%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SEU241+1 : TPTP v9.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n013.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 05:27:22 AM UTC 2025
% Result : Theorem 0.20s 0.39s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : SEU241+1 : TPTP v9.0.0. Released v3.3.0.
% 0.03/0.13 % Command : run_E %s %d THM
% 0.13/0.34 % Computer : n013.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Fri Jun 20 06:28:23 EDT 2025
% 0.13/0.34 % CPUTime :
% 0.20/0.39 % SZS status Theorem
% 0.20/0.39 % SZS output start Proof
% 0.20/0.39 tff(in_type, type, (
% 0.20/0.39 in: ( $i * $i ) > $o)).
% 0.20/0.39 tff(tptp_fun_A_3_type, type, (
% 0.20/0.39 tptp_fun_A_3: $i)).
% 0.20/0.39 tff(ordered_pair_type, type, (
% 0.20/0.39 ordered_pair: ( $i * $i ) > $i)).
% 0.20/0.39 tff(tptp_fun_C_1_type, type, (
% 0.20/0.39 tptp_fun_C_1: ( $i * $i ) > $i)).
% 0.20/0.39 tff(set_union2_type, type, (
% 0.20/0.39 set_union2: ( $i * $i ) > $i)).
% 0.20/0.39 tff(relation_rng_type, type, (
% 0.20/0.39 relation_rng: $i > $i)).
% 0.20/0.39 tff(relation_dom_type, type, (
% 0.20/0.39 relation_dom: $i > $i)).
% 0.20/0.39 tff(tptp_fun_D_0_type, type, (
% 0.20/0.39 tptp_fun_D_0: ( $i * $i ) > $i)).
% 0.20/0.39 tff(is_antisymmetric_in_type, type, (
% 0.20/0.39 is_antisymmetric_in: ( $i * $i ) > $o)).
% 0.20/0.39 tff(relation_field_type, type, (
% 0.20/0.39 relation_field: $i > $i)).
% 0.20/0.39 tff(relation_type, type, (
% 0.20/0.39 relation: $i > $o)).
% 0.20/0.39 tff(tptp_fun_C_4_type, type, (
% 0.20/0.39 tptp_fun_C_4: $i)).
% 0.20/0.39 tff(tptp_fun_B_5_type, type, (
% 0.20/0.39 tptp_fun_B_5: $i)).
% 0.20/0.39 tff(antisymmetric_type, type, (
% 0.20/0.39 antisymmetric: $i > $o)).
% 0.20/0.39 tff(1,plain,
% 0.20/0.39 ((relation(A!3) & ((antisymmetric(A!3) | ![B: $i, C: $i] : ((~(in(ordered_pair(B, C), A!3) & in(ordered_pair(C, B), A!3))) | (B = C))) & ((~antisymmetric(A!3)) | (~((~(in(ordered_pair(B!5, C!4), A!3) & in(ordered_pair(C!4, B!5), A!3))) | (B!5 = C!4)))))) <=> (relation(A!3) & (antisymmetric(A!3) | ![B: $i, C: $i] : ((~(in(ordered_pair(B, C), A!3) & in(ordered_pair(C, B), A!3))) | (B = C))) & ((~antisymmetric(A!3)) | (~((~(in(ordered_pair(B!5, C!4), A!3) & in(ordered_pair(C!4, B!5), A!3))) | (B!5 = C!4)))))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(2,plain,
% 0.20/0.39 ((antisymmetric(A!3) | ![B: $i, C: $i] : ((~(in(ordered_pair(B, C), A!3) & in(ordered_pair(C, B), A!3))) | (B = C))) <=> (antisymmetric(A!3) | ![B: $i, C: $i] : ((~(in(ordered_pair(B, C), A!3) & in(ordered_pair(C, B), A!3))) | (B = C)))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(3,plain,
% 0.20/0.39 (((antisymmetric(A!3) | ![B: $i, C: $i] : ((~(in(ordered_pair(B, C), A!3) & in(ordered_pair(C, B), A!3))) | (B = C))) & ((~antisymmetric(A!3)) | (~((~(in(ordered_pair(B!5, C!4), A!3) & in(ordered_pair(C!4, B!5), A!3))) | (B!5 = C!4))))) <=> ((antisymmetric(A!3) | ![B: $i, C: $i] : ((~(in(ordered_pair(B, C), A!3) & in(ordered_pair(C, B), A!3))) | (B = C))) & ((~antisymmetric(A!3)) | (~((~(in(ordered_pair(B!5, C!4), A!3) & in(ordered_pair(C!4, B!5), A!3))) | (B!5 = C!4)))))),
% 0.20/0.39 inference(monotonicity,[status(thm)],[2])).
% 0.20/0.39 tff(4,plain,
% 0.20/0.39 ((relation(A!3) & ((antisymmetric(A!3) | ![B: $i, C: $i] : ((~(in(ordered_pair(B, C), A!3) & in(ordered_pair(C, B), A!3))) | (B = C))) & ((~antisymmetric(A!3)) | (~((~(in(ordered_pair(B!5, C!4), A!3) & in(ordered_pair(C!4, B!5), A!3))) | (B!5 = C!4)))))) <=> (relation(A!3) & ((antisymmetric(A!3) | ![B: $i, C: $i] : ((~(in(ordered_pair(B, C), A!3) & in(ordered_pair(C, B), A!3))) | (B = C))) & ((~antisymmetric(A!3)) | (~((~(in(ordered_pair(B!5, C!4), A!3) & in(ordered_pair(C!4, B!5), A!3))) | (B!5 = C!4))))))),
% 0.20/0.39 inference(monotonicity,[status(thm)],[3])).
% 0.20/0.39 tff(5,plain,
% 0.20/0.39 ((relation(A!3) & ((antisymmetric(A!3) | ![B: $i, C: $i] : ((~(in(ordered_pair(B, C), A!3) & in(ordered_pair(C, B), A!3))) | (B = C))) & ((~antisymmetric(A!3)) | (~((~(in(ordered_pair(B!5, C!4), A!3) & in(ordered_pair(C!4, B!5), A!3))) | (B!5 = C!4)))))) <=> (relation(A!3) & (antisymmetric(A!3) | ![B: $i, C: $i] : ((~(in(ordered_pair(B, C), A!3) & in(ordered_pair(C, B), A!3))) | (B = C))) & ((~antisymmetric(A!3)) | (~((~(in(ordered_pair(B!5, C!4), A!3) & in(ordered_pair(C!4, B!5), A!3))) | (B!5 = C!4)))))),
% 0.20/0.39 inference(transitivity,[status(thm)],[4, 1])).
% 0.20/0.39 tff(6,plain,
% 0.20/0.39 ((~![A: $i] : ((~relation(A)) | (antisymmetric(A) <=> ![B: $i, C: $i] : ((~(in(ordered_pair(B, C), A) & in(ordered_pair(C, B), A))) | (B = C))))) <=> (~![A: $i] : ((~relation(A)) | (antisymmetric(A) <=> ![B: $i, C: $i] : ((~(in(ordered_pair(B, C), A) & in(ordered_pair(C, B), A))) | (B = C)))))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(7,plain,
% 0.20/0.39 ((~![A: $i] : (relation(A) => (antisymmetric(A) <=> ![B: $i, C: $i] : ((in(ordered_pair(B, C), A) & in(ordered_pair(C, B), A)) => (B = C))))) <=> (~![A: $i] : ((~relation(A)) | (antisymmetric(A) <=> ![B: $i, C: $i] : ((~(in(ordered_pair(B, C), A) & in(ordered_pair(C, B), A))) | (B = C)))))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(8,axiom,(~![A: $i] : (relation(A) => (antisymmetric(A) <=> ![B: $i, C: $i] : ((in(ordered_pair(B, C), A) & in(ordered_pair(C, B), A)) => (B = C))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','l3_wellord1')).
% 0.20/0.40 tff(9,plain,
% 0.20/0.40 (~![A: $i] : ((~relation(A)) | (antisymmetric(A) <=> ![B: $i, C: $i] : ((~(in(ordered_pair(B, C), A) & in(ordered_pair(C, B), A))) | (B = C))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[8, 7])).
% 0.20/0.40 tff(10,plain,
% 0.20/0.40 (~![A: $i] : ((~relation(A)) | (antisymmetric(A) <=> ![B: $i, C: $i] : ((~(in(ordered_pair(B, C), A) & in(ordered_pair(C, B), A))) | (B = C))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[9, 6])).
% 0.20/0.40 tff(11,plain,
% 0.20/0.40 (~![A: $i] : ((~relation(A)) | (antisymmetric(A) <=> ![B: $i, C: $i] : ((~(in(ordered_pair(B, C), A) & in(ordered_pair(C, B), A))) | (B = C))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[10, 6])).
% 0.20/0.40 tff(12,plain,
% 0.20/0.40 (~![A: $i] : ((~relation(A)) | (antisymmetric(A) <=> ![B: $i, C: $i] : ((~(in(ordered_pair(B, C), A) & in(ordered_pair(C, B), A))) | (B = C))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[11, 6])).
% 0.20/0.40 tff(13,plain,
% 0.20/0.40 (relation(A!3) & (antisymmetric(A!3) | ![B: $i, C: $i] : ((~(in(ordered_pair(B, C), A!3) & in(ordered_pair(C, B), A!3))) | (B = C))) & ((~antisymmetric(A!3)) | (~((~(in(ordered_pair(B!5, C!4), A!3) & in(ordered_pair(C!4, B!5), A!3))) | (B!5 = C!4))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[12, 5])).
% 0.20/0.40 tff(14,plain,
% 0.20/0.40 (relation(A!3)),
% 0.20/0.40 inference(and_elim,[status(thm)],[13])).
% 0.20/0.40 tff(15,plain,
% 0.20/0.40 (^[A: $i] : refl(((~relation(A)) | (relation_field(A) = set_union2(relation_dom(A), relation_rng(A)))) <=> ((~relation(A)) | (relation_field(A) = set_union2(relation_dom(A), relation_rng(A)))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(16,plain,
% 0.20/0.40 (![A: $i] : ((~relation(A)) | (relation_field(A) = set_union2(relation_dom(A), relation_rng(A)))) <=> ![A: $i] : ((~relation(A)) | (relation_field(A) = set_union2(relation_dom(A), relation_rng(A))))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[15])).
% 0.20/0.40 tff(17,plain,
% 0.20/0.40 (![A: $i] : ((~relation(A)) | (relation_field(A) = set_union2(relation_dom(A), relation_rng(A)))) <=> ![A: $i] : ((~relation(A)) | (relation_field(A) = set_union2(relation_dom(A), relation_rng(A))))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(18,plain,
% 0.20/0.40 (^[A: $i] : rewrite((relation(A) => (relation_field(A) = set_union2(relation_dom(A), relation_rng(A)))) <=> ((~relation(A)) | (relation_field(A) = set_union2(relation_dom(A), relation_rng(A)))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(19,plain,
% 0.20/0.40 (![A: $i] : (relation(A) => (relation_field(A) = set_union2(relation_dom(A), relation_rng(A)))) <=> ![A: $i] : ((~relation(A)) | (relation_field(A) = set_union2(relation_dom(A), relation_rng(A))))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[18])).
% 0.20/0.40 tff(20,axiom,(![A: $i] : (relation(A) => (relation_field(A) = set_union2(relation_dom(A), relation_rng(A))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d6_relat_1')).
% 0.20/0.40 tff(21,plain,
% 0.20/0.40 (![A: $i] : ((~relation(A)) | (relation_field(A) = set_union2(relation_dom(A), relation_rng(A))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[20, 19])).
% 0.20/0.40 tff(22,plain,
% 0.20/0.40 (![A: $i] : ((~relation(A)) | (relation_field(A) = set_union2(relation_dom(A), relation_rng(A))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[21, 17])).
% 0.20/0.40 tff(23,plain,(
% 0.20/0.40 ![A: $i] : ((~relation(A)) | (relation_field(A) = set_union2(relation_dom(A), relation_rng(A))))),
% 0.20/0.40 inference(skolemize,[status(sab)],[22])).
% 0.20/0.40 tff(24,plain,
% 0.20/0.40 (![A: $i] : ((~relation(A)) | (relation_field(A) = set_union2(relation_dom(A), relation_rng(A))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[23, 16])).
% 0.20/0.40 tff(25,plain,
% 0.20/0.40 (((~![A: $i] : ((~relation(A)) | (relation_field(A) = set_union2(relation_dom(A), relation_rng(A))))) | ((~relation(A!3)) | (relation_field(A!3) = set_union2(relation_dom(A!3), relation_rng(A!3))))) <=> ((~![A: $i] : ((~relation(A)) | (relation_field(A) = set_union2(relation_dom(A), relation_rng(A))))) | (~relation(A!3)) | (relation_field(A!3) = set_union2(relation_dom(A!3), relation_rng(A!3))))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(26,plain,
% 0.20/0.40 ((~![A: $i] : ((~relation(A)) | (relation_field(A) = set_union2(relation_dom(A), relation_rng(A))))) | ((~relation(A!3)) | (relation_field(A!3) = set_union2(relation_dom(A!3), relation_rng(A!3))))),
% 0.20/0.40 inference(quant_inst,[status(thm)],[])).
