TSTP Solution File: SEU240+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SEU240+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% 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 : Tue Sep 20 07:28:26 EDT 2022
% Result : Theorem 0.12s 0.40s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SEU240+1 : TPTP v8.1.0. Released v3.3.0.
% 0.11/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n001.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Sat Sep 3 11:18:55 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 0.12/0.40 % SZS status Theorem
% 0.12/0.40 % SZS output start Proof
% 0.12/0.40 tff(in_type, type, (
% 0.12/0.40 in: ( $i * $i ) > $o)).
% 0.12/0.40 tff(tptp_fun_A_4_type, type, (
% 0.12/0.40 tptp_fun_A_4: $i)).
% 0.12/0.40 tff(ordered_pair_type, type, (
% 0.12/0.40 ordered_pair: ( $i * $i ) > $i)).
% 0.12/0.40 tff(tptp_fun_E_0_type, type, (
% 0.12/0.40 tptp_fun_E_0: ( $i * $i ) > $i)).
% 0.12/0.40 tff(set_union2_type, type, (
% 0.12/0.40 set_union2: ( $i * $i ) > $i)).
% 0.12/0.40 tff(relation_rng_type, type, (
% 0.12/0.40 relation_rng: $i > $i)).
% 0.12/0.40 tff(relation_dom_type, type, (
% 0.12/0.40 relation_dom: $i > $i)).
% 0.12/0.40 tff(tptp_fun_D_1_type, type, (
% 0.12/0.40 tptp_fun_D_1: ( $i * $i ) > $i)).
% 0.12/0.40 tff(tptp_fun_C_2_type, type, (
% 0.12/0.40 tptp_fun_C_2: ( $i * $i ) > $i)).
% 0.12/0.40 tff(is_transitive_in_type, type, (
% 0.12/0.40 is_transitive_in: ( $i * $i ) > $o)).
% 0.12/0.40 tff(relation_field_type, type, (
% 0.12/0.40 relation_field: $i > $i)).
% 0.12/0.40 tff(relation_type, type, (
% 0.12/0.40 relation: $i > $o)).
% 0.12/0.40 tff(tptp_fun_D_5_type, type, (
% 0.12/0.40 tptp_fun_D_5: $i)).
% 0.12/0.40 tff(tptp_fun_B_7_type, type, (
% 0.12/0.40 tptp_fun_B_7: $i)).
% 0.12/0.40 tff(tptp_fun_C_6_type, type, (
% 0.12/0.40 tptp_fun_C_6: $i)).
% 0.12/0.40 tff(transitive_type, type, (
% 0.12/0.40 transitive: $i > $o)).
% 0.12/0.40 tff(1,plain,
% 0.12/0.40 ((relation(A!4) & ((transitive(A!4) | ![B: $i, C: $i, D: $i] : ((~(in(ordered_pair(B, C), A!4) & in(ordered_pair(C, D), A!4))) | in(ordered_pair(B, D), A!4))) & ((~transitive(A!4)) | (~((~(in(ordered_pair(B!7, C!6), A!4) & in(ordered_pair(C!6, D!5), A!4))) | in(ordered_pair(B!7, D!5), A!4)))))) <=> (relation(A!4) & (transitive(A!4) | ![B: $i, C: $i, D: $i] : ((~(in(ordered_pair(B, C), A!4) & in(ordered_pair(C, D), A!4))) | in(ordered_pair(B, D), A!4))) & ((~transitive(A!4)) | (~((~(in(ordered_pair(B!7, C!6), A!4) & in(ordered_pair(C!6, D!5), A!4))) | in(ordered_pair(B!7, D!5), A!4)))))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(2,plain,
% 0.12/0.40 ((transitive(A!4) | ![B: $i, C: $i, D: $i] : ((~(in(ordered_pair(B, C), A!4) & in(ordered_pair(C, D), A!4))) | in(ordered_pair(B, D), A!4))) <=> (transitive(A!4) | ![B: $i, C: $i, D: $i] : ((~(in(ordered_pair(B, C), A!4) & in(ordered_pair(C, D), A!4))) | in(ordered_pair(B, D), A!4)))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(3,plain,
% 0.12/0.40 (((transitive(A!4) | ![B: $i, C: $i, D: $i] : ((~(in(ordered_pair(B, C), A!4) & in(ordered_pair(C, D), A!4))) | in(ordered_pair(B, D), A!4))) & ((~transitive(A!4)) | (~((~(in(ordered_pair(B!7, C!6), A!4) & in(ordered_pair(C!6, D!5), A!4))) | in(ordered_pair(B!7, D!5), A!4))))) <=> ((transitive(A!4) | ![B: $i, C: $i, D: $i] : ((~(in(ordered_pair(B, C), A!4) & in(ordered_pair(C, D), A!4))) | in(ordered_pair(B, D), A!4))) & ((~transitive(A!4)) | (~((~(in(ordered_pair(B!7, C!6), A!4) & in(ordered_pair(C!6, D!5), A!4))) | in(ordered_pair(B!7, D!5), A!4)))))),
% 0.12/0.40 inference(monotonicity,[status(thm)],[2])).
% 0.12/0.40 tff(4,plain,
% 0.12/0.40 ((~(~relation(A!4))) <=> relation(A!4)),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(5,plain,
% 0.12/0.40 (((~(~relation(A!4))) & ((transitive(A!4) | ![B: $i, C: $i, D: $i] : ((~(in(ordered_pair(B, C), A!4) & in(ordered_pair(C, D), A!4))) | in(ordered_pair(B, D), A!4))) & ((~transitive(A!4)) | (~((~(in(ordered_pair(B!7, C!6), A!4) & in(ordered_pair(C!6, D!5), A!4))) | in(ordered_pair(B!7, D!5), A!4)))))) <=> (relation(A!4) & ((transitive(A!4) | ![B: $i, C: $i, D: $i] : ((~(in(ordered_pair(B, C), A!4) & in(ordered_pair(C, D), A!4))) | in(ordered_pair(B, D), A!4))) & ((~transitive(A!4)) | (~((~(in(ordered_pair(B!7, C!6), A!4) & in(ordered_pair(C!6, D!5), A!4))) | in(ordered_pair(B!7, D!5), A!4))))))),
% 0.12/0.40 inference(monotonicity,[status(thm)],[4, 3])).
% 0.12/0.40 tff(6,plain,
% 0.12/0.40 (((~(~relation(A!4))) & ((transitive(A!4) | ![B: $i, C: $i, D: $i] : ((~(in(ordered_pair(B, C), A!4) & in(ordered_pair(C, D), A!4))) | in(ordered_pair(B, D), A!4))) & ((~transitive(A!4)) | (~((~(in(ordered_pair(B!7, C!6), A!4) & in(ordered_pair(C!6, D!5), A!4))) | in(ordered_pair(B!7, D!5), A!4)))))) <=> (relation(A!4) & (transitive(A!4) | ![B: $i, C: $i, D: $i] : ((~(in(ordered_pair(B, C), A!4) & in(ordered_pair(C, D), A!4))) | in(ordered_pair(B, D), A!4))) & ((~transitive(A!4)) | (~((~(in(ordered_pair(B!7, C!6), A!4) & in(ordered_pair(C!6, D!5), A!4))) | in(ordered_pair(B!7, D!5), A!4)))))),
% 0.12/0.40 inference(transitivity,[status(thm)],[5, 1])).
% 0.12/0.40 tff(7,plain,
% 0.12/0.40 ((~![A: $i] : ((~relation(A)) | (transitive(A) <=> ![B: $i, C: $i, D: $i] : ((~(in(ordered_pair(B, C), A) & in(ordered_pair(C, D), A))) | in(ordered_pair(B, D), A))))) <=> (~![A: $i] : ((~relation(A)) | (transitive(A) <=> ![B: $i, C: $i, D: $i] : ((~(in(ordered_pair(B, C), A) & in(ordered_pair(C, D), A))) | in(ordered_pair(B, D), A)))))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(8,plain,
% 0.12/0.40 ((~![A: $i] : (relation(A) => (transitive(A) <=> ![B: $i, C: $i, D: $i] : ((in(ordered_pair(B, C), A) & in(ordered_pair(C, D), A)) => in(ordered_pair(B, D), A))))) <=> (~![A: $i] : ((~relation(A)) | (transitive(A) <=> ![B: $i, C: $i, D: $i] : ((~(in(ordered_pair(B, C), A) & in(ordered_pair(C, D), A))) | in(ordered_pair(B, D), A)))))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(9,axiom,(~![A: $i] : (relation(A) => (transitive(A) <=> ![B: $i, C: $i, D: $i] : ((in(ordered_pair(B, C), A) & in(ordered_pair(C, D), A)) => in(ordered_pair(B, D), A))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','l2_wellord1')).
% 0.12/0.40 tff(10,plain,
% 0.12/0.40 (~![A: $i] : ((~relation(A)) | (transitive(A) <=> ![B: $i, C: $i, D: $i] : ((~(in(ordered_pair(B, C), A) & in(ordered_pair(C, D), A))) | in(ordered_pair(B, D), A))))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[9, 8])).
% 0.12/0.40 tff(11,plain,
% 0.12/0.40 (~![A: $i] : ((~relation(A)) | (transitive(A) <=> ![B: $i, C: $i, D: $i] : ((~(in(ordered_pair(B, C), A) & in(ordered_pair(C, D), A))) | in(ordered_pair(B, D), A))))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[10, 7])).
% 0.12/0.40 tff(12,plain,
% 0.12/0.40 (~![A: $i] : ((~relation(A)) | (transitive(A) <=> ![B: $i, C: $i, D: $i] : ((~(in(ordered_pair(B, C), A) & in(ordered_pair(C, D), A))) | in(ordered_pair(B, D), A))))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[11, 7])).
% 0.12/0.40 tff(13,plain,
% 0.12/0.40 (~![A: $i] : ((~relation(A)) | (transitive(A) <=> ![B: $i, C: $i, D: $i] : ((~(in(ordered_pair(B, C), A) & in(ordered_pair(C, D), A))) | in(ordered_pair(B, D), A))))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[12, 7])).
% 0.12/0.40 tff(14,plain,
% 0.12/0.40 (~![A: $i] : ((~relation(A)) | (transitive(A) <=> ![B: $i, C: $i, D: $i] : ((~(in(ordered_pair(B, C), A) & in(ordered_pair(C, D), A))) | in(ordered_pair(B, D), A))))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[13, 7])).
% 0.12/0.40 tff(15,plain,
% 0.12/0.40 (~![A: $i] : ((~relation(A)) | (transitive(A) <=> ![B: $i, C: $i, D: $i] : ((~(in(ordered_pair(B, C), A) & in(ordered_pair(C, D), A))) | in(ordered_pair(B, D), A))))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[14, 7])).
% 0.12/0.40 tff(16,plain,
% 0.12/0.40 (~![A: $i] : ((~relation(A)) | (transitive(A) <=> ![B: $i, C: $i, D: $i] : ((~(in(ordered_pair(B, C), A) & in(ordered_pair(C, D), A))) | in(ordered_pair(B, D), A))))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[15, 7])).
% 0.12/0.40 tff(17,plain,
% 0.12/0.40 (relation(A!4) & (transitive(A!4) | ![B: $i, C: $i, D: $i] : ((~(in(ordered_pair(B, C), A!4) & in(ordered_pair(C, D), A!4))) | in(ordered_pair(B, D), A!4))) & ((~transitive(A!4)) | (~((~(in(ordered_pair(B!7, C!6), A!4) & in(ordered_pair(C!6, D!5), A!4))) | in(ordered_pair(B!7, D!5), A!4))))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[16, 6])).
% 0.12/0.40 tff(18,plain,
% 0.12/0.40 (relation(A!4)),
% 0.12/0.40 inference(and_elim,[status(thm)],[17])).
% 0.12/0.40 tff(19,plain,
% 0.12/0.40 (^[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)))))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(20,plain,
% 0.12/0.40 (![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))))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[19])).
% 0.12/0.40 tff(21,plain,
% 0.12/0.40 (![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))))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(22,plain,
% 0.12/0.40 (^[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)))))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(23,plain,
% 0.12/0.40 (![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))))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[22])).
% 0.12/0.40 tff(24,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')).
% 0.12/0.40 tff(25,plain,
% 0.12/0.40 (![A: $i] : ((~relation(A)) | (relation_field(A) = set_union2(relation_dom(A), relation_rng(A))))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[24, 23])).
% 0.12/0.40 tff(26,plain,
% 0.12/0.40 (![A: $i] : ((~relation(A)) | (relation_field(A) = set_union2(relation_dom(A), relation_rng(A))))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[25, 21])).
% 0.12/0.40 tff(27,plain,(
% 0.12/0.40 ![A: $i] : ((~relation(A)) | (relation_field(A) = set_union2(relation_dom(A), relation_rng(A))))),
% 0.12/0.40 inference(skolemize,[status(sab)],[26])).
