%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SEU254+1 : TPTP v9.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n006.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 05:27:24 AM UTC 2025
% Result : Theorem 0.11s 0.37s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU254+1 : TPTP v9.0.0. Released v3.3.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.11/0.32 % Computer : n006.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Fri Jun 20 06:29:05 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.11/0.37 % SZS status Theorem
% 0.11/0.37 % SZS output start Proof
% 0.11/0.37 tff(in_type, type, (
% 0.11/0.37 in: ( $i * $i ) > $o)).
% 0.11/0.37 tff(tptp_fun_A_10_type, type, (
% 0.11/0.37 tptp_fun_A_10: $i)).
% 0.11/0.37 tff(tptp_fun_D_1_type, type, (
% 0.11/0.37 tptp_fun_D_1: $i > $i)).
% 0.11/0.37 tff(relation_restriction_type, type, (
% 0.11/0.37 relation_restriction: ( $i * $i ) > $i)).
% 0.11/0.37 tff(tptp_fun_B_9_type, type, (
% 0.11/0.37 tptp_fun_B_9: $i)).
% 0.11/0.37 tff(tptp_fun_B_3_type, type, (
% 0.11/0.37 tptp_fun_B_3: $i > $i)).
% 0.11/0.37 tff(cartesian_product2_type, type, (
% 0.11/0.37 cartesian_product2: ( $i * $i ) > $i)).
% 0.11/0.37 tff(ordered_pair_type, type, (
% 0.11/0.37 ordered_pair: ( $i * $i ) > $i)).
% 0.11/0.37 tff(relation_type, type, (
% 0.11/0.37 relation: $i > $o)).
% 0.11/0.37 tff(transitive_type, type, (
% 0.11/0.37 transitive: $i > $o)).
% 0.11/0.37 tff(tptp_fun_C_2_type, type, (
% 0.11/0.37 tptp_fun_C_2: $i > $i)).
% 0.11/0.37 tff(1,plain,
% 0.11/0.37 (^[A: $i, B: $i, C: $i, D: $i] : refl((~(((~in(A, C)) | (~in(B, D))) <=> in(ordered_pair(A, B), cartesian_product2(C, D)))) <=> (~(((~in(A, C)) | (~in(B, D))) <=> in(ordered_pair(A, B), cartesian_product2(C, D)))))),
% 0.11/0.37 inference(bind,[status(th)],[])).
% 0.11/0.37 tff(2,plain,
% 0.11/0.37 (![A: $i, B: $i, C: $i, D: $i] : (~(((~in(A, C)) | (~in(B, D))) <=> in(ordered_pair(A, B), cartesian_product2(C, D)))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~(((~in(A, C)) | (~in(B, D))) <=> in(ordered_pair(A, B), cartesian_product2(C, D))))),
% 0.11/0.37 inference(quant_intro,[status(thm)],[1])).
% 0.11/0.37 tff(3,plain,
% 0.11/0.37 (^[A: $i, B: $i, C: $i, D: $i] : trans(trans(monotonicity(rewrite((in(A, C) & in(B, D)) <=> (~((~in(A, C)) | (~in(B, D))))), ((in(ordered_pair(A, B), cartesian_product2(C, D)) <=> (in(A, C) & in(B, D))) <=> (in(ordered_pair(A, B), cartesian_product2(C, D)) <=> (~((~in(A, C)) | (~in(B, D))))))), rewrite((in(ordered_pair(A, B), cartesian_product2(C, D)) <=> (~((~in(A, C)) | (~in(B, D))))) <=> (~(((~in(A, C)) | (~in(B, D))) <=> in(ordered_pair(A, B), cartesian_product2(C, D))))), ((in(ordered_pair(A, B), cartesian_product2(C, D)) <=> (in(A, C) & in(B, D))) <=> (~(((~in(A, C)) | (~in(B, D))) <=> in(ordered_pair(A, B), cartesian_product2(C, D)))))), rewrite((~(((~in(A, C)) | (~in(B, D))) <=> in(ordered_pair(A, B), cartesian_product2(C, D)))) <=> (~(((~in(A, C)) | (~in(B, D))) <=> in(ordered_pair(A, B), cartesian_product2(C, D))))), ((in(ordered_pair(A, B), cartesian_product2(C, D)) <=> (in(A, C) & in(B, D))) <=> (~(((~in(A, C)) | (~in(B, D))) <=> in(ordered_pair(A, B), cartesian_product2(C, D))))))),
% 0.11/0.37 inference(bind,[status(th)],[])).
% 0.11/0.37 tff(4,plain,
% 0.11/0.37 (![A: $i, B: $i, C: $i, D: $i] : (in(ordered_pair(A, B), cartesian_product2(C, D)) <=> (in(A, C) & in(B, D))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~(((~in(A, C)) | (~in(B, D))) <=> in(ordered_pair(A, B), cartesian_product2(C, D))))),
% 0.11/0.37 inference(quant_intro,[status(thm)],[3])).
% 0.11/0.37 tff(5,plain,
% 0.11/0.37 (![A: $i, B: $i, C: $i, D: $i] : (in(ordered_pair(A, B), cartesian_product2(C, D)) <=> (in(A, C) & in(B, D))) <=> ![A: $i, B: $i, C: $i, D: $i] : (in(ordered_pair(A, B), cartesian_product2(C, D)) <=> (in(A, C) & in(B, D)))),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(6,axiom,(![A: $i, B: $i, C: $i, D: $i] : (in(ordered_pair(A, B), cartesian_product2(C, D)) <=> (in(A, C) & in(B, D)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t106_zfmisc_1')).
% 0.11/0.37 tff(7,plain,
% 0.11/0.37 (![A: $i, B: $i, C: $i, D: $i] : (in(ordered_pair(A, B), cartesian_product2(C, D)) <=> (in(A, C) & in(B, D)))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.11/0.37 tff(8,plain,(
% 0.11/0.37 ![A: $i, B: $i, C: $i, D: $i] : (in(ordered_pair(A, B), cartesian_product2(C, D)) <=> (in(A, C) & in(B, D)))),
% 0.11/0.37 inference(skolemize,[status(sab)],[7])).
% 0.11/0.37 tff(9,plain,
% 0.11/0.37 (![A: $i, B: $i, C: $i, D: $i] : (~(((~in(A, C)) | (~in(B, D))) <=> in(ordered_pair(A, B), cartesian_product2(C, D))))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[8, 4])).
% 0.11/0.37 tff(10,plain,
% 0.11/0.37 (![A: $i, B: $i, C: $i, D: $i] : (~(((~in(A, C)) | (~in(B, D))) <=> in(ordered_pair(A, B), cartesian_product2(C, D))))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[9, 2])).
% 0.11/0.37 tff(11,plain,
% 0.11/0.37 ((~![A: $i, B: $i, C: $i, D: $i] : (~(((~in(A, C)) | (~in(B, D))) <=> in(ordered_pair(A, B), cartesian_product2(C, D))))) | (~(((~in(tptp_fun_B_3(relation_restriction(B!9, A!10)), A!10)) | (~in(tptp_fun_D_1(relation_restriction(B!9, A!10)), A!10))) <=> in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), cartesian_product2(A!10, A!10))))),
% 0.11/0.37 inference(quant_inst,[status(thm)],[])).
% 0.11/0.37 tff(12,plain,
% 0.11/0.37 (~(((~in(tptp_fun_B_3(relation_restriction(B!9, A!10)), A!10)) | (~in(tptp_fun_D_1(relation_restriction(B!9, A!10)), A!10))) <=> in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), cartesian_product2(A!10, A!10)))),
% 0.11/0.37 inference(unit_resolution,[status(thm)],[11, 10])).
% 0.11/0.37 tff(13,plain,
% 0.11/0.37 ((~(transitive(relation_restriction(B!9, A!10)) | (~relation(B!9)) | (~transitive(B!9)))) <=> (~(transitive(relation_restriction(B!9, A!10)) | (~relation(B!9)) | (~transitive(B!9))))),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(14,plain,
% 0.11/0.37 ((~![A: $i, B: $i] : (transitive(relation_restriction(B, A)) | (~relation(B)) | (~transitive(B)))) <=> (~![A: $i, B: $i] : (transitive(relation_restriction(B, A)) | (~relation(B)) | (~transitive(B))))),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(15,plain,
% 0.11/0.37 ((~![A: $i, B: $i] : (relation(B) => (transitive(B) => transitive(relation_restriction(B, A))))) <=> (~![A: $i, B: $i] : (transitive(relation_restriction(B, A)) | (~relation(B)) | (~transitive(B))))),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(16,axiom,(~![A: $i, B: $i] : (relation(B) => (transitive(B) => transitive(relation_restriction(B, A))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t24_wellord1')).
% 0.11/0.37 tff(17,plain,
% 0.11/0.37 (~![A: $i, B: $i] : (transitive(relation_restriction(B, A)) | (~relation(B)) | (~transitive(B)))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[16, 15])).
% 0.11/0.37 tff(18,plain,
% 0.11/0.37 (~![A: $i, B: $i] : (transitive(relation_restriction(B, A)) | (~relation(B)) | (~transitive(B)))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[17, 14])).
% 0.11/0.37 tff(19,plain,
% 0.11/0.37 (~![A: $i, B: $i] : (transitive(relation_restriction(B, A)) | (~relation(B)) | (~transitive(B)))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[18, 14])).
% 0.11/0.37 tff(20,plain,
% 0.11/0.37 (~![A: $i, B: $i] : (transitive(relation_restriction(B, A)) | (~relation(B)) | (~transitive(B)))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[19, 14])).
% 0.11/0.37 tff(21,plain,(
% 0.11/0.37 ~(transitive(relation_restriction(B!9, A!10)) | (~relation(B!9)) | (~transitive(B!9)))),
% 0.11/0.37 inference(skolemize,[status(sab)],[20])).
% 0.11/0.37 tff(22,plain,
% 0.11/0.37 (~(transitive(relation_restriction(B!9, A!10)) | (~relation(B!9)) | (~transitive(B!9)))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[21, 13])).
% 0.11/0.37 tff(23,plain,
% 0.11/0.37 (relation(B!9)),
% 0.11/0.37 inference(or_elim,[status(thm)],[22])).
% 0.11/0.37 tff(24,plain,
% 0.11/0.37 (^[A: $i, B: $i, C: $i] : refl(((~relation(C)) | (~(((~in(A, C)) | (~in(A, cartesian_product2(B, B)))) <=> in(A, relation_restriction(C, B))))) <=> ((~relation(C)) | (~(((~in(A, C)) | (~in(A, cartesian_product2(B, B)))) <=> in(A, relation_restriction(C, B))))))),
% 0.11/0.37 inference(bind,[status(th)],[])).
% 0.11/0.37 tff(25,plain,
% 0.11/0.37 (![A: $i, B: $i, C: $i] : ((~relation(C)) | (~(((~in(A, C)) | (~in(A, cartesian_product2(B, B)))) <=> in(A, relation_restriction(C, B))))) <=> ![A: $i, B: $i, C: $i] : ((~relation(C)) | (~(((~in(A, C)) | (~in(A, cartesian_product2(B, B)))) <=> in(A, relation_restriction(C, B)))))),
% 0.11/0.37 inference(quant_intro,[status(thm)],[24])).
% 0.11/0.37 tff(26,plain,
% 0.11/0.37 (^[A: $i, B: $i, C: $i] : rewrite(((~relation(C)) | (in(A, relation_restriction(C, B)) <=> (in(A, C) & in(A, cartesian_product2(B, B))))) <=> ((~relation(C)) | (~(((~in(A, C)) | (~in(A, cartesian_product2(B, B)))) <=> in(A, relation_restriction(C, B))))))),
% 0.11/0.37 inference(bind,[status(th)],[])).
