%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SEU202+1 : TPTP v9.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n008.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:27:13 AM UTC 2025
% Result : Theorem 0.19s 0.40s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU202+1 : TPTP v9.0.0. Released v3.3.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n008.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 06:16:33 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.19/0.40 % SZS status Theorem
% 0.19/0.40 % SZS output start Proof
% 0.19/0.40 tff(in_type, type, (
% 0.19/0.40 in: ( $i * $i ) > $o)).
% 0.19/0.40 tff(relation_rng_restriction_type, type, (
% 0.19/0.40 relation_rng_restriction: ( $i * $i ) > $i)).
% 0.19/0.40 tff(tptp_fun_C_11_type, type, (
% 0.19/0.40 tptp_fun_C_11: $i)).
% 0.19/0.40 tff(tptp_fun_A_13_type, type, (
% 0.19/0.40 tptp_fun_A_13: $i)).
% 0.19/0.40 tff(ordered_pair_type, type, (
% 0.19/0.40 ordered_pair: ( $i * $i ) > $i)).
% 0.19/0.40 tff(tptp_fun_E_2_type, type, (
% 0.19/0.40 tptp_fun_E_2: ( $i * $i * $i ) > $i)).
% 0.19/0.40 tff(relation_dom_restriction_type, type, (
% 0.19/0.40 relation_dom_restriction: ( $i * $i ) > $i)).
% 0.19/0.40 tff(tptp_fun_B_12_type, type, (
% 0.19/0.40 tptp_fun_B_12: $i)).
% 0.19/0.40 tff(tptp_fun_D_3_type, type, (
% 0.19/0.40 tptp_fun_D_3: ( $i * $i * $i ) > $i)).
% 0.19/0.40 tff(relation_type, type, (
% 0.19/0.40 relation: $i > $o)).
% 0.19/0.40 tff(tptp_fun_E_0_type, type, (
% 0.19/0.40 tptp_fun_E_0: ( $i * $i * $i ) > $i)).
% 0.19/0.40 tff(tptp_fun_D_1_type, type, (
% 0.19/0.40 tptp_fun_D_1: ( $i * $i * $i ) > $i)).
% 0.19/0.40 tff(1,assumption,(~in(ordered_pair(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13)), relation_dom_restriction(C!11, B!12))), introduced(assumption)).
% 0.19/0.40 tff(2,plain,
% 0.19/0.40 ((~![A: $i, B: $i, C: $i] : ((~relation(C)) | (relation_dom_restriction(relation_rng_restriction(A, C), B) = relation_rng_restriction(A, relation_dom_restriction(C, B))))) <=> (~![A: $i, B: $i, C: $i] : ((~relation(C)) | (relation_dom_restriction(relation_rng_restriction(A, C), B) = relation_rng_restriction(A, relation_dom_restriction(C, B)))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(3,plain,
% 0.19/0.40 ((~![A: $i, B: $i, C: $i] : (relation(C) => (relation_dom_restriction(relation_rng_restriction(A, C), B) = relation_rng_restriction(A, relation_dom_restriction(C, B))))) <=> (~![A: $i, B: $i, C: $i] : ((~relation(C)) | (relation_dom_restriction(relation_rng_restriction(A, C), B) = relation_rng_restriction(A, relation_dom_restriction(C, B)))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(4,axiom,(~![A: $i, B: $i, C: $i] : (relation(C) => (relation_dom_restriction(relation_rng_restriction(A, C), B) = relation_rng_restriction(A, relation_dom_restriction(C, B))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t140_relat_1')).
% 0.19/0.40 tff(5,plain,
% 0.19/0.40 (~![A: $i, B: $i, C: $i] : ((~relation(C)) | (relation_dom_restriction(relation_rng_restriction(A, C), B) = relation_rng_restriction(A, relation_dom_restriction(C, B))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.19/0.40 tff(6,plain,
% 0.19/0.40 (~![A: $i, B: $i, C: $i] : ((~relation(C)) | (relation_dom_restriction(relation_rng_restriction(A, C), B) = relation_rng_restriction(A, relation_dom_restriction(C, B))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[5, 2])).
% 0.19/0.40 tff(7,plain,
% 0.19/0.40 (~![A: $i, B: $i, C: $i] : ((~relation(C)) | (relation_dom_restriction(relation_rng_restriction(A, C), B) = relation_rng_restriction(A, relation_dom_restriction(C, B))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.19/0.40 tff(8,plain,
% 0.19/0.40 (~![A: $i, B: $i, C: $i] : ((~relation(C)) | (relation_dom_restriction(relation_rng_restriction(A, C), B) = relation_rng_restriction(A, relation_dom_restriction(C, B))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[7, 2])).
% 0.19/0.40 tff(9,plain,(
% 0.19/0.40 ~((~relation(C!11)) | (relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12) = relation_rng_restriction(A!13, relation_dom_restriction(C!11, B!12))))),
% 0.19/0.40 inference(skolemize,[status(sab)],[8])).
% 0.19/0.40 tff(10,plain,
% 0.19/0.40 (relation(C!11)),
% 0.19/0.40 inference(or_elim,[status(thm)],[9])).
% 0.19/0.40 tff(11,plain,
% 0.19/0.40 (^[A: $i, B: $i] : refl(((~relation(A)) | relation(relation_dom_restriction(A, B))) <=> ((~relation(A)) | relation(relation_dom_restriction(A, B))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(12,plain,
% 0.19/0.40 (![A: $i, B: $i] : ((~relation(A)) | relation(relation_dom_restriction(A, B))) <=> ![A: $i, B: $i] : ((~relation(A)) | relation(relation_dom_restriction(A, B)))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[11])).
% 0.19/0.40 tff(13,plain,
% 0.19/0.40 (![A: $i, B: $i] : ((~relation(A)) | relation(relation_dom_restriction(A, B))) <=> ![A: $i, B: $i] : ((~relation(A)) | relation(relation_dom_restriction(A, B)))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(14,plain,
% 0.19/0.40 (^[A: $i, B: $i] : rewrite((relation(A) => relation(relation_dom_restriction(A, B))) <=> ((~relation(A)) | relation(relation_dom_restriction(A, B))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(15,plain,
% 0.19/0.40 (![A: $i, B: $i] : (relation(A) => relation(relation_dom_restriction(A, B))) <=> ![A: $i, B: $i] : ((~relation(A)) | relation(relation_dom_restriction(A, B)))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[14])).
% 0.19/0.40 tff(16,axiom,(![A: $i, B: $i] : (relation(A) => relation(relation_dom_restriction(A, B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_k7_relat_1')).
% 0.19/0.40 tff(17,plain,
% 0.19/0.40 (![A: $i, B: $i] : ((~relation(A)) | relation(relation_dom_restriction(A, B)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[16, 15])).
% 0.19/0.40 tff(18,plain,
% 0.19/0.40 (![A: $i, B: $i] : ((~relation(A)) | relation(relation_dom_restriction(A, B)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[17, 13])).
% 0.19/0.40 tff(19,plain,(
% 0.19/0.40 ![A: $i, B: $i] : ((~relation(A)) | relation(relation_dom_restriction(A, B)))),
% 0.19/0.40 inference(skolemize,[status(sab)],[18])).
% 0.19/0.40 tff(20,plain,
% 0.19/0.40 (![A: $i, B: $i] : ((~relation(A)) | relation(relation_dom_restriction(A, B)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[19, 12])).
% 0.19/0.40 tff(21,plain,
% 0.19/0.40 (((~![A: $i, B: $i] : ((~relation(A)) | relation(relation_dom_restriction(A, B)))) | ((~relation(C!11)) | relation(relation_dom_restriction(C!11, B!12)))) <=> ((~![A: $i, B: $i] : ((~relation(A)) | relation(relation_dom_restriction(A, B)))) | (~relation(C!11)) | relation(relation_dom_restriction(C!11, B!12)))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(22,plain,
% 0.19/0.40 ((~![A: $i, B: $i] : ((~relation(A)) | relation(relation_dom_restriction(A, B)))) | ((~relation(C!11)) | relation(relation_dom_restriction(C!11, B!12)))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(23,plain,
% 0.19/0.40 ((~![A: $i, B: $i] : ((~relation(A)) | relation(relation_dom_restriction(A, B)))) | (~relation(C!11)) | relation(relation_dom_restriction(C!11, B!12))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[22, 21])).
% 0.19/0.40 tff(24,plain,
% 0.19/0.40 (relation(relation_dom_restriction(C!11, B!12))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[23, 20, 10])).
% 0.19/0.40 tff(25,plain,
% 0.19/0.40 (^[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_1(C, B, A), B)) | (~in(ordered_pair(tptp_fun_D_1(C, B, A), tptp_fun_E_0(C, B, A)), A))) <=> in(ordered_pair(tptp_fun_D_1(C, B, A), tptp_fun_E_0(C, B, A)), C)))))))) <=> ((~relation(A)) | ![B: $i, C: $i] : ((~relation(C)) | (~((~((C = relation_dom_restriction(A, B)) | (((~in(tptp_fun_D_1(C, B, A), B)) | (~in(ordered_pair(tptp_fun_D_1(C, B, A), tptp_fun_E_0(C, B, A)), A))) <=> in(ordered_pair(tptp_fun_D_1(C, B, A), tptp_fun_E_0(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))))))))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(26,plain,
% 0.19/0.40 (![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_1(C, B, A), B)) | (~in(ordered_pair(tptp_fun_D_1(C, B, A), tptp_fun_E_0(C, B, A)), A))) <=> in(ordered_pair(tptp_fun_D_1(C, B, A), tptp_fun_E_0(C, B, A)), C)))))))) <=> ![A: $i] : ((~relation(A)) | ![B: $i, C: $i] : ((~relation(C)) | (~((~((C = relation_dom_restriction(A, B)) | (((~in(tptp_fun_D_1(C, B, A), B)) | (~in(ordered_pair(tptp_fun_D_1(C, B, A), tptp_fun_E_0(C, B, A)), A))) <=> in(ordered_pair(tptp_fun_D_1(C, B, A), tptp_fun_E_0(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)))))))))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[25])).
% 0.19/0.40 tff(27,plain,
% 0.19/0.40 (^[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_1(C, B, A), B)) | (~in(ordered_pair(tptp_fun_D_1(C, B, A), tptp_fun_E_0(C, B, A)), A))) <=> in(ordered_pair(tptp_fun_D_1(C, B, A), tptp_fun_E_0(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_1(C, B, A), B)) | (~in(ordered_pair(tptp_fun_D_1(C, B, A), tptp_fun_E_0(C, B, A)), A))) <=> in(ordered_pair(tptp_fun_D_1(C, B, A), tptp_fun_E_0(C, B, A)), C)))))))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(28,plain,
% 0.19/0.40 (![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_1(C, B, A), B)) | (~in(ordered_pair(tptp_fun_D_1(C, B, A), tptp_fun_E_0(C, B, A)), A))) <=> in(ordered_pair(tptp_fun_D_1(C, B, A), tptp_fun_E_0(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_1(C, B, A), B)) | (~in(ordered_pair(tptp_fun_D_1(C, B, A), tptp_fun_E_0(C, B, A)), A))) <=> in(ordered_pair(tptp_fun_D_1(C, B, A), tptp_fun_E_0(C, B, A)), C))))))))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[27])).
% 0.19/0.40 tff(29,plain,
% 0.19/0.40 (^[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_1(C, B, A), B)) | (~in(ordered_pair(tptp_fun_D_1(C, B, A), tptp_fun_E_0(C, B, A)), A))) <=> in(ordered_pair(tptp_fun_D_1(C, B, A), tptp_fun_E_0(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_1(C, B, A), B)) | (~in(ordered_pair(tptp_fun_D_1(C, B, A), tptp_fun_E_0(C, B, A)), A))) <=> in(ordered_pair(tptp_fun_D_1(C, B, A), tptp_fun_E_0(C, B, A)), C)))))))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(30,plain,
% 0.19/0.40 (![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_1(C, B, A), B)) | (~in(ordered_pair(tptp_fun_D_1(C, B, A), tptp_fun_E_0(C, B, A)), A))) <=> in(ordered_pair(tptp_fun_D_1(C, B, A), tptp_fun_E_0(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_1(C, B, A), B)) | (~in(ordered_pair(tptp_fun_D_1(C, B, A), tptp_fun_E_0(C, B, A)), A))) <=> in(ordered_pair(tptp_fun_D_1(C, B, A), tptp_fun_E_0(C, B, A)), C))))))))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[29])).
% 0.19/0.40 tff(31,plain,
% 0.19/0.40 (![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_1(C, B, A), B)) | (~in(ordered_pair(tptp_fun_D_1(C, B, A), tptp_fun_E_0(C, B, A)), A))) <=> in(ordered_pair(tptp_fun_D_1(C, B, A), tptp_fun_E_0(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_1(C, B, A), B)) | (~in(ordered_pair(tptp_fun_D_1(C, B, A), tptp_fun_E_0(C, B, A)), A))) <=> in(ordered_pair(tptp_fun_D_1(C, B, A), tptp_fun_E_0(C, B, A)), C))))))))),
% 0.19/0.40 inference(transitivity,[status(thm)],[30, 28])).
% 0.19/0.40 tff(32,plain,
% 0.19/0.40 (^[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_1(C, B, A), tptp_fun_E_0(C, B, A)), C) <=> (in(tptp_fun_D_1(C, B, A), B) & in(ordered_pair(tptp_fun_D_1(C, B, A), tptp_fun_E_0(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_1(C, B, A), B)) | (~in(ordered_pair(tptp_fun_D_1(C, B, A), tptp_fun_E_0(C, B, A)), A))) <=> in(ordered_pair(tptp_fun_D_1(C, B, A), tptp_fun_E_0(C, B, A)), C)))))))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(33,plain,
% 0.19/0.40 (![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_1(C, B, A), tptp_fun_E_0(C, B, A)), C) <=> (in(tptp_fun_D_1(C, B, A), B) & in(ordered_pair(tptp_fun_D_1(C, B, A), tptp_fun_E_0(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_1(C, B, A), B)) | (~in(ordered_pair(tptp_fun_D_1(C, B, A), tptp_fun_E_0(C, B, A)), A))) <=> in(ordered_pair(tptp_fun_D_1(C, B, A), tptp_fun_E_0(C, B, A)), C))))))))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[32])).
% 0.19/0.40 tff(34,plain,
% 0.19/0.40 (![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))))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(35,plain,
% 0.19/0.40 (^[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))))))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(36,plain,
% 0.19/0.40 (![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))))))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[35])).
% 0.19/0.40 tff(37,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')).
% 0.19/0.40 tff(38,plain,
% 0.19/0.40 (![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))))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[37, 36])).
% 0.19/0.40 tff(39,plain,
% 0.19/0.40 (![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))))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[38, 34])).
% 0.19/0.41 tff(40,plain,(
% 0.19/0.41 ![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_1(C, B, A), tptp_fun_E_0(C, B, A)), C) <=> (in(tptp_fun_D_1(C, B, A), B) & in(ordered_pair(tptp_fun_D_1(C, B, A), tptp_fun_E_0(C, B, A)), A))))))))),
% 0.19/0.41 inference(skolemize,[status(sab)],[39])).
% 0.19/0.41 tff(41,plain,
% 0.19/0.41 (![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_1(C, B, A), B)) | (~in(ordered_pair(tptp_fun_D_1(C, B, A), tptp_fun_E_0(C, B, A)), A))) <=> in(ordered_pair(tptp_fun_D_1(C, B, A), tptp_fun_E_0(C, B, A)), C))))))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[40, 33])).
% 0.19/0.41 tff(42,plain,
% 0.19/0.41 (![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_1(C, B, A), B)) | (~in(ordered_pair(tptp_fun_D_1(C, B, A), tptp_fun_E_0(C, B, A)), A))) <=> in(ordered_pair(tptp_fun_D_1(C, B, A), tptp_fun_E_0(C, B, A)), C))))))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[41, 31])).
% 0.19/0.41 tff(43,plain,
% 0.19/0.41 (![A: $i] : ((~relation(A)) | ![B: $i, C: $i] : ((~relation(C)) | (~((~((C = relation_dom_restriction(A, B)) | (((~in(tptp_fun_D_1(C, B, A), B)) | (~in(ordered_pair(tptp_fun_D_1(C, B, A), tptp_fun_E_0(C, B, A)), A))) <=> in(ordered_pair(tptp_fun_D_1(C, B, A), tptp_fun_E_0(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)))))))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[42, 26])).
