%------------------------------------------------------------------------------
% File     : Z3---4.8.9.0
% Problem  : SEU271+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm  : none
% Format   : tptp
% Command  : z3_tptp -proof -model -t:%d -file:%s

% Computer : n011.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 : Tue Sep 20 07:28:37 EDT 2022

% Result   : Theorem 0.19s 0.41s
% Output   : Proof 0.20s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : SEU271+1 : TPTP v8.1.0. Released v3.3.0.
% 0.12/0.13  % Command  : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34  % Computer : n011.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 300
% 0.13/0.34  % DateTime : Sat Sep  3 11:17:43 EDT 2022
% 0.19/0.35  % CPUTime  : 
% 0.19/0.35  Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.19/0.35  Usage: tptp [options] [-file:]file
% 0.19/0.35    -h, -?       prints this message.
% 0.19/0.35    -smt2        print SMT-LIB2 benchmark.
% 0.19/0.35    -m, -model   generate model.
% 0.19/0.35    -p, -proof   generate proof.
% 0.19/0.35    -c, -core    generate unsat core of named formulas.
% 0.19/0.35    -st, -statistics display statistics.
% 0.19/0.35    -t:timeout   set timeout (in second).
% 0.19/0.35    -smt2status  display status in smt2 format instead of SZS.
% 0.19/0.35    -check_status check the status produced by Z3 against annotation in benchmark.
% 0.19/0.35    -<param>:<value> configuration parameter and value.
% 0.19/0.35    -o:<output-file> file to place output in.
% 0.19/0.41  % SZS status Theorem
% 0.19/0.41  % SZS output start Proof
% 0.19/0.41  tff(subset_type, type, (
% 0.19/0.41     subset: ( $i * $i ) > $o)).
% 0.19/0.41  tff(tptp_fun_C_3_type, type, (
% 0.19/0.41     tptp_fun_C_3: ( $i * $i ) > $i)).
% 0.19/0.41  tff(inclusion_relation_type, type, (
% 0.19/0.41     inclusion_relation: $i > $i)).
% 0.19/0.41  tff(tptp_fun_A_14_type, type, (
% 0.19/0.41     tptp_fun_A_14: $i)).
% 0.19/0.41  tff(set_union2_type, type, (
% 0.19/0.41     set_union2: ( $i * $i ) > $i)).
% 0.19/0.41  tff(relation_rng_type, type, (
% 0.19/0.41     relation_rng: $i > $i)).
% 0.19/0.41  tff(relation_dom_type, type, (
% 0.19/0.41     relation_dom: $i > $i)).
% 0.19/0.41  tff(tptp_fun_D_2_type, type, (
% 0.19/0.41     tptp_fun_D_2: ( $i * $i ) > $i)).
% 0.19/0.41  tff(in_type, type, (
% 0.19/0.41     in: ( $i * $i ) > $o)).
% 0.19/0.41  tff(ordered_pair_type, type, (
% 0.19/0.41     ordered_pair: ( $i * $i ) > $i)).
% 0.19/0.41  tff(relation_field_type, type, (
% 0.19/0.41     relation_field: $i > $i)).
% 0.19/0.41  tff(relation_type, type, (
% 0.19/0.41     relation: $i > $o)).
% 0.19/0.41  tff(tptp_fun_D_0_type, type, (
% 0.19/0.41     tptp_fun_D_0: ( $i * $i ) > $i)).
% 0.19/0.41  tff(tptp_fun_C_1_type, type, (
% 0.19/0.41     tptp_fun_C_1: ( $i * $i ) > $i)).
% 0.19/0.41  tff(is_antisymmetric_in_type, type, (
% 0.19/0.41     is_antisymmetric_in: ( $i * $i ) > $o)).
% 0.19/0.41  tff(antisymmetric_type, type, (
% 0.19/0.41     antisymmetric: $i > $o)).
% 0.19/0.41  tff(1,plain,
% 0.19/0.41      (^[A: $i] : refl(relation(inclusion_relation(A)) <=> relation(inclusion_relation(A)))),
% 0.19/0.41      inference(bind,[status(th)],[])).
% 0.19/0.41  tff(2,plain,
% 0.19/0.41      (![A: $i] : relation(inclusion_relation(A)) <=> ![A: $i] : relation(inclusion_relation(A))),
% 0.19/0.41      inference(quant_intro,[status(thm)],[1])).
% 0.19/0.41  tff(3,plain,
% 0.19/0.41      (![A: $i] : relation(inclusion_relation(A)) <=> ![A: $i] : relation(inclusion_relation(A))),
% 0.19/0.41      inference(rewrite,[status(thm)],[])).
% 0.19/0.41  tff(4,axiom,(![A: $i] : relation(inclusion_relation(A))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_k1_wellord2')).
% 0.19/0.41  tff(5,plain,
% 0.19/0.41      (![A: $i] : relation(inclusion_relation(A))),
% 0.19/0.41      inference(modus_ponens,[status(thm)],[4, 3])).
% 0.19/0.41  tff(6,plain,(
% 0.19/0.41      ![A: $i] : relation(inclusion_relation(A))),
% 0.19/0.41      inference(skolemize,[status(sab)],[5])).
% 0.19/0.41  tff(7,plain,
% 0.19/0.41      (![A: $i] : relation(inclusion_relation(A))),
% 0.19/0.41      inference(modus_ponens,[status(thm)],[6, 2])).
% 0.19/0.41  tff(8,plain,
% 0.19/0.41      ((~![A: $i] : relation(inclusion_relation(A))) | relation(inclusion_relation(A!14))),
% 0.19/0.41      inference(quant_inst,[status(thm)],[])).
% 0.19/0.41  tff(9,plain,
% 0.19/0.41      (relation(inclusion_relation(A!14))),
% 0.19/0.41      inference(unit_resolution,[status(thm)],[8, 7])).
% 0.19/0.41  tff(10,plain,
% 0.19/0.41      (^[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)))))),
% 0.19/0.41      inference(bind,[status(th)],[])).
% 0.19/0.41  tff(11,plain,
% 0.19/0.41      (![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))))),
% 0.19/0.41      inference(quant_intro,[status(thm)],[10])).
% 0.19/0.41  tff(12,plain,
% 0.19/0.41      (![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))))),
% 0.19/0.41      inference(rewrite,[status(thm)],[])).
% 0.19/0.41  tff(13,plain,
% 0.19/0.41      (^[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)))))),
% 0.19/0.41      inference(bind,[status(th)],[])).
% 0.19/0.41  tff(14,plain,
% 0.19/0.41      (![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))))),
% 0.19/0.41      inference(quant_intro,[status(thm)],[13])).
% 0.19/0.41  tff(15,axiom,(![A: $i] : (relation(A) => (relation_field(A) = set_union2(relation_dom(A), relation_rng(A))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d6_relat_1')).
% 0.19/0.41  tff(16,plain,
% 0.19/0.41      (![A: $i] : ((~relation(A)) | (relation_field(A) = set_union2(relation_dom(A), relation_rng(A))))),
% 0.19/0.41      inference(modus_ponens,[status(thm)],[15, 14])).
% 0.19/0.41  tff(17,plain,
% 0.19/0.41      (![A: $i] : ((~relation(A)) | (relation_field(A) = set_union2(relation_dom(A), relation_rng(A))))),
% 0.19/0.41      inference(modus_ponens,[status(thm)],[16, 12])).
% 0.19/0.41  tff(18,plain,(
% 0.19/0.41      ![A: $i] : ((~relation(A)) | (relation_field(A) = set_union2(relation_dom(A), relation_rng(A))))),
% 0.19/0.41      inference(skolemize,[status(sab)],[17])).
% 0.19/0.41  tff(19,plain,
% 0.19/0.41      (![A: $i] : ((~relation(A)) | (relation_field(A) = set_union2(relation_dom(A), relation_rng(A))))),
% 0.19/0.41      inference(modus_ponens,[status(thm)],[18, 11])).
% 0.19/0.41  tff(20,plain,
% 0.19/0.41      (((~![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)))))),
% 0.19/0.41      inference(rewrite,[status(thm)],[])).
% 0.19/0.41  tff(21,plain,
% 0.19/0.41      ((~![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)))))),
% 0.19/0.41      inference(quant_inst,[status(thm)],[])).
% 0.19/0.41  tff(22,plain,
% 0.19/0.41      ((~![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))))),
% 0.19/0.41      inference(modus_ponens,[status(thm)],[21, 20])).
% 0.19/0.41  tff(23,plain,
% 0.19/0.41      (relation_field(inclusion_relation(A!14)) = set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14)))),
% 0.19/0.41      inference(unit_resolution,[status(thm)],[22, 19, 9])).
% 0.19/0.41  tff(24,plain,
% 0.19/0.41      (^[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))))))))))))),
% 0.19/0.41      inference(bind,[status(th)],[])).
% 0.19/0.41  tff(25,plain,
% 0.19/0.41      (![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)))))))))))),
% 0.19/0.41      inference(quant_intro,[status(thm)],[24])).
% 0.19/0.41  tff(26,plain,
% 0.19/0.41      (^[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))))))))))),
% 0.19/0.42      inference(bind,[status(th)],[])).
% 0.19/0.42  tff(27,plain,
% 0.19/0.42      (![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)))))))))),
% 0.19/0.42      inference(quant_intro,[status(thm)],[26])).
% 0.19/0.42  tff(28,plain,
% 0.19/0.42      (^[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))))))))))),
% 0.19/0.42      inference(bind,[status(th)],[])).
