%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SEU186+1 : TPTP v9.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n015.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 05:27:10 AM UTC 2025
% Result : Theorem 0.14s 0.44s
% Output : Proof 0.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.14 % Problem : SEU186+1 : TPTP v9.0.0. Released v3.3.0.
% 0.03/0.14 % Command : run_E %s %d THM
% 0.14/0.36 % Computer : n015.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 06:14:10 EDT 2025
% 0.14/0.36 % CPUTime :
% 0.14/0.44 % SZS status Theorem
% 0.14/0.44 % SZS output start Proof
% 0.14/0.44 tff(empty_type, type, (
% 0.14/0.44 empty: $i > $o)).
% 0.14/0.44 tff(tptp_fun_A_8_type, type, (
% 0.14/0.44 tptp_fun_A_8: $i)).
% 0.14/0.44 tff(in_type, type, (
% 0.14/0.44 in: ( $i * $i ) > $o)).
% 0.14/0.44 tff(tptp_fun_B_3_type, type, (
% 0.14/0.44 tptp_fun_B_3: $i > $i)).
% 0.14/0.44 tff(ordered_pair_type, type, (
% 0.14/0.44 ordered_pair: ( $i * $i ) > $i)).
% 0.14/0.44 tff(tptp_fun_D_0_type, type, (
% 0.14/0.44 tptp_fun_D_0: $i > $i)).
% 0.14/0.44 tff(tptp_fun_C_1_type, type, (
% 0.14/0.44 tptp_fun_C_1: $i > $i)).
% 0.14/0.44 tff(relation_type, type, (
% 0.14/0.44 relation: $i > $o)).
% 0.14/0.44 tff(tptp_fun_B_2_type, type, (
% 0.14/0.44 tptp_fun_B_2: $i > $i)).
% 0.14/0.44 tff(empty_set_type, type, (
% 0.14/0.44 empty_set: $i)).
% 0.14/0.44 tff(element_type, type, (
% 0.14/0.44 element: ( $i * $i ) > $o)).
% 0.14/0.44 tff(1,assumption,(in(tptp_fun_B_3(A!8), A!8)), introduced(assumption)).
% 0.14/0.44 tff(2,plain,
% 0.14/0.44 (^[A: $i] : refl((~((~((~relation(A)) | ![B: $i] : ((~in(B, A)) | (B = ordered_pair(tptp_fun_C_1(B), tptp_fun_D_0(B)))))) | (~(relation(A) | (~((~in(tptp_fun_B_2(A), A)) | (~![C: $i, D: $i] : (~(tptp_fun_B_2(A) = ordered_pair(C, D)))))))))) <=> (~((~((~relation(A)) | ![B: $i] : ((~in(B, A)) | (B = ordered_pair(tptp_fun_C_1(B), tptp_fun_D_0(B)))))) | (~(relation(A) | (~((~in(tptp_fun_B_2(A), A)) | (~![C: $i, D: $i] : (~(tptp_fun_B_2(A) = ordered_pair(C, D)))))))))))),
% 0.14/0.44 inference(bind,[status(th)],[])).
% 0.14/0.44 tff(3,plain,
% 0.14/0.44 (![A: $i] : (~((~((~relation(A)) | ![B: $i] : ((~in(B, A)) | (B = ordered_pair(tptp_fun_C_1(B), tptp_fun_D_0(B)))))) | (~(relation(A) | (~((~in(tptp_fun_B_2(A), A)) | (~![C: $i, D: $i] : (~(tptp_fun_B_2(A) = ordered_pair(C, D)))))))))) <=> ![A: $i] : (~((~((~relation(A)) | ![B: $i] : ((~in(B, A)) | (B = ordered_pair(tptp_fun_C_1(B), tptp_fun_D_0(B)))))) | (~(relation(A) | (~((~in(tptp_fun_B_2(A), A)) | (~![C: $i, D: $i] : (~(tptp_fun_B_2(A) = ordered_pair(C, D))))))))))),
% 0.14/0.44 inference(quant_intro,[status(thm)],[2])).
% 0.14/0.44 tff(4,plain,
% 0.14/0.44 (^[A: $i] : rewrite((~((~((~relation(A)) | ![B: $i] : ((~in(B, A)) | (B = ordered_pair(tptp_fun_C_1(B), tptp_fun_D_0(B)))))) | (~(relation(A) | (~((~in(tptp_fun_B_2(A), A)) | (~![C: $i, D: $i] : (~(tptp_fun_B_2(A) = ordered_pair(C, D)))))))))) <=> (~((~((~relation(A)) | ![B: $i] : ((~in(B, A)) | (B = ordered_pair(tptp_fun_C_1(B), tptp_fun_D_0(B)))))) | (~(relation(A) | (~((~in(tptp_fun_B_2(A), A)) | (~![C: $i, D: $i] : (~(tptp_fun_B_2(A) = ordered_pair(C, D)))))))))))),
% 0.14/0.44 inference(bind,[status(th)],[])).
