%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SEU270+1 : TPTP v9.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n009.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:27:27 AM UTC 2025
% Result : Theorem 0.19s 0.38s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SEU270+1 : TPTP v9.0.0. Released v3.3.0.
% 0.03/0.11 % Command : run_E %s %d THM
% 0.11/0.32 % Computer : n009.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Fri Jun 20 06:33:18 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.19/0.38 % SZS status Theorem
% 0.19/0.38 % SZS output start Proof
% 0.19/0.38 tff(ordinal_subset_type, type, (
% 0.19/0.38 ordinal_subset: ( $i * $i ) > $o)).
% 0.19/0.38 tff(tptp_fun_D_2_type, type, (
% 0.19/0.38 tptp_fun_D_2: ( $i * $i ) > $i)).
% 0.19/0.38 tff(inclusion_relation_type, type, (
% 0.19/0.38 inclusion_relation: $i > $i)).
% 0.19/0.38 tff(tptp_fun_A_14_type, type, (
% 0.19/0.38 tptp_fun_A_14: $i)).
% 0.19/0.38 tff(set_union2_type, type, (
% 0.19/0.38 set_union2: ( $i * $i ) > $i)).
% 0.19/0.38 tff(relation_rng_type, type, (
% 0.19/0.38 relation_rng: $i > $i)).
% 0.19/0.38 tff(relation_dom_type, type, (
% 0.19/0.38 relation_dom: $i > $i)).
% 0.19/0.38 tff(tptp_fun_C_3_type, type, (
% 0.19/0.38 tptp_fun_C_3: ( $i * $i ) > $i)).
% 0.19/0.38 tff(subset_type, type, (
% 0.19/0.38 subset: ( $i * $i ) > $o)).
% 0.19/0.38 tff(ordinal_type, type, (
% 0.19/0.38 ordinal: $i > $o)).
% 0.19/0.38 tff(relation_field_type, type, (
% 0.19/0.38 relation_field: $i > $i)).
% 0.19/0.38 tff(in_type, type, (
% 0.19/0.38 in: ( $i * $i ) > $o)).
% 0.19/0.38 tff(ordered_pair_type, type, (
% 0.19/0.38 ordered_pair: ( $i * $i ) > $i)).
% 0.19/0.38 tff(relation_type, type, (
% 0.19/0.38 relation: $i > $o)).
% 0.19/0.38 tff(tptp_fun_D_0_type, type, (
% 0.19/0.38 tptp_fun_D_0: ( $i * $i ) > $i)).
% 0.19/0.38 tff(tptp_fun_C_1_type, type, (
% 0.19/0.38 tptp_fun_C_1: ( $i * $i ) > $i)).
% 0.19/0.38 tff(connected_type, type, (
% 0.19/0.38 connected: $i > $o)).
% 0.19/0.38 tff(is_connected_in_type, type, (
% 0.19/0.38 is_connected_in: ( $i * $i ) > $o)).
% 0.19/0.38 tff(1,plain,
% 0.19/0.38 (^[A: $i] : refl(relation(inclusion_relation(A)) <=> relation(inclusion_relation(A)))),
% 0.19/0.38 inference(bind,[status(th)],[])).
% 0.19/0.38 tff(2,plain,
% 0.19/0.38 (![A: $i] : relation(inclusion_relation(A)) <=> ![A: $i] : relation(inclusion_relation(A))),
% 0.19/0.38 inference(quant_intro,[status(thm)],[1])).
% 0.19/0.38 tff(3,plain,
% 0.19/0.38 (![A: $i] : relation(inclusion_relation(A)) <=> ![A: $i] : relation(inclusion_relation(A))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(4,axiom,(![A: $i] : relation(inclusion_relation(A))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_k1_wellord2')).
% 0.19/0.38 tff(5,plain,
% 0.19/0.38 (![A: $i] : relation(inclusion_relation(A))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.19/0.38 tff(6,plain,(
% 0.19/0.38 ![A: $i] : relation(inclusion_relation(A))),
% 0.19/0.38 inference(skolemize,[status(sab)],[5])).
% 0.19/0.38 tff(7,plain,
% 0.19/0.38 (![A: $i] : relation(inclusion_relation(A))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.19/0.38 tff(8,plain,
% 0.19/0.38 ((~![A: $i] : relation(inclusion_relation(A))) | relation(inclusion_relation(A!14))),
% 0.19/0.38 inference(quant_inst,[status(thm)],[])).
% 0.19/0.38 tff(9,plain,
% 0.19/0.38 (relation(inclusion_relation(A!14))),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.19/0.38 tff(10,plain,
% 0.19/0.38 (^[A: $i, B: $i] : rewrite(((~relation(B)) | (~((~((~(B = inclusion_relation(A))) | (~((~(relation_field(B) = A)) | (~![C: $i, D: $i] : ((in(ordered_pair(C, D), B) <=> subset(C, D)) | (~in(C, A)) | (~in(D, A)))))))) | (~((B = inclusion_relation(A)) | (~(relation_field(B) = A)) | (~((in(ordered_pair(tptp_fun_C_1(B, A), tptp_fun_D_0(B, A)), B) <=> subset(tptp_fun_C_1(B, A), tptp_fun_D_0(B, A))) | (~in(tptp_fun_C_1(B, A), A)) | (~in(tptp_fun_D_0(B, A), A))))))))) <=> ((~relation(B)) | (~((~((B = inclusion_relation(A)) | (~(relation_field(B) = A)) | (~((in(ordered_pair(tptp_fun_C_1(B, A), tptp_fun_D_0(B, A)), B) <=> subset(tptp_fun_C_1(B, A), tptp_fun_D_0(B, A))) | (~in(tptp_fun_C_1(B, A), A)) | (~in(tptp_fun_D_0(B, A), A)))))) | (~((~(B = inclusion_relation(A))) | (~((~(relation_field(B) = A)) | (~![C: $i, D: $i] : ((in(ordered_pair(C, D), B) <=> subset(C, D)) | (~in(C, A)) | (~in(D, A))))))))))))),
% 0.19/0.38 inference(bind,[status(th)],[])).
% 0.19/0.38 tff(11,plain,
% 0.19/0.38 (![A: $i, B: $i] : ((~relation(B)) | (~((~((~(B = inclusion_relation(A))) | (~((~(relation_field(B) = A)) | (~![C: $i, D: $i] : ((in(ordered_pair(C, D), B) <=> subset(C, D)) | (~in(C, A)) | (~in(D, A)))))))) | (~((B = inclusion_relation(A)) | (~(relation_field(B) = A)) | (~((in(ordered_pair(tptp_fun_C_1(B, A), tptp_fun_D_0(B, A)), B) <=> subset(tptp_fun_C_1(B, A), tptp_fun_D_0(B, A))) | (~in(tptp_fun_C_1(B, A), A)) | (~in(tptp_fun_D_0(B, A), A))))))))) <=> ![A: $i, B: $i] : ((~relation(B)) | (~((~((B = inclusion_relation(A)) | (~(relation_field(B) = A)) | (~((in(ordered_pair(tptp_fun_C_1(B, A), tptp_fun_D_0(B, A)), B) <=> subset(tptp_fun_C_1(B, A), tptp_fun_D_0(B, A))) | (~in(tptp_fun_C_1(B, A), A)) | (~in(tptp_fun_D_0(B, A), A)))))) | (~((~(B = inclusion_relation(A))) | (~((~(relation_field(B) = A)) | (~![C: $i, D: $i] : ((in(ordered_pair(C, D), B) <=> subset(C, D)) | (~in(C, A)) | (~in(D, A)))))))))))),
% 0.19/0.38 inference(quant_intro,[status(thm)],[10])).
% 0.19/0.38 tff(12,plain,
% 0.19/0.38 (^[A: $i, B: $i] : refl(((~relation(B)) | (~((~((~(B = inclusion_relation(A))) | (~((~(relation_field(B) = A)) | (~![C: $i, D: $i] : ((in(ordered_pair(C, D), B) <=> subset(C, D)) | (~in(C, A)) | (~in(D, A)))))))) | (~((B = inclusion_relation(A)) | (~(relation_field(B) = A)) | (~((in(ordered_pair(tptp_fun_C_1(B, A), tptp_fun_D_0(B, A)), B) <=> subset(tptp_fun_C_1(B, A), tptp_fun_D_0(B, A))) | (~in(tptp_fun_C_1(B, A), A)) | (~in(tptp_fun_D_0(B, A), A))))))))) <=> ((~relation(B)) | (~((~((~(B = inclusion_relation(A))) | (~((~(relation_field(B) = A)) | (~![C: $i, D: $i] : ((in(ordered_pair(C, D), B) <=> subset(C, D)) | (~in(C, A)) | (~in(D, A)))))))) | (~((B = inclusion_relation(A)) | (~(relation_field(B) = A)) | (~((in(ordered_pair(tptp_fun_C_1(B, A), tptp_fun_D_0(B, A)), B) <=> subset(tptp_fun_C_1(B, A), tptp_fun_D_0(B, A))) | (~in(tptp_fun_C_1(B, A), A)) | (~in(tptp_fun_D_0(B, A), A))))))))))),
% 0.19/0.38 inference(bind,[status(th)],[])).
% 0.19/0.38 tff(13,plain,
% 0.19/0.38 (![A: $i, B: $i] : ((~relation(B)) | (~((~((~(B = inclusion_relation(A))) | (~((~(relation_field(B) = A)) | (~![C: $i, D: $i] : ((in(ordered_pair(C, D), B) <=> subset(C, D)) | (~in(C, A)) | (~in(D, A)))))))) | (~((B = inclusion_relation(A)) | (~(relation_field(B) = A)) | (~((in(ordered_pair(tptp_fun_C_1(B, A), tptp_fun_D_0(B, A)), B) <=> subset(tptp_fun_C_1(B, A), tptp_fun_D_0(B, A))) | (~in(tptp_fun_C_1(B, A), A)) | (~in(tptp_fun_D_0(B, A), A))))))))) <=> ![A: $i, B: $i] : ((~relation(B)) | (~((~((~(B = inclusion_relation(A))) | (~((~(relation_field(B) = A)) | (~![C: $i, D: $i] : ((in(ordered_pair(C, D), B) <=> subset(C, D)) | (~in(C, A)) | (~in(D, A)))))))) | (~((B = inclusion_relation(A)) | (~(relation_field(B) = A)) | (~((in(ordered_pair(tptp_fun_C_1(B, A), tptp_fun_D_0(B, A)), B) <=> subset(tptp_fun_C_1(B, A), tptp_fun_D_0(B, A))) | (~in(tptp_fun_C_1(B, A), A)) | (~in(tptp_fun_D_0(B, A), A)))))))))),
% 0.19/0.38 inference(quant_intro,[status(thm)],[12])).
% 0.19/0.38 tff(14,plain,
% 0.19/0.38 (^[A: $i, B: $i] : rewrite(((~relation(B)) | (~((~((~(B = inclusion_relation(A))) | (~((~(relation_field(B) = A)) | (~![C: $i, D: $i] : ((in(ordered_pair(C, D), B) <=> subset(C, D)) | (~in(C, A)) | (~in(D, A)))))))) | (~((B = inclusion_relation(A)) | (~(relation_field(B) = A)) | (~((in(ordered_pair(tptp_fun_C_1(B, A), tptp_fun_D_0(B, A)), B) <=> subset(tptp_fun_C_1(B, A), tptp_fun_D_0(B, A))) | (~in(tptp_fun_C_1(B, A), A)) | (~in(tptp_fun_D_0(B, A), A))))))))) <=> ((~relation(B)) | (~((~((~(B = inclusion_relation(A))) | (~((~(relation_field(B) = A)) | (~![C: $i, D: $i] : ((in(ordered_pair(C, D), B) <=> subset(C, D)) | (~in(C, A)) | (~in(D, A)))))))) | (~((B = inclusion_relation(A)) | (~(relation_field(B) = A)) | (~((in(ordered_pair(tptp_fun_C_1(B, A), tptp_fun_D_0(B, A)), B) <=> subset(tptp_fun_C_1(B, A), tptp_fun_D_0(B, A))) | (~in(tptp_fun_C_1(B, A), A)) | (~in(tptp_fun_D_0(B, A), A))))))))))),
% 0.19/0.38 inference(bind,[status(th)],[])).
% 0.19/0.38 tff(15,plain,
% 0.19/0.38 (![A: $i, B: $i] : ((~relation(B)) | (~((~((~(B = inclusion_relation(A))) | (~((~(relation_field(B) = A)) | (~![C: $i, D: $i] : ((in(ordered_pair(C, D), B) <=> subset(C, D)) | (~in(C, A)) | (~in(D, A)))))))) | (~((B = inclusion_relation(A)) | (~(relation_field(B) = A)) | (~((in(ordered_pair(tptp_fun_C_1(B, A), tptp_fun_D_0(B, A)), B) <=> subset(tptp_fun_C_1(B, A), tptp_fun_D_0(B, A))) | (~in(tptp_fun_C_1(B, A), A)) | (~in(tptp_fun_D_0(B, A), A))))))))) <=> ![A: $i, B: $i] : ((~relation(B)) | (~((~((~(B = inclusion_relation(A))) | (~((~(relation_field(B) = A)) | (~![C: $i, D: $i] : ((in(ordered_pair(C, D), B) <=> subset(C, D)) | (~in(C, A)) | (~in(D, A)))))))) | (~((B = inclusion_relation(A)) | (~(relation_field(B) = A)) | (~((in(ordered_pair(tptp_fun_C_1(B, A), tptp_fun_D_0(B, A)), B) <=> subset(tptp_fun_C_1(B, A), tptp_fun_D_0(B, A))) | (~in(tptp_fun_C_1(B, A), A)) | (~in(tptp_fun_D_0(B, A), A)))))))))),
% 0.19/0.38 inference(quant_intro,[status(thm)],[14])).
% 0.19/0.38 tff(16,plain,
% 0.19/0.38 (![A: $i, B: $i] : ((~relation(B)) | (~((~((~(B = inclusion_relation(A))) | (~((~(relation_field(B) = A)) | (~![C: $i, D: $i] : ((in(ordered_pair(C, D), B) <=> subset(C, D)) | (~in(C, A)) | (~in(D, A)))))))) | (~((B = inclusion_relation(A)) | (~(relation_field(B) = A)) | (~((in(ordered_pair(tptp_fun_C_1(B, A), tptp_fun_D_0(B, A)), B) <=> subset(tptp_fun_C_1(B, A), tptp_fun_D_0(B, A))) | (~in(tptp_fun_C_1(B, A), A)) | (~in(tptp_fun_D_0(B, A), A))))))))) <=> ![A: $i, B: $i] : ((~relation(B)) | (~((~((~(B = inclusion_relation(A))) | (~((~(relation_field(B) = A)) | (~![C: $i, D: $i] : ((in(ordered_pair(C, D), B) <=> subset(C, D)) | (~in(C, A)) | (~in(D, A)))))))) | (~((B = inclusion_relation(A)) | (~(relation_field(B) = A)) | (~((in(ordered_pair(tptp_fun_C_1(B, A), tptp_fun_D_0(B, A)), B) <=> subset(tptp_fun_C_1(B, A), tptp_fun_D_0(B, A))) | (~in(tptp_fun_C_1(B, A), A)) | (~in(tptp_fun_D_0(B, A), A)))))))))),
% 0.19/0.38 inference(transitivity,[status(thm)],[15, 13])).
% 0.19/0.38 tff(17,plain,
% 0.19/0.38 (^[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_1(B, A), A) & in(tptp_fun_D_0(B, A), A))) | (in(ordered_pair(tptp_fun_C_1(B, A), tptp_fun_D_0(B, A)), B) <=> subset(tptp_fun_C_1(B, A), tptp_fun_D_0(B, A)))))))) <=> ((~relation(B)) | (~((~((~(B = inclusion_relation(A))) | (~((~(relation_field(B) = A)) | (~![C: $i, D: $i] : ((in(ordered_pair(C, D), B) <=> subset(C, D)) | (~in(C, A)) | (~in(D, A)))))))) | (~((B = inclusion_relation(A)) | (~(relation_field(B) = A)) | (~((in(ordered_pair(tptp_fun_C_1(B, A), tptp_fun_D_0(B, A)), B) <=> subset(tptp_fun_C_1(B, A), tptp_fun_D_0(B, A))) | (~in(tptp_fun_C_1(B, A), A)) | (~in(tptp_fun_D_0(B, A), A))))))))))),
% 0.19/0.38 inference(bind,[status(th)],[])).
% 0.19/0.38 tff(18,plain,
% 0.19/0.38 (![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_1(B, A), A) & in(tptp_fun_D_0(B, A), A))) | (in(ordered_pair(tptp_fun_C_1(B, A), tptp_fun_D_0(B, A)), B) <=> subset(tptp_fun_C_1(B, A), tptp_fun_D_0(B, A)))))))) <=> ![A: $i, B: $i] : ((~relation(B)) | (~((~((~(B = inclusion_relation(A))) | (~((~(relation_field(B) = A)) | (~![C: $i, D: $i] : ((in(ordered_pair(C, D), B) <=> subset(C, D)) | (~in(C, A)) | (~in(D, A)))))))) | (~((B = inclusion_relation(A)) | (~(relation_field(B) = A)) | (~((in(ordered_pair(tptp_fun_C_1(B, A), tptp_fun_D_0(B, A)), B) <=> subset(tptp_fun_C_1(B, A), tptp_fun_D_0(B, A))) | (~in(tptp_fun_C_1(B, A), A)) | (~in(tptp_fun_D_0(B, A), A)))))))))),
% 0.19/0.38 inference(quant_intro,[status(thm)],[17])).
% 0.19/0.38 tff(19,plain,
% 0.19/0.38 (^[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_1(B, A), A) & in(tptp_fun_D_0(B, A), A))) | (in(ordered_pair(tptp_fun_C_1(B, A), tptp_fun_D_0(B, A)), B) <=> subset(tptp_fun_C_1(B, A), tptp_fun_D_0(B, A))))))))) <=> ((~relation(B)) | (((~(B = inclusion_relation(A))) | ((relation_field(B) = A) & ![C: $i, D: $i] : ((~(in(C, A) & in(D, A))) | (in(ordered_pair(C, D), B) <=> subset(C, D))))) & ((B = inclusion_relation(A)) | (~(relation_field(B) = A)) | (~((~(in(tptp_fun_C_1(B, A), A) & in(tptp_fun_D_0(B, A), A))) | (in(ordered_pair(tptp_fun_C_1(B, A), tptp_fun_D_0(B, A)), B) <=> subset(tptp_fun_C_1(B, A), tptp_fun_D_0(B, A)))))))))),
% 0.19/0.38 inference(bind,[status(th)],[])).