% 0.19/0.41 tff(44,plain,
% 0.19/0.41 (((~![A: $i] : ((~relation(A)) | ![B: $i, C: $i] : ((~relation(C)) | (~((~((C = relation_dom_restriction(A, B)) | (((~in(tptp_fun_D_1(C, B, A), B)) | (~in(ordered_pair(tptp_fun_D_1(C, B, A), tptp_fun_E_0(C, B, A)), A))) <=> in(ordered_pair(tptp_fun_D_1(C, B, A), tptp_fun_E_0(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(C!11)) | ![B: $i, C: $i] : ((~relation(C)) | (~((~((C = relation_dom_restriction(C!11, B)) | (((~in(tptp_fun_D_1(C, B, C!11), B)) | (~in(ordered_pair(tptp_fun_D_1(C, B, C!11), tptp_fun_E_0(C, B, C!11)), C!11))) <=> in(ordered_pair(tptp_fun_D_1(C, B, C!11), tptp_fun_E_0(C, B, C!11)), C)))) | (~((~(C = relation_dom_restriction(C!11, B))) | ![D: $i, E: $i] : (~(((~in(D, B)) | (~in(ordered_pair(D, E), C!11))) <=> 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_1(C, B, A), B)) | (~in(ordered_pair(tptp_fun_D_1(C, B, A), tptp_fun_E_0(C, B, A)), A))) <=> in(ordered_pair(tptp_fun_D_1(C, B, A), tptp_fun_E_0(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(C!11)) | ![B: $i, C: $i] : ((~relation(C)) | (~((~((C = relation_dom_restriction(C!11, B)) | (((~in(tptp_fun_D_1(C, B, C!11), B)) | (~in(ordered_pair(tptp_fun_D_1(C, B, C!11), tptp_fun_E_0(C, B, C!11)), C!11))) <=> in(ordered_pair(tptp_fun_D_1(C, B, C!11), tptp_fun_E_0(C, B, C!11)), C)))) | (~((~(C = relation_dom_restriction(C!11, B))) | ![D: $i, E: $i] : (~(((~in(D, B)) | (~in(ordered_pair(D, E), C!11))) <=> in(ordered_pair(D, E), C)))))))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(45,plain,
% 0.19/0.41 ((~![A: $i] : ((~relation(A)) | ![B: $i, C: $i] : ((~relation(C)) | (~((~((C = relation_dom_restriction(A, B)) | (((~in(tptp_fun_D_1(C, B, A), B)) | (~in(ordered_pair(tptp_fun_D_1(C, B, A), tptp_fun_E_0(C, B, A)), A))) <=> in(ordered_pair(tptp_fun_D_1(C, B, A), tptp_fun_E_0(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(C!11)) | ![B: $i, C: $i] : ((~relation(C)) | (~((~((C = relation_dom_restriction(C!11, B)) | (((~in(tptp_fun_D_1(C, B, C!11), B)) | (~in(ordered_pair(tptp_fun_D_1(C, B, C!11), tptp_fun_E_0(C, B, C!11)), C!11))) <=> in(ordered_pair(tptp_fun_D_1(C, B, C!11), tptp_fun_E_0(C, B, C!11)), C)))) | (~((~(C = relation_dom_restriction(C!11, B))) | ![D: $i, E: $i] : (~(((~in(D, B)) | (~in(ordered_pair(D, E), C!11))) <=> in(ordered_pair(D, E), C)))))))))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(46,plain,
% 0.19/0.41 ((~![A: $i] : ((~relation(A)) | ![B: $i, C: $i] : ((~relation(C)) | (~((~((C = relation_dom_restriction(A, B)) | (((~in(tptp_fun_D_1(C, B, A), B)) | (~in(ordered_pair(tptp_fun_D_1(C, B, A), tptp_fun_E_0(C, B, A)), A))) <=> in(ordered_pair(tptp_fun_D_1(C, B, A), tptp_fun_E_0(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(C!11)) | ![B: $i, C: $i] : ((~relation(C)) | (~((~((C = relation_dom_restriction(C!11, B)) | (((~in(tptp_fun_D_1(C, B, C!11), B)) | (~in(ordered_pair(tptp_fun_D_1(C, B, C!11), tptp_fun_E_0(C, B, C!11)), C!11))) <=> in(ordered_pair(tptp_fun_D_1(C, B, C!11), tptp_fun_E_0(C, B, C!11)), C)))) | (~((~(C = relation_dom_restriction(C!11, B))) | ![D: $i, E: $i] : (~(((~in(D, B)) | (~in(ordered_pair(D, E), C!11))) <=> in(ordered_pair(D, E), C))))))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[45, 44])).
% 0.19/0.41 tff(47,plain,
% 0.19/0.41 (![B: $i, C: $i] : ((~relation(C)) | (~((~((C = relation_dom_restriction(C!11, B)) | (((~in(tptp_fun_D_1(C, B, C!11), B)) | (~in(ordered_pair(tptp_fun_D_1(C, B, C!11), tptp_fun_E_0(C, B, C!11)), C!11))) <=> in(ordered_pair(tptp_fun_D_1(C, B, C!11), tptp_fun_E_0(C, B, C!11)), C)))) | (~((~(C = relation_dom_restriction(C!11, B))) | ![D: $i, E: $i] : (~(((~in(D, B)) | (~in(ordered_pair(D, E), C!11))) <=> in(ordered_pair(D, E), C))))))))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[46, 43, 10])).
% 0.19/0.41 tff(48,plain,
% 0.19/0.41 (((~![B: $i, C: $i] : ((~relation(C)) | (~((~((C = relation_dom_restriction(C!11, B)) | (((~in(tptp_fun_D_1(C, B, C!11), B)) | (~in(ordered_pair(tptp_fun_D_1(C, B, C!11), tptp_fun_E_0(C, B, C!11)), C!11))) <=> in(ordered_pair(tptp_fun_D_1(C, B, C!11), tptp_fun_E_0(C, B, C!11)), C)))) | (~((~(C = relation_dom_restriction(C!11, B))) | ![D: $i, E: $i] : (~(((~in(D, B)) | (~in(ordered_pair(D, E), C!11))) <=> in(ordered_pair(D, E), C))))))))) | ((~relation(relation_dom_restriction(C!11, B!12))) | ![D: $i, E: $i] : (~(((~in(D, B!12)) | (~in(ordered_pair(D, E), C!11))) <=> in(ordered_pair(D, E), relation_dom_restriction(C!11, B!12)))))) <=> ((~![B: $i, C: $i] : ((~relation(C)) | (~((~((C = relation_dom_restriction(C!11, B)) | (((~in(tptp_fun_D_1(C, B, C!11), B)) | (~in(ordered_pair(tptp_fun_D_1(C, B, C!11), tptp_fun_E_0(C, B, C!11)), C!11))) <=> in(ordered_pair(tptp_fun_D_1(C, B, C!11), tptp_fun_E_0(C, B, C!11)), C)))) | (~((~(C = relation_dom_restriction(C!11, B))) | ![D: $i, E: $i] : (~(((~in(D, B)) | (~in(ordered_pair(D, E), C!11))) <=> in(ordered_pair(D, E), C))))))))) | (~relation(relation_dom_restriction(C!11, B!12))) | ![D: $i, E: $i] : (~(((~in(D, B!12)) | (~in(ordered_pair(D, E), C!11))) <=> in(ordered_pair(D, E), relation_dom_restriction(C!11, B!12)))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(49,plain,
% 0.19/0.41 (((~relation(relation_dom_restriction(C!11, B!12))) | (~((~((relation_dom_restriction(C!11, B!12) = relation_dom_restriction(C!11, B!12)) | (((~in(tptp_fun_D_1(relation_dom_restriction(C!11, B!12), B!12, C!11), B!12)) | (~in(ordered_pair(tptp_fun_D_1(relation_dom_restriction(C!11, B!12), B!12, C!11), tptp_fun_E_0(relation_dom_restriction(C!11, B!12), B!12, C!11)), C!11))) <=> in(ordered_pair(tptp_fun_D_1(relation_dom_restriction(C!11, B!12), B!12, C!11), tptp_fun_E_0(relation_dom_restriction(C!11, B!12), B!12, C!11)), relation_dom_restriction(C!11, B!12))))) | (~((~(relation_dom_restriction(C!11, B!12) = relation_dom_restriction(C!11, B!12))) | ![D: $i, E: $i] : (~(((~in(D, B!12)) | (~in(ordered_pair(D, E), C!11))) <=> in(ordered_pair(D, E), relation_dom_restriction(C!11, B!12))))))))) <=> ((~relation(relation_dom_restriction(C!11, B!12))) | ![D: $i, E: $i] : (~(((~in(D, B!12)) | (~in(ordered_pair(D, E), C!11))) <=> in(ordered_pair(D, E), relation_dom_restriction(C!11, B!12)))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(50,plain,
% 0.19/0.41 (((~![B: $i, C: $i] : ((~relation(C)) | (~((~((C = relation_dom_restriction(C!11, B)) | (((~in(tptp_fun_D_1(C, B, C!11), B)) | (~in(ordered_pair(tptp_fun_D_1(C, B, C!11), tptp_fun_E_0(C, B, C!11)), C!11))) <=> in(ordered_pair(tptp_fun_D_1(C, B, C!11), tptp_fun_E_0(C, B, C!11)), C)))) | (~((~(C = relation_dom_restriction(C!11, B))) | ![D: $i, E: $i] : (~(((~in(D, B)) | (~in(ordered_pair(D, E), C!11))) <=> in(ordered_pair(D, E), C))))))))) | ((~relation(relation_dom_restriction(C!11, B!12))) | (~((~((relation_dom_restriction(C!11, B!12) = relation_dom_restriction(C!11, B!12)) | (((~in(tptp_fun_D_1(relation_dom_restriction(C!11, B!12), B!12, C!11), B!12)) | (~in(ordered_pair(tptp_fun_D_1(relation_dom_restriction(C!11, B!12), B!12, C!11), tptp_fun_E_0(relation_dom_restriction(C!11, B!12), B!12, C!11)), C!11))) <=> in(ordered_pair(tptp_fun_D_1(relation_dom_restriction(C!11, B!12), B!12, C!11), tptp_fun_E_0(relation_dom_restriction(C!11, B!12), B!12, C!11)), relation_dom_restriction(C!11, B!12))))) | (~((~(relation_dom_restriction(C!11, B!12) = relation_dom_restriction(C!11, B!12))) | ![D: $i, E: $i] : (~(((~in(D, B!12)) | (~in(ordered_pair(D, E), C!11))) <=> in(ordered_pair(D, E), relation_dom_restriction(C!11, B!12)))))))))) <=> ((~![B: $i, C: $i] : ((~relation(C)) | (~((~((C = relation_dom_restriction(C!11, B)) | (((~in(tptp_fun_D_1(C, B, C!11), B)) | (~in(ordered_pair(tptp_fun_D_1(C, B, C!11), tptp_fun_E_0(C, B, C!11)), C!11))) <=> in(ordered_pair(tptp_fun_D_1(C, B, C!11), tptp_fun_E_0(C, B, C!11)), C)))) | (~((~(C = relation_dom_restriction(C!11, B))) | ![D: $i, E: $i] : (~(((~in(D, B)) | (~in(ordered_pair(D, E), C!11))) <=> in(ordered_pair(D, E), C))))))))) | ((~relation(relation_dom_restriction(C!11, B!12))) | ![D: $i, E: $i] : (~(((~in(D, B!12)) | (~in(ordered_pair(D, E), C!11))) <=> in(ordered_pair(D, E), relation_dom_restriction(C!11, B!12))))))),
% 0.19/0.41 inference(monotonicity,[status(thm)],[49])).
% 0.19/0.41 tff(51,plain,
% 0.19/0.41 (((~![B: $i, C: $i] : ((~relation(C)) | (~((~((C = relation_dom_restriction(C!11, B)) | (((~in(tptp_fun_D_1(C, B, C!11), B)) | (~in(ordered_pair(tptp_fun_D_1(C, B, C!11), tptp_fun_E_0(C, B, C!11)), C!11))) <=> in(ordered_pair(tptp_fun_D_1(C, B, C!11), tptp_fun_E_0(C, B, C!11)), C)))) | (~((~(C = relation_dom_restriction(C!11, B))) | ![D: $i, E: $i] : (~(((~in(D, B)) | (~in(ordered_pair(D, E), C!11))) <=> in(ordered_pair(D, E), C))))))))) | ((~relation(relation_dom_restriction(C!11, B!12))) | (~((~((relation_dom_restriction(C!11, B!12) = relation_dom_restriction(C!11, B!12)) | (((~in(tptp_fun_D_1(relation_dom_restriction(C!11, B!12), B!12, C!11), B!12)) | (~in(ordered_pair(tptp_fun_D_1(relation_dom_restriction(C!11, B!12), B!12, C!11), tptp_fun_E_0(relation_dom_restriction(C!11, B!12), B!12, C!11)), C!11))) <=> in(ordered_pair(tptp_fun_D_1(relation_dom_restriction(C!11, B!12), B!12, C!11), tptp_fun_E_0(relation_dom_restriction(C!11, B!12), B!12, C!11)), relation_dom_restriction(C!11, B!12))))) | (~((~(relation_dom_restriction(C!11, B!12) = relation_dom_restriction(C!11, B!12))) | ![D: $i, E: $i] : (~(((~in(D, B!12)) | (~in(ordered_pair(D, E), C!11))) <=> in(ordered_pair(D, E), relation_dom_restriction(C!11, B!12)))))))))) <=> ((~![B: $i, C: $i] : ((~relation(C)) | (~((~((C = relation_dom_restriction(C!11, B)) | (((~in(tptp_fun_D_1(C, B, C!11), B)) | (~in(ordered_pair(tptp_fun_D_1(C, B, C!11), tptp_fun_E_0(C, B, C!11)), C!11))) <=> in(ordered_pair(tptp_fun_D_1(C, B, C!11), tptp_fun_E_0(C, B, C!11)), C)))) | (~((~(C = relation_dom_restriction(C!11, B))) | ![D: $i, E: $i] : (~(((~in(D, B)) | (~in(ordered_pair(D, E), C!11))) <=> in(ordered_pair(D, E), C))))))))) | (~relation(relation_dom_restriction(C!11, B!12))) | ![D: $i, E: $i] : (~(((~in(D, B!12)) | (~in(ordered_pair(D, E), C!11))) <=> in(ordered_pair(D, E), relation_dom_restriction(C!11, B!12)))))),
% 0.19/0.41 inference(transitivity,[status(thm)],[50, 48])).
% 0.19/0.41 tff(52,plain,
% 0.19/0.41 ((~![B: $i, C: $i] : ((~relation(C)) | (~((~((C = relation_dom_restriction(C!11, B)) | (((~in(tptp_fun_D_1(C, B, C!11), B)) | (~in(ordered_pair(tptp_fun_D_1(C, B, C!11), tptp_fun_E_0(C, B, C!11)), C!11))) <=> in(ordered_pair(tptp_fun_D_1(C, B, C!11), tptp_fun_E_0(C, B, C!11)), C)))) | (~((~(C = relation_dom_restriction(C!11, B))) | ![D: $i, E: $i] : (~(((~in(D, B)) | (~in(ordered_pair(D, E), C!11))) <=> in(ordered_pair(D, E), C))))))))) | ((~relation(relation_dom_restriction(C!11, B!12))) | (~((~((relation_dom_restriction(C!11, B!12) = relation_dom_restriction(C!11, B!12)) | (((~in(tptp_fun_D_1(relation_dom_restriction(C!11, B!12), B!12, C!11), B!12)) | (~in(ordered_pair(tptp_fun_D_1(relation_dom_restriction(C!11, B!12), B!12, C!11), tptp_fun_E_0(relation_dom_restriction(C!11, B!12), B!12, C!11)), C!11))) <=> in(ordered_pair(tptp_fun_D_1(relation_dom_restriction(C!11, B!12), B!12, C!11), tptp_fun_E_0(relation_dom_restriction(C!11, B!12), B!12, C!11)), relation_dom_restriction(C!11, B!12))))) | (~((~(relation_dom_restriction(C!11, B!12) = relation_dom_restriction(C!11, B!12))) | ![D: $i, E: $i] : (~(((~in(D, B!12)) | (~in(ordered_pair(D, E), C!11))) <=> in(ordered_pair(D, E), relation_dom_restriction(C!11, B!12)))))))))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(53,plain,
% 0.19/0.42 ((~![B: $i, C: $i] : ((~relation(C)) | (~((~((C = relation_dom_restriction(C!11, B)) | (((~in(tptp_fun_D_1(C, B, C!11), B)) | (~in(ordered_pair(tptp_fun_D_1(C, B, C!11), tptp_fun_E_0(C, B, C!11)), C!11))) <=> in(ordered_pair(tptp_fun_D_1(C, B, C!11), tptp_fun_E_0(C, B, C!11)), C)))) | (~((~(C = relation_dom_restriction(C!11, B))) | ![D: $i, E: $i] : (~(((~in(D, B)) | (~in(ordered_pair(D, E), C!11))) <=> in(ordered_pair(D, E), C))))))))) | (~relation(relation_dom_restriction(C!11, B!12))) | ![D: $i, E: $i] : (~(((~in(D, B!12)) | (~in(ordered_pair(D, E), C!11))) <=> in(ordered_pair(D, E), relation_dom_restriction(C!11, B!12))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[52, 51])).
% 0.19/0.42 tff(54,plain,
% 0.19/0.42 (![D: $i, E: $i] : (~(((~in(D, B!12)) | (~in(ordered_pair(D, E), C!11))) <=> in(ordered_pair(D, E), relation_dom_restriction(C!11, B!12))))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[53, 47, 24])).
% 0.19/0.42 tff(55,plain,
% 0.19/0.42 ((~![D: $i, E: $i] : (~(((~in(D, B!12)) | (~in(ordered_pair(D, E), C!11))) <=> in(ordered_pair(D, E), relation_dom_restriction(C!11, B!12))))) | (~(((~in(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), B!12)) | (~in(ordered_pair(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13)), C!11))) <=> in(ordered_pair(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13)), relation_dom_restriction(C!11, B!12))))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(56,plain,
% 0.19/0.42 (~(((~in(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), B!12)) | (~in(ordered_pair(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13)), C!11))) <=> in(ordered_pair(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13)), relation_dom_restriction(C!11, B!12)))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[55, 54])).
% 0.19/0.42 tff(57,plain,
% 0.19/0.42 ((((~in(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), B!12)) | (~in(ordered_pair(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13)), C!11))) <=> in(ordered_pair(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13)), relation_dom_restriction(C!11, B!12))) | ((~in(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), B!12)) | (~in(ordered_pair(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13)), C!11))) | in(ordered_pair(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13)), relation_dom_restriction(C!11, B!12))),
% 0.19/0.42 inference(tautology,[status(thm)],[])).
% 0.19/0.42 tff(58,plain,
% 0.19/0.42 (((~in(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), B!12)) | (~in(ordered_pair(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13)), C!11))) | in(ordered_pair(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13)), relation_dom_restriction(C!11, B!12))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[57, 56])).
% 0.19/0.42 tff(59,plain,
% 0.19/0.42 ((~in(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), B!12)) | (~in(ordered_pair(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13)), C!11))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[58, 1])).
% 0.19/0.42 tff(60,plain,
% 0.19/0.42 (((~in(tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), A!13)) | (~in(ordered_pair(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13)), relation_dom_restriction(C!11, B!12)))) | in(ordered_pair(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13)), relation_dom_restriction(C!11, B!12))),
% 0.19/0.42 inference(tautology,[status(thm)],[])).
% 0.19/0.42 tff(61,plain,
% 0.19/0.42 ((~in(tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), A!13)) | (~in(ordered_pair(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13)), relation_dom_restriction(C!11, B!12)))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[60, 1])).
