%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SEU193+2 : TPTP v9.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n007.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 05:27:11 AM UTC 2025
% Result : Theorem 4.20s 4.39s
% Output : Proof 4.23s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU193+2 : TPTP v9.0.0. Released v3.3.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n007.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 20 06:17:05 EDT 2025
% 0.12/0.33 % CPUTime :
% 4.20/4.39 % SZS status Theorem
% 4.20/4.39 % SZS output start Proof
% 4.20/4.39 tff(in_type, type, (
% 4.20/4.39 in: ( $i * $i ) > $o)).
% 4.20/4.39 tff(relation_dom_restriction_type, type, (
% 4.20/4.39 relation_dom_restriction: ( $i * $i ) > $i)).
% 4.20/4.39 tff(tptp_fun_A_55_type, type, (
% 4.20/4.39 tptp_fun_A_55: $i)).
% 4.20/4.39 tff(tptp_fun_B_54_type, type, (
% 4.20/4.39 tptp_fun_B_54: $i)).
% 4.20/4.39 tff(ordered_pair_type, type, (
% 4.20/4.39 ordered_pair: ( $i * $i ) > $i)).
% 4.20/4.39 tff(tptp_fun_D_20_type, type, (
% 4.20/4.39 tptp_fun_D_20: ( $i * $i ) > $i)).
% 4.20/4.39 tff(tptp_fun_C_21_type, type, (
% 4.20/4.39 tptp_fun_C_21: ( $i * $i ) > $i)).
% 4.20/4.39 tff(subset_type, type, (
% 4.20/4.39 subset: ( $i * $i ) > $o)).
% 4.20/4.39 tff(relation_type, type, (
% 4.20/4.39 relation: $i > $o)).
% 4.20/4.39 tff(tptp_fun_E_2_type, type, (
% 4.20/4.39 tptp_fun_E_2: ( $i * $i * $i ) > $i)).
% 4.20/4.39 tff(tptp_fun_D_3_type, type, (
% 4.20/4.39 tptp_fun_D_3: ( $i * $i * $i ) > $i)).
% 4.20/4.39 tff(1,plain,
% 4.20/4.39 ((~![A: $i, B: $i] : ((~relation(B)) | subset(relation_dom_restriction(B, A), B))) <=> (~![A: $i, B: $i] : ((~relation(B)) | subset(relation_dom_restriction(B, A), B)))),
% 4.20/4.39 inference(rewrite,[status(thm)],[])).
% 4.20/4.39 tff(2,plain,
% 4.20/4.39 ((~![A: $i, B: $i] : (relation(B) => subset(relation_dom_restriction(B, A), B))) <=> (~![A: $i, B: $i] : ((~relation(B)) | subset(relation_dom_restriction(B, A), B)))),
% 4.20/4.39 inference(rewrite,[status(thm)],[])).
% 4.20/4.39 tff(3,axiom,(~![A: $i, B: $i] : (relation(B) => subset(relation_dom_restriction(B, A), B))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t88_relat_1')).
% 4.20/4.39 tff(4,plain,
% 4.20/4.39 (~![A: $i, B: $i] : ((~relation(B)) | subset(relation_dom_restriction(B, A), B))),
% 4.20/4.39 inference(modus_ponens,[status(thm)],[3, 2])).
% 4.20/4.39 tff(5,plain,
% 4.20/4.39 (~![A: $i, B: $i] : ((~relation(B)) | subset(relation_dom_restriction(B, A), B))),
% 4.20/4.39 inference(modus_ponens,[status(thm)],[4, 1])).
% 4.20/4.39 tff(6,plain,
% 4.20/4.39 (~![A: $i, B: $i] : ((~relation(B)) | subset(relation_dom_restriction(B, A), B))),
% 4.20/4.39 inference(modus_ponens,[status(thm)],[5, 1])).
% 4.20/4.39 tff(7,plain,
% 4.20/4.39 (~![A: $i, B: $i] : ((~relation(B)) | subset(relation_dom_restriction(B, A), B))),
% 4.20/4.39 inference(modus_ponens,[status(thm)],[6, 1])).
% 4.20/4.39 tff(8,plain,(
% 4.20/4.39 ~((~relation(B!54)) | subset(relation_dom_restriction(B!54, A!55), B!54))),
% 4.20/4.39 inference(skolemize,[status(sab)],[7])).
% 4.20/4.39 tff(9,plain,
% 4.20/4.39 (relation(B!54)),
% 4.20/4.39 inference(or_elim,[status(thm)],[8])).
% 4.20/4.39 tff(10,plain,
% 4.20/4.39 (^[A: $i, B: $i] : refl(((~relation(A)) | relation(relation_dom_restriction(A, B))) <=> ((~relation(A)) | relation(relation_dom_restriction(A, B))))),
% 4.20/4.39 inference(bind,[status(th)],[])).
% 4.20/4.39 tff(11,plain,
% 4.20/4.39 (![A: $i, B: $i] : ((~relation(A)) | relation(relation_dom_restriction(A, B))) <=> ![A: $i, B: $i] : ((~relation(A)) | relation(relation_dom_restriction(A, B)))),
% 4.20/4.39 inference(quant_intro,[status(thm)],[10])).
% 4.20/4.39 tff(12,plain,
% 4.20/4.39 (![A: $i, B: $i] : ((~relation(A)) | relation(relation_dom_restriction(A, B))) <=> ![A: $i, B: $i] : ((~relation(A)) | relation(relation_dom_restriction(A, B)))),
% 4.20/4.39 inference(rewrite,[status(thm)],[])).
% 4.20/4.39 tff(13,plain,
% 4.20/4.39 (^[A: $i, B: $i] : rewrite((relation(A) => relation(relation_dom_restriction(A, B))) <=> ((~relation(A)) | relation(relation_dom_restriction(A, B))))),
% 4.20/4.39 inference(bind,[status(th)],[])).
% 4.20/4.39 tff(14,plain,
% 4.20/4.39 (![A: $i, B: $i] : (relation(A) => relation(relation_dom_restriction(A, B))) <=> ![A: $i, B: $i] : ((~relation(A)) | relation(relation_dom_restriction(A, B)))),
% 4.20/4.39 inference(quant_intro,[status(thm)],[13])).
% 4.20/4.39 tff(15,axiom,(![A: $i, B: $i] : (relation(A) => relation(relation_dom_restriction(A, B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_k7_relat_1')).
% 4.20/4.39 tff(16,plain,
% 4.20/4.39 (![A: $i, B: $i] : ((~relation(A)) | relation(relation_dom_restriction(A, B)))),
% 4.20/4.39 inference(modus_ponens,[status(thm)],[15, 14])).
% 4.20/4.39 tff(17,plain,
% 4.20/4.39 (![A: $i, B: $i] : ((~relation(A)) | relation(relation_dom_restriction(A, B)))),
% 4.20/4.39 inference(modus_ponens,[status(thm)],[16, 12])).
% 4.20/4.39 tff(18,plain,(
% 4.20/4.39 ![A: $i, B: $i] : ((~relation(A)) | relation(relation_dom_restriction(A, B)))),
% 4.20/4.39 inference(skolemize,[status(sab)],[17])).
% 4.20/4.39 tff(19,plain,
% 4.20/4.39 (![A: $i, B: $i] : ((~relation(A)) | relation(relation_dom_restriction(A, B)))),
% 4.20/4.39 inference(modus_ponens,[status(thm)],[18, 11])).
% 4.20/4.39 tff(20,plain,
% 4.20/4.39 (((~![A: $i, B: $i] : ((~relation(A)) | relation(relation_dom_restriction(A, B)))) | ((~relation(B!54)) | relation(relation_dom_restriction(B!54, A!55)))) <=> ((~![A: $i, B: $i] : ((~relation(A)) | relation(relation_dom_restriction(A, B)))) | (~relation(B!54)) | relation(relation_dom_restriction(B!54, A!55)))),
% 4.20/4.39 inference(rewrite,[status(thm)],[])).
% 4.20/4.39 tff(21,plain,
% 4.20/4.39 ((~![A: $i, B: $i] : ((~relation(A)) | relation(relation_dom_restriction(A, B)))) | ((~relation(B!54)) | relation(relation_dom_restriction(B!54, A!55)))),
% 4.20/4.39 inference(quant_inst,[status(thm)],[])).
% 4.20/4.39 tff(22,plain,
% 4.20/4.39 ((~![A: $i, B: $i] : ((~relation(A)) | relation(relation_dom_restriction(A, B)))) | (~relation(B!54)) | relation(relation_dom_restriction(B!54, A!55))),
% 4.20/4.39 inference(modus_ponens,[status(thm)],[21, 20])).
% 4.20/4.39 tff(23,plain,
% 4.20/4.39 (relation(relation_dom_restriction(B!54, A!55))),
% 4.20/4.39 inference(unit_resolution,[status(thm)],[22, 19, 9])).