% 0.19/0.38 tff(20,plain,
% 0.19/0.38 (![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_1(B, A), A) & in(tptp_fun_D_0(B, A), A))) | (in(ordered_pair(tptp_fun_C_1(B, A), tptp_fun_D_0(B, A)), B) <=> subset(tptp_fun_C_1(B, A), tptp_fun_D_0(B, A))))))))) <=> ![A: $i, B: $i] : ((~relation(B)) | (((~(B = inclusion_relation(A))) | ((relation_field(B) = A) & ![C: $i, D: $i] : ((~(in(C, A) & in(D, A))) | (in(ordered_pair(C, D), B) <=> subset(C, D))))) & ((B = inclusion_relation(A)) | (~(relation_field(B) = A)) | (~((~(in(tptp_fun_C_1(B, A), A) & in(tptp_fun_D_0(B, A), A))) | (in(ordered_pair(tptp_fun_C_1(B, A), tptp_fun_D_0(B, A)), B) <=> subset(tptp_fun_C_1(B, A), tptp_fun_D_0(B, A))))))))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[19])).
% 0.19/0.39 tff(21,plain,
% 0.19/0.39 (![A: $i, B: $i] : ((~relation(B)) | ((B = inclusion_relation(A)) <=> ((relation_field(B) = A) & ![C: $i, D: $i] : ((~(in(C, A) & in(D, A))) | (in(ordered_pair(C, D), B) <=> subset(C, D)))))) <=> ![A: $i, B: $i] : ((~relation(B)) | ((B = inclusion_relation(A)) <=> ((relation_field(B) = A) & ![C: $i, D: $i] : ((~(in(C, A) & in(D, A))) | (in(ordered_pair(C, D), B) <=> subset(C, D))))))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(22,plain,
% 0.19/0.39 (^[A: $i, B: $i] : trans(monotonicity(rewrite(((B = inclusion_relation(A)) <=> ((relation_field(B) = A) & ![C: $i, D: $i] : ((in(C, A) & in(D, A)) => (in(ordered_pair(C, D), B) <=> subset(C, D))))) <=> ((B = inclusion_relation(A)) <=> ((relation_field(B) = A) & ![C: $i, D: $i] : ((~(in(C, A) & in(D, A))) | (in(ordered_pair(C, D), B) <=> subset(C, D)))))), ((relation(B) => ((B = inclusion_relation(A)) <=> ((relation_field(B) = A) & ![C: $i, D: $i] : ((in(C, A) & in(D, A)) => (in(ordered_pair(C, D), B) <=> subset(C, D)))))) <=> (relation(B) => ((B = inclusion_relation(A)) <=> ((relation_field(B) = A) & ![C: $i, D: $i] : ((~(in(C, A) & in(D, A))) | (in(ordered_pair(C, D), B) <=> subset(C, D)))))))), rewrite((relation(B) => ((B = inclusion_relation(A)) <=> ((relation_field(B) = A) & ![C: $i, D: $i] : ((~(in(C, A) & in(D, A))) | (in(ordered_pair(C, D), B) <=> subset(C, D)))))) <=> ((~relation(B)) | ((B = inclusion_relation(A)) <=> ((relation_field(B) = A) & ![C: $i, D: $i] : ((~(in(C, A) & in(D, A))) | (in(ordered_pair(C, D), B) <=> subset(C, D))))))), ((relation(B) => ((B = inclusion_relation(A)) <=> ((relation_field(B) = A) & ![C: $i, D: $i] : ((in(C, A) & in(D, A)) => (in(ordered_pair(C, D), B) <=> subset(C, D)))))) <=> ((~relation(B)) | ((B = inclusion_relation(A)) <=> ((relation_field(B) = A) & ![C: $i, D: $i] : ((~(in(C, A) & in(D, A))) | (in(ordered_pair(C, D), B) <=> subset(C, D))))))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(23,plain,
% 0.19/0.39 (![A: $i, B: $i] : (relation(B) => ((B = inclusion_relation(A)) <=> ((relation_field(B) = A) & ![C: $i, D: $i] : ((in(C, A) & in(D, A)) => (in(ordered_pair(C, D), B) <=> subset(C, D)))))) <=> ![A: $i, B: $i] : ((~relation(B)) | ((B = inclusion_relation(A)) <=> ((relation_field(B) = A) & ![C: $i, D: $i] : ((~(in(C, A) & in(D, A))) | (in(ordered_pair(C, D), B) <=> subset(C, D))))))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[22])).
% 0.19/0.39 tff(24,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')).
% 0.19/0.39 tff(25,plain,
% 0.19/0.39 (![A: $i, B: $i] : ((~relation(B)) | ((B = inclusion_relation(A)) <=> ((relation_field(B) = A) & ![C: $i, D: $i] : ((~(in(C, A) & in(D, A))) | (in(ordered_pair(C, D), B) <=> subset(C, D))))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[24, 23])).
% 0.19/0.39 tff(26,plain,
% 0.19/0.39 (![A: $i, B: $i] : ((~relation(B)) | ((B = inclusion_relation(A)) <=> ((relation_field(B) = A) & ![C: $i, D: $i] : ((~(in(C, A) & in(D, A))) | (in(ordered_pair(C, D), B) <=> subset(C, D))))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[25, 21])).
% 0.19/0.39 tff(27,plain,(
% 0.19/0.39 ![A: $i, B: $i] : ((~relation(B)) | (((~(B = inclusion_relation(A))) | ((relation_field(B) = A) & ![C: $i, D: $i] : ((~(in(C, A) & in(D, A))) | (in(ordered_pair(C, D), B) <=> subset(C, D))))) & ((B = inclusion_relation(A)) | ((~(relation_field(B) = A)) | (~((~(in(tptp_fun_C_1(B, A), A) & in(tptp_fun_D_0(B, A), A))) | (in(ordered_pair(tptp_fun_C_1(B, A), tptp_fun_D_0(B, A)), B) <=> subset(tptp_fun_C_1(B, A), tptp_fun_D_0(B, A)))))))))),
% 0.19/0.39 inference(skolemize,[status(sab)],[26])).
% 0.19/0.39 tff(28,plain,
% 0.19/0.39 (![A: $i, B: $i] : ((~relation(B)) | (((~(B = inclusion_relation(A))) | ((relation_field(B) = A) & ![C: $i, D: $i] : ((~(in(C, A) & in(D, A))) | (in(ordered_pair(C, D), B) <=> subset(C, D))))) & ((B = inclusion_relation(A)) | (~(relation_field(B) = A)) | (~((~(in(tptp_fun_C_1(B, A), A) & in(tptp_fun_D_0(B, A), A))) | (in(ordered_pair(tptp_fun_C_1(B, A), tptp_fun_D_0(B, A)), B) <=> subset(tptp_fun_C_1(B, A), tptp_fun_D_0(B, A))))))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[27, 20])).
% 0.19/0.39 tff(29,plain,
% 0.19/0.39 (![A: $i, B: $i] : ((~relation(B)) | (~((~((~(B = inclusion_relation(A))) | (~((~(relation_field(B) = A)) | (~![C: $i, D: $i] : ((in(ordered_pair(C, D), B) <=> subset(C, D)) | (~in(C, A)) | (~in(D, A)))))))) | (~((B = inclusion_relation(A)) | (~(relation_field(B) = A)) | (~((in(ordered_pair(tptp_fun_C_1(B, A), tptp_fun_D_0(B, A)), B) <=> subset(tptp_fun_C_1(B, A), tptp_fun_D_0(B, A))) | (~in(tptp_fun_C_1(B, A), A)) | (~in(tptp_fun_D_0(B, A), A)))))))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[28, 18])).
% 0.19/0.39 tff(30,plain,
% 0.19/0.39 (![A: $i, B: $i] : ((~relation(B)) | (~((~((~(B = inclusion_relation(A))) | (~((~(relation_field(B) = A)) | (~![C: $i, D: $i] : ((in(ordered_pair(C, D), B) <=> subset(C, D)) | (~in(C, A)) | (~in(D, A)))))))) | (~((B = inclusion_relation(A)) | (~(relation_field(B) = A)) | (~((in(ordered_pair(tptp_fun_C_1(B, A), tptp_fun_D_0(B, A)), B) <=> subset(tptp_fun_C_1(B, A), tptp_fun_D_0(B, A))) | (~in(tptp_fun_C_1(B, A), A)) | (~in(tptp_fun_D_0(B, A), A)))))))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[29, 16])).
% 0.19/0.39 tff(31,plain,
% 0.19/0.39 (![A: $i, B: $i] : ((~relation(B)) | (~((~((B = inclusion_relation(A)) | (~(relation_field(B) = A)) | (~((in(ordered_pair(tptp_fun_C_1(B, A), tptp_fun_D_0(B, A)), B) <=> subset(tptp_fun_C_1(B, A), tptp_fun_D_0(B, A))) | (~in(tptp_fun_C_1(B, A), A)) | (~in(tptp_fun_D_0(B, A), A)))))) | (~((~(B = inclusion_relation(A))) | (~((~(relation_field(B) = A)) | (~![C: $i, D: $i] : ((in(ordered_pair(C, D), B) <=> subset(C, D)) | (~in(C, A)) | (~in(D, A)))))))))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[30, 11])).
% 0.19/0.39 tff(32,plain,
% 0.19/0.39 (((~![A: $i, B: $i] : ((~relation(B)) | (~((~((B = inclusion_relation(A)) | (~(relation_field(B) = A)) | (~((in(ordered_pair(tptp_fun_C_1(B, A), tptp_fun_D_0(B, A)), B) <=> subset(tptp_fun_C_1(B, A), tptp_fun_D_0(B, A))) | (~in(tptp_fun_C_1(B, A), A)) | (~in(tptp_fun_D_0(B, A), A)))))) | (~((~(B = inclusion_relation(A))) | (~((~(relation_field(B) = A)) | (~![C: $i, D: $i] : ((in(ordered_pair(C, D), B) <=> subset(C, D)) | (~in(C, A)) | (~in(D, A)))))))))))) | ((~relation(inclusion_relation(A!14))) | (~((~(relation_field(inclusion_relation(A!14)) = A!14)) | (~![C: $i, D: $i] : ((~in(C, A!14)) | (~in(D, A!14)) | (in(ordered_pair(C, D), inclusion_relation(A!14)) <=> subset(C, D)))))))) <=> ((~![A: $i, B: $i] : ((~relation(B)) | (~((~((B = inclusion_relation(A)) | (~(relation_field(B) = A)) | (~((in(ordered_pair(tptp_fun_C_1(B, A), tptp_fun_D_0(B, A)), B) <=> subset(tptp_fun_C_1(B, A), tptp_fun_D_0(B, A))) | (~in(tptp_fun_C_1(B, A), A)) | (~in(tptp_fun_D_0(B, A), A)))))) | (~((~(B = inclusion_relation(A))) | (~((~(relation_field(B) = A)) | (~![C: $i, D: $i] : ((in(ordered_pair(C, D), B) <=> subset(C, D)) | (~in(C, A)) | (~in(D, A)))))))))))) | (~relation(inclusion_relation(A!14))) | (~((~(relation_field(inclusion_relation(A!14)) = A!14)) | (~![C: $i, D: $i] : ((~in(C, A!14)) | (~in(D, A!14)) | (in(ordered_pair(C, D), inclusion_relation(A!14)) <=> subset(C, D)))))))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(33,plain,
% 0.19/0.39 (((~relation(inclusion_relation(A!14))) | (~((~((inclusion_relation(A!14) = inclusion_relation(A!14)) | (~(relation_field(inclusion_relation(A!14)) = A!14)) | (~((in(ordered_pair(tptp_fun_C_1(inclusion_relation(A!14), A!14), tptp_fun_D_0(inclusion_relation(A!14), A!14)), inclusion_relation(A!14)) <=> subset(tptp_fun_C_1(inclusion_relation(A!14), A!14), tptp_fun_D_0(inclusion_relation(A!14), A!14))) | (~in(tptp_fun_C_1(inclusion_relation(A!14), A!14), A!14)) | (~in(tptp_fun_D_0(inclusion_relation(A!14), A!14), A!14)))))) | (~((~(inclusion_relation(A!14) = inclusion_relation(A!14))) | (~((~(relation_field(inclusion_relation(A!14)) = A!14)) | (~![C: $i, D: $i] : ((in(ordered_pair(C, D), inclusion_relation(A!14)) <=> subset(C, D)) | (~in(C, A!14)) | (~in(D, A!14))))))))))) <=> ((~relation(inclusion_relation(A!14))) | (~((~(relation_field(inclusion_relation(A!14)) = A!14)) | (~![C: $i, D: $i] : ((~in(C, A!14)) | (~in(D, A!14)) | (in(ordered_pair(C, D), inclusion_relation(A!14)) <=> subset(C, D)))))))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(34,plain,
% 0.19/0.39 (((~![A: $i, B: $i] : ((~relation(B)) | (~((~((B = inclusion_relation(A)) | (~(relation_field(B) = A)) | (~((in(ordered_pair(tptp_fun_C_1(B, A), tptp_fun_D_0(B, A)), B) <=> subset(tptp_fun_C_1(B, A), tptp_fun_D_0(B, A))) | (~in(tptp_fun_C_1(B, A), A)) | (~in(tptp_fun_D_0(B, A), A)))))) | (~((~(B = inclusion_relation(A))) | (~((~(relation_field(B) = A)) | (~![C: $i, D: $i] : ((in(ordered_pair(C, D), B) <=> subset(C, D)) | (~in(C, A)) | (~in(D, A)))))))))))) | ((~relation(inclusion_relation(A!14))) | (~((~((inclusion_relation(A!14) = inclusion_relation(A!14)) | (~(relation_field(inclusion_relation(A!14)) = A!14)) | (~((in(ordered_pair(tptp_fun_C_1(inclusion_relation(A!14), A!14), tptp_fun_D_0(inclusion_relation(A!14), A!14)), inclusion_relation(A!14)) <=> subset(tptp_fun_C_1(inclusion_relation(A!14), A!14), tptp_fun_D_0(inclusion_relation(A!14), A!14))) | (~in(tptp_fun_C_1(inclusion_relation(A!14), A!14), A!14)) | (~in(tptp_fun_D_0(inclusion_relation(A!14), A!14), A!14)))))) | (~((~(inclusion_relation(A!14) = inclusion_relation(A!14))) | (~((~(relation_field(inclusion_relation(A!14)) = A!14)) | (~![C: $i, D: $i] : ((in(ordered_pair(C, D), inclusion_relation(A!14)) <=> subset(C, D)) | (~in(C, A!14)) | (~in(D, A!14)))))))))))) <=> ((~![A: $i, B: $i] : ((~relation(B)) | (~((~((B = inclusion_relation(A)) | (~(relation_field(B) = A)) | (~((in(ordered_pair(tptp_fun_C_1(B, A), tptp_fun_D_0(B, A)), B) <=> subset(tptp_fun_C_1(B, A), tptp_fun_D_0(B, A))) | (~in(tptp_fun_C_1(B, A), A)) | (~in(tptp_fun_D_0(B, A), A)))))) | (~((~(B = inclusion_relation(A))) | (~((~(relation_field(B) = A)) | (~![C: $i, D: $i] : ((in(ordered_pair(C, D), B) <=> subset(C, D)) | (~in(C, A)) | (~in(D, A)))))))))))) | ((~relation(inclusion_relation(A!14))) | (~((~(relation_field(inclusion_relation(A!14)) = A!14)) | (~![C: $i, D: $i] : ((~in(C, A!14)) | (~in(D, A!14)) | (in(ordered_pair(C, D), inclusion_relation(A!14)) <=> subset(C, D))))))))),
% 0.19/0.39 inference(monotonicity,[status(thm)],[33])).
% 0.19/0.39 tff(35,plain,
% 0.19/0.39 (((~![A: $i, B: $i] : ((~relation(B)) | (~((~((B = inclusion_relation(A)) | (~(relation_field(B) = A)) | (~((in(ordered_pair(tptp_fun_C_1(B, A), tptp_fun_D_0(B, A)), B) <=> subset(tptp_fun_C_1(B, A), tptp_fun_D_0(B, A))) | (~in(tptp_fun_C_1(B, A), A)) | (~in(tptp_fun_D_0(B, A), A)))))) | (~((~(B = inclusion_relation(A))) | (~((~(relation_field(B) = A)) | (~![C: $i, D: $i] : ((in(ordered_pair(C, D), B) <=> subset(C, D)) | (~in(C, A)) | (~in(D, A)))))))))))) | ((~relation(inclusion_relation(A!14))) | (~((~((inclusion_relation(A!14) = inclusion_relation(A!14)) | (~(relation_field(inclusion_relation(A!14)) = A!14)) | (~((in(ordered_pair(tptp_fun_C_1(inclusion_relation(A!14), A!14), tptp_fun_D_0(inclusion_relation(A!14), A!14)), inclusion_relation(A!14)) <=> subset(tptp_fun_C_1(inclusion_relation(A!14), A!14), tptp_fun_D_0(inclusion_relation(A!14), A!14))) | (~in(tptp_fun_C_1(inclusion_relation(A!14), A!14), A!14)) | (~in(tptp_fun_D_0(inclusion_relation(A!14), A!14), A!14)))))) | (~((~(inclusion_relation(A!14) = inclusion_relation(A!14))) | (~((~(relation_field(inclusion_relation(A!14)) = A!14)) | (~![C: $i, D: $i] : ((in(ordered_pair(C, D), inclusion_relation(A!14)) <=> subset(C, D)) | (~in(C, A!14)) | (~in(D, A!14)))))))))))) <=> ((~![A: $i, B: $i] : ((~relation(B)) | (~((~((B = inclusion_relation(A)) | (~(relation_field(B) = A)) | (~((in(ordered_pair(tptp_fun_C_1(B, A), tptp_fun_D_0(B, A)), B) <=> subset(tptp_fun_C_1(B, A), tptp_fun_D_0(B, A))) | (~in(tptp_fun_C_1(B, A), A)) | (~in(tptp_fun_D_0(B, A), A)))))) | (~((~(B = inclusion_relation(A))) | (~((~(relation_field(B) = A)) | (~![C: $i, D: $i] : ((in(ordered_pair(C, D), B) <=> subset(C, D)) | (~in(C, A)) | (~in(D, A)))))))))))) | (~relation(inclusion_relation(A!14))) | (~((~(relation_field(inclusion_relation(A!14)) = A!14)) | (~![C: $i, D: $i] : ((~in(C, A!14)) | (~in(D, A!14)) | (in(ordered_pair(C, D), inclusion_relation(A!14)) <=> subset(C, D)))))))),
% 0.19/0.39 inference(transitivity,[status(thm)],[34, 32])).
