%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SEU195+2 : TPTP v9.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n005.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:27:12 AM UTC 2025
% Result : Theorem 1.80s 1.96s
% Output : Proof 1.80s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SEU195+2 : TPTP v9.0.0. Released v3.3.0.
% 0.06/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n005.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 20 06:16:05 EDT 2025
% 0.12/0.33 % CPUTime :
% 1.80/1.96 % SZS status Theorem
% 1.80/1.96 % SZS output start Proof
% 1.80/1.96 tff(in_type, type, (
% 1.80/1.96 in: ( $i * $i ) > $o)).
% 1.80/1.96 tff(relation_composition_type, type, (
% 1.80/1.96 relation_composition: ( $i * $i ) > $i)).
% 1.80/1.96 tff(tptp_fun_B_56_type, type, (
% 1.80/1.96 tptp_fun_B_56: $i)).
% 1.80/1.96 tff(identity_relation_type, type, (
% 1.80/1.96 identity_relation: $i > $i)).
% 1.80/1.96 tff(tptp_fun_A_57_type, type, (
% 1.80/1.96 tptp_fun_A_57: $i)).
% 1.80/1.96 tff(ordered_pair_type, type, (
% 1.80/1.96 ordered_pair: ( $i * $i ) > $i)).
% 1.80/1.96 tff(tptp_fun_E_2_type, type, (
% 1.80/1.96 tptp_fun_E_2: ( $i * $i * $i ) > $i)).
% 1.80/1.96 tff(tptp_fun_D_3_type, type, (
% 1.80/1.96 tptp_fun_D_3: ( $i * $i * $i ) > $i)).
% 1.80/1.96 tff(relation_dom_restriction_type, type, (
% 1.80/1.96 relation_dom_restriction: ( $i * $i ) > $i)).
% 1.80/1.96 tff(relation_type, type, (
% 1.80/1.96 relation: $i > $o)).
% 1.80/1.96 tff(1,plain,
% 1.80/1.96 (^[A: $i] : refl(relation(identity_relation(A)) <=> relation(identity_relation(A)))),
% 1.80/1.96 inference(bind,[status(th)],[])).
% 1.80/1.96 tff(2,plain,
% 1.80/1.96 (![A: $i] : relation(identity_relation(A)) <=> ![A: $i] : relation(identity_relation(A))),
% 1.80/1.96 inference(quant_intro,[status(thm)],[1])).
% 1.80/1.96 tff(3,plain,
% 1.80/1.96 (![A: $i] : relation(identity_relation(A)) <=> ![A: $i] : relation(identity_relation(A))),
% 1.80/1.96 inference(rewrite,[status(thm)],[])).
% 1.80/1.96 tff(4,axiom,(![A: $i] : relation(identity_relation(A))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_k6_relat_1')).
% 1.80/1.96 tff(5,plain,
% 1.80/1.96 (![A: $i] : relation(identity_relation(A))),
% 1.80/1.96 inference(modus_ponens,[status(thm)],[4, 3])).
% 1.80/1.96 tff(6,plain,(
% 1.80/1.96 ![A: $i] : relation(identity_relation(A))),
% 1.80/1.96 inference(skolemize,[status(sab)],[5])).
% 1.80/1.96 tff(7,plain,
% 1.80/1.96 (![A: $i] : relation(identity_relation(A))),
% 1.80/1.96 inference(modus_ponens,[status(thm)],[6, 2])).
% 1.80/1.96 tff(8,plain,
% 1.80/1.96 ((~![A: $i] : relation(identity_relation(A))) | relation(identity_relation(A!57))),
% 1.80/1.96 inference(quant_inst,[status(thm)],[])).
% 1.80/1.96 tff(9,plain,
% 1.80/1.96 (relation(identity_relation(A!57))),
% 1.80/1.96 inference(unit_resolution,[status(thm)],[8, 7])).
% 1.80/1.96 tff(10,plain,
% 1.80/1.96 ((~![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))))),
% 1.80/1.96 inference(rewrite,[status(thm)],[])).
% 1.80/1.96 tff(11,plain,
% 1.80/1.96 ((~![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))))),
% 1.80/1.96 inference(rewrite,[status(thm)],[])).
% 1.80/1.96 tff(12,axiom,(~![A: $i, B: $i] : (relation(B) => (relation_dom_restriction(B, A) = relation_composition(identity_relation(A), B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t94_relat_1')).
% 1.80/1.96 tff(13,plain,
% 1.80/1.96 (~![A: $i, B: $i] : ((~relation(B)) | (relation_dom_restriction(B, A) = relation_composition(identity_relation(A), B)))),
% 1.80/1.96 inference(modus_ponens,[status(thm)],[12, 11])).
% 1.80/1.96 tff(14,plain,
% 1.80/1.96 (~![A: $i, B: $i] : ((~relation(B)) | (relation_dom_restriction(B, A) = relation_composition(identity_relation(A), B)))),
% 1.80/1.96 inference(modus_ponens,[status(thm)],[13, 10])).
% 1.80/1.96 tff(15,plain,
% 1.80/1.96 (~![A: $i, B: $i] : ((~relation(B)) | (relation_dom_restriction(B, A) = relation_composition(identity_relation(A), B)))),
% 1.80/1.96 inference(modus_ponens,[status(thm)],[14, 10])).
% 1.80/1.96 tff(16,plain,
% 1.80/1.96 (~![A: $i, B: $i] : ((~relation(B)) | (relation_dom_restriction(B, A) = relation_composition(identity_relation(A), B)))),
% 1.80/1.96 inference(modus_ponens,[status(thm)],[15, 10])).
% 1.80/1.96 tff(17,plain,(
% 1.80/1.96 ~((~relation(B!56)) | (relation_dom_restriction(B!56, A!57) = relation_composition(identity_relation(A!57), B!56)))),
% 1.80/1.96 inference(skolemize,[status(sab)],[16])).
% 1.80/1.96 tff(18,plain,
% 1.80/1.96 (relation(B!56)),
% 1.80/1.96 inference(or_elim,[status(thm)],[17])).
% 1.80/1.96 tff(19,plain,
% 1.80/1.96 (^[A: $i, B: $i] : refl((relation(relation_composition(A, B)) | (~relation(B)) | (~relation(A))) <=> (relation(relation_composition(A, B)) | (~relation(B)) | (~relation(A))))),
% 1.80/1.96 inference(bind,[status(th)],[])).
% 1.80/1.96 tff(20,plain,
% 1.80/1.96 (![A: $i, B: $i] : (relation(relation_composition(A, B)) | (~relation(B)) | (~relation(A))) <=> ![A: $i, B: $i] : (relation(relation_composition(A, B)) | (~relation(B)) | (~relation(A)))),
% 1.80/1.96 inference(quant_intro,[status(thm)],[19])).
% 1.80/1.96 tff(21,plain,
% 1.80/1.96 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite((relation(A) & relation(B)) <=> (~((~relation(B)) | (~relation(A))))), ((~(relation(A) & relation(B))) <=> (~(~((~relation(B)) | (~relation(A))))))), rewrite((~(~((~relation(B)) | (~relation(A))))) <=> ((~relation(B)) | (~relation(A)))), ((~(relation(A) & relation(B))) <=> ((~relation(B)) | (~relation(A))))), ((relation(relation_composition(A, B)) | (~(relation(A) & relation(B)))) <=> (relation(relation_composition(A, B)) | ((~relation(B)) | (~relation(A)))))), rewrite((relation(relation_composition(A, B)) | ((~relation(B)) | (~relation(A)))) <=> (relation(relation_composition(A, B)) | (~relation(B)) | (~relation(A)))), ((relation(relation_composition(A, B)) | (~(relation(A) & relation(B)))) <=> (relation(relation_composition(A, B)) | (~relation(B)) | (~relation(A)))))),
% 1.80/1.96 inference(bind,[status(th)],[])).
% 1.80/1.96 tff(22,plain,
% 1.80/1.96 (![A: $i, B: $i] : (relation(relation_composition(A, B)) | (~(relation(A) & relation(B)))) <=> ![A: $i, B: $i] : (relation(relation_composition(A, B)) | (~relation(B)) | (~relation(A)))),
% 1.80/1.96 inference(quant_intro,[status(thm)],[21])).
% 1.80/1.96 tff(23,plain,
% 1.80/1.96 (![A: $i, B: $i] : (relation(relation_composition(A, B)) | (~(relation(A) & relation(B)))) <=> ![A: $i, B: $i] : (relation(relation_composition(A, B)) | (~(relation(A) & relation(B))))),
% 1.80/1.96 inference(rewrite,[status(thm)],[])).
% 1.80/1.96 tff(24,plain,
% 1.80/1.96 (^[A: $i, B: $i] : rewrite(((relation(A) & relation(B)) => relation(relation_composition(A, B))) <=> (relation(relation_composition(A, B)) | (~(relation(A) & relation(B)))))),
% 1.80/1.96 inference(bind,[status(th)],[])).
% 1.80/1.96 tff(25,plain,
% 1.80/1.96 (![A: $i, B: $i] : ((relation(A) & relation(B)) => relation(relation_composition(A, B))) <=> ![A: $i, B: $i] : (relation(relation_composition(A, B)) | (~(relation(A) & relation(B))))),
% 1.80/1.96 inference(quant_intro,[status(thm)],[24])).
% 1.80/1.96 tff(26,axiom,(![A: $i, B: $i] : ((relation(A) & relation(B)) => relation(relation_composition(A, B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_k5_relat_1')).
% 1.80/1.96 tff(27,plain,
% 1.80/1.96 (![A: $i, B: $i] : (relation(relation_composition(A, B)) | (~(relation(A) & relation(B))))),
% 1.80/1.96 inference(modus_ponens,[status(thm)],[26, 25])).
% 1.80/1.96 tff(28,plain,
% 1.80/1.96 (![A: $i, B: $i] : (relation(relation_composition(A, B)) | (~(relation(A) & relation(B))))),
% 1.80/1.96 inference(modus_ponens,[status(thm)],[27, 23])).
