%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SET956+1 : TPTP v9.0.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n012.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:26:43 AM UTC 2025
% Result : Theorem 0.19s 0.38s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : SET956+1 : TPTP v9.0.0. Released v3.2.0.
% 0.12/0.13 % Command : run_E %s %d THM
% 0.13/0.34 % Computer : n012.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Fri Jun 20 05:51:55 EDT 2025
% 0.19/0.34 % CPUTime :
% 0.19/0.38 % SZS status Theorem
% 0.19/0.38 % SZS output start Proof
% 0.19/0.38 tff(in_type, type, (
% 0.19/0.38 in: ( $i * $i ) > $o)).
% 0.19/0.38 tff(tptp_fun_A_8_type, type, (
% 0.19/0.38 tptp_fun_A_8: $i)).
% 0.19/0.38 tff(ordered_pair_type, type, (
% 0.19/0.38 ordered_pair: ( $i * $i ) > $i)).
% 0.19/0.38 tff(tptp_fun_F_3_type, type, (
% 0.19/0.38 tptp_fun_F_3: ( $i * $i * $i ) > $i)).
% 0.19/0.38 tff(tptp_fun_B_7_type, type, (
% 0.19/0.38 tptp_fun_B_7: $i)).
% 0.19/0.38 tff(tptp_fun_C_6_type, type, (
% 0.19/0.38 tptp_fun_C_6: $i)).
% 0.19/0.38 tff(tptp_fun_C_0_type, type, (
% 0.19/0.38 tptp_fun_C_0: ( $i * $i ) > $i)).
% 0.19/0.38 tff(tptp_fun_D_5_type, type, (
% 0.19/0.38 tptp_fun_D_5: $i)).
% 0.19/0.38 tff(tptp_fun_E_4_type, type, (
% 0.19/0.38 tptp_fun_E_4: ( $i * $i * $i ) > $i)).
% 0.19/0.38 tff(subset_type, type, (
% 0.19/0.38 subset: ( $i * $i ) > $o)).
% 0.19/0.38 tff(cartesian_product2_type, type, (
% 0.19/0.38 cartesian_product2: ( $i * $i ) > $i)).
% 0.19/0.38 tff(1,plain,
% 0.19/0.38 (^[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))))))))),
% 0.19/0.38 inference(bind,[status(th)],[])).
% 0.19/0.38 tff(2,plain,
% 0.19/0.38 (![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)))))))),
% 0.19/0.38 inference(quant_intro,[status(thm)],[1])).
% 0.19/0.38 tff(3,plain,
% 0.19/0.38 (^[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))))))))),
% 0.19/0.38 inference(bind,[status(th)],[])).
% 0.19/0.38 tff(4,plain,
% 0.19/0.38 (![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)))))))),
% 0.19/0.38 inference(quant_intro,[status(thm)],[3])).
% 0.19/0.38 tff(5,plain,
% 0.19/0.38 (![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)))))))),
% 0.19/0.38 inference(transitivity,[status(thm)],[4, 2])).
% 0.19/0.38 tff(6,plain,
% 0.19/0.38 (^[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)))))))))),
% 0.19/0.38 inference(bind,[status(th)],[])).
% 0.19/0.38 tff(7,plain,
% 0.19/0.38 (![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)))))))),
% 0.19/0.38 inference(quant_intro,[status(thm)],[6])).
% 0.19/0.38 tff(8,plain,
% 0.19/0.38 (![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)))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(9,plain,
% 0.19/0.38 (^[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))))),
% 0.19/0.38 inference(bind,[status(th)],[])).
% 0.19/0.38 tff(10,plain,
% 0.19/0.38 (![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)))),
% 0.19/0.38 inference(quant_intro,[status(thm)],[9])).
% 0.19/0.38 tff(11,axiom,(![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : (in(C, A) => in(C, B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d3_tarski')).
% 0.19/0.38 tff(12,plain,
% 0.19/0.38 (![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B)))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[11, 10])).
% 0.19/0.38 tff(13,plain,
% 0.19/0.38 (![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B)))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[12, 8])).
% 0.19/0.38 tff(14,plain,(
% 0.19/0.38 ![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)))))),
% 0.19/0.38 inference(skolemize,[status(sab)],[13])).
% 0.19/0.38 tff(15,plain,
% 0.19/0.38 (![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)))))))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[14, 7])).
% 0.19/0.38 tff(16,plain,
% 0.19/0.38 (![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)))))))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[15, 5])).
% 0.19/0.38 tff(17,plain,
% 0.19/0.38 ((~![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!8, D!5)) | ![C: $i] : ((~in(C, A!8)) | in(C, D!5)))) | (~(subset(A!8, D!5) | (~((~in(tptp_fun_C_0(D!5, A!8), A!8)) | in(tptp_fun_C_0(D!5, A!8), D!5)))))))),
% 0.19/0.38 inference(quant_inst,[status(thm)],[])).