% 0.19/0.39 tff(36,plain,
% 0.19/0.39 ((~![A: $i, B: $i] : ((~relation(B)) | (~((~((B = inclusion_relation(A)) | (~(relation_field(B) = A)) | (~((in(ordered_pair(tptp_fun_C_1(B, A), tptp_fun_D_0(B, A)), B) <=> subset(tptp_fun_C_1(B, A), tptp_fun_D_0(B, A))) | (~in(tptp_fun_C_1(B, A), A)) | (~in(tptp_fun_D_0(B, A), A)))))) | (~((~(B = inclusion_relation(A))) | (~((~(relation_field(B) = A)) | (~![C: $i, D: $i] : ((in(ordered_pair(C, D), B) <=> subset(C, D)) | (~in(C, A)) | (~in(D, A)))))))))))) | ((~relation(inclusion_relation(A!14))) | (~((~((inclusion_relation(A!14) = inclusion_relation(A!14)) | (~(relation_field(inclusion_relation(A!14)) = A!14)) | (~((in(ordered_pair(tptp_fun_C_1(inclusion_relation(A!14), A!14), tptp_fun_D_0(inclusion_relation(A!14), A!14)), inclusion_relation(A!14)) <=> subset(tptp_fun_C_1(inclusion_relation(A!14), A!14), tptp_fun_D_0(inclusion_relation(A!14), A!14))) | (~in(tptp_fun_C_1(inclusion_relation(A!14), A!14), A!14)) | (~in(tptp_fun_D_0(inclusion_relation(A!14), A!14), A!14)))))) | (~((~(inclusion_relation(A!14) = inclusion_relation(A!14))) | (~((~(relation_field(inclusion_relation(A!14)) = A!14)) | (~![C: $i, D: $i] : ((in(ordered_pair(C, D), inclusion_relation(A!14)) <=> subset(C, D)) | (~in(C, A!14)) | (~in(D, A!14)))))))))))),
% 0.19/0.39 inference(quant_inst,[status(thm)],[])).
% 0.19/0.39 tff(37,plain,
% 0.19/0.39 ((~![A: $i, B: $i] : ((~relation(B)) | (~((~((B = inclusion_relation(A)) | (~(relation_field(B) = A)) | (~((in(ordered_pair(tptp_fun_C_1(B, A), tptp_fun_D_0(B, A)), B) <=> subset(tptp_fun_C_1(B, A), tptp_fun_D_0(B, A))) | (~in(tptp_fun_C_1(B, A), A)) | (~in(tptp_fun_D_0(B, A), A)))))) | (~((~(B = inclusion_relation(A))) | (~((~(relation_field(B) = A)) | (~![C: $i, D: $i] : ((in(ordered_pair(C, D), B) <=> subset(C, D)) | (~in(C, A)) | (~in(D, A)))))))))))) | (~relation(inclusion_relation(A!14))) | (~((~(relation_field(inclusion_relation(A!14)) = A!14)) | (~![C: $i, D: $i] : ((~in(C, A!14)) | (~in(D, A!14)) | (in(ordered_pair(C, D), inclusion_relation(A!14)) <=> subset(C, D))))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[36, 35])).
% 0.19/0.39 tff(38,plain,
% 0.19/0.39 (~((~(relation_field(inclusion_relation(A!14)) = A!14)) | (~![C: $i, D: $i] : ((~in(C, A!14)) | (~in(D, A!14)) | (in(ordered_pair(C, D), inclusion_relation(A!14)) <=> subset(C, D)))))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[37, 31, 9])).
% 0.19/0.39 tff(39,plain,
% 0.19/0.39 (((~(relation_field(inclusion_relation(A!14)) = A!14)) | (~![C: $i, D: $i] : ((~in(C, A!14)) | (~in(D, A!14)) | (in(ordered_pair(C, D), inclusion_relation(A!14)) <=> subset(C, D))))) | (relation_field(inclusion_relation(A!14)) = A!14)),
% 0.19/0.39 inference(tautology,[status(thm)],[])).
% 0.19/0.39 tff(40,plain,
% 0.19/0.39 (relation_field(inclusion_relation(A!14)) = A!14),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[39, 38])).
% 0.19/0.39 tff(41,plain,
% 0.19/0.39 (^[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)))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(42,plain,
% 0.19/0.39 (![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))))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[41])).
% 0.19/0.39 tff(43,plain,
% 0.19/0.39 (![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))))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(44,plain,
% 0.19/0.39 (^[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)))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(45,plain,
% 0.19/0.39 (![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))))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[44])).
% 0.19/0.39 tff(46,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')).
% 0.19/0.39 tff(47,plain,
% 0.19/0.39 (![A: $i] : ((~relation(A)) | (relation_field(A) = set_union2(relation_dom(A), relation_rng(A))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[46, 45])).
% 0.19/0.39 tff(48,plain,
% 0.19/0.39 (![A: $i] : ((~relation(A)) | (relation_field(A) = set_union2(relation_dom(A), relation_rng(A))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[47, 43])).
% 0.19/0.39 tff(49,plain,(
% 0.19/0.39 ![A: $i] : ((~relation(A)) | (relation_field(A) = set_union2(relation_dom(A), relation_rng(A))))),
% 0.19/0.39 inference(skolemize,[status(sab)],[48])).
% 0.19/0.39 tff(50,plain,
% 0.19/0.39 (![A: $i] : ((~relation(A)) | (relation_field(A) = set_union2(relation_dom(A), relation_rng(A))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[49, 42])).
% 0.19/0.39 tff(51,plain,
% 0.19/0.39 (((~![A: $i] : ((~relation(A)) | (relation_field(A) = set_union2(relation_dom(A), relation_rng(A))))) | ((~relation(inclusion_relation(A!14))) | (relation_field(inclusion_relation(A!14)) = set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14)))))) <=> ((~![A: $i] : ((~relation(A)) | (relation_field(A) = set_union2(relation_dom(A), relation_rng(A))))) | (~relation(inclusion_relation(A!14))) | (relation_field(inclusion_relation(A!14)) = set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14)))))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(52,plain,
% 0.19/0.39 ((~![A: $i] : ((~relation(A)) | (relation_field(A) = set_union2(relation_dom(A), relation_rng(A))))) | ((~relation(inclusion_relation(A!14))) | (relation_field(inclusion_relation(A!14)) = set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14)))))),
% 0.19/0.39 inference(quant_inst,[status(thm)],[])).
% 0.19/0.39 tff(53,plain,
% 0.19/0.39 ((~![A: $i] : ((~relation(A)) | (relation_field(A) = set_union2(relation_dom(A), relation_rng(A))))) | (~relation(inclusion_relation(A!14))) | (relation_field(inclusion_relation(A!14)) = set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[52, 51])).
% 0.19/0.39 tff(54,plain,
% 0.19/0.39 (relation_field(inclusion_relation(A!14)) = set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14)))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[53, 50, 9])).
% 0.19/0.39 tff(55,plain,
% 0.19/0.39 (set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))) = relation_field(inclusion_relation(A!14))),
% 0.19/0.39 inference(symmetry,[status(thm)],[54])).
% 0.19/0.39 tff(56,plain,
% 0.19/0.39 (set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))) = A!14),
% 0.19/0.39 inference(transitivity,[status(thm)],[55, 40])).
% 0.19/0.39 tff(57,plain,
% 0.19/0.39 (ordinal(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14)))) <=> ordinal(A!14)),
% 0.19/0.39 inference(monotonicity,[status(thm)],[56])).
% 0.19/0.39 tff(58,plain,
% 0.19/0.39 (ordinal(A!14) <=> ordinal(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))))),
% 0.19/0.39 inference(symmetry,[status(thm)],[57])).
% 0.19/0.39 tff(59,plain,
% 0.19/0.39 ((~![A: $i] : (connected(inclusion_relation(A)) | (~ordinal(A)))) <=> (~![A: $i] : (connected(inclusion_relation(A)) | (~ordinal(A))))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(60,plain,
% 0.19/0.39 ((~![A: $i] : (ordinal(A) => connected(inclusion_relation(A)))) <=> (~![A: $i] : (connected(inclusion_relation(A)) | (~ordinal(A))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(61,axiom,(~![A: $i] : (ordinal(A) => connected(inclusion_relation(A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t4_wellord2')).
% 0.19/0.40 tff(62,plain,
% 0.19/0.40 (~![A: $i] : (connected(inclusion_relation(A)) | (~ordinal(A)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[61, 60])).
% 0.19/0.40 tff(63,plain,
% 0.19/0.40 (~![A: $i] : (connected(inclusion_relation(A)) | (~ordinal(A)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[62, 59])).
% 0.19/0.40 tff(64,plain,
% 0.19/0.40 (~![A: $i] : (connected(inclusion_relation(A)) | (~ordinal(A)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[63, 59])).
% 0.19/0.40 tff(65,plain,
% 0.19/0.40 (~![A: $i] : (connected(inclusion_relation(A)) | (~ordinal(A)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[64, 59])).
% 0.19/0.40 tff(66,plain,(
% 0.19/0.40 ~(connected(inclusion_relation(A!14)) | (~ordinal(A!14)))),
% 0.19/0.40 inference(skolemize,[status(sab)],[65])).
% 0.19/0.40 tff(67,plain,
% 0.19/0.40 (ordinal(A!14)),
% 0.19/0.40 inference(or_elim,[status(thm)],[66])).
% 0.19/0.40 tff(68,plain,
% 0.19/0.40 (ordinal(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[67, 58])).
% 0.19/0.40 tff(69,plain,
% 0.19/0.40 (^[A: $i] : refl(((~relation(A)) | ![B: $i] : (~((~((~is_connected_in(A, B)) | ![C: $i, D: $i] : (in(ordered_pair(D, C), A) | (C = D) | in(ordered_pair(C, D), A) | (~in(C, B)) | (~in(D, B))))) | (~(is_connected_in(A, B) | (~((~in(tptp_fun_C_3(B, A), B)) | (~in(tptp_fun_D_2(B, A), B)) | (tptp_fun_C_3(B, A) = tptp_fun_D_2(B, A)) | in(ordered_pair(tptp_fun_C_3(B, A), tptp_fun_D_2(B, A)), A) | in(ordered_pair(tptp_fun_D_2(B, A), tptp_fun_C_3(B, A)), A)))))))) <=> ((~relation(A)) | ![B: $i] : (~((~((~is_connected_in(A, B)) | ![C: $i, D: $i] : (in(ordered_pair(D, C), A) | (C = D) | in(ordered_pair(C, D), A) | (~in(C, B)) | (~in(D, B))))) | (~(is_connected_in(A, B) | (~((~in(tptp_fun_C_3(B, A), B)) | (~in(tptp_fun_D_2(B, A), B)) | (tptp_fun_C_3(B, A) = tptp_fun_D_2(B, A)) | in(ordered_pair(tptp_fun_C_3(B, A), tptp_fun_D_2(B, A)), A) | in(ordered_pair(tptp_fun_D_2(B, A), tptp_fun_C_3(B, A)), A)))))))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(70,plain,
% 0.19/0.40 (![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~is_connected_in(A, B)) | ![C: $i, D: $i] : (in(ordered_pair(D, C), A) | (C = D) | in(ordered_pair(C, D), A) | (~in(C, B)) | (~in(D, B))))) | (~(is_connected_in(A, B) | (~((~in(tptp_fun_C_3(B, A), B)) | (~in(tptp_fun_D_2(B, A), B)) | (tptp_fun_C_3(B, A) = tptp_fun_D_2(B, A)) | in(ordered_pair(tptp_fun_C_3(B, A), tptp_fun_D_2(B, A)), A) | in(ordered_pair(tptp_fun_D_2(B, A), tptp_fun_C_3(B, A)), A)))))))) <=> ![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~is_connected_in(A, B)) | ![C: $i, D: $i] : (in(ordered_pair(D, C), A) | (C = D) | in(ordered_pair(C, D), A) | (~in(C, B)) | (~in(D, B))))) | (~(is_connected_in(A, B) | (~((~in(tptp_fun_C_3(B, A), B)) | (~in(tptp_fun_D_2(B, A), B)) | (tptp_fun_C_3(B, A) = tptp_fun_D_2(B, A)) | in(ordered_pair(tptp_fun_C_3(B, A), tptp_fun_D_2(B, A)), A) | in(ordered_pair(tptp_fun_D_2(B, A), tptp_fun_C_3(B, A)), A))))))))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[69])).
% 0.19/0.40 tff(71,plain,
% 0.19/0.40 (^[A: $i] : rewrite(((~relation(A)) | ![B: $i] : (~((~((~is_connected_in(A, B)) | ![C: $i, D: $i] : (in(ordered_pair(D, C), A) | (C = D) | in(ordered_pair(C, D), A) | (~in(C, B)) | (~in(D, B))))) | (~(is_connected_in(A, B) | (~((~in(tptp_fun_C_3(B, A), B)) | (~in(tptp_fun_D_2(B, A), B)) | (tptp_fun_C_3(B, A) = tptp_fun_D_2(B, A)) | in(ordered_pair(tptp_fun_C_3(B, A), tptp_fun_D_2(B, A)), A) | in(ordered_pair(tptp_fun_D_2(B, A), tptp_fun_C_3(B, A)), A)))))))) <=> ((~relation(A)) | ![B: $i] : (~((~((~is_connected_in(A, B)) | ![C: $i, D: $i] : (in(ordered_pair(D, C), A) | (C = D) | in(ordered_pair(C, D), A) | (~in(C, B)) | (~in(D, B))))) | (~(is_connected_in(A, B) | (~((~in(tptp_fun_C_3(B, A), B)) | (~in(tptp_fun_D_2(B, A), B)) | (tptp_fun_C_3(B, A) = tptp_fun_D_2(B, A)) | in(ordered_pair(tptp_fun_C_3(B, A), tptp_fun_D_2(B, A)), A) | in(ordered_pair(tptp_fun_D_2(B, A), tptp_fun_C_3(B, A)), A)))))))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(72,plain,
% 0.19/0.40 (![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~is_connected_in(A, B)) | ![C: $i, D: $i] : (in(ordered_pair(D, C), A) | (C = D) | in(ordered_pair(C, D), A) | (~in(C, B)) | (~in(D, B))))) | (~(is_connected_in(A, B) | (~((~in(tptp_fun_C_3(B, A), B)) | (~in(tptp_fun_D_2(B, A), B)) | (tptp_fun_C_3(B, A) = tptp_fun_D_2(B, A)) | in(ordered_pair(tptp_fun_C_3(B, A), tptp_fun_D_2(B, A)), A) | in(ordered_pair(tptp_fun_D_2(B, A), tptp_fun_C_3(B, A)), A)))))))) <=> ![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~is_connected_in(A, B)) | ![C: $i, D: $i] : (in(ordered_pair(D, C), A) | (C = D) | in(ordered_pair(C, D), A) | (~in(C, B)) | (~in(D, B))))) | (~(is_connected_in(A, B) | (~((~in(tptp_fun_C_3(B, A), B)) | (~in(tptp_fun_D_2(B, A), B)) | (tptp_fun_C_3(B, A) = tptp_fun_D_2(B, A)) | in(ordered_pair(tptp_fun_C_3(B, A), tptp_fun_D_2(B, A)), A) | in(ordered_pair(tptp_fun_D_2(B, A), tptp_fun_C_3(B, A)), A))))))))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[71])).
% 0.19/0.40 tff(73,plain,
% 0.19/0.40 (![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~is_connected_in(A, B)) | ![C: $i, D: $i] : (in(ordered_pair(D, C), A) | (C = D) | in(ordered_pair(C, D), A) | (~in(C, B)) | (~in(D, B))))) | (~(is_connected_in(A, B) | (~((~in(tptp_fun_C_3(B, A), B)) | (~in(tptp_fun_D_2(B, A), B)) | (tptp_fun_C_3(B, A) = tptp_fun_D_2(B, A)) | in(ordered_pair(tptp_fun_C_3(B, A), tptp_fun_D_2(B, A)), A) | in(ordered_pair(tptp_fun_D_2(B, A), tptp_fun_C_3(B, A)), A)))))))) <=> ![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~is_connected_in(A, B)) | ![C: $i, D: $i] : (in(ordered_pair(D, C), A) | (C = D) | in(ordered_pair(C, D), A) | (~in(C, B)) | (~in(D, B))))) | (~(is_connected_in(A, B) | (~((~in(tptp_fun_C_3(B, A), B)) | (~in(tptp_fun_D_2(B, A), B)) | (tptp_fun_C_3(B, A) = tptp_fun_D_2(B, A)) | in(ordered_pair(tptp_fun_C_3(B, A), tptp_fun_D_2(B, A)), A) | in(ordered_pair(tptp_fun_D_2(B, A), tptp_fun_C_3(B, A)), A))))))))),
% 0.19/0.40 inference(transitivity,[status(thm)],[72, 70])).
% 0.19/0.40 tff(74,plain,
% 0.19/0.40 (^[A: $i] : rewrite(((~relation(A)) | ![B: $i] : (((~is_connected_in(A, B)) | ![C: $i, D: $i] : (~(in(C, B) & in(D, B) & (~(C = D)) & (~in(ordered_pair(C, D), A)) & (~in(ordered_pair(D, C), A))))) & (is_connected_in(A, B) | (in(tptp_fun_C_3(B, A), B) & in(tptp_fun_D_2(B, A), B) & (~(tptp_fun_C_3(B, A) = tptp_fun_D_2(B, A))) & (~in(ordered_pair(tptp_fun_C_3(B, A), tptp_fun_D_2(B, A)), A)) & (~in(ordered_pair(tptp_fun_D_2(B, A), tptp_fun_C_3(B, A)), A)))))) <=> ((~relation(A)) | ![B: $i] : (~((~((~is_connected_in(A, B)) | ![C: $i, D: $i] : (in(ordered_pair(D, C), A) | (C = D) | in(ordered_pair(C, D), A) | (~in(C, B)) | (~in(D, B))))) | (~(is_connected_in(A, B) | (~((~in(tptp_fun_C_3(B, A), B)) | (~in(tptp_fun_D_2(B, A), B)) | (tptp_fun_C_3(B, A) = tptp_fun_D_2(B, A)) | in(ordered_pair(tptp_fun_C_3(B, A), tptp_fun_D_2(B, A)), A) | in(ordered_pair(tptp_fun_D_2(B, A), tptp_fun_C_3(B, A)), A)))))))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(75,plain,
% 0.19/0.40 (![A: $i] : ((~relation(A)) | ![B: $i] : (((~is_connected_in(A, B)) | ![C: $i, D: $i] : (~(in(C, B) & in(D, B) & (~(C = D)) & (~in(ordered_pair(C, D), A)) & (~in(ordered_pair(D, C), A))))) & (is_connected_in(A, B) | (in(tptp_fun_C_3(B, A), B) & in(tptp_fun_D_2(B, A), B) & (~(tptp_fun_C_3(B, A) = tptp_fun_D_2(B, A))) & (~in(ordered_pair(tptp_fun_C_3(B, A), tptp_fun_D_2(B, A)), A)) & (~in(ordered_pair(tptp_fun_D_2(B, A), tptp_fun_C_3(B, A)), A)))))) <=> ![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~is_connected_in(A, B)) | ![C: $i, D: $i] : (in(ordered_pair(D, C), A) | (C = D) | in(ordered_pair(C, D), A) | (~in(C, B)) | (~in(D, B))))) | (~(is_connected_in(A, B) | (~((~in(tptp_fun_C_3(B, A), B)) | (~in(tptp_fun_D_2(B, A), B)) | (tptp_fun_C_3(B, A) = tptp_fun_D_2(B, A)) | in(ordered_pair(tptp_fun_C_3(B, A), tptp_fun_D_2(B, A)), A) | in(ordered_pair(tptp_fun_D_2(B, A), tptp_fun_C_3(B, A)), A))))))))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[74])).