% 1.80/1.96 tff(29,plain,(
% 1.80/1.96 ![A: $i, B: $i] : (relation(relation_composition(A, B)) | (~(relation(A) & relation(B))))),
% 1.80/1.96 inference(skolemize,[status(sab)],[28])).
% 1.80/1.96 tff(30,plain,
% 1.80/1.96 (![A: $i, B: $i] : (relation(relation_composition(A, B)) | (~relation(B)) | (~relation(A)))),
% 1.80/1.96 inference(modus_ponens,[status(thm)],[29, 22])).
% 1.80/1.96 tff(31,plain,
% 1.80/1.96 (![A: $i, B: $i] : (relation(relation_composition(A, B)) | (~relation(B)) | (~relation(A)))),
% 1.80/1.96 inference(modus_ponens,[status(thm)],[30, 20])).
% 1.80/1.96 tff(32,plain,
% 1.80/1.96 (((~![A: $i, B: $i] : (relation(relation_composition(A, B)) | (~relation(B)) | (~relation(A)))) | ((~relation(B!56)) | relation(relation_composition(identity_relation(A!57), B!56)) | (~relation(identity_relation(A!57))))) <=> ((~![A: $i, B: $i] : (relation(relation_composition(A, B)) | (~relation(B)) | (~relation(A)))) | (~relation(B!56)) | relation(relation_composition(identity_relation(A!57), B!56)) | (~relation(identity_relation(A!57))))),
% 1.80/1.96 inference(rewrite,[status(thm)],[])).
% 1.80/1.96 tff(33,plain,
% 1.80/1.96 ((relation(relation_composition(identity_relation(A!57), B!56)) | (~relation(B!56)) | (~relation(identity_relation(A!57)))) <=> ((~relation(B!56)) | relation(relation_composition(identity_relation(A!57), B!56)) | (~relation(identity_relation(A!57))))),
% 1.80/1.96 inference(rewrite,[status(thm)],[])).
% 1.80/1.96 tff(34,plain,
% 1.80/1.96 (((~![A: $i, B: $i] : (relation(relation_composition(A, B)) | (~relation(B)) | (~relation(A)))) | (relation(relation_composition(identity_relation(A!57), B!56)) | (~relation(B!56)) | (~relation(identity_relation(A!57))))) <=> ((~![A: $i, B: $i] : (relation(relation_composition(A, B)) | (~relation(B)) | (~relation(A)))) | ((~relation(B!56)) | relation(relation_composition(identity_relation(A!57), B!56)) | (~relation(identity_relation(A!57)))))),
% 1.80/1.96 inference(monotonicity,[status(thm)],[33])).
% 1.80/1.96 tff(35,plain,
% 1.80/1.96 (((~![A: $i, B: $i] : (relation(relation_composition(A, B)) | (~relation(B)) | (~relation(A)))) | (relation(relation_composition(identity_relation(A!57), B!56)) | (~relation(B!56)) | (~relation(identity_relation(A!57))))) <=> ((~![A: $i, B: $i] : (relation(relation_composition(A, B)) | (~relation(B)) | (~relation(A)))) | (~relation(B!56)) | relation(relation_composition(identity_relation(A!57), B!56)) | (~relation(identity_relation(A!57))))),
% 1.80/1.96 inference(transitivity,[status(thm)],[34, 32])).
% 1.80/1.96 tff(36,plain,
% 1.80/1.96 ((~![A: $i, B: $i] : (relation(relation_composition(A, B)) | (~relation(B)) | (~relation(A)))) | (relation(relation_composition(identity_relation(A!57), B!56)) | (~relation(B!56)) | (~relation(identity_relation(A!57))))),
% 1.80/1.96 inference(quant_inst,[status(thm)],[])).
% 1.80/1.96 tff(37,plain,
% 1.80/1.96 ((~![A: $i, B: $i] : (relation(relation_composition(A, B)) | (~relation(B)) | (~relation(A)))) | (~relation(B!56)) | relation(relation_composition(identity_relation(A!57), B!56)) | (~relation(identity_relation(A!57)))),
% 1.80/1.96 inference(modus_ponens,[status(thm)],[36, 35])).
% 1.80/1.96 tff(38,plain,
% 1.80/1.96 (relation(relation_composition(identity_relation(A!57), B!56)) | (~relation(identity_relation(A!57)))),
% 1.80/1.96 inference(unit_resolution,[status(thm)],[37, 31, 18])).
% 1.80/1.96 tff(39,plain,
% 1.80/1.96 (relation(relation_composition(identity_relation(A!57), B!56))),
% 1.80/1.96 inference(unit_resolution,[status(thm)],[38, 9])).
% 1.80/1.96 tff(40,plain,
% 1.80/1.96 (^[A: $i] : rewrite(((~relation(A)) | ![B: $i, C: $i] : ((~relation(C)) | (~((~((~(C = relation_dom_restriction(A, B))) | ![D: $i, E: $i] : (~(((~in(D, B)) | (~in(ordered_pair(D, E), A))) <=> in(ordered_pair(D, E), C))))) | (~((C = relation_dom_restriction(A, B)) | (((~in(tptp_fun_D_3(C, B, A), B)) | (~in(ordered_pair(tptp_fun_D_3(C, B, A), tptp_fun_E_2(C, B, A)), A))) <=> in(ordered_pair(tptp_fun_D_3(C, B, A), tptp_fun_E_2(C, B, A)), C)))))))) <=> ((~relation(A)) | ![B: $i, C: $i] : ((~relation(C)) | (~((~((C = relation_dom_restriction(A, B)) | (((~in(tptp_fun_D_3(C, B, A), B)) | (~in(ordered_pair(tptp_fun_D_3(C, B, A), tptp_fun_E_2(C, B, A)), A))) <=> in(ordered_pair(tptp_fun_D_3(C, B, A), tptp_fun_E_2(C, B, A)), C)))) | (~((~(C = relation_dom_restriction(A, B))) | ![D: $i, E: $i] : (~(((~in(D, B)) | (~in(ordered_pair(D, E), A))) <=> in(ordered_pair(D, E), C))))))))))),
% 1.80/1.96 inference(bind,[status(th)],[])).
% 1.80/1.96 tff(41,plain,
% 1.80/1.96 (![A: $i] : ((~relation(A)) | ![B: $i, C: $i] : ((~relation(C)) | (~((~((~(C = relation_dom_restriction(A, B))) | ![D: $i, E: $i] : (~(((~in(D, B)) | (~in(ordered_pair(D, E), A))) <=> in(ordered_pair(D, E), C))))) | (~((C = relation_dom_restriction(A, B)) | (((~in(tptp_fun_D_3(C, B, A), B)) | (~in(ordered_pair(tptp_fun_D_3(C, B, A), tptp_fun_E_2(C, B, A)), A))) <=> in(ordered_pair(tptp_fun_D_3(C, B, A), tptp_fun_E_2(C, B, A)), C)))))))) <=> ![A: $i] : ((~relation(A)) | ![B: $i, C: $i] : ((~relation(C)) | (~((~((C = relation_dom_restriction(A, B)) | (((~in(tptp_fun_D_3(C, B, A), B)) | (~in(ordered_pair(tptp_fun_D_3(C, B, A), tptp_fun_E_2(C, B, A)), A))) <=> in(ordered_pair(tptp_fun_D_3(C, B, A), tptp_fun_E_2(C, B, A)), C)))) | (~((~(C = relation_dom_restriction(A, B))) | ![D: $i, E: $i] : (~(((~in(D, B)) | (~in(ordered_pair(D, E), A))) <=> in(ordered_pair(D, E), C)))))))))),
% 1.80/1.96 inference(quant_intro,[status(thm)],[40])).
% 1.80/1.96 tff(42,plain,
% 1.80/1.96 (^[A: $i] : refl(((~relation(A)) | ![B: $i, C: $i] : ((~relation(C)) | (~((~((~(C = relation_dom_restriction(A, B))) | ![D: $i, E: $i] : (~(((~in(D, B)) | (~in(ordered_pair(D, E), A))) <=> in(ordered_pair(D, E), C))))) | (~((C = relation_dom_restriction(A, B)) | (((~in(tptp_fun_D_3(C, B, A), B)) | (~in(ordered_pair(tptp_fun_D_3(C, B, A), tptp_fun_E_2(C, B, A)), A))) <=> in(ordered_pair(tptp_fun_D_3(C, B, A), tptp_fun_E_2(C, B, A)), C)))))))) <=> ((~relation(A)) | ![B: $i, C: $i] : ((~relation(C)) | (~((~((~(C = relation_dom_restriction(A, B))) | ![D: $i, E: $i] : (~(((~in(D, B)) | (~in(ordered_pair(D, E), A))) <=> in(ordered_pair(D, E), C))))) | (~((C = relation_dom_restriction(A, B)) | (((~in(tptp_fun_D_3(C, B, A), B)) | (~in(ordered_pair(tptp_fun_D_3(C, B, A), tptp_fun_E_2(C, B, A)), A))) <=> in(ordered_pair(tptp_fun_D_3(C, B, A), tptp_fun_E_2(C, B, A)), C)))))))))),
% 1.80/1.96 inference(bind,[status(th)],[])).
% 1.80/1.96 tff(43,plain,
% 1.80/1.96 (![A: $i] : ((~relation(A)) | ![B: $i, C: $i] : ((~relation(C)) | (~((~((~(C = relation_dom_restriction(A, B))) | ![D: $i, E: $i] : (~(((~in(D, B)) | (~in(ordered_pair(D, E), A))) <=> in(ordered_pair(D, E), C))))) | (~((C = relation_dom_restriction(A, B)) | (((~in(tptp_fun_D_3(C, B, A), B)) | (~in(ordered_pair(tptp_fun_D_3(C, B, A), tptp_fun_E_2(C, B, A)), A))) <=> in(ordered_pair(tptp_fun_D_3(C, B, A), tptp_fun_E_2(C, B, A)), C)))))))) <=> ![A: $i] : ((~relation(A)) | ![B: $i, C: $i] : ((~relation(C)) | (~((~((~(C = relation_dom_restriction(A, B))) | ![D: $i, E: $i] : (~(((~in(D, B)) | (~in(ordered_pair(D, E), A))) <=> in(ordered_pair(D, E), C))))) | (~((C = relation_dom_restriction(A, B)) | (((~in(tptp_fun_D_3(C, B, A), B)) | (~in(ordered_pair(tptp_fun_D_3(C, B, A), tptp_fun_E_2(C, B, A)), A))) <=> in(ordered_pair(tptp_fun_D_3(C, B, A), tptp_fun_E_2(C, B, A)), C))))))))),
% 1.80/1.96 inference(quant_intro,[status(thm)],[42])).