% 4.20/4.39 tff(24,plain,
% 4.20/4.39 (^[A: $i] : refl(((~relation(A)) | ![B: $i] : ((~relation(B)) | (~((~((~subset(A, B)) | ![C: $i, D: $i] : ((~in(ordered_pair(C, D), A)) | in(ordered_pair(C, D), B)))) | (~(subset(A, B) | (~((~in(ordered_pair(tptp_fun_C_21(B, A), tptp_fun_D_20(B, A)), A)) | in(ordered_pair(tptp_fun_C_21(B, A), tptp_fun_D_20(B, A)), B))))))))) <=> ((~relation(A)) | ![B: $i] : ((~relation(B)) | (~((~((~subset(A, B)) | ![C: $i, D: $i] : ((~in(ordered_pair(C, D), A)) | in(ordered_pair(C, D), B)))) | (~(subset(A, B) | (~((~in(ordered_pair(tptp_fun_C_21(B, A), tptp_fun_D_20(B, A)), A)) | in(ordered_pair(tptp_fun_C_21(B, A), tptp_fun_D_20(B, A)), B))))))))))),
% 4.20/4.39 inference(bind,[status(th)],[])).
% 4.20/4.39 tff(25,plain,
% 4.20/4.39 (![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | (~((~((~subset(A, B)) | ![C: $i, D: $i] : ((~in(ordered_pair(C, D), A)) | in(ordered_pair(C, D), B)))) | (~(subset(A, B) | (~((~in(ordered_pair(tptp_fun_C_21(B, A), tptp_fun_D_20(B, A)), A)) | in(ordered_pair(tptp_fun_C_21(B, A), tptp_fun_D_20(B, A)), B))))))))) <=> ![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | (~((~((~subset(A, B)) | ![C: $i, D: $i] : ((~in(ordered_pair(C, D), A)) | in(ordered_pair(C, D), B)))) | (~(subset(A, B) | (~((~in(ordered_pair(tptp_fun_C_21(B, A), tptp_fun_D_20(B, A)), A)) | in(ordered_pair(tptp_fun_C_21(B, A), tptp_fun_D_20(B, A)), B)))))))))),
% 4.20/4.39 inference(quant_intro,[status(thm)],[24])).
% 4.20/4.39 tff(26,plain,
% 4.20/4.39 (^[A: $i] : rewrite(((~relation(A)) | ![B: $i] : ((~relation(B)) | (~((~((~subset(A, B)) | ![C: $i, D: $i] : ((~in(ordered_pair(C, D), A)) | in(ordered_pair(C, D), B)))) | (~(subset(A, B) | (~((~in(ordered_pair(tptp_fun_C_21(B, A), tptp_fun_D_20(B, A)), A)) | in(ordered_pair(tptp_fun_C_21(B, A), tptp_fun_D_20(B, A)), B))))))))) <=> ((~relation(A)) | ![B: $i] : ((~relation(B)) | (~((~((~subset(A, B)) | ![C: $i, D: $i] : ((~in(ordered_pair(C, D), A)) | in(ordered_pair(C, D), B)))) | (~(subset(A, B) | (~((~in(ordered_pair(tptp_fun_C_21(B, A), tptp_fun_D_20(B, A)), A)) | in(ordered_pair(tptp_fun_C_21(B, A), tptp_fun_D_20(B, A)), B))))))))))),
% 4.20/4.39 inference(bind,[status(th)],[])).
% 4.20/4.39 tff(27,plain,
% 4.20/4.39 (![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | (~((~((~subset(A, B)) | ![C: $i, D: $i] : ((~in(ordered_pair(C, D), A)) | in(ordered_pair(C, D), B)))) | (~(subset(A, B) | (~((~in(ordered_pair(tptp_fun_C_21(B, A), tptp_fun_D_20(B, A)), A)) | in(ordered_pair(tptp_fun_C_21(B, A), tptp_fun_D_20(B, A)), B))))))))) <=> ![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | (~((~((~subset(A, B)) | ![C: $i, D: $i] : ((~in(ordered_pair(C, D), A)) | in(ordered_pair(C, D), B)))) | (~(subset(A, B) | (~((~in(ordered_pair(tptp_fun_C_21(B, A), tptp_fun_D_20(B, A)), A)) | in(ordered_pair(tptp_fun_C_21(B, A), tptp_fun_D_20(B, A)), B)))))))))),
% 4.20/4.39 inference(quant_intro,[status(thm)],[26])).
% 4.20/4.39 tff(28,plain,
% 4.20/4.39 (![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | (~((~((~subset(A, B)) | ![C: $i, D: $i] : ((~in(ordered_pair(C, D), A)) | in(ordered_pair(C, D), B)))) | (~(subset(A, B) | (~((~in(ordered_pair(tptp_fun_C_21(B, A), tptp_fun_D_20(B, A)), A)) | in(ordered_pair(tptp_fun_C_21(B, A), tptp_fun_D_20(B, A)), B))))))))) <=> ![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | (~((~((~subset(A, B)) | ![C: $i, D: $i] : ((~in(ordered_pair(C, D), A)) | in(ordered_pair(C, D), B)))) | (~(subset(A, B) | (~((~in(ordered_pair(tptp_fun_C_21(B, A), tptp_fun_D_20(B, A)), A)) | in(ordered_pair(tptp_fun_C_21(B, A), tptp_fun_D_20(B, A)), B)))))))))),
% 4.20/4.39 inference(transitivity,[status(thm)],[27, 25])).
% 4.20/4.39 tff(29,plain,
% 4.20/4.39 (^[A: $i] : rewrite(((~relation(A)) | ![B: $i] : ((~relation(B)) | (((~subset(A, B)) | ![C: $i, D: $i] : ((~in(ordered_pair(C, D), A)) | in(ordered_pair(C, D), B))) & (subset(A, B) | (~((~in(ordered_pair(tptp_fun_C_21(B, A), tptp_fun_D_20(B, A)), A)) | in(ordered_pair(tptp_fun_C_21(B, A), tptp_fun_D_20(B, A)), B))))))) <=> ((~relation(A)) | ![B: $i] : ((~relation(B)) | (~((~((~subset(A, B)) | ![C: $i, D: $i] : ((~in(ordered_pair(C, D), A)) | in(ordered_pair(C, D), B)))) | (~(subset(A, B) | (~((~in(ordered_pair(tptp_fun_C_21(B, A), tptp_fun_D_20(B, A)), A)) | in(ordered_pair(tptp_fun_C_21(B, A), tptp_fun_D_20(B, A)), B))))))))))),
% 4.20/4.39 inference(bind,[status(th)],[])).
% 4.20/4.39 tff(30,plain,
% 4.20/4.39 (![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | (((~subset(A, B)) | ![C: $i, D: $i] : ((~in(ordered_pair(C, D), A)) | in(ordered_pair(C, D), B))) & (subset(A, B) | (~((~in(ordered_pair(tptp_fun_C_21(B, A), tptp_fun_D_20(B, A)), A)) | in(ordered_pair(tptp_fun_C_21(B, A), tptp_fun_D_20(B, A)), B))))))) <=> ![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | (~((~((~subset(A, B)) | ![C: $i, D: $i] : ((~in(ordered_pair(C, D), A)) | in(ordered_pair(C, D), B)))) | (~(subset(A, B) | (~((~in(ordered_pair(tptp_fun_C_21(B, A), tptp_fun_D_20(B, A)), A)) | in(ordered_pair(tptp_fun_C_21(B, A), tptp_fun_D_20(B, A)), B)))))))))),
% 4.20/4.39 inference(quant_intro,[status(thm)],[29])).
% 4.20/4.39 tff(31,plain,
% 4.20/4.39 (![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | (subset(A, B) <=> ![C: $i, D: $i] : ((~in(ordered_pair(C, D), A)) | in(ordered_pair(C, D), B))))) <=> ![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | (subset(A, B) <=> ![C: $i, D: $i] : ((~in(ordered_pair(C, D), A)) | in(ordered_pair(C, D), B)))))),
% 4.20/4.39 inference(rewrite,[status(thm)],[])).