% 0.19/0.40 tff(76,plain,
% 0.19/0.40 (![A: $i] : ((~relation(A)) | ![B: $i] : (is_connected_in(A, B) <=> ![C: $i, D: $i] : (~(in(C, B) & in(D, B) & (~(C = D)) & (~in(ordered_pair(C, D), A)) & (~in(ordered_pair(D, C), A)))))) <=> ![A: $i] : ((~relation(A)) | ![B: $i] : (is_connected_in(A, B) <=> ![C: $i, D: $i] : (~(in(C, B) & in(D, B) & (~(C = D)) & (~in(ordered_pair(C, D), A)) & (~in(ordered_pair(D, C), A))))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(77,plain,
% 0.19/0.40 (^[A: $i] : trans(monotonicity(quant_intro(proof_bind(^[B: $i] : rewrite((is_connected_in(A, B) <=> ![C: $i, D: $i] : (~((((in(C, B) & in(D, B)) & (~(C = D))) & (~in(ordered_pair(C, D), A))) & (~in(ordered_pair(D, C), A))))) <=> (is_connected_in(A, B) <=> ![C: $i, D: $i] : (~(in(C, B) & in(D, B) & (~(C = D)) & (~in(ordered_pair(C, D), A)) & (~in(ordered_pair(D, C), A))))))), (![B: $i] : (is_connected_in(A, B) <=> ![C: $i, D: $i] : (~((((in(C, B) & in(D, B)) & (~(C = D))) & (~in(ordered_pair(C, D), A))) & (~in(ordered_pair(D, C), A))))) <=> ![B: $i] : (is_connected_in(A, B) <=> ![C: $i, D: $i] : (~(in(C, B) & in(D, B) & (~(C = D)) & (~in(ordered_pair(C, D), A)) & (~in(ordered_pair(D, C), A))))))), ((relation(A) => ![B: $i] : (is_connected_in(A, B) <=> ![C: $i, D: $i] : (~((((in(C, B) & in(D, B)) & (~(C = D))) & (~in(ordered_pair(C, D), A))) & (~in(ordered_pair(D, C), A)))))) <=> (relation(A) => ![B: $i] : (is_connected_in(A, B) <=> ![C: $i, D: $i] : (~(in(C, B) & in(D, B) & (~(C = D)) & (~in(ordered_pair(C, D), A)) & (~in(ordered_pair(D, C), A)))))))), rewrite((relation(A) => ![B: $i] : (is_connected_in(A, B) <=> ![C: $i, D: $i] : (~(in(C, B) & in(D, B) & (~(C = D)) & (~in(ordered_pair(C, D), A)) & (~in(ordered_pair(D, C), A)))))) <=> ((~relation(A)) | ![B: $i] : (is_connected_in(A, B) <=> ![C: $i, D: $i] : (~(in(C, B) & in(D, B) & (~(C = D)) & (~in(ordered_pair(C, D), A)) & (~in(ordered_pair(D, C), A))))))), ((relation(A) => ![B: $i] : (is_connected_in(A, B) <=> ![C: $i, D: $i] : (~((((in(C, B) & in(D, B)) & (~(C = D))) & (~in(ordered_pair(C, D), A))) & (~in(ordered_pair(D, C), A)))))) <=> ((~relation(A)) | ![B: $i] : (is_connected_in(A, B) <=> ![C: $i, D: $i] : (~(in(C, B) & in(D, B) & (~(C = D)) & (~in(ordered_pair(C, D), A)) & (~in(ordered_pair(D, C), A))))))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(78,plain,
% 0.19/0.40 (![A: $i] : (relation(A) => ![B: $i] : (is_connected_in(A, B) <=> ![C: $i, D: $i] : (~((((in(C, B) & in(D, B)) & (~(C = D))) & (~in(ordered_pair(C, D), A))) & (~in(ordered_pair(D, C), A)))))) <=> ![A: $i] : ((~relation(A)) | ![B: $i] : (is_connected_in(A, B) <=> ![C: $i, D: $i] : (~(in(C, B) & in(D, B) & (~(C = D)) & (~in(ordered_pair(C, D), A)) & (~in(ordered_pair(D, C), A))))))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[77])).
% 0.19/0.40 tff(79,axiom,(![A: $i] : (relation(A) => ![B: $i] : (is_connected_in(A, B) <=> ![C: $i, D: $i] : (~((((in(C, B) & in(D, B)) & (~(C = D))) & (~in(ordered_pair(C, D), A))) & (~in(ordered_pair(D, C), A))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d6_relat_2')).
% 0.19/0.40 tff(80,plain,
% 0.19/0.40 (![A: $i] : ((~relation(A)) | ![B: $i] : (is_connected_in(A, B) <=> ![C: $i, D: $i] : (~(in(C, B) & in(D, B) & (~(C = D)) & (~in(ordered_pair(C, D), A)) & (~in(ordered_pair(D, C), A))))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[79, 78])).
% 0.19/0.40 tff(81,plain,
% 0.19/0.40 (![A: $i] : ((~relation(A)) | ![B: $i] : (is_connected_in(A, B) <=> ![C: $i, D: $i] : (~(in(C, B) & in(D, B) & (~(C = D)) & (~in(ordered_pair(C, D), A)) & (~in(ordered_pair(D, C), A))))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[80, 76])).
% 0.19/0.40 tff(82,plain,(
% 0.19/0.40 ![A: $i] : ((~relation(A)) | ![B: $i] : (((~is_connected_in(A, B)) | ![C: $i, D: $i] : (~(in(C, B) & in(D, B) & (~(C = D)) & (~in(ordered_pair(C, D), A)) & (~in(ordered_pair(D, C), A))))) & (is_connected_in(A, B) | (in(tptp_fun_C_3(B, A), B) & in(tptp_fun_D_2(B, A), B) & (~(tptp_fun_C_3(B, A) = tptp_fun_D_2(B, A))) & (~in(ordered_pair(tptp_fun_C_3(B, A), tptp_fun_D_2(B, A)), A)) & (~in(ordered_pair(tptp_fun_D_2(B, A), tptp_fun_C_3(B, A)), A))))))),
% 0.19/0.40 inference(skolemize,[status(sab)],[81])).
% 0.19/0.40 tff(83,plain,
% 0.19/0.40 (![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~is_connected_in(A, B)) | ![C: $i, D: $i] : (in(ordered_pair(D, C), A) | (C = D) | in(ordered_pair(C, D), A) | (~in(C, B)) | (~in(D, B))))) | (~(is_connected_in(A, B) | (~((~in(tptp_fun_C_3(B, A), B)) | (~in(tptp_fun_D_2(B, A), B)) | (tptp_fun_C_3(B, A) = tptp_fun_D_2(B, A)) | in(ordered_pair(tptp_fun_C_3(B, A), tptp_fun_D_2(B, A)), A) | in(ordered_pair(tptp_fun_D_2(B, A), tptp_fun_C_3(B, A)), A))))))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[82, 75])).
% 0.19/0.40 tff(84,plain,
% 0.19/0.40 (![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~is_connected_in(A, B)) | ![C: $i, D: $i] : (in(ordered_pair(D, C), A) | (C = D) | in(ordered_pair(C, D), A) | (~in(C, B)) | (~in(D, B))))) | (~(is_connected_in(A, B) | (~((~in(tptp_fun_C_3(B, A), B)) | (~in(tptp_fun_D_2(B, A), B)) | (tptp_fun_C_3(B, A) = tptp_fun_D_2(B, A)) | in(ordered_pair(tptp_fun_C_3(B, A), tptp_fun_D_2(B, A)), A) | in(ordered_pair(tptp_fun_D_2(B, A), tptp_fun_C_3(B, A)), A))))))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[83, 73])).
% 0.19/0.40 tff(85,plain,
% 0.19/0.40 (((~![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~is_connected_in(A, B)) | ![C: $i, D: $i] : (in(ordered_pair(D, C), A) | (C = D) | in(ordered_pair(C, D), A) | (~in(C, B)) | (~in(D, B))))) | (~(is_connected_in(A, B) | (~((~in(tptp_fun_C_3(B, A), B)) | (~in(tptp_fun_D_2(B, A), B)) | (tptp_fun_C_3(B, A) = tptp_fun_D_2(B, A)) | in(ordered_pair(tptp_fun_C_3(B, A), tptp_fun_D_2(B, A)), A) | in(ordered_pair(tptp_fun_D_2(B, A), tptp_fun_C_3(B, A)), A))))))))) | ((~relation(inclusion_relation(A!14))) | ![B: $i] : (~((~((~is_connected_in(inclusion_relation(A!14), B)) | ![C: $i, D: $i] : ((C = D) | (~in(C, B)) | (~in(D, B)) | in(ordered_pair(D, C), inclusion_relation(A!14)) | in(ordered_pair(C, D), inclusion_relation(A!14))))) | (~(is_connected_in(inclusion_relation(A!14), B) | (~((~in(tptp_fun_C_3(B, inclusion_relation(A!14)), B)) | (~in(tptp_fun_D_2(B, inclusion_relation(A!14)), B)) | (tptp_fun_C_3(B, inclusion_relation(A!14)) = tptp_fun_D_2(B, inclusion_relation(A!14))) | in(ordered_pair(tptp_fun_C_3(B, inclusion_relation(A!14)), tptp_fun_D_2(B, inclusion_relation(A!14))), inclusion_relation(A!14)) | in(ordered_pair(tptp_fun_D_2(B, inclusion_relation(A!14)), tptp_fun_C_3(B, inclusion_relation(A!14))), inclusion_relation(A!14)))))))))) <=> ((~![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~is_connected_in(A, B)) | ![C: $i, D: $i] : (in(ordered_pair(D, C), A) | (C = D) | in(ordered_pair(C, D), A) | (~in(C, B)) | (~in(D, B))))) | (~(is_connected_in(A, B) | (~((~in(tptp_fun_C_3(B, A), B)) | (~in(tptp_fun_D_2(B, A), B)) | (tptp_fun_C_3(B, A) = tptp_fun_D_2(B, A)) | in(ordered_pair(tptp_fun_C_3(B, A), tptp_fun_D_2(B, A)), A) | in(ordered_pair(tptp_fun_D_2(B, A), tptp_fun_C_3(B, A)), A))))))))) | (~relation(inclusion_relation(A!14))) | ![B: $i] : (~((~((~is_connected_in(inclusion_relation(A!14), B)) | ![C: $i, D: $i] : ((C = D) | (~in(C, B)) | (~in(D, B)) | in(ordered_pair(D, C), inclusion_relation(A!14)) | in(ordered_pair(C, D), inclusion_relation(A!14))))) | (~(is_connected_in(inclusion_relation(A!14), B) | (~((~in(tptp_fun_C_3(B, inclusion_relation(A!14)), B)) | (~in(tptp_fun_D_2(B, inclusion_relation(A!14)), B)) | (tptp_fun_C_3(B, inclusion_relation(A!14)) = tptp_fun_D_2(B, inclusion_relation(A!14))) | in(ordered_pair(tptp_fun_C_3(B, inclusion_relation(A!14)), tptp_fun_D_2(B, inclusion_relation(A!14))), inclusion_relation(A!14)) | in(ordered_pair(tptp_fun_D_2(B, inclusion_relation(A!14)), tptp_fun_C_3(B, inclusion_relation(A!14))), inclusion_relation(A!14)))))))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(86,plain,
% 0.19/0.40 (((~relation(inclusion_relation(A!14))) | ![B: $i] : (~((~((~is_connected_in(inclusion_relation(A!14), B)) | ![C: $i, D: $i] : (in(ordered_pair(D, C), inclusion_relation(A!14)) | (C = D) | in(ordered_pair(C, D), inclusion_relation(A!14)) | (~in(C, B)) | (~in(D, B))))) | (~(is_connected_in(inclusion_relation(A!14), B) | (~((~in(tptp_fun_C_3(B, inclusion_relation(A!14)), B)) | (~in(tptp_fun_D_2(B, inclusion_relation(A!14)), B)) | (tptp_fun_C_3(B, inclusion_relation(A!14)) = tptp_fun_D_2(B, inclusion_relation(A!14))) | in(ordered_pair(tptp_fun_C_3(B, inclusion_relation(A!14)), tptp_fun_D_2(B, inclusion_relation(A!14))), inclusion_relation(A!14)) | in(ordered_pair(tptp_fun_D_2(B, inclusion_relation(A!14)), tptp_fun_C_3(B, inclusion_relation(A!14))), inclusion_relation(A!14))))))))) <=> ((~relation(inclusion_relation(A!14))) | ![B: $i] : (~((~((~is_connected_in(inclusion_relation(A!14), B)) | ![C: $i, D: $i] : ((C = D) | (~in(C, B)) | (~in(D, B)) | in(ordered_pair(D, C), inclusion_relation(A!14)) | in(ordered_pair(C, D), inclusion_relation(A!14))))) | (~(is_connected_in(inclusion_relation(A!14), B) | (~((~in(tptp_fun_C_3(B, inclusion_relation(A!14)), B)) | (~in(tptp_fun_D_2(B, inclusion_relation(A!14)), B)) | (tptp_fun_C_3(B, inclusion_relation(A!14)) = tptp_fun_D_2(B, inclusion_relation(A!14))) | in(ordered_pair(tptp_fun_C_3(B, inclusion_relation(A!14)), tptp_fun_D_2(B, inclusion_relation(A!14))), inclusion_relation(A!14)) | in(ordered_pair(tptp_fun_D_2(B, inclusion_relation(A!14)), tptp_fun_C_3(B, inclusion_relation(A!14))), inclusion_relation(A!14)))))))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(87,plain,
% 0.19/0.40 (((~![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~is_connected_in(A, B)) | ![C: $i, D: $i] : (in(ordered_pair(D, C), A) | (C = D) | in(ordered_pair(C, D), A) | (~in(C, B)) | (~in(D, B))))) | (~(is_connected_in(A, B) | (~((~in(tptp_fun_C_3(B, A), B)) | (~in(tptp_fun_D_2(B, A), B)) | (tptp_fun_C_3(B, A) = tptp_fun_D_2(B, A)) | in(ordered_pair(tptp_fun_C_3(B, A), tptp_fun_D_2(B, A)), A) | in(ordered_pair(tptp_fun_D_2(B, A), tptp_fun_C_3(B, A)), A))))))))) | ((~relation(inclusion_relation(A!14))) | ![B: $i] : (~((~((~is_connected_in(inclusion_relation(A!14), B)) | ![C: $i, D: $i] : (in(ordered_pair(D, C), inclusion_relation(A!14)) | (C = D) | in(ordered_pair(C, D), inclusion_relation(A!14)) | (~in(C, B)) | (~in(D, B))))) | (~(is_connected_in(inclusion_relation(A!14), B) | (~((~in(tptp_fun_C_3(B, inclusion_relation(A!14)), B)) | (~in(tptp_fun_D_2(B, inclusion_relation(A!14)), B)) | (tptp_fun_C_3(B, inclusion_relation(A!14)) = tptp_fun_D_2(B, inclusion_relation(A!14))) | in(ordered_pair(tptp_fun_C_3(B, inclusion_relation(A!14)), tptp_fun_D_2(B, inclusion_relation(A!14))), inclusion_relation(A!14)) | in(ordered_pair(tptp_fun_D_2(B, inclusion_relation(A!14)), tptp_fun_C_3(B, inclusion_relation(A!14))), inclusion_relation(A!14)))))))))) <=> ((~![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~is_connected_in(A, B)) | ![C: $i, D: $i] : (in(ordered_pair(D, C), A) | (C = D) | in(ordered_pair(C, D), A) | (~in(C, B)) | (~in(D, B))))) | (~(is_connected_in(A, B) | (~((~in(tptp_fun_C_3(B, A), B)) | (~in(tptp_fun_D_2(B, A), B)) | (tptp_fun_C_3(B, A) = tptp_fun_D_2(B, A)) | in(ordered_pair(tptp_fun_C_3(B, A), tptp_fun_D_2(B, A)), A) | in(ordered_pair(tptp_fun_D_2(B, A), tptp_fun_C_3(B, A)), A))))))))) | ((~relation(inclusion_relation(A!14))) | ![B: $i] : (~((~((~is_connected_in(inclusion_relation(A!14), B)) | ![C: $i, D: $i] : ((C = D) | (~in(C, B)) | (~in(D, B)) | in(ordered_pair(D, C), inclusion_relation(A!14)) | in(ordered_pair(C, D), inclusion_relation(A!14))))) | (~(is_connected_in(inclusion_relation(A!14), B) | (~((~in(tptp_fun_C_3(B, inclusion_relation(A!14)), B)) | (~in(tptp_fun_D_2(B, inclusion_relation(A!14)), B)) | (tptp_fun_C_3(B, inclusion_relation(A!14)) = tptp_fun_D_2(B, inclusion_relation(A!14))) | in(ordered_pair(tptp_fun_C_3(B, inclusion_relation(A!14)), tptp_fun_D_2(B, inclusion_relation(A!14))), inclusion_relation(A!14)) | in(ordered_pair(tptp_fun_D_2(B, inclusion_relation(A!14)), tptp_fun_C_3(B, inclusion_relation(A!14))), inclusion_relation(A!14))))))))))),
% 0.19/0.40 inference(monotonicity,[status(thm)],[86])).