% 1.80/1.96 tff(44,plain,
% 1.80/1.96 (^[A: $i] : rewrite(((~relation(A)) | ![B: $i, C: $i] : ((~relation(C)) | (~((~((~(C = relation_dom_restriction(A, B))) | ![D: $i, E: $i] : (~(((~in(D, B)) | (~in(ordered_pair(D, E), A))) <=> in(ordered_pair(D, E), C))))) | (~((C = relation_dom_restriction(A, B)) | (((~in(tptp_fun_D_3(C, B, A), B)) | (~in(ordered_pair(tptp_fun_D_3(C, B, A), tptp_fun_E_2(C, B, A)), A))) <=> in(ordered_pair(tptp_fun_D_3(C, B, A), tptp_fun_E_2(C, B, A)), C)))))))) <=> ((~relation(A)) | ![B: $i, C: $i] : ((~relation(C)) | (~((~((~(C = relation_dom_restriction(A, B))) | ![D: $i, E: $i] : (~(((~in(D, B)) | (~in(ordered_pair(D, E), A))) <=> in(ordered_pair(D, E), C))))) | (~((C = relation_dom_restriction(A, B)) | (((~in(tptp_fun_D_3(C, B, A), B)) | (~in(ordered_pair(tptp_fun_D_3(C, B, A), tptp_fun_E_2(C, B, A)), A))) <=> in(ordered_pair(tptp_fun_D_3(C, B, A), tptp_fun_E_2(C, B, A)), C)))))))))),
% 1.80/1.96 inference(bind,[status(th)],[])).
% 1.80/1.96 tff(45,plain,
% 1.80/1.96 (![A: $i] : ((~relation(A)) | ![B: $i, C: $i] : ((~relation(C)) | (~((~((~(C = relation_dom_restriction(A, B))) | ![D: $i, E: $i] : (~(((~in(D, B)) | (~in(ordered_pair(D, E), A))) <=> in(ordered_pair(D, E), C))))) | (~((C = relation_dom_restriction(A, B)) | (((~in(tptp_fun_D_3(C, B, A), B)) | (~in(ordered_pair(tptp_fun_D_3(C, B, A), tptp_fun_E_2(C, B, A)), A))) <=> in(ordered_pair(tptp_fun_D_3(C, B, A), tptp_fun_E_2(C, B, A)), C)))))))) <=> ![A: $i] : ((~relation(A)) | ![B: $i, C: $i] : ((~relation(C)) | (~((~((~(C = relation_dom_restriction(A, B))) | ![D: $i, E: $i] : (~(((~in(D, B)) | (~in(ordered_pair(D, E), A))) <=> in(ordered_pair(D, E), C))))) | (~((C = relation_dom_restriction(A, B)) | (((~in(tptp_fun_D_3(C, B, A), B)) | (~in(ordered_pair(tptp_fun_D_3(C, B, A), tptp_fun_E_2(C, B, A)), A))) <=> in(ordered_pair(tptp_fun_D_3(C, B, A), tptp_fun_E_2(C, B, A)), C))))))))),
% 1.80/1.96 inference(quant_intro,[status(thm)],[44])).
% 1.80/1.96 tff(46,plain,
% 1.80/1.96 (![A: $i] : ((~relation(A)) | ![B: $i, C: $i] : ((~relation(C)) | (~((~((~(C = relation_dom_restriction(A, B))) | ![D: $i, E: $i] : (~(((~in(D, B)) | (~in(ordered_pair(D, E), A))) <=> in(ordered_pair(D, E), C))))) | (~((C = relation_dom_restriction(A, B)) | (((~in(tptp_fun_D_3(C, B, A), B)) | (~in(ordered_pair(tptp_fun_D_3(C, B, A), tptp_fun_E_2(C, B, A)), A))) <=> in(ordered_pair(tptp_fun_D_3(C, B, A), tptp_fun_E_2(C, B, A)), C)))))))) <=> ![A: $i] : ((~relation(A)) | ![B: $i, C: $i] : ((~relation(C)) | (~((~((~(C = relation_dom_restriction(A, B))) | ![D: $i, E: $i] : (~(((~in(D, B)) | (~in(ordered_pair(D, E), A))) <=> in(ordered_pair(D, E), C))))) | (~((C = relation_dom_restriction(A, B)) | (((~in(tptp_fun_D_3(C, B, A), B)) | (~in(ordered_pair(tptp_fun_D_3(C, B, A), tptp_fun_E_2(C, B, A)), A))) <=> in(ordered_pair(tptp_fun_D_3(C, B, A), tptp_fun_E_2(C, B, A)), C))))))))),
% 1.80/1.96 inference(transitivity,[status(thm)],[45, 43])).
% 1.80/1.96 tff(47,plain,
% 1.80/1.96 (^[A: $i] : rewrite(((~relation(A)) | ![B: $i, C: $i] : ((~relation(C)) | (((~(C = relation_dom_restriction(A, B))) | ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (in(D, B) & in(ordered_pair(D, E), A)))) & ((C = relation_dom_restriction(A, B)) | (~(in(ordered_pair(tptp_fun_D_3(C, B, A), tptp_fun_E_2(C, B, A)), C) <=> (in(tptp_fun_D_3(C, B, A), B) & in(ordered_pair(tptp_fun_D_3(C, B, A), tptp_fun_E_2(C, B, A)), A)))))))) <=> ((~relation(A)) | ![B: $i, C: $i] : ((~relation(C)) | (~((~((~(C = relation_dom_restriction(A, B))) | ![D: $i, E: $i] : (~(((~in(D, B)) | (~in(ordered_pair(D, E), A))) <=> in(ordered_pair(D, E), C))))) | (~((C = relation_dom_restriction(A, B)) | (((~in(tptp_fun_D_3(C, B, A), B)) | (~in(ordered_pair(tptp_fun_D_3(C, B, A), tptp_fun_E_2(C, B, A)), A))) <=> in(ordered_pair(tptp_fun_D_3(C, B, A), tptp_fun_E_2(C, B, A)), C)))))))))),
% 1.80/1.96 inference(bind,[status(th)],[])).
% 1.80/1.96 tff(48,plain,
% 1.80/1.96 (![A: $i] : ((~relation(A)) | ![B: $i, C: $i] : ((~relation(C)) | (((~(C = relation_dom_restriction(A, B))) | ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (in(D, B) & in(ordered_pair(D, E), A)))) & ((C = relation_dom_restriction(A, B)) | (~(in(ordered_pair(tptp_fun_D_3(C, B, A), tptp_fun_E_2(C, B, A)), C) <=> (in(tptp_fun_D_3(C, B, A), B) & in(ordered_pair(tptp_fun_D_3(C, B, A), tptp_fun_E_2(C, B, A)), A)))))))) <=> ![A: $i] : ((~relation(A)) | ![B: $i, C: $i] : ((~relation(C)) | (~((~((~(C = relation_dom_restriction(A, B))) | ![D: $i, E: $i] : (~(((~in(D, B)) | (~in(ordered_pair(D, E), A))) <=> in(ordered_pair(D, E), C))))) | (~((C = relation_dom_restriction(A, B)) | (((~in(tptp_fun_D_3(C, B, A), B)) | (~in(ordered_pair(tptp_fun_D_3(C, B, A), tptp_fun_E_2(C, B, A)), A))) <=> in(ordered_pair(tptp_fun_D_3(C, B, A), tptp_fun_E_2(C, B, A)), C))))))))),
% 1.80/1.96 inference(quant_intro,[status(thm)],[47])).
% 1.80/1.96 tff(49,plain,
% 1.80/1.96 (![A: $i] : ((~relation(A)) | ![B: $i, C: $i] : ((~relation(C)) | ((C = relation_dom_restriction(A, B)) <=> ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (in(D, B) & in(ordered_pair(D, E), A)))))) <=> ![A: $i] : ((~relation(A)) | ![B: $i, C: $i] : ((~relation(C)) | ((C = relation_dom_restriction(A, B)) <=> ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (in(D, B) & in(ordered_pair(D, E), A))))))),
% 1.80/1.96 inference(rewrite,[status(thm)],[])).
% 1.80/1.96 tff(50,plain,
% 1.80/1.96 (^[A: $i] : trans(monotonicity(quant_intro(proof_bind(^[B: $i, C: $i] : trans(monotonicity(rewrite(((C = relation_dom_restriction(A, B)) <=> ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (in(D, B) & in(ordered_pair(D, E), A)))) <=> ((C = relation_dom_restriction(A, B)) <=> ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (in(D, B) & in(ordered_pair(D, E), A))))), ((relation(C) => ((C = relation_dom_restriction(A, B)) <=> ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (in(D, B) & in(ordered_pair(D, E), A))))) <=> (relation(C) => ((C = relation_dom_restriction(A, B)) <=> ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (in(D, B) & in(ordered_pair(D, E), A))))))), rewrite((relation(C) => ((C = relation_dom_restriction(A, B)) <=> ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (in(D, B) & in(ordered_pair(D, E), A))))) <=> ((~relation(C)) | ((C = relation_dom_restriction(A, B)) <=> ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (in(D, B) & in(ordered_pair(D, E), A)))))), ((relation(C) => ((C = relation_dom_restriction(A, B)) <=> ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (in(D, B) & in(ordered_pair(D, E), A))))) <=> ((~relation(C)) | ((C = relation_dom_restriction(A, B)) <=> ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (in(D, B) & in(ordered_pair(D, E), A)))))))), (![B: $i, C: $i] : (relation(C) => ((C = relation_dom_restriction(A, B)) <=> ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (in(D, B) & in(ordered_pair(D, E), A))))) <=> ![B: $i, C: $i] : ((~relation(C)) | ((C = relation_dom_restriction(A, B)) <=> ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (in(D, B) & in(ordered_pair(D, E), A))))))), ((relation(A) => ![B: $i, C: $i] : (relation(C) => ((C = relation_dom_restriction(A, B)) <=> ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (in(D, B) & in(ordered_pair(D, E), A)))))) <=> (relation(A) => ![B: $i, C: $i] : ((~relation(C)) | ((C = relation_dom_restriction(A, B)) <=> ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (in(D, B) & in(ordered_pair(D, E), A)))))))), rewrite((relation(A) => ![B: $i, C: $i] : ((~relation(C)) | ((C = relation_dom_restriction(A, B)) <=> ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (in(D, B) & in(ordered_pair(D, E), A)))))) <=> ((~relation(A)) | ![B: $i, C: $i] : ((~relation(C)) | ((C = relation_dom_restriction(A, B)) <=> ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (in(D, B) & in(ordered_pair(D, E), A))))))), ((relation(A) => ![B: $i, C: $i] : (relation(C) => ((C = relation_dom_restriction(A, B)) <=> ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (in(D, B) & in(ordered_pair(D, E), A)))))) <=> ((~relation(A)) | ![B: $i, C: $i] : ((~relation(C)) | ((C = relation_dom_restriction(A, B)) <=> ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (in(D, B) & in(ordered_pair(D, E), A))))))))),
% 1.80/1.96 inference(bind,[status(th)],[])).
