%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN349+1 : TPTP v9.0.0. Released v2.0.0.
% 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 05:38:51 AM UTC 2025
% Result : Theorem 0.14s 0.40s
% Output : Proof 0.14s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.14/0.14 % Problem : SYN349+1 : TPTP v9.0.0. Released v2.0.0.
% 0.14/0.14 % Command : run_E %s %d THM
% 0.14/0.36 % Computer : n013.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Fri Jun 20 12:31:38 EDT 2025
% 0.14/0.36 % CPUTime :
% 0.14/0.40 % SZS status Theorem
% 0.14/0.40 % SZS output start Proof
% 0.14/0.40 tff(big_f_type, type, (
% 0.14/0.40 big_f: ( $i * $i ) > $o)).
% 0.14/0.40 tff(tptp_fun_X2_0_type, type, (
% 0.14/0.40 tptp_fun_X2_0: $i > $i)).
% 0.14/0.40 tff(elem_2_type, type, (
% 0.14/0.40 elem_2: $i)).
% 0.14/0.40 tff(tptp_fun_X4_1_type, type, (
% 0.14/0.40 tptp_fun_X4_1: ( $i * $i ) > $i)).
% 0.14/0.40 tff(1,assumption,(~big_f(elem!2, tptp_fun_X4_1(tptp_fun_X2_0(elem!2), elem!2))), introduced(assumption)).
% 0.14/0.40 tff(2,plain,
% 0.14/0.40 (![X1: $i] : ![X3: $i] : (~((~(big_f(X1, tptp_fun_X4_1(X3, X1)) <=> big_f(tptp_fun_X2_0(X1), tptp_fun_X4_1(X3, X1)))) | (((big_f(X1, tptp_fun_X4_1(X3, X1)) <=> big_f(tptp_fun_X4_1(X3, X1), X3)) <=> big_f(X3, tptp_fun_X4_1(X3, X1))) <=> big_f(tptp_fun_X4_1(X3, X1), tptp_fun_X2_0(X1))))) <=> ![X1: $i, X3: $i] : (~((~(big_f(X1, tptp_fun_X4_1(X3, X1)) <=> big_f(tptp_fun_X2_0(X1), tptp_fun_X4_1(X3, X1)))) | (((big_f(X1, tptp_fun_X4_1(X3, X1)) <=> big_f(tptp_fun_X4_1(X3, X1), X3)) <=> big_f(X3, tptp_fun_X4_1(X3, X1))) <=> big_f(tptp_fun_X4_1(X3, X1), tptp_fun_X2_0(X1)))))),
% 0.14/0.40 inference(pull_quant,[status(thm)],[])).
% 0.14/0.40 tff(3,plain,
% 0.14/0.40 ((~?[X1: $i] : ![X2: $i] : ?[X3: $i] : ![X4: $i] : ((~(big_f(X1, X4) <=> big_f(X2, X4))) | (((big_f(X1, X4) <=> big_f(X4, X3)) <=> big_f(X3, X4)) <=> big_f(X4, X2)))) <=> (~?[X1: $i] : ![X2: $i] : ?[X3: $i] : ![X4: $i] : ((~(big_f(X1, X4) <=> big_f(X2, X4))) | (((big_f(X1, X4) <=> big_f(X4, X3)) <=> big_f(X3, X4)) <=> big_f(X4, X2))))),
% 0.14/0.40 inference(rewrite,[status(thm)],[])).
% 0.14/0.40 tff(4,plain,
% 0.14/0.40 ((~?[X1: $i] : ![X2: $i] : ?[X3: $i] : ![X4: $i] : ((big_f(X1, X4) <=> big_f(X2, X4)) => (((big_f(X1, X4) <=> big_f(X4, X3)) <=> big_f(X3, X4)) <=> big_f(X4, X2)))) <=> (~?[X1: $i] : ![X2: $i] : ?[X3: $i] : ![X4: $i] : ((~(big_f(X1, X4) <=> big_f(X2, X4))) | (((big_f(X1, X4) <=> big_f(X4, X3)) <=> big_f(X3, X4)) <=> big_f(X4, X2))))),
% 0.14/0.40 inference(rewrite,[status(thm)],[])).
% 0.14/0.40 tff(5,axiom,(~?[X1: $i] : ![X2: $i] : ?[X3: $i] : ![X4: $i] : ((big_f(X1, X4) <=> big_f(X2, X4)) => (((big_f(X1, X4) <=> big_f(X4, X3)) <=> big_f(X3, X4)) <=> big_f(X4, X2)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','church_46_17_5')).
% 0.14/0.40 tff(6,plain,
% 0.14/0.40 (~?[X1: $i] : ![X2: $i] : ?[X3: $i] : ![X4: $i] : ((~(big_f(X1, X4) <=> big_f(X2, X4))) | (((big_f(X1, X4) <=> big_f(X4, X3)) <=> big_f(X3, X4)) <=> big_f(X4, X2)))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.14/0.40 tff(7,plain,
% 0.14/0.40 (~?[X1: $i] : ![X2: $i] : ?[X3: $i] : ![X4: $i] : ((~(big_f(X1, X4) <=> big_f(X2, X4))) | (((big_f(X1, X4) <=> big_f(X4, X3)) <=> big_f(X3, X4)) <=> big_f(X4, X2)))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[6, 3])).