% 0.11/0.37 tff(27,plain,
% 0.11/0.37 (![A: $i, B: $i, C: $i] : ((~relation(C)) | (in(A, relation_restriction(C, B)) <=> (in(A, C) & in(A, cartesian_product2(B, B))))) <=> ![A: $i, B: $i, C: $i] : ((~relation(C)) | (~(((~in(A, C)) | (~in(A, cartesian_product2(B, B)))) <=> in(A, relation_restriction(C, B)))))),
% 0.11/0.37 inference(quant_intro,[status(thm)],[26])).
% 0.11/0.37 tff(28,plain,
% 0.11/0.37 (![A: $i, B: $i, C: $i] : ((~relation(C)) | (in(A, relation_restriction(C, B)) <=> (in(A, C) & in(A, cartesian_product2(B, B))))) <=> ![A: $i, B: $i, C: $i] : ((~relation(C)) | (in(A, relation_restriction(C, B)) <=> (in(A, C) & in(A, cartesian_product2(B, B)))))),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(29,plain,
% 0.11/0.37 (^[A: $i, B: $i, C: $i] : rewrite((relation(C) => (in(A, relation_restriction(C, B)) <=> (in(A, C) & in(A, cartesian_product2(B, B))))) <=> ((~relation(C)) | (in(A, relation_restriction(C, B)) <=> (in(A, C) & in(A, cartesian_product2(B, B))))))),
% 0.11/0.37 inference(bind,[status(th)],[])).
% 0.11/0.37 tff(30,plain,
% 0.11/0.37 (![A: $i, B: $i, C: $i] : (relation(C) => (in(A, relation_restriction(C, B)) <=> (in(A, C) & in(A, cartesian_product2(B, B))))) <=> ![A: $i, B: $i, C: $i] : ((~relation(C)) | (in(A, relation_restriction(C, B)) <=> (in(A, C) & in(A, cartesian_product2(B, B)))))),
% 0.11/0.37 inference(quant_intro,[status(thm)],[29])).
% 0.11/0.37 tff(31,axiom,(![A: $i, B: $i, C: $i] : (relation(C) => (in(A, relation_restriction(C, B)) <=> (in(A, C) & in(A, cartesian_product2(B, B)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t16_wellord1')).
% 0.11/0.37 tff(32,plain,
% 0.11/0.37 (![A: $i, B: $i, C: $i] : ((~relation(C)) | (in(A, relation_restriction(C, B)) <=> (in(A, C) & in(A, cartesian_product2(B, B)))))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[31, 30])).
% 0.11/0.37 tff(33,plain,
% 0.11/0.37 (![A: $i, B: $i, C: $i] : ((~relation(C)) | (in(A, relation_restriction(C, B)) <=> (in(A, C) & in(A, cartesian_product2(B, B)))))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[32, 28])).
% 0.11/0.37 tff(34,plain,(
% 0.11/0.37 ![A: $i, B: $i, C: $i] : ((~relation(C)) | (in(A, relation_restriction(C, B)) <=> (in(A, C) & in(A, cartesian_product2(B, B)))))),
% 0.11/0.37 inference(skolemize,[status(sab)],[33])).
% 0.11/0.37 tff(35,plain,
% 0.11/0.37 (![A: $i, B: $i, C: $i] : ((~relation(C)) | (~(((~in(A, C)) | (~in(A, cartesian_product2(B, B)))) <=> in(A, relation_restriction(C, B)))))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[34, 27])).
% 0.11/0.37 tff(36,plain,
% 0.11/0.37 (![A: $i, B: $i, C: $i] : ((~relation(C)) | (~(((~in(A, C)) | (~in(A, cartesian_product2(B, B)))) <=> in(A, relation_restriction(C, B)))))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[35, 25])).
% 0.11/0.37 tff(37,plain,
% 0.11/0.37 (((~![A: $i, B: $i, C: $i] : ((~relation(C)) | (~(((~in(A, C)) | (~in(A, cartesian_product2(B, B)))) <=> in(A, relation_restriction(C, B)))))) | ((~relation(B!9)) | (~(((~in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), B!9)) | (~in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), cartesian_product2(A!10, A!10)))) <=> in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), relation_restriction(B!9, A!10)))))) <=> ((~![A: $i, B: $i, C: $i] : ((~relation(C)) | (~(((~in(A, C)) | (~in(A, cartesian_product2(B, B)))) <=> in(A, relation_restriction(C, B)))))) | (~relation(B!9)) | (~(((~in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), B!9)) | (~in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), cartesian_product2(A!10, A!10)))) <=> in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), relation_restriction(B!9, A!10)))))),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(38,plain,
% 0.11/0.37 ((~![A: $i, B: $i, C: $i] : ((~relation(C)) | (~(((~in(A, C)) | (~in(A, cartesian_product2(B, B)))) <=> in(A, relation_restriction(C, B)))))) | ((~relation(B!9)) | (~(((~in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), B!9)) | (~in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), cartesian_product2(A!10, A!10)))) <=> in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), relation_restriction(B!9, A!10)))))),
% 0.11/0.37 inference(quant_inst,[status(thm)],[])).
% 0.11/0.37 tff(39,plain,
% 0.11/0.37 ((~![A: $i, B: $i, C: $i] : ((~relation(C)) | (~(((~in(A, C)) | (~in(A, cartesian_product2(B, B)))) <=> in(A, relation_restriction(C, B)))))) | (~relation(B!9)) | (~(((~in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), B!9)) | (~in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), cartesian_product2(A!10, A!10)))) <=> in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), relation_restriction(B!9, A!10))))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[38, 37])).
% 0.11/0.38 tff(40,plain,
% 0.11/0.38 (~(((~in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), B!9)) | (~in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), cartesian_product2(A!10, A!10)))) <=> in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), relation_restriction(B!9, A!10)))),
% 0.11/0.38 inference(unit_resolution,[status(thm)],[39, 36, 23])).
% 0.11/0.38 tff(41,plain,
% 0.11/0.38 (^[A: $i, B: $i] : refl(((~relation(A)) | relation(relation_restriction(A, B))) <=> ((~relation(A)) | relation(relation_restriction(A, B))))),
% 0.11/0.38 inference(bind,[status(th)],[])).
% 0.11/0.38 tff(42,plain,
% 0.11/0.38 (![A: $i, B: $i] : ((~relation(A)) | relation(relation_restriction(A, B))) <=> ![A: $i, B: $i] : ((~relation(A)) | relation(relation_restriction(A, B)))),
% 0.11/0.38 inference(quant_intro,[status(thm)],[41])).
% 0.11/0.38 tff(43,plain,
% 0.11/0.38 (![A: $i, B: $i] : ((~relation(A)) | relation(relation_restriction(A, B))) <=> ![A: $i, B: $i] : ((~relation(A)) | relation(relation_restriction(A, B)))),
% 0.11/0.38 inference(rewrite,[status(thm)],[])).
% 0.11/0.38 tff(44,plain,
% 0.11/0.38 (^[A: $i, B: $i] : rewrite((relation(A) => relation(relation_restriction(A, B))) <=> ((~relation(A)) | relation(relation_restriction(A, B))))),
% 0.11/0.38 inference(bind,[status(th)],[])).
% 0.11/0.38 tff(45,plain,
% 0.11/0.38 (![A: $i, B: $i] : (relation(A) => relation(relation_restriction(A, B))) <=> ![A: $i, B: $i] : ((~relation(A)) | relation(relation_restriction(A, B)))),
% 0.11/0.38 inference(quant_intro,[status(thm)],[44])).
% 0.11/0.38 tff(46,axiom,(![A: $i, B: $i] : (relation(A) => relation(relation_restriction(A, B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_k2_wellord1')).
% 0.11/0.38 tff(47,plain,
% 0.11/0.38 (![A: $i, B: $i] : ((~relation(A)) | relation(relation_restriction(A, B)))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[46, 45])).
% 0.11/0.38 tff(48,plain,
% 0.11/0.38 (![A: $i, B: $i] : ((~relation(A)) | relation(relation_restriction(A, B)))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[47, 43])).
% 0.11/0.38 tff(49,plain,(
% 0.11/0.38 ![A: $i, B: $i] : ((~relation(A)) | relation(relation_restriction(A, B)))),
% 0.11/0.38 inference(skolemize,[status(sab)],[48])).
% 0.11/0.38 tff(50,plain,
% 0.11/0.38 (![A: $i, B: $i] : ((~relation(A)) | relation(relation_restriction(A, B)))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[49, 42])).
% 0.11/0.38 tff(51,plain,
% 0.11/0.38 (((~![A: $i, B: $i] : ((~relation(A)) | relation(relation_restriction(A, B)))) | ((~relation(B!9)) | relation(relation_restriction(B!9, A!10)))) <=> ((~![A: $i, B: $i] : ((~relation(A)) | relation(relation_restriction(A, B)))) | (~relation(B!9)) | relation(relation_restriction(B!9, A!10)))),
% 0.11/0.38 inference(rewrite,[status(thm)],[])).
% 0.11/0.38 tff(52,plain,
% 0.11/0.38 ((~![A: $i, B: $i] : ((~relation(A)) | relation(relation_restriction(A, B)))) | ((~relation(B!9)) | relation(relation_restriction(B!9, A!10)))),
% 0.11/0.38 inference(quant_inst,[status(thm)],[])).
% 0.11/0.38 tff(53,plain,
% 0.11/0.38 ((~![A: $i, B: $i] : ((~relation(A)) | relation(relation_restriction(A, B)))) | (~relation(B!9)) | relation(relation_restriction(B!9, A!10))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[52, 51])).
% 0.11/0.38 tff(54,plain,
% 0.11/0.38 (relation(relation_restriction(B!9, A!10))),
% 0.11/0.38 inference(unit_resolution,[status(thm)],[53, 50, 23])).
% 0.11/0.38 tff(55,plain,
% 0.11/0.38 (^[A: $i] : refl(((~relation(A)) | (~((~((~transitive(A)) | ![B: $i, C: $i, D: $i] : (in(ordered_pair(B, D), A) | (~in(ordered_pair(B, C), A)) | (~in(ordered_pair(C, D), A))))) | (~(transitive(A) | (~(in(ordered_pair(tptp_fun_B_3(A), tptp_fun_D_1(A)), A) | (~in(ordered_pair(tptp_fun_B_3(A), tptp_fun_C_2(A)), A)) | (~in(ordered_pair(tptp_fun_C_2(A), tptp_fun_D_1(A)), A))))))))) <=> ((~relation(A)) | (~((~((~transitive(A)) | ![B: $i, C: $i, D: $i] : (in(ordered_pair(B, D), A) | (~in(ordered_pair(B, C), A)) | (~in(ordered_pair(C, D), A))))) | (~(transitive(A) | (~(in(ordered_pair(tptp_fun_B_3(A), tptp_fun_D_1(A)), A) | (~in(ordered_pair(tptp_fun_B_3(A), tptp_fun_C_2(A)), A)) | (~in(ordered_pair(tptp_fun_C_2(A), tptp_fun_D_1(A)), A))))))))))),
% 0.11/0.38 inference(bind,[status(th)],[])).
% 0.11/0.38 tff(56,plain,
% 0.11/0.38 (![A: $i] : ((~relation(A)) | (~((~((~transitive(A)) | ![B: $i, C: $i, D: $i] : (in(ordered_pair(B, D), A) | (~in(ordered_pair(B, C), A)) | (~in(ordered_pair(C, D), A))))) | (~(transitive(A) | (~(in(ordered_pair(tptp_fun_B_3(A), tptp_fun_D_1(A)), A) | (~in(ordered_pair(tptp_fun_B_3(A), tptp_fun_C_2(A)), A)) | (~in(ordered_pair(tptp_fun_C_2(A), tptp_fun_D_1(A)), A))))))))) <=> ![A: $i] : ((~relation(A)) | (~((~((~transitive(A)) | ![B: $i, C: $i, D: $i] : (in(ordered_pair(B, D), A) | (~in(ordered_pair(B, C), A)) | (~in(ordered_pair(C, D), A))))) | (~(transitive(A) | (~(in(ordered_pair(tptp_fun_B_3(A), tptp_fun_D_1(A)), A) | (~in(ordered_pair(tptp_fun_B_3(A), tptp_fun_C_2(A)), A)) | (~in(ordered_pair(tptp_fun_C_2(A), tptp_fun_D_1(A)), A)))))))))),
% 0.11/0.38 inference(quant_intro,[status(thm)],[55])).
