%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SEU240+1 : TPTP v9.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n003.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:27:21 AM UTC 2025
% Result : Theorem 0.12s 0.38s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU240+1 : TPTP v9.0.0. Released v3.3.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n003.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 20 06:28:24 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.12/0.38 % SZS status Theorem
% 0.12/0.38 % SZS output start Proof
% 0.12/0.38 tff(in_type, type, (
% 0.12/0.38 in: ( $i * $i ) > $o)).
% 0.12/0.38 tff(tptp_fun_A_4_type, type, (
% 0.12/0.38 tptp_fun_A_4: $i)).
% 0.12/0.38 tff(ordered_pair_type, type, (
% 0.12/0.38 ordered_pair: ( $i * $i ) > $i)).
% 0.12/0.38 tff(tptp_fun_E_0_type, type, (
% 0.12/0.38 tptp_fun_E_0: ( $i * $i ) > $i)).
% 0.12/0.38 tff(set_union2_type, type, (
% 0.12/0.38 set_union2: ( $i * $i ) > $i)).
% 0.12/0.38 tff(relation_rng_type, type, (
% 0.12/0.38 relation_rng: $i > $i)).
% 0.12/0.38 tff(relation_dom_type, type, (
% 0.12/0.38 relation_dom: $i > $i)).
% 0.12/0.38 tff(tptp_fun_D_1_type, type, (
% 0.12/0.38 tptp_fun_D_1: ( $i * $i ) > $i)).
% 0.12/0.38 tff(tptp_fun_C_2_type, type, (
% 0.12/0.38 tptp_fun_C_2: ( $i * $i ) > $i)).
% 0.12/0.38 tff(is_transitive_in_type, type, (
% 0.12/0.38 is_transitive_in: ( $i * $i ) > $o)).
% 0.12/0.38 tff(relation_field_type, type, (
% 0.12/0.38 relation_field: $i > $i)).
% 0.12/0.38 tff(relation_type, type, (
% 0.12/0.38 relation: $i > $o)).
% 0.12/0.38 tff(tptp_fun_D_5_type, type, (
% 0.12/0.38 tptp_fun_D_5: $i)).
% 0.12/0.38 tff(tptp_fun_B_7_type, type, (
% 0.12/0.38 tptp_fun_B_7: $i)).
% 0.12/0.38 tff(tptp_fun_C_6_type, type, (
% 0.12/0.38 tptp_fun_C_6: $i)).
% 0.12/0.38 tff(transitive_type, type, (
% 0.12/0.38 transitive: $i > $o)).
% 0.12/0.38 tff(1,plain,
% 0.12/0.38 ((relation(A!4) & ((transitive(A!4) | ![B: $i, C: $i, D: $i] : ((~(in(ordered_pair(B, C), A!4) & in(ordered_pair(C, D), A!4))) | in(ordered_pair(B, D), A!4))) & ((~transitive(A!4)) | (~((~(in(ordered_pair(B!7, C!6), A!4) & in(ordered_pair(C!6, D!5), A!4))) | in(ordered_pair(B!7, D!5), A!4)))))) <=> (relation(A!4) & (transitive(A!4) | ![B: $i, C: $i, D: $i] : ((~(in(ordered_pair(B, C), A!4) & in(ordered_pair(C, D), A!4))) | in(ordered_pair(B, D), A!4))) & ((~transitive(A!4)) | (~((~(in(ordered_pair(B!7, C!6), A!4) & in(ordered_pair(C!6, D!5), A!4))) | in(ordered_pair(B!7, D!5), A!4)))))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(2,plain,
% 0.12/0.38 ((transitive(A!4) | ![B: $i, C: $i, D: $i] : ((~(in(ordered_pair(B, C), A!4) & in(ordered_pair(C, D), A!4))) | in(ordered_pair(B, D), A!4))) <=> (transitive(A!4) | ![B: $i, C: $i, D: $i] : ((~(in(ordered_pair(B, C), A!4) & in(ordered_pair(C, D), A!4))) | in(ordered_pair(B, D), A!4)))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(3,plain,
% 0.12/0.38 (((transitive(A!4) | ![B: $i, C: $i, D: $i] : ((~(in(ordered_pair(B, C), A!4) & in(ordered_pair(C, D), A!4))) | in(ordered_pair(B, D), A!4))) & ((~transitive(A!4)) | (~((~(in(ordered_pair(B!7, C!6), A!4) & in(ordered_pair(C!6, D!5), A!4))) | in(ordered_pair(B!7, D!5), A!4))))) <=> ((transitive(A!4) | ![B: $i, C: $i, D: $i] : ((~(in(ordered_pair(B, C), A!4) & in(ordered_pair(C, D), A!4))) | in(ordered_pair(B, D), A!4))) & ((~transitive(A!4)) | (~((~(in(ordered_pair(B!7, C!6), A!4) & in(ordered_pair(C!6, D!5), A!4))) | in(ordered_pair(B!7, D!5), A!4)))))),
% 0.12/0.38 inference(monotonicity,[status(thm)],[2])).
% 0.12/0.38 tff(4,plain,
% 0.12/0.38 ((relation(A!4) & ((transitive(A!4) | ![B: $i, C: $i, D: $i] : ((~(in(ordered_pair(B, C), A!4) & in(ordered_pair(C, D), A!4))) | in(ordered_pair(B, D), A!4))) & ((~transitive(A!4)) | (~((~(in(ordered_pair(B!7, C!6), A!4) & in(ordered_pair(C!6, D!5), A!4))) | in(ordered_pair(B!7, D!5), A!4)))))) <=> (relation(A!4) & ((transitive(A!4) | ![B: $i, C: $i, D: $i] : ((~(in(ordered_pair(B, C), A!4) & in(ordered_pair(C, D), A!4))) | in(ordered_pair(B, D), A!4))) & ((~transitive(A!4)) | (~((~(in(ordered_pair(B!7, C!6), A!4) & in(ordered_pair(C!6, D!5), A!4))) | in(ordered_pair(B!7, D!5), A!4))))))),
% 0.12/0.38 inference(monotonicity,[status(thm)],[3])).
% 0.12/0.38 tff(5,plain,
% 0.12/0.38 ((relation(A!4) & ((transitive(A!4) | ![B: $i, C: $i, D: $i] : ((~(in(ordered_pair(B, C), A!4) & in(ordered_pair(C, D), A!4))) | in(ordered_pair(B, D), A!4))) & ((~transitive(A!4)) | (~((~(in(ordered_pair(B!7, C!6), A!4) & in(ordered_pair(C!6, D!5), A!4))) | in(ordered_pair(B!7, D!5), A!4)))))) <=> (relation(A!4) & (transitive(A!4) | ![B: $i, C: $i, D: $i] : ((~(in(ordered_pair(B, C), A!4) & in(ordered_pair(C, D), A!4))) | in(ordered_pair(B, D), A!4))) & ((~transitive(A!4)) | (~((~(in(ordered_pair(B!7, C!6), A!4) & in(ordered_pair(C!6, D!5), A!4))) | in(ordered_pair(B!7, D!5), A!4)))))),
% 0.12/0.38 inference(transitivity,[status(thm)],[4, 1])).
% 0.12/0.38 tff(6,plain,
% 0.12/0.38 ((~![A: $i] : ((~relation(A)) | (transitive(A) <=> ![B: $i, C: $i, D: $i] : ((~(in(ordered_pair(B, C), A) & in(ordered_pair(C, D), A))) | in(ordered_pair(B, D), A))))) <=> (~![A: $i] : ((~relation(A)) | (transitive(A) <=> ![B: $i, C: $i, D: $i] : ((~(in(ordered_pair(B, C), A) & in(ordered_pair(C, D), A))) | in(ordered_pair(B, D), A)))))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(7,plain,
% 0.12/0.39 ((~![A: $i] : (relation(A) => (transitive(A) <=> ![B: $i, C: $i, D: $i] : ((in(ordered_pair(B, C), A) & in(ordered_pair(C, D), A)) => in(ordered_pair(B, D), A))))) <=> (~![A: $i] : ((~relation(A)) | (transitive(A) <=> ![B: $i, C: $i, D: $i] : ((~(in(ordered_pair(B, C), A) & in(ordered_pair(C, D), A))) | in(ordered_pair(B, D), A)))))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(8,axiom,(~![A: $i] : (relation(A) => (transitive(A) <=> ![B: $i, C: $i, D: $i] : ((in(ordered_pair(B, C), A) & in(ordered_pair(C, D), A)) => in(ordered_pair(B, D), A))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','l2_wellord1')).
% 0.12/0.39 tff(9,plain,
% 0.12/0.39 (~![A: $i] : ((~relation(A)) | (transitive(A) <=> ![B: $i, C: $i, D: $i] : ((~(in(ordered_pair(B, C), A) & in(ordered_pair(C, D), A))) | in(ordered_pair(B, D), A))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[8, 7])).
% 0.12/0.39 tff(10,plain,
% 0.12/0.39 (~![A: $i] : ((~relation(A)) | (transitive(A) <=> ![B: $i, C: $i, D: $i] : ((~(in(ordered_pair(B, C), A) & in(ordered_pair(C, D), A))) | in(ordered_pair(B, D), A))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[9, 6])).
% 0.12/0.39 tff(11,plain,
% 0.12/0.39 (~![A: $i] : ((~relation(A)) | (transitive(A) <=> ![B: $i, C: $i, D: $i] : ((~(in(ordered_pair(B, C), A) & in(ordered_pair(C, D), A))) | in(ordered_pair(B, D), A))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[10, 6])).
% 0.12/0.39 tff(12,plain,
% 0.12/0.39 (~![A: $i] : ((~relation(A)) | (transitive(A) <=> ![B: $i, C: $i, D: $i] : ((~(in(ordered_pair(B, C), A) & in(ordered_pair(C, D), A))) | in(ordered_pair(B, D), A))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[11, 6])).
% 0.12/0.39 tff(13,plain,
% 0.12/0.39 (relation(A!4) & (transitive(A!4) | ![B: $i, C: $i, D: $i] : ((~(in(ordered_pair(B, C), A!4) & in(ordered_pair(C, D), A!4))) | in(ordered_pair(B, D), A!4))) & ((~transitive(A!4)) | (~((~(in(ordered_pair(B!7, C!6), A!4) & in(ordered_pair(C!6, D!5), A!4))) | in(ordered_pair(B!7, D!5), A!4))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[12, 5])).
% 0.12/0.39 tff(14,plain,
% 0.12/0.39 (relation(A!4)),
% 0.12/0.39 inference(and_elim,[status(thm)],[13])).
% 0.12/0.39 tff(15,plain,
% 0.12/0.39 (^[A: $i] : refl(((~relation(A)) | (relation_field(A) = set_union2(relation_dom(A), relation_rng(A)))) <=> ((~relation(A)) | (relation_field(A) = set_union2(relation_dom(A), relation_rng(A)))))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(16,plain,
% 0.12/0.39 (![A: $i] : ((~relation(A)) | (relation_field(A) = set_union2(relation_dom(A), relation_rng(A)))) <=> ![A: $i] : ((~relation(A)) | (relation_field(A) = set_union2(relation_dom(A), relation_rng(A))))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[15])).
% 0.12/0.39 tff(17,plain,
% 0.12/0.39 (![A: $i] : ((~relation(A)) | (relation_field(A) = set_union2(relation_dom(A), relation_rng(A)))) <=> ![A: $i] : ((~relation(A)) | (relation_field(A) = set_union2(relation_dom(A), relation_rng(A))))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(18,plain,
% 0.12/0.39 (^[A: $i] : rewrite((relation(A) => (relation_field(A) = set_union2(relation_dom(A), relation_rng(A)))) <=> ((~relation(A)) | (relation_field(A) = set_union2(relation_dom(A), relation_rng(A)))))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(19,plain,
% 0.12/0.39 (![A: $i] : (relation(A) => (relation_field(A) = set_union2(relation_dom(A), relation_rng(A)))) <=> ![A: $i] : ((~relation(A)) | (relation_field(A) = set_union2(relation_dom(A), relation_rng(A))))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[18])).
% 0.12/0.39 tff(20,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')).
% 0.12/0.39 tff(21,plain,
% 0.12/0.39 (![A: $i] : ((~relation(A)) | (relation_field(A) = set_union2(relation_dom(A), relation_rng(A))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[20, 19])).
% 0.12/0.39 tff(22,plain,
% 0.12/0.39 (![A: $i] : ((~relation(A)) | (relation_field(A) = set_union2(relation_dom(A), relation_rng(A))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[21, 17])).
% 0.12/0.39 tff(23,plain,(
% 0.12/0.39 ![A: $i] : ((~relation(A)) | (relation_field(A) = set_union2(relation_dom(A), relation_rng(A))))),
% 0.12/0.39 inference(skolemize,[status(sab)],[22])).
% 0.12/0.39 tff(24,plain,
% 0.12/0.39 (![A: $i] : ((~relation(A)) | (relation_field(A) = set_union2(relation_dom(A), relation_rng(A))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[23, 16])).
% 0.12/0.39 tff(25,plain,
% 0.12/0.39 (((~![A: $i] : ((~relation(A)) | (relation_field(A) = set_union2(relation_dom(A), relation_rng(A))))) | ((~relation(A!4)) | (relation_field(A!4) = set_union2(relation_dom(A!4), relation_rng(A!4))))) <=> ((~![A: $i] : ((~relation(A)) | (relation_field(A) = set_union2(relation_dom(A), relation_rng(A))))) | (~relation(A!4)) | (relation_field(A!4) = set_union2(relation_dom(A!4), relation_rng(A!4))))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(26,plain,
% 0.12/0.39 ((~![A: $i] : ((~relation(A)) | (relation_field(A) = set_union2(relation_dom(A), relation_rng(A))))) | ((~relation(A!4)) | (relation_field(A!4) = set_union2(relation_dom(A!4), relation_rng(A!4))))),
% 0.12/0.39 inference(quant_inst,[status(thm)],[])).
% 0.12/0.39 tff(27,plain,
% 0.12/0.39 ((~![A: $i] : ((~relation(A)) | (relation_field(A) = set_union2(relation_dom(A), relation_rng(A))))) | (~relation(A!4)) | (relation_field(A!4) = set_union2(relation_dom(A!4), relation_rng(A!4)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[26, 25])).
% 0.12/0.39 tff(28,plain,
% 0.12/0.39 (relation_field(A!4) = set_union2(relation_dom(A!4), relation_rng(A!4))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[27, 24, 14])).
% 0.12/0.39 tff(29,plain,
% 0.12/0.39 (set_union2(relation_dom(A!4), relation_rng(A!4)) = relation_field(A!4)),
% 0.12/0.39 inference(symmetry,[status(thm)],[28])).
% 0.12/0.39 tff(30,plain,
% 0.12/0.39 (is_transitive_in(A!4, set_union2(relation_dom(A!4), relation_rng(A!4))) <=> is_transitive_in(A!4, relation_field(A!4))),
% 0.12/0.39 inference(monotonicity,[status(thm)],[29])).
% 0.12/0.39 tff(31,plain,
% 0.12/0.39 (is_transitive_in(A!4, relation_field(A!4)) <=> is_transitive_in(A!4, set_union2(relation_dom(A!4), relation_rng(A!4)))),
% 0.12/0.39 inference(symmetry,[status(thm)],[30])).
% 0.12/0.39 tff(32,plain,
% 0.12/0.39 ((~is_transitive_in(A!4, relation_field(A!4))) <=> (~is_transitive_in(A!4, set_union2(relation_dom(A!4), relation_rng(A!4))))),
% 0.12/0.39 inference(monotonicity,[status(thm)],[31])).