% 0.20/0.40 tff(27,plain,
% 0.20/0.40 ((~![A: $i] : ((~relation(A)) | (relation_field(A) = set_union2(relation_dom(A), relation_rng(A))))) | (~relation(A!3)) | (relation_field(A!3) = set_union2(relation_dom(A!3), relation_rng(A!3)))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[26, 25])).
% 0.20/0.40 tff(28,plain,
% 0.20/0.40 (relation_field(A!3) = set_union2(relation_dom(A!3), relation_rng(A!3))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[27, 24, 14])).
% 0.20/0.40 tff(29,plain,
% 0.20/0.40 (set_union2(relation_dom(A!3), relation_rng(A!3)) = relation_field(A!3)),
% 0.20/0.40 inference(symmetry,[status(thm)],[28])).
% 0.20/0.40 tff(30,plain,
% 0.20/0.40 (is_antisymmetric_in(A!3, set_union2(relation_dom(A!3), relation_rng(A!3))) <=> is_antisymmetric_in(A!3, relation_field(A!3))),
% 0.20/0.40 inference(monotonicity,[status(thm)],[29])).
% 0.20/0.40 tff(31,plain,
% 0.20/0.40 (is_antisymmetric_in(A!3, relation_field(A!3)) <=> is_antisymmetric_in(A!3, set_union2(relation_dom(A!3), relation_rng(A!3)))),
% 0.20/0.40 inference(symmetry,[status(thm)],[30])).
% 0.20/0.40 tff(32,plain,
% 0.20/0.40 ((~is_antisymmetric_in(A!3, relation_field(A!3))) <=> (~is_antisymmetric_in(A!3, set_union2(relation_dom(A!3), relation_rng(A!3))))),
% 0.20/0.40 inference(monotonicity,[status(thm)],[31])).
% 0.20/0.40 tff(33,assumption,(~((B!5 = C!4) | (~in(ordered_pair(B!5, C!4), A!3)) | (~in(ordered_pair(C!4, B!5), A!3)))), introduced(assumption)).
% 0.20/0.40 tff(34,plain,
% 0.20/0.40 (((B!5 = C!4) | (~in(ordered_pair(B!5, C!4), A!3)) | (~in(ordered_pair(C!4, B!5), A!3))) | in(ordered_pair(C!4, B!5), A!3)),
% 0.20/0.40 inference(tautology,[status(thm)],[])).
% 0.20/0.40 tff(35,plain,
% 0.20/0.40 (in(ordered_pair(C!4, B!5), A!3)),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[34, 33])).
% 0.20/0.40 tff(36,plain,
% 0.20/0.40 (((B!5 = C!4) | (~in(ordered_pair(B!5, C!4), A!3)) | (~in(ordered_pair(C!4, B!5), A!3))) | in(ordered_pair(B!5, C!4), A!3)),
% 0.20/0.40 inference(tautology,[status(thm)],[])).
% 0.20/0.40 tff(37,plain,
% 0.20/0.40 (in(ordered_pair(B!5, C!4), A!3)),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[36, 33])).
% 0.20/0.40 tff(38,plain,
% 0.20/0.40 (((B!5 = C!4) | (~in(ordered_pair(B!5, C!4), A!3)) | (~in(ordered_pair(C!4, B!5), A!3))) | (~(B!5 = C!4))),
% 0.20/0.40 inference(tautology,[status(thm)],[])).
% 0.20/0.40 tff(39,plain,
% 0.20/0.40 (~(B!5 = C!4)),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[38, 33])).
% 0.20/0.40 tff(40,plain,
% 0.20/0.40 ((~is_antisymmetric_in(A!3, set_union2(relation_dom(A!3), relation_rng(A!3)))) <=> (~is_antisymmetric_in(A!3, relation_field(A!3)))),
% 0.20/0.40 inference(monotonicity,[status(thm)],[30])).
% 0.20/0.40 tff(41,plain,
% 0.20/0.40 (in(C!4, set_union2(relation_dom(A!3), relation_rng(A!3))) <=> in(C!4, relation_field(A!3))),
% 0.20/0.40 inference(monotonicity,[status(thm)],[29])).
% 0.20/0.40 tff(42,plain,
% 0.20/0.40 (in(C!4, relation_field(A!3)) <=> in(C!4, set_union2(relation_dom(A!3), relation_rng(A!3)))),
% 0.20/0.40 inference(symmetry,[status(thm)],[41])).
% 0.20/0.40 tff(43,plain,
% 0.20/0.40 (^[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)))))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(44,plain,
% 0.20/0.40 (![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))))))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[43])).
% 0.20/0.40 tff(45,plain,
% 0.20/0.40 (^[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))))))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(46,plain,
% 0.20/0.40 (![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))))))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[45])).
% 0.20/0.40 tff(47,plain,
% 0.20/0.40 (![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)))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(48,plain,
% 0.20/0.40 (^[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)))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(49,plain,
% 0.20/0.40 (![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)))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[48])).
% 0.20/0.40 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/sandbox/benchmark/theBenchmark.p','t30_relat_1')).
% 0.20/0.40 tff(51,plain,
% 0.20/0.40 (![A: $i, B: $i, C: $i] : ((in(A, relation_field(C)) & in(B, relation_field(C))) | (~relation(C)) | (~in(ordered_pair(A, B), C)))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[50, 49])).
% 0.20/0.40 tff(52,plain,
% 0.20/0.40 (![A: $i, B: $i, C: $i] : ((in(A, relation_field(C)) & in(B, relation_field(C))) | (~relation(C)) | (~in(ordered_pair(A, B), C)))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[51, 47])).
% 0.20/0.40 tff(53,plain,(
% 0.20/0.40 ![A: $i, B: $i, C: $i] : ((in(A, relation_field(C)) & in(B, relation_field(C))) | (~relation(C)) | (~in(ordered_pair(A, B), C)))),
% 0.20/0.40 inference(skolemize,[status(sab)],[52])).
% 0.20/0.40 tff(54,plain,
% 0.20/0.40 (![A: $i, B: $i, C: $i] : ((~relation(C)) | (~in(ordered_pair(A, B), C)) | (~((~in(A, relation_field(C))) | (~in(B, relation_field(C))))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[53, 46])).
% 0.20/0.40 tff(55,plain,
% 0.20/0.40 (![A: $i, B: $i, C: $i] : ((~relation(C)) | (~in(ordered_pair(A, B), C)) | (~((~in(A, relation_field(C))) | (~in(B, relation_field(C))))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[54, 44])).
% 0.20/0.40 tff(56,assumption,(in(ordered_pair(C!4, B!5), A!3)), introduced(assumption)).
% 0.20/0.40 tff(57,plain,
% 0.20/0.40 (((~![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!3)) | (~in(ordered_pair(C!4, B!5), A!3)) | (~((~in(C!4, relation_field(A!3))) | (~in(B!5, relation_field(A!3))))))) <=> ((~![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!3)) | (~in(ordered_pair(C!4, B!5), A!3)) | (~((~in(C!4, relation_field(A!3))) | (~in(B!5, relation_field(A!3))))))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(58,plain,
% 0.20/0.40 ((~![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!3)) | (~in(ordered_pair(C!4, B!5), A!3)) | (~((~in(C!4, relation_field(A!3))) | (~in(B!5, relation_field(A!3))))))),
% 0.20/0.40 inference(quant_inst,[status(thm)],[])).
% 0.20/0.40 tff(59,plain,
% 0.20/0.40 ((~![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!3)) | (~in(ordered_pair(C!4, B!5), A!3)) | (~((~in(C!4, relation_field(A!3))) | (~in(B!5, relation_field(A!3)))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[58, 57])).
% 0.20/0.40 tff(60,plain,
% 0.20/0.40 (~((~in(C!4, relation_field(A!3))) | (~in(B!5, relation_field(A!3))))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[59, 14, 56, 55])).
% 0.20/0.40 tff(61,plain,
% 0.20/0.40 (((~in(C!4, relation_field(A!3))) | (~in(B!5, relation_field(A!3)))) | in(C!4, relation_field(A!3))),
% 0.20/0.40 inference(tautology,[status(thm)],[])).
% 0.20/0.40 tff(62,plain,
% 0.20/0.40 (in(C!4, relation_field(A!3))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[61, 60])).
% 0.20/0.40 tff(63,plain,
% 0.20/0.40 (in(C!4, set_union2(relation_dom(A!3), relation_rng(A!3)))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[62, 42])).
% 0.20/0.40 tff(64,plain,
% 0.20/0.40 (in(B!5, set_union2(relation_dom(A!3), relation_rng(A!3))) <=> in(B!5, relation_field(A!3))),
% 0.20/0.40 inference(monotonicity,[status(thm)],[29])).
% 0.20/0.40 tff(65,plain,
% 0.20/0.40 (in(B!5, relation_field(A!3)) <=> in(B!5, set_union2(relation_dom(A!3), relation_rng(A!3)))),
% 0.20/0.40 inference(symmetry,[status(thm)],[64])).
% 0.20/0.40 tff(66,plain,
% 0.20/0.40 (((~in(C!4, relation_field(A!3))) | (~in(B!5, relation_field(A!3)))) | in(B!5, relation_field(A!3))),
% 0.20/0.40 inference(tautology,[status(thm)],[])).
% 0.20/0.40 tff(67,plain,
% 0.20/0.40 (in(B!5, relation_field(A!3))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[66, 60])).
% 0.20/0.40 tff(68,plain,
% 0.20/0.40 (in(B!5, set_union2(relation_dom(A!3), relation_rng(A!3)))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[67, 65])).
% 0.20/0.40 tff(69,assumption,(![C: $i, D: $i] : ((C = D) | (~in(ordered_pair(C, D), A!3)) | (~in(ordered_pair(D, C), A!3)) | (~in(C, set_union2(relation_dom(A!3), relation_rng(A!3)))) | (~in(D, set_union2(relation_dom(A!3), relation_rng(A!3)))))), introduced(assumption)).
% 0.20/0.40 tff(70,assumption,(in(ordered_pair(B!5, C!4), A!3)), introduced(assumption)).
% 0.20/0.40 tff(71,assumption,(~(B!5 = C!4)), introduced(assumption)).
% 0.20/0.40 tff(72,plain,
% 0.20/0.40 (((~![C: $i, D: $i] : ((C = D) | (~in(ordered_pair(C, D), A!3)) | (~in(ordered_pair(D, C), A!3)) | (~in(C, set_union2(relation_dom(A!3), relation_rng(A!3)))) | (~in(D, set_union2(relation_dom(A!3), relation_rng(A!3)))))) | ((B!5 = C!4) | (~in(ordered_pair(B!5, C!4), A!3)) | (~in(ordered_pair(C!4, B!5), A!3)) | (~in(B!5, set_union2(relation_dom(A!3), relation_rng(A!3)))) | (~in(C!4, set_union2(relation_dom(A!3), relation_rng(A!3)))))) <=> ((~![C: $i, D: $i] : ((C = D) | (~in(ordered_pair(C, D), A!3)) | (~in(ordered_pair(D, C), A!3)) | (~in(C, set_union2(relation_dom(A!3), relation_rng(A!3)))) | (~in(D, set_union2(relation_dom(A!3), relation_rng(A!3)))))) | (B!5 = C!4) | (~in(ordered_pair(B!5, C!4), A!3)) | (~in(ordered_pair(C!4, B!5), A!3)) | (~in(B!5, set_union2(relation_dom(A!3), relation_rng(A!3)))) | (~in(C!4, set_union2(relation_dom(A!3), relation_rng(A!3)))))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(73,plain,
% 0.20/0.40 ((~![C: $i, D: $i] : ((C = D) | (~in(ordered_pair(C, D), A!3)) | (~in(ordered_pair(D, C), A!3)) | (~in(C, set_union2(relation_dom(A!3), relation_rng(A!3)))) | (~in(D, set_union2(relation_dom(A!3), relation_rng(A!3)))))) | ((B!5 = C!4) | (~in(ordered_pair(B!5, C!4), A!3)) | (~in(ordered_pair(C!4, B!5), A!3)) | (~in(B!5, set_union2(relation_dom(A!3), relation_rng(A!3)))) | (~in(C!4, set_union2(relation_dom(A!3), relation_rng(A!3)))))),
% 0.20/0.40 inference(quant_inst,[status(thm)],[])).
% 0.20/0.40 tff(74,plain,
% 0.20/0.40 ((~![C: $i, D: $i] : ((C = D) | (~in(ordered_pair(C, D), A!3)) | (~in(ordered_pair(D, C), A!3)) | (~in(C, set_union2(relation_dom(A!3), relation_rng(A!3)))) | (~in(D, set_union2(relation_dom(A!3), relation_rng(A!3)))))) | (B!5 = C!4) | (~in(ordered_pair(B!5, C!4), A!3)) | (~in(ordered_pair(C!4, B!5), A!3)) | (~in(B!5, set_union2(relation_dom(A!3), relation_rng(A!3)))) | (~in(C!4, set_union2(relation_dom(A!3), relation_rng(A!3))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[73, 72])).
% 0.20/0.41 tff(75,plain,
% 0.20/0.41 ($false),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[74, 71, 70, 56, 69, 68, 63])).
