%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SEU200+2 : TPTP v9.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n001.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 05:27:13 AM UTC 2025
% Result : Theorem 0.20s 0.50s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SEU200+2 : TPTP v9.0.0. Released v3.3.0.
% 0.07/0.13 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n001.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Fri Jun 20 06:19:20 EDT 2025
% 0.12/0.35 % CPUTime :
% 0.20/0.50 % SZS status Theorem
% 0.20/0.50 % SZS output start Proof
% 0.20/0.50 tff(subset_type, type, (
% 0.20/0.50 subset: ( $i * $i ) > $o)).
% 0.20/0.50 tff(relation_rng_type, type, (
% 0.20/0.50 relation_rng: $i > $i)).
% 0.20/0.50 tff(tptp_fun_B_52_type, type, (
% 0.20/0.50 tptp_fun_B_52: $i)).
% 0.20/0.50 tff(relation_rng_restriction_type, type, (
% 0.20/0.50 relation_rng_restriction: ( $i * $i ) > $i)).
% 0.20/0.50 tff(tptp_fun_A_53_type, type, (
% 0.20/0.50 tptp_fun_A_53: $i)).
% 0.20/0.50 tff(relation_dom_type, type, (
% 0.20/0.50 relation_dom: $i > $i)).
% 0.20/0.50 tff(relation_type, type, (
% 0.20/0.50 relation: $i > $o)).
% 0.20/0.50 tff(1,plain,
% 0.20/0.50 ((~![A: $i, B: $i] : ((~relation(B)) | subset(relation_rng(relation_rng_restriction(A, B)), relation_rng(B)))) <=> (~![A: $i, B: $i] : ((~relation(B)) | subset(relation_rng(relation_rng_restriction(A, B)), relation_rng(B))))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(2,plain,
% 0.20/0.50 ((~![A: $i, B: $i] : (relation(B) => subset(relation_rng(relation_rng_restriction(A, B)), relation_rng(B)))) <=> (~![A: $i, B: $i] : ((~relation(B)) | subset(relation_rng(relation_rng_restriction(A, B)), relation_rng(B))))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(3,axiom,(~![A: $i, B: $i] : (relation(B) => subset(relation_rng(relation_rng_restriction(A, B)), relation_rng(B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t118_relat_1')).
% 0.20/0.50 tff(4,plain,
% 0.20/0.50 (~![A: $i, B: $i] : ((~relation(B)) | subset(relation_rng(relation_rng_restriction(A, B)), relation_rng(B)))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[3, 2])).
% 0.20/0.50 tff(5,plain,
% 0.20/0.50 (~![A: $i, B: $i] : ((~relation(B)) | subset(relation_rng(relation_rng_restriction(A, B)), relation_rng(B)))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[4, 1])).
% 0.20/0.50 tff(6,plain,
% 0.20/0.50 (~![A: $i, B: $i] : ((~relation(B)) | subset(relation_rng(relation_rng_restriction(A, B)), relation_rng(B)))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[5, 1])).
% 0.20/0.50 tff(7,plain,
% 0.20/0.50 (~![A: $i, B: $i] : ((~relation(B)) | subset(relation_rng(relation_rng_restriction(A, B)), relation_rng(B)))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[6, 1])).
% 0.20/0.50 tff(8,plain,(
% 0.20/0.50 ~((~relation(B!52)) | subset(relation_rng(relation_rng_restriction(A!53, B!52)), relation_rng(B!52)))),
% 0.20/0.50 inference(skolemize,[status(sab)],[7])).
% 0.20/0.50 tff(9,plain,
% 0.20/0.50 (~subset(relation_rng(relation_rng_restriction(A!53, B!52)), relation_rng(B!52))),
% 0.20/0.50 inference(or_elim,[status(thm)],[8])).