% 0.12/0.40 tff(28,plain,
% 0.12/0.40 (![A: $i] : ((~relation(A)) | (relation_field(A) = set_union2(relation_dom(A), relation_rng(A))))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[27, 20])).
% 0.12/0.40 tff(29,plain,
% 0.12/0.40 (((~![A: $i] : ((~relation(A)) | (relation_field(A) = set_union2(relation_dom(A), relation_rng(A))))) | ((~relation(A!4)) | (relation_field(A!4) = set_union2(relation_dom(A!4), relation_rng(A!4))))) <=> ((~![A: $i] : ((~relation(A)) | (relation_field(A) = set_union2(relation_dom(A), relation_rng(A))))) | (~relation(A!4)) | (relation_field(A!4) = set_union2(relation_dom(A!4), relation_rng(A!4))))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(30,plain,
% 0.12/0.40 ((~![A: $i] : ((~relation(A)) | (relation_field(A) = set_union2(relation_dom(A), relation_rng(A))))) | ((~relation(A!4)) | (relation_field(A!4) = set_union2(relation_dom(A!4), relation_rng(A!4))))),
% 0.12/0.40 inference(quant_inst,[status(thm)],[])).
% 0.12/0.40 tff(31,plain,
% 0.12/0.40 ((~![A: $i] : ((~relation(A)) | (relation_field(A) = set_union2(relation_dom(A), relation_rng(A))))) | (~relation(A!4)) | (relation_field(A!4) = set_union2(relation_dom(A!4), relation_rng(A!4)))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[30, 29])).
% 0.12/0.40 tff(32,plain,
% 0.12/0.40 (relation_field(A!4) = set_union2(relation_dom(A!4), relation_rng(A!4))),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[31, 28, 18])).
% 0.12/0.40 tff(33,plain,
% 0.12/0.40 (set_union2(relation_dom(A!4), relation_rng(A!4)) = relation_field(A!4)),
% 0.12/0.40 inference(symmetry,[status(thm)],[32])).
% 0.12/0.40 tff(34,plain,
% 0.12/0.40 (is_transitive_in(A!4, set_union2(relation_dom(A!4), relation_rng(A!4))) <=> is_transitive_in(A!4, relation_field(A!4))),
% 0.12/0.40 inference(monotonicity,[status(thm)],[33])).
% 0.12/0.40 tff(35,plain,
% 0.12/0.40 (is_transitive_in(A!4, relation_field(A!4)) <=> is_transitive_in(A!4, set_union2(relation_dom(A!4), relation_rng(A!4)))),
% 0.12/0.40 inference(symmetry,[status(thm)],[34])).
% 0.12/0.40 tff(36,plain,
% 0.12/0.40 ((~is_transitive_in(A!4, relation_field(A!4))) <=> (~is_transitive_in(A!4, set_union2(relation_dom(A!4), relation_rng(A!4))))),
% 0.12/0.40 inference(monotonicity,[status(thm)],[35])).
% 0.12/0.40 tff(37,assumption,(~(in(ordered_pair(B!7, D!5), A!4) | (~in(ordered_pair(B!7, C!6), A!4)) | (~in(ordered_pair(C!6, D!5), A!4)))), introduced(assumption)).
% 0.12/0.40 tff(38,plain,
% 0.12/0.40 ((in(ordered_pair(B!7, D!5), A!4) | (~in(ordered_pair(B!7, C!6), A!4)) | (~in(ordered_pair(C!6, D!5), A!4))) | in(ordered_pair(C!6, D!5), A!4)),
% 0.12/0.40 inference(tautology,[status(thm)],[])).
% 0.12/0.40 tff(39,plain,
% 0.12/0.40 (in(ordered_pair(C!6, D!5), A!4)),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[38, 37])).
% 0.12/0.40 tff(40,plain,
% 0.12/0.40 ((in(ordered_pair(B!7, D!5), A!4) | (~in(ordered_pair(B!7, C!6), A!4)) | (~in(ordered_pair(C!6, D!5), A!4))) | in(ordered_pair(B!7, C!6), A!4)),
% 0.12/0.40 inference(tautology,[status(thm)],[])).
% 0.12/0.40 tff(41,plain,
% 0.12/0.40 (in(ordered_pair(B!7, C!6), A!4)),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[40, 37])).
% 0.12/0.40 tff(42,plain,
% 0.12/0.40 ((in(ordered_pair(B!7, D!5), A!4) | (~in(ordered_pair(B!7, C!6), A!4)) | (~in(ordered_pair(C!6, D!5), A!4))) | (~in(ordered_pair(B!7, D!5), A!4))),
% 0.12/0.40 inference(tautology,[status(thm)],[])).
% 0.12/0.40 tff(43,plain,
% 0.12/0.40 (~in(ordered_pair(B!7, D!5), A!4)),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[42, 37])).
% 0.12/0.40 tff(44,plain,
% 0.12/0.40 ((~is_transitive_in(A!4, set_union2(relation_dom(A!4), relation_rng(A!4)))) <=> (~is_transitive_in(A!4, relation_field(A!4)))),
% 0.12/0.40 inference(monotonicity,[status(thm)],[34])).
% 0.12/0.40 tff(45,plain,
% 0.12/0.40 (in(B!7, set_union2(relation_dom(A!4), relation_rng(A!4))) <=> in(B!7, relation_field(A!4))),
% 0.12/0.40 inference(monotonicity,[status(thm)],[33])).
% 0.12/0.40 tff(46,plain,
% 0.12/0.40 (in(B!7, relation_field(A!4)) <=> in(B!7, set_union2(relation_dom(A!4), relation_rng(A!4)))),
% 0.12/0.40 inference(symmetry,[status(thm)],[45])).
% 0.12/0.40 tff(47,plain,
% 0.12/0.40 (^[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)))))))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(48,plain,
% 0.12/0.40 (![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))))))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[47])).
% 0.12/0.40 tff(49,plain,
% 0.12/0.40 (^[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))))))))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(50,plain,
% 0.12/0.40 (![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))))))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[49])).
% 0.12/0.40 tff(51,plain,
% 0.12/0.40 (![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)))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(52,plain,
% 0.12/0.40 (^[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)))))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(53,plain,
% 0.12/0.40 (![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)))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[52])).
% 0.12/0.40 tff(54,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')).
% 0.12/0.40 tff(55,plain,
% 0.12/0.40 (![A: $i, B: $i, C: $i] : ((in(A, relation_field(C)) & in(B, relation_field(C))) | (~relation(C)) | (~in(ordered_pair(A, B), C)))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[54, 53])).
% 0.12/0.40 tff(56,plain,
% 0.12/0.40 (![A: $i, B: $i, C: $i] : ((in(A, relation_field(C)) & in(B, relation_field(C))) | (~relation(C)) | (~in(ordered_pair(A, B), C)))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[55, 51])).
% 0.12/0.40 tff(57,plain,(
% 0.12/0.40 ![A: $i, B: $i, C: $i] : ((in(A, relation_field(C)) & in(B, relation_field(C))) | (~relation(C)) | (~in(ordered_pair(A, B), C)))),
% 0.12/0.40 inference(skolemize,[status(sab)],[56])).
% 0.12/0.40 tff(58,plain,
% 0.12/0.40 (![A: $i, B: $i, C: $i] : ((~relation(C)) | (~in(ordered_pair(A, B), C)) | (~((~in(A, relation_field(C))) | (~in(B, relation_field(C))))))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[57, 50])).
% 0.12/0.40 tff(59,plain,
% 0.12/0.40 (![A: $i, B: $i, C: $i] : ((~relation(C)) | (~in(ordered_pair(A, B), C)) | (~((~in(A, relation_field(C))) | (~in(B, relation_field(C))))))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[58, 48])).
% 0.12/0.40 tff(60,assumption,(in(ordered_pair(B!7, C!6), A!4)), introduced(assumption)).
% 0.12/0.40 tff(61,plain,
% 0.12/0.40 (((~![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!4)) | (~in(ordered_pair(B!7, C!6), A!4)) | (~((~in(B!7, relation_field(A!4))) | (~in(C!6, relation_field(A!4))))))) <=> ((~![A: $i, B: $i, C: $i] : ((~relation(C)) | (~in(ordered_pair(A, B), C)) | (~((~in(A, relation_field(C))) | (~in(B, relation_field(C))))))) | (~relation(A!4)) | (~in(ordered_pair(B!7, C!6), A!4)) | (~((~in(B!7, relation_field(A!4))) | (~in(C!6, relation_field(A!4))))))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(62,plain,
% 0.12/0.40 ((~![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!4)) | (~in(ordered_pair(B!7, C!6), A!4)) | (~((~in(B!7, relation_field(A!4))) | (~in(C!6, relation_field(A!4))))))),
% 0.12/0.40 inference(quant_inst,[status(thm)],[])).
% 0.12/0.40 tff(63,plain,
% 0.12/0.40 ((~![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!4)) | (~in(ordered_pair(B!7, C!6), A!4)) | (~((~in(B!7, relation_field(A!4))) | (~in(C!6, relation_field(A!4)))))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[62, 61])).
% 0.12/0.40 tff(64,plain,
% 0.12/0.40 (~((~in(B!7, relation_field(A!4))) | (~in(C!6, relation_field(A!4))))),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[63, 18, 60, 59])).
% 0.12/0.40 tff(65,plain,
% 0.12/0.40 (((~in(B!7, relation_field(A!4))) | (~in(C!6, relation_field(A!4)))) | in(B!7, relation_field(A!4))),
% 0.12/0.40 inference(tautology,[status(thm)],[])).
% 0.12/0.40 tff(66,plain,
% 0.12/0.40 (in(B!7, relation_field(A!4))),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[65, 64])).
% 0.12/0.40 tff(67,plain,
% 0.12/0.40 (in(B!7, set_union2(relation_dom(A!4), relation_rng(A!4)))),
% 0.12/0.41 inference(modus_ponens,[status(thm)],[66, 46])).
% 0.12/0.41 tff(68,plain,
% 0.12/0.41 (in(C!6, set_union2(relation_dom(A!4), relation_rng(A!4))) <=> in(C!6, relation_field(A!4))),
% 0.12/0.41 inference(monotonicity,[status(thm)],[33])).
% 0.12/0.41 tff(69,plain,
% 0.12/0.41 (in(C!6, relation_field(A!4)) <=> in(C!6, set_union2(relation_dom(A!4), relation_rng(A!4)))),
% 0.12/0.41 inference(symmetry,[status(thm)],[68])).
% 0.12/0.41 tff(70,assumption,(in(ordered_pair(C!6, D!5), A!4)), introduced(assumption)).
% 0.12/0.41 tff(71,plain,
% 0.12/0.41 (((~![A: $i, B: $i, C: $i] : ((~relation(C)) | (~in(ordered_pair(A, B), C)) | (~((~in(A, relation_field(C))) | (~in(B, relation_field(C))))))) | ((~relation(A!4)) | (~in(ordered_pair(C!6, D!5), A!4)) | (~((~in(C!6, relation_field(A!4))) | (~in(D!5, relation_field(A!4))))))) <=> ((~![A: $i, B: $i, C: $i] : ((~relation(C)) | (~in(ordered_pair(A, B), C)) | (~((~in(A, relation_field(C))) | (~in(B, relation_field(C))))))) | (~relation(A!4)) | (~in(ordered_pair(C!6, D!5), A!4)) | (~((~in(C!6, relation_field(A!4))) | (~in(D!5, relation_field(A!4))))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(72,plain,
% 0.19/0.41 ((~![A: $i, B: $i, C: $i] : ((~relation(C)) | (~in(ordered_pair(A, B), C)) | (~((~in(A, relation_field(C))) | (~in(B, relation_field(C))))))) | ((~relation(A!4)) | (~in(ordered_pair(C!6, D!5), A!4)) | (~((~in(C!6, relation_field(A!4))) | (~in(D!5, relation_field(A!4))))))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(73,plain,
% 0.19/0.41 ((~![A: $i, B: $i, C: $i] : ((~relation(C)) | (~in(ordered_pair(A, B), C)) | (~((~in(A, relation_field(C))) | (~in(B, relation_field(C))))))) | (~relation(A!4)) | (~in(ordered_pair(C!6, D!5), A!4)) | (~((~in(C!6, relation_field(A!4))) | (~in(D!5, relation_field(A!4)))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[72, 71])).
% 0.19/0.41 tff(74,plain,
% 0.19/0.41 (~((~in(C!6, relation_field(A!4))) | (~in(D!5, relation_field(A!4))))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[73, 18, 70, 59])).
% 0.19/0.41 tff(75,plain,
% 0.19/0.41 (((~in(C!6, relation_field(A!4))) | (~in(D!5, relation_field(A!4)))) | in(C!6, relation_field(A!4))),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(76,plain,
% 0.19/0.41 (in(C!6, relation_field(A!4))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[75, 74])).
% 0.19/0.41 tff(77,plain,
% 0.19/0.41 (in(C!6, set_union2(relation_dom(A!4), relation_rng(A!4)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[76, 69])).
