%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SET954+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 0.12s 0.37s
% Output : Proof 0.12s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12 % Problem : SET954+1 : TPTP v9.0.0. Released v3.2.0.
% 0.08/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n012.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 20 05:52:10 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.12/0.37 % SZS status Theorem
% 0.12/0.37 % SZS output start Proof
% 0.12/0.37 tff(in_type, type, (
% 0.12/0.37 in: ( $i * $i ) > $o)).
% 0.12/0.37 tff(cartesian_product2_type, type, (
% 0.12/0.37 cartesian_product2: ( $i * $i ) > $i)).
% 0.12/0.37 tff(tptp_fun_C_3_type, type, (
% 0.12/0.37 tptp_fun_C_3: $i)).
% 0.12/0.37 tff(tptp_fun_D_2_type, type, (
% 0.12/0.37 tptp_fun_D_2: $i)).
% 0.12/0.37 tff(ordered_pair_type, type, (
% 0.12/0.37 ordered_pair: ( $i * $i ) > $i)).
% 0.12/0.37 tff(tptp_fun_A_5_type, type, (
% 0.12/0.37 tptp_fun_A_5: $i)).
% 0.12/0.37 tff(tptp_fun_B_4_type, type, (
% 0.12/0.37 tptp_fun_B_4: $i)).
% 0.12/0.37 tff(1,plain,
% 0.12/0.37 (^[A: $i, B: $i, C: $i, D: $i] : refl((~(((~in(A, C)) | (~in(B, D))) <=> in(ordered_pair(A, B), cartesian_product2(C, D)))) <=> (~(((~in(A, C)) | (~in(B, D))) <=> in(ordered_pair(A, B), cartesian_product2(C, D)))))),
% 0.12/0.37 inference(bind,[status(th)],[])).
% 0.12/0.37 tff(2,plain,
% 0.12/0.37 (![A: $i, B: $i, C: $i, D: $i] : (~(((~in(A, C)) | (~in(B, D))) <=> in(ordered_pair(A, B), cartesian_product2(C, D)))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~(((~in(A, C)) | (~in(B, D))) <=> in(ordered_pair(A, B), cartesian_product2(C, D))))),
% 0.12/0.37 inference(quant_intro,[status(thm)],[1])).
% 0.12/0.37 tff(3,plain,
% 0.12/0.37 (^[A: $i, B: $i, C: $i, D: $i] : trans(trans(monotonicity(rewrite((in(A, C) & in(B, D)) <=> (~((~in(A, C)) | (~in(B, D))))), ((in(ordered_pair(A, B), cartesian_product2(C, D)) <=> (in(A, C) & in(B, D))) <=> (in(ordered_pair(A, B), cartesian_product2(C, D)) <=> (~((~in(A, C)) | (~in(B, D))))))), rewrite((in(ordered_pair(A, B), cartesian_product2(C, D)) <=> (~((~in(A, C)) | (~in(B, D))))) <=> (~(((~in(A, C)) | (~in(B, D))) <=> in(ordered_pair(A, B), cartesian_product2(C, D))))), ((in(ordered_pair(A, B), cartesian_product2(C, D)) <=> (in(A, C) & in(B, D))) <=> (~(((~in(A, C)) | (~in(B, D))) <=> in(ordered_pair(A, B), cartesian_product2(C, D)))))), rewrite((~(((~in(A, C)) | (~in(B, D))) <=> in(ordered_pair(A, B), cartesian_product2(C, D)))) <=> (~(((~in(A, C)) | (~in(B, D))) <=> in(ordered_pair(A, B), cartesian_product2(C, D))))), ((in(ordered_pair(A, B), cartesian_product2(C, D)) <=> (in(A, C) & in(B, D))) <=> (~(((~in(A, C)) | (~in(B, D))) <=> in(ordered_pair(A, B), cartesian_product2(C, D))))))),
% 0.12/0.37 inference(bind,[status(th)],[])).
% 0.12/0.37 tff(4,plain,
% 0.12/0.37 (![A: $i, B: $i, C: $i, D: $i] : (in(ordered_pair(A, B), cartesian_product2(C, D)) <=> (in(A, C) & in(B, D))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~(((~in(A, C)) | (~in(B, D))) <=> in(ordered_pair(A, B), cartesian_product2(C, D))))),
% 0.12/0.37 inference(quant_intro,[status(thm)],[3])).