% 0.20/0.50 tff(10,plain,
% 0.20/0.50 (((~subset(relation_dom(relation_rng_restriction(A!53, B!52)), relation_dom(B!52))) | (~subset(relation_rng(relation_rng_restriction(A!53, B!52)), relation_rng(B!52)))) | subset(relation_rng(relation_rng_restriction(A!53, B!52)), relation_rng(B!52))),
% 0.20/0.50 inference(tautology,[status(thm)],[])).
% 0.20/0.50 tff(11,plain,
% 0.20/0.50 ((~subset(relation_dom(relation_rng_restriction(A!53, B!52)), relation_dom(B!52))) | (~subset(relation_rng(relation_rng_restriction(A!53, B!52)), relation_rng(B!52)))),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[10, 9])).
% 0.20/0.50 tff(12,plain,
% 0.20/0.50 (relation(B!52)),
% 0.20/0.50 inference(or_elim,[status(thm)],[8])).
% 0.20/0.50 tff(13,plain,
% 0.20/0.50 (^[A: $i, B: $i] : refl(((~relation(B)) | relation(relation_rng_restriction(A, B))) <=> ((~relation(B)) | relation(relation_rng_restriction(A, B))))),
% 0.20/0.50 inference(bind,[status(th)],[])).
% 0.20/0.50 tff(14,plain,
% 0.20/0.50 (![A: $i, B: $i] : ((~relation(B)) | relation(relation_rng_restriction(A, B))) <=> ![A: $i, B: $i] : ((~relation(B)) | relation(relation_rng_restriction(A, B)))),
% 0.20/0.50 inference(quant_intro,[status(thm)],[13])).
% 0.20/0.50 tff(15,plain,
% 0.20/0.50 (![A: $i, B: $i] : ((~relation(B)) | relation(relation_rng_restriction(A, B))) <=> ![A: $i, B: $i] : ((~relation(B)) | relation(relation_rng_restriction(A, B)))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(16,plain,
% 0.20/0.50 (^[A: $i, B: $i] : rewrite((relation(B) => relation(relation_rng_restriction(A, B))) <=> ((~relation(B)) | relation(relation_rng_restriction(A, B))))),
% 0.20/0.50 inference(bind,[status(th)],[])).
% 0.20/0.50 tff(17,plain,
% 0.20/0.50 (![A: $i, B: $i] : (relation(B) => relation(relation_rng_restriction(A, B))) <=> ![A: $i, B: $i] : ((~relation(B)) | relation(relation_rng_restriction(A, B)))),
% 0.20/0.50 inference(quant_intro,[status(thm)],[16])).
% 0.20/0.50 tff(18,axiom,(![A: $i, B: $i] : (relation(B) => relation(relation_rng_restriction(A, B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_k8_relat_1')).
% 0.20/0.50 tff(19,plain,
% 0.20/0.50 (![A: $i, B: $i] : ((~relation(B)) | relation(relation_rng_restriction(A, B)))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[18, 17])).
% 0.20/0.50 tff(20,plain,
% 0.20/0.50 (![A: $i, B: $i] : ((~relation(B)) | relation(relation_rng_restriction(A, B)))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[19, 15])).
% 0.20/0.50 tff(21,plain,(
% 0.20/0.50 ![A: $i, B: $i] : ((~relation(B)) | relation(relation_rng_restriction(A, B)))),
% 0.20/0.50 inference(skolemize,[status(sab)],[20])).
% 0.20/0.50 tff(22,plain,
% 0.20/0.50 (![A: $i, B: $i] : ((~relation(B)) | relation(relation_rng_restriction(A, B)))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[21, 14])).
% 0.20/0.50 tff(23,plain,
% 0.20/0.50 (((~![A: $i, B: $i] : ((~relation(B)) | relation(relation_rng_restriction(A, B)))) | ((~relation(B!52)) | relation(relation_rng_restriction(A!53, B!52)))) <=> ((~![A: $i, B: $i] : ((~relation(B)) | relation(relation_rng_restriction(A, B)))) | (~relation(B!52)) | relation(relation_rng_restriction(A!53, B!52)))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(24,plain,
% 0.20/0.50 ((~![A: $i, B: $i] : ((~relation(B)) | relation(relation_rng_restriction(A, B)))) | ((~relation(B!52)) | relation(relation_rng_restriction(A!53, B!52)))),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(25,plain,
% 0.20/0.50 ((~![A: $i, B: $i] : ((~relation(B)) | relation(relation_rng_restriction(A, B)))) | (~relation(B!52)) | relation(relation_rng_restriction(A!53, B!52))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[24, 23])).