% 0.12/0.39 tff(33,assumption,(~(in(ordered_pair(B!7, D!5), A!4) | (~in(ordered_pair(B!7, C!6), A!4)) | (~in(ordered_pair(C!6, D!5), A!4)))), introduced(assumption)).
% 0.12/0.39 tff(34,plain,
% 0.12/0.39 ((in(ordered_pair(B!7, D!5), A!4) | (~in(ordered_pair(B!7, C!6), A!4)) | (~in(ordered_pair(C!6, D!5), A!4))) | in(ordered_pair(C!6, D!5), A!4)),
% 0.12/0.39 inference(tautology,[status(thm)],[])).
% 0.12/0.39 tff(35,plain,
% 0.12/0.39 (in(ordered_pair(C!6, D!5), A!4)),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[34, 33])).
% 0.12/0.39 tff(36,plain,
% 0.12/0.39 ((in(ordered_pair(B!7, D!5), A!4) | (~in(ordered_pair(B!7, C!6), A!4)) | (~in(ordered_pair(C!6, D!5), A!4))) | in(ordered_pair(B!7, C!6), A!4)),
% 0.12/0.39 inference(tautology,[status(thm)],[])).
% 0.12/0.39 tff(37,plain,
% 0.12/0.39 (in(ordered_pair(B!7, C!6), A!4)),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[36, 33])).
% 0.12/0.39 tff(38,plain,
% 0.12/0.39 ((in(ordered_pair(B!7, D!5), A!4) | (~in(ordered_pair(B!7, C!6), A!4)) | (~in(ordered_pair(C!6, D!5), A!4))) | (~in(ordered_pair(B!7, D!5), A!4))),
% 0.12/0.39 inference(tautology,[status(thm)],[])).
% 0.12/0.39 tff(39,plain,
% 0.12/0.39 (~in(ordered_pair(B!7, D!5), A!4)),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[38, 33])).
% 0.12/0.39 tff(40,plain,
% 0.12/0.39 ((~is_transitive_in(A!4, set_union2(relation_dom(A!4), relation_rng(A!4)))) <=> (~is_transitive_in(A!4, relation_field(A!4)))),
% 0.12/0.39 inference(monotonicity,[status(thm)],[30])).
% 0.12/0.39 tff(41,plain,
% 0.12/0.39 (in(B!7, set_union2(relation_dom(A!4), relation_rng(A!4))) <=> in(B!7, relation_field(A!4))),
% 0.12/0.39 inference(monotonicity,[status(thm)],[29])).
% 0.12/0.39 tff(42,plain,
% 0.12/0.39 (in(B!7, relation_field(A!4)) <=> in(B!7, set_union2(relation_dom(A!4), relation_rng(A!4)))),
% 0.12/0.39 inference(symmetry,[status(thm)],[41])).
% 0.12/0.39 tff(43,plain,
% 0.12/0.39 (^[A: $i, B: $i, C: $i] : refl(((~relation(C)) | (~in(ordered_pair(A, B), C)) | (~((~in(A, relation_field(C))) | (~in(B, relation_field(C)))))) <=> ((~relation(C)) | (~in(ordered_pair(A, B), C)) | (~((~in(A, relation_field(C))) | (~in(B, relation_field(C)))))))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(44,plain,
% 0.12/0.39 (![A: $i, B: $i, C: $i] : ((~relation(C)) | (~in(ordered_pair(A, B), C)) | (~((~in(A, relation_field(C))) | (~in(B, relation_field(C)))))) <=> ![A: $i, B: $i, C: $i] : ((~relation(C)) | (~in(ordered_pair(A, B), C)) | (~((~in(A, relation_field(C))) | (~in(B, relation_field(C))))))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[43])).
% 0.12/0.39 tff(45,plain,
% 0.12/0.39 (^[A: $i, B: $i, C: $i] : trans(monotonicity(rewrite((in(A, relation_field(C)) & in(B, relation_field(C))) <=> (~((~in(A, relation_field(C))) | (~in(B, relation_field(C)))))), (((in(A, relation_field(C)) & in(B, relation_field(C))) | (~relation(C)) | (~in(ordered_pair(A, B), C))) <=> ((~((~in(A, relation_field(C))) | (~in(B, relation_field(C))))) | (~relation(C)) | (~in(ordered_pair(A, B), C))))), rewrite(((~((~in(A, relation_field(C))) | (~in(B, relation_field(C))))) | (~relation(C)) | (~in(ordered_pair(A, B), C))) <=> ((~relation(C)) | (~in(ordered_pair(A, B), C)) | (~((~in(A, relation_field(C))) | (~in(B, relation_field(C))))))), (((in(A, relation_field(C)) & in(B, relation_field(C))) | (~relation(C)) | (~in(ordered_pair(A, B), C))) <=> ((~relation(C)) | (~in(ordered_pair(A, B), C)) | (~((~in(A, relation_field(C))) | (~in(B, relation_field(C))))))))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(46,plain,
% 0.12/0.39 (![A: $i, B: $i, C: $i] : ((in(A, relation_field(C)) & in(B, relation_field(C))) | (~relation(C)) | (~in(ordered_pair(A, B), C))) <=> ![A: $i, B: $i, C: $i] : ((~relation(C)) | (~in(ordered_pair(A, B), C)) | (~((~in(A, relation_field(C))) | (~in(B, relation_field(C))))))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[45])).
% 0.12/0.39 tff(47,plain,
% 0.12/0.39 (![A: $i, B: $i, C: $i] : ((in(A, relation_field(C)) & in(B, relation_field(C))) | (~relation(C)) | (~in(ordered_pair(A, B), C))) <=> ![A: $i, B: $i, C: $i] : ((in(A, relation_field(C)) & in(B, relation_field(C))) | (~relation(C)) | (~in(ordered_pair(A, B), C)))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(48,plain,
% 0.12/0.39 (^[A: $i, B: $i, C: $i] : trans(monotonicity(rewrite((in(ordered_pair(A, B), C) => (in(A, relation_field(C)) & in(B, relation_field(C)))) <=> ((~in(ordered_pair(A, B), C)) | (in(A, relation_field(C)) & in(B, relation_field(C))))), ((relation(C) => (in(ordered_pair(A, B), C) => (in(A, relation_field(C)) & in(B, relation_field(C))))) <=> (relation(C) => ((~in(ordered_pair(A, B), C)) | (in(A, relation_field(C)) & in(B, relation_field(C))))))), rewrite((relation(C) => ((~in(ordered_pair(A, B), C)) | (in(A, relation_field(C)) & in(B, relation_field(C))))) <=> ((in(A, relation_field(C)) & in(B, relation_field(C))) | (~relation(C)) | (~in(ordered_pair(A, B), C)))), ((relation(C) => (in(ordered_pair(A, B), C) => (in(A, relation_field(C)) & in(B, relation_field(C))))) <=> ((in(A, relation_field(C)) & in(B, relation_field(C))) | (~relation(C)) | (~in(ordered_pair(A, B), C)))))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(49,plain,
% 0.12/0.39 (![A: $i, B: $i, C: $i] : (relation(C) => (in(ordered_pair(A, B), C) => (in(A, relation_field(C)) & in(B, relation_field(C))))) <=> ![A: $i, B: $i, C: $i] : ((in(A, relation_field(C)) & in(B, relation_field(C))) | (~relation(C)) | (~in(ordered_pair(A, B), C)))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[48])).
% 0.12/0.39 tff(50,axiom,(![A: $i, B: $i, C: $i] : (relation(C) => (in(ordered_pair(A, B), C) => (in(A, relation_field(C)) & in(B, relation_field(C)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t30_relat_1')).
% 0.12/0.39 tff(51,plain,
% 0.12/0.39 (![A: $i, B: $i, C: $i] : ((in(A, relation_field(C)) & in(B, relation_field(C))) | (~relation(C)) | (~in(ordered_pair(A, B), C)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[50, 49])).
% 0.12/0.39 tff(52,plain,
% 0.12/0.39 (![A: $i, B: $i, C: $i] : ((in(A, relation_field(C)) & in(B, relation_field(C))) | (~relation(C)) | (~in(ordered_pair(A, B), C)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[51, 47])).
% 0.12/0.39 tff(53,plain,(
% 0.12/0.39 ![A: $i, B: $i, C: $i] : ((in(A, relation_field(C)) & in(B, relation_field(C))) | (~relation(C)) | (~in(ordered_pair(A, B), C)))),
% 0.12/0.39 inference(skolemize,[status(sab)],[52])).
% 0.12/0.39 tff(54,plain,
% 0.12/0.39 (![A: $i, B: $i, C: $i] : ((~relation(C)) | (~in(ordered_pair(A, B), C)) | (~((~in(A, relation_field(C))) | (~in(B, relation_field(C))))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[53, 46])).
% 0.12/0.39 tff(55,plain,
% 0.12/0.39 (![A: $i, B: $i, C: $i] : ((~relation(C)) | (~in(ordered_pair(A, B), C)) | (~((~in(A, relation_field(C))) | (~in(B, relation_field(C))))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[54, 44])).
% 0.12/0.39 tff(56,assumption,(in(ordered_pair(B!7, C!6), A!4)), introduced(assumption)).
% 0.12/0.39 tff(57,plain,
% 0.12/0.39 (((~![A: $i, B: $i, C: $i] : ((~relation(C)) | (~in(ordered_pair(A, B), C)) | (~((~in(A, relation_field(C))) | (~in(B, relation_field(C))))))) | ((~relation(A!4)) | (~in(ordered_pair(B!7, C!6), A!4)) | (~((~in(B!7, relation_field(A!4))) | (~in(C!6, relation_field(A!4))))))) <=> ((~![A: $i, B: $i, C: $i] : ((~relation(C)) | (~in(ordered_pair(A, B), C)) | (~((~in(A, relation_field(C))) | (~in(B, relation_field(C))))))) | (~relation(A!4)) | (~in(ordered_pair(B!7, C!6), A!4)) | (~((~in(B!7, relation_field(A!4))) | (~in(C!6, relation_field(A!4))))))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(58,plain,
% 0.12/0.39 ((~![A: $i, B: $i, C: $i] : ((~relation(C)) | (~in(ordered_pair(A, B), C)) | (~((~in(A, relation_field(C))) | (~in(B, relation_field(C))))))) | ((~relation(A!4)) | (~in(ordered_pair(B!7, C!6), A!4)) | (~((~in(B!7, relation_field(A!4))) | (~in(C!6, relation_field(A!4))))))),
% 0.12/0.39 inference(quant_inst,[status(thm)],[])).
% 0.12/0.39 tff(59,plain,
% 0.12/0.39 ((~![A: $i, B: $i, C: $i] : ((~relation(C)) | (~in(ordered_pair(A, B), C)) | (~((~in(A, relation_field(C))) | (~in(B, relation_field(C))))))) | (~relation(A!4)) | (~in(ordered_pair(B!7, C!6), A!4)) | (~((~in(B!7, relation_field(A!4))) | (~in(C!6, relation_field(A!4)))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[58, 57])).
% 0.12/0.39 tff(60,plain,
% 0.12/0.39 (~((~in(B!7, relation_field(A!4))) | (~in(C!6, relation_field(A!4))))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[59, 14, 56, 55])).
% 0.12/0.39 tff(61,plain,
% 0.12/0.39 (((~in(B!7, relation_field(A!4))) | (~in(C!6, relation_field(A!4)))) | in(B!7, relation_field(A!4))),
% 0.12/0.39 inference(tautology,[status(thm)],[])).
% 0.12/0.39 tff(62,plain,
% 0.12/0.39 (in(B!7, relation_field(A!4))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[61, 60])).
% 0.12/0.39 tff(63,plain,
% 0.12/0.39 (in(B!7, set_union2(relation_dom(A!4), relation_rng(A!4)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[62, 42])).
% 0.12/0.39 tff(64,plain,
% 0.12/0.39 (in(C!6, set_union2(relation_dom(A!4), relation_rng(A!4))) <=> in(C!6, relation_field(A!4))),
% 0.12/0.39 inference(monotonicity,[status(thm)],[29])).
% 0.12/0.39 tff(65,plain,
% 0.12/0.39 (in(C!6, relation_field(A!4)) <=> in(C!6, set_union2(relation_dom(A!4), relation_rng(A!4)))),
% 0.12/0.39 inference(symmetry,[status(thm)],[64])).
% 0.12/0.39 tff(66,assumption,(in(ordered_pair(C!6, D!5), A!4)), introduced(assumption)).
% 0.12/0.39 tff(67,plain,
% 0.12/0.39 (((~![A: $i, B: $i, C: $i] : ((~relation(C)) | (~in(ordered_pair(A, B), C)) | (~((~in(A, relation_field(C))) | (~in(B, relation_field(C))))))) | ((~relation(A!4)) | (~in(ordered_pair(C!6, D!5), A!4)) | (~((~in(C!6, relation_field(A!4))) | (~in(D!5, relation_field(A!4))))))) <=> ((~![A: $i, B: $i, C: $i] : ((~relation(C)) | (~in(ordered_pair(A, B), C)) | (~((~in(A, relation_field(C))) | (~in(B, relation_field(C))))))) | (~relation(A!4)) | (~in(ordered_pair(C!6, D!5), A!4)) | (~((~in(C!6, relation_field(A!4))) | (~in(D!5, relation_field(A!4))))))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(68,plain,
% 0.12/0.39 ((~![A: $i, B: $i, C: $i] : ((~relation(C)) | (~in(ordered_pair(A, B), C)) | (~((~in(A, relation_field(C))) | (~in(B, relation_field(C))))))) | ((~relation(A!4)) | (~in(ordered_pair(C!6, D!5), A!4)) | (~((~in(C!6, relation_field(A!4))) | (~in(D!5, relation_field(A!4))))))),
% 0.12/0.39 inference(quant_inst,[status(thm)],[])).
% 0.12/0.39 tff(69,plain,
% 0.12/0.39 ((~![A: $i, B: $i, C: $i] : ((~relation(C)) | (~in(ordered_pair(A, B), C)) | (~((~in(A, relation_field(C))) | (~in(B, relation_field(C))))))) | (~relation(A!4)) | (~in(ordered_pair(C!6, D!5), A!4)) | (~((~in(C!6, relation_field(A!4))) | (~in(D!5, relation_field(A!4)))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[68, 67])).
% 0.12/0.39 tff(70,plain,
% 0.12/0.39 (~((~in(C!6, relation_field(A!4))) | (~in(D!5, relation_field(A!4))))),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[69, 14, 66, 55])).
% 0.21/0.40 tff(71,plain,
% 0.21/0.40 (((~in(C!6, relation_field(A!4))) | (~in(D!5, relation_field(A!4)))) | in(C!6, relation_field(A!4))),
% 0.21/0.40 inference(tautology,[status(thm)],[])).
% 0.21/0.40 tff(72,plain,
% 0.21/0.40 (in(C!6, relation_field(A!4))),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[71, 70])).
% 0.21/0.40 tff(73,plain,
% 0.21/0.40 (in(C!6, set_union2(relation_dom(A!4), relation_rng(A!4)))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[72, 65])).
% 0.21/0.40 tff(74,plain,
% 0.21/0.40 (in(D!5, set_union2(relation_dom(A!4), relation_rng(A!4))) <=> in(D!5, relation_field(A!4))),
% 0.21/0.40 inference(monotonicity,[status(thm)],[29])).
