%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SEU196+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 05:27:12 AM UTC 2025
% Result : Theorem 0.12s 0.38s
% Output : Proof 0.12s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SEU196+1 : TPTP v9.0.0. Released v3.3.0.
% 0.11/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n008.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 06:16:18 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.12/0.38 % SZS status Theorem
% 0.12/0.38 % SZS output start Proof
% 0.12/0.38 tff(subset_type, type, (
% 0.12/0.38 subset: ( $i * $i ) > $o)).
% 0.12/0.38 tff(relation_rng_type, type, (
% 0.12/0.38 relation_rng: $i > $i)).
% 0.12/0.38 tff(tptp_fun_B_7_type, type, (
% 0.12/0.38 tptp_fun_B_7: $i)).
% 0.12/0.38 tff(relation_dom_restriction_type, type, (
% 0.12/0.38 relation_dom_restriction: ( $i * $i ) > $i)).
% 0.12/0.38 tff(tptp_fun_A_8_type, type, (
% 0.12/0.38 tptp_fun_A_8: $i)).
% 0.12/0.38 tff(relation_dom_type, type, (
% 0.12/0.38 relation_dom: $i > $i)).
% 0.12/0.38 tff(relation_type, type, (
% 0.12/0.38 relation: $i > $o)).
% 0.12/0.38 tff(1,plain,
% 0.12/0.38 ((~![A: $i, B: $i] : ((~relation(B)) | subset(relation_rng(relation_dom_restriction(B, A)), relation_rng(B)))) <=> (~![A: $i, B: $i] : ((~relation(B)) | subset(relation_rng(relation_dom_restriction(B, A)), relation_rng(B))))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(2,plain,
% 0.12/0.38 ((~![A: $i, B: $i] : (relation(B) => subset(relation_rng(relation_dom_restriction(B, A)), relation_rng(B)))) <=> (~![A: $i, B: $i] : ((~relation(B)) | subset(relation_rng(relation_dom_restriction(B, A)), relation_rng(B))))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(3,axiom,(~![A: $i, B: $i] : (relation(B) => subset(relation_rng(relation_dom_restriction(B, A)), relation_rng(B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t99_relat_1')).
% 0.12/0.38 tff(4,plain,
% 0.12/0.38 (~![A: $i, B: $i] : ((~relation(B)) | subset(relation_rng(relation_dom_restriction(B, A)), relation_rng(B)))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[3, 2])).
% 0.12/0.38 tff(5,plain,
% 0.12/0.38 (~![A: $i, B: $i] : ((~relation(B)) | subset(relation_rng(relation_dom_restriction(B, A)), relation_rng(B)))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[4, 1])).
% 0.12/0.38 tff(6,plain,
% 0.12/0.38 (~![A: $i, B: $i] : ((~relation(B)) | subset(relation_rng(relation_dom_restriction(B, A)), relation_rng(B)))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[5, 1])).
% 0.12/0.38 tff(7,plain,
% 0.12/0.38 (~![A: $i, B: $i] : ((~relation(B)) | subset(relation_rng(relation_dom_restriction(B, A)), relation_rng(B)))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[6, 1])).
% 0.12/0.38 tff(8,plain,(
% 0.12/0.38 ~((~relation(B!7)) | subset(relation_rng(relation_dom_restriction(B!7, A!8)), relation_rng(B!7)))),
% 0.12/0.38 inference(skolemize,[status(sab)],[7])).
% 0.12/0.38 tff(9,plain,
% 0.12/0.38 (~subset(relation_rng(relation_dom_restriction(B!7, A!8)), relation_rng(B!7))),
% 0.12/0.38 inference(or_elim,[status(thm)],[8])).
% 0.12/0.38 tff(10,plain,
% 0.12/0.38 (((~subset(relation_dom(relation_dom_restriction(B!7, A!8)), relation_dom(B!7))) | (~subset(relation_rng(relation_dom_restriction(B!7, A!8)), relation_rng(B!7)))) | subset(relation_rng(relation_dom_restriction(B!7, A!8)), relation_rng(B!7))),
% 0.12/0.38 inference(tautology,[status(thm)],[])).