% 0.20/0.41 tff(76,plain,((~![C: $i, D: $i] : ((C = D) | (~in(ordered_pair(C, D), A!3)) | (~in(ordered_pair(D, C), A!3)) | (~in(C, set_union2(relation_dom(A!3), relation_rng(A!3)))) | (~in(D, set_union2(relation_dom(A!3), relation_rng(A!3)))))) | (B!5 = C!4) | (~in(ordered_pair(B!5, C!4), A!3)) | (~in(ordered_pair(C!4, B!5), A!3))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.41 tff(77,plain,
% 0.20/0.41 (~![C: $i, D: $i] : ((C = D) | (~in(ordered_pair(C, D), A!3)) | (~in(ordered_pair(D, C), A!3)) | (~in(C, set_union2(relation_dom(A!3), relation_rng(A!3)))) | (~in(D, set_union2(relation_dom(A!3), relation_rng(A!3)))))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[76, 39, 37, 35])).
% 0.20/0.41 tff(78,plain,
% 0.20/0.41 (^[A: $i] : refl(((~relation(A)) | ![B: $i] : (~((~((~is_antisymmetric_in(A, B)) | ![C: $i, D: $i] : ((C = D) | (~in(C, B)) | (~in(D, B)) | (~in(ordered_pair(C, D), A)) | (~in(ordered_pair(D, C), A))))) | (~(is_antisymmetric_in(A, B) | (~((tptp_fun_C_1(B, A) = tptp_fun_D_0(B, A)) | (~in(tptp_fun_C_1(B, A), B)) | (~in(tptp_fun_D_0(B, A), B)) | (~in(ordered_pair(tptp_fun_C_1(B, A), tptp_fun_D_0(B, A)), A)) | (~in(ordered_pair(tptp_fun_D_0(B, A), tptp_fun_C_1(B, A)), A))))))))) <=> ((~relation(A)) | ![B: $i] : (~((~((~is_antisymmetric_in(A, B)) | ![C: $i, D: $i] : ((C = D) | (~in(C, B)) | (~in(D, B)) | (~in(ordered_pair(C, D), A)) | (~in(ordered_pair(D, C), A))))) | (~(is_antisymmetric_in(A, B) | (~((tptp_fun_C_1(B, A) = tptp_fun_D_0(B, A)) | (~in(tptp_fun_C_1(B, A), B)) | (~in(tptp_fun_D_0(B, A), B)) | (~in(ordered_pair(tptp_fun_C_1(B, A), tptp_fun_D_0(B, A)), A)) | (~in(ordered_pair(tptp_fun_D_0(B, A), tptp_fun_C_1(B, A)), A))))))))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(79,plain,
% 0.20/0.41 (![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~is_antisymmetric_in(A, B)) | ![C: $i, D: $i] : ((C = D) | (~in(C, B)) | (~in(D, B)) | (~in(ordered_pair(C, D), A)) | (~in(ordered_pair(D, C), A))))) | (~(is_antisymmetric_in(A, B) | (~((tptp_fun_C_1(B, A) = tptp_fun_D_0(B, A)) | (~in(tptp_fun_C_1(B, A), B)) | (~in(tptp_fun_D_0(B, A), B)) | (~in(ordered_pair(tptp_fun_C_1(B, A), tptp_fun_D_0(B, A)), A)) | (~in(ordered_pair(tptp_fun_D_0(B, A), tptp_fun_C_1(B, A)), A))))))))) <=> ![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~is_antisymmetric_in(A, B)) | ![C: $i, D: $i] : ((C = D) | (~in(C, B)) | (~in(D, B)) | (~in(ordered_pair(C, D), A)) | (~in(ordered_pair(D, C), A))))) | (~(is_antisymmetric_in(A, B) | (~((tptp_fun_C_1(B, A) = tptp_fun_D_0(B, A)) | (~in(tptp_fun_C_1(B, A), B)) | (~in(tptp_fun_D_0(B, A), B)) | (~in(ordered_pair(tptp_fun_C_1(B, A), tptp_fun_D_0(B, A)), A)) | (~in(ordered_pair(tptp_fun_D_0(B, A), tptp_fun_C_1(B, A)), A)))))))))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[78])).
% 0.20/0.41 tff(80,plain,
% 0.20/0.41 (^[A: $i] : rewrite(((~relation(A)) | ![B: $i] : (~((~((~is_antisymmetric_in(A, B)) | ![C: $i, D: $i] : ((C = D) | (~in(C, B)) | (~in(D, B)) | (~in(ordered_pair(C, D), A)) | (~in(ordered_pair(D, C), A))))) | (~(is_antisymmetric_in(A, B) | (~((tptp_fun_C_1(B, A) = tptp_fun_D_0(B, A)) | (~in(tptp_fun_C_1(B, A), B)) | (~in(tptp_fun_D_0(B, A), B)) | (~in(ordered_pair(tptp_fun_C_1(B, A), tptp_fun_D_0(B, A)), A)) | (~in(ordered_pair(tptp_fun_D_0(B, A), tptp_fun_C_1(B, A)), A))))))))) <=> ((~relation(A)) | ![B: $i] : (~((~((~is_antisymmetric_in(A, B)) | ![C: $i, D: $i] : ((C = D) | (~in(C, B)) | (~in(D, B)) | (~in(ordered_pair(C, D), A)) | (~in(ordered_pair(D, C), A))))) | (~(is_antisymmetric_in(A, B) | (~((tptp_fun_C_1(B, A) = tptp_fun_D_0(B, A)) | (~in(tptp_fun_C_1(B, A), B)) | (~in(tptp_fun_D_0(B, A), B)) | (~in(ordered_pair(tptp_fun_C_1(B, A), tptp_fun_D_0(B, A)), A)) | (~in(ordered_pair(tptp_fun_D_0(B, A), tptp_fun_C_1(B, A)), A))))))))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(81,plain,
% 0.20/0.41 (![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~is_antisymmetric_in(A, B)) | ![C: $i, D: $i] : ((C = D) | (~in(C, B)) | (~in(D, B)) | (~in(ordered_pair(C, D), A)) | (~in(ordered_pair(D, C), A))))) | (~(is_antisymmetric_in(A, B) | (~((tptp_fun_C_1(B, A) = tptp_fun_D_0(B, A)) | (~in(tptp_fun_C_1(B, A), B)) | (~in(tptp_fun_D_0(B, A), B)) | (~in(ordered_pair(tptp_fun_C_1(B, A), tptp_fun_D_0(B, A)), A)) | (~in(ordered_pair(tptp_fun_D_0(B, A), tptp_fun_C_1(B, A)), A))))))))) <=> ![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~is_antisymmetric_in(A, B)) | ![C: $i, D: $i] : ((C = D) | (~in(C, B)) | (~in(D, B)) | (~in(ordered_pair(C, D), A)) | (~in(ordered_pair(D, C), A))))) | (~(is_antisymmetric_in(A, B) | (~((tptp_fun_C_1(B, A) = tptp_fun_D_0(B, A)) | (~in(tptp_fun_C_1(B, A), B)) | (~in(tptp_fun_D_0(B, A), B)) | (~in(ordered_pair(tptp_fun_C_1(B, A), tptp_fun_D_0(B, A)), A)) | (~in(ordered_pair(tptp_fun_D_0(B, A), tptp_fun_C_1(B, A)), A)))))))))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[80])).
% 0.20/0.41 tff(82,plain,
% 0.20/0.41 (![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~is_antisymmetric_in(A, B)) | ![C: $i, D: $i] : ((C = D) | (~in(C, B)) | (~in(D, B)) | (~in(ordered_pair(C, D), A)) | (~in(ordered_pair(D, C), A))))) | (~(is_antisymmetric_in(A, B) | (~((tptp_fun_C_1(B, A) = tptp_fun_D_0(B, A)) | (~in(tptp_fun_C_1(B, A), B)) | (~in(tptp_fun_D_0(B, A), B)) | (~in(ordered_pair(tptp_fun_C_1(B, A), tptp_fun_D_0(B, A)), A)) | (~in(ordered_pair(tptp_fun_D_0(B, A), tptp_fun_C_1(B, A)), A))))))))) <=> ![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~is_antisymmetric_in(A, B)) | ![C: $i, D: $i] : ((C = D) | (~in(C, B)) | (~in(D, B)) | (~in(ordered_pair(C, D), A)) | (~in(ordered_pair(D, C), A))))) | (~(is_antisymmetric_in(A, B) | (~((tptp_fun_C_1(B, A) = tptp_fun_D_0(B, A)) | (~in(tptp_fun_C_1(B, A), B)) | (~in(tptp_fun_D_0(B, A), B)) | (~in(ordered_pair(tptp_fun_C_1(B, A), tptp_fun_D_0(B, A)), A)) | (~in(ordered_pair(tptp_fun_D_0(B, A), tptp_fun_C_1(B, A)), A)))))))))),
% 0.20/0.41 inference(transitivity,[status(thm)],[81, 79])).
% 0.20/0.41 tff(83,plain,
% 0.20/0.41 (^[A: $i] : rewrite(((~relation(A)) | ![B: $i] : (((~is_antisymmetric_in(A, B)) | ![C: $i, D: $i] : ((~(in(C, B) & in(D, B) & in(ordered_pair(C, D), A) & in(ordered_pair(D, C), A))) | (C = D))) & (is_antisymmetric_in(A, B) | (~((~(in(tptp_fun_C_1(B, A), B) & in(tptp_fun_D_0(B, A), B) & in(ordered_pair(tptp_fun_C_1(B, A), tptp_fun_D_0(B, A)), A) & in(ordered_pair(tptp_fun_D_0(B, A), tptp_fun_C_1(B, A)), A))) | (tptp_fun_C_1(B, A) = tptp_fun_D_0(B, A))))))) <=> ((~relation(A)) | ![B: $i] : (~((~((~is_antisymmetric_in(A, B)) | ![C: $i, D: $i] : ((C = D) | (~in(C, B)) | (~in(D, B)) | (~in(ordered_pair(C, D), A)) | (~in(ordered_pair(D, C), A))))) | (~(is_antisymmetric_in(A, B) | (~((tptp_fun_C_1(B, A) = tptp_fun_D_0(B, A)) | (~in(tptp_fun_C_1(B, A), B)) | (~in(tptp_fun_D_0(B, A), B)) | (~in(ordered_pair(tptp_fun_C_1(B, A), tptp_fun_D_0(B, A)), A)) | (~in(ordered_pair(tptp_fun_D_0(B, A), tptp_fun_C_1(B, A)), A))))))))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(84,plain,
% 0.20/0.41 (![A: $i] : ((~relation(A)) | ![B: $i] : (((~is_antisymmetric_in(A, B)) | ![C: $i, D: $i] : ((~(in(C, B) & in(D, B) & in(ordered_pair(C, D), A) & in(ordered_pair(D, C), A))) | (C = D))) & (is_antisymmetric_in(A, B) | (~((~(in(tptp_fun_C_1(B, A), B) & in(tptp_fun_D_0(B, A), B) & in(ordered_pair(tptp_fun_C_1(B, A), tptp_fun_D_0(B, A)), A) & in(ordered_pair(tptp_fun_D_0(B, A), tptp_fun_C_1(B, A)), A))) | (tptp_fun_C_1(B, A) = tptp_fun_D_0(B, A))))))) <=> ![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~is_antisymmetric_in(A, B)) | ![C: $i, D: $i] : ((C = D) | (~in(C, B)) | (~in(D, B)) | (~in(ordered_pair(C, D), A)) | (~in(ordered_pair(D, C), A))))) | (~(is_antisymmetric_in(A, B) | (~((tptp_fun_C_1(B, A) = tptp_fun_D_0(B, A)) | (~in(tptp_fun_C_1(B, A), B)) | (~in(tptp_fun_D_0(B, A), B)) | (~in(ordered_pair(tptp_fun_C_1(B, A), tptp_fun_D_0(B, A)), A)) | (~in(ordered_pair(tptp_fun_D_0(B, A), tptp_fun_C_1(B, A)), A)))))))))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[83])).