% 0.19/0.41 tff(78,plain,
% 0.19/0.41 (in(D!5, set_union2(relation_dom(A!4), relation_rng(A!4))) <=> in(D!5, relation_field(A!4))),
% 0.19/0.41 inference(monotonicity,[status(thm)],[33])).
% 0.19/0.41 tff(79,plain,
% 0.19/0.41 (in(D!5, relation_field(A!4)) <=> in(D!5, set_union2(relation_dom(A!4), relation_rng(A!4)))),
% 0.19/0.41 inference(symmetry,[status(thm)],[78])).
% 0.19/0.41 tff(80,plain,
% 0.19/0.41 (((~in(C!6, relation_field(A!4))) | (~in(D!5, relation_field(A!4)))) | in(D!5, relation_field(A!4))),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(81,plain,
% 0.19/0.41 (in(D!5, relation_field(A!4))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[80, 74])).
% 0.19/0.41 tff(82,plain,
% 0.19/0.41 (in(D!5, set_union2(relation_dom(A!4), relation_rng(A!4)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[81, 79])).
% 0.19/0.41 tff(83,assumption,(![C: $i, D: $i, E: $i] : (in(ordered_pair(C, E), A!4) | (~in(ordered_pair(C, D), A!4)) | (~in(ordered_pair(D, E), A!4)) | (~in(C, set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(E, set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(D, set_union2(relation_dom(A!4), relation_rng(A!4)))))), introduced(assumption)).
% 0.19/0.41 tff(84,assumption,(~in(ordered_pair(B!7, D!5), A!4)), introduced(assumption)).
% 0.19/0.41 tff(85,plain,
% 0.19/0.41 (((~![C: $i, D: $i, E: $i] : (in(ordered_pair(C, E), A!4) | (~in(ordered_pair(C, D), A!4)) | (~in(ordered_pair(D, E), A!4)) | (~in(C, set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(E, set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(D, set_union2(relation_dom(A!4), relation_rng(A!4)))))) | (in(ordered_pair(B!7, D!5), A!4) | (~in(ordered_pair(B!7, C!6), A!4)) | (~in(ordered_pair(C!6, D!5), A!4)) | (~in(D!5, set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(C!6, set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(B!7, set_union2(relation_dom(A!4), relation_rng(A!4)))))) <=> ((~![C: $i, D: $i, E: $i] : (in(ordered_pair(C, E), A!4) | (~in(ordered_pair(C, D), A!4)) | (~in(ordered_pair(D, E), A!4)) | (~in(C, set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(E, set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(D, set_union2(relation_dom(A!4), relation_rng(A!4)))))) | in(ordered_pair(B!7, D!5), A!4) | (~in(ordered_pair(B!7, C!6), A!4)) | (~in(ordered_pair(C!6, D!5), A!4)) | (~in(D!5, set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(C!6, set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(B!7, set_union2(relation_dom(A!4), relation_rng(A!4)))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(86,plain,
% 0.19/0.41 ((in(ordered_pair(B!7, D!5), A!4) | (~in(ordered_pair(B!7, C!6), A!4)) | (~in(ordered_pair(C!6, D!5), A!4)) | (~in(B!7, set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(D!5, set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(C!6, set_union2(relation_dom(A!4), relation_rng(A!4))))) <=> (in(ordered_pair(B!7, D!5), A!4) | (~in(ordered_pair(B!7, C!6), A!4)) | (~in(ordered_pair(C!6, D!5), A!4)) | (~in(D!5, set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(C!6, set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(B!7, set_union2(relation_dom(A!4), relation_rng(A!4)))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(87,plain,
% 0.19/0.41 (((~![C: $i, D: $i, E: $i] : (in(ordered_pair(C, E), A!4) | (~in(ordered_pair(C, D), A!4)) | (~in(ordered_pair(D, E), A!4)) | (~in(C, set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(E, set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(D, set_union2(relation_dom(A!4), relation_rng(A!4)))))) | (in(ordered_pair(B!7, D!5), A!4) | (~in(ordered_pair(B!7, C!6), A!4)) | (~in(ordered_pair(C!6, D!5), A!4)) | (~in(B!7, set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(D!5, set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(C!6, set_union2(relation_dom(A!4), relation_rng(A!4)))))) <=> ((~![C: $i, D: $i, E: $i] : (in(ordered_pair(C, E), A!4) | (~in(ordered_pair(C, D), A!4)) | (~in(ordered_pair(D, E), A!4)) | (~in(C, set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(E, set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(D, set_union2(relation_dom(A!4), relation_rng(A!4)))))) | (in(ordered_pair(B!7, D!5), A!4) | (~in(ordered_pair(B!7, C!6), A!4)) | (~in(ordered_pair(C!6, D!5), A!4)) | (~in(D!5, set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(C!6, set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(B!7, set_union2(relation_dom(A!4), relation_rng(A!4))))))),
% 0.19/0.41 inference(monotonicity,[status(thm)],[86])).
% 0.19/0.41 tff(88,plain,
% 0.19/0.41 (((~![C: $i, D: $i, E: $i] : (in(ordered_pair(C, E), A!4) | (~in(ordered_pair(C, D), A!4)) | (~in(ordered_pair(D, E), A!4)) | (~in(C, set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(E, set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(D, set_union2(relation_dom(A!4), relation_rng(A!4)))))) | (in(ordered_pair(B!7, D!5), A!4) | (~in(ordered_pair(B!7, C!6), A!4)) | (~in(ordered_pair(C!6, D!5), A!4)) | (~in(B!7, set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(D!5, set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(C!6, set_union2(relation_dom(A!4), relation_rng(A!4)))))) <=> ((~![C: $i, D: $i, E: $i] : (in(ordered_pair(C, E), A!4) | (~in(ordered_pair(C, D), A!4)) | (~in(ordered_pair(D, E), A!4)) | (~in(C, set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(E, set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(D, set_union2(relation_dom(A!4), relation_rng(A!4)))))) | in(ordered_pair(B!7, D!5), A!4) | (~in(ordered_pair(B!7, C!6), A!4)) | (~in(ordered_pair(C!6, D!5), A!4)) | (~in(D!5, set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(C!6, set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(B!7, set_union2(relation_dom(A!4), relation_rng(A!4)))))),
% 0.19/0.41 inference(transitivity,[status(thm)],[87, 85])).
% 0.19/0.41 tff(89,plain,
% 0.19/0.41 ((~![C: $i, D: $i, E: $i] : (in(ordered_pair(C, E), A!4) | (~in(ordered_pair(C, D), A!4)) | (~in(ordered_pair(D, E), A!4)) | (~in(C, set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(E, set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(D, set_union2(relation_dom(A!4), relation_rng(A!4)))))) | (in(ordered_pair(B!7, D!5), A!4) | (~in(ordered_pair(B!7, C!6), A!4)) | (~in(ordered_pair(C!6, D!5), A!4)) | (~in(B!7, set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(D!5, set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(C!6, set_union2(relation_dom(A!4), relation_rng(A!4)))))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(90,plain,
% 0.19/0.41 ((~![C: $i, D: $i, E: $i] : (in(ordered_pair(C, E), A!4) | (~in(ordered_pair(C, D), A!4)) | (~in(ordered_pair(D, E), A!4)) | (~in(C, set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(E, set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(D, set_union2(relation_dom(A!4), relation_rng(A!4)))))) | in(ordered_pair(B!7, D!5), A!4) | (~in(ordered_pair(B!7, C!6), A!4)) | (~in(ordered_pair(C!6, D!5), A!4)) | (~in(D!5, set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(C!6, set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(B!7, set_union2(relation_dom(A!4), relation_rng(A!4))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[89, 88])).
% 0.19/0.41 tff(91,plain,
% 0.19/0.41 ($false),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[90, 84, 60, 70, 83, 82, 77, 67])).
% 0.19/0.41 tff(92,plain,((~![C: $i, D: $i, E: $i] : (in(ordered_pair(C, E), A!4) | (~in(ordered_pair(C, D), A!4)) | (~in(ordered_pair(D, E), A!4)) | (~in(C, set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(E, set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(D, set_union2(relation_dom(A!4), relation_rng(A!4)))))) | in(ordered_pair(B!7, D!5), A!4) | (~in(ordered_pair(B!7, C!6), A!4)) | (~in(ordered_pair(C!6, D!5), A!4))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.41 tff(93,plain,
% 0.19/0.41 (~![C: $i, D: $i, E: $i] : (in(ordered_pair(C, E), A!4) | (~in(ordered_pair(C, D), A!4)) | (~in(ordered_pair(D, E), A!4)) | (~in(C, set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(E, set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(D, set_union2(relation_dom(A!4), relation_rng(A!4)))))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[92, 43, 41, 39])).
% 0.19/0.41 tff(94,plain,
% 0.19/0.41 (^[A: $i] : refl(((~relation(A)) | ![B: $i] : (~((~((~is_transitive_in(A, B)) | ![C: $i, D: $i, E: $i] : (in(ordered_pair(C, E), A) | (~in(C, B)) | (~in(D, B)) | (~in(E, B)) | (~in(ordered_pair(C, D), A)) | (~in(ordered_pair(D, E), A))))) | (~(is_transitive_in(A, B) | (~(in(ordered_pair(tptp_fun_C_2(B, A), tptp_fun_E_0(B, A)), A) | (~in(tptp_fun_C_2(B, A), B)) | (~in(tptp_fun_D_1(B, A), B)) | (~in(tptp_fun_E_0(B, A), B)) | (~in(ordered_pair(tptp_fun_C_2(B, A), tptp_fun_D_1(B, A)), A)) | (~in(ordered_pair(tptp_fun_D_1(B, A), tptp_fun_E_0(B, A)), A))))))))) <=> ((~relation(A)) | ![B: $i] : (~((~((~is_transitive_in(A, B)) | ![C: $i, D: $i, E: $i] : (in(ordered_pair(C, E), A) | (~in(C, B)) | (~in(D, B)) | (~in(E, B)) | (~in(ordered_pair(C, D), A)) | (~in(ordered_pair(D, E), A))))) | (~(is_transitive_in(A, B) | (~(in(ordered_pair(tptp_fun_C_2(B, A), tptp_fun_E_0(B, A)), A) | (~in(tptp_fun_C_2(B, A), B)) | (~in(tptp_fun_D_1(B, A), B)) | (~in(tptp_fun_E_0(B, A), B)) | (~in(ordered_pair(tptp_fun_C_2(B, A), tptp_fun_D_1(B, A)), A)) | (~in(ordered_pair(tptp_fun_D_1(B, A), tptp_fun_E_0(B, A)), A))))))))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(95,plain,
% 0.19/0.41 (![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~is_transitive_in(A, B)) | ![C: $i, D: $i, E: $i] : (in(ordered_pair(C, E), A) | (~in(C, B)) | (~in(D, B)) | (~in(E, B)) | (~in(ordered_pair(C, D), A)) | (~in(ordered_pair(D, E), A))))) | (~(is_transitive_in(A, B) | (~(in(ordered_pair(tptp_fun_C_2(B, A), tptp_fun_E_0(B, A)), A) | (~in(tptp_fun_C_2(B, A), B)) | (~in(tptp_fun_D_1(B, A), B)) | (~in(tptp_fun_E_0(B, A), B)) | (~in(ordered_pair(tptp_fun_C_2(B, A), tptp_fun_D_1(B, A)), A)) | (~in(ordered_pair(tptp_fun_D_1(B, A), tptp_fun_E_0(B, A)), A))))))))) <=> ![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~is_transitive_in(A, B)) | ![C: $i, D: $i, E: $i] : (in(ordered_pair(C, E), A) | (~in(C, B)) | (~in(D, B)) | (~in(E, B)) | (~in(ordered_pair(C, D), A)) | (~in(ordered_pair(D, E), A))))) | (~(is_transitive_in(A, B) | (~(in(ordered_pair(tptp_fun_C_2(B, A), tptp_fun_E_0(B, A)), A) | (~in(tptp_fun_C_2(B, A), B)) | (~in(tptp_fun_D_1(B, A), B)) | (~in(tptp_fun_E_0(B, A), B)) | (~in(ordered_pair(tptp_fun_C_2(B, A), tptp_fun_D_1(B, A)), A)) | (~in(ordered_pair(tptp_fun_D_1(B, A), tptp_fun_E_0(B, A)), A)))))))))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[94])).