% 0.14/0.44 tff(5,plain,
% 0.14/0.44 (![A: $i] : (~((~((~relation(A)) | ![B: $i] : ((~in(B, A)) | (B = ordered_pair(tptp_fun_C_1(B), tptp_fun_D_0(B)))))) | (~(relation(A) | (~((~in(tptp_fun_B_2(A), A)) | (~![C: $i, D: $i] : (~(tptp_fun_B_2(A) = ordered_pair(C, D)))))))))) <=> ![A: $i] : (~((~((~relation(A)) | ![B: $i] : ((~in(B, A)) | (B = ordered_pair(tptp_fun_C_1(B), tptp_fun_D_0(B)))))) | (~(relation(A) | (~((~in(tptp_fun_B_2(A), A)) | (~![C: $i, D: $i] : (~(tptp_fun_B_2(A) = ordered_pair(C, D))))))))))),
% 0.14/0.44 inference(quant_intro,[status(thm)],[4])).
% 0.14/0.44 tff(6,plain,
% 0.14/0.44 (![A: $i] : (~((~((~relation(A)) | ![B: $i] : ((~in(B, A)) | (B = ordered_pair(tptp_fun_C_1(B), tptp_fun_D_0(B)))))) | (~(relation(A) | (~((~in(tptp_fun_B_2(A), A)) | (~![C: $i, D: $i] : (~(tptp_fun_B_2(A) = ordered_pair(C, D)))))))))) <=> ![A: $i] : (~((~((~relation(A)) | ![B: $i] : ((~in(B, A)) | (B = ordered_pair(tptp_fun_C_1(B), tptp_fun_D_0(B)))))) | (~(relation(A) | (~((~in(tptp_fun_B_2(A), A)) | (~![C: $i, D: $i] : (~(tptp_fun_B_2(A) = ordered_pair(C, D))))))))))),
% 0.14/0.44 inference(transitivity,[status(thm)],[5, 3])).
% 0.14/0.44 tff(7,plain,
% 0.14/0.44 (^[A: $i] : trans(monotonicity(rewrite(((~relation(A)) | ![B: $i] : ((~in(B, A)) | (B = ordered_pair(tptp_fun_C_1(B), tptp_fun_D_0(B))))) <=> ((~relation(A)) | ![B: $i] : ((~in(B, A)) | (B = ordered_pair(tptp_fun_C_1(B), tptp_fun_D_0(B)))))), rewrite((relation(A) | (in(tptp_fun_B_2(A), A) & ![C: $i, D: $i] : (~(tptp_fun_B_2(A) = ordered_pair(C, D))))) <=> (relation(A) | (~((~in(tptp_fun_B_2(A), A)) | (~![C: $i, D: $i] : (~(tptp_fun_B_2(A) = ordered_pair(C, D)))))))), ((((~relation(A)) | ![B: $i] : ((~in(B, A)) | (B = ordered_pair(tptp_fun_C_1(B), tptp_fun_D_0(B))))) & (relation(A) | (in(tptp_fun_B_2(A), A) & ![C: $i, D: $i] : (~(tptp_fun_B_2(A) = ordered_pair(C, D)))))) <=> (((~relation(A)) | ![B: $i] : ((~in(B, A)) | (B = ordered_pair(tptp_fun_C_1(B), tptp_fun_D_0(B))))) & (relation(A) | (~((~in(tptp_fun_B_2(A), A)) | (~![C: $i, D: $i] : (~(tptp_fun_B_2(A) = ordered_pair(C, D)))))))))), rewrite((((~relation(A)) | ![B: $i] : ((~in(B, A)) | (B = ordered_pair(tptp_fun_C_1(B), tptp_fun_D_0(B))))) & (relation(A) | (~((~in(tptp_fun_B_2(A), A)) | (~![C: $i, D: $i] : (~(tptp_fun_B_2(A) = ordered_pair(C, D)))))))) <=> (~((~((~relation(A)) | ![B: $i] : ((~in(B, A)) | (B = ordered_pair(tptp_fun_C_1(B), tptp_fun_D_0(B)))))) | (~(relation(A) | (~((~in(tptp_fun_B_2(A), A)) | (~![C: $i, D: $i] : (~(tptp_fun_B_2(A) = ordered_pair(C, D))))))))))), ((((~relation(A)) | ![B: $i] : ((~in(B, A)) | (B = ordered_pair(tptp_fun_C_1(B), tptp_fun_D_0(B))))) & (relation(A) | (in(tptp_fun_B_2(A), A) & ![C: $i, D: $i] : (~(tptp_fun_B_2(A) = ordered_pair(C, D)))))) <=> (~((~((~relation(A)) | ![B: $i] : ((~in(B, A)) | (B = ordered_pair(tptp_fun_C_1(B), tptp_fun_D_0(B)))))) | (~(relation(A) | (~((~in(tptp_fun_B_2(A), A)) | (~![C: $i, D: $i] : (~(tptp_fun_B_2(A) = ordered_pair(C, D))))))))))))),
% 0.22/0.44 inference(bind,[status(th)],[])).
