%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SET958+1 : TPTP v9.0.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n006.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 05:26:43 AM UTC 2025
% Result : Theorem 0.20s 0.38s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : SET958+1 : TPTP v9.0.0. Released v3.2.0.
% 0.03/0.13 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n006.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Fri Jun 20 05:52:35 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.20/0.38 % SZS status Theorem
% 0.20/0.38 % SZS output start Proof
% 0.20/0.38 tff(in_type, type, (
% 0.20/0.38 in: ( $i * $i ) > $o)).
% 0.20/0.38 tff(tptp_fun_A_4_type, type, (
% 0.20/0.38 tptp_fun_A_4: $i)).
% 0.20/0.38 tff(ordered_pair_type, type, (
% 0.20/0.38 ordered_pair: ( $i * $i ) > $i)).
% 0.20/0.38 tff(tptp_fun_E_5_type, type, (
% 0.20/0.38 tptp_fun_E_5: $i > $i)).
% 0.20/0.38 tff(tptp_fun_C_0_type, type, (
% 0.20/0.38 tptp_fun_C_0: ( $i * $i ) > $i)).
% 0.20/0.38 tff(tptp_fun_B_3_type, type, (
% 0.20/0.38 tptp_fun_B_3: $i)).
% 0.20/0.38 tff(tptp_fun_D_6_type, type, (
% 0.20/0.38 tptp_fun_D_6: $i > $i)).
% 0.20/0.38 tff(subset_type, type, (
% 0.20/0.38 subset: ( $i * $i ) > $o)).
% 0.20/0.38 tff(1,plain,
% 0.20/0.38 (^[A: $i, B: $i] : refl((~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B))))))) <=> (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B))))))))),
% 0.20/0.38 inference(bind,[status(th)],[])).
% 0.20/0.38 tff(2,plain,
% 0.20/0.38 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B))))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B)))))))),
% 0.20/0.38 inference(quant_intro,[status(thm)],[1])).
% 0.20/0.38 tff(3,plain,
% 0.20/0.38 (^[A: $i, B: $i] : rewrite((~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B))))))) <=> (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B))))))))),
% 0.20/0.38 inference(bind,[status(th)],[])).
% 0.20/0.38 tff(4,plain,
% 0.20/0.38 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B))))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B)))))))),
% 0.20/0.38 inference(quant_intro,[status(thm)],[3])).
% 0.20/0.38 tff(5,plain,
% 0.20/0.38 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B))))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B)))))))),
% 0.20/0.38 inference(transitivity,[status(thm)],[4, 2])).
% 0.20/0.38 tff(6,plain,
% 0.20/0.38 (^[A: $i, B: $i] : trans(monotonicity(rewrite(((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) <=> ((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))), rewrite((subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B)))) <=> (subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B))))), ((((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B))))) <=> (((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B))))))), rewrite((((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B))))) <=> (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B)))))))), ((((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B))))) <=> (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B)))))))))),
% 0.20/0.38 inference(bind,[status(th)],[])).
% 0.20/0.38 tff(7,plain,
% 0.20/0.38 (![A: $i, B: $i] : (((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B)))))))),
% 0.20/0.38 inference(quant_intro,[status(thm)],[6])).
% 0.20/0.38 tff(8,plain,
% 0.20/0.38 (![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B))) <=> ![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B)))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(9,plain,
% 0.20/0.38 (^[A: $i, B: $i] : rewrite((subset(A, B) <=> ![C: $i] : (in(C, A) => in(C, B))) <=> (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B))))),
% 0.20/0.38 inference(bind,[status(th)],[])).
% 0.20/0.38 tff(10,plain,
% 0.20/0.38 (![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : (in(C, A) => in(C, B))) <=> ![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B)))),
% 0.20/0.38 inference(quant_intro,[status(thm)],[9])).
% 0.20/0.38 tff(11,axiom,(![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : (in(C, A) => in(C, B)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d3_tarski')).
% 0.20/0.38 tff(12,plain,
% 0.20/0.38 (![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B)))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[11, 10])).
% 0.20/0.38 tff(13,plain,
% 0.20/0.38 (![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B)))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[12, 8])).
% 0.20/0.38 tff(14,plain,(
% 0.20/0.38 ![A: $i, B: $i] : (((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B)))))),
% 0.20/0.38 inference(skolemize,[status(sab)],[13])).
% 0.20/0.38 tff(15,plain,
% 0.20/0.38 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B)))))))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[14, 7])).
