%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SEU020+1 : TPTP v9.0.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n009.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:26:48 AM UTC 2025
% Result : Theorem 0.18s 0.38s
% Output : Proof 0.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SEU020+1 : TPTP v9.0.0. Released v3.2.0.
% 0.11/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n009.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 05:57:33 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.18/0.38 % SZS status Theorem
% 0.18/0.38 % SZS output start Proof
% 0.18/0.38 tff(one_to_one_type, type, (
% 0.18/0.38 one_to_one: $i > $o)).
% 0.18/0.38 tff(relation_composition_type, type, (
% 0.18/0.38 relation_composition: ( $i * $i ) > $i)).
% 0.18/0.38 tff(tptp_fun_B_10_type, type, (
% 0.18/0.38 tptp_fun_B_10: $i)).
% 0.18/0.38 tff(tptp_fun_A_9_type, type, (
% 0.18/0.38 tptp_fun_A_9: $i)).
% 0.18/0.38 tff(identity_relation_type, type, (
% 0.18/0.38 identity_relation: $i > $i)).
% 0.18/0.38 tff(relation_dom_type, type, (
% 0.18/0.38 relation_dom: $i > $i)).
% 0.18/0.38 tff(function_type, type, (
% 0.18/0.38 function: $i > $o)).
% 0.18/0.38 tff(relation_type, type, (
% 0.18/0.38 relation: $i > $o)).
% 0.18/0.38 tff(subset_type, type, (
% 0.18/0.38 subset: ( $i * $i ) > $o)).
% 0.18/0.38 tff(relation_rng_type, type, (
% 0.18/0.38 relation_rng: $i > $i)).
% 0.18/0.38 tff(1,plain,
% 0.18/0.38 (((~one_to_one(A!9)) & (relation(A!9) & function(A!9)) & (relation(B!10) & function(B!10) & (relation_composition(A!9, B!10) = identity_relation(relation_dom(A!9))))) <=> ((~one_to_one(A!9)) & relation(A!9) & function(A!9) & relation(B!10) & function(B!10) & (relation_composition(A!9, B!10) = identity_relation(relation_dom(A!9))))),
% 0.18/0.38 inference(rewrite,[status(thm)],[])).
% 0.18/0.38 tff(2,plain,
% 0.18/0.38 ((~![A: $i] : (one_to_one(A) | (~(relation(A) & function(A))) | (~?[B: $i] : (relation(B) & function(B) & (relation_composition(A, B) = identity_relation(relation_dom(A))))))) <=> (~![A: $i] : (one_to_one(A) | (~(relation(A) & function(A))) | (~?[B: $i] : (relation(B) & function(B) & (relation_composition(A, B) = identity_relation(relation_dom(A)))))))),
% 0.18/0.38 inference(rewrite,[status(thm)],[])).
% 0.18/0.38 tff(3,plain,
% 0.18/0.38 ((~![A: $i] : ((relation(A) & function(A)) => (?[B: $i] : ((relation(B) & function(B)) & (relation_composition(A, B) = identity_relation(relation_dom(A)))) => one_to_one(A)))) <=> (~![A: $i] : (one_to_one(A) | (~(relation(A) & function(A))) | (~?[B: $i] : (relation(B) & function(B) & (relation_composition(A, B) = identity_relation(relation_dom(A)))))))),
% 0.18/0.38 inference(rewrite,[status(thm)],[])).
% 0.18/0.38 tff(4,axiom,(~![A: $i] : ((relation(A) & function(A)) => (?[B: $i] : ((relation(B) & function(B)) & (relation_composition(A, B) = identity_relation(relation_dom(A)))) => one_to_one(A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t53_funct_1')).
% 0.18/0.38 tff(5,plain,
% 0.18/0.38 (~![A: $i] : (one_to_one(A) | (~(relation(A) & function(A))) | (~?[B: $i] : (relation(B) & function(B) & (relation_composition(A, B) = identity_relation(relation_dom(A))))))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.18/0.38 tff(6,plain,
% 0.18/0.38 (~![A: $i] : (one_to_one(A) | (~(relation(A) & function(A))) | (~?[B: $i] : (relation(B) & function(B) & (relation_composition(A, B) = identity_relation(relation_dom(A))))))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[5, 2])).
% 0.18/0.38 tff(7,plain,
% 0.18/0.38 (~![A: $i] : (one_to_one(A) | (~(relation(A) & function(A))) | (~?[B: $i] : (relation(B) & function(B) & (relation_composition(A, B) = identity_relation(relation_dom(A))))))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.18/0.38 tff(8,plain,
% 0.18/0.38 (~![A: $i] : (one_to_one(A) | (~(relation(A) & function(A))) | (~?[B: $i] : (relation(B) & function(B) & (relation_composition(A, B) = identity_relation(relation_dom(A))))))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[7, 2])).
% 0.18/0.38 tff(9,plain,
% 0.18/0.38 ((~one_to_one(A!9)) & relation(A!9) & function(A!9) & relation(B!10) & function(B!10) & (relation_composition(A!9, B!10) = identity_relation(relation_dom(A!9)))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[8, 1])).
% 0.18/0.38 tff(10,plain,
% 0.18/0.38 (relation_composition(A!9, B!10) = identity_relation(relation_dom(A!9))),
% 0.18/0.38 inference(and_elim,[status(thm)],[9])).
% 0.18/0.38 tff(11,plain,
% 0.18/0.38 (one_to_one(relation_composition(A!9, B!10)) <=> one_to_one(identity_relation(relation_dom(A!9)))),
% 0.18/0.38 inference(monotonicity,[status(thm)],[10])).
% 0.18/0.38 tff(12,plain,
% 0.18/0.38 (one_to_one(identity_relation(relation_dom(A!9))) <=> one_to_one(relation_composition(A!9, B!10))),
% 0.18/0.38 inference(symmetry,[status(thm)],[11])).
% 0.18/0.38 tff(13,plain,
% 0.18/0.38 (^[A: $i] : refl(one_to_one(identity_relation(A)) <=> one_to_one(identity_relation(A)))),
% 0.18/0.38 inference(bind,[status(th)],[])).
% 0.18/0.38 tff(14,plain,
% 0.18/0.38 (![A: $i] : one_to_one(identity_relation(A)) <=> ![A: $i] : one_to_one(identity_relation(A))),
% 0.18/0.38 inference(quant_intro,[status(thm)],[13])).
% 0.18/0.38 tff(15,plain,
% 0.18/0.38 (![A: $i] : one_to_one(identity_relation(A)) <=> ![A: $i] : one_to_one(identity_relation(A))),
% 0.18/0.38 inference(rewrite,[status(thm)],[])).
% 0.18/0.38 tff(16,axiom,(![A: $i] : one_to_one(identity_relation(A))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t52_funct_1')).
% 0.18/0.38 tff(17,plain,
% 0.18/0.38 (![A: $i] : one_to_one(identity_relation(A))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[16, 15])).
% 0.18/0.38 tff(18,plain,(
% 0.18/0.38 ![A: $i] : one_to_one(identity_relation(A))),
% 0.18/0.38 inference(skolemize,[status(sab)],[17])).
% 0.18/0.38 tff(19,plain,
% 0.18/0.38 (![A: $i] : one_to_one(identity_relation(A))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[18, 14])).
% 0.18/0.38 tff(20,plain,
% 0.18/0.38 ((~![A: $i] : one_to_one(identity_relation(A))) | one_to_one(identity_relation(relation_dom(A!9)))),
% 0.18/0.38 inference(quant_inst,[status(thm)],[])).
% 0.18/0.38 tff(21,plain,
% 0.18/0.38 (one_to_one(identity_relation(relation_dom(A!9)))),
% 0.18/0.38 inference(unit_resolution,[status(thm)],[20, 19])).
% 0.18/0.38 tff(22,plain,
% 0.18/0.38 (one_to_one(relation_composition(A!9, B!10))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[21, 12])).
% 0.18/0.38 tff(23,plain,
% 0.18/0.38 (^[A: $i] : refl((~((~(relation_dom(identity_relation(A)) = A)) | (~(relation_rng(identity_relation(A)) = A)))) <=> (~((~(relation_dom(identity_relation(A)) = A)) | (~(relation_rng(identity_relation(A)) = A)))))),
% 0.18/0.38 inference(bind,[status(th)],[])).