% 0.11/0.38 tff(57,plain,
% 0.11/0.38 (^[A: $i] : rewrite(((~relation(A)) | (~((~((~transitive(A)) | ![B: $i, C: $i, D: $i] : (in(ordered_pair(B, D), A) | (~in(ordered_pair(B, C), A)) | (~in(ordered_pair(C, D), A))))) | (~(transitive(A) | (~(in(ordered_pair(tptp_fun_B_3(A), tptp_fun_D_1(A)), A) | (~in(ordered_pair(tptp_fun_B_3(A), tptp_fun_C_2(A)), A)) | (~in(ordered_pair(tptp_fun_C_2(A), tptp_fun_D_1(A)), A))))))))) <=> ((~relation(A)) | (~((~((~transitive(A)) | ![B: $i, C: $i, D: $i] : (in(ordered_pair(B, D), A) | (~in(ordered_pair(B, C), A)) | (~in(ordered_pair(C, D), A))))) | (~(transitive(A) | (~(in(ordered_pair(tptp_fun_B_3(A), tptp_fun_D_1(A)), A) | (~in(ordered_pair(tptp_fun_B_3(A), tptp_fun_C_2(A)), A)) | (~in(ordered_pair(tptp_fun_C_2(A), tptp_fun_D_1(A)), A))))))))))),
% 0.11/0.38 inference(bind,[status(th)],[])).
% 0.11/0.38 tff(58,plain,
% 0.11/0.38 (![A: $i] : ((~relation(A)) | (~((~((~transitive(A)) | ![B: $i, C: $i, D: $i] : (in(ordered_pair(B, D), A) | (~in(ordered_pair(B, C), A)) | (~in(ordered_pair(C, D), A))))) | (~(transitive(A) | (~(in(ordered_pair(tptp_fun_B_3(A), tptp_fun_D_1(A)), A) | (~in(ordered_pair(tptp_fun_B_3(A), tptp_fun_C_2(A)), A)) | (~in(ordered_pair(tptp_fun_C_2(A), tptp_fun_D_1(A)), A))))))))) <=> ![A: $i] : ((~relation(A)) | (~((~((~transitive(A)) | ![B: $i, C: $i, D: $i] : (in(ordered_pair(B, D), A) | (~in(ordered_pair(B, C), A)) | (~in(ordered_pair(C, D), A))))) | (~(transitive(A) | (~(in(ordered_pair(tptp_fun_B_3(A), tptp_fun_D_1(A)), A) | (~in(ordered_pair(tptp_fun_B_3(A), tptp_fun_C_2(A)), A)) | (~in(ordered_pair(tptp_fun_C_2(A), tptp_fun_D_1(A)), A)))))))))),
% 0.11/0.38 inference(quant_intro,[status(thm)],[57])).
% 0.11/0.38 tff(59,plain,
% 0.11/0.38 (![A: $i] : ((~relation(A)) | (~((~((~transitive(A)) | ![B: $i, C: $i, D: $i] : (in(ordered_pair(B, D), A) | (~in(ordered_pair(B, C), A)) | (~in(ordered_pair(C, D), A))))) | (~(transitive(A) | (~(in(ordered_pair(tptp_fun_B_3(A), tptp_fun_D_1(A)), A) | (~in(ordered_pair(tptp_fun_B_3(A), tptp_fun_C_2(A)), A)) | (~in(ordered_pair(tptp_fun_C_2(A), tptp_fun_D_1(A)), A))))))))) <=> ![A: $i] : ((~relation(A)) | (~((~((~transitive(A)) | ![B: $i, C: $i, D: $i] : (in(ordered_pair(B, D), A) | (~in(ordered_pair(B, C), A)) | (~in(ordered_pair(C, D), A))))) | (~(transitive(A) | (~(in(ordered_pair(tptp_fun_B_3(A), tptp_fun_D_1(A)), A) | (~in(ordered_pair(tptp_fun_B_3(A), tptp_fun_C_2(A)), A)) | (~in(ordered_pair(tptp_fun_C_2(A), tptp_fun_D_1(A)), A)))))))))),
% 0.11/0.38 inference(transitivity,[status(thm)],[58, 56])).
% 0.11/0.38 tff(60,plain,
% 0.11/0.38 (^[A: $i] : rewrite(((~relation(A)) | (((~transitive(A)) | ![B: $i, C: $i, D: $i] : ((~(in(ordered_pair(B, C), A) & in(ordered_pair(C, D), A))) | in(ordered_pair(B, D), A))) & (transitive(A) | (~((~(in(ordered_pair(tptp_fun_B_3(A), tptp_fun_C_2(A)), A) & in(ordered_pair(tptp_fun_C_2(A), tptp_fun_D_1(A)), A))) | in(ordered_pair(tptp_fun_B_3(A), tptp_fun_D_1(A)), A)))))) <=> ((~relation(A)) | (~((~((~transitive(A)) | ![B: $i, C: $i, D: $i] : (in(ordered_pair(B, D), A) | (~in(ordered_pair(B, C), A)) | (~in(ordered_pair(C, D), A))))) | (~(transitive(A) | (~(in(ordered_pair(tptp_fun_B_3(A), tptp_fun_D_1(A)), A) | (~in(ordered_pair(tptp_fun_B_3(A), tptp_fun_C_2(A)), A)) | (~in(ordered_pair(tptp_fun_C_2(A), tptp_fun_D_1(A)), A))))))))))),
% 0.11/0.38 inference(bind,[status(th)],[])).
% 0.11/0.38 tff(61,plain,
% 0.11/0.38 (![A: $i] : ((~relation(A)) | (((~transitive(A)) | ![B: $i, C: $i, D: $i] : ((~(in(ordered_pair(B, C), A) & in(ordered_pair(C, D), A))) | in(ordered_pair(B, D), A))) & (transitive(A) | (~((~(in(ordered_pair(tptp_fun_B_3(A), tptp_fun_C_2(A)), A) & in(ordered_pair(tptp_fun_C_2(A), tptp_fun_D_1(A)), A))) | in(ordered_pair(tptp_fun_B_3(A), tptp_fun_D_1(A)), A)))))) <=> ![A: $i] : ((~relation(A)) | (~((~((~transitive(A)) | ![B: $i, C: $i, D: $i] : (in(ordered_pair(B, D), A) | (~in(ordered_pair(B, C), A)) | (~in(ordered_pair(C, D), A))))) | (~(transitive(A) | (~(in(ordered_pair(tptp_fun_B_3(A), tptp_fun_D_1(A)), A) | (~in(ordered_pair(tptp_fun_B_3(A), tptp_fun_C_2(A)), A)) | (~in(ordered_pair(tptp_fun_C_2(A), tptp_fun_D_1(A)), A)))))))))),
% 0.11/0.38 inference(quant_intro,[status(thm)],[60])).
% 0.11/0.38 tff(62,plain,
% 0.11/0.38 (![A: $i] : ((~relation(A)) | (transitive(A) <=> ![B: $i, C: $i, D: $i] : ((~(in(ordered_pair(B, C), A) & in(ordered_pair(C, D), A))) | in(ordered_pair(B, D), A)))) <=> ![A: $i] : ((~relation(A)) | (transitive(A) <=> ![B: $i, C: $i, D: $i] : ((~(in(ordered_pair(B, C), A) & in(ordered_pair(C, D), A))) | in(ordered_pair(B, D), A))))),
% 0.11/0.38 inference(rewrite,[status(thm)],[])).
% 0.11/0.38 tff(63,plain,
% 0.11/0.38 (^[A: $i] : trans(monotonicity(rewrite((transitive(A) <=> ![B: $i, C: $i, D: $i] : ((in(ordered_pair(B, C), A) & in(ordered_pair(C, D), A)) => in(ordered_pair(B, D), A))) <=> (transitive(A) <=> ![B: $i, C: $i, D: $i] : ((~(in(ordered_pair(B, C), A) & in(ordered_pair(C, D), A))) | in(ordered_pair(B, D), A)))), ((relation(A) => (transitive(A) <=> ![B: $i, C: $i, D: $i] : ((in(ordered_pair(B, C), A) & in(ordered_pair(C, D), A)) => in(ordered_pair(B, D), A)))) <=> (relation(A) => (transitive(A) <=> ![B: $i, C: $i, D: $i] : ((~(in(ordered_pair(B, C), A) & in(ordered_pair(C, D), A))) | in(ordered_pair(B, D), A)))))), rewrite((relation(A) => (transitive(A) <=> ![B: $i, C: $i, D: $i] : ((~(in(ordered_pair(B, C), A) & in(ordered_pair(C, D), A))) | in(ordered_pair(B, D), A)))) <=> ((~relation(A)) | (transitive(A) <=> ![B: $i, C: $i, D: $i] : ((~(in(ordered_pair(B, C), A) & in(ordered_pair(C, D), A))) | in(ordered_pair(B, D), A))))), ((relation(A) => (transitive(A) <=> ![B: $i, C: $i, D: $i] : ((in(ordered_pair(B, C), A) & in(ordered_pair(C, D), A)) => in(ordered_pair(B, D), A)))) <=> ((~relation(A)) | (transitive(A) <=> ![B: $i, C: $i, D: $i] : ((~(in(ordered_pair(B, C), A) & in(ordered_pair(C, D), A))) | in(ordered_pair(B, D), A))))))),
% 0.11/0.38 inference(bind,[status(th)],[])).
% 0.11/0.38 tff(64,plain,
% 0.11/0.38 (![A: $i] : (relation(A) => (transitive(A) <=> ![B: $i, C: $i, D: $i] : ((in(ordered_pair(B, C), A) & in(ordered_pair(C, D), A)) => in(ordered_pair(B, D), A)))) <=> ![A: $i] : ((~relation(A)) | (transitive(A) <=> ![B: $i, C: $i, D: $i] : ((~(in(ordered_pair(B, C), A) & in(ordered_pair(C, D), A))) | in(ordered_pair(B, D), A))))),
% 0.11/0.38 inference(quant_intro,[status(thm)],[63])).
% 0.11/0.38 tff(65,axiom,(![A: $i] : (relation(A) => (transitive(A) <=> ![B: $i, C: $i, D: $i] : ((in(ordered_pair(B, C), A) & in(ordered_pair(C, D), A)) => in(ordered_pair(B, D), A))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','l2_wellord1')).
% 0.11/0.38 tff(66,plain,
% 0.11/0.38 (![A: $i] : ((~relation(A)) | (transitive(A) <=> ![B: $i, C: $i, D: $i] : ((~(in(ordered_pair(B, C), A) & in(ordered_pair(C, D), A))) | in(ordered_pair(B, D), A))))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[65, 64])).
% 0.11/0.38 tff(67,plain,
% 0.11/0.38 (![A: $i] : ((~relation(A)) | (transitive(A) <=> ![B: $i, C: $i, D: $i] : ((~(in(ordered_pair(B, C), A) & in(ordered_pair(C, D), A))) | in(ordered_pair(B, D), A))))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[66, 62])).
