%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SEU239+1 : TPTP v9.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n001.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 0.13s 0.38s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SEU239+1 : TPTP v9.0.0. Released v3.3.0.
% 0.06/0.12 % Command : run_E %s %d THM
% 0.13/0.33 % Computer : n001.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Fri Jun 20 06:31:50 EDT 2025
% 0.13/0.33 % CPUTime :
% 0.13/0.38 % SZS status Theorem
% 0.13/0.38 % SZS output start Proof
% 0.13/0.38 tff(in_type, type, (
% 0.13/0.38 in: ( $i * $i ) > $o)).
% 0.13/0.38 tff(relation_field_type, type, (
% 0.13/0.38 relation_field: $i > $i)).
% 0.13/0.38 tff(tptp_fun_A_2_type, type, (
% 0.13/0.38 tptp_fun_A_2: $i)).
% 0.13/0.38 tff(tptp_fun_C_0_type, type, (
% 0.13/0.38 tptp_fun_C_0: ( $i * $i ) > $i)).
% 0.13/0.38 tff(set_union2_type, type, (
% 0.13/0.38 set_union2: ( $i * $i ) > $i)).
% 0.13/0.38 tff(relation_rng_type, type, (
% 0.13/0.38 relation_rng: $i > $i)).
% 0.13/0.38 tff(relation_dom_type, type, (
% 0.13/0.38 relation_dom: $i > $i)).
% 0.13/0.38 tff(relation_type, type, (
% 0.13/0.38 relation: $i > $o)).
% 0.13/0.38 tff(ordered_pair_type, type, (
% 0.13/0.38 ordered_pair: ( $i * $i ) > $i)).
% 0.13/0.38 tff(tptp_fun_B_3_type, type, (
% 0.13/0.38 tptp_fun_B_3: $i)).
% 0.13/0.38 tff(reflexive_type, type, (
% 0.13/0.38 reflexive: $i > $o)).
% 0.13/0.38 tff(is_reflexive_in_type, type, (
% 0.13/0.38 is_reflexive_in: ( $i * $i ) > $o)).
% 0.13/0.38 tff(1,plain,
% 0.13/0.38 ((relation(A!2) & ((reflexive(A!2) | ![B: $i] : ((~in(B, relation_field(A!2))) | in(ordered_pair(B, B), A!2))) & ((~reflexive(A!2)) | (~((~in(B!3, relation_field(A!2))) | in(ordered_pair(B!3, B!3), A!2)))))) <=> (relation(A!2) & (reflexive(A!2) | ![B: $i] : ((~in(B, relation_field(A!2))) | in(ordered_pair(B, B), A!2))) & ((~reflexive(A!2)) | (~((~in(B!3, relation_field(A!2))) | in(ordered_pair(B!3, B!3), A!2)))))),
% 0.13/0.38 inference(rewrite,[status(thm)],[])).
% 0.13/0.38 tff(2,plain,
% 0.13/0.38 ((reflexive(A!2) | ![B: $i] : ((~in(B, relation_field(A!2))) | in(ordered_pair(B, B), A!2))) <=> (reflexive(A!2) | ![B: $i] : ((~in(B, relation_field(A!2))) | in(ordered_pair(B, B), A!2)))),
% 0.13/0.38 inference(rewrite,[status(thm)],[])).
% 0.13/0.38 tff(3,plain,
% 0.13/0.38 (((reflexive(A!2) | ![B: $i] : ((~in(B, relation_field(A!2))) | in(ordered_pair(B, B), A!2))) & ((~reflexive(A!2)) | (~((~in(B!3, relation_field(A!2))) | in(ordered_pair(B!3, B!3), A!2))))) <=> ((reflexive(A!2) | ![B: $i] : ((~in(B, relation_field(A!2))) | in(ordered_pair(B, B), A!2))) & ((~reflexive(A!2)) | (~((~in(B!3, relation_field(A!2))) | in(ordered_pair(B!3, B!3), A!2)))))),
% 0.13/0.38 inference(monotonicity,[status(thm)],[2])).
% 0.13/0.38 tff(4,plain,
% 0.13/0.38 ((relation(A!2) & ((reflexive(A!2) | ![B: $i] : ((~in(B, relation_field(A!2))) | in(ordered_pair(B, B), A!2))) & ((~reflexive(A!2)) | (~((~in(B!3, relation_field(A!2))) | in(ordered_pair(B!3, B!3), A!2)))))) <=> (relation(A!2) & ((reflexive(A!2) | ![B: $i] : ((~in(B, relation_field(A!2))) | in(ordered_pair(B, B), A!2))) & ((~reflexive(A!2)) | (~((~in(B!3, relation_field(A!2))) | in(ordered_pair(B!3, B!3), A!2))))))),
% 0.13/0.38 inference(monotonicity,[status(thm)],[3])).
% 0.13/0.38 tff(5,plain,
% 0.13/0.38 ((relation(A!2) & ((reflexive(A!2) | ![B: $i] : ((~in(B, relation_field(A!2))) | in(ordered_pair(B, B), A!2))) & ((~reflexive(A!2)) | (~((~in(B!3, relation_field(A!2))) | in(ordered_pair(B!3, B!3), A!2)))))) <=> (relation(A!2) & (reflexive(A!2) | ![B: $i] : ((~in(B, relation_field(A!2))) | in(ordered_pair(B, B), A!2))) & ((~reflexive(A!2)) | (~((~in(B!3, relation_field(A!2))) | in(ordered_pair(B!3, B!3), A!2)))))),
% 0.13/0.38 inference(transitivity,[status(thm)],[4, 1])).
% 0.13/0.38 tff(6,plain,
% 0.13/0.38 ((~![A: $i] : ((~relation(A)) | (reflexive(A) <=> ![B: $i] : ((~in(B, relation_field(A))) | in(ordered_pair(B, B), A))))) <=> (~![A: $i] : ((~relation(A)) | (reflexive(A) <=> ![B: $i] : ((~in(B, relation_field(A))) | in(ordered_pair(B, B), A)))))),
% 0.13/0.38 inference(rewrite,[status(thm)],[])).
% 0.13/0.38 tff(7,plain,
% 0.13/0.38 ((~![A: $i] : (relation(A) => (reflexive(A) <=> ![B: $i] : (in(B, relation_field(A)) => in(ordered_pair(B, B), A))))) <=> (~![A: $i] : ((~relation(A)) | (reflexive(A) <=> ![B: $i] : ((~in(B, relation_field(A))) | in(ordered_pair(B, B), A)))))),
% 0.13/0.38 inference(rewrite,[status(thm)],[])).
% 0.13/0.38 tff(8,axiom,(~![A: $i] : (relation(A) => (reflexive(A) <=> ![B: $i] : (in(B, relation_field(A)) => in(ordered_pair(B, B), A))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','l1_wellord1')).
% 0.13/0.38 tff(9,plain,
% 0.13/0.38 (~![A: $i] : ((~relation(A)) | (reflexive(A) <=> ![B: $i] : ((~in(B, relation_field(A))) | in(ordered_pair(B, B), A))))),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[8, 7])).
% 0.13/0.38 tff(10,plain,
% 0.13/0.38 (~![A: $i] : ((~relation(A)) | (reflexive(A) <=> ![B: $i] : ((~in(B, relation_field(A))) | in(ordered_pair(B, B), A))))),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[9, 6])).
% 0.13/0.38 tff(11,plain,
% 0.13/0.38 (~![A: $i] : ((~relation(A)) | (reflexive(A) <=> ![B: $i] : ((~in(B, relation_field(A))) | in(ordered_pair(B, B), A))))),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[10, 6])).
% 0.13/0.38 tff(12,plain,
% 0.13/0.38 (~![A: $i] : ((~relation(A)) | (reflexive(A) <=> ![B: $i] : ((~in(B, relation_field(A))) | in(ordered_pair(B, B), A))))),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[11, 6])).
% 0.13/0.38 tff(13,plain,
% 0.13/0.38 (relation(A!2) & (reflexive(A!2) | ![B: $i] : ((~in(B, relation_field(A!2))) | in(ordered_pair(B, B), A!2))) & ((~reflexive(A!2)) | (~((~in(B!3, relation_field(A!2))) | in(ordered_pair(B!3, B!3), A!2))))),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[12, 5])).
% 0.13/0.38 tff(14,plain,
% 0.13/0.38 (relation(A!2)),
% 0.13/0.38 inference(and_elim,[status(thm)],[13])).
% 0.13/0.38 tff(15,plain,
% 0.13/0.38 (^[A: $i] : refl(((~relation(A)) | (relation_field(A) = set_union2(relation_dom(A), relation_rng(A)))) <=> ((~relation(A)) | (relation_field(A) = set_union2(relation_dom(A), relation_rng(A)))))),
% 0.13/0.38 inference(bind,[status(th)],[])).
