%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SEU263+1 : TPTP v9.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n009.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 05:27:25 AM UTC 2025
% Result : Theorem 0.19s 0.37s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.12 % Problem : SEU263+1 : TPTP v9.0.0. Released v3.3.0.
% 0.02/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n009.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Fri Jun 20 06:30:48 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.19/0.37 % SZS status Theorem
% 0.19/0.37 % SZS output start Proof
% 0.19/0.37 tff(subset_type, type, (
% 0.19/0.37 subset: ( $i * $i ) > $o)).
% 0.19/0.37 tff(cartesian_product2_type, type, (
% 0.19/0.37 cartesian_product2: ( $i * $i ) > $i)).
% 0.19/0.37 tff(tptp_fun_B_5_type, type, (
% 0.19/0.37 tptp_fun_B_5: $i)).
% 0.19/0.37 tff(tptp_fun_C_4_type, type, (
% 0.19/0.37 tptp_fun_C_4: $i)).
% 0.19/0.37 tff(relation_rng_type, type, (
% 0.19/0.37 relation_rng: $i > $i)).
% 0.19/0.37 tff(tptp_fun_D_3_type, type, (
% 0.19/0.37 tptp_fun_D_3: $i)).
% 0.19/0.37 tff(relation_dom_type, type, (
% 0.19/0.37 relation_dom: $i > $i)).
% 0.19/0.37 tff(tptp_fun_A_6_type, type, (
% 0.19/0.37 tptp_fun_A_6: $i)).
% 0.19/0.37 tff(relation_of2_as_subset_type, type, (
% 0.19/0.37 relation_of2_as_subset: ( $i * $i * $i ) > $o)).
% 0.19/0.37 tff(relation_of2_type, type, (
% 0.19/0.37 relation_of2: ( $i * $i * $i ) > $o)).
% 0.19/0.37 tff(relation_type, type, (
% 0.19/0.37 relation: $i > $o)).
% 0.19/0.37 tff(element_type, type, (
% 0.19/0.37 element: ( $i * $i ) > $o)).
% 0.19/0.37 tff(powerset_type, type, (
% 0.19/0.37 powerset: $i > $i)).
% 0.19/0.37 tff(1,plain,
% 0.19/0.37 ((~(relation_of2_as_subset(D!3, C!4, B!5) | (~subset(relation_rng(D!3), B!5)) | (~relation_of2_as_subset(D!3, C!4, A!6)))) <=> (~(relation_of2_as_subset(D!3, C!4, B!5) | (~subset(relation_rng(D!3), B!5)) | (~relation_of2_as_subset(D!3, C!4, A!6))))),
% 0.19/0.37 inference(rewrite,[status(thm)],[])).
% 0.19/0.37 tff(2,plain,
% 0.19/0.37 ((~![A: $i, B: $i, C: $i, D: $i] : (relation_of2_as_subset(D, C, B) | (~subset(relation_rng(D), B)) | (~relation_of2_as_subset(D, C, A)))) <=> (~![A: $i, B: $i, C: $i, D: $i] : (relation_of2_as_subset(D, C, B) | (~subset(relation_rng(D), B)) | (~relation_of2_as_subset(D, C, A))))),
% 0.19/0.37 inference(rewrite,[status(thm)],[])).
% 0.19/0.37 tff(3,plain,
% 0.19/0.37 ((~![A: $i, B: $i, C: $i, D: $i] : (relation_of2_as_subset(D, C, A) => (subset(relation_rng(D), B) => relation_of2_as_subset(D, C, B)))) <=> (~![A: $i, B: $i, C: $i, D: $i] : (relation_of2_as_subset(D, C, B) | (~subset(relation_rng(D), B)) | (~relation_of2_as_subset(D, C, A))))),
% 0.19/0.37 inference(rewrite,[status(thm)],[])).
% 0.19/0.37 tff(4,axiom,(~![A: $i, B: $i, C: $i, D: $i] : (relation_of2_as_subset(D, C, A) => (subset(relation_rng(D), B) => relation_of2_as_subset(D, C, B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t14_relset_1')).
% 0.19/0.37 tff(5,plain,
% 0.19/0.37 (~![A: $i, B: $i, C: $i, D: $i] : (relation_of2_as_subset(D, C, B) | (~subset(relation_rng(D), B)) | (~relation_of2_as_subset(D, C, A)))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.19/0.37 tff(6,plain,
% 0.19/0.37 (~![A: $i, B: $i, C: $i, D: $i] : (relation_of2_as_subset(D, C, B) | (~subset(relation_rng(D), B)) | (~relation_of2_as_subset(D, C, A)))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[5, 2])).
% 0.19/0.37 tff(7,plain,
% 0.19/0.37 (~![A: $i, B: $i, C: $i, D: $i] : (relation_of2_as_subset(D, C, B) | (~subset(relation_rng(D), B)) | (~relation_of2_as_subset(D, C, A)))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.19/0.37 tff(8,plain,
% 0.19/0.37 (~![A: $i, B: $i, C: $i, D: $i] : (relation_of2_as_subset(D, C, B) | (~subset(relation_rng(D), B)) | (~relation_of2_as_subset(D, C, A)))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[7, 2])).
% 0.19/0.37 tff(9,plain,(
% 0.19/0.37 ~(relation_of2_as_subset(D!3, C!4, B!5) | (~subset(relation_rng(D!3), B!5)) | (~relation_of2_as_subset(D!3, C!4, A!6)))),
% 0.19/0.37 inference(skolemize,[status(sab)],[8])).
% 0.19/0.37 tff(10,plain,
% 0.19/0.37 (~(relation_of2_as_subset(D!3, C!4, B!5) | (~subset(relation_rng(D!3), B!5)) | (~relation_of2_as_subset(D!3, C!4, A!6)))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[9, 1])).
% 0.19/0.37 tff(11,plain,
% 0.19/0.37 (relation_of2_as_subset(D!3, C!4, A!6)),
% 0.19/0.37 inference(or_elim,[status(thm)],[10])).
% 0.19/0.37 tff(12,plain,
% 0.19/0.37 (^[A: $i, B: $i, C: $i] : refl(((~relation_of2_as_subset(C, A, B)) | (~((~subset(relation_dom(C), A)) | (~subset(relation_rng(C), B))))) <=> ((~relation_of2_as_subset(C, A, B)) | (~((~subset(relation_dom(C), A)) | (~subset(relation_rng(C), B))))))),
% 0.19/0.37 inference(bind,[status(th)],[])).