% 0.21/0.40 tff(75,plain,
% 0.21/0.40 (in(D!5, relation_field(A!4)) <=> in(D!5, set_union2(relation_dom(A!4), relation_rng(A!4)))),
% 0.21/0.40 inference(symmetry,[status(thm)],[74])).
% 0.21/0.40 tff(76,plain,
% 0.21/0.40 (((~in(C!6, relation_field(A!4))) | (~in(D!5, relation_field(A!4)))) | in(D!5, relation_field(A!4))),
% 0.21/0.40 inference(tautology,[status(thm)],[])).
% 0.21/0.40 tff(77,plain,
% 0.21/0.40 (in(D!5, relation_field(A!4))),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[76, 70])).
% 0.21/0.40 tff(78,plain,
% 0.21/0.40 (in(D!5, set_union2(relation_dom(A!4), relation_rng(A!4)))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[77, 75])).
% 0.21/0.40 tff(79,assumption,(![C: $i, D: $i, E: $i] : (in(ordered_pair(C, E), A!4) | (~in(ordered_pair(C, D), A!4)) | (~in(ordered_pair(D, E), A!4)) | (~in(C, set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(D, set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(E, set_union2(relation_dom(A!4), relation_rng(A!4)))))), introduced(assumption)).
% 0.21/0.40 tff(80,assumption,(~in(ordered_pair(B!7, D!5), A!4)), introduced(assumption)).
% 0.21/0.40 tff(81,plain,
% 0.21/0.40 (((~![C: $i, D: $i, E: $i] : (in(ordered_pair(C, E), A!4) | (~in(ordered_pair(C, D), A!4)) | (~in(ordered_pair(D, E), A!4)) | (~in(C, set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(D, set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(E, set_union2(relation_dom(A!4), relation_rng(A!4)))))) | (in(ordered_pair(B!7, D!5), A!4) | (~in(ordered_pair(B!7, C!6), A!4)) | (~in(ordered_pair(C!6, D!5), A!4)) | (~in(D!5, set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(C!6, set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(B!7, set_union2(relation_dom(A!4), relation_rng(A!4)))))) <=> ((~![C: $i, D: $i, E: $i] : (in(ordered_pair(C, E), A!4) | (~in(ordered_pair(C, D), A!4)) | (~in(ordered_pair(D, E), A!4)) | (~in(C, set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(D, set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(E, set_union2(relation_dom(A!4), relation_rng(A!4)))))) | in(ordered_pair(B!7, D!5), A!4) | (~in(ordered_pair(B!7, C!6), A!4)) | (~in(ordered_pair(C!6, D!5), A!4)) | (~in(D!5, set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(C!6, set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(B!7, set_union2(relation_dom(A!4), relation_rng(A!4)))))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(82,plain,
% 0.21/0.40 ((in(ordered_pair(B!7, D!5), A!4) | (~in(ordered_pair(B!7, C!6), A!4)) | (~in(ordered_pair(C!6, D!5), A!4)) | (~in(B!7, set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(C!6, set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(D!5, set_union2(relation_dom(A!4), relation_rng(A!4))))) <=> (in(ordered_pair(B!7, D!5), A!4) | (~in(ordered_pair(B!7, C!6), A!4)) | (~in(ordered_pair(C!6, D!5), A!4)) | (~in(D!5, set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(C!6, set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(B!7, set_union2(relation_dom(A!4), relation_rng(A!4)))))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(83,plain,
% 0.21/0.40 (((~![C: $i, D: $i, E: $i] : (in(ordered_pair(C, E), A!4) | (~in(ordered_pair(C, D), A!4)) | (~in(ordered_pair(D, E), A!4)) | (~in(C, set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(D, set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(E, set_union2(relation_dom(A!4), relation_rng(A!4)))))) | (in(ordered_pair(B!7, D!5), A!4) | (~in(ordered_pair(B!7, C!6), A!4)) | (~in(ordered_pair(C!6, D!5), A!4)) | (~in(B!7, set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(C!6, set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(D!5, set_union2(relation_dom(A!4), relation_rng(A!4)))))) <=> ((~![C: $i, D: $i, E: $i] : (in(ordered_pair(C, E), A!4) | (~in(ordered_pair(C, D), A!4)) | (~in(ordered_pair(D, E), A!4)) | (~in(C, set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(D, set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(E, set_union2(relation_dom(A!4), relation_rng(A!4)))))) | (in(ordered_pair(B!7, D!5), A!4) | (~in(ordered_pair(B!7, C!6), A!4)) | (~in(ordered_pair(C!6, D!5), A!4)) | (~in(D!5, set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(C!6, set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(B!7, set_union2(relation_dom(A!4), relation_rng(A!4))))))),
% 0.21/0.40 inference(monotonicity,[status(thm)],[82])).
% 0.21/0.40 tff(84,plain,
% 0.21/0.40 (((~![C: $i, D: $i, E: $i] : (in(ordered_pair(C, E), A!4) | (~in(ordered_pair(C, D), A!4)) | (~in(ordered_pair(D, E), A!4)) | (~in(C, set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(D, set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(E, set_union2(relation_dom(A!4), relation_rng(A!4)))))) | (in(ordered_pair(B!7, D!5), A!4) | (~in(ordered_pair(B!7, C!6), A!4)) | (~in(ordered_pair(C!6, D!5), A!4)) | (~in(B!7, set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(C!6, set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(D!5, set_union2(relation_dom(A!4), relation_rng(A!4)))))) <=> ((~![C: $i, D: $i, E: $i] : (in(ordered_pair(C, E), A!4) | (~in(ordered_pair(C, D), A!4)) | (~in(ordered_pair(D, E), A!4)) | (~in(C, set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(D, set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(E, set_union2(relation_dom(A!4), relation_rng(A!4)))))) | in(ordered_pair(B!7, D!5), A!4) | (~in(ordered_pair(B!7, C!6), A!4)) | (~in(ordered_pair(C!6, D!5), A!4)) | (~in(D!5, set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(C!6, set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(B!7, set_union2(relation_dom(A!4), relation_rng(A!4)))))),
% 0.21/0.40 inference(transitivity,[status(thm)],[83, 81])).
% 0.21/0.40 tff(85,plain,
% 0.21/0.40 ((~![C: $i, D: $i, E: $i] : (in(ordered_pair(C, E), A!4) | (~in(ordered_pair(C, D), A!4)) | (~in(ordered_pair(D, E), A!4)) | (~in(C, set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(D, set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(E, set_union2(relation_dom(A!4), relation_rng(A!4)))))) | (in(ordered_pair(B!7, D!5), A!4) | (~in(ordered_pair(B!7, C!6), A!4)) | (~in(ordered_pair(C!6, D!5), A!4)) | (~in(B!7, set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(C!6, set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(D!5, set_union2(relation_dom(A!4), relation_rng(A!4)))))),
% 0.21/0.40 inference(quant_inst,[status(thm)],[])).
% 0.21/0.40 tff(86,plain,
% 0.21/0.40 ((~![C: $i, D: $i, E: $i] : (in(ordered_pair(C, E), A!4) | (~in(ordered_pair(C, D), A!4)) | (~in(ordered_pair(D, E), A!4)) | (~in(C, set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(D, set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(E, set_union2(relation_dom(A!4), relation_rng(A!4)))))) | in(ordered_pair(B!7, D!5), A!4) | (~in(ordered_pair(B!7, C!6), A!4)) | (~in(ordered_pair(C!6, D!5), A!4)) | (~in(D!5, set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(C!6, set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(B!7, set_union2(relation_dom(A!4), relation_rng(A!4))))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[85, 84])).
% 0.21/0.40 tff(87,plain,
% 0.21/0.40 ($false),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[86, 80, 56, 66, 79, 78, 73, 63])).
% 0.21/0.40 tff(88,plain,((~![C: $i, D: $i, E: $i] : (in(ordered_pair(C, E), A!4) | (~in(ordered_pair(C, D), A!4)) | (~in(ordered_pair(D, E), A!4)) | (~in(C, set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(D, set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(E, set_union2(relation_dom(A!4), relation_rng(A!4)))))) | in(ordered_pair(B!7, D!5), A!4) | (~in(ordered_pair(B!7, C!6), A!4)) | (~in(ordered_pair(C!6, D!5), A!4))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.40 tff(89,plain,
% 0.21/0.40 (~![C: $i, D: $i, E: $i] : (in(ordered_pair(C, E), A!4) | (~in(ordered_pair(C, D), A!4)) | (~in(ordered_pair(D, E), A!4)) | (~in(C, set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(D, set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(E, set_union2(relation_dom(A!4), relation_rng(A!4)))))),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[88, 39, 37, 35])).
% 0.21/0.40 tff(90,plain,
% 0.21/0.40 (^[A: $i] : refl(((~relation(A)) | ![B: $i] : (~((~((~is_transitive_in(A, B)) | ![C: $i, D: $i, E: $i] : (in(ordered_pair(C, E), A) | (~in(C, B)) | (~in(D, B)) | (~in(E, B)) | (~in(ordered_pair(C, D), A)) | (~in(ordered_pair(D, E), A))))) | (~(is_transitive_in(A, B) | (~(in(ordered_pair(tptp_fun_C_2(B, A), tptp_fun_E_0(B, A)), A) | (~in(tptp_fun_C_2(B, A), B)) | (~in(tptp_fun_D_1(B, A), B)) | (~in(tptp_fun_E_0(B, A), B)) | (~in(ordered_pair(tptp_fun_C_2(B, A), tptp_fun_D_1(B, A)), A)) | (~in(ordered_pair(tptp_fun_D_1(B, A), tptp_fun_E_0(B, A)), A))))))))) <=> ((~relation(A)) | ![B: $i] : (~((~((~is_transitive_in(A, B)) | ![C: $i, D: $i, E: $i] : (in(ordered_pair(C, E), A) | (~in(C, B)) | (~in(D, B)) | (~in(E, B)) | (~in(ordered_pair(C, D), A)) | (~in(ordered_pair(D, E), A))))) | (~(is_transitive_in(A, B) | (~(in(ordered_pair(tptp_fun_C_2(B, A), tptp_fun_E_0(B, A)), A) | (~in(tptp_fun_C_2(B, A), B)) | (~in(tptp_fun_D_1(B, A), B)) | (~in(tptp_fun_E_0(B, A), B)) | (~in(ordered_pair(tptp_fun_C_2(B, A), tptp_fun_D_1(B, A)), A)) | (~in(ordered_pair(tptp_fun_D_1(B, A), tptp_fun_E_0(B, A)), A))))))))))),
% 0.21/0.40 inference(bind,[status(th)],[])).
% 0.21/0.40 tff(91,plain,
% 0.21/0.40 (![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~is_transitive_in(A, B)) | ![C: $i, D: $i, E: $i] : (in(ordered_pair(C, E), A) | (~in(C, B)) | (~in(D, B)) | (~in(E, B)) | (~in(ordered_pair(C, D), A)) | (~in(ordered_pair(D, E), A))))) | (~(is_transitive_in(A, B) | (~(in(ordered_pair(tptp_fun_C_2(B, A), tptp_fun_E_0(B, A)), A) | (~in(tptp_fun_C_2(B, A), B)) | (~in(tptp_fun_D_1(B, A), B)) | (~in(tptp_fun_E_0(B, A), B)) | (~in(ordered_pair(tptp_fun_C_2(B, A), tptp_fun_D_1(B, A)), A)) | (~in(ordered_pair(tptp_fun_D_1(B, A), tptp_fun_E_0(B, A)), A))))))))) <=> ![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~is_transitive_in(A, B)) | ![C: $i, D: $i, E: $i] : (in(ordered_pair(C, E), A) | (~in(C, B)) | (~in(D, B)) | (~in(E, B)) | (~in(ordered_pair(C, D), A)) | (~in(ordered_pair(D, E), A))))) | (~(is_transitive_in(A, B) | (~(in(ordered_pair(tptp_fun_C_2(B, A), tptp_fun_E_0(B, A)), A) | (~in(tptp_fun_C_2(B, A), B)) | (~in(tptp_fun_D_1(B, A), B)) | (~in(tptp_fun_E_0(B, A), B)) | (~in(ordered_pair(tptp_fun_C_2(B, A), tptp_fun_D_1(B, A)), A)) | (~in(ordered_pair(tptp_fun_D_1(B, A), tptp_fun_E_0(B, A)), A)))))))))),
% 0.21/0.40 inference(quant_intro,[status(thm)],[90])).
% 0.21/0.40 tff(92,plain,
% 0.21/0.40 (^[A: $i] : rewrite(((~relation(A)) | ![B: $i] : (~((~((~is_transitive_in(A, B)) | ![C: $i, D: $i, E: $i] : (in(ordered_pair(C, E), A) | (~in(C, B)) | (~in(D, B)) | (~in(E, B)) | (~in(ordered_pair(C, D), A)) | (~in(ordered_pair(D, E), A))))) | (~(is_transitive_in(A, B) | (~(in(ordered_pair(tptp_fun_C_2(B, A), tptp_fun_E_0(B, A)), A) | (~in(tptp_fun_C_2(B, A), B)) | (~in(tptp_fun_D_1(B, A), B)) | (~in(tptp_fun_E_0(B, A), B)) | (~in(ordered_pair(tptp_fun_C_2(B, A), tptp_fun_D_1(B, A)), A)) | (~in(ordered_pair(tptp_fun_D_1(B, A), tptp_fun_E_0(B, A)), A))))))))) <=> ((~relation(A)) | ![B: $i] : (~((~((~is_transitive_in(A, B)) | ![C: $i, D: $i, E: $i] : (in(ordered_pair(C, E), A) | (~in(C, B)) | (~in(D, B)) | (~in(E, B)) | (~in(ordered_pair(C, D), A)) | (~in(ordered_pair(D, E), A))))) | (~(is_transitive_in(A, B) | (~(in(ordered_pair(tptp_fun_C_2(B, A), tptp_fun_E_0(B, A)), A) | (~in(tptp_fun_C_2(B, A), B)) | (~in(tptp_fun_D_1(B, A), B)) | (~in(tptp_fun_E_0(B, A), B)) | (~in(ordered_pair(tptp_fun_C_2(B, A), tptp_fun_D_1(B, A)), A)) | (~in(ordered_pair(tptp_fun_D_1(B, A), tptp_fun_E_0(B, A)), A))))))))))),
% 0.21/0.40 inference(bind,[status(th)],[])).
% 0.21/0.40 tff(93,plain,
% 0.21/0.40 (![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~is_transitive_in(A, B)) | ![C: $i, D: $i, E: $i] : (in(ordered_pair(C, E), A) | (~in(C, B)) | (~in(D, B)) | (~in(E, B)) | (~in(ordered_pair(C, D), A)) | (~in(ordered_pair(D, E), A))))) | (~(is_transitive_in(A, B) | (~(in(ordered_pair(tptp_fun_C_2(B, A), tptp_fun_E_0(B, A)), A) | (~in(tptp_fun_C_2(B, A), B)) | (~in(tptp_fun_D_1(B, A), B)) | (~in(tptp_fun_E_0(B, A), B)) | (~in(ordered_pair(tptp_fun_C_2(B, A), tptp_fun_D_1(B, A)), A)) | (~in(ordered_pair(tptp_fun_D_1(B, A), tptp_fun_E_0(B, A)), A))))))))) <=> ![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~is_transitive_in(A, B)) | ![C: $i, D: $i, E: $i] : (in(ordered_pair(C, E), A) | (~in(C, B)) | (~in(D, B)) | (~in(E, B)) | (~in(ordered_pair(C, D), A)) | (~in(ordered_pair(D, E), A))))) | (~(is_transitive_in(A, B) | (~(in(ordered_pair(tptp_fun_C_2(B, A), tptp_fun_E_0(B, A)), A) | (~in(tptp_fun_C_2(B, A), B)) | (~in(tptp_fun_D_1(B, A), B)) | (~in(tptp_fun_E_0(B, A), B)) | (~in(ordered_pair(tptp_fun_C_2(B, A), tptp_fun_D_1(B, A)), A)) | (~in(ordered_pair(tptp_fun_D_1(B, A), tptp_fun_E_0(B, A)), A)))))))))),
% 0.21/0.40 inference(quant_intro,[status(thm)],[92])).