% 0.13/0.38 tff(16,plain,
% 0.13/0.38 (![A: $i] : ((~relation(A)) | (relation_field(A) = set_union2(relation_dom(A), relation_rng(A)))) <=> ![A: $i] : ((~relation(A)) | (relation_field(A) = set_union2(relation_dom(A), relation_rng(A))))),
% 0.13/0.38 inference(quant_intro,[status(thm)],[15])).
% 0.13/0.38 tff(17,plain,
% 0.13/0.38 (![A: $i] : ((~relation(A)) | (relation_field(A) = set_union2(relation_dom(A), relation_rng(A)))) <=> ![A: $i] : ((~relation(A)) | (relation_field(A) = set_union2(relation_dom(A), relation_rng(A))))),
% 0.13/0.38 inference(rewrite,[status(thm)],[])).
% 0.13/0.38 tff(18,plain,
% 0.13/0.38 (^[A: $i] : rewrite((relation(A) => (relation_field(A) = set_union2(relation_dom(A), relation_rng(A)))) <=> ((~relation(A)) | (relation_field(A) = set_union2(relation_dom(A), relation_rng(A)))))),
% 0.13/0.38 inference(bind,[status(th)],[])).
% 0.13/0.38 tff(19,plain,
% 0.13/0.38 (![A: $i] : (relation(A) => (relation_field(A) = set_union2(relation_dom(A), relation_rng(A)))) <=> ![A: $i] : ((~relation(A)) | (relation_field(A) = set_union2(relation_dom(A), relation_rng(A))))),
% 0.13/0.38 inference(quant_intro,[status(thm)],[18])).
% 0.13/0.38 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')).
% 0.13/0.38 tff(21,plain,
% 0.13/0.38 (![A: $i] : ((~relation(A)) | (relation_field(A) = set_union2(relation_dom(A), relation_rng(A))))),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[20, 19])).
% 0.13/0.38 tff(22,plain,
% 0.13/0.38 (![A: $i] : ((~relation(A)) | (relation_field(A) = set_union2(relation_dom(A), relation_rng(A))))),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[21, 17])).
% 0.13/0.38 tff(23,plain,(
% 0.13/0.38 ![A: $i] : ((~relation(A)) | (relation_field(A) = set_union2(relation_dom(A), relation_rng(A))))),
% 0.13/0.38 inference(skolemize,[status(sab)],[22])).
% 0.13/0.38 tff(24,plain,
% 0.13/0.38 (![A: $i] : ((~relation(A)) | (relation_field(A) = set_union2(relation_dom(A), relation_rng(A))))),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[23, 16])).
% 0.13/0.38 tff(25,plain,
% 0.13/0.38 (((~![A: $i] : ((~relation(A)) | (relation_field(A) = set_union2(relation_dom(A), relation_rng(A))))) | ((~relation(A!2)) | (relation_field(A!2) = set_union2(relation_dom(A!2), relation_rng(A!2))))) <=> ((~![A: $i] : ((~relation(A)) | (relation_field(A) = set_union2(relation_dom(A), relation_rng(A))))) | (~relation(A!2)) | (relation_field(A!2) = set_union2(relation_dom(A!2), relation_rng(A!2))))),
% 0.13/0.38 inference(rewrite,[status(thm)],[])).
% 0.13/0.38 tff(26,plain,
% 0.13/0.38 ((~![A: $i] : ((~relation(A)) | (relation_field(A) = set_union2(relation_dom(A), relation_rng(A))))) | ((~relation(A!2)) | (relation_field(A!2) = set_union2(relation_dom(A!2), relation_rng(A!2))))),
% 0.13/0.38 inference(quant_inst,[status(thm)],[])).
% 0.13/0.38 tff(27,plain,
% 0.13/0.38 ((~![A: $i] : ((~relation(A)) | (relation_field(A) = set_union2(relation_dom(A), relation_rng(A))))) | (~relation(A!2)) | (relation_field(A!2) = set_union2(relation_dom(A!2), relation_rng(A!2)))),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[26, 25])).
% 0.13/0.38 tff(28,plain,
% 0.13/0.38 (relation_field(A!2) = set_union2(relation_dom(A!2), relation_rng(A!2))),
% 0.13/0.38 inference(unit_resolution,[status(thm)],[27, 24, 14])).
% 0.13/0.38 tff(29,plain,
% 0.13/0.38 (in(tptp_fun_C_0(set_union2(relation_dom(A!2), relation_rng(A!2)), A!2), relation_field(A!2)) <=> in(tptp_fun_C_0(set_union2(relation_dom(A!2), relation_rng(A!2)), A!2), set_union2(relation_dom(A!2), relation_rng(A!2)))),
% 0.13/0.38 inference(monotonicity,[status(thm)],[28])).
% 0.13/0.38 tff(30,plain,
% 0.13/0.38 (in(tptp_fun_C_0(set_union2(relation_dom(A!2), relation_rng(A!2)), A!2), set_union2(relation_dom(A!2), relation_rng(A!2))) <=> in(tptp_fun_C_0(set_union2(relation_dom(A!2), relation_rng(A!2)), A!2), relation_field(A!2))),
% 0.13/0.38 inference(symmetry,[status(thm)],[29])).
% 0.13/0.38 tff(31,plain,
% 0.13/0.38 (set_union2(relation_dom(A!2), relation_rng(A!2)) = relation_field(A!2)),
% 0.13/0.38 inference(symmetry,[status(thm)],[28])).
% 0.13/0.38 tff(32,plain,
% 0.13/0.38 (is_reflexive_in(A!2, set_union2(relation_dom(A!2), relation_rng(A!2))) <=> is_reflexive_in(A!2, relation_field(A!2))),
% 0.13/0.38 inference(monotonicity,[status(thm)],[31])).
% 0.13/0.38 tff(33,plain,
% 0.13/0.38 (is_reflexive_in(A!2, relation_field(A!2)) <=> is_reflexive_in(A!2, set_union2(relation_dom(A!2), relation_rng(A!2)))),
% 0.13/0.38 inference(symmetry,[status(thm)],[32])).
% 0.13/0.38 tff(34,plain,
% 0.13/0.38 ((~is_reflexive_in(A!2, relation_field(A!2))) <=> (~is_reflexive_in(A!2, set_union2(relation_dom(A!2), relation_rng(A!2))))),
% 0.13/0.38 inference(monotonicity,[status(thm)],[33])).
% 0.13/0.38 tff(35,assumption,(~((~in(B!3, relation_field(A!2))) | in(ordered_pair(B!3, B!3), A!2))), introduced(assumption)).
% 0.13/0.38 tff(36,plain,
% 0.13/0.38 (((~in(B!3, relation_field(A!2))) | in(ordered_pair(B!3, B!3), A!2)) | (~in(ordered_pair(B!3, B!3), A!2))),
% 0.13/0.38 inference(tautology,[status(thm)],[])).
% 0.13/0.38 tff(37,plain,
% 0.13/0.38 (~in(ordered_pair(B!3, B!3), A!2)),
% 0.13/0.38 inference(unit_resolution,[status(thm)],[36, 35])).
% 0.13/0.38 tff(38,plain,
% 0.13/0.38 (((~in(B!3, relation_field(A!2))) | in(ordered_pair(B!3, B!3), A!2)) | in(B!3, relation_field(A!2))),
% 0.13/0.38 inference(tautology,[status(thm)],[])).
% 0.13/0.38 tff(39,plain,
% 0.13/0.38 (in(B!3, relation_field(A!2))),
% 0.13/0.38 inference(unit_resolution,[status(thm)],[38, 35])).
% 0.13/0.38 tff(40,plain,
% 0.13/0.38 ((~is_reflexive_in(A!2, set_union2(relation_dom(A!2), relation_rng(A!2)))) <=> (~is_reflexive_in(A!2, relation_field(A!2)))),
% 0.13/0.38 inference(monotonicity,[status(thm)],[32])).
% 0.13/0.38 tff(41,plain,
% 0.13/0.38 (in(B!3, set_union2(relation_dom(A!2), relation_rng(A!2))) <=> in(B!3, relation_field(A!2))),
% 0.13/0.38 inference(monotonicity,[status(thm)],[31])).
% 0.13/0.38 tff(42,plain,
% 0.13/0.38 (in(B!3, relation_field(A!2)) <=> in(B!3, set_union2(relation_dom(A!2), relation_rng(A!2)))),
% 0.13/0.38 inference(symmetry,[status(thm)],[41])).
% 0.13/0.38 tff(43,plain,
% 0.13/0.38 (in(B!3, set_union2(relation_dom(A!2), relation_rng(A!2)))),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[39, 42])).
% 0.13/0.38 tff(44,assumption,(in(B!3, set_union2(relation_dom(A!2), relation_rng(A!2)))), introduced(assumption)).