% 4.20/4.39 tff(32,plain,
% 4.20/4.39 (^[A: $i] : trans(monotonicity(quant_intro(proof_bind(^[B: $i] : trans(monotonicity(rewrite((subset(A, B) <=> ![C: $i, D: $i] : (in(ordered_pair(C, D), A) => in(ordered_pair(C, D), B))) <=> (subset(A, B) <=> ![C: $i, D: $i] : ((~in(ordered_pair(C, D), A)) | in(ordered_pair(C, D), B)))), ((relation(B) => (subset(A, B) <=> ![C: $i, D: $i] : (in(ordered_pair(C, D), A) => in(ordered_pair(C, D), B)))) <=> (relation(B) => (subset(A, B) <=> ![C: $i, D: $i] : ((~in(ordered_pair(C, D), A)) | in(ordered_pair(C, D), B)))))), rewrite((relation(B) => (subset(A, B) <=> ![C: $i, D: $i] : ((~in(ordered_pair(C, D), A)) | in(ordered_pair(C, D), B)))) <=> ((~relation(B)) | (subset(A, B) <=> ![C: $i, D: $i] : ((~in(ordered_pair(C, D), A)) | in(ordered_pair(C, D), B))))), ((relation(B) => (subset(A, B) <=> ![C: $i, D: $i] : (in(ordered_pair(C, D), A) => in(ordered_pair(C, D), B)))) <=> ((~relation(B)) | (subset(A, B) <=> ![C: $i, D: $i] : ((~in(ordered_pair(C, D), A)) | in(ordered_pair(C, D), B))))))), (![B: $i] : (relation(B) => (subset(A, B) <=> ![C: $i, D: $i] : (in(ordered_pair(C, D), A) => in(ordered_pair(C, D), B)))) <=> ![B: $i] : ((~relation(B)) | (subset(A, B) <=> ![C: $i, D: $i] : ((~in(ordered_pair(C, D), A)) | in(ordered_pair(C, D), B)))))), ((relation(A) => ![B: $i] : (relation(B) => (subset(A, B) <=> ![C: $i, D: $i] : (in(ordered_pair(C, D), A) => in(ordered_pair(C, D), B))))) <=> (relation(A) => ![B: $i] : ((~relation(B)) | (subset(A, B) <=> ![C: $i, D: $i] : ((~in(ordered_pair(C, D), A)) | in(ordered_pair(C, D), B))))))), rewrite((relation(A) => ![B: $i] : ((~relation(B)) | (subset(A, B) <=> ![C: $i, D: $i] : ((~in(ordered_pair(C, D), A)) | in(ordered_pair(C, D), B))))) <=> ((~relation(A)) | ![B: $i] : ((~relation(B)) | (subset(A, B) <=> ![C: $i, D: $i] : ((~in(ordered_pair(C, D), A)) | in(ordered_pair(C, D), B)))))), ((relation(A) => ![B: $i] : (relation(B) => (subset(A, B) <=> ![C: $i, D: $i] : (in(ordered_pair(C, D), A) => in(ordered_pair(C, D), B))))) <=> ((~relation(A)) | ![B: $i] : ((~relation(B)) | (subset(A, B) <=> ![C: $i, D: $i] : ((~in(ordered_pair(C, D), A)) | in(ordered_pair(C, D), B)))))))),
% 4.20/4.39 inference(bind,[status(th)],[])).
% 4.20/4.39 tff(33,plain,
% 4.20/4.39 (![A: $i] : (relation(A) => ![B: $i] : (relation(B) => (subset(A, B) <=> ![C: $i, D: $i] : (in(ordered_pair(C, D), A) => in(ordered_pair(C, D), B))))) <=> ![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | (subset(A, B) <=> ![C: $i, D: $i] : ((~in(ordered_pair(C, D), A)) | in(ordered_pair(C, D), B)))))),
% 4.20/4.39 inference(quant_intro,[status(thm)],[32])).
% 4.20/4.39 tff(34,axiom,(![A: $i] : (relation(A) => ![B: $i] : (relation(B) => (subset(A, B) <=> ![C: $i, D: $i] : (in(ordered_pair(C, D), A) => in(ordered_pair(C, D), B)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d3_relat_1')).
% 4.20/4.39 tff(35,plain,
% 4.20/4.39 (![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | (subset(A, B) <=> ![C: $i, D: $i] : ((~in(ordered_pair(C, D), A)) | in(ordered_pair(C, D), B)))))),
% 4.20/4.39 inference(modus_ponens,[status(thm)],[34, 33])).
% 4.20/4.39 tff(36,plain,
% 4.20/4.39 (![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | (subset(A, B) <=> ![C: $i, D: $i] : ((~in(ordered_pair(C, D), A)) | in(ordered_pair(C, D), B)))))),
% 4.20/4.39 inference(modus_ponens,[status(thm)],[35, 31])).
% 4.20/4.39 tff(37,plain,(
% 4.20/4.39 ![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | (((~subset(A, B)) | ![C: $i, D: $i] : ((~in(ordered_pair(C, D), A)) | in(ordered_pair(C, D), B))) & (subset(A, B) | (~((~in(ordered_pair(tptp_fun_C_21(B, A), tptp_fun_D_20(B, A)), A)) | in(ordered_pair(tptp_fun_C_21(B, A), tptp_fun_D_20(B, A)), B)))))))),
% 4.20/4.39 inference(skolemize,[status(sab)],[36])).
% 4.20/4.39 tff(38,plain,
% 4.20/4.39 (![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | (~((~((~subset(A, B)) | ![C: $i, D: $i] : ((~in(ordered_pair(C, D), A)) | in(ordered_pair(C, D), B)))) | (~(subset(A, B) | (~((~in(ordered_pair(tptp_fun_C_21(B, A), tptp_fun_D_20(B, A)), A)) | in(ordered_pair(tptp_fun_C_21(B, A), tptp_fun_D_20(B, A)), B)))))))))),
% 4.20/4.39 inference(modus_ponens,[status(thm)],[37, 30])).
% 4.20/4.39 tff(39,plain,
% 4.20/4.39 (![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | (~((~((~subset(A, B)) | ![C: $i, D: $i] : ((~in(ordered_pair(C, D), A)) | in(ordered_pair(C, D), B)))) | (~(subset(A, B) | (~((~in(ordered_pair(tptp_fun_C_21(B, A), tptp_fun_D_20(B, A)), A)) | in(ordered_pair(tptp_fun_C_21(B, A), tptp_fun_D_20(B, A)), B)))))))))),
% 4.20/4.39 inference(modus_ponens,[status(thm)],[38, 28])).
% 4.20/4.39 tff(40,plain,
% 4.20/4.39 (((~![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | (~((~((~subset(A, B)) | ![C: $i, D: $i] : ((~in(ordered_pair(C, D), A)) | in(ordered_pair(C, D), B)))) | (~(subset(A, B) | (~((~in(ordered_pair(tptp_fun_C_21(B, A), tptp_fun_D_20(B, A)), A)) | in(ordered_pair(tptp_fun_C_21(B, A), tptp_fun_D_20(B, A)), B)))))))))) | ((~relation(relation_dom_restriction(B!54, A!55))) | ![B: $i] : ((~relation(B)) | (~((~((~subset(relation_dom_restriction(B!54, A!55), B)) | ![C: $i, D: $i] : ((~in(ordered_pair(C, D), relation_dom_restriction(B!54, A!55))) | in(ordered_pair(C, D), B)))) | (~(subset(relation_dom_restriction(B!54, A!55), B) | (~((~in(ordered_pair(tptp_fun_C_21(B, relation_dom_restriction(B!54, A!55)), tptp_fun_D_20(B, relation_dom_restriction(B!54, A!55))), relation_dom_restriction(B!54, A!55))) | in(ordered_pair(tptp_fun_C_21(B, relation_dom_restriction(B!54, A!55)), tptp_fun_D_20(B, relation_dom_restriction(B!54, A!55))), B)))))))))) <=> ((~![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | (~((~((~subset(A, B)) | ![C: $i, D: $i] : ((~in(ordered_pair(C, D), A)) | in(ordered_pair(C, D), B)))) | (~(subset(A, B) | (~((~in(ordered_pair(tptp_fun_C_21(B, A), tptp_fun_D_20(B, A)), A)) | in(ordered_pair(tptp_fun_C_21(B, A), tptp_fun_D_20(B, A)), B)))))))))) | (~relation(relation_dom_restriction(B!54, A!55))) | ![B: $i] : ((~relation(B)) | (~((~((~subset(relation_dom_restriction(B!54, A!55), B)) | ![C: $i, D: $i] : ((~in(ordered_pair(C, D), relation_dom_restriction(B!54, A!55))) | in(ordered_pair(C, D), B)))) | (~(subset(relation_dom_restriction(B!54, A!55), B) | (~((~in(ordered_pair(tptp_fun_C_21(B, relation_dom_restriction(B!54, A!55)), tptp_fun_D_20(B, relation_dom_restriction(B!54, A!55))), relation_dom_restriction(B!54, A!55))) | in(ordered_pair(tptp_fun_C_21(B, relation_dom_restriction(B!54, A!55)), tptp_fun_D_20(B, relation_dom_restriction(B!54, A!55))), B)))))))))),
% 4.20/4.39 inference(rewrite,[status(thm)],[])).
