%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SEU268+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 05:27:26 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
% 0.06/0.12 % Problem : SEU268+1 : TPTP v9.0.0. Released v3.3.0.
% 0.06/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n009.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 20 06:32:33 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_C_0_type, type, (
% 0.20/0.38 tptp_fun_C_0: ( $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_13_type, type, (
% 0.20/0.38 tptp_fun_A_13: $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(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_1_type, type, (
% 0.20/0.38 tptp_fun_D_1: ( $i * $i ) > $i)).
% 0.20/0.38 tff(tptp_fun_C_2_type, type, (
% 0.20/0.38 tptp_fun_C_2: ( $i * $i ) > $i)).
% 0.20/0.38 tff(is_reflexive_in_type, type, (
% 0.20/0.38 is_reflexive_in: ( $i * $i ) > $o)).
% 0.20/0.38 tff(reflexive_type, type, (
% 0.20/0.38 reflexive: $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!13))),
% 0.20/0.38 inference(quant_inst,[status(thm)],[])).
% 0.20/0.38 tff(9,plain,
% 0.20/0.38 (relation(inclusion_relation(A!13))),
% 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!13))) | (relation_field(inclusion_relation(A!13)) = set_union2(relation_dom(inclusion_relation(A!13)), relation_rng(inclusion_relation(A!13)))))) <=> ((~![A: $i] : ((~relation(A)) | (relation_field(A) = set_union2(relation_dom(A), relation_rng(A))))) | (~relation(inclusion_relation(A!13))) | (relation_field(inclusion_relation(A!13)) = set_union2(relation_dom(inclusion_relation(A!13)), relation_rng(inclusion_relation(A!13)))))),
% 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!13))) | (relation_field(inclusion_relation(A!13)) = set_union2(relation_dom(inclusion_relation(A!13)), relation_rng(inclusion_relation(A!13)))))),
% 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!13))) | (relation_field(inclusion_relation(A!13)) = set_union2(relation_dom(inclusion_relation(A!13)), relation_rng(inclusion_relation(A!13))))),
% 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!13)) = set_union2(relation_dom(inclusion_relation(A!13)), relation_rng(inclusion_relation(A!13)))),
% 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_2(B, A), tptp_fun_D_1(B, A)), B) <=> subset(tptp_fun_C_2(B, A), tptp_fun_D_1(B, A))) | (~in(tptp_fun_C_2(B, A), A)) | (~in(tptp_fun_D_1(B, A), A))))))))) <=> ((~relation(B)) | (~((~((B = inclusion_relation(A)) | (~(relation_field(B) = A)) | (~((in(ordered_pair(tptp_fun_C_2(B, A), tptp_fun_D_1(B, A)), B) <=> subset(tptp_fun_C_2(B, A), tptp_fun_D_1(B, A))) | (~in(tptp_fun_C_2(B, A), A)) | (~in(tptp_fun_D_1(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_2(B, A), tptp_fun_D_1(B, A)), B) <=> subset(tptp_fun_C_2(B, A), tptp_fun_D_1(B, A))) | (~in(tptp_fun_C_2(B, A), A)) | (~in(tptp_fun_D_1(B, A), A))))))))) <=> ![A: $i, B: $i] : ((~relation(B)) | (~((~((B = inclusion_relation(A)) | (~(relation_field(B) = A)) | (~((in(ordered_pair(tptp_fun_C_2(B, A), tptp_fun_D_1(B, A)), B) <=> subset(tptp_fun_C_2(B, A), tptp_fun_D_1(B, A))) | (~in(tptp_fun_C_2(B, A), A)) | (~in(tptp_fun_D_1(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_2(B, A), tptp_fun_D_1(B, A)), B) <=> subset(tptp_fun_C_2(B, A), tptp_fun_D_1(B, A))) | (~in(tptp_fun_C_2(B, A), A)) | (~in(tptp_fun_D_1(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_2(B, A), tptp_fun_D_1(B, A)), B) <=> subset(tptp_fun_C_2(B, A), tptp_fun_D_1(B, A))) | (~in(tptp_fun_C_2(B, A), A)) | (~in(tptp_fun_D_1(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_2(B, A), tptp_fun_D_1(B, A)), B) <=> subset(tptp_fun_C_2(B, A), tptp_fun_D_1(B, A))) | (~in(tptp_fun_C_2(B, A), A)) | (~in(tptp_fun_D_1(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_2(B, A), tptp_fun_D_1(B, A)), B) <=> subset(tptp_fun_C_2(B, A), tptp_fun_D_1(B, A))) | (~in(tptp_fun_C_2(B, A), A)) | (~in(tptp_fun_D_1(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_2(B, A), tptp_fun_D_1(B, A)), B) <=> subset(tptp_fun_C_2(B, A), tptp_fun_D_1(B, A))) | (~in(tptp_fun_C_2(B, A), A)) | (~in(tptp_fun_D_1(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_2(B, A), tptp_fun_D_1(B, A)), B) <=> subset(tptp_fun_C_2(B, A), tptp_fun_D_1(B, A))) | (~in(tptp_fun_C_2(B, A), A)) | (~in(tptp_fun_D_1(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_2(B, A), tptp_fun_D_1(B, A)), B) <=> subset(tptp_fun_C_2(B, A), tptp_fun_D_1(B, A))) | (~in(tptp_fun_C_2(B, A), A)) | (~in(tptp_fun_D_1(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_2(B, A), tptp_fun_D_1(B, A)), B) <=> subset(tptp_fun_C_2(B, A), tptp_fun_D_1(B, A))) | (~in(tptp_fun_C_2(B, A), A)) | (~in(tptp_fun_D_1(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_2(B, A), tptp_fun_D_1(B, A)), B) <=> subset(tptp_fun_C_2(B, A), tptp_fun_D_1(B, A))) | (~in(tptp_fun_C_2(B, A), A)) | (~in(tptp_fun_D_1(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_2(B, A), tptp_fun_D_1(B, A)), B) <=> subset(tptp_fun_C_2(B, A), tptp_fun_D_1(B, A))) | (~in(tptp_fun_C_2(B, A), A)) | (~in(tptp_fun_D_1(B, A), A)))))))))),
% 0.20/0.38 inference(transitivity,[status(thm)],[29, 27])).
% 0.20/0.38 tff(31,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(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_2(B, A), A) & in(tptp_fun_D_1(B, A), A))) | (in(ordered_pair(tptp_fun_C_2(B, A), tptp_fun_D_1(B, A)), B) <=> subset(tptp_fun_C_2(B, A), tptp_fun_D_1(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_2(B, A), tptp_fun_D_1(B, A)), B) <=> subset(tptp_fun_C_2(B, A), tptp_fun_D_1(B, A))) | (~in(tptp_fun_C_2(B, A), A)) | (~in(tptp_fun_D_1(B, A), A))))))))))),
% 0.20/0.38 inference(bind,[status(th)],[])).
% 0.20/0.38 tff(32,plain,
% 0.20/0.38 (![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_2(B, A), A) & in(tptp_fun_D_1(B, A), A))) | (in(ordered_pair(tptp_fun_C_2(B, A), tptp_fun_D_1(B, A)), B) <=> subset(tptp_fun_C_2(B, A), tptp_fun_D_1(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_2(B, A), tptp_fun_D_1(B, A)), B) <=> subset(tptp_fun_C_2(B, A), tptp_fun_D_1(B, A))) | (~in(tptp_fun_C_2(B, A), A)) | (~in(tptp_fun_D_1(B, A), A)))))))))),
% 0.20/0.38 inference(quant_intro,[status(thm)],[31])).
% 0.20/0.38 tff(33,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(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_2(B, A), A) & in(tptp_fun_D_1(B, A), A))) | (in(ordered_pair(tptp_fun_C_2(B, A), tptp_fun_D_1(B, A)), B) <=> subset(tptp_fun_C_2(B, A), tptp_fun_D_1(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_2(B, A), A) & in(tptp_fun_D_1(B, A), A))) | (in(ordered_pair(tptp_fun_C_2(B, A), tptp_fun_D_1(B, A)), B) <=> subset(tptp_fun_C_2(B, A), tptp_fun_D_1(B, A)))))))))),
% 0.20/0.38 inference(bind,[status(th)],[])).
% 0.20/0.38 tff(34,plain,
% 0.20/0.38 (![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_2(B, A), A) & in(tptp_fun_D_1(B, A), A))) | (in(ordered_pair(tptp_fun_C_2(B, A), tptp_fun_D_1(B, A)), B) <=> subset(tptp_fun_C_2(B, A), tptp_fun_D_1(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_2(B, A), A) & in(tptp_fun_D_1(B, A), A))) | (in(ordered_pair(tptp_fun_C_2(B, A), tptp_fun_D_1(B, A)), B) <=> subset(tptp_fun_C_2(B, A), tptp_fun_D_1(B, A))))))))),
% 0.20/0.38 inference(quant_intro,[status(thm)],[33])).
% 0.20/0.38 tff(35,plain,
% 0.20/0.38 (![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))))))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(36,plain,
% 0.20/0.38 (^[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))))))))),
% 0.20/0.38 inference(bind,[status(th)],[])).
% 0.20/0.38 tff(37,plain,
% 0.20/0.38 (![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))))))),
% 0.20/0.38 inference(quant_intro,[status(thm)],[36])).
% 0.20/0.38 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')).
% 0.20/0.38 tff(39,plain,
% 0.20/0.38 (![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))))))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[38, 37])).
% 0.20/0.38 tff(40,plain,
% 0.20/0.38 (![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))))))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[39, 35])).
% 0.20/0.38 tff(41,plain,(
% 0.20/0.38 ![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_2(B, A), A) & in(tptp_fun_D_1(B, A), A))) | (in(ordered_pair(tptp_fun_C_2(B, A), tptp_fun_D_1(B, A)), B) <=> subset(tptp_fun_C_2(B, A), tptp_fun_D_1(B, A)))))))))),
% 0.20/0.38 inference(skolemize,[status(sab)],[40])).
