%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SEU167+3 : TPTP v9.0.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n002.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 05:27:07 AM UTC 2025
% Result : Theorem 0.15s 0.40s
% Output : Proof 0.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14 % Problem : SEU167+3 : TPTP v9.0.0. Released v3.2.0.
% 0.08/0.14 % Command : run_E %s %d THM
% 0.15/0.35 % Computer : n002.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Fri Jun 20 06:11:01 EDT 2025
% 0.15/0.36 % CPUTime :
% 0.15/0.40 % SZS status Theorem
% 0.15/0.40 % SZS output start Proof
% 0.15/0.40 tff(subset_type, type, (
% 0.15/0.40 subset: ( $i * $i ) > $o)).
% 0.15/0.40 tff(cartesian_product2_type, type, (
% 0.15/0.40 cartesian_product2: ( $i * $i ) > $i)).
% 0.15/0.40 tff(tptp_fun_D_2_type, type, (
% 0.15/0.40 tptp_fun_D_2: $i)).
% 0.15/0.40 tff(tptp_fun_A_5_type, type, (
% 0.15/0.40 tptp_fun_A_5: $i)).
% 0.15/0.40 tff(tptp_fun_C_3_type, type, (
% 0.15/0.40 tptp_fun_C_3: $i)).
% 0.15/0.40 tff(tptp_fun_B_4_type, type, (
% 0.15/0.40 tptp_fun_B_4: $i)).
% 0.15/0.40 tff(1,plain,
% 0.15/0.40 ((~![A: $i, B: $i, C: $i, D: $i] : ((~(subset(A, B) & subset(C, D))) | subset(cartesian_product2(A, C), cartesian_product2(B, D)))) <=> (~![A: $i, B: $i, C: $i, D: $i] : ((~(subset(A, B) & subset(C, D))) | subset(cartesian_product2(A, C), cartesian_product2(B, D))))),
% 0.15/0.40 inference(rewrite,[status(thm)],[])).
% 0.15/0.40 tff(2,plain,
% 0.15/0.40 ((~![A: $i, B: $i, C: $i, D: $i] : ((subset(A, B) & subset(C, D)) => subset(cartesian_product2(A, C), cartesian_product2(B, D)))) <=> (~![A: $i, B: $i, C: $i, D: $i] : ((~(subset(A, B) & subset(C, D))) | subset(cartesian_product2(A, C), cartesian_product2(B, D))))),
% 0.15/0.40 inference(rewrite,[status(thm)],[])).
% 0.15/0.40 tff(3,axiom,(~![A: $i, B: $i, C: $i, D: $i] : ((subset(A, B) & subset(C, D)) => subset(cartesian_product2(A, C), cartesian_product2(B, D)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t119_zfmisc_1')).
% 0.15/0.40 tff(4,plain,
% 0.15/0.40 (~![A: $i, B: $i, C: $i, D: $i] : ((~(subset(A, B) & subset(C, D))) | subset(cartesian_product2(A, C), cartesian_product2(B, D)))),
% 0.15/0.40 inference(modus_ponens,[status(thm)],[3, 2])).
% 0.15/0.40 tff(5,plain,
% 0.15/0.40 (~![A: $i, B: $i, C: $i, D: $i] : ((~(subset(A, B) & subset(C, D))) | subset(cartesian_product2(A, C), cartesian_product2(B, D)))),
% 0.15/0.40 inference(modus_ponens,[status(thm)],[4, 1])).
% 0.15/0.40 tff(6,plain,
% 0.15/0.40 (~![A: $i, B: $i, C: $i, D: $i] : ((~(subset(A, B) & subset(C, D))) | subset(cartesian_product2(A, C), cartesian_product2(B, D)))),
% 0.15/0.40 inference(modus_ponens,[status(thm)],[5, 1])).
% 0.15/0.40 tff(7,plain,
% 0.15/0.40 (~![A: $i, B: $i, C: $i, D: $i] : ((~(subset(A, B) & subset(C, D))) | subset(cartesian_product2(A, C), cartesian_product2(B, D)))),
% 0.15/0.40 inference(modus_ponens,[status(thm)],[6, 1])).