% 0.19/0.38 tff(18,plain,
% 0.19/0.38 (~((~((~subset(A!8, D!5)) | ![C: $i] : ((~in(C, A!8)) | in(C, D!5)))) | (~(subset(A!8, D!5) | (~((~in(tptp_fun_C_0(D!5, A!8), A!8)) | in(tptp_fun_C_0(D!5, A!8), D!5))))))),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[17, 16])).
% 0.19/0.38 tff(19,plain,
% 0.19/0.38 (((~((~subset(A!8, D!5)) | ![C: $i] : ((~in(C, A!8)) | in(C, D!5)))) | (~(subset(A!8, D!5) | (~((~in(tptp_fun_C_0(D!5, A!8), A!8)) | in(tptp_fun_C_0(D!5, A!8), D!5)))))) | (subset(A!8, D!5) | (~((~in(tptp_fun_C_0(D!5, A!8), A!8)) | in(tptp_fun_C_0(D!5, A!8), D!5))))),
% 0.19/0.38 inference(tautology,[status(thm)],[])).
% 0.19/0.38 tff(20,plain,
% 0.19/0.38 (subset(A!8, D!5) | (~((~in(tptp_fun_C_0(D!5, A!8), A!8)) | in(tptp_fun_C_0(D!5, A!8), D!5)))),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[19, 18])).
% 0.19/0.38 tff(21,plain,
% 0.19/0.38 (((subset(A!8, cartesian_product2(B!7, C!6)) & ![E: $i, F: $i] : ((~in(ordered_pair(E, F), A!8)) | in(ordered_pair(E, F), D!5))) & (~subset(A!8, D!5))) <=> (subset(A!8, cartesian_product2(B!7, C!6)) & ![E: $i, F: $i] : ((~in(ordered_pair(E, F), A!8)) | in(ordered_pair(E, F), D!5)) & (~subset(A!8, D!5)))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(22,plain,
% 0.19/0.38 ((subset(A!8, cartesian_product2(B!7, C!6)) & ![E: $i, F: $i] : ((~in(ordered_pair(E, F), A!8)) | in(ordered_pair(E, F), D!5))) <=> (subset(A!8, cartesian_product2(B!7, C!6)) & ![E: $i, F: $i] : ((~in(ordered_pair(E, F), A!8)) | in(ordered_pair(E, F), D!5)))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(23,plain,
% 0.19/0.38 (((subset(A!8, cartesian_product2(B!7, C!6)) & ![E: $i, F: $i] : ((~in(ordered_pair(E, F), A!8)) | in(ordered_pair(E, F), D!5))) & (~subset(A!8, D!5))) <=> ((subset(A!8, cartesian_product2(B!7, C!6)) & ![E: $i, F: $i] : ((~in(ordered_pair(E, F), A!8)) | in(ordered_pair(E, F), D!5))) & (~subset(A!8, D!5)))),
% 0.19/0.39 inference(monotonicity,[status(thm)],[22])).
% 0.19/0.39 tff(24,plain,
% 0.19/0.39 (((subset(A!8, cartesian_product2(B!7, C!6)) & ![E: $i, F: $i] : ((~in(ordered_pair(E, F), A!8)) | in(ordered_pair(E, F), D!5))) & (~subset(A!8, D!5))) <=> (subset(A!8, cartesian_product2(B!7, C!6)) & ![E: $i, F: $i] : ((~in(ordered_pair(E, F), A!8)) | in(ordered_pair(E, F), D!5)) & (~subset(A!8, D!5)))),
% 0.19/0.39 inference(transitivity,[status(thm)],[23, 21])).
% 0.19/0.39 tff(25,plain,
% 0.19/0.39 ((~![A: $i, B: $i, C: $i, D: $i] : ((~(subset(A, cartesian_product2(B, C)) & ![E: $i, F: $i] : ((~in(ordered_pair(E, F), A)) | in(ordered_pair(E, F), D)))) | subset(A, D))) <=> (~![A: $i, B: $i, C: $i, D: $i] : ((~(subset(A, cartesian_product2(B, C)) & ![E: $i, F: $i] : ((~in(ordered_pair(E, F), A)) | in(ordered_pair(E, F), D)))) | subset(A, D)))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(26,plain,
% 0.19/0.39 ((~![A: $i, B: $i, C: $i, D: $i] : ((subset(A, cartesian_product2(B, C)) & ![E: $i, F: $i] : (in(ordered_pair(E, F), A) => in(ordered_pair(E, F), D))) => subset(A, D))) <=> (~![A: $i, B: $i, C: $i, D: $i] : ((~(subset(A, cartesian_product2(B, C)) & ![E: $i, F: $i] : ((~in(ordered_pair(E, F), A)) | in(ordered_pair(E, F), D)))) | subset(A, D)))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(27,axiom,(~![A: $i, B: $i, C: $i, D: $i] : ((subset(A, cartesian_product2(B, C)) & ![E: $i, F: $i] : (in(ordered_pair(E, F), A) => in(ordered_pair(E, F), D))) => subset(A, D))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t109_zfmisc_1')).