% 0.19/0.40 tff(88,plain,
% 0.19/0.40 (((~![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~is_connected_in(A, B)) | ![C: $i, D: $i] : (in(ordered_pair(D, C), A) | (C = D) | in(ordered_pair(C, D), A) | (~in(C, B)) | (~in(D, B))))) | (~(is_connected_in(A, B) | (~((~in(tptp_fun_C_3(B, A), B)) | (~in(tptp_fun_D_2(B, A), B)) | (tptp_fun_C_3(B, A) = tptp_fun_D_2(B, A)) | in(ordered_pair(tptp_fun_C_3(B, A), tptp_fun_D_2(B, A)), A) | in(ordered_pair(tptp_fun_D_2(B, A), tptp_fun_C_3(B, A)), A))))))))) | ((~relation(inclusion_relation(A!14))) | ![B: $i] : (~((~((~is_connected_in(inclusion_relation(A!14), B)) | ![C: $i, D: $i] : (in(ordered_pair(D, C), inclusion_relation(A!14)) | (C = D) | in(ordered_pair(C, D), inclusion_relation(A!14)) | (~in(C, B)) | (~in(D, B))))) | (~(is_connected_in(inclusion_relation(A!14), B) | (~((~in(tptp_fun_C_3(B, inclusion_relation(A!14)), B)) | (~in(tptp_fun_D_2(B, inclusion_relation(A!14)), B)) | (tptp_fun_C_3(B, inclusion_relation(A!14)) = tptp_fun_D_2(B, inclusion_relation(A!14))) | in(ordered_pair(tptp_fun_C_3(B, inclusion_relation(A!14)), tptp_fun_D_2(B, inclusion_relation(A!14))), inclusion_relation(A!14)) | in(ordered_pair(tptp_fun_D_2(B, inclusion_relation(A!14)), tptp_fun_C_3(B, inclusion_relation(A!14))), inclusion_relation(A!14)))))))))) <=> ((~![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~is_connected_in(A, B)) | ![C: $i, D: $i] : (in(ordered_pair(D, C), A) | (C = D) | in(ordered_pair(C, D), A) | (~in(C, B)) | (~in(D, B))))) | (~(is_connected_in(A, B) | (~((~in(tptp_fun_C_3(B, A), B)) | (~in(tptp_fun_D_2(B, A), B)) | (tptp_fun_C_3(B, A) = tptp_fun_D_2(B, A)) | in(ordered_pair(tptp_fun_C_3(B, A), tptp_fun_D_2(B, A)), A) | in(ordered_pair(tptp_fun_D_2(B, A), tptp_fun_C_3(B, A)), A))))))))) | (~relation(inclusion_relation(A!14))) | ![B: $i] : (~((~((~is_connected_in(inclusion_relation(A!14), B)) | ![C: $i, D: $i] : ((C = D) | (~in(C, B)) | (~in(D, B)) | in(ordered_pair(D, C), inclusion_relation(A!14)) | in(ordered_pair(C, D), inclusion_relation(A!14))))) | (~(is_connected_in(inclusion_relation(A!14), B) | (~((~in(tptp_fun_C_3(B, inclusion_relation(A!14)), B)) | (~in(tptp_fun_D_2(B, inclusion_relation(A!14)), B)) | (tptp_fun_C_3(B, inclusion_relation(A!14)) = tptp_fun_D_2(B, inclusion_relation(A!14))) | in(ordered_pair(tptp_fun_C_3(B, inclusion_relation(A!14)), tptp_fun_D_2(B, inclusion_relation(A!14))), inclusion_relation(A!14)) | in(ordered_pair(tptp_fun_D_2(B, inclusion_relation(A!14)), tptp_fun_C_3(B, inclusion_relation(A!14))), inclusion_relation(A!14)))))))))),
% 0.19/0.41 inference(transitivity,[status(thm)],[87, 85])).
% 0.19/0.41 tff(89,plain,
% 0.19/0.41 ((~![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~is_connected_in(A, B)) | ![C: $i, D: $i] : (in(ordered_pair(D, C), A) | (C = D) | in(ordered_pair(C, D), A) | (~in(C, B)) | (~in(D, B))))) | (~(is_connected_in(A, B) | (~((~in(tptp_fun_C_3(B, A), B)) | (~in(tptp_fun_D_2(B, A), B)) | (tptp_fun_C_3(B, A) = tptp_fun_D_2(B, A)) | in(ordered_pair(tptp_fun_C_3(B, A), tptp_fun_D_2(B, A)), A) | in(ordered_pair(tptp_fun_D_2(B, A), tptp_fun_C_3(B, A)), A))))))))) | ((~relation(inclusion_relation(A!14))) | ![B: $i] : (~((~((~is_connected_in(inclusion_relation(A!14), B)) | ![C: $i, D: $i] : (in(ordered_pair(D, C), inclusion_relation(A!14)) | (C = D) | in(ordered_pair(C, D), inclusion_relation(A!14)) | (~in(C, B)) | (~in(D, B))))) | (~(is_connected_in(inclusion_relation(A!14), B) | (~((~in(tptp_fun_C_3(B, inclusion_relation(A!14)), B)) | (~in(tptp_fun_D_2(B, inclusion_relation(A!14)), B)) | (tptp_fun_C_3(B, inclusion_relation(A!14)) = tptp_fun_D_2(B, inclusion_relation(A!14))) | in(ordered_pair(tptp_fun_C_3(B, inclusion_relation(A!14)), tptp_fun_D_2(B, inclusion_relation(A!14))), inclusion_relation(A!14)) | in(ordered_pair(tptp_fun_D_2(B, inclusion_relation(A!14)), tptp_fun_C_3(B, inclusion_relation(A!14))), inclusion_relation(A!14)))))))))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(90,plain,
% 0.19/0.41 ((~![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~is_connected_in(A, B)) | ![C: $i, D: $i] : (in(ordered_pair(D, C), A) | (C = D) | in(ordered_pair(C, D), A) | (~in(C, B)) | (~in(D, B))))) | (~(is_connected_in(A, B) | (~((~in(tptp_fun_C_3(B, A), B)) | (~in(tptp_fun_D_2(B, A), B)) | (tptp_fun_C_3(B, A) = tptp_fun_D_2(B, A)) | in(ordered_pair(tptp_fun_C_3(B, A), tptp_fun_D_2(B, A)), A) | in(ordered_pair(tptp_fun_D_2(B, A), tptp_fun_C_3(B, A)), A))))))))) | (~relation(inclusion_relation(A!14))) | ![B: $i] : (~((~((~is_connected_in(inclusion_relation(A!14), B)) | ![C: $i, D: $i] : ((C = D) | (~in(C, B)) | (~in(D, B)) | in(ordered_pair(D, C), inclusion_relation(A!14)) | in(ordered_pair(C, D), inclusion_relation(A!14))))) | (~(is_connected_in(inclusion_relation(A!14), B) | (~((~in(tptp_fun_C_3(B, inclusion_relation(A!14)), B)) | (~in(tptp_fun_D_2(B, inclusion_relation(A!14)), B)) | (tptp_fun_C_3(B, inclusion_relation(A!14)) = tptp_fun_D_2(B, inclusion_relation(A!14))) | in(ordered_pair(tptp_fun_C_3(B, inclusion_relation(A!14)), tptp_fun_D_2(B, inclusion_relation(A!14))), inclusion_relation(A!14)) | in(ordered_pair(tptp_fun_D_2(B, inclusion_relation(A!14)), tptp_fun_C_3(B, inclusion_relation(A!14))), inclusion_relation(A!14))))))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[89, 88])).
% 0.19/0.41 tff(91,plain,
% 0.19/0.41 (![B: $i] : (~((~((~is_connected_in(inclusion_relation(A!14), B)) | ![C: $i, D: $i] : ((C = D) | (~in(C, B)) | (~in(D, B)) | in(ordered_pair(D, C), inclusion_relation(A!14)) | in(ordered_pair(C, D), inclusion_relation(A!14))))) | (~(is_connected_in(inclusion_relation(A!14), B) | (~((~in(tptp_fun_C_3(B, inclusion_relation(A!14)), B)) | (~in(tptp_fun_D_2(B, inclusion_relation(A!14)), B)) | (tptp_fun_C_3(B, inclusion_relation(A!14)) = tptp_fun_D_2(B, inclusion_relation(A!14))) | in(ordered_pair(tptp_fun_C_3(B, inclusion_relation(A!14)), tptp_fun_D_2(B, inclusion_relation(A!14))), inclusion_relation(A!14)) | in(ordered_pair(tptp_fun_D_2(B, inclusion_relation(A!14)), tptp_fun_C_3(B, inclusion_relation(A!14))), inclusion_relation(A!14))))))))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[90, 84, 9])).
% 0.19/0.41 tff(92,plain,
% 0.19/0.41 (((~![B: $i] : (~((~((~is_connected_in(inclusion_relation(A!14), B)) | ![C: $i, D: $i] : ((C = D) | (~in(C, B)) | (~in(D, B)) | in(ordered_pair(D, C), inclusion_relation(A!14)) | in(ordered_pair(C, D), inclusion_relation(A!14))))) | (~(is_connected_in(inclusion_relation(A!14), B) | (~((~in(tptp_fun_C_3(B, inclusion_relation(A!14)), B)) | (~in(tptp_fun_D_2(B, inclusion_relation(A!14)), B)) | (tptp_fun_C_3(B, inclusion_relation(A!14)) = tptp_fun_D_2(B, inclusion_relation(A!14))) | in(ordered_pair(tptp_fun_C_3(B, inclusion_relation(A!14)), tptp_fun_D_2(B, inclusion_relation(A!14))), inclusion_relation(A!14)) | in(ordered_pair(tptp_fun_D_2(B, inclusion_relation(A!14)), tptp_fun_C_3(B, inclusion_relation(A!14))), inclusion_relation(A!14))))))))) | (~((~((~is_connected_in(inclusion_relation(A!14), set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))))) | ![C: $i, D: $i] : ((C = D) | in(ordered_pair(D, C), inclusion_relation(A!14)) | in(ordered_pair(C, D), inclusion_relation(A!14)) | (~in(C, set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))))) | (~in(D, set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14)))))))) | (~((~((~in(tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)), set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))))) | (~in(tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)), set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))))) | (tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)) = tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14))) | in(ordered_pair(tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)), tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14))), inclusion_relation(A!14)) | in(ordered_pair(tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)), tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14))), inclusion_relation(A!14)))) | is_connected_in(inclusion_relation(A!14), set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))))))))) <=> ((~![B: $i] : (~((~((~is_connected_in(inclusion_relation(A!14), B)) | ![C: $i, D: $i] : ((C = D) | (~in(C, B)) | (~in(D, B)) | in(ordered_pair(D, C), inclusion_relation(A!14)) | in(ordered_pair(C, D), inclusion_relation(A!14))))) | (~(is_connected_in(inclusion_relation(A!14), B) | (~((~in(tptp_fun_C_3(B, inclusion_relation(A!14)), B)) | (~in(tptp_fun_D_2(B, inclusion_relation(A!14)), B)) | (tptp_fun_C_3(B, inclusion_relation(A!14)) = tptp_fun_D_2(B, inclusion_relation(A!14))) | in(ordered_pair(tptp_fun_C_3(B, inclusion_relation(A!14)), tptp_fun_D_2(B, inclusion_relation(A!14))), inclusion_relation(A!14)) | in(ordered_pair(tptp_fun_D_2(B, inclusion_relation(A!14)), tptp_fun_C_3(B, inclusion_relation(A!14))), inclusion_relation(A!14))))))))) | (~((~((~is_connected_in(inclusion_relation(A!14), set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))))) | ![C: $i, D: $i] : ((C = D) | in(ordered_pair(D, C), inclusion_relation(A!14)) | in(ordered_pair(C, D), inclusion_relation(A!14)) | (~in(C, set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))))) | (~in(D, set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14)))))))) | (~((~((~in(tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)), set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))))) | (~in(tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)), set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))))) | (tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)) = tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14))) | in(ordered_pair(tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)), tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14))), inclusion_relation(A!14)) | in(ordered_pair(tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)), tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14))), inclusion_relation(A!14)))) | is_connected_in(inclusion_relation(A!14), set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14)))))))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(93,plain,
% 0.19/0.41 ((~((~((~is_connected_in(inclusion_relation(A!14), set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))))) | ![C: $i, D: $i] : ((C = D) | (~in(C, set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))))) | (~in(D, set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))))) | in(ordered_pair(D, C), inclusion_relation(A!14)) | in(ordered_pair(C, D), inclusion_relation(A!14))))) | (~(is_connected_in(inclusion_relation(A!14), set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14)))) | (~((~in(tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)), set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))))) | (~in(tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)), set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))))) | (tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)) = tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14))) | in(ordered_pair(tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)), tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14))), inclusion_relation(A!14)) | in(ordered_pair(tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)), tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14))), inclusion_relation(A!14)))))))) <=> (~((~((~is_connected_in(inclusion_relation(A!14), set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))))) | ![C: $i, D: $i] : ((C = D) | in(ordered_pair(D, C), inclusion_relation(A!14)) | in(ordered_pair(C, D), inclusion_relation(A!14)) | (~in(C, set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))))) | (~in(D, set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14)))))))) | (~((~((~in(tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)), set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))))) | (~in(tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)), set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))))) | (tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)) = tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14))) | in(ordered_pair(tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)), tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14))), inclusion_relation(A!14)) | in(ordered_pair(tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)), tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14))), inclusion_relation(A!14)))) | is_connected_in(inclusion_relation(A!14), set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))))))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(94,plain,
% 0.19/0.41 (((~![B: $i] : (~((~((~is_connected_in(inclusion_relation(A!14), B)) | ![C: $i, D: $i] : ((C = D) | (~in(C, B)) | (~in(D, B)) | in(ordered_pair(D, C), inclusion_relation(A!14)) | in(ordered_pair(C, D), inclusion_relation(A!14))))) | (~(is_connected_in(inclusion_relation(A!14), B) | (~((~in(tptp_fun_C_3(B, inclusion_relation(A!14)), B)) | (~in(tptp_fun_D_2(B, inclusion_relation(A!14)), B)) | (tptp_fun_C_3(B, inclusion_relation(A!14)) = tptp_fun_D_2(B, inclusion_relation(A!14))) | in(ordered_pair(tptp_fun_C_3(B, inclusion_relation(A!14)), tptp_fun_D_2(B, inclusion_relation(A!14))), inclusion_relation(A!14)) | in(ordered_pair(tptp_fun_D_2(B, inclusion_relation(A!14)), tptp_fun_C_3(B, inclusion_relation(A!14))), inclusion_relation(A!14))))))))) | (~((~((~is_connected_in(inclusion_relation(A!14), set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))))) | ![C: $i, D: $i] : ((C = D) | (~in(C, set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))))) | (~in(D, set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))))) | in(ordered_pair(D, C), inclusion_relation(A!14)) | in(ordered_pair(C, D), inclusion_relation(A!14))))) | (~(is_connected_in(inclusion_relation(A!14), set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14)))) | (~((~in(tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)), set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))))) | (~in(tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)), set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))))) | (tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)) = tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14))) | in(ordered_pair(tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)), tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14))), inclusion_relation(A!14)) | in(ordered_pair(tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)), tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14))), inclusion_relation(A!14))))))))) <=> ((~![B: $i] : (~((~((~is_connected_in(inclusion_relation(A!14), B)) | ![C: $i, D: $i] : ((C = D) | (~in(C, B)) | (~in(D, B)) | in(ordered_pair(D, C), inclusion_relation(A!14)) | in(ordered_pair(C, D), inclusion_relation(A!14))))) | (~(is_connected_in(inclusion_relation(A!14), B) | (~((~in(tptp_fun_C_3(B, inclusion_relation(A!14)), B)) | (~in(tptp_fun_D_2(B, inclusion_relation(A!14)), B)) | (tptp_fun_C_3(B, inclusion_relation(A!14)) = tptp_fun_D_2(B, inclusion_relation(A!14))) | in(ordered_pair(tptp_fun_C_3(B, inclusion_relation(A!14)), tptp_fun_D_2(B, inclusion_relation(A!14))), inclusion_relation(A!14)) | in(ordered_pair(tptp_fun_D_2(B, inclusion_relation(A!14)), tptp_fun_C_3(B, inclusion_relation(A!14))), inclusion_relation(A!14))))))))) | (~((~((~is_connected_in(inclusion_relation(A!14), set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))))) | ![C: $i, D: $i] : ((C = D) | in(ordered_pair(D, C), inclusion_relation(A!14)) | in(ordered_pair(C, D), inclusion_relation(A!14)) | (~in(C, set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))))) | (~in(D, set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14)))))))) | (~((~((~in(tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)), set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))))) | (~in(tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)), set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))))) | (tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)) = tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14))) | in(ordered_pair(tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)), tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14))), inclusion_relation(A!14)) | in(ordered_pair(tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)), tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14))), inclusion_relation(A!14)))) | is_connected_in(inclusion_relation(A!14), set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14)))))))))),
% 0.19/0.42 inference(monotonicity,[status(thm)],[93])).
% 0.19/0.42 tff(95,plain,
% 0.19/0.42 (((~![B: $i] : (~((~((~is_connected_in(inclusion_relation(A!14), B)) | ![C: $i, D: $i] : ((C = D) | (~in(C, B)) | (~in(D, B)) | in(ordered_pair(D, C), inclusion_relation(A!14)) | in(ordered_pair(C, D), inclusion_relation(A!14))))) | (~(is_connected_in(inclusion_relation(A!14), B) | (~((~in(tptp_fun_C_3(B, inclusion_relation(A!14)), B)) | (~in(tptp_fun_D_2(B, inclusion_relation(A!14)), B)) | (tptp_fun_C_3(B, inclusion_relation(A!14)) = tptp_fun_D_2(B, inclusion_relation(A!14))) | in(ordered_pair(tptp_fun_C_3(B, inclusion_relation(A!14)), tptp_fun_D_2(B, inclusion_relation(A!14))), inclusion_relation(A!14)) | in(ordered_pair(tptp_fun_D_2(B, inclusion_relation(A!14)), tptp_fun_C_3(B, inclusion_relation(A!14))), inclusion_relation(A!14))))))))) | (~((~((~is_connected_in(inclusion_relation(A!14), set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))))) | ![C: $i, D: $i] : ((C = D) | (~in(C, set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))))) | (~in(D, set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))))) | in(ordered_pair(D, C), inclusion_relation(A!14)) | in(ordered_pair(C, D), inclusion_relation(A!14))))) | (~(is_connected_in(inclusion_relation(A!14), set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14)))) | (~((~in(tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)), set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))))) | (~in(tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)), set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))))) | (tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)) = tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14))) | in(ordered_pair(tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)), tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14))), inclusion_relation(A!14)) | in(ordered_pair(tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)), tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14))), inclusion_relation(A!14))))))))) <=> ((~![B: $i] : (~((~((~is_connected_in(inclusion_relation(A!14), B)) | ![C: $i, D: $i] : ((C = D) | (~in(C, B)) | (~in(D, B)) | in(ordered_pair(D, C), inclusion_relation(A!14)) | in(ordered_pair(C, D), inclusion_relation(A!14))))) | (~(is_connected_in(inclusion_relation(A!14), B) | (~((~in(tptp_fun_C_3(B, inclusion_relation(A!14)), B)) | (~in(tptp_fun_D_2(B, inclusion_relation(A!14)), B)) | (tptp_fun_C_3(B, inclusion_relation(A!14)) = tptp_fun_D_2(B, inclusion_relation(A!14))) | in(ordered_pair(tptp_fun_C_3(B, inclusion_relation(A!14)), tptp_fun_D_2(B, inclusion_relation(A!14))), inclusion_relation(A!14)) | in(ordered_pair(tptp_fun_D_2(B, inclusion_relation(A!14)), tptp_fun_C_3(B, inclusion_relation(A!14))), inclusion_relation(A!14))))))))) | (~((~((~is_connected_in(inclusion_relation(A!14), set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))))) | ![C: $i, D: $i] : ((C = D) | in(ordered_pair(D, C), inclusion_relation(A!14)) | in(ordered_pair(C, D), inclusion_relation(A!14)) | (~in(C, set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))))) | (~in(D, set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14)))))))) | (~((~((~in(tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)), set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))))) | (~in(tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)), set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))))) | (tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)) = tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14))) | in(ordered_pair(tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)), tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14))), inclusion_relation(A!14)) | in(ordered_pair(tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)), tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14))), inclusion_relation(A!14)))) | is_connected_in(inclusion_relation(A!14), set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14)))))))))),
% 0.19/0.42 inference(transitivity,[status(thm)],[94, 92])).