% 0.14/0.40 tff(8,plain,
% 0.14/0.40 (~?[X1: $i] : ![X2: $i] : ?[X3: $i] : ![X4: $i] : ((~(big_f(X1, X4) <=> big_f(X2, X4))) | (((big_f(X1, X4) <=> big_f(X4, X3)) <=> big_f(X3, X4)) <=> big_f(X4, X2)))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.14/0.40 tff(9,plain,
% 0.14/0.40 (~?[X1: $i] : ![X2: $i] : ?[X3: $i] : ![X4: $i] : ((~(big_f(X1, X4) <=> big_f(X2, X4))) | (((big_f(X1, X4) <=> big_f(X4, X3)) <=> big_f(X3, X4)) <=> big_f(X4, X2)))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[8, 3])).
% 0.14/0.40 tff(10,plain,
% 0.14/0.40 (^[X1: $i] : trans(sk($oeq((~![X2: $i] : ?[X3: $i] : ![X4: $i] : ((~(big_f(X1, X4) <=> big_f(X2, X4))) | (((big_f(X1, X4) <=> big_f(X4, X3)) <=> big_f(X3, X4)) <=> big_f(X4, X2)))), (~?[X3: $i] : ![X4: $i] : ((~(big_f(X1, X4) <=> big_f(tptp_fun_X2_0(X1), X4))) | (((big_f(X1, X4) <=> big_f(X4, X3)) <=> big_f(X3, X4)) <=> big_f(X4, tptp_fun_X2_0(X1))))))), nnf_neg(proof_bind(^[X3: $i] : sk($oeq((~![X4: $i] : ((~(big_f(X1, X4) <=> big_f(tptp_fun_X2_0(X1), X4))) | (((big_f(X1, X4) <=> big_f(X4, X3)) <=> big_f(X3, X4)) <=> big_f(X4, tptp_fun_X2_0(X1))))), (~((~(big_f(X1, tptp_fun_X4_1(X3, X1)) <=> big_f(tptp_fun_X2_0(X1), tptp_fun_X4_1(X3, X1)))) | (((big_f(X1, tptp_fun_X4_1(X3, X1)) <=> big_f(tptp_fun_X4_1(X3, X1), X3)) <=> big_f(X3, tptp_fun_X4_1(X3, X1))) <=> big_f(tptp_fun_X4_1(X3, X1), tptp_fun_X2_0(X1)))))))), $oeq((~?[X3: $i] : ![X4: $i] : ((~(big_f(X1, X4) <=> big_f(tptp_fun_X2_0(X1), X4))) | (((big_f(X1, X4) <=> big_f(X4, X3)) <=> big_f(X3, X4)) <=> big_f(X4, tptp_fun_X2_0(X1))))), ![X3: $i] : (~((~(big_f(X1, tptp_fun_X4_1(X3, X1)) <=> big_f(tptp_fun_X2_0(X1), tptp_fun_X4_1(X3, X1)))) | (((big_f(X1, tptp_fun_X4_1(X3, X1)) <=> big_f(tptp_fun_X4_1(X3, X1), X3)) <=> big_f(X3, tptp_fun_X4_1(X3, X1))) <=> big_f(tptp_fun_X4_1(X3, X1), tptp_fun_X2_0(X1))))))), $oeq((~![X2: $i] : ?[X3: $i] : ![X4: $i] : ((~(big_f(X1, X4) <=> big_f(X2, X4))) | (((big_f(X1, X4) <=> big_f(X4, X3)) <=> big_f(X3, X4)) <=> big_f(X4, X2)))), ![X3: $i] : (~((~(big_f(X1, tptp_fun_X4_1(X3, X1)) <=> big_f(tptp_fun_X2_0(X1), tptp_fun_X4_1(X3, X1)))) | (((big_f(X1, tptp_fun_X4_1(X3, X1)) <=> big_f(tptp_fun_X4_1(X3, X1), X3)) <=> big_f(X3, tptp_fun_X4_1(X3, X1))) <=> big_f(tptp_fun_X4_1(X3, X1), tptp_fun_X2_0(X1)))))))),
% 0.14/0.41 inference(bind,[status(th)],[])).
% 0.14/0.41 tff(11,plain,(
% 0.14/0.41 ![X1: $i] : ![X3: $i] : (~((~(big_f(X1, tptp_fun_X4_1(X3, X1)) <=> big_f(tptp_fun_X2_0(X1), tptp_fun_X4_1(X3, X1)))) | (((big_f(X1, tptp_fun_X4_1(X3, X1)) <=> big_f(tptp_fun_X4_1(X3, X1), X3)) <=> big_f(X3, tptp_fun_X4_1(X3, X1))) <=> big_f(tptp_fun_X4_1(X3, X1), tptp_fun_X2_0(X1)))))),
% 0.14/0.41 inference(nnf-neg,[status(sab)],[9, 10])).
