%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN459-1 : TPTP v9.0.0. Released v2.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n013.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 05:39:11 AM UTC 2025
% Result : Unsatisfiable 0.72s 0.87s
% Output : Proof 0.88s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SYN459-1 : TPTP v9.0.0. Released v2.1.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.11/0.32 % Computer : n013.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Fri Jun 20 12:36:23 EDT 2025
% 0.11/0.32 % CPUTime :
% 0.72/0.87 % SZS status Unsatisfiable
% 0.72/0.87 % SZS output start Proof
% 0.72/0.87 tff(c2_1_type, type, (
% 0.72/0.87 c2_1: $i > $o)).
% 0.72/0.87 tff(a200_type, type, (
% 0.72/0.87 a200: $i)).
% 0.72/0.87 tff(c0_1_type, type, (
% 0.72/0.87 c0_1: $i > $o)).
% 0.72/0.87 tff(hskp10_type, type, (
% 0.72/0.87 hskp10: $o)).
% 0.72/0.87 tff(c1_1_type, type, (
% 0.72/0.87 c1_1: $i > $o)).
% 0.72/0.87 tff(c3_1_type, type, (
% 0.72/0.87 c3_1: $i > $o)).
% 0.72/0.87 tff(ndr1_0_type, type, (
% 0.72/0.87 ndr1_0: $o)).
% 0.72/0.87 tff(a191_type, type, (
% 0.72/0.87 a191: $i)).
% 0.72/0.87 tff(hskp2_type, type, (
% 0.72/0.87 hskp2: $o)).
% 0.72/0.87 tff(a221_type, type, (
% 0.72/0.87 a221: $i)).
% 0.72/0.87 tff(a214_type, type, (
% 0.72/0.87 a214: $i)).
% 0.72/0.87 tff(hskp5_type, type, (
% 0.72/0.87 hskp5: $o)).
% 0.72/0.87 tff(a194_type, type, (
% 0.72/0.87 a194: $i)).
% 0.72/0.87 tff(a190_type, type, (
% 0.72/0.87 a190: $i)).
% 0.72/0.87 tff(hskp1_type, type, (
% 0.72/0.87 hskp1: $o)).
% 0.72/0.87 tff(hskp19_type, type, (
% 0.72/0.87 hskp19: $o)).
% 0.72/0.87 tff(a215_type, type, (
% 0.72/0.87 a215: $i)).
% 0.72/0.87 tff(hskp15_type, type, (
% 0.72/0.87 hskp15: $o)).
% 0.72/0.87 tff(a230_type, type, (
% 0.72/0.87 a230: $i)).
% 0.72/0.87 tff(hskp25_type, type, (
% 0.72/0.87 hskp25: $o)).
% 0.72/0.87 tff(a225_type, type, (
% 0.72/0.87 a225: $i)).
% 0.72/0.87 tff(a195_type, type, (
% 0.72/0.87 a195: $i)).
% 0.72/0.87 tff(hskp6_type, type, (
% 0.72/0.87 hskp6: $o)).
% 0.72/0.87 tff(a209_type, type, (
% 0.72/0.87 a209: $i)).
% 0.72/0.87 tff(hskp13_type, type, (
% 0.72/0.87 hskp13: $o)).
% 0.72/0.87 tff(a257_type, type, (
% 0.72/0.87 a257: $i)).
% 0.72/0.87 tff(hskp21_type, type, (
% 0.72/0.87 hskp21: $o)).
% 0.72/0.87 tff(hskp24_type, type, (
% 0.72/0.87 hskp24: $o)).
% 0.72/0.87 tff(a189_type, type, (
% 0.72/0.87 a189: $i)).
% 0.72/0.87 tff(hskp23_type, type, (
% 0.72/0.87 hskp23: $o)).
% 0.72/0.87 tff(a199_type, type, (
% 0.72/0.87 a199: $i)).
% 0.72/0.87 tff(hskp9_type, type, (
% 0.72/0.87 hskp9: $o)).
% 0.72/0.87 tff(hskp0_type, type, (
% 0.72/0.87 hskp0: $o)).
% 0.72/0.87 tff(a188_type, type, (
% 0.72/0.87 a188: $i)).
% 0.72/0.87 tff(a210_type, type, (
% 0.72/0.87 a210: $i)).
% 0.72/0.87 tff(hskp14_type, type, (
% 0.72/0.87 hskp14: $o)).
% 0.72/0.87 tff(hskp7_type, type, (
% 0.72/0.87 hskp7: $o)).
% 0.72/0.87 tff(a197_type, type, (
% 0.72/0.87 a197: $i)).
% 0.72/0.87 tff(hskp8_type, type, (
% 0.72/0.87 hskp8: $o)).
% 0.72/0.87 tff(a198_type, type, (
% 0.72/0.87 a198: $i)).
% 0.72/0.87 tff(hskp22_type, type, (
% 0.72/0.87 hskp22: $o)).
% 0.72/0.87 tff(a259_type, type, (
% 0.72/0.87 a259: $i)).
% 0.72/0.87 tff(hskp16_type, type, (
% 0.72/0.87 hskp16: $o)).
% 0.72/0.87 tff(1,plain,
% 0.72/0.87 (^[V: $i, U: $i] : refl((hskp10 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V)) <=> (hskp10 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V)))),
% 0.72/0.87 inference(bind,[status(th)],[])).
% 0.72/0.87 tff(2,plain,
% 0.72/0.87 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V)) <=> ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))),
% 0.72/0.87 inference(quant_intro,[status(thm)],[1])).
% 0.72/0.87 tff(3,plain,
% 0.72/0.87 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V)) <=> ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))),
% 0.72/0.87 inference(rewrite,[status(thm)],[])).
% 0.72/0.87 tff(4,plain,
% 0.72/0.87 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~ndr1_0) | (~c1_1(U))) | (~c3_1(U))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)))), (((((~ndr1_0) | (~c1_1(U))) | (~c3_1(U))) | c1_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | c1_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | c1_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V))), (((((~ndr1_0) | (~c1_1(U))) | (~c3_1(U))) | c1_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V)))), ((((((~ndr1_0) | (~c1_1(U))) | (~c3_1(U))) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V))), ((((((~ndr1_0) | (~c1_1(U))) | (~c3_1(U))) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V)))), (((((((~ndr1_0) | (~c1_1(U))) | (~c3_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))), (((((((~ndr1_0) | (~c1_1(U))) | (~c3_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V)))), ((((((((~ndr1_0) | (~c1_1(U))) | (~c3_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V)) | c0_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))), ((((((((~ndr1_0) | (~c1_1(U))) | (~c3_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V)))), (((((((((~ndr1_0) | (~c1_1(U))) | (~c3_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) | hskp10) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V)) | hskp10))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V)) | hskp10) <=> (hskp10 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))), (((((((((~ndr1_0) | (~c1_1(U))) | (~c3_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) | hskp10) <=> (hskp10 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))))),
% 0.72/0.87 inference(bind,[status(th)],[])).
% 0.72/0.87 tff(5,plain,
% 0.72/0.87 (![V: $i, U: $i] : ((((((((~ndr1_0) | (~c1_1(U))) | (~c3_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) | hskp10) <=> ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))),
% 0.72/0.87 inference(quant_intro,[status(thm)],[4])).
% 0.72/0.87 tff(6,axiom,(![V: $i, U: $i] : ((((((((~ndr1_0) | (~c1_1(U))) | (~c3_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) | hskp10)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause134')).
% 0.72/0.87 tff(7,plain,
% 0.72/0.87 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))),
% 0.72/0.87 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.72/0.87 tff(8,plain,
% 0.72/0.87 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))),
% 0.72/0.87 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.72/0.87 tff(9,plain,(
% 0.72/0.87 ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))),
% 0.72/0.87 inference(skolemize,[status(sab)],[8])).
% 0.72/0.87 tff(10,plain,
% 0.72/0.87 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))),
% 0.72/0.87 inference(modus_ponens,[status(thm)],[9, 2])).
% 0.72/0.87 tff(11,assumption,(~c2_1(a194)), introduced(assumption)).
% 0.72/0.87 tff(12,assumption,(~c1_1(a194)), introduced(assumption)).
% 0.72/0.87 tff(13,assumption,(~c3_1(a190)), introduced(assumption)).
% 0.72/0.87 tff(14,assumption,(~hskp2), introduced(assumption)).
% 0.72/0.87 tff(15,assumption,(c1_1(a214)), introduced(assumption)).
% 0.72/0.87 tff(16,plain,
% 0.72/0.87 (^[V: $i, U: $i] : refl((hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))) <=> (hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))))),
% 0.72/0.87 inference(bind,[status(th)],[])).
% 0.72/0.87 tff(17,plain,
% 0.72/0.87 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 0.72/0.87 inference(quant_intro,[status(thm)],[16])).
% 0.72/0.87 tff(18,plain,
% 0.72/0.87 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 0.72/0.87 inference(rewrite,[status(thm)],[])).
% 0.72/0.87 tff(19,plain,
% 0.72/0.87 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c0_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c0_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(V)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(V))))), (((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)))), (((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V))))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V))))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V))))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | hskp2) <=> (((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))) | hskp2))), rewrite((((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))) | hskp2) <=> (hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | hskp2) <=> (hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))))),
% 0.72/0.87 inference(bind,[status(th)],[])).
% 0.72/0.87 tff(20,plain,
% 0.72/0.87 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | hskp2) <=> ![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 0.72/0.87 inference(quant_intro,[status(thm)],[19])).
% 0.72/0.87 tff(21,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | hskp2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause138')).
% 0.72/0.87 tff(22,plain,
% 0.72/0.87 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 0.72/0.87 inference(modus_ponens,[status(thm)],[21, 20])).
% 0.72/0.87 tff(23,plain,
% 0.72/0.87 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 0.72/0.87 inference(modus_ponens,[status(thm)],[22, 18])).
% 0.72/0.87 tff(24,plain,(
% 0.72/0.87 ![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 0.72/0.87 inference(skolemize,[status(sab)],[23])).
% 0.72/0.87 tff(25,plain,
% 0.72/0.87 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 0.72/0.87 inference(modus_ponens,[status(thm)],[24, 17])).
% 0.72/0.87 tff(26,plain,
% 0.72/0.87 (^[V: $i, U: $i] : refl((hskp5 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V))) <=> (hskp5 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V))))),
% 0.72/0.87 inference(bind,[status(th)],[])).
% 0.72/0.87 tff(27,plain,
% 0.72/0.87 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.72/0.87 inference(quant_intro,[status(thm)],[26])).
% 0.72/0.87 tff(28,plain,
% 0.72/0.87 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.72/0.87 inference(rewrite,[status(thm)],[])).
% 0.72/0.87 tff(29,plain,
% 0.72/0.87 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c2_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c2_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(V)))), ((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(V))))), (((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(V))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(V))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(V)))), (((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(V))))), ((((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | (~c1_1(V)))), ((((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | (~c1_1(V))))), (((((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | (~c1_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)))), (((((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V))))), ((((((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V))) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))), ((((((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V))))), (((((((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c3_1(V)) | hskp5) <=> (((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V))) | hskp5))), rewrite((((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V))) | hskp5) <=> (hskp5 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))), (((((((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c3_1(V)) | hskp5) <=> (hskp5 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))))),
% 0.72/0.87 inference(bind,[status(th)],[])).
% 0.72/0.87 tff(30,plain,
% 0.72/0.87 (![V: $i, U: $i] : ((((((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c3_1(V)) | hskp5) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.72/0.87 inference(quant_intro,[status(thm)],[29])).
% 0.72/0.87 tff(31,axiom,(![V: $i, U: $i] : ((((((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c3_1(V)) | hskp5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause133')).
% 0.72/0.87 tff(32,plain,
% 0.72/0.87 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.72/0.87 inference(modus_ponens,[status(thm)],[31, 30])).
% 0.72/0.87 tff(33,plain,
% 0.72/0.87 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.72/0.87 inference(modus_ponens,[status(thm)],[32, 28])).
% 0.72/0.87 tff(34,plain,(
% 0.72/0.87 ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.72/0.87 inference(skolemize,[status(sab)],[33])).
% 0.72/0.87 tff(35,plain,
% 0.72/0.87 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.72/0.87 inference(modus_ponens,[status(thm)],[34, 27])).
% 0.72/0.87 tff(36,assumption,(~hskp15), introduced(assumption)).
% 0.72/0.87 tff(37,assumption,(hskp2), introduced(assumption)).
% 0.72/0.87 tff(38,plain,
% 0.72/0.87 (((~hskp2) | (~c3_1(a191))) <=> ((~hskp2) | (~c3_1(a191)))),
% 0.72/0.87 inference(rewrite,[status(thm)],[])).
% 0.72/0.87 tff(39,plain,
% 0.72/0.87 (((~c3_1(a191)) | (~hskp2)) <=> ((~hskp2) | (~c3_1(a191)))),
% 0.72/0.87 inference(rewrite,[status(thm)],[])).
% 0.72/0.87 tff(40,axiom,((~c3_1(a191)) | (~hskp2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause107')).
% 0.72/0.87 tff(41,plain,
% 0.72/0.87 ((~hskp2) | (~c3_1(a191))),
% 0.72/0.87 inference(modus_ponens,[status(thm)],[40, 39])).
% 0.72/0.87 tff(42,plain,
% 0.72/0.87 ((~hskp2) | (~c3_1(a191))),
% 0.72/0.87 inference(modus_ponens,[status(thm)],[41, 38])).
% 0.72/0.87 tff(43,plain,
% 0.72/0.87 (~c3_1(a191)),
% 0.72/0.87 inference(unit_resolution,[status(thm)],[42, 37])).
% 0.72/0.87 tff(44,plain,
% 0.72/0.87 (((~hskp2) | (~c2_1(a191))) <=> ((~hskp2) | (~c2_1(a191)))),
% 0.72/0.87 inference(rewrite,[status(thm)],[])).
% 0.72/0.87 tff(45,plain,
% 0.72/0.87 (((~c2_1(a191)) | (~hskp2)) <=> ((~hskp2) | (~c2_1(a191)))),
% 0.72/0.87 inference(rewrite,[status(thm)],[])).
% 0.72/0.87 tff(46,axiom,((~c2_1(a191)) | (~hskp2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause106')).
% 0.72/0.87 tff(47,plain,
% 0.72/0.87 ((~hskp2) | (~c2_1(a191))),
% 0.72/0.87 inference(modus_ponens,[status(thm)],[46, 45])).
% 0.72/0.87 tff(48,plain,
% 0.72/0.87 ((~hskp2) | (~c2_1(a191))),
% 0.72/0.87 inference(modus_ponens,[status(thm)],[47, 44])).
% 0.72/0.87 tff(49,plain,
% 0.72/0.87 (~c2_1(a191)),
% 0.72/0.87 inference(unit_resolution,[status(thm)],[48, 37])).
% 0.72/0.87 tff(50,plain,
% 0.72/0.87 (((~hskp2) | (~c1_1(a191))) <=> ((~hskp2) | (~c1_1(a191)))),
% 0.72/0.87 inference(rewrite,[status(thm)],[])).
% 0.72/0.87 tff(51,plain,
% 0.72/0.87 (((~c1_1(a191)) | (~hskp2)) <=> ((~hskp2) | (~c1_1(a191)))),
% 0.72/0.87 inference(rewrite,[status(thm)],[])).
% 0.72/0.87 tff(52,axiom,((~c1_1(a191)) | (~hskp2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause105')).
% 0.72/0.87 tff(53,plain,
% 0.72/0.87 ((~hskp2) | (~c1_1(a191))),
% 0.72/0.87 inference(modus_ponens,[status(thm)],[52, 51])).
% 0.72/0.87 tff(54,plain,
% 0.72/0.87 ((~hskp2) | (~c1_1(a191))),
% 0.72/0.87 inference(modus_ponens,[status(thm)],[53, 50])).
% 0.72/0.87 tff(55,plain,
% 0.72/0.87 (~c1_1(a191)),
% 0.72/0.87 inference(unit_resolution,[status(thm)],[54, 37])).
% 0.72/0.87 tff(56,plain,
% 0.72/0.87 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c1_1(U) | c2_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) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W))))),
% 0.72/0.87 inference(bind,[status(th)],[])).
% 0.72/0.87 tff(57,plain,
% 0.72/0.87 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_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) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 0.72/0.87 inference(quant_intro,[status(thm)],[56])).
% 0.72/0.87 tff(58,plain,
% 0.72/0.87 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_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) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 0.72/0.87 inference(rewrite,[status(thm)],[])).
% 0.72/0.87 tff(59,plain,
% 0.72/0.87 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c0_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c0_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(V)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(V))))), (((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)))), (((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c2_1(W))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))) | (~c2_1(W))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c2_1(W)))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c2_1(W))))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c1_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c2_1(W))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c2_1(W))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c2_1(W)))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c2_1(W))))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c1_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c2_1(W))) | c2_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c2_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c2_1(W)))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c2_1(W))))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c1_1(U)) | c2_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c2_1(W))) | c0_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c2_1(W))) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | (~c2_1(W)))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c1_1(U)) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | (~c2_1(W))))), ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | (~c2_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | (~c2_1(W))) | c0_1(W)) <=> ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)))), ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W) | (~c2_1(W))))), (((((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c0_1(W)) | c1_1(W)) <=> (((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W) | (~c2_1(W))) | c1_1(W)))), rewrite((((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W) | (~c2_1(W))) | c1_1(W)) <=> ((~ndr1_0) | c1_1(U) | c2_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)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))))),
% 0.72/0.88 inference(bind,[status(th)],[])).
% 0.72/0.88 tff(60,plain,
% 0.72/0.88 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c0_1(W)) | c1_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 0.72/0.88 inference(quant_intro,[status(thm)],[59])).
% 0.72/0.88 tff(61,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c0_1(W)) | c1_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause155')).
% 0.72/0.88 tff(62,plain,
% 0.72/0.88 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 0.72/0.88 inference(modus_ponens,[status(thm)],[61, 60])).
% 0.72/0.88 tff(63,plain,
% 0.72/0.88 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 0.72/0.88 inference(modus_ponens,[status(thm)],[62, 58])).
% 0.72/0.88 tff(64,plain,(
% 0.72/0.88 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 0.72/0.88 inference(skolemize,[status(sab)],[63])).
% 0.72/0.88 tff(65,plain,
% 0.72/0.88 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 0.72/0.88 inference(modus_ponens,[status(thm)],[64, 57])).
% 0.72/0.88 tff(66,assumption,(~c2_1(a191)), introduced(assumption)).
% 0.72/0.88 tff(67,assumption,(~c1_1(a191)), introduced(assumption)).
% 0.72/0.88 tff(68,assumption,(~c3_1(a191)), introduced(assumption)).
% 0.72/0.88 tff(69,assumption,(~hskp5), introduced(assumption)).
% 0.72/0.88 tff(70,plain,
% 0.72/0.88 ((hskp21 | hskp15 | hskp5) <=> (hskp21 | hskp15 | hskp5)),
% 0.72/0.88 inference(rewrite,[status(thm)],[])).
% 0.72/0.88 tff(71,plain,
% 0.72/0.88 (((hskp15 | hskp5) | hskp21) <=> (hskp21 | hskp15 | hskp5)),
% 0.72/0.88 inference(rewrite,[status(thm)],[])).
% 0.72/0.88 tff(72,plain,
% 0.72/0.88 ((hskp5 | hskp15) <=> (hskp15 | hskp5)),
% 0.72/0.88 inference(rewrite,[status(thm)],[])).
% 0.72/0.88 tff(73,plain,
% 0.72/0.88 (((hskp5 | hskp15) | hskp21) <=> ((hskp15 | hskp5) | hskp21)),
% 0.72/0.88 inference(monotonicity,[status(thm)],[72])).
% 0.72/0.88 tff(74,plain,
% 0.72/0.88 (((hskp5 | hskp15) | hskp21) <=> (hskp21 | hskp15 | hskp5)),
% 0.72/0.88 inference(transitivity,[status(thm)],[73, 71])).
% 0.72/0.88 tff(75,axiom,((hskp5 | hskp15) | hskp21), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause30')).
% 0.72/0.88 tff(76,plain,
% 0.72/0.88 (hskp21 | hskp15 | hskp5),
% 0.72/0.88 inference(modus_ponens,[status(thm)],[75, 74])).
% 0.72/0.88 tff(77,plain,
% 0.72/0.88 (hskp21 | hskp15 | hskp5),
% 0.72/0.88 inference(modus_ponens,[status(thm)],[76, 70])).
% 0.72/0.88 tff(78,plain,
% 0.72/0.88 (hskp21 | hskp15 | hskp5),
% 0.72/0.88 inference(modus_ponens,[status(thm)],[77, 70])).
% 0.72/0.88 tff(79,plain,
% 0.72/0.88 (hskp21 | hskp15 | hskp5),
% 0.72/0.88 inference(modus_ponens,[status(thm)],[78, 70])).
% 0.72/0.88 tff(80,plain,
% 0.72/0.88 (hskp21 | hskp15 | hskp5),
% 0.72/0.88 inference(modus_ponens,[status(thm)],[79, 70])).
% 0.72/0.88 tff(81,plain,
% 0.72/0.88 (hskp21),
% 0.72/0.88 inference(unit_resolution,[status(thm)],[80, 69, 36])).
% 0.72/0.88 tff(82,plain,
% 0.72/0.88 (((~hskp21) | (~c1_1(a257))) <=> ((~hskp21) | (~c1_1(a257)))),
% 0.72/0.88 inference(rewrite,[status(thm)],[])).
% 0.72/0.88 tff(83,plain,
% 0.72/0.88 (((~c1_1(a257)) | (~hskp21)) <=> ((~hskp21) | (~c1_1(a257)))),
% 0.72/0.88 inference(rewrite,[status(thm)],[])).
% 0.72/0.88 tff(84,axiom,((~c1_1(a257)) | (~hskp21)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause72')).
% 0.72/0.88 tff(85,plain,
% 0.72/0.88 ((~hskp21) | (~c1_1(a257))),
% 0.72/0.88 inference(modus_ponens,[status(thm)],[84, 83])).
% 0.72/0.88 tff(86,plain,
% 0.72/0.88 ((~hskp21) | (~c1_1(a257))),
% 0.72/0.88 inference(modus_ponens,[status(thm)],[85, 82])).
% 0.72/0.88 tff(87,plain,
% 0.72/0.88 (~c1_1(a257)),
% 0.72/0.88 inference(unit_resolution,[status(thm)],[86, 81])).
% 0.72/0.88 tff(88,plain,
% 0.72/0.88 (((~hskp21) | (~c3_1(a257))) <=> ((~hskp21) | (~c3_1(a257)))),
% 0.72/0.88 inference(rewrite,[status(thm)],[])).
% 0.72/0.88 tff(89,plain,
% 0.72/0.88 (((~c3_1(a257)) | (~hskp21)) <=> ((~hskp21) | (~c3_1(a257)))),
% 0.72/0.88 inference(rewrite,[status(thm)],[])).
% 0.72/0.88 tff(90,axiom,((~c3_1(a257)) | (~hskp21)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause73')).
% 0.72/0.88 tff(91,plain,
% 0.72/0.88 ((~hskp21) | (~c3_1(a257))),
% 0.72/0.88 inference(modus_ponens,[status(thm)],[90, 89])).
% 0.72/0.88 tff(92,plain,
% 0.72/0.88 ((~hskp21) | (~c3_1(a257))),
% 0.72/0.88 inference(modus_ponens,[status(thm)],[91, 88])).
% 0.72/0.88 tff(93,plain,
% 0.72/0.88 (~c3_1(a257)),
% 0.72/0.88 inference(unit_resolution,[status(thm)],[92, 81])).
% 0.72/0.88 tff(94,plain,
% 0.72/0.88 (((~hskp21) | c2_1(a257)) <=> ((~hskp21) | c2_1(a257))),
% 0.72/0.88 inference(rewrite,[status(thm)],[])).
% 0.72/0.88 tff(95,axiom,((~hskp21) | c2_1(a257)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause44')).
% 0.72/0.88 tff(96,plain,
% 0.72/0.88 ((~hskp21) | c2_1(a257)),
% 0.72/0.88 inference(modus_ponens,[status(thm)],[95, 94])).
% 0.72/0.88 tff(97,plain,
% 0.72/0.88 ((~hskp21) | c2_1(a257)),
% 0.72/0.88 inference(modus_ponens,[status(thm)],[96, 94])).
% 0.72/0.88 tff(98,plain,
% 0.72/0.88 ((~hskp21) | c2_1(a257)),
% 0.72/0.88 inference(modus_ponens,[status(thm)],[97, 94])).
% 0.72/0.88 tff(99,plain,
% 0.72/0.88 ((~hskp21) | c2_1(a257)),
% 0.72/0.88 inference(modus_ponens,[status(thm)],[98, 94])).
% 0.72/0.88 tff(100,plain,
% 0.72/0.88 ((~hskp21) | c2_1(a257)),
% 0.72/0.88 inference(modus_ponens,[status(thm)],[99, 94])).
% 0.72/0.88 tff(101,plain,
% 0.72/0.88 (c2_1(a257)),
% 0.72/0.88 inference(unit_resolution,[status(thm)],[100, 81])).
% 0.72/0.88 tff(102,assumption,(~hskp1), introduced(assumption)).
% 0.72/0.88 tff(103,plain,
% 0.72/0.88 (^[U: $i] : refl((hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)) <=> (hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)))),
% 0.72/0.88 inference(bind,[status(th)],[])).
% 0.72/0.88 tff(104,plain,
% 0.72/0.88 (![U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)) <=> ![U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))),
% 0.72/0.88 inference(quant_intro,[status(thm)],[103])).
% 0.72/0.88 tff(105,plain,
% 0.72/0.88 (![U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)) <=> ![U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))),
% 0.72/0.88 inference(rewrite,[status(thm)],[])).
% 0.72/0.88 tff(106,plain,
% 0.72/0.88 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ndr1_0) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U))), ((((~ndr1_0) | c0_1(U)) | c1_1(U)) <=> (((~ndr1_0) | c0_1(U)) | c1_1(U)))), rewrite((((~ndr1_0) | c0_1(U)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U))), ((((~ndr1_0) | c0_1(U)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U)))), (((((~ndr1_0) | c0_1(U)) | c1_1(U)) | 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)) | hskp1) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)) | hskp1))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)) | hskp1) <=> (hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))), ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) | hskp1) <=> (hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))))),
% 0.72/0.88 inference(bind,[status(th)],[])).
% 0.72/0.88 tff(107,plain,
% 0.72/0.88 (![U: $i] : (((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) | hskp1) <=> ![U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))),
% 0.72/0.88 inference(quant_intro,[status(thm)],[106])).
% 0.72/0.88 tff(108,axiom,(![U: $i] : (((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) | hskp1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause112')).
% 0.72/0.88 tff(109,plain,
% 0.72/0.88 (![U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))),
% 0.72/0.88 inference(modus_ponens,[status(thm)],[108, 107])).
% 0.72/0.88 tff(110,plain,
% 0.72/0.88 (![U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))),
% 0.72/0.88 inference(modus_ponens,[status(thm)],[109, 105])).
% 0.72/0.88 tff(111,plain,(
% 0.72/0.88 ![U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))),
% 0.72/0.88 inference(skolemize,[status(sab)],[110])).
% 0.72/0.88 tff(112,plain,
% 0.72/0.88 (![U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))),
% 0.72/0.88 inference(modus_ponens,[status(thm)],[111, 104])).
% 0.72/0.88 tff(113,assumption,(~c3_1(a257)), introduced(assumption)).
% 0.72/0.88 tff(114,assumption,(~c1_1(a257)), introduced(assumption)).
% 0.72/0.88 tff(115,assumption,(~ndr1_0), introduced(assumption)).
% 0.72/0.88 tff(116,plain,
% 0.72/0.88 ((ndr1_0 | (~hskp2)) <=> (ndr1_0 | (~hskp2))),
% 0.72/0.88 inference(rewrite,[status(thm)],[])).
% 0.72/0.88 tff(117,plain,
% 0.72/0.88 (((~hskp2) | ndr1_0) <=> (ndr1_0 | (~hskp2))),
% 0.72/0.88 inference(rewrite,[status(thm)],[])).
% 0.72/0.88 tff(118,axiom,((~hskp2) | ndr1_0), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause24')).
% 0.72/0.88 tff(119,plain,
% 0.72/0.88 (ndr1_0 | (~hskp2)),
% 0.72/0.88 inference(modus_ponens,[status(thm)],[118, 117])).
% 0.72/0.88 tff(120,plain,
% 0.72/0.88 (ndr1_0 | (~hskp2)),
% 0.72/0.88 inference(modus_ponens,[status(thm)],[119, 116])).
% 0.72/0.88 tff(121,plain,
% 0.72/0.88 (~hskp2),
% 0.72/0.88 inference(unit_resolution,[status(thm)],[120, 115])).
% 0.72/0.88 tff(122,plain,
% 0.72/0.88 (((~hskp25) | ndr1_0) <=> ((~hskp25) | ndr1_0)),
% 0.72/0.88 inference(rewrite,[status(thm)],[])).
% 0.72/0.88 tff(123,axiom,((~hskp25) | ndr1_0), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause1')).
% 0.72/0.88 tff(124,plain,
% 0.72/0.88 ((~hskp25) | ndr1_0),
% 0.72/0.88 inference(modus_ponens,[status(thm)],[123, 122])).
% 0.72/0.88 tff(125,plain,
% 0.72/0.88 ((~hskp25) | ndr1_0),
% 0.72/0.88 inference(modus_ponens,[status(thm)],[124, 122])).
% 0.72/0.88 tff(126,plain,
% 0.72/0.88 ((~hskp25) | ndr1_0),
% 0.72/0.88 inference(modus_ponens,[status(thm)],[125, 122])).
% 0.72/0.88 tff(127,plain,
% 0.72/0.88 ((~hskp25) | ndr1_0),
% 0.72/0.88 inference(modus_ponens,[status(thm)],[126, 122])).
% 0.72/0.88 tff(128,plain,
% 0.72/0.88 ((~hskp25) | ndr1_0),
% 0.72/0.88 inference(modus_ponens,[status(thm)],[127, 122])).
% 0.72/0.88 tff(129,plain,
% 0.72/0.88 (~hskp25),
% 0.72/0.88 inference(unit_resolution,[status(thm)],[128, 115])).
% 0.72/0.88 tff(130,plain,
% 0.72/0.88 ((ndr1_0 | (~hskp15)) <=> (ndr1_0 | (~hskp15))),
% 0.72/0.88 inference(rewrite,[status(thm)],[])).
% 0.72/0.88 tff(131,plain,
% 0.72/0.88 (((~hskp15) | ndr1_0) <=> (ndr1_0 | (~hskp15))),
% 0.72/0.88 inference(rewrite,[status(thm)],[])).
% 0.72/0.88 tff(132,axiom,((~hskp15) | ndr1_0), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause11')).
% 0.72/0.88 tff(133,plain,
% 0.72/0.88 (ndr1_0 | (~hskp15)),
% 0.72/0.88 inference(modus_ponens,[status(thm)],[132, 131])).
% 0.72/0.88 tff(134,plain,
% 0.72/0.88 (ndr1_0 | (~hskp15)),
% 0.72/0.88 inference(modus_ponens,[status(thm)],[133, 130])).
% 0.72/0.88 tff(135,plain,
% 0.72/0.88 (~hskp15),
% 0.72/0.88 inference(unit_resolution,[status(thm)],[134, 115])).
% 0.72/0.88 tff(136,plain,
% 0.72/0.88 ((hskp25 | hskp15 | hskp2) <=> (hskp25 | hskp15 | hskp2)),
% 0.72/0.88 inference(rewrite,[status(thm)],[])).
% 0.72/0.88 tff(137,plain,
% 0.72/0.88 (((hskp25 | hskp15) | hskp2) <=> (hskp25 | hskp15 | hskp2)),
% 0.72/0.88 inference(rewrite,[status(thm)],[])).
% 0.72/0.88 tff(138,plain,
% 0.72/0.88 ((hskp25 | hskp15) <=> (hskp25 | hskp15)),
% 0.72/0.88 inference(rewrite,[status(thm)],[])).
% 0.72/0.88 tff(139,plain,
% 0.72/0.88 (((hskp25 | hskp15) | hskp2) <=> ((hskp25 | hskp15) | hskp2)),
% 0.72/0.88 inference(monotonicity,[status(thm)],[138])).
% 0.72/0.88 tff(140,plain,
% 0.72/0.88 (((hskp25 | hskp15) | hskp2) <=> (hskp25 | hskp15 | hskp2)),
% 0.72/0.88 inference(transitivity,[status(thm)],[139, 137])).
% 0.72/0.88 tff(141,axiom,((hskp25 | hskp15) | hskp2), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause27')).
% 0.72/0.88 tff(142,plain,
% 0.72/0.88 (hskp25 | hskp15 | hskp2),
% 0.72/0.88 inference(modus_ponens,[status(thm)],[141, 140])).
% 0.72/0.88 tff(143,plain,
% 0.72/0.88 (hskp25 | hskp15 | hskp2),
% 0.72/0.88 inference(modus_ponens,[status(thm)],[142, 136])).
% 0.72/0.88 tff(144,plain,
% 0.72/0.88 (hskp25 | hskp15 | hskp2),
% 0.72/0.88 inference(modus_ponens,[status(thm)],[143, 136])).
% 0.72/0.88 tff(145,plain,
% 0.72/0.88 (hskp25 | hskp15 | hskp2),
% 0.72/0.88 inference(modus_ponens,[status(thm)],[144, 136])).
% 0.72/0.88 tff(146,plain,
% 0.72/0.88 (hskp25 | hskp15 | hskp2),
% 0.72/0.88 inference(modus_ponens,[status(thm)],[145, 136])).
% 0.72/0.88 tff(147,plain,
% 0.72/0.88 ($false),
% 0.72/0.88 inference(unit_resolution,[status(thm)],[146, 135, 129, 121])).
% 0.72/0.88 tff(148,plain,(ndr1_0), inference(lemma,lemma(discharge,[]))).
% 0.72/0.88 tff(149,plain,
% 0.72/0.88 (((~![U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp1 | c1_1(a257) | c3_1(a257) | (~ndr1_0) | c0_1(a257))) <=> ((~![U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | hskp1 | c1_1(a257) | c3_1(a257) | (~ndr1_0) | c0_1(a257))),
% 0.72/0.88 inference(rewrite,[status(thm)],[])).
% 0.72/0.88 tff(150,plain,
% 0.72/0.88 ((hskp1 | (~ndr1_0) | c3_1(a257) | c1_1(a257) | c0_1(a257)) <=> (hskp1 | c1_1(a257) | c3_1(a257) | (~ndr1_0) | c0_1(a257))),
% 0.72/0.88 inference(rewrite,[status(thm)],[])).
% 0.72/0.88 tff(151,plain,
% 0.72/0.88 (((~![U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp1 | (~ndr1_0) | c3_1(a257) | c1_1(a257) | c0_1(a257))) <=> ((~![U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp1 | c1_1(a257) | c3_1(a257) | (~ndr1_0) | c0_1(a257)))),
% 0.72/0.88 inference(monotonicity,[status(thm)],[150])).
% 0.72/0.88 tff(152,plain,
% 0.72/0.88 (((~![U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp1 | (~ndr1_0) | c3_1(a257) | c1_1(a257) | c0_1(a257))) <=> ((~![U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | hskp1 | c1_1(a257) | c3_1(a257) | (~ndr1_0) | c0_1(a257))),
% 0.72/0.88 inference(transitivity,[status(thm)],[151, 149])).
% 0.72/0.88 tff(153,plain,
% 0.72/0.88 ((~![U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp1 | (~ndr1_0) | c3_1(a257) | c1_1(a257) | c0_1(a257))),
% 0.72/0.88 inference(quant_inst,[status(thm)],[])).
% 0.72/0.88 tff(154,plain,
% 0.72/0.88 ((~![U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | hskp1 | c1_1(a257) | c3_1(a257) | (~ndr1_0) | c0_1(a257)),
% 0.72/0.88 inference(modus_ponens,[status(thm)],[153, 152])).
% 0.72/0.88 tff(155,plain,
% 0.72/0.88 (hskp1 | c0_1(a257)),
% 0.72/0.88 inference(unit_resolution,[status(thm)],[154, 148, 114, 113, 112])).
% 0.72/0.88 tff(156,plain,
% 0.72/0.88 (c0_1(a257)),
% 0.72/0.88 inference(unit_resolution,[status(thm)],[155, 102])).
% 0.72/0.88 tff(157,plain,
% 0.72/0.88 (((~![U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp1 | c1_1(a191) | c3_1(a191) | (~ndr1_0) | c0_1(a191))) <=> ((~![U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | hskp1 | c1_1(a191) | c3_1(a191) | (~ndr1_0) | c0_1(a191))),
% 0.72/0.88 inference(rewrite,[status(thm)],[])).
% 0.72/0.88 tff(158,plain,
% 0.72/0.88 ((hskp1 | (~ndr1_0) | c3_1(a191) | c1_1(a191) | c0_1(a191)) <=> (hskp1 | c1_1(a191) | c3_1(a191) | (~ndr1_0) | c0_1(a191))),
% 0.72/0.88 inference(rewrite,[status(thm)],[])).
% 0.72/0.88 tff(159,plain,
% 0.72/0.88 (((~![U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp1 | (~ndr1_0) | c3_1(a191) | c1_1(a191) | c0_1(a191))) <=> ((~![U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp1 | c1_1(a191) | c3_1(a191) | (~ndr1_0) | c0_1(a191)))),
% 0.72/0.88 inference(monotonicity,[status(thm)],[158])).
% 0.72/0.88 tff(160,plain,
% 0.72/0.88 (((~![U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp1 | (~ndr1_0) | c3_1(a191) | c1_1(a191) | c0_1(a191))) <=> ((~![U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | hskp1 | c1_1(a191) | c3_1(a191) | (~ndr1_0) | c0_1(a191))),
% 0.72/0.88 inference(transitivity,[status(thm)],[159, 157])).
% 0.72/0.88 tff(161,plain,
% 0.72/0.88 ((~![U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp1 | (~ndr1_0) | c3_1(a191) | c1_1(a191) | c0_1(a191))),
% 0.72/0.88 inference(quant_inst,[status(thm)],[])).
% 0.72/0.88 tff(162,plain,
% 0.72/0.88 ((~![U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | hskp1 | c1_1(a191) | c3_1(a191) | (~ndr1_0) | c0_1(a191)),
% 0.72/0.88 inference(modus_ponens,[status(thm)],[161, 160])).
% 0.72/0.88 tff(163,plain,
% 0.72/0.88 (hskp1 | c0_1(a191)),
% 0.72/0.88 inference(unit_resolution,[status(thm)],[162, 148, 67, 68, 112])).
% 0.72/0.88 tff(164,plain,
% 0.72/0.88 (c0_1(a191)),
% 0.72/0.88 inference(unit_resolution,[status(thm)],[163, 102])).
% 0.72/0.88 tff(165,plain,
% 0.72/0.88 (^[V: $i, U: $i] : refl((hskp1 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V))) <=> (hskp1 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V))))),
% 0.72/0.88 inference(bind,[status(th)],[])).
% 0.72/0.88 tff(166,plain,
% 0.72/0.88 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))),
% 0.72/0.88 inference(quant_intro,[status(thm)],[165])).
% 0.72/0.88 tff(167,plain,
% 0.72/0.88 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))),
% 0.72/0.88 inference(rewrite,[status(thm)],[])).
% 0.72/0.88 tff(168,plain,
% 0.72/0.88 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c3_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c3_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c3_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c3_1(U)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c3_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c3_1(U)) | c1_1(V)) | c2_1(V)) | hskp1) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V))) | hskp1))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V))) | hskp1) <=> (hskp1 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c3_1(U)) | c1_1(V)) | c2_1(V)) | hskp1) <=> (hskp1 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))))),
% 0.72/0.88 inference(bind,[status(th)],[])).
% 0.72/0.88 tff(169,plain,
% 0.72/0.88 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c3_1(U)) | c1_1(V)) | c2_1(V)) | hskp1) <=> ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))),
% 0.72/0.88 inference(quant_intro,[status(thm)],[168])).
% 0.72/0.88 tff(170,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c3_1(U)) | c1_1(V)) | c2_1(V)) | hskp1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause140')).
% 0.72/0.88 tff(171,plain,
% 0.72/0.88 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))),
% 0.72/0.88 inference(modus_ponens,[status(thm)],[170, 169])).
% 0.72/0.88 tff(172,plain,
% 0.72/0.88 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))),
% 0.72/0.88 inference(modus_ponens,[status(thm)],[171, 167])).
% 0.72/0.88 tff(173,plain,(
% 0.72/0.88 ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))),
% 0.72/0.88 inference(skolemize,[status(sab)],[172])).
% 0.72/0.88 tff(174,plain,
% 0.72/0.88 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))),
% 0.72/0.88 inference(modus_ponens,[status(thm)],[173, 166])).
% 0.72/0.88 tff(175,assumption,(c2_1(a257)), introduced(assumption)).
% 0.72/0.88 tff(176,plain,
% 0.72/0.88 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp1 | c3_1(a257) | c1_1(a191) | c2_1(a191) | (~ndr1_0) | (~c0_1(a191)) | (~c0_1(a257)) | (~c2_1(a257)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | hskp1 | c3_1(a257) | c1_1(a191) | c2_1(a191) | (~ndr1_0) | (~c0_1(a191)) | (~c0_1(a257)) | (~c2_1(a257)))),
% 0.72/0.88 inference(rewrite,[status(thm)],[])).
% 0.72/0.88 tff(177,plain,
% 0.72/0.88 ((hskp1 | (~ndr1_0) | c3_1(a257) | (~c2_1(a257)) | (~c0_1(a257)) | c1_1(a191) | c2_1(a191) | (~c0_1(a191))) <=> (hskp1 | c3_1(a257) | c1_1(a191) | c2_1(a191) | (~ndr1_0) | (~c0_1(a191)) | (~c0_1(a257)) | (~c2_1(a257)))),
% 0.72/0.88 inference(rewrite,[status(thm)],[])).
% 0.72/0.88 tff(178,plain,
% 0.72/0.88 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp1 | (~ndr1_0) | c3_1(a257) | (~c2_1(a257)) | (~c0_1(a257)) | c1_1(a191) | c2_1(a191) | (~c0_1(a191)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp1 | c3_1(a257) | c1_1(a191) | c2_1(a191) | (~ndr1_0) | (~c0_1(a191)) | (~c0_1(a257)) | (~c2_1(a257))))),
% 0.72/0.88 inference(monotonicity,[status(thm)],[177])).
% 0.72/0.88 tff(179,plain,
% 0.72/0.88 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp1 | (~ndr1_0) | c3_1(a257) | (~c2_1(a257)) | (~c0_1(a257)) | c1_1(a191) | c2_1(a191) | (~c0_1(a191)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | hskp1 | c3_1(a257) | c1_1(a191) | c2_1(a191) | (~ndr1_0) | (~c0_1(a191)) | (~c0_1(a257)) | (~c2_1(a257)))),
% 0.72/0.88 inference(transitivity,[status(thm)],[178, 176])).
% 0.72/0.88 tff(180,plain,
% 0.72/0.88 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp1 | (~ndr1_0) | c3_1(a257) | (~c2_1(a257)) | (~c0_1(a257)) | c1_1(a191) | c2_1(a191) | (~c0_1(a191)))),
% 0.72/0.88 inference(quant_inst,[status(thm)],[])).
% 0.72/0.88 tff(181,plain,
% 0.72/0.88 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | hskp1 | c3_1(a257) | c1_1(a191) | c2_1(a191) | (~ndr1_0) | (~c0_1(a191)) | (~c0_1(a257)) | (~c2_1(a257))),
% 0.72/0.88 inference(modus_ponens,[status(thm)],[180, 179])).
% 0.72/0.88 tff(182,plain,
% 0.72/0.88 (hskp1 | (~c0_1(a191)) | (~c0_1(a257))),
% 0.72/0.88 inference(unit_resolution,[status(thm)],[181, 148, 175, 113, 67, 66, 174])).
% 0.72/0.88 tff(183,plain,
% 0.72/0.88 ($false),
% 0.72/0.88 inference(unit_resolution,[status(thm)],[182, 164, 102, 156])).
% 0.72/0.88 tff(184,plain,(hskp1 | (~c2_1(a257)) | c3_1(a257) | c1_1(a191) | c2_1(a191) | c1_1(a257) | c3_1(a191)), inference(lemma,lemma(discharge,[]))).
% 0.72/0.88 tff(185,plain,
% 0.72/0.88 (hskp1),
% 0.72/0.88 inference(unit_resolution,[status(thm)],[184, 101, 93, 67, 66, 87, 68])).
% 0.72/0.88 tff(186,plain,
% 0.72/0.88 (((~hskp1) | c2_1(a190)) <=> ((~hskp1) | c2_1(a190))),
% 0.72/0.88 inference(rewrite,[status(thm)],[])).
% 0.72/0.88 tff(187,axiom,((~hskp1) | c2_1(a190)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause69')).
% 0.72/0.88 tff(188,plain,
% 0.72/0.88 ((~hskp1) | c2_1(a190)),
% 0.72/0.88 inference(modus_ponens,[status(thm)],[187, 186])).
% 0.72/0.88 tff(189,plain,
% 0.72/0.88 ((~hskp1) | c2_1(a190)),
% 0.72/0.88 inference(modus_ponens,[status(thm)],[188, 186])).
% 0.72/0.88 tff(190,plain,
% 0.72/0.88 ((~hskp1) | c2_1(a190)),
% 0.72/0.88 inference(modus_ponens,[status(thm)],[189, 186])).
% 0.72/0.88 tff(191,plain,
% 0.72/0.88 ((~hskp1) | c2_1(a190)),
% 0.72/0.88 inference(modus_ponens,[status(thm)],[190, 186])).
% 0.72/0.88 tff(192,plain,
% 0.72/0.88 ((~hskp1) | c2_1(a190)),
% 0.72/0.88 inference(modus_ponens,[status(thm)],[191, 186])).
% 0.72/0.88 tff(193,plain,
% 0.72/0.88 (c2_1(a190)),
% 0.72/0.88 inference(unit_resolution,[status(thm)],[192, 185])).
% 0.72/0.88 tff(194,plain,
% 0.72/0.88 (((~hskp1) | c0_1(a190)) <=> ((~hskp1) | c0_1(a190))),
% 0.72/0.88 inference(rewrite,[status(thm)],[])).
% 0.72/0.88 tff(195,axiom,((~hskp1) | c0_1(a190)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause68')).
% 0.72/0.88 tff(196,plain,
% 0.72/0.88 ((~hskp1) | c0_1(a190)),
% 0.72/0.88 inference(modus_ponens,[status(thm)],[195, 194])).
% 0.72/0.88 tff(197,plain,
% 0.72/0.88 ((~hskp1) | c0_1(a190)),
% 0.72/0.88 inference(modus_ponens,[status(thm)],[196, 194])).
% 0.72/0.88 tff(198,plain,
% 0.72/0.88 ((~hskp1) | c0_1(a190)),
% 0.72/0.88 inference(modus_ponens,[status(thm)],[197, 194])).
% 0.72/0.88 tff(199,plain,
% 0.72/0.88 ((~hskp1) | c0_1(a190)),
% 0.72/0.88 inference(modus_ponens,[status(thm)],[198, 194])).
% 0.72/0.88 tff(200,plain,
% 0.72/0.88 ((~hskp1) | c0_1(a190)),
% 0.72/0.88 inference(modus_ponens,[status(thm)],[199, 194])).
% 0.72/0.88 tff(201,plain,
% 0.72/0.88 (c0_1(a190)),
% 0.72/0.88 inference(unit_resolution,[status(thm)],[200, 185])).
% 0.72/0.88 tff(202,plain,
% 0.72/0.88 (^[V: $i, U: $i] : refl((hskp19 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V))) <=> (hskp19 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V))))),
% 0.72/0.88 inference(bind,[status(th)],[])).
% 0.72/0.88 tff(203,plain,
% 0.72/0.88 (![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))),
% 0.72/0.88 inference(quant_intro,[status(thm)],[202])).
% 0.72/0.88 tff(204,plain,
% 0.72/0.88 (![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))),
% 0.72/0.88 inference(rewrite,[status(thm)],[])).
% 0.72/0.88 tff(205,plain,
% 0.72/0.88 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c1_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V))) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c1_1(V)) | c3_1(V)) | hskp19) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V))) | hskp19))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V))) | hskp19) <=> (hskp19 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c1_1(V)) | c3_1(V)) | hskp19) <=> (hskp19 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))))),
% 0.72/0.88 inference(bind,[status(th)],[])).
% 0.72/0.88 tff(206,plain,
% 0.72/0.88 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c1_1(V)) | c3_1(V)) | hskp19) <=> ![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))),
% 0.72/0.88 inference(quant_intro,[status(thm)],[205])).
% 0.72/0.88 tff(207,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c1_1(V)) | c3_1(V)) | hskp19)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause143')).
% 0.72/0.88 tff(208,plain,
% 0.72/0.88 (![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))),
% 0.72/0.88 inference(modus_ponens,[status(thm)],[207, 206])).
% 0.72/0.88 tff(209,plain,
% 0.72/0.88 (![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))),
% 0.72/0.88 inference(modus_ponens,[status(thm)],[208, 204])).
% 0.72/0.88 tff(210,plain,(
% 0.72/0.88 ![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))),
% 0.72/0.88 inference(skolemize,[status(sab)],[209])).
% 0.72/0.88 tff(211,plain,
% 0.72/0.88 (![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))),
% 0.72/0.88 inference(modus_ponens,[status(thm)],[210, 203])).
% 0.72/0.88 tff(212,plain,
% 0.72/0.88 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp19 | c1_1(a257) | c3_1(a257) | c3_1(a190) | (~ndr1_0) | (~c2_1(a190)) | (~c0_1(a190)) | (~c2_1(a257)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp19 | c1_1(a257) | c3_1(a257) | c3_1(a190) | (~ndr1_0) | (~c2_1(a190)) | (~c0_1(a190)) | (~c2_1(a257)))),
% 0.72/0.88 inference(rewrite,[status(thm)],[])).
% 0.72/0.88 tff(213,plain,
% 0.72/0.88 ((hskp19 | (~ndr1_0) | c3_1(a190) | (~c2_1(a190)) | (~c0_1(a190)) | c3_1(a257) | c1_1(a257) | (~c2_1(a257))) <=> (hskp19 | c1_1(a257) | c3_1(a257) | c3_1(a190) | (~ndr1_0) | (~c2_1(a190)) | (~c0_1(a190)) | (~c2_1(a257)))),
% 0.72/0.89 inference(rewrite,[status(thm)],[])).
% 0.72/0.89 tff(214,plain,
% 0.72/0.89 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp19 | (~ndr1_0) | c3_1(a190) | (~c2_1(a190)) | (~c0_1(a190)) | c3_1(a257) | c1_1(a257) | (~c2_1(a257)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp19 | c1_1(a257) | c3_1(a257) | c3_1(a190) | (~ndr1_0) | (~c2_1(a190)) | (~c0_1(a190)) | (~c2_1(a257))))),
% 0.72/0.89 inference(monotonicity,[status(thm)],[213])).
% 0.72/0.89 tff(215,plain,
% 0.72/0.89 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp19 | (~ndr1_0) | c3_1(a190) | (~c2_1(a190)) | (~c0_1(a190)) | c3_1(a257) | c1_1(a257) | (~c2_1(a257)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp19 | c1_1(a257) | c3_1(a257) | c3_1(a190) | (~ndr1_0) | (~c2_1(a190)) | (~c0_1(a190)) | (~c2_1(a257)))),
% 0.72/0.89 inference(transitivity,[status(thm)],[214, 212])).
% 0.72/0.89 tff(216,plain,
% 0.72/0.89 ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp19 | (~ndr1_0) | c3_1(a190) | (~c2_1(a190)) | (~c0_1(a190)) | c3_1(a257) | c1_1(a257) | (~c2_1(a257)))),
% 0.72/0.89 inference(quant_inst,[status(thm)],[])).
% 0.72/0.89 tff(217,plain,
% 0.72/0.89 ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp19 | c1_1(a257) | c3_1(a257) | c3_1(a190) | (~ndr1_0) | (~c2_1(a190)) | (~c0_1(a190)) | (~c2_1(a257))),
% 0.72/0.89 inference(modus_ponens,[status(thm)],[216, 215])).
% 0.72/0.89 tff(218,plain,
% 0.72/0.89 (hskp19 | (~c2_1(a190)) | (~c0_1(a190))),
% 0.72/0.89 inference(unit_resolution,[status(thm)],[217, 148, 101, 87, 93, 13, 211])).
% 0.72/0.89 tff(219,plain,
% 0.72/0.89 (hskp19),
% 0.72/0.89 inference(unit_resolution,[status(thm)],[218, 201, 193])).
% 0.72/0.89 tff(220,plain,
% 0.72/0.89 (((~hskp19) | c3_1(a225)) <=> ((~hskp19) | c3_1(a225))),
% 0.72/0.89 inference(rewrite,[status(thm)],[])).
% 0.72/0.89 tff(221,axiom,((~hskp19) | c3_1(a225)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause47')).
% 0.72/0.89 tff(222,plain,
% 0.72/0.89 ((~hskp19) | c3_1(a225)),
% 0.72/0.89 inference(modus_ponens,[status(thm)],[221, 220])).
% 0.72/0.89 tff(223,plain,
% 0.72/0.89 ((~hskp19) | c3_1(a225)),
% 0.72/0.89 inference(modus_ponens,[status(thm)],[222, 220])).
% 0.72/0.89 tff(224,plain,
% 0.72/0.89 ((~hskp19) | c3_1(a225)),
% 0.72/0.89 inference(modus_ponens,[status(thm)],[223, 220])).
% 0.72/0.89 tff(225,plain,
% 0.72/0.89 ((~hskp19) | c3_1(a225)),
% 0.72/0.89 inference(modus_ponens,[status(thm)],[224, 220])).
% 0.72/0.89 tff(226,plain,
% 0.72/0.89 ((~hskp19) | c3_1(a225)),
% 0.72/0.89 inference(modus_ponens,[status(thm)],[225, 220])).
% 0.72/0.89 tff(227,plain,
% 0.72/0.89 (c3_1(a225)),
% 0.72/0.89 inference(unit_resolution,[status(thm)],[226, 219])).
% 0.72/0.89 tff(228,plain,
% 0.72/0.89 (((~hskp19) | (~c0_1(a225))) <=> ((~hskp19) | (~c0_1(a225)))),
% 0.72/0.89 inference(rewrite,[status(thm)],[])).
% 0.72/0.89 tff(229,plain,
% 0.72/0.89 (((~c0_1(a225)) | (~hskp19)) <=> ((~hskp19) | (~c0_1(a225)))),
% 0.72/0.89 inference(rewrite,[status(thm)],[])).
% 0.72/0.89 tff(230,axiom,((~c0_1(a225)) | (~hskp19)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause75')).
% 0.72/0.89 tff(231,plain,
% 0.72/0.89 ((~hskp19) | (~c0_1(a225))),
% 0.72/0.89 inference(modus_ponens,[status(thm)],[230, 229])).
% 0.72/0.89 tff(232,plain,
% 0.72/0.89 ((~hskp19) | (~c0_1(a225))),
% 0.72/0.89 inference(modus_ponens,[status(thm)],[231, 228])).
% 0.72/0.89 tff(233,plain,
% 0.72/0.89 (~c0_1(a225)),
% 0.72/0.89 inference(unit_resolution,[status(thm)],[232, 219])).
% 0.72/0.89 tff(234,assumption,(c3_1(a225)), introduced(assumption)).
% 0.72/0.89 tff(235,assumption,(~c0_1(a225)), introduced(assumption)).
% 0.72/0.89 tff(236,assumption,(~hskp13), introduced(assumption)).
% 0.72/0.89 tff(237,plain,
% 0.72/0.89 (^[V: $i, U: $i] : refl((hskp13 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V)) <=> (hskp13 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V)))),
% 0.72/0.89 inference(bind,[status(th)],[])).
% 0.72/0.89 tff(238,plain,
% 0.72/0.89 (![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V)) <=> ![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))),
% 0.72/0.89 inference(quant_intro,[status(thm)],[237])).
% 0.72/0.89 tff(239,plain,
% 0.72/0.89 (![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V)) <=> ![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))),
% 0.72/0.89 inference(rewrite,[status(thm)],[])).
% 0.72/0.89 tff(240,plain,
% 0.72/0.89 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~ndr1_0) | (~c2_1(U))) | (~c3_1(U))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)))), (((((~ndr1_0) | (~c2_1(U))) | (~c3_1(U))) | c1_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U))) | c1_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U))) | c1_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V))), (((((~ndr1_0) | (~c2_1(U))) | (~c3_1(U))) | c1_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V)))), ((((((~ndr1_0) | (~c2_1(U))) | (~c3_1(U))) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c2_1(V))), ((((((~ndr1_0) | (~c2_1(U))) | (~c3_1(U))) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c2_1(V)))), (((((((~ndr1_0) | (~c2_1(U))) | (~c3_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c2_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))), (((((((~ndr1_0) | (~c2_1(U))) | (~c3_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V)))), ((((((((~ndr1_0) | (~c2_1(U))) | (~c3_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V)) | c0_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))), ((((((((~ndr1_0) | (~c2_1(U))) | (~c3_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V)))), (((((((((~ndr1_0) | (~c2_1(U))) | (~c3_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) | hskp13) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V)) | hskp13))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V)) | hskp13) <=> (hskp13 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))), (((((((((~ndr1_0) | (~c2_1(U))) | (~c3_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) | hskp13) <=> (hskp13 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))))),
% 0.72/0.89 inference(bind,[status(th)],[])).
% 0.72/0.89 tff(241,plain,
% 0.72/0.89 (![V: $i, U: $i] : ((((((((~ndr1_0) | (~c2_1(U))) | (~c3_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) | hskp13) <=> ![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))),
% 0.72/0.89 inference(quant_intro,[status(thm)],[240])).
% 0.72/0.89 tff(242,axiom,(![V: $i, U: $i] : ((((((((~ndr1_0) | (~c2_1(U))) | (~c3_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) | hskp13)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause135')).
% 0.72/0.89 tff(243,plain,
% 0.72/0.89 (![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))),
% 0.72/0.89 inference(modus_ponens,[status(thm)],[242, 241])).
% 0.72/0.89 tff(244,plain,
% 0.72/0.89 (![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))),
% 0.72/0.89 inference(modus_ponens,[status(thm)],[243, 239])).
% 0.72/0.89 tff(245,plain,(
% 0.72/0.89 ![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))),
% 0.72/0.89 inference(skolemize,[status(sab)],[244])).
% 0.72/0.89 tff(246,plain,
% 0.72/0.89 (![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))),
% 0.72/0.89 inference(modus_ponens,[status(thm)],[245, 238])).
% 0.72/0.89 tff(247,plain,
% 0.72/0.89 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp13 | c0_1(a225) | c1_1(a191) | c2_1(a191) | c3_1(a191) | (~ndr1_0) | (~c2_1(a225)) | (~c3_1(a225)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp13 | c0_1(a225) | c1_1(a191) | c2_1(a191) | c3_1(a191) | (~ndr1_0) | (~c2_1(a225)) | (~c3_1(a225)))),
% 0.72/0.89 inference(rewrite,[status(thm)],[])).
% 0.72/0.89 tff(248,plain,
% 0.72/0.89 ((hskp13 | (~ndr1_0) | c0_1(a225) | (~c3_1(a225)) | (~c2_1(a225)) | c3_1(a191) | c1_1(a191) | c2_1(a191)) <=> (hskp13 | c0_1(a225) | c1_1(a191) | c2_1(a191) | c3_1(a191) | (~ndr1_0) | (~c2_1(a225)) | (~c3_1(a225)))),
% 0.72/0.89 inference(rewrite,[status(thm)],[])).
% 0.72/0.89 tff(249,plain,
% 0.72/0.89 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp13 | (~ndr1_0) | c0_1(a225) | (~c3_1(a225)) | (~c2_1(a225)) | c3_1(a191) | c1_1(a191) | c2_1(a191))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp13 | c0_1(a225) | c1_1(a191) | c2_1(a191) | c3_1(a191) | (~ndr1_0) | (~c2_1(a225)) | (~c3_1(a225))))),
% 0.72/0.89 inference(monotonicity,[status(thm)],[248])).
% 0.72/0.89 tff(250,plain,
% 0.72/0.89 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp13 | (~ndr1_0) | c0_1(a225) | (~c3_1(a225)) | (~c2_1(a225)) | c3_1(a191) | c1_1(a191) | c2_1(a191))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp13 | c0_1(a225) | c1_1(a191) | c2_1(a191) | c3_1(a191) | (~ndr1_0) | (~c2_1(a225)) | (~c3_1(a225)))),
% 0.72/0.89 inference(transitivity,[status(thm)],[249, 247])).
% 0.72/0.89 tff(251,plain,
% 0.72/0.89 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp13 | (~ndr1_0) | c0_1(a225) | (~c3_1(a225)) | (~c2_1(a225)) | c3_1(a191) | c1_1(a191) | c2_1(a191))),
% 0.72/0.89 inference(quant_inst,[status(thm)],[])).
% 0.72/0.89 tff(252,plain,
% 0.72/0.89 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp13 | c0_1(a225) | c1_1(a191) | c2_1(a191) | c3_1(a191) | (~ndr1_0) | (~c2_1(a225)) | (~c3_1(a225))),
% 0.72/0.89 inference(modus_ponens,[status(thm)],[251, 250])).
% 0.72/0.89 tff(253,plain,
% 0.72/0.89 (hskp13 | (~c2_1(a225))),
% 0.72/0.89 inference(unit_resolution,[status(thm)],[252, 148, 234, 235, 67, 66, 68, 246])).
% 0.72/0.89 tff(254,plain,
% 0.72/0.89 (~c2_1(a225)),
% 0.72/0.89 inference(unit_resolution,[status(thm)],[253, 236])).
% 0.72/0.89 tff(255,plain,
% 0.72/0.89 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W)) <=> ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W)))),
% 0.72/0.89 inference(bind,[status(th)],[])).
% 0.72/0.89 tff(256,plain,
% 0.72/0.89 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.72/0.89 inference(quant_intro,[status(thm)],[255])).
% 0.72/0.89 tff(257,plain,
% 0.72/0.89 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.72/0.89 inference(rewrite,[status(thm)],[])).
% 0.72/0.89 tff(258,plain,
% 0.72/0.89 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~ndr1_0) | (~c3_1(U))) | c1_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | c1_1(V))), (((((~ndr1_0) | (~c3_1(U))) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | c1_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | c1_1(V) | c2_1(V))), (((((~ndr1_0) | (~c3_1(U))) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | c1_1(V) | c2_1(V)))), ((((((~ndr1_0) | (~c3_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | c1_1(V) | c2_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | c1_1(V) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))), ((((((~ndr1_0) | (~c3_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c2_1(V)))), (((((((~ndr1_0) | (~c3_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c2_1(V)) | c0_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c2_1(V)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))), (((((((~ndr1_0) | (~c3_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c2_1(V)))), ((((((((~ndr1_0) | (~c3_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c2_1(V)) | c2_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c2_1(V)) | c2_1(U)) <=> ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))), ((((((((~ndr1_0) | (~c3_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c2_1(V)))), (((((((((~ndr1_0) | (~c3_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) | c2_1(U)) | c0_1(W)) <=> (((~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c2_1(V)) | c0_1(W)))), rewrite((((~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c2_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c0_1(W))), (((((((((~ndr1_0) | (~c3_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) | c2_1(U)) | c0_1(W)) <=> ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c0_1(W)))), ((((((((((~ndr1_0) | (~c3_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) | c2_1(U)) | c0_1(W)) | c1_1(W)) <=> (((~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c0_1(W)) | c1_1(W)))), rewrite((((~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c1_1(W) | c0_1(W))), ((((((((((~ndr1_0) | (~c3_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) | c2_1(U)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c1_1(W) | c0_1(W)))), (((((((((((~ndr1_0) | (~c3_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) | c2_1(U)) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> (((~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c1_1(W) | c0_1(W)) | c2_1(W)))), rewrite((((~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c1_1(W) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))), (((((((((((~ndr1_0) | (~c3_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) | c2_1(U)) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))))),
% 0.72/0.89 inference(bind,[status(th)],[])).
% 0.72/0.89 tff(259,plain,
% 0.72/0.89 (![W: $i, V: $i, U: $i] : ((((((((((~ndr1_0) | (~c3_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) | c2_1(U)) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.72/0.89 inference(quant_intro,[status(thm)],[258])).
% 0.72/0.89 tff(260,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~ndr1_0) | (~c3_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) | c2_1(U)) | c0_1(W)) | c1_1(W)) | c2_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause151')).
% 0.72/0.89 tff(261,plain,
% 0.72/0.89 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.72/0.89 inference(modus_ponens,[status(thm)],[260, 259])).
% 0.72/0.89 tff(262,plain,
% 0.72/0.89 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.72/0.89 inference(modus_ponens,[status(thm)],[261, 257])).
% 0.72/0.89 tff(263,plain,(
% 0.72/0.89 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.72/0.89 inference(skolemize,[status(sab)],[262])).
% 0.72/0.89 tff(264,plain,
% 0.72/0.89 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.72/0.89 inference(modus_ponens,[status(thm)],[263, 256])).
% 0.72/0.89 tff(265,plain,
% 0.72/0.89 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a225) | c1_1(a191) | c2_1(a191) | c3_1(a191) | (~ndr1_0) | c0_1(a191) | c2_1(a225) | (~c3_1(a225)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a225) | c1_1(a191) | c2_1(a191) | c3_1(a191) | (~ndr1_0) | c0_1(a191) | c2_1(a225) | (~c3_1(a225)))),
% 0.72/0.89 inference(rewrite,[status(thm)],[])).
% 0.72/0.89 tff(266,plain,
% 0.72/0.89 (((~ndr1_0) | c0_1(a225) | c2_1(a225) | (~c3_1(a225)) | c3_1(a191) | c1_1(a191) | c2_1(a191) | c2_1(a191) | c1_1(a191) | c0_1(a191)) <=> (c0_1(a225) | c1_1(a191) | c2_1(a191) | c3_1(a191) | (~ndr1_0) | c0_1(a191) | c2_1(a225) | (~c3_1(a225)))),
% 0.72/0.89 inference(rewrite,[status(thm)],[])).
% 0.72/0.89 tff(267,plain,
% 0.72/0.89 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c0_1(a225) | c2_1(a225) | (~c3_1(a225)) | c3_1(a191) | c1_1(a191) | c2_1(a191) | c2_1(a191) | c1_1(a191) | c0_1(a191))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a225) | c1_1(a191) | c2_1(a191) | c3_1(a191) | (~ndr1_0) | c0_1(a191) | c2_1(a225) | (~c3_1(a225))))),
% 0.72/0.89 inference(monotonicity,[status(thm)],[266])).
% 0.72/0.89 tff(268,plain,
% 0.72/0.89 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c0_1(a225) | c2_1(a225) | (~c3_1(a225)) | c3_1(a191) | c1_1(a191) | c2_1(a191) | c2_1(a191) | c1_1(a191) | c0_1(a191))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a225) | c1_1(a191) | c2_1(a191) | c3_1(a191) | (~ndr1_0) | c0_1(a191) | c2_1(a225) | (~c3_1(a225)))),
% 0.72/0.89 inference(transitivity,[status(thm)],[267, 265])).
% 0.72/0.89 tff(269,plain,
% 0.72/0.89 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c0_1(a225) | c2_1(a225) | (~c3_1(a225)) | c3_1(a191) | c1_1(a191) | c2_1(a191) | c2_1(a191) | c1_1(a191) | c0_1(a191))),
% 0.72/0.89 inference(quant_inst,[status(thm)],[])).
% 0.72/0.89 tff(270,plain,
% 0.72/0.89 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a225) | c1_1(a191) | c2_1(a191) | c3_1(a191) | (~ndr1_0) | c0_1(a191) | c2_1(a225) | (~c3_1(a225))),
% 0.72/0.89 inference(modus_ponens,[status(thm)],[269, 268])).
% 0.72/0.89 tff(271,plain,
% 0.72/0.89 (c0_1(a191) | c2_1(a225)),
% 0.72/0.89 inference(unit_resolution,[status(thm)],[270, 148, 234, 235, 67, 66, 68, 264])).
% 0.72/0.89 tff(272,plain,
% 0.72/0.89 (c0_1(a191)),
% 0.72/0.89 inference(unit_resolution,[status(thm)],[271, 254])).
% 0.72/0.89 tff(273,plain,
% 0.72/0.89 (^[V: $i, U: $i] : refl((hskp13 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V))) <=> (hskp13 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V))))),
% 0.72/0.89 inference(bind,[status(th)],[])).
% 0.72/0.89 tff(274,plain,
% 0.72/0.89 (![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))),
% 0.72/0.89 inference(quant_intro,[status(thm)],[273])).
% 0.72/0.89 tff(275,plain,
% 0.72/0.89 (![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))),
% 0.72/0.89 inference(rewrite,[status(thm)],[])).
% 0.72/0.89 tff(276,plain,
% 0.72/0.89 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c3_1(U)) | (~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)))), rewrite((((~c3_1(U)) | (~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(V)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(V))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(V))) | c2_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c0_1(V))))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c0_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c0_1(V))) | c3_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V))))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(V)) | c3_1(V)) | hskp13) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V))) | hskp13))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V))) | hskp13) <=> (hskp13 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(V)) | c3_1(V)) | hskp13) <=> (hskp13 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))))),
% 0.72/0.89 inference(bind,[status(th)],[])).
% 0.72/0.89 tff(277,plain,
% 0.72/0.89 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(V)) | c3_1(V)) | hskp13) <=> ![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))),
% 0.72/0.89 inference(quant_intro,[status(thm)],[276])).
% 0.72/0.89 tff(278,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(V)) | c3_1(V)) | hskp13)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause149')).
% 0.72/0.89 tff(279,plain,
% 0.72/0.89 (![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))),
% 0.72/0.89 inference(modus_ponens,[status(thm)],[278, 277])).
% 0.72/0.89 tff(280,plain,
% 0.72/0.89 (![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))),
% 0.72/0.89 inference(modus_ponens,[status(thm)],[279, 275])).
% 0.72/0.89 tff(281,plain,(
% 0.72/0.89 ![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))),
% 0.72/0.89 inference(skolemize,[status(sab)],[280])).
% 0.72/0.89 tff(282,plain,
% 0.72/0.89 (![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))),
% 0.72/0.89 inference(modus_ponens,[status(thm)],[281, 274])).
% 0.72/0.89 tff(283,plain,
% 0.72/0.89 (^[V: $i, U: $i] : refl((hskp10 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V))) <=> (hskp10 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V))))),
% 0.72/0.89 inference(bind,[status(th)],[])).
% 0.72/0.89 tff(284,plain,
% 0.72/0.89 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))),
% 0.72/0.89 inference(quant_intro,[status(thm)],[283])).
% 0.72/0.89 tff(285,plain,
% 0.72/0.89 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))),
% 0.72/0.89 inference(rewrite,[status(thm)],[])).
% 0.72/0.89 tff(286,plain,
% 0.72/0.89 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c0_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c0_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(V)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(V))))), (((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(V)))), (((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(V))))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | (~c3_1(V)))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | (~c3_1(V))))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | (~c3_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V))))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V))))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp10) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V))) | hskp10))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V))) | hskp10) <=> (hskp10 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp10) <=> (hskp10 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))))),
% 0.72/0.89 inference(bind,[status(th)],[])).
% 0.72/0.89 tff(287,plain,
% 0.72/0.89 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp10) <=> ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))),
% 0.72/0.89 inference(quant_intro,[status(thm)],[286])).
% 0.72/0.89 tff(288,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp10)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause132')).
% 0.72/0.89 tff(289,plain,
% 0.72/0.89 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))),
% 0.72/0.89 inference(modus_ponens,[status(thm)],[288, 287])).
% 0.72/0.89 tff(290,plain,
% 0.72/0.89 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))),
% 0.72/0.89 inference(modus_ponens,[status(thm)],[289, 285])).
% 0.72/0.89 tff(291,plain,(
% 0.72/0.89 ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))),
% 0.72/0.89 inference(skolemize,[status(sab)],[290])).
% 0.72/0.89 tff(292,plain,
% 0.72/0.89 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))),
% 0.72/0.89 inference(modus_ponens,[status(thm)],[291, 284])).
% 0.72/0.89 tff(293,plain,
% 0.72/0.89 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp10 | c0_1(a225) | c2_1(a191) | c3_1(a191) | (~ndr1_0) | (~c0_1(a191)) | c2_1(a225) | (~c3_1(a225)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp10 | c0_1(a225) | c2_1(a191) | c3_1(a191) | (~ndr1_0) | (~c0_1(a191)) | c2_1(a225) | (~c3_1(a225)))),
% 0.72/0.89 inference(rewrite,[status(thm)],[])).
% 0.72/0.89 tff(294,plain,
% 0.72/0.89 ((hskp10 | (~ndr1_0) | c3_1(a191) | c2_1(a191) | (~c0_1(a191)) | c0_1(a225) | c2_1(a225) | (~c3_1(a225))) <=> (hskp10 | c0_1(a225) | c2_1(a191) | c3_1(a191) | (~ndr1_0) | (~c0_1(a191)) | c2_1(a225) | (~c3_1(a225)))),
% 0.72/0.89 inference(rewrite,[status(thm)],[])).
% 0.72/0.89 tff(295,plain,
% 0.72/0.89 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp10 | (~ndr1_0) | c3_1(a191) | c2_1(a191) | (~c0_1(a191)) | c0_1(a225) | c2_1(a225) | (~c3_1(a225)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp10 | c0_1(a225) | c2_1(a191) | c3_1(a191) | (~ndr1_0) | (~c0_1(a191)) | c2_1(a225) | (~c3_1(a225))))),
% 0.72/0.89 inference(monotonicity,[status(thm)],[294])).
% 0.72/0.89 tff(296,plain,
% 0.72/0.89 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp10 | (~ndr1_0) | c3_1(a191) | c2_1(a191) | (~c0_1(a191)) | c0_1(a225) | c2_1(a225) | (~c3_1(a225)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp10 | c0_1(a225) | c2_1(a191) | c3_1(a191) | (~ndr1_0) | (~c0_1(a191)) | c2_1(a225) | (~c3_1(a225)))),
% 0.72/0.89 inference(transitivity,[status(thm)],[295, 293])).
% 0.72/0.89 tff(297,plain,
% 0.72/0.89 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp10 | (~ndr1_0) | c3_1(a191) | c2_1(a191) | (~c0_1(a191)) | c0_1(a225) | c2_1(a225) | (~c3_1(a225)))),
% 0.72/0.89 inference(quant_inst,[status(thm)],[])).
% 0.72/0.89 tff(298,plain,
% 0.72/0.89 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp10 | c0_1(a225) | c2_1(a191) | c3_1(a191) | (~ndr1_0) | (~c0_1(a191)) | c2_1(a225) | (~c3_1(a225))),
% 0.72/0.89 inference(modus_ponens,[status(thm)],[297, 296])).
% 0.72/0.89 tff(299,plain,
% 0.72/0.89 (hskp10 | (~c0_1(a191)) | c2_1(a225)),
% 0.72/0.89 inference(unit_resolution,[status(thm)],[298, 148, 234, 235, 66, 68, 292])).
% 0.72/0.89 tff(300,plain,
% 0.72/0.89 (hskp10),
% 0.72/0.89 inference(unit_resolution,[status(thm)],[299, 272, 254])).
% 0.72/0.89 tff(301,plain,
% 0.72/0.89 (((~hskp10) | c0_1(a200)) <=> ((~hskp10) | c0_1(a200))),
% 0.72/0.89 inference(rewrite,[status(thm)],[])).
% 0.72/0.89 tff(302,axiom,((~hskp10) | c0_1(a200)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause57')).
% 0.72/0.89 tff(303,plain,
% 0.72/0.89 ((~hskp10) | c0_1(a200)),
% 0.72/0.89 inference(modus_ponens,[status(thm)],[302, 301])).
% 0.72/0.89 tff(304,plain,
% 0.72/0.89 ((~hskp10) | c0_1(a200)),
% 0.72/0.89 inference(modus_ponens,[status(thm)],[303, 301])).
% 0.72/0.89 tff(305,plain,
% 0.72/0.89 ((~hskp10) | c0_1(a200)),
% 0.72/0.89 inference(modus_ponens,[status(thm)],[304, 301])).
% 0.72/0.89 tff(306,plain,
% 0.72/0.89 ((~hskp10) | c0_1(a200)),
% 0.72/0.89 inference(modus_ponens,[status(thm)],[305, 301])).
% 0.72/0.89 tff(307,plain,
% 0.72/0.89 ((~hskp10) | c0_1(a200)),
% 0.72/0.89 inference(modus_ponens,[status(thm)],[306, 301])).
% 0.72/0.89 tff(308,plain,
% 0.72/0.89 (c0_1(a200)),
% 0.72/0.89 inference(unit_resolution,[status(thm)],[307, 300])).
% 0.72/0.89 tff(309,plain,
% 0.72/0.89 (((~hskp10) | c3_1(a200)) <=> ((~hskp10) | c3_1(a200))),
% 0.72/0.89 inference(rewrite,[status(thm)],[])).
% 0.72/0.89 tff(310,axiom,((~hskp10) | c3_1(a200)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause58')).
% 0.72/0.89 tff(311,plain,
% 0.72/0.89 ((~hskp10) | c3_1(a200)),
% 0.72/0.89 inference(modus_ponens,[status(thm)],[310, 309])).
% 0.72/0.89 tff(312,plain,
% 0.72/0.89 ((~hskp10) | c3_1(a200)),
% 0.72/0.89 inference(modus_ponens,[status(thm)],[311, 309])).
% 0.72/0.89 tff(313,plain,
% 0.72/0.89 ((~hskp10) | c3_1(a200)),
% 0.72/0.89 inference(modus_ponens,[status(thm)],[312, 309])).
% 0.72/0.89 tff(314,plain,
% 0.72/0.89 ((~hskp10) | c3_1(a200)),
% 0.72/0.89 inference(modus_ponens,[status(thm)],[313, 309])).
% 0.72/0.89 tff(315,plain,
% 0.72/0.89 ((~hskp10) | c3_1(a200)),
% 0.72/0.89 inference(modus_ponens,[status(thm)],[314, 309])).
% 0.72/0.89 tff(316,plain,
% 0.72/0.89 (c3_1(a200)),
% 0.72/0.89 inference(unit_resolution,[status(thm)],[315, 300])).
% 0.72/0.89 tff(317,plain,
% 0.72/0.89 (^[V: $i, U: $i] : refl((hskp24 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V))) <=> (hskp24 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V))))),
% 0.72/0.89 inference(bind,[status(th)],[])).
% 0.72/0.89 tff(318,plain,
% 0.72/0.89 (![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))),
% 0.72/0.89 inference(quant_intro,[status(thm)],[317])).
% 0.72/0.89 tff(319,plain,
% 0.72/0.89 (![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))),
% 0.72/0.89 inference(rewrite,[status(thm)],[])).
% 0.72/0.89 tff(320,plain,
% 0.72/0.89 (^[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) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V))))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V))))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c1_1(V)) | c2_1(V)) | hskp24) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V))) | hskp24))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V))) | hskp24) <=> (hskp24 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c1_1(V)) | c2_1(V)) | hskp24) <=> (hskp24 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))))),
% 0.72/0.90 inference(bind,[status(th)],[])).
% 0.72/0.90 tff(321,plain,
% 0.72/0.90 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c1_1(V)) | c2_1(V)) | hskp24) <=> ![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))),
% 0.72/0.90 inference(quant_intro,[status(thm)],[320])).
% 0.72/0.90 tff(322,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c1_1(V)) | c2_1(V)) | hskp24)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause139')).
% 0.72/0.90 tff(323,plain,
% 0.72/0.90 (![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))),
% 0.72/0.90 inference(modus_ponens,[status(thm)],[322, 321])).
% 0.72/0.90 tff(324,plain,
% 0.72/0.90 (![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))),
% 0.72/0.90 inference(modus_ponens,[status(thm)],[323, 319])).
% 0.72/0.90 tff(325,plain,(
% 0.72/0.90 ![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))),
% 0.72/0.90 inference(skolemize,[status(sab)],[324])).
% 0.72/0.90 tff(326,plain,
% 0.72/0.90 (![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))),
% 0.72/0.90 inference(modus_ponens,[status(thm)],[325, 318])).
% 0.72/0.90 tff(327,assumption,(~c1_1(a200)), introduced(assumption)).
% 0.72/0.90 tff(328,plain,
% 0.72/0.90 (((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp24 | c1_1(a200) | c1_1(a191) | c2_1(a191) | (~ndr1_0) | (~c0_1(a191)) | (~c3_1(a200)) | (~c0_1(a200)))) <=> ((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | hskp24 | c1_1(a200) | c1_1(a191) | c2_1(a191) | (~ndr1_0) | (~c0_1(a191)) | (~c3_1(a200)) | (~c0_1(a200)))),
% 0.72/0.90 inference(rewrite,[status(thm)],[])).
% 0.72/0.90 tff(329,plain,
% 0.72/0.90 ((hskp24 | (~ndr1_0) | c1_1(a200) | (~c3_1(a200)) | (~c0_1(a200)) | c1_1(a191) | c2_1(a191) | (~c0_1(a191))) <=> (hskp24 | c1_1(a200) | c1_1(a191) | c2_1(a191) | (~ndr1_0) | (~c0_1(a191)) | (~c3_1(a200)) | (~c0_1(a200)))),
% 0.72/0.90 inference(rewrite,[status(thm)],[])).
% 0.72/0.90 tff(330,plain,
% 0.72/0.90 (((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp24 | (~ndr1_0) | c1_1(a200) | (~c3_1(a200)) | (~c0_1(a200)) | c1_1(a191) | c2_1(a191) | (~c0_1(a191)))) <=> ((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp24 | c1_1(a200) | c1_1(a191) | c2_1(a191) | (~ndr1_0) | (~c0_1(a191)) | (~c3_1(a200)) | (~c0_1(a200))))),
% 0.72/0.90 inference(monotonicity,[status(thm)],[329])).