% 0.19/0.42  tff(29,plain,
% 0.19/0.42      (![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)))))))))),
% 0.19/0.42      inference(quant_intro,[status(thm)],[28])).
% 0.19/0.42  tff(30,plain,
% 0.19/0.42      (![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)))))))))),
% 0.19/0.42      inference(transitivity,[status(thm)],[29, 27])).
% 0.19/0.42  tff(31,plain,
% 0.19/0.42      (^[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))))))))))),
% 0.19/0.42      inference(bind,[status(th)],[])).
% 0.19/0.42  tff(32,plain,
% 0.19/0.42      (![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)))))))))),
% 0.19/0.42      inference(quant_intro,[status(thm)],[31])).
% 0.19/0.42  tff(33,plain,
% 0.19/0.42      (^[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)))))))))),
% 0.19/0.42      inference(bind,[status(th)],[])).
% 0.19/0.42  tff(34,plain,
% 0.19/0.42      (![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))))))))),
% 0.19/0.42      inference(quant_intro,[status(thm)],[33])).
% 0.19/0.42  tff(35,plain,
% 0.19/0.42      (![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))))))),
% 0.19/0.42      inference(rewrite,[status(thm)],[])).
% 0.19/0.42  tff(36,plain,
% 0.19/0.42      (^[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))))))))),
% 0.19/0.42      inference(bind,[status(th)],[])).
% 0.19/0.42  tff(37,plain,
% 0.19/0.42      (![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))))))),
% 0.19/0.42      inference(quant_intro,[status(thm)],[36])).
% 0.19/0.42  tff(38,axiom,(![A: $i, B: $i] : (relation(B) => ((B = inclusion_relation(A)) <=> ((relation_field(B) = A) & ![C: $i, D: $i] : ((in(C, A) & in(D, A)) => (in(ordered_pair(C, D), B) <=> subset(C, D))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d1_wellord2')).
% 0.19/0.42  tff(39,plain,
% 0.19/0.42      (![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))))))),
% 0.19/0.42      inference(modus_ponens,[status(thm)],[38, 37])).
% 0.19/0.42  tff(40,plain,
% 0.19/0.42      (![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))))))),
% 0.19/0.42      inference(modus_ponens,[status(thm)],[39, 35])).
% 0.19/0.42  tff(41,plain,(
% 0.19/0.42      ![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)))))))))),
% 0.19/0.42      inference(skolemize,[status(sab)],[40])).
% 0.19/0.42  tff(42,plain,
% 0.19/0.42      (![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))))))))),
% 0.19/0.42      inference(modus_ponens,[status(thm)],[41, 34])).
% 0.19/0.42  tff(43,plain,
% 0.19/0.42      (![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)))))))))),
% 0.19/0.42      inference(modus_ponens,[status(thm)],[42, 32])).
% 0.19/0.42  tff(44,plain,
% 0.19/0.42      (![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)))))))))),
% 0.19/0.42      inference(modus_ponens,[status(thm)],[43, 30])).
% 0.19/0.42  tff(45,plain,
% 0.19/0.42      (![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)))))))))))),
% 0.19/0.42      inference(modus_ponens,[status(thm)],[44, 25])).
% 0.19/0.42  tff(46,plain,
% 0.19/0.42      (((~![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)))))))),
% 0.19/0.42      inference(rewrite,[status(thm)],[])).
% 0.19/0.42  tff(47,plain,
% 0.19/0.42      (((~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)))))))),
% 0.19/0.42      inference(rewrite,[status(thm)],[])).
% 0.19/0.42  tff(48,plain,
% 0.19/0.42      (((~![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))))))))),
% 0.19/0.42      inference(monotonicity,[status(thm)],[47])).
% 0.19/0.42  tff(49,plain,
% 0.19/0.42      (((~![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)))))))),
% 0.19/0.43      inference(transitivity,[status(thm)],[48, 46])).
% 0.19/0.43  tff(50,plain,
% 0.19/0.43      ((~![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)))))))))))),
% 0.19/0.43      inference(quant_inst,[status(thm)],[])).
% 0.19/0.43  tff(51,plain,
% 0.19/0.43      ((~![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))))))),
% 0.19/0.43      inference(modus_ponens,[status(thm)],[50, 49])).
% 0.19/0.43  tff(52,plain,
% 0.19/0.43      (~((~(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)))))),
% 0.19/0.43      inference(unit_resolution,[status(thm)],[51, 45, 9])).
% 0.19/0.43  tff(53,plain,
% 0.19/0.43      (((~(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)),
% 0.19/0.43      inference(tautology,[status(thm)],[])).
% 0.19/0.43  tff(54,plain,
% 0.19/0.43      (relation_field(inclusion_relation(A!14)) = A!14),
% 0.19/0.43      inference(unit_resolution,[status(thm)],[53, 52])).
% 0.19/0.43  tff(55,plain,
% 0.19/0.43      (A!14 = relation_field(inclusion_relation(A!14))),
% 0.19/0.43      inference(symmetry,[status(thm)],[54])).
% 0.19/0.43  tff(56,plain,
% 0.19/0.43      (A!14 = set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14)))),
% 0.19/0.43      inference(transitivity,[status(thm)],[55, 23])).
% 0.19/0.43  tff(57,plain,
% 0.19/0.43      (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))))),
% 0.19/0.43      inference(monotonicity,[status(thm)],[56])).
% 0.19/0.43  tff(58,plain,
% 0.19/0.43      (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)),
% 0.19/0.43      inference(symmetry,[status(thm)],[57])).
% 0.19/0.43  tff(59,plain,
% 0.19/0.43      (^[A: $i] : refl(((~relation(A)) | ![B: $i] : (~((~((~is_antisymmetric_in(A, B)) | ![C: $i, D: $i] : ((C = D) | (~in(D, B)) | (~in(ordered_pair(C, D), A)) | (~in(ordered_pair(D, C), A)) | (~in(C, B))))) | (~(is_antisymmetric_in(A, B) | (~((tptp_fun_C_3(B, A) = tptp_fun_D_2(B, A)) | (~in(tptp_fun_C_3(B, A), B)) | (~in(tptp_fun_D_2(B, A), B)) | (~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_antisymmetric_in(A, B)) | ![C: $i, D: $i] : ((C = D) | (~in(D, B)) | (~in(ordered_pair(C, D), A)) | (~in(ordered_pair(D, C), A)) | (~in(C, B))))) | (~(is_antisymmetric_in(A, B) | (~((tptp_fun_C_3(B, A) = tptp_fun_D_2(B, A)) | (~in(tptp_fun_C_3(B, A), B)) | (~in(tptp_fun_D_2(B, A), B)) | (~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))))))))))),
% 0.19/0.43      inference(bind,[status(th)],[])).
% 0.19/0.43  tff(60,plain,
% 0.19/0.43      (![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~is_antisymmetric_in(A, B)) | ![C: $i, D: $i] : ((C = D) | (~in(D, B)) | (~in(ordered_pair(C, D), A)) | (~in(ordered_pair(D, C), A)) | (~in(C, B))))) | (~(is_antisymmetric_in(A, B) | (~((tptp_fun_C_3(B, A) = tptp_fun_D_2(B, A)) | (~in(tptp_fun_C_3(B, A), B)) | (~in(tptp_fun_D_2(B, A), B)) | (~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_antisymmetric_in(A, B)) | ![C: $i, D: $i] : ((C = D) | (~in(D, B)) | (~in(ordered_pair(C, D), A)) | (~in(ordered_pair(D, C), A)) | (~in(C, B))))) | (~(is_antisymmetric_in(A, B) | (~((tptp_fun_C_3(B, A) = tptp_fun_D_2(B, A)) | (~in(tptp_fun_C_3(B, A), B)) | (~in(tptp_fun_D_2(B, A), B)) | (~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)))))))))),
% 0.19/0.43      inference(quant_intro,[status(thm)],[59])).
% 0.19/0.43  tff(61,plain,
% 0.19/0.43      (^[A: $i] : rewrite(((~relation(A)) | ![B: $i] : (~((~((~is_antisymmetric_in(A, B)) | ![C: $i, D: $i] : ((C = D) | (~in(D, B)) | (~in(ordered_pair(C, D), A)) | (~in(ordered_pair(D, C), A)) | (~in(C, B))))) | (~(is_antisymmetric_in(A, B) | (~((tptp_fun_C_3(B, A) = tptp_fun_D_2(B, A)) | (~in(tptp_fun_C_3(B, A), B)) | (~in(tptp_fun_D_2(B, A), B)) | (~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_antisymmetric_in(A, B)) | ![C: $i, D: $i] : ((C = D) | (~in(D, B)) | (~in(ordered_pair(C, D), A)) | (~in(ordered_pair(D, C), A)) | (~in(C, B))))) | (~(is_antisymmetric_in(A, B) | (~((tptp_fun_C_3(B, A) = tptp_fun_D_2(B, A)) | (~in(tptp_fun_C_3(B, A), B)) | (~in(tptp_fun_D_2(B, A), B)) | (~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))))))))))),
% 0.19/0.43      inference(bind,[status(th)],[])).