% 0.11/0.38 tff(68,plain,(
% 0.11/0.38 ![A: $i] : ((~relation(A)) | (((~transitive(A)) | ![B: $i, C: $i, D: $i] : ((~(in(ordered_pair(B, C), A) & in(ordered_pair(C, D), A))) | in(ordered_pair(B, D), A))) & (transitive(A) | (~((~(in(ordered_pair(tptp_fun_B_3(A), tptp_fun_C_2(A)), A) & in(ordered_pair(tptp_fun_C_2(A), tptp_fun_D_1(A)), A))) | in(ordered_pair(tptp_fun_B_3(A), tptp_fun_D_1(A)), A))))))),
% 0.11/0.38 inference(skolemize,[status(sab)],[67])).
% 0.11/0.38 tff(69,plain,
% 0.11/0.38 (![A: $i] : ((~relation(A)) | (~((~((~transitive(A)) | ![B: $i, C: $i, D: $i] : (in(ordered_pair(B, D), A) | (~in(ordered_pair(B, C), A)) | (~in(ordered_pair(C, D), A))))) | (~(transitive(A) | (~(in(ordered_pair(tptp_fun_B_3(A), tptp_fun_D_1(A)), A) | (~in(ordered_pair(tptp_fun_B_3(A), tptp_fun_C_2(A)), A)) | (~in(ordered_pair(tptp_fun_C_2(A), tptp_fun_D_1(A)), A)))))))))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[68, 61])).
% 0.11/0.38 tff(70,plain,
% 0.11/0.38 (![A: $i] : ((~relation(A)) | (~((~((~transitive(A)) | ![B: $i, C: $i, D: $i] : (in(ordered_pair(B, D), A) | (~in(ordered_pair(B, C), A)) | (~in(ordered_pair(C, D), A))))) | (~(transitive(A) | (~(in(ordered_pair(tptp_fun_B_3(A), tptp_fun_D_1(A)), A) | (~in(ordered_pair(tptp_fun_B_3(A), tptp_fun_C_2(A)), A)) | (~in(ordered_pair(tptp_fun_C_2(A), tptp_fun_D_1(A)), A)))))))))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[69, 59])).
% 0.11/0.38 tff(71,plain,
% 0.11/0.38 (((~![A: $i] : ((~relation(A)) | (~((~((~transitive(A)) | ![B: $i, C: $i, D: $i] : (in(ordered_pair(B, D), A) | (~in(ordered_pair(B, C), A)) | (~in(ordered_pair(C, D), A))))) | (~(transitive(A) | (~(in(ordered_pair(tptp_fun_B_3(A), tptp_fun_D_1(A)), A) | (~in(ordered_pair(tptp_fun_B_3(A), tptp_fun_C_2(A)), A)) | (~in(ordered_pair(tptp_fun_C_2(A), tptp_fun_D_1(A)), A)))))))))) | ((~relation(relation_restriction(B!9, A!10))) | (~((~((~transitive(relation_restriction(B!9, A!10))) | ![B: $i, C: $i, D: $i] : (in(ordered_pair(B, D), relation_restriction(B!9, A!10)) | (~in(ordered_pair(B, C), relation_restriction(B!9, A!10))) | (~in(ordered_pair(C, D), relation_restriction(B!9, A!10)))))) | (~(transitive(relation_restriction(B!9, A!10)) | (~((~in(ordered_pair(tptp_fun_C_2(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), relation_restriction(B!9, A!10))) | (~in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_C_2(relation_restriction(B!9, A!10))), relation_restriction(B!9, A!10))) | in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), relation_restriction(B!9, A!10)))))))))) <=> ((~![A: $i] : ((~relation(A)) | (~((~((~transitive(A)) | ![B: $i, C: $i, D: $i] : (in(ordered_pair(B, D), A) | (~in(ordered_pair(B, C), A)) | (~in(ordered_pair(C, D), A))))) | (~(transitive(A) | (~(in(ordered_pair(tptp_fun_B_3(A), tptp_fun_D_1(A)), A) | (~in(ordered_pair(tptp_fun_B_3(A), tptp_fun_C_2(A)), A)) | (~in(ordered_pair(tptp_fun_C_2(A), tptp_fun_D_1(A)), A)))))))))) | (~relation(relation_restriction(B!9, A!10))) | (~((~((~transitive(relation_restriction(B!9, A!10))) | ![B: $i, C: $i, D: $i] : (in(ordered_pair(B, D), relation_restriction(B!9, A!10)) | (~in(ordered_pair(B, C), relation_restriction(B!9, A!10))) | (~in(ordered_pair(C, D), relation_restriction(B!9, A!10)))))) | (~(transitive(relation_restriction(B!9, A!10)) | (~((~in(ordered_pair(tptp_fun_C_2(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), relation_restriction(B!9, A!10))) | (~in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_C_2(relation_restriction(B!9, A!10))), relation_restriction(B!9, A!10))) | in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), relation_restriction(B!9, A!10)))))))))),
% 0.11/0.38 inference(rewrite,[status(thm)],[])).
% 0.11/0.38 tff(72,plain,
% 0.11/0.38 (((~relation(relation_restriction(B!9, A!10))) | (~((~((~transitive(relation_restriction(B!9, A!10))) | ![B: $i, C: $i, D: $i] : (in(ordered_pair(B, D), relation_restriction(B!9, A!10)) | (~in(ordered_pair(B, C), relation_restriction(B!9, A!10))) | (~in(ordered_pair(C, D), relation_restriction(B!9, A!10)))))) | (~(transitive(relation_restriction(B!9, A!10)) | (~(in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), relation_restriction(B!9, A!10)) | (~in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_C_2(relation_restriction(B!9, A!10))), relation_restriction(B!9, A!10))) | (~in(ordered_pair(tptp_fun_C_2(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), relation_restriction(B!9, A!10)))))))))) <=> ((~relation(relation_restriction(B!9, A!10))) | (~((~((~transitive(relation_restriction(B!9, A!10))) | ![B: $i, C: $i, D: $i] : (in(ordered_pair(B, D), relation_restriction(B!9, A!10)) | (~in(ordered_pair(B, C), relation_restriction(B!9, A!10))) | (~in(ordered_pair(C, D), relation_restriction(B!9, A!10)))))) | (~(transitive(relation_restriction(B!9, A!10)) | (~((~in(ordered_pair(tptp_fun_C_2(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), relation_restriction(B!9, A!10))) | (~in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_C_2(relation_restriction(B!9, A!10))), relation_restriction(B!9, A!10))) | in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), relation_restriction(B!9, A!10)))))))))),
% 0.11/0.39 inference(rewrite,[status(thm)],[])).
% 0.11/0.39 tff(73,plain,
% 0.11/0.39 (((~![A: $i] : ((~relation(A)) | (~((~((~transitive(A)) | ![B: $i, C: $i, D: $i] : (in(ordered_pair(B, D), A) | (~in(ordered_pair(B, C), A)) | (~in(ordered_pair(C, D), A))))) | (~(transitive(A) | (~(in(ordered_pair(tptp_fun_B_3(A), tptp_fun_D_1(A)), A) | (~in(ordered_pair(tptp_fun_B_3(A), tptp_fun_C_2(A)), A)) | (~in(ordered_pair(tptp_fun_C_2(A), tptp_fun_D_1(A)), A)))))))))) | ((~relation(relation_restriction(B!9, A!10))) | (~((~((~transitive(relation_restriction(B!9, A!10))) | ![B: $i, C: $i, D: $i] : (in(ordered_pair(B, D), relation_restriction(B!9, A!10)) | (~in(ordered_pair(B, C), relation_restriction(B!9, A!10))) | (~in(ordered_pair(C, D), relation_restriction(B!9, A!10)))))) | (~(transitive(relation_restriction(B!9, A!10)) | (~(in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), relation_restriction(B!9, A!10)) | (~in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_C_2(relation_restriction(B!9, A!10))), relation_restriction(B!9, A!10))) | (~in(ordered_pair(tptp_fun_C_2(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), relation_restriction(B!9, A!10))))))))))) <=> ((~![A: $i] : ((~relation(A)) | (~((~((~transitive(A)) | ![B: $i, C: $i, D: $i] : (in(ordered_pair(B, D), A) | (~in(ordered_pair(B, C), A)) | (~in(ordered_pair(C, D), A))))) | (~(transitive(A) | (~(in(ordered_pair(tptp_fun_B_3(A), tptp_fun_D_1(A)), A) | (~in(ordered_pair(tptp_fun_B_3(A), tptp_fun_C_2(A)), A)) | (~in(ordered_pair(tptp_fun_C_2(A), tptp_fun_D_1(A)), A)))))))))) | ((~relation(relation_restriction(B!9, A!10))) | (~((~((~transitive(relation_restriction(B!9, A!10))) | ![B: $i, C: $i, D: $i] : (in(ordered_pair(B, D), relation_restriction(B!9, A!10)) | (~in(ordered_pair(B, C), relation_restriction(B!9, A!10))) | (~in(ordered_pair(C, D), relation_restriction(B!9, A!10)))))) | (~(transitive(relation_restriction(B!9, A!10)) | (~((~in(ordered_pair(tptp_fun_C_2(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), relation_restriction(B!9, A!10))) | (~in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_C_2(relation_restriction(B!9, A!10))), relation_restriction(B!9, A!10))) | in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), relation_restriction(B!9, A!10))))))))))),
% 0.11/0.39 inference(monotonicity,[status(thm)],[72])).
% 0.11/0.39 tff(74,plain,
% 0.11/0.39 (((~![A: $i] : ((~relation(A)) | (~((~((~transitive(A)) | ![B: $i, C: $i, D: $i] : (in(ordered_pair(B, D), A) | (~in(ordered_pair(B, C), A)) | (~in(ordered_pair(C, D), A))))) | (~(transitive(A) | (~(in(ordered_pair(tptp_fun_B_3(A), tptp_fun_D_1(A)), A) | (~in(ordered_pair(tptp_fun_B_3(A), tptp_fun_C_2(A)), A)) | (~in(ordered_pair(tptp_fun_C_2(A), tptp_fun_D_1(A)), A)))))))))) | ((~relation(relation_restriction(B!9, A!10))) | (~((~((~transitive(relation_restriction(B!9, A!10))) | ![B: $i, C: $i, D: $i] : (in(ordered_pair(B, D), relation_restriction(B!9, A!10)) | (~in(ordered_pair(B, C), relation_restriction(B!9, A!10))) | (~in(ordered_pair(C, D), relation_restriction(B!9, A!10)))))) | (~(transitive(relation_restriction(B!9, A!10)) | (~(in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), relation_restriction(B!9, A!10)) | (~in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_C_2(relation_restriction(B!9, A!10))), relation_restriction(B!9, A!10))) | (~in(ordered_pair(tptp_fun_C_2(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), relation_restriction(B!9, A!10))))))))))) <=> ((~![A: $i] : ((~relation(A)) | (~((~((~transitive(A)) | ![B: $i, C: $i, D: $i] : (in(ordered_pair(B, D), A) | (~in(ordered_pair(B, C), A)) | (~in(ordered_pair(C, D), A))))) | (~(transitive(A) | (~(in(ordered_pair(tptp_fun_B_3(A), tptp_fun_D_1(A)), A) | (~in(ordered_pair(tptp_fun_B_3(A), tptp_fun_C_2(A)), A)) | (~in(ordered_pair(tptp_fun_C_2(A), tptp_fun_D_1(A)), A)))))))))) | (~relation(relation_restriction(B!9, A!10))) | (~((~((~transitive(relation_restriction(B!9, A!10))) | ![B: $i, C: $i, D: $i] : (in(ordered_pair(B, D), relation_restriction(B!9, A!10)) | (~in(ordered_pair(B, C), relation_restriction(B!9, A!10))) | (~in(ordered_pair(C, D), relation_restriction(B!9, A!10)))))) | (~(transitive(relation_restriction(B!9, A!10)) | (~((~in(ordered_pair(tptp_fun_C_2(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), relation_restriction(B!9, A!10))) | (~in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_C_2(relation_restriction(B!9, A!10))), relation_restriction(B!9, A!10))) | in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), relation_restriction(B!9, A!10)))))))))),
% 0.11/0.39 inference(transitivity,[status(thm)],[73, 71])).