% 0.19/0.42 tff(62,plain,
% 0.19/0.42 (^[A: $i, B: $i] : refl(((~relation(B)) | relation(relation_rng_restriction(A, B))) <=> ((~relation(B)) | relation(relation_rng_restriction(A, B))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(63,plain,
% 0.19/0.42 (![A: $i, B: $i] : ((~relation(B)) | relation(relation_rng_restriction(A, B))) <=> ![A: $i, B: $i] : ((~relation(B)) | relation(relation_rng_restriction(A, B)))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[62])).
% 0.19/0.42 tff(64,plain,
% 0.19/0.42 (![A: $i, B: $i] : ((~relation(B)) | relation(relation_rng_restriction(A, B))) <=> ![A: $i, B: $i] : ((~relation(B)) | relation(relation_rng_restriction(A, B)))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(65,plain,
% 0.19/0.42 (^[A: $i, B: $i] : rewrite((relation(B) => relation(relation_rng_restriction(A, B))) <=> ((~relation(B)) | relation(relation_rng_restriction(A, B))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(66,plain,
% 0.19/0.42 (![A: $i, B: $i] : (relation(B) => relation(relation_rng_restriction(A, B))) <=> ![A: $i, B: $i] : ((~relation(B)) | relation(relation_rng_restriction(A, B)))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[65])).
% 0.19/0.42 tff(67,axiom,(![A: $i, B: $i] : (relation(B) => relation(relation_rng_restriction(A, B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_k8_relat_1')).
% 0.19/0.42 tff(68,plain,
% 0.19/0.42 (![A: $i, B: $i] : ((~relation(B)) | relation(relation_rng_restriction(A, B)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[67, 66])).
% 0.19/0.42 tff(69,plain,
% 0.19/0.42 (![A: $i, B: $i] : ((~relation(B)) | relation(relation_rng_restriction(A, B)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[68, 64])).
% 0.19/0.42 tff(70,plain,(
% 0.19/0.42 ![A: $i, B: $i] : ((~relation(B)) | relation(relation_rng_restriction(A, B)))),
% 0.19/0.42 inference(skolemize,[status(sab)],[69])).
% 0.19/0.42 tff(71,plain,
% 0.19/0.42 (![A: $i, B: $i] : ((~relation(B)) | relation(relation_rng_restriction(A, B)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[70, 63])).
% 0.19/0.42 tff(72,plain,
% 0.19/0.42 (((~![A: $i, B: $i] : ((~relation(B)) | relation(relation_rng_restriction(A, B)))) | ((~relation(C!11)) | relation(relation_rng_restriction(A!13, C!11)))) <=> ((~![A: $i, B: $i] : ((~relation(B)) | relation(relation_rng_restriction(A, B)))) | (~relation(C!11)) | relation(relation_rng_restriction(A!13, C!11)))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(73,plain,
% 0.19/0.42 ((~![A: $i, B: $i] : ((~relation(B)) | relation(relation_rng_restriction(A, B)))) | ((~relation(C!11)) | relation(relation_rng_restriction(A!13, C!11)))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(74,plain,
% 0.19/0.42 ((~![A: $i, B: $i] : ((~relation(B)) | relation(relation_rng_restriction(A, B)))) | (~relation(C!11)) | relation(relation_rng_restriction(A!13, C!11))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[73, 72])).
% 0.19/0.42 tff(75,plain,
% 0.19/0.42 (relation(relation_rng_restriction(A!13, C!11))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[74, 71, 10])).
% 0.19/0.42 tff(76,plain,
% 0.19/0.42 (((~![A: $i, B: $i] : ((~relation(A)) | relation(relation_dom_restriction(A, B)))) | ((~relation(relation_rng_restriction(A!13, C!11))) | relation(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12)))) <=> ((~![A: $i, B: $i] : ((~relation(A)) | relation(relation_dom_restriction(A, B)))) | (~relation(relation_rng_restriction(A!13, C!11))) | relation(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12)))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(77,plain,
% 0.19/0.42 ((~![A: $i, B: $i] : ((~relation(A)) | relation(relation_dom_restriction(A, B)))) | ((~relation(relation_rng_restriction(A!13, C!11))) | relation(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12)))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(78,plain,
% 0.19/0.42 ((~![A: $i, B: $i] : ((~relation(A)) | relation(relation_dom_restriction(A, B)))) | (~relation(relation_rng_restriction(A!13, C!11))) | relation(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[77, 76])).
% 0.19/0.42 tff(79,plain,
% 0.19/0.42 (relation(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[78, 20, 75])).
% 0.19/0.42 tff(80,plain,
% 0.19/0.42 (^[A: $i, B: $i] : rewrite(((~relation(B)) | ![C: $i] : ((~relation(C)) | (~((~((~(C = relation_rng_restriction(A, B))) | ![D: $i, E: $i] : (~(((~in(E, A)) | (~in(ordered_pair(D, E), B))) <=> in(ordered_pair(D, E), C))))) | (~((C = relation_rng_restriction(A, B)) | (((~in(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)), B))) <=> in(ordered_pair(tptp_fun_D_3(C, B, A), tptp_fun_E_2(C, B, A)), C)))))))) <=> ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~((~((C = relation_rng_restriction(A, B)) | (((~in(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)), B))) <=> in(ordered_pair(tptp_fun_D_3(C, B, A), tptp_fun_E_2(C, B, A)), C)))) | (~((~(C = relation_rng_restriction(A, B))) | ![D: $i, E: $i] : (~(((~in(E, A)) | (~in(ordered_pair(D, E), B))) <=> in(ordered_pair(D, E), C))))))))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(81,plain,
% 0.19/0.42 (![A: $i, B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~((~((~(C = relation_rng_restriction(A, B))) | ![D: $i, E: $i] : (~(((~in(E, A)) | (~in(ordered_pair(D, E), B))) <=> in(ordered_pair(D, E), C))))) | (~((C = relation_rng_restriction(A, B)) | (((~in(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)), B))) <=> in(ordered_pair(tptp_fun_D_3(C, B, A), tptp_fun_E_2(C, B, A)), C)))))))) <=> ![A: $i, B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~((~((C = relation_rng_restriction(A, B)) | (((~in(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)), B))) <=> in(ordered_pair(tptp_fun_D_3(C, B, A), tptp_fun_E_2(C, B, A)), C)))) | (~((~(C = relation_rng_restriction(A, B))) | ![D: $i, E: $i] : (~(((~in(E, A)) | (~in(ordered_pair(D, E), B))) <=> in(ordered_pair(D, E), C)))))))))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[80])).
% 0.19/0.42 tff(82,plain,
% 0.19/0.42 (^[A: $i, B: $i] : refl(((~relation(B)) | ![C: $i] : ((~relation(C)) | (~((~((~(C = relation_rng_restriction(A, B))) | ![D: $i, E: $i] : (~(((~in(E, A)) | (~in(ordered_pair(D, E), B))) <=> in(ordered_pair(D, E), C))))) | (~((C = relation_rng_restriction(A, B)) | (((~in(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)), B))) <=> in(ordered_pair(tptp_fun_D_3(C, B, A), tptp_fun_E_2(C, B, A)), C)))))))) <=> ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~((~((~(C = relation_rng_restriction(A, B))) | ![D: $i, E: $i] : (~(((~in(E, A)) | (~in(ordered_pair(D, E), B))) <=> in(ordered_pair(D, E), C))))) | (~((C = relation_rng_restriction(A, B)) | (((~in(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)), B))) <=> in(ordered_pair(tptp_fun_D_3(C, B, A), tptp_fun_E_2(C, B, A)), C)))))))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(83,plain,
% 0.19/0.42 (![A: $i, B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~((~((~(C = relation_rng_restriction(A, B))) | ![D: $i, E: $i] : (~(((~in(E, A)) | (~in(ordered_pair(D, E), B))) <=> in(ordered_pair(D, E), C))))) | (~((C = relation_rng_restriction(A, B)) | (((~in(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)), B))) <=> in(ordered_pair(tptp_fun_D_3(C, B, A), tptp_fun_E_2(C, B, A)), C)))))))) <=> ![A: $i, B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~((~((~(C = relation_rng_restriction(A, B))) | ![D: $i, E: $i] : (~(((~in(E, A)) | (~in(ordered_pair(D, E), B))) <=> in(ordered_pair(D, E), C))))) | (~((C = relation_rng_restriction(A, B)) | (((~in(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)), B))) <=> in(ordered_pair(tptp_fun_D_3(C, B, A), tptp_fun_E_2(C, B, A)), C))))))))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[82])).
% 0.19/0.42 tff(84,plain,
% 0.19/0.42 (^[A: $i, B: $i] : rewrite(((~relation(B)) | ![C: $i] : ((~relation(C)) | (~((~((~(C = relation_rng_restriction(A, B))) | ![D: $i, E: $i] : (~(((~in(E, A)) | (~in(ordered_pair(D, E), B))) <=> in(ordered_pair(D, E), C))))) | (~((C = relation_rng_restriction(A, B)) | (((~in(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)), B))) <=> in(ordered_pair(tptp_fun_D_3(C, B, A), tptp_fun_E_2(C, B, A)), C)))))))) <=> ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~((~((~(C = relation_rng_restriction(A, B))) | ![D: $i, E: $i] : (~(((~in(E, A)) | (~in(ordered_pair(D, E), B))) <=> in(ordered_pair(D, E), C))))) | (~((C = relation_rng_restriction(A, B)) | (((~in(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)), B))) <=> in(ordered_pair(tptp_fun_D_3(C, B, A), tptp_fun_E_2(C, B, A)), C)))))))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(85,plain,
% 0.19/0.42 (![A: $i, B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~((~((~(C = relation_rng_restriction(A, B))) | ![D: $i, E: $i] : (~(((~in(E, A)) | (~in(ordered_pair(D, E), B))) <=> in(ordered_pair(D, E), C))))) | (~((C = relation_rng_restriction(A, B)) | (((~in(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)), B))) <=> in(ordered_pair(tptp_fun_D_3(C, B, A), tptp_fun_E_2(C, B, A)), C)))))))) <=> ![A: $i, B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~((~((~(C = relation_rng_restriction(A, B))) | ![D: $i, E: $i] : (~(((~in(E, A)) | (~in(ordered_pair(D, E), B))) <=> in(ordered_pair(D, E), C))))) | (~((C = relation_rng_restriction(A, B)) | (((~in(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)), B))) <=> in(ordered_pair(tptp_fun_D_3(C, B, A), tptp_fun_E_2(C, B, A)), C))))))))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[84])).
% 0.19/0.42 tff(86,plain,
% 0.19/0.42 (![A: $i, B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~((~((~(C = relation_rng_restriction(A, B))) | ![D: $i, E: $i] : (~(((~in(E, A)) | (~in(ordered_pair(D, E), B))) <=> in(ordered_pair(D, E), C))))) | (~((C = relation_rng_restriction(A, B)) | (((~in(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)), B))) <=> in(ordered_pair(tptp_fun_D_3(C, B, A), tptp_fun_E_2(C, B, A)), C)))))))) <=> ![A: $i, B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~((~((~(C = relation_rng_restriction(A, B))) | ![D: $i, E: $i] : (~(((~in(E, A)) | (~in(ordered_pair(D, E), B))) <=> in(ordered_pair(D, E), C))))) | (~((C = relation_rng_restriction(A, B)) | (((~in(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)), B))) <=> in(ordered_pair(tptp_fun_D_3(C, B, A), tptp_fun_E_2(C, B, A)), C))))))))),
% 0.19/0.42 inference(transitivity,[status(thm)],[85, 83])).
% 0.19/0.42 tff(87,plain,
% 0.19/0.42 (^[A: $i, B: $i] : rewrite(((~relation(B)) | ![C: $i] : ((~relation(C)) | (((~(C = relation_rng_restriction(A, B))) | ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (in(E, A) & in(ordered_pair(D, E), B)))) & ((C = relation_rng_restriction(A, B)) | (~(in(ordered_pair(tptp_fun_D_3(C, B, A), tptp_fun_E_2(C, B, A)), C) <=> (in(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)), B)))))))) <=> ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~((~((~(C = relation_rng_restriction(A, B))) | ![D: $i, E: $i] : (~(((~in(E, A)) | (~in(ordered_pair(D, E), B))) <=> in(ordered_pair(D, E), C))))) | (~((C = relation_rng_restriction(A, B)) | (((~in(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)), B))) <=> in(ordered_pair(tptp_fun_D_3(C, B, A), tptp_fun_E_2(C, B, A)), C)))))))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(88,plain,
% 0.19/0.42 (![A: $i, B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (((~(C = relation_rng_restriction(A, B))) | ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (in(E, A) & in(ordered_pair(D, E), B)))) & ((C = relation_rng_restriction(A, B)) | (~(in(ordered_pair(tptp_fun_D_3(C, B, A), tptp_fun_E_2(C, B, A)), C) <=> (in(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)), B)))))))) <=> ![A: $i, B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~((~((~(C = relation_rng_restriction(A, B))) | ![D: $i, E: $i] : (~(((~in(E, A)) | (~in(ordered_pair(D, E), B))) <=> in(ordered_pair(D, E), C))))) | (~((C = relation_rng_restriction(A, B)) | (((~in(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)), B))) <=> in(ordered_pair(tptp_fun_D_3(C, B, A), tptp_fun_E_2(C, B, A)), C))))))))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[87])).
% 0.19/0.42 tff(89,plain,
% 0.19/0.42 (![A: $i, B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | ((C = relation_rng_restriction(A, B)) <=> ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (in(E, A) & in(ordered_pair(D, E), B)))))) <=> ![A: $i, B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | ((C = relation_rng_restriction(A, B)) <=> ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (in(E, A) & in(ordered_pair(D, E), B))))))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(90,plain,
% 0.19/0.43 (^[A: $i, B: $i] : trans(monotonicity(quant_intro(proof_bind(^[C: $i] : trans(monotonicity(rewrite(((C = relation_rng_restriction(A, B)) <=> ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (in(E, A) & in(ordered_pair(D, E), B)))) <=> ((C = relation_rng_restriction(A, B)) <=> ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (in(E, A) & in(ordered_pair(D, E), B))))), ((relation(C) => ((C = relation_rng_restriction(A, B)) <=> ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (in(E, A) & in(ordered_pair(D, E), B))))) <=> (relation(C) => ((C = relation_rng_restriction(A, B)) <=> ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (in(E, A) & in(ordered_pair(D, E), B))))))), rewrite((relation(C) => ((C = relation_rng_restriction(A, B)) <=> ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (in(E, A) & in(ordered_pair(D, E), B))))) <=> ((~relation(C)) | ((C = relation_rng_restriction(A, B)) <=> ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (in(E, A) & in(ordered_pair(D, E), B)))))), ((relation(C) => ((C = relation_rng_restriction(A, B)) <=> ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (in(E, A) & in(ordered_pair(D, E), B))))) <=> ((~relation(C)) | ((C = relation_rng_restriction(A, B)) <=> ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (in(E, A) & in(ordered_pair(D, E), B)))))))), (![C: $i] : (relation(C) => ((C = relation_rng_restriction(A, B)) <=> ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (in(E, A) & in(ordered_pair(D, E), B))))) <=> ![C: $i] : ((~relation(C)) | ((C = relation_rng_restriction(A, B)) <=> ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (in(E, A) & in(ordered_pair(D, E), B))))))), ((relation(B) => ![C: $i] : (relation(C) => ((C = relation_rng_restriction(A, B)) <=> ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (in(E, A) & in(ordered_pair(D, E), B)))))) <=> (relation(B) => ![C: $i] : ((~relation(C)) | ((C = relation_rng_restriction(A, B)) <=> ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (in(E, A) & in(ordered_pair(D, E), B)))))))), rewrite((relation(B) => ![C: $i] : ((~relation(C)) | ((C = relation_rng_restriction(A, B)) <=> ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (in(E, A) & in(ordered_pair(D, E), B)))))) <=> ((~relation(B)) | ![C: $i] : ((~relation(C)) | ((C = relation_rng_restriction(A, B)) <=> ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (in(E, A) & in(ordered_pair(D, E), B))))))), ((relation(B) => ![C: $i] : (relation(C) => ((C = relation_rng_restriction(A, B)) <=> ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (in(E, A) & in(ordered_pair(D, E), B)))))) <=> ((~relation(B)) | ![C: $i] : ((~relation(C)) | ((C = relation_rng_restriction(A, B)) <=> ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (in(E, A) & in(ordered_pair(D, E), B))))))))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(91,plain,
% 0.19/0.43 (![A: $i, B: $i] : (relation(B) => ![C: $i] : (relation(C) => ((C = relation_rng_restriction(A, B)) <=> ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (in(E, A) & in(ordered_pair(D, E), B)))))) <=> ![A: $i, B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | ((C = relation_rng_restriction(A, B)) <=> ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (in(E, A) & in(ordered_pair(D, E), B))))))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[90])).
% 0.19/0.43 tff(92,axiom,(![A: $i, B: $i] : (relation(B) => ![C: $i] : (relation(C) => ((C = relation_rng_restriction(A, B)) <=> ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (in(E, A) & in(ordered_pair(D, E), B))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d12_relat_1')).
% 0.19/0.43 tff(93,plain,
% 0.19/0.43 (![A: $i, B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | ((C = relation_rng_restriction(A, B)) <=> ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (in(E, A) & in(ordered_pair(D, E), B))))))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[92, 91])).
% 0.19/0.43 tff(94,plain,
% 0.19/0.43 (![A: $i, B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | ((C = relation_rng_restriction(A, B)) <=> ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (in(E, A) & in(ordered_pair(D, E), B))))))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[93, 89])).
% 0.19/0.43 tff(95,plain,(
% 0.19/0.43 ![A: $i, B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (((~(C = relation_rng_restriction(A, B))) | ![D: $i, E: $i] : (in(ordered_pair(D, E), C) <=> (in(E, A) & in(ordered_pair(D, E), B)))) & ((C = relation_rng_restriction(A, B)) | (~(in(ordered_pair(tptp_fun_D_3(C, B, A), tptp_fun_E_2(C, B, A)), C) <=> (in(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)), B))))))))),
% 0.19/0.43 inference(skolemize,[status(sab)],[94])).