% 0.72/0.90 tff(331,plain,
% 0.72/0.90 (((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp24 | (~ndr1_0) | c1_1(a200) | (~c3_1(a200)) | (~c0_1(a200)) | c1_1(a191) | c2_1(a191) | (~c0_1(a191)))) <=> ((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | hskp24 | c1_1(a200) | c1_1(a191) | c2_1(a191) | (~ndr1_0) | (~c0_1(a191)) | (~c3_1(a200)) | (~c0_1(a200)))),
% 0.72/0.90 inference(transitivity,[status(thm)],[330, 328])).
% 0.72/0.90 tff(332,plain,
% 0.72/0.90 ((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp24 | (~ndr1_0) | c1_1(a200) | (~c3_1(a200)) | (~c0_1(a200)) | c1_1(a191) | c2_1(a191) | (~c0_1(a191)))),
% 0.72/0.90 inference(quant_inst,[status(thm)],[])).
% 0.72/0.90 tff(333,plain,
% 0.72/0.90 ((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | hskp24 | c1_1(a200) | c1_1(a191) | c2_1(a191) | (~ndr1_0) | (~c0_1(a191)) | (~c3_1(a200)) | (~c0_1(a200))),
% 0.72/0.90 inference(modus_ponens,[status(thm)],[332, 331])).
% 0.72/0.90 tff(334,plain,
% 0.72/0.90 (hskp24 | (~c0_1(a191)) | (~c3_1(a200)) | (~c0_1(a200))),
% 0.72/0.90 inference(unit_resolution,[status(thm)],[333, 148, 327, 67, 66, 326])).
% 0.72/0.90 tff(335,plain,
% 0.72/0.90 (hskp24),
% 0.72/0.90 inference(unit_resolution,[status(thm)],[334, 316, 272, 308])).
% 0.72/0.90 tff(336,plain,
% 0.72/0.90 (((~hskp24) | c3_1(a215)) <=> ((~hskp24) | c3_1(a215))),
% 0.72/0.90 inference(rewrite,[status(thm)],[])).
% 0.72/0.90 tff(337,axiom,((~hskp24) | c3_1(a215)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause39')).
% 0.72/0.90 tff(338,plain,
% 0.72/0.90 ((~hskp24) | c3_1(a215)),
% 0.72/0.90 inference(modus_ponens,[status(thm)],[337, 336])).
% 0.72/0.90 tff(339,plain,
% 0.72/0.90 ((~hskp24) | c3_1(a215)),
% 0.72/0.90 inference(modus_ponens,[status(thm)],[338, 336])).
% 0.72/0.90 tff(340,plain,
% 0.72/0.90 ((~hskp24) | c3_1(a215)),
% 0.72/0.90 inference(modus_ponens,[status(thm)],[339, 336])).
% 0.72/0.90 tff(341,plain,
% 0.72/0.90 ((~hskp24) | c3_1(a215)),
% 0.72/0.90 inference(modus_ponens,[status(thm)],[340, 336])).
% 0.72/0.90 tff(342,plain,
% 0.72/0.90 ((~hskp24) | c3_1(a215)),
% 0.72/0.90 inference(modus_ponens,[status(thm)],[341, 336])).
% 0.72/0.90 tff(343,plain,
% 0.72/0.90 (c3_1(a215)),
% 0.72/0.90 inference(unit_resolution,[status(thm)],[342, 335])).
% 0.72/0.90 tff(344,plain,
% 0.72/0.90 (((~hskp24) | c2_1(a215)) <=> ((~hskp24) | c2_1(a215))),
% 0.72/0.90 inference(rewrite,[status(thm)],[])).
% 0.72/0.90 tff(345,axiom,((~hskp24) | c2_1(a215)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause38')).
% 0.72/0.90 tff(346,plain,
% 0.72/0.90 ((~hskp24) | c2_1(a215)),
% 0.72/0.90 inference(modus_ponens,[status(thm)],[345, 344])).
% 0.72/0.90 tff(347,plain,
% 0.72/0.90 ((~hskp24) | c2_1(a215)),
% 0.72/0.90 inference(modus_ponens,[status(thm)],[346, 344])).
% 0.72/0.90 tff(348,plain,
% 0.72/0.90 ((~hskp24) | c2_1(a215)),
% 0.72/0.90 inference(modus_ponens,[status(thm)],[347, 344])).
% 0.72/0.90 tff(349,plain,
% 0.72/0.90 ((~hskp24) | c2_1(a215)),
% 0.72/0.90 inference(modus_ponens,[status(thm)],[348, 344])).
% 0.72/0.90 tff(350,plain,
% 0.72/0.90 ((~hskp24) | c2_1(a215)),
% 0.72/0.90 inference(modus_ponens,[status(thm)],[349, 344])).
% 0.72/0.90 tff(351,plain,
% 0.72/0.90 (c2_1(a215)),
% 0.72/0.90 inference(unit_resolution,[status(thm)],[350, 335])).
% 0.72/0.90 tff(352,plain,
% 0.72/0.90 (((~hskp24) | c1_1(a215)) <=> ((~hskp24) | c1_1(a215))),
% 0.72/0.90 inference(rewrite,[status(thm)],[])).
% 0.72/0.90 tff(353,axiom,((~hskp24) | c1_1(a215)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause37')).
% 0.72/0.90 tff(354,plain,
% 0.72/0.90 ((~hskp24) | c1_1(a215)),
% 0.72/0.90 inference(modus_ponens,[status(thm)],[353, 352])).
% 0.72/0.90 tff(355,plain,
% 0.72/0.90 ((~hskp24) | c1_1(a215)),
% 0.72/0.90 inference(modus_ponens,[status(thm)],[354, 352])).
% 0.72/0.90 tff(356,plain,
% 0.72/0.90 ((~hskp24) | c1_1(a215)),
% 0.72/0.90 inference(modus_ponens,[status(thm)],[355, 352])).
% 0.72/0.90 tff(357,plain,
% 0.72/0.90 ((~hskp24) | c1_1(a215)),
% 0.72/0.90 inference(modus_ponens,[status(thm)],[356, 352])).
% 0.72/0.90 tff(358,plain,
% 0.72/0.90 ((~hskp24) | c1_1(a215)),
% 0.72/0.90 inference(modus_ponens,[status(thm)],[357, 352])).
% 0.72/0.90 tff(359,plain,
% 0.72/0.90 (c1_1(a215)),
% 0.72/0.90 inference(unit_resolution,[status(thm)],[358, 335])).
% 0.72/0.90 tff(360,plain,
% 0.72/0.90 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp13 | c2_1(a191) | c3_1(a191) | (~ndr1_0) | (~c0_1(a191)) | (~c1_1(a215)) | (~c2_1(a215)) | (~c3_1(a215)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | hskp13 | c2_1(a191) | c3_1(a191) | (~ndr1_0) | (~c0_1(a191)) | (~c1_1(a215)) | (~c2_1(a215)) | (~c3_1(a215)))),
% 0.72/0.90 inference(rewrite,[status(thm)],[])).
% 0.72/0.90 tff(361,plain,
% 0.72/0.90 ((hskp13 | (~ndr1_0) | (~c3_1(a215)) | (~c1_1(a215)) | (~c2_1(a215)) | c3_1(a191) | c2_1(a191) | (~c0_1(a191))) <=> (hskp13 | c2_1(a191) | c3_1(a191) | (~ndr1_0) | (~c0_1(a191)) | (~c1_1(a215)) | (~c2_1(a215)) | (~c3_1(a215)))),
% 0.72/0.90 inference(rewrite,[status(thm)],[])).
% 0.72/0.90 tff(362,plain,
% 0.72/0.90 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp13 | (~ndr1_0) | (~c3_1(a215)) | (~c1_1(a215)) | (~c2_1(a215)) | c3_1(a191) | c2_1(a191) | (~c0_1(a191)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp13 | c2_1(a191) | c3_1(a191) | (~ndr1_0) | (~c0_1(a191)) | (~c1_1(a215)) | (~c2_1(a215)) | (~c3_1(a215))))),
% 0.72/0.90 inference(monotonicity,[status(thm)],[361])).
% 0.72/0.90 tff(363,plain,
% 0.72/0.90 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp13 | (~ndr1_0) | (~c3_1(a215)) | (~c1_1(a215)) | (~c2_1(a215)) | c3_1(a191) | c2_1(a191) | (~c0_1(a191)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | hskp13 | c2_1(a191) | c3_1(a191) | (~ndr1_0) | (~c0_1(a191)) | (~c1_1(a215)) | (~c2_1(a215)) | (~c3_1(a215)))),
% 0.72/0.90 inference(transitivity,[status(thm)],[362, 360])).
% 0.72/0.90 tff(364,plain,
% 0.72/0.90 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp13 | (~ndr1_0) | (~c3_1(a215)) | (~c1_1(a215)) | (~c2_1(a215)) | c3_1(a191) | c2_1(a191) | (~c0_1(a191)))),
% 0.72/0.90 inference(quant_inst,[status(thm)],[])).
% 0.72/0.90 tff(365,plain,
% 0.72/0.90 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | hskp13 | c2_1(a191) | c3_1(a191) | (~ndr1_0) | (~c0_1(a191)) | (~c1_1(a215)) | (~c2_1(a215)) | (~c3_1(a215))),
% 0.72/0.90 inference(modus_ponens,[status(thm)],[364, 363])).
% 0.72/0.90 tff(366,plain,
% 0.72/0.90 ($false),
% 0.72/0.90 inference(unit_resolution,[status(thm)],[365, 148, 236, 359, 351, 343, 66, 68, 282, 272])).
% 0.72/0.90 tff(367,plain,(hskp13 | c2_1(a191) | c3_1(a191) | c1_1(a200) | c1_1(a191) | (~c3_1(a225)) | c0_1(a225)), inference(lemma,lemma(discharge,[]))).
% 0.72/0.90 tff(368,plain,
% 0.72/0.90 (c1_1(a200)),
% 0.72/0.90 inference(unit_resolution,[status(thm)],[367, 236, 68, 234, 67, 66, 235])).
% 0.72/0.90 tff(369,plain,
% 0.72/0.90 (((~hskp10) | (~c1_1(a200))) <=> ((~hskp10) | (~c1_1(a200)))),
% 0.72/0.90 inference(rewrite,[status(thm)],[])).
% 0.72/0.90 tff(370,plain,
% 0.72/0.90 (((~c1_1(a200)) | (~hskp10)) <=> ((~hskp10) | (~c1_1(a200)))),
% 0.72/0.90 inference(rewrite,[status(thm)],[])).
% 0.72/0.90 tff(371,axiom,((~c1_1(a200)) | (~hskp10)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause92')).
% 0.72/0.90 tff(372,plain,
% 0.72/0.90 ((~hskp10) | (~c1_1(a200))),
% 0.72/0.90 inference(modus_ponens,[status(thm)],[371, 370])).
% 0.72/0.90 tff(373,plain,
% 0.72/0.90 ((~hskp10) | (~c1_1(a200))),
% 0.72/0.90 inference(modus_ponens,[status(thm)],[372, 369])).
% 0.72/0.90 tff(374,plain,
% 0.72/0.90 (~hskp10),
% 0.72/0.90 inference(unit_resolution,[status(thm)],[373, 368])).
% 0.72/0.90 tff(375,assumption,(c0_1(a191)), introduced(assumption)).
% 0.72/0.90 tff(376,plain,
% 0.72/0.90 (hskp10 | c2_1(a225)),
% 0.72/0.90 inference(unit_resolution,[status(thm)],[298, 148, 234, 235, 66, 68, 292, 375])).
% 0.72/0.90 tff(377,plain,
% 0.72/0.90 ($false),
% 0.72/0.90 inference(unit_resolution,[status(thm)],[376, 374, 254])).
% 0.72/0.90 tff(378,plain,(hskp13 | (~c3_1(a225)) | c0_1(a225) | c2_1(a191) | c3_1(a191) | (~c0_1(a191)) | c1_1(a191)), inference(lemma,lemma(discharge,[]))).
% 0.72/0.90 tff(379,plain,
% 0.72/0.90 (~c0_1(a191)),
% 0.72/0.90 inference(unit_resolution,[status(thm)],[378, 236, 235, 66, 68, 234, 67])).
% 0.72/0.90 tff(380,plain,
% 0.72/0.90 ($false),
% 0.72/0.90 inference(unit_resolution,[status(thm)],[271, 254, 379])).
% 0.72/0.90 tff(381,plain,(hskp13 | (~c3_1(a225)) | c0_1(a225) | c1_1(a191) | c2_1(a191) | c3_1(a191)), inference(lemma,lemma(discharge,[]))).
% 0.72/0.90 tff(382,plain,
% 0.72/0.90 (hskp13),
% 0.72/0.90 inference(unit_resolution,[status(thm)],[381, 233, 227, 67, 66, 68])).
% 0.72/0.90 tff(383,plain,
% 0.72/0.90 (((~hskp13) | (~c0_1(a209))) <=> ((~hskp13) | (~c0_1(a209)))),
% 0.72/0.90 inference(rewrite,[status(thm)],[])).
% 0.72/0.90 tff(384,plain,
% 0.72/0.90 (((~c0_1(a209)) | (~hskp13)) <=> ((~hskp13) | (~c0_1(a209)))),
% 0.72/0.90 inference(rewrite,[status(thm)],[])).
% 0.72/0.90 tff(385,axiom,((~c0_1(a209)) | (~hskp13)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause86')).
% 0.72/0.90 tff(386,plain,
% 0.72/0.90 ((~hskp13) | (~c0_1(a209))),
% 0.72/0.90 inference(modus_ponens,[status(thm)],[385, 384])).
% 0.72/0.90 tff(387,plain,
% 0.72/0.90 ((~hskp13) | (~c0_1(a209))),
% 0.72/0.90 inference(modus_ponens,[status(thm)],[386, 383])).
% 0.72/0.90 tff(388,plain,
% 0.72/0.90 (~c0_1(a209)),
% 0.72/0.90 inference(unit_resolution,[status(thm)],[387, 382])).
% 0.72/0.90 tff(389,plain,
% 0.72/0.90 (((~hskp13) | c3_1(a209)) <=> ((~hskp13) | c3_1(a209))),
% 0.72/0.90 inference(rewrite,[status(thm)],[])).
% 0.72/0.90 tff(390,axiom,((~hskp13) | c3_1(a209)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause55')).
% 0.72/0.90 tff(391,plain,
% 0.72/0.90 ((~hskp13) | c3_1(a209)),
% 0.72/0.90 inference(modus_ponens,[status(thm)],[390, 389])).
% 0.72/0.90 tff(392,plain,
% 0.72/0.90 ((~hskp13) | c3_1(a209)),
% 0.72/0.90 inference(modus_ponens,[status(thm)],[391, 389])).
% 0.72/0.90 tff(393,plain,
% 0.72/0.90 ((~hskp13) | c3_1(a209)),
% 0.72/0.90 inference(modus_ponens,[status(thm)],[392, 389])).
% 0.72/0.90 tff(394,plain,
% 0.72/0.90 ((~hskp13) | c3_1(a209)),
% 0.72/0.90 inference(modus_ponens,[status(thm)],[393, 389])).
% 0.72/0.90 tff(395,plain,
% 0.72/0.90 ((~hskp13) | c3_1(a209)),
% 0.72/0.90 inference(modus_ponens,[status(thm)],[394, 389])).
% 0.72/0.90 tff(396,plain,
% 0.72/0.90 (c3_1(a209)),
% 0.72/0.90 inference(unit_resolution,[status(thm)],[395, 382])).
% 0.72/0.90 tff(397,plain,
% 0.72/0.90 (((~hskp13) | c1_1(a209)) <=> ((~hskp13) | c1_1(a209))),
% 0.72/0.90 inference(rewrite,[status(thm)],[])).
% 0.72/0.90 tff(398,axiom,((~hskp13) | c1_1(a209)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause54')).
% 0.72/0.90 tff(399,plain,
% 0.72/0.90 ((~hskp13) | c1_1(a209)),
% 0.72/0.90 inference(modus_ponens,[status(thm)],[398, 397])).
% 0.72/0.90 tff(400,plain,
% 0.72/0.90 ((~hskp13) | c1_1(a209)),
% 0.72/0.90 inference(modus_ponens,[status(thm)],[399, 397])).
% 0.72/0.90 tff(401,plain,
% 0.72/0.90 ((~hskp13) | c1_1(a209)),
% 0.72/0.90 inference(modus_ponens,[status(thm)],[400, 397])).
% 0.72/0.90 tff(402,plain,
% 0.72/0.90 ((~hskp13) | c1_1(a209)),
% 0.72/0.90 inference(modus_ponens,[status(thm)],[401, 397])).
% 0.72/0.90 tff(403,plain,
% 0.72/0.90 ((~hskp13) | c1_1(a209)),
% 0.72/0.90 inference(modus_ponens,[status(thm)],[402, 397])).
% 0.72/0.90 tff(404,plain,
% 0.72/0.90 (c1_1(a209)),
% 0.72/0.90 inference(unit_resolution,[status(thm)],[403, 382])).
% 0.72/0.90 tff(405,plain,
% 0.72/0.90 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp10 | c0_1(a209) | c1_1(a191) | c2_1(a191) | c3_1(a191) | (~ndr1_0) | (~c1_1(a209)) | (~c3_1(a209)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp10 | c0_1(a209) | c1_1(a191) | c2_1(a191) | c3_1(a191) | (~ndr1_0) | (~c1_1(a209)) | (~c3_1(a209)))),
% 0.72/0.90 inference(rewrite,[status(thm)],[])).
% 0.72/0.90 tff(406,plain,
% 0.72/0.90 ((hskp10 | (~ndr1_0) | c0_1(a209) | (~c3_1(a209)) | (~c1_1(a209)) | c3_1(a191) | c1_1(a191) | c2_1(a191)) <=> (hskp10 | c0_1(a209) | c1_1(a191) | c2_1(a191) | c3_1(a191) | (~ndr1_0) | (~c1_1(a209)) | (~c3_1(a209)))),
% 0.72/0.90 inference(rewrite,[status(thm)],[])).
% 0.72/0.90 tff(407,plain,
% 0.72/0.90 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp10 | (~ndr1_0) | c0_1(a209) | (~c3_1(a209)) | (~c1_1(a209)) | c3_1(a191) | c1_1(a191) | c2_1(a191))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp10 | c0_1(a209) | c1_1(a191) | c2_1(a191) | c3_1(a191) | (~ndr1_0) | (~c1_1(a209)) | (~c3_1(a209))))),
% 0.72/0.90 inference(monotonicity,[status(thm)],[406])).
% 0.72/0.90 tff(408,plain,
% 0.72/0.90 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp10 | (~ndr1_0) | c0_1(a209) | (~c3_1(a209)) | (~c1_1(a209)) | c3_1(a191) | c1_1(a191) | c2_1(a191))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp10 | c0_1(a209) | c1_1(a191) | c2_1(a191) | c3_1(a191) | (~ndr1_0) | (~c1_1(a209)) | (~c3_1(a209)))),
% 0.72/0.90 inference(transitivity,[status(thm)],[407, 405])).
% 0.72/0.90 tff(409,plain,
% 0.72/0.90 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp10 | (~ndr1_0) | c0_1(a209) | (~c3_1(a209)) | (~c1_1(a209)) | c3_1(a191) | c1_1(a191) | c2_1(a191))),
% 0.72/0.90 inference(quant_inst,[status(thm)],[])).
% 0.72/0.90 tff(410,plain,
% 0.72/0.90 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp10 | c0_1(a209) | c1_1(a191) | c2_1(a191) | c3_1(a191) | (~ndr1_0) | (~c1_1(a209)) | (~c3_1(a209))),
% 0.72/0.90 inference(modus_ponens,[status(thm)],[409, 408])).
% 0.72/0.90 tff(411,plain,
% 0.72/0.90 (hskp10),
% 0.72/0.90 inference(unit_resolution,[status(thm)],[410, 148, 404, 396, 388, 67, 66, 68, 10])).
% 0.72/0.90 tff(412,plain,
% 0.72/0.90 (~c1_1(a200)),
% 0.72/0.90 inference(unit_resolution,[status(thm)],[373, 411])).
% 0.72/0.90 tff(413,plain,
% 0.72/0.90 (((~hskp19) | (~c1_1(a225))) <=> ((~hskp19) | (~c1_1(a225)))),
% 0.72/0.90 inference(rewrite,[status(thm)],[])).
% 0.72/0.90 tff(414,plain,
% 0.72/0.90 (((~c1_1(a225)) | (~hskp19)) <=> ((~hskp19) | (~c1_1(a225)))),
% 0.72/0.90 inference(rewrite,[status(thm)],[])).
% 0.72/0.90 tff(415,axiom,((~c1_1(a225)) | (~hskp19)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause76')).
% 0.72/0.90 tff(416,plain,
% 0.72/0.90 ((~hskp19) | (~c1_1(a225))),
% 0.72/0.90 inference(modus_ponens,[status(thm)],[415, 414])).
% 0.72/0.90 tff(417,plain,
% 0.72/0.90 ((~hskp19) | (~c1_1(a225))),
% 0.72/0.90 inference(modus_ponens,[status(thm)],[416, 413])).
% 0.72/0.90 tff(418,plain,
% 0.72/0.90 (~c1_1(a225)),
% 0.72/0.90 inference(unit_resolution,[status(thm)],[417, 219])).
% 0.72/0.90 tff(419,plain,
% 0.72/0.90 (c0_1(a200)),
% 0.72/0.90 inference(unit_resolution,[status(thm)],[307, 411])).
% 0.72/0.90 tff(420,assumption,(~c2_1(a200)), introduced(assumption)).
% 0.72/0.90 tff(421,assumption,(~c0_1(a209)), introduced(assumption)).
% 0.72/0.90 tff(422,assumption,(c0_1(a200)), introduced(assumption)).
% 0.72/0.90 tff(423,assumption,(c3_1(a209)), introduced(assumption)).
% 0.72/0.90 tff(424,assumption,(c1_1(a209)), introduced(assumption)).
% 0.72/0.90 tff(425,plain,
% 0.72/0.90 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_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(a257) | c0_1(a209) | c1_1(a200) | (~ndr1_0) | c2_1(a200) | (~c0_1(a200)) | (~c1_1(a209)) | (~c3_1(a209)) | c0_1(a257) | (~c2_1(a257)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_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(a257) | c0_1(a209) | c1_1(a200) | (~ndr1_0) | c2_1(a200) | (~c0_1(a200)) | (~c1_1(a209)) | (~c3_1(a209)) | c0_1(a257) | (~c2_1(a257)))),
% 0.72/0.90 inference(rewrite,[status(thm)],[])).
% 0.72/0.90 tff(426,plain,
% 0.72/0.90 (((~ndr1_0) | c1_1(a200) | c2_1(a200) | (~c0_1(a200)) | c0_1(a209) | (~c3_1(a209)) | (~c1_1(a209)) | c1_1(a257) | c0_1(a257) | (~c2_1(a257))) <=> (c1_1(a257) | c0_1(a209) | c1_1(a200) | (~ndr1_0) | c2_1(a200) | (~c0_1(a200)) | (~c1_1(a209)) | (~c3_1(a209)) | c0_1(a257) | (~c2_1(a257)))),
% 0.72/0.90 inference(rewrite,[status(thm)],[])).
% 0.72/0.90 tff(427,plain,
% 0.72/0.90 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_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) | c1_1(a200) | c2_1(a200) | (~c0_1(a200)) | c0_1(a209) | (~c3_1(a209)) | (~c1_1(a209)) | c1_1(a257) | c0_1(a257) | (~c2_1(a257)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_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(a257) | c0_1(a209) | c1_1(a200) | (~ndr1_0) | c2_1(a200) | (~c0_1(a200)) | (~c1_1(a209)) | (~c3_1(a209)) | c0_1(a257) | (~c2_1(a257))))),
% 0.72/0.90 inference(monotonicity,[status(thm)],[426])).
% 0.72/0.90 tff(428,plain,
% 0.72/0.90 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_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) | c1_1(a200) | c2_1(a200) | (~c0_1(a200)) | c0_1(a209) | (~c3_1(a209)) | (~c1_1(a209)) | c1_1(a257) | c0_1(a257) | (~c2_1(a257)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_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(a257) | c0_1(a209) | c1_1(a200) | (~ndr1_0) | c2_1(a200) | (~c0_1(a200)) | (~c1_1(a209)) | (~c3_1(a209)) | c0_1(a257) | (~c2_1(a257)))),
% 0.72/0.90 inference(transitivity,[status(thm)],[427, 425])).
% 0.72/0.90 tff(429,plain,
% 0.72/0.90 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_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) | c1_1(a200) | c2_1(a200) | (~c0_1(a200)) | c0_1(a209) | (~c3_1(a209)) | (~c1_1(a209)) | c1_1(a257) | c0_1(a257) | (~c2_1(a257)))),
% 0.72/0.90 inference(quant_inst,[status(thm)],[])).
% 0.72/0.90 tff(430,plain,
% 0.72/0.90 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_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(a257) | c0_1(a209) | c1_1(a200) | (~ndr1_0) | c2_1(a200) | (~c0_1(a200)) | (~c1_1(a209)) | (~c3_1(a209)) | c0_1(a257) | (~c2_1(a257))),
% 0.72/0.90 inference(modus_ponens,[status(thm)],[429, 428])).
% 0.72/0.90 tff(431,plain,
% 0.72/0.90 (c2_1(a200) | c0_1(a257)),
% 0.72/0.90 inference(unit_resolution,[status(thm)],[430, 148, 175, 424, 423, 422, 114, 421, 327, 65])).
% 0.72/0.90 tff(432,plain,
% 0.72/0.90 (c0_1(a257)),
% 0.72/0.90 inference(unit_resolution,[status(thm)],[431, 420])).
% 0.72/0.90 tff(433,assumption,(~c1_1(a225)), introduced(assumption)).
% 0.72/0.90 tff(434,plain,
% 0.72/0.90 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_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(a225) | c1_1(a225) | c0_1(a209) | c1_1(a200) | (~ndr1_0) | c2_1(a200) | (~c0_1(a200)) | (~c1_1(a209)) | (~c3_1(a209)) | (~c2_1(a225)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_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(a225) | c1_1(a225) | c0_1(a209) | c1_1(a200) | (~ndr1_0) | c2_1(a200) | (~c0_1(a200)) | (~c1_1(a209)) | (~c3_1(a209)) | (~c2_1(a225)))),
% 0.72/0.90 inference(rewrite,[status(thm)],[])).
% 0.72/0.90 tff(435,plain,
% 0.72/0.90 (((~ndr1_0) | c1_1(a200) | c2_1(a200) | (~c0_1(a200)) | c0_1(a209) | (~c3_1(a209)) | (~c1_1(a209)) | c1_1(a225) | c0_1(a225) | (~c2_1(a225))) <=> (c0_1(a225) | c1_1(a225) | c0_1(a209) | c1_1(a200) | (~ndr1_0) | c2_1(a200) | (~c0_1(a200)) | (~c1_1(a209)) | (~c3_1(a209)) | (~c2_1(a225)))),
% 0.72/0.90 inference(rewrite,[status(thm)],[])).
% 0.72/0.90 tff(436,plain,
% 0.72/0.90 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_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) | c1_1(a200) | c2_1(a200) | (~c0_1(a200)) | c0_1(a209) | (~c3_1(a209)) | (~c1_1(a209)) | c1_1(a225) | c0_1(a225) | (~c2_1(a225)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_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(a225) | c1_1(a225) | c0_1(a209) | c1_1(a200) | (~ndr1_0) | c2_1(a200) | (~c0_1(a200)) | (~c1_1(a209)) | (~c3_1(a209)) | (~c2_1(a225))))),
% 0.72/0.90 inference(monotonicity,[status(thm)],[435])).
% 0.72/0.90 tff(437,plain,
% 0.72/0.90 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_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) | c1_1(a200) | c2_1(a200) | (~c0_1(a200)) | c0_1(a209) | (~c3_1(a209)) | (~c1_1(a209)) | c1_1(a225) | c0_1(a225) | (~c2_1(a225)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_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(a225) | c1_1(a225) | c0_1(a209) | c1_1(a200) | (~ndr1_0) | c2_1(a200) | (~c0_1(a200)) | (~c1_1(a209)) | (~c3_1(a209)) | (~c2_1(a225)))),
% 0.72/0.90 inference(transitivity,[status(thm)],[436, 434])).
% 0.72/0.90 tff(438,plain,
% 0.72/0.90 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_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) | c1_1(a200) | c2_1(a200) | (~c0_1(a200)) | c0_1(a209) | (~c3_1(a209)) | (~c1_1(a209)) | c1_1(a225) | c0_1(a225) | (~c2_1(a225)))),
% 0.72/0.90 inference(quant_inst,[status(thm)],[])).
% 0.72/0.90 tff(439,plain,
% 0.72/0.90 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_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(a225) | c1_1(a225) | c0_1(a209) | c1_1(a200) | (~ndr1_0) | c2_1(a200) | (~c0_1(a200)) | (~c1_1(a209)) | (~c3_1(a209)) | (~c2_1(a225))),
% 0.72/0.90 inference(modus_ponens,[status(thm)],[438, 437])).
% 0.72/0.90 tff(440,plain,
% 0.72/0.90 (c2_1(a200) | (~c2_1(a225))),
% 0.72/0.90 inference(unit_resolution,[status(thm)],[439, 148, 424, 423, 422, 235, 433, 421, 327, 65])).
% 0.72/0.90 tff(441,plain,
% 0.72/0.90 (~c2_1(a225)),
% 0.72/0.90 inference(unit_resolution,[status(thm)],[440, 420])).
% 0.72/0.90 tff(442,plain,
% 0.72/0.90 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W))) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W))))),
% 0.72/0.90 inference(bind,[status(th)],[])).
% 0.72/0.90 tff(443,plain,
% 0.72/0.90 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))),
% 0.72/0.90 inference(quant_intro,[status(thm)],[442])).
% 0.72/0.90 tff(444,plain,
% 0.72/0.90 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))),
% 0.72/0.90 inference(rewrite,[status(thm)],[])).
% 0.72/0.90 tff(445,plain,
% 0.72/0.90 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(W))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V))) | (~c3_1(W))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(W)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(W))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(W))) | c3_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(W))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(W))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(W)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(W))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(W))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(W))) | c3_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(W))) | c1_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(W))) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(W)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(W))) | c3_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(W))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(W))) | c3_1(U)) | c1_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(W))) | c3_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(W))) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | (~c3_1(W)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(W))) | c3_1(U)) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | (~c3_1(W))))), ((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(W))) | c3_1(U)) | c1_1(V)) | c3_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | (~c3_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | (~c3_1(W))) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)))), ((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(W))) | c3_1(U)) | c1_1(V)) | c3_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c3_1(W))))), (((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(W))) | c3_1(U)) | c1_1(V)) | c3_1(V)) | c0_1(W)) | c2_1(W)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_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)) | c3_1(V) | c1_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)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))), (((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(W))) | c3_1(U)) | c1_1(V)) | c3_1(V)) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))))),
% 0.72/0.91 inference(bind,[status(th)],[])).
% 0.72/0.91 tff(446,plain,
% 0.72/0.91 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(W))) | c3_1(U)) | c1_1(V)) | c3_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)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))),
% 0.72/0.91 inference(quant_intro,[status(thm)],[445])).
% 0.72/0.91 tff(447,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(W))) | c3_1(U)) | c1_1(V)) | c3_1(V)) | c0_1(W)) | c2_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause156')).
% 0.72/0.91 tff(448,plain,
% 0.72/0.91 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))),
% 0.72/0.91 inference(modus_ponens,[status(thm)],[447, 446])).
% 0.72/0.91 tff(449,plain,
% 0.72/0.91 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))),
% 0.72/0.91 inference(modus_ponens,[status(thm)],[448, 444])).
% 0.72/0.91 tff(450,plain,(
% 0.72/0.91 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))),
% 0.72/0.91 inference(skolemize,[status(sab)],[449])).
% 0.72/0.91 tff(451,plain,
% 0.72/0.91 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))),
% 0.72/0.91 inference(modus_ponens,[status(thm)],[450, 443])).
% 0.72/0.91 tff(452,plain,
% 0.72/0.91 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c1_1(a257) | c3_1(a257) | c0_1(a225) | (~ndr1_0) | c2_1(a225) | (~c3_1(a225)) | (~c0_1(a257)) | (~c2_1(a257)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c1_1(a257) | c3_1(a257) | c0_1(a225) | (~ndr1_0) | c2_1(a225) | (~c3_1(a225)) | (~c0_1(a257)) | (~c2_1(a257)))),
% 0.72/0.91 inference(rewrite,[status(thm)],[])).
% 0.72/0.91 tff(453,plain,
% 0.72/0.91 (((~ndr1_0) | c3_1(a257) | (~c2_1(a257)) | (~c0_1(a257)) | c3_1(a257) | c1_1(a257) | (~c2_1(a257)) | c2_1(a225) | c0_1(a225) | (~c3_1(a225))) <=> (c1_1(a257) | c3_1(a257) | c0_1(a225) | (~ndr1_0) | c2_1(a225) | (~c3_1(a225)) | (~c0_1(a257)) | (~c2_1(a257)))),
% 0.72/0.91 inference(rewrite,[status(thm)],[])).
% 0.72/0.91 tff(454,plain,
% 0.72/0.91 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a257) | (~c2_1(a257)) | (~c0_1(a257)) | c3_1(a257) | c1_1(a257) | (~c2_1(a257)) | c2_1(a225) | c0_1(a225) | (~c3_1(a225)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c1_1(a257) | c3_1(a257) | c0_1(a225) | (~ndr1_0) | c2_1(a225) | (~c3_1(a225)) | (~c0_1(a257)) | (~c2_1(a257))))),
% 0.72/0.91 inference(monotonicity,[status(thm)],[453])).
% 0.72/0.91 tff(455,plain,
% 0.72/0.91 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a257) | (~c2_1(a257)) | (~c0_1(a257)) | c3_1(a257) | c1_1(a257) | (~c2_1(a257)) | c2_1(a225) | c0_1(a225) | (~c3_1(a225)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c1_1(a257) | c3_1(a257) | c0_1(a225) | (~ndr1_0) | c2_1(a225) | (~c3_1(a225)) | (~c0_1(a257)) | (~c2_1(a257)))),
% 0.72/0.91 inference(transitivity,[status(thm)],[454, 452])).
% 0.72/0.91 tff(456,plain,
% 0.72/0.91 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a257) | (~c2_1(a257)) | (~c0_1(a257)) | c3_1(a257) | c1_1(a257) | (~c2_1(a257)) | c2_1(a225) | c0_1(a225) | (~c3_1(a225)))),
% 0.72/0.91 inference(quant_inst,[status(thm)],[])).
% 0.72/0.91 tff(457,plain,
% 0.72/0.91 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c1_1(a257) | c3_1(a257) | c0_1(a225) | (~ndr1_0) | c2_1(a225) | (~c3_1(a225)) | (~c0_1(a257)) | (~c2_1(a257))),
% 0.72/0.91 inference(modus_ponens,[status(thm)],[456, 455])).
% 0.72/0.91 tff(458,plain,
% 0.72/0.91 ($false),
% 0.72/0.91 inference(unit_resolution,[status(thm)],[457, 148, 175, 234, 114, 113, 235, 451, 441, 432])).
% 0.72/0.91 tff(459,plain,(c2_1(a200) | (~c2_1(a257)) | (~c3_1(a225)) | c1_1(a257) | c3_1(a257) | c0_1(a225) | (~c1_1(a209)) | (~c3_1(a209)) | (~c0_1(a200)) | c1_1(a225) | c0_1(a209) | c1_1(a200)), inference(lemma,lemma(discharge,[]))).
% 0.72/0.91 tff(460,plain,
% 0.72/0.91 (c2_1(a200)),
% 0.72/0.91 inference(unit_resolution,[status(thm)],[459, 101, 227, 87, 93, 233, 404, 396, 419, 418, 388, 412])).
% 0.72/0.91 tff(461,plain,
% 0.72/0.91 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W))))),
% 0.72/0.91 inference(bind,[status(th)],[])).
% 0.72/0.91 tff(462,plain,
% 0.72/0.91 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))),
% 0.72/0.91 inference(quant_intro,[status(thm)],[461])).
% 0.72/0.91 tff(463,plain,
% 0.72/0.91 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))),
% 0.72/0.91 inference(rewrite,[status(thm)],[])).
% 0.72/0.91 tff(464,plain,
% 0.72/0.91 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(V))) | (~c0_1(W))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V))) | (~c0_1(W))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V))) | (~c0_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | (~c0_1(W)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(V))) | (~c0_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | (~c0_1(W))))), ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(V))) | (~c0_1(W))) | c1_1(W)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | (~c0_1(W))) | c1_1(W)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | (~c0_1(W))) | c1_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c0_1(W)))), ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(V))) | (~c0_1(W))) | c1_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c0_1(W))))), (((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(V))) | (~c0_1(W))) | c1_1(W)) | c3_1(W)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c0_1(W))) | c3_1(W)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c0_1(W))) | c3_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))), (((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(V))) | (~c0_1(W))) | c1_1(W)) | c3_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))))),
% 0.72/0.91 inference(bind,[status(th)],[])).
% 0.72/0.91 tff(465,plain,
% 0.72/0.91 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(V))) | (~c0_1(W))) | c1_1(W)) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))),
% 0.72/0.91 inference(quant_intro,[status(thm)],[464])).
% 0.72/0.91 tff(466,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(V))) | (~c0_1(W))) | c1_1(W)) | c3_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause163')).
% 0.72/0.91 tff(467,plain,
% 0.72/0.91 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))),
% 0.72/0.91 inference(modus_ponens,[status(thm)],[466, 465])).
% 0.72/0.91 tff(468,plain,
% 0.72/0.91 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))),
% 0.72/0.91 inference(modus_ponens,[status(thm)],[467, 463])).
% 0.72/0.91 tff(469,plain,(
% 0.72/0.91 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))),
% 0.72/0.91 inference(skolemize,[status(sab)],[468])).
% 0.72/0.91 tff(470,plain,
% 0.72/0.91 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))),
% 0.72/0.91 inference(modus_ponens,[status(thm)],[469, 462])).
% 0.72/0.91 tff(471,plain,
% 0.72/0.91 (c3_1(a200)),
% 0.72/0.91 inference(unit_resolution,[status(thm)],[315, 411])).
% 0.72/0.91 tff(472,plain,
% 0.72/0.91 (^[U: $i] : refl((hskp23 | hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))) <=> (hskp23 | hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))))),
% 0.72/0.91 inference(bind,[status(th)],[])).
% 0.72/0.91 tff(473,plain,
% 0.72/0.91 (![U: $i] : (hskp23 | hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp23 | hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))),
% 0.72/0.91 inference(quant_intro,[status(thm)],[472])).
% 0.72/0.91 tff(474,plain,
% 0.72/0.91 (![U: $i] : (hskp23 | hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp23 | hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))),
% 0.72/0.91 inference(rewrite,[status(thm)],[])).
% 0.72/0.91 tff(475,plain,
% 0.72/0.91 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp23) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))) | hskp23))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))) | hskp23) <=> (hskp23 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp23) <=> (hskp23 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp23) | hskp5) <=> ((hskp23 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))) | hskp5))), rewrite(((hskp23 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))) | hskp5) <=> (hskp23 | hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp23) | hskp5) <=> (hskp23 | hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))))),
% 0.72/0.91 inference(bind,[status(th)],[])).
% 0.72/0.91 tff(476,plain,
% 0.72/0.91 (![U: $i] : ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp23) | hskp5) <=> ![U: $i] : (hskp23 | hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))),
% 0.72/0.91 inference(quant_intro,[status(thm)],[475])).
% 0.72/0.91 tff(477,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp23) | hskp5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause127')).
% 0.72/0.91 tff(478,plain,
% 0.72/0.91 (![U: $i] : (hskp23 | hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))),
% 0.72/0.91 inference(modus_ponens,[status(thm)],[477, 476])).
% 0.72/0.91 tff(479,plain,
% 0.72/0.91 (![U: $i] : (hskp23 | hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))),
% 0.72/0.91 inference(modus_ponens,[status(thm)],[478, 474])).
% 0.72/0.91 tff(480,plain,(
% 0.72/0.91 ![U: $i] : (hskp23 | hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))),
% 0.72/0.91 inference(skolemize,[status(sab)],[479])).
% 0.72/0.91 tff(481,plain,
% 0.72/0.91 (![U: $i] : (hskp23 | hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))),
% 0.72/0.91 inference(modus_ponens,[status(thm)],[480, 473])).
% 0.72/0.91 tff(482,plain,
% 0.72/0.91 (((~![U: $i] : (hskp23 | hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | (hskp23 | hskp5 | (~ndr1_0) | (~c2_1(a200)) | (~c3_1(a200)) | (~c0_1(a200)))) <=> ((~![U: $i] : (hskp23 | hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | hskp23 | hskp5 | (~ndr1_0) | (~c2_1(a200)) | (~c3_1(a200)) | (~c0_1(a200)))),
% 0.72/0.91 inference(rewrite,[status(thm)],[])).
% 0.72/0.91 tff(483,plain,
% 0.72/0.91 ((hskp23 | hskp5 | (~ndr1_0) | (~c3_1(a200)) | (~c2_1(a200)) | (~c0_1(a200))) <=> (hskp23 | hskp5 | (~ndr1_0) | (~c2_1(a200)) | (~c3_1(a200)) | (~c0_1(a200)))),
% 0.72/0.91 inference(rewrite,[status(thm)],[])).
% 0.72/0.91 tff(484,plain,
% 0.72/0.91 (((~![U: $i] : (hskp23 | hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | (hskp23 | hskp5 | (~ndr1_0) | (~c3_1(a200)) | (~c2_1(a200)) | (~c0_1(a200)))) <=> ((~![U: $i] : (hskp23 | hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | (hskp23 | hskp5 | (~ndr1_0) | (~c2_1(a200)) | (~c3_1(a200)) | (~c0_1(a200))))),
% 0.72/0.91 inference(monotonicity,[status(thm)],[483])).
% 0.72/0.91 tff(485,plain,
% 0.72/0.91 (((~![U: $i] : (hskp23 | hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | (hskp23 | hskp5 | (~ndr1_0) | (~c3_1(a200)) | (~c2_1(a200)) | (~c0_1(a200)))) <=> ((~![U: $i] : (hskp23 | hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | hskp23 | hskp5 | (~ndr1_0) | (~c2_1(a200)) | (~c3_1(a200)) | (~c0_1(a200)))),
% 0.72/0.91 inference(transitivity,[status(thm)],[484, 482])).
% 0.72/0.91 tff(486,plain,
% 0.72/0.91 ((~![U: $i] : (hskp23 | hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | (hskp23 | hskp5 | (~ndr1_0) | (~c3_1(a200)) | (~c2_1(a200)) | (~c0_1(a200)))),
% 0.72/0.91 inference(quant_inst,[status(thm)],[])).
% 0.72/0.91 tff(487,plain,
% 0.72/0.91 ((~![U: $i] : (hskp23 | hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | hskp23 | hskp5 | (~ndr1_0) | (~c2_1(a200)) | (~c3_1(a200)) | (~c0_1(a200))),
% 0.72/0.91 inference(modus_ponens,[status(thm)],[486, 485])).
% 0.72/0.91 tff(488,plain,
% 0.72/0.91 (hskp23 | (~c2_1(a200))),
% 0.72/0.91 inference(unit_resolution,[status(thm)],[487, 148, 69, 419, 471, 481])).
% 0.72/0.91 tff(489,plain,
% 0.72/0.91 (hskp23),
% 0.72/0.91 inference(unit_resolution,[status(thm)],[488, 460])).
% 0.72/0.91 tff(490,plain,
% 0.72/0.91 (((~hskp23) | c3_1(a189)) <=> ((~hskp23) | c3_1(a189))),
% 0.72/0.91 inference(rewrite,[status(thm)],[])).
% 0.72/0.91 tff(491,axiom,((~hskp23) | c3_1(a189)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause42')).
% 0.72/0.91 tff(492,plain,
% 0.72/0.91 ((~hskp23) | c3_1(a189)),
% 0.72/0.91 inference(modus_ponens,[status(thm)],[491, 490])).
% 0.72/0.91 tff(493,plain,
% 0.72/0.91 ((~hskp23) | c3_1(a189)),
% 0.72/0.91 inference(modus_ponens,[status(thm)],[492, 490])).
% 0.72/0.91 tff(494,plain,
% 0.72/0.91 ((~hskp23) | c3_1(a189)),
% 0.72/0.91 inference(modus_ponens,[status(thm)],[493, 490])).
% 0.72/0.91 tff(495,plain,
% 0.72/0.91 ((~hskp23) | c3_1(a189)),
% 0.72/0.91 inference(modus_ponens,[status(thm)],[494, 490])).
% 0.72/0.91 tff(496,plain,
% 0.72/0.91 ((~hskp23) | c3_1(a189)),
% 0.72/0.91 inference(modus_ponens,[status(thm)],[495, 490])).
% 0.72/0.91 tff(497,plain,
% 0.72/0.91 (c3_1(a189)),
% 0.72/0.91 inference(unit_resolution,[status(thm)],[496, 489])).
% 0.72/0.91 tff(498,plain,
% 0.72/0.91 (((~hskp23) | c1_1(a189)) <=> ((~hskp23) | c1_1(a189))),
% 0.72/0.91 inference(rewrite,[status(thm)],[])).
% 0.72/0.91 tff(499,axiom,((~hskp23) | c1_1(a189)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause41')).
% 0.72/0.91 tff(500,plain,
% 0.72/0.91 ((~hskp23) | c1_1(a189)),
% 0.72/0.91 inference(modus_ponens,[status(thm)],[499, 498])).
% 0.72/0.91 tff(501,plain,
% 0.72/0.91 ((~hskp23) | c1_1(a189)),
% 0.72/0.91 inference(modus_ponens,[status(thm)],[500, 498])).
% 0.72/0.91 tff(502,plain,
% 0.72/0.91 ((~hskp23) | c1_1(a189)),
% 0.72/0.91 inference(modus_ponens,[status(thm)],[501, 498])).
% 0.72/0.91 tff(503,plain,
% 0.72/0.91 ((~hskp23) | c1_1(a189)),
% 0.72/0.91 inference(modus_ponens,[status(thm)],[502, 498])).
% 0.72/0.91 tff(504,plain,
% 0.72/0.91 ((~hskp23) | c1_1(a189)),
% 0.72/0.91 inference(modus_ponens,[status(thm)],[503, 498])).
% 0.72/0.91 tff(505,plain,
% 0.72/0.91 (c1_1(a189)),
% 0.72/0.91 inference(unit_resolution,[status(thm)],[504, 489])).
% 0.72/0.91 tff(506,plain,
% 0.72/0.91 (((~hskp23) | c0_1(a189)) <=> ((~hskp23) | c0_1(a189))),
% 0.72/0.91 inference(rewrite,[status(thm)],[])).
% 0.72/0.91 tff(507,axiom,((~hskp23) | c0_1(a189)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause40')).
% 0.72/0.91 tff(508,plain,
% 0.72/0.91 ((~hskp23) | c0_1(a189)),
% 0.72/0.91 inference(modus_ponens,[status(thm)],[507, 506])).
% 0.72/0.91 tff(509,plain,
% 0.72/0.91 ((~hskp23) | c0_1(a189)),
% 0.72/0.91 inference(modus_ponens,[status(thm)],[508, 506])).
% 0.72/0.91 tff(510,plain,
% 0.72/0.91 ((~hskp23) | c0_1(a189)),
% 0.72/0.91 inference(modus_ponens,[status(thm)],[509, 506])).
% 0.72/0.91 tff(511,plain,
% 0.72/0.91 ((~hskp23) | c0_1(a189)),
% 0.72/0.91 inference(modus_ponens,[status(thm)],[510, 506])).
% 0.72/0.91 tff(512,plain,
% 0.72/0.91 ((~hskp23) | c0_1(a189)),
% 0.72/0.91 inference(modus_ponens,[status(thm)],[511, 506])).
% 0.72/0.91 tff(513,plain,
% 0.72/0.91 (c0_1(a189)),
% 0.72/0.91 inference(unit_resolution,[status(thm)],[512, 489])).
% 0.72/0.91 tff(514,plain,
% 0.72/0.91 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | (c1_1(a191) | c3_1(a191) | (~ndr1_0) | (~c0_1(a191)) | (~c2_1(a200)) | (~c3_1(a200)) | (~c0_1(a200)) | (~c3_1(a189)) | (~c0_1(a189)) | (~c1_1(a189)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | c1_1(a191) | c3_1(a191) | (~ndr1_0) | (~c0_1(a191)) | (~c2_1(a200)) | (~c3_1(a200)) | (~c0_1(a200)) | (~c3_1(a189)) | (~c0_1(a189)) | (~c1_1(a189)))),
% 0.72/0.91 inference(rewrite,[status(thm)],[])).
% 0.72/0.91 tff(515,plain,
% 0.72/0.91 (((~ndr1_0) | (~c3_1(a200)) | (~c2_1(a200)) | (~c0_1(a200)) | (~c3_1(a189)) | (~c1_1(a189)) | (~c0_1(a189)) | c1_1(a191) | c3_1(a191) | (~c0_1(a191))) <=> (c1_1(a191) | c3_1(a191) | (~ndr1_0) | (~c0_1(a191)) | (~c2_1(a200)) | (~c3_1(a200)) | (~c0_1(a200)) | (~c3_1(a189)) | (~c0_1(a189)) | (~c1_1(a189)))),
% 0.72/0.91 inference(rewrite,[status(thm)],[])).
% 0.72/0.91 tff(516,plain,
% 0.72/0.91 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c3_1(a200)) | (~c2_1(a200)) | (~c0_1(a200)) | (~c3_1(a189)) | (~c1_1(a189)) | (~c0_1(a189)) | c1_1(a191) | c3_1(a191) | (~c0_1(a191)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | (c1_1(a191) | c3_1(a191) | (~ndr1_0) | (~c0_1(a191)) | (~c2_1(a200)) | (~c3_1(a200)) | (~c0_1(a200)) | (~c3_1(a189)) | (~c0_1(a189)) | (~c1_1(a189))))),
% 0.72/0.91 inference(monotonicity,[status(thm)],[515])).
% 0.72/0.91 tff(517,plain,
% 0.72/0.91 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c3_1(a200)) | (~c2_1(a200)) | (~c0_1(a200)) | (~c3_1(a189)) | (~c1_1(a189)) | (~c0_1(a189)) | c1_1(a191) | c3_1(a191) | (~c0_1(a191)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | c1_1(a191) | c3_1(a191) | (~ndr1_0) | (~c0_1(a191)) | (~c2_1(a200)) | (~c3_1(a200)) | (~c0_1(a200)) | (~c3_1(a189)) | (~c0_1(a189)) | (~c1_1(a189)))),
% 0.72/0.91 inference(transitivity,[status(thm)],[516, 514])).
% 0.72/0.91 tff(518,plain,
% 0.72/0.91 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c3_1(a200)) | (~c2_1(a200)) | (~c0_1(a200)) | (~c3_1(a189)) | (~c1_1(a189)) | (~c0_1(a189)) | c1_1(a191) | c3_1(a191) | (~c0_1(a191)))),
% 0.72/0.91 inference(quant_inst,[status(thm)],[])).
% 0.72/0.91 tff(519,plain,
% 0.72/0.91 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | c1_1(a191) | c3_1(a191) | (~ndr1_0) | (~c0_1(a191)) | (~c2_1(a200)) | (~c3_1(a200)) | (~c0_1(a200)) | (~c3_1(a189)) | (~c0_1(a189)) | (~c1_1(a189))),
% 0.72/0.91 inference(modus_ponens,[status(thm)],[518, 517])).
% 0.72/0.91 tff(520,plain,
% 0.72/0.91 (~c0_1(a191)),
% 0.72/0.91 inference(unit_resolution,[status(thm)],[519, 148, 513, 505, 497, 419, 471, 67, 68, 470, 460])).
% 0.72/0.91 tff(521,plain,
% 0.72/0.91 (^[U: $i] : refl((hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U)) <=> (hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U)))),
% 0.72/0.91 inference(bind,[status(th)],[])).
% 0.72/0.91 tff(522,plain,
% 0.72/0.91 (![U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U)) <=> ![U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))),
% 0.72/0.91 inference(quant_intro,[status(thm)],[521])).
% 0.72/0.91 tff(523,plain,
% 0.72/0.91 (![U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U)) <=> ![U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))),
% 0.72/0.91 inference(rewrite,[status(thm)],[])).
% 0.72/0.91 tff(524,plain,
% 0.72/0.91 (^[U: $i] : 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)) | hskp6) <=> (((~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U)) | hskp6))), rewrite((((~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U)) | hskp6) <=> (hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))), ((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp6) <=> (hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))))),
% 0.72/0.91 inference(bind,[status(th)],[])).
% 0.72/0.91 tff(525,plain,
% 0.72/0.91 (![U: $i] : (((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp6) <=> ![U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))),
% 0.72/0.91 inference(quant_intro,[status(thm)],[524])).
% 0.72/0.91 tff(526,axiom,(![U: $i] : (((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause113')).
% 0.72/0.91 tff(527,plain,
% 0.72/0.91 (![U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))),
% 0.72/0.91 inference(modus_ponens,[status(thm)],[526, 525])).
% 0.72/0.91 tff(528,plain,
% 0.72/0.91 (![U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))),
% 0.72/0.91 inference(modus_ponens,[status(thm)],[527, 523])).
% 0.72/0.91 tff(529,plain,(
% 0.72/0.91 ![U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))),
% 0.72/0.91 inference(skolemize,[status(sab)],[528])).
% 0.72/0.91 tff(530,plain,
% 0.72/0.91 (![U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))),
% 0.72/0.91 inference(modus_ponens,[status(thm)],[529, 522])).
% 0.72/0.91 tff(531,plain,
% 0.72/0.91 (((~![U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp6 | c2_1(a191) | c3_1(a191) | (~ndr1_0) | c0_1(a191))) <=> ((~![U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | hskp6 | c2_1(a191) | c3_1(a191) | (~ndr1_0) | c0_1(a191))),
% 0.72/0.91 inference(rewrite,[status(thm)],[])).
% 0.72/0.91 tff(532,plain,
% 0.72/0.91 ((hskp6 | (~ndr1_0) | c3_1(a191) | c0_1(a191) | c2_1(a191)) <=> (hskp6 | c2_1(a191) | c3_1(a191) | (~ndr1_0) | c0_1(a191))),
% 0.72/0.91 inference(rewrite,[status(thm)],[])).
% 0.72/0.91 tff(533,plain,
% 0.72/0.91 (((~![U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp6 | (~ndr1_0) | c3_1(a191) | c0_1(a191) | c2_1(a191))) <=> ((~![U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp6 | c2_1(a191) | c3_1(a191) | (~ndr1_0) | c0_1(a191)))),
% 0.72/0.91 inference(monotonicity,[status(thm)],[532])).
% 0.72/0.91 tff(534,plain,
% 0.72/0.91 (((~![U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp6 | (~ndr1_0) | c3_1(a191) | c0_1(a191) | c2_1(a191))) <=> ((~![U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | hskp6 | c2_1(a191) | c3_1(a191) | (~ndr1_0) | c0_1(a191))),
% 0.72/0.91 inference(transitivity,[status(thm)],[533, 531])).
% 0.72/0.91 tff(535,plain,
% 0.72/0.91 ((~![U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp6 | (~ndr1_0) | c3_1(a191) | c0_1(a191) | c2_1(a191))),
% 0.72/0.91 inference(quant_inst,[status(thm)],[])).
% 0.72/0.91 tff(536,plain,
% 0.72/0.91 ((~![U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | hskp6 | c2_1(a191) | c3_1(a191) | (~ndr1_0) | c0_1(a191)),
% 0.72/0.91 inference(modus_ponens,[status(thm)],[535, 534])).
% 0.72/0.91 tff(537,plain,
% 0.72/0.91 (hskp6 | c0_1(a191)),
% 0.72/0.91 inference(unit_resolution,[status(thm)],[536, 148, 66, 68, 530])).
% 0.72/0.91 tff(538,plain,
% 0.72/0.91 (hskp6),
% 0.72/0.91 inference(unit_resolution,[status(thm)],[537, 520])).
% 0.72/0.91 tff(539,plain,
% 0.72/0.91 (((~hskp6) | (~c3_1(a195))) <=> ((~hskp6) | (~c3_1(a195)))),
% 0.72/0.91 inference(rewrite,[status(thm)],[])).
% 0.72/0.91 tff(540,plain,
% 0.72/0.91 (((~c3_1(a195)) | (~hskp6)) <=> ((~hskp6) | (~c3_1(a195)))),
% 0.72/0.91 inference(rewrite,[status(thm)],[])).
% 0.72/0.91 tff(541,axiom,((~c3_1(a195)) | (~hskp6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause99')).
% 0.72/0.91 tff(542,plain,
% 0.72/0.91 ((~hskp6) | (~c3_1(a195))),
% 0.72/0.91 inference(modus_ponens,[status(thm)],[541, 540])).
% 0.72/0.91 tff(543,plain,
% 0.72/0.91 ((~hskp6) | (~c3_1(a195))),
% 0.72/0.91 inference(modus_ponens,[status(thm)],[542, 539])).
% 0.72/0.91 tff(544,plain,
% 0.72/0.91 (~c3_1(a195)),
% 0.72/0.91 inference(unit_resolution,[status(thm)],[543, 538])).
% 0.72/0.91 tff(545,plain,
% 0.72/0.91 (((~hskp6) | c0_1(a195)) <=> ((~hskp6) | c0_1(a195))),
% 0.72/0.91 inference(rewrite,[status(thm)],[])).
% 0.72/0.91 tff(546,axiom,((~hskp6) | c0_1(a195)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause63')).
% 0.72/0.91 tff(547,plain,
% 0.72/0.91 ((~hskp6) | c0_1(a195)),
% 0.72/0.91 inference(modus_ponens,[status(thm)],[546, 545])).
% 0.72/0.91 tff(548,plain,
% 0.72/0.91 ((~hskp6) | c0_1(a195)),
% 0.72/0.91 inference(modus_ponens,[status(thm)],[547, 545])).
% 0.72/0.91 tff(549,plain,
% 0.72/0.91 ((~hskp6) | c0_1(a195)),
% 0.72/0.91 inference(modus_ponens,[status(thm)],[548, 545])).
% 0.72/0.91 tff(550,plain,
% 0.72/0.91 ((~hskp6) | c0_1(a195)),
% 0.72/0.91 inference(modus_ponens,[status(thm)],[549, 545])).
% 0.72/0.91 tff(551,plain,
% 0.72/0.91 ((~hskp6) | c0_1(a195)),
% 0.72/0.91 inference(modus_ponens,[status(thm)],[550, 545])).
% 0.72/0.91 tff(552,plain,
% 0.72/0.91 (c0_1(a195)),
% 0.72/0.91 inference(unit_resolution,[status(thm)],[551, 538])).
% 0.72/0.91 tff(553,plain,
% 0.72/0.91 (((~hskp6) | (~c1_1(a195))) <=> ((~hskp6) | (~c1_1(a195)))),
% 0.72/0.91 inference(rewrite,[status(thm)],[])).
% 0.72/0.91 tff(554,plain,
% 0.72/0.91 (((~c1_1(a195)) | (~hskp6)) <=> ((~hskp6) | (~c1_1(a195)))),
% 0.72/0.91 inference(rewrite,[status(thm)],[])).
% 0.72/0.91 tff(555,axiom,((~c1_1(a195)) | (~hskp6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause98')).
% 0.72/0.91 tff(556,plain,
% 0.72/0.91 ((~hskp6) | (~c1_1(a195))),
% 0.72/0.91 inference(modus_ponens,[status(thm)],[555, 554])).
% 0.72/0.91 tff(557,plain,
% 0.72/0.91 ((~hskp6) | (~c1_1(a195))),
% 0.72/0.91 inference(modus_ponens,[status(thm)],[556, 553])).
% 0.72/0.91 tff(558,plain,
% 0.72/0.91 (~c1_1(a195)),
% 0.72/0.91 inference(unit_resolution,[status(thm)],[557, 538])).
% 0.72/0.91 tff(559,assumption,(c2_1(a200)), introduced(assumption)).
% 0.72/0.91 tff(560,assumption,(~c3_1(a195)), introduced(assumption)).
% 0.72/0.91 tff(561,assumption,(~c1_1(a195)), introduced(assumption)).
% 0.72/0.91 tff(562,assumption,(c0_1(a195)), introduced(assumption)).
% 0.72/0.91 tff(563,assumption,(c3_1(a200)), introduced(assumption)).
% 0.72/0.91 tff(564,plain,
% 0.72/0.91 (hskp23 | (~c2_1(a200))),
% 0.72/0.91 inference(unit_resolution,[status(thm)],[487, 148, 69, 422, 563, 481])).
% 0.72/0.91 tff(565,plain,
% 0.72/0.91 (hskp23),
% 0.72/0.91 inference(unit_resolution,[status(thm)],[564, 559])).
% 0.72/0.91 tff(566,plain,
% 0.72/0.91 (c3_1(a189)),
% 0.72/0.91 inference(unit_resolution,[status(thm)],[496, 565])).
% 0.72/0.91 tff(567,plain,
% 0.72/0.91 (c1_1(a189)),
% 0.72/0.91 inference(unit_resolution,[status(thm)],[504, 565])).
% 0.72/0.91 tff(568,plain,
% 0.72/0.91 (c0_1(a189)),
% 0.72/0.91 inference(unit_resolution,[status(thm)],[512, 565])).
% 0.72/0.91 tff(569,plain,
% 0.72/0.91 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | (c1_1(a195) | c3_1(a195) | (~ndr1_0) | (~c0_1(a195)) | (~c2_1(a200)) | (~c3_1(a200)) | (~c0_1(a200)) | (~c3_1(a189)) | (~c0_1(a189)) | (~c1_1(a189)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | c1_1(a195) | c3_1(a195) | (~ndr1_0) | (~c0_1(a195)) | (~c2_1(a200)) | (~c3_1(a200)) | (~c0_1(a200)) | (~c3_1(a189)) | (~c0_1(a189)) | (~c1_1(a189)))),
% 0.72/0.91 inference(rewrite,[status(thm)],[])).
% 0.72/0.91 tff(570,plain,
% 0.72/0.91 (((~ndr1_0) | (~c3_1(a200)) | (~c2_1(a200)) | (~c0_1(a200)) | (~c3_1(a189)) | (~c1_1(a189)) | (~c0_1(a189)) | c1_1(a195) | c3_1(a195) | (~c0_1(a195))) <=> (c1_1(a195) | c3_1(a195) | (~ndr1_0) | (~c0_1(a195)) | (~c2_1(a200)) | (~c3_1(a200)) | (~c0_1(a200)) | (~c3_1(a189)) | (~c0_1(a189)) | (~c1_1(a189)))),
% 0.72/0.91 inference(rewrite,[status(thm)],[])).
% 0.72/0.91 tff(571,plain,
% 0.72/0.91 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c3_1(a200)) | (~c2_1(a200)) | (~c0_1(a200)) | (~c3_1(a189)) | (~c1_1(a189)) | (~c0_1(a189)) | c1_1(a195) | c3_1(a195) | (~c0_1(a195)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | (c1_1(a195) | c3_1(a195) | (~ndr1_0) | (~c0_1(a195)) | (~c2_1(a200)) | (~c3_1(a200)) | (~c0_1(a200)) | (~c3_1(a189)) | (~c0_1(a189)) | (~c1_1(a189))))),
% 0.72/0.91 inference(monotonicity,[status(thm)],[570])).
% 0.72/0.91 tff(572,plain,
% 0.72/0.91 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c3_1(a200)) | (~c2_1(a200)) | (~c0_1(a200)) | (~c3_1(a189)) | (~c1_1(a189)) | (~c0_1(a189)) | c1_1(a195) | c3_1(a195) | (~c0_1(a195)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | c1_1(a195) | c3_1(a195) | (~ndr1_0) | (~c0_1(a195)) | (~c2_1(a200)) | (~c3_1(a200)) | (~c0_1(a200)) | (~c3_1(a189)) | (~c0_1(a189)) | (~c1_1(a189)))),
% 0.72/0.91 inference(transitivity,[status(thm)],[571, 569])).
% 0.72/0.91 tff(573,plain,
% 0.72/0.91 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c3_1(a200)) | (~c2_1(a200)) | (~c0_1(a200)) | (~c3_1(a189)) | (~c1_1(a189)) | (~c0_1(a189)) | c1_1(a195) | c3_1(a195) | (~c0_1(a195)))),
% 0.72/0.91 inference(quant_inst,[status(thm)],[])).
% 0.72/0.91 tff(574,plain,
% 0.72/0.91 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | c1_1(a195) | c3_1(a195) | (~ndr1_0) | (~c0_1(a195)) | (~c2_1(a200)) | (~c3_1(a200)) | (~c0_1(a200)) | (~c3_1(a189)) | (~c0_1(a189)) | (~c1_1(a189))),
% 0.72/0.91 inference(modus_ponens,[status(thm)],[573, 572])).
% 0.72/0.91 tff(575,plain,
% 0.72/0.91 ($false),
% 0.72/0.91 inference(unit_resolution,[status(thm)],[574, 148, 568, 567, 566, 422, 563, 562, 561, 560, 470, 559])).
% 0.72/0.91 tff(576,plain,((~c2_1(a200)) | (~c0_1(a200)) | (~c3_1(a200)) | (~c0_1(a195)) | c1_1(a195) | c3_1(a195) | hskp5), inference(lemma,lemma(discharge,[]))).
% 0.72/0.91 tff(577,plain,
% 0.72/0.91 ($false),
% 0.72/0.91 inference(unit_resolution,[status(thm)],[576, 558, 552, 471, 419, 460, 544, 69])).
% 0.72/0.91 tff(578,plain,(hskp5 | c2_1(a191) | c3_1(a191) | c1_1(a191) | c3_1(a190) | hskp15), inference(lemma,lemma(discharge,[]))).
% 0.72/0.91 tff(579,plain,
% 0.72/0.91 (hskp5),
% 0.72/0.91 inference(unit_resolution,[status(thm)],[578, 13, 68, 67, 66, 36])).
% 0.72/0.91 tff(580,plain,
% 0.72/0.91 (((~hskp5) | (~c2_1(a194))) <=> ((~hskp5) | (~c2_1(a194)))),
% 0.72/0.91 inference(rewrite,[status(thm)],[])).
% 0.72/0.91 tff(581,plain,
% 0.72/0.91 (((~c2_1(a194)) | (~hskp5)) <=> ((~hskp5) | (~c2_1(a194)))),
% 0.72/0.91 inference(rewrite,[status(thm)],[])).
% 0.72/0.91 tff(582,axiom,((~c2_1(a194)) | (~hskp5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause101')).
% 0.72/0.91 tff(583,plain,
% 0.72/0.91 ((~hskp5) | (~c2_1(a194))),
% 0.72/0.91 inference(modus_ponens,[status(thm)],[582, 581])).
% 0.72/0.91 tff(584,plain,
% 0.72/0.91 ((~hskp5) | (~c2_1(a194))),
% 0.72/0.91 inference(modus_ponens,[status(thm)],[583, 580])).
% 0.72/0.92 tff(585,plain,
% 0.72/0.92 (~c2_1(a194)),
% 0.72/0.92 inference(unit_resolution,[status(thm)],[584, 579])).
% 0.72/0.92 tff(586,plain,
% 0.72/0.92 (((~hskp5) | (~c1_1(a194))) <=> ((~hskp5) | (~c1_1(a194)))),
% 0.72/0.92 inference(rewrite,[status(thm)],[])).
% 0.72/0.92 tff(587,plain,
% 0.72/0.92 (((~c1_1(a194)) | (~hskp5)) <=> ((~hskp5) | (~c1_1(a194)))),
% 0.72/0.92 inference(rewrite,[status(thm)],[])).
% 0.72/0.92 tff(588,axiom,((~c1_1(a194)) | (~hskp5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause100')).
% 0.72/0.92 tff(589,plain,
% 0.72/0.92 ((~hskp5) | (~c1_1(a194))),
% 0.72/0.92 inference(modus_ponens,[status(thm)],[588, 587])).
% 0.72/0.92 tff(590,plain,
% 0.72/0.92 ((~hskp5) | (~c1_1(a194))),
% 0.72/0.92 inference(modus_ponens,[status(thm)],[589, 586])).
% 0.72/0.92 tff(591,plain,
% 0.72/0.92 (~c1_1(a194)),
% 0.72/0.92 inference(unit_resolution,[status(thm)],[590, 579])).
% 0.72/0.92 tff(592,plain,
% 0.72/0.92 (((~hskp5) | c0_1(a194)) <=> ((~hskp5) | c0_1(a194))),
% 0.72/0.92 inference(rewrite,[status(thm)],[])).
% 0.72/0.92 tff(593,axiom,((~hskp5) | c0_1(a194)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause64')).
% 0.72/0.92 tff(594,plain,
% 0.72/0.92 ((~hskp5) | c0_1(a194)),
% 0.72/0.92 inference(modus_ponens,[status(thm)],[593, 592])).
% 0.72/0.92 tff(595,plain,
% 0.72/0.92 ((~hskp5) | c0_1(a194)),
% 0.72/0.92 inference(modus_ponens,[status(thm)],[594, 592])).
% 0.72/0.92 tff(596,plain,
% 0.72/0.92 ((~hskp5) | c0_1(a194)),
% 0.72/0.92 inference(modus_ponens,[status(thm)],[595, 592])).
% 0.72/0.92 tff(597,plain,
% 0.72/0.92 ((~hskp5) | c0_1(a194)),
% 0.72/0.92 inference(modus_ponens,[status(thm)],[596, 592])).
% 0.72/0.92 tff(598,plain,
% 0.72/0.92 ((~hskp5) | c0_1(a194)),
% 0.72/0.92 inference(modus_ponens,[status(thm)],[597, 592])).
% 0.72/0.92 tff(599,plain,
% 0.72/0.92 (c0_1(a194)),
% 0.72/0.92 inference(unit_resolution,[status(thm)],[598, 579])).
% 0.72/0.92 tff(600,assumption,(hskp0), introduced(assumption)).
% 0.72/0.92 tff(601,plain,
% 0.72/0.92 (((~hskp0) | (~c3_1(a188))) <=> ((~hskp0) | (~c3_1(a188)))),
% 0.72/0.92 inference(rewrite,[status(thm)],[])).
% 0.72/0.92 tff(602,plain,
% 0.72/0.92 (((~c3_1(a188)) | (~hskp0)) <=> ((~hskp0) | (~c3_1(a188)))),
% 0.72/0.92 inference(rewrite,[status(thm)],[])).
% 0.72/0.92 tff(603,axiom,((~c3_1(a188)) | (~hskp0)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause111')).
% 0.72/0.92 tff(604,plain,
% 0.72/0.92 ((~hskp0) | (~c3_1(a188))),
% 0.72/0.92 inference(modus_ponens,[status(thm)],[603, 602])).
% 0.72/0.92 tff(605,plain,
% 0.72/0.92 ((~hskp0) | (~c3_1(a188))),
% 0.72/0.92 inference(modus_ponens,[status(thm)],[604, 601])).
% 0.72/0.92 tff(606,plain,
% 0.72/0.92 (~c3_1(a188)),
% 0.72/0.92 inference(unit_resolution,[status(thm)],[605, 600])).
% 0.72/0.92 tff(607,plain,
% 0.72/0.92 (((~hskp0) | (~c1_1(a188))) <=> ((~hskp0) | (~c1_1(a188)))),
% 0.72/0.92 inference(rewrite,[status(thm)],[])).
% 0.72/0.92 tff(608,plain,
% 0.72/0.92 (((~c1_1(a188)) | (~hskp0)) <=> ((~hskp0) | (~c1_1(a188)))),
% 0.72/0.92 inference(rewrite,[status(thm)],[])).
% 0.72/0.92 tff(609,axiom,((~c1_1(a188)) | (~hskp0)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause110')).
% 0.72/0.92 tff(610,plain,
% 0.72/0.92 ((~hskp0) | (~c1_1(a188))),
% 0.72/0.92 inference(modus_ponens,[status(thm)],[609, 608])).
% 0.72/0.92 tff(611,plain,
% 0.72/0.92 ((~hskp0) | (~c1_1(a188))),
% 0.72/0.92 inference(modus_ponens,[status(thm)],[610, 607])).
% 0.72/0.92 tff(612,plain,
% 0.72/0.92 (~c1_1(a188)),
% 0.72/0.92 inference(unit_resolution,[status(thm)],[611, 600])).
% 0.72/0.92 tff(613,plain,
% 0.72/0.92 (((~hskp0) | (~c0_1(a188))) <=> ((~hskp0) | (~c0_1(a188)))),
% 0.72/0.92 inference(rewrite,[status(thm)],[])).
% 0.72/0.92 tff(614,plain,
% 0.72/0.92 (((~c0_1(a188)) | (~hskp0)) <=> ((~hskp0) | (~c0_1(a188)))),
% 0.72/0.92 inference(rewrite,[status(thm)],[])).
% 0.72/0.92 tff(615,axiom,((~c0_1(a188)) | (~hskp0)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause109')).
% 0.72/0.92 tff(616,plain,
% 0.72/0.92 ((~hskp0) | (~c0_1(a188))),
% 0.72/0.92 inference(modus_ponens,[status(thm)],[615, 614])).
% 0.72/0.92 tff(617,plain,
% 0.72/0.92 ((~hskp0) | (~c0_1(a188))),
% 0.72/0.92 inference(modus_ponens,[status(thm)],[616, 613])).
% 0.72/0.92 tff(618,plain,
% 0.72/0.92 (~c0_1(a188)),
% 0.72/0.92 inference(unit_resolution,[status(thm)],[617, 600])).
% 0.72/0.92 tff(619,plain,
% 0.72/0.92 (((~![U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp1 | c0_1(a188) | c1_1(a188) | c3_1(a188) | (~ndr1_0))) <=> ((~![U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | hskp1 | c0_1(a188) | c1_1(a188) | c3_1(a188) | (~ndr1_0))),
% 0.72/0.92 inference(rewrite,[status(thm)],[])).
% 0.72/0.92 tff(620,plain,
% 0.72/0.92 ((hskp1 | (~ndr1_0) | c3_1(a188) | c1_1(a188) | c0_1(a188)) <=> (hskp1 | c0_1(a188) | c1_1(a188) | c3_1(a188) | (~ndr1_0))),
% 0.72/0.92 inference(rewrite,[status(thm)],[])).
% 0.72/0.92 tff(621,plain,
% 0.72/0.92 (((~![U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp1 | (~ndr1_0) | c3_1(a188) | c1_1(a188) | c0_1(a188))) <=> ((~![U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp1 | c0_1(a188) | c1_1(a188) | c3_1(a188) | (~ndr1_0)))),
% 0.72/0.92 inference(monotonicity,[status(thm)],[620])).
% 0.72/0.92 tff(622,plain,
% 0.72/0.92 (((~![U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp1 | (~ndr1_0) | c3_1(a188) | c1_1(a188) | c0_1(a188))) <=> ((~![U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | hskp1 | c0_1(a188) | c1_1(a188) | c3_1(a188) | (~ndr1_0))),
% 0.72/0.92 inference(transitivity,[status(thm)],[621, 619])).
% 0.72/0.92 tff(623,plain,
% 0.72/0.92 ((~![U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp1 | (~ndr1_0) | c3_1(a188) | c1_1(a188) | c0_1(a188))),
% 0.72/0.92 inference(quant_inst,[status(thm)],[])).
% 0.72/0.92 tff(624,plain,
% 0.72/0.92 ((~![U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | hskp1 | c0_1(a188) | c1_1(a188) | c3_1(a188) | (~ndr1_0)),
% 0.72/0.92 inference(modus_ponens,[status(thm)],[623, 622])).
% 0.72/0.92 tff(625,plain,
% 0.72/0.92 ($false),
% 0.72/0.92 inference(unit_resolution,[status(thm)],[624, 148, 102, 618, 612, 606, 112])).
% 0.72/0.92 tff(626,plain,((~hskp0) | hskp1), inference(lemma,lemma(discharge,[]))).
% 0.72/0.92 tff(627,plain,
% 0.72/0.92 (~hskp0),
% 0.72/0.92 inference(unit_resolution,[status(thm)],[626, 102])).
% 0.72/0.92 tff(628,plain,
% 0.72/0.92 ((hskp9 | hskp1 | hskp0) <=> (hskp9 | hskp1 | hskp0)),
% 0.72/0.92 inference(rewrite,[status(thm)],[])).
% 0.72/0.92 tff(629,plain,
% 0.72/0.92 (((hskp1 | hskp9) | hskp0) <=> (hskp9 | hskp1 | hskp0)),
% 0.72/0.92 inference(rewrite,[status(thm)],[])).
% 0.72/0.92 tff(630,axiom,((hskp1 | hskp9) | hskp0), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause29')).
% 0.72/0.92 tff(631,plain,
% 0.72/0.92 (hskp9 | hskp1 | hskp0),
% 0.72/0.92 inference(modus_ponens,[status(thm)],[630, 629])).
% 0.72/0.92 tff(632,plain,
% 0.72/0.92 (hskp9 | hskp1 | hskp0),
% 0.72/0.92 inference(modus_ponens,[status(thm)],[631, 628])).
% 0.72/0.92 tff(633,plain,
% 0.72/0.92 (hskp9 | hskp1 | hskp0),
% 0.72/0.92 inference(modus_ponens,[status(thm)],[632, 628])).
% 0.72/0.92 tff(634,plain,
% 0.72/0.92 (hskp9 | hskp1 | hskp0),
% 0.72/0.92 inference(modus_ponens,[status(thm)],[633, 628])).
% 0.72/0.92 tff(635,plain,
% 0.72/0.92 (hskp9 | hskp1 | hskp0),
% 0.72/0.92 inference(modus_ponens,[status(thm)],[634, 628])).
% 0.72/0.92 tff(636,plain,
% 0.72/0.92 (hskp9),
% 0.72/0.92 inference(unit_resolution,[status(thm)],[635, 627, 102])).
% 0.72/0.92 tff(637,plain,
% 0.72/0.92 (((~hskp9) | (~c1_1(a199))) <=> ((~hskp9) | (~c1_1(a199)))),
% 0.72/0.92 inference(rewrite,[status(thm)],[])).
% 0.72/0.92 tff(638,plain,
% 0.72/0.92 (((~c1_1(a199)) | (~hskp9)) <=> ((~hskp9) | (~c1_1(a199)))),
% 0.72/0.92 inference(rewrite,[status(thm)],[])).
% 0.72/0.92 tff(639,axiom,((~c1_1(a199)) | (~hskp9)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause94')).
% 0.72/0.92 tff(640,plain,
% 0.72/0.92 ((~hskp9) | (~c1_1(a199))),
% 0.72/0.92 inference(modus_ponens,[status(thm)],[639, 638])).
% 0.72/0.92 tff(641,plain,
% 0.72/0.92 ((~hskp9) | (~c1_1(a199))),
% 0.72/0.92 inference(modus_ponens,[status(thm)],[640, 637])).
% 0.72/0.92 tff(642,plain,
% 0.72/0.92 (~c1_1(a199)),
% 0.72/0.92 inference(unit_resolution,[status(thm)],[641, 636])).
% 0.72/0.92 tff(643,plain,
% 0.72/0.92 (((~hskp9) | (~c0_1(a199))) <=> ((~hskp9) | (~c0_1(a199)))),
% 0.72/0.92 inference(rewrite,[status(thm)],[])).
% 0.72/0.92 tff(644,plain,
% 0.72/0.92 (((~c0_1(a199)) | (~hskp9)) <=> ((~hskp9) | (~c0_1(a199)))),
% 0.72/0.92 inference(rewrite,[status(thm)],[])).
% 0.72/0.92 tff(645,axiom,((~c0_1(a199)) | (~hskp9)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause93')).
% 0.72/0.92 tff(646,plain,
% 0.72/0.92 ((~hskp9) | (~c0_1(a199))),
% 0.72/0.92 inference(modus_ponens,[status(thm)],[645, 644])).
% 0.72/0.92 tff(647,plain,
% 0.72/0.92 ((~hskp9) | (~c0_1(a199))),
% 0.72/0.92 inference(modus_ponens,[status(thm)],[646, 643])).
% 0.72/0.92 tff(648,plain,
% 0.72/0.92 (~c0_1(a199)),
% 0.72/0.92 inference(unit_resolution,[status(thm)],[647, 636])).
% 0.72/0.92 tff(649,plain,
% 0.72/0.92 (((~![U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp1 | c0_1(a199) | c1_1(a199) | (~ndr1_0) | c3_1(a199))) <=> ((~![U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | hskp1 | c0_1(a199) | c1_1(a199) | (~ndr1_0) | c3_1(a199))),
% 0.72/0.92 inference(rewrite,[status(thm)],[])).
% 0.72/0.92 tff(650,plain,
% 0.72/0.92 ((hskp1 | (~ndr1_0) | c3_1(a199) | c1_1(a199) | c0_1(a199)) <=> (hskp1 | c0_1(a199) | c1_1(a199) | (~ndr1_0) | c3_1(a199))),
% 0.72/0.92 inference(rewrite,[status(thm)],[])).
% 0.72/0.92 tff(651,plain,
% 0.72/0.92 (((~![U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp1 | (~ndr1_0) | c3_1(a199) | c1_1(a199) | c0_1(a199))) <=> ((~![U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp1 | c0_1(a199) | c1_1(a199) | (~ndr1_0) | c3_1(a199)))),
% 0.72/0.92 inference(monotonicity,[status(thm)],[650])).
% 0.72/0.92 tff(652,plain,
% 0.72/0.92 (((~![U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp1 | (~ndr1_0) | c3_1(a199) | c1_1(a199) | c0_1(a199))) <=> ((~![U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | hskp1 | c0_1(a199) | c1_1(a199) | (~ndr1_0) | c3_1(a199))),
% 0.72/0.92 inference(transitivity,[status(thm)],[651, 649])).
% 0.72/0.92 tff(653,plain,
% 0.72/0.92 ((~![U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp1 | (~ndr1_0) | c3_1(a199) | c1_1(a199) | c0_1(a199))),
% 0.72/0.92 inference(quant_inst,[status(thm)],[])).
% 0.72/0.92 tff(654,plain,
% 0.72/0.92 ((~![U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | hskp1 | c0_1(a199) | c1_1(a199) | (~ndr1_0) | c3_1(a199)),
% 0.72/0.92 inference(modus_ponens,[status(thm)],[653, 652])).