% 0.12/0.37 tff(5,plain,
% 0.12/0.37 (![A: $i, B: $i, C: $i, D: $i] : (in(ordered_pair(A, B), cartesian_product2(C, D)) <=> (in(A, C) & in(B, D))) <=> ![A: $i, B: $i, C: $i, D: $i] : (in(ordered_pair(A, B), cartesian_product2(C, D)) <=> (in(A, C) & in(B, D)))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(6,axiom,(![A: $i, B: $i, C: $i, D: $i] : (in(ordered_pair(A, B), cartesian_product2(C, D)) <=> (in(A, C) & in(B, D)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','l55_zfmisc_1')).
% 0.12/0.37 tff(7,plain,
% 0.12/0.37 (![A: $i, B: $i, C: $i, D: $i] : (in(ordered_pair(A, B), cartesian_product2(C, D)) <=> (in(A, C) & in(B, D)))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.12/0.37 tff(8,plain,(
% 0.12/0.37 ![A: $i, B: $i, C: $i, D: $i] : (in(ordered_pair(A, B), cartesian_product2(C, D)) <=> (in(A, C) & in(B, D)))),
% 0.12/0.37 inference(skolemize,[status(sab)],[7])).
% 0.12/0.37 tff(9,plain,
% 0.12/0.37 (![A: $i, B: $i, C: $i, D: $i] : (~(((~in(A, C)) | (~in(B, D))) <=> in(ordered_pair(A, B), cartesian_product2(C, D))))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[8, 4])).
% 0.12/0.37 tff(10,plain,
% 0.12/0.37 (![A: $i, B: $i, C: $i, D: $i] : (~(((~in(A, C)) | (~in(B, D))) <=> in(ordered_pair(A, B), cartesian_product2(C, D))))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[9, 2])).
% 0.12/0.37 tff(11,plain,
% 0.12/0.37 (((~![A: $i, B: $i, C: $i, D: $i] : (~(((~in(A, C)) | (~in(B, D))) <=> in(ordered_pair(A, B), cartesian_product2(C, D))))) | (~(((~in(A!5, C!3)) | (~in(B!4, D!2))) <=> in(ordered_pair(B!4, A!5), cartesian_product2(D!2, C!3))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (~(((~in(A, C)) | (~in(B, D))) <=> in(ordered_pair(A, B), cartesian_product2(C, D))))) | (~(((~in(A!5, C!3)) | (~in(B!4, D!2))) <=> in(ordered_pair(B!4, A!5), cartesian_product2(D!2, C!3)))))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(12,plain,
% 0.12/0.37 ((~(((~in(A!5, C!3)) | (~in(B!4, D!2))) <=> in(ordered_pair(B!4, A!5), cartesian_product2(D!2, C!3)))) <=> (~(((~in(A!5, C!3)) | (~in(B!4, D!2))) <=> in(ordered_pair(B!4, A!5), cartesian_product2(D!2, C!3))))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(13,plain,
% 0.12/0.37 ((((~in(B!4, D!2)) | (~in(A!5, C!3))) <=> in(ordered_pair(B!4, A!5), cartesian_product2(D!2, C!3))) <=> (((~in(A!5, C!3)) | (~in(B!4, D!2))) <=> in(ordered_pair(B!4, A!5), cartesian_product2(D!2, C!3)))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(14,plain,
% 0.12/0.37 ((~(((~in(B!4, D!2)) | (~in(A!5, C!3))) <=> in(ordered_pair(B!4, A!5), cartesian_product2(D!2, C!3)))) <=> (~(((~in(A!5, C!3)) | (~in(B!4, D!2))) <=> in(ordered_pair(B!4, A!5), cartesian_product2(D!2, C!3))))),
% 0.12/0.37 inference(monotonicity,[status(thm)],[13])).
% 0.12/0.37 tff(15,plain,
% 0.12/0.37 ((~(((~in(B!4, D!2)) | (~in(A!5, C!3))) <=> in(ordered_pair(B!4, A!5), cartesian_product2(D!2, C!3)))) <=> (~(((~in(A!5, C!3)) | (~in(B!4, D!2))) <=> in(ordered_pair(B!4, A!5), cartesian_product2(D!2, C!3))))),
% 0.12/0.37 inference(transitivity,[status(thm)],[14, 12])).