% 0.19/0.41 tff(96,plain,
% 0.19/0.41 (^[A: $i] : rewrite(((~relation(A)) | ![B: $i] : (~((~((~is_transitive_in(A, B)) | ![C: $i, D: $i, E: $i] : (in(ordered_pair(C, E), A) | (~in(C, B)) | (~in(D, B)) | (~in(E, B)) | (~in(ordered_pair(C, D), A)) | (~in(ordered_pair(D, E), A))))) | (~(is_transitive_in(A, B) | (~(in(ordered_pair(tptp_fun_C_2(B, A), tptp_fun_E_0(B, A)), A) | (~in(tptp_fun_C_2(B, A), B)) | (~in(tptp_fun_D_1(B, A), B)) | (~in(tptp_fun_E_0(B, A), B)) | (~in(ordered_pair(tptp_fun_C_2(B, A), tptp_fun_D_1(B, A)), A)) | (~in(ordered_pair(tptp_fun_D_1(B, A), tptp_fun_E_0(B, A)), A))))))))) <=> ((~relation(A)) | ![B: $i] : (~((~((~is_transitive_in(A, B)) | ![C: $i, D: $i, E: $i] : (in(ordered_pair(C, E), A) | (~in(C, B)) | (~in(D, B)) | (~in(E, B)) | (~in(ordered_pair(C, D), A)) | (~in(ordered_pair(D, E), A))))) | (~(is_transitive_in(A, B) | (~(in(ordered_pair(tptp_fun_C_2(B, A), tptp_fun_E_0(B, A)), A) | (~in(tptp_fun_C_2(B, A), B)) | (~in(tptp_fun_D_1(B, A), B)) | (~in(tptp_fun_E_0(B, A), B)) | (~in(ordered_pair(tptp_fun_C_2(B, A), tptp_fun_D_1(B, A)), A)) | (~in(ordered_pair(tptp_fun_D_1(B, A), tptp_fun_E_0(B, A)), A))))))))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(97,plain,
% 0.19/0.42 (![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~is_transitive_in(A, B)) | ![C: $i, D: $i, E: $i] : (in(ordered_pair(C, E), A) | (~in(C, B)) | (~in(D, B)) | (~in(E, B)) | (~in(ordered_pair(C, D), A)) | (~in(ordered_pair(D, E), A))))) | (~(is_transitive_in(A, B) | (~(in(ordered_pair(tptp_fun_C_2(B, A), tptp_fun_E_0(B, A)), A) | (~in(tptp_fun_C_2(B, A), B)) | (~in(tptp_fun_D_1(B, A), B)) | (~in(tptp_fun_E_0(B, A), B)) | (~in(ordered_pair(tptp_fun_C_2(B, A), tptp_fun_D_1(B, A)), A)) | (~in(ordered_pair(tptp_fun_D_1(B, A), tptp_fun_E_0(B, A)), A))))))))) <=> ![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~is_transitive_in(A, B)) | ![C: $i, D: $i, E: $i] : (in(ordered_pair(C, E), A) | (~in(C, B)) | (~in(D, B)) | (~in(E, B)) | (~in(ordered_pair(C, D), A)) | (~in(ordered_pair(D, E), A))))) | (~(is_transitive_in(A, B) | (~(in(ordered_pair(tptp_fun_C_2(B, A), tptp_fun_E_0(B, A)), A) | (~in(tptp_fun_C_2(B, A), B)) | (~in(tptp_fun_D_1(B, A), B)) | (~in(tptp_fun_E_0(B, A), B)) | (~in(ordered_pair(tptp_fun_C_2(B, A), tptp_fun_D_1(B, A)), A)) | (~in(ordered_pair(tptp_fun_D_1(B, A), tptp_fun_E_0(B, A)), A)))))))))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[96])).
% 0.19/0.42 tff(98,plain,
% 0.19/0.42 (![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~is_transitive_in(A, B)) | ![C: $i, D: $i, E: $i] : (in(ordered_pair(C, E), A) | (~in(C, B)) | (~in(D, B)) | (~in(E, B)) | (~in(ordered_pair(C, D), A)) | (~in(ordered_pair(D, E), A))))) | (~(is_transitive_in(A, B) | (~(in(ordered_pair(tptp_fun_C_2(B, A), tptp_fun_E_0(B, A)), A) | (~in(tptp_fun_C_2(B, A), B)) | (~in(tptp_fun_D_1(B, A), B)) | (~in(tptp_fun_E_0(B, A), B)) | (~in(ordered_pair(tptp_fun_C_2(B, A), tptp_fun_D_1(B, A)), A)) | (~in(ordered_pair(tptp_fun_D_1(B, A), tptp_fun_E_0(B, A)), A))))))))) <=> ![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~is_transitive_in(A, B)) | ![C: $i, D: $i, E: $i] : (in(ordered_pair(C, E), A) | (~in(C, B)) | (~in(D, B)) | (~in(E, B)) | (~in(ordered_pair(C, D), A)) | (~in(ordered_pair(D, E), A))))) | (~(is_transitive_in(A, B) | (~(in(ordered_pair(tptp_fun_C_2(B, A), tptp_fun_E_0(B, A)), A) | (~in(tptp_fun_C_2(B, A), B)) | (~in(tptp_fun_D_1(B, A), B)) | (~in(tptp_fun_E_0(B, A), B)) | (~in(ordered_pair(tptp_fun_C_2(B, A), tptp_fun_D_1(B, A)), A)) | (~in(ordered_pair(tptp_fun_D_1(B, A), tptp_fun_E_0(B, A)), A)))))))))),
% 0.19/0.42 inference(transitivity,[status(thm)],[97, 95])).
% 0.19/0.42 tff(99,plain,
% 0.19/0.42 (^[A: $i] : rewrite(((~relation(A)) | ![B: $i] : (((~is_transitive_in(A, B)) | ![C: $i, D: $i, E: $i] : ((~(in(C, B) & in(D, B) & in(E, B) & in(ordered_pair(C, D), A) & in(ordered_pair(D, E), A))) | in(ordered_pair(C, E), A))) & (is_transitive_in(A, B) | (~((~(in(tptp_fun_C_2(B, A), B) & in(tptp_fun_D_1(B, A), B) & in(tptp_fun_E_0(B, A), B) & in(ordered_pair(tptp_fun_C_2(B, A), tptp_fun_D_1(B, A)), A) & in(ordered_pair(tptp_fun_D_1(B, A), tptp_fun_E_0(B, A)), A))) | in(ordered_pair(tptp_fun_C_2(B, A), tptp_fun_E_0(B, A)), A)))))) <=> ((~relation(A)) | ![B: $i] : (~((~((~is_transitive_in(A, B)) | ![C: $i, D: $i, E: $i] : (in(ordered_pair(C, E), A) | (~in(C, B)) | (~in(D, B)) | (~in(E, B)) | (~in(ordered_pair(C, D), A)) | (~in(ordered_pair(D, E), A))))) | (~(is_transitive_in(A, B) | (~(in(ordered_pair(tptp_fun_C_2(B, A), tptp_fun_E_0(B, A)), A) | (~in(tptp_fun_C_2(B, A), B)) | (~in(tptp_fun_D_1(B, A), B)) | (~in(tptp_fun_E_0(B, A), B)) | (~in(ordered_pair(tptp_fun_C_2(B, A), tptp_fun_D_1(B, A)), A)) | (~in(ordered_pair(tptp_fun_D_1(B, A), tptp_fun_E_0(B, A)), A))))))))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(100,plain,
% 0.19/0.42 (![A: $i] : ((~relation(A)) | ![B: $i] : (((~is_transitive_in(A, B)) | ![C: $i, D: $i, E: $i] : ((~(in(C, B) & in(D, B) & in(E, B) & in(ordered_pair(C, D), A) & in(ordered_pair(D, E), A))) | in(ordered_pair(C, E), A))) & (is_transitive_in(A, B) | (~((~(in(tptp_fun_C_2(B, A), B) & in(tptp_fun_D_1(B, A), B) & in(tptp_fun_E_0(B, A), B) & in(ordered_pair(tptp_fun_C_2(B, A), tptp_fun_D_1(B, A)), A) & in(ordered_pair(tptp_fun_D_1(B, A), tptp_fun_E_0(B, A)), A))) | in(ordered_pair(tptp_fun_C_2(B, A), tptp_fun_E_0(B, A)), A)))))) <=> ![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~is_transitive_in(A, B)) | ![C: $i, D: $i, E: $i] : (in(ordered_pair(C, E), A) | (~in(C, B)) | (~in(D, B)) | (~in(E, B)) | (~in(ordered_pair(C, D), A)) | (~in(ordered_pair(D, E), A))))) | (~(is_transitive_in(A, B) | (~(in(ordered_pair(tptp_fun_C_2(B, A), tptp_fun_E_0(B, A)), A) | (~in(tptp_fun_C_2(B, A), B)) | (~in(tptp_fun_D_1(B, A), B)) | (~in(tptp_fun_E_0(B, A), B)) | (~in(ordered_pair(tptp_fun_C_2(B, A), tptp_fun_D_1(B, A)), A)) | (~in(ordered_pair(tptp_fun_D_1(B, A), tptp_fun_E_0(B, A)), A)))))))))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[99])).
% 0.19/0.42 tff(101,plain,
% 0.19/0.42 (![A: $i] : ((~relation(A)) | ![B: $i] : (is_transitive_in(A, B) <=> ![C: $i, D: $i, E: $i] : ((~(in(C, B) & in(D, B) & in(E, B) & in(ordered_pair(C, D), A) & in(ordered_pair(D, E), A))) | in(ordered_pair(C, E), A)))) <=> ![A: $i] : ((~relation(A)) | ![B: $i] : (is_transitive_in(A, B) <=> ![C: $i, D: $i, E: $i] : ((~(in(C, B) & in(D, B) & in(E, B) & in(ordered_pair(C, D), A) & in(ordered_pair(D, E), A))) | in(ordered_pair(C, E), A))))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(102,plain,
% 0.19/0.42 (^[A: $i] : trans(monotonicity(quant_intro(proof_bind(^[B: $i] : rewrite((is_transitive_in(A, B) <=> ![C: $i, D: $i, E: $i] : (((((in(C, B) & in(D, B)) & in(E, B)) & in(ordered_pair(C, D), A)) & in(ordered_pair(D, E), A)) => in(ordered_pair(C, E), A))) <=> (is_transitive_in(A, B) <=> ![C: $i, D: $i, E: $i] : ((~(in(C, B) & in(D, B) & in(E, B) & in(ordered_pair(C, D), A) & in(ordered_pair(D, E), A))) | in(ordered_pair(C, E), A))))), (![B: $i] : (is_transitive_in(A, B) <=> ![C: $i, D: $i, E: $i] : (((((in(C, B) & in(D, B)) & in(E, B)) & in(ordered_pair(C, D), A)) & in(ordered_pair(D, E), A)) => in(ordered_pair(C, E), A))) <=> ![B: $i] : (is_transitive_in(A, B) <=> ![C: $i, D: $i, E: $i] : ((~(in(C, B) & in(D, B) & in(E, B) & in(ordered_pair(C, D), A) & in(ordered_pair(D, E), A))) | in(ordered_pair(C, E), A))))), ((relation(A) => ![B: $i] : (is_transitive_in(A, B) <=> ![C: $i, D: $i, E: $i] : (((((in(C, B) & in(D, B)) & in(E, B)) & in(ordered_pair(C, D), A)) & in(ordered_pair(D, E), A)) => in(ordered_pair(C, E), A)))) <=> (relation(A) => ![B: $i] : (is_transitive_in(A, B) <=> ![C: $i, D: $i, E: $i] : ((~(in(C, B) & in(D, B) & in(E, B) & in(ordered_pair(C, D), A) & in(ordered_pair(D, E), A))) | in(ordered_pair(C, E), A)))))), rewrite((relation(A) => ![B: $i] : (is_transitive_in(A, B) <=> ![C: $i, D: $i, E: $i] : ((~(in(C, B) & in(D, B) & in(E, B) & in(ordered_pair(C, D), A) & in(ordered_pair(D, E), A))) | in(ordered_pair(C, E), A)))) <=> ((~relation(A)) | ![B: $i] : (is_transitive_in(A, B) <=> ![C: $i, D: $i, E: $i] : ((~(in(C, B) & in(D, B) & in(E, B) & in(ordered_pair(C, D), A) & in(ordered_pair(D, E), A))) | in(ordered_pair(C, E), A))))), ((relation(A) => ![B: $i] : (is_transitive_in(A, B) <=> ![C: $i, D: $i, E: $i] : (((((in(C, B) & in(D, B)) & in(E, B)) & in(ordered_pair(C, D), A)) & in(ordered_pair(D, E), A)) => in(ordered_pair(C, E), A)))) <=> ((~relation(A)) | ![B: $i] : (is_transitive_in(A, B) <=> ![C: $i, D: $i, E: $i] : ((~(in(C, B) & in(D, B) & in(E, B) & in(ordered_pair(C, D), A) & in(ordered_pair(D, E), A))) | in(ordered_pair(C, E), A))))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(103,plain,
% 0.19/0.42 (![A: $i] : (relation(A) => ![B: $i] : (is_transitive_in(A, B) <=> ![C: $i, D: $i, E: $i] : (((((in(C, B) & in(D, B)) & in(E, B)) & in(ordered_pair(C, D), A)) & in(ordered_pair(D, E), A)) => in(ordered_pair(C, E), A)))) <=> ![A: $i] : ((~relation(A)) | ![B: $i] : (is_transitive_in(A, B) <=> ![C: $i, D: $i, E: $i] : ((~(in(C, B) & in(D, B) & in(E, B) & in(ordered_pair(C, D), A) & in(ordered_pair(D, E), A))) | in(ordered_pair(C, E), A))))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[102])).