% 0.19/0.37 tff(13,plain,
% 0.19/0.37 (![A: $i, B: $i, C: $i] : ((~relation_of2_as_subset(C, A, B)) | (~((~subset(relation_dom(C), A)) | (~subset(relation_rng(C), B))))) <=> ![A: $i, B: $i, C: $i] : ((~relation_of2_as_subset(C, A, B)) | (~((~subset(relation_dom(C), A)) | (~subset(relation_rng(C), B)))))),
% 0.19/0.37 inference(quant_intro,[status(thm)],[12])).
% 0.19/0.37 tff(14,plain,
% 0.19/0.37 (^[A: $i, B: $i, C: $i] : rewrite(((~relation_of2_as_subset(C, A, B)) | (subset(relation_dom(C), A) & subset(relation_rng(C), B))) <=> ((~relation_of2_as_subset(C, A, B)) | (~((~subset(relation_dom(C), A)) | (~subset(relation_rng(C), B))))))),
% 0.19/0.37 inference(bind,[status(th)],[])).
% 0.19/0.37 tff(15,plain,
% 0.19/0.37 (![A: $i, B: $i, C: $i] : ((~relation_of2_as_subset(C, A, B)) | (subset(relation_dom(C), A) & subset(relation_rng(C), B))) <=> ![A: $i, B: $i, C: $i] : ((~relation_of2_as_subset(C, A, B)) | (~((~subset(relation_dom(C), A)) | (~subset(relation_rng(C), B)))))),
% 0.19/0.37 inference(quant_intro,[status(thm)],[14])).
% 0.19/0.37 tff(16,plain,
% 0.19/0.37 (![A: $i, B: $i, C: $i] : ((~relation_of2_as_subset(C, A, B)) | (subset(relation_dom(C), A) & subset(relation_rng(C), B))) <=> ![A: $i, B: $i, C: $i] : ((~relation_of2_as_subset(C, A, B)) | (subset(relation_dom(C), A) & subset(relation_rng(C), B)))),
% 0.19/0.37 inference(rewrite,[status(thm)],[])).
% 0.19/0.37 tff(17,plain,
% 0.19/0.37 (^[A: $i, B: $i, C: $i] : rewrite((relation_of2_as_subset(C, A, B) => (subset(relation_dom(C), A) & subset(relation_rng(C), B))) <=> ((~relation_of2_as_subset(C, A, B)) | (subset(relation_dom(C), A) & subset(relation_rng(C), B))))),
% 0.19/0.37 inference(bind,[status(th)],[])).
% 0.19/0.37 tff(18,plain,
% 0.19/0.37 (![A: $i, B: $i, C: $i] : (relation_of2_as_subset(C, A, B) => (subset(relation_dom(C), A) & subset(relation_rng(C), B))) <=> ![A: $i, B: $i, C: $i] : ((~relation_of2_as_subset(C, A, B)) | (subset(relation_dom(C), A) & subset(relation_rng(C), B)))),
% 0.19/0.37 inference(quant_intro,[status(thm)],[17])).
% 0.19/0.37 tff(19,axiom,(![A: $i, B: $i, C: $i] : (relation_of2_as_subset(C, A, B) => (subset(relation_dom(C), A) & subset(relation_rng(C), B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t12_relset_1')).
% 0.19/0.37 tff(20,plain,
% 0.19/0.37 (![A: $i, B: $i, C: $i] : ((~relation_of2_as_subset(C, A, B)) | (subset(relation_dom(C), A) & subset(relation_rng(C), B)))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[19, 18])).
% 0.19/0.37 tff(21,plain,
% 0.19/0.37 (![A: $i, B: $i, C: $i] : ((~relation_of2_as_subset(C, A, B)) | (subset(relation_dom(C), A) & subset(relation_rng(C), B)))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[20, 16])).
% 0.19/0.37 tff(22,plain,(
% 0.19/0.37 ![A: $i, B: $i, C: $i] : ((~relation_of2_as_subset(C, A, B)) | (subset(relation_dom(C), A) & subset(relation_rng(C), B)))),
% 0.19/0.37 inference(skolemize,[status(sab)],[21])).
% 0.19/0.37 tff(23,plain,
% 0.19/0.37 (![A: $i, B: $i, C: $i] : ((~relation_of2_as_subset(C, A, B)) | (~((~subset(relation_dom(C), A)) | (~subset(relation_rng(C), B)))))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[22, 15])).
% 0.19/0.37 tff(24,plain,
% 0.19/0.37 (![A: $i, B: $i, C: $i] : ((~relation_of2_as_subset(C, A, B)) | (~((~subset(relation_dom(C), A)) | (~subset(relation_rng(C), B)))))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[23, 13])).
% 0.19/0.37 tff(25,plain,
% 0.19/0.37 (((~![A: $i, B: $i, C: $i] : ((~relation_of2_as_subset(C, A, B)) | (~((~subset(relation_dom(C), A)) | (~subset(relation_rng(C), B)))))) | ((~relation_of2_as_subset(D!3, C!4, A!6)) | (~((~subset(relation_dom(D!3), C!4)) | (~subset(relation_rng(D!3), A!6)))))) <=> ((~![A: $i, B: $i, C: $i] : ((~relation_of2_as_subset(C, A, B)) | (~((~subset(relation_dom(C), A)) | (~subset(relation_rng(C), B)))))) | (~relation_of2_as_subset(D!3, C!4, A!6)) | (~((~subset(relation_dom(D!3), C!4)) | (~subset(relation_rng(D!3), A!6)))))),
% 0.19/0.37 inference(rewrite,[status(thm)],[])).
% 0.19/0.37 tff(26,plain,
% 0.19/0.37 ((~![A: $i, B: $i, C: $i] : ((~relation_of2_as_subset(C, A, B)) | (~((~subset(relation_dom(C), A)) | (~subset(relation_rng(C), B)))))) | ((~relation_of2_as_subset(D!3, C!4, A!6)) | (~((~subset(relation_dom(D!3), C!4)) | (~subset(relation_rng(D!3), A!6)))))),
% 0.19/0.37 inference(quant_inst,[status(thm)],[])).
% 0.19/0.37 tff(27,plain,
% 0.19/0.37 ((~![A: $i, B: $i, C: $i] : ((~relation_of2_as_subset(C, A, B)) | (~((~subset(relation_dom(C), A)) | (~subset(relation_rng(C), B)))))) | (~relation_of2_as_subset(D!3, C!4, A!6)) | (~((~subset(relation_dom(D!3), C!4)) | (~subset(relation_rng(D!3), A!6))))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[26, 25])).
% 0.19/0.37 tff(28,plain,
% 0.19/0.37 (~((~subset(relation_dom(D!3), C!4)) | (~subset(relation_rng(D!3), A!6)))),
% 0.19/0.37 inference(unit_resolution,[status(thm)],[27, 24, 11])).