% 0.20/0.38 tff(42,plain,
% 0.20/0.38 (![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_2(B, A), A) & in(tptp_fun_D_1(B, A), A))) | (in(ordered_pair(tptp_fun_C_2(B, A), tptp_fun_D_1(B, A)), B) <=> subset(tptp_fun_C_2(B, A), tptp_fun_D_1(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_2(B, A), tptp_fun_D_1(B, A)), B) <=> subset(tptp_fun_C_2(B, A), tptp_fun_D_1(B, A))) | (~in(tptp_fun_C_2(B, A), A)) | (~in(tptp_fun_D_1(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_2(B, A), tptp_fun_D_1(B, A)), B) <=> subset(tptp_fun_C_2(B, A), tptp_fun_D_1(B, A))) | (~in(tptp_fun_C_2(B, A), A)) | (~in(tptp_fun_D_1(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_2(B, A), tptp_fun_D_1(B, A)), B) <=> subset(tptp_fun_C_2(B, A), tptp_fun_D_1(B, A))) | (~in(tptp_fun_C_2(B, A), A)) | (~in(tptp_fun_D_1(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_2(B, A), tptp_fun_D_1(B, A)), B) <=> subset(tptp_fun_C_2(B, A), tptp_fun_D_1(B, A))) | (~in(tptp_fun_C_2(B, A), A)) | (~in(tptp_fun_D_1(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!13))) | (~((~(relation_field(inclusion_relation(A!13)) = A!13)) | (~![C: $i, D: $i] : ((~in(C, A!13)) | (~in(D, A!13)) | (in(ordered_pair(C, D), inclusion_relation(A!13)) <=> subset(C, D)))))))) <=> ((~![A: $i, B: $i] : ((~relation(B)) | (~((~((B = inclusion_relation(A)) | (~(relation_field(B) = A)) | (~((in(ordered_pair(tptp_fun_C_2(B, A), tptp_fun_D_1(B, A)), B) <=> subset(tptp_fun_C_2(B, A), tptp_fun_D_1(B, A))) | (~in(tptp_fun_C_2(B, A), A)) | (~in(tptp_fun_D_1(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!13))) | (~((~(relation_field(inclusion_relation(A!13)) = A!13)) | (~![C: $i, D: $i] : ((~in(C, A!13)) | (~in(D, A!13)) | (in(ordered_pair(C, D), inclusion_relation(A!13)) <=> 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!13))) | (~((~((inclusion_relation(A!13) = inclusion_relation(A!13)) | (~(relation_field(inclusion_relation(A!13)) = A!13)) | (~((in(ordered_pair(tptp_fun_C_2(inclusion_relation(A!13), A!13), tptp_fun_D_1(inclusion_relation(A!13), A!13)), inclusion_relation(A!13)) <=> subset(tptp_fun_C_2(inclusion_relation(A!13), A!13), tptp_fun_D_1(inclusion_relation(A!13), A!13))) | (~in(tptp_fun_C_2(inclusion_relation(A!13), A!13), A!13)) | (~in(tptp_fun_D_1(inclusion_relation(A!13), A!13), A!13)))))) | (~((~(inclusion_relation(A!13) = inclusion_relation(A!13))) | (~((~(relation_field(inclusion_relation(A!13)) = A!13)) | (~![C: $i, D: $i] : ((in(ordered_pair(C, D), inclusion_relation(A!13)) <=> subset(C, D)) | (~in(C, A!13)) | (~in(D, A!13))))))))))) <=> ((~relation(inclusion_relation(A!13))) | (~((~(relation_field(inclusion_relation(A!13)) = A!13)) | (~![C: $i, D: $i] : ((~in(C, A!13)) | (~in(D, A!13)) | (in(ordered_pair(C, D), inclusion_relation(A!13)) <=> 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_2(B, A), tptp_fun_D_1(B, A)), B) <=> subset(tptp_fun_C_2(B, A), tptp_fun_D_1(B, A))) | (~in(tptp_fun_C_2(B, A), A)) | (~in(tptp_fun_D_1(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!13))) | (~((~((inclusion_relation(A!13) = inclusion_relation(A!13)) | (~(relation_field(inclusion_relation(A!13)) = A!13)) | (~((in(ordered_pair(tptp_fun_C_2(inclusion_relation(A!13), A!13), tptp_fun_D_1(inclusion_relation(A!13), A!13)), inclusion_relation(A!13)) <=> subset(tptp_fun_C_2(inclusion_relation(A!13), A!13), tptp_fun_D_1(inclusion_relation(A!13), A!13))) | (~in(tptp_fun_C_2(inclusion_relation(A!13), A!13), A!13)) | (~in(tptp_fun_D_1(inclusion_relation(A!13), A!13), A!13)))))) | (~((~(inclusion_relation(A!13) = inclusion_relation(A!13))) | (~((~(relation_field(inclusion_relation(A!13)) = A!13)) | (~![C: $i, D: $i] : ((in(ordered_pair(C, D), inclusion_relation(A!13)) <=> subset(C, D)) | (~in(C, A!13)) | (~in(D, A!13)))))))))))) <=> ((~![A: $i, B: $i] : ((~relation(B)) | (~((~((B = inclusion_relation(A)) | (~(relation_field(B) = A)) | (~((in(ordered_pair(tptp_fun_C_2(B, A), tptp_fun_D_1(B, A)), B) <=> subset(tptp_fun_C_2(B, A), tptp_fun_D_1(B, A))) | (~in(tptp_fun_C_2(B, A), A)) | (~in(tptp_fun_D_1(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!13))) | (~((~(relation_field(inclusion_relation(A!13)) = A!13)) | (~![C: $i, D: $i] : ((~in(C, A!13)) | (~in(D, A!13)) | (in(ordered_pair(C, D), inclusion_relation(A!13)) <=> 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_2(B, A), tptp_fun_D_1(B, A)), B) <=> subset(tptp_fun_C_2(B, A), tptp_fun_D_1(B, A))) | (~in(tptp_fun_C_2(B, A), A)) | (~in(tptp_fun_D_1(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!13))) | (~((~((inclusion_relation(A!13) = inclusion_relation(A!13)) | (~(relation_field(inclusion_relation(A!13)) = A!13)) | (~((in(ordered_pair(tptp_fun_C_2(inclusion_relation(A!13), A!13), tptp_fun_D_1(inclusion_relation(A!13), A!13)), inclusion_relation(A!13)) <=> subset(tptp_fun_C_2(inclusion_relation(A!13), A!13), tptp_fun_D_1(inclusion_relation(A!13), A!13))) | (~in(tptp_fun_C_2(inclusion_relation(A!13), A!13), A!13)) | (~in(tptp_fun_D_1(inclusion_relation(A!13), A!13), A!13)))))) | (~((~(inclusion_relation(A!13) = inclusion_relation(A!13))) | (~((~(relation_field(inclusion_relation(A!13)) = A!13)) | (~![C: $i, D: $i] : ((in(ordered_pair(C, D), inclusion_relation(A!13)) <=> subset(C, D)) | (~in(C, A!13)) | (~in(D, A!13)))))))))))) <=> ((~![A: $i, B: $i] : ((~relation(B)) | (~((~((B = inclusion_relation(A)) | (~(relation_field(B) = A)) | (~((in(ordered_pair(tptp_fun_C_2(B, A), tptp_fun_D_1(B, A)), B) <=> subset(tptp_fun_C_2(B, A), tptp_fun_D_1(B, A))) | (~in(tptp_fun_C_2(B, A), A)) | (~in(tptp_fun_D_1(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!13))) | (~((~(relation_field(inclusion_relation(A!13)) = A!13)) | (~![C: $i, D: $i] : ((~in(C, A!13)) | (~in(D, A!13)) | (in(ordered_pair(C, D), inclusion_relation(A!13)) <=> 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_2(B, A), tptp_fun_D_1(B, A)), B) <=> subset(tptp_fun_C_2(B, A), tptp_fun_D_1(B, A))) | (~in(tptp_fun_C_2(B, A), A)) | (~in(tptp_fun_D_1(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!13))) | (~((~((inclusion_relation(A!13) = inclusion_relation(A!13)) | (~(relation_field(inclusion_relation(A!13)) = A!13)) | (~((in(ordered_pair(tptp_fun_C_2(inclusion_relation(A!13), A!13), tptp_fun_D_1(inclusion_relation(A!13), A!13)), inclusion_relation(A!13)) <=> subset(tptp_fun_C_2(inclusion_relation(A!13), A!13), tptp_fun_D_1(inclusion_relation(A!13), A!13))) | (~in(tptp_fun_C_2(inclusion_relation(A!13), A!13), A!13)) | (~in(tptp_fun_D_1(inclusion_relation(A!13), A!13), A!13)))))) | (~((~(inclusion_relation(A!13) = inclusion_relation(A!13))) | (~((~(relation_field(inclusion_relation(A!13)) = A!13)) | (~![C: $i, D: $i] : ((in(ordered_pair(C, D), inclusion_relation(A!13)) <=> subset(C, D)) | (~in(C, A!13)) | (~in(D, A!13)))))))))))),
% 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_2(B, A), tptp_fun_D_1(B, A)), B) <=> subset(tptp_fun_C_2(B, A), tptp_fun_D_1(B, A))) | (~in(tptp_fun_C_2(B, A), A)) | (~in(tptp_fun_D_1(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!13))) | (~((~(relation_field(inclusion_relation(A!13)) = A!13)) | (~![C: $i, D: $i] : ((~in(C, A!13)) | (~in(D, A!13)) | (in(ordered_pair(C, D), inclusion_relation(A!13)) <=> 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!13)) = A!13)) | (~![C: $i, D: $i] : ((~in(C, A!13)) | (~in(D, A!13)) | (in(ordered_pair(C, D), inclusion_relation(A!13)) <=> 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!13)) = A!13)) | (~![C: $i, D: $i] : ((~in(C, A!13)) | (~in(D, A!13)) | (in(ordered_pair(C, D), inclusion_relation(A!13)) <=> subset(C, D))))) | (relation_field(inclusion_relation(A!13)) = A!13)),
% 0.20/0.39 inference(tautology,[status(thm)],[])).
% 0.20/0.39 tff(54,plain,
% 0.20/0.39 (relation_field(inclusion_relation(A!13)) = A!13),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[53, 52])).
% 0.20/0.39 tff(55,plain,
% 0.20/0.39 (A!13 = relation_field(inclusion_relation(A!13))),
% 0.20/0.39 inference(symmetry,[status(thm)],[54])).
% 0.20/0.39 tff(56,plain,
% 0.20/0.39 (A!13 = set_union2(relation_dom(inclusion_relation(A!13)), relation_rng(inclusion_relation(A!13)))),
% 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_0(set_union2(relation_dom(inclusion_relation(A!13)), relation_rng(inclusion_relation(A!13))), inclusion_relation(A!13)), A!13) <=> in(tptp_fun_C_0(set_union2(relation_dom(inclusion_relation(A!13)), relation_rng(inclusion_relation(A!13))), inclusion_relation(A!13)), set_union2(relation_dom(inclusion_relation(A!13)), relation_rng(inclusion_relation(A!13))))),
% 0.20/0.39 inference(monotonicity,[status(thm)],[56])).
% 0.20/0.39 tff(58,plain,
% 0.20/0.39 (in(tptp_fun_C_0(set_union2(relation_dom(inclusion_relation(A!13)), relation_rng(inclusion_relation(A!13))), inclusion_relation(A!13)), set_union2(relation_dom(inclusion_relation(A!13)), relation_rng(inclusion_relation(A!13)))) <=> in(tptp_fun_C_0(set_union2(relation_dom(inclusion_relation(A!13)), relation_rng(inclusion_relation(A!13))), inclusion_relation(A!13)), A!13)),
% 0.20/0.39 inference(symmetry,[status(thm)],[57])).
% 0.20/0.39 tff(59,plain,
% 0.20/0.39 (^[A: $i] : refl(((~relation(A)) | ![B: $i] : (~((~((~is_reflexive_in(A, B)) | ![C: $i] : ((~in(C, B)) | in(ordered_pair(C, C), A)))) | (~(is_reflexive_in(A, B) | (~((~in(tptp_fun_C_0(B, A), B)) | in(ordered_pair(tptp_fun_C_0(B, A), tptp_fun_C_0(B, A)), A)))))))) <=> ((~relation(A)) | ![B: $i] : (~((~((~is_reflexive_in(A, B)) | ![C: $i] : ((~in(C, B)) | in(ordered_pair(C, C), A)))) | (~(is_reflexive_in(A, B) | (~((~in(tptp_fun_C_0(B, A), B)) | in(ordered_pair(tptp_fun_C_0(B, A), tptp_fun_C_0(B, A)), A)))))))))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(60,plain,
% 0.20/0.39 (![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~is_reflexive_in(A, B)) | ![C: $i] : ((~in(C, B)) | in(ordered_pair(C, C), A)))) | (~(is_reflexive_in(A, B) | (~((~in(tptp_fun_C_0(B, A), B)) | in(ordered_pair(tptp_fun_C_0(B, A), tptp_fun_C_0(B, A)), A)))))))) <=> ![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~is_reflexive_in(A, B)) | ![C: $i] : ((~in(C, B)) | in(ordered_pair(C, C), A)))) | (~(is_reflexive_in(A, B) | (~((~in(tptp_fun_C_0(B, A), B)) | in(ordered_pair(tptp_fun_C_0(B, A), tptp_fun_C_0(B, A)), A))))))))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[59])).