% 4.20/4.39 tff(41,plain,
% 4.20/4.39 ((~![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | (~((~((~subset(A, B)) | ![C: $i, D: $i] : ((~in(ordered_pair(C, D), A)) | in(ordered_pair(C, D), B)))) | (~(subset(A, B) | (~((~in(ordered_pair(tptp_fun_C_21(B, A), tptp_fun_D_20(B, A)), A)) | in(ordered_pair(tptp_fun_C_21(B, A), tptp_fun_D_20(B, A)), B)))))))))) | ((~relation(relation_dom_restriction(B!54, A!55))) | ![B: $i] : ((~relation(B)) | (~((~((~subset(relation_dom_restriction(B!54, A!55), B)) | ![C: $i, D: $i] : ((~in(ordered_pair(C, D), relation_dom_restriction(B!54, A!55))) | in(ordered_pair(C, D), B)))) | (~(subset(relation_dom_restriction(B!54, A!55), B) | (~((~in(ordered_pair(tptp_fun_C_21(B, relation_dom_restriction(B!54, A!55)), tptp_fun_D_20(B, relation_dom_restriction(B!54, A!55))), relation_dom_restriction(B!54, A!55))) | in(ordered_pair(tptp_fun_C_21(B, relation_dom_restriction(B!54, A!55)), tptp_fun_D_20(B, relation_dom_restriction(B!54, A!55))), B)))))))))),
% 4.20/4.39 inference(quant_inst,[status(thm)],[])).
% 4.20/4.39 tff(42,plain,
% 4.20/4.39 ((~![A: $i] : ((~relation(A)) | ![B: $i] : ((~relation(B)) | (~((~((~subset(A, B)) | ![C: $i, D: $i] : ((~in(ordered_pair(C, D), A)) | in(ordered_pair(C, D), B)))) | (~(subset(A, B) | (~((~in(ordered_pair(tptp_fun_C_21(B, A), tptp_fun_D_20(B, A)), A)) | in(ordered_pair(tptp_fun_C_21(B, A), tptp_fun_D_20(B, A)), B)))))))))) | (~relation(relation_dom_restriction(B!54, A!55))) | ![B: $i] : ((~relation(B)) | (~((~((~subset(relation_dom_restriction(B!54, A!55), B)) | ![C: $i, D: $i] : ((~in(ordered_pair(C, D), relation_dom_restriction(B!54, A!55))) | in(ordered_pair(C, D), B)))) | (~(subset(relation_dom_restriction(B!54, A!55), B) | (~((~in(ordered_pair(tptp_fun_C_21(B, relation_dom_restriction(B!54, A!55)), tptp_fun_D_20(B, relation_dom_restriction(B!54, A!55))), relation_dom_restriction(B!54, A!55))) | in(ordered_pair(tptp_fun_C_21(B, relation_dom_restriction(B!54, A!55)), tptp_fun_D_20(B, relation_dom_restriction(B!54, A!55))), B))))))))),
% 4.20/4.39 inference(modus_ponens,[status(thm)],[41, 40])).
% 4.20/4.39 tff(43,plain,
% 4.20/4.39 (![B: $i] : ((~relation(B)) | (~((~((~subset(relation_dom_restriction(B!54, A!55), B)) | ![C: $i, D: $i] : ((~in(ordered_pair(C, D), relation_dom_restriction(B!54, A!55))) | in(ordered_pair(C, D), B)))) | (~(subset(relation_dom_restriction(B!54, A!55), B) | (~((~in(ordered_pair(tptp_fun_C_21(B, relation_dom_restriction(B!54, A!55)), tptp_fun_D_20(B, relation_dom_restriction(B!54, A!55))), relation_dom_restriction(B!54, A!55))) | in(ordered_pair(tptp_fun_C_21(B, relation_dom_restriction(B!54, A!55)), tptp_fun_D_20(B, relation_dom_restriction(B!54, A!55))), B))))))))),
% 4.20/4.39 inference(unit_resolution,[status(thm)],[42, 39, 23])).
% 4.20/4.39 tff(44,plain,
% 4.20/4.39 (((~![B: $i] : ((~relation(B)) | (~((~((~subset(relation_dom_restriction(B!54, A!55), B)) | ![C: $i, D: $i] : ((~in(ordered_pair(C, D), relation_dom_restriction(B!54, A!55))) | in(ordered_pair(C, D), B)))) | (~(subset(relation_dom_restriction(B!54, A!55), B) | (~((~in(ordered_pair(tptp_fun_C_21(B, relation_dom_restriction(B!54, A!55)), tptp_fun_D_20(B, relation_dom_restriction(B!54, A!55))), relation_dom_restriction(B!54, A!55))) | in(ordered_pair(tptp_fun_C_21(B, relation_dom_restriction(B!54, A!55)), tptp_fun_D_20(B, relation_dom_restriction(B!54, A!55))), B))))))))) | ((~relation(B!54)) | (~((~((~subset(relation_dom_restriction(B!54, A!55), B!54)) | ![C: $i, D: $i] : ((~in(ordered_pair(C, D), relation_dom_restriction(B!54, A!55))) | in(ordered_pair(C, D), B!54)))) | (~(subset(relation_dom_restriction(B!54, A!55), B!54) | (~((~in(ordered_pair(tptp_fun_C_21(B!54, relation_dom_restriction(B!54, A!55)), tptp_fun_D_20(B!54, relation_dom_restriction(B!54, A!55))), relation_dom_restriction(B!54, A!55))) | in(ordered_pair(tptp_fun_C_21(B!54, relation_dom_restriction(B!54, A!55)), tptp_fun_D_20(B!54, relation_dom_restriction(B!54, A!55))), B!54))))))))) <=> ((~![B: $i] : ((~relation(B)) | (~((~((~subset(relation_dom_restriction(B!54, A!55), B)) | ![C: $i, D: $i] : ((~in(ordered_pair(C, D), relation_dom_restriction(B!54, A!55))) | in(ordered_pair(C, D), B)))) | (~(subset(relation_dom_restriction(B!54, A!55), B) | (~((~in(ordered_pair(tptp_fun_C_21(B, relation_dom_restriction(B!54, A!55)), tptp_fun_D_20(B, relation_dom_restriction(B!54, A!55))), relation_dom_restriction(B!54, A!55))) | in(ordered_pair(tptp_fun_C_21(B, relation_dom_restriction(B!54, A!55)), tptp_fun_D_20(B, relation_dom_restriction(B!54, A!55))), B))))))))) | (~relation(B!54)) | (~((~((~subset(relation_dom_restriction(B!54, A!55), B!54)) | ![C: $i, D: $i] : ((~in(ordered_pair(C, D), relation_dom_restriction(B!54, A!55))) | in(ordered_pair(C, D), B!54)))) | (~(subset(relation_dom_restriction(B!54, A!55), B!54) | (~((~in(ordered_pair(tptp_fun_C_21(B!54, relation_dom_restriction(B!54, A!55)), tptp_fun_D_20(B!54, relation_dom_restriction(B!54, A!55))), relation_dom_restriction(B!54, A!55))) | in(ordered_pair(tptp_fun_C_21(B!54, relation_dom_restriction(B!54, A!55)), tptp_fun_D_20(B!54, relation_dom_restriction(B!54, A!55))), B!54))))))))),
% 4.20/4.39 inference(rewrite,[status(thm)],[])).
% 4.20/4.39 tff(45,plain,
% 4.20/4.39 ((~![B: $i] : ((~relation(B)) | (~((~((~subset(relation_dom_restriction(B!54, A!55), B)) | ![C: $i, D: $i] : ((~in(ordered_pair(C, D), relation_dom_restriction(B!54, A!55))) | in(ordered_pair(C, D), B)))) | (~(subset(relation_dom_restriction(B!54, A!55), B) | (~((~in(ordered_pair(tptp_fun_C_21(B, relation_dom_restriction(B!54, A!55)), tptp_fun_D_20(B, relation_dom_restriction(B!54, A!55))), relation_dom_restriction(B!54, A!55))) | in(ordered_pair(tptp_fun_C_21(B, relation_dom_restriction(B!54, A!55)), tptp_fun_D_20(B, relation_dom_restriction(B!54, A!55))), B))))))))) | ((~relation(B!54)) | (~((~((~subset(relation_dom_restriction(B!54, A!55), B!54)) | ![C: $i, D: $i] : ((~in(ordered_pair(C, D), relation_dom_restriction(B!54, A!55))) | in(ordered_pair(C, D), B!54)))) | (~(subset(relation_dom_restriction(B!54, A!55), B!54) | (~((~in(ordered_pair(tptp_fun_C_21(B!54, relation_dom_restriction(B!54, A!55)), tptp_fun_D_20(B!54, relation_dom_restriction(B!54, A!55))), relation_dom_restriction(B!54, A!55))) | in(ordered_pair(tptp_fun_C_21(B!54, relation_dom_restriction(B!54, A!55)), tptp_fun_D_20(B!54, relation_dom_restriction(B!54, A!55))), B!54))))))))),
% 4.20/4.39 inference(quant_inst,[status(thm)],[])).