% 0.19/0.43  tff(62,plain,
% 0.19/0.43      (![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~is_antisymmetric_in(A, B)) | ![C: $i, D: $i] : ((C = D) | (~in(D, B)) | (~in(ordered_pair(C, D), A)) | (~in(ordered_pair(D, C), A)) | (~in(C, B))))) | (~(is_antisymmetric_in(A, B) | (~((tptp_fun_C_3(B, A) = tptp_fun_D_2(B, A)) | (~in(tptp_fun_C_3(B, A), B)) | (~in(tptp_fun_D_2(B, A), B)) | (~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_antisymmetric_in(A, B)) | ![C: $i, D: $i] : ((C = D) | (~in(D, B)) | (~in(ordered_pair(C, D), A)) | (~in(ordered_pair(D, C), A)) | (~in(C, B))))) | (~(is_antisymmetric_in(A, B) | (~((tptp_fun_C_3(B, A) = tptp_fun_D_2(B, A)) | (~in(tptp_fun_C_3(B, A), B)) | (~in(tptp_fun_D_2(B, A), B)) | (~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)))))))))),
% 0.19/0.43      inference(quant_intro,[status(thm)],[61])).
% 0.19/0.43  tff(63,plain,
% 0.20/0.43      (![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~is_antisymmetric_in(A, B)) | ![C: $i, D: $i] : ((C = D) | (~in(D, B)) | (~in(ordered_pair(C, D), A)) | (~in(ordered_pair(D, C), A)) | (~in(C, B))))) | (~(is_antisymmetric_in(A, B) | (~((tptp_fun_C_3(B, A) = tptp_fun_D_2(B, A)) | (~in(tptp_fun_C_3(B, A), B)) | (~in(tptp_fun_D_2(B, A), B)) | (~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_antisymmetric_in(A, B)) | ![C: $i, D: $i] : ((C = D) | (~in(D, B)) | (~in(ordered_pair(C, D), A)) | (~in(ordered_pair(D, C), A)) | (~in(C, B))))) | (~(is_antisymmetric_in(A, B) | (~((tptp_fun_C_3(B, A) = tptp_fun_D_2(B, A)) | (~in(tptp_fun_C_3(B, A), B)) | (~in(tptp_fun_D_2(B, A), B)) | (~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)))))))))),
% 0.20/0.43      inference(transitivity,[status(thm)],[62, 60])).
% 0.20/0.43  tff(64,plain,
% 0.20/0.43      (^[A: $i] : rewrite(((~relation(A)) | ![B: $i] : (((~is_antisymmetric_in(A, B)) | ![C: $i, D: $i] : ((~(in(C, B) & in(D, B) & in(ordered_pair(C, D), A) & in(ordered_pair(D, C), A))) | (C = D))) & (is_antisymmetric_in(A, B) | (~((~(in(tptp_fun_C_3(B, A), B) & in(tptp_fun_D_2(B, A), B) & 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))) | (tptp_fun_C_3(B, A) = tptp_fun_D_2(B, A))))))) <=> ((~relation(A)) | ![B: $i] : (~((~((~is_antisymmetric_in(A, B)) | ![C: $i, D: $i] : ((C = D) | (~in(D, B)) | (~in(ordered_pair(C, D), A)) | (~in(ordered_pair(D, C), A)) | (~in(C, B))))) | (~(is_antisymmetric_in(A, B) | (~((tptp_fun_C_3(B, A) = tptp_fun_D_2(B, A)) | (~in(tptp_fun_C_3(B, A), B)) | (~in(tptp_fun_D_2(B, A), B)) | (~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))))))))))),
% 0.20/0.43      inference(bind,[status(th)],[])).
% 0.20/0.43  tff(65,plain,
% 0.20/0.43      (![A: $i] : ((~relation(A)) | ![B: $i] : (((~is_antisymmetric_in(A, B)) | ![C: $i, D: $i] : ((~(in(C, B) & in(D, B) & in(ordered_pair(C, D), A) & in(ordered_pair(D, C), A))) | (C = D))) & (is_antisymmetric_in(A, B) | (~((~(in(tptp_fun_C_3(B, A), B) & in(tptp_fun_D_2(B, A), B) & 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))) | (tptp_fun_C_3(B, A) = tptp_fun_D_2(B, A))))))) <=> ![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~is_antisymmetric_in(A, B)) | ![C: $i, D: $i] : ((C = D) | (~in(D, B)) | (~in(ordered_pair(C, D), A)) | (~in(ordered_pair(D, C), A)) | (~in(C, B))))) | (~(is_antisymmetric_in(A, B) | (~((tptp_fun_C_3(B, A) = tptp_fun_D_2(B, A)) | (~in(tptp_fun_C_3(B, A), B)) | (~in(tptp_fun_D_2(B, A), B)) | (~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)))))))))),
% 0.20/0.43      inference(quant_intro,[status(thm)],[64])).
% 0.20/0.43  tff(66,plain,
% 0.20/0.43      (![A: $i] : ((~relation(A)) | ![B: $i] : (is_antisymmetric_in(A, B) <=> ![C: $i, D: $i] : ((~(in(C, B) & in(D, B) & in(ordered_pair(C, D), A) & in(ordered_pair(D, C), A))) | (C = D)))) <=> ![A: $i] : ((~relation(A)) | ![B: $i] : (is_antisymmetric_in(A, B) <=> ![C: $i, D: $i] : ((~(in(C, B) & in(D, B) & in(ordered_pair(C, D), A) & in(ordered_pair(D, C), A))) | (C = D))))),
% 0.20/0.43      inference(rewrite,[status(thm)],[])).
% 0.20/0.43  tff(67,plain,
% 0.20/0.43      (^[A: $i] : trans(monotonicity(quant_intro(proof_bind(^[B: $i] : rewrite((is_antisymmetric_in(A, B) <=> ![C: $i, D: $i] : ((((in(C, B) & in(D, B)) & in(ordered_pair(C, D), A)) & in(ordered_pair(D, C), A)) => (C = D))) <=> (is_antisymmetric_in(A, B) <=> ![C: $i, D: $i] : ((~(in(C, B) & in(D, B) & in(ordered_pair(C, D), A) & in(ordered_pair(D, C), A))) | (C = D))))), (![B: $i] : (is_antisymmetric_in(A, B) <=> ![C: $i, D: $i] : ((((in(C, B) & in(D, B)) & in(ordered_pair(C, D), A)) & in(ordered_pair(D, C), A)) => (C = D))) <=> ![B: $i] : (is_antisymmetric_in(A, B) <=> ![C: $i, D: $i] : ((~(in(C, B) & in(D, B) & in(ordered_pair(C, D), A) & in(ordered_pair(D, C), A))) | (C = D))))), ((relation(A) => ![B: $i] : (is_antisymmetric_in(A, B) <=> ![C: $i, D: $i] : ((((in(C, B) & in(D, B)) & in(ordered_pair(C, D), A)) & in(ordered_pair(D, C), A)) => (C = D)))) <=> (relation(A) => ![B: $i] : (is_antisymmetric_in(A, B) <=> ![C: $i, D: $i] : ((~(in(C, B) & in(D, B) & in(ordered_pair(C, D), A) & in(ordered_pair(D, C), A))) | (C = D)))))), rewrite((relation(A) => ![B: $i] : (is_antisymmetric_in(A, B) <=> ![C: $i, D: $i] : ((~(in(C, B) & in(D, B) & in(ordered_pair(C, D), A) & in(ordered_pair(D, C), A))) | (C = D)))) <=> ((~relation(A)) | ![B: $i] : (is_antisymmetric_in(A, B) <=> ![C: $i, D: $i] : ((~(in(C, B) & in(D, B) & in(ordered_pair(C, D), A) & in(ordered_pair(D, C), A))) | (C = D))))), ((relation(A) => ![B: $i] : (is_antisymmetric_in(A, B) <=> ![C: $i, D: $i] : ((((in(C, B) & in(D, B)) & in(ordered_pair(C, D), A)) & in(ordered_pair(D, C), A)) => (C = D)))) <=> ((~relation(A)) | ![B: $i] : (is_antisymmetric_in(A, B) <=> ![C: $i, D: $i] : ((~(in(C, B) & in(D, B) & in(ordered_pair(C, D), A) & in(ordered_pair(D, C), A))) | (C = D))))))),
% 0.20/0.43      inference(bind,[status(th)],[])).
% 0.20/0.43  tff(68,plain,
% 0.20/0.43      (![A: $i] : (relation(A) => ![B: $i] : (is_antisymmetric_in(A, B) <=> ![C: $i, D: $i] : ((((in(C, B) & in(D, B)) & in(ordered_pair(C, D), A)) & in(ordered_pair(D, C), A)) => (C = D)))) <=> ![A: $i] : ((~relation(A)) | ![B: $i] : (is_antisymmetric_in(A, B) <=> ![C: $i, D: $i] : ((~(in(C, B) & in(D, B) & in(ordered_pair(C, D), A) & in(ordered_pair(D, C), A))) | (C = D))))),
% 0.20/0.43      inference(quant_intro,[status(thm)],[67])).
% 0.20/0.43  tff(69,axiom,(![A: $i] : (relation(A) => ![B: $i] : (is_antisymmetric_in(A, B) <=> ![C: $i, D: $i] : ((((in(C, B) & in(D, B)) & in(ordered_pair(C, D), A)) & in(ordered_pair(D, C), A)) => (C = D))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d4_relat_2')).
% 0.20/0.43  tff(70,plain,
% 0.20/0.43      (![A: $i] : ((~relation(A)) | ![B: $i] : (is_antisymmetric_in(A, B) <=> ![C: $i, D: $i] : ((~(in(C, B) & in(D, B) & in(ordered_pair(C, D), A) & in(ordered_pair(D, C), A))) | (C = D))))),
% 0.20/0.43      inference(modus_ponens,[status(thm)],[69, 68])).
% 0.20/0.43  tff(71,plain,
% 0.20/0.43      (![A: $i] : ((~relation(A)) | ![B: $i] : (is_antisymmetric_in(A, B) <=> ![C: $i, D: $i] : ((~(in(C, B) & in(D, B) & in(ordered_pair(C, D), A) & in(ordered_pair(D, C), A))) | (C = D))))),
% 0.20/0.43      inference(modus_ponens,[status(thm)],[70, 66])).