% 0.19/0.37 tff(29,plain,
% 0.19/0.37 (((~subset(relation_dom(D!3), C!4)) | (~subset(relation_rng(D!3), A!6))) | subset(relation_dom(D!3), C!4)),
% 0.19/0.37 inference(tautology,[status(thm)],[])).
% 0.19/0.37 tff(30,plain,
% 0.19/0.37 (subset(relation_dom(D!3), C!4)),
% 0.19/0.37 inference(unit_resolution,[status(thm)],[29, 28])).
% 0.19/0.37 tff(31,plain,
% 0.19/0.37 (subset(relation_rng(D!3), B!5)),
% 0.19/0.37 inference(or_elim,[status(thm)],[10])).
% 0.19/0.37 tff(32,plain,
% 0.19/0.37 (^[A: $i, B: $i, C: $i, D: $i] : refl((subset(cartesian_product2(A, C), cartesian_product2(B, D)) | (~subset(A, B)) | (~subset(C, D))) <=> (subset(cartesian_product2(A, C), cartesian_product2(B, D)) | (~subset(A, B)) | (~subset(C, D))))),
% 0.19/0.37 inference(bind,[status(th)],[])).
% 0.19/0.37 tff(33,plain,
% 0.19/0.37 (![A: $i, B: $i, C: $i, D: $i] : (subset(cartesian_product2(A, C), cartesian_product2(B, D)) | (~subset(A, B)) | (~subset(C, D))) <=> ![A: $i, B: $i, C: $i, D: $i] : (subset(cartesian_product2(A, C), cartesian_product2(B, D)) | (~subset(A, B)) | (~subset(C, D)))),
% 0.19/0.37 inference(quant_intro,[status(thm)],[32])).
% 0.19/0.37 tff(34,plain,
% 0.19/0.37 (^[A: $i, B: $i, C: $i, D: $i] : trans(monotonicity(trans(monotonicity(rewrite((subset(A, B) & subset(C, D)) <=> (~((~subset(A, B)) | (~subset(C, D))))), ((~(subset(A, B) & subset(C, D))) <=> (~(~((~subset(A, B)) | (~subset(C, D))))))), rewrite((~(~((~subset(A, B)) | (~subset(C, D))))) <=> ((~subset(A, B)) | (~subset(C, D)))), ((~(subset(A, B) & subset(C, D))) <=> ((~subset(A, B)) | (~subset(C, D))))), (((~(subset(A, B) & subset(C, D))) | subset(cartesian_product2(A, C), cartesian_product2(B, D))) <=> (((~subset(A, B)) | (~subset(C, D))) | subset(cartesian_product2(A, C), cartesian_product2(B, D))))), rewrite((((~subset(A, B)) | (~subset(C, D))) | subset(cartesian_product2(A, C), cartesian_product2(B, D))) <=> (subset(cartesian_product2(A, C), cartesian_product2(B, D)) | (~subset(A, B)) | (~subset(C, D)))), (((~(subset(A, B) & subset(C, D))) | subset(cartesian_product2(A, C), cartesian_product2(B, D))) <=> (subset(cartesian_product2(A, C), cartesian_product2(B, D)) | (~subset(A, B)) | (~subset(C, D)))))),
% 0.19/0.37 inference(bind,[status(th)],[])).
% 0.19/0.37 tff(35,plain,
% 0.19/0.37 (![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(cartesian_product2(A, C), cartesian_product2(B, D)) | (~subset(A, B)) | (~subset(C, D)))),
% 0.19/0.37 inference(quant_intro,[status(thm)],[34])).
% 0.19/0.37 tff(36,plain,
% 0.19/0.37 (![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)))),
% 0.19/0.37 inference(rewrite,[status(thm)],[])).
% 0.19/0.37 tff(37,plain,
% 0.19/0.37 (^[A: $i, B: $i, C: $i, D: $i] : rewrite(((subset(A, B) & subset(C, D)) => subset(cartesian_product2(A, C), cartesian_product2(B, D))) <=> ((~(subset(A, B) & subset(C, D))) | subset(cartesian_product2(A, C), cartesian_product2(B, D))))),
% 0.19/0.37 inference(bind,[status(th)],[])).
% 0.19/0.37 tff(38,plain,
% 0.19/0.37 (![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)))),
% 0.19/0.37 inference(quant_intro,[status(thm)],[37])).
% 0.19/0.37 tff(39,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')).
% 0.19/0.37 tff(40,plain,
% 0.19/0.37 (![A: $i, B: $i, C: $i, D: $i] : ((~(subset(A, B) & subset(C, D))) | subset(cartesian_product2(A, C), cartesian_product2(B, D)))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[39, 38])).
% 0.19/0.37 tff(41,plain,
% 0.19/0.37 (![A: $i, B: $i, C: $i, D: $i] : ((~(subset(A, B) & subset(C, D))) | subset(cartesian_product2(A, C), cartesian_product2(B, D)))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[40, 36])).
% 0.19/0.37 tff(42,plain,(
% 0.19/0.37 ![A: $i, B: $i, C: $i, D: $i] : ((~(subset(A, B) & subset(C, D))) | subset(cartesian_product2(A, C), cartesian_product2(B, D)))),
% 0.19/0.37 inference(skolemize,[status(sab)],[41])).
% 0.19/0.37 tff(43,plain,
% 0.19/0.37 (![A: $i, B: $i, C: $i, D: $i] : (subset(cartesian_product2(A, C), cartesian_product2(B, D)) | (~subset(A, B)) | (~subset(C, D)))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[42, 35])).
% 0.19/0.37 tff(44,plain,
% 0.19/0.37 (![A: $i, B: $i, C: $i, D: $i] : (subset(cartesian_product2(A, C), cartesian_product2(B, D)) | (~subset(A, B)) | (~subset(C, D)))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[43, 33])).
% 0.19/0.37 tff(45,plain,
% 0.19/0.37 (((~![A: $i, B: $i, C: $i, D: $i] : (subset(cartesian_product2(A, C), cartesian_product2(B, D)) | (~subset(A, B)) | (~subset(C, D)))) | ((~subset(relation_rng(D!3), B!5)) | (~subset(relation_dom(D!3), C!4)) | subset(cartesian_product2(relation_dom(D!3), relation_rng(D!3)), cartesian_product2(C!4, B!5)))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (subset(cartesian_product2(A, C), cartesian_product2(B, D)) | (~subset(A, B)) | (~subset(C, D)))) | (~subset(relation_rng(D!3), B!5)) | (~subset(relation_dom(D!3), C!4)) | subset(cartesian_product2(relation_dom(D!3), relation_rng(D!3)), cartesian_product2(C!4, B!5)))),
% 0.19/0.37 inference(rewrite,[status(thm)],[])).