% 0.19/0.39 tff(28,plain,
% 0.19/0.39 (~![A: $i, B: $i, C: $i, D: $i] : ((~(subset(A, cartesian_product2(B, C)) & ![E: $i, F: $i] : ((~in(ordered_pair(E, F), A)) | in(ordered_pair(E, F), D)))) | subset(A, D))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[27, 26])).
% 0.19/0.39 tff(29,plain,
% 0.19/0.39 (~![A: $i, B: $i, C: $i, D: $i] : ((~(subset(A, cartesian_product2(B, C)) & ![E: $i, F: $i] : ((~in(ordered_pair(E, F), A)) | in(ordered_pair(E, F), D)))) | subset(A, D))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[28, 25])).
% 0.19/0.39 tff(30,plain,
% 0.19/0.39 (~![A: $i, B: $i, C: $i, D: $i] : ((~(subset(A, cartesian_product2(B, C)) & ![E: $i, F: $i] : ((~in(ordered_pair(E, F), A)) | in(ordered_pair(E, F), D)))) | subset(A, D))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[29, 25])).
% 0.19/0.39 tff(31,plain,
% 0.19/0.39 (~![A: $i, B: $i, C: $i, D: $i] : ((~(subset(A, cartesian_product2(B, C)) & ![E: $i, F: $i] : ((~in(ordered_pair(E, F), A)) | in(ordered_pair(E, F), D)))) | subset(A, D))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[30, 25])).
% 0.19/0.39 tff(32,plain,
% 0.19/0.39 (subset(A!8, cartesian_product2(B!7, C!6)) & ![E: $i, F: $i] : ((~in(ordered_pair(E, F), A!8)) | in(ordered_pair(E, F), D!5)) & (~subset(A!8, D!5))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[31, 24])).
% 0.19/0.39 tff(33,plain,
% 0.19/0.39 (~subset(A!8, D!5)),
% 0.19/0.39 inference(and_elim,[status(thm)],[32])).
% 0.19/0.39 tff(34,plain,
% 0.19/0.39 ((~(subset(A!8, D!5) | (~((~in(tptp_fun_C_0(D!5, A!8), A!8)) | in(tptp_fun_C_0(D!5, A!8), D!5))))) | subset(A!8, D!5) | (~((~in(tptp_fun_C_0(D!5, A!8), A!8)) | in(tptp_fun_C_0(D!5, A!8), D!5)))),
% 0.19/0.39 inference(tautology,[status(thm)],[])).
% 0.19/0.39 tff(35,plain,
% 0.19/0.39 ((~(subset(A!8, D!5) | (~((~in(tptp_fun_C_0(D!5, A!8), A!8)) | in(tptp_fun_C_0(D!5, A!8), D!5))))) | (~((~in(tptp_fun_C_0(D!5, A!8), A!8)) | in(tptp_fun_C_0(D!5, A!8), D!5)))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[34, 33])).
% 0.19/0.39 tff(36,plain,
% 0.19/0.39 (~((~in(tptp_fun_C_0(D!5, A!8), A!8)) | in(tptp_fun_C_0(D!5, A!8), D!5))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[35, 20])).
% 0.19/0.39 tff(37,plain,
% 0.19/0.39 (((~in(tptp_fun_C_0(D!5, A!8), A!8)) | in(tptp_fun_C_0(D!5, A!8), D!5)) | in(tptp_fun_C_0(D!5, A!8), A!8)),
% 0.19/0.39 inference(tautology,[status(thm)],[])).
% 0.19/0.39 tff(38,plain,
% 0.19/0.39 (in(tptp_fun_C_0(D!5, A!8), A!8)),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[37, 36])).
% 0.19/0.39 tff(39,plain,
% 0.19/0.39 (subset(A!8, cartesian_product2(B!7, C!6))),
% 0.19/0.39 inference(and_elim,[status(thm)],[32])).