% 0.20/0.43  tff(72,plain,(
% 0.20/0.43      ![A: $i] : ((~relation(A)) | ![B: $i] : (((~is_antisymmetric_in(A, B)) | ![C: $i, D: $i] : ((~(in(C, B) & in(D, B) & in(ordered_pair(C, D), A) & in(ordered_pair(D, C), A))) | (C = D))) & (is_antisymmetric_in(A, B) | (~((~(in(tptp_fun_C_3(B, A), B) & in(tptp_fun_D_2(B, A), B) & 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))) | (tptp_fun_C_3(B, A) = tptp_fun_D_2(B, A)))))))),
% 0.20/0.43      inference(skolemize,[status(sab)],[71])).
% 0.20/0.43  tff(73,plain,
% 0.20/0.43      (![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~is_antisymmetric_in(A, B)) | ![C: $i, D: $i] : ((C = D) | (~in(D, B)) | (~in(ordered_pair(C, D), A)) | (~in(ordered_pair(D, C), A)) | (~in(C, B))))) | (~(is_antisymmetric_in(A, B) | (~((tptp_fun_C_3(B, A) = tptp_fun_D_2(B, A)) | (~in(tptp_fun_C_3(B, A), B)) | (~in(tptp_fun_D_2(B, A), B)) | (~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)))))))))),
% 0.20/0.43      inference(modus_ponens,[status(thm)],[72, 65])).
% 0.20/0.43  tff(74,plain,
% 0.20/0.43      (![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~is_antisymmetric_in(A, B)) | ![C: $i, D: $i] : ((C = D) | (~in(D, B)) | (~in(ordered_pair(C, D), A)) | (~in(ordered_pair(D, C), A)) | (~in(C, B))))) | (~(is_antisymmetric_in(A, B) | (~((tptp_fun_C_3(B, A) = tptp_fun_D_2(B, A)) | (~in(tptp_fun_C_3(B, A), B)) | (~in(tptp_fun_D_2(B, A), B)) | (~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)))))))))),
% 0.20/0.43      inference(modus_ponens,[status(thm)],[73, 63])).
% 0.20/0.43  tff(75,plain,
% 0.20/0.43      (((~![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~is_antisymmetric_in(A, B)) | ![C: $i, D: $i] : ((C = D) | (~in(D, B)) | (~in(ordered_pair(C, D), A)) | (~in(ordered_pair(D, C), A)) | (~in(C, B))))) | (~(is_antisymmetric_in(A, B) | (~((tptp_fun_C_3(B, A) = tptp_fun_D_2(B, A)) | (~in(tptp_fun_C_3(B, A), B)) | (~in(tptp_fun_D_2(B, A), B)) | (~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_antisymmetric_in(inclusion_relation(A!14), B)) | ![C: $i, D: $i] : ((C = D) | (~in(D, B)) | (~in(C, B)) | (~in(ordered_pair(C, D), inclusion_relation(A!14))) | (~in(ordered_pair(D, C), inclusion_relation(A!14)))))) | (~(is_antisymmetric_in(inclusion_relation(A!14), B) | (~((tptp_fun_C_3(B, inclusion_relation(A!14)) = tptp_fun_D_2(B, inclusion_relation(A!14))) | (~in(tptp_fun_C_3(B, inclusion_relation(A!14)), B)) | (~in(tptp_fun_D_2(B, inclusion_relation(A!14)), B)) | (~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_antisymmetric_in(A, B)) | ![C: $i, D: $i] : ((C = D) | (~in(D, B)) | (~in(ordered_pair(C, D), A)) | (~in(ordered_pair(D, C), A)) | (~in(C, B))))) | (~(is_antisymmetric_in(A, B) | (~((tptp_fun_C_3(B, A) = tptp_fun_D_2(B, A)) | (~in(tptp_fun_C_3(B, A), B)) | (~in(tptp_fun_D_2(B, A), B)) | (~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_antisymmetric_in(inclusion_relation(A!14), B)) | ![C: $i, D: $i] : ((C = D) | (~in(D, B)) | (~in(C, B)) | (~in(ordered_pair(C, D), inclusion_relation(A!14))) | (~in(ordered_pair(D, C), inclusion_relation(A!14)))))) | (~(is_antisymmetric_in(inclusion_relation(A!14), B) | (~((tptp_fun_C_3(B, inclusion_relation(A!14)) = tptp_fun_D_2(B, inclusion_relation(A!14))) | (~in(tptp_fun_C_3(B, inclusion_relation(A!14)), B)) | (~in(tptp_fun_D_2(B, inclusion_relation(A!14)), B)) | (~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))))))))))),
% 0.20/0.43      inference(rewrite,[status(thm)],[])).
% 0.20/0.43  tff(76,plain,
% 0.20/0.43      (((~relation(inclusion_relation(A!14))) | ![B: $i] : (~((~((~is_antisymmetric_in(inclusion_relation(A!14), B)) | ![C: $i, D: $i] : ((C = D) | (~in(D, B)) | (~in(ordered_pair(C, D), inclusion_relation(A!14))) | (~in(ordered_pair(D, C), inclusion_relation(A!14))) | (~in(C, B))))) | (~(is_antisymmetric_in(inclusion_relation(A!14), B) | (~((tptp_fun_C_3(B, inclusion_relation(A!14)) = tptp_fun_D_2(B, inclusion_relation(A!14))) | (~in(tptp_fun_C_3(B, inclusion_relation(A!14)), B)) | (~in(tptp_fun_D_2(B, inclusion_relation(A!14)), B)) | (~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_antisymmetric_in(inclusion_relation(A!14), B)) | ![C: $i, D: $i] : ((C = D) | (~in(D, B)) | (~in(C, B)) | (~in(ordered_pair(C, D), inclusion_relation(A!14))) | (~in(ordered_pair(D, C), inclusion_relation(A!14)))))) | (~(is_antisymmetric_in(inclusion_relation(A!14), B) | (~((tptp_fun_C_3(B, inclusion_relation(A!14)) = tptp_fun_D_2(B, inclusion_relation(A!14))) | (~in(tptp_fun_C_3(B, inclusion_relation(A!14)), B)) | (~in(tptp_fun_D_2(B, inclusion_relation(A!14)), B)) | (~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))))))))))),
% 0.20/0.44      inference(rewrite,[status(thm)],[])).
% 0.20/0.44  tff(77,plain,
% 0.20/0.44      (((~![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~is_antisymmetric_in(A, B)) | ![C: $i, D: $i] : ((C = D) | (~in(D, B)) | (~in(ordered_pair(C, D), A)) | (~in(ordered_pair(D, C), A)) | (~in(C, B))))) | (~(is_antisymmetric_in(A, B) | (~((tptp_fun_C_3(B, A) = tptp_fun_D_2(B, A)) | (~in(tptp_fun_C_3(B, A), B)) | (~in(tptp_fun_D_2(B, A), B)) | (~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_antisymmetric_in(inclusion_relation(A!14), B)) | ![C: $i, D: $i] : ((C = D) | (~in(D, B)) | (~in(ordered_pair(C, D), inclusion_relation(A!14))) | (~in(ordered_pair(D, C), inclusion_relation(A!14))) | (~in(C, B))))) | (~(is_antisymmetric_in(inclusion_relation(A!14), B) | (~((tptp_fun_C_3(B, inclusion_relation(A!14)) = tptp_fun_D_2(B, inclusion_relation(A!14))) | (~in(tptp_fun_C_3(B, inclusion_relation(A!14)), B)) | (~in(tptp_fun_D_2(B, inclusion_relation(A!14)), B)) | (~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_antisymmetric_in(A, B)) | ![C: $i, D: $i] : ((C = D) | (~in(D, B)) | (~in(ordered_pair(C, D), A)) | (~in(ordered_pair(D, C), A)) | (~in(C, B))))) | (~(is_antisymmetric_in(A, B) | (~((tptp_fun_C_3(B, A) = tptp_fun_D_2(B, A)) | (~in(tptp_fun_C_3(B, A), B)) | (~in(tptp_fun_D_2(B, A), B)) | (~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_antisymmetric_in(inclusion_relation(A!14), B)) | ![C: $i, D: $i] : ((C = D) | (~in(D, B)) | (~in(C, B)) | (~in(ordered_pair(C, D), inclusion_relation(A!14))) | (~in(ordered_pair(D, C), inclusion_relation(A!14)))))) | (~(is_antisymmetric_in(inclusion_relation(A!14), B) | (~((tptp_fun_C_3(B, inclusion_relation(A!14)) = tptp_fun_D_2(B, inclusion_relation(A!14))) | (~in(tptp_fun_C_3(B, inclusion_relation(A!14)), B)) | (~in(tptp_fun_D_2(B, inclusion_relation(A!14)), B)) | (~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)))))))))))),
% 0.20/0.44      inference(monotonicity,[status(thm)],[76])).