% 0.22/0.44 tff(8,plain,
% 0.22/0.44 (![A: $i] : (((~relation(A)) | ![B: $i] : ((~in(B, A)) | (B = ordered_pair(tptp_fun_C_1(B), tptp_fun_D_0(B))))) & (relation(A) | (in(tptp_fun_B_2(A), A) & ![C: $i, D: $i] : (~(tptp_fun_B_2(A) = ordered_pair(C, D)))))) <=> ![A: $i] : (~((~((~relation(A)) | ![B: $i] : ((~in(B, A)) | (B = ordered_pair(tptp_fun_C_1(B), tptp_fun_D_0(B)))))) | (~(relation(A) | (~((~in(tptp_fun_B_2(A), A)) | (~![C: $i, D: $i] : (~(tptp_fun_B_2(A) = ordered_pair(C, D))))))))))),
% 0.22/0.44 inference(quant_intro,[status(thm)],[7])).
% 0.22/0.44 tff(9,plain,
% 0.22/0.44 (![A: $i] : (relation(A) <=> ![B: $i] : (~(in(B, A) & ![C: $i, D: $i] : (~(B = ordered_pair(C, D)))))) <=> ![A: $i] : (relation(A) <=> ![B: $i] : (~(in(B, A) & ![C: $i, D: $i] : (~(B = ordered_pair(C, D))))))),
% 0.22/0.44 inference(rewrite,[status(thm)],[])).
% 0.22/0.44 tff(10,axiom,(![A: $i] : (relation(A) <=> ![B: $i] : (~(in(B, A) & ![C: $i, D: $i] : (~(B = ordered_pair(C, D))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d1_relat_1')).
% 0.22/0.44 tff(11,plain,
% 0.22/0.44 (![A: $i] : (relation(A) <=> ![B: $i] : (~(in(B, A) & ![C: $i, D: $i] : (~(B = ordered_pair(C, D))))))),
% 0.22/0.44 inference(modus_ponens,[status(thm)],[10, 9])).
% 0.22/0.44 tff(12,plain,(
% 0.22/0.44 ![A: $i] : (((~relation(A)) | ![B: $i] : ((~in(B, A)) | (B = ordered_pair(tptp_fun_C_1(B), tptp_fun_D_0(B))))) & (relation(A) | (in(tptp_fun_B_2(A), A) & ![C: $i, D: $i] : (~(tptp_fun_B_2(A) = ordered_pair(C, D))))))),
% 0.22/0.44 inference(skolemize,[status(sab)],[11])).
% 0.22/0.44 tff(13,plain,
% 0.22/0.44 (![A: $i] : (~((~((~relation(A)) | ![B: $i] : ((~in(B, A)) | (B = ordered_pair(tptp_fun_C_1(B), tptp_fun_D_0(B)))))) | (~(relation(A) | (~((~in(tptp_fun_B_2(A), A)) | (~![C: $i, D: $i] : (~(tptp_fun_B_2(A) = ordered_pair(C, D))))))))))),
% 0.22/0.44 inference(modus_ponens,[status(thm)],[12, 8])).
% 0.22/0.44 tff(14,plain,
% 0.22/0.44 (![A: $i] : (~((~((~relation(A)) | ![B: $i] : ((~in(B, A)) | (B = ordered_pair(tptp_fun_C_1(B), tptp_fun_D_0(B)))))) | (~(relation(A) | (~((~in(tptp_fun_B_2(A), A)) | (~![C: $i, D: $i] : (~(tptp_fun_B_2(A) = ordered_pair(C, D))))))))))),
% 0.22/0.44 inference(modus_ponens,[status(thm)],[13, 6])).
% 0.22/0.44 tff(15,plain,
% 0.22/0.44 ((~![A: $i] : (~((~((~relation(A)) | ![B: $i] : ((~in(B, A)) | (B = ordered_pair(tptp_fun_C_1(B), tptp_fun_D_0(B)))))) | (~(relation(A) | (~((~in(tptp_fun_B_2(A), A)) | (~![C: $i, D: $i] : (~(tptp_fun_B_2(A) = ordered_pair(C, D))))))))))) | (~((~((~relation(A!8)) | ![B: $i] : ((~in(B, A!8)) | (B = ordered_pair(tptp_fun_C_1(B), tptp_fun_D_0(B)))))) | (~(relation(A!8) | (~((~in(tptp_fun_B_2(A!8), A!8)) | (~![C: $i, D: $i] : (~(tptp_fun_B_2(A!8) = ordered_pair(C, D))))))))))),
% 0.22/0.44 inference(quant_inst,[status(thm)],[])).
% 0.22/0.44 tff(16,plain,
% 0.22/0.44 (~((~((~relation(A!8)) | ![B: $i] : ((~in(B, A!8)) | (B = ordered_pair(tptp_fun_C_1(B), tptp_fun_D_0(B)))))) | (~(relation(A!8) | (~((~in(tptp_fun_B_2(A!8), A!8)) | (~![C: $i, D: $i] : (~(tptp_fun_B_2(A!8) = ordered_pair(C, D)))))))))),
% 0.22/0.44 inference(unit_resolution,[status(thm)],[15, 14])).