% 0.18/0.38 tff(24,plain,
% 0.18/0.38 (![A: $i] : (~((~(relation_dom(identity_relation(A)) = A)) | (~(relation_rng(identity_relation(A)) = A)))) <=> ![A: $i] : (~((~(relation_dom(identity_relation(A)) = A)) | (~(relation_rng(identity_relation(A)) = A))))),
% 0.18/0.38 inference(quant_intro,[status(thm)],[23])).
% 0.18/0.38 tff(25,plain,
% 0.18/0.38 (^[A: $i] : rewrite(((relation_dom(identity_relation(A)) = A) & (relation_rng(identity_relation(A)) = A)) <=> (~((~(relation_dom(identity_relation(A)) = A)) | (~(relation_rng(identity_relation(A)) = A)))))),
% 0.18/0.38 inference(bind,[status(th)],[])).
% 0.18/0.38 tff(26,plain,
% 0.18/0.38 (![A: $i] : ((relation_dom(identity_relation(A)) = A) & (relation_rng(identity_relation(A)) = A)) <=> ![A: $i] : (~((~(relation_dom(identity_relation(A)) = A)) | (~(relation_rng(identity_relation(A)) = A))))),
% 0.18/0.38 inference(quant_intro,[status(thm)],[25])).
% 0.18/0.38 tff(27,plain,
% 0.18/0.38 (![A: $i] : ((relation_dom(identity_relation(A)) = A) & (relation_rng(identity_relation(A)) = A)) <=> ![A: $i] : ((relation_dom(identity_relation(A)) = A) & (relation_rng(identity_relation(A)) = A))),
% 0.18/0.38 inference(rewrite,[status(thm)],[])).
% 0.18/0.38 tff(28,axiom,(![A: $i] : ((relation_dom(identity_relation(A)) = A) & (relation_rng(identity_relation(A)) = A))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t71_relat_1')).
% 0.18/0.38 tff(29,plain,
% 0.18/0.38 (![A: $i] : ((relation_dom(identity_relation(A)) = A) & (relation_rng(identity_relation(A)) = A))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[28, 27])).
% 0.18/0.38 tff(30,plain,(
% 0.18/0.38 ![A: $i] : ((relation_dom(identity_relation(A)) = A) & (relation_rng(identity_relation(A)) = A))),
% 0.18/0.38 inference(skolemize,[status(sab)],[29])).
% 0.18/0.38 tff(31,plain,
% 0.18/0.38 (![A: $i] : (~((~(relation_dom(identity_relation(A)) = A)) | (~(relation_rng(identity_relation(A)) = A))))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[30, 26])).
% 0.18/0.38 tff(32,plain,
% 0.18/0.38 (![A: $i] : (~((~(relation_dom(identity_relation(A)) = A)) | (~(relation_rng(identity_relation(A)) = A))))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[31, 24])).
% 0.18/0.38 tff(33,plain,
% 0.18/0.38 ((~![A: $i] : (~((~(relation_dom(identity_relation(A)) = A)) | (~(relation_rng(identity_relation(A)) = A))))) | (~((~(relation_dom(identity_relation(relation_dom(A!9))) = relation_dom(A!9))) | (~(relation_rng(identity_relation(relation_dom(A!9))) = relation_dom(A!9)))))),
% 0.18/0.38 inference(quant_inst,[status(thm)],[])).
% 0.18/0.38 tff(34,plain,
% 0.18/0.38 (~((~(relation_dom(identity_relation(relation_dom(A!9))) = relation_dom(A!9))) | (~(relation_rng(identity_relation(relation_dom(A!9))) = relation_dom(A!9))))),
% 0.18/0.38 inference(unit_resolution,[status(thm)],[33, 32])).
% 0.18/0.38 tff(35,plain,
% 0.18/0.38 (((~(relation_dom(identity_relation(relation_dom(A!9))) = relation_dom(A!9))) | (~(relation_rng(identity_relation(relation_dom(A!9))) = relation_dom(A!9)))) | (relation_dom(identity_relation(relation_dom(A!9))) = relation_dom(A!9))),
% 0.18/0.38 inference(tautology,[status(thm)],[])).
% 0.18/0.38 tff(36,plain,
% 0.18/0.38 (relation_dom(identity_relation(relation_dom(A!9))) = relation_dom(A!9)),
% 0.18/0.38 inference(unit_resolution,[status(thm)],[35, 34])).
% 0.18/0.38 tff(37,plain,
% 0.18/0.38 (relation_dom(relation_composition(A!9, B!10)) = relation_dom(identity_relation(relation_dom(A!9)))),
% 0.18/0.38 inference(monotonicity,[status(thm)],[10])).
% 0.18/0.38 tff(38,plain,
% 0.18/0.38 (relation_dom(relation_composition(A!9, B!10)) = relation_dom(A!9)),
% 0.18/0.38 inference(transitivity,[status(thm)],[37, 36])).
% 0.18/0.38 tff(39,plain,
% 0.18/0.38 (function(B!10)),
% 0.18/0.38 inference(and_elim,[status(thm)],[9])).
% 0.18/0.38 tff(40,plain,
% 0.18/0.38 (relation(B!10)),
% 0.18/0.38 inference(and_elim,[status(thm)],[9])).
% 0.18/0.38 tff(41,plain,
% 0.18/0.38 (^[A: $i] : refl(((~relation(A)) | (~function(A)) | ![B: $i] : (subset(relation_rng(B), relation_dom(A)) | (~(relation_dom(relation_composition(B, A)) = relation_dom(B))) | (~relation(B)) | (~function(B)))) <=> ((~relation(A)) | (~function(A)) | ![B: $i] : (subset(relation_rng(B), relation_dom(A)) | (~(relation_dom(relation_composition(B, A)) = relation_dom(B))) | (~relation(B)) | (~function(B)))))),
% 0.18/0.38 inference(bind,[status(th)],[])).
% 0.18/0.38 tff(42,plain,
% 0.18/0.38 (![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i] : (subset(relation_rng(B), relation_dom(A)) | (~(relation_dom(relation_composition(B, A)) = relation_dom(B))) | (~relation(B)) | (~function(B)))) <=> ![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i] : (subset(relation_rng(B), relation_dom(A)) | (~(relation_dom(relation_composition(B, A)) = relation_dom(B))) | (~relation(B)) | (~function(B))))),
% 0.18/0.38 inference(quant_intro,[status(thm)],[41])).
% 0.18/0.38 tff(43,plain,
% 0.18/0.38 (^[A: $i] : rewrite(((~relation(A)) | (~function(A)) | ![B: $i] : (subset(relation_rng(B), relation_dom(A)) | (~(relation_dom(relation_composition(B, A)) = relation_dom(B))) | (~relation(B)) | (~function(B)))) <=> ((~relation(A)) | (~function(A)) | ![B: $i] : (subset(relation_rng(B), relation_dom(A)) | (~(relation_dom(relation_composition(B, A)) = relation_dom(B))) | (~relation(B)) | (~function(B)))))),
% 0.18/0.38 inference(bind,[status(th)],[])).
% 0.18/0.38 tff(44,plain,
% 0.18/0.38 (![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i] : (subset(relation_rng(B), relation_dom(A)) | (~(relation_dom(relation_composition(B, A)) = relation_dom(B))) | (~relation(B)) | (~function(B)))) <=> ![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i] : (subset(relation_rng(B), relation_dom(A)) | (~(relation_dom(relation_composition(B, A)) = relation_dom(B))) | (~relation(B)) | (~function(B))))),
% 0.18/0.38 inference(quant_intro,[status(thm)],[43])).
% 0.18/0.38 tff(45,plain,
% 0.18/0.38 (![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i] : (subset(relation_rng(B), relation_dom(A)) | (~(relation_dom(relation_composition(B, A)) = relation_dom(B))) | (~relation(B)) | (~function(B)))) <=> ![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i] : (subset(relation_rng(B), relation_dom(A)) | (~(relation_dom(relation_composition(B, A)) = relation_dom(B))) | (~relation(B)) | (~function(B))))),
% 0.18/0.38 inference(transitivity,[status(thm)],[44, 42])).
