%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SEU264+1 : TPTP v9.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n008.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 05:27:26 AM UTC 2025
% Result : Theorem 0.13s 0.39s
% Output : Proof 0.13s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : SEU264+1 : TPTP v9.0.0. Released v3.3.0.
% 0.08/0.13 % Command : run_E %s %d THM
% 0.13/0.35 % Computer : n008.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Fri Jun 20 06:31:03 EDT 2025
% 0.13/0.35 % CPUTime :
% 0.13/0.39 % SZS status Theorem
% 0.13/0.39 % SZS output start Proof
% 0.13/0.39 tff(subset_type, type, (
% 0.13/0.39 subset: ( $i * $i ) > $o)).
% 0.13/0.39 tff(tptp_fun_A_6_type, type, (
% 0.13/0.39 tptp_fun_A_6: $i)).
% 0.13/0.39 tff(relation_rng_type, type, (
% 0.13/0.39 relation_rng: $i > $i)).
% 0.13/0.39 tff(tptp_fun_D_3_type, type, (
% 0.13/0.39 tptp_fun_D_3: $i)).
% 0.13/0.39 tff(tptp_fun_C_4_type, type, (
% 0.13/0.39 tptp_fun_C_4: $i)).
% 0.13/0.39 tff(relation_dom_type, type, (
% 0.13/0.39 relation_dom: $i > $i)).
% 0.13/0.39 tff(relation_of2_as_subset_type, type, (
% 0.13/0.39 relation_of2_as_subset: ( $i * $i * $i ) > $o)).
% 0.13/0.39 tff(tptp_fun_B_5_type, type, (
% 0.13/0.39 tptp_fun_B_5: $i)).
% 0.13/0.39 tff(1,plain,
% 0.13/0.39 ((~(relation_of2_as_subset(D!3, C!4, B!5) | (~relation_of2_as_subset(D!3, C!4, A!6)) | (~subset(A!6, B!5)))) <=> (~(relation_of2_as_subset(D!3, C!4, B!5) | (~relation_of2_as_subset(D!3, C!4, A!6)) | (~subset(A!6, B!5))))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(2,plain,
% 0.13/0.39 ((~![A: $i, B: $i, C: $i, D: $i] : (relation_of2_as_subset(D, C, B) | (~relation_of2_as_subset(D, C, A)) | (~subset(A, B)))) <=> (~![A: $i, B: $i, C: $i, D: $i] : (relation_of2_as_subset(D, C, B) | (~relation_of2_as_subset(D, C, A)) | (~subset(A, B))))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(3,plain,
% 0.13/0.39 ((~![A: $i, B: $i, C: $i, D: $i] : (relation_of2_as_subset(D, C, A) => (subset(A, B) => relation_of2_as_subset(D, C, B)))) <=> (~![A: $i, B: $i, C: $i, D: $i] : (relation_of2_as_subset(D, C, B) | (~relation_of2_as_subset(D, C, A)) | (~subset(A, B))))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(4,axiom,(~![A: $i, B: $i, C: $i, D: $i] : (relation_of2_as_subset(D, C, A) => (subset(A, B) => relation_of2_as_subset(D, C, B)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t16_relset_1')).
% 0.13/0.39 tff(5,plain,
% 0.13/0.39 (~![A: $i, B: $i, C: $i, D: $i] : (relation_of2_as_subset(D, C, B) | (~relation_of2_as_subset(D, C, A)) | (~subset(A, B)))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.13/0.39 tff(6,plain,
% 0.13/0.39 (~![A: $i, B: $i, C: $i, D: $i] : (relation_of2_as_subset(D, C, B) | (~relation_of2_as_subset(D, C, A)) | (~subset(A, B)))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[5, 2])).