% 0.13/0.38 tff(45,assumption,(![C: $i] : ((~in(C, set_union2(relation_dom(A!2), relation_rng(A!2)))) | in(ordered_pair(C, C), A!2))), introduced(assumption)).
% 0.13/0.38 tff(46,assumption,(~in(ordered_pair(B!3, B!3), A!2)), introduced(assumption)).
% 0.13/0.38 tff(47,plain,
% 0.13/0.38 (((~![C: $i] : ((~in(C, set_union2(relation_dom(A!2), relation_rng(A!2)))) | in(ordered_pair(C, C), A!2))) | ((~in(B!3, set_union2(relation_dom(A!2), relation_rng(A!2)))) | in(ordered_pair(B!3, B!3), A!2))) <=> ((~![C: $i] : ((~in(C, set_union2(relation_dom(A!2), relation_rng(A!2)))) | in(ordered_pair(C, C), A!2))) | (~in(B!3, set_union2(relation_dom(A!2), relation_rng(A!2)))) | in(ordered_pair(B!3, B!3), A!2))),
% 0.13/0.38 inference(rewrite,[status(thm)],[])).
% 0.13/0.38 tff(48,plain,
% 0.13/0.38 ((~![C: $i] : ((~in(C, set_union2(relation_dom(A!2), relation_rng(A!2)))) | in(ordered_pair(C, C), A!2))) | ((~in(B!3, set_union2(relation_dom(A!2), relation_rng(A!2)))) | in(ordered_pair(B!3, B!3), A!2))),
% 0.13/0.38 inference(quant_inst,[status(thm)],[])).
% 0.13/0.38 tff(49,plain,
% 0.13/0.38 ((~![C: $i] : ((~in(C, set_union2(relation_dom(A!2), relation_rng(A!2)))) | in(ordered_pair(C, C), A!2))) | (~in(B!3, set_union2(relation_dom(A!2), relation_rng(A!2)))) | in(ordered_pair(B!3, B!3), A!2)),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[48, 47])).
% 0.13/0.38 tff(50,plain,
% 0.13/0.38 ($false),
% 0.13/0.38 inference(unit_resolution,[status(thm)],[49, 46, 45, 44])).
% 0.13/0.38 tff(51,plain,((~![C: $i] : ((~in(C, set_union2(relation_dom(A!2), relation_rng(A!2)))) | in(ordered_pair(C, C), A!2))) | in(ordered_pair(B!3, B!3), A!2) | (~in(B!3, set_union2(relation_dom(A!2), relation_rng(A!2))))), inference(lemma,lemma(discharge,[]))).
% 0.13/0.38 tff(52,plain,
% 0.13/0.38 (~![C: $i] : ((~in(C, set_union2(relation_dom(A!2), relation_rng(A!2)))) | in(ordered_pair(C, C), A!2))),
% 0.13/0.38 inference(unit_resolution,[status(thm)],[51, 37, 43])).
% 0.13/0.38 tff(53,plain,
% 0.13/0.38 (^[A: $i] : refl(((~relation(A)) | ![B: $i] : (~((~((~is_reflexive_in(A, B)) | ![C: $i] : ((~in(C, B)) | in(ordered_pair(C, C), A)))) | (~(is_reflexive_in(A, B) | (~((~in(tptp_fun_C_0(B, A), B)) | in(ordered_pair(tptp_fun_C_0(B, A), tptp_fun_C_0(B, A)), A)))))))) <=> ((~relation(A)) | ![B: $i] : (~((~((~is_reflexive_in(A, B)) | ![C: $i] : ((~in(C, B)) | in(ordered_pair(C, C), A)))) | (~(is_reflexive_in(A, B) | (~((~in(tptp_fun_C_0(B, A), B)) | in(ordered_pair(tptp_fun_C_0(B, A), tptp_fun_C_0(B, A)), A)))))))))),
% 0.13/0.38 inference(bind,[status(th)],[])).
% 0.13/0.38 tff(54,plain,
% 0.13/0.38 (![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~is_reflexive_in(A, B)) | ![C: $i] : ((~in(C, B)) | in(ordered_pair(C, C), A)))) | (~(is_reflexive_in(A, B) | (~((~in(tptp_fun_C_0(B, A), B)) | in(ordered_pair(tptp_fun_C_0(B, A), tptp_fun_C_0(B, A)), A)))))))) <=> ![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~is_reflexive_in(A, B)) | ![C: $i] : ((~in(C, B)) | in(ordered_pair(C, C), A)))) | (~(is_reflexive_in(A, B) | (~((~in(tptp_fun_C_0(B, A), B)) | in(ordered_pair(tptp_fun_C_0(B, A), tptp_fun_C_0(B, A)), A))))))))),
% 0.13/0.38 inference(quant_intro,[status(thm)],[53])).
% 0.13/0.38 tff(55,plain,
% 0.13/0.38 (^[A: $i] : rewrite(((~relation(A)) | ![B: $i] : (~((~((~is_reflexive_in(A, B)) | ![C: $i] : ((~in(C, B)) | in(ordered_pair(C, C), A)))) | (~(is_reflexive_in(A, B) | (~((~in(tptp_fun_C_0(B, A), B)) | in(ordered_pair(tptp_fun_C_0(B, A), tptp_fun_C_0(B, A)), A)))))))) <=> ((~relation(A)) | ![B: $i] : (~((~((~is_reflexive_in(A, B)) | ![C: $i] : ((~in(C, B)) | in(ordered_pair(C, C), A)))) | (~(is_reflexive_in(A, B) | (~((~in(tptp_fun_C_0(B, A), B)) | in(ordered_pair(tptp_fun_C_0(B, A), tptp_fun_C_0(B, A)), A)))))))))),
% 0.13/0.38 inference(bind,[status(th)],[])).
% 0.13/0.38 tff(56,plain,
% 0.13/0.38 (![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~is_reflexive_in(A, B)) | ![C: $i] : ((~in(C, B)) | in(ordered_pair(C, C), A)))) | (~(is_reflexive_in(A, B) | (~((~in(tptp_fun_C_0(B, A), B)) | in(ordered_pair(tptp_fun_C_0(B, A), tptp_fun_C_0(B, A)), A)))))))) <=> ![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~is_reflexive_in(A, B)) | ![C: $i] : ((~in(C, B)) | in(ordered_pair(C, C), A)))) | (~(is_reflexive_in(A, B) | (~((~in(tptp_fun_C_0(B, A), B)) | in(ordered_pair(tptp_fun_C_0(B, A), tptp_fun_C_0(B, A)), A))))))))),
% 0.13/0.38 inference(quant_intro,[status(thm)],[55])).
% 0.13/0.38 tff(57,plain,
% 0.13/0.38 (![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~is_reflexive_in(A, B)) | ![C: $i] : ((~in(C, B)) | in(ordered_pair(C, C), A)))) | (~(is_reflexive_in(A, B) | (~((~in(tptp_fun_C_0(B, A), B)) | in(ordered_pair(tptp_fun_C_0(B, A), tptp_fun_C_0(B, A)), A)))))))) <=> ![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~is_reflexive_in(A, B)) | ![C: $i] : ((~in(C, B)) | in(ordered_pair(C, C), A)))) | (~(is_reflexive_in(A, B) | (~((~in(tptp_fun_C_0(B, A), B)) | in(ordered_pair(tptp_fun_C_0(B, A), tptp_fun_C_0(B, A)), A))))))))),
% 0.13/0.38 inference(transitivity,[status(thm)],[56, 54])).
% 0.13/0.38 tff(58,plain,
% 0.13/0.38 (^[A: $i] : rewrite(((~relation(A)) | ![B: $i] : (((~is_reflexive_in(A, B)) | ![C: $i] : ((~in(C, B)) | in(ordered_pair(C, C), A))) & (is_reflexive_in(A, B) | (~((~in(tptp_fun_C_0(B, A), B)) | in(ordered_pair(tptp_fun_C_0(B, A), tptp_fun_C_0(B, A)), A)))))) <=> ((~relation(A)) | ![B: $i] : (~((~((~is_reflexive_in(A, B)) | ![C: $i] : ((~in(C, B)) | in(ordered_pair(C, C), A)))) | (~(is_reflexive_in(A, B) | (~((~in(tptp_fun_C_0(B, A), B)) | in(ordered_pair(tptp_fun_C_0(B, A), tptp_fun_C_0(B, A)), A)))))))))),
% 0.13/0.38 inference(bind,[status(th)],[])).
% 0.13/0.38 tff(59,plain,
% 0.13/0.38 (![A: $i] : ((~relation(A)) | ![B: $i] : (((~is_reflexive_in(A, B)) | ![C: $i] : ((~in(C, B)) | in(ordered_pair(C, C), A))) & (is_reflexive_in(A, B) | (~((~in(tptp_fun_C_0(B, A), B)) | in(ordered_pair(tptp_fun_C_0(B, A), tptp_fun_C_0(B, A)), A)))))) <=> ![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~is_reflexive_in(A, B)) | ![C: $i] : ((~in(C, B)) | in(ordered_pair(C, C), A)))) | (~(is_reflexive_in(A, B) | (~((~in(tptp_fun_C_0(B, A), B)) | in(ordered_pair(tptp_fun_C_0(B, A), tptp_fun_C_0(B, A)), A))))))))),
% 0.13/0.39 inference(quant_intro,[status(thm)],[58])).