% 0.18/0.38 tff(46,plain,
% 0.18/0.38 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite((relation(A) & function(A)) <=> (~((~relation(A)) | (~function(A))))), ((~(relation(A) & function(A))) <=> (~(~((~relation(A)) | (~function(A))))))), rewrite((~(~((~relation(A)) | (~function(A))))) <=> ((~relation(A)) | (~function(A)))), ((~(relation(A) & function(A))) <=> ((~relation(A)) | (~function(A))))), quant_intro(proof_bind(^[B: $i] : trans(monotonicity(trans(monotonicity(rewrite((relation(B) & function(B)) <=> (~((~relation(B)) | (~function(B))))), ((~(relation(B) & function(B))) <=> (~(~((~relation(B)) | (~function(B))))))), rewrite((~(~((~relation(B)) | (~function(B))))) <=> ((~relation(B)) | (~function(B)))), ((~(relation(B) & function(B))) <=> ((~relation(B)) | (~function(B))))), ((subset(relation_rng(B), relation_dom(A)) | (~(relation_dom(relation_composition(B, A)) = relation_dom(B))) | (~(relation(B) & function(B)))) <=> (subset(relation_rng(B), relation_dom(A)) | (~(relation_dom(relation_composition(B, A)) = relation_dom(B))) | ((~relation(B)) | (~function(B)))))), rewrite((subset(relation_rng(B), relation_dom(A)) | (~(relation_dom(relation_composition(B, A)) = relation_dom(B))) | ((~relation(B)) | (~function(B)))) <=> (subset(relation_rng(B), relation_dom(A)) | (~(relation_dom(relation_composition(B, A)) = relation_dom(B))) | (~relation(B)) | (~function(B)))), ((subset(relation_rng(B), relation_dom(A)) | (~(relation_dom(relation_composition(B, A)) = relation_dom(B))) | (~(relation(B) & function(B)))) <=> (subset(relation_rng(B), relation_dom(A)) | (~(relation_dom(relation_composition(B, A)) = relation_dom(B))) | (~relation(B)) | (~function(B)))))), (![B: $i] : (subset(relation_rng(B), relation_dom(A)) | (~(relation_dom(relation_composition(B, A)) = relation_dom(B))) | (~(relation(B) & function(B)))) <=> ![B: $i] : (subset(relation_rng(B), relation_dom(A)) | (~(relation_dom(relation_composition(B, A)) = relation_dom(B))) | (~relation(B)) | (~function(B))))), (((~(relation(A) & function(A))) | ![B: $i] : (subset(relation_rng(B), relation_dom(A)) | (~(relation_dom(relation_composition(B, A)) = relation_dom(B))) | (~(relation(B) & function(B))))) <=> (((~relation(A)) | (~function(A))) | ![B: $i] : (subset(relation_rng(B), relation_dom(A)) | (~(relation_dom(relation_composition(B, A)) = relation_dom(B))) | (~relation(B)) | (~function(B)))))), rewrite((((~relation(A)) | (~function(A))) | ![B: $i] : (subset(relation_rng(B), relation_dom(A)) | (~(relation_dom(relation_composition(B, A)) = relation_dom(B))) | (~relation(B)) | (~function(B)))) <=> ((~relation(A)) | (~function(A)) | ![B: $i] : (subset(relation_rng(B), relation_dom(A)) | (~(relation_dom(relation_composition(B, A)) = relation_dom(B))) | (~relation(B)) | (~function(B))))), (((~(relation(A) & function(A))) | ![B: $i] : (subset(relation_rng(B), relation_dom(A)) | (~(relation_dom(relation_composition(B, A)) = relation_dom(B))) | (~(relation(B) & function(B))))) <=> ((~relation(A)) | (~function(A)) | ![B: $i] : (subset(relation_rng(B), relation_dom(A)) | (~(relation_dom(relation_composition(B, A)) = relation_dom(B))) | (~relation(B)) | (~function(B))))))),
% 0.18/0.38 inference(bind,[status(th)],[])).
% 0.18/0.38 tff(47,plain,
% 0.18/0.38 (![A: $i] : ((~(relation(A) & function(A))) | ![B: $i] : (subset(relation_rng(B), relation_dom(A)) | (~(relation_dom(relation_composition(B, A)) = relation_dom(B))) | (~(relation(B) & function(B))))) <=> ![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i] : (subset(relation_rng(B), relation_dom(A)) | (~(relation_dom(relation_composition(B, A)) = relation_dom(B))) | (~relation(B)) | (~function(B))))),
% 0.18/0.38 inference(quant_intro,[status(thm)],[46])).
% 0.18/0.38 tff(48,plain,
% 0.18/0.38 (![A: $i] : ((~(relation(A) & function(A))) | ![B: $i] : (subset(relation_rng(B), relation_dom(A)) | (~(relation_dom(relation_composition(B, A)) = relation_dom(B))) | (~(relation(B) & function(B))))) <=> ![A: $i] : ((~(relation(A) & function(A))) | ![B: $i] : (subset(relation_rng(B), relation_dom(A)) | (~(relation_dom(relation_composition(B, A)) = relation_dom(B))) | (~(relation(B) & function(B)))))),
% 0.18/0.38 inference(rewrite,[status(thm)],[])).
% 0.18/0.38 tff(49,plain,
% 0.18/0.38 (^[A: $i] : trans(monotonicity(quant_intro(proof_bind(^[B: $i] : trans(monotonicity(rewrite(((relation_dom(relation_composition(B, A)) = relation_dom(B)) => subset(relation_rng(B), relation_dom(A))) <=> ((~(relation_dom(relation_composition(B, A)) = relation_dom(B))) | subset(relation_rng(B), relation_dom(A)))), (((relation(B) & function(B)) => ((relation_dom(relation_composition(B, A)) = relation_dom(B)) => subset(relation_rng(B), relation_dom(A)))) <=> ((relation(B) & function(B)) => ((~(relation_dom(relation_composition(B, A)) = relation_dom(B))) | subset(relation_rng(B), relation_dom(A)))))), rewrite(((relation(B) & function(B)) => ((~(relation_dom(relation_composition(B, A)) = relation_dom(B))) | subset(relation_rng(B), relation_dom(A)))) <=> (subset(relation_rng(B), relation_dom(A)) | (~(relation_dom(relation_composition(B, A)) = relation_dom(B))) | (~(relation(B) & function(B))))), (((relation(B) & function(B)) => ((relation_dom(relation_composition(B, A)) = relation_dom(B)) => subset(relation_rng(B), relation_dom(A)))) <=> (subset(relation_rng(B), relation_dom(A)) | (~(relation_dom(relation_composition(B, A)) = relation_dom(B))) | (~(relation(B) & function(B))))))), (![B: $i] : ((relation(B) & function(B)) => ((relation_dom(relation_composition(B, A)) = relation_dom(B)) => subset(relation_rng(B), relation_dom(A)))) <=> ![B: $i] : (subset(relation_rng(B), relation_dom(A)) | (~(relation_dom(relation_composition(B, A)) = relation_dom(B))) | (~(relation(B) & function(B)))))), (((relation(A) & function(A)) => ![B: $i] : ((relation(B) & function(B)) => ((relation_dom(relation_composition(B, A)) = relation_dom(B)) => subset(relation_rng(B), relation_dom(A))))) <=> ((relation(A) & function(A)) => ![B: $i] : (subset(relation_rng(B), relation_dom(A)) | (~(relation_dom(relation_composition(B, A)) = relation_dom(B))) | (~(relation(B) & function(B))))))), rewrite(((relation(A) & function(A)) => ![B: $i] : (subset(relation_rng(B), relation_dom(A)) | (~(relation_dom(relation_composition(B, A)) = relation_dom(B))) | (~(relation(B) & function(B))))) <=> ((~(relation(A) & function(A))) | ![B: $i] : (subset(relation_rng(B), relation_dom(A)) | (~(relation_dom(relation_composition(B, A)) = relation_dom(B))) | (~(relation(B) & function(B)))))), (((relation(A) & function(A)) => ![B: $i] : ((relation(B) & function(B)) => ((relation_dom(relation_composition(B, A)) = relation_dom(B)) => subset(relation_rng(B), relation_dom(A))))) <=> ((~(relation(A) & function(A))) | ![B: $i] : (subset(relation_rng(B), relation_dom(A)) | (~(relation_dom(relation_composition(B, A)) = relation_dom(B))) | (~(relation(B) & function(B)))))))),
% 0.18/0.39 inference(bind,[status(th)],[])).