% 0.20/0.44  tff(78,plain,
% 0.20/0.44      (((~![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~is_antisymmetric_in(A, B)) | ![C: $i, D: $i] : ((C = D) | (~in(D, B)) | (~in(ordered_pair(C, D), A)) | (~in(ordered_pair(D, C), A)) | (~in(C, B))))) | (~(is_antisymmetric_in(A, B) | (~((tptp_fun_C_3(B, A) = tptp_fun_D_2(B, A)) | (~in(tptp_fun_C_3(B, A), B)) | (~in(tptp_fun_D_2(B, A), B)) | (~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_antisymmetric_in(inclusion_relation(A!14), B)) | ![C: $i, D: $i] : ((C = D) | (~in(D, B)) | (~in(ordered_pair(C, D), inclusion_relation(A!14))) | (~in(ordered_pair(D, C), inclusion_relation(A!14))) | (~in(C, B))))) | (~(is_antisymmetric_in(inclusion_relation(A!14), B) | (~((tptp_fun_C_3(B, inclusion_relation(A!14)) = tptp_fun_D_2(B, inclusion_relation(A!14))) | (~in(tptp_fun_C_3(B, inclusion_relation(A!14)), B)) | (~in(tptp_fun_D_2(B, inclusion_relation(A!14)), B)) | (~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_antisymmetric_in(A, B)) | ![C: $i, D: $i] : ((C = D) | (~in(D, B)) | (~in(ordered_pair(C, D), A)) | (~in(ordered_pair(D, C), A)) | (~in(C, B))))) | (~(is_antisymmetric_in(A, B) | (~((tptp_fun_C_3(B, A) = tptp_fun_D_2(B, A)) | (~in(tptp_fun_C_3(B, A), B)) | (~in(tptp_fun_D_2(B, A), B)) | (~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_antisymmetric_in(inclusion_relation(A!14), B)) | ![C: $i, D: $i] : ((C = D) | (~in(D, B)) | (~in(C, B)) | (~in(ordered_pair(C, D), inclusion_relation(A!14))) | (~in(ordered_pair(D, C), inclusion_relation(A!14)))))) | (~(is_antisymmetric_in(inclusion_relation(A!14), B) | (~((tptp_fun_C_3(B, inclusion_relation(A!14)) = tptp_fun_D_2(B, inclusion_relation(A!14))) | (~in(tptp_fun_C_3(B, inclusion_relation(A!14)), B)) | (~in(tptp_fun_D_2(B, inclusion_relation(A!14)), B)) | (~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))))))))))),
% 0.20/0.44      inference(transitivity,[status(thm)],[77, 75])).
% 0.20/0.44  tff(79,plain,
% 0.20/0.44      ((~![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~is_antisymmetric_in(A, B)) | ![C: $i, D: $i] : ((C = D) | (~in(D, B)) | (~in(ordered_pair(C, D), A)) | (~in(ordered_pair(D, C), A)) | (~in(C, B))))) | (~(is_antisymmetric_in(A, B) | (~((tptp_fun_C_3(B, A) = tptp_fun_D_2(B, A)) | (~in(tptp_fun_C_3(B, A), B)) | (~in(tptp_fun_D_2(B, A), B)) | (~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_antisymmetric_in(inclusion_relation(A!14), B)) | ![C: $i, D: $i] : ((C = D) | (~in(D, B)) | (~in(ordered_pair(C, D), inclusion_relation(A!14))) | (~in(ordered_pair(D, C), inclusion_relation(A!14))) | (~in(C, B))))) | (~(is_antisymmetric_in(inclusion_relation(A!14), B) | (~((tptp_fun_C_3(B, inclusion_relation(A!14)) = tptp_fun_D_2(B, inclusion_relation(A!14))) | (~in(tptp_fun_C_3(B, inclusion_relation(A!14)), B)) | (~in(tptp_fun_D_2(B, inclusion_relation(A!14)), B)) | (~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))))))))))),
% 0.20/0.44      inference(quant_inst,[status(thm)],[])).
% 0.20/0.44  tff(80,plain,
% 0.20/0.44      ((~![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~is_antisymmetric_in(A, B)) | ![C: $i, D: $i] : ((C = D) | (~in(D, B)) | (~in(ordered_pair(C, D), A)) | (~in(ordered_pair(D, C), A)) | (~in(C, B))))) | (~(is_antisymmetric_in(A, B) | (~((tptp_fun_C_3(B, A) = tptp_fun_D_2(B, A)) | (~in(tptp_fun_C_3(B, A), B)) | (~in(tptp_fun_D_2(B, A), B)) | (~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_antisymmetric_in(inclusion_relation(A!14), B)) | ![C: $i, D: $i] : ((C = D) | (~in(D, B)) | (~in(C, B)) | (~in(ordered_pair(C, D), inclusion_relation(A!14))) | (~in(ordered_pair(D, C), inclusion_relation(A!14)))))) | (~(is_antisymmetric_in(inclusion_relation(A!14), B) | (~((tptp_fun_C_3(B, inclusion_relation(A!14)) = tptp_fun_D_2(B, inclusion_relation(A!14))) | (~in(tptp_fun_C_3(B, inclusion_relation(A!14)), B)) | (~in(tptp_fun_D_2(B, inclusion_relation(A!14)), B)) | (~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)))))))))),
% 0.20/0.44      inference(modus_ponens,[status(thm)],[79, 78])).
% 0.20/0.44  tff(81,plain,
% 0.20/0.44      (![B: $i] : (~((~((~is_antisymmetric_in(inclusion_relation(A!14), B)) | ![C: $i, D: $i] : ((C = D) | (~in(D, B)) | (~in(C, B)) | (~in(ordered_pair(C, D), inclusion_relation(A!14))) | (~in(ordered_pair(D, C), inclusion_relation(A!14)))))) | (~(is_antisymmetric_in(inclusion_relation(A!14), B) | (~((tptp_fun_C_3(B, inclusion_relation(A!14)) = tptp_fun_D_2(B, inclusion_relation(A!14))) | (~in(tptp_fun_C_3(B, inclusion_relation(A!14)), B)) | (~in(tptp_fun_D_2(B, inclusion_relation(A!14)), B)) | (~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)))))))))),
% 0.20/0.44      inference(unit_resolution,[status(thm)],[80, 74, 9])).
% 0.20/0.44  tff(82,plain,
% 0.20/0.44      (((~![B: $i] : (~((~((~is_antisymmetric_in(inclusion_relation(A!14), B)) | ![C: $i, D: $i] : ((C = D) | (~in(D, B)) | (~in(C, B)) | (~in(ordered_pair(C, D), inclusion_relation(A!14))) | (~in(ordered_pair(D, C), inclusion_relation(A!14)))))) | (~(is_antisymmetric_in(inclusion_relation(A!14), B) | (~((tptp_fun_C_3(B, inclusion_relation(A!14)) = tptp_fun_D_2(B, inclusion_relation(A!14))) | (~in(tptp_fun_C_3(B, inclusion_relation(A!14)), B)) | (~in(tptp_fun_D_2(B, inclusion_relation(A!14)), B)) | (~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_antisymmetric_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(C, D), inclusion_relation(A!14))) | (~in(ordered_pair(D, C), inclusion_relation(A!14))) | (~in(D, set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))))) | (~in(C, set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14)))))))) | (~(is_antisymmetric_in(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(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))))) | (~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_antisymmetric_in(inclusion_relation(A!14), B)) | ![C: $i, D: $i] : ((C = D) | (~in(D, B)) | (~in(C, B)) | (~in(ordered_pair(C, D), inclusion_relation(A!14))) | (~in(ordered_pair(D, C), inclusion_relation(A!14)))))) | (~(is_antisymmetric_in(inclusion_relation(A!14), B) | (~((tptp_fun_C_3(B, inclusion_relation(A!14)) = tptp_fun_D_2(B, inclusion_relation(A!14))) | (~in(tptp_fun_C_3(B, inclusion_relation(A!14)), B)) | (~in(tptp_fun_D_2(B, inclusion_relation(A!14)), B)) | (~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_antisymmetric_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(C, D), inclusion_relation(A!14))) | (~in(ordered_pair(D, C), inclusion_relation(A!14))) | (~in(D, set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))))) | (~in(C, set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14)))))))) | (~(is_antisymmetric_in(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(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))))) | (~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))))))))))),
% 0.20/0.44      inference(rewrite,[status(thm)],[])).
% 0.20/0.44  tff(83,plain,
% 0.20/0.44      ((~((~((~is_antisymmetric_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(D, set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))))) | (~in(C, set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))))) | (~in(ordered_pair(C, D), inclusion_relation(A!14))) | (~in(ordered_pair(D, C), inclusion_relation(A!14)))))) | (~(is_antisymmetric_in(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(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))))) | (~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_antisymmetric_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(C, D), inclusion_relation(A!14))) | (~in(ordered_pair(D, C), inclusion_relation(A!14))) | (~in(D, set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))))) | (~in(C, set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14)))))))) | (~(is_antisymmetric_in(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(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))))) | (~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)))))))))),
% 0.20/0.45      inference(rewrite,[status(thm)],[])).