% 0.20/0.41 tff(85,plain,
% 0.20/0.41 (![A: $i] : ((~relation(A)) | ![B: $i] : (is_antisymmetric_in(A, B) <=> ![C: $i, D: $i] : ((~(in(C, B) & in(D, B) & in(ordered_pair(C, D), A) & in(ordered_pair(D, C), A))) | (C = D)))) <=> ![A: $i] : ((~relation(A)) | ![B: $i] : (is_antisymmetric_in(A, B) <=> ![C: $i, D: $i] : ((~(in(C, B) & in(D, B) & in(ordered_pair(C, D), A) & in(ordered_pair(D, C), A))) | (C = D))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(86,plain,
% 0.20/0.41 (^[A: $i] : trans(monotonicity(quant_intro(proof_bind(^[B: $i] : rewrite((is_antisymmetric_in(A, B) <=> ![C: $i, D: $i] : ((((in(C, B) & in(D, B)) & in(ordered_pair(C, D), A)) & in(ordered_pair(D, C), A)) => (C = D))) <=> (is_antisymmetric_in(A, B) <=> ![C: $i, D: $i] : ((~(in(C, B) & in(D, B) & in(ordered_pair(C, D), A) & in(ordered_pair(D, C), A))) | (C = D))))), (![B: $i] : (is_antisymmetric_in(A, B) <=> ![C: $i, D: $i] : ((((in(C, B) & in(D, B)) & in(ordered_pair(C, D), A)) & in(ordered_pair(D, C), A)) => (C = D))) <=> ![B: $i] : (is_antisymmetric_in(A, B) <=> ![C: $i, D: $i] : ((~(in(C, B) & in(D, B) & in(ordered_pair(C, D), A) & in(ordered_pair(D, C), A))) | (C = D))))), ((relation(A) => ![B: $i] : (is_antisymmetric_in(A, B) <=> ![C: $i, D: $i] : ((((in(C, B) & in(D, B)) & in(ordered_pair(C, D), A)) & in(ordered_pair(D, C), A)) => (C = D)))) <=> (relation(A) => ![B: $i] : (is_antisymmetric_in(A, B) <=> ![C: $i, D: $i] : ((~(in(C, B) & in(D, B) & in(ordered_pair(C, D), A) & in(ordered_pair(D, C), A))) | (C = D)))))), rewrite((relation(A) => ![B: $i] : (is_antisymmetric_in(A, B) <=> ![C: $i, D: $i] : ((~(in(C, B) & in(D, B) & in(ordered_pair(C, D), A) & in(ordered_pair(D, C), A))) | (C = D)))) <=> ((~relation(A)) | ![B: $i] : (is_antisymmetric_in(A, B) <=> ![C: $i, D: $i] : ((~(in(C, B) & in(D, B) & in(ordered_pair(C, D), A) & in(ordered_pair(D, C), A))) | (C = D))))), ((relation(A) => ![B: $i] : (is_antisymmetric_in(A, B) <=> ![C: $i, D: $i] : ((((in(C, B) & in(D, B)) & in(ordered_pair(C, D), A)) & in(ordered_pair(D, C), A)) => (C = D)))) <=> ((~relation(A)) | ![B: $i] : (is_antisymmetric_in(A, B) <=> ![C: $i, D: $i] : ((~(in(C, B) & in(D, B) & in(ordered_pair(C, D), A) & in(ordered_pair(D, C), A))) | (C = D))))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(87,plain,
% 0.20/0.41 (![A: $i] : (relation(A) => ![B: $i] : (is_antisymmetric_in(A, B) <=> ![C: $i, D: $i] : ((((in(C, B) & in(D, B)) & in(ordered_pair(C, D), A)) & in(ordered_pair(D, C), A)) => (C = D)))) <=> ![A: $i] : ((~relation(A)) | ![B: $i] : (is_antisymmetric_in(A, B) <=> ![C: $i, D: $i] : ((~(in(C, B) & in(D, B) & in(ordered_pair(C, D), A) & in(ordered_pair(D, C), A))) | (C = D))))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[86])).
% 0.20/0.41 tff(88,axiom,(![A: $i] : (relation(A) => ![B: $i] : (is_antisymmetric_in(A, B) <=> ![C: $i, D: $i] : ((((in(C, B) & in(D, B)) & in(ordered_pair(C, D), A)) & in(ordered_pair(D, C), A)) => (C = D))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d4_relat_2')).
% 0.20/0.41 tff(89,plain,
% 0.20/0.41 (![A: $i] : ((~relation(A)) | ![B: $i] : (is_antisymmetric_in(A, B) <=> ![C: $i, D: $i] : ((~(in(C, B) & in(D, B) & in(ordered_pair(C, D), A) & in(ordered_pair(D, C), A))) | (C = D))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[88, 87])).
% 0.20/0.41 tff(90,plain,
% 0.20/0.41 (![A: $i] : ((~relation(A)) | ![B: $i] : (is_antisymmetric_in(A, B) <=> ![C: $i, D: $i] : ((~(in(C, B) & in(D, B) & in(ordered_pair(C, D), A) & in(ordered_pair(D, C), A))) | (C = D))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[89, 85])).
% 0.20/0.41 tff(91,plain,(
% 0.20/0.41 ![A: $i] : ((~relation(A)) | ![B: $i] : (((~is_antisymmetric_in(A, B)) | ![C: $i, D: $i] : ((~(in(C, B) & in(D, B) & in(ordered_pair(C, D), A) & in(ordered_pair(D, C), A))) | (C = D))) & (is_antisymmetric_in(A, B) | (~((~(in(tptp_fun_C_1(B, A), B) & in(tptp_fun_D_0(B, A), B) & in(ordered_pair(tptp_fun_C_1(B, A), tptp_fun_D_0(B, A)), A) & in(ordered_pair(tptp_fun_D_0(B, A), tptp_fun_C_1(B, A)), A))) | (tptp_fun_C_1(B, A) = tptp_fun_D_0(B, A)))))))),
% 0.20/0.41 inference(skolemize,[status(sab)],[90])).
% 0.20/0.41 tff(92,plain,
% 0.20/0.41 (![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~is_antisymmetric_in(A, B)) | ![C: $i, D: $i] : ((C = D) | (~in(C, B)) | (~in(D, B)) | (~in(ordered_pair(C, D), A)) | (~in(ordered_pair(D, C), A))))) | (~(is_antisymmetric_in(A, B) | (~((tptp_fun_C_1(B, A) = tptp_fun_D_0(B, A)) | (~in(tptp_fun_C_1(B, A), B)) | (~in(tptp_fun_D_0(B, A), B)) | (~in(ordered_pair(tptp_fun_C_1(B, A), tptp_fun_D_0(B, A)), A)) | (~in(ordered_pair(tptp_fun_D_0(B, A), tptp_fun_C_1(B, A)), A)))))))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[91, 84])).
% 0.20/0.41 tff(93,plain,
% 0.20/0.41 (![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~is_antisymmetric_in(A, B)) | ![C: $i, D: $i] : ((C = D) | (~in(C, B)) | (~in(D, B)) | (~in(ordered_pair(C, D), A)) | (~in(ordered_pair(D, C), A))))) | (~(is_antisymmetric_in(A, B) | (~((tptp_fun_C_1(B, A) = tptp_fun_D_0(B, A)) | (~in(tptp_fun_C_1(B, A), B)) | (~in(tptp_fun_D_0(B, A), B)) | (~in(ordered_pair(tptp_fun_C_1(B, A), tptp_fun_D_0(B, A)), A)) | (~in(ordered_pair(tptp_fun_D_0(B, A), tptp_fun_C_1(B, A)), A)))))))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[92, 82])).
% 0.20/0.41 tff(94,plain,
% 0.20/0.41 (((~![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~is_antisymmetric_in(A, B)) | ![C: $i, D: $i] : ((C = D) | (~in(C, B)) | (~in(D, B)) | (~in(ordered_pair(C, D), A)) | (~in(ordered_pair(D, C), A))))) | (~(is_antisymmetric_in(A, B) | (~((tptp_fun_C_1(B, A) = tptp_fun_D_0(B, A)) | (~in(tptp_fun_C_1(B, A), B)) | (~in(tptp_fun_D_0(B, A), B)) | (~in(ordered_pair(tptp_fun_C_1(B, A), tptp_fun_D_0(B, A)), A)) | (~in(ordered_pair(tptp_fun_D_0(B, A), tptp_fun_C_1(B, A)), A)))))))))) | ((~relation(A!3)) | ![B: $i] : (~((~((~is_antisymmetric_in(A!3, B)) | ![C: $i, D: $i] : ((C = D) | (~in(C, B)) | (~in(D, B)) | (~in(ordered_pair(C, D), A!3)) | (~in(ordered_pair(D, C), A!3))))) | (~(is_antisymmetric_in(A!3, B) | (~((~in(ordered_pair(tptp_fun_D_0(B, A!3), tptp_fun_C_1(B, A!3)), A!3)) | (~in(ordered_pair(tptp_fun_C_1(B, A!3), tptp_fun_D_0(B, A!3)), A!3)) | (~in(tptp_fun_D_0(B, A!3), B)) | (~in(tptp_fun_C_1(B, A!3), B)) | (tptp_fun_C_1(B, A!3) = tptp_fun_D_0(B, A!3)))))))))) <=> ((~![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~is_antisymmetric_in(A, B)) | ![C: $i, D: $i] : ((C = D) | (~in(C, B)) | (~in(D, B)) | (~in(ordered_pair(C, D), A)) | (~in(ordered_pair(D, C), A))))) | (~(is_antisymmetric_in(A, B) | (~((tptp_fun_C_1(B, A) = tptp_fun_D_0(B, A)) | (~in(tptp_fun_C_1(B, A), B)) | (~in(tptp_fun_D_0(B, A), B)) | (~in(ordered_pair(tptp_fun_C_1(B, A), tptp_fun_D_0(B, A)), A)) | (~in(ordered_pair(tptp_fun_D_0(B, A), tptp_fun_C_1(B, A)), A)))))))))) | (~relation(A!3)) | ![B: $i] : (~((~((~is_antisymmetric_in(A!3, B)) | ![C: $i, D: $i] : ((C = D) | (~in(C, B)) | (~in(D, B)) | (~in(ordered_pair(C, D), A!3)) | (~in(ordered_pair(D, C), A!3))))) | (~(is_antisymmetric_in(A!3, B) | (~((~in(ordered_pair(tptp_fun_D_0(B, A!3), tptp_fun_C_1(B, A!3)), A!3)) | (~in(ordered_pair(tptp_fun_C_1(B, A!3), tptp_fun_D_0(B, A!3)), A!3)) | (~in(tptp_fun_D_0(B, A!3), B)) | (~in(tptp_fun_C_1(B, A!3), B)) | (tptp_fun_C_1(B, A!3) = tptp_fun_D_0(B, A!3)))))))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(95,plain,
% 0.20/0.41 (((~relation(A!3)) | ![B: $i] : (~((~((~is_antisymmetric_in(A!3, B)) | ![C: $i, D: $i] : ((C = D) | (~in(C, B)) | (~in(D, B)) | (~in(ordered_pair(C, D), A!3)) | (~in(ordered_pair(D, C), A!3))))) | (~(is_antisymmetric_in(A!3, B) | (~((tptp_fun_C_1(B, A!3) = tptp_fun_D_0(B, A!3)) | (~in(tptp_fun_C_1(B, A!3), B)) | (~in(tptp_fun_D_0(B, A!3), B)) | (~in(ordered_pair(tptp_fun_C_1(B, A!3), tptp_fun_D_0(B, A!3)), A!3)) | (~in(ordered_pair(tptp_fun_D_0(B, A!3), tptp_fun_C_1(B, A!3)), A!3))))))))) <=> ((~relation(A!3)) | ![B: $i] : (~((~((~is_antisymmetric_in(A!3, B)) | ![C: $i, D: $i] : ((C = D) | (~in(C, B)) | (~in(D, B)) | (~in(ordered_pair(C, D), A!3)) | (~in(ordered_pair(D, C), A!3))))) | (~(is_antisymmetric_in(A!3, B) | (~((~in(ordered_pair(tptp_fun_D_0(B, A!3), tptp_fun_C_1(B, A!3)), A!3)) | (~in(ordered_pair(tptp_fun_C_1(B, A!3), tptp_fun_D_0(B, A!3)), A!3)) | (~in(tptp_fun_D_0(B, A!3), B)) | (~in(tptp_fun_C_1(B, A!3), B)) | (tptp_fun_C_1(B, A!3) = tptp_fun_D_0(B, A!3)))))))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(96,plain,
% 0.20/0.41 (((~![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~is_antisymmetric_in(A, B)) | ![C: $i, D: $i] : ((C = D) | (~in(C, B)) | (~in(D, B)) | (~in(ordered_pair(C, D), A)) | (~in(ordered_pair(D, C), A))))) | (~(is_antisymmetric_in(A, B) | (~((tptp_fun_C_1(B, A) = tptp_fun_D_0(B, A)) | (~in(tptp_fun_C_1(B, A), B)) | (~in(tptp_fun_D_0(B, A), B)) | (~in(ordered_pair(tptp_fun_C_1(B, A), tptp_fun_D_0(B, A)), A)) | (~in(ordered_pair(tptp_fun_D_0(B, A), tptp_fun_C_1(B, A)), A)))))))))) | ((~relation(A!3)) | ![B: $i] : (~((~((~is_antisymmetric_in(A!3, B)) | ![C: $i, D: $i] : ((C = D) | (~in(C, B)) | (~in(D, B)) | (~in(ordered_pair(C, D), A!3)) | (~in(ordered_pair(D, C), A!3))))) | (~(is_antisymmetric_in(A!3, B) | (~((tptp_fun_C_1(B, A!3) = tptp_fun_D_0(B, A!3)) | (~in(tptp_fun_C_1(B, A!3), B)) | (~in(tptp_fun_D_0(B, A!3), B)) | (~in(ordered_pair(tptp_fun_C_1(B, A!3), tptp_fun_D_0(B, A!3)), A!3)) | (~in(ordered_pair(tptp_fun_D_0(B, A!3), tptp_fun_C_1(B, A!3)), A!3)))))))))) <=> ((~![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~is_antisymmetric_in(A, B)) | ![C: $i, D: $i] : ((C = D) | (~in(C, B)) | (~in(D, B)) | (~in(ordered_pair(C, D), A)) | (~in(ordered_pair(D, C), A))))) | (~(is_antisymmetric_in(A, B) | (~((tptp_fun_C_1(B, A) = tptp_fun_D_0(B, A)) | (~in(tptp_fun_C_1(B, A), B)) | (~in(tptp_fun_D_0(B, A), B)) | (~in(ordered_pair(tptp_fun_C_1(B, A), tptp_fun_D_0(B, A)), A)) | (~in(ordered_pair(tptp_fun_D_0(B, A), tptp_fun_C_1(B, A)), A)))))))))) | ((~relation(A!3)) | ![B: $i] : (~((~((~is_antisymmetric_in(A!3, B)) | ![C: $i, D: $i] : ((C = D) | (~in(C, B)) | (~in(D, B)) | (~in(ordered_pair(C, D), A!3)) | (~in(ordered_pair(D, C), A!3))))) | (~(is_antisymmetric_in(A!3, B) | (~((~in(ordered_pair(tptp_fun_D_0(B, A!3), tptp_fun_C_1(B, A!3)), A!3)) | (~in(ordered_pair(tptp_fun_C_1(B, A!3), tptp_fun_D_0(B, A!3)), A!3)) | (~in(tptp_fun_D_0(B, A!3), B)) | (~in(tptp_fun_C_1(B, A!3), B)) | (tptp_fun_C_1(B, A!3) = tptp_fun_D_0(B, A!3))))))))))),
% 0.20/0.41 inference(monotonicity,[status(thm)],[95])).
