%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SEU269+1 : TPTP v9.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n009.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 05:27:27 AM UTC 2025
% Result : Theorem 0.20s 0.38s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12 % Problem : SEU269+1 : TPTP v9.0.0. Released v3.3.0.
% 0.08/0.12 % Command : run_E %s %d THM
% 0.12/0.32 % Computer : n009.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 300
% 0.12/0.32 % DateTime : Fri Jun 20 06:32:18 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.20/0.38 % SZS status Theorem
% 0.20/0.38 % SZS output start Proof
% 0.20/0.38 tff(subset_type, type, (
% 0.20/0.38 subset: ( $i * $i ) > $o)).
% 0.20/0.38 tff(tptp_fun_D_3_type, type, (
% 0.20/0.38 tptp_fun_D_3: ( $i * $i ) > $i)).
% 0.20/0.38 tff(inclusion_relation_type, type, (
% 0.20/0.38 inclusion_relation: $i > $i)).
% 0.20/0.38 tff(tptp_fun_A_15_type, type, (
% 0.20/0.38 tptp_fun_A_15: $i)).
% 0.20/0.38 tff(set_union2_type, type, (
% 0.20/0.38 set_union2: ( $i * $i ) > $i)).
% 0.20/0.38 tff(relation_rng_type, type, (
% 0.20/0.38 relation_rng: $i > $i)).
% 0.20/0.38 tff(relation_dom_type, type, (
% 0.20/0.38 relation_dom: $i > $i)).
% 0.20/0.38 tff(tptp_fun_C_4_type, type, (
% 0.20/0.38 tptp_fun_C_4: ( $i * $i ) > $i)).
% 0.20/0.38 tff(in_type, type, (
% 0.20/0.38 in: ( $i * $i ) > $o)).
% 0.20/0.38 tff(ordered_pair_type, type, (
% 0.20/0.38 ordered_pair: ( $i * $i ) > $i)).
% 0.20/0.38 tff(relation_field_type, type, (
% 0.20/0.38 relation_field: $i > $i)).
% 0.20/0.38 tff(relation_type, type, (
% 0.20/0.38 relation: $i > $o)).
% 0.20/0.38 tff(tptp_fun_D_0_type, type, (
% 0.20/0.38 tptp_fun_D_0: ( $i * $i ) > $i)).
% 0.20/0.38 tff(tptp_fun_C_1_type, type, (
% 0.20/0.38 tptp_fun_C_1: ( $i * $i ) > $i)).
% 0.20/0.38 tff(tptp_fun_E_2_type, type, (
% 0.20/0.38 tptp_fun_E_2: ( $i * $i ) > $i)).
% 0.20/0.38 tff(is_transitive_in_type, type, (
% 0.20/0.38 is_transitive_in: ( $i * $i ) > $o)).
% 0.20/0.38 tff(transitive_type, type, (
% 0.20/0.38 transitive: $i > $o)).
% 0.20/0.38 tff(1,plain,
% 0.20/0.38 (^[A: $i] : refl(relation(inclusion_relation(A)) <=> relation(inclusion_relation(A)))),
% 0.20/0.38 inference(bind,[status(th)],[])).
% 0.20/0.38 tff(2,plain,
% 0.20/0.38 (![A: $i] : relation(inclusion_relation(A)) <=> ![A: $i] : relation(inclusion_relation(A))),
% 0.20/0.38 inference(quant_intro,[status(thm)],[1])).
% 0.20/0.38 tff(3,plain,
% 0.20/0.38 (![A: $i] : relation(inclusion_relation(A)) <=> ![A: $i] : relation(inclusion_relation(A))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(4,axiom,(![A: $i] : relation(inclusion_relation(A))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_k1_wellord2')).
% 0.20/0.38 tff(5,plain,
% 0.20/0.38 (![A: $i] : relation(inclusion_relation(A))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.20/0.38 tff(6,plain,(
% 0.20/0.38 ![A: $i] : relation(inclusion_relation(A))),
% 0.20/0.38 inference(skolemize,[status(sab)],[5])).
% 0.20/0.38 tff(7,plain,
% 0.20/0.38 (![A: $i] : relation(inclusion_relation(A))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.20/0.38 tff(8,plain,
% 0.20/0.38 ((~![A: $i] : relation(inclusion_relation(A))) | relation(inclusion_relation(A!15))),
% 0.20/0.38 inference(quant_inst,[status(thm)],[])).
% 0.20/0.38 tff(9,plain,
% 0.20/0.38 (relation(inclusion_relation(A!15))),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.20/0.38 tff(10,plain,
% 0.20/0.38 (^[A: $i] : refl(((~relation(A)) | (relation_field(A) = set_union2(relation_dom(A), relation_rng(A)))) <=> ((~relation(A)) | (relation_field(A) = set_union2(relation_dom(A), relation_rng(A)))))),
% 0.20/0.38 inference(bind,[status(th)],[])).
% 0.20/0.38 tff(11,plain,
% 0.20/0.38 (![A: $i] : ((~relation(A)) | (relation_field(A) = set_union2(relation_dom(A), relation_rng(A)))) <=> ![A: $i] : ((~relation(A)) | (relation_field(A) = set_union2(relation_dom(A), relation_rng(A))))),
% 0.20/0.38 inference(quant_intro,[status(thm)],[10])).
% 0.20/0.38 tff(12,plain,
% 0.20/0.38 (![A: $i] : ((~relation(A)) | (relation_field(A) = set_union2(relation_dom(A), relation_rng(A)))) <=> ![A: $i] : ((~relation(A)) | (relation_field(A) = set_union2(relation_dom(A), relation_rng(A))))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(13,plain,
% 0.20/0.38 (^[A: $i] : rewrite((relation(A) => (relation_field(A) = set_union2(relation_dom(A), relation_rng(A)))) <=> ((~relation(A)) | (relation_field(A) = set_union2(relation_dom(A), relation_rng(A)))))),
% 0.20/0.38 inference(bind,[status(th)],[])).
% 0.20/0.38 tff(14,plain,
% 0.20/0.38 (![A: $i] : (relation(A) => (relation_field(A) = set_union2(relation_dom(A), relation_rng(A)))) <=> ![A: $i] : ((~relation(A)) | (relation_field(A) = set_union2(relation_dom(A), relation_rng(A))))),
% 0.20/0.38 inference(quant_intro,[status(thm)],[13])).
% 0.20/0.38 tff(15,axiom,(![A: $i] : (relation(A) => (relation_field(A) = set_union2(relation_dom(A), relation_rng(A))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d6_relat_1')).
% 0.20/0.38 tff(16,plain,
% 0.20/0.38 (![A: $i] : ((~relation(A)) | (relation_field(A) = set_union2(relation_dom(A), relation_rng(A))))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[15, 14])).
% 0.20/0.38 tff(17,plain,
% 0.20/0.38 (![A: $i] : ((~relation(A)) | (relation_field(A) = set_union2(relation_dom(A), relation_rng(A))))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[16, 12])).
% 0.20/0.38 tff(18,plain,(
% 0.20/0.38 ![A: $i] : ((~relation(A)) | (relation_field(A) = set_union2(relation_dom(A), relation_rng(A))))),
% 0.20/0.38 inference(skolemize,[status(sab)],[17])).
% 0.20/0.38 tff(19,plain,
% 0.20/0.38 (![A: $i] : ((~relation(A)) | (relation_field(A) = set_union2(relation_dom(A), relation_rng(A))))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[18, 11])).
% 0.20/0.38 tff(20,plain,
% 0.20/0.38 (((~![A: $i] : ((~relation(A)) | (relation_field(A) = set_union2(relation_dom(A), relation_rng(A))))) | ((~relation(inclusion_relation(A!15))) | (relation_field(inclusion_relation(A!15)) = set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15)))))) <=> ((~![A: $i] : ((~relation(A)) | (relation_field(A) = set_union2(relation_dom(A), relation_rng(A))))) | (~relation(inclusion_relation(A!15))) | (relation_field(inclusion_relation(A!15)) = set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15)))))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(21,plain,
% 0.20/0.38 ((~![A: $i] : ((~relation(A)) | (relation_field(A) = set_union2(relation_dom(A), relation_rng(A))))) | ((~relation(inclusion_relation(A!15))) | (relation_field(inclusion_relation(A!15)) = set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15)))))),
% 0.20/0.38 inference(quant_inst,[status(thm)],[])).
% 0.20/0.38 tff(22,plain,
% 0.20/0.38 ((~![A: $i] : ((~relation(A)) | (relation_field(A) = set_union2(relation_dom(A), relation_rng(A))))) | (~relation(inclusion_relation(A!15))) | (relation_field(inclusion_relation(A!15)) = set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[21, 20])).
% 0.20/0.38 tff(23,plain,
% 0.20/0.38 (relation_field(inclusion_relation(A!15)) = set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15)))),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[22, 19, 9])).
% 0.20/0.38 tff(24,plain,
% 0.20/0.38 (^[A: $i, B: $i] : rewrite(((~relation(B)) | (~((~((~(B = inclusion_relation(A))) | (~((~(relation_field(B) = A)) | (~![C: $i, D: $i] : ((in(ordered_pair(C, D), B) <=> subset(C, D)) | (~in(C, A)) | (~in(D, A)))))))) | (~((B = inclusion_relation(A)) | (~(relation_field(B) = A)) | (~((in(ordered_pair(tptp_fun_C_1(B, A), tptp_fun_D_0(B, A)), B) <=> subset(tptp_fun_C_1(B, A), tptp_fun_D_0(B, A))) | (~in(tptp_fun_C_1(B, A), A)) | (~in(tptp_fun_D_0(B, A), A))))))))) <=> ((~relation(B)) | (~((~((B = inclusion_relation(A)) | (~(relation_field(B) = A)) | (~((in(ordered_pair(tptp_fun_C_1(B, A), tptp_fun_D_0(B, A)), B) <=> subset(tptp_fun_C_1(B, A), tptp_fun_D_0(B, A))) | (~in(tptp_fun_C_1(B, A), A)) | (~in(tptp_fun_D_0(B, A), A)))))) | (~((~(B = inclusion_relation(A))) | (~((~(relation_field(B) = A)) | (~![C: $i, D: $i] : ((in(ordered_pair(C, D), B) <=> subset(C, D)) | (~in(C, A)) | (~in(D, A))))))))))))),
% 0.20/0.38 inference(bind,[status(th)],[])).
% 0.20/0.38 tff(25,plain,
% 0.20/0.38 (![A: $i, B: $i] : ((~relation(B)) | (~((~((~(B = inclusion_relation(A))) | (~((~(relation_field(B) = A)) | (~![C: $i, D: $i] : ((in(ordered_pair(C, D), B) <=> subset(C, D)) | (~in(C, A)) | (~in(D, A)))))))) | (~((B = inclusion_relation(A)) | (~(relation_field(B) = A)) | (~((in(ordered_pair(tptp_fun_C_1(B, A), tptp_fun_D_0(B, A)), B) <=> subset(tptp_fun_C_1(B, A), tptp_fun_D_0(B, A))) | (~in(tptp_fun_C_1(B, A), A)) | (~in(tptp_fun_D_0(B, A), A))))))))) <=> ![A: $i, B: $i] : ((~relation(B)) | (~((~((B = inclusion_relation(A)) | (~(relation_field(B) = A)) | (~((in(ordered_pair(tptp_fun_C_1(B, A), tptp_fun_D_0(B, A)), B) <=> subset(tptp_fun_C_1(B, A), tptp_fun_D_0(B, A))) | (~in(tptp_fun_C_1(B, A), A)) | (~in(tptp_fun_D_0(B, A), A)))))) | (~((~(B = inclusion_relation(A))) | (~((~(relation_field(B) = A)) | (~![C: $i, D: $i] : ((in(ordered_pair(C, D), B) <=> subset(C, D)) | (~in(C, A)) | (~in(D, A)))))))))))),
% 0.20/0.38 inference(quant_intro,[status(thm)],[24])).
% 0.20/0.38 tff(26,plain,
% 0.20/0.38 (^[A: $i, B: $i] : refl(((~relation(B)) | (~((~((~(B = inclusion_relation(A))) | (~((~(relation_field(B) = A)) | (~![C: $i, D: $i] : ((in(ordered_pair(C, D), B) <=> subset(C, D)) | (~in(C, A)) | (~in(D, A)))))))) | (~((B = inclusion_relation(A)) | (~(relation_field(B) = A)) | (~((in(ordered_pair(tptp_fun_C_1(B, A), tptp_fun_D_0(B, A)), B) <=> subset(tptp_fun_C_1(B, A), tptp_fun_D_0(B, A))) | (~in(tptp_fun_C_1(B, A), A)) | (~in(tptp_fun_D_0(B, A), A))))))))) <=> ((~relation(B)) | (~((~((~(B = inclusion_relation(A))) | (~((~(relation_field(B) = A)) | (~![C: $i, D: $i] : ((in(ordered_pair(C, D), B) <=> subset(C, D)) | (~in(C, A)) | (~in(D, A)))))))) | (~((B = inclusion_relation(A)) | (~(relation_field(B) = A)) | (~((in(ordered_pair(tptp_fun_C_1(B, A), tptp_fun_D_0(B, A)), B) <=> subset(tptp_fun_C_1(B, A), tptp_fun_D_0(B, A))) | (~in(tptp_fun_C_1(B, A), A)) | (~in(tptp_fun_D_0(B, A), A))))))))))),
% 0.20/0.38 inference(bind,[status(th)],[])).
% 0.20/0.38 tff(27,plain,
% 0.20/0.38 (![A: $i, B: $i] : ((~relation(B)) | (~((~((~(B = inclusion_relation(A))) | (~((~(relation_field(B) = A)) | (~![C: $i, D: $i] : ((in(ordered_pair(C, D), B) <=> subset(C, D)) | (~in(C, A)) | (~in(D, A)))))))) | (~((B = inclusion_relation(A)) | (~(relation_field(B) = A)) | (~((in(ordered_pair(tptp_fun_C_1(B, A), tptp_fun_D_0(B, A)), B) <=> subset(tptp_fun_C_1(B, A), tptp_fun_D_0(B, A))) | (~in(tptp_fun_C_1(B, A), A)) | (~in(tptp_fun_D_0(B, A), A))))))))) <=> ![A: $i, B: $i] : ((~relation(B)) | (~((~((~(B = inclusion_relation(A))) | (~((~(relation_field(B) = A)) | (~![C: $i, D: $i] : ((in(ordered_pair(C, D), B) <=> subset(C, D)) | (~in(C, A)) | (~in(D, A)))))))) | (~((B = inclusion_relation(A)) | (~(relation_field(B) = A)) | (~((in(ordered_pair(tptp_fun_C_1(B, A), tptp_fun_D_0(B, A)), B) <=> subset(tptp_fun_C_1(B, A), tptp_fun_D_0(B, A))) | (~in(tptp_fun_C_1(B, A), A)) | (~in(tptp_fun_D_0(B, A), A)))))))))),
% 0.20/0.38 inference(quant_intro,[status(thm)],[26])).
% 0.20/0.38 tff(28,plain,
% 0.20/0.38 (^[A: $i, B: $i] : rewrite(((~relation(B)) | (~((~((~(B = inclusion_relation(A))) | (~((~(relation_field(B) = A)) | (~![C: $i, D: $i] : ((in(ordered_pair(C, D), B) <=> subset(C, D)) | (~in(C, A)) | (~in(D, A)))))))) | (~((B = inclusion_relation(A)) | (~(relation_field(B) = A)) | (~((in(ordered_pair(tptp_fun_C_1(B, A), tptp_fun_D_0(B, A)), B) <=> subset(tptp_fun_C_1(B, A), tptp_fun_D_0(B, A))) | (~in(tptp_fun_C_1(B, A), A)) | (~in(tptp_fun_D_0(B, A), A))))))))) <=> ((~relation(B)) | (~((~((~(B = inclusion_relation(A))) | (~((~(relation_field(B) = A)) | (~![C: $i, D: $i] : ((in(ordered_pair(C, D), B) <=> subset(C, D)) | (~in(C, A)) | (~in(D, A)))))))) | (~((B = inclusion_relation(A)) | (~(relation_field(B) = A)) | (~((in(ordered_pair(tptp_fun_C_1(B, A), tptp_fun_D_0(B, A)), B) <=> subset(tptp_fun_C_1(B, A), tptp_fun_D_0(B, A))) | (~in(tptp_fun_C_1(B, A), A)) | (~in(tptp_fun_D_0(B, A), A))))))))))),
% 0.20/0.38 inference(bind,[status(th)],[])).
% 0.20/0.38 tff(29,plain,
% 0.20/0.38 (![A: $i, B: $i] : ((~relation(B)) | (~((~((~(B = inclusion_relation(A))) | (~((~(relation_field(B) = A)) | (~![C: $i, D: $i] : ((in(ordered_pair(C, D), B) <=> subset(C, D)) | (~in(C, A)) | (~in(D, A)))))))) | (~((B = inclusion_relation(A)) | (~(relation_field(B) = A)) | (~((in(ordered_pair(tptp_fun_C_1(B, A), tptp_fun_D_0(B, A)), B) <=> subset(tptp_fun_C_1(B, A), tptp_fun_D_0(B, A))) | (~in(tptp_fun_C_1(B, A), A)) | (~in(tptp_fun_D_0(B, A), A))))))))) <=> ![A: $i, B: $i] : ((~relation(B)) | (~((~((~(B = inclusion_relation(A))) | (~((~(relation_field(B) = A)) | (~![C: $i, D: $i] : ((in(ordered_pair(C, D), B) <=> subset(C, D)) | (~in(C, A)) | (~in(D, A)))))))) | (~((B = inclusion_relation(A)) | (~(relation_field(B) = A)) | (~((in(ordered_pair(tptp_fun_C_1(B, A), tptp_fun_D_0(B, A)), B) <=> subset(tptp_fun_C_1(B, A), tptp_fun_D_0(B, A))) | (~in(tptp_fun_C_1(B, A), A)) | (~in(tptp_fun_D_0(B, A), A)))))))))),
% 0.20/0.38 inference(quant_intro,[status(thm)],[28])).
% 0.20/0.38 tff(30,plain,
% 0.20/0.38 (![A: $i, B: $i] : ((~relation(B)) | (~((~((~(B = inclusion_relation(A))) | (~((~(relation_field(B) = A)) | (~![C: $i, D: $i] : ((in(ordered_pair(C, D), B) <=> subset(C, D)) | (~in(C, A)) | (~in(D, A)))))))) | (~((B = inclusion_relation(A)) | (~(relation_field(B) = A)) | (~((in(ordered_pair(tptp_fun_C_1(B, A), tptp_fun_D_0(B, A)), B) <=> subset(tptp_fun_C_1(B, A), tptp_fun_D_0(B, A))) | (~in(tptp_fun_C_1(B, A), A)) | (~in(tptp_fun_D_0(B, A), A))))))))) <=> ![A: $i, B: $i] : ((~relation(B)) | (~((~((~(B = inclusion_relation(A))) | (~((~(relation_field(B) = A)) | (~![C: $i, D: $i] : ((in(ordered_pair(C, D), B) <=> subset(C, D)) | (~in(C, A)) | (~in(D, A)))))))) | (~((B = inclusion_relation(A)) | (~(relation_field(B) = A)) | (~((in(ordered_pair(tptp_fun_C_1(B, A), tptp_fun_D_0(B, A)), B) <=> subset(tptp_fun_C_1(B, A), tptp_fun_D_0(B, A))) | (~in(tptp_fun_C_1(B, A), A)) | (~in(tptp_fun_D_0(B, A), A)))))))))),
% 0.20/0.39 inference(transitivity,[status(thm)],[29, 27])).