% 0.11/0.39 tff(75,plain,
% 0.11/0.39 ((~![A: $i] : ((~relation(A)) | (~((~((~transitive(A)) | ![B: $i, C: $i, D: $i] : (in(ordered_pair(B, D), A) | (~in(ordered_pair(B, C), A)) | (~in(ordered_pair(C, D), A))))) | (~(transitive(A) | (~(in(ordered_pair(tptp_fun_B_3(A), tptp_fun_D_1(A)), A) | (~in(ordered_pair(tptp_fun_B_3(A), tptp_fun_C_2(A)), A)) | (~in(ordered_pair(tptp_fun_C_2(A), tptp_fun_D_1(A)), A)))))))))) | ((~relation(relation_restriction(B!9, A!10))) | (~((~((~transitive(relation_restriction(B!9, A!10))) | ![B: $i, C: $i, D: $i] : (in(ordered_pair(B, D), relation_restriction(B!9, A!10)) | (~in(ordered_pair(B, C), relation_restriction(B!9, A!10))) | (~in(ordered_pair(C, D), relation_restriction(B!9, A!10)))))) | (~(transitive(relation_restriction(B!9, A!10)) | (~(in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), relation_restriction(B!9, A!10)) | (~in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_C_2(relation_restriction(B!9, A!10))), relation_restriction(B!9, A!10))) | (~in(ordered_pair(tptp_fun_C_2(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), relation_restriction(B!9, A!10))))))))))),
% 0.11/0.39 inference(quant_inst,[status(thm)],[])).
% 0.11/0.39 tff(76,plain,
% 0.11/0.39 ((~![A: $i] : ((~relation(A)) | (~((~((~transitive(A)) | ![B: $i, C: $i, D: $i] : (in(ordered_pair(B, D), A) | (~in(ordered_pair(B, C), A)) | (~in(ordered_pair(C, D), A))))) | (~(transitive(A) | (~(in(ordered_pair(tptp_fun_B_3(A), tptp_fun_D_1(A)), A) | (~in(ordered_pair(tptp_fun_B_3(A), tptp_fun_C_2(A)), A)) | (~in(ordered_pair(tptp_fun_C_2(A), tptp_fun_D_1(A)), A)))))))))) | (~relation(relation_restriction(B!9, A!10))) | (~((~((~transitive(relation_restriction(B!9, A!10))) | ![B: $i, C: $i, D: $i] : (in(ordered_pair(B, D), relation_restriction(B!9, A!10)) | (~in(ordered_pair(B, C), relation_restriction(B!9, A!10))) | (~in(ordered_pair(C, D), relation_restriction(B!9, A!10)))))) | (~(transitive(relation_restriction(B!9, A!10)) | (~((~in(ordered_pair(tptp_fun_C_2(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), relation_restriction(B!9, A!10))) | (~in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_C_2(relation_restriction(B!9, A!10))), relation_restriction(B!9, A!10))) | in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), relation_restriction(B!9, A!10))))))))),
% 0.11/0.39 inference(modus_ponens,[status(thm)],[75, 74])).
% 0.11/0.39 tff(77,plain,
% 0.11/0.39 (~((~((~transitive(relation_restriction(B!9, A!10))) | ![B: $i, C: $i, D: $i] : (in(ordered_pair(B, D), relation_restriction(B!9, A!10)) | (~in(ordered_pair(B, C), relation_restriction(B!9, A!10))) | (~in(ordered_pair(C, D), relation_restriction(B!9, A!10)))))) | (~(transitive(relation_restriction(B!9, A!10)) | (~((~in(ordered_pair(tptp_fun_C_2(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), relation_restriction(B!9, A!10))) | (~in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_C_2(relation_restriction(B!9, A!10))), relation_restriction(B!9, A!10))) | in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), relation_restriction(B!9, A!10)))))))),
% 0.11/0.39 inference(unit_resolution,[status(thm)],[76, 70, 54])).
% 0.11/0.39 tff(78,plain,
% 0.11/0.39 (((~((~transitive(relation_restriction(B!9, A!10))) | ![B: $i, C: $i, D: $i] : (in(ordered_pair(B, D), relation_restriction(B!9, A!10)) | (~in(ordered_pair(B, C), relation_restriction(B!9, A!10))) | (~in(ordered_pair(C, D), relation_restriction(B!9, A!10)))))) | (~(transitive(relation_restriction(B!9, A!10)) | (~((~in(ordered_pair(tptp_fun_C_2(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), relation_restriction(B!9, A!10))) | (~in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_C_2(relation_restriction(B!9, A!10))), relation_restriction(B!9, A!10))) | in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), relation_restriction(B!9, A!10))))))) | (transitive(relation_restriction(B!9, A!10)) | (~((~in(ordered_pair(tptp_fun_C_2(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), relation_restriction(B!9, A!10))) | (~in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_C_2(relation_restriction(B!9, A!10))), relation_restriction(B!9, A!10))) | in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), relation_restriction(B!9, A!10)))))),
% 0.11/0.39 inference(tautology,[status(thm)],[])).
% 0.11/0.39 tff(79,plain,
% 0.11/0.39 (transitive(relation_restriction(B!9, A!10)) | (~((~in(ordered_pair(tptp_fun_C_2(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), relation_restriction(B!9, A!10))) | (~in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_C_2(relation_restriction(B!9, A!10))), relation_restriction(B!9, A!10))) | in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), relation_restriction(B!9, A!10))))),
% 0.11/0.39 inference(unit_resolution,[status(thm)],[78, 77])).
% 0.11/0.39 tff(80,plain,
% 0.11/0.39 (~transitive(relation_restriction(B!9, A!10))),
% 0.11/0.39 inference(or_elim,[status(thm)],[22])).
% 0.11/0.39 tff(81,plain,
% 0.11/0.39 ((~(transitive(relation_restriction(B!9, A!10)) | (~((~in(ordered_pair(tptp_fun_C_2(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), relation_restriction(B!9, A!10))) | (~in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_C_2(relation_restriction(B!9, A!10))), relation_restriction(B!9, A!10))) | in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), relation_restriction(B!9, A!10)))))) | transitive(relation_restriction(B!9, A!10)) | (~((~in(ordered_pair(tptp_fun_C_2(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), relation_restriction(B!9, A!10))) | (~in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_C_2(relation_restriction(B!9, A!10))), relation_restriction(B!9, A!10))) | in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), relation_restriction(B!9, A!10))))),
% 0.11/0.39 inference(tautology,[status(thm)],[])).
% 0.11/0.39 tff(82,plain,
% 0.11/0.39 ((~(transitive(relation_restriction(B!9, A!10)) | (~((~in(ordered_pair(tptp_fun_C_2(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), relation_restriction(B!9, A!10))) | (~in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_C_2(relation_restriction(B!9, A!10))), relation_restriction(B!9, A!10))) | in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), relation_restriction(B!9, A!10)))))) | (~((~in(ordered_pair(tptp_fun_C_2(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), relation_restriction(B!9, A!10))) | (~in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_C_2(relation_restriction(B!9, A!10))), relation_restriction(B!9, A!10))) | in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), relation_restriction(B!9, A!10))))),
% 0.11/0.39 inference(unit_resolution,[status(thm)],[81, 80])).
% 0.11/0.39 tff(83,plain,
% 0.11/0.39 (~((~in(ordered_pair(tptp_fun_C_2(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), relation_restriction(B!9, A!10))) | (~in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_C_2(relation_restriction(B!9, A!10))), relation_restriction(B!9, A!10))) | in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), relation_restriction(B!9, A!10)))),
% 0.11/0.39 inference(unit_resolution,[status(thm)],[82, 79])).
% 0.11/0.39 tff(84,plain,
% 0.11/0.39 (((~in(ordered_pair(tptp_fun_C_2(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), relation_restriction(B!9, A!10))) | (~in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_C_2(relation_restriction(B!9, A!10))), relation_restriction(B!9, A!10))) | in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), relation_restriction(B!9, A!10))) | (~in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), relation_restriction(B!9, A!10)))),
% 0.11/0.39 inference(tautology,[status(thm)],[])).
% 0.11/0.39 tff(85,plain,
% 0.11/0.39 (~in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), relation_restriction(B!9, A!10))),
% 0.11/0.39 inference(unit_resolution,[status(thm)],[84, 83])).
% 0.11/0.39 tff(86,plain,
% 0.11/0.39 ((((~in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), B!9)) | (~in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), cartesian_product2(A!10, A!10)))) <=> in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), relation_restriction(B!9, A!10))) | ((~in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), B!9)) | (~in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), cartesian_product2(A!10, A!10)))) | in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), relation_restriction(B!9, A!10))),
% 0.11/0.39 inference(tautology,[status(thm)],[])).
% 0.11/0.39 tff(87,plain,
% 0.11/0.39 ((((~in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), B!9)) | (~in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), cartesian_product2(A!10, A!10)))) <=> in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), relation_restriction(B!9, A!10))) | ((~in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), B!9)) | (~in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), cartesian_product2(A!10, A!10))))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[86, 85])).
% 0.19/0.40 tff(88,plain,
% 0.19/0.40 ((~in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), B!9)) | (~in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), cartesian_product2(A!10, A!10)))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[87, 40])).
% 0.19/0.40 tff(89,plain,
% 0.19/0.40 (((~![A: $i, B: $i, C: $i] : ((~relation(C)) | (~(((~in(A, C)) | (~in(A, cartesian_product2(B, B)))) <=> in(A, relation_restriction(C, B)))))) | ((~relation(B!9)) | (~(((~in(ordered_pair(tptp_fun_C_2(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), B!9)) | (~in(ordered_pair(tptp_fun_C_2(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), cartesian_product2(A!10, A!10)))) <=> in(ordered_pair(tptp_fun_C_2(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), relation_restriction(B!9, A!10)))))) <=> ((~![A: $i, B: $i, C: $i] : ((~relation(C)) | (~(((~in(A, C)) | (~in(A, cartesian_product2(B, B)))) <=> in(A, relation_restriction(C, B)))))) | (~relation(B!9)) | (~(((~in(ordered_pair(tptp_fun_C_2(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), B!9)) | (~in(ordered_pair(tptp_fun_C_2(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), cartesian_product2(A!10, A!10)))) <=> in(ordered_pair(tptp_fun_C_2(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), relation_restriction(B!9, A!10)))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(90,plain,
% 0.19/0.40 ((~![A: $i, B: $i, C: $i] : ((~relation(C)) | (~(((~in(A, C)) | (~in(A, cartesian_product2(B, B)))) <=> in(A, relation_restriction(C, B)))))) | ((~relation(B!9)) | (~(((~in(ordered_pair(tptp_fun_C_2(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), B!9)) | (~in(ordered_pair(tptp_fun_C_2(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), cartesian_product2(A!10, A!10)))) <=> in(ordered_pair(tptp_fun_C_2(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), relation_restriction(B!9, A!10)))))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(91,plain,
% 0.19/0.40 ((~![A: $i, B: $i, C: $i] : ((~relation(C)) | (~(((~in(A, C)) | (~in(A, cartesian_product2(B, B)))) <=> in(A, relation_restriction(C, B)))))) | (~relation(B!9)) | (~(((~in(ordered_pair(tptp_fun_C_2(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), B!9)) | (~in(ordered_pair(tptp_fun_C_2(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), cartesian_product2(A!10, A!10)))) <=> in(ordered_pair(tptp_fun_C_2(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), relation_restriction(B!9, A!10))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[90, 89])).