% 0.20/0.41 tff(97,plain,
% 0.20/0.41 (((~![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~is_antisymmetric_in(A, B)) | ![C: $i, D: $i] : ((C = D) | (~in(C, B)) | (~in(D, B)) | (~in(ordered_pair(C, D), A)) | (~in(ordered_pair(D, C), A))))) | (~(is_antisymmetric_in(A, B) | (~((tptp_fun_C_1(B, A) = tptp_fun_D_0(B, A)) | (~in(tptp_fun_C_1(B, A), B)) | (~in(tptp_fun_D_0(B, A), B)) | (~in(ordered_pair(tptp_fun_C_1(B, A), tptp_fun_D_0(B, A)), A)) | (~in(ordered_pair(tptp_fun_D_0(B, A), tptp_fun_C_1(B, A)), A)))))))))) | ((~relation(A!3)) | ![B: $i] : (~((~((~is_antisymmetric_in(A!3, B)) | ![C: $i, D: $i] : ((C = D) | (~in(C, B)) | (~in(D, B)) | (~in(ordered_pair(C, D), A!3)) | (~in(ordered_pair(D, C), A!3))))) | (~(is_antisymmetric_in(A!3, B) | (~((tptp_fun_C_1(B, A!3) = tptp_fun_D_0(B, A!3)) | (~in(tptp_fun_C_1(B, A!3), B)) | (~in(tptp_fun_D_0(B, A!3), B)) | (~in(ordered_pair(tptp_fun_C_1(B, A!3), tptp_fun_D_0(B, A!3)), A!3)) | (~in(ordered_pair(tptp_fun_D_0(B, A!3), tptp_fun_C_1(B, A!3)), A!3)))))))))) <=> ((~![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~is_antisymmetric_in(A, B)) | ![C: $i, D: $i] : ((C = D) | (~in(C, B)) | (~in(D, B)) | (~in(ordered_pair(C, D), A)) | (~in(ordered_pair(D, C), A))))) | (~(is_antisymmetric_in(A, B) | (~((tptp_fun_C_1(B, A) = tptp_fun_D_0(B, A)) | (~in(tptp_fun_C_1(B, A), B)) | (~in(tptp_fun_D_0(B, A), B)) | (~in(ordered_pair(tptp_fun_C_1(B, A), tptp_fun_D_0(B, A)), A)) | (~in(ordered_pair(tptp_fun_D_0(B, A), tptp_fun_C_1(B, A)), A)))))))))) | (~relation(A!3)) | ![B: $i] : (~((~((~is_antisymmetric_in(A!3, B)) | ![C: $i, D: $i] : ((C = D) | (~in(C, B)) | (~in(D, B)) | (~in(ordered_pair(C, D), A!3)) | (~in(ordered_pair(D, C), A!3))))) | (~(is_antisymmetric_in(A!3, B) | (~((~in(ordered_pair(tptp_fun_D_0(B, A!3), tptp_fun_C_1(B, A!3)), A!3)) | (~in(ordered_pair(tptp_fun_C_1(B, A!3), tptp_fun_D_0(B, A!3)), A!3)) | (~in(tptp_fun_D_0(B, A!3), B)) | (~in(tptp_fun_C_1(B, A!3), B)) | (tptp_fun_C_1(B, A!3) = tptp_fun_D_0(B, A!3)))))))))),
% 0.20/0.41 inference(transitivity,[status(thm)],[96, 94])).
% 0.20/0.42 tff(98,plain,
% 0.20/0.42 ((~![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~is_antisymmetric_in(A, B)) | ![C: $i, D: $i] : ((C = D) | (~in(C, B)) | (~in(D, B)) | (~in(ordered_pair(C, D), A)) | (~in(ordered_pair(D, C), A))))) | (~(is_antisymmetric_in(A, B) | (~((tptp_fun_C_1(B, A) = tptp_fun_D_0(B, A)) | (~in(tptp_fun_C_1(B, A), B)) | (~in(tptp_fun_D_0(B, A), B)) | (~in(ordered_pair(tptp_fun_C_1(B, A), tptp_fun_D_0(B, A)), A)) | (~in(ordered_pair(tptp_fun_D_0(B, A), tptp_fun_C_1(B, A)), A)))))))))) | ((~relation(A!3)) | ![B: $i] : (~((~((~is_antisymmetric_in(A!3, B)) | ![C: $i, D: $i] : ((C = D) | (~in(C, B)) | (~in(D, B)) | (~in(ordered_pair(C, D), A!3)) | (~in(ordered_pair(D, C), A!3))))) | (~(is_antisymmetric_in(A!3, B) | (~((tptp_fun_C_1(B, A!3) = tptp_fun_D_0(B, A!3)) | (~in(tptp_fun_C_1(B, A!3), B)) | (~in(tptp_fun_D_0(B, A!3), B)) | (~in(ordered_pair(tptp_fun_C_1(B, A!3), tptp_fun_D_0(B, A!3)), A!3)) | (~in(ordered_pair(tptp_fun_D_0(B, A!3), tptp_fun_C_1(B, A!3)), A!3)))))))))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(99,plain,
% 0.20/0.42 ((~![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~is_antisymmetric_in(A, B)) | ![C: $i, D: $i] : ((C = D) | (~in(C, B)) | (~in(D, B)) | (~in(ordered_pair(C, D), A)) | (~in(ordered_pair(D, C), A))))) | (~(is_antisymmetric_in(A, B) | (~((tptp_fun_C_1(B, A) = tptp_fun_D_0(B, A)) | (~in(tptp_fun_C_1(B, A), B)) | (~in(tptp_fun_D_0(B, A), B)) | (~in(ordered_pair(tptp_fun_C_1(B, A), tptp_fun_D_0(B, A)), A)) | (~in(ordered_pair(tptp_fun_D_0(B, A), tptp_fun_C_1(B, A)), A)))))))))) | (~relation(A!3)) | ![B: $i] : (~((~((~is_antisymmetric_in(A!3, B)) | ![C: $i, D: $i] : ((C = D) | (~in(C, B)) | (~in(D, B)) | (~in(ordered_pair(C, D), A!3)) | (~in(ordered_pair(D, C), A!3))))) | (~(is_antisymmetric_in(A!3, B) | (~((~in(ordered_pair(tptp_fun_D_0(B, A!3), tptp_fun_C_1(B, A!3)), A!3)) | (~in(ordered_pair(tptp_fun_C_1(B, A!3), tptp_fun_D_0(B, A!3)), A!3)) | (~in(tptp_fun_D_0(B, A!3), B)) | (~in(tptp_fun_C_1(B, A!3), B)) | (tptp_fun_C_1(B, A!3) = tptp_fun_D_0(B, A!3))))))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[98, 97])).
% 0.20/0.42 tff(100,plain,
% 0.20/0.42 (![B: $i] : (~((~((~is_antisymmetric_in(A!3, B)) | ![C: $i, D: $i] : ((C = D) | (~in(C, B)) | (~in(D, B)) | (~in(ordered_pair(C, D), A!3)) | (~in(ordered_pair(D, C), A!3))))) | (~(is_antisymmetric_in(A!3, B) | (~((~in(ordered_pair(tptp_fun_D_0(B, A!3), tptp_fun_C_1(B, A!3)), A!3)) | (~in(ordered_pair(tptp_fun_C_1(B, A!3), tptp_fun_D_0(B, A!3)), A!3)) | (~in(tptp_fun_D_0(B, A!3), B)) | (~in(tptp_fun_C_1(B, A!3), B)) | (tptp_fun_C_1(B, A!3) = tptp_fun_D_0(B, A!3))))))))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[99, 93, 14])).
% 0.20/0.42 tff(101,plain,
% 0.20/0.42 (((~![B: $i] : (~((~((~is_antisymmetric_in(A!3, B)) | ![C: $i, D: $i] : ((C = D) | (~in(C, B)) | (~in(D, B)) | (~in(ordered_pair(C, D), A!3)) | (~in(ordered_pair(D, C), A!3))))) | (~(is_antisymmetric_in(A!3, B) | (~((~in(ordered_pair(tptp_fun_D_0(B, A!3), tptp_fun_C_1(B, A!3)), A!3)) | (~in(ordered_pair(tptp_fun_C_1(B, A!3), tptp_fun_D_0(B, A!3)), A!3)) | (~in(tptp_fun_D_0(B, A!3), B)) | (~in(tptp_fun_C_1(B, A!3), B)) | (tptp_fun_C_1(B, A!3) = tptp_fun_D_0(B, A!3))))))))) | (~((~((~is_antisymmetric_in(A!3, set_union2(relation_dom(A!3), relation_rng(A!3)))) | ![C: $i, D: $i] : ((C = D) | (~in(ordered_pair(C, D), A!3)) | (~in(ordered_pair(D, C), A!3)) | (~in(C, set_union2(relation_dom(A!3), relation_rng(A!3)))) | (~in(D, set_union2(relation_dom(A!3), relation_rng(A!3))))))) | (~(is_antisymmetric_in(A!3, set_union2(relation_dom(A!3), relation_rng(A!3))) | (~((tptp_fun_C_1(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3) = tptp_fun_D_0(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3)) | (~in(tptp_fun_C_1(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3), set_union2(relation_dom(A!3), relation_rng(A!3)))) | (~in(tptp_fun_D_0(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3), set_union2(relation_dom(A!3), relation_rng(A!3)))) | (~in(ordered_pair(tptp_fun_C_1(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3), tptp_fun_D_0(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3)), A!3)) | (~in(ordered_pair(tptp_fun_D_0(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3), tptp_fun_C_1(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3)), A!3))))))))) <=> ((~![B: $i] : (~((~((~is_antisymmetric_in(A!3, B)) | ![C: $i, D: $i] : ((C = D) | (~in(C, B)) | (~in(D, B)) | (~in(ordered_pair(C, D), A!3)) | (~in(ordered_pair(D, C), A!3))))) | (~(is_antisymmetric_in(A!3, B) | (~((~in(ordered_pair(tptp_fun_D_0(B, A!3), tptp_fun_C_1(B, A!3)), A!3)) | (~in(ordered_pair(tptp_fun_C_1(B, A!3), tptp_fun_D_0(B, A!3)), A!3)) | (~in(tptp_fun_D_0(B, A!3), B)) | (~in(tptp_fun_C_1(B, A!3), B)) | (tptp_fun_C_1(B, A!3) = tptp_fun_D_0(B, A!3))))))))) | (~((~((~is_antisymmetric_in(A!3, set_union2(relation_dom(A!3), relation_rng(A!3)))) | ![C: $i, D: $i] : ((C = D) | (~in(ordered_pair(C, D), A!3)) | (~in(ordered_pair(D, C), A!3)) | (~in(C, set_union2(relation_dom(A!3), relation_rng(A!3)))) | (~in(D, set_union2(relation_dom(A!3), relation_rng(A!3))))))) | (~(is_antisymmetric_in(A!3, set_union2(relation_dom(A!3), relation_rng(A!3))) | (~((tptp_fun_C_1(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3) = tptp_fun_D_0(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3)) | (~in(tptp_fun_C_1(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3), set_union2(relation_dom(A!3), relation_rng(A!3)))) | (~in(tptp_fun_D_0(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3), set_union2(relation_dom(A!3), relation_rng(A!3)))) | (~in(ordered_pair(tptp_fun_C_1(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3), tptp_fun_D_0(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3)), A!3)) | (~in(ordered_pair(tptp_fun_D_0(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3), tptp_fun_C_1(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3)), A!3)))))))))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(102,plain,
% 0.20/0.42 ((~((~((~is_antisymmetric_in(A!3, set_union2(relation_dom(A!3), relation_rng(A!3)))) | ![C: $i, D: $i] : ((C = D) | (~in(C, set_union2(relation_dom(A!3), relation_rng(A!3)))) | (~in(D, set_union2(relation_dom(A!3), relation_rng(A!3)))) | (~in(ordered_pair(C, D), A!3)) | (~in(ordered_pair(D, C), A!3))))) | (~(is_antisymmetric_in(A!3, set_union2(relation_dom(A!3), relation_rng(A!3))) | (~((~in(ordered_pair(tptp_fun_D_0(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3), tptp_fun_C_1(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3)), A!3)) | (~in(ordered_pair(tptp_fun_C_1(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3), tptp_fun_D_0(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3)), A!3)) | (~in(tptp_fun_D_0(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3), set_union2(relation_dom(A!3), relation_rng(A!3)))) | (~in(tptp_fun_C_1(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3), set_union2(relation_dom(A!3), relation_rng(A!3)))) | (tptp_fun_C_1(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3) = tptp_fun_D_0(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3)))))))) <=> (~((~((~is_antisymmetric_in(A!3, set_union2(relation_dom(A!3), relation_rng(A!3)))) | ![C: $i, D: $i] : ((C = D) | (~in(ordered_pair(C, D), A!3)) | (~in(ordered_pair(D, C), A!3)) | (~in(C, set_union2(relation_dom(A!3), relation_rng(A!3)))) | (~in(D, set_union2(relation_dom(A!3), relation_rng(A!3))))))) | (~(is_antisymmetric_in(A!3, set_union2(relation_dom(A!3), relation_rng(A!3))) | (~((tptp_fun_C_1(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3) = tptp_fun_D_0(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3)) | (~in(tptp_fun_C_1(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3), set_union2(relation_dom(A!3), relation_rng(A!3)))) | (~in(tptp_fun_D_0(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3), set_union2(relation_dom(A!3), relation_rng(A!3)))) | (~in(ordered_pair(tptp_fun_C_1(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3), tptp_fun_D_0(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3)), A!3)) | (~in(ordered_pair(tptp_fun_D_0(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3), tptp_fun_C_1(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3)), A!3))))))))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(103,plain,