% 0.20/0.38 tff(16,plain,
% 0.20/0.38 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B)))))))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[15, 5])).
% 0.20/0.38 tff(17,plain,
% 0.20/0.38 ((~![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B)))))))) | (~((~((~subset(A!4, B!3)) | ![C: $i] : ((~in(C, A!4)) | in(C, B!3)))) | (~(subset(A!4, B!3) | (~((~in(tptp_fun_C_0(B!3, A!4), A!4)) | in(tptp_fun_C_0(B!3, A!4), B!3)))))))),
% 0.20/0.38 inference(quant_inst,[status(thm)],[])).
% 0.20/0.38 tff(18,plain,
% 0.20/0.38 (~((~((~subset(A!4, B!3)) | ![C: $i] : ((~in(C, A!4)) | in(C, B!3)))) | (~(subset(A!4, B!3) | (~((~in(tptp_fun_C_0(B!3, A!4), A!4)) | in(tptp_fun_C_0(B!3, A!4), B!3))))))),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[17, 16])).
% 0.20/0.38 tff(19,plain,
% 0.20/0.38 (((~((~subset(A!4, B!3)) | ![C: $i] : ((~in(C, A!4)) | in(C, B!3)))) | (~(subset(A!4, B!3) | (~((~in(tptp_fun_C_0(B!3, A!4), A!4)) | in(tptp_fun_C_0(B!3, A!4), B!3)))))) | (subset(A!4, B!3) | (~((~in(tptp_fun_C_0(B!3, A!4), A!4)) | in(tptp_fun_C_0(B!3, A!4), B!3))))),
% 0.20/0.38 inference(tautology,[status(thm)],[])).
% 0.20/0.38 tff(20,plain,
% 0.20/0.38 (subset(A!4, B!3) | (~((~in(tptp_fun_C_0(B!3, A!4), A!4)) | in(tptp_fun_C_0(B!3, A!4), B!3)))),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[19, 18])).
% 0.20/0.38 tff(21,plain,
% 0.20/0.38 (((![C: $i] : ((~in(C, A!4)) | (C = ordered_pair(tptp_fun_D_6(C), tptp_fun_E_5(C)))) & ![C: $i, D: $i] : ((~in(ordered_pair(C, D), A!4)) | in(ordered_pair(C, D), B!3))) & (~subset(A!4, B!3))) <=> (![C: $i] : ((~in(C, A!4)) | (C = ordered_pair(tptp_fun_D_6(C), tptp_fun_E_5(C)))) & ![C: $i, D: $i] : ((~in(ordered_pair(C, D), A!4)) | in(ordered_pair(C, D), B!3)) & (~subset(A!4, B!3)))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(22,plain,
% 0.20/0.38 ((![C: $i] : ((~in(C, A!4)) | (C = ordered_pair(tptp_fun_D_6(C), tptp_fun_E_5(C)))) & ![C: $i, D: $i] : ((~in(ordered_pair(C, D), A!4)) | in(ordered_pair(C, D), B!3))) <=> (![C: $i] : ((~in(C, A!4)) | (C = ordered_pair(tptp_fun_D_6(C), tptp_fun_E_5(C)))) & ![C: $i, D: $i] : ((~in(ordered_pair(C, D), A!4)) | in(ordered_pair(C, D), B!3)))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(23,plain,
% 0.20/0.38 (((![C: $i] : ((~in(C, A!4)) | (C = ordered_pair(tptp_fun_D_6(C), tptp_fun_E_5(C)))) & ![C: $i, D: $i] : ((~in(ordered_pair(C, D), A!4)) | in(ordered_pair(C, D), B!3))) & (~subset(A!4, B!3))) <=> ((![C: $i] : ((~in(C, A!4)) | (C = ordered_pair(tptp_fun_D_6(C), tptp_fun_E_5(C)))) & ![C: $i, D: $i] : ((~in(ordered_pair(C, D), A!4)) | in(ordered_pair(C, D), B!3))) & (~subset(A!4, B!3)))),
% 0.20/0.39 inference(monotonicity,[status(thm)],[22])).