% 1.80/1.96 tff(51,plain,
% 1.80/1.96 (![A: $i] : (relation(A) => ![B: $i, C: $i] : (relation(C) => ((C = relation_dom_restriction(A, B)) <=> ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (in(D, B) & in(ordered_pair(D, E), A)))))) <=> ![A: $i] : ((~relation(A)) | ![B: $i, C: $i] : ((~relation(C)) | ((C = relation_dom_restriction(A, B)) <=> ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (in(D, B) & in(ordered_pair(D, E), A))))))),
% 1.80/1.96 inference(quant_intro,[status(thm)],[50])).
% 1.80/1.96 tff(52,axiom,(![A: $i] : (relation(A) => ![B: $i, C: $i] : (relation(C) => ((C = relation_dom_restriction(A, B)) <=> ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (in(D, B) & in(ordered_pair(D, E), A))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d11_relat_1')).
% 1.80/1.96 tff(53,plain,
% 1.80/1.96 (![A: $i] : ((~relation(A)) | ![B: $i, C: $i] : ((~relation(C)) | ((C = relation_dom_restriction(A, B)) <=> ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (in(D, B) & in(ordered_pair(D, E), A))))))),
% 1.80/1.96 inference(modus_ponens,[status(thm)],[52, 51])).
% 1.80/1.96 tff(54,plain,
% 1.80/1.96 (![A: $i] : ((~relation(A)) | ![B: $i, C: $i] : ((~relation(C)) | ((C = relation_dom_restriction(A, B)) <=> ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (in(D, B) & in(ordered_pair(D, E), A))))))),
% 1.80/1.96 inference(modus_ponens,[status(thm)],[53, 49])).
% 1.80/1.96 tff(55,plain,(
% 1.80/1.96 ![A: $i] : ((~relation(A)) | ![B: $i, C: $i] : ((~relation(C)) | (((~(C = relation_dom_restriction(A, B))) | ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (in(D, B) & in(ordered_pair(D, E), A)))) & ((C = relation_dom_restriction(A, B)) | (~(in(ordered_pair(tptp_fun_D_3(C, B, A), tptp_fun_E_2(C, B, A)), C) <=> (in(tptp_fun_D_3(C, B, A), B) & in(ordered_pair(tptp_fun_D_3(C, B, A), tptp_fun_E_2(C, B, A)), A))))))))),
% 1.80/1.96 inference(skolemize,[status(sab)],[54])).
% 1.80/1.96 tff(56,plain,
% 1.80/1.96 (![A: $i] : ((~relation(A)) | ![B: $i, C: $i] : ((~relation(C)) | (~((~((~(C = relation_dom_restriction(A, B))) | ![D: $i, E: $i] : (~(((~in(D, B)) | (~in(ordered_pair(D, E), A))) <=> in(ordered_pair(D, E), C))))) | (~((C = relation_dom_restriction(A, B)) | (((~in(tptp_fun_D_3(C, B, A), B)) | (~in(ordered_pair(tptp_fun_D_3(C, B, A), tptp_fun_E_2(C, B, A)), A))) <=> in(ordered_pair(tptp_fun_D_3(C, B, A), tptp_fun_E_2(C, B, A)), C))))))))),
% 1.80/1.96 inference(modus_ponens,[status(thm)],[55, 48])).
% 1.80/1.96 tff(57,plain,
% 1.80/1.96 (![A: $i] : ((~relation(A)) | ![B: $i, C: $i] : ((~relation(C)) | (~((~((~(C = relation_dom_restriction(A, B))) | ![D: $i, E: $i] : (~(((~in(D, B)) | (~in(ordered_pair(D, E), A))) <=> in(ordered_pair(D, E), C))))) | (~((C = relation_dom_restriction(A, B)) | (((~in(tptp_fun_D_3(C, B, A), B)) | (~in(ordered_pair(tptp_fun_D_3(C, B, A), tptp_fun_E_2(C, B, A)), A))) <=> in(ordered_pair(tptp_fun_D_3(C, B, A), tptp_fun_E_2(C, B, A)), C))))))))),
% 1.80/1.96 inference(modus_ponens,[status(thm)],[56, 46])).
% 1.80/1.96 tff(58,plain,
% 1.80/1.96 (![A: $i] : ((~relation(A)) | ![B: $i, C: $i] : ((~relation(C)) | (~((~((C = relation_dom_restriction(A, B)) | (((~in(tptp_fun_D_3(C, B, A), B)) | (~in(ordered_pair(tptp_fun_D_3(C, B, A), tptp_fun_E_2(C, B, A)), A))) <=> in(ordered_pair(tptp_fun_D_3(C, B, A), tptp_fun_E_2(C, B, A)), C)))) | (~((~(C = relation_dom_restriction(A, B))) | ![D: $i, E: $i] : (~(((~in(D, B)) | (~in(ordered_pair(D, E), A))) <=> in(ordered_pair(D, E), C)))))))))),
% 1.80/1.96 inference(modus_ponens,[status(thm)],[57, 41])).
% 1.80/1.96 tff(59,plain,
% 1.80/1.96 (((~![A: $i] : ((~relation(A)) | ![B: $i, C: $i] : ((~relation(C)) | (~((~((C = relation_dom_restriction(A, B)) | (((~in(tptp_fun_D_3(C, B, A), B)) | (~in(ordered_pair(tptp_fun_D_3(C, B, A), tptp_fun_E_2(C, B, A)), A))) <=> in(ordered_pair(tptp_fun_D_3(C, B, A), tptp_fun_E_2(C, B, A)), C)))) | (~((~(C = relation_dom_restriction(A, B))) | ![D: $i, E: $i] : (~(((~in(D, B)) | (~in(ordered_pair(D, E), A))) <=> in(ordered_pair(D, E), C)))))))))) | ((~relation(B!56)) | ![B: $i, C: $i] : ((~relation(C)) | (~((~((C = relation_dom_restriction(B!56, B)) | (((~in(tptp_fun_D_3(C, B, B!56), B)) | (~in(ordered_pair(tptp_fun_D_3(C, B, B!56), tptp_fun_E_2(C, B, B!56)), B!56))) <=> in(ordered_pair(tptp_fun_D_3(C, B, B!56), tptp_fun_E_2(C, B, B!56)), C)))) | (~((~(C = relation_dom_restriction(B!56, B))) | ![D: $i, E: $i] : (~(((~in(D, B)) | (~in(ordered_pair(D, E), B!56))) <=> in(ordered_pair(D, E), C)))))))))) <=> ((~![A: $i] : ((~relation(A)) | ![B: $i, C: $i] : ((~relation(C)) | (~((~((C = relation_dom_restriction(A, B)) | (((~in(tptp_fun_D_3(C, B, A), B)) | (~in(ordered_pair(tptp_fun_D_3(C, B, A), tptp_fun_E_2(C, B, A)), A))) <=> in(ordered_pair(tptp_fun_D_3(C, B, A), tptp_fun_E_2(C, B, A)), C)))) | (~((~(C = relation_dom_restriction(A, B))) | ![D: $i, E: $i] : (~(((~in(D, B)) | (~in(ordered_pair(D, E), A))) <=> in(ordered_pair(D, E), C)))))))))) | (~relation(B!56)) | ![B: $i, C: $i] : ((~relation(C)) | (~((~((C = relation_dom_restriction(B!56, B)) | (((~in(tptp_fun_D_3(C, B, B!56), B)) | (~in(ordered_pair(tptp_fun_D_3(C, B, B!56), tptp_fun_E_2(C, B, B!56)), B!56))) <=> in(ordered_pair(tptp_fun_D_3(C, B, B!56), tptp_fun_E_2(C, B, B!56)), C)))) | (~((~(C = relation_dom_restriction(B!56, B))) | ![D: $i, E: $i] : (~(((~in(D, B)) | (~in(ordered_pair(D, E), B!56))) <=> in(ordered_pair(D, E), C)))))))))),
% 1.80/1.96 inference(rewrite,[status(thm)],[])).