% 0.19/0.39 tff(40,plain,
% 0.19/0.39 (^[A: $i, B: $i, C: $i, D: $i] : refl(((~subset(A, cartesian_product2(B, C))) | (~in(D, A)) | (~((~in(tptp_fun_E_4(D, C, B), B)) | (~in(tptp_fun_F_3(D, C, B), C)) | (~(D = ordered_pair(tptp_fun_E_4(D, C, B), tptp_fun_F_3(D, C, B))))))) <=> ((~subset(A, cartesian_product2(B, C))) | (~in(D, A)) | (~((~in(tptp_fun_E_4(D, C, B), B)) | (~in(tptp_fun_F_3(D, C, B), C)) | (~(D = ordered_pair(tptp_fun_E_4(D, C, B), tptp_fun_F_3(D, C, B))))))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(41,plain,
% 0.19/0.39 (![A: $i, B: $i, C: $i, D: $i] : ((~subset(A, cartesian_product2(B, C))) | (~in(D, A)) | (~((~in(tptp_fun_E_4(D, C, B), B)) | (~in(tptp_fun_F_3(D, C, B), C)) | (~(D = ordered_pair(tptp_fun_E_4(D, C, B), tptp_fun_F_3(D, C, B))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : ((~subset(A, cartesian_product2(B, C))) | (~in(D, A)) | (~((~in(tptp_fun_E_4(D, C, B), B)) | (~in(tptp_fun_F_3(D, C, B), C)) | (~(D = ordered_pair(tptp_fun_E_4(D, C, B), tptp_fun_F_3(D, C, B)))))))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[40])).
% 0.19/0.39 tff(42,plain,
% 0.19/0.39 (^[A: $i, B: $i, C: $i, D: $i] : trans(monotonicity(rewrite((in(tptp_fun_E_4(D, C, B), B) & in(tptp_fun_F_3(D, C, B), C) & (D = ordered_pair(tptp_fun_E_4(D, C, B), tptp_fun_F_3(D, C, B)))) <=> (~((~in(tptp_fun_E_4(D, C, B), B)) | (~in(tptp_fun_F_3(D, C, B), C)) | (~(D = ordered_pair(tptp_fun_E_4(D, C, B), tptp_fun_F_3(D, C, B))))))), (((~subset(A, cartesian_product2(B, C))) | (~in(D, A)) | (in(tptp_fun_E_4(D, C, B), B) & in(tptp_fun_F_3(D, C, B), C) & (D = ordered_pair(tptp_fun_E_4(D, C, B), tptp_fun_F_3(D, C, B))))) <=> ((~subset(A, cartesian_product2(B, C))) | (~in(D, A)) | (~((~in(tptp_fun_E_4(D, C, B), B)) | (~in(tptp_fun_F_3(D, C, B), C)) | (~(D = ordered_pair(tptp_fun_E_4(D, C, B), tptp_fun_F_3(D, C, B))))))))), rewrite(((~subset(A, cartesian_product2(B, C))) | (~in(D, A)) | (~((~in(tptp_fun_E_4(D, C, B), B)) | (~in(tptp_fun_F_3(D, C, B), C)) | (~(D = ordered_pair(tptp_fun_E_4(D, C, B), tptp_fun_F_3(D, C, B))))))) <=> ((~subset(A, cartesian_product2(B, C))) | (~in(D, A)) | (~((~in(tptp_fun_E_4(D, C, B), B)) | (~in(tptp_fun_F_3(D, C, B), C)) | (~(D = ordered_pair(tptp_fun_E_4(D, C, B), tptp_fun_F_3(D, C, B)))))))), (((~subset(A, cartesian_product2(B, C))) | (~in(D, A)) | (in(tptp_fun_E_4(D, C, B), B) & in(tptp_fun_F_3(D, C, B), C) & (D = ordered_pair(tptp_fun_E_4(D, C, B), tptp_fun_F_3(D, C, B))))) <=> ((~subset(A, cartesian_product2(B, C))) | (~in(D, A)) | (~((~in(tptp_fun_E_4(D, C, B), B)) | (~in(tptp_fun_F_3(D, C, B), C)) | (~(D = ordered_pair(tptp_fun_E_4(D, C, B), tptp_fun_F_3(D, C, B)))))))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(43,plain,
% 0.19/0.39 (![A: $i, B: $i, C: $i, D: $i] : ((~subset(A, cartesian_product2(B, C))) | (~in(D, A)) | (in(tptp_fun_E_4(D, C, B), B) & in(tptp_fun_F_3(D, C, B), C) & (D = ordered_pair(tptp_fun_E_4(D, C, B), tptp_fun_F_3(D, C, B))))) <=> ![A: $i, B: $i, C: $i, D: $i] : ((~subset(A, cartesian_product2(B, C))) | (~in(D, A)) | (~((~in(tptp_fun_E_4(D, C, B), B)) | (~in(tptp_fun_F_3(D, C, B), C)) | (~(D = ordered_pair(tptp_fun_E_4(D, C, B), tptp_fun_F_3(D, C, B)))))))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[42])).
