[])).
% 0.87/1.04 tff(1906,plain,
% 0.87/1.04 (![V: $i, U: $i] : (hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 0.87/1.04 inference(quant_intro,[status(thm)],[1905])).
% 0.87/1.04 tff(1907,plain,
% 0.87/1.04 (![V: $i, U: $i] : (hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 0.87/1.04 inference(rewrite,[status(thm)],[])).
% 0.87/1.04 tff(1908,plain,
% 0.87/1.04 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_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)) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_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)) | (~c1_1(U)) | (~c3_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))) | c2_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c0_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c0_1(V))) | c2_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c2_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V))))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c2_1(V)) | hskp26) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V))) | hskp26))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V))) | hskp26) <=> (hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c2_1(V)) | hskp26) <=> (hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))))),
% 0.87/1.04 inference(bind,[status(th)],[])).
% 0.87/1.04 tff(1909,plain,
% 0.87/1.04 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c2_1(V)) | hskp26) <=> ![V: $i, U: $i] : (hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 0.87/1.04 inference(quant_intro,[status(thm)],[1908])).
% 0.87/1.04 tff(1910,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c2_1(V)) | hskp26)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause165')).
% 0.87/1.04 tff(1911,plain,
% 0.87/1.04 (![V: $i, U: $i] : (hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 0.87/1.04 inference(modus_ponens,[status(thm)],[1910, 1909])).
% 0.87/1.04 tff(1912,plain,
% 0.87/1.04 (![V: $i, U: $i] : (hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 0.87/1.04 inference(modus_ponens,[status(thm)],[1911, 1907])).
% 0.87/1.04 tff(1913,plain,(
% 0.87/1.04 ![V: $i, U: $i] : (hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 0.87/1.04 inference(skolemize,[status(sab)],[1912])).
% 0.87/1.04 tff(1914,plain,
% 0.87/1.04 (![V: $i, U: $i] : (hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 0.87/1.04 inference(modus_ponens,[status(thm)],[1913, 1906])).
% 0.87/1.04 tff(1915,plain,
% 0.87/1.04 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp26 | c2_1(a221) | (~ndr1_0) | (~c1_1(a221)) | (~c0_1(a221)) | (~c2_1(a229)) | (~c1_1(a229)) | (~c3_1(a229)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp26 | c2_1(a221) | (~ndr1_0) | (~c1_1(a221)) | (~c0_1(a221)) | (~c2_1(a229)) | (~c1_1(a229)) | (~c3_1(a229)))),
% 0.87/1.04 inference(rewrite,[status(thm)],[])).
% 0.87/1.04 tff(1916,plain,
% 0.87/1.04 ((hskp26 | (~ndr1_0) | (~c2_1(a229)) | (~c1_1(a229)) | (~c3_1(a229)) | c2_1(a221) | (~c1_1(a221)) | (~c0_1(a221))) <=> (hskp26 | c2_1(a221) | (~ndr1_0) | (~c1_1(a221)) | (~c0_1(a221)) | (~c2_1(a229)) | (~c1_1(a229)) | (~c3_1(a229)))),
% 0.87/1.04 inference(rewrite,[status(thm)],[])).
% 0.87/1.04 tff(1917,plain,
% 0.87/1.04 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp26 | (~ndr1_0) | (~c2_1(a229)) | (~c1_1(a229)) | (~c3_1(a229)) | c2_1(a221) | (~c1_1(a221)) | (~c0_1(a221)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp26 | c2_1(a221) | (~ndr1_0) | (~c1_1(a221)) | (~c0_1(a221)) | (~c2_1(a229)) | (~c1_1(a229)) | (~c3_1(a229))))),
% 0.87/1.04 inference(monotonicity,[status(thm)],[1916])).
% 0.87/1.04 tff(1918,plain,
% 0.87/1.04 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp26 | (~ndr1_0) | (~c2_1(a229)) | (~c1_1(a229)) | (~c3_1(a229)) | c2_1(a221) | (~c1_1(a221)) | (~c0_1(a221)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp26 | c2_1(a221) | (~ndr1_0) | (~c1_1(a221)) | (~c0_1(a221)) | (~c2_1(a229)) | (~c1_1(a229)) | (~c3_1(a229)))),
% 0.87/1.04 inference(transitivity,[status(thm)],[1917, 1915])).
% 0.87/1.04 tff(1919,plain,
% 0.87/1.04 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp26 | (~ndr1_0) | (~c2_1(a229)) | (~c1_1(a229)) | (~c3_1(a229)) | c2_1(a221) | (~c1_1(a221)) | (~c0_1(a221)))),
% 0.87/1.04 inference(quant_inst,[status(thm)],[])).
% 0.87/1.04 tff(1920,plain,
% 0.87/1.04 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp26 | c2_1(a221) | (~ndr1_0) | (~c1_1(a221)) | (~c0_1(a221)) | (~c2_1(a229)) | (~c1_1(a229)) | (~c3_1(a229))),
% 0.87/1.04 inference(modus_ponens,[status(thm)],[1919, 1918])).
% 0.87/1.04 tff(1921,plain,
% 0.87/1.04 (hskp26 | (~c1_1(a229))),
% 0.87/1.04 inference(unit_resolution,[status(thm)],[1920, 122, 1053, 1045, 1835, 1833, 1834, 1914])).
% 0.87/1.04 tff(1922,plain,
% 0.87/1.04 (hskp26),
% 0.87/1.04 inference(unit_resolution,[status(thm)],[1921, 1853])).
% 0.87/1.04 tff(1923,plain,
% 0.87/1.04 (((~hskp26) | c3_1(a223)) <=> ((~hskp26) | c3_1(a223))),
% 0.87/1.04 inference(rewrite,[status(thm)],[])).
% 0.87/1.04 tff(1924,axiom,((~hskp26) | c3_1(a223)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause44')).
% 0.87/1.04 tff(1925,plain,
% 0.87/1.04 ((~hskp26) | c3_1(a223)),
% 0.87/1.04 inference(modus_ponens,[status(thm)],[1924, 1923])).
% 0.87/1.04 tff(1926,plain,
% 0.87/1.04 ((~hskp26) | c3_1(a223)),
% 0.87/1.04 inference(modus_ponens,[status(thm)],[1925, 1923])).
% 0.87/1.04 tff(1927,plain,
% 0.87/1.04 ((~hskp26) | c3_1(a223)),
% 0.87/1.04 inference(modus_ponens,[status(thm)],[1926, 1923])).
% 0.87/1.04 tff(1928,plain,
% 0.87/1.04 ((~hskp26) | c3_1(a223)),
% 0.87/1.04 inference(modus_ponens,[status(thm)],[1927, 1923])).
% 0.87/1.04 tff(1929,plain,
% 0.87/1.04 ((~hskp26) | c3_1(a223)),
% 0.87/1.04 inference(modus_ponens,[status(thm)],[1928, 1923])).
% 0.87/1.04 tff(1930,plain,
% 0.87/1.04 (c3_1(a223)),
% 0.87/1.04 inference(unit_resolution,[status(thm)],[1929, 1922])).
% 0.87/1.04 tff(1931,plain,
% 0.87/1.04 (((~hskp26) | c2_1(a223)) <=> ((~hskp26) | c2_1(a223))),
% 0.87/1.04 inference(rewrite,[status(thm)],[])).
% 0.87/1.04 tff(1932,axiom,((~hskp26) | c2_1(a223)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause43')).
% 0.87/1.04 tff(1933,plain,
% 0.87/1.04 ((~hskp26) | c2_1(a223)),
% 0.87/1.04 inference(modus_ponens,[status(thm)],[1932, 1931])).
% 0.87/1.04 tff(1934,plain,
% 0.87/1.04 ((~hskp26) | c2_1(a223)),
% 0.87/1.04 inference(modus_ponens,[status(thm)],[1933, 1931])).
% 0.87/1.04 tff(1935,plain,
% 0.87/1.04 ((~hskp26) | c2_1(a223)),
% 0.87/1.04 inference(modus_ponens,[status(thm)],[1934, 1931])).
% 0.87/1.04 tff(1936,plain,
% 0.87/1.04 ((~hskp26) | c2_1(a223)),
% 0.87/1.04 inference(modus_ponens,[status(thm)],[1935, 1931])).
% 0.87/1.04 tff(1937,plain,
% 0.87/1.04 ((~hskp26) | c2_1(a223)),
% 0.87/1.04 inference(modus_ponens,[status(thm)],[1936, 1931])).
% 0.87/1.04 tff(1938,plain,
% 0.87/1.04 (c2_1(a223)),
% 0.87/1.04 inference(unit_resolution,[status(thm)],[1937, 1922])).
% 0.87/1.05 tff(1939,plain,
% 0.87/1.05 (((~hskp26) | c1_1(a223)) <=> ((~hskp26) | c1_1(a223))),
% 0.87/1.05 inference(rewrite,[status(thm)],[])).
% 0.87/1.05 tff(1940,axiom,((~hskp26) | c1_1(a223)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause42')).
% 0.87/1.05 tff(1941,plain,
% 0.87/1.05 ((~hskp26) | c1_1(a223)),
% 0.87/1.05 inference(modus_ponens,[status(thm)],[1940, 1939])).
% 0.87/1.05 tff(1942,plain,
% 0.87/1.05 ((~hskp26) | c1_1(a223)),
% 0.87/1.05 inference(modus_ponens,[status(thm)],[1941, 1939])).
% 0.87/1.05 tff(1943,plain,
% 0.87/1.05 ((~hskp26) | c1_1(a223)),
% 0.87/1.05 inference(modus_ponens,[status(thm)],[1942, 1939])).
% 0.87/1.05 tff(1944,plain,
% 0.87/1.05 ((~hskp26) | c1_1(a223)),
% 0.87/1.05 inference(modus_ponens,[status(thm)],[1943, 1939])).
% 0.87/1.05 tff(1945,plain,
% 0.87/1.05 ((~hskp26) | c1_1(a223)),
% 0.87/1.05 inference(modus_ponens,[status(thm)],[1944, 1939])).
% 0.87/1.05 tff(1946,plain,
% 0.87/1.05 (c1_1(a223)),
% 0.87/1.05 inference(unit_resolution,[status(thm)],[1945, 1922])).
% 0.87/1.05 tff(1947,plain,
% 0.87/1.05 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | (c1_1(a236) | c2_1(a236) | c0_1(a229) | (~ndr1_0) | (~c1_1(a223)) | (~c3_1(a223)) | (~c2_1(a223)) | (~c2_1(a229)) | (~c3_1(a229)) | (~c0_1(a236)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | c1_1(a236) | c2_1(a236) | c0_1(a229) | (~ndr1_0) | (~c1_1(a223)) | (~c3_1(a223)) | (~c2_1(a223)) | (~c2_1(a229)) | (~c3_1(a229)) | (~c0_1(a236)))),
% 0.87/1.05 inference(rewrite,[status(thm)],[])).
% 0.87/1.05 tff(1948,plain,
% 0.87/1.05 (((~ndr1_0) | (~c2_1(a223)) | (~c1_1(a223)) | (~c3_1(a223)) | c2_1(a236) | c1_1(a236) | (~c0_1(a236)) | c0_1(a229) | (~c2_1(a229)) | (~c3_1(a229))) <=> (c1_1(a236) | c2_1(a236) | c0_1(a229) | (~ndr1_0) | (~c1_1(a223)) | (~c3_1(a223)) | (~c2_1(a223)) | (~c2_1(a229)) | (~c3_1(a229)) | (~c0_1(a236)))),
% 0.87/1.05 inference(rewrite,[status(thm)],[])).
% 0.87/1.05 tff(1949,plain,
% 0.87/1.05 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a223)) | (~c1_1(a223)) | (~c3_1(a223)) | c2_1(a236) | c1_1(a236) | (~c0_1(a236)) | c0_1(a229) | (~c2_1(a229)) | (~c3_1(a229)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | (c1_1(a236) | c2_1(a236) | c0_1(a229) | (~ndr1_0) | (~c1_1(a223)) | (~c3_1(a223)) | (~c2_1(a223)) | (~c2_1(a229)) | (~c3_1(a229)) | (~c0_1(a236))))),
% 0.87/1.05 inference(monotonicity,[status(thm)],[1948])).
% 0.87/1.05 tff(1950,plain,
% 0.87/1.05 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a223)) | (~c1_1(a223)) | (~c3_1(a223)) | c2_1(a236) | c1_1(a236) | (~c0_1(a236)) | c0_1(a229) | (~c2_1(a229)) | (~c3_1(a229)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | c1_1(a236) | c2_1(a236) | c0_1(a229) | (~ndr1_0) | (~c1_1(a223)) | (~c3_1(a223)) | (~c2_1(a223)) | (~c2_1(a229)) | (~c3_1(a229)) | (~c0_1(a236)))),
% 0.87/1.05 inference(transitivity,[status(thm)],[1949, 1947])).
% 0.87/1.05 tff(1951,plain,
% 0.87/1.05 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a223)) | (~c1_1(a223)) | (~c3_1(a223)) | c2_1(a236) | c1_1(a236) | (~c0_1(a236)) | c0_1(a229) | (~c2_1(a229)) | (~c3_1(a229)))),
% 0.87/1.05 inference(quant_inst,[status(thm)],[])).
% 0.87/1.05 tff(1952,plain,
% 0.87/1.05 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | c1_1(a236) | c2_1(a236) | c0_1(a229) | (~ndr1_0) | (~c1_1(a223)) | (~c3_1(a223)) | (~c2_1(a223)) | (~c2_1(a229)) | (~c3_1(a229)) | (~c0_1(a236))),
% 0.87/1.05 inference(modus_ponens,[status(thm)],[1951, 1950])).
% 0.87/1.05 tff(1953,plain,
% 0.87/1.05 ($false),
% 0.87/1.05 inference(unit_resolution,[status(thm)],[1952, 122, 1946, 1938, 1930, 1053, 1045, 1897, 1896, 1044, 1269, 1904])).
% 0.87/1.05 tff(1954,plain,(hskp8), inference(lemma,lemma(discharge,[]))).
% 0.87/1.05 tff(1955,plain,
% 0.87/1.05 (((~hskp8) | (~c3_1(a225))) <=> ((~hskp8) | (~c3_1(a225)))),
% 0.87/1.05 inference(rewrite,[status(thm)],[])).
% 0.87/1.05 tff(1956,plain,
% 0.87/1.05 (((~c3_1(a225)) | (~hskp8)) <=> ((~hskp8) | (~c3_1(a225)))),
% 0.87/1.05 inference(rewrite,[status(thm)],[])).
% 0.87/1.05 tff(1957,axiom,((~c3_1(a225)) | (~hskp8)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause110')).
% 0.87/1.05 tff(1958,plain,
% 0.87/1.05 ((~hskp8) | (~c3_1(a225))),
% 0.87/1.05 inference(modus_ponens,[status(thm)],[1957, 1956])).
% 0.87/1.05 tff(1959,plain,
% 0.87/1.05 ((~hskp8) | (~c3_1(a225))),
% 0.87/1.05 inference(modus_ponens,[status(thm)],[1958, 1955])).
% 0.87/1.05 tff(1960,plain,
% 0.87/1.05 (~c3_1(a225)),
% 0.87/1.05 inference(unit_resolution,[status(thm)],[1959, 1954])).
% 0.87/1.05 tff(1961,plain,
% 0.87/1.05 (((~hskp8) | (~c2_1(a225))) <=> ((~hskp8) | (~c2_1(a225)))),
% 0.87/1.05 inference(rewrite,[status(thm)],[])).
% 0.87/1.05 tff(1962,plain,
% 0.87/1.05 (((~c2_1(a225)) | (~hskp8)) <=> ((~hskp8) | (~c2_1(a225)))),
% 0.87/1.05 inference(rewrite,[status(thm)],[])).
% 0.87/1.05 tff(1963,axiom,((~c2_1(a225)) | (~hskp8)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause109')).
% 0.87/1.05 tff(1964,plain,
% 0.87/1.05 ((~hskp8) | (~c2_1(a225))),
% 0.87/1.05 inference(modus_ponens,[status(thm)],[1963, 1962])).
% 0.87/1.05 tff(1965,plain,
% 0.87/1.05 ((~hskp8) | (~c2_1(a225))),
% 0.87/1.05 inference(modus_ponens,[status(thm)],[1964, 1961])).
% 0.87/1.05 tff(1966,plain,
% 0.87/1.05 (~c2_1(a225)),
% 0.87/1.05 inference(unit_resolution,[status(thm)],[1965, 1954])).
% 0.87/1.05 tff(1967,plain,
% 0.87/1.05 (((~hskp8) | c0_1(a225)) <=> ((~hskp8) | c0_1(a225))),
% 0.87/1.05 inference(rewrite,[status(thm)],[])).
% 0.87/1.05 tff(1968,axiom,((~hskp8) | c0_1(a225)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause66')).
% 0.87/1.05 tff(1969,plain,
% 0.87/1.05 ((~hskp8) | c0_1(a225)),
% 0.87/1.05 inference(modus_ponens,[status(thm)],[1968, 1967])).
% 0.87/1.05 tff(1970,plain,
% 0.87/1.05 ((~hskp8) | c0_1(a225)),
% 0.87/1.05 inference(modus_ponens,[status(thm)],[1969, 1967])).
% 0.87/1.05 tff(1971,plain,
% 0.87/1.05 ((~hskp8) | c0_1(a225)),
% 0.87/1.05 inference(modus_ponens,[status(thm)],[1970, 1967])).
% 0.87/1.05 tff(1972,plain,
% 0.87/1.05 ((~hskp8) | c0_1(a225)),
% 0.87/1.05 inference(modus_ponens,[status(thm)],[1971, 1967])).
% 0.87/1.05 tff(1973,plain,
% 0.87/1.05 ((~hskp8) | c0_1(a225)),
% 0.87/1.05 inference(modus_ponens,[status(thm)],[1972, 1967])).
% 0.87/1.05 tff(1974,plain,
% 0.87/1.05 (c0_1(a225)),
% 0.87/1.05 inference(unit_resolution,[status(thm)],[1973, 1954])).
% 0.87/1.05 tff(1975,plain,
% 0.87/1.05 (((~![U: $i] : (hskp15 | hskp0 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp15 | hskp0 | c2_1(a225) | c3_1(a225) | (~ndr1_0) | (~c0_1(a225)))) <=> ((~![U: $i] : (hskp15 | hskp0 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | hskp15 | hskp0 | c2_1(a225) | c3_1(a225) | (~ndr1_0) | (~c0_1(a225)))),
% 0.87/1.05 inference(rewrite,[status(thm)],[])).
% 0.87/1.05 tff(1976,plain,
% 0.87/1.05 ((hskp15 | hskp0 | (~ndr1_0) | c3_1(a225) | c2_1(a225) | (~c0_1(a225))) <=> (hskp15 | hskp0 | c2_1(a225) | c3_1(a225) | (~ndr1_0) | (~c0_1(a225)))),
% 0.87/1.05 inference(rewrite,[status(thm)],[])).
% 0.87/1.05 tff(1977,plain,
% 0.87/1.05 (((~![U: $i] : (hskp15 | hskp0 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp15 | hskp0 | (~ndr1_0) | c3_1(a225) | c2_1(a225) | (~c0_1(a225)))) <=> ((~![U: $i] : (hskp15 | hskp0 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp15 | hskp0 | c2_1(a225) | c3_1(a225) | (~ndr1_0) | (~c0_1(a225))))),
% 0.87/1.05 inference(monotonicity,[status(thm)],[1976])).
% 0.87/1.05 tff(1978,plain,
% 0.87/1.05 (((~![U: $i] : (hskp15 | hskp0 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp15 | hskp0 | (~ndr1_0) | c3_1(a225) | c2_1(a225) | (~c0_1(a225)))) <=> ((~![U: $i] : (hskp15 | hskp0 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | hskp15 | hskp0 | c2_1(a225) | c3_1(a225) | (~ndr1_0) | (~c0_1(a225)))),
% 0.87/1.05 inference(transitivity,[status(thm)],[1977, 1975])).
% 0.87/1.05 tff(1979,plain,
% 0.87/1.05 ((~![U: $i] : (hskp15 | hskp0 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp15 | hskp0 | (~ndr1_0) | c3_1(a225) | c2_1(a225) | (~c0_1(a225)))),
% 0.87/1.05 inference(quant_inst,[status(thm)],[])).
% 0.87/1.05 tff(1980,plain,
% 0.87/1.05 ((~![U: $i] : (hskp15 | hskp0 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | hskp15 | hskp0 | c2_1(a225) | c3_1(a225) | (~ndr1_0) | (~c0_1(a225))),
% 0.87/1.05 inference(modus_ponens,[status(thm)],[1979, 1978])).
% 0.87/1.05 tff(1981,plain,
% 0.87/1.05 (hskp15 | hskp0),
% 0.87/1.05 inference(unit_resolution,[status(thm)],[1980, 122, 1974, 1966, 1960, 202])).
% 0.87/1.05 tff(1982,plain,
% 0.87/1.05 (hskp15),
% 0.87/1.05 inference(unit_resolution,[status(thm)],[1981, 64])).
% 0.87/1.05 tff(1983,plain,
% 0.87/1.05 (hskp27),
% 0.87/1.05 inference(unit_resolution,[status(thm)],[1086, 1982])).
% 0.87/1.05 tff(1984,plain,
% 0.87/1.05 (c3_1(a232)),
% 0.87/1.05 inference(unit_resolution,[status(thm)],[247, 1983])).
% 0.87/1.05 tff(1985,plain,
% 0.87/1.05 (c2_1(a232)),
% 0.87/1.05 inference(unit_resolution,[status(thm)],[255, 1983])).
% 0.87/1.05 tff(1986,plain,
% 0.87/1.05 (c0_1(a232)),
% 0.87/1.05 inference(unit_resolution,[status(thm)],[263, 1983])).
% 0.87/1.05 tff(1987,plain,
% 0.87/1.05 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp0 | c2_1(a225) | c3_1(a225) | (~ndr1_0) | (~c2_1(a232)) | (~c3_1(a232)) | (~c0_1(a232)) | c1_1(a225))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp0 | c2_1(a225) | c3_1(a225) | (~ndr1_0) | (~c2_1(a232)) | (~c3_1(a232)) | (~c0_1(a232)) | c1_1(a225))),
% 0.87/1.05 inference(rewrite,[status(thm)],[])).
% 0.87/1.05 tff(1988,plain,
% 0.87/1.05 ((hskp0 | (~ndr1_0) | (~c2_1(a232)) | (~c0_1(a232)) | (~c3_1(a232)) | c3_1(a225) | c2_1(a225) | c1_1(a225)) <=> (hskp0 | c2_1(a225) | c3_1(a225) | (~ndr1_0) | (~c2_1(a232)) | (~c3_1(a232)) | (~c0_1(a232)) | c1_1(a225))),
% 0.87/1.05 inference(rewrite,[status(thm)],[])).
% 0.87/1.05 tff(1989,plain,
% 0.87/1.05 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp0 | (~ndr1_0) | (~c2_1(a232)) | (~c0_1(a232)) | (~c3_1(a232)) | c3_1(a225) | c2_1(a225) | c1_1(a225))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp0 | c2_1(a225) | c3_1(a225) | (~ndr1_0) | (~c2_1(a232)) | (~c3_1(a232)) | (~c0_1(a232)) | c1_1(a225)))),
% 0.87/1.05 inference(monotonicity,[status(thm)],[1988])).