% 1.80/1.96 tff(60,plain,
% 1.80/1.96 ((~![A: $i] : ((~relation(A)) | ![B: $i, C: $i] : ((~relation(C)) | (~((~((C = relation_dom_restriction(A, B)) | (((~in(tptp_fun_D_3(C, B, A), B)) | (~in(ordered_pair(tptp_fun_D_3(C, B, A), tptp_fun_E_2(C, B, A)), A))) <=> in(ordered_pair(tptp_fun_D_3(C, B, A), tptp_fun_E_2(C, B, A)), C)))) | (~((~(C = relation_dom_restriction(A, B))) | ![D: $i, E: $i] : (~(((~in(D, B)) | (~in(ordered_pair(D, E), A))) <=> in(ordered_pair(D, E), C)))))))))) | ((~relation(B!56)) | ![B: $i, C: $i] : ((~relation(C)) | (~((~((C = relation_dom_restriction(B!56, B)) | (((~in(tptp_fun_D_3(C, B, B!56), B)) | (~in(ordered_pair(tptp_fun_D_3(C, B, B!56), tptp_fun_E_2(C, B, B!56)), B!56))) <=> in(ordered_pair(tptp_fun_D_3(C, B, B!56), tptp_fun_E_2(C, B, B!56)), C)))) | (~((~(C = relation_dom_restriction(B!56, B))) | ![D: $i, E: $i] : (~(((~in(D, B)) | (~in(ordered_pair(D, E), B!56))) <=> in(ordered_pair(D, E), C)))))))))),
% 1.80/1.96 inference(quant_inst,[status(thm)],[])).
% 1.80/1.96 tff(61,plain,
% 1.80/1.96 ((~![A: $i] : ((~relation(A)) | ![B: $i, C: $i] : ((~relation(C)) | (~((~((C = relation_dom_restriction(A, B)) | (((~in(tptp_fun_D_3(C, B, A), B)) | (~in(ordered_pair(tptp_fun_D_3(C, B, A), tptp_fun_E_2(C, B, A)), A))) <=> in(ordered_pair(tptp_fun_D_3(C, B, A), tptp_fun_E_2(C, B, A)), C)))) | (~((~(C = relation_dom_restriction(A, B))) | ![D: $i, E: $i] : (~(((~in(D, B)) | (~in(ordered_pair(D, E), A))) <=> in(ordered_pair(D, E), C)))))))))) | (~relation(B!56)) | ![B: $i, C: $i] : ((~relation(C)) | (~((~((C = relation_dom_restriction(B!56, B)) | (((~in(tptp_fun_D_3(C, B, B!56), B)) | (~in(ordered_pair(tptp_fun_D_3(C, B, B!56), tptp_fun_E_2(C, B, B!56)), B!56))) <=> in(ordered_pair(tptp_fun_D_3(C, B, B!56), tptp_fun_E_2(C, B, B!56)), C)))) | (~((~(C = relation_dom_restriction(B!56, B))) | ![D: $i, E: $i] : (~(((~in(D, B)) | (~in(ordered_pair(D, E), B!56))) <=> in(ordered_pair(D, E), C))))))))),
% 1.80/1.97 inference(modus_ponens,[status(thm)],[60, 59])).
% 1.80/1.97 tff(62,plain,
% 1.80/1.97 (![B: $i, C: $i] : ((~relation(C)) | (~((~((C = relation_dom_restriction(B!56, B)) | (((~in(tptp_fun_D_3(C, B, B!56), B)) | (~in(ordered_pair(tptp_fun_D_3(C, B, B!56), tptp_fun_E_2(C, B, B!56)), B!56))) <=> in(ordered_pair(tptp_fun_D_3(C, B, B!56), tptp_fun_E_2(C, B, B!56)), C)))) | (~((~(C = relation_dom_restriction(B!56, B))) | ![D: $i, E: $i] : (~(((~in(D, B)) | (~in(ordered_pair(D, E), B!56))) <=> in(ordered_pair(D, E), C))))))))),
% 1.80/1.97 inference(unit_resolution,[status(thm)],[61, 58, 18])).
% 1.80/1.97 tff(63,plain,
% 1.80/1.97 (((~![B: $i, C: $i] : ((~relation(C)) | (~((~((C = relation_dom_restriction(B!56, B)) | (((~in(tptp_fun_D_3(C, B, B!56), B)) | (~in(ordered_pair(tptp_fun_D_3(C, B, B!56), tptp_fun_E_2(C, B, B!56)), B!56))) <=> in(ordered_pair(tptp_fun_D_3(C, B, B!56), tptp_fun_E_2(C, B, B!56)), C)))) | (~((~(C = relation_dom_restriction(B!56, B))) | ![D: $i, E: $i] : (~(((~in(D, B)) | (~in(ordered_pair(D, E), B!56))) <=> in(ordered_pair(D, E), C))))))))) | ((~relation(relation_composition(identity_relation(A!57), B!56))) | (~((~((~(relation_composition(identity_relation(A!57), B!56) = relation_dom_restriction(B!56, A!57))) | ![D: $i, E: $i] : (~(((~in(D, A!57)) | (~in(ordered_pair(D, E), B!56))) <=> in(ordered_pair(D, E), relation_composition(identity_relation(A!57), B!56)))))) | (~((relation_composition(identity_relation(A!57), B!56) = relation_dom_restriction(B!56, A!57)) | (((~in(tptp_fun_D_3(relation_composition(identity_relation(A!57), B!56), A!57, B!56), A!57)) | (~in(ordered_pair(tptp_fun_D_3(relation_composition(identity_relation(A!57), B!56), A!57, B!56), tptp_fun_E_2(relation_composition(identity_relation(A!57), B!56), A!57, B!56)), B!56))) <=> in(ordered_pair(tptp_fun_D_3(relation_composition(identity_relation(A!57), B!56), A!57, B!56), tptp_fun_E_2(relation_composition(identity_relation(A!57), B!56), A!57, B!56)), relation_composition(identity_relation(A!57), B!56))))))))) <=> ((~![B: $i, C: $i] : ((~relation(C)) | (~((~((C = relation_dom_restriction(B!56, B)) | (((~in(tptp_fun_D_3(C, B, B!56), B)) | (~in(ordered_pair(tptp_fun_D_3(C, B, B!56), tptp_fun_E_2(C, B, B!56)), B!56))) <=> in(ordered_pair(tptp_fun_D_3(C, B, B!56), tptp_fun_E_2(C, B, B!56)), C)))) | (~((~(C = relation_dom_restriction(B!56, B))) | ![D: $i, E: $i] : (~(((~in(D, B)) | (~in(ordered_pair(D, E), B!56))) <=> in(ordered_pair(D, E), C))))))))) | (~relation(relation_composition(identity_relation(A!57), B!56))) | (~((~((~(relation_composition(identity_relation(A!57), B!56) = relation_dom_restriction(B!56, A!57))) | ![D: $i, E: $i] : (~(((~in(D, A!57)) | (~in(ordered_pair(D, E), B!56))) <=> in(ordered_pair(D, E), relation_composition(identity_relation(A!57), B!56)))))) | (~((relation_composition(identity_relation(A!57), B!56) = relation_dom_restriction(B!56, A!57)) | (((~in(tptp_fun_D_3(relation_composition(identity_relation(A!57), B!56), A!57, B!56), A!57)) | (~in(ordered_pair(tptp_fun_D_3(relation_composition(identity_relation(A!57), B!56), A!57, B!56), tptp_fun_E_2(relation_composition(identity_relation(A!57), B!56), A!57, B!56)), B!56))) <=> in(ordered_pair(tptp_fun_D_3(relation_composition(identity_relation(A!57), B!56), A!57, B!56), tptp_fun_E_2(relation_composition(identity_relation(A!57), B!56), A!57, B!56)), relation_composition(identity_relation(A!57), B!56))))))))),
% 1.80/1.97 inference(rewrite,[status(thm)],[])).
% 1.80/1.97 tff(64,plain,
% 1.80/1.97 (((~relation(relation_composition(identity_relation(A!57), B!56))) | (~((~((relation_composition(identity_relation(A!57), B!56) = relation_dom_restriction(B!56, A!57)) | (((~in(tptp_fun_D_3(relation_composition(identity_relation(A!57), B!56), A!57, B!56), A!57)) | (~in(ordered_pair(tptp_fun_D_3(relation_composition(identity_relation(A!57), B!56), A!57, B!56), tptp_fun_E_2(relation_composition(identity_relation(A!57), B!56), A!57, B!56)), B!56))) <=> in(ordered_pair(tptp_fun_D_3(relation_composition(identity_relation(A!57), B!56), A!57, B!56), tptp_fun_E_2(relation_composition(identity_relation(A!57), B!56), A!57, B!56)), relation_composition(identity_relation(A!57), B!56))))) | (~((~(relation_composition(identity_relation(A!57), B!56) = relation_dom_restriction(B!56, A!57))) | ![D: $i, E: $i] : (~(((~in(D, A!57)) | (~in(ordered_pair(D, E), B!56))) <=> in(ordered_pair(D, E), relation_composition(identity_relation(A!57), B!56))))))))) <=> ((~relation(relation_composition(identity_relation(A!57), B!56))) | (~((~((~(relation_composition(identity_relation(A!57), B!56) = relation_dom_restriction(B!56, A!57))) | ![D: $i, E: $i] : (~(((~in(D, A!57)) | (~in(ordered_pair(D, E), B!56))) <=> in(ordered_pair(D, E), relation_composition(identity_relation(A!57), B!56)))))) | (~((relation_composition(identity_relation(A!57), B!56) = relation_dom_restriction(B!56, A!57)) | (((~in(tptp_fun_D_3(relation_composition(identity_relation(A!57), B!56), A!57, B!56), A!57)) | (~in(ordered_pair(tptp_fun_D_3(relation_composition(identity_relation(A!57), B!56), A!57, B!56), tptp_fun_E_2(relation_composition(identity_relation(A!57), B!56), A!57, B!56)), B!56))) <=> in(ordered_pair(tptp_fun_D_3(relation_composition(identity_relation(A!57), B!56), A!57, B!56), tptp_fun_E_2(relation_composition(identity_relation(A!57), B!56), A!57, B!56)), relation_composition(identity_relation(A!57), B!56))))))))),
% 1.80/1.97 inference(rewrite,[status(thm)],[])).