% 0.20/0.39 tff(61,plain,
% 0.20/0.39 (^[A: $i] : rewrite(((~relation(A)) | ![B: $i] : (~((~((~is_reflexive_in(A, B)) | ![C: $i] : ((~in(C, B)) | in(ordered_pair(C, C), A)))) | (~(is_reflexive_in(A, B) | (~((~in(tptp_fun_C_0(B, A), B)) | in(ordered_pair(tptp_fun_C_0(B, A), tptp_fun_C_0(B, A)), A)))))))) <=> ((~relation(A)) | ![B: $i] : (~((~((~is_reflexive_in(A, B)) | ![C: $i] : ((~in(C, B)) | in(ordered_pair(C, C), A)))) | (~(is_reflexive_in(A, B) | (~((~in(tptp_fun_C_0(B, A), B)) | in(ordered_pair(tptp_fun_C_0(B, A), tptp_fun_C_0(B, A)), A)))))))))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(62,plain,
% 0.20/0.39 (![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~is_reflexive_in(A, B)) | ![C: $i] : ((~in(C, B)) | in(ordered_pair(C, C), A)))) | (~(is_reflexive_in(A, B) | (~((~in(tptp_fun_C_0(B, A), B)) | in(ordered_pair(tptp_fun_C_0(B, A), tptp_fun_C_0(B, A)), A)))))))) <=> ![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~is_reflexive_in(A, B)) | ![C: $i] : ((~in(C, B)) | in(ordered_pair(C, C), A)))) | (~(is_reflexive_in(A, B) | (~((~in(tptp_fun_C_0(B, A), B)) | in(ordered_pair(tptp_fun_C_0(B, A), tptp_fun_C_0(B, A)), A))))))))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[61])).
% 0.20/0.39 tff(63,plain,
% 0.20/0.39 (![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~is_reflexive_in(A, B)) | ![C: $i] : ((~in(C, B)) | in(ordered_pair(C, C), A)))) | (~(is_reflexive_in(A, B) | (~((~in(tptp_fun_C_0(B, A), B)) | in(ordered_pair(tptp_fun_C_0(B, A), tptp_fun_C_0(B, A)), A)))))))) <=> ![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~is_reflexive_in(A, B)) | ![C: $i] : ((~in(C, B)) | in(ordered_pair(C, C), A)))) | (~(is_reflexive_in(A, B) | (~((~in(tptp_fun_C_0(B, A), B)) | in(ordered_pair(tptp_fun_C_0(B, A), tptp_fun_C_0(B, A)), A))))))))),
% 0.20/0.39 inference(transitivity,[status(thm)],[62, 60])).
% 0.20/0.39 tff(64,plain,
% 0.20/0.39 (^[A: $i] : rewrite(((~relation(A)) | ![B: $i] : (((~is_reflexive_in(A, B)) | ![C: $i] : ((~in(C, B)) | in(ordered_pair(C, C), A))) & (is_reflexive_in(A, B) | (~((~in(tptp_fun_C_0(B, A), B)) | in(ordered_pair(tptp_fun_C_0(B, A), tptp_fun_C_0(B, A)), A)))))) <=> ((~relation(A)) | ![B: $i] : (~((~((~is_reflexive_in(A, B)) | ![C: $i] : ((~in(C, B)) | in(ordered_pair(C, C), A)))) | (~(is_reflexive_in(A, B) | (~((~in(tptp_fun_C_0(B, A), B)) | in(ordered_pair(tptp_fun_C_0(B, A), tptp_fun_C_0(B, A)), A)))))))))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(65,plain,
% 0.20/0.39 (![A: $i] : ((~relation(A)) | ![B: $i] : (((~is_reflexive_in(A, B)) | ![C: $i] : ((~in(C, B)) | in(ordered_pair(C, C), A))) & (is_reflexive_in(A, B) | (~((~in(tptp_fun_C_0(B, A), B)) | in(ordered_pair(tptp_fun_C_0(B, A), tptp_fun_C_0(B, A)), A)))))) <=> ![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~is_reflexive_in(A, B)) | ![C: $i] : ((~in(C, B)) | in(ordered_pair(C, C), A)))) | (~(is_reflexive_in(A, B) | (~((~in(tptp_fun_C_0(B, A), B)) | in(ordered_pair(tptp_fun_C_0(B, A), tptp_fun_C_0(B, A)), A))))))))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[64])).
% 0.20/0.39 tff(66,plain,
% 0.20/0.39 (![A: $i] : ((~relation(A)) | ![B: $i] : (is_reflexive_in(A, B) <=> ![C: $i] : ((~in(C, B)) | in(ordered_pair(C, C), A)))) <=> ![A: $i] : ((~relation(A)) | ![B: $i] : (is_reflexive_in(A, B) <=> ![C: $i] : ((~in(C, B)) | in(ordered_pair(C, C), 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_reflexive_in(A, B) <=> ![C: $i] : (in(C, B) => in(ordered_pair(C, C), A))) <=> (is_reflexive_in(A, B) <=> ![C: $i] : ((~in(C, B)) | in(ordered_pair(C, C), A))))), (![B: $i] : (is_reflexive_in(A, B) <=> ![C: $i] : (in(C, B) => in(ordered_pair(C, C), A))) <=> ![B: $i] : (is_reflexive_in(A, B) <=> ![C: $i] : ((~in(C, B)) | in(ordered_pair(C, C), A))))), ((relation(A) => ![B: $i] : (is_reflexive_in(A, B) <=> ![C: $i] : (in(C, B) => in(ordered_pair(C, C), A)))) <=> (relation(A) => ![B: $i] : (is_reflexive_in(A, B) <=> ![C: $i] : ((~in(C, B)) | in(ordered_pair(C, C), A)))))), rewrite((relation(A) => ![B: $i] : (is_reflexive_in(A, B) <=> ![C: $i] : ((~in(C, B)) | in(ordered_pair(C, C), A)))) <=> ((~relation(A)) | ![B: $i] : (is_reflexive_in(A, B) <=> ![C: $i] : ((~in(C, B)) | in(ordered_pair(C, C), A))))), ((relation(A) => ![B: $i] : (is_reflexive_in(A, B) <=> ![C: $i] : (in(C, B) => in(ordered_pair(C, C), A)))) <=> ((~relation(A)) | ![B: $i] : (is_reflexive_in(A, B) <=> ![C: $i] : ((~in(C, B)) | in(ordered_pair(C, C), 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_reflexive_in(A, B) <=> ![C: $i] : (in(C, B) => in(ordered_pair(C, C), A)))) <=> ![A: $i] : ((~relation(A)) | ![B: $i] : (is_reflexive_in(A, B) <=> ![C: $i] : ((~in(C, B)) | in(ordered_pair(C, C), 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_reflexive_in(A, B) <=> ![C: $i] : (in(C, B) => in(ordered_pair(C, C), A))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d1_relat_2')).
% 0.20/0.40 tff(70,plain,
% 0.20/0.40 (![A: $i] : ((~relation(A)) | ![B: $i] : (is_reflexive_in(A, B) <=> ![C: $i] : ((~in(C, B)) | in(ordered_pair(C, C), 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_reflexive_in(A, B) <=> ![C: $i] : ((~in(C, B)) | in(ordered_pair(C, C), 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_reflexive_in(A, B)) | ![C: $i] : ((~in(C, B)) | in(ordered_pair(C, C), A))) & (is_reflexive_in(A, B) | (~((~in(tptp_fun_C_0(B, A), B)) | in(ordered_pair(tptp_fun_C_0(B, A), tptp_fun_C_0(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_reflexive_in(A, B)) | ![C: $i] : ((~in(C, B)) | in(ordered_pair(C, C), A)))) | (~(is_reflexive_in(A, B) | (~((~in(tptp_fun_C_0(B, A), B)) | in(ordered_pair(tptp_fun_C_0(B, A), tptp_fun_C_0(B, A)), A))))))))),
% 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_reflexive_in(A, B)) | ![C: $i] : ((~in(C, B)) | in(ordered_pair(C, C), A)))) | (~(is_reflexive_in(A, B) | (~((~in(tptp_fun_C_0(B, A), B)) | in(ordered_pair(tptp_fun_C_0(B, A), tptp_fun_C_0(B, A)), A))))))))),
% 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_reflexive_in(A, B)) | ![C: $i] : ((~in(C, B)) | in(ordered_pair(C, C), A)))) | (~(is_reflexive_in(A, B) | (~((~in(tptp_fun_C_0(B, A), B)) | in(ordered_pair(tptp_fun_C_0(B, A), tptp_fun_C_0(B, A)), A))))))))) | ((~relation(inclusion_relation(A!13))) | ![B: $i] : (~((~((~is_reflexive_in(inclusion_relation(A!13), B)) | ![C: $i] : ((~in(C, B)) | in(ordered_pair(C, C), inclusion_relation(A!13))))) | (~(is_reflexive_in(inclusion_relation(A!13), B) | (~((~in(tptp_fun_C_0(B, inclusion_relation(A!13)), B)) | in(ordered_pair(tptp_fun_C_0(B, inclusion_relation(A!13)), tptp_fun_C_0(B, inclusion_relation(A!13))), inclusion_relation(A!13)))))))))) <=> ((~![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~is_reflexive_in(A, B)) | ![C: $i] : ((~in(C, B)) | in(ordered_pair(C, C), A)))) | (~(is_reflexive_in(A, B) | (~((~in(tptp_fun_C_0(B, A), B)) | in(ordered_pair(tptp_fun_C_0(B, A), tptp_fun_C_0(B, A)), A))))))))) | (~relation(inclusion_relation(A!13))) | ![B: $i] : (~((~((~is_reflexive_in(inclusion_relation(A!13), B)) | ![C: $i] : ((~in(C, B)) | in(ordered_pair(C, C), inclusion_relation(A!13))))) | (~(is_reflexive_in(inclusion_relation(A!13), B) | (~((~in(tptp_fun_C_0(B, inclusion_relation(A!13)), B)) | in(ordered_pair(tptp_fun_C_0(B, inclusion_relation(A!13)), tptp_fun_C_0(B, inclusion_relation(A!13))), inclusion_relation(A!13)))))))))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(76,plain,
% 0.20/0.40 ((~![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~is_reflexive_in(A, B)) | ![C: $i] : ((~in(C, B)) | in(ordered_pair(C, C), A)))) | (~(is_reflexive_in(A, B) | (~((~in(tptp_fun_C_0(B, A), B)) | in(ordered_pair(tptp_fun_C_0(B, A), tptp_fun_C_0(B, A)), A))))))))) | ((~relation(inclusion_relation(A!13))) | ![B: $i] : (~((~((~is_reflexive_in(inclusion_relation(A!13), B)) | ![C: $i] : ((~in(C, B)) | in(ordered_pair(C, C), inclusion_relation(A!13))))) | (~(is_reflexive_in(inclusion_relation(A!13), B) | (~((~in(tptp_fun_C_0(B, inclusion_relation(A!13)), B)) | in(ordered_pair(tptp_fun_C_0(B, inclusion_relation(A!13)), tptp_fun_C_0(B, inclusion_relation(A!13))), inclusion_relation(A!13)))))))))),
% 0.20/0.40 inference(quant_inst,[status(thm)],[])).