% 0.12/0.38 tff(11,plain,
% 0.12/0.38 ((~subset(relation_dom(relation_dom_restriction(B!7, A!8)), relation_dom(B!7))) | (~subset(relation_rng(relation_dom_restriction(B!7, A!8)), relation_rng(B!7)))),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[10, 9])).
% 0.12/0.38 tff(12,plain,
% 0.12/0.38 (relation(B!7)),
% 0.12/0.38 inference(or_elim,[status(thm)],[8])).
% 0.12/0.38 tff(13,plain,
% 0.12/0.38 (^[A: $i, B: $i] : refl(((~relation(A)) | relation(relation_dom_restriction(A, B))) <=> ((~relation(A)) | relation(relation_dom_restriction(A, B))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(14,plain,
% 0.12/0.38 (![A: $i, B: $i] : ((~relation(A)) | relation(relation_dom_restriction(A, B))) <=> ![A: $i, B: $i] : ((~relation(A)) | relation(relation_dom_restriction(A, B)))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[13])).
% 0.12/0.38 tff(15,plain,
% 0.12/0.38 (![A: $i, B: $i] : ((~relation(A)) | relation(relation_dom_restriction(A, B))) <=> ![A: $i, B: $i] : ((~relation(A)) | relation(relation_dom_restriction(A, B)))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(16,plain,
% 0.12/0.38 (^[A: $i, B: $i] : rewrite((relation(A) => relation(relation_dom_restriction(A, B))) <=> ((~relation(A)) | relation(relation_dom_restriction(A, B))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(17,plain,
% 0.12/0.38 (![A: $i, B: $i] : (relation(A) => relation(relation_dom_restriction(A, B))) <=> ![A: $i, B: $i] : ((~relation(A)) | relation(relation_dom_restriction(A, B)))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[16])).
% 0.12/0.38 tff(18,axiom,(![A: $i, B: $i] : (relation(A) => relation(relation_dom_restriction(A, B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_k7_relat_1')).
% 0.12/0.38 tff(19,plain,
% 0.12/0.38 (![A: $i, B: $i] : ((~relation(A)) | relation(relation_dom_restriction(A, B)))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[18, 17])).
% 0.12/0.38 tff(20,plain,
% 0.12/0.38 (![A: $i, B: $i] : ((~relation(A)) | relation(relation_dom_restriction(A, B)))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[19, 15])).
% 0.12/0.38 tff(21,plain,(
% 0.12/0.38 ![A: $i, B: $i] : ((~relation(A)) | relation(relation_dom_restriction(A, B)))),
% 0.12/0.38 inference(skolemize,[status(sab)],[20])).
% 0.12/0.38 tff(22,plain,
% 0.12/0.38 (![A: $i, B: $i] : ((~relation(A)) | relation(relation_dom_restriction(A, B)))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[21, 14])).
% 0.12/0.38 tff(23,plain,
% 0.12/0.38 (((~![A: $i, B: $i] : ((~relation(A)) | relation(relation_dom_restriction(A, B)))) | ((~relation(B!7)) | relation(relation_dom_restriction(B!7, A!8)))) <=> ((~![A: $i, B: $i] : ((~relation(A)) | relation(relation_dom_restriction(A, B)))) | (~relation(B!7)) | relation(relation_dom_restriction(B!7, A!8)))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(24,plain,
% 0.12/0.38 ((~![A: $i, B: $i] : ((~relation(A)) | relation(relation_dom_restriction(A, B)))) | ((~relation(B!7)) | relation(relation_dom_restriction(B!7, A!8)))),
% 0.12/0.38 inference(quant_inst,[status(thm)],[])).
% 0.12/0.38 tff(25,plain,
% 0.12/0.38 ((~![A: $i, B: $i] : ((~relation(A)) | relation(relation_dom_restriction(A, B)))) | (~relation(B!7)) | relation(relation_dom_restriction(B!7, A!8))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[24, 23])).