% 0.20/0.39 tff(24,plain,
% 0.20/0.39 (((![C: $i] : ((~in(C, A!4)) | (C = ordered_pair(tptp_fun_D_6(C), tptp_fun_E_5(C)))) & ![C: $i, D: $i] : ((~in(ordered_pair(C, D), A!4)) | in(ordered_pair(C, D), B!3))) & (~subset(A!4, B!3))) <=> (![C: $i] : ((~in(C, A!4)) | (C = ordered_pair(tptp_fun_D_6(C), tptp_fun_E_5(C)))) & ![C: $i, D: $i] : ((~in(ordered_pair(C, D), A!4)) | in(ordered_pair(C, D), B!3)) & (~subset(A!4, B!3)))),
% 0.20/0.39 inference(transitivity,[status(thm)],[23, 21])).
% 0.20/0.39 tff(25,plain,
% 0.20/0.39 ((~![A: $i, B: $i] : ((~(![C: $i] : (~(in(C, A) & ![D: $i, E: $i] : (~(C = ordered_pair(D, E))))) & ![C: $i, D: $i] : ((~in(ordered_pair(C, D), A)) | in(ordered_pair(C, D), B)))) | subset(A, B))) <=> (~![A: $i, B: $i] : ((~(![C: $i] : (~(in(C, A) & ![D: $i, E: $i] : (~(C = ordered_pair(D, E))))) & ![C: $i, D: $i] : ((~in(ordered_pair(C, D), A)) | in(ordered_pair(C, D), B)))) | subset(A, B)))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(26,plain,
% 0.20/0.39 ((~![A: $i, B: $i] : ((![C: $i] : (~(in(C, A) & ![D: $i, E: $i] : (~(C = ordered_pair(D, E))))) & ![C: $i, D: $i] : (in(ordered_pair(C, D), A) => in(ordered_pair(C, D), B))) => subset(A, B))) <=> (~![A: $i, B: $i] : ((~(![C: $i] : (~(in(C, A) & ![D: $i, E: $i] : (~(C = ordered_pair(D, E))))) & ![C: $i, D: $i] : ((~in(ordered_pair(C, D), A)) | in(ordered_pair(C, D), B)))) | subset(A, B)))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(27,axiom,(~![A: $i, B: $i] : ((![C: $i] : (~(in(C, A) & ![D: $i, E: $i] : (~(C = ordered_pair(D, E))))) & ![C: $i, D: $i] : (in(ordered_pair(C, D), A) => in(ordered_pair(C, D), B))) => subset(A, B))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t111_zfmisc_1')).
% 0.20/0.39 tff(28,plain,
% 0.20/0.39 (~![A: $i, B: $i] : ((~(![C: $i] : (~(in(C, A) & ![D: $i, E: $i] : (~(C = ordered_pair(D, E))))) & ![C: $i, D: $i] : ((~in(ordered_pair(C, D), A)) | in(ordered_pair(C, D), B)))) | subset(A, B))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[27, 26])).
% 0.20/0.39 tff(29,plain,
% 0.20/0.39 (~![A: $i, B: $i] : ((~(![C: $i] : (~(in(C, A) & ![D: $i, E: $i] : (~(C = ordered_pair(D, E))))) & ![C: $i, D: $i] : ((~in(ordered_pair(C, D), A)) | in(ordered_pair(C, D), B)))) | subset(A, B))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[28, 25])).
% 0.20/0.39 tff(30,plain,
% 0.20/0.39 (~![A: $i, B: $i] : ((~(![C: $i] : (~(in(C, A) & ![D: $i, E: $i] : (~(C = ordered_pair(D, E))))) & ![C: $i, D: $i] : ((~in(ordered_pair(C, D), A)) | in(ordered_pair(C, D), B)))) | subset(A, B))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[29, 25])).
% 0.20/0.39 tff(31,plain,
% 0.20/0.39 (~![A: $i, B: $i] : ((~(![C: $i] : (~(in(C, A) & ![D: $i, E: $i] : (~(C = ordered_pair(D, E))))) & ![C: $i, D: $i] : ((~in(ordered_pair(C, D), A)) | in(ordered_pair(C, D), B)))) | subset(A, B))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[30, 25])).
% 0.20/0.39 tff(32,plain,
% 0.20/0.39 (![C: $i] : ((~in(C, A!4)) | (C = ordered_pair(tptp_fun_D_6(C), tptp_fun_E_5(C)))) & ![C: $i, D: $i] : ((~in(ordered_pair(C, D), A!4)) | in(ordered_pair(C, D), B!3)) & (~subset(A!4, B!3))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[31, 24])).
% 0.20/0.39 tff(33,plain,
% 0.20/0.39 (~subset(A!4, B!3)),
% 0.20/0.39 inference(and_elim,[status(thm)],[32])).
