%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SEU196+2 : TPTP v9.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n010.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 0.19s 0.46s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SEU196+2 : TPTP v9.0.0. Released v3.3.0.
% 0.11/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n010.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 06:17:56 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.19/0.46 % SZS status Theorem
% 0.19/0.46 % SZS output start Proof
% 0.19/0.46 tff(subset_type, type, (
% 0.19/0.46 subset: ( $i * $i ) > $o)).
% 0.19/0.46 tff(relation_rng_type, type, (
% 0.19/0.46 relation_rng: $i > $i)).
% 0.19/0.46 tff(tptp_fun_B_56_type, type, (
% 0.19/0.46 tptp_fun_B_56: $i)).
% 0.19/0.46 tff(relation_dom_restriction_type, type, (
% 0.19/0.46 relation_dom_restriction: ( $i * $i ) > $i)).
% 0.19/0.46 tff(tptp_fun_A_57_type, type, (
% 0.19/0.46 tptp_fun_A_57: $i)).
% 0.19/0.46 tff(relation_dom_type, type, (
% 0.19/0.46 relation_dom: $i > $i)).
% 0.19/0.46 tff(relation_type, type, (
% 0.19/0.46 relation: $i > $o)).
% 0.19/0.46 tff(1,plain,
% 0.19/0.46 ((~![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))))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(2,plain,
% 0.19/0.46 ((~![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))))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 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')).
% 0.19/0.46 tff(4,plain,
% 0.19/0.46 (~![A: $i, B: $i] : ((~relation(B)) | subset(relation_rng(relation_dom_restriction(B, A)), relation_rng(B)))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[3, 2])).
% 0.19/0.46 tff(5,plain,
% 0.19/0.46 (~![A: $i, B: $i] : ((~relation(B)) | subset(relation_rng(relation_dom_restriction(B, A)), relation_rng(B)))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[4, 1])).
% 0.19/0.46 tff(6,plain,
% 0.19/0.46 (~![A: $i, B: $i] : ((~relation(B)) | subset(relation_rng(relation_dom_restriction(B, A)), relation_rng(B)))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[5, 1])).
% 0.19/0.46 tff(7,plain,
% 0.19/0.46 (~![A: $i, B: $i] : ((~relation(B)) | subset(relation_rng(relation_dom_restriction(B, A)), relation_rng(B)))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[6, 1])).
% 0.19/0.46 tff(8,plain,(
% 0.19/0.46 ~((~relation(B!56)) | subset(relation_rng(relation_dom_restriction(B!56, A!57)), relation_rng(B!56)))),
% 0.19/0.46 inference(skolemize,[status(sab)],[7])).
% 0.19/0.46 tff(9,plain,
% 0.19/0.46 (~subset(relation_rng(relation_dom_restriction(B!56, A!57)), relation_rng(B!56))),
% 0.19/0.46 inference(or_elim,[status(thm)],[8])).
% 0.19/0.46 tff(10,plain,
% 0.19/0.46 (((~subset(relation_dom(relation_dom_restriction(B!56, A!57)), relation_dom(B!56))) | (~subset(relation_rng(relation_dom_restriction(B!56, A!57)), relation_rng(B!56)))) | subset(relation_rng(relation_dom_restriction(B!56, A!57)), relation_rng(B!56))),
% 0.19/0.46 inference(tautology,[status(thm)],[])).
% 0.19/0.46 tff(11,plain,
% 0.19/0.46 ((~subset(relation_dom(relation_dom_restriction(B!56, A!57)), relation_dom(B!56))) | (~subset(relation_rng(relation_dom_restriction(B!56, A!57)), relation_rng(B!56)))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[10, 9])).
% 0.19/0.46 tff(12,plain,
% 0.19/0.46 (relation(B!56)),
% 0.19/0.46 inference(or_elim,[status(thm)],[8])).
% 0.19/0.46 tff(13,plain,
% 0.19/0.46 (^[A: $i, B: $i] : refl(((~relation(B)) | subset(relation_dom_restriction(B, A), B)) <=> ((~relation(B)) | subset(relation_dom_restriction(B, A), B)))),
% 0.19/0.46 inference(bind,[status(th)],[])).
% 0.19/0.46 tff(14,plain,
% 0.19/0.46 (![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))),
% 0.19/0.46 inference(quant_intro,[status(thm)],[13])).
% 0.19/0.46 tff(15,plain,
% 0.19/0.46 (![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))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(16,plain,
% 0.19/0.46 (^[A: $i, B: $i] : rewrite((relation(B) => subset(relation_dom_restriction(B, A), B)) <=> ((~relation(B)) | subset(relation_dom_restriction(B, A), B)))),
% 0.19/0.46 inference(bind,[status(th)],[])).