% 0.22/0.44 tff(17,plain,
% 0.22/0.44 (((~((~relation(A!8)) | ![B: $i] : ((~in(B, A!8)) | (B = ordered_pair(tptp_fun_C_1(B), tptp_fun_D_0(B)))))) | (~(relation(A!8) | (~((~in(tptp_fun_B_2(A!8), A!8)) | (~![C: $i, D: $i] : (~(tptp_fun_B_2(A!8) = ordered_pair(C, D))))))))) | ((~relation(A!8)) | ![B: $i] : ((~in(B, A!8)) | (B = ordered_pair(tptp_fun_C_1(B), tptp_fun_D_0(B)))))),
% 0.22/0.44 inference(tautology,[status(thm)],[])).
% 0.22/0.44 tff(18,plain,
% 0.22/0.44 ((~relation(A!8)) | ![B: $i] : ((~in(B, A!8)) | (B = ordered_pair(tptp_fun_C_1(B), tptp_fun_D_0(B))))),
% 0.22/0.44 inference(unit_resolution,[status(thm)],[17, 16])).
% 0.22/0.44 tff(19,plain,
% 0.22/0.44 (((~(A!8 = empty_set)) & ![B: $i, C: $i] : (~in(ordered_pair(B, C), A!8)) & relation(A!8)) <=> ((~(A!8 = empty_set)) & ![B: $i, C: $i] : (~in(ordered_pair(B, C), A!8)) & relation(A!8))),
% 0.22/0.44 inference(rewrite,[status(thm)],[])).
% 0.22/0.44 tff(20,plain,
% 0.22/0.44 ((~![A: $i] : ((A = empty_set) | (~![B: $i, C: $i] : (~in(ordered_pair(B, C), A))) | (~relation(A)))) <=> (~![A: $i] : ((A = empty_set) | (~![B: $i, C: $i] : (~in(ordered_pair(B, C), A))) | (~relation(A))))),
% 0.22/0.44 inference(rewrite,[status(thm)],[])).
% 0.22/0.44 tff(21,plain,
% 0.22/0.44 ((~![A: $i] : (relation(A) => (![B: $i, C: $i] : (~in(ordered_pair(B, C), A)) => (A = empty_set)))) <=> (~![A: $i] : ((A = empty_set) | (~![B: $i, C: $i] : (~in(ordered_pair(B, C), A))) | (~relation(A))))),
% 0.22/0.44 inference(rewrite,[status(thm)],[])).
% 0.22/0.44 tff(22,axiom,(~![A: $i] : (relation(A) => (![B: $i, C: $i] : (~in(ordered_pair(B, C), A)) => (A = empty_set)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t56_relat_1')).
% 0.22/0.44 tff(23,plain,
% 0.22/0.44 (~![A: $i] : ((A = empty_set) | (~![B: $i, C: $i] : (~in(ordered_pair(B, C), A))) | (~relation(A)))),
% 0.22/0.44 inference(modus_ponens,[status(thm)],[22, 21])).
% 0.22/0.44 tff(24,plain,
% 0.22/0.44 (~![A: $i] : ((A = empty_set) | (~![B: $i, C: $i] : (~in(ordered_pair(B, C), A))) | (~relation(A)))),
% 0.22/0.44 inference(modus_ponens,[status(thm)],[23, 20])).
% 0.22/0.44 tff(25,plain,
% 0.22/0.44 (~![A: $i] : ((A = empty_set) | (~![B: $i, C: $i] : (~in(ordered_pair(B, C), A))) | (~relation(A)))),
% 0.22/0.44 inference(modus_ponens,[status(thm)],[24, 20])).
% 0.22/0.44 tff(26,plain,
% 0.22/0.44 (~![A: $i] : ((A = empty_set) | (~![B: $i, C: $i] : (~in(ordered_pair(B, C), A))) | (~relation(A)))),
% 0.22/0.44 inference(modus_ponens,[status(thm)],[25, 20])).
% 0.22/0.44 tff(27,plain,
% 0.22/0.44 ((~(A!8 = empty_set)) & ![B: $i, C: $i] : (~in(ordered_pair(B, C), A!8)) & relation(A!8)),
% 0.22/0.44 inference(modus_ponens,[status(thm)],[26, 19])).
% 0.22/0.44 tff(28,plain,
% 0.22/0.44 (relation(A!8)),
% 0.22/0.44 inference(and_elim,[status(thm)],[27])).
% 0.22/0.44 tff(29,plain,
% 0.22/0.44 ((~((~relation(A!8)) | ![B: $i] : ((~in(B, A!8)) | (B = ordered_pair(tptp_fun_C_1(B), tptp_fun_D_0(B)))))) | (~relation(A!8)) | ![B: $i] : ((~in(B, A!8)) | (B = ordered_pair(tptp_fun_C_1(B), tptp_fun_D_0(B))))),
% 0.22/0.44 inference(tautology,[status(thm)],[])).
% 0.22/0.44 tff(30,plain,
% 0.22/0.44 ((~((~relation(A!8)) | ![B: $i] : ((~in(B, A!8)) | (B = ordered_pair(tptp_fun_C_1(B), tptp_fun_D_0(B)))))) | ![B: $i] : ((~in(B, A!8)) | (B = ordered_pair(tptp_fun_C_1(B), tptp_fun_D_0(B))))),
% 0.22/0.44 inference(unit_resolution,[status(thm)],[29, 28])).