% 0.19/0.39 tff(44,plain,
% 0.19/0.39 (![A: $i, B: $i, C: $i, D: $i] : (~(subset(A, cartesian_product2(B, C)) & in(D, A) & ![E: $i, F: $i] : (~(in(E, B) & in(F, C) & (D = ordered_pair(E, F)))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~(subset(A, cartesian_product2(B, C)) & in(D, A) & ![E: $i, F: $i] : (~(in(E, B) & in(F, C) & (D = ordered_pair(E, F))))))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(45,plain,
% 0.19/0.39 (^[A: $i, B: $i, C: $i, D: $i] : rewrite((~((subset(A, cartesian_product2(B, C)) & in(D, A)) & ![E: $i, F: $i] : (~((in(E, B) & in(F, C)) & (D = ordered_pair(E, F)))))) <=> (~(subset(A, cartesian_product2(B, C)) & in(D, A) & ![E: $i, F: $i] : (~(in(E, B) & in(F, C) & (D = ordered_pair(E, F)))))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(46,plain,
% 0.19/0.39 (![A: $i, B: $i, C: $i, D: $i] : (~((subset(A, cartesian_product2(B, C)) & in(D, A)) & ![E: $i, F: $i] : (~((in(E, B) & in(F, C)) & (D = ordered_pair(E, F)))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~(subset(A, cartesian_product2(B, C)) & in(D, A) & ![E: $i, F: $i] : (~(in(E, B) & in(F, C) & (D = ordered_pair(E, F))))))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[45])).
% 0.19/0.39 tff(47,axiom,(![A: $i, B: $i, C: $i, D: $i] : (~((subset(A, cartesian_product2(B, C)) & in(D, A)) & ![E: $i, F: $i] : (~((in(E, B) & in(F, C)) & (D = ordered_pair(E, F))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t103_zfmisc_1')).
% 0.19/0.39 tff(48,plain,
% 0.19/0.39 (![A: $i, B: $i, C: $i, D: $i] : (~(subset(A, cartesian_product2(B, C)) & in(D, A) & ![E: $i, F: $i] : (~(in(E, B) & in(F, C) & (D = ordered_pair(E, F))))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[47, 46])).
% 0.19/0.39 tff(49,plain,
% 0.19/0.39 (![A: $i, B: $i, C: $i, D: $i] : (~(subset(A, cartesian_product2(B, C)) & in(D, A) & ![E: $i, F: $i] : (~(in(E, B) & in(F, C) & (D = ordered_pair(E, F))))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[48, 44])).
% 0.19/0.39 tff(50,plain,(
% 0.19/0.39 ![A: $i, B: $i, C: $i, D: $i] : ((~subset(A, cartesian_product2(B, C))) | (~in(D, A)) | (in(tptp_fun_E_4(D, C, B), B) & in(tptp_fun_F_3(D, C, B), C) & (D = ordered_pair(tptp_fun_E_4(D, C, B), tptp_fun_F_3(D, C, B)))))),
% 0.19/0.39 inference(skolemize,[status(sab)],[49])).
% 0.19/0.39 tff(51,plain,
% 0.19/0.39 (![A: $i, B: $i, C: $i, D: $i] : ((~subset(A, cartesian_product2(B, C))) | (~in(D, A)) | (~((~in(tptp_fun_E_4(D, C, B), B)) | (~in(tptp_fun_F_3(D, C, B), C)) | (~(D = ordered_pair(tptp_fun_E_4(D, C, B), tptp_fun_F_3(D, C, B)))))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[50, 43])).
% 0.19/0.39 tff(52,plain,
% 0.19/0.39 (![A: $i, B: $i, C: $i, D: $i] : ((~subset(A, cartesian_product2(B, C))) | (~in(D, A)) | (~((~in(tptp_fun_E_4(D, C, B), B)) | (~in(tptp_fun_F_3(D, C, B), C)) | (~(D = ordered_pair(tptp_fun_E_4(D, C, B), tptp_fun_F_3(D, C, B)))))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[51, 41])).