% 0.19/0.42 tff(96,plain,
% 0.19/0.42 ((~![B: $i] : (~((~((~is_connected_in(inclusion_relation(A!14), B)) | ![C: $i, D: $i] : ((C = D) | (~in(C, B)) | (~in(D, B)) | in(ordered_pair(D, C), inclusion_relation(A!14)) | in(ordered_pair(C, D), inclusion_relation(A!14))))) | (~(is_connected_in(inclusion_relation(A!14), B) | (~((~in(tptp_fun_C_3(B, inclusion_relation(A!14)), B)) | (~in(tptp_fun_D_2(B, inclusion_relation(A!14)), B)) | (tptp_fun_C_3(B, inclusion_relation(A!14)) = tptp_fun_D_2(B, inclusion_relation(A!14))) | in(ordered_pair(tptp_fun_C_3(B, inclusion_relation(A!14)), tptp_fun_D_2(B, inclusion_relation(A!14))), inclusion_relation(A!14)) | in(ordered_pair(tptp_fun_D_2(B, inclusion_relation(A!14)), tptp_fun_C_3(B, inclusion_relation(A!14))), inclusion_relation(A!14))))))))) | (~((~((~is_connected_in(inclusion_relation(A!14), set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))))) | ![C: $i, D: $i] : ((C = D) | (~in(C, set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))))) | (~in(D, set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))))) | in(ordered_pair(D, C), inclusion_relation(A!14)) | in(ordered_pair(C, D), inclusion_relation(A!14))))) | (~(is_connected_in(inclusion_relation(A!14), set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14)))) | (~((~in(tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)), set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))))) | (~in(tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)), set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))))) | (tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)) = tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14))) | in(ordered_pair(tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)), tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14))), inclusion_relation(A!14)) | in(ordered_pair(tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)), tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14))), inclusion_relation(A!14))))))))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(97,plain,
% 0.19/0.42 ((~![B: $i] : (~((~((~is_connected_in(inclusion_relation(A!14), B)) | ![C: $i, D: $i] : ((C = D) | (~in(C, B)) | (~in(D, B)) | in(ordered_pair(D, C), inclusion_relation(A!14)) | in(ordered_pair(C, D), inclusion_relation(A!14))))) | (~(is_connected_in(inclusion_relation(A!14), B) | (~((~in(tptp_fun_C_3(B, inclusion_relation(A!14)), B)) | (~in(tptp_fun_D_2(B, inclusion_relation(A!14)), B)) | (tptp_fun_C_3(B, inclusion_relation(A!14)) = tptp_fun_D_2(B, inclusion_relation(A!14))) | in(ordered_pair(tptp_fun_C_3(B, inclusion_relation(A!14)), tptp_fun_D_2(B, inclusion_relation(A!14))), inclusion_relation(A!14)) | in(ordered_pair(tptp_fun_D_2(B, inclusion_relation(A!14)), tptp_fun_C_3(B, inclusion_relation(A!14))), inclusion_relation(A!14))))))))) | (~((~((~is_connected_in(inclusion_relation(A!14), set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))))) | ![C: $i, D: $i] : ((C = D) | in(ordered_pair(D, C), inclusion_relation(A!14)) | in(ordered_pair(C, D), inclusion_relation(A!14)) | (~in(C, set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))))) | (~in(D, set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14)))))))) | (~((~((~in(tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)), set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))))) | (~in(tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)), set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))))) | (tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)) = tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14))) | in(ordered_pair(tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)), tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14))), inclusion_relation(A!14)) | in(ordered_pair(tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)), tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14))), inclusion_relation(A!14)))) | is_connected_in(inclusion_relation(A!14), set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))))))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[96, 95])).
% 0.19/0.42 tff(98,plain,
% 0.19/0.42 (~((~((~is_connected_in(inclusion_relation(A!14), set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))))) | ![C: $i, D: $i] : ((C = D) | in(ordered_pair(D, C), inclusion_relation(A!14)) | in(ordered_pair(C, D), inclusion_relation(A!14)) | (~in(C, set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))))) | (~in(D, set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14)))))))) | (~((~((~in(tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)), set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))))) | (~in(tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)), set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))))) | (tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)) = tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14))) | in(ordered_pair(tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)), tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14))), inclusion_relation(A!14)) | in(ordered_pair(tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)), tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14))), inclusion_relation(A!14)))) | is_connected_in(inclusion_relation(A!14), set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14)))))))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[97, 91])).
% 0.19/0.42 tff(99,plain,
% 0.19/0.42 (((~((~is_connected_in(inclusion_relation(A!14), set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))))) | ![C: $i, D: $i] : ((C = D) | in(ordered_pair(D, C), inclusion_relation(A!14)) | in(ordered_pair(C, D), inclusion_relation(A!14)) | (~in(C, set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))))) | (~in(D, set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14)))))))) | (~((~((~in(tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)), set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))))) | (~in(tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)), set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))))) | (tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)) = tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14))) | in(ordered_pair(tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)), tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14))), inclusion_relation(A!14)) | in(ordered_pair(tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)), tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14))), inclusion_relation(A!14)))) | is_connected_in(inclusion_relation(A!14), set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))))))) | ((~((~in(tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)), set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))))) | (~in(tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)), set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))))) | (tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)) = tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14))) | in(ordered_pair(tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)), tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14))), inclusion_relation(A!14)) | in(ordered_pair(tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)), tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14))), inclusion_relation(A!14)))) | is_connected_in(inclusion_relation(A!14), set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14)))))),
% 0.19/0.43 inference(tautology,[status(thm)],[])).
% 0.19/0.43 tff(100,plain,
% 0.19/0.43 ((~((~in(tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)), set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))))) | (~in(tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)), set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))))) | (tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)) = tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14))) | in(ordered_pair(tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)), tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14))), inclusion_relation(A!14)) | in(ordered_pair(tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)), tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14))), inclusion_relation(A!14)))) | is_connected_in(inclusion_relation(A!14), set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[99, 98])).
% 0.19/0.43 tff(101,plain,
% 0.19/0.43 (is_connected_in(inclusion_relation(A!14), set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14)))) <=> is_connected_in(inclusion_relation(A!14), relation_field(inclusion_relation(A!14)))),
% 0.19/0.43 inference(monotonicity,[status(thm)],[55])).
% 0.19/0.43 tff(102,plain,
% 0.19/0.43 (is_connected_in(inclusion_relation(A!14), relation_field(inclusion_relation(A!14))) <=> is_connected_in(inclusion_relation(A!14), set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))))),
% 0.19/0.43 inference(symmetry,[status(thm)],[101])).
% 0.19/0.43 tff(103,plain,
% 0.19/0.43 ((~is_connected_in(inclusion_relation(A!14), relation_field(inclusion_relation(A!14)))) <=> (~is_connected_in(inclusion_relation(A!14), set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14)))))),
% 0.19/0.43 inference(monotonicity,[status(thm)],[102])).
% 0.19/0.43 tff(104,plain,
% 0.19/0.43 (^[A: $i] : refl(((~relation(A)) | (connected(A) <=> is_connected_in(A, relation_field(A)))) <=> ((~relation(A)) | (connected(A) <=> is_connected_in(A, relation_field(A)))))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(105,plain,
% 0.19/0.43 (![A: $i] : ((~relation(A)) | (connected(A) <=> is_connected_in(A, relation_field(A)))) <=> ![A: $i] : ((~relation(A)) | (connected(A) <=> is_connected_in(A, relation_field(A))))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[104])).
% 0.19/0.43 tff(106,plain,
% 0.19/0.43 (![A: $i] : ((~relation(A)) | (connected(A) <=> is_connected_in(A, relation_field(A)))) <=> ![A: $i] : ((~relation(A)) | (connected(A) <=> is_connected_in(A, relation_field(A))))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(107,plain,
% 0.19/0.43 (^[A: $i] : rewrite((relation(A) => (connected(A) <=> is_connected_in(A, relation_field(A)))) <=> ((~relation(A)) | (connected(A) <=> is_connected_in(A, relation_field(A)))))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(108,plain,
% 0.19/0.43 (![A: $i] : (relation(A) => (connected(A) <=> is_connected_in(A, relation_field(A)))) <=> ![A: $i] : ((~relation(A)) | (connected(A) <=> is_connected_in(A, relation_field(A))))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[107])).
% 0.19/0.43 tff(109,axiom,(![A: $i] : (relation(A) => (connected(A) <=> is_connected_in(A, relation_field(A))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d14_relat_2')).
% 0.19/0.43 tff(110,plain,
% 0.19/0.43 (![A: $i] : ((~relation(A)) | (connected(A) <=> is_connected_in(A, relation_field(A))))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[109, 108])).
% 0.19/0.43 tff(111,plain,
% 0.19/0.43 (![A: $i] : ((~relation(A)) | (connected(A) <=> is_connected_in(A, relation_field(A))))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[110, 106])).
% 0.19/0.43 tff(112,plain,(
% 0.19/0.43 ![A: $i] : ((~relation(A)) | (connected(A) <=> is_connected_in(A, relation_field(A))))),
% 0.19/0.43 inference(skolemize,[status(sab)],[111])).
% 0.19/0.43 tff(113,plain,
% 0.19/0.43 (![A: $i] : ((~relation(A)) | (connected(A) <=> is_connected_in(A, relation_field(A))))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[112, 105])).
% 0.19/0.43 tff(114,plain,
% 0.19/0.43 (((~![A: $i] : ((~relation(A)) | (connected(A) <=> is_connected_in(A, relation_field(A))))) | ((~relation(inclusion_relation(A!14))) | (connected(inclusion_relation(A!14)) <=> is_connected_in(inclusion_relation(A!14), relation_field(inclusion_relation(A!14)))))) <=> ((~![A: $i] : ((~relation(A)) | (connected(A) <=> is_connected_in(A, relation_field(A))))) | (~relation(inclusion_relation(A!14))) | (connected(inclusion_relation(A!14)) <=> is_connected_in(inclusion_relation(A!14), relation_field(inclusion_relation(A!14)))))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(115,plain,
% 0.19/0.43 ((~![A: $i] : ((~relation(A)) | (connected(A) <=> is_connected_in(A, relation_field(A))))) | ((~relation(inclusion_relation(A!14))) | (connected(inclusion_relation(A!14)) <=> is_connected_in(inclusion_relation(A!14), relation_field(inclusion_relation(A!14)))))),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(116,plain,
% 0.19/0.43 ((~![A: $i] : ((~relation(A)) | (connected(A) <=> is_connected_in(A, relation_field(A))))) | (~relation(inclusion_relation(A!14))) | (connected(inclusion_relation(A!14)) <=> is_connected_in(inclusion_relation(A!14), relation_field(inclusion_relation(A!14))))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[115, 114])).
% 0.19/0.43 tff(117,plain,
% 0.19/0.43 ((~relation(inclusion_relation(A!14))) | (connected(inclusion_relation(A!14)) <=> is_connected_in(inclusion_relation(A!14), relation_field(inclusion_relation(A!14))))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[116, 113])).
% 0.19/0.43 tff(118,plain,
% 0.19/0.43 (connected(inclusion_relation(A!14)) <=> is_connected_in(inclusion_relation(A!14), relation_field(inclusion_relation(A!14)))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[117, 9])).
% 0.19/0.43 tff(119,plain,
% 0.19/0.43 (~connected(inclusion_relation(A!14))),
% 0.19/0.43 inference(or_elim,[status(thm)],[66])).
% 0.19/0.43 tff(120,plain,
% 0.19/0.43 ((~(connected(inclusion_relation(A!14)) <=> is_connected_in(inclusion_relation(A!14), relation_field(inclusion_relation(A!14))))) | connected(inclusion_relation(A!14)) | (~is_connected_in(inclusion_relation(A!14), relation_field(inclusion_relation(A!14))))),
% 0.19/0.43 inference(tautology,[status(thm)],[])).
% 0.19/0.43 tff(121,plain,
% 0.19/0.43 ((~(connected(inclusion_relation(A!14)) <=> is_connected_in(inclusion_relation(A!14), relation_field(inclusion_relation(A!14))))) | (~is_connected_in(inclusion_relation(A!14), relation_field(inclusion_relation(A!14))))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[120, 119])).
% 0.19/0.43 tff(122,plain,
% 0.19/0.43 (~is_connected_in(inclusion_relation(A!14), relation_field(inclusion_relation(A!14)))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[121, 118])).
% 0.19/0.43 tff(123,plain,
% 0.19/0.43 (~is_connected_in(inclusion_relation(A!14), set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[122, 103])).
% 0.19/0.43 tff(124,plain,
% 0.19/0.43 ((~((~((~in(tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)), set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))))) | (~in(tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)), set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))))) | (tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)) = tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14))) | in(ordered_pair(tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)), tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14))), inclusion_relation(A!14)) | in(ordered_pair(tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)), tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14))), inclusion_relation(A!14)))) | is_connected_in(inclusion_relation(A!14), set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14)))))) | (~((~in(tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)), set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))))) | (~in(tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)), set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))))) | (tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)) = tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14))) | in(ordered_pair(tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)), tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14))), inclusion_relation(A!14)) | in(ordered_pair(tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)), tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14))), inclusion_relation(A!14)))) | is_connected_in(inclusion_relation(A!14), set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))))),
% 0.19/0.43 inference(tautology,[status(thm)],[])).
% 0.19/0.43 tff(125,plain,
% 0.19/0.43 (~((~in(tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)), set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))))) | (~in(tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)), set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))))) | (tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)) = tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14))) | in(ordered_pair(tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)), tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14))), inclusion_relation(A!14)) | in(ordered_pair(tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)), tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14))), inclusion_relation(A!14)))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[124, 123, 100])).
% 0.19/0.43 tff(126,plain,
% 0.19/0.43 (((~in(tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)), set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))))) | (~in(tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)), set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))))) | (tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)) = tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14))) | in(ordered_pair(tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)), tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14))), inclusion_relation(A!14)) | in(ordered_pair(tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)), tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14))), inclusion_relation(A!14))) | in(tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)), set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))))),
% 0.19/0.43 inference(tautology,[status(thm)],[])).
% 0.19/0.43 tff(127,plain,
% 0.19/0.43 (in(tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)), set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[126, 125])).
% 0.19/0.43 tff(128,plain,
% 0.19/0.43 (^[A: $i, B: $i] : refl((ordinal(A) | (~in(A, B)) | (~ordinal(B))) <=> (ordinal(A) | (~in(A, B)) | (~ordinal(B))))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(129,plain,
% 0.19/0.43 (![A: $i, B: $i] : (ordinal(A) | (~in(A, B)) | (~ordinal(B))) <=> ![A: $i, B: $i] : (ordinal(A) | (~in(A, B)) | (~ordinal(B)))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[128])).
% 0.19/0.43 tff(130,plain,
% 0.19/0.43 (![A: $i, B: $i] : (ordinal(A) | (~in(A, B)) | (~ordinal(B))) <=> ![A: $i, B: $i] : (ordinal(A) | (~in(A, B)) | (~ordinal(B)))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(131,plain,
% 0.19/0.43 (^[A: $i, B: $i] : trans(monotonicity(rewrite((in(A, B) => ordinal(A)) <=> (ordinal(A) | (~in(A, B)))), ((ordinal(B) => (in(A, B) => ordinal(A))) <=> (ordinal(B) => (ordinal(A) | (~in(A, B)))))), rewrite((ordinal(B) => (ordinal(A) | (~in(A, B)))) <=> (ordinal(A) | (~in(A, B)) | (~ordinal(B)))), ((ordinal(B) => (in(A, B) => ordinal(A))) <=> (ordinal(A) | (~in(A, B)) | (~ordinal(B)))))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(132,plain,
% 0.19/0.43 (![A: $i, B: $i] : (ordinal(B) => (in(A, B) => ordinal(A))) <=> ![A: $i, B: $i] : (ordinal(A) | (~in(A, B)) | (~ordinal(B)))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[131])).
% 0.19/0.43 tff(133,axiom,(![A: $i, B: $i] : (ordinal(B) => (in(A, B) => ordinal(A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t23_ordinal1')).
% 0.19/0.43 tff(134,plain,
% 0.19/0.43 (![A: $i, B: $i] : (ordinal(A) | (~in(A, B)) | (~ordinal(B)))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[133, 132])).
% 0.19/0.43 tff(135,plain,
% 0.19/0.43 (![A: $i, B: $i] : (ordinal(A) | (~in(A, B)) | (~ordinal(B)))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[134, 130])).
% 0.19/0.43 tff(136,plain,(
% 0.19/0.43 ![A: $i, B: $i] : (ordinal(A) | (~in(A, B)) | (~ordinal(B)))),
% 0.19/0.43 inference(skolemize,[status(sab)],[135])).
% 0.19/0.43 tff(137,plain,
% 0.19/0.43 (![A: $i, B: $i] : (ordinal(A) | (~in(A, B)) | (~ordinal(B)))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[136, 129])).
% 0.19/0.43 tff(138,plain,
% 0.19/0.43 (((~![A: $i, B: $i] : (ordinal(A) | (~in(A, B)) | (~ordinal(B)))) | ((~in(tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)), set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))))) | (~ordinal(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))))) | ordinal(tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14))))) <=> ((~![A: $i, B: $i] : (ordinal(A) | (~in(A, B)) | (~ordinal(B)))) | (~in(tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)), set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))))) | (~ordinal(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))))) | ordinal(tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14))))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(139,plain,
% 0.19/0.43 ((ordinal(tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14))) | (~in(tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)), set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))))) | (~ordinal(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14)))))) <=> ((~in(tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)), set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))))) | (~ordinal(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))))) | ordinal(tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14))))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(140,plain,
% 0.19/0.43 (((~![A: $i, B: $i] : (ordinal(A) | (~in(A, B)) | (~ordinal(B)))) | (ordinal(tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14))) | (~in(tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)), set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))))) | (~ordinal(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))))))) <=> ((~![A: $i, B: $i] : (ordinal(A) | (~in(A, B)) | (~ordinal(B)))) | ((~in(tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)), set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))))) | (~ordinal(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))))) | ordinal(tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)))))),
% 0.19/0.43 inference(monotonicity,[status(thm)],[139])).