% 0.15/0.40 tff(8,plain,(
% 0.15/0.40 ~((~(subset(A!5, B!4) & subset(C!3, D!2))) | subset(cartesian_product2(A!5, C!3), cartesian_product2(B!4, D!2)))),
% 0.15/0.40 inference(skolemize,[status(sab)],[7])).
% 0.15/0.40 tff(9,plain,
% 0.15/0.40 (subset(A!5, B!4) & subset(C!3, D!2)),
% 0.15/0.40 inference(or_elim,[status(thm)],[8])).
% 0.15/0.40 tff(10,plain,
% 0.15/0.40 (subset(C!3, D!2)),
% 0.15/0.40 inference(and_elim,[status(thm)],[9])).
% 0.15/0.40 tff(11,plain,
% 0.15/0.40 (^[A: $i, B: $i, C: $i] : refl(((~subset(A, B)) | (~((~subset(cartesian_product2(A, C), cartesian_product2(B, C))) | (~subset(cartesian_product2(C, A), cartesian_product2(C, B)))))) <=> ((~subset(A, B)) | (~((~subset(cartesian_product2(A, C), cartesian_product2(B, C))) | (~subset(cartesian_product2(C, A), cartesian_product2(C, B)))))))),
% 0.15/0.40 inference(bind,[status(th)],[])).
% 0.15/0.40 tff(12,plain,
% 0.15/0.40 (![A: $i, B: $i, C: $i] : ((~subset(A, B)) | (~((~subset(cartesian_product2(A, C), cartesian_product2(B, C))) | (~subset(cartesian_product2(C, A), cartesian_product2(C, B)))))) <=> ![A: $i, B: $i, C: $i] : ((~subset(A, B)) | (~((~subset(cartesian_product2(A, C), cartesian_product2(B, C))) | (~subset(cartesian_product2(C, A), cartesian_product2(C, B))))))),
% 0.15/0.40 inference(quant_intro,[status(thm)],[11])).
% 0.15/0.40 tff(13,plain,
% 0.15/0.40 (^[A: $i, B: $i, C: $i] : rewrite(((~subset(A, B)) | (subset(cartesian_product2(A, C), cartesian_product2(B, C)) & subset(cartesian_product2(C, A), cartesian_product2(C, B)))) <=> ((~subset(A, B)) | (~((~subset(cartesian_product2(A, C), cartesian_product2(B, C))) | (~subset(cartesian_product2(C, A), cartesian_product2(C, B)))))))),
% 0.15/0.40 inference(bind,[status(th)],[])).
% 0.15/0.40 tff(14,plain,
% 0.15/0.40 (![A: $i, B: $i, C: $i] : ((~subset(A, B)) | (subset(cartesian_product2(A, C), cartesian_product2(B, C)) & subset(cartesian_product2(C, A), cartesian_product2(C, B)))) <=> ![A: $i, B: $i, C: $i] : ((~subset(A, B)) | (~((~subset(cartesian_product2(A, C), cartesian_product2(B, C))) | (~subset(cartesian_product2(C, A), cartesian_product2(C, B))))))),
% 0.15/0.40 inference(quant_intro,[status(thm)],[13])).
% 0.15/0.40 tff(15,plain,
% 0.15/0.40 (![A: $i, B: $i, C: $i] : ((~subset(A, B)) | (subset(cartesian_product2(A, C), cartesian_product2(B, C)) & subset(cartesian_product2(C, A), cartesian_product2(C, B)))) <=> ![A: $i, B: $i, C: $i] : ((~subset(A, B)) | (subset(cartesian_product2(A, C), cartesian_product2(B, C)) & subset(cartesian_product2(C, A), cartesian_product2(C, B))))),
% 0.15/0.40 inference(rewrite,[status(thm)],[])).
% 0.15/0.40 tff(16,plain,
% 0.15/0.40 (^[A: $i, B: $i, C: $i] : rewrite((subset(A, B) => (subset(cartesian_product2(A, C), cartesian_product2(B, C)) & subset(cartesian_product2(C, A), cartesian_product2(C, B)))) <=> ((~subset(A, B)) | (subset(cartesian_product2(A, C), cartesian_product2(B, C)) & subset(cartesian_product2(C, A), cartesian_product2(C, B)))))),
% 0.15/0.40 inference(bind,[status(th)],[])).