% 0.19/0.42 tff(104,axiom,(![A: $i] : (relation(A) => ![B: $i] : (is_transitive_in(A, B) <=> ![C: $i, D: $i, E: $i] : (((((in(C, B) & in(D, B)) & in(E, B)) & in(ordered_pair(C, D), A)) & in(ordered_pair(D, E), A)) => in(ordered_pair(C, E), A))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d8_relat_2')).
% 0.19/0.42 tff(105,plain,
% 0.19/0.42 (![A: $i] : ((~relation(A)) | ![B: $i] : (is_transitive_in(A, B) <=> ![C: $i, D: $i, E: $i] : ((~(in(C, B) & in(D, B) & in(E, B) & in(ordered_pair(C, D), A) & in(ordered_pair(D, E), A))) | in(ordered_pair(C, E), A))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[104, 103])).
% 0.19/0.42 tff(106,plain,
% 0.19/0.42 (![A: $i] : ((~relation(A)) | ![B: $i] : (is_transitive_in(A, B) <=> ![C: $i, D: $i, E: $i] : ((~(in(C, B) & in(D, B) & in(E, B) & in(ordered_pair(C, D), A) & in(ordered_pair(D, E), A))) | in(ordered_pair(C, E), A))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[105, 101])).
% 0.19/0.42 tff(107,plain,(
% 0.19/0.42 ![A: $i] : ((~relation(A)) | ![B: $i] : (((~is_transitive_in(A, B)) | ![C: $i, D: $i, E: $i] : ((~(in(C, B) & in(D, B) & in(E, B) & in(ordered_pair(C, D), A) & in(ordered_pair(D, E), A))) | in(ordered_pair(C, E), A))) & (is_transitive_in(A, B) | (~((~(in(tptp_fun_C_2(B, A), B) & in(tptp_fun_D_1(B, A), B) & in(tptp_fun_E_0(B, A), B) & in(ordered_pair(tptp_fun_C_2(B, A), tptp_fun_D_1(B, A)), A) & in(ordered_pair(tptp_fun_D_1(B, A), tptp_fun_E_0(B, A)), A))) | in(ordered_pair(tptp_fun_C_2(B, A), tptp_fun_E_0(B, A)), A))))))),
% 0.19/0.42 inference(skolemize,[status(sab)],[106])).
% 0.19/0.42 tff(108,plain,
% 0.19/0.42 (![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~is_transitive_in(A, B)) | ![C: $i, D: $i, E: $i] : (in(ordered_pair(C, E), A) | (~in(C, B)) | (~in(D, B)) | (~in(E, B)) | (~in(ordered_pair(C, D), A)) | (~in(ordered_pair(D, E), A))))) | (~(is_transitive_in(A, B) | (~(in(ordered_pair(tptp_fun_C_2(B, A), tptp_fun_E_0(B, A)), A) | (~in(tptp_fun_C_2(B, A), B)) | (~in(tptp_fun_D_1(B, A), B)) | (~in(tptp_fun_E_0(B, A), B)) | (~in(ordered_pair(tptp_fun_C_2(B, A), tptp_fun_D_1(B, A)), A)) | (~in(ordered_pair(tptp_fun_D_1(B, A), tptp_fun_E_0(B, A)), A)))))))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[107, 100])).
% 0.19/0.42 tff(109,plain,
% 0.19/0.42 (![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~is_transitive_in(A, B)) | ![C: $i, D: $i, E: $i] : (in(ordered_pair(C, E), A) | (~in(C, B)) | (~in(D, B)) | (~in(E, B)) | (~in(ordered_pair(C, D), A)) | (~in(ordered_pair(D, E), A))))) | (~(is_transitive_in(A, B) | (~(in(ordered_pair(tptp_fun_C_2(B, A), tptp_fun_E_0(B, A)), A) | (~in(tptp_fun_C_2(B, A), B)) | (~in(tptp_fun_D_1(B, A), B)) | (~in(tptp_fun_E_0(B, A), B)) | (~in(ordered_pair(tptp_fun_C_2(B, A), tptp_fun_D_1(B, A)), A)) | (~in(ordered_pair(tptp_fun_D_1(B, A), tptp_fun_E_0(B, A)), A)))))))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[108, 98])).
% 0.19/0.42 tff(110,plain,
% 0.19/0.42 (((~![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~is_transitive_in(A, B)) | ![C: $i, D: $i, E: $i] : (in(ordered_pair(C, E), A) | (~in(C, B)) | (~in(D, B)) | (~in(E, B)) | (~in(ordered_pair(C, D), A)) | (~in(ordered_pair(D, E), A))))) | (~(is_transitive_in(A, B) | (~(in(ordered_pair(tptp_fun_C_2(B, A), tptp_fun_E_0(B, A)), A) | (~in(tptp_fun_C_2(B, A), B)) | (~in(tptp_fun_D_1(B, A), B)) | (~in(tptp_fun_E_0(B, A), B)) | (~in(ordered_pair(tptp_fun_C_2(B, A), tptp_fun_D_1(B, A)), A)) | (~in(ordered_pair(tptp_fun_D_1(B, A), tptp_fun_E_0(B, A)), A)))))))))) | ((~relation(A!4)) | ![B: $i] : (~((~((~is_transitive_in(A!4, B)) | ![C: $i, D: $i, E: $i] : (in(ordered_pair(C, E), A!4) | (~in(C, B)) | (~in(D, B)) | (~in(E, B)) | (~in(ordered_pair(C, D), A!4)) | (~in(ordered_pair(D, E), A!4))))) | (~(is_transitive_in(A!4, B) | (~(in(ordered_pair(tptp_fun_C_2(B, A!4), tptp_fun_E_0(B, A!4)), A!4) | (~in(tptp_fun_C_2(B, A!4), B)) | (~in(tptp_fun_D_1(B, A!4), B)) | (~in(tptp_fun_E_0(B, A!4), B)) | (~in(ordered_pair(tptp_fun_C_2(B, A!4), tptp_fun_D_1(B, A!4)), A!4)) | (~in(ordered_pair(tptp_fun_D_1(B, A!4), tptp_fun_E_0(B, A!4)), A!4)))))))))) <=> ((~![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~is_transitive_in(A, B)) | ![C: $i, D: $i, E: $i] : (in(ordered_pair(C, E), A) | (~in(C, B)) | (~in(D, B)) | (~in(E, B)) | (~in(ordered_pair(C, D), A)) | (~in(ordered_pair(D, E), A))))) | (~(is_transitive_in(A, B) | (~(in(ordered_pair(tptp_fun_C_2(B, A), tptp_fun_E_0(B, A)), A) | (~in(tptp_fun_C_2(B, A), B)) | (~in(tptp_fun_D_1(B, A), B)) | (~in(tptp_fun_E_0(B, A), B)) | (~in(ordered_pair(tptp_fun_C_2(B, A), tptp_fun_D_1(B, A)), A)) | (~in(ordered_pair(tptp_fun_D_1(B, A), tptp_fun_E_0(B, A)), A)))))))))) | (~relation(A!4)) | ![B: $i] : (~((~((~is_transitive_in(A!4, B)) | ![C: $i, D: $i, E: $i] : (in(ordered_pair(C, E), A!4) | (~in(C, B)) | (~in(D, B)) | (~in(E, B)) | (~in(ordered_pair(C, D), A!4)) | (~in(ordered_pair(D, E), A!4))))) | (~(is_transitive_in(A!4, B) | (~(in(ordered_pair(tptp_fun_C_2(B, A!4), tptp_fun_E_0(B, A!4)), A!4) | (~in(tptp_fun_C_2(B, A!4), B)) | (~in(tptp_fun_D_1(B, A!4), B)) | (~in(tptp_fun_E_0(B, A!4), B)) | (~in(ordered_pair(tptp_fun_C_2(B, A!4), tptp_fun_D_1(B, A!4)), A!4)) | (~in(ordered_pair(tptp_fun_D_1(B, A!4), tptp_fun_E_0(B, A!4)), A!4)))))))))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(111,plain,
% 0.19/0.42 ((~![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~is_transitive_in(A, B)) | ![C: $i, D: $i, E: $i] : (in(ordered_pair(C, E), A) | (~in(C, B)) | (~in(D, B)) | (~in(E, B)) | (~in(ordered_pair(C, D), A)) | (~in(ordered_pair(D, E), A))))) | (~(is_transitive_in(A, B) | (~(in(ordered_pair(tptp_fun_C_2(B, A), tptp_fun_E_0(B, A)), A) | (~in(tptp_fun_C_2(B, A), B)) | (~in(tptp_fun_D_1(B, A), B)) | (~in(tptp_fun_E_0(B, A), B)) | (~in(ordered_pair(tptp_fun_C_2(B, A), tptp_fun_D_1(B, A)), A)) | (~in(ordered_pair(tptp_fun_D_1(B, A), tptp_fun_E_0(B, A)), A)))))))))) | ((~relation(A!4)) | ![B: $i] : (~((~((~is_transitive_in(A!4, B)) | ![C: $i, D: $i, E: $i] : (in(ordered_pair(C, E), A!4) | (~in(C, B)) | (~in(D, B)) | (~in(E, B)) | (~in(ordered_pair(C, D), A!4)) | (~in(ordered_pair(D, E), A!4))))) | (~(is_transitive_in(A!4, B) | (~(in(ordered_pair(tptp_fun_C_2(B, A!4), tptp_fun_E_0(B, A!4)), A!4) | (~in(tptp_fun_C_2(B, A!4), B)) | (~in(tptp_fun_D_1(B, A!4), B)) | (~in(tptp_fun_E_0(B, A!4), B)) | (~in(ordered_pair(tptp_fun_C_2(B, A!4), tptp_fun_D_1(B, A!4)), A!4)) | (~in(ordered_pair(tptp_fun_D_1(B, A!4), tptp_fun_E_0(B, A!4)), A!4)))))))))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(112,plain,
% 0.19/0.42 ((~![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~is_transitive_in(A, B)) | ![C: $i, D: $i, E: $i] : (in(ordered_pair(C, E), A) | (~in(C, B)) | (~in(D, B)) | (~in(E, B)) | (~in(ordered_pair(C, D), A)) | (~in(ordered_pair(D, E), A))))) | (~(is_transitive_in(A, B) | (~(in(ordered_pair(tptp_fun_C_2(B, A), tptp_fun_E_0(B, A)), A) | (~in(tptp_fun_C_2(B, A), B)) | (~in(tptp_fun_D_1(B, A), B)) | (~in(tptp_fun_E_0(B, A), B)) | (~in(ordered_pair(tptp_fun_C_2(B, A), tptp_fun_D_1(B, A)), A)) | (~in(ordered_pair(tptp_fun_D_1(B, A), tptp_fun_E_0(B, A)), A)))))))))) | (~relation(A!4)) | ![B: $i] : (~((~((~is_transitive_in(A!4, B)) | ![C: $i, D: $i, E: $i] : (in(ordered_pair(C, E), A!4) | (~in(C, B)) | (~in(D, B)) | (~in(E, B)) | (~in(ordered_pair(C, D), A!4)) | (~in(ordered_pair(D, E), A!4))))) | (~(is_transitive_in(A!4, B) | (~(in(ordered_pair(tptp_fun_C_2(B, A!4), tptp_fun_E_0(B, A!4)), A!4) | (~in(tptp_fun_C_2(B, A!4), B)) | (~in(tptp_fun_D_1(B, A!4), B)) | (~in(tptp_fun_E_0(B, A!4), B)) | (~in(ordered_pair(tptp_fun_C_2(B, A!4), tptp_fun_D_1(B, A!4)), A!4)) | (~in(ordered_pair(tptp_fun_D_1(B, A!4), tptp_fun_E_0(B, A!4)), A!4))))))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[111, 110])).
% 0.19/0.42 tff(113,plain,
% 0.19/0.42 (![B: $i] : (~((~((~is_transitive_in(A!4, B)) | ![C: $i, D: $i, E: $i] : (in(ordered_pair(C, E), A!4) | (~in(C, B)) | (~in(D, B)) | (~in(E, B)) | (~in(ordered_pair(C, D), A!4)) | (~in(ordered_pair(D, E), A!4))))) | (~(is_transitive_in(A!4, B) | (~(in(ordered_pair(tptp_fun_C_2(B, A!4), tptp_fun_E_0(B, A!4)), A!4) | (~in(tptp_fun_C_2(B, A!4), B)) | (~in(tptp_fun_D_1(B, A!4), B)) | (~in(tptp_fun_E_0(B, A!4), B)) | (~in(ordered_pair(tptp_fun_C_2(B, A!4), tptp_fun_D_1(B, A!4)), A!4)) | (~in(ordered_pair(tptp_fun_D_1(B, A!4), tptp_fun_E_0(B, A!4)), A!4))))))))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[112, 109, 18])).