% 0.12/0.38 tff(26,plain,
% 0.12/0.38 (relation(relation_dom_restriction(B!7, A!8))),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[25, 22, 12])).
% 0.12/0.38 tff(27,plain,
% 0.12/0.38 (^[A: $i] : refl(((~relation(A)) | ![B: $i] : ((~subset(A, B)) | (~relation(B)) | (~((~subset(relation_dom(A), relation_dom(B))) | (~subset(relation_rng(A), relation_rng(B))))))) <=> ((~relation(A)) | ![B: $i] : ((~subset(A, B)) | (~relation(B)) | (~((~subset(relation_dom(A), relation_dom(B))) | (~subset(relation_rng(A), relation_rng(B))))))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(28,plain,
% 0.12/0.38 (![A: $i] : ((~relation(A)) | ![B: $i] : ((~subset(A, B)) | (~relation(B)) | (~((~subset(relation_dom(A), relation_dom(B))) | (~subset(relation_rng(A), relation_rng(B))))))) <=> ![A: $i] : ((~relation(A)) | ![B: $i] : ((~subset(A, B)) | (~relation(B)) | (~((~subset(relation_dom(A), relation_dom(B))) | (~subset(relation_rng(A), relation_rng(B)))))))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[27])).
% 0.12/0.38 tff(29,plain,
% 0.12/0.38 (^[A: $i] : rewrite(((~relation(A)) | ![B: $i] : ((~subset(A, B)) | (~relation(B)) | (~((~subset(relation_dom(A), relation_dom(B))) | (~subset(relation_rng(A), relation_rng(B))))))) <=> ((~relation(A)) | ![B: $i] : ((~subset(A, B)) | (~relation(B)) | (~((~subset(relation_dom(A), relation_dom(B))) | (~subset(relation_rng(A), relation_rng(B))))))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(30,plain,
% 0.12/0.38 (![A: $i] : ((~relation(A)) | ![B: $i] : ((~subset(A, B)) | (~relation(B)) | (~((~subset(relation_dom(A), relation_dom(B))) | (~subset(relation_rng(A), relation_rng(B))))))) <=> ![A: $i] : ((~relation(A)) | ![B: $i] : ((~subset(A, B)) | (~relation(B)) | (~((~subset(relation_dom(A), relation_dom(B))) | (~subset(relation_rng(A), relation_rng(B)))))))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[29])).
% 0.12/0.38 tff(31,plain,
% 0.12/0.38 (![A: $i] : ((~relation(A)) | ![B: $i] : ((~subset(A, B)) | (~relation(B)) | (~((~subset(relation_dom(A), relation_dom(B))) | (~subset(relation_rng(A), relation_rng(B))))))) <=> ![A: $i] : ((~relation(A)) | ![B: $i] : ((~subset(A, B)) | (~relation(B)) | (~((~subset(relation_dom(A), relation_dom(B))) | (~subset(relation_rng(A), relation_rng(B)))))))),
% 0.12/0.38 inference(transitivity,[status(thm)],[30, 28])).
% 0.12/0.38 tff(32,plain,
% 0.12/0.38 (^[A: $i] : rewrite(((~relation(A)) | ![B: $i] : ((subset(relation_dom(A), relation_dom(B)) & subset(relation_rng(A), relation_rng(B))) | (~subset(A, B)) | (~relation(B)))) <=> ((~relation(A)) | ![B: $i] : ((~subset(A, B)) | (~relation(B)) | (~((~subset(relation_dom(A), relation_dom(B))) | (~subset(relation_rng(A), relation_rng(B))))))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(33,plain,
% 0.12/0.38 (![A: $i] : ((~relation(A)) | ![B: $i] : ((subset(relation_dom(A), relation_dom(B)) & subset(relation_rng(A), relation_rng(B))) | (~subset(A, B)) | (~relation(B)))) <=> ![A: $i] : ((~relation(A)) | ![B: $i] : ((~subset(A, B)) | (~relation(B)) | (~((~subset(relation_dom(A), relation_dom(B))) | (~subset(relation_rng(A), relation_rng(B)))))))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[32])).