% 0.15/0.40 tff(17,plain,
% 0.15/0.40 (![A: $i, B: $i, C: $i] : (subset(A, B) => (subset(cartesian_product2(A, C), cartesian_product2(B, C)) & subset(cartesian_product2(C, A), cartesian_product2(C, B)))) <=> ![A: $i, B: $i, C: $i] : ((~subset(A, B)) | (subset(cartesian_product2(A, C), cartesian_product2(B, C)) & subset(cartesian_product2(C, A), cartesian_product2(C, B))))),
% 0.15/0.40 inference(quant_intro,[status(thm)],[16])).
% 0.15/0.40 tff(18,axiom,(![A: $i, B: $i, C: $i] : (subset(A, B) => (subset(cartesian_product2(A, C), cartesian_product2(B, C)) & subset(cartesian_product2(C, A), cartesian_product2(C, B))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t118_zfmisc_1')).
% 0.15/0.40 tff(19,plain,
% 0.15/0.40 (![A: $i, B: $i, C: $i] : ((~subset(A, B)) | (subset(cartesian_product2(A, C), cartesian_product2(B, C)) & subset(cartesian_product2(C, A), cartesian_product2(C, B))))),
% 0.15/0.40 inference(modus_ponens,[status(thm)],[18, 17])).
% 0.15/0.40 tff(20,plain,
% 0.15/0.40 (![A: $i, B: $i, C: $i] : ((~subset(A, B)) | (subset(cartesian_product2(A, C), cartesian_product2(B, C)) & subset(cartesian_product2(C, A), cartesian_product2(C, B))))),
% 0.15/0.40 inference(modus_ponens,[status(thm)],[19, 15])).
% 0.15/0.40 tff(21,plain,(
% 0.15/0.40 ![A: $i, B: $i, C: $i] : ((~subset(A, B)) | (subset(cartesian_product2(A, C), cartesian_product2(B, C)) & subset(cartesian_product2(C, A), cartesian_product2(C, B))))),
% 0.15/0.40 inference(skolemize,[status(sab)],[20])).
% 0.15/0.40 tff(22,plain,
% 0.15/0.40 (![A: $i, B: $i, C: $i] : ((~subset(A, B)) | (~((~subset(cartesian_product2(A, C), cartesian_product2(B, C))) | (~subset(cartesian_product2(C, A), cartesian_product2(C, B))))))),
% 0.15/0.40 inference(modus_ponens,[status(thm)],[21, 14])).
% 0.15/0.40 tff(23,plain,
% 0.15/0.40 (![A: $i, B: $i, C: $i] : ((~subset(A, B)) | (~((~subset(cartesian_product2(A, C), cartesian_product2(B, C))) | (~subset(cartesian_product2(C, A), cartesian_product2(C, B))))))),
% 0.15/0.40 inference(modus_ponens,[status(thm)],[22, 12])).
% 0.15/0.40 tff(24,plain,
% 0.15/0.40 (((~![A: $i, B: $i, C: $i] : ((~subset(A, B)) | (~((~subset(cartesian_product2(A, C), cartesian_product2(B, C))) | (~subset(cartesian_product2(C, A), cartesian_product2(C, B))))))) | ((~subset(C!3, D!2)) | (~((~subset(cartesian_product2(C!3, A!5), cartesian_product2(D!2, A!5))) | (~subset(cartesian_product2(A!5, C!3), cartesian_product2(A!5, D!2))))))) <=> ((~![A: $i, B: $i, C: $i] : ((~subset(A, B)) | (~((~subset(cartesian_product2(A, C), cartesian_product2(B, C))) | (~subset(cartesian_product2(C, A), cartesian_product2(C, B))))))) | (~subset(C!3, D!2)) | (~((~subset(cartesian_product2(C!3, A!5), cartesian_product2(D!2, A!5))) | (~subset(cartesian_product2(A!5, C!3), cartesian_product2(A!5, D!2))))))),
% 0.15/0.40 inference(rewrite,[status(thm)],[])).