% 0.20/0.39 tff(31,plain,
% 0.20/0.39 (^[A: $i, B: $i] : rewrite(((~relation(B)) | (((~(B = inclusion_relation(A))) | ((relation_field(B) = A) & ![C: $i, D: $i] : ((~(in(C, A) & in(D, A))) | (in(ordered_pair(C, D), B) <=> subset(C, D))))) & ((B = inclusion_relation(A)) | (~(relation_field(B) = A)) | (~((~(in(tptp_fun_C_1(B, A), A) & in(tptp_fun_D_0(B, A), A))) | (in(ordered_pair(tptp_fun_C_1(B, A), tptp_fun_D_0(B, A)), B) <=> subset(tptp_fun_C_1(B, A), tptp_fun_D_0(B, A)))))))) <=> ((~relation(B)) | (~((~((~(B = inclusion_relation(A))) | (~((~(relation_field(B) = A)) | (~![C: $i, D: $i] : ((in(ordered_pair(C, D), B) <=> subset(C, D)) | (~in(C, A)) | (~in(D, A)))))))) | (~((B = inclusion_relation(A)) | (~(relation_field(B) = A)) | (~((in(ordered_pair(tptp_fun_C_1(B, A), tptp_fun_D_0(B, A)), B) <=> subset(tptp_fun_C_1(B, A), tptp_fun_D_0(B, A))) | (~in(tptp_fun_C_1(B, A), A)) | (~in(tptp_fun_D_0(B, A), A))))))))))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(32,plain,
% 0.20/0.39 (![A: $i, B: $i] : ((~relation(B)) | (((~(B = inclusion_relation(A))) | ((relation_field(B) = A) & ![C: $i, D: $i] : ((~(in(C, A) & in(D, A))) | (in(ordered_pair(C, D), B) <=> subset(C, D))))) & ((B = inclusion_relation(A)) | (~(relation_field(B) = A)) | (~((~(in(tptp_fun_C_1(B, A), A) & in(tptp_fun_D_0(B, A), A))) | (in(ordered_pair(tptp_fun_C_1(B, A), tptp_fun_D_0(B, A)), B) <=> subset(tptp_fun_C_1(B, A), tptp_fun_D_0(B, A)))))))) <=> ![A: $i, B: $i] : ((~relation(B)) | (~((~((~(B = inclusion_relation(A))) | (~((~(relation_field(B) = A)) | (~![C: $i, D: $i] : ((in(ordered_pair(C, D), B) <=> subset(C, D)) | (~in(C, A)) | (~in(D, A)))))))) | (~((B = inclusion_relation(A)) | (~(relation_field(B) = A)) | (~((in(ordered_pair(tptp_fun_C_1(B, A), tptp_fun_D_0(B, A)), B) <=> subset(tptp_fun_C_1(B, A), tptp_fun_D_0(B, A))) | (~in(tptp_fun_C_1(B, A), A)) | (~in(tptp_fun_D_0(B, A), A)))))))))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[31])).
% 0.20/0.39 tff(33,plain,
% 0.20/0.39 (^[A: $i, B: $i] : rewrite(((~relation(B)) | (((~(B = inclusion_relation(A))) | ((relation_field(B) = A) & ![C: $i, D: $i] : ((~(in(C, A) & in(D, A))) | (in(ordered_pair(C, D), B) <=> subset(C, D))))) & ((B = inclusion_relation(A)) | ((~(relation_field(B) = A)) | (~((~(in(tptp_fun_C_1(B, A), A) & in(tptp_fun_D_0(B, A), A))) | (in(ordered_pair(tptp_fun_C_1(B, A), tptp_fun_D_0(B, A)), B) <=> subset(tptp_fun_C_1(B, A), tptp_fun_D_0(B, A))))))))) <=> ((~relation(B)) | (((~(B = inclusion_relation(A))) | ((relation_field(B) = A) & ![C: $i, D: $i] : ((~(in(C, A) & in(D, A))) | (in(ordered_pair(C, D), B) <=> subset(C, D))))) & ((B = inclusion_relation(A)) | (~(relation_field(B) = A)) | (~((~(in(tptp_fun_C_1(B, A), A) & in(tptp_fun_D_0(B, A), A))) | (in(ordered_pair(tptp_fun_C_1(B, A), tptp_fun_D_0(B, A)), B) <=> subset(tptp_fun_C_1(B, A), tptp_fun_D_0(B, A)))))))))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(34,plain,
% 0.20/0.39 (![A: $i, B: $i] : ((~relation(B)) | (((~(B = inclusion_relation(A))) | ((relation_field(B) = A) & ![C: $i, D: $i] : ((~(in(C, A) & in(D, A))) | (in(ordered_pair(C, D), B) <=> subset(C, D))))) & ((B = inclusion_relation(A)) | ((~(relation_field(B) = A)) | (~((~(in(tptp_fun_C_1(B, A), A) & in(tptp_fun_D_0(B, A), A))) | (in(ordered_pair(tptp_fun_C_1(B, A), tptp_fun_D_0(B, A)), B) <=> subset(tptp_fun_C_1(B, A), tptp_fun_D_0(B, A))))))))) <=> ![A: $i, B: $i] : ((~relation(B)) | (((~(B = inclusion_relation(A))) | ((relation_field(B) = A) & ![C: $i, D: $i] : ((~(in(C, A) & in(D, A))) | (in(ordered_pair(C, D), B) <=> subset(C, D))))) & ((B = inclusion_relation(A)) | (~(relation_field(B) = A)) | (~((~(in(tptp_fun_C_1(B, A), A) & in(tptp_fun_D_0(B, A), A))) | (in(ordered_pair(tptp_fun_C_1(B, A), tptp_fun_D_0(B, A)), B) <=> subset(tptp_fun_C_1(B, A), tptp_fun_D_0(B, A))))))))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[33])).
% 0.20/0.39 tff(35,plain,
% 0.20/0.39 (![A: $i, B: $i] : ((~relation(B)) | ((B = inclusion_relation(A)) <=> ((relation_field(B) = A) & ![C: $i, D: $i] : ((~(in(C, A) & in(D, A))) | (in(ordered_pair(C, D), B) <=> subset(C, D)))))) <=> ![A: $i, B: $i] : ((~relation(B)) | ((B = inclusion_relation(A)) <=> ((relation_field(B) = A) & ![C: $i, D: $i] : ((~(in(C, A) & in(D, A))) | (in(ordered_pair(C, D), B) <=> subset(C, D))))))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(36,plain,
% 0.20/0.39 (^[A: $i, B: $i] : trans(monotonicity(rewrite(((B = inclusion_relation(A)) <=> ((relation_field(B) = A) & ![C: $i, D: $i] : ((in(C, A) & in(D, A)) => (in(ordered_pair(C, D), B) <=> subset(C, D))))) <=> ((B = inclusion_relation(A)) <=> ((relation_field(B) = A) & ![C: $i, D: $i] : ((~(in(C, A) & in(D, A))) | (in(ordered_pair(C, D), B) <=> subset(C, D)))))), ((relation(B) => ((B = inclusion_relation(A)) <=> ((relation_field(B) = A) & ![C: $i, D: $i] : ((in(C, A) & in(D, A)) => (in(ordered_pair(C, D), B) <=> subset(C, D)))))) <=> (relation(B) => ((B = inclusion_relation(A)) <=> ((relation_field(B) = A) & ![C: $i, D: $i] : ((~(in(C, A) & in(D, A))) | (in(ordered_pair(C, D), B) <=> subset(C, D)))))))), rewrite((relation(B) => ((B = inclusion_relation(A)) <=> ((relation_field(B) = A) & ![C: $i, D: $i] : ((~(in(C, A) & in(D, A))) | (in(ordered_pair(C, D), B) <=> subset(C, D)))))) <=> ((~relation(B)) | ((B = inclusion_relation(A)) <=> ((relation_field(B) = A) & ![C: $i, D: $i] : ((~(in(C, A) & in(D, A))) | (in(ordered_pair(C, D), B) <=> subset(C, D))))))), ((relation(B) => ((B = inclusion_relation(A)) <=> ((relation_field(B) = A) & ![C: $i, D: $i] : ((in(C, A) & in(D, A)) => (in(ordered_pair(C, D), B) <=> subset(C, D)))))) <=> ((~relation(B)) | ((B = inclusion_relation(A)) <=> ((relation_field(B) = A) & ![C: $i, D: $i] : ((~(in(C, A) & in(D, A))) | (in(ordered_pair(C, D), B) <=> subset(C, D))))))))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(37,plain,
% 0.20/0.39 (![A: $i, B: $i] : (relation(B) => ((B = inclusion_relation(A)) <=> ((relation_field(B) = A) & ![C: $i, D: $i] : ((in(C, A) & in(D, A)) => (in(ordered_pair(C, D), B) <=> subset(C, D)))))) <=> ![A: $i, B: $i] : ((~relation(B)) | ((B = inclusion_relation(A)) <=> ((relation_field(B) = A) & ![C: $i, D: $i] : ((~(in(C, A) & in(D, A))) | (in(ordered_pair(C, D), B) <=> subset(C, D))))))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[36])).
% 0.20/0.39 tff(38,axiom,(![A: $i, B: $i] : (relation(B) => ((B = inclusion_relation(A)) <=> ((relation_field(B) = A) & ![C: $i, D: $i] : ((in(C, A) & in(D, A)) => (in(ordered_pair(C, D), B) <=> subset(C, D))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d1_wellord2')).
% 0.20/0.39 tff(39,plain,
% 0.20/0.39 (![A: $i, B: $i] : ((~relation(B)) | ((B = inclusion_relation(A)) <=> ((relation_field(B) = A) & ![C: $i, D: $i] : ((~(in(C, A) & in(D, A))) | (in(ordered_pair(C, D), B) <=> subset(C, D))))))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[38, 37])).
% 0.20/0.39 tff(40,plain,
% 0.20/0.39 (![A: $i, B: $i] : ((~relation(B)) | ((B = inclusion_relation(A)) <=> ((relation_field(B) = A) & ![C: $i, D: $i] : ((~(in(C, A) & in(D, A))) | (in(ordered_pair(C, D), B) <=> subset(C, D))))))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[39, 35])).
% 0.20/0.39 tff(41,plain,(
% 0.20/0.39 ![A: $i, B: $i] : ((~relation(B)) | (((~(B = inclusion_relation(A))) | ((relation_field(B) = A) & ![C: $i, D: $i] : ((~(in(C, A) & in(D, A))) | (in(ordered_pair(C, D), B) <=> subset(C, D))))) & ((B = inclusion_relation(A)) | ((~(relation_field(B) = A)) | (~((~(in(tptp_fun_C_1(B, A), A) & in(tptp_fun_D_0(B, A), A))) | (in(ordered_pair(tptp_fun_C_1(B, A), tptp_fun_D_0(B, A)), B) <=> subset(tptp_fun_C_1(B, A), tptp_fun_D_0(B, A)))))))))),
% 0.20/0.39 inference(skolemize,[status(sab)],[40])).
% 0.20/0.39 tff(42,plain,
% 0.20/0.39 (![A: $i, B: $i] : ((~relation(B)) | (((~(B = inclusion_relation(A))) | ((relation_field(B) = A) & ![C: $i, D: $i] : ((~(in(C, A) & in(D, A))) | (in(ordered_pair(C, D), B) <=> subset(C, D))))) & ((B = inclusion_relation(A)) | (~(relation_field(B) = A)) | (~((~(in(tptp_fun_C_1(B, A), A) & in(tptp_fun_D_0(B, A), A))) | (in(ordered_pair(tptp_fun_C_1(B, A), tptp_fun_D_0(B, A)), B) <=> subset(tptp_fun_C_1(B, A), tptp_fun_D_0(B, A))))))))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[41, 34])).
% 0.20/0.39 tff(43,plain,
% 0.20/0.39 (![A: $i, B: $i] : ((~relation(B)) | (~((~((~(B = inclusion_relation(A))) | (~((~(relation_field(B) = A)) | (~![C: $i, D: $i] : ((in(ordered_pair(C, D), B) <=> subset(C, D)) | (~in(C, A)) | (~in(D, A)))))))) | (~((B = inclusion_relation(A)) | (~(relation_field(B) = A)) | (~((in(ordered_pair(tptp_fun_C_1(B, A), tptp_fun_D_0(B, A)), B) <=> subset(tptp_fun_C_1(B, A), tptp_fun_D_0(B, A))) | (~in(tptp_fun_C_1(B, A), A)) | (~in(tptp_fun_D_0(B, A), A)))))))))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[42, 32])).
% 0.20/0.39 tff(44,plain,
% 0.20/0.39 (![A: $i, B: $i] : ((~relation(B)) | (~((~((~(B = inclusion_relation(A))) | (~((~(relation_field(B) = A)) | (~![C: $i, D: $i] : ((in(ordered_pair(C, D), B) <=> subset(C, D)) | (~in(C, A)) | (~in(D, A)))))))) | (~((B = inclusion_relation(A)) | (~(relation_field(B) = A)) | (~((in(ordered_pair(tptp_fun_C_1(B, A), tptp_fun_D_0(B, A)), B) <=> subset(tptp_fun_C_1(B, A), tptp_fun_D_0(B, A))) | (~in(tptp_fun_C_1(B, A), A)) | (~in(tptp_fun_D_0(B, A), A)))))))))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[43, 30])).
% 0.20/0.39 tff(45,plain,
% 0.20/0.39 (![A: $i, B: $i] : ((~relation(B)) | (~((~((B = inclusion_relation(A)) | (~(relation_field(B) = A)) | (~((in(ordered_pair(tptp_fun_C_1(B, A), tptp_fun_D_0(B, A)), B) <=> subset(tptp_fun_C_1(B, A), tptp_fun_D_0(B, A))) | (~in(tptp_fun_C_1(B, A), A)) | (~in(tptp_fun_D_0(B, A), A)))))) | (~((~(B = inclusion_relation(A))) | (~((~(relation_field(B) = A)) | (~![C: $i, D: $i] : ((in(ordered_pair(C, D), B) <=> subset(C, D)) | (~in(C, A)) | (~in(D, A)))))))))))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[44, 25])).
% 0.20/0.39 tff(46,plain,
% 0.20/0.39 (((~![A: $i, B: $i] : ((~relation(B)) | (~((~((B = inclusion_relation(A)) | (~(relation_field(B) = A)) | (~((in(ordered_pair(tptp_fun_C_1(B, A), tptp_fun_D_0(B, A)), B) <=> subset(tptp_fun_C_1(B, A), tptp_fun_D_0(B, A))) | (~in(tptp_fun_C_1(B, A), A)) | (~in(tptp_fun_D_0(B, A), A)))))) | (~((~(B = inclusion_relation(A))) | (~((~(relation_field(B) = A)) | (~![C: $i, D: $i] : ((in(ordered_pair(C, D), B) <=> subset(C, D)) | (~in(C, A)) | (~in(D, A)))))))))))) | ((~relation(inclusion_relation(A!15))) | (~((~(relation_field(inclusion_relation(A!15)) = A!15)) | (~![C: $i, D: $i] : ((~in(C, A!15)) | (~in(D, A!15)) | (in(ordered_pair(C, D), inclusion_relation(A!15)) <=> subset(C, D)))))))) <=> ((~![A: $i, B: $i] : ((~relation(B)) | (~((~((B = inclusion_relation(A)) | (~(relation_field(B) = A)) | (~((in(ordered_pair(tptp_fun_C_1(B, A), tptp_fun_D_0(B, A)), B) <=> subset(tptp_fun_C_1(B, A), tptp_fun_D_0(B, A))) | (~in(tptp_fun_C_1(B, A), A)) | (~in(tptp_fun_D_0(B, A), A)))))) | (~((~(B = inclusion_relation(A))) | (~((~(relation_field(B) = A)) | (~![C: $i, D: $i] : ((in(ordered_pair(C, D), B) <=> subset(C, D)) | (~in(C, A)) | (~in(D, A)))))))))))) | (~relation(inclusion_relation(A!15))) | (~((~(relation_field(inclusion_relation(A!15)) = A!15)) | (~![C: $i, D: $i] : ((~in(C, A!15)) | (~in(D, A!15)) | (in(ordered_pair(C, D), inclusion_relation(A!15)) <=> subset(C, D)))))))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(47,plain,
% 0.20/0.39 (((~relation(inclusion_relation(A!15))) | (~((~((inclusion_relation(A!15) = inclusion_relation(A!15)) | (~(relation_field(inclusion_relation(A!15)) = A!15)) | (~((in(ordered_pair(tptp_fun_C_1(inclusion_relation(A!15), A!15), tptp_fun_D_0(inclusion_relation(A!15), A!15)), inclusion_relation(A!15)) <=> subset(tptp_fun_C_1(inclusion_relation(A!15), A!15), tptp_fun_D_0(inclusion_relation(A!15), A!15))) | (~in(tptp_fun_C_1(inclusion_relation(A!15), A!15), A!15)) | (~in(tptp_fun_D_0(inclusion_relation(A!15), A!15), A!15)))))) | (~((~(inclusion_relation(A!15) = inclusion_relation(A!15))) | (~((~(relation_field(inclusion_relation(A!15)) = A!15)) | (~![C: $i, D: $i] : ((in(ordered_pair(C, D), inclusion_relation(A!15)) <=> subset(C, D)) | (~in(C, A!15)) | (~in(D, A!15))))))))))) <=> ((~relation(inclusion_relation(A!15))) | (~((~(relation_field(inclusion_relation(A!15)) = A!15)) | (~![C: $i, D: $i] : ((~in(C, A!15)) | (~in(D, A!15)) | (in(ordered_pair(C, D), inclusion_relation(A!15)) <=> subset(C, D)))))))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(48,plain,
% 0.20/0.39 (((~![A: $i, B: $i] : ((~relation(B)) | (~((~((B = inclusion_relation(A)) | (~(relation_field(B) = A)) | (~((in(ordered_pair(tptp_fun_C_1(B, A), tptp_fun_D_0(B, A)), B) <=> subset(tptp_fun_C_1(B, A), tptp_fun_D_0(B, A))) | (~in(tptp_fun_C_1(B, A), A)) | (~in(tptp_fun_D_0(B, A), A)))))) | (~((~(B = inclusion_relation(A))) | (~((~(relation_field(B) = A)) | (~![C: $i, D: $i] : ((in(ordered_pair(C, D), B) <=> subset(C, D)) | (~in(C, A)) | (~in(D, A)))))))))))) | ((~relation(inclusion_relation(A!15))) | (~((~((inclusion_relation(A!15) = inclusion_relation(A!15)) | (~(relation_field(inclusion_relation(A!15)) = A!15)) | (~((in(ordered_pair(tptp_fun_C_1(inclusion_relation(A!15), A!15), tptp_fun_D_0(inclusion_relation(A!15), A!15)), inclusion_relation(A!15)) <=> subset(tptp_fun_C_1(inclusion_relation(A!15), A!15), tptp_fun_D_0(inclusion_relation(A!15), A!15))) | (~in(tptp_fun_C_1(inclusion_relation(A!15), A!15), A!15)) | (~in(tptp_fun_D_0(inclusion_relation(A!15), A!15), A!15)))))) | (~((~(inclusion_relation(A!15) = inclusion_relation(A!15))) | (~((~(relation_field(inclusion_relation(A!15)) = A!15)) | (~![C: $i, D: $i] : ((in(ordered_pair(C, D), inclusion_relation(A!15)) <=> subset(C, D)) | (~in(C, A!15)) | (~in(D, A!15)))))))))))) <=> ((~![A: $i, B: $i] : ((~relation(B)) | (~((~((B = inclusion_relation(A)) | (~(relation_field(B) = A)) | (~((in(ordered_pair(tptp_fun_C_1(B, A), tptp_fun_D_0(B, A)), B) <=> subset(tptp_fun_C_1(B, A), tptp_fun_D_0(B, A))) | (~in(tptp_fun_C_1(B, A), A)) | (~in(tptp_fun_D_0(B, A), A)))))) | (~((~(B = inclusion_relation(A))) | (~((~(relation_field(B) = A)) | (~![C: $i, D: $i] : ((in(ordered_pair(C, D), B) <=> subset(C, D)) | (~in(C, A)) | (~in(D, A)))))))))))) | ((~relation(inclusion_relation(A!15))) | (~((~(relation_field(inclusion_relation(A!15)) = A!15)) | (~![C: $i, D: $i] : ((~in(C, A!15)) | (~in(D, A!15)) | (in(ordered_pair(C, D), inclusion_relation(A!15)) <=> subset(C, D))))))))),
% 0.20/0.39 inference(monotonicity,[status(thm)],[47])).