% 0.14/0.41 tff(12,plain,
% 0.14/0.41 (![X1: $i, X3: $i] : (~((~(big_f(X1, tptp_fun_X4_1(X3, X1)) <=> big_f(tptp_fun_X2_0(X1), tptp_fun_X4_1(X3, X1)))) | (((big_f(X1, tptp_fun_X4_1(X3, X1)) <=> big_f(tptp_fun_X4_1(X3, X1), X3)) <=> big_f(X3, tptp_fun_X4_1(X3, X1))) <=> big_f(tptp_fun_X4_1(X3, X1), tptp_fun_X2_0(X1)))))),
% 0.14/0.41 inference(modus_ponens,[status(thm)],[11, 2])).
% 0.14/0.41 tff(13,plain,
% 0.14/0.41 ((~![X1: $i, X3: $i] : (~((~(big_f(X1, tptp_fun_X4_1(X3, X1)) <=> big_f(tptp_fun_X2_0(X1), tptp_fun_X4_1(X3, X1)))) | (((big_f(X1, tptp_fun_X4_1(X3, X1)) <=> big_f(tptp_fun_X4_1(X3, X1), X3)) <=> big_f(X3, tptp_fun_X4_1(X3, X1))) <=> big_f(tptp_fun_X4_1(X3, X1), tptp_fun_X2_0(X1)))))) | (~((~(big_f(elem!2, tptp_fun_X4_1(tptp_fun_X2_0(elem!2), elem!2)) <=> big_f(tptp_fun_X2_0(elem!2), tptp_fun_X4_1(tptp_fun_X2_0(elem!2), elem!2)))) | (((big_f(elem!2, tptp_fun_X4_1(tptp_fun_X2_0(elem!2), elem!2)) <=> big_f(tptp_fun_X4_1(tptp_fun_X2_0(elem!2), elem!2), tptp_fun_X2_0(elem!2))) <=> big_f(tptp_fun_X2_0(elem!2), tptp_fun_X4_1(tptp_fun_X2_0(elem!2), elem!2))) <=> big_f(tptp_fun_X4_1(tptp_fun_X2_0(elem!2), elem!2), tptp_fun_X2_0(elem!2)))))),
% 0.14/0.41 inference(quant_inst,[status(thm)],[])).
% 0.14/0.41 tff(14,plain,
% 0.14/0.41 (~((~(big_f(elem!2, tptp_fun_X4_1(tptp_fun_X2_0(elem!2), elem!2)) <=> big_f(tptp_fun_X2_0(elem!2), tptp_fun_X4_1(tptp_fun_X2_0(elem!2), elem!2)))) | (((big_f(elem!2, tptp_fun_X4_1(tptp_fun_X2_0(elem!2), elem!2)) <=> big_f(tptp_fun_X4_1(tptp_fun_X2_0(elem!2), elem!2), tptp_fun_X2_0(elem!2))) <=> big_f(tptp_fun_X2_0(elem!2), tptp_fun_X4_1(tptp_fun_X2_0(elem!2), elem!2))) <=> big_f(tptp_fun_X4_1(tptp_fun_X2_0(elem!2), elem!2), tptp_fun_X2_0(elem!2))))),
% 0.14/0.41 inference(unit_resolution,[status(thm)],[13, 12])).
% 0.14/0.41 tff(15,plain,
% 0.14/0.41 (((~(big_f(elem!2, tptp_fun_X4_1(tptp_fun_X2_0(elem!2), elem!2)) <=> big_f(tptp_fun_X2_0(elem!2), tptp_fun_X4_1(tptp_fun_X2_0(elem!2), elem!2)))) | (((big_f(elem!2, tptp_fun_X4_1(tptp_fun_X2_0(elem!2), elem!2)) <=> big_f(tptp_fun_X4_1(tptp_fun_X2_0(elem!2), elem!2), tptp_fun_X2_0(elem!2))) <=> big_f(tptp_fun_X2_0(elem!2), tptp_fun_X4_1(tptp_fun_X2_0(elem!2), elem!2))) <=> big_f(tptp_fun_X4_1(tptp_fun_X2_0(elem!2), elem!2), tptp_fun_X2_0(elem!2)))) | (~(((big_f(elem!2, tptp_fun_X4_1(tptp_fun_X2_0(elem!2), elem!2)) <=> big_f(tptp_fun_X4_1(tptp_fun_X2_0(elem!2), elem!2), tptp_fun_X2_0(elem!2))) <=> big_f(tptp_fun_X2_0(elem!2), tptp_fun_X4_1(tptp_fun_X2_0(elem!2), elem!2))) <=> big_f(tptp_fun_X4_1(tptp_fun_X2_0(elem!2), elem!2), tptp_fun_X2_0(elem!2))))),
% 0.14/0.41 inference(tautology,[status(thm)],[])).