% 0.19/0.37 tff(46,plain,
% 0.19/0.37 ((subset(cartesian_product2(relation_dom(D!3), relation_rng(D!3)), cartesian_product2(C!4, B!5)) | (~subset(relation_dom(D!3), C!4)) | (~subset(relation_rng(D!3), B!5))) <=> ((~subset(relation_rng(D!3), B!5)) | (~subset(relation_dom(D!3), C!4)) | subset(cartesian_product2(relation_dom(D!3), relation_rng(D!3)), cartesian_product2(C!4, B!5)))),
% 0.19/0.37 inference(rewrite,[status(thm)],[])).
% 0.19/0.37 tff(47,plain,
% 0.19/0.37 (((~![A: $i, B: $i, C: $i, D: $i] : (subset(cartesian_product2(A, C), cartesian_product2(B, D)) | (~subset(A, B)) | (~subset(C, D)))) | (subset(cartesian_product2(relation_dom(D!3), relation_rng(D!3)), cartesian_product2(C!4, B!5)) | (~subset(relation_dom(D!3), C!4)) | (~subset(relation_rng(D!3), B!5)))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (subset(cartesian_product2(A, C), cartesian_product2(B, D)) | (~subset(A, B)) | (~subset(C, D)))) | ((~subset(relation_rng(D!3), B!5)) | (~subset(relation_dom(D!3), C!4)) | subset(cartesian_product2(relation_dom(D!3), relation_rng(D!3)), cartesian_product2(C!4, B!5))))),
% 0.19/0.37 inference(monotonicity,[status(thm)],[46])).
% 0.19/0.37 tff(48,plain,
% 0.19/0.37 (((~![A: $i, B: $i, C: $i, D: $i] : (subset(cartesian_product2(A, C), cartesian_product2(B, D)) | (~subset(A, B)) | (~subset(C, D)))) | (subset(cartesian_product2(relation_dom(D!3), relation_rng(D!3)), cartesian_product2(C!4, B!5)) | (~subset(relation_dom(D!3), C!4)) | (~subset(relation_rng(D!3), B!5)))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (subset(cartesian_product2(A, C), cartesian_product2(B, D)) | (~subset(A, B)) | (~subset(C, D)))) | (~subset(relation_rng(D!3), B!5)) | (~subset(relation_dom(D!3), C!4)) | subset(cartesian_product2(relation_dom(D!3), relation_rng(D!3)), cartesian_product2(C!4, B!5)))),
% 0.19/0.37 inference(transitivity,[status(thm)],[47, 45])).
% 0.19/0.37 tff(49,plain,
% 0.19/0.37 ((~![A: $i, B: $i, C: $i, D: $i] : (subset(cartesian_product2(A, C), cartesian_product2(B, D)) | (~subset(A, B)) | (~subset(C, D)))) | (subset(cartesian_product2(relation_dom(D!3), relation_rng(D!3)), cartesian_product2(C!4, B!5)) | (~subset(relation_dom(D!3), C!4)) | (~subset(relation_rng(D!3), B!5)))),
% 0.19/0.37 inference(quant_inst,[status(thm)],[])).
% 0.19/0.37 tff(50,plain,
% 0.19/0.37 ((~![A: $i, B: $i, C: $i, D: $i] : (subset(cartesian_product2(A, C), cartesian_product2(B, D)) | (~subset(A, B)) | (~subset(C, D)))) | (~subset(relation_rng(D!3), B!5)) | (~subset(relation_dom(D!3), C!4)) | subset(cartesian_product2(relation_dom(D!3), relation_rng(D!3)), cartesian_product2(C!4, B!5))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[49, 48])).
% 0.19/0.37 tff(51,plain,
% 0.19/0.37 (subset(cartesian_product2(relation_dom(D!3), relation_rng(D!3)), cartesian_product2(C!4, B!5))),
% 0.19/0.37 inference(unit_resolution,[status(thm)],[50, 44, 31, 30])).
% 0.19/0.37 tff(52,plain,
% 0.19/0.37 (^[A: $i, B: $i, C: $i] : refl((relation_of2(C, A, B) <=> subset(C, cartesian_product2(A, B))) <=> (relation_of2(C, A, B) <=> subset(C, cartesian_product2(A, B))))),
% 0.19/0.37 inference(bind,[status(th)],[])).
% 0.19/0.37 tff(53,plain,
% 0.19/0.37 (![A: $i, B: $i, C: $i] : (relation_of2(C, A, B) <=> subset(C, cartesian_product2(A, B))) <=> ![A: $i, B: $i, C: $i] : (relation_of2(C, A, B) <=> subset(C, cartesian_product2(A, B)))),
% 0.19/0.38 inference(quant_intro,[status(thm)],[52])).
% 0.19/0.38 tff(54,plain,
% 0.19/0.38 (![A: $i, B: $i, C: $i] : (relation_of2(C, A, B) <=> subset(C, cartesian_product2(A, B))) <=> ![A: $i, B: $i, C: $i] : (relation_of2(C, A, B) <=> subset(C, cartesian_product2(A, B)))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(55,axiom,(![A: $i, B: $i, C: $i] : (relation_of2(C, A, B) <=> subset(C, cartesian_product2(A, B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d1_relset_1')).
% 0.19/0.38 tff(56,plain,
% 0.19/0.38 (![A: $i, B: $i, C: $i] : (relation_of2(C, A, B) <=> subset(C, cartesian_product2(A, B)))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[55, 54])).
% 0.19/0.38 tff(57,plain,(
% 0.19/0.38 ![A: $i, B: $i, C: $i] : (relation_of2(C, A, B) <=> subset(C, cartesian_product2(A, B)))),
% 0.19/0.38 inference(skolemize,[status(sab)],[56])).
% 0.19/0.38 tff(58,plain,
% 0.19/0.38 (![A: $i, B: $i, C: $i] : (relation_of2(C, A, B) <=> subset(C, cartesian_product2(A, B)))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[57, 53])).
% 0.19/0.38 tff(59,plain,
% 0.19/0.38 ((~![A: $i, B: $i, C: $i] : (relation_of2(C, A, B) <=> subset(C, cartesian_product2(A, B)))) | (relation_of2(D!3, C!4, B!5) <=> subset(D!3, cartesian_product2(C!4, B!5)))),
% 0.19/0.38 inference(quant_inst,[status(thm)],[])).
% 0.19/0.38 tff(60,plain,
% 0.19/0.38 (relation_of2(D!3, C!4, B!5) <=> subset(D!3, cartesian_product2(C!4, B!5))),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[59, 58])).