% 0.20/0.39 tff(49,plain,
% 0.20/0.39 (((~![A: $i, B: $i] : ((~relation(B)) | (~((~((B = inclusion_relation(A)) | (~(relation_field(B) = A)) | (~((in(ordered_pair(tptp_fun_C_1(B, A), tptp_fun_D_0(B, A)), B) <=> subset(tptp_fun_C_1(B, A), tptp_fun_D_0(B, A))) | (~in(tptp_fun_C_1(B, A), A)) | (~in(tptp_fun_D_0(B, A), A)))))) | (~((~(B = inclusion_relation(A))) | (~((~(relation_field(B) = A)) | (~![C: $i, D: $i] : ((in(ordered_pair(C, D), B) <=> subset(C, D)) | (~in(C, A)) | (~in(D, A)))))))))))) | ((~relation(inclusion_relation(A!15))) | (~((~((inclusion_relation(A!15) = inclusion_relation(A!15)) | (~(relation_field(inclusion_relation(A!15)) = A!15)) | (~((in(ordered_pair(tptp_fun_C_1(inclusion_relation(A!15), A!15), tptp_fun_D_0(inclusion_relation(A!15), A!15)), inclusion_relation(A!15)) <=> subset(tptp_fun_C_1(inclusion_relation(A!15), A!15), tptp_fun_D_0(inclusion_relation(A!15), A!15))) | (~in(tptp_fun_C_1(inclusion_relation(A!15), A!15), A!15)) | (~in(tptp_fun_D_0(inclusion_relation(A!15), A!15), A!15)))))) | (~((~(inclusion_relation(A!15) = inclusion_relation(A!15))) | (~((~(relation_field(inclusion_relation(A!15)) = A!15)) | (~![C: $i, D: $i] : ((in(ordered_pair(C, D), inclusion_relation(A!15)) <=> subset(C, D)) | (~in(C, A!15)) | (~in(D, A!15)))))))))))) <=> ((~![A: $i, B: $i] : ((~relation(B)) | (~((~((B = inclusion_relation(A)) | (~(relation_field(B) = A)) | (~((in(ordered_pair(tptp_fun_C_1(B, A), tptp_fun_D_0(B, A)), B) <=> subset(tptp_fun_C_1(B, A), tptp_fun_D_0(B, A))) | (~in(tptp_fun_C_1(B, A), A)) | (~in(tptp_fun_D_0(B, A), A)))))) | (~((~(B = inclusion_relation(A))) | (~((~(relation_field(B) = A)) | (~![C: $i, D: $i] : ((in(ordered_pair(C, D), B) <=> subset(C, D)) | (~in(C, A)) | (~in(D, A)))))))))))) | (~relation(inclusion_relation(A!15))) | (~((~(relation_field(inclusion_relation(A!15)) = A!15)) | (~![C: $i, D: $i] : ((~in(C, A!15)) | (~in(D, A!15)) | (in(ordered_pair(C, D), inclusion_relation(A!15)) <=> subset(C, D)))))))),
% 0.20/0.39 inference(transitivity,[status(thm)],[48, 46])).
% 0.20/0.39 tff(50,plain,
% 0.20/0.39 ((~![A: $i, B: $i] : ((~relation(B)) | (~((~((B = inclusion_relation(A)) | (~(relation_field(B) = A)) | (~((in(ordered_pair(tptp_fun_C_1(B, A), tptp_fun_D_0(B, A)), B) <=> subset(tptp_fun_C_1(B, A), tptp_fun_D_0(B, A))) | (~in(tptp_fun_C_1(B, A), A)) | (~in(tptp_fun_D_0(B, A), A)))))) | (~((~(B = inclusion_relation(A))) | (~((~(relation_field(B) = A)) | (~![C: $i, D: $i] : ((in(ordered_pair(C, D), B) <=> subset(C, D)) | (~in(C, A)) | (~in(D, A)))))))))))) | ((~relation(inclusion_relation(A!15))) | (~((~((inclusion_relation(A!15) = inclusion_relation(A!15)) | (~(relation_field(inclusion_relation(A!15)) = A!15)) | (~((in(ordered_pair(tptp_fun_C_1(inclusion_relation(A!15), A!15), tptp_fun_D_0(inclusion_relation(A!15), A!15)), inclusion_relation(A!15)) <=> subset(tptp_fun_C_1(inclusion_relation(A!15), A!15), tptp_fun_D_0(inclusion_relation(A!15), A!15))) | (~in(tptp_fun_C_1(inclusion_relation(A!15), A!15), A!15)) | (~in(tptp_fun_D_0(inclusion_relation(A!15), A!15), A!15)))))) | (~((~(inclusion_relation(A!15) = inclusion_relation(A!15))) | (~((~(relation_field(inclusion_relation(A!15)) = A!15)) | (~![C: $i, D: $i] : ((in(ordered_pair(C, D), inclusion_relation(A!15)) <=> subset(C, D)) | (~in(C, A!15)) | (~in(D, A!15)))))))))))),
% 0.20/0.39 inference(quant_inst,[status(thm)],[])).
% 0.20/0.39 tff(51,plain,
% 0.20/0.39 ((~![A: $i, B: $i] : ((~relation(B)) | (~((~((B = inclusion_relation(A)) | (~(relation_field(B) = A)) | (~((in(ordered_pair(tptp_fun_C_1(B, A), tptp_fun_D_0(B, A)), B) <=> subset(tptp_fun_C_1(B, A), tptp_fun_D_0(B, A))) | (~in(tptp_fun_C_1(B, A), A)) | (~in(tptp_fun_D_0(B, A), A)))))) | (~((~(B = inclusion_relation(A))) | (~((~(relation_field(B) = A)) | (~![C: $i, D: $i] : ((in(ordered_pair(C, D), B) <=> subset(C, D)) | (~in(C, A)) | (~in(D, A)))))))))))) | (~relation(inclusion_relation(A!15))) | (~((~(relation_field(inclusion_relation(A!15)) = A!15)) | (~![C: $i, D: $i] : ((~in(C, A!15)) | (~in(D, A!15)) | (in(ordered_pair(C, D), inclusion_relation(A!15)) <=> subset(C, D))))))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[50, 49])).
% 0.20/0.39 tff(52,plain,
% 0.20/0.39 (~((~(relation_field(inclusion_relation(A!15)) = A!15)) | (~![C: $i, D: $i] : ((~in(C, A!15)) | (~in(D, A!15)) | (in(ordered_pair(C, D), inclusion_relation(A!15)) <=> subset(C, D)))))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[51, 45, 9])).
% 0.20/0.39 tff(53,plain,
% 0.20/0.39 (((~(relation_field(inclusion_relation(A!15)) = A!15)) | (~![C: $i, D: $i] : ((~in(C, A!15)) | (~in(D, A!15)) | (in(ordered_pair(C, D), inclusion_relation(A!15)) <=> subset(C, D))))) | (relation_field(inclusion_relation(A!15)) = A!15)),
% 0.20/0.39 inference(tautology,[status(thm)],[])).
% 0.20/0.39 tff(54,plain,
% 0.20/0.39 (relation_field(inclusion_relation(A!15)) = A!15),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[53, 52])).
% 0.20/0.39 tff(55,plain,
% 0.20/0.39 (A!15 = relation_field(inclusion_relation(A!15))),
% 0.20/0.39 inference(symmetry,[status(thm)],[54])).
% 0.20/0.39 tff(56,plain,
% 0.20/0.39 (A!15 = set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15)))),
% 0.20/0.39 inference(transitivity,[status(thm)],[55, 23])).
% 0.20/0.39 tff(57,plain,
% 0.20/0.39 (in(tptp_fun_C_4(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), A!15) <=> in(tptp_fun_C_4(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))))),
% 0.20/0.39 inference(monotonicity,[status(thm)],[56])).
% 0.20/0.39 tff(58,plain,
% 0.20/0.39 (in(tptp_fun_C_4(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15)))) <=> in(tptp_fun_C_4(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), A!15)),
% 0.20/0.40 inference(symmetry,[status(thm)],[57])).
% 0.20/0.40 tff(59,plain,
% 0.20/0.40 (^[A: $i] : refl(((~relation(A)) | ![B: $i] : (~((~((~is_transitive_in(A, B)) | ![C: $i, D: $i, E: $i] : (in(ordered_pair(C, E), A) | (~in(D, B)) | (~in(E, B)) | (~in(C, B)) | (~in(ordered_pair(C, D), A)) | (~in(ordered_pair(D, E), A))))) | (~(is_transitive_in(A, B) | (~(in(ordered_pair(tptp_fun_C_4(B, A), tptp_fun_E_2(B, A)), A) | (~in(tptp_fun_D_3(B, A), B)) | (~in(tptp_fun_E_2(B, A), B)) | (~in(ordered_pair(tptp_fun_C_4(B, A), tptp_fun_D_3(B, A)), A)) | (~in(ordered_pair(tptp_fun_D_3(B, A), tptp_fun_E_2(B, A)), A)) | (~in(tptp_fun_C_4(B, A), B))))))))) <=> ((~relation(A)) | ![B: $i] : (~((~((~is_transitive_in(A, B)) | ![C: $i, D: $i, E: $i] : (in(ordered_pair(C, E), A) | (~in(D, B)) | (~in(E, B)) | (~in(C, B)) | (~in(ordered_pair(C, D), A)) | (~in(ordered_pair(D, E), A))))) | (~(is_transitive_in(A, B) | (~(in(ordered_pair(tptp_fun_C_4(B, A), tptp_fun_E_2(B, A)), A) | (~in(tptp_fun_D_3(B, A), B)) | (~in(tptp_fun_E_2(B, A), B)) | (~in(ordered_pair(tptp_fun_C_4(B, A), tptp_fun_D_3(B, A)), A)) | (~in(ordered_pair(tptp_fun_D_3(B, A), tptp_fun_E_2(B, A)), A)) | (~in(tptp_fun_C_4(B, A), B))))))))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(60,plain,
% 0.20/0.40 (![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~is_transitive_in(A, B)) | ![C: $i, D: $i, E: $i] : (in(ordered_pair(C, E), A) | (~in(D, B)) | (~in(E, B)) | (~in(C, B)) | (~in(ordered_pair(C, D), A)) | (~in(ordered_pair(D, E), A))))) | (~(is_transitive_in(A, B) | (~(in(ordered_pair(tptp_fun_C_4(B, A), tptp_fun_E_2(B, A)), A) | (~in(tptp_fun_D_3(B, A), B)) | (~in(tptp_fun_E_2(B, A), B)) | (~in(ordered_pair(tptp_fun_C_4(B, A), tptp_fun_D_3(B, A)), A)) | (~in(ordered_pair(tptp_fun_D_3(B, A), tptp_fun_E_2(B, A)), A)) | (~in(tptp_fun_C_4(B, A), B))))))))) <=> ![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~is_transitive_in(A, B)) | ![C: $i, D: $i, E: $i] : (in(ordered_pair(C, E), A) | (~in(D, B)) | (~in(E, B)) | (~in(C, B)) | (~in(ordered_pair(C, D), A)) | (~in(ordered_pair(D, E), A))))) | (~(is_transitive_in(A, B) | (~(in(ordered_pair(tptp_fun_C_4(B, A), tptp_fun_E_2(B, A)), A) | (~in(tptp_fun_D_3(B, A), B)) | (~in(tptp_fun_E_2(B, A), B)) | (~in(ordered_pair(tptp_fun_C_4(B, A), tptp_fun_D_3(B, A)), A)) | (~in(ordered_pair(tptp_fun_D_3(B, A), tptp_fun_E_2(B, A)), A)) | (~in(tptp_fun_C_4(B, A), B)))))))))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[59])).
% 0.20/0.40 tff(61,plain,
% 0.20/0.40 (^[A: $i] : rewrite(((~relation(A)) | ![B: $i] : (~((~((~is_transitive_in(A, B)) | ![C: $i, D: $i, E: $i] : (in(ordered_pair(C, E), A) | (~in(D, B)) | (~in(E, B)) | (~in(C, B)) | (~in(ordered_pair(C, D), A)) | (~in(ordered_pair(D, E), A))))) | (~(is_transitive_in(A, B) | (~(in(ordered_pair(tptp_fun_C_4(B, A), tptp_fun_E_2(B, A)), A) | (~in(tptp_fun_D_3(B, A), B)) | (~in(tptp_fun_E_2(B, A), B)) | (~in(ordered_pair(tptp_fun_C_4(B, A), tptp_fun_D_3(B, A)), A)) | (~in(ordered_pair(tptp_fun_D_3(B, A), tptp_fun_E_2(B, A)), A)) | (~in(tptp_fun_C_4(B, A), B))))))))) <=> ((~relation(A)) | ![B: $i] : (~((~((~is_transitive_in(A, B)) | ![C: $i, D: $i, E: $i] : (in(ordered_pair(C, E), A) | (~in(D, B)) | (~in(E, B)) | (~in(C, B)) | (~in(ordered_pair(C, D), A)) | (~in(ordered_pair(D, E), A))))) | (~(is_transitive_in(A, B) | (~(in(ordered_pair(tptp_fun_C_4(B, A), tptp_fun_E_2(B, A)), A) | (~in(tptp_fun_D_3(B, A), B)) | (~in(tptp_fun_E_2(B, A), B)) | (~in(ordered_pair(tptp_fun_C_4(B, A), tptp_fun_D_3(B, A)), A)) | (~in(ordered_pair(tptp_fun_D_3(B, A), tptp_fun_E_2(B, A)), A)) | (~in(tptp_fun_C_4(B, A), B))))))))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(62,plain,
% 0.20/0.40 (![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~is_transitive_in(A, B)) | ![C: $i, D: $i, E: $i] : (in(ordered_pair(C, E), A) | (~in(D, B)) | (~in(E, B)) | (~in(C, B)) | (~in(ordered_pair(C, D), A)) | (~in(ordered_pair(D, E), A))))) | (~(is_transitive_in(A, B) | (~(in(ordered_pair(tptp_fun_C_4(B, A), tptp_fun_E_2(B, A)), A) | (~in(tptp_fun_D_3(B, A), B)) | (~in(tptp_fun_E_2(B, A), B)) | (~in(ordered_pair(tptp_fun_C_4(B, A), tptp_fun_D_3(B, A)), A)) | (~in(ordered_pair(tptp_fun_D_3(B, A), tptp_fun_E_2(B, A)), A)) | (~in(tptp_fun_C_4(B, A), B))))))))) <=> ![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~is_transitive_in(A, B)) | ![C: $i, D: $i, E: $i] : (in(ordered_pair(C, E), A) | (~in(D, B)) | (~in(E, B)) | (~in(C, B)) | (~in(ordered_pair(C, D), A)) | (~in(ordered_pair(D, E), A))))) | (~(is_transitive_in(A, B) | (~(in(ordered_pair(tptp_fun_C_4(B, A), tptp_fun_E_2(B, A)), A) | (~in(tptp_fun_D_3(B, A), B)) | (~in(tptp_fun_E_2(B, A), B)) | (~in(ordered_pair(tptp_fun_C_4(B, A), tptp_fun_D_3(B, A)), A)) | (~in(ordered_pair(tptp_fun_D_3(B, A), tptp_fun_E_2(B, A)), A)) | (~in(tptp_fun_C_4(B, A), B)))))))))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[61])).
% 0.20/0.40 tff(63,plain,
% 0.20/0.40 (![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~is_transitive_in(A, B)) | ![C: $i, D: $i, E: $i] : (in(ordered_pair(C, E), A) | (~in(D, B)) | (~in(E, B)) | (~in(C, B)) | (~in(ordered_pair(C, D), A)) | (~in(ordered_pair(D, E), A))))) | (~(is_transitive_in(A, B) | (~(in(ordered_pair(tptp_fun_C_4(B, A), tptp_fun_E_2(B, A)), A) | (~in(tptp_fun_D_3(B, A), B)) | (~in(tptp_fun_E_2(B, A), B)) | (~in(ordered_pair(tptp_fun_C_4(B, A), tptp_fun_D_3(B, A)), A)) | (~in(ordered_pair(tptp_fun_D_3(B, A), tptp_fun_E_2(B, A)), A)) | (~in(tptp_fun_C_4(B, A), B))))))))) <=> ![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~is_transitive_in(A, B)) | ![C: $i, D: $i, E: $i] : (in(ordered_pair(C, E), A) | (~in(D, B)) | (~in(E, B)) | (~in(C, B)) | (~in(ordered_pair(C, D), A)) | (~in(ordered_pair(D, E), A))))) | (~(is_transitive_in(A, B) | (~(in(ordered_pair(tptp_fun_C_4(B, A), tptp_fun_E_2(B, A)), A) | (~in(tptp_fun_D_3(B, A), B)) | (~in(tptp_fun_E_2(B, A), B)) | (~in(ordered_pair(tptp_fun_C_4(B, A), tptp_fun_D_3(B, A)), A)) | (~in(ordered_pair(tptp_fun_D_3(B, A), tptp_fun_E_2(B, A)), A)) | (~in(tptp_fun_C_4(B, A), B)))))))))),
% 0.20/0.40 inference(transitivity,[status(thm)],[62, 60])).