% 0.13/0.39 tff(60,plain,
% 0.13/0.39 (![A: $i] : ((~relation(A)) | ![B: $i] : (is_reflexive_in(A, B) <=> ![C: $i] : ((~in(C, B)) | in(ordered_pair(C, C), A)))) <=> ![A: $i] : ((~relation(A)) | ![B: $i] : (is_reflexive_in(A, B) <=> ![C: $i] : ((~in(C, B)) | in(ordered_pair(C, C), A))))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(61,plain,
% 0.13/0.39 (^[A: $i] : trans(monotonicity(quant_intro(proof_bind(^[B: $i] : rewrite((is_reflexive_in(A, B) <=> ![C: $i] : (in(C, B) => in(ordered_pair(C, C), A))) <=> (is_reflexive_in(A, B) <=> ![C: $i] : ((~in(C, B)) | in(ordered_pair(C, C), A))))), (![B: $i] : (is_reflexive_in(A, B) <=> ![C: $i] : (in(C, B) => in(ordered_pair(C, C), A))) <=> ![B: $i] : (is_reflexive_in(A, B) <=> ![C: $i] : ((~in(C, B)) | in(ordered_pair(C, C), A))))), ((relation(A) => ![B: $i] : (is_reflexive_in(A, B) <=> ![C: $i] : (in(C, B) => in(ordered_pair(C, C), A)))) <=> (relation(A) => ![B: $i] : (is_reflexive_in(A, B) <=> ![C: $i] : ((~in(C, B)) | in(ordered_pair(C, C), A)))))), rewrite((relation(A) => ![B: $i] : (is_reflexive_in(A, B) <=> ![C: $i] : ((~in(C, B)) | in(ordered_pair(C, C), A)))) <=> ((~relation(A)) | ![B: $i] : (is_reflexive_in(A, B) <=> ![C: $i] : ((~in(C, B)) | in(ordered_pair(C, C), A))))), ((relation(A) => ![B: $i] : (is_reflexive_in(A, B) <=> ![C: $i] : (in(C, B) => in(ordered_pair(C, C), A)))) <=> ((~relation(A)) | ![B: $i] : (is_reflexive_in(A, B) <=> ![C: $i] : ((~in(C, B)) | in(ordered_pair(C, C), A))))))),
% 0.13/0.39 inference(bind,[status(th)],[])).
% 0.13/0.39 tff(62,plain,
% 0.13/0.39 (![A: $i] : (relation(A) => ![B: $i] : (is_reflexive_in(A, B) <=> ![C: $i] : (in(C, B) => in(ordered_pair(C, C), A)))) <=> ![A: $i] : ((~relation(A)) | ![B: $i] : (is_reflexive_in(A, B) <=> ![C: $i] : ((~in(C, B)) | in(ordered_pair(C, C), A))))),
% 0.13/0.39 inference(quant_intro,[status(thm)],[61])).
% 0.13/0.39 tff(63,axiom,(![A: $i] : (relation(A) => ![B: $i] : (is_reflexive_in(A, B) <=> ![C: $i] : (in(C, B) => in(ordered_pair(C, C), A))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d1_relat_2')).
% 0.13/0.39 tff(64,plain,
% 0.13/0.39 (![A: $i] : ((~relation(A)) | ![B: $i] : (is_reflexive_in(A, B) <=> ![C: $i] : ((~in(C, B)) | in(ordered_pair(C, C), A))))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[63, 62])).
% 0.13/0.39 tff(65,plain,
% 0.13/0.39 (![A: $i] : ((~relation(A)) | ![B: $i] : (is_reflexive_in(A, B) <=> ![C: $i] : ((~in(C, B)) | in(ordered_pair(C, C), A))))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[64, 60])).
% 0.13/0.39 tff(66,plain,(
% 0.13/0.39 ![A: $i] : ((~relation(A)) | ![B: $i] : (((~is_reflexive_in(A, B)) | ![C: $i] : ((~in(C, B)) | in(ordered_pair(C, C), A))) & (is_reflexive_in(A, B) | (~((~in(tptp_fun_C_0(B, A), B)) | in(ordered_pair(tptp_fun_C_0(B, A), tptp_fun_C_0(B, A)), A))))))),
% 0.13/0.39 inference(skolemize,[status(sab)],[65])).
% 0.13/0.39 tff(67,plain,
% 0.13/0.39 (![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~is_reflexive_in(A, B)) | ![C: $i] : ((~in(C, B)) | in(ordered_pair(C, C), A)))) | (~(is_reflexive_in(A, B) | (~((~in(tptp_fun_C_0(B, A), B)) | in(ordered_pair(tptp_fun_C_0(B, A), tptp_fun_C_0(B, A)), A))))))))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[66, 59])).
% 0.13/0.39 tff(68,plain,
% 0.13/0.39 (![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~is_reflexive_in(A, B)) | ![C: $i] : ((~in(C, B)) | in(ordered_pair(C, C), A)))) | (~(is_reflexive_in(A, B) | (~((~in(tptp_fun_C_0(B, A), B)) | in(ordered_pair(tptp_fun_C_0(B, A), tptp_fun_C_0(B, A)), A))))))))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[67, 57])).
% 0.13/0.39 tff(69,plain,
% 0.13/0.39 (((~![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~is_reflexive_in(A, B)) | ![C: $i] : ((~in(C, B)) | in(ordered_pair(C, C), A)))) | (~(is_reflexive_in(A, B) | (~((~in(tptp_fun_C_0(B, A), B)) | in(ordered_pair(tptp_fun_C_0(B, A), tptp_fun_C_0(B, A)), A))))))))) | ((~relation(A!2)) | ![B: $i] : (~((~((~is_reflexive_in(A!2, B)) | ![C: $i] : ((~in(C, B)) | in(ordered_pair(C, C), A!2)))) | (~(is_reflexive_in(A!2, B) | (~((~in(tptp_fun_C_0(B, A!2), B)) | in(ordered_pair(tptp_fun_C_0(B, A!2), tptp_fun_C_0(B, A!2)), A!2))))))))) <=> ((~![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~is_reflexive_in(A, B)) | ![C: $i] : ((~in(C, B)) | in(ordered_pair(C, C), A)))) | (~(is_reflexive_in(A, B) | (~((~in(tptp_fun_C_0(B, A), B)) | in(ordered_pair(tptp_fun_C_0(B, A), tptp_fun_C_0(B, A)), A))))))))) | (~relation(A!2)) | ![B: $i] : (~((~((~is_reflexive_in(A!2, B)) | ![C: $i] : ((~in(C, B)) | in(ordered_pair(C, C), A!2)))) | (~(is_reflexive_in(A!2, B) | (~((~in(tptp_fun_C_0(B, A!2), B)) | in(ordered_pair(tptp_fun_C_0(B, A!2), tptp_fun_C_0(B, A!2)), A!2))))))))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(70,plain,
% 0.13/0.39 ((~![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~is_reflexive_in(A, B)) | ![C: $i] : ((~in(C, B)) | in(ordered_pair(C, C), A)))) | (~(is_reflexive_in(A, B) | (~((~in(tptp_fun_C_0(B, A), B)) | in(ordered_pair(tptp_fun_C_0(B, A), tptp_fun_C_0(B, A)), A))))))))) | ((~relation(A!2)) | ![B: $i] : (~((~((~is_reflexive_in(A!2, B)) | ![C: $i] : ((~in(C, B)) | in(ordered_pair(C, C), A!2)))) | (~(is_reflexive_in(A!2, B) | (~((~in(tptp_fun_C_0(B, A!2), B)) | in(ordered_pair(tptp_fun_C_0(B, A!2), tptp_fun_C_0(B, A!2)), A!2))))))))),
% 0.13/0.39 inference(quant_inst,[status(thm)],[])).
% 0.13/0.39 tff(71,plain,
% 0.13/0.39 ((~![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~is_reflexive_in(A, B)) | ![C: $i] : ((~in(C, B)) | in(ordered_pair(C, C), A)))) | (~(is_reflexive_in(A, B) | (~((~in(tptp_fun_C_0(B, A), B)) | in(ordered_pair(tptp_fun_C_0(B, A), tptp_fun_C_0(B, A)), A))))))))) | (~relation(A!2)) | ![B: $i] : (~((~((~is_reflexive_in(A!2, B)) | ![C: $i] : ((~in(C, B)) | in(ordered_pair(C, C), A!2)))) | (~(is_reflexive_in(A!2, B) | (~((~in(tptp_fun_C_0(B, A!2), B)) | in(ordered_pair(tptp_fun_C_0(B, A!2), tptp_fun_C_0(B, A!2)), A!2)))))))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[70, 69])).