% 0.12/0.38 tff(34,plain,
% 0.12/0.38 (![A: $i] : ((~relation(A)) | ![B: $i] : ((subset(relation_dom(A), relation_dom(B)) & subset(relation_rng(A), relation_rng(B))) | (~subset(A, B)) | (~relation(B)))) <=> ![A: $i] : ((~relation(A)) | ![B: $i] : ((subset(relation_dom(A), relation_dom(B)) & subset(relation_rng(A), relation_rng(B))) | (~subset(A, B)) | (~relation(B))))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(35,plain,
% 0.12/0.38 (^[A: $i] : trans(monotonicity(quant_intro(proof_bind(^[B: $i] : trans(monotonicity(rewrite((subset(A, B) => (subset(relation_dom(A), relation_dom(B)) & subset(relation_rng(A), relation_rng(B)))) <=> ((~subset(A, B)) | (subset(relation_dom(A), relation_dom(B)) & subset(relation_rng(A), relation_rng(B))))), ((relation(B) => (subset(A, B) => (subset(relation_dom(A), relation_dom(B)) & subset(relation_rng(A), relation_rng(B))))) <=> (relation(B) => ((~subset(A, B)) | (subset(relation_dom(A), relation_dom(B)) & subset(relation_rng(A), relation_rng(B))))))), rewrite((relation(B) => ((~subset(A, B)) | (subset(relation_dom(A), relation_dom(B)) & subset(relation_rng(A), relation_rng(B))))) <=> ((subset(relation_dom(A), relation_dom(B)) & subset(relation_rng(A), relation_rng(B))) | (~subset(A, B)) | (~relation(B)))), ((relation(B) => (subset(A, B) => (subset(relation_dom(A), relation_dom(B)) & subset(relation_rng(A), relation_rng(B))))) <=> ((subset(relation_dom(A), relation_dom(B)) & subset(relation_rng(A), relation_rng(B))) | (~subset(A, B)) | (~relation(B)))))), (![B: $i] : (relation(B) => (subset(A, B) => (subset(relation_dom(A), relation_dom(B)) & subset(relation_rng(A), relation_rng(B))))) <=> ![B: $i] : ((subset(relation_dom(A), relation_dom(B)) & subset(relation_rng(A), relation_rng(B))) | (~subset(A, B)) | (~relation(B))))), ((relation(A) => ![B: $i] : (relation(B) => (subset(A, B) => (subset(relation_dom(A), relation_dom(B)) & subset(relation_rng(A), relation_rng(B)))))) <=> (relation(A) => ![B: $i] : ((subset(relation_dom(A), relation_dom(B)) & subset(relation_rng(A), relation_rng(B))) | (~subset(A, B)) | (~relation(B)))))), rewrite((relation(A) => ![B: $i] : ((subset(relation_dom(A), relation_dom(B)) & subset(relation_rng(A), relation_rng(B))) | (~subset(A, B)) | (~relation(B)))) <=> ((~relation(A)) | ![B: $i] : ((subset(relation_dom(A), relation_dom(B)) & subset(relation_rng(A), relation_rng(B))) | (~subset(A, B)) | (~relation(B))))), ((relation(A) => ![B: $i] : (relation(B) => (subset(A, B) => (subset(relation_dom(A), relation_dom(B)) & subset(relation_rng(A), relation_rng(B)))))) <=> ((~relation(A)) | ![B: $i] : ((subset(relation_dom(A), relation_dom(B)) & subset(relation_rng(A), relation_rng(B))) | (~subset(A, B)) | (~relation(B))))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(36,plain,
% 0.12/0.38 (![A: $i] : (relation(A) => ![B: $i] : (relation(B) => (subset(A, B) => (subset(relation_dom(A), relation_dom(B)) & subset(relation_rng(A), relation_rng(B)))))) <=> ![A: $i] : ((~relation(A)) | ![B: $i] : ((subset(relation_dom(A), relation_dom(B)) & subset(relation_rng(A), relation_rng(B))) | (~subset(A, B)) | (~relation(B))))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[35])).