% 0.72/0.92 tff(655,plain,
% 0.72/0.92 (c3_1(a199)),
% 0.72/0.92 inference(unit_resolution,[status(thm)],[654, 148, 102, 648, 642, 112])).
% 0.72/0.92 tff(656,plain,
% 0.72/0.92 (((~hskp9) | c2_1(a199)) <=> ((~hskp9) | c2_1(a199))),
% 0.72/0.92 inference(rewrite,[status(thm)],[])).
% 0.72/0.92 tff(657,axiom,((~hskp9) | c2_1(a199)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause59')).
% 0.72/0.92 tff(658,plain,
% 0.72/0.92 ((~hskp9) | c2_1(a199)),
% 0.72/0.92 inference(modus_ponens,[status(thm)],[657, 656])).
% 0.72/0.92 tff(659,plain,
% 0.72/0.92 ((~hskp9) | c2_1(a199)),
% 0.72/0.92 inference(modus_ponens,[status(thm)],[658, 656])).
% 0.72/0.92 tff(660,plain,
% 0.72/0.92 ((~hskp9) | c2_1(a199)),
% 0.72/0.92 inference(modus_ponens,[status(thm)],[659, 656])).
% 0.72/0.92 tff(661,plain,
% 0.72/0.92 ((~hskp9) | c2_1(a199)),
% 0.72/0.92 inference(modus_ponens,[status(thm)],[660, 656])).
% 0.72/0.92 tff(662,plain,
% 0.72/0.92 ((~hskp9) | c2_1(a199)),
% 0.72/0.92 inference(modus_ponens,[status(thm)],[661, 656])).
% 0.72/0.92 tff(663,plain,
% 0.72/0.92 (c2_1(a199)),
% 0.72/0.92 inference(unit_resolution,[status(thm)],[662, 636])).
% 0.72/0.92 tff(664,plain,
% 0.72/0.92 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp13 | c0_1(a199) | c1_1(a191) | c2_1(a191) | c3_1(a191) | (~ndr1_0) | (~c2_1(a199)) | (~c3_1(a199)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp13 | c0_1(a199) | c1_1(a191) | c2_1(a191) | c3_1(a191) | (~ndr1_0) | (~c2_1(a199)) | (~c3_1(a199)))),
% 0.72/0.92 inference(rewrite,[status(thm)],[])).
% 0.72/0.92 tff(665,plain,
% 0.72/0.92 ((hskp13 | (~ndr1_0) | c0_1(a199) | (~c3_1(a199)) | (~c2_1(a199)) | c3_1(a191) | c1_1(a191) | c2_1(a191)) <=> (hskp13 | c0_1(a199) | c1_1(a191) | c2_1(a191) | c3_1(a191) | (~ndr1_0) | (~c2_1(a199)) | (~c3_1(a199)))),
% 0.72/0.92 inference(rewrite,[status(thm)],[])).
% 0.72/0.92 tff(666,plain,
% 0.72/0.92 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp13 | (~ndr1_0) | c0_1(a199) | (~c3_1(a199)) | (~c2_1(a199)) | c3_1(a191) | c1_1(a191) | c2_1(a191))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp13 | c0_1(a199) | c1_1(a191) | c2_1(a191) | c3_1(a191) | (~ndr1_0) | (~c2_1(a199)) | (~c3_1(a199))))),
% 0.72/0.92 inference(monotonicity,[status(thm)],[665])).
% 0.72/0.92 tff(667,plain,
% 0.72/0.92 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp13 | (~ndr1_0) | c0_1(a199) | (~c3_1(a199)) | (~c2_1(a199)) | c3_1(a191) | c1_1(a191) | c2_1(a191))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp13 | c0_1(a199) | c1_1(a191) | c2_1(a191) | c3_1(a191) | (~ndr1_0) | (~c2_1(a199)) | (~c3_1(a199)))),
% 0.72/0.92 inference(transitivity,[status(thm)],[666, 664])).
% 0.72/0.92 tff(668,plain,
% 0.72/0.92 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp13 | (~ndr1_0) | c0_1(a199) | (~c3_1(a199)) | (~c2_1(a199)) | c3_1(a191) | c1_1(a191) | c2_1(a191))),
% 0.72/0.92 inference(quant_inst,[status(thm)],[])).
% 0.72/0.92 tff(669,plain,
% 0.72/0.92 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp13 | c0_1(a199) | c1_1(a191) | c2_1(a191) | c3_1(a191) | (~ndr1_0) | (~c2_1(a199)) | (~c3_1(a199))),
% 0.72/0.92 inference(modus_ponens,[status(thm)],[668, 667])).
% 0.72/0.92 tff(670,plain,
% 0.72/0.92 (hskp13 | (~c3_1(a199))),
% 0.72/0.92 inference(unit_resolution,[status(thm)],[669, 148, 663, 648, 67, 66, 68, 246])).
% 0.72/0.92 tff(671,plain,
% 0.72/0.92 (hskp13),
% 0.72/0.92 inference(unit_resolution,[status(thm)],[670, 655])).
% 0.72/0.92 tff(672,plain,
% 0.72/0.92 (~c0_1(a209)),
% 0.72/0.92 inference(unit_resolution,[status(thm)],[387, 671])).
% 0.72/0.92 tff(673,assumption,(c0_1(a194)), introduced(assumption)).
% 0.72/0.92 tff(674,plain,
% 0.72/0.92 (c3_1(a209)),
% 0.72/0.92 inference(unit_resolution,[status(thm)],[395, 671])).
% 0.72/0.92 tff(675,plain,
% 0.72/0.92 (c1_1(a209)),
% 0.72/0.92 inference(unit_resolution,[status(thm)],[403, 671])).
% 0.72/0.92 tff(676,plain,
% 0.72/0.92 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_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(a209) | c0_1(a199) | c1_1(a199) | c1_1(a194) | c2_1(a194) | (~ndr1_0) | (~c0_1(a194)) | (~c2_1(a199)) | (~c1_1(a209)) | (~c3_1(a209)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_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(a209) | c0_1(a199) | c1_1(a199) | c1_1(a194) | c2_1(a194) | (~ndr1_0) | (~c0_1(a194)) | (~c2_1(a199)) | (~c1_1(a209)) | (~c3_1(a209)))),
% 0.72/0.92 inference(rewrite,[status(thm)],[])).
% 0.72/0.92 tff(677,plain,
% 0.72/0.92 (((~ndr1_0) | c1_1(a194) | c2_1(a194) | (~c0_1(a194)) | c0_1(a209) | (~c3_1(a209)) | (~c1_1(a209)) | c1_1(a199) | c0_1(a199) | (~c2_1(a199))) <=> (c0_1(a209) | c0_1(a199) | c1_1(a199) | c1_1(a194) | c2_1(a194) | (~ndr1_0) | (~c0_1(a194)) | (~c2_1(a199)) | (~c1_1(a209)) | (~c3_1(a209)))),
% 0.72/0.92 inference(rewrite,[status(thm)],[])).
% 0.72/0.92 tff(678,plain,
% 0.72/0.92 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_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) | c1_1(a194) | c2_1(a194) | (~c0_1(a194)) | c0_1(a209) | (~c3_1(a209)) | (~c1_1(a209)) | c1_1(a199) | c0_1(a199) | (~c2_1(a199)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_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(a209) | c0_1(a199) | c1_1(a199) | c1_1(a194) | c2_1(a194) | (~ndr1_0) | (~c0_1(a194)) | (~c2_1(a199)) | (~c1_1(a209)) | (~c3_1(a209))))),
% 0.72/0.92 inference(monotonicity,[status(thm)],[677])).
% 0.72/0.92 tff(679,plain,
% 0.72/0.92 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_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) | c1_1(a194) | c2_1(a194) | (~c0_1(a194)) | c0_1(a209) | (~c3_1(a209)) | (~c1_1(a209)) | c1_1(a199) | c0_1(a199) | (~c2_1(a199)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_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(a209) | c0_1(a199) | c1_1(a199) | c1_1(a194) | c2_1(a194) | (~ndr1_0) | (~c0_1(a194)) | (~c2_1(a199)) | (~c1_1(a209)) | (~c3_1(a209)))),
% 0.72/0.92 inference(transitivity,[status(thm)],[678, 676])).
% 0.72/0.92 tff(680,plain,
% 0.72/0.92 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_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) | c1_1(a194) | c2_1(a194) | (~c0_1(a194)) | c0_1(a209) | (~c3_1(a209)) | (~c1_1(a209)) | c1_1(a199) | c0_1(a199) | (~c2_1(a199)))),
% 0.72/0.92 inference(quant_inst,[status(thm)],[])).
% 0.72/0.92 tff(681,plain,
% 0.72/0.92 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a209) | c0_1(a199) | c1_1(a199) | c1_1(a194) | c2_1(a194) | (~ndr1_0) | (~c0_1(a194)) | (~c2_1(a199)) | (~c1_1(a209)) | (~c3_1(a209))),
% 0.72/0.92 inference(modus_ponens,[status(thm)],[680, 679])).
% 0.72/0.92 tff(682,plain,
% 0.72/0.92 ($false),
% 0.72/0.92 inference(unit_resolution,[status(thm)],[681, 148, 675, 674, 663, 673, 672, 648, 642, 12, 11, 65])).
% 0.72/0.92 tff(683,plain,(hskp1 | (~c0_1(a194)) | c1_1(a194) | c2_1(a194) | c1_1(a191) | c2_1(a191) | c3_1(a191)), inference(lemma,lemma(discharge,[]))).
% 0.72/0.92 tff(684,plain,
% 0.72/0.92 (hskp1),
% 0.72/0.92 inference(unit_resolution,[status(thm)],[683, 599, 591, 585, 67, 66, 68])).
% 0.72/0.92 tff(685,plain,
% 0.72/0.92 (c0_1(a190)),
% 0.72/0.92 inference(unit_resolution,[status(thm)],[200, 684])).
% 0.72/0.92 tff(686,assumption,(~c2_1(a190)), introduced(assumption)).
% 0.72/0.92 tff(687,plain,
% 0.72/0.92 (~hskp1),
% 0.72/0.92 inference(unit_resolution,[status(thm)],[192, 686])).
% 0.72/0.92 tff(688,plain,
% 0.72/0.92 (~hskp0),
% 0.72/0.92 inference(unit_resolution,[status(thm)],[626, 687])).
% 0.72/0.92 tff(689,plain,
% 0.72/0.92 (hskp9),
% 0.72/0.92 inference(unit_resolution,[status(thm)],[635, 688, 687])).
% 0.72/0.92 tff(690,plain,
% 0.72/0.92 (~c0_1(a199)),
% 0.72/0.92 inference(unit_resolution,[status(thm)],[647, 689])).
% 0.72/0.92 tff(691,plain,
% 0.72/0.92 (~c1_1(a199)),
% 0.72/0.92 inference(unit_resolution,[status(thm)],[641, 689])).
% 0.72/0.92 tff(692,plain,
% 0.72/0.92 (((~![U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp1 | c0_1(a195) | c1_1(a195) | c3_1(a195) | (~ndr1_0))) <=> ((~![U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | hskp1 | c0_1(a195) | c1_1(a195) | c3_1(a195) | (~ndr1_0))),
% 0.72/0.92 inference(rewrite,[status(thm)],[])).
% 0.72/0.92 tff(693,plain,
% 0.72/0.92 ((hskp1 | (~ndr1_0) | c3_1(a195) | c1_1(a195) | c0_1(a195)) <=> (hskp1 | c0_1(a195) | c1_1(a195) | c3_1(a195) | (~ndr1_0))),
% 0.72/0.92 inference(rewrite,[status(thm)],[])).
% 0.72/0.92 tff(694,plain,
% 0.72/0.92 (((~![U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp1 | (~ndr1_0) | c3_1(a195) | c1_1(a195) | c0_1(a195))) <=> ((~![U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp1 | c0_1(a195) | c1_1(a195) | c3_1(a195) | (~ndr1_0)))),
% 0.72/0.92 inference(monotonicity,[status(thm)],[693])).
% 0.72/0.92 tff(695,plain,
% 0.72/0.92 (((~![U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp1 | (~ndr1_0) | c3_1(a195) | c1_1(a195) | c0_1(a195))) <=> ((~![U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | hskp1 | c0_1(a195) | c1_1(a195) | c3_1(a195) | (~ndr1_0))),
% 0.72/0.92 inference(transitivity,[status(thm)],[694, 692])).
% 0.72/0.92 tff(696,plain,
% 0.72/0.92 ((~![U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp1 | (~ndr1_0) | c3_1(a195) | c1_1(a195) | c0_1(a195))),
% 0.72/0.92 inference(quant_inst,[status(thm)],[])).
% 0.72/0.92 tff(697,plain,
% 0.72/0.92 ((~![U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | hskp1 | c0_1(a195) | c1_1(a195) | c3_1(a195) | (~ndr1_0)),
% 0.72/0.92 inference(modus_ponens,[status(thm)],[696, 695])).
% 0.72/0.92 tff(698,plain,
% 0.72/0.92 (hskp1 | c0_1(a195) | c1_1(a195)),
% 0.72/0.92 inference(unit_resolution,[status(thm)],[697, 148, 560, 112])).
% 0.72/0.92 tff(699,plain,
% 0.72/0.92 (c0_1(a195)),
% 0.72/0.92 inference(unit_resolution,[status(thm)],[698, 687, 561])).
% 0.72/0.92 tff(700,plain,
% 0.72/0.92 (c0_1(a191)),
% 0.72/0.92 inference(unit_resolution,[status(thm)],[163, 687])).
% 0.72/0.92 tff(701,plain,
% 0.72/0.92 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp1 | c3_1(a195) | c1_1(a191) | c2_1(a191) | (~ndr1_0) | (~c0_1(a191)) | (~c2_1(a195)) | (~c0_1(a195)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | hskp1 | c3_1(a195) | c1_1(a191) | c2_1(a191) | (~ndr1_0) | (~c0_1(a191)) | (~c2_1(a195)) | (~c0_1(a195)))),
% 0.72/0.92 inference(rewrite,[status(thm)],[])).
% 0.72/0.92 tff(702,plain,
% 0.72/0.92 ((hskp1 | (~ndr1_0) | c3_1(a195) | (~c2_1(a195)) | (~c0_1(a195)) | c1_1(a191) | c2_1(a191) | (~c0_1(a191))) <=> (hskp1 | c3_1(a195) | c1_1(a191) | c2_1(a191) | (~ndr1_0) | (~c0_1(a191)) | (~c2_1(a195)) | (~c0_1(a195)))),
% 0.72/0.92 inference(rewrite,[status(thm)],[])).
% 0.72/0.92 tff(703,plain,
% 0.72/0.92 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp1 | (~ndr1_0) | c3_1(a195) | (~c2_1(a195)) | (~c0_1(a195)) | c1_1(a191) | c2_1(a191) | (~c0_1(a191)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp1 | c3_1(a195) | c1_1(a191) | c2_1(a191) | (~ndr1_0) | (~c0_1(a191)) | (~c2_1(a195)) | (~c0_1(a195))))),
% 0.72/0.92 inference(monotonicity,[status(thm)],[702])).
% 0.72/0.92 tff(704,plain,
% 0.72/0.92 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp1 | (~ndr1_0) | c3_1(a195) | (~c2_1(a195)) | (~c0_1(a195)) | c1_1(a191) | c2_1(a191) | (~c0_1(a191)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | hskp1 | c3_1(a195) | c1_1(a191) | c2_1(a191) | (~ndr1_0) | (~c0_1(a191)) | (~c2_1(a195)) | (~c0_1(a195)))),
% 0.72/0.92 inference(transitivity,[status(thm)],[703, 701])).
% 0.72/0.92 tff(705,plain,
% 0.72/0.92 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp1 | (~ndr1_0) | c3_1(a195) | (~c2_1(a195)) | (~c0_1(a195)) | c1_1(a191) | c2_1(a191) | (~c0_1(a191)))),
% 0.72/0.92 inference(quant_inst,[status(thm)],[])).
% 0.72/0.92 tff(706,plain,
% 0.72/0.92 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | hskp1 | c3_1(a195) | c1_1(a191) | c2_1(a191) | (~ndr1_0) | (~c0_1(a191)) | (~c2_1(a195)) | (~c0_1(a195))),
% 0.72/0.92 inference(modus_ponens,[status(thm)],[705, 704])).
% 0.72/0.92 tff(707,plain,
% 0.72/0.92 (hskp1 | (~c0_1(a191)) | (~c2_1(a195)) | (~c0_1(a195))),
% 0.72/0.92 inference(unit_resolution,[status(thm)],[706, 148, 560, 67, 66, 174])).
% 0.72/0.92 tff(708,plain,
% 0.72/0.92 (~c2_1(a195)),
% 0.72/0.92 inference(unit_resolution,[status(thm)],[707, 700, 699, 687])).
% 0.72/0.92 tff(709,assumption,(~c1_1(a199)), introduced(assumption)).
% 0.72/0.92 tff(710,assumption,(~c0_1(a199)), introduced(assumption)).
% 0.72/0.92 tff(711,plain,
% 0.72/0.92 (hskp1 | c0_1(a199) | c3_1(a199)),
% 0.72/0.92 inference(unit_resolution,[status(thm)],[654, 148, 709, 112])).
% 0.72/0.92 tff(712,plain,
% 0.72/0.92 (c3_1(a199)),
% 0.72/0.92 inference(unit_resolution,[status(thm)],[711, 687, 710])).
% 0.72/0.92 tff(713,plain,
% 0.72/0.92 (^[V: $i, U: $i] : refl((hskp15 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V)) <=> (hskp15 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V)))),
% 0.72/0.92 inference(bind,[status(th)],[])).
% 0.72/0.92 tff(714,plain,
% 0.72/0.92 (![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V)) <=> ![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))),
% 0.72/0.92 inference(quant_intro,[status(thm)],[713])).
% 0.72/0.92 tff(715,plain,
% 0.72/0.92 (![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V)) <=> ![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))),
% 0.72/0.92 inference(rewrite,[status(thm)],[])).
% 0.72/0.92 tff(716,plain,
% 0.72/0.92 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c1_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U))))), (((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))), (((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U))))), ((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U))) | c1_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U))) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V))), ((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V)))), (((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c2_1(V))), (((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c2_1(V)))), ((((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c2_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))), ((((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V)))), (((((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | hskp15) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V)) | hskp15))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V)) | hskp15) <=> (hskp15 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))), (((((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | hskp15) <=> (hskp15 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))))),
% 0.72/0.92 inference(bind,[status(th)],[])).
% 0.72/0.92 tff(717,plain,
% 0.72/0.92 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | hskp15) <=> ![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))),
% 0.72/0.92 inference(quant_intro,[status(thm)],[716])).
% 0.72/0.92 tff(718,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | hskp15)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause130')).
% 0.72/0.92 tff(719,plain,
% 0.72/0.92 (![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))),
% 0.72/0.92 inference(modus_ponens,[status(thm)],[718, 717])).
% 0.72/0.92 tff(720,plain,
% 0.72/0.92 (![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))),
% 0.72/0.92 inference(modus_ponens,[status(thm)],[719, 715])).
% 0.72/0.92 tff(721,plain,(
% 0.72/0.92 ![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))),
% 0.72/0.92 inference(skolemize,[status(sab)],[720])).
% 0.72/0.92 tff(722,plain,
% 0.72/0.92 (![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))),
% 0.72/0.92 inference(modus_ponens,[status(thm)],[721, 714])).
% 0.72/0.92 tff(723,plain,
% 0.72/0.92 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp15 | c2_1(a190) | c1_1(a191) | c2_1(a191) | c3_1(a191) | c3_1(a190) | (~ndr1_0) | (~c1_1(a190)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp15 | c2_1(a190) | c1_1(a191) | c2_1(a191) | c3_1(a191) | c3_1(a190) | (~ndr1_0) | (~c1_1(a190)))),
% 0.72/0.92 inference(rewrite,[status(thm)],[])).
% 0.72/0.92 tff(724,plain,
% 0.72/0.92 ((hskp15 | (~ndr1_0) | c3_1(a190) | c2_1(a190) | (~c1_1(a190)) | c3_1(a191) | c1_1(a191) | c2_1(a191)) <=> (hskp15 | c2_1(a190) | c1_1(a191) | c2_1(a191) | c3_1(a191) | c3_1(a190) | (~ndr1_0) | (~c1_1(a190)))),
% 0.72/0.92 inference(rewrite,[status(thm)],[])).
% 0.72/0.92 tff(725,plain,
% 0.72/0.92 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp15 | (~ndr1_0) | c3_1(a190) | c2_1(a190) | (~c1_1(a190)) | c3_1(a191) | c1_1(a191) | c2_1(a191))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp15 | c2_1(a190) | c1_1(a191) | c2_1(a191) | c3_1(a191) | c3_1(a190) | (~ndr1_0) | (~c1_1(a190))))),
% 0.72/0.92 inference(monotonicity,[status(thm)],[724])).
% 0.72/0.92 tff(726,plain,
% 0.72/0.92 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp15 | (~ndr1_0) | c3_1(a190) | c2_1(a190) | (~c1_1(a190)) | c3_1(a191) | c1_1(a191) | c2_1(a191))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp15 | c2_1(a190) | c1_1(a191) | c2_1(a191) | c3_1(a191) | c3_1(a190) | (~ndr1_0) | (~c1_1(a190)))),
% 0.72/0.92 inference(transitivity,[status(thm)],[725, 723])).
% 0.72/0.92 tff(727,plain,
% 0.72/0.92 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp15 | (~ndr1_0) | c3_1(a190) | c2_1(a190) | (~c1_1(a190)) | c3_1(a191) | c1_1(a191) | c2_1(a191))),
% 0.72/0.92 inference(quant_inst,[status(thm)],[])).
% 0.72/0.92 tff(728,plain,
% 0.72/0.92 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp15 | c2_1(a190) | c1_1(a191) | c2_1(a191) | c3_1(a191) | c3_1(a190) | (~ndr1_0) | (~c1_1(a190))),
% 0.72/0.92 inference(modus_ponens,[status(thm)],[727, 726])).
% 0.72/0.92 tff(729,plain,
% 0.72/0.92 (c2_1(a190) | (~c1_1(a190))),
% 0.72/0.92 inference(unit_resolution,[status(thm)],[728, 148, 36, 67, 66, 68, 13, 722])).
% 0.72/0.92 tff(730,plain,
% 0.72/0.92 (~c1_1(a190)),
% 0.72/0.92 inference(unit_resolution,[status(thm)],[729, 686])).
% 0.72/0.92 tff(731,plain,
% 0.72/0.92 (^[V: $i, U: $i] : refl((hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V))) <=> (hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V))))),
% 0.72/0.92 inference(bind,[status(th)],[])).
% 0.72/0.92 tff(732,plain,
% 0.72/0.92 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))),
% 0.72/0.92 inference(quant_intro,[status(thm)],[731])).
% 0.72/0.92 tff(733,plain,
% 0.72/0.92 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))),
% 0.72/0.92 inference(rewrite,[status(thm)],[])).
% 0.72/0.92 tff(734,plain,
% 0.72/0.92 (^[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)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c0_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(V)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(V))))), (((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(V)))), (((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(V))))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | (~c3_1(V)))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | (~c3_1(V))))), (((((((~c0_1(U)) | (~ndr1_0)) | (~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))) | c1_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | (~c3_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)))), (((((((~c0_1(U)) | (~ndr1_0)) | (~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))))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V))))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | hskp1) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V))) | hskp1))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V))) | hskp1) <=> (hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | hskp1) <=> (hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))))),
% 0.72/0.93 inference(bind,[status(th)],[])).
% 0.72/0.93 tff(735,plain,
% 0.72/0.93 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | hskp1) <=> ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))),
% 0.72/0.93 inference(quant_intro,[status(thm)],[734])).
% 0.72/0.93 tff(736,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | hskp1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause136')).
% 0.72/0.93 tff(737,plain,
% 0.72/0.93 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))),
% 0.72/0.93 inference(modus_ponens,[status(thm)],[736, 735])).
% 0.72/0.93 tff(738,plain,
% 0.72/0.93 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))),
% 0.72/0.93 inference(modus_ponens,[status(thm)],[737, 733])).
% 0.72/0.93 tff(739,plain,(
% 0.72/0.93 ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))),
% 0.72/0.93 inference(skolemize,[status(sab)],[738])).
% 0.72/0.93 tff(740,plain,
% 0.72/0.93 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))),
% 0.72/0.93 inference(modus_ponens,[status(thm)],[739, 732])).
% 0.72/0.93 tff(741,plain,
% 0.72/0.93 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp1 | c2_1(a199) | c1_1(a199) | c2_1(a191) | c3_1(a191) | (~ndr1_0) | (~c0_1(a191)) | (~c3_1(a199)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | hskp1 | c2_1(a199) | c1_1(a199) | c2_1(a191) | c3_1(a191) | (~ndr1_0) | (~c0_1(a191)) | (~c3_1(a199)))),
% 0.72/0.93 inference(rewrite,[status(thm)],[])).
% 0.72/0.93 tff(742,plain,
% 0.72/0.93 ((hskp1 | (~ndr1_0) | c3_1(a191) | c2_1(a191) | (~c0_1(a191)) | c1_1(a199) | c2_1(a199) | (~c3_1(a199))) <=> (hskp1 | c2_1(a199) | c1_1(a199) | c2_1(a191) | c3_1(a191) | (~ndr1_0) | (~c0_1(a191)) | (~c3_1(a199)))),
% 0.72/0.93 inference(rewrite,[status(thm)],[])).
% 0.72/0.93 tff(743,plain,
% 0.72/0.93 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp1 | (~ndr1_0) | c3_1(a191) | c2_1(a191) | (~c0_1(a191)) | c1_1(a199) | c2_1(a199) | (~c3_1(a199)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp1 | c2_1(a199) | c1_1(a199) | c2_1(a191) | c3_1(a191) | (~ndr1_0) | (~c0_1(a191)) | (~c3_1(a199))))),
% 0.72/0.93 inference(monotonicity,[status(thm)],[742])).
% 0.72/0.93 tff(744,plain,
% 0.72/0.93 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp1 | (~ndr1_0) | c3_1(a191) | c2_1(a191) | (~c0_1(a191)) | c1_1(a199) | c2_1(a199) | (~c3_1(a199)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | hskp1 | c2_1(a199) | c1_1(a199) | c2_1(a191) | c3_1(a191) | (~ndr1_0) | (~c0_1(a191)) | (~c3_1(a199)))),
% 0.72/0.93 inference(transitivity,[status(thm)],[743, 741])).
% 0.72/0.93 tff(745,plain,
% 0.72/0.93 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp1 | (~ndr1_0) | c3_1(a191) | c2_1(a191) | (~c0_1(a191)) | c1_1(a199) | c2_1(a199) | (~c3_1(a199)))),
% 0.72/0.93 inference(quant_inst,[status(thm)],[])).
% 0.72/0.93 tff(746,plain,
% 0.72/0.93 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | hskp1 | c2_1(a199) | c1_1(a199) | c2_1(a191) | c3_1(a191) | (~ndr1_0) | (~c0_1(a191)) | (~c3_1(a199))),
% 0.72/0.93 inference(modus_ponens,[status(thm)],[745, 744])).
% 0.72/0.93 tff(747,plain,
% 0.72/0.93 (hskp1 | c2_1(a199) | (~c0_1(a191)) | (~c3_1(a199))),
% 0.72/0.93 inference(unit_resolution,[status(thm)],[746, 148, 709, 66, 68, 740])).
% 0.72/0.93 tff(748,plain,
% 0.72/0.93 (c2_1(a199)),
% 0.72/0.93 inference(unit_resolution,[status(thm)],[747, 712, 700, 687])).
% 0.72/0.93 tff(749,plain,
% 0.72/0.93 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp13 | c2_1(a190) | c0_1(a199) | c3_1(a190) | (~ndr1_0) | c1_1(a190) | (~c2_1(a199)) | (~c3_1(a199)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp13 | c2_1(a190) | c0_1(a199) | c3_1(a190) | (~ndr1_0) | c1_1(a190) | (~c2_1(a199)) | (~c3_1(a199)))),
% 0.72/0.93 inference(rewrite,[status(thm)],[])).
% 0.72/0.93 tff(750,plain,
% 0.72/0.93 ((hskp13 | (~ndr1_0) | c0_1(a199) | (~c3_1(a199)) | (~c2_1(a199)) | c3_1(a190) | c1_1(a190) | c2_1(a190)) <=> (hskp13 | c2_1(a190) | c0_1(a199) | c3_1(a190) | (~ndr1_0) | c1_1(a190) | (~c2_1(a199)) | (~c3_1(a199)))),
% 0.72/0.93 inference(rewrite,[status(thm)],[])).
% 0.72/0.93 tff(751,plain,
% 0.72/0.93 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp13 | (~ndr1_0) | c0_1(a199) | (~c3_1(a199)) | (~c2_1(a199)) | c3_1(a190) | c1_1(a190) | c2_1(a190))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp13 | c2_1(a190) | c0_1(a199) | c3_1(a190) | (~ndr1_0) | c1_1(a190) | (~c2_1(a199)) | (~c3_1(a199))))),
% 0.72/0.93 inference(monotonicity,[status(thm)],[750])).
% 0.72/0.93 tff(752,plain,
% 0.72/0.93 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp13 | (~ndr1_0) | c0_1(a199) | (~c3_1(a199)) | (~c2_1(a199)) | c3_1(a190) | c1_1(a190) | c2_1(a190))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp13 | c2_1(a190) | c0_1(a199) | c3_1(a190) | (~ndr1_0) | c1_1(a190) | (~c2_1(a199)) | (~c3_1(a199)))),
% 0.72/0.93 inference(transitivity,[status(thm)],[751, 749])).
% 0.72/0.93 tff(753,plain,
% 0.72/0.93 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp13 | (~ndr1_0) | c0_1(a199) | (~c3_1(a199)) | (~c2_1(a199)) | c3_1(a190) | c1_1(a190) | c2_1(a190))),
% 0.72/0.93 inference(quant_inst,[status(thm)],[])).
% 0.72/0.93 tff(754,plain,
% 0.72/0.93 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp13 | c2_1(a190) | c0_1(a199) | c3_1(a190) | (~ndr1_0) | c1_1(a190) | (~c2_1(a199)) | (~c3_1(a199))),
% 0.79/0.93 inference(modus_ponens,[status(thm)],[753, 752])).
% 0.79/0.93 tff(755,plain,
% 0.79/0.93 (hskp13 | c2_1(a190) | c1_1(a190) | (~c2_1(a199)) | (~c3_1(a199))),
% 0.79/0.93 inference(unit_resolution,[status(thm)],[754, 148, 710, 13, 246])).
% 0.79/0.93 tff(756,plain,
% 0.79/0.93 (hskp13),
% 0.79/0.93 inference(unit_resolution,[status(thm)],[755, 748, 686, 730, 712])).
% 0.79/0.93 tff(757,plain,
% 0.79/0.93 (~c0_1(a209)),
% 0.79/0.93 inference(unit_resolution,[status(thm)],[387, 756])).
% 0.79/0.93 tff(758,plain,
% 0.79/0.93 (c3_1(a209)),
% 0.79/0.93 inference(unit_resolution,[status(thm)],[395, 756])).
% 0.79/0.93 tff(759,plain,
% 0.79/0.93 (c1_1(a209)),
% 0.79/0.93 inference(unit_resolution,[status(thm)],[403, 756])).
% 0.79/0.93 tff(760,plain,
% 0.79/0.93 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_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(a209) | c0_1(a199) | c1_1(a199) | c1_1(a195) | (~ndr1_0) | c2_1(a195) | (~c0_1(a195)) | (~c2_1(a199)) | (~c1_1(a209)) | (~c3_1(a209)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_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(a209) | c0_1(a199) | c1_1(a199) | c1_1(a195) | (~ndr1_0) | c2_1(a195) | (~c0_1(a195)) | (~c2_1(a199)) | (~c1_1(a209)) | (~c3_1(a209)))),
% 0.79/0.93 inference(rewrite,[status(thm)],[])).
% 0.79/0.93 tff(761,plain,
% 0.79/0.93 (((~ndr1_0) | c1_1(a195) | c2_1(a195) | (~c0_1(a195)) | c0_1(a209) | (~c3_1(a209)) | (~c1_1(a209)) | c1_1(a199) | c0_1(a199) | (~c2_1(a199))) <=> (c0_1(a209) | c0_1(a199) | c1_1(a199) | c1_1(a195) | (~ndr1_0) | c2_1(a195) | (~c0_1(a195)) | (~c2_1(a199)) | (~c1_1(a209)) | (~c3_1(a209)))),
% 0.79/0.93 inference(rewrite,[status(thm)],[])).
% 0.79/0.93 tff(762,plain,
% 0.79/0.93 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_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) | c1_1(a195) | c2_1(a195) | (~c0_1(a195)) | c0_1(a209) | (~c3_1(a209)) | (~c1_1(a209)) | c1_1(a199) | c0_1(a199) | (~c2_1(a199)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_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(a209) | c0_1(a199) | c1_1(a199) | c1_1(a195) | (~ndr1_0) | c2_1(a195) | (~c0_1(a195)) | (~c2_1(a199)) | (~c1_1(a209)) | (~c3_1(a209))))),
% 0.79/0.93 inference(monotonicity,[status(thm)],[761])).
% 0.79/0.93 tff(763,plain,
% 0.79/0.93 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_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) | c1_1(a195) | c2_1(a195) | (~c0_1(a195)) | c0_1(a209) | (~c3_1(a209)) | (~c1_1(a209)) | c1_1(a199) | c0_1(a199) | (~c2_1(a199)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_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(a209) | c0_1(a199) | c1_1(a199) | c1_1(a195) | (~ndr1_0) | c2_1(a195) | (~c0_1(a195)) | (~c2_1(a199)) | (~c1_1(a209)) | (~c3_1(a209)))),
% 0.79/0.93 inference(transitivity,[status(thm)],[762, 760])).
% 0.79/0.93 tff(764,plain,
% 0.79/0.93 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_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) | c1_1(a195) | c2_1(a195) | (~c0_1(a195)) | c0_1(a209) | (~c3_1(a209)) | (~c1_1(a209)) | c1_1(a199) | c0_1(a199) | (~c2_1(a199)))),
% 0.79/0.93 inference(quant_inst,[status(thm)],[])).
% 0.79/0.93 tff(765,plain,
% 0.79/0.93 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a209) | c0_1(a199) | c1_1(a199) | c1_1(a195) | (~ndr1_0) | c2_1(a195) | (~c0_1(a195)) | (~c2_1(a199)) | (~c1_1(a209)) | (~c3_1(a209))),
% 0.79/0.93 inference(modus_ponens,[status(thm)],[764, 763])).
% 0.79/0.93 tff(766,plain,
% 0.79/0.93 ($false),
% 0.79/0.93 inference(unit_resolution,[status(thm)],[765, 148, 759, 758, 748, 699, 757, 710, 709, 561, 65, 708])).
% 0.79/0.93 tff(767,plain,(c2_1(a190) | c0_1(a199) | c1_1(a199) | c1_1(a195) | c3_1(a190) | c2_1(a191) | c3_1(a191) | c3_1(a195) | c1_1(a191) | hskp15), inference(lemma,lemma(discharge,[]))).
% 0.79/0.93 tff(768,plain,
% 0.79/0.93 ($false),
% 0.79/0.93 inference(unit_resolution,[status(thm)],[767, 691, 690, 686, 561, 13, 66, 68, 560, 67, 36])).
% 0.79/0.93 tff(769,plain,(c2_1(a190) | c1_1(a195) | c3_1(a190) | c2_1(a191) | c3_1(a191) | c3_1(a195) | c1_1(a191) | hskp15), inference(lemma,lemma(discharge,[]))).
% 0.79/0.93 tff(770,plain,
% 0.79/0.93 (c2_1(a190)),
% 0.79/0.93 inference(unit_resolution,[status(thm)],[769, 561, 13, 66, 68, 560, 67, 36])).
% 0.79/0.93 tff(771,assumption,(~c0_1(a195)), introduced(assumption)).
% 0.79/0.93 tff(772,plain,
% 0.79/0.93 (~hskp6),
% 0.79/0.93 inference(unit_resolution,[status(thm)],[551, 771])).
% 0.79/0.93 tff(773,plain,
% 0.79/0.93 (((~![U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp6 | c0_1(a195) | c3_1(a195) | (~ndr1_0) | c2_1(a195))) <=> ((~![U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | hskp6 | c0_1(a195) | c3_1(a195) | (~ndr1_0) | c2_1(a195))),
% 0.79/0.93 inference(rewrite,[status(thm)],[])).
% 0.79/0.93 tff(774,plain,
% 0.79/0.93 ((hskp6 | (~ndr1_0) | c3_1(a195) | c0_1(a195) | c2_1(a195)) <=> (hskp6 | c0_1(a195) | c3_1(a195) | (~ndr1_0) | c2_1(a195))),
% 0.79/0.93 inference(rewrite,[status(thm)],[])).
% 0.79/0.93 tff(775,plain,
% 0.79/0.93 (((~![U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp6 | (~ndr1_0) | c3_1(a195) | c0_1(a195) | c2_1(a195))) <=> ((~![U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp6 | c0_1(a195) | c3_1(a195) | (~ndr1_0) | c2_1(a195)))),
% 0.79/0.93 inference(monotonicity,[status(thm)],[774])).
% 0.79/0.93 tff(776,plain,
% 0.79/0.93 (((~![U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp6 | (~ndr1_0) | c3_1(a195) | c0_1(a195) | c2_1(a195))) <=> ((~![U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | hskp6 | c0_1(a195) | c3_1(a195) | (~ndr1_0) | c2_1(a195))),
% 0.79/0.93 inference(transitivity,[status(thm)],[775, 773])).
% 0.79/0.93 tff(777,plain,
% 0.79/0.93 ((~![U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp6 | (~ndr1_0) | c3_1(a195) | c0_1(a195) | c2_1(a195))),
% 0.79/0.93 inference(quant_inst,[status(thm)],[])).
% 0.79/0.93 tff(778,plain,
% 0.79/0.93 ((~![U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | hskp6 | c0_1(a195) | c3_1(a195) | (~ndr1_0) | c2_1(a195)),
% 0.79/0.93 inference(modus_ponens,[status(thm)],[777, 776])).
% 0.79/0.93 tff(779,plain,
% 0.79/0.93 (hskp6 | c0_1(a195) | c2_1(a195)),
% 0.79/0.93 inference(unit_resolution,[status(thm)],[778, 148, 560, 530])).
% 0.79/0.93 tff(780,plain,
% 0.79/0.93 (c2_1(a195)),
% 0.79/0.93 inference(unit_resolution,[status(thm)],[779, 772, 771])).
% 0.79/0.93 tff(781,plain,
% 0.79/0.93 (c0_1(a191)),
% 0.79/0.93 inference(unit_resolution,[status(thm)],[537, 772])).
% 0.79/0.93 tff(782,plain,
% 0.79/0.93 (hskp1),
% 0.79/0.93 inference(unit_resolution,[status(thm)],[698, 771, 561])).
% 0.79/0.93 tff(783,plain,
% 0.79/0.93 (c0_1(a190)),
% 0.79/0.93 inference(unit_resolution,[status(thm)],[200, 782])).
% 0.79/0.93 tff(784,assumption,(c2_1(a190)), introduced(assumption)).
% 0.79/0.93 tff(785,plain,
% 0.79/0.93 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp19 | c1_1(a195) | c3_1(a195) | c3_1(a190) | (~ndr1_0) | (~c2_1(a190)) | (~c0_1(a190)) | (~c2_1(a195)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp19 | c1_1(a195) | c3_1(a195) | c3_1(a190) | (~ndr1_0) | (~c2_1(a190)) | (~c0_1(a190)) | (~c2_1(a195)))),
% 0.79/0.93 inference(rewrite,[status(thm)],[])).
% 0.79/0.93 tff(786,plain,
% 0.79/0.93 ((hskp19 | (~ndr1_0) | c3_1(a190) | (~c2_1(a190)) | (~c0_1(a190)) | c3_1(a195) | c1_1(a195) | (~c2_1(a195))) <=> (hskp19 | c1_1(a195) | c3_1(a195) | c3_1(a190) | (~ndr1_0) | (~c2_1(a190)) | (~c0_1(a190)) | (~c2_1(a195)))),
% 0.79/0.93 inference(rewrite,[status(thm)],[])).
% 0.79/0.93 tff(787,plain,
% 0.79/0.93 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp19 | (~ndr1_0) | c3_1(a190) | (~c2_1(a190)) | (~c0_1(a190)) | c3_1(a195) | c1_1(a195) | (~c2_1(a195)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp19 | c1_1(a195) | c3_1(a195) | c3_1(a190) | (~ndr1_0) | (~c2_1(a190)) | (~c0_1(a190)) | (~c2_1(a195))))),
% 0.79/0.93 inference(monotonicity,[status(thm)],[786])).
% 0.79/0.93 tff(788,plain,
% 0.79/0.93 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp19 | (~ndr1_0) | c3_1(a190) | (~c2_1(a190)) | (~c0_1(a190)) | c3_1(a195) | c1_1(a195) | (~c2_1(a195)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp19 | c1_1(a195) | c3_1(a195) | c3_1(a190) | (~ndr1_0) | (~c2_1(a190)) | (~c0_1(a190)) | (~c2_1(a195)))),
% 0.79/0.93 inference(transitivity,[status(thm)],[787, 785])).
% 0.79/0.93 tff(789,plain,
% 0.79/0.93 ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp19 | (~ndr1_0) | c3_1(a190) | (~c2_1(a190)) | (~c0_1(a190)) | c3_1(a195) | c1_1(a195) | (~c2_1(a195)))),
% 0.79/0.93 inference(quant_inst,[status(thm)],[])).
% 0.79/0.93 tff(790,plain,
% 0.79/0.93 ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp19 | c1_1(a195) | c3_1(a195) | c3_1(a190) | (~ndr1_0) | (~c2_1(a190)) | (~c0_1(a190)) | (~c2_1(a195))),
% 0.79/0.93 inference(modus_ponens,[status(thm)],[789, 788])).
% 0.79/0.93 tff(791,plain,
% 0.79/0.93 (hskp19 | c1_1(a195) | (~c2_1(a190)) | (~c0_1(a190)) | (~c2_1(a195))),
% 0.79/0.93 inference(unit_resolution,[status(thm)],[790, 148, 560, 13, 211])).
% 0.79/0.93 tff(792,plain,
% 0.79/0.93 (hskp19),
% 0.79/0.93 inference(unit_resolution,[status(thm)],[791, 780, 784, 561, 783])).
% 0.79/0.93 tff(793,plain,
% 0.79/0.93 (~c0_1(a225)),
% 0.79/0.93 inference(unit_resolution,[status(thm)],[232, 792])).
% 0.79/0.93 tff(794,plain,
% 0.79/0.93 (c3_1(a225)),
% 0.79/0.93 inference(unit_resolution,[status(thm)],[226, 792])).
% 0.79/0.93 tff(795,plain,
% 0.79/0.93 (hskp13),
% 0.79/0.93 inference(unit_resolution,[status(thm)],[378, 794, 793, 66, 68, 781, 67])).
% 0.79/0.93 tff(796,plain,
% 0.79/0.93 (~c0_1(a209)),
% 0.79/0.93 inference(unit_resolution,[status(thm)],[387, 795])).
% 0.79/0.93 tff(797,plain,
% 0.79/0.93 (c3_1(a209)),
% 0.79/0.93 inference(unit_resolution,[status(thm)],[395, 795])).
% 0.79/0.93 tff(798,plain,
% 0.79/0.93 (c1_1(a209)),
% 0.79/0.93 inference(unit_resolution,[status(thm)],[403, 795])).
% 0.79/0.93 tff(799,plain,
% 0.79/0.93 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_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(a195) | c0_1(a209) | c1_1(a195) | c1_1(a191) | c2_1(a191) | (~ndr1_0) | (~c0_1(a191)) | (~c2_1(a195)) | (~c1_1(a209)) | (~c3_1(a209)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_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(a195) | c0_1(a209) | c1_1(a195) | c1_1(a191) | c2_1(a191) | (~ndr1_0) | (~c0_1(a191)) | (~c2_1(a195)) | (~c1_1(a209)) | (~c3_1(a209)))),
% 0.79/0.93 inference(rewrite,[status(thm)],[])).
% 0.79/0.93 tff(800,plain,
% 0.79/0.93 (((~ndr1_0) | c1_1(a191) | c2_1(a191) | (~c0_1(a191)) | c0_1(a209) | (~c3_1(a209)) | (~c1_1(a209)) | c1_1(a195) | c0_1(a195) | (~c2_1(a195))) <=> (c0_1(a195) | c0_1(a209) | c1_1(a195) | c1_1(a191) | c2_1(a191) | (~ndr1_0) | (~c0_1(a191)) | (~c2_1(a195)) | (~c1_1(a209)) | (~c3_1(a209)))),
% 0.79/0.93 inference(rewrite,[status(thm)],[])).
% 0.79/0.93 tff(801,plain,
% 0.79/0.93 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_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) | c1_1(a191) | c2_1(a191) | (~c0_1(a191)) | c0_1(a209) | (~c3_1(a209)) | (~c1_1(a209)) | c1_1(a195) | c0_1(a195) | (~c2_1(a195)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_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(a195) | c0_1(a209) | c1_1(a195) | c1_1(a191) | c2_1(a191) | (~ndr1_0) | (~c0_1(a191)) | (~c2_1(a195)) | (~c1_1(a209)) | (~c3_1(a209))))),
% 0.79/0.93 inference(monotonicity,[status(thm)],[800])).
% 0.79/0.93 tff(802,plain,
% 0.79/0.93 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_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) | c1_1(a191) | c2_1(a191) | (~c0_1(a191)) | c0_1(a209) | (~c3_1(a209)) | (~c1_1(a209)) | c1_1(a195) | c0_1(a195) | (~c2_1(a195)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_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(a195) | c0_1(a209) | c1_1(a195) | c1_1(a191) | c2_1(a191) | (~ndr1_0) | (~c0_1(a191)) | (~c2_1(a195)) | (~c1_1(a209)) | (~c3_1(a209)))),
% 0.79/0.93 inference(transitivity,[status(thm)],[801, 799])).
% 0.79/0.93 tff(803,plain,
% 0.79/0.93 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_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) | c1_1(a191) | c2_1(a191) | (~c0_1(a191)) | c0_1(a209) | (~c3_1(a209)) | (~c1_1(a209)) | c1_1(a195) | c0_1(a195) | (~c2_1(a195)))),
% 0.79/0.93 inference(quant_inst,[status(thm)],[])).
% 0.79/0.93 tff(804,plain,
% 0.79/0.93 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a195) | c0_1(a209) | c1_1(a195) | c1_1(a191) | c2_1(a191) | (~ndr1_0) | (~c0_1(a191)) | (~c2_1(a195)) | (~c1_1(a209)) | (~c3_1(a209))),
% 0.79/0.93 inference(modus_ponens,[status(thm)],[803, 802])).
% 0.79/0.93 tff(805,plain,
% 0.79/0.93 ($false),
% 0.79/0.93 inference(unit_resolution,[status(thm)],[804, 148, 798, 797, 771, 796, 561, 67, 66, 65, 781, 780])).
% 0.79/0.93 tff(806,plain,(c0_1(a195) | c1_1(a195) | c1_1(a191) | c2_1(a191) | c3_1(a191) | (~c2_1(a190)) | c3_1(a195) | c3_1(a190)), inference(lemma,lemma(discharge,[]))).
% 0.79/0.93 tff(807,plain,
% 0.79/0.93 (c0_1(a195)),
% 0.79/0.93 inference(unit_resolution,[status(thm)],[806, 561, 67, 66, 68, 770, 560, 13])).
% 0.79/0.93 tff(808,plain,
% 0.79/0.93 (c0_1(a195)),
% 0.79/0.93 inference(unit_resolution,[status(thm)],[698, 102, 561])).
% 0.79/0.93 tff(809,plain,
% 0.79/0.93 (~c2_1(a195)),
% 0.79/0.93 inference(unit_resolution,[status(thm)],[707, 164, 808, 102])).
% 0.79/0.93 tff(810,plain,
% 0.79/0.93 (c3_1(a199)),
% 0.79/0.93 inference(unit_resolution,[status(thm)],[711, 102, 710])).
% 0.79/0.93 tff(811,plain,
% 0.79/0.93 (c2_1(a199)),
% 0.79/0.93 inference(unit_resolution,[status(thm)],[747, 810, 164, 102])).
% 0.79/0.93 tff(812,plain,
% 0.79/0.93 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp13 | c0_1(a199) | c1_1(a195) | c3_1(a195) | (~ndr1_0) | c2_1(a195) | (~c2_1(a199)) | (~c3_1(a199)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp13 | c0_1(a199) | c1_1(a195) | c3_1(a195) | (~ndr1_0) | c2_1(a195) | (~c2_1(a199)) | (~c3_1(a199)))),
% 0.79/0.93 inference(rewrite,[status(thm)],[])).
% 0.79/0.93 tff(813,plain,
% 0.79/0.93 ((hskp13 | (~ndr1_0) | c0_1(a199) | (~c3_1(a199)) | (~c2_1(a199)) | c3_1(a195) | c1_1(a195) | c2_1(a195)) <=> (hskp13 | c0_1(a199) | c1_1(a195) | c3_1(a195) | (~ndr1_0) | c2_1(a195) | (~c2_1(a199)) | (~c3_1(a199)))),
% 0.79/0.93 inference(rewrite,[status(thm)],[])).
% 0.79/0.93 tff(814,plain,
% 0.79/0.93 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp13 | (~ndr1_0) | c0_1(a199) | (~c3_1(a199)) | (~c2_1(a199)) | c3_1(a195) | c1_1(a195) | c2_1(a195))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp13 | c0_1(a199) | c1_1(a195) | c3_1(a195) | (~ndr1_0) | c2_1(a195) | (~c2_1(a199)) | (~c3_1(a199))))),
% 0.79/0.93 inference(monotonicity,[status(thm)],[813])).
% 0.79/0.93 tff(815,plain,
% 0.79/0.93 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp13 | (~ndr1_0) | c0_1(a199) | (~c3_1(a199)) | (~c2_1(a199)) | c3_1(a195) | c1_1(a195) | c2_1(a195))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp13 | c0_1(a199) | c1_1(a195) | c3_1(a195) | (~ndr1_0) | c2_1(a195) | (~c2_1(a199)) | (~c3_1(a199)))),
% 0.79/0.93 inference(transitivity,[status(thm)],[814, 812])).
% 0.79/0.93 tff(816,plain,
% 0.79/0.93 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp13 | (~ndr1_0) | c0_1(a199) | (~c3_1(a199)) | (~c2_1(a199)) | c3_1(a195) | c1_1(a195) | c2_1(a195))),
% 0.79/0.93 inference(quant_inst,[status(thm)],[])).
% 0.79/0.93 tff(817,plain,
% 0.79/0.93 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp13 | c0_1(a199) | c1_1(a195) | c3_1(a195) | (~ndr1_0) | c2_1(a195) | (~c2_1(a199)) | (~c3_1(a199))),
% 0.79/0.93 inference(modus_ponens,[status(thm)],[816, 815])).
% 0.79/0.93 tff(818,plain,
% 0.79/0.93 (hskp13 | c2_1(a195) | (~c2_1(a199)) | (~c3_1(a199))),
% 0.79/0.93 inference(unit_resolution,[status(thm)],[817, 148, 710, 561, 560, 246])).
% 0.79/0.93 tff(819,plain,
% 0.79/0.93 (hskp13),
% 0.79/0.93 inference(unit_resolution,[status(thm)],[818, 811, 809, 810])).
% 0.79/0.93 tff(820,plain,
% 0.79/0.93 (~c0_1(a209)),
% 0.79/0.93 inference(unit_resolution,[status(thm)],[387, 819])).
% 0.79/0.93 tff(821,plain,
% 0.79/0.93 (c3_1(a209)),
% 0.79/0.93 inference(unit_resolution,[status(thm)],[395, 819])).
% 0.79/0.93 tff(822,plain,
% 0.79/0.93 (c1_1(a209)),
% 0.79/0.93 inference(unit_resolution,[status(thm)],[403, 819])).
% 0.79/0.93 tff(823,plain,
% 0.79/0.93 ($false),
% 0.79/0.93 inference(unit_resolution,[status(thm)],[765, 148, 822, 821, 811, 808, 820, 710, 709, 561, 65, 809])).
% 0.79/0.93 tff(824,plain,(hskp1 | c0_1(a199) | c1_1(a199) | c1_1(a195) | c3_1(a195) | c2_1(a191) | c3_1(a191) | c1_1(a191)), inference(lemma,lemma(discharge,[]))).
% 0.79/0.93 tff(825,plain,
% 0.79/0.93 ($false),
% 0.79/0.93 inference(unit_resolution,[status(thm)],[824, 642, 648, 102, 561, 560, 66, 68, 67])).
% 0.79/0.93 tff(826,plain,(hskp1 | c1_1(a195) | c3_1(a195) | c2_1(a191) | c3_1(a191) | c1_1(a191)), inference(lemma,lemma(discharge,[]))).
% 0.79/0.93 tff(827,plain,
% 0.79/0.93 (hskp1),
% 0.79/0.93 inference(unit_resolution,[status(thm)],[826, 561, 560, 66, 68, 67])).
% 0.79/0.93 tff(828,plain,
% 0.79/0.93 (c0_1(a190)),
% 0.79/0.93 inference(unit_resolution,[status(thm)],[200, 827])).
% 0.79/0.93 tff(829,assumption,(c0_1(a190)), introduced(assumption)).
% 0.79/0.93 tff(830,assumption,(~hskp19), introduced(assumption)).
% 0.79/0.93 tff(831,plain,
% 0.79/0.93 (~c2_1(a195)),
% 0.79/0.93 inference(unit_resolution,[status(thm)],[791, 830, 784, 561, 829])).
% 0.79/0.93 tff(832,plain,
% 0.79/0.93 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp19 | c3_1(a190) | (~ndr1_0) | (~c2_1(a190)) | (~c0_1(a190)) | c1_1(a190))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp19 | c3_1(a190) | (~ndr1_0) | (~c2_1(a190)) | (~c0_1(a190)) | c1_1(a190))),
% 0.79/0.93 inference(rewrite,[status(thm)],[])).
% 0.79/0.93 tff(833,plain,
% 0.79/0.93 ((hskp19 | (~ndr1_0) | c3_1(a190) | (~c2_1(a190)) | (~c0_1(a190)) | c3_1(a190) | c1_1(a190) | (~c2_1(a190))) <=> (hskp19 | c3_1(a190) | (~ndr1_0) | (~c2_1(a190)) | (~c0_1(a190)) | c1_1(a190))),
% 0.79/0.93 inference(rewrite,[status(thm)],[])).
% 0.79/0.93 tff(834,plain,
% 0.79/0.93 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp19 | (~ndr1_0) | c3_1(a190) | (~c2_1(a190)) | (~c0_1(a190)) | c3_1(a190) | c1_1(a190) | (~c2_1(a190)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp19 | c3_1(a190) | (~ndr1_0) | (~c2_1(a190)) | (~c0_1(a190)) | c1_1(a190)))),
% 0.79/0.93 inference(monotonicity,[status(thm)],[833])).
% 0.79/0.93 tff(835,plain,
% 0.79/0.93 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp19 | (~ndr1_0) | c3_1(a190) | (~c2_1(a190)) | (~c0_1(a190)) | c3_1(a190) | c1_1(a190) | (~c2_1(a190)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp19 | c3_1(a190) | (~ndr1_0) | (~c2_1(a190)) | (~c0_1(a190)) | c1_1(a190))),
% 0.79/0.93 inference(transitivity,[status(thm)],[834, 832])).
% 0.79/0.93 tff(836,plain,
% 0.79/0.93 ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp19 | (~ndr1_0) | c3_1(a190) | (~c2_1(a190)) | (~c0_1(a190)) | c3_1(a190) | c1_1(a190) | (~c2_1(a190)))),
% 0.79/0.93 inference(quant_inst,[status(thm)],[])).
% 0.79/0.93 tff(837,plain,
% 0.79/0.93 ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp19 | c3_1(a190) | (~ndr1_0) | (~c2_1(a190)) | (~c0_1(a190)) | c1_1(a190)),
% 0.79/0.93 inference(modus_ponens,[status(thm)],[836, 835])).
% 0.79/0.93 tff(838,plain,
% 0.79/0.93 (hskp19 | (~c2_1(a190)) | (~c0_1(a190)) | c1_1(a190)),
% 0.79/0.93 inference(unit_resolution,[status(thm)],[837, 148, 13, 211])).
% 0.79/0.93 tff(839,plain,
% 0.79/0.93 (c1_1(a190)),
% 0.79/0.93 inference(unit_resolution,[status(thm)],[838, 830, 784, 829])).
% 0.79/0.93 tff(840,plain,
% 0.79/0.93 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W))))),
% 0.79/0.93 inference(bind,[status(th)],[])).
% 0.79/0.93 tff(841,plain,
% 0.79/0.93 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))),
% 0.79/0.94 inference(quant_intro,[status(thm)],[840])).
% 0.79/0.94 tff(842,plain,
% 0.79/0.94 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))),
% 0.79/0.94 inference(rewrite,[status(thm)],[])).
% 0.79/0.94 tff(843,plain,
% 0.79/0.94 (^[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))) <=> ((~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> (((~c1_1(U)) | (~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c1_1(U)) | (~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c0_1(W))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c0_1(W))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c0_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c0_1(W)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c0_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c0_1(W))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c0_1(W))) | c2_1(V)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c0_1(W))) | c2_1(V)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c0_1(W))) | c2_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V)) | (~c0_1(W)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c0_1(W))) | c2_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V)) | (~c0_1(W))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c0_1(W))) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V)) | (~c0_1(W))) | c3_1(V)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V)) | (~c0_1(W))) | c3_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | (~c0_1(W)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c0_1(W))) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | (~c0_1(W))))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c0_1(W))) | c2_1(V)) | c3_1(V)) | c1_1(W)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | (~c0_1(W))) | c1_1(W)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | (~c0_1(W))) | c1_1(W)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c1_1(W) | (~c0_1(W)))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c0_1(W))) | c2_1(V)) | c3_1(V)) | c1_1(W)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c1_1(W) | (~c0_1(W))))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c0_1(W))) | c2_1(V)) | c3_1(V)) | c1_1(W)) | c2_1(W)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c1_1(W) | (~c0_1(W))) | c2_1(W)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c1_1(W) | (~c0_1(W))) | c2_1(W)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c0_1(W))) | c2_1(V)) | c3_1(V)) | c1_1(W)) | c2_1(W)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))))),
% 0.79/0.94 inference(bind,[status(th)],[])).
% 0.79/0.94 tff(844,plain,
% 0.79/0.94 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c0_1(W))) | c2_1(V)) | c3_1(V)) | c1_1(W)) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))),
% 0.79/0.94 inference(quant_intro,[status(thm)],[843])).
% 0.79/0.94 tff(845,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c0_1(W))) | c2_1(V)) | c3_1(V)) | c1_1(W)) | c2_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause159')).
% 0.79/0.94 tff(846,plain,
% 0.79/0.94 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))),
% 0.79/0.94 inference(modus_ponens,[status(thm)],[845, 844])).
% 0.79/0.94 tff(847,plain,
% 0.79/0.94 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))),
% 0.79/0.94 inference(modus_ponens,[status(thm)],[846, 842])).
% 0.79/0.94 tff(848,plain,(
% 0.79/0.94 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))),
% 0.79/0.94 inference(skolemize,[status(sab)],[847])).
% 0.79/0.94 tff(849,plain,
% 0.79/0.94 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))),
% 0.79/0.94 inference(modus_ponens,[status(thm)],[848, 841])).
% 0.79/0.94 tff(850,plain,
% 0.79/0.94 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | (c1_1(a195) | c3_1(a195) | (~ndr1_0) | (~c2_1(a190)) | (~c0_1(a190)) | (~c1_1(a190)) | c2_1(a195) | (~c0_1(a195)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | c1_1(a195) | c3_1(a195) | (~ndr1_0) | (~c2_1(a190)) | (~c0_1(a190)) | (~c1_1(a190)) | c2_1(a195) | (~c0_1(a195)))),
% 0.79/0.94 inference(rewrite,[status(thm)],[])).
% 0.79/0.94 tff(851,plain,
% 0.79/0.94 (((~ndr1_0) | (~c1_1(a190)) | (~c2_1(a190)) | (~c0_1(a190)) | c3_1(a195) | c2_1(a195) | (~c0_1(a195)) | c2_1(a195) | c1_1(a195) | (~c0_1(a195))) <=> (c1_1(a195) | c3_1(a195) | (~ndr1_0) | (~c2_1(a190)) | (~c0_1(a190)) | (~c1_1(a190)) | c2_1(a195) | (~c0_1(a195)))),
% 0.79/0.94 inference(rewrite,[status(thm)],[])).
% 0.79/0.94 tff(852,plain,
% 0.79/0.94 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c1_1(a190)) | (~c2_1(a190)) | (~c0_1(a190)) | c3_1(a195) | c2_1(a195) | (~c0_1(a195)) | c2_1(a195) | c1_1(a195) | (~c0_1(a195)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | (c1_1(a195) | c3_1(a195) | (~ndr1_0) | (~c2_1(a190)) | (~c0_1(a190)) | (~c1_1(a190)) | c2_1(a195) | (~c0_1(a195))))),
% 0.79/0.94 inference(monotonicity,[status(thm)],[851])).
% 0.79/0.94 tff(853,plain,
% 0.79/0.94 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c1_1(a190)) | (~c2_1(a190)) | (~c0_1(a190)) | c3_1(a195) | c2_1(a195) | (~c0_1(a195)) | c2_1(a195) | c1_1(a195) | (~c0_1(a195)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | c1_1(a195) | c3_1(a195) | (~ndr1_0) | (~c2_1(a190)) | (~c0_1(a190)) | (~c1_1(a190)) | c2_1(a195) | (~c0_1(a195)))),
% 0.79/0.94 inference(transitivity,[status(thm)],[852, 850])).
% 0.79/0.94 tff(854,plain,
% 0.79/0.94 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c1_1(a190)) | (~c2_1(a190)) | (~c0_1(a190)) | c3_1(a195) | c2_1(a195) | (~c0_1(a195)) | c2_1(a195) | c1_1(a195) | (~c0_1(a195)))),
% 0.79/0.94 inference(quant_inst,[status(thm)],[])).
% 0.79/0.94 tff(855,plain,
% 0.79/0.94 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | c1_1(a195) | c3_1(a195) | (~ndr1_0) | (~c2_1(a190)) | (~c0_1(a190)) | (~c1_1(a190)) | c2_1(a195) | (~c0_1(a195))),
% 0.79/0.94 inference(modus_ponens,[status(thm)],[854, 853])).
% 0.79/0.94 tff(856,plain,
% 0.79/0.94 ($false),
% 0.79/0.94 inference(unit_resolution,[status(thm)],[855, 148, 562, 829, 784, 561, 560, 849, 839, 831])).
% 0.79/0.94 tff(857,plain,(hskp19 | (~c0_1(a195)) | (~c0_1(a190)) | (~c2_1(a190)) | c1_1(a195) | c3_1(a195) | c3_1(a190)), inference(lemma,lemma(discharge,[]))).
% 0.79/0.94 tff(858,plain,
% 0.79/0.94 (hskp19),
% 0.79/0.94 inference(unit_resolution,[status(thm)],[857, 828, 770, 807, 561, 560, 13])).
% 0.79/0.94 tff(859,plain,
% 0.79/0.94 (~c0_1(a225)),
% 0.79/0.94 inference(unit_resolution,[status(thm)],[232, 858])).
% 0.79/0.94 tff(860,plain,
% 0.79/0.94 (c3_1(a225)),
% 0.79/0.94 inference(unit_resolution,[status(thm)],[226, 858])).
% 0.79/0.94 tff(861,plain,
% 0.79/0.94 (hskp13),
% 0.79/0.94 inference(unit_resolution,[status(thm)],[381, 860, 859, 67, 66, 68])).
% 0.79/0.94 tff(862,plain,
% 0.79/0.94 (~c0_1(a209)),
% 0.79/0.94 inference(unit_resolution,[status(thm)],[387, 861])).
% 0.79/0.94 tff(863,plain,
% 0.79/0.94 (c3_1(a209)),
% 0.79/0.94 inference(unit_resolution,[status(thm)],[395, 861])).
% 0.79/0.94 tff(864,plain,
% 0.79/0.94 (c1_1(a209)),
% 0.79/0.94 inference(unit_resolution,[status(thm)],[403, 861])).
% 0.79/0.94 tff(865,plain,
% 0.79/0.94 (hskp10),
% 0.79/0.94 inference(unit_resolution,[status(thm)],[410, 148, 864, 863, 862, 67, 66, 68, 10])).
% 0.79/0.94 tff(866,plain,
% 0.79/0.94 (c0_1(a200)),
% 0.79/0.94 inference(unit_resolution,[status(thm)],[307, 865])).
% 0.79/0.94 tff(867,plain,
% 0.79/0.94 (~c1_1(a225)),
% 0.79/0.94 inference(unit_resolution,[status(thm)],[417, 858])).
% 0.79/0.94 tff(868,plain,
% 0.79/0.94 (c3_1(a200)),
% 0.79/0.94 inference(unit_resolution,[status(thm)],[315, 865])).
% 0.79/0.94 tff(869,plain,
% 0.79/0.94 (~c1_1(a200)),
% 0.79/0.94 inference(unit_resolution,[status(thm)],[373, 865])).
% 0.79/0.94 tff(870,assumption,(c2_1(a225)), introduced(assumption)).
% 0.79/0.94 tff(871,plain,
% 0.79/0.94 (c2_1(a200) | (~c0_1(a200)) | (~c2_1(a225))),
% 0.79/0.94 inference(unit_resolution,[status(thm)],[439, 148, 424, 423, 235, 433, 421, 327, 65])).
% 0.79/0.94 tff(872,plain,
% 0.79/0.94 (c2_1(a200)),
% 0.79/0.94 inference(unit_resolution,[status(thm)],[871, 870, 422])).
% 0.79/0.94 tff(873,plain,
% 0.79/0.94 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_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(a225) | c1_1(a225) | c0_1(a209) | c1_1(a194) | c2_1(a194) | (~ndr1_0) | (~c0_1(a194)) | (~c1_1(a209)) | (~c3_1(a209)) | (~c2_1(a225)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_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(a225) | c1_1(a225) | c0_1(a209) | c1_1(a194) | c2_1(a194) | (~ndr1_0) | (~c0_1(a194)) | (~c1_1(a209)) | (~c3_1(a209)) | (~c2_1(a225)))),
% 0.79/0.94 inference(rewrite,[status(thm)],[])).
% 0.79/0.94 tff(874,plain,
% 0.79/0.94 (((~ndr1_0) | c1_1(a194) | c2_1(a194) | (~c0_1(a194)) | c0_1(a209) | (~c3_1(a209)) | (~c1_1(a209)) | c1_1(a225) | c0_1(a225) | (~c2_1(a225))) <=> (c0_1(a225) | c1_1(a225) | c0_1(a209) | c1_1(a194) | c2_1(a194) | (~ndr1_0) | (~c0_1(a194)) | (~c1_1(a209)) | (~c3_1(a209)) | (~c2_1(a225)))),
% 0.79/0.94 inference(rewrite,[status(thm)],[])).
% 0.79/0.94 tff(875,plain,
% 0.79/0.94 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_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) | c1_1(a194) | c2_1(a194) | (~c0_1(a194)) | c0_1(a209) | (~c3_1(a209)) | (~c1_1(a209)) | c1_1(a225) | c0_1(a225) | (~c2_1(a225)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_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(a225) | c1_1(a225) | c0_1(a209) | c1_1(a194) | c2_1(a194) | (~ndr1_0) | (~c0_1(a194)) | (~c1_1(a209)) | (~c3_1(a209)) | (~c2_1(a225))))),
% 0.79/0.94 inference(monotonicity,[status(thm)],[874])).
% 0.79/0.94 tff(876,plain,
% 0.79/0.94 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_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) | c1_1(a194) | c2_1(a194) | (~c0_1(a194)) | c0_1(a209) | (~c3_1(a209)) | (~c1_1(a209)) | c1_1(a225) | c0_1(a225) | (~c2_1(a225)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_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(a225) | c1_1(a225) | c0_1(a209) | c1_1(a194) | c2_1(a194) | (~ndr1_0) | (~c0_1(a194)) | (~c1_1(a209)) | (~c3_1(a209)) | (~c2_1(a225)))),
% 0.79/0.94 inference(transitivity,[status(thm)],[875, 873])).
% 0.79/0.94 tff(877,plain,
% 0.79/0.94 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_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) | c1_1(a194) | c2_1(a194) | (~c0_1(a194)) | c0_1(a209) | (~c3_1(a209)) | (~c1_1(a209)) | c1_1(a225) | c0_1(a225) | (~c2_1(a225)))),
% 0.79/0.94 inference(quant_inst,[status(thm)],[])).
% 0.79/0.94 tff(878,plain,
% 0.79/0.94 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a225) | c1_1(a225) | c0_1(a209) | c1_1(a194) | c2_1(a194) | (~ndr1_0) | (~c0_1(a194)) | (~c1_1(a209)) | (~c3_1(a209)) | (~c2_1(a225))),
% 0.79/0.94 inference(modus_ponens,[status(thm)],[877, 876])).
% 0.79/0.94 tff(879,plain,
% 0.79/0.94 ((~c0_1(a194)) | (~c2_1(a225))),
% 0.79/0.94 inference(unit_resolution,[status(thm)],[878, 148, 424, 423, 235, 433, 421, 12, 11, 65])).
% 0.79/0.94 tff(880,plain,
% 0.79/0.94 (~c0_1(a194)),
% 0.79/0.94 inference(unit_resolution,[status(thm)],[879, 870])).
% 0.79/0.94 tff(881,plain,
% 0.79/0.94 (~hskp5),
% 0.79/0.94 inference(unit_resolution,[status(thm)],[598, 880])).
% 0.79/0.94 tff(882,plain,
% 0.79/0.94 (hskp23 | hskp5 | (~c2_1(a200))),
% 0.79/0.94 inference(unit_resolution,[status(thm)],[487, 148, 422, 563, 481])).
% 0.79/0.94 tff(883,plain,
% 0.79/0.94 (hskp23),
% 0.79/0.94 inference(unit_resolution,[status(thm)],[882, 881, 872])).
% 0.79/0.94 tff(884,plain,
% 0.79/0.94 (c3_1(a189)),
% 0.79/0.94 inference(unit_resolution,[status(thm)],[496, 883])).
% 0.79/0.94 tff(885,plain,
% 0.79/0.94 (c1_1(a189)),
% 0.79/0.94 inference(unit_resolution,[status(thm)],[504, 883])).
% 0.79/0.94 tff(886,plain,
% 0.79/0.94 (c0_1(a189)),
% 0.79/0.94 inference(unit_resolution,[status(thm)],[512, 883])).
% 0.79/0.94 tff(887,plain,
% 0.79/0.94 ($false),
% 0.79/0.94 inference(unit_resolution,[status(thm)],[574, 148, 886, 885, 884, 422, 563, 562, 561, 560, 470, 872])).
% 0.79/0.94 tff(888,plain,((~c2_1(a225)) | (~c0_1(a200)) | (~c3_1(a200)) | (~c0_1(a195)) | c1_1(a195) | c3_1(a195) | (~c1_1(a209)) | (~c3_1(a209)) | c0_1(a225) | c1_1(a225) | c0_1(a209) | c1_1(a200) | c1_1(a194) | c2_1(a194)), inference(lemma,lemma(discharge,[]))).
% 0.79/0.94 tff(889,plain,
% 0.79/0.94 (~c2_1(a225)),
% 0.79/0.94 inference(unit_resolution,[status(thm)],[888, 869, 868, 807, 561, 560, 864, 863, 859, 867, 862, 866, 12, 11])).
% 0.79/0.94 tff(890,plain,
% 0.79/0.94 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a225) | c1_1(a195) | c3_1(a195) | (~ndr1_0) | (~c2_1(a195)) | (~c0_1(a195)) | c2_1(a225) | (~c3_1(a225)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a225) | c1_1(a195) | c3_1(a195) | (~ndr1_0) | (~c2_1(a195)) | (~c0_1(a195)) | c2_1(a225) | (~c3_1(a225)))),
% 0.79/0.94 inference(rewrite,[status(thm)],[])).
% 0.79/0.94 tff(891,plain,
% 0.79/0.94 (((~ndr1_0) | c3_1(a195) | (~c2_1(a195)) | (~c0_1(a195)) | c3_1(a195) | c1_1(a195) | (~c2_1(a195)) | c2_1(a225) | c0_1(a225) | (~c3_1(a225))) <=> (c0_1(a225) | c1_1(a195) | c3_1(a195) | (~ndr1_0) | (~c2_1(a195)) | (~c0_1(a195)) | c2_1(a225) | (~c3_1(a225)))),
% 0.79/0.94 inference(rewrite,[status(thm)],[])).
% 0.79/0.94 tff(892,plain,
% 0.79/0.94 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a195) | (~c2_1(a195)) | (~c0_1(a195)) | c3_1(a195) | c1_1(a195) | (~c2_1(a195)) | c2_1(a225) | c0_1(a225) | (~c3_1(a225)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a225) | c1_1(a195) | c3_1(a195) | (~ndr1_0) | (~c2_1(a195)) | (~c0_1(a195)) | c2_1(a225) | (~c3_1(a225))))),
% 0.79/0.94 inference(monotonicity,[status(thm)],[891])).
% 0.79/0.94 tff(893,plain,
% 0.79/0.94 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a195) | (~c2_1(a195)) | (~c0_1(a195)) | c3_1(a195) | c1_1(a195) | (~c2_1(a195)) | c2_1(a225) | c0_1(a225) | (~c3_1(a225)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a225) | c1_1(a195) | c3_1(a195) | (~ndr1_0) | (~c2_1(a195)) | (~c0_1(a195)) | c2_1(a225) | (~c3_1(a225)))),
% 0.79/0.94 inference(transitivity,[status(thm)],[892, 890])).
% 0.79/0.94 tff(894,plain,
% 0.79/0.94 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a195) | (~c2_1(a195)) | (~c0_1(a195)) | c3_1(a195) | c1_1(a195) | (~c2_1(a195)) | c2_1(a225) | c0_1(a225) | (~c3_1(a225)))),
% 0.79/0.94 inference(quant_inst,[status(thm)],[])).
% 0.79/0.94 tff(895,plain,
% 0.79/0.94 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a225) | c1_1(a195) | c3_1(a195) | (~ndr1_0) | (~c2_1(a195)) | (~c0_1(a195)) | c2_1(a225) | (~c3_1(a225))),
% 0.79/0.94 inference(modus_ponens,[status(thm)],[894, 893])).
% 0.79/0.94 tff(896,plain,
% 0.79/0.94 (~c2_1(a195)),
% 0.79/0.94 inference(unit_resolution,[status(thm)],[895, 148, 860, 807, 859, 561, 560, 451, 889])).
% 0.79/0.94 tff(897,plain,
% 0.79/0.94 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a225) | c1_1(a225) | c1_1(a195) | c3_1(a195) | (~ndr1_0) | c2_1(a195) | c2_1(a225) | (~c3_1(a225)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a225) | c1_1(a225) | c1_1(a195) | c3_1(a195) | (~ndr1_0) | c2_1(a195) | c2_1(a225) | (~c3_1(a225)))),
% 0.79/0.94 inference(rewrite,[status(thm)],[])).
% 0.79/0.94 tff(898,plain,
% 0.79/0.94 (((~ndr1_0) | c0_1(a225) | c2_1(a225) | (~c3_1(a225)) | c3_1(a195) | c1_1(a195) | c2_1(a195) | c2_1(a225) | c1_1(a225) | c0_1(a225)) <=> (c0_1(a225) | c1_1(a225) | c1_1(a195) | c3_1(a195) | (~ndr1_0) | c2_1(a195) | c2_1(a225) | (~c3_1(a225)))),
% 0.79/0.94 inference(rewrite,[status(thm)],[])).
% 0.79/0.94 tff(899,plain,
% 0.79/0.94 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c0_1(a225) | c2_1(a225) | (~c3_1(a225)) | c3_1(a195) | c1_1(a195) | c2_1(a195) | c2_1(a225) | c1_1(a225) | c0_1(a225))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a225) | c1_1(a225) | c1_1(a195) | c3_1(a195) | (~ndr1_0) | c2_1(a195) | c2_1(a225) | (~c3_1(a225))))),
% 0.79/0.94 inference(monotonicity,[status(thm)],[898])).
% 0.79/0.94 tff(900,plain,
% 0.79/0.94 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c0_1(a225) | c2_1(a225) | (~c3_1(a225)) | c3_1(a195) | c1_1(a195) | c2_1(a195) | c2_1(a225) | c1_1(a225) | c0_1(a225))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a225) | c1_1(a225) | c1_1(a195) | c3_1(a195) | (~ndr1_0) | c2_1(a195) | c2_1(a225) | (~c3_1(a225)))),
% 0.79/0.94 inference(transitivity,[status(thm)],[899, 897])).
% 0.79/0.94 tff(901,plain,
% 0.79/0.94 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c0_1(a225) | c2_1(a225) | (~c3_1(a225)) | c3_1(a195) | c1_1(a195) | c2_1(a195) | c2_1(a225) | c1_1(a225) | c0_1(a225))),
% 0.79/0.94 inference(quant_inst,[status(thm)],[])).
% 0.79/0.94 tff(902,plain,
% 0.79/0.94 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a225) | c1_1(a225) | c1_1(a195) | c3_1(a195) | (~ndr1_0) | c2_1(a195) | c2_1(a225) | (~c3_1(a225))),
% 0.79/0.94 inference(modus_ponens,[status(thm)],[901, 900])).
% 0.79/0.94 tff(903,plain,
% 0.79/0.94 ($false),
% 0.79/0.94 inference(unit_resolution,[status(thm)],[902, 148, 860, 859, 867, 561, 560, 264, 896, 889])).
% 0.79/0.94 tff(904,plain,(c1_1(a195) | c3_1(a195) | c1_1(a194) | c2_1(a194) | c1_1(a191) | c2_1(a191) | c3_1(a191) | c3_1(a190) | hskp15), inference(lemma,lemma(discharge,[]))).
% 0.79/0.94 tff(905,plain,
% 0.79/0.94 (c1_1(a195)),
% 0.79/0.94 inference(unit_resolution,[status(thm)],[904, 560, 12, 11, 67, 66, 68, 13, 36])).
% 0.79/0.94 tff(906,plain,
% 0.79/0.94 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp15 | (~c1_1(a195)) | c3_1(a195) | c1_1(a191) | c2_1(a191) | c3_1(a191) | (~ndr1_0) | c2_1(a195))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp15 | (~c1_1(a195)) | c3_1(a195) | c1_1(a191) | c2_1(a191) | c3_1(a191) | (~ndr1_0) | c2_1(a195))),
% 0.79/0.94 inference(rewrite,[status(thm)],[])).
% 0.79/0.94 tff(907,plain,
% 0.79/0.94 ((hskp15 | (~ndr1_0) | c3_1(a195) | c2_1(a195) | (~c1_1(a195)) | c3_1(a191) | c1_1(a191) | c2_1(a191)) <=> (hskp15 | (~c1_1(a195)) | c3_1(a195) | c1_1(a191) | c2_1(a191) | c3_1(a191) | (~ndr1_0) | c2_1(a195))),
% 0.79/0.94 inference(rewrite,[status(thm)],[])).
% 0.79/0.94 tff(908,plain,
% 0.79/0.94 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp15 | (~ndr1_0) | c3_1(a195) | c2_1(a195) | (~c1_1(a195)) | c3_1(a191) | c1_1(a191) | c2_1(a191))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp15 | (~c1_1(a195)) | c3_1(a195) | c1_1(a191) | c2_1(a191) | c3_1(a191) | (~ndr1_0) | c2_1(a195)))),
% 0.79/0.94 inference(monotonicity,[status(thm)],[907])).
% 0.79/0.94 tff(909,plain,
% 0.79/0.94 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp15 | (~ndr1_0) | c3_1(a195) | c2_1(a195) | (~c1_1(a195)) | c3_1(a191) | c1_1(a191) | c2_1(a191))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp15 | (~c1_1(a195)) | c3_1(a195) | c1_1(a191) | c2_1(a191) | c3_1(a191) | (~ndr1_0) | c2_1(a195))),
% 0.79/0.94 inference(transitivity,[status(thm)],[908, 906])).
% 0.79/0.94 tff(910,plain,
% 0.79/0.94 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp15 | (~ndr1_0) | c3_1(a195) | c2_1(a195) | (~c1_1(a195)) | c3_1(a191) | c1_1(a191) | c2_1(a191))),
% 0.79/0.94 inference(quant_inst,[status(thm)],[])).
% 0.79/0.94 tff(911,plain,
% 0.79/0.94 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp15 | (~c1_1(a195)) | c3_1(a195) | c1_1(a191) | c2_1(a191) | c3_1(a191) | (~ndr1_0) | c2_1(a195)),
% 0.79/0.94 inference(modus_ponens,[status(thm)],[910, 909])).
% 0.79/0.94 tff(912,plain,
% 0.79/0.94 ((~c1_1(a195)) | c2_1(a195)),
% 0.79/0.94 inference(unit_resolution,[status(thm)],[911, 148, 36, 560, 67, 66, 68, 722])).
% 0.79/0.94 tff(913,plain,
% 0.79/0.94 (c2_1(a195)),
% 0.79/0.94 inference(unit_resolution,[status(thm)],[912, 905])).
% 0.79/0.94 tff(914,plain,
% 0.79/0.94 (~hskp6),
% 0.79/0.94 inference(unit_resolution,[status(thm)],[557, 905])).
% 0.79/0.94 tff(915,plain,
% 0.79/0.94 (c0_1(a191)),
% 0.79/0.94 inference(unit_resolution,[status(thm)],[537, 914])).
% 0.79/0.94 tff(916,plain,
% 0.79/0.94 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | ((~c1_1(a195)) | c1_1(a191) | c2_1(a191) | c3_1(a191) | (~ndr1_0) | (~c0_1(a191)) | (~c2_1(a195)) | (~c0_1(a195)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | (~c1_1(a195)) | c1_1(a191) | c2_1(a191) | c3_1(a191) | (~ndr1_0) | (~c0_1(a191)) | (~c2_1(a195)) | (~c0_1(a195)))),
% 0.79/0.94 inference(rewrite,[status(thm)],[])).