% 0.13/0.39 tff(72,plain,
% 0.13/0.39 (![B: $i] : (~((~((~is_reflexive_in(A!2, B)) | ![C: $i] : ((~in(C, B)) | in(ordered_pair(C, C), A!2)))) | (~(is_reflexive_in(A!2, B) | (~((~in(tptp_fun_C_0(B, A!2), B)) | in(ordered_pair(tptp_fun_C_0(B, A!2), tptp_fun_C_0(B, A!2)), A!2)))))))),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[71, 68, 14])).
% 0.13/0.39 tff(73,plain,
% 0.13/0.39 (((~![B: $i] : (~((~((~is_reflexive_in(A!2, B)) | ![C: $i] : ((~in(C, B)) | in(ordered_pair(C, C), A!2)))) | (~(is_reflexive_in(A!2, B) | (~((~in(tptp_fun_C_0(B, A!2), B)) | in(ordered_pair(tptp_fun_C_0(B, A!2), tptp_fun_C_0(B, A!2)), A!2)))))))) | (~((~((~is_reflexive_in(A!2, set_union2(relation_dom(A!2), relation_rng(A!2)))) | ![C: $i] : ((~in(C, set_union2(relation_dom(A!2), relation_rng(A!2)))) | in(ordered_pair(C, C), A!2)))) | (~((~((~in(tptp_fun_C_0(set_union2(relation_dom(A!2), relation_rng(A!2)), A!2), set_union2(relation_dom(A!2), relation_rng(A!2)))) | in(ordered_pair(tptp_fun_C_0(set_union2(relation_dom(A!2), relation_rng(A!2)), A!2), tptp_fun_C_0(set_union2(relation_dom(A!2), relation_rng(A!2)), A!2)), A!2))) | is_reflexive_in(A!2, set_union2(relation_dom(A!2), relation_rng(A!2)))))))) <=> ((~![B: $i] : (~((~((~is_reflexive_in(A!2, B)) | ![C: $i] : ((~in(C, B)) | in(ordered_pair(C, C), A!2)))) | (~(is_reflexive_in(A!2, B) | (~((~in(tptp_fun_C_0(B, A!2), B)) | in(ordered_pair(tptp_fun_C_0(B, A!2), tptp_fun_C_0(B, A!2)), A!2)))))))) | (~((~((~is_reflexive_in(A!2, set_union2(relation_dom(A!2), relation_rng(A!2)))) | ![C: $i] : ((~in(C, set_union2(relation_dom(A!2), relation_rng(A!2)))) | in(ordered_pair(C, C), A!2)))) | (~((~((~in(tptp_fun_C_0(set_union2(relation_dom(A!2), relation_rng(A!2)), A!2), set_union2(relation_dom(A!2), relation_rng(A!2)))) | in(ordered_pair(tptp_fun_C_0(set_union2(relation_dom(A!2), relation_rng(A!2)), A!2), tptp_fun_C_0(set_union2(relation_dom(A!2), relation_rng(A!2)), A!2)), A!2))) | is_reflexive_in(A!2, set_union2(relation_dom(A!2), relation_rng(A!2))))))))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(74,plain,
% 0.13/0.39 ((~((~((~is_reflexive_in(A!2, set_union2(relation_dom(A!2), relation_rng(A!2)))) | ![C: $i] : ((~in(C, set_union2(relation_dom(A!2), relation_rng(A!2)))) | in(ordered_pair(C, C), A!2)))) | (~(is_reflexive_in(A!2, set_union2(relation_dom(A!2), relation_rng(A!2))) | (~((~in(tptp_fun_C_0(set_union2(relation_dom(A!2), relation_rng(A!2)), A!2), set_union2(relation_dom(A!2), relation_rng(A!2)))) | in(ordered_pair(tptp_fun_C_0(set_union2(relation_dom(A!2), relation_rng(A!2)), A!2), tptp_fun_C_0(set_union2(relation_dom(A!2), relation_rng(A!2)), A!2)), A!2))))))) <=> (~((~((~is_reflexive_in(A!2, set_union2(relation_dom(A!2), relation_rng(A!2)))) | ![C: $i] : ((~in(C, set_union2(relation_dom(A!2), relation_rng(A!2)))) | in(ordered_pair(C, C), A!2)))) | (~((~((~in(tptp_fun_C_0(set_union2(relation_dom(A!2), relation_rng(A!2)), A!2), set_union2(relation_dom(A!2), relation_rng(A!2)))) | in(ordered_pair(tptp_fun_C_0(set_union2(relation_dom(A!2), relation_rng(A!2)), A!2), tptp_fun_C_0(set_union2(relation_dom(A!2), relation_rng(A!2)), A!2)), A!2))) | is_reflexive_in(A!2, set_union2(relation_dom(A!2), relation_rng(A!2)))))))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(75,plain,
% 0.13/0.39 (((~![B: $i] : (~((~((~is_reflexive_in(A!2, B)) | ![C: $i] : ((~in(C, B)) | in(ordered_pair(C, C), A!2)))) | (~(is_reflexive_in(A!2, B) | (~((~in(tptp_fun_C_0(B, A!2), B)) | in(ordered_pair(tptp_fun_C_0(B, A!2), tptp_fun_C_0(B, A!2)), A!2)))))))) | (~((~((~is_reflexive_in(A!2, set_union2(relation_dom(A!2), relation_rng(A!2)))) | ![C: $i] : ((~in(C, set_union2(relation_dom(A!2), relation_rng(A!2)))) | in(ordered_pair(C, C), A!2)))) | (~(is_reflexive_in(A!2, set_union2(relation_dom(A!2), relation_rng(A!2))) | (~((~in(tptp_fun_C_0(set_union2(relation_dom(A!2), relation_rng(A!2)), A!2), set_union2(relation_dom(A!2), relation_rng(A!2)))) | in(ordered_pair(tptp_fun_C_0(set_union2(relation_dom(A!2), relation_rng(A!2)), A!2), tptp_fun_C_0(set_union2(relation_dom(A!2), relation_rng(A!2)), A!2)), A!2)))))))) <=> ((~![B: $i] : (~((~((~is_reflexive_in(A!2, B)) | ![C: $i] : ((~in(C, B)) | in(ordered_pair(C, C), A!2)))) | (~(is_reflexive_in(A!2, B) | (~((~in(tptp_fun_C_0(B, A!2), B)) | in(ordered_pair(tptp_fun_C_0(B, A!2), tptp_fun_C_0(B, A!2)), A!2)))))))) | (~((~((~is_reflexive_in(A!2, set_union2(relation_dom(A!2), relation_rng(A!2)))) | ![C: $i] : ((~in(C, set_union2(relation_dom(A!2), relation_rng(A!2)))) | in(ordered_pair(C, C), A!2)))) | (~((~((~in(tptp_fun_C_0(set_union2(relation_dom(A!2), relation_rng(A!2)), A!2), set_union2(relation_dom(A!2), relation_rng(A!2)))) | in(ordered_pair(tptp_fun_C_0(set_union2(relation_dom(A!2), relation_rng(A!2)), A!2), tptp_fun_C_0(set_union2(relation_dom(A!2), relation_rng(A!2)), A!2)), A!2))) | is_reflexive_in(A!2, set_union2(relation_dom(A!2), relation_rng(A!2))))))))),
% 0.13/0.39 inference(monotonicity,[status(thm)],[74])).