% 0.22/0.44 tff(31,plain,
% 0.22/0.44 (![B: $i] : ((~in(B, A!8)) | (B = ordered_pair(tptp_fun_C_1(B), tptp_fun_D_0(B))))),
% 0.22/0.44 inference(unit_resolution,[status(thm)],[30, 18])).
% 0.22/0.44 tff(32,plain,
% 0.22/0.44 (((~![B: $i] : ((~in(B, A!8)) | (B = ordered_pair(tptp_fun_C_1(B), tptp_fun_D_0(B))))) | ((~in(tptp_fun_B_3(A!8), A!8)) | (tptp_fun_B_3(A!8) = ordered_pair(tptp_fun_C_1(tptp_fun_B_3(A!8)), tptp_fun_D_0(tptp_fun_B_3(A!8)))))) <=> ((~![B: $i] : ((~in(B, A!8)) | (B = ordered_pair(tptp_fun_C_1(B), tptp_fun_D_0(B))))) | (~in(tptp_fun_B_3(A!8), A!8)) | (tptp_fun_B_3(A!8) = ordered_pair(tptp_fun_C_1(tptp_fun_B_3(A!8)), tptp_fun_D_0(tptp_fun_B_3(A!8)))))),
% 0.22/0.44 inference(rewrite,[status(thm)],[])).
% 0.22/0.44 tff(33,plain,
% 0.22/0.44 ((~![B: $i] : ((~in(B, A!8)) | (B = ordered_pair(tptp_fun_C_1(B), tptp_fun_D_0(B))))) | ((~in(tptp_fun_B_3(A!8), A!8)) | (tptp_fun_B_3(A!8) = ordered_pair(tptp_fun_C_1(tptp_fun_B_3(A!8)), tptp_fun_D_0(tptp_fun_B_3(A!8)))))),
% 0.22/0.44 inference(quant_inst,[status(thm)],[])).
% 0.22/0.44 tff(34,plain,
% 0.22/0.44 ((~![B: $i] : ((~in(B, A!8)) | (B = ordered_pair(tptp_fun_C_1(B), tptp_fun_D_0(B))))) | (~in(tptp_fun_B_3(A!8), A!8)) | (tptp_fun_B_3(A!8) = ordered_pair(tptp_fun_C_1(tptp_fun_B_3(A!8)), tptp_fun_D_0(tptp_fun_B_3(A!8))))),
% 0.22/0.45 inference(modus_ponens,[status(thm)],[33, 32])).
% 0.22/0.45 tff(35,plain,
% 0.22/0.45 (tptp_fun_B_3(A!8) = ordered_pair(tptp_fun_C_1(tptp_fun_B_3(A!8)), tptp_fun_D_0(tptp_fun_B_3(A!8)))),
% 0.22/0.45 inference(unit_resolution,[status(thm)],[34, 31, 1])).
% 0.22/0.45 tff(36,plain,
% 0.22/0.45 (ordered_pair(tptp_fun_C_1(tptp_fun_B_3(A!8)), tptp_fun_D_0(tptp_fun_B_3(A!8))) = tptp_fun_B_3(A!8)),
% 0.22/0.45 inference(symmetry,[status(thm)],[35])).
% 0.22/0.45 tff(37,plain,
% 0.22/0.45 (in(ordered_pair(tptp_fun_C_1(tptp_fun_B_3(A!8)), tptp_fun_D_0(tptp_fun_B_3(A!8))), A!8) <=> in(tptp_fun_B_3(A!8), A!8)),
% 0.22/0.45 inference(monotonicity,[status(thm)],[36])).
% 0.22/0.45 tff(38,plain,
% 0.22/0.45 (in(tptp_fun_B_3(A!8), A!8) <=> in(ordered_pair(tptp_fun_C_1(tptp_fun_B_3(A!8)), tptp_fun_D_0(tptp_fun_B_3(A!8))), A!8)),
% 0.22/0.45 inference(symmetry,[status(thm)],[37])).
% 0.22/0.45 tff(39,plain,
% 0.22/0.45 (in(ordered_pair(tptp_fun_C_1(tptp_fun_B_3(A!8)), tptp_fun_D_0(tptp_fun_B_3(A!8))), A!8)),
% 0.22/0.45 inference(modus_ponens,[status(thm)],[1, 38])).
% 0.22/0.45 tff(40,plain,
% 0.22/0.45 (^[B: $i, C: $i] : refl((~in(ordered_pair(B, C), A!8)) <=> (~in(ordered_pair(B, C), A!8)))),
% 0.22/0.45 inference(bind,[status(th)],[])).
% 0.22/0.45 tff(41,plain,
% 0.22/0.45 (![B: $i, C: $i] : (~in(ordered_pair(B, C), A!8)) <=> ![B: $i, C: $i] : (~in(ordered_pair(B, C), A!8))),
% 0.22/0.45 inference(quant_intro,[status(thm)],[40])).
% 0.22/0.45 tff(42,plain,
% 0.22/0.45 (![B: $i, C: $i] : (~in(ordered_pair(B, C), A!8))),
% 0.22/0.45 inference(and_elim,[status(thm)],[27])).