% 0.21/0.40 tff(94,plain,
% 0.21/0.40 (![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~is_transitive_in(A, B)) | ![C: $i, D: $i, E: $i] : (in(ordered_pair(C, E), A) | (~in(C, B)) | (~in(D, B)) | (~in(E, B)) | (~in(ordered_pair(C, D), A)) | (~in(ordered_pair(D, E), A))))) | (~(is_transitive_in(A, B) | (~(in(ordered_pair(tptp_fun_C_2(B, A), tptp_fun_E_0(B, A)), A) | (~in(tptp_fun_C_2(B, A), B)) | (~in(tptp_fun_D_1(B, A), B)) | (~in(tptp_fun_E_0(B, A), B)) | (~in(ordered_pair(tptp_fun_C_2(B, A), tptp_fun_D_1(B, A)), A)) | (~in(ordered_pair(tptp_fun_D_1(B, A), tptp_fun_E_0(B, A)), A))))))))) <=> ![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~is_transitive_in(A, B)) | ![C: $i, D: $i, E: $i] : (in(ordered_pair(C, E), A) | (~in(C, B)) | (~in(D, B)) | (~in(E, B)) | (~in(ordered_pair(C, D), A)) | (~in(ordered_pair(D, E), A))))) | (~(is_transitive_in(A, B) | (~(in(ordered_pair(tptp_fun_C_2(B, A), tptp_fun_E_0(B, A)), A) | (~in(tptp_fun_C_2(B, A), B)) | (~in(tptp_fun_D_1(B, A), B)) | (~in(tptp_fun_E_0(B, A), B)) | (~in(ordered_pair(tptp_fun_C_2(B, A), tptp_fun_D_1(B, A)), A)) | (~in(ordered_pair(tptp_fun_D_1(B, A), tptp_fun_E_0(B, A)), A)))))))))),
% 0.21/0.40 inference(transitivity,[status(thm)],[93, 91])).
% 0.21/0.40 tff(95,plain,
% 0.21/0.40 (^[A: $i] : rewrite(((~relation(A)) | ![B: $i] : (((~is_transitive_in(A, B)) | ![C: $i, D: $i, E: $i] : ((~(in(C, B) & in(D, B) & in(E, B) & in(ordered_pair(C, D), A) & in(ordered_pair(D, E), A))) | in(ordered_pair(C, E), A))) & (is_transitive_in(A, B) | (~((~(in(tptp_fun_C_2(B, A), B) & in(tptp_fun_D_1(B, A), B) & in(tptp_fun_E_0(B, A), B) & in(ordered_pair(tptp_fun_C_2(B, A), tptp_fun_D_1(B, A)), A) & in(ordered_pair(tptp_fun_D_1(B, A), tptp_fun_E_0(B, A)), A))) | in(ordered_pair(tptp_fun_C_2(B, A), tptp_fun_E_0(B, A)), A)))))) <=> ((~relation(A)) | ![B: $i] : (~((~((~is_transitive_in(A, B)) | ![C: $i, D: $i, E: $i] : (in(ordered_pair(C, E), A) | (~in(C, B)) | (~in(D, B)) | (~in(E, B)) | (~in(ordered_pair(C, D), A)) | (~in(ordered_pair(D, E), A))))) | (~(is_transitive_in(A, B) | (~(in(ordered_pair(tptp_fun_C_2(B, A), tptp_fun_E_0(B, A)), A) | (~in(tptp_fun_C_2(B, A), B)) | (~in(tptp_fun_D_1(B, A), B)) | (~in(tptp_fun_E_0(B, A), B)) | (~in(ordered_pair(tptp_fun_C_2(B, A), tptp_fun_D_1(B, A)), A)) | (~in(ordered_pair(tptp_fun_D_1(B, A), tptp_fun_E_0(B, A)), A))))))))))),
% 0.21/0.40 inference(bind,[status(th)],[])).
% 0.21/0.40 tff(96,plain,
% 0.21/0.40 (![A: $i] : ((~relation(A)) | ![B: $i] : (((~is_transitive_in(A, B)) | ![C: $i, D: $i, E: $i] : ((~(in(C, B) & in(D, B) & in(E, B) & in(ordered_pair(C, D), A) & in(ordered_pair(D, E), A))) | in(ordered_pair(C, E), A))) & (is_transitive_in(A, B) | (~((~(in(tptp_fun_C_2(B, A), B) & in(tptp_fun_D_1(B, A), B) & in(tptp_fun_E_0(B, A), B) & in(ordered_pair(tptp_fun_C_2(B, A), tptp_fun_D_1(B, A)), A) & in(ordered_pair(tptp_fun_D_1(B, A), tptp_fun_E_0(B, A)), A))) | in(ordered_pair(tptp_fun_C_2(B, A), tptp_fun_E_0(B, A)), A)))))) <=> ![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~is_transitive_in(A, B)) | ![C: $i, D: $i, E: $i] : (in(ordered_pair(C, E), A) | (~in(C, B)) | (~in(D, B)) | (~in(E, B)) | (~in(ordered_pair(C, D), A)) | (~in(ordered_pair(D, E), A))))) | (~(is_transitive_in(A, B) | (~(in(ordered_pair(tptp_fun_C_2(B, A), tptp_fun_E_0(B, A)), A) | (~in(tptp_fun_C_2(B, A), B)) | (~in(tptp_fun_D_1(B, A), B)) | (~in(tptp_fun_E_0(B, A), B)) | (~in(ordered_pair(tptp_fun_C_2(B, A), tptp_fun_D_1(B, A)), A)) | (~in(ordered_pair(tptp_fun_D_1(B, A), tptp_fun_E_0(B, A)), A)))))))))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[95])).
% 0.21/0.41 tff(97,plain,
% 0.21/0.41 (![A: $i] : ((~relation(A)) | ![B: $i] : (is_transitive_in(A, B) <=> ![C: $i, D: $i, E: $i] : ((~(in(C, B) & in(D, B) & in(E, B) & in(ordered_pair(C, D), A) & in(ordered_pair(D, E), A))) | in(ordered_pair(C, E), A)))) <=> ![A: $i] : ((~relation(A)) | ![B: $i] : (is_transitive_in(A, B) <=> ![C: $i, D: $i, E: $i] : ((~(in(C, B) & in(D, B) & in(E, B) & in(ordered_pair(C, D), A) & in(ordered_pair(D, E), A))) | in(ordered_pair(C, E), A))))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(98,plain,
% 0.21/0.41 (^[A: $i] : trans(monotonicity(quant_intro(proof_bind(^[B: $i] : rewrite((is_transitive_in(A, B) <=> ![C: $i, D: $i, E: $i] : (((((in(C, B) & in(D, B)) & in(E, B)) & in(ordered_pair(C, D), A)) & in(ordered_pair(D, E), A)) => in(ordered_pair(C, E), A))) <=> (is_transitive_in(A, B) <=> ![C: $i, D: $i, E: $i] : ((~(in(C, B) & in(D, B) & in(E, B) & in(ordered_pair(C, D), A) & in(ordered_pair(D, E), A))) | in(ordered_pair(C, E), A))))), (![B: $i] : (is_transitive_in(A, B) <=> ![C: $i, D: $i, E: $i] : (((((in(C, B) & in(D, B)) & in(E, B)) & in(ordered_pair(C, D), A)) & in(ordered_pair(D, E), A)) => in(ordered_pair(C, E), A))) <=> ![B: $i] : (is_transitive_in(A, B) <=> ![C: $i, D: $i, E: $i] : ((~(in(C, B) & in(D, B) & in(E, B) & in(ordered_pair(C, D), A) & in(ordered_pair(D, E), A))) | in(ordered_pair(C, E), A))))), ((relation(A) => ![B: $i] : (is_transitive_in(A, B) <=> ![C: $i, D: $i, E: $i] : (((((in(C, B) & in(D, B)) & in(E, B)) & in(ordered_pair(C, D), A)) & in(ordered_pair(D, E), A)) => in(ordered_pair(C, E), A)))) <=> (relation(A) => ![B: $i] : (is_transitive_in(A, B) <=> ![C: $i, D: $i, E: $i] : ((~(in(C, B) & in(D, B) & in(E, B) & in(ordered_pair(C, D), A) & in(ordered_pair(D, E), A))) | in(ordered_pair(C, E), A)))))), rewrite((relation(A) => ![B: $i] : (is_transitive_in(A, B) <=> ![C: $i, D: $i, E: $i] : ((~(in(C, B) & in(D, B) & in(E, B) & in(ordered_pair(C, D), A) & in(ordered_pair(D, E), A))) | in(ordered_pair(C, E), A)))) <=> ((~relation(A)) | ![B: $i] : (is_transitive_in(A, B) <=> ![C: $i, D: $i, E: $i] : ((~(in(C, B) & in(D, B) & in(E, B) & in(ordered_pair(C, D), A) & in(ordered_pair(D, E), A))) | in(ordered_pair(C, E), A))))), ((relation(A) => ![B: $i] : (is_transitive_in(A, B) <=> ![C: $i, D: $i, E: $i] : (((((in(C, B) & in(D, B)) & in(E, B)) & in(ordered_pair(C, D), A)) & in(ordered_pair(D, E), A)) => in(ordered_pair(C, E), A)))) <=> ((~relation(A)) | ![B: $i] : (is_transitive_in(A, B) <=> ![C: $i, D: $i, E: $i] : ((~(in(C, B) & in(D, B) & in(E, B) & in(ordered_pair(C, D), A) & in(ordered_pair(D, E), A))) | in(ordered_pair(C, E), A))))))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(99,plain,
% 0.21/0.41 (![A: $i] : (relation(A) => ![B: $i] : (is_transitive_in(A, B) <=> ![C: $i, D: $i, E: $i] : (((((in(C, B) & in(D, B)) & in(E, B)) & in(ordered_pair(C, D), A)) & in(ordered_pair(D, E), A)) => in(ordered_pair(C, E), A)))) <=> ![A: $i] : ((~relation(A)) | ![B: $i] : (is_transitive_in(A, B) <=> ![C: $i, D: $i, E: $i] : ((~(in(C, B) & in(D, B) & in(E, B) & in(ordered_pair(C, D), A) & in(ordered_pair(D, E), A))) | in(ordered_pair(C, E), A))))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[98])).
% 0.21/0.41 tff(100,axiom,(![A: $i] : (relation(A) => ![B: $i] : (is_transitive_in(A, B) <=> ![C: $i, D: $i, E: $i] : (((((in(C, B) & in(D, B)) & in(E, B)) & in(ordered_pair(C, D), A)) & in(ordered_pair(D, E), A)) => in(ordered_pair(C, E), A))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d8_relat_2')).
% 0.21/0.41 tff(101,plain,
% 0.21/0.41 (![A: $i] : ((~relation(A)) | ![B: $i] : (is_transitive_in(A, B) <=> ![C: $i, D: $i, E: $i] : ((~(in(C, B) & in(D, B) & in(E, B) & in(ordered_pair(C, D), A) & in(ordered_pair(D, E), A))) | in(ordered_pair(C, E), A))))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[100, 99])).
% 0.21/0.41 tff(102,plain,
% 0.21/0.41 (![A: $i] : ((~relation(A)) | ![B: $i] : (is_transitive_in(A, B) <=> ![C: $i, D: $i, E: $i] : ((~(in(C, B) & in(D, B) & in(E, B) & in(ordered_pair(C, D), A) & in(ordered_pair(D, E), A))) | in(ordered_pair(C, E), A))))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[101, 97])).
% 0.21/0.41 tff(103,plain,(
% 0.21/0.41 ![A: $i] : ((~relation(A)) | ![B: $i] : (((~is_transitive_in(A, B)) | ![C: $i, D: $i, E: $i] : ((~(in(C, B) & in(D, B) & in(E, B) & in(ordered_pair(C, D), A) & in(ordered_pair(D, E), A))) | in(ordered_pair(C, E), A))) & (is_transitive_in(A, B) | (~((~(in(tptp_fun_C_2(B, A), B) & in(tptp_fun_D_1(B, A), B) & in(tptp_fun_E_0(B, A), B) & in(ordered_pair(tptp_fun_C_2(B, A), tptp_fun_D_1(B, A)), A) & in(ordered_pair(tptp_fun_D_1(B, A), tptp_fun_E_0(B, A)), A))) | in(ordered_pair(tptp_fun_C_2(B, A), tptp_fun_E_0(B, A)), A))))))),
% 0.21/0.41 inference(skolemize,[status(sab)],[102])).
% 0.21/0.41 tff(104,plain,
% 0.21/0.41 (![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~is_transitive_in(A, B)) | ![C: $i, D: $i, E: $i] : (in(ordered_pair(C, E), A) | (~in(C, B)) | (~in(D, B)) | (~in(E, B)) | (~in(ordered_pair(C, D), A)) | (~in(ordered_pair(D, E), A))))) | (~(is_transitive_in(A, B) | (~(in(ordered_pair(tptp_fun_C_2(B, A), tptp_fun_E_0(B, A)), A) | (~in(tptp_fun_C_2(B, A), B)) | (~in(tptp_fun_D_1(B, A), B)) | (~in(tptp_fun_E_0(B, A), B)) | (~in(ordered_pair(tptp_fun_C_2(B, A), tptp_fun_D_1(B, A)), A)) | (~in(ordered_pair(tptp_fun_D_1(B, A), tptp_fun_E_0(B, A)), A)))))))))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[103, 96])).
% 0.21/0.41 tff(105,plain,
% 0.21/0.41 (![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~is_transitive_in(A, B)) | ![C: $i, D: $i, E: $i] : (in(ordered_pair(C, E), A) | (~in(C, B)) | (~in(D, B)) | (~in(E, B)) | (~in(ordered_pair(C, D), A)) | (~in(ordered_pair(D, E), A))))) | (~(is_transitive_in(A, B) | (~(in(ordered_pair(tptp_fun_C_2(B, A), tptp_fun_E_0(B, A)), A) | (~in(tptp_fun_C_2(B, A), B)) | (~in(tptp_fun_D_1(B, A), B)) | (~in(tptp_fun_E_0(B, A), B)) | (~in(ordered_pair(tptp_fun_C_2(B, A), tptp_fun_D_1(B, A)), A)) | (~in(ordered_pair(tptp_fun_D_1(B, A), tptp_fun_E_0(B, A)), A)))))))))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[104, 94])).