% 0.19/0.39 tff(53,plain,
% 0.19/0.39 (((~![A: $i, B: $i, C: $i, D: $i] : ((~subset(A, cartesian_product2(B, C))) | (~in(D, A)) | (~((~in(tptp_fun_E_4(D, C, B), B)) | (~in(tptp_fun_F_3(D, C, B), C)) | (~(D = ordered_pair(tptp_fun_E_4(D, C, B), tptp_fun_F_3(D, C, B)))))))) | ((~subset(A!8, cartesian_product2(B!7, C!6))) | (~in(tptp_fun_C_0(D!5, A!8), A!8)) | (~((~in(tptp_fun_E_4(tptp_fun_C_0(D!5, A!8), C!6, B!7), B!7)) | (~in(tptp_fun_F_3(tptp_fun_C_0(D!5, A!8), C!6, B!7), C!6)) | (~(tptp_fun_C_0(D!5, A!8) = ordered_pair(tptp_fun_E_4(tptp_fun_C_0(D!5, A!8), C!6, B!7), tptp_fun_F_3(tptp_fun_C_0(D!5, A!8), C!6, B!7)))))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : ((~subset(A, cartesian_product2(B, C))) | (~in(D, A)) | (~((~in(tptp_fun_E_4(D, C, B), B)) | (~in(tptp_fun_F_3(D, C, B), C)) | (~(D = ordered_pair(tptp_fun_E_4(D, C, B), tptp_fun_F_3(D, C, B)))))))) | (~subset(A!8, cartesian_product2(B!7, C!6))) | (~in(tptp_fun_C_0(D!5, A!8), A!8)) | (~((~in(tptp_fun_E_4(tptp_fun_C_0(D!5, A!8), C!6, B!7), B!7)) | (~in(tptp_fun_F_3(tptp_fun_C_0(D!5, A!8), C!6, B!7), C!6)) | (~(tptp_fun_C_0(D!5, A!8) = ordered_pair(tptp_fun_E_4(tptp_fun_C_0(D!5, A!8), C!6, B!7), tptp_fun_F_3(tptp_fun_C_0(D!5, A!8), C!6, B!7)))))))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(54,plain,
% 0.19/0.39 ((~![A: $i, B: $i, C: $i, D: $i] : ((~subset(A, cartesian_product2(B, C))) | (~in(D, A)) | (~((~in(tptp_fun_E_4(D, C, B), B)) | (~in(tptp_fun_F_3(D, C, B), C)) | (~(D = ordered_pair(tptp_fun_E_4(D, C, B), tptp_fun_F_3(D, C, B)))))))) | ((~subset(A!8, cartesian_product2(B!7, C!6))) | (~in(tptp_fun_C_0(D!5, A!8), A!8)) | (~((~in(tptp_fun_E_4(tptp_fun_C_0(D!5, A!8), C!6, B!7), B!7)) | (~in(tptp_fun_F_3(tptp_fun_C_0(D!5, A!8), C!6, B!7), C!6)) | (~(tptp_fun_C_0(D!5, A!8) = ordered_pair(tptp_fun_E_4(tptp_fun_C_0(D!5, A!8), C!6, B!7), tptp_fun_F_3(tptp_fun_C_0(D!5, A!8), C!6, B!7)))))))),
% 0.19/0.39 inference(quant_inst,[status(thm)],[])).
% 0.19/0.39 tff(55,plain,
% 0.19/0.39 ((~![A: $i, B: $i, C: $i, D: $i] : ((~subset(A, cartesian_product2(B, C))) | (~in(D, A)) | (~((~in(tptp_fun_E_4(D, C, B), B)) | (~in(tptp_fun_F_3(D, C, B), C)) | (~(D = ordered_pair(tptp_fun_E_4(D, C, B), tptp_fun_F_3(D, C, B)))))))) | (~subset(A!8, cartesian_product2(B!7, C!6))) | (~in(tptp_fun_C_0(D!5, A!8), A!8)) | (~((~in(tptp_fun_E_4(tptp_fun_C_0(D!5, A!8), C!6, B!7), B!7)) | (~in(tptp_fun_F_3(tptp_fun_C_0(D!5, A!8), C!6, B!7), C!6)) | (~(tptp_fun_C_0(D!5, A!8) = ordered_pair(tptp_fun_E_4(tptp_fun_C_0(D!5, A!8), C!6, B!7), tptp_fun_F_3(tptp_fun_C_0(D!5, A!8), C!6, B!7))))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[54, 53])).
% 0.19/0.39 tff(56,plain,
% 0.19/0.39 (~((~in(tptp_fun_E_4(tptp_fun_C_0(D!5, A!8), C!6, B!7), B!7)) | (~in(tptp_fun_F_3(tptp_fun_C_0(D!5, A!8), C!6, B!7), C!6)) | (~(tptp_fun_C_0(D!5, A!8) = ordered_pair(tptp_fun_E_4(tptp_fun_C_0(D!5, A!8), C!6, B!7), tptp_fun_F_3(tptp_fun_C_0(D!5, A!8), C!6, B!7)))))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[55, 52, 39, 38])).