% 0.20/0.50 tff(26,plain,
% 0.20/0.50 (relation(relation_rng_restriction(A!53, B!52))),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[25, 22, 12])).
% 0.20/0.50 tff(27,plain,
% 0.20/0.50 (^[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))))))))),
% 0.20/0.50 inference(bind,[status(th)],[])).
% 0.20/0.50 tff(28,plain,
% 0.20/0.50 (![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)))))))),
% 0.20/0.50 inference(quant_intro,[status(thm)],[27])).
% 0.20/0.50 tff(29,plain,
% 0.20/0.50 (^[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))))))))),
% 0.20/0.50 inference(bind,[status(th)],[])).
% 0.20/0.50 tff(30,plain,
% 0.20/0.50 (![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)))))))),
% 0.20/0.50 inference(quant_intro,[status(thm)],[29])).
% 0.20/0.50 tff(31,plain,
% 0.20/0.50 (![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)))))))),
% 0.20/0.50 inference(transitivity,[status(thm)],[30, 28])).
% 0.20/0.50 tff(32,plain,
% 0.20/0.50 (^[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))))))))),
% 0.20/0.50 inference(bind,[status(th)],[])).
% 0.20/0.50 tff(33,plain,
% 0.20/0.50 (![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)))))))),
% 0.20/0.50 inference(quant_intro,[status(thm)],[32])).
% 0.20/0.50 tff(34,plain,
% 0.20/0.50 (![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))))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(35,plain,
% 0.20/0.50 (^[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))))))),
% 0.20/0.50 inference(bind,[status(th)],[])).
% 0.20/0.50 tff(36,plain,
% 0.20/0.50 (![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))))),
% 0.20/0.50 inference(quant_intro,[status(thm)],[35])).
% 0.20/0.50 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')).
% 0.20/0.50 tff(38,plain,
% 0.20/0.50 (![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))))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[37, 36])).
% 0.20/0.50 tff(39,plain,
% 0.20/0.50 (![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))))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[38, 34])).
% 0.20/0.50 tff(40,plain,(
% 0.20/0.50 ![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))))),
% 0.20/0.50 inference(skolemize,[status(sab)],[39])).
% 0.20/0.50 tff(41,plain,
% 0.20/0.50 (![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)))))))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[40, 33])).
% 0.20/0.50 tff(42,plain,
% 0.20/0.50 (![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)))))))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[41, 31])).
% 0.20/0.50 tff(43,plain,
% 0.20/0.50 (((~![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_rng_restriction(A!53, B!52))) | ![B: $i] : ((~relation(B)) | (~subset(relation_rng_restriction(A!53, B!52), B)) | (~((~subset(relation_dom(relation_rng_restriction(A!53, B!52)), relation_dom(B))) | (~subset(relation_rng(relation_rng_restriction(A!53, B!52)), 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_rng_restriction(A!53, B!52))) | ![B: $i] : ((~relation(B)) | (~subset(relation_rng_restriction(A!53, B!52), B)) | (~((~subset(relation_dom(relation_rng_restriction(A!53, B!52)), relation_dom(B))) | (~subset(relation_rng(relation_rng_restriction(A!53, B!52)), relation_rng(B)))))))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(44,plain,
% 0.20/0.50 ((~![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_rng_restriction(A!53, B!52))) | ![B: $i] : ((~relation(B)) | (~subset(relation_rng_restriction(A!53, B!52), B)) | (~((~subset(relation_dom(relation_rng_restriction(A!53, B!52)), relation_dom(B))) | (~subset(relation_rng(relation_rng_restriction(A!53, B!52)), relation_rng(B)))))))),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(45,plain,
% 0.20/0.50 ((~![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_rng_restriction(A!53, B!52))) | ![B: $i] : ((~relation(B)) | (~subset(relation_rng_restriction(A!53, B!52), B)) | (~((~subset(relation_dom(relation_rng_restriction(A!53, B!52)), relation_dom(B))) | (~subset(relation_rng(relation_rng_restriction(A!53, B!52)), relation_rng(B))))))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[44, 43])).
