%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SEU225+2 : TPTP v9.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n011.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 05:27:18 AM UTC 2025
% Result : Theorem 1.38s 1.57s
% Output : Proof 1.38s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14 % Problem : SEU225+2 : TPTP v9.0.0. Released v3.3.0.
% 0.08/0.14 % Command : run_E %s %d THM
% 0.13/0.35 % Computer : n011.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Fri Jun 20 06:22:56 EDT 2025
% 0.13/0.35 % CPUTime :
% 1.38/1.57 % SZS status Theorem
% 1.38/1.57 % SZS output start Proof
% 1.38/1.57 tff(apply_type, type, (
% 1.38/1.57 apply: ( $i * $i ) > $i)).
% 1.38/1.57 tff(tptp_fun_B_77_type, type, (
% 1.38/1.57 tptp_fun_B_77: $i)).
% 1.38/1.57 tff(tptp_fun_C_76_type, type, (
% 1.38/1.57 tptp_fun_C_76: $i)).
% 1.38/1.57 tff(relation_dom_restriction_type, type, (
% 1.38/1.57 relation_dom_restriction: ( $i * $i ) > $i)).
% 1.38/1.57 tff(tptp_fun_A_78_type, type, (
% 1.38/1.57 tptp_fun_A_78: $i)).
% 1.38/1.57 tff(identity_relation_type, type, (
% 1.38/1.57 identity_relation: $i > $i)).
% 1.38/1.57 tff(in_type, type, (
% 1.38/1.57 in: ( $i * $i ) > $o)).
% 1.38/1.57 tff(function_type, type, (
% 1.38/1.57 function: $i > $o)).
% 1.38/1.57 tff(relation_type, type, (
% 1.38/1.57 relation: $i > $o)).
% 1.38/1.57 tff(relation_composition_type, type, (
% 1.38/1.57 relation_composition: ( $i * $i ) > $i)).
% 1.38/1.57 tff(relation_dom_type, type, (
% 1.38/1.57 relation_dom: $i > $i)).
% 1.38/1.57 tff(relation_rng_type, type, (
% 1.38/1.57 relation_rng: $i > $i)).
% 1.38/1.57 tff(1,plain,
% 1.38/1.57 ((~((apply(relation_dom_restriction(C!76, A!78), B!77) = apply(C!76, B!77)) | (~(relation(C!76) & function(C!76))) | (~in(B!77, A!78)))) <=> (~((apply(relation_dom_restriction(C!76, A!78), B!77) = apply(C!76, B!77)) | (~(relation(C!76) & function(C!76))) | (~in(B!77, A!78))))),
% 1.38/1.57 inference(rewrite,[status(thm)],[])).
% 1.38/1.57 tff(2,plain,
% 1.38/1.57 ((~![A: $i, B: $i, C: $i] : ((apply(relation_dom_restriction(C, A), B) = apply(C, B)) | (~(relation(C) & function(C))) | (~in(B, A)))) <=> (~![A: $i, B: $i, C: $i] : ((apply(relation_dom_restriction(C, A), B) = apply(C, B)) | (~(relation(C) & function(C))) | (~in(B, A))))),
% 1.38/1.57 inference(rewrite,[status(thm)],[])).
% 1.38/1.57 tff(3,plain,
% 1.38/1.57 ((~![A: $i, B: $i, C: $i] : ((relation(C) & function(C)) => (in(B, A) => (apply(relation_dom_restriction(C, A), B) = apply(C, B))))) <=> (~![A: $i, B: $i, C: $i] : ((apply(relation_dom_restriction(C, A), B) = apply(C, B)) | (~(relation(C) & function(C))) | (~in(B, A))))),
% 1.38/1.57 inference(rewrite,[status(thm)],[])).
% 1.38/1.57 tff(4,axiom,(~![A: $i, B: $i, C: $i] : ((relation(C) & function(C)) => (in(B, A) => (apply(relation_dom_restriction(C, A), B) = apply(C, B))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t72_funct_1')).
% 1.38/1.57 tff(5,plain,
% 1.38/1.57 (~![A: $i, B: $i, C: $i] : ((apply(relation_dom_restriction(C, A), B) = apply(C, B)) | (~(relation(C) & function(C))) | (~in(B, A)))),
% 1.38/1.57 inference(modus_ponens,[status(thm)],[4, 3])).
% 1.38/1.57 tff(6,plain,
% 1.38/1.57 (~![A: $i, B: $i, C: $i] : ((apply(relation_dom_restriction(C, A), B) = apply(C, B)) | (~(relation(C) & function(C))) | (~in(B, A)))),
% 1.38/1.57 inference(modus_ponens,[status(thm)],[5, 2])).
% 1.38/1.57 tff(7,plain,
% 1.38/1.57 (~![A: $i, B: $i, C: $i] : ((apply(relation_dom_restriction(C, A), B) = apply(C, B)) | (~(relation(C) & function(C))) | (~in(B, A)))),
% 1.38/1.57 inference(modus_ponens,[status(thm)],[6, 2])).
% 1.38/1.57 tff(8,plain,
% 1.38/1.57 (~![A: $i, B: $i, C: $i] : ((apply(relation_dom_restriction(C, A), B) = apply(C, B)) | (~(relation(C) & function(C))) | (~in(B, A)))),
% 1.38/1.57 inference(modus_ponens,[status(thm)],[7, 2])).
% 1.38/1.57 tff(9,plain,(
% 1.38/1.57 ~((apply(relation_dom_restriction(C!76, A!78), B!77) = apply(C!76, B!77)) | (~(relation(C!76) & function(C!76))) | (~in(B!77, A!78)))),
% 1.38/1.57 inference(skolemize,[status(sab)],[8])).
% 1.38/1.57 tff(10,plain,
% 1.38/1.57 (~((apply(relation_dom_restriction(C!76, A!78), B!77) = apply(C!76, B!77)) | (~(relation(C!76) & function(C!76))) | (~in(B!77, A!78)))),
% 1.38/1.57 inference(modus_ponens,[status(thm)],[9, 1])).
% 1.38/1.57 tff(11,plain,
% 1.38/1.57 (in(B!77, A!78)),
% 1.38/1.57 inference(or_elim,[status(thm)],[10])).