% 0.79/0.94 tff(917,plain,
% 0.79/0.94 (((~ndr1_0) | (~c1_1(a195)) | (~c2_1(a195)) | (~c0_1(a195)) | c3_1(a191) | c2_1(a191) | (~c0_1(a191)) | c2_1(a191) | c1_1(a191) | (~c0_1(a191))) <=> ((~c1_1(a195)) | c1_1(a191) | c2_1(a191) | c3_1(a191) | (~ndr1_0) | (~c0_1(a191)) | (~c2_1(a195)) | (~c0_1(a195)))),
% 0.79/0.94 inference(rewrite,[status(thm)],[])).
% 0.79/0.94 tff(918,plain,
% 0.79/0.94 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c1_1(a195)) | (~c2_1(a195)) | (~c0_1(a195)) | c3_1(a191) | c2_1(a191) | (~c0_1(a191)) | c2_1(a191) | c1_1(a191) | (~c0_1(a191)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | ((~c1_1(a195)) | c1_1(a191) | c2_1(a191) | c3_1(a191) | (~ndr1_0) | (~c0_1(a191)) | (~c2_1(a195)) | (~c0_1(a195))))),
% 0.79/0.94 inference(monotonicity,[status(thm)],[917])).
% 0.79/0.94 tff(919,plain,
% 0.79/0.94 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c1_1(a195)) | (~c2_1(a195)) | (~c0_1(a195)) | c3_1(a191) | c2_1(a191) | (~c0_1(a191)) | c2_1(a191) | c1_1(a191) | (~c0_1(a191)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | (~c1_1(a195)) | c1_1(a191) | c2_1(a191) | c3_1(a191) | (~ndr1_0) | (~c0_1(a191)) | (~c2_1(a195)) | (~c0_1(a195)))),
% 0.79/0.94 inference(transitivity,[status(thm)],[918, 916])).
% 0.79/0.94 tff(920,plain,
% 0.79/0.94 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c1_1(a195)) | (~c2_1(a195)) | (~c0_1(a195)) | c3_1(a191) | c2_1(a191) | (~c0_1(a191)) | c2_1(a191) | c1_1(a191) | (~c0_1(a191)))),
% 0.79/0.94 inference(quant_inst,[status(thm)],[])).
% 0.79/0.94 tff(921,plain,
% 0.79/0.94 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | (~c1_1(a195)) | c1_1(a191) | c2_1(a191) | c3_1(a191) | (~ndr1_0) | (~c0_1(a191)) | (~c2_1(a195)) | (~c0_1(a195))),
% 0.79/0.94 inference(modus_ponens,[status(thm)],[920, 919])).
% 0.79/0.94 tff(922,plain,
% 0.79/0.94 (~c0_1(a195)),
% 0.79/0.94 inference(unit_resolution,[status(thm)],[921, 148, 905, 67, 66, 68, 849, 915, 913])).
% 0.79/0.94 tff(923,plain,
% 0.79/0.94 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp5 | c0_1(a195) | (~c1_1(a195)) | c3_1(a195) | (~ndr1_0) | (~c2_1(a195)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp5 | c0_1(a195) | (~c1_1(a195)) | c3_1(a195) | (~ndr1_0) | (~c2_1(a195)))),
% 0.79/0.94 inference(rewrite,[status(thm)],[])).
% 0.79/0.94 tff(924,plain,
% 0.79/0.94 ((hskp5 | (~ndr1_0) | c3_1(a195) | c0_1(a195) | (~c2_1(a195)) | c3_1(a195) | c0_1(a195) | (~c1_1(a195))) <=> (hskp5 | c0_1(a195) | (~c1_1(a195)) | c3_1(a195) | (~ndr1_0) | (~c2_1(a195)))),
% 0.79/0.95 inference(rewrite,[status(thm)],[])).
% 0.79/0.95 tff(925,plain,
% 0.79/0.95 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp5 | (~ndr1_0) | c3_1(a195) | c0_1(a195) | (~c2_1(a195)) | c3_1(a195) | c0_1(a195) | (~c1_1(a195)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp5 | c0_1(a195) | (~c1_1(a195)) | c3_1(a195) | (~ndr1_0) | (~c2_1(a195))))),
% 0.79/0.95 inference(monotonicity,[status(thm)],[924])).
% 0.79/0.95 tff(926,plain,
% 0.79/0.95 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp5 | (~ndr1_0) | c3_1(a195) | c0_1(a195) | (~c2_1(a195)) | c3_1(a195) | c0_1(a195) | (~c1_1(a195)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp5 | c0_1(a195) | (~c1_1(a195)) | c3_1(a195) | (~ndr1_0) | (~c2_1(a195)))),
% 0.79/0.95 inference(transitivity,[status(thm)],[925, 923])).
% 0.79/0.95 tff(927,plain,
% 0.79/0.95 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp5 | (~ndr1_0) | c3_1(a195) | c0_1(a195) | (~c2_1(a195)) | c3_1(a195) | c0_1(a195) | (~c1_1(a195)))),
% 0.79/0.95 inference(quant_inst,[status(thm)],[])).
% 0.79/0.95 tff(928,plain,
% 0.79/0.95 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp5 | c0_1(a195) | (~c1_1(a195)) | c3_1(a195) | (~ndr1_0) | (~c2_1(a195))),
% 0.79/0.95 inference(modus_ponens,[status(thm)],[927, 926])).
% 0.79/0.95 tff(929,plain,
% 0.79/0.95 (hskp5 | c0_1(a195) | (~c1_1(a195)) | (~c2_1(a195))),
% 0.79/0.95 inference(unit_resolution,[status(thm)],[928, 148, 560, 35])).
% 0.79/0.95 tff(930,plain,
% 0.79/0.95 (hskp5),
% 0.79/0.95 inference(unit_resolution,[status(thm)],[929, 922, 905, 913])).
% 0.79/0.95 tff(931,plain,
% 0.79/0.95 (c0_1(a194)),
% 0.79/0.95 inference(unit_resolution,[status(thm)],[598, 930])).
% 0.79/0.95 tff(932,assumption,(c2_1(a195)), introduced(assumption)).
% 0.79/0.95 tff(933,plain,
% 0.79/0.95 (^[V: $i, U: $i] : refl((hskp6 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))) <=> (hskp6 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))))),
% 0.79/0.95 inference(bind,[status(th)],[])).
% 0.79/0.95 tff(934,plain,
% 0.79/0.95 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 0.79/0.95 inference(quant_intro,[status(thm)],[933])).
% 0.79/0.95 tff(935,plain,
% 0.79/0.95 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 0.79/0.95 inference(rewrite,[status(thm)],[])).
% 0.79/0.95 tff(936,plain,
% 0.79/0.95 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c0_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c0_1(V)) | hskp6) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))) | hskp6))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))) | hskp6) <=> (hskp6 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c0_1(V)) | hskp6) <=> (hskp6 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))))),
% 0.79/0.95 inference(bind,[status(th)],[])).
% 0.79/0.95 tff(937,plain,
% 0.79/0.95 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c0_1(V)) | hskp6) <=> ![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 0.79/0.95 inference(quant_intro,[status(thm)],[936])).
% 0.79/0.95 tff(938,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c0_1(V)) | hskp6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause152')).
% 0.79/0.95 tff(939,plain,
% 0.79/0.95 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 0.79/0.95 inference(modus_ponens,[status(thm)],[938, 937])).
% 0.79/0.95 tff(940,plain,
% 0.79/0.95 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 0.79/0.95 inference(modus_ponens,[status(thm)],[939, 935])).
% 0.79/0.95 tff(941,plain,(
% 0.79/0.95 ![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 0.79/0.95 inference(skolemize,[status(sab)],[940])).
% 0.79/0.95 tff(942,plain,
% 0.79/0.95 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 0.79/0.95 inference(modus_ponens,[status(thm)],[941, 934])).
% 0.79/0.95 tff(943,assumption,(c1_1(a195)), introduced(assumption)).
% 0.79/0.95 tff(944,plain,
% 0.79/0.95 (~hskp6),
% 0.79/0.95 inference(unit_resolution,[status(thm)],[557, 943])).
% 0.79/0.95 tff(945,plain,
% 0.79/0.95 (c0_1(a191)),
% 0.79/0.95 inference(unit_resolution,[status(thm)],[537, 944])).
% 0.79/0.95 tff(946,plain,
% 0.79/0.95 (~c0_1(a195)),
% 0.79/0.95 inference(unit_resolution,[status(thm)],[921, 148, 943, 67, 66, 68, 849, 945, 932])).
% 0.79/0.95 tff(947,plain,
% 0.79/0.95 (^[V: $i, U: $i] : refl((hskp14 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))) <=> (hskp14 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))))),
% 0.79/0.95 inference(bind,[status(th)],[])).
% 0.79/0.95 tff(948,plain,
% 0.79/0.95 (![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 0.79/0.95 inference(quant_intro,[status(thm)],[947])).
% 0.79/0.95 tff(949,plain,
% 0.79/0.95 (![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 0.79/0.95 inference(rewrite,[status(thm)],[])).
% 0.79/0.95 tff(950,plain,
% 0.79/0.95 (^[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) | (~c3_1(U)) | (~c2_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c2_1(V)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c2_1(V))))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c2_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V))))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V))))), ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))), ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) | hskp14) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))) | hskp14))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))) | hskp14) <=> (hskp14 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) | hskp14) <=> (hskp14 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))))),
% 0.79/0.95 inference(bind,[status(th)],[])).
% 0.79/0.95 tff(951,plain,
% 0.79/0.95 (![V: $i, U: $i] : ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) | hskp14) <=> ![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 0.79/0.95 inference(quant_intro,[status(thm)],[950])).
% 0.79/0.95 tff(952,axiom,(![V: $i, U: $i] : ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) | hskp14)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause147')).
% 0.79/0.95 tff(953,plain,
% 0.79/0.95 (![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 0.79/0.95 inference(modus_ponens,[status(thm)],[952, 951])).
% 0.79/0.95 tff(954,plain,
% 0.79/0.95 (![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 0.79/0.95 inference(modus_ponens,[status(thm)],[953, 949])).
% 0.79/0.95 tff(955,plain,(
% 0.79/0.95 ![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 0.79/0.95 inference(skolemize,[status(sab)],[954])).
% 0.79/0.95 tff(956,plain,
% 0.79/0.95 (![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 0.79/0.95 inference(modus_ponens,[status(thm)],[955, 948])).
% 0.79/0.95 tff(957,plain,
% 0.79/0.95 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp14 | c0_1(a199) | c1_1(a199) | (~ndr1_0) | (~c2_1(a199)) | (~c3_1(a199)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp14 | c0_1(a199) | c1_1(a199) | (~ndr1_0) | (~c2_1(a199)) | (~c3_1(a199)))),
% 0.79/0.95 inference(rewrite,[status(thm)],[])).
% 0.79/0.95 tff(958,plain,
% 0.79/0.95 ((hskp14 | (~ndr1_0) | c1_1(a199) | (~c3_1(a199)) | (~c2_1(a199)) | c0_1(a199) | (~c3_1(a199)) | (~c2_1(a199))) <=> (hskp14 | c0_1(a199) | c1_1(a199) | (~ndr1_0) | (~c2_1(a199)) | (~c3_1(a199)))),
% 0.79/0.95 inference(rewrite,[status(thm)],[])).
% 0.79/0.95 tff(959,plain,
% 0.79/0.95 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp14 | (~ndr1_0) | c1_1(a199) | (~c3_1(a199)) | (~c2_1(a199)) | c0_1(a199) | (~c3_1(a199)) | (~c2_1(a199)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp14 | c0_1(a199) | c1_1(a199) | (~ndr1_0) | (~c2_1(a199)) | (~c3_1(a199))))),
% 0.79/0.95 inference(monotonicity,[status(thm)],[958])).
% 0.79/0.95 tff(960,plain,
% 0.79/0.95 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp14 | (~ndr1_0) | c1_1(a199) | (~c3_1(a199)) | (~c2_1(a199)) | c0_1(a199) | (~c3_1(a199)) | (~c2_1(a199)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp14 | c0_1(a199) | c1_1(a199) | (~ndr1_0) | (~c2_1(a199)) | (~c3_1(a199)))),
% 0.79/0.95 inference(transitivity,[status(thm)],[959, 957])).
% 0.79/0.95 tff(961,plain,
% 0.79/0.95 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp14 | (~ndr1_0) | c1_1(a199) | (~c3_1(a199)) | (~c2_1(a199)) | c0_1(a199) | (~c3_1(a199)) | (~c2_1(a199)))),
% 0.79/0.95 inference(quant_inst,[status(thm)],[])).
% 0.79/0.95 tff(962,plain,
% 0.79/0.95 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp14 | c0_1(a199) | c1_1(a199) | (~ndr1_0) | (~c2_1(a199)) | (~c3_1(a199))),
% 0.79/0.95 inference(modus_ponens,[status(thm)],[961, 960])).
% 0.79/0.95 tff(963,plain,
% 0.79/0.95 (hskp14 | (~c3_1(a199))),
% 0.79/0.95 inference(unit_resolution,[status(thm)],[962, 148, 663, 648, 642, 956])).
% 0.79/0.95 tff(964,plain,
% 0.79/0.95 (hskp14),
% 0.79/0.95 inference(unit_resolution,[status(thm)],[963, 655])).
% 0.79/0.95 tff(965,plain,
% 0.79/0.95 (((~hskp14) | c3_1(a210)) <=> ((~hskp14) | c3_1(a210))),
% 0.79/0.95 inference(rewrite,[status(thm)],[])).
% 0.79/0.95 tff(966,axiom,((~hskp14) | c3_1(a210)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause53')).
% 0.79/0.95 tff(967,plain,
% 0.79/0.95 ((~hskp14) | c3_1(a210)),
% 0.79/0.95 inference(modus_ponens,[status(thm)],[966, 965])).
% 0.79/0.95 tff(968,plain,
% 0.79/0.95 ((~hskp14) | c3_1(a210)),
% 0.79/0.95 inference(modus_ponens,[status(thm)],[967, 965])).
% 0.79/0.95 tff(969,plain,
% 0.79/0.95 ((~hskp14) | c3_1(a210)),
% 0.79/0.95 inference(modus_ponens,[status(thm)],[968, 965])).
% 0.79/0.95 tff(970,plain,
% 0.79/0.95 ((~hskp14) | c3_1(a210)),
% 0.79/0.95 inference(modus_ponens,[status(thm)],[969, 965])).
% 0.79/0.95 tff(971,plain,
% 0.79/0.95 ((~hskp14) | c3_1(a210)),
% 0.79/0.95 inference(modus_ponens,[status(thm)],[970, 965])).
% 0.79/0.95 tff(972,plain,
% 0.79/0.95 (c3_1(a210)),
% 0.79/0.95 inference(unit_resolution,[status(thm)],[971, 964])).
% 0.79/0.95 tff(973,plain,
% 0.79/0.95 (((~hskp14) | c2_1(a210)) <=> ((~hskp14) | c2_1(a210))),
% 0.79/0.95 inference(rewrite,[status(thm)],[])).
% 0.79/0.95 tff(974,axiom,((~hskp14) | c2_1(a210)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause52')).
% 0.79/0.95 tff(975,plain,
% 0.79/0.95 ((~hskp14) | c2_1(a210)),
% 0.79/0.95 inference(modus_ponens,[status(thm)],[974, 973])).
% 0.79/0.95 tff(976,plain,
% 0.79/0.95 ((~hskp14) | c2_1(a210)),
% 0.79/0.95 inference(modus_ponens,[status(thm)],[975, 973])).
% 0.79/0.95 tff(977,plain,
% 0.79/0.95 ((~hskp14) | c2_1(a210)),
% 0.79/0.95 inference(modus_ponens,[status(thm)],[976, 973])).
% 0.79/0.95 tff(978,plain,
% 0.79/0.95 ((~hskp14) | c2_1(a210)),
% 0.79/0.95 inference(modus_ponens,[status(thm)],[977, 973])).
% 0.79/0.95 tff(979,plain,
% 0.79/0.95 ((~hskp14) | c2_1(a210)),
% 0.79/0.95 inference(modus_ponens,[status(thm)],[978, 973])).
% 0.79/0.95 tff(980,plain,
% 0.79/0.95 (c2_1(a210)),
% 0.79/0.95 inference(unit_resolution,[status(thm)],[979, 964])).
% 0.79/0.95 tff(981,plain,
% 0.79/0.95 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp6 | c0_1(a195) | (~c1_1(a195)) | (~ndr1_0) | (~c2_1(a195)) | (~c2_1(a210)) | (~c3_1(a210)) | (~c0_1(a210)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp6 | c0_1(a195) | (~c1_1(a195)) | (~ndr1_0) | (~c2_1(a195)) | (~c2_1(a210)) | (~c3_1(a210)) | (~c0_1(a210)))),
% 0.79/0.95 inference(rewrite,[status(thm)],[])).
% 0.79/0.95 tff(982,plain,
% 0.79/0.95 ((hskp6 | (~ndr1_0) | (~c3_1(a210)) | (~c2_1(a210)) | (~c0_1(a210)) | c0_1(a195) | (~c1_1(a195)) | (~c2_1(a195))) <=> (hskp6 | c0_1(a195) | (~c1_1(a195)) | (~ndr1_0) | (~c2_1(a195)) | (~c2_1(a210)) | (~c3_1(a210)) | (~c0_1(a210)))),
% 0.79/0.95 inference(rewrite,[status(thm)],[])).
% 0.79/0.95 tff(983,plain,
% 0.79/0.95 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp6 | (~ndr1_0) | (~c3_1(a210)) | (~c2_1(a210)) | (~c0_1(a210)) | c0_1(a195) | (~c1_1(a195)) | (~c2_1(a195)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp6 | c0_1(a195) | (~c1_1(a195)) | (~ndr1_0) | (~c2_1(a195)) | (~c2_1(a210)) | (~c3_1(a210)) | (~c0_1(a210))))),
% 0.79/0.95 inference(monotonicity,[status(thm)],[982])).
% 0.79/0.95 tff(984,plain,
% 0.79/0.95 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp6 | (~ndr1_0) | (~c3_1(a210)) | (~c2_1(a210)) | (~c0_1(a210)) | c0_1(a195) | (~c1_1(a195)) | (~c2_1(a195)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp6 | c0_1(a195) | (~c1_1(a195)) | (~ndr1_0) | (~c2_1(a195)) | (~c2_1(a210)) | (~c3_1(a210)) | (~c0_1(a210)))),
% 0.79/0.95 inference(transitivity,[status(thm)],[983, 981])).
% 0.79/0.95 tff(985,plain,
% 0.79/0.95 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp6 | (~ndr1_0) | (~c3_1(a210)) | (~c2_1(a210)) | (~c0_1(a210)) | c0_1(a195) | (~c1_1(a195)) | (~c2_1(a195)))),
% 0.79/0.95 inference(quant_inst,[status(thm)],[])).
% 0.79/0.95 tff(986,plain,
% 0.79/0.95 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp6 | c0_1(a195) | (~c1_1(a195)) | (~ndr1_0) | (~c2_1(a195)) | (~c2_1(a210)) | (~c3_1(a210)) | (~c0_1(a210))),
% 0.79/0.95 inference(modus_ponens,[status(thm)],[985, 984])).
% 0.79/0.95 tff(987,plain,
% 0.79/0.95 (~c0_1(a210)),
% 0.79/0.95 inference(unit_resolution,[status(thm)],[986, 148, 944, 980, 972, 946, 943, 942, 932])).
% 0.79/0.95 tff(988,plain,
% 0.79/0.95 (((~hskp14) | (~c1_1(a210))) <=> ((~hskp14) | (~c1_1(a210)))),
% 0.79/0.95 inference(rewrite,[status(thm)],[])).
% 0.79/0.95 tff(989,plain,
% 0.79/0.95 (((~c1_1(a210)) | (~hskp14)) <=> ((~hskp14) | (~c1_1(a210)))),
% 0.79/0.95 inference(rewrite,[status(thm)],[])).
% 0.79/0.95 tff(990,axiom,((~c1_1(a210)) | (~hskp14)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause85')).
% 0.79/0.95 tff(991,plain,
% 0.79/0.95 ((~hskp14) | (~c1_1(a210))),
% 0.79/0.95 inference(modus_ponens,[status(thm)],[990, 989])).
% 0.79/0.95 tff(992,plain,
% 0.79/0.95 ((~hskp14) | (~c1_1(a210))),
% 0.79/0.95 inference(modus_ponens,[status(thm)],[991, 988])).
% 0.79/0.95 tff(993,plain,
% 0.79/0.95 (~c1_1(a210)),
% 0.79/0.95 inference(unit_resolution,[status(thm)],[992, 964])).
% 0.79/0.95 tff(994,plain,
% 0.79/0.95 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_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(a210) | c0_1(a209) | c1_1(a194) | c2_1(a194) | (~ndr1_0) | (~c0_1(a194)) | (~c1_1(a209)) | (~c3_1(a209)) | (~c2_1(a210)) | c0_1(a210))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_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(a210) | c0_1(a209) | c1_1(a194) | c2_1(a194) | (~ndr1_0) | (~c0_1(a194)) | (~c1_1(a209)) | (~c3_1(a209)) | (~c2_1(a210)) | c0_1(a210))),
% 0.79/0.95 inference(rewrite,[status(thm)],[])).
% 0.79/0.95 tff(995,plain,
% 0.79/0.95 (((~ndr1_0) | c1_1(a194) | c2_1(a194) | (~c0_1(a194)) | c0_1(a209) | (~c3_1(a209)) | (~c1_1(a209)) | c1_1(a210) | c0_1(a210) | (~c2_1(a210))) <=> (c1_1(a210) | c0_1(a209) | c1_1(a194) | c2_1(a194) | (~ndr1_0) | (~c0_1(a194)) | (~c1_1(a209)) | (~c3_1(a209)) | (~c2_1(a210)) | c0_1(a210))),
% 0.79/0.95 inference(rewrite,[status(thm)],[])).
% 0.79/0.95 tff(996,plain,
% 0.79/0.95 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_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) | c1_1(a194) | c2_1(a194) | (~c0_1(a194)) | c0_1(a209) | (~c3_1(a209)) | (~c1_1(a209)) | c1_1(a210) | c0_1(a210) | (~c2_1(a210)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_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(a210) | c0_1(a209) | c1_1(a194) | c2_1(a194) | (~ndr1_0) | (~c0_1(a194)) | (~c1_1(a209)) | (~c3_1(a209)) | (~c2_1(a210)) | c0_1(a210)))),
% 0.79/0.95 inference(monotonicity,[status(thm)],[995])).
% 0.79/0.95 tff(997,plain,
% 0.79/0.95 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_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) | c1_1(a194) | c2_1(a194) | (~c0_1(a194)) | c0_1(a209) | (~c3_1(a209)) | (~c1_1(a209)) | c1_1(a210) | c0_1(a210) | (~c2_1(a210)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_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(a210) | c0_1(a209) | c1_1(a194) | c2_1(a194) | (~ndr1_0) | (~c0_1(a194)) | (~c1_1(a209)) | (~c3_1(a209)) | (~c2_1(a210)) | c0_1(a210))),
% 0.79/0.95 inference(transitivity,[status(thm)],[996, 994])).
% 0.79/0.95 tff(998,plain,
% 0.79/0.95 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_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) | c1_1(a194) | c2_1(a194) | (~c0_1(a194)) | c0_1(a209) | (~c3_1(a209)) | (~c1_1(a209)) | c1_1(a210) | c0_1(a210) | (~c2_1(a210)))),
% 0.79/0.95 inference(quant_inst,[status(thm)],[])).
% 0.79/0.95 tff(999,plain,
% 0.79/0.95 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a210) | c0_1(a209) | c1_1(a194) | c2_1(a194) | (~ndr1_0) | (~c0_1(a194)) | (~c1_1(a209)) | (~c3_1(a209)) | (~c2_1(a210)) | c0_1(a210)),
% 0.79/0.95 inference(modus_ponens,[status(thm)],[998, 997])).
% 0.79/0.95 tff(1000,plain,
% 0.79/0.95 ($false),
% 0.79/0.95 inference(unit_resolution,[status(thm)],[999, 148, 980, 675, 674, 673, 993, 672, 12, 11, 65, 987])).
% 0.79/0.95 tff(1001,plain,(hskp1 | (~c0_1(a194)) | c1_1(a194) | c2_1(a194) | (~c1_1(a195)) | (~c2_1(a195)) | c1_1(a191) | c2_1(a191) | c3_1(a191)), inference(lemma,lemma(discharge,[]))).
% 0.79/0.95 tff(1002,plain,
% 0.79/0.95 (hskp1),
% 0.79/0.95 inference(unit_resolution,[status(thm)],[1001, 931, 12, 11, 905, 913, 67, 66, 68])).
% 0.79/0.95 tff(1003,plain,
% 0.79/0.95 (c0_1(a190)),
% 0.79/0.95 inference(unit_resolution,[status(thm)],[200, 1002])).
% 0.79/0.95 tff(1004,plain,
% 0.79/0.95 (c2_1(a190)),
% 0.79/0.95 inference(unit_resolution,[status(thm)],[192, 1002])).
% 0.79/0.95 tff(1005,assumption,(c1_1(a190)), introduced(assumption)).
% 0.79/0.95 tff(1006,plain,
% 0.79/0.95 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | (c1_1(a194) | c2_1(a194) | c2_1(a191) | c3_1(a191) | (~ndr1_0) | (~c2_1(a190)) | (~c0_1(a190)) | (~c1_1(a190)) | (~c0_1(a191)) | (~c0_1(a194)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | c1_1(a194) | c2_1(a194) | c2_1(a191) | c3_1(a191) | (~ndr1_0) | (~c2_1(a190)) | (~c0_1(a190)) | (~c1_1(a190)) | (~c0_1(a191)) | (~c0_1(a194)))),
% 0.79/0.95 inference(rewrite,[status(thm)],[])).
% 0.79/0.95 tff(1007,plain,
% 0.79/0.95 (((~ndr1_0) | (~c1_1(a190)) | (~c2_1(a190)) | (~c0_1(a190)) | c3_1(a191) | c2_1(a191) | (~c0_1(a191)) | c2_1(a194) | c1_1(a194) | (~c0_1(a194))) <=> (c1_1(a194) | c2_1(a194) | c2_1(a191) | c3_1(a191) | (~ndr1_0) | (~c2_1(a190)) | (~c0_1(a190)) | (~c1_1(a190)) | (~c0_1(a191)) | (~c0_1(a194)))),
% 0.79/0.95 inference(rewrite,[status(thm)],[])).
% 0.79/0.95 tff(1008,plain,
% 0.79/0.95 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c1_1(a190)) | (~c2_1(a190)) | (~c0_1(a190)) | c3_1(a191) | c2_1(a191) | (~c0_1(a191)) | c2_1(a194) | c1_1(a194) | (~c0_1(a194)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | (c1_1(a194) | c2_1(a194) | c2_1(a191) | c3_1(a191) | (~ndr1_0) | (~c2_1(a190)) | (~c0_1(a190)) | (~c1_1(a190)) | (~c0_1(a191)) | (~c0_1(a194))))),
% 0.79/0.95 inference(monotonicity,[status(thm)],[1007])).
% 0.79/0.95 tff(1009,plain,
% 0.79/0.95 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c1_1(a190)) | (~c2_1(a190)) | (~c0_1(a190)) | c3_1(a191) | c2_1(a191) | (~c0_1(a191)) | c2_1(a194) | c1_1(a194) | (~c0_1(a194)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | c1_1(a194) | c2_1(a194) | c2_1(a191) | c3_1(a191) | (~ndr1_0) | (~c2_1(a190)) | (~c0_1(a190)) | (~c1_1(a190)) | (~c0_1(a191)) | (~c0_1(a194)))),
% 0.79/0.95 inference(transitivity,[status(thm)],[1008, 1006])).
% 0.79/0.95 tff(1010,plain,
% 0.79/0.95 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c1_1(a190)) | (~c2_1(a190)) | (~c0_1(a190)) | c3_1(a191) | c2_1(a191) | (~c0_1(a191)) | c2_1(a194) | c1_1(a194) | (~c0_1(a194)))),
% 0.79/0.95 inference(quant_inst,[status(thm)],[])).
% 0.79/0.95 tff(1011,plain,
% 0.79/0.95 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | c1_1(a194) | c2_1(a194) | c2_1(a191) | c3_1(a191) | (~ndr1_0) | (~c2_1(a190)) | (~c0_1(a190)) | (~c1_1(a190)) | (~c0_1(a191)) | (~c0_1(a194))),
% 0.79/0.95 inference(modus_ponens,[status(thm)],[1010, 1009])).
% 0.79/0.95 tff(1012,plain,
% 0.79/0.95 ($false),
% 0.79/0.95 inference(unit_resolution,[status(thm)],[1011, 148, 673, 829, 784, 12, 11, 66, 68, 849, 375, 1005])).
% 0.79/0.95 tff(1013,plain,((~c1_1(a190)) | (~c0_1(a194)) | (~c0_1(a190)) | (~c2_1(a190)) | c1_1(a194) | c2_1(a194) | c2_1(a191) | c3_1(a191) | (~c0_1(a191))), inference(lemma,lemma(discharge,[]))).
% 0.79/0.95 tff(1014,plain,
% 0.79/0.95 (~c1_1(a190)),
% 0.79/0.95 inference(unit_resolution,[status(thm)],[1013, 931, 1003, 1004, 12, 11, 66, 68, 915])).
% 0.79/0.95 tff(1015,plain,
% 0.79/0.95 (hskp19),
% 0.79/0.95 inference(unit_resolution,[status(thm)],[838, 1014, 1004, 1003])).
% 0.79/0.95 tff(1016,plain,
% 0.79/0.95 (c3_1(a225)),
% 0.79/0.95 inference(unit_resolution,[status(thm)],[226, 1015])).
% 0.79/0.95 tff(1017,plain,
% 0.79/0.95 (~c0_1(a225)),
% 0.79/0.95 inference(unit_resolution,[status(thm)],[232, 1015])).
% 0.79/0.95 tff(1018,plain,
% 0.79/0.95 (hskp13),
% 0.79/0.95 inference(unit_resolution,[status(thm)],[378, 1017, 915, 66, 68, 1016, 67])).
% 0.79/0.95 tff(1019,plain,
% 0.79/0.95 (~c0_1(a209)),
% 0.79/0.95 inference(unit_resolution,[status(thm)],[387, 1018])).
% 0.79/0.95 tff(1020,plain,
% 0.79/0.95 (~c1_1(a225)),
% 0.79/0.95 inference(unit_resolution,[status(thm)],[417, 1015])).
% 0.79/0.95 tff(1021,plain,
% 0.79/0.95 (c3_1(a209)),
% 0.79/0.95 inference(unit_resolution,[status(thm)],[395, 1018])).
% 0.79/0.95 tff(1022,plain,
% 0.79/0.95 (c1_1(a209)),
% 0.79/0.95 inference(unit_resolution,[status(thm)],[403, 1018])).
% 0.79/0.95 tff(1023,plain,
% 0.79/0.95 (~c2_1(a225)),
% 0.79/0.95 inference(unit_resolution,[status(thm)],[878, 148, 1022, 1021, 931, 1017, 1020, 1019, 12, 11, 65])).
% 0.79/0.95 tff(1024,plain,
% 0.79/0.95 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W))) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W))))),
% 0.79/0.95 inference(bind,[status(th)],[])).
% 0.79/0.95 tff(1025,plain,
% 0.79/0.95 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))),
% 0.79/0.95 inference(quant_intro,[status(thm)],[1024])).
% 0.79/0.95 tff(1026,plain,
% 0.79/0.95 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))),
% 0.79/0.95 inference(rewrite,[status(thm)],[])).
% 0.79/0.95 tff(1027,plain,
% 0.79/0.95 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V))))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V))))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c3_1(W))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V))) | (~c3_1(W))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c3_1(W)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c3_1(W))))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c3_1(W))) | c1_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c3_1(W))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c3_1(W))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c3_1(W)))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c3_1(W))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c3_1(W))))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c3_1(W))) | c1_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c3_1(W))) | c0_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c3_1(W))) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | (~c3_1(W)))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c3_1(W))) | c1_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | (~c3_1(W))))), ((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c3_1(W))) | c1_1(U)) | c0_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | (~c3_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | (~c3_1(W))) | c0_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)))), ((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c3_1(W))) | c1_1(U)) | c0_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | (~c3_1(W))))), (((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c3_1(W))) | c1_1(U)) | c0_1(V)) | c0_1(W)) | c2_1(W)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | (~c3_1(W))) | c2_1(W)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | (~c3_1(W))) | c2_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))), (((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c3_1(W))) | c1_1(U)) | c0_1(V)) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))))),
% 0.79/0.95 inference(bind,[status(th)],[])).
% 0.79/0.95 tff(1028,plain,
% 0.79/0.95 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c3_1(W))) | c1_1(U)) | c0_1(V)) | c0_1(W)) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))),
% 0.79/0.95 inference(quant_intro,[status(thm)],[1027])).
% 0.79/0.95 tff(1029,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c3_1(W))) | c1_1(U)) | c0_1(V)) | c0_1(W)) | c2_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause157')).
% 0.79/0.95 tff(1030,plain,
% 0.79/0.95 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))),
% 0.79/0.96 inference(modus_ponens,[status(thm)],[1029, 1028])).
% 0.79/0.96 tff(1031,plain,
% 0.79/0.96 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))),
% 0.79/0.96 inference(modus_ponens,[status(thm)],[1030, 1026])).
% 0.79/0.96 tff(1032,plain,(
% 0.79/0.96 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))),
% 0.79/0.96 inference(skolemize,[status(sab)],[1031])).
% 0.79/0.96 tff(1033,plain,
% 0.79/0.96 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))),
% 0.79/0.96 inference(modus_ponens,[status(thm)],[1032, 1025])).
% 0.79/0.96 tff(1034,plain,
% 0.79/0.96 (hskp10),
% 0.79/0.96 inference(unit_resolution,[status(thm)],[298, 148, 1016, 1017, 66, 68, 292, 915, 1023])).
% 0.79/0.96 tff(1035,plain,
% 0.79/0.96 (~c1_1(a200)),
% 0.79/0.96 inference(unit_resolution,[status(thm)],[373, 1034])).
% 0.79/0.96 tff(1036,plain,
% 0.79/0.96 (c3_1(a200)),
% 0.79/0.96 inference(unit_resolution,[status(thm)],[315, 1034])).
% 0.79/0.96 tff(1037,plain,
% 0.79/0.96 (c0_1(a200)),
% 0.79/0.96 inference(unit_resolution,[status(thm)],[307, 1034])).
% 0.79/0.96 tff(1038,plain,
% 0.79/0.96 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a195) | c0_1(a225) | c1_1(a200) | (~c1_1(a195)) | (~ndr1_0) | (~c2_1(a195)) | (~c3_1(a200)) | (~c0_1(a200)) | c2_1(a225) | (~c3_1(a225)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a195) | c0_1(a225) | c1_1(a200) | (~c1_1(a195)) | (~ndr1_0) | (~c2_1(a195)) | (~c3_1(a200)) | (~c0_1(a200)) | c2_1(a225) | (~c3_1(a225)))),
% 0.79/0.96 inference(rewrite,[status(thm)],[])).
% 0.79/0.96 tff(1039,plain,
% 0.79/0.96 (((~ndr1_0) | c1_1(a200) | (~c3_1(a200)) | (~c0_1(a200)) | c0_1(a195) | (~c1_1(a195)) | (~c2_1(a195)) | c2_1(a225) | c0_1(a225) | (~c3_1(a225))) <=> (c0_1(a195) | c0_1(a225) | c1_1(a200) | (~c1_1(a195)) | (~ndr1_0) | (~c2_1(a195)) | (~c3_1(a200)) | (~c0_1(a200)) | c2_1(a225) | (~c3_1(a225)))),
% 0.79/0.96 inference(rewrite,[status(thm)],[])).
% 0.79/0.96 tff(1040,plain,
% 0.79/0.96 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a200) | (~c3_1(a200)) | (~c0_1(a200)) | c0_1(a195) | (~c1_1(a195)) | (~c2_1(a195)) | c2_1(a225) | c0_1(a225) | (~c3_1(a225)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a195) | c0_1(a225) | c1_1(a200) | (~c1_1(a195)) | (~ndr1_0) | (~c2_1(a195)) | (~c3_1(a200)) | (~c0_1(a200)) | c2_1(a225) | (~c3_1(a225))))),
% 0.79/0.96 inference(monotonicity,[status(thm)],[1039])).
% 0.79/0.96 tff(1041,plain,
% 0.79/0.96 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a200) | (~c3_1(a200)) | (~c0_1(a200)) | c0_1(a195) | (~c1_1(a195)) | (~c2_1(a195)) | c2_1(a225) | c0_1(a225) | (~c3_1(a225)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a195) | c0_1(a225) | c1_1(a200) | (~c1_1(a195)) | (~ndr1_0) | (~c2_1(a195)) | (~c3_1(a200)) | (~c0_1(a200)) | c2_1(a225) | (~c3_1(a225)))),
% 0.79/0.96 inference(transitivity,[status(thm)],[1040, 1038])).
% 0.79/0.96 tff(1042,plain,
% 0.79/0.96 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a200) | (~c3_1(a200)) | (~c0_1(a200)) | c0_1(a195) | (~c1_1(a195)) | (~c2_1(a195)) | c2_1(a225) | c0_1(a225) | (~c3_1(a225)))),
% 0.79/0.96 inference(quant_inst,[status(thm)],[])).
% 0.79/0.96 tff(1043,plain,
% 0.79/0.96 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a195) | c0_1(a225) | c1_1(a200) | (~c1_1(a195)) | (~ndr1_0) | (~c2_1(a195)) | (~c3_1(a200)) | (~c0_1(a200)) | c2_1(a225) | (~c3_1(a225))),
% 0.79/0.96 inference(modus_ponens,[status(thm)],[1042, 1041])).
% 0.79/0.96 tff(1044,plain,
% 0.79/0.96 ($false),
% 0.79/0.96 inference(unit_resolution,[status(thm)],[1043, 148, 1016, 1037, 1036, 922, 1017, 1035, 905, 1033, 913, 1023])).
% 0.79/0.96 tff(1045,plain,(c3_1(a195) | c2_1(a191) | c3_1(a191) | c1_1(a194) | c2_1(a194) | c1_1(a191) | c3_1(a190) | hskp15), inference(lemma,lemma(discharge,[]))).
% 0.79/0.96 tff(1046,plain,
% 0.79/0.96 (c3_1(a195)),
% 0.79/0.96 inference(unit_resolution,[status(thm)],[1045, 591, 68, 66, 585, 67, 13, 36])).
% 0.79/0.96 tff(1047,plain,
% 0.79/0.96 (~hskp6),
% 0.79/0.96 inference(unit_resolution,[status(thm)],[543, 1046])).
% 0.79/0.96 tff(1048,plain,
% 0.79/0.96 (c0_1(a191)),
% 0.79/0.96 inference(unit_resolution,[status(thm)],[537, 1047])).
% 0.79/0.96 tff(1049,plain,
% 0.79/0.96 (c2_1(a190)),
% 0.79/0.96 inference(unit_resolution,[status(thm)],[192, 684])).
% 0.79/0.96 tff(1050,plain,
% 0.79/0.96 (~c1_1(a190)),
% 0.79/0.96 inference(unit_resolution,[status(thm)],[1013, 685, 599, 1049, 591, 585, 66, 68, 1048])).
% 0.79/0.96 tff(1051,plain,
% 0.79/0.96 (hskp19),
% 0.79/0.96 inference(unit_resolution,[status(thm)],[838, 1049, 1050, 685])).
% 0.79/0.96 tff(1052,plain,
% 0.79/0.96 (c3_1(a225)),
% 0.79/0.96 inference(unit_resolution,[status(thm)],[226, 1051])).
% 0.79/0.96 tff(1053,plain,
% 0.79/0.96 (~c0_1(a225)),
% 0.79/0.96 inference(unit_resolution,[status(thm)],[232, 1051])).
% 0.79/0.96 tff(1054,plain,
% 0.79/0.96 (hskp13),
% 0.79/0.96 inference(unit_resolution,[status(thm)],[381, 1053, 1052, 67, 66, 68])).
% 0.79/0.96 tff(1055,plain,
% 0.79/0.96 (~c0_1(a209)),
% 0.79/0.96 inference(unit_resolution,[status(thm)],[387, 1054])).
% 0.79/0.96 tff(1056,plain,
% 0.79/0.96 (~c1_1(a225)),
% 0.79/0.96 inference(unit_resolution,[status(thm)],[417, 1051])).
% 0.79/0.96 tff(1057,plain,
% 0.79/0.96 (c3_1(a209)),
% 0.79/0.96 inference(unit_resolution,[status(thm)],[395, 1054])).
% 0.79/0.96 tff(1058,plain,
% 0.79/0.96 (c1_1(a209)),
% 0.79/0.96 inference(unit_resolution,[status(thm)],[403, 1054])).
% 0.79/0.96 tff(1059,plain,
% 0.79/0.96 (~c2_1(a225)),
% 0.79/0.96 inference(unit_resolution,[status(thm)],[878, 148, 1058, 1057, 599, 1053, 1056, 1055, 591, 585, 65])).
% 0.79/0.96 tff(1060,plain,
% 0.79/0.96 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a225) | c3_1(a190) | (~ndr1_0) | (~c2_1(a190)) | (~c0_1(a190)) | c1_1(a190) | c2_1(a225) | (~c3_1(a225)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a225) | c3_1(a190) | (~ndr1_0) | (~c2_1(a190)) | (~c0_1(a190)) | c1_1(a190) | c2_1(a225) | (~c3_1(a225)))),
% 0.79/0.96 inference(rewrite,[status(thm)],[])).
% 0.79/0.96 tff(1061,plain,
% 0.79/0.96 (((~ndr1_0) | c3_1(a190) | (~c2_1(a190)) | (~c0_1(a190)) | c3_1(a190) | c1_1(a190) | (~c2_1(a190)) | c2_1(a225) | c0_1(a225) | (~c3_1(a225))) <=> (c0_1(a225) | c3_1(a190) | (~ndr1_0) | (~c2_1(a190)) | (~c0_1(a190)) | c1_1(a190) | c2_1(a225) | (~c3_1(a225)))),
% 0.79/0.96 inference(rewrite,[status(thm)],[])).
% 0.79/0.96 tff(1062,plain,
% 0.79/0.96 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a190) | (~c2_1(a190)) | (~c0_1(a190)) | c3_1(a190) | c1_1(a190) | (~c2_1(a190)) | c2_1(a225) | c0_1(a225) | (~c3_1(a225)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a225) | c3_1(a190) | (~ndr1_0) | (~c2_1(a190)) | (~c0_1(a190)) | c1_1(a190) | c2_1(a225) | (~c3_1(a225))))),
% 0.79/0.96 inference(monotonicity,[status(thm)],[1061])).
% 0.79/0.96 tff(1063,plain,
% 0.79/0.96 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a190) | (~c2_1(a190)) | (~c0_1(a190)) | c3_1(a190) | c1_1(a190) | (~c2_1(a190)) | c2_1(a225) | c0_1(a225) | (~c3_1(a225)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a225) | c3_1(a190) | (~ndr1_0) | (~c2_1(a190)) | (~c0_1(a190)) | c1_1(a190) | c2_1(a225) | (~c3_1(a225)))),
% 0.79/0.96 inference(transitivity,[status(thm)],[1062, 1060])).
% 0.79/0.96 tff(1064,plain,
% 0.79/0.96 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a190) | (~c2_1(a190)) | (~c0_1(a190)) | c3_1(a190) | c1_1(a190) | (~c2_1(a190)) | c2_1(a225) | c0_1(a225) | (~c3_1(a225)))),
% 0.82/0.96 inference(quant_inst,[status(thm)],[])).
% 0.82/0.96 tff(1065,plain,
% 0.82/0.96 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a225) | c3_1(a190) | (~ndr1_0) | (~c2_1(a190)) | (~c0_1(a190)) | c1_1(a190) | c2_1(a225) | (~c3_1(a225))),
% 0.82/0.96 inference(modus_ponens,[status(thm)],[1064, 1063])).
% 0.82/0.96 tff(1066,plain,
% 0.82/0.96 ($false),
% 0.82/0.96 inference(unit_resolution,[status(thm)],[1065, 148, 1052, 685, 1049, 1053, 13, 451, 1050, 1059])).
% 0.82/0.96 tff(1067,plain,(c3_1(a190) | c1_1(a191) | c2_1(a191) | c3_1(a191) | hskp15), inference(lemma,lemma(discharge,[]))).
% 0.82/0.96 tff(1068,plain,
% 0.82/0.96 (c3_1(a190)),
% 0.82/0.96 inference(unit_resolution,[status(thm)],[1067, 55, 49, 43, 36])).
% 0.82/0.96 tff(1069,plain,
% 0.82/0.96 (((~hskp1) | (~c3_1(a190))) <=> ((~hskp1) | (~c3_1(a190)))),
% 0.82/0.96 inference(rewrite,[status(thm)],[])).
% 0.82/0.96 tff(1070,plain,
% 0.82/0.96 (((~c3_1(a190)) | (~hskp1)) <=> ((~hskp1) | (~c3_1(a190)))),
% 0.82/0.96 inference(rewrite,[status(thm)],[])).
% 0.82/0.96 tff(1071,axiom,((~c3_1(a190)) | (~hskp1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause108')).
% 0.82/0.96 tff(1072,plain,
% 0.82/0.96 ((~hskp1) | (~c3_1(a190))),
% 0.82/0.96 inference(modus_ponens,[status(thm)],[1071, 1070])).
% 0.82/0.96 tff(1073,plain,
% 0.82/0.96 ((~hskp1) | (~c3_1(a190))),
% 0.82/0.96 inference(modus_ponens,[status(thm)],[1072, 1069])).
% 0.82/0.96 tff(1074,plain,
% 0.82/0.96 (~hskp1),
% 0.82/0.96 inference(unit_resolution,[status(thm)],[1073, 1068])).
% 0.82/0.96 tff(1075,plain,
% 0.82/0.96 (hskp1 | c0_1(a191)),
% 0.82/0.96 inference(unit_resolution,[status(thm)],[162, 148, 55, 43, 112])).
% 0.82/0.96 tff(1076,plain,
% 0.82/0.96 (c0_1(a191)),
% 0.82/0.96 inference(unit_resolution,[status(thm)],[1075, 1074])).
% 0.82/0.96 tff(1077,plain,
% 0.82/0.96 (~hskp0),
% 0.82/0.96 inference(unit_resolution,[status(thm)],[626, 1074])).
% 0.82/0.96 tff(1078,plain,
% 0.82/0.96 (hskp9),
% 0.82/0.96 inference(unit_resolution,[status(thm)],[635, 1077, 1074])).
% 0.82/0.96 tff(1079,plain,
% 0.82/0.96 (~c1_1(a199)),
% 0.82/0.96 inference(unit_resolution,[status(thm)],[641, 1078])).
% 0.82/0.96 tff(1080,plain,
% 0.82/0.96 (~c0_1(a199)),
% 0.82/0.96 inference(unit_resolution,[status(thm)],[647, 1078])).
% 0.82/0.96 tff(1081,plain,
% 0.82/0.96 (c3_1(a199)),
% 0.82/0.96 inference(unit_resolution,[status(thm)],[654, 148, 1074, 1080, 1079, 112])).
% 0.82/0.96 tff(1082,plain,
% 0.82/0.96 (c2_1(a199)),
% 0.82/0.96 inference(unit_resolution,[status(thm)],[662, 1078])).
% 0.82/0.96 tff(1083,plain,
% 0.82/0.96 (hskp13 | (~c3_1(a199))),
% 0.82/0.96 inference(unit_resolution,[status(thm)],[669, 148, 1082, 1080, 55, 49, 43, 246])).
% 0.82/0.96 tff(1084,plain,
% 0.82/0.96 (hskp13),
% 0.82/0.96 inference(unit_resolution,[status(thm)],[1083, 1081])).
% 0.82/0.96 tff(1085,plain,
% 0.82/0.96 (~c0_1(a209)),
% 0.82/0.96 inference(unit_resolution,[status(thm)],[387, 1084])).
% 0.82/0.96 tff(1086,plain,
% 0.82/0.96 (c3_1(a209)),
% 0.82/0.96 inference(unit_resolution,[status(thm)],[395, 1084])).
% 0.82/0.96 tff(1087,plain,
% 0.82/0.96 (c1_1(a209)),
% 0.82/0.96 inference(unit_resolution,[status(thm)],[403, 1084])).
% 0.82/0.96 tff(1088,plain,
% 0.82/0.96 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_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(a209) | c0_1(a199) | c1_1(a199) | c1_1(a191) | c2_1(a191) | (~ndr1_0) | (~c0_1(a191)) | (~c2_1(a199)) | (~c1_1(a209)) | (~c3_1(a209)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_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(a209) | c0_1(a199) | c1_1(a199) | c1_1(a191) | c2_1(a191) | (~ndr1_0) | (~c0_1(a191)) | (~c2_1(a199)) | (~c1_1(a209)) | (~c3_1(a209)))),
% 0.82/0.96 inference(rewrite,[status(thm)],[])).
% 0.82/0.96 tff(1089,plain,
% 0.82/0.96 (((~ndr1_0) | c1_1(a191) | c2_1(a191) | (~c0_1(a191)) | c0_1(a209) | (~c3_1(a209)) | (~c1_1(a209)) | c1_1(a199) | c0_1(a199) | (~c2_1(a199))) <=> (c0_1(a209) | c0_1(a199) | c1_1(a199) | c1_1(a191) | c2_1(a191) | (~ndr1_0) | (~c0_1(a191)) | (~c2_1(a199)) | (~c1_1(a209)) | (~c3_1(a209)))),
% 0.82/0.96 inference(rewrite,[status(thm)],[])).
% 0.82/0.96 tff(1090,plain,
% 0.82/0.96 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_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) | c1_1(a191) | c2_1(a191) | (~c0_1(a191)) | c0_1(a209) | (~c3_1(a209)) | (~c1_1(a209)) | c1_1(a199) | c0_1(a199) | (~c2_1(a199)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_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(a209) | c0_1(a199) | c1_1(a199) | c1_1(a191) | c2_1(a191) | (~ndr1_0) | (~c0_1(a191)) | (~c2_1(a199)) | (~c1_1(a209)) | (~c3_1(a209))))),
% 0.82/0.96 inference(monotonicity,[status(thm)],[1089])).
% 0.82/0.96 tff(1091,plain,
% 0.82/0.96 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_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) | c1_1(a191) | c2_1(a191) | (~c0_1(a191)) | c0_1(a209) | (~c3_1(a209)) | (~c1_1(a209)) | c1_1(a199) | c0_1(a199) | (~c2_1(a199)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_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(a209) | c0_1(a199) | c1_1(a199) | c1_1(a191) | c2_1(a191) | (~ndr1_0) | (~c0_1(a191)) | (~c2_1(a199)) | (~c1_1(a209)) | (~c3_1(a209)))),
% 0.82/0.96 inference(transitivity,[status(thm)],[1090, 1088])).
% 0.82/0.96 tff(1092,plain,
% 0.82/0.96 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_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) | c1_1(a191) | c2_1(a191) | (~c0_1(a191)) | c0_1(a209) | (~c3_1(a209)) | (~c1_1(a209)) | c1_1(a199) | c0_1(a199) | (~c2_1(a199)))),
% 0.82/0.96 inference(quant_inst,[status(thm)],[])).
% 0.82/0.96 tff(1093,plain,
% 0.82/0.96 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a209) | c0_1(a199) | c1_1(a199) | c1_1(a191) | c2_1(a191) | (~ndr1_0) | (~c0_1(a191)) | (~c2_1(a199)) | (~c1_1(a209)) | (~c3_1(a209))),
% 0.82/0.96 inference(modus_ponens,[status(thm)],[1092, 1091])).
% 0.82/0.96 tff(1094,plain,
% 0.82/0.96 ($false),
% 0.82/0.96 inference(unit_resolution,[status(thm)],[1093, 148, 1087, 1086, 1082, 1085, 1080, 1079, 55, 49, 65, 1076])).
% 0.82/0.96 tff(1095,plain,((~hskp2) | hskp15), inference(lemma,lemma(discharge,[]))).
% 0.82/0.96 tff(1096,plain,
% 0.82/0.96 (~hskp2),
% 0.82/0.96 inference(unit_resolution,[status(thm)],[1095, 36])).
% 0.82/0.96 tff(1097,plain,
% 0.82/0.96 (hskp25),
% 0.82/0.96 inference(unit_resolution,[status(thm)],[146, 1096, 36])).
% 0.82/0.96 tff(1098,plain,
% 0.82/0.96 (((~hskp25) | c0_1(a230)) <=> ((~hskp25) | c0_1(a230))),
% 0.82/0.96 inference(rewrite,[status(thm)],[])).
% 0.82/0.96 tff(1099,axiom,((~hskp25) | c0_1(a230)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause34')).
% 0.82/0.96 tff(1100,plain,
% 0.82/0.96 ((~hskp25) | c0_1(a230)),
% 0.82/0.96 inference(modus_ponens,[status(thm)],[1099, 1098])).
% 0.82/0.96 tff(1101,plain,
% 0.82/0.96 ((~hskp25) | c0_1(a230)),
% 0.82/0.96 inference(modus_ponens,[status(thm)],[1100, 1098])).
% 0.82/0.96 tff(1102,plain,
% 0.82/0.96 ((~hskp25) | c0_1(a230)),
% 0.82/0.96 inference(modus_ponens,[status(thm)],[1101, 1098])).
% 0.82/0.96 tff(1103,plain,
% 0.82/0.96 ((~hskp25) | c0_1(a230)),
% 0.82/0.96 inference(modus_ponens,[status(thm)],[1102, 1098])).
% 0.82/0.96 tff(1104,plain,
% 0.82/0.96 ((~hskp25) | c0_1(a230)),
% 0.82/0.96 inference(modus_ponens,[status(thm)],[1103, 1098])).
% 0.82/0.96 tff(1105,plain,
% 0.82/0.96 (c0_1(a230)),
% 0.82/0.96 inference(unit_resolution,[status(thm)],[1104, 1097])).
% 0.82/0.96 tff(1106,plain,
% 0.82/0.96 (((~hskp25) | c2_1(a230)) <=> ((~hskp25) | c2_1(a230))),
% 0.82/0.96 inference(rewrite,[status(thm)],[])).
% 0.82/0.96 tff(1107,axiom,((~hskp25) | c2_1(a230)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause36')).
% 0.82/0.96 tff(1108,plain,
% 0.82/0.96 ((~hskp25) | c2_1(a230)),
% 0.82/0.96 inference(modus_ponens,[status(thm)],[1107, 1106])).
% 0.82/0.96 tff(1109,plain,
% 0.82/0.96 ((~hskp25) | c2_1(a230)),
% 0.82/0.96 inference(modus_ponens,[status(thm)],[1108, 1106])).
% 0.82/0.96 tff(1110,plain,
% 0.82/0.96 ((~hskp25) | c2_1(a230)),
% 0.82/0.96 inference(modus_ponens,[status(thm)],[1109, 1106])).
% 0.82/0.96 tff(1111,plain,
% 0.82/0.96 ((~hskp25) | c2_1(a230)),
% 0.82/0.96 inference(modus_ponens,[status(thm)],[1110, 1106])).
% 0.82/0.96 tff(1112,plain,
% 0.82/0.96 ((~hskp25) | c2_1(a230)),
% 0.82/0.96 inference(modus_ponens,[status(thm)],[1111, 1106])).
% 0.82/0.96 tff(1113,plain,
% 0.82/0.96 (c2_1(a230)),
% 0.82/0.96 inference(unit_resolution,[status(thm)],[1112, 1097])).
% 0.82/0.96 tff(1114,plain,
% 0.82/0.96 (((~hskp25) | c1_1(a230)) <=> ((~hskp25) | c1_1(a230))),
% 0.82/0.96 inference(rewrite,[status(thm)],[])).
% 0.82/0.96 tff(1115,axiom,((~hskp25) | c1_1(a230)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause35')).
% 0.82/0.96 tff(1116,plain,
% 0.82/0.96 ((~hskp25) | c1_1(a230)),
% 0.82/0.96 inference(modus_ponens,[status(thm)],[1115, 1114])).
% 0.82/0.96 tff(1117,plain,
% 0.82/0.96 ((~hskp25) | c1_1(a230)),
% 0.82/0.96 inference(modus_ponens,[status(thm)],[1116, 1114])).
% 0.82/0.96 tff(1118,plain,
% 0.82/0.96 ((~hskp25) | c1_1(a230)),
% 0.82/0.96 inference(modus_ponens,[status(thm)],[1117, 1114])).
% 0.82/0.96 tff(1119,plain,
% 0.82/0.96 ((~hskp25) | c1_1(a230)),
% 0.82/0.96 inference(modus_ponens,[status(thm)],[1118, 1114])).
% 0.82/0.96 tff(1120,plain,
% 0.82/0.96 ((~hskp25) | c1_1(a230)),
% 0.82/0.96 inference(modus_ponens,[status(thm)],[1119, 1114])).
% 0.82/0.96 tff(1121,plain,
% 0.82/0.96 (c1_1(a230)),
% 0.82/0.96 inference(unit_resolution,[status(thm)],[1120, 1097])).
% 0.82/0.96 tff(1122,plain,
% 0.82/0.96 (^[U: $i] : refl((hskp2 | hskp1 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) <=> (hskp2 | hskp1 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))))),
% 0.82/0.96 inference(bind,[status(th)],[])).
% 0.82/0.96 tff(1123,plain,
% 0.82/0.96 (![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 0.82/0.96 inference(quant_intro,[status(thm)],[1122])).
% 0.82/0.96 tff(1124,plain,
% 0.82/0.96 (![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 0.82/0.96 inference(rewrite,[status(thm)],[])).
% 0.82/0.96 tff(1125,plain,
% 0.82/0.96 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) <=> ((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp1) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | hskp1))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | hskp1) <=> (hskp1 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp1) <=> (hskp1 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp1) | hskp2) <=> ((hskp1 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | hskp2))), rewrite(((hskp1 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | hskp2) <=> (hskp2 | hskp1 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp1) | hskp2) <=> (hskp2 | hskp1 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))))),
% 0.82/0.96 inference(bind,[status(th)],[])).
% 0.82/0.96 tff(1126,plain,
% 0.82/0.96 (![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp1) | hskp2) <=> ![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 0.82/0.96 inference(quant_intro,[status(thm)],[1125])).
% 0.82/0.96 tff(1127,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp1) | hskp2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause126')).
% 0.82/0.96 tff(1128,plain,
% 0.82/0.96 (![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 0.82/0.96 inference(modus_ponens,[status(thm)],[1127, 1126])).
% 0.82/0.96 tff(1129,plain,
% 0.82/0.96 (![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 0.82/0.96 inference(modus_ponens,[status(thm)],[1128, 1124])).
% 0.82/0.96 tff(1130,plain,(
% 0.82/0.96 ![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 0.82/0.96 inference(skolemize,[status(sab)],[1129])).
% 0.82/0.96 tff(1131,plain,
% 0.82/0.96 (![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 0.82/0.96 inference(modus_ponens,[status(thm)],[1130, 1123])).
% 0.82/0.96 tff(1132,assumption,(c1_1(a230)), introduced(assumption)).
% 0.82/0.96 tff(1133,assumption,(c0_1(a230)), introduced(assumption)).
% 0.82/0.96 tff(1134,plain,
% 0.82/0.96 (((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp2 | hskp1 | (~ndr1_0) | (~c0_1(a230)) | (~c3_1(a230)) | (~c1_1(a230)))) <=> ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp2 | hskp1 | (~ndr1_0) | (~c0_1(a230)) | (~c3_1(a230)) | (~c1_1(a230)))),
% 0.82/0.96 inference(rewrite,[status(thm)],[])).
% 0.82/0.96 tff(1135,plain,
% 0.82/0.96 ((hskp2 | hskp1 | (~ndr1_0) | (~c3_1(a230)) | (~c1_1(a230)) | (~c0_1(a230))) <=> (hskp2 | hskp1 | (~ndr1_0) | (~c0_1(a230)) | (~c3_1(a230)) | (~c1_1(a230)))),
% 0.82/0.96 inference(rewrite,[status(thm)],[])).
% 0.82/0.96 tff(1136,plain,
% 0.82/0.96 (((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp2 | hskp1 | (~ndr1_0) | (~c3_1(a230)) | (~c1_1(a230)) | (~c0_1(a230)))) <=> ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp2 | hskp1 | (~ndr1_0) | (~c0_1(a230)) | (~c3_1(a230)) | (~c1_1(a230))))),
% 0.82/0.96 inference(monotonicity,[status(thm)],[1135])).
% 0.82/0.96 tff(1137,plain,
% 0.82/0.96 (((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp2 | hskp1 | (~ndr1_0) | (~c3_1(a230)) | (~c1_1(a230)) | (~c0_1(a230)))) <=> ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp2 | hskp1 | (~ndr1_0) | (~c0_1(a230)) | (~c3_1(a230)) | (~c1_1(a230)))),
% 0.82/0.96 inference(transitivity,[status(thm)],[1136, 1134])).
% 0.82/0.96 tff(1138,plain,
% 0.82/0.96 ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp2 | hskp1 | (~ndr1_0) | (~c3_1(a230)) | (~c1_1(a230)) | (~c0_1(a230)))),
% 0.82/0.96 inference(quant_inst,[status(thm)],[])).
% 0.82/0.96 tff(1139,plain,
% 0.82/0.96 ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp2 | hskp1 | (~ndr1_0) | (~c0_1(a230)) | (~c3_1(a230)) | (~c1_1(a230))),
% 0.82/0.96 inference(modus_ponens,[status(thm)],[1138, 1137])).
% 0.82/0.96 tff(1140,plain,
% 0.82/0.96 (hskp1 | (~c3_1(a230))),
% 0.82/0.96 inference(unit_resolution,[status(thm)],[1139, 148, 14, 1133, 1132, 1131])).
% 0.82/0.96 tff(1141,plain,
% 0.82/0.96 (~c3_1(a230)),
% 0.82/0.96 inference(unit_resolution,[status(thm)],[1140, 102])).
% 0.82/0.96 tff(1142,plain,
% 0.82/0.96 (^[V: $i, U: $i] : refl((hskp2 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) <=> (hskp2 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))))),
% 0.82/0.96 inference(bind,[status(th)],[])).
% 0.82/0.96 tff(1143,plain,
% 0.82/0.96 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.82/0.96 inference(quant_intro,[status(thm)],[1142])).
% 0.82/0.96 tff(1144,plain,
% 0.82/0.96 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.82/0.96 inference(rewrite,[status(thm)],[])).
% 0.82/0.96 tff(1145,plain,
% 0.82/0.96 (^[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)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | c1_1(V)) | hskp2) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) | hskp2))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) | hskp2) <=> (hskp2 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | c1_1(V)) | hskp2) <=> (hskp2 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))))),
% 0.82/0.96 inference(bind,[status(th)],[])).
% 0.82/0.96 tff(1146,plain,
% 0.82/0.96 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | c1_1(V)) | hskp2) <=> ![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.82/0.96 inference(quant_intro,[status(thm)],[1145])).
% 0.82/0.96 tff(1147,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | c1_1(V)) | hskp2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause137')).
% 0.82/0.96 tff(1148,plain,
% 0.82/0.96 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.82/0.96 inference(modus_ponens,[status(thm)],[1147, 1146])).
% 0.82/0.96 tff(1149,plain,
% 0.82/0.96 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.82/0.96 inference(modus_ponens,[status(thm)],[1148, 1144])).
% 0.82/0.96 tff(1150,plain,(
% 0.82/0.96 ![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.82/0.96 inference(skolemize,[status(sab)],[1149])).
% 0.82/0.96 tff(1151,plain,
% 0.82/0.96 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.82/0.96 inference(modus_ponens,[status(thm)],[1150, 1143])).
% 0.82/0.96 tff(1152,plain,
% 0.82/0.96 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp2 | c0_1(a199) | c1_1(a199) | (~ndr1_0) | c3_1(a230) | (~c0_1(a230)) | (~c1_1(a230)) | (~c3_1(a199)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp2 | c0_1(a199) | c1_1(a199) | (~ndr1_0) | c3_1(a230) | (~c0_1(a230)) | (~c1_1(a230)) | (~c3_1(a199)))),
% 0.82/0.96 inference(rewrite,[status(thm)],[])).
% 0.82/0.96 tff(1153,plain,
% 0.82/0.96 ((hskp2 | (~ndr1_0) | c3_1(a230) | (~c1_1(a230)) | (~c0_1(a230)) | c1_1(a199) | c0_1(a199) | (~c3_1(a199))) <=> (hskp2 | c0_1(a199) | c1_1(a199) | (~ndr1_0) | c3_1(a230) | (~c0_1(a230)) | (~c1_1(a230)) | (~c3_1(a199)))),
% 0.82/0.96 inference(rewrite,[status(thm)],[])).
% 0.82/0.96 tff(1154,plain,
% 0.82/0.96 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp2 | (~ndr1_0) | c3_1(a230) | (~c1_1(a230)) | (~c0_1(a230)) | c1_1(a199) | c0_1(a199) | (~c3_1(a199)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp2 | c0_1(a199) | c1_1(a199) | (~ndr1_0) | c3_1(a230) | (~c0_1(a230)) | (~c1_1(a230)) | (~c3_1(a199))))),
% 0.82/0.96 inference(monotonicity,[status(thm)],[1153])).
% 0.82/0.96 tff(1155,plain,
% 0.82/0.96 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp2 | (~ndr1_0) | c3_1(a230) | (~c1_1(a230)) | (~c0_1(a230)) | c1_1(a199) | c0_1(a199) | (~c3_1(a199)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp2 | c0_1(a199) | c1_1(a199) | (~ndr1_0) | c3_1(a230) | (~c0_1(a230)) | (~c1_1(a230)) | (~c3_1(a199)))),
% 0.82/0.96 inference(transitivity,[status(thm)],[1154, 1152])).
% 0.82/0.96 tff(1156,plain,
% 0.82/0.96 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp2 | (~ndr1_0) | c3_1(a230) | (~c1_1(a230)) | (~c0_1(a230)) | c1_1(a199) | c0_1(a199) | (~c3_1(a199)))),
% 0.82/0.96 inference(quant_inst,[status(thm)],[])).
% 0.82/0.96 tff(1157,plain,
% 0.82/0.96 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp2 | c0_1(a199) | c1_1(a199) | (~ndr1_0) | c3_1(a230) | (~c0_1(a230)) | (~c1_1(a230)) | (~c3_1(a199))),
% 0.82/0.96 inference(modus_ponens,[status(thm)],[1156, 1155])).
% 0.82/0.96 tff(1158,plain,
% 0.82/0.96 (~c3_1(a199)),
% 0.82/0.96 inference(unit_resolution,[status(thm)],[1157, 148, 14, 1133, 1132, 648, 642, 1151, 1141])).
% 0.82/0.96 tff(1159,plain,
% 0.82/0.96 ($false),
% 0.82/0.96 inference(unit_resolution,[status(thm)],[654, 148, 102, 648, 642, 112, 1158])).
% 0.82/0.96 tff(1160,plain,(hskp1 | hskp2 | (~c0_1(a230)) | (~c1_1(a230))), inference(lemma,lemma(discharge,[]))).
% 0.82/0.96 tff(1161,plain,
% 0.82/0.96 (hskp1),
% 0.82/0.96 inference(unit_resolution,[status(thm)],[1160, 1096, 1105, 1121])).
% 0.82/0.96 tff(1162,plain,
% 0.82/0.96 (~c3_1(a190)),
% 0.82/0.96 inference(unit_resolution,[status(thm)],[1073, 1161])).
% 0.82/0.96 tff(1163,plain,
% 0.82/0.96 (hskp1),
% 0.82/0.96 inference(unit_resolution,[status(thm)],[1160, 14, 1133, 1132])).
% 0.82/0.96 tff(1164,plain,
% 0.82/0.96 (~c3_1(a190)),
% 0.82/0.96 inference(unit_resolution,[status(thm)],[1073, 1163])).
% 0.82/0.96 tff(1165,plain,
% 0.82/0.96 (c0_1(a190)),
% 0.82/0.96 inference(unit_resolution,[status(thm)],[200, 1163])).
% 0.82/0.96 tff(1166,plain,
% 0.82/0.96 (c2_1(a190)),
% 0.82/0.96 inference(unit_resolution,[status(thm)],[192, 1163])).
% 0.82/0.96 tff(1167,plain,
% 0.82/0.96 (hskp19),
% 0.82/0.96 inference(unit_resolution,[status(thm)],[857, 562, 560, 1166, 561, 1165, 1164])).
% 0.82/0.96 tff(1168,plain,
% 0.82/0.96 (~c1_1(a225)),
% 0.82/0.96 inference(unit_resolution,[status(thm)],[417, 1167])).
% 0.82/0.96 tff(1169,plain,
% 0.82/0.96 (~c0_1(a225)),
% 0.82/0.96 inference(unit_resolution,[status(thm)],[232, 1167])).
% 0.82/0.96 tff(1170,plain,
% 0.82/0.96 (c3_1(a225)),
% 0.82/0.96 inference(unit_resolution,[status(thm)],[226, 1167])).
% 0.82/0.96 tff(1171,assumption,(~c3_1(a230)), introduced(assumption)).
% 0.82/0.96 tff(1172,plain,
% 0.82/0.96 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp2 | c0_1(a225) | c1_1(a225) | (~ndr1_0) | c3_1(a230) | (~c0_1(a230)) | (~c1_1(a230)) | (~c3_1(a225)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp2 | c0_1(a225) | c1_1(a225) | (~ndr1_0) | c3_1(a230) | (~c0_1(a230)) | (~c1_1(a230)) | (~c3_1(a225)))),
% 0.82/0.96 inference(rewrite,[status(thm)],[])).
% 0.82/0.96 tff(1173,plain,
% 0.82/0.96 ((hskp2 | (~ndr1_0) | c3_1(a230) | (~c1_1(a230)) | (~c0_1(a230)) | c1_1(a225) | c0_1(a225) | (~c3_1(a225))) <=> (hskp2 | c0_1(a225) | c1_1(a225) | (~ndr1_0) | c3_1(a230) | (~c0_1(a230)) | (~c1_1(a230)) | (~c3_1(a225)))),
% 0.82/0.96 inference(rewrite,[status(thm)],[])).
% 0.82/0.96 tff(1174,plain,
% 0.82/0.96 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp2 | (~ndr1_0) | c3_1(a230) | (~c1_1(a230)) | (~c0_1(a230)) | c1_1(a225) | c0_1(a225) | (~c3_1(a225)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp2 | c0_1(a225) | c1_1(a225) | (~ndr1_0) | c3_1(a230) | (~c0_1(a230)) | (~c1_1(a230)) | (~c3_1(a225))))),
% 0.82/0.96 inference(monotonicity,[status(thm)],[1173])).
% 0.82/0.96 tff(1175,plain,
% 0.82/0.96 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp2 | (~ndr1_0) | c3_1(a230) | (~c1_1(a230)) | (~c0_1(a230)) | c1_1(a225) | c0_1(a225) | (~c3_1(a225)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp2 | c0_1(a225) | c1_1(a225) | (~ndr1_0) | c3_1(a230) | (~c0_1(a230)) | (~c1_1(a230)) | (~c3_1(a225)))),
% 0.82/0.96 inference(transitivity,[status(thm)],[1174, 1172])).
% 0.82/0.97 tff(1176,plain,
% 0.82/0.97 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp2 | (~ndr1_0) | c3_1(a230) | (~c1_1(a230)) | (~c0_1(a230)) | c1_1(a225) | c0_1(a225) | (~c3_1(a225)))),
% 0.82/0.97 inference(quant_inst,[status(thm)],[])).
% 0.82/0.97 tff(1177,plain,
% 0.82/0.97 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp2 | c0_1(a225) | c1_1(a225) | (~ndr1_0) | c3_1(a230) | (~c0_1(a230)) | (~c1_1(a230)) | (~c3_1(a225))),
% 0.82/0.97 inference(modus_ponens,[status(thm)],[1176, 1175])).
% 0.82/0.97 tff(1178,plain,
% 0.82/0.97 ($false),
% 0.82/0.97 inference(unit_resolution,[status(thm)],[1177, 148, 14, 1133, 1132, 234, 235, 433, 1151, 1171])).
% 0.82/0.97 tff(1179,plain,(c3_1(a230) | hskp2 | (~c0_1(a230)) | (~c1_1(a230)) | (~c3_1(a225)) | c0_1(a225) | c1_1(a225)), inference(lemma,lemma(discharge,[]))).
% 0.82/0.97 tff(1180,plain,
% 0.82/0.97 (c3_1(a230)),
% 0.82/0.97 inference(unit_resolution,[status(thm)],[1179, 1170, 1133, 1132, 14, 1169, 1168])).
% 0.82/0.97 tff(1181,assumption,(c2_1(a230)), introduced(assumption)).
% 0.82/0.97 tff(1182,plain,
% 0.82/0.97 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | (c1_1(a195) | c3_1(a195) | (~ndr1_0) | (~c2_1(a230)) | (~c0_1(a230)) | (~c3_1(a230)) | (~c1_1(a230)) | (~c0_1(a195)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | c1_1(a195) | c3_1(a195) | (~ndr1_0) | (~c2_1(a230)) | (~c0_1(a230)) | (~c3_1(a230)) | (~c1_1(a230)) | (~c0_1(a195)))),
% 0.82/0.97 inference(rewrite,[status(thm)],[])).
% 0.82/0.97 tff(1183,plain,
% 0.82/0.97 (((~ndr1_0) | (~c3_1(a230)) | (~c2_1(a230)) | (~c0_1(a230)) | (~c3_1(a230)) | (~c1_1(a230)) | (~c0_1(a230)) | c1_1(a195) | c3_1(a195) | (~c0_1(a195))) <=> (c1_1(a195) | c3_1(a195) | (~ndr1_0) | (~c2_1(a230)) | (~c0_1(a230)) | (~c3_1(a230)) | (~c1_1(a230)) | (~c0_1(a195)))),
% 0.82/0.97 inference(rewrite,[status(thm)],[])).
% 0.82/0.97 tff(1184,plain,
% 0.82/0.97 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c3_1(a230)) | (~c2_1(a230)) | (~c0_1(a230)) | (~c3_1(a230)) | (~c1_1(a230)) | (~c0_1(a230)) | c1_1(a195) | c3_1(a195) | (~c0_1(a195)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | (c1_1(a195) | c3_1(a195) | (~ndr1_0) | (~c2_1(a230)) | (~c0_1(a230)) | (~c3_1(a230)) | (~c1_1(a230)) | (~c0_1(a195))))),
% 0.82/0.97 inference(monotonicity,[status(thm)],[1183])).
% 0.82/0.97 tff(1185,plain,
% 0.82/0.97 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c3_1(a230)) | (~c2_1(a230)) | (~c0_1(a230)) | (~c3_1(a230)) | (~c1_1(a230)) | (~c0_1(a230)) | c1_1(a195) | c3_1(a195) | (~c0_1(a195)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | c1_1(a195) | c3_1(a195) | (~ndr1_0) | (~c2_1(a230)) | (~c0_1(a230)) | (~c3_1(a230)) | (~c1_1(a230)) | (~c0_1(a195)))),
% 0.82/0.97 inference(transitivity,[status(thm)],[1184, 1182])).
% 0.82/0.97 tff(1186,plain,
% 0.82/0.97 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c3_1(a230)) | (~c2_1(a230)) | (~c0_1(a230)) | (~c3_1(a230)) | (~c1_1(a230)) | (~c0_1(a230)) | c1_1(a195) | c3_1(a195) | (~c0_1(a195)))),
% 0.82/0.97 inference(quant_inst,[status(thm)],[])).
% 0.82/0.97 tff(1187,plain,
% 0.82/0.97 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | c1_1(a195) | c3_1(a195) | (~ndr1_0) | (~c2_1(a230)) | (~c0_1(a230)) | (~c3_1(a230)) | (~c1_1(a230)) | (~c0_1(a195))),
% 0.82/0.97 inference(modus_ponens,[status(thm)],[1186, 1185])).
% 0.82/0.97 tff(1188,plain,
% 0.82/0.97 ($false),
% 0.82/0.97 inference(unit_resolution,[status(thm)],[1187, 148, 1133, 1132, 1181, 562, 561, 560, 470, 1180])).
% 0.82/0.97 tff(1189,plain,((~c0_1(a195)) | (~c0_1(a230)) | (~c1_1(a230)) | (~c2_1(a230)) | c1_1(a195) | c3_1(a195) | hskp2), inference(lemma,lemma(discharge,[]))).
% 0.82/0.97 tff(1190,plain,
% 0.82/0.97 (~c0_1(a195)),
% 0.82/0.97 inference(unit_resolution,[status(thm)],[1189, 561, 1121, 1113, 1105, 560, 1096])).
% 0.82/0.97 tff(1191,assumption,(~hskp6), introduced(assumption)).
% 0.82/0.97 tff(1192,assumption,(~c0_1(a194)), introduced(assumption)).
% 0.82/0.97 tff(1193,plain,
% 0.82/0.97 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a194) | c1_1(a195) | c3_1(a195) | c2_1(a194) | c3_1(a190) | (~ndr1_0) | (~c2_1(a190)) | (~c0_1(a190)) | (~c3_1(a194)) | (~c2_1(a195)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a194) | c1_1(a195) | c3_1(a195) | c2_1(a194) | c3_1(a190) | (~ndr1_0) | (~c2_1(a190)) | (~c0_1(a190)) | (~c3_1(a194)) | (~c2_1(a195)))),
% 0.82/0.97 inference(rewrite,[status(thm)],[])).
% 0.82/0.97 tff(1194,plain,
% 0.82/0.97 (((~ndr1_0) | c3_1(a190) | (~c2_1(a190)) | (~c0_1(a190)) | c3_1(a195) | c1_1(a195) | (~c2_1(a195)) | c2_1(a194) | c0_1(a194) | (~c3_1(a194))) <=> (c0_1(a194) | c1_1(a195) | c3_1(a195) | c2_1(a194) | c3_1(a190) | (~ndr1_0) | (~c2_1(a190)) | (~c0_1(a190)) | (~c3_1(a194)) | (~c2_1(a195)))),
% 0.82/0.97 inference(rewrite,[status(thm)],[])).
% 0.82/0.97 tff(1195,plain,
% 0.82/0.97 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a190) | (~c2_1(a190)) | (~c0_1(a190)) | c3_1(a195) | c1_1(a195) | (~c2_1(a195)) | c2_1(a194) | c0_1(a194) | (~c3_1(a194)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a194) | c1_1(a195) | c3_1(a195) | c2_1(a194) | c3_1(a190) | (~ndr1_0) | (~c2_1(a190)) | (~c0_1(a190)) | (~c3_1(a194)) | (~c2_1(a195))))),
% 0.82/0.97 inference(monotonicity,[status(thm)],[1194])).
% 0.82/0.97 tff(1196,plain,
% 0.82/0.97 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a190) | (~c2_1(a190)) | (~c0_1(a190)) | c3_1(a195) | c1_1(a195) | (~c2_1(a195)) | c2_1(a194) | c0_1(a194) | (~c3_1(a194)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a194) | c1_1(a195) | c3_1(a195) | c2_1(a194) | c3_1(a190) | (~ndr1_0) | (~c2_1(a190)) | (~c0_1(a190)) | (~c3_1(a194)) | (~c2_1(a195)))),
% 0.82/0.97 inference(transitivity,[status(thm)],[1195, 1193])).
% 0.82/0.97 tff(1197,plain,
% 0.82/0.97 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a190) | (~c2_1(a190)) | (~c0_1(a190)) | c3_1(a195) | c1_1(a195) | (~c2_1(a195)) | c2_1(a194) | c0_1(a194) | (~c3_1(a194)))),
% 0.82/0.97 inference(quant_inst,[status(thm)],[])).
% 0.82/0.97 tff(1198,plain,
% 0.82/0.97 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a194) | c1_1(a195) | c3_1(a195) | c2_1(a194) | c3_1(a190) | (~ndr1_0) | (~c2_1(a190)) | (~c0_1(a190)) | (~c3_1(a194)) | (~c2_1(a195))),
% 0.82/0.97 inference(modus_ponens,[status(thm)],[1197, 1196])).
% 0.82/0.97 tff(1199,plain,
% 0.82/0.97 (c0_1(a194) | (~c3_1(a194)) | (~c2_1(a195))),
% 0.82/0.97 inference(unit_resolution,[status(thm)],[1198, 148, 829, 784, 561, 560, 11, 13, 451])).
% 0.82/0.97 tff(1200,plain,
% 0.82/0.97 (~c3_1(a194)),
% 0.82/0.97 inference(unit_resolution,[status(thm)],[1199, 1192, 932])).
% 0.82/0.97 tff(1201,plain,
% 0.82/0.97 (((~![U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp6 | c0_1(a194) | c2_1(a194) | (~ndr1_0) | c3_1(a194))) <=> ((~![U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | hskp6 | c0_1(a194) | c2_1(a194) | (~ndr1_0) | c3_1(a194))),
% 0.82/0.97 inference(rewrite,[status(thm)],[])).
% 0.82/0.97 tff(1202,plain,
% 0.82/0.97 ((hskp6 | (~ndr1_0) | c3_1(a194) | c0_1(a194) | c2_1(a194)) <=> (hskp6 | c0_1(a194) | c2_1(a194) | (~ndr1_0) | c3_1(a194))),
% 0.82/0.97 inference(rewrite,[status(thm)],[])).
% 0.82/0.97 tff(1203,plain,
% 0.82/0.97 (((~![U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp6 | (~ndr1_0) | c3_1(a194) | c0_1(a194) | c2_1(a194))) <=> ((~![U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp6 | c0_1(a194) | c2_1(a194) | (~ndr1_0) | c3_1(a194)))),
% 0.82/0.97 inference(monotonicity,[status(thm)],[1202])).