% 4.20/4.39 tff(46,plain,
% 4.20/4.39 ((~![B: $i] : ((~relation(B)) | (~((~((~subset(relation_dom_restriction(B!54, A!55), B)) | ![C: $i, D: $i] : ((~in(ordered_pair(C, D), relation_dom_restriction(B!54, A!55))) | in(ordered_pair(C, D), B)))) | (~(subset(relation_dom_restriction(B!54, A!55), B) | (~((~in(ordered_pair(tptp_fun_C_21(B, relation_dom_restriction(B!54, A!55)), tptp_fun_D_20(B, relation_dom_restriction(B!54, A!55))), relation_dom_restriction(B!54, A!55))) | in(ordered_pair(tptp_fun_C_21(B, relation_dom_restriction(B!54, A!55)), tptp_fun_D_20(B, relation_dom_restriction(B!54, A!55))), B))))))))) | (~relation(B!54)) | (~((~((~subset(relation_dom_restriction(B!54, A!55), B!54)) | ![C: $i, D: $i] : ((~in(ordered_pair(C, D), relation_dom_restriction(B!54, A!55))) | in(ordered_pair(C, D), B!54)))) | (~(subset(relation_dom_restriction(B!54, A!55), B!54) | (~((~in(ordered_pair(tptp_fun_C_21(B!54, relation_dom_restriction(B!54, A!55)), tptp_fun_D_20(B!54, relation_dom_restriction(B!54, A!55))), relation_dom_restriction(B!54, A!55))) | in(ordered_pair(tptp_fun_C_21(B!54, relation_dom_restriction(B!54, A!55)), tptp_fun_D_20(B!54, relation_dom_restriction(B!54, A!55))), B!54)))))))),
% 4.20/4.39 inference(modus_ponens,[status(thm)],[45, 44])).
% 4.20/4.39 tff(47,plain,
% 4.20/4.39 (~((~((~subset(relation_dom_restriction(B!54, A!55), B!54)) | ![C: $i, D: $i] : ((~in(ordered_pair(C, D), relation_dom_restriction(B!54, A!55))) | in(ordered_pair(C, D), B!54)))) | (~(subset(relation_dom_restriction(B!54, A!55), B!54) | (~((~in(ordered_pair(tptp_fun_C_21(B!54, relation_dom_restriction(B!54, A!55)), tptp_fun_D_20(B!54, relation_dom_restriction(B!54, A!55))), relation_dom_restriction(B!54, A!55))) | in(ordered_pair(tptp_fun_C_21(B!54, relation_dom_restriction(B!54, A!55)), tptp_fun_D_20(B!54, relation_dom_restriction(B!54, A!55))), B!54))))))),
% 4.20/4.40 inference(unit_resolution,[status(thm)],[46, 9, 43])).
% 4.20/4.40 tff(48,plain,
% 4.20/4.40 (((~((~subset(relation_dom_restriction(B!54, A!55), B!54)) | ![C: $i, D: $i] : ((~in(ordered_pair(C, D), relation_dom_restriction(B!54, A!55))) | in(ordered_pair(C, D), B!54)))) | (~(subset(relation_dom_restriction(B!54, A!55), B!54) | (~((~in(ordered_pair(tptp_fun_C_21(B!54, relation_dom_restriction(B!54, A!55)), tptp_fun_D_20(B!54, relation_dom_restriction(B!54, A!55))), relation_dom_restriction(B!54, A!55))) | in(ordered_pair(tptp_fun_C_21(B!54, relation_dom_restriction(B!54, A!55)), tptp_fun_D_20(B!54, relation_dom_restriction(B!54, A!55))), B!54)))))) | (subset(relation_dom_restriction(B!54, A!55), B!54) | (~((~in(ordered_pair(tptp_fun_C_21(B!54, relation_dom_restriction(B!54, A!55)), tptp_fun_D_20(B!54, relation_dom_restriction(B!54, A!55))), relation_dom_restriction(B!54, A!55))) | in(ordered_pair(tptp_fun_C_21(B!54, relation_dom_restriction(B!54, A!55)), tptp_fun_D_20(B!54, relation_dom_restriction(B!54, A!55))), B!54))))),
% 4.20/4.40 inference(tautology,[status(thm)],[])).
% 4.20/4.40 tff(49,plain,
% 4.20/4.40 (subset(relation_dom_restriction(B!54, A!55), B!54) | (~((~in(ordered_pair(tptp_fun_C_21(B!54, relation_dom_restriction(B!54, A!55)), tptp_fun_D_20(B!54, relation_dom_restriction(B!54, A!55))), relation_dom_restriction(B!54, A!55))) | in(ordered_pair(tptp_fun_C_21(B!54, relation_dom_restriction(B!54, A!55)), tptp_fun_D_20(B!54, relation_dom_restriction(B!54, A!55))), B!54)))),
% 4.20/4.40 inference(unit_resolution,[status(thm)],[48, 47])).
% 4.20/4.40 tff(50,plain,
% 4.20/4.40 (~subset(relation_dom_restriction(B!54, A!55), B!54)),
% 4.20/4.40 inference(or_elim,[status(thm)],[8])).
% 4.20/4.40 tff(51,plain,
% 4.20/4.40 ((~(subset(relation_dom_restriction(B!54, A!55), B!54) | (~((~in(ordered_pair(tptp_fun_C_21(B!54, relation_dom_restriction(B!54, A!55)), tptp_fun_D_20(B!54, relation_dom_restriction(B!54, A!55))), relation_dom_restriction(B!54, A!55))) | in(ordered_pair(tptp_fun_C_21(B!54, relation_dom_restriction(B!54, A!55)), tptp_fun_D_20(B!54, relation_dom_restriction(B!54, A!55))), B!54))))) | subset(relation_dom_restriction(B!54, A!55), B!54) | (~((~in(ordered_pair(tptp_fun_C_21(B!54, relation_dom_restriction(B!54, A!55)), tptp_fun_D_20(B!54, relation_dom_restriction(B!54, A!55))), relation_dom_restriction(B!54, A!55))) | in(ordered_pair(tptp_fun_C_21(B!54, relation_dom_restriction(B!54, A!55)), tptp_fun_D_20(B!54, relation_dom_restriction(B!54, A!55))), B!54)))),
% 4.20/4.40 inference(tautology,[status(thm)],[])).
% 4.20/4.40 tff(52,plain,
% 4.20/4.40 ((~(subset(relation_dom_restriction(B!54, A!55), B!54) | (~((~in(ordered_pair(tptp_fun_C_21(B!54, relation_dom_restriction(B!54, A!55)), tptp_fun_D_20(B!54, relation_dom_restriction(B!54, A!55))), relation_dom_restriction(B!54, A!55))) | in(ordered_pair(tptp_fun_C_21(B!54, relation_dom_restriction(B!54, A!55)), tptp_fun_D_20(B!54, relation_dom_restriction(B!54, A!55))), B!54))))) | (~((~in(ordered_pair(tptp_fun_C_21(B!54, relation_dom_restriction(B!54, A!55)), tptp_fun_D_20(B!54, relation_dom_restriction(B!54, A!55))), relation_dom_restriction(B!54, A!55))) | in(ordered_pair(tptp_fun_C_21(B!54, relation_dom_restriction(B!54, A!55)), tptp_fun_D_20(B!54, relation_dom_restriction(B!54, A!55))), B!54)))),
% 4.20/4.40 inference(unit_resolution,[status(thm)],[51, 50])).
% 4.20/4.40 tff(53,plain,
% 4.20/4.40 (~((~in(ordered_pair(tptp_fun_C_21(B!54, relation_dom_restriction(B!54, A!55)), tptp_fun_D_20(B!54, relation_dom_restriction(B!54, A!55))), relation_dom_restriction(B!54, A!55))) | in(ordered_pair(tptp_fun_C_21(B!54, relation_dom_restriction(B!54, A!55)), tptp_fun_D_20(B!54, relation_dom_restriction(B!54, A!55))), B!54))),
% 4.20/4.40 inference(unit_resolution,[status(thm)],[52, 49])).
% 4.20/4.40 tff(54,plain,
% 4.20/4.40 (((~in(ordered_pair(tptp_fun_C_21(B!54, relation_dom_restriction(B!54, A!55)), tptp_fun_D_20(B!54, relation_dom_restriction(B!54, A!55))), relation_dom_restriction(B!54, A!55))) | in(ordered_pair(tptp_fun_C_21(B!54, relation_dom_restriction(B!54, A!55)), tptp_fun_D_20(B!54, relation_dom_restriction(B!54, A!55))), B!54)) | (~in(ordered_pair(tptp_fun_C_21(B!54, relation_dom_restriction(B!54, A!55)), tptp_fun_D_20(B!54, relation_dom_restriction(B!54, A!55))), B!54))),
% 4.23/4.40 inference(tautology,[status(thm)],[])).