% 1.38/1.57 tff(12,plain,
% 1.38/1.57 (^[A: $i, B: $i] : refl(((~in(B, A)) | (apply(identity_relation(A), B) = B)) <=> ((~in(B, A)) | (apply(identity_relation(A), B) = B)))),
% 1.38/1.57 inference(bind,[status(th)],[])).
% 1.38/1.57 tff(13,plain,
% 1.38/1.57 (![A: $i, B: $i] : ((~in(B, A)) | (apply(identity_relation(A), B) = B)) <=> ![A: $i, B: $i] : ((~in(B, A)) | (apply(identity_relation(A), B) = B))),
% 1.38/1.57 inference(quant_intro,[status(thm)],[12])).
% 1.38/1.57 tff(14,plain,
% 1.38/1.57 (![A: $i, B: $i] : ((~in(B, A)) | (apply(identity_relation(A), B) = B)) <=> ![A: $i, B: $i] : ((~in(B, A)) | (apply(identity_relation(A), B) = B))),
% 1.38/1.57 inference(rewrite,[status(thm)],[])).
% 1.38/1.57 tff(15,plain,
% 1.38/1.57 (^[A: $i, B: $i] : rewrite((in(B, A) => (apply(identity_relation(A), B) = B)) <=> ((~in(B, A)) | (apply(identity_relation(A), B) = B)))),
% 1.38/1.57 inference(bind,[status(th)],[])).
% 1.38/1.58 tff(16,plain,
% 1.38/1.58 (![A: $i, B: $i] : (in(B, A) => (apply(identity_relation(A), B) = B)) <=> ![A: $i, B: $i] : ((~in(B, A)) | (apply(identity_relation(A), B) = B))),
% 1.38/1.58 inference(quant_intro,[status(thm)],[15])).
% 1.38/1.58 tff(17,axiom,(![A: $i, B: $i] : (in(B, A) => (apply(identity_relation(A), B) = B))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t35_funct_1')).
% 1.38/1.58 tff(18,plain,
% 1.38/1.58 (![A: $i, B: $i] : ((~in(B, A)) | (apply(identity_relation(A), B) = B))),
% 1.38/1.58 inference(modus_ponens,[status(thm)],[17, 16])).
% 1.38/1.58 tff(19,plain,
% 1.38/1.58 (![A: $i, B: $i] : ((~in(B, A)) | (apply(identity_relation(A), B) = B))),
% 1.38/1.58 inference(modus_ponens,[status(thm)],[18, 14])).
% 1.38/1.58 tff(20,plain,(
% 1.38/1.58 ![A: $i, B: $i] : ((~in(B, A)) | (apply(identity_relation(A), B) = B))),
% 1.38/1.58 inference(skolemize,[status(sab)],[19])).
% 1.38/1.58 tff(21,plain,
% 1.38/1.58 (![A: $i, B: $i] : ((~in(B, A)) | (apply(identity_relation(A), B) = B))),
% 1.38/1.58 inference(modus_ponens,[status(thm)],[20, 13])).
% 1.38/1.58 tff(22,plain,
% 1.38/1.58 (((~![A: $i, B: $i] : ((~in(B, A)) | (apply(identity_relation(A), B) = B))) | ((~in(B!77, A!78)) | (apply(identity_relation(A!78), B!77) = B!77))) <=> ((~![A: $i, B: $i] : ((~in(B, A)) | (apply(identity_relation(A), B) = B))) | (~in(B!77, A!78)) | (apply(identity_relation(A!78), B!77) = B!77))),
% 1.38/1.58 inference(rewrite,[status(thm)],[])).
% 1.38/1.58 tff(23,plain,
% 1.38/1.58 ((~![A: $i, B: $i] : ((~in(B, A)) | (apply(identity_relation(A), B) = B))) | ((~in(B!77, A!78)) | (apply(identity_relation(A!78), B!77) = B!77))),
% 1.38/1.58 inference(quant_inst,[status(thm)],[])).
% 1.38/1.58 tff(24,plain,
% 1.38/1.58 ((~![A: $i, B: $i] : ((~in(B, A)) | (apply(identity_relation(A), B) = B))) | (~in(B!77, A!78)) | (apply(identity_relation(A!78), B!77) = B!77)),
% 1.38/1.58 inference(modus_ponens,[status(thm)],[23, 22])).
% 1.38/1.58 tff(25,plain,
% 1.38/1.58 (apply(identity_relation(A!78), B!77) = B!77),
% 1.38/1.58 inference(unit_resolution,[status(thm)],[24, 21, 11])).
% 1.38/1.58 tff(26,plain,
% 1.38/1.58 (B!77 = apply(identity_relation(A!78), B!77)),
% 1.38/1.58 inference(symmetry,[status(thm)],[25])).
% 1.38/1.58 tff(27,plain,
% 1.38/1.58 (apply(C!76, B!77) = apply(C!76, apply(identity_relation(A!78), B!77))),
% 1.38/1.58 inference(monotonicity,[status(thm)],[26])).
% 1.38/1.58 tff(28,plain,
% 1.38/1.58 (apply(C!76, apply(identity_relation(A!78), B!77)) = apply(C!76, B!77)),
% 1.38/1.58 inference(symmetry,[status(thm)],[27])).
% 1.38/1.58 tff(29,plain,
% 1.38/1.58 (^[A: $i] : refl(relation(identity_relation(A)) <=> relation(identity_relation(A)))),
% 1.38/1.58 inference(bind,[status(th)],[])).
% 1.38/1.58 tff(30,plain,
% 1.38/1.58 (![A: $i] : relation(identity_relation(A)) <=> ![A: $i] : relation(identity_relation(A))),
% 1.38/1.58 inference(quant_intro,[status(thm)],[29])).
% 1.38/1.58 tff(31,plain,
% 1.38/1.58 (![A: $i] : relation(identity_relation(A)) <=> ![A: $i] : relation(identity_relation(A))),
% 1.38/1.58 inference(rewrite,[status(thm)],[])).
% 1.38/1.58 tff(32,axiom,(![A: $i] : relation(identity_relation(A))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_k6_relat_1')).
% 1.38/1.58 tff(33,plain,
% 1.38/1.58 (![A: $i] : relation(identity_relation(A))),
% 1.38/1.58 inference(modus_ponens,[status(thm)],[32, 31])).