% 0.21/0.41 tff(106,plain,
% 0.21/0.41 (((~![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~is_transitive_in(A, B)) | ![C: $i, D: $i, E: $i] : (in(ordered_pair(C, E), A) | (~in(C, B)) | (~in(D, B)) | (~in(E, B)) | (~in(ordered_pair(C, D), A)) | (~in(ordered_pair(D, E), A))))) | (~(is_transitive_in(A, B) | (~(in(ordered_pair(tptp_fun_C_2(B, A), tptp_fun_E_0(B, A)), A) | (~in(tptp_fun_C_2(B, A), B)) | (~in(tptp_fun_D_1(B, A), B)) | (~in(tptp_fun_E_0(B, A), B)) | (~in(ordered_pair(tptp_fun_C_2(B, A), tptp_fun_D_1(B, A)), A)) | (~in(ordered_pair(tptp_fun_D_1(B, A), tptp_fun_E_0(B, A)), A)))))))))) | ((~relation(A!4)) | ![B: $i] : (~((~((~is_transitive_in(A!4, B)) | ![C: $i, D: $i, E: $i] : (in(ordered_pair(C, E), A!4) | (~in(C, B)) | (~in(D, B)) | (~in(E, B)) | (~in(ordered_pair(C, D), A!4)) | (~in(ordered_pair(D, E), A!4))))) | (~(is_transitive_in(A!4, B) | (~((~in(ordered_pair(tptp_fun_D_1(B, A!4), tptp_fun_E_0(B, A!4)), A!4)) | (~in(ordered_pair(tptp_fun_C_2(B, A!4), tptp_fun_D_1(B, A!4)), A!4)) | (~in(tptp_fun_E_0(B, A!4), B)) | (~in(tptp_fun_D_1(B, A!4), B)) | (~in(tptp_fun_C_2(B, A!4), B)) | in(ordered_pair(tptp_fun_C_2(B, A!4), tptp_fun_E_0(B, A!4)), A!4))))))))) <=> ((~![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~is_transitive_in(A, B)) | ![C: $i, D: $i, E: $i] : (in(ordered_pair(C, E), A) | (~in(C, B)) | (~in(D, B)) | (~in(E, B)) | (~in(ordered_pair(C, D), A)) | (~in(ordered_pair(D, E), A))))) | (~(is_transitive_in(A, B) | (~(in(ordered_pair(tptp_fun_C_2(B, A), tptp_fun_E_0(B, A)), A) | (~in(tptp_fun_C_2(B, A), B)) | (~in(tptp_fun_D_1(B, A), B)) | (~in(tptp_fun_E_0(B, A), B)) | (~in(ordered_pair(tptp_fun_C_2(B, A), tptp_fun_D_1(B, A)), A)) | (~in(ordered_pair(tptp_fun_D_1(B, A), tptp_fun_E_0(B, A)), A)))))))))) | (~relation(A!4)) | ![B: $i] : (~((~((~is_transitive_in(A!4, B)) | ![C: $i, D: $i, E: $i] : (in(ordered_pair(C, E), A!4) | (~in(C, B)) | (~in(D, B)) | (~in(E, B)) | (~in(ordered_pair(C, D), A!4)) | (~in(ordered_pair(D, E), A!4))))) | (~(is_transitive_in(A!4, B) | (~((~in(ordered_pair(tptp_fun_D_1(B, A!4), tptp_fun_E_0(B, A!4)), A!4)) | (~in(ordered_pair(tptp_fun_C_2(B, A!4), tptp_fun_D_1(B, A!4)), A!4)) | (~in(tptp_fun_E_0(B, A!4), B)) | (~in(tptp_fun_D_1(B, A!4), B)) | (~in(tptp_fun_C_2(B, A!4), B)) | in(ordered_pair(tptp_fun_C_2(B, A!4), tptp_fun_E_0(B, A!4)), A!4))))))))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(107,plain,
% 0.21/0.41 (((~relation(A!4)) | ![B: $i] : (~((~((~is_transitive_in(A!4, B)) | ![C: $i, D: $i, E: $i] : (in(ordered_pair(C, E), A!4) | (~in(C, B)) | (~in(D, B)) | (~in(E, B)) | (~in(ordered_pair(C, D), A!4)) | (~in(ordered_pair(D, E), A!4))))) | (~(is_transitive_in(A!4, B) | (~(in(ordered_pair(tptp_fun_C_2(B, A!4), tptp_fun_E_0(B, A!4)), A!4) | (~in(tptp_fun_C_2(B, A!4), B)) | (~in(tptp_fun_D_1(B, A!4), B)) | (~in(tptp_fun_E_0(B, A!4), B)) | (~in(ordered_pair(tptp_fun_C_2(B, A!4), tptp_fun_D_1(B, A!4)), A!4)) | (~in(ordered_pair(tptp_fun_D_1(B, A!4), tptp_fun_E_0(B, A!4)), A!4))))))))) <=> ((~relation(A!4)) | ![B: $i] : (~((~((~is_transitive_in(A!4, B)) | ![C: $i, D: $i, E: $i] : (in(ordered_pair(C, E), A!4) | (~in(C, B)) | (~in(D, B)) | (~in(E, B)) | (~in(ordered_pair(C, D), A!4)) | (~in(ordered_pair(D, E), A!4))))) | (~(is_transitive_in(A!4, B) | (~((~in(ordered_pair(tptp_fun_D_1(B, A!4), tptp_fun_E_0(B, A!4)), A!4)) | (~in(ordered_pair(tptp_fun_C_2(B, A!4), tptp_fun_D_1(B, A!4)), A!4)) | (~in(tptp_fun_E_0(B, A!4), B)) | (~in(tptp_fun_D_1(B, A!4), B)) | (~in(tptp_fun_C_2(B, A!4), B)) | in(ordered_pair(tptp_fun_C_2(B, A!4), tptp_fun_E_0(B, A!4)), A!4))))))))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(108,plain,
% 0.21/0.41 (((~![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~is_transitive_in(A, B)) | ![C: $i, D: $i, E: $i] : (in(ordered_pair(C, E), A) | (~in(C, B)) | (~in(D, B)) | (~in(E, B)) | (~in(ordered_pair(C, D), A)) | (~in(ordered_pair(D, E), A))))) | (~(is_transitive_in(A, B) | (~(in(ordered_pair(tptp_fun_C_2(B, A), tptp_fun_E_0(B, A)), A) | (~in(tptp_fun_C_2(B, A), B)) | (~in(tptp_fun_D_1(B, A), B)) | (~in(tptp_fun_E_0(B, A), B)) | (~in(ordered_pair(tptp_fun_C_2(B, A), tptp_fun_D_1(B, A)), A)) | (~in(ordered_pair(tptp_fun_D_1(B, A), tptp_fun_E_0(B, A)), A)))))))))) | ((~relation(A!4)) | ![B: $i] : (~((~((~is_transitive_in(A!4, B)) | ![C: $i, D: $i, E: $i] : (in(ordered_pair(C, E), A!4) | (~in(C, B)) | (~in(D, B)) | (~in(E, B)) | (~in(ordered_pair(C, D), A!4)) | (~in(ordered_pair(D, E), A!4))))) | (~(is_transitive_in(A!4, B) | (~(in(ordered_pair(tptp_fun_C_2(B, A!4), tptp_fun_E_0(B, A!4)), A!4) | (~in(tptp_fun_C_2(B, A!4), B)) | (~in(tptp_fun_D_1(B, A!4), B)) | (~in(tptp_fun_E_0(B, A!4), B)) | (~in(ordered_pair(tptp_fun_C_2(B, A!4), tptp_fun_D_1(B, A!4)), A!4)) | (~in(ordered_pair(tptp_fun_D_1(B, A!4), tptp_fun_E_0(B, A!4)), A!4)))))))))) <=> ((~![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~is_transitive_in(A, B)) | ![C: $i, D: $i, E: $i] : (in(ordered_pair(C, E), A) | (~in(C, B)) | (~in(D, B)) | (~in(E, B)) | (~in(ordered_pair(C, D), A)) | (~in(ordered_pair(D, E), A))))) | (~(is_transitive_in(A, B) | (~(in(ordered_pair(tptp_fun_C_2(B, A), tptp_fun_E_0(B, A)), A) | (~in(tptp_fun_C_2(B, A), B)) | (~in(tptp_fun_D_1(B, A), B)) | (~in(tptp_fun_E_0(B, A), B)) | (~in(ordered_pair(tptp_fun_C_2(B, A), tptp_fun_D_1(B, A)), A)) | (~in(ordered_pair(tptp_fun_D_1(B, A), tptp_fun_E_0(B, A)), A)))))))))) | ((~relation(A!4)) | ![B: $i] : (~((~((~is_transitive_in(A!4, B)) | ![C: $i, D: $i, E: $i] : (in(ordered_pair(C, E), A!4) | (~in(C, B)) | (~in(D, B)) | (~in(E, B)) | (~in(ordered_pair(C, D), A!4)) | (~in(ordered_pair(D, E), A!4))))) | (~(is_transitive_in(A!4, B) | (~((~in(ordered_pair(tptp_fun_D_1(B, A!4), tptp_fun_E_0(B, A!4)), A!4)) | (~in(ordered_pair(tptp_fun_C_2(B, A!4), tptp_fun_D_1(B, A!4)), A!4)) | (~in(tptp_fun_E_0(B, A!4), B)) | (~in(tptp_fun_D_1(B, A!4), B)) | (~in(tptp_fun_C_2(B, A!4), B)) | in(ordered_pair(tptp_fun_C_2(B, A!4), tptp_fun_E_0(B, A!4)), A!4)))))))))),
% 0.21/0.41 inference(monotonicity,[status(thm)],[107])).
% 0.21/0.41 tff(109,plain,
% 0.21/0.41 (((~![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~is_transitive_in(A, B)) | ![C: $i, D: $i, E: $i] : (in(ordered_pair(C, E), A) | (~in(C, B)) | (~in(D, B)) | (~in(E, B)) | (~in(ordered_pair(C, D), A)) | (~in(ordered_pair(D, E), A))))) | (~(is_transitive_in(A, B) | (~(in(ordered_pair(tptp_fun_C_2(B, A), tptp_fun_E_0(B, A)), A) | (~in(tptp_fun_C_2(B, A), B)) | (~in(tptp_fun_D_1(B, A), B)) | (~in(tptp_fun_E_0(B, A), B)) | (~in(ordered_pair(tptp_fun_C_2(B, A), tptp_fun_D_1(B, A)), A)) | (~in(ordered_pair(tptp_fun_D_1(B, A), tptp_fun_E_0(B, A)), A)))))))))) | ((~relation(A!4)) | ![B: $i] : (~((~((~is_transitive_in(A!4, B)) | ![C: $i, D: $i, E: $i] : (in(ordered_pair(C, E), A!4) | (~in(C, B)) | (~in(D, B)) | (~in(E, B)) | (~in(ordered_pair(C, D), A!4)) | (~in(ordered_pair(D, E), A!4))))) | (~(is_transitive_in(A!4, B) | (~(in(ordered_pair(tptp_fun_C_2(B, A!4), tptp_fun_E_0(B, A!4)), A!4) | (~in(tptp_fun_C_2(B, A!4), B)) | (~in(tptp_fun_D_1(B, A!4), B)) | (~in(tptp_fun_E_0(B, A!4), B)) | (~in(ordered_pair(tptp_fun_C_2(B, A!4), tptp_fun_D_1(B, A!4)), A!4)) | (~in(ordered_pair(tptp_fun_D_1(B, A!4), tptp_fun_E_0(B, A!4)), A!4)))))))))) <=> ((~![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~is_transitive_in(A, B)) | ![C: $i, D: $i, E: $i] : (in(ordered_pair(C, E), A) | (~in(C, B)) | (~in(D, B)) | (~in(E, B)) | (~in(ordered_pair(C, D), A)) | (~in(ordered_pair(D, E), A))))) | (~(is_transitive_in(A, B) | (~(in(ordered_pair(tptp_fun_C_2(B, A), tptp_fun_E_0(B, A)), A) | (~in(tptp_fun_C_2(B, A), B)) | (~in(tptp_fun_D_1(B, A), B)) | (~in(tptp_fun_E_0(B, A), B)) | (~in(ordered_pair(tptp_fun_C_2(B, A), tptp_fun_D_1(B, A)), A)) | (~in(ordered_pair(tptp_fun_D_1(B, A), tptp_fun_E_0(B, A)), A)))))))))) | (~relation(A!4)) | ![B: $i] : (~((~((~is_transitive_in(A!4, B)) | ![C: $i, D: $i, E: $i] : (in(ordered_pair(C, E), A!4) | (~in(C, B)) | (~in(D, B)) | (~in(E, B)) | (~in(ordered_pair(C, D), A!4)) | (~in(ordered_pair(D, E), A!4))))) | (~(is_transitive_in(A!4, B) | (~((~in(ordered_pair(tptp_fun_D_1(B, A!4), tptp_fun_E_0(B, A!4)), A!4)) | (~in(ordered_pair(tptp_fun_C_2(B, A!4), tptp_fun_D_1(B, A!4)), A!4)) | (~in(tptp_fun_E_0(B, A!4), B)) | (~in(tptp_fun_D_1(B, A!4), B)) | (~in(tptp_fun_C_2(B, A!4), B)) | in(ordered_pair(tptp_fun_C_2(B, A!4), tptp_fun_E_0(B, A!4)), A!4))))))))),
% 0.21/0.41 inference(transitivity,[status(thm)],[108, 106])).
% 0.21/0.41 tff(110,plain,
% 0.21/0.41 ((~![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~is_transitive_in(A, B)) | ![C: $i, D: $i, E: $i] : (in(ordered_pair(C, E), A) | (~in(C, B)) | (~in(D, B)) | (~in(E, B)) | (~in(ordered_pair(C, D), A)) | (~in(ordered_pair(D, E), A))))) | (~(is_transitive_in(A, B) | (~(in(ordered_pair(tptp_fun_C_2(B, A), tptp_fun_E_0(B, A)), A) | (~in(tptp_fun_C_2(B, A), B)) | (~in(tptp_fun_D_1(B, A), B)) | (~in(tptp_fun_E_0(B, A), B)) | (~in(ordered_pair(tptp_fun_C_2(B, A), tptp_fun_D_1(B, A)), A)) | (~in(ordered_pair(tptp_fun_D_1(B, A), tptp_fun_E_0(B, A)), A)))))))))) | ((~relation(A!4)) | ![B: $i] : (~((~((~is_transitive_in(A!4, B)) | ![C: $i, D: $i, E: $i] : (in(ordered_pair(C, E), A!4) | (~in(C, B)) | (~in(D, B)) | (~in(E, B)) | (~in(ordered_pair(C, D), A!4)) | (~in(ordered_pair(D, E), A!4))))) | (~(is_transitive_in(A!4, B) | (~(in(ordered_pair(tptp_fun_C_2(B, A!4), tptp_fun_E_0(B, A!4)), A!4) | (~in(tptp_fun_C_2(B, A!4), B)) | (~in(tptp_fun_D_1(B, A!4), B)) | (~in(tptp_fun_E_0(B, A!4), B)) | (~in(ordered_pair(tptp_fun_C_2(B, A!4), tptp_fun_D_1(B, A!4)), A!4)) | (~in(ordered_pair(tptp_fun_D_1(B, A!4), tptp_fun_E_0(B, A!4)), A!4)))))))))),
% 0.21/0.41 inference(quant_inst,[status(thm)],[])).