% 0.13/0.39 tff(76,plain,
% 0.13/0.39 (((~![B: $i] : (~((~((~is_reflexive_in(A!2, B)) | ![C: $i] : ((~in(C, B)) | in(ordered_pair(C, C), A!2)))) | (~(is_reflexive_in(A!2, B) | (~((~in(tptp_fun_C_0(B, A!2), B)) | in(ordered_pair(tptp_fun_C_0(B, A!2), tptp_fun_C_0(B, A!2)), A!2)))))))) | (~((~((~is_reflexive_in(A!2, set_union2(relation_dom(A!2), relation_rng(A!2)))) | ![C: $i] : ((~in(C, set_union2(relation_dom(A!2), relation_rng(A!2)))) | in(ordered_pair(C, C), A!2)))) | (~(is_reflexive_in(A!2, set_union2(relation_dom(A!2), relation_rng(A!2))) | (~((~in(tptp_fun_C_0(set_union2(relation_dom(A!2), relation_rng(A!2)), A!2), set_union2(relation_dom(A!2), relation_rng(A!2)))) | in(ordered_pair(tptp_fun_C_0(set_union2(relation_dom(A!2), relation_rng(A!2)), A!2), tptp_fun_C_0(set_union2(relation_dom(A!2), relation_rng(A!2)), A!2)), A!2)))))))) <=> ((~![B: $i] : (~((~((~is_reflexive_in(A!2, B)) | ![C: $i] : ((~in(C, B)) | in(ordered_pair(C, C), A!2)))) | (~(is_reflexive_in(A!2, B) | (~((~in(tptp_fun_C_0(B, A!2), B)) | in(ordered_pair(tptp_fun_C_0(B, A!2), tptp_fun_C_0(B, A!2)), A!2)))))))) | (~((~((~is_reflexive_in(A!2, set_union2(relation_dom(A!2), relation_rng(A!2)))) | ![C: $i] : ((~in(C, set_union2(relation_dom(A!2), relation_rng(A!2)))) | in(ordered_pair(C, C), A!2)))) | (~((~((~in(tptp_fun_C_0(set_union2(relation_dom(A!2), relation_rng(A!2)), A!2), set_union2(relation_dom(A!2), relation_rng(A!2)))) | in(ordered_pair(tptp_fun_C_0(set_union2(relation_dom(A!2), relation_rng(A!2)), A!2), tptp_fun_C_0(set_union2(relation_dom(A!2), relation_rng(A!2)), A!2)), A!2))) | is_reflexive_in(A!2, set_union2(relation_dom(A!2), relation_rng(A!2))))))))),
% 0.21/0.39 inference(transitivity,[status(thm)],[75, 73])).
% 0.21/0.39 tff(77,plain,
% 0.21/0.39 ((~![B: $i] : (~((~((~is_reflexive_in(A!2, B)) | ![C: $i] : ((~in(C, B)) | in(ordered_pair(C, C), A!2)))) | (~(is_reflexive_in(A!2, B) | (~((~in(tptp_fun_C_0(B, A!2), B)) | in(ordered_pair(tptp_fun_C_0(B, A!2), tptp_fun_C_0(B, A!2)), A!2)))))))) | (~((~((~is_reflexive_in(A!2, set_union2(relation_dom(A!2), relation_rng(A!2)))) | ![C: $i] : ((~in(C, set_union2(relation_dom(A!2), relation_rng(A!2)))) | in(ordered_pair(C, C), A!2)))) | (~(is_reflexive_in(A!2, set_union2(relation_dom(A!2), relation_rng(A!2))) | (~((~in(tptp_fun_C_0(set_union2(relation_dom(A!2), relation_rng(A!2)), A!2), set_union2(relation_dom(A!2), relation_rng(A!2)))) | in(ordered_pair(tptp_fun_C_0(set_union2(relation_dom(A!2), relation_rng(A!2)), A!2), tptp_fun_C_0(set_union2(relation_dom(A!2), relation_rng(A!2)), A!2)), A!2)))))))),
% 0.21/0.39 inference(quant_inst,[status(thm)],[])).
% 0.21/0.39 tff(78,plain,
% 0.21/0.39 ((~![B: $i] : (~((~((~is_reflexive_in(A!2, B)) | ![C: $i] : ((~in(C, B)) | in(ordered_pair(C, C), A!2)))) | (~(is_reflexive_in(A!2, B) | (~((~in(tptp_fun_C_0(B, A!2), B)) | in(ordered_pair(tptp_fun_C_0(B, A!2), tptp_fun_C_0(B, A!2)), A!2)))))))) | (~((~((~is_reflexive_in(A!2, set_union2(relation_dom(A!2), relation_rng(A!2)))) | ![C: $i] : ((~in(C, set_union2(relation_dom(A!2), relation_rng(A!2)))) | in(ordered_pair(C, C), A!2)))) | (~((~((~in(tptp_fun_C_0(set_union2(relation_dom(A!2), relation_rng(A!2)), A!2), set_union2(relation_dom(A!2), relation_rng(A!2)))) | in(ordered_pair(tptp_fun_C_0(set_union2(relation_dom(A!2), relation_rng(A!2)), A!2), tptp_fun_C_0(set_union2(relation_dom(A!2), relation_rng(A!2)), A!2)), A!2))) | is_reflexive_in(A!2, set_union2(relation_dom(A!2), relation_rng(A!2)))))))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[77, 76])).
% 0.21/0.39 tff(79,plain,
% 0.21/0.39 (~((~((~is_reflexive_in(A!2, set_union2(relation_dom(A!2), relation_rng(A!2)))) | ![C: $i] : ((~in(C, set_union2(relation_dom(A!2), relation_rng(A!2)))) | in(ordered_pair(C, C), A!2)))) | (~((~((~in(tptp_fun_C_0(set_union2(relation_dom(A!2), relation_rng(A!2)), A!2), set_union2(relation_dom(A!2), relation_rng(A!2)))) | in(ordered_pair(tptp_fun_C_0(set_union2(relation_dom(A!2), relation_rng(A!2)), A!2), tptp_fun_C_0(set_union2(relation_dom(A!2), relation_rng(A!2)), A!2)), A!2))) | is_reflexive_in(A!2, set_union2(relation_dom(A!2), relation_rng(A!2))))))),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[78, 72])).
% 0.21/0.39 tff(80,plain,
% 0.21/0.39 (((~((~is_reflexive_in(A!2, set_union2(relation_dom(A!2), relation_rng(A!2)))) | ![C: $i] : ((~in(C, set_union2(relation_dom(A!2), relation_rng(A!2)))) | in(ordered_pair(C, C), A!2)))) | (~((~((~in(tptp_fun_C_0(set_union2(relation_dom(A!2), relation_rng(A!2)), A!2), set_union2(relation_dom(A!2), relation_rng(A!2)))) | in(ordered_pair(tptp_fun_C_0(set_union2(relation_dom(A!2), relation_rng(A!2)), A!2), tptp_fun_C_0(set_union2(relation_dom(A!2), relation_rng(A!2)), A!2)), A!2))) | is_reflexive_in(A!2, set_union2(relation_dom(A!2), relation_rng(A!2)))))) | ((~is_reflexive_in(A!2, set_union2(relation_dom(A!2), relation_rng(A!2)))) | ![C: $i] : ((~in(C, set_union2(relation_dom(A!2), relation_rng(A!2)))) | in(ordered_pair(C, C), A!2)))),
% 0.21/0.39 inference(tautology,[status(thm)],[])).
% 0.21/0.39 tff(81,plain,
% 0.21/0.39 ((~is_reflexive_in(A!2, set_union2(relation_dom(A!2), relation_rng(A!2)))) | ![C: $i] : ((~in(C, set_union2(relation_dom(A!2), relation_rng(A!2)))) | in(ordered_pair(C, C), A!2))),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[80, 79])).
% 0.21/0.39 tff(82,plain,
% 0.21/0.39 ((~((~is_reflexive_in(A!2, set_union2(relation_dom(A!2), relation_rng(A!2)))) | ![C: $i] : ((~in(C, set_union2(relation_dom(A!2), relation_rng(A!2)))) | in(ordered_pair(C, C), A!2)))) | (~is_reflexive_in(A!2, set_union2(relation_dom(A!2), relation_rng(A!2)))) | ![C: $i] : ((~in(C, set_union2(relation_dom(A!2), relation_rng(A!2)))) | in(ordered_pair(C, C), A!2))),
% 0.21/0.40 inference(tautology,[status(thm)],[])).
% 0.21/0.40 tff(83,plain,
% 0.21/0.40 ((~is_reflexive_in(A!2, set_union2(relation_dom(A!2), relation_rng(A!2)))) | ![C: $i] : ((~in(C, set_union2(relation_dom(A!2), relation_rng(A!2)))) | in(ordered_pair(C, C), A!2))),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[82, 81])).
% 0.21/0.40 tff(84,plain,
% 0.21/0.40 (~is_reflexive_in(A!2, set_union2(relation_dom(A!2), relation_rng(A!2)))),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[83, 52])).
% 0.21/0.40 tff(85,plain,
% 0.21/0.40 (~is_reflexive_in(A!2, relation_field(A!2))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[84, 40])).
% 0.21/0.40 tff(86,plain,
% 0.21/0.40 (^[A: $i] : refl(((~relation(A)) | (reflexive(A) <=> is_reflexive_in(A, relation_field(A)))) <=> ((~relation(A)) | (reflexive(A) <=> is_reflexive_in(A, relation_field(A)))))),
% 0.21/0.40 inference(bind,[status(th)],[])).
% 0.21/0.40 tff(87,plain,
% 0.21/0.40 (![A: $i] : ((~relation(A)) | (reflexive(A) <=> is_reflexive_in(A, relation_field(A)))) <=> ![A: $i] : ((~relation(A)) | (reflexive(A) <=> is_reflexive_in(A, relation_field(A))))),
% 0.21/0.40 inference(quant_intro,[status(thm)],[86])).