% 0.20/0.45  tff(84,plain,
% 0.20/0.45      (((~![B: $i] : (~((~((~is_antisymmetric_in(inclusion_relation(A!14), B)) | ![C: $i, D: $i] : ((C = D) | (~in(D, B)) | (~in(C, B)) | (~in(ordered_pair(C, D), inclusion_relation(A!14))) | (~in(ordered_pair(D, C), inclusion_relation(A!14)))))) | (~(is_antisymmetric_in(inclusion_relation(A!14), B) | (~((tptp_fun_C_3(B, inclusion_relation(A!14)) = tptp_fun_D_2(B, inclusion_relation(A!14))) | (~in(tptp_fun_C_3(B, inclusion_relation(A!14)), B)) | (~in(tptp_fun_D_2(B, inclusion_relation(A!14)), B)) | (~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_antisymmetric_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(D, set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))))) | (~in(C, set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))))) | (~in(ordered_pair(C, D), inclusion_relation(A!14))) | (~in(ordered_pair(D, C), inclusion_relation(A!14)))))) | (~(is_antisymmetric_in(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(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))))) | (~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_antisymmetric_in(inclusion_relation(A!14), B)) | ![C: $i, D: $i] : ((C = D) | (~in(D, B)) | (~in(C, B)) | (~in(ordered_pair(C, D), inclusion_relation(A!14))) | (~in(ordered_pair(D, C), inclusion_relation(A!14)))))) | (~(is_antisymmetric_in(inclusion_relation(A!14), B) | (~((tptp_fun_C_3(B, inclusion_relation(A!14)) = tptp_fun_D_2(B, inclusion_relation(A!14))) | (~in(tptp_fun_C_3(B, inclusion_relation(A!14)), B)) | (~in(tptp_fun_D_2(B, inclusion_relation(A!14)), B)) | (~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_antisymmetric_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(C, D), inclusion_relation(A!14))) | (~in(ordered_pair(D, C), inclusion_relation(A!14))) | (~in(D, set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))))) | (~in(C, set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14)))))))) | (~(is_antisymmetric_in(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(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))))) | (~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))))))))))),
% 0.20/0.45      inference(monotonicity,[status(thm)],[83])).
% 0.20/0.45  tff(85,plain,
% 0.20/0.45      (((~![B: $i] : (~((~((~is_antisymmetric_in(inclusion_relation(A!14), B)) | ![C: $i, D: $i] : ((C = D) | (~in(D, B)) | (~in(C, B)) | (~in(ordered_pair(C, D), inclusion_relation(A!14))) | (~in(ordered_pair(D, C), inclusion_relation(A!14)))))) | (~(is_antisymmetric_in(inclusion_relation(A!14), B) | (~((tptp_fun_C_3(B, inclusion_relation(A!14)) = tptp_fun_D_2(B, inclusion_relation(A!14))) | (~in(tptp_fun_C_3(B, inclusion_relation(A!14)), B)) | (~in(tptp_fun_D_2(B, inclusion_relation(A!14)), B)) | (~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_antisymmetric_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(D, set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))))) | (~in(C, set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))))) | (~in(ordered_pair(C, D), inclusion_relation(A!14))) | (~in(ordered_pair(D, C), inclusion_relation(A!14)))))) | (~(is_antisymmetric_in(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(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))))) | (~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_antisymmetric_in(inclusion_relation(A!14), B)) | ![C: $i, D: $i] : ((C = D) | (~in(D, B)) | (~in(C, B)) | (~in(ordered_pair(C, D), inclusion_relation(A!14))) | (~in(ordered_pair(D, C), inclusion_relation(A!14)))))) | (~(is_antisymmetric_in(inclusion_relation(A!14), B) | (~((tptp_fun_C_3(B, inclusion_relation(A!14)) = tptp_fun_D_2(B, inclusion_relation(A!14))) | (~in(tptp_fun_C_3(B, inclusion_relation(A!14)), B)) | (~in(tptp_fun_D_2(B, inclusion_relation(A!14)), B)) | (~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_antisymmetric_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(C, D), inclusion_relation(A!14))) | (~in(ordered_pair(D, C), inclusion_relation(A!14))) | (~in(D, set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))))) | (~in(C, set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14)))))))) | (~(is_antisymmetric_in(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(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))))) | (~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))))))))))),
% 0.20/0.45      inference(transitivity,[status(thm)],[84, 82])).
% 0.20/0.45  tff(86,plain,
% 0.20/0.45      ((~![B: $i] : (~((~((~is_antisymmetric_in(inclusion_relation(A!14), B)) | ![C: $i, D: $i] : ((C = D) | (~in(D, B)) | (~in(C, B)) | (~in(ordered_pair(C, D), inclusion_relation(A!14))) | (~in(ordered_pair(D, C), inclusion_relation(A!14)))))) | (~(is_antisymmetric_in(inclusion_relation(A!14), B) | (~((tptp_fun_C_3(B, inclusion_relation(A!14)) = tptp_fun_D_2(B, inclusion_relation(A!14))) | (~in(tptp_fun_C_3(B, inclusion_relation(A!14)), B)) | (~in(tptp_fun_D_2(B, inclusion_relation(A!14)), B)) | (~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_antisymmetric_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(D, set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))))) | (~in(C, set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))))) | (~in(ordered_pair(C, D), inclusion_relation(A!14))) | (~in(ordered_pair(D, C), inclusion_relation(A!14)))))) | (~(is_antisymmetric_in(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(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))))) | (~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)))))))))),
% 0.20/0.45      inference(quant_inst,[status(thm)],[])).
% 0.20/0.45  tff(87,plain,
% 0.20/0.45      ((~![B: $i] : (~((~((~is_antisymmetric_in(inclusion_relation(A!14), B)) | ![C: $i, D: $i] : ((C = D) | (~in(D, B)) | (~in(C, B)) | (~in(ordered_pair(C, D), inclusion_relation(A!14))) | (~in(ordered_pair(D, C), inclusion_relation(A!14)))))) | (~(is_antisymmetric_in(inclusion_relation(A!14), B) | (~((tptp_fun_C_3(B, inclusion_relation(A!14)) = tptp_fun_D_2(B, inclusion_relation(A!14))) | (~in(tptp_fun_C_3(B, inclusion_relation(A!14)), B)) | (~in(tptp_fun_D_2(B, inclusion_relation(A!14)), B)) | (~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_antisymmetric_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(C, D), inclusion_relation(A!14))) | (~in(ordered_pair(D, C), inclusion_relation(A!14))) | (~in(D, set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))))) | (~in(C, set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14)))))))) | (~(is_antisymmetric_in(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(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))))) | (~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)))))))))),
% 0.20/0.45      inference(modus_ponens,[status(thm)],[86, 85])).
% 0.20/0.45  tff(88,plain,
% 0.20/0.45      (~((~((~is_antisymmetric_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(C, D), inclusion_relation(A!14))) | (~in(ordered_pair(D, C), inclusion_relation(A!14))) | (~in(D, set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))))) | (~in(C, set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14)))))))) | (~(is_antisymmetric_in(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(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))))) | (~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))))))))),
% 0.20/0.46      inference(unit_resolution,[status(thm)],[87, 81])).
% 0.20/0.46  tff(89,plain,
% 0.20/0.46      (((~((~is_antisymmetric_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(C, D), inclusion_relation(A!14))) | (~in(ordered_pair(D, C), inclusion_relation(A!14))) | (~in(D, set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))))) | (~in(C, set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14)))))))) | (~(is_antisymmetric_in(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(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))))) | (~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_antisymmetric_in(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(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))))) | (~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))))))),
% 0.20/0.46      inference(tautology,[status(thm)],[])).
% 0.20/0.46  tff(90,plain,
% 0.20/0.46      (is_antisymmetric_in(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(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))))) | (~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)))))),
% 0.20/0.46      inference(unit_resolution,[status(thm)],[89, 88])).
% 0.20/0.46  tff(91,plain,
% 0.20/0.46      (set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))) = relation_field(inclusion_relation(A!14))),
% 0.20/0.46      inference(symmetry,[status(thm)],[23])).
% 0.20/0.46  tff(92,plain,
% 0.20/0.46      (is_antisymmetric_in(inclusion_relation(A!14), set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14)))) <=> is_antisymmetric_in(inclusion_relation(A!14), relation_field(inclusion_relation(A!14)))),
% 0.20/0.46      inference(monotonicity,[status(thm)],[91])).
% 0.20/0.46  tff(93,plain,
% 0.20/0.46      (is_antisymmetric_in(inclusion_relation(A!14), relation_field(inclusion_relation(A!14))) <=> is_antisymmetric_in(inclusion_relation(A!14), set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))))),
% 0.20/0.46      inference(symmetry,[status(thm)],[92])).
% 0.20/0.46  tff(94,plain,
% 0.20/0.46      ((~is_antisymmetric_in(inclusion_relation(A!14), relation_field(inclusion_relation(A!14)))) <=> (~is_antisymmetric_in(inclusion_relation(A!14), set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14)))))),
% 0.20/0.46      inference(monotonicity,[status(thm)],[93])).
% 0.20/0.46  tff(95,plain,
% 0.20/0.46      (^[A: $i] : refl(((~relation(A)) | (antisymmetric(A) <=> is_antisymmetric_in(A, relation_field(A)))) <=> ((~relation(A)) | (antisymmetric(A) <=> is_antisymmetric_in(A, relation_field(A)))))),
% 0.20/0.46      inference(bind,[status(th)],[])).
% 0.20/0.46  tff(96,plain,
% 0.20/0.46      (![A: $i] : ((~relation(A)) | (antisymmetric(A) <=> is_antisymmetric_in(A, relation_field(A)))) <=> ![A: $i] : ((~relation(A)) | (antisymmetric(A) <=> is_antisymmetric_in(A, relation_field(A))))),
% 0.20/0.46      inference(quant_intro,[status(thm)],[95])).
% 0.20/0.46  tff(97,plain,
% 0.20/0.46      (![A: $i] : ((~relation(A)) | (antisymmetric(A) <=> is_antisymmetric_in(A, relation_field(A)))) <=> ![A: $i] : ((~relation(A)) | (antisymmetric(A) <=> is_antisymmetric_in(A, relation_field(A))))),
% 0.20/0.46      inference(rewrite,[status(thm)],[])).
% 0.20/0.46  tff(98,plain,
% 0.20/0.46      (^[A: $i] : rewrite((relation(A) => (antisymmetric(A) <=> is_antisymmetric_in(A, relation_field(A)))) <=> ((~relation(A)) | (antisymmetric(A) <=> is_antisymmetric_in(A, relation_field(A)))))),
% 0.20/0.46      inference(bind,[status(th)],[])).