% 0.19/0.43 tff(96,plain,
% 0.19/0.43 (![A: $i, B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~((~((~(C = relation_rng_restriction(A, B))) | ![D: $i, E: $i] : (~(((~in(E, A)) | (~in(ordered_pair(D, E), B))) <=> in(ordered_pair(D, E), C))))) | (~((C = relation_rng_restriction(A, B)) | (((~in(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)), B))) <=> in(ordered_pair(tptp_fun_D_3(C, B, A), tptp_fun_E_2(C, B, A)), C))))))))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[95, 88])).
% 0.19/0.43 tff(97,plain,
% 0.19/0.43 (![A: $i, B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~((~((~(C = relation_rng_restriction(A, B))) | ![D: $i, E: $i] : (~(((~in(E, A)) | (~in(ordered_pair(D, E), B))) <=> in(ordered_pair(D, E), C))))) | (~((C = relation_rng_restriction(A, B)) | (((~in(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)), B))) <=> in(ordered_pair(tptp_fun_D_3(C, B, A), tptp_fun_E_2(C, B, A)), C))))))))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[96, 86])).
% 0.19/0.43 tff(98,plain,
% 0.19/0.43 (![A: $i, B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~((~((C = relation_rng_restriction(A, B)) | (((~in(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)), B))) <=> in(ordered_pair(tptp_fun_D_3(C, B, A), tptp_fun_E_2(C, B, A)), C)))) | (~((~(C = relation_rng_restriction(A, B))) | ![D: $i, E: $i] : (~(((~in(E, A)) | (~in(ordered_pair(D, E), B))) <=> in(ordered_pair(D, E), C)))))))))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[97, 81])).
% 0.19/0.43 tff(99,plain,
% 0.19/0.43 (((~![A: $i, B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~((~((C = relation_rng_restriction(A, B)) | (((~in(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)), B))) <=> in(ordered_pair(tptp_fun_D_3(C, B, A), tptp_fun_E_2(C, B, A)), C)))) | (~((~(C = relation_rng_restriction(A, B))) | ![D: $i, E: $i] : (~(((~in(E, A)) | (~in(ordered_pair(D, E), B))) <=> in(ordered_pair(D, E), C)))))))))) | ((~relation(relation_dom_restriction(C!11, B!12))) | ![C: $i] : ((~relation(C)) | (~((~((~(C = relation_rng_restriction(A!13, relation_dom_restriction(C!11, B!12)))) | ![D: $i, E: $i] : (~(((~in(E, A!13)) | (~in(ordered_pair(D, E), relation_dom_restriction(C!11, B!12)))) <=> in(ordered_pair(D, E), C))))) | (~((C = relation_rng_restriction(A!13, relation_dom_restriction(C!11, B!12))) | (((~in(tptp_fun_E_2(C, relation_dom_restriction(C!11, B!12), A!13), A!13)) | (~in(ordered_pair(tptp_fun_D_3(C, relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(C, relation_dom_restriction(C!11, B!12), A!13)), relation_dom_restriction(C!11, B!12)))) <=> in(ordered_pair(tptp_fun_D_3(C, relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(C, relation_dom_restriction(C!11, B!12), A!13)), C))))))))) <=> ((~![A: $i, B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~((~((C = relation_rng_restriction(A, B)) | (((~in(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)), B))) <=> in(ordered_pair(tptp_fun_D_3(C, B, A), tptp_fun_E_2(C, B, A)), C)))) | (~((~(C = relation_rng_restriction(A, B))) | ![D: $i, E: $i] : (~(((~in(E, A)) | (~in(ordered_pair(D, E), B))) <=> in(ordered_pair(D, E), C)))))))))) | (~relation(relation_dom_restriction(C!11, B!12))) | ![C: $i] : ((~relation(C)) | (~((~((~(C = relation_rng_restriction(A!13, relation_dom_restriction(C!11, B!12)))) | ![D: $i, E: $i] : (~(((~in(E, A!13)) | (~in(ordered_pair(D, E), relation_dom_restriction(C!11, B!12)))) <=> in(ordered_pair(D, E), C))))) | (~((C = relation_rng_restriction(A!13, relation_dom_restriction(C!11, B!12))) | (((~in(tptp_fun_E_2(C, relation_dom_restriction(C!11, B!12), A!13), A!13)) | (~in(ordered_pair(tptp_fun_D_3(C, relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(C, relation_dom_restriction(C!11, B!12), A!13)), relation_dom_restriction(C!11, B!12)))) <=> in(ordered_pair(tptp_fun_D_3(C, relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(C, relation_dom_restriction(C!11, B!12), A!13)), C))))))))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(100,plain,
% 0.19/0.43 (((~relation(relation_dom_restriction(C!11, B!12))) | ![C: $i] : ((~relation(C)) | (~((~((C = relation_rng_restriction(A!13, relation_dom_restriction(C!11, B!12))) | (((~in(tptp_fun_E_2(C, relation_dom_restriction(C!11, B!12), A!13), A!13)) | (~in(ordered_pair(tptp_fun_D_3(C, relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(C, relation_dom_restriction(C!11, B!12), A!13)), relation_dom_restriction(C!11, B!12)))) <=> in(ordered_pair(tptp_fun_D_3(C, relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(C, relation_dom_restriction(C!11, B!12), A!13)), C)))) | (~((~(C = relation_rng_restriction(A!13, relation_dom_restriction(C!11, B!12)))) | ![D: $i, E: $i] : (~(((~in(E, A!13)) | (~in(ordered_pair(D, E), relation_dom_restriction(C!11, B!12)))) <=> in(ordered_pair(D, E), C))))))))) <=> ((~relation(relation_dom_restriction(C!11, B!12))) | ![C: $i] : ((~relation(C)) | (~((~((~(C = relation_rng_restriction(A!13, relation_dom_restriction(C!11, B!12)))) | ![D: $i, E: $i] : (~(((~in(E, A!13)) | (~in(ordered_pair(D, E), relation_dom_restriction(C!11, B!12)))) <=> in(ordered_pair(D, E), C))))) | (~((C = relation_rng_restriction(A!13, relation_dom_restriction(C!11, B!12))) | (((~in(tptp_fun_E_2(C, relation_dom_restriction(C!11, B!12), A!13), A!13)) | (~in(ordered_pair(tptp_fun_D_3(C, relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(C, relation_dom_restriction(C!11, B!12), A!13)), relation_dom_restriction(C!11, B!12)))) <=> in(ordered_pair(tptp_fun_D_3(C, relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(C, relation_dom_restriction(C!11, B!12), A!13)), C))))))))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(101,plain,
% 0.19/0.43 (((~![A: $i, B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~((~((C = relation_rng_restriction(A, B)) | (((~in(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)), B))) <=> in(ordered_pair(tptp_fun_D_3(C, B, A), tptp_fun_E_2(C, B, A)), C)))) | (~((~(C = relation_rng_restriction(A, B))) | ![D: $i, E: $i] : (~(((~in(E, A)) | (~in(ordered_pair(D, E), B))) <=> in(ordered_pair(D, E), C)))))))))) | ((~relation(relation_dom_restriction(C!11, B!12))) | ![C: $i] : ((~relation(C)) | (~((~((C = relation_rng_restriction(A!13, relation_dom_restriction(C!11, B!12))) | (((~in(tptp_fun_E_2(C, relation_dom_restriction(C!11, B!12), A!13), A!13)) | (~in(ordered_pair(tptp_fun_D_3(C, relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(C, relation_dom_restriction(C!11, B!12), A!13)), relation_dom_restriction(C!11, B!12)))) <=> in(ordered_pair(tptp_fun_D_3(C, relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(C, relation_dom_restriction(C!11, B!12), A!13)), C)))) | (~((~(C = relation_rng_restriction(A!13, relation_dom_restriction(C!11, B!12)))) | ![D: $i, E: $i] : (~(((~in(E, A!13)) | (~in(ordered_pair(D, E), relation_dom_restriction(C!11, B!12)))) <=> in(ordered_pair(D, E), C)))))))))) <=> ((~![A: $i, B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~((~((C = relation_rng_restriction(A, B)) | (((~in(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)), B))) <=> in(ordered_pair(tptp_fun_D_3(C, B, A), tptp_fun_E_2(C, B, A)), C)))) | (~((~(C = relation_rng_restriction(A, B))) | ![D: $i, E: $i] : (~(((~in(E, A)) | (~in(ordered_pair(D, E), B))) <=> in(ordered_pair(D, E), C)))))))))) | ((~relation(relation_dom_restriction(C!11, B!12))) | ![C: $i] : ((~relation(C)) | (~((~((~(C = relation_rng_restriction(A!13, relation_dom_restriction(C!11, B!12)))) | ![D: $i, E: $i] : (~(((~in(E, A!13)) | (~in(ordered_pair(D, E), relation_dom_restriction(C!11, B!12)))) <=> in(ordered_pair(D, E), C))))) | (~((C = relation_rng_restriction(A!13, relation_dom_restriction(C!11, B!12))) | (((~in(tptp_fun_E_2(C, relation_dom_restriction(C!11, B!12), A!13), A!13)) | (~in(ordered_pair(tptp_fun_D_3(C, relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(C, relation_dom_restriction(C!11, B!12), A!13)), relation_dom_restriction(C!11, B!12)))) <=> in(ordered_pair(tptp_fun_D_3(C, relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(C, relation_dom_restriction(C!11, B!12), A!13)), C)))))))))),
% 0.19/0.43 inference(monotonicity,[status(thm)],[100])).
% 0.19/0.43 tff(102,plain,
% 0.19/0.43 (((~![A: $i, B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~((~((C = relation_rng_restriction(A, B)) | (((~in(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)), B))) <=> in(ordered_pair(tptp_fun_D_3(C, B, A), tptp_fun_E_2(C, B, A)), C)))) | (~((~(C = relation_rng_restriction(A, B))) | ![D: $i, E: $i] : (~(((~in(E, A)) | (~in(ordered_pair(D, E), B))) <=> in(ordered_pair(D, E), C)))))))))) | ((~relation(relation_dom_restriction(C!11, B!12))) | ![C: $i] : ((~relation(C)) | (~((~((C = relation_rng_restriction(A!13, relation_dom_restriction(C!11, B!12))) | (((~in(tptp_fun_E_2(C, relation_dom_restriction(C!11, B!12), A!13), A!13)) | (~in(ordered_pair(tptp_fun_D_3(C, relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(C, relation_dom_restriction(C!11, B!12), A!13)), relation_dom_restriction(C!11, B!12)))) <=> in(ordered_pair(tptp_fun_D_3(C, relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(C, relation_dom_restriction(C!11, B!12), A!13)), C)))) | (~((~(C = relation_rng_restriction(A!13, relation_dom_restriction(C!11, B!12)))) | ![D: $i, E: $i] : (~(((~in(E, A!13)) | (~in(ordered_pair(D, E), relation_dom_restriction(C!11, B!12)))) <=> in(ordered_pair(D, E), C)))))))))) <=> ((~![A: $i, B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~((~((C = relation_rng_restriction(A, B)) | (((~in(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)), B))) <=> in(ordered_pair(tptp_fun_D_3(C, B, A), tptp_fun_E_2(C, B, A)), C)))) | (~((~(C = relation_rng_restriction(A, B))) | ![D: $i, E: $i] : (~(((~in(E, A)) | (~in(ordered_pair(D, E), B))) <=> in(ordered_pair(D, E), C)))))))))) | (~relation(relation_dom_restriction(C!11, B!12))) | ![C: $i] : ((~relation(C)) | (~((~((~(C = relation_rng_restriction(A!13, relation_dom_restriction(C!11, B!12)))) | ![D: $i, E: $i] : (~(((~in(E, A!13)) | (~in(ordered_pair(D, E), relation_dom_restriction(C!11, B!12)))) <=> in(ordered_pair(D, E), C))))) | (~((C = relation_rng_restriction(A!13, relation_dom_restriction(C!11, B!12))) | (((~in(tptp_fun_E_2(C, relation_dom_restriction(C!11, B!12), A!13), A!13)) | (~in(ordered_pair(tptp_fun_D_3(C, relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(C, relation_dom_restriction(C!11, B!12), A!13)), relation_dom_restriction(C!11, B!12)))) <=> in(ordered_pair(tptp_fun_D_3(C, relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(C, relation_dom_restriction(C!11, B!12), A!13)), C))))))))),
% 0.19/0.43 inference(transitivity,[status(thm)],[101, 99])).
% 0.19/0.43 tff(103,plain,
% 0.19/0.43 ((~![A: $i, B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~((~((C = relation_rng_restriction(A, B)) | (((~in(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)), B))) <=> in(ordered_pair(tptp_fun_D_3(C, B, A), tptp_fun_E_2(C, B, A)), C)))) | (~((~(C = relation_rng_restriction(A, B))) | ![D: $i, E: $i] : (~(((~in(E, A)) | (~in(ordered_pair(D, E), B))) <=> in(ordered_pair(D, E), C)))))))))) | ((~relation(relation_dom_restriction(C!11, B!12))) | ![C: $i] : ((~relation(C)) | (~((~((C = relation_rng_restriction(A!13, relation_dom_restriction(C!11, B!12))) | (((~in(tptp_fun_E_2(C, relation_dom_restriction(C!11, B!12), A!13), A!13)) | (~in(ordered_pair(tptp_fun_D_3(C, relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(C, relation_dom_restriction(C!11, B!12), A!13)), relation_dom_restriction(C!11, B!12)))) <=> in(ordered_pair(tptp_fun_D_3(C, relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(C, relation_dom_restriction(C!11, B!12), A!13)), C)))) | (~((~(C = relation_rng_restriction(A!13, relation_dom_restriction(C!11, B!12)))) | ![D: $i, E: $i] : (~(((~in(E, A!13)) | (~in(ordered_pair(D, E), relation_dom_restriction(C!11, B!12)))) <=> in(ordered_pair(D, E), C)))))))))),
% 0.19/0.44 inference(quant_inst,[status(thm)],[])).
% 0.19/0.44 tff(104,plain,
% 0.19/0.44 ((~![A: $i, B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~((~((C = relation_rng_restriction(A, B)) | (((~in(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)), B))) <=> in(ordered_pair(tptp_fun_D_3(C, B, A), tptp_fun_E_2(C, B, A)), C)))) | (~((~(C = relation_rng_restriction(A, B))) | ![D: $i, E: $i] : (~(((~in(E, A)) | (~in(ordered_pair(D, E), B))) <=> in(ordered_pair(D, E), C)))))))))) | (~relation(relation_dom_restriction(C!11, B!12))) | ![C: $i] : ((~relation(C)) | (~((~((~(C = relation_rng_restriction(A!13, relation_dom_restriction(C!11, B!12)))) | ![D: $i, E: $i] : (~(((~in(E, A!13)) | (~in(ordered_pair(D, E), relation_dom_restriction(C!11, B!12)))) <=> in(ordered_pair(D, E), C))))) | (~((C = relation_rng_restriction(A!13, relation_dom_restriction(C!11, B!12))) | (((~in(tptp_fun_E_2(C, relation_dom_restriction(C!11, B!12), A!13), A!13)) | (~in(ordered_pair(tptp_fun_D_3(C, relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(C, relation_dom_restriction(C!11, B!12), A!13)), relation_dom_restriction(C!11, B!12)))) <=> in(ordered_pair(tptp_fun_D_3(C, relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(C, relation_dom_restriction(C!11, B!12), A!13)), C)))))))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[103, 102])).
% 0.19/0.44 tff(105,plain,
% 0.19/0.44 ((~relation(relation_dom_restriction(C!11, B!12))) | ![C: $i] : ((~relation(C)) | (~((~((~(C = relation_rng_restriction(A!13, relation_dom_restriction(C!11, B!12)))) | ![D: $i, E: $i] : (~(((~in(E, A!13)) | (~in(ordered_pair(D, E), relation_dom_restriction(C!11, B!12)))) <=> in(ordered_pair(D, E), C))))) | (~((C = relation_rng_restriction(A!13, relation_dom_restriction(C!11, B!12))) | (((~in(tptp_fun_E_2(C, relation_dom_restriction(C!11, B!12), A!13), A!13)) | (~in(ordered_pair(tptp_fun_D_3(C, relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(C, relation_dom_restriction(C!11, B!12), A!13)), relation_dom_restriction(C!11, B!12)))) <=> in(ordered_pair(tptp_fun_D_3(C, relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(C, relation_dom_restriction(C!11, B!12), A!13)), C)))))))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[104, 98])).
% 0.19/0.44 tff(106,plain,
% 0.19/0.44 (![C: $i] : ((~relation(C)) | (~((~((~(C = relation_rng_restriction(A!13, relation_dom_restriction(C!11, B!12)))) | ![D: $i, E: $i] : (~(((~in(E, A!13)) | (~in(ordered_pair(D, E), relation_dom_restriction(C!11, B!12)))) <=> in(ordered_pair(D, E), C))))) | (~((C = relation_rng_restriction(A!13, relation_dom_restriction(C!11, B!12))) | (((~in(tptp_fun_E_2(C, relation_dom_restriction(C!11, B!12), A!13), A!13)) | (~in(ordered_pair(tptp_fun_D_3(C, relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(C, relation_dom_restriction(C!11, B!12), A!13)), relation_dom_restriction(C!11, B!12)))) <=> in(ordered_pair(tptp_fun_D_3(C, relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(C, relation_dom_restriction(C!11, B!12), A!13)), C)))))))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[105, 24])).