% 1.80/1.97 tff(65,plain,
% 1.80/1.97 (((~![B: $i, C: $i] : ((~relation(C)) | (~((~((C = relation_dom_restriction(B!56, B)) | (((~in(tptp_fun_D_3(C, B, B!56), B)) | (~in(ordered_pair(tptp_fun_D_3(C, B, B!56), tptp_fun_E_2(C, B, B!56)), B!56))) <=> in(ordered_pair(tptp_fun_D_3(C, B, B!56), tptp_fun_E_2(C, B, B!56)), C)))) | (~((~(C = relation_dom_restriction(B!56, B))) | ![D: $i, E: $i] : (~(((~in(D, B)) | (~in(ordered_pair(D, E), B!56))) <=> in(ordered_pair(D, E), C))))))))) | ((~relation(relation_composition(identity_relation(A!57), B!56))) | (~((~((relation_composition(identity_relation(A!57), B!56) = relation_dom_restriction(B!56, A!57)) | (((~in(tptp_fun_D_3(relation_composition(identity_relation(A!57), B!56), A!57, B!56), A!57)) | (~in(ordered_pair(tptp_fun_D_3(relation_composition(identity_relation(A!57), B!56), A!57, B!56), tptp_fun_E_2(relation_composition(identity_relation(A!57), B!56), A!57, B!56)), B!56))) <=> in(ordered_pair(tptp_fun_D_3(relation_composition(identity_relation(A!57), B!56), A!57, B!56), tptp_fun_E_2(relation_composition(identity_relation(A!57), B!56), A!57, B!56)), relation_composition(identity_relation(A!57), B!56))))) | (~((~(relation_composition(identity_relation(A!57), B!56) = relation_dom_restriction(B!56, A!57))) | ![D: $i, E: $i] : (~(((~in(D, A!57)) | (~in(ordered_pair(D, E), B!56))) <=> in(ordered_pair(D, E), relation_composition(identity_relation(A!57), B!56)))))))))) <=> ((~![B: $i, C: $i] : ((~relation(C)) | (~((~((C = relation_dom_restriction(B!56, B)) | (((~in(tptp_fun_D_3(C, B, B!56), B)) | (~in(ordered_pair(tptp_fun_D_3(C, B, B!56), tptp_fun_E_2(C, B, B!56)), B!56))) <=> in(ordered_pair(tptp_fun_D_3(C, B, B!56), tptp_fun_E_2(C, B, B!56)), C)))) | (~((~(C = relation_dom_restriction(B!56, B))) | ![D: $i, E: $i] : (~(((~in(D, B)) | (~in(ordered_pair(D, E), B!56))) <=> in(ordered_pair(D, E), C))))))))) | ((~relation(relation_composition(identity_relation(A!57), B!56))) | (~((~((~(relation_composition(identity_relation(A!57), B!56) = relation_dom_restriction(B!56, A!57))) | ![D: $i, E: $i] : (~(((~in(D, A!57)) | (~in(ordered_pair(D, E), B!56))) <=> in(ordered_pair(D, E), relation_composition(identity_relation(A!57), B!56)))))) | (~((relation_composition(identity_relation(A!57), B!56) = relation_dom_restriction(B!56, A!57)) | (((~in(tptp_fun_D_3(relation_composition(identity_relation(A!57), B!56), A!57, B!56), A!57)) | (~in(ordered_pair(tptp_fun_D_3(relation_composition(identity_relation(A!57), B!56), A!57, B!56), tptp_fun_E_2(relation_composition(identity_relation(A!57), B!56), A!57, B!56)), B!56))) <=> in(ordered_pair(tptp_fun_D_3(relation_composition(identity_relation(A!57), B!56), A!57, B!56), tptp_fun_E_2(relation_composition(identity_relation(A!57), B!56), A!57, B!56)), relation_composition(identity_relation(A!57), B!56)))))))))),
% 1.80/1.97 inference(monotonicity,[status(thm)],[64])).
% 1.80/1.97 tff(66,plain,
% 1.80/1.97 (((~![B: $i, C: $i] : ((~relation(C)) | (~((~((C = relation_dom_restriction(B!56, B)) | (((~in(tptp_fun_D_3(C, B, B!56), B)) | (~in(ordered_pair(tptp_fun_D_3(C, B, B!56), tptp_fun_E_2(C, B, B!56)), B!56))) <=> in(ordered_pair(tptp_fun_D_3(C, B, B!56), tptp_fun_E_2(C, B, B!56)), C)))) | (~((~(C = relation_dom_restriction(B!56, B))) | ![D: $i, E: $i] : (~(((~in(D, B)) | (~in(ordered_pair(D, E), B!56))) <=> in(ordered_pair(D, E), C))))))))) | ((~relation(relation_composition(identity_relation(A!57), B!56))) | (~((~((relation_composition(identity_relation(A!57), B!56) = relation_dom_restriction(B!56, A!57)) | (((~in(tptp_fun_D_3(relation_composition(identity_relation(A!57), B!56), A!57, B!56), A!57)) | (~in(ordered_pair(tptp_fun_D_3(relation_composition(identity_relation(A!57), B!56), A!57, B!56), tptp_fun_E_2(relation_composition(identity_relation(A!57), B!56), A!57, B!56)), B!56))) <=> in(ordered_pair(tptp_fun_D_3(relation_composition(identity_relation(A!57), B!56), A!57, B!56), tptp_fun_E_2(relation_composition(identity_relation(A!57), B!56), A!57, B!56)), relation_composition(identity_relation(A!57), B!56))))) | (~((~(relation_composition(identity_relation(A!57), B!56) = relation_dom_restriction(B!56, A!57))) | ![D: $i, E: $i] : (~(((~in(D, A!57)) | (~in(ordered_pair(D, E), B!56))) <=> in(ordered_pair(D, E), relation_composition(identity_relation(A!57), B!56)))))))))) <=> ((~![B: $i, C: $i] : ((~relation(C)) | (~((~((C = relation_dom_restriction(B!56, B)) | (((~in(tptp_fun_D_3(C, B, B!56), B)) | (~in(ordered_pair(tptp_fun_D_3(C, B, B!56), tptp_fun_E_2(C, B, B!56)), B!56))) <=> in(ordered_pair(tptp_fun_D_3(C, B, B!56), tptp_fun_E_2(C, B, B!56)), C)))) | (~((~(C = relation_dom_restriction(B!56, B))) | ![D: $i, E: $i] : (~(((~in(D, B)) | (~in(ordered_pair(D, E), B!56))) <=> in(ordered_pair(D, E), C))))))))) | (~relation(relation_composition(identity_relation(A!57), B!56))) | (~((~((~(relation_composition(identity_relation(A!57), B!56) = relation_dom_restriction(B!56, A!57))) | ![D: $i, E: $i] : (~(((~in(D, A!57)) | (~in(ordered_pair(D, E), B!56))) <=> in(ordered_pair(D, E), relation_composition(identity_relation(A!57), B!56)))))) | (~((relation_composition(identity_relation(A!57), B!56) = relation_dom_restriction(B!56, A!57)) | (((~in(tptp_fun_D_3(relation_composition(identity_relation(A!57), B!56), A!57, B!56), A!57)) | (~in(ordered_pair(tptp_fun_D_3(relation_composition(identity_relation(A!57), B!56), A!57, B!56), tptp_fun_E_2(relation_composition(identity_relation(A!57), B!56), A!57, B!56)), B!56))) <=> in(ordered_pair(tptp_fun_D_3(relation_composition(identity_relation(A!57), B!56), A!57, B!56), tptp_fun_E_2(relation_composition(identity_relation(A!57), B!56), A!57, B!56)), relation_composition(identity_relation(A!57), B!56))))))))),
% 1.80/1.97 inference(transitivity,[status(thm)],[65, 63])).
% 1.80/1.97 tff(67,plain,
% 1.80/1.97 ((~![B: $i, C: $i] : ((~relation(C)) | (~((~((C = relation_dom_restriction(B!56, B)) | (((~in(tptp_fun_D_3(C, B, B!56), B)) | (~in(ordered_pair(tptp_fun_D_3(C, B, B!56), tptp_fun_E_2(C, B, B!56)), B!56))) <=> in(ordered_pair(tptp_fun_D_3(C, B, B!56), tptp_fun_E_2(C, B, B!56)), C)))) | (~((~(C = relation_dom_restriction(B!56, B))) | ![D: $i, E: $i] : (~(((~in(D, B)) | (~in(ordered_pair(D, E), B!56))) <=> in(ordered_pair(D, E), C))))))))) | ((~relation(relation_composition(identity_relation(A!57), B!56))) | (~((~((relation_composition(identity_relation(A!57), B!56) = relation_dom_restriction(B!56, A!57)) | (((~in(tptp_fun_D_3(relation_composition(identity_relation(A!57), B!56), A!57, B!56), A!57)) | (~in(ordered_pair(tptp_fun_D_3(relation_composition(identity_relation(A!57), B!56), A!57, B!56), tptp_fun_E_2(relation_composition(identity_relation(A!57), B!56), A!57, B!56)), B!56))) <=> in(ordered_pair(tptp_fun_D_3(relation_composition(identity_relation(A!57), B!56), A!57, B!56), tptp_fun_E_2(relation_composition(identity_relation(A!57), B!56), A!57, B!56)), relation_composition(identity_relation(A!57), B!56))))) | (~((~(relation_composition(identity_relation(A!57), B!56) = relation_dom_restriction(B!56, A!57))) | ![D: $i, E: $i] : (~(((~in(D, A!57)) | (~in(ordered_pair(D, E), B!56))) <=> in(ordered_pair(D, E), relation_composition(identity_relation(A!57), B!56)))))))))),
% 1.80/1.97 inference(quant_inst,[status(thm)],[])).