% 1.38/1.58 tff(34,plain,(
% 1.38/1.58 ![A: $i] : relation(identity_relation(A))),
% 1.38/1.58 inference(skolemize,[status(sab)],[33])).
% 1.38/1.58 tff(35,plain,
% 1.38/1.58 (![A: $i] : relation(identity_relation(A))),
% 1.38/1.58 inference(modus_ponens,[status(thm)],[34, 30])).
% 1.38/1.58 tff(36,plain,
% 1.38/1.58 ((~![A: $i] : relation(identity_relation(A))) | relation(identity_relation(A!78))),
% 1.38/1.58 inference(quant_inst,[status(thm)],[])).
% 1.38/1.58 tff(37,plain,
% 1.38/1.58 (relation(identity_relation(A!78))),
% 1.38/1.58 inference(unit_resolution,[status(thm)],[36, 35])).
% 1.38/1.58 tff(38,plain,
% 1.38/1.58 (^[A: $i] : refl((~((~relation(identity_relation(A))) | (~function(identity_relation(A))))) <=> (~((~relation(identity_relation(A))) | (~function(identity_relation(A))))))),
% 1.38/1.58 inference(bind,[status(th)],[])).
% 1.38/1.58 tff(39,plain,
% 1.38/1.58 (![A: $i] : (~((~relation(identity_relation(A))) | (~function(identity_relation(A))))) <=> ![A: $i] : (~((~relation(identity_relation(A))) | (~function(identity_relation(A)))))),
% 1.38/1.58 inference(quant_intro,[status(thm)],[38])).
% 1.38/1.58 tff(40,plain,
% 1.38/1.58 (^[A: $i] : rewrite((relation(identity_relation(A)) & function(identity_relation(A))) <=> (~((~relation(identity_relation(A))) | (~function(identity_relation(A))))))),
% 1.38/1.58 inference(bind,[status(th)],[])).
% 1.38/1.58 tff(41,plain,
% 1.38/1.58 (![A: $i] : (relation(identity_relation(A)) & function(identity_relation(A))) <=> ![A: $i] : (~((~relation(identity_relation(A))) | (~function(identity_relation(A)))))),
% 1.38/1.58 inference(quant_intro,[status(thm)],[40])).
% 1.38/1.58 tff(42,plain,
% 1.38/1.58 (![A: $i] : (relation(identity_relation(A)) & function(identity_relation(A))) <=> ![A: $i] : (relation(identity_relation(A)) & function(identity_relation(A)))),
% 1.38/1.58 inference(rewrite,[status(thm)],[])).
% 1.38/1.58 tff(43,axiom,(![A: $i] : (relation(identity_relation(A)) & function(identity_relation(A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','fc2_funct_1')).
% 1.38/1.58 tff(44,plain,
% 1.38/1.58 (![A: $i] : (relation(identity_relation(A)) & function(identity_relation(A)))),
% 1.38/1.58 inference(modus_ponens,[status(thm)],[43, 42])).
% 1.38/1.58 tff(45,plain,(
% 1.38/1.58 ![A: $i] : (relation(identity_relation(A)) & function(identity_relation(A)))),
% 1.38/1.58 inference(skolemize,[status(sab)],[44])).
% 1.38/1.58 tff(46,plain,
% 1.38/1.58 (![A: $i] : (~((~relation(identity_relation(A))) | (~function(identity_relation(A)))))),
% 1.38/1.58 inference(modus_ponens,[status(thm)],[45, 41])).
% 1.38/1.58 tff(47,plain,
% 1.38/1.58 (![A: $i] : (~((~relation(identity_relation(A))) | (~function(identity_relation(A)))))),
% 1.38/1.58 inference(modus_ponens,[status(thm)],[46, 39])).
% 1.38/1.58 tff(48,plain,
% 1.38/1.58 ((~![A: $i] : (~((~relation(identity_relation(A))) | (~function(identity_relation(A)))))) | (~((~relation(identity_relation(A!78))) | (~function(identity_relation(A!78)))))),
% 1.38/1.58 inference(quant_inst,[status(thm)],[])).
% 1.38/1.58 tff(49,plain,
% 1.38/1.58 (~((~relation(identity_relation(A!78))) | (~function(identity_relation(A!78))))),
% 1.38/1.58 inference(unit_resolution,[status(thm)],[48, 47])).
% 1.38/1.58 tff(50,plain,
% 1.38/1.58 (((~relation(identity_relation(A!78))) | (~function(identity_relation(A!78)))) | function(identity_relation(A!78))),
% 1.38/1.58 inference(tautology,[status(thm)],[])).
% 1.38/1.58 tff(51,plain,
% 1.38/1.58 (function(identity_relation(A!78))),
% 1.38/1.58 inference(unit_resolution,[status(thm)],[50, 49])).
% 1.38/1.58 tff(52,plain,
% 1.38/1.58 (^[A: $i, B: $i] : refl(((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~relation(C)) | (~in(A, relation_dom(B))) | (~function(C)))) <=> ((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~relation(C)) | (~in(A, relation_dom(B))) | (~function(C)))))),
% 1.38/1.58 inference(bind,[status(th)],[])).
% 1.38/1.58 tff(53,plain,
% 1.38/1.58 (![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~relation(C)) | (~in(A, relation_dom(B))) | (~function(C)))) <=> ![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~relation(C)) | (~in(A, relation_dom(B))) | (~function(C))))),
% 1.38/1.58 inference(quant_intro,[status(thm)],[52])).
% 1.38/1.58 tff(54,plain,
% 1.38/1.58 (^[A: $i, B: $i] : rewrite(((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~relation(C)) | (~in(A, relation_dom(B))) | (~function(C)))) <=> ((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~relation(C)) | (~in(A, relation_dom(B))) | (~function(C)))))),
% 1.38/1.58 inference(bind,[status(th)],[])).
% 1.38/1.58 tff(55,plain,
% 1.38/1.58 (![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~relation(C)) | (~in(A, relation_dom(B))) | (~function(C)))) <=> ![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~relation(C)) | (~in(A, relation_dom(B))) | (~function(C))))),
% 1.38/1.58 inference(quant_intro,[status(thm)],[54])).
% 1.38/1.58 tff(56,plain,
% 1.38/1.58 (![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~relation(C)) | (~in(A, relation_dom(B))) | (~function(C)))) <=> ![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~relation(C)) | (~in(A, relation_dom(B))) | (~function(C))))),
% 1.38/1.58 inference(transitivity,[status(thm)],[55, 53])).