% 0.20/0.39 tff(34,plain,
% 0.20/0.39 ((~(subset(A!4, B!3) | (~((~in(tptp_fun_C_0(B!3, A!4), A!4)) | in(tptp_fun_C_0(B!3, A!4), B!3))))) | subset(A!4, B!3) | (~((~in(tptp_fun_C_0(B!3, A!4), A!4)) | in(tptp_fun_C_0(B!3, A!4), B!3)))),
% 0.20/0.39 inference(tautology,[status(thm)],[])).
% 0.20/0.39 tff(35,plain,
% 0.20/0.39 ((~(subset(A!4, B!3) | (~((~in(tptp_fun_C_0(B!3, A!4), A!4)) | in(tptp_fun_C_0(B!3, A!4), B!3))))) | (~((~in(tptp_fun_C_0(B!3, A!4), A!4)) | in(tptp_fun_C_0(B!3, A!4), B!3)))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[34, 33])).
% 0.20/0.39 tff(36,plain,
% 0.20/0.39 (~((~in(tptp_fun_C_0(B!3, A!4), A!4)) | in(tptp_fun_C_0(B!3, A!4), B!3))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[35, 20])).
% 0.20/0.39 tff(37,plain,
% 0.20/0.39 (((~in(tptp_fun_C_0(B!3, A!4), A!4)) | in(tptp_fun_C_0(B!3, A!4), B!3)) | in(tptp_fun_C_0(B!3, A!4), A!4)),
% 0.20/0.39 inference(tautology,[status(thm)],[])).
% 0.20/0.39 tff(38,plain,
% 0.20/0.39 (in(tptp_fun_C_0(B!3, A!4), A!4)),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[37, 36])).
% 0.20/0.39 tff(39,plain,
% 0.20/0.39 (^[C: $i] : refl(((~in(C, A!4)) | (C = ordered_pair(tptp_fun_D_6(C), tptp_fun_E_5(C)))) <=> ((~in(C, A!4)) | (C = ordered_pair(tptp_fun_D_6(C), tptp_fun_E_5(C)))))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(40,plain,
% 0.20/0.39 (![C: $i] : ((~in(C, A!4)) | (C = ordered_pair(tptp_fun_D_6(C), tptp_fun_E_5(C)))) <=> ![C: $i] : ((~in(C, A!4)) | (C = ordered_pair(tptp_fun_D_6(C), tptp_fun_E_5(C))))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[39])).
% 0.20/0.39 tff(41,plain,
% 0.20/0.39 (![C: $i] : ((~in(C, A!4)) | (C = ordered_pair(tptp_fun_D_6(C), tptp_fun_E_5(C))))),
% 0.20/0.39 inference(and_elim,[status(thm)],[32])).
% 0.20/0.39 tff(42,plain,
% 0.20/0.39 (![C: $i] : ((~in(C, A!4)) | (C = ordered_pair(tptp_fun_D_6(C), tptp_fun_E_5(C))))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[41, 40])).
% 0.20/0.39 tff(43,plain,
% 0.20/0.39 (((~![C: $i] : ((~in(C, A!4)) | (C = ordered_pair(tptp_fun_D_6(C), tptp_fun_E_5(C))))) | ((~in(tptp_fun_C_0(B!3, A!4), A!4)) | (tptp_fun_C_0(B!3, A!4) = ordered_pair(tptp_fun_D_6(tptp_fun_C_0(B!3, A!4)), tptp_fun_E_5(tptp_fun_C_0(B!3, A!4)))))) <=> ((~![C: $i] : ((~in(C, A!4)) | (C = ordered_pair(tptp_fun_D_6(C), tptp_fun_E_5(C))))) | (~in(tptp_fun_C_0(B!3, A!4), A!4)) | (tptp_fun_C_0(B!3, A!4) = ordered_pair(tptp_fun_D_6(tptp_fun_C_0(B!3, A!4)), tptp_fun_E_5(tptp_fun_C_0(B!3, A!4)))))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(44,plain,
% 0.20/0.39 ((~![C: $i] : ((~in(C, A!4)) | (C = ordered_pair(tptp_fun_D_6(C), tptp_fun_E_5(C))))) | ((~in(tptp_fun_C_0(B!3, A!4), A!4)) | (tptp_fun_C_0(B!3, A!4) = ordered_pair(tptp_fun_D_6(tptp_fun_C_0(B!3, A!4)), tptp_fun_E_5(tptp_fun_C_0(B!3, A!4)))))),
% 0.20/0.39 inference(quant_inst,[status(thm)],[])).