% 0.20/0.40 tff(77,plain,
% 0.20/0.40 ((~![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~is_reflexive_in(A, B)) | ![C: $i] : ((~in(C, B)) | in(ordered_pair(C, C), A)))) | (~(is_reflexive_in(A, B) | (~((~in(tptp_fun_C_0(B, A), B)) | in(ordered_pair(tptp_fun_C_0(B, A), tptp_fun_C_0(B, A)), A))))))))) | (~relation(inclusion_relation(A!13))) | ![B: $i] : (~((~((~is_reflexive_in(inclusion_relation(A!13), B)) | ![C: $i] : ((~in(C, B)) | in(ordered_pair(C, C), inclusion_relation(A!13))))) | (~(is_reflexive_in(inclusion_relation(A!13), B) | (~((~in(tptp_fun_C_0(B, inclusion_relation(A!13)), B)) | in(ordered_pair(tptp_fun_C_0(B, inclusion_relation(A!13)), tptp_fun_C_0(B, inclusion_relation(A!13))), inclusion_relation(A!13))))))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[76, 75])).
% 0.20/0.40 tff(78,plain,
% 0.20/0.40 (![B: $i] : (~((~((~is_reflexive_in(inclusion_relation(A!13), B)) | ![C: $i] : ((~in(C, B)) | in(ordered_pair(C, C), inclusion_relation(A!13))))) | (~(is_reflexive_in(inclusion_relation(A!13), B) | (~((~in(tptp_fun_C_0(B, inclusion_relation(A!13)), B)) | in(ordered_pair(tptp_fun_C_0(B, inclusion_relation(A!13)), tptp_fun_C_0(B, inclusion_relation(A!13))), inclusion_relation(A!13))))))))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[77, 74, 9])).
% 0.20/0.40 tff(79,plain,
% 0.20/0.40 (((~![B: $i] : (~((~((~is_reflexive_in(inclusion_relation(A!13), B)) | ![C: $i] : ((~in(C, B)) | in(ordered_pair(C, C), inclusion_relation(A!13))))) | (~(is_reflexive_in(inclusion_relation(A!13), B) | (~((~in(tptp_fun_C_0(B, inclusion_relation(A!13)), B)) | in(ordered_pair(tptp_fun_C_0(B, inclusion_relation(A!13)), tptp_fun_C_0(B, inclusion_relation(A!13))), inclusion_relation(A!13))))))))) | (~((~((~is_reflexive_in(inclusion_relation(A!13), set_union2(relation_dom(inclusion_relation(A!13)), relation_rng(inclusion_relation(A!13))))) | ![C: $i] : ((~in(C, set_union2(relation_dom(inclusion_relation(A!13)), relation_rng(inclusion_relation(A!13))))) | in(ordered_pair(C, C), inclusion_relation(A!13))))) | (~((~((~in(tptp_fun_C_0(set_union2(relation_dom(inclusion_relation(A!13)), relation_rng(inclusion_relation(A!13))), inclusion_relation(A!13)), set_union2(relation_dom(inclusion_relation(A!13)), relation_rng(inclusion_relation(A!13))))) | in(ordered_pair(tptp_fun_C_0(set_union2(relation_dom(inclusion_relation(A!13)), relation_rng(inclusion_relation(A!13))), inclusion_relation(A!13)), tptp_fun_C_0(set_union2(relation_dom(inclusion_relation(A!13)), relation_rng(inclusion_relation(A!13))), inclusion_relation(A!13))), inclusion_relation(A!13)))) | is_reflexive_in(inclusion_relation(A!13), set_union2(relation_dom(inclusion_relation(A!13)), relation_rng(inclusion_relation(A!13))))))))) <=> ((~![B: $i] : (~((~((~is_reflexive_in(inclusion_relation(A!13), B)) | ![C: $i] : ((~in(C, B)) | in(ordered_pair(C, C), inclusion_relation(A!13))))) | (~(is_reflexive_in(inclusion_relation(A!13), B) | (~((~in(tptp_fun_C_0(B, inclusion_relation(A!13)), B)) | in(ordered_pair(tptp_fun_C_0(B, inclusion_relation(A!13)), tptp_fun_C_0(B, inclusion_relation(A!13))), inclusion_relation(A!13))))))))) | (~((~((~is_reflexive_in(inclusion_relation(A!13), set_union2(relation_dom(inclusion_relation(A!13)), relation_rng(inclusion_relation(A!13))))) | ![C: $i] : ((~in(C, set_union2(relation_dom(inclusion_relation(A!13)), relation_rng(inclusion_relation(A!13))))) | in(ordered_pair(C, C), inclusion_relation(A!13))))) | (~((~((~in(tptp_fun_C_0(set_union2(relation_dom(inclusion_relation(A!13)), relation_rng(inclusion_relation(A!13))), inclusion_relation(A!13)), set_union2(relation_dom(inclusion_relation(A!13)), relation_rng(inclusion_relation(A!13))))) | in(ordered_pair(tptp_fun_C_0(set_union2(relation_dom(inclusion_relation(A!13)), relation_rng(inclusion_relation(A!13))), inclusion_relation(A!13)), tptp_fun_C_0(set_union2(relation_dom(inclusion_relation(A!13)), relation_rng(inclusion_relation(A!13))), inclusion_relation(A!13))), inclusion_relation(A!13)))) | is_reflexive_in(inclusion_relation(A!13), set_union2(relation_dom(inclusion_relation(A!13)), relation_rng(inclusion_relation(A!13)))))))))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(80,plain,
% 0.20/0.40 ((~((~((~is_reflexive_in(inclusion_relation(A!13), set_union2(relation_dom(inclusion_relation(A!13)), relation_rng(inclusion_relation(A!13))))) | ![C: $i] : ((~in(C, set_union2(relation_dom(inclusion_relation(A!13)), relation_rng(inclusion_relation(A!13))))) | in(ordered_pair(C, C), inclusion_relation(A!13))))) | (~(is_reflexive_in(inclusion_relation(A!13), set_union2(relation_dom(inclusion_relation(A!13)), relation_rng(inclusion_relation(A!13)))) | (~((~in(tptp_fun_C_0(set_union2(relation_dom(inclusion_relation(A!13)), relation_rng(inclusion_relation(A!13))), inclusion_relation(A!13)), set_union2(relation_dom(inclusion_relation(A!13)), relation_rng(inclusion_relation(A!13))))) | in(ordered_pair(tptp_fun_C_0(set_union2(relation_dom(inclusion_relation(A!13)), relation_rng(inclusion_relation(A!13))), inclusion_relation(A!13)), tptp_fun_C_0(set_union2(relation_dom(inclusion_relation(A!13)), relation_rng(inclusion_relation(A!13))), inclusion_relation(A!13))), inclusion_relation(A!13)))))))) <=> (~((~((~is_reflexive_in(inclusion_relation(A!13), set_union2(relation_dom(inclusion_relation(A!13)), relation_rng(inclusion_relation(A!13))))) | ![C: $i] : ((~in(C, set_union2(relation_dom(inclusion_relation(A!13)), relation_rng(inclusion_relation(A!13))))) | in(ordered_pair(C, C), inclusion_relation(A!13))))) | (~((~((~in(tptp_fun_C_0(set_union2(relation_dom(inclusion_relation(A!13)), relation_rng(inclusion_relation(A!13))), inclusion_relation(A!13)), set_union2(relation_dom(inclusion_relation(A!13)), relation_rng(inclusion_relation(A!13))))) | in(ordered_pair(tptp_fun_C_0(set_union2(relation_dom(inclusion_relation(A!13)), relation_rng(inclusion_relation(A!13))), inclusion_relation(A!13)), tptp_fun_C_0(set_union2(relation_dom(inclusion_relation(A!13)), relation_rng(inclusion_relation(A!13))), inclusion_relation(A!13))), inclusion_relation(A!13)))) | is_reflexive_in(inclusion_relation(A!13), set_union2(relation_dom(inclusion_relation(A!13)), relation_rng(inclusion_relation(A!13))))))))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(81,plain,
% 0.20/0.40 (((~![B: $i] : (~((~((~is_reflexive_in(inclusion_relation(A!13), B)) | ![C: $i] : ((~in(C, B)) | in(ordered_pair(C, C), inclusion_relation(A!13))))) | (~(is_reflexive_in(inclusion_relation(A!13), B) | (~((~in(tptp_fun_C_0(B, inclusion_relation(A!13)), B)) | in(ordered_pair(tptp_fun_C_0(B, inclusion_relation(A!13)), tptp_fun_C_0(B, inclusion_relation(A!13))), inclusion_relation(A!13))))))))) | (~((~((~is_reflexive_in(inclusion_relation(A!13), set_union2(relation_dom(inclusion_relation(A!13)), relation_rng(inclusion_relation(A!13))))) | ![C: $i] : ((~in(C, set_union2(relation_dom(inclusion_relation(A!13)), relation_rng(inclusion_relation(A!13))))) | in(ordered_pair(C, C), inclusion_relation(A!13))))) | (~(is_reflexive_in(inclusion_relation(A!13), set_union2(relation_dom(inclusion_relation(A!13)), relation_rng(inclusion_relation(A!13)))) | (~((~in(tptp_fun_C_0(set_union2(relation_dom(inclusion_relation(A!13)), relation_rng(inclusion_relation(A!13))), inclusion_relation(A!13)), set_union2(relation_dom(inclusion_relation(A!13)), relation_rng(inclusion_relation(A!13))))) | in(ordered_pair(tptp_fun_C_0(set_union2(relation_dom(inclusion_relation(A!13)), relation_rng(inclusion_relation(A!13))), inclusion_relation(A!13)), tptp_fun_C_0(set_union2(relation_dom(inclusion_relation(A!13)), relation_rng(inclusion_relation(A!13))), inclusion_relation(A!13))), inclusion_relation(A!13))))))))) <=> ((~![B: $i] : (~((~((~is_reflexive_in(inclusion_relation(A!13), B)) | ![C: $i] : ((~in(C, B)) | in(ordered_pair(C, C), inclusion_relation(A!13))))) | (~(is_reflexive_in(inclusion_relation(A!13), B) | (~((~in(tptp_fun_C_0(B, inclusion_relation(A!13)), B)) | in(ordered_pair(tptp_fun_C_0(B, inclusion_relation(A!13)), tptp_fun_C_0(B, inclusion_relation(A!13))), inclusion_relation(A!13))))))))) | (~((~((~is_reflexive_in(inclusion_relation(A!13), set_union2(relation_dom(inclusion_relation(A!13)), relation_rng(inclusion_relation(A!13))))) | ![C: $i] : ((~in(C, set_union2(relation_dom(inclusion_relation(A!13)), relation_rng(inclusion_relation(A!13))))) | in(ordered_pair(C, C), inclusion_relation(A!13))))) | (~((~((~in(tptp_fun_C_0(set_union2(relation_dom(inclusion_relation(A!13)), relation_rng(inclusion_relation(A!13))), inclusion_relation(A!13)), set_union2(relation_dom(inclusion_relation(A!13)), relation_rng(inclusion_relation(A!13))))) | in(ordered_pair(tptp_fun_C_0(set_union2(relation_dom(inclusion_relation(A!13)), relation_rng(inclusion_relation(A!13))), inclusion_relation(A!13)), tptp_fun_C_0(set_union2(relation_dom(inclusion_relation(A!13)), relation_rng(inclusion_relation(A!13))), inclusion_relation(A!13))), inclusion_relation(A!13)))) | is_reflexive_in(inclusion_relation(A!13), set_union2(relation_dom(inclusion_relation(A!13)), relation_rng(inclusion_relation(A!13)))))))))),
% 0.20/0.40 inference(monotonicity,[status(thm)],[80])).