% 4.23/4.40 tff(55,plain,
% 4.23/4.40 (~in(ordered_pair(tptp_fun_C_21(B!54, relation_dom_restriction(B!54, A!55)), tptp_fun_D_20(B!54, relation_dom_restriction(B!54, A!55))), B!54)),
% 4.23/4.40 inference(unit_resolution,[status(thm)],[54, 53])).
% 4.23/4.40 tff(56,plain,
% 4.23/4.40 (((~in(tptp_fun_C_21(B!54, relation_dom_restriction(B!54, A!55)), A!55)) | (~in(ordered_pair(tptp_fun_C_21(B!54, relation_dom_restriction(B!54, A!55)), tptp_fun_D_20(B!54, relation_dom_restriction(B!54, A!55))), B!54))) | in(ordered_pair(tptp_fun_C_21(B!54, relation_dom_restriction(B!54, A!55)), tptp_fun_D_20(B!54, relation_dom_restriction(B!54, A!55))), B!54)),
% 4.23/4.40 inference(tautology,[status(thm)],[])).
% 4.23/4.40 tff(57,plain,
% 4.23/4.40 ((~in(tptp_fun_C_21(B!54, relation_dom_restriction(B!54, A!55)), A!55)) | (~in(ordered_pair(tptp_fun_C_21(B!54, relation_dom_restriction(B!54, A!55)), tptp_fun_D_20(B!54, relation_dom_restriction(B!54, A!55))), B!54))),
% 4.23/4.40 inference(unit_resolution,[status(thm)],[56, 55])).
% 4.23/4.40 tff(58,plain,
% 4.23/4.40 (((~in(ordered_pair(tptp_fun_C_21(B!54, relation_dom_restriction(B!54, A!55)), tptp_fun_D_20(B!54, relation_dom_restriction(B!54, A!55))), relation_dom_restriction(B!54, A!55))) | in(ordered_pair(tptp_fun_C_21(B!54, relation_dom_restriction(B!54, A!55)), tptp_fun_D_20(B!54, relation_dom_restriction(B!54, A!55))), B!54)) | in(ordered_pair(tptp_fun_C_21(B!54, relation_dom_restriction(B!54, A!55)), tptp_fun_D_20(B!54, relation_dom_restriction(B!54, A!55))), relation_dom_restriction(B!54, A!55))),
% 4.23/4.40 inference(tautology,[status(thm)],[])).
% 4.23/4.40 tff(59,plain,
% 4.23/4.40 (in(ordered_pair(tptp_fun_C_21(B!54, relation_dom_restriction(B!54, A!55)), tptp_fun_D_20(B!54, relation_dom_restriction(B!54, A!55))), relation_dom_restriction(B!54, A!55))),
% 4.23/4.40 inference(unit_resolution,[status(thm)],[58, 53])).
% 4.23/4.40 tff(60,plain,
% 4.23/4.40 ((((~in(tptp_fun_C_21(B!54, relation_dom_restriction(B!54, A!55)), A!55)) | (~in(ordered_pair(tptp_fun_C_21(B!54, relation_dom_restriction(B!54, A!55)), tptp_fun_D_20(B!54, relation_dom_restriction(B!54, A!55))), B!54))) <=> in(ordered_pair(tptp_fun_C_21(B!54, relation_dom_restriction(B!54, A!55)), tptp_fun_D_20(B!54, relation_dom_restriction(B!54, A!55))), relation_dom_restriction(B!54, A!55))) | (~((~in(tptp_fun_C_21(B!54, relation_dom_restriction(B!54, A!55)), A!55)) | (~in(ordered_pair(tptp_fun_C_21(B!54, relation_dom_restriction(B!54, A!55)), tptp_fun_D_20(B!54, relation_dom_restriction(B!54, A!55))), B!54)))) | (~in(ordered_pair(tptp_fun_C_21(B!54, relation_dom_restriction(B!54, A!55)), tptp_fun_D_20(B!54, relation_dom_restriction(B!54, A!55))), relation_dom_restriction(B!54, A!55)))),
% 4.23/4.40 inference(tautology,[status(thm)],[])).
% 4.23/4.40 tff(61,plain,
% 4.23/4.40 (((~in(tptp_fun_C_21(B!54, relation_dom_restriction(B!54, A!55)), A!55)) | (~in(ordered_pair(tptp_fun_C_21(B!54, relation_dom_restriction(B!54, A!55)), tptp_fun_D_20(B!54, relation_dom_restriction(B!54, A!55))), B!54))) <=> in(ordered_pair(tptp_fun_C_21(B!54, relation_dom_restriction(B!54, A!55)), tptp_fun_D_20(B!54, relation_dom_restriction(B!54, A!55))), relation_dom_restriction(B!54, A!55))),
% 4.23/4.40 inference(unit_resolution,[status(thm)],[60, 59, 57])).
% 4.23/4.40 tff(62,plain,
% 4.23/4.40 (^[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))))))))))),
% 4.23/4.40 inference(bind,[status(th)],[])).
% 4.23/4.40 tff(63,plain,
% 4.23/4.40 (![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)))))))))),
% 4.23/4.40 inference(quant_intro,[status(thm)],[62])).
% 4.23/4.40 tff(64,plain,
% 4.23/4.40 (^[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)))))))))),
% 4.23/4.40 inference(bind,[status(th)],[])).
% 4.23/4.40 tff(65,plain,
% 4.23/4.40 (![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))))))))),
% 4.23/4.40 inference(quant_intro,[status(thm)],[64])).
% 4.23/4.40 tff(66,plain,
% 4.23/4.40 (^[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)))))))))),
% 4.23/4.40 inference(bind,[status(th)],[])).
% 4.23/4.40 tff(67,plain,
% 4.23/4.40 (![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))))))))),
% 4.23/4.40 inference(quant_intro,[status(thm)],[66])).
% 4.23/4.40 tff(68,plain,
% 4.23/4.40 (![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))))))))),
% 4.23/4.40 inference(transitivity,[status(thm)],[67, 65])).
% 4.23/4.40 tff(69,plain,
% 4.23/4.40 (^[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)))))))))),
% 4.23/4.40 inference(bind,[status(th)],[])).
% 4.23/4.40 tff(70,plain,
% 4.23/4.40 (![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))))))))),
% 4.23/4.40 inference(quant_intro,[status(thm)],[69])).
% 4.23/4.40 tff(71,plain,
% 4.23/4.40 (![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))))))),
% 4.23/4.40 inference(rewrite,[status(thm)],[])).
% 4.23/4.40 tff(72,plain,
% 4.23/4.40 (^[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))))))))),
% 4.23/4.40 inference(bind,[status(th)],[])).
% 4.23/4.40 tff(73,plain,
% 4.23/4.40 (![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))))))),
% 4.23/4.40 inference(quant_intro,[status(thm)],[72])).
% 4.23/4.40 tff(74,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')).
% 4.23/4.40 tff(75,plain,
% 4.23/4.40 (![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))))))),
% 4.23/4.40 inference(modus_ponens,[status(thm)],[74, 73])).
% 4.23/4.40 tff(76,plain,
% 4.23/4.40 (![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))))))),
% 4.23/4.40 inference(modus_ponens,[status(thm)],[75, 71])).
% 4.23/4.40 tff(77,plain,(
% 4.23/4.40 ![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))))))))),
% 4.23/4.40 inference(skolemize,[status(sab)],[76])).
% 4.23/4.40 tff(78,plain,
% 4.23/4.40 (![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))))))))),
% 4.23/4.40 inference(modus_ponens,[status(thm)],[77, 70])).
% 4.23/4.40 tff(79,plain,
% 4.23/4.40 (![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))))))))),
% 4.23/4.40 inference(modus_ponens,[status(thm)],[78, 68])).
% 4.23/4.40 tff(80,plain,
% 4.23/4.40 (![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)))))))))),
% 4.23/4.40 inference(modus_ponens,[status(thm)],[79, 63])).
% 4.23/4.40 tff(81,plain,
% 4.23/4.40 (((~![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!54)) | ![B: $i, C: $i] : ((~relation(C)) | (~((~((C = relation_dom_restriction(B!54, B)) | (((~in(tptp_fun_D_3(C, B, B!54), B)) | (~in(ordered_pair(tptp_fun_D_3(C, B, B!54), tptp_fun_E_2(C, B, B!54)), B!54))) <=> in(ordered_pair(tptp_fun_D_3(C, B, B!54), tptp_fun_E_2(C, B, B!54)), C)))) | (~((~(C = relation_dom_restriction(B!54, B))) | ![D: $i, E: $i] : (~(((~in(D, B)) | (~in(ordered_pair(D, E), B!54))) <=> 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!54)) | ![B: $i, C: $i] : ((~relation(C)) | (~((~((C = relation_dom_restriction(B!54, B)) | (((~in(tptp_fun_D_3(C, B, B!54), B)) | (~in(ordered_pair(tptp_fun_D_3(C, B, B!54), tptp_fun_E_2(C, B, B!54)), B!54))) <=> in(ordered_pair(tptp_fun_D_3(C, B, B!54), tptp_fun_E_2(C, B, B!54)), C)))) | (~((~(C = relation_dom_restriction(B!54, B))) | ![D: $i, E: $i] : (~(((~in(D, B)) | (~in(ordered_pair(D, E), B!54))) <=> in(ordered_pair(D, E), C)))))))))),
% 4.23/4.40 inference(rewrite,[status(thm)],[])).