% 0.20/0.50 tff(46,plain,
% 0.20/0.50 (![B: $i] : ((~relation(B)) | (~subset(relation_rng_restriction(A!53, B!52), B)) | (~((~subset(relation_dom(relation_rng_restriction(A!53, B!52)), relation_dom(B))) | (~subset(relation_rng(relation_rng_restriction(A!53, B!52)), relation_rng(B))))))),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[45, 42, 26])).
% 0.20/0.50 tff(47,plain,
% 0.20/0.50 (^[A: $i, B: $i] : refl(((~relation(B)) | subset(relation_rng_restriction(A, B), B)) <=> ((~relation(B)) | subset(relation_rng_restriction(A, B), B)))),
% 0.20/0.50 inference(bind,[status(th)],[])).
% 0.20/0.50 tff(48,plain,
% 0.20/0.50 (![A: $i, B: $i] : ((~relation(B)) | subset(relation_rng_restriction(A, B), B)) <=> ![A: $i, B: $i] : ((~relation(B)) | subset(relation_rng_restriction(A, B), B))),
% 0.20/0.50 inference(quant_intro,[status(thm)],[47])).
% 0.20/0.50 tff(49,plain,
% 0.20/0.50 (![A: $i, B: $i] : ((~relation(B)) | subset(relation_rng_restriction(A, B), B)) <=> ![A: $i, B: $i] : ((~relation(B)) | subset(relation_rng_restriction(A, B), B))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(50,plain,
% 0.20/0.50 (^[A: $i, B: $i] : rewrite((relation(B) => subset(relation_rng_restriction(A, B), B)) <=> ((~relation(B)) | subset(relation_rng_restriction(A, B), B)))),
% 0.20/0.50 inference(bind,[status(th)],[])).
% 0.20/0.50 tff(51,plain,
% 0.20/0.50 (![A: $i, B: $i] : (relation(B) => subset(relation_rng_restriction(A, B), B)) <=> ![A: $i, B: $i] : ((~relation(B)) | subset(relation_rng_restriction(A, B), B))),
% 0.20/0.50 inference(quant_intro,[status(thm)],[50])).
% 0.20/0.50 tff(52,axiom,(![A: $i, B: $i] : (relation(B) => subset(relation_rng_restriction(A, B), B))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t117_relat_1')).
% 0.20/0.50 tff(53,plain,
% 0.20/0.50 (![A: $i, B: $i] : ((~relation(B)) | subset(relation_rng_restriction(A, B), B))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[52, 51])).
% 0.20/0.50 tff(54,plain,
% 0.20/0.50 (![A: $i, B: $i] : ((~relation(B)) | subset(relation_rng_restriction(A, B), B))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[53, 49])).
% 0.20/0.50 tff(55,plain,(
% 0.20/0.50 ![A: $i, B: $i] : ((~relation(B)) | subset(relation_rng_restriction(A, B), B))),
% 0.20/0.50 inference(skolemize,[status(sab)],[54])).
% 0.20/0.50 tff(56,plain,
% 0.20/0.50 (![A: $i, B: $i] : ((~relation(B)) | subset(relation_rng_restriction(A, B), B))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[55, 48])).