% 0.87/1.05 tff(1990,plain,
% 0.87/1.05 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp0 | (~ndr1_0) | (~c2_1(a232)) | (~c0_1(a232)) | (~c3_1(a232)) | c3_1(a225) | c2_1(a225) | c1_1(a225))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp0 | c2_1(a225) | c3_1(a225) | (~ndr1_0) | (~c2_1(a232)) | (~c3_1(a232)) | (~c0_1(a232)) | c1_1(a225))),
% 0.87/1.05 inference(transitivity,[status(thm)],[1989, 1987])).
% 0.87/1.05 tff(1991,plain,
% 0.87/1.05 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp0 | (~ndr1_0) | (~c2_1(a232)) | (~c0_1(a232)) | (~c3_1(a232)) | c3_1(a225) | c2_1(a225) | c1_1(a225))),
% 0.87/1.05 inference(quant_inst,[status(thm)],[])).
% 0.87/1.05 tff(1992,plain,
% 0.87/1.05 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp0 | c2_1(a225) | c3_1(a225) | (~ndr1_0) | (~c2_1(a232)) | (~c3_1(a232)) | (~c0_1(a232)) | c1_1(a225)),
% 0.87/1.05 inference(modus_ponens,[status(thm)],[1991, 1990])).
% 0.87/1.05 tff(1993,plain,
% 0.87/1.05 (c1_1(a225)),
% 0.87/1.05 inference(unit_resolution,[status(thm)],[1992, 122, 64, 1986, 1985, 1984, 1966, 1960, 42])).
% 0.87/1.05 tff(1994,plain,
% 0.87/1.05 (((~![U: $i] : (hskp12 | hskp0 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp12 | hskp0 | c3_1(a225) | (~ndr1_0) | (~c0_1(a225)) | (~c1_1(a225)))) <=> ((~![U: $i] : (hskp12 | hskp0 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp12 | hskp0 | c3_1(a225) | (~ndr1_0) | (~c0_1(a225)) | (~c1_1(a225)))),
% 0.87/1.05 inference(rewrite,[status(thm)],[])).
% 0.87/1.05 tff(1995,plain,
% 0.87/1.05 ((hskp12 | hskp0 | (~ndr1_0) | c3_1(a225) | (~c1_1(a225)) | (~c0_1(a225))) <=> (hskp12 | hskp0 | c3_1(a225) | (~ndr1_0) | (~c0_1(a225)) | (~c1_1(a225)))),
% 0.87/1.05 inference(rewrite,[status(thm)],[])).
% 0.87/1.05 tff(1996,plain,
% 0.87/1.05 (((~![U: $i] : (hskp12 | hskp0 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp12 | hskp0 | (~ndr1_0) | c3_1(a225) | (~c1_1(a225)) | (~c0_1(a225)))) <=> ((~![U: $i] : (hskp12 | hskp0 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp12 | hskp0 | c3_1(a225) | (~ndr1_0) | (~c0_1(a225)) | (~c1_1(a225))))),
% 0.87/1.05 inference(monotonicity,[status(thm)],[1995])).
% 0.87/1.05 tff(1997,plain,
% 0.87/1.05 (((~![U: $i] : (hskp12 | hskp0 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp12 | hskp0 | (~ndr1_0) | c3_1(a225) | (~c1_1(a225)) | (~c0_1(a225)))) <=> ((~![U: $i] : (hskp12 | hskp0 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp12 | hskp0 | c3_1(a225) | (~ndr1_0) | (~c0_1(a225)) | (~c1_1(a225)))),
% 0.87/1.05 inference(transitivity,[status(thm)],[1996, 1994])).
% 0.87/1.05 tff(1998,plain,
% 0.87/1.05 ((~![U: $i] : (hskp12 | hskp0 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp12 | hskp0 | (~ndr1_0) | c3_1(a225) | (~c1_1(a225)) | (~c0_1(a225)))),
% 0.87/1.05 inference(quant_inst,[status(thm)],[])).
% 0.87/1.05 tff(1999,plain,
% 0.87/1.05 ((~![U: $i] : (hskp12 | hskp0 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp12 | hskp0 | c3_1(a225) | (~ndr1_0) | (~c0_1(a225)) | (~c1_1(a225))),
% 0.87/1.05 inference(modus_ponens,[status(thm)],[1998, 1997])).
% 0.87/1.05 tff(2000,plain,
% 0.87/1.05 (hskp12 | hskp0 | (~c1_1(a225))),
% 0.87/1.05 inference(unit_resolution,[status(thm)],[1999, 122, 1974, 1960, 63])).
% 0.87/1.05 tff(2001,plain,
% 0.87/1.05 (hskp12),
% 0.87/1.05 inference(unit_resolution,[status(thm)],[2000, 1993, 64])).
% 0.87/1.05 tff(2002,plain,
% 0.87/1.05 (~c3_1(a235)),
% 0.87/1.05 inference(unit_resolution,[status(thm)],[1296, 2001])).
% 0.87/1.05 tff(2003,plain,
% 0.87/1.05 (~c1_1(a235)),
% 0.87/1.05 inference(unit_resolution,[status(thm)],[1377, 2001])).
% 0.87/1.05 tff(2004,plain,
% 0.87/1.05 (~c0_1(a235)),
% 0.87/1.05 inference(unit_resolution,[status(thm)],[1302, 2001])).
% 0.87/1.05 tff(2005,plain,
% 0.87/1.05 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a235) | c1_1(a235) | c3_1(a235) | c2_1(a225) | (~ndr1_0) | (~c0_1(a225)) | (~c1_1(a225)) | (~c2_1(a235)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a235) | c1_1(a235) | c3_1(a235) | c2_1(a225) | (~ndr1_0) | (~c0_1(a225)) | (~c1_1(a225)) | (~c2_1(a235)))),
% 0.87/1.05 inference(rewrite,[status(thm)],[])).
% 0.87/1.05 tff(2006,plain,
% 0.87/1.05 (((~ndr1_0) | c2_1(a225) | (~c1_1(a225)) | (~c0_1(a225)) | c3_1(a235) | c1_1(a235) | (~c2_1(a235)) | c1_1(a235) | c0_1(a235) | (~c2_1(a235))) <=> (c0_1(a235) | c1_1(a235) | c3_1(a235) | c2_1(a225) | (~ndr1_0) | (~c0_1(a225)) | (~c1_1(a225)) | (~c2_1(a235)))),
% 0.87/1.05 inference(rewrite,[status(thm)],[])).
% 0.87/1.05 tff(2007,plain,
% 0.87/1.05 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a225) | (~c1_1(a225)) | (~c0_1(a225)) | c3_1(a235) | c1_1(a235) | (~c2_1(a235)) | c1_1(a235) | c0_1(a235) | (~c2_1(a235)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a235) | c1_1(a235) | c3_1(a235) | c2_1(a225) | (~ndr1_0) | (~c0_1(a225)) | (~c1_1(a225)) | (~c2_1(a235))))),
% 0.87/1.05 inference(monotonicity,[status(thm)],[2006])).
% 0.87/1.05 tff(2008,plain,
% 0.87/1.05 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a225) | (~c1_1(a225)) | (~c0_1(a225)) | c3_1(a235) | c1_1(a235) | (~c2_1(a235)) | c1_1(a235) | c0_1(a235) | (~c2_1(a235)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a235) | c1_1(a235) | c3_1(a235) | c2_1(a225) | (~ndr1_0) | (~c0_1(a225)) | (~c1_1(a225)) | (~c2_1(a235)))),
% 0.87/1.05 inference(transitivity,[status(thm)],[2007, 2005])).
% 0.87/1.05 tff(2009,plain,
% 0.87/1.05 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a225) | (~c1_1(a225)) | (~c0_1(a225)) | c3_1(a235) | c1_1(a235) | (~c2_1(a235)) | c1_1(a235) | c0_1(a235) | (~c2_1(a235)))),
% 0.87/1.05 inference(quant_inst,[status(thm)],[])).
% 0.87/1.05 tff(2010,plain,
% 0.87/1.05 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a235) | c1_1(a235) | c3_1(a235) | c2_1(a225) | (~ndr1_0) | (~c0_1(a225)) | (~c1_1(a225)) | (~c2_1(a235))),
% 0.87/1.05 inference(modus_ponens,[status(thm)],[2009, 2008])).
% 0.87/1.05 tff(2011,plain,
% 0.87/1.05 (~c2_1(a235)),
% 0.87/1.05 inference(unit_resolution,[status(thm)],[2010, 122, 1974, 2004, 2003, 2002, 1966, 1320, 1993])).
% 0.87/1.05 tff(2012,plain,
% 0.87/1.05 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp0 | c1_1(a235) | c3_1(a235) | (~ndr1_0) | (~c2_1(a232)) | (~c3_1(a232)) | (~c0_1(a232)) | c2_1(a235))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp0 | c1_1(a235) | c3_1(a235) | (~ndr1_0) | (~c2_1(a232)) | (~c3_1(a232)) | (~c0_1(a232)) | c2_1(a235))),
% 0.87/1.05 inference(rewrite,[status(thm)],[])).
% 0.87/1.05 tff(2013,plain,
% 0.87/1.05 ((hskp0 | (~ndr1_0) | (~c2_1(a232)) | (~c0_1(a232)) | (~c3_1(a232)) | c3_1(a235) | c2_1(a235) | c1_1(a235)) <=> (hskp0 | c1_1(a235) | c3_1(a235) | (~ndr1_0) | (~c2_1(a232)) | (~c3_1(a232)) | (~c0_1(a232)) | c2_1(a235))),
% 0.87/1.05 inference(rewrite,[status(thm)],[])).
% 0.87/1.05 tff(2014,plain,
% 0.87/1.05 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp0 | (~ndr1_0) | (~c2_1(a232)) | (~c0_1(a232)) | (~c3_1(a232)) | c3_1(a235) | c2_1(a235) | c1_1(a235))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp0 | c1_1(a235) | c3_1(a235) | (~ndr1_0) | (~c2_1(a232)) | (~c3_1(a232)) | (~c0_1(a232)) | c2_1(a235)))),
% 0.87/1.05 inference(monotonicity,[status(thm)],[2013])).
% 0.87/1.05 tff(2015,plain,
% 0.87/1.05 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp0 | (~ndr1_0) | (~c2_1(a232)) | (~c0_1(a232)) | (~c3_1(a232)) | c3_1(a235) | c2_1(a235) | c1_1(a235))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp0 | c1_1(a235) | c3_1(a235) | (~ndr1_0) | (~c2_1(a232)) | (~c3_1(a232)) | (~c0_1(a232)) | c2_1(a235))),
% 0.87/1.05 inference(transitivity,[status(thm)],[2014, 2012])).
% 0.87/1.05 tff(2016,plain,
% 0.87/1.05 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp0 | (~ndr1_0) | (~c2_1(a232)) | (~c0_1(a232)) | (~c3_1(a232)) | c3_1(a235) | c2_1(a235) | c1_1(a235))),
% 0.87/1.05 inference(quant_inst,[status(thm)],[])).
% 0.87/1.05 tff(2017,plain,
% 0.87/1.05 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp0 | c1_1(a235) | c3_1(a235) | (~ndr1_0) | (~c2_1(a232)) | (~c3_1(a232)) | (~c0_1(a232)) | c2_1(a235)),
% 0.87/1.05 inference(modus_ponens,[status(thm)],[2016, 2015])).
% 0.87/1.05 tff(2018,plain,
% 0.87/1.05 ($false),
% 0.87/1.05 inference(unit_resolution,[status(thm)],[2017, 122, 64, 1986, 1985, 1984, 2003, 2002, 42, 2011])).
% 0.87/1.05 tff(2019,plain,(hskp0), inference(lemma,lemma(discharge,[]))).
% 0.87/1.05 tff(2020,plain,
% 0.87/1.05 (~c2_1(a213)),
% 0.87/1.05 inference(unit_resolution,[status(thm)],[278, 2019])).
% 0.87/1.05 tff(2021,plain,
% 0.87/1.05 (c1_1(a213)),
% 0.87/1.05 inference(unit_resolution,[status(thm)],[294, 2019])).
% 0.87/1.05 tff(2022,plain,
% 0.87/1.05 (hskp11 | hskp10 | c0_1(a213)),
% 0.87/1.05 inference(unit_resolution,[status(thm)],[388, 122, 2021, 2020, 32])).
% 0.87/1.05 tff(2023,plain,
% 0.87/1.05 (hskp11),
% 0.87/1.05 inference(unit_resolution,[status(thm)],[2022, 22, 21])).
% 0.87/1.05 tff(2024,plain,
% 0.87/1.05 (~c1_1(a230)),
% 0.87/1.05 inference(unit_resolution,[status(thm)],[442, 2023])).
% 0.87/1.05 tff(2025,plain,
% 0.87/1.05 (c2_1(a230)),
% 0.87/1.05 inference(unit_resolution,[status(thm)],[478, 2023])).
% 0.87/1.05 tff(2026,plain,
% 0.87/1.05 (c3_1(a230)),
% 0.87/1.05 inference(unit_resolution,[status(thm)],[470, 2023])).
% 0.87/1.05 tff(2027,plain,
% 0.87/1.05 (c3_1(a213)),
% 0.87/1.05 inference(unit_resolution,[status(thm)],[286, 2019])).
% 0.87/1.05 tff(2028,plain,
% 0.87/1.05 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | (c1_1(a230) | c2_1(a225) | c3_1(a225) | c2_1(a213) | (~ndr1_0) | (~c3_1(a213)) | c0_1(a213) | (~c0_1(a225)) | (~c3_1(a230)) | (~c2_1(a230)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a230) | c2_1(a225) | c3_1(a225) | c2_1(a213) | (~ndr1_0) | (~c3_1(a213)) | c0_1(a213) | (~c0_1(a225)) | (~c3_1(a230)) | (~c2_1(a230)))),
% 0.87/1.05 inference(rewrite,[status(thm)],[])).
% 0.87/1.05 tff(2029,plain,
% 0.87/1.05 (((~ndr1_0) | c3_1(a225) | c2_1(a225) | (~c0_1(a225)) | c1_1(a230) | (~c3_1(a230)) | (~c2_1(a230)) | c0_1(a213) | c2_1(a213) | (~c3_1(a213))) <=> (c1_1(a230) | c2_1(a225) | c3_1(a225) | c2_1(a213) | (~ndr1_0) | (~c3_1(a213)) | c0_1(a213) | (~c0_1(a225)) | (~c3_1(a230)) | (~c2_1(a230)))),
% 0.87/1.05 inference(rewrite,[status(thm)],[])).
% 0.87/1.05 tff(2030,plain,
% 0.87/1.05 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a225) | c2_1(a225) | (~c0_1(a225)) | c1_1(a230) | (~c3_1(a230)) | (~c2_1(a230)) | c0_1(a213) | c2_1(a213) | (~c3_1(a213)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | (c1_1(a230) | c2_1(a225) | c3_1(a225) | c2_1(a213) | (~ndr1_0) | (~c3_1(a213)) | c0_1(a213) | (~c0_1(a225)) | (~c3_1(a230)) | (~c2_1(a230))))),
% 0.87/1.05 inference(monotonicity,[status(thm)],[2029])).
% 0.87/1.05 tff(2031,plain,
% 0.87/1.05 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a225) | c2_1(a225) | (~c0_1(a225)) | c1_1(a230) | (~c3_1(a230)) | (~c2_1(a230)) | c0_1(a213) | c2_1(a213) | (~c3_1(a213)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a230) | c2_1(a225) | c3_1(a225) | c2_1(a213) | (~ndr1_0) | (~c3_1(a213)) | c0_1(a213) | (~c0_1(a225)) | (~c3_1(a230)) | (~c2_1(a230)))),
% 0.87/1.05 inference(transitivity,[status(thm)],[2030, 2028])).
% 0.87/1.05 tff(2032,plain,
% 0.87/1.05 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a225) | c2_1(a225) | (~c0_1(a225)) | c1_1(a230) | (~c3_1(a230)) | (~c2_1(a230)) | c0_1(a213) | c2_1(a213) | (~c3_1(a213)))),
% 0.87/1.05 inference(quant_inst,[status(thm)],[])).
% 0.87/1.05 tff(2033,plain,
% 0.87/1.05 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a230) | c2_1(a225) | c3_1(a225) | c2_1(a213) | (~ndr1_0) | (~c3_1(a213)) | c0_1(a213) | (~c0_1(a225)) | (~c3_1(a230)) | (~c2_1(a230))),
% 0.87/1.05 inference(modus_ponens,[status(thm)],[2032, 2031])).
% 0.87/1.05 tff(2034,plain,
% 0.87/1.05 ($false),
% 0.87/1.05 inference(unit_resolution,[status(thm)],[2033, 122, 566, 565, 1974, 2027, 559, 1966, 1960, 2020, 10, 22])).
% 0.87/1.05 tff(2035,plain,(c0_1(a213) | (~c2_1(a230)) | (~c3_1(a230)) | c1_1(a230)), inference(lemma,lemma(discharge,[]))).
% 0.87/1.05 tff(2036,plain,
% 0.87/1.05 ($false),
% 0.87/1.05 inference(unit_resolution,[status(thm)],[2035, 2026, 2025, 22, 2024])).
% 0.87/1.05 tff(2037,plain,(c0_1(a213) | hskp10), inference(lemma,lemma(discharge,[]))).
% 0.87/1.05 tff(2038,plain,
% 0.87/1.05 (c0_1(a213)),
% 0.87/1.05 inference(unit_resolution,[status(thm)],[2037, 20])).
% 0.87/1.05 tff(2039,plain,
% 0.87/1.05 (^[V: $i, U: $i] : refl((hskp3 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V))) <=> (hskp3 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V))))),
% 0.87/1.05 inference(bind,[status(th)],[])).
% 0.87/1.05 tff(2040,plain,
% 0.87/1.05 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 0.87/1.05 inference(quant_intro,[status(thm)],[2039])).
% 0.87/1.05 tff(2041,plain,
% 0.87/1.05 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 0.87/1.05 inference(rewrite,[status(thm)],[])).
% 0.87/1.05 tff(2042,plain,
% 0.87/1.05 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) <=> ((~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c1_1(U)) | (~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)))), rewrite((((~c1_1(U)) | (~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | (~c0_1(V))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c0_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c0_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c3_1(V)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c0_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c0_1(V))) | c3_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c3_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c3_1(V)) | hskp3) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V))) | hskp3))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V))) | hskp3) <=> (hskp3 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c3_1(V)) | hskp3) <=> (hskp3 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))))),
% 0.87/1.05 inference(bind,[status(th)],[])).
% 0.87/1.05 tff(2043,plain,
% 0.87/1.05 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c3_1(V)) | hskp3) <=> ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 0.87/1.05 inference(quant_intro,[status(thm)],[2042])).
% 0.87/1.05 tff(2044,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c3_1(V)) | hskp3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause166')).
% 0.87/1.05 tff(2045,plain,
% 0.87/1.05 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 0.87/1.05 inference(modus_ponens,[status(thm)],[2044, 2043])).
% 0.87/1.05 tff(2046,plain,
% 0.87/1.05 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 0.87/1.05 inference(modus_ponens,[status(thm)],[2045, 2041])).
% 0.87/1.05 tff(2047,plain,(
% 0.87/1.05 ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 0.87/1.05 inference(skolemize,[status(sab)],[2046])).
% 0.87/1.05 tff(2048,plain,
% 0.87/1.05 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 0.87/1.05 inference(modus_ponens,[status(thm)],[2047, 2040])).
% 0.87/1.05 tff(2049,assumption,(hskp11), introduced(assumption)).
% 0.87/1.05 tff(2050,plain,
% 0.87/1.05 (~c1_1(a230)),
% 0.87/1.05 inference(unit_resolution,[status(thm)],[442, 2049])).
% 0.87/1.05 tff(2051,plain,
% 0.87/1.05 (c3_1(a230)),
% 0.87/1.05 inference(unit_resolution,[status(thm)],[470, 2049])).
% 0.87/1.05 tff(2052,plain,
% 0.87/1.05 (c2_1(a230)),
% 0.87/1.05 inference(unit_resolution,[status(thm)],[478, 2049])).
% 0.87/1.05 tff(2053,plain,
% 0.87/1.05 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp27 | c1_1(a230) | c2_1(a225) | c3_1(a225) | (~ndr1_0) | (~c0_1(a225)) | (~c3_1(a230)) | (~c2_1(a230)))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp27 | c1_1(a230) | c2_1(a225) | c3_1(a225) | (~ndr1_0) | (~c0_1(a225)) | (~c3_1(a230)) | (~c2_1(a230)))),
% 0.87/1.05 inference(rewrite,[status(thm)],[])).
% 0.87/1.05 tff(2054,plain,
% 0.87/1.05 ((hskp27 | (~ndr1_0) | c3_1(a225) | c2_1(a225) | (~c0_1(a225)) | c1_1(a230) | (~c3_1(a230)) | (~c2_1(a230))) <=> (hskp27 | c1_1(a230) | c2_1(a225) | c3_1(a225) | (~ndr1_0) | (~c0_1(a225)) | (~c3_1(a230)) | (~c2_1(a230)))),
% 0.87/1.05 inference(rewrite,[status(thm)],[])).
% 0.87/1.05 tff(2055,plain,
% 0.87/1.05 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp27 | (~ndr1_0) | c3_1(a225) | c2_1(a225) | (~c0_1(a225)) | c1_1(a230) | (~c3_1(a230)) | (~c2_1(a230)))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp27 | c1_1(a230) | c2_1(a225) | c3_1(a225) | (~ndr1_0) | (~c0_1(a225)) | (~c3_1(a230)) | (~c2_1(a230))))),
% 0.87/1.05 inference(monotonicity,[status(thm)],[2054])).
% 0.87/1.05 tff(2056,plain,
% 0.87/1.05 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp27 | (~ndr1_0) | c3_1(a225) | c2_1(a225) | (~c0_1(a225)) | c1_1(a230) | (~c3_1(a230)) | (~c2_1(a230)))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp27 | c1_1(a230) | c2_1(a225) | c3_1(a225) | (~ndr1_0) | (~c0_1(a225)) | (~c3_1(a230)) | (~c2_1(a230)))),
% 0.87/1.05 inference(transitivity,[status(thm)],[2055, 2053])).
% 0.87/1.05 tff(2057,plain,
% 0.87/1.05 ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp27 | (~ndr1_0) | c3_1(a225) | c2_1(a225) | (~c0_1(a225)) | c1_1(a230) | (~c3_1(a230)) | (~c2_1(a230)))),
% 0.87/1.05 inference(quant_inst,[status(thm)],[])).
% 0.87/1.05 tff(2058,plain,
% 0.87/1.05 ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp27 | c1_1(a230) | c2_1(a225) | c3_1(a225) | (~ndr1_0) | (~c0_1(a225)) | (~c3_1(a230)) | (~c2_1(a230))),
% 0.87/1.05 inference(modus_ponens,[status(thm)],[2057, 2056])).