% 0.15/0.40 tff(25,plain,
% 0.15/0.40 ((~![A: $i, B: $i, C: $i] : ((~subset(A, B)) | (~((~subset(cartesian_product2(A, C), cartesian_product2(B, C))) | (~subset(cartesian_product2(C, A), cartesian_product2(C, B))))))) | ((~subset(C!3, D!2)) | (~((~subset(cartesian_product2(C!3, A!5), cartesian_product2(D!2, A!5))) | (~subset(cartesian_product2(A!5, C!3), cartesian_product2(A!5, D!2))))))),
% 0.15/0.40 inference(quant_inst,[status(thm)],[])).
% 0.15/0.40 tff(26,plain,
% 0.15/0.40 ((~![A: $i, B: $i, C: $i] : ((~subset(A, B)) | (~((~subset(cartesian_product2(A, C), cartesian_product2(B, C))) | (~subset(cartesian_product2(C, A), cartesian_product2(C, B))))))) | (~subset(C!3, D!2)) | (~((~subset(cartesian_product2(C!3, A!5), cartesian_product2(D!2, A!5))) | (~subset(cartesian_product2(A!5, C!3), cartesian_product2(A!5, D!2)))))),
% 0.15/0.41 inference(modus_ponens,[status(thm)],[25, 24])).
% 0.15/0.41 tff(27,plain,
% 0.15/0.41 (~((~subset(cartesian_product2(C!3, A!5), cartesian_product2(D!2, A!5))) | (~subset(cartesian_product2(A!5, C!3), cartesian_product2(A!5, D!2))))),
% 0.15/0.41 inference(unit_resolution,[status(thm)],[26, 23, 10])).
% 0.15/0.41 tff(28,plain,
% 0.15/0.41 (((~subset(cartesian_product2(C!3, A!5), cartesian_product2(D!2, A!5))) | (~subset(cartesian_product2(A!5, C!3), cartesian_product2(A!5, D!2)))) | subset(cartesian_product2(A!5, C!3), cartesian_product2(A!5, D!2))),
% 0.15/0.41 inference(tautology,[status(thm)],[])).
% 0.15/0.41 tff(29,plain,
% 0.15/0.41 (subset(cartesian_product2(A!5, C!3), cartesian_product2(A!5, D!2))),
% 0.15/0.41 inference(unit_resolution,[status(thm)],[28, 27])).
% 0.15/0.41 tff(30,plain,
% 0.15/0.41 (subset(A!5, B!4)),
% 0.15/0.41 inference(and_elim,[status(thm)],[9])).
% 0.15/0.41 tff(31,plain,
% 0.15/0.41 (((~![A: $i, B: $i, C: $i] : ((~subset(A, B)) | (~((~subset(cartesian_product2(A, C), cartesian_product2(B, C))) | (~subset(cartesian_product2(C, A), cartesian_product2(C, B))))))) | ((~subset(A!5, B!4)) | (~((~subset(cartesian_product2(A!5, D!2), cartesian_product2(B!4, D!2))) | (~subset(cartesian_product2(D!2, A!5), cartesian_product2(D!2, B!4))))))) <=> ((~![A: $i, B: $i, C: $i] : ((~subset(A, B)) | (~((~subset(cartesian_product2(A, C), cartesian_product2(B, C))) | (~subset(cartesian_product2(C, A), cartesian_product2(C, B))))))) | (~subset(A!5, B!4)) | (~((~subset(cartesian_product2(A!5, D!2), cartesian_product2(B!4, D!2))) | (~subset(cartesian_product2(D!2, A!5), cartesian_product2(D!2, B!4))))))),
% 0.15/0.41 inference(rewrite,[status(thm)],[])).