% 0.20/0.40 tff(64,plain,
% 0.20/0.40 (^[A: $i] : rewrite(((~relation(A)) | ![B: $i] : (((~is_transitive_in(A, B)) | ![C: $i, D: $i, E: $i] : ((~(in(C, B) & in(D, B) & in(E, B) & in(ordered_pair(C, D), A) & in(ordered_pair(D, E), A))) | in(ordered_pair(C, E), A))) & (is_transitive_in(A, B) | (~((~(in(tptp_fun_C_4(B, A), B) & in(tptp_fun_D_3(B, A), B) & in(tptp_fun_E_2(B, A), B) & in(ordered_pair(tptp_fun_C_4(B, A), tptp_fun_D_3(B, A)), A) & in(ordered_pair(tptp_fun_D_3(B, A), tptp_fun_E_2(B, A)), A))) | in(ordered_pair(tptp_fun_C_4(B, A), tptp_fun_E_2(B, A)), A)))))) <=> ((~relation(A)) | ![B: $i] : (~((~((~is_transitive_in(A, B)) | ![C: $i, D: $i, E: $i] : (in(ordered_pair(C, E), A) | (~in(D, B)) | (~in(E, B)) | (~in(C, B)) | (~in(ordered_pair(C, D), A)) | (~in(ordered_pair(D, E), A))))) | (~(is_transitive_in(A, B) | (~(in(ordered_pair(tptp_fun_C_4(B, A), tptp_fun_E_2(B, A)), A) | (~in(tptp_fun_D_3(B, A), B)) | (~in(tptp_fun_E_2(B, A), B)) | (~in(ordered_pair(tptp_fun_C_4(B, A), tptp_fun_D_3(B, A)), A)) | (~in(ordered_pair(tptp_fun_D_3(B, A), tptp_fun_E_2(B, A)), A)) | (~in(tptp_fun_C_4(B, A), B))))))))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(65,plain,
% 0.20/0.40 (![A: $i] : ((~relation(A)) | ![B: $i] : (((~is_transitive_in(A, B)) | ![C: $i, D: $i, E: $i] : ((~(in(C, B) & in(D, B) & in(E, B) & in(ordered_pair(C, D), A) & in(ordered_pair(D, E), A))) | in(ordered_pair(C, E), A))) & (is_transitive_in(A, B) | (~((~(in(tptp_fun_C_4(B, A), B) & in(tptp_fun_D_3(B, A), B) & in(tptp_fun_E_2(B, A), B) & in(ordered_pair(tptp_fun_C_4(B, A), tptp_fun_D_3(B, A)), A) & in(ordered_pair(tptp_fun_D_3(B, A), tptp_fun_E_2(B, A)), A))) | in(ordered_pair(tptp_fun_C_4(B, A), tptp_fun_E_2(B, A)), A)))))) <=> ![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~is_transitive_in(A, B)) | ![C: $i, D: $i, E: $i] : (in(ordered_pair(C, E), A) | (~in(D, B)) | (~in(E, B)) | (~in(C, B)) | (~in(ordered_pair(C, D), A)) | (~in(ordered_pair(D, E), A))))) | (~(is_transitive_in(A, B) | (~(in(ordered_pair(tptp_fun_C_4(B, A), tptp_fun_E_2(B, A)), A) | (~in(tptp_fun_D_3(B, A), B)) | (~in(tptp_fun_E_2(B, A), B)) | (~in(ordered_pair(tptp_fun_C_4(B, A), tptp_fun_D_3(B, A)), A)) | (~in(ordered_pair(tptp_fun_D_3(B, A), tptp_fun_E_2(B, A)), A)) | (~in(tptp_fun_C_4(B, A), B)))))))))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[64])).
% 0.20/0.40 tff(66,plain,
% 0.20/0.40 (![A: $i] : ((~relation(A)) | ![B: $i] : (is_transitive_in(A, B) <=> ![C: $i, D: $i, E: $i] : ((~(in(C, B) & in(D, B) & in(E, B) & in(ordered_pair(C, D), A) & in(ordered_pair(D, E), A))) | in(ordered_pair(C, E), A)))) <=> ![A: $i] : ((~relation(A)) | ![B: $i] : (is_transitive_in(A, B) <=> ![C: $i, D: $i, E: $i] : ((~(in(C, B) & in(D, B) & in(E, B) & in(ordered_pair(C, D), A) & in(ordered_pair(D, E), A))) | in(ordered_pair(C, E), A))))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(67,plain,
% 0.20/0.40 (^[A: $i] : trans(monotonicity(quant_intro(proof_bind(^[B: $i] : rewrite((is_transitive_in(A, B) <=> ![C: $i, D: $i, E: $i] : (((((in(C, B) & in(D, B)) & in(E, B)) & in(ordered_pair(C, D), A)) & in(ordered_pair(D, E), A)) => in(ordered_pair(C, E), A))) <=> (is_transitive_in(A, B) <=> ![C: $i, D: $i, E: $i] : ((~(in(C, B) & in(D, B) & in(E, B) & in(ordered_pair(C, D), A) & in(ordered_pair(D, E), A))) | in(ordered_pair(C, E), A))))), (![B: $i] : (is_transitive_in(A, B) <=> ![C: $i, D: $i, E: $i] : (((((in(C, B) & in(D, B)) & in(E, B)) & in(ordered_pair(C, D), A)) & in(ordered_pair(D, E), A)) => in(ordered_pair(C, E), A))) <=> ![B: $i] : (is_transitive_in(A, B) <=> ![C: $i, D: $i, E: $i] : ((~(in(C, B) & in(D, B) & in(E, B) & in(ordered_pair(C, D), A) & in(ordered_pair(D, E), A))) | in(ordered_pair(C, E), A))))), ((relation(A) => ![B: $i] : (is_transitive_in(A, B) <=> ![C: $i, D: $i, E: $i] : (((((in(C, B) & in(D, B)) & in(E, B)) & in(ordered_pair(C, D), A)) & in(ordered_pair(D, E), A)) => in(ordered_pair(C, E), A)))) <=> (relation(A) => ![B: $i] : (is_transitive_in(A, B) <=> ![C: $i, D: $i, E: $i] : ((~(in(C, B) & in(D, B) & in(E, B) & in(ordered_pair(C, D), A) & in(ordered_pair(D, E), A))) | in(ordered_pair(C, E), A)))))), rewrite((relation(A) => ![B: $i] : (is_transitive_in(A, B) <=> ![C: $i, D: $i, E: $i] : ((~(in(C, B) & in(D, B) & in(E, B) & in(ordered_pair(C, D), A) & in(ordered_pair(D, E), A))) | in(ordered_pair(C, E), A)))) <=> ((~relation(A)) | ![B: $i] : (is_transitive_in(A, B) <=> ![C: $i, D: $i, E: $i] : ((~(in(C, B) & in(D, B) & in(E, B) & in(ordered_pair(C, D), A) & in(ordered_pair(D, E), A))) | in(ordered_pair(C, E), A))))), ((relation(A) => ![B: $i] : (is_transitive_in(A, B) <=> ![C: $i, D: $i, E: $i] : (((((in(C, B) & in(D, B)) & in(E, B)) & in(ordered_pair(C, D), A)) & in(ordered_pair(D, E), A)) => in(ordered_pair(C, E), A)))) <=> ((~relation(A)) | ![B: $i] : (is_transitive_in(A, B) <=> ![C: $i, D: $i, E: $i] : ((~(in(C, B) & in(D, B) & in(E, B) & in(ordered_pair(C, D), A) & in(ordered_pair(D, E), A))) | in(ordered_pair(C, E), A))))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(68,plain,
% 0.20/0.40 (![A: $i] : (relation(A) => ![B: $i] : (is_transitive_in(A, B) <=> ![C: $i, D: $i, E: $i] : (((((in(C, B) & in(D, B)) & in(E, B)) & in(ordered_pair(C, D), A)) & in(ordered_pair(D, E), A)) => in(ordered_pair(C, E), A)))) <=> ![A: $i] : ((~relation(A)) | ![B: $i] : (is_transitive_in(A, B) <=> ![C: $i, D: $i, E: $i] : ((~(in(C, B) & in(D, B) & in(E, B) & in(ordered_pair(C, D), A) & in(ordered_pair(D, E), A))) | in(ordered_pair(C, E), A))))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[67])).
% 0.20/0.40 tff(69,axiom,(![A: $i] : (relation(A) => ![B: $i] : (is_transitive_in(A, B) <=> ![C: $i, D: $i, E: $i] : (((((in(C, B) & in(D, B)) & in(E, B)) & in(ordered_pair(C, D), A)) & in(ordered_pair(D, E), A)) => in(ordered_pair(C, E), A))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d8_relat_2')).
% 0.20/0.40 tff(70,plain,
% 0.20/0.40 (![A: $i] : ((~relation(A)) | ![B: $i] : (is_transitive_in(A, B) <=> ![C: $i, D: $i, E: $i] : ((~(in(C, B) & in(D, B) & in(E, B) & in(ordered_pair(C, D), A) & in(ordered_pair(D, E), A))) | in(ordered_pair(C, E), A))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[69, 68])).
% 0.20/0.40 tff(71,plain,
% 0.20/0.40 (![A: $i] : ((~relation(A)) | ![B: $i] : (is_transitive_in(A, B) <=> ![C: $i, D: $i, E: $i] : ((~(in(C, B) & in(D, B) & in(E, B) & in(ordered_pair(C, D), A) & in(ordered_pair(D, E), A))) | in(ordered_pair(C, E), A))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[70, 66])).
% 0.20/0.40 tff(72,plain,(
% 0.20/0.40 ![A: $i] : ((~relation(A)) | ![B: $i] : (((~is_transitive_in(A, B)) | ![C: $i, D: $i, E: $i] : ((~(in(C, B) & in(D, B) & in(E, B) & in(ordered_pair(C, D), A) & in(ordered_pair(D, E), A))) | in(ordered_pair(C, E), A))) & (is_transitive_in(A, B) | (~((~(in(tptp_fun_C_4(B, A), B) & in(tptp_fun_D_3(B, A), B) & in(tptp_fun_E_2(B, A), B) & in(ordered_pair(tptp_fun_C_4(B, A), tptp_fun_D_3(B, A)), A) & in(ordered_pair(tptp_fun_D_3(B, A), tptp_fun_E_2(B, A)), A))) | in(ordered_pair(tptp_fun_C_4(B, A), tptp_fun_E_2(B, A)), A))))))),
% 0.20/0.40 inference(skolemize,[status(sab)],[71])).
% 0.20/0.40 tff(73,plain,
% 0.20/0.40 (![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~is_transitive_in(A, B)) | ![C: $i, D: $i, E: $i] : (in(ordered_pair(C, E), A) | (~in(D, B)) | (~in(E, B)) | (~in(C, B)) | (~in(ordered_pair(C, D), A)) | (~in(ordered_pair(D, E), A))))) | (~(is_transitive_in(A, B) | (~(in(ordered_pair(tptp_fun_C_4(B, A), tptp_fun_E_2(B, A)), A) | (~in(tptp_fun_D_3(B, A), B)) | (~in(tptp_fun_E_2(B, A), B)) | (~in(ordered_pair(tptp_fun_C_4(B, A), tptp_fun_D_3(B, A)), A)) | (~in(ordered_pair(tptp_fun_D_3(B, A), tptp_fun_E_2(B, A)), A)) | (~in(tptp_fun_C_4(B, A), B)))))))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[72, 65])).
% 0.20/0.40 tff(74,plain,
% 0.20/0.40 (![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~is_transitive_in(A, B)) | ![C: $i, D: $i, E: $i] : (in(ordered_pair(C, E), A) | (~in(D, B)) | (~in(E, B)) | (~in(C, B)) | (~in(ordered_pair(C, D), A)) | (~in(ordered_pair(D, E), A))))) | (~(is_transitive_in(A, B) | (~(in(ordered_pair(tptp_fun_C_4(B, A), tptp_fun_E_2(B, A)), A) | (~in(tptp_fun_D_3(B, A), B)) | (~in(tptp_fun_E_2(B, A), B)) | (~in(ordered_pair(tptp_fun_C_4(B, A), tptp_fun_D_3(B, A)), A)) | (~in(ordered_pair(tptp_fun_D_3(B, A), tptp_fun_E_2(B, A)), A)) | (~in(tptp_fun_C_4(B, A), B)))))))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[73, 63])).
% 0.20/0.40 tff(75,plain,
% 0.20/0.40 (((~![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~is_transitive_in(A, B)) | ![C: $i, D: $i, E: $i] : (in(ordered_pair(C, E), A) | (~in(D, B)) | (~in(E, B)) | (~in(C, B)) | (~in(ordered_pair(C, D), A)) | (~in(ordered_pair(D, E), A))))) | (~(is_transitive_in(A, B) | (~(in(ordered_pair(tptp_fun_C_4(B, A), tptp_fun_E_2(B, A)), A) | (~in(tptp_fun_D_3(B, A), B)) | (~in(tptp_fun_E_2(B, A), B)) | (~in(ordered_pair(tptp_fun_C_4(B, A), tptp_fun_D_3(B, A)), A)) | (~in(ordered_pair(tptp_fun_D_3(B, A), tptp_fun_E_2(B, A)), A)) | (~in(tptp_fun_C_4(B, A), B)))))))))) | ((~relation(inclusion_relation(A!15))) | ![B: $i] : (~((~((~is_transitive_in(inclusion_relation(A!15), B)) | ![C: $i, D: $i, E: $i] : ((~in(D, B)) | (~in(E, B)) | (~in(C, B)) | in(ordered_pair(C, E), inclusion_relation(A!15)) | (~in(ordered_pair(C, D), inclusion_relation(A!15))) | (~in(ordered_pair(D, E), inclusion_relation(A!15)))))) | (~(is_transitive_in(inclusion_relation(A!15), B) | (~((~in(tptp_fun_C_4(B, inclusion_relation(A!15)), B)) | (~in(ordered_pair(tptp_fun_D_3(B, inclusion_relation(A!15)), tptp_fun_E_2(B, inclusion_relation(A!15))), inclusion_relation(A!15))) | (~in(ordered_pair(tptp_fun_C_4(B, inclusion_relation(A!15)), tptp_fun_D_3(B, inclusion_relation(A!15))), inclusion_relation(A!15))) | (~in(tptp_fun_E_2(B, inclusion_relation(A!15)), B)) | (~in(tptp_fun_D_3(B, inclusion_relation(A!15)), B)) | in(ordered_pair(tptp_fun_C_4(B, inclusion_relation(A!15)), tptp_fun_E_2(B, inclusion_relation(A!15))), inclusion_relation(A!15)))))))))) <=> ((~![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~is_transitive_in(A, B)) | ![C: $i, D: $i, E: $i] : (in(ordered_pair(C, E), A) | (~in(D, B)) | (~in(E, B)) | (~in(C, B)) | (~in(ordered_pair(C, D), A)) | (~in(ordered_pair(D, E), A))))) | (~(is_transitive_in(A, B) | (~(in(ordered_pair(tptp_fun_C_4(B, A), tptp_fun_E_2(B, A)), A) | (~in(tptp_fun_D_3(B, A), B)) | (~in(tptp_fun_E_2(B, A), B)) | (~in(ordered_pair(tptp_fun_C_4(B, A), tptp_fun_D_3(B, A)), A)) | (~in(ordered_pair(tptp_fun_D_3(B, A), tptp_fun_E_2(B, A)), A)) | (~in(tptp_fun_C_4(B, A), B)))))))))) | (~relation(inclusion_relation(A!15))) | ![B: $i] : (~((~((~is_transitive_in(inclusion_relation(A!15), B)) | ![C: $i, D: $i, E: $i] : ((~in(D, B)) | (~in(E, B)) | (~in(C, B)) | in(ordered_pair(C, E), inclusion_relation(A!15)) | (~in(ordered_pair(C, D), inclusion_relation(A!15))) | (~in(ordered_pair(D, E), inclusion_relation(A!15)))))) | (~(is_transitive_in(inclusion_relation(A!15), B) | (~((~in(tptp_fun_C_4(B, inclusion_relation(A!15)), B)) | (~in(ordered_pair(tptp_fun_D_3(B, inclusion_relation(A!15)), tptp_fun_E_2(B, inclusion_relation(A!15))), inclusion_relation(A!15))) | (~in(ordered_pair(tptp_fun_C_4(B, inclusion_relation(A!15)), tptp_fun_D_3(B, inclusion_relation(A!15))), inclusion_relation(A!15))) | (~in(tptp_fun_E_2(B, inclusion_relation(A!15)), B)) | (~in(tptp_fun_D_3(B, inclusion_relation(A!15)), B)) | in(ordered_pair(tptp_fun_C_4(B, inclusion_relation(A!15)), tptp_fun_E_2(B, inclusion_relation(A!15))), inclusion_relation(A!15)))))))))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(76,plain,
% 0.20/0.40 (((~relation(inclusion_relation(A!15))) | ![B: $i] : (~((~((~is_transitive_in(inclusion_relation(A!15), B)) | ![C: $i, D: $i, E: $i] : (in(ordered_pair(C, E), inclusion_relation(A!15)) | (~in(D, B)) | (~in(E, B)) | (~in(C, B)) | (~in(ordered_pair(C, D), inclusion_relation(A!15))) | (~in(ordered_pair(D, E), inclusion_relation(A!15)))))) | (~(is_transitive_in(inclusion_relation(A!15), B) | (~(in(ordered_pair(tptp_fun_C_4(B, inclusion_relation(A!15)), tptp_fun_E_2(B, inclusion_relation(A!15))), inclusion_relation(A!15)) | (~in(tptp_fun_D_3(B, inclusion_relation(A!15)), B)) | (~in(tptp_fun_E_2(B, inclusion_relation(A!15)), B)) | (~in(ordered_pair(tptp_fun_C_4(B, inclusion_relation(A!15)), tptp_fun_D_3(B, inclusion_relation(A!15))), inclusion_relation(A!15))) | (~in(ordered_pair(tptp_fun_D_3(B, inclusion_relation(A!15)), tptp_fun_E_2(B, inclusion_relation(A!15))), inclusion_relation(A!15))) | (~in(tptp_fun_C_4(B, inclusion_relation(A!15)), B))))))))) <=> ((~relation(inclusion_relation(A!15))) | ![B: $i] : (~((~((~is_transitive_in(inclusion_relation(A!15), B)) | ![C: $i, D: $i, E: $i] : ((~in(D, B)) | (~in(E, B)) | (~in(C, B)) | in(ordered_pair(C, E), inclusion_relation(A!15)) | (~in(ordered_pair(C, D), inclusion_relation(A!15))) | (~in(ordered_pair(D, E), inclusion_relation(A!15)))))) | (~(is_transitive_in(inclusion_relation(A!15), B) | (~((~in(tptp_fun_C_4(B, inclusion_relation(A!15)), B)) | (~in(ordered_pair(tptp_fun_D_3(B, inclusion_relation(A!15)), tptp_fun_E_2(B, inclusion_relation(A!15))), inclusion_relation(A!15))) | (~in(ordered_pair(tptp_fun_C_4(B, inclusion_relation(A!15)), tptp_fun_D_3(B, inclusion_relation(A!15))), inclusion_relation(A!15))) | (~in(tptp_fun_E_2(B, inclusion_relation(A!15)), B)) | (~in(tptp_fun_D_3(B, inclusion_relation(A!15)), B)) | in(ordered_pair(tptp_fun_C_4(B, inclusion_relation(A!15)), tptp_fun_E_2(B, inclusion_relation(A!15))), inclusion_relation(A!15)))))))))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(77,plain,
% 0.20/0.40 (((~![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~is_transitive_in(A, B)) | ![C: $i, D: $i, E: $i] : (in(ordered_pair(C, E), A) | (~in(D, B)) | (~in(E, B)) | (~in(C, B)) | (~in(ordered_pair(C, D), A)) | (~in(ordered_pair(D, E), A))))) | (~(is_transitive_in(A, B) | (~(in(ordered_pair(tptp_fun_C_4(B, A), tptp_fun_E_2(B, A)), A) | (~in(tptp_fun_D_3(B, A), B)) | (~in(tptp_fun_E_2(B, A), B)) | (~in(ordered_pair(tptp_fun_C_4(B, A), tptp_fun_D_3(B, A)), A)) | (~in(ordered_pair(tptp_fun_D_3(B, A), tptp_fun_E_2(B, A)), A)) | (~in(tptp_fun_C_4(B, A), B)))))))))) | ((~relation(inclusion_relation(A!15))) | ![B: $i] : (~((~((~is_transitive_in(inclusion_relation(A!15), B)) | ![C: $i, D: $i, E: $i] : (in(ordered_pair(C, E), inclusion_relation(A!15)) | (~in(D, B)) | (~in(E, B)) | (~in(C, B)) | (~in(ordered_pair(C, D), inclusion_relation(A!15))) | (~in(ordered_pair(D, E), inclusion_relation(A!15)))))) | (~(is_transitive_in(inclusion_relation(A!15), B) | (~(in(ordered_pair(tptp_fun_C_4(B, inclusion_relation(A!15)), tptp_fun_E_2(B, inclusion_relation(A!15))), inclusion_relation(A!15)) | (~in(tptp_fun_D_3(B, inclusion_relation(A!15)), B)) | (~in(tptp_fun_E_2(B, inclusion_relation(A!15)), B)) | (~in(ordered_pair(tptp_fun_C_4(B, inclusion_relation(A!15)), tptp_fun_D_3(B, inclusion_relation(A!15))), inclusion_relation(A!15))) | (~in(ordered_pair(tptp_fun_D_3(B, inclusion_relation(A!15)), tptp_fun_E_2(B, inclusion_relation(A!15))), inclusion_relation(A!15))) | (~in(tptp_fun_C_4(B, inclusion_relation(A!15)), B)))))))))) <=> ((~![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~is_transitive_in(A, B)) | ![C: $i, D: $i, E: $i] : (in(ordered_pair(C, E), A) | (~in(D, B)) | (~in(E, B)) | (~in(C, B)) | (~in(ordered_pair(C, D), A)) | (~in(ordered_pair(D, E), A))))) | (~(is_transitive_in(A, B) | (~(in(ordered_pair(tptp_fun_C_4(B, A), tptp_fun_E_2(B, A)), A) | (~in(tptp_fun_D_3(B, A), B)) | (~in(tptp_fun_E_2(B, A), B)) | (~in(ordered_pair(tptp_fun_C_4(B, A), tptp_fun_D_3(B, A)), A)) | (~in(ordered_pair(tptp_fun_D_3(B, A), tptp_fun_E_2(B, A)), A)) | (~in(tptp_fun_C_4(B, A), B)))))))))) | ((~relation(inclusion_relation(A!15))) | ![B: $i] : (~((~((~is_transitive_in(inclusion_relation(A!15), B)) | ![C: $i, D: $i, E: $i] : ((~in(D, B)) | (~in(E, B)) | (~in(C, B)) | in(ordered_pair(C, E), inclusion_relation(A!15)) | (~in(ordered_pair(C, D), inclusion_relation(A!15))) | (~in(ordered_pair(D, E), inclusion_relation(A!15)))))) | (~(is_transitive_in(inclusion_relation(A!15), B) | (~((~in(tptp_fun_C_4(B, inclusion_relation(A!15)), B)) | (~in(ordered_pair(tptp_fun_D_3(B, inclusion_relation(A!15)), tptp_fun_E_2(B, inclusion_relation(A!15))), inclusion_relation(A!15))) | (~in(ordered_pair(tptp_fun_C_4(B, inclusion_relation(A!15)), tptp_fun_D_3(B, inclusion_relation(A!15))), inclusion_relation(A!15))) | (~in(tptp_fun_E_2(B, inclusion_relation(A!15)), B)) | (~in(tptp_fun_D_3(B, inclusion_relation(A!15)), B)) | in(ordered_pair(tptp_fun_C_4(B, inclusion_relation(A!15)), tptp_fun_E_2(B, inclusion_relation(A!15))), inclusion_relation(A!15))))))))))),
% 0.20/0.41 inference(monotonicity,[status(thm)],[76])).