% 0.82/0.97 tff(1204,plain,
% 0.82/0.97 (((~![U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp6 | (~ndr1_0) | c3_1(a194) | c0_1(a194) | c2_1(a194))) <=> ((~![U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | hskp6 | c0_1(a194) | c2_1(a194) | (~ndr1_0) | c3_1(a194))),
% 0.82/0.97 inference(transitivity,[status(thm)],[1203, 1201])).
% 0.82/0.97 tff(1205,plain,
% 0.82/0.97 ((~![U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp6 | (~ndr1_0) | c3_1(a194) | c0_1(a194) | c2_1(a194))),
% 0.82/0.97 inference(quant_inst,[status(thm)],[])).
% 0.82/0.97 tff(1206,plain,
% 0.82/0.97 ((~![U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | hskp6 | c0_1(a194) | c2_1(a194) | (~ndr1_0) | c3_1(a194)),
% 0.82/0.97 inference(modus_ponens,[status(thm)],[1205, 1204])).
% 0.82/0.97 tff(1207,plain,
% 0.82/0.97 (hskp6 | c0_1(a194) | c3_1(a194)),
% 0.82/0.97 inference(unit_resolution,[status(thm)],[1206, 148, 11, 530])).
% 0.82/0.97 tff(1208,plain,
% 0.82/0.97 ($false),
% 0.82/0.97 inference(unit_resolution,[status(thm)],[1207, 1200, 1192, 1191])).
% 0.82/0.97 tff(1209,plain,(c0_1(a194) | hskp6 | c2_1(a194) | (~c2_1(a195)) | (~c0_1(a190)) | (~c2_1(a190)) | c1_1(a195) | c3_1(a195) | c3_1(a190)), inference(lemma,lemma(discharge,[]))).
% 0.82/0.97 tff(1210,plain,
% 0.82/0.97 (c0_1(a194)),
% 0.82/0.97 inference(unit_resolution,[status(thm)],[1209, 772, 11, 780, 1165, 1166, 561, 560, 1164])).
% 0.82/0.97 tff(1211,plain,
% 0.82/0.97 (hskp19 | c1_1(a195) | (~c2_1(a195))),
% 0.82/0.97 inference(unit_resolution,[status(thm)],[790, 148, 1165, 1166, 560, 1164, 211])).
% 0.82/0.97 tff(1212,plain,
% 0.82/0.97 (hskp19),
% 0.82/0.97 inference(unit_resolution,[status(thm)],[1211, 780, 561])).
% 0.82/0.97 tff(1213,plain,
% 0.82/0.97 (~c1_1(a225)),
% 0.82/0.97 inference(unit_resolution,[status(thm)],[417, 1212])).
% 0.82/0.97 tff(1214,plain,
% 0.82/0.97 (~c0_1(a225)),
% 0.82/0.97 inference(unit_resolution,[status(thm)],[232, 1212])).
% 0.82/0.97 tff(1215,plain,
% 0.82/0.97 (c3_1(a225)),
% 0.82/0.97 inference(unit_resolution,[status(thm)],[226, 1212])).
% 0.82/0.97 tff(1216,plain,
% 0.82/0.97 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp2 | c0_1(a225) | c1_1(a225) | c3_1(a190) | (~ndr1_0) | (~c0_1(a190)) | (~c1_1(a190)) | (~c3_1(a225)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp2 | c0_1(a225) | c1_1(a225) | c3_1(a190) | (~ndr1_0) | (~c0_1(a190)) | (~c1_1(a190)) | (~c3_1(a225)))),
% 0.82/0.97 inference(rewrite,[status(thm)],[])).
% 0.82/0.97 tff(1217,plain,
% 0.82/0.97 ((hskp2 | (~ndr1_0) | c3_1(a190) | (~c1_1(a190)) | (~c0_1(a190)) | c1_1(a225) | c0_1(a225) | (~c3_1(a225))) <=> (hskp2 | c0_1(a225) | c1_1(a225) | c3_1(a190) | (~ndr1_0) | (~c0_1(a190)) | (~c1_1(a190)) | (~c3_1(a225)))),
% 0.82/0.97 inference(rewrite,[status(thm)],[])).
% 0.82/0.97 tff(1218,plain,
% 0.82/0.97 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp2 | (~ndr1_0) | c3_1(a190) | (~c1_1(a190)) | (~c0_1(a190)) | c1_1(a225) | c0_1(a225) | (~c3_1(a225)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp2 | c0_1(a225) | c1_1(a225) | c3_1(a190) | (~ndr1_0) | (~c0_1(a190)) | (~c1_1(a190)) | (~c3_1(a225))))),
% 0.82/0.97 inference(monotonicity,[status(thm)],[1217])).
% 0.82/0.97 tff(1219,plain,
% 0.82/0.97 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp2 | (~ndr1_0) | c3_1(a190) | (~c1_1(a190)) | (~c0_1(a190)) | c1_1(a225) | c0_1(a225) | (~c3_1(a225)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp2 | c0_1(a225) | c1_1(a225) | c3_1(a190) | (~ndr1_0) | (~c0_1(a190)) | (~c1_1(a190)) | (~c3_1(a225)))),
% 0.82/0.97 inference(transitivity,[status(thm)],[1218, 1216])).
% 0.82/0.97 tff(1220,plain,
% 0.82/0.97 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp2 | (~ndr1_0) | c3_1(a190) | (~c1_1(a190)) | (~c0_1(a190)) | c1_1(a225) | c0_1(a225) | (~c3_1(a225)))),
% 0.82/0.97 inference(quant_inst,[status(thm)],[])).
% 0.82/0.97 tff(1221,plain,
% 0.82/0.97 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp2 | c0_1(a225) | c1_1(a225) | c3_1(a190) | (~ndr1_0) | (~c0_1(a190)) | (~c1_1(a190)) | (~c3_1(a225))),
% 0.82/0.97 inference(modus_ponens,[status(thm)],[1220, 1219])).
% 0.82/0.97 tff(1222,plain,
% 0.82/0.97 (~c1_1(a190)),
% 0.82/0.97 inference(unit_resolution,[status(thm)],[1221, 148, 14, 1215, 1165, 1214, 1213, 1164, 1151])).
% 0.82/0.97 tff(1223,assumption,(~c1_1(a190)), introduced(assumption)).
% 0.82/0.97 tff(1224,assumption,(hskp24), introduced(assumption)).
% 0.82/0.97 tff(1225,plain,
% 0.82/0.97 (c3_1(a215)),
% 0.82/0.97 inference(unit_resolution,[status(thm)],[342, 1224])).
% 0.82/0.97 tff(1226,plain,
% 0.82/0.97 (c2_1(a215)),
% 0.82/0.97 inference(unit_resolution,[status(thm)],[350, 1224])).
% 0.82/0.97 tff(1227,plain,
% 0.82/0.97 (c1_1(a215)),
% 0.82/0.97 inference(unit_resolution,[status(thm)],[358, 1224])).
% 0.82/0.97 tff(1228,plain,
% 0.82/0.97 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | (c3_1(a190) | (~ndr1_0) | (~c0_1(a190)) | c1_1(a190) | (~c0_1(a215)) | (~c1_1(a215)) | (~c2_1(a215)) | (~c3_1(a215)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | c3_1(a190) | (~ndr1_0) | (~c0_1(a190)) | c1_1(a190) | (~c0_1(a215)) | (~c1_1(a215)) | (~c2_1(a215)) | (~c3_1(a215)))),
% 0.82/0.97 inference(rewrite,[status(thm)],[])).
% 0.82/0.97 tff(1229,plain,
% 0.82/0.97 (((~ndr1_0) | (~c3_1(a215)) | (~c2_1(a215)) | (~c0_1(a215)) | (~c3_1(a215)) | (~c1_1(a215)) | (~c0_1(a215)) | c1_1(a190) | c3_1(a190) | (~c0_1(a190))) <=> (c3_1(a190) | (~ndr1_0) | (~c0_1(a190)) | c1_1(a190) | (~c0_1(a215)) | (~c1_1(a215)) | (~c2_1(a215)) | (~c3_1(a215)))),
% 0.82/0.97 inference(rewrite,[status(thm)],[])).
% 0.82/0.97 tff(1230,plain,
% 0.82/0.97 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c3_1(a215)) | (~c2_1(a215)) | (~c0_1(a215)) | (~c3_1(a215)) | (~c1_1(a215)) | (~c0_1(a215)) | c1_1(a190) | c3_1(a190) | (~c0_1(a190)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | (c3_1(a190) | (~ndr1_0) | (~c0_1(a190)) | c1_1(a190) | (~c0_1(a215)) | (~c1_1(a215)) | (~c2_1(a215)) | (~c3_1(a215))))),
% 0.82/0.97 inference(monotonicity,[status(thm)],[1229])).
% 0.82/0.97 tff(1231,plain,
% 0.82/0.97 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c3_1(a215)) | (~c2_1(a215)) | (~c0_1(a215)) | (~c3_1(a215)) | (~c1_1(a215)) | (~c0_1(a215)) | c1_1(a190) | c3_1(a190) | (~c0_1(a190)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | c3_1(a190) | (~ndr1_0) | (~c0_1(a190)) | c1_1(a190) | (~c0_1(a215)) | (~c1_1(a215)) | (~c2_1(a215)) | (~c3_1(a215)))),
% 0.82/0.97 inference(transitivity,[status(thm)],[1230, 1228])).
% 0.82/0.97 tff(1232,plain,
% 0.82/0.97 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c3_1(a215)) | (~c2_1(a215)) | (~c0_1(a215)) | (~c3_1(a215)) | (~c1_1(a215)) | (~c0_1(a215)) | c1_1(a190) | c3_1(a190) | (~c0_1(a190)))),
% 0.82/0.97 inference(quant_inst,[status(thm)],[])).
% 0.82/0.97 tff(1233,plain,
% 0.82/0.97 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | c3_1(a190) | (~ndr1_0) | (~c0_1(a190)) | c1_1(a190) | (~c0_1(a215)) | (~c1_1(a215)) | (~c2_1(a215)) | (~c3_1(a215))),
% 0.82/0.97 inference(modus_ponens,[status(thm)],[1232, 1231])).
% 0.82/0.97 tff(1234,plain,
% 0.82/0.97 (~c0_1(a215)),
% 0.82/0.97 inference(unit_resolution,[status(thm)],[1233, 148, 1227, 1226, 1225, 829, 13, 470, 1223])).
% 0.82/0.97 tff(1235,plain,
% 0.82/0.97 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_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(a195) | c1_1(a195) | c1_1(a194) | c2_1(a194) | (~ndr1_0) | (~c0_1(a194)) | (~c2_1(a195)) | (~c1_1(a215)) | c0_1(a215) | (~c3_1(a215)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_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(a195) | c1_1(a195) | c1_1(a194) | c2_1(a194) | (~ndr1_0) | (~c0_1(a194)) | (~c2_1(a195)) | (~c1_1(a215)) | c0_1(a215) | (~c3_1(a215)))),
% 0.82/0.97 inference(rewrite,[status(thm)],[])).
% 0.82/0.97 tff(1236,plain,
% 0.82/0.97 (((~ndr1_0) | c1_1(a194) | c2_1(a194) | (~c0_1(a194)) | c0_1(a215) | (~c3_1(a215)) | (~c1_1(a215)) | c1_1(a195) | c0_1(a195) | (~c2_1(a195))) <=> (c0_1(a195) | c1_1(a195) | c1_1(a194) | c2_1(a194) | (~ndr1_0) | (~c0_1(a194)) | (~c2_1(a195)) | (~c1_1(a215)) | c0_1(a215) | (~c3_1(a215)))),
% 0.82/0.97 inference(rewrite,[status(thm)],[])).
% 0.82/0.97 tff(1237,plain,
% 0.82/0.97 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_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) | c1_1(a194) | c2_1(a194) | (~c0_1(a194)) | c0_1(a215) | (~c3_1(a215)) | (~c1_1(a215)) | c1_1(a195) | c0_1(a195) | (~c2_1(a195)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_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(a195) | c1_1(a195) | c1_1(a194) | c2_1(a194) | (~ndr1_0) | (~c0_1(a194)) | (~c2_1(a195)) | (~c1_1(a215)) | c0_1(a215) | (~c3_1(a215))))),
% 0.82/0.97 inference(monotonicity,[status(thm)],[1236])).
% 0.82/0.97 tff(1238,plain,
% 0.82/0.97 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_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) | c1_1(a194) | c2_1(a194) | (~c0_1(a194)) | c0_1(a215) | (~c3_1(a215)) | (~c1_1(a215)) | c1_1(a195) | c0_1(a195) | (~c2_1(a195)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_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(a195) | c1_1(a195) | c1_1(a194) | c2_1(a194) | (~ndr1_0) | (~c0_1(a194)) | (~c2_1(a195)) | (~c1_1(a215)) | c0_1(a215) | (~c3_1(a215)))),
% 0.82/0.97 inference(transitivity,[status(thm)],[1237, 1235])).
% 0.82/0.97 tff(1239,plain,
% 0.82/0.97 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_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) | c1_1(a194) | c2_1(a194) | (~c0_1(a194)) | c0_1(a215) | (~c3_1(a215)) | (~c1_1(a215)) | c1_1(a195) | c0_1(a195) | (~c2_1(a195)))),
% 0.82/0.97 inference(quant_inst,[status(thm)],[])).
% 0.82/0.97 tff(1240,plain,
% 0.82/0.97 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a195) | c1_1(a195) | c1_1(a194) | c2_1(a194) | (~ndr1_0) | (~c0_1(a194)) | (~c2_1(a195)) | (~c1_1(a215)) | c0_1(a215) | (~c3_1(a215))),
% 0.82/0.97 inference(modus_ponens,[status(thm)],[1239, 1238])).
% 0.82/0.97 tff(1241,plain,
% 0.82/0.97 ($false),
% 0.82/0.97 inference(unit_resolution,[status(thm)],[1240, 148, 1227, 1225, 771, 673, 561, 12, 11, 65, 932, 1234])).
% 0.82/0.97 tff(1242,plain,((~hskp24) | c0_1(a195) | (~c0_1(a194)) | c1_1(a195) | c1_1(a194) | c2_1(a194) | (~c2_1(a195)) | (~c0_1(a190)) | c3_1(a190) | c1_1(a190)), inference(lemma,lemma(discharge,[]))).
% 0.82/0.97 tff(1243,plain,
% 0.82/0.97 (~hskp24),
% 0.82/0.97 inference(unit_resolution,[status(thm)],[1242, 771, 1210, 561, 12, 11, 780, 1165, 1164, 1222])).
% 0.82/0.97 tff(1244,plain,
% 0.82/0.97 (((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp24 | c1_1(a194) | c2_1(a194) | (~ndr1_0) | (~c3_1(a194)) | (~c0_1(a194)))) <=> ((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | hskp24 | c1_1(a194) | c2_1(a194) | (~ndr1_0) | (~c3_1(a194)) | (~c0_1(a194)))),
% 0.82/0.97 inference(rewrite,[status(thm)],[])).
% 0.82/0.97 tff(1245,plain,
% 0.82/0.97 ((hskp24 | (~ndr1_0) | c1_1(a194) | (~c3_1(a194)) | (~c0_1(a194)) | c1_1(a194) | c2_1(a194) | (~c0_1(a194))) <=> (hskp24 | c1_1(a194) | c2_1(a194) | (~ndr1_0) | (~c3_1(a194)) | (~c0_1(a194)))),
% 0.82/0.97 inference(rewrite,[status(thm)],[])).
% 0.82/0.97 tff(1246,plain,
% 0.82/0.97 (((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp24 | (~ndr1_0) | c1_1(a194) | (~c3_1(a194)) | (~c0_1(a194)) | c1_1(a194) | c2_1(a194) | (~c0_1(a194)))) <=> ((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp24 | c1_1(a194) | c2_1(a194) | (~ndr1_0) | (~c3_1(a194)) | (~c0_1(a194))))),
% 0.82/0.97 inference(monotonicity,[status(thm)],[1245])).
% 0.82/0.97 tff(1247,plain,
% 0.82/0.97 (((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp24 | (~ndr1_0) | c1_1(a194) | (~c3_1(a194)) | (~c0_1(a194)) | c1_1(a194) | c2_1(a194) | (~c0_1(a194)))) <=> ((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | hskp24 | c1_1(a194) | c2_1(a194) | (~ndr1_0) | (~c3_1(a194)) | (~c0_1(a194)))),
% 0.82/0.97 inference(transitivity,[status(thm)],[1246, 1244])).
% 0.82/0.97 tff(1248,plain,
% 0.82/0.97 ((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp24 | (~ndr1_0) | c1_1(a194) | (~c3_1(a194)) | (~c0_1(a194)) | c1_1(a194) | c2_1(a194) | (~c0_1(a194)))),
% 0.82/0.97 inference(quant_inst,[status(thm)],[])).
% 0.82/0.97 tff(1249,plain,
% 0.82/0.97 ((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | hskp24 | c1_1(a194) | c2_1(a194) | (~ndr1_0) | (~c3_1(a194)) | (~c0_1(a194))),
% 0.82/0.97 inference(modus_ponens,[status(thm)],[1248, 1247])).
% 0.82/0.97 tff(1250,plain,
% 0.82/0.97 (hskp24 | c2_1(a194) | (~c3_1(a194)) | (~c0_1(a194))),
% 0.82/0.97 inference(unit_resolution,[status(thm)],[1249, 148, 12, 326])).
% 0.82/0.97 tff(1251,plain,
% 0.82/0.97 (~c3_1(a194)),
% 0.82/0.97 inference(unit_resolution,[status(thm)],[1250, 1243, 11, 1210])).
% 0.82/0.97 tff(1252,plain,
% 0.82/0.97 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W))))),
% 0.82/0.97 inference(bind,[status(th)],[])).
% 0.82/0.97 tff(1253,plain,
% 0.82/0.97 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))),
% 0.82/0.97 inference(quant_intro,[status(thm)],[1252])).
% 0.82/0.97 tff(1254,plain,
% 0.82/0.97 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))),
% 0.82/0.97 inference(rewrite,[status(thm)],[])).
% 0.82/0.97 tff(1255,plain,
% 0.82/0.97 (^[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))) <=> ((~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> (((~c1_1(U)) | (~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c1_1(U)) | (~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c0_1(W))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c0_1(W))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c0_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c0_1(W)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c0_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c0_1(W))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c0_1(W))) | (~c2_1(W))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c0_1(W))) | (~c2_1(W))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c0_1(W))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(W)) | (~c0_1(W)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c0_1(W))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(W)) | (~c0_1(W))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c0_1(W))) | (~c2_1(W))) | c2_1(V)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(W)) | (~c0_1(W))) | c2_1(V)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(W)) | (~c0_1(W))) | c2_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V)) | (~c2_1(W)) | (~c0_1(W)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c0_1(W))) | (~c2_1(W))) | c2_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V)) | (~c2_1(W)) | (~c0_1(W))))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c0_1(W))) | (~c2_1(W))) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V)) | (~c2_1(W)) | (~c0_1(W))) | c3_1(V)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V)) | (~c2_1(W)) | (~c0_1(W))) | c3_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | (~c2_1(W)) | (~c0_1(W)))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c0_1(W))) | (~c2_1(W))) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | (~c2_1(W)) | (~c0_1(W))))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c0_1(W))) | (~c2_1(W))) | c2_1(V)) | c3_1(V)) | c1_1(W)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | (~c2_1(W)) | (~c0_1(W))) | c1_1(W)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | (~c2_1(W)) | (~c0_1(W))) | c1_1(W)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c0_1(W))) | (~c2_1(W))) | c2_1(V)) | c3_1(V)) | c1_1(W)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))))),
% 0.82/0.97 inference(bind,[status(th)],[])).
% 0.82/0.97 tff(1256,plain,
% 0.82/0.97 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c0_1(W))) | (~c2_1(W))) | c2_1(V)) | c3_1(V)) | c1_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))),
% 0.82/0.97 inference(quant_intro,[status(thm)],[1255])).
% 0.82/0.97 tff(1257,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c0_1(W))) | (~c2_1(W))) | c2_1(V)) | c3_1(V)) | c1_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause160')).
% 0.82/0.97 tff(1258,plain,
% 0.82/0.97 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))),
% 0.82/0.98 inference(modus_ponens,[status(thm)],[1257, 1256])).
% 0.82/0.98 tff(1259,plain,
% 0.82/0.98 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))),
% 0.82/0.98 inference(modus_ponens,[status(thm)],[1258, 1254])).
% 0.82/0.98 tff(1260,plain,(
% 0.82/0.98 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))),
% 0.82/0.98 inference(skolemize,[status(sab)],[1259])).
% 0.82/0.98 tff(1261,plain,
% 0.82/0.98 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))),
% 0.82/0.98 inference(modus_ponens,[status(thm)],[1260, 1253])).
% 0.82/0.98 tff(1262,plain,
% 0.82/0.98 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))) | (c2_1(a194) | (~ndr1_0) | (~c2_1(a230)) | (~c0_1(a230)) | (~c1_1(a230)) | (~c2_1(a190)) | (~c0_1(a190)) | c1_1(a190) | c3_1(a194) | (~c0_1(a194)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))) | c2_1(a194) | (~ndr1_0) | (~c2_1(a230)) | (~c0_1(a230)) | (~c1_1(a230)) | (~c2_1(a190)) | (~c0_1(a190)) | c1_1(a190) | c3_1(a194) | (~c0_1(a194)))),
% 0.82/0.98 inference(rewrite,[status(thm)],[])).
% 0.82/0.98 tff(1263,plain,
% 0.82/0.98 (((~ndr1_0) | (~c1_1(a230)) | (~c2_1(a230)) | (~c0_1(a230)) | c3_1(a194) | c2_1(a194) | (~c0_1(a194)) | c1_1(a190) | (~c2_1(a190)) | (~c0_1(a190))) <=> (c2_1(a194) | (~ndr1_0) | (~c2_1(a230)) | (~c0_1(a230)) | (~c1_1(a230)) | (~c2_1(a190)) | (~c0_1(a190)) | c1_1(a190) | c3_1(a194) | (~c0_1(a194)))),
% 0.82/0.98 inference(rewrite,[status(thm)],[])).
% 0.82/0.98 tff(1264,plain,
% 0.82/0.98 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | (~c1_1(a230)) | (~c2_1(a230)) | (~c0_1(a230)) | c3_1(a194) | c2_1(a194) | (~c0_1(a194)) | c1_1(a190) | (~c2_1(a190)) | (~c0_1(a190)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))) | (c2_1(a194) | (~ndr1_0) | (~c2_1(a230)) | (~c0_1(a230)) | (~c1_1(a230)) | (~c2_1(a190)) | (~c0_1(a190)) | c1_1(a190) | c3_1(a194) | (~c0_1(a194))))),
% 0.82/0.98 inference(monotonicity,[status(thm)],[1263])).
% 0.82/0.98 tff(1265,plain,
% 0.82/0.98 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | (~c1_1(a230)) | (~c2_1(a230)) | (~c0_1(a230)) | c3_1(a194) | c2_1(a194) | (~c0_1(a194)) | c1_1(a190) | (~c2_1(a190)) | (~c0_1(a190)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))) | c2_1(a194) | (~ndr1_0) | (~c2_1(a230)) | (~c0_1(a230)) | (~c1_1(a230)) | (~c2_1(a190)) | (~c0_1(a190)) | c1_1(a190) | c3_1(a194) | (~c0_1(a194)))),
% 0.82/0.98 inference(transitivity,[status(thm)],[1264, 1262])).
% 0.82/0.98 tff(1266,plain,
% 0.82/0.98 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | (~c1_1(a230)) | (~c2_1(a230)) | (~c0_1(a230)) | c3_1(a194) | c2_1(a194) | (~c0_1(a194)) | c1_1(a190) | (~c2_1(a190)) | (~c0_1(a190)))),
% 0.82/0.98 inference(quant_inst,[status(thm)],[])).
% 0.82/0.98 tff(1267,plain,
% 0.82/0.98 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))) | c2_1(a194) | (~ndr1_0) | (~c2_1(a230)) | (~c0_1(a230)) | (~c1_1(a230)) | (~c2_1(a190)) | (~c0_1(a190)) | c1_1(a190) | c3_1(a194) | (~c0_1(a194))),
% 0.82/0.98 inference(modus_ponens,[status(thm)],[1266, 1265])).
% 0.82/0.98 tff(1268,plain,
% 0.82/0.98 ($false),
% 0.82/0.98 inference(unit_resolution,[status(thm)],[1267, 148, 1133, 1132, 1181, 1210, 1165, 1166, 11, 1261, 1222, 1251])).
% 0.82/0.98 tff(1269,plain,(c0_1(a195) | (~c0_1(a230)) | (~c1_1(a230)) | (~c2_1(a230)) | c2_1(a194) | c1_1(a194) | c1_1(a195) | c3_1(a195) | hskp2), inference(lemma,lemma(discharge,[]))).
% 0.82/0.98 tff(1270,plain,
% 0.82/0.98 (c1_1(a194)),
% 0.82/0.98 inference(unit_resolution,[status(thm)],[1269, 771, 1121, 1113, 1105, 11, 561, 560, 1096])).
% 0.82/0.98 tff(1271,plain,
% 0.82/0.98 (~hskp5),
% 0.82/0.98 inference(unit_resolution,[status(thm)],[590, 1270])).
% 0.82/0.98 tff(1272,plain,
% 0.82/0.98 (hskp21),
% 0.82/0.98 inference(unit_resolution,[status(thm)],[80, 1271, 36])).
% 0.82/0.98 tff(1273,plain,
% 0.82/0.98 (~c3_1(a257)),
% 0.82/0.98 inference(unit_resolution,[status(thm)],[92, 1272])).
% 0.82/0.98 tff(1274,plain,
% 0.82/0.98 (~c1_1(a257)),
% 0.82/0.98 inference(unit_resolution,[status(thm)],[86, 1272])).
% 0.82/0.98 tff(1275,plain,
% 0.82/0.98 (c2_1(a190)),
% 0.82/0.98 inference(unit_resolution,[status(thm)],[192, 1161])).
% 0.82/0.98 tff(1276,plain,
% 0.82/0.98 (c0_1(a190)),
% 0.82/0.98 inference(unit_resolution,[status(thm)],[200, 1161])).
% 0.82/0.98 tff(1277,plain,
% 0.82/0.98 (c2_1(a257)),
% 0.82/0.98 inference(unit_resolution,[status(thm)],[100, 1272])).
% 0.82/0.98 tff(1278,assumption,(~c2_1(a225)), introduced(assumption)).
% 0.82/0.98 tff(1279,plain,
% 0.82/0.98 (hskp19),
% 0.82/0.98 inference(unit_resolution,[status(thm)],[217, 148, 175, 829, 784, 114, 113, 13, 211])).
% 0.82/0.98 tff(1280,plain,
% 0.82/0.98 (~c0_1(a225)),
% 0.82/0.98 inference(unit_resolution,[status(thm)],[232, 1279])).
% 0.82/0.98 tff(1281,plain,
% 0.82/0.98 (c3_1(a225)),
% 0.82/0.98 inference(unit_resolution,[status(thm)],[226, 1279])).
% 0.82/0.98 tff(1282,plain,
% 0.82/0.98 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c1_1(a257) | c3_1(a257) | c0_1(a225) | c3_1(a190) | (~ndr1_0) | (~c2_1(a190)) | (~c0_1(a190)) | c2_1(a225) | (~c3_1(a225)) | (~c2_1(a257)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c1_1(a257) | c3_1(a257) | c0_1(a225) | c3_1(a190) | (~ndr1_0) | (~c2_1(a190)) | (~c0_1(a190)) | c2_1(a225) | (~c3_1(a225)) | (~c2_1(a257)))),
% 0.82/0.98 inference(rewrite,[status(thm)],[])).
% 0.82/0.98 tff(1283,plain,
% 0.82/0.98 (((~ndr1_0) | c3_1(a190) | (~c2_1(a190)) | (~c0_1(a190)) | c3_1(a257) | c1_1(a257) | (~c2_1(a257)) | c2_1(a225) | c0_1(a225) | (~c3_1(a225))) <=> (c1_1(a257) | c3_1(a257) | c0_1(a225) | c3_1(a190) | (~ndr1_0) | (~c2_1(a190)) | (~c0_1(a190)) | c2_1(a225) | (~c3_1(a225)) | (~c2_1(a257)))),
% 0.82/0.98 inference(rewrite,[status(thm)],[])).
% 0.82/0.98 tff(1284,plain,
% 0.82/0.98 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a190) | (~c2_1(a190)) | (~c0_1(a190)) | c3_1(a257) | c1_1(a257) | (~c2_1(a257)) | c2_1(a225) | c0_1(a225) | (~c3_1(a225)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c1_1(a257) | c3_1(a257) | c0_1(a225) | c3_1(a190) | (~ndr1_0) | (~c2_1(a190)) | (~c0_1(a190)) | c2_1(a225) | (~c3_1(a225)) | (~c2_1(a257))))),
% 0.82/0.98 inference(monotonicity,[status(thm)],[1283])).
% 0.82/0.98 tff(1285,plain,
% 0.82/0.98 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a190) | (~c2_1(a190)) | (~c0_1(a190)) | c3_1(a257) | c1_1(a257) | (~c2_1(a257)) | c2_1(a225) | c0_1(a225) | (~c3_1(a225)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c1_1(a257) | c3_1(a257) | c0_1(a225) | c3_1(a190) | (~ndr1_0) | (~c2_1(a190)) | (~c0_1(a190)) | c2_1(a225) | (~c3_1(a225)) | (~c2_1(a257)))),
% 0.82/0.98 inference(transitivity,[status(thm)],[1284, 1282])).
% 0.82/0.98 tff(1286,plain,
% 0.82/0.98 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a190) | (~c2_1(a190)) | (~c0_1(a190)) | c3_1(a257) | c1_1(a257) | (~c2_1(a257)) | c2_1(a225) | c0_1(a225) | (~c3_1(a225)))),
% 0.82/0.98 inference(quant_inst,[status(thm)],[])).
% 0.82/0.98 tff(1287,plain,
% 0.82/0.98 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c1_1(a257) | c3_1(a257) | c0_1(a225) | c3_1(a190) | (~ndr1_0) | (~c2_1(a190)) | (~c0_1(a190)) | c2_1(a225) | (~c3_1(a225)) | (~c2_1(a257))),
% 0.82/0.98 inference(modus_ponens,[status(thm)],[1286, 1285])).
% 0.82/0.98 tff(1288,plain,
% 0.82/0.98 ($false),
% 0.82/0.98 inference(unit_resolution,[status(thm)],[1287, 148, 175, 1281, 829, 784, 114, 113, 1280, 13, 451, 1278])).
% 0.82/0.98 tff(1289,plain,(c2_1(a225) | (~c2_1(a257)) | (~c0_1(a190)) | (~c2_1(a190)) | c1_1(a257) | c3_1(a257) | c3_1(a190)), inference(lemma,lemma(discharge,[]))).
% 0.82/0.98 tff(1290,plain,
% 0.82/0.98 (c2_1(a225)),
% 0.82/0.98 inference(unit_resolution,[status(thm)],[1289, 1277, 1276, 1275, 1274, 1273, 1162])).
% 0.82/0.98 tff(1291,plain,
% 0.82/0.98 (^[V: $i, U: $i] : refl((hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))) <=> (hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))))),
% 0.82/0.98 inference(bind,[status(th)],[])).
% 0.82/0.98 tff(1292,plain,
% 0.82/0.98 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 0.82/0.98 inference(quant_intro,[status(thm)],[1291])).
% 0.82/0.98 tff(1293,plain,
% 0.82/0.98 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 0.82/0.98 inference(rewrite,[status(thm)],[])).
% 0.82/0.98 tff(1294,plain,
% 0.82/0.98 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) <=> ((~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> (((~c1_1(U)) | (~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c1_1(U)) | (~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c0_1(V)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c0_1(V)) | hskp7) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))) | hskp7))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))) | hskp7) <=> (hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c0_1(V)) | hskp7) <=> (hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))))),
% 0.82/0.98 inference(bind,[status(th)],[])).
% 0.82/0.98 tff(1295,plain,
% 0.82/0.98 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c0_1(V)) | hskp7) <=> ![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 0.82/0.98 inference(quant_intro,[status(thm)],[1294])).
% 0.82/0.98 tff(1296,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c0_1(V)) | hskp7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause153')).
% 0.82/0.98 tff(1297,plain,
% 0.82/0.98 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 0.82/0.98 inference(modus_ponens,[status(thm)],[1296, 1295])).
% 0.82/0.98 tff(1298,plain,
% 0.82/0.98 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 0.82/0.98 inference(modus_ponens,[status(thm)],[1297, 1293])).
% 0.82/0.98 tff(1299,plain,(
% 0.82/0.98 ![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 0.82/0.98 inference(skolemize,[status(sab)],[1298])).
% 0.82/0.98 tff(1300,plain,
% 0.82/0.98 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 0.82/0.98 inference(modus_ponens,[status(thm)],[1299, 1292])).
% 0.82/0.98 tff(1301,plain,
% 0.82/0.98 (hskp19 | c1_1(a195) | (~c2_1(a195))),
% 0.82/0.98 inference(unit_resolution,[status(thm)],[790, 148, 1276, 1275, 560, 1162, 211])).
% 0.82/0.98 tff(1302,plain,
% 0.82/0.98 (hskp19),
% 0.82/0.98 inference(unit_resolution,[status(thm)],[1301, 780, 561])).
% 0.82/0.98 tff(1303,plain,
% 0.82/0.98 (~c0_1(a225)),
% 0.82/0.98 inference(unit_resolution,[status(thm)],[232, 1302])).
% 0.82/0.98 tff(1304,plain,
% 0.82/0.98 (c3_1(a225)),
% 0.82/0.98 inference(unit_resolution,[status(thm)],[226, 1302])).
% 0.82/0.98 tff(1305,assumption,(hskp7), introduced(assumption)).
% 0.82/0.98 tff(1306,plain,
% 0.82/0.98 (((~hskp7) | (~c0_1(a197))) <=> ((~hskp7) | (~c0_1(a197)))),
% 0.82/0.98 inference(rewrite,[status(thm)],[])).
% 0.82/0.98 tff(1307,plain,
% 0.82/0.98 (((~c0_1(a197)) | (~hskp7)) <=> ((~hskp7) | (~c0_1(a197)))),
% 0.82/0.98 inference(rewrite,[status(thm)],[])).
% 0.82/0.98 tff(1308,axiom,((~c0_1(a197)) | (~hskp7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause96')).
% 0.82/0.98 tff(1309,plain,
% 0.82/0.98 ((~hskp7) | (~c0_1(a197))),
% 0.82/0.98 inference(modus_ponens,[status(thm)],[1308, 1307])).
% 0.82/0.98 tff(1310,plain,
% 0.82/0.98 ((~hskp7) | (~c0_1(a197))),
% 0.82/0.98 inference(modus_ponens,[status(thm)],[1309, 1306])).
% 0.82/0.98 tff(1311,plain,
% 0.82/0.98 (~c0_1(a197)),
% 0.82/0.98 inference(unit_resolution,[status(thm)],[1310, 1305])).
% 0.82/0.98 tff(1312,plain,
% 0.82/0.98 (((~hskp7) | (~c2_1(a197))) <=> ((~hskp7) | (~c2_1(a197)))),
% 0.82/0.98 inference(rewrite,[status(thm)],[])).
% 0.82/0.98 tff(1313,plain,
% 0.82/0.98 (((~c2_1(a197)) | (~hskp7)) <=> ((~hskp7) | (~c2_1(a197)))),
% 0.82/0.98 inference(rewrite,[status(thm)],[])).
% 0.82/0.98 tff(1314,axiom,((~c2_1(a197)) | (~hskp7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause97')).
% 0.82/0.98 tff(1315,plain,
% 0.82/0.98 ((~hskp7) | (~c2_1(a197))),
% 0.82/0.98 inference(modus_ponens,[status(thm)],[1314, 1313])).
% 0.82/0.98 tff(1316,plain,
% 0.82/0.98 ((~hskp7) | (~c2_1(a197))),
% 0.82/0.98 inference(modus_ponens,[status(thm)],[1315, 1312])).
% 0.82/0.98 tff(1317,plain,
% 0.82/0.98 (~c2_1(a197)),
% 0.82/0.98 inference(unit_resolution,[status(thm)],[1316, 1305])).
% 0.82/0.98 tff(1318,plain,
% 0.82/0.98 (c2_1(a190)),
% 0.82/0.98 inference(unit_resolution,[status(thm)],[192, 782])).
% 0.82/0.98 tff(1319,assumption,(~c0_1(a197)), introduced(assumption)).
% 0.82/0.98 tff(1320,assumption,(~c2_1(a197)), introduced(assumption)).
% 0.82/0.98 tff(1321,plain,
% 0.82/0.98 (((~![U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp6 | c0_1(a197) | c2_1(a197) | (~ndr1_0) | c3_1(a197))) <=> ((~![U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | hskp6 | c0_1(a197) | c2_1(a197) | (~ndr1_0) | c3_1(a197))),
% 0.82/0.98 inference(rewrite,[status(thm)],[])).
% 0.82/0.98 tff(1322,plain,
% 0.82/0.98 ((hskp6 | (~ndr1_0) | c3_1(a197) | c0_1(a197) | c2_1(a197)) <=> (hskp6 | c0_1(a197) | c2_1(a197) | (~ndr1_0) | c3_1(a197))),
% 0.82/0.98 inference(rewrite,[status(thm)],[])).
% 0.82/0.98 tff(1323,plain,
% 0.82/0.98 (((~![U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp6 | (~ndr1_0) | c3_1(a197) | c0_1(a197) | c2_1(a197))) <=> ((~![U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp6 | c0_1(a197) | c2_1(a197) | (~ndr1_0) | c3_1(a197)))),
% 0.82/0.98 inference(monotonicity,[status(thm)],[1322])).
% 0.82/0.98 tff(1324,plain,
% 0.82/0.98 (((~![U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp6 | (~ndr1_0) | c3_1(a197) | c0_1(a197) | c2_1(a197))) <=> ((~![U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | hskp6 | c0_1(a197) | c2_1(a197) | (~ndr1_0) | c3_1(a197))),
% 0.82/0.98 inference(transitivity,[status(thm)],[1323, 1321])).
% 0.82/0.98 tff(1325,plain,
% 0.82/0.98 ((~![U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp6 | (~ndr1_0) | c3_1(a197) | c0_1(a197) | c2_1(a197))),
% 0.82/0.98 inference(quant_inst,[status(thm)],[])).
% 0.82/0.98 tff(1326,plain,
% 0.82/0.98 ((~![U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | hskp6 | c0_1(a197) | c2_1(a197) | (~ndr1_0) | c3_1(a197)),
% 0.82/0.98 inference(modus_ponens,[status(thm)],[1325, 1324])).
% 0.82/0.98 tff(1327,plain,
% 0.82/0.98 (hskp6 | c0_1(a197) | c3_1(a197)),
% 0.82/0.98 inference(unit_resolution,[status(thm)],[1326, 148, 1320, 530])).
% 0.82/0.98 tff(1328,plain,
% 0.82/0.98 (c3_1(a197)),
% 0.82/0.98 inference(unit_resolution,[status(thm)],[1327, 772, 1319])).
% 0.82/0.98 tff(1329,plain,
% 0.82/0.98 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a197) | c2_1(a197) | c1_1(a195) | c3_1(a195) | c3_1(a190) | (~ndr1_0) | (~c2_1(a190)) | (~c0_1(a190)) | (~c2_1(a195)) | (~c3_1(a197)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a197) | c2_1(a197) | c1_1(a195) | c3_1(a195) | c3_1(a190) | (~ndr1_0) | (~c2_1(a190)) | (~c0_1(a190)) | (~c2_1(a195)) | (~c3_1(a197)))),
% 0.82/0.98 inference(rewrite,[status(thm)],[])).
% 0.82/0.98 tff(1330,plain,
% 0.82/0.98 (((~ndr1_0) | c3_1(a190) | (~c2_1(a190)) | (~c0_1(a190)) | c3_1(a195) | c1_1(a195) | (~c2_1(a195)) | c2_1(a197) | c0_1(a197) | (~c3_1(a197))) <=> (c0_1(a197) | c2_1(a197) | c1_1(a195) | c3_1(a195) | c3_1(a190) | (~ndr1_0) | (~c2_1(a190)) | (~c0_1(a190)) | (~c2_1(a195)) | (~c3_1(a197)))),
% 0.82/0.98 inference(rewrite,[status(thm)],[])).
% 0.82/0.98 tff(1331,plain,
% 0.82/0.98 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a190) | (~c2_1(a190)) | (~c0_1(a190)) | c3_1(a195) | c1_1(a195) | (~c2_1(a195)) | c2_1(a197) | c0_1(a197) | (~c3_1(a197)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a197) | c2_1(a197) | c1_1(a195) | c3_1(a195) | c3_1(a190) | (~ndr1_0) | (~c2_1(a190)) | (~c0_1(a190)) | (~c2_1(a195)) | (~c3_1(a197))))),
% 0.82/0.98 inference(monotonicity,[status(thm)],[1330])).
% 0.82/0.98 tff(1332,plain,
% 0.82/0.98 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a190) | (~c2_1(a190)) | (~c0_1(a190)) | c3_1(a195) | c1_1(a195) | (~c2_1(a195)) | c2_1(a197) | c0_1(a197) | (~c3_1(a197)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a197) | c2_1(a197) | c1_1(a195) | c3_1(a195) | c3_1(a190) | (~ndr1_0) | (~c2_1(a190)) | (~c0_1(a190)) | (~c2_1(a195)) | (~c3_1(a197)))),
% 0.82/0.98 inference(transitivity,[status(thm)],[1331, 1329])).
% 0.82/0.98 tff(1333,plain,
% 0.82/0.98 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a190) | (~c2_1(a190)) | (~c0_1(a190)) | c3_1(a195) | c1_1(a195) | (~c2_1(a195)) | c2_1(a197) | c0_1(a197) | (~c3_1(a197)))),
% 0.82/0.98 inference(quant_inst,[status(thm)],[])).
% 0.82/0.98 tff(1334,plain,
% 0.82/0.98 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a197) | c2_1(a197) | c1_1(a195) | c3_1(a195) | c3_1(a190) | (~ndr1_0) | (~c2_1(a190)) | (~c0_1(a190)) | (~c2_1(a195)) | (~c3_1(a197))),
% 0.82/0.98 inference(modus_ponens,[status(thm)],[1333, 1332])).
% 0.82/0.98 tff(1335,plain,
% 0.82/0.98 (c0_1(a197) | (~c2_1(a190)) | (~c0_1(a190)) | (~c2_1(a195)) | (~c3_1(a197))),
% 0.82/0.98 inference(unit_resolution,[status(thm)],[1334, 148, 1320, 561, 560, 13, 451])).
% 0.82/0.98 tff(1336,plain,
% 0.82/0.98 ($false),
% 0.82/0.98 inference(unit_resolution,[status(thm)],[1335, 1328, 780, 1319, 783, 1318])).
% 0.82/0.98 tff(1337,plain,(c0_1(a195) | c0_1(a197) | c2_1(a197) | c1_1(a195) | c3_1(a195) | c3_1(a190)), inference(lemma,lemma(discharge,[]))).
% 0.82/0.98 tff(1338,plain,
% 0.82/0.98 ($false),
% 0.82/0.98 inference(unit_resolution,[status(thm)],[1337, 1317, 1311, 771, 561, 560, 13])).
% 0.82/0.98 tff(1339,plain,((~hskp7) | c0_1(a195) | c1_1(a195) | c3_1(a195) | c3_1(a190)), inference(lemma,lemma(discharge,[]))).
% 0.82/0.98 tff(1340,plain,
% 0.82/0.98 (~hskp7),
% 0.82/0.98 inference(unit_resolution,[status(thm)],[1339, 771, 561, 560, 1162])).
% 0.82/0.98 tff(1341,plain,
% 0.82/0.98 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp7 | c0_1(a225) | (~ndr1_0) | (~c2_1(a230)) | (~c0_1(a230)) | (~c1_1(a230)) | (~c2_1(a225)) | (~c3_1(a225)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp7 | c0_1(a225) | (~ndr1_0) | (~c2_1(a230)) | (~c0_1(a230)) | (~c1_1(a230)) | (~c2_1(a225)) | (~c3_1(a225)))),
% 0.82/0.98 inference(rewrite,[status(thm)],[])).
% 0.82/0.98 tff(1342,plain,
% 0.82/0.98 ((hskp7 | (~ndr1_0) | (~c1_1(a230)) | (~c2_1(a230)) | (~c0_1(a230)) | c0_1(a225) | (~c3_1(a225)) | (~c2_1(a225))) <=> (hskp7 | c0_1(a225) | (~ndr1_0) | (~c2_1(a230)) | (~c0_1(a230)) | (~c1_1(a230)) | (~c2_1(a225)) | (~c3_1(a225)))),
% 0.82/0.98 inference(rewrite,[status(thm)],[])).
% 0.82/0.98 tff(1343,plain,
% 0.82/0.98 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp7 | (~ndr1_0) | (~c1_1(a230)) | (~c2_1(a230)) | (~c0_1(a230)) | c0_1(a225) | (~c3_1(a225)) | (~c2_1(a225)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp7 | c0_1(a225) | (~ndr1_0) | (~c2_1(a230)) | (~c0_1(a230)) | (~c1_1(a230)) | (~c2_1(a225)) | (~c3_1(a225))))),
% 0.82/0.98 inference(monotonicity,[status(thm)],[1342])).
% 0.82/0.98 tff(1344,plain,
% 0.82/0.98 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp7 | (~ndr1_0) | (~c1_1(a230)) | (~c2_1(a230)) | (~c0_1(a230)) | c0_1(a225) | (~c3_1(a225)) | (~c2_1(a225)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp7 | c0_1(a225) | (~ndr1_0) | (~c2_1(a230)) | (~c0_1(a230)) | (~c1_1(a230)) | (~c2_1(a225)) | (~c3_1(a225)))),
% 0.82/0.98 inference(transitivity,[status(thm)],[1343, 1341])).
% 0.82/0.98 tff(1345,plain,
% 0.82/0.98 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp7 | (~ndr1_0) | (~c1_1(a230)) | (~c2_1(a230)) | (~c0_1(a230)) | c0_1(a225) | (~c3_1(a225)) | (~c2_1(a225)))),
% 0.82/0.98 inference(quant_inst,[status(thm)],[])).
% 0.82/0.98 tff(1346,plain,
% 0.82/0.98 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp7 | c0_1(a225) | (~ndr1_0) | (~c2_1(a230)) | (~c0_1(a230)) | (~c1_1(a230)) | (~c2_1(a225)) | (~c3_1(a225))),
% 0.82/0.98 inference(modus_ponens,[status(thm)],[1345, 1344])).
% 0.82/0.98 tff(1347,plain,
% 0.82/0.98 ($false),
% 0.82/0.98 inference(unit_resolution,[status(thm)],[1346, 148, 1340, 1105, 1121, 1113, 1304, 1303, 1300, 1290])).
% 0.82/0.98 tff(1348,plain,(c0_1(a195) | hskp15 | c1_1(a195) | c3_1(a195) | c2_1(a194)), inference(lemma,lemma(discharge,[]))).
% 0.82/0.98 tff(1349,plain,
% 0.82/0.98 (c2_1(a194)),
% 0.82/0.98 inference(unit_resolution,[status(thm)],[1348, 1190, 561, 560, 36])).
% 0.82/0.98 tff(1350,plain,
% 0.82/0.98 (~hskp5),
% 0.82/0.98 inference(unit_resolution,[status(thm)],[584, 1349])).
% 0.82/0.98 tff(1351,plain,
% 0.82/0.98 (hskp21),
% 0.82/0.98 inference(unit_resolution,[status(thm)],[80, 1350, 36])).
% 0.82/0.98 tff(1352,plain,
% 0.82/0.98 (~c3_1(a257)),
% 0.82/0.98 inference(unit_resolution,[status(thm)],[92, 1351])).
% 0.82/0.98 tff(1353,plain,
% 0.82/0.98 (~c1_1(a257)),
% 0.82/0.98 inference(unit_resolution,[status(thm)],[86, 1351])).
% 0.82/0.98 tff(1354,plain,
% 0.82/0.98 (c2_1(a257)),
% 0.82/0.98 inference(unit_resolution,[status(thm)],[100, 1351])).
% 0.82/0.98 tff(1355,plain,
% 0.82/0.98 (c2_1(a225)),
% 0.82/0.98 inference(unit_resolution,[status(thm)],[1289, 1354, 1276, 1275, 1353, 1352, 1162])).
% 0.82/0.98 tff(1356,plain,
% 0.82/0.98 (~hskp6),
% 0.82/0.98 inference(unit_resolution,[status(thm)],[551, 1190])).
% 0.82/0.98 tff(1357,plain,
% 0.82/0.98 (c2_1(a195)),
% 0.82/0.98 inference(unit_resolution,[status(thm)],[779, 1356, 1190])).
% 0.82/0.98 tff(1358,plain,
% 0.82/0.98 (hskp19),
% 0.82/0.98 inference(unit_resolution,[status(thm)],[1301, 1357, 561])).
% 0.82/0.98 tff(1359,plain,
% 0.82/0.98 (~c0_1(a225)),
% 0.82/0.98 inference(unit_resolution,[status(thm)],[232, 1358])).
% 0.82/0.98 tff(1360,plain,
% 0.82/0.98 (c3_1(a225)),
% 0.82/0.98 inference(unit_resolution,[status(thm)],[226, 1358])).
% 0.82/0.98 tff(1361,plain,
% 0.82/0.98 (~hskp7),
% 0.82/0.98 inference(unit_resolution,[status(thm)],[1339, 1190, 561, 560, 1162])).
% 0.82/0.98 tff(1362,plain,
% 0.82/0.98 ($false),
% 0.82/0.98 inference(unit_resolution,[status(thm)],[1346, 148, 1361, 1105, 1121, 1113, 1360, 1359, 1300, 1355])).
% 0.82/0.98 tff(1363,plain,(c1_1(a195) | hskp15 | c3_1(a195)), inference(lemma,lemma(discharge,[]))).
% 0.82/0.98 tff(1364,plain,
% 0.82/0.98 (c1_1(a195)),
% 0.82/0.98 inference(unit_resolution,[status(thm)],[1363, 560, 36])).
% 0.82/0.98 tff(1365,plain,
% 0.82/0.98 (c0_1(a194) | c3_1(a194)),
% 0.82/0.98 inference(unit_resolution,[status(thm)],[1206, 148, 944, 11, 530])).
% 0.82/0.98 tff(1366,plain,
% 0.82/0.98 (c3_1(a194)),
% 0.82/0.98 inference(unit_resolution,[status(thm)],[1365, 1192])).
% 0.82/0.98 tff(1367,plain,
% 0.82/0.98 (c2_1(a195)),
% 0.82/0.98 inference(unit_resolution,[status(thm)],[779, 771, 944])).
% 0.82/0.98 tff(1368,plain,
% 0.82/0.98 (hskp5),
% 0.82/0.98 inference(unit_resolution,[status(thm)],[929, 1367, 943, 771])).
% 0.82/0.98 tff(1369,plain,
% 0.82/0.98 (~c2_1(a194)),
% 0.82/0.98 inference(unit_resolution,[status(thm)],[584, 1368])).
% 0.82/0.98 tff(1370,plain,
% 0.82/0.98 (~c1_1(a194)),
% 0.82/0.98 inference(unit_resolution,[status(thm)],[590, 1368])).
% 0.82/0.98 tff(1371,plain,
% 0.82/0.98 (c0_1(a194)),
% 0.82/0.98 inference(unit_resolution,[status(thm)],[598, 1368])).
% 0.82/0.98 tff(1372,plain,
% 0.82/0.98 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp2 | c0_1(a195) | (~c1_1(a195)) | c1_1(a194) | c2_1(a194) | (~ndr1_0) | (~c0_1(a194)) | (~c2_1(a195)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp2 | c0_1(a195) | (~c1_1(a195)) | c1_1(a194) | c2_1(a194) | (~ndr1_0) | (~c0_1(a194)) | (~c2_1(a195)))),
% 0.82/0.98 inference(rewrite,[status(thm)],[])).
% 0.82/0.98 tff(1373,plain,
% 0.82/0.98 ((hskp2 | (~ndr1_0) | c1_1(a194) | c2_1(a194) | (~c0_1(a194)) | c0_1(a195) | (~c1_1(a195)) | (~c2_1(a195))) <=> (hskp2 | c0_1(a195) | (~c1_1(a195)) | c1_1(a194) | c2_1(a194) | (~ndr1_0) | (~c0_1(a194)) | (~c2_1(a195)))),
% 0.82/0.98 inference(rewrite,[status(thm)],[])).
% 0.82/0.98 tff(1374,plain,
% 0.82/0.98 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp2 | (~ndr1_0) | c1_1(a194) | c2_1(a194) | (~c0_1(a194)) | c0_1(a195) | (~c1_1(a195)) | (~c2_1(a195)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp2 | c0_1(a195) | (~c1_1(a195)) | c1_1(a194) | c2_1(a194) | (~ndr1_0) | (~c0_1(a194)) | (~c2_1(a195))))),
% 0.82/0.98 inference(monotonicity,[status(thm)],[1373])).
% 0.82/0.98 tff(1375,plain,
% 0.82/0.98 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp2 | (~ndr1_0) | c1_1(a194) | c2_1(a194) | (~c0_1(a194)) | c0_1(a195) | (~c1_1(a195)) | (~c2_1(a195)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp2 | c0_1(a195) | (~c1_1(a195)) | c1_1(a194) | c2_1(a194) | (~ndr1_0) | (~c0_1(a194)) | (~c2_1(a195)))),
% 0.82/0.98 inference(transitivity,[status(thm)],[1374, 1372])).
% 0.82/0.98 tff(1376,plain,
% 0.82/0.98 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp2 | (~ndr1_0) | c1_1(a194) | c2_1(a194) | (~c0_1(a194)) | c0_1(a195) | (~c1_1(a195)) | (~c2_1(a195)))),
% 0.82/0.98 inference(quant_inst,[status(thm)],[])).
% 0.82/0.98 tff(1377,plain,
% 0.82/0.98 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp2 | c0_1(a195) | (~c1_1(a195)) | c1_1(a194) | c2_1(a194) | (~ndr1_0) | (~c0_1(a194)) | (~c2_1(a195))),
% 0.82/0.98 inference(modus_ponens,[status(thm)],[1376, 1375])).
% 0.82/0.98 tff(1378,plain,
% 0.82/0.98 ($false),
% 0.82/0.98 inference(unit_resolution,[status(thm)],[1377, 148, 14, 771, 1371, 943, 1370, 1369, 25, 1367])).
% 0.82/0.98 tff(1379,plain,(c0_1(a195) | hskp2 | (~c1_1(a195)) | c3_1(a195)), inference(lemma,lemma(discharge,[]))).
% 0.82/0.98 tff(1380,plain,
% 0.82/0.98 (c0_1(a195)),
% 0.82/0.98 inference(unit_resolution,[status(thm)],[1379, 943, 14, 560])).
% 0.82/0.98 tff(1381,plain,
% 0.82/0.98 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp2 | c0_1(a194) | (~c1_1(a195)) | c3_1(a195) | c1_1(a194) | (~ndr1_0) | (~c3_1(a194)) | (~c0_1(a195)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp2 | c0_1(a194) | (~c1_1(a195)) | c3_1(a195) | c1_1(a194) | (~ndr1_0) | (~c3_1(a194)) | (~c0_1(a195)))),
% 0.82/0.98 inference(rewrite,[status(thm)],[])).
% 0.82/0.98 tff(1382,plain,
% 0.82/0.98 ((hskp2 | (~ndr1_0) | c3_1(a195) | (~c1_1(a195)) | (~c0_1(a195)) | c1_1(a194) | c0_1(a194) | (~c3_1(a194))) <=> (hskp2 | c0_1(a194) | (~c1_1(a195)) | c3_1(a195) | c1_1(a194) | (~ndr1_0) | (~c3_1(a194)) | (~c0_1(a195)))),
% 0.82/0.98 inference(rewrite,[status(thm)],[])).
% 0.82/0.98 tff(1383,plain,
% 0.82/0.98 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp2 | (~ndr1_0) | c3_1(a195) | (~c1_1(a195)) | (~c0_1(a195)) | c1_1(a194) | c0_1(a194) | (~c3_1(a194)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp2 | c0_1(a194) | (~c1_1(a195)) | c3_1(a195) | c1_1(a194) | (~ndr1_0) | (~c3_1(a194)) | (~c0_1(a195))))),
% 0.82/0.98 inference(monotonicity,[status(thm)],[1382])).
% 0.82/0.98 tff(1384,plain,
% 0.82/0.98 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp2 | (~ndr1_0) | c3_1(a195) | (~c1_1(a195)) | (~c0_1(a195)) | c1_1(a194) | c0_1(a194) | (~c3_1(a194)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp2 | c0_1(a194) | (~c1_1(a195)) | c3_1(a195) | c1_1(a194) | (~ndr1_0) | (~c3_1(a194)) | (~c0_1(a195)))),
% 0.82/0.98 inference(transitivity,[status(thm)],[1383, 1381])).
% 0.82/0.98 tff(1385,plain,
% 0.82/0.98 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp2 | (~ndr1_0) | c3_1(a195) | (~c1_1(a195)) | (~c0_1(a195)) | c1_1(a194) | c0_1(a194) | (~c3_1(a194)))),
% 0.82/0.98 inference(quant_inst,[status(thm)],[])).
% 0.82/0.98 tff(1386,plain,
% 0.82/0.98 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp2 | c0_1(a194) | (~c1_1(a195)) | c3_1(a195) | c1_1(a194) | (~ndr1_0) | (~c3_1(a194)) | (~c0_1(a195))),
% 0.82/0.98 inference(modus_ponens,[status(thm)],[1385, 1384])).
% 0.82/0.98 tff(1387,plain,
% 0.82/0.98 (c0_1(a194) | (~c3_1(a194))),
% 0.82/0.98 inference(unit_resolution,[status(thm)],[1386, 148, 14, 1380, 943, 560, 12, 1151])).
% 0.82/0.98 tff(1388,plain,
% 0.82/0.98 ($false),
% 0.82/0.98 inference(unit_resolution,[status(thm)],[1387, 1366, 1192])).
% 0.82/0.98 tff(1389,plain,(c0_1(a194) | hskp2 | (~c1_1(a195)) | c3_1(a195) | c1_1(a194) | c2_1(a194)), inference(lemma,lemma(discharge,[]))).
% 0.82/0.98 tff(1390,plain,
% 0.82/0.98 (c0_1(a194)),
% 0.82/0.98 inference(unit_resolution,[status(thm)],[1389, 12, 943, 560, 14, 11])).
% 0.82/0.98 tff(1391,assumption,(~c3_1(a194)), introduced(assumption)).
% 0.82/0.98 tff(1392,plain,
% 0.82/0.98 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | (c1_1(a194) | c2_1(a194) | (~ndr1_0) | (~c2_1(a230)) | (~c0_1(a230)) | (~c1_1(a230)) | c3_1(a194) | (~c0_1(a194)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | c1_1(a194) | c2_1(a194) | (~ndr1_0) | (~c2_1(a230)) | (~c0_1(a230)) | (~c1_1(a230)) | c3_1(a194) | (~c0_1(a194)))),
% 0.82/0.98 inference(rewrite,[status(thm)],[])).
% 0.82/0.99 tff(1393,plain,
% 0.82/0.99 (((~ndr1_0) | (~c1_1(a230)) | (~c2_1(a230)) | (~c0_1(a230)) | c3_1(a194) | c2_1(a194) | (~c0_1(a194)) | c2_1(a194) | c1_1(a194) | (~c0_1(a194))) <=> (c1_1(a194) | c2_1(a194) | (~ndr1_0) | (~c2_1(a230)) | (~c0_1(a230)) | (~c1_1(a230)) | c3_1(a194) | (~c0_1(a194)))),
% 0.82/0.99 inference(rewrite,[status(thm)],[])).
% 0.82/0.99 tff(1394,plain,
% 0.82/0.99 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c1_1(a230)) | (~c2_1(a230)) | (~c0_1(a230)) | c3_1(a194) | c2_1(a194) | (~c0_1(a194)) | c2_1(a194) | c1_1(a194) | (~c0_1(a194)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | (c1_1(a194) | c2_1(a194) | (~ndr1_0) | (~c2_1(a230)) | (~c0_1(a230)) | (~c1_1(a230)) | c3_1(a194) | (~c0_1(a194))))),
% 0.82/0.99 inference(monotonicity,[status(thm)],[1393])).
% 0.82/0.99 tff(1395,plain,
% 0.82/0.99 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c1_1(a230)) | (~c2_1(a230)) | (~c0_1(a230)) | c3_1(a194) | c2_1(a194) | (~c0_1(a194)) | c2_1(a194) | c1_1(a194) | (~c0_1(a194)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | c1_1(a194) | c2_1(a194) | (~ndr1_0) | (~c2_1(a230)) | (~c0_1(a230)) | (~c1_1(a230)) | c3_1(a194) | (~c0_1(a194)))),
% 0.82/0.99 inference(transitivity,[status(thm)],[1394, 1392])).
% 0.82/0.99 tff(1396,plain,
% 0.82/0.99 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c1_1(a230)) | (~c2_1(a230)) | (~c0_1(a230)) | c3_1(a194) | c2_1(a194) | (~c0_1(a194)) | c2_1(a194) | c1_1(a194) | (~c0_1(a194)))),
% 0.82/0.99 inference(quant_inst,[status(thm)],[])).
% 0.82/0.99 tff(1397,plain,
% 0.82/0.99 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | c1_1(a194) | c2_1(a194) | (~ndr1_0) | (~c2_1(a230)) | (~c0_1(a230)) | (~c1_1(a230)) | c3_1(a194) | (~c0_1(a194))),
% 0.82/0.99 inference(modus_ponens,[status(thm)],[1396, 1395])).
% 0.82/0.99 tff(1398,plain,
% 0.82/0.99 ($false),
% 0.82/0.99 inference(unit_resolution,[status(thm)],[1397, 148, 1133, 1132, 1181, 673, 12, 11, 849, 1391])).
% 0.82/0.99 tff(1399,plain,(c3_1(a194) | (~c0_1(a230)) | (~c1_1(a230)) | (~c2_1(a230)) | (~c0_1(a194)) | c1_1(a194) | c2_1(a194)), inference(lemma,lemma(discharge,[]))).
% 0.82/0.99 tff(1400,plain,
% 0.82/0.99 (c3_1(a194)),
% 0.82/0.99 inference(unit_resolution,[status(thm)],[1399, 1390, 1132, 1181, 1133, 12, 11])).
% 0.82/0.99 tff(1401,plain,
% 0.82/0.99 (^[V: $i, U: $i] : refl((hskp13 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V))) <=> (hskp13 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V))))),
% 0.82/0.99 inference(bind,[status(th)],[])).
% 0.82/0.99 tff(1402,plain,
% 0.82/0.99 (![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))),
% 0.82/0.99 inference(quant_intro,[status(thm)],[1401])).
% 0.82/0.99 tff(1403,plain,
% 0.82/0.99 (![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))),
% 0.82/0.99 inference(rewrite,[status(thm)],[])).
% 0.82/0.99 tff(1404,plain,
% 0.82/0.99 (^[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)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c1_1(V)) | c2_1(V)) | hskp13) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V))) | hskp13))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V))) | hskp13) <=> (hskp13 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c1_1(V)) | c2_1(V)) | hskp13) <=> (hskp13 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))))),
% 0.82/0.99 inference(bind,[status(th)],[])).
% 0.82/0.99 tff(1405,plain,
% 0.82/0.99 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c1_1(V)) | c2_1(V)) | hskp13) <=> ![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))),
% 0.82/0.99 inference(quant_intro,[status(thm)],[1404])).
% 0.82/0.99 tff(1406,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c1_1(V)) | c2_1(V)) | hskp13)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause141')).
% 0.82/0.99 tff(1407,plain,
% 0.82/0.99 (![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))),
% 0.82/0.99 inference(modus_ponens,[status(thm)],[1406, 1405])).
% 0.82/0.99 tff(1408,plain,
% 0.82/0.99 (![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))),
% 0.82/0.99 inference(modus_ponens,[status(thm)],[1407, 1403])).
% 0.82/0.99 tff(1409,plain,(
% 0.82/0.99 ![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))),
% 0.82/0.99 inference(skolemize,[status(sab)],[1408])).
% 0.82/0.99 tff(1410,plain,
% 0.82/0.99 (![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))),
% 0.82/0.99 inference(modus_ponens,[status(thm)],[1409, 1402])).
% 0.82/0.99 tff(1411,plain,
% 0.82/0.99 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp13 | (~c1_1(a195)) | c3_1(a195) | c1_1(a194) | c2_1(a194) | (~ndr1_0) | (~c3_1(a194)) | (~c0_1(a195)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | hskp13 | (~c1_1(a195)) | c3_1(a195) | c1_1(a194) | c2_1(a194) | (~ndr1_0) | (~c3_1(a194)) | (~c0_1(a195)))),
% 0.82/0.99 inference(rewrite,[status(thm)],[])).
% 0.82/0.99 tff(1412,plain,
% 0.82/0.99 ((hskp13 | (~ndr1_0) | c3_1(a195) | (~c1_1(a195)) | (~c0_1(a195)) | c1_1(a194) | c2_1(a194) | (~c3_1(a194))) <=> (hskp13 | (~c1_1(a195)) | c3_1(a195) | c1_1(a194) | c2_1(a194) | (~ndr1_0) | (~c3_1(a194)) | (~c0_1(a195)))),
% 0.82/0.99 inference(rewrite,[status(thm)],[])).
% 0.82/0.99 tff(1413,plain,
% 0.82/0.99 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp13 | (~ndr1_0) | c3_1(a195) | (~c1_1(a195)) | (~c0_1(a195)) | c1_1(a194) | c2_1(a194) | (~c3_1(a194)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp13 | (~c1_1(a195)) | c3_1(a195) | c1_1(a194) | c2_1(a194) | (~ndr1_0) | (~c3_1(a194)) | (~c0_1(a195))))),
% 0.82/0.99 inference(monotonicity,[status(thm)],[1412])).
% 0.82/0.99 tff(1414,plain,
% 0.82/0.99 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp13 | (~ndr1_0) | c3_1(a195) | (~c1_1(a195)) | (~c0_1(a195)) | c1_1(a194) | c2_1(a194) | (~c3_1(a194)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | hskp13 | (~c1_1(a195)) | c3_1(a195) | c1_1(a194) | c2_1(a194) | (~ndr1_0) | (~c3_1(a194)) | (~c0_1(a195)))),
% 0.82/0.99 inference(transitivity,[status(thm)],[1413, 1411])).
% 0.82/0.99 tff(1415,plain,
% 0.82/0.99 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp13 | (~ndr1_0) | c3_1(a195) | (~c1_1(a195)) | (~c0_1(a195)) | c1_1(a194) | c2_1(a194) | (~c3_1(a194)))),
% 0.82/0.99 inference(quant_inst,[status(thm)],[])).
% 0.82/0.99 tff(1416,plain,
% 0.82/0.99 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | hskp13 | (~c1_1(a195)) | c3_1(a195) | c1_1(a194) | c2_1(a194) | (~ndr1_0) | (~c3_1(a194)) | (~c0_1(a195))),
% 0.82/0.99 inference(modus_ponens,[status(thm)],[1415, 1414])).
% 0.82/0.99 tff(1417,plain,
% 0.82/0.99 (hskp13),
% 0.82/0.99 inference(unit_resolution,[status(thm)],[1416, 148, 1380, 943, 560, 12, 11, 1410, 1400])).
% 0.82/0.99 tff(1418,plain,
% 0.82/0.99 (~c0_1(a209)),
% 0.82/0.99 inference(unit_resolution,[status(thm)],[387, 1417])).
% 0.82/0.99 tff(1419,plain,
% 0.82/0.99 (c1_1(a209)),
% 0.82/0.99 inference(unit_resolution,[status(thm)],[403, 1417])).
% 0.82/0.99 tff(1420,plain,
% 0.82/0.99 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp2 | c0_1(a209) | c1_1(a194) | c2_1(a194) | (~ndr1_0) | (~c0_1(a194)) | (~c1_1(a209)) | (~c2_1(a209)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp2 | c0_1(a209) | c1_1(a194) | c2_1(a194) | (~ndr1_0) | (~c0_1(a194)) | (~c1_1(a209)) | (~c2_1(a209)))),
% 0.82/0.99 inference(rewrite,[status(thm)],[])).
% 0.82/0.99 tff(1421,plain,
% 0.82/0.99 ((hskp2 | (~ndr1_0) | c1_1(a194) | c2_1(a194) | (~c0_1(a194)) | c0_1(a209) | (~c1_1(a209)) | (~c2_1(a209))) <=> (hskp2 | c0_1(a209) | c1_1(a194) | c2_1(a194) | (~ndr1_0) | (~c0_1(a194)) | (~c1_1(a209)) | (~c2_1(a209)))),
% 0.82/0.99 inference(rewrite,[status(thm)],[])).
% 0.82/0.99 tff(1422,plain,
% 0.82/0.99 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp2 | (~ndr1_0) | c1_1(a194) | c2_1(a194) | (~c0_1(a194)) | c0_1(a209) | (~c1_1(a209)) | (~c2_1(a209)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp2 | c0_1(a209) | c1_1(a194) | c2_1(a194) | (~ndr1_0) | (~c0_1(a194)) | (~c1_1(a209)) | (~c2_1(a209))))),
% 0.82/0.99 inference(monotonicity,[status(thm)],[1421])).
% 0.82/0.99 tff(1423,plain,
% 0.82/0.99 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp2 | (~ndr1_0) | c1_1(a194) | c2_1(a194) | (~c0_1(a194)) | c0_1(a209) | (~c1_1(a209)) | (~c2_1(a209)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp2 | c0_1(a209) | c1_1(a194) | c2_1(a194) | (~ndr1_0) | (~c0_1(a194)) | (~c1_1(a209)) | (~c2_1(a209)))),
% 0.82/0.99 inference(transitivity,[status(thm)],[1422, 1420])).
% 0.82/0.99 tff(1424,plain,
% 0.82/0.99 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp2 | (~ndr1_0) | c1_1(a194) | c2_1(a194) | (~c0_1(a194)) | c0_1(a209) | (~c1_1(a209)) | (~c2_1(a209)))),
% 0.82/0.99 inference(quant_inst,[status(thm)],[])).
% 0.82/0.99 tff(1425,plain,
% 0.82/0.99 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp2 | c0_1(a209) | c1_1(a194) | c2_1(a194) | (~ndr1_0) | (~c0_1(a194)) | (~c1_1(a209)) | (~c2_1(a209))),
% 0.82/0.99 inference(modus_ponens,[status(thm)],[1424, 1423])).
% 0.82/0.99 tff(1426,plain,
% 0.82/0.99 (~c2_1(a209)),
% 0.82/0.99 inference(unit_resolution,[status(thm)],[1425, 148, 14, 1419, 1390, 1418, 12, 11, 25])).
% 0.82/0.99 tff(1427,plain,
% 0.82/0.99 (c3_1(a209)),
% 0.82/0.99 inference(unit_resolution,[status(thm)],[395, 1417])).
% 0.82/0.99 tff(1428,assumption,(c3_1(a194)), introduced(assumption)).
% 0.82/0.99 tff(1429,assumption,(~hskp0), introduced(assumption)).
% 0.82/0.99 tff(1430,plain,
% 0.82/0.99 (hskp24),
% 0.82/0.99 inference(unit_resolution,[status(thm)],[1249, 148, 673, 12, 11, 326, 1428])).
% 0.82/0.99 tff(1431,plain,
% 0.82/0.99 (c3_1(a215)),
% 0.82/0.99 inference(unit_resolution,[status(thm)],[342, 1430])).
% 0.82/0.99 tff(1432,assumption,(~c2_1(a209)), introduced(assumption)).
% 0.82/0.99 tff(1433,plain,
% 0.82/0.99 (c1_1(a215)),
% 0.82/0.99 inference(unit_resolution,[status(thm)],[358, 1430])).
% 0.82/0.99 tff(1434,plain,
% 0.82/0.99 (c2_1(a215)),
% 0.82/0.99 inference(unit_resolution,[status(thm)],[350, 1430])).
% 0.82/0.99 tff(1435,assumption,(c2_1(a215)), introduced(assumption)).
% 0.82/0.99 tff(1436,assumption,(c1_1(a215)), introduced(assumption)).
% 0.82/0.99 tff(1437,assumption,(~hskp9), introduced(assumption)).
% 0.82/0.99 tff(1438,plain,
% 0.82/0.99 (^[V: $i, U: $i] : refl((hskp9 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V))) <=> (hskp9 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V))))),
% 0.82/0.99 inference(bind,[status(th)],[])).
% 0.82/0.99 tff(1439,plain,
% 0.82/0.99 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))),
% 0.82/0.99 inference(quant_intro,[status(thm)],[1438])).
% 0.82/0.99 tff(1440,plain,
% 0.82/0.99 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))),
% 0.82/0.99 inference(rewrite,[status(thm)],[])).
% 0.82/0.99 tff(1441,plain,
% 0.82/0.99 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) <=> ((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c1_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_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) | (~c3_1(U)) | (~c1_1(U)) | (~c0_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) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V))) | c2_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_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) | (~c3_1(U)) | (~c1_1(U)) | (~c0_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)) | hskp9) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V))) | hskp9))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V))) | hskp9) <=> (hskp9 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_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)) | hskp9) <=> (hskp9 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))))),
% 0.82/0.99 inference(bind,[status(th)],[])).
% 0.82/0.99 tff(1442,plain,
% 0.82/0.99 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) | c2_1(V)) | hskp9) <=> ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))),
% 0.82/0.99 inference(quant_intro,[status(thm)],[1441])).
% 0.82/0.99 tff(1443,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)) | hskp9)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause148')).
% 0.82/0.99 tff(1444,plain,
% 0.82/0.99 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))),
% 0.82/0.99 inference(modus_ponens,[status(thm)],[1443, 1442])).
% 0.82/0.99 tff(1445,plain,
% 0.82/0.99 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))),
% 0.82/0.99 inference(modus_ponens,[status(thm)],[1444, 1440])).
% 0.82/0.99 tff(1446,plain,(
% 0.82/0.99 ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))),
% 0.82/0.99 inference(skolemize,[status(sab)],[1445])).
% 0.82/0.99 tff(1447,plain,
% 0.82/0.99 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))),
% 0.82/0.99 inference(modus_ponens,[status(thm)],[1446, 1439])).
% 0.82/0.99 tff(1448,assumption,(c3_1(a215)), introduced(assumption)).
% 0.82/0.99 tff(1449,plain,
% 0.82/0.99 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp9 | c1_1(a194) | c2_1(a194) | (~ndr1_0) | (~c0_1(a194)) | (~c0_1(a215)) | (~c1_1(a215)) | (~c3_1(a215)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | hskp9 | c1_1(a194) | c2_1(a194) | (~ndr1_0) | (~c0_1(a194)) | (~c0_1(a215)) | (~c1_1(a215)) | (~c3_1(a215)))),
% 0.82/0.99 inference(rewrite,[status(thm)],[])).
% 0.82/0.99 tff(1450,plain,
% 0.82/0.99 ((hskp9 | (~ndr1_0) | (~c3_1(a215)) | (~c1_1(a215)) | (~c0_1(a215)) | c1_1(a194) | c2_1(a194) | (~c0_1(a194))) <=> (hskp9 | c1_1(a194) | c2_1(a194) | (~ndr1_0) | (~c0_1(a194)) | (~c0_1(a215)) | (~c1_1(a215)) | (~c3_1(a215)))),
% 0.82/0.99 inference(rewrite,[status(thm)],[])).
% 0.82/0.99 tff(1451,plain,
% 0.82/0.99 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp9 | (~ndr1_0) | (~c3_1(a215)) | (~c1_1(a215)) | (~c0_1(a215)) | c1_1(a194) | c2_1(a194) | (~c0_1(a194)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp9 | c1_1(a194) | c2_1(a194) | (~ndr1_0) | (~c0_1(a194)) | (~c0_1(a215)) | (~c1_1(a215)) | (~c3_1(a215))))),
% 0.82/0.99 inference(monotonicity,[status(thm)],[1450])).
% 0.82/0.99 tff(1452,plain,
% 0.82/0.99 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp9 | (~ndr1_0) | (~c3_1(a215)) | (~c1_1(a215)) | (~c0_1(a215)) | c1_1(a194) | c2_1(a194) | (~c0_1(a194)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | hskp9 | c1_1(a194) | c2_1(a194) | (~ndr1_0) | (~c0_1(a194)) | (~c0_1(a215)) | (~c1_1(a215)) | (~c3_1(a215)))),
% 0.82/0.99 inference(transitivity,[status(thm)],[1451, 1449])).
% 0.82/0.99 tff(1453,plain,
% 0.82/0.99 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp9 | (~ndr1_0) | (~c3_1(a215)) | (~c1_1(a215)) | (~c0_1(a215)) | c1_1(a194) | c2_1(a194) | (~c0_1(a194)))),
% 0.82/0.99 inference(quant_inst,[status(thm)],[])).
% 0.82/0.99 tff(1454,plain,
% 0.82/0.99 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | hskp9 | c1_1(a194) | c2_1(a194) | (~ndr1_0) | (~c0_1(a194)) | (~c0_1(a215)) | (~c1_1(a215)) | (~c3_1(a215))),
% 0.82/0.99 inference(modus_ponens,[status(thm)],[1453, 1452])).
% 0.82/0.99 tff(1455,plain,
% 0.82/0.99 (hskp9 | (~c0_1(a215))),
% 0.82/0.99 inference(unit_resolution,[status(thm)],[1454, 148, 1436, 1448, 673, 12, 11, 1447])).
% 0.82/0.99 tff(1456,plain,
% 0.82/0.99 (~c0_1(a215)),
% 0.82/0.99 inference(unit_resolution,[status(thm)],[1455, 1437])).
% 0.82/0.99 tff(1457,plain,
% 0.82/0.99 (^[U: $i] : refl((hskp9 | hskp8 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U))) <=> (hskp9 | hskp8 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U))))),
% 0.82/0.99 inference(bind,[status(th)],[])).
% 0.82/0.99 tff(1458,plain,
% 0.82/0.99 (![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U))) <=> ![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))),
% 0.82/0.99 inference(quant_intro,[status(thm)],[1457])).
% 0.82/0.99 tff(1459,plain,
% 0.82/0.99 (![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U))) <=> ![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))),
% 0.82/0.99 inference(rewrite,[status(thm)],[])).
% 0.82/0.99 tff(1460,plain,
% 0.82/0.99 (^[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)) | hskp8) <=> (((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U))) | hskp8))), rewrite((((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U))) | hskp8) <=> (hskp8 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))), ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp8) <=> (hskp8 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U))))), (((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp8) | hskp9) <=> ((hskp8 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U))) | hskp9))), rewrite(((hskp8 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U))) | hskp9) <=> (hskp9 | hskp8 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))), (((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp8) | hskp9) <=> (hskp9 | hskp8 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))))),
% 0.82/0.99 inference(bind,[status(th)],[])).
% 0.82/0.99 tff(1461,plain,
% 0.82/0.99 (![U: $i] : ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp8) | hskp9) <=> ![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))),
% 0.82/0.99 inference(quant_intro,[status(thm)],[1460])).
% 0.82/0.99 tff(1462,axiom,(![U: $i] : ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp8) | hskp9)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause115')).
% 0.82/0.99 tff(1463,plain,
% 0.82/0.99 (![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))),
% 0.82/0.99 inference(modus_ponens,[status(thm)],[1462, 1461])).
% 0.82/0.99 tff(1464,plain,
% 0.82/0.99 (![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))),
% 0.82/0.99 inference(modus_ponens,[status(thm)],[1463, 1459])).
% 0.82/0.99 tff(1465,plain,(
% 0.82/0.99 ![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))),
% 0.82/0.99 inference(skolemize,[status(sab)],[1464])).
% 0.82/0.99 tff(1466,plain,
% 0.82/0.99 (![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))),
% 0.82/0.99 inference(modus_ponens,[status(thm)],[1465, 1458])).
% 0.82/0.99 tff(1467,plain,
% 0.82/0.99 (((~![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp9 | hskp8 | c0_1(a209) | (~ndr1_0) | (~c1_1(a209)) | c2_1(a209))) <=> ((~![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | hskp9 | hskp8 | c0_1(a209) | (~ndr1_0) | (~c1_1(a209)) | c2_1(a209))),
% 0.82/0.99 inference(rewrite,[status(thm)],[])).
% 0.82/0.99 tff(1468,plain,
% 0.82/0.99 ((hskp9 | hskp8 | (~ndr1_0) | c0_1(a209) | c2_1(a209) | (~c1_1(a209))) <=> (hskp9 | hskp8 | c0_1(a209) | (~ndr1_0) | (~c1_1(a209)) | c2_1(a209))),
% 0.82/0.99 inference(rewrite,[status(thm)],[])).
% 0.82/0.99 tff(1469,plain,
% 0.82/0.99 (((~![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp9 | hskp8 | (~ndr1_0) | c0_1(a209) | c2_1(a209) | (~c1_1(a209)))) <=> ((~![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp9 | hskp8 | c0_1(a209) | (~ndr1_0) | (~c1_1(a209)) | c2_1(a209)))),
% 0.82/0.99 inference(monotonicity,[status(thm)],[1468])).
% 0.82/0.99 tff(1470,plain,
% 0.82/0.99 (((~![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp9 | hskp8 | (~ndr1_0) | c0_1(a209) | c2_1(a209) | (~c1_1(a209)))) <=> ((~![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | hskp9 | hskp8 | c0_1(a209) | (~ndr1_0) | (~c1_1(a209)) | c2_1(a209))),
% 0.82/0.99 inference(transitivity,[status(thm)],[1469, 1467])).
% 0.82/0.99 tff(1471,plain,
% 0.82/0.99 ((~![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp9 | hskp8 | (~ndr1_0) | c0_1(a209) | c2_1(a209) | (~c1_1(a209)))),
% 0.82/0.99 inference(quant_inst,[status(thm)],[])).
% 0.82/0.99 tff(1472,plain,
% 0.82/0.99 ((~![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | hskp9 | hskp8 | c0_1(a209) | (~ndr1_0) | (~c1_1(a209)) | c2_1(a209)),
% 0.82/0.99 inference(modus_ponens,[status(thm)],[1471, 1470])).