% 0.19/0.43 tff(114,plain,
% 0.19/0.43 (((~![B: $i] : (~((~((~is_transitive_in(A!4, B)) | ![C: $i, D: $i, E: $i] : (in(ordered_pair(C, E), A!4) | (~in(C, B)) | (~in(D, B)) | (~in(E, B)) | (~in(ordered_pair(C, D), A!4)) | (~in(ordered_pair(D, E), A!4))))) | (~(is_transitive_in(A!4, B) | (~(in(ordered_pair(tptp_fun_C_2(B, A!4), tptp_fun_E_0(B, A!4)), A!4) | (~in(tptp_fun_C_2(B, A!4), B)) | (~in(tptp_fun_D_1(B, A!4), B)) | (~in(tptp_fun_E_0(B, A!4), B)) | (~in(ordered_pair(tptp_fun_C_2(B, A!4), tptp_fun_D_1(B, A!4)), A!4)) | (~in(ordered_pair(tptp_fun_D_1(B, A!4), tptp_fun_E_0(B, A!4)), A!4))))))))) | (~((~((~is_transitive_in(A!4, set_union2(relation_dom(A!4), relation_rng(A!4)))) | ![C: $i, D: $i, E: $i] : (in(ordered_pair(C, E), A!4) | (~in(ordered_pair(C, D), A!4)) | (~in(ordered_pair(D, E), A!4)) | (~in(C, set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(E, set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(D, set_union2(relation_dom(A!4), relation_rng(A!4))))))) | (~(is_transitive_in(A!4, set_union2(relation_dom(A!4), relation_rng(A!4))) | (~(in(ordered_pair(tptp_fun_C_2(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), tptp_fun_E_0(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4)), A!4) | (~in(tptp_fun_C_2(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(tptp_fun_D_1(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(tptp_fun_E_0(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(ordered_pair(tptp_fun_C_2(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), tptp_fun_D_1(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4)), A!4)) | (~in(ordered_pair(tptp_fun_D_1(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), tptp_fun_E_0(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4)), A!4))))))))) <=> ((~![B: $i] : (~((~((~is_transitive_in(A!4, B)) | ![C: $i, D: $i, E: $i] : (in(ordered_pair(C, E), A!4) | (~in(C, B)) | (~in(D, B)) | (~in(E, B)) | (~in(ordered_pair(C, D), A!4)) | (~in(ordered_pair(D, E), A!4))))) | (~(is_transitive_in(A!4, B) | (~(in(ordered_pair(tptp_fun_C_2(B, A!4), tptp_fun_E_0(B, A!4)), A!4) | (~in(tptp_fun_C_2(B, A!4), B)) | (~in(tptp_fun_D_1(B, A!4), B)) | (~in(tptp_fun_E_0(B, A!4), B)) | (~in(ordered_pair(tptp_fun_C_2(B, A!4), tptp_fun_D_1(B, A!4)), A!4)) | (~in(ordered_pair(tptp_fun_D_1(B, A!4), tptp_fun_E_0(B, A!4)), A!4))))))))) | (~((~((~is_transitive_in(A!4, set_union2(relation_dom(A!4), relation_rng(A!4)))) | ![C: $i, D: $i, E: $i] : (in(ordered_pair(C, E), A!4) | (~in(ordered_pair(C, D), A!4)) | (~in(ordered_pair(D, E), A!4)) | (~in(C, set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(E, set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(D, set_union2(relation_dom(A!4), relation_rng(A!4))))))) | (~(is_transitive_in(A!4, set_union2(relation_dom(A!4), relation_rng(A!4))) | (~(in(ordered_pair(tptp_fun_C_2(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), tptp_fun_E_0(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4)), A!4) | (~in(tptp_fun_C_2(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(tptp_fun_D_1(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(tptp_fun_E_0(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(ordered_pair(tptp_fun_C_2(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), tptp_fun_D_1(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4)), A!4)) | (~in(ordered_pair(tptp_fun_D_1(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), tptp_fun_E_0(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4)), A!4)))))))))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(115,plain,
% 0.19/0.43 ((~((~((~is_transitive_in(A!4, set_union2(relation_dom(A!4), relation_rng(A!4)))) | ![C: $i, D: $i, E: $i] : (in(ordered_pair(C, E), A!4) | (~in(C, set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(D, set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(E, set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(ordered_pair(C, D), A!4)) | (~in(ordered_pair(D, E), A!4))))) | (~(is_transitive_in(A!4, set_union2(relation_dom(A!4), relation_rng(A!4))) | (~(in(ordered_pair(tptp_fun_C_2(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), tptp_fun_E_0(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4)), A!4) | (~in(tptp_fun_C_2(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(tptp_fun_D_1(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(tptp_fun_E_0(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(ordered_pair(tptp_fun_C_2(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), tptp_fun_D_1(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4)), A!4)) | (~in(ordered_pair(tptp_fun_D_1(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), tptp_fun_E_0(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4)), A!4)))))))) <=> (~((~((~is_transitive_in(A!4, set_union2(relation_dom(A!4), relation_rng(A!4)))) | ![C: $i, D: $i, E: $i] : (in(ordered_pair(C, E), A!4) | (~in(ordered_pair(C, D), A!4)) | (~in(ordered_pair(D, E), A!4)) | (~in(C, set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(E, set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(D, set_union2(relation_dom(A!4), relation_rng(A!4))))))) | (~(is_transitive_in(A!4, set_union2(relation_dom(A!4), relation_rng(A!4))) | (~(in(ordered_pair(tptp_fun_C_2(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), tptp_fun_E_0(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4)), A!4) | (~in(tptp_fun_C_2(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(tptp_fun_D_1(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(tptp_fun_E_0(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(ordered_pair(tptp_fun_C_2(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), tptp_fun_D_1(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4)), A!4)) | (~in(ordered_pair(tptp_fun_D_1(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), tptp_fun_E_0(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4)), A!4))))))))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(116,plain,
% 0.19/0.43 (((~![B: $i] : (~((~((~is_transitive_in(A!4, B)) | ![C: $i, D: $i, E: $i] : (in(ordered_pair(C, E), A!4) | (~in(C, B)) | (~in(D, B)) | (~in(E, B)) | (~in(ordered_pair(C, D), A!4)) | (~in(ordered_pair(D, E), A!4))))) | (~(is_transitive_in(A!4, B) | (~(in(ordered_pair(tptp_fun_C_2(B, A!4), tptp_fun_E_0(B, A!4)), A!4) | (~in(tptp_fun_C_2(B, A!4), B)) | (~in(tptp_fun_D_1(B, A!4), B)) | (~in(tptp_fun_E_0(B, A!4), B)) | (~in(ordered_pair(tptp_fun_C_2(B, A!4), tptp_fun_D_1(B, A!4)), A!4)) | (~in(ordered_pair(tptp_fun_D_1(B, A!4), tptp_fun_E_0(B, A!4)), A!4))))))))) | (~((~((~is_transitive_in(A!4, set_union2(relation_dom(A!4), relation_rng(A!4)))) | ![C: $i, D: $i, E: $i] : (in(ordered_pair(C, E), A!4) | (~in(C, set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(D, set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(E, set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(ordered_pair(C, D), A!4)) | (~in(ordered_pair(D, E), A!4))))) | (~(is_transitive_in(A!4, set_union2(relation_dom(A!4), relation_rng(A!4))) | (~(in(ordered_pair(tptp_fun_C_2(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), tptp_fun_E_0(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4)), A!4) | (~in(tptp_fun_C_2(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(tptp_fun_D_1(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(tptp_fun_E_0(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(ordered_pair(tptp_fun_C_2(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), tptp_fun_D_1(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4)), A!4)) | (~in(ordered_pair(tptp_fun_D_1(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), tptp_fun_E_0(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4)), A!4))))))))) <=> ((~![B: $i] : (~((~((~is_transitive_in(A!4, B)) | ![C: $i, D: $i, E: $i] : (in(ordered_pair(C, E), A!4) | (~in(C, B)) | (~in(D, B)) | (~in(E, B)) | (~in(ordered_pair(C, D), A!4)) | (~in(ordered_pair(D, E), A!4))))) | (~(is_transitive_in(A!4, B) | (~(in(ordered_pair(tptp_fun_C_2(B, A!4), tptp_fun_E_0(B, A!4)), A!4) | (~in(tptp_fun_C_2(B, A!4), B)) | (~in(tptp_fun_D_1(B, A!4), B)) | (~in(tptp_fun_E_0(B, A!4), B)) | (~in(ordered_pair(tptp_fun_C_2(B, A!4), tptp_fun_D_1(B, A!4)), A!4)) | (~in(ordered_pair(tptp_fun_D_1(B, A!4), tptp_fun_E_0(B, A!4)), A!4))))))))) | (~((~((~is_transitive_in(A!4, set_union2(relation_dom(A!4), relation_rng(A!4)))) | ![C: $i, D: $i, E: $i] : (in(ordered_pair(C, E), A!4) | (~in(ordered_pair(C, D), A!4)) | (~in(ordered_pair(D, E), A!4)) | (~in(C, set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(E, set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(D, set_union2(relation_dom(A!4), relation_rng(A!4))))))) | (~(is_transitive_in(A!4, set_union2(relation_dom(A!4), relation_rng(A!4))) | (~(in(ordered_pair(tptp_fun_C_2(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), tptp_fun_E_0(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4)), A!4) | (~in(tptp_fun_C_2(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(tptp_fun_D_1(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(tptp_fun_E_0(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(ordered_pair(tptp_fun_C_2(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), tptp_fun_D_1(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4)), A!4)) | (~in(ordered_pair(tptp_fun_D_1(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), tptp_fun_E_0(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4)), A!4)))))))))),
% 0.19/0.43 inference(monotonicity,[status(thm)],[115])).
% 0.19/0.43 tff(117,plain,
% 0.19/0.43 (((~![B: $i] : (~((~((~is_transitive_in(A!4, B)) | ![C: $i, D: $i, E: $i] : (in(ordered_pair(C, E), A!4) | (~in(C, B)) | (~in(D, B)) | (~in(E, B)) | (~in(ordered_pair(C, D), A!4)) | (~in(ordered_pair(D, E), A!4))))) | (~(is_transitive_in(A!4, B) | (~(in(ordered_pair(tptp_fun_C_2(B, A!4), tptp_fun_E_0(B, A!4)), A!4) | (~in(tptp_fun_C_2(B, A!4), B)) | (~in(tptp_fun_D_1(B, A!4), B)) | (~in(tptp_fun_E_0(B, A!4), B)) | (~in(ordered_pair(tptp_fun_C_2(B, A!4), tptp_fun_D_1(B, A!4)), A!4)) | (~in(ordered_pair(tptp_fun_D_1(B, A!4), tptp_fun_E_0(B, A!4)), A!4))))))))) | (~((~((~is_transitive_in(A!4, set_union2(relation_dom(A!4), relation_rng(A!4)))) | ![C: $i, D: $i, E: $i] : (in(ordered_pair(C, E), A!4) | (~in(C, set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(D, set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(E, set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(ordered_pair(C, D), A!4)) | (~in(ordered_pair(D, E), A!4))))) | (~(is_transitive_in(A!4, set_union2(relation_dom(A!4), relation_rng(A!4))) | (~(in(ordered_pair(tptp_fun_C_2(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), tptp_fun_E_0(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4)), A!4) | (~in(tptp_fun_C_2(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(tptp_fun_D_1(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(tptp_fun_E_0(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(ordered_pair(tptp_fun_C_2(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), tptp_fun_D_1(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4)), A!4)) | (~in(ordered_pair(tptp_fun_D_1(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), tptp_fun_E_0(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4)), A!4))))))))) <=> ((~![B: $i] : (~((~((~is_transitive_in(A!4, B)) | ![C: $i, D: $i, E: $i] : (in(ordered_pair(C, E), A!4) | (~in(C, B)) | (~in(D, B)) | (~in(E, B)) | (~in(ordered_pair(C, D), A!4)) | (~in(ordered_pair(D, E), A!4))))) | (~(is_transitive_in(A!4, B) | (~(in(ordered_pair(tptp_fun_C_2(B, A!4), tptp_fun_E_0(B, A!4)), A!4) | (~in(tptp_fun_C_2(B, A!4), B)) | (~in(tptp_fun_D_1(B, A!4), B)) | (~in(tptp_fun_E_0(B, A!4), B)) | (~in(ordered_pair(tptp_fun_C_2(B, A!4), tptp_fun_D_1(B, A!4)), A!4)) | (~in(ordered_pair(tptp_fun_D_1(B, A!4), tptp_fun_E_0(B, A!4)), A!4))))))))) | (~((~((~is_transitive_in(A!4, set_union2(relation_dom(A!4), relation_rng(A!4)))) | ![C: $i, D: $i, E: $i] : (in(ordered_pair(C, E), A!4) | (~in(ordered_pair(C, D), A!4)) | (~in(ordered_pair(D, E), A!4)) | (~in(C, set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(E, set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(D, set_union2(relation_dom(A!4), relation_rng(A!4))))))) | (~(is_transitive_in(A!4, set_union2(relation_dom(A!4), relation_rng(A!4))) | (~(in(ordered_pair(tptp_fun_C_2(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), tptp_fun_E_0(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4)), A!4) | (~in(tptp_fun_C_2(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(tptp_fun_D_1(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(tptp_fun_E_0(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(ordered_pair(tptp_fun_C_2(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), tptp_fun_D_1(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4)), A!4)) | (~in(ordered_pair(tptp_fun_D_1(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), tptp_fun_E_0(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4)), A!4)))))))))),
% 0.19/0.44 inference(transitivity,[status(thm)],[116, 114])).