% 0.19/0.46 tff(17,plain,
% 0.19/0.46 (![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))),
% 0.19/0.46 inference(quant_intro,[status(thm)],[16])).
% 0.19/0.46 tff(18,axiom,(![A: $i, B: $i] : (relation(B) => subset(relation_dom_restriction(B, A), B))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t88_relat_1')).
% 0.19/0.46 tff(19,plain,
% 0.19/0.46 (![A: $i, B: $i] : ((~relation(B)) | subset(relation_dom_restriction(B, A), B))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[18, 17])).
% 0.19/0.46 tff(20,plain,
% 0.19/0.46 (![A: $i, B: $i] : ((~relation(B)) | subset(relation_dom_restriction(B, A), B))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[19, 15])).
% 0.19/0.46 tff(21,plain,(
% 0.19/0.46 ![A: $i, B: $i] : ((~relation(B)) | subset(relation_dom_restriction(B, A), B))),
% 0.19/0.46 inference(skolemize,[status(sab)],[20])).
% 0.19/0.46 tff(22,plain,
% 0.19/0.46 (![A: $i, B: $i] : ((~relation(B)) | subset(relation_dom_restriction(B, A), B))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[21, 14])).
% 0.19/0.46 tff(23,plain,
% 0.19/0.46 (((~![A: $i, B: $i] : ((~relation(B)) | subset(relation_dom_restriction(B, A), B))) | ((~relation(B!56)) | subset(relation_dom_restriction(B!56, A!57), B!56))) <=> ((~![A: $i, B: $i] : ((~relation(B)) | subset(relation_dom_restriction(B, A), B))) | (~relation(B!56)) | subset(relation_dom_restriction(B!56, A!57), B!56))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(24,plain,
% 0.19/0.46 ((~![A: $i, B: $i] : ((~relation(B)) | subset(relation_dom_restriction(B, A), B))) | ((~relation(B!56)) | subset(relation_dom_restriction(B!56, A!57), B!56))),
% 0.19/0.46 inference(quant_inst,[status(thm)],[])).
% 0.19/0.46 tff(25,plain,
% 0.19/0.46 ((~![A: $i, B: $i] : ((~relation(B)) | subset(relation_dom_restriction(B, A), B))) | (~relation(B!56)) | subset(relation_dom_restriction(B!56, A!57), B!56)),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[24, 23])).
% 0.19/0.46 tff(26,plain,
% 0.19/0.46 (subset(relation_dom_restriction(B!56, A!57), B!56)),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[25, 22, 12])).
% 0.19/0.46 tff(27,plain,
% 0.19/0.46 (^[A: $i, B: $i] : refl(((~relation(A)) | relation(relation_dom_restriction(A, B))) <=> ((~relation(A)) | relation(relation_dom_restriction(A, B))))),
% 0.19/0.46 inference(bind,[status(th)],[])).
% 0.19/0.46 tff(28,plain,
% 0.19/0.46 (![A: $i, B: $i] : ((~relation(A)) | relation(relation_dom_restriction(A, B))) <=> ![A: $i, B: $i] : ((~relation(A)) | relation(relation_dom_restriction(A, B)))),
% 0.19/0.46 inference(quant_intro,[status(thm)],[27])).
% 0.19/0.46 tff(29,plain,
% 0.19/0.46 (![A: $i, B: $i] : ((~relation(A)) | relation(relation_dom_restriction(A, B))) <=> ![A: $i, B: $i] : ((~relation(A)) | relation(relation_dom_restriction(A, B)))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(30,plain,
% 0.19/0.46 (^[A: $i, B: $i] : rewrite((relation(A) => relation(relation_dom_restriction(A, B))) <=> ((~relation(A)) | relation(relation_dom_restriction(A, B))))),
% 0.19/0.46 inference(bind,[status(th)],[])).
% 0.19/0.46 tff(31,plain,
% 0.19/0.46 (![A: $i, B: $i] : (relation(A) => relation(relation_dom_restriction(A, B))) <=> ![A: $i, B: $i] : ((~relation(A)) | relation(relation_dom_restriction(A, B)))),
% 0.19/0.46 inference(quant_intro,[status(thm)],[30])).
% 0.19/0.46 tff(32,axiom,(![A: $i, B: $i] : (relation(A) => relation(relation_dom_restriction(A, B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_k7_relat_1')).