% 4.23/4.40 tff(82,plain,
% 4.23/4.40 ((~![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!54)) | ![B: $i, C: $i] : ((~relation(C)) | (~((~((C = relation_dom_restriction(B!54, B)) | (((~in(tptp_fun_D_3(C, B, B!54), B)) | (~in(ordered_pair(tptp_fun_D_3(C, B, B!54), tptp_fun_E_2(C, B, B!54)), B!54))) <=> in(ordered_pair(tptp_fun_D_3(C, B, B!54), tptp_fun_E_2(C, B, B!54)), C)))) | (~((~(C = relation_dom_restriction(B!54, B))) | ![D: $i, E: $i] : (~(((~in(D, B)) | (~in(ordered_pair(D, E), B!54))) <=> in(ordered_pair(D, E), C)))))))))),
% 4.23/4.40 inference(quant_inst,[status(thm)],[])).
% 4.23/4.40 tff(83,plain,
% 4.23/4.40 ((~![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!54)) | ![B: $i, C: $i] : ((~relation(C)) | (~((~((C = relation_dom_restriction(B!54, B)) | (((~in(tptp_fun_D_3(C, B, B!54), B)) | (~in(ordered_pair(tptp_fun_D_3(C, B, B!54), tptp_fun_E_2(C, B, B!54)), B!54))) <=> in(ordered_pair(tptp_fun_D_3(C, B, B!54), tptp_fun_E_2(C, B, B!54)), C)))) | (~((~(C = relation_dom_restriction(B!54, B))) | ![D: $i, E: $i] : (~(((~in(D, B)) | (~in(ordered_pair(D, E), B!54))) <=> in(ordered_pair(D, E), C))))))))),
% 4.23/4.40 inference(modus_ponens,[status(thm)],[82, 81])).
% 4.23/4.40 tff(84,plain,
% 4.23/4.40 (![B: $i, C: $i] : ((~relation(C)) | (~((~((C = relation_dom_restriction(B!54, B)) | (((~in(tptp_fun_D_3(C, B, B!54), B)) | (~in(ordered_pair(tptp_fun_D_3(C, B, B!54), tptp_fun_E_2(C, B, B!54)), B!54))) <=> in(ordered_pair(tptp_fun_D_3(C, B, B!54), tptp_fun_E_2(C, B, B!54)), C)))) | (~((~(C = relation_dom_restriction(B!54, B))) | ![D: $i, E: $i] : (~(((~in(D, B)) | (~in(ordered_pair(D, E), B!54))) <=> in(ordered_pair(D, E), C))))))))),
% 4.23/4.40 inference(unit_resolution,[status(thm)],[83, 80, 9])).
% 4.23/4.40 tff(85,plain,
% 4.23/4.40 (((~![B: $i, C: $i] : ((~relation(C)) | (~((~((C = relation_dom_restriction(B!54, B)) | (((~in(tptp_fun_D_3(C, B, B!54), B)) | (~in(ordered_pair(tptp_fun_D_3(C, B, B!54), tptp_fun_E_2(C, B, B!54)), B!54))) <=> in(ordered_pair(tptp_fun_D_3(C, B, B!54), tptp_fun_E_2(C, B, B!54)), C)))) | (~((~(C = relation_dom_restriction(B!54, B))) | ![D: $i, E: $i] : (~(((~in(D, B)) | (~in(ordered_pair(D, E), B!54))) <=> in(ordered_pair(D, E), C))))))))) | ((~relation(relation_dom_restriction(B!54, A!55))) | ![D: $i, E: $i] : (~(((~in(D, A!55)) | (~in(ordered_pair(D, E), B!54))) <=> in(ordered_pair(D, E), relation_dom_restriction(B!54, A!55)))))) <=> ((~![B: $i, C: $i] : ((~relation(C)) | (~((~((C = relation_dom_restriction(B!54, B)) | (((~in(tptp_fun_D_3(C, B, B!54), B)) | (~in(ordered_pair(tptp_fun_D_3(C, B, B!54), tptp_fun_E_2(C, B, B!54)), B!54))) <=> in(ordered_pair(tptp_fun_D_3(C, B, B!54), tptp_fun_E_2(C, B, B!54)), C)))) | (~((~(C = relation_dom_restriction(B!54, B))) | ![D: $i, E: $i] : (~(((~in(D, B)) | (~in(ordered_pair(D, E), B!54))) <=> in(ordered_pair(D, E), C))))))))) | (~relation(relation_dom_restriction(B!54, A!55))) | ![D: $i, E: $i] : (~(((~in(D, A!55)) | (~in(ordered_pair(D, E), B!54))) <=> in(ordered_pair(D, E), relation_dom_restriction(B!54, A!55)))))),
% 4.23/4.40 inference(rewrite,[status(thm)],[])).
% 4.23/4.40 tff(86,plain,
% 4.23/4.40 (((~relation(relation_dom_restriction(B!54, A!55))) | (~((~((relation_dom_restriction(B!54, A!55) = relation_dom_restriction(B!54, A!55)) | (((~in(tptp_fun_D_3(relation_dom_restriction(B!54, A!55), A!55, B!54), A!55)) | (~in(ordered_pair(tptp_fun_D_3(relation_dom_restriction(B!54, A!55), A!55, B!54), tptp_fun_E_2(relation_dom_restriction(B!54, A!55), A!55, B!54)), B!54))) <=> in(ordered_pair(tptp_fun_D_3(relation_dom_restriction(B!54, A!55), A!55, B!54), tptp_fun_E_2(relation_dom_restriction(B!54, A!55), A!55, B!54)), relation_dom_restriction(B!54, A!55))))) | (~((~(relation_dom_restriction(B!54, A!55) = relation_dom_restriction(B!54, A!55))) | ![D: $i, E: $i] : (~(((~in(D, A!55)) | (~in(ordered_pair(D, E), B!54))) <=> in(ordered_pair(D, E), relation_dom_restriction(B!54, A!55))))))))) <=> ((~relation(relation_dom_restriction(B!54, A!55))) | ![D: $i, E: $i] : (~(((~in(D, A!55)) | (~in(ordered_pair(D, E), B!54))) <=> in(ordered_pair(D, E), relation_dom_restriction(B!54, A!55)))))),
% 4.23/4.40 inference(rewrite,[status(thm)],[])).
% 4.23/4.40 tff(87,plain,
% 4.23/4.40 (((~![B: $i, C: $i] : ((~relation(C)) | (~((~((C = relation_dom_restriction(B!54, B)) | (((~in(tptp_fun_D_3(C, B, B!54), B)) | (~in(ordered_pair(tptp_fun_D_3(C, B, B!54), tptp_fun_E_2(C, B, B!54)), B!54))) <=> in(ordered_pair(tptp_fun_D_3(C, B, B!54), tptp_fun_E_2(C, B, B!54)), C)))) | (~((~(C = relation_dom_restriction(B!54, B))) | ![D: $i, E: $i] : (~(((~in(D, B)) | (~in(ordered_pair(D, E), B!54))) <=> in(ordered_pair(D, E), C))))))))) | ((~relation(relation_dom_restriction(B!54, A!55))) | (~((~((relation_dom_restriction(B!54, A!55) = relation_dom_restriction(B!54, A!55)) | (((~in(tptp_fun_D_3(relation_dom_restriction(B!54, A!55), A!55, B!54), A!55)) | (~in(ordered_pair(tptp_fun_D_3(relation_dom_restriction(B!54, A!55), A!55, B!54), tptp_fun_E_2(relation_dom_restriction(B!54, A!55), A!55, B!54)), B!54))) <=> in(ordered_pair(tptp_fun_D_3(relation_dom_restriction(B!54, A!55), A!55, B!54), tptp_fun_E_2(relation_dom_restriction(B!54, A!55), A!55, B!54)), relation_dom_restriction(B!54, A!55))))) | (~((~(relation_dom_restriction(B!54, A!55) = relation_dom_restriction(B!54, A!55))) | ![D: $i, E: $i] : (~(((~in(D, A!55)) | (~in(ordered_pair(D, E), B!54))) <=> in(ordered_pair(D, E), relation_dom_restriction(B!54, A!55)))))))))) <=> ((~![B: $i, C: $i] : ((~relation(C)) | (~((~((C = relation_dom_restriction(B!54, B)) | (((~in(tptp_fun_D_3(C, B, B!54), B)) | (~in(ordered_pair(tptp_fun_D_3(C, B, B!54), tptp_fun_E_2(C, B, B!54)), B!54))) <=> in(ordered_pair(tptp_fun_D_3(C, B, B!54), tptp_fun_E_2(C, B, B!54)), C)))) | (~((~(C = relation_dom_restriction(B!54, B))) | ![D: $i, E: $i] : (~(((~in(D, B)) | (~in(ordered_pair(D, E), B!54))) <=> in(ordered_pair(D, E), C))))))))) | ((~relation(relation_dom_restriction(B!54, A!55))) | ![D: $i, E: $i] : (~(((~in(D, A!55)) | (~in(ordered_pair(D, E), B!54))) <=> in(ordered_pair(D, E), relation_dom_restriction(B!54, A!55))))))),
% 4.23/4.40 inference(monotonicity,[status(thm)],[86])).