% 0.20/0.41 tff(78,plain,
% 0.20/0.41 (((~![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~is_transitive_in(A, B)) | ![C: $i, D: $i, E: $i] : (in(ordered_pair(C, E), A) | (~in(D, B)) | (~in(E, B)) | (~in(C, B)) | (~in(ordered_pair(C, D), A)) | (~in(ordered_pair(D, E), A))))) | (~(is_transitive_in(A, B) | (~(in(ordered_pair(tptp_fun_C_4(B, A), tptp_fun_E_2(B, A)), A) | (~in(tptp_fun_D_3(B, A), B)) | (~in(tptp_fun_E_2(B, A), B)) | (~in(ordered_pair(tptp_fun_C_4(B, A), tptp_fun_D_3(B, A)), A)) | (~in(ordered_pair(tptp_fun_D_3(B, A), tptp_fun_E_2(B, A)), A)) | (~in(tptp_fun_C_4(B, A), B)))))))))) | ((~relation(inclusion_relation(A!15))) | ![B: $i] : (~((~((~is_transitive_in(inclusion_relation(A!15), B)) | ![C: $i, D: $i, E: $i] : (in(ordered_pair(C, E), inclusion_relation(A!15)) | (~in(D, B)) | (~in(E, B)) | (~in(C, B)) | (~in(ordered_pair(C, D), inclusion_relation(A!15))) | (~in(ordered_pair(D, E), inclusion_relation(A!15)))))) | (~(is_transitive_in(inclusion_relation(A!15), B) | (~(in(ordered_pair(tptp_fun_C_4(B, inclusion_relation(A!15)), tptp_fun_E_2(B, inclusion_relation(A!15))), inclusion_relation(A!15)) | (~in(tptp_fun_D_3(B, inclusion_relation(A!15)), B)) | (~in(tptp_fun_E_2(B, inclusion_relation(A!15)), B)) | (~in(ordered_pair(tptp_fun_C_4(B, inclusion_relation(A!15)), tptp_fun_D_3(B, inclusion_relation(A!15))), inclusion_relation(A!15))) | (~in(ordered_pair(tptp_fun_D_3(B, inclusion_relation(A!15)), tptp_fun_E_2(B, inclusion_relation(A!15))), inclusion_relation(A!15))) | (~in(tptp_fun_C_4(B, inclusion_relation(A!15)), B)))))))))) <=> ((~![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~is_transitive_in(A, B)) | ![C: $i, D: $i, E: $i] : (in(ordered_pair(C, E), A) | (~in(D, B)) | (~in(E, B)) | (~in(C, B)) | (~in(ordered_pair(C, D), A)) | (~in(ordered_pair(D, E), A))))) | (~(is_transitive_in(A, B) | (~(in(ordered_pair(tptp_fun_C_4(B, A), tptp_fun_E_2(B, A)), A) | (~in(tptp_fun_D_3(B, A), B)) | (~in(tptp_fun_E_2(B, A), B)) | (~in(ordered_pair(tptp_fun_C_4(B, A), tptp_fun_D_3(B, A)), A)) | (~in(ordered_pair(tptp_fun_D_3(B, A), tptp_fun_E_2(B, A)), A)) | (~in(tptp_fun_C_4(B, A), B)))))))))) | (~relation(inclusion_relation(A!15))) | ![B: $i] : (~((~((~is_transitive_in(inclusion_relation(A!15), B)) | ![C: $i, D: $i, E: $i] : ((~in(D, B)) | (~in(E, B)) | (~in(C, B)) | in(ordered_pair(C, E), inclusion_relation(A!15)) | (~in(ordered_pair(C, D), inclusion_relation(A!15))) | (~in(ordered_pair(D, E), inclusion_relation(A!15)))))) | (~(is_transitive_in(inclusion_relation(A!15), B) | (~((~in(tptp_fun_C_4(B, inclusion_relation(A!15)), B)) | (~in(ordered_pair(tptp_fun_D_3(B, inclusion_relation(A!15)), tptp_fun_E_2(B, inclusion_relation(A!15))), inclusion_relation(A!15))) | (~in(ordered_pair(tptp_fun_C_4(B, inclusion_relation(A!15)), tptp_fun_D_3(B, inclusion_relation(A!15))), inclusion_relation(A!15))) | (~in(tptp_fun_E_2(B, inclusion_relation(A!15)), B)) | (~in(tptp_fun_D_3(B, inclusion_relation(A!15)), B)) | in(ordered_pair(tptp_fun_C_4(B, inclusion_relation(A!15)), tptp_fun_E_2(B, inclusion_relation(A!15))), inclusion_relation(A!15)))))))))),
% 0.20/0.41 inference(transitivity,[status(thm)],[77, 75])).
% 0.20/0.41 tff(79,plain,
% 0.20/0.41 ((~![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~is_transitive_in(A, B)) | ![C: $i, D: $i, E: $i] : (in(ordered_pair(C, E), A) | (~in(D, B)) | (~in(E, B)) | (~in(C, B)) | (~in(ordered_pair(C, D), A)) | (~in(ordered_pair(D, E), A))))) | (~(is_transitive_in(A, B) | (~(in(ordered_pair(tptp_fun_C_4(B, A), tptp_fun_E_2(B, A)), A) | (~in(tptp_fun_D_3(B, A), B)) | (~in(tptp_fun_E_2(B, A), B)) | (~in(ordered_pair(tptp_fun_C_4(B, A), tptp_fun_D_3(B, A)), A)) | (~in(ordered_pair(tptp_fun_D_3(B, A), tptp_fun_E_2(B, A)), A)) | (~in(tptp_fun_C_4(B, A), B)))))))))) | ((~relation(inclusion_relation(A!15))) | ![B: $i] : (~((~((~is_transitive_in(inclusion_relation(A!15), B)) | ![C: $i, D: $i, E: $i] : (in(ordered_pair(C, E), inclusion_relation(A!15)) | (~in(D, B)) | (~in(E, B)) | (~in(C, B)) | (~in(ordered_pair(C, D), inclusion_relation(A!15))) | (~in(ordered_pair(D, E), inclusion_relation(A!15)))))) | (~(is_transitive_in(inclusion_relation(A!15), B) | (~(in(ordered_pair(tptp_fun_C_4(B, inclusion_relation(A!15)), tptp_fun_E_2(B, inclusion_relation(A!15))), inclusion_relation(A!15)) | (~in(tptp_fun_D_3(B, inclusion_relation(A!15)), B)) | (~in(tptp_fun_E_2(B, inclusion_relation(A!15)), B)) | (~in(ordered_pair(tptp_fun_C_4(B, inclusion_relation(A!15)), tptp_fun_D_3(B, inclusion_relation(A!15))), inclusion_relation(A!15))) | (~in(ordered_pair(tptp_fun_D_3(B, inclusion_relation(A!15)), tptp_fun_E_2(B, inclusion_relation(A!15))), inclusion_relation(A!15))) | (~in(tptp_fun_C_4(B, inclusion_relation(A!15)), B)))))))))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(80,plain,
% 0.20/0.41 ((~![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~is_transitive_in(A, B)) | ![C: $i, D: $i, E: $i] : (in(ordered_pair(C, E), A) | (~in(D, B)) | (~in(E, B)) | (~in(C, B)) | (~in(ordered_pair(C, D), A)) | (~in(ordered_pair(D, E), A))))) | (~(is_transitive_in(A, B) | (~(in(ordered_pair(tptp_fun_C_4(B, A), tptp_fun_E_2(B, A)), A) | (~in(tptp_fun_D_3(B, A), B)) | (~in(tptp_fun_E_2(B, A), B)) | (~in(ordered_pair(tptp_fun_C_4(B, A), tptp_fun_D_3(B, A)), A)) | (~in(ordered_pair(tptp_fun_D_3(B, A), tptp_fun_E_2(B, A)), A)) | (~in(tptp_fun_C_4(B, A), B)))))))))) | (~relation(inclusion_relation(A!15))) | ![B: $i] : (~((~((~is_transitive_in(inclusion_relation(A!15), B)) | ![C: $i, D: $i, E: $i] : ((~in(D, B)) | (~in(E, B)) | (~in(C, B)) | in(ordered_pair(C, E), inclusion_relation(A!15)) | (~in(ordered_pair(C, D), inclusion_relation(A!15))) | (~in(ordered_pair(D, E), inclusion_relation(A!15)))))) | (~(is_transitive_in(inclusion_relation(A!15), B) | (~((~in(tptp_fun_C_4(B, inclusion_relation(A!15)), B)) | (~in(ordered_pair(tptp_fun_D_3(B, inclusion_relation(A!15)), tptp_fun_E_2(B, inclusion_relation(A!15))), inclusion_relation(A!15))) | (~in(ordered_pair(tptp_fun_C_4(B, inclusion_relation(A!15)), tptp_fun_D_3(B, inclusion_relation(A!15))), inclusion_relation(A!15))) | (~in(tptp_fun_E_2(B, inclusion_relation(A!15)), B)) | (~in(tptp_fun_D_3(B, inclusion_relation(A!15)), B)) | in(ordered_pair(tptp_fun_C_4(B, inclusion_relation(A!15)), tptp_fun_E_2(B, inclusion_relation(A!15))), inclusion_relation(A!15))))))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[79, 78])).
% 0.20/0.41 tff(81,plain,
% 0.20/0.41 (![B: $i] : (~((~((~is_transitive_in(inclusion_relation(A!15), B)) | ![C: $i, D: $i, E: $i] : ((~in(D, B)) | (~in(E, B)) | (~in(C, B)) | in(ordered_pair(C, E), inclusion_relation(A!15)) | (~in(ordered_pair(C, D), inclusion_relation(A!15))) | (~in(ordered_pair(D, E), inclusion_relation(A!15)))))) | (~(is_transitive_in(inclusion_relation(A!15), B) | (~((~in(tptp_fun_C_4(B, inclusion_relation(A!15)), B)) | (~in(ordered_pair(tptp_fun_D_3(B, inclusion_relation(A!15)), tptp_fun_E_2(B, inclusion_relation(A!15))), inclusion_relation(A!15))) | (~in(ordered_pair(tptp_fun_C_4(B, inclusion_relation(A!15)), tptp_fun_D_3(B, inclusion_relation(A!15))), inclusion_relation(A!15))) | (~in(tptp_fun_E_2(B, inclusion_relation(A!15)), B)) | (~in(tptp_fun_D_3(B, inclusion_relation(A!15)), B)) | in(ordered_pair(tptp_fun_C_4(B, inclusion_relation(A!15)), tptp_fun_E_2(B, inclusion_relation(A!15))), inclusion_relation(A!15))))))))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[80, 74, 9])).