% 0.19/0.40 tff(92,plain,
% 0.19/0.40 (~(((~in(ordered_pair(tptp_fun_C_2(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), B!9)) | (~in(ordered_pair(tptp_fun_C_2(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), cartesian_product2(A!10, A!10)))) <=> in(ordered_pair(tptp_fun_C_2(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), relation_restriction(B!9, A!10)))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[91, 36, 23])).
% 0.19/0.40 tff(93,plain,
% 0.19/0.40 (((~in(ordered_pair(tptp_fun_C_2(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), relation_restriction(B!9, A!10))) | (~in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_C_2(relation_restriction(B!9, A!10))), relation_restriction(B!9, A!10))) | in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), relation_restriction(B!9, A!10))) | in(ordered_pair(tptp_fun_C_2(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), relation_restriction(B!9, A!10))),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(94,plain,
% 0.19/0.40 (in(ordered_pair(tptp_fun_C_2(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), relation_restriction(B!9, A!10))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[93, 83])).
% 0.19/0.40 tff(95,plain,
% 0.19/0.40 ((((~in(ordered_pair(tptp_fun_C_2(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), B!9)) | (~in(ordered_pair(tptp_fun_C_2(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), cartesian_product2(A!10, A!10)))) <=> in(ordered_pair(tptp_fun_C_2(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), relation_restriction(B!9, A!10))) | (~((~in(ordered_pair(tptp_fun_C_2(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), B!9)) | (~in(ordered_pair(tptp_fun_C_2(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), cartesian_product2(A!10, A!10))))) | (~in(ordered_pair(tptp_fun_C_2(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), relation_restriction(B!9, A!10)))),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(96,plain,
% 0.19/0.40 ((((~in(ordered_pair(tptp_fun_C_2(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), B!9)) | (~in(ordered_pair(tptp_fun_C_2(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), cartesian_product2(A!10, A!10)))) <=> in(ordered_pair(tptp_fun_C_2(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), relation_restriction(B!9, A!10))) | (~((~in(ordered_pair(tptp_fun_C_2(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), B!9)) | (~in(ordered_pair(tptp_fun_C_2(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), cartesian_product2(A!10, A!10)))))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[95, 94])).
% 0.19/0.40 tff(97,plain,
% 0.19/0.40 (~((~in(ordered_pair(tptp_fun_C_2(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), B!9)) | (~in(ordered_pair(tptp_fun_C_2(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), cartesian_product2(A!10, A!10))))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[96, 92])).
% 0.19/0.40 tff(98,plain,
% 0.19/0.40 (((~in(ordered_pair(tptp_fun_C_2(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), B!9)) | (~in(ordered_pair(tptp_fun_C_2(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), cartesian_product2(A!10, A!10)))) | in(ordered_pair(tptp_fun_C_2(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), B!9)),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(99,plain,
% 0.19/0.40 (in(ordered_pair(tptp_fun_C_2(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), B!9)),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[98, 97])).
% 0.19/0.40 tff(100,plain,
% 0.19/0.40 (((~![A: $i, B: $i, C: $i] : ((~relation(C)) | (~(((~in(A, C)) | (~in(A, cartesian_product2(B, B)))) <=> in(A, relation_restriction(C, B)))))) | ((~relation(B!9)) | (~(((~in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_C_2(relation_restriction(B!9, A!10))), B!9)) | (~in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_C_2(relation_restriction(B!9, A!10))), cartesian_product2(A!10, A!10)))) <=> in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_C_2(relation_restriction(B!9, A!10))), relation_restriction(B!9, A!10)))))) <=> ((~![A: $i, B: $i, C: $i] : ((~relation(C)) | (~(((~in(A, C)) | (~in(A, cartesian_product2(B, B)))) <=> in(A, relation_restriction(C, B)))))) | (~relation(B!9)) | (~(((~in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_C_2(relation_restriction(B!9, A!10))), B!9)) | (~in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_C_2(relation_restriction(B!9, A!10))), cartesian_product2(A!10, A!10)))) <=> in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_C_2(relation_restriction(B!9, A!10))), relation_restriction(B!9, A!10)))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(101,plain,
% 0.19/0.40 ((~![A: $i, B: $i, C: $i] : ((~relation(C)) | (~(((~in(A, C)) | (~in(A, cartesian_product2(B, B)))) <=> in(A, relation_restriction(C, B)))))) | ((~relation(B!9)) | (~(((~in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_C_2(relation_restriction(B!9, A!10))), B!9)) | (~in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_C_2(relation_restriction(B!9, A!10))), cartesian_product2(A!10, A!10)))) <=> in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_C_2(relation_restriction(B!9, A!10))), relation_restriction(B!9, A!10)))))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(102,plain,
% 0.19/0.40 ((~![A: $i, B: $i, C: $i] : ((~relation(C)) | (~(((~in(A, C)) | (~in(A, cartesian_product2(B, B)))) <=> in(A, relation_restriction(C, B)))))) | (~relation(B!9)) | (~(((~in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_C_2(relation_restriction(B!9, A!10))), B!9)) | (~in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_C_2(relation_restriction(B!9, A!10))), cartesian_product2(A!10, A!10)))) <=> in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_C_2(relation_restriction(B!9, A!10))), relation_restriction(B!9, A!10))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[101, 100])).
% 0.19/0.40 tff(103,plain,
% 0.19/0.40 (~(((~in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_C_2(relation_restriction(B!9, A!10))), B!9)) | (~in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_C_2(relation_restriction(B!9, A!10))), cartesian_product2(A!10, A!10)))) <=> in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_C_2(relation_restriction(B!9, A!10))), relation_restriction(B!9, A!10)))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[102, 36, 23])).
% 0.19/0.40 tff(104,plain,
% 0.19/0.40 (((~in(ordered_pair(tptp_fun_C_2(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), relation_restriction(B!9, A!10))) | (~in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_C_2(relation_restriction(B!9, A!10))), relation_restriction(B!9, A!10))) | in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), relation_restriction(B!9, A!10))) | in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_C_2(relation_restriction(B!9, A!10))), relation_restriction(B!9, A!10))),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(105,plain,
% 0.19/0.40 (in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_C_2(relation_restriction(B!9, A!10))), relation_restriction(B!9, A!10))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[104, 83])).
% 0.19/0.40 tff(106,plain,
% 0.19/0.40 ((((~in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_C_2(relation_restriction(B!9, A!10))), B!9)) | (~in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_C_2(relation_restriction(B!9, A!10))), cartesian_product2(A!10, A!10)))) <=> in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_C_2(relation_restriction(B!9, A!10))), relation_restriction(B!9, A!10))) | (~((~in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_C_2(relation_restriction(B!9, A!10))), B!9)) | (~in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_C_2(relation_restriction(B!9, A!10))), cartesian_product2(A!10, A!10))))) | (~in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_C_2(relation_restriction(B!9, A!10))), relation_restriction(B!9, A!10)))),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(107,plain,
% 0.19/0.40 ((((~in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_C_2(relation_restriction(B!9, A!10))), B!9)) | (~in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_C_2(relation_restriction(B!9, A!10))), cartesian_product2(A!10, A!10)))) <=> in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_C_2(relation_restriction(B!9, A!10))), relation_restriction(B!9, A!10))) | (~((~in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_C_2(relation_restriction(B!9, A!10))), B!9)) | (~in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_C_2(relation_restriction(B!9, A!10))), cartesian_product2(A!10, A!10)))))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[106, 105])).
% 0.19/0.41 tff(108,plain,
% 0.19/0.41 (~((~in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_C_2(relation_restriction(B!9, A!10))), B!9)) | (~in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_C_2(relation_restriction(B!9, A!10))), cartesian_product2(A!10, A!10))))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[107, 103])).
% 0.19/0.41 tff(109,plain,
% 0.19/0.41 (((~in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_C_2(relation_restriction(B!9, A!10))), B!9)) | (~in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_C_2(relation_restriction(B!9, A!10))), cartesian_product2(A!10, A!10)))) | in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_C_2(relation_restriction(B!9, A!10))), B!9)),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(110,plain,
% 0.19/0.41 (in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_C_2(relation_restriction(B!9, A!10))), B!9)),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[109, 108])).
% 0.19/0.41 tff(111,plain,
% 0.19/0.41 (((~![A: $i] : ((~relation(A)) | (~((~((~transitive(A)) | ![B: $i, C: $i, D: $i] : (in(ordered_pair(B, D), A) | (~in(ordered_pair(B, C), A)) | (~in(ordered_pair(C, D), A))))) | (~(transitive(A) | (~(in(ordered_pair(tptp_fun_B_3(A), tptp_fun_D_1(A)), A) | (~in(ordered_pair(tptp_fun_B_3(A), tptp_fun_C_2(A)), A)) | (~in(ordered_pair(tptp_fun_C_2(A), tptp_fun_D_1(A)), A)))))))))) | ((~relation(B!9)) | (~((~((~transitive(B!9)) | ![B: $i, C: $i, D: $i] : (in(ordered_pair(B, D), B!9) | (~in(ordered_pair(B, C), B!9)) | (~in(ordered_pair(C, D), B!9))))) | (~(transitive(B!9) | (~((~in(ordered_pair(tptp_fun_C_2(B!9), tptp_fun_D_1(B!9)), B!9)) | (~in(ordered_pair(tptp_fun_B_3(B!9), tptp_fun_C_2(B!9)), B!9)) | in(ordered_pair(tptp_fun_B_3(B!9), tptp_fun_D_1(B!9)), B!9))))))))) <=> ((~![A: $i] : ((~relation(A)) | (~((~((~transitive(A)) | ![B: $i, C: $i, D: $i] : (in(ordered_pair(B, D), A) | (~in(ordered_pair(B, C), A)) | (~in(ordered_pair(C, D), A))))) | (~(transitive(A) | (~(in(ordered_pair(tptp_fun_B_3(A), tptp_fun_D_1(A)), A) | (~in(ordered_pair(tptp_fun_B_3(A), tptp_fun_C_2(A)), A)) | (~in(ordered_pair(tptp_fun_C_2(A), tptp_fun_D_1(A)), A)))))))))) | (~relation(B!9)) | (~((~((~transitive(B!9)) | ![B: $i, C: $i, D: $i] : (in(ordered_pair(B, D), B!9) | (~in(ordered_pair(B, C), B!9)) | (~in(ordered_pair(C, D), B!9))))) | (~(transitive(B!9) | (~((~in(ordered_pair(tptp_fun_C_2(B!9), tptp_fun_D_1(B!9)), B!9)) | (~in(ordered_pair(tptp_fun_B_3(B!9), tptp_fun_C_2(B!9)), B!9)) | in(ordered_pair(tptp_fun_B_3(B!9), tptp_fun_D_1(B!9)), B!9))))))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(112,plain,
% 0.19/0.41 (((~relation(B!9)) | (~((~((~transitive(B!9)) | ![B: $i, C: $i, D: $i] : (in(ordered_pair(B, D), B!9) | (~in(ordered_pair(B, C), B!9)) | (~in(ordered_pair(C, D), B!9))))) | (~(transitive(B!9) | (~(in(ordered_pair(tptp_fun_B_3(B!9), tptp_fun_D_1(B!9)), B!9) | (~in(ordered_pair(tptp_fun_B_3(B!9), tptp_fun_C_2(B!9)), B!9)) | (~in(ordered_pair(tptp_fun_C_2(B!9), tptp_fun_D_1(B!9)), B!9))))))))) <=> ((~relation(B!9)) | (~((~((~transitive(B!9)) | ![B: $i, C: $i, D: $i] : (in(ordered_pair(B, D), B!9) | (~in(ordered_pair(B, C), B!9)) | (~in(ordered_pair(C, D), B!9))))) | (~(transitive(B!9) | (~((~in(ordered_pair(tptp_fun_C_2(B!9), tptp_fun_D_1(B!9)), B!9)) | (~in(ordered_pair(tptp_fun_B_3(B!9), tptp_fun_C_2(B!9)), B!9)) | in(ordered_pair(tptp_fun_B_3(B!9), tptp_fun_D_1(B!9)), B!9))))))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(113,plain,
% 0.19/0.41 (((~![A: $i] : ((~relation(A)) | (~((~((~transitive(A)) | ![B: $i, C: $i, D: $i] : (in(ordered_pair(B, D), A) | (~in(ordered_pair(B, C), A)) | (~in(ordered_pair(C, D), A))))) | (~(transitive(A) | (~(in(ordered_pair(tptp_fun_B_3(A), tptp_fun_D_1(A)), A) | (~in(ordered_pair(tptp_fun_B_3(A), tptp_fun_C_2(A)), A)) | (~in(ordered_pair(tptp_fun_C_2(A), tptp_fun_D_1(A)), A)))))))))) | ((~relation(B!9)) | (~((~((~transitive(B!9)) | ![B: $i, C: $i, D: $i] : (in(ordered_pair(B, D), B!9) | (~in(ordered_pair(B, C), B!9)) | (~in(ordered_pair(C, D), B!9))))) | (~(transitive(B!9) | (~(in(ordered_pair(tptp_fun_B_3(B!9), tptp_fun_D_1(B!9)), B!9) | (~in(ordered_pair(tptp_fun_B_3(B!9), tptp_fun_C_2(B!9)), B!9)) | (~in(ordered_pair(tptp_fun_C_2(B!9), tptp_fun_D_1(B!9)), B!9)))))))))) <=> ((~![A: $i] : ((~relation(A)) | (~((~((~transitive(A)) | ![B: $i, C: $i, D: $i] : (in(ordered_pair(B, D), A) | (~in(ordered_pair(B, C), A)) | (~in(ordered_pair(C, D), A))))) | (~(transitive(A) | (~(in(ordered_pair(tptp_fun_B_3(A), tptp_fun_D_1(A)), A) | (~in(ordered_pair(tptp_fun_B_3(A), tptp_fun_C_2(A)), A)) | (~in(ordered_pair(tptp_fun_C_2(A), tptp_fun_D_1(A)), A)))))))))) | ((~relation(B!9)) | (~((~((~transitive(B!9)) | ![B: $i, C: $i, D: $i] : (in(ordered_pair(B, D), B!9) | (~in(ordered_pair(B, C), B!9)) | (~in(ordered_pair(C, D), B!9))))) | (~(transitive(B!9) | (~((~in(ordered_pair(tptp_fun_C_2(B!9), tptp_fun_D_1(B!9)), B!9)) | (~in(ordered_pair(tptp_fun_B_3(B!9), tptp_fun_C_2(B!9)), B!9)) | in(ordered_pair(tptp_fun_B_3(B!9), tptp_fun_D_1(B!9)), B!9)))))))))),
% 0.19/0.41 inference(monotonicity,[status(thm)],[112])).