% 4.23/4.40 tff(88,plain,
% 4.23/4.40 (((~![B: $i, C: $i] : ((~relation(C)) | (~((~((C = relation_dom_restriction(B!54, B)) | (((~in(tptp_fun_D_3(C, B, B!54), B)) | (~in(ordered_pair(tptp_fun_D_3(C, B, B!54), tptp_fun_E_2(C, B, B!54)), B!54))) <=> in(ordered_pair(tptp_fun_D_3(C, B, B!54), tptp_fun_E_2(C, B, B!54)), C)))) | (~((~(C = relation_dom_restriction(B!54, B))) | ![D: $i, E: $i] : (~(((~in(D, B)) | (~in(ordered_pair(D, E), B!54))) <=> in(ordered_pair(D, E), C))))))))) | ((~relation(relation_dom_restriction(B!54, A!55))) | (~((~((relation_dom_restriction(B!54, A!55) = relation_dom_restriction(B!54, A!55)) | (((~in(tptp_fun_D_3(relation_dom_restriction(B!54, A!55), A!55, B!54), A!55)) | (~in(ordered_pair(tptp_fun_D_3(relation_dom_restriction(B!54, A!55), A!55, B!54), tptp_fun_E_2(relation_dom_restriction(B!54, A!55), A!55, B!54)), B!54))) <=> in(ordered_pair(tptp_fun_D_3(relation_dom_restriction(B!54, A!55), A!55, B!54), tptp_fun_E_2(relation_dom_restriction(B!54, A!55), A!55, B!54)), relation_dom_restriction(B!54, A!55))))) | (~((~(relation_dom_restriction(B!54, A!55) = relation_dom_restriction(B!54, A!55))) | ![D: $i, E: $i] : (~(((~in(D, A!55)) | (~in(ordered_pair(D, E), B!54))) <=> in(ordered_pair(D, E), relation_dom_restriction(B!54, A!55)))))))))) <=> ((~![B: $i, C: $i] : ((~relation(C)) | (~((~((C = relation_dom_restriction(B!54, B)) | (((~in(tptp_fun_D_3(C, B, B!54), B)) | (~in(ordered_pair(tptp_fun_D_3(C, B, B!54), tptp_fun_E_2(C, B, B!54)), B!54))) <=> in(ordered_pair(tptp_fun_D_3(C, B, B!54), tptp_fun_E_2(C, B, B!54)), C)))) | (~((~(C = relation_dom_restriction(B!54, B))) | ![D: $i, E: $i] : (~(((~in(D, B)) | (~in(ordered_pair(D, E), B!54))) <=> in(ordered_pair(D, E), C))))))))) | (~relation(relation_dom_restriction(B!54, A!55))) | ![D: $i, E: $i] : (~(((~in(D, A!55)) | (~in(ordered_pair(D, E), B!54))) <=> in(ordered_pair(D, E), relation_dom_restriction(B!54, A!55)))))),
% 4.23/4.42 inference(transitivity,[status(thm)],[87, 85])).
% 4.23/4.42 tff(89,plain,
% 4.23/4.42 ((~![B: $i, C: $i] : ((~relation(C)) | (~((~((C = relation_dom_restriction(B!54, B)) | (((~in(tptp_fun_D_3(C, B, B!54), B)) | (~in(ordered_pair(tptp_fun_D_3(C, B, B!54), tptp_fun_E_2(C, B, B!54)), B!54))) <=> in(ordered_pair(tptp_fun_D_3(C, B, B!54), tptp_fun_E_2(C, B, B!54)), C)))) | (~((~(C = relation_dom_restriction(B!54, B))) | ![D: $i, E: $i] : (~(((~in(D, B)) | (~in(ordered_pair(D, E), B!54))) <=> in(ordered_pair(D, E), C))))))))) | ((~relation(relation_dom_restriction(B!54, A!55))) | (~((~((relation_dom_restriction(B!54, A!55) = relation_dom_restriction(B!54, A!55)) | (((~in(tptp_fun_D_3(relation_dom_restriction(B!54, A!55), A!55, B!54), A!55)) | (~in(ordered_pair(tptp_fun_D_3(relation_dom_restriction(B!54, A!55), A!55, B!54), tptp_fun_E_2(relation_dom_restriction(B!54, A!55), A!55, B!54)), B!54))) <=> in(ordered_pair(tptp_fun_D_3(relation_dom_restriction(B!54, A!55), A!55, B!54), tptp_fun_E_2(relation_dom_restriction(B!54, A!55), A!55, B!54)), relation_dom_restriction(B!54, A!55))))) | (~((~(relation_dom_restriction(B!54, A!55) = relation_dom_restriction(B!54, A!55))) | ![D: $i, E: $i] : (~(((~in(D, A!55)) | (~in(ordered_pair(D, E), B!54))) <=> in(ordered_pair(D, E), relation_dom_restriction(B!54, A!55)))))))))),
% 4.23/4.42 inference(quant_inst,[status(thm)],[])).
% 4.23/4.42 tff(90,plain,
% 4.23/4.42 ((~![B: $i, C: $i] : ((~relation(C)) | (~((~((C = relation_dom_restriction(B!54, B)) | (((~in(tptp_fun_D_3(C, B, B!54), B)) | (~in(ordered_pair(tptp_fun_D_3(C, B, B!54), tptp_fun_E_2(C, B, B!54)), B!54))) <=> in(ordered_pair(tptp_fun_D_3(C, B, B!54), tptp_fun_E_2(C, B, B!54)), C)))) | (~((~(C = relation_dom_restriction(B!54, B))) | ![D: $i, E: $i] : (~(((~in(D, B)) | (~in(ordered_pair(D, E), B!54))) <=> in(ordered_pair(D, E), C))))))))) | (~relation(relation_dom_restriction(B!54, A!55))) | ![D: $i, E: $i] : (~(((~in(D, A!55)) | (~in(ordered_pair(D, E), B!54))) <=> in(ordered_pair(D, E), relation_dom_restriction(B!54, A!55))))),
% 4.23/4.42 inference(modus_ponens,[status(thm)],[89, 88])).
% 4.23/4.42 tff(91,plain,
% 4.23/4.42 (![D: $i, E: $i] : (~(((~in(D, A!55)) | (~in(ordered_pair(D, E), B!54))) <=> in(ordered_pair(D, E), relation_dom_restriction(B!54, A!55))))),
% 4.23/4.42 inference(unit_resolution,[status(thm)],[90, 84, 23])).
% 4.23/4.42 tff(92,plain,
% 4.23/4.42 ((~![D: $i, E: $i] : (~(((~in(D, A!55)) | (~in(ordered_pair(D, E), B!54))) <=> in(ordered_pair(D, E), relation_dom_restriction(B!54, A!55))))) | (~(((~in(tptp_fun_C_21(B!54, relation_dom_restriction(B!54, A!55)), A!55)) | (~in(ordered_pair(tptp_fun_C_21(B!54, relation_dom_restriction(B!54, A!55)), tptp_fun_D_20(B!54, relation_dom_restriction(B!54, A!55))), B!54))) <=> in(ordered_pair(tptp_fun_C_21(B!54, relation_dom_restriction(B!54, A!55)), tptp_fun_D_20(B!54, relation_dom_restriction(B!54, A!55))), relation_dom_restriction(B!54, A!55))))),
% 4.23/4.42 inference(quant_inst,[status(thm)],[])).
% 4.23/4.42 tff(93,plain,
% 4.23/4.42 ($false),
% 4.23/4.42 inference(unit_resolution,[status(thm)],[92, 91, 61])).
% 4.23/4.42 % SZS output end Proof
% 4.27/4.43 % E exiting
%------------------------------------------------------------------------------