% 0.19/0.44 tff(107,plain,
% 0.19/0.44 (((~![C: $i] : ((~relation(C)) | (~((~((~(C = relation_rng_restriction(A!13, relation_dom_restriction(C!11, B!12)))) | ![D: $i, E: $i] : (~(((~in(E, A!13)) | (~in(ordered_pair(D, E), relation_dom_restriction(C!11, B!12)))) <=> in(ordered_pair(D, E), C))))) | (~((C = relation_rng_restriction(A!13, relation_dom_restriction(C!11, B!12))) | (((~in(tptp_fun_E_2(C, relation_dom_restriction(C!11, B!12), A!13), A!13)) | (~in(ordered_pair(tptp_fun_D_3(C, relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(C, relation_dom_restriction(C!11, B!12), A!13)), relation_dom_restriction(C!11, B!12)))) <=> in(ordered_pair(tptp_fun_D_3(C, relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(C, relation_dom_restriction(C!11, B!12), A!13)), C)))))))) | ((~relation(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12))) | (~((~((~(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12) = relation_rng_restriction(A!13, relation_dom_restriction(C!11, B!12)))) | ![D: $i, E: $i] : (~(((~in(E, A!13)) | (~in(ordered_pair(D, E), relation_dom_restriction(C!11, B!12)))) <=> in(ordered_pair(D, E), relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12)))))) | (~((relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12) = relation_rng_restriction(A!13, relation_dom_restriction(C!11, B!12))) | (((~in(tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), A!13)) | (~in(ordered_pair(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13)), relation_dom_restriction(C!11, B!12)))) <=> in(ordered_pair(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13)), relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12))))))))) <=> ((~![C: $i] : ((~relation(C)) | (~((~((~(C = relation_rng_restriction(A!13, relation_dom_restriction(C!11, B!12)))) | ![D: $i, E: $i] : (~(((~in(E, A!13)) | (~in(ordered_pair(D, E), relation_dom_restriction(C!11, B!12)))) <=> in(ordered_pair(D, E), C))))) | (~((C = relation_rng_restriction(A!13, relation_dom_restriction(C!11, B!12))) | (((~in(tptp_fun_E_2(C, relation_dom_restriction(C!11, B!12), A!13), A!13)) | (~in(ordered_pair(tptp_fun_D_3(C, relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(C, relation_dom_restriction(C!11, B!12), A!13)), relation_dom_restriction(C!11, B!12)))) <=> in(ordered_pair(tptp_fun_D_3(C, relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(C, relation_dom_restriction(C!11, B!12), A!13)), C)))))))) | (~relation(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12))) | (~((~((~(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12) = relation_rng_restriction(A!13, relation_dom_restriction(C!11, B!12)))) | ![D: $i, E: $i] : (~(((~in(E, A!13)) | (~in(ordered_pair(D, E), relation_dom_restriction(C!11, B!12)))) <=> in(ordered_pair(D, E), relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12)))))) | (~((relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12) = relation_rng_restriction(A!13, relation_dom_restriction(C!11, B!12))) | (((~in(tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), A!13)) | (~in(ordered_pair(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13)), relation_dom_restriction(C!11, B!12)))) <=> in(ordered_pair(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13)), relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12))))))))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(108,plain,
% 0.19/0.44 ((~![C: $i] : ((~relation(C)) | (~((~((~(C = relation_rng_restriction(A!13, relation_dom_restriction(C!11, B!12)))) | ![D: $i, E: $i] : (~(((~in(E, A!13)) | (~in(ordered_pair(D, E), relation_dom_restriction(C!11, B!12)))) <=> in(ordered_pair(D, E), C))))) | (~((C = relation_rng_restriction(A!13, relation_dom_restriction(C!11, B!12))) | (((~in(tptp_fun_E_2(C, relation_dom_restriction(C!11, B!12), A!13), A!13)) | (~in(ordered_pair(tptp_fun_D_3(C, relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(C, relation_dom_restriction(C!11, B!12), A!13)), relation_dom_restriction(C!11, B!12)))) <=> in(ordered_pair(tptp_fun_D_3(C, relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(C, relation_dom_restriction(C!11, B!12), A!13)), C)))))))) | ((~relation(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12))) | (~((~((~(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12) = relation_rng_restriction(A!13, relation_dom_restriction(C!11, B!12)))) | ![D: $i, E: $i] : (~(((~in(E, A!13)) | (~in(ordered_pair(D, E), relation_dom_restriction(C!11, B!12)))) <=> in(ordered_pair(D, E), relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12)))))) | (~((relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12) = relation_rng_restriction(A!13, relation_dom_restriction(C!11, B!12))) | (((~in(tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), A!13)) | (~in(ordered_pair(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13)), relation_dom_restriction(C!11, B!12)))) <=> in(ordered_pair(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13)), relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12))))))))),
% 0.19/0.44 inference(quant_inst,[status(thm)],[])).
% 0.19/0.44 tff(109,plain,
% 0.19/0.44 ((~![C: $i] : ((~relation(C)) | (~((~((~(C = relation_rng_restriction(A!13, relation_dom_restriction(C!11, B!12)))) | ![D: $i, E: $i] : (~(((~in(E, A!13)) | (~in(ordered_pair(D, E), relation_dom_restriction(C!11, B!12)))) <=> in(ordered_pair(D, E), C))))) | (~((C = relation_rng_restriction(A!13, relation_dom_restriction(C!11, B!12))) | (((~in(tptp_fun_E_2(C, relation_dom_restriction(C!11, B!12), A!13), A!13)) | (~in(ordered_pair(tptp_fun_D_3(C, relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(C, relation_dom_restriction(C!11, B!12), A!13)), relation_dom_restriction(C!11, B!12)))) <=> in(ordered_pair(tptp_fun_D_3(C, relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(C, relation_dom_restriction(C!11, B!12), A!13)), C)))))))) | (~relation(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12))) | (~((~((~(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12) = relation_rng_restriction(A!13, relation_dom_restriction(C!11, B!12)))) | ![D: $i, E: $i] : (~(((~in(E, A!13)) | (~in(ordered_pair(D, E), relation_dom_restriction(C!11, B!12)))) <=> in(ordered_pair(D, E), relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12)))))) | (~((relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12) = relation_rng_restriction(A!13, relation_dom_restriction(C!11, B!12))) | (((~in(tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), A!13)) | (~in(ordered_pair(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13)), relation_dom_restriction(C!11, B!12)))) <=> in(ordered_pair(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13)), relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12)))))))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[108, 107])).
% 0.19/0.45 tff(110,plain,
% 0.19/0.45 (~((~((~(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12) = relation_rng_restriction(A!13, relation_dom_restriction(C!11, B!12)))) | ![D: $i, E: $i] : (~(((~in(E, A!13)) | (~in(ordered_pair(D, E), relation_dom_restriction(C!11, B!12)))) <=> in(ordered_pair(D, E), relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12)))))) | (~((relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12) = relation_rng_restriction(A!13, relation_dom_restriction(C!11, B!12))) | (((~in(tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), A!13)) | (~in(ordered_pair(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13)), relation_dom_restriction(C!11, B!12)))) <=> in(ordered_pair(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13)), relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12))))))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[109, 106, 79])).
% 0.19/0.45 tff(111,plain,
% 0.19/0.45 (((~((~(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12) = relation_rng_restriction(A!13, relation_dom_restriction(C!11, B!12)))) | ![D: $i, E: $i] : (~(((~in(E, A!13)) | (~in(ordered_pair(D, E), relation_dom_restriction(C!11, B!12)))) <=> in(ordered_pair(D, E), relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12)))))) | (~((relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12) = relation_rng_restriction(A!13, relation_dom_restriction(C!11, B!12))) | (((~in(tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), A!13)) | (~in(ordered_pair(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13)), relation_dom_restriction(C!11, B!12)))) <=> in(ordered_pair(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13)), relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12)))))) | ((relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12) = relation_rng_restriction(A!13, relation_dom_restriction(C!11, B!12))) | (((~in(tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), A!13)) | (~in(ordered_pair(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13)), relation_dom_restriction(C!11, B!12)))) <=> in(ordered_pair(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13)), relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12))))),
% 0.19/0.45 inference(tautology,[status(thm)],[])).
% 0.19/0.45 tff(112,plain,
% 0.19/0.45 ((relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12) = relation_rng_restriction(A!13, relation_dom_restriction(C!11, B!12))) | (((~in(tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), A!13)) | (~in(ordered_pair(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13)), relation_dom_restriction(C!11, B!12)))) <=> in(ordered_pair(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13)), relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12)))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[111, 110])).
% 0.19/0.45 tff(113,plain,
% 0.19/0.45 (~(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12) = relation_rng_restriction(A!13, relation_dom_restriction(C!11, B!12)))),
% 0.19/0.45 inference(or_elim,[status(thm)],[9])).
% 0.19/0.45 tff(114,plain,
% 0.19/0.45 ((~((relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12) = relation_rng_restriction(A!13, relation_dom_restriction(C!11, B!12))) | (((~in(tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), A!13)) | (~in(ordered_pair(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13)), relation_dom_restriction(C!11, B!12)))) <=> in(ordered_pair(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13)), relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12))))) | (relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12) = relation_rng_restriction(A!13, relation_dom_restriction(C!11, B!12))) | (((~in(tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), A!13)) | (~in(ordered_pair(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13)), relation_dom_restriction(C!11, B!12)))) <=> in(ordered_pair(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13)), relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12)))),
% 0.19/0.45 inference(tautology,[status(thm)],[])).
% 0.19/0.45 tff(115,plain,
% 0.19/0.45 ((~((relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12) = relation_rng_restriction(A!13, relation_dom_restriction(C!11, B!12))) | (((~in(tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), A!13)) | (~in(ordered_pair(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13)), relation_dom_restriction(C!11, B!12)))) <=> in(ordered_pair(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13)), relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12))))) | (((~in(tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), A!13)) | (~in(ordered_pair(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13)), relation_dom_restriction(C!11, B!12)))) <=> in(ordered_pair(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13)), relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12)))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[114, 113])).
% 0.19/0.45 tff(116,plain,
% 0.19/0.45 (((~in(tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), A!13)) | (~in(ordered_pair(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13)), relation_dom_restriction(C!11, B!12)))) <=> in(ordered_pair(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13)), relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[115, 112])).
% 0.19/0.45 tff(117,plain,
% 0.19/0.45 ((~(((~in(tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), A!13)) | (~in(ordered_pair(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13)), relation_dom_restriction(C!11, B!12)))) <=> in(ordered_pair(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13)), relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12)))) | (~((~in(tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), A!13)) | (~in(ordered_pair(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13)), relation_dom_restriction(C!11, B!12))))) | in(ordered_pair(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13)), relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12))),
% 0.19/0.45 inference(tautology,[status(thm)],[])).
% 0.19/0.45 tff(118,plain,
% 0.19/0.45 ((~((~in(tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), A!13)) | (~in(ordered_pair(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13)), relation_dom_restriction(C!11, B!12))))) | in(ordered_pair(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13)), relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[117, 116])).
% 0.19/0.45 tff(119,plain,
% 0.19/0.45 (in(ordered_pair(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13)), relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[118, 61])).
% 0.19/0.45 tff(120,plain,
% 0.19/0.45 (((~![A: $i] : ((~relation(A)) | ![B: $i, C: $i] : ((~relation(C)) | (~((~((C = relation_dom_restriction(A, B)) | (((~in(tptp_fun_D_1(C, B, A), B)) | (~in(ordered_pair(tptp_fun_D_1(C, B, A), tptp_fun_E_0(C, B, A)), A))) <=> in(ordered_pair(tptp_fun_D_1(C, B, A), tptp_fun_E_0(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(relation_rng_restriction(A!13, C!11))) | ![B: $i, C: $i] : ((~relation(C)) | (~((~((~(C = relation_dom_restriction(relation_rng_restriction(A!13, C!11), B))) | ![D: $i, E: $i] : (~(((~in(D, B)) | (~in(ordered_pair(D, E), relation_rng_restriction(A!13, C!11)))) <=> in(ordered_pair(D, E), C))))) | (~((C = relation_dom_restriction(relation_rng_restriction(A!13, C!11), B)) | (((~in(tptp_fun_D_1(C, B, relation_rng_restriction(A!13, C!11)), B)) | (~in(ordered_pair(tptp_fun_D_1(C, B, relation_rng_restriction(A!13, C!11)), tptp_fun_E_0(C, B, relation_rng_restriction(A!13, C!11))), relation_rng_restriction(A!13, C!11)))) <=> in(ordered_pair(tptp_fun_D_1(C, B, relation_rng_restriction(A!13, C!11)), tptp_fun_E_0(C, B, relation_rng_restriction(A!13, C!11))), C))))))))) <=> ((~![A: $i] : ((~relation(A)) | ![B: $i, C: $i] : ((~relation(C)) | (~((~((C = relation_dom_restriction(A, B)) | (((~in(tptp_fun_D_1(C, B, A), B)) | (~in(ordered_pair(tptp_fun_D_1(C, B, A), tptp_fun_E_0(C, B, A)), A))) <=> in(ordered_pair(tptp_fun_D_1(C, B, A), tptp_fun_E_0(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(relation_rng_restriction(A!13, C!11))) | ![B: $i, C: $i] : ((~relation(C)) | (~((~((~(C = relation_dom_restriction(relation_rng_restriction(A!13, C!11), B))) | ![D: $i, E: $i] : (~(((~in(D, B)) | (~in(ordered_pair(D, E), relation_rng_restriction(A!13, C!11)))) <=> in(ordered_pair(D, E), C))))) | (~((C = relation_dom_restriction(relation_rng_restriction(A!13, C!11), B)) | (((~in(tptp_fun_D_1(C, B, relation_rng_restriction(A!13, C!11)), B)) | (~in(ordered_pair(tptp_fun_D_1(C, B, relation_rng_restriction(A!13, C!11)), tptp_fun_E_0(C, B, relation_rng_restriction(A!13, C!11))), relation_rng_restriction(A!13, C!11)))) <=> in(ordered_pair(tptp_fun_D_1(C, B, relation_rng_restriction(A!13, C!11)), tptp_fun_E_0(C, B, relation_rng_restriction(A!13, C!11))), C))))))))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(121,plain,
% 0.19/0.45 (((~relation(relation_rng_restriction(A!13, C!11))) | ![B: $i, C: $i] : ((~relation(C)) | (~((~((C = relation_dom_restriction(relation_rng_restriction(A!13, C!11), B)) | (((~in(tptp_fun_D_1(C, B, relation_rng_restriction(A!13, C!11)), B)) | (~in(ordered_pair(tptp_fun_D_1(C, B, relation_rng_restriction(A!13, C!11)), tptp_fun_E_0(C, B, relation_rng_restriction(A!13, C!11))), relation_rng_restriction(A!13, C!11)))) <=> in(ordered_pair(tptp_fun_D_1(C, B, relation_rng_restriction(A!13, C!11)), tptp_fun_E_0(C, B, relation_rng_restriction(A!13, C!11))), C)))) | (~((~(C = relation_dom_restriction(relation_rng_restriction(A!13, C!11), B))) | ![D: $i, E: $i] : (~(((~in(D, B)) | (~in(ordered_pair(D, E), relation_rng_restriction(A!13, C!11)))) <=> in(ordered_pair(D, E), C))))))))) <=> ((~relation(relation_rng_restriction(A!13, C!11))) | ![B: $i, C: $i] : ((~relation(C)) | (~((~((~(C = relation_dom_restriction(relation_rng_restriction(A!13, C!11), B))) | ![D: $i, E: $i] : (~(((~in(D, B)) | (~in(ordered_pair(D, E), relation_rng_restriction(A!13, C!11)))) <=> in(ordered_pair(D, E), C))))) | (~((C = relation_dom_restriction(relation_rng_restriction(A!13, C!11), B)) | (((~in(tptp_fun_D_1(C, B, relation_rng_restriction(A!13, C!11)), B)) | (~in(ordered_pair(tptp_fun_D_1(C, B, relation_rng_restriction(A!13, C!11)), tptp_fun_E_0(C, B, relation_rng_restriction(A!13, C!11))), relation_rng_restriction(A!13, C!11)))) <=> in(ordered_pair(tptp_fun_D_1(C, B, relation_rng_restriction(A!13, C!11)), tptp_fun_E_0(C, B, relation_rng_restriction(A!13, C!11))), C))))))))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(122,plain,
% 0.19/0.46 (((~![A: $i] : ((~relation(A)) | ![B: $i, C: $i] : ((~relation(C)) | (~((~((C = relation_dom_restriction(A, B)) | (((~in(tptp_fun_D_1(C, B, A), B)) | (~in(ordered_pair(tptp_fun_D_1(C, B, A), tptp_fun_E_0(C, B, A)), A))) <=> in(ordered_pair(tptp_fun_D_1(C, B, A), tptp_fun_E_0(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(relation_rng_restriction(A!13, C!11))) | ![B: $i, C: $i] : ((~relation(C)) | (~((~((C = relation_dom_restriction(relation_rng_restriction(A!13, C!11), B)) | (((~in(tptp_fun_D_1(C, B, relation_rng_restriction(A!13, C!11)), B)) | (~in(ordered_pair(tptp_fun_D_1(C, B, relation_rng_restriction(A!13, C!11)), tptp_fun_E_0(C, B, relation_rng_restriction(A!13, C!11))), relation_rng_restriction(A!13, C!11)))) <=> in(ordered_pair(tptp_fun_D_1(C, B, relation_rng_restriction(A!13, C!11)), tptp_fun_E_0(C, B, relation_rng_restriction(A!13, C!11))), C)))) | (~((~(C = relation_dom_restriction(relation_rng_restriction(A!13, C!11), B))) | ![D: $i, E: $i] : (~(((~in(D, B)) | (~in(ordered_pair(D, E), relation_rng_restriction(A!13, C!11)))) <=> 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_1(C, B, A), B)) | (~in(ordered_pair(tptp_fun_D_1(C, B, A), tptp_fun_E_0(C, B, A)), A))) <=> in(ordered_pair(tptp_fun_D_1(C, B, A), tptp_fun_E_0(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(relation_rng_restriction(A!13, C!11))) | ![B: $i, C: $i] : ((~relation(C)) | (~((~((~(C = relation_dom_restriction(relation_rng_restriction(A!13, C!11), B))) | ![D: $i, E: $i] : (~(((~in(D, B)) | (~in(ordered_pair(D, E), relation_rng_restriction(A!13, C!11)))) <=> in(ordered_pair(D, E), C))))) | (~((C = relation_dom_restriction(relation_rng_restriction(A!13, C!11), B)) | (((~in(tptp_fun_D_1(C, B, relation_rng_restriction(A!13, C!11)), B)) | (~in(ordered_pair(tptp_fun_D_1(C, B, relation_rng_restriction(A!13, C!11)), tptp_fun_E_0(C, B, relation_rng_restriction(A!13, C!11))), relation_rng_restriction(A!13, C!11)))) <=> in(ordered_pair(tptp_fun_D_1(C, B, relation_rng_restriction(A!13, C!11)), tptp_fun_E_0(C, B, relation_rng_restriction(A!13, C!11))), C)))))))))),
% 0.19/0.46 inference(monotonicity,[status(thm)],[121])).