% 1.80/1.97 tff(68,plain,
% 1.80/1.97 ((~![B: $i, C: $i] : ((~relation(C)) | (~((~((C = relation_dom_restriction(B!56, B)) | (((~in(tptp_fun_D_3(C, B, B!56), B)) | (~in(ordered_pair(tptp_fun_D_3(C, B, B!56), tptp_fun_E_2(C, B, B!56)), B!56))) <=> in(ordered_pair(tptp_fun_D_3(C, B, B!56), tptp_fun_E_2(C, B, B!56)), C)))) | (~((~(C = relation_dom_restriction(B!56, B))) | ![D: $i, E: $i] : (~(((~in(D, B)) | (~in(ordered_pair(D, E), B!56))) <=> in(ordered_pair(D, E), C))))))))) | (~relation(relation_composition(identity_relation(A!57), B!56))) | (~((~((~(relation_composition(identity_relation(A!57), B!56) = relation_dom_restriction(B!56, A!57))) | ![D: $i, E: $i] : (~(((~in(D, A!57)) | (~in(ordered_pair(D, E), B!56))) <=> in(ordered_pair(D, E), relation_composition(identity_relation(A!57), B!56)))))) | (~((relation_composition(identity_relation(A!57), B!56) = relation_dom_restriction(B!56, A!57)) | (((~in(tptp_fun_D_3(relation_composition(identity_relation(A!57), B!56), A!57, B!56), A!57)) | (~in(ordered_pair(tptp_fun_D_3(relation_composition(identity_relation(A!57), B!56), A!57, B!56), tptp_fun_E_2(relation_composition(identity_relation(A!57), B!56), A!57, B!56)), B!56))) <=> in(ordered_pair(tptp_fun_D_3(relation_composition(identity_relation(A!57), B!56), A!57, B!56), tptp_fun_E_2(relation_composition(identity_relation(A!57), B!56), A!57, B!56)), relation_composition(identity_relation(A!57), B!56)))))))),
% 1.80/1.97 inference(modus_ponens,[status(thm)],[67, 66])).
% 1.80/1.97 tff(69,plain,
% 1.80/1.97 (~((~((~(relation_composition(identity_relation(A!57), B!56) = relation_dom_restriction(B!56, A!57))) | ![D: $i, E: $i] : (~(((~in(D, A!57)) | (~in(ordered_pair(D, E), B!56))) <=> in(ordered_pair(D, E), relation_composition(identity_relation(A!57), B!56)))))) | (~((relation_composition(identity_relation(A!57), B!56) = relation_dom_restriction(B!56, A!57)) | (((~in(tptp_fun_D_3(relation_composition(identity_relation(A!57), B!56), A!57, B!56), A!57)) | (~in(ordered_pair(tptp_fun_D_3(relation_composition(identity_relation(A!57), B!56), A!57, B!56), tptp_fun_E_2(relation_composition(identity_relation(A!57), B!56), A!57, B!56)), B!56))) <=> in(ordered_pair(tptp_fun_D_3(relation_composition(identity_relation(A!57), B!56), A!57, B!56), tptp_fun_E_2(relation_composition(identity_relation(A!57), B!56), A!57, B!56)), relation_composition(identity_relation(A!57), B!56))))))),
% 1.80/1.97 inference(unit_resolution,[status(thm)],[68, 62, 39])).
% 1.80/1.97 tff(70,plain,
% 1.80/1.97 (((~((~(relation_composition(identity_relation(A!57), B!56) = relation_dom_restriction(B!56, A!57))) | ![D: $i, E: $i] : (~(((~in(D, A!57)) | (~in(ordered_pair(D, E), B!56))) <=> in(ordered_pair(D, E), relation_composition(identity_relation(A!57), B!56)))))) | (~((relation_composition(identity_relation(A!57), B!56) = relation_dom_restriction(B!56, A!57)) | (((~in(tptp_fun_D_3(relation_composition(identity_relation(A!57), B!56), A!57, B!56), A!57)) | (~in(ordered_pair(tptp_fun_D_3(relation_composition(identity_relation(A!57), B!56), A!57, B!56), tptp_fun_E_2(relation_composition(identity_relation(A!57), B!56), A!57, B!56)), B!56))) <=> in(ordered_pair(tptp_fun_D_3(relation_composition(identity_relation(A!57), B!56), A!57, B!56), tptp_fun_E_2(relation_composition(identity_relation(A!57), B!56), A!57, B!56)), relation_composition(identity_relation(A!57), B!56)))))) | ((relation_composition(identity_relation(A!57), B!56) = relation_dom_restriction(B!56, A!57)) | (((~in(tptp_fun_D_3(relation_composition(identity_relation(A!57), B!56), A!57, B!56), A!57)) | (~in(ordered_pair(tptp_fun_D_3(relation_composition(identity_relation(A!57), B!56), A!57, B!56), tptp_fun_E_2(relation_composition(identity_relation(A!57), B!56), A!57, B!56)), B!56))) <=> in(ordered_pair(tptp_fun_D_3(relation_composition(identity_relation(A!57), B!56), A!57, B!56), tptp_fun_E_2(relation_composition(identity_relation(A!57), B!56), A!57, B!56)), relation_composition(identity_relation(A!57), B!56))))),
% 1.80/1.97 inference(tautology,[status(thm)],[])).
% 1.80/1.97 tff(71,plain,
% 1.80/1.97 ((relation_composition(identity_relation(A!57), B!56) = relation_dom_restriction(B!56, A!57)) | (((~in(tptp_fun_D_3(relation_composition(identity_relation(A!57), B!56), A!57, B!56), A!57)) | (~in(ordered_pair(tptp_fun_D_3(relation_composition(identity_relation(A!57), B!56), A!57, B!56), tptp_fun_E_2(relation_composition(identity_relation(A!57), B!56), A!57, B!56)), B!56))) <=> in(ordered_pair(tptp_fun_D_3(relation_composition(identity_relation(A!57), B!56), A!57, B!56), tptp_fun_E_2(relation_composition(identity_relation(A!57), B!56), A!57, B!56)), relation_composition(identity_relation(A!57), B!56)))),
% 1.80/1.97 inference(unit_resolution,[status(thm)],[70, 69])).
% 1.80/1.97 tff(72,plain,
% 1.80/1.97 ((relation_composition(identity_relation(A!57), B!56) = relation_dom_restriction(B!56, A!57)) <=> (relation_dom_restriction(B!56, A!57) = relation_composition(identity_relation(A!57), B!56))),
% 1.80/1.97 inference(commutativity,[status(thm)],[])).
% 1.80/1.97 tff(73,plain,
% 1.80/1.97 ((relation_dom_restriction(B!56, A!57) = relation_composition(identity_relation(A!57), B!56)) <=> (relation_composition(identity_relation(A!57), B!56) = relation_dom_restriction(B!56, A!57))),
% 1.80/1.97 inference(symmetry,[status(thm)],[72])).
% 1.80/1.97 tff(74,plain,
% 1.80/1.97 ((~(relation_dom_restriction(B!56, A!57) = relation_composition(identity_relation(A!57), B!56))) <=> (~(relation_composition(identity_relation(A!57), B!56) = relation_dom_restriction(B!56, A!57)))),
% 1.80/1.97 inference(monotonicity,[status(thm)],[73])).
% 1.80/1.97 tff(75,plain,
% 1.80/1.97 (~(relation_dom_restriction(B!56, A!57) = relation_composition(identity_relation(A!57), B!56))),
% 1.80/1.97 inference(or_elim,[status(thm)],[17])).
% 1.80/1.97 tff(76,plain,
% 1.80/1.97 (~(relation_composition(identity_relation(A!57), B!56) = relation_dom_restriction(B!56, A!57))),
% 1.80/1.97 inference(modus_ponens,[status(thm)],[75, 74])).
% 1.80/1.97 tff(77,plain,
% 1.80/1.97 ((~((relation_composition(identity_relation(A!57), B!56) = relation_dom_restriction(B!56, A!57)) | (((~in(tptp_fun_D_3(relation_composition(identity_relation(A!57), B!56), A!57, B!56), A!57)) | (~in(ordered_pair(tptp_fun_D_3(relation_composition(identity_relation(A!57), B!56), A!57, B!56), tptp_fun_E_2(relation_composition(identity_relation(A!57), B!56), A!57, B!56)), B!56))) <=> in(ordered_pair(tptp_fun_D_3(relation_composition(identity_relation(A!57), B!56), A!57, B!56), tptp_fun_E_2(relation_composition(identity_relation(A!57), B!56), A!57, B!56)), relation_composition(identity_relation(A!57), B!56))))) | (relation_composition(identity_relation(A!57), B!56) = relation_dom_restriction(B!56, A!57)) | (((~in(tptp_fun_D_3(relation_composition(identity_relation(A!57), B!56), A!57, B!56), A!57)) | (~in(ordered_pair(tptp_fun_D_3(relation_composition(identity_relation(A!57), B!56), A!57, B!56), tptp_fun_E_2(relation_composition(identity_relation(A!57), B!56), A!57, B!56)), B!56))) <=> in(ordered_pair(tptp_fun_D_3(relation_composition(identity_relation(A!57), B!56), A!57, B!56), tptp_fun_E_2(relation_composition(identity_relation(A!57), B!56), A!57, B!56)), relation_composition(identity_relation(A!57), B!56)))),
% 1.80/1.97 inference(tautology,[status(thm)],[])).
% 1.80/1.97 tff(78,plain,
% 1.80/1.97 (((~in(tptp_fun_D_3(relation_composition(identity_relation(A!57), B!56), A!57, B!56), A!57)) | (~in(ordered_pair(tptp_fun_D_3(relation_composition(identity_relation(A!57), B!56), A!57, B!56), tptp_fun_E_2(relation_composition(identity_relation(A!57), B!56), A!57, B!56)), B!56))) <=> in(ordered_pair(tptp_fun_D_3(relation_composition(identity_relation(A!57), B!56), A!57, B!56), tptp_fun_E_2(relation_composition(identity_relation(A!57), B!56), A!57, B!56)), relation_composition(identity_relation(A!57), B!56))),
% 1.80/1.97 inference(unit_resolution,[status(thm)],[77, 76, 71])).
% 1.80/1.97 tff(79,plain,
% 1.80/1.97 (^[A: $i, B: $i, C: $i, D: $i] : refl(((~relation(D)) | (~(((~in(A, C)) | (~in(ordered_pair(A, B), D))) <=> in(ordered_pair(A, B), relation_composition(identity_relation(C), D))))) <=> ((~relation(D)) | (~(((~in(A, C)) | (~in(ordered_pair(A, B), D))) <=> in(ordered_pair(A, B), relation_composition(identity_relation(C), D))))))),
% 1.80/1.97 inference(bind,[status(th)],[])).