% 0.13/0.39 tff(7,plain,
% 0.13/0.39 (~![A: $i, B: $i, C: $i, D: $i] : (relation_of2_as_subset(D, C, B) | (~relation_of2_as_subset(D, C, A)) | (~subset(A, B)))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.13/0.39 tff(8,plain,
% 0.13/0.39 (~![A: $i, B: $i, C: $i, D: $i] : (relation_of2_as_subset(D, C, B) | (~relation_of2_as_subset(D, C, A)) | (~subset(A, B)))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[7, 2])).
% 0.13/0.39 tff(9,plain,(
% 0.13/0.39 ~(relation_of2_as_subset(D!3, C!4, B!5) | (~relation_of2_as_subset(D!3, C!4, A!6)) | (~subset(A!6, B!5)))),
% 0.13/0.39 inference(skolemize,[status(sab)],[8])).
% 0.13/0.39 tff(10,plain,
% 0.13/0.39 (~(relation_of2_as_subset(D!3, C!4, B!5) | (~relation_of2_as_subset(D!3, C!4, A!6)) | (~subset(A!6, B!5)))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[9, 1])).
% 0.13/0.39 tff(11,plain,
% 0.13/0.39 (relation_of2_as_subset(D!3, C!4, A!6)),
% 0.13/0.39 inference(or_elim,[status(thm)],[10])).
% 0.13/0.39 tff(12,plain,
% 0.13/0.39 (^[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))))))),
% 0.13/0.39 inference(bind,[status(th)],[])).
% 0.13/0.39 tff(13,plain,
% 0.13/0.39 (![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)))))),
% 0.13/0.39 inference(quant_intro,[status(thm)],[12])).
% 0.13/0.39 tff(14,plain,
% 0.13/0.39 (^[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))))))),
% 0.13/0.39 inference(bind,[status(th)],[])).
% 0.13/0.39 tff(15,plain,
% 0.13/0.39 (![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)))))),
% 0.13/0.39 inference(quant_intro,[status(thm)],[14])).
% 0.13/0.39 tff(16,plain,
% 0.13/0.39 (![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)))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(17,plain,
% 0.13/0.39 (^[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))))),
% 0.13/0.39 inference(bind,[status(th)],[])).
% 0.13/0.39 tff(18,plain,
% 0.13/0.39 (![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)))),
% 0.13/0.39 inference(quant_intro,[status(thm)],[17])).
% 0.13/0.39 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/sandbox2/benchmark/theBenchmark.p','t12_relset_1')).
% 0.13/0.39 tff(20,plain,
% 0.13/0.39 (![A: $i, B: $i, C: $i] : ((~relation_of2_as_subset(C, A, B)) | (subset(relation_dom(C), A) & subset(relation_rng(C), B)))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[19, 18])).
% 0.13/0.39 tff(21,plain,
% 0.13/0.39 (![A: $i, B: $i, C: $i] : ((~relation_of2_as_subset(C, A, B)) | (subset(relation_dom(C), A) & subset(relation_rng(C), B)))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[20, 16])).
% 0.13/0.39 tff(22,plain,(
% 0.13/0.39 ![A: $i, B: $i, C: $i] : ((~relation_of2_as_subset(C, A, B)) | (subset(relation_dom(C), A) & subset(relation_rng(C), B)))),
% 0.13/0.39 inference(skolemize,[status(sab)],[21])).
% 0.13/0.39 tff(23,plain,
% 0.13/0.39 (![A: $i, B: $i, C: $i] : ((~relation_of2_as_subset(C, A, B)) | (~((~subset(relation_dom(C), A)) | (~subset(relation_rng(C), B)))))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[22, 15])).
% 0.13/0.39 tff(24,plain,
% 0.13/0.39 (![A: $i, B: $i, C: $i] : ((~relation_of2_as_subset(C, A, B)) | (~((~subset(relation_dom(C), A)) | (~subset(relation_rng(C), B)))))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[23, 13])).