% 0.20/0.40 tff(82,plain,
% 0.20/0.40 (((~![B: $i] : (~((~((~is_reflexive_in(inclusion_relation(A!13), B)) | ![C: $i] : ((~in(C, B)) | in(ordered_pair(C, C), inclusion_relation(A!13))))) | (~(is_reflexive_in(inclusion_relation(A!13), B) | (~((~in(tptp_fun_C_0(B, inclusion_relation(A!13)), B)) | in(ordered_pair(tptp_fun_C_0(B, inclusion_relation(A!13)), tptp_fun_C_0(B, inclusion_relation(A!13))), inclusion_relation(A!13))))))))) | (~((~((~is_reflexive_in(inclusion_relation(A!13), set_union2(relation_dom(inclusion_relation(A!13)), relation_rng(inclusion_relation(A!13))))) | ![C: $i] : ((~in(C, set_union2(relation_dom(inclusion_relation(A!13)), relation_rng(inclusion_relation(A!13))))) | in(ordered_pair(C, C), inclusion_relation(A!13))))) | (~(is_reflexive_in(inclusion_relation(A!13), set_union2(relation_dom(inclusion_relation(A!13)), relation_rng(inclusion_relation(A!13)))) | (~((~in(tptp_fun_C_0(set_union2(relation_dom(inclusion_relation(A!13)), relation_rng(inclusion_relation(A!13))), inclusion_relation(A!13)), set_union2(relation_dom(inclusion_relation(A!13)), relation_rng(inclusion_relation(A!13))))) | in(ordered_pair(tptp_fun_C_0(set_union2(relation_dom(inclusion_relation(A!13)), relation_rng(inclusion_relation(A!13))), inclusion_relation(A!13)), tptp_fun_C_0(set_union2(relation_dom(inclusion_relation(A!13)), relation_rng(inclusion_relation(A!13))), inclusion_relation(A!13))), inclusion_relation(A!13))))))))) <=> ((~![B: $i] : (~((~((~is_reflexive_in(inclusion_relation(A!13), B)) | ![C: $i] : ((~in(C, B)) | in(ordered_pair(C, C), inclusion_relation(A!13))))) | (~(is_reflexive_in(inclusion_relation(A!13), B) | (~((~in(tptp_fun_C_0(B, inclusion_relation(A!13)), B)) | in(ordered_pair(tptp_fun_C_0(B, inclusion_relation(A!13)), tptp_fun_C_0(B, inclusion_relation(A!13))), inclusion_relation(A!13))))))))) | (~((~((~is_reflexive_in(inclusion_relation(A!13), set_union2(relation_dom(inclusion_relation(A!13)), relation_rng(inclusion_relation(A!13))))) | ![C: $i] : ((~in(C, set_union2(relation_dom(inclusion_relation(A!13)), relation_rng(inclusion_relation(A!13))))) | in(ordered_pair(C, C), inclusion_relation(A!13))))) | (~((~((~in(tptp_fun_C_0(set_union2(relation_dom(inclusion_relation(A!13)), relation_rng(inclusion_relation(A!13))), inclusion_relation(A!13)), set_union2(relation_dom(inclusion_relation(A!13)), relation_rng(inclusion_relation(A!13))))) | in(ordered_pair(tptp_fun_C_0(set_union2(relation_dom(inclusion_relation(A!13)), relation_rng(inclusion_relation(A!13))), inclusion_relation(A!13)), tptp_fun_C_0(set_union2(relation_dom(inclusion_relation(A!13)), relation_rng(inclusion_relation(A!13))), inclusion_relation(A!13))), inclusion_relation(A!13)))) | is_reflexive_in(inclusion_relation(A!13), set_union2(relation_dom(inclusion_relation(A!13)), relation_rng(inclusion_relation(A!13)))))))))),
% 0.20/0.40 inference(transitivity,[status(thm)],[81, 79])).
% 0.20/0.40 tff(83,plain,
% 0.20/0.40 ((~![B: $i] : (~((~((~is_reflexive_in(inclusion_relation(A!13), B)) | ![C: $i] : ((~in(C, B)) | in(ordered_pair(C, C), inclusion_relation(A!13))))) | (~(is_reflexive_in(inclusion_relation(A!13), B) | (~((~in(tptp_fun_C_0(B, inclusion_relation(A!13)), B)) | in(ordered_pair(tptp_fun_C_0(B, inclusion_relation(A!13)), tptp_fun_C_0(B, inclusion_relation(A!13))), inclusion_relation(A!13))))))))) | (~((~((~is_reflexive_in(inclusion_relation(A!13), set_union2(relation_dom(inclusion_relation(A!13)), relation_rng(inclusion_relation(A!13))))) | ![C: $i] : ((~in(C, set_union2(relation_dom(inclusion_relation(A!13)), relation_rng(inclusion_relation(A!13))))) | in(ordered_pair(C, C), inclusion_relation(A!13))))) | (~(is_reflexive_in(inclusion_relation(A!13), set_union2(relation_dom(inclusion_relation(A!13)), relation_rng(inclusion_relation(A!13)))) | (~((~in(tptp_fun_C_0(set_union2(relation_dom(inclusion_relation(A!13)), relation_rng(inclusion_relation(A!13))), inclusion_relation(A!13)), set_union2(relation_dom(inclusion_relation(A!13)), relation_rng(inclusion_relation(A!13))))) | in(ordered_pair(tptp_fun_C_0(set_union2(relation_dom(inclusion_relation(A!13)), relation_rng(inclusion_relation(A!13))), inclusion_relation(A!13)), tptp_fun_C_0(set_union2(relation_dom(inclusion_relation(A!13)), relation_rng(inclusion_relation(A!13))), inclusion_relation(A!13))), inclusion_relation(A!13))))))))),
% 0.20/0.40 inference(quant_inst,[status(thm)],[])).
% 0.20/0.40 tff(84,plain,
% 0.20/0.40 ((~![B: $i] : (~((~((~is_reflexive_in(inclusion_relation(A!13), B)) | ![C: $i] : ((~in(C, B)) | in(ordered_pair(C, C), inclusion_relation(A!13))))) | (~(is_reflexive_in(inclusion_relation(A!13), B) | (~((~in(tptp_fun_C_0(B, inclusion_relation(A!13)), B)) | in(ordered_pair(tptp_fun_C_0(B, inclusion_relation(A!13)), tptp_fun_C_0(B, inclusion_relation(A!13))), inclusion_relation(A!13))))))))) | (~((~((~is_reflexive_in(inclusion_relation(A!13), set_union2(relation_dom(inclusion_relation(A!13)), relation_rng(inclusion_relation(A!13))))) | ![C: $i] : ((~in(C, set_union2(relation_dom(inclusion_relation(A!13)), relation_rng(inclusion_relation(A!13))))) | in(ordered_pair(C, C), inclusion_relation(A!13))))) | (~((~((~in(tptp_fun_C_0(set_union2(relation_dom(inclusion_relation(A!13)), relation_rng(inclusion_relation(A!13))), inclusion_relation(A!13)), set_union2(relation_dom(inclusion_relation(A!13)), relation_rng(inclusion_relation(A!13))))) | in(ordered_pair(tptp_fun_C_0(set_union2(relation_dom(inclusion_relation(A!13)), relation_rng(inclusion_relation(A!13))), inclusion_relation(A!13)), tptp_fun_C_0(set_union2(relation_dom(inclusion_relation(A!13)), relation_rng(inclusion_relation(A!13))), inclusion_relation(A!13))), inclusion_relation(A!13)))) | is_reflexive_in(inclusion_relation(A!13), set_union2(relation_dom(inclusion_relation(A!13)), relation_rng(inclusion_relation(A!13))))))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[83, 82])).
% 0.20/0.40 tff(85,plain,
% 0.20/0.40 (~((~((~is_reflexive_in(inclusion_relation(A!13), set_union2(relation_dom(inclusion_relation(A!13)), relation_rng(inclusion_relation(A!13))))) | ![C: $i] : ((~in(C, set_union2(relation_dom(inclusion_relation(A!13)), relation_rng(inclusion_relation(A!13))))) | in(ordered_pair(C, C), inclusion_relation(A!13))))) | (~((~((~in(tptp_fun_C_0(set_union2(relation_dom(inclusion_relation(A!13)), relation_rng(inclusion_relation(A!13))), inclusion_relation(A!13)), set_union2(relation_dom(inclusion_relation(A!13)), relation_rng(inclusion_relation(A!13))))) | in(ordered_pair(tptp_fun_C_0(set_union2(relation_dom(inclusion_relation(A!13)), relation_rng(inclusion_relation(A!13))), inclusion_relation(A!13)), tptp_fun_C_0(set_union2(relation_dom(inclusion_relation(A!13)), relation_rng(inclusion_relation(A!13))), inclusion_relation(A!13))), inclusion_relation(A!13)))) | is_reflexive_in(inclusion_relation(A!13), set_union2(relation_dom(inclusion_relation(A!13)), relation_rng(inclusion_relation(A!13)))))))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[84, 78])).
% 0.20/0.41 tff(86,plain,
% 0.20/0.41 (((~((~is_reflexive_in(inclusion_relation(A!13), set_union2(relation_dom(inclusion_relation(A!13)), relation_rng(inclusion_relation(A!13))))) | ![C: $i] : ((~in(C, set_union2(relation_dom(inclusion_relation(A!13)), relation_rng(inclusion_relation(A!13))))) | in(ordered_pair(C, C), inclusion_relation(A!13))))) | (~((~((~in(tptp_fun_C_0(set_union2(relation_dom(inclusion_relation(A!13)), relation_rng(inclusion_relation(A!13))), inclusion_relation(A!13)), set_union2(relation_dom(inclusion_relation(A!13)), relation_rng(inclusion_relation(A!13))))) | in(ordered_pair(tptp_fun_C_0(set_union2(relation_dom(inclusion_relation(A!13)), relation_rng(inclusion_relation(A!13))), inclusion_relation(A!13)), tptp_fun_C_0(set_union2(relation_dom(inclusion_relation(A!13)), relation_rng(inclusion_relation(A!13))), inclusion_relation(A!13))), inclusion_relation(A!13)))) | is_reflexive_in(inclusion_relation(A!13), set_union2(relation_dom(inclusion_relation(A!13)), relation_rng(inclusion_relation(A!13))))))) | ((~((~in(tptp_fun_C_0(set_union2(relation_dom(inclusion_relation(A!13)), relation_rng(inclusion_relation(A!13))), inclusion_relation(A!13)), set_union2(relation_dom(inclusion_relation(A!13)), relation_rng(inclusion_relation(A!13))))) | in(ordered_pair(tptp_fun_C_0(set_union2(relation_dom(inclusion_relation(A!13)), relation_rng(inclusion_relation(A!13))), inclusion_relation(A!13)), tptp_fun_C_0(set_union2(relation_dom(inclusion_relation(A!13)), relation_rng(inclusion_relation(A!13))), inclusion_relation(A!13))), inclusion_relation(A!13)))) | is_reflexive_in(inclusion_relation(A!13), set_union2(relation_dom(inclusion_relation(A!13)), relation_rng(inclusion_relation(A!13)))))),
% 0.20/0.41 inference(tautology,[status(thm)],[])).
% 0.20/0.41 tff(87,plain,
% 0.20/0.41 ((~((~in(tptp_fun_C_0(set_union2(relation_dom(inclusion_relation(A!13)), relation_rng(inclusion_relation(A!13))), inclusion_relation(A!13)), set_union2(relation_dom(inclusion_relation(A!13)), relation_rng(inclusion_relation(A!13))))) | in(ordered_pair(tptp_fun_C_0(set_union2(relation_dom(inclusion_relation(A!13)), relation_rng(inclusion_relation(A!13))), inclusion_relation(A!13)), tptp_fun_C_0(set_union2(relation_dom(inclusion_relation(A!13)), relation_rng(inclusion_relation(A!13))), inclusion_relation(A!13))), inclusion_relation(A!13)))) | is_reflexive_in(inclusion_relation(A!13), set_union2(relation_dom(inclusion_relation(A!13)), relation_rng(inclusion_relation(A!13))))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[86, 85])).