% 0.19/0.46 tff(33,plain,
% 0.19/0.46 (![A: $i, B: $i] : ((~relation(A)) | relation(relation_dom_restriction(A, B)))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[32, 31])).
% 0.19/0.46 tff(34,plain,
% 0.19/0.46 (![A: $i, B: $i] : ((~relation(A)) | relation(relation_dom_restriction(A, B)))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[33, 29])).
% 0.19/0.46 tff(35,plain,(
% 0.19/0.46 ![A: $i, B: $i] : ((~relation(A)) | relation(relation_dom_restriction(A, B)))),
% 0.19/0.46 inference(skolemize,[status(sab)],[34])).
% 0.19/0.46 tff(36,plain,
% 0.19/0.46 (![A: $i, B: $i] : ((~relation(A)) | relation(relation_dom_restriction(A, B)))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[35, 28])).
% 0.19/0.46 tff(37,plain,
% 0.19/0.46 (((~![A: $i, B: $i] : ((~relation(A)) | relation(relation_dom_restriction(A, B)))) | ((~relation(B!56)) | relation(relation_dom_restriction(B!56, A!57)))) <=> ((~![A: $i, B: $i] : ((~relation(A)) | relation(relation_dom_restriction(A, B)))) | (~relation(B!56)) | relation(relation_dom_restriction(B!56, A!57)))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(38,plain,
% 0.19/0.46 ((~![A: $i, B: $i] : ((~relation(A)) | relation(relation_dom_restriction(A, B)))) | ((~relation(B!56)) | relation(relation_dom_restriction(B!56, A!57)))),
% 0.19/0.46 inference(quant_inst,[status(thm)],[])).
% 0.19/0.47 tff(39,plain,
% 0.19/0.47 ((~![A: $i, B: $i] : ((~relation(A)) | relation(relation_dom_restriction(A, B)))) | (~relation(B!56)) | relation(relation_dom_restriction(B!56, A!57))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[38, 37])).
% 0.19/0.47 tff(40,plain,
% 0.19/0.47 (relation(relation_dom_restriction(B!56, A!57))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[39, 36, 12])).
% 0.19/0.47 tff(41,plain,
% 0.19/0.47 (^[A: $i] : refl(((~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] : ((~relation(B)) | (~subset(A, B)) | (~((~subset(relation_dom(A), relation_dom(B))) | (~subset(relation_rng(A), relation_rng(B))))))))),
% 0.19/0.47 inference(bind,[status(th)],[])).
% 0.19/0.47 tff(42,plain,
% 0.19/0.47 (![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] : ((~relation(B)) | (~subset(A, B)) | (~((~subset(relation_dom(A), relation_dom(B))) | (~subset(relation_rng(A), relation_rng(B)))))))),
% 0.19/0.47 inference(quant_intro,[status(thm)],[41])).
% 0.19/0.47 tff(43,plain,
% 0.19/0.47 (^[A: $i] : rewrite(((~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] : ((~relation(B)) | (~subset(A, B)) | (~((~subset(relation_dom(A), relation_dom(B))) | (~subset(relation_rng(A), relation_rng(B))))))))),
% 0.19/0.47 inference(bind,[status(th)],[])).
% 0.19/0.47 tff(44,plain,
% 0.19/0.47 (![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] : ((~relation(B)) | (~subset(A, B)) | (~((~subset(relation_dom(A), relation_dom(B))) | (~subset(relation_rng(A), relation_rng(B)))))))),
% 0.19/0.47 inference(quant_intro,[status(thm)],[43])).
% 0.19/0.47 tff(45,plain,
% 0.19/0.47 (![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] : ((~relation(B)) | (~subset(A, B)) | (~((~subset(relation_dom(A), relation_dom(B))) | (~subset(relation_rng(A), relation_rng(B)))))))),
% 0.19/0.47 inference(transitivity,[status(thm)],[44, 42])).
% 0.19/0.47 tff(46,plain,
% 0.19/0.47 (^[A: $i] : rewrite(((~relation(A)) | ![B: $i] : ((subset(relation_dom(A), relation_dom(B)) & subset(relation_rng(A), relation_rng(B))) | (~relation(B)) | (~subset(A, B)))) <=> ((~relation(A)) | ![B: $i] : ((~relation(B)) | (~subset(A, B)) | (~((~subset(relation_dom(A), relation_dom(B))) | (~subset(relation_rng(A), relation_rng(B))))))))),
% 0.19/0.47 inference(bind,[status(th)],[])).