% 0.20/0.41 tff(82,plain,
% 0.20/0.41 (((~![B: $i] : (~((~((~is_transitive_in(inclusion_relation(A!15), B)) | ![C: $i, D: $i, E: $i] : ((~in(D, B)) | (~in(E, B)) | (~in(C, B)) | in(ordered_pair(C, E), inclusion_relation(A!15)) | (~in(ordered_pair(C, D), inclusion_relation(A!15))) | (~in(ordered_pair(D, E), inclusion_relation(A!15)))))) | (~(is_transitive_in(inclusion_relation(A!15), B) | (~((~in(tptp_fun_C_4(B, inclusion_relation(A!15)), B)) | (~in(ordered_pair(tptp_fun_D_3(B, inclusion_relation(A!15)), tptp_fun_E_2(B, inclusion_relation(A!15))), inclusion_relation(A!15))) | (~in(ordered_pair(tptp_fun_C_4(B, inclusion_relation(A!15)), tptp_fun_D_3(B, inclusion_relation(A!15))), inclusion_relation(A!15))) | (~in(tptp_fun_E_2(B, inclusion_relation(A!15)), B)) | (~in(tptp_fun_D_3(B, inclusion_relation(A!15)), B)) | in(ordered_pair(tptp_fun_C_4(B, inclusion_relation(A!15)), tptp_fun_E_2(B, inclusion_relation(A!15))), inclusion_relation(A!15))))))))) | (~((~((~is_transitive_in(inclusion_relation(A!15), set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))))) | ![C: $i, D: $i, E: $i] : (in(ordered_pair(C, E), inclusion_relation(A!15)) | (~in(ordered_pair(C, D), inclusion_relation(A!15))) | (~in(ordered_pair(D, E), inclusion_relation(A!15))) | (~in(D, set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))))) | (~in(E, set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))))) | (~in(C, set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15)))))))) | (~(is_transitive_in(inclusion_relation(A!15), set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15)))) | (~((~in(tptp_fun_D_3(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))))) | (~in(ordered_pair(tptp_fun_C_4(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), tptp_fun_D_3(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15))), inclusion_relation(A!15))) | in(ordered_pair(tptp_fun_C_4(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), tptp_fun_E_2(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15))), inclusion_relation(A!15)) | (~in(tptp_fun_E_2(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))))) | (~in(ordered_pair(tptp_fun_D_3(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), tptp_fun_E_2(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15))), inclusion_relation(A!15))) | (~in(tptp_fun_C_4(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15)))))))))))) <=> ((~![B: $i] : (~((~((~is_transitive_in(inclusion_relation(A!15), B)) | ![C: $i, D: $i, E: $i] : ((~in(D, B)) | (~in(E, B)) | (~in(C, B)) | in(ordered_pair(C, E), inclusion_relation(A!15)) | (~in(ordered_pair(C, D), inclusion_relation(A!15))) | (~in(ordered_pair(D, E), inclusion_relation(A!15)))))) | (~(is_transitive_in(inclusion_relation(A!15), B) | (~((~in(tptp_fun_C_4(B, inclusion_relation(A!15)), B)) | (~in(ordered_pair(tptp_fun_D_3(B, inclusion_relation(A!15)), tptp_fun_E_2(B, inclusion_relation(A!15))), inclusion_relation(A!15))) | (~in(ordered_pair(tptp_fun_C_4(B, inclusion_relation(A!15)), tptp_fun_D_3(B, inclusion_relation(A!15))), inclusion_relation(A!15))) | (~in(tptp_fun_E_2(B, inclusion_relation(A!15)), B)) | (~in(tptp_fun_D_3(B, inclusion_relation(A!15)), B)) | in(ordered_pair(tptp_fun_C_4(B, inclusion_relation(A!15)), tptp_fun_E_2(B, inclusion_relation(A!15))), inclusion_relation(A!15))))))))) | (~((~((~is_transitive_in(inclusion_relation(A!15), set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))))) | ![C: $i, D: $i, E: $i] : (in(ordered_pair(C, E), inclusion_relation(A!15)) | (~in(ordered_pair(C, D), inclusion_relation(A!15))) | (~in(ordered_pair(D, E), inclusion_relation(A!15))) | (~in(D, set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))))) | (~in(E, set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))))) | (~in(C, set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15)))))))) | (~(is_transitive_in(inclusion_relation(A!15), set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15)))) | (~((~in(tptp_fun_D_3(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))))) | (~in(ordered_pair(tptp_fun_C_4(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), tptp_fun_D_3(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15))), inclusion_relation(A!15))) | in(ordered_pair(tptp_fun_C_4(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), tptp_fun_E_2(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15))), inclusion_relation(A!15)) | (~in(tptp_fun_E_2(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))))) | (~in(ordered_pair(tptp_fun_D_3(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), tptp_fun_E_2(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15))), inclusion_relation(A!15))) | (~in(tptp_fun_C_4(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))))))))))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(83,plain,
% 0.20/0.41 ((~((~((~is_transitive_in(inclusion_relation(A!15), set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))))) | ![C: $i, D: $i, E: $i] : ((~in(D, set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))))) | (~in(E, set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))))) | (~in(C, set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))))) | in(ordered_pair(C, E), inclusion_relation(A!15)) | (~in(ordered_pair(C, D), inclusion_relation(A!15))) | (~in(ordered_pair(D, E), inclusion_relation(A!15)))))) | (~(is_transitive_in(inclusion_relation(A!15), set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15)))) | (~((~in(tptp_fun_C_4(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))))) | (~in(ordered_pair(tptp_fun_D_3(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), tptp_fun_E_2(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15))), inclusion_relation(A!15))) | (~in(ordered_pair(tptp_fun_C_4(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), tptp_fun_D_3(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15))), inclusion_relation(A!15))) | (~in(tptp_fun_E_2(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))))) | (~in(tptp_fun_D_3(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))))) | in(ordered_pair(tptp_fun_C_4(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), tptp_fun_E_2(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15))), inclusion_relation(A!15)))))))) <=> (~((~((~is_transitive_in(inclusion_relation(A!15), set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))))) | ![C: $i, D: $i, E: $i] : (in(ordered_pair(C, E), inclusion_relation(A!15)) | (~in(ordered_pair(C, D), inclusion_relation(A!15))) | (~in(ordered_pair(D, E), inclusion_relation(A!15))) | (~in(D, set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))))) | (~in(E, set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))))) | (~in(C, set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15)))))))) | (~(is_transitive_in(inclusion_relation(A!15), set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15)))) | (~((~in(tptp_fun_D_3(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))))) | (~in(ordered_pair(tptp_fun_C_4(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), tptp_fun_D_3(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15))), inclusion_relation(A!15))) | in(ordered_pair(tptp_fun_C_4(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), tptp_fun_E_2(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15))), inclusion_relation(A!15)) | (~in(tptp_fun_E_2(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))))) | (~in(ordered_pair(tptp_fun_D_3(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), tptp_fun_E_2(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15))), inclusion_relation(A!15))) | (~in(tptp_fun_C_4(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15)))))))))))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(84,plain,
% 0.20/0.42 (((~![B: $i] : (~((~((~is_transitive_in(inclusion_relation(A!15), B)) | ![C: $i, D: $i, E: $i] : ((~in(D, B)) | (~in(E, B)) | (~in(C, B)) | in(ordered_pair(C, E), inclusion_relation(A!15)) | (~in(ordered_pair(C, D), inclusion_relation(A!15))) | (~in(ordered_pair(D, E), inclusion_relation(A!15)))))) | (~(is_transitive_in(inclusion_relation(A!15), B) | (~((~in(tptp_fun_C_4(B, inclusion_relation(A!15)), B)) | (~in(ordered_pair(tptp_fun_D_3(B, inclusion_relation(A!15)), tptp_fun_E_2(B, inclusion_relation(A!15))), inclusion_relation(A!15))) | (~in(ordered_pair(tptp_fun_C_4(B, inclusion_relation(A!15)), tptp_fun_D_3(B, inclusion_relation(A!15))), inclusion_relation(A!15))) | (~in(tptp_fun_E_2(B, inclusion_relation(A!15)), B)) | (~in(tptp_fun_D_3(B, inclusion_relation(A!15)), B)) | in(ordered_pair(tptp_fun_C_4(B, inclusion_relation(A!15)), tptp_fun_E_2(B, inclusion_relation(A!15))), inclusion_relation(A!15))))))))) | (~((~((~is_transitive_in(inclusion_relation(A!15), set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))))) | ![C: $i, D: $i, E: $i] : ((~in(D, set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))))) | (~in(E, set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))))) | (~in(C, set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))))) | in(ordered_pair(C, E), inclusion_relation(A!15)) | (~in(ordered_pair(C, D), inclusion_relation(A!15))) | (~in(ordered_pair(D, E), inclusion_relation(A!15)))))) | (~(is_transitive_in(inclusion_relation(A!15), set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15)))) | (~((~in(tptp_fun_C_4(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))))) | (~in(ordered_pair(tptp_fun_D_3(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), tptp_fun_E_2(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15))), inclusion_relation(A!15))) | (~in(ordered_pair(tptp_fun_C_4(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), tptp_fun_D_3(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15))), inclusion_relation(A!15))) | (~in(tptp_fun_E_2(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))))) | (~in(tptp_fun_D_3(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))))) | in(ordered_pair(tptp_fun_C_4(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), tptp_fun_E_2(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15))), inclusion_relation(A!15))))))))) <=> ((~![B: $i] : (~((~((~is_transitive_in(inclusion_relation(A!15), B)) | ![C: $i, D: $i, E: $i] : ((~in(D, B)) | (~in(E, B)) | (~in(C, B)) | in(ordered_pair(C, E), inclusion_relation(A!15)) | (~in(ordered_pair(C, D), inclusion_relation(A!15))) | (~in(ordered_pair(D, E), inclusion_relation(A!15)))))) | (~(is_transitive_in(inclusion_relation(A!15), B) | (~((~in(tptp_fun_C_4(B, inclusion_relation(A!15)), B)) | (~in(ordered_pair(tptp_fun_D_3(B, inclusion_relation(A!15)), tptp_fun_E_2(B, inclusion_relation(A!15))), inclusion_relation(A!15))) | (~in(ordered_pair(tptp_fun_C_4(B, inclusion_relation(A!15)), tptp_fun_D_3(B, inclusion_relation(A!15))), inclusion_relation(A!15))) | (~in(tptp_fun_E_2(B, inclusion_relation(A!15)), B)) | (~in(tptp_fun_D_3(B, inclusion_relation(A!15)), B)) | in(ordered_pair(tptp_fun_C_4(B, inclusion_relation(A!15)), tptp_fun_E_2(B, inclusion_relation(A!15))), inclusion_relation(A!15))))))))) | (~((~((~is_transitive_in(inclusion_relation(A!15), set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))))) | ![C: $i, D: $i, E: $i] : (in(ordered_pair(C, E), inclusion_relation(A!15)) | (~in(ordered_pair(C, D), inclusion_relation(A!15))) | (~in(ordered_pair(D, E), inclusion_relation(A!15))) | (~in(D, set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))))) | (~in(E, set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))))) | (~in(C, set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15)))))))) | (~(is_transitive_in(inclusion_relation(A!15), set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15)))) | (~((~in(tptp_fun_D_3(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))))) | (~in(ordered_pair(tptp_fun_C_4(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), tptp_fun_D_3(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15))), inclusion_relation(A!15))) | in(ordered_pair(tptp_fun_C_4(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), tptp_fun_E_2(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15))), inclusion_relation(A!15)) | (~in(tptp_fun_E_2(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))))) | (~in(ordered_pair(tptp_fun_D_3(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), tptp_fun_E_2(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15))), inclusion_relation(A!15))) | (~in(tptp_fun_C_4(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))))))))))))),
% 0.20/0.42 inference(monotonicity,[status(thm)],[83])).
% 0.20/0.42 tff(85,plain,
% 0.20/0.42 (((~![B: $i] : (~((~((~is_transitive_in(inclusion_relation(A!15), B)) | ![C: $i, D: $i, E: $i] : ((~in(D, B)) | (~in(E, B)) | (~in(C, B)) | in(ordered_pair(C, E), inclusion_relation(A!15)) | (~in(ordered_pair(C, D), inclusion_relation(A!15))) | (~in(ordered_pair(D, E), inclusion_relation(A!15)))))) | (~(is_transitive_in(inclusion_relation(A!15), B) | (~((~in(tptp_fun_C_4(B, inclusion_relation(A!15)), B)) | (~in(ordered_pair(tptp_fun_D_3(B, inclusion_relation(A!15)), tptp_fun_E_2(B, inclusion_relation(A!15))), inclusion_relation(A!15))) | (~in(ordered_pair(tptp_fun_C_4(B, inclusion_relation(A!15)), tptp_fun_D_3(B, inclusion_relation(A!15))), inclusion_relation(A!15))) | (~in(tptp_fun_E_2(B, inclusion_relation(A!15)), B)) | (~in(tptp_fun_D_3(B, inclusion_relation(A!15)), B)) | in(ordered_pair(tptp_fun_C_4(B, inclusion_relation(A!15)), tptp_fun_E_2(B, inclusion_relation(A!15))), inclusion_relation(A!15))))))))) | (~((~((~is_transitive_in(inclusion_relation(A!15), set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))))) | ![C: $i, D: $i, E: $i] : ((~in(D, set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))))) | (~in(E, set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))))) | (~in(C, set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))))) | in(ordered_pair(C, E), inclusion_relation(A!15)) | (~in(ordered_pair(C, D), inclusion_relation(A!15))) | (~in(ordered_pair(D, E), inclusion_relation(A!15)))))) | (~(is_transitive_in(inclusion_relation(A!15), set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15)))) | (~((~in(tptp_fun_C_4(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))))) | (~in(ordered_pair(tptp_fun_D_3(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), tptp_fun_E_2(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15))), inclusion_relation(A!15))) | (~in(ordered_pair(tptp_fun_C_4(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), tptp_fun_D_3(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15))), inclusion_relation(A!15))) | (~in(tptp_fun_E_2(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))))) | (~in(tptp_fun_D_3(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))))) | in(ordered_pair(tptp_fun_C_4(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), tptp_fun_E_2(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15))), inclusion_relation(A!15))))))))) <=> ((~![B: $i] : (~((~((~is_transitive_in(inclusion_relation(A!15), B)) | ![C: $i, D: $i, E: $i] : ((~in(D, B)) | (~in(E, B)) | (~in(C, B)) | in(ordered_pair(C, E), inclusion_relation(A!15)) | (~in(ordered_pair(C, D), inclusion_relation(A!15))) | (~in(ordered_pair(D, E), inclusion_relation(A!15)))))) | (~(is_transitive_in(inclusion_relation(A!15), B) | (~((~in(tptp_fun_C_4(B, inclusion_relation(A!15)), B)) | (~in(ordered_pair(tptp_fun_D_3(B, inclusion_relation(A!15)), tptp_fun_E_2(B, inclusion_relation(A!15))), inclusion_relation(A!15))) | (~in(ordered_pair(tptp_fun_C_4(B, inclusion_relation(A!15)), tptp_fun_D_3(B, inclusion_relation(A!15))), inclusion_relation(A!15))) | (~in(tptp_fun_E_2(B, inclusion_relation(A!15)), B)) | (~in(tptp_fun_D_3(B, inclusion_relation(A!15)), B)) | in(ordered_pair(tptp_fun_C_4(B, inclusion_relation(A!15)), tptp_fun_E_2(B, inclusion_relation(A!15))), inclusion_relation(A!15))))))))) | (~((~((~is_transitive_in(inclusion_relation(A!15), set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))))) | ![C: $i, D: $i, E: $i] : (in(ordered_pair(C, E), inclusion_relation(A!15)) | (~in(ordered_pair(C, D), inclusion_relation(A!15))) | (~in(ordered_pair(D, E), inclusion_relation(A!15))) | (~in(D, set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))))) | (~in(E, set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))))) | (~in(C, set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15)))))))) | (~(is_transitive_in(inclusion_relation(A!15), set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15)))) | (~((~in(tptp_fun_D_3(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))))) | (~in(ordered_pair(tptp_fun_C_4(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), tptp_fun_D_3(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15))), inclusion_relation(A!15))) | in(ordered_pair(tptp_fun_C_4(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), tptp_fun_E_2(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15))), inclusion_relation(A!15)) | (~in(tptp_fun_E_2(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))))) | (~in(ordered_pair(tptp_fun_D_3(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), tptp_fun_E_2(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15))), inclusion_relation(A!15))) | (~in(tptp_fun_C_4(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))))))))))))),
% 0.20/0.42 inference(transitivity,[status(thm)],[84, 82])).
% 0.20/0.42 tff(86,plain,
% 0.20/0.42 ((~![B: $i] : (~((~((~is_transitive_in(inclusion_relation(A!15), B)) | ![C: $i, D: $i, E: $i] : ((~in(D, B)) | (~in(E, B)) | (~in(C, B)) | in(ordered_pair(C, E), inclusion_relation(A!15)) | (~in(ordered_pair(C, D), inclusion_relation(A!15))) | (~in(ordered_pair(D, E), inclusion_relation(A!15)))))) | (~(is_transitive_in(inclusion_relation(A!15), B) | (~((~in(tptp_fun_C_4(B, inclusion_relation(A!15)), B)) | (~in(ordered_pair(tptp_fun_D_3(B, inclusion_relation(A!15)), tptp_fun_E_2(B, inclusion_relation(A!15))), inclusion_relation(A!15))) | (~in(ordered_pair(tptp_fun_C_4(B, inclusion_relation(A!15)), tptp_fun_D_3(B, inclusion_relation(A!15))), inclusion_relation(A!15))) | (~in(tptp_fun_E_2(B, inclusion_relation(A!15)), B)) | (~in(tptp_fun_D_3(B, inclusion_relation(A!15)), B)) | in(ordered_pair(tptp_fun_C_4(B, inclusion_relation(A!15)), tptp_fun_E_2(B, inclusion_relation(A!15))), inclusion_relation(A!15))))))))) | (~((~((~is_transitive_in(inclusion_relation(A!15), set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))))) | ![C: $i, D: $i, E: $i] : ((~in(D, set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))))) | (~in(E, set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))))) | (~in(C, set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))))) | in(ordered_pair(C, E), inclusion_relation(A!15)) | (~in(ordered_pair(C, D), inclusion_relation(A!15))) | (~in(ordered_pair(D, E), inclusion_relation(A!15)))))) | (~(is_transitive_in(inclusion_relation(A!15), set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15)))) | (~((~in(tptp_fun_C_4(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))))) | (~in(ordered_pair(tptp_fun_D_3(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), tptp_fun_E_2(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15))), inclusion_relation(A!15))) | (~in(ordered_pair(tptp_fun_C_4(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), tptp_fun_D_3(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15))), inclusion_relation(A!15))) | (~in(tptp_fun_E_2(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))))) | (~in(tptp_fun_D_3(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))))) | in(ordered_pair(tptp_fun_C_4(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), tptp_fun_E_2(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15))), inclusion_relation(A!15))))))))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(87,plain,
% 0.20/0.43 ((~![B: $i] : (~((~((~is_transitive_in(inclusion_relation(A!15), B)) | ![C: $i, D: $i, E: $i] : ((~in(D, B)) | (~in(E, B)) | (~in(C, B)) | in(ordered_pair(C, E), inclusion_relation(A!15)) | (~in(ordered_pair(C, D), inclusion_relation(A!15))) | (~in(ordered_pair(D, E), inclusion_relation(A!15)))))) | (~(is_transitive_in(inclusion_relation(A!15), B) | (~((~in(tptp_fun_C_4(B, inclusion_relation(A!15)), B)) | (~in(ordered_pair(tptp_fun_D_3(B, inclusion_relation(A!15)), tptp_fun_E_2(B, inclusion_relation(A!15))), inclusion_relation(A!15))) | (~in(ordered_pair(tptp_fun_C_4(B, inclusion_relation(A!15)), tptp_fun_D_3(B, inclusion_relation(A!15))), inclusion_relation(A!15))) | (~in(tptp_fun_E_2(B, inclusion_relation(A!15)), B)) | (~in(tptp_fun_D_3(B, inclusion_relation(A!15)), B)) | in(ordered_pair(tptp_fun_C_4(B, inclusion_relation(A!15)), tptp_fun_E_2(B, inclusion_relation(A!15))), inclusion_relation(A!15))))))))) | (~((~((~is_transitive_in(inclusion_relation(A!15), set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))))) | ![C: $i, D: $i, E: $i] : (in(ordered_pair(C, E), inclusion_relation(A!15)) | (~in(ordered_pair(C, D), inclusion_relation(A!15))) | (~in(ordered_pair(D, E), inclusion_relation(A!15))) | (~in(D, set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))))) | (~in(E, set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))))) | (~in(C, set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15)))))))) | (~(is_transitive_in(inclusion_relation(A!15), set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15)))) | (~((~in(tptp_fun_D_3(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))))) | (~in(ordered_pair(tptp_fun_C_4(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), tptp_fun_D_3(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15))), inclusion_relation(A!15))) | in(ordered_pair(tptp_fun_C_4(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), tptp_fun_E_2(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15))), inclusion_relation(A!15)) | (~in(tptp_fun_E_2(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))))) | (~in(ordered_pair(tptp_fun_D_3(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), tptp_fun_E_2(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15))), inclusion_relation(A!15))) | (~in(tptp_fun_C_4(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15)))))))))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[86, 85])).
% 0.20/0.43 tff(88,plain,
% 0.20/0.43 (~((~((~is_transitive_in(inclusion_relation(A!15), set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))))) | ![C: $i, D: $i, E: $i] : (in(ordered_pair(C, E), inclusion_relation(A!15)) | (~in(ordered_pair(C, D), inclusion_relation(A!15))) | (~in(ordered_pair(D, E), inclusion_relation(A!15))) | (~in(D, set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))))) | (~in(E, set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))))) | (~in(C, set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15)))))))) | (~(is_transitive_in(inclusion_relation(A!15), set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15)))) | (~((~in(tptp_fun_D_3(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))))) | (~in(ordered_pair(tptp_fun_C_4(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), tptp_fun_D_3(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15))), inclusion_relation(A!15))) | in(ordered_pair(tptp_fun_C_4(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), tptp_fun_E_2(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15))), inclusion_relation(A!15)) | (~in(tptp_fun_E_2(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))))) | (~in(ordered_pair(tptp_fun_D_3(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), tptp_fun_E_2(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15))), inclusion_relation(A!15))) | (~in(tptp_fun_C_4(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))))))))))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[87, 81])).
% 0.20/0.43 tff(89,plain,
% 0.20/0.43 (((~((~is_transitive_in(inclusion_relation(A!15), set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))))) | ![C: $i, D: $i, E: $i] : (in(ordered_pair(C, E), inclusion_relation(A!15)) | (~in(ordered_pair(C, D), inclusion_relation(A!15))) | (~in(ordered_pair(D, E), inclusion_relation(A!15))) | (~in(D, set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))))) | (~in(E, set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))))) | (~in(C, set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15)))))))) | (~(is_transitive_in(inclusion_relation(A!15), set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15)))) | (~((~in(tptp_fun_D_3(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))))) | (~in(ordered_pair(tptp_fun_C_4(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), tptp_fun_D_3(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15))), inclusion_relation(A!15))) | in(ordered_pair(tptp_fun_C_4(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), tptp_fun_E_2(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15))), inclusion_relation(A!15)) | (~in(tptp_fun_E_2(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))))) | (~in(ordered_pair(tptp_fun_D_3(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), tptp_fun_E_2(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15))), inclusion_relation(A!15))) | (~in(tptp_fun_C_4(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15)))))))))) | (is_transitive_in(inclusion_relation(A!15), set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15)))) | (~((~in(tptp_fun_D_3(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))))) | (~in(ordered_pair(tptp_fun_C_4(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), tptp_fun_D_3(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15))), inclusion_relation(A!15))) | in(ordered_pair(tptp_fun_C_4(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), tptp_fun_E_2(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15))), inclusion_relation(A!15)) | (~in(tptp_fun_E_2(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))))) | (~in(ordered_pair(tptp_fun_D_3(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), tptp_fun_E_2(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15))), inclusion_relation(A!15))) | (~in(tptp_fun_C_4(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))))))))),
% 0.20/0.43 inference(tautology,[status(thm)],[])).