% 0.19/0.39 tff(57,plain,
% 0.19/0.39 (((~in(tptp_fun_E_4(tptp_fun_C_0(D!5, A!8), C!6, B!7), B!7)) | (~in(tptp_fun_F_3(tptp_fun_C_0(D!5, A!8), C!6, B!7), C!6)) | (~(tptp_fun_C_0(D!5, A!8) = ordered_pair(tptp_fun_E_4(tptp_fun_C_0(D!5, A!8), C!6, B!7), tptp_fun_F_3(tptp_fun_C_0(D!5, A!8), C!6, B!7))))) | (tptp_fun_C_0(D!5, A!8) = ordered_pair(tptp_fun_E_4(tptp_fun_C_0(D!5, A!8), C!6, B!7), tptp_fun_F_3(tptp_fun_C_0(D!5, A!8), C!6, B!7)))),
% 0.19/0.39 inference(tautology,[status(thm)],[])).
% 0.19/0.39 tff(58,plain,
% 0.19/0.39 (tptp_fun_C_0(D!5, A!8) = ordered_pair(tptp_fun_E_4(tptp_fun_C_0(D!5, A!8), C!6, B!7), tptp_fun_F_3(tptp_fun_C_0(D!5, A!8), C!6, B!7))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[57, 56])).
% 0.19/0.39 tff(59,plain,
% 0.19/0.39 (ordered_pair(tptp_fun_E_4(tptp_fun_C_0(D!5, A!8), C!6, B!7), tptp_fun_F_3(tptp_fun_C_0(D!5, A!8), C!6, B!7)) = tptp_fun_C_0(D!5, A!8)),
% 0.19/0.39 inference(symmetry,[status(thm)],[58])).
% 0.19/0.39 tff(60,plain,
% 0.19/0.39 (in(ordered_pair(tptp_fun_E_4(tptp_fun_C_0(D!5, A!8), C!6, B!7), tptp_fun_F_3(tptp_fun_C_0(D!5, A!8), C!6, B!7)), A!8) <=> in(tptp_fun_C_0(D!5, A!8), A!8)),
% 0.19/0.39 inference(monotonicity,[status(thm)],[59])).
% 0.19/0.39 tff(61,plain,
% 0.19/0.39 (in(tptp_fun_C_0(D!5, A!8), A!8) <=> in(ordered_pair(tptp_fun_E_4(tptp_fun_C_0(D!5, A!8), C!6, B!7), tptp_fun_F_3(tptp_fun_C_0(D!5, A!8), C!6, B!7)), A!8)),
% 0.19/0.39 inference(symmetry,[status(thm)],[60])).
% 0.19/0.39 tff(62,plain,
% 0.19/0.39 (in(ordered_pair(tptp_fun_E_4(tptp_fun_C_0(D!5, A!8), C!6, B!7), tptp_fun_F_3(tptp_fun_C_0(D!5, A!8), C!6, B!7)), A!8)),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[38, 61])).
% 0.19/0.39 tff(63,plain,
% 0.19/0.39 (in(ordered_pair(tptp_fun_E_4(tptp_fun_C_0(D!5, A!8), C!6, B!7), tptp_fun_F_3(tptp_fun_C_0(D!5, A!8), C!6, B!7)), D!5) <=> in(tptp_fun_C_0(D!5, A!8), D!5)),
% 0.19/0.39 inference(monotonicity,[status(thm)],[59])).
% 0.19/0.39 tff(64,plain,
% 0.19/0.39 (in(tptp_fun_C_0(D!5, A!8), D!5) <=> in(ordered_pair(tptp_fun_E_4(tptp_fun_C_0(D!5, A!8), C!6, B!7), tptp_fun_F_3(tptp_fun_C_0(D!5, A!8), C!6, B!7)), D!5)),
% 0.19/0.39 inference(symmetry,[status(thm)],[63])).
% 0.19/0.39 tff(65,plain,
% 0.19/0.39 ((~in(tptp_fun_C_0(D!5, A!8), D!5)) <=> (~in(ordered_pair(tptp_fun_E_4(tptp_fun_C_0(D!5, A!8), C!6, B!7), tptp_fun_F_3(tptp_fun_C_0(D!5, A!8), C!6, B!7)), D!5))),
% 0.19/0.39 inference(monotonicity,[status(thm)],[64])).
% 0.19/0.39 tff(66,plain,
% 0.19/0.39 (((~in(tptp_fun_C_0(D!5, A!8), A!8)) | in(tptp_fun_C_0(D!5, A!8), D!5)) | (~in(tptp_fun_C_0(D!5, A!8), D!5))),
% 0.19/0.39 inference(tautology,[status(thm)],[])).
% 0.19/0.39 tff(67,plain,
% 0.19/0.39 (~in(tptp_fun_C_0(D!5, A!8), D!5)),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[66, 36])).
% 0.19/0.39 tff(68,plain,
% 0.19/0.39 (~in(ordered_pair(tptp_fun_E_4(tptp_fun_C_0(D!5, A!8), C!6, B!7), tptp_fun_F_3(tptp_fun_C_0(D!5, A!8), C!6, B!7)), D!5)),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[67, 65])).