% 0.20/0.39 tff(45,plain,
% 0.20/0.39 ((~![C: $i] : ((~in(C, A!4)) | (C = ordered_pair(tptp_fun_D_6(C), tptp_fun_E_5(C))))) | (~in(tptp_fun_C_0(B!3, A!4), A!4)) | (tptp_fun_C_0(B!3, A!4) = ordered_pair(tptp_fun_D_6(tptp_fun_C_0(B!3, A!4)), tptp_fun_E_5(tptp_fun_C_0(B!3, A!4))))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[44, 43])).
% 0.20/0.39 tff(46,plain,
% 0.20/0.39 (tptp_fun_C_0(B!3, A!4) = ordered_pair(tptp_fun_D_6(tptp_fun_C_0(B!3, A!4)), tptp_fun_E_5(tptp_fun_C_0(B!3, A!4)))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[45, 42, 38])).
% 0.20/0.39 tff(47,plain,
% 0.20/0.39 (ordered_pair(tptp_fun_D_6(tptp_fun_C_0(B!3, A!4)), tptp_fun_E_5(tptp_fun_C_0(B!3, A!4))) = tptp_fun_C_0(B!3, A!4)),
% 0.20/0.39 inference(symmetry,[status(thm)],[46])).
% 0.20/0.39 tff(48,plain,
% 0.20/0.39 (in(ordered_pair(tptp_fun_D_6(tptp_fun_C_0(B!3, A!4)), tptp_fun_E_5(tptp_fun_C_0(B!3, A!4))), A!4) <=> in(tptp_fun_C_0(B!3, A!4), A!4)),
% 0.20/0.39 inference(monotonicity,[status(thm)],[47])).
% 0.20/0.39 tff(49,plain,
% 0.20/0.39 (in(tptp_fun_C_0(B!3, A!4), A!4) <=> in(ordered_pair(tptp_fun_D_6(tptp_fun_C_0(B!3, A!4)), tptp_fun_E_5(tptp_fun_C_0(B!3, A!4))), A!4)),
% 0.20/0.39 inference(symmetry,[status(thm)],[48])).
% 0.20/0.39 tff(50,plain,
% 0.20/0.39 (in(ordered_pair(tptp_fun_D_6(tptp_fun_C_0(B!3, A!4)), tptp_fun_E_5(tptp_fun_C_0(B!3, A!4))), A!4)),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[38, 49])).
% 0.20/0.39 tff(51,plain,
% 0.20/0.39 (in(ordered_pair(tptp_fun_D_6(tptp_fun_C_0(B!3, A!4)), tptp_fun_E_5(tptp_fun_C_0(B!3, A!4))), B!3) <=> in(tptp_fun_C_0(B!3, A!4), B!3)),
% 0.20/0.39 inference(monotonicity,[status(thm)],[47])).
% 0.20/0.39 tff(52,plain,
% 0.20/0.39 (in(tptp_fun_C_0(B!3, A!4), B!3) <=> in(ordered_pair(tptp_fun_D_6(tptp_fun_C_0(B!3, A!4)), tptp_fun_E_5(tptp_fun_C_0(B!3, A!4))), B!3)),
% 0.20/0.39 inference(symmetry,[status(thm)],[51])).
% 0.20/0.39 tff(53,plain,
% 0.20/0.39 ((~in(tptp_fun_C_0(B!3, A!4), B!3)) <=> (~in(ordered_pair(tptp_fun_D_6(tptp_fun_C_0(B!3, A!4)), tptp_fun_E_5(tptp_fun_C_0(B!3, A!4))), B!3))),
% 0.20/0.39 inference(monotonicity,[status(thm)],[52])).
% 0.20/0.39 tff(54,plain,
% 0.20/0.39 (((~in(tptp_fun_C_0(B!3, A!4), A!4)) | in(tptp_fun_C_0(B!3, A!4), B!3)) | (~in(tptp_fun_C_0(B!3, A!4), B!3))),
% 0.20/0.39 inference(tautology,[status(thm)],[])).
% 0.20/0.39 tff(55,plain,
% 0.20/0.39 (~in(tptp_fun_C_0(B!3, A!4), B!3)),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[54, 36])).
% 0.20/0.39 tff(56,plain,
% 0.20/0.39 (~in(ordered_pair(tptp_fun_D_6(tptp_fun_C_0(B!3, A!4)), tptp_fun_E_5(tptp_fun_C_0(B!3, A!4))), B!3)),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[55, 53])).