% 0.19/0.38 tff(61,plain,
% 0.19/0.38 (^[A: $i, B: $i, C: $i] : refl((relation_of2_as_subset(C, A, B) <=> relation_of2(C, A, B)) <=> (relation_of2_as_subset(C, A, B) <=> relation_of2(C, A, B)))),
% 0.19/0.38 inference(bind,[status(th)],[])).
% 0.19/0.38 tff(62,plain,
% 0.19/0.38 (![A: $i, B: $i, C: $i] : (relation_of2_as_subset(C, A, B) <=> relation_of2(C, A, B)) <=> ![A: $i, B: $i, C: $i] : (relation_of2_as_subset(C, A, B) <=> relation_of2(C, A, B))),
% 0.19/0.38 inference(quant_intro,[status(thm)],[61])).
% 0.19/0.38 tff(63,plain,
% 0.19/0.38 (![A: $i, B: $i, C: $i] : (relation_of2_as_subset(C, A, B) <=> relation_of2(C, A, B)) <=> ![A: $i, B: $i, C: $i] : (relation_of2_as_subset(C, A, B) <=> relation_of2(C, A, B))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(64,axiom,(![A: $i, B: $i, C: $i] : (relation_of2_as_subset(C, A, B) <=> relation_of2(C, A, B))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','redefinition_m2_relset_1')).
% 0.19/0.38 tff(65,plain,
% 0.19/0.38 (![A: $i, B: $i, C: $i] : (relation_of2_as_subset(C, A, B) <=> relation_of2(C, A, B))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[64, 63])).
% 0.19/0.38 tff(66,plain,(
% 0.19/0.38 ![A: $i, B: $i, C: $i] : (relation_of2_as_subset(C, A, B) <=> relation_of2(C, A, B))),
% 0.19/0.38 inference(skolemize,[status(sab)],[65])).
% 0.19/0.38 tff(67,plain,
% 0.19/0.38 (![A: $i, B: $i, C: $i] : (relation_of2_as_subset(C, A, B) <=> relation_of2(C, A, B))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[66, 62])).
% 0.19/0.38 tff(68,plain,
% 0.19/0.38 ((~![A: $i, B: $i, C: $i] : (relation_of2_as_subset(C, A, B) <=> relation_of2(C, A, B))) | (relation_of2_as_subset(D!3, C!4, B!5) <=> relation_of2(D!3, C!4, B!5))),
% 0.19/0.38 inference(quant_inst,[status(thm)],[])).
% 0.19/0.38 tff(69,plain,
% 0.19/0.38 (relation_of2_as_subset(D!3, C!4, B!5) <=> relation_of2(D!3, C!4, B!5)),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[68, 67])).
% 0.19/0.38 tff(70,plain,
% 0.19/0.38 (~relation_of2_as_subset(D!3, C!4, B!5)),
% 0.19/0.38 inference(or_elim,[status(thm)],[10])).
% 0.19/0.38 tff(71,plain,
% 0.19/0.38 ((~(relation_of2_as_subset(D!3, C!4, B!5) <=> relation_of2(D!3, C!4, B!5))) | relation_of2_as_subset(D!3, C!4, B!5) | (~relation_of2(D!3, C!4, B!5))),
% 0.19/0.38 inference(tautology,[status(thm)],[])).
% 0.19/0.38 tff(72,plain,
% 0.19/0.38 ((~(relation_of2_as_subset(D!3, C!4, B!5) <=> relation_of2(D!3, C!4, B!5))) | (~relation_of2(D!3, C!4, B!5))),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[71, 70])).
% 0.19/0.38 tff(73,plain,
% 0.19/0.38 (~relation_of2(D!3, C!4, B!5)),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[72, 69])).
% 0.19/0.38 tff(74,plain,
% 0.19/0.38 ((~(relation_of2(D!3, C!4, B!5) <=> subset(D!3, cartesian_product2(C!4, B!5)))) | relation_of2(D!3, C!4, B!5) | (~subset(D!3, cartesian_product2(C!4, B!5)))),
% 0.19/0.38 inference(tautology,[status(thm)],[])).
% 0.19/0.38 tff(75,plain,
% 0.19/0.38 ((~(relation_of2(D!3, C!4, B!5) <=> subset(D!3, cartesian_product2(C!4, B!5)))) | (~subset(D!3, cartesian_product2(C!4, B!5)))),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[74, 73])).
% 0.19/0.38 tff(76,plain,
% 0.19/0.38 (~subset(D!3, cartesian_product2(C!4, B!5))),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[75, 60])).
% 0.19/0.38 tff(77,plain,
% 0.19/0.38 (^[A: $i, B: $i, C: $i] : refl(((~relation_of2_as_subset(C, A, B)) | element(C, powerset(cartesian_product2(A, B)))) <=> ((~relation_of2_as_subset(C, A, B)) | element(C, powerset(cartesian_product2(A, B)))))),
% 0.19/0.38 inference(bind,[status(th)],[])).
% 0.19/0.38 tff(78,plain,
% 0.19/0.38 (![A: $i, B: $i, C: $i] : ((~relation_of2_as_subset(C, A, B)) | element(C, powerset(cartesian_product2(A, B)))) <=> ![A: $i, B: $i, C: $i] : ((~relation_of2_as_subset(C, A, B)) | element(C, powerset(cartesian_product2(A, B))))),
% 0.19/0.38 inference(quant_intro,[status(thm)],[77])).
% 0.19/0.38 tff(79,plain,
% 0.19/0.38 (![A: $i, B: $i, C: $i] : ((~relation_of2_as_subset(C, A, B)) | element(C, powerset(cartesian_product2(A, B)))) <=> ![A: $i, B: $i, C: $i] : ((~relation_of2_as_subset(C, A, B)) | element(C, powerset(cartesian_product2(A, B))))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(80,plain,
% 0.19/0.38 (^[A: $i, B: $i, C: $i] : rewrite((relation_of2_as_subset(C, A, B) => element(C, powerset(cartesian_product2(A, B)))) <=> ((~relation_of2_as_subset(C, A, B)) | element(C, powerset(cartesian_product2(A, B)))))),
% 0.19/0.38 inference(bind,[status(th)],[])).
% 0.19/0.38 tff(81,plain,
% 0.19/0.38 (![A: $i, B: $i, C: $i] : (relation_of2_as_subset(C, A, B) => element(C, powerset(cartesian_product2(A, B)))) <=> ![A: $i, B: $i, C: $i] : ((~relation_of2_as_subset(C, A, B)) | element(C, powerset(cartesian_product2(A, B))))),
% 0.19/0.38 inference(quant_intro,[status(thm)],[80])).