% 1.38/1.58 tff(57,plain,
% 1.38/1.58 (^[A: $i, 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))))), quant_intro(proof_bind(^[C: $i] : trans(monotonicity(trans(monotonicity(rewrite((relation(C) & function(C)) <=> (~((~relation(C)) | (~function(C))))), ((~(relation(C) & function(C))) <=> (~(~((~relation(C)) | (~function(C))))))), rewrite((~(~((~relation(C)) | (~function(C))))) <=> ((~relation(C)) | (~function(C)))), ((~(relation(C) & function(C))) <=> ((~relation(C)) | (~function(C))))), (((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~(relation(C) & function(C))) | (~in(A, relation_dom(B)))) <=> ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | ((~relation(C)) | (~function(C))) | (~in(A, relation_dom(B)))))), rewrite(((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | ((~relation(C)) | (~function(C))) | (~in(A, relation_dom(B)))) <=> ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~relation(C)) | (~in(A, relation_dom(B))) | (~function(C)))), (((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~(relation(C) & function(C))) | (~in(A, relation_dom(B)))) <=> ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~relation(C)) | (~in(A, relation_dom(B))) | (~function(C)))))), (![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~(relation(C) & function(C))) | (~in(A, relation_dom(B)))) <=> ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~relation(C)) | (~in(A, relation_dom(B))) | (~function(C))))), (((~(relation(B) & function(B))) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~(relation(C) & function(C))) | (~in(A, relation_dom(B))))) <=> (((~relation(B)) | (~function(B))) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~relation(C)) | (~in(A, relation_dom(B))) | (~function(C)))))), rewrite((((~relation(B)) | (~function(B))) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~relation(C)) | (~in(A, relation_dom(B))) | (~function(C)))) <=> ((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~relation(C)) | (~in(A, relation_dom(B))) | (~function(C))))), (((~(relation(B) & function(B))) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~(relation(C) & function(C))) | (~in(A, relation_dom(B))))) <=> ((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~relation(C)) | (~in(A, relation_dom(B))) | (~function(C))))))),
% 1.38/1.58 inference(bind,[status(th)],[])).
% 1.38/1.58 tff(58,plain,
% 1.38/1.58 (![A: $i, B: $i] : ((~(relation(B) & function(B))) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~(relation(C) & function(C))) | (~in(A, relation_dom(B))))) <=> ![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~relation(C)) | (~in(A, relation_dom(B))) | (~function(C))))),
% 1.38/1.58 inference(quant_intro,[status(thm)],[57])).
% 1.38/1.58 tff(59,plain,
% 1.38/1.58 (![A: $i, B: $i] : ((~(relation(B) & function(B))) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~(relation(C) & function(C))) | (~in(A, relation_dom(B))))) <=> ![A: $i, B: $i] : ((~(relation(B) & function(B))) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~(relation(C) & function(C))) | (~in(A, relation_dom(B)))))),
% 1.38/1.58 inference(rewrite,[status(thm)],[])).
% 1.38/1.58 tff(60,plain,
% 1.38/1.58 (^[A: $i, B: $i] : trans(monotonicity(quant_intro(proof_bind(^[C: $i] : trans(monotonicity(rewrite((in(A, relation_dom(B)) => (apply(relation_composition(B, C), A) = apply(C, apply(B, A)))) <=> ((~in(A, relation_dom(B))) | (apply(relation_composition(B, C), A) = apply(C, apply(B, A))))), (((relation(C) & function(C)) => (in(A, relation_dom(B)) => (apply(relation_composition(B, C), A) = apply(C, apply(B, A))))) <=> ((relation(C) & function(C)) => ((~in(A, relation_dom(B))) | (apply(relation_composition(B, C), A) = apply(C, apply(B, A))))))), rewrite(((relation(C) & function(C)) => ((~in(A, relation_dom(B))) | (apply(relation_composition(B, C), A) = apply(C, apply(B, A))))) <=> ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~(relation(C) & function(C))) | (~in(A, relation_dom(B))))), (((relation(C) & function(C)) => (in(A, relation_dom(B)) => (apply(relation_composition(B, C), A) = apply(C, apply(B, A))))) <=> ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~(relation(C) & function(C))) | (~in(A, relation_dom(B))))))), (![C: $i] : ((relation(C) & function(C)) => (in(A, relation_dom(B)) => (apply(relation_composition(B, C), A) = apply(C, apply(B, A))))) <=> ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~(relation(C) & function(C))) | (~in(A, relation_dom(B)))))), (((relation(B) & function(B)) => ![C: $i] : ((relation(C) & function(C)) => (in(A, relation_dom(B)) => (apply(relation_composition(B, C), A) = apply(C, apply(B, A)))))) <=> ((relation(B) & function(B)) => ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~(relation(C) & function(C))) | (~in(A, relation_dom(B))))))), rewrite(((relation(B) & function(B)) => ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~(relation(C) & function(C))) | (~in(A, relation_dom(B))))) <=> ((~(relation(B) & function(B))) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~(relation(C) & function(C))) | (~in(A, relation_dom(B)))))), (((relation(B) & function(B)) => ![C: $i] : ((relation(C) & function(C)) => (in(A, relation_dom(B)) => (apply(relation_composition(B, C), A) = apply(C, apply(B, A)))))) <=> ((~(relation(B) & function(B))) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~(relation(C) & function(C))) | (~in(A, relation_dom(B)))))))),
% 1.38/1.58 inference(bind,[status(th)],[])).
% 1.38/1.58 tff(61,plain,
% 1.38/1.58 (![A: $i, B: $i] : ((relation(B) & function(B)) => ![C: $i] : ((relation(C) & function(C)) => (in(A, relation_dom(B)) => (apply(relation_composition(B, C), A) = apply(C, apply(B, A)))))) <=> ![A: $i, B: $i] : ((~(relation(B) & function(B))) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~(relation(C) & function(C))) | (~in(A, relation_dom(B)))))),
% 1.38/1.58 inference(quant_intro,[status(thm)],[60])).
% 1.38/1.58 tff(62,axiom,(![A: $i, B: $i] : ((relation(B) & function(B)) => ![C: $i] : ((relation(C) & function(C)) => (in(A, relation_dom(B)) => (apply(relation_composition(B, C), A) = apply(C, apply(B, A))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t23_funct_1')).