% 0.20/0.42 (((~![B: $i] : (~((~((~is_antisymmetric_in(A!3, B)) | ![C: $i, D: $i] : ((C = D) | (~in(C, B)) | (~in(D, B)) | (~in(ordered_pair(C, D), A!3)) | (~in(ordered_pair(D, C), A!3))))) | (~(is_antisymmetric_in(A!3, B) | (~((~in(ordered_pair(tptp_fun_D_0(B, A!3), tptp_fun_C_1(B, A!3)), A!3)) | (~in(ordered_pair(tptp_fun_C_1(B, A!3), tptp_fun_D_0(B, A!3)), A!3)) | (~in(tptp_fun_D_0(B, A!3), B)) | (~in(tptp_fun_C_1(B, A!3), B)) | (tptp_fun_C_1(B, A!3) = tptp_fun_D_0(B, A!3))))))))) | (~((~((~is_antisymmetric_in(A!3, set_union2(relation_dom(A!3), relation_rng(A!3)))) | ![C: $i, D: $i] : ((C = D) | (~in(C, set_union2(relation_dom(A!3), relation_rng(A!3)))) | (~in(D, set_union2(relation_dom(A!3), relation_rng(A!3)))) | (~in(ordered_pair(C, D), A!3)) | (~in(ordered_pair(D, C), A!3))))) | (~(is_antisymmetric_in(A!3, set_union2(relation_dom(A!3), relation_rng(A!3))) | (~((~in(ordered_pair(tptp_fun_D_0(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3), tptp_fun_C_1(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3)), A!3)) | (~in(ordered_pair(tptp_fun_C_1(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3), tptp_fun_D_0(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3)), A!3)) | (~in(tptp_fun_D_0(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3), set_union2(relation_dom(A!3), relation_rng(A!3)))) | (~in(tptp_fun_C_1(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3), set_union2(relation_dom(A!3), relation_rng(A!3)))) | (tptp_fun_C_1(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3) = tptp_fun_D_0(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3))))))))) <=> ((~![B: $i] : (~((~((~is_antisymmetric_in(A!3, B)) | ![C: $i, D: $i] : ((C = D) | (~in(C, B)) | (~in(D, B)) | (~in(ordered_pair(C, D), A!3)) | (~in(ordered_pair(D, C), A!3))))) | (~(is_antisymmetric_in(A!3, B) | (~((~in(ordered_pair(tptp_fun_D_0(B, A!3), tptp_fun_C_1(B, A!3)), A!3)) | (~in(ordered_pair(tptp_fun_C_1(B, A!3), tptp_fun_D_0(B, A!3)), A!3)) | (~in(tptp_fun_D_0(B, A!3), B)) | (~in(tptp_fun_C_1(B, A!3), B)) | (tptp_fun_C_1(B, A!3) = tptp_fun_D_0(B, A!3))))))))) | (~((~((~is_antisymmetric_in(A!3, set_union2(relation_dom(A!3), relation_rng(A!3)))) | ![C: $i, D: $i] : ((C = D) | (~in(ordered_pair(C, D), A!3)) | (~in(ordered_pair(D, C), A!3)) | (~in(C, set_union2(relation_dom(A!3), relation_rng(A!3)))) | (~in(D, set_union2(relation_dom(A!3), relation_rng(A!3))))))) | (~(is_antisymmetric_in(A!3, set_union2(relation_dom(A!3), relation_rng(A!3))) | (~((tptp_fun_C_1(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3) = tptp_fun_D_0(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3)) | (~in(tptp_fun_C_1(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3), set_union2(relation_dom(A!3), relation_rng(A!3)))) | (~in(tptp_fun_D_0(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3), set_union2(relation_dom(A!3), relation_rng(A!3)))) | (~in(ordered_pair(tptp_fun_C_1(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3), tptp_fun_D_0(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3)), A!3)) | (~in(ordered_pair(tptp_fun_D_0(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3), tptp_fun_C_1(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3)), A!3)))))))))),
% 0.20/0.42 inference(monotonicity,[status(thm)],[102])).
% 0.20/0.42 tff(104,plain,
% 0.20/0.42 (((~![B: $i] : (~((~((~is_antisymmetric_in(A!3, B)) | ![C: $i, D: $i] : ((C = D) | (~in(C, B)) | (~in(D, B)) | (~in(ordered_pair(C, D), A!3)) | (~in(ordered_pair(D, C), A!3))))) | (~(is_antisymmetric_in(A!3, B) | (~((~in(ordered_pair(tptp_fun_D_0(B, A!3), tptp_fun_C_1(B, A!3)), A!3)) | (~in(ordered_pair(tptp_fun_C_1(B, A!3), tptp_fun_D_0(B, A!3)), A!3)) | (~in(tptp_fun_D_0(B, A!3), B)) | (~in(tptp_fun_C_1(B, A!3), B)) | (tptp_fun_C_1(B, A!3) = tptp_fun_D_0(B, A!3))))))))) | (~((~((~is_antisymmetric_in(A!3, set_union2(relation_dom(A!3), relation_rng(A!3)))) | ![C: $i, D: $i] : ((C = D) | (~in(C, set_union2(relation_dom(A!3), relation_rng(A!3)))) | (~in(D, set_union2(relation_dom(A!3), relation_rng(A!3)))) | (~in(ordered_pair(C, D), A!3)) | (~in(ordered_pair(D, C), A!3))))) | (~(is_antisymmetric_in(A!3, set_union2(relation_dom(A!3), relation_rng(A!3))) | (~((~in(ordered_pair(tptp_fun_D_0(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3), tptp_fun_C_1(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3)), A!3)) | (~in(ordered_pair(tptp_fun_C_1(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3), tptp_fun_D_0(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3)), A!3)) | (~in(tptp_fun_D_0(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3), set_union2(relation_dom(A!3), relation_rng(A!3)))) | (~in(tptp_fun_C_1(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3), set_union2(relation_dom(A!3), relation_rng(A!3)))) | (tptp_fun_C_1(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3) = tptp_fun_D_0(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3))))))))) <=> ((~![B: $i] : (~((~((~is_antisymmetric_in(A!3, B)) | ![C: $i, D: $i] : ((C = D) | (~in(C, B)) | (~in(D, B)) | (~in(ordered_pair(C, D), A!3)) | (~in(ordered_pair(D, C), A!3))))) | (~(is_antisymmetric_in(A!3, B) | (~((~in(ordered_pair(tptp_fun_D_0(B, A!3), tptp_fun_C_1(B, A!3)), A!3)) | (~in(ordered_pair(tptp_fun_C_1(B, A!3), tptp_fun_D_0(B, A!3)), A!3)) | (~in(tptp_fun_D_0(B, A!3), B)) | (~in(tptp_fun_C_1(B, A!3), B)) | (tptp_fun_C_1(B, A!3) = tptp_fun_D_0(B, A!3))))))))) | (~((~((~is_antisymmetric_in(A!3, set_union2(relation_dom(A!3), relation_rng(A!3)))) | ![C: $i, D: $i] : ((C = D) | (~in(ordered_pair(C, D), A!3)) | (~in(ordered_pair(D, C), A!3)) | (~in(C, set_union2(relation_dom(A!3), relation_rng(A!3)))) | (~in(D, set_union2(relation_dom(A!3), relation_rng(A!3))))))) | (~(is_antisymmetric_in(A!3, set_union2(relation_dom(A!3), relation_rng(A!3))) | (~((tptp_fun_C_1(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3) = tptp_fun_D_0(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3)) | (~in(tptp_fun_C_1(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3), set_union2(relation_dom(A!3), relation_rng(A!3)))) | (~in(tptp_fun_D_0(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3), set_union2(relation_dom(A!3), relation_rng(A!3)))) | (~in(ordered_pair(tptp_fun_C_1(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3), tptp_fun_D_0(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3)), A!3)) | (~in(ordered_pair(tptp_fun_D_0(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3), tptp_fun_C_1(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3)), A!3)))))))))),
% 0.20/0.43 inference(transitivity,[status(thm)],[103, 101])).
% 0.20/0.43 tff(105,plain,
% 0.20/0.43 ((~![B: $i] : (~((~((~is_antisymmetric_in(A!3, B)) | ![C: $i, D: $i] : ((C = D) | (~in(C, B)) | (~in(D, B)) | (~in(ordered_pair(C, D), A!3)) | (~in(ordered_pair(D, C), A!3))))) | (~(is_antisymmetric_in(A!3, B) | (~((~in(ordered_pair(tptp_fun_D_0(B, A!3), tptp_fun_C_1(B, A!3)), A!3)) | (~in(ordered_pair(tptp_fun_C_1(B, A!3), tptp_fun_D_0(B, A!3)), A!3)) | (~in(tptp_fun_D_0(B, A!3), B)) | (~in(tptp_fun_C_1(B, A!3), B)) | (tptp_fun_C_1(B, A!3) = tptp_fun_D_0(B, A!3))))))))) | (~((~((~is_antisymmetric_in(A!3, set_union2(relation_dom(A!3), relation_rng(A!3)))) | ![C: $i, D: $i] : ((C = D) | (~in(C, set_union2(relation_dom(A!3), relation_rng(A!3)))) | (~in(D, set_union2(relation_dom(A!3), relation_rng(A!3)))) | (~in(ordered_pair(C, D), A!3)) | (~in(ordered_pair(D, C), A!3))))) | (~(is_antisymmetric_in(A!3, set_union2(relation_dom(A!3), relation_rng(A!3))) | (~((~in(ordered_pair(tptp_fun_D_0(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3), tptp_fun_C_1(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3)), A!3)) | (~in(ordered_pair(tptp_fun_C_1(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3), tptp_fun_D_0(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3)), A!3)) | (~in(tptp_fun_D_0(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3), set_union2(relation_dom(A!3), relation_rng(A!3)))) | (~in(tptp_fun_C_1(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3), set_union2(relation_dom(A!3), relation_rng(A!3)))) | (tptp_fun_C_1(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3) = tptp_fun_D_0(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3))))))))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(106,plain,
% 0.20/0.43 ((~![B: $i] : (~((~((~is_antisymmetric_in(A!3, B)) | ![C: $i, D: $i] : ((C = D) | (~in(C, B)) | (~in(D, B)) | (~in(ordered_pair(C, D), A!3)) | (~in(ordered_pair(D, C), A!3))))) | (~(is_antisymmetric_in(A!3, B) | (~((~in(ordered_pair(tptp_fun_D_0(B, A!3), tptp_fun_C_1(B, A!3)), A!3)) | (~in(ordered_pair(tptp_fun_C_1(B, A!3), tptp_fun_D_0(B, A!3)), A!3)) | (~in(tptp_fun_D_0(B, A!3), B)) | (~in(tptp_fun_C_1(B, A!3), B)) | (tptp_fun_C_1(B, A!3) = tptp_fun_D_0(B, A!3))))))))) | (~((~((~is_antisymmetric_in(A!3, set_union2(relation_dom(A!3), relation_rng(A!3)))) | ![C: $i, D: $i] : ((C = D) | (~in(ordered_pair(C, D), A!3)) | (~in(ordered_pair(D, C), A!3)) | (~in(C, set_union2(relation_dom(A!3), relation_rng(A!3)))) | (~in(D, set_union2(relation_dom(A!3), relation_rng(A!3))))))) | (~(is_antisymmetric_in(A!3, set_union2(relation_dom(A!3), relation_rng(A!3))) | (~((tptp_fun_C_1(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3) = tptp_fun_D_0(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3)) | (~in(tptp_fun_C_1(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3), set_union2(relation_dom(A!3), relation_rng(A!3)))) | (~in(tptp_fun_D_0(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3), set_union2(relation_dom(A!3), relation_rng(A!3)))) | (~in(ordered_pair(tptp_fun_C_1(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3), tptp_fun_D_0(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3)), A!3)) | (~in(ordered_pair(tptp_fun_D_0(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3), tptp_fun_C_1(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3)), A!3))))))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[105, 104])).