% 0.14/0.41 tff(16,plain,
% 0.14/0.41 (~(((big_f(elem!2, tptp_fun_X4_1(tptp_fun_X2_0(elem!2), elem!2)) <=> big_f(tptp_fun_X4_1(tptp_fun_X2_0(elem!2), elem!2), tptp_fun_X2_0(elem!2))) <=> big_f(tptp_fun_X2_0(elem!2), tptp_fun_X4_1(tptp_fun_X2_0(elem!2), elem!2))) <=> big_f(tptp_fun_X4_1(tptp_fun_X2_0(elem!2), elem!2), tptp_fun_X2_0(elem!2)))),
% 0.14/0.41 inference(unit_resolution,[status(thm)],[15, 14])).
% 0.14/0.41 tff(17,assumption,(~(big_f(elem!2, tptp_fun_X4_1(tptp_fun_X2_0(elem!2), elem!2)) <=> big_f(tptp_fun_X4_1(tptp_fun_X2_0(elem!2), elem!2), tptp_fun_X2_0(elem!2)))), introduced(assumption)).
% 0.14/0.41 tff(18,plain,
% 0.14/0.41 ((big_f(elem!2, tptp_fun_X4_1(tptp_fun_X2_0(elem!2), elem!2)) <=> big_f(tptp_fun_X4_1(tptp_fun_X2_0(elem!2), elem!2), tptp_fun_X2_0(elem!2))) | big_f(elem!2, tptp_fun_X4_1(tptp_fun_X2_0(elem!2), elem!2)) | big_f(tptp_fun_X4_1(tptp_fun_X2_0(elem!2), elem!2), tptp_fun_X2_0(elem!2))),
% 0.14/0.41 inference(tautology,[status(thm)],[])).
% 0.14/0.41 tff(19,plain,
% 0.14/0.41 (big_f(tptp_fun_X4_1(tptp_fun_X2_0(elem!2), elem!2), tptp_fun_X2_0(elem!2))),
% 0.14/0.41 inference(unit_resolution,[status(thm)],[18, 1, 17])).
% 0.14/0.41 tff(20,plain,
% 0.14/0.41 (((~(big_f(elem!2, tptp_fun_X4_1(tptp_fun_X2_0(elem!2), elem!2)) <=> big_f(tptp_fun_X2_0(elem!2), tptp_fun_X4_1(tptp_fun_X2_0(elem!2), elem!2)))) | (((big_f(elem!2, tptp_fun_X4_1(tptp_fun_X2_0(elem!2), elem!2)) <=> big_f(tptp_fun_X4_1(tptp_fun_X2_0(elem!2), elem!2), tptp_fun_X2_0(elem!2))) <=> big_f(tptp_fun_X2_0(elem!2), tptp_fun_X4_1(tptp_fun_X2_0(elem!2), elem!2))) <=> big_f(tptp_fun_X4_1(tptp_fun_X2_0(elem!2), elem!2), tptp_fun_X2_0(elem!2)))) | (big_f(elem!2, tptp_fun_X4_1(tptp_fun_X2_0(elem!2), elem!2)) <=> big_f(tptp_fun_X2_0(elem!2), tptp_fun_X4_1(tptp_fun_X2_0(elem!2), elem!2)))),
% 0.14/0.41 inference(tautology,[status(thm)],[])).
% 0.14/0.41 tff(21,plain,
% 0.14/0.41 (big_f(elem!2, tptp_fun_X4_1(tptp_fun_X2_0(elem!2), elem!2)) <=> big_f(tptp_fun_X2_0(elem!2), tptp_fun_X4_1(tptp_fun_X2_0(elem!2), elem!2))),
% 0.14/0.41 inference(unit_resolution,[status(thm)],[20, 14])).
% 0.14/0.41 tff(22,plain,
% 0.14/0.41 ((~(big_f(elem!2, tptp_fun_X4_1(tptp_fun_X2_0(elem!2), elem!2)) <=> big_f(tptp_fun_X2_0(elem!2), tptp_fun_X4_1(tptp_fun_X2_0(elem!2), elem!2)))) | big_f(elem!2, tptp_fun_X4_1(tptp_fun_X2_0(elem!2), elem!2)) | (~big_f(tptp_fun_X2_0(elem!2), tptp_fun_X4_1(tptp_fun_X2_0(elem!2), elem!2)))),
% 0.14/0.41 inference(tautology,[status(thm)],[])).
% 0.14/0.41 tff(23,plain,
% 0.14/0.41 (~big_f(tptp_fun_X2_0(elem!2), tptp_fun_X4_1(tptp_fun_X2_0(elem!2), elem!2))),
% 0.14/0.41 inference(unit_resolution,[status(thm)],[22, 1, 21])).