% 1.38/1.58 tff(63,plain,
% 1.38/1.58 (![A: $i, B: $i] : ((~(relation(B) & function(B))) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~(relation(C) & function(C))) | (~in(A, relation_dom(B)))))),
% 1.38/1.58 inference(modus_ponens,[status(thm)],[62, 61])).
% 1.38/1.58 tff(64,plain,
% 1.38/1.58 (![A: $i, B: $i] : ((~(relation(B) & function(B))) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~(relation(C) & function(C))) | (~in(A, relation_dom(B)))))),
% 1.38/1.58 inference(modus_ponens,[status(thm)],[63, 59])).
% 1.38/1.58 tff(65,plain,(
% 1.38/1.58 ![A: $i, B: $i] : ((~(relation(B) & function(B))) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~(relation(C) & function(C))) | (~in(A, relation_dom(B)))))),
% 1.38/1.58 inference(skolemize,[status(sab)],[64])).
% 1.38/1.58 tff(66,plain,
% 1.38/1.58 (![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~relation(C)) | (~in(A, relation_dom(B))) | (~function(C))))),
% 1.38/1.58 inference(modus_ponens,[status(thm)],[65, 58])).
% 1.38/1.58 tff(67,plain,
% 1.38/1.58 (![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~relation(C)) | (~in(A, relation_dom(B))) | (~function(C))))),
% 1.38/1.58 inference(modus_ponens,[status(thm)],[66, 56])).
% 1.38/1.58 tff(68,plain,
% 1.38/1.58 (((~![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~relation(C)) | (~in(A, relation_dom(B))) | (~function(C))))) | ((~relation(identity_relation(A!78))) | (~function(identity_relation(A!78))) | ![C: $i] : ((~relation(C)) | (~function(C)) | (~in(B!77, relation_dom(identity_relation(A!78)))) | (apply(relation_composition(identity_relation(A!78), C), B!77) = apply(C, apply(identity_relation(A!78), B!77)))))) <=> ((~![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~relation(C)) | (~in(A, relation_dom(B))) | (~function(C))))) | (~relation(identity_relation(A!78))) | (~function(identity_relation(A!78))) | ![C: $i] : ((~relation(C)) | (~function(C)) | (~in(B!77, relation_dom(identity_relation(A!78)))) | (apply(relation_composition(identity_relation(A!78), C), B!77) = apply(C, apply(identity_relation(A!78), B!77)))))),
% 1.38/1.58 inference(rewrite,[status(thm)],[])).
% 1.38/1.58 tff(69,plain,
% 1.38/1.58 (((~relation(identity_relation(A!78))) | (~function(identity_relation(A!78))) | ![C: $i] : ((~relation(C)) | (~function(C)) | (~in(B!77, relation_dom(identity_relation(A!78)))) | (apply(relation_composition(identity_relation(A!78), C), B!77) = apply(C, apply(identity_relation(A!78), B!77))))) <=> ((~relation(identity_relation(A!78))) | (~function(identity_relation(A!78))) | ![C: $i] : ((~relation(C)) | (~function(C)) | (~in(B!77, relation_dom(identity_relation(A!78)))) | (apply(relation_composition(identity_relation(A!78), C), B!77) = apply(C, apply(identity_relation(A!78), B!77)))))),
% 1.38/1.58 inference(rewrite,[status(thm)],[])).
% 1.38/1.58 tff(70,plain,
% 1.38/1.58 (^[C: $i] : rewrite(((apply(relation_composition(identity_relation(A!78), C), B!77) = apply(C, apply(identity_relation(A!78), B!77))) | (~relation(C)) | (~in(B!77, relation_dom(identity_relation(A!78)))) | (~function(C))) <=> ((~relation(C)) | (~function(C)) | (~in(B!77, relation_dom(identity_relation(A!78)))) | (apply(relation_composition(identity_relation(A!78), C), B!77) = apply(C, apply(identity_relation(A!78), B!77)))))),
% 1.38/1.58 inference(bind,[status(th)],[])).
% 1.38/1.58 tff(71,plain,
% 1.38/1.58 (![C: $i] : ((apply(relation_composition(identity_relation(A!78), C), B!77) = apply(C, apply(identity_relation(A!78), B!77))) | (~relation(C)) | (~in(B!77, relation_dom(identity_relation(A!78)))) | (~function(C))) <=> ![C: $i] : ((~relation(C)) | (~function(C)) | (~in(B!77, relation_dom(identity_relation(A!78)))) | (apply(relation_composition(identity_relation(A!78), C), B!77) = apply(C, apply(identity_relation(A!78), B!77))))),
% 1.38/1.58 inference(quant_intro,[status(thm)],[70])).
% 1.38/1.58 tff(72,plain,
% 1.38/1.58 (((~relation(identity_relation(A!78))) | (~function(identity_relation(A!78))) | ![C: $i] : ((apply(relation_composition(identity_relation(A!78), C), B!77) = apply(C, apply(identity_relation(A!78), B!77))) | (~relation(C)) | (~in(B!77, relation_dom(identity_relation(A!78)))) | (~function(C)))) <=> ((~relation(identity_relation(A!78))) | (~function(identity_relation(A!78))) | ![C: $i] : ((~relation(C)) | (~function(C)) | (~in(B!77, relation_dom(identity_relation(A!78)))) | (apply(relation_composition(identity_relation(A!78), C), B!77) = apply(C, apply(identity_relation(A!78), B!77)))))),
% 1.38/1.58 inference(monotonicity,[status(thm)],[71])).
% 1.38/1.58 tff(73,plain,
% 1.38/1.58 (((~relation(identity_relation(A!78))) | (~function(identity_relation(A!78))) | ![C: $i] : ((apply(relation_composition(identity_relation(A!78), C), B!77) = apply(C, apply(identity_relation(A!78), B!77))) | (~relation(C)) | (~in(B!77, relation_dom(identity_relation(A!78)))) | (~function(C)))) <=> ((~relation(identity_relation(A!78))) | (~function(identity_relation(A!78))) | ![C: $i] : ((~relation(C)) | (~function(C)) | (~in(B!77, relation_dom(identity_relation(A!78)))) | (apply(relation_composition(identity_relation(A!78), C), B!77) = apply(C, apply(identity_relation(A!78), B!77)))))),
% 1.38/1.58 inference(transitivity,[status(thm)],[72, 69])).