% 0.82/0.99 tff(1473,plain,
% 0.82/0.99 (hskp9 | hskp8 | c2_1(a209)),
% 0.82/0.99 inference(unit_resolution,[status(thm)],[1472, 148, 424, 421, 1466])).
% 0.82/0.99 tff(1474,plain,
% 0.82/0.99 (hskp8),
% 0.82/0.99 inference(unit_resolution,[status(thm)],[1473, 1437, 1432])).
% 0.82/0.99 tff(1475,assumption,(~c0_1(a215)), introduced(assumption)).
% 0.82/0.99 tff(1476,plain,
% 0.82/0.99 (^[V: $i, U: $i] : refl((hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))) <=> (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))))),
% 0.82/0.99 inference(bind,[status(th)],[])).
% 0.82/0.99 tff(1477,plain,
% 0.82/0.99 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 0.82/0.99 inference(quant_intro,[status(thm)],[1476])).
% 0.82/0.99 tff(1478,plain,
% 0.82/0.99 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 0.82/0.99 inference(rewrite,[status(thm)],[])).
% 0.82/0.99 tff(1479,plain,
% 0.82/0.99 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V))))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V))))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V))))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c2_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c2_1(U)) | c0_1(V)) | hskp0) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))) | hskp0))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))) | hskp0) <=> (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c2_1(U)) | c0_1(V)) | hskp0) <=> (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))))),
% 0.82/0.99 inference(bind,[status(th)],[])).
% 0.82/0.99 tff(1480,plain,
% 0.82/0.99 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c2_1(U)) | c0_1(V)) | hskp0) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 0.82/0.99 inference(quant_intro,[status(thm)],[1479])).
% 0.82/0.99 tff(1481,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c2_1(U)) | c0_1(V)) | hskp0)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause145')).
% 0.82/0.99 tff(1482,plain,
% 0.82/0.99 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 0.82/0.99 inference(modus_ponens,[status(thm)],[1481, 1480])).
% 0.82/0.99 tff(1483,plain,
% 0.82/0.99 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 0.82/0.99 inference(modus_ponens,[status(thm)],[1482, 1478])).
% 0.82/0.99 tff(1484,plain,(
% 0.82/0.99 ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 0.82/0.99 inference(skolemize,[status(sab)],[1483])).
% 0.82/0.99 tff(1485,plain,
% 0.82/0.99 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 0.82/0.99 inference(modus_ponens,[status(thm)],[1484, 1477])).
% 0.82/0.99 tff(1486,assumption,(hskp8), introduced(assumption)).
% 0.82/0.99 tff(1487,plain,
% 0.82/0.99 (((~hskp8) | (~c2_1(a198))) <=> ((~hskp8) | (~c2_1(a198)))),
% 0.82/0.99 inference(rewrite,[status(thm)],[])).
% 0.82/0.99 tff(1488,plain,
% 0.82/0.99 (((~c2_1(a198)) | (~hskp8)) <=> ((~hskp8) | (~c2_1(a198)))),
% 0.82/0.99 inference(rewrite,[status(thm)],[])).
% 0.82/0.99 tff(1489,axiom,((~c2_1(a198)) | (~hskp8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause95')).
% 0.82/0.99 tff(1490,plain,
% 0.82/0.99 ((~hskp8) | (~c2_1(a198))),
% 0.82/0.99 inference(modus_ponens,[status(thm)],[1489, 1488])).
% 0.82/0.99 tff(1491,plain,
% 0.82/0.99 ((~hskp8) | (~c2_1(a198))),
% 0.82/0.99 inference(modus_ponens,[status(thm)],[1490, 1487])).
% 0.82/0.99 tff(1492,plain,
% 0.82/0.99 (~c2_1(a198)),
% 0.82/0.99 inference(unit_resolution,[status(thm)],[1491, 1486])).
% 0.82/0.99 tff(1493,plain,
% 0.82/0.99 (((~hskp8) | c3_1(a198)) <=> ((~hskp8) | c3_1(a198))),
% 0.82/0.99 inference(rewrite,[status(thm)],[])).
% 0.82/0.99 tff(1494,axiom,((~hskp8) | c3_1(a198)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause61')).
% 0.82/0.99 tff(1495,plain,
% 0.82/0.99 ((~hskp8) | c3_1(a198)),
% 0.82/0.99 inference(modus_ponens,[status(thm)],[1494, 1493])).
% 0.82/0.99 tff(1496,plain,
% 0.82/0.99 ((~hskp8) | c3_1(a198)),
% 0.82/0.99 inference(modus_ponens,[status(thm)],[1495, 1493])).
% 0.82/0.99 tff(1497,plain,
% 0.82/0.99 ((~hskp8) | c3_1(a198)),
% 0.82/0.99 inference(modus_ponens,[status(thm)],[1496, 1493])).
% 0.82/0.99 tff(1498,plain,
% 0.82/0.99 ((~hskp8) | c3_1(a198)),
% 0.82/0.99 inference(modus_ponens,[status(thm)],[1497, 1493])).
% 0.82/0.99 tff(1499,plain,
% 0.82/0.99 ((~hskp8) | c3_1(a198)),
% 0.82/0.99 inference(modus_ponens,[status(thm)],[1498, 1493])).
% 0.82/0.99 tff(1500,plain,
% 0.82/0.99 (c3_1(a198)),
% 0.82/0.99 inference(unit_resolution,[status(thm)],[1499, 1486])).
% 0.82/0.99 tff(1501,plain,
% 0.82/0.99 (((~hskp8) | c1_1(a198)) <=> ((~hskp8) | c1_1(a198))),
% 0.82/0.99 inference(rewrite,[status(thm)],[])).
% 0.82/0.99 tff(1502,axiom,((~hskp8) | c1_1(a198)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause60')).
% 0.82/0.99 tff(1503,plain,
% 0.82/0.99 ((~hskp8) | c1_1(a198)),
% 0.82/0.99 inference(modus_ponens,[status(thm)],[1502, 1501])).
% 0.82/0.99 tff(1504,plain,
% 0.82/0.99 ((~hskp8) | c1_1(a198)),
% 0.82/0.99 inference(modus_ponens,[status(thm)],[1503, 1501])).
% 0.82/0.99 tff(1505,plain,
% 0.82/0.99 ((~hskp8) | c1_1(a198)),
% 0.82/0.99 inference(modus_ponens,[status(thm)],[1504, 1501])).
% 0.82/0.99 tff(1506,plain,
% 0.82/0.99 ((~hskp8) | c1_1(a198)),
% 0.82/0.99 inference(modus_ponens,[status(thm)],[1505, 1501])).
% 0.82/0.99 tff(1507,plain,
% 0.82/0.99 ((~hskp8) | c1_1(a198)),
% 0.82/0.99 inference(modus_ponens,[status(thm)],[1506, 1501])).
% 0.82/0.99 tff(1508,plain,
% 0.82/0.99 (c1_1(a198)),
% 0.82/0.99 inference(unit_resolution,[status(thm)],[1507, 1486])).
% 0.82/0.99 tff(1509,plain,
% 0.82/0.99 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp0 | c2_1(a198) | (~ndr1_0) | (~c3_1(a198)) | (~c1_1(a198)) | (~c1_1(a215)) | (~c2_1(a215)) | c0_1(a215))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp0 | c2_1(a198) | (~ndr1_0) | (~c3_1(a198)) | (~c1_1(a198)) | (~c1_1(a215)) | (~c2_1(a215)) | c0_1(a215))),
% 0.82/0.99 inference(rewrite,[status(thm)],[])).
% 0.82/0.99 tff(1510,plain,
% 0.82/0.99 ((hskp0 | (~ndr1_0) | c2_1(a198) | (~c3_1(a198)) | (~c1_1(a198)) | c0_1(a215) | (~c1_1(a215)) | (~c2_1(a215))) <=> (hskp0 | c2_1(a198) | (~ndr1_0) | (~c3_1(a198)) | (~c1_1(a198)) | (~c1_1(a215)) | (~c2_1(a215)) | c0_1(a215))),
% 0.82/0.99 inference(rewrite,[status(thm)],[])).
% 0.82/0.99 tff(1511,plain,
% 0.82/0.99 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp0 | (~ndr1_0) | c2_1(a198) | (~c3_1(a198)) | (~c1_1(a198)) | c0_1(a215) | (~c1_1(a215)) | (~c2_1(a215)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp0 | c2_1(a198) | (~ndr1_0) | (~c3_1(a198)) | (~c1_1(a198)) | (~c1_1(a215)) | (~c2_1(a215)) | c0_1(a215)))),
% 0.82/0.99 inference(monotonicity,[status(thm)],[1510])).
% 0.82/0.99 tff(1512,plain,
% 0.82/0.99 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp0 | (~ndr1_0) | c2_1(a198) | (~c3_1(a198)) | (~c1_1(a198)) | c0_1(a215) | (~c1_1(a215)) | (~c2_1(a215)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp0 | c2_1(a198) | (~ndr1_0) | (~c3_1(a198)) | (~c1_1(a198)) | (~c1_1(a215)) | (~c2_1(a215)) | c0_1(a215))),
% 0.82/0.99 inference(transitivity,[status(thm)],[1511, 1509])).
% 0.82/0.99 tff(1513,plain,
% 0.82/0.99 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp0 | (~ndr1_0) | c2_1(a198) | (~c3_1(a198)) | (~c1_1(a198)) | c0_1(a215) | (~c1_1(a215)) | (~c2_1(a215)))),
% 0.82/0.99 inference(quant_inst,[status(thm)],[])).
% 0.82/0.99 tff(1514,plain,
% 0.82/0.99 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp0 | c2_1(a198) | (~ndr1_0) | (~c3_1(a198)) | (~c1_1(a198)) | (~c1_1(a215)) | (~c2_1(a215)) | c0_1(a215)),
% 0.82/0.99 inference(modus_ponens,[status(thm)],[1513, 1512])).
% 0.82/0.99 tff(1515,plain,
% 0.82/0.99 ($false),
% 0.82/0.99 inference(unit_resolution,[status(thm)],[1514, 148, 1429, 1436, 1435, 1508, 1500, 1492, 1485, 1475])).
% 0.82/0.99 tff(1516,plain,((~hskp8) | hskp0 | (~c1_1(a215)) | (~c2_1(a215)) | c0_1(a215)), inference(lemma,lemma(discharge,[]))).
% 0.82/0.99 tff(1517,plain,
% 0.82/0.99 ($false),
% 0.82/0.99 inference(unit_resolution,[status(thm)],[1516, 1474, 1456, 1436, 1435, 1429])).
% 0.82/0.99 tff(1518,plain,(hskp9 | (~c1_1(a215)) | (~c2_1(a215)) | hskp0 | c2_1(a209) | (~c1_1(a209)) | c0_1(a209) | (~c3_1(a215)) | (~c0_1(a194)) | c1_1(a194) | c2_1(a194)), inference(lemma,lemma(discharge,[]))).
% 0.82/0.99 tff(1519,plain,
% 0.82/0.99 (hskp9),
% 0.82/0.99 inference(unit_resolution,[status(thm)],[1518, 1429, 1434, 1433, 1432, 424, 421, 1431, 673, 12, 11])).
% 0.82/0.99 tff(1520,plain,
% 0.82/0.99 (~c0_1(a199)),
% 0.82/1.00 inference(unit_resolution,[status(thm)],[647, 1519])).
% 0.82/1.00 tff(1521,plain,
% 0.82/1.00 (~c1_1(a199)),
% 0.82/1.00 inference(unit_resolution,[status(thm)],[641, 1519])).
% 0.82/1.00 tff(1522,plain,
% 0.82/1.00 (c0_1(a199) | (~c2_1(a199))),
% 0.82/1.00 inference(unit_resolution,[status(thm)],[681, 148, 424, 423, 673, 421, 709, 12, 11, 65])).
% 0.82/1.00 tff(1523,plain,
% 0.82/1.00 (~c2_1(a199)),
% 0.82/1.00 inference(unit_resolution,[status(thm)],[1522, 710])).
% 0.82/1.00 tff(1524,plain,
% 0.82/1.00 (^[V: $i, U: $i] : refl((hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V)) <=> (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V)))),
% 0.82/1.00 inference(bind,[status(th)],[])).
% 0.82/1.00 tff(1525,plain,
% 0.82/1.00 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V)) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))),
% 0.82/1.00 inference(quant_intro,[status(thm)],[1524])).
% 0.82/1.00 tff(1526,plain,
% 0.82/1.00 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V)) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))),
% 0.82/1.00 inference(rewrite,[status(thm)],[])).
% 0.82/1.00 tff(1527,plain,
% 0.82/1.00 (^[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) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_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) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V)) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V)))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V)))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp0) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V)) | hskp0))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V)) | hskp0) <=> (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp0) <=> (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))))),
% 0.82/1.00 inference(bind,[status(th)],[])).
% 0.82/1.00 tff(1528,plain,
% 0.82/1.00 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp0) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))),
% 0.82/1.00 inference(quant_intro,[status(thm)],[1527])).
% 0.82/1.00 tff(1529,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp0)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause131')).
% 0.82/1.00 tff(1530,plain,
% 0.82/1.00 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))),
% 0.82/1.00 inference(modus_ponens,[status(thm)],[1529, 1528])).
% 0.82/1.00 tff(1531,plain,
% 0.82/1.00 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))),
% 0.82/1.00 inference(modus_ponens,[status(thm)],[1530, 1526])).
% 0.82/1.00 tff(1532,plain,(
% 0.82/1.00 ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))),
% 0.82/1.00 inference(skolemize,[status(sab)],[1531])).
% 0.82/1.00 tff(1533,plain,
% 0.82/1.00 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))),
% 0.82/1.00 inference(modus_ponens,[status(thm)],[1532, 1525])).
% 0.82/1.00 tff(1534,plain,
% 0.82/1.00 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | (hskp0 | c2_1(a199) | c0_1(a199) | c1_1(a199) | c2_1(a194) | (~ndr1_0) | (~c3_1(a194)) | (~c0_1(a194)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | hskp0 | c2_1(a199) | c0_1(a199) | c1_1(a199) | c2_1(a194) | (~ndr1_0) | (~c3_1(a194)) | (~c0_1(a194)))),
% 0.82/1.00 inference(rewrite,[status(thm)],[])).
% 0.82/1.00 tff(1535,plain,
% 0.82/1.00 ((hskp0 | (~ndr1_0) | c2_1(a194) | (~c3_1(a194)) | (~c0_1(a194)) | c1_1(a199) | c0_1(a199) | c2_1(a199)) <=> (hskp0 | c2_1(a199) | c0_1(a199) | c1_1(a199) | c2_1(a194) | (~ndr1_0) | (~c3_1(a194)) | (~c0_1(a194)))),
% 0.82/1.00 inference(rewrite,[status(thm)],[])).
% 0.82/1.00 tff(1536,plain,
% 0.82/1.00 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | (hskp0 | (~ndr1_0) | c2_1(a194) | (~c3_1(a194)) | (~c0_1(a194)) | c1_1(a199) | c0_1(a199) | c2_1(a199))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | (hskp0 | c2_1(a199) | c0_1(a199) | c1_1(a199) | c2_1(a194) | (~ndr1_0) | (~c3_1(a194)) | (~c0_1(a194))))),
% 0.82/1.00 inference(monotonicity,[status(thm)],[1535])).
% 0.82/1.00 tff(1537,plain,
% 0.82/1.00 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | (hskp0 | (~ndr1_0) | c2_1(a194) | (~c3_1(a194)) | (~c0_1(a194)) | c1_1(a199) | c0_1(a199) | c2_1(a199))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | hskp0 | c2_1(a199) | c0_1(a199) | c1_1(a199) | c2_1(a194) | (~ndr1_0) | (~c3_1(a194)) | (~c0_1(a194)))),
% 0.82/1.00 inference(transitivity,[status(thm)],[1536, 1534])).
% 0.82/1.00 tff(1538,plain,
% 0.82/1.00 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | (hskp0 | (~ndr1_0) | c2_1(a194) | (~c3_1(a194)) | (~c0_1(a194)) | c1_1(a199) | c0_1(a199) | c2_1(a199))),
% 0.82/1.00 inference(quant_inst,[status(thm)],[])).
% 0.82/1.00 tff(1539,plain,
% 0.82/1.00 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | hskp0 | c2_1(a199) | c0_1(a199) | c1_1(a199) | c2_1(a194) | (~ndr1_0) | (~c3_1(a194)) | (~c0_1(a194))),
% 0.82/1.00 inference(modus_ponens,[status(thm)],[1538, 1537])).
% 0.82/1.00 tff(1540,plain,
% 0.82/1.00 (c2_1(a199) | c0_1(a199)),
% 0.82/1.00 inference(unit_resolution,[status(thm)],[1539, 148, 1429, 673, 709, 11, 1533, 1428])).
% 0.82/1.00 tff(1541,plain,
% 0.82/1.00 ($false),
% 0.82/1.00 inference(unit_resolution,[status(thm)],[1540, 1523, 710])).
% 0.82/1.00 tff(1542,plain,(c0_1(a199) | hskp0 | (~c0_1(a194)) | c1_1(a199) | c2_1(a194) | (~c3_1(a194)) | (~c1_1(a209)) | (~c3_1(a209)) | c0_1(a209) | c1_1(a194)), inference(lemma,lemma(discharge,[]))).
% 0.82/1.00 tff(1543,plain,
% 0.82/1.00 ($false),
% 0.82/1.00 inference(unit_resolution,[status(thm)],[1542, 1521, 1520, 673, 1429, 11, 1428, 424, 423, 421, 12])).
% 0.82/1.00 tff(1544,plain,(hskp0 | (~c0_1(a194)) | c2_1(a194) | (~c3_1(a194)) | (~c1_1(a209)) | (~c3_1(a209)) | c0_1(a209) | c1_1(a194) | c2_1(a209)), inference(lemma,lemma(discharge,[]))).
% 0.82/1.00 tff(1545,plain,
% 0.82/1.00 (hskp0),
% 0.82/1.00 inference(unit_resolution,[status(thm)],[1544, 1390, 11, 1400, 1419, 1427, 1418, 12, 1426])).
% 0.82/1.00 tff(1546,plain,
% 0.82/1.00 (~c3_1(a188)),
% 0.82/1.00 inference(unit_resolution,[status(thm)],[605, 1545])).
% 0.82/1.00 tff(1547,plain,
% 0.82/1.00 (~c0_1(a188)),
% 0.82/1.00 inference(unit_resolution,[status(thm)],[617, 1545])).
% 0.82/1.00 tff(1548,plain,
% 0.82/1.00 (((~![U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp6 | c0_1(a188) | c3_1(a188) | (~ndr1_0) | c2_1(a188))) <=> ((~![U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | hskp6 | c0_1(a188) | c3_1(a188) | (~ndr1_0) | c2_1(a188))),
% 0.82/1.00 inference(rewrite,[status(thm)],[])).
% 0.82/1.00 tff(1549,plain,
% 0.82/1.00 ((hskp6 | (~ndr1_0) | c3_1(a188) | c0_1(a188) | c2_1(a188)) <=> (hskp6 | c0_1(a188) | c3_1(a188) | (~ndr1_0) | c2_1(a188))),
% 0.82/1.00 inference(rewrite,[status(thm)],[])).
% 0.82/1.00 tff(1550,plain,
% 0.82/1.00 (((~![U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp6 | (~ndr1_0) | c3_1(a188) | c0_1(a188) | c2_1(a188))) <=> ((~![U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp6 | c0_1(a188) | c3_1(a188) | (~ndr1_0) | c2_1(a188)))),
% 0.82/1.00 inference(monotonicity,[status(thm)],[1549])).
% 0.82/1.00 tff(1551,plain,
% 0.82/1.00 (((~![U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp6 | (~ndr1_0) | c3_1(a188) | c0_1(a188) | c2_1(a188))) <=> ((~![U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | hskp6 | c0_1(a188) | c3_1(a188) | (~ndr1_0) | c2_1(a188))),
% 0.82/1.00 inference(transitivity,[status(thm)],[1550, 1548])).
% 0.82/1.00 tff(1552,plain,
% 0.82/1.00 ((~![U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp6 | (~ndr1_0) | c3_1(a188) | c0_1(a188) | c2_1(a188))),
% 0.82/1.00 inference(quant_inst,[status(thm)],[])).
% 0.82/1.00 tff(1553,plain,
% 0.82/1.00 ((~![U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | hskp6 | c0_1(a188) | c3_1(a188) | (~ndr1_0) | c2_1(a188)),
% 0.82/1.00 inference(modus_ponens,[status(thm)],[1552, 1551])).
% 0.82/1.00 tff(1554,plain,
% 0.82/1.00 (c2_1(a188)),
% 0.82/1.00 inference(unit_resolution,[status(thm)],[1553, 148, 944, 1547, 1546, 530])).
% 0.82/1.00 tff(1555,plain,
% 0.82/1.00 (~c1_1(a188)),
% 0.82/1.00 inference(unit_resolution,[status(thm)],[611, 1545])).
% 0.82/1.00 tff(1556,plain,
% 0.82/1.00 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_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(a209) | c1_1(a194) | c2_1(a194) | c0_1(a188) | c1_1(a188) | (~ndr1_0) | (~c2_1(a188)) | (~c0_1(a194)) | (~c1_1(a209)) | (~c3_1(a209)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_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(a209) | c1_1(a194) | c2_1(a194) | c0_1(a188) | c1_1(a188) | (~ndr1_0) | (~c2_1(a188)) | (~c0_1(a194)) | (~c1_1(a209)) | (~c3_1(a209)))),
% 0.82/1.00 inference(rewrite,[status(thm)],[])).
% 0.82/1.00 tff(1557,plain,
% 0.82/1.00 (((~ndr1_0) | c1_1(a194) | c2_1(a194) | (~c0_1(a194)) | c0_1(a209) | (~c3_1(a209)) | (~c1_1(a209)) | c1_1(a188) | c0_1(a188) | (~c2_1(a188))) <=> (c0_1(a209) | c1_1(a194) | c2_1(a194) | c0_1(a188) | c1_1(a188) | (~ndr1_0) | (~c2_1(a188)) | (~c0_1(a194)) | (~c1_1(a209)) | (~c3_1(a209)))),
% 0.82/1.00 inference(rewrite,[status(thm)],[])).
% 0.82/1.00 tff(1558,plain,
% 0.82/1.00 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_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) | c1_1(a194) | c2_1(a194) | (~c0_1(a194)) | c0_1(a209) | (~c3_1(a209)) | (~c1_1(a209)) | c1_1(a188) | c0_1(a188) | (~c2_1(a188)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_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(a209) | c1_1(a194) | c2_1(a194) | c0_1(a188) | c1_1(a188) | (~ndr1_0) | (~c2_1(a188)) | (~c0_1(a194)) | (~c1_1(a209)) | (~c3_1(a209))))),
% 0.82/1.00 inference(monotonicity,[status(thm)],[1557])).
% 0.82/1.00 tff(1559,plain,
% 0.82/1.00 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_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) | c1_1(a194) | c2_1(a194) | (~c0_1(a194)) | c0_1(a209) | (~c3_1(a209)) | (~c1_1(a209)) | c1_1(a188) | c0_1(a188) | (~c2_1(a188)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_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(a209) | c1_1(a194) | c2_1(a194) | c0_1(a188) | c1_1(a188) | (~ndr1_0) | (~c2_1(a188)) | (~c0_1(a194)) | (~c1_1(a209)) | (~c3_1(a209)))),
% 0.82/1.00 inference(transitivity,[status(thm)],[1558, 1556])).
% 0.82/1.00 tff(1560,plain,
% 0.82/1.00 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_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) | c1_1(a194) | c2_1(a194) | (~c0_1(a194)) | c0_1(a209) | (~c3_1(a209)) | (~c1_1(a209)) | c1_1(a188) | c0_1(a188) | (~c2_1(a188)))),
% 0.82/1.00 inference(quant_inst,[status(thm)],[])).
% 0.82/1.00 tff(1561,plain,
% 0.82/1.00 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a209) | c1_1(a194) | c2_1(a194) | c0_1(a188) | c1_1(a188) | (~ndr1_0) | (~c2_1(a188)) | (~c0_1(a194)) | (~c1_1(a209)) | (~c3_1(a209))),
% 0.82/1.00 inference(modus_ponens,[status(thm)],[1560, 1559])).
% 0.82/1.00 tff(1562,plain,
% 0.82/1.00 ($false),
% 0.82/1.00 inference(unit_resolution,[status(thm)],[1561, 148, 1419, 1427, 1390, 1418, 12, 11, 1547, 1555, 65, 1554])).
% 0.82/1.00 tff(1563,plain,(c1_1(a194) | c2_1(a194) | hskp2 | (~c1_1(a195)) | c3_1(a195) | (~c1_1(a230)) | (~c2_1(a230)) | (~c0_1(a230))), inference(lemma,lemma(discharge,[]))).
% 0.82/1.00 tff(1564,plain,
% 0.82/1.00 (c1_1(a194)),
% 0.82/1.00 inference(unit_resolution,[status(thm)],[1563, 11, 1096, 1364, 560, 1121, 1113, 1105])).
% 0.82/1.00 tff(1565,plain,
% 0.82/1.00 (~hskp5),
% 0.82/1.00 inference(unit_resolution,[status(thm)],[590, 1564])).
% 0.82/1.00 tff(1566,plain,
% 0.82/1.00 (hskp21),
% 0.82/1.00 inference(unit_resolution,[status(thm)],[80, 1565, 36])).
% 0.82/1.00 tff(1567,plain,
% 0.82/1.00 (~c3_1(a257)),
% 0.82/1.00 inference(unit_resolution,[status(thm)],[92, 1566])).
% 0.82/1.00 tff(1568,plain,
% 0.82/1.00 (~c1_1(a257)),
% 0.82/1.00 inference(unit_resolution,[status(thm)],[86, 1566])).
% 0.82/1.00 tff(1569,plain,
% 0.82/1.00 (c2_1(a257)),
% 0.82/1.00 inference(unit_resolution,[status(thm)],[100, 1566])).
% 0.82/1.00 tff(1570,plain,
% 0.82/1.00 (~hskp6),
% 0.82/1.00 inference(unit_resolution,[status(thm)],[557, 1364])).
% 0.82/1.00 tff(1571,plain,
% 0.82/1.00 (c0_1(a195)),
% 0.82/1.00 inference(unit_resolution,[status(thm)],[1379, 1364, 1096, 560])).
% 0.82/1.00 tff(1572,assumption,(~c3_1(a225)), introduced(assumption)).
% 0.82/1.00 tff(1573,plain,
% 0.82/1.00 (((~![U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp6 | c3_1(a225) | c0_1(a225) | (~ndr1_0) | c2_1(a225))) <=> ((~![U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | hskp6 | c3_1(a225) | c0_1(a225) | (~ndr1_0) | c2_1(a225))),
% 0.82/1.00 inference(rewrite,[status(thm)],[])).
% 0.82/1.00 tff(1574,plain,
% 0.82/1.00 ((hskp6 | (~ndr1_0) | c3_1(a225) | c0_1(a225) | c2_1(a225)) <=> (hskp6 | c3_1(a225) | c0_1(a225) | (~ndr1_0) | c2_1(a225))),
% 0.82/1.00 inference(rewrite,[status(thm)],[])).
% 0.82/1.00 tff(1575,plain,
% 0.82/1.00 (((~![U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp6 | (~ndr1_0) | c3_1(a225) | c0_1(a225) | c2_1(a225))) <=> ((~![U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp6 | c3_1(a225) | c0_1(a225) | (~ndr1_0) | c2_1(a225)))),
% 0.82/1.00 inference(monotonicity,[status(thm)],[1574])).
% 0.82/1.00 tff(1576,plain,
% 0.82/1.00 (((~![U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp6 | (~ndr1_0) | c3_1(a225) | c0_1(a225) | c2_1(a225))) <=> ((~![U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | hskp6 | c3_1(a225) | c0_1(a225) | (~ndr1_0) | c2_1(a225))),
% 0.82/1.00 inference(transitivity,[status(thm)],[1575, 1573])).
% 0.82/1.00 tff(1577,plain,
% 0.82/1.00 ((~![U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp6 | (~ndr1_0) | c3_1(a225) | c0_1(a225) | c2_1(a225))),
% 0.82/1.00 inference(quant_inst,[status(thm)],[])).
% 0.82/1.00 tff(1578,plain,
% 0.82/1.00 ((~![U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | hskp6 | c3_1(a225) | c0_1(a225) | (~ndr1_0) | c2_1(a225)),
% 0.82/1.00 inference(modus_ponens,[status(thm)],[1577, 1576])).
% 0.82/1.00 tff(1579,plain,
% 0.82/1.00 (c3_1(a225) | c2_1(a225)),
% 0.82/1.00 inference(unit_resolution,[status(thm)],[1578, 148, 1191, 235, 530])).
% 0.82/1.00 tff(1580,plain,
% 0.82/1.00 (c2_1(a225)),
% 0.82/1.00 inference(unit_resolution,[status(thm)],[1579, 1572])).
% 0.82/1.00 tff(1581,plain,
% 0.82/1.00 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | c3_1(W)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | c3_1(W)))),
% 0.82/1.00 inference(bind,[status(th)],[])).
% 0.82/1.00 tff(1582,plain,
% 0.82/1.00 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | c3_1(W))),
% 0.82/1.00 inference(quant_intro,[status(thm)],[1581])).
% 0.82/1.00 tff(1583,plain,
% 0.82/1.00 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | c3_1(W))),
% 0.82/1.00 inference(rewrite,[status(thm)],[])).
% 0.82/1.00 tff(1584,plain,
% 0.82/1.00 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) <=> ((~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> (((~c1_1(U)) | (~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c1_1(U)) | (~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c2_1(W))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(W)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(W))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | c2_1(V)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(W))) | c2_1(V)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(W))) | c2_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V)) | (~c2_1(W)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | c2_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V)) | (~c2_1(W))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V)) | (~c2_1(W))) | c3_1(V)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V)) | (~c2_1(W))) | c3_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | (~c2_1(W)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | (~c2_1(W))))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | c2_1(V)) | c3_1(V)) | c0_1(W)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | (~c2_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | (~c2_1(W))) | c0_1(W)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | c2_1(V)) | c3_1(V)) | c0_1(W)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W))))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c3_1(W)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W))) | c3_1(W)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W))) | c3_1(W)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | c3_1(W))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c3_1(W)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | c3_1(W))))),
% 0.82/1.00 inference(bind,[status(th)],[])).
% 0.82/1.00 tff(1585,plain,
% 0.82/1.00 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | c3_1(W))),
% 0.82/1.00 inference(quant_intro,[status(thm)],[1584])).
% 0.82/1.00 tff(1586,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c3_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause158')).
% 0.82/1.00 tff(1587,plain,
% 0.82/1.00 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | c3_1(W))),
% 0.82/1.00 inference(modus_ponens,[status(thm)],[1586, 1585])).
% 0.82/1.00 tff(1588,plain,
% 0.82/1.00 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | c3_1(W))),
% 0.82/1.00 inference(modus_ponens,[status(thm)],[1587, 1583])).
% 0.82/1.00 tff(1589,plain,(
% 0.82/1.00 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | c3_1(W))),
% 0.82/1.00 inference(skolemize,[status(sab)],[1588])).
% 0.82/1.00 tff(1590,plain,
% 0.82/1.00 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | c3_1(W))),
% 0.82/1.00 inference(modus_ponens,[status(thm)],[1589, 1582])).
% 0.82/1.00 tff(1591,plain,
% 0.82/1.00 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | c3_1(W))) | (c3_1(a225) | c0_1(a225) | c3_1(a195) | (~ndr1_0) | (~c2_1(a230)) | (~c0_1(a230)) | (~c1_1(a230)) | c2_1(a195) | (~c0_1(a195)) | (~c2_1(a225)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | c3_1(W))) | c3_1(a225) | c0_1(a225) | c3_1(a195) | (~ndr1_0) | (~c2_1(a230)) | (~c0_1(a230)) | (~c1_1(a230)) | c2_1(a195) | (~c0_1(a195)) | (~c2_1(a225)))),
% 0.82/1.00 inference(rewrite,[status(thm)],[])).
% 0.82/1.00 tff(1592,plain,
% 0.82/1.00 (((~ndr1_0) | (~c1_1(a230)) | (~c2_1(a230)) | (~c0_1(a230)) | c3_1(a195) | c2_1(a195) | (~c0_1(a195)) | c0_1(a225) | (~c2_1(a225)) | c3_1(a225)) <=> (c3_1(a225) | c0_1(a225) | c3_1(a195) | (~ndr1_0) | (~c2_1(a230)) | (~c0_1(a230)) | (~c1_1(a230)) | c2_1(a195) | (~c0_1(a195)) | (~c2_1(a225)))),
% 0.82/1.00 inference(rewrite,[status(thm)],[])).
% 0.82/1.00 tff(1593,plain,
% 0.82/1.00 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | c3_1(W))) | ((~ndr1_0) | (~c1_1(a230)) | (~c2_1(a230)) | (~c0_1(a230)) | c3_1(a195) | c2_1(a195) | (~c0_1(a195)) | c0_1(a225) | (~c2_1(a225)) | c3_1(a225))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | c3_1(W))) | (c3_1(a225) | c0_1(a225) | c3_1(a195) | (~ndr1_0) | (~c2_1(a230)) | (~c0_1(a230)) | (~c1_1(a230)) | c2_1(a195) | (~c0_1(a195)) | (~c2_1(a225))))),
% 0.82/1.00 inference(monotonicity,[status(thm)],[1592])).
% 0.82/1.00 tff(1594,plain,
% 0.82/1.00 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | c3_1(W))) | ((~ndr1_0) | (~c1_1(a230)) | (~c2_1(a230)) | (~c0_1(a230)) | c3_1(a195) | c2_1(a195) | (~c0_1(a195)) | c0_1(a225) | (~c2_1(a225)) | c3_1(a225))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | c3_1(W))) | c3_1(a225) | c0_1(a225) | c3_1(a195) | (~ndr1_0) | (~c2_1(a230)) | (~c0_1(a230)) | (~c1_1(a230)) | c2_1(a195) | (~c0_1(a195)) | (~c2_1(a225)))),
% 0.82/1.00 inference(transitivity,[status(thm)],[1593, 1591])).
% 0.82/1.00 tff(1595,plain,
% 0.82/1.00 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | c3_1(W))) | ((~ndr1_0) | (~c1_1(a230)) | (~c2_1(a230)) | (~c0_1(a230)) | c3_1(a195) | c2_1(a195) | (~c0_1(a195)) | c0_1(a225) | (~c2_1(a225)) | c3_1(a225))),
% 0.82/1.00 inference(quant_inst,[status(thm)],[])).
% 0.82/1.00 tff(1596,plain,
% 0.82/1.00 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | c3_1(W))) | c3_1(a225) | c0_1(a225) | c3_1(a195) | (~ndr1_0) | (~c2_1(a230)) | (~c0_1(a230)) | (~c1_1(a230)) | c2_1(a195) | (~c0_1(a195)) | (~c2_1(a225))),
% 0.82/1.00 inference(modus_ponens,[status(thm)],[1595, 1594])).
% 0.82/1.00 tff(1597,plain,
% 0.82/1.00 (c3_1(a225) | c2_1(a195) | (~c2_1(a225))),
% 0.82/1.00 inference(unit_resolution,[status(thm)],[1596, 148, 1133, 1132, 1181, 562, 235, 560, 1590])).
% 0.82/1.00 tff(1598,plain,
% 0.82/1.00 (c2_1(a195)),
% 0.82/1.00 inference(unit_resolution,[status(thm)],[1597, 1580, 1572])).
% 0.82/1.00 tff(1599,plain,
% 0.82/1.00 (~hskp19),
% 0.82/1.00 inference(unit_resolution,[status(thm)],[226, 1572])).
% 0.82/1.00 tff(1600,plain,
% 0.82/1.00 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp19 | c3_1(a225) | c1_1(a225) | c3_1(a195) | (~ndr1_0) | (~c2_1(a195)) | (~c0_1(a195)) | (~c2_1(a225)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp19 | c3_1(a225) | c1_1(a225) | c3_1(a195) | (~ndr1_0) | (~c2_1(a195)) | (~c0_1(a195)) | (~c2_1(a225)))),
% 0.82/1.00 inference(rewrite,[status(thm)],[])).
% 0.82/1.00 tff(1601,plain,
% 0.82/1.00 ((hskp19 | (~ndr1_0) | c3_1(a195) | (~c2_1(a195)) | (~c0_1(a195)) | c3_1(a225) | c1_1(a225) | (~c2_1(a225))) <=> (hskp19 | c3_1(a225) | c1_1(a225) | c3_1(a195) | (~ndr1_0) | (~c2_1(a195)) | (~c0_1(a195)) | (~c2_1(a225)))),
% 0.82/1.00 inference(rewrite,[status(thm)],[])).
% 0.82/1.00 tff(1602,plain,
% 0.82/1.00 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp19 | (~ndr1_0) | c3_1(a195) | (~c2_1(a195)) | (~c0_1(a195)) | c3_1(a225) | c1_1(a225) | (~c2_1(a225)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp19 | c3_1(a225) | c1_1(a225) | c3_1(a195) | (~ndr1_0) | (~c2_1(a195)) | (~c0_1(a195)) | (~c2_1(a225))))),
% 0.82/1.00 inference(monotonicity,[status(thm)],[1601])).
% 0.82/1.00 tff(1603,plain,
% 0.82/1.00 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp19 | (~ndr1_0) | c3_1(a195) | (~c2_1(a195)) | (~c0_1(a195)) | c3_1(a225) | c1_1(a225) | (~c2_1(a225)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp19 | c3_1(a225) | c1_1(a225) | c3_1(a195) | (~ndr1_0) | (~c2_1(a195)) | (~c0_1(a195)) | (~c2_1(a225)))),
% 0.82/1.00 inference(transitivity,[status(thm)],[1602, 1600])).
% 0.82/1.00 tff(1604,plain,
% 0.82/1.00 ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp19 | (~ndr1_0) | c3_1(a195) | (~c2_1(a195)) | (~c0_1(a195)) | c3_1(a225) | c1_1(a225) | (~c2_1(a225)))),
% 0.82/1.00 inference(quant_inst,[status(thm)],[])).
% 0.82/1.00 tff(1605,plain,
% 0.82/1.00 ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp19 | c3_1(a225) | c1_1(a225) | c3_1(a195) | (~ndr1_0) | (~c2_1(a195)) | (~c0_1(a195)) | (~c2_1(a225))),
% 0.82/1.00 inference(modus_ponens,[status(thm)],[1604, 1603])).
% 0.82/1.00 tff(1606,plain,
% 0.82/1.00 (c1_1(a225)),
% 0.82/1.00 inference(unit_resolution,[status(thm)],[1605, 148, 1599, 1572, 562, 560, 211, 1580, 1598])).
% 0.82/1.00 tff(1607,plain,
% 0.82/1.00 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp5 | c3_1(a225) | c0_1(a225) | (~c1_1(a225)) | (~ndr1_0) | (~c2_1(a225)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp5 | c3_1(a225) | c0_1(a225) | (~c1_1(a225)) | (~ndr1_0) | (~c2_1(a225)))),
% 0.82/1.00 inference(rewrite,[status(thm)],[])).
% 0.82/1.00 tff(1608,plain,
% 0.82/1.00 ((hskp5 | (~ndr1_0) | c3_1(a225) | c0_1(a225) | (~c2_1(a225)) | c3_1(a225) | c0_1(a225) | (~c1_1(a225))) <=> (hskp5 | c3_1(a225) | c0_1(a225) | (~c1_1(a225)) | (~ndr1_0) | (~c2_1(a225)))),
% 0.82/1.00 inference(rewrite,[status(thm)],[])).
% 0.82/1.00 tff(1609,plain,
% 0.82/1.00 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp5 | (~ndr1_0) | c3_1(a225) | c0_1(a225) | (~c2_1(a225)) | c3_1(a225) | c0_1(a225) | (~c1_1(a225)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp5 | c3_1(a225) | c0_1(a225) | (~c1_1(a225)) | (~ndr1_0) | (~c2_1(a225))))),
% 0.82/1.00 inference(monotonicity,[status(thm)],[1608])).
% 0.82/1.00 tff(1610,plain,
% 0.82/1.00 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp5 | (~ndr1_0) | c3_1(a225) | c0_1(a225) | (~c2_1(a225)) | c3_1(a225) | c0_1(a225) | (~c1_1(a225)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp5 | c3_1(a225) | c0_1(a225) | (~c1_1(a225)) | (~ndr1_0) | (~c2_1(a225)))),
% 0.82/1.00 inference(transitivity,[status(thm)],[1609, 1607])).
% 0.82/1.00 tff(1611,plain,
% 0.82/1.00 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp5 | (~ndr1_0) | c3_1(a225) | c0_1(a225) | (~c2_1(a225)) | c3_1(a225) | c0_1(a225) | (~c1_1(a225)))),
% 0.82/1.00 inference(quant_inst,[status(thm)],[])).
% 0.82/1.00 tff(1612,plain,
% 0.82/1.00 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp5 | c3_1(a225) | c0_1(a225) | (~c1_1(a225)) | (~ndr1_0) | (~c2_1(a225))),
% 0.82/1.00 inference(modus_ponens,[status(thm)],[1611, 1610])).
% 0.82/1.00 tff(1613,plain,
% 0.82/1.00 (hskp5),
% 0.82/1.00 inference(unit_resolution,[status(thm)],[1612, 148, 1572, 235, 1606, 35, 1580])).
% 0.82/1.00 tff(1614,plain,
% 0.82/1.00 (~c1_1(a194)),
% 0.82/1.00 inference(unit_resolution,[status(thm)],[590, 1613])).
% 0.82/1.00 tff(1615,plain,
% 0.82/1.00 (c0_1(a194)),
% 0.82/1.00 inference(unit_resolution,[status(thm)],[598, 1613])).
% 0.82/1.00 tff(1616,plain,
% 0.82/1.00 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp2 | c0_1(a225) | (~c1_1(a225)) | c1_1(a194) | c2_1(a194) | (~ndr1_0) | (~c0_1(a194)) | (~c2_1(a225)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp2 | c0_1(a225) | (~c1_1(a225)) | c1_1(a194) | c2_1(a194) | (~ndr1_0) | (~c0_1(a194)) | (~c2_1(a225)))),
% 0.82/1.00 inference(rewrite,[status(thm)],[])).
% 0.82/1.00 tff(1617,plain,
% 0.82/1.00 ((hskp2 | (~ndr1_0) | c1_1(a194) | c2_1(a194) | (~c0_1(a194)) | c0_1(a225) | (~c1_1(a225)) | (~c2_1(a225))) <=> (hskp2 | c0_1(a225) | (~c1_1(a225)) | c1_1(a194) | c2_1(a194) | (~ndr1_0) | (~c0_1(a194)) | (~c2_1(a225)))),
% 0.82/1.00 inference(rewrite,[status(thm)],[])).
% 0.82/1.00 tff(1618,plain,
% 0.82/1.00 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp2 | (~ndr1_0) | c1_1(a194) | c2_1(a194) | (~c0_1(a194)) | c0_1(a225) | (~c1_1(a225)) | (~c2_1(a225)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp2 | c0_1(a225) | (~c1_1(a225)) | c1_1(a194) | c2_1(a194) | (~ndr1_0) | (~c0_1(a194)) | (~c2_1(a225))))),
% 0.82/1.00 inference(monotonicity,[status(thm)],[1617])).
% 0.82/1.01 tff(1619,plain,
% 0.82/1.01 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp2 | (~ndr1_0) | c1_1(a194) | c2_1(a194) | (~c0_1(a194)) | c0_1(a225) | (~c1_1(a225)) | (~c2_1(a225)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp2 | c0_1(a225) | (~c1_1(a225)) | c1_1(a194) | c2_1(a194) | (~ndr1_0) | (~c0_1(a194)) | (~c2_1(a225)))),
% 0.82/1.01 inference(transitivity,[status(thm)],[1618, 1616])).
% 0.82/1.01 tff(1620,plain,
% 0.82/1.01 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp2 | (~ndr1_0) | c1_1(a194) | c2_1(a194) | (~c0_1(a194)) | c0_1(a225) | (~c1_1(a225)) | (~c2_1(a225)))),
% 0.82/1.01 inference(quant_inst,[status(thm)],[])).
% 0.82/1.01 tff(1621,plain,
% 0.82/1.01 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp2 | c0_1(a225) | (~c1_1(a225)) | c1_1(a194) | c2_1(a194) | (~ndr1_0) | (~c0_1(a194)) | (~c2_1(a225))),
% 0.82/1.01 inference(modus_ponens,[status(thm)],[1620, 1619])).
% 0.82/1.01 tff(1622,plain,
% 0.82/1.01 ($false),
% 0.82/1.01 inference(unit_resolution,[status(thm)],[1621, 148, 14, 1615, 235, 1606, 1614, 11, 25, 1580])).
% 0.82/1.01 tff(1623,plain,(c3_1(a225) | hskp2 | c0_1(a225) | c2_1(a194) | (~c0_1(a195)) | c3_1(a195) | (~c0_1(a230)) | (~c1_1(a230)) | (~c2_1(a230)) | hskp6), inference(lemma,lemma(discharge,[]))).
% 0.82/1.01 tff(1624,plain,
% 0.82/1.01 (c3_1(a225)),
% 0.82/1.01 inference(unit_resolution,[status(thm)],[1623, 235, 1096, 11, 1571, 560, 1105, 1121, 1113, 1570])).
% 0.82/1.01 tff(1625,plain,
% 0.82/1.01 (c3_1(a225)),
% 0.82/1.01 inference(unit_resolution,[status(thm)],[1623, 235, 14, 11, 1380, 560, 1133, 1132, 1181, 944])).
% 0.82/1.01 tff(1626,plain,
% 0.82/1.01 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp2 | c0_1(a225) | c1_1(a225) | (~c1_1(a195)) | c3_1(a195) | (~ndr1_0) | (~c0_1(a195)) | (~c3_1(a225)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp2 | c0_1(a225) | c1_1(a225) | (~c1_1(a195)) | c3_1(a195) | (~ndr1_0) | (~c0_1(a195)) | (~c3_1(a225)))),
% 0.82/1.01 inference(rewrite,[status(thm)],[])).
% 0.82/1.01 tff(1627,plain,
% 0.82/1.01 ((hskp2 | (~ndr1_0) | c3_1(a195) | (~c1_1(a195)) | (~c0_1(a195)) | c1_1(a225) | c0_1(a225) | (~c3_1(a225))) <=> (hskp2 | c0_1(a225) | c1_1(a225) | (~c1_1(a195)) | c3_1(a195) | (~ndr1_0) | (~c0_1(a195)) | (~c3_1(a225)))),
% 0.82/1.01 inference(rewrite,[status(thm)],[])).
% 0.82/1.01 tff(1628,plain,
% 0.82/1.01 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp2 | (~ndr1_0) | c3_1(a195) | (~c1_1(a195)) | (~c0_1(a195)) | c1_1(a225) | c0_1(a225) | (~c3_1(a225)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp2 | c0_1(a225) | c1_1(a225) | (~c1_1(a195)) | c3_1(a195) | (~ndr1_0) | (~c0_1(a195)) | (~c3_1(a225))))),
% 0.82/1.01 inference(monotonicity,[status(thm)],[1627])).
% 0.82/1.01 tff(1629,plain,
% 0.82/1.01 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp2 | (~ndr1_0) | c3_1(a195) | (~c1_1(a195)) | (~c0_1(a195)) | c1_1(a225) | c0_1(a225) | (~c3_1(a225)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp2 | c0_1(a225) | c1_1(a225) | (~c1_1(a195)) | c3_1(a195) | (~ndr1_0) | (~c0_1(a195)) | (~c3_1(a225)))),
% 0.82/1.01 inference(transitivity,[status(thm)],[1628, 1626])).
% 0.82/1.01 tff(1630,plain,
% 0.82/1.01 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp2 | (~ndr1_0) | c3_1(a195) | (~c1_1(a195)) | (~c0_1(a195)) | c1_1(a225) | c0_1(a225) | (~c3_1(a225)))),
% 0.82/1.01 inference(quant_inst,[status(thm)],[])).
% 0.82/1.01 tff(1631,plain,
% 0.82/1.01 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp2 | c0_1(a225) | c1_1(a225) | (~c1_1(a195)) | c3_1(a195) | (~ndr1_0) | (~c0_1(a195)) | (~c3_1(a225))),
% 0.82/1.01 inference(modus_ponens,[status(thm)],[1630, 1629])).
% 0.82/1.01 tff(1632,plain,
% 0.82/1.01 ($false),
% 0.82/1.01 inference(unit_resolution,[status(thm)],[1631, 148, 14, 234, 1380, 235, 433, 943, 560, 1151])).
% 0.82/1.01 tff(1633,plain,(c1_1(a225) | hskp2 | (~c3_1(a225)) | c0_1(a225) | (~c1_1(a195)) | c3_1(a195)), inference(lemma,lemma(discharge,[]))).
% 0.82/1.01 tff(1634,plain,
% 0.82/1.01 (c1_1(a225)),
% 0.82/1.01 inference(unit_resolution,[status(thm)],[1633, 1625, 14, 235, 943, 560])).
% 0.82/1.01 tff(1635,plain,
% 0.82/1.01 (~c2_1(a225)),
% 0.82/1.01 inference(unit_resolution,[status(thm)],[1621, 148, 14, 1390, 235, 1634, 12, 11, 25])).
% 0.82/1.01 tff(1636,assumption,(c1_1(a225)), introduced(assumption)).
% 0.82/1.01 tff(1637,plain,
% 0.82/1.01 (((~![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp9 | hskp8 | c0_1(a225) | (~c1_1(a225)) | (~ndr1_0) | c2_1(a225))) <=> ((~![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | hskp9 | hskp8 | c0_1(a225) | (~c1_1(a225)) | (~ndr1_0) | c2_1(a225))),
% 0.82/1.01 inference(rewrite,[status(thm)],[])).
% 0.82/1.01 tff(1638,plain,
% 0.82/1.01 ((hskp9 | hskp8 | (~ndr1_0) | c0_1(a225) | c2_1(a225) | (~c1_1(a225))) <=> (hskp9 | hskp8 | c0_1(a225) | (~c1_1(a225)) | (~ndr1_0) | c2_1(a225))),
% 0.82/1.01 inference(rewrite,[status(thm)],[])).
% 0.82/1.01 tff(1639,plain,
% 0.82/1.01 (((~![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp9 | hskp8 | (~ndr1_0) | c0_1(a225) | c2_1(a225) | (~c1_1(a225)))) <=> ((~![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp9 | hskp8 | c0_1(a225) | (~c1_1(a225)) | (~ndr1_0) | c2_1(a225)))),
% 0.82/1.01 inference(monotonicity,[status(thm)],[1638])).
% 0.82/1.01 tff(1640,plain,
% 0.82/1.01 (((~![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp9 | hskp8 | (~ndr1_0) | c0_1(a225) | c2_1(a225) | (~c1_1(a225)))) <=> ((~![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | hskp9 | hskp8 | c0_1(a225) | (~c1_1(a225)) | (~ndr1_0) | c2_1(a225))),
% 0.82/1.01 inference(transitivity,[status(thm)],[1639, 1637])).
% 0.82/1.01 tff(1641,plain,
% 0.82/1.01 ((~![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp9 | hskp8 | (~ndr1_0) | c0_1(a225) | c2_1(a225) | (~c1_1(a225)))),
% 0.82/1.01 inference(quant_inst,[status(thm)],[])).
% 0.82/1.01 tff(1642,plain,
% 0.82/1.01 ((~![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | hskp9 | hskp8 | c0_1(a225) | (~c1_1(a225)) | (~ndr1_0) | c2_1(a225)),
% 0.82/1.01 inference(modus_ponens,[status(thm)],[1641, 1640])).
% 0.82/1.01 tff(1643,plain,
% 0.82/1.01 (hskp9 | hskp8 | (~c1_1(a225)) | c2_1(a225)),
% 0.82/1.01 inference(unit_resolution,[status(thm)],[1642, 148, 235, 1466])).
% 0.82/1.01 tff(1644,plain,
% 0.82/1.01 (hskp8),
% 0.82/1.01 inference(unit_resolution,[status(thm)],[1643, 1437, 1636, 1278])).
% 0.82/1.01 tff(1645,plain,
% 0.82/1.01 ($false),
% 0.82/1.01 inference(unit_resolution,[status(thm)],[1516, 1456, 1644, 1436, 1435, 1429])).
% 0.82/1.01 tff(1646,plain,(hskp9 | (~c1_1(a215)) | (~c2_1(a215)) | hskp0 | (~c3_1(a215)) | (~c0_1(a194)) | c1_1(a194) | c2_1(a194) | (~c1_1(a225)) | c2_1(a225) | c0_1(a225)), inference(lemma,lemma(discharge,[]))).
% 0.82/1.01 tff(1647,plain,
% 0.82/1.01 (hskp9),
% 0.82/1.01 inference(unit_resolution,[status(thm)],[1646, 1429, 1434, 1433, 1431, 673, 12, 11, 1636, 1278, 235])).
% 0.82/1.01 tff(1648,plain,
% 0.82/1.01 (~c0_1(a199)),
% 0.82/1.01 inference(unit_resolution,[status(thm)],[647, 1647])).
% 0.82/1.01 tff(1649,plain,
% 0.82/1.01 (~c1_1(a199)),
% 0.82/1.01 inference(unit_resolution,[status(thm)],[641, 1647])).
% 0.82/1.01 tff(1650,plain,
% 0.82/1.01 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_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(a225) | (~c1_1(a225)) | c0_1(a199) | c1_1(a199) | c1_1(a194) | c2_1(a194) | (~ndr1_0) | (~c0_1(a194)) | (~c2_1(a199)) | (~c3_1(a225)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_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(a225) | (~c1_1(a225)) | c0_1(a199) | c1_1(a199) | c1_1(a194) | c2_1(a194) | (~ndr1_0) | (~c0_1(a194)) | (~c2_1(a199)) | (~c3_1(a225)))),
% 0.82/1.01 inference(rewrite,[status(thm)],[])).
% 0.82/1.01 tff(1651,plain,
% 0.82/1.01 (((~ndr1_0) | c1_1(a194) | c2_1(a194) | (~c0_1(a194)) | c0_1(a225) | (~c3_1(a225)) | (~c1_1(a225)) | c1_1(a199) | c0_1(a199) | (~c2_1(a199))) <=> (c0_1(a225) | (~c1_1(a225)) | c0_1(a199) | c1_1(a199) | c1_1(a194) | c2_1(a194) | (~ndr1_0) | (~c0_1(a194)) | (~c2_1(a199)) | (~c3_1(a225)))),
% 0.82/1.01 inference(rewrite,[status(thm)],[])).
% 0.82/1.01 tff(1652,plain,
% 0.82/1.01 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_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) | c1_1(a194) | c2_1(a194) | (~c0_1(a194)) | c0_1(a225) | (~c3_1(a225)) | (~c1_1(a225)) | c1_1(a199) | c0_1(a199) | (~c2_1(a199)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_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(a225) | (~c1_1(a225)) | c0_1(a199) | c1_1(a199) | c1_1(a194) | c2_1(a194) | (~ndr1_0) | (~c0_1(a194)) | (~c2_1(a199)) | (~c3_1(a225))))),
% 0.82/1.01 inference(monotonicity,[status(thm)],[1651])).
% 0.82/1.01 tff(1653,plain,
% 0.82/1.01 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_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) | c1_1(a194) | c2_1(a194) | (~c0_1(a194)) | c0_1(a225) | (~c3_1(a225)) | (~c1_1(a225)) | c1_1(a199) | c0_1(a199) | (~c2_1(a199)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_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(a225) | (~c1_1(a225)) | c0_1(a199) | c1_1(a199) | c1_1(a194) | c2_1(a194) | (~ndr1_0) | (~c0_1(a194)) | (~c2_1(a199)) | (~c3_1(a225)))),
% 0.82/1.01 inference(transitivity,[status(thm)],[1652, 1650])).
% 0.82/1.01 tff(1654,plain,
% 0.82/1.01 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_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) | c1_1(a194) | c2_1(a194) | (~c0_1(a194)) | c0_1(a225) | (~c3_1(a225)) | (~c1_1(a225)) | c1_1(a199) | c0_1(a199) | (~c2_1(a199)))),
% 0.82/1.01 inference(quant_inst,[status(thm)],[])).
% 0.82/1.01 tff(1655,plain,
% 0.82/1.01 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a225) | (~c1_1(a225)) | c0_1(a199) | c1_1(a199) | c1_1(a194) | c2_1(a194) | (~ndr1_0) | (~c0_1(a194)) | (~c2_1(a199)) | (~c3_1(a225))),
% 0.82/1.01 inference(modus_ponens,[status(thm)],[1654, 1653])).
% 0.82/1.01 tff(1656,plain,
% 0.82/1.01 (~c2_1(a199)),
% 0.82/1.01 inference(unit_resolution,[status(thm)],[1655, 148, 234, 673, 235, 1636, 710, 709, 12, 11, 65])).
% 0.82/1.01 tff(1657,plain,
% 0.82/1.01 ($false),
% 0.82/1.01 inference(unit_resolution,[status(thm)],[1539, 148, 1429, 1656, 673, 710, 709, 11, 1533, 1428])).
% 0.82/1.01 tff(1658,plain,(c1_1(a199) | hskp0 | (~c0_1(a194)) | c0_1(a199) | c2_1(a194) | (~c3_1(a194)) | (~c3_1(a225)) | c0_1(a225) | (~c1_1(a225)) | c1_1(a194)), inference(lemma,lemma(discharge,[]))).
% 0.82/1.01 tff(1659,plain,
% 0.82/1.01 ($false),
% 0.82/1.01 inference(unit_resolution,[status(thm)],[1658, 1649, 1648, 673, 1429, 11, 1428, 234, 235, 1636, 12])).
% 0.82/1.01 tff(1660,plain,(hskp0 | (~c0_1(a194)) | c2_1(a194) | (~c3_1(a194)) | (~c3_1(a225)) | c0_1(a225) | (~c1_1(a225)) | c1_1(a194) | c2_1(a225)), inference(lemma,lemma(discharge,[]))).
% 0.82/1.01 tff(1661,plain,
% 0.82/1.01 (hskp0),
% 0.82/1.01 inference(unit_resolution,[status(thm)],[1660, 1390, 11, 1400, 1625, 235, 1634, 12, 1635])).
% 0.82/1.01 tff(1662,plain,
% 0.82/1.01 (~c3_1(a188)),
% 0.82/1.01 inference(unit_resolution,[status(thm)],[605, 1661])).
% 0.82/1.01 tff(1663,plain,
% 0.82/1.01 (~c0_1(a188)),
% 0.82/1.01 inference(unit_resolution,[status(thm)],[617, 1661])).
% 0.82/1.01 tff(1664,plain,
% 0.82/1.01 (c2_1(a188)),
% 0.82/1.01 inference(unit_resolution,[status(thm)],[1553, 148, 944, 1663, 1662, 530])).
% 0.82/1.01 tff(1665,plain,
% 0.82/1.01 (~c1_1(a188)),
% 0.82/1.01 inference(unit_resolution,[status(thm)],[611, 1661])).
% 0.82/1.01 tff(1666,plain,
% 0.82/1.01 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_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(a225) | (~c1_1(a225)) | c1_1(a194) | c2_1(a194) | c0_1(a188) | c1_1(a188) | (~ndr1_0) | (~c2_1(a188)) | (~c0_1(a194)) | (~c3_1(a225)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_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(a225) | (~c1_1(a225)) | c1_1(a194) | c2_1(a194) | c0_1(a188) | c1_1(a188) | (~ndr1_0) | (~c2_1(a188)) | (~c0_1(a194)) | (~c3_1(a225)))),
% 0.82/1.01 inference(rewrite,[status(thm)],[])).
% 0.82/1.01 tff(1667,plain,
% 0.82/1.01 (((~ndr1_0) | c1_1(a194) | c2_1(a194) | (~c0_1(a194)) | c0_1(a225) | (~c3_1(a225)) | (~c1_1(a225)) | c1_1(a188) | c0_1(a188) | (~c2_1(a188))) <=> (c0_1(a225) | (~c1_1(a225)) | c1_1(a194) | c2_1(a194) | c0_1(a188) | c1_1(a188) | (~ndr1_0) | (~c2_1(a188)) | (~c0_1(a194)) | (~c3_1(a225)))),
% 0.82/1.01 inference(rewrite,[status(thm)],[])).
% 0.82/1.01 tff(1668,plain,
% 0.82/1.01 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_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) | c1_1(a194) | c2_1(a194) | (~c0_1(a194)) | c0_1(a225) | (~c3_1(a225)) | (~c1_1(a225)) | c1_1(a188) | c0_1(a188) | (~c2_1(a188)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_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(a225) | (~c1_1(a225)) | c1_1(a194) | c2_1(a194) | c0_1(a188) | c1_1(a188) | (~ndr1_0) | (~c2_1(a188)) | (~c0_1(a194)) | (~c3_1(a225))))),
% 0.82/1.01 inference(monotonicity,[status(thm)],[1667])).
% 0.82/1.01 tff(1669,plain,
% 0.82/1.01 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_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) | c1_1(a194) | c2_1(a194) | (~c0_1(a194)) | c0_1(a225) | (~c3_1(a225)) | (~c1_1(a225)) | c1_1(a188) | c0_1(a188) | (~c2_1(a188)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_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(a225) | (~c1_1(a225)) | c1_1(a194) | c2_1(a194) | c0_1(a188) | c1_1(a188) | (~ndr1_0) | (~c2_1(a188)) | (~c0_1(a194)) | (~c3_1(a225)))),
% 0.82/1.01 inference(transitivity,[status(thm)],[1668, 1666])).
% 0.82/1.01 tff(1670,plain,
% 0.82/1.01 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_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) | c1_1(a194) | c2_1(a194) | (~c0_1(a194)) | c0_1(a225) | (~c3_1(a225)) | (~c1_1(a225)) | c1_1(a188) | c0_1(a188) | (~c2_1(a188)))),
% 0.82/1.01 inference(quant_inst,[status(thm)],[])).
% 0.82/1.01 tff(1671,plain,
% 0.82/1.01 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a225) | (~c1_1(a225)) | c1_1(a194) | c2_1(a194) | c0_1(a188) | c1_1(a188) | (~ndr1_0) | (~c2_1(a188)) | (~c0_1(a194)) | (~c3_1(a225))),
% 0.82/1.01 inference(modus_ponens,[status(thm)],[1670, 1669])).
% 0.82/1.01 tff(1672,plain,
% 0.82/1.01 ($false),
% 0.82/1.01 inference(unit_resolution,[status(thm)],[1671, 148, 1625, 1390, 235, 1634, 12, 11, 1663, 1665, 65, 1664])).
% 0.82/1.01 tff(1673,plain,(c1_1(a194) | c0_1(a225) | c2_1(a194) | hskp2 | (~c1_1(a230)) | (~c2_1(a230)) | (~c0_1(a230)) | (~c1_1(a195)) | c3_1(a195)), inference(lemma,lemma(discharge,[]))).
% 0.82/1.01 tff(1674,plain,
% 0.82/1.01 (c1_1(a194)),
% 0.82/1.01 inference(unit_resolution,[status(thm)],[1673, 235, 11, 1096, 1121, 1113, 1105, 1364, 560])).
% 0.82/1.01 tff(1675,plain,
% 0.82/1.01 (~hskp5),
% 0.82/1.01 inference(unit_resolution,[status(thm)],[590, 1674])).
% 0.82/1.01 tff(1676,plain,
% 0.82/1.01 (hskp21),
% 0.82/1.01 inference(unit_resolution,[status(thm)],[80, 1675, 36])).
% 0.82/1.01 tff(1677,plain,
% 0.82/1.01 (~c3_1(a257)),
% 0.82/1.01 inference(unit_resolution,[status(thm)],[92, 1676])).
% 0.82/1.01 tff(1678,plain,
% 0.82/1.01 (c2_1(a257)),
% 0.82/1.01 inference(unit_resolution,[status(thm)],[100, 1676])).
% 0.82/1.01 tff(1679,plain,
% 0.82/1.01 (~c1_1(a257)),
% 0.82/1.01 inference(unit_resolution,[status(thm)],[86, 1676])).
% 0.82/1.01 tff(1680,plain,
% 0.82/1.01 (c2_1(a225)),
% 0.82/1.01 inference(unit_resolution,[status(thm)],[1289, 1679, 1276, 1275, 1678, 1677, 1162])).
% 0.82/1.01 tff(1681,plain,
% 0.82/1.01 (hskp7 | (~c2_1(a225)) | (~c3_1(a225))),
% 0.82/1.01 inference(unit_resolution,[status(thm)],[1346, 148, 1105, 1121, 1113, 235, 1300])).
% 0.82/1.01 tff(1682,plain,
% 0.82/1.01 (hskp7),
% 0.82/1.01 inference(unit_resolution,[status(thm)],[1681, 1680, 1624])).
% 0.82/1.01 tff(1683,plain,
% 0.82/1.01 (~c2_1(a197)),
% 0.82/1.01 inference(unit_resolution,[status(thm)],[1316, 1682])).
% 0.82/1.01 tff(1684,plain,
% 0.82/1.01 (~c0_1(a197)),
% 0.82/1.01 inference(unit_resolution,[status(thm)],[1310, 1682])).
% 0.82/1.01 tff(1685,plain,
% 0.82/1.01 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c1_1(a257) | c3_1(a257) | c0_1(a197) | c2_1(a197) | c3_1(a190) | (~ndr1_0) | (~c2_1(a190)) | (~c0_1(a190)) | (~c3_1(a197)) | (~c2_1(a257)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c1_1(a257) | c3_1(a257) | c0_1(a197) | c2_1(a197) | c3_1(a190) | (~ndr1_0) | (~c2_1(a190)) | (~c0_1(a190)) | (~c3_1(a197)) | (~c2_1(a257)))),
% 0.82/1.01 inference(rewrite,[status(thm)],[])).
% 0.82/1.01 tff(1686,plain,
% 0.82/1.01 (((~ndr1_0) | c3_1(a190) | (~c2_1(a190)) | (~c0_1(a190)) | c3_1(a257) | c1_1(a257) | (~c2_1(a257)) | c2_1(a197) | c0_1(a197) | (~c3_1(a197))) <=> (c1_1(a257) | c3_1(a257) | c0_1(a197) | c2_1(a197) | c3_1(a190) | (~ndr1_0) | (~c2_1(a190)) | (~c0_1(a190)) | (~c3_1(a197)) | (~c2_1(a257)))),
% 0.82/1.01 inference(rewrite,[status(thm)],[])).
% 0.82/1.01 tff(1687,plain,
% 0.82/1.01 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a190) | (~c2_1(a190)) | (~c0_1(a190)) | c3_1(a257) | c1_1(a257) | (~c2_1(a257)) | c2_1(a197) | c0_1(a197) | (~c3_1(a197)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c1_1(a257) | c3_1(a257) | c0_1(a197) | c2_1(a197) | c3_1(a190) | (~ndr1_0) | (~c2_1(a190)) | (~c0_1(a190)) | (~c3_1(a197)) | (~c2_1(a257))))),
% 0.82/1.01 inference(monotonicity,[status(thm)],[1686])).
% 0.82/1.01 tff(1688,plain,
% 0.82/1.01 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a190) | (~c2_1(a190)) | (~c0_1(a190)) | c3_1(a257) | c1_1(a257) | (~c2_1(a257)) | c2_1(a197) | c0_1(a197) | (~c3_1(a197)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c1_1(a257) | c3_1(a257) | c0_1(a197) | c2_1(a197) | c3_1(a190) | (~ndr1_0) | (~c2_1(a190)) | (~c0_1(a190)) | (~c3_1(a197)) | (~c2_1(a257)))),
% 0.82/1.01 inference(transitivity,[status(thm)],[1687, 1685])).
% 0.82/1.01 tff(1689,plain,
% 0.82/1.01 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a190) | (~c2_1(a190)) | (~c0_1(a190)) | c3_1(a257) | c1_1(a257) | (~c2_1(a257)) | c2_1(a197) | c0_1(a197) | (~c3_1(a197)))),
% 0.82/1.01 inference(quant_inst,[status(thm)],[])).
% 0.82/1.01 tff(1690,plain,
% 0.82/1.01 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c1_1(a257) | c3_1(a257) | c0_1(a197) | c2_1(a197) | c3_1(a190) | (~ndr1_0) | (~c2_1(a190)) | (~c0_1(a190)) | (~c3_1(a197)) | (~c2_1(a257))),
% 0.82/1.01 inference(modus_ponens,[status(thm)],[1689, 1688])).
% 0.82/1.01 tff(1691,plain,
% 0.82/1.01 (~c3_1(a197)),
% 0.82/1.01 inference(unit_resolution,[status(thm)],[1690, 148, 1678, 1276, 1275, 1679, 1677, 1684, 1683, 1162, 451])).
% 0.82/1.01 tff(1692,plain,
% 0.82/1.01 ($false),
% 0.82/1.01 inference(unit_resolution,[status(thm)],[1326, 148, 1570, 1684, 1683, 530, 1691])).
% 0.82/1.01 tff(1693,plain,(c0_1(a225) | hskp15 | c2_1(a194) | c3_1(a195)), inference(lemma,lemma(discharge,[]))).
% 0.82/1.01 tff(1694,plain,
% 0.82/1.01 (c0_1(a225)),
% 0.82/1.01 inference(unit_resolution,[status(thm)],[1693, 11, 36, 560])).
% 0.82/1.01 tff(1695,plain,
% 0.82/1.01 (~hskp19),
% 0.82/1.01 inference(unit_resolution,[status(thm)],[232, 1694])).
% 0.82/1.01 tff(1696,plain,
% 0.82/1.01 ($false),
% 0.82/1.01 inference(unit_resolution,[status(thm)],[217, 148, 1695, 1569, 1276, 1275, 1568, 1567, 1162, 211])).
% 0.82/1.01 tff(1697,plain,(c2_1(a194) | hskp15 | c3_1(a195)), inference(lemma,lemma(discharge,[]))).
% 0.82/1.01 tff(1698,plain,
% 0.82/1.01 (c2_1(a194)),
% 0.82/1.01 inference(unit_resolution,[status(thm)],[1697, 560, 36])).
% 0.82/1.01 tff(1699,plain,
% 0.82/1.01 (~hskp5),
% 0.82/1.01 inference(unit_resolution,[status(thm)],[584, 1698])).
% 0.82/1.01 tff(1700,plain,
% 0.82/1.01 (hskp21),
% 0.82/1.01 inference(unit_resolution,[status(thm)],[80, 1699, 36])).
% 0.82/1.01 tff(1701,plain,
% 0.82/1.01 (~c3_1(a257)),
% 0.82/1.01 inference(unit_resolution,[status(thm)],[92, 1700])).
% 0.82/1.01 tff(1702,plain,
% 0.82/1.01 (~c1_1(a257)),
% 0.82/1.01 inference(unit_resolution,[status(thm)],[86, 1700])).
% 0.82/1.01 tff(1703,plain,
% 0.82/1.01 (c2_1(a257)),
% 0.82/1.01 inference(unit_resolution,[status(thm)],[100, 1700])).
% 0.82/1.01 tff(1704,plain,
% 0.82/1.01 (hskp19),
% 0.82/1.01 inference(unit_resolution,[status(thm)],[217, 148, 1703, 1276, 1275, 1702, 1701, 1162, 211])).
% 0.82/1.01 tff(1705,plain,
% 0.82/1.01 (~c0_1(a225)),
% 0.82/1.01 inference(unit_resolution,[status(thm)],[232, 1704])).
% 0.82/1.01 tff(1706,plain,
% 0.82/1.01 (c3_1(a225)),
% 0.82/1.01 inference(unit_resolution,[status(thm)],[226, 1704])).
% 0.82/1.01 tff(1707,plain,
% 0.82/1.01 (~c1_1(a225)),
% 0.82/1.01 inference(unit_resolution,[status(thm)],[417, 1704])).
% 0.82/1.01 tff(1708,plain,
% 0.82/1.01 ($false),
% 0.82/1.01 inference(unit_resolution,[status(thm)],[1633, 1707, 1706, 1096, 1705, 1364, 560])).
% 0.82/1.01 tff(1709,plain,(c3_1(a195) | hskp15), inference(lemma,lemma(discharge,[]))).
% 0.82/1.01 tff(1710,plain,
% 0.82/1.01 (c3_1(a195)),
% 0.82/1.01 inference(unit_resolution,[status(thm)],[1709, 36])).
% 0.82/1.01 tff(1711,plain,
% 0.82/1.01 (~hskp6),
% 0.82/1.01 inference(unit_resolution,[status(thm)],[543, 1710])).
% 0.82/1.01 tff(1712,plain,
% 0.82/1.01 (hskp19 | c1_1(a190)),
% 0.82/1.01 inference(unit_resolution,[status(thm)],[837, 148, 1165, 1166, 1164, 211])).
% 0.82/1.01 tff(1713,plain,
% 0.82/1.01 (hskp19),
% 0.82/1.01 inference(unit_resolution,[status(thm)],[1712, 1223])).
% 0.82/1.01 tff(1714,plain,
% 0.82/1.01 (c3_1(a225)),
% 0.82/1.01 inference(unit_resolution,[status(thm)],[226, 1713])).
% 0.82/1.01 tff(1715,plain,
% 0.82/1.01 (~c0_1(a225)),
% 0.82/1.01 inference(unit_resolution,[status(thm)],[232, 1713])).
% 0.82/1.01 tff(1716,plain,
% 0.82/1.01 (~c1_1(a225)),
% 0.82/1.01 inference(unit_resolution,[status(thm)],[417, 1713])).
% 0.82/1.01 tff(1717,plain,
% 0.82/1.01 (c3_1(a230)),
% 0.82/1.01 inference(unit_resolution,[status(thm)],[1179, 1716, 1133, 1132, 14, 235, 234])).
% 0.82/1.01 tff(1718,plain,
% 0.82/1.01 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | (c3_1(a190) | (~ndr1_0) | (~c2_1(a230)) | (~c0_1(a230)) | (~c3_1(a230)) | (~c1_1(a230)) | (~c0_1(a190)) | c1_1(a190))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | c3_1(a190) | (~ndr1_0) | (~c2_1(a230)) | (~c0_1(a230)) | (~c3_1(a230)) | (~c1_1(a230)) | (~c0_1(a190)) | c1_1(a190))),
% 0.82/1.01 inference(rewrite,[status(thm)],[])).
% 0.82/1.01 tff(1719,plain,
% 0.82/1.01 (((~ndr1_0) | (~c3_1(a230)) | (~c2_1(a230)) | (~c0_1(a230)) | (~c3_1(a230)) | (~c1_1(a230)) | (~c0_1(a230)) | c1_1(a190) | c3_1(a190) | (~c0_1(a190))) <=> (c3_1(a190) | (~ndr1_0) | (~c2_1(a230)) | (~c0_1(a230)) | (~c3_1(a230)) | (~c1_1(a230)) | (~c0_1(a190)) | c1_1(a190))),
% 0.82/1.01 inference(rewrite,[status(thm)],[])).
% 0.82/1.01 tff(1720,plain,
% 0.82/1.01 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c3_1(a230)) | (~c2_1(a230)) | (~c0_1(a230)) | (~c3_1(a230)) | (~c1_1(a230)) | (~c0_1(a230)) | c1_1(a190) | c3_1(a190) | (~c0_1(a190)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | (c3_1(a190) | (~ndr1_0) | (~c2_1(a230)) | (~c0_1(a230)) | (~c3_1(a230)) | (~c1_1(a230)) | (~c0_1(a190)) | c1_1(a190)))),
% 0.82/1.01 inference(monotonicity,[status(thm)],[1719])).
% 0.82/1.01 tff(1721,plain,
% 0.82/1.01 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c3_1(a230)) | (~c2_1(a230)) | (~c0_1(a230)) | (~c3_1(a230)) | (~c1_1(a230)) | (~c0_1(a230)) | c1_1(a190) | c3_1(a190) | (~c0_1(a190)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | c3_1(a190) | (~ndr1_0) | (~c2_1(a230)) | (~c0_1(a230)) | (~c3_1(a230)) | (~c1_1(a230)) | (~c0_1(a190)) | c1_1(a190))),
% 0.82/1.01 inference(transitivity,[status(thm)],[1720, 1718])).
% 0.82/1.01 tff(1722,plain,
% 0.82/1.01 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c3_1(a230)) | (~c2_1(a230)) | (~c0_1(a230)) | (~c3_1(a230)) | (~c1_1(a230)) | (~c0_1(a230)) | c1_1(a190) | c3_1(a190) | (~c0_1(a190)))),
% 0.82/1.01 inference(quant_inst,[status(thm)],[])).
% 0.82/1.01 tff(1723,plain,
% 0.82/1.01 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | c3_1(a190) | (~ndr1_0) | (~c2_1(a230)) | (~c0_1(a230)) | (~c3_1(a230)) | (~c1_1(a230)) | (~c0_1(a190)) | c1_1(a190)),
% 0.82/1.01 inference(modus_ponens,[status(thm)],[1722, 1721])).
% 0.82/1.01 tff(1724,plain,
% 0.82/1.01 ($false),
% 0.82/1.01 inference(unit_resolution,[status(thm)],[1723, 148, 1133, 1132, 1181, 1165, 1164, 470, 1223, 1717])).
% 0.82/1.01 tff(1725,plain,(c1_1(a190) | (~c0_1(a230)) | (~c1_1(a230)) | (~c2_1(a230)) | hskp2 | c0_1(a225) | (~c3_1(a225))), inference(lemma,lemma(discharge,[]))).
% 0.82/1.01 tff(1726,plain,
% 0.82/1.01 ($false),
% 0.82/1.01 inference(unit_resolution,[status(thm)],[1725, 1715, 1714, 1132, 1181, 14, 1223, 1133])).
% 0.82/1.01 tff(1727,plain,(c1_1(a190) | (~c1_1(a230)) | (~c2_1(a230)) | hskp2 | (~c0_1(a230))), inference(lemma,lemma(discharge,[]))).
% 0.82/1.01 tff(1728,plain,
% 0.82/1.01 (c1_1(a190)),
% 0.82/1.01 inference(unit_resolution,[status(thm)],[1727, 1121, 1113, 1096, 1105])).
% 0.82/1.01 tff(1729,assumption,(hskp19), introduced(assumption)).
% 0.82/1.01 tff(1730,plain,
% 0.82/1.01 (~c1_1(a225)),
% 0.82/1.01 inference(unit_resolution,[status(thm)],[417, 1729])).
% 0.82/1.01 tff(1731,plain,
% 0.82/1.01 (~c0_1(a225)),
% 0.82/1.01 inference(unit_resolution,[status(thm)],[232, 1729])).
% 0.82/1.01 tff(1732,plain,
% 0.82/1.01 (c3_1(a225)),
% 0.82/1.01 inference(unit_resolution,[status(thm)],[226, 1729])).
% 0.82/1.01 tff(1733,plain,
% 0.82/1.01 ($false),
% 0.82/1.01 inference(unit_resolution,[status(thm)],[1221, 148, 14, 1732, 829, 1731, 1730, 13, 1151, 1005])).
% 0.82/1.01 tff(1734,plain,((~hskp19) | hskp2 | (~c0_1(a190)) | c3_1(a190) | (~c1_1(a190))), inference(lemma,lemma(discharge,[]))).
% 0.82/1.01 tff(1735,plain,
% 0.82/1.01 (~hskp19),
% 0.82/1.01 inference(unit_resolution,[status(thm)],[1734, 1096, 1276, 1162, 1728])).
% 0.82/1.01 tff(1736,assumption,(hskp21), introduced(assumption)).
% 0.82/1.01 tff(1737,plain,
% 0.82/1.01 (~c3_1(a257)),
% 0.82/1.01 inference(unit_resolution,[status(thm)],[92, 1736])).
% 0.82/1.01 tff(1738,plain,
% 0.82/1.01 (~c1_1(a257)),
% 0.82/1.01 inference(unit_resolution,[status(thm)],[86, 1736])).
% 0.82/1.01 tff(1739,plain,
% 0.82/1.01 (c2_1(a257)),
% 0.82/1.01 inference(unit_resolution,[status(thm)],[100, 1736])).
% 0.82/1.01 tff(1740,plain,
% 0.82/1.01 ($false),
% 0.82/1.01 inference(unit_resolution,[status(thm)],[217, 148, 830, 1739, 829, 784, 1738, 1737, 13, 211])).
% 0.82/1.01 tff(1741,plain,((~hskp21) | hskp19 | (~c0_1(a190)) | (~c2_1(a190)) | c3_1(a190)), inference(lemma,lemma(discharge,[]))).
% 0.82/1.01 tff(1742,plain,
% 0.82/1.01 (~hskp21),
% 0.82/1.01 inference(unit_resolution,[status(thm)],[1741, 1735, 1276, 1275, 1162])).
% 0.82/1.01 tff(1743,plain,
% 0.82/1.01 (hskp5),
% 0.82/1.01 inference(unit_resolution,[status(thm)],[80, 1742, 36])).
% 0.82/1.01 tff(1744,plain,
% 0.82/1.01 (~c1_1(a194)),
% 0.82/1.01 inference(unit_resolution,[status(thm)],[590, 1743])).
% 0.82/1.01 tff(1745,plain,
% 0.82/1.01 (~c2_1(a194)),
% 0.82/1.01 inference(unit_resolution,[status(thm)],[584, 1743])).
% 0.82/1.01 tff(1746,plain,
% 0.82/1.01 (c0_1(a194) | c3_1(a194)),
% 0.82/1.01 inference(unit_resolution,[status(thm)],[1206, 148, 1191, 11, 530])).
% 0.82/1.01 tff(1747,plain,
% 0.82/1.01 (c3_1(a194)),
% 0.82/1.01 inference(unit_resolution,[status(thm)],[1746, 1192])).
% 0.82/1.01 tff(1748,plain,
% 0.82/1.01 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp2 | c0_1(a194) | c1_1(a194) | c3_1(a190) | (~ndr1_0) | (~c0_1(a190)) | (~c1_1(a190)) | (~c3_1(a194)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp2 | c0_1(a194) | c1_1(a194) | c3_1(a190) | (~ndr1_0) | (~c0_1(a190)) | (~c1_1(a190)) | (~c3_1(a194)))),
% 0.82/1.01 inference(rewrite,[status(thm)],[])).