% 0.19/0.38 tff(82,axiom,(![A: $i, B: $i, C: $i] : (relation_of2_as_subset(C, A, B) => element(C, powerset(cartesian_product2(A, B))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_m2_relset_1')).
% 0.19/0.38 tff(83,plain,
% 0.19/0.38 (![A: $i, B: $i, C: $i] : ((~relation_of2_as_subset(C, A, B)) | element(C, powerset(cartesian_product2(A, B))))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[82, 81])).
% 0.19/0.38 tff(84,plain,
% 0.19/0.38 (![A: $i, B: $i, C: $i] : ((~relation_of2_as_subset(C, A, B)) | element(C, powerset(cartesian_product2(A, B))))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[83, 79])).
% 0.19/0.38 tff(85,plain,(
% 0.19/0.38 ![A: $i, B: $i, C: $i] : ((~relation_of2_as_subset(C, A, B)) | element(C, powerset(cartesian_product2(A, B))))),
% 0.19/0.38 inference(skolemize,[status(sab)],[84])).
% 0.19/0.38 tff(86,plain,
% 0.19/0.38 (![A: $i, B: $i, C: $i] : ((~relation_of2_as_subset(C, A, B)) | element(C, powerset(cartesian_product2(A, B))))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[85, 78])).
% 0.19/0.38 tff(87,plain,
% 0.19/0.38 (((~![A: $i, B: $i, C: $i] : ((~relation_of2_as_subset(C, A, B)) | element(C, powerset(cartesian_product2(A, B))))) | ((~relation_of2_as_subset(D!3, C!4, A!6)) | element(D!3, powerset(cartesian_product2(C!4, A!6))))) <=> ((~![A: $i, B: $i, C: $i] : ((~relation_of2_as_subset(C, A, B)) | element(C, powerset(cartesian_product2(A, B))))) | (~relation_of2_as_subset(D!3, C!4, A!6)) | element(D!3, powerset(cartesian_product2(C!4, A!6))))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(88,plain,
% 0.19/0.38 ((~![A: $i, B: $i, C: $i] : ((~relation_of2_as_subset(C, A, B)) | element(C, powerset(cartesian_product2(A, B))))) | ((~relation_of2_as_subset(D!3, C!4, A!6)) | element(D!3, powerset(cartesian_product2(C!4, A!6))))),
% 0.19/0.38 inference(quant_inst,[status(thm)],[])).
% 0.19/0.38 tff(89,plain,
% 0.19/0.38 ((~![A: $i, B: $i, C: $i] : ((~relation_of2_as_subset(C, A, B)) | element(C, powerset(cartesian_product2(A, B))))) | (~relation_of2_as_subset(D!3, C!4, A!6)) | element(D!3, powerset(cartesian_product2(C!4, A!6)))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[88, 87])).
% 0.19/0.38 tff(90,plain,
% 0.19/0.38 (element(D!3, powerset(cartesian_product2(C!4, A!6)))),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[89, 86, 11])).
% 0.19/0.38 tff(91,plain,
% 0.19/0.38 (^[A: $i, B: $i, C: $i] : refl((relation(C) | (~element(C, powerset(cartesian_product2(A, B))))) <=> (relation(C) | (~element(C, powerset(cartesian_product2(A, B))))))),
% 0.19/0.38 inference(bind,[status(th)],[])).
% 0.19/0.38 tff(92,plain,
% 0.19/0.38 (![A: $i, B: $i, C: $i] : (relation(C) | (~element(C, powerset(cartesian_product2(A, B))))) <=> ![A: $i, B: $i, C: $i] : (relation(C) | (~element(C, powerset(cartesian_product2(A, B)))))),
% 0.19/0.38 inference(quant_intro,[status(thm)],[91])).
% 0.19/0.38 tff(93,plain,
% 0.19/0.38 (![A: $i, B: $i, C: $i] : (relation(C) | (~element(C, powerset(cartesian_product2(A, B))))) <=> ![A: $i, B: $i, C: $i] : (relation(C) | (~element(C, powerset(cartesian_product2(A, B)))))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(94,plain,
% 0.19/0.38 (^[A: $i, B: $i, C: $i] : rewrite((element(C, powerset(cartesian_product2(A, B))) => relation(C)) <=> (relation(C) | (~element(C, powerset(cartesian_product2(A, B))))))),
% 0.19/0.38 inference(bind,[status(th)],[])).
% 0.19/0.38 tff(95,plain,
% 0.19/0.38 (![A: $i, B: $i, C: $i] : (element(C, powerset(cartesian_product2(A, B))) => relation(C)) <=> ![A: $i, B: $i, C: $i] : (relation(C) | (~element(C, powerset(cartesian_product2(A, B)))))),
% 0.19/0.38 inference(quant_intro,[status(thm)],[94])).
% 0.19/0.38 tff(96,axiom,(![A: $i, B: $i, C: $i] : (element(C, powerset(cartesian_product2(A, B))) => relation(C))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','cc1_relset_1')).
% 0.19/0.38 tff(97,plain,
% 0.19/0.38 (![A: $i, B: $i, C: $i] : (relation(C) | (~element(C, powerset(cartesian_product2(A, B)))))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[96, 95])).
% 0.19/0.38 tff(98,plain,
% 0.19/0.38 (![A: $i, B: $i, C: $i] : (relation(C) | (~element(C, powerset(cartesian_product2(A, B)))))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[97, 93])).
% 0.19/0.38 tff(99,plain,(
% 0.19/0.38 ![A: $i, B: $i, C: $i] : (relation(C) | (~element(C, powerset(cartesian_product2(A, B)))))),
% 0.19/0.38 inference(skolemize,[status(sab)],[98])).
% 0.19/0.38 tff(100,plain,
% 0.19/0.38 (![A: $i, B: $i, C: $i] : (relation(C) | (~element(C, powerset(cartesian_product2(A, B)))))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[99, 92])).
% 0.19/0.38 tff(101,plain,
% 0.19/0.38 (((~![A: $i, B: $i, C: $i] : (relation(C) | (~element(C, powerset(cartesian_product2(A, B)))))) | (relation(D!3) | (~element(D!3, powerset(cartesian_product2(C!4, A!6)))))) <=> ((~![A: $i, B: $i, C: $i] : (relation(C) | (~element(C, powerset(cartesian_product2(A, B)))))) | relation(D!3) | (~element(D!3, powerset(cartesian_product2(C!4, A!6)))))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(102,plain,
% 0.19/0.38 ((~![A: $i, B: $i, C: $i] : (relation(C) | (~element(C, powerset(cartesian_product2(A, B)))))) | (relation(D!3) | (~element(D!3, powerset(cartesian_product2(C!4, A!6)))))),
% 0.19/0.38 inference(quant_inst,[status(thm)],[])).