% 0.13/0.39 tff(25,plain,
% 0.13/0.39 (((~![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)))))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(26,plain,
% 0.13/0.39 ((~![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)))))),
% 0.13/0.39 inference(quant_inst,[status(thm)],[])).
% 0.13/0.39 tff(27,plain,
% 0.13/0.39 ((~![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))))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[26, 25])).
% 0.13/0.39 tff(28,plain,
% 0.13/0.39 (~((~subset(relation_dom(D!3), C!4)) | (~subset(relation_rng(D!3), A!6)))),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[27, 24, 11])).
% 0.13/0.39 tff(29,plain,
% 0.13/0.39 (((~subset(relation_dom(D!3), C!4)) | (~subset(relation_rng(D!3), A!6))) | subset(relation_rng(D!3), A!6)),
% 0.13/0.39 inference(tautology,[status(thm)],[])).
% 0.13/0.39 tff(30,plain,
% 0.13/0.39 (subset(relation_rng(D!3), A!6)),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[29, 28])).
% 0.13/0.39 tff(31,plain,
% 0.13/0.39 (~relation_of2_as_subset(D!3, C!4, B!5)),
% 0.13/0.39 inference(or_elim,[status(thm)],[10])).
% 0.13/0.39 tff(32,plain,
% 0.13/0.39 (^[A: $i, B: $i, C: $i, D: $i] : refl((relation_of2_as_subset(D, C, B) | (~subset(relation_rng(D), B)) | (~relation_of2_as_subset(D, C, A))) <=> (relation_of2_as_subset(D, C, B) | (~subset(relation_rng(D), B)) | (~relation_of2_as_subset(D, C, A))))),
% 0.13/0.39 inference(bind,[status(th)],[])).
% 0.13/0.39 tff(33,plain,
% 0.13/0.39 (![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)))),
% 0.13/0.39 inference(quant_intro,[status(thm)],[32])).
% 0.13/0.39 tff(34,plain,
% 0.13/0.39 (![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)))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(35,plain,
% 0.13/0.39 (^[A: $i, B: $i, C: $i, D: $i] : trans(monotonicity(rewrite((subset(relation_rng(D), B) => relation_of2_as_subset(D, C, B)) <=> ((~subset(relation_rng(D), B)) | relation_of2_as_subset(D, C, B))), ((relation_of2_as_subset(D, C, A) => (subset(relation_rng(D), B) => relation_of2_as_subset(D, C, B))) <=> (relation_of2_as_subset(D, C, A) => ((~subset(relation_rng(D), B)) | relation_of2_as_subset(D, C, B))))), rewrite((relation_of2_as_subset(D, C, A) => ((~subset(relation_rng(D), B)) | relation_of2_as_subset(D, C, B))) <=> (relation_of2_as_subset(D, C, B) | (~subset(relation_rng(D), B)) | (~relation_of2_as_subset(D, C, A)))), ((relation_of2_as_subset(D, C, A) => (subset(relation_rng(D), B) => relation_of2_as_subset(D, C, B))) <=> (relation_of2_as_subset(D, C, B) | (~subset(relation_rng(D), B)) | (~relation_of2_as_subset(D, C, A)))))),
% 0.13/0.39 inference(bind,[status(th)],[])).
% 0.13/0.39 tff(36,plain,
% 0.13/0.39 (![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)))),
% 0.13/0.39 inference(quant_intro,[status(thm)],[35])).
% 0.13/0.39 tff(37,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/sandbox2/benchmark/theBenchmark.p','t14_relset_1')).
% 0.13/0.39 tff(38,plain,
% 0.13/0.39 (![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)))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[37, 36])).
% 0.13/0.39 tff(39,plain,
% 0.13/0.39 (![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)))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[38, 34])).
% 0.13/0.39 tff(40,plain,(
% 0.13/0.39 ![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)))),
% 0.13/0.39 inference(skolemize,[status(sab)],[39])).
% 0.13/0.39 tff(41,plain,
% 0.13/0.39 (![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)))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[40, 33])).