% 0.20/0.43 tff(90,plain,
% 0.20/0.43 (is_transitive_in(inclusion_relation(A!15), set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15)))) | (~((~in(tptp_fun_D_3(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))))) | (~in(ordered_pair(tptp_fun_C_4(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), tptp_fun_D_3(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15))), inclusion_relation(A!15))) | in(ordered_pair(tptp_fun_C_4(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), tptp_fun_E_2(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15))), inclusion_relation(A!15)) | (~in(tptp_fun_E_2(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))))) | (~in(ordered_pair(tptp_fun_D_3(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), tptp_fun_E_2(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15))), inclusion_relation(A!15))) | (~in(tptp_fun_C_4(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15)))))))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[89, 88])).
% 0.20/0.43 tff(91,plain,
% 0.20/0.43 (set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))) = relation_field(inclusion_relation(A!15))),
% 0.20/0.43 inference(symmetry,[status(thm)],[23])).
% 0.20/0.43 tff(92,plain,
% 0.20/0.43 (is_transitive_in(inclusion_relation(A!15), set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15)))) <=> is_transitive_in(inclusion_relation(A!15), relation_field(inclusion_relation(A!15)))),
% 0.20/0.43 inference(monotonicity,[status(thm)],[91])).
% 0.20/0.43 tff(93,plain,
% 0.20/0.43 (is_transitive_in(inclusion_relation(A!15), relation_field(inclusion_relation(A!15))) <=> is_transitive_in(inclusion_relation(A!15), set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))))),
% 0.20/0.43 inference(symmetry,[status(thm)],[92])).
% 0.20/0.43 tff(94,plain,
% 0.20/0.43 ((~is_transitive_in(inclusion_relation(A!15), relation_field(inclusion_relation(A!15)))) <=> (~is_transitive_in(inclusion_relation(A!15), set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15)))))),
% 0.20/0.43 inference(monotonicity,[status(thm)],[93])).
% 0.20/0.43 tff(95,plain,
% 0.20/0.43 (^[A: $i] : refl(((~relation(A)) | (transitive(A) <=> is_transitive_in(A, relation_field(A)))) <=> ((~relation(A)) | (transitive(A) <=> is_transitive_in(A, relation_field(A)))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(96,plain,
% 0.20/0.43 (![A: $i] : ((~relation(A)) | (transitive(A) <=> is_transitive_in(A, relation_field(A)))) <=> ![A: $i] : ((~relation(A)) | (transitive(A) <=> is_transitive_in(A, relation_field(A))))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[95])).
% 0.20/0.43 tff(97,plain,
% 0.20/0.43 (![A: $i] : ((~relation(A)) | (transitive(A) <=> is_transitive_in(A, relation_field(A)))) <=> ![A: $i] : ((~relation(A)) | (transitive(A) <=> is_transitive_in(A, relation_field(A))))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(98,plain,
% 0.20/0.43 (^[A: $i] : rewrite((relation(A) => (transitive(A) <=> is_transitive_in(A, relation_field(A)))) <=> ((~relation(A)) | (transitive(A) <=> is_transitive_in(A, relation_field(A)))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(99,plain,
% 0.20/0.43 (![A: $i] : (relation(A) => (transitive(A) <=> is_transitive_in(A, relation_field(A)))) <=> ![A: $i] : ((~relation(A)) | (transitive(A) <=> is_transitive_in(A, relation_field(A))))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[98])).
% 0.20/0.43 tff(100,axiom,(![A: $i] : (relation(A) => (transitive(A) <=> is_transitive_in(A, relation_field(A))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d16_relat_2')).
% 0.20/0.43 tff(101,plain,
% 0.20/0.43 (![A: $i] : ((~relation(A)) | (transitive(A) <=> is_transitive_in(A, relation_field(A))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[100, 99])).
% 0.20/0.43 tff(102,plain,
% 0.20/0.43 (![A: $i] : ((~relation(A)) | (transitive(A) <=> is_transitive_in(A, relation_field(A))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[101, 97])).
% 0.20/0.43 tff(103,plain,(
% 0.20/0.43 ![A: $i] : ((~relation(A)) | (transitive(A) <=> is_transitive_in(A, relation_field(A))))),
% 0.20/0.43 inference(skolemize,[status(sab)],[102])).
% 0.20/0.43 tff(104,plain,
% 0.20/0.43 (![A: $i] : ((~relation(A)) | (transitive(A) <=> is_transitive_in(A, relation_field(A))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[103, 96])).
% 0.20/0.43 tff(105,plain,
% 0.20/0.43 (((~![A: $i] : ((~relation(A)) | (transitive(A) <=> is_transitive_in(A, relation_field(A))))) | ((~relation(inclusion_relation(A!15))) | (transitive(inclusion_relation(A!15)) <=> is_transitive_in(inclusion_relation(A!15), relation_field(inclusion_relation(A!15)))))) <=> ((~![A: $i] : ((~relation(A)) | (transitive(A) <=> is_transitive_in(A, relation_field(A))))) | (~relation(inclusion_relation(A!15))) | (transitive(inclusion_relation(A!15)) <=> is_transitive_in(inclusion_relation(A!15), relation_field(inclusion_relation(A!15)))))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(106,plain,
% 0.20/0.43 ((~![A: $i] : ((~relation(A)) | (transitive(A) <=> is_transitive_in(A, relation_field(A))))) | ((~relation(inclusion_relation(A!15))) | (transitive(inclusion_relation(A!15)) <=> is_transitive_in(inclusion_relation(A!15), relation_field(inclusion_relation(A!15)))))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(107,plain,
% 0.20/0.43 ((~![A: $i] : ((~relation(A)) | (transitive(A) <=> is_transitive_in(A, relation_field(A))))) | (~relation(inclusion_relation(A!15))) | (transitive(inclusion_relation(A!15)) <=> is_transitive_in(inclusion_relation(A!15), relation_field(inclusion_relation(A!15))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[106, 105])).
% 0.20/0.43 tff(108,plain,
% 0.20/0.43 ((~relation(inclusion_relation(A!15))) | (transitive(inclusion_relation(A!15)) <=> is_transitive_in(inclusion_relation(A!15), relation_field(inclusion_relation(A!15))))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[107, 104])).
% 0.20/0.43 tff(109,plain,
% 0.20/0.43 (transitive(inclusion_relation(A!15)) <=> is_transitive_in(inclusion_relation(A!15), relation_field(inclusion_relation(A!15)))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[108, 9])).
% 0.20/0.43 tff(110,plain,
% 0.20/0.43 ((~![A: $i] : transitive(inclusion_relation(A))) <=> (~![A: $i] : transitive(inclusion_relation(A)))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(111,axiom,(~![A: $i] : transitive(inclusion_relation(A))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t3_wellord2')).
% 0.20/0.43 tff(112,plain,
% 0.20/0.43 (~![A: $i] : transitive(inclusion_relation(A))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[111, 110])).
% 0.20/0.43 tff(113,plain,
% 0.20/0.43 (~![A: $i] : transitive(inclusion_relation(A))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[112, 110])).
% 0.20/0.43 tff(114,plain,
% 0.20/0.43 (~![A: $i] : transitive(inclusion_relation(A))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[113, 110])).
% 0.20/0.43 tff(115,plain,
% 0.20/0.43 (~![A: $i] : transitive(inclusion_relation(A))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[114, 110])).
% 0.20/0.43 tff(116,plain,(
% 0.20/0.43 ~transitive(inclusion_relation(A!15))),
% 0.20/0.43 inference(skolemize,[status(sab)],[115])).
% 0.20/0.43 tff(117,plain,
% 0.20/0.43 ((~(transitive(inclusion_relation(A!15)) <=> is_transitive_in(inclusion_relation(A!15), relation_field(inclusion_relation(A!15))))) | transitive(inclusion_relation(A!15)) | (~is_transitive_in(inclusion_relation(A!15), relation_field(inclusion_relation(A!15))))),
% 0.20/0.43 inference(tautology,[status(thm)],[])).
% 0.20/0.43 tff(118,plain,
% 0.20/0.43 ((~(transitive(inclusion_relation(A!15)) <=> is_transitive_in(inclusion_relation(A!15), relation_field(inclusion_relation(A!15))))) | (~is_transitive_in(inclusion_relation(A!15), relation_field(inclusion_relation(A!15))))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[117, 116])).
% 0.20/0.43 tff(119,plain,
% 0.20/0.43 (~is_transitive_in(inclusion_relation(A!15), relation_field(inclusion_relation(A!15)))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[118, 109])).
% 0.20/0.43 tff(120,plain,
% 0.20/0.43 (~is_transitive_in(inclusion_relation(A!15), set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[119, 94])).
% 0.20/0.43 tff(121,plain,
% 0.20/0.43 ((~(is_transitive_in(inclusion_relation(A!15), set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15)))) | (~((~in(tptp_fun_D_3(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))))) | (~in(ordered_pair(tptp_fun_C_4(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), tptp_fun_D_3(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15))), inclusion_relation(A!15))) | in(ordered_pair(tptp_fun_C_4(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), tptp_fun_E_2(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15))), inclusion_relation(A!15)) | (~in(tptp_fun_E_2(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))))) | (~in(ordered_pair(tptp_fun_D_3(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), tptp_fun_E_2(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15))), inclusion_relation(A!15))) | (~in(tptp_fun_C_4(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))))))))) | is_transitive_in(inclusion_relation(A!15), set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15)))) | (~((~in(tptp_fun_D_3(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))))) | (~in(ordered_pair(tptp_fun_C_4(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), tptp_fun_D_3(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15))), inclusion_relation(A!15))) | in(ordered_pair(tptp_fun_C_4(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), tptp_fun_E_2(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15))), inclusion_relation(A!15)) | (~in(tptp_fun_E_2(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))))) | (~in(ordered_pair(tptp_fun_D_3(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), tptp_fun_E_2(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15))), inclusion_relation(A!15))) | (~in(tptp_fun_C_4(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15)))))))),
% 0.20/0.44 inference(tautology,[status(thm)],[])).
% 0.20/0.44 tff(122,plain,
% 0.20/0.44 (~((~in(tptp_fun_D_3(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))))) | (~in(ordered_pair(tptp_fun_C_4(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), tptp_fun_D_3(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15))), inclusion_relation(A!15))) | in(ordered_pair(tptp_fun_C_4(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), tptp_fun_E_2(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15))), inclusion_relation(A!15)) | (~in(tptp_fun_E_2(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))))) | (~in(ordered_pair(tptp_fun_D_3(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), tptp_fun_E_2(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15))), inclusion_relation(A!15))) | (~in(tptp_fun_C_4(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))))))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[121, 120, 90])).
% 0.20/0.44 tff(123,plain,
% 0.20/0.44 (((~in(tptp_fun_D_3(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))))) | (~in(ordered_pair(tptp_fun_C_4(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), tptp_fun_D_3(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15))), inclusion_relation(A!15))) | in(ordered_pair(tptp_fun_C_4(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), tptp_fun_E_2(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15))), inclusion_relation(A!15)) | (~in(tptp_fun_E_2(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))))) | (~in(ordered_pair(tptp_fun_D_3(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), tptp_fun_E_2(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15))), inclusion_relation(A!15))) | (~in(tptp_fun_C_4(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15)))))) | in(tptp_fun_C_4(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))))),
% 0.20/0.44 inference(tautology,[status(thm)],[])).
% 0.20/0.44 tff(124,plain,
% 0.20/0.44 (in(tptp_fun_C_4(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[123, 122])).
% 0.20/0.44 tff(125,plain,
% 0.20/0.44 (in(tptp_fun_C_4(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), A!15)),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[124, 58])).
% 0.20/0.44 tff(126,plain,
% 0.20/0.44 (in(tptp_fun_D_3(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), A!15) <=> in(tptp_fun_D_3(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))))),
% 0.20/0.44 inference(monotonicity,[status(thm)],[56])).
% 0.20/0.44 tff(127,plain,
% 0.20/0.44 (in(tptp_fun_D_3(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15)))) <=> in(tptp_fun_D_3(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), A!15)),
% 0.20/0.44 inference(symmetry,[status(thm)],[126])).
% 0.20/0.44 tff(128,plain,
% 0.20/0.44 (((~in(tptp_fun_D_3(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))))) | (~in(ordered_pair(tptp_fun_C_4(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), tptp_fun_D_3(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15))), inclusion_relation(A!15))) | in(ordered_pair(tptp_fun_C_4(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), tptp_fun_E_2(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15))), inclusion_relation(A!15)) | (~in(tptp_fun_E_2(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))))) | (~in(ordered_pair(tptp_fun_D_3(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), tptp_fun_E_2(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15))), inclusion_relation(A!15))) | (~in(tptp_fun_C_4(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15)))))) | in(tptp_fun_D_3(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))))),
% 0.20/0.44 inference(tautology,[status(thm)],[])).
% 0.20/0.44 tff(129,plain,
% 0.20/0.44 (in(tptp_fun_D_3(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[128, 122])).
% 0.20/0.44 tff(130,plain,
% 0.20/0.44 (in(tptp_fun_D_3(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), A!15)),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[129, 127])).
% 0.20/0.44 tff(131,plain,
% 0.20/0.44 (((~(relation_field(inclusion_relation(A!15)) = A!15)) | (~![C: $i, D: $i] : ((~in(C, A!15)) | (~in(D, A!15)) | (in(ordered_pair(C, D), inclusion_relation(A!15)) <=> subset(C, D))))) | ![C: $i, D: $i] : ((~in(C, A!15)) | (~in(D, A!15)) | (in(ordered_pair(C, D), inclusion_relation(A!15)) <=> subset(C, D)))),
% 0.20/0.44 inference(tautology,[status(thm)],[])).
% 0.20/0.44 tff(132,plain,
% 0.20/0.44 (![C: $i, D: $i] : ((~in(C, A!15)) | (~in(D, A!15)) | (in(ordered_pair(C, D), inclusion_relation(A!15)) <=> subset(C, D)))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[131, 52])).
% 0.20/0.44 tff(133,plain,
% 0.20/0.44 (((~![C: $i, D: $i] : ((~in(C, A!15)) | (~in(D, A!15)) | (in(ordered_pair(C, D), inclusion_relation(A!15)) <=> subset(C, D)))) | ((~in(tptp_fun_C_4(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), A!15)) | (~in(tptp_fun_D_3(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), A!15)) | (in(ordered_pair(tptp_fun_C_4(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), tptp_fun_D_3(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15))), inclusion_relation(A!15)) <=> subset(tptp_fun_C_4(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), tptp_fun_D_3(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)))))) <=> ((~![C: $i, D: $i] : ((~in(C, A!15)) | (~in(D, A!15)) | (in(ordered_pair(C, D), inclusion_relation(A!15)) <=> subset(C, D)))) | (~in(tptp_fun_C_4(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), A!15)) | (~in(tptp_fun_D_3(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), A!15)) | (in(ordered_pair(tptp_fun_C_4(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), tptp_fun_D_3(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15))), inclusion_relation(A!15)) <=> subset(tptp_fun_C_4(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), tptp_fun_D_3(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)))))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(134,plain,
% 0.20/0.44 ((~![C: $i, D: $i] : ((~in(C, A!15)) | (~in(D, A!15)) | (in(ordered_pair(C, D), inclusion_relation(A!15)) <=> subset(C, D)))) | ((~in(tptp_fun_C_4(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), A!15)) | (~in(tptp_fun_D_3(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), A!15)) | (in(ordered_pair(tptp_fun_C_4(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), tptp_fun_D_3(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15))), inclusion_relation(A!15)) <=> subset(tptp_fun_C_4(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), tptp_fun_D_3(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)))))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(135,plain,
% 0.20/0.44 ((~![C: $i, D: $i] : ((~in(C, A!15)) | (~in(D, A!15)) | (in(ordered_pair(C, D), inclusion_relation(A!15)) <=> subset(C, D)))) | (~in(tptp_fun_C_4(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), A!15)) | (~in(tptp_fun_D_3(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), A!15)) | (in(ordered_pair(tptp_fun_C_4(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), tptp_fun_D_3(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15))), inclusion_relation(A!15)) <=> subset(tptp_fun_C_4(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), tptp_fun_D_3(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15))))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[134, 133])).
% 0.20/0.44 tff(136,plain,
% 0.20/0.44 ((~in(tptp_fun_C_4(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), A!15)) | (~in(tptp_fun_D_3(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), A!15)) | (in(ordered_pair(tptp_fun_C_4(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), tptp_fun_D_3(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15))), inclusion_relation(A!15)) <=> subset(tptp_fun_C_4(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), tptp_fun_D_3(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15))))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[135, 132])).
% 0.20/0.44 tff(137,plain,
% 0.20/0.44 (in(ordered_pair(tptp_fun_C_4(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), tptp_fun_D_3(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15))), inclusion_relation(A!15)) <=> subset(tptp_fun_C_4(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), tptp_fun_D_3(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[136, 130, 125])).
% 0.20/0.44 tff(138,plain,
% 0.20/0.44 (((~in(tptp_fun_D_3(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))))) | (~in(ordered_pair(tptp_fun_C_4(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), tptp_fun_D_3(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15))), inclusion_relation(A!15))) | in(ordered_pair(tptp_fun_C_4(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), tptp_fun_E_2(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15))), inclusion_relation(A!15)) | (~in(tptp_fun_E_2(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))))) | (~in(ordered_pair(tptp_fun_D_3(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), tptp_fun_E_2(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15))), inclusion_relation(A!15))) | (~in(tptp_fun_C_4(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15)))))) | in(ordered_pair(tptp_fun_C_4(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), tptp_fun_D_3(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15))), inclusion_relation(A!15))),
% 0.20/0.44 inference(tautology,[status(thm)],[])).
% 0.20/0.44 tff(139,plain,
% 0.20/0.44 (in(ordered_pair(tptp_fun_C_4(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), tptp_fun_D_3(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15))), inclusion_relation(A!15))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[138, 122])).
% 0.20/0.44 tff(140,plain,
% 0.20/0.44 ((~(in(ordered_pair(tptp_fun_C_4(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), tptp_fun_D_3(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15))), inclusion_relation(A!15)) <=> subset(tptp_fun_C_4(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), tptp_fun_D_3(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15))))) | (~in(ordered_pair(tptp_fun_C_4(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), tptp_fun_D_3(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15))), inclusion_relation(A!15))) | subset(tptp_fun_C_4(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), tptp_fun_D_3(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)))),
% 0.20/0.44 inference(tautology,[status(thm)],[])).
% 0.20/0.44 tff(141,plain,
% 0.20/0.44 ((~(in(ordered_pair(tptp_fun_C_4(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), tptp_fun_D_3(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15))), inclusion_relation(A!15)) <=> subset(tptp_fun_C_4(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), tptp_fun_D_3(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15))))) | subset(tptp_fun_C_4(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), tptp_fun_D_3(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[140, 139])).
% 0.20/0.45 tff(142,plain,
% 0.20/0.45 (subset(tptp_fun_C_4(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), tptp_fun_D_3(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[141, 137])).
% 0.20/0.45 tff(143,plain,
% 0.20/0.45 (in(tptp_fun_E_2(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), A!15) <=> in(tptp_fun_E_2(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))))),
% 0.20/0.45 inference(monotonicity,[status(thm)],[56])).
% 0.20/0.45 tff(144,plain,
% 0.20/0.45 (in(tptp_fun_E_2(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15)))) <=> in(tptp_fun_E_2(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), A!15)),
% 0.20/0.45 inference(symmetry,[status(thm)],[143])).