% 0.21/0.40 tff(88,plain,
% 0.21/0.40 (![A: $i] : ((~relation(A)) | (reflexive(A) <=> is_reflexive_in(A, relation_field(A)))) <=> ![A: $i] : ((~relation(A)) | (reflexive(A) <=> is_reflexive_in(A, relation_field(A))))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(89,plain,
% 0.21/0.40 (^[A: $i] : rewrite((relation(A) => (reflexive(A) <=> is_reflexive_in(A, relation_field(A)))) <=> ((~relation(A)) | (reflexive(A) <=> is_reflexive_in(A, relation_field(A)))))),
% 0.21/0.40 inference(bind,[status(th)],[])).
% 0.21/0.40 tff(90,plain,
% 0.21/0.40 (![A: $i] : (relation(A) => (reflexive(A) <=> is_reflexive_in(A, relation_field(A)))) <=> ![A: $i] : ((~relation(A)) | (reflexive(A) <=> is_reflexive_in(A, relation_field(A))))),
% 0.21/0.40 inference(quant_intro,[status(thm)],[89])).
% 0.21/0.40 tff(91,axiom,(![A: $i] : (relation(A) => (reflexive(A) <=> is_reflexive_in(A, relation_field(A))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d9_relat_2')).
% 0.21/0.40 tff(92,plain,
% 0.21/0.40 (![A: $i] : ((~relation(A)) | (reflexive(A) <=> is_reflexive_in(A, relation_field(A))))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[91, 90])).
% 0.21/0.40 tff(93,plain,
% 0.21/0.40 (![A: $i] : ((~relation(A)) | (reflexive(A) <=> is_reflexive_in(A, relation_field(A))))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[92, 88])).
% 0.21/0.40 tff(94,plain,(
% 0.21/0.40 ![A: $i] : ((~relation(A)) | (reflexive(A) <=> is_reflexive_in(A, relation_field(A))))),
% 0.21/0.40 inference(skolemize,[status(sab)],[93])).
% 0.21/0.40 tff(95,plain,
% 0.21/0.40 (![A: $i] : ((~relation(A)) | (reflexive(A) <=> is_reflexive_in(A, relation_field(A))))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[94, 87])).
% 0.21/0.40 tff(96,plain,
% 0.21/0.40 (((~![A: $i] : ((~relation(A)) | (reflexive(A) <=> is_reflexive_in(A, relation_field(A))))) | ((~relation(A!2)) | (reflexive(A!2) <=> is_reflexive_in(A!2, relation_field(A!2))))) <=> ((~![A: $i] : ((~relation(A)) | (reflexive(A) <=> is_reflexive_in(A, relation_field(A))))) | (~relation(A!2)) | (reflexive(A!2) <=> is_reflexive_in(A!2, relation_field(A!2))))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(97,plain,
% 0.21/0.40 ((~![A: $i] : ((~relation(A)) | (reflexive(A) <=> is_reflexive_in(A, relation_field(A))))) | ((~relation(A!2)) | (reflexive(A!2) <=> is_reflexive_in(A!2, relation_field(A!2))))),
% 0.21/0.40 inference(quant_inst,[status(thm)],[])).
% 0.21/0.40 tff(98,plain,
% 0.21/0.40 ((~![A: $i] : ((~relation(A)) | (reflexive(A) <=> is_reflexive_in(A, relation_field(A))))) | (~relation(A!2)) | (reflexive(A!2) <=> is_reflexive_in(A!2, relation_field(A!2)))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[97, 96])).
% 0.21/0.40 tff(99,plain,
% 0.21/0.40 (reflexive(A!2) <=> is_reflexive_in(A!2, relation_field(A!2))),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[98, 95, 14])).
% 0.21/0.40 tff(100,plain,
% 0.21/0.40 ((~(reflexive(A!2) <=> is_reflexive_in(A!2, relation_field(A!2)))) | (~reflexive(A!2)) | is_reflexive_in(A!2, relation_field(A!2))),
% 0.21/0.40 inference(tautology,[status(thm)],[])).
% 0.21/0.40 tff(101,plain,
% 0.21/0.40 ((~reflexive(A!2)) | is_reflexive_in(A!2, relation_field(A!2))),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[100, 99])).
% 0.21/0.40 tff(102,plain,
% 0.21/0.40 (~reflexive(A!2)),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[101, 85])).
% 0.21/0.40 tff(103,plain,
% 0.21/0.40 ((reflexive(A!2) | ![B: $i] : ((~in(B, relation_field(A!2))) | in(ordered_pair(B, B), A!2))) <=> (reflexive(A!2) | ![B: $i] : ((~in(B, relation_field(A!2))) | in(ordered_pair(B, B), A!2)))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(104,plain,
% 0.21/0.40 (reflexive(A!2) | ![B: $i] : ((~in(B, relation_field(A!2))) | in(ordered_pair(B, B), A!2))),
% 0.21/0.40 inference(and_elim,[status(thm)],[13])).
% 0.21/0.40 tff(105,plain,
% 0.21/0.40 (reflexive(A!2) | ![B: $i] : ((~in(B, relation_field(A!2))) | in(ordered_pair(B, B), A!2))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[104, 103])).
% 0.21/0.40 tff(106,plain,
% 0.21/0.40 (![B: $i] : ((~in(B, relation_field(A!2))) | in(ordered_pair(B, B), A!2))),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[105, 102])).
% 0.21/0.40 tff(107,plain,
% 0.21/0.40 (((~![B: $i] : ((~in(B, relation_field(A!2))) | in(ordered_pair(B, B), A!2))) | ((~in(B!3, relation_field(A!2))) | in(ordered_pair(B!3, B!3), A!2))) <=> ((~![B: $i] : ((~in(B, relation_field(A!2))) | in(ordered_pair(B, B), A!2))) | (~in(B!3, relation_field(A!2))) | in(ordered_pair(B!3, B!3), A!2))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(108,plain,
% 0.21/0.40 ((~![B: $i] : ((~in(B, relation_field(A!2))) | in(ordered_pair(B, B), A!2))) | ((~in(B!3, relation_field(A!2))) | in(ordered_pair(B!3, B!3), A!2))),
% 0.21/0.40 inference(quant_inst,[status(thm)],[])).
% 0.21/0.40 tff(109,plain,
% 0.21/0.40 ((~![B: $i] : ((~in(B, relation_field(A!2))) | in(ordered_pair(B, B), A!2))) | (~in(B!3, relation_field(A!2))) | in(ordered_pair(B!3, B!3), A!2)),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[108, 107])).
% 0.21/0.40 tff(110,plain,
% 0.21/0.40 ($false),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[109, 106, 39, 37])).
% 0.21/0.40 tff(111,plain,((~in(B!3, relation_field(A!2))) | in(ordered_pair(B!3, B!3), A!2)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.40 tff(112,plain,
% 0.21/0.40 ((~reflexive(A!2)) | (~((~in(B!3, relation_field(A!2))) | in(ordered_pair(B!3, B!3), A!2)))),
% 0.21/0.40 inference(and_elim,[status(thm)],[13])).
% 0.21/0.40 tff(113,plain,
% 0.21/0.40 (~reflexive(A!2)),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[112, 111])).
% 0.21/0.40 tff(114,plain,
% 0.21/0.40 ((~(reflexive(A!2) <=> is_reflexive_in(A!2, relation_field(A!2)))) | reflexive(A!2) | (~is_reflexive_in(A!2, relation_field(A!2)))),
% 0.21/0.40 inference(tautology,[status(thm)],[])).
% 0.21/0.40 tff(115,plain,
% 0.21/0.40 (reflexive(A!2) | (~is_reflexive_in(A!2, relation_field(A!2)))),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[114, 99])).
% 0.21/0.40 tff(116,plain,
% 0.21/0.40 (~is_reflexive_in(A!2, relation_field(A!2))),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[115, 113])).
% 0.21/0.40 tff(117,plain,
% 0.21/0.40 (~is_reflexive_in(A!2, set_union2(relation_dom(A!2), relation_rng(A!2)))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[116, 34])).
% 0.21/0.40 tff(118,plain,
% 0.21/0.40 (((~((~is_reflexive_in(A!2, set_union2(relation_dom(A!2), relation_rng(A!2)))) | ![C: $i] : ((~in(C, set_union2(relation_dom(A!2), relation_rng(A!2)))) | in(ordered_pair(C, C), A!2)))) | (~((~((~in(tptp_fun_C_0(set_union2(relation_dom(A!2), relation_rng(A!2)), A!2), set_union2(relation_dom(A!2), relation_rng(A!2)))) | in(ordered_pair(tptp_fun_C_0(set_union2(relation_dom(A!2), relation_rng(A!2)), A!2), tptp_fun_C_0(set_union2(relation_dom(A!2), relation_rng(A!2)), A!2)), A!2))) | is_reflexive_in(A!2, set_union2(relation_dom(A!2), relation_rng(A!2)))))) | ((~((~in(tptp_fun_C_0(set_union2(relation_dom(A!2), relation_rng(A!2)), A!2), set_union2(relation_dom(A!2), relation_rng(A!2)))) | in(ordered_pair(tptp_fun_C_0(set_union2(relation_dom(A!2), relation_rng(A!2)), A!2), tptp_fun_C_0(set_union2(relation_dom(A!2), relation_rng(A!2)), A!2)), A!2))) | is_reflexive_in(A!2, set_union2(relation_dom(A!2), relation_rng(A!2))))),
% 0.21/0.40 inference(tautology,[status(thm)],[])).