% 1.38/1.58 tff(74,plain,
% 1.38/1.58 (((~![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~relation(C)) | (~in(A, relation_dom(B))) | (~function(C))))) | ((~relation(identity_relation(A!78))) | (~function(identity_relation(A!78))) | ![C: $i] : ((apply(relation_composition(identity_relation(A!78), C), B!77) = apply(C, apply(identity_relation(A!78), B!77))) | (~relation(C)) | (~in(B!77, relation_dom(identity_relation(A!78)))) | (~function(C))))) <=> ((~![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~relation(C)) | (~in(A, relation_dom(B))) | (~function(C))))) | ((~relation(identity_relation(A!78))) | (~function(identity_relation(A!78))) | ![C: $i] : ((~relation(C)) | (~function(C)) | (~in(B!77, relation_dom(identity_relation(A!78)))) | (apply(relation_composition(identity_relation(A!78), C), B!77) = apply(C, apply(identity_relation(A!78), B!77))))))),
% 1.38/1.58 inference(monotonicity,[status(thm)],[73])).
% 1.38/1.58 tff(75,plain,
% 1.38/1.58 (((~![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~relation(C)) | (~in(A, relation_dom(B))) | (~function(C))))) | ((~relation(identity_relation(A!78))) | (~function(identity_relation(A!78))) | ![C: $i] : ((apply(relation_composition(identity_relation(A!78), C), B!77) = apply(C, apply(identity_relation(A!78), B!77))) | (~relation(C)) | (~in(B!77, relation_dom(identity_relation(A!78)))) | (~function(C))))) <=> ((~![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~relation(C)) | (~in(A, relation_dom(B))) | (~function(C))))) | (~relation(identity_relation(A!78))) | (~function(identity_relation(A!78))) | ![C: $i] : ((~relation(C)) | (~function(C)) | (~in(B!77, relation_dom(identity_relation(A!78)))) | (apply(relation_composition(identity_relation(A!78), C), B!77) = apply(C, apply(identity_relation(A!78), B!77)))))),
% 1.38/1.58 inference(transitivity,[status(thm)],[74, 68])).
% 1.38/1.58 tff(76,plain,
% 1.38/1.58 ((~![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~relation(C)) | (~in(A, relation_dom(B))) | (~function(C))))) | ((~relation(identity_relation(A!78))) | (~function(identity_relation(A!78))) | ![C: $i] : ((apply(relation_composition(identity_relation(A!78), C), B!77) = apply(C, apply(identity_relation(A!78), B!77))) | (~relation(C)) | (~in(B!77, relation_dom(identity_relation(A!78)))) | (~function(C))))),
% 1.38/1.58 inference(quant_inst,[status(thm)],[])).
% 1.38/1.58 tff(77,plain,
% 1.38/1.58 ((~![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~relation(C)) | (~in(A, relation_dom(B))) | (~function(C))))) | (~relation(identity_relation(A!78))) | (~function(identity_relation(A!78))) | ![C: $i] : ((~relation(C)) | (~function(C)) | (~in(B!77, relation_dom(identity_relation(A!78)))) | (apply(relation_composition(identity_relation(A!78), C), B!77) = apply(C, apply(identity_relation(A!78), B!77))))),
% 1.38/1.58 inference(modus_ponens,[status(thm)],[76, 75])).
% 1.38/1.58 tff(78,plain,
% 1.38/1.58 ((~relation(identity_relation(A!78))) | (~function(identity_relation(A!78))) | ![C: $i] : ((~relation(C)) | (~function(C)) | (~in(B!77, relation_dom(identity_relation(A!78)))) | (apply(relation_composition(identity_relation(A!78), C), B!77) = apply(C, apply(identity_relation(A!78), B!77))))),
% 1.38/1.58 inference(unit_resolution,[status(thm)],[77, 67])).
% 1.38/1.58 tff(79,plain,
% 1.38/1.58 (![C: $i] : ((~relation(C)) | (~function(C)) | (~in(B!77, relation_dom(identity_relation(A!78)))) | (apply(relation_composition(identity_relation(A!78), C), B!77) = apply(C, apply(identity_relation(A!78), B!77))))),
% 1.38/1.58 inference(unit_resolution,[status(thm)],[78, 51, 37])).
% 1.38/1.58 tff(80,plain,
% 1.38/1.58 (^[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)))))),
% 1.38/1.58 inference(bind,[status(th)],[])).
% 1.38/1.58 tff(81,plain,
% 1.38/1.58 (![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))))),
% 1.38/1.58 inference(quant_intro,[status(thm)],[80])).
% 1.38/1.58 tff(82,plain,
% 1.38/1.58 (^[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)))))),
% 1.38/1.58 inference(bind,[status(th)],[])).
% 1.38/1.58 tff(83,plain,
% 1.38/1.58 (![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))))),
% 1.38/1.58 inference(quant_intro,[status(thm)],[82])).
% 1.38/1.58 tff(84,plain,
% 1.38/1.58 (![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))),
% 1.38/1.58 inference(rewrite,[status(thm)],[])).
% 1.38/1.58 tff(85,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')).
% 1.38/1.58 tff(86,plain,
% 1.38/1.58 (![A: $i] : ((relation_dom(identity_relation(A)) = A) & (relation_rng(identity_relation(A)) = A))),
% 1.38/1.58 inference(modus_ponens,[status(thm)],[85, 84])).
% 1.38/1.58 tff(87,plain,(
% 1.38/1.58 ![A: $i] : ((relation_dom(identity_relation(A)) = A) & (relation_rng(identity_relation(A)) = A))),
% 1.38/1.58 inference(skolemize,[status(sab)],[86])).
% 1.38/1.58 tff(88,plain,
% 1.38/1.58 (![A: $i] : (~((~(relation_dom(identity_relation(A)) = A)) | (~(relation_rng(identity_relation(A)) = A))))),
% 1.38/1.58 inference(modus_ponens,[status(thm)],[87, 83])).
% 1.38/1.58 tff(89,plain,
% 1.38/1.58 (![A: $i] : (~((~(relation_dom(identity_relation(A)) = A)) | (~(relation_rng(identity_relation(A)) = A))))),
% 1.38/1.58 inference(modus_ponens,[status(thm)],[88, 81])).