% 0.12/0.38 tff(37,axiom,(![A: $i] : (relation(A) => ![B: $i] : (relation(B) => (subset(A, B) => (subset(relation_dom(A), relation_dom(B)) & subset(relation_rng(A), relation_rng(B))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t25_relat_1')).
% 0.12/0.38 tff(38,plain,
% 0.12/0.38 (![A: $i] : ((~relation(A)) | ![B: $i] : ((subset(relation_dom(A), relation_dom(B)) & subset(relation_rng(A), relation_rng(B))) | (~subset(A, B)) | (~relation(B))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[37, 36])).
% 0.12/0.38 tff(39,plain,
% 0.12/0.38 (![A: $i] : ((~relation(A)) | ![B: $i] : ((subset(relation_dom(A), relation_dom(B)) & subset(relation_rng(A), relation_rng(B))) | (~subset(A, B)) | (~relation(B))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[38, 34])).
% 0.12/0.38 tff(40,plain,(
% 0.12/0.38 ![A: $i] : ((~relation(A)) | ![B: $i] : ((subset(relation_dom(A), relation_dom(B)) & subset(relation_rng(A), relation_rng(B))) | (~subset(A, B)) | (~relation(B))))),
% 0.12/0.38 inference(skolemize,[status(sab)],[39])).
% 0.12/0.38 tff(41,plain,
% 0.12/0.38 (![A: $i] : ((~relation(A)) | ![B: $i] : ((~subset(A, B)) | (~relation(B)) | (~((~subset(relation_dom(A), relation_dom(B))) | (~subset(relation_rng(A), relation_rng(B)))))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[40, 33])).
% 0.12/0.38 tff(42,plain,
% 0.12/0.38 (![A: $i] : ((~relation(A)) | ![B: $i] : ((~subset(A, B)) | (~relation(B)) | (~((~subset(relation_dom(A), relation_dom(B))) | (~subset(relation_rng(A), relation_rng(B)))))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[41, 31])).
% 0.12/0.38 tff(43,plain,
% 0.12/0.38 (((~![A: $i] : ((~relation(A)) | ![B: $i] : ((~subset(A, B)) | (~relation(B)) | (~((~subset(relation_dom(A), relation_dom(B))) | (~subset(relation_rng(A), relation_rng(B)))))))) | ((~relation(relation_dom_restriction(B!7, A!8))) | ![B: $i] : ((~relation(B)) | (~subset(relation_dom_restriction(B!7, A!8), B)) | (~((~subset(relation_dom(relation_dom_restriction(B!7, A!8)), relation_dom(B))) | (~subset(relation_rng(relation_dom_restriction(B!7, A!8)), relation_rng(B)))))))) <=> ((~![A: $i] : ((~relation(A)) | ![B: $i] : ((~subset(A, B)) | (~relation(B)) | (~((~subset(relation_dom(A), relation_dom(B))) | (~subset(relation_rng(A), relation_rng(B)))))))) | (~relation(relation_dom_restriction(B!7, A!8))) | ![B: $i] : ((~relation(B)) | (~subset(relation_dom_restriction(B!7, A!8), B)) | (~((~subset(relation_dom(relation_dom_restriction(B!7, A!8)), relation_dom(B))) | (~subset(relation_rng(relation_dom_restriction(B!7, A!8)), relation_rng(B)))))))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(44,plain,
% 0.12/0.38 (((~relation(relation_dom_restriction(B!7, A!8))) | ![B: $i] : ((~subset(relation_dom_restriction(B!7, A!8), B)) | (~relation(B)) | (~((~subset(relation_dom(relation_dom_restriction(B!7, A!8)), relation_dom(B))) | (~subset(relation_rng(relation_dom_restriction(B!7, A!8)), relation_rng(B))))))) <=> ((~relation(relation_dom_restriction(B!7, A!8))) | ![B: $i] : ((~relation(B)) | (~subset(relation_dom_restriction(B!7, A!8), B)) | (~((~subset(relation_dom(relation_dom_restriction(B!7, A!8)), relation_dom(B))) | (~subset(relation_rng(relation_dom_restriction(B!7, A!8)), relation_rng(B)))))))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(45,plain,