% 0.21/0.41 tff(111,plain,
% 0.21/0.41 ((~![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~is_transitive_in(A, B)) | ![C: $i, D: $i, E: $i] : (in(ordered_pair(C, E), A) | (~in(C, B)) | (~in(D, B)) | (~in(E, B)) | (~in(ordered_pair(C, D), A)) | (~in(ordered_pair(D, E), A))))) | (~(is_transitive_in(A, B) | (~(in(ordered_pair(tptp_fun_C_2(B, A), tptp_fun_E_0(B, A)), A) | (~in(tptp_fun_C_2(B, A), B)) | (~in(tptp_fun_D_1(B, A), B)) | (~in(tptp_fun_E_0(B, A), B)) | (~in(ordered_pair(tptp_fun_C_2(B, A), tptp_fun_D_1(B, A)), A)) | (~in(ordered_pair(tptp_fun_D_1(B, A), tptp_fun_E_0(B, A)), A)))))))))) | (~relation(A!4)) | ![B: $i] : (~((~((~is_transitive_in(A!4, B)) | ![C: $i, D: $i, E: $i] : (in(ordered_pair(C, E), A!4) | (~in(C, B)) | (~in(D, B)) | (~in(E, B)) | (~in(ordered_pair(C, D), A!4)) | (~in(ordered_pair(D, E), A!4))))) | (~(is_transitive_in(A!4, B) | (~((~in(ordered_pair(tptp_fun_D_1(B, A!4), tptp_fun_E_0(B, A!4)), A!4)) | (~in(ordered_pair(tptp_fun_C_2(B, A!4), tptp_fun_D_1(B, A!4)), A!4)) | (~in(tptp_fun_E_0(B, A!4), B)) | (~in(tptp_fun_D_1(B, A!4), B)) | (~in(tptp_fun_C_2(B, A!4), B)) | in(ordered_pair(tptp_fun_C_2(B, A!4), tptp_fun_E_0(B, A!4)), A!4)))))))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[110, 109])).
% 0.21/0.42 tff(112,plain,
% 0.21/0.42 (![B: $i] : (~((~((~is_transitive_in(A!4, B)) | ![C: $i, D: $i, E: $i] : (in(ordered_pair(C, E), A!4) | (~in(C, B)) | (~in(D, B)) | (~in(E, B)) | (~in(ordered_pair(C, D), A!4)) | (~in(ordered_pair(D, E), A!4))))) | (~(is_transitive_in(A!4, B) | (~((~in(ordered_pair(tptp_fun_D_1(B, A!4), tptp_fun_E_0(B, A!4)), A!4)) | (~in(ordered_pair(tptp_fun_C_2(B, A!4), tptp_fun_D_1(B, A!4)), A!4)) | (~in(tptp_fun_E_0(B, A!4), B)) | (~in(tptp_fun_D_1(B, A!4), B)) | (~in(tptp_fun_C_2(B, A!4), B)) | in(ordered_pair(tptp_fun_C_2(B, A!4), tptp_fun_E_0(B, A!4)), A!4)))))))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[111, 105, 14])).
% 0.21/0.42 tff(113,plain,
% 0.21/0.42 (((~![B: $i] : (~((~((~is_transitive_in(A!4, B)) | ![C: $i, D: $i, E: $i] : (in(ordered_pair(C, E), A!4) | (~in(C, B)) | (~in(D, B)) | (~in(E, B)) | (~in(ordered_pair(C, D), A!4)) | (~in(ordered_pair(D, E), A!4))))) | (~(is_transitive_in(A!4, B) | (~((~in(ordered_pair(tptp_fun_D_1(B, A!4), tptp_fun_E_0(B, A!4)), A!4)) | (~in(ordered_pair(tptp_fun_C_2(B, A!4), tptp_fun_D_1(B, A!4)), A!4)) | (~in(tptp_fun_E_0(B, A!4), B)) | (~in(tptp_fun_D_1(B, A!4), B)) | (~in(tptp_fun_C_2(B, A!4), B)) | in(ordered_pair(tptp_fun_C_2(B, A!4), tptp_fun_E_0(B, A!4)), A!4)))))))) | (~((~((~is_transitive_in(A!4, set_union2(relation_dom(A!4), relation_rng(A!4)))) | ![C: $i, D: $i, E: $i] : (in(ordered_pair(C, E), A!4) | (~in(ordered_pair(C, D), A!4)) | (~in(ordered_pair(D, E), A!4)) | (~in(C, set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(D, set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(E, set_union2(relation_dom(A!4), relation_rng(A!4))))))) | (~(is_transitive_in(A!4, set_union2(relation_dom(A!4), relation_rng(A!4))) | (~(in(ordered_pair(tptp_fun_C_2(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), tptp_fun_E_0(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4)), A!4) | (~in(tptp_fun_C_2(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(tptp_fun_D_1(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(tptp_fun_E_0(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(ordered_pair(tptp_fun_C_2(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), tptp_fun_D_1(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4)), A!4)) | (~in(ordered_pair(tptp_fun_D_1(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), tptp_fun_E_0(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4)), A!4))))))))) <=> ((~![B: $i] : (~((~((~is_transitive_in(A!4, B)) | ![C: $i, D: $i, E: $i] : (in(ordered_pair(C, E), A!4) | (~in(C, B)) | (~in(D, B)) | (~in(E, B)) | (~in(ordered_pair(C, D), A!4)) | (~in(ordered_pair(D, E), A!4))))) | (~(is_transitive_in(A!4, B) | (~((~in(ordered_pair(tptp_fun_D_1(B, A!4), tptp_fun_E_0(B, A!4)), A!4)) | (~in(ordered_pair(tptp_fun_C_2(B, A!4), tptp_fun_D_1(B, A!4)), A!4)) | (~in(tptp_fun_E_0(B, A!4), B)) | (~in(tptp_fun_D_1(B, A!4), B)) | (~in(tptp_fun_C_2(B, A!4), B)) | in(ordered_pair(tptp_fun_C_2(B, A!4), tptp_fun_E_0(B, A!4)), A!4)))))))) | (~((~((~is_transitive_in(A!4, set_union2(relation_dom(A!4), relation_rng(A!4)))) | ![C: $i, D: $i, E: $i] : (in(ordered_pair(C, E), A!4) | (~in(ordered_pair(C, D), A!4)) | (~in(ordered_pair(D, E), A!4)) | (~in(C, set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(D, set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(E, set_union2(relation_dom(A!4), relation_rng(A!4))))))) | (~(is_transitive_in(A!4, set_union2(relation_dom(A!4), relation_rng(A!4))) | (~(in(ordered_pair(tptp_fun_C_2(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), tptp_fun_E_0(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4)), A!4) | (~in(tptp_fun_C_2(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(tptp_fun_D_1(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(tptp_fun_E_0(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(ordered_pair(tptp_fun_C_2(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), tptp_fun_D_1(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4)), A!4)) | (~in(ordered_pair(tptp_fun_D_1(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), tptp_fun_E_0(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4)), A!4)))))))))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(114,plain,
% 0.21/0.42 ((~((~((~is_transitive_in(A!4, set_union2(relation_dom(A!4), relation_rng(A!4)))) | ![C: $i, D: $i, E: $i] : (in(ordered_pair(C, E), A!4) | (~in(C, set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(D, set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(E, set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(ordered_pair(C, D), A!4)) | (~in(ordered_pair(D, E), A!4))))) | (~(is_transitive_in(A!4, set_union2(relation_dom(A!4), relation_rng(A!4))) | (~((~in(ordered_pair(tptp_fun_D_1(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), tptp_fun_E_0(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4)), A!4)) | (~in(ordered_pair(tptp_fun_C_2(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), tptp_fun_D_1(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4)), A!4)) | (~in(tptp_fun_E_0(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(tptp_fun_D_1(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(tptp_fun_C_2(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), set_union2(relation_dom(A!4), relation_rng(A!4)))) | in(ordered_pair(tptp_fun_C_2(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), tptp_fun_E_0(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4)), A!4))))))) <=> (~((~((~is_transitive_in(A!4, set_union2(relation_dom(A!4), relation_rng(A!4)))) | ![C: $i, D: $i, E: $i] : (in(ordered_pair(C, E), A!4) | (~in(ordered_pair(C, D), A!4)) | (~in(ordered_pair(D, E), A!4)) | (~in(C, set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(D, set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(E, set_union2(relation_dom(A!4), relation_rng(A!4))))))) | (~(is_transitive_in(A!4, set_union2(relation_dom(A!4), relation_rng(A!4))) | (~(in(ordered_pair(tptp_fun_C_2(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), tptp_fun_E_0(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4)), A!4) | (~in(tptp_fun_C_2(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(tptp_fun_D_1(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(tptp_fun_E_0(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(ordered_pair(tptp_fun_C_2(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), tptp_fun_D_1(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4)), A!4)) | (~in(ordered_pair(tptp_fun_D_1(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), tptp_fun_E_0(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4)), A!4))))))))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(115,plain,
% 0.21/0.42 (((~![B: $i] : (~((~((~is_transitive_in(A!4, B)) | ![C: $i, D: $i, E: $i] : (in(ordered_pair(C, E), A!4) | (~in(C, B)) | (~in(D, B)) | (~in(E, B)) | (~in(ordered_pair(C, D), A!4)) | (~in(ordered_pair(D, E), A!4))))) | (~(is_transitive_in(A!4, B) | (~((~in(ordered_pair(tptp_fun_D_1(B, A!4), tptp_fun_E_0(B, A!4)), A!4)) | (~in(ordered_pair(tptp_fun_C_2(B, A!4), tptp_fun_D_1(B, A!4)), A!4)) | (~in(tptp_fun_E_0(B, A!4), B)) | (~in(tptp_fun_D_1(B, A!4), B)) | (~in(tptp_fun_C_2(B, A!4), B)) | in(ordered_pair(tptp_fun_C_2(B, A!4), tptp_fun_E_0(B, A!4)), A!4)))))))) | (~((~((~is_transitive_in(A!4, set_union2(relation_dom(A!4), relation_rng(A!4)))) | ![C: $i, D: $i, E: $i] : (in(ordered_pair(C, E), A!4) | (~in(C, set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(D, set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(E, set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(ordered_pair(C, D), A!4)) | (~in(ordered_pair(D, E), A!4))))) | (~(is_transitive_in(A!4, set_union2(relation_dom(A!4), relation_rng(A!4))) | (~((~in(ordered_pair(tptp_fun_D_1(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), tptp_fun_E_0(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4)), A!4)) | (~in(ordered_pair(tptp_fun_C_2(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), tptp_fun_D_1(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4)), A!4)) | (~in(tptp_fun_E_0(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(tptp_fun_D_1(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(tptp_fun_C_2(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), set_union2(relation_dom(A!4), relation_rng(A!4)))) | in(ordered_pair(tptp_fun_C_2(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), tptp_fun_E_0(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4)), A!4)))))))) <=> ((~![B: $i] : (~((~((~is_transitive_in(A!4, B)) | ![C: $i, D: $i, E: $i] : (in(ordered_pair(C, E), A!4) | (~in(C, B)) | (~in(D, B)) | (~in(E, B)) | (~in(ordered_pair(C, D), A!4)) | (~in(ordered_pair(D, E), A!4))))) | (~(is_transitive_in(A!4, B) | (~((~in(ordered_pair(tptp_fun_D_1(B, A!4), tptp_fun_E_0(B, A!4)), A!4)) | (~in(ordered_pair(tptp_fun_C_2(B, A!4), tptp_fun_D_1(B, A!4)), A!4)) | (~in(tptp_fun_E_0(B, A!4), B)) | (~in(tptp_fun_D_1(B, A!4), B)) | (~in(tptp_fun_C_2(B, A!4), B)) | in(ordered_pair(tptp_fun_C_2(B, A!4), tptp_fun_E_0(B, A!4)), A!4)))))))) | (~((~((~is_transitive_in(A!4, set_union2(relation_dom(A!4), relation_rng(A!4)))) | ![C: $i, D: $i, E: $i] : (in(ordered_pair(C, E), A!4) | (~in(ordered_pair(C, D), A!4)) | (~in(ordered_pair(D, E), A!4)) | (~in(C, set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(D, set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(E, set_union2(relation_dom(A!4), relation_rng(A!4))))))) | (~(is_transitive_in(A!4, set_union2(relation_dom(A!4), relation_rng(A!4))) | (~(in(ordered_pair(tptp_fun_C_2(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), tptp_fun_E_0(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4)), A!4) | (~in(tptp_fun_C_2(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(tptp_fun_D_1(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(tptp_fun_E_0(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(ordered_pair(tptp_fun_C_2(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), tptp_fun_D_1(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4)), A!4)) | (~in(ordered_pair(tptp_fun_D_1(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), tptp_fun_E_0(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4)), A!4)))))))))),
% 0.21/0.42 inference(monotonicity,[status(thm)],[114])).
% 0.21/0.42 tff(116,plain,
% 0.21/0.42 (((~![B: $i] : (~((~((~is_transitive_in(A!4, B)) | ![C: $i, D: $i, E: $i] : (in(ordered_pair(C, E), A!4) | (~in(C, B)) | (~in(D, B)) | (~in(E, B)) | (~in(ordered_pair(C, D), A!4)) | (~in(ordered_pair(D, E), A!4))))) | (~(is_transitive_in(A!4, B) | (~((~in(ordered_pair(tptp_fun_D_1(B, A!4), tptp_fun_E_0(B, A!4)), A!4)) | (~in(ordered_pair(tptp_fun_C_2(B, A!4), tptp_fun_D_1(B, A!4)), A!4)) | (~in(tptp_fun_E_0(B, A!4), B)) | (~in(tptp_fun_D_1(B, A!4), B)) | (~in(tptp_fun_C_2(B, A!4), B)) | in(ordered_pair(tptp_fun_C_2(B, A!4), tptp_fun_E_0(B, A!4)), A!4)))))))) | (~((~((~is_transitive_in(A!4, set_union2(relation_dom(A!4), relation_rng(A!4)))) | ![C: $i, D: $i, E: $i] : (in(ordered_pair(C, E), A!4) | (~in(C, set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(D, set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(E, set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(ordered_pair(C, D), A!4)) | (~in(ordered_pair(D, E), A!4))))) | (~(is_transitive_in(A!4, set_union2(relation_dom(A!4), relation_rng(A!4))) | (~((~in(ordered_pair(tptp_fun_D_1(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), tptp_fun_E_0(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4)), A!4)) | (~in(ordered_pair(tptp_fun_C_2(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), tptp_fun_D_1(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4)), A!4)) | (~in(tptp_fun_E_0(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(tptp_fun_D_1(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(tptp_fun_C_2(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), set_union2(relation_dom(A!4), relation_rng(A!4)))) | in(ordered_pair(tptp_fun_C_2(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), tptp_fun_E_0(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4)), A!4)))))))) <=> ((~![B: $i] : (~((~((~is_transitive_in(A!4, B)) | ![C: $i, D: $i, E: $i] : (in(ordered_pair(C, E), A!4) | (~in(C, B)) | (~in(D, B)) | (~in(E, B)) | (~in(ordered_pair(C, D), A!4)) | (~in(ordered_pair(D, E), A!4))))) | (~(is_transitive_in(A!4, B) | (~((~in(ordered_pair(tptp_fun_D_1(B, A!4), tptp_fun_E_0(B, A!4)), A!4)) | (~in(ordered_pair(tptp_fun_C_2(B, A!4), tptp_fun_D_1(B, A!4)), A!4)) | (~in(tptp_fun_E_0(B, A!4), B)) | (~in(tptp_fun_D_1(B, A!4), B)) | (~in(tptp_fun_C_2(B, A!4), B)) | in(ordered_pair(tptp_fun_C_2(B, A!4), tptp_fun_E_0(B, A!4)), A!4)))))))) | (~((~((~is_transitive_in(A!4, set_union2(relation_dom(A!4), relation_rng(A!4)))) | ![C: $i, D: $i, E: $i] : (in(ordered_pair(C, E), A!4) | (~in(ordered_pair(C, D), A!4)) | (~in(ordered_pair(D, E), A!4)) | (~in(C, set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(D, set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(E, set_union2(relation_dom(A!4), relation_rng(A!4))))))) | (~(is_transitive_in(A!4, set_union2(relation_dom(A!4), relation_rng(A!4))) | (~(in(ordered_pair(tptp_fun_C_2(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), tptp_fun_E_0(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4)), A!4) | (~in(tptp_fun_C_2(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(tptp_fun_D_1(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(tptp_fun_E_0(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(ordered_pair(tptp_fun_C_2(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), tptp_fun_D_1(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4)), A!4)) | (~in(ordered_pair(tptp_fun_D_1(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), tptp_fun_E_0(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4)), A!4)))))))))),
% 0.21/0.43 inference(transitivity,[status(thm)],[115, 113])).