% 0.19/0.38 tff(103,plain,
% 0.19/0.38 ((~![A: $i, B: $i, C: $i] : (relation(C) | (~element(C, powerset(cartesian_product2(A, B)))))) | relation(D!3) | (~element(D!3, powerset(cartesian_product2(C!4, A!6))))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[102, 101])).
% 0.19/0.38 tff(104,plain,
% 0.19/0.38 (relation(D!3)),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[103, 100, 90])).
% 0.19/0.38 tff(105,plain,
% 0.19/0.38 (^[A: $i] : refl(((~relation(A)) | subset(A, cartesian_product2(relation_dom(A), relation_rng(A)))) <=> ((~relation(A)) | subset(A, cartesian_product2(relation_dom(A), relation_rng(A)))))),
% 0.19/0.38 inference(bind,[status(th)],[])).
% 0.19/0.38 tff(106,plain,
% 0.19/0.38 (![A: $i] : ((~relation(A)) | subset(A, cartesian_product2(relation_dom(A), relation_rng(A)))) <=> ![A: $i] : ((~relation(A)) | subset(A, cartesian_product2(relation_dom(A), relation_rng(A))))),
% 0.19/0.38 inference(quant_intro,[status(thm)],[105])).
% 0.19/0.38 tff(107,plain,
% 0.19/0.38 (![A: $i] : ((~relation(A)) | subset(A, cartesian_product2(relation_dom(A), relation_rng(A)))) <=> ![A: $i] : ((~relation(A)) | subset(A, cartesian_product2(relation_dom(A), relation_rng(A))))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(108,plain,
% 0.19/0.38 (^[A: $i] : rewrite((relation(A) => subset(A, cartesian_product2(relation_dom(A), relation_rng(A)))) <=> ((~relation(A)) | subset(A, cartesian_product2(relation_dom(A), relation_rng(A)))))),
% 0.19/0.38 inference(bind,[status(th)],[])).
% 0.19/0.38 tff(109,plain,
% 0.19/0.38 (![A: $i] : (relation(A) => subset(A, cartesian_product2(relation_dom(A), relation_rng(A)))) <=> ![A: $i] : ((~relation(A)) | subset(A, cartesian_product2(relation_dom(A), relation_rng(A))))),
% 0.19/0.38 inference(quant_intro,[status(thm)],[108])).
% 0.19/0.38 tff(110,axiom,(![A: $i] : (relation(A) => subset(A, cartesian_product2(relation_dom(A), relation_rng(A))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t21_relat_1')).
% 0.19/0.38 tff(111,plain,
% 0.19/0.38 (![A: $i] : ((~relation(A)) | subset(A, cartesian_product2(relation_dom(A), relation_rng(A))))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[110, 109])).
% 0.19/0.38 tff(112,plain,
% 0.19/0.38 (![A: $i] : ((~relation(A)) | subset(A, cartesian_product2(relation_dom(A), relation_rng(A))))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[111, 107])).
% 0.19/0.38 tff(113,plain,(
% 0.19/0.38 ![A: $i] : ((~relation(A)) | subset(A, cartesian_product2(relation_dom(A), relation_rng(A))))),
% 0.19/0.38 inference(skolemize,[status(sab)],[112])).
% 0.19/0.38 tff(114,plain,
% 0.19/0.38 (![A: $i] : ((~relation(A)) | subset(A, cartesian_product2(relation_dom(A), relation_rng(A))))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[113, 106])).
% 0.19/0.38 tff(115,plain,
% 0.19/0.38 (((~![A: $i] : ((~relation(A)) | subset(A, cartesian_product2(relation_dom(A), relation_rng(A))))) | ((~relation(D!3)) | subset(D!3, cartesian_product2(relation_dom(D!3), relation_rng(D!3))))) <=> ((~![A: $i] : ((~relation(A)) | subset(A, cartesian_product2(relation_dom(A), relation_rng(A))))) | (~relation(D!3)) | subset(D!3, cartesian_product2(relation_dom(D!3), relation_rng(D!3))))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(116,plain,
% 0.19/0.38 ((~![A: $i] : ((~relation(A)) | subset(A, cartesian_product2(relation_dom(A), relation_rng(A))))) | ((~relation(D!3)) | subset(D!3, cartesian_product2(relation_dom(D!3), relation_rng(D!3))))),
% 0.19/0.38 inference(quant_inst,[status(thm)],[])).
% 0.19/0.38 tff(117,plain,
% 0.19/0.38 ((~![A: $i] : ((~relation(A)) | subset(A, cartesian_product2(relation_dom(A), relation_rng(A))))) | (~relation(D!3)) | subset(D!3, cartesian_product2(relation_dom(D!3), relation_rng(D!3)))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[116, 115])).
% 0.19/0.38 tff(118,plain,
% 0.19/0.38 ((~relation(D!3)) | subset(D!3, cartesian_product2(relation_dom(D!3), relation_rng(D!3)))),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[117, 114])).
% 0.19/0.38 tff(119,plain,
% 0.19/0.38 (subset(D!3, cartesian_product2(relation_dom(D!3), relation_rng(D!3)))),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[118, 104])).
% 0.19/0.38 tff(120,plain,
% 0.19/0.38 (![A: $i, B: $i, C: $i] : (subset(A, C) | (~subset(B, C)) | (~subset(A, B))) <=> ![A: $i, B: $i, C: $i] : (subset(A, C) | (~subset(B, C)) | (~subset(A, B)))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(121,plain,
% 0.19/0.38 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(rewrite((subset(A, B) & subset(B, C)) <=> (~((~subset(B, C)) | (~subset(A, B))))), ((~(subset(A, B) & subset(B, C))) <=> (~(~((~subset(B, C)) | (~subset(A, B))))))), rewrite((~(~((~subset(B, C)) | (~subset(A, B))))) <=> ((~subset(B, C)) | (~subset(A, B)))), ((~(subset(A, B) & subset(B, C))) <=> ((~subset(B, C)) | (~subset(A, B))))), (((~(subset(A, B) & subset(B, C))) | subset(A, C)) <=> (((~subset(B, C)) | (~subset(A, B))) | subset(A, C)))), rewrite((((~subset(B, C)) | (~subset(A, B))) | subset(A, C)) <=> (subset(A, C) | (~subset(B, C)) | (~subset(A, B)))), (((~(subset(A, B) & subset(B, C))) | subset(A, C)) <=> (subset(A, C) | (~subset(B, C)) | (~subset(A, B)))))),
% 0.19/0.38 inference(bind,[status(th)],[])).