% 0.19/0.41 tff(114,plain,
% 0.19/0.41 (((~![A: $i] : ((~relation(A)) | (~((~((~transitive(A)) | ![B: $i, C: $i, D: $i] : (in(ordered_pair(B, D), A) | (~in(ordered_pair(B, C), A)) | (~in(ordered_pair(C, D), A))))) | (~(transitive(A) | (~(in(ordered_pair(tptp_fun_B_3(A), tptp_fun_D_1(A)), A) | (~in(ordered_pair(tptp_fun_B_3(A), tptp_fun_C_2(A)), A)) | (~in(ordered_pair(tptp_fun_C_2(A), tptp_fun_D_1(A)), A)))))))))) | ((~relation(B!9)) | (~((~((~transitive(B!9)) | ![B: $i, C: $i, D: $i] : (in(ordered_pair(B, D), B!9) | (~in(ordered_pair(B, C), B!9)) | (~in(ordered_pair(C, D), B!9))))) | (~(transitive(B!9) | (~(in(ordered_pair(tptp_fun_B_3(B!9), tptp_fun_D_1(B!9)), B!9) | (~in(ordered_pair(tptp_fun_B_3(B!9), tptp_fun_C_2(B!9)), B!9)) | (~in(ordered_pair(tptp_fun_C_2(B!9), tptp_fun_D_1(B!9)), B!9)))))))))) <=> ((~![A: $i] : ((~relation(A)) | (~((~((~transitive(A)) | ![B: $i, C: $i, D: $i] : (in(ordered_pair(B, D), A) | (~in(ordered_pair(B, C), A)) | (~in(ordered_pair(C, D), A))))) | (~(transitive(A) | (~(in(ordered_pair(tptp_fun_B_3(A), tptp_fun_D_1(A)), A) | (~in(ordered_pair(tptp_fun_B_3(A), tptp_fun_C_2(A)), A)) | (~in(ordered_pair(tptp_fun_C_2(A), tptp_fun_D_1(A)), A)))))))))) | (~relation(B!9)) | (~((~((~transitive(B!9)) | ![B: $i, C: $i, D: $i] : (in(ordered_pair(B, D), B!9) | (~in(ordered_pair(B, C), B!9)) | (~in(ordered_pair(C, D), B!9))))) | (~(transitive(B!9) | (~((~in(ordered_pair(tptp_fun_C_2(B!9), tptp_fun_D_1(B!9)), B!9)) | (~in(ordered_pair(tptp_fun_B_3(B!9), tptp_fun_C_2(B!9)), B!9)) | in(ordered_pair(tptp_fun_B_3(B!9), tptp_fun_D_1(B!9)), B!9))))))))),
% 0.19/0.41 inference(transitivity,[status(thm)],[113, 111])).
% 0.19/0.41 tff(115,plain,
% 0.19/0.41 ((~![A: $i] : ((~relation(A)) | (~((~((~transitive(A)) | ![B: $i, C: $i, D: $i] : (in(ordered_pair(B, D), A) | (~in(ordered_pair(B, C), A)) | (~in(ordered_pair(C, D), A))))) | (~(transitive(A) | (~(in(ordered_pair(tptp_fun_B_3(A), tptp_fun_D_1(A)), A) | (~in(ordered_pair(tptp_fun_B_3(A), tptp_fun_C_2(A)), A)) | (~in(ordered_pair(tptp_fun_C_2(A), tptp_fun_D_1(A)), A)))))))))) | ((~relation(B!9)) | (~((~((~transitive(B!9)) | ![B: $i, C: $i, D: $i] : (in(ordered_pair(B, D), B!9) | (~in(ordered_pair(B, C), B!9)) | (~in(ordered_pair(C, D), B!9))))) | (~(transitive(B!9) | (~(in(ordered_pair(tptp_fun_B_3(B!9), tptp_fun_D_1(B!9)), B!9) | (~in(ordered_pair(tptp_fun_B_3(B!9), tptp_fun_C_2(B!9)), B!9)) | (~in(ordered_pair(tptp_fun_C_2(B!9), tptp_fun_D_1(B!9)), B!9)))))))))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(116,plain,
% 0.19/0.41 ((~![A: $i] : ((~relation(A)) | (~((~((~transitive(A)) | ![B: $i, C: $i, D: $i] : (in(ordered_pair(B, D), A) | (~in(ordered_pair(B, C), A)) | (~in(ordered_pair(C, D), A))))) | (~(transitive(A) | (~(in(ordered_pair(tptp_fun_B_3(A), tptp_fun_D_1(A)), A) | (~in(ordered_pair(tptp_fun_B_3(A), tptp_fun_C_2(A)), A)) | (~in(ordered_pair(tptp_fun_C_2(A), tptp_fun_D_1(A)), A)))))))))) | (~relation(B!9)) | (~((~((~transitive(B!9)) | ![B: $i, C: $i, D: $i] : (in(ordered_pair(B, D), B!9) | (~in(ordered_pair(B, C), B!9)) | (~in(ordered_pair(C, D), B!9))))) | (~(transitive(B!9) | (~((~in(ordered_pair(tptp_fun_C_2(B!9), tptp_fun_D_1(B!9)), B!9)) | (~in(ordered_pair(tptp_fun_B_3(B!9), tptp_fun_C_2(B!9)), B!9)) | in(ordered_pair(tptp_fun_B_3(B!9), tptp_fun_D_1(B!9)), B!9)))))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[115, 114])).
% 0.19/0.41 tff(117,plain,
% 0.19/0.41 (~((~((~transitive(B!9)) | ![B: $i, C: $i, D: $i] : (in(ordered_pair(B, D), B!9) | (~in(ordered_pair(B, C), B!9)) | (~in(ordered_pair(C, D), B!9))))) | (~(transitive(B!9) | (~((~in(ordered_pair(tptp_fun_C_2(B!9), tptp_fun_D_1(B!9)), B!9)) | (~in(ordered_pair(tptp_fun_B_3(B!9), tptp_fun_C_2(B!9)), B!9)) | in(ordered_pair(tptp_fun_B_3(B!9), tptp_fun_D_1(B!9)), B!9))))))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[116, 70, 23])).
% 0.19/0.41 tff(118,plain,
% 0.19/0.41 (((~((~transitive(B!9)) | ![B: $i, C: $i, D: $i] : (in(ordered_pair(B, D), B!9) | (~in(ordered_pair(B, C), B!9)) | (~in(ordered_pair(C, D), B!9))))) | (~(transitive(B!9) | (~((~in(ordered_pair(tptp_fun_C_2(B!9), tptp_fun_D_1(B!9)), B!9)) | (~in(ordered_pair(tptp_fun_B_3(B!9), tptp_fun_C_2(B!9)), B!9)) | in(ordered_pair(tptp_fun_B_3(B!9), tptp_fun_D_1(B!9)), B!9)))))) | ((~transitive(B!9)) | ![B: $i, C: $i, D: $i] : (in(ordered_pair(B, D), B!9) | (~in(ordered_pair(B, C), B!9)) | (~in(ordered_pair(C, D), B!9))))),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(119,plain,
% 0.19/0.41 ((~transitive(B!9)) | ![B: $i, C: $i, D: $i] : (in(ordered_pair(B, D), B!9) | (~in(ordered_pair(B, C), B!9)) | (~in(ordered_pair(C, D), B!9)))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[118, 117])).
% 0.19/0.41 tff(120,plain,
% 0.19/0.41 (transitive(B!9)),
% 0.19/0.41 inference(or_elim,[status(thm)],[22])).
% 0.19/0.41 tff(121,plain,
% 0.19/0.41 ((~((~transitive(B!9)) | ![B: $i, C: $i, D: $i] : (in(ordered_pair(B, D), B!9) | (~in(ordered_pair(B, C), B!9)) | (~in(ordered_pair(C, D), B!9))))) | (~transitive(B!9)) | ![B: $i, C: $i, D: $i] : (in(ordered_pair(B, D), B!9) | (~in(ordered_pair(B, C), B!9)) | (~in(ordered_pair(C, D), B!9)))),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(122,plain,
% 0.19/0.41 ((~((~transitive(B!9)) | ![B: $i, C: $i, D: $i] : (in(ordered_pair(B, D), B!9) | (~in(ordered_pair(B, C), B!9)) | (~in(ordered_pair(C, D), B!9))))) | ![B: $i, C: $i, D: $i] : (in(ordered_pair(B, D), B!9) | (~in(ordered_pair(B, C), B!9)) | (~in(ordered_pair(C, D), B!9)))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[121, 120])).
% 0.19/0.41 tff(123,plain,
% 0.19/0.41 (![B: $i, C: $i, D: $i] : (in(ordered_pair(B, D), B!9) | (~in(ordered_pair(B, C), B!9)) | (~in(ordered_pair(C, D), B!9)))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[122, 119])).