% 0.19/0.43 tff(141,plain,
% 0.19/0.43 (((~![A: $i, B: $i] : (ordinal(A) | (~in(A, B)) | (~ordinal(B)))) | (ordinal(tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14))) | (~in(tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)), set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))))) | (~ordinal(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))))))) <=> ((~![A: $i, B: $i] : (ordinal(A) | (~in(A, B)) | (~ordinal(B)))) | (~in(tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)), set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))))) | (~ordinal(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))))) | ordinal(tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14))))),
% 0.19/0.44 inference(transitivity,[status(thm)],[140, 138])).
% 0.19/0.44 tff(142,plain,
% 0.19/0.44 ((~![A: $i, B: $i] : (ordinal(A) | (~in(A, B)) | (~ordinal(B)))) | (ordinal(tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14))) | (~in(tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)), set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))))) | (~ordinal(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))))))),
% 0.19/0.44 inference(quant_inst,[status(thm)],[])).
% 0.19/0.44 tff(143,plain,
% 0.19/0.44 ((~![A: $i, B: $i] : (ordinal(A) | (~in(A, B)) | (~ordinal(B)))) | (~in(tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)), set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))))) | (~ordinal(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))))) | ordinal(tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[142, 141])).
% 0.19/0.44 tff(144,plain,
% 0.19/0.44 ((~ordinal(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))))) | ordinal(tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[143, 137, 127])).
% 0.19/0.44 tff(145,plain,
% 0.19/0.44 (ordinal(tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[144, 68])).
% 0.19/0.44 tff(146,plain,
% 0.19/0.44 (((~in(tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)), set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))))) | (~in(tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)), set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))))) | (tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)) = tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14))) | in(ordered_pair(tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)), tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14))), inclusion_relation(A!14)) | in(ordered_pair(tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)), tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14))), inclusion_relation(A!14))) | in(tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)), set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))))),
% 0.19/0.44 inference(tautology,[status(thm)],[])).
% 0.19/0.44 tff(147,plain,
% 0.19/0.44 (in(tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)), set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[146, 125])).
% 0.19/0.44 tff(148,plain,
% 0.19/0.44 (((~![A: $i, B: $i] : (ordinal(A) | (~in(A, B)) | (~ordinal(B)))) | ((~in(tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)), set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))))) | ordinal(tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14))) | (~ordinal(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))))))) <=> ((~![A: $i, B: $i] : (ordinal(A) | (~in(A, B)) | (~ordinal(B)))) | (~in(tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)), set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))))) | ordinal(tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14))) | (~ordinal(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))))))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(149,plain,
% 0.19/0.44 ((ordinal(tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14))) | (~in(tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)), set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))))) | (~ordinal(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14)))))) <=> ((~in(tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)), set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))))) | ordinal(tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14))) | (~ordinal(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))))))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(150,plain,
% 0.19/0.44 (((~![A: $i, B: $i] : (ordinal(A) | (~in(A, B)) | (~ordinal(B)))) | (ordinal(tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14))) | (~in(tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)), set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))))) | (~ordinal(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))))))) <=> ((~![A: $i, B: $i] : (ordinal(A) | (~in(A, B)) | (~ordinal(B)))) | ((~in(tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)), set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))))) | ordinal(tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14))) | (~ordinal(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14)))))))),
% 0.19/0.44 inference(monotonicity,[status(thm)],[149])).
% 0.19/0.44 tff(151,plain,
% 0.19/0.44 (((~![A: $i, B: $i] : (ordinal(A) | (~in(A, B)) | (~ordinal(B)))) | (ordinal(tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14))) | (~in(tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)), set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))))) | (~ordinal(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))))))) <=> ((~![A: $i, B: $i] : (ordinal(A) | (~in(A, B)) | (~ordinal(B)))) | (~in(tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)), set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))))) | ordinal(tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14))) | (~ordinal(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))))))),
% 0.19/0.44 inference(transitivity,[status(thm)],[150, 148])).
% 0.19/0.44 tff(152,plain,
% 0.19/0.44 ((~![A: $i, B: $i] : (ordinal(A) | (~in(A, B)) | (~ordinal(B)))) | (ordinal(tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14))) | (~in(tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)), set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))))) | (~ordinal(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))))))),
% 0.19/0.44 inference(quant_inst,[status(thm)],[])).
% 0.19/0.44 tff(153,plain,
% 0.19/0.44 ((~![A: $i, B: $i] : (ordinal(A) | (~in(A, B)) | (~ordinal(B)))) | (~in(tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)), set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))))) | ordinal(tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14))) | (~ordinal(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14)))))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[152, 151])).
% 0.19/0.44 tff(154,plain,
% 0.19/0.44 (ordinal(tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14))) | (~ordinal(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14)))))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[153, 137, 147])).
% 0.19/0.44 tff(155,plain,
% 0.19/0.44 (ordinal(tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[154, 68])).
% 0.19/0.44 tff(156,plain,
% 0.19/0.44 (^[A: $i, B: $i] : refl(((ordinal_subset(A, B) <=> subset(A, B)) | (~ordinal(B)) | (~ordinal(A))) <=> ((ordinal_subset(A, B) <=> subset(A, B)) | (~ordinal(B)) | (~ordinal(A))))),
% 0.19/0.44 inference(bind,[status(th)],[])).
% 0.19/0.44 tff(157,plain,
% 0.19/0.44 (![A: $i, B: $i] : ((ordinal_subset(A, B) <=> subset(A, B)) | (~ordinal(B)) | (~ordinal(A))) <=> ![A: $i, B: $i] : ((ordinal_subset(A, B) <=> subset(A, B)) | (~ordinal(B)) | (~ordinal(A)))),
% 0.19/0.44 inference(quant_intro,[status(thm)],[156])).
% 0.19/0.44 tff(158,plain,
% 0.19/0.44 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite((ordinal(A) & ordinal(B)) <=> (~((~ordinal(B)) | (~ordinal(A))))), ((~(ordinal(A) & ordinal(B))) <=> (~(~((~ordinal(B)) | (~ordinal(A))))))), rewrite((~(~((~ordinal(B)) | (~ordinal(A))))) <=> ((~ordinal(B)) | (~ordinal(A)))), ((~(ordinal(A) & ordinal(B))) <=> ((~ordinal(B)) | (~ordinal(A))))), (((~(ordinal(A) & ordinal(B))) | (ordinal_subset(A, B) <=> subset(A, B))) <=> (((~ordinal(B)) | (~ordinal(A))) | (ordinal_subset(A, B) <=> subset(A, B))))), rewrite((((~ordinal(B)) | (~ordinal(A))) | (ordinal_subset(A, B) <=> subset(A, B))) <=> ((ordinal_subset(A, B) <=> subset(A, B)) | (~ordinal(B)) | (~ordinal(A)))), (((~(ordinal(A) & ordinal(B))) | (ordinal_subset(A, B) <=> subset(A, B))) <=> ((ordinal_subset(A, B) <=> subset(A, B)) | (~ordinal(B)) | (~ordinal(A)))))),
% 0.19/0.44 inference(bind,[status(th)],[])).
% 0.19/0.44 tff(159,plain,
% 0.19/0.44 (![A: $i, B: $i] : ((~(ordinal(A) & ordinal(B))) | (ordinal_subset(A, B) <=> subset(A, B))) <=> ![A: $i, B: $i] : ((ordinal_subset(A, B) <=> subset(A, B)) | (~ordinal(B)) | (~ordinal(A)))),
% 0.19/0.44 inference(quant_intro,[status(thm)],[158])).
% 0.19/0.44 tff(160,plain,
% 0.19/0.44 (![A: $i, B: $i] : ((~(ordinal(A) & ordinal(B))) | (ordinal_subset(A, B) <=> subset(A, B))) <=> ![A: $i, B: $i] : ((~(ordinal(A) & ordinal(B))) | (ordinal_subset(A, B) <=> subset(A, B)))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(161,plain,
% 0.19/0.44 (^[A: $i, B: $i] : rewrite(((ordinal(A) & ordinal(B)) => (ordinal_subset(A, B) <=> subset(A, B))) <=> ((~(ordinal(A) & ordinal(B))) | (ordinal_subset(A, B) <=> subset(A, B))))),
% 0.19/0.44 inference(bind,[status(th)],[])).
% 0.19/0.44 tff(162,plain,
% 0.19/0.44 (![A: $i, B: $i] : ((ordinal(A) & ordinal(B)) => (ordinal_subset(A, B) <=> subset(A, B))) <=> ![A: $i, B: $i] : ((~(ordinal(A) & ordinal(B))) | (ordinal_subset(A, B) <=> subset(A, B)))),
% 0.19/0.44 inference(quant_intro,[status(thm)],[161])).
% 0.19/0.44 tff(163,axiom,(![A: $i, B: $i] : ((ordinal(A) & ordinal(B)) => (ordinal_subset(A, B) <=> subset(A, B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','redefinition_r1_ordinal1')).
% 0.19/0.44 tff(164,plain,
% 0.19/0.44 (![A: $i, B: $i] : ((~(ordinal(A) & ordinal(B))) | (ordinal_subset(A, B) <=> subset(A, B)))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[163, 162])).
% 0.19/0.44 tff(165,plain,
% 0.19/0.44 (![A: $i, B: $i] : ((~(ordinal(A) & ordinal(B))) | (ordinal_subset(A, B) <=> subset(A, B)))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[164, 160])).
% 0.19/0.44 tff(166,plain,(
% 0.19/0.44 ![A: $i, B: $i] : ((~(ordinal(A) & ordinal(B))) | (ordinal_subset(A, B) <=> subset(A, B)))),
% 0.19/0.44 inference(skolemize,[status(sab)],[165])).
% 0.19/0.44 tff(167,plain,
% 0.19/0.44 (![A: $i, B: $i] : ((ordinal_subset(A, B) <=> subset(A, B)) | (~ordinal(B)) | (~ordinal(A)))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[166, 159])).
% 0.19/0.44 tff(168,plain,
% 0.19/0.44 (![A: $i, B: $i] : ((ordinal_subset(A, B) <=> subset(A, B)) | (~ordinal(B)) | (~ordinal(A)))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[167, 157])).
% 0.19/0.44 tff(169,plain,
% 0.19/0.44 (((~![A: $i, B: $i] : ((ordinal_subset(A, B) <=> subset(A, B)) | (~ordinal(B)) | (~ordinal(A)))) | ((~ordinal(tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)))) | (~ordinal(tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)))) | (ordinal_subset(tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)), tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14))) <=> subset(tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)), tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)))))) <=> ((~![A: $i, B: $i] : ((ordinal_subset(A, B) <=> subset(A, B)) | (~ordinal(B)) | (~ordinal(A)))) | (~ordinal(tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)))) | (~ordinal(tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)))) | (ordinal_subset(tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)), tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14))) <=> subset(tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)), tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)))))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(170,plain,
% 0.19/0.44 (((ordinal_subset(tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)), tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14))) <=> subset(tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)), tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)))) | (~ordinal(tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)))) | (~ordinal(tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14))))) <=> ((~ordinal(tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)))) | (~ordinal(tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)))) | (ordinal_subset(tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)), tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14))) <=> subset(tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)), tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)))))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(171,plain,
% 0.19/0.44 (((~![A: $i, B: $i] : ((ordinal_subset(A, B) <=> subset(A, B)) | (~ordinal(B)) | (~ordinal(A)))) | ((ordinal_subset(tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)), tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14))) <=> subset(tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)), tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)))) | (~ordinal(tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)))) | (~ordinal(tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)))))) <=> ((~![A: $i, B: $i] : ((ordinal_subset(A, B) <=> subset(A, B)) | (~ordinal(B)) | (~ordinal(A)))) | ((~ordinal(tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)))) | (~ordinal(tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)))) | (ordinal_subset(tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)), tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14))) <=> subset(tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)), tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14))))))),
% 0.19/0.44 inference(monotonicity,[status(thm)],[170])).
% 0.19/0.44 tff(172,plain,
% 0.19/0.44 (((~![A: $i, B: $i] : ((ordinal_subset(A, B) <=> subset(A, B)) | (~ordinal(B)) | (~ordinal(A)))) | ((ordinal_subset(tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)), tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14))) <=> subset(tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)), tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)))) | (~ordinal(tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)))) | (~ordinal(tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)))))) <=> ((~![A: $i, B: $i] : ((ordinal_subset(A, B) <=> subset(A, B)) | (~ordinal(B)) | (~ordinal(A)))) | (~ordinal(tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)))) | (~ordinal(tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)))) | (ordinal_subset(tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)), tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14))) <=> subset(tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)), tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)))))),
% 0.19/0.45 inference(transitivity,[status(thm)],[171, 169])).
% 0.19/0.45 tff(173,plain,
% 0.19/0.45 ((~![A: $i, B: $i] : ((ordinal_subset(A, B) <=> subset(A, B)) | (~ordinal(B)) | (~ordinal(A)))) | ((ordinal_subset(tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)), tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14))) <=> subset(tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)), tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)))) | (~ordinal(tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)))) | (~ordinal(tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)))))),
% 0.19/0.45 inference(quant_inst,[status(thm)],[])).
% 0.19/0.45 tff(174,plain,
% 0.19/0.45 ((~![A: $i, B: $i] : ((ordinal_subset(A, B) <=> subset(A, B)) | (~ordinal(B)) | (~ordinal(A)))) | (~ordinal(tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)))) | (~ordinal(tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)))) | (ordinal_subset(tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)), tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14))) <=> subset(tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)), tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14))))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[173, 172])).
% 0.19/0.45 tff(175,plain,
% 0.19/0.45 (ordinal_subset(tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)), tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14))) <=> subset(tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)), tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[174, 168, 155, 145])).
% 0.19/0.45 tff(176,plain,
% 0.19/0.45 (A!14 = relation_field(inclusion_relation(A!14))),
% 0.19/0.45 inference(symmetry,[status(thm)],[40])).
% 0.19/0.45 tff(177,plain,
% 0.19/0.45 (A!14 = set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14)))),
% 0.19/0.45 inference(transitivity,[status(thm)],[176, 54])).
% 0.19/0.45 tff(178,plain,
% 0.19/0.45 (in(tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)), A!14) <=> in(tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)), set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))))),
% 0.19/0.45 inference(monotonicity,[status(thm)],[177])).
% 0.19/0.45 tff(179,plain,
% 0.19/0.45 (in(tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)), set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14)))) <=> in(tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)), A!14)),
% 0.19/0.45 inference(symmetry,[status(thm)],[178])).
% 0.19/0.45 tff(180,plain,
% 0.19/0.45 (in(tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)), A!14)),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[147, 179])).
% 0.19/0.45 tff(181,plain,
% 0.19/0.45 (in(tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)), A!14) <=> in(tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)), set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))))),
% 0.19/0.45 inference(monotonicity,[status(thm)],[177])).
% 0.19/0.45 tff(182,plain,
% 0.19/0.45 (in(tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)), set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14)))) <=> in(tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)), A!14)),
% 0.19/0.45 inference(symmetry,[status(thm)],[181])).
% 0.19/0.45 tff(183,plain,
% 0.19/0.45 (in(tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)), A!14)),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[127, 182])).
% 0.19/0.45 tff(184,plain,
% 0.19/0.45 (((~(relation_field(inclusion_relation(A!14)) = A!14)) | (~![C: $i, D: $i] : ((~in(C, A!14)) | (~in(D, A!14)) | (in(ordered_pair(C, D), inclusion_relation(A!14)) <=> subset(C, D))))) | ![C: $i, D: $i] : ((~in(C, A!14)) | (~in(D, A!14)) | (in(ordered_pair(C, D), inclusion_relation(A!14)) <=> subset(C, D)))),
% 0.19/0.45 inference(tautology,[status(thm)],[])).
% 0.19/0.45 tff(185,plain,
% 0.19/0.45 (![C: $i, D: $i] : ((~in(C, A!14)) | (~in(D, A!14)) | (in(ordered_pair(C, D), inclusion_relation(A!14)) <=> subset(C, D)))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[184, 38])).
% 0.19/0.45 tff(186,plain,
% 0.19/0.45 (((~![C: $i, D: $i] : ((~in(C, A!14)) | (~in(D, A!14)) | (in(ordered_pair(C, D), inclusion_relation(A!14)) <=> subset(C, D)))) | ((~in(tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)), A!14)) | (~in(tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)), A!14)) | (in(ordered_pair(tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)), tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14))), inclusion_relation(A!14)) <=> subset(tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)), tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)))))) <=> ((~![C: $i, D: $i] : ((~in(C, A!14)) | (~in(D, A!14)) | (in(ordered_pair(C, D), inclusion_relation(A!14)) <=> subset(C, D)))) | (~in(tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)), A!14)) | (~in(tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)), A!14)) | (in(ordered_pair(tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)), tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14))), inclusion_relation(A!14)) <=> subset(tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)), tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)))))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(187,plain,
% 0.19/0.45 ((~![C: $i, D: $i] : ((~in(C, A!14)) | (~in(D, A!14)) | (in(ordered_pair(C, D), inclusion_relation(A!14)) <=> subset(C, D)))) | ((~in(tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)), A!14)) | (~in(tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)), A!14)) | (in(ordered_pair(tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)), tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14))), inclusion_relation(A!14)) <=> subset(tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)), tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)))))),
% 0.19/0.45 inference(quant_inst,[status(thm)],[])).
% 0.19/0.45 tff(188,plain,
% 0.19/0.45 ((~![C: $i, D: $i] : ((~in(C, A!14)) | (~in(D, A!14)) | (in(ordered_pair(C, D), inclusion_relation(A!14)) <=> subset(C, D)))) | (~in(tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)), A!14)) | (~in(tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)), A!14)) | (in(ordered_pair(tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)), tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14))), inclusion_relation(A!14)) <=> subset(tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)), tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14))))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[187, 186])).
% 0.19/0.45 tff(189,plain,
% 0.19/0.45 ((~in(tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)), A!14)) | (~in(tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)), A!14)) | (in(ordered_pair(tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)), tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14))), inclusion_relation(A!14)) <=> subset(tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)), tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14))))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[188, 185])).
% 0.19/0.45 tff(190,plain,
% 0.19/0.45 (in(ordered_pair(tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)), tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14))), inclusion_relation(A!14)) <=> subset(tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)), tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[189, 183, 180])).
% 0.19/0.45 tff(191,plain,
% 0.19/0.45 (((~in(tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)), set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))))) | (~in(tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)), set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))))) | (tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)) = tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14))) | in(ordered_pair(tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)), tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14))), inclusion_relation(A!14)) | in(ordered_pair(tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)), tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14))), inclusion_relation(A!14))) | (~in(ordered_pair(tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)), tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14))), inclusion_relation(A!14)))),
% 0.19/0.45 inference(tautology,[status(thm)],[])).
% 0.19/0.45 tff(192,plain,
% 0.19/0.45 (~in(ordered_pair(tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)), tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14))), inclusion_relation(A!14))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[191, 125])).
% 0.19/0.45 tff(193,plain,
% 0.19/0.45 ((~(in(ordered_pair(tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)), tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14))), inclusion_relation(A!14)) <=> subset(tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)), tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14))))) | in(ordered_pair(tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)), tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14))), inclusion_relation(A!14)) | (~subset(tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)), tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14))))),
% 0.19/0.45 inference(tautology,[status(thm)],[])).