% 0.20/0.46  tff(99,plain,
% 0.20/0.46      (![A: $i] : (relation(A) => (antisymmetric(A) <=> is_antisymmetric_in(A, relation_field(A)))) <=> ![A: $i] : ((~relation(A)) | (antisymmetric(A) <=> is_antisymmetric_in(A, relation_field(A))))),
% 0.20/0.46      inference(quant_intro,[status(thm)],[98])).
% 0.20/0.46  tff(100,axiom,(![A: $i] : (relation(A) => (antisymmetric(A) <=> is_antisymmetric_in(A, relation_field(A))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d12_relat_2')).
% 0.20/0.46  tff(101,plain,
% 0.20/0.46      (![A: $i] : ((~relation(A)) | (antisymmetric(A) <=> is_antisymmetric_in(A, relation_field(A))))),
% 0.20/0.46      inference(modus_ponens,[status(thm)],[100, 99])).
% 0.20/0.46  tff(102,plain,
% 0.20/0.46      (![A: $i] : ((~relation(A)) | (antisymmetric(A) <=> is_antisymmetric_in(A, relation_field(A))))),
% 0.20/0.46      inference(modus_ponens,[status(thm)],[101, 97])).
% 0.20/0.46  tff(103,plain,(
% 0.20/0.46      ![A: $i] : ((~relation(A)) | (antisymmetric(A) <=> is_antisymmetric_in(A, relation_field(A))))),
% 0.20/0.46      inference(skolemize,[status(sab)],[102])).
% 0.20/0.46  tff(104,plain,
% 0.20/0.46      (![A: $i] : ((~relation(A)) | (antisymmetric(A) <=> is_antisymmetric_in(A, relation_field(A))))),
% 0.20/0.46      inference(modus_ponens,[status(thm)],[103, 96])).
% 0.20/0.46  tff(105,plain,
% 0.20/0.46      (((~![A: $i] : ((~relation(A)) | (antisymmetric(A) <=> is_antisymmetric_in(A, relation_field(A))))) | ((~relation(inclusion_relation(A!14))) | (antisymmetric(inclusion_relation(A!14)) <=> is_antisymmetric_in(inclusion_relation(A!14), relation_field(inclusion_relation(A!14)))))) <=> ((~![A: $i] : ((~relation(A)) | (antisymmetric(A) <=> is_antisymmetric_in(A, relation_field(A))))) | (~relation(inclusion_relation(A!14))) | (antisymmetric(inclusion_relation(A!14)) <=> is_antisymmetric_in(inclusion_relation(A!14), relation_field(inclusion_relation(A!14)))))),
% 0.20/0.46      inference(rewrite,[status(thm)],[])).
% 0.20/0.46  tff(106,plain,
% 0.20/0.46      ((~![A: $i] : ((~relation(A)) | (antisymmetric(A) <=> is_antisymmetric_in(A, relation_field(A))))) | ((~relation(inclusion_relation(A!14))) | (antisymmetric(inclusion_relation(A!14)) <=> is_antisymmetric_in(inclusion_relation(A!14), relation_field(inclusion_relation(A!14)))))),
% 0.20/0.46      inference(quant_inst,[status(thm)],[])).
% 0.20/0.46  tff(107,plain,
% 0.20/0.46      ((~![A: $i] : ((~relation(A)) | (antisymmetric(A) <=> is_antisymmetric_in(A, relation_field(A))))) | (~relation(inclusion_relation(A!14))) | (antisymmetric(inclusion_relation(A!14)) <=> is_antisymmetric_in(inclusion_relation(A!14), relation_field(inclusion_relation(A!14))))),
% 0.20/0.46      inference(modus_ponens,[status(thm)],[106, 105])).
% 0.20/0.46  tff(108,plain,
% 0.20/0.46      ((~relation(inclusion_relation(A!14))) | (antisymmetric(inclusion_relation(A!14)) <=> is_antisymmetric_in(inclusion_relation(A!14), relation_field(inclusion_relation(A!14))))),
% 0.20/0.46      inference(unit_resolution,[status(thm)],[107, 104])).
% 0.20/0.46  tff(109,plain,
% 0.20/0.46      (antisymmetric(inclusion_relation(A!14)) <=> is_antisymmetric_in(inclusion_relation(A!14), relation_field(inclusion_relation(A!14)))),
% 0.20/0.46      inference(unit_resolution,[status(thm)],[108, 9])).
% 0.20/0.46  tff(110,plain,
% 0.20/0.46      ((~![A: $i] : antisymmetric(inclusion_relation(A))) <=> (~![A: $i] : antisymmetric(inclusion_relation(A)))),
% 0.20/0.46      inference(rewrite,[status(thm)],[])).
% 0.20/0.46  tff(111,axiom,(~![A: $i] : antisymmetric(inclusion_relation(A))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t5_wellord2')).
% 0.20/0.46  tff(112,plain,
% 0.20/0.46      (~![A: $i] : antisymmetric(inclusion_relation(A))),
% 0.20/0.46      inference(modus_ponens,[status(thm)],[111, 110])).
% 0.20/0.46  tff(113,plain,
% 0.20/0.46      (~![A: $i] : antisymmetric(inclusion_relation(A))),
% 0.20/0.46      inference(modus_ponens,[status(thm)],[112, 110])).
% 0.20/0.46  tff(114,plain,
% 0.20/0.46      (~![A: $i] : antisymmetric(inclusion_relation(A))),
% 0.20/0.46      inference(modus_ponens,[status(thm)],[113, 110])).
% 0.20/0.46  tff(115,plain,
% 0.20/0.46      (~![A: $i] : antisymmetric(inclusion_relation(A))),
% 0.20/0.46      inference(modus_ponens,[status(thm)],[114, 110])).
% 0.20/0.46  tff(116,plain,
% 0.20/0.46      (~![A: $i] : antisymmetric(inclusion_relation(A))),
% 0.20/0.46      inference(modus_ponens,[status(thm)],[115, 110])).
% 0.20/0.46  tff(117,plain,
% 0.20/0.46      (~![A: $i] : antisymmetric(inclusion_relation(A))),
% 0.20/0.46      inference(modus_ponens,[status(thm)],[116, 110])).
% 0.20/0.46  tff(118,plain,
% 0.20/0.46      (~![A: $i] : antisymmetric(inclusion_relation(A))),
% 0.20/0.46      inference(modus_ponens,[status(thm)],[117, 110])).
% 0.20/0.46  tff(119,plain,(
% 0.20/0.46      ~antisymmetric(inclusion_relation(A!14))),
% 0.20/0.46      inference(skolemize,[status(sab)],[118])).
% 0.20/0.46  tff(120,plain,
% 0.20/0.46      ((~(antisymmetric(inclusion_relation(A!14)) <=> is_antisymmetric_in(inclusion_relation(A!14), relation_field(inclusion_relation(A!14))))) | antisymmetric(inclusion_relation(A!14)) | (~is_antisymmetric_in(inclusion_relation(A!14), relation_field(inclusion_relation(A!14))))),
% 0.20/0.46      inference(tautology,[status(thm)],[])).
% 0.20/0.46  tff(121,plain,
% 0.20/0.46      ((~(antisymmetric(inclusion_relation(A!14)) <=> is_antisymmetric_in(inclusion_relation(A!14), relation_field(inclusion_relation(A!14))))) | (~is_antisymmetric_in(inclusion_relation(A!14), relation_field(inclusion_relation(A!14))))),
% 0.20/0.46      inference(unit_resolution,[status(thm)],[120, 119])).
% 0.20/0.46  tff(122,plain,
% 0.20/0.46      (~is_antisymmetric_in(inclusion_relation(A!14), relation_field(inclusion_relation(A!14)))),
% 0.20/0.46      inference(unit_resolution,[status(thm)],[121, 109])).
% 0.20/0.46  tff(123,plain,
% 0.20/0.46      (~is_antisymmetric_in(inclusion_relation(A!14), set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))))),
% 0.20/0.46      inference(modus_ponens,[status(thm)],[122, 94])).
% 0.20/0.46  tff(124,plain,
% 0.20/0.46      ((~(is_antisymmetric_in(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(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))))) | (~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_antisymmetric_in(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(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))))) | (~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)))))),
% 0.20/0.46      inference(tautology,[status(thm)],[])).
% 0.20/0.46  tff(125,plain,
% 0.20/0.46      (~((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(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))))) | (~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))))),
% 0.20/0.46      inference(unit_resolution,[status(thm)],[124, 123, 90])).
% 0.20/0.46  tff(126,plain,
% 0.20/0.46      (((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(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))))) | (~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))))),
% 0.20/0.46      inference(tautology,[status(thm)],[])).
% 0.20/0.46  tff(127,plain,
% 0.20/0.46      (in(tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)), set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))))),
% 0.20/0.46      inference(unit_resolution,[status(thm)],[126, 125])).
% 0.20/0.46  tff(128,plain,
% 0.20/0.46      (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)),
% 0.20/0.46      inference(modus_ponens,[status(thm)],[127, 58])).
% 0.20/0.46  tff(129,plain,
% 0.20/0.46      (in(tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)), 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))))),
% 0.20/0.46      inference(monotonicity,[status(thm)],[56])).
% 0.20/0.46  tff(130,plain,
% 0.20/0.46      (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_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)), A!14)),
% 0.20/0.46      inference(symmetry,[status(thm)],[129])).