% 0.19/0.44 tff(118,plain,
% 0.19/0.44 ((~![B: $i] : (~((~((~is_transitive_in(A!4, B)) | ![C: $i, D: $i, E: $i] : (in(ordered_pair(C, E), A!4) | (~in(C, B)) | (~in(D, B)) | (~in(E, B)) | (~in(ordered_pair(C, D), A!4)) | (~in(ordered_pair(D, E), A!4))))) | (~(is_transitive_in(A!4, B) | (~(in(ordered_pair(tptp_fun_C_2(B, A!4), tptp_fun_E_0(B, A!4)), A!4) | (~in(tptp_fun_C_2(B, A!4), B)) | (~in(tptp_fun_D_1(B, A!4), B)) | (~in(tptp_fun_E_0(B, A!4), B)) | (~in(ordered_pair(tptp_fun_C_2(B, A!4), tptp_fun_D_1(B, A!4)), A!4)) | (~in(ordered_pair(tptp_fun_D_1(B, A!4), tptp_fun_E_0(B, A!4)), A!4))))))))) | (~((~((~is_transitive_in(A!4, set_union2(relation_dom(A!4), relation_rng(A!4)))) | ![C: $i, D: $i, E: $i] : (in(ordered_pair(C, E), A!4) | (~in(C, set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(D, set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(E, set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(ordered_pair(C, D), A!4)) | (~in(ordered_pair(D, E), A!4))))) | (~(is_transitive_in(A!4, set_union2(relation_dom(A!4), relation_rng(A!4))) | (~(in(ordered_pair(tptp_fun_C_2(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), tptp_fun_E_0(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4)), A!4) | (~in(tptp_fun_C_2(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(tptp_fun_D_1(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(tptp_fun_E_0(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(ordered_pair(tptp_fun_C_2(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), tptp_fun_D_1(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4)), A!4)) | (~in(ordered_pair(tptp_fun_D_1(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), tptp_fun_E_0(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4)), A!4))))))))),
% 0.19/0.44 inference(quant_inst,[status(thm)],[])).
% 0.19/0.44 tff(119,plain,
% 0.19/0.44 ((~![B: $i] : (~((~((~is_transitive_in(A!4, B)) | ![C: $i, D: $i, E: $i] : (in(ordered_pair(C, E), A!4) | (~in(C, B)) | (~in(D, B)) | (~in(E, B)) | (~in(ordered_pair(C, D), A!4)) | (~in(ordered_pair(D, E), A!4))))) | (~(is_transitive_in(A!4, B) | (~(in(ordered_pair(tptp_fun_C_2(B, A!4), tptp_fun_E_0(B, A!4)), A!4) | (~in(tptp_fun_C_2(B, A!4), B)) | (~in(tptp_fun_D_1(B, A!4), B)) | (~in(tptp_fun_E_0(B, A!4), B)) | (~in(ordered_pair(tptp_fun_C_2(B, A!4), tptp_fun_D_1(B, A!4)), A!4)) | (~in(ordered_pair(tptp_fun_D_1(B, A!4), tptp_fun_E_0(B, A!4)), A!4))))))))) | (~((~((~is_transitive_in(A!4, set_union2(relation_dom(A!4), relation_rng(A!4)))) | ![C: $i, D: $i, E: $i] : (in(ordered_pair(C, E), A!4) | (~in(ordered_pair(C, D), A!4)) | (~in(ordered_pair(D, E), A!4)) | (~in(C, set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(E, set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(D, set_union2(relation_dom(A!4), relation_rng(A!4))))))) | (~(is_transitive_in(A!4, set_union2(relation_dom(A!4), relation_rng(A!4))) | (~(in(ordered_pair(tptp_fun_C_2(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), tptp_fun_E_0(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4)), A!4) | (~in(tptp_fun_C_2(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(tptp_fun_D_1(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(tptp_fun_E_0(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(ordered_pair(tptp_fun_C_2(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), tptp_fun_D_1(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4)), A!4)) | (~in(ordered_pair(tptp_fun_D_1(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), tptp_fun_E_0(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4)), A!4))))))))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[118, 117])).
% 0.19/0.44 tff(120,plain,
% 0.19/0.44 (~((~((~is_transitive_in(A!4, set_union2(relation_dom(A!4), relation_rng(A!4)))) | ![C: $i, D: $i, E: $i] : (in(ordered_pair(C, E), A!4) | (~in(ordered_pair(C, D), A!4)) | (~in(ordered_pair(D, E), A!4)) | (~in(C, set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(E, set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(D, set_union2(relation_dom(A!4), relation_rng(A!4))))))) | (~(is_transitive_in(A!4, set_union2(relation_dom(A!4), relation_rng(A!4))) | (~(in(ordered_pair(tptp_fun_C_2(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), tptp_fun_E_0(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4)), A!4) | (~in(tptp_fun_C_2(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(tptp_fun_D_1(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(tptp_fun_E_0(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(ordered_pair(tptp_fun_C_2(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), tptp_fun_D_1(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4)), A!4)) | (~in(ordered_pair(tptp_fun_D_1(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), tptp_fun_E_0(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4)), A!4)))))))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[119, 113])).
% 0.19/0.44 tff(121,plain,
% 0.19/0.44 (((~((~is_transitive_in(A!4, set_union2(relation_dom(A!4), relation_rng(A!4)))) | ![C: $i, D: $i, E: $i] : (in(ordered_pair(C, E), A!4) | (~in(ordered_pair(C, D), A!4)) | (~in(ordered_pair(D, E), A!4)) | (~in(C, set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(E, set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(D, set_union2(relation_dom(A!4), relation_rng(A!4))))))) | (~(is_transitive_in(A!4, set_union2(relation_dom(A!4), relation_rng(A!4))) | (~(in(ordered_pair(tptp_fun_C_2(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), tptp_fun_E_0(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4)), A!4) | (~in(tptp_fun_C_2(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(tptp_fun_D_1(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(tptp_fun_E_0(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(ordered_pair(tptp_fun_C_2(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), tptp_fun_D_1(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4)), A!4)) | (~in(ordered_pair(tptp_fun_D_1(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), tptp_fun_E_0(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4)), A!4))))))) | ((~is_transitive_in(A!4, set_union2(relation_dom(A!4), relation_rng(A!4)))) | ![C: $i, D: $i, E: $i] : (in(ordered_pair(C, E), A!4) | (~in(ordered_pair(C, D), A!4)) | (~in(ordered_pair(D, E), A!4)) | (~in(C, set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(E, set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(D, set_union2(relation_dom(A!4), relation_rng(A!4))))))),
% 0.19/0.44 inference(tautology,[status(thm)],[])).
% 0.19/0.44 tff(122,plain,
% 0.19/0.44 ((~is_transitive_in(A!4, set_union2(relation_dom(A!4), relation_rng(A!4)))) | ![C: $i, D: $i, E: $i] : (in(ordered_pair(C, E), A!4) | (~in(ordered_pair(C, D), A!4)) | (~in(ordered_pair(D, E), A!4)) | (~in(C, set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(E, set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(D, set_union2(relation_dom(A!4), relation_rng(A!4)))))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[121, 120])).
% 0.19/0.44 tff(123,plain,
% 0.19/0.44 ((~((~is_transitive_in(A!4, set_union2(relation_dom(A!4), relation_rng(A!4)))) | ![C: $i, D: $i, E: $i] : (in(ordered_pair(C, E), A!4) | (~in(ordered_pair(C, D), A!4)) | (~in(ordered_pair(D, E), A!4)) | (~in(C, set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(E, set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(D, set_union2(relation_dom(A!4), relation_rng(A!4))))))) | (~is_transitive_in(A!4, set_union2(relation_dom(A!4), relation_rng(A!4)))) | ![C: $i, D: $i, E: $i] : (in(ordered_pair(C, E), A!4) | (~in(ordered_pair(C, D), A!4)) | (~in(ordered_pair(D, E), A!4)) | (~in(C, set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(E, set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(D, set_union2(relation_dom(A!4), relation_rng(A!4)))))),
% 0.19/0.44 inference(tautology,[status(thm)],[])).
% 0.19/0.44 tff(124,plain,
% 0.19/0.44 ((~is_transitive_in(A!4, set_union2(relation_dom(A!4), relation_rng(A!4)))) | ![C: $i, D: $i, E: $i] : (in(ordered_pair(C, E), A!4) | (~in(ordered_pair(C, D), A!4)) | (~in(ordered_pair(D, E), A!4)) | (~in(C, set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(E, set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(D, set_union2(relation_dom(A!4), relation_rng(A!4)))))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[123, 122])).
% 0.19/0.44 tff(125,plain,
% 0.19/0.44 (~is_transitive_in(A!4, set_union2(relation_dom(A!4), relation_rng(A!4)))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[124, 93])).
% 0.19/0.44 tff(126,plain,
% 0.19/0.44 (~is_transitive_in(A!4, relation_field(A!4))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[125, 44])).
% 0.19/0.44 tff(127,plain,
% 0.19/0.44 (^[A: $i] : refl(((~relation(A)) | (transitive(A) <=> is_transitive_in(A, relation_field(A)))) <=> ((~relation(A)) | (transitive(A) <=> is_transitive_in(A, relation_field(A)))))),
% 0.19/0.44 inference(bind,[status(th)],[])).
% 0.19/0.44 tff(128,plain,
% 0.19/0.44 (![A: $i] : ((~relation(A)) | (transitive(A) <=> is_transitive_in(A, relation_field(A)))) <=> ![A: $i] : ((~relation(A)) | (transitive(A) <=> is_transitive_in(A, relation_field(A))))),
% 0.19/0.44 inference(quant_intro,[status(thm)],[127])).
% 0.19/0.44 tff(129,plain,
% 0.19/0.44 (![A: $i] : ((~relation(A)) | (transitive(A) <=> is_transitive_in(A, relation_field(A)))) <=> ![A: $i] : ((~relation(A)) | (transitive(A) <=> is_transitive_in(A, relation_field(A))))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(130,plain,
% 0.19/0.45 (^[A: $i] : rewrite((relation(A) => (transitive(A) <=> is_transitive_in(A, relation_field(A)))) <=> ((~relation(A)) | (transitive(A) <=> is_transitive_in(A, relation_field(A)))))),
% 0.19/0.45 inference(bind,[status(th)],[])).
% 0.19/0.45 tff(131,plain,
% 0.19/0.45 (![A: $i] : (relation(A) => (transitive(A) <=> is_transitive_in(A, relation_field(A)))) <=> ![A: $i] : ((~relation(A)) | (transitive(A) <=> is_transitive_in(A, relation_field(A))))),
% 0.19/0.45 inference(quant_intro,[status(thm)],[130])).
% 0.19/0.45 tff(132,axiom,(![A: $i] : (relation(A) => (transitive(A) <=> is_transitive_in(A, relation_field(A))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d16_relat_2')).
% 0.19/0.45 tff(133,plain,
% 0.19/0.45 (![A: $i] : ((~relation(A)) | (transitive(A) <=> is_transitive_in(A, relation_field(A))))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[132, 131])).
% 0.19/0.45 tff(134,plain,
% 0.19/0.45 (![A: $i] : ((~relation(A)) | (transitive(A) <=> is_transitive_in(A, relation_field(A))))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[133, 129])).
% 0.19/0.45 tff(135,plain,(
% 0.19/0.45 ![A: $i] : ((~relation(A)) | (transitive(A) <=> is_transitive_in(A, relation_field(A))))),
% 0.19/0.45 inference(skolemize,[status(sab)],[134])).
% 0.19/0.45 tff(136,plain,
% 0.19/0.45 (![A: $i] : ((~relation(A)) | (transitive(A) <=> is_transitive_in(A, relation_field(A))))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[135, 128])).
% 0.19/0.45 tff(137,plain,
% 0.19/0.45 (((~![A: $i] : ((~relation(A)) | (transitive(A) <=> is_transitive_in(A, relation_field(A))))) | ((~relation(A!4)) | (transitive(A!4) <=> is_transitive_in(A!4, relation_field(A!4))))) <=> ((~![A: $i] : ((~relation(A)) | (transitive(A) <=> is_transitive_in(A, relation_field(A))))) | (~relation(A!4)) | (transitive(A!4) <=> is_transitive_in(A!4, relation_field(A!4))))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(138,plain,
% 0.19/0.45 ((~![A: $i] : ((~relation(A)) | (transitive(A) <=> is_transitive_in(A, relation_field(A))))) | ((~relation(A!4)) | (transitive(A!4) <=> is_transitive_in(A!4, relation_field(A!4))))),
% 0.19/0.45 inference(quant_inst,[status(thm)],[])).