% 0.14/0.41 tff(24,plain,
% 0.14/0.41 (((big_f(elem!2, tptp_fun_X4_1(tptp_fun_X2_0(elem!2), elem!2)) <=> big_f(tptp_fun_X4_1(tptp_fun_X2_0(elem!2), elem!2), tptp_fun_X2_0(elem!2))) <=> big_f(tptp_fun_X2_0(elem!2), tptp_fun_X4_1(tptp_fun_X2_0(elem!2), elem!2))) | (big_f(elem!2, tptp_fun_X4_1(tptp_fun_X2_0(elem!2), elem!2)) <=> big_f(tptp_fun_X4_1(tptp_fun_X2_0(elem!2), elem!2), tptp_fun_X2_0(elem!2))) | big_f(tptp_fun_X2_0(elem!2), tptp_fun_X4_1(tptp_fun_X2_0(elem!2), elem!2))),
% 0.14/0.41 inference(tautology,[status(thm)],[])).
% 0.14/0.41 tff(25,plain,
% 0.14/0.41 ((big_f(elem!2, tptp_fun_X4_1(tptp_fun_X2_0(elem!2), elem!2)) <=> big_f(tptp_fun_X4_1(tptp_fun_X2_0(elem!2), elem!2), tptp_fun_X2_0(elem!2))) <=> big_f(tptp_fun_X2_0(elem!2), tptp_fun_X4_1(tptp_fun_X2_0(elem!2), elem!2))),
% 0.14/0.41 inference(unit_resolution,[status(thm)],[24, 23, 17])).
% 0.14/0.41 tff(26,plain,
% 0.14/0.41 ((((big_f(elem!2, tptp_fun_X4_1(tptp_fun_X2_0(elem!2), elem!2)) <=> big_f(tptp_fun_X4_1(tptp_fun_X2_0(elem!2), elem!2), tptp_fun_X2_0(elem!2))) <=> big_f(tptp_fun_X2_0(elem!2), tptp_fun_X4_1(tptp_fun_X2_0(elem!2), elem!2))) <=> big_f(tptp_fun_X4_1(tptp_fun_X2_0(elem!2), elem!2), tptp_fun_X2_0(elem!2))) | (~((big_f(elem!2, tptp_fun_X4_1(tptp_fun_X2_0(elem!2), elem!2)) <=> big_f(tptp_fun_X4_1(tptp_fun_X2_0(elem!2), elem!2), tptp_fun_X2_0(elem!2))) <=> big_f(tptp_fun_X2_0(elem!2), tptp_fun_X4_1(tptp_fun_X2_0(elem!2), elem!2)))) | (~big_f(tptp_fun_X4_1(tptp_fun_X2_0(elem!2), elem!2), tptp_fun_X2_0(elem!2)))),
% 0.14/0.41 inference(tautology,[status(thm)],[])).
% 0.14/0.41 tff(27,plain,
% 0.14/0.41 ($false),
% 0.14/0.41 inference(unit_resolution,[status(thm)],[26, 25, 19, 16])).
% 0.14/0.41 tff(28,plain,(big_f(elem!2, tptp_fun_X4_1(tptp_fun_X2_0(elem!2), elem!2)) | (big_f(elem!2, tptp_fun_X4_1(tptp_fun_X2_0(elem!2), elem!2)) <=> big_f(tptp_fun_X4_1(tptp_fun_X2_0(elem!2), elem!2), tptp_fun_X2_0(elem!2)))), inference(lemma,lemma(discharge,[]))).
% 0.14/0.41 tff(29,plain,
% 0.14/0.41 (big_f(elem!2, tptp_fun_X4_1(tptp_fun_X2_0(elem!2), elem!2))),
% 0.14/0.41 inference(unit_resolution,[status(thm)],[28, 17])).
% 0.14/0.41 tff(30,plain,
% 0.14/0.41 ((big_f(elem!2, tptp_fun_X4_1(tptp_fun_X2_0(elem!2), elem!2)) <=> big_f(tptp_fun_X4_1(tptp_fun_X2_0(elem!2), elem!2), tptp_fun_X2_0(elem!2))) | (~big_f(elem!2, tptp_fun_X4_1(tptp_fun_X2_0(elem!2), elem!2))) | (~big_f(tptp_fun_X4_1(tptp_fun_X2_0(elem!2), elem!2), tptp_fun_X2_0(elem!2)))),
% 0.14/0.41 inference(tautology,[status(thm)],[])).
% 0.14/0.41 tff(31,plain,
% 0.14/0.41 (~big_f(tptp_fun_X4_1(tptp_fun_X2_0(elem!2), elem!2), tptp_fun_X2_0(elem!2))),
% 0.14/0.41 inference(unit_resolution,[status(thm)],[30, 29, 17])).
% 0.14/0.41 tff(32,plain,
% 0.14/0.41 ((~(big_f(elem!2, tptp_fun_X4_1(tptp_fun_X2_0(elem!2), elem!2)) <=> big_f(tptp_fun_X2_0(elem!2), tptp_fun_X4_1(tptp_fun_X2_0(elem!2), elem!2)))) | (~big_f(elem!2, tptp_fun_X4_1(tptp_fun_X2_0(elem!2), elem!2))) | big_f(tptp_fun_X2_0(elem!2), tptp_fun_X4_1(tptp_fun_X2_0(elem!2), elem!2))),
% 0.14/0.41 inference(tautology,[status(thm)],[])).