% 0.87/1.05 tff(2059,plain,
% 0.87/1.05 ($false),
% 0.87/1.05 inference(unit_resolution,[status(thm)],[2058, 122, 1080, 2052, 2051, 1974, 2050, 1966, 1960, 463])).
% 0.87/1.05 tff(2060,plain,((~hskp11) | hskp27), inference(lemma,lemma(discharge,[]))).
% 0.87/1.05 tff(2061,plain,
% 0.87/1.05 (~hskp11),
% 0.87/1.05 inference(unit_resolution,[status(thm)],[2060, 1080])).
% 0.87/1.05 tff(2062,plain,
% 0.87/1.05 ((hskp15 | hskp11 | hskp7) <=> (hskp15 | hskp11 | hskp7)),
% 0.87/1.05 inference(rewrite,[status(thm)],[])).
% 0.87/1.05 tff(2063,plain,
% 0.87/1.05 (((hskp15 | hskp7) | hskp11) <=> (hskp15 | hskp11 | hskp7)),
% 0.87/1.05 inference(rewrite,[status(thm)],[])).
% 0.87/1.05 tff(2064,axiom,((hskp15 | hskp7) | hskp11), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause31')).
% 0.87/1.05 tff(2065,plain,
% 0.87/1.05 (hskp15 | hskp11 | hskp7),
% 0.87/1.05 inference(modus_ponens,[status(thm)],[2064, 2063])).
% 0.87/1.05 tff(2066,plain,
% 0.87/1.05 (hskp15 | hskp11 | hskp7),
% 0.87/1.05 inference(modus_ponens,[status(thm)],[2065, 2062])).
% 0.87/1.05 tff(2067,plain,
% 0.87/1.05 (hskp15 | hskp11 | hskp7),
% 0.87/1.05 inference(modus_ponens,[status(thm)],[2066, 2062])).
% 0.87/1.05 tff(2068,plain,
% 0.87/1.05 (hskp15 | hskp11 | hskp7),
% 0.87/1.05 inference(modus_ponens,[status(thm)],[2067, 2062])).
% 0.87/1.05 tff(2069,plain,
% 0.87/1.05 (hskp15 | hskp11 | hskp7),
% 0.87/1.05 inference(modus_ponens,[status(thm)],[2068, 2062])).
% 0.87/1.05 tff(2070,plain,
% 0.87/1.05 (hskp7),
% 0.87/1.05 inference(unit_resolution,[status(thm)],[2069, 2061, 1163])).
% 0.87/1.05 tff(2071,plain,
% 0.87/1.05 (((~hskp7) | c0_1(a224)) <=> ((~hskp7) | c0_1(a224))),
% 0.87/1.05 inference(rewrite,[status(thm)],[])).
% 0.87/1.05 tff(2072,axiom,((~hskp7) | c0_1(a224)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause67')).
% 0.87/1.05 tff(2073,plain,
% 0.87/1.05 ((~hskp7) | c0_1(a224)),
% 0.87/1.06 inference(modus_ponens,[status(thm)],[2072, 2071])).
% 0.87/1.06 tff(2074,plain,
% 0.87/1.06 ((~hskp7) | c0_1(a224)),
% 0.87/1.06 inference(modus_ponens,[status(thm)],[2073, 2071])).
% 0.87/1.06 tff(2075,plain,
% 0.87/1.06 ((~hskp7) | c0_1(a224)),
% 0.87/1.06 inference(modus_ponens,[status(thm)],[2074, 2071])).
% 0.87/1.06 tff(2076,plain,
% 0.87/1.06 ((~hskp7) | c0_1(a224)),
% 0.87/1.06 inference(modus_ponens,[status(thm)],[2075, 2071])).
% 0.87/1.06 tff(2077,plain,
% 0.87/1.06 ((~hskp7) | c0_1(a224)),
% 0.87/1.06 inference(modus_ponens,[status(thm)],[2076, 2071])).
% 0.87/1.06 tff(2078,plain,
% 0.87/1.06 (c0_1(a224)),
% 0.87/1.06 inference(unit_resolution,[status(thm)],[2077, 2070])).
% 0.87/1.06 tff(2079,plain,
% 0.87/1.06 (c0_1(a213)),
% 0.87/1.06 inference(unit_resolution,[status(thm)],[2022, 2061, 21])).
% 0.87/1.06 tff(2080,plain,
% 0.87/1.06 (hskp20),
% 0.87/1.06 inference(unit_resolution,[status(thm)],[436, 2061, 21, 2021, 2020])).
% 0.87/1.06 tff(2081,plain,
% 0.87/1.06 (~c3_1(a259)),
% 0.87/1.06 inference(unit_resolution,[status(thm)],[354, 2080])).
% 0.87/1.06 tff(2082,plain,
% 0.87/1.06 (c1_1(a259)),
% 0.87/1.06 inference(unit_resolution,[status(thm)],[362, 2080])).
% 0.87/1.06 tff(2083,plain,
% 0.87/1.06 (c0_1(a259)),
% 0.87/1.06 inference(unit_resolution,[status(thm)],[370, 2080])).
% 0.87/1.06 tff(2084,plain,
% 0.87/1.06 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp3 | c3_1(a259) | (~ndr1_0) | (~c1_1(a213)) | (~c3_1(a213)) | (~c0_1(a213)) | (~c0_1(a259)) | (~c1_1(a259)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp3 | c3_1(a259) | (~ndr1_0) | (~c1_1(a213)) | (~c3_1(a213)) | (~c0_1(a213)) | (~c0_1(a259)) | (~c1_1(a259)))),
% 0.87/1.06 inference(rewrite,[status(thm)],[])).
% 0.87/1.06 tff(2085,plain,
% 0.87/1.06 ((hskp3 | (~ndr1_0) | (~c1_1(a213)) | (~c0_1(a213)) | (~c3_1(a213)) | c3_1(a259) | (~c1_1(a259)) | (~c0_1(a259))) <=> (hskp3 | c3_1(a259) | (~ndr1_0) | (~c1_1(a213)) | (~c3_1(a213)) | (~c0_1(a213)) | (~c0_1(a259)) | (~c1_1(a259)))),
% 0.87/1.06 inference(rewrite,[status(thm)],[])).
% 0.87/1.06 tff(2086,plain,
% 0.87/1.06 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp3 | (~ndr1_0) | (~c1_1(a213)) | (~c0_1(a213)) | (~c3_1(a213)) | c3_1(a259) | (~c1_1(a259)) | (~c0_1(a259)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp3 | c3_1(a259) | (~ndr1_0) | (~c1_1(a213)) | (~c3_1(a213)) | (~c0_1(a213)) | (~c0_1(a259)) | (~c1_1(a259))))),
% 0.87/1.06 inference(monotonicity,[status(thm)],[2085])).
% 0.87/1.06 tff(2087,plain,
% 0.87/1.06 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp3 | (~ndr1_0) | (~c1_1(a213)) | (~c0_1(a213)) | (~c3_1(a213)) | c3_1(a259) | (~c1_1(a259)) | (~c0_1(a259)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp3 | c3_1(a259) | (~ndr1_0) | (~c1_1(a213)) | (~c3_1(a213)) | (~c0_1(a213)) | (~c0_1(a259)) | (~c1_1(a259)))),
% 0.87/1.06 inference(transitivity,[status(thm)],[2086, 2084])).
% 0.87/1.06 tff(2088,plain,
% 0.87/1.06 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp3 | (~ndr1_0) | (~c1_1(a213)) | (~c0_1(a213)) | (~c3_1(a213)) | c3_1(a259) | (~c1_1(a259)) | (~c0_1(a259)))),
% 0.87/1.06 inference(quant_inst,[status(thm)],[])).
% 0.87/1.06 tff(2089,plain,
% 0.87/1.06 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp3 | c3_1(a259) | (~ndr1_0) | (~c1_1(a213)) | (~c3_1(a213)) | (~c0_1(a213)) | (~c0_1(a259)) | (~c1_1(a259))),
% 0.87/1.06 inference(modus_ponens,[status(thm)],[2088, 2087])).
% 0.87/1.06 tff(2090,plain,
% 0.87/1.06 (hskp3),
% 0.87/1.06 inference(unit_resolution,[status(thm)],[2089, 122, 2083, 2082, 2021, 2027, 2081, 2048, 2079])).
% 0.87/1.06 tff(2091,plain,
% 0.87/1.06 (~c2_1(a216)),
% 0.87/1.06 inference(unit_resolution,[status(thm)],[312, 2090])).
% 0.87/1.06 tff(2092,plain,
% 0.87/1.06 (~c0_1(a216)),
% 0.87/1.06 inference(unit_resolution,[status(thm)],[318, 2090])).
% 0.87/1.06 tff(2093,plain,
% 0.87/1.06 (((~hskp7) | (~c1_1(a224))) <=> ((~hskp7) | (~c1_1(a224)))),
% 0.87/1.06 inference(rewrite,[status(thm)],[])).
% 0.87/1.06 tff(2094,plain,
% 0.87/1.06 (((~c1_1(a224)) | (~hskp7)) <=> ((~hskp7) | (~c1_1(a224)))),
% 0.87/1.06 inference(rewrite,[status(thm)],[])).
% 0.87/1.06 tff(2095,axiom,((~c1_1(a224)) | (~hskp7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause111')).
% 0.87/1.06 tff(2096,plain,
% 0.87/1.06 ((~hskp7) | (~c1_1(a224))),
% 0.87/1.06 inference(modus_ponens,[status(thm)],[2095, 2094])).
% 0.87/1.06 tff(2097,plain,
% 0.87/1.06 ((~hskp7) | (~c1_1(a224))),
% 0.87/1.06 inference(modus_ponens,[status(thm)],[2096, 2093])).
% 0.87/1.06 tff(2098,plain,
% 0.87/1.06 (~c1_1(a224)),
% 0.87/1.06 inference(unit_resolution,[status(thm)],[2097, 2070])).
% 0.87/1.06 tff(2099,plain,
% 0.87/1.06 (~c2_1(a259)),
% 0.87/1.06 inference(unit_resolution,[status(thm)],[1225, 122, 1080, 2083, 2081, 192])).
% 0.87/1.06 tff(2100,plain,
% 0.87/1.06 (((~hskp7) | c3_1(a224)) <=> ((~hskp7) | c3_1(a224))),
% 0.87/1.06 inference(rewrite,[status(thm)],[])).
% 0.87/1.06 tff(2101,axiom,((~hskp7) | c3_1(a224)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause68')).
% 0.87/1.06 tff(2102,plain,
% 0.87/1.06 ((~hskp7) | c3_1(a224)),
% 0.87/1.06 inference(modus_ponens,[status(thm)],[2101, 2100])).
% 0.87/1.06 tff(2103,plain,
% 0.87/1.06 ((~hskp7) | c3_1(a224)),
% 0.87/1.06 inference(modus_ponens,[status(thm)],[2102, 2100])).
% 0.87/1.06 tff(2104,plain,
% 0.87/1.06 ((~hskp7) | c3_1(a224)),
% 0.87/1.06 inference(modus_ponens,[status(thm)],[2103, 2100])).
% 0.87/1.06 tff(2105,plain,
% 0.87/1.06 ((~hskp7) | c3_1(a224)),
% 0.87/1.06 inference(modus_ponens,[status(thm)],[2104, 2100])).
% 0.87/1.06 tff(2106,plain,
% 0.87/1.06 ((~hskp7) | c3_1(a224)),
% 0.87/1.06 inference(modus_ponens,[status(thm)],[2105, 2100])).
% 0.87/1.06 tff(2107,plain,
% 0.87/1.06 (c3_1(a224)),
% 0.87/1.06 inference(unit_resolution,[status(thm)],[2106, 2070])).
% 0.87/1.06 tff(2108,plain,
% 0.87/1.06 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp27 | c3_1(a259) | c1_1(a224) | (~ndr1_0) | (~c3_1(a224)) | (~c2_1(a224)) | c2_1(a259) | (~c0_1(a259)))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp27 | c3_1(a259) | c1_1(a224) | (~ndr1_0) | (~c3_1(a224)) | (~c2_1(a224)) | c2_1(a259) | (~c0_1(a259)))),
% 0.87/1.06 inference(rewrite,[status(thm)],[])).
% 0.87/1.06 tff(2109,plain,
% 0.87/1.06 ((hskp27 | (~ndr1_0) | c3_1(a259) | c2_1(a259) | (~c0_1(a259)) | c1_1(a224) | (~c3_1(a224)) | (~c2_1(a224))) <=> (hskp27 | c3_1(a259) | c1_1(a224) | (~ndr1_0) | (~c3_1(a224)) | (~c2_1(a224)) | c2_1(a259) | (~c0_1(a259)))),
% 0.87/1.06 inference(rewrite,[status(thm)],[])).
% 0.87/1.06 tff(2110,plain,
% 0.87/1.06 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp27 | (~ndr1_0) | c3_1(a259) | c2_1(a259) | (~c0_1(a259)) | c1_1(a224) | (~c3_1(a224)) | (~c2_1(a224)))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp27 | c3_1(a259) | c1_1(a224) | (~ndr1_0) | (~c3_1(a224)) | (~c2_1(a224)) | c2_1(a259) | (~c0_1(a259))))),
% 0.87/1.06 inference(monotonicity,[status(thm)],[2109])).
% 0.87/1.06 tff(2111,plain,
% 0.87/1.06 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp27 | (~ndr1_0) | c3_1(a259) | c2_1(a259) | (~c0_1(a259)) | c1_1(a224) | (~c3_1(a224)) | (~c2_1(a224)))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp27 | c3_1(a259) | c1_1(a224) | (~ndr1_0) | (~c3_1(a224)) | (~c2_1(a224)) | c2_1(a259) | (~c0_1(a259)))),
% 0.87/1.06 inference(transitivity,[status(thm)],[2110, 2108])).
% 0.87/1.06 tff(2112,plain,
% 0.87/1.06 ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp27 | (~ndr1_0) | c3_1(a259) | c2_1(a259) | (~c0_1(a259)) | c1_1(a224) | (~c3_1(a224)) | (~c2_1(a224)))),
% 0.87/1.06 inference(quant_inst,[status(thm)],[])).
% 0.87/1.06 tff(2113,plain,
% 0.87/1.06 ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp27 | c3_1(a259) | c1_1(a224) | (~ndr1_0) | (~c3_1(a224)) | (~c2_1(a224)) | c2_1(a259) | (~c0_1(a259))),
% 0.87/1.06 inference(modus_ponens,[status(thm)],[2112, 2111])).
% 0.87/1.06 tff(2114,plain,
% 0.87/1.06 (~c2_1(a224)),
% 0.87/1.06 inference(unit_resolution,[status(thm)],[2113, 122, 1080, 2083, 2107, 2081, 2098, 463, 2099])).
% 0.87/1.06 tff(2115,plain,
% 0.87/1.06 (c3_1(a216)),
% 0.87/1.06 inference(unit_resolution,[status(thm)],[328, 2090])).
% 0.87/1.06 tff(2116,assumption,(~c2_1(a224)), introduced(assumption)).
% 0.87/1.06 tff(2117,assumption,(~c1_1(a224)), introduced(assumption)).
% 0.87/1.06 tff(2118,assumption,(c0_1(a224)), introduced(assumption)).
% 0.87/1.06 tff(2119,plain,
% 0.87/1.06 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | (c1_1(a224) | c0_1(a216) | c2_1(a216) | c2_1(a213) | (~ndr1_0) | (~c1_1(a213)) | (~c3_1(a213)) | (~c3_1(a216)) | c2_1(a224) | (~c0_1(a224)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a224) | c0_1(a216) | c2_1(a216) | c2_1(a213) | (~ndr1_0) | (~c1_1(a213)) | (~c3_1(a213)) | (~c3_1(a216)) | c2_1(a224) | (~c0_1(a224)))),
% 0.87/1.06 inference(rewrite,[status(thm)],[])).
% 0.87/1.06 tff(2120,plain,
% 0.87/1.06 (((~ndr1_0) | c2_1(a213) | (~c1_1(a213)) | (~c3_1(a213)) | c2_1(a224) | c1_1(a224) | (~c0_1(a224)) | c0_1(a216) | c2_1(a216) | (~c3_1(a216))) <=> (c1_1(a224) | c0_1(a216) | c2_1(a216) | c2_1(a213) | (~ndr1_0) | (~c1_1(a213)) | (~c3_1(a213)) | (~c3_1(a216)) | c2_1(a224) | (~c0_1(a224)))),
% 0.87/1.06 inference(rewrite,[status(thm)],[])).
% 0.87/1.06 tff(2121,plain,
% 0.87/1.06 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a213) | (~c1_1(a213)) | (~c3_1(a213)) | c2_1(a224) | c1_1(a224) | (~c0_1(a224)) | c0_1(a216) | c2_1(a216) | (~c3_1(a216)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | (c1_1(a224) | c0_1(a216) | c2_1(a216) | c2_1(a213) | (~ndr1_0) | (~c1_1(a213)) | (~c3_1(a213)) | (~c3_1(a216)) | c2_1(a224) | (~c0_1(a224))))),
% 0.87/1.06 inference(monotonicity,[status(thm)],[2120])).
% 0.87/1.06 tff(2122,plain,
% 0.87/1.06 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a213) | (~c1_1(a213)) | (~c3_1(a213)) | c2_1(a224) | c1_1(a224) | (~c0_1(a224)) | c0_1(a216) | c2_1(a216) | (~c3_1(a216)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a224) | c0_1(a216) | c2_1(a216) | c2_1(a213) | (~ndr1_0) | (~c1_1(a213)) | (~c3_1(a213)) | (~c3_1(a216)) | c2_1(a224) | (~c0_1(a224)))),
% 0.87/1.06 inference(transitivity,[status(thm)],[2121, 2119])).
% 0.87/1.06 tff(2123,plain,
% 0.87/1.06 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a213) | (~c1_1(a213)) | (~c3_1(a213)) | c2_1(a224) | c1_1(a224) | (~c0_1(a224)) | c0_1(a216) | c2_1(a216) | (~c3_1(a216)))),
% 0.87/1.06 inference(quant_inst,[status(thm)],[])).
% 0.87/1.06 tff(2124,plain,
% 0.87/1.06 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a224) | c0_1(a216) | c2_1(a216) | c2_1(a213) | (~ndr1_0) | (~c1_1(a213)) | (~c3_1(a213)) | (~c3_1(a216)) | c2_1(a224) | (~c0_1(a224))),
% 0.87/1.06 inference(modus_ponens,[status(thm)],[2123, 2122])).
% 0.87/1.06 tff(2125,plain,
% 0.87/1.06 ($false),
% 0.87/1.06 inference(unit_resolution,[status(thm)],[2124, 122, 2118, 1747, 321, 320, 2117, 1726, 1725, 306, 305, 2116])).
% 0.87/1.06 tff(2126,plain,(c2_1(a224) | (~c0_1(a224)) | (~c3_1(a216)) | (~c1_1(a213)) | (~c3_1(a213)) | c1_1(a224) | c0_1(a216) | c2_1(a216) | c2_1(a213)), inference(lemma,lemma(discharge,[]))).
% 0.87/1.06 tff(2127,plain,
% 0.87/1.06 ($false),
% 0.87/1.06 inference(unit_resolution,[status(thm)],[2126, 2115, 2114, 2020, 2021, 2027, 2098, 2092, 2091, 2078])).
% 0.87/1.06 tff(2128,plain,(hskp27 | hskp10 | hskp15), inference(lemma,lemma(discharge,[]))).
% 0.87/1.06 tff(2129,plain,
% 0.87/1.06 (hskp27),
% 0.87/1.06 inference(unit_resolution,[status(thm)],[2128, 1163, 20])).
% 0.87/1.06 tff(2130,plain,
% 0.87/1.06 (c3_1(a232)),
% 0.87/1.06 inference(unit_resolution,[status(thm)],[247, 2129])).
% 0.87/1.06 tff(2131,plain,
% 0.87/1.06 (c0_1(a232)),
% 0.87/1.06 inference(unit_resolution,[status(thm)],[263, 2129])).
% 0.87/1.06 tff(2132,plain,
% 0.87/1.06 (c2_1(a232)),
% 0.87/1.06 inference(unit_resolution,[status(thm)],[255, 2129])).
% 0.87/1.06 tff(2133,plain,
% 0.87/1.06 (((~![U: $i] : (hskp28 | hskp15 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp28 | hskp15 | (~ndr1_0) | (~c2_1(a232)) | c1_1(a232) | (~c0_1(a232)))) <=> ((~![U: $i] : (hskp28 | hskp15 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp28 | hskp15 | (~ndr1_0) | (~c2_1(a232)) | c1_1(a232) | (~c0_1(a232)))),
% 0.87/1.06 inference(rewrite,[status(thm)],[])).
% 0.87/1.06 tff(2134,plain,
% 0.87/1.06 ((hskp28 | hskp15 | (~ndr1_0) | c1_1(a232) | (~c2_1(a232)) | (~c0_1(a232))) <=> (hskp28 | hskp15 | (~ndr1_0) | (~c2_1(a232)) | c1_1(a232) | (~c0_1(a232)))),
% 0.87/1.06 inference(rewrite,[status(thm)],[])).
% 0.87/1.06 tff(2135,plain,
% 0.87/1.06 (((~![U: $i] : (hskp28 | hskp15 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp28 | hskp15 | (~ndr1_0) | c1_1(a232) | (~c2_1(a232)) | (~c0_1(a232)))) <=> ((~![U: $i] : (hskp28 | hskp15 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp28 | hskp15 | (~ndr1_0) | (~c2_1(a232)) | c1_1(a232) | (~c0_1(a232))))),
% 0.87/1.06 inference(monotonicity,[status(thm)],[2134])).
% 0.87/1.06 tff(2136,plain,
% 0.87/1.06 (((~![U: $i] : (hskp28 | hskp15 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp28 | hskp15 | (~ndr1_0) | c1_1(a232) | (~c2_1(a232)) | (~c0_1(a232)))) <=> ((~![U: $i] : (hskp28 | hskp15 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp28 | hskp15 | (~ndr1_0) | (~c2_1(a232)) | c1_1(a232) | (~c0_1(a232)))),
% 0.87/1.06 inference(transitivity,[status(thm)],[2135, 2133])).
% 0.87/1.06 tff(2137,plain,
% 0.87/1.06 ((~![U: $i] : (hskp28 | hskp15 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp28 | hskp15 | (~ndr1_0) | c1_1(a232) | (~c2_1(a232)) | (~c0_1(a232)))),
% 0.87/1.06 inference(quant_inst,[status(thm)],[])).
% 0.87/1.06 tff(2138,plain,
% 0.87/1.06 ((~![U: $i] : (hskp28 | hskp15 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp28 | hskp15 | (~ndr1_0) | (~c2_1(a232)) | c1_1(a232) | (~c0_1(a232))),
% 0.87/1.06 inference(modus_ponens,[status(thm)],[2137, 2136])).
% 0.87/1.06 tff(2139,plain,
% 0.87/1.06 (hskp28 | c1_1(a232)),
% 0.87/1.06 inference(unit_resolution,[status(thm)],[2138, 122, 1163, 768, 767, 1182])).
% 0.87/1.06 tff(2140,plain,
% 0.87/1.06 (c1_1(a232)),
% 0.87/1.06 inference(unit_resolution,[status(thm)],[2139, 683])).