% 0.12/0.38 (((~![A: $i] : ((~relation(A)) | ![B: $i] : ((~subset(A, B)) | (~relation(B)) | (~((~subset(relation_dom(A), relation_dom(B))) | (~subset(relation_rng(A), relation_rng(B)))))))) | ((~relation(relation_dom_restriction(B!7, A!8))) | ![B: $i] : ((~subset(relation_dom_restriction(B!7, A!8), B)) | (~relation(B)) | (~((~subset(relation_dom(relation_dom_restriction(B!7, A!8)), relation_dom(B))) | (~subset(relation_rng(relation_dom_restriction(B!7, A!8)), relation_rng(B)))))))) <=> ((~![A: $i] : ((~relation(A)) | ![B: $i] : ((~subset(A, B)) | (~relation(B)) | (~((~subset(relation_dom(A), relation_dom(B))) | (~subset(relation_rng(A), relation_rng(B)))))))) | ((~relation(relation_dom_restriction(B!7, A!8))) | ![B: $i] : ((~relation(B)) | (~subset(relation_dom_restriction(B!7, A!8), B)) | (~((~subset(relation_dom(relation_dom_restriction(B!7, A!8)), relation_dom(B))) | (~subset(relation_rng(relation_dom_restriction(B!7, A!8)), relation_rng(B))))))))),
% 0.12/0.38 inference(monotonicity,[status(thm)],[44])).
% 0.12/0.38 tff(46,plain,
% 0.12/0.38 (((~![A: $i] : ((~relation(A)) | ![B: $i] : ((~subset(A, B)) | (~relation(B)) | (~((~subset(relation_dom(A), relation_dom(B))) | (~subset(relation_rng(A), relation_rng(B)))))))) | ((~relation(relation_dom_restriction(B!7, A!8))) | ![B: $i] : ((~subset(relation_dom_restriction(B!7, A!8), B)) | (~relation(B)) | (~((~subset(relation_dom(relation_dom_restriction(B!7, A!8)), relation_dom(B))) | (~subset(relation_rng(relation_dom_restriction(B!7, A!8)), relation_rng(B)))))))) <=> ((~![A: $i] : ((~relation(A)) | ![B: $i] : ((~subset(A, B)) | (~relation(B)) | (~((~subset(relation_dom(A), relation_dom(B))) | (~subset(relation_rng(A), relation_rng(B)))))))) | (~relation(relation_dom_restriction(B!7, A!8))) | ![B: $i] : ((~relation(B)) | (~subset(relation_dom_restriction(B!7, A!8), B)) | (~((~subset(relation_dom(relation_dom_restriction(B!7, A!8)), relation_dom(B))) | (~subset(relation_rng(relation_dom_restriction(B!7, A!8)), relation_rng(B)))))))),
% 0.12/0.38 inference(transitivity,[status(thm)],[45, 43])).
% 0.12/0.38 tff(47,plain,
% 0.12/0.38 ((~![A: $i] : ((~relation(A)) | ![B: $i] : ((~subset(A, B)) | (~relation(B)) | (~((~subset(relation_dom(A), relation_dom(B))) | (~subset(relation_rng(A), relation_rng(B)))))))) | ((~relation(relation_dom_restriction(B!7, A!8))) | ![B: $i] : ((~subset(relation_dom_restriction(B!7, A!8), B)) | (~relation(B)) | (~((~subset(relation_dom(relation_dom_restriction(B!7, A!8)), relation_dom(B))) | (~subset(relation_rng(relation_dom_restriction(B!7, A!8)), relation_rng(B)))))))),
% 0.12/0.38 inference(quant_inst,[status(thm)],[])).