% 0.20/0.43 tff(107,plain,
% 0.20/0.43 (~((~((~is_antisymmetric_in(A!3, set_union2(relation_dom(A!3), relation_rng(A!3)))) | ![C: $i, D: $i] : ((C = D) | (~in(ordered_pair(C, D), A!3)) | (~in(ordered_pair(D, C), A!3)) | (~in(C, set_union2(relation_dom(A!3), relation_rng(A!3)))) | (~in(D, set_union2(relation_dom(A!3), relation_rng(A!3))))))) | (~(is_antisymmetric_in(A!3, set_union2(relation_dom(A!3), relation_rng(A!3))) | (~((tptp_fun_C_1(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3) = tptp_fun_D_0(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3)) | (~in(tptp_fun_C_1(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3), set_union2(relation_dom(A!3), relation_rng(A!3)))) | (~in(tptp_fun_D_0(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3), set_union2(relation_dom(A!3), relation_rng(A!3)))) | (~in(ordered_pair(tptp_fun_C_1(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3), tptp_fun_D_0(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3)), A!3)) | (~in(ordered_pair(tptp_fun_D_0(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3), tptp_fun_C_1(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3)), A!3)))))))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[106, 100])).
% 0.20/0.43 tff(108,plain,
% 0.20/0.43 (((~((~is_antisymmetric_in(A!3, set_union2(relation_dom(A!3), relation_rng(A!3)))) | ![C: $i, D: $i] : ((C = D) | (~in(ordered_pair(C, D), A!3)) | (~in(ordered_pair(D, C), A!3)) | (~in(C, set_union2(relation_dom(A!3), relation_rng(A!3)))) | (~in(D, set_union2(relation_dom(A!3), relation_rng(A!3))))))) | (~(is_antisymmetric_in(A!3, set_union2(relation_dom(A!3), relation_rng(A!3))) | (~((tptp_fun_C_1(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3) = tptp_fun_D_0(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3)) | (~in(tptp_fun_C_1(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3), set_union2(relation_dom(A!3), relation_rng(A!3)))) | (~in(tptp_fun_D_0(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3), set_union2(relation_dom(A!3), relation_rng(A!3)))) | (~in(ordered_pair(tptp_fun_C_1(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3), tptp_fun_D_0(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3)), A!3)) | (~in(ordered_pair(tptp_fun_D_0(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3), tptp_fun_C_1(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3)), A!3))))))) | ((~is_antisymmetric_in(A!3, set_union2(relation_dom(A!3), relation_rng(A!3)))) | ![C: $i, D: $i] : ((C = D) | (~in(ordered_pair(C, D), A!3)) | (~in(ordered_pair(D, C), A!3)) | (~in(C, set_union2(relation_dom(A!3), relation_rng(A!3)))) | (~in(D, set_union2(relation_dom(A!3), relation_rng(A!3))))))),
% 0.20/0.43 inference(tautology,[status(thm)],[])).
% 0.20/0.43 tff(109,plain,
% 0.20/0.43 ((~is_antisymmetric_in(A!3, set_union2(relation_dom(A!3), relation_rng(A!3)))) | ![C: $i, D: $i] : ((C = D) | (~in(ordered_pair(C, D), A!3)) | (~in(ordered_pair(D, C), A!3)) | (~in(C, set_union2(relation_dom(A!3), relation_rng(A!3)))) | (~in(D, set_union2(relation_dom(A!3), relation_rng(A!3)))))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[108, 107])).
% 0.20/0.43 tff(110,plain,
% 0.20/0.43 ((~((~is_antisymmetric_in(A!3, set_union2(relation_dom(A!3), relation_rng(A!3)))) | ![C: $i, D: $i] : ((C = D) | (~in(ordered_pair(C, D), A!3)) | (~in(ordered_pair(D, C), A!3)) | (~in(C, set_union2(relation_dom(A!3), relation_rng(A!3)))) | (~in(D, set_union2(relation_dom(A!3), relation_rng(A!3))))))) | (~is_antisymmetric_in(A!3, set_union2(relation_dom(A!3), relation_rng(A!3)))) | ![C: $i, D: $i] : ((C = D) | (~in(ordered_pair(C, D), A!3)) | (~in(ordered_pair(D, C), A!3)) | (~in(C, set_union2(relation_dom(A!3), relation_rng(A!3)))) | (~in(D, set_union2(relation_dom(A!3), relation_rng(A!3)))))),
% 0.20/0.43 inference(tautology,[status(thm)],[])).
% 0.20/0.43 tff(111,plain,
% 0.20/0.43 ((~is_antisymmetric_in(A!3, set_union2(relation_dom(A!3), relation_rng(A!3)))) | ![C: $i, D: $i] : ((C = D) | (~in(ordered_pair(C, D), A!3)) | (~in(ordered_pair(D, C), A!3)) | (~in(C, set_union2(relation_dom(A!3), relation_rng(A!3)))) | (~in(D, set_union2(relation_dom(A!3), relation_rng(A!3)))))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[110, 109])).
% 0.20/0.43 tff(112,plain,
% 0.20/0.43 (~is_antisymmetric_in(A!3, set_union2(relation_dom(A!3), relation_rng(A!3)))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[111, 77])).
% 0.20/0.43 tff(113,plain,
% 0.20/0.43 (~is_antisymmetric_in(A!3, relation_field(A!3))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[112, 40])).
% 0.20/0.43 tff(114,plain,
% 0.20/0.43 (^[A: $i] : refl(((~relation(A)) | (antisymmetric(A) <=> is_antisymmetric_in(A, relation_field(A)))) <=> ((~relation(A)) | (antisymmetric(A) <=> is_antisymmetric_in(A, relation_field(A)))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(115,plain,
% 0.20/0.43 (![A: $i] : ((~relation(A)) | (antisymmetric(A) <=> is_antisymmetric_in(A, relation_field(A)))) <=> ![A: $i] : ((~relation(A)) | (antisymmetric(A) <=> is_antisymmetric_in(A, relation_field(A))))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[114])).
% 0.20/0.43 tff(116,plain,
% 0.20/0.43 (![A: $i] : ((~relation(A)) | (antisymmetric(A) <=> is_antisymmetric_in(A, relation_field(A)))) <=> ![A: $i] : ((~relation(A)) | (antisymmetric(A) <=> is_antisymmetric_in(A, relation_field(A))))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(117,plain,
% 0.20/0.43 (^[A: $i] : rewrite((relation(A) => (antisymmetric(A) <=> is_antisymmetric_in(A, relation_field(A)))) <=> ((~relation(A)) | (antisymmetric(A) <=> is_antisymmetric_in(A, relation_field(A)))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(118,plain,
% 0.20/0.43 (![A: $i] : (relation(A) => (antisymmetric(A) <=> is_antisymmetric_in(A, relation_field(A)))) <=> ![A: $i] : ((~relation(A)) | (antisymmetric(A) <=> is_antisymmetric_in(A, relation_field(A))))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[117])).
% 0.20/0.43 tff(119,axiom,(![A: $i] : (relation(A) => (antisymmetric(A) <=> is_antisymmetric_in(A, relation_field(A))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d12_relat_2')).
% 0.20/0.43 tff(120,plain,
% 0.20/0.43 (![A: $i] : ((~relation(A)) | (antisymmetric(A) <=> is_antisymmetric_in(A, relation_field(A))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[119, 118])).
% 0.20/0.43 tff(121,plain,
% 0.20/0.43 (![A: $i] : ((~relation(A)) | (antisymmetric(A) <=> is_antisymmetric_in(A, relation_field(A))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[120, 116])).
% 0.20/0.43 tff(122,plain,(
% 0.20/0.43 ![A: $i] : ((~relation(A)) | (antisymmetric(A) <=> is_antisymmetric_in(A, relation_field(A))))),
% 0.20/0.43 inference(skolemize,[status(sab)],[121])).
% 0.20/0.43 tff(123,plain,
% 0.20/0.43 (![A: $i] : ((~relation(A)) | (antisymmetric(A) <=> is_antisymmetric_in(A, relation_field(A))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[122, 115])).
% 0.20/0.43 tff(124,plain,
% 0.20/0.43 (((~![A: $i] : ((~relation(A)) | (antisymmetric(A) <=> is_antisymmetric_in(A, relation_field(A))))) | ((~relation(A!3)) | (antisymmetric(A!3) <=> is_antisymmetric_in(A!3, relation_field(A!3))))) <=> ((~![A: $i] : ((~relation(A)) | (antisymmetric(A) <=> is_antisymmetric_in(A, relation_field(A))))) | (~relation(A!3)) | (antisymmetric(A!3) <=> is_antisymmetric_in(A!3, relation_field(A!3))))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(125,plain,
% 0.20/0.43 ((~![A: $i] : ((~relation(A)) | (antisymmetric(A) <=> is_antisymmetric_in(A, relation_field(A))))) | ((~relation(A!3)) | (antisymmetric(A!3) <=> is_antisymmetric_in(A!3, relation_field(A!3))))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(126,plain,
% 0.20/0.43 ((~![A: $i] : ((~relation(A)) | (antisymmetric(A) <=> is_antisymmetric_in(A, relation_field(A))))) | (~relation(A!3)) | (antisymmetric(A!3) <=> is_antisymmetric_in(A!3, relation_field(A!3)))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[125, 124])).
% 0.20/0.43 tff(127,plain,
% 0.20/0.43 (antisymmetric(A!3) <=> is_antisymmetric_in(A!3, relation_field(A!3))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[126, 123, 14])).
% 0.20/0.43 tff(128,plain,
% 0.20/0.43 ((~(antisymmetric(A!3) <=> is_antisymmetric_in(A!3, relation_field(A!3)))) | (~antisymmetric(A!3)) | is_antisymmetric_in(A!3, relation_field(A!3))),
% 0.20/0.43 inference(tautology,[status(thm)],[])).
% 0.20/0.43 tff(129,plain,
% 0.20/0.43 ((~antisymmetric(A!3)) | is_antisymmetric_in(A!3, relation_field(A!3))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[128, 127])).
% 0.20/0.43 tff(130,plain,
% 0.20/0.43 (~antisymmetric(A!3)),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[129, 113])).
% 0.20/0.43 tff(131,plain,
% 0.20/0.43 ((antisymmetric(A!3) | ![B: $i, C: $i] : ((B = C) | (~in(ordered_pair(B, C), A!3)) | (~in(ordered_pair(C, B), A!3)))) <=> (antisymmetric(A!3) | ![B: $i, C: $i] : ((B = C) | (~in(ordered_pair(B, C), A!3)) | (~in(ordered_pair(C, B), A!3))))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(132,plain,
% 0.20/0.43 ((antisymmetric(A!3) | ![B: $i, C: $i] : ((~(in(ordered_pair(B, C), A!3) & in(ordered_pair(C, B), A!3))) | (B = C))) <=> (antisymmetric(A!3) | ![B: $i, C: $i] : ((B = C) | (~in(ordered_pair(B, C), A!3)) | (~in(ordered_pair(C, B), A!3))))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(133,plain,
% 0.20/0.43 (antisymmetric(A!3) | ![B: $i, C: $i] : ((~(in(ordered_pair(B, C), A!3) & in(ordered_pair(C, B), A!3))) | (B = C))),
% 0.20/0.43 inference(and_elim,[status(thm)],[13])).
% 0.20/0.43 tff(134,plain,
% 0.20/0.43 (antisymmetric(A!3) | ![B: $i, C: $i] : ((B = C) | (~in(ordered_pair(B, C), A!3)) | (~in(ordered_pair(C, B), A!3)))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[133, 132])).
% 0.20/0.43 tff(135,plain,
% 0.20/0.43 (antisymmetric(A!3) | ![B: $i, C: $i] : ((B = C) | (~in(ordered_pair(B, C), A!3)) | (~in(ordered_pair(C, B), A!3)))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[134, 131])).
% 0.20/0.43 tff(136,plain,
% 0.20/0.43 (![B: $i, C: $i] : ((B = C) | (~in(ordered_pair(B, C), A!3)) | (~in(ordered_pair(C, B), A!3)))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[135, 130])).
% 0.20/0.43 tff(137,plain,
% 0.20/0.43 (((~![B: $i, C: $i] : ((B = C) | (~in(ordered_pair(B, C), A!3)) | (~in(ordered_pair(C, B), A!3)))) | ((B!5 = C!4) | (~in(ordered_pair(B!5, C!4), A!3)) | (~in(ordered_pair(C!4, B!5), A!3)))) <=> ((~![B: $i, C: $i] : ((B = C) | (~in(ordered_pair(B, C), A!3)) | (~in(ordered_pair(C, B), A!3)))) | (B!5 = C!4) | (~in(ordered_pair(B!5, C!4), A!3)) | (~in(ordered_pair(C!4, B!5), A!3)))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(138,plain,
% 0.20/0.43 ((~![B: $i, C: $i] : ((B = C) | (~in(ordered_pair(B, C), A!3)) | (~in(ordered_pair(C, B), A!3)))) | ((B!5 = C!4) | (~in(ordered_pair(B!5, C!4), A!3)) | (~in(ordered_pair(C!4, B!5), A!3)))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(139,plain,
% 0.20/0.43 ((~![B: $i, C: $i] : ((B = C) | (~in(ordered_pair(B, C), A!3)) | (~in(ordered_pair(C, B), A!3)))) | (B!5 = C!4) | (~in(ordered_pair(B!5, C!4), A!3)) | (~in(ordered_pair(C!4, B!5), A!3))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[138, 137])).