% 0.87/1.06 tff(2141,plain,
% 0.87/1.06 (~hskp14),
% 0.87/1.06 inference(unit_resolution,[status(thm)],[1194, 683, 1163])).
% 0.87/1.06 tff(2142,plain,
% 0.87/1.06 (hskp15 | hskp14 | c0_1(a213)),
% 0.87/1.06 inference(unit_resolution,[status(thm)],[1517, 122, 2021, 2027, 1134])).
% 0.87/1.06 tff(2143,plain,
% 0.87/1.06 (c0_1(a213)),
% 0.87/1.06 inference(unit_resolution,[status(thm)],[2142, 2141, 1163])).
% 0.87/1.06 tff(2144,plain,
% 0.87/1.06 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp20 | (~ndr1_0) | (~c1_1(a213)) | (~c3_1(a213)) | (~c0_1(a213)) | (~c2_1(a232)) | (~c1_1(a232)) | (~c0_1(a232)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | hskp20 | (~ndr1_0) | (~c1_1(a213)) | (~c3_1(a213)) | (~c0_1(a213)) | (~c2_1(a232)) | (~c1_1(a232)) | (~c0_1(a232)))),
% 0.87/1.06 inference(rewrite,[status(thm)],[])).
% 0.87/1.06 tff(2145,plain,
% 0.87/1.06 ((hskp20 | (~ndr1_0) | (~c1_1(a213)) | (~c0_1(a213)) | (~c3_1(a213)) | (~c1_1(a232)) | (~c2_1(a232)) | (~c0_1(a232))) <=> (hskp20 | (~ndr1_0) | (~c1_1(a213)) | (~c3_1(a213)) | (~c0_1(a213)) | (~c2_1(a232)) | (~c1_1(a232)) | (~c0_1(a232)))),
% 0.87/1.06 inference(rewrite,[status(thm)],[])).
% 0.87/1.06 tff(2146,plain,
% 0.87/1.06 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp20 | (~ndr1_0) | (~c1_1(a213)) | (~c0_1(a213)) | (~c3_1(a213)) | (~c1_1(a232)) | (~c2_1(a232)) | (~c0_1(a232)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp20 | (~ndr1_0) | (~c1_1(a213)) | (~c3_1(a213)) | (~c0_1(a213)) | (~c2_1(a232)) | (~c1_1(a232)) | (~c0_1(a232))))),
% 0.87/1.06 inference(monotonicity,[status(thm)],[2145])).
% 0.87/1.06 tff(2147,plain,
% 0.87/1.06 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp20 | (~ndr1_0) | (~c1_1(a213)) | (~c0_1(a213)) | (~c3_1(a213)) | (~c1_1(a232)) | (~c2_1(a232)) | (~c0_1(a232)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | hskp20 | (~ndr1_0) | (~c1_1(a213)) | (~c3_1(a213)) | (~c0_1(a213)) | (~c2_1(a232)) | (~c1_1(a232)) | (~c0_1(a232)))),
% 0.87/1.06 inference(transitivity,[status(thm)],[2146, 2144])).
% 0.87/1.06 tff(2148,plain,
% 0.87/1.06 ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp20 | (~ndr1_0) | (~c1_1(a213)) | (~c0_1(a213)) | (~c3_1(a213)) | (~c1_1(a232)) | (~c2_1(a232)) | (~c0_1(a232)))),
% 0.87/1.06 inference(quant_inst,[status(thm)],[])).
% 0.87/1.06 tff(2149,plain,
% 0.87/1.06 ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | hskp20 | (~ndr1_0) | (~c1_1(a213)) | (~c3_1(a213)) | (~c0_1(a213)) | (~c2_1(a232)) | (~c1_1(a232)) | (~c0_1(a232))),
% 0.87/1.06 inference(modus_ponens,[status(thm)],[2148, 2147])).
% 0.87/1.06 tff(2150,plain,
% 0.87/1.06 ($false),
% 0.87/1.06 inference(unit_resolution,[status(thm)],[2149, 122, 132, 768, 767, 2021, 2027, 1013, 2143, 2140])).
% 0.87/1.06 tff(2151,plain,(hskp28 | hskp20 | (~c0_1(a232)) | (~c2_1(a232)) | hskp15), inference(lemma,lemma(discharge,[]))).
% 0.87/1.06 tff(2152,plain,
% 0.87/1.06 (hskp28),
% 0.87/1.06 inference(unit_resolution,[status(thm)],[2151, 132, 768, 767, 1163])).
% 0.87/1.06 tff(2153,plain,
% 0.87/1.06 (c2_1(a246)),
% 0.87/1.06 inference(unit_resolution,[status(thm)],[699, 2152])).
% 0.87/1.06 tff(2154,plain,
% 0.87/1.06 (c1_1(a246)),
% 0.87/1.06 inference(unit_resolution,[status(thm)],[707, 2152])).
% 0.87/1.06 tff(2155,plain,
% 0.87/1.06 (c0_1(a246)),
% 0.87/1.06 inference(unit_resolution,[status(thm)],[715, 2152])).
% 0.87/1.06 tff(2156,plain,
% 0.87/1.06 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp20 | (~ndr1_0) | (~c1_1(a213)) | (~c3_1(a213)) | (~c0_1(a213)) | (~c0_1(a246)) | (~c1_1(a246)) | (~c2_1(a246)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | hskp20 | (~ndr1_0) | (~c1_1(a213)) | (~c3_1(a213)) | (~c0_1(a213)) | (~c0_1(a246)) | (~c1_1(a246)) | (~c2_1(a246)))),
% 0.87/1.06 inference(rewrite,[status(thm)],[])).
% 0.87/1.06 tff(2157,plain,
% 0.87/1.06 ((hskp20 | (~ndr1_0) | (~c1_1(a213)) | (~c0_1(a213)) | (~c3_1(a213)) | (~c1_1(a246)) | (~c2_1(a246)) | (~c0_1(a246))) <=> (hskp20 | (~ndr1_0) | (~c1_1(a213)) | (~c3_1(a213)) | (~c0_1(a213)) | (~c0_1(a246)) | (~c1_1(a246)) | (~c2_1(a246)))),
% 0.87/1.06 inference(rewrite,[status(thm)],[])).
% 0.87/1.06 tff(2158,plain,
% 0.87/1.06 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp20 | (~ndr1_0) | (~c1_1(a213)) | (~c0_1(a213)) | (~c3_1(a213)) | (~c1_1(a246)) | (~c2_1(a246)) | (~c0_1(a246)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp20 | (~ndr1_0) | (~c1_1(a213)) | (~c3_1(a213)) | (~c0_1(a213)) | (~c0_1(a246)) | (~c1_1(a246)) | (~c2_1(a246))))),
% 0.87/1.06 inference(monotonicity,[status(thm)],[2157])).
% 0.87/1.06 tff(2159,plain,
% 0.87/1.06 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp20 | (~ndr1_0) | (~c1_1(a213)) | (~c0_1(a213)) | (~c3_1(a213)) | (~c1_1(a246)) | (~c2_1(a246)) | (~c0_1(a246)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | hskp20 | (~ndr1_0) | (~c1_1(a213)) | (~c3_1(a213)) | (~c0_1(a213)) | (~c0_1(a246)) | (~c1_1(a246)) | (~c2_1(a246)))),
% 0.87/1.06 inference(transitivity,[status(thm)],[2158, 2156])).
% 0.87/1.06 tff(2160,plain,
% 0.87/1.06 ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp20 | (~ndr1_0) | (~c1_1(a213)) | (~c0_1(a213)) | (~c3_1(a213)) | (~c1_1(a246)) | (~c2_1(a246)) | (~c0_1(a246)))),
% 0.87/1.06 inference(quant_inst,[status(thm)],[])).
% 0.87/1.06 tff(2161,plain,
% 0.87/1.06 ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | hskp20 | (~ndr1_0) | (~c1_1(a213)) | (~c3_1(a213)) | (~c0_1(a213)) | (~c0_1(a246)) | (~c1_1(a246)) | (~c2_1(a246))),
% 0.87/1.06 inference(modus_ponens,[status(thm)],[2160, 2159])).
% 0.87/1.06 tff(2162,plain,
% 0.87/1.06 (~c0_1(a213)),
% 0.87/1.06 inference(unit_resolution,[status(thm)],[2161, 122, 132, 2155, 2154, 2153, 2021, 2027, 1013])).
% 0.87/1.06 tff(2163,plain,
% 0.87/1.06 (hskp20 | hskp13),
% 0.87/1.06 inference(unit_resolution,[status(thm)],[936, 122, 2021, 2027, 2020, 74])).
% 0.87/1.06 tff(2164,plain,
% 0.87/1.06 (hskp13),
% 0.87/1.06 inference(unit_resolution,[status(thm)],[2163, 132])).
% 0.87/1.06 tff(2165,plain,
% 0.87/1.06 (~c3_1(a236)),
% 0.87/1.06 inference(unit_resolution,[status(thm)],[752, 2164])).
% 0.87/1.06 tff(2166,plain,
% 0.87/1.06 (~c2_1(a236)),
% 0.87/1.06 inference(unit_resolution,[status(thm)],[758, 2164])).
% 0.87/1.06 tff(2167,plain,
% 0.87/1.06 (~c1_1(a236)),
% 0.87/1.06 inference(unit_resolution,[status(thm)],[764, 2164])).
% 0.87/1.06 tff(2168,plain,
% 0.87/1.06 (hskp17),
% 0.87/1.06 inference(unit_resolution,[status(thm)],[947, 122, 768, 767, 766, 2167, 2166, 2165, 453])).
% 0.87/1.06 tff(2169,plain,
% 0.87/1.06 (~c2_1(a243)),
% 0.87/1.06 inference(unit_resolution,[status(thm)],[501, 2168])).
% 0.87/1.06 tff(2170,plain,
% 0.87/1.06 (~c1_1(a243)),
% 0.87/1.06 inference(unit_resolution,[status(thm)],[530, 2168])).
% 0.87/1.06 tff(2171,plain,
% 0.87/1.06 (~c0_1(a243)),
% 0.87/1.06 inference(unit_resolution,[status(thm)],[507, 2168])).
% 0.87/1.06 tff(2172,plain,
% 0.87/1.06 ($false),
% 0.87/1.06 inference(unit_resolution,[status(thm)],[722, 122, 2155, 2154, 2153, 2021, 2027, 2171, 2170, 2169, 627, 2162])).
% 0.87/1.06 tff(2173,plain,(hskp20 | (~c0_1(a232)) | (~c2_1(a232)) | hskp15 | (~c3_1(a232))), inference(lemma,lemma(discharge,[]))).
% 0.87/1.06 tff(2174,plain,
% 0.87/1.06 (hskp20),
% 0.87/1.06 inference(unit_resolution,[status(thm)],[2173, 2132, 1163, 2131, 2130])).
% 0.87/1.06 tff(2175,plain,
% 0.87/1.06 (~c3_1(a259)),
% 0.87/1.06 inference(unit_resolution,[status(thm)],[354, 2174])).
% 0.87/1.06 tff(2176,plain,
% 0.87/1.06 (c1_1(a259)),
% 0.87/1.06 inference(unit_resolution,[status(thm)],[362, 2174])).
% 0.87/1.06 tff(2177,plain,
% 0.87/1.06 (c0_1(a259)),
% 0.87/1.06 inference(unit_resolution,[status(thm)],[370, 2174])).
% 0.87/1.06 tff(2178,plain,
% 0.87/1.06 (hskp3),
% 0.87/1.06 inference(unit_resolution,[status(thm)],[2089, 122, 2177, 2176, 2021, 2027, 2175, 2048, 2038])).
% 0.87/1.06 tff(2179,plain,
% 0.87/1.06 (~c0_1(a216)),
% 0.87/1.06 inference(unit_resolution,[status(thm)],[318, 2178])).
% 0.87/1.06 tff(2180,plain,
% 0.87/1.06 (c3_1(a216)),
% 0.87/1.06 inference(unit_resolution,[status(thm)],[328, 2178])).
% 0.87/1.06 tff(2181,plain,
% 0.87/1.06 (c1_1(a216)),
% 0.87/1.06 inference(unit_resolution,[status(thm)],[890, 122, 2180, 2021, 2027, 2179, 583, 2038])).
% 0.87/1.06 tff(2182,plain,
% 0.87/1.06 (((~![U: $i] : (hskp15 | hskp14 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp15 | hskp14 | c0_1(a216) | (~ndr1_0) | (~c1_1(a216)) | (~c3_1(a216)))) <=> ((~![U: $i] : (hskp15 | hskp14 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))) | hskp15 | hskp14 | c0_1(a216) | (~ndr1_0) | (~c1_1(a216)) | (~c3_1(a216)))),
% 0.87/1.06 inference(rewrite,[status(thm)],[])).
% 0.87/1.06 tff(2183,plain,
% 0.87/1.06 ((hskp15 | hskp14 | (~ndr1_0) | c0_1(a216) | (~c1_1(a216)) | (~c3_1(a216))) <=> (hskp15 | hskp14 | c0_1(a216) | (~ndr1_0) | (~c1_1(a216)) | (~c3_1(a216)))),
% 0.87/1.06 inference(rewrite,[status(thm)],[])).
% 0.87/1.06 tff(2184,plain,
% 0.87/1.06 (((~![U: $i] : (hskp15 | hskp14 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp15 | hskp14 | (~ndr1_0) | c0_1(a216) | (~c1_1(a216)) | (~c3_1(a216)))) <=> ((~![U: $i] : (hskp15 | hskp14 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp15 | hskp14 | c0_1(a216) | (~ndr1_0) | (~c1_1(a216)) | (~c3_1(a216))))),
% 0.87/1.06 inference(monotonicity,[status(thm)],[2183])).
% 0.87/1.06 tff(2185,plain,
% 0.87/1.06 (((~![U: $i] : (hskp15 | hskp14 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp15 | hskp14 | (~ndr1_0) | c0_1(a216) | (~c1_1(a216)) | (~c3_1(a216)))) <=> ((~![U: $i] : (hskp15 | hskp14 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))) | hskp15 | hskp14 | c0_1(a216) | (~ndr1_0) | (~c1_1(a216)) | (~c3_1(a216)))),
% 0.87/1.06 inference(transitivity,[status(thm)],[2184, 2182])).
% 0.87/1.06 tff(2186,plain,
% 0.87/1.06 ((~![U: $i] : (hskp15 | hskp14 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp15 | hskp14 | (~ndr1_0) | c0_1(a216) | (~c1_1(a216)) | (~c3_1(a216)))),
% 0.87/1.06 inference(quant_inst,[status(thm)],[])).
% 0.87/1.06 tff(2187,plain,
% 0.87/1.06 ((~![U: $i] : (hskp15 | hskp14 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))) | hskp15 | hskp14 | c0_1(a216) | (~ndr1_0) | (~c1_1(a216)) | (~c3_1(a216))),
% 0.87/1.06 inference(modus_ponens,[status(thm)],[2186, 2185])).
% 0.87/1.06 tff(2188,plain,
% 0.87/1.06 (hskp14 | (~c1_1(a216))),
% 0.87/1.06 inference(unit_resolution,[status(thm)],[2187, 122, 1163, 2180, 2179, 1134])).
% 0.87/1.06 tff(2189,plain,
% 0.87/1.06 (hskp14),
% 0.87/1.06 inference(unit_resolution,[status(thm)],[2188, 2181])).
% 0.87/1.06 tff(2190,plain,
% 0.87/1.06 (c0_1(a237)),
% 0.87/1.06 inference(unit_resolution,[status(thm)],[1157, 2189])).
% 0.87/1.06 tff(2191,plain,
% 0.87/1.06 (~c1_1(a237)),
% 0.87/1.06 inference(unit_resolution,[status(thm)],[1169, 2189])).
% 0.87/1.06 tff(2192,assumption,(~c2_1(a229)), introduced(assumption)).
% 0.87/1.06 tff(2193,plain,
% 0.87/1.06 (hskp20),
% 0.87/1.06 inference(unit_resolution,[status(thm)],[2173, 2131, 2132, 1163, 2130])).
% 0.87/1.06 tff(2194,plain,
% 0.87/1.06 (~c3_1(a259)),
% 0.87/1.06 inference(unit_resolution,[status(thm)],[354, 2193])).
% 0.87/1.06 tff(2195,plain,
% 0.87/1.06 (c1_1(a259)),
% 0.87/1.06 inference(unit_resolution,[status(thm)],[362, 2193])).
% 0.87/1.06 tff(2196,plain,
% 0.87/1.06 (c0_1(a259)),
% 0.87/1.06 inference(unit_resolution,[status(thm)],[370, 2193])).
% 0.87/1.06 tff(2197,plain,
% 0.87/1.06 (hskp28 | c1_1(a232)),
% 0.87/1.06 inference(unit_resolution,[status(thm)],[2138, 122, 1163, 2131, 2132, 1182])).
% 0.87/1.06 tff(2198,plain,
% 0.87/1.06 (c1_1(a232)),
% 0.87/1.06 inference(unit_resolution,[status(thm)],[2197, 683])).
% 0.87/1.06 tff(2199,plain,
% 0.87/1.06 (hskp3 | (~c0_1(a213))),
% 0.87/1.06 inference(unit_resolution,[status(thm)],[2089, 122, 2196, 2195, 2021, 2027, 2194, 2048])).
% 0.87/1.06 tff(2200,plain,
% 0.87/1.06 (hskp3),
% 0.87/1.06 inference(unit_resolution,[status(thm)],[2199, 2143])).
% 0.87/1.06 tff(2201,plain,
% 0.87/1.06 (~c0_1(a216)),
% 0.87/1.06 inference(unit_resolution,[status(thm)],[318, 2200])).
% 0.87/1.06 tff(2202,plain,
% 0.87/1.06 (c3_1(a216)),
% 0.87/1.06 inference(unit_resolution,[status(thm)],[328, 2200])).
% 0.87/1.06 tff(2203,plain,
% 0.87/1.06 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (c0_1(a216) | (~ndr1_0) | c1_1(a216) | (~c3_1(a216)) | (~c1_1(a232)) | (~c3_1(a232)) | (~c0_1(a232)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | c0_1(a216) | (~ndr1_0) | c1_1(a216) | (~c3_1(a216)) | (~c1_1(a232)) | (~c3_1(a232)) | (~c0_1(a232)))),
% 0.87/1.06 inference(rewrite,[status(thm)],[])).
% 0.87/1.06 tff(2204,plain,
% 0.87/1.06 (((~ndr1_0) | (~c1_1(a232)) | (~c0_1(a232)) | (~c3_1(a232)) | c0_1(a216) | c1_1(a216) | (~c3_1(a216))) <=> (c0_1(a216) | (~ndr1_0) | c1_1(a216) | (~c3_1(a216)) | (~c1_1(a232)) | (~c3_1(a232)) | (~c0_1(a232)))),
% 0.87/1.06 inference(rewrite,[status(thm)],[])).
% 0.87/1.06 tff(2205,plain,
% 0.87/1.06 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | ((~ndr1_0) | (~c1_1(a232)) | (~c0_1(a232)) | (~c3_1(a232)) | c0_1(a216) | c1_1(a216) | (~c3_1(a216)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (c0_1(a216) | (~ndr1_0) | c1_1(a216) | (~c3_1(a216)) | (~c1_1(a232)) | (~c3_1(a232)) | (~c0_1(a232))))),
% 0.87/1.06 inference(monotonicity,[status(thm)],[2204])).
% 0.87/1.06 tff(2206,plain,
% 0.87/1.06 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | ((~ndr1_0) | (~c1_1(a232)) | (~c0_1(a232)) | (~c3_1(a232)) | c0_1(a216) | c1_1(a216) | (~c3_1(a216)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | c0_1(a216) | (~ndr1_0) | c1_1(a216) | (~c3_1(a216)) | (~c1_1(a232)) | (~c3_1(a232)) | (~c0_1(a232)))),
% 0.87/1.06 inference(transitivity,[status(thm)],[2205, 2203])).
% 0.87/1.06 tff(2207,plain,
% 0.87/1.06 ((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | ((~ndr1_0) | (~c1_1(a232)) | (~c0_1(a232)) | (~c3_1(a232)) | c0_1(a216) | c1_1(a216) | (~c3_1(a216)))),
% 0.87/1.06 inference(quant_inst,[status(thm)],[])).
% 0.87/1.06 tff(2208,plain,
% 0.87/1.06 ((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | c0_1(a216) | (~ndr1_0) | c1_1(a216) | (~c3_1(a216)) | (~c1_1(a232)) | (~c3_1(a232)) | (~c0_1(a232))),
% 0.87/1.06 inference(modus_ponens,[status(thm)],[2207, 2206])).
% 0.87/1.06 tff(2209,plain,
% 0.87/1.06 (c1_1(a216)),
% 0.87/1.06 inference(unit_resolution,[status(thm)],[2208, 122, 2131, 2130, 2202, 2201, 583, 2198])).
% 0.87/1.06 tff(2210,plain,
% 0.87/1.06 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | (c3_1(a229) | c3_1(a259) | c0_1(a229) | (~ndr1_0) | (~c2_1(a232)) | (~c1_1(a232)) | (~c0_1(a232)) | (~c1_1(a229)) | (~c0_1(a259)) | (~c1_1(a259)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c3_1(a229) | c3_1(a259) | c0_1(a229) | (~ndr1_0) | (~c2_1(a232)) | (~c1_1(a232)) | (~c0_1(a232)) | (~c1_1(a229)) | (~c0_1(a259)) | (~c1_1(a259)))),
% 0.87/1.07 inference(rewrite,[status(thm)],[])).
% 0.87/1.07 tff(2211,plain,
% 0.87/1.07 (((~ndr1_0) | (~c2_1(a232)) | (~c1_1(a232)) | (~c0_1(a232)) | c3_1(a259) | (~c1_1(a259)) | (~c0_1(a259)) | c0_1(a229) | c3_1(a229) | (~c1_1(a229))) <=> (c3_1(a229) | c3_1(a259) | c0_1(a229) | (~ndr1_0) | (~c2_1(a232)) | (~c1_1(a232)) | (~c0_1(a232)) | (~c1_1(a229)) | (~c0_1(a259)) | (~c1_1(a259)))),
% 0.87/1.07 inference(rewrite,[status(thm)],[])).
% 0.87/1.07 tff(2212,plain,
% 0.87/1.07 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a232)) | (~c1_1(a232)) | (~c0_1(a232)) | c3_1(a259) | (~c1_1(a259)) | (~c0_1(a259)) | c0_1(a229) | c3_1(a229) | (~c1_1(a229)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | (c3_1(a229) | c3_1(a259) | c0_1(a229) | (~ndr1_0) | (~c2_1(a232)) | (~c1_1(a232)) | (~c0_1(a232)) | (~c1_1(a229)) | (~c0_1(a259)) | (~c1_1(a259))))),
% 0.87/1.07 inference(monotonicity,[status(thm)],[2211])).