% 0.19/0.46 tff(123,plain,
% 0.19/0.46 (((~![A: $i] : ((~relation(A)) | ![B: $i, C: $i] : ((~relation(C)) | (~((~((C = relation_dom_restriction(A, B)) | (((~in(tptp_fun_D_1(C, B, A), B)) | (~in(ordered_pair(tptp_fun_D_1(C, B, A), tptp_fun_E_0(C, B, A)), A))) <=> in(ordered_pair(tptp_fun_D_1(C, B, A), tptp_fun_E_0(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(relation_rng_restriction(A!13, C!11))) | ![B: $i, C: $i] : ((~relation(C)) | (~((~((C = relation_dom_restriction(relation_rng_restriction(A!13, C!11), B)) | (((~in(tptp_fun_D_1(C, B, relation_rng_restriction(A!13, C!11)), B)) | (~in(ordered_pair(tptp_fun_D_1(C, B, relation_rng_restriction(A!13, C!11)), tptp_fun_E_0(C, B, relation_rng_restriction(A!13, C!11))), relation_rng_restriction(A!13, C!11)))) <=> in(ordered_pair(tptp_fun_D_1(C, B, relation_rng_restriction(A!13, C!11)), tptp_fun_E_0(C, B, relation_rng_restriction(A!13, C!11))), C)))) | (~((~(C = relation_dom_restriction(relation_rng_restriction(A!13, C!11), B))) | ![D: $i, E: $i] : (~(((~in(D, B)) | (~in(ordered_pair(D, E), relation_rng_restriction(A!13, C!11)))) <=> 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_1(C, B, A), B)) | (~in(ordered_pair(tptp_fun_D_1(C, B, A), tptp_fun_E_0(C, B, A)), A))) <=> in(ordered_pair(tptp_fun_D_1(C, B, A), tptp_fun_E_0(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(relation_rng_restriction(A!13, C!11))) | ![B: $i, C: $i] : ((~relation(C)) | (~((~((~(C = relation_dom_restriction(relation_rng_restriction(A!13, C!11), B))) | ![D: $i, E: $i] : (~(((~in(D, B)) | (~in(ordered_pair(D, E), relation_rng_restriction(A!13, C!11)))) <=> in(ordered_pair(D, E), C))))) | (~((C = relation_dom_restriction(relation_rng_restriction(A!13, C!11), B)) | (((~in(tptp_fun_D_1(C, B, relation_rng_restriction(A!13, C!11)), B)) | (~in(ordered_pair(tptp_fun_D_1(C, B, relation_rng_restriction(A!13, C!11)), tptp_fun_E_0(C, B, relation_rng_restriction(A!13, C!11))), relation_rng_restriction(A!13, C!11)))) <=> in(ordered_pair(tptp_fun_D_1(C, B, relation_rng_restriction(A!13, C!11)), tptp_fun_E_0(C, B, relation_rng_restriction(A!13, C!11))), C))))))))),
% 0.19/0.46 inference(transitivity,[status(thm)],[122, 120])).
% 0.19/0.46 tff(124,plain,
% 0.19/0.46 ((~![A: $i] : ((~relation(A)) | ![B: $i, C: $i] : ((~relation(C)) | (~((~((C = relation_dom_restriction(A, B)) | (((~in(tptp_fun_D_1(C, B, A), B)) | (~in(ordered_pair(tptp_fun_D_1(C, B, A), tptp_fun_E_0(C, B, A)), A))) <=> in(ordered_pair(tptp_fun_D_1(C, B, A), tptp_fun_E_0(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(relation_rng_restriction(A!13, C!11))) | ![B: $i, C: $i] : ((~relation(C)) | (~((~((C = relation_dom_restriction(relation_rng_restriction(A!13, C!11), B)) | (((~in(tptp_fun_D_1(C, B, relation_rng_restriction(A!13, C!11)), B)) | (~in(ordered_pair(tptp_fun_D_1(C, B, relation_rng_restriction(A!13, C!11)), tptp_fun_E_0(C, B, relation_rng_restriction(A!13, C!11))), relation_rng_restriction(A!13, C!11)))) <=> in(ordered_pair(tptp_fun_D_1(C, B, relation_rng_restriction(A!13, C!11)), tptp_fun_E_0(C, B, relation_rng_restriction(A!13, C!11))), C)))) | (~((~(C = relation_dom_restriction(relation_rng_restriction(A!13, C!11), B))) | ![D: $i, E: $i] : (~(((~in(D, B)) | (~in(ordered_pair(D, E), relation_rng_restriction(A!13, C!11)))) <=> in(ordered_pair(D, E), C)))))))))),
% 0.19/0.46 inference(quant_inst,[status(thm)],[])).
% 0.19/0.46 tff(125,plain,
% 0.19/0.46 ((~![A: $i] : ((~relation(A)) | ![B: $i, C: $i] : ((~relation(C)) | (~((~((C = relation_dom_restriction(A, B)) | (((~in(tptp_fun_D_1(C, B, A), B)) | (~in(ordered_pair(tptp_fun_D_1(C, B, A), tptp_fun_E_0(C, B, A)), A))) <=> in(ordered_pair(tptp_fun_D_1(C, B, A), tptp_fun_E_0(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(relation_rng_restriction(A!13, C!11))) | ![B: $i, C: $i] : ((~relation(C)) | (~((~((~(C = relation_dom_restriction(relation_rng_restriction(A!13, C!11), B))) | ![D: $i, E: $i] : (~(((~in(D, B)) | (~in(ordered_pair(D, E), relation_rng_restriction(A!13, C!11)))) <=> in(ordered_pair(D, E), C))))) | (~((C = relation_dom_restriction(relation_rng_restriction(A!13, C!11), B)) | (((~in(tptp_fun_D_1(C, B, relation_rng_restriction(A!13, C!11)), B)) | (~in(ordered_pair(tptp_fun_D_1(C, B, relation_rng_restriction(A!13, C!11)), tptp_fun_E_0(C, B, relation_rng_restriction(A!13, C!11))), relation_rng_restriction(A!13, C!11)))) <=> in(ordered_pair(tptp_fun_D_1(C, B, relation_rng_restriction(A!13, C!11)), tptp_fun_E_0(C, B, relation_rng_restriction(A!13, C!11))), C)))))))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[124, 123])).
% 0.19/0.46 tff(126,plain,
% 0.19/0.46 (![B: $i, C: $i] : ((~relation(C)) | (~((~((~(C = relation_dom_restriction(relation_rng_restriction(A!13, C!11), B))) | ![D: $i, E: $i] : (~(((~in(D, B)) | (~in(ordered_pair(D, E), relation_rng_restriction(A!13, C!11)))) <=> in(ordered_pair(D, E), C))))) | (~((C = relation_dom_restriction(relation_rng_restriction(A!13, C!11), B)) | (((~in(tptp_fun_D_1(C, B, relation_rng_restriction(A!13, C!11)), B)) | (~in(ordered_pair(tptp_fun_D_1(C, B, relation_rng_restriction(A!13, C!11)), tptp_fun_E_0(C, B, relation_rng_restriction(A!13, C!11))), relation_rng_restriction(A!13, C!11)))) <=> in(ordered_pair(tptp_fun_D_1(C, B, relation_rng_restriction(A!13, C!11)), tptp_fun_E_0(C, B, relation_rng_restriction(A!13, C!11))), C)))))))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[125, 43, 75])).
% 0.19/0.46 tff(127,plain,
% 0.19/0.46 (((~![B: $i, C: $i] : ((~relation(C)) | (~((~((~(C = relation_dom_restriction(relation_rng_restriction(A!13, C!11), B))) | ![D: $i, E: $i] : (~(((~in(D, B)) | (~in(ordered_pair(D, E), relation_rng_restriction(A!13, C!11)))) <=> in(ordered_pair(D, E), C))))) | (~((C = relation_dom_restriction(relation_rng_restriction(A!13, C!11), B)) | (((~in(tptp_fun_D_1(C, B, relation_rng_restriction(A!13, C!11)), B)) | (~in(ordered_pair(tptp_fun_D_1(C, B, relation_rng_restriction(A!13, C!11)), tptp_fun_E_0(C, B, relation_rng_restriction(A!13, C!11))), relation_rng_restriction(A!13, C!11)))) <=> in(ordered_pair(tptp_fun_D_1(C, B, relation_rng_restriction(A!13, C!11)), tptp_fun_E_0(C, B, relation_rng_restriction(A!13, C!11))), C)))))))) | ((~relation(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12))) | ![D: $i, E: $i] : (~(((~in(D, B!12)) | (~in(ordered_pair(D, E), relation_rng_restriction(A!13, C!11)))) <=> in(ordered_pair(D, E), relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12)))))) <=> ((~![B: $i, C: $i] : ((~relation(C)) | (~((~((~(C = relation_dom_restriction(relation_rng_restriction(A!13, C!11), B))) | ![D: $i, E: $i] : (~(((~in(D, B)) | (~in(ordered_pair(D, E), relation_rng_restriction(A!13, C!11)))) <=> in(ordered_pair(D, E), C))))) | (~((C = relation_dom_restriction(relation_rng_restriction(A!13, C!11), B)) | (((~in(tptp_fun_D_1(C, B, relation_rng_restriction(A!13, C!11)), B)) | (~in(ordered_pair(tptp_fun_D_1(C, B, relation_rng_restriction(A!13, C!11)), tptp_fun_E_0(C, B, relation_rng_restriction(A!13, C!11))), relation_rng_restriction(A!13, C!11)))) <=> in(ordered_pair(tptp_fun_D_1(C, B, relation_rng_restriction(A!13, C!11)), tptp_fun_E_0(C, B, relation_rng_restriction(A!13, C!11))), C)))))))) | (~relation(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12))) | ![D: $i, E: $i] : (~(((~in(D, B!12)) | (~in(ordered_pair(D, E), relation_rng_restriction(A!13, C!11)))) <=> in(ordered_pair(D, E), relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12)))))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(128,plain,
% 0.19/0.46 (((~relation(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12))) | (~((~((~(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12) = relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12))) | ![D: $i, E: $i] : (~(((~in(D, B!12)) | (~in(ordered_pair(D, E), relation_rng_restriction(A!13, C!11)))) <=> in(ordered_pair(D, E), relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12)))))) | (~((relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12) = relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12)) | (((~in(tptp_fun_D_1(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), B!12, relation_rng_restriction(A!13, C!11)), B!12)) | (~in(ordered_pair(tptp_fun_D_1(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), B!12, relation_rng_restriction(A!13, C!11)), tptp_fun_E_0(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), B!12, relation_rng_restriction(A!13, C!11))), relation_rng_restriction(A!13, C!11)))) <=> in(ordered_pair(tptp_fun_D_1(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), B!12, relation_rng_restriction(A!13, C!11)), tptp_fun_E_0(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), B!12, relation_rng_restriction(A!13, C!11))), relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12)))))))) <=> ((~relation(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12))) | ![D: $i, E: $i] : (~(((~in(D, B!12)) | (~in(ordered_pair(D, E), relation_rng_restriction(A!13, C!11)))) <=> in(ordered_pair(D, E), relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12)))))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(129,plain,
% 0.19/0.46 (((~![B: $i, C: $i] : ((~relation(C)) | (~((~((~(C = relation_dom_restriction(relation_rng_restriction(A!13, C!11), B))) | ![D: $i, E: $i] : (~(((~in(D, B)) | (~in(ordered_pair(D, E), relation_rng_restriction(A!13, C!11)))) <=> in(ordered_pair(D, E), C))))) | (~((C = relation_dom_restriction(relation_rng_restriction(A!13, C!11), B)) | (((~in(tptp_fun_D_1(C, B, relation_rng_restriction(A!13, C!11)), B)) | (~in(ordered_pair(tptp_fun_D_1(C, B, relation_rng_restriction(A!13, C!11)), tptp_fun_E_0(C, B, relation_rng_restriction(A!13, C!11))), relation_rng_restriction(A!13, C!11)))) <=> in(ordered_pair(tptp_fun_D_1(C, B, relation_rng_restriction(A!13, C!11)), tptp_fun_E_0(C, B, relation_rng_restriction(A!13, C!11))), C)))))))) | ((~relation(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12))) | (~((~((~(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12) = relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12))) | ![D: $i, E: $i] : (~(((~in(D, B!12)) | (~in(ordered_pair(D, E), relation_rng_restriction(A!13, C!11)))) <=> in(ordered_pair(D, E), relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12)))))) | (~((relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12) = relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12)) | (((~in(tptp_fun_D_1(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), B!12, relation_rng_restriction(A!13, C!11)), B!12)) | (~in(ordered_pair(tptp_fun_D_1(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), B!12, relation_rng_restriction(A!13, C!11)), tptp_fun_E_0(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), B!12, relation_rng_restriction(A!13, C!11))), relation_rng_restriction(A!13, C!11)))) <=> in(ordered_pair(tptp_fun_D_1(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), B!12, relation_rng_restriction(A!13, C!11)), tptp_fun_E_0(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), B!12, relation_rng_restriction(A!13, C!11))), relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12))))))))) <=> ((~![B: $i, C: $i] : ((~relation(C)) | (~((~((~(C = relation_dom_restriction(relation_rng_restriction(A!13, C!11), B))) | ![D: $i, E: $i] : (~(((~in(D, B)) | (~in(ordered_pair(D, E), relation_rng_restriction(A!13, C!11)))) <=> in(ordered_pair(D, E), C))))) | (~((C = relation_dom_restriction(relation_rng_restriction(A!13, C!11), B)) | (((~in(tptp_fun_D_1(C, B, relation_rng_restriction(A!13, C!11)), B)) | (~in(ordered_pair(tptp_fun_D_1(C, B, relation_rng_restriction(A!13, C!11)), tptp_fun_E_0(C, B, relation_rng_restriction(A!13, C!11))), relation_rng_restriction(A!13, C!11)))) <=> in(ordered_pair(tptp_fun_D_1(C, B, relation_rng_restriction(A!13, C!11)), tptp_fun_E_0(C, B, relation_rng_restriction(A!13, C!11))), C)))))))) | ((~relation(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12))) | ![D: $i, E: $i] : (~(((~in(D, B!12)) | (~in(ordered_pair(D, E), relation_rng_restriction(A!13, C!11)))) <=> in(ordered_pair(D, E), relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12))))))),
% 0.19/0.46 inference(monotonicity,[status(thm)],[128])).
% 0.19/0.46 tff(130,plain,
% 0.19/0.46 (((~![B: $i, C: $i] : ((~relation(C)) | (~((~((~(C = relation_dom_restriction(relation_rng_restriction(A!13, C!11), B))) | ![D: $i, E: $i] : (~(((~in(D, B)) | (~in(ordered_pair(D, E), relation_rng_restriction(A!13, C!11)))) <=> in(ordered_pair(D, E), C))))) | (~((C = relation_dom_restriction(relation_rng_restriction(A!13, C!11), B)) | (((~in(tptp_fun_D_1(C, B, relation_rng_restriction(A!13, C!11)), B)) | (~in(ordered_pair(tptp_fun_D_1(C, B, relation_rng_restriction(A!13, C!11)), tptp_fun_E_0(C, B, relation_rng_restriction(A!13, C!11))), relation_rng_restriction(A!13, C!11)))) <=> in(ordered_pair(tptp_fun_D_1(C, B, relation_rng_restriction(A!13, C!11)), tptp_fun_E_0(C, B, relation_rng_restriction(A!13, C!11))), C)))))))) | ((~relation(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12))) | (~((~((~(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12) = relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12))) | ![D: $i, E: $i] : (~(((~in(D, B!12)) | (~in(ordered_pair(D, E), relation_rng_restriction(A!13, C!11)))) <=> in(ordered_pair(D, E), relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12)))))) | (~((relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12) = relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12)) | (((~in(tptp_fun_D_1(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), B!12, relation_rng_restriction(A!13, C!11)), B!12)) | (~in(ordered_pair(tptp_fun_D_1(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), B!12, relation_rng_restriction(A!13, C!11)), tptp_fun_E_0(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), B!12, relation_rng_restriction(A!13, C!11))), relation_rng_restriction(A!13, C!11)))) <=> in(ordered_pair(tptp_fun_D_1(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), B!12, relation_rng_restriction(A!13, C!11)), tptp_fun_E_0(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), B!12, relation_rng_restriction(A!13, C!11))), relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12))))))))) <=> ((~![B: $i, C: $i] : ((~relation(C)) | (~((~((~(C = relation_dom_restriction(relation_rng_restriction(A!13, C!11), B))) | ![D: $i, E: $i] : (~(((~in(D, B)) | (~in(ordered_pair(D, E), relation_rng_restriction(A!13, C!11)))) <=> in(ordered_pair(D, E), C))))) | (~((C = relation_dom_restriction(relation_rng_restriction(A!13, C!11), B)) | (((~in(tptp_fun_D_1(C, B, relation_rng_restriction(A!13, C!11)), B)) | (~in(ordered_pair(tptp_fun_D_1(C, B, relation_rng_restriction(A!13, C!11)), tptp_fun_E_0(C, B, relation_rng_restriction(A!13, C!11))), relation_rng_restriction(A!13, C!11)))) <=> in(ordered_pair(tptp_fun_D_1(C, B, relation_rng_restriction(A!13, C!11)), tptp_fun_E_0(C, B, relation_rng_restriction(A!13, C!11))), C)))))))) | (~relation(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12))) | ![D: $i, E: $i] : (~(((~in(D, B!12)) | (~in(ordered_pair(D, E), relation_rng_restriction(A!13, C!11)))) <=> in(ordered_pair(D, E), relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12)))))),
% 0.19/0.47 inference(transitivity,[status(thm)],[129, 127])).