% 0.15/0.41 tff(32,plain,
% 0.15/0.41 ((~![A: $i, B: $i, C: $i] : ((~subset(A, B)) | (~((~subset(cartesian_product2(A, C), cartesian_product2(B, C))) | (~subset(cartesian_product2(C, A), cartesian_product2(C, B))))))) | ((~subset(A!5, B!4)) | (~((~subset(cartesian_product2(A!5, D!2), cartesian_product2(B!4, D!2))) | (~subset(cartesian_product2(D!2, A!5), cartesian_product2(D!2, B!4))))))),
% 0.15/0.41 inference(quant_inst,[status(thm)],[])).
% 0.15/0.41 tff(33,plain,
% 0.15/0.41 ((~![A: $i, B: $i, C: $i] : ((~subset(A, B)) | (~((~subset(cartesian_product2(A, C), cartesian_product2(B, C))) | (~subset(cartesian_product2(C, A), cartesian_product2(C, B))))))) | (~subset(A!5, B!4)) | (~((~subset(cartesian_product2(A!5, D!2), cartesian_product2(B!4, D!2))) | (~subset(cartesian_product2(D!2, A!5), cartesian_product2(D!2, B!4)))))),
% 0.15/0.41 inference(modus_ponens,[status(thm)],[32, 31])).
% 0.15/0.41 tff(34,plain,
% 0.15/0.41 (~((~subset(cartesian_product2(A!5, D!2), cartesian_product2(B!4, D!2))) | (~subset(cartesian_product2(D!2, A!5), cartesian_product2(D!2, B!4))))),
% 0.15/0.41 inference(unit_resolution,[status(thm)],[33, 23, 30])).
% 0.15/0.41 tff(35,plain,
% 0.15/0.41 (((~subset(cartesian_product2(A!5, D!2), cartesian_product2(B!4, D!2))) | (~subset(cartesian_product2(D!2, A!5), cartesian_product2(D!2, B!4)))) | subset(cartesian_product2(A!5, D!2), cartesian_product2(B!4, D!2))),
% 0.15/0.41 inference(tautology,[status(thm)],[])).
% 0.15/0.41 tff(36,plain,
% 0.15/0.41 (subset(cartesian_product2(A!5, D!2), cartesian_product2(B!4, D!2))),
% 0.15/0.41 inference(unit_resolution,[status(thm)],[35, 34])).
% 0.15/0.41 tff(37,plain,
% 0.15/0.41 (![A: $i, B: $i, C: $i] : (subset(A, C) | (~subset(A, B)) | (~subset(B, C))) <=> ![A: $i, B: $i, C: $i] : (subset(A, C) | (~subset(A, B)) | (~subset(B, C)))),
% 0.15/0.41 inference(rewrite,[status(thm)],[])).
% 0.15/0.41 tff(38,plain,
% 0.15/0.41 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(rewrite((subset(A, B) & subset(B, C)) <=> (~((~subset(A, B)) | (~subset(B, C))))), ((~(subset(A, B) & subset(B, C))) <=> (~(~((~subset(A, B)) | (~subset(B, C))))))), rewrite((~(~((~subset(A, B)) | (~subset(B, C))))) <=> ((~subset(A, B)) | (~subset(B, C)))), ((~(subset(A, B) & subset(B, C))) <=> ((~subset(A, B)) | (~subset(B, C))))), (((~(subset(A, B) & subset(B, C))) | subset(A, C)) <=> (((~subset(A, B)) | (~subset(B, C))) | subset(A, C)))), rewrite((((~subset(A, B)) | (~subset(B, C))) | subset(A, C)) <=> (subset(A, C) | (~subset(A, B)) | (~subset(B, C)))), (((~(subset(A, B) & subset(B, C))) | subset(A, C)) <=> (subset(A, C) | (~subset(A, B)) | (~subset(B, C)))))),
% 0.22/0.41 inference(bind,[status(th)],[])).
% 0.22/0.41 tff(39,plain,
% 0.22/0.41 (![A: $i, B: $i, C: $i] : ((~(subset(A, B) & subset(B, C))) | subset(A, C)) <=> ![A: $i, B: $i, C: $i] : (subset(A, C) | (~subset(A, B)) | (~subset(B, C)))),
% 0.22/0.41 inference(quant_intro,[status(thm)],[38])).