% 0.19/0.39 tff(69,plain,
% 0.19/0.39 (^[E: $i, F: $i] : refl(((~in(ordered_pair(E, F), A!8)) | in(ordered_pair(E, F), D!5)) <=> ((~in(ordered_pair(E, F), A!8)) | in(ordered_pair(E, F), D!5)))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(70,plain,
% 0.19/0.39 (![E: $i, F: $i] : ((~in(ordered_pair(E, F), A!8)) | in(ordered_pair(E, F), D!5)) <=> ![E: $i, F: $i] : ((~in(ordered_pair(E, F), A!8)) | in(ordered_pair(E, F), D!5))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[69])).
% 0.19/0.39 tff(71,plain,
% 0.19/0.39 (![E: $i, F: $i] : ((~in(ordered_pair(E, F), A!8)) | in(ordered_pair(E, F), D!5))),
% 0.19/0.39 inference(and_elim,[status(thm)],[32])).
% 0.19/0.39 tff(72,plain,
% 0.19/0.39 (![E: $i, F: $i] : ((~in(ordered_pair(E, F), A!8)) | in(ordered_pair(E, F), D!5))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[71, 70])).
% 0.19/0.39 tff(73,plain,
% 0.19/0.39 (((~![E: $i, F: $i] : ((~in(ordered_pair(E, F), A!8)) | in(ordered_pair(E, F), D!5))) | ((~in(ordered_pair(tptp_fun_E_4(tptp_fun_C_0(D!5, A!8), C!6, B!7), tptp_fun_F_3(tptp_fun_C_0(D!5, A!8), C!6, B!7)), A!8)) | in(ordered_pair(tptp_fun_E_4(tptp_fun_C_0(D!5, A!8), C!6, B!7), tptp_fun_F_3(tptp_fun_C_0(D!5, A!8), C!6, B!7)), D!5))) <=> ((~![E: $i, F: $i] : ((~in(ordered_pair(E, F), A!8)) | in(ordered_pair(E, F), D!5))) | (~in(ordered_pair(tptp_fun_E_4(tptp_fun_C_0(D!5, A!8), C!6, B!7), tptp_fun_F_3(tptp_fun_C_0(D!5, A!8), C!6, B!7)), A!8)) | in(ordered_pair(tptp_fun_E_4(tptp_fun_C_0(D!5, A!8), C!6, B!7), tptp_fun_F_3(tptp_fun_C_0(D!5, A!8), C!6, B!7)), D!5))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(74,plain,
% 0.19/0.40 ((~![E: $i, F: $i] : ((~in(ordered_pair(E, F), A!8)) | in(ordered_pair(E, F), D!5))) | ((~in(ordered_pair(tptp_fun_E_4(tptp_fun_C_0(D!5, A!8), C!6, B!7), tptp_fun_F_3(tptp_fun_C_0(D!5, A!8), C!6, B!7)), A!8)) | in(ordered_pair(tptp_fun_E_4(tptp_fun_C_0(D!5, A!8), C!6, B!7), tptp_fun_F_3(tptp_fun_C_0(D!5, A!8), C!6, B!7)), D!5))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(75,plain,
% 0.19/0.40 ((~![E: $i, F: $i] : ((~in(ordered_pair(E, F), A!8)) | in(ordered_pair(E, F), D!5))) | (~in(ordered_pair(tptp_fun_E_4(tptp_fun_C_0(D!5, A!8), C!6, B!7), tptp_fun_F_3(tptp_fun_C_0(D!5, A!8), C!6, B!7)), A!8)) | in(ordered_pair(tptp_fun_E_4(tptp_fun_C_0(D!5, A!8), C!6, B!7), tptp_fun_F_3(tptp_fun_C_0(D!5, A!8), C!6, B!7)), D!5)),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[74, 73])).
% 0.19/0.40 tff(76,plain,
% 0.19/0.40 ((~in(ordered_pair(tptp_fun_E_4(tptp_fun_C_0(D!5, A!8), C!6, B!7), tptp_fun_F_3(tptp_fun_C_0(D!5, A!8), C!6, B!7)), A!8)) | in(ordered_pair(tptp_fun_E_4(tptp_fun_C_0(D!5, A!8), C!6, B!7), tptp_fun_F_3(tptp_fun_C_0(D!5, A!8), C!6, B!7)), D!5)),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[75, 72])).
% 0.19/0.40 tff(77,plain,
% 0.19/0.40 ($false),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[76, 68, 62])).
% 0.19/0.40 % SZS output end Proof
% 0.19/0.40 % E exiting
%------------------------------------------------------------------------------