% 0.20/0.41 tff(88,plain,
% 0.20/0.41 (set_union2(relation_dom(inclusion_relation(A!13)), relation_rng(inclusion_relation(A!13))) = relation_field(inclusion_relation(A!13))),
% 0.20/0.41 inference(symmetry,[status(thm)],[23])).
% 0.20/0.41 tff(89,plain,
% 0.20/0.41 (is_reflexive_in(inclusion_relation(A!13), set_union2(relation_dom(inclusion_relation(A!13)), relation_rng(inclusion_relation(A!13)))) <=> is_reflexive_in(inclusion_relation(A!13), relation_field(inclusion_relation(A!13)))),
% 0.20/0.41 inference(monotonicity,[status(thm)],[88])).
% 0.20/0.41 tff(90,plain,
% 0.20/0.41 (is_reflexive_in(inclusion_relation(A!13), relation_field(inclusion_relation(A!13))) <=> is_reflexive_in(inclusion_relation(A!13), set_union2(relation_dom(inclusion_relation(A!13)), relation_rng(inclusion_relation(A!13))))),
% 0.20/0.41 inference(symmetry,[status(thm)],[89])).
% 0.20/0.41 tff(91,plain,
% 0.20/0.41 ((~is_reflexive_in(inclusion_relation(A!13), relation_field(inclusion_relation(A!13)))) <=> (~is_reflexive_in(inclusion_relation(A!13), set_union2(relation_dom(inclusion_relation(A!13)), relation_rng(inclusion_relation(A!13)))))),
% 0.20/0.41 inference(monotonicity,[status(thm)],[90])).
% 0.20/0.41 tff(92,plain,
% 0.20/0.41 (^[A: $i] : refl(((~relation(A)) | (reflexive(A) <=> is_reflexive_in(A, relation_field(A)))) <=> ((~relation(A)) | (reflexive(A) <=> is_reflexive_in(A, relation_field(A)))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(93,plain,
% 0.20/0.41 (![A: $i] : ((~relation(A)) | (reflexive(A) <=> is_reflexive_in(A, relation_field(A)))) <=> ![A: $i] : ((~relation(A)) | (reflexive(A) <=> is_reflexive_in(A, relation_field(A))))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[92])).
% 0.20/0.41 tff(94,plain,
% 0.20/0.41 (![A: $i] : ((~relation(A)) | (reflexive(A) <=> is_reflexive_in(A, relation_field(A)))) <=> ![A: $i] : ((~relation(A)) | (reflexive(A) <=> is_reflexive_in(A, relation_field(A))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(95,plain,
% 0.20/0.41 (^[A: $i] : rewrite((relation(A) => (reflexive(A) <=> is_reflexive_in(A, relation_field(A)))) <=> ((~relation(A)) | (reflexive(A) <=> is_reflexive_in(A, relation_field(A)))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(96,plain,
% 0.20/0.41 (![A: $i] : (relation(A) => (reflexive(A) <=> is_reflexive_in(A, relation_field(A)))) <=> ![A: $i] : ((~relation(A)) | (reflexive(A) <=> is_reflexive_in(A, relation_field(A))))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[95])).
% 0.20/0.41 tff(97,axiom,(![A: $i] : (relation(A) => (reflexive(A) <=> is_reflexive_in(A, relation_field(A))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d9_relat_2')).
% 0.20/0.41 tff(98,plain,
% 0.20/0.41 (![A: $i] : ((~relation(A)) | (reflexive(A) <=> is_reflexive_in(A, relation_field(A))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[97, 96])).
% 0.20/0.41 tff(99,plain,
% 0.20/0.41 (![A: $i] : ((~relation(A)) | (reflexive(A) <=> is_reflexive_in(A, relation_field(A))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[98, 94])).
% 0.20/0.41 tff(100,plain,(
% 0.20/0.41 ![A: $i] : ((~relation(A)) | (reflexive(A) <=> is_reflexive_in(A, relation_field(A))))),
% 0.20/0.41 inference(skolemize,[status(sab)],[99])).
% 0.20/0.41 tff(101,plain,
% 0.20/0.41 (![A: $i] : ((~relation(A)) | (reflexive(A) <=> is_reflexive_in(A, relation_field(A))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[100, 93])).
% 0.20/0.41 tff(102,plain,
% 0.20/0.41 (((~![A: $i] : ((~relation(A)) | (reflexive(A) <=> is_reflexive_in(A, relation_field(A))))) | ((~relation(inclusion_relation(A!13))) | (reflexive(inclusion_relation(A!13)) <=> is_reflexive_in(inclusion_relation(A!13), relation_field(inclusion_relation(A!13)))))) <=> ((~![A: $i] : ((~relation(A)) | (reflexive(A) <=> is_reflexive_in(A, relation_field(A))))) | (~relation(inclusion_relation(A!13))) | (reflexive(inclusion_relation(A!13)) <=> is_reflexive_in(inclusion_relation(A!13), relation_field(inclusion_relation(A!13)))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(103,plain,
% 0.20/0.41 ((~![A: $i] : ((~relation(A)) | (reflexive(A) <=> is_reflexive_in(A, relation_field(A))))) | ((~relation(inclusion_relation(A!13))) | (reflexive(inclusion_relation(A!13)) <=> is_reflexive_in(inclusion_relation(A!13), relation_field(inclusion_relation(A!13)))))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(104,plain,
% 0.20/0.41 ((~![A: $i] : ((~relation(A)) | (reflexive(A) <=> is_reflexive_in(A, relation_field(A))))) | (~relation(inclusion_relation(A!13))) | (reflexive(inclusion_relation(A!13)) <=> is_reflexive_in(inclusion_relation(A!13), relation_field(inclusion_relation(A!13))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[103, 102])).
% 0.20/0.41 tff(105,plain,
% 0.20/0.41 ((~relation(inclusion_relation(A!13))) | (reflexive(inclusion_relation(A!13)) <=> is_reflexive_in(inclusion_relation(A!13), relation_field(inclusion_relation(A!13))))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[104, 101])).
% 0.20/0.41 tff(106,plain,
% 0.20/0.41 (reflexive(inclusion_relation(A!13)) <=> is_reflexive_in(inclusion_relation(A!13), relation_field(inclusion_relation(A!13)))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[105, 9])).
% 0.20/0.41 tff(107,plain,
% 0.20/0.41 ((~![A: $i] : reflexive(inclusion_relation(A))) <=> (~![A: $i] : reflexive(inclusion_relation(A)))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(108,axiom,(~![A: $i] : reflexive(inclusion_relation(A))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t2_wellord2')).
% 0.20/0.41 tff(109,plain,
% 0.20/0.41 (~![A: $i] : reflexive(inclusion_relation(A))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[108, 107])).
% 0.20/0.41 tff(110,plain,
% 0.20/0.41 (~![A: $i] : reflexive(inclusion_relation(A))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[109, 107])).
% 0.20/0.41 tff(111,plain,
% 0.20/0.41 (~![A: $i] : reflexive(inclusion_relation(A))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[110, 107])).
% 0.20/0.41 tff(112,plain,
% 0.20/0.41 (~![A: $i] : reflexive(inclusion_relation(A))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[111, 107])).
% 0.20/0.41 tff(113,plain,(
% 0.20/0.41 ~reflexive(inclusion_relation(A!13))),
% 0.20/0.41 inference(skolemize,[status(sab)],[112])).
% 0.20/0.41 tff(114,plain,
% 0.20/0.41 ((~(reflexive(inclusion_relation(A!13)) <=> is_reflexive_in(inclusion_relation(A!13), relation_field(inclusion_relation(A!13))))) | reflexive(inclusion_relation(A!13)) | (~is_reflexive_in(inclusion_relation(A!13), relation_field(inclusion_relation(A!13))))),
% 0.20/0.41 inference(tautology,[status(thm)],[])).
% 0.20/0.41 tff(115,plain,
% 0.20/0.41 ((~(reflexive(inclusion_relation(A!13)) <=> is_reflexive_in(inclusion_relation(A!13), relation_field(inclusion_relation(A!13))))) | (~is_reflexive_in(inclusion_relation(A!13), relation_field(inclusion_relation(A!13))))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[114, 113])).
% 0.20/0.41 tff(116,plain,
% 0.20/0.41 (~is_reflexive_in(inclusion_relation(A!13), relation_field(inclusion_relation(A!13)))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[115, 106])).
% 0.20/0.41 tff(117,plain,
% 0.20/0.41 (~is_reflexive_in(inclusion_relation(A!13), set_union2(relation_dom(inclusion_relation(A!13)), relation_rng(inclusion_relation(A!13))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[116, 91])).
% 0.20/0.41 tff(118,plain,
% 0.20/0.41 ((~((~((~in(tptp_fun_C_0(set_union2(relation_dom(inclusion_relation(A!13)), relation_rng(inclusion_relation(A!13))), inclusion_relation(A!13)), set_union2(relation_dom(inclusion_relation(A!13)), relation_rng(inclusion_relation(A!13))))) | in(ordered_pair(tptp_fun_C_0(set_union2(relation_dom(inclusion_relation(A!13)), relation_rng(inclusion_relation(A!13))), inclusion_relation(A!13)), tptp_fun_C_0(set_union2(relation_dom(inclusion_relation(A!13)), relation_rng(inclusion_relation(A!13))), inclusion_relation(A!13))), inclusion_relation(A!13)))) | is_reflexive_in(inclusion_relation(A!13), set_union2(relation_dom(inclusion_relation(A!13)), relation_rng(inclusion_relation(A!13)))))) | (~((~in(tptp_fun_C_0(set_union2(relation_dom(inclusion_relation(A!13)), relation_rng(inclusion_relation(A!13))), inclusion_relation(A!13)), set_union2(relation_dom(inclusion_relation(A!13)), relation_rng(inclusion_relation(A!13))))) | in(ordered_pair(tptp_fun_C_0(set_union2(relation_dom(inclusion_relation(A!13)), relation_rng(inclusion_relation(A!13))), inclusion_relation(A!13)), tptp_fun_C_0(set_union2(relation_dom(inclusion_relation(A!13)), relation_rng(inclusion_relation(A!13))), inclusion_relation(A!13))), inclusion_relation(A!13)))) | is_reflexive_in(inclusion_relation(A!13), set_union2(relation_dom(inclusion_relation(A!13)), relation_rng(inclusion_relation(A!13))))),
% 0.20/0.41 inference(tautology,[status(thm)],[])).
% 0.20/0.41 tff(119,plain,
% 0.20/0.41 (~((~in(tptp_fun_C_0(set_union2(relation_dom(inclusion_relation(A!13)), relation_rng(inclusion_relation(A!13))), inclusion_relation(A!13)), set_union2(relation_dom(inclusion_relation(A!13)), relation_rng(inclusion_relation(A!13))))) | in(ordered_pair(tptp_fun_C_0(set_union2(relation_dom(inclusion_relation(A!13)), relation_rng(inclusion_relation(A!13))), inclusion_relation(A!13)), tptp_fun_C_0(set_union2(relation_dom(inclusion_relation(A!13)), relation_rng(inclusion_relation(A!13))), inclusion_relation(A!13))), inclusion_relation(A!13)))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[118, 117, 87])).