% 0.12/0.38 tff(48,plain,
% 0.12/0.38 ((~![A: $i] : ((~relation(A)) | ![B: $i] : ((~subset(A, B)) | (~relation(B)) | (~((~subset(relation_dom(A), relation_dom(B))) | (~subset(relation_rng(A), relation_rng(B)))))))) | (~relation(relation_dom_restriction(B!7, A!8))) | ![B: $i] : ((~relation(B)) | (~subset(relation_dom_restriction(B!7, A!8), B)) | (~((~subset(relation_dom(relation_dom_restriction(B!7, A!8)), relation_dom(B))) | (~subset(relation_rng(relation_dom_restriction(B!7, A!8)), relation_rng(B))))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[47, 46])).
% 0.12/0.38 tff(49,plain,
% 0.12/0.38 (![B: $i] : ((~relation(B)) | (~subset(relation_dom_restriction(B!7, A!8), B)) | (~((~subset(relation_dom(relation_dom_restriction(B!7, A!8)), relation_dom(B))) | (~subset(relation_rng(relation_dom_restriction(B!7, A!8)), relation_rng(B))))))),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[48, 42, 26])).
% 0.12/0.38 tff(50,plain,
% 0.12/0.38 (^[A: $i, B: $i] : refl(((~relation(B)) | subset(relation_dom_restriction(B, A), B)) <=> ((~relation(B)) | subset(relation_dom_restriction(B, A), B)))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(51,plain,
% 0.12/0.38 (![A: $i, B: $i] : ((~relation(B)) | subset(relation_dom_restriction(B, A), B)) <=> ![A: $i, B: $i] : ((~relation(B)) | subset(relation_dom_restriction(B, A), B))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[50])).
% 0.12/0.38 tff(52,plain,
% 0.12/0.38 (![A: $i, B: $i] : ((~relation(B)) | subset(relation_dom_restriction(B, A), B)) <=> ![A: $i, B: $i] : ((~relation(B)) | subset(relation_dom_restriction(B, A), B))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(53,plain,
% 0.12/0.38 (^[A: $i, B: $i] : rewrite((relation(B) => subset(relation_dom_restriction(B, A), B)) <=> ((~relation(B)) | subset(relation_dom_restriction(B, A), B)))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(54,plain,
% 0.12/0.38 (![A: $i, B: $i] : (relation(B) => subset(relation_dom_restriction(B, A), B)) <=> ![A: $i, B: $i] : ((~relation(B)) | subset(relation_dom_restriction(B, A), B))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[53])).
% 0.12/0.38 tff(55,axiom,(![A: $i, B: $i] : (relation(B) => subset(relation_dom_restriction(B, A), B))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t88_relat_1')).
% 0.12/0.38 tff(56,plain,
% 0.12/0.38 (![A: $i, B: $i] : ((~relation(B)) | subset(relation_dom_restriction(B, A), B))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[55, 54])).
% 0.12/0.38 tff(57,plain,
% 0.12/0.38 (![A: $i, B: $i] : ((~relation(B)) | subset(relation_dom_restriction(B, A), B))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[56, 52])).
% 0.12/0.38 tff(58,plain,(
% 0.12/0.38 ![A: $i, B: $i] : ((~relation(B)) | subset(relation_dom_restriction(B, A), B))),
% 0.12/0.38 inference(skolemize,[status(sab)],[57])).
% 0.12/0.38 tff(59,plain,
% 0.12/0.38 (![A: $i, B: $i] : ((~relation(B)) | subset(relation_dom_restriction(B, A), B))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[58, 51])).
% 0.12/0.38 tff(60,plain,
% 0.12/0.38 (((~![A: $i, B: $i] : ((~relation(B)) | subset(relation_dom_restriction(B, A), B))) | ((~relation(B!7)) | subset(relation_dom_restriction(B!7, A!8), B!7))) <=> ((~![A: $i, B: $i] : ((~relation(B)) | subset(relation_dom_restriction(B, A), B))) | (~relation(B!7)) | subset(relation_dom_restriction(B!7, A!8), B!7))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(61,plain,
% 0.12/0.39 ((~![A: $i, B: $i] : ((~relation(B)) | subset(relation_dom_restriction(B, A), B))) | ((~relation(B!7)) | subset(relation_dom_restriction(B!7, A!8), B!7))),
% 0.12/0.39 inference(quant_inst,[status(thm)],[])).