% 0.20/0.46  tff(131,plain,
% 0.20/0.46      (((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(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))))) | (~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))))),
% 0.20/0.46      inference(tautology,[status(thm)],[])).
% 0.20/0.46  tff(132,plain,
% 0.20/0.46      (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))))),
% 0.20/0.46      inference(unit_resolution,[status(thm)],[131, 125])).
% 0.20/0.46  tff(133,plain,
% 0.20/0.46      (in(tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)), A!14)),
% 0.20/0.46      inference(modus_ponens,[status(thm)],[132, 130])).
% 0.20/0.46  tff(134,plain,
% 0.20/0.46      (((~(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)))),
% 0.20/0.46      inference(tautology,[status(thm)],[])).
% 0.20/0.46  tff(135,plain,
% 0.20/0.46      (![C: $i, D: $i] : ((~in(C, A!14)) | (~in(D, A!14)) | (in(ordered_pair(C, D), inclusion_relation(A!14)) <=> subset(C, D)))),
% 0.20/0.46      inference(unit_resolution,[status(thm)],[134, 52])).
% 0.20/0.46  tff(136,plain,
% 0.20/0.46      (((~![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_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)))))),
% 0.20/0.47      inference(rewrite,[status(thm)],[])).
% 0.20/0.47  tff(137,plain,
% 0.20/0.47      ((~![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)))))),
% 0.20/0.47      inference(quant_inst,[status(thm)],[])).
% 0.20/0.47  tff(138,plain,
% 0.20/0.47      ((~![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))))),
% 0.20/0.47      inference(modus_ponens,[status(thm)],[137, 136])).
% 0.20/0.47  tff(139,plain,
% 0.20/0.47      ((~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))))),
% 0.20/0.47      inference(unit_resolution,[status(thm)],[138, 135])).
% 0.20/0.47  tff(140,plain,
% 0.20/0.47      (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)))),
% 0.20/0.47      inference(unit_resolution,[status(thm)],[139, 133, 128])).
% 0.20/0.47  tff(141,plain,
% 0.20/0.47      (((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(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))))) | (~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))),
% 0.20/0.47      inference(tautology,[status(thm)],[])).
% 0.20/0.47  tff(142,plain,
% 0.20/0.47      (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))),
% 0.20/0.47      inference(unit_resolution,[status(thm)],[141, 125])).
% 0.20/0.47  tff(143,plain,
% 0.20/0.47      ((~(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)))),
% 0.20/0.47      inference(tautology,[status(thm)],[])).
% 0.20/0.47  tff(144,plain,
% 0.20/0.47      ((~(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)))),
% 0.20/0.47      inference(unit_resolution,[status(thm)],[143, 142])).
% 0.20/0.47  tff(145,plain,
% 0.20/0.47      (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)))),
% 0.20/0.47      inference(unit_resolution,[status(thm)],[144, 140])).
% 0.20/0.47  tff(146,plain,
% 0.20/0.47      (((~![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)))))),
% 0.20/0.47      inference(rewrite,[status(thm)],[])).
% 0.20/0.47  tff(147,plain,
% 0.20/0.47      ((~![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)))))),
% 0.20/0.47      inference(quant_inst,[status(thm)],[])).
% 0.20/0.47  tff(148,plain,
% 0.20/0.47      ((~![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))))),
% 0.20/0.47      inference(modus_ponens,[status(thm)],[147, 146])).
% 0.20/0.47  tff(149,plain,
% 0.20/0.47      ((~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))))),
% 0.20/0.47      inference(unit_resolution,[status(thm)],[148, 135])).
% 0.20/0.47  tff(150,plain,
% 0.20/0.47      (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)))),
% 0.20/0.47      inference(unit_resolution,[status(thm)],[149, 133, 128])).
% 0.20/0.47  tff(151,plain,
% 0.20/0.47      (((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(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))))) | (~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))),
% 0.20/0.47      inference(tautology,[status(thm)],[])).
% 0.20/0.47  tff(152,plain,
% 0.20/0.47      (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))),
% 0.20/0.47      inference(unit_resolution,[status(thm)],[151, 125])).
% 0.20/0.47  tff(153,plain,
% 0.20/0.47      ((~(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)))),
% 0.20/0.47      inference(tautology,[status(thm)],[])).
% 0.20/0.47  tff(154,plain,
% 0.20/0.47      ((~(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)))),
% 0.20/0.47      inference(unit_resolution,[status(thm)],[153, 152])).
% 0.20/0.47  tff(155,plain,
% 0.20/0.47      (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)))),
% 0.20/0.47      inference(unit_resolution,[status(thm)],[154, 150])).
% 0.20/0.47  tff(156,plain,
% 0.20/0.47      ((~((~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_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_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_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))))),
% 0.20/0.47      inference(tautology,[status(thm)],[])).
% 0.20/0.47  tff(157,plain,
% 0.20/0.47      (~((~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_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)))))),
% 0.20/0.47      inference(unit_resolution,[status(thm)],[156, 155, 145])).
% 0.20/0.47  tff(158,plain,
% 0.20/0.47      (((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(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))))) | (~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)))) | (~(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))))),
% 0.20/0.47      inference(tautology,[status(thm)],[])).
% 0.20/0.47  tff(159,plain,
% 0.20/0.47      (~(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)))),
% 0.20/0.47      inference(unit_resolution,[status(thm)],[158, 125])).
% 0.20/0.47  tff(160,plain,
% 0.20/0.47      ((~((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)))) | (~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)))))))) | (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)))) | (~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)))))),
% 0.20/0.47      inference(tautology,[status(thm)],[])).
% 0.20/0.47  tff(161,plain,
% 0.20/0.47      (~((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)))) | (~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)))))))),
% 0.20/0.47      inference(unit_resolution,[status(thm)],[160, 159, 157])).
% 0.20/0.47  tff(162,plain,
% 0.20/0.47      (^[A: $i, B: $i] : refl(((A = B) <=> (~((~subset(A, B)) | (~subset(B, A))))) <=> ((A = B) <=> (~((~subset(A, B)) | (~subset(B, A))))))),
% 0.20/0.47      inference(bind,[status(th)],[])).
% 0.20/0.47  tff(163,plain,
% 0.20/0.47      (![A: $i, B: $i] : ((A = B) <=> (~((~subset(A, B)) | (~subset(B, A))))) <=> ![A: $i, B: $i] : ((A = B) <=> (~((~subset(A, B)) | (~subset(B, A)))))),
% 0.20/0.47      inference(quant_intro,[status(thm)],[162])).
% 0.20/0.47  tff(164,plain,
% 0.20/0.47      (^[A: $i, B: $i] : rewrite(((A = B) <=> (subset(A, B) & subset(B, A))) <=> ((A = B) <=> (~((~subset(A, B)) | (~subset(B, A))))))),
% 0.20/0.47      inference(bind,[status(th)],[])).
% 0.20/0.47  tff(165,plain,
% 0.20/0.47      (![A: $i, B: $i] : ((A = B) <=> (subset(A, B) & subset(B, A))) <=> ![A: $i, B: $i] : ((A = B) <=> (~((~subset(A, B)) | (~subset(B, A)))))),
% 0.20/0.47      inference(quant_intro,[status(thm)],[164])).
% 0.20/0.47  tff(166,plain,
% 0.20/0.47      (![A: $i, B: $i] : ((A = B) <=> (subset(A, B) & subset(B, A))) <=> ![A: $i, B: $i] : ((A = B) <=> (subset(A, B) & subset(B, A)))),
% 0.20/0.47      inference(rewrite,[status(thm)],[])).
% 0.20/0.47  tff(167,axiom,(![A: $i, B: $i] : ((A = B) <=> (subset(A, B) & subset(B, A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d10_xboole_0')).
% 0.20/0.47  tff(168,plain,
% 0.20/0.47      (![A: $i, B: $i] : ((A = B) <=> (subset(A, B) & subset(B, A)))),
% 0.20/0.47      inference(modus_ponens,[status(thm)],[167, 166])).
% 0.20/0.47  tff(169,plain,(
% 0.20/0.47      ![A: $i, B: $i] : ((A = B) <=> (subset(A, B) & subset(B, A)))),
% 0.20/0.47      inference(skolemize,[status(sab)],[168])).
% 0.20/0.47  tff(170,plain,
% 0.20/0.47      (![A: $i, B: $i] : ((A = B) <=> (~((~subset(A, B)) | (~subset(B, A)))))),
% 0.20/0.47      inference(modus_ponens,[status(thm)],[169, 165])).
% 0.20/0.47  tff(171,plain,
% 0.20/0.47      (![A: $i, B: $i] : ((A = B) <=> (~((~subset(A, B)) | (~subset(B, A)))))),
% 0.20/0.47      inference(modus_ponens,[status(thm)],[170, 163])).
% 0.20/0.47  tff(172,plain,
% 0.20/0.47      ((~![A: $i, B: $i] : ((A = B) <=> (~((~subset(A, B)) | (~subset(B, A)))))) | ((tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)) = tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14))) <=> (~((~subset(tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)), tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)))) | (~subset(tptp_fun_D_2(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)), tptp_fun_C_3(set_union2(relation_dom(inclusion_relation(A!14)), relation_rng(inclusion_relation(A!14))), inclusion_relation(A!14)))))))),
% 0.20/0.48      inference(quant_inst,[status(thm)],[])).
% 0.20/0.48  tff(173,plain,
% 0.20/0.48      ($false),
% 0.20/0.48      inference(unit_resolution,[status(thm)],[172, 171, 161])).
% 0.20/0.48  % SZS output end Proof
%------------------------------------------------------------------------------