% 1.80/1.97 tff(80,plain,
% 1.80/1.97 (![A: $i, B: $i, C: $i, D: $i] : ((~relation(D)) | (~(((~in(A, C)) | (~in(ordered_pair(A, B), D))) <=> in(ordered_pair(A, B), relation_composition(identity_relation(C), D))))) <=> ![A: $i, B: $i, C: $i, D: $i] : ((~relation(D)) | (~(((~in(A, C)) | (~in(ordered_pair(A, B), D))) <=> in(ordered_pair(A, B), relation_composition(identity_relation(C), D)))))),
% 1.80/1.97 inference(quant_intro,[status(thm)],[79])).
% 1.80/1.97 tff(81,plain,
% 1.80/1.97 (^[A: $i, B: $i, C: $i, D: $i] : rewrite(((~relation(D)) | (in(ordered_pair(A, B), relation_composition(identity_relation(C), D)) <=> (in(A, C) & in(ordered_pair(A, B), D)))) <=> ((~relation(D)) | (~(((~in(A, C)) | (~in(ordered_pair(A, B), D))) <=> in(ordered_pair(A, B), relation_composition(identity_relation(C), D))))))),
% 1.80/1.97 inference(bind,[status(th)],[])).
% 1.80/1.97 tff(82,plain,
% 1.80/1.97 (![A: $i, B: $i, C: $i, D: $i] : ((~relation(D)) | (in(ordered_pair(A, B), relation_composition(identity_relation(C), D)) <=> (in(A, C) & in(ordered_pair(A, B), D)))) <=> ![A: $i, B: $i, C: $i, D: $i] : ((~relation(D)) | (~(((~in(A, C)) | (~in(ordered_pair(A, B), D))) <=> in(ordered_pair(A, B), relation_composition(identity_relation(C), D)))))),
% 1.80/1.97 inference(quant_intro,[status(thm)],[81])).
% 1.80/1.97 tff(83,plain,
% 1.80/1.97 (![A: $i, B: $i, C: $i, D: $i] : ((~relation(D)) | (in(ordered_pair(A, B), relation_composition(identity_relation(C), D)) <=> (in(A, C) & in(ordered_pair(A, B), D)))) <=> ![A: $i, B: $i, C: $i, D: $i] : ((~relation(D)) | (in(ordered_pair(A, B), relation_composition(identity_relation(C), D)) <=> (in(A, C) & in(ordered_pair(A, B), D))))),
% 1.80/1.97 inference(rewrite,[status(thm)],[])).
% 1.80/1.97 tff(84,plain,
% 1.80/1.97 (^[A: $i, B: $i, C: $i, D: $i] : rewrite((relation(D) => (in(ordered_pair(A, B), relation_composition(identity_relation(C), D)) <=> (in(A, C) & in(ordered_pair(A, B), D)))) <=> ((~relation(D)) | (in(ordered_pair(A, B), relation_composition(identity_relation(C), D)) <=> (in(A, C) & in(ordered_pair(A, B), D)))))),
% 1.80/1.97 inference(bind,[status(th)],[])).
% 1.80/1.97 tff(85,plain,
% 1.80/1.97 (![A: $i, B: $i, C: $i, D: $i] : (relation(D) => (in(ordered_pair(A, B), relation_composition(identity_relation(C), D)) <=> (in(A, C) & in(ordered_pair(A, B), D)))) <=> ![A: $i, B: $i, C: $i, D: $i] : ((~relation(D)) | (in(ordered_pair(A, B), relation_composition(identity_relation(C), D)) <=> (in(A, C) & in(ordered_pair(A, B), D))))),
% 1.80/1.97 inference(quant_intro,[status(thm)],[84])).
% 1.80/1.97 tff(86,axiom,(![A: $i, B: $i, C: $i, D: $i] : (relation(D) => (in(ordered_pair(A, B), relation_composition(identity_relation(C), D)) <=> (in(A, C) & in(ordered_pair(A, B), D))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t74_relat_1')).
% 1.80/1.97 tff(87,plain,
% 1.80/1.97 (![A: $i, B: $i, C: $i, D: $i] : ((~relation(D)) | (in(ordered_pair(A, B), relation_composition(identity_relation(C), D)) <=> (in(A, C) & in(ordered_pair(A, B), D))))),
% 1.80/1.97 inference(modus_ponens,[status(thm)],[86, 85])).
% 1.80/1.97 tff(88,plain,
% 1.80/1.97 (![A: $i, B: $i, C: $i, D: $i] : ((~relation(D)) | (in(ordered_pair(A, B), relation_composition(identity_relation(C), D)) <=> (in(A, C) & in(ordered_pair(A, B), D))))),
% 1.80/1.97 inference(modus_ponens,[status(thm)],[87, 83])).
% 1.80/1.97 tff(89,plain,(
% 1.80/1.97 ![A: $i, B: $i, C: $i, D: $i] : ((~relation(D)) | (in(ordered_pair(A, B), relation_composition(identity_relation(C), D)) <=> (in(A, C) & in(ordered_pair(A, B), D))))),
% 1.80/1.97 inference(skolemize,[status(sab)],[88])).
% 1.80/1.97 tff(90,plain,
% 1.80/1.97 (![A: $i, B: $i, C: $i, D: $i] : ((~relation(D)) | (~(((~in(A, C)) | (~in(ordered_pair(A, B), D))) <=> in(ordered_pair(A, B), relation_composition(identity_relation(C), D)))))),
% 1.80/1.97 inference(modus_ponens,[status(thm)],[89, 82])).
% 1.80/1.97 tff(91,plain,
% 1.80/1.97 (![A: $i, B: $i, C: $i, D: $i] : ((~relation(D)) | (~(((~in(A, C)) | (~in(ordered_pair(A, B), D))) <=> in(ordered_pair(A, B), relation_composition(identity_relation(C), D)))))),
% 1.80/1.97 inference(modus_ponens,[status(thm)],[90, 80])).
% 1.80/1.97 tff(92,plain,
% 1.80/1.97 (((~![A: $i, B: $i, C: $i, D: $i] : ((~relation(D)) | (~(((~in(A, C)) | (~in(ordered_pair(A, B), D))) <=> in(ordered_pair(A, B), relation_composition(identity_relation(C), D)))))) | ((~relation(B!56)) | (~(((~in(tptp_fun_D_3(relation_composition(identity_relation(A!57), B!56), A!57, B!56), A!57)) | (~in(ordered_pair(tptp_fun_D_3(relation_composition(identity_relation(A!57), B!56), A!57, B!56), tptp_fun_E_2(relation_composition(identity_relation(A!57), B!56), A!57, B!56)), B!56))) <=> in(ordered_pair(tptp_fun_D_3(relation_composition(identity_relation(A!57), B!56), A!57, B!56), tptp_fun_E_2(relation_composition(identity_relation(A!57), B!56), A!57, B!56)), relation_composition(identity_relation(A!57), B!56)))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : ((~relation(D)) | (~(((~in(A, C)) | (~in(ordered_pair(A, B), D))) <=> in(ordered_pair(A, B), relation_composition(identity_relation(C), D)))))) | (~relation(B!56)) | (~(((~in(tptp_fun_D_3(relation_composition(identity_relation(A!57), B!56), A!57, B!56), A!57)) | (~in(ordered_pair(tptp_fun_D_3(relation_composition(identity_relation(A!57), B!56), A!57, B!56), tptp_fun_E_2(relation_composition(identity_relation(A!57), B!56), A!57, B!56)), B!56))) <=> in(ordered_pair(tptp_fun_D_3(relation_composition(identity_relation(A!57), B!56), A!57, B!56), tptp_fun_E_2(relation_composition(identity_relation(A!57), B!56), A!57, B!56)), relation_composition(identity_relation(A!57), B!56)))))),
% 1.80/1.98 inference(rewrite,[status(thm)],[])).
% 1.80/1.98 tff(93,plain,
% 1.80/1.98 ((~![A: $i, B: $i, C: $i, D: $i] : ((~relation(D)) | (~(((~in(A, C)) | (~in(ordered_pair(A, B), D))) <=> in(ordered_pair(A, B), relation_composition(identity_relation(C), D)))))) | ((~relation(B!56)) | (~(((~in(tptp_fun_D_3(relation_composition(identity_relation(A!57), B!56), A!57, B!56), A!57)) | (~in(ordered_pair(tptp_fun_D_3(relation_composition(identity_relation(A!57), B!56), A!57, B!56), tptp_fun_E_2(relation_composition(identity_relation(A!57), B!56), A!57, B!56)), B!56))) <=> in(ordered_pair(tptp_fun_D_3(relation_composition(identity_relation(A!57), B!56), A!57, B!56), tptp_fun_E_2(relation_composition(identity_relation(A!57), B!56), A!57, B!56)), relation_composition(identity_relation(A!57), B!56)))))),
% 1.80/1.98 inference(quant_inst,[status(thm)],[])).
% 1.80/1.98 tff(94,plain,
% 1.80/1.98 ((~![A: $i, B: $i, C: $i, D: $i] : ((~relation(D)) | (~(((~in(A, C)) | (~in(ordered_pair(A, B), D))) <=> in(ordered_pair(A, B), relation_composition(identity_relation(C), D)))))) | (~relation(B!56)) | (~(((~in(tptp_fun_D_3(relation_composition(identity_relation(A!57), B!56), A!57, B!56), A!57)) | (~in(ordered_pair(tptp_fun_D_3(relation_composition(identity_relation(A!57), B!56), A!57, B!56), tptp_fun_E_2(relation_composition(identity_relation(A!57), B!56), A!57, B!56)), B!56))) <=> in(ordered_pair(tptp_fun_D_3(relation_composition(identity_relation(A!57), B!56), A!57, B!56), tptp_fun_E_2(relation_composition(identity_relation(A!57), B!56), A!57, B!56)), relation_composition(identity_relation(A!57), B!56))))),
% 1.80/1.98 inference(modus_ponens,[status(thm)],[93, 92])).
% 1.80/1.98 tff(95,plain,
% 1.80/1.98 ($false),
% 1.80/1.98 inference(unit_resolution,[status(thm)],[94, 91, 18, 78])).
% 1.80/1.98 % SZS output end Proof
% 1.84/1.99 % E exiting
%------------------------------------------------------------------------------