% 0.20/0.45 tff(145,plain,
% 0.20/0.45 (((~in(tptp_fun_D_3(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))))) | (~in(ordered_pair(tptp_fun_C_4(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), tptp_fun_D_3(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15))), inclusion_relation(A!15))) | in(ordered_pair(tptp_fun_C_4(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), tptp_fun_E_2(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15))), inclusion_relation(A!15)) | (~in(tptp_fun_E_2(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))))) | (~in(ordered_pair(tptp_fun_D_3(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), tptp_fun_E_2(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15))), inclusion_relation(A!15))) | (~in(tptp_fun_C_4(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15)))))) | in(tptp_fun_E_2(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))))),
% 0.20/0.45 inference(tautology,[status(thm)],[])).
% 0.20/0.45 tff(146,plain,
% 0.20/0.45 (in(tptp_fun_E_2(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[145, 122])).
% 0.20/0.45 tff(147,plain,
% 0.20/0.45 (in(tptp_fun_E_2(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), A!15)),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[146, 144])).
% 0.20/0.45 tff(148,plain,
% 0.20/0.45 (((~![C: $i, D: $i] : ((~in(C, A!15)) | (~in(D, A!15)) | (in(ordered_pair(C, D), inclusion_relation(A!15)) <=> subset(C, D)))) | ((~in(tptp_fun_D_3(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), A!15)) | (~in(tptp_fun_E_2(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), A!15)) | (in(ordered_pair(tptp_fun_D_3(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), tptp_fun_E_2(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15))), inclusion_relation(A!15)) <=> subset(tptp_fun_D_3(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), tptp_fun_E_2(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)))))) <=> ((~![C: $i, D: $i] : ((~in(C, A!15)) | (~in(D, A!15)) | (in(ordered_pair(C, D), inclusion_relation(A!15)) <=> subset(C, D)))) | (~in(tptp_fun_D_3(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), A!15)) | (~in(tptp_fun_E_2(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), A!15)) | (in(ordered_pair(tptp_fun_D_3(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), tptp_fun_E_2(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15))), inclusion_relation(A!15)) <=> subset(tptp_fun_D_3(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), tptp_fun_E_2(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)))))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(149,plain,
% 0.20/0.45 ((~![C: $i, D: $i] : ((~in(C, A!15)) | (~in(D, A!15)) | (in(ordered_pair(C, D), inclusion_relation(A!15)) <=> subset(C, D)))) | ((~in(tptp_fun_D_3(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), A!15)) | (~in(tptp_fun_E_2(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), A!15)) | (in(ordered_pair(tptp_fun_D_3(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), tptp_fun_E_2(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15))), inclusion_relation(A!15)) <=> subset(tptp_fun_D_3(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), tptp_fun_E_2(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)))))),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(150,plain,
% 0.20/0.45 ((~![C: $i, D: $i] : ((~in(C, A!15)) | (~in(D, A!15)) | (in(ordered_pair(C, D), inclusion_relation(A!15)) <=> subset(C, D)))) | (~in(tptp_fun_D_3(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), A!15)) | (~in(tptp_fun_E_2(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), A!15)) | (in(ordered_pair(tptp_fun_D_3(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), tptp_fun_E_2(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15))), inclusion_relation(A!15)) <=> subset(tptp_fun_D_3(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), tptp_fun_E_2(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15))))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[149, 148])).
% 0.20/0.45 tff(151,plain,
% 0.20/0.45 ((~in(tptp_fun_D_3(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), A!15)) | (~in(tptp_fun_E_2(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), A!15)) | (in(ordered_pair(tptp_fun_D_3(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), tptp_fun_E_2(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15))), inclusion_relation(A!15)) <=> subset(tptp_fun_D_3(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), tptp_fun_E_2(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15))))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[150, 132])).
% 0.20/0.45 tff(152,plain,
% 0.20/0.45 (in(ordered_pair(tptp_fun_D_3(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), tptp_fun_E_2(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15))), inclusion_relation(A!15)) <=> subset(tptp_fun_D_3(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), tptp_fun_E_2(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[151, 130, 147])).
% 0.20/0.45 tff(153,plain,
% 0.20/0.45 (((~in(tptp_fun_D_3(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))))) | (~in(ordered_pair(tptp_fun_C_4(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), tptp_fun_D_3(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15))), inclusion_relation(A!15))) | in(ordered_pair(tptp_fun_C_4(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), tptp_fun_E_2(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15))), inclusion_relation(A!15)) | (~in(tptp_fun_E_2(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))))) | (~in(ordered_pair(tptp_fun_D_3(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), tptp_fun_E_2(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15))), inclusion_relation(A!15))) | (~in(tptp_fun_C_4(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15)))))) | in(ordered_pair(tptp_fun_D_3(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), tptp_fun_E_2(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15))), inclusion_relation(A!15))),
% 0.20/0.45 inference(tautology,[status(thm)],[])).
% 0.20/0.45 tff(154,plain,
% 0.20/0.45 (in(ordered_pair(tptp_fun_D_3(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), tptp_fun_E_2(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15))), inclusion_relation(A!15))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[153, 122])).
% 0.20/0.45 tff(155,plain,
% 0.20/0.45 ((~(in(ordered_pair(tptp_fun_D_3(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), tptp_fun_E_2(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15))), inclusion_relation(A!15)) <=> subset(tptp_fun_D_3(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), tptp_fun_E_2(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15))))) | (~in(ordered_pair(tptp_fun_D_3(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), tptp_fun_E_2(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15))), inclusion_relation(A!15))) | subset(tptp_fun_D_3(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), tptp_fun_E_2(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)))),
% 0.20/0.45 inference(tautology,[status(thm)],[])).
% 0.20/0.45 tff(156,plain,
% 0.20/0.45 ((~(in(ordered_pair(tptp_fun_D_3(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), tptp_fun_E_2(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15))), inclusion_relation(A!15)) <=> subset(tptp_fun_D_3(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), tptp_fun_E_2(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15))))) | subset(tptp_fun_D_3(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), tptp_fun_E_2(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[155, 154])).
% 0.20/0.45 tff(157,plain,
% 0.20/0.45 (subset(tptp_fun_D_3(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), tptp_fun_E_2(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[156, 152])).
% 0.20/0.45 tff(158,plain,
% 0.20/0.45 (((~![C: $i, D: $i] : ((~in(C, A!15)) | (~in(D, A!15)) | (in(ordered_pair(C, D), inclusion_relation(A!15)) <=> subset(C, D)))) | ((~in(tptp_fun_C_4(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), A!15)) | (~in(tptp_fun_E_2(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), A!15)) | (in(ordered_pair(tptp_fun_C_4(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), tptp_fun_E_2(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15))), inclusion_relation(A!15)) <=> subset(tptp_fun_C_4(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), tptp_fun_E_2(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)))))) <=> ((~![C: $i, D: $i] : ((~in(C, A!15)) | (~in(D, A!15)) | (in(ordered_pair(C, D), inclusion_relation(A!15)) <=> subset(C, D)))) | (~in(tptp_fun_C_4(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), A!15)) | (~in(tptp_fun_E_2(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), A!15)) | (in(ordered_pair(tptp_fun_C_4(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), tptp_fun_E_2(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15))), inclusion_relation(A!15)) <=> subset(tptp_fun_C_4(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), tptp_fun_E_2(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)))))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(159,plain,
% 0.20/0.45 ((~![C: $i, D: $i] : ((~in(C, A!15)) | (~in(D, A!15)) | (in(ordered_pair(C, D), inclusion_relation(A!15)) <=> subset(C, D)))) | ((~in(tptp_fun_C_4(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), A!15)) | (~in(tptp_fun_E_2(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), A!15)) | (in(ordered_pair(tptp_fun_C_4(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), tptp_fun_E_2(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15))), inclusion_relation(A!15)) <=> subset(tptp_fun_C_4(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), tptp_fun_E_2(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)))))),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(160,plain,
% 0.20/0.45 ((~![C: $i, D: $i] : ((~in(C, A!15)) | (~in(D, A!15)) | (in(ordered_pair(C, D), inclusion_relation(A!15)) <=> subset(C, D)))) | (~in(tptp_fun_C_4(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), A!15)) | (~in(tptp_fun_E_2(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), A!15)) | (in(ordered_pair(tptp_fun_C_4(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), tptp_fun_E_2(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15))), inclusion_relation(A!15)) <=> subset(tptp_fun_C_4(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), tptp_fun_E_2(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15))))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[159, 158])).
% 0.20/0.45 tff(161,plain,
% 0.20/0.45 ((~in(tptp_fun_C_4(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), A!15)) | (~in(tptp_fun_E_2(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), A!15)) | (in(ordered_pair(tptp_fun_C_4(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), tptp_fun_E_2(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15))), inclusion_relation(A!15)) <=> subset(tptp_fun_C_4(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), tptp_fun_E_2(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15))))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[160, 132])).
% 0.20/0.46 tff(162,plain,
% 0.20/0.46 (in(ordered_pair(tptp_fun_C_4(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), tptp_fun_E_2(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15))), inclusion_relation(A!15)) <=> subset(tptp_fun_C_4(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), tptp_fun_E_2(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[161, 147, 125])).
% 0.20/0.46 tff(163,plain,
% 0.20/0.46 (((~in(tptp_fun_D_3(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))))) | (~in(ordered_pair(tptp_fun_C_4(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), tptp_fun_D_3(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15))), inclusion_relation(A!15))) | in(ordered_pair(tptp_fun_C_4(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), tptp_fun_E_2(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15))), inclusion_relation(A!15)) | (~in(tptp_fun_E_2(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))))) | (~in(ordered_pair(tptp_fun_D_3(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), tptp_fun_E_2(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15))), inclusion_relation(A!15))) | (~in(tptp_fun_C_4(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15)))))) | (~in(ordered_pair(tptp_fun_C_4(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), tptp_fun_E_2(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15))), inclusion_relation(A!15)))),
% 0.20/0.46 inference(tautology,[status(thm)],[])).
% 0.20/0.46 tff(164,plain,
% 0.20/0.46 (~in(ordered_pair(tptp_fun_C_4(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), tptp_fun_E_2(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15))), inclusion_relation(A!15))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[163, 122])).
% 0.20/0.46 tff(165,plain,
% 0.20/0.46 ((~(in(ordered_pair(tptp_fun_C_4(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), tptp_fun_E_2(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15))), inclusion_relation(A!15)) <=> subset(tptp_fun_C_4(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), tptp_fun_E_2(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15))))) | in(ordered_pair(tptp_fun_C_4(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), tptp_fun_E_2(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15))), inclusion_relation(A!15)) | (~subset(tptp_fun_C_4(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), tptp_fun_E_2(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15))))),
% 0.20/0.46 inference(tautology,[status(thm)],[])).
% 0.20/0.46 tff(166,plain,
% 0.20/0.46 ((~(in(ordered_pair(tptp_fun_C_4(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), tptp_fun_E_2(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15))), inclusion_relation(A!15)) <=> subset(tptp_fun_C_4(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), tptp_fun_E_2(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15))))) | (~subset(tptp_fun_C_4(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), tptp_fun_E_2(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15))))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[165, 164])).
% 0.20/0.46 tff(167,plain,
% 0.20/0.46 (~subset(tptp_fun_C_4(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), tptp_fun_E_2(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[166, 162])).
% 0.20/0.46 tff(168,plain,
% 0.20/0.46 (![A: $i, B: $i, C: $i] : (subset(A, C) | (~subset(A, B)) | (~subset(B, C))) <=> ![A: $i, B: $i, C: $i] : (subset(A, C) | (~subset(A, B)) | (~subset(B, C)))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(169,plain,
% 0.20/0.46 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(rewrite((subset(A, B) & subset(B, C)) <=> (~((~subset(A, B)) | (~subset(B, C))))), ((~(subset(A, B) & subset(B, C))) <=> (~(~((~subset(A, B)) | (~subset(B, C))))))), rewrite((~(~((~subset(A, B)) | (~subset(B, C))))) <=> ((~subset(A, B)) | (~subset(B, C)))), ((~(subset(A, B) & subset(B, C))) <=> ((~subset(A, B)) | (~subset(B, C))))), (((~(subset(A, B) & subset(B, C))) | subset(A, C)) <=> (((~subset(A, B)) | (~subset(B, C))) | subset(A, C)))), rewrite((((~subset(A, B)) | (~subset(B, C))) | subset(A, C)) <=> (subset(A, C) | (~subset(A, B)) | (~subset(B, C)))), (((~(subset(A, B) & subset(B, C))) | subset(A, C)) <=> (subset(A, C) | (~subset(A, B)) | (~subset(B, C)))))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(170,plain,
% 0.20/0.46 (![A: $i, B: $i, C: $i] : ((~(subset(A, B) & subset(B, C))) | subset(A, C)) <=> ![A: $i, B: $i, C: $i] : (subset(A, C) | (~subset(A, B)) | (~subset(B, C)))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[169])).
% 0.20/0.46 tff(171,plain,
% 0.20/0.46 (![A: $i, B: $i, C: $i] : ((~(subset(A, B) & subset(B, C))) | subset(A, C)) <=> ![A: $i, B: $i, C: $i] : ((~(subset(A, B) & subset(B, C))) | subset(A, C))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(172,plain,
% 0.20/0.46 (^[A: $i, B: $i, C: $i] : rewrite(((subset(A, B) & subset(B, C)) => subset(A, C)) <=> ((~(subset(A, B) & subset(B, C))) | subset(A, C)))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(173,plain,
% 0.20/0.46 (![A: $i, B: $i, C: $i] : ((subset(A, B) & subset(B, C)) => subset(A, C)) <=> ![A: $i, B: $i, C: $i] : ((~(subset(A, B) & subset(B, C))) | subset(A, C))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[172])).
% 0.20/0.46 tff(174,axiom,(![A: $i, B: $i, C: $i] : ((subset(A, B) & subset(B, C)) => subset(A, C))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t1_xboole_1')).
% 0.20/0.46 tff(175,plain,
% 0.20/0.46 (![A: $i, B: $i, C: $i] : ((~(subset(A, B) & subset(B, C))) | subset(A, C))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[174, 173])).
% 0.20/0.46 tff(176,plain,
% 0.20/0.46 (![A: $i, B: $i, C: $i] : ((~(subset(A, B) & subset(B, C))) | subset(A, C))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[175, 171])).
% 0.20/0.46 tff(177,plain,(
% 0.20/0.46 ![A: $i, B: $i, C: $i] : ((~(subset(A, B) & subset(B, C))) | subset(A, C))),
% 0.20/0.46 inference(skolemize,[status(sab)],[176])).
% 0.20/0.46 tff(178,plain,
% 0.20/0.46 (![A: $i, B: $i, C: $i] : (subset(A, C) | (~subset(A, B)) | (~subset(B, C)))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[177, 170])).
% 0.20/0.46 tff(179,plain,
% 0.20/0.46 (![A: $i, B: $i, C: $i] : (subset(A, C) | (~subset(A, B)) | (~subset(B, C)))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[178, 168])).
% 0.20/0.46 tff(180,plain,
% 0.20/0.46 (((~![A: $i, B: $i, C: $i] : (subset(A, C) | (~subset(A, B)) | (~subset(B, C)))) | (subset(tptp_fun_C_4(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), tptp_fun_E_2(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15))) | (~subset(tptp_fun_D_3(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), tptp_fun_E_2(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)))) | (~subset(tptp_fun_C_4(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), tptp_fun_D_3(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)))))) <=> ((~![A: $i, B: $i, C: $i] : (subset(A, C) | (~subset(A, B)) | (~subset(B, C)))) | subset(tptp_fun_C_4(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), tptp_fun_E_2(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15))) | (~subset(tptp_fun_D_3(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), tptp_fun_E_2(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)))) | (~subset(tptp_fun_C_4(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), tptp_fun_D_3(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)))))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(181,plain,
% 0.20/0.46 ((subset(tptp_fun_C_4(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), tptp_fun_E_2(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15))) | (~subset(tptp_fun_C_4(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), tptp_fun_D_3(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)))) | (~subset(tptp_fun_D_3(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), tptp_fun_E_2(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15))))) <=> (subset(tptp_fun_C_4(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), tptp_fun_E_2(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15))) | (~subset(tptp_fun_D_3(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), tptp_fun_E_2(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)))) | (~subset(tptp_fun_C_4(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), tptp_fun_D_3(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)))))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(182,plain,
% 0.20/0.46 (((~![A: $i, B: $i, C: $i] : (subset(A, C) | (~subset(A, B)) | (~subset(B, C)))) | (subset(tptp_fun_C_4(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), tptp_fun_E_2(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15))) | (~subset(tptp_fun_C_4(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), tptp_fun_D_3(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)))) | (~subset(tptp_fun_D_3(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), tptp_fun_E_2(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)))))) <=> ((~![A: $i, B: $i, C: $i] : (subset(A, C) | (~subset(A, B)) | (~subset(B, C)))) | (subset(tptp_fun_C_4(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), tptp_fun_E_2(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15))) | (~subset(tptp_fun_D_3(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), tptp_fun_E_2(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)))) | (~subset(tptp_fun_C_4(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), tptp_fun_D_3(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15))))))),
% 0.20/0.46 inference(monotonicity,[status(thm)],[181])).
% 0.20/0.46 tff(183,plain,
% 0.20/0.46 (((~![A: $i, B: $i, C: $i] : (subset(A, C) | (~subset(A, B)) | (~subset(B, C)))) | (subset(tptp_fun_C_4(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), tptp_fun_E_2(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15))) | (~subset(tptp_fun_C_4(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), tptp_fun_D_3(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)))) | (~subset(tptp_fun_D_3(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), tptp_fun_E_2(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)))))) <=> ((~![A: $i, B: $i, C: $i] : (subset(A, C) | (~subset(A, B)) | (~subset(B, C)))) | subset(tptp_fun_C_4(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), tptp_fun_E_2(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15))) | (~subset(tptp_fun_D_3(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), tptp_fun_E_2(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)))) | (~subset(tptp_fun_C_4(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), tptp_fun_D_3(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)))))),
% 0.20/0.46 inference(transitivity,[status(thm)],[182, 180])).
% 0.20/0.46 tff(184,plain,
% 0.20/0.46 ((~![A: $i, B: $i, C: $i] : (subset(A, C) | (~subset(A, B)) | (~subset(B, C)))) | (subset(tptp_fun_C_4(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), tptp_fun_E_2(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15))) | (~subset(tptp_fun_C_4(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), tptp_fun_D_3(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)))) | (~subset(tptp_fun_D_3(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), tptp_fun_E_2(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)))))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(185,plain,
% 0.20/0.47 ((~![A: $i, B: $i, C: $i] : (subset(A, C) | (~subset(A, B)) | (~subset(B, C)))) | subset(tptp_fun_C_4(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), tptp_fun_E_2(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15))) | (~subset(tptp_fun_D_3(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), tptp_fun_E_2(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)))) | (~subset(tptp_fun_C_4(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15)), tptp_fun_D_3(set_union2(relation_dom(inclusion_relation(A!15)), relation_rng(inclusion_relation(A!15))), inclusion_relation(A!15))))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[184, 183])).
% 0.20/0.47 tff(186,plain,
% 0.20/0.47 ($false),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[185, 179, 167, 157, 142])).
% 0.20/0.47 % SZS output end Proof
% 0.20/0.47 % E exiting
%------------------------------------------------------------------------------