% 0.13/0.39 tff(42,plain,
% 0.13/0.39 (((~![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)))) | (relation_of2_as_subset(D!3, C!4, B!5) | (~relation_of2_as_subset(D!3, C!4, A!6)) | (~subset(relation_rng(D!3), B!5)))) <=> ((~![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)))) | relation_of2_as_subset(D!3, C!4, B!5) | (~relation_of2_as_subset(D!3, C!4, A!6)) | (~subset(relation_rng(D!3), B!5)))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(43,plain,
% 0.13/0.39 ((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) | (~relation_of2_as_subset(D!3, C!4, A!6)) | (~subset(relation_rng(D!3), B!5)))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(44,plain,
% 0.13/0.39 (((~![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)))) | (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)))) <=> ((~![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)))) | (relation_of2_as_subset(D!3, C!4, B!5) | (~relation_of2_as_subset(D!3, C!4, A!6)) | (~subset(relation_rng(D!3), B!5))))),
% 0.13/0.40 inference(monotonicity,[status(thm)],[43])).
% 0.13/0.40 tff(45,plain,
% 0.13/0.40 (((~![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)))) | (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)))) <=> ((~![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)))) | relation_of2_as_subset(D!3, C!4, B!5) | (~relation_of2_as_subset(D!3, C!4, A!6)) | (~subset(relation_rng(D!3), B!5)))),
% 0.13/0.40 inference(transitivity,[status(thm)],[44, 42])).
% 0.13/0.40 tff(46,plain,
% 0.13/0.40 ((~![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)))) | (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)))),
% 0.13/0.40 inference(quant_inst,[status(thm)],[])).
% 0.13/0.40 tff(47,plain,
% 0.13/0.40 ((~![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)))) | relation_of2_as_subset(D!3, C!4, B!5) | (~relation_of2_as_subset(D!3, C!4, A!6)) | (~subset(relation_rng(D!3), B!5))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[46, 45])).
% 0.13/0.40 tff(48,plain,
% 0.13/0.40 (~subset(relation_rng(D!3), B!5)),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[47, 41, 31, 11])).
% 0.13/0.40 tff(49,plain,
% 0.13/0.40 (![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)))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(50,plain,
% 0.13/0.40 (^[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)))))),
% 0.13/0.40 inference(bind,[status(th)],[])).
% 0.13/0.40 tff(51,plain,
% 0.13/0.40 (![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)))),
% 0.13/0.40 inference(quant_intro,[status(thm)],[50])).
% 0.13/0.40 tff(52,plain,
% 0.13/0.40 (![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))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(53,plain,
% 0.13/0.40 (^[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)))),
% 0.13/0.40 inference(bind,[status(th)],[])).
% 0.13/0.40 tff(54,plain,
% 0.13/0.40 (![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))),
% 0.13/0.40 inference(quant_intro,[status(thm)],[53])).
% 0.13/0.40 tff(55,axiom,(![A: $i, B: $i, C: $i] : ((subset(A, B) & subset(B, C)) => subset(A, C))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t1_xboole_1')).
% 0.13/0.40 tff(56,plain,
% 0.13/0.40 (![A: $i, B: $i, C: $i] : ((~(subset(A, B) & subset(B, C))) | subset(A, C))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[55, 54])).
% 0.13/0.40 tff(57,plain,
% 0.13/0.40 (![A: $i, B: $i, C: $i] : ((~(subset(A, B) & subset(B, C))) | subset(A, C))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[56, 52])).
% 0.13/0.40 tff(58,plain,(
% 0.13/0.40 ![A: $i, B: $i, C: $i] : ((~(subset(A, B) & subset(B, C))) | subset(A, C))),
% 0.13/0.40 inference(skolemize,[status(sab)],[57])).