% 0.87/1.07 tff(2213,plain,
% 0.87/1.07 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a232)) | (~c1_1(a232)) | (~c0_1(a232)) | c3_1(a259) | (~c1_1(a259)) | (~c0_1(a259)) | c0_1(a229) | c3_1(a229) | (~c1_1(a229)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c3_1(a229) | c3_1(a259) | c0_1(a229) | (~ndr1_0) | (~c2_1(a232)) | (~c1_1(a232)) | (~c0_1(a232)) | (~c1_1(a229)) | (~c0_1(a259)) | (~c1_1(a259)))),
% 0.87/1.07 inference(transitivity,[status(thm)],[2212, 2210])).
% 0.87/1.07 tff(2214,plain,
% 0.87/1.07 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a232)) | (~c1_1(a232)) | (~c0_1(a232)) | c3_1(a259) | (~c1_1(a259)) | (~c0_1(a259)) | c0_1(a229) | c3_1(a229) | (~c1_1(a229)))),
% 0.87/1.07 inference(quant_inst,[status(thm)],[])).
% 0.87/1.07 tff(2215,plain,
% 0.87/1.07 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c3_1(a229) | c3_1(a259) | c0_1(a229) | (~ndr1_0) | (~c2_1(a232)) | (~c1_1(a232)) | (~c0_1(a232)) | (~c1_1(a229)) | (~c0_1(a259)) | (~c1_1(a259))),
% 0.87/1.07 inference(modus_ponens,[status(thm)],[2214, 2213])).
% 0.87/1.07 tff(2216,plain,
% 0.87/1.07 ((~c1_1(a232)) | (~c1_1(a229))),
% 0.87/1.07 inference(unit_resolution,[status(thm)],[2215, 122, 2131, 2132, 2196, 2195, 12, 2194, 11, 993])).
% 0.87/1.07 tff(2217,plain,
% 0.87/1.07 (~c1_1(a229)),
% 0.87/1.07 inference(unit_resolution,[status(thm)],[2216, 2198])).
% 0.87/1.07 tff(2218,plain,
% 0.87/1.07 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c2_1(a229) | c0_1(a229) | c0_1(a216) | (~ndr1_0) | (~c1_1(a216)) | (~c3_1(a216)) | (~c2_1(a232)) | (~c1_1(a232)) | (~c0_1(a232)) | c1_1(a229))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c2_1(a229) | c0_1(a229) | c0_1(a216) | (~ndr1_0) | (~c1_1(a216)) | (~c3_1(a216)) | (~c2_1(a232)) | (~c1_1(a232)) | (~c0_1(a232)) | c1_1(a229))),
% 0.87/1.07 inference(rewrite,[status(thm)],[])).
% 0.87/1.07 tff(2219,plain,
% 0.87/1.07 (((~ndr1_0) | (~c2_1(a232)) | (~c1_1(a232)) | (~c0_1(a232)) | c0_1(a216) | (~c3_1(a216)) | (~c1_1(a216)) | c1_1(a229) | c0_1(a229) | c2_1(a229)) <=> (c2_1(a229) | c0_1(a229) | c0_1(a216) | (~ndr1_0) | (~c1_1(a216)) | (~c3_1(a216)) | (~c2_1(a232)) | (~c1_1(a232)) | (~c0_1(a232)) | c1_1(a229))),
% 0.87/1.07 inference(rewrite,[status(thm)],[])).
% 0.87/1.07 tff(2220,plain,
% 0.87/1.07 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | (~c2_1(a232)) | (~c1_1(a232)) | (~c0_1(a232)) | c0_1(a216) | (~c3_1(a216)) | (~c1_1(a216)) | c1_1(a229) | c0_1(a229) | c2_1(a229))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c2_1(a229) | c0_1(a229) | c0_1(a216) | (~ndr1_0) | (~c1_1(a216)) | (~c3_1(a216)) | (~c2_1(a232)) | (~c1_1(a232)) | (~c0_1(a232)) | c1_1(a229)))),
% 0.87/1.07 inference(monotonicity,[status(thm)],[2219])).
% 0.87/1.07 tff(2221,plain,
% 0.87/1.07 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | (~c2_1(a232)) | (~c1_1(a232)) | (~c0_1(a232)) | c0_1(a216) | (~c3_1(a216)) | (~c1_1(a216)) | c1_1(a229) | c0_1(a229) | c2_1(a229))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c2_1(a229) | c0_1(a229) | c0_1(a216) | (~ndr1_0) | (~c1_1(a216)) | (~c3_1(a216)) | (~c2_1(a232)) | (~c1_1(a232)) | (~c0_1(a232)) | c1_1(a229))),
% 0.87/1.07 inference(transitivity,[status(thm)],[2220, 2218])).
% 0.87/1.07 tff(2222,plain,
% 0.87/1.07 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | (~c2_1(a232)) | (~c1_1(a232)) | (~c0_1(a232)) | c0_1(a216) | (~c3_1(a216)) | (~c1_1(a216)) | c1_1(a229) | c0_1(a229) | c2_1(a229))),
% 0.87/1.07 inference(quant_inst,[status(thm)],[])).
% 0.87/1.07 tff(2223,plain,
% 0.87/1.07 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c2_1(a229) | c0_1(a229) | c0_1(a216) | (~ndr1_0) | (~c1_1(a216)) | (~c3_1(a216)) | (~c2_1(a232)) | (~c1_1(a232)) | (~c0_1(a232)) | c1_1(a229)),
% 0.87/1.07 inference(modus_ponens,[status(thm)],[2222, 2221])).
% 0.87/1.07 tff(2224,plain,
% 0.87/1.07 ($false),
% 0.87/1.07 inference(unit_resolution,[status(thm)],[2223, 122, 2131, 2132, 2192, 2202, 11, 2201, 627, 2198, 2217, 2209])).
% 0.87/1.07 tff(2225,plain,(hskp28 | c2_1(a229) | c0_1(a229) | c3_1(a229) | hskp15), inference(lemma,lemma(discharge,[]))).
% 0.87/1.07 tff(2226,plain,
% 0.87/1.07 (hskp28),
% 0.87/1.07 inference(unit_resolution,[status(thm)],[2225, 1163, 11, 12, 2192])).
% 0.87/1.07 tff(2227,plain,
% 0.87/1.07 (c2_1(a246)),
% 0.87/1.07 inference(unit_resolution,[status(thm)],[699, 2226])).
% 0.87/1.07 tff(2228,plain,
% 0.87/1.07 (c1_1(a246)),
% 0.87/1.07 inference(unit_resolution,[status(thm)],[707, 2226])).
% 0.87/1.07 tff(2229,plain,
% 0.87/1.07 (c0_1(a246)),
% 0.87/1.07 inference(unit_resolution,[status(thm)],[715, 2226])).
% 0.87/1.07 tff(2230,plain,
% 0.87/1.07 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | (c3_1(a229) | c3_1(a259) | c0_1(a229) | (~ndr1_0) | (~c0_1(a246)) | (~c1_1(a246)) | (~c2_1(a246)) | (~c1_1(a229)) | (~c0_1(a259)) | (~c1_1(a259)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c3_1(a229) | c3_1(a259) | c0_1(a229) | (~ndr1_0) | (~c0_1(a246)) | (~c1_1(a246)) | (~c2_1(a246)) | (~c1_1(a229)) | (~c0_1(a259)) | (~c1_1(a259)))),
% 0.87/1.07 inference(rewrite,[status(thm)],[])).
% 0.87/1.07 tff(2231,plain,
% 0.87/1.07 (((~ndr1_0) | (~c2_1(a246)) | (~c1_1(a246)) | (~c0_1(a246)) | c3_1(a259) | (~c1_1(a259)) | (~c0_1(a259)) | c0_1(a229) | c3_1(a229) | (~c1_1(a229))) <=> (c3_1(a229) | c3_1(a259) | c0_1(a229) | (~ndr1_0) | (~c0_1(a246)) | (~c1_1(a246)) | (~c2_1(a246)) | (~c1_1(a229)) | (~c0_1(a259)) | (~c1_1(a259)))),
% 0.87/1.07 inference(rewrite,[status(thm)],[])).
% 0.87/1.07 tff(2232,plain,
% 0.87/1.07 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a246)) | (~c1_1(a246)) | (~c0_1(a246)) | c3_1(a259) | (~c1_1(a259)) | (~c0_1(a259)) | c0_1(a229) | c3_1(a229) | (~c1_1(a229)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | (c3_1(a229) | c3_1(a259) | c0_1(a229) | (~ndr1_0) | (~c0_1(a246)) | (~c1_1(a246)) | (~c2_1(a246)) | (~c1_1(a229)) | (~c0_1(a259)) | (~c1_1(a259))))),
% 0.87/1.07 inference(monotonicity,[status(thm)],[2231])).
% 0.87/1.07 tff(2233,plain,
% 0.87/1.07 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a246)) | (~c1_1(a246)) | (~c0_1(a246)) | c3_1(a259) | (~c1_1(a259)) | (~c0_1(a259)) | c0_1(a229) | c3_1(a229) | (~c1_1(a229)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c3_1(a229) | c3_1(a259) | c0_1(a229) | (~ndr1_0) | (~c0_1(a246)) | (~c1_1(a246)) | (~c2_1(a246)) | (~c1_1(a229)) | (~c0_1(a259)) | (~c1_1(a259)))),
% 0.87/1.07 inference(transitivity,[status(thm)],[2232, 2230])).
% 0.87/1.07 tff(2234,plain,
% 0.87/1.07 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a246)) | (~c1_1(a246)) | (~c0_1(a246)) | c3_1(a259) | (~c1_1(a259)) | (~c0_1(a259)) | c0_1(a229) | c3_1(a229) | (~c1_1(a229)))),
% 0.87/1.07 inference(quant_inst,[status(thm)],[])).
% 0.87/1.07 tff(2235,plain,
% 0.87/1.07 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c3_1(a229) | c3_1(a259) | c0_1(a229) | (~ndr1_0) | (~c0_1(a246)) | (~c1_1(a246)) | (~c2_1(a246)) | (~c1_1(a229)) | (~c0_1(a259)) | (~c1_1(a259))),
% 0.87/1.07 inference(modus_ponens,[status(thm)],[2234, 2233])).
% 0.87/1.07 tff(2236,plain,
% 0.87/1.07 (~c1_1(a229)),
% 0.87/1.07 inference(unit_resolution,[status(thm)],[2235, 122, 2229, 2228, 2227, 2196, 2195, 12, 2194, 11, 993])).
% 0.87/1.07 tff(2237,plain,
% 0.87/1.07 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp17 | c2_1(a229) | c3_1(a229) | (~ndr1_0) | (~c2_1(a232)) | (~c3_1(a232)) | (~c0_1(a232)) | c1_1(a229))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp17 | c2_1(a229) | c3_1(a229) | (~ndr1_0) | (~c2_1(a232)) | (~c3_1(a232)) | (~c0_1(a232)) | c1_1(a229))),
% 0.87/1.07 inference(rewrite,[status(thm)],[])).
% 0.87/1.07 tff(2238,plain,
% 0.87/1.07 ((hskp17 | (~ndr1_0) | (~c2_1(a232)) | (~c0_1(a232)) | (~c3_1(a232)) | c3_1(a229) | c2_1(a229) | c1_1(a229)) <=> (hskp17 | c2_1(a229) | c3_1(a229) | (~ndr1_0) | (~c2_1(a232)) | (~c3_1(a232)) | (~c0_1(a232)) | c1_1(a229))),
% 0.87/1.07 inference(rewrite,[status(thm)],[])).
% 0.87/1.07 tff(2239,plain,
% 0.87/1.07 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp17 | (~ndr1_0) | (~c2_1(a232)) | (~c0_1(a232)) | (~c3_1(a232)) | c3_1(a229) | c2_1(a229) | c1_1(a229))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp17 | c2_1(a229) | c3_1(a229) | (~ndr1_0) | (~c2_1(a232)) | (~c3_1(a232)) | (~c0_1(a232)) | c1_1(a229)))),
% 0.87/1.07 inference(monotonicity,[status(thm)],[2238])).
% 0.87/1.07 tff(2240,plain,
% 0.87/1.07 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp17 | (~ndr1_0) | (~c2_1(a232)) | (~c0_1(a232)) | (~c3_1(a232)) | c3_1(a229) | c2_1(a229) | c1_1(a229))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp17 | c2_1(a229) | c3_1(a229) | (~ndr1_0) | (~c2_1(a232)) | (~c3_1(a232)) | (~c0_1(a232)) | c1_1(a229))),
% 0.87/1.07 inference(transitivity,[status(thm)],[2239, 2237])).
% 0.87/1.07 tff(2241,plain,
% 0.87/1.07 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp17 | (~ndr1_0) | (~c2_1(a232)) | (~c0_1(a232)) | (~c3_1(a232)) | c3_1(a229) | c2_1(a229) | c1_1(a229))),
% 0.87/1.07 inference(quant_inst,[status(thm)],[])).
% 0.87/1.07 tff(2242,plain,
% 0.87/1.07 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp17 | c2_1(a229) | c3_1(a229) | (~ndr1_0) | (~c2_1(a232)) | (~c3_1(a232)) | (~c0_1(a232)) | c1_1(a229)),
% 0.87/1.07 inference(modus_ponens,[status(thm)],[2241, 2240])).
% 0.87/1.07 tff(2243,plain,
% 0.87/1.07 (hskp17 | c1_1(a229)),
% 0.87/1.07 inference(unit_resolution,[status(thm)],[2242, 122, 2131, 2132, 2130, 2192, 12, 453])).
% 0.87/1.07 tff(2244,plain,
% 0.87/1.07 (hskp17),
% 0.87/1.07 inference(unit_resolution,[status(thm)],[2243, 2236])).
% 0.87/1.07 tff(2245,plain,
% 0.87/1.07 (~c2_1(a243)),
% 0.87/1.07 inference(unit_resolution,[status(thm)],[501, 2244])).
% 0.87/1.07 tff(2246,plain,
% 0.87/1.07 (~c1_1(a243)),
% 0.87/1.07 inference(unit_resolution,[status(thm)],[530, 2244])).
% 0.87/1.07 tff(2247,plain,
% 0.87/1.07 (~c0_1(a243)),
% 0.87/1.07 inference(unit_resolution,[status(thm)],[507, 2244])).
% 0.87/1.07 tff(2248,plain,
% 0.87/1.07 ($false),
% 0.87/1.07 inference(unit_resolution,[status(thm)],[722, 122, 1679, 1678, 1694, 2021, 2027, 1575, 1574, 1573, 627, 22])).
% 0.87/1.07 tff(2249,plain,(c0_1(a213) | (~c0_1(a246)) | (~c1_1(a246)) | (~c2_1(a246)) | c0_1(a243) | c1_1(a243) | c2_1(a243)), inference(lemma,lemma(discharge,[]))).
% 0.87/1.07 tff(2250,plain,
% 0.87/1.07 (c0_1(a213)),
% 0.87/1.07 inference(unit_resolution,[status(thm)],[2249, 2229, 2228, 2227, 2247, 2246, 2245])).
% 0.87/1.07 tff(2251,plain,
% 0.87/1.07 (^[V: $i, U: $i] : refl((hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V)) <=> (hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V)))),
% 0.87/1.07 inference(bind,[status(th)],[])).
% 0.87/1.07 tff(2252,plain,
% 0.87/1.07 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))),
% 0.87/1.07 inference(quant_intro,[status(thm)],[2251])).
% 0.87/1.07 tff(2253,plain,
% 0.87/1.07 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))),
% 0.87/1.07 inference(rewrite,[status(thm)],[])).
% 0.87/1.07 tff(2254,plain,
% 0.87/1.07 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) <=> ((~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c1_1(U)) | (~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)))), rewrite((((~c1_1(U)) | (~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U))) | c0_1(V)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U))) | c0_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp7) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V)) | hskp7))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V)) | hskp7) <=> (hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp7) <=> (hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))))),
% 0.87/1.07 inference(bind,[status(th)],[])).
% 0.87/1.07 tff(2255,plain,
% 0.87/1.07 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp7) <=> ![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))),
% 0.87/1.07 inference(quant_intro,[status(thm)],[2254])).
% 0.87/1.07 tff(2256,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause151')).
% 0.87/1.07 tff(2257,plain,
% 0.87/1.07 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))),
% 0.87/1.07 inference(modus_ponens,[status(thm)],[2256, 2255])).
% 0.87/1.07 tff(2258,plain,
% 0.87/1.07 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))),
% 0.87/1.07 inference(modus_ponens,[status(thm)],[2257, 2253])).
% 0.87/1.07 tff(2259,plain,(
% 0.87/1.07 ![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))),
% 0.87/1.07 inference(skolemize,[status(sab)],[2258])).
% 0.87/1.07 tff(2260,plain,
% 0.87/1.07 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))),
% 0.87/1.07 inference(modus_ponens,[status(thm)],[2259, 2252])).
% 0.87/1.07 tff(2261,plain,
% 0.87/1.07 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp7 | c2_1(a229) | c3_1(a229) | c0_1(a229) | (~ndr1_0) | (~c1_1(a213)) | (~c3_1(a213)) | (~c0_1(a213)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp7 | c2_1(a229) | c3_1(a229) | c0_1(a229) | (~ndr1_0) | (~c1_1(a213)) | (~c3_1(a213)) | (~c0_1(a213)))),
% 0.87/1.07 inference(rewrite,[status(thm)],[])).
% 0.87/1.07 tff(2262,plain,
% 0.87/1.07 ((hskp7 | (~ndr1_0) | (~c1_1(a213)) | (~c0_1(a213)) | (~c3_1(a213)) | c3_1(a229) | c2_1(a229) | c0_1(a229)) <=> (hskp7 | c2_1(a229) | c3_1(a229) | c0_1(a229) | (~ndr1_0) | (~c1_1(a213)) | (~c3_1(a213)) | (~c0_1(a213)))),
% 0.87/1.07 inference(rewrite,[status(thm)],[])).
% 0.87/1.07 tff(2263,plain,
% 0.87/1.07 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp7 | (~ndr1_0) | (~c1_1(a213)) | (~c0_1(a213)) | (~c3_1(a213)) | c3_1(a229) | c2_1(a229) | c0_1(a229))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp7 | c2_1(a229) | c3_1(a229) | c0_1(a229) | (~ndr1_0) | (~c1_1(a213)) | (~c3_1(a213)) | (~c0_1(a213))))),
% 0.87/1.07 inference(monotonicity,[status(thm)],[2262])).
% 0.87/1.07 tff(2264,plain,
% 0.87/1.07 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp7 | (~ndr1_0) | (~c1_1(a213)) | (~c0_1(a213)) | (~c3_1(a213)) | c3_1(a229) | c2_1(a229) | c0_1(a229))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp7 | c2_1(a229) | c3_1(a229) | c0_1(a229) | (~ndr1_0) | (~c1_1(a213)) | (~c3_1(a213)) | (~c0_1(a213)))),
% 0.87/1.07 inference(transitivity,[status(thm)],[2263, 2261])).
% 0.87/1.07 tff(2265,plain,
% 0.87/1.07 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp7 | (~ndr1_0) | (~c1_1(a213)) | (~c0_1(a213)) | (~c3_1(a213)) | c3_1(a229) | c2_1(a229) | c0_1(a229))),
% 0.87/1.07 inference(quant_inst,[status(thm)],[])).
% 0.87/1.07 tff(2266,plain,
% 0.87/1.07 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp7 | c2_1(a229) | c3_1(a229) | c0_1(a229) | (~ndr1_0) | (~c1_1(a213)) | (~c3_1(a213)) | (~c0_1(a213))),
% 0.87/1.07 inference(modus_ponens,[status(thm)],[2265, 2264])).
% 0.87/1.07 tff(2267,plain,
% 0.87/1.07 (hskp7 | c2_1(a229) | (~c0_1(a213))),
% 0.87/1.07 inference(unit_resolution,[status(thm)],[2266, 122, 12, 2021, 2027, 11, 2260])).
% 0.87/1.07 tff(2268,plain,
% 0.87/1.07 (hskp7),
% 0.87/1.07 inference(unit_resolution,[status(thm)],[2267, 2250, 2192])).
% 0.87/1.07 tff(2269,plain,
% 0.87/1.07 (c0_1(a224)),
% 0.87/1.07 inference(unit_resolution,[status(thm)],[2077, 2268])).
% 0.87/1.07 tff(2270,plain,
% 0.87/1.07 (hskp3),
% 0.87/1.07 inference(unit_resolution,[status(thm)],[2199, 2250])).
% 0.87/1.07 tff(2271,plain,
% 0.87/1.07 (~c2_1(a216)),
% 0.87/1.07 inference(unit_resolution,[status(thm)],[312, 2270])).
% 0.87/1.07 tff(2272,plain,
% 0.87/1.07 (~c0_1(a216)),
% 0.87/1.07 inference(unit_resolution,[status(thm)],[318, 2270])).
% 0.87/1.07 tff(2273,plain,
% 0.87/1.07 (~c1_1(a224)),
% 0.87/1.07 inference(unit_resolution,[status(thm)],[2097, 2268])).
% 0.87/1.07 tff(2274,plain,
% 0.87/1.07 (c3_1(a216)),
% 0.87/1.07 inference(unit_resolution,[status(thm)],[328, 2270])).
% 0.87/1.07 tff(2275,plain,
% 0.87/1.07 (c2_1(a224)),
% 0.87/1.07 inference(unit_resolution,[status(thm)],[2126, 2274, 2020, 2021, 2027, 2273, 2272, 2271, 2269])).
% 0.87/1.07 tff(2276,plain,
% 0.87/1.07 (c3_1(a224)),
% 0.87/1.07 inference(unit_resolution,[status(thm)],[2106, 2268])).
% 0.87/1.07 tff(2277,plain,
% 0.87/1.07 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | (c2_1(a225) | c3_1(a225) | c1_1(a224) | c0_1(a216) | c2_1(a216) | (~ndr1_0) | (~c3_1(a216)) | (~c3_1(a224)) | (~c2_1(a224)) | (~c0_1(a225)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c2_1(a225) | c3_1(a225) | c1_1(a224) | c0_1(a216) | c2_1(a216) | (~ndr1_0) | (~c3_1(a216)) | (~c3_1(a224)) | (~c2_1(a224)) | (~c0_1(a225)))),
% 0.87/1.07 inference(rewrite,[status(thm)],[])).
% 0.87/1.07 tff(2278,plain,
% 0.87/1.07 (((~ndr1_0) | c3_1(a225) | c2_1(a225) | (~c0_1(a225)) | c1_1(a224) | (~c3_1(a224)) | (~c2_1(a224)) | c0_1(a216) | c2_1(a216) | (~c3_1(a216))) <=> (c2_1(a225) | c3_1(a225) | c1_1(a224) | c0_1(a216) | c2_1(a216) | (~ndr1_0) | (~c3_1(a216)) | (~c3_1(a224)) | (~c2_1(a224)) | (~c0_1(a225)))),
% 0.87/1.07 inference(rewrite,[status(thm)],[])).
% 0.87/1.07 tff(2279,plain,
% 0.87/1.07 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a225) | c2_1(a225) | (~c0_1(a225)) | c1_1(a224) | (~c3_1(a224)) | (~c2_1(a224)) | c0_1(a216) | c2_1(a216) | (~c3_1(a216)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | (c2_1(a225) | c3_1(a225) | c1_1(a224) | c0_1(a216) | c2_1(a216) | (~ndr1_0) | (~c3_1(a216)) | (~c3_1(a224)) | (~c2_1(a224)) | (~c0_1(a225))))),
% 0.87/1.07 inference(monotonicity,[status(thm)],[2278])).