% 0.20/0.41 tff(120,plain,
% 0.20/0.41 (((~in(tptp_fun_C_0(set_union2(relation_dom(inclusion_relation(A!13)), relation_rng(inclusion_relation(A!13))), inclusion_relation(A!13)), set_union2(relation_dom(inclusion_relation(A!13)), relation_rng(inclusion_relation(A!13))))) | in(ordered_pair(tptp_fun_C_0(set_union2(relation_dom(inclusion_relation(A!13)), relation_rng(inclusion_relation(A!13))), inclusion_relation(A!13)), tptp_fun_C_0(set_union2(relation_dom(inclusion_relation(A!13)), relation_rng(inclusion_relation(A!13))), inclusion_relation(A!13))), inclusion_relation(A!13))) | in(tptp_fun_C_0(set_union2(relation_dom(inclusion_relation(A!13)), relation_rng(inclusion_relation(A!13))), inclusion_relation(A!13)), set_union2(relation_dom(inclusion_relation(A!13)), relation_rng(inclusion_relation(A!13))))),
% 0.20/0.41 inference(tautology,[status(thm)],[])).
% 0.20/0.41 tff(121,plain,
% 0.20/0.41 (in(tptp_fun_C_0(set_union2(relation_dom(inclusion_relation(A!13)), relation_rng(inclusion_relation(A!13))), inclusion_relation(A!13)), set_union2(relation_dom(inclusion_relation(A!13)), relation_rng(inclusion_relation(A!13))))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[120, 119])).
% 0.20/0.41 tff(122,plain,
% 0.20/0.41 (in(tptp_fun_C_0(set_union2(relation_dom(inclusion_relation(A!13)), relation_rng(inclusion_relation(A!13))), inclusion_relation(A!13)), A!13)),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[121, 58])).
% 0.20/0.41 tff(123,plain,
% 0.20/0.41 (((~(relation_field(inclusion_relation(A!13)) = A!13)) | (~![C: $i, D: $i] : ((~in(C, A!13)) | (~in(D, A!13)) | (in(ordered_pair(C, D), inclusion_relation(A!13)) <=> subset(C, D))))) | ![C: $i, D: $i] : ((~in(C, A!13)) | (~in(D, A!13)) | (in(ordered_pair(C, D), inclusion_relation(A!13)) <=> subset(C, D)))),
% 0.20/0.41 inference(tautology,[status(thm)],[])).
% 0.20/0.41 tff(124,plain,
% 0.20/0.41 (![C: $i, D: $i] : ((~in(C, A!13)) | (~in(D, A!13)) | (in(ordered_pair(C, D), inclusion_relation(A!13)) <=> subset(C, D)))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[123, 52])).
% 0.20/0.41 tff(125,plain,
% 0.20/0.41 (((~![C: $i, D: $i] : ((~in(C, A!13)) | (~in(D, A!13)) | (in(ordered_pair(C, D), inclusion_relation(A!13)) <=> subset(C, D)))) | ((~in(tptp_fun_C_0(set_union2(relation_dom(inclusion_relation(A!13)), relation_rng(inclusion_relation(A!13))), inclusion_relation(A!13)), A!13)) | (in(ordered_pair(tptp_fun_C_0(set_union2(relation_dom(inclusion_relation(A!13)), relation_rng(inclusion_relation(A!13))), inclusion_relation(A!13)), tptp_fun_C_0(set_union2(relation_dom(inclusion_relation(A!13)), relation_rng(inclusion_relation(A!13))), inclusion_relation(A!13))), inclusion_relation(A!13)) <=> subset(tptp_fun_C_0(set_union2(relation_dom(inclusion_relation(A!13)), relation_rng(inclusion_relation(A!13))), inclusion_relation(A!13)), tptp_fun_C_0(set_union2(relation_dom(inclusion_relation(A!13)), relation_rng(inclusion_relation(A!13))), inclusion_relation(A!13)))))) <=> ((~![C: $i, D: $i] : ((~in(C, A!13)) | (~in(D, A!13)) | (in(ordered_pair(C, D), inclusion_relation(A!13)) <=> subset(C, D)))) | (~in(tptp_fun_C_0(set_union2(relation_dom(inclusion_relation(A!13)), relation_rng(inclusion_relation(A!13))), inclusion_relation(A!13)), A!13)) | (in(ordered_pair(tptp_fun_C_0(set_union2(relation_dom(inclusion_relation(A!13)), relation_rng(inclusion_relation(A!13))), inclusion_relation(A!13)), tptp_fun_C_0(set_union2(relation_dom(inclusion_relation(A!13)), relation_rng(inclusion_relation(A!13))), inclusion_relation(A!13))), inclusion_relation(A!13)) <=> subset(tptp_fun_C_0(set_union2(relation_dom(inclusion_relation(A!13)), relation_rng(inclusion_relation(A!13))), inclusion_relation(A!13)), tptp_fun_C_0(set_union2(relation_dom(inclusion_relation(A!13)), relation_rng(inclusion_relation(A!13))), inclusion_relation(A!13)))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(126,plain,
% 0.20/0.41 (((~in(tptp_fun_C_0(set_union2(relation_dom(inclusion_relation(A!13)), relation_rng(inclusion_relation(A!13))), inclusion_relation(A!13)), A!13)) | (~in(tptp_fun_C_0(set_union2(relation_dom(inclusion_relation(A!13)), relation_rng(inclusion_relation(A!13))), inclusion_relation(A!13)), A!13)) | (in(ordered_pair(tptp_fun_C_0(set_union2(relation_dom(inclusion_relation(A!13)), relation_rng(inclusion_relation(A!13))), inclusion_relation(A!13)), tptp_fun_C_0(set_union2(relation_dom(inclusion_relation(A!13)), relation_rng(inclusion_relation(A!13))), inclusion_relation(A!13))), inclusion_relation(A!13)) <=> subset(tptp_fun_C_0(set_union2(relation_dom(inclusion_relation(A!13)), relation_rng(inclusion_relation(A!13))), inclusion_relation(A!13)), tptp_fun_C_0(set_union2(relation_dom(inclusion_relation(A!13)), relation_rng(inclusion_relation(A!13))), inclusion_relation(A!13))))) <=> ((~in(tptp_fun_C_0(set_union2(relation_dom(inclusion_relation(A!13)), relation_rng(inclusion_relation(A!13))), inclusion_relation(A!13)), A!13)) | (in(ordered_pair(tptp_fun_C_0(set_union2(relation_dom(inclusion_relation(A!13)), relation_rng(inclusion_relation(A!13))), inclusion_relation(A!13)), tptp_fun_C_0(set_union2(relation_dom(inclusion_relation(A!13)), relation_rng(inclusion_relation(A!13))), inclusion_relation(A!13))), inclusion_relation(A!13)) <=> subset(tptp_fun_C_0(set_union2(relation_dom(inclusion_relation(A!13)), relation_rng(inclusion_relation(A!13))), inclusion_relation(A!13)), tptp_fun_C_0(set_union2(relation_dom(inclusion_relation(A!13)), relation_rng(inclusion_relation(A!13))), inclusion_relation(A!13)))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(127,plain,
% 0.20/0.41 (((~![C: $i, D: $i] : ((~in(C, A!13)) | (~in(D, A!13)) | (in(ordered_pair(C, D), inclusion_relation(A!13)) <=> subset(C, D)))) | ((~in(tptp_fun_C_0(set_union2(relation_dom(inclusion_relation(A!13)), relation_rng(inclusion_relation(A!13))), inclusion_relation(A!13)), A!13)) | (~in(tptp_fun_C_0(set_union2(relation_dom(inclusion_relation(A!13)), relation_rng(inclusion_relation(A!13))), inclusion_relation(A!13)), A!13)) | (in(ordered_pair(tptp_fun_C_0(set_union2(relation_dom(inclusion_relation(A!13)), relation_rng(inclusion_relation(A!13))), inclusion_relation(A!13)), tptp_fun_C_0(set_union2(relation_dom(inclusion_relation(A!13)), relation_rng(inclusion_relation(A!13))), inclusion_relation(A!13))), inclusion_relation(A!13)) <=> subset(tptp_fun_C_0(set_union2(relation_dom(inclusion_relation(A!13)), relation_rng(inclusion_relation(A!13))), inclusion_relation(A!13)), tptp_fun_C_0(set_union2(relation_dom(inclusion_relation(A!13)), relation_rng(inclusion_relation(A!13))), inclusion_relation(A!13)))))) <=> ((~![C: $i, D: $i] : ((~in(C, A!13)) | (~in(D, A!13)) | (in(ordered_pair(C, D), inclusion_relation(A!13)) <=> subset(C, D)))) | ((~in(tptp_fun_C_0(set_union2(relation_dom(inclusion_relation(A!13)), relation_rng(inclusion_relation(A!13))), inclusion_relation(A!13)), A!13)) | (in(ordered_pair(tptp_fun_C_0(set_union2(relation_dom(inclusion_relation(A!13)), relation_rng(inclusion_relation(A!13))), inclusion_relation(A!13)), tptp_fun_C_0(set_union2(relation_dom(inclusion_relation(A!13)), relation_rng(inclusion_relation(A!13))), inclusion_relation(A!13))), inclusion_relation(A!13)) <=> subset(tptp_fun_C_0(set_union2(relation_dom(inclusion_relation(A!13)), relation_rng(inclusion_relation(A!13))), inclusion_relation(A!13)), tptp_fun_C_0(set_union2(relation_dom(inclusion_relation(A!13)), relation_rng(inclusion_relation(A!13))), inclusion_relation(A!13))))))),
% 0.20/0.41 inference(monotonicity,[status(thm)],[126])).
% 0.20/0.41 tff(128,plain,
% 0.20/0.41 (((~![C: $i, D: $i] : ((~in(C, A!13)) | (~in(D, A!13)) | (in(ordered_pair(C, D), inclusion_relation(A!13)) <=> subset(C, D)))) | ((~in(tptp_fun_C_0(set_union2(relation_dom(inclusion_relation(A!13)), relation_rng(inclusion_relation(A!13))), inclusion_relation(A!13)), A!13)) | (~in(tptp_fun_C_0(set_union2(relation_dom(inclusion_relation(A!13)), relation_rng(inclusion_relation(A!13))), inclusion_relation(A!13)), A!13)) | (in(ordered_pair(tptp_fun_C_0(set_union2(relation_dom(inclusion_relation(A!13)), relation_rng(inclusion_relation(A!13))), inclusion_relation(A!13)), tptp_fun_C_0(set_union2(relation_dom(inclusion_relation(A!13)), relation_rng(inclusion_relation(A!13))), inclusion_relation(A!13))), inclusion_relation(A!13)) <=> subset(tptp_fun_C_0(set_union2(relation_dom(inclusion_relation(A!13)), relation_rng(inclusion_relation(A!13))), inclusion_relation(A!13)), tptp_fun_C_0(set_union2(relation_dom(inclusion_relation(A!13)), relation_rng(inclusion_relation(A!13))), inclusion_relation(A!13)))))) <=> ((~![C: $i, D: $i] : ((~in(C, A!13)) | (~in(D, A!13)) | (in(ordered_pair(C, D), inclusion_relation(A!13)) <=> subset(C, D)))) | (~in(tptp_fun_C_0(set_union2(relation_dom(inclusion_relation(A!13)), relation_rng(inclusion_relation(A!13))), inclusion_relation(A!13)), A!13)) | (in(ordered_pair(tptp_fun_C_0(set_union2(relation_dom(inclusion_relation(A!13)), relation_rng(inclusion_relation(A!13))), inclusion_relation(A!13)), tptp_fun_C_0(set_union2(relation_dom(inclusion_relation(A!13)), relation_rng(inclusion_relation(A!13))), inclusion_relation(A!13))), inclusion_relation(A!13)) <=> subset(tptp_fun_C_0(set_union2(relation_dom(inclusion_relation(A!13)), relation_rng(inclusion_relation(A!13))), inclusion_relation(A!13)), tptp_fun_C_0(set_union2(relation_dom(inclusion_relation(A!13)), relation_rng(inclusion_relation(A!13))), inclusion_relation(A!13)))))),
% 0.20/0.42 inference(transitivity,[status(thm)],[127, 125])).