% 0.14/0.41 tff(33,plain,
% 0.14/0.41 (big_f(tptp_fun_X2_0(elem!2), tptp_fun_X4_1(tptp_fun_X2_0(elem!2), elem!2))),
% 0.14/0.41 inference(unit_resolution,[status(thm)],[32, 29, 21])).
% 0.14/0.41 tff(34,plain,
% 0.14/0.41 ((~((big_f(elem!2, tptp_fun_X4_1(tptp_fun_X2_0(elem!2), elem!2)) <=> big_f(tptp_fun_X4_1(tptp_fun_X2_0(elem!2), elem!2), tptp_fun_X2_0(elem!2))) <=> big_f(tptp_fun_X2_0(elem!2), tptp_fun_X4_1(tptp_fun_X2_0(elem!2), elem!2)))) | (big_f(elem!2, tptp_fun_X4_1(tptp_fun_X2_0(elem!2), elem!2)) <=> big_f(tptp_fun_X4_1(tptp_fun_X2_0(elem!2), elem!2), tptp_fun_X2_0(elem!2))) | (~big_f(tptp_fun_X2_0(elem!2), tptp_fun_X4_1(tptp_fun_X2_0(elem!2), elem!2)))),
% 0.14/0.41 inference(tautology,[status(thm)],[])).
% 0.14/0.41 tff(35,plain,
% 0.14/0.41 (~((big_f(elem!2, tptp_fun_X4_1(tptp_fun_X2_0(elem!2), elem!2)) <=> big_f(tptp_fun_X4_1(tptp_fun_X2_0(elem!2), elem!2), tptp_fun_X2_0(elem!2))) <=> big_f(tptp_fun_X2_0(elem!2), tptp_fun_X4_1(tptp_fun_X2_0(elem!2), elem!2)))),
% 0.14/0.41 inference(unit_resolution,[status(thm)],[34, 33, 17])).
% 0.14/0.41 tff(36,plain,
% 0.14/0.41 ((((big_f(elem!2, tptp_fun_X4_1(tptp_fun_X2_0(elem!2), elem!2)) <=> big_f(tptp_fun_X4_1(tptp_fun_X2_0(elem!2), elem!2), tptp_fun_X2_0(elem!2))) <=> big_f(tptp_fun_X2_0(elem!2), tptp_fun_X4_1(tptp_fun_X2_0(elem!2), elem!2))) <=> big_f(tptp_fun_X4_1(tptp_fun_X2_0(elem!2), elem!2), tptp_fun_X2_0(elem!2))) | ((big_f(elem!2, tptp_fun_X4_1(tptp_fun_X2_0(elem!2), elem!2)) <=> big_f(tptp_fun_X4_1(tptp_fun_X2_0(elem!2), elem!2), tptp_fun_X2_0(elem!2))) <=> big_f(tptp_fun_X2_0(elem!2), tptp_fun_X4_1(tptp_fun_X2_0(elem!2), elem!2))) | big_f(tptp_fun_X4_1(tptp_fun_X2_0(elem!2), elem!2), tptp_fun_X2_0(elem!2))),
% 0.14/0.41 inference(tautology,[status(thm)],[])).
% 0.14/0.41 tff(37,plain,
% 0.14/0.41 ($false),
% 0.14/0.41 inference(unit_resolution,[status(thm)],[36, 35, 31, 16])).
% 0.14/0.41 tff(38,plain,(big_f(elem!2, tptp_fun_X4_1(tptp_fun_X2_0(elem!2), elem!2)) <=> big_f(tptp_fun_X4_1(tptp_fun_X2_0(elem!2), elem!2), tptp_fun_X2_0(elem!2))), inference(lemma,lemma(discharge,[]))).
% 0.14/0.41 tff(39,plain,
% 0.14/0.41 ((~(big_f(elem!2, tptp_fun_X4_1(tptp_fun_X2_0(elem!2), elem!2)) <=> big_f(tptp_fun_X4_1(tptp_fun_X2_0(elem!2), elem!2), tptp_fun_X2_0(elem!2)))) | big_f(elem!2, tptp_fun_X4_1(tptp_fun_X2_0(elem!2), elem!2)) | (~big_f(tptp_fun_X4_1(tptp_fun_X2_0(elem!2), elem!2), tptp_fun_X2_0(elem!2)))),
% 0.14/0.41 inference(tautology,[status(thm)],[])).
% 0.14/0.41 tff(40,plain,
% 0.14/0.41 (big_f(elem!2, tptp_fun_X4_1(tptp_fun_X2_0(elem!2), elem!2)) | (~big_f(tptp_fun_X4_1(tptp_fun_X2_0(elem!2), elem!2), tptp_fun_X2_0(elem!2)))),
% 0.14/0.41 inference(unit_resolution,[status(thm)],[39, 38])).