% 0.19/0.38 tff(122,plain,
% 0.19/0.38 (![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(B, C)) | (~subset(A, B)))),
% 0.19/0.38 inference(quant_intro,[status(thm)],[121])).
% 0.19/0.38 tff(123,plain,
% 0.19/0.38 (![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))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(124,plain,
% 0.19/0.38 (^[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)))),
% 0.19/0.38 inference(bind,[status(th)],[])).
% 0.19/0.38 tff(125,plain,
% 0.19/0.38 (![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))),
% 0.19/0.38 inference(quant_intro,[status(thm)],[124])).
% 0.19/0.38 tff(126,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')).
% 0.19/0.38 tff(127,plain,
% 0.19/0.38 (![A: $i, B: $i, C: $i] : ((~(subset(A, B) & subset(B, C))) | subset(A, C))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[126, 125])).
% 0.19/0.38 tff(128,plain,
% 0.19/0.38 (![A: $i, B: $i, C: $i] : ((~(subset(A, B) & subset(B, C))) | subset(A, C))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[127, 123])).
% 0.19/0.38 tff(129,plain,(
% 0.19/0.38 ![A: $i, B: $i, C: $i] : ((~(subset(A, B) & subset(B, C))) | subset(A, C))),
% 0.19/0.38 inference(skolemize,[status(sab)],[128])).
% 0.19/0.38 tff(130,plain,
% 0.19/0.38 (![A: $i, B: $i, C: $i] : (subset(A, C) | (~subset(B, C)) | (~subset(A, B)))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[129, 122])).
% 0.19/0.38 tff(131,plain,
% 0.19/0.38 (![A: $i, B: $i, C: $i] : (subset(A, C) | (~subset(B, C)) | (~subset(A, B)))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[130, 120])).
% 0.19/0.38 tff(132,plain,
% 0.19/0.38 (((~![A: $i, B: $i, C: $i] : (subset(A, C) | (~subset(B, C)) | (~subset(A, B)))) | (subset(D!3, cartesian_product2(C!4, B!5)) | (~subset(D!3, cartesian_product2(relation_dom(D!3), relation_rng(D!3)))) | (~subset(cartesian_product2(relation_dom(D!3), relation_rng(D!3)), cartesian_product2(C!4, B!5))))) <=> ((~![A: $i, B: $i, C: $i] : (subset(A, C) | (~subset(B, C)) | (~subset(A, B)))) | subset(D!3, cartesian_product2(C!4, B!5)) | (~subset(D!3, cartesian_product2(relation_dom(D!3), relation_rng(D!3)))) | (~subset(cartesian_product2(relation_dom(D!3), relation_rng(D!3)), cartesian_product2(C!4, B!5))))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(133,plain,
% 0.19/0.38 ((subset(D!3, cartesian_product2(C!4, B!5)) | (~subset(cartesian_product2(relation_dom(D!3), relation_rng(D!3)), cartesian_product2(C!4, B!5))) | (~subset(D!3, cartesian_product2(relation_dom(D!3), relation_rng(D!3))))) <=> (subset(D!3, cartesian_product2(C!4, B!5)) | (~subset(D!3, cartesian_product2(relation_dom(D!3), relation_rng(D!3)))) | (~subset(cartesian_product2(relation_dom(D!3), relation_rng(D!3)), cartesian_product2(C!4, B!5))))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(134,plain,
% 0.19/0.38 (((~![A: $i, B: $i, C: $i] : (subset(A, C) | (~subset(B, C)) | (~subset(A, B)))) | (subset(D!3, cartesian_product2(C!4, B!5)) | (~subset(cartesian_product2(relation_dom(D!3), relation_rng(D!3)), cartesian_product2(C!4, B!5))) | (~subset(D!3, cartesian_product2(relation_dom(D!3), relation_rng(D!3)))))) <=> ((~![A: $i, B: $i, C: $i] : (subset(A, C) | (~subset(B, C)) | (~subset(A, B)))) | (subset(D!3, cartesian_product2(C!4, B!5)) | (~subset(D!3, cartesian_product2(relation_dom(D!3), relation_rng(D!3)))) | (~subset(cartesian_product2(relation_dom(D!3), relation_rng(D!3)), cartesian_product2(C!4, B!5)))))),
% 0.19/0.38 inference(monotonicity,[status(thm)],[133])).
% 0.19/0.38 tff(135,plain,
% 0.19/0.38 (((~![A: $i, B: $i, C: $i] : (subset(A, C) | (~subset(B, C)) | (~subset(A, B)))) | (subset(D!3, cartesian_product2(C!4, B!5)) | (~subset(cartesian_product2(relation_dom(D!3), relation_rng(D!3)), cartesian_product2(C!4, B!5))) | (~subset(D!3, cartesian_product2(relation_dom(D!3), relation_rng(D!3)))))) <=> ((~![A: $i, B: $i, C: $i] : (subset(A, C) | (~subset(B, C)) | (~subset(A, B)))) | subset(D!3, cartesian_product2(C!4, B!5)) | (~subset(D!3, cartesian_product2(relation_dom(D!3), relation_rng(D!3)))) | (~subset(cartesian_product2(relation_dom(D!3), relation_rng(D!3)), cartesian_product2(C!4, B!5))))),
% 0.19/0.38 inference(transitivity,[status(thm)],[134, 132])).
% 0.19/0.38 tff(136,plain,
% 0.19/0.38 ((~![A: $i, B: $i, C: $i] : (subset(A, C) | (~subset(B, C)) | (~subset(A, B)))) | (subset(D!3, cartesian_product2(C!4, B!5)) | (~subset(cartesian_product2(relation_dom(D!3), relation_rng(D!3)), cartesian_product2(C!4, B!5))) | (~subset(D!3, cartesian_product2(relation_dom(D!3), relation_rng(D!3)))))),
% 0.19/0.38 inference(quant_inst,[status(thm)],[])).
% 0.19/0.38 tff(137,plain,
% 0.19/0.38 ((~![A: $i, B: $i, C: $i] : (subset(A, C) | (~subset(B, C)) | (~subset(A, B)))) | subset(D!3, cartesian_product2(C!4, B!5)) | (~subset(D!3, cartesian_product2(relation_dom(D!3), relation_rng(D!3)))) | (~subset(cartesian_product2(relation_dom(D!3), relation_rng(D!3)), cartesian_product2(C!4, B!5)))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[136, 135])).
% 0.19/0.38 tff(138,plain,
% 0.19/0.38 ($false),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[137, 131, 119, 76, 51])).
% 0.19/0.39 % SZS output end Proof
% 0.19/0.39 % E exiting
%------------------------------------------------------------------------------