% 0.20/0.42 tff(129,plain,
% 0.20/0.42 ((~![C: $i, D: $i] : ((~in(C, A!13)) | (~in(D, A!13)) | (in(ordered_pair(C, D), inclusion_relation(A!13)) <=> subset(C, D)))) | ((~in(tptp_fun_C_0(set_union2(relation_dom(inclusion_relation(A!13)), relation_rng(inclusion_relation(A!13))), inclusion_relation(A!13)), A!13)) | (~in(tptp_fun_C_0(set_union2(relation_dom(inclusion_relation(A!13)), relation_rng(inclusion_relation(A!13))), inclusion_relation(A!13)), A!13)) | (in(ordered_pair(tptp_fun_C_0(set_union2(relation_dom(inclusion_relation(A!13)), relation_rng(inclusion_relation(A!13))), inclusion_relation(A!13)), tptp_fun_C_0(set_union2(relation_dom(inclusion_relation(A!13)), relation_rng(inclusion_relation(A!13))), inclusion_relation(A!13))), inclusion_relation(A!13)) <=> subset(tptp_fun_C_0(set_union2(relation_dom(inclusion_relation(A!13)), relation_rng(inclusion_relation(A!13))), inclusion_relation(A!13)), tptp_fun_C_0(set_union2(relation_dom(inclusion_relation(A!13)), relation_rng(inclusion_relation(A!13))), inclusion_relation(A!13)))))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(130,plain,
% 0.20/0.42 ((~![C: $i, D: $i] : ((~in(C, A!13)) | (~in(D, A!13)) | (in(ordered_pair(C, D), inclusion_relation(A!13)) <=> subset(C, D)))) | (~in(tptp_fun_C_0(set_union2(relation_dom(inclusion_relation(A!13)), relation_rng(inclusion_relation(A!13))), inclusion_relation(A!13)), A!13)) | (in(ordered_pair(tptp_fun_C_0(set_union2(relation_dom(inclusion_relation(A!13)), relation_rng(inclusion_relation(A!13))), inclusion_relation(A!13)), tptp_fun_C_0(set_union2(relation_dom(inclusion_relation(A!13)), relation_rng(inclusion_relation(A!13))), inclusion_relation(A!13))), inclusion_relation(A!13)) <=> subset(tptp_fun_C_0(set_union2(relation_dom(inclusion_relation(A!13)), relation_rng(inclusion_relation(A!13))), inclusion_relation(A!13)), tptp_fun_C_0(set_union2(relation_dom(inclusion_relation(A!13)), relation_rng(inclusion_relation(A!13))), inclusion_relation(A!13))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[129, 128])).
% 0.20/0.42 tff(131,plain,
% 0.20/0.42 ((~in(tptp_fun_C_0(set_union2(relation_dom(inclusion_relation(A!13)), relation_rng(inclusion_relation(A!13))), inclusion_relation(A!13)), A!13)) | (in(ordered_pair(tptp_fun_C_0(set_union2(relation_dom(inclusion_relation(A!13)), relation_rng(inclusion_relation(A!13))), inclusion_relation(A!13)), tptp_fun_C_0(set_union2(relation_dom(inclusion_relation(A!13)), relation_rng(inclusion_relation(A!13))), inclusion_relation(A!13))), inclusion_relation(A!13)) <=> subset(tptp_fun_C_0(set_union2(relation_dom(inclusion_relation(A!13)), relation_rng(inclusion_relation(A!13))), inclusion_relation(A!13)), tptp_fun_C_0(set_union2(relation_dom(inclusion_relation(A!13)), relation_rng(inclusion_relation(A!13))), inclusion_relation(A!13))))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[130, 124])).
% 0.20/0.42 tff(132,plain,
% 0.20/0.42 (in(ordered_pair(tptp_fun_C_0(set_union2(relation_dom(inclusion_relation(A!13)), relation_rng(inclusion_relation(A!13))), inclusion_relation(A!13)), tptp_fun_C_0(set_union2(relation_dom(inclusion_relation(A!13)), relation_rng(inclusion_relation(A!13))), inclusion_relation(A!13))), inclusion_relation(A!13)) <=> subset(tptp_fun_C_0(set_union2(relation_dom(inclusion_relation(A!13)), relation_rng(inclusion_relation(A!13))), inclusion_relation(A!13)), tptp_fun_C_0(set_union2(relation_dom(inclusion_relation(A!13)), relation_rng(inclusion_relation(A!13))), inclusion_relation(A!13)))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[131, 122])).
% 0.20/0.42 tff(133,plain,
% 0.20/0.42 (((~in(tptp_fun_C_0(set_union2(relation_dom(inclusion_relation(A!13)), relation_rng(inclusion_relation(A!13))), inclusion_relation(A!13)), set_union2(relation_dom(inclusion_relation(A!13)), relation_rng(inclusion_relation(A!13))))) | in(ordered_pair(tptp_fun_C_0(set_union2(relation_dom(inclusion_relation(A!13)), relation_rng(inclusion_relation(A!13))), inclusion_relation(A!13)), tptp_fun_C_0(set_union2(relation_dom(inclusion_relation(A!13)), relation_rng(inclusion_relation(A!13))), inclusion_relation(A!13))), inclusion_relation(A!13))) | (~in(ordered_pair(tptp_fun_C_0(set_union2(relation_dom(inclusion_relation(A!13)), relation_rng(inclusion_relation(A!13))), inclusion_relation(A!13)), tptp_fun_C_0(set_union2(relation_dom(inclusion_relation(A!13)), relation_rng(inclusion_relation(A!13))), inclusion_relation(A!13))), inclusion_relation(A!13)))),
% 0.20/0.42 inference(tautology,[status(thm)],[])).
% 0.20/0.42 tff(134,plain,
% 0.20/0.42 (~in(ordered_pair(tptp_fun_C_0(set_union2(relation_dom(inclusion_relation(A!13)), relation_rng(inclusion_relation(A!13))), inclusion_relation(A!13)), tptp_fun_C_0(set_union2(relation_dom(inclusion_relation(A!13)), relation_rng(inclusion_relation(A!13))), inclusion_relation(A!13))), inclusion_relation(A!13))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[133, 119])).
% 0.20/0.42 tff(135,plain,
% 0.20/0.42 ((~(in(ordered_pair(tptp_fun_C_0(set_union2(relation_dom(inclusion_relation(A!13)), relation_rng(inclusion_relation(A!13))), inclusion_relation(A!13)), tptp_fun_C_0(set_union2(relation_dom(inclusion_relation(A!13)), relation_rng(inclusion_relation(A!13))), inclusion_relation(A!13))), inclusion_relation(A!13)) <=> subset(tptp_fun_C_0(set_union2(relation_dom(inclusion_relation(A!13)), relation_rng(inclusion_relation(A!13))), inclusion_relation(A!13)), tptp_fun_C_0(set_union2(relation_dom(inclusion_relation(A!13)), relation_rng(inclusion_relation(A!13))), inclusion_relation(A!13))))) | in(ordered_pair(tptp_fun_C_0(set_union2(relation_dom(inclusion_relation(A!13)), relation_rng(inclusion_relation(A!13))), inclusion_relation(A!13)), tptp_fun_C_0(set_union2(relation_dom(inclusion_relation(A!13)), relation_rng(inclusion_relation(A!13))), inclusion_relation(A!13))), inclusion_relation(A!13)) | (~subset(tptp_fun_C_0(set_union2(relation_dom(inclusion_relation(A!13)), relation_rng(inclusion_relation(A!13))), inclusion_relation(A!13)), tptp_fun_C_0(set_union2(relation_dom(inclusion_relation(A!13)), relation_rng(inclusion_relation(A!13))), inclusion_relation(A!13))))),
% 0.20/0.42 inference(tautology,[status(thm)],[])).
% 0.20/0.42 tff(136,plain,
% 0.20/0.42 ((~(in(ordered_pair(tptp_fun_C_0(set_union2(relation_dom(inclusion_relation(A!13)), relation_rng(inclusion_relation(A!13))), inclusion_relation(A!13)), tptp_fun_C_0(set_union2(relation_dom(inclusion_relation(A!13)), relation_rng(inclusion_relation(A!13))), inclusion_relation(A!13))), inclusion_relation(A!13)) <=> subset(tptp_fun_C_0(set_union2(relation_dom(inclusion_relation(A!13)), relation_rng(inclusion_relation(A!13))), inclusion_relation(A!13)), tptp_fun_C_0(set_union2(relation_dom(inclusion_relation(A!13)), relation_rng(inclusion_relation(A!13))), inclusion_relation(A!13))))) | (~subset(tptp_fun_C_0(set_union2(relation_dom(inclusion_relation(A!13)), relation_rng(inclusion_relation(A!13))), inclusion_relation(A!13)), tptp_fun_C_0(set_union2(relation_dom(inclusion_relation(A!13)), relation_rng(inclusion_relation(A!13))), inclusion_relation(A!13))))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[135, 134])).
% 0.20/0.42 tff(137,plain,
% 0.20/0.42 (~subset(tptp_fun_C_0(set_union2(relation_dom(inclusion_relation(A!13)), relation_rng(inclusion_relation(A!13))), inclusion_relation(A!13)), tptp_fun_C_0(set_union2(relation_dom(inclusion_relation(A!13)), relation_rng(inclusion_relation(A!13))), inclusion_relation(A!13)))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[136, 132])).
% 0.20/0.42 tff(138,plain,
% 0.20/0.42 (^[A: $i] : refl(subset(A, A) <=> subset(A, A))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(139,plain,
% 0.20/0.42 (![A: $i] : subset(A, A) <=> ![A: $i] : subset(A, A)),
% 0.20/0.42 inference(quant_intro,[status(thm)],[138])).
% 0.20/0.42 tff(140,plain,
% 0.20/0.42 (![A: $i] : subset(A, A) <=> ![A: $i] : subset(A, A)),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(141,plain,
% 0.20/0.42 (![A: $i, B: $i] : subset(A, A) <=> ![A: $i] : subset(A, A)),
% 0.20/0.42 inference(elim_unused_vars,[status(thm)],[])).
% 0.20/0.42 tff(142,axiom,(![A: $i, B: $i] : subset(A, A)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','reflexivity_r1_tarski')).
% 0.20/0.42 tff(143,plain,
% 0.20/0.42 (![A: $i] : subset(A, A)),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[142, 141])).
% 0.20/0.42 tff(144,plain,
% 0.20/0.42 (![A: $i] : subset(A, A)),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[143, 140])).
% 0.20/0.42 tff(145,plain,(
% 0.20/0.42 ![A: $i] : subset(A, A)),
% 0.20/0.42 inference(skolemize,[status(sab)],[144])).
% 0.20/0.42 tff(146,plain,
% 0.20/0.42 (![A: $i] : subset(A, A)),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[145, 139])).
% 0.20/0.42 tff(147,plain,
% 0.20/0.42 ((~![A: $i] : subset(A, A)) | subset(tptp_fun_C_0(set_union2(relation_dom(inclusion_relation(A!13)), relation_rng(inclusion_relation(A!13))), inclusion_relation(A!13)), tptp_fun_C_0(set_union2(relation_dom(inclusion_relation(A!13)), relation_rng(inclusion_relation(A!13))), inclusion_relation(A!13)))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(148,plain,
% 0.20/0.42 ($false),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[147, 146, 137])).
% 0.20/0.42 % SZS output end Proof
% 0.20/0.42 % E exiting
%------------------------------------------------------------------------------