% 0.82/1.01 tff(1749,plain,
% 0.82/1.01 ((hskp2 | (~ndr1_0) | c3_1(a190) | (~c1_1(a190)) | (~c0_1(a190)) | c1_1(a194) | c0_1(a194) | (~c3_1(a194))) <=> (hskp2 | c0_1(a194) | c1_1(a194) | c3_1(a190) | (~ndr1_0) | (~c0_1(a190)) | (~c1_1(a190)) | (~c3_1(a194)))),
% 0.82/1.01 inference(rewrite,[status(thm)],[])).
% 0.82/1.01 tff(1750,plain,
% 0.82/1.01 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp2 | (~ndr1_0) | c3_1(a190) | (~c1_1(a190)) | (~c0_1(a190)) | c1_1(a194) | c0_1(a194) | (~c3_1(a194)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp2 | c0_1(a194) | c1_1(a194) | c3_1(a190) | (~ndr1_0) | (~c0_1(a190)) | (~c1_1(a190)) | (~c3_1(a194))))),
% 0.82/1.01 inference(monotonicity,[status(thm)],[1749])).
% 0.82/1.01 tff(1751,plain,
% 0.82/1.01 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp2 | (~ndr1_0) | c3_1(a190) | (~c1_1(a190)) | (~c0_1(a190)) | c1_1(a194) | c0_1(a194) | (~c3_1(a194)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp2 | c0_1(a194) | c1_1(a194) | c3_1(a190) | (~ndr1_0) | (~c0_1(a190)) | (~c1_1(a190)) | (~c3_1(a194)))),
% 0.82/1.01 inference(transitivity,[status(thm)],[1750, 1748])).
% 0.82/1.01 tff(1752,plain,
% 0.82/1.01 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp2 | (~ndr1_0) | c3_1(a190) | (~c1_1(a190)) | (~c0_1(a190)) | c1_1(a194) | c0_1(a194) | (~c3_1(a194)))),
% 0.82/1.01 inference(quant_inst,[status(thm)],[])).
% 0.82/1.01 tff(1753,plain,
% 0.82/1.01 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp2 | c0_1(a194) | c1_1(a194) | c3_1(a190) | (~ndr1_0) | (~c0_1(a190)) | (~c1_1(a190)) | (~c3_1(a194))),
% 0.82/1.01 inference(modus_ponens,[status(thm)],[1752, 1751])).
% 0.82/1.01 tff(1754,plain,
% 0.82/1.01 (c0_1(a194) | (~c1_1(a190)) | (~c3_1(a194))),
% 0.82/1.01 inference(unit_resolution,[status(thm)],[1753, 148, 14, 829, 12, 13, 1151])).
% 0.82/1.01 tff(1755,plain,
% 0.82/1.01 (~c1_1(a190)),
% 0.82/1.01 inference(unit_resolution,[status(thm)],[1754, 1192, 1747])).
% 0.82/1.01 tff(1756,plain,
% 0.82/1.01 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a194) | c2_1(a194) | c3_1(a190) | (~ndr1_0) | (~c2_1(a190)) | (~c0_1(a190)) | c1_1(a190) | (~c3_1(a194)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a194) | c2_1(a194) | c3_1(a190) | (~ndr1_0) | (~c2_1(a190)) | (~c0_1(a190)) | c1_1(a190) | (~c3_1(a194)))),
% 0.82/1.01 inference(rewrite,[status(thm)],[])).
% 0.82/1.01 tff(1757,plain,
% 0.82/1.01 (((~ndr1_0) | c3_1(a190) | (~c2_1(a190)) | (~c0_1(a190)) | c3_1(a190) | c1_1(a190) | (~c2_1(a190)) | c2_1(a194) | c0_1(a194) | (~c3_1(a194))) <=> (c0_1(a194) | c2_1(a194) | c3_1(a190) | (~ndr1_0) | (~c2_1(a190)) | (~c0_1(a190)) | c1_1(a190) | (~c3_1(a194)))),
% 0.82/1.01 inference(rewrite,[status(thm)],[])).
% 0.82/1.01 tff(1758,plain,
% 0.82/1.01 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a190) | (~c2_1(a190)) | (~c0_1(a190)) | c3_1(a190) | c1_1(a190) | (~c2_1(a190)) | c2_1(a194) | c0_1(a194) | (~c3_1(a194)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a194) | c2_1(a194) | c3_1(a190) | (~ndr1_0) | (~c2_1(a190)) | (~c0_1(a190)) | c1_1(a190) | (~c3_1(a194))))),
% 0.82/1.01 inference(monotonicity,[status(thm)],[1757])).
% 0.82/1.01 tff(1759,plain,
% 0.82/1.01 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a190) | (~c2_1(a190)) | (~c0_1(a190)) | c3_1(a190) | c1_1(a190) | (~c2_1(a190)) | c2_1(a194) | c0_1(a194) | (~c3_1(a194)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a194) | c2_1(a194) | c3_1(a190) | (~ndr1_0) | (~c2_1(a190)) | (~c0_1(a190)) | c1_1(a190) | (~c3_1(a194)))),
% 0.82/1.01 inference(transitivity,[status(thm)],[1758, 1756])).
% 0.82/1.01 tff(1760,plain,
% 0.82/1.01 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a190) | (~c2_1(a190)) | (~c0_1(a190)) | c3_1(a190) | c1_1(a190) | (~c2_1(a190)) | c2_1(a194) | c0_1(a194) | (~c3_1(a194)))),
% 0.82/1.01 inference(quant_inst,[status(thm)],[])).
% 0.82/1.01 tff(1761,plain,
% 0.82/1.01 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a194) | c2_1(a194) | c3_1(a190) | (~ndr1_0) | (~c2_1(a190)) | (~c0_1(a190)) | c1_1(a190) | (~c3_1(a194))),
% 0.82/1.02 inference(modus_ponens,[status(thm)],[1760, 1759])).
% 0.82/1.02 tff(1762,plain,
% 0.82/1.02 (c0_1(a194) | c1_1(a190) | (~c3_1(a194))),
% 0.82/1.02 inference(unit_resolution,[status(thm)],[1761, 148, 829, 784, 11, 13, 451])).
% 0.82/1.02 tff(1763,plain,
% 0.82/1.02 ($false),
% 0.82/1.02 inference(unit_resolution,[status(thm)],[1762, 1755, 1747, 1192])).
% 0.82/1.02 tff(1764,plain,(c0_1(a194) | (~c0_1(a190)) | (~c2_1(a190)) | c2_1(a194) | c3_1(a190) | hskp2 | c1_1(a194) | hskp6), inference(lemma,lemma(discharge,[]))).
% 0.82/1.02 tff(1765,plain,
% 0.82/1.02 (c0_1(a194)),
% 0.82/1.02 inference(unit_resolution,[status(thm)],[1764, 12, 1166, 11, 1164, 14, 1165, 1191])).
% 0.82/1.02 tff(1766,plain,
% 0.82/1.02 (c3_1(a194)),
% 0.82/1.02 inference(unit_resolution,[status(thm)],[1399, 1765, 1132, 1181, 11, 12, 1133])).
% 0.82/1.02 tff(1767,plain,
% 0.82/1.02 (c1_1(a190)),
% 0.82/1.02 inference(unit_resolution,[status(thm)],[1727, 1132, 1181, 14, 1133])).
% 0.82/1.02 tff(1768,assumption,(hskp13), introduced(assumption)).
% 0.82/1.02 tff(1769,plain,
% 0.82/1.02 (~c0_1(a209)),
% 0.82/1.02 inference(unit_resolution,[status(thm)],[387, 1768])).
% 0.82/1.02 tff(1770,plain,
% 0.82/1.02 (c0_1(a194)),
% 0.82/1.02 inference(unit_resolution,[status(thm)],[1764, 12, 784, 11, 13, 14, 829, 1191])).
% 0.82/1.02 tff(1771,plain,
% 0.82/1.02 (c1_1(a209)),
% 0.82/1.02 inference(unit_resolution,[status(thm)],[403, 1768])).
% 0.82/1.02 tff(1772,plain,
% 0.82/1.02 (~c2_1(a209)),
% 0.82/1.02 inference(unit_resolution,[status(thm)],[1425, 148, 14, 1771, 1770, 1769, 12, 11, 25])).
% 0.82/1.02 tff(1773,plain,
% 0.82/1.02 (c3_1(a209)),
% 0.82/1.02 inference(unit_resolution,[status(thm)],[395, 1768])).
% 0.82/1.02 tff(1774,plain,
% 0.82/1.02 (hskp0),
% 0.82/1.02 inference(unit_resolution,[status(thm)],[1544, 1772, 11, 1428, 1771, 1773, 1769, 12, 1770])).
% 0.82/1.02 tff(1775,plain,
% 0.82/1.02 (~c3_1(a188)),
% 0.82/1.02 inference(unit_resolution,[status(thm)],[605, 1774])).
% 0.82/1.02 tff(1776,plain,
% 0.82/1.02 (~c1_1(a188)),
% 0.82/1.02 inference(unit_resolution,[status(thm)],[611, 1774])).
% 0.82/1.02 tff(1777,plain,
% 0.82/1.02 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a209) | c3_1(a190) | c1_1(a188) | c3_1(a188) | (~ndr1_0) | (~c2_1(a188)) | (~c2_1(a190)) | (~c0_1(a190)) | c2_1(a209) | (~c3_1(a209)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a209) | c3_1(a190) | c1_1(a188) | c3_1(a188) | (~ndr1_0) | (~c2_1(a188)) | (~c2_1(a190)) | (~c0_1(a190)) | c2_1(a209) | (~c3_1(a209)))),
% 0.82/1.02 inference(rewrite,[status(thm)],[])).
% 0.82/1.02 tff(1778,plain,
% 0.82/1.02 (((~ndr1_0) | c3_1(a190) | (~c2_1(a190)) | (~c0_1(a190)) | c3_1(a188) | c1_1(a188) | (~c2_1(a188)) | c2_1(a209) | c0_1(a209) | (~c3_1(a209))) <=> (c0_1(a209) | c3_1(a190) | c1_1(a188) | c3_1(a188) | (~ndr1_0) | (~c2_1(a188)) | (~c2_1(a190)) | (~c0_1(a190)) | c2_1(a209) | (~c3_1(a209)))),
% 0.82/1.02 inference(rewrite,[status(thm)],[])).
% 0.82/1.02 tff(1779,plain,
% 0.82/1.02 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a190) | (~c2_1(a190)) | (~c0_1(a190)) | c3_1(a188) | c1_1(a188) | (~c2_1(a188)) | c2_1(a209) | c0_1(a209) | (~c3_1(a209)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a209) | c3_1(a190) | c1_1(a188) | c3_1(a188) | (~ndr1_0) | (~c2_1(a188)) | (~c2_1(a190)) | (~c0_1(a190)) | c2_1(a209) | (~c3_1(a209))))),
% 0.82/1.02 inference(monotonicity,[status(thm)],[1778])).
% 0.82/1.02 tff(1780,plain,
% 0.82/1.02 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a190) | (~c2_1(a190)) | (~c0_1(a190)) | c3_1(a188) | c1_1(a188) | (~c2_1(a188)) | c2_1(a209) | c0_1(a209) | (~c3_1(a209)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a209) | c3_1(a190) | c1_1(a188) | c3_1(a188) | (~ndr1_0) | (~c2_1(a188)) | (~c2_1(a190)) | (~c0_1(a190)) | c2_1(a209) | (~c3_1(a209)))),
% 0.82/1.02 inference(transitivity,[status(thm)],[1779, 1777])).
% 0.82/1.02 tff(1781,plain,
% 0.82/1.02 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a190) | (~c2_1(a190)) | (~c0_1(a190)) | c3_1(a188) | c1_1(a188) | (~c2_1(a188)) | c2_1(a209) | c0_1(a209) | (~c3_1(a209)))),
% 0.82/1.02 inference(quant_inst,[status(thm)],[])).
% 0.82/1.02 tff(1782,plain,
% 0.82/1.02 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a209) | c3_1(a190) | c1_1(a188) | c3_1(a188) | (~ndr1_0) | (~c2_1(a188)) | (~c2_1(a190)) | (~c0_1(a190)) | c2_1(a209) | (~c3_1(a209))),
% 0.82/1.02 inference(modus_ponens,[status(thm)],[1781, 1780])).
% 0.82/1.02 tff(1783,plain,
% 0.82/1.02 (~c2_1(a188)),
% 0.82/1.02 inference(unit_resolution,[status(thm)],[1782, 148, 1773, 829, 784, 1769, 13, 1776, 1775, 451, 1772])).
% 0.82/1.02 tff(1784,plain,
% 0.82/1.02 (~c0_1(a188)),
% 0.82/1.02 inference(unit_resolution,[status(thm)],[617, 1774])).
% 0.82/1.02 tff(1785,plain,
% 0.82/1.02 ($false),
% 0.82/1.02 inference(unit_resolution,[status(thm)],[1553, 148, 1191, 1784, 1775, 530, 1783])).
% 0.82/1.02 tff(1786,plain,((~hskp13) | hskp6 | (~c0_1(a190)) | (~c2_1(a190)) | c3_1(a190) | c2_1(a194) | (~c3_1(a194)) | c1_1(a194) | hskp2), inference(lemma,lemma(discharge,[]))).
% 0.82/1.02 tff(1787,plain,
% 0.82/1.02 (~hskp13),
% 0.82/1.02 inference(unit_resolution,[status(thm)],[1786, 1766, 1165, 1166, 1164, 11, 1191, 12, 14])).
% 0.82/1.02 tff(1788,plain,
% 0.82/1.02 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp13 | c1_1(a194) | c2_1(a194) | c3_1(a190) | (~ndr1_0) | (~c0_1(a190)) | (~c1_1(a190)) | (~c3_1(a194)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | hskp13 | c1_1(a194) | c2_1(a194) | c3_1(a190) | (~ndr1_0) | (~c0_1(a190)) | (~c1_1(a190)) | (~c3_1(a194)))),
% 0.82/1.02 inference(rewrite,[status(thm)],[])).
% 0.82/1.02 tff(1789,plain,
% 0.82/1.02 ((hskp13 | (~ndr1_0) | c3_1(a190) | (~c1_1(a190)) | (~c0_1(a190)) | c1_1(a194) | c2_1(a194) | (~c3_1(a194))) <=> (hskp13 | c1_1(a194) | c2_1(a194) | c3_1(a190) | (~ndr1_0) | (~c0_1(a190)) | (~c1_1(a190)) | (~c3_1(a194)))),
% 0.82/1.02 inference(rewrite,[status(thm)],[])).
% 0.82/1.02 tff(1790,plain,
% 0.82/1.02 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp13 | (~ndr1_0) | c3_1(a190) | (~c1_1(a190)) | (~c0_1(a190)) | c1_1(a194) | c2_1(a194) | (~c3_1(a194)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp13 | c1_1(a194) | c2_1(a194) | c3_1(a190) | (~ndr1_0) | (~c0_1(a190)) | (~c1_1(a190)) | (~c3_1(a194))))),
% 0.82/1.02 inference(monotonicity,[status(thm)],[1789])).
% 0.82/1.02 tff(1791,plain,
% 0.82/1.02 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp13 | (~ndr1_0) | c3_1(a190) | (~c1_1(a190)) | (~c0_1(a190)) | c1_1(a194) | c2_1(a194) | (~c3_1(a194)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | hskp13 | c1_1(a194) | c2_1(a194) | c3_1(a190) | (~ndr1_0) | (~c0_1(a190)) | (~c1_1(a190)) | (~c3_1(a194)))),
% 0.82/1.02 inference(transitivity,[status(thm)],[1790, 1788])).
% 0.82/1.02 tff(1792,plain,
% 0.82/1.02 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp13 | (~ndr1_0) | c3_1(a190) | (~c1_1(a190)) | (~c0_1(a190)) | c1_1(a194) | c2_1(a194) | (~c3_1(a194)))),
% 0.82/1.02 inference(quant_inst,[status(thm)],[])).
% 0.82/1.02 tff(1793,plain,
% 0.82/1.02 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | hskp13 | c1_1(a194) | c2_1(a194) | c3_1(a190) | (~ndr1_0) | (~c0_1(a190)) | (~c1_1(a190)) | (~c3_1(a194))),
% 0.82/1.02 inference(modus_ponens,[status(thm)],[1792, 1791])).
% 0.82/1.02 tff(1794,plain,
% 0.82/1.02 ($false),
% 0.82/1.02 inference(unit_resolution,[status(thm)],[1793, 148, 1787, 1165, 12, 11, 1164, 1410, 1767, 1766])).
% 0.82/1.02 tff(1795,plain,(c1_1(a194) | c2_1(a194) | hskp6 | hskp2 | (~c1_1(a230)) | (~c2_1(a230)) | (~c0_1(a230))), inference(lemma,lemma(discharge,[]))).
% 0.82/1.02 tff(1796,plain,
% 0.82/1.02 ($false),
% 0.82/1.02 inference(unit_resolution,[status(thm)],[1795, 1745, 1744, 1711, 1096, 1121, 1113, 1105])).
% 0.82/1.02 tff(1797,plain,(hskp15), inference(lemma,lemma(discharge,[]))).
% 0.82/1.02 tff(1798,plain,
% 0.82/1.02 (((~hskp15) | (~c3_1(a214))) <=> ((~hskp15) | (~c3_1(a214)))),
% 0.82/1.02 inference(rewrite,[status(thm)],[])).
% 0.82/1.02 tff(1799,plain,
% 0.82/1.02 (((~c3_1(a214)) | (~hskp15)) <=> ((~hskp15) | (~c3_1(a214)))),
% 0.82/1.02 inference(rewrite,[status(thm)],[])).
% 0.82/1.02 tff(1800,axiom,((~c3_1(a214)) | (~hskp15)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause84')).
% 0.82/1.02 tff(1801,plain,
% 0.82/1.02 ((~hskp15) | (~c3_1(a214))),
% 0.82/1.02 inference(modus_ponens,[status(thm)],[1800, 1799])).
% 0.82/1.02 tff(1802,plain,
% 0.82/1.02 ((~hskp15) | (~c3_1(a214))),
% 0.82/1.02 inference(modus_ponens,[status(thm)],[1801, 1798])).
% 0.82/1.02 tff(1803,plain,
% 0.82/1.02 (~c3_1(a214)),
% 0.82/1.02 inference(unit_resolution,[status(thm)],[1802, 1797])).
% 0.82/1.02 tff(1804,plain,
% 0.82/1.02 (((~hskp15) | (~c0_1(a214))) <=> ((~hskp15) | (~c0_1(a214)))),
% 0.82/1.02 inference(rewrite,[status(thm)],[])).
% 0.82/1.02 tff(1805,plain,
% 0.82/1.02 (((~c0_1(a214)) | (~hskp15)) <=> ((~hskp15) | (~c0_1(a214)))),
% 0.82/1.02 inference(rewrite,[status(thm)],[])).
% 0.82/1.02 tff(1806,axiom,((~c0_1(a214)) | (~hskp15)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause83')).
% 0.82/1.02 tff(1807,plain,
% 0.82/1.02 ((~hskp15) | (~c0_1(a214))),
% 0.82/1.02 inference(modus_ponens,[status(thm)],[1806, 1805])).
% 0.82/1.02 tff(1808,plain,
% 0.82/1.02 ((~hskp15) | (~c0_1(a214))),
% 0.82/1.02 inference(modus_ponens,[status(thm)],[1807, 1804])).
% 0.82/1.02 tff(1809,plain,
% 0.82/1.02 (~c0_1(a214)),
% 0.82/1.02 inference(unit_resolution,[status(thm)],[1808, 1797])).
% 0.82/1.02 tff(1810,plain,
% 0.82/1.02 (((~hskp15) | c2_1(a214)) <=> ((~hskp15) | c2_1(a214))),
% 0.82/1.02 inference(rewrite,[status(thm)],[])).
% 0.82/1.02 tff(1811,axiom,((~hskp15) | c2_1(a214)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause51')).
% 0.82/1.02 tff(1812,plain,
% 0.82/1.02 ((~hskp15) | c2_1(a214)),
% 0.82/1.02 inference(modus_ponens,[status(thm)],[1811, 1810])).
% 0.82/1.02 tff(1813,plain,
% 0.82/1.02 ((~hskp15) | c2_1(a214)),
% 0.82/1.02 inference(modus_ponens,[status(thm)],[1812, 1810])).
% 0.82/1.02 tff(1814,plain,
% 0.82/1.02 ((~hskp15) | c2_1(a214)),
% 0.82/1.02 inference(modus_ponens,[status(thm)],[1813, 1810])).
% 0.82/1.02 tff(1815,plain,
% 0.82/1.02 ((~hskp15) | c2_1(a214)),
% 0.82/1.02 inference(modus_ponens,[status(thm)],[1814, 1810])).
% 0.82/1.02 tff(1816,plain,
% 0.82/1.02 ((~hskp15) | c2_1(a214)),
% 0.82/1.02 inference(modus_ponens,[status(thm)],[1815, 1810])).
% 0.82/1.02 tff(1817,plain,
% 0.82/1.02 (c2_1(a214)),
% 0.82/1.02 inference(unit_resolution,[status(thm)],[1816, 1797])).
% 0.82/1.02 tff(1818,plain,
% 0.82/1.02 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp5 | c0_1(a214) | c3_1(a214) | (~ndr1_0) | (~c1_1(a214)) | (~c2_1(a214)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp5 | c0_1(a214) | c3_1(a214) | (~ndr1_0) | (~c1_1(a214)) | (~c2_1(a214)))),
% 0.82/1.02 inference(rewrite,[status(thm)],[])).
% 0.82/1.02 tff(1819,plain,
% 0.82/1.02 ((hskp5 | (~ndr1_0) | c3_1(a214) | c0_1(a214) | (~c2_1(a214)) | c3_1(a214) | c0_1(a214) | (~c1_1(a214))) <=> (hskp5 | c0_1(a214) | c3_1(a214) | (~ndr1_0) | (~c1_1(a214)) | (~c2_1(a214)))),
% 0.82/1.02 inference(rewrite,[status(thm)],[])).
% 0.82/1.02 tff(1820,plain,
% 0.82/1.02 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp5 | (~ndr1_0) | c3_1(a214) | c0_1(a214) | (~c2_1(a214)) | c3_1(a214) | c0_1(a214) | (~c1_1(a214)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp5 | c0_1(a214) | c3_1(a214) | (~ndr1_0) | (~c1_1(a214)) | (~c2_1(a214))))),
% 0.82/1.02 inference(monotonicity,[status(thm)],[1819])).
% 0.82/1.02 tff(1821,plain,
% 0.82/1.02 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp5 | (~ndr1_0) | c3_1(a214) | c0_1(a214) | (~c2_1(a214)) | c3_1(a214) | c0_1(a214) | (~c1_1(a214)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp5 | c0_1(a214) | c3_1(a214) | (~ndr1_0) | (~c1_1(a214)) | (~c2_1(a214)))),
% 0.82/1.02 inference(transitivity,[status(thm)],[1820, 1818])).
% 0.82/1.02 tff(1822,plain,
% 0.82/1.02 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp5 | (~ndr1_0) | c3_1(a214) | c0_1(a214) | (~c2_1(a214)) | c3_1(a214) | c0_1(a214) | (~c1_1(a214)))),
% 0.82/1.02 inference(quant_inst,[status(thm)],[])).
% 0.82/1.02 tff(1823,plain,
% 0.82/1.02 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp5 | c0_1(a214) | c3_1(a214) | (~ndr1_0) | (~c1_1(a214)) | (~c2_1(a214))),
% 0.82/1.02 inference(modus_ponens,[status(thm)],[1822, 1821])).
% 0.82/1.02 tff(1824,plain,
% 0.82/1.02 (hskp5 | (~c1_1(a214))),
% 0.82/1.02 inference(unit_resolution,[status(thm)],[1823, 148, 1817, 1809, 1803, 35])).
% 0.82/1.02 tff(1825,plain,
% 0.82/1.02 (hskp5),
% 0.82/1.02 inference(unit_resolution,[status(thm)],[1824, 15])).
% 0.82/1.02 tff(1826,plain,
% 0.82/1.02 (~c1_1(a194)),
% 0.82/1.02 inference(unit_resolution,[status(thm)],[590, 1825])).
% 0.82/1.02 tff(1827,plain,
% 0.82/1.02 (c0_1(a194)),
% 0.82/1.02 inference(unit_resolution,[status(thm)],[598, 1825])).
% 0.82/1.02 tff(1828,plain,
% 0.82/1.02 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp2 | c0_1(a214) | c1_1(a194) | c2_1(a194) | (~ndr1_0) | (~c0_1(a194)) | (~c1_1(a214)) | (~c2_1(a214)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp2 | c0_1(a214) | c1_1(a194) | c2_1(a194) | (~ndr1_0) | (~c0_1(a194)) | (~c1_1(a214)) | (~c2_1(a214)))),
% 0.82/1.02 inference(rewrite,[status(thm)],[])).
% 0.82/1.02 tff(1829,plain,
% 0.82/1.02 ((hskp2 | (~ndr1_0) | c1_1(a194) | c2_1(a194) | (~c0_1(a194)) | c0_1(a214) | (~c1_1(a214)) | (~c2_1(a214))) <=> (hskp2 | c0_1(a214) | c1_1(a194) | c2_1(a194) | (~ndr1_0) | (~c0_1(a194)) | (~c1_1(a214)) | (~c2_1(a214)))),
% 0.82/1.02 inference(rewrite,[status(thm)],[])).
% 0.82/1.02 tff(1830,plain,
% 0.82/1.02 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp2 | (~ndr1_0) | c1_1(a194) | c2_1(a194) | (~c0_1(a194)) | c0_1(a214) | (~c1_1(a214)) | (~c2_1(a214)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp2 | c0_1(a214) | c1_1(a194) | c2_1(a194) | (~ndr1_0) | (~c0_1(a194)) | (~c1_1(a214)) | (~c2_1(a214))))),
% 0.82/1.02 inference(monotonicity,[status(thm)],[1829])).
% 0.82/1.02 tff(1831,plain,
% 0.82/1.02 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp2 | (~ndr1_0) | c1_1(a194) | c2_1(a194) | (~c0_1(a194)) | c0_1(a214) | (~c1_1(a214)) | (~c2_1(a214)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp2 | c0_1(a214) | c1_1(a194) | c2_1(a194) | (~ndr1_0) | (~c0_1(a194)) | (~c1_1(a214)) | (~c2_1(a214)))),
% 0.82/1.02 inference(transitivity,[status(thm)],[1830, 1828])).
% 0.82/1.02 tff(1832,plain,
% 0.82/1.02 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp2 | (~ndr1_0) | c1_1(a194) | c2_1(a194) | (~c0_1(a194)) | c0_1(a214) | (~c1_1(a214)) | (~c2_1(a214)))),
% 0.82/1.02 inference(quant_inst,[status(thm)],[])).
% 0.82/1.02 tff(1833,plain,
% 0.82/1.02 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp2 | c0_1(a214) | c1_1(a194) | c2_1(a194) | (~ndr1_0) | (~c0_1(a194)) | (~c1_1(a214)) | (~c2_1(a214))),
% 0.82/1.02 inference(modus_ponens,[status(thm)],[1832, 1831])).
% 0.82/1.02 tff(1834,plain,
% 0.82/1.02 ($false),
% 0.82/1.02 inference(unit_resolution,[status(thm)],[1833, 148, 14, 1817, 1827, 1809, 1826, 11, 25, 15])).
% 0.82/1.02 tff(1835,plain,((~c1_1(a214)) | hskp2 | c2_1(a194)), inference(lemma,lemma(discharge,[]))).
% 0.82/1.02 tff(1836,plain,
% 0.82/1.02 (~c1_1(a214)),
% 0.82/1.02 inference(unit_resolution,[status(thm)],[1835, 14, 11])).
% 0.82/1.02 tff(1837,plain,
% 0.82/1.02 (((~![U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp1 | c0_1(a214) | c3_1(a214) | (~ndr1_0) | c1_1(a214))) <=> ((~![U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | hskp1 | c0_1(a214) | c3_1(a214) | (~ndr1_0) | c1_1(a214))),
% 0.82/1.02 inference(rewrite,[status(thm)],[])).
% 0.82/1.02 tff(1838,plain,
% 0.82/1.02 ((hskp1 | (~ndr1_0) | c3_1(a214) | c1_1(a214) | c0_1(a214)) <=> (hskp1 | c0_1(a214) | c3_1(a214) | (~ndr1_0) | c1_1(a214))),
% 0.82/1.02 inference(rewrite,[status(thm)],[])).
% 0.82/1.02 tff(1839,plain,
% 0.82/1.02 (((~![U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp1 | (~ndr1_0) | c3_1(a214) | c1_1(a214) | c0_1(a214))) <=> ((~![U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp1 | c0_1(a214) | c3_1(a214) | (~ndr1_0) | c1_1(a214)))),
% 0.82/1.02 inference(monotonicity,[status(thm)],[1838])).
% 0.82/1.02 tff(1840,plain,
% 0.82/1.02 (((~![U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp1 | (~ndr1_0) | c3_1(a214) | c1_1(a214) | c0_1(a214))) <=> ((~![U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | hskp1 | c0_1(a214) | c3_1(a214) | (~ndr1_0) | c1_1(a214))),
% 0.82/1.02 inference(transitivity,[status(thm)],[1839, 1837])).
% 0.82/1.02 tff(1841,plain,
% 0.82/1.02 ((~![U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp1 | (~ndr1_0) | c3_1(a214) | c1_1(a214) | c0_1(a214))),
% 0.82/1.02 inference(quant_inst,[status(thm)],[])).
% 0.82/1.02 tff(1842,plain,
% 0.82/1.02 ((~![U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | hskp1 | c0_1(a214) | c3_1(a214) | (~ndr1_0) | c1_1(a214)),
% 0.82/1.02 inference(modus_ponens,[status(thm)],[1841, 1840])).
% 0.82/1.02 tff(1843,plain,
% 0.82/1.02 (hskp1 | c1_1(a214)),
% 0.82/1.02 inference(unit_resolution,[status(thm)],[1842, 148, 1809, 1803, 112])).
% 0.82/1.02 tff(1844,plain,
% 0.82/1.02 (hskp1),
% 0.82/1.02 inference(unit_resolution,[status(thm)],[1843, 1836])).
% 0.82/1.02 tff(1845,plain,
% 0.82/1.02 (c0_1(a190)),
% 0.82/1.02 inference(unit_resolution,[status(thm)],[200, 1844])).
% 0.82/1.02 tff(1846,plain,
% 0.82/1.02 (c2_1(a190)),
% 0.82/1.02 inference(unit_resolution,[status(thm)],[192, 1844])).
% 0.82/1.02 tff(1847,plain,
% 0.82/1.02 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp19 | c3_1(a214) | c3_1(a190) | (~ndr1_0) | (~c2_1(a190)) | (~c0_1(a190)) | c1_1(a214) | (~c2_1(a214)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp19 | c3_1(a214) | c3_1(a190) | (~ndr1_0) | (~c2_1(a190)) | (~c0_1(a190)) | c1_1(a214) | (~c2_1(a214)))),
% 0.82/1.02 inference(rewrite,[status(thm)],[])).
% 0.82/1.02 tff(1848,plain,
% 0.82/1.02 ((hskp19 | (~ndr1_0) | c3_1(a190) | (~c2_1(a190)) | (~c0_1(a190)) | c3_1(a214) | c1_1(a214) | (~c2_1(a214))) <=> (hskp19 | c3_1(a214) | c3_1(a190) | (~ndr1_0) | (~c2_1(a190)) | (~c0_1(a190)) | c1_1(a214) | (~c2_1(a214)))),
% 0.82/1.02 inference(rewrite,[status(thm)],[])).
% 0.82/1.02 tff(1849,plain,
% 0.82/1.02 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp19 | (~ndr1_0) | c3_1(a190) | (~c2_1(a190)) | (~c0_1(a190)) | c3_1(a214) | c1_1(a214) | (~c2_1(a214)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp19 | c3_1(a214) | c3_1(a190) | (~ndr1_0) | (~c2_1(a190)) | (~c0_1(a190)) | c1_1(a214) | (~c2_1(a214))))),
% 0.82/1.02 inference(monotonicity,[status(thm)],[1848])).
% 0.82/1.02 tff(1850,plain,
% 0.82/1.02 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp19 | (~ndr1_0) | c3_1(a190) | (~c2_1(a190)) | (~c0_1(a190)) | c3_1(a214) | c1_1(a214) | (~c2_1(a214)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp19 | c3_1(a214) | c3_1(a190) | (~ndr1_0) | (~c2_1(a190)) | (~c0_1(a190)) | c1_1(a214) | (~c2_1(a214)))),
% 0.82/1.02 inference(transitivity,[status(thm)],[1849, 1847])).
% 0.82/1.02 tff(1851,plain,
% 0.82/1.02 ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp19 | (~ndr1_0) | c3_1(a190) | (~c2_1(a190)) | (~c0_1(a190)) | c3_1(a214) | c1_1(a214) | (~c2_1(a214)))),
% 0.82/1.02 inference(quant_inst,[status(thm)],[])).
% 0.82/1.02 tff(1852,plain,
% 0.82/1.02 ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp19 | c3_1(a214) | c3_1(a190) | (~ndr1_0) | (~c2_1(a190)) | (~c0_1(a190)) | c1_1(a214) | (~c2_1(a214))),
% 0.82/1.02 inference(modus_ponens,[status(thm)],[1851, 1850])).
% 0.82/1.02 tff(1853,plain,
% 0.82/1.02 (hskp19 | (~c2_1(a190)) | (~c0_1(a190)) | c1_1(a214)),
% 0.82/1.02 inference(unit_resolution,[status(thm)],[1852, 148, 1817, 1803, 13, 211])).
% 0.82/1.02 tff(1854,plain,
% 0.82/1.02 (hskp19),
% 0.82/1.02 inference(unit_resolution,[status(thm)],[1853, 1845, 1846, 1836])).
% 0.82/1.02 tff(1855,plain,
% 0.82/1.02 (~c1_1(a190)),
% 0.82/1.02 inference(unit_resolution,[status(thm)],[1734, 1854, 1845, 13, 14])).
% 0.82/1.02 tff(1856,assumption,(~c1_1(a214)), introduced(assumption)).
% 0.82/1.02 tff(1857,assumption,(hskp22), introduced(assumption)).
% 0.82/1.02 tff(1858,plain,
% 0.82/1.02 (((~hskp22) | (~c2_1(a259))) <=> ((~hskp22) | (~c2_1(a259)))),
% 0.82/1.02 inference(rewrite,[status(thm)],[])).
% 0.82/1.02 tff(1859,plain,
% 0.82/1.02 (((~c2_1(a259)) | (~hskp22)) <=> ((~hskp22) | (~c2_1(a259)))),
% 0.82/1.02 inference(rewrite,[status(thm)],[])).
% 0.82/1.02 tff(1860,axiom,((~c2_1(a259)) | (~hskp22)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause71')).
% 0.82/1.02 tff(1861,plain,
% 0.82/1.02 ((~hskp22) | (~c2_1(a259))),
% 0.82/1.02 inference(modus_ponens,[status(thm)],[1860, 1859])).
% 0.82/1.02 tff(1862,plain,
% 0.82/1.02 ((~hskp22) | (~c2_1(a259))),
% 0.82/1.02 inference(modus_ponens,[status(thm)],[1861, 1858])).
% 0.82/1.02 tff(1863,plain,
% 0.82/1.02 (~c2_1(a259)),
% 0.82/1.02 inference(unit_resolution,[status(thm)],[1862, 1857])).
% 0.82/1.02 tff(1864,plain,
% 0.82/1.02 (((~hskp22) | (~c0_1(a259))) <=> ((~hskp22) | (~c0_1(a259)))),
% 0.82/1.02 inference(rewrite,[status(thm)],[])).
% 0.82/1.02 tff(1865,plain,
% 0.82/1.02 (((~c0_1(a259)) | (~hskp22)) <=> ((~hskp22) | (~c0_1(a259)))),
% 0.82/1.02 inference(rewrite,[status(thm)],[])).
% 0.82/1.02 tff(1866,axiom,((~c0_1(a259)) | (~hskp22)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause70')).
% 0.82/1.02 tff(1867,plain,
% 0.82/1.02 ((~hskp22) | (~c0_1(a259))),
% 0.82/1.02 inference(modus_ponens,[status(thm)],[1866, 1865])).
% 0.82/1.02 tff(1868,plain,
% 0.82/1.02 ((~hskp22) | (~c0_1(a259))),
% 0.82/1.02 inference(modus_ponens,[status(thm)],[1867, 1864])).
% 0.82/1.02 tff(1869,plain,
% 0.82/1.02 (~c0_1(a259)),
% 0.82/1.02 inference(unit_resolution,[status(thm)],[1868, 1857])).
% 0.82/1.02 tff(1870,plain,
% 0.82/1.02 (hskp1),
% 0.82/1.02 inference(unit_resolution,[status(thm)],[1843, 1856])).
% 0.82/1.02 tff(1871,plain,
% 0.82/1.02 (c2_1(a190)),
% 0.82/1.02 inference(unit_resolution,[status(thm)],[192, 1870])).
% 0.82/1.02 tff(1872,plain,
% 0.82/1.02 (c0_1(a190)),
% 0.82/1.02 inference(unit_resolution,[status(thm)],[200, 1870])).
% 0.82/1.02 tff(1873,plain,
% 0.82/1.02 (((~hskp22) | c3_1(a259)) <=> ((~hskp22) | c3_1(a259))),
% 0.82/1.02 inference(rewrite,[status(thm)],[])).
% 0.82/1.02 tff(1874,axiom,((~hskp22) | c3_1(a259)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause43')).
% 0.82/1.02 tff(1875,plain,
% 0.82/1.02 ((~hskp22) | c3_1(a259)),
% 0.82/1.02 inference(modus_ponens,[status(thm)],[1874, 1873])).
% 0.82/1.02 tff(1876,plain,
% 0.82/1.02 ((~hskp22) | c3_1(a259)),
% 0.82/1.02 inference(modus_ponens,[status(thm)],[1875, 1873])).
% 0.82/1.02 tff(1877,plain,
% 0.82/1.02 ((~hskp22) | c3_1(a259)),
% 0.82/1.02 inference(modus_ponens,[status(thm)],[1876, 1873])).
% 0.82/1.02 tff(1878,plain,
% 0.82/1.02 ((~hskp22) | c3_1(a259)),
% 0.82/1.02 inference(modus_ponens,[status(thm)],[1877, 1873])).
% 0.82/1.02 tff(1879,plain,
% 0.82/1.02 ((~hskp22) | c3_1(a259)),
% 0.82/1.02 inference(modus_ponens,[status(thm)],[1878, 1873])).
% 0.82/1.02 tff(1880,plain,
% 0.82/1.02 (c3_1(a259)),
% 0.82/1.02 inference(unit_resolution,[status(thm)],[1879, 1857])).
% 0.82/1.02 tff(1881,plain,
% 0.82/1.02 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a259) | c2_1(a259) | c3_1(a214) | c3_1(a190) | (~ndr1_0) | (~c2_1(a190)) | (~c0_1(a190)) | c1_1(a214) | (~c2_1(a214)) | (~c3_1(a259)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a259) | c2_1(a259) | c3_1(a214) | c3_1(a190) | (~ndr1_0) | (~c2_1(a190)) | (~c0_1(a190)) | c1_1(a214) | (~c2_1(a214)) | (~c3_1(a259)))),
% 0.82/1.02 inference(rewrite,[status(thm)],[])).
% 0.82/1.02 tff(1882,plain,
% 0.82/1.02 (((~ndr1_0) | c3_1(a190) | (~c2_1(a190)) | (~c0_1(a190)) | c3_1(a214) | c1_1(a214) | (~c2_1(a214)) | c2_1(a259) | c0_1(a259) | (~c3_1(a259))) <=> (c0_1(a259) | c2_1(a259) | c3_1(a214) | c3_1(a190) | (~ndr1_0) | (~c2_1(a190)) | (~c0_1(a190)) | c1_1(a214) | (~c2_1(a214)) | (~c3_1(a259)))),
% 0.82/1.02 inference(rewrite,[status(thm)],[])).
% 0.82/1.02 tff(1883,plain,
% 0.82/1.02 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a190) | (~c2_1(a190)) | (~c0_1(a190)) | c3_1(a214) | c1_1(a214) | (~c2_1(a214)) | c2_1(a259) | c0_1(a259) | (~c3_1(a259)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a259) | c2_1(a259) | c3_1(a214) | c3_1(a190) | (~ndr1_0) | (~c2_1(a190)) | (~c0_1(a190)) | c1_1(a214) | (~c2_1(a214)) | (~c3_1(a259))))),
% 0.82/1.02 inference(monotonicity,[status(thm)],[1882])).
% 0.82/1.02 tff(1884,plain,
% 0.82/1.02 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a190) | (~c2_1(a190)) | (~c0_1(a190)) | c3_1(a214) | c1_1(a214) | (~c2_1(a214)) | c2_1(a259) | c0_1(a259) | (~c3_1(a259)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a259) | c2_1(a259) | c3_1(a214) | c3_1(a190) | (~ndr1_0) | (~c2_1(a190)) | (~c0_1(a190)) | c1_1(a214) | (~c2_1(a214)) | (~c3_1(a259)))),
% 0.82/1.02 inference(transitivity,[status(thm)],[1883, 1881])).
% 0.82/1.02 tff(1885,plain,
% 0.82/1.02 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a190) | (~c2_1(a190)) | (~c0_1(a190)) | c3_1(a214) | c1_1(a214) | (~c2_1(a214)) | c2_1(a259) | c0_1(a259) | (~c3_1(a259)))),
% 0.82/1.02 inference(quant_inst,[status(thm)],[])).
% 0.82/1.02 tff(1886,plain,
% 0.82/1.02 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a259) | c2_1(a259) | c3_1(a214) | c3_1(a190) | (~ndr1_0) | (~c2_1(a190)) | (~c0_1(a190)) | c1_1(a214) | (~c2_1(a214)) | (~c3_1(a259))),
% 0.82/1.02 inference(modus_ponens,[status(thm)],[1885, 1884])).
% 0.82/1.02 tff(1887,plain,
% 0.82/1.02 ($false),
% 0.82/1.02 inference(unit_resolution,[status(thm)],[1886, 148, 1880, 1817, 1872, 1871, 1869, 1863, 1803, 13, 451, 1856])).
% 0.82/1.02 tff(1888,plain,((~hskp22) | c3_1(a190) | c1_1(a214)), inference(lemma,lemma(discharge,[]))).
% 0.82/1.02 tff(1889,plain,
% 0.82/1.02 (~hskp22),
% 0.82/1.02 inference(unit_resolution,[status(thm)],[1888, 1836, 13])).
% 0.82/1.02 tff(1890,plain,
% 0.82/1.02 ((hskp24 | hskp22 | hskp2) <=> (hskp24 | hskp22 | hskp2)),
% 0.82/1.02 inference(rewrite,[status(thm)],[])).
% 0.82/1.02 tff(1891,plain,
% 0.82/1.02 (((hskp24 | hskp22) | hskp2) <=> (hskp24 | hskp22 | hskp2)),
% 0.82/1.02 inference(rewrite,[status(thm)],[])).
% 0.82/1.02 tff(1892,plain,
% 0.82/1.02 ((hskp24 | hskp22) <=> (hskp24 | hskp22)),
% 0.82/1.02 inference(rewrite,[status(thm)],[])).
% 0.82/1.02 tff(1893,plain,
% 0.82/1.02 (((hskp24 | hskp22) | hskp2) <=> ((hskp24 | hskp22) | hskp2)),
% 0.82/1.02 inference(monotonicity,[status(thm)],[1892])).
% 0.82/1.02 tff(1894,plain,
% 0.82/1.02 (((hskp24 | hskp22) | hskp2) <=> (hskp24 | hskp22 | hskp2)),
% 0.82/1.02 inference(transitivity,[status(thm)],[1893, 1891])).
% 0.82/1.02 tff(1895,axiom,((hskp24 | hskp22) | hskp2), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause31')).
% 0.82/1.02 tff(1896,plain,
% 0.82/1.02 (hskp24 | hskp22 | hskp2),
% 0.82/1.02 inference(modus_ponens,[status(thm)],[1895, 1894])).
% 0.82/1.02 tff(1897,plain,
% 0.82/1.02 (hskp24 | hskp22 | hskp2),
% 0.82/1.02 inference(modus_ponens,[status(thm)],[1896, 1890])).
% 0.82/1.02 tff(1898,plain,
% 0.82/1.02 (hskp24 | hskp22 | hskp2),
% 0.82/1.02 inference(modus_ponens,[status(thm)],[1897, 1890])).
% 0.82/1.02 tff(1899,plain,
% 0.82/1.02 (hskp24 | hskp22 | hskp2),
% 0.82/1.02 inference(modus_ponens,[status(thm)],[1898, 1890])).
% 0.82/1.02 tff(1900,plain,
% 0.82/1.02 (hskp24 | hskp22 | hskp2),
% 0.82/1.02 inference(modus_ponens,[status(thm)],[1899, 1890])).
% 0.82/1.02 tff(1901,plain,
% 0.82/1.02 (hskp24),
% 0.82/1.02 inference(unit_resolution,[status(thm)],[1900, 1889, 14])).
% 0.82/1.02 tff(1902,plain,
% 0.82/1.02 (c3_1(a215)),
% 0.82/1.02 inference(unit_resolution,[status(thm)],[342, 1901])).
% 0.82/1.02 tff(1903,plain,
% 0.82/1.02 (c2_1(a215)),
% 0.82/1.02 inference(unit_resolution,[status(thm)],[350, 1901])).
% 0.82/1.02 tff(1904,plain,
% 0.82/1.02 (c1_1(a215)),
% 0.82/1.02 inference(unit_resolution,[status(thm)],[358, 1901])).
% 0.82/1.02 tff(1905,plain,
% 0.82/1.02 (~c0_1(a215)),
% 0.82/1.02 inference(unit_resolution,[status(thm)],[1233, 148, 1904, 1903, 1902, 1845, 13, 470, 1855])).
% 0.82/1.02 tff(1906,plain,
% 0.82/1.02 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W))) <=> ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W))))),
% 0.82/1.02 inference(bind,[status(th)],[])).
% 0.82/1.02 tff(1907,plain,
% 0.82/1.02 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 0.82/1.02 inference(quant_intro,[status(thm)],[1906])).
% 0.82/1.02 tff(1908,plain,
% 0.82/1.02 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 0.82/1.02 inference(rewrite,[status(thm)],[])).
% 0.82/1.02 tff(1909,plain,
% 0.82/1.02 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c3_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)))), ((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c3_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(V)))), ((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(V))))), (((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(V)) | (~c2_1(V)))), (((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(V)) | (~c2_1(V))))), ((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c2_1(W))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(V)) | (~c2_1(V))) | (~c2_1(W))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(V)) | (~c2_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c2_1(W)))), ((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c2_1(W))))), (((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c2_1(W))) | c1_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c2_1(W))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c2_1(W))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c2_1(W)))), (((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c2_1(W))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c2_1(W))))), ((((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c2_1(W))) | c1_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c2_1(W))) | c2_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c2_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c2_1(W)))), ((((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c2_1(W))) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c2_1(W))))), (((((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c2_1(W))) | c1_1(U)) | c2_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c2_1(W))) | c0_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c2_1(W))) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | (~c2_1(W)))), (((((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c2_1(W))) | c1_1(U)) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | (~c2_1(W))))), ((((((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c2_1(W))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | (~c2_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | (~c2_1(W))) | c0_1(W)) <=> ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)))), ((((((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c2_1(W))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W))))), (((((((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c2_1(W))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c0_1(W)) | c1_1(W)) <=> (((~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W))) | c1_1(W)))), rewrite((((~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W))) | c1_1(W)) <=> ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))), (((((((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c2_1(W))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))))),
% 0.82/1.02 inference(bind,[status(th)],[])).
% 0.82/1.02 tff(1910,plain,
% 0.82/1.02 (![W: $i, V: $i, U: $i] : ((((((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c2_1(W))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c0_1(W)) | c1_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 0.82/1.02 inference(quant_intro,[status(thm)],[1909])).
% 0.82/1.02 tff(1911,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c2_1(W))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c0_1(W)) | c1_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause154')).
% 0.82/1.02 tff(1912,plain,
% 0.82/1.02 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 0.82/1.02 inference(modus_ponens,[status(thm)],[1911, 1910])).
% 0.82/1.02 tff(1913,plain,
% 0.82/1.02 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 0.88/1.03 inference(modus_ponens,[status(thm)],[1912, 1908])).
% 0.88/1.03 tff(1914,plain,(
% 0.88/1.03 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 0.88/1.03 inference(skolemize,[status(sab)],[1913])).
% 0.88/1.03 tff(1915,plain,
% 0.88/1.03 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 0.88/1.03 inference(modus_ponens,[status(thm)],[1914, 1907])).
% 0.88/1.03 tff(1916,plain,
% 0.88/1.03 (~c1_1(a225)),
% 0.88/1.03 inference(unit_resolution,[status(thm)],[417, 1854])).
% 0.88/1.03 tff(1917,plain,
% 0.88/1.03 (c3_1(a225)),
% 0.88/1.03 inference(unit_resolution,[status(thm)],[226, 1854])).
% 0.88/1.03 tff(1918,plain,
% 0.88/1.03 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a225) | c0_1(a214) | (~ndr1_0) | (~c1_1(a215)) | (~c2_1(a215)) | c0_1(a215) | c1_1(a214) | (~c2_1(a214)) | c2_1(a225) | (~c3_1(a225)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a225) | c0_1(a214) | (~ndr1_0) | (~c1_1(a215)) | (~c2_1(a215)) | c0_1(a215) | c1_1(a214) | (~c2_1(a214)) | c2_1(a225) | (~c3_1(a225)))),
% 0.88/1.03 inference(rewrite,[status(thm)],[])).
% 0.88/1.03 tff(1919,plain,
% 0.88/1.03 (((~ndr1_0) | c1_1(a225) | c2_1(a225) | (~c3_1(a225)) | c0_1(a215) | (~c1_1(a215)) | (~c2_1(a215)) | c1_1(a214) | c0_1(a214) | (~c2_1(a214))) <=> (c1_1(a225) | c0_1(a214) | (~ndr1_0) | (~c1_1(a215)) | (~c2_1(a215)) | c0_1(a215) | c1_1(a214) | (~c2_1(a214)) | c2_1(a225) | (~c3_1(a225)))),
% 0.88/1.03 inference(rewrite,[status(thm)],[])).
% 0.88/1.03 tff(1920,plain,
% 0.88/1.03 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a225) | c2_1(a225) | (~c3_1(a225)) | c0_1(a215) | (~c1_1(a215)) | (~c2_1(a215)) | c1_1(a214) | c0_1(a214) | (~c2_1(a214)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a225) | c0_1(a214) | (~ndr1_0) | (~c1_1(a215)) | (~c2_1(a215)) | c0_1(a215) | c1_1(a214) | (~c2_1(a214)) | c2_1(a225) | (~c3_1(a225))))),
% 0.88/1.03 inference(monotonicity,[status(thm)],[1919])).
% 0.88/1.03 tff(1921,plain,
% 0.88/1.03 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a225) | c2_1(a225) | (~c3_1(a225)) | c0_1(a215) | (~c1_1(a215)) | (~c2_1(a215)) | c1_1(a214) | c0_1(a214) | (~c2_1(a214)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a225) | c0_1(a214) | (~ndr1_0) | (~c1_1(a215)) | (~c2_1(a215)) | c0_1(a215) | c1_1(a214) | (~c2_1(a214)) | c2_1(a225) | (~c3_1(a225)))),
% 0.88/1.03 inference(transitivity,[status(thm)],[1920, 1918])).
% 0.88/1.03 tff(1922,plain,
% 0.88/1.03 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a225) | c2_1(a225) | (~c3_1(a225)) | c0_1(a215) | (~c1_1(a215)) | (~c2_1(a215)) | c1_1(a214) | c0_1(a214) | (~c2_1(a214)))),
% 0.88/1.03 inference(quant_inst,[status(thm)],[])).
% 0.88/1.03 tff(1923,plain,
% 0.88/1.03 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a225) | c0_1(a214) | (~ndr1_0) | (~c1_1(a215)) | (~c2_1(a215)) | c0_1(a215) | c1_1(a214) | (~c2_1(a214)) | c2_1(a225) | (~c3_1(a225))),
% 0.88/1.03 inference(modus_ponens,[status(thm)],[1922, 1921])).
% 0.88/1.03 tff(1924,plain,
% 0.88/1.03 (c2_1(a225)),
% 0.88/1.03 inference(unit_resolution,[status(thm)],[1923, 148, 1904, 1903, 1917, 1817, 1916, 1809, 1915, 1905, 1836])).
% 0.88/1.03 tff(1925,plain,
% 0.88/1.03 (~c0_1(a225)),
% 0.88/1.03 inference(unit_resolution,[status(thm)],[232, 1854])).
% 0.88/1.03 tff(1926,plain,
% 0.88/1.03 (c0_1(a194) | (~c2_1(a190)) | (~c0_1(a190)) | c1_1(a190) | (~c3_1(a194))),
% 0.88/1.03 inference(unit_resolution,[status(thm)],[1761, 148, 11, 13, 451])).
% 0.88/1.03 tff(1927,plain,
% 0.88/1.03 (~c3_1(a194)),
% 0.88/1.03 inference(unit_resolution,[status(thm)],[1926, 1192, 1846, 1845, 1855])).
% 0.88/1.03 tff(1928,plain,
% 0.88/1.03 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a194) | c0_1(a225) | c1_1(a194) | c2_1(a194) | (~ndr1_0) | c3_1(a194) | c2_1(a225) | (~c3_1(a225)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a194) | c0_1(a225) | c1_1(a194) | c2_1(a194) | (~ndr1_0) | c3_1(a194) | c2_1(a225) | (~c3_1(a225)))),
% 0.88/1.03 inference(rewrite,[status(thm)],[])).
% 0.88/1.03 tff(1929,plain,
% 0.88/1.03 (((~ndr1_0) | c0_1(a225) | c2_1(a225) | (~c3_1(a225)) | c3_1(a194) | c1_1(a194) | c2_1(a194) | c2_1(a194) | c1_1(a194) | c0_1(a194)) <=> (c0_1(a194) | c0_1(a225) | c1_1(a194) | c2_1(a194) | (~ndr1_0) | c3_1(a194) | c2_1(a225) | (~c3_1(a225)))),
% 0.88/1.03 inference(rewrite,[status(thm)],[])).
% 0.88/1.03 tff(1930,plain,
% 0.88/1.03 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c0_1(a225) | c2_1(a225) | (~c3_1(a225)) | c3_1(a194) | c1_1(a194) | c2_1(a194) | c2_1(a194) | c1_1(a194) | c0_1(a194))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a194) | c0_1(a225) | c1_1(a194) | c2_1(a194) | (~ndr1_0) | c3_1(a194) | c2_1(a225) | (~c3_1(a225))))),
% 0.88/1.03 inference(monotonicity,[status(thm)],[1929])).
% 0.88/1.03 tff(1931,plain,
% 0.88/1.03 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c0_1(a225) | c2_1(a225) | (~c3_1(a225)) | c3_1(a194) | c1_1(a194) | c2_1(a194) | c2_1(a194) | c1_1(a194) | c0_1(a194))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a194) | c0_1(a225) | c1_1(a194) | c2_1(a194) | (~ndr1_0) | c3_1(a194) | c2_1(a225) | (~c3_1(a225)))),
% 0.88/1.03 inference(transitivity,[status(thm)],[1930, 1928])).
% 0.88/1.03 tff(1932,plain,
% 0.88/1.03 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c0_1(a225) | c2_1(a225) | (~c3_1(a225)) | c3_1(a194) | c1_1(a194) | c2_1(a194) | c2_1(a194) | c1_1(a194) | c0_1(a194))),
% 0.88/1.03 inference(quant_inst,[status(thm)],[])).
% 0.88/1.03 tff(1933,plain,
% 0.88/1.03 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a194) | c0_1(a225) | c1_1(a194) | c2_1(a194) | (~ndr1_0) | c3_1(a194) | c2_1(a225) | (~c3_1(a225))),
% 0.88/1.03 inference(modus_ponens,[status(thm)],[1932, 1931])).
% 0.88/1.03 tff(1934,plain,
% 0.88/1.03 (c2_1(a225)),
% 0.88/1.03 inference(unit_resolution,[status(thm)],[1933, 148, 1917, 1192, 1925, 12, 11, 264, 1927])).
% 0.88/1.03 tff(1935,plain,
% 0.88/1.03 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp13 | c0_1(a225) | c1_1(a194) | c2_1(a194) | (~ndr1_0) | c3_1(a194) | (~c2_1(a225)) | (~c3_1(a225)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp13 | c0_1(a225) | c1_1(a194) | c2_1(a194) | (~ndr1_0) | c3_1(a194) | (~c2_1(a225)) | (~c3_1(a225)))),
% 0.88/1.03 inference(rewrite,[status(thm)],[])).
% 0.88/1.03 tff(1936,plain,
% 0.88/1.03 ((hskp13 | (~ndr1_0) | c0_1(a225) | (~c3_1(a225)) | (~c2_1(a225)) | c3_1(a194) | c1_1(a194) | c2_1(a194)) <=> (hskp13 | c0_1(a225) | c1_1(a194) | c2_1(a194) | (~ndr1_0) | c3_1(a194) | (~c2_1(a225)) | (~c3_1(a225)))),
% 0.88/1.03 inference(rewrite,[status(thm)],[])).
% 0.88/1.03 tff(1937,plain,
% 0.88/1.03 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp13 | (~ndr1_0) | c0_1(a225) | (~c3_1(a225)) | (~c2_1(a225)) | c3_1(a194) | c1_1(a194) | c2_1(a194))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp13 | c0_1(a225) | c1_1(a194) | c2_1(a194) | (~ndr1_0) | c3_1(a194) | (~c2_1(a225)) | (~c3_1(a225))))),
% 0.88/1.03 inference(monotonicity,[status(thm)],[1936])).
% 0.88/1.03 tff(1938,plain,
% 0.88/1.03 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp13 | (~ndr1_0) | c0_1(a225) | (~c3_1(a225)) | (~c2_1(a225)) | c3_1(a194) | c1_1(a194) | c2_1(a194))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp13 | c0_1(a225) | c1_1(a194) | c2_1(a194) | (~ndr1_0) | c3_1(a194) | (~c2_1(a225)) | (~c3_1(a225)))),
% 0.88/1.03 inference(transitivity,[status(thm)],[1937, 1935])).
% 0.88/1.03 tff(1939,plain,
% 0.88/1.03 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp13 | (~ndr1_0) | c0_1(a225) | (~c3_1(a225)) | (~c2_1(a225)) | c3_1(a194) | c1_1(a194) | c2_1(a194))),
% 0.88/1.03 inference(quant_inst,[status(thm)],[])).
% 0.88/1.03 tff(1940,plain,
% 0.88/1.03 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp13 | c0_1(a225) | c1_1(a194) | c2_1(a194) | (~ndr1_0) | c3_1(a194) | (~c2_1(a225)) | (~c3_1(a225))),
% 0.88/1.03 inference(modus_ponens,[status(thm)],[1939, 1938])).
% 0.88/1.03 tff(1941,plain,
% 0.88/1.03 (hskp13),
% 0.88/1.03 inference(unit_resolution,[status(thm)],[1940, 148, 1917, 1925, 12, 11, 246, 1934, 1927])).
% 0.88/1.03 tff(1942,plain,
% 0.88/1.03 (~c0_1(a209)),
% 0.88/1.03 inference(unit_resolution,[status(thm)],[387, 1941])).
% 0.88/1.03 tff(1943,plain,
% 0.88/1.03 (c3_1(a209)),
% 0.88/1.03 inference(unit_resolution,[status(thm)],[395, 1941])).
% 0.88/1.03 tff(1944,plain,
% 0.88/1.03 (c1_1(a209)),
% 0.88/1.03 inference(unit_resolution,[status(thm)],[403, 1941])).
% 0.88/1.03 tff(1945,plain,
% 0.88/1.03 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp10 | c0_1(a209) | c1_1(a194) | c2_1(a194) | (~ndr1_0) | c3_1(a194) | (~c1_1(a209)) | (~c3_1(a209)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp10 | c0_1(a209) | c1_1(a194) | c2_1(a194) | (~ndr1_0) | c3_1(a194) | (~c1_1(a209)) | (~c3_1(a209)))),
% 0.88/1.03 inference(rewrite,[status(thm)],[])).
% 0.88/1.03 tff(1946,plain,
% 0.88/1.03 ((hskp10 | (~ndr1_0) | c0_1(a209) | (~c3_1(a209)) | (~c1_1(a209)) | c3_1(a194) | c1_1(a194) | c2_1(a194)) <=> (hskp10 | c0_1(a209) | c1_1(a194) | c2_1(a194) | (~ndr1_0) | c3_1(a194) | (~c1_1(a209)) | (~c3_1(a209)))),
% 0.88/1.03 inference(rewrite,[status(thm)],[])).
% 0.88/1.03 tff(1947,plain,
% 0.88/1.03 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp10 | (~ndr1_0) | c0_1(a209) | (~c3_1(a209)) | (~c1_1(a209)) | c3_1(a194) | c1_1(a194) | c2_1(a194))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp10 | c0_1(a209) | c1_1(a194) | c2_1(a194) | (~ndr1_0) | c3_1(a194) | (~c1_1(a209)) | (~c3_1(a209))))),
% 0.88/1.03 inference(monotonicity,[status(thm)],[1946])).
% 0.88/1.03 tff(1948,plain,
% 0.88/1.03 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp10 | (~ndr1_0) | c0_1(a209) | (~c3_1(a209)) | (~c1_1(a209)) | c3_1(a194) | c1_1(a194) | c2_1(a194))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp10 | c0_1(a209) | c1_1(a194) | c2_1(a194) | (~ndr1_0) | c3_1(a194) | (~c1_1(a209)) | (~c3_1(a209)))),
% 0.88/1.03 inference(transitivity,[status(thm)],[1947, 1945])).
% 0.88/1.03 tff(1949,plain,
% 0.88/1.03 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp10 | (~ndr1_0) | c0_1(a209) | (~c3_1(a209)) | (~c1_1(a209)) | c3_1(a194) | c1_1(a194) | c2_1(a194))),
% 0.88/1.03 inference(quant_inst,[status(thm)],[])).
% 0.88/1.03 tff(1950,plain,
% 0.88/1.03 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp10 | c0_1(a209) | c1_1(a194) | c2_1(a194) | (~ndr1_0) | c3_1(a194) | (~c1_1(a209)) | (~c3_1(a209))),
% 0.88/1.03 inference(modus_ponens,[status(thm)],[1949, 1948])).
% 0.88/1.03 tff(1951,plain,
% 0.88/1.03 (hskp10),
% 0.88/1.03 inference(unit_resolution,[status(thm)],[1950, 148, 1944, 1943, 1942, 12, 11, 10, 1927])).
% 0.88/1.03 tff(1952,plain,
% 0.88/1.03 (c0_1(a200)),
% 0.88/1.03 inference(unit_resolution,[status(thm)],[307, 1951])).
% 0.88/1.03 tff(1953,plain,
% 0.88/1.03 (hskp6),
% 0.88/1.03 inference(unit_resolution,[status(thm)],[1764, 1192, 1846, 11, 13, 14, 1845, 12])).
% 0.88/1.03 tff(1954,plain,
% 0.88/1.03 (~c3_1(a195)),
% 0.88/1.03 inference(unit_resolution,[status(thm)],[543, 1953])).
% 0.88/1.03 tff(1955,plain,
% 0.88/1.03 (~c1_1(a195)),
% 0.88/1.03 inference(unit_resolution,[status(thm)],[557, 1953])).
% 0.88/1.03 tff(1956,plain,
% 0.88/1.03 (c0_1(a195)),
% 0.88/1.03 inference(unit_resolution,[status(thm)],[551, 1953])).
% 0.88/1.03 tff(1957,plain,
% 0.88/1.03 (c3_1(a200)),
% 0.88/1.03 inference(unit_resolution,[status(thm)],[315, 1951])).
% 0.88/1.03 tff(1958,plain,
% 0.88/1.03 (~c1_1(a200)),
% 0.88/1.03 inference(unit_resolution,[status(thm)],[373, 1951])).
% 0.88/1.03 tff(1959,plain,
% 0.88/1.03 ($false),
% 0.88/1.03 inference(unit_resolution,[status(thm)],[888, 1958, 1957, 11, 1956, 1955, 1954, 1934, 1943, 1925, 1916, 1942, 1944, 12, 1952])).
% 0.88/1.03 tff(1960,plain,(c0_1(a194) | c2_1(a194) | c1_1(a194) | c3_1(a190) | hskp2), inference(lemma,lemma(discharge,[]))).
% 0.88/1.03 tff(1961,plain,
% 0.88/1.03 (c0_1(a194)),
% 0.88/1.03 inference(unit_resolution,[status(thm)],[1960, 12, 11, 13, 14])).
% 0.88/1.03 tff(1962,plain,
% 0.88/1.03 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_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(a225) | c1_1(a225) | c1_1(a194) | c2_1(a194) | (~ndr1_0) | (~c0_1(a194)) | (~c1_1(a215)) | c0_1(a215) | (~c3_1(a215)) | (~c2_1(a225)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_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(a225) | c1_1(a225) | c1_1(a194) | c2_1(a194) | (~ndr1_0) | (~c0_1(a194)) | (~c1_1(a215)) | c0_1(a215) | (~c3_1(a215)) | (~c2_1(a225)))),
% 0.88/1.03 inference(rewrite,[status(thm)],[])).
% 0.88/1.03 tff(1963,plain,
% 0.88/1.03 (((~ndr1_0) | c1_1(a194) | c2_1(a194) | (~c0_1(a194)) | c0_1(a215) | (~c3_1(a215)) | (~c1_1(a215)) | c1_1(a225) | c0_1(a225) | (~c2_1(a225))) <=> (c0_1(a225) | c1_1(a225) | c1_1(a194) | c2_1(a194) | (~ndr1_0) | (~c0_1(a194)) | (~c1_1(a215)) | c0_1(a215) | (~c3_1(a215)) | (~c2_1(a225)))),
% 0.88/1.03 inference(rewrite,[status(thm)],[])).
% 0.88/1.03 tff(1964,plain,
% 0.88/1.03 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_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) | c1_1(a194) | c2_1(a194) | (~c0_1(a194)) | c0_1(a215) | (~c3_1(a215)) | (~c1_1(a215)) | c1_1(a225) | c0_1(a225) | (~c2_1(a225)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_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(a225) | c1_1(a225) | c1_1(a194) | c2_1(a194) | (~ndr1_0) | (~c0_1(a194)) | (~c1_1(a215)) | c0_1(a215) | (~c3_1(a215)) | (~c2_1(a225))))),
% 0.88/1.03 inference(monotonicity,[status(thm)],[1963])).
% 0.88/1.03 tff(1965,plain,
% 0.88/1.03 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_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) | c1_1(a194) | c2_1(a194) | (~c0_1(a194)) | c0_1(a215) | (~c3_1(a215)) | (~c1_1(a215)) | c1_1(a225) | c0_1(a225) | (~c2_1(a225)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_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(a225) | c1_1(a225) | c1_1(a194) | c2_1(a194) | (~ndr1_0) | (~c0_1(a194)) | (~c1_1(a215)) | c0_1(a215) | (~c3_1(a215)) | (~c2_1(a225)))),
% 0.88/1.03 inference(transitivity,[status(thm)],[1964, 1962])).
% 0.88/1.03 tff(1966,plain,
% 0.88/1.03 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_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) | c1_1(a194) | c2_1(a194) | (~c0_1(a194)) | c0_1(a215) | (~c3_1(a215)) | (~c1_1(a215)) | c1_1(a225) | c0_1(a225) | (~c2_1(a225)))),
% 0.88/1.03 inference(quant_inst,[status(thm)],[])).
% 0.88/1.03 tff(1967,plain,
% 0.88/1.03 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a225) | c1_1(a225) | c1_1(a194) | c2_1(a194) | (~ndr1_0) | (~c0_1(a194)) | (~c1_1(a215)) | c0_1(a215) | (~c3_1(a215)) | (~c2_1(a225))),
% 0.88/1.03 inference(modus_ponens,[status(thm)],[1966, 1965])).
% 0.88/1.03 tff(1968,plain,
% 0.88/1.03 ($false),
% 0.88/1.03 inference(unit_resolution,[status(thm)],[1967, 148, 1904, 1902, 1961, 1925, 1916, 12, 11, 65, 1924, 1905])).
% 0.88/1.03 tff(1969,plain,(c1_1(a194) | c2_1(a194) | c3_1(a190) | hskp2), inference(lemma,lemma(discharge,[]))).
% 0.88/1.03 tff(1970,plain,
% 0.88/1.03 (c1_1(a194)),
% 0.88/1.03 inference(unit_resolution,[status(thm)],[1969, 14, 13, 11])).
% 0.88/1.03 tff(1971,plain,
% 0.88/1.03 (~c3_1(a194)),
% 0.88/1.03 inference(unit_resolution,[status(thm)],[1926, 1192, 784, 829, 1223])).
% 0.88/1.03 tff(1972,assumption,(c1_1(a194)), introduced(assumption)).
% 0.88/1.03 tff(1973,plain,
% 0.88/1.03 (~hskp5),
% 0.88/1.03 inference(unit_resolution,[status(thm)],[590, 1972])).
% 0.88/1.03 tff(1974,plain,
% 0.88/1.03 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp5 | c0_1(a194) | c0_1(a214) | c3_1(a214) | (~c1_1(a194)) | (~ndr1_0) | c3_1(a194) | (~c2_1(a214)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp5 | c0_1(a194) | c0_1(a214) | c3_1(a214) | (~c1_1(a194)) | (~ndr1_0) | c3_1(a194) | (~c2_1(a214)))),
% 0.88/1.03 inference(rewrite,[status(thm)],[])).
% 0.88/1.03 tff(1975,plain,
% 0.88/1.03 ((hskp5 | (~ndr1_0) | c3_1(a214) | c0_1(a214) | (~c2_1(a214)) | c3_1(a194) | c0_1(a194) | (~c1_1(a194))) <=> (hskp5 | c0_1(a194) | c0_1(a214) | c3_1(a214) | (~c1_1(a194)) | (~ndr1_0) | c3_1(a194) | (~c2_1(a214)))),
% 0.88/1.03 inference(rewrite,[status(thm)],[])).
% 0.88/1.03 tff(1976,plain,
% 0.88/1.03 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp5 | (~ndr1_0) | c3_1(a214) | c0_1(a214) | (~c2_1(a214)) | c3_1(a194) | c0_1(a194) | (~c1_1(a194)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp5 | c0_1(a194) | c0_1(a214) | c3_1(a214) | (~c1_1(a194)) | (~ndr1_0) | c3_1(a194) | (~c2_1(a214))))),
% 0.88/1.03 inference(monotonicity,[status(thm)],[1975])).
% 0.88/1.03 tff(1977,plain,
% 0.88/1.03 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp5 | (~ndr1_0) | c3_1(a214) | c0_1(a214) | (~c2_1(a214)) | c3_1(a194) | c0_1(a194) | (~c1_1(a194)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp5 | c0_1(a194) | c0_1(a214) | c3_1(a214) | (~c1_1(a194)) | (~ndr1_0) | c3_1(a194) | (~c2_1(a214)))),
% 0.88/1.03 inference(transitivity,[status(thm)],[1976, 1974])).
% 0.88/1.03 tff(1978,plain,
% 0.88/1.03 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp5 | (~ndr1_0) | c3_1(a214) | c0_1(a214) | (~c2_1(a214)) | c3_1(a194) | c0_1(a194) | (~c1_1(a194)))),
% 0.88/1.03 inference(quant_inst,[status(thm)],[])).
% 0.88/1.03 tff(1979,plain,
% 0.88/1.03 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp5 | c0_1(a194) | c0_1(a214) | c3_1(a214) | (~c1_1(a194)) | (~ndr1_0) | c3_1(a194) | (~c2_1(a214))),
% 0.88/1.03 inference(modus_ponens,[status(thm)],[1978, 1977])).
% 0.88/1.03 tff(1980,plain,
% 0.88/1.03 ($false),
% 0.88/1.03 inference(unit_resolution,[status(thm)],[1979, 148, 1973, 1817, 1192, 1809, 1803, 1972, 35, 1971])).
% 0.88/1.03 tff(1981,plain,(c0_1(a194) | (~c1_1(a194)) | (~c2_1(a190)) | (~c0_1(a190)) | c1_1(a190) | c2_1(a194) | c3_1(a190)), inference(lemma,lemma(discharge,[]))).
% 0.88/1.03 tff(1982,plain,
% 0.88/1.03 (c0_1(a194)),
% 0.88/1.03 inference(unit_resolution,[status(thm)],[1981, 1970, 1846, 1845, 1855, 11, 13])).
% 0.88/1.03 tff(1983,assumption,(hskp25), introduced(assumption)).
% 0.88/1.03 tff(1984,plain,
% 0.88/1.03 (c1_1(a230)),
% 0.88/1.03 inference(unit_resolution,[status(thm)],[1120, 1983])).
% 0.88/1.03 tff(1985,plain,
% 0.88/1.03 (c0_1(a230)),
% 0.88/1.03 inference(unit_resolution,[status(thm)],[1104, 1983])).
% 0.88/1.03 tff(1986,plain,
% 0.88/1.03 (c2_1(a230)),
% 0.88/1.03 inference(unit_resolution,[status(thm)],[1112, 1983])).
% 0.88/1.03 tff(1987,plain,
% 0.88/1.03 ($false),
% 0.88/1.03 inference(unit_resolution,[status(thm)],[1727, 1986, 1985, 1223, 14, 1984])).
% 0.88/1.03 tff(1988,plain,((~hskp25) | c1_1(a190) | hskp2), inference(lemma,lemma(discharge,[]))).
% 0.88/1.03 tff(1989,plain,
% 0.88/1.03 (~hskp25),
% 0.88/1.03 inference(unit_resolution,[status(thm)],[1988, 1855, 14])).
% 0.88/1.03 tff(1990,plain,
% 0.88/1.03 (^[U: $i] : refl((hskp25 | hskp16 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) <=> (hskp25 | hskp16 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))))),
% 0.88/1.03 inference(bind,[status(th)],[])).
% 0.88/1.03 tff(1991,plain,
% 0.88/1.03 (![U: $i] : (hskp25 | hskp16 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp25 | hskp16 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 0.88/1.03 inference(quant_intro,[status(thm)],[1990])).
% 0.88/1.03 tff(1992,plain,
% 0.88/1.03 (![U: $i] : (hskp25 | hskp16 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp25 | hskp16 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 0.88/1.03 inference(rewrite,[status(thm)],[])).
% 0.88/1.03 tff(1993,plain,
% 0.88/1.03 (^[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)) | 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)) | hskp25) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) | hskp25))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) | hskp25) <=> (hskp25 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp25) <=> (hskp25 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp25) | hskp16) <=> ((hskp25 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) | hskp16))), rewrite(((hskp25 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) | hskp16) <=> (hskp25 | hskp16 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp25) | hskp16) <=> (hskp25 | hskp16 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))))),
% 0.88/1.03 inference(bind,[status(th)],[])).
% 0.88/1.03 tff(1994,plain,
% 0.88/1.03 (![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp25) | hskp16) <=> ![U: $i] : (hskp25 | hskp16 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 0.88/1.03 inference(quant_intro,[status(thm)],[1993])).
% 0.88/1.03 tff(1995,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp25) | hskp16)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause121')).
% 0.88/1.03 tff(1996,plain,
% 0.88/1.03 (![U: $i] : (hskp25 | hskp16 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 0.88/1.03 inference(modus_ponens,[status(thm)],[1995, 1994])).
% 0.88/1.03 tff(1997,plain,
% 0.88/1.03 (![U: $i] : (hskp25 | hskp16 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 0.88/1.03 inference(modus_ponens,[status(thm)],[1996, 1992])).
% 0.88/1.03 tff(1998,plain,(
% 0.88/1.03 ![U: $i] : (hskp25 | hskp16 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 0.88/1.03 inference(skolemize,[status(sab)],[1997])).
% 0.88/1.03 tff(1999,plain,
% 0.88/1.03 (![U: $i] : (hskp25 | hskp16 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 0.88/1.03 inference(modus_ponens,[status(thm)],[1998, 1991])).
% 0.88/1.03 tff(2000,plain,
% 0.88/1.03 (((~![U: $i] : (hskp25 | hskp16 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp25 | hskp16 | (~c1_1(a194)) | c2_1(a194) | (~ndr1_0) | (~c0_1(a194)))) <=> ((~![U: $i] : (hskp25 | hskp16 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp25 | hskp16 | (~c1_1(a194)) | c2_1(a194) | (~ndr1_0) | (~c0_1(a194)))),
% 0.88/1.03 inference(rewrite,[status(thm)],[])).
% 0.88/1.03 tff(2001,plain,
% 0.88/1.03 ((hskp25 | hskp16 | (~ndr1_0) | c2_1(a194) | (~c1_1(a194)) | (~c0_1(a194))) <=> (hskp25 | hskp16 | (~c1_1(a194)) | c2_1(a194) | (~ndr1_0) | (~c0_1(a194)))),
% 0.88/1.03 inference(rewrite,[status(thm)],[])).
% 0.88/1.03 tff(2002,plain,
% 0.88/1.03 (((~![U: $i] : (hskp25 | hskp16 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp25 | hskp16 | (~ndr1_0) | c2_1(a194) | (~c1_1(a194)) | (~c0_1(a194)))) <=> ((~![U: $i] : (hskp25 | hskp16 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp25 | hskp16 | (~c1_1(a194)) | c2_1(a194) | (~ndr1_0) | (~c0_1(a194))))),
% 0.88/1.03 inference(monotonicity,[status(thm)],[2001])).
% 0.88/1.03 tff(2003,plain,
% 0.88/1.03 (((~![U: $i] : (hskp25 | hskp16 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp25 | hskp16 | (~ndr1_0) | c2_1(a194) | (~c1_1(a194)) | (~c0_1(a194)))) <=> ((~![U: $i] : (hskp25 | hskp16 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp25 | hskp16 | (~c1_1(a194)) | c2_1(a194) | (~ndr1_0) | (~c0_1(a194)))),
% 0.88/1.03 inference(transitivity,[status(thm)],[2002, 2000])).
% 0.88/1.03 tff(2004,plain,
% 0.88/1.03 ((~![U: $i] : (hskp25 | hskp16 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp25 | hskp16 | (~ndr1_0) | c2_1(a194) | (~c1_1(a194)) | (~c0_1(a194)))),
% 0.88/1.03 inference(quant_inst,[status(thm)],[])).
% 0.88/1.03 tff(2005,plain,
% 0.88/1.03 ((~![U: $i] : (hskp25 | hskp16 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp25 | hskp16 | (~c1_1(a194)) | c2_1(a194) | (~ndr1_0) | (~c0_1(a194))),
% 0.88/1.03 inference(modus_ponens,[status(thm)],[2004, 2003])).
% 0.88/1.03 tff(2006,plain,
% 0.88/1.03 (hskp25 | hskp16 | (~c1_1(a194)) | (~c0_1(a194))),
% 0.88/1.03 inference(unit_resolution,[status(thm)],[2005, 148, 11, 1999])).
% 0.88/1.03 tff(2007,plain,
% 0.88/1.03 (hskp16),
% 0.88/1.03 inference(unit_resolution,[status(thm)],[2006, 1989, 1970, 1982])).
% 0.88/1.03 tff(2008,plain,
% 0.88/1.03 (((~hskp16) | (~c2_1(a221))) <=> ((~hskp16) | (~c2_1(a221)))),
% 0.88/1.03 inference(rewrite,[status(thm)],[])).
% 0.88/1.03 tff(2009,plain,
% 0.88/1.03 (((~c2_1(a221)) | (~hskp16)) <=> ((~hskp16) | (~c2_1(a221)))),
% 0.88/1.03 inference(rewrite,[status(thm)],[])).
% 0.88/1.03 tff(2010,axiom,((~c2_1(a221)) | (~hskp16)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause82')).
% 0.88/1.03 tff(2011,plain,
% 0.88/1.03 ((~hskp16) | (~c2_1(a221))),
% 0.88/1.03 inference(modus_ponens,[status(thm)],[2010, 2009])).
% 0.88/1.03 tff(2012,plain,
% 0.88/1.03 ((~hskp16) | (~c2_1(a221))),
% 0.88/1.03 inference(modus_ponens,[status(thm)],[2011, 2008])).
% 0.88/1.03 tff(2013,plain,
% 0.88/1.03 (~c2_1(a221)),
% 0.88/1.03 inference(unit_resolution,[status(thm)],[2012, 2007])).
% 0.88/1.03 tff(2014,plain,
% 0.88/1.03 (((~hskp16) | (~c1_1(a221))) <=> ((~hskp16) | (~c1_1(a221)))),
% 0.88/1.03 inference(rewrite,[status(thm)],[])).
% 0.88/1.03 tff(2015,plain,
% 0.88/1.03 (((~c1_1(a221)) | (~hskp16)) <=> ((~hskp16) | (~c1_1(a221)))),
% 0.88/1.03 inference(rewrite,[status(thm)],[])).
% 0.88/1.03 tff(2016,axiom,((~c1_1(a221)) | (~hskp16)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause81')).
% 0.88/1.03 tff(2017,plain,
% 0.88/1.03 ((~hskp16) | (~c1_1(a221))),
% 0.88/1.03 inference(modus_ponens,[status(thm)],[2016, 2015])).
% 0.88/1.03 tff(2018,plain,
% 0.88/1.03 ((~hskp16) | (~c1_1(a221))),
% 0.88/1.03 inference(modus_ponens,[status(thm)],[2017, 2014])).
% 0.88/1.03 tff(2019,plain,
% 0.88/1.03 (~c1_1(a221)),
% 0.88/1.03 inference(unit_resolution,[status(thm)],[2018, 2007])).
% 0.88/1.03 tff(2020,plain,
% 0.88/1.03 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a225) | c1_1(a225) | c1_1(a221) | c2_1(a221) | (~ndr1_0) | (~c1_1(a215)) | (~c2_1(a215)) | c0_1(a215) | (~c3_1(a221)) | (~c2_1(a225)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a225) | c1_1(a225) | c1_1(a221) | c2_1(a221) | (~ndr1_0) | (~c1_1(a215)) | (~c2_1(a215)) | c0_1(a215) | (~c3_1(a221)) | (~c2_1(a225)))),
% 0.88/1.03 inference(rewrite,[status(thm)],[])).