% 0.20/0.39 tff(57,plain,
% 0.20/0.39 (^[C: $i, D: $i] : refl(((~in(ordered_pair(C, D), A!4)) | in(ordered_pair(C, D), B!3)) <=> ((~in(ordered_pair(C, D), A!4)) | in(ordered_pair(C, D), B!3)))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(58,plain,
% 0.20/0.39 (![C: $i, D: $i] : ((~in(ordered_pair(C, D), A!4)) | in(ordered_pair(C, D), B!3)) <=> ![C: $i, D: $i] : ((~in(ordered_pair(C, D), A!4)) | in(ordered_pair(C, D), B!3))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[57])).
% 0.20/0.39 tff(59,plain,
% 0.20/0.39 (![C: $i, D: $i] : ((~in(ordered_pair(C, D), A!4)) | in(ordered_pair(C, D), B!3))),
% 0.20/0.39 inference(and_elim,[status(thm)],[32])).
% 0.20/0.39 tff(60,plain,
% 0.20/0.39 (![C: $i, D: $i] : ((~in(ordered_pair(C, D), A!4)) | in(ordered_pair(C, D), B!3))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[59, 58])).
% 0.20/0.39 tff(61,plain,
% 0.20/0.39 (((~![C: $i, D: $i] : ((~in(ordered_pair(C, D), A!4)) | in(ordered_pair(C, D), B!3))) | ((~in(ordered_pair(tptp_fun_D_6(tptp_fun_C_0(B!3, A!4)), tptp_fun_E_5(tptp_fun_C_0(B!3, A!4))), A!4)) | in(ordered_pair(tptp_fun_D_6(tptp_fun_C_0(B!3, A!4)), tptp_fun_E_5(tptp_fun_C_0(B!3, A!4))), B!3))) <=> ((~![C: $i, D: $i] : ((~in(ordered_pair(C, D), A!4)) | in(ordered_pair(C, D), B!3))) | (~in(ordered_pair(tptp_fun_D_6(tptp_fun_C_0(B!3, A!4)), tptp_fun_E_5(tptp_fun_C_0(B!3, A!4))), A!4)) | in(ordered_pair(tptp_fun_D_6(tptp_fun_C_0(B!3, A!4)), tptp_fun_E_5(tptp_fun_C_0(B!3, A!4))), B!3))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(62,plain,
% 0.20/0.39 ((~![C: $i, D: $i] : ((~in(ordered_pair(C, D), A!4)) | in(ordered_pair(C, D), B!3))) | ((~in(ordered_pair(tptp_fun_D_6(tptp_fun_C_0(B!3, A!4)), tptp_fun_E_5(tptp_fun_C_0(B!3, A!4))), A!4)) | in(ordered_pair(tptp_fun_D_6(tptp_fun_C_0(B!3, A!4)), tptp_fun_E_5(tptp_fun_C_0(B!3, A!4))), B!3))),
% 0.20/0.39 inference(quant_inst,[status(thm)],[])).
% 0.20/0.39 tff(63,plain,
% 0.20/0.39 ((~![C: $i, D: $i] : ((~in(ordered_pair(C, D), A!4)) | in(ordered_pair(C, D), B!3))) | (~in(ordered_pair(tptp_fun_D_6(tptp_fun_C_0(B!3, A!4)), tptp_fun_E_5(tptp_fun_C_0(B!3, A!4))), A!4)) | in(ordered_pair(tptp_fun_D_6(tptp_fun_C_0(B!3, A!4)), tptp_fun_E_5(tptp_fun_C_0(B!3, A!4))), B!3)),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[62, 61])).
% 0.20/0.39 tff(64,plain,
% 0.20/0.39 ((~in(ordered_pair(tptp_fun_D_6(tptp_fun_C_0(B!3, A!4)), tptp_fun_E_5(tptp_fun_C_0(B!3, A!4))), A!4)) | in(ordered_pair(tptp_fun_D_6(tptp_fun_C_0(B!3, A!4)), tptp_fun_E_5(tptp_fun_C_0(B!3, A!4))), B!3)),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[63, 60])).
% 0.20/0.39 tff(65,plain,
% 0.20/0.39 ($false),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[64, 56, 50])).
% 0.20/0.39 % SZS output end Proof
% 0.20/0.39 % E exiting
%------------------------------------------------------------------------------