% 0.19/0.47 tff(47,plain,
% 0.19/0.47 (![A: $i] : ((~relation(A)) | ![B: $i] : ((subset(relation_dom(A), relation_dom(B)) & subset(relation_rng(A), relation_rng(B))) | (~relation(B)) | (~subset(A, B)))) <=> ![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)))))))),
% 0.19/0.47 inference(quant_intro,[status(thm)],[46])).
% 0.19/0.47 tff(48,plain,
% 0.19/0.47 (![A: $i] : ((~relation(A)) | ![B: $i] : ((subset(relation_dom(A), relation_dom(B)) & subset(relation_rng(A), relation_rng(B))) | (~relation(B)) | (~subset(A, B)))) <=> ![A: $i] : ((~relation(A)) | ![B: $i] : ((subset(relation_dom(A), relation_dom(B)) & subset(relation_rng(A), relation_rng(B))) | (~relation(B)) | (~subset(A, B))))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(49,plain,
% 0.19/0.47 (^[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))) | (~relation(B)) | (~subset(A, 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))) | (~relation(B)) | (~subset(A, 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))) | (~relation(B)) | (~subset(A, 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))) | (~relation(B)) | (~subset(A, B)))))), rewrite((relation(A) => ![B: $i] : ((subset(relation_dom(A), relation_dom(B)) & subset(relation_rng(A), relation_rng(B))) | (~relation(B)) | (~subset(A, B)))) <=> ((~relation(A)) | ![B: $i] : ((subset(relation_dom(A), relation_dom(B)) & subset(relation_rng(A), relation_rng(B))) | (~relation(B)) | (~subset(A, 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))) | (~relation(B)) | (~subset(A, B))))))),
% 0.19/0.47 inference(bind,[status(th)],[])).
% 0.19/0.47 tff(50,plain,
% 0.19/0.47 (![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))) | (~relation(B)) | (~subset(A, B))))),
% 0.19/0.47 inference(quant_intro,[status(thm)],[49])).
% 0.19/0.47 tff(51,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')).
% 0.19/0.47 tff(52,plain,
% 0.19/0.47 (![A: $i] : ((~relation(A)) | ![B: $i] : ((subset(relation_dom(A), relation_dom(B)) & subset(relation_rng(A), relation_rng(B))) | (~relation(B)) | (~subset(A, B))))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[51, 50])).
% 0.19/0.47 tff(53,plain,
% 0.19/0.47 (![A: $i] : ((~relation(A)) | ![B: $i] : ((subset(relation_dom(A), relation_dom(B)) & subset(relation_rng(A), relation_rng(B))) | (~relation(B)) | (~subset(A, B))))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[52, 48])).
% 0.19/0.47 tff(54,plain,(
% 0.19/0.47 ![A: $i] : ((~relation(A)) | ![B: $i] : ((subset(relation_dom(A), relation_dom(B)) & subset(relation_rng(A), relation_rng(B))) | (~relation(B)) | (~subset(A, B))))),
% 0.19/0.47 inference(skolemize,[status(sab)],[53])).
% 0.19/0.47 tff(55,plain,
% 0.19/0.47 (![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)))))))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[54, 47])).
% 0.19/0.47 tff(56,plain,
% 0.19/0.47 (![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)))))))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[55, 45])).
% 0.19/0.47 tff(57,plain,
% 0.19/0.47 (((~![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)))))))) | ((~relation(relation_dom_restriction(B!56, A!57))) | ![B: $i] : ((~relation(B)) | (~subset(relation_dom_restriction(B!56, A!57), B)) | (~((~subset(relation_dom(relation_dom_restriction(B!56, A!57)), relation_dom(B))) | (~subset(relation_rng(relation_dom_restriction(B!56, A!57)), relation_rng(B)))))))) <=> ((~![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)))))))) | (~relation(relation_dom_restriction(B!56, A!57))) | ![B: $i] : ((~relation(B)) | (~subset(relation_dom_restriction(B!56, A!57), B)) | (~((~subset(relation_dom(relation_dom_restriction(B!56, A!57)), relation_dom(B))) | (~subset(relation_rng(relation_dom_restriction(B!56, A!57)), relation_rng(B)))))))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(58,plain,
% 0.19/0.47 ((~![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)))))))) | ((~relation(relation_dom_restriction(B!56, A!57))) | ![B: $i] : ((~relation(B)) | (~subset(relation_dom_restriction(B!56, A!57), B)) | (~((~subset(relation_dom(relation_dom_restriction(B!56, A!57)), relation_dom(B))) | (~subset(relation_rng(relation_dom_restriction(B!56, A!57)), relation_rng(B)))))))),
% 0.19/0.47 inference(quant_inst,[status(thm)],[])).