% 0.12/0.39 tff(62,plain,
% 0.12/0.39 ((~![A: $i, B: $i] : ((~relation(B)) | subset(relation_dom_restriction(B, A), B))) | (~relation(B!7)) | subset(relation_dom_restriction(B!7, A!8), B!7)),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[61, 60])).
% 0.12/0.39 tff(63,plain,
% 0.12/0.39 (subset(relation_dom_restriction(B!7, A!8), B!7)),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[62, 59, 12])).
% 0.12/0.39 tff(64,plain,
% 0.12/0.39 (((~![B: $i] : ((~relation(B)) | (~subset(relation_dom_restriction(B!7, A!8), B)) | (~((~subset(relation_dom(relation_dom_restriction(B!7, A!8)), relation_dom(B))) | (~subset(relation_rng(relation_dom_restriction(B!7, A!8)), relation_rng(B))))))) | ((~relation(B!7)) | (~subset(relation_dom_restriction(B!7, A!8), B!7)) | (~((~subset(relation_dom(relation_dom_restriction(B!7, A!8)), relation_dom(B!7))) | (~subset(relation_rng(relation_dom_restriction(B!7, A!8)), relation_rng(B!7))))))) <=> ((~![B: $i] : ((~relation(B)) | (~subset(relation_dom_restriction(B!7, A!8), B)) | (~((~subset(relation_dom(relation_dom_restriction(B!7, A!8)), relation_dom(B))) | (~subset(relation_rng(relation_dom_restriction(B!7, A!8)), relation_rng(B))))))) | (~relation(B!7)) | (~subset(relation_dom_restriction(B!7, A!8), B!7)) | (~((~subset(relation_dom(relation_dom_restriction(B!7, A!8)), relation_dom(B!7))) | (~subset(relation_rng(relation_dom_restriction(B!7, A!8)), relation_rng(B!7))))))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(65,plain,
% 0.12/0.39 ((~![B: $i] : ((~relation(B)) | (~subset(relation_dom_restriction(B!7, A!8), B)) | (~((~subset(relation_dom(relation_dom_restriction(B!7, A!8)), relation_dom(B))) | (~subset(relation_rng(relation_dom_restriction(B!7, A!8)), relation_rng(B))))))) | ((~relation(B!7)) | (~subset(relation_dom_restriction(B!7, A!8), B!7)) | (~((~subset(relation_dom(relation_dom_restriction(B!7, A!8)), relation_dom(B!7))) | (~subset(relation_rng(relation_dom_restriction(B!7, A!8)), relation_rng(B!7))))))),
% 0.12/0.39 inference(quant_inst,[status(thm)],[])).
% 0.12/0.39 tff(66,plain,
% 0.12/0.39 ((~![B: $i] : ((~relation(B)) | (~subset(relation_dom_restriction(B!7, A!8), B)) | (~((~subset(relation_dom(relation_dom_restriction(B!7, A!8)), relation_dom(B))) | (~subset(relation_rng(relation_dom_restriction(B!7, A!8)), relation_rng(B))))))) | (~relation(B!7)) | (~subset(relation_dom_restriction(B!7, A!8), B!7)) | (~((~subset(relation_dom(relation_dom_restriction(B!7, A!8)), relation_dom(B!7))) | (~subset(relation_rng(relation_dom_restriction(B!7, A!8)), relation_rng(B!7)))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[65, 64])).
% 0.12/0.39 tff(67,plain,
% 0.12/0.39 ($false),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[66, 12, 63, 49, 11])).
% 0.12/0.39 % SZS output end Proof
% 0.12/0.39 % E exiting
%------------------------------------------------------------------------------