% 0.14/0.41 tff(41,plain,
% 0.14/0.41 (~big_f(tptp_fun_X4_1(tptp_fun_X2_0(elem!2), elem!2), tptp_fun_X2_0(elem!2))),
% 0.14/0.41 inference(unit_resolution,[status(thm)],[40, 1])).
% 0.14/0.41 tff(42,plain,
% 0.14/0.41 (big_f(elem!2, tptp_fun_X4_1(tptp_fun_X2_0(elem!2), elem!2)) | (~big_f(tptp_fun_X2_0(elem!2), tptp_fun_X4_1(tptp_fun_X2_0(elem!2), elem!2)))),
% 0.14/0.41 inference(unit_resolution,[status(thm)],[22, 21])).
% 0.14/0.41 tff(43,plain,
% 0.14/0.41 (~big_f(tptp_fun_X2_0(elem!2), tptp_fun_X4_1(tptp_fun_X2_0(elem!2), elem!2))),
% 0.14/0.41 inference(unit_resolution,[status(thm)],[42, 1])).
% 0.14/0.41 tff(44,plain,
% 0.14/0.41 ((~((big_f(elem!2, tptp_fun_X4_1(tptp_fun_X2_0(elem!2), elem!2)) <=> big_f(tptp_fun_X4_1(tptp_fun_X2_0(elem!2), elem!2), tptp_fun_X2_0(elem!2))) <=> big_f(tptp_fun_X2_0(elem!2), tptp_fun_X4_1(tptp_fun_X2_0(elem!2), elem!2)))) | (~(big_f(elem!2, tptp_fun_X4_1(tptp_fun_X2_0(elem!2), elem!2)) <=> big_f(tptp_fun_X4_1(tptp_fun_X2_0(elem!2), elem!2), tptp_fun_X2_0(elem!2)))) | big_f(tptp_fun_X2_0(elem!2), tptp_fun_X4_1(tptp_fun_X2_0(elem!2), elem!2))),
% 0.14/0.41 inference(tautology,[status(thm)],[])).
% 0.14/0.41 tff(45,plain,
% 0.14/0.41 ((~((big_f(elem!2, tptp_fun_X4_1(tptp_fun_X2_0(elem!2), elem!2)) <=> big_f(tptp_fun_X4_1(tptp_fun_X2_0(elem!2), elem!2), tptp_fun_X2_0(elem!2))) <=> big_f(tptp_fun_X2_0(elem!2), tptp_fun_X4_1(tptp_fun_X2_0(elem!2), elem!2)))) | big_f(tptp_fun_X2_0(elem!2), tptp_fun_X4_1(tptp_fun_X2_0(elem!2), elem!2))),
% 0.14/0.41 inference(unit_resolution,[status(thm)],[44, 38])).
% 0.14/0.41 tff(46,plain,
% 0.14/0.41 (~((big_f(elem!2, tptp_fun_X4_1(tptp_fun_X2_0(elem!2), elem!2)) <=> big_f(tptp_fun_X4_1(tptp_fun_X2_0(elem!2), elem!2), tptp_fun_X2_0(elem!2))) <=> big_f(tptp_fun_X2_0(elem!2), tptp_fun_X4_1(tptp_fun_X2_0(elem!2), elem!2)))),
% 0.14/0.41 inference(unit_resolution,[status(thm)],[45, 43])).
% 0.14/0.41 tff(47,plain,
% 0.14/0.41 (((big_f(elem!2, tptp_fun_X4_1(tptp_fun_X2_0(elem!2), elem!2)) <=> big_f(tptp_fun_X4_1(tptp_fun_X2_0(elem!2), elem!2), tptp_fun_X2_0(elem!2))) <=> big_f(tptp_fun_X2_0(elem!2), tptp_fun_X4_1(tptp_fun_X2_0(elem!2), elem!2))) | big_f(tptp_fun_X4_1(tptp_fun_X2_0(elem!2), elem!2), tptp_fun_X2_0(elem!2))),
% 0.14/0.41 inference(unit_resolution,[status(thm)],[36, 16])).
% 0.14/0.41 tff(48,plain,
% 0.14/0.41 ($false),
% 0.14/0.41 inference(unit_resolution,[status(thm)],[47, 46, 41])).
% 0.14/0.41 tff(49,plain,(big_f(elem!2, tptp_fun_X4_1(tptp_fun_X2_0(elem!2), elem!2))), inference(lemma,lemma(discharge,[]))).
% 0.14/0.41 tff(50,plain,
% 0.14/0.41 ((~(big_f(elem!2, tptp_fun_X4_1(tptp_fun_X2_0(elem!2), elem!2)) <=> big_f(tptp_fun_X4_1(tptp_fun_X2_0(elem!2), elem!2), tptp_fun_X2_0(elem!2)))) | (~big_f(elem!2, tptp_fun_X4_1(tptp_fun_X2_0(elem!2), elem!2))) | big_f(tptp_fun_X4_1(tptp_fun_X2_0(elem!2), elem!2), tptp_fun_X2_0(elem!2))),
% 0.14/0.41 inference(tautology,[status(thm)],[])).