% 0.19/0.47 tff(131,plain,
% 0.19/0.47 ((~![B: $i, C: $i] : ((~relation(C)) | (~((~((~(C = relation_dom_restriction(relation_rng_restriction(A!13, C!11), B))) | ![D: $i, E: $i] : (~(((~in(D, B)) | (~in(ordered_pair(D, E), relation_rng_restriction(A!13, C!11)))) <=> in(ordered_pair(D, E), C))))) | (~((C = relation_dom_restriction(relation_rng_restriction(A!13, C!11), B)) | (((~in(tptp_fun_D_1(C, B, relation_rng_restriction(A!13, C!11)), B)) | (~in(ordered_pair(tptp_fun_D_1(C, B, relation_rng_restriction(A!13, C!11)), tptp_fun_E_0(C, B, relation_rng_restriction(A!13, C!11))), relation_rng_restriction(A!13, C!11)))) <=> in(ordered_pair(tptp_fun_D_1(C, B, relation_rng_restriction(A!13, C!11)), tptp_fun_E_0(C, B, relation_rng_restriction(A!13, C!11))), C)))))))) | ((~relation(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12))) | (~((~((~(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12) = relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12))) | ![D: $i, E: $i] : (~(((~in(D, B!12)) | (~in(ordered_pair(D, E), relation_rng_restriction(A!13, C!11)))) <=> in(ordered_pair(D, E), relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12)))))) | (~((relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12) = relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12)) | (((~in(tptp_fun_D_1(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), B!12, relation_rng_restriction(A!13, C!11)), B!12)) | (~in(ordered_pair(tptp_fun_D_1(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), B!12, relation_rng_restriction(A!13, C!11)), tptp_fun_E_0(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), B!12, relation_rng_restriction(A!13, C!11))), relation_rng_restriction(A!13, C!11)))) <=> in(ordered_pair(tptp_fun_D_1(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), B!12, relation_rng_restriction(A!13, C!11)), tptp_fun_E_0(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), B!12, relation_rng_restriction(A!13, C!11))), relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12))))))))),
% 0.19/0.47 inference(quant_inst,[status(thm)],[])).
% 0.19/0.47 tff(132,plain,
% 0.19/0.47 ((~![B: $i, C: $i] : ((~relation(C)) | (~((~((~(C = relation_dom_restriction(relation_rng_restriction(A!13, C!11), B))) | ![D: $i, E: $i] : (~(((~in(D, B)) | (~in(ordered_pair(D, E), relation_rng_restriction(A!13, C!11)))) <=> in(ordered_pair(D, E), C))))) | (~((C = relation_dom_restriction(relation_rng_restriction(A!13, C!11), B)) | (((~in(tptp_fun_D_1(C, B, relation_rng_restriction(A!13, C!11)), B)) | (~in(ordered_pair(tptp_fun_D_1(C, B, relation_rng_restriction(A!13, C!11)), tptp_fun_E_0(C, B, relation_rng_restriction(A!13, C!11))), relation_rng_restriction(A!13, C!11)))) <=> in(ordered_pair(tptp_fun_D_1(C, B, relation_rng_restriction(A!13, C!11)), tptp_fun_E_0(C, B, relation_rng_restriction(A!13, C!11))), C)))))))) | (~relation(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12))) | ![D: $i, E: $i] : (~(((~in(D, B!12)) | (~in(ordered_pair(D, E), relation_rng_restriction(A!13, C!11)))) <=> in(ordered_pair(D, E), relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12))))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[131, 130])).
% 0.19/0.47 tff(133,plain,
% 0.19/0.47 (![D: $i, E: $i] : (~(((~in(D, B!12)) | (~in(ordered_pair(D, E), relation_rng_restriction(A!13, C!11)))) <=> in(ordered_pair(D, E), relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12))))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[132, 79, 126])).
% 0.19/0.47 tff(134,plain,
% 0.19/0.47 ((~![D: $i, E: $i] : (~(((~in(D, B!12)) | (~in(ordered_pair(D, E), relation_rng_restriction(A!13, C!11)))) <=> in(ordered_pair(D, E), relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12))))) | (~(((~in(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), B!12)) | (~in(ordered_pair(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13)), relation_rng_restriction(A!13, C!11)))) <=> in(ordered_pair(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13)), relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12))))),
% 0.19/0.47 inference(quant_inst,[status(thm)],[])).
% 0.19/0.47 tff(135,plain,
% 0.19/0.47 (~(((~in(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), B!12)) | (~in(ordered_pair(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13)), relation_rng_restriction(A!13, C!11)))) <=> in(ordered_pair(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13)), relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12)))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[134, 133])).
% 0.19/0.47 tff(136,plain,
% 0.19/0.47 ((((~in(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), B!12)) | (~in(ordered_pair(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13)), relation_rng_restriction(A!13, C!11)))) <=> in(ordered_pair(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13)), relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12))) | (~((~in(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), B!12)) | (~in(ordered_pair(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13)), relation_rng_restriction(A!13, C!11))))) | (~in(ordered_pair(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13)), relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12)))),
% 0.19/0.47 inference(tautology,[status(thm)],[])).
% 0.19/0.47 tff(137,plain,
% 0.19/0.47 ((~((~in(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), B!12)) | (~in(ordered_pair(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13)), relation_rng_restriction(A!13, C!11))))) | (~in(ordered_pair(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13)), relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12)))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[136, 135])).
% 0.19/0.47 tff(138,plain,
% 0.19/0.47 (~((~in(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), B!12)) | (~in(ordered_pair(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13)), relation_rng_restriction(A!13, C!11))))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[137, 119])).
% 0.19/0.47 tff(139,plain,
% 0.19/0.47 (((~in(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), B!12)) | (~in(ordered_pair(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13)), relation_rng_restriction(A!13, C!11)))) | in(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), B!12)),
% 0.19/0.47 inference(tautology,[status(thm)],[])).
% 0.19/0.47 tff(140,plain,
% 0.19/0.47 (in(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), B!12)),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[139, 138])).
% 0.19/0.48 tff(141,plain,
% 0.19/0.48 ((~((~in(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), B!12)) | (~in(ordered_pair(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13)), C!11)))) | (~in(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), B!12)) | (~in(ordered_pair(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13)), C!11))),
% 0.19/0.48 inference(tautology,[status(thm)],[])).
% 0.19/0.48 tff(142,plain,
% 0.19/0.48 (~in(ordered_pair(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13)), C!11)),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[141, 140, 59])).
% 0.19/0.48 tff(143,plain,
% 0.19/0.48 (((~in(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), B!12)) | (~in(ordered_pair(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13)), relation_rng_restriction(A!13, C!11)))) | in(ordered_pair(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13)), relation_rng_restriction(A!13, C!11))),
% 0.19/0.48 inference(tautology,[status(thm)],[])).
% 0.19/0.48 tff(144,plain,
% 0.19/0.48 (in(ordered_pair(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13)), relation_rng_restriction(A!13, C!11))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[143, 138])).
% 0.19/0.48 tff(145,plain,
% 0.19/0.48 (((~![A: $i, B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~((~((C = relation_rng_restriction(A, B)) | (((~in(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)), B))) <=> in(ordered_pair(tptp_fun_D_3(C, B, A), tptp_fun_E_2(C, B, A)), C)))) | (~((~(C = relation_rng_restriction(A, B))) | ![D: $i, E: $i] : (~(((~in(E, A)) | (~in(ordered_pair(D, E), B))) <=> in(ordered_pair(D, E), C)))))))))) | ((~relation(C!11)) | ![C: $i] : ((~relation(C)) | (~((~((C = relation_rng_restriction(A!13, C!11)) | (((~in(tptp_fun_E_2(C, C!11, A!13), A!13)) | (~in(ordered_pair(tptp_fun_D_3(C, C!11, A!13), tptp_fun_E_2(C, C!11, A!13)), C!11))) <=> in(ordered_pair(tptp_fun_D_3(C, C!11, A!13), tptp_fun_E_2(C, C!11, A!13)), C)))) | (~((~(C = relation_rng_restriction(A!13, C!11))) | ![D: $i, E: $i] : (~(((~in(E, A!13)) | (~in(ordered_pair(D, E), C!11))) <=> in(ordered_pair(D, E), C)))))))))) <=> ((~![A: $i, B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~((~((C = relation_rng_restriction(A, B)) | (((~in(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)), B))) <=> in(ordered_pair(tptp_fun_D_3(C, B, A), tptp_fun_E_2(C, B, A)), C)))) | (~((~(C = relation_rng_restriction(A, B))) | ![D: $i, E: $i] : (~(((~in(E, A)) | (~in(ordered_pair(D, E), B))) <=> in(ordered_pair(D, E), C)))))))))) | (~relation(C!11)) | ![C: $i] : ((~relation(C)) | (~((~((C = relation_rng_restriction(A!13, C!11)) | (((~in(tptp_fun_E_2(C, C!11, A!13), A!13)) | (~in(ordered_pair(tptp_fun_D_3(C, C!11, A!13), tptp_fun_E_2(C, C!11, A!13)), C!11))) <=> in(ordered_pair(tptp_fun_D_3(C, C!11, A!13), tptp_fun_E_2(C, C!11, A!13)), C)))) | (~((~(C = relation_rng_restriction(A!13, C!11))) | ![D: $i, E: $i] : (~(((~in(E, A!13)) | (~in(ordered_pair(D, E), C!11))) <=> in(ordered_pair(D, E), C)))))))))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(146,plain,
% 0.19/0.48 ((~![A: $i, B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~((~((C = relation_rng_restriction(A, B)) | (((~in(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)), B))) <=> in(ordered_pair(tptp_fun_D_3(C, B, A), tptp_fun_E_2(C, B, A)), C)))) | (~((~(C = relation_rng_restriction(A, B))) | ![D: $i, E: $i] : (~(((~in(E, A)) | (~in(ordered_pair(D, E), B))) <=> in(ordered_pair(D, E), C)))))))))) | ((~relation(C!11)) | ![C: $i] : ((~relation(C)) | (~((~((C = relation_rng_restriction(A!13, C!11)) | (((~in(tptp_fun_E_2(C, C!11, A!13), A!13)) | (~in(ordered_pair(tptp_fun_D_3(C, C!11, A!13), tptp_fun_E_2(C, C!11, A!13)), C!11))) <=> in(ordered_pair(tptp_fun_D_3(C, C!11, A!13), tptp_fun_E_2(C, C!11, A!13)), C)))) | (~((~(C = relation_rng_restriction(A!13, C!11))) | ![D: $i, E: $i] : (~(((~in(E, A!13)) | (~in(ordered_pair(D, E), C!11))) <=> in(ordered_pair(D, E), C)))))))))),
% 0.19/0.48 inference(quant_inst,[status(thm)],[])).
% 0.19/0.48 tff(147,plain,
% 0.19/0.48 ((~![A: $i, B: $i] : ((~relation(B)) | ![C: $i] : ((~relation(C)) | (~((~((C = relation_rng_restriction(A, B)) | (((~in(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)), B))) <=> in(ordered_pair(tptp_fun_D_3(C, B, A), tptp_fun_E_2(C, B, A)), C)))) | (~((~(C = relation_rng_restriction(A, B))) | ![D: $i, E: $i] : (~(((~in(E, A)) | (~in(ordered_pair(D, E), B))) <=> in(ordered_pair(D, E), C)))))))))) | (~relation(C!11)) | ![C: $i] : ((~relation(C)) | (~((~((C = relation_rng_restriction(A!13, C!11)) | (((~in(tptp_fun_E_2(C, C!11, A!13), A!13)) | (~in(ordered_pair(tptp_fun_D_3(C, C!11, A!13), tptp_fun_E_2(C, C!11, A!13)), C!11))) <=> in(ordered_pair(tptp_fun_D_3(C, C!11, A!13), tptp_fun_E_2(C, C!11, A!13)), C)))) | (~((~(C = relation_rng_restriction(A!13, C!11))) | ![D: $i, E: $i] : (~(((~in(E, A!13)) | (~in(ordered_pair(D, E), C!11))) <=> in(ordered_pair(D, E), C))))))))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[146, 145])).
% 0.19/0.48 tff(148,plain,
% 0.19/0.48 (![C: $i] : ((~relation(C)) | (~((~((C = relation_rng_restriction(A!13, C!11)) | (((~in(tptp_fun_E_2(C, C!11, A!13), A!13)) | (~in(ordered_pair(tptp_fun_D_3(C, C!11, A!13), tptp_fun_E_2(C, C!11, A!13)), C!11))) <=> in(ordered_pair(tptp_fun_D_3(C, C!11, A!13), tptp_fun_E_2(C, C!11, A!13)), C)))) | (~((~(C = relation_rng_restriction(A!13, C!11))) | ![D: $i, E: $i] : (~(((~in(E, A!13)) | (~in(ordered_pair(D, E), C!11))) <=> in(ordered_pair(D, E), C))))))))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[147, 98, 10])).
% 0.19/0.48 tff(149,plain,
% 0.19/0.48 (((~![C: $i] : ((~relation(C)) | (~((~((C = relation_rng_restriction(A!13, C!11)) | (((~in(tptp_fun_E_2(C, C!11, A!13), A!13)) | (~in(ordered_pair(tptp_fun_D_3(C, C!11, A!13), tptp_fun_E_2(C, C!11, A!13)), C!11))) <=> in(ordered_pair(tptp_fun_D_3(C, C!11, A!13), tptp_fun_E_2(C, C!11, A!13)), C)))) | (~((~(C = relation_rng_restriction(A!13, C!11))) | ![D: $i, E: $i] : (~(((~in(E, A!13)) | (~in(ordered_pair(D, E), C!11))) <=> in(ordered_pair(D, E), C))))))))) | ((~relation(relation_rng_restriction(A!13, C!11))) | ![D: $i, E: $i] : (~(((~in(E, A!13)) | (~in(ordered_pair(D, E), C!11))) <=> in(ordered_pair(D, E), relation_rng_restriction(A!13, C!11)))))) <=> ((~![C: $i] : ((~relation(C)) | (~((~((C = relation_rng_restriction(A!13, C!11)) | (((~in(tptp_fun_E_2(C, C!11, A!13), A!13)) | (~in(ordered_pair(tptp_fun_D_3(C, C!11, A!13), tptp_fun_E_2(C, C!11, A!13)), C!11))) <=> in(ordered_pair(tptp_fun_D_3(C, C!11, A!13), tptp_fun_E_2(C, C!11, A!13)), C)))) | (~((~(C = relation_rng_restriction(A!13, C!11))) | ![D: $i, E: $i] : (~(((~in(E, A!13)) | (~in(ordered_pair(D, E), C!11))) <=> in(ordered_pair(D, E), C))))))))) | (~relation(relation_rng_restriction(A!13, C!11))) | ![D: $i, E: $i] : (~(((~in(E, A!13)) | (~in(ordered_pair(D, E), C!11))) <=> in(ordered_pair(D, E), relation_rng_restriction(A!13, C!11)))))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(150,plain,
% 0.19/0.48 (((~relation(relation_rng_restriction(A!13, C!11))) | (~((~((relation_rng_restriction(A!13, C!11) = relation_rng_restriction(A!13, C!11)) | (((~in(tptp_fun_E_2(relation_rng_restriction(A!13, C!11), C!11, A!13), A!13)) | (~in(ordered_pair(tptp_fun_D_3(relation_rng_restriction(A!13, C!11), C!11, A!13), tptp_fun_E_2(relation_rng_restriction(A!13, C!11), C!11, A!13)), C!11))) <=> in(ordered_pair(tptp_fun_D_3(relation_rng_restriction(A!13, C!11), C!11, A!13), tptp_fun_E_2(relation_rng_restriction(A!13, C!11), C!11, A!13)), relation_rng_restriction(A!13, C!11))))) | (~((~(relation_rng_restriction(A!13, C!11) = relation_rng_restriction(A!13, C!11))) | ![D: $i, E: $i] : (~(((~in(E, A!13)) | (~in(ordered_pair(D, E), C!11))) <=> in(ordered_pair(D, E), relation_rng_restriction(A!13, C!11))))))))) <=> ((~relation(relation_rng_restriction(A!13, C!11))) | ![D: $i, E: $i] : (~(((~in(E, A!13)) | (~in(ordered_pair(D, E), C!11))) <=> in(ordered_pair(D, E), relation_rng_restriction(A!13, C!11)))))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(151,plain,
% 0.19/0.48 (((~![C: $i] : ((~relation(C)) | (~((~((C = relation_rng_restriction(A!13, C!11)) | (((~in(tptp_fun_E_2(C, C!11, A!13), A!13)) | (~in(ordered_pair(tptp_fun_D_3(C, C!11, A!13), tptp_fun_E_2(C, C!11, A!13)), C!11))) <=> in(ordered_pair(tptp_fun_D_3(C, C!11, A!13), tptp_fun_E_2(C, C!11, A!13)), C)))) | (~((~(C = relation_rng_restriction(A!13, C!11))) | ![D: $i, E: $i] : (~(((~in(E, A!13)) | (~in(ordered_pair(D, E), C!11))) <=> in(ordered_pair(D, E), C))))))))) | ((~relation(relation_rng_restriction(A!13, C!11))) | (~((~((relation_rng_restriction(A!13, C!11) = relation_rng_restriction(A!13, C!11)) | (((~in(tptp_fun_E_2(relation_rng_restriction(A!13, C!11), C!11, A!13), A!13)) | (~in(ordered_pair(tptp_fun_D_3(relation_rng_restriction(A!13, C!11), C!11, A!13), tptp_fun_E_2(relation_rng_restriction(A!13, C!11), C!11, A!13)), C!11))) <=> in(ordered_pair(tptp_fun_D_3(relation_rng_restriction(A!13, C!11), C!11, A!13), tptp_fun_E_2(relation_rng_restriction(A!13, C!11), C!11, A!13)), relation_rng_restriction(A!13, C!11))))) | (~((~(relation_rng_restriction(A!13, C!11) = relation_rng_restriction(A!13, C!11))) | ![D: $i, E: $i] : (~(((~in(E, A!13)) | (~in(ordered_pair(D, E), C!11))) <=> in(ordered_pair(D, E), relation_rng_restriction(A!13, C!11)))))))))) <=> ((~![C: $i] : ((~relation(C)) | (~((~((C = relation_rng_restriction(A!13, C!11)) | (((~in(tptp_fun_E_2(C, C!11, A!13), A!13)) | (~in(ordered_pair(tptp_fun_D_3(C, C!11, A!13), tptp_fun_E_2(C, C!11, A!13)), C!11))) <=> in(ordered_pair(tptp_fun_D_3(C, C!11, A!13), tptp_fun_E_2(C, C!11, A!13)), C)))) | (~((~(C = relation_rng_restriction(A!13, C!11))) | ![D: $i, E: $i] : (~(((~in(E, A!13)) | (~in(ordered_pair(D, E), C!11))) <=> in(ordered_pair(D, E), C))))))))) | ((~relation(relation_rng_restriction(A!13, C!11))) | ![D: $i, E: $i] : (~(((~in(E, A!13)) | (~in(ordered_pair(D, E), C!11))) <=> in(ordered_pair(D, E), relation_rng_restriction(A!13, C!11))))))),
% 0.19/0.48 inference(monotonicity,[status(thm)],[150])).