% 0.19/0.45 tff(194,plain,
% 0.19/0.45 ((~(in(ordered_pair(tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)), tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14))), inclusion_relation(A!14)) <=> subset(tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)), tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14))))) | (~subset(tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)), tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14))))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[193, 192])).
% 0.19/0.45 tff(195,plain,
% 0.19/0.45 (~subset(tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)), tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[194, 190])).
% 0.19/0.45 tff(196,plain,
% 0.19/0.45 ((~(ordinal_subset(tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)), tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14))) <=> subset(tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)), tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14))))) | (~ordinal_subset(tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)), tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)))) | subset(tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)), tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)))),
% 0.19/0.45 inference(tautology,[status(thm)],[])).
% 0.19/0.45 tff(197,plain,
% 0.19/0.45 ((~(ordinal_subset(tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)), tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14))) <=> subset(tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)), tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14))))) | (~ordinal_subset(tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)), tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14))))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[196, 195])).
% 0.19/0.45 tff(198,plain,
% 0.19/0.45 (~ordinal_subset(tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)), tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[197, 175])).
% 0.19/0.45 tff(199,plain,
% 0.19/0.45 (((~![A: $i, B: $i] : ((ordinal_subset(A, B) <=> subset(A, B)) | (~ordinal(B)) | (~ordinal(A)))) | ((~ordinal(tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)))) | (~ordinal(tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)))) | (ordinal_subset(tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)), tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14))) <=> subset(tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)), tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)))))) <=> ((~![A: $i, B: $i] : ((ordinal_subset(A, B) <=> subset(A, B)) | (~ordinal(B)) | (~ordinal(A)))) | (~ordinal(tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)))) | (~ordinal(tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)))) | (ordinal_subset(tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)), tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14))) <=> subset(tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)), tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)))))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(200,plain,
% 0.19/0.45 (((ordinal_subset(tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)), tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14))) <=> subset(tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)), tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)))) | (~ordinal(tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)))) | (~ordinal(tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14))))) <=> ((~ordinal(tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)))) | (~ordinal(tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)))) | (ordinal_subset(tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)), tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14))) <=> subset(tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)), tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)))))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(201,plain,
% 0.19/0.45 (((~![A: $i, B: $i] : ((ordinal_subset(A, B) <=> subset(A, B)) | (~ordinal(B)) | (~ordinal(A)))) | ((ordinal_subset(tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)), tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14))) <=> subset(tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)), tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)))) | (~ordinal(tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)))) | (~ordinal(tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)))))) <=> ((~![A: $i, B: $i] : ((ordinal_subset(A, B) <=> subset(A, B)) | (~ordinal(B)) | (~ordinal(A)))) | ((~ordinal(tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)))) | (~ordinal(tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)))) | (ordinal_subset(tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)), tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14))) <=> subset(tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)), tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14))))))),
% 0.19/0.46 inference(monotonicity,[status(thm)],[200])).
% 0.19/0.46 tff(202,plain,
% 0.19/0.46 (((~![A: $i, B: $i] : ((ordinal_subset(A, B) <=> subset(A, B)) | (~ordinal(B)) | (~ordinal(A)))) | ((ordinal_subset(tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)), tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14))) <=> subset(tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)), tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)))) | (~ordinal(tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)))) | (~ordinal(tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)))))) <=> ((~![A: $i, B: $i] : ((ordinal_subset(A, B) <=> subset(A, B)) | (~ordinal(B)) | (~ordinal(A)))) | (~ordinal(tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)))) | (~ordinal(tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)))) | (ordinal_subset(tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)), tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14))) <=> subset(tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)), tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)))))),
% 0.19/0.46 inference(transitivity,[status(thm)],[201, 199])).
% 0.19/0.46 tff(203,plain,
% 0.19/0.46 ((~![A: $i, B: $i] : ((ordinal_subset(A, B) <=> subset(A, B)) | (~ordinal(B)) | (~ordinal(A)))) | ((ordinal_subset(tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)), tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14))) <=> subset(tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)), tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)))) | (~ordinal(tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)))) | (~ordinal(tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)))))),
% 0.19/0.46 inference(quant_inst,[status(thm)],[])).
% 0.19/0.46 tff(204,plain,
% 0.19/0.46 ((~![A: $i, B: $i] : ((ordinal_subset(A, B) <=> subset(A, B)) | (~ordinal(B)) | (~ordinal(A)))) | (~ordinal(tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)))) | (~ordinal(tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)))) | (ordinal_subset(tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)), tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14))) <=> subset(tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)), tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14))))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[203, 202])).
% 0.19/0.46 tff(205,plain,
% 0.19/0.46 (ordinal_subset(tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)), tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14))) <=> subset(tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)), tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[204, 168, 155, 145])).
% 0.19/0.46 tff(206,plain,
% 0.19/0.46 (((~![C: $i, D: $i] : ((~in(C, A!14)) | (~in(D, A!14)) | (in(ordered_pair(C, D), inclusion_relation(A!14)) <=> subset(C, D)))) | ((~in(tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)), A!14)) | (~in(tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)), A!14)) | (in(ordered_pair(tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)), tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14))), inclusion_relation(A!14)) <=> subset(tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)), tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)))))) <=> ((~![C: $i, D: $i] : ((~in(C, A!14)) | (~in(D, A!14)) | (in(ordered_pair(C, D), inclusion_relation(A!14)) <=> subset(C, D)))) | (~in(tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)), A!14)) | (~in(tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)), A!14)) | (in(ordered_pair(tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)), tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14))), inclusion_relation(A!14)) <=> subset(tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)), tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)))))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(207,plain,
% 0.19/0.46 ((~![C: $i, D: $i] : ((~in(C, A!14)) | (~in(D, A!14)) | (in(ordered_pair(C, D), inclusion_relation(A!14)) <=> subset(C, D)))) | ((~in(tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)), A!14)) | (~in(tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)), A!14)) | (in(ordered_pair(tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)), tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14))), inclusion_relation(A!14)) <=> subset(tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)), tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)))))),
% 0.19/0.46 inference(quant_inst,[status(thm)],[])).
% 0.19/0.46 tff(208,plain,
% 0.19/0.46 ((~![C: $i, D: $i] : ((~in(C, A!14)) | (~in(D, A!14)) | (in(ordered_pair(C, D), inclusion_relation(A!14)) <=> subset(C, D)))) | (~in(tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)), A!14)) | (~in(tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)), A!14)) | (in(ordered_pair(tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)), tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14))), inclusion_relation(A!14)) <=> subset(tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)), tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14))))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[207, 206])).
% 0.19/0.46 tff(209,plain,
% 0.19/0.46 ((~in(tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)), A!14)) | (~in(tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)), A!14)) | (in(ordered_pair(tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)), tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14))), inclusion_relation(A!14)) <=> subset(tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)), tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14))))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[208, 185])).
% 0.19/0.46 tff(210,plain,
% 0.19/0.46 (in(ordered_pair(tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)), tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14))), inclusion_relation(A!14)) <=> subset(tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)), tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[209, 183, 180])).
% 0.19/0.46 tff(211,plain,
% 0.19/0.46 (((~in(tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)), set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))))) | (~in(tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)), set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))))) | (tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)) = tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14))) | in(ordered_pair(tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)), tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14))), inclusion_relation(A!14)) | in(ordered_pair(tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)), tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14))), inclusion_relation(A!14))) | (~in(ordered_pair(tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)), tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14))), inclusion_relation(A!14)))),
% 0.19/0.46 inference(tautology,[status(thm)],[])).
% 0.19/0.46 tff(212,plain,
% 0.19/0.46 (~in(ordered_pair(tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)), tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14))), inclusion_relation(A!14))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[211, 125])).
% 0.19/0.46 tff(213,plain,
% 0.19/0.46 ((~(in(ordered_pair(tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)), tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14))), inclusion_relation(A!14)) <=> subset(tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)), tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14))))) | in(ordered_pair(tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)), tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14))), inclusion_relation(A!14)) | (~subset(tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)), tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14))))),
% 0.19/0.46 inference(tautology,[status(thm)],[])).
% 0.19/0.46 tff(214,plain,
% 0.19/0.46 ((~(in(ordered_pair(tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)), tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14))), inclusion_relation(A!14)) <=> subset(tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)), tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14))))) | (~subset(tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)), tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14))))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[213, 212])).
% 0.19/0.46 tff(215,plain,
% 0.19/0.46 (~subset(tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)), tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[214, 210])).
% 0.19/0.46 tff(216,plain,
% 0.19/0.46 ((~(ordinal_subset(tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)), tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14))) <=> subset(tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)), tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14))))) | (~ordinal_subset(tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)), tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)))) | subset(tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)), tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)))),
% 0.19/0.46 inference(tautology,[status(thm)],[])).
% 0.19/0.46 tff(217,plain,
% 0.19/0.46 ((~(ordinal_subset(tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)), tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14))) <=> subset(tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)), tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14))))) | (~ordinal_subset(tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)), tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14))))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[216, 215])).
% 0.19/0.46 tff(218,plain,
% 0.19/0.46 (~ordinal_subset(tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)), tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[217, 205])).
% 0.19/0.46 tff(219,plain,
% 0.19/0.46 (^[A: $i, B: $i] : refl((ordinal_subset(B, A) | ordinal_subset(A, B) | (~ordinal(B)) | (~ordinal(A))) <=> (ordinal_subset(B, A) | ordinal_subset(A, B) | (~ordinal(B)) | (~ordinal(A))))),
% 0.19/0.46 inference(bind,[status(th)],[])).
% 0.19/0.46 tff(220,plain,
% 0.19/0.46 (![A: $i, B: $i] : (ordinal_subset(B, A) | ordinal_subset(A, B) | (~ordinal(B)) | (~ordinal(A))) <=> ![A: $i, B: $i] : (ordinal_subset(B, A) | ordinal_subset(A, B) | (~ordinal(B)) | (~ordinal(A)))),
% 0.19/0.46 inference(quant_intro,[status(thm)],[219])).
% 0.19/0.46 tff(221,plain,
% 0.19/0.46 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite((ordinal(A) & ordinal(B)) <=> (~((~ordinal(B)) | (~ordinal(A))))), ((~(ordinal(A) & ordinal(B))) <=> (~(~((~ordinal(B)) | (~ordinal(A))))))), rewrite((~(~((~ordinal(B)) | (~ordinal(A))))) <=> ((~ordinal(B)) | (~ordinal(A)))), ((~(ordinal(A) & ordinal(B))) <=> ((~ordinal(B)) | (~ordinal(A))))), ((ordinal_subset(B, A) | ordinal_subset(A, B) | (~(ordinal(A) & ordinal(B)))) <=> (ordinal_subset(B, A) | ordinal_subset(A, B) | ((~ordinal(B)) | (~ordinal(A)))))), rewrite((ordinal_subset(B, A) | ordinal_subset(A, B) | ((~ordinal(B)) | (~ordinal(A)))) <=> (ordinal_subset(B, A) | ordinal_subset(A, B) | (~ordinal(B)) | (~ordinal(A)))), ((ordinal_subset(B, A) | ordinal_subset(A, B) | (~(ordinal(A) & ordinal(B)))) <=> (ordinal_subset(B, A) | ordinal_subset(A, B) | (~ordinal(B)) | (~ordinal(A)))))),
% 0.19/0.46 inference(bind,[status(th)],[])).
% 0.19/0.46 tff(222,plain,
% 0.19/0.46 (![A: $i, B: $i] : (ordinal_subset(B, A) | ordinal_subset(A, B) | (~(ordinal(A) & ordinal(B)))) <=> ![A: $i, B: $i] : (ordinal_subset(B, A) | ordinal_subset(A, B) | (~ordinal(B)) | (~ordinal(A)))),
% 0.19/0.46 inference(quant_intro,[status(thm)],[221])).
% 0.19/0.46 tff(223,plain,
% 0.19/0.46 (![A: $i, B: $i] : (ordinal_subset(B, A) | ordinal_subset(A, B) | (~(ordinal(A) & ordinal(B)))) <=> ![A: $i, B: $i] : (ordinal_subset(B, A) | ordinal_subset(A, B) | (~(ordinal(A) & ordinal(B))))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(224,plain,
% 0.19/0.46 (^[A: $i, B: $i] : trans(monotonicity(rewrite((ordinal_subset(A, B) | ordinal_subset(B, A)) <=> (ordinal_subset(B, A) | ordinal_subset(A, B))), (((ordinal(A) & ordinal(B)) => (ordinal_subset(A, B) | ordinal_subset(B, A))) <=> ((ordinal(A) & ordinal(B)) => (ordinal_subset(B, A) | ordinal_subset(A, B))))), rewrite(((ordinal(A) & ordinal(B)) => (ordinal_subset(B, A) | ordinal_subset(A, B))) <=> (ordinal_subset(B, A) | ordinal_subset(A, B) | (~(ordinal(A) & ordinal(B))))), (((ordinal(A) & ordinal(B)) => (ordinal_subset(A, B) | ordinal_subset(B, A))) <=> (ordinal_subset(B, A) | ordinal_subset(A, B) | (~(ordinal(A) & ordinal(B))))))),
% 0.19/0.46 inference(bind,[status(th)],[])).
% 0.19/0.46 tff(225,plain,
% 0.19/0.46 (![A: $i, B: $i] : ((ordinal(A) & ordinal(B)) => (ordinal_subset(A, B) | ordinal_subset(B, A))) <=> ![A: $i, B: $i] : (ordinal_subset(B, A) | ordinal_subset(A, B) | (~(ordinal(A) & ordinal(B))))),
% 0.19/0.46 inference(quant_intro,[status(thm)],[224])).
% 0.19/0.46 tff(226,axiom,(![A: $i, B: $i] : ((ordinal(A) & ordinal(B)) => (ordinal_subset(A, B) | ordinal_subset(B, A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','connectedness_r1_ordinal1')).
% 0.19/0.46 tff(227,plain,
% 0.19/0.46 (![A: $i, B: $i] : (ordinal_subset(B, A) | ordinal_subset(A, B) | (~(ordinal(A) & ordinal(B))))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[226, 225])).
% 0.19/0.46 tff(228,plain,
% 0.19/0.46 (![A: $i, B: $i] : (ordinal_subset(B, A) | ordinal_subset(A, B) | (~(ordinal(A) & ordinal(B))))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[227, 223])).
% 0.19/0.46 tff(229,plain,(
% 0.19/0.46 ![A: $i, B: $i] : (ordinal_subset(B, A) | ordinal_subset(A, B) | (~(ordinal(A) & ordinal(B))))),
% 0.19/0.46 inference(skolemize,[status(sab)],[228])).
% 0.19/0.46 tff(230,plain,
% 0.19/0.46 (![A: $i, B: $i] : (ordinal_subset(B, A) | ordinal_subset(A, B) | (~ordinal(B)) | (~ordinal(A)))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[229, 222])).
% 0.19/0.46 tff(231,plain,
% 0.19/0.46 (![A: $i, B: $i] : (ordinal_subset(B, A) | ordinal_subset(A, B) | (~ordinal(B)) | (~ordinal(A)))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[230, 220])).
% 0.19/0.46 tff(232,plain,
% 0.19/0.46 (((~![A: $i, B: $i] : (ordinal_subset(B, A) | ordinal_subset(A, B) | (~ordinal(B)) | (~ordinal(A)))) | ((~ordinal(tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)))) | (~ordinal(tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)))) | ordinal_subset(tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)), tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14))) | ordinal_subset(tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)), tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14))))) <=> ((~![A: $i, B: $i] : (ordinal_subset(B, A) | ordinal_subset(A, B) | (~ordinal(B)) | (~ordinal(A)))) | (~ordinal(tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)))) | (~ordinal(tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)))) | ordinal_subset(tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)), tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14))) | ordinal_subset(tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)), tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14))))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(233,plain,
% 0.19/0.46 ((ordinal_subset(tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)), tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14))) | ordinal_subset(tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)), tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14))) | (~ordinal(tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)))) | (~ordinal(tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14))))) <=> ((~ordinal(tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)))) | (~ordinal(tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)))) | ordinal_subset(tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)), tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14))) | ordinal_subset(tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)), tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14))))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(234,plain,
% 0.19/0.46 (((~![A: $i, B: $i] : (ordinal_subset(B, A) | ordinal_subset(A, B) | (~ordinal(B)) | (~ordinal(A)))) | (ordinal_subset(tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)), tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14))) | ordinal_subset(tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)), tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14))) | (~ordinal(tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)))) | (~ordinal(tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)))))) <=> ((~![A: $i, B: $i] : (ordinal_subset(B, A) | ordinal_subset(A, B) | (~ordinal(B)) | (~ordinal(A)))) | ((~ordinal(tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)))) | (~ordinal(tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)))) | ordinal_subset(tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)), tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14))) | ordinal_subset(tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)), tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)))))),
% 0.19/0.46 inference(monotonicity,[status(thm)],[233])).
% 0.19/0.46 tff(235,plain,
% 0.19/0.46 (((~![A: $i, B: $i] : (ordinal_subset(B, A) | ordinal_subset(A, B) | (~ordinal(B)) | (~ordinal(A)))) | (ordinal_subset(tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)), tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14))) | ordinal_subset(tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)), tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14))) | (~ordinal(tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)))) | (~ordinal(tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)))))) <=> ((~![A: $i, B: $i] : (ordinal_subset(B, A) | ordinal_subset(A, B) | (~ordinal(B)) | (~ordinal(A)))) | (~ordinal(tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)))) | (~ordinal(tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)))) | ordinal_subset(tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)), tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14))) | ordinal_subset(tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)), tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14))))),
% 0.19/0.47 inference(transitivity,[status(thm)],[234, 232])).
% 0.19/0.47 tff(236,plain,
% 0.19/0.47 ((~![A: $i, B: $i] : (ordinal_subset(B, A) | ordinal_subset(A, B) | (~ordinal(B)) | (~ordinal(A)))) | (ordinal_subset(tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)), tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14))) | ordinal_subset(tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)), tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14))) | (~ordinal(tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)))) | (~ordinal(tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)))))),
% 0.19/0.47 inference(quant_inst,[status(thm)],[])).
% 0.19/0.47 tff(237,plain,
% 0.19/0.47 ((~![A: $i, B: $i] : (ordinal_subset(B, A) | ordinal_subset(A, B) | (~ordinal(B)) | (~ordinal(A)))) | (~ordinal(tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)))) | (~ordinal(tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)))) | ordinal_subset(tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)), tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14))) | ordinal_subset(tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)), tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[236, 235])).
% 0.19/0.47 tff(238,plain,
% 0.19/0.47 ($false),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[237, 231, 155, 145, 218, 198])).
% 0.19/0.47 % SZS output end Proof
% 0.19/0.47 % E exiting
%------------------------------------------------------------------------------