% 0.22/0.41 tff(40,plain,
% 0.22/0.41 (![A: $i, B: $i, C: $i] : ((~(subset(A, B) & subset(B, C))) | subset(A, C)) <=> ![A: $i, B: $i, C: $i] : ((~(subset(A, B) & subset(B, C))) | subset(A, C))),
% 0.22/0.41 inference(rewrite,[status(thm)],[])).
% 0.22/0.41 tff(41,plain,
% 0.22/0.41 (^[A: $i, B: $i, C: $i] : rewrite(((subset(A, B) & subset(B, C)) => subset(A, C)) <=> ((~(subset(A, B) & subset(B, C))) | subset(A, C)))),
% 0.22/0.41 inference(bind,[status(th)],[])).
% 0.22/0.41 tff(42,plain,
% 0.22/0.41 (![A: $i, B: $i, C: $i] : ((subset(A, B) & subset(B, C)) => subset(A, C)) <=> ![A: $i, B: $i, C: $i] : ((~(subset(A, B) & subset(B, C))) | subset(A, C))),
% 0.22/0.41 inference(quant_intro,[status(thm)],[41])).
% 0.22/0.41 tff(43,axiom,(![A: $i, B: $i, C: $i] : ((subset(A, B) & subset(B, C)) => subset(A, C))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t1_xboole_1')).
% 0.22/0.41 tff(44,plain,
% 0.22/0.41 (![A: $i, B: $i, C: $i] : ((~(subset(A, B) & subset(B, C))) | subset(A, C))),
% 0.22/0.41 inference(modus_ponens,[status(thm)],[43, 42])).
% 0.22/0.41 tff(45,plain,
% 0.22/0.41 (![A: $i, B: $i, C: $i] : ((~(subset(A, B) & subset(B, C))) | subset(A, C))),
% 0.22/0.41 inference(modus_ponens,[status(thm)],[44, 40])).
% 0.22/0.41 tff(46,plain,(
% 0.22/0.41 ![A: $i, B: $i, C: $i] : ((~(subset(A, B) & subset(B, C))) | subset(A, C))),
% 0.22/0.41 inference(skolemize,[status(sab)],[45])).
% 0.22/0.41 tff(47,plain,
% 0.22/0.41 (![A: $i, B: $i, C: $i] : (subset(A, C) | (~subset(A, B)) | (~subset(B, C)))),
% 0.22/0.41 inference(modus_ponens,[status(thm)],[46, 39])).
% 0.22/0.41 tff(48,plain,
% 0.22/0.41 (![A: $i, B: $i, C: $i] : (subset(A, C) | (~subset(A, B)) | (~subset(B, C)))),
% 0.22/0.41 inference(modus_ponens,[status(thm)],[47, 37])).
% 0.22/0.41 tff(49,plain,
% 0.22/0.41 (~subset(cartesian_product2(A!5, C!3), cartesian_product2(B!4, D!2))),
% 0.22/0.41 inference(or_elim,[status(thm)],[8])).
% 0.22/0.41 tff(50,plain,
% 0.22/0.41 (((~![A: $i, B: $i, C: $i] : (subset(A, C) | (~subset(A, B)) | (~subset(B, C)))) | (subset(cartesian_product2(A!5, C!3), cartesian_product2(B!4, D!2)) | (~subset(cartesian_product2(A!5, D!2), cartesian_product2(B!4, D!2))) | (~subset(cartesian_product2(A!5, C!3), cartesian_product2(A!5, D!2))))) <=> ((~![A: $i, B: $i, C: $i] : (subset(A, C) | (~subset(A, B)) | (~subset(B, C)))) | subset(cartesian_product2(A!5, C!3), cartesian_product2(B!4, D!2)) | (~subset(cartesian_product2(A!5, D!2), cartesian_product2(B!4, D!2))) | (~subset(cartesian_product2(A!5, C!3), cartesian_product2(A!5, D!2))))),
% 0.22/0.41 inference(rewrite,[status(thm)],[])).