% 0.18/0.39 tff(50,plain,
% 0.18/0.39 (![A: $i] : ((relation(A) & function(A)) => ![B: $i] : ((relation(B) & function(B)) => ((relation_dom(relation_composition(B, A)) = relation_dom(B)) => subset(relation_rng(B), relation_dom(A))))) <=> ![A: $i] : ((~(relation(A) & function(A))) | ![B: $i] : (subset(relation_rng(B), relation_dom(A)) | (~(relation_dom(relation_composition(B, A)) = relation_dom(B))) | (~(relation(B) & function(B)))))),
% 0.18/0.39 inference(quant_intro,[status(thm)],[49])).
% 0.18/0.39 tff(51,axiom,(![A: $i] : ((relation(A) & function(A)) => ![B: $i] : ((relation(B) & function(B)) => ((relation_dom(relation_composition(B, A)) = relation_dom(B)) => subset(relation_rng(B), relation_dom(A)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t27_funct_1')).
% 0.18/0.39 tff(52,plain,
% 0.18/0.39 (![A: $i] : ((~(relation(A) & function(A))) | ![B: $i] : (subset(relation_rng(B), relation_dom(A)) | (~(relation_dom(relation_composition(B, A)) = relation_dom(B))) | (~(relation(B) & function(B)))))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[51, 50])).
% 0.18/0.39 tff(53,plain,
% 0.18/0.39 (![A: $i] : ((~(relation(A) & function(A))) | ![B: $i] : (subset(relation_rng(B), relation_dom(A)) | (~(relation_dom(relation_composition(B, A)) = relation_dom(B))) | (~(relation(B) & function(B)))))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[52, 48])).
% 0.18/0.39 tff(54,plain,(
% 0.18/0.39 ![A: $i] : ((~(relation(A) & function(A))) | ![B: $i] : (subset(relation_rng(B), relation_dom(A)) | (~(relation_dom(relation_composition(B, A)) = relation_dom(B))) | (~(relation(B) & function(B)))))),
% 0.18/0.39 inference(skolemize,[status(sab)],[53])).
% 0.18/0.39 tff(55,plain,
% 0.18/0.39 (![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i] : (subset(relation_rng(B), relation_dom(A)) | (~(relation_dom(relation_composition(B, A)) = relation_dom(B))) | (~relation(B)) | (~function(B))))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[54, 47])).
% 0.18/0.39 tff(56,plain,
% 0.18/0.39 (![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i] : (subset(relation_rng(B), relation_dom(A)) | (~(relation_dom(relation_composition(B, A)) = relation_dom(B))) | (~relation(B)) | (~function(B))))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[55, 45])).
% 0.18/0.39 tff(57,plain,
% 0.18/0.39 (((~![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i] : (subset(relation_rng(B), relation_dom(A)) | (~(relation_dom(relation_composition(B, A)) = relation_dom(B))) | (~relation(B)) | (~function(B))))) | ((~function(B!10)) | (~relation(B!10)) | ![B: $i] : ((~relation(B)) | (~function(B)) | subset(relation_rng(B), relation_dom(B!10)) | (~(relation_dom(relation_composition(B, B!10)) = relation_dom(B)))))) <=> ((~![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i] : (subset(relation_rng(B), relation_dom(A)) | (~(relation_dom(relation_composition(B, A)) = relation_dom(B))) | (~relation(B)) | (~function(B))))) | (~function(B!10)) | (~relation(B!10)) | ![B: $i] : ((~relation(B)) | (~function(B)) | subset(relation_rng(B), relation_dom(B!10)) | (~(relation_dom(relation_composition(B, B!10)) = relation_dom(B)))))),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(58,plain,
% 0.18/0.39 (((~relation(B!10)) | (~function(B!10)) | ![B: $i] : ((~relation(B)) | (~function(B)) | subset(relation_rng(B), relation_dom(B!10)) | (~(relation_dom(relation_composition(B, B!10)) = relation_dom(B))))) <=> ((~function(B!10)) | (~relation(B!10)) | ![B: $i] : ((~relation(B)) | (~function(B)) | subset(relation_rng(B), relation_dom(B!10)) | (~(relation_dom(relation_composition(B, B!10)) = relation_dom(B)))))),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(59,plain,
% 0.18/0.39 (^[B: $i] : rewrite((subset(relation_rng(B), relation_dom(B!10)) | (~(relation_dom(relation_composition(B, B!10)) = relation_dom(B))) | (~relation(B)) | (~function(B))) <=> ((~relation(B)) | (~function(B)) | subset(relation_rng(B), relation_dom(B!10)) | (~(relation_dom(relation_composition(B, B!10)) = relation_dom(B)))))),
% 0.18/0.39 inference(bind,[status(th)],[])).
% 0.18/0.39 tff(60,plain,
% 0.18/0.39 (![B: $i] : (subset(relation_rng(B), relation_dom(B!10)) | (~(relation_dom(relation_composition(B, B!10)) = relation_dom(B))) | (~relation(B)) | (~function(B))) <=> ![B: $i] : ((~relation(B)) | (~function(B)) | subset(relation_rng(B), relation_dom(B!10)) | (~(relation_dom(relation_composition(B, B!10)) = relation_dom(B))))),
% 0.18/0.39 inference(quant_intro,[status(thm)],[59])).
% 0.18/0.39 tff(61,plain,
% 0.18/0.39 (((~relation(B!10)) | (~function(B!10)) | ![B: $i] : (subset(relation_rng(B), relation_dom(B!10)) | (~(relation_dom(relation_composition(B, B!10)) = relation_dom(B))) | (~relation(B)) | (~function(B)))) <=> ((~relation(B!10)) | (~function(B!10)) | ![B: $i] : ((~relation(B)) | (~function(B)) | subset(relation_rng(B), relation_dom(B!10)) | (~(relation_dom(relation_composition(B, B!10)) = relation_dom(B)))))),
% 0.18/0.39 inference(monotonicity,[status(thm)],[60])).
% 0.18/0.39 tff(62,plain,
% 0.18/0.39 (((~relation(B!10)) | (~function(B!10)) | ![B: $i] : (subset(relation_rng(B), relation_dom(B!10)) | (~(relation_dom(relation_composition(B, B!10)) = relation_dom(B))) | (~relation(B)) | (~function(B)))) <=> ((~function(B!10)) | (~relation(B!10)) | ![B: $i] : ((~relation(B)) | (~function(B)) | subset(relation_rng(B), relation_dom(B!10)) | (~(relation_dom(relation_composition(B, B!10)) = relation_dom(B)))))),
% 0.18/0.39 inference(transitivity,[status(thm)],[61, 58])).
% 0.18/0.39 tff(63,plain,
% 0.18/0.39 (((~![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i] : (subset(relation_rng(B), relation_dom(A)) | (~(relation_dom(relation_composition(B, A)) = relation_dom(B))) | (~relation(B)) | (~function(B))))) | ((~relation(B!10)) | (~function(B!10)) | ![B: $i] : (subset(relation_rng(B), relation_dom(B!10)) | (~(relation_dom(relation_composition(B, B!10)) = relation_dom(B))) | (~relation(B)) | (~function(B))))) <=> ((~![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i] : (subset(relation_rng(B), relation_dom(A)) | (~(relation_dom(relation_composition(B, A)) = relation_dom(B))) | (~relation(B)) | (~function(B))))) | ((~function(B!10)) | (~relation(B!10)) | ![B: $i] : ((~relation(B)) | (~function(B)) | subset(relation_rng(B), relation_dom(B!10)) | (~(relation_dom(relation_composition(B, B!10)) = relation_dom(B))))))),
% 0.18/0.39 inference(monotonicity,[status(thm)],[62])).