% 0.19/0.45 tff(139,plain,
% 0.19/0.45 ((~![A: $i] : ((~relation(A)) | (transitive(A) <=> is_transitive_in(A, relation_field(A))))) | (~relation(A!4)) | (transitive(A!4) <=> is_transitive_in(A!4, relation_field(A!4)))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[138, 137])).
% 0.19/0.45 tff(140,plain,
% 0.19/0.45 (transitive(A!4) <=> is_transitive_in(A!4, relation_field(A!4))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[139, 136, 18])).
% 0.19/0.45 tff(141,plain,
% 0.19/0.45 ((~(transitive(A!4) <=> is_transitive_in(A!4, relation_field(A!4)))) | (~transitive(A!4)) | is_transitive_in(A!4, relation_field(A!4))),
% 0.19/0.45 inference(tautology,[status(thm)],[])).
% 0.19/0.45 tff(142,plain,
% 0.19/0.45 ((~transitive(A!4)) | is_transitive_in(A!4, relation_field(A!4))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[141, 140])).
% 0.19/0.45 tff(143,plain,
% 0.19/0.45 (~transitive(A!4)),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[142, 126])).
% 0.19/0.45 tff(144,plain,
% 0.19/0.45 ((transitive(A!4) | ![B: $i, C: $i, D: $i] : (in(ordered_pair(B, D), A!4) | (~in(ordered_pair(B, C), A!4)) | (~in(ordered_pair(C, D), A!4)))) <=> (transitive(A!4) | ![B: $i, C: $i, D: $i] : (in(ordered_pair(B, D), A!4) | (~in(ordered_pair(B, C), A!4)) | (~in(ordered_pair(C, D), A!4))))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(145,plain,
% 0.19/0.45 ((transitive(A!4) | ![B: $i, C: $i, D: $i] : ((~(in(ordered_pair(B, C), A!4) & in(ordered_pair(C, D), A!4))) | in(ordered_pair(B, D), A!4))) <=> (transitive(A!4) | ![B: $i, C: $i, D: $i] : (in(ordered_pair(B, D), A!4) | (~in(ordered_pair(B, C), A!4)) | (~in(ordered_pair(C, D), A!4))))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(146,plain,
% 0.19/0.45 (transitive(A!4) | ![B: $i, C: $i, D: $i] : ((~(in(ordered_pair(B, C), A!4) & in(ordered_pair(C, D), A!4))) | in(ordered_pair(B, D), A!4))),
% 0.19/0.45 inference(and_elim,[status(thm)],[17])).
% 0.19/0.45 tff(147,plain,
% 0.19/0.45 (transitive(A!4) | ![B: $i, C: $i, D: $i] : (in(ordered_pair(B, D), A!4) | (~in(ordered_pair(B, C), A!4)) | (~in(ordered_pair(C, D), A!4)))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[146, 145])).
% 0.19/0.45 tff(148,plain,
% 0.19/0.45 (transitive(A!4) | ![B: $i, C: $i, D: $i] : (in(ordered_pair(B, D), A!4) | (~in(ordered_pair(B, C), A!4)) | (~in(ordered_pair(C, D), A!4)))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[147, 144])).
% 0.19/0.45 tff(149,plain,
% 0.19/0.45 (![B: $i, C: $i, D: $i] : (in(ordered_pair(B, D), A!4) | (~in(ordered_pair(B, C), A!4)) | (~in(ordered_pair(C, D), A!4)))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[148, 143])).
% 0.19/0.45 tff(150,plain,
% 0.19/0.45 (((~![B: $i, C: $i, D: $i] : (in(ordered_pair(B, D), A!4) | (~in(ordered_pair(B, C), A!4)) | (~in(ordered_pair(C, D), A!4)))) | (in(ordered_pair(B!7, D!5), A!4) | (~in(ordered_pair(B!7, C!6), A!4)) | (~in(ordered_pair(C!6, D!5), A!4)))) <=> ((~![B: $i, C: $i, D: $i] : (in(ordered_pair(B, D), A!4) | (~in(ordered_pair(B, C), A!4)) | (~in(ordered_pair(C, D), A!4)))) | in(ordered_pair(B!7, D!5), A!4) | (~in(ordered_pair(B!7, C!6), A!4)) | (~in(ordered_pair(C!6, D!5), A!4)))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(151,plain,
% 0.19/0.45 ((~![B: $i, C: $i, D: $i] : (in(ordered_pair(B, D), A!4) | (~in(ordered_pair(B, C), A!4)) | (~in(ordered_pair(C, D), A!4)))) | (in(ordered_pair(B!7, D!5), A!4) | (~in(ordered_pair(B!7, C!6), A!4)) | (~in(ordered_pair(C!6, D!5), A!4)))),
% 0.19/0.45 inference(quant_inst,[status(thm)],[])).
% 0.19/0.45 tff(152,plain,
% 0.19/0.45 ((~![B: $i, C: $i, D: $i] : (in(ordered_pair(B, D), A!4) | (~in(ordered_pair(B, C), A!4)) | (~in(ordered_pair(C, D), A!4)))) | in(ordered_pair(B!7, D!5), A!4) | (~in(ordered_pair(B!7, C!6), A!4)) | (~in(ordered_pair(C!6, D!5), A!4))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[151, 150])).
% 0.19/0.45 tff(153,plain,
% 0.19/0.45 ($false),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[152, 149, 43, 41, 39])).
% 0.19/0.45 tff(154,plain,(in(ordered_pair(B!7, D!5), A!4) | (~in(ordered_pair(B!7, C!6), A!4)) | (~in(ordered_pair(C!6, D!5), A!4))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.45 tff(155,plain,
% 0.19/0.45 (((~transitive(A!4)) | (~((~(in(ordered_pair(B!7, C!6), A!4) & in(ordered_pair(C!6, D!5), A!4))) | in(ordered_pair(B!7, D!5), A!4)))) <=> ((~transitive(A!4)) | (~(in(ordered_pair(B!7, D!5), A!4) | (~in(ordered_pair(B!7, C!6), A!4)) | (~in(ordered_pair(C!6, D!5), A!4)))))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(156,plain,
% 0.19/0.45 ((~transitive(A!4)) | (~((~(in(ordered_pair(B!7, C!6), A!4) & in(ordered_pair(C!6, D!5), A!4))) | in(ordered_pair(B!7, D!5), A!4)))),
% 0.19/0.45 inference(and_elim,[status(thm)],[17])).
% 0.19/0.45 tff(157,plain,
% 0.19/0.45 ((~transitive(A!4)) | (~(in(ordered_pair(B!7, D!5), A!4) | (~in(ordered_pair(B!7, C!6), A!4)) | (~in(ordered_pair(C!6, D!5), A!4))))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[156, 155])).
% 0.19/0.45 tff(158,plain,
% 0.19/0.45 (~transitive(A!4)),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[157, 154])).
% 0.19/0.45 tff(159,plain,
% 0.19/0.45 ((~(transitive(A!4) <=> is_transitive_in(A!4, relation_field(A!4)))) | transitive(A!4) | (~is_transitive_in(A!4, relation_field(A!4)))),
% 0.19/0.45 inference(tautology,[status(thm)],[])).
% 0.19/0.45 tff(160,plain,
% 0.19/0.45 (transitive(A!4) | (~is_transitive_in(A!4, relation_field(A!4)))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[159, 140])).
% 0.19/0.45 tff(161,plain,
% 0.19/0.45 (~is_transitive_in(A!4, relation_field(A!4))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[160, 158])).
% 0.19/0.45 tff(162,plain,
% 0.19/0.45 (~is_transitive_in(A!4, set_union2(relation_dom(A!4), relation_rng(A!4)))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[161, 36])).
% 0.19/0.45 tff(163,plain,
% 0.19/0.45 (((~((~is_transitive_in(A!4, set_union2(relation_dom(A!4), relation_rng(A!4)))) | ![C: $i, D: $i, E: $i] : (in(ordered_pair(C, E), A!4) | (~in(ordered_pair(C, D), A!4)) | (~in(ordered_pair(D, E), A!4)) | (~in(C, set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(E, set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(D, set_union2(relation_dom(A!4), relation_rng(A!4))))))) | (~(is_transitive_in(A!4, set_union2(relation_dom(A!4), relation_rng(A!4))) | (~(in(ordered_pair(tptp_fun_C_2(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), tptp_fun_E_0(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4)), A!4) | (~in(tptp_fun_C_2(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(tptp_fun_D_1(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(tptp_fun_E_0(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(ordered_pair(tptp_fun_C_2(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), tptp_fun_D_1(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4)), A!4)) | (~in(ordered_pair(tptp_fun_D_1(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), tptp_fun_E_0(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4)), A!4))))))) | (is_transitive_in(A!4, set_union2(relation_dom(A!4), relation_rng(A!4))) | (~(in(ordered_pair(tptp_fun_C_2(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), tptp_fun_E_0(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4)), A!4) | (~in(tptp_fun_C_2(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(tptp_fun_D_1(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(tptp_fun_E_0(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(ordered_pair(tptp_fun_C_2(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), tptp_fun_D_1(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4)), A!4)) | (~in(ordered_pair(tptp_fun_D_1(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), tptp_fun_E_0(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4)), A!4)))))),
% 0.19/0.45 inference(tautology,[status(thm)],[])).
% 0.19/0.45 tff(164,plain,
% 0.19/0.45 (is_transitive_in(A!4, set_union2(relation_dom(A!4), relation_rng(A!4))) | (~(in(ordered_pair(tptp_fun_C_2(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), tptp_fun_E_0(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4)), A!4) | (~in(tptp_fun_C_2(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(tptp_fun_D_1(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(tptp_fun_E_0(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(ordered_pair(tptp_fun_C_2(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), tptp_fun_D_1(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4)), A!4)) | (~in(ordered_pair(tptp_fun_D_1(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), tptp_fun_E_0(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4)), A!4))))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[163, 120])).
% 0.19/0.45 tff(165,plain,
% 0.19/0.45 ((~(is_transitive_in(A!4, set_union2(relation_dom(A!4), relation_rng(A!4))) | (~(in(ordered_pair(tptp_fun_C_2(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), tptp_fun_E_0(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4)), A!4) | (~in(tptp_fun_C_2(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(tptp_fun_D_1(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(tptp_fun_E_0(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(ordered_pair(tptp_fun_C_2(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), tptp_fun_D_1(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4)), A!4)) | (~in(ordered_pair(tptp_fun_D_1(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), tptp_fun_E_0(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4)), A!4)))))) | is_transitive_in(A!4, set_union2(relation_dom(A!4), relation_rng(A!4))) | (~(in(ordered_pair(tptp_fun_C_2(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), tptp_fun_E_0(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4)), A!4) | (~in(tptp_fun_C_2(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(tptp_fun_D_1(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(tptp_fun_E_0(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(ordered_pair(tptp_fun_C_2(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), tptp_fun_D_1(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4)), A!4)) | (~in(ordered_pair(tptp_fun_D_1(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), tptp_fun_E_0(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4)), A!4))))),
% 0.19/0.46 inference(tautology,[status(thm)],[])).
% 0.19/0.46 tff(166,plain,
% 0.19/0.46 (is_transitive_in(A!4, set_union2(relation_dom(A!4), relation_rng(A!4))) | (~(in(ordered_pair(tptp_fun_C_2(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), tptp_fun_E_0(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4)), A!4) | (~in(tptp_fun_C_2(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(tptp_fun_D_1(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(tptp_fun_E_0(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(ordered_pair(tptp_fun_C_2(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), tptp_fun_D_1(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4)), A!4)) | (~in(ordered_pair(tptp_fun_D_1(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), tptp_fun_E_0(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4)), A!4))))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[165, 164])).
% 0.19/0.46 tff(167,plain,
% 0.19/0.46 (~(in(ordered_pair(tptp_fun_C_2(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), tptp_fun_E_0(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4)), A!4) | (~in(tptp_fun_C_2(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(tptp_fun_D_1(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(tptp_fun_E_0(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(ordered_pair(tptp_fun_C_2(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), tptp_fun_D_1(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4)), A!4)) | (~in(ordered_pair(tptp_fun_D_1(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), tptp_fun_E_0(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4)), A!4)))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[166, 162])).
% 0.19/0.46 tff(168,plain,
% 0.19/0.46 ((in(ordered_pair(tptp_fun_C_2(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), tptp_fun_E_0(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4)), A!4) | (~in(tptp_fun_C_2(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(tptp_fun_D_1(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(tptp_fun_E_0(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(ordered_pair(tptp_fun_C_2(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), tptp_fun_D_1(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4)), A!4)) | (~in(ordered_pair(tptp_fun_D_1(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), tptp_fun_E