% 1.38/1.58 tff(90,plain,
% 1.38/1.58 ((~![A: $i] : (~((~(relation_dom(identity_relation(A)) = A)) | (~(relation_rng(identity_relation(A)) = A))))) | (~((~(relation_dom(identity_relation(A!78)) = A!78)) | (~(relation_rng(identity_relation(A!78)) = A!78))))),
% 1.38/1.58 inference(quant_inst,[status(thm)],[])).
% 1.38/1.58 tff(91,plain,
% 1.38/1.58 (~((~(relation_dom(identity_relation(A!78)) = A!78)) | (~(relation_rng(identity_relation(A!78)) = A!78)))),
% 1.38/1.58 inference(unit_resolution,[status(thm)],[90, 89])).
% 1.38/1.58 tff(92,plain,
% 1.38/1.58 (((~(relation_dom(identity_relation(A!78)) = A!78)) | (~(relation_rng(identity_relation(A!78)) = A!78))) | (relation_dom(identity_relation(A!78)) = A!78)),
% 1.38/1.58 inference(tautology,[status(thm)],[])).
% 1.38/1.58 tff(93,plain,
% 1.38/1.58 (relation_dom(identity_relation(A!78)) = A!78),
% 1.38/1.58 inference(unit_resolution,[status(thm)],[92, 91])).
% 1.38/1.58 tff(94,plain,
% 1.38/1.58 (in(B!77, relation_dom(identity_relation(A!78))) <=> in(B!77, A!78)),
% 1.38/1.58 inference(monotonicity,[status(thm)],[93])).
% 1.38/1.58 tff(95,plain,
% 1.38/1.58 (in(B!77, A!78) <=> in(B!77, relation_dom(identity_relation(A!78)))),
% 1.38/1.58 inference(symmetry,[status(thm)],[94])).
% 1.38/1.58 tff(96,plain,
% 1.38/1.58 (in(B!77, relation_dom(identity_relation(A!78)))),
% 1.38/1.58 inference(modus_ponens,[status(thm)],[11, 95])).
% 1.38/1.58 tff(97,plain,
% 1.38/1.58 (relation(C!76) & function(C!76)),
% 1.38/1.58 inference(or_elim,[status(thm)],[10])).
% 1.38/1.58 tff(98,plain,
% 1.38/1.58 (function(C!76)),
% 1.38/1.58 inference(and_elim,[status(thm)],[97])).
% 1.38/1.58 tff(99,plain,
% 1.38/1.58 (relation(C!76)),
% 1.38/1.58 inference(and_elim,[status(thm)],[97])).
% 1.38/1.58 tff(100,plain,
% 1.38/1.58 (((~![C: $i] : ((~relation(C)) | (~function(C)) | (~in(B!77, relation_dom(identity_relation(A!78)))) | (apply(relation_composition(identity_relation(A!78), C), B!77) = apply(C, apply(identity_relation(A!78), B!77))))) | ((~relation(C!76)) | (~function(C!76)) | (~in(B!77, relation_dom(identity_relation(A!78)))) | (apply(relation_composition(identity_relation(A!78), C!76), B!77) = apply(C!76, apply(identity_relation(A!78), B!77))))) <=> ((~![C: $i] : ((~relation(C)) | (~function(C)) | (~in(B!77, relation_dom(identity_relation(A!78)))) | (apply(relation_composition(identity_relation(A!78), C), B!77) = apply(C, apply(identity_relation(A!78), B!77))))) | (~relation(C!76)) | (~function(C!76)) | (~in(B!77, relation_dom(identity_relation(A!78)))) | (apply(relation_composition(identity_relation(A!78), C!76), B!77) = apply(C!76, apply(identity_relation(A!78), B!77))))),
% 1.38/1.58 inference(rewrite,[status(thm)],[])).
% 1.38/1.58 tff(101,plain,
% 1.38/1.58 ((~![C: $i] : ((~relation(C)) | (~function(C)) | (~in(B!77, relation_dom(identity_relation(A!78)))) | (apply(relation_composition(identity_relation(A!78), C), B!77) = apply(C, apply(identity_relation(A!78), B!77))))) | ((~relation(C!76)) | (~function(C!76)) | (~in(B!77, relation_dom(identity_relation(A!78)))) | (apply(relation_composition(identity_relation(A!78), C!76), B!77) = apply(C!76, apply(identity_relation(A!78), B!77))))),
% 1.38/1.58 inference(quant_inst,[status(thm)],[])).
% 1.38/1.58 tff(102,plain,
% 1.38/1.58 ((~![C: $i] : ((~relation(C)) | (~function(C)) | (~in(B!77, relation_dom(identity_relation(A!78)))) | (apply(relation_composition(identity_relation(A!78), C), B!77) = apply(C, apply(identity_relation(A!78), B!77))))) | (~relation(C!76)) | (~function(C!76)) | (~in(B!77, relation_dom(identity_relation(A!78)))) | (apply(relation_composition(identity_relation(A!78), C!76), B!77) = apply(C!76, apply(identity_relation(A!78), B!77)))),
% 1.38/1.58 inference(modus_ponens,[status(thm)],[101, 100])).
% 1.38/1.58 tff(103,plain,
% 1.38/1.58 (apply(relation_composition(identity_relation(A!78), C!76), B!77) = apply(C!76, apply(identity_relation(A!78), B!77))),
% 1.38/1.58 inference(unit_resolution,[status(thm)],[102, 99, 98, 96, 79])).
% 1.38/1.58 tff(104,plain,
% 1.38/1.58 (^[A: $i, B: $i] : refl(((~relation(B)) | (relation_dom_restriction(B, A) = relation_composition(identity_relation(A), B))) <=> ((~relation(B)) | (relation_dom_restriction(B, A) = relation_composition(identity_relation(A), B))))),
% 1.38/1.58 inference(bind,[status(th)],[])).
% 1.38/1.58 tff(105,plain,
% 1.38/1.58 (![A: $i, B: $i] : ((~relation(B)) | (relation_dom_restriction(B, A) = relation_composition(identity_relation(A), B))) <=> ![A: $i, B: $i] : ((~relation(B)) | (relation_dom_restriction(B, A) = relation_composition(identity_relation(A), B)))),
% 1.38/1.58 inference(quant_intro,[status(thm)],[104])).