% 0.88/1.03 tff(2021,plain,
% 0.88/1.03 (((~ndr1_0) | c1_1(a221) | c2_1(a221) | (~c3_1(a221)) | c0_1(a215) | (~c1_1(a215)) | (~c2_1(a215)) | c1_1(a225) | c0_1(a225) | (~c2_1(a225))) <=> (c0_1(a225) | c1_1(a225) | c1_1(a221) | c2_1(a221) | (~ndr1_0) | (~c1_1(a215)) | (~c2_1(a215)) | c0_1(a215) | (~c3_1(a221)) | (~c2_1(a225)))),
% 0.88/1.03 inference(rewrite,[status(thm)],[])).
% 0.88/1.03 tff(2022,plain,
% 0.88/1.03 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a221) | c2_1(a221) | (~c3_1(a221)) | c0_1(a215) | (~c1_1(a215)) | (~c2_1(a215)) | c1_1(a225) | c0_1(a225) | (~c2_1(a225)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a225) | c1_1(a225) | c1_1(a221) | c2_1(a221) | (~ndr1_0) | (~c1_1(a215)) | (~c2_1(a215)) | c0_1(a215) | (~c3_1(a221)) | (~c2_1(a225))))),
% 0.88/1.03 inference(monotonicity,[status(thm)],[2021])).
% 0.88/1.03 tff(2023,plain,
% 0.88/1.03 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a221) | c2_1(a221) | (~c3_1(a221)) | c0_1(a215) | (~c1_1(a215)) | (~c2_1(a215)) | c1_1(a225) | c0_1(a225) | (~c2_1(a225)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a225) | c1_1(a225) | c1_1(a221) | c2_1(a221) | (~ndr1_0) | (~c1_1(a215)) | (~c2_1(a215)) | c0_1(a215) | (~c3_1(a221)) | (~c2_1(a225)))),
% 0.88/1.03 inference(transitivity,[status(thm)],[2022, 2020])).
% 0.88/1.03 tff(2024,plain,
% 0.88/1.03 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a221) | c2_1(a221) | (~c3_1(a221)) | c0_1(a215) | (~c1_1(a215)) | (~c2_1(a215)) | c1_1(a225) | c0_1(a225) | (~c2_1(a225)))),
% 0.88/1.03 inference(quant_inst,[status(thm)],[])).
% 0.88/1.03 tff(2025,plain,
% 0.88/1.03 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a225) | c1_1(a225) | c1_1(a221) | c2_1(a221) | (~ndr1_0) | (~c1_1(a215)) | (~c2_1(a215)) | c0_1(a215) | (~c3_1(a221)) | (~c2_1(a225))),
% 0.88/1.03 inference(modus_ponens,[status(thm)],[2024, 2023])).
% 0.88/1.03 tff(2026,plain,
% 0.88/1.03 (~c3_1(a221)),
% 0.88/1.03 inference(unit_resolution,[status(thm)],[2025, 148, 1904, 1903, 1925, 1916, 2019, 2013, 1915, 1924, 1905])).
% 0.88/1.03 tff(2027,plain,
% 0.88/1.03 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp10 | c1_1(a221) | c2_1(a221) | (~ndr1_0) | (~c1_1(a215)) | c0_1(a215) | (~c3_1(a215)) | c3_1(a221))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp10 | c1_1(a221) | c2_1(a221) | (~ndr1_0) | (~c1_1(a215)) | c0_1(a215) | (~c3_1(a215)) | c3_1(a221))),
% 0.88/1.03 inference(rewrite,[status(thm)],[])).
% 0.88/1.03 tff(2028,plain,
% 0.88/1.03 ((hskp10 | (~ndr1_0) | c0_1(a215) | (~c3_1(a215)) | (~c1_1(a215)) | c3_1(a221) | c1_1(a221) | c2_1(a221)) <=> (hskp10 | c1_1(a221) | c2_1(a221) | (~ndr1_0) | (~c1_1(a215)) | c0_1(a215) | (~c3_1(a215)) | c3_1(a221))),
% 0.88/1.04 inference(rewrite,[status(thm)],[])).
% 0.88/1.04 tff(2029,plain,
% 0.88/1.04 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp10 | (~ndr1_0) | c0_1(a215) | (~c3_1(a215)) | (~c1_1(a215)) | c3_1(a221) | c1_1(a221) | c2_1(a221))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp10 | c1_1(a221) | c2_1(a221) | (~ndr1_0) | (~c1_1(a215)) | c0_1(a215) | (~c3_1(a215)) | c3_1(a221)))),
% 0.88/1.04 inference(monotonicity,[status(thm)],[2028])).
% 0.88/1.04 tff(2030,plain,
% 0.88/1.04 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp10 | (~ndr1_0) | c0_1(a215) | (~c3_1(a215)) | (~c1_1(a215)) | c3_1(a221) | c1_1(a221) | c2_1(a221))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp10 | c1_1(a221) | c2_1(a221) | (~ndr1_0) | (~c1_1(a215)) | c0_1(a215) | (~c3_1(a215)) | c3_1(a221))),
% 0.88/1.04 inference(transitivity,[status(thm)],[2029, 2027])).
% 0.88/1.04 tff(2031,plain,
% 0.88/1.04 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp10 | (~ndr1_0) | c0_1(a215) | (~c3_1(a215)) | (~c1_1(a215)) | c3_1(a221) | c1_1(a221) | c2_1(a221))),
% 0.88/1.04 inference(quant_inst,[status(thm)],[])).
% 0.88/1.04 tff(2032,plain,
% 0.88/1.04 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp10 | c1_1(a221) | c2_1(a221) | (~ndr1_0) | (~c1_1(a215)) | c0_1(a215) | (~c3_1(a215)) | c3_1(a221)),
% 0.88/1.04 inference(modus_ponens,[status(thm)],[2031, 2030])).
% 0.88/1.04 tff(2033,plain,
% 0.88/1.04 (hskp10),
% 0.88/1.04 inference(unit_resolution,[status(thm)],[2032, 148, 1904, 1902, 2019, 2013, 10, 1905, 2026])).
% 0.88/1.04 tff(2034,plain,
% 0.88/1.04 (c0_1(a200)),
% 0.88/1.04 inference(unit_resolution,[status(thm)],[307, 2033])).
% 0.88/1.04 tff(2035,assumption,(hskp16), introduced(assumption)).
% 0.88/1.04 tff(2036,plain,
% 0.88/1.04 (~c2_1(a221)),
% 0.88/1.04 inference(unit_resolution,[status(thm)],[2012, 2035])).
% 0.88/1.04 tff(2037,plain,
% 0.88/1.04 (((~hskp16) | (~c0_1(a221))) <=> ((~hskp16) | (~c0_1(a221)))),
% 0.88/1.04 inference(rewrite,[status(thm)],[])).
% 0.88/1.04 tff(2038,plain,
% 0.88/1.04 (((~c0_1(a221)) | (~hskp16)) <=> ((~hskp16) | (~c0_1(a221)))),
% 0.88/1.04 inference(rewrite,[status(thm)],[])).
% 0.88/1.04 tff(2039,axiom,((~c0_1(a221)) | (~hskp16)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause80')).
% 0.88/1.04 tff(2040,plain,
% 0.88/1.04 ((~hskp16) | (~c0_1(a221))),
% 0.88/1.04 inference(modus_ponens,[status(thm)],[2039, 2038])).
% 0.88/1.04 tff(2041,plain,
% 0.88/1.04 ((~hskp16) | (~c0_1(a221))),
% 0.88/1.04 inference(modus_ponens,[status(thm)],[2040, 2037])).
% 0.88/1.04 tff(2042,plain,
% 0.88/1.04 (~c0_1(a221)),
% 0.88/1.04 inference(unit_resolution,[status(thm)],[2041, 2035])).
% 0.88/1.04 tff(2043,plain,
% 0.88/1.04 (((~![U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp6 | c0_1(a221) | c2_1(a221) | (~ndr1_0) | c3_1(a221))) <=> ((~![U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | hskp6 | c0_1(a221) | c2_1(a221) | (~ndr1_0) | c3_1(a221))),
% 0.88/1.04 inference(rewrite,[status(thm)],[])).
% 0.88/1.04 tff(2044,plain,
% 0.88/1.04 ((hskp6 | (~ndr1_0) | c3_1(a221) | c0_1(a221) | c2_1(a221)) <=> (hskp6 | c0_1(a221) | c2_1(a221) | (~ndr1_0) | c3_1(a221))),
% 0.88/1.04 inference(rewrite,[status(thm)],[])).
% 0.88/1.04 tff(2045,plain,
% 0.88/1.04 (((~![U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp6 | (~ndr1_0) | c3_1(a221) | c0_1(a221) | c2_1(a221))) <=> ((~![U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp6 | c0_1(a221) | c2_1(a221) | (~ndr1_0) | c3_1(a221)))),
% 0.88/1.04 inference(monotonicity,[status(thm)],[2044])).
% 0.88/1.04 tff(2046,plain,
% 0.88/1.04 (((~![U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp6 | (~ndr1_0) | c3_1(a221) | c0_1(a221) | c2_1(a221))) <=> ((~![U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | hskp6 | c0_1(a221) | c2_1(a221) | (~ndr1_0) | c3_1(a221))),
% 0.88/1.04 inference(transitivity,[status(thm)],[2045, 2043])).
% 0.88/1.04 tff(2047,plain,
% 0.88/1.04 ((~![U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp6 | (~ndr1_0) | c3_1(a221) | c0_1(a221) | c2_1(a221))),
% 0.88/1.04 inference(quant_inst,[status(thm)],[])).
% 0.88/1.04 tff(2048,plain,
% 0.88/1.04 ((~![U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | hskp6 | c0_1(a221) | c2_1(a221) | (~ndr1_0) | c3_1(a221)),
% 0.88/1.04 inference(modus_ponens,[status(thm)],[2047, 2046])).
% 0.88/1.04 tff(2049,plain,
% 0.88/1.04 (c3_1(a221)),
% 0.88/1.04 inference(unit_resolution,[status(thm)],[2048, 148, 1191, 2042, 2036, 530])).
% 0.88/1.04 tff(2050,plain,
% 0.88/1.04 (~c1_1(a221)),
% 0.88/1.04 inference(unit_resolution,[status(thm)],[2018, 2035])).
% 0.88/1.04 tff(2051,plain,
% 0.88/1.04 ($false),
% 0.88/1.04 inference(unit_resolution,[status(thm)],[2025, 148, 1436, 1435, 235, 433, 2050, 2036, 1915, 870, 1475, 2049])).
% 0.88/1.04 tff(2052,plain,((~hskp16) | (~c1_1(a215)) | (~c2_1(a215)) | c0_1(a225) | c1_1(a225) | (~c2_1(a225)) | c0_1(a215) | hskp6), inference(lemma,lemma(discharge,[]))).
% 0.88/1.04 tff(2053,plain,
% 0.88/1.04 (hskp6),
% 0.88/1.04 inference(unit_resolution,[status(thm)],[2052, 2007, 1903, 1925, 1916, 1924, 1905, 1904])).
% 0.88/1.04 tff(2054,plain,
% 0.88/1.04 (~c3_1(a195)),
% 0.88/1.04 inference(unit_resolution,[status(thm)],[543, 2053])).
% 0.88/1.04 tff(2055,plain,
% 0.88/1.04 (~c1_1(a195)),
% 0.88/1.04 inference(unit_resolution,[status(thm)],[557, 2053])).
% 0.88/1.04 tff(2056,plain,
% 0.88/1.04 (c0_1(a195)),
% 0.88/1.04 inference(unit_resolution,[status(thm)],[551, 2053])).
% 0.88/1.04 tff(2057,plain,
% 0.88/1.04 (~hskp5),
% 0.88/1.04 inference(unit_resolution,[status(thm)],[590, 1970])).
% 0.88/1.04 tff(2058,plain,
% 0.88/1.04 (c3_1(a200)),
% 0.88/1.04 inference(unit_resolution,[status(thm)],[315, 2033])).
% 0.88/1.04 tff(2059,plain,
% 0.88/1.04 (~c2_1(a200)),
% 0.88/1.04 inference(unit_resolution,[status(thm)],[576, 2058, 2057, 2056, 2055, 2054, 2034])).
% 0.88/1.04 tff(2060,plain,
% 0.88/1.04 (~c1_1(a200)),
% 0.88/1.04 inference(unit_resolution,[status(thm)],[373, 2033])).
% 0.88/1.04 tff(2061,plain,
% 0.88/1.04 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp13 | c0_1(a225) | c1_1(a221) | c2_1(a221) | (~ndr1_0) | c3_1(a221) | (~c2_1(a225)) | (~c3_1(a225)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp13 | c0_1(a225) | c1_1(a221) | c2_1(a221) | (~ndr1_0) | c3_1(a221) | (~c2_1(a225)) | (~c3_1(a225)))),
% 0.88/1.04 inference(rewrite,[status(thm)],[])).
% 0.88/1.04 tff(2062,plain,
% 0.88/1.04 ((hskp13 | (~ndr1_0) | c0_1(a225) | (~c3_1(a225)) | (~c2_1(a225)) | c3_1(a221) | c1_1(a221) | c2_1(a221)) <=> (hskp13 | c0_1(a225) | c1_1(a221) | c2_1(a221) | (~ndr1_0) | c3_1(a221) | (~c2_1(a225)) | (~c3_1(a225)))),
% 0.88/1.04 inference(rewrite,[status(thm)],[])).
% 0.88/1.04 tff(2063,plain,
% 0.88/1.04 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp13 | (~ndr1_0) | c0_1(a225) | (~c3_1(a225)) | (~c2_1(a225)) | c3_1(a221) | c1_1(a221) | c2_1(a221))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp13 | c0_1(a225) | c1_1(a221) | c2_1(a221) | (~ndr1_0) | c3_1(a221) | (~c2_1(a225)) | (~c3_1(a225))))),
% 0.88/1.04 inference(monotonicity,[status(thm)],[2062])).
% 0.88/1.04 tff(2064,plain,
% 0.88/1.04 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp13 | (~ndr1_0) | c0_1(a225) | (~c3_1(a225)) | (~c2_1(a225)) | c3_1(a221) | c1_1(a221) | c2_1(a221))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp13 | c0_1(a225) | c1_1(a221) | c2_1(a221) | (~ndr1_0) | c3_1(a221) | (~c2_1(a225)) | (~c3_1(a225)))),
% 0.88/1.04 inference(transitivity,[status(thm)],[2063, 2061])).
% 0.88/1.04 tff(2065,plain,
% 0.88/1.04 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp13 | (~ndr1_0) | c0_1(a225) | (~c3_1(a225)) | (~c2_1(a225)) | c3_1(a221) | c1_1(a221) | c2_1(a221))),
% 0.88/1.04 inference(quant_inst,[status(thm)],[])).
% 0.88/1.04 tff(2066,plain,
% 0.88/1.04 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp13 | c0_1(a225) | c1_1(a221) | c2_1(a221) | (~ndr1_0) | c3_1(a221) | (~c2_1(a225)) | (~c3_1(a225))),
% 0.88/1.04 inference(modus_ponens,[status(thm)],[2065, 2064])).
% 0.88/1.04 tff(2067,plain,
% 0.88/1.04 (hskp13),
% 0.88/1.04 inference(unit_resolution,[status(thm)],[2066, 148, 1917, 1925, 2019, 2013, 246, 1924, 2026])).
% 0.88/1.04 tff(2068,plain,
% 0.88/1.04 (~c0_1(a209)),
% 0.88/1.04 inference(unit_resolution,[status(thm)],[387, 2067])).
% 0.88/1.04 tff(2069,plain,
% 0.88/1.04 (c3_1(a209)),
% 0.88/1.04 inference(unit_resolution,[status(thm)],[395, 2067])).
% 0.88/1.04 tff(2070,plain,
% 0.88/1.04 (c1_1(a209)),
% 0.88/1.04 inference(unit_resolution,[status(thm)],[403, 2067])).
% 0.88/1.04 tff(2071,plain,
% 0.88/1.04 ($false),
% 0.88/1.04 inference(unit_resolution,[status(thm)],[439, 148, 2070, 2069, 2034, 1925, 1916, 2068, 2060, 65, 1924, 2059])).
% 0.88/1.04 tff(2072,plain,(hskp2 | c2_1(a194) | c3_1(a190)), inference(lemma,lemma(discharge,[]))).
% 0.88/1.04 tff(2073,plain,
% 0.88/1.04 (hskp2),
% 0.88/1.04 inference(unit_resolution,[status(thm)],[2072, 13, 11])).
% 0.88/1.04 tff(2074,plain,
% 0.88/1.04 (~c3_1(a191)),
% 0.88/1.04 inference(unit_resolution,[status(thm)],[42, 2073])).
% 0.88/1.04 tff(2075,plain,
% 0.88/1.04 (~c2_1(a191)),
% 0.88/1.04 inference(unit_resolution,[status(thm)],[48, 2073])).
% 0.88/1.04 tff(2076,plain,
% 0.88/1.04 (~c1_1(a191)),
% 0.88/1.04 inference(unit_resolution,[status(thm)],[54, 2073])).
% 0.88/1.04 tff(2077,plain,
% 0.88/1.04 (~c0_1(a194)),
% 0.88/1.04 inference(unit_resolution,[status(thm)],[683, 102, 67, 11, 66, 12, 68])).
% 0.88/1.04 tff(2078,plain,
% 0.88/1.04 (c1_1(a214)),
% 0.88/1.04 inference(unit_resolution,[status(thm)],[1843, 102])).
% 0.88/1.04 tff(2079,plain,
% 0.88/1.04 (hskp5),
% 0.88/1.04 inference(unit_resolution,[status(thm)],[1824, 2078])).
% 0.88/1.04 tff(2080,plain,
% 0.88/1.04 ($false),
% 0.88/1.04 inference(unit_resolution,[status(thm)],[598, 2079, 2077])).
% 0.88/1.04 tff(2081,plain,(hskp1 | c1_1(a191) | c2_1(a194) | c2_1(a191) | c1_1(a194) | c3_1(a191)), inference(lemma,lemma(discharge,[]))).
% 0.88/1.04 tff(2082,plain,
% 0.88/1.04 (hskp1),
% 0.88/1.04 inference(unit_resolution,[status(thm)],[2081, 12, 11, 2075, 2076, 2074])).
% 0.88/1.04 tff(2083,plain,
% 0.88/1.04 (c0_1(a190)),
% 0.88/1.04 inference(unit_resolution,[status(thm)],[200, 2082])).
% 0.88/1.04 tff(2084,plain,
% 0.88/1.04 (c2_1(a190)),
% 0.88/1.04 inference(unit_resolution,[status(thm)],[192, 2082])).
% 0.88/1.04 tff(2085,plain,
% 0.88/1.04 (~hskp5),
% 0.88/1.04 inference(unit_resolution,[status(thm)],[598, 1192])).
% 0.88/1.04 tff(2086,plain,
% 0.88/1.04 (~c1_1(a214)),
% 0.88/1.04 inference(unit_resolution,[status(thm)],[1824, 2085])).
% 0.88/1.04 tff(2087,plain,
% 0.88/1.04 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a194) | c3_1(a214) | c2_1(a194) | c3_1(a190) | (~ndr1_0) | (~c2_1(a190)) | (~c0_1(a190)) | (~c3_1(a194)) | c1_1(a214) | (~c2_1(a214)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a194) | c3_1(a214) | c2_1(a194) | c3_1(a190) | (~ndr1_0) | (~c2_1(a190)) | (~c0_1(a190)) | (~c3_1(a194)) | c1_1(a214) | (~c2_1(a214)))),
% 0.88/1.04 inference(rewrite,[status(thm)],[])).
% 0.88/1.04 tff(2088,plain,
% 0.88/1.04 (((~ndr1_0) | c3_1(a190) | (~c2_1(a190)) | (~c0_1(a190)) | c3_1(a214) | c1_1(a214) | (~c2_1(a214)) | c2_1(a194) | c0_1(a194) | (~c3_1(a194))) <=> (c0_1(a194) | c3_1(a214) | c2_1(a194) | c3_1(a190) | (~ndr1_0) | (~c2_1(a190)) | (~c0_1(a190)) | (~c3_1(a194)) | c1_1(a214) | (~c2_1(a214)))),
% 0.88/1.04 inference(rewrite,[status(thm)],[])).
% 0.88/1.04 tff(2089,plain,
% 0.88/1.04 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a190) | (~c2_1(a190)) | (~c0_1(a190)) | c3_1(a214) | c1_1(a214) | (~c2_1(a214)) | c2_1(a194) | c0_1(a194) | (~c3_1(a194)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a194) | c3_1(a214) | c2_1(a194) | c3_1(a190) | (~ndr1_0) | (~c2_1(a190)) | (~c0_1(a190)) | (~c3_1(a194)) | c1_1(a214) | (~c2_1(a214))))),
% 0.88/1.04 inference(monotonicity,[status(thm)],[2088])).
% 0.88/1.04 tff(2090,plain,
% 0.88/1.04 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a190) | (~c2_1(a190)) | (~c0_1(a190)) | c3_1(a214) | c1_1(a214) | (~c2_1(a214)) | c2_1(a194) | c0_1(a194) | (~c3_1(a194)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a194) | c3_1(a214) | c2_1(a194) | c3_1(a190) | (~ndr1_0) | (~c2_1(a190)) | (~c0_1(a190)) | (~c3_1(a194)) | c1_1(a214) | (~c2_1(a214)))),
% 0.88/1.04 inference(transitivity,[status(thm)],[2089, 2087])).
% 0.88/1.04 tff(2091,plain,
% 0.88/1.04 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a190) | (~c2_1(a190)) | (~c0_1(a190)) | c3_1(a214) | c1_1(a214) | (~c2_1(a214)) | c2_1(a194) | c0_1(a194) | (~c3_1(a194)))),
% 0.88/1.04 inference(quant_inst,[status(thm)],[])).
% 0.88/1.04 tff(2092,plain,
% 0.88/1.04 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a194) | c3_1(a214) | c2_1(a194) | c3_1(a190) | (~ndr1_0) | (~c2_1(a190)) | (~c0_1(a190)) | (~c3_1(a194)) | c1_1(a214) | (~c2_1(a214))),
% 0.88/1.04 inference(modus_ponens,[status(thm)],[2091, 2090])).
% 0.88/1.04 tff(2093,plain,
% 0.88/1.04 (c0_1(a194) | (~c2_1(a190)) | (~c0_1(a190)) | (~c3_1(a194)) | c1_1(a214)),
% 0.88/1.04 inference(unit_resolution,[status(thm)],[2092, 148, 1817, 1803, 11, 13, 451])).
% 0.88/1.04 tff(2094,plain,
% 0.88/1.04 (~c3_1(a194)),
% 0.88/1.04 inference(unit_resolution,[status(thm)],[2093, 2086, 2084, 2083, 1192])).
% 0.88/1.04 tff(2095,plain,
% 0.88/1.04 (hskp19),
% 0.88/1.04 inference(unit_resolution,[status(thm)],[1853, 2086, 2084, 2083])).
% 0.88/1.04 tff(2096,plain,
% 0.88/1.04 (c3_1(a225)),
% 0.88/1.04 inference(unit_resolution,[status(thm)],[226, 2095])).
% 0.88/1.04 tff(2097,plain,
% 0.88/1.04 (~c0_1(a225)),
% 0.88/1.04 inference(unit_resolution,[status(thm)],[232, 2095])).
% 0.88/1.04 tff(2098,plain,
% 0.88/1.04 (hskp13),
% 0.88/1.04 inference(unit_resolution,[status(thm)],[381, 2097, 2076, 2096, 2075, 2074])).
% 0.88/1.04 tff(2099,plain,
% 0.88/1.04 (~c0_1(a209)),
% 0.88/1.04 inference(unit_resolution,[status(thm)],[387, 2098])).
% 0.88/1.04 tff(2100,plain,
% 0.88/1.04 (c3_1(a209)),
% 0.88/1.04 inference(unit_resolution,[status(thm)],[395, 2098])).
% 0.88/1.04 tff(2101,plain,
% 0.88/1.04 (c1_1(a209)),
% 0.88/1.04 inference(unit_resolution,[status(thm)],[403, 2098])).
% 0.88/1.04 tff(2102,plain,
% 0.88/1.04 (hskp10),
% 0.88/1.04 inference(unit_resolution,[status(thm)],[1950, 148, 2101, 2100, 2099, 12, 11, 10, 2094])).
% 0.88/1.04 tff(2103,plain,
% 0.88/1.04 (c0_1(a200)),
% 0.88/1.04 inference(unit_resolution,[status(thm)],[307, 2102])).
% 0.88/1.04 tff(2104,plain,
% 0.88/1.04 (c2_1(a225)),
% 0.88/1.04 inference(unit_resolution,[status(thm)],[1933, 148, 2096, 1192, 2097, 12, 11, 264, 2094])).
% 0.88/1.04 tff(2105,plain,
% 0.88/1.04 (~c1_1(a225)),
% 0.88/1.04 inference(unit_resolution,[status(thm)],[417, 2095])).
% 0.88/1.04 tff(2106,plain,
% 0.88/1.04 (hskp6),
% 0.88/1.04 inference(unit_resolution,[status(thm)],[1207, 2094, 1192])).
% 0.88/1.04 tff(2107,plain,
% 0.88/1.04 (c0_1(a195)),
% 0.88/1.04 inference(unit_resolution,[status(thm)],[551, 2106])).
% 0.88/1.04 tff(2108,plain,
% 0.88/1.04 (~c3_1(a195)),
% 0.88/1.04 inference(unit_resolution,[status(thm)],[543, 2106])).
% 0.88/1.04 tff(2109,plain,
% 0.88/1.04 (~c1_1(a195)),
% 0.88/1.04 inference(unit_resolution,[status(thm)],[557, 2106])).
% 0.88/1.04 tff(2110,plain,
% 0.88/1.04 (c3_1(a200)),
% 0.88/1.04 inference(unit_resolution,[status(thm)],[315, 2102])).
% 0.88/1.04 tff(2111,plain,
% 0.88/1.04 (~c1_1(a200)),
% 0.88/1.04 inference(unit_resolution,[status(thm)],[373, 2102])).
% 0.88/1.04 tff(2112,plain,
% 0.88/1.04 ($false),
% 0.88/1.04 inference(unit_resolution,[status(thm)],[888, 2111, 2110, 11, 12, 2109, 2108, 2107, 2100, 2097, 2105, 2099, 2101, 2104, 2103])).
% 0.88/1.04 tff(2113,plain,(c0_1(a194) | c2_1(a194) | c1_1(a194) | c3_1(a190)), inference(lemma,lemma(discharge,[]))).
% 0.88/1.04 tff(2114,plain,
% 0.88/1.04 (c0_1(a194)),
% 0.88/1.04 inference(unit_resolution,[status(thm)],[2113, 13, 11, 12])).
% 0.88/1.04 tff(2115,plain,
% 0.88/1.04 (hskp1),
% 0.88/1.04 inference(unit_resolution,[status(thm)],[683, 2114, 2076, 11, 2075, 12, 2074])).
% 0.88/1.04 tff(2116,plain,
% 0.88/1.04 (c0_1(a190)),
% 0.88/1.04 inference(unit_resolution,[status(thm)],[200, 2115])).
% 0.88/1.04 tff(2117,plain,
% 0.88/1.04 (c2_1(a190)),
% 0.88/1.04 inference(unit_resolution,[status(thm)],[192, 2115])).
% 0.88/1.04 tff(2118,plain,
% 0.88/1.04 (hskp19 | c1_1(a190)),
% 0.88/1.04 inference(unit_resolution,[status(thm)],[837, 148, 2116, 2117, 13, 211])).
% 0.88/1.04 tff(2119,plain,
% 0.88/1.04 (c1_1(a190)),
% 0.88/1.04 inference(unit_resolution,[status(thm)],[2118, 830])).
% 0.88/1.04 tff(2120,plain,
% 0.88/1.04 (~c0_1(a191)),
% 0.88/1.04 inference(unit_resolution,[status(thm)],[1013, 2119, 2116, 2117, 12, 11, 2075, 2074, 2114])).
% 0.88/1.04 tff(2121,plain,
% 0.88/1.04 (hskp6 | c0_1(a191)),
% 0.88/1.04 inference(unit_resolution,[status(thm)],[536, 148, 2075, 2074, 530])).
% 0.88/1.04 tff(2122,plain,
% 0.88/1.04 (hskp6),
% 0.88/1.04 inference(unit_resolution,[status(thm)],[2121, 2120])).
% 0.88/1.04 tff(2123,plain,
% 0.88/1.04 (c0_1(a195)),
% 0.88/1.04 inference(unit_resolution,[status(thm)],[551, 2122])).
% 0.88/1.04 tff(2124,plain,
% 0.88/1.04 (~c1_1(a195)),
% 0.88/1.04 inference(unit_resolution,[status(thm)],[557, 2122])).
% 0.88/1.04 tff(2125,plain,
% 0.88/1.04 (~c3_1(a195)),
% 0.88/1.04 inference(unit_resolution,[status(thm)],[543, 2122])).
% 0.88/1.04 tff(2126,plain,
% 0.88/1.04 ($false),
% 0.88/1.04 inference(unit_resolution,[status(thm)],[857, 2125, 2124, 830, 2117, 2123, 2116, 13])).
% 0.88/1.04 tff(2127,plain,(hskp19 | c3_1(a190) | c1_1(a194) | c2_1(a194)), inference(lemma,lemma(discharge,[]))).
% 0.88/1.04 tff(2128,plain,
% 0.88/1.04 (hskp19),
% 0.88/1.04 inference(unit_resolution,[status(thm)],[2127, 13, 12, 11])).
% 0.88/1.04 tff(2129,plain,
% 0.88/1.04 (~c0_1(a225)),
% 0.88/1.04 inference(unit_resolution,[status(thm)],[232, 2128])).
% 0.88/1.04 tff(2130,plain,
% 0.88/1.04 (hskp13),
% 0.88/1.04 inference(unit_resolution,[status(thm)],[381, 1732, 2076, 235, 2075, 2074])).
% 0.88/1.04 tff(2131,plain,
% 0.88/1.04 (~c0_1(a209)),
% 0.88/1.04 inference(unit_resolution,[status(thm)],[387, 2130])).
% 0.88/1.04 tff(2132,plain,
% 0.88/1.04 (c0_1(a194)),
% 0.88/1.04 inference(unit_resolution,[status(thm)],[2113, 12, 11, 13])).
% 0.88/1.04 tff(2133,plain,
% 0.88/1.04 (c3_1(a209)),
% 0.88/1.04 inference(unit_resolution,[status(thm)],[395, 2130])).
% 0.88/1.04 tff(2134,plain,
% 0.88/1.04 (c1_1(a209)),
% 0.88/1.04 inference(unit_resolution,[status(thm)],[403, 2130])).
% 0.88/1.04 tff(2135,plain,
% 0.88/1.04 (~c2_1(a225)),
% 0.88/1.04 inference(unit_resolution,[status(thm)],[878, 148, 2134, 2133, 2132, 235, 1730, 2131, 12, 11, 65])).
% 0.88/1.04 tff(2136,plain,
% 0.88/1.04 (hskp10),
% 0.88/1.04 inference(unit_resolution,[status(thm)],[410, 148, 2134, 2133, 2131, 2076, 2075, 2074, 10])).
% 0.88/1.04 tff(2137,plain,
% 0.88/1.04 (~c1_1(a200)),
% 0.88/1.04 inference(unit_resolution,[status(thm)],[373, 2136])).
% 0.88/1.04 tff(2138,plain,
% 0.88/1.04 (c3_1(a200)),
% 0.88/1.04 inference(unit_resolution,[status(thm)],[315, 2136])).
% 0.88/1.04 tff(2139,plain,
% 0.88/1.04 (c0_1(a200)),
% 0.88/1.04 inference(unit_resolution,[status(thm)],[307, 2136])).
% 0.88/1.04 tff(2140,plain,
% 0.88/1.04 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a225) | c0_1(a214) | c1_1(a200) | (~ndr1_0) | (~c3_1(a200)) | (~c0_1(a200)) | (~c1_1(a214)) | (~c2_1(a214)) | c2_1(a225) | (~c3_1(a225)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a225) | c0_1(a214) | c1_1(a200) | (~ndr1_0) | (~c3_1(a200)) | (~c0_1(a200)) | (~c1_1(a214)) | (~c2_1(a214)) | c2_1(a225) | (~c3_1(a225)))),
% 0.88/1.04 inference(rewrite,[status(thm)],[])).
% 0.88/1.04 tff(2141,plain,
% 0.88/1.04 (((~ndr1_0) | c1_1(a200) | (~c3_1(a200)) | (~c0_1(a200)) | c0_1(a214) | (~c1_1(a214)) | (~c2_1(a214)) | c2_1(a225) | c0_1(a225) | (~c3_1(a225))) <=> (c0_1(a225) | c0_1(a214) | c1_1(a200) | (~ndr1_0) | (~c3_1(a200)) | (~c0_1(a200)) | (~c1_1(a214)) | (~c2_1(a214)) | c2_1(a225) | (~c3_1(a225)))),
% 0.88/1.04 inference(rewrite,[status(thm)],[])).
% 0.88/1.04 tff(2142,plain,
% 0.88/1.04 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a200) | (~c3_1(a200)) | (~c0_1(a200)) | c0_1(a214) | (~c1_1(a214)) | (~c2_1(a214)) | c2_1(a225) | c0_1(a225) | (~c3_1(a225)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a225) | c0_1(a214) | c1_1(a200) | (~ndr1_0) | (~c3_1(a200)) | (~c0_1(a200)) | (~c1_1(a214)) | (~c2_1(a214)) | c2_1(a225) | (~c3_1(a225))))),
% 0.88/1.04 inference(monotonicity,[status(thm)],[2141])).
% 0.88/1.04 tff(2143,plain,
% 0.88/1.04 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a200) | (~c3_1(a200)) | (~c0_1(a200)) | c0_1(a214) | (~c1_1(a214)) | (~c2_1(a214)) | c2_1(a225) | c0_1(a225) | (~c3_1(a225)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a225) | c0_1(a214) | c1_1(a200) | (~ndr1_0) | (~c3_1(a200)) | (~c0_1(a200)) | (~c1_1(a214)) | (~c2_1(a214)) | c2_1(a225) | (~c3_1(a225)))),
% 0.88/1.04 inference(transitivity,[status(thm)],[2142, 2140])).
% 0.88/1.04 tff(2144,plain,
% 0.88/1.04 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a200) | (~c3_1(a200)) | (~c0_1(a200)) | c0_1(a214) | (~c1_1(a214)) | (~c2_1(a214)) | c2_1(a225) | c0_1(a225) | (~c3_1(a225)))),
% 0.88/1.04 inference(quant_inst,[status(thm)],[])).
% 0.88/1.04 tff(2145,plain,
% 0.88/1.04 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a225) | c0_1(a214) | c1_1(a200) | (~ndr1_0) | (~c3_1(a200)) | (~c0_1(a200)) | (~c1_1(a214)) | (~c2_1(a214)) | c2_1(a225) | (~c3_1(a225))),
% 0.88/1.04 inference(modus_ponens,[status(thm)],[2144, 2143])).
% 0.88/1.04 tff(2146,plain,
% 0.88/1.04 (~c1_1(a214)),
% 0.88/1.04 inference(unit_resolution,[status(thm)],[2145, 148, 1732, 1817, 2139, 2138, 235, 1809, 2137, 1033, 2135])).
% 0.88/1.04 tff(2147,plain,
% 0.88/1.04 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a225) | c3_1(a214) | c3_1(a190) | (~ndr1_0) | (~c2_1(a190)) | (~c0_1(a190)) | c1_1(a214) | (~c2_1(a214)) | c2_1(a225) | (~c3_1(a225)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a225) | c3_1(a214) | c3_1(a190) | (~ndr1_0) | (~c2_1(a190)) | (~c0_1(a190)) | c1_1(a214) | (~c2_1(a214)) | c2_1(a225) | (~c3_1(a225)))),
% 0.88/1.04 inference(rewrite,[status(thm)],[])).
% 0.88/1.04 tff(2148,plain,
% 0.88/1.04 (((~ndr1_0) | c3_1(a190) | (~c2_1(a190)) | (~c0_1(a190)) | c3_1(a214) | c1_1(a214) | (~c2_1(a214)) | c2_1(a225) | c0_1(a225) | (~c3_1(a225))) <=> (c0_1(a225) | c3_1(a214) | c3_1(a190) | (~ndr1_0) | (~c2_1(a190)) | (~c0_1(a190)) | c1_1(a214) | (~c2_1(a214)) | c2_1(a225) | (~c3_1(a225)))),
% 0.88/1.04 inference(rewrite,[status(thm)],[])).
% 0.88/1.04 tff(2149,plain,
% 0.88/1.04 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a190) | (~c2_1(a190)) | (~c0_1(a190)) | c3_1(a214) | c1_1(a214) | (~c2_1(a214)) | c2_1(a225) | c0_1(a225) | (~c3_1(a225)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a225) | c3_1(a214) | c3_1(a190) | (~ndr1_0) | (~c2_1(a190)) | (~c0_1(a190)) | c1_1(a214) | (~c2_1(a214)) | c2_1(a225) | (~c3_1(a225))))),
% 0.88/1.04 inference(monotonicity,[status(thm)],[2148])).
% 0.88/1.04 tff(2150,plain,
% 0.88/1.04 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a190) | (~c2_1(a190)) | (~c0_1(a190)) | c3_1(a214) | c1_1(a214) | (~c2_1(a214)) | c2_1(a225) | c0_1(a225) | (~c3_1(a225)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a225) | c3_1(a214) | c3_1(a190) | (~ndr1_0) | (~c2_1(a190)) | (~c0_1(a190)) | c1_1(a214) | (~c2_1(a214)) | c2_1(a225) | (~c3_1(a225)))),
% 0.88/1.04 inference(transitivity,[status(thm)],[2149, 2147])).
% 0.88/1.04 tff(2151,plain,
% 0.88/1.04 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a190) | (~c2_1(a190)) | (~c0_1(a190)) | c3_1(a214) | c1_1(a214) | (~c2_1(a214)) | c2_1(a225) | c0_1(a225) | (~c3_1(a225)))),
% 0.88/1.04 inference(quant_inst,[status(thm)],[])).
% 0.88/1.04 tff(2152,plain,
% 0.88/1.04 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a225) | c3_1(a214) | c3_1(a190) | (~ndr1_0) | (~c2_1(a190)) | (~c0_1(a190)) | c1_1(a214) | (~c2_1(a214)) | c2_1(a225) | (~c3_1(a225))),
% 0.88/1.04 inference(modus_ponens,[status(thm)],[2151, 2150])).
% 0.88/1.04 tff(2153,plain,
% 0.88/1.04 ($false),
% 0.88/1.04 inference(unit_resolution,[status(thm)],[2152, 148, 1732, 1817, 2083, 2084, 235, 1803, 13, 451, 2135, 2146])).
% 0.88/1.04 tff(2154,plain,((~hskp19) | c0_1(a225) | c3_1(a190) | c1_1(a194) | c2_1(a194)), inference(lemma,lemma(discharge,[]))).
% 0.88/1.04 tff(2155,plain,
% 0.88/1.04 ($false),
% 0.88/1.04 inference(unit_resolution,[status(thm)],[2154, 2129, 2128, 13, 12, 11])).
% 0.88/1.04 tff(2156,plain,(c3_1(a190) | c1_1(a194) | c2_1(a194)), inference(lemma,lemma(discharge,[]))).
% 0.88/1.04 tff(2157,plain,
% 0.88/1.04 (c3_1(a190)),
% 0.88/1.04 inference(unit_resolution,[status(thm)],[2156, 12, 11])).
% 0.88/1.04 tff(2158,plain,
% 0.88/1.04 (~hskp1),
% 0.88/1.04 inference(unit_resolution,[status(thm)],[1073, 2157])).
% 0.88/1.04 tff(2159,plain,
% 0.88/1.04 (c1_1(a214)),
% 0.88/1.04 inference(unit_resolution,[status(thm)],[1843, 2158])).
% 0.88/1.04 tff(2160,plain,
% 0.88/1.04 (hskp2),
% 0.88/1.04 inference(unit_resolution,[status(thm)],[1835, 2159, 11])).
% 0.88/1.04 tff(2161,plain,
% 0.88/1.04 (~c3_1(a191)),
% 0.88/1.04 inference(unit_resolution,[status(thm)],[42, 2160])).
% 0.88/1.04 tff(2162,plain,
% 0.88/1.04 (~c2_1(a191)),
% 0.88/1.04 inference(unit_resolution,[status(thm)],[48, 2160])).
% 0.88/1.04 tff(2163,plain,
% 0.88/1.04 (hskp5),
% 0.88/1.04 inference(unit_resolution,[status(thm)],[1824, 2159])).
% 0.88/1.04 tff(2164,plain,
% 0.88/1.04 (c0_1(a194)),
% 0.88/1.04 inference(unit_resolution,[status(thm)],[598, 2163])).
% 0.88/1.04 tff(2165,plain,
% 0.88/1.04 (~c1_1(a191)),
% 0.88/1.04 inference(unit_resolution,[status(thm)],[54, 2160])).
% 0.88/1.04 tff(2166,plain,
% 0.88/1.04 ($false),
% 0.88/1.04 inference(unit_resolution,[status(thm)],[683, 2165, 2164, 2158, 11, 2162, 12, 2161])).
% 0.88/1.04 tff(2167,plain,(c1_1(a194) | c2_1(a194)), inference(lemma,lemma(discharge,[]))).
% 0.88/1.04 tff(2168,plain,
% 0.88/1.04 (c1_1(a194)),
% 0.88/1.04 inference(unit_resolution,[status(thm)],[2167, 11])).
% 0.88/1.04 tff(2169,plain,
% 0.88/1.04 (~hskp5),
% 0.88/1.04 inference(unit_resolution,[status(thm)],[590, 2168])).
% 0.88/1.04 tff(2170,plain,
% 0.88/1.04 (~c1_1(a214)),
% 0.88/1.04 inference(unit_resolution,[status(thm)],[1824, 2169])).
% 0.88/1.04 tff(2171,plain,
% 0.88/1.04 (hskp1),
% 0.88/1.04 inference(unit_resolution,[status(thm)],[1843, 2170])).
% 0.88/1.04 tff(2172,plain,
% 0.88/1.04 (~c3_1(a190)),
% 0.88/1.04 inference(unit_resolution,[status(thm)],[1073, 2171])).
% 0.88/1.04 tff(2173,plain,
% 0.88/1.04 (hskp2),
% 0.88/1.04 inference(unit_resolution,[status(thm)],[2072, 2172, 11])).
% 0.88/1.04 tff(2174,plain,
% 0.88/1.04 (~c3_1(a191)),
% 0.88/1.04 inference(unit_resolution,[status(thm)],[42, 2173])).
% 0.88/1.04 tff(2175,plain,
% 0.88/1.04 (~c2_1(a191)),
% 0.88/1.04 inference(unit_resolution,[status(thm)],[48, 2173])).
% 0.88/1.04 tff(2176,plain,
% 0.88/1.04 (~c1_1(a191)),
% 0.88/1.04 inference(unit_resolution,[status(thm)],[54, 2173])).
% 0.88/1.04 tff(2177,plain,
% 0.88/1.04 (c2_1(a190)),
% 0.88/1.04 inference(unit_resolution,[status(thm)],[192, 2171])).
% 0.88/1.04 tff(2178,plain,
% 0.88/1.04 (c0_1(a190)),
% 0.88/1.04 inference(unit_resolution,[status(thm)],[200, 2171])).
% 0.88/1.04 tff(2179,plain,
% 0.88/1.04 (hskp19),
% 0.88/1.04 inference(unit_resolution,[status(thm)],[1852, 148, 1817, 2178, 2177, 1803, 2172, 211, 2170])).
% 0.88/1.04 tff(2180,plain,
% 0.88/1.04 (~c0_1(a225)),
% 0.88/1.04 inference(unit_resolution,[status(thm)],[232, 2179])).
% 0.88/1.04 tff(2181,plain,
% 0.88/1.04 (c3_1(a225)),
% 0.88/1.04 inference(unit_resolution,[status(thm)],[226, 2179])).
% 0.88/1.04 tff(2182,plain,
% 0.88/1.04 (hskp13),
% 0.88/1.04 inference(unit_resolution,[status(thm)],[381, 2181, 2176, 2180, 2175, 2174])).
% 0.88/1.04 tff(2183,plain,
% 0.88/1.04 (~c0_1(a209)),
% 0.88/1.04 inference(unit_resolution,[status(thm)],[387, 2182])).
% 0.88/1.04 tff(2184,plain,
% 0.88/1.04 (c3_1(a209)),
% 0.88/1.04 inference(unit_resolution,[status(thm)],[395, 2182])).
% 0.88/1.04 tff(2185,plain,
% 0.88/1.04 (c1_1(a209)),
% 0.88/1.04 inference(unit_resolution,[status(thm)],[403, 2182])).
% 0.88/1.04 tff(2186,plain,
% 0.88/1.04 (hskp10),
% 0.88/1.04 inference(unit_resolution,[status(thm)],[410, 148, 2185, 2184, 2183, 2176, 2175, 2174, 10])).
% 0.88/1.04 tff(2187,plain,
% 0.88/1.04 (c0_1(a200)),
% 0.88/1.04 inference(unit_resolution,[status(thm)],[307, 2186])).
% 0.88/1.04 tff(2188,plain,
% 0.88/1.04 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_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(a214) | c0_1(a209) | c1_1(a191) | c2_1(a191) | (~ndr1_0) | (~c0_1(a191)) | (~c1_1(a209)) | (~c3_1(a209)) | c1_1(a214) | (~c2_1(a214)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_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(a214) | c0_1(a209) | c1_1(a191) | c2_1(a191) | (~ndr1_0) | (~c0_1(a191)) | (~c1_1(a209)) | (~c3_1(a209)) | c1_1(a214) | (~c2_1(a214)))),
% 0.88/1.04 inference(rewrite,[status(thm)],[])).
% 0.88/1.04 tff(2189,plain,
% 0.88/1.04 (((~ndr1_0) | c1_1(a191) | c2_1(a191) | (~c0_1(a191)) | c0_1(a209) | (~c3_1(a209)) | (~c1_1(a209)) | c1_1(a214) | c0_1(a214) | (~c2_1(a214))) <=> (c0_1(a214) | c0_1(a209) | c1_1(a191) | c2_1(a191) | (~ndr1_0) | (~c0_1(a191)) | (~c1_1(a209)) | (~c3_1(a209)) | c1_1(a214) | (~c2_1(a214)))),
% 0.88/1.04 inference(rewrite,[status(thm)],[])).
% 0.88/1.04 tff(2190,plain,
% 0.88/1.04 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_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) | c1_1(a191) | c2_1(a191) | (~c0_1(a191)) | c0_1(a209) | (~c3_1(a209)) | (~c1_1(a209)) | c1_1(a214) | c0_1(a214) | (~c2_1(a214)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_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(a214) | c0_1(a209) | c1_1(a191) | c2_1(a191) | (~ndr1_0) | (~c0_1(a191)) | (~c1_1(a209)) | (~c3_1(a209)) | c1_1(a214) | (~c2_1(a214))))),
% 0.88/1.04 inference(monotonicity,[status(thm)],[2189])).
% 0.88/1.04 tff(2191,plain,
% 0.88/1.04 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_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) | c1_1(a191) | c2_1(a191) | (~c0_1(a191)) | c0_1(a209) | (~c3_1(a209)) | (~c1_1(a209)) | c1_1(a214) | c0_1(a214) | (~c2_1(a214)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_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(a214) | c0_1(a209) | c1_1(a191) | c2_1(a191) | (~ndr1_0) | (~c0_1(a191)) | (~c1_1(a209)) | (~c3_1(a209)) | c1_1(a214) | (~c2_1(a214)))),
% 0.88/1.04 inference(transitivity,[status(thm)],[2190, 2188])).
% 0.88/1.04 tff(2192,plain,
% 0.88/1.04 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_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) | c1_1(a191) | c2_1(a191) | (~c0_1(a191)) | c0_1(a209) | (~c3_1(a209)) | (~c1_1(a209)) | c1_1(a214) | c0_1(a214) | (~c2_1(a214)))),
% 0.88/1.04 inference(quant_inst,[status(thm)],[])).
% 0.88/1.04 tff(2193,plain,
% 0.88/1.04 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a214) | c0_1(a209) | c1_1(a191) | c2_1(a191) | (~ndr1_0) | (~c0_1(a191)) | (~c1_1(a209)) | (~c3_1(a209)) | c1_1(a214) | (~c2_1(a214))),
% 0.88/1.04 inference(modus_ponens,[status(thm)],[2192, 2191])).
% 0.88/1.04 tff(2194,plain,
% 0.88/1.04 (~c0_1(a191)),
% 0.88/1.04 inference(unit_resolution,[status(thm)],[2193, 148, 1817, 2185, 2184, 1809, 2183, 2176, 2175, 65, 2170])).
% 0.88/1.04 tff(2195,plain,
% 0.88/1.04 (hskp6 | c0_1(a191)),
% 0.88/1.04 inference(unit_resolution,[status(thm)],[536, 148, 2175, 2174, 530])).
% 0.88/1.04 tff(2196,plain,
% 0.88/1.04 (hskp6),
% 0.88/1.04 inference(unit_resolution,[status(thm)],[2195, 2194])).
% 0.88/1.04 tff(2197,plain,
% 0.88/1.04 (~c3_1(a195)),
% 0.88/1.04 inference(unit_resolution,[status(thm)],[543, 2196])).
% 0.88/1.04 tff(2198,plain,
% 0.88/1.04 (~c1_1(a195)),
% 0.88/1.04 inference(unit_resolution,[status(thm)],[557, 2196])).
% 0.88/1.04 tff(2199,plain,
% 0.88/1.04 (c0_1(a195)),
% 0.88/1.04 inference(unit_resolution,[status(thm)],[551, 2196])).
% 0.88/1.04 tff(2200,plain,
% 0.88/1.04 (c3_1(a200)),
% 0.88/1.04 inference(unit_resolution,[status(thm)],[315, 2186])).
% 0.88/1.04 tff(2201,plain,
% 0.88/1.04 (~c2_1(a200)),
% 0.88/1.04 inference(unit_resolution,[status(thm)],[576, 2200, 2169, 2199, 2198, 2197, 2187])).
% 0.88/1.04 tff(2202,plain,
% 0.88/1.04 (c0_1(a191) | c2_1(a225)),
% 0.88/1.04 inference(unit_resolution,[status(thm)],[270, 148, 2181, 2180, 2176, 2175, 2174, 264])).
% 0.88/1.04 tff(2203,plain,
% 0.88/1.04 (c2_1(a225)),
% 0.88/1.04 inference(unit_resolution,[status(thm)],[2202, 2194])).
% 0.88/1.04 tff(2204,plain,
% 0.88/1.04 (~c1_1(a200)),
% 0.88/1.04 inference(unit_resolution,[status(thm)],[373, 2186])).
% 0.88/1.04 tff(2205,plain,
% 0.88/1.04 (~c1_1(a225)),
% 0.88/1.04 inference(unit_resolution,[status(thm)],[417, 2179])).
% 0.88/1.04 tff(2206,plain,
% 0.88/1.04 ($false),
% 0.88/1.04 inference(unit_resolution,[status(thm)],[439, 148, 2185, 2184, 2187, 2180, 2205, 2183, 2204, 65, 2203, 2201])).
% 0.88/1.04 tff(2207,plain,(c2_1(a194)), inference(lemma,lemma(discharge,[]))).
% 0.88/1.04 tff(2208,plain,
% 0.88/1.04 (~hskp5),
% 0.88/1.04 inference(unit_resolution,[status(thm)],[584, 2207])).
% 0.88/1.04 tff(2209,plain,
% 0.88/1.04 (~c1_1(a214)),
% 0.88/1.04 inference(unit_resolution,[status(thm)],[1824, 2208])).
% 0.88/1.04 tff(2210,plain,
% 0.88/1.04 (hskp1),
% 0.88/1.04 inference(unit_resolution,[status(thm)],[1843, 2209])).
% 0.88/1.04 tff(2211,plain,
% 0.88/1.04 (~c3_1(a190)),
% 0.88/1.04 inference(unit_resolution,[status(thm)],[1073, 2210])).
% 0.88/1.04 tff(2212,plain,
% 0.88/1.04 (c2_1(a190)),
% 0.88/1.04 inference(unit_resolution,[status(thm)],[192, 2210])).
% 0.88/1.04 tff(2213,plain,
% 0.88/1.04 (c0_1(a190)),
% 0.88/1.04 inference(unit_resolution,[status(thm)],[200, 2210])).
% 0.88/1.04 tff(2214,plain,
% 0.88/1.04 (hskp19),
% 0.88/1.04 inference(unit_resolution,[status(thm)],[1852, 148, 1817, 2213, 2212, 1803, 2211, 211, 2209])).
% 0.88/1.04 tff(2215,plain,
% 0.88/1.04 (~c1_1(a190)),
% 0.88/1.04 inference(unit_resolution,[status(thm)],[1734, 14, 2213, 2211, 2214])).
% 0.88/1.04 tff(2216,plain,
% 0.88/1.04 (~hskp25),
% 0.88/1.04 inference(unit_resolution,[status(thm)],[1988, 14, 2215])).
% 0.88/1.04 tff(2217,assumption,(~hskp16), introduced(assumption)).
% 0.88/1.04 tff(2218,plain,
% 0.88/1.04 (^[U: $i] : refl((hskp23 | hskp16 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U))) <=> (hskp23 | hskp16 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U))))),
% 0.88/1.04 inference(bind,[status(th)],[])).
% 0.88/1.04 tff(2219,plain,
% 0.88/1.04 (![U: $i] : (hskp23 | hskp16 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp23 | hskp16 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))),
% 0.88/1.04 inference(quant_intro,[status(thm)],[2218])).
% 0.88/1.04 tff(2220,plain,
% 0.88/1.04 (![U: $i] : (hskp23 | hskp16 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp23 | hskp16 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))),
% 0.88/1.04 inference(rewrite,[status(thm)],[])).
% 0.88/1.04 tff(2221,plain,
% 0.88/1.04 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c0_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) <=> (((~ndr1_0) | (~c0_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U))))), (((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))), (((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U))))), ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp23) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U))) | hskp23))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U))) | hskp23) <=> (hskp23 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))), ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp23) <=> (hskp23 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U))))), (((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp23) | hskp16) <=> ((hskp23 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U))) | hskp16))), rewrite(((hskp23 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U))) | hskp16) <=> (hskp23 | hskp16 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))), (((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp23) | hskp16) <=> (hskp23 | hskp16 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))))),
% 0.88/1.04 inference(bind,[status(th)],[])).
% 0.88/1.04 tff(2222,plain,
% 0.88/1.04 (![U: $i] : ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp23) | hskp16) <=> ![U: $i] : (hskp23 | hskp16 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))),
% 0.88/1.04 inference(quant_intro,[status(thm)],[2221])).
% 0.88/1.04 tff(2223,axiom,(![U: $i] : ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp23) | hskp16)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause117')).
% 0.88/1.04 tff(2224,plain,
% 0.88/1.04 (![U: $i] : (hskp23 | hskp16 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))),
% 0.88/1.04 inference(modus_ponens,[status(thm)],[2223, 2222])).
% 0.88/1.04 tff(2225,plain,
% 0.88/1.04 (![U: $i] : (hskp23 | hskp16 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))),
% 0.88/1.04 inference(modus_ponens,[status(thm)],[2224, 2220])).
% 0.88/1.04 tff(2226,plain,(
% 0.88/1.04 ![U: $i] : (hskp23 | hskp16 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))),
% 0.88/1.04 inference(skolemize,[status(sab)],[2225])).
% 0.88/1.04 tff(2227,plain,
% 0.88/1.04 (![U: $i] : (hskp23 | hskp16 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))),
% 0.88/1.04 inference(modus_ponens,[status(thm)],[2226, 2219])).
% 0.88/1.04 tff(2228,plain,
% 0.88/1.04 (((~![U: $i] : (hskp23 | hskp16 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp23 | hskp16 | c3_1(a190) | (~ndr1_0) | (~c0_1(a190)) | c1_1(a190))) <=> ((~![U: $i] : (hskp23 | hskp16 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))) | hskp23 | hskp16 | c3_1(a190) | (~ndr1_0) | (~c0_1(a190)) | c1_1(a190))),
% 0.88/1.04 inference(rewrite,[status(thm)],[])).
% 0.88/1.05 tff(2229,plain,
% 0.88/1.05 ((hskp23 | hskp16 | (~ndr1_0) | c3_1(a190) | c1_1(a190) | (~c0_1(a190))) <=> (hskp23 | hskp16 | c3_1(a190) | (~ndr1_0) | (~c0_1(a190)) | c1_1(a190))),
% 0.88/1.05 inference(rewrite,[status(thm)],[])).
% 0.88/1.05 tff(2230,plain,
% 0.88/1.05 (((~![U: $i] : (hskp23 | hskp16 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp23 | hskp16 | (~ndr1_0) | c3_1(a190) | c1_1(a190) | (~c0_1(a190)))) <=> ((~![U: $i] : (hskp23 | hskp16 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp23 | hskp16 | c3_1(a190) | (~ndr1_0) | (~c0_1(a190)) | c1_1(a190)))),
% 0.88/1.05 inference(monotonicity,[status(thm)],[2229])).
% 0.88/1.05 tff(2231,plain,
% 0.88/1.05 (((~![U: $i] : (hskp23 | hskp16 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp23 | hskp16 | (~ndr1_0) | c3_1(a190) | c1_1(a190) | (~c0_1(a190)))) <=> ((~![U: $i] : (hskp23 | hskp16 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))) | hskp23 | hskp16 | c3_1(a190) | (~ndr1_0) | (~c0_1(a190)) | c1_1(a190))),
% 0.88/1.05 inference(transitivity,[status(thm)],[2230, 2228])).
% 0.88/1.05 tff(2232,plain,
% 0.88/1.05 ((~![U: $i] : (hskp23 | hskp16 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp23 | hskp16 | (~ndr1_0) | c3_1(a190) | c1_1(a190) | (~c0_1(a190)))),
% 0.88/1.05 inference(quant_inst,[status(thm)],[])).
% 0.88/1.05 tff(2233,plain,
% 0.88/1.05 ((~![U: $i] : (hskp23 | hskp16 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))) | hskp23 | hskp16 | c3_1(a190) | (~ndr1_0) | (~c0_1(a190)) | c1_1(a190)),
% 0.88/1.05 inference(modus_ponens,[status(thm)],[2232, 2231])).
% 0.88/1.05 tff(2234,plain,
% 0.88/1.05 (hskp23 | hskp16 | c1_1(a190)),
% 0.88/1.05 inference(unit_resolution,[status(thm)],[2233, 148, 2213, 2211, 2227])).
% 0.88/1.05 tff(2235,plain,
% 0.88/1.05 (hskp23),
% 0.88/1.05 inference(unit_resolution,[status(thm)],[2234, 2217, 1223])).
% 0.88/1.05 tff(2236,plain,
% 0.88/1.05 (c1_1(a189)),
% 0.88/1.05 inference(unit_resolution,[status(thm)],[504, 2235])).
% 0.88/1.05 tff(2237,plain,
% 0.88/1.05 (c0_1(a189)),
% 0.88/1.05 inference(unit_resolution,[status(thm)],[512, 2235])).
% 0.88/1.05 tff(2238,assumption,(~hskp25), introduced(assumption)).
% 0.88/1.05 tff(2239,plain,
% 0.88/1.05 (((~![U: $i] : (hskp25 | hskp16 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp25 | hskp16 | (~ndr1_0) | c2_1(a189) | (~c0_1(a189)) | (~c1_1(a189)))) <=> ((~![U: $i] : (hskp25 | hskp16 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp25 | hskp16 | (~ndr1_0) | c2_1(a189) | (~c0_1(a189)) | (~c1_1(a189)))),
% 0.88/1.05 inference(rewrite,[status(thm)],[])).
% 0.88/1.05 tff(2240,plain,
% 0.88/1.05 ((hskp25 | hskp16 | (~ndr1_0) | c2_1(a189) | (~c1_1(a189)) | (~c0_1(a189))) <=> (hskp25 | hskp16 | (~ndr1_0) | c2_1(a189) | (~c0_1(a189)) | (~c1_1(a189)))),
% 0.88/1.05 inference(rewrite,[status(thm)],[])).
% 0.88/1.05 tff(2241,plain,
% 0.88/1.05 (((~![U: $i] : (hskp25 | hskp16 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp25 | hskp16 | (~ndr1_0) | c2_1(a189) | (~c1_1(a189)) | (~c0_1(a189)))) <=> ((~![U: $i] : (hskp25 | hskp16 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp25 | hskp16 | (~ndr1_0) | c2_1(a189) | (~c0_1(a189)) | (~c1_1(a189))))),
% 0.88/1.05 inference(monotonicity,[status(thm)],[2240])).
% 0.88/1.05 tff(2242,plain,
% 0.88/1.05 (((~![U: $i] : (hskp25 | hskp16 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp25 | hskp16 | (~ndr1_0) | c2_1(a189) | (~c1_1(a189)) | (~c0_1(a189)))) <=> ((~![U: $i] : (hskp25 | hskp16 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp25 | hskp16 | (~ndr1_0) | c2_1(a189) | (~c0_1(a189)) | (~c1_1(a189)))),
% 0.88/1.05 inference(transitivity,[status(thm)],[2241, 2239])).
% 0.88/1.05 tff(2243,plain,
% 0.88/1.05 ((~![U: $i] : (hskp25 | hskp16 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp25 | hskp16 | (~ndr1_0) | c2_1(a189) | (~c1_1(a189)) | (~c0_1(a189)))),
% 0.88/1.05 inference(quant_inst,[status(thm)],[])).
% 0.88/1.05 tff(2244,plain,
% 0.88/1.05 ((~![U: $i] : (hskp25 | hskp16 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp25 | hskp16 | (~ndr1_0) | c2_1(a189) | (~c0_1(a189)) | (~c1_1(a189))),
% 0.88/1.05 inference(modus_ponens,[status(thm)],[2243, 2242])).
% 0.88/1.05 tff(2245,plain,
% 0.88/1.05 (c2_1(a189)),
% 0.88/1.05 inference(unit_resolution,[status(thm)],[2244, 2238, 148, 2217, 2237, 2236, 1999])).
% 0.88/1.05 tff(2246,plain,
% 0.88/1.05 (c3_1(a189)),
% 0.88/1.05 inference(unit_resolution,[status(thm)],[496, 2235])).
% 0.88/1.05 tff(2247,plain,
% 0.88/1.05 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | (c3_1(a190) | (~ndr1_0) | (~c0_1(a190)) | c1_1(a190) | (~c3_1(a189)) | (~c2_1(a189)) | (~c0_1(a189)) | (~c1_1(a189)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | c3_1(a190) | (~ndr1_0) | (~c0_1(a190)) | c1_1(a190) | (~c3_1(a189)) | (~c2_1(a189)) | (~c0_1(a189)) | (~c1_1(a189)))),
% 0.88/1.05 inference(rewrite,[status(thm)],[])).
% 0.88/1.05 tff(2248,plain,
% 0.88/1.05 (((~ndr1_0) | (~c3_1(a189)) | (~c2_1(a189)) | (~c0_1(a189)) | (~c3_1(a189)) | (~c1_1(a189)) | (~c0_1(a189)) | c1_1(a190) | c3_1(a190) | (~c0_1(a190))) <=> (c3_1(a190) | (~ndr1_0) | (~c0_1(a190)) | c1_1(a190) | (~c3_1(a189)) | (~c2_1(a189)) | (~c0_1(a189)) | (~c1_1(a189)))),
% 0.88/1.05 inference(rewrite,[status(thm)],[])).
% 0.88/1.05 tff(2249,plain,
% 0.88/1.05 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c3_1(a189)) | (~c2_1(a189)) | (~c0_1(a189)) | (~c3_1(a189)) | (~c1_1(a189)) | (~c0_1(a189)) | c1_1(a190) | c3_1(a190) | (~c0_1(a190)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | (c3_1(a190) | (~ndr1_0) | (~c0_1(a190)) | c1_1(a190) | (~c3_1(a189)) | (~c2_1(a189)) | (~c0_1(a189)) | (~c1_1(a189))))),
% 0.88/1.05 inference(monotonicity,[status(thm)],[2248])).
% 0.88/1.05 tff(2250,plain,
% 0.88/1.05 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c3_1(a189)) | (~c2_1(a189)) | (~c0_1(a189)) | (~c3_1(a189)) | (~c1_1(a189)) | (~c0_1(a189)) | c1_1(a190) | c3_1(a190) | (~c0_1(a190)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | c3_1(a190) | (~ndr1_0) | (~c0_1(a190)) | c1_1(a190) | (~c3_1(a189)) | (~c2_1(a189)) | (~c0_1(a189)) | (~c1_1(a189)))),
% 0.88/1.05 inference(transitivity,[status(thm)],[2249, 2247])).
% 0.88/1.05 tff(2251,plain,
% 0.88/1.05 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c3_1(a189)) | (~c2_1(a189)) | (~c0_1(a189)) | (~c3_1(a189)) | (~c1_1(a189)) | (~c0_1(a189)) | c1_1(a190) | c3_1(a190) | (~c0_1(a190)))),
% 0.88/1.05 inference(quant_inst,[status(thm)],[])).
% 0.88/1.05 tff(2252,plain,
% 0.88/1.05 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | c3_1(a190) | (~ndr1_0) | (~c0_1(a190)) | c1_1(a190) | (~c3_1(a189)) | (~c2_1(a189)) | (~c0_1(a189)) | (~c1_1(a189))),
% 0.88/1.05 inference(modus_ponens,[status(thm)],[2251, 2250])).
% 0.88/1.05 tff(2253,plain,
% 0.88/1.05 ($false),
% 0.88/1.05 inference(unit_resolution,[status(thm)],[2252, 148, 2237, 2236, 2246, 2213, 2211, 470, 1223, 2245])).
% 0.88/1.05 tff(2254,plain,(hskp16 | c1_1(a190) | hskp25), inference(lemma,lemma(discharge,[]))).
% 0.88/1.05 tff(2255,plain,
% 0.88/1.05 (hskp16),
% 0.88/1.05 inference(unit_resolution,[status(thm)],[2254, 2215, 2216])).
% 0.88/1.05 tff(2256,plain,
% 0.88/1.05 (~c2_1(a221)),
% 0.88/1.05 inference(unit_resolution,[status(thm)],[2012, 2255])).
% 0.88/1.05 tff(2257,plain,
% 0.88/1.05 (~c0_1(a221)),
% 0.88/1.05 inference(unit_resolution,[status(thm)],[2041, 2255])).
% 0.88/1.05 tff(2258,plain,
% 0.88/1.05 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a221) | c2_1(a221) | c3_1(a214) | c3_1(a190) | (~ndr1_0) | (~c2_1(a190)) | (~c0_1(a190)) | c1_1(a214) | (~c2_1(a214)) | (~c3_1(a221)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a221) | c2_1(a221) | c3_1(a214) | c3_1(a190) | (~ndr1_0) | (~c2_1(a190)) | (~c0_1(a190)) | c1_1(a214) | (~c2_1(a214)) | (~c3_1(a221)))),
% 0.88/1.05 inference(rewrite,[status(thm)],[])).
% 0.88/1.05 tff(2259,plain,
% 0.88/1.05 (((~ndr1_0) | c3_1(a190) | (~c2_1(a190)) | (~c0_1(a190)) | c3_1(a214) | c1_1(a214) | (~c2_1(a214)) | c2_1(a221) | c0_1(a221) | (~c3_1(a221))) <=> (c0_1(a221) | c2_1(a221) | c3_1(a214) | c3_1(a190) | (~ndr1_0) | (~c2_1(a190)) | (~c0_1(a190)) | c1_1(a214) | (~c2_1(a214)) | (~c3_1(a221)))),
% 0.88/1.05 inference(rewrite,[status(thm)],[])).
% 0.88/1.05 tff(2260,plain,
% 0.88/1.05 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a190) | (~c2_1(a190)) | (~c0_1(a190)) | c3_1(a214) | c1_1(a214) | (~c2_1(a214)) | c2_1(a221) | c0_1(a221) | (~c3_1(a221)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a221) | c2_1(a221) | c3_1(a214) | c3_1(a190) | (~ndr1_0) | (~c2_1(a190)) | (~c0_1(a190)) | c1_1(a214) | (~c2_1(a214)) | (~c3_1(a221))))),
% 0.88/1.05 inference(monotonicity,[status(thm)],[2259])).
% 0.88/1.05 tff(2261,plain,
% 0.88/1.05 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a190) | (~c2_1(a190)) | (~c0_1(a190)) | c3_1(a214) | c1_1(a214) | (~c2_1(a214)) | c2_1(a221) | c0_1(a221) | (~c3_1(a221)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a221) | c2_1(a221) | c3_1(a214) | c3_1(a190) | (~ndr1_0) | (~c2_1(a190)) | (~c0_1(a190)) | c1_1(a214) | (~c2_1(a214)) | (~c3_1(a221)))),
% 0.88/1.05 inference(transitivity,[status(thm)],[2260, 2258])).
% 0.88/1.05 tff(2262,plain,
% 0.88/1.05 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a190) | (~c2_1(a190)) | (~c0_1(a190)) | c3_1(a214) | c1_1(a214) | (~c2_1(a214)) | c2_1(a221) | c0_1(a221) | (~c3_1(a221)))),
% 0.88/1.05 inference(quant_inst,[status(thm)],[])).
% 0.88/1.05 tff(2263,plain,
% 0.88/1.05 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a221) | c2_1(a221) | c3_1(a214) | c3_1(a190) | (~ndr1_0) | (~c2_1(a190)) | (~c0_1(a190)) | c1_1(a214) | (~c2_1(a214)) | (~c3_1(a221))),
% 0.88/1.05 inference(modus_ponens,[status(thm)],[2262, 2261])).
% 0.88/1.05 tff(2264,plain,
% 0.88/1.05 (~c3_1(a221)),
% 0.88/1.05 inference(unit_resolution,[status(thm)],[2263, 148, 1817, 2213, 2212, 2257, 2256, 1803, 2211, 451, 2209])).
% 0.88/1.05 tff(2265,plain,
% 0.88/1.05 (~hskp22),
% 0.88/1.05 inference(unit_resolution,[status(thm)],[1888, 2211, 2209])).
% 0.88/1.05 tff(2266,plain,
% 0.88/1.05 (hskp24),
% 0.88/1.05 inference(unit_resolution,[status(thm)],[1900, 14, 2265])).
% 0.88/1.05 tff(2267,plain,
% 0.88/1.05 (c3_1(a215)),
% 0.88/1.05 inference(unit_resolution,[status(thm)],[342, 2266])).
% 0.88/1.05 tff(2268,plain,
% 0.88/1.05 (c2_1(a215)),
% 0.88/1.05 inference(unit_resolution,[status(thm)],[350, 2266])).
% 0.88/1.05 tff(2269,plain,
% 0.88/1.05 (c1_1(a215)),
% 0.88/1.05 inference(unit_resolution,[status(thm)],[358, 2266])).
% 0.88/1.05 tff(2270,plain,
% 0.88/1.05 (~c0_1(a215)),
% 0.88/1.05 inference(unit_resolution,[status(thm)],[1233, 148, 2269, 2268, 2267, 2213, 2211, 470, 2215])).
% 0.88/1.05 tff(2271,plain,
% 0.88/1.05 (~c1_1(a221)),
% 0.88/1.05 inference(unit_resolution,[status(thm)],[2018, 2255])).
% 0.88/1.05 tff(2272,plain,
% 0.88/1.05 (hskp10),
% 0.88/1.05 inference(unit_resolution,[status(thm)],[2032, 148, 2269, 2267, 2271, 2256, 10, 2270, 2264])).
% 0.88/1.05 tff(2273,plain,
% 0.88/1.05 (c0_1(a200)),
% 0.88/1.05 inference(unit_resolution,[status(thm)],[307, 2272])).
% 0.88/1.05 tff(2274,plain,
% 0.88/1.05 (hskp6),
% 0.88/1.05 inference(unit_resolution,[status(thm)],[2048, 148, 2257, 2256, 530, 2264])).
% 0.88/1.05 tff(2275,plain,
% 0.88/1.05 (~c3_1(a195)),
% 0.88/1.05 inference(unit_resolution,[status(thm)],[543, 2274])).
% 0.88/1.05 tff(2276,plain,
% 0.88/1.05 (~c1_1(a195)),
% 0.88/1.05 inference(unit_resolution,[status(thm)],[557, 2274])).
% 0.88/1.05 tff(2277,plain,
% 0.88/1.05 (c0_1(a195)),
% 0.88/1.05 inference(unit_resolution,[status(thm)],[551, 2274])).
% 0.88/1.05 tff(2278,plain,
% 0.88/1.05 (c3_1(a200)),
% 0.88/1.05 inference(unit_resolution,[status(thm)],[315, 2272])).
% 0.88/1.05 tff(2279,plain,
% 0.88/1.05 (~c2_1(a200)),
% 0.88/1.05 inference(unit_resolution,[status(thm)],[576, 2278, 2208, 2277, 2276, 2275, 2273])).
% 0.88/1.05 tff(2280,plain,
% 0.88/1.05 (~c1_1(a225)),
% 0.88/1.05 inference(unit_resolution,[status(thm)],[417, 2214])).
% 0.88/1.05 tff(2281,plain,
% 0.88/1.05 (c3_1(a225)),
% 0.88/1.05 inference(unit_resolution,[status(thm)],[226, 2214])).
% 0.88/1.05 tff(2282,plain,
% 0.88/1.05 (c2_1(a225)),
% 0.88/1.05 inference(unit_resolution,[status(thm)],[1923, 148, 2269, 2268, 2281, 1817, 2280, 1809, 1915, 2270, 2209])).
% 0.88/1.05 tff(2283,plain,
% 0.88/1.05 (~c1_1(a200)),
% 0.88/1.05 inference(unit_resolution,[status(thm)],[373, 2272])).
% 0.88/1.05 tff(2284,plain,
% 0.88/1.05 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp13 | c1_1(a221) | c2_1(a221) | (~ndr1_0) | (~c2_1(a215)) | c0_1(a215) | (~c3_1(a215)) | c3_1(a221))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp13 | c1_1(a221) | c2_1(a221) | (~ndr1_0) | (~c2_1(a215)) | c0_1(a215) | (~c3_1(a215)) | c3_1(a221))),
% 0.88/1.05 inference(rewrite,[status(thm)],[])).
% 0.88/1.05 tff(2285,plain,
% 0.88/1.05 ((hskp13 | (~ndr1_0) | c0_1(a215) | (~c3_1(a215)) | (~c2_1(a215)) | c3_1(a221) | c1_1(a221) | c2_1(a221)) <=> (hskp13 | c1_1(a221) | c2_1(a221) | (~ndr1_0) | (~c2_1(a215)) | c0_1(a215) | (~c3_1(a215)) | c3_1(a221))),
% 0.88/1.05 inference(rewrite,[status(thm)],[])).
% 0.88/1.05 tff(2286,plain,
% 0.88/1.05 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp13 | (~ndr1_0) | c0_1(a215) | (~c3_1(a215)) | (~c2_1(a215)) | c3_1(a221) | c1_1(a221) | c2_1(a221))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp13 | c1_1(a221) | c2_1(a221) | (~ndr1_0) | (~c2_1(a215)) | c0_1(a215) | (~c3_1(a215)) | c3_1(a221)))),
% 0.88/1.05 inference(monotonicity,[status(thm)],[2285])).
% 0.88/1.05 tff(2287,plain,
% 0.88/1.05 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp13 | (~ndr1_0) | c0_1(a215) | (~c3_1(a215)) | (~c2_1(a215)) | c3_1(a221) | c1_1(a221) | c2_1(a221))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp13 | c1_1(a221) | c2_1(a221) | (~ndr1_0) | (~c2_1(a215)) | c0_1(a215) | (~c3_1(a215)) | c3_1(a221))),
% 0.88/1.05 inference(transitivity,[status(thm)],[2286, 2284])).
% 0.88/1.05 tff(2288,plain,
% 0.88/1.05 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp13 | (~ndr1_0) | c0_1(a215) | (~c3_1(a215)) | (~c2_1(a215)) | c3_1(a221) | c1_1(a221) | c2_1(a221))),
% 0.88/1.05 inference(quant_inst,[status(thm)],[])).
% 0.88/1.05 tff(2289,plain,
% 0.88/1.05 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp13 | c1_1(a221) | c2_1(a221) | (~ndr1_0) | (~c2_1(a215)) | c0_1(a215) | (~c3_1(a215)) | c3_1(a221)),
% 0.88/1.05 inference(modus_ponens,[status(thm)],[2288, 2287])).
% 0.88/1.05 tff(2290,plain,
% 0.88/1.05 (hskp13),
% 0.88/1.05 inference(unit_resolution,[status(thm)],[2289, 148, 2268, 2267, 2271, 2256, 246, 2270, 2264])).
% 0.88/1.05 tff(2291,plain,
% 0.88/1.05 (~c0_1(a209)),
% 0.88/1.05 inference(unit_resolution,[status(thm)],[387, 2290])).
% 0.88/1.05 tff(2292,plain,
% 0.88/1.05 (~c0_1(a225)),
% 0.88/1.05 inference(unit_resolution,[status(thm)],[232, 2214])).
% 0.88/1.05 tff(2293,plain,
% 0.88/1.05 (c3_1(a209)),
% 0.88/1.05 inference(unit_resolution,[status(thm)],[395, 2290])).
% 0.88/1.05 tff(2294,plain,
% 0.88/1.05 (c1_1(a209)),
% 0.88/1.05 inference(unit_resolution,[status(thm)],[403, 2290])).
% 0.88/1.05 tff(2295,plain,
% 0.88/1.05 ($false),
% 0.88/1.05 inference(unit_resolution,[status(thm)],[439, 148, 2294, 2293, 2273, 2292, 2280, 2291, 2283, 65, 2282, 2279])).
% 0.88/1.05 tff(2296,plain,(hskp2), inference(lemma,lemma(discharge,[]))).
% 0.88/1.05 tff(2297,plain,
% 0.88/1.05 (~c3_1(a191)),
% 0.88/1.05 inference(unit_resolution,[status(thm)],[42, 2296])).
% 0.88/1.05 tff(2298,plain,
% 0.88/1.05 (~c2_1(a191)),
% 0.88/1.05 inference(unit_resolution,[status(thm)],[48, 2296])).
% 0.88/1.05 tff(2299,plain,
% 0.88/1.05 (~c1_1(a191)),
% 0.88/1.05 inference(unit_resolution,[status(thm)],[54, 2296])).
% 0.88/1.05 tff(2300,plain,
% 0.88/1.05 (hskp13),
% 0.88/1.05 inference(unit_resolution,[status(thm)],[381, 2299, 2281, 2292, 2298, 2297])).
% 0.88/1.05 tff(2301,plain,
% 0.88/1.05 (~c0_1(a209)),
% 0.88/1.05 inference(unit_resolution,[status(thm)],[387, 2300])).
% 0.88/1.05 tff(2302,plain,
% 0.88/1.05 (c3_1(a209)),
% 0.88/1.05 inference(unit_resolution,[status(thm)],[395, 2300])).
% 0.88/1.05 tff(2303,plain,
% 0.88/1.05 (c1_1(a209)),
% 0.88/1.05 inference(unit_resolution,[status(thm)],[403, 2300])).
% 0.88/1.05 tff(2304,plain,
% 0.88/1.05 (hskp10),
% 0.88/1.05 inference(unit_resolution,[status(thm)],[410, 148, 2303, 2302, 2301, 2299, 2298, 2297, 10])).
% 0.88/1.05 tff(2305,plain,
% 0.88/1.05 (c0_1(a200)),
% 0.88/1.05 inference(unit_resolution,[status(thm)],[307, 2304])).
% 0.88/1.05 tff(2306,plain,
% 0.88/1.05 (~c0_1(a191)),
% 0.88/1.05 inference(unit_resolution,[status(thm)],[2193, 148, 1817, 2303, 2302, 1809, 2301, 2299, 2298, 65, 2209])).
% 0.88/1.05 tff(2307,plain,
% 0.88/1.05 (hskp6),
% 0.88/1.05 inference(unit_resolution,[status(thm)],[536, 148, 2298, 2297, 530, 2306])).
% 0.88/1.05 tff(2308,plain,
% 0.88/1.05 (~c3_1(a195)),
% 0.88/1.05 inference(unit_resolution,[status(thm)],[543, 2307])).
% 0.88/1.05 tff(2309,plain,
% 0.88/1.05 (~c1_1(a195)),
% 0.88/1.05 inference(unit_resolution,[status(thm)],[557, 2307])).
% 0.88/1.05 tff(2310,plain,
% 0.88/1.05 (c0_1(a195)),
% 0.88/1.05 inference(unit_resolution,[status(thm)],[551, 2307])).
% 0.88/1.05 tff(2311,plain,
% 0.88/1.05 (c3_1(a200)),
% 0.88/1.05 inference(unit_resolution,[status(thm)],[315, 2304])).
% 0.88/1.05 tff(2312,plain,
% 0.88/1.05 (~c2_1(a200)),
% 0.88/1.05 inference(unit_resolution,[status(thm)],[576, 2311, 2208, 2310, 2309, 2308, 2305])).
% 0.88/1.05 tff(2313,plain,
% 0.88/1.05 (c2_1(a225)),
% 0.88/1.05 inference(unit_resolution,[status(thm)],[270, 148, 2281, 2292, 2299, 2298, 2297, 264, 2306])).
% 0.88/1.05 tff(2314,plain,
% 0.88/1.05 (~c1_1(a200)),
% 0.88/1.05 inference(unit_resolution,[status(thm)],[373, 2304])).
% 0.88/1.05 tff(2315,plain,
% 0.88/1.05 ($false),
% 0.88/1.05 inference(unit_resolution,[status(thm)],[439, 148, 2303, 2302, 2305, 2292, 2280, 2301, 2314, 65, 2313, 2312])).
% 0.88/1.05 % SZS output end Proof
% 0.88/1.05 % E exiting
%------------------------------------------------------------------------------