% 0.19/0.48 tff(152,plain,
% 0.19/0.48 (((~![C: $i] : ((~relation(C)) | (~((~((C = relation_rng_restriction(A!13, C!11)) | (((~in(tptp_fun_E_2(C, C!11, A!13), A!13)) | (~in(ordered_pair(tptp_fun_D_3(C, C!11, A!13), tptp_fun_E_2(C, C!11, A!13)), C!11))) <=> in(ordered_pair(tptp_fun_D_3(C, C!11, A!13), tptp_fun_E_2(C, C!11, A!13)), C)))) | (~((~(C = relation_rng_restriction(A!13, C!11))) | ![D: $i, E: $i] : (~(((~in(E, A!13)) | (~in(ordered_pair(D, E), C!11))) <=> in(ordered_pair(D, E), C))))))))) | ((~relation(relation_rng_restriction(A!13, C!11))) | (~((~((relation_rng_restriction(A!13, C!11) = relation_rng_restriction(A!13, C!11)) | (((~in(tptp_fun_E_2(relation_rng_restriction(A!13, C!11), C!11, A!13), A!13)) | (~in(ordered_pair(tptp_fun_D_3(relation_rng_restriction(A!13, C!11), C!11, A!13), tptp_fun_E_2(relation_rng_restriction(A!13, C!11), C!11, A!13)), C!11))) <=> in(ordered_pair(tptp_fun_D_3(relation_rng_restriction(A!13, C!11), C!11, A!13), tptp_fun_E_2(relation_rng_restriction(A!13, C!11), C!11, A!13)), relation_rng_restriction(A!13, C!11))))) | (~((~(relation_rng_restriction(A!13, C!11) = relation_rng_restriction(A!13, C!11))) | ![D: $i, E: $i] : (~(((~in(E, A!13)) | (~in(ordered_pair(D, E), C!11))) <=> in(ordered_pair(D, E), relation_rng_restriction(A!13, C!11)))))))))) <=> ((~![C: $i] : ((~relation(C)) | (~((~((C = relation_rng_restriction(A!13, C!11)) | (((~in(tptp_fun_E_2(C, C!11, A!13), A!13)) | (~in(ordered_pair(tptp_fun_D_3(C, C!11, A!13), tptp_fun_E_2(C, C!11, A!13)), C!11))) <=> in(ordered_pair(tptp_fun_D_3(C, C!11, A!13), tptp_fun_E_2(C, C!11, A!13)), C)))) | (~((~(C = relation_rng_restriction(A!13, C!11))) | ![D: $i, E: $i] : (~(((~in(E, A!13)) | (~in(ordered_pair(D, E), C!11))) <=> in(ordered_pair(D, E), C))))))))) | (~relation(relation_rng_restriction(A!13, C!11))) | ![D: $i, E: $i] : (~(((~in(E, A!13)) | (~in(ordered_pair(D, E), C!11))) <=> in(ordered_pair(D, E), relation_rng_restriction(A!13, C!11)))))),
% 0.19/0.48 inference(transitivity,[status(thm)],[151, 149])).
% 0.19/0.48 tff(153,plain,
% 0.19/0.48 ((~![C: $i] : ((~relation(C)) | (~((~((C = relation_rng_restriction(A!13, C!11)) | (((~in(tptp_fun_E_2(C, C!11, A!13), A!13)) | (~in(ordered_pair(tptp_fun_D_3(C, C!11, A!13), tptp_fun_E_2(C, C!11, A!13)), C!11))) <=> in(ordered_pair(tptp_fun_D_3(C, C!11, A!13), tptp_fun_E_2(C, C!11, A!13)), C)))) | (~((~(C = relation_rng_restriction(A!13, C!11))) | ![D: $i, E: $i] : (~(((~in(E, A!13)) | (~in(ordered_pair(D, E), C!11))) <=> in(ordered_pair(D, E), C))))))))) | ((~relation(relation_rng_restriction(A!13, C!11))) | (~((~((relation_rng_restriction(A!13, C!11) = relation_rng_restriction(A!13, C!11)) | (((~in(tptp_fun_E_2(relation_rng_restriction(A!13, C!11), C!11, A!13), A!13)) | (~in(ordered_pair(tptp_fun_D_3(relation_rng_restriction(A!13, C!11), C!11, A!13), tptp_fun_E_2(relation_rng_restriction(A!13, C!11), C!11, A!13)), C!11))) <=> in(ordered_pair(tptp_fun_D_3(relation_rng_restriction(A!13, C!11), C!11, A!13), tptp_fun_E_2(relation_rng_restriction(A!13, C!11), C!11, A!13)), relation_rng_restriction(A!13, C!11))))) | (~((~(relation_rng_restriction(A!13, C!11) = relation_rng_restriction(A!13, C!11))) | ![D: $i, E: $i] : (~(((~in(E, A!13)) | (~in(ordered_pair(D, E), C!11))) <=> in(ordered_pair(D, E), relation_rng_restriction(A!13, C!11)))))))))),
% 0.19/0.48 inference(quant_inst,[status(thm)],[])).
% 0.19/0.48 tff(154,plain,
% 0.19/0.48 ((~![C: $i] : ((~relation(C)) | (~((~((C = relation_rng_restriction(A!13, C!11)) | (((~in(tptp_fun_E_2(C, C!11, A!13), A!13)) | (~in(ordered_pair(tptp_fun_D_3(C, C!11, A!13), tptp_fun_E_2(C, C!11, A!13)), C!11))) <=> in(ordered_pair(tptp_fun_D_3(C, C!11, A!13), tptp_fun_E_2(C, C!11, A!13)), C)))) | (~((~(C = relation_rng_restriction(A!13, C!11))) | ![D: $i, E: $i] : (~(((~in(E, A!13)) | (~in(ordered_pair(D, E), C!11))) <=> in(ordered_pair(D, E), C))))))))) | (~relation(relation_rng_restriction(A!13, C!11))) | ![D: $i, E: $i] : (~(((~in(E, A!13)) | (~in(ordered_pair(D, E), C!11))) <=> in(ordered_pair(D, E), relation_rng_restriction(A!13, C!11))))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[153, 152])).
% 0.19/0.48 tff(155,plain,
% 0.19/0.48 (![D: $i, E: $i] : (~(((~in(E, A!13)) | (~in(ordered_pair(D, E), C!11))) <=> in(ordered_pair(D, E), relation_rng_restriction(A!13, C!11))))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[154, 148, 75])).
% 0.19/0.48 tff(156,plain,
% 0.19/0.48 ((~![D: $i, E: $i] : (~(((~in(E, A!13)) | (~in(ordered_pair(D, E), C!11))) <=> in(ordered_pair(D, E), relation_rng_restriction(A!13, C!11))))) | (~(((~in(tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), A!13)) | (~in(ordered_pair(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13)), C!11))) <=> in(ordered_pair(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13)), relation_rng_restriction(A!13, C!11))))),
% 0.19/0.49 inference(quant_inst,[status(thm)],[])).
% 0.19/0.49 tff(157,plain,
% 0.19/0.49 (~(((~in(tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), A!13)) | (~in(ordered_pair(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13)), C!11))) <=> in(ordered_pair(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13)), relation_rng_restriction(A!13, C!11)))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[156, 155])).
% 0.19/0.49 tff(158,plain,
% 0.19/0.49 ((((~in(tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), A!13)) | (~in(ordered_pair(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13)), C!11))) <=> in(ordered_pair(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13)), relation_rng_restriction(A!13, C!11))) | (~((~in(tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), A!13)) | (~in(ordered_pair(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13)), C!11)))) | (~in(ordered_pair(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13)), relation_rng_restriction(A!13, C!11)))),
% 0.19/0.49 inference(tautology,[status(thm)],[])).
% 0.19/0.49 tff(159,plain,
% 0.19/0.49 ((~((~in(tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), A!13)) | (~in(ordered_pair(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13)), C!11)))) | (~in(ordered_pair(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13)), relation_rng_restriction(A!13, C!11)))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[158, 157])).
% 0.19/0.49 tff(160,plain,
% 0.19/0.49 (~((~in(tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), A!13)) | (~in(ordered_pair(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13)), C!11)))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[159, 144])).
% 0.19/0.49 tff(161,plain,
% 0.19/0.49 (((~in(tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), A!13)) | (~in(ordered_pair(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13)), C!11))) | in(ordered_pair(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13)), C!11)),
% 0.19/0.49 inference(tautology,[status(thm)],[])).
% 0.19/0.49 tff(162,plain,
% 0.19/0.49 ($false),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[161, 160, 142])).
% 0.19/0.49 tff(163,plain,(in(ordered_pair(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13)), relation_dom_restriction(C!11, B!12))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.49 tff(164,plain,
% 0.19/0.49 ((((~in(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), B!12)) | (~in(ordered_pair(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13)), C!11))) <=> in(ordered_pair(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13)), relation_dom_restriction(C!11, B!12))) | (~((~in(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), B!12)) | (~in(ordered_pair(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13)), C!11)))) | (~in(ordered_pair(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13)), relation_dom_restriction(C!11, B!12)))),
% 0.19/0.49 inference(tautology,[status(thm)],[])).
% 0.19/0.49 tff(165,plain,
% 0.19/0.49 ((~((~in(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), B!12)) | (~in(ordered_pair(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13)), C!11)))) | (~in(ordered_pair(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13)), relation_dom_restriction(C!11, B!12)))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[164, 56])).
% 0.19/0.49 tff(166,plain,
% 0.19/0.49 (~((~in(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), B!12)) | (~in(ordered_pair(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13)), C!11)))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[165, 163])).
% 0.19/0.49 tff(167,plain,
% 0.19/0.49 (((~in(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), B!12)) | (~in(ordered_pair(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13)), C!11))) | in(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), B!12)),
% 0.19/0.49 inference(tautology,[status(thm)],[])).
% 0.19/0.49 tff(168,plain,
% 0.19/0.49 (in(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), B!12)),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[167, 166])).
% 0.19/0.49 tff(169,assumption,(~in(ordered_pair(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13)), relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12))), introduced(assumption)).
% 0.19/0.49 tff(170,plain,
% 0.19/0.49 ((((~in(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), B!12)) | (~in(ordered_pair(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13)), relation_rng_restriction(A!13, C!11)))) <=> in(ordered_pair(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13)), relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12))) | ((~in(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), B!12)) | (~in(ordered_pair(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13)), relation_rng_restriction(A!13, C!11)))) | in(ordered_pair(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13)), relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12))),
% 0.19/0.49 inference(tautology,[status(thm)],[])).
% 0.19/0.49 tff(171,plain,
% 0.19/0.49 (((~in(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), B!12)) | (~in(ordered_pair(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13)), relation_rng_restriction(A!13, C!11)))) | in(ordered_pair(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13)), relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[170, 135])).
% 0.19/0.49 tff(172,plain,
% 0.19/0.49 ((~in(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), B!12)) | (~in(ordered_pair(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13)), relation_rng_restriction(A!13, C!11)))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[171, 169])).
% 0.19/0.49 tff(173,plain,
% 0.19/0.49 ((~((~in(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), B!12)) | (~in(ordered_pair(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13)), relation_rng_restriction(A!13, C!11))))) | (~in(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), B!12)) | (~in(ordered_pair(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13)), relation_rng_restriction(A!13, C!11)))),
% 0.19/0.49 inference(tautology,[status(thm)],[])).
% 0.19/0.49 tff(174,plain,
% 0.19/0.49 (~in(ordered_pair(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13)), relation_rng_restriction(A!13, C!11))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[173, 172, 168])).
% 0.19/0.49 tff(175,plain,
% 0.19/0.49 (((~in(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), B!12)) | (~in(ordered_pair(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13)), C!11))) | in(ordered_pair(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13)), C!11)),
% 0.19/0.49 inference(tautology,[status(thm)],[])).
% 0.19/0.49 tff(176,plain,
% 0.19/0.49 (in(ordered_pair(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13)), C!11)),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[175, 166])).
% 0.19/0.49 tff(177,plain,
% 0.19/0.49 (~((~in(tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), A!13)) | (~in(ordered_pair(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13)), relation_dom_restriction(C!11, B!12))))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[118, 169])).
% 0.19/0.49 tff(178,plain,
% 0.19/0.49 (((~in(tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), A!13)) | (~in(ordered_pair(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13)), relation_dom_restriction(C!11, B!12)))) | in(tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), A!13)),
% 0.19/0.49 inference(tautology,[status(thm)],[])).
% 0.19/0.49 tff(179,plain,
% 0.19/0.49 (in(tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), A!13)),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[178, 177])).
% 0.19/0.49 tff(180,plain,
% 0.19/0.49 ((~((~in(tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), A!13)) | (~in(ordered_pair(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13)), C!11)))) | (~in(tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), A!13)) | (~in(ordered_pair(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13)), C!11))),
% 0.19/0.49 inference(tautology,[status(thm)],[])).
% 0.19/0.49 tff(181,plain,
% 0.19/0.49 (~((~in(tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), A!13)) | (~in(ordered_pair(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13)), C!11)))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[180, 179, 176])).
% 0.19/0.49 tff(182,plain,
% 0.19/0.49 ((((~in(tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), A!13)) | (~in(ordered_pair(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13)), C!11))) <=> in(ordered_pair(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13)), relation_rng_restriction(A!13, C!11))) | ((~in(tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), A!13)) | (~in(ordered_pair(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13)), C!11))) | in(ordered_pair(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13)), relation_rng_restriction(A!13, C!11))),
% 0.19/0.49 inference(tautology,[status(thm)],[])).
% 0.19/0.49 tff(183,plain,
% 0.19/0.49 (((~in(tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), A!13)) | (~in(ordered_pair(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13)), C!11))) | in(ordered_pair(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13)), relation_rng_restriction(A!13, C!11))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[182, 157])).
% 0.19/0.49 tff(184,plain,
% 0.19/0.49 ($false),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[183, 181, 174])).
% 0.19/0.49 tff(185,plain,(in(ordered_pair(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13)), relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.49 tff(186,plain,
% 0.19/0.49 (~((~in(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), B!12)) | (~in(ordered_pair(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13)), relation_rng_restriction(A!13, C!11))))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[137, 185])).
% 0.19/0.49 tff(187,plain,
% 0.19/0.49 (in(ordered_pair(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13)), relation_rng_restriction(A!13, C!11))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[143, 186])).
% 0.19/0.49 tff(188,plain,
% 0.19/0.49 ((~(((~in(tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), A!13)) | (~in(ordered_pair(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13)), relation_dom_restriction(C!11, B!12)))) <=> in(ordered_pair(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13)), relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12)))) | ((~in(tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), A!13)) | (~in(ordered_pair(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13)), relation_dom_restriction(C!11, B!12)))) | (~in(ordered_pair(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13)), relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12)))),
% 0.19/0.49 inference(tautology,[status(thm)],[])).
% 0.19/0.49 tff(189,plain,
% 0.19/0.49 (((~in(tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), A!13)) | (~in(ordered_pair(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13)), relation_dom_restriction(C!11, B!12)))) | (~in(ordered_pair(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13)), relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12)))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[188, 116])).
% 0.19/0.49 tff(190,plain,
% 0.19/0.49 ((~in(tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), A!13)) | (~in(ordered_pair(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13)), relation_dom_restriction(C!11, B!12)))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[189, 185])).
% 0.19/0.50 tff(191,plain,
% 0.19/0.50 ((~((~in(tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), A!13)) | (~in(ordered_pair(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13)), relation_dom_restriction(C!11, B!12))))) | (~in(tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), A!13)) | (~in(ordered_pair(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13)), relation_dom_restriction(C!11, B!12)))),
% 0.19/0.50 inference(tautology,[status(thm)],[])).
% 0.19/0.50 tff(192,plain,
% 0.19/0.50 (~in(tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), A!13)),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[191, 190, 163])).
% 0.19/0.50 tff(193,plain,
% 0.19/0.50 (((~in(tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), A!13)) | (~in(ordered_pair(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13)), C!11))) | in(tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), A!13)),
% 0.19/0.50 inference(tautology,[status(thm)],[])).
% 0.19/0.50 tff(194,plain,
% 0.19/0.50 ((~in(tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), A!13)) | (~in(ordered_pair(tptp_fun_D_3(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13), tptp_fun_E_2(relation_dom_restriction(relation_rng_restriction(A!13, C!11), B!12), relation_dom_restriction(C!11, B!12), A!13)), C!11))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[193, 192])).
% 0.19/0.50 tff(195,plain,
% 0.19/0.50 ($false),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[159, 194, 187])).
% 0.19/0.50 % SZS output end Proof
% 0.19/0.50 % E exiting
%------------------------------------------------------------------------------