% 0.87/1.07 tff(2280,plain,
% 0.87/1.07 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a225) | c2_1(a225) | (~c0_1(a225)) | c1_1(a224) | (~c3_1(a224)) | (~c2_1(a224)) | c0_1(a216) | c2_1(a216) | (~c3_1(a216)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c2_1(a225) | c3_1(a225) | c1_1(a224) | c0_1(a216) | c2_1(a216) | (~ndr1_0) | (~c3_1(a216)) | (~c3_1(a224)) | (~c2_1(a224)) | (~c0_1(a225)))),
% 0.87/1.07 inference(transitivity,[status(thm)],[2279, 2277])).
% 0.87/1.07 tff(2281,plain,
% 0.87/1.07 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a225) | c2_1(a225) | (~c0_1(a225)) | c1_1(a224) | (~c3_1(a224)) | (~c2_1(a224)) | c0_1(a216) | c2_1(a216) | (~c3_1(a216)))),
% 0.87/1.07 inference(quant_inst,[status(thm)],[])).
% 0.87/1.07 tff(2282,plain,
% 0.87/1.07 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c2_1(a225) | c3_1(a225) | c1_1(a224) | c0_1(a216) | c2_1(a216) | (~ndr1_0) | (~c3_1(a216)) | (~c3_1(a224)) | (~c2_1(a224)) | (~c0_1(a225))),
% 0.87/1.07 inference(modus_ponens,[status(thm)],[2281, 2280])).
% 0.87/1.07 tff(2283,plain,
% 0.87/1.07 ($false),
% 0.87/1.07 inference(unit_resolution,[status(thm)],[2282, 122, 1974, 2276, 2274, 1966, 1960, 2273, 2272, 2271, 10, 2275])).
% 0.87/1.07 tff(2284,plain,(hskp15 | c2_1(a229) | c3_1(a229) | c0_1(a229)), inference(lemma,lemma(discharge,[]))).
% 0.87/1.07 tff(2285,plain,
% 0.87/1.07 (c2_1(a229)),
% 0.87/1.07 inference(unit_resolution,[status(thm)],[2284, 1163, 12, 11])).
% 0.87/1.07 tff(2286,plain,
% 0.87/1.07 (~c2_1(a216)),
% 0.87/1.07 inference(unit_resolution,[status(thm)],[312, 2178])).
% 0.87/1.07 tff(2287,plain,
% 0.87/1.07 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp9 | c3_1(a229) | c3_1(a259) | c0_1(a229) | (~ndr1_0) | (~c2_1(a229)) | (~c0_1(a259)) | (~c1_1(a259)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp9 | c3_1(a229) | c3_1(a259) | c0_1(a229) | (~ndr1_0) | (~c2_1(a229)) | (~c0_1(a259)) | (~c1_1(a259)))),
% 0.87/1.07 inference(rewrite,[status(thm)],[])).
% 0.87/1.07 tff(2288,plain,
% 0.87/1.07 ((hskp9 | (~ndr1_0) | c3_1(a259) | (~c1_1(a259)) | (~c0_1(a259)) | c3_1(a229) | c0_1(a229) | (~c2_1(a229))) <=> (hskp9 | c3_1(a229) | c3_1(a259) | c0_1(a229) | (~ndr1_0) | (~c2_1(a229)) | (~c0_1(a259)) | (~c1_1(a259)))),
% 0.87/1.07 inference(rewrite,[status(thm)],[])).
% 0.87/1.07 tff(2289,plain,
% 0.87/1.07 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp9 | (~ndr1_0) | c3_1(a259) | (~c1_1(a259)) | (~c0_1(a259)) | c3_1(a229) | c0_1(a229) | (~c2_1(a229)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp9 | c3_1(a229) | c3_1(a259) | c0_1(a229) | (~ndr1_0) | (~c2_1(a229)) | (~c0_1(a259)) | (~c1_1(a259))))),
% 0.87/1.07 inference(monotonicity,[status(thm)],[2288])).
% 0.87/1.07 tff(2290,plain,
% 0.87/1.07 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp9 | (~ndr1_0) | c3_1(a259) | (~c1_1(a259)) | (~c0_1(a259)) | c3_1(a229) | c0_1(a229) | (~c2_1(a229)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp9 | c3_1(a229) | c3_1(a259) | c0_1(a229) | (~ndr1_0) | (~c2_1(a229)) | (~c0_1(a259)) | (~c1_1(a259)))),
% 0.87/1.07 inference(transitivity,[status(thm)],[2289, 2287])).
% 0.87/1.07 tff(2291,plain,
% 0.87/1.07 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp9 | (~ndr1_0) | c3_1(a259) | (~c1_1(a259)) | (~c0_1(a259)) | c3_1(a229) | c0_1(a229) | (~c2_1(a229)))),
% 0.87/1.07 inference(quant_inst,[status(thm)],[])).
% 0.87/1.07 tff(2292,plain,
% 0.87/1.07 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp9 | c3_1(a229) | c3_1(a259) | c0_1(a229) | (~ndr1_0) | (~c2_1(a229)) | (~c0_1(a259)) | (~c1_1(a259))),
% 0.87/1.07 inference(modus_ponens,[status(thm)],[2291, 2290])).
% 0.87/1.07 tff(2293,plain,
% 0.87/1.07 (hskp9),
% 0.87/1.07 inference(unit_resolution,[status(thm)],[2292, 122, 2177, 2176, 2285, 12, 2175, 11, 1359])).
% 0.87/1.07 tff(2294,plain,
% 0.87/1.07 (~c2_1(a228)),
% 0.87/1.07 inference(unit_resolution,[status(thm)],[1371, 2293])).
% 0.87/1.07 tff(2295,plain,
% 0.87/1.07 (~c1_1(a228)),
% 0.87/1.07 inference(unit_resolution,[status(thm)],[1398, 2293])).
% 0.87/1.07 tff(2296,plain,
% 0.87/1.07 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | (c1_1(a228) | c2_1(a228) | c0_1(a216) | c2_1(a216) | c2_1(a213) | (~ndr1_0) | (~c1_1(a213)) | (~c3_1(a213)) | (~c3_1(a216)) | (~c0_1(a228)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a228) | c2_1(a228) | c0_1(a216) | c2_1(a216) | c2_1(a213) | (~ndr1_0) | (~c1_1(a213)) | (~c3_1(a213)) | (~c3_1(a216)) | (~c0_1(a228)))),
% 0.87/1.07 inference(rewrite,[status(thm)],[])).
% 0.87/1.07 tff(2297,plain,
% 0.87/1.07 (((~ndr1_0) | c2_1(a213) | (~c1_1(a213)) | (~c3_1(a213)) | c2_1(a228) | c1_1(a228) | (~c0_1(a228)) | c0_1(a216) | c2_1(a216) | (~c3_1(a216))) <=> (c1_1(a228) | c2_1(a228) | c0_1(a216) | c2_1(a216) | c2_1(a213) | (~ndr1_0) | (~c1_1(a213)) | (~c3_1(a213)) | (~c3_1(a216)) | (~c0_1(a228)))),
% 0.87/1.08 inference(rewrite,[status(thm)],[])).
% 0.87/1.08 tff(2298,plain,
% 0.87/1.08 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a213) | (~c1_1(a213)) | (~c3_1(a213)) | c2_1(a228) | c1_1(a228) | (~c0_1(a228)) | c0_1(a216) | c2_1(a216) | (~c3_1(a216)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | (c1_1(a228) | c2_1(a228) | c0_1(a216) | c2_1(a216) | c2_1(a213) | (~ndr1_0) | (~c1_1(a213)) | (~c3_1(a213)) | (~c3_1(a216)) | (~c0_1(a228))))),
% 0.87/1.08 inference(monotonicity,[status(thm)],[2297])).
% 0.87/1.08 tff(2299,plain,
% 0.87/1.08 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a213) | (~c1_1(a213)) | (~c3_1(a213)) | c2_1(a228) | c1_1(a228) | (~c0_1(a228)) | c0_1(a216) | c2_1(a216) | (~c3_1(a216)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a228) | c2_1(a228) | c0_1(a216) | c2_1(a216) | c2_1(a213) | (~ndr1_0) | (~c1_1(a213)) | (~c3_1(a213)) | (~c3_1(a216)) | (~c0_1(a228)))),
% 0.87/1.08 inference(transitivity,[status(thm)],[2298, 2296])).
% 0.87/1.08 tff(2300,plain,
% 0.87/1.08 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a213) | (~c1_1(a213)) | (~c3_1(a213)) | c2_1(a228) | c1_1(a228) | (~c0_1(a228)) | c0_1(a216) | c2_1(a216) | (~c3_1(a216)))),
% 0.87/1.08 inference(quant_inst,[status(thm)],[])).
% 0.87/1.08 tff(2301,plain,
% 0.87/1.08 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a228) | c2_1(a228) | c0_1(a216) | c2_1(a216) | c2_1(a213) | (~ndr1_0) | (~c1_1(a213)) | (~c3_1(a213)) | (~c3_1(a216)) | (~c0_1(a228))),
% 0.87/1.08 inference(modus_ponens,[status(thm)],[2300, 2299])).
% 0.87/1.08 tff(2302,plain,
% 0.87/1.08 (~c0_1(a228)),
% 0.87/1.08 inference(unit_resolution,[status(thm)],[2301, 122, 2180, 2021, 2027, 2295, 2294, 2179, 2286, 2020, 305])).
% 0.87/1.08 tff(2303,plain,
% 0.87/1.08 (c3_1(a228)),
% 0.87/1.08 inference(unit_resolution,[status(thm)],[1385, 2293])).
% 0.87/1.08 tff(2304,plain,
% 0.87/1.08 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c3_1(a229) | c1_1(a228) | c2_1(a216) | (~ndr1_0) | (~c1_1(a216)) | (~c3_1(a216)) | (~c3_1(a228)) | c0_1(a228) | (~c2_1(a229)) | c1_1(a229))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c3_1(a229) | c1_1(a228) | c2_1(a216) | (~ndr1_0) | (~c1_1(a216)) | (~c3_1(a216)) | (~c3_1(a228)) | c0_1(a228) | (~c2_1(a229)) | c1_1(a229))),
% 0.87/1.08 inference(rewrite,[status(thm)],[])).
% 0.87/1.08 tff(2305,plain,
% 0.87/1.08 (((~ndr1_0) | c2_1(a216) | (~c1_1(a216)) | (~c3_1(a216)) | c3_1(a229) | c1_1(a229) | (~c2_1(a229)) | c1_1(a228) | c0_1(a228) | (~c3_1(a228))) <=> (c3_1(a229) | c1_1(a228) | c2_1(a216) | (~ndr1_0) | (~c1_1(a216)) | (~c3_1(a216)) | (~c3_1(a228)) | c0_1(a228) | (~c2_1(a229)) | c1_1(a229))),
% 0.87/1.08 inference(rewrite,[status(thm)],[])).
% 0.87/1.08 tff(2306,plain,
% 0.87/1.08 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a216) | (~c1_1(a216)) | (~c3_1(a216)) | c3_1(a229) | c1_1(a229) | (~c2_1(a229)) | c1_1(a228) | c0_1(a228) | (~c3_1(a228)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c3_1(a229) | c1_1(a228) | c2_1(a216) | (~ndr1_0) | (~c1_1(a216)) | (~c3_1(a216)) | (~c3_1(a228)) | c0_1(a228) | (~c2_1(a229)) | c1_1(a229)))),
% 0.87/1.08 inference(monotonicity,[status(thm)],[2305])).
% 0.91/1.08 tff(2307,plain,
% 0.91/1.08 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a216) | (~c1_1(a216)) | (~c3_1(a216)) | c3_1(a229) | c1_1(a229) | (~c2_1(a229)) | c1_1(a228) | c0_1(a228) | (~c3_1(a228)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c3_1(a229) | c1_1(a228) | c2_1(a216) | (~ndr1_0) | (~c1_1(a216)) | (~c3_1(a216)) | (~c3_1(a228)) | c0_1(a228) | (~c2_1(a229)) | c1_1(a229))),
% 0.91/1.08 inference(transitivity,[status(thm)],[2306, 2304])).
% 0.91/1.08 tff(2308,plain,
% 0.91/1.08 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a216) | (~c1_1(a216)) | (~c3_1(a216)) | c3_1(a229) | c1_1(a229) | (~c2_1(a229)) | c1_1(a228) | c0_1(a228) | (~c3_1(a228)))),
% 0.91/1.08 inference(quant_inst,[status(thm)],[])).
% 0.91/1.08 tff(2309,plain,
% 0.91/1.08 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c3_1(a229) | c1_1(a228) | c2_1(a216) | (~ndr1_0) | (~c1_1(a216)) | (~c3_1(a216)) | (~c3_1(a228)) | c0_1(a228) | (~c2_1(a229)) | c1_1(a229)),
% 0.91/1.08 inference(modus_ponens,[status(thm)],[2308, 2307])).
% 0.91/1.08 tff(2310,plain,
% 0.91/1.08 (c1_1(a229)),
% 0.91/1.08 inference(unit_resolution,[status(thm)],[2309, 122, 2285, 12, 2303, 2180, 2295, 2286, 735, 2302, 2181])).
% 0.91/1.08 tff(2311,plain,
% 0.91/1.08 (c2_1(a237)),
% 0.91/1.08 inference(unit_resolution,[status(thm)],[1149, 2189])).
% 0.91/1.08 tff(2312,plain,
% 0.91/1.08 (c3_1(a237)),
% 0.91/1.08 inference(unit_resolution,[status(thm)],[1723, 2311, 2310, 2285, 2191, 11, 2190])).
% 0.91/1.08 tff(2313,plain,
% 0.91/1.08 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | (c1_1(a237) | c2_1(a228) | c2_1(a225) | c3_1(a225) | (~ndr1_0) | (~c0_1(a225)) | (~c3_1(a228)) | c0_1(a228) | (~c3_1(a237)) | (~c2_1(a237)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a237) | c2_1(a228) | c2_1(a225) | c3_1(a225) | (~ndr1_0) | (~c0_1(a225)) | (~c3_1(a228)) | c0_1(a228) | (~c3_1(a237)) | (~c2_1(a237)))),
% 0.91/1.08 inference(rewrite,[status(thm)],[])).
% 0.91/1.08 tff(2314,plain,
% 0.91/1.08 (((~ndr1_0) | c3_1(a225) | c2_1(a225) | (~c0_1(a225)) | c1_1(a237) | (~c3_1(a237)) | (~c2_1(a237)) | c0_1(a228) | c2_1(a228) | (~c3_1(a228))) <=> (c1_1(a237) | c2_1(a228) | c2_1(a225) | c3_1(a225) | (~ndr1_0) | (~c0_1(a225)) | (~c3_1(a228)) | c0_1(a228) | (~c3_1(a237)) | (~c2_1(a237)))),
% 0.91/1.08 inference(rewrite,[status(thm)],[])).
% 0.91/1.08 tff(2315,plain,
% 0.91/1.08 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a225) | c2_1(a225) | (~c0_1(a225)) | c1_1(a237) | (~c3_1(a237)) | (~c2_1(a237)) | c0_1(a228) | c2_1(a228) | (~c3_1(a228)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | (c1_1(a237) | c2_1(a228) | c2_1(a225) | c3_1(a225) | (~ndr1_0) | (~c0_1(a225)) | (~c3_1(a228)) | c0_1(a228) | (~c3_1(a237)) | (~c2_1(a237))))),
% 0.91/1.08 inference(monotonicity,[status(thm)],[2314])).
% 0.91/1.08 tff(2316,plain,
% 0.91/1.08 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a225) | c2_1(a225) | (~c0_1(a225)) | c1_1(a237) | (~c3_1(a237)) | (~c2_1(a237)) | c0_1(a228) | c2_1(a228) | (~c3_1(a228)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a237) | c2_1(a228) | c2_1(a225) | c3_1(a225) | (~ndr1_0) | (~c0_1(a225)) | (~c3_1(a228)) | c0_1(a228) | (~c3_1(a237)) | (~c2_1(a237)))),
% 0.91/1.08 inference(transitivity,[status(thm)],[2315, 2313])).
% 0.91/1.08 tff(2317,plain,
% 0.91/1.08 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a225) | c2_1(a225) | (~c0_1(a225)) | c1_1(a237) | (~c3_1(a237)) | (~c2_1(a237)) | c0_1(a228) | c2_1(a228) | (~c3_1(a228)))),
% 0.91/1.08 inference(quant_inst,[status(thm)],[])).
% 0.91/1.08 tff(2318,plain,
% 0.91/1.08 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a237) | c2_1(a228) | c2_1(a225) | c3_1(a225) | (~ndr1_0) | (~c0_1(a225)) | (~c3_1(a228)) | c0_1(a228) | (~c3_1(a237)) | (~c2_1(a237))),
% 0.91/1.08 inference(modus_ponens,[status(thm)],[2317, 2316])).
% 0.91/1.08 tff(2319,plain,
% 0.91/1.08 ($false),
% 0.91/1.08 inference(unit_resolution,[status(thm)],[2318, 122, 2311, 2303, 1974, 2191, 2294, 1966, 1960, 10, 2302, 2312])).
% 0.91/1.08 tff(2320,plain,(hskp15 | c0_1(a229) | c3_1(a229)), inference(lemma,lemma(discharge,[]))).
% 0.91/1.08 tff(2321,plain,
% 0.91/1.08 (hskp15),
% 0.91/1.08 inference(unit_resolution,[status(thm)],[2320, 12, 11])).
% 0.91/1.08 tff(2322,plain,
% 0.91/1.08 (hskp27),
% 0.91/1.08 inference(unit_resolution,[status(thm)],[1086, 2321])).
% 0.91/1.08 tff(2323,plain,
% 0.91/1.08 (c3_1(a232)),
% 0.91/1.08 inference(unit_resolution,[status(thm)],[247, 2322])).
% 0.91/1.08 tff(2324,plain,
% 0.91/1.08 (c2_1(a232)),
% 0.91/1.08 inference(unit_resolution,[status(thm)],[255, 2322])).
% 0.91/1.08 tff(2325,plain,
% 0.91/1.08 (c0_1(a238)),
% 0.91/1.08 inference(unit_resolution,[status(thm)],[232, 2321])).
% 0.91/1.08 tff(2326,plain,
% 0.91/1.08 (~c3_1(a238)),
% 0.91/1.08 inference(unit_resolution,[status(thm)],[216, 2321])).
% 0.91/1.08 tff(2327,plain,
% 0.91/1.08 (c2_1(a238)),
% 0.91/1.08 inference(unit_resolution,[status(thm)],[224, 2321])).
% 0.91/1.08 tff(2328,plain,
% 0.91/1.08 (c0_1(a232)),
% 0.91/1.08 inference(unit_resolution,[status(thm)],[263, 2322])).
% 0.91/1.08 tff(2329,plain,
% 0.91/1.08 (hskp11),
% 0.91/1.08 inference(unit_resolution,[status(thm)],[436, 132, 21, 2021, 2020])).
% 0.91/1.08 tff(2330,plain,
% 0.91/1.08 (~c1_1(a230)),
% 0.91/1.08 inference(unit_resolution,[status(thm)],[442, 2329])).
% 0.91/1.08 tff(2331,plain,
% 0.91/1.08 (c3_1(a230)),
% 0.91/1.08 inference(unit_resolution,[status(thm)],[470, 2329])).
% 0.91/1.08 tff(2332,plain,
% 0.91/1.08 (c2_1(a230)),
% 0.91/1.08 inference(unit_resolution,[status(thm)],[478, 2329])).
% 0.91/1.08 tff(2333,plain,
% 0.91/1.08 (c0_1(a213)),
% 0.91/1.08 inference(unit_resolution,[status(thm)],[2035, 2332, 2331, 2330])).
% 0.91/1.08 tff(2334,plain,
% 0.91/1.08 (hskp21 | hskp20 | (~c0_1(a213))),
% 0.91/1.08 inference(unit_resolution,[status(thm)],[406, 122, 2021, 2020, 400])).
% 0.91/1.08 tff(2335,plain,
% 0.91/1.08 (hskp21),
% 0.91/1.08 inference(unit_resolution,[status(thm)],[2334, 2333, 132])).
% 0.91/1.08 tff(2336,plain,
% 0.91/1.08 (c1_1(a260)),
% 0.91/1.08 inference(unit_resolution,[status(thm)],[427, 2335])).
% 0.91/1.08 tff(2337,plain,
% 0.91/1.08 (~c0_1(a260)),
% 0.91/1.08 inference(unit_resolution,[status(thm)],[419, 2335])).
% 0.91/1.08 tff(2338,plain,
% 0.91/1.08 (~hskp28),
% 0.91/1.08 inference(unit_resolution,[status(thm)],[1592, 2337, 2336, 132, 2171, 2170, 2169])).
% 0.91/1.08 tff(2339,assumption,(~c3_1(a238)), introduced(assumption)).
% 0.91/1.08 tff(2340,plain,
% 0.91/1.08 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp28 | c3_1(a238) | c2_1(a213) | (~ndr1_0) | (~c1_1(a213)) | (~c0_1(a213)) | c1_1(a238) | (~c2_1(a238)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp28 | c3_1(a238) | c2_1(a213) | (~ndr1_0) | (~c1_1(a213)) | (~c0_1(a213)) | c1_1(a238) | (~c2_1(a238)))),
% 0.91/1.08 inference(rewrite,[status(thm)],[])).
% 0.91/1.08 tff(2341,plain,
% 0.91/1.08 ((hskp28 | (~ndr1_0) | c2_1(a213) | (~c1_1(a213)) | (~c0_1(a213)) | c3_1(a238) | c1_1(a238) | (~c2_1(a238))) <=> (hskp28 | c3_1(a238) | c2_1(a213) | (~ndr1_0) | (~c1_1(a213)) | (~c0_1(a213)) | c1_1(a238) | (~c2_1(a238)))),
% 0.91/1.08 inference(rewrite,[status(thm)],[])).
% 0.91/1.08 tff(2342,plain,
% 0.91/1.08 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp28 | (~ndr1_0) | c2_1(a213) | (~c1_1(a213)) | (~c0_1(a213)) | c3_1(a238) | c1_1(a238) | (~c2_1(a238)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp28 | c3_1(a238) | c2_1(a213) | (~ndr1_0) | (~c1_1(a213)) | (~c0_1(a213)) | c1_1(a238) | (~c2_1(a238))))),
% 0.91/1.08 inference(monotonicity,[status(thm)],[2341])).
% 0.91/1.08 tff(2343,plain,
% 0.91/1.08 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp28 | (~ndr1_0) | c2_1(a213) | (~c1_1(a213)) | (~c0_1(a213)) | c3_1(a238) | c1_1(a238) | (~c2_1(a238)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp28 | c3_1(a238) | c2_1(a213) | (~ndr1_0) | (~c1_1(a213)) | (~c0_1(a213)) | c1_1(a238) | (~c2_1(a238)))),
% 0.91/1.08 inference(transitivity,[status(thm)],[2342, 2340])).