% 0.20/0.50 tff(57,plain,
% 0.20/0.50 (((~![A: $i, B: $i] : ((~relation(B)) | subset(relation_rng_restriction(A, B), B))) | ((~relation(B!52)) | subset(relation_rng_restriction(A!53, B!52), B!52))) <=> ((~![A: $i, B: $i] : ((~relation(B)) | subset(relation_rng_restriction(A, B), B))) | (~relation(B!52)) | subset(relation_rng_restriction(A!53, B!52), B!52))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(58,plain,
% 0.20/0.50 ((~![A: $i, B: $i] : ((~relation(B)) | subset(relation_rng_restriction(A, B), B))) | ((~relation(B!52)) | subset(relation_rng_restriction(A!53, B!52), B!52))),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(59,plain,
% 0.20/0.50 ((~![A: $i, B: $i] : ((~relation(B)) | subset(relation_rng_restriction(A, B), B))) | (~relation(B!52)) | subset(relation_rng_restriction(A!53, B!52), B!52)),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[58, 57])).
% 0.20/0.50 tff(60,plain,
% 0.20/0.50 (subset(relation_rng_restriction(A!53, B!52), B!52)),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[59, 56, 12])).
% 0.20/0.50 tff(61,plain,
% 0.20/0.50 (((~![B: $i] : ((~relation(B)) | (~subset(relation_rng_restriction(A!53, B!52), B)) | (~((~subset(relation_dom(relation_rng_restriction(A!53, B!52)), relation_dom(B))) | (~subset(relation_rng(relation_rng_restriction(A!53, B!52)), relation_rng(B))))))) | ((~relation(B!52)) | (~subset(relation_rng_restriction(A!53, B!52), B!52)) | (~((~subset(relation_dom(relation_rng_restriction(A!53, B!52)), relation_dom(B!52))) | (~subset(relation_rng(relation_rng_restriction(A!53, B!52)), relation_rng(B!52))))))) <=> ((~![B: $i] : ((~relation(B)) | (~subset(relation_rng_restriction(A!53, B!52), B)) | (~((~subset(relation_dom(relation_rng_restriction(A!53, B!52)), relation_dom(B))) | (~subset(relation_rng(relation_rng_restriction(A!53, B!52)), relation_rng(B))))))) | (~relation(B!52)) | (~subset(relation_rng_restriction(A!53, B!52), B!52)) | (~((~subset(relation_dom(relation_rng_restriction(A!53, B!52)), relation_dom(B!52))) | (~subset(relation_rng(relation_rng_restriction(A!53, B!52)), relation_rng(B!52))))))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(62,plain,
% 0.20/0.50 ((~![B: $i] : ((~relation(B)) | (~subset(relation_rng_restriction(A!53, B!52), B)) | (~((~subset(relation_dom(relation_rng_restriction(A!53, B!52)), relation_dom(B))) | (~subset(relation_rng(relation_rng_restriction(A!53, B!52)), relation_rng(B))))))) | ((~relation(B!52)) | (~subset(relation_rng_restriction(A!53, B!52), B!52)) | (~((~subset(relation_dom(relation_rng_restriction(A!53, B!52)), relation_dom(B!52))) | (~subset(relation_rng(relation_rng_restriction(A!53, B!52)), relation_rng(B!52))))))),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(63,plain,
% 0.20/0.50 ((~![B: $i] : ((~relation(B)) | (~subset(relation_rng_restriction(A!53, B!52), B)) | (~((~subset(relation_dom(relation_rng_restriction(A!53, B!52)), relation_dom(B))) | (~subset(relation_rng(relation_rng_restriction(A!53, B!52)), relation_rng(B))))))) | (~relation(B!52)) | (~subset(relation_rng_restriction(A!53, B!52), B!52)) | (~((~subset(relation_dom(relation_rng_restriction(A!53, B!52)), relation_dom(B!52))) | (~subset(relation_rng(relation_rng_restriction(A!53, B!52)), relation_rng(B!52)))))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[62, 61])).
% 0.20/0.51 tff(64,plain,
% 0.20/0.51 ($false),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[63, 12, 60, 46, 11])).
% 0.20/0.51 % SZS output end Proof
% 0.20/0.51 % E exiting
%------------------------------------------------------------------------------