% 0.13/0.40 tff(59,plain,
% 0.13/0.40 (![A: $i, B: $i, C: $i] : (subset(A, C) | (~subset(A, B)) | (~subset(B, C)))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[58, 51])).
% 0.13/0.40 tff(60,plain,
% 0.13/0.40 (![A: $i, B: $i, C: $i] : (subset(A, C) | (~subset(A, B)) | (~subset(B, C)))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[59, 49])).
% 0.13/0.40 tff(61,plain,
% 0.13/0.40 (subset(A!6, B!5)),
% 0.13/0.40 inference(or_elim,[status(thm)],[10])).
% 0.13/0.40 tff(62,plain,
% 0.13/0.40 (((~![A: $i, B: $i, C: $i] : (subset(A, C) | (~subset(A, B)) | (~subset(B, C)))) | ((~subset(A!6, B!5)) | subset(relation_rng(D!3), B!5) | (~subset(relation_rng(D!3), A!6)))) <=> ((~![A: $i, B: $i, C: $i] : (subset(A, C) | (~subset(A, B)) | (~subset(B, C)))) | (~subset(A!6, B!5)) | subset(relation_rng(D!3), B!5) | (~subset(relation_rng(D!3), A!6)))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(63,plain,
% 0.13/0.40 ((subset(relation_rng(D!3), B!5) | (~subset(relation_rng(D!3), A!6)) | (~subset(A!6, B!5))) <=> ((~subset(A!6, B!5)) | subset(relation_rng(D!3), B!5) | (~subset(relation_rng(D!3), A!6)))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(64,plain,
% 0.13/0.40 (((~![A: $i, B: $i, C: $i] : (subset(A, C) | (~subset(A, B)) | (~subset(B, C)))) | (subset(relation_rng(D!3), B!5) | (~subset(relation_rng(D!3), A!6)) | (~subset(A!6, B!5)))) <=> ((~![A: $i, B: $i, C: $i] : (subset(A, C) | (~subset(A, B)) | (~subset(B, C)))) | ((~subset(A!6, B!5)) | subset(relation_rng(D!3), B!5) | (~subset(relation_rng(D!3), A!6))))),
% 0.13/0.40 inference(monotonicity,[status(thm)],[63])).
% 0.13/0.40 tff(65,plain,
% 0.13/0.40 (((~![A: $i, B: $i, C: $i] : (subset(A, C) | (~subset(A, B)) | (~subset(B, C)))) | (subset(relation_rng(D!3), B!5) | (~subset(relation_rng(D!3), A!6)) | (~subset(A!6, B!5)))) <=> ((~![A: $i, B: $i, C: $i] : (subset(A, C) | (~subset(A, B)) | (~subset(B, C)))) | (~subset(A!6, B!5)) | subset(relation_rng(D!3), B!5) | (~subset(relation_rng(D!3), A!6)))),
% 0.13/0.40 inference(transitivity,[status(thm)],[64, 62])).
% 0.13/0.40 tff(66,plain,
% 0.13/0.40 ((~![A: $i, B: $i, C: $i] : (subset(A, C) | (~subset(A, B)) | (~subset(B, C)))) | (subset(relation_rng(D!3), B!5) | (~subset(relation_rng(D!3), A!6)) | (~subset(A!6, B!5)))),
% 0.13/0.40 inference(quant_inst,[status(thm)],[])).
% 0.13/0.40 tff(67,plain,
% 0.13/0.40 ((~![A: $i, B: $i, C: $i] : (subset(A, C) | (~subset(A, B)) | (~subset(B, C)))) | (~subset(A!6, B!5)) | subset(relation_rng(D!3), B!5) | (~subset(relation_rng(D!3), A!6))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[66, 65])).
% 0.13/0.40 tff(68,plain,
% 0.13/0.40 ($false),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[67, 61, 60, 48, 30])).
% 0.13/0.40 % SZS output end Proof
% 0.13/0.40 % E exiting
%------------------------------------------------------------------------------