% 0.21/0.43 tff(117,plain,
% 0.21/0.43 ((~![B: $i] : (~((~((~is_transitive_in(A!4, B)) | ![C: $i, D: $i, E: $i] : (in(ordered_pair(C, E), A!4) | (~in(C, B)) | (~in(D, B)) | (~in(E, B)) | (~in(ordered_pair(C, D), A!4)) | (~in(ordered_pair(D, E), A!4))))) | (~(is_transitive_in(A!4, B) | (~((~in(ordered_pair(tptp_fun_D_1(B, A!4), tptp_fun_E_0(B, A!4)), A!4)) | (~in(ordered_pair(tptp_fun_C_2(B, A!4), tptp_fun_D_1(B, A!4)), A!4)) | (~in(tptp_fun_E_0(B, A!4), B)) | (~in(tptp_fun_D_1(B, A!4), B)) | (~in(tptp_fun_C_2(B, A!4), B)) | in(ordered_pair(tptp_fun_C_2(B, A!4), tptp_fun_E_0(B, A!4)), A!4)))))))) | (~((~((~is_transitive_in(A!4, set_union2(relation_dom(A!4), relation_rng(A!4)))) | ![C: $i, D: $i, E: $i] : (in(ordered_pair(C, E), A!4) | (~in(C, set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(D, set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(E, set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(ordered_pair(C, D), A!4)) | (~in(ordered_pair(D, E), A!4))))) | (~(is_transitive_in(A!4, set_union2(relation_dom(A!4), relation_rng(A!4))) | (~((~in(ordered_pair(tptp_fun_D_1(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), tptp_fun_E_0(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4)), A!4)) | (~in(ordered_pair(tptp_fun_C_2(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), tptp_fun_D_1(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4)), A!4)) | (~in(tptp_fun_E_0(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(tptp_fun_D_1(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(tptp_fun_C_2(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), set_union2(relation_dom(A!4), relation_rng(A!4)))) | in(ordered_pair(tptp_fun_C_2(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), tptp_fun_E_0(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4)), A!4)))))))),
% 0.21/0.43 inference(quant_inst,[status(thm)],[])).
% 0.21/0.43 tff(118,plain,
% 0.21/0.43 ((~![B: $i] : (~((~((~is_transitive_in(A!4, B)) | ![C: $i, D: $i, E: $i] : (in(ordered_pair(C, E), A!4) | (~in(C, B)) | (~in(D, B)) | (~in(E, B)) | (~in(ordered_pair(C, D), A!4)) | (~in(ordered_pair(D, E), A!4))))) | (~(is_transitive_in(A!4, B) | (~((~in(ordered_pair(tptp_fun_D_1(B, A!4), tptp_fun_E_0(B, A!4)), A!4)) | (~in(ordered_pair(tptp_fun_C_2(B, A!4), tptp_fun_D_1(B, A!4)), A!4)) | (~in(tptp_fun_E_0(B, A!4), B)) | (~in(tptp_fun_D_1(B, A!4), B)) | (~in(tptp_fun_C_2(B, A!4), B)) | in(ordered_pair(tptp_fun_C_2(B, A!4), tptp_fun_E_0(B, A!4)), A!4)))))))) | (~((~((~is_transitive_in(A!4, set_union2(relation_dom(A!4), relation_rng(A!4)))) | ![C: $i, D: $i, E: $i] : (in(ordered_pair(C, E), A!4) | (~in(ordered_pair(C, D), A!4)) | (~in(ordered_pair(D, E), A!4)) | (~in(C, set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(D, set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(E, set_union2(relation_dom(A!4), relation_rng(A!4))))))) | (~(is_transitive_in(A!4, set_union2(relation_dom(A!4), relation_rng(A!4))) | (~(in(ordered_pair(tptp_fun_C_2(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), tptp_fun_E_0(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4)), A!4) | (~in(tptp_fun_C_2(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(tptp_fun_D_1(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(tptp_fun_E_0(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(ordered_pair(tptp_fun_C_2(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), tptp_fun_D_1(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4)), A!4)) | (~in(ordered_pair(tptp_fun_D_1(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), tptp_fun_E_0(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4)), A!4))))))))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[117, 116])).
% 0.21/0.43 tff(119,plain,
% 0.21/0.43 (~((~((~is_transitive_in(A!4, set_union2(relation_dom(A!4), relation_rng(A!4)))) | ![C: $i, D: $i, E: $i] : (in(ordered_pair(C, E), A!4) | (~in(ordered_pair(C, D), A!4)) | (~in(ordered_pair(D, E), A!4)) | (~in(C, set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(D, set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(E, set_union2(relation_dom(A!4), relation_rng(A!4))))))) | (~(is_transitive_in(A!4, set_union2(relation_dom(A!4), relation_rng(A!4))) | (~(in(ordered_pair(tptp_fun_C_2(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), tptp_fun_E_0(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4)), A!4) | (~in(tptp_fun_C_2(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(tptp_fun_D_1(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(tptp_fun_E_0(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(ordered_pair(tptp_fun_C_2(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), tptp_fun_D_1(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4)), A!4)) | (~in(ordered_pair(tptp_fun_D_1(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), tptp_fun_E_0(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4)), A!4)))))))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[118, 112])).
% 0.21/0.43 tff(120,plain,
% 0.21/0.43 (((~((~is_transitive_in(A!4, set_union2(relation_dom(A!4), relation_rng(A!4)))) | ![C: $i, D: $i, E: $i] : (in(ordered_pair(C, E), A!4) | (~in(ordered_pair(C, D), A!4)) | (~in(ordered_pair(D, E), A!4)) | (~in(C, set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(D, set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(E, set_union2(relation_dom(A!4), relation_rng(A!4))))))) | (~(is_transitive_in(A!4, set_union2(relation_dom(A!4), relation_rng(A!4))) | (~(in(ordered_pair(tptp_fun_C_2(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), tptp_fun_E_0(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4)), A!4) | (~in(tptp_fun_C_2(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(tptp_fun_D_1(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(tptp_fun_E_0(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(ordered_pair(tptp_fun_C_2(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), tptp_fun_D_1(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4)), A!4)) | (~in(ordered_pair(tptp_fun_D_1(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), tptp_fun_E_0(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4)), A!4))))))) | ((~is_transitive_in(A!4, set_union2(relation_dom(A!4), relation_rng(A!4)))) | ![C: $i, D: $i, E: $i] : (in(ordered_pair(C, E), A!4) | (~in(ordered_pair(C, D), A!4)) | (~in(ordered_pair(D, E), A!4)) | (~in(C, set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(D, set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(E, set_union2(relation_dom(A!4), relation_rng(A!4))))))),
% 0.21/0.43 inference(tautology,[status(thm)],[])).
% 0.21/0.43 tff(121,plain,
% 0.21/0.43 ((~is_transitive_in(A!4, set_union2(relation_dom(A!4), relation_rng(A!4)))) | ![C: $i, D: $i, E: $i] : (in(ordered_pair(C, E), A!4) | (~in(ordered_pair(C, D), A!4)) | (~in(ordered_pair(D, E), A!4)) | (~in(C, set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(D, set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(E, set_union2(relation_dom(A!4), relation_rng(A!4)))))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[120, 119])).
% 0.21/0.43 tff(122,plain,
% 0.21/0.43 ((~((~is_transitive_in(A!4, set_union2(relation_dom(A!4), relation_rng(A!4)))) | ![C: $i, D: $i, E: $i] : (in(ordered_pair(C, E), A!4) | (~in(ordered_pair(C, D), A!4)) | (~in(ordered_pair(D, E), A!4)) | (~in(C, set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(D, set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(E, set_union2(relation_dom(A!4), relation_rng(A!4))))))) | (~is_transitive_in(A!4, set_union2(relation_dom(A!4), relation_rng(A!4)))) | ![C: $i, D: $i, E: $i] : (in(ordered_pair(C, E), A!4) | (~in(ordered_pair(C, D), A!4)) | (~in(ordered_pair(D, E), A!4)) | (~in(C, set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(D, set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(E, set_union2(relation_dom(A!4), relation_rng(A!4)))))),
% 0.21/0.43 inference(tautology,[status(thm)],[])).
% 0.21/0.43 tff(123,plain,
% 0.21/0.43 ((~is_transitive_in(A!4, set_union2(relation_dom(A!4), relation_rng(A!4)))) | ![C: $i, D: $i, E: $i] : (in(ordered_pair(C, E), A!4) | (~in(ordered_pair(C, D), A!4)) | (~in(ordered_pair(D, E), A!4)) | (~in(C, set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(D, set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(E, set_union2(relation_dom(A!4), relation_rng(A!4)))))),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[122, 121])).
% 0.21/0.44 tff(124,plain,
% 0.21/0.44 (~is_transitive_in(A!4, set_union2(relation_dom(A!4), relation_rng(A!4)))),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[123, 89])).
% 0.21/0.44 tff(125,plain,
% 0.21/0.44 (~is_transitive_in(A!4, relation_field(A!4))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[124, 40])).
% 0.21/0.44 tff(126,plain,
% 0.21/0.44 (^[A: $i] : refl(((~relation(A)) | (transitive(A) <=> is_transitive_in(A, relation_field(A)))) <=> ((~relation(A)) | (transitive(A) <=> is_transitive_in(A, relation_field(A)))))),
% 0.21/0.44 inference(bind,[status(th)],[])).
% 0.21/0.44 tff(127,plain,
% 0.21/0.44 (![A: $i] : ((~relation(A)) | (transitive(A) <=> is_transitive_in(A, relation_field(A)))) <=> ![A: $i] : ((~relation(A)) | (transitive(A) <=> is_transitive_in(A, relation_field(A))))),
% 0.21/0.44 inference(quant_intro,[status(thm)],[126])).
% 0.21/0.44 tff(128,plain,
% 0.21/0.44 (![A: $i] : ((~relation(A)) | (transitive(A) <=> is_transitive_in(A, relation_field(A)))) <=> ![A: $i] : ((~relation(A)) | (transitive(A) <=> is_transitive_in(A, relation_field(A))))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(129,plain,
% 0.21/0.44 (^[A: $i] : rewrite((relation(A) => (transitive(A) <=> is_transitive_in(A, relation_field(A)))) <=> ((~relation(A)) | (transitive(A) <=> is_transitive_in(A, relation_field(A)))))),
% 0.21/0.44 inference(bind,[status(th)],[])).
% 0.21/0.44 tff(130,plain,
% 0.21/0.44 (![A: $i] : (relation(A) => (transitive(A) <=> is_transitive_in(A, relation_field(A)))) <=> ![A: $i] : ((~relation(A)) | (transitive(A) <=> is_transitive_in(A, relation_field(A))))),
% 0.21/0.44 inference(quant_intro,[status(thm)],[129])).
% 0.21/0.44 tff(131,axiom,(![A: $i] : (relation(A) => (transitive(A) <=> is_transitive_in(A, relation_field(A))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d16_relat_2')).
% 0.21/0.44 tff(132,plain,
% 0.21/0.44 (![A: $i] : ((~relation(A)) | (transitive(A) <=> is_transitive_in(A, relation_field(A))))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[131, 130])).
% 0.21/0.44 tff(133,plain,
% 0.21/0.44 (![A: $i] : ((~relation(A)) | (transitive(A) <=> is_transitive_in(A, relation_field(A))))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[132, 128])).
% 0.21/0.44 tff(134,plain,(
% 0.21/0.44 ![A: $i] : ((~relation(A)) | (transitive(A) <=> is_transitive_in(A, relation_field(A))))),
% 0.21/0.44 inference(skolemize,[status(sab)],[133])).
% 0.21/0.44 tff(135,plain,
% 0.21/0.44 (![A: $i] : ((~relation(A)) | (transitive(A) <=> is_transitive_in(A, relation_field(A))))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[134, 127])).
% 0.21/0.44 tff(136,plain,
% 0.21/0.44 (((~![A: $i] : ((~relation(A)) | (transitive(A) <=> is_transitive_in(A, relation_field(A))))) | ((~relation(A!4)) | (transitive(A!4) <=> is_transitive_in(A!4, relation_field(A!4))))) <=> ((~![A: $i] : ((~relation(A)) | (transitive(A) <=> is_transitive_in(A, relation_field(A))))) | (~relation(A!4)) | (transitive(A!4) <=> is_transitive_in(A!4, relation_field(A!4))))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(137,plain,
% 0.21/0.44 ((~![A: $i] : ((~relation(A)) | (transitive(A) <=> is_transitive_in(A, relation_field(A))))) | ((~relation(A!4)) | (transitive(A!4) <=> is_transitive_in(A!4, relation_field(A!4))))),
% 0.21/0.44 inference(quant_inst,[status(thm)],[])).
% 0.21/0.44 tff(138,plain,
% 0.21/0.44 ((~![A: $i] : ((~relation(A)) | (transitive(A) <=> is_transitive_in(A, relation_field(A))))) | (~relation(A!4)) | (transitive(A!4) <=> is_transitive_in(A!4, relation_field(A!4)))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[137, 136])).
% 0.21/0.44 tff(139,plain,
% 0.21/0.44 (transitive(A!4) <=> is_transitive_in(A!4, relation_field(A!4))),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[138, 135, 14])).
% 0.21/0.44 tff(140,plain,
% 0.21/0.44 ((~(transitive(A!4) <=> is_transitive_in(A!4, relation_field(A!4)))) | (~transitive(A!4)) | is_transitive_in(A!4, relation_field(A!4))),
% 0.21/0.44 inference(tautology,[status(thm)],[])).
% 0.21/0.44 tff(141,plain,
% 0.21/0.44 ((~transitive(A!4)) | is_transitive_in(A!4, relation_field(A!4))),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[140, 139])).
% 0.21/0.44 tff(142,plain,
% 0.21/0.44 (~transitive(A!4)),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[141, 125])).
% 0.21/0.44 tff(143,plain,
% 0.21/0.44 ((transitive(A!4) | ![B: $i, C: $i, D: $i] : (in(ordered_pair(B, D), A!4) | (~in(ordered_pair(B, C), A!4)) | (~in(ordered_pair(C, D), A!4)))) <=> (transitive(A!4) | ![B: $i, C: $i, D: $i] : (in(ordered_pair(B, D), A!4) | (~in(ordered_pair(B, C), A!4)) | (~in(ordered_pair(C, D), A!4))))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(144,plain,
% 0.21/0.44 ((transitive(A!4) | ![B: $i, C: $i, D: $i] : ((~(in(ordered_pair(B, C), A!4) & in(ordered_pair(C, D), A!4))) | in(ordered_pair(B, D), A!4))) <=> (transitive(A!4) | ![B: $i, C: $i, D: $i] : (in(ordered_pair(B, D), A!4) | (~in(ordered_pair(B, C), A!4)) | (~in(ordered_pair(C, D), A!4))))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(145,plain,
% 0.21/0.44 (transitive(A!4) | ![B: $i, C: $i, D: $i] : ((~(in(ordered_pair(B, C), A!4) & in(ordered_pair(C, D), A!4))) | in(ordered_pair(B, D), A!4))),
% 0.21/0.44 inference(and_elim,[status(thm)],[13])).