% 0.22/0.45 tff(43,plain,
% 0.22/0.45 (![B: $i, C: $i] : (~in(ordered_pair(B, C), A!8))),
% 0.22/0.45 inference(modus_ponens,[status(thm)],[42, 41])).
% 0.22/0.45 tff(44,plain,
% 0.22/0.45 ((~![B: $i, C: $i] : (~in(ordered_pair(B, C), A!8))) | (~in(ordered_pair(tptp_fun_C_1(tptp_fun_B_3(A!8)), tptp_fun_D_0(tptp_fun_B_3(A!8))), A!8))),
% 0.22/0.45 inference(quant_inst,[status(thm)],[])).
% 0.22/0.45 tff(45,plain,
% 0.22/0.45 (~in(ordered_pair(tptp_fun_C_1(tptp_fun_B_3(A!8)), tptp_fun_D_0(tptp_fun_B_3(A!8))), A!8)),
% 0.22/0.45 inference(unit_resolution,[status(thm)],[44, 43])).
% 0.22/0.45 tff(46,plain,
% 0.22/0.45 ($false),
% 0.22/0.45 inference(unit_resolution,[status(thm)],[45, 39])).
% 0.22/0.45 tff(47,plain,(~in(tptp_fun_B_3(A!8), A!8)), inference(lemma,lemma(discharge,[]))).
% 0.22/0.45 tff(48,plain,
% 0.22/0.45 (![A: $i] : ?[B: $i] : element(B, A) <=> ![A: $i] : ?[B: $i] : element(B, A)),
% 0.22/0.45 inference(rewrite,[status(thm)],[])).
% 0.22/0.45 tff(49,axiom,(![A: $i] : ?[B: $i] : element(B, A)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','existence_m1_subset_1')).
% 0.22/0.45 tff(50,plain,
% 0.22/0.45 (![A: $i] : ?[B: $i] : element(B, A)),
% 0.22/0.45 inference(modus_ponens,[status(thm)],[49, 48])).
% 0.22/0.45 tff(51,plain,(
% 0.22/0.45 ![A: $i] : element(tptp_fun_B_3(A), A)),
% 0.22/0.45 inference(skolemize,[status(sab)],[50])).
% 0.22/0.45 tff(52,plain,
% 0.22/0.45 ((~![A: $i] : element(tptp_fun_B_3(A), A)) | element(tptp_fun_B_3(A!8), A!8)),
% 0.22/0.45 inference(quant_inst,[status(thm)],[])).
% 0.22/0.45 tff(53,plain,
% 0.22/0.45 (element(tptp_fun_B_3(A!8), A!8)),
% 0.22/0.45 inference(unit_resolution,[status(thm)],[52, 51])).
% 0.22/0.45 tff(54,plain,
% 0.22/0.45 (^[A: $i, B: $i] : refl((empty(B) | in(A, B) | (~element(A, B))) <=> (empty(B) | in(A, B) | (~element(A, B))))),
% 0.22/0.45 inference(bind,[status(th)],[])).
% 0.22/0.45 tff(55,plain,
% 0.22/0.45 (![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B))) <=> ![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))),
% 0.22/0.45 inference(quant_intro,[status(thm)],[54])).
% 0.22/0.45 tff(56,plain,
% 0.22/0.45 (![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B))) <=> ![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))),
% 0.22/0.45 inference(rewrite,[status(thm)],[])).
% 0.22/0.45 tff(57,plain,
% 0.22/0.45 (^[A: $i, B: $i] : rewrite((element(A, B) => (empty(B) | in(A, B))) <=> (empty(B) | in(A, B) | (~element(A, B))))),
% 0.22/0.45 inference(bind,[status(th)],[])).
% 0.22/0.45 tff(58,plain,
% 0.22/0.45 (![A: $i, B: $i] : (element(A, B) => (empty(B) | in(A, B))) <=> ![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))),
% 0.22/0.45 inference(quant_intro,[status(thm)],[57])).
% 0.22/0.45 tff(59,axiom,(![A: $i, B: $i] : (element(A, B) => (empty(B) | in(A, B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t2_subset')).
% 0.22/0.45 tff(60,plain,
% 0.22/0.45 (![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))),
% 0.22/0.45 inference(modus_ponens,[status(thm)],[59, 58])).
% 0.22/0.45 tff(61,plain,
% 0.22/0.45 (![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))),
% 0.22/0.45 inference(modus_ponens,[status(thm)],[60, 56])).
% 0.22/0.45 tff(62,plain,(
% 0.22/0.45 ![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))),
% 0.22/0.45 inference(skolemize,[status(sab)],[61])).
% 0.22/0.45 tff(63,plain,
% 0.22/0.45 (![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))),
% 0.22/0.45 inference(modus_ponens,[status(thm)],[62, 55])).
% 0.22/0.45 tff(64,plain,
% 0.22/0.45 (((~![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))) | (empty(A!8) | (~element(tptp_fun_B_3(A!8), A!8)) | in(tptp_fun_B_3(A!8), A!8))) <=> ((~![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))) | empty(A!8) | (~element(tptp_fun_B_3(A!8), A!8)) | in(tptp_fun_B_3(A!8), A!8))),
% 0.22/0.45 inference(rewrite,[status(thm)],[])).