% 0.12/0.37 tff(16,plain,
% 0.12/0.37 (((~![A: $i, B: $i, C: $i, D: $i] : (~(((~in(A, C)) | (~in(B, D))) <=> in(ordered_pair(A, B), cartesian_product2(C, D))))) | (~(((~in(B!4, D!2)) | (~in(A!5, C!3))) <=> in(ordered_pair(B!4, A!5), cartesian_product2(D!2, C!3))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (~(((~in(A, C)) | (~in(B, D))) <=> in(ordered_pair(A, B), cartesian_product2(C, D))))) | (~(((~in(A!5, C!3)) | (~in(B!4, D!2))) <=> in(ordered_pair(B!4, A!5), cartesian_product2(D!2, C!3)))))),
% 0.12/0.37 inference(monotonicity,[status(thm)],[15])).
% 0.12/0.37 tff(17,plain,
% 0.12/0.37 (((~![A: $i, B: $i, C: $i, D: $i] : (~(((~in(A, C)) | (~in(B, D))) <=> in(ordered_pair(A, B), cartesian_product2(C, D))))) | (~(((~in(B!4, D!2)) | (~in(A!5, C!3))) <=> in(ordered_pair(B!4, A!5), cartesian_product2(D!2, C!3))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (~(((~in(A, C)) | (~in(B, D))) <=> in(ordered_pair(A, B), cartesian_product2(C, D))))) | (~(((~in(A!5, C!3)) | (~in(B!4, D!2))) <=> in(ordered_pair(B!4, A!5), cartesian_product2(D!2, C!3)))))),
% 0.12/0.37 inference(transitivity,[status(thm)],[16, 11])).
% 0.12/0.37 tff(18,plain,
% 0.12/0.37 ((~![A: $i, B: $i, C: $i, D: $i] : (~(((~in(A, C)) | (~in(B, D))) <=> in(ordered_pair(A, B), cartesian_product2(C, D))))) | (~(((~in(B!4, D!2)) | (~in(A!5, C!3))) <=> in(ordered_pair(B!4, A!5), cartesian_product2(D!2, C!3))))),
% 0.12/0.37 inference(quant_inst,[status(thm)],[])).
% 0.12/0.37 tff(19,plain,
% 0.12/0.37 ((~![A: $i, B: $i, C: $i, D: $i] : (~(((~in(A, C)) | (~in(B, D))) <=> in(ordered_pair(A, B), cartesian_product2(C, D))))) | (~(((~in(A!5, C!3)) | (~in(B!4, D!2))) <=> in(ordered_pair(B!4, A!5), cartesian_product2(D!2, C!3))))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[18, 17])).
% 0.12/0.37 tff(20,plain,
% 0.12/0.37 (~(((~in(A!5, C!3)) | (~in(B!4, D!2))) <=> in(ordered_pair(B!4, A!5), cartesian_product2(D!2, C!3)))),
% 0.12/0.37 inference(unit_resolution,[status(thm)],[19, 10])).
% 0.12/0.37 tff(21,plain,
% 0.12/0.37 ((~![A: $i, B: $i, C: $i, D: $i] : (~(((~in(A, C)) | (~in(B, D))) <=> in(ordered_pair(A, B), cartesian_product2(C, D))))) | (~(((~in(A!5, C!3)) | (~in(B!4, D!2))) <=> in(ordered_pair(A!5, B!4), cartesian_product2(C!3, D!2))))),
% 0.12/0.37 inference(quant_inst,[status(thm)],[])).
% 0.12/0.37 tff(22,plain,
% 0.12/0.37 (~(((~in(A!5, C!3)) | (~in(B!4, D!2))) <=> in(ordered_pair(A!5, B!4), cartesian_product2(C!3, D!2)))),
% 0.12/0.37 inference(unit_resolution,[status(thm)],[21, 10])).
% 0.12/0.37 tff(23,plain,
% 0.12/0.37 ((~![A: $i, B: $i, C: $i, D: $i] : ((~in(ordered_pair(A, B), cartesian_product2(C, D))) | in(ordered_pair(B, A), cartesian_product2(D, C)))) <=> (~![A: $i, B: $i, C: $i, D: $i] : ((~in(ordered_pair(A, B), cartesian_product2(C, D))) | in(ordered_pair(B, A), cartesian_product2(D, C))))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(24,plain,
% 0.12/0.37 ((~![A: $i, B: $i, C: $i, D: $i] : (in(ordered_pair(A, B), cartesian_product2(C, D)) => in(ordered_pair(B, A), cartesian_product2(D, C)))) <=> (~![A: $i, B: $i, C: $i, D: $i] : ((~in(ordered_pair(A, B), cartesian_product2(C, D))) | in(ordered_pair(B, A), cartesian_product2(D, C))))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(25,axiom,(~![A: $i, B: $i, C: $i, D: $i] : (in(ordered_pair(A, B), cartesian_product2(C, D)) => in(ordered_pair(B, A), cartesian_product2(D, C)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t107_zfmisc_1')).