% 0.21/0.40 tff(119,plain,
% 0.21/0.40 ((~((~in(tptp_fun_C_0(set_union2(relation_dom(A!2), relation_rng(A!2)), A!2), set_union2(relation_dom(A!2), relation_rng(A!2)))) | in(ordered_pair(tptp_fun_C_0(set_union2(relation_dom(A!2), relation_rng(A!2)), A!2), tptp_fun_C_0(set_union2(relation_dom(A!2), relation_rng(A!2)), A!2)), A!2))) | is_reflexive_in(A!2, set_union2(relation_dom(A!2), relation_rng(A!2)))),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[118, 79])).
% 0.21/0.40 tff(120,plain,
% 0.21/0.40 ((~((~((~in(tptp_fun_C_0(set_union2(relation_dom(A!2), relation_rng(A!2)), A!2), set_union2(relation_dom(A!2), relation_rng(A!2)))) | in(ordered_pair(tptp_fun_C_0(set_union2(relation_dom(A!2), relation_rng(A!2)), A!2), tptp_fun_C_0(set_union2(relation_dom(A!2), relation_rng(A!2)), A!2)), A!2))) | is_reflexive_in(A!2, set_union2(relation_dom(A!2), relation_rng(A!2))))) | (~((~in(tptp_fun_C_0(set_union2(relation_dom(A!2), relation_rng(A!2)), A!2), set_union2(relation_dom(A!2), relation_rng(A!2)))) | in(ordered_pair(tptp_fun_C_0(set_union2(relation_dom(A!2), relation_rng(A!2)), A!2), tptp_fun_C_0(set_union2(relation_dom(A!2), relation_rng(A!2)), A!2)), A!2))) | is_reflexive_in(A!2, set_union2(relation_dom(A!2), relation_rng(A!2)))),
% 0.21/0.40 inference(tautology,[status(thm)],[])).
% 0.21/0.40 tff(121,plain,
% 0.21/0.40 ((~((~in(tptp_fun_C_0(set_union2(relation_dom(A!2), relation_rng(A!2)), A!2), set_union2(relation_dom(A!2), relation_rng(A!2)))) | in(ordered_pair(tptp_fun_C_0(set_union2(relation_dom(A!2), relation_rng(A!2)), A!2), tptp_fun_C_0(set_union2(relation_dom(A!2), relation_rng(A!2)), A!2)), A!2))) | is_reflexive_in(A!2, set_union2(relation_dom(A!2), relation_rng(A!2)))),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[120, 119])).
% 0.21/0.40 tff(122,plain,
% 0.21/0.40 (~((~in(tptp_fun_C_0(set_union2(relation_dom(A!2), relation_rng(A!2)), A!2), set_union2(relation_dom(A!2), relation_rng(A!2)))) | in(ordered_pair(tptp_fun_C_0(set_union2(relation_dom(A!2), relation_rng(A!2)), A!2), tptp_fun_C_0(set_union2(relation_dom(A!2), relation_rng(A!2)), A!2)), A!2))),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[121, 117])).
% 0.21/0.40 tff(123,plain,
% 0.21/0.40 (((~in(tptp_fun_C_0(set_union2(relation_dom(A!2), relation_rng(A!2)), A!2), set_union2(relation_dom(A!2), relation_rng(A!2)))) | in(ordered_pair(tptp_fun_C_0(set_union2(relation_dom(A!2), relation_rng(A!2)), A!2), tptp_fun_C_0(set_union2(relation_dom(A!2), relation_rng(A!2)), A!2)), A!2)) | in(tptp_fun_C_0(set_union2(relation_dom(A!2), relation_rng(A!2)), A!2), set_union2(relation_dom(A!2), relation_rng(A!2)))),
% 0.21/0.40 inference(tautology,[status(thm)],[])).
% 0.21/0.40 tff(124,plain,
% 0.21/0.40 (in(tptp_fun_C_0(set_union2(relation_dom(A!2), relation_rng(A!2)), A!2), set_union2(relation_dom(A!2), relation_rng(A!2)))),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[123, 122])).
% 0.21/0.40 tff(125,plain,
% 0.21/0.40 (in(tptp_fun_C_0(set_union2(relation_dom(A!2), relation_rng(A!2)), A!2), relation_field(A!2))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[124, 30])).
% 0.21/0.40 tff(126,plain,
% 0.21/0.40 (((~in(tptp_fun_C_0(set_union2(relation_dom(A!2), relation_rng(A!2)), A!2), set_union2(relation_dom(A!2), relation_rng(A!2)))) | in(ordered_pair(tptp_fun_C_0(set_union2(relation_dom(A!2), relation_rng(A!2)), A!2), tptp_fun_C_0(set_union2(relation_dom(A!2), relation_rng(A!2)), A!2)), A!2)) | (~in(ordered_pair(tptp_fun_C_0(set_union2(relation_dom(A!2), relation_rng(A!2)), A!2), tptp_fun_C_0(set_union2(relation_dom(A!2), relation_rng(A!2)), A!2)), A!2))),
% 0.21/0.40 inference(tautology,[status(thm)],[])).
% 0.21/0.40 tff(127,plain,
% 0.21/0.40 (~in(ordered_pair(tptp_fun_C_0(set_union2(relation_dom(A!2), relation_rng(A!2)), A!2), tptp_fun_C_0(set_union2(relation_dom(A!2), relation_rng(A!2)), A!2)), A!2)),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[126, 122])).
% 0.21/0.40 tff(128,plain,
% 0.21/0.40 (![B: $i] : ((~in(B, relation_field(A!2))) | in(ordered_pair(B, B), A!2))),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[105, 113])).
% 0.21/0.40 tff(129,plain,
% 0.21/0.40 (((~![B: $i] : ((~in(B, relation_field(A!2))) | in(ordered_pair(B, B), A!2))) | ((~in(tptp_fun_C_0(set_union2(relation_dom(A!2), relation_rng(A!2)), A!2), relation_field(A!2))) | in(ordered_pair(tptp_fun_C_0(set_union2(relation_dom(A!2), relation_rng(A!2)), A!2), tptp_fun_C_0(set_union2(relation_dom(A!2), relation_rng(A!2)), A!2)), A!2))) <=> ((~![B: $i] : ((~in(B, relation_field(A!2))) | in(ordered_pair(B, B), A!2))) | (~in(tptp_fun_C_0(set_union2(relation_dom(A!2), relation_rng(A!2)), A!2), relation_field(A!2))) | in(ordered_pair(tptp_fun_C_0(set_union2(relation_dom(A!2), relation_rng(A!2)), A!2), tptp_fun_C_0(set_union2(relation_dom(A!2), relation_rng(A!2)), A!2)), A!2))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(130,plain,
% 0.21/0.40 ((~![B: $i] : ((~in(B, relation_field(A!2))) | in(ordered_pair(B, B), A!2))) | ((~in(tptp_fun_C_0(set_union2(relation_dom(A!2), relation_rng(A!2)), A!2), relation_field(A!2))) | in(ordered_pair(tptp_fun_C_0(set_union2(relation_dom(A!2), relation_rng(A!2)), A!2), tptp_fun_C_0(set_union2(relation_dom(A!2), relation_rng(A!2)), A!2)), A!2))),
% 0.21/0.41 inference(quant_inst,[status(thm)],[])).
% 0.21/0.41 tff(131,plain,
% 0.21/0.41 ((~![B: $i] : ((~in(B, relation_field(A!2))) | in(ordered_pair(B, B), A!2))) | (~in(tptp_fun_C_0(set_union2(relation_dom(A!2), relation_rng(A!2)), A!2), relation_field(A!2))) | in(ordered_pair(tptp_fun_C_0(set_union2(relation_dom(A!2), relation_rng(A!2)), A!2), tptp_fun_C_0(set_union2(relation_dom(A!2), relation_rng(A!2)), A!2)), A!2)),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[130, 129])).
% 0.21/0.41 tff(132,plain,
% 0.21/0.41 (~in(tptp_fun_C_0(set_union2(relation_dom(A!2), relation_rng(A!2)), A!2), relation_field(A!2))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[131, 128, 127])).
% 0.21/0.41 tff(133,plain,
% 0.21/0.41 ($false),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[132, 125])).
% 0.21/0.41 % SZS output end Proof
% 0.21/0.41 % E exiting
%------------------------------------------------------------------------------