% 0.19/0.41 tff(124,plain,
% 0.19/0.41 (((~![B: $i, C: $i, D: $i] : (in(ordered_pair(B, D), B!9) | (~in(ordered_pair(B, C), B!9)) | (~in(ordered_pair(C, D), B!9)))) | (in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), B!9) | (~in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_C_2(relation_restriction(B!9, A!10))), B!9)) | (~in(ordered_pair(tptp_fun_C_2(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), B!9)))) <=> ((~![B: $i, C: $i, D: $i] : (in(ordered_pair(B, D), B!9) | (~in(ordered_pair(B, C), B!9)) | (~in(ordered_pair(C, D), B!9)))) | in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), B!9) | (~in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_C_2(relation_restriction(B!9, A!10))), B!9)) | (~in(ordered_pair(tptp_fun_C_2(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), B!9)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(125,plain,
% 0.19/0.41 ((~![B: $i, C: $i, D: $i] : (in(ordered_pair(B, D), B!9) | (~in(ordered_pair(B, C), B!9)) | (~in(ordered_pair(C, D), B!9)))) | (in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), B!9) | (~in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_C_2(relation_restriction(B!9, A!10))), B!9)) | (~in(ordered_pair(tptp_fun_C_2(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), B!9)))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(126,plain,
% 0.19/0.41 ((~![B: $i, C: $i, D: $i] : (in(ordered_pair(B, D), B!9) | (~in(ordered_pair(B, C), B!9)) | (~in(ordered_pair(C, D), B!9)))) | in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), B!9) | (~in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_C_2(relation_restriction(B!9, A!10))), B!9)) | (~in(ordered_pair(tptp_fun_C_2(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), B!9))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[125, 124])).
% 0.19/0.41 tff(127,plain,
% 0.19/0.41 (in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), B!9) | (~in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_C_2(relation_restriction(B!9, A!10))), B!9)) | (~in(ordered_pair(tptp_fun_C_2(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), B!9))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[126, 123])).
% 0.19/0.41 tff(128,plain,
% 0.19/0.41 (in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), B!9)),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[127, 110, 99])).
% 0.19/0.41 tff(129,plain,
% 0.19/0.41 ((~((~in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), B!9)) | (~in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), cartesian_product2(A!10, A!10))))) | (~in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), B!9)) | (~in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), cartesian_product2(A!10, A!10)))),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(130,plain,
% 0.19/0.41 (~in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), cartesian_product2(A!10, A!10))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[129, 128, 88])).
% 0.19/0.41 tff(131,plain,
% 0.19/0.41 ((((~in(tptp_fun_B_3(relation_restriction(B!9, A!10)), A!10)) | (~in(tptp_fun_D_1(relation_restriction(B!9, A!10)), A!10))) <=> in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), cartesian_product2(A!10, A!10))) | ((~in(tptp_fun_B_3(relation_restriction(B!9, A!10)), A!10)) | (~in(tptp_fun_D_1(relation_restriction(B!9, A!10)), A!10))) | in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), cartesian_product2(A!10, A!10))),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(132,plain,
% 0.19/0.41 ((((~in(tptp_fun_B_3(relation_restriction(B!9, A!10)), A!10)) | (~in(tptp_fun_D_1(relation_restriction(B!9, A!10)), A!10))) <=> in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), cartesian_product2(A!10, A!10))) | ((~in(tptp_fun_B_3(relation_restriction(B!9, A!10)), A!10)) | (~in(tptp_fun_D_1(relation_restriction(B!9, A!10)), A!10)))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[131, 130])).
% 0.19/0.41 tff(133,plain,
% 0.19/0.41 ((~in(tptp_fun_B_3(relation_restriction(B!9, A!10)), A!10)) | (~in(tptp_fun_D_1(relation_restriction(B!9, A!10)), A!10))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[132, 12])).
% 0.19/0.41 tff(134,plain,
% 0.19/0.41 ((~![A: $i, B: $i, C: $i, D: $i] : (~(((~in(A, C)) | (~in(B, D))) <=> in(ordered_pair(A, B), cartesian_product2(C, D))))) | (~(((~in(tptp_fun_C_2(relation_restriction(B!9, A!10)), A!10)) | (~in(tptp_fun_D_1(relation_restriction(B!9, A!10)), A!10))) <=> in(ordered_pair(tptp_fun_C_2(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), cartesian_product2(A!10, A!10))))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(135,plain,
% 0.19/0.42 (~(((~in(tptp_fun_C_2(relation_restriction(B!9, A!10)), A!10)) | (~in(tptp_fun_D_1(relation_restriction(B!9, A!10)), A!10))) <=> in(ordered_pair(tptp_fun_C_2(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), cartesian_product2(A!10, A!10)))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[134, 10])).
% 0.19/0.42 tff(136,plain,
% 0.19/0.42 (((~in(ordered_pair(tptp_fun_C_2(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), B!9)) | (~in(ordered_pair(tptp_fun_C_2(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), cartesian_product2(A!10, A!10)))) | in(ordered_pair(tptp_fun_C_2(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), cartesian_product2(A!10, A!10))),
% 0.19/0.42 inference(tautology,[status(thm)],[])).
% 0.19/0.42 tff(137,plain,
% 0.19/0.42 (in(ordered_pair(tptp_fun_C_2(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), cartesian_product2(A!10, A!10))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[136, 97])).
% 0.19/0.42 tff(138,plain,
% 0.19/0.42 ((((~in(tptp_fun_C_2(relation_restriction(B!9, A!10)), A!10)) | (~in(tptp_fun_D_1(relation_restriction(B!9, A!10)), A!10))) <=> in(ordered_pair(tptp_fun_C_2(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), cartesian_product2(A!10, A!10))) | (~((~in(tptp_fun_C_2(relation_restriction(B!9, A!10)), A!10)) | (~in(tptp_fun_D_1(relation_restriction(B!9, A!10)), A!10)))) | (~in(ordered_pair(tptp_fun_C_2(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), cartesian_product2(A!10, A!10)))),
% 0.19/0.42 inference(tautology,[status(thm)],[])).
% 0.19/0.42 tff(139,plain,
% 0.19/0.42 ((((~in(tptp_fun_C_2(relation_restriction(B!9, A!10)), A!10)) | (~in(tptp_fun_D_1(relation_restriction(B!9, A!10)), A!10))) <=> in(ordered_pair(tptp_fun_C_2(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), cartesian_product2(A!10, A!10))) | (~((~in(tptp_fun_C_2(relation_restriction(B!9, A!10)), A!10)) | (~in(tptp_fun_D_1(relation_restriction(B!9, A!10)), A!10))))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[138, 137])).
% 0.19/0.42 tff(140,plain,
% 0.19/0.42 (~((~in(tptp_fun_C_2(relation_restriction(B!9, A!10)), A!10)) | (~in(tptp_fun_D_1(relation_restriction(B!9, A!10)), A!10)))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[139, 135])).
% 0.19/0.42 tff(141,plain,
% 0.19/0.42 (((~in(tptp_fun_C_2(relation_restriction(B!9, A!10)), A!10)) | (~in(tptp_fun_D_1(relation_restriction(B!9, A!10)), A!10))) | in(tptp_fun_D_1(relation_restriction(B!9, A!10)), A!10)),
% 0.19/0.42 inference(tautology,[status(thm)],[])).
% 0.19/0.42 tff(142,plain,
% 0.19/0.42 (in(tptp_fun_D_1(relation_restriction(B!9, A!10)), A!10)),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[141, 140])).
% 0.19/0.42 tff(143,plain,
% 0.19/0.42 ((~![A: $i, B: $i, C: $i, D: $i] : (~(((~in(A, C)) | (~in(B, D))) <=> in(ordered_pair(A, B), cartesian_product2(C, D))))) | (~(((~in(tptp_fun_B_3(relation_restriction(B!9, A!10)), A!10)) | (~in(tptp_fun_C_2(relation_restriction(B!9, A!10)), A!10))) <=> in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_C_2(relation_restriction(B!9, A!10))), cartesian_product2(A!10, A!10))))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(144,plain,
% 0.19/0.42 (~(((~in(tptp_fun_B_3(relation_restriction(B!9, A!10)), A!10)) | (~in(tptp_fun_C_2(relation_restriction(B!9, A!10)), A!10))) <=> in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_C_2(relation_restriction(B!9, A!10))), cartesian_product2(A!10, A!10)))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[143, 10])).
% 0.19/0.42 tff(145,plain,
% 0.19/0.42 (((~in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_C_2(relation_restriction(B!9, A!10))), B!9)) | (~in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_C_2(relation_restriction(B!9, A!10))), cartesian_product2(A!10, A!10)))) | in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_C_2(relation_restriction(B!9, A!10))), cartesian_product2(A!10, A!10))),
% 0.19/0.42 inference(tautology,[status(thm)],[])).
% 0.19/0.42 tff(146,plain,
% 0.19/0.42 (in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_C_2(relation_restriction(B!9, A!10))), cartesian_product2(A!10, A!10))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[145, 108])).
% 0.19/0.42 tff(147,plain,
% 0.19/0.42 ((((~in(tptp_fun_B_3(relation_restriction(B!9, A!10)), A!10)) | (~in(tptp_fun_C_2(relation_restriction(B!9, A!10)), A!10))) <=> in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_C_2(relation_restriction(B!9, A!10))), cartesian_product2(A!10, A!10))) | (~((~in(tptp_fun_B_3(relation_restriction(B!9, A!10)), A!10)) | (~in(tptp_fun_C_2(relation_restriction(B!9, A!10)), A!10)))) | (~in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_C_2(relation_restriction(B!9, A!10))), cartesian_product2(A!10, A!10)))),
% 0.19/0.42 inference(tautology,[status(thm)],[])).
% 0.19/0.42 tff(148,plain,
% 0.19/0.42 ((((~in(tptp_fun_B_3(relation_restriction(B!9, A!10)), A!10)) | (~in(tptp_fun_C_2(relation_restriction(B!9, A!10)), A!10))) <=> in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_C_2(relation_restriction(B!9, A!10))), cartesian_product2(A!10, A!10))) | (~((~in(tptp_fun_B_3(relation_restriction(B!9, A!10)), A!10)) | (~in(tptp_fun_C_2(relation_restriction(B!9, A!10)), A!10))))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[147, 146])).
% 0.19/0.42 tff(149,plain,
% 0.19/0.42 (~((~in(tptp_fun_B_3(relation_restriction(B!9, A!10)), A!10)) | (~in(tptp_fun_C_2(relation_restriction(B!9, A!10)), A!10)))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[148, 144])).
% 0.19/0.42 tff(150,plain,
% 0.19/0.42 (((~in(tptp_fun_B_3(relation_restriction(B!9, A!10)), A!10)) | (~in(tptp_fun_C_2(relation_restriction(B!9, A!10)), A!10))) | in(tptp_fun_B_3(relation_restriction(B!9, A!10)), A!10)),
% 0.19/0.42 inference(tautology,[status(thm)],[])).
% 0.19/0.42 tff(151,plain,
% 0.19/0.42 (in(tptp_fun_B_3(relation_restriction(B!9, A!10)), A!10)),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[150, 149])).
% 0.19/0.42 tff(152,plain,
% 0.19/0.42 ((~((~in(tptp_fun_B_3(relation_restriction(B!9, A!10)), A!10)) | (~in(tptp_fun_D_1(relation_restriction(B!9, A!10)), A!10)))) | (~in(tptp_fun_B_3(relation_restriction(B!9, A!10)), A!10)) | (~in(tptp_fun_D_1(relation_restriction(B!9, A!10)), A!10))),
% 0.19/0.42 inference(tautology,[status(thm)],[])).
% 0.19/0.42 tff(153,plain,
% 0.19/0.42 ($false),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[152, 151, 142, 133])).
% 0.19/0.42 % SZS output end Proof
% 0.19/0.42 % E exiting
%------------------------------------------------------------------------------