% 0.21/0.44 tff(146,plain,
% 0.21/0.44 (transitive(A!4) | ![B: $i, C: $i, D: $i] : (in(ordered_pair(B, D), A!4) | (~in(ordered_pair(B, C), A!4)) | (~in(ordered_pair(C, D), A!4)))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[145, 144])).
% 0.21/0.44 tff(147,plain,
% 0.21/0.44 (transitive(A!4) | ![B: $i, C: $i, D: $i] : (in(ordered_pair(B, D), A!4) | (~in(ordered_pair(B, C), A!4)) | (~in(ordered_pair(C, D), A!4)))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[146, 143])).
% 0.21/0.44 tff(148,plain,
% 0.21/0.44 (![B: $i, C: $i, D: $i] : (in(ordered_pair(B, D), A!4) | (~in(ordered_pair(B, C), A!4)) | (~in(ordered_pair(C, D), A!4)))),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[147, 142])).
% 0.21/0.44 tff(149,plain,
% 0.21/0.44 (((~![B: $i, C: $i, D: $i] : (in(ordered_pair(B, D), A!4) | (~in(ordered_pair(B, C), A!4)) | (~in(ordered_pair(C, D), A!4)))) | (in(ordered_pair(B!7, D!5), A!4) | (~in(ordered_pair(B!7, C!6), A!4)) | (~in(ordered_pair(C!6, D!5), A!4)))) <=> ((~![B: $i, C: $i, D: $i] : (in(ordered_pair(B, D), A!4) | (~in(ordered_pair(B, C), A!4)) | (~in(ordered_pair(C, D), A!4)))) | in(ordered_pair(B!7, D!5), A!4) | (~in(ordered_pair(B!7, C!6), A!4)) | (~in(ordered_pair(C!6, D!5), A!4)))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(150,plain,
% 0.21/0.44 ((~![B: $i, C: $i, D: $i] : (in(ordered_pair(B, D), A!4) | (~in(ordered_pair(B, C), A!4)) | (~in(ordered_pair(C, D), A!4)))) | (in(ordered_pair(B!7, D!5), A!4) | (~in(ordered_pair(B!7, C!6), A!4)) | (~in(ordered_pair(C!6, D!5), A!4)))),
% 0.21/0.44 inference(quant_inst,[status(thm)],[])).
% 0.21/0.44 tff(151,plain,
% 0.21/0.44 ((~![B: $i, C: $i, D: $i] : (in(ordered_pair(B, D), A!4) | (~in(ordered_pair(B, C), A!4)) | (~in(ordered_pair(C, D), A!4)))) | in(ordered_pair(B!7, D!5), A!4) | (~in(ordered_pair(B!7, C!6), A!4)) | (~in(ordered_pair(C!6, D!5), A!4))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[150, 149])).
% 0.21/0.44 tff(152,plain,
% 0.21/0.44 ($false),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[151, 148, 39, 37, 35])).
% 0.21/0.44 tff(153,plain,(in(ordered_pair(B!7, D!5), A!4) | (~in(ordered_pair(B!7, C!6), A!4)) | (~in(ordered_pair(C!6, D!5), A!4))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.44 tff(154,plain,
% 0.21/0.44 (((~transitive(A!4)) | (~((~(in(ordered_pair(B!7, C!6), A!4) & in(ordered_pair(C!6, D!5), A!4))) | in(ordered_pair(B!7, D!5), A!4)))) <=> ((~transitive(A!4)) | (~(in(ordered_pair(B!7, D!5), A!4) | (~in(ordered_pair(B!7, C!6), A!4)) | (~in(ordered_pair(C!6, D!5), A!4)))))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(155,plain,
% 0.21/0.44 ((~transitive(A!4)) | (~((~(in(ordered_pair(B!7, C!6), A!4) & in(ordered_pair(C!6, D!5), A!4))) | in(ordered_pair(B!7, D!5), A!4)))),
% 0.21/0.44 inference(and_elim,[status(thm)],[13])).
% 0.21/0.44 tff(156,plain,
% 0.21/0.44 ((~transitive(A!4)) | (~(in(ordered_pair(B!7, D!5), A!4) | (~in(ordered_pair(B!7, C!6), A!4)) | (~in(ordered_pair(C!6, D!5), A!4))))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[155, 154])).
% 0.21/0.44 tff(157,plain,
% 0.21/0.44 (~transitive(A!4)),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[156, 153])).
% 0.21/0.44 tff(158,plain,
% 0.21/0.44 ((~(transitive(A!4) <=> is_transitive_in(A!4, relation_field(A!4)))) | transitive(A!4) | (~is_transitive_in(A!4, relation_field(A!4)))),
% 0.21/0.44 inference(tautology,[status(thm)],[])).
% 0.21/0.44 tff(159,plain,
% 0.21/0.44 (transitive(A!4) | (~is_transitive_in(A!4, relation_field(A!4)))),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[158, 139])).
% 0.21/0.44 tff(160,plain,
% 0.21/0.44 (~is_transitive_in(A!4, relation_field(A!4))),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[159, 157])).
% 0.21/0.44 tff(161,plain,
% 0.21/0.44 (~is_transitive_in(A!4, set_union2(relation_dom(A!4), relation_rng(A!4)))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[160, 32])).
% 0.21/0.44 tff(162,plain,
% 0.21/0.44 (((~((~is_transitive_in(A!4, set_union2(relation_dom(A!4), relation_rng(A!4)))) | ![C: $i, D: $i, E: $i] : (in(ordered_pair(C, E), A!4) | (~in(ordered_pair(C, D), A!4)) | (~in(ordered_pair(D, E), A!4)) | (~in(C, set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(D, set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(E, set_union2(relation_dom(A!4), relation_rng(A!4))))))) | (~(is_transitive_in(A!4, set_union2(relation_dom(A!4), relation_rng(A!4))) | (~(in(ordered_pair(tptp_fun_C_2(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), tptp_fun_E_0(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4)), A!4) | (~in(tptp_fun_C_2(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(tptp_fun_D_1(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(tptp_fun_E_0(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(ordered_pair(tptp_fun_C_2(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), tptp_fun_D_1(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4)), A!4)) | (~in(ordered_pair(tptp_fun_D_1(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), tptp_fun_E_0(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4)), A!4))))))) | (is_transitive_in(A!4, set_union2(relation_dom(A!4), relation_rng(A!4))) | (~(in(ordered_pair(tptp_fun_C_2(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), tptp_fun_E_0(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4)), A!4) | (~in(tptp_fun_C_2(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(tptp_fun_D_1(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(tptp_fun_E_0(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(ordered_pair(tptp_fun_C_2(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), tptp_fun_D_1(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4)), A!4)) | (~in(ordered_pair(tptp_fun_D_1(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), tptp_fun_E_0(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4)), A!4)))))),
% 0.21/0.44 inference(tautology,[status(thm)],[])).
% 0.21/0.44 tff(163,plain,
% 0.21/0.44 (is_transitive_in(A!4, set_union2(relation_dom(A!4), relation_rng(A!4))) | (~(in(ordered_pair(tptp_fun_C_2(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), tptp_fun_E_0(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4)), A!4) | (~in(tptp_fun_C_2(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(tptp_fun_D_1(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(tptp_fun_E_0(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(ordered_pair(tptp_fun_C_2(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), tptp_fun_D_1(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4)), A!4)) | (~in(ordered_pair(tptp_fun_D_1(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), tptp_fun_E_0(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4)), A!4))))),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[162, 119])).
% 0.21/0.44 tff(164,plain,
% 0.21/0.44 ((~(is_transitive_in(A!4, set_union2(relation_dom(A!4), relation_rng(A!4))) | (~(in(ordered_pair(tptp_fun_C_2(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), tptp_fun_E_0(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4)), A!4) | (~in(tptp_fun_C_2(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(tptp_fun_D_1(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(tptp_fun_E_0(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(ordered_pair(tptp_fun_C_2(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), tptp_fun_D_1(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4)), A!4)) | (~in(ordered_pair(tptp_fun_D_1(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), tptp_fun_E_0(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4)), A!4)))))) | is_transitive_in(A!4, set_union2(relation_dom(A!4), relation_rng(A!4))) | (~(in(ordered_pair(tptp_fun_C_2(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), tptp_fun_E_0(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4)), A!4) | (~in(tptp_fun_C_2(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(tptp_fun_D_1(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(tptp_fun_E_0(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(ordered_pair(tptp_fun_C_2(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), tptp_fun_D_1(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4)), A!4)) | (~in(ordered_pair(tptp_fun_D_1(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), tptp_fun_E_0(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4)), A!4))))),
% 0.21/0.45 inference(tautology,[status(thm)],[])).
% 0.21/0.45 tff(165,plain,
% 0.21/0.45 (is_transitive_in(A!4, set_union2(relation_dom(A!4), relation_rng(A!4))) | (~(in(ordered_pair(tptp_fun_C_2(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), tptp_fun_E_0(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4)), A!4) | (~in(tptp_fun_C_2(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(tptp_fun_D_1(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(tptp_fun_E_0(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(ordered_pair(tptp_fun_C_2(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), tptp_fun_D_1(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4)), A!4)) | (~in(ordered_pair(tptp_fun_D_1(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), tptp_fun_E_0(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4)), A!4))))),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[164, 163])).
% 0.21/0.45 tff(166,plain,
% 0.21/0.45 (~(in(ordered_pair(tptp_fun_C_2(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), tptp_fun_E_0(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4)), A!4) | (~in(tptp_fun_C_2(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(tptp_fun_D_1(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(tptp_fun_E_0(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(ordered_pair(tptp_fun_C_2(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), tptp_fun_D_1(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4)), A!4)) | (~in(ordered_pair(tptp_fun_D_1(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), tptp_fun_E_0(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4)), A!4)))),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[165, 161])).
% 0.21/0.45 tff(167,plain,
% 0.21/0.45 ((in(ordered_pair(tptp_fun_C_2(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), tptp_fun_E_0(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4)), A!4) | (~in(tptp_fun_C_2(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(tptp_fun_D_1(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(tptp_fun_E_0(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(ordered_pair(tptp_fun_C_2(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), tptp_fun_D_1(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4)), A!4)) | (~in(ordered_pair(tptp_fun_D_1(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), tptp_fun_E_0(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4)), A!4))) | in(ordered_pair(tptp_fun_D_1(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), tptp_fun_E_0(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4)), A!4)),
% 0.21/0.45 inference(tautology,[status(thm)],[])).
% 0.21/0.45 tff(168,plain,
% 0.21/0.45 (in(ordered_pair(tptp_fun_D_1(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), tptp_fun_E_0(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4)), A!4)),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[167, 166])).
% 0.21/0.45 tff(169,plain,
% 0.21/0.45 ((in(ordered_pair(tptp_fun_C_2(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), tptp_fun_E_0(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4)), A!4) | (~in(tptp_fun_C_2(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(tptp_fun_D_1(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(tptp_fun_E_0(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(ordered_pair(tptp_fun_C_2(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), tptp_fun_D_1(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4)), A!4)) | (~in(ordered_pair(tptp_fun_D_1(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), tptp_fun_E_0(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4)), A!4))) | in(ordered_pair(tptp_fun_C_2(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), tptp_fun_D_1(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4)), A!4)),
% 0.21/0.45 inference(tautology,[status(thm)],[])).
% 0.21/0.45 tff(170,plain,
% 0.21/0.45 (in(ordered_pair(tptp_fun_C_2(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), tptp_fun_D_1(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4)), A!4)),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[169, 166])).
% 0.21/0.45 tff(171,plain,
% 0.21/0.45 ((in(ordered_pair(tptp_fun_C_2(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), tptp_fun_E_0(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4)), A!4) | (~in(tptp_fun_C_2(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(tptp_fun_D_1(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(tptp_fun_E_0(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(ordered_pair(tptp_fun_C_2(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), tptp_fun_D_1(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4)), A!4)) | (~in(ordered_pair(tptp_fun_D_1(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), tptp_fun_E_0(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4)), A!4))) | (~in(ordered_pair(tptp_fun_C_2(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), tptp_fun_E_0(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4)), A!4))),
% 0.21/0.45 inference(tautology,[status(thm)],[])).
% 0.21/0.45 tff(172,plain,
% 0.21/0.45 (~in(ordered_pair(tptp_fun_C_2(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), tptp_fun_E_0(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4)), A!4)),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[171, 166])).
% 0.21/0.45 tff(173,plain,
% 0.21/0.45 (![B: $i, C: $i, D: $i] : (in(ordered_pair(B, D), A!4) | (~in(ordered_pair(B, C), A!4)) | (~in(ordered_pair(C, D), A!4)))),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[147, 157])).
% 0.21/0.45 tff(174,plain,
% 0.21/0.45 (((~![B: $i, C: $i, D: $i] : (in(ordered_pair(B, D), A!4) | (~in(ordered_pair(B, C), A!4)) | (~in(ordered_pair(C, D), A!4)))) | (in(ordered_pair(tptp_fun_C_2(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), tptp_fun_E_0(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4)), A!4) | (~in(ordered_pair(tptp_fun_C_2(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), tptp_fun_D_1(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4)), A!4)) | (~in(ordered_pair(tptp_fun_D_1(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), tptp_fun_E_0(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4)), A!4)))) <=> ((~![B: $i, C: $i, D: $i] : (in(ordered_pair(B, D), A!4) | (~in(ordered_pair(B, C), A!4)) | (~in(ordered_pair(C, D), A!4)))) | in(ordered_pair(tptp_fun_C_2(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), tptp_fun_E_0(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4)), A!4) | (~in(ordered_pair(tptp_fun_C_2(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), tptp_fun_D_1(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4)), A!4)) | (~in(ordered_pair(tptp_fun_D_1(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), tptp_fun_E_0(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4)), A!4)))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(175,plain,
% 0.21/0.45 ((~![B: $i, C: $i, D: $i] : (in(ordered_pair(B, D), A!4) | (~in(ordered_pair(B, C), A!4)) | (~in(ordered_pair(C, D), A!4)))) | (in(ordered_pair(tptp_fun_C_2(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), tptp_fun_E_0(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4)), A!4) | (~in(ordered_pair(tptp_fun_C_2(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), tptp_fun_D_1(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4)), A!4)) | (~in(ordered_pair(tptp_fun_D_1(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), tptp_fun_E_0(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4)), A!4)))),
% 0.21/0.45 inference(quant_inst,[status(thm)],[])).
% 0.21/0.45 tff(176,plain,
% 0.21/0.45 ((~![B: $i, C: $i, D: $i] : (in(ordered_pair(B, D), A!4) | (~in(ordered_pair(B, C), A!4)) | (~in(ordered_pair(C, D), A!4)))) | in(ordered_pair(tptp_fun_C_2(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), tptp_fun_E_0(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4)), A!4) | (~in(ordered_pair(tptp_fun_C_2(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), tptp_fun_D_1(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4)), A!4)) | (~in(ordered_pair(tptp_fun_D_1(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), tptp_fun_E_0(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4)), A!4))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[175, 174])).
% 0.21/0.45 tff(177,plain,
% 0.21/0.45 ($false),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[176, 173, 172, 170, 168])).
% 0.21/0.45 % SZS output end Proof
% 0.21/0.45 % E exiting
%------------------------------------------------------------------------------