% 0.18/0.39 tff(64,plain,
% 0.18/0.39 (((~![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i] : (subset(relation_rng(B), relation_dom(A)) | (~(relation_dom(relation_composition(B, A)) = relation_dom(B))) | (~relation(B)) | (~function(B))))) | ((~relation(B!10)) | (~function(B!10)) | ![B: $i] : (subset(relation_rng(B), relation_dom(B!10)) | (~(relation_dom(relation_composition(B, B!10)) = relation_dom(B))) | (~relation(B)) | (~function(B))))) <=> ((~![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i] : (subset(relation_rng(B), relation_dom(A)) | (~(relation_dom(relation_composition(B, A)) = relation_dom(B))) | (~relation(B)) | (~function(B))))) | (~function(B!10)) | (~relation(B!10)) | ![B: $i] : ((~relation(B)) | (~function(B)) | subset(relation_rng(B), relation_dom(B!10)) | (~(relation_dom(relation_composition(B, B!10)) = relation_dom(B)))))),
% 0.18/0.39 inference(transitivity,[status(thm)],[63, 57])).
% 0.18/0.39 tff(65,plain,
% 0.18/0.39 ((~![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i] : (subset(relation_rng(B), relation_dom(A)) | (~(relation_dom(relation_composition(B, A)) = relation_dom(B))) | (~relation(B)) | (~function(B))))) | ((~relation(B!10)) | (~function(B!10)) | ![B: $i] : (subset(relation_rng(B), relation_dom(B!10)) | (~(relation_dom(relation_composition(B, B!10)) = relation_dom(B))) | (~relation(B)) | (~function(B))))),
% 0.18/0.39 inference(quant_inst,[status(thm)],[])).
% 0.18/0.39 tff(66,plain,
% 0.18/0.39 ((~![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i] : (subset(relation_rng(B), relation_dom(A)) | (~(relation_dom(relation_composition(B, A)) = relation_dom(B))) | (~relation(B)) | (~function(B))))) | (~function(B!10)) | (~relation(B!10)) | ![B: $i] : ((~relation(B)) | (~function(B)) | subset(relation_rng(B), relation_dom(B!10)) | (~(relation_dom(relation_composition(B, B!10)) = relation_dom(B))))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[65, 64])).
% 0.18/0.39 tff(67,plain,
% 0.18/0.39 (![B: $i] : ((~relation(B)) | (~function(B)) | subset(relation_rng(B), relation_dom(B!10)) | (~(relation_dom(relation_composition(B, B!10)) = relation_dom(B))))),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[66, 56, 40, 39])).
% 0.18/0.39 tff(68,plain,
% 0.18/0.39 (function(A!9)),
% 0.18/0.39 inference(and_elim,[status(thm)],[9])).
% 0.18/0.39 tff(69,plain,
% 0.18/0.39 (relation(A!9)),
% 0.18/0.39 inference(and_elim,[status(thm)],[9])).
% 0.18/0.39 tff(70,plain,
% 0.18/0.39 (((~![B: $i] : ((~relation(B)) | (~function(B)) | subset(relation_rng(B), relation_dom(B!10)) | (~(relation_dom(relation_composition(B, B!10)) = relation_dom(B))))) | ((~function(A!9)) | (~relation(A!9)) | subset(relation_rng(A!9), relation_dom(B!10)) | (~(relation_dom(relation_composition(A!9, B!10)) = relation_dom(A!9))))) <=> ((~![B: $i] : ((~relation(B)) | (~function(B)) | subset(relation_rng(B), relation_dom(B!10)) | (~(relation_dom(relation_composition(B, B!10)) = relation_dom(B))))) | (~function(A!9)) | (~relation(A!9)) | subset(relation_rng(A!9), relation_dom(B!10)) | (~(relation_dom(relation_composition(A!9, B!10)) = relation_dom(A!9))))),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(71,plain,
% 0.18/0.39 (((~relation(A!9)) | (~function(A!9)) | subset(relation_rng(A!9), relation_dom(B!10)) | (~(relation_dom(relation_composition(A!9, B!10)) = relation_dom(A!9)))) <=> ((~function(A!9)) | (~relation(A!9)) | subset(relation_rng(A!9), relation_dom(B!10)) | (~(relation_dom(relation_composition(A!9, B!10)) = relation_dom(A!9))))),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(72,plain,
% 0.18/0.39 (((~![B: $i] : ((~relation(B)) | (~function(B)) | subset(relation_rng(B), relation_dom(B!10)) | (~(relation_dom(relation_composition(B, B!10)) = relation_dom(B))))) | ((~relation(A!9)) | (~function(A!9)) | subset(relation_rng(A!9), relation_dom(B!10)) | (~(relation_dom(relation_composition(A!9, B!10)) = relation_dom(A!9))))) <=> ((~![B: $i] : ((~relation(B)) | (~function(B)) | subset(relation_rng(B), relation_dom(B!10)) | (~(relation_dom(relation_composition(B, B!10)) = relation_dom(B))))) | ((~function(A!9)) | (~relation(A!9)) | subset(relation_rng(A!9), relation_dom(B!10)) | (~(relation_dom(relation_composition(A!9, B!10)) = relation_dom(A!9)))))),
% 0.18/0.39 inference(monotonicity,[status(thm)],[71])).
% 0.18/0.39 tff(73,plain,
% 0.18/0.39 (((~![B: $i] : ((~relation(B)) | (~function(B)) | subset(relation_rng(B), relation_dom(B!10)) | (~(relation_dom(relation_composition(B, B!10)) = relation_dom(B))))) | ((~relation(A!9)) | (~function(A!9)) | subset(relation_rng(A!9), relation_dom(B!10)) | (~(relation_dom(relation_composition(A!9, B!10)) = relation_dom(A!9))))) <=> ((~![B: $i] : ((~relation(B)) | (~function(B)) | subset(relation_rng(B), relation_dom(B!10)) | (~(relation_dom(relation_composition(B, B!10)) = relation_dom(B))))) | (~function(A!9)) | (~relation(A!9)) | subset(relation_rng(A!9), relation_dom(B!10)) | (~(relation_dom(relation_composition(A!9, B!10)) = relation_dom(A!9))))),
% 0.18/0.39 inference(transitivity,[status(thm)],[72, 70])).
% 0.18/0.39 tff(74,plain,
% 0.18/0.39 ((~![B: $i] : ((~relation(B)) | (~function(B)) | subset(relation_rng(B), relation_dom(B!10)) | (~(relation_dom(relation_composition(B, B!10)) = relation_dom(B))))) | ((~relation(A!9)) | (~function(A!9)) | subset(relation_rng(A!9), relation_dom(B!10)) | (~(relation_dom(relation_composition(A!9, B!10)) = relation_dom(A!9))))),
% 0.18/0.39 inference(quant_inst,[status(thm)],[])).
% 0.18/0.39 tff(75,plain,
% 0.18/0.39 ((~![B: $i] : ((~relation(B)) | (~function(B)) | subset(relation_rng(B), relation_dom(B!10)) | (~(relation_dom(relation_composition(B, B!10)) = relation_dom(B))))) | (~function(A!9)) | (~relation(A!9)) | subset(relation_rng(A!9), relation_dom(B!10)) | (~(relation_dom(relation_composition(A!9, B!10)) = relation_dom(A!9)))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[74, 73])).
% 0.18/0.39 tff(76,plain,
% 0.18/0.39 (subset(relation_rng(A!9), relation_dom(B!10)) | (~(relation_dom(relation_composition(A!9, B!10)) = relation_dom(A!9)))),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[75, 69, 68, 67])).
% 0.18/0.39 tff(77,plain,
% 0.18/0.39 (subset(relation_rng(A!9), relation_dom(B!10))),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[76, 38])).
% 0.18/0.39 tff(78,plain,
% 0.18/0.39 (^[A: $i] : refl(((~relation(A)) | (~function(A)) | ![B: $i] : (one_to_one(B) | (~relation(B)) | (~function(B)) | (~one_to_one(relation_composition(B, A))) | (~subset(relation_rng(B), relation_dom(A))))) <=> ((~relation(A)) | (~function(A)) | ![B: $i] : (one_to_one(B) | (~relation(B)) | (~function(B)) | (~one_to_one(relation_composition(B, A))) | (~subset(relation_rng(B), relation_dom(A))))))),
% 0.18/0.39 inference(bind,[status(th)],[])).