% 0.91/1.08 tff(2344,plain,
% 0.91/1.08 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp28 | (~ndr1_0) | c2_1(a213) | (~c1_1(a213)) | (~c0_1(a213)) | c3_1(a238) | c1_1(a238) | (~c2_1(a238)))),
% 0.91/1.08 inference(quant_inst,[status(thm)],[])).
% 0.91/1.08 tff(2345,plain,
% 0.91/1.08 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp28 | c3_1(a238) | c2_1(a213) | (~ndr1_0) | (~c1_1(a213)) | (~c0_1(a213)) | c1_1(a238) | (~c2_1(a238))),
% 0.91/1.08 inference(modus_ponens,[status(thm)],[2344, 2343])).
% 0.91/1.08 tff(2346,plain,
% 0.91/1.08 (hskp28 | (~c0_1(a213)) | c1_1(a238)),
% 0.91/1.08 inference(unit_resolution,[status(thm)],[2345, 122, 1877, 2021, 2339, 2020, 682])).
% 0.91/1.08 tff(2347,plain,
% 0.91/1.08 (c1_1(a238)),
% 0.91/1.08 inference(unit_resolution,[status(thm)],[2346, 2338, 2333])).
% 0.91/1.08 tff(2348,plain,
% 0.91/1.08 (c3_1(a260)),
% 0.91/1.08 inference(unit_resolution,[status(thm)],[1613, 122, 2336, 1878, 1877, 2337, 2339, 993, 2347])).
% 0.91/1.08 tff(2349,plain,
% 0.91/1.08 ($false),
% 0.91/1.08 inference(unit_resolution,[status(thm)],[1621, 122, 2336, 1878, 1877, 2337, 2171, 2170, 2169, 627, 2347, 2348])).
% 0.91/1.08 tff(2350,plain,(hskp20 | (~c0_1(a238)) | (~c2_1(a238)) | c3_1(a238) | (~c0_1(a232)) | (~c2_1(a232)) | (~c3_1(a232)) | hskp10), inference(lemma,lemma(discharge,[]))).
% 0.91/1.08 tff(2351,plain,
% 0.91/1.08 (hskp20),
% 0.91/1.08 inference(unit_resolution,[status(thm)],[2350, 2328, 2327, 2326, 2325, 2324, 2323, 20])).
% 0.91/1.08 tff(2352,plain,
% 0.91/1.08 (~c3_1(a259)),
% 0.91/1.08 inference(unit_resolution,[status(thm)],[354, 2351])).
% 0.91/1.08 tff(2353,plain,
% 0.91/1.08 (c1_1(a259)),
% 0.91/1.08 inference(unit_resolution,[status(thm)],[362, 2351])).
% 0.91/1.08 tff(2354,plain,
% 0.91/1.08 (c0_1(a259)),
% 0.91/1.08 inference(unit_resolution,[status(thm)],[370, 2351])).
% 0.91/1.08 tff(2355,plain,
% 0.91/1.08 (hskp3),
% 0.91/1.08 inference(unit_resolution,[status(thm)],[2089, 122, 2354, 2353, 2021, 2027, 2352, 2048, 2038])).
% 0.91/1.08 tff(2356,plain,
% 0.91/1.08 (~c2_1(a216)),
% 0.91/1.08 inference(unit_resolution,[status(thm)],[312, 2355])).
% 0.91/1.08 tff(2357,plain,
% 0.91/1.08 (~c0_1(a216)),
% 0.91/1.08 inference(unit_resolution,[status(thm)],[318, 2355])).
% 0.91/1.08 tff(2358,plain,
% 0.91/1.08 (c3_1(a216)),
% 0.91/1.08 inference(unit_resolution,[status(thm)],[328, 2355])).
% 0.91/1.08 tff(2359,plain,
% 0.91/1.08 (c1_1(a216)),
% 0.91/1.08 inference(unit_resolution,[status(thm)],[890, 122, 2358, 2021, 2027, 2357, 583, 2038])).
% 0.91/1.08 tff(2360,plain,
% 0.91/1.08 (hskp11),
% 0.91/1.08 inference(unit_resolution,[status(thm)],[898, 122, 20, 2357, 2356, 32, 2359])).
% 0.91/1.08 tff(2361,plain,
% 0.91/1.08 (~c1_1(a230)),
% 0.91/1.08 inference(unit_resolution,[status(thm)],[442, 2360])).
% 0.91/1.08 tff(2362,plain,
% 0.91/1.08 (c3_1(a230)),
% 0.91/1.08 inference(unit_resolution,[status(thm)],[470, 2360])).
% 0.91/1.08 tff(2363,plain,
% 0.91/1.08 (c2_1(a230)),
% 0.91/1.08 inference(unit_resolution,[status(thm)],[478, 2360])).
% 0.91/1.08 tff(2364,plain,
% 0.91/1.08 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | (c1_1(a230) | c2_1(a225) | c3_1(a225) | c0_1(a216) | c2_1(a216) | (~ndr1_0) | (~c3_1(a216)) | (~c0_1(a225)) | (~c3_1(a230)) | (~c2_1(a230)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a230) | c2_1(a225) | c3_1(a225) | c0_1(a216) | c2_1(a216) | (~ndr1_0) | (~c3_1(a216)) | (~c0_1(a225)) | (~c3_1(a230)) | (~c2_1(a230)))),
% 0.91/1.08 inference(rewrite,[status(thm)],[])).
% 0.91/1.08 tff(2365,plain,
% 0.91/1.08 (((~ndr1_0) | c3_1(a225) | c2_1(a225) | (~c0_1(a225)) | c1_1(a230) | (~c3_1(a230)) | (~c2_1(a230)) | c0_1(a216) | c2_1(a216) | (~c3_1(a216))) <=> (c1_1(a230) | c2_1(a225) | c3_1(a225) | c0_1(a216) | c2_1(a216) | (~ndr1_0) | (~c3_1(a216)) | (~c0_1(a225)) | (~c3_1(a230)) | (~c2_1(a230)))),
% 0.91/1.08 inference(rewrite,[status(thm)],[])).
% 0.91/1.08 tff(2366,plain,
% 0.91/1.08 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a225) | c2_1(a225) | (~c0_1(a225)) | c1_1(a230) | (~c3_1(a230)) | (~c2_1(a230)) | c0_1(a216) | c2_1(a216) | (~c3_1(a216)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | (c1_1(a230) | c2_1(a225) | c3_1(a225) | c0_1(a216) | c2_1(a216) | (~ndr1_0) | (~c3_1(a216)) | (~c0_1(a225)) | (~c3_1(a230)) | (~c2_1(a230))))),
% 0.91/1.08 inference(monotonicity,[status(thm)],[2365])).
% 0.91/1.08 tff(2367,plain,
% 0.91/1.08 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a225) | c2_1(a225) | (~c0_1(a225)) | c1_1(a230) | (~c3_1(a230)) | (~c2_1(a230)) | c0_1(a216) | c2_1(a216) | (~c3_1(a216)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a230) | c2_1(a225) | c3_1(a225) | c0_1(a216) | c2_1(a216) | (~ndr1_0) | (~c3_1(a216)) | (~c0_1(a225)) | (~c3_1(a230)) | (~c2_1(a230)))),
% 0.91/1.08 inference(transitivity,[status(thm)],[2366, 2364])).
% 0.91/1.08 tff(2368,plain,
% 0.91/1.08 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a225) | c2_1(a225) | (~c0_1(a225)) | c1_1(a230) | (~c3_1(a230)) | (~c2_1(a230)) | c0_1(a216) | c2_1(a216) | (~c3_1(a216)))),
% 0.91/1.08 inference(quant_inst,[status(thm)],[])).
% 0.91/1.08 tff(2369,plain,
% 0.91/1.08 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a230) | c2_1(a225) | c3_1(a225) | c0_1(a216) | c2_1(a216) | (~ndr1_0) | (~c3_1(a216)) | (~c0_1(a225)) | (~c3_1(a230)) | (~c2_1(a230))),
% 0.91/1.08 inference(modus_ponens,[status(thm)],[2368, 2367])).
% 0.91/1.08 tff(2370,plain,
% 0.91/1.08 ($false),
% 0.91/1.08 inference(unit_resolution,[status(thm)],[2369, 122, 2363, 2362, 1974, 2358, 2361, 1966, 1960, 2357, 2356, 10])).
% 0.91/1.08 tff(2371,plain,(c3_1(a229) | c0_1(a229)), inference(lemma,lemma(discharge,[]))).
% 0.91/1.08 tff(2372,plain,
% 0.91/1.08 (c3_1(a229)),
% 0.91/1.08 inference(unit_resolution,[status(thm)],[2371, 11])).
% 0.91/1.08 tff(2373,plain,
% 0.91/1.08 (hskp14),
% 0.91/1.08 inference(unit_resolution,[status(thm)],[1528, 1163, 2021, 2027, 11, 2372])).
% 0.91/1.08 tff(2374,plain,
% 0.91/1.08 (c0_1(a237)),
% 0.91/1.08 inference(unit_resolution,[status(thm)],[1157, 2373])).
% 0.91/1.08 tff(2375,plain,
% 0.91/1.08 (~c1_1(a237)),
% 0.91/1.08 inference(unit_resolution,[status(thm)],[1169, 2373])).
% 0.91/1.08 tff(2376,plain,
% 0.91/1.08 (c2_1(a237)),
% 0.91/1.08 inference(unit_resolution,[status(thm)],[1149, 2373])).
% 0.91/1.08 tff(2377,plain,
% 0.91/1.08 (hskp28),
% 0.91/1.08 inference(unit_resolution,[status(thm)],[1596, 1163, 2021, 2027, 11, 2372])).
% 0.91/1.08 tff(2378,plain,
% 0.91/1.08 (c2_1(a246)),
% 0.91/1.08 inference(unit_resolution,[status(thm)],[699, 2377])).
% 0.91/1.08 tff(2379,plain,
% 0.91/1.08 (c1_1(a246)),
% 0.91/1.08 inference(unit_resolution,[status(thm)],[707, 2377])).
% 0.91/1.08 tff(2380,plain,
% 0.91/1.08 (c0_1(a246)),
% 0.91/1.08 inference(unit_resolution,[status(thm)],[715, 2377])).
% 0.91/1.08 tff(2381,plain,
% 0.91/1.08 (c1_1(a229)),
% 0.91/1.08 inference(unit_resolution,[status(thm)],[1702, 1678, 2372, 1694, 1183, 2021, 2027, 11, 2020, 1648, 1647, 1679])).
% 0.91/1.08 tff(2382,plain,
% 0.91/1.08 (hskp10),
% 0.91/1.08 inference(unit_resolution,[status(thm)],[2037, 22])).
% 0.91/1.08 tff(2383,plain,
% 0.91/1.08 (c2_1(a229)),
% 0.91/1.08 inference(unit_resolution,[status(thm)],[1052, 2382])).
% 0.91/1.08 tff(2384,plain,
% 0.91/1.08 (c3_1(a237)),
% 0.91/1.08 inference(unit_resolution,[status(thm)],[1723, 2383, 1647, 2381, 1183, 11, 1648])).
% 0.91/1.08 tff(2385,plain,
% 0.91/1.08 (hskp13 | (~c3_1(a237))),
% 0.91/1.08 inference(unit_resolution,[status(thm)],[1742, 122, 1647, 2372, 1183, 11, 1736, 2381])).
% 0.91/1.08 tff(2386,plain,
% 0.91/1.08 (hskp13),
% 0.91/1.08 inference(unit_resolution,[status(thm)],[2385, 2384])).
% 0.91/1.08 tff(2387,plain,
% 0.91/1.08 (~c2_1(a236)),
% 0.91/1.08 inference(unit_resolution,[status(thm)],[758, 2386])).
% 0.91/1.08 tff(2388,plain,
% 0.91/1.08 (~c1_1(a236)),
% 0.91/1.08 inference(unit_resolution,[status(thm)],[764, 2386])).
% 0.91/1.08 tff(2389,plain,
% 0.91/1.08 (~c0_1(a236)),
% 0.91/1.08 inference(unit_resolution,[status(thm)],[1488, 122, 2383, 2372, 2388, 2387, 11, 1269, 2381])).
% 0.91/1.08 tff(2390,plain,
% 0.91/1.08 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c1_1(a236) | c2_1(a236) | (~ndr1_0) | (~c1_1(a213)) | (~c3_1(a213)) | c0_1(a213) | (~c0_1(a246)) | (~c1_1(a246)) | (~c2_1(a246)) | c0_1(a236))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c1_1(a236) | c2_1(a236) | (~ndr1_0) | (~c1_1(a213)) | (~c3_1(a213)) | c0_1(a213) | (~c0_1(a246)) | (~c1_1(a246)) | (~c2_1(a246)) | c0_1(a236))),
% 0.91/1.08 inference(rewrite,[status(thm)],[])).
% 0.91/1.08 tff(2391,plain,
% 0.91/1.08 (((~ndr1_0) | (~c2_1(a246)) | (~c1_1(a246)) | (~c0_1(a246)) | c0_1(a213) | (~c3_1(a213)) | (~c1_1(a213)) | c1_1(a236) | c0_1(a236) | c2_1(a236)) <=> (c1_1(a236) | c2_1(a236) | (~ndr1_0) | (~c1_1(a213)) | (~c3_1(a213)) | c0_1(a213) | (~c0_1(a246)) | (~c1_1(a246)) | (~c2_1(a246)) | c0_1(a236))),
% 0.91/1.08 inference(rewrite,[status(thm)],[])).
% 0.91/1.08 tff(2392,plain,
% 0.91/1.08 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | (~c2_1(a246)) | (~c1_1(a246)) | (~c0_1(a246)) | c0_1(a213) | (~c3_1(a213)) | (~c1_1(a213)) | c1_1(a236) | c0_1(a236) | c2_1(a236))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c1_1(a236) | c2_1(a236) | (~ndr1_0) | (~c1_1(a213)) | (~c3_1(a213)) | c0_1(a213) | (~c0_1(a246)) | (~c1_1(a246)) | (~c2_1(a246)) | c0_1(a236)))),
% 0.91/1.08 inference(monotonicity,[status(thm)],[2391])).
% 0.91/1.08 tff(2393,plain,
% 0.91/1.08 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | (~c2_1(a246)) | (~c1_1(a246)) | (~c0_1(a246)) | c0_1(a213) | (~c3_1(a213)) | (~c1_1(a213)) | c1_1(a236) | c0_1(a236) | c2_1(a236))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c1_1(a236) | c2_1(a236) | (~ndr1_0) | (~c1_1(a213)) | (~c3_1(a213)) | c0_1(a213) | (~c0_1(a246)) | (~c1_1(a246)) | (~c2_1(a246)) | c0_1(a236))),
% 0.91/1.08 inference(transitivity,[status(thm)],[2392, 2390])).
% 0.91/1.08 tff(2394,plain,
% 0.91/1.08 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | (~c2_1(a246)) | (~c1_1(a246)) | (~c0_1(a246)) | c0_1(a213) | (~c3_1(a213)) | (~c1_1(a213)) | c1_1(a236) | c0_1(a236) | c2_1(a236))),
% 0.91/1.08 inference(quant_inst,[status(thm)],[])).
% 0.91/1.08 tff(2395,plain,
% 0.91/1.08 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c1_1(a236) | c2_1(a236) | (~ndr1_0) | (~c1_1(a213)) | (~c3_1(a213)) | c0_1(a213) | (~c0_1(a246)) | (~c1_1(a246)) | (~c2_1(a246)) | c0_1(a236)),
% 0.91/1.08 inference(modus_ponens,[status(thm)],[2394, 2393])).
% 0.91/1.08 tff(2396,plain,
% 0.91/1.08 ($false),
% 0.91/1.08 inference(unit_resolution,[status(thm)],[2395, 122, 1679, 1678, 1694, 2021, 2027, 2388, 2387, 627, 22, 2389])).
% 0.91/1.08 tff(2397,plain,(c0_1(a213) | (~c0_1(a246)) | (~c1_1(a246)) | (~c2_1(a246)) | c0_1(a229) | (~c2_1(a237)) | c1_1(a237) | (~c0_1(a237))), inference(lemma,lemma(discharge,[]))).
% 0.91/1.08 tff(2398,plain,
% 0.91/1.08 (c0_1(a213)),
% 0.91/1.08 inference(unit_resolution,[status(thm)],[2397, 2380, 2379, 2378, 11, 2376, 2375, 2374])).
% 0.91/1.08 tff(2399,plain,
% 0.91/1.08 (hskp27 | c3_1(a237)),
% 0.91/1.08 inference(unit_resolution,[status(thm)],[1161, 122, 1648, 1647, 192])).
% 0.91/1.08 tff(2400,plain,
% 0.91/1.08 (c3_1(a237)),
% 0.91/1.08 inference(unit_resolution,[status(thm)],[2399, 1080])).
% 0.91/1.08 tff(2401,plain,
% 0.91/1.08 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp27 | c1_1(a237) | c2_1(a225) | c3_1(a225) | (~ndr1_0) | (~c0_1(a225)) | (~c3_1(a237)) | (~c2_1(a237)))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp27 | c1_1(a237) | c2_1(a225) | c3_1(a225) | (~ndr1_0) | (~c0_1(a225)) | (~c3_1(a237)) | (~c2_1(a237)))),
% 0.91/1.08 inference(rewrite,[status(thm)],[])).
% 0.91/1.08 tff(2402,plain,
% 0.91/1.08 ((hskp27 | (~ndr1_0) | c3_1(a225) | c2_1(a225) | (~c0_1(a225)) | c1_1(a237) | (~c3_1(a237)) | (~c2_1(a237))) <=> (hskp27 | c1_1(a237) | c2_1(a225) | c3_1(a225) | (~ndr1_0) | (~c0_1(a225)) | (~c3_1(a237)) | (~c2_1(a237)))),
% 0.91/1.08 inference(rewrite,[status(thm)],[])).
% 0.91/1.08 tff(2403,plain,
% 0.91/1.08 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp27 | (~ndr1_0) | c3_1(a225) | c2_1(a225) | (~c0_1(a225)) | c1_1(a237) | (~c3_1(a237)) | (~c2_1(a237)))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp27 | c1_1(a237) | c2_1(a225) | c3_1(a225) | (~ndr1_0) | (~c0_1(a225)) | (~c3_1(a237)) | (~c2_1(a237))))),
% 0.91/1.08 inference(monotonicity,[status(thm)],[2402])).
% 0.91/1.08 tff(2404,plain,
% 0.91/1.08 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp27 | (~ndr1_0) | c3_1(a225) | c2_1(a225) | (~c0_1(a225)) | c1_1(a237) | (~c3_1(a237)) | (~c2_1(a237)))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp27 | c1_1(a237) | c2_1(a225) | c3_1(a225) | (~ndr1_0) | (~c0_1(a225)) | (~c3_1(a237)) | (~c2_1(a237)))),
% 0.91/1.08 inference(transitivity,[status(thm)],[2403, 2401])).
% 0.91/1.08 tff(2405,plain,
% 0.91/1.08 ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp27 | (~ndr1_0) | c3_1(a225) | c2_1(a225) | (~c0_1(a225)) | c1_1(a237) | (~c3_1(a237)) | (~c2_1(a237)))),
% 0.91/1.08 inference(quant_inst,[status(thm)],[])).
% 0.91/1.08 tff(2406,plain,
% 0.91/1.08 ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp27 | c1_1(a237) | c2_1(a225) | c3_1(a225) | (~ndr1_0) | (~c0_1(a225)) | (~c3_1(a237)) | (~c2_1(a237))),
% 0.91/1.08 inference(modus_ponens,[status(thm)],[2405, 2404])).
% 0.91/1.08 tff(2407,plain,
% 0.91/1.08 (hskp27 | (~c3_1(a237))),
% 0.91/1.08 inference(unit_resolution,[status(thm)],[2406, 122, 1647, 1974, 1183, 1966, 1960, 463])).
% 0.91/1.08 tff(2408,plain,
% 0.91/1.08 ($false),
% 0.91/1.08 inference(unit_resolution,[status(thm)],[2407, 2400, 1080])).
% 0.91/1.08 tff(2409,plain,(hskp27 | (~c2_1(a237)) | c1_1(a237) | (~c0_1(a237))), inference(lemma,lemma(discharge,[]))).
% 0.91/1.08 tff(2410,plain,
% 0.91/1.08 (hskp27),
% 0.91/1.08 inference(unit_resolution,[status(thm)],[2409, 2376, 2375, 2374])).
% 0.91/1.08 tff(2411,plain,
% 0.91/1.08 (c3_1(a232)),
% 0.91/1.08 inference(unit_resolution,[status(thm)],[247, 2410])).
% 0.91/1.08 tff(2412,plain,
% 0.91/1.08 (c0_1(a232)),
% 0.91/1.08 inference(unit_resolution,[status(thm)],[263, 2410])).
% 0.91/1.08 tff(2413,plain,
% 0.91/1.08 (c2_1(a232)),
% 0.91/1.08 inference(unit_resolution,[status(thm)],[255, 2410])).
% 0.91/1.08 tff(2414,plain,
% 0.91/1.08 (hskp20),
% 0.91/1.08 inference(unit_resolution,[status(thm)],[2173, 2413, 1163, 2412, 2411])).
% 0.91/1.08 tff(2415,plain,
% 0.91/1.08 (~c3_1(a259)),
% 0.91/1.08 inference(unit_resolution,[status(thm)],[354, 2414])).
% 0.91/1.08 tff(2416,plain,
% 0.91/1.08 (c1_1(a259)),
% 0.91/1.08 inference(unit_resolution,[status(thm)],[362, 2414])).
% 0.91/1.08 tff(2417,plain,
% 0.91/1.08 (c0_1(a259)),
% 0.91/1.08 inference(unit_resolution,[status(thm)],[370, 2414])).
% 0.91/1.08 tff(2418,plain,
% 0.91/1.08 (hskp3 | (~c0_1(a213))),
% 0.91/1.08 inference(unit_resolution,[status(thm)],[2089, 122, 2417, 2416, 2021, 2027, 2415, 2048])).
% 0.91/1.08 tff(2419,plain,
% 0.91/1.08 (hskp3),
% 0.91/1.08 inference(unit_resolution,[status(thm)],[2418, 2398])).
% 0.91/1.08 tff(2420,plain,
% 0.91/1.08 (~c2_1(a216)),
% 0.91/1.08 inference(unit_resolution,[status(thm)],[312, 2419])).
% 0.91/1.08 tff(2421,plain,
% 0.91/1.08 (~c0_1(a216)),
% 0.91/1.08 inference(unit_resolution,[status(thm)],[318, 2419])).
% 0.91/1.08 tff(2422,plain,
% 0.91/1.08 (c3_1(a216)),
% 0.91/1.08 inference(unit_resolution,[status(thm)],[328, 2419])).
% 0.91/1.08 tff(2423,plain,
% 0.91/1.08 (~c2_1(a229)),
% 0.91/1.08 inference(unit_resolution,[status(thm)],[1769, 2421, 11, 2372, 1163, 2420, 2422, 2021, 2027, 2020])).
% 0.91/1.08 tff(2424,plain,
% 0.91/1.08 (c1_1(a229)),
% 0.91/1.08 inference(unit_resolution,[status(thm)],[1702, 2379, 2372, 2378, 2375, 2021, 2027, 11, 2020, 2374, 2376, 2380])).