% 0.12/0.38 tff(26,plain,
% 0.12/0.38 (~![A: $i, B: $i, C: $i, D: $i] : ((~in(ordered_pair(A, B), cartesian_product2(C, D))) | in(ordered_pair(B, A), cartesian_product2(D, C)))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[25, 24])).
% 0.12/0.38 tff(27,plain,
% 0.12/0.38 (~![A: $i, B: $i, C: $i, D: $i] : ((~in(ordered_pair(A, B), cartesian_product2(C, D))) | in(ordered_pair(B, A), cartesian_product2(D, C)))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[26, 23])).
% 0.12/0.38 tff(28,plain,
% 0.12/0.38 (~![A: $i, B: $i, C: $i, D: $i] : ((~in(ordered_pair(A, B), cartesian_product2(C, D))) | in(ordered_pair(B, A), cartesian_product2(D, C)))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[27, 23])).
% 0.12/0.38 tff(29,plain,
% 0.12/0.38 (~![A: $i, B: $i, C: $i, D: $i] : ((~in(ordered_pair(A, B), cartesian_product2(C, D))) | in(ordered_pair(B, A), cartesian_product2(D, C)))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[28, 23])).
% 0.12/0.38 tff(30,plain,(
% 0.12/0.38 ~((~in(ordered_pair(A!5, B!4), cartesian_product2(C!3, D!2))) | in(ordered_pair(B!4, A!5), cartesian_product2(D!2, C!3)))),
% 0.12/0.38 inference(skolemize,[status(sab)],[29])).
% 0.12/0.38 tff(31,plain,
% 0.12/0.38 (in(ordered_pair(A!5, B!4), cartesian_product2(C!3, D!2))),
% 0.12/0.38 inference(or_elim,[status(thm)],[30])).
% 0.12/0.38 tff(32,plain,
% 0.12/0.38 ((((~in(A!5, C!3)) | (~in(B!4, D!2))) <=> in(ordered_pair(A!5, B!4), cartesian_product2(C!3, D!2))) | (~((~in(A!5, C!3)) | (~in(B!4, D!2)))) | (~in(ordered_pair(A!5, B!4), cartesian_product2(C!3, D!2)))),
% 0.12/0.38 inference(tautology,[status(thm)],[])).
% 0.12/0.38 tff(33,plain,
% 0.12/0.38 ((((~in(A!5, C!3)) | (~in(B!4, D!2))) <=> in(ordered_pair(A!5, B!4), cartesian_product2(C!3, D!2))) | (~((~in(A!5, C!3)) | (~in(B!4, D!2))))),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[32, 31])).
% 0.12/0.38 tff(34,plain,
% 0.12/0.38 (~((~in(A!5, C!3)) | (~in(B!4, D!2)))),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[33, 22])).
% 0.12/0.38 tff(35,plain,
% 0.12/0.38 (~in(ordered_pair(B!4, A!5), cartesian_product2(D!2, C!3))),
% 0.12/0.38 inference(or_elim,[status(thm)],[30])).
% 0.12/0.38 tff(36,plain,
% 0.12/0.38 ((((~in(A!5, C!3)) | (~in(B!4, D!2))) <=> in(ordered_pair(B!4, A!5), cartesian_product2(D!2, C!3))) | ((~in(A!5, C!3)) | (~in(B!4, D!2))) | in(ordered_pair(B!4, A!5), cartesian_product2(D!2, C!3))),
% 0.12/0.38 inference(tautology,[status(thm)],[])).
% 0.12/0.38 tff(37,plain,
% 0.12/0.38 ((((~in(A!5, C!3)) | (~in(B!4, D!2))) <=> in(ordered_pair(B!4, A!5), cartesian_product2(D!2, C!3))) | ((~in(A!5, C!3)) | (~in(B!4, D!2)))),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[36, 35])).
% 0.12/0.38 tff(38,plain,
% 0.12/0.38 ($false),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[37, 34, 20])).
% 0.12/0.38 % SZS output end Proof
% 0.12/0.38 % E exiting
%------------------------------------------------------------------------------