% 0.18/0.39 tff(79,plain,
% 0.18/0.39 (![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i] : (one_to_one(B) | (~relation(B)) | (~function(B)) | (~one_to_one(relation_composition(B, A))) | (~subset(relation_rng(B), relation_dom(A))))) <=> ![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i] : (one_to_one(B) | (~relation(B)) | (~function(B)) | (~one_to_one(relation_composition(B, A))) | (~subset(relation_rng(B), relation_dom(A)))))),
% 0.18/0.39 inference(quant_intro,[status(thm)],[78])).
% 0.18/0.39 tff(80,plain,
% 0.18/0.39 (^[A: $i] : rewrite(((~relation(A)) | (~function(A)) | ![B: $i] : (one_to_one(B) | (~relation(B)) | (~function(B)) | (~one_to_one(relation_composition(B, A))) | (~subset(relation_rng(B), relation_dom(A))))) <=> ((~relation(A)) | (~function(A)) | ![B: $i] : (one_to_one(B) | (~relation(B)) | (~function(B)) | (~one_to_one(relation_composition(B, A))) | (~subset(relation_rng(B), relation_dom(A))))))),
% 0.18/0.39 inference(bind,[status(th)],[])).
% 0.18/0.39 tff(81,plain,
% 0.18/0.39 (![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i] : (one_to_one(B) | (~relation(B)) | (~function(B)) | (~one_to_one(relation_composition(B, A))) | (~subset(relation_rng(B), relation_dom(A))))) <=> ![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i] : (one_to_one(B) | (~relation(B)) | (~function(B)) | (~one_to_one(relation_composition(B, A))) | (~subset(relation_rng(B), relation_dom(A)))))),
% 0.18/0.39 inference(quant_intro,[status(thm)],[80])).
% 0.18/0.39 tff(82,plain,
% 0.18/0.39 (![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i] : (one_to_one(B) | (~relation(B)) | (~function(B)) | (~one_to_one(relation_composition(B, A))) | (~subset(relation_rng(B), relation_dom(A))))) <=> ![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i] : (one_to_one(B) | (~relation(B)) | (~function(B)) | (~one_to_one(relation_composition(B, A))) | (~subset(relation_rng(B), relation_dom(A)))))),
% 0.18/0.39 inference(transitivity,[status(thm)],[81, 79])).
% 0.18/0.39 tff(83,plain,
% 0.18/0.39 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite((relation(A) & function(A)) <=> (~((~relation(A)) | (~function(A))))), ((~(relation(A) & function(A))) <=> (~(~((~relation(A)) | (~function(A))))))), rewrite((~(~((~relation(A)) | (~function(A))))) <=> ((~relation(A)) | (~function(A)))), ((~(relation(A) & function(A))) <=> ((~relation(A)) | (~function(A))))), quant_intro(proof_bind(^[B: $i] : trans(monotonicity(trans(monotonicity(rewrite((relation(B) & function(B)) <=> (~((~relation(B)) | (~function(B))))), ((~(relation(B) & function(B))) <=> (~(~((~relation(B)) | (~function(B))))))), rewrite((~(~((~relation(B)) | (~function(B))))) <=> ((~relation(B)) | (~function(B)))), ((~(relation(B) & function(B))) <=> ((~relation(B)) | (~function(B))))), trans(monotonicity(rewrite((one_to_one(relation_composition(B, A)) & subset(relation_rng(B), relation_dom(A))) <=> (~((~one_to_one(relation_composition(B, A))) | (~subset(relation_rng(B), relation_dom(A)))))), ((~(one_to_one(relation_composition(B, A)) & subset(relation_rng(B), relation_dom(A)))) <=> (~(~((~one_to_one(relation_composition(B, A))) | (~subset(relation_rng(B), relation_dom(A)))))))), rewrite((~(~((~one_to_one(relation_composition(B, A))) | (~subset(relation_rng(B), relation_dom(A)))))) <=> ((~one_to_one(relation_composition(B, A))) | (~subset(relation_rng(B), relation_dom(A))))), ((~(one_to_one(relation_composition(B, A)) & subset(relation_rng(B), relation_dom(A)))) <=> ((~one_to_one(relation_composition(B, A))) | (~subset(relation_rng(B), relation_dom(A)))))), ((one_to_one(B) | (~(relation(B) & function(B))) | (~(one_to_one(relation_composition(B, A)) & subset(relation_rng(B), relation_dom(A))))) <=> (one_to_one(B) | ((~relation(B)) | (~function(B))) | ((~one_to_one(relation_composition(B, A))) | (~subset(relation_rng(B), relation_dom(A))))))), rewrite((one_to_one(B) | ((~relation(B)) | (~function(B))) | ((~one_to_one(relation_composition(B, A))) | (~subset(relation_rng(B), relation_dom(A))))) <=> (one_to_one(B) | (~relation(B)) | (~function(B)) | (~one_to_one(relation_composition(B, A))) | (~subset(relation_rng(B), relation_dom(A))))), ((one_to_one(B) | (~(relation(B) & function(B))) | (~(one_to_one(relation_composition(B, A)) & subset(relation_rng(B), relation_dom(A))))) <=> (one_to_one(B) | (~relation(B)) | (~function(B)) | (~one_to_one(relation_composition(B, A))) | (~subset(relation_rng(B), relation_dom(A))))))), (![B: $i] : (one_to_one(B) | (~(relation(B) & function(B))) | (~(one_to_one(relation_composition(B, A)) & subset(relation_rng(B), relation_dom(A))))) <=> ![B: $i] : (one_to_one(B) | (~relation(B)) | (~function(B)) | (~one_to_one(relation_composition(B, A))) | (~subset(relation_rng(B), relation_dom(A)))))), (((~(relation(A) & function(A))) | ![B: $i] : (one_to_one(B) | (~(relation(B) & function(B))) | (~(one_to_one(relation_composition(B, A)) & subset(relation_rng(B), relation_dom(A)))))) <=> (((~relation(A)) | (~function(A))) | ![B: $i] : (one_to_one(B) | (~relation(B)) | (~function(B)) | (~one_to_one(relation_composition(B, A))) | (~subset(relation_rng(B), relation_dom(A))))))), rewrite((((~relation(A)) | (~function(A))) | ![B: $i] : (one_to_one(B) | (~relation(B)) | (~function(B)) | (~one_to_one(relation_composition(B, A))) | (~subset(relation_rng(B), relation_dom(A))))) <=> ((~relation(A)) | (~function(A)) | ![B: $i] : (one_to_one(B) | (~relation(B)) | (~function(B)) | (~one_to_one(relation_composition(B, A))) | (~subset(relation_rng(B), relation_dom(A)))))), (((~(relation(A) & function(A))) | ![B: $i] : (one_to_one(B) | (~(relation(B) & function(B))) | (~(one_to_one(relation_composition(B, A)) & subset(relation_rng(B), relation_dom(A)))))) <=> ((~relation(A)) | (~function(A)) | ![B: $i] : (one_to_one(B) | (~relation(B)) | (~function(B)) | (~one_to_one(relation_composition(B, A))) | (~subset(relation_rng(B), relation_dom(A)))))))),
% 0.18/0.39 inference(bind,[status(th)],[])).
% 0.18/0.39 tff(84,plain,
% 0.18/0.39 (![A: $i] : ((~(relation(A) & function(A))) | ![B: $i] : (one_to_one(B) | (~(relation(B) & function(B))) | (~(one_to_one(relation_composition(B, A)) & subset(relation_rng(B), relation_dom(A)))))) <=> ![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i] : (one_to_one(B) | (~relation(B)) | (~function(B)) | (~one_to_one(relation_composition(B, A))) | (~subset(relation_rng(B), relation_dom(A)))))),
% 0.18/0.39 inference(quant_intro,[status(thm)],[83])).