% 0.22/0.41 tff(51,plain,
% 0.22/0.41 ((subset(cartesian_product2(A!5, C!3), cartesian_product2(B!4, D!2)) | (~subset(cartesian_product2(A!5, C!3), cartesian_product2(A!5, D!2))) | (~subset(cartesian_product2(A!5, D!2), cartesian_product2(B!4, D!2)))) <=> (subset(cartesian_product2(A!5, C!3), cartesian_product2(B!4, D!2)) | (~subset(cartesian_product2(A!5, D!2), cartesian_product2(B!4, D!2))) | (~subset(cartesian_product2(A!5, C!3), cartesian_product2(A!5, D!2))))),
% 0.22/0.41 inference(rewrite,[status(thm)],[])).
% 0.22/0.41 tff(52,plain,
% 0.22/0.41 (((~![A: $i, B: $i, C: $i] : (subset(A, C) | (~subset(A, B)) | (~subset(B, C)))) | (subset(cartesian_product2(A!5, C!3), cartesian_product2(B!4, D!2)) | (~subset(cartesian_product2(A!5, C!3), cartesian_product2(A!5, D!2))) | (~subset(cartesian_product2(A!5, D!2), cartesian_product2(B!4, D!2))))) <=> ((~![A: $i, B: $i, C: $i] : (subset(A, C) | (~subset(A, B)) | (~subset(B, C)))) | (subset(cartesian_product2(A!5, C!3), cartesian_product2(B!4, D!2)) | (~subset(cartesian_product2(A!5, D!2), cartesian_product2(B!4, D!2))) | (~subset(cartesian_product2(A!5, C!3), cartesian_product2(A!5, D!2)))))),
% 0.22/0.41 inference(monotonicity,[status(thm)],[51])).
% 0.22/0.41 tff(53,plain,
% 0.22/0.41 (((~![A: $i, B: $i, C: $i] : (subset(A, C) | (~subset(A, B)) | (~subset(B, C)))) | (subset(cartesian_product2(A!5, C!3), cartesian_product2(B!4, D!2)) | (~subset(cartesian_product2(A!5, C!3), cartesian_product2(A!5, D!2))) | (~subset(cartesian_product2(A!5, D!2), cartesian_product2(B!4, D!2))))) <=> ((~![A: $i, B: $i, C: $i] : (subset(A, C) | (~subset(A, B)) | (~subset(B, C)))) | subset(cartesian_product2(A!5, C!3), cartesian_product2(B!4, D!2)) | (~subset(cartesian_product2(A!5, D!2), cartesian_product2(B!4, D!2))) | (~subset(cartesian_product2(A!5, C!3), cartesian_product2(A!5, D!2))))),
% 0.22/0.41 inference(transitivity,[status(thm)],[52, 50])).
% 0.22/0.41 tff(54,plain,
% 0.22/0.41 ((~![A: $i, B: $i, C: $i] : (subset(A, C) | (~subset(A, B)) | (~subset(B, C)))) | (subset(cartesian_product2(A!5, C!3), cartesian_product2(B!4, D!2)) | (~subset(cartesian_product2(A!5, C!3), cartesian_product2(A!5, D!2))) | (~subset(cartesian_product2(A!5, D!2), cartesian_product2(B!4, D!2))))),
% 0.22/0.41 inference(quant_inst,[status(thm)],[])).
% 0.22/0.41 tff(55,plain,
% 0.22/0.41 ((~![A: $i, B: $i, C: $i] : (subset(A, C) | (~subset(A, B)) | (~subset(B, C)))) | subset(cartesian_product2(A!5, C!3), cartesian_product2(B!4, D!2)) | (~subset(cartesian_product2(A!5, D!2), cartesian_product2(B!4, D!2))) | (~subset(cartesian_product2(A!5, C!3), cartesian_product2(A!5, D!2)))),
% 0.22/0.41 inference(modus_ponens,[status(thm)],[54, 53])).
% 0.22/0.41 tff(56,plain,
% 0.22/0.41 ($false),
% 0.22/0.41 inference(unit_resolution,[status(thm)],[55, 49, 48, 36, 29])).
% 0.22/0.41 % SZS output end Proof
% 0.22/0.41 % E exiting
%------------------------------------------------------------------------------