% 1.38/1.58 tff(106,plain,
% 1.38/1.58 (![A: $i, B: $i] : ((~relation(B)) | (relation_dom_restriction(B, A) = relation_composition(identity_relation(A), B))) <=> ![A: $i, B: $i] : ((~relation(B)) | (relation_dom_restriction(B, A) = relation_composition(identity_relation(A), B)))),
% 1.38/1.58 inference(rewrite,[status(thm)],[])).
% 1.38/1.58 tff(107,plain,
% 1.38/1.58 (^[A: $i, B: $i] : rewrite((relation(B) => (relation_dom_restriction(B, A) = relation_composition(identity_relation(A), B))) <=> ((~relation(B)) | (relation_dom_restriction(B, A) = relation_composition(identity_relation(A), B))))),
% 1.38/1.58 inference(bind,[status(th)],[])).
% 1.38/1.58 tff(108,plain,
% 1.38/1.58 (![A: $i, B: $i] : (relation(B) => (relation_dom_restriction(B, A) = relation_composition(identity_relation(A), B))) <=> ![A: $i, B: $i] : ((~relation(B)) | (relation_dom_restriction(B, A) = relation_composition(identity_relation(A), B)))),
% 1.38/1.58 inference(quant_intro,[status(thm)],[107])).
% 1.38/1.58 tff(109,axiom,(![A: $i, B: $i] : (relation(B) => (relation_dom_restriction(B, A) = relation_composition(identity_relation(A), B)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t94_relat_1')).
% 1.38/1.58 tff(110,plain,
% 1.38/1.58 (![A: $i, B: $i] : ((~relation(B)) | (relation_dom_restriction(B, A) = relation_composition(identity_relation(A), B)))),
% 1.38/1.58 inference(modus_ponens,[status(thm)],[109, 108])).
% 1.38/1.58 tff(111,plain,
% 1.38/1.58 (![A: $i, B: $i] : ((~relation(B)) | (relation_dom_restriction(B, A) = relation_composition(identity_relation(A), B)))),
% 1.38/1.58 inference(modus_ponens,[status(thm)],[110, 106])).
% 1.38/1.58 tff(112,plain,(
% 1.38/1.58 ![A: $i, B: $i] : ((~relation(B)) | (relation_dom_restriction(B, A) = relation_composition(identity_relation(A), B)))),
% 1.38/1.58 inference(skolemize,[status(sab)],[111])).
% 1.38/1.58 tff(113,plain,
% 1.38/1.58 (![A: $i, B: $i] : ((~relation(B)) | (relation_dom_restriction(B, A) = relation_composition(identity_relation(A), B)))),
% 1.38/1.59 inference(modus_ponens,[status(thm)],[112, 105])).
% 1.38/1.59 tff(114,plain,
% 1.38/1.59 (((~![A: $i, B: $i] : ((~relation(B)) | (relation_dom_restriction(B, A) = relation_composition(identity_relation(A), B)))) | ((~relation(C!76)) | (relation_dom_restriction(C!76, A!78) = relation_composition(identity_relation(A!78), C!76)))) <=> ((~![A: $i, B: $i] : ((~relation(B)) | (relation_dom_restriction(B, A) = relation_composition(identity_relation(A), B)))) | (~relation(C!76)) | (relation_dom_restriction(C!76, A!78) = relation_composition(identity_relation(A!78), C!76)))),
% 1.38/1.59 inference(rewrite,[status(thm)],[])).
% 1.38/1.59 tff(115,plain,
% 1.38/1.59 ((~![A: $i, B: $i] : ((~relation(B)) | (relation_dom_restriction(B, A) = relation_composition(identity_relation(A), B)))) | ((~relation(C!76)) | (relation_dom_restriction(C!76, A!78) = relation_composition(identity_relation(A!78), C!76)))),
% 1.38/1.59 inference(quant_inst,[status(thm)],[])).
% 1.38/1.59 tff(116,plain,
% 1.38/1.59 ((~![A: $i, B: $i] : ((~relation(B)) | (relation_dom_restriction(B, A) = relation_composition(identity_relation(A), B)))) | (~relation(C!76)) | (relation_dom_restriction(C!76, A!78) = relation_composition(identity_relation(A!78), C!76))),
% 1.38/1.59 inference(modus_ponens,[status(thm)],[115, 114])).
% 1.38/1.59 tff(117,plain,
% 1.38/1.59 (relation_dom_restriction(C!76, A!78) = relation_composition(identity_relation(A!78), C!76)),
% 1.38/1.59 inference(unit_resolution,[status(thm)],[116, 99, 113])).
% 1.38/1.59 tff(118,plain,
% 1.38/1.59 (relation_composition(identity_relation(A!78), C!76) = relation_dom_restriction(C!76, A!78)),
% 1.38/1.59 inference(symmetry,[status(thm)],[117])).
% 1.38/1.59 tff(119,plain,
% 1.38/1.59 (apply(relation_composition(identity_relation(A!78), C!76), B!77) = apply(relation_dom_restriction(C!76, A!78), B!77)),
% 1.38/1.59 inference(monotonicity,[status(thm)],[118])).
% 1.38/1.59 tff(120,plain,
% 1.38/1.59 (apply(relation_dom_restriction(C!76, A!78), B!77) = apply(relation_composition(identity_relation(A!78), C!76), B!77)),
% 1.38/1.59 inference(symmetry,[status(thm)],[119])).
% 1.38/1.59 tff(121,plain,
% 1.38/1.59 (apply(relation_dom_restriction(C!76, A!78), B!77) = apply(C!76, B!77)),
% 1.38/1.59 inference(transitivity,[status(thm)],[120, 103, 28])).
% 1.38/1.59 tff(122,plain,
% 1.38/1.59 (~(apply(relation_dom_restriction(C!76, A!78), B!77) = apply(C!76, B!77))),
% 1.38/1.59 inference(or_elim,[status(thm)],[10])).
% 1.38/1.59 tff(123,plain,
% 1.38/1.59 ($false),
% 1.38/1.59 inference(unit_resolution,[status(thm)],[122, 121])).
% 1.38/1.59 % SZS output end Proof
% 1.38/1.60 % E exiting
%------------------------------------------------------------------------------