% 0.18/0.39 tff(85,plain,
% 0.18/0.39 (![A: $i] : ((~(relation(A) & function(A))) | ![B: $i] : (one_to_one(B) | (~(relation(B) & function(B))) | (~(one_to_one(relation_composition(B, A)) & subset(relation_rng(B), relation_dom(A)))))) <=> ![A: $i] : ((~(relation(A) & function(A))) | ![B: $i] : (one_to_one(B) | (~(relation(B) & function(B))) | (~(one_to_one(relation_composition(B, A)) & subset(relation_rng(B), relation_dom(A))))))),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(86,plain,
% 0.18/0.39 (^[A: $i] : trans(monotonicity(quant_intro(proof_bind(^[B: $i] : trans(monotonicity(rewrite(((one_to_one(relation_composition(B, A)) & subset(relation_rng(B), relation_dom(A))) => one_to_one(B)) <=> (one_to_one(B) | (~(one_to_one(relation_composition(B, A)) & subset(relation_rng(B), relation_dom(A)))))), (((relation(B) & function(B)) => ((one_to_one(relation_composition(B, A)) & subset(relation_rng(B), relation_dom(A))) => one_to_one(B))) <=> ((relation(B) & function(B)) => (one_to_one(B) | (~(one_to_one(relation_composition(B, A)) & subset(relation_rng(B), relation_dom(A)))))))), rewrite(((relation(B) & function(B)) => (one_to_one(B) | (~(one_to_one(relation_composition(B, A)) & subset(relation_rng(B), relation_dom(A)))))) <=> (one_to_one(B) | (~(relation(B) & function(B))) | (~(one_to_one(relation_composition(B, A)) & subset(relation_rng(B), relation_dom(A)))))), (((relation(B) & function(B)) => ((one_to_one(relation_composition(B, A)) & subset(relation_rng(B), relation_dom(A))) => one_to_one(B))) <=> (one_to_one(B) | (~(relation(B) & function(B))) | (~(one_to_one(relation_composition(B, A)) & subset(relation_rng(B), relation_dom(A)))))))), (![B: $i] : ((relation(B) & function(B)) => ((one_to_one(relation_composition(B, A)) & subset(relation_rng(B), relation_dom(A))) => one_to_one(B))) <=> ![B: $i] : (one_to_one(B) | (~(relation(B) & function(B))) | (~(one_to_one(relation_composition(B, A)) & subset(relation_rng(B), relation_dom(A))))))), (((relation(A) & function(A)) => ![B: $i] : ((relation(B) & function(B)) => ((one_to_one(relation_composition(B, A)) & subset(relation_rng(B), relation_dom(A))) => one_to_one(B)))) <=> ((relation(A) & function(A)) => ![B: $i] : (one_to_one(B) | (~(relation(B) & function(B))) | (~(one_to_one(relation_composition(B, A)) & subset(relation_rng(B), relation_dom(A)))))))), rewrite(((relation(A) & function(A)) => ![B: $i] : (one_to_one(B) | (~(relation(B) & function(B))) | (~(one_to_one(relation_composition(B, A)) & subset(relation_rng(B), relation_dom(A)))))) <=> ((~(relation(A) & function(A))) | ![B: $i] : (one_to_one(B) | (~(relation(B) & function(B))) | (~(one_to_one(relation_composition(B, A)) & subset(relation_rng(B), relation_dom(A))))))), (((relation(A) & function(A)) => ![B: $i] : ((relation(B) & function(B)) => ((one_to_one(relation_composition(B, A)) & subset(relation_rng(B), relation_dom(A))) => one_to_one(B)))) <=> ((~(relation(A) & function(A))) | ![B: $i] : (one_to_one(B) | (~(relation(B) & function(B))) | (~(one_to_one(relation_composition(B, A)) & subset(relation_rng(B), relation_dom(A))))))))),
% 0.18/0.39 inference(bind,[status(th)],[])).
% 0.18/0.39 tff(87,plain,
% 0.18/0.39 (![A: $i] : ((relation(A) & function(A)) => ![B: $i] : ((relation(B) & function(B)) => ((one_to_one(relation_composition(B, A)) & subset(relation_rng(B), relation_dom(A))) => one_to_one(B)))) <=> ![A: $i] : ((~(relation(A) & function(A))) | ![B: $i] : (one_to_one(B) | (~(relation(B) & function(B))) | (~(one_to_one(relation_composition(B, A)) & subset(relation_rng(B), relation_dom(A))))))),
% 0.18/0.39 inference(quant_intro,[status(thm)],[86])).
% 0.18/0.39 tff(88,axiom,(![A: $i] : ((relation(A) & function(A)) => ![B: $i] : ((relation(B) & function(B)) => ((one_to_one(relation_composition(B, A)) & subset(relation_rng(B), relation_dom(A))) => one_to_one(B))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t47_funct_1')).
% 0.18/0.39 tff(89,plain,
% 0.18/0.39 (![A: $i] : ((~(relation(A) & function(A))) | ![B: $i] : (one_to_one(B) | (~(relation(B) & function(B))) | (~(one_to_one(relation_composition(B, A)) & subset(relation_rng(B), relation_dom(A))))))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[88, 87])).
% 0.18/0.39 tff(90,plain,
% 0.18/0.39 (![A: $i] : ((~(relation(A) & function(A))) | ![B: $i] : (one_to_one(B) | (~(relation(B) & function(B))) | (~(one_to_one(relation_composition(B, A)) & subset(relation_rng(B), relation_dom(A))))))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[89, 85])).
% 0.18/0.40 tff(91,plain,(
% 0.18/0.40 ![A: $i] : ((~(relation(A) & function(A))) | ![B: $i] : (one_to_one(B) | (~(relation(B) & function(B))) | (~(one_to_one(relation_composition(B, A)) & subset(relation_rng(B), relation_dom(A))))))),
% 0.18/0.40 inference(skolemize,[status(sab)],[90])).
% 0.18/0.40 tff(92,plain,
% 0.18/0.40 (![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i] : (one_to_one(B) | (~relation(B)) | (~function(B)) | (~one_to_one(relation_composition(B, A))) | (~subset(relation_rng(B), relation_dom(A)))))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[91, 84])).
% 0.18/0.40 tff(93,plain,
% 0.18/0.40 (![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i] : (one_to_one(B) | (~relation(B)) | (~function(B)) | (~one_to_one(relation_composition(B, A))) | (~subset(relation_rng(B), relation_dom(A)))))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[92, 82])).
% 0.18/0.40 tff(94,plain,
% 0.18/0.40 (((~![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i] : (one_to_one(B) | (~relation(B)) | (~function(B)) | (~one_to_one(relation_composition(B, A))) | (~subset(relation_rng(B), relation_dom(A)))))) | (![B: $i] : (one_to_one(B) | (~relation(B)) | (~function(B)) | (~one_to_one(relation_composition(B, B!10))) | (~subset(relation_rng(B), relation_dom(B!10)))) | (~function(B!10)) | (~relation(B!10)))) <=> ((~![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i] : (one_to_one(B) | (~relation(B)) | (~function(B)) | (~one_to_one(relation_composition(B, A))) | (~subset(relation_rng(B), relation_dom(A)))))) | ![B: $i] : (one_to_one(B) | (~relation(B)) | (~function(B)) | (~one_to_one(relation_composition(B, B!10))) | (~subset(relation_rng(B), relation_dom(B!10)))) | (~function(B!10)) | (~relation(B!10)))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(95,plain,
% 0.18/0.40 (((~relation(B!10)) | (~function(B!10)) | ![B: $i] : (one_to_one(B) | (~relation(B)) | (~function(B)) | (~one_to_one(relation_composition(B, B!10))) | (~subset(relation_rng(B), relation_dom(B!10))))) <=> (![B: $i] : (one_to_one(B) | (~relation(B)) | (~function(B)) | (~one_to_one(relation_composition(B, B!10))) | (~subset(relation_rng(B), relation_dom(B!10)))) | (~function(B!10)) | (~relation(B!10)))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(96,plain,
% 0.18/0.40 (((~![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i] : (one_to_one(B) | (~relation(B)) | (~function(B)) | (~one_to_one(relation_composition(B, A))) | (~subset(relation_rng(B), relation_dom(A)))))) | ((~relation(B!10)) | (~function(B!10)) | ![B: $i] : (one_to_one(B) | (~relation(B)) | (~function(B)) | (~one_to_one(relation_composition(B, B!10))) | (~subset(relation_rng(B), relation_dom(B!10)))))) <=> ((~![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i] : (one_to_one(B) | (~relation(B)) | (~function(B)) | (~one_to_one(relation_composition(B, A))) | (~subset(relation_rng(B), relation_dom(A)))))) | (![B: $i] : (one_to_one(B) | (~relation(B)) | (~function(B)) | (~one_to_one(relation_composition(B, B!10))) | (~subset(relation_rng(B), relation_dom(B!10)))) | (~function(B!10)) | (~relation(B!10))))),
% 0.18/0.40 inference(monotonicity,[status(thm)],[95])).