% 0.22/0.45 tff(65,plain,
% 0.22/0.45 ((empty(A!8) | in(tptp_fun_B_3(A!8), A!8) | (~element(tptp_fun_B_3(A!8), A!8))) <=> (empty(A!8) | (~element(tptp_fun_B_3(A!8), A!8)) | in(tptp_fun_B_3(A!8), A!8))),
% 0.22/0.45 inference(rewrite,[status(thm)],[])).
% 0.22/0.45 tff(66,plain,
% 0.22/0.45 (((~![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))) | (empty(A!8) | in(tptp_fun_B_3(A!8), A!8) | (~element(tptp_fun_B_3(A!8), A!8)))) <=> ((~![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))) | (empty(A!8) | (~element(tptp_fun_B_3(A!8), A!8)) | in(tptp_fun_B_3(A!8), A!8)))),
% 0.22/0.45 inference(monotonicity,[status(thm)],[65])).
% 0.22/0.45 tff(67,plain,
% 0.22/0.45 (((~![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))) | (empty(A!8) | in(tptp_fun_B_3(A!8), A!8) | (~element(tptp_fun_B_3(A!8), A!8)))) <=> ((~![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))) | empty(A!8) | (~element(tptp_fun_B_3(A!8), A!8)) | in(tptp_fun_B_3(A!8), A!8))),
% 0.22/0.45 inference(transitivity,[status(thm)],[66, 64])).
% 0.22/0.45 tff(68,plain,
% 0.22/0.45 ((~![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))) | (empty(A!8) | in(tptp_fun_B_3(A!8), A!8) | (~element(tptp_fun_B_3(A!8), A!8)))),
% 0.22/0.45 inference(quant_inst,[status(thm)],[])).
% 0.22/0.45 tff(69,plain,
% 0.22/0.45 ((~![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))) | empty(A!8) | (~element(tptp_fun_B_3(A!8), A!8)) | in(tptp_fun_B_3(A!8), A!8)),
% 0.22/0.45 inference(modus_ponens,[status(thm)],[68, 67])).
% 0.22/0.45 tff(70,plain,
% 0.22/0.45 (empty(A!8) | in(tptp_fun_B_3(A!8), A!8)),
% 0.22/0.45 inference(unit_resolution,[status(thm)],[69, 63, 53])).
% 0.22/0.45 tff(71,plain,
% 0.22/0.45 (empty(A!8)),
% 0.22/0.45 inference(unit_resolution,[status(thm)],[70, 47])).
% 0.22/0.45 tff(72,plain,
% 0.22/0.45 (^[A: $i, B: $i] : refl(((~empty(B)) | (A = B) | (~empty(A))) <=> ((~empty(B)) | (A = B) | (~empty(A))))),
% 0.22/0.45 inference(bind,[status(th)],[])).
% 0.22/0.45 tff(73,plain,
% 0.22/0.45 (![A: $i, B: $i] : ((~empty(B)) | (A = B) | (~empty(A))) <=> ![A: $i, B: $i] : ((~empty(B)) | (A = B) | (~empty(A)))),
% 0.22/0.45 inference(quant_intro,[status(thm)],[72])).
% 0.22/0.45 tff(74,plain,
% 0.22/0.45 (^[A: $i, B: $i] : trans(monotonicity(rewrite((empty(A) & (~(A = B)) & empty(B)) <=> (~((~empty(B)) | (A = B) | (~empty(A))))), ((~(empty(A) & (~(A = B)) & empty(B))) <=> (~(~((~empty(B)) | (A = B) | (~empty(A))))))), rewrite((~(~((~empty(B)) | (A = B) | (~empty(A))))) <=> ((~empty(B)) | (A = B) | (~empty(A)))), ((~(empty(A) & (~(A = B)) & empty(B))) <=> ((~empty(B)) | (A = B) | (~empty(A)))))),
% 0.22/0.45 inference(bind,[status(th)],[])).
% 0.22/0.45 tff(75,plain,
% 0.22/0.45 (![A: $i, B: $i] : (~(empty(A) & (~(A = B)) & empty(B))) <=> ![A: $i, B: $i] : ((~empty(B)) | (A = B) | (~empty(A)))),
% 0.22/0.45 inference(quant_intro,[status(thm)],[74])).
% 0.22/0.45 tff(76,plain,
% 0.22/0.45 (![A: $i, B: $i] : (~(empty(A) & (~(A = B)) & empty(B))) <=> ![A: $i, B: $i] : (~(empty(A) & (~(A = B)) & empty(B)))),
% 0.22/0.45 inference(rewrite,[status(thm)],[])).
% 0.22/0.45 tff(77,plain,
% 0.22/0.45 (^[A: $i, B: $i] : rewrite((~((empty(A) & (~(A = B))) & empty(B))) <=> (~(empty(A) & (~(A = B)) & empty(B))))),
% 0.22/0.45 inference(bind,[status(th)],[])).
% 0.22/0.45 tff(78,plain,
% 0.22/0.45 (![A: $i, B: $i] : (~((empty(A) & (~(A = B))) & empty(B))) <=> ![A: $i, B: $i] : (~(empty(A) & (~(A = B)) & empty(B)))),
% 0.22/0.45 inference(quant_intro,[status(thm)],[77])).