% 0.19/0.47 tff(59,plain,
% 0.19/0.47 ((~![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)))))))) | (~relation(relation_dom_restriction(B!56, A!57))) | ![B: $i] : ((~relation(B)) | (~subset(relation_dom_restriction(B!56, A!57), B)) | (~((~subset(relation_dom(relation_dom_restriction(B!56, A!57)), relation_dom(B))) | (~subset(relation_rng(relation_dom_restriction(B!56, A!57)), relation_rng(B))))))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[58, 57])).
% 0.19/0.47 tff(60,plain,
% 0.19/0.47 ((~relation(relation_dom_restriction(B!56, A!57))) | ![B: $i] : ((~relation(B)) | (~subset(relation_dom_restriction(B!56, A!57), B)) | (~((~subset(relation_dom(relation_dom_restriction(B!56, A!57)), relation_dom(B))) | (~subset(relation_rng(relation_dom_restriction(B!56, A!57)), relation_rng(B))))))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[59, 56])).
% 0.19/0.47 tff(61,plain,
% 0.19/0.47 (![B: $i] : ((~relation(B)) | (~subset(relation_dom_restriction(B!56, A!57), B)) | (~((~subset(relation_dom(relation_dom_restriction(B!56, A!57)), relation_dom(B))) | (~subset(relation_rng(relation_dom_restriction(B!56, A!57)), relation_rng(B))))))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[60, 40])).
% 0.19/0.47 tff(62,plain,
% 0.19/0.47 (((~![B: $i] : ((~relation(B)) | (~subset(relation_dom_restriction(B!56, A!57), B)) | (~((~subset(relation_dom(relation_dom_restriction(B!56, A!57)), relation_dom(B))) | (~subset(relation_rng(relation_dom_restriction(B!56, A!57)), relation_rng(B))))))) | ((~relation(B!56)) | (~subset(relation_dom_restriction(B!56, A!57), B!56)) | (~((~subset(relation_dom(relation_dom_restriction(B!56, A!57)), relation_dom(B!56))) | (~subset(relation_rng(relation_dom_restriction(B!56, A!57)), relation_rng(B!56))))))) <=> ((~![B: $i] : ((~relation(B)) | (~subset(relation_dom_restriction(B!56, A!57), B)) | (~((~subset(relation_dom(relation_dom_restriction(B!56, A!57)), relation_dom(B))) | (~subset(relation_rng(relation_dom_restriction(B!56, A!57)), relation_rng(B))))))) | (~relation(B!56)) | (~subset(relation_dom_restriction(B!56, A!57), B!56)) | (~((~subset(relation_dom(relation_dom_restriction(B!56, A!57)), relation_dom(B!56))) | (~subset(relation_rng(relation_dom_restriction(B!56, A!57)), relation_rng(B!56))))))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(63,plain,
% 0.19/0.47 ((~![B: $i] : ((~relation(B)) | (~subset(relation_dom_restriction(B!56, A!57), B)) | (~((~subset(relation_dom(relation_dom_restriction(B!56, A!57)), relation_dom(B))) | (~subset(relation_rng(relation_dom_restriction(B!56, A!57)), relation_rng(B))))))) | ((~relation(B!56)) | (~subset(relation_dom_restriction(B!56, A!57), B!56)) | (~((~subset(relation_dom(relation_dom_restriction(B!56, A!57)), relation_dom(B!56))) | (~subset(relation_rng(relation_dom_restriction(B!56, A!57)), relation_rng(B!56))))))),
% 0.19/0.47 inference(quant_inst,[status(thm)],[])).
% 0.19/0.47 tff(64,plain,
% 0.19/0.47 ((~![B: $i] : ((~relation(B)) | (~subset(relation_dom_restriction(B!56, A!57), B)) | (~((~subset(relation_dom(relation_dom_restriction(B!56, A!57)), relation_dom(B))) | (~subset(relation_rng(relation_dom_restriction(B!56, A!57)), relation_rng(B))))))) | (~relation(B!56)) | (~subset(relation_dom_restriction(B!56, A!57), B!56)) | (~((~subset(relation_dom(relation_dom_restriction(B!56, A!57)), relation_dom(B!56))) | (~subset(relation_rng(relation_dom_restriction(B!56, A!57)), relation_rng(B!56)))))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[63, 62])).
% 0.19/0.47 tff(65,plain,
% 0.19/0.47 ($false),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[64, 12, 61, 26, 11])).
% 0.19/0.47 % SZS output end Proof
% 0.19/0.48 % E exiting
%------------------------------------------------------------------------------