% 0.18/0.40 tff(97,plain,
% 0.18/0.40 (((~![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i] : (one_to_one(B) | (~relation(B)) | (~function(B)) | (~one_to_one(relation_composition(B, A))) | (~subset(relation_rng(B), relation_dom(A)))))) | ((~relation(B!10)) | (~function(B!10)) | ![B: $i] : (one_to_one(B) | (~relation(B)) | (~function(B)) | (~one_to_one(relation_composition(B, B!10))) | (~subset(relation_rng(B), relation_dom(B!10)))))) <=> ((~![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i] : (one_to_one(B) | (~relation(B)) | (~function(B)) | (~one_to_one(relation_composition(B, A))) | (~subset(relation_rng(B), relation_dom(A)))))) | ![B: $i] : (one_to_one(B) | (~relation(B)) | (~function(B)) | (~one_to_one(relation_composition(B, B!10))) | (~subset(relation_rng(B), relation_dom(B!10)))) | (~function(B!10)) | (~relation(B!10)))),
% 0.18/0.40 inference(transitivity,[status(thm)],[96, 94])).
% 0.18/0.40 tff(98,plain,
% 0.18/0.40 ((~![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i] : (one_to_one(B) | (~relation(B)) | (~function(B)) | (~one_to_one(relation_composition(B, A))) | (~subset(relation_rng(B), relation_dom(A)))))) | ((~relation(B!10)) | (~function(B!10)) | ![B: $i] : (one_to_one(B) | (~relation(B)) | (~function(B)) | (~one_to_one(relation_composition(B, B!10))) | (~subset(relation_rng(B), relation_dom(B!10)))))),
% 0.18/0.40 inference(quant_inst,[status(thm)],[])).
% 0.18/0.40 tff(99,plain,
% 0.18/0.40 ((~![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i] : (one_to_one(B) | (~relation(B)) | (~function(B)) | (~one_to_one(relation_composition(B, A))) | (~subset(relation_rng(B), relation_dom(A)))))) | ![B: $i] : (one_to_one(B) | (~relation(B)) | (~function(B)) | (~one_to_one(relation_composition(B, B!10))) | (~subset(relation_rng(B), relation_dom(B!10)))) | (~function(B!10)) | (~relation(B!10))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[98, 97])).
% 0.18/0.40 tff(100,plain,
% 0.18/0.40 (![B: $i] : (one_to_one(B) | (~relation(B)) | (~function(B)) | (~one_to_one(relation_composition(B, B!10))) | (~subset(relation_rng(B), relation_dom(B!10))))),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[99, 93, 40, 39])).
% 0.18/0.40 tff(101,plain,
% 0.18/0.40 (~one_to_one(A!9)),
% 0.18/0.40 inference(and_elim,[status(thm)],[9])).
% 0.18/0.40 tff(102,plain,
% 0.18/0.40 (((~![B: $i] : (one_to_one(B) | (~relation(B)) | (~function(B)) | (~one_to_one(relation_composition(B, B!10))) | (~subset(relation_rng(B), relation_dom(B!10))))) | (one_to_one(A!9) | (~function(A!9)) | (~relation(A!9)) | (~one_to_one(relation_composition(A!9, B!10))) | (~subset(relation_rng(A!9), relation_dom(B!10))))) <=> ((~![B: $i] : (one_to_one(B) | (~relation(B)) | (~function(B)) | (~one_to_one(relation_composition(B, B!10))) | (~subset(relation_rng(B), relation_dom(B!10))))) | one_to_one(A!9) | (~function(A!9)) | (~relation(A!9)) | (~one_to_one(relation_composition(A!9, B!10))) | (~subset(relation_rng(A!9), relation_dom(B!10))))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(103,plain,
% 0.18/0.40 ((one_to_one(A!9) | (~relation(A!9)) | (~function(A!9)) | (~one_to_one(relation_composition(A!9, B!10))) | (~subset(relation_rng(A!9), relation_dom(B!10)))) <=> (one_to_one(A!9) | (~function(A!9)) | (~relation(A!9)) | (~one_to_one(relation_composition(A!9, B!10))) | (~subset(relation_rng(A!9), relation_dom(B!10))))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(104,plain,
% 0.18/0.40 (((~![B: $i] : (one_to_one(B) | (~relation(B)) | (~function(B)) | (~one_to_one(relation_composition(B, B!10))) | (~subset(relation_rng(B), relation_dom(B!10))))) | (one_to_one(A!9) | (~relation(A!9)) | (~function(A!9)) | (~one_to_one(relation_composition(A!9, B!10))) | (~subset(relation_rng(A!9), relation_dom(B!10))))) <=> ((~![B: $i] : (one_to_one(B) | (~relation(B)) | (~function(B)) | (~one_to_one(relation_composition(B, B!10))) | (~subset(relation_rng(B), relation_dom(B!10))))) | (one_to_one(A!9) | (~function(A!9)) | (~relation(A!9)) | (~one_to_one(relation_composition(A!9, B!10))) | (~subset(relation_rng(A!9), relation_dom(B!10)))))),
% 0.18/0.40 inference(monotonicity,[status(thm)],[103])).
% 0.18/0.40 tff(105,plain,
% 0.18/0.40 (((~![B: $i] : (one_to_one(B) | (~relation(B)) | (~function(B)) | (~one_to_one(relation_composition(B, B!10))) | (~subset(relation_rng(B), relation_dom(B!10))))) | (one_to_one(A!9) | (~relation(A!9)) | (~function(A!9)) | (~one_to_one(relation_composition(A!9, B!10))) | (~subset(relation_rng(A!9), relation_dom(B!10))))) <=> ((~![B: $i] : (one_to_one(B) | (~relation(B)) | (~function(B)) | (~one_to_one(relation_composition(B, B!10))) | (~subset(relation_rng(B), relation_dom(B!10))))) | one_to_one(A!9) | (~function(A!9)) | (~relation(A!9)) | (~one_to_one(relation_composition(A!9, B!10))) | (~subset(relation_rng(A!9), relation_dom(B!10))))),
% 0.18/0.40 inference(transitivity,[status(thm)],[104, 102])).
% 0.18/0.40 tff(106,plain,
% 0.18/0.40 ((~![B: $i] : (one_to_one(B) | (~relation(B)) | (~function(B)) | (~one_to_one(relation_composition(B, B!10))) | (~subset(relation_rng(B), relation_dom(B!10))))) | (one_to_one(A!9) | (~relation(A!9)) | (~function(A!9)) | (~one_to_one(relation_composition(A!9, B!10))) | (~subset(relation_rng(A!9), relation_dom(B!10))))),
% 0.18/0.40 inference(quant_inst,[status(thm)],[])).
% 0.18/0.40 tff(107,plain,
% 0.18/0.40 ((~![B: $i] : (one_to_one(B) | (~relation(B)) | (~function(B)) | (~one_to_one(relation_composition(B, B!10))) | (~subset(relation_rng(B), relation_dom(B!10))))) | one_to_one(A!9) | (~function(A!9)) | (~relation(A!9)) | (~one_to_one(relation_composition(A!9, B!10))) | (~subset(relation_rng(A!9), relation_dom(B!10)))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[106, 105])).
% 0.18/0.40 tff(108,plain,
% 0.18/0.40 ((~one_to_one(relation_composition(A!9, B!10))) | (~subset(relation_rng(A!9), relation_dom(B!10)))),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[107, 101, 69, 68, 100])).
% 0.18/0.40 tff(109,plain,
% 0.18/0.40 ($false),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[108, 77, 22])).
% 0.18/0.40 % SZS output end Proof
% 0.18/0.40 % E exiting
%------------------------------------------------------------------------------