% 0.22/0.45 tff(79,axiom,(![A: $i, B: $i] : (~((empty(A) & (~(A = B))) & empty(B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t8_boole')).
% 0.22/0.45 tff(80,plain,
% 0.22/0.45 (![A: $i, B: $i] : (~(empty(A) & (~(A = B)) & empty(B)))),
% 0.22/0.45 inference(modus_ponens,[status(thm)],[79, 78])).
% 0.22/0.45 tff(81,plain,
% 0.22/0.45 (![A: $i, B: $i] : (~(empty(A) & (~(A = B)) & empty(B)))),
% 0.22/0.45 inference(modus_ponens,[status(thm)],[80, 76])).
% 0.22/0.45 tff(82,plain,(
% 0.22/0.45 ![A: $i, B: $i] : (~(empty(A) & (~(A = B)) & empty(B)))),
% 0.22/0.45 inference(skolemize,[status(sab)],[81])).
% 0.22/0.45 tff(83,plain,
% 0.22/0.45 (![A: $i, B: $i] : ((~empty(B)) | (A = B) | (~empty(A)))),
% 0.22/0.45 inference(modus_ponens,[status(thm)],[82, 75])).
% 0.22/0.45 tff(84,plain,
% 0.22/0.45 (![A: $i, B: $i] : ((~empty(B)) | (A = B) | (~empty(A)))),
% 0.22/0.45 inference(modus_ponens,[status(thm)],[83, 73])).
% 0.22/0.45 tff(85,plain,
% 0.22/0.45 (~(A!8 = empty_set)),
% 0.22/0.45 inference(and_elim,[status(thm)],[27])).
% 0.22/0.45 tff(86,plain,
% 0.22/0.45 (empty(empty_set) <=> empty(empty_set)),
% 0.22/0.45 inference(rewrite,[status(thm)],[])).
% 0.22/0.45 tff(87,axiom,(empty(empty_set)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','fc1_xboole_0')).
% 0.22/0.45 tff(88,plain,
% 0.22/0.45 (empty(empty_set)),
% 0.22/0.45 inference(modus_ponens,[status(thm)],[87, 86])).
% 0.22/0.45 tff(89,plain,
% 0.22/0.45 (((~![A: $i, B: $i] : ((~empty(B)) | (A = B) | (~empty(A)))) | ((A!8 = empty_set) | (~empty(empty_set)) | (~empty(A!8)))) <=> ((~![A: $i, B: $i] : ((~empty(B)) | (A = B) | (~empty(A)))) | (A!8 = empty_set) | (~empty(empty_set)) | (~empty(A!8)))),
% 0.22/0.45 inference(rewrite,[status(thm)],[])).
% 0.22/0.45 tff(90,plain,
% 0.22/0.45 (((~empty(empty_set)) | (A!8 = empty_set) | (~empty(A!8))) <=> ((A!8 = empty_set) | (~empty(empty_set)) | (~empty(A!8)))),
% 0.22/0.45 inference(rewrite,[status(thm)],[])).
% 0.22/0.45 tff(91,plain,
% 0.22/0.45 (((~![A: $i, B: $i] : ((~empty(B)) | (A = B) | (~empty(A)))) | ((~empty(empty_set)) | (A!8 = empty_set) | (~empty(A!8)))) <=> ((~![A: $i, B: $i] : ((~empty(B)) | (A = B) | (~empty(A)))) | ((A!8 = empty_set) | (~empty(empty_set)) | (~empty(A!8))))),
% 0.22/0.45 inference(monotonicity,[status(thm)],[90])).
% 0.22/0.45 tff(92,plain,
% 0.22/0.45 (((~![A: $i, B: $i] : ((~empty(B)) | (A = B) | (~empty(A)))) | ((~empty(empty_set)) | (A!8 = empty_set) | (~empty(A!8)))) <=> ((~![A: $i, B: $i] : ((~empty(B)) | (A = B) | (~empty(A)))) | (A!8 = empty_set) | (~empty(empty_set)) | (~empty(A!8)))),
% 0.22/0.45 inference(transitivity,[status(thm)],[91, 89])).
% 0.22/0.45 tff(93,plain,
% 0.22/0.45 ((~![A: $i, B: $i] : ((~empty(B)) | (A = B) | (~empty(A)))) | ((~empty(empty_set)) | (A!8 = empty_set) | (~empty(A!8)))),
% 0.22/0.45 inference(quant_inst,[status(thm)],[])).
% 0.22/0.45 tff(94,plain,
% 0.22/0.45 ((~![A: $i, B: $i] : ((~empty(B)) | (A = B) | (~empty(A)))) | (A!8 = empty_set) | (~empty(empty_set)) | (~empty(A!8))),
% 0.22/0.45 inference(modus_ponens,[status(thm)],[93, 92])).
% 0.22/0.45 tff(95,plain,
% 0.22/0.45 ($false),
% 0.22/0.45 inference(unit_resolution,[status(thm)],[94, 88, 85, 84, 71])).
% 0.22/0.45 % SZS output end Proof
% 0.22/0.45 % E exiting
%------------------------------------------------------------------------------