% 0.20/0.43 tff(140,plain,
% 0.20/0.43 ($false),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[139, 136, 39, 37, 35])).
% 0.20/0.43 tff(141,plain,((B!5 = C!4) | (~in(ordered_pair(B!5, C!4), A!3)) | (~in(ordered_pair(C!4, B!5), A!3))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.44 tff(142,plain,
% 0.20/0.44 (((~antisymmetric(A!3)) | (~((~(in(ordered_pair(B!5, C!4), A!3) & in(ordered_pair(C!4, B!5), A!3))) | (B!5 = C!4)))) <=> ((~antisymmetric(A!3)) | (~((B!5 = C!4) | (~in(ordered_pair(B!5, C!4), A!3)) | (~in(ordered_pair(C!4, B!5), A!3)))))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(143,plain,
% 0.20/0.44 ((~antisymmetric(A!3)) | (~((~(in(ordered_pair(B!5, C!4), A!3) & in(ordered_pair(C!4, B!5), A!3))) | (B!5 = C!4)))),
% 0.20/0.44 inference(and_elim,[status(thm)],[13])).
% 0.20/0.44 tff(144,plain,
% 0.20/0.44 ((~antisymmetric(A!3)) | (~((B!5 = C!4) | (~in(ordered_pair(B!5, C!4), A!3)) | (~in(ordered_pair(C!4, B!5), A!3))))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[143, 142])).
% 0.20/0.44 tff(145,plain,
% 0.20/0.44 (~antisymmetric(A!3)),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[144, 141])).
% 0.20/0.44 tff(146,plain,
% 0.20/0.44 ((~(antisymmetric(A!3) <=> is_antisymmetric_in(A!3, relation_field(A!3)))) | antisymmetric(A!3) | (~is_antisymmetric_in(A!3, relation_field(A!3)))),
% 0.20/0.44 inference(tautology,[status(thm)],[])).
% 0.20/0.44 tff(147,plain,
% 0.20/0.44 (antisymmetric(A!3) | (~is_antisymmetric_in(A!3, relation_field(A!3)))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[146, 127])).
% 0.20/0.44 tff(148,plain,
% 0.20/0.44 (~is_antisymmetric_in(A!3, relation_field(A!3))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[147, 145])).
% 0.20/0.44 tff(149,plain,
% 0.20/0.44 (~is_antisymmetric_in(A!3, set_union2(relation_dom(A!3), relation_rng(A!3)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[148, 32])).
% 0.20/0.44 tff(150,plain,
% 0.20/0.44 (((~((~is_antisymmetric_in(A!3, set_union2(relation_dom(A!3), relation_rng(A!3)))) | ![C: $i, D: $i] : ((C = D) | (~in(ordered_pair(C, D), A!3)) | (~in(ordered_pair(D, C), A!3)) | (~in(C, set_union2(relation_dom(A!3), relation_rng(A!3)))) | (~in(D, set_union2(relation_dom(A!3), relation_rng(A!3))))))) | (~(is_antisymmetric_in(A!3, set_union2(relation_dom(A!3), relation_rng(A!3))) | (~((tptp_fun_C_1(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3) = tptp_fun_D_0(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3)) | (~in(tptp_fun_C_1(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3), set_union2(relation_dom(A!3), relation_rng(A!3)))) | (~in(tptp_fun_D_0(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3), set_union2(relation_dom(A!3), relation_rng(A!3)))) | (~in(ordered_pair(tptp_fun_C_1(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3), tptp_fun_D_0(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3)), A!3)) | (~in(ordered_pair(tptp_fun_D_0(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3), tptp_fun_C_1(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3)), A!3))))))) | (is_antisymmetric_in(A!3, set_union2(relation_dom(A!3), relation_rng(A!3))) | (~((tptp_fun_C_1(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3) = tptp_fun_D_0(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3)) | (~in(tptp_fun_C_1(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3), set_union2(relation_dom(A!3), relation_rng(A!3)))) | (~in(tptp_fun_D_0(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3), set_union2(relation_dom(A!3), relation_rng(A!3)))) | (~in(ordered_pair(tptp_fun_C_1(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3), tptp_fun_D_0(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3)), A!3)) | (~in(ordered_pair(tptp_fun_D_0(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3), tptp_fun_C_1(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3)), A!3)))))),
% 0.20/0.44 inference(tautology,[status(thm)],[])).
% 0.20/0.44 tff(151,plain,
% 0.20/0.44 (is_antisymmetric_in(A!3, set_union2(relation_dom(A!3), relation_rng(A!3))) | (~((tptp_fun_C_1(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3) = tptp_fun_D_0(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3)) | (~in(tptp_fun_C_1(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3), set_union2(relation_dom(A!3), relation_rng(A!3)))) | (~in(tptp_fun_D_0(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3), set_union2(relation_dom(A!3), relation_rng(A!3)))) | (~in(ordered_pair(tptp_fun_C_1(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3), tptp_fun_D_0(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3)), A!3)) | (~in(ordered_pair(tptp_fun_D_0(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3), tptp_fun_C_1(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3)), A!3))))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[150, 107])).
% 0.20/0.44 tff(152,plain,
% 0.20/0.44 ((~(is_antisymmetric_in(A!3, set_union2(relation_dom(A!3), relation_rng(A!3))) | (~((tptp_fun_C_1(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3) = tptp_fun_D_0(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3)) | (~in(tptp_fun_C_1(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3), set_union2(relation_dom(A!3), relation_rng(A!3)))) | (~in(tptp_fun_D_0(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3), set_union2(relation_dom(A!3), relation_rng(A!3)))) | (~in(ordered_pair(tptp_fun_C_1(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3), tptp_fun_D_0(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3)), A!3)) | (~in(ordered_pair(tptp_fun_D_0(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3), tptp_fun_C_1(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3)), A!3)))))) | is_antisymmetric_in(A!3, set_union2(relation_dom(A!3), relation_rng(A!3))) | (~((tptp_fun_C_1(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3) = tptp_fun_D_0(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3)) | (~in(tptp_fun_C_1(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3), set_union2(relation_dom(A!3), relation_rng(A!3)))) | (~in(tptp_fun_D_0(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3), set_union2(relation_dom(A!3), relation_rng(A!3)))) | (~in(ordered_pair(tptp_fun_C_1(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3), tptp_fun_D_0(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3)), A!3)) | (~in(ordered_pair(tptp_fun_D_0(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3), tptp_fun_C_1(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3)), A!3))))),
% 0.20/0.44 inference(tautology,[status(thm)],[])).
% 0.20/0.44 tff(153,plain,
% 0.20/0.44 (is_antisymmetric_in(A!3, set_union2(relation_dom(A!3), relation_rng(A!3))) | (~((tptp_fun_C_1(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3) = tptp_fun_D_0(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3)) | (~in(tptp_fun_C_1(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3), set_union2(relation_dom(A!3), relation_rng(A!3)))) | (~in(tptp_fun_D_0(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3), set_union2(relation_dom(A!3), relation_rng(A!3)))) | (~in(ordered_pair(tptp_fun_C_1(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3), tptp_fun_D_0(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3)), A!3)) | (~in(ordered_pair(tptp_fun_D_0(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3), tptp_fun_C_1(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3)), A!3))))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[152, 151])).
% 0.20/0.44 tff(154,plain,
% 0.20/0.44 (~((tptp_fun_C_1(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3) = tptp_fun_D_0(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3)) | (~in(tptp_fun_C_1(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3), set_union2(relation_dom(A!3), relation_rng(A!3)))) | (~in(tptp_fun_D_0(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3), set_union2(relation_dom(A!3), relation_rng(A!3)))) | (~in(ordered_pair(tptp_fun_C_1(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3), tptp_fun_D_0(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3)), A!3)) | (~in(ordered_pair(tptp_fun_D_0(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3), tptp_fun_C_1(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3)), A!3)))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[153, 149])).
% 0.20/0.44 tff(155,plain,
% 0.20/0.44 (((tptp_fun_C_1(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3) = tptp_fun_D_0(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3)) | (~in(tptp_fun_C_1(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3), set_union2(relation_dom(A!3), relation_rng(A!3)))) | (~in(tptp_fun_D_0(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3), set_union2(relation_dom(A!3), relation_rng(A!3)))) | (~in(ordered_pair(tptp_fun_C_1(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3), tptp_fun_D_0(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3)), A!3)) | (~in(ordered_pair(tptp_fun_D_0(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3), tptp_fun_C_1(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3)), A!3))) | in(ordered_pair(tptp_fun_D_0(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3), tptp_fun_C_1(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3)), A!3)),
% 0.20/0.44 inference(tautology,[status(thm)],[])).
% 0.20/0.44 tff(156,plain,
% 0.20/0.44 (in(ordered_pair(tptp_fun_D_0(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3), tptp_fun_C_1(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3)), A!3)),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[155, 154])).
% 0.20/0.44 tff(157,plain,
% 0.20/0.44 (((tptp_fun_C_1(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3) = tptp_fun_D_0(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3)) | (~in(tptp_fun_C_1(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3), set_union2(relation_dom(A!3), relation_rng(A!3)))) | (~in(tptp_fun_D_0(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3), set_union2(relation_dom(A!3), relation_rng(A!3)))) | (~in(ordered_pair(tptp_fun_C_1(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3), tptp_fun_D_0(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3)), A!3)) | (~in(ordered_pair(tptp_fun_D_0(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3), tptp_fun_C_1(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3)), A!3))) | in(ordered_pair(tptp_fun_C_1(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3), tptp_fun_D_0(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3)), A!3)),
% 0.20/0.44 inference(tautology,[status(thm)],[])).
% 0.20/0.44 tff(158,plain,
% 0.20/0.44 (in(ordered_pair(tptp_fun_C_1(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3), tptp_fun_D_0(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3)), A!3)),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[157, 154])).
% 0.20/0.44 tff(159,plain,
% 0.20/0.44 (((tptp_fun_C_1(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3) = tptp_fun_D_0(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3)) | (~in(tptp_fun_C_1(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3), set_union2(relation_dom(A!3), relation_rng(A!3)))) | (~in(tptp_fun_D_0(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3), set_union2(relation_dom(A!3), relation_rng(A!3)))) | (~in(ordered_pair(tptp_fun_C_1(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3), tptp_fun_D_0(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3)), A!3)) | (~in(ordered_pair(tptp_fun_D_0(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3), tptp_fun_C_1(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3)), A!3))) | (~(tptp_fun_C_1(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3) = tptp_fun_D_0(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3)))),
% 0.20/0.44 inference(tautology,[status(thm)],[])).
% 0.20/0.44 tff(160,plain,
% 0.20/0.44 (~(tptp_fun_C_1(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3) = tptp_fun_D_0(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[159, 154])).
% 0.20/0.44 tff(161,plain,
% 0.20/0.44 (![B: $i, C: $i] : ((B = C) | (~in(ordered_pair(B, C), A!3)) | (~in(ordered_pair(C, B), A!3)))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[135, 145])).
% 0.20/0.44 tff(162,plain,
% 0.20/0.44 (((~![B: $i, C: $i] : ((B = C) | (~in(ordered_pair(B, C), A!3)) | (~in(ordered_pair(C, B), A!3)))) | ((tptp_fun_C_1(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3) = tptp_fun_D_0(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3)) | (~in(ordered_pair(tptp_fun_C_1(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3), tptp_fun_D_0(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3)), A!3)) | (~in(ordered_pair(tptp_fun_D_0(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3), tptp_fun_C_1(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3)), A!3)))) <=> ((~![B: $i, C: $i] : ((B = C) | (~in(ordered_pair(B, C), A!3)) | (~in(ordered_pair(C, B), A!3)))) | (tptp_fun_C_1(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3) = tptp_fun_D_0(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3)) | (~in(ordered_pair(tptp_fun_C_1(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3), tptp_fun_D_0(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3)), A!3)) | (~in(ordered_pair(tptp_fun_D_0(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3), tptp_fun_C_1(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3)), A!3)))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(163,plain,
% 0.20/0.45 ((~![B: $i, C: $i] : ((B = C) | (~in(ordered_pair(B, C), A!3)) | (~in(ordered_pair(C, B), A!3)))) | ((tptp_fun_C_1(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3) = tptp_fun_D_0(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3)) | (~in(ordered_pair(tptp_fun_C_1(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3), tptp_fun_D_0(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3)), A!3)) | (~in(ordered_pair(tptp_fun_D_0(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3), tptp_fun_C_1(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3)), A!3)))),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(164,plain,
% 0.20/0.45 ((~![B: $i, C: $i] : ((B = C) | (~in(ordered_pair(B, C), A!3)) | (~in(ordered_pair(C, B), A!3)))) | (tptp_fun_C_1(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3) = tptp_fun_D_0(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3)) | (~in(ordered_pair(tptp_fun_C_1(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3), tptp_fun_D_0(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3)), A!3)) | (~in(ordered_pair(tptp_fun_D_0(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3), tptp_fun_C_1(set_union2(relation_dom(A!3), relation_rng(A!3)), A!3)), A!3))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[163, 162])).
% 0.20/0.45 tff(165,plain,
% 0.20/0.45 ($false),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[164, 161, 160, 158, 156])).
% 0.20/0.45 % SZS output end Proof
% 0.20/0.45 % E exiting
%------------------------------------------------------------------------------