% 0.91/1.08 tff(2425,plain,
% 0.91/1.08 (~hskp10),
% 0.91/1.08 inference(unit_resolution,[status(thm)],[1052, 2423])).
% 0.91/1.08 tff(2426,plain,
% 0.91/1.08 (((~![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp11 | hskp10 | c2_1(a229) | c0_1(a229) | (~ndr1_0) | (~c1_1(a229)))) <=> ((~![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | hskp11 | hskp10 | c2_1(a229) | c0_1(a229) | (~ndr1_0) | (~c1_1(a229)))),
% 0.91/1.08 inference(rewrite,[status(thm)],[])).
% 0.91/1.08 tff(2427,plain,
% 0.91/1.08 ((hskp11 | hskp10 | (~ndr1_0) | c0_1(a229) | c2_1(a229) | (~c1_1(a229))) <=> (hskp11 | hskp10 | c2_1(a229) | c0_1(a229) | (~ndr1_0) | (~c1_1(a229)))),
% 0.91/1.08 inference(rewrite,[status(thm)],[])).
% 0.91/1.08 tff(2428,plain,
% 0.91/1.08 (((~![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp11 | hskp10 | (~ndr1_0) | c0_1(a229) | c2_1(a229) | (~c1_1(a229)))) <=> ((~![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp11 | hskp10 | c2_1(a229) | c0_1(a229) | (~ndr1_0) | (~c1_1(a229))))),
% 0.91/1.08 inference(monotonicity,[status(thm)],[2427])).
% 0.91/1.08 tff(2429,plain,
% 0.91/1.08 (((~![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp11 | hskp10 | (~ndr1_0) | c0_1(a229) | c2_1(a229) | (~c1_1(a229)))) <=> ((~![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | hskp11 | hskp10 | c2_1(a229) | c0_1(a229) | (~ndr1_0) | (~c1_1(a229)))),
% 0.91/1.08 inference(transitivity,[status(thm)],[2428, 2426])).
% 0.91/1.08 tff(2430,plain,
% 0.91/1.08 ((~![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp11 | hskp10 | (~ndr1_0) | c0_1(a229) | c2_1(a229) | (~c1_1(a229)))),
% 0.91/1.08 inference(quant_inst,[status(thm)],[])).
% 0.91/1.08 tff(2431,plain,
% 0.91/1.08 ((~![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | hskp11 | hskp10 | c2_1(a229) | c0_1(a229) | (~ndr1_0) | (~c1_1(a229))),
% 0.91/1.08 inference(modus_ponens,[status(thm)],[2430, 2429])).
% 0.91/1.08 tff(2432,plain,
% 0.91/1.08 (hskp11 | hskp10 | c2_1(a229) | (~c1_1(a229))),
% 0.91/1.08 inference(unit_resolution,[status(thm)],[2431, 122, 11, 32])).
% 0.91/1.08 tff(2433,plain,
% 0.91/1.08 (hskp11),
% 0.91/1.08 inference(unit_resolution,[status(thm)],[2432, 2425, 2424, 2423])).
% 0.91/1.08 tff(2434,plain,
% 0.91/1.08 (~c1_1(a230)),
% 0.91/1.08 inference(unit_resolution,[status(thm)],[442, 2433])).
% 0.91/1.08 tff(2435,plain,
% 0.91/1.08 (c3_1(a230)),
% 0.91/1.08 inference(unit_resolution,[status(thm)],[470, 2433])).
% 0.91/1.08 tff(2436,plain,
% 0.91/1.08 (c2_1(a230)),
% 0.91/1.08 inference(unit_resolution,[status(thm)],[478, 2433])).
% 0.91/1.08 tff(2437,plain,
% 0.91/1.08 ($false),
% 0.91/1.08 inference(unit_resolution,[status(thm)],[2369, 122, 2436, 2435, 1974, 2422, 2434, 1966, 1960, 2421, 2420, 10])).
% 0.91/1.08 tff(2438,plain,(hskp15 | c0_1(a229)), inference(lemma,lemma(discharge,[]))).
% 0.91/1.08 tff(2439,plain,
% 0.91/1.08 (hskp15),
% 0.91/1.08 inference(unit_resolution,[status(thm)],[2438, 11])).
% 0.91/1.08 tff(2440,plain,
% 0.91/1.08 (hskp27),
% 0.91/1.08 inference(unit_resolution,[status(thm)],[1086, 2439])).
% 0.91/1.08 tff(2441,plain,
% 0.91/1.08 (c2_1(a232)),
% 0.91/1.08 inference(unit_resolution,[status(thm)],[255, 2440])).
% 0.91/1.08 tff(2442,plain,
% 0.91/1.08 (c0_1(a232)),
% 0.91/1.08 inference(unit_resolution,[status(thm)],[263, 2440])).
% 0.91/1.08 tff(2443,plain,
% 0.91/1.08 (hskp6),
% 0.91/1.08 inference(unit_resolution,[status(thm)],[1831, 2383, 2027, 2021, 2372, 2020, 11])).
% 0.91/1.08 tff(2444,plain,
% 0.91/1.08 (c1_1(a221)),
% 0.91/1.08 inference(unit_resolution,[status(thm)],[1116, 2443])).
% 0.91/1.08 tff(2445,plain,
% 0.91/1.08 (c0_1(a221)),
% 0.91/1.08 inference(unit_resolution,[status(thm)],[1101, 2443])).
% 0.91/1.08 tff(2446,plain,
% 0.91/1.08 (c3_1(a232)),
% 0.91/1.08 inference(unit_resolution,[status(thm)],[247, 2440])).
% 0.91/1.08 tff(2447,plain,
% 0.91/1.08 (~c2_1(a221)),
% 0.91/1.08 inference(unit_resolution,[status(thm)],[1093, 2443])).
% 0.91/1.08 tff(2448,plain,
% 0.91/1.08 (c1_1(a229)),
% 0.91/1.08 inference(unit_resolution,[status(thm)],[1852, 2447, 2021, 2446, 2027, 2445, 2020, 2372, 2444, 11, 2442, 2441])).
% 0.91/1.08 tff(2449,plain,
% 0.91/1.08 (hskp20),
% 0.91/1.08 inference(unit_resolution,[status(thm)],[1624, 2383, 2027, 2021, 11, 2372, 2020])).
% 0.91/1.08 tff(2450,plain,
% 0.91/1.08 (c1_1(a259)),
% 0.91/1.08 inference(unit_resolution,[status(thm)],[362, 2449])).
% 0.91/1.08 tff(2451,plain,
% 0.91/1.08 (c0_1(a259)),
% 0.91/1.08 inference(unit_resolution,[status(thm)],[370, 2449])).
% 0.91/1.08 tff(2452,plain,
% 0.91/1.08 (c2_1(a238)),
% 0.91/1.08 inference(unit_resolution,[status(thm)],[224, 2439])).
% 0.91/1.08 tff(2453,plain,
% 0.91/1.08 (~c3_1(a259)),
% 0.91/1.08 inference(unit_resolution,[status(thm)],[354, 2449])).
% 0.91/1.08 tff(2454,plain,
% 0.91/1.08 (c0_1(a238)),
% 0.91/1.08 inference(unit_resolution,[status(thm)],[232, 2439])).
% 0.91/1.08 tff(2455,plain,
% 0.91/1.08 (~c3_1(a238)),
% 0.91/1.08 inference(unit_resolution,[status(thm)],[216, 2439])).
% 0.91/1.08 tff(2456,plain,
% 0.91/1.08 ((~c2_1(a229)) | (~c1_1(a229)) | c1_1(a238)),
% 0.91/1.08 inference(unit_resolution,[status(thm)],[1862, 122, 2454, 2452, 2455, 11, 1715])).
% 0.91/1.08 tff(2457,plain,
% 0.91/1.08 (c1_1(a238)),
% 0.91/1.08 inference(unit_resolution,[status(thm)],[2456, 2448, 2383])).
% 0.91/1.08 tff(2458,plain,
% 0.91/1.08 (hskp13),
% 0.91/1.08 inference(unit_resolution,[status(thm)],[1894, 2457, 11, 2454, 2453, 2452, 2448, 2451, 2450, 2372])).
% 0.91/1.08 tff(2459,plain,
% 0.91/1.08 (~c2_1(a236)),
% 0.91/1.08 inference(unit_resolution,[status(thm)],[758, 2458])).
% 0.91/1.08 tff(2460,plain,
% 0.91/1.08 (~c1_1(a236)),
% 0.91/1.08 inference(unit_resolution,[status(thm)],[764, 2458])).
% 0.91/1.08 tff(2461,plain,
% 0.91/1.08 (~c0_1(a236)),
% 0.91/1.08 inference(unit_resolution,[status(thm)],[1488, 122, 2383, 2372, 2460, 2459, 11, 1269, 2448])).
% 0.91/1.08 tff(2462,plain,
% 0.91/1.08 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c1_1(a236) | c2_1(a236) | (~ndr1_0) | (~c1_1(a213)) | (~c3_1(a213)) | c0_1(a213) | c0_1(a236) | (~c2_1(a238)) | (~c0_1(a238)) | (~c1_1(a238)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c1_1(a236) | c2_1(a236) | (~ndr1_0) | (~c1_1(a213)) | (~c3_1(a213)) | c0_1(a213) | c0_1(a236) | (~c2_1(a238)) | (~c0_1(a238)) | (~c1_1(a238)))),
% 0.91/1.08 inference(rewrite,[status(thm)],[])).
% 0.91/1.08 tff(2463,plain,
% 0.91/1.08 (((~ndr1_0) | (~c2_1(a238)) | (~c1_1(a238)) | (~c0_1(a238)) | c0_1(a213) | (~c3_1(a213)) | (~c1_1(a213)) | c1_1(a236) | c0_1(a236) | c2_1(a236)) <=> (c1_1(a236) | c2_1(a236) | (~ndr1_0) | (~c1_1(a213)) | (~c3_1(a213)) | c0_1(a213) | c0_1(a236) | (~c2_1(a238)) | (~c0_1(a238)) | (~c1_1(a238)))),
% 0.91/1.08 inference(rewrite,[status(thm)],[])).
% 0.91/1.08 tff(2464,plain,
% 0.91/1.08 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | (~c2_1(a238)) | (~c1_1(a238)) | (~c0_1(a238)) | c0_1(a213) | (~c3_1(a213)) | (~c1_1(a213)) | c1_1(a236) | c0_1(a236) | c2_1(a236))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c1_1(a236) | c2_1(a236) | (~ndr1_0) | (~c1_1(a213)) | (~c3_1(a213)) | c0_1(a213) | c0_1(a236) | (~c2_1(a238)) | (~c0_1(a238)) | (~c1_1(a238))))),
% 0.91/1.08 inference(monotonicity,[status(thm)],[2463])).
% 0.91/1.08 tff(2465,plain,
% 0.91/1.08 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | (~c2_1(a238)) | (~c1_1(a238)) | (~c0_1(a238)) | c0_1(a213) | (~c3_1(a213)) | (~c1_1(a213)) | c1_1(a236) | c0_1(a236) | c2_1(a236))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c1_1(a236) | c2_1(a236) | (~ndr1_0) | (~c1_1(a213)) | (~c3_1(a213)) | c0_1(a213) | c0_1(a236) | (~c2_1(a238)) | (~c0_1(a238)) | (~c1_1(a238)))),
% 0.91/1.08 inference(transitivity,[status(thm)],[2464, 2462])).
% 0.91/1.08 tff(2466,plain,
% 0.91/1.08 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | (~c2_1(a238)) | (~c1_1(a238)) | (~c0_1(a238)) | c0_1(a213) | (~c3_1(a213)) | (~c1_1(a213)) | c1_1(a236) | c0_1(a236) | c2_1(a236))),
% 0.91/1.08 inference(quant_inst,[status(thm)],[])).
% 0.91/1.08 tff(2467,plain,
% 0.91/1.08 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c1_1(a236) | c2_1(a236) | (~ndr1_0) | (~c1_1(a213)) | (~c3_1(a213)) | c0_1(a213) | c0_1(a236) | (~c2_1(a238)) | (~c0_1(a238)) | (~c1_1(a238))),
% 0.91/1.08 inference(modus_ponens,[status(thm)],[2466, 2465])).
% 0.91/1.08 tff(2468,plain,
% 0.91/1.08 ($false),
% 0.91/1.08 inference(unit_resolution,[status(thm)],[2467, 122, 2454, 2452, 2021, 2027, 2460, 2459, 627, 22, 2457, 2461])).
% 0.91/1.09 tff(2469,plain,(c0_1(a213) | c0_1(a229)), inference(lemma,lemma(discharge,[]))).
% 0.91/1.09 tff(2470,plain,
% 0.91/1.09 (c0_1(a213)),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[2469, 11])).
% 0.91/1.09 tff(2471,plain,
% 0.91/1.09 ((~c0_1(a213)) | c1_1(a229) | (~c3_1(a229))),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[1525, 122, 2021, 2027, 11, 583])).
% 0.91/1.09 tff(2472,plain,
% 0.91/1.09 (c1_1(a229)),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[2471, 2470, 2372])).
% 0.91/1.09 tff(2473,plain,
% 0.91/1.09 (~c2_1(a229)),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[1624, 132, 2027, 2021, 11, 2372, 2020])).
% 0.91/1.09 tff(2474,plain,
% 0.91/1.09 (hskp10),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[2350, 132, 2452, 2455, 2454, 2441, 2446, 2442])).
% 0.91/1.09 tff(2475,plain,
% 0.91/1.09 ($false),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[1052, 2474, 2473])).
% 0.91/1.09 tff(2476,plain,(hskp20 | c0_1(a229)), inference(lemma,lemma(discharge,[]))).
% 0.91/1.09 tff(2477,plain,
% 0.91/1.09 (hskp20),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[2476, 11])).
% 0.91/1.09 tff(2478,plain,
% 0.91/1.09 (c1_1(a259)),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[362, 2477])).
% 0.91/1.09 tff(2479,plain,
% 0.91/1.09 (c0_1(a259)),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[370, 2477])).
% 0.91/1.09 tff(2480,plain,
% 0.91/1.09 (~c3_1(a259)),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[354, 2477])).
% 0.91/1.09 tff(2481,plain,
% 0.91/1.09 (~hskp10),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[1052, 2192])).
% 0.91/1.09 tff(2482,plain,
% 0.91/1.09 (hskp11),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[2432, 2481, 2472, 2192])).
% 0.91/1.09 tff(2483,plain,
% 0.91/1.09 (~c1_1(a230)),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[442, 2482])).
% 0.91/1.09 tff(2484,plain,
% 0.91/1.09 (c3_1(a230)),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[470, 2482])).
% 0.91/1.09 tff(2485,plain,
% 0.91/1.09 (c2_1(a230)),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[478, 2482])).
% 0.91/1.09 tff(2486,plain,
% 0.91/1.09 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | (c2_1(a229) | c1_1(a230) | c0_1(a229) | c2_1(a225) | c3_1(a225) | (~ndr1_0) | (~c0_1(a225)) | (~c3_1(a229)) | (~c3_1(a230)) | (~c2_1(a230)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c2_1(a229) | c1_1(a230) | c0_1(a229) | c2_1(a225) | c3_1(a225) | (~ndr1_0) | (~c0_1(a225)) | (~c3_1(a229)) | (~c3_1(a230)) | (~c2_1(a230)))),
% 0.91/1.09 inference(rewrite,[status(thm)],[])).
% 0.91/1.09 tff(2487,plain,
% 0.91/1.09 (((~ndr1_0) | c3_1(a225) | c2_1(a225) | (~c0_1(a225)) | c1_1(a230) | (~c3_1(a230)) | (~c2_1(a230)) | c0_1(a229) | c2_1(a229) | (~c3_1(a229))) <=> (c2_1(a229) | c1_1(a230) | c0_1(a229) | c2_1(a225) | c3_1(a225) | (~ndr1_0) | (~c0_1(a225)) | (~c3_1(a229)) | (~c3_1(a230)) | (~c2_1(a230)))),
% 0.91/1.09 inference(rewrite,[status(thm)],[])).
% 0.91/1.09 tff(2488,plain,
% 0.91/1.09 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a225) | c2_1(a225) | (~c0_1(a225)) | c1_1(a230) | (~c3_1(a230)) | (~c2_1(a230)) | c0_1(a229) | c2_1(a229) | (~c3_1(a229)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | (c2_1(a229) | c1_1(a230) | c0_1(a229) | c2_1(a225) | c3_1(a225) | (~ndr1_0) | (~c0_1(a225)) | (~c3_1(a229)) | (~c3_1(a230)) | (~c2_1(a230))))),
% 0.91/1.09 inference(monotonicity,[status(thm)],[2487])).
% 0.91/1.09 tff(2489,plain,
% 0.91/1.09 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a225) | c2_1(a225) | (~c0_1(a225)) | c1_1(a230) | (~c3_1(a230)) | (~c2_1(a230)) | c0_1(a229) | c2_1(a229) | (~c3_1(a229)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c2_1(a229) | c1_1(a230) | c0_1(a229) | c2_1(a225) | c3_1(a225) | (~ndr1_0) | (~c0_1(a225)) | (~c3_1(a229)) | (~c3_1(a230)) | (~c2_1(a230)))),
% 0.91/1.09 inference(transitivity,[status(thm)],[2488, 2486])).
% 0.91/1.09 tff(2490,plain,
% 0.91/1.09 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a225) | c2_1(a225) | (~c0_1(a225)) | c1_1(a230) | (~c3_1(a230)) | (~c2_1(a230)) | c0_1(a229) | c2_1(a229) | (~c3_1(a229)))),
% 0.91/1.09 inference(quant_inst,[status(thm)],[])).
% 0.91/1.09 tff(2491,plain,
% 0.91/1.09 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c2_1(a229) | c1_1(a230) | c0_1(a229) | c2_1(a225) | c3_1(a225) | (~ndr1_0) | (~c0_1(a225)) | (~c3_1(a229)) | (~c3_1(a230)) | (~c2_1(a230))),
% 0.91/1.09 inference(modus_ponens,[status(thm)],[2490, 2489])).
% 0.91/1.09 tff(2492,plain,
% 0.91/1.09 ($false),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[2491, 122, 2485, 2484, 2192, 2372, 1974, 2483, 11, 1966, 1960, 10])).
% 0.91/1.09 tff(2493,plain,(c2_1(a229) | c0_1(a229)), inference(lemma,lemma(discharge,[]))).
% 0.91/1.09 tff(2494,plain,
% 0.91/1.09 (c2_1(a229)),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[2493, 11])).
% 0.91/1.09 tff(2495,plain,
% 0.91/1.09 (c1_1(a238)),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[2456, 2494, 2472])).
% 0.91/1.09 tff(2496,plain,
% 0.91/1.09 (hskp13),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[1894, 2495, 11, 2454, 2480, 2452, 2472, 2479, 2478, 2372])).
% 0.91/1.09 tff(2497,plain,
% 0.91/1.09 (~c2_1(a236)),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[758, 2496])).
% 0.91/1.09 tff(2498,plain,
% 0.91/1.09 (~c1_1(a236)),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[764, 2496])).
% 0.91/1.09 tff(2499,plain,
% 0.91/1.09 (~c0_1(a236)),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[1488, 122, 2494, 2372, 2498, 2497, 11, 1269, 2472])).
% 0.91/1.09 tff(2500,plain,
% 0.91/1.09 ($false),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[1903, 122, 2454, 2452, 2372, 2498, 2497, 11, 627, 2472, 2495, 2499])).
% 0.91/1.09 tff(2501,plain,(c0_1(a229)), inference(lemma,lemma(discharge,[]))).
% 0.91/1.09 tff(2502,plain,
% 0.91/1.09 (~hskp10),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[1043, 2501])).
% 0.91/1.09 tff(2503,plain,
% 0.91/1.09 (c0_1(a213)),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[2037, 2502])).
% 0.91/1.09 tff(2504,plain,
% 0.91/1.09 (hskp11),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[436, 132, 2502, 2021, 2020])).
% 0.91/1.09 tff(2505,plain,
% 0.91/1.09 (hskp27),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[2060, 2504])).
% 0.91/1.09 tff(2506,plain,
% 0.91/1.09 (c0_1(a232)),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[263, 2505])).
% 0.91/1.09 tff(2507,plain,
% 0.91/1.09 (c3_1(a232)),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[247, 2505])).
% 0.91/1.09 tff(2508,plain,
% 0.91/1.09 (c2_1(a232)),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[255, 2505])).
% 0.91/1.09 tff(2509,plain,
% 0.91/1.09 (hskp15),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[2173, 2508, 132, 2506, 2507])).
% 0.91/1.09 tff(2510,plain,
% 0.91/1.09 (c0_1(a238)),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[232, 2509])).
% 0.91/1.09 tff(2511,plain,
% 0.91/1.09 (c2_1(a238)),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[224, 2509])).
% 0.91/1.09 tff(2512,plain,
% 0.91/1.09 (~c3_1(a238)),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[216, 2509])).
% 0.91/1.09 tff(2513,plain,
% 0.91/1.09 ($false),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[2350, 2512, 2511, 2502, 132, 2510, 2508, 2507, 2506])).
% 0.91/1.09 tff(2514,plain,(hskp20), inference(lemma,lemma(discharge,[]))).
% 0.91/1.09 tff(2515,plain,
% 0.91/1.09 (~c3_1(a259)),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[354, 2514])).
% 0.91/1.09 tff(2516,plain,
% 0.91/1.09 (c1_1(a259)),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[362, 2514])).
% 0.91/1.09 tff(2517,plain,
% 0.91/1.09 (c0_1(a259)),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[370, 2514])).
% 0.91/1.09 tff(2518,plain,
% 0.91/1.09 (hskp3),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[2089, 122, 2517, 2516, 2021, 2027, 2515, 2048, 2503])).
% 0.91/1.09 tff(2519,plain,
% 0.91/1.09 (~c2_1(a216)),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[312, 2518])).
% 0.91/1.09 tff(2520,plain,
% 0.91/1.09 (~c0_1(a216)),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[318, 2518])).
% 0.91/1.09 tff(2521,plain,
% 0.91/1.09 (c3_1(a216)),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[328, 2518])).
% 0.91/1.09 tff(2522,plain,
% 0.91/1.09 (c1_1(a216)),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[890, 122, 2521, 2021, 2027, 2520, 583, 2503])).
% 0.91/1.09 tff(2523,plain,
% 0.91/1.09 (hskp11),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[898, 122, 2502, 2520, 2519, 32, 2522])).
% 0.91/1.09 tff(2524,plain,
% 0.91/1.09 (~c1_1(a230)),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[442, 2523])).
% 0.91/1.09 tff(2525,plain,
% 0.91/1.09 (c3_1(a230)),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[470, 2523])).
% 0.91/1.09 tff(2526,plain,
% 0.91/1.09 (c2_1(a230)),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[478, 2523])).
% 0.91/1.09 tff(2527,plain,
% 0.91/1.09 ($false),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[2369, 122, 2526, 2525, 1974, 2521, 2524, 1966, 1960, 2520, 2519, 10])).
% 0.91/1.09 % SZS output end Proof
% 0.91/1.09 % E exiting
%------------------------------------------------------------------------------