% 0.14/0.41 tff(51,plain,
% 0.14/0.41 ((~big_f(elem!2, tptp_fun_X4_1(tptp_fun_X2_0(elem!2), elem!2))) | big_f(tptp_fun_X4_1(tptp_fun_X2_0(elem!2), elem!2), tptp_fun_X2_0(elem!2))),
% 0.14/0.41 inference(unit_resolution,[status(thm)],[50, 38])).
% 0.14/0.41 tff(52,plain,
% 0.14/0.41 (big_f(tptp_fun_X4_1(tptp_fun_X2_0(elem!2), elem!2), tptp_fun_X2_0(elem!2))),
% 0.14/0.41 inference(unit_resolution,[status(thm)],[51, 49])).
% 0.14/0.41 tff(53,plain,
% 0.14/0.41 ((~big_f(elem!2, tptp_fun_X4_1(tptp_fun_X2_0(elem!2), elem!2))) | big_f(tptp_fun_X2_0(elem!2), tptp_fun_X4_1(tptp_fun_X2_0(elem!2), elem!2))),
% 0.14/0.41 inference(unit_resolution,[status(thm)],[32, 21])).
% 0.14/0.41 tff(54,plain,
% 0.14/0.41 (big_f(tptp_fun_X2_0(elem!2), tptp_fun_X4_1(tptp_fun_X2_0(elem!2), elem!2))),
% 0.14/0.41 inference(unit_resolution,[status(thm)],[53, 49])).
% 0.14/0.41 tff(55,plain,
% 0.14/0.41 (((big_f(elem!2, tptp_fun_X4_1(tptp_fun_X2_0(elem!2), elem!2)) <=> big_f(tptp_fun_X4_1(tptp_fun_X2_0(elem!2), elem!2), tptp_fun_X2_0(elem!2))) <=> big_f(tptp_fun_X2_0(elem!2), tptp_fun_X4_1(tptp_fun_X2_0(elem!2), elem!2))) | (~(big_f(elem!2, tptp_fun_X4_1(tptp_fun_X2_0(elem!2), elem!2)) <=> big_f(tptp_fun_X4_1(tptp_fun_X2_0(elem!2), elem!2), tptp_fun_X2_0(elem!2)))) | (~big_f(tptp_fun_X2_0(elem!2), tptp_fun_X4_1(tptp_fun_X2_0(elem!2), elem!2)))),
% 0.14/0.41 inference(tautology,[status(thm)],[])).
% 0.14/0.41 tff(56,plain,
% 0.14/0.41 (((big_f(elem!2, tptp_fun_X4_1(tptp_fun_X2_0(elem!2), elem!2)) <=> big_f(tptp_fun_X4_1(tptp_fun_X2_0(elem!2), elem!2), tptp_fun_X2_0(elem!2))) <=> big_f(tptp_fun_X2_0(elem!2), tptp_fun_X4_1(tptp_fun_X2_0(elem!2), elem!2))) | (~big_f(tptp_fun_X2_0(elem!2), tptp_fun_X4_1(tptp_fun_X2_0(elem!2), elem!2)))),
% 0.14/0.41 inference(unit_resolution,[status(thm)],[55, 38])).
% 0.14/0.41 tff(57,plain,
% 0.14/0.41 ((big_f(elem!2, tptp_fun_X4_1(tptp_fun_X2_0(elem!2), elem!2)) <=> big_f(tptp_fun_X4_1(tptp_fun_X2_0(elem!2), elem!2), tptp_fun_X2_0(elem!2))) <=> big_f(tptp_fun_X2_0(elem!2), tptp_fun_X4_1(tptp_fun_X2_0(elem!2), elem!2))),
% 0.14/0.41 inference(unit_resolution,[status(thm)],[56, 54])).
% 0.14/0.41 tff(58,plain,
% 0.14/0.41 ((~((big_f(elem!2, tptp_fun_X4_1(tptp_fun_X2_0(elem!2), elem!2)) <=> big_f(tptp_fun_X4_1(tptp_fun_X2_0(elem!2), elem!2), tptp_fun_X2_0(elem!2))) <=> big_f(tptp_fun_X2_0(elem!2), tptp_fun_X4_1(tptp_fun_X2_0(elem!2), elem!2)))) | (~big_f(tptp_fun_X4_1(tptp_fun_X2_0(elem!2), elem!2), tptp_fun_X2_0(elem!2)))),
% 0.14/0.41 inference(unit_resolution,[status(thm)],[26, 16])).
% 0.14/0.41 tff(59,plain,
% 0.14/0.41 ($false),
% 0.14/0.41 inference(unit_resolution,[status(thm)],[58, 57, 52])).
% 0.14/0.41 % SZS output end Proof
% 0.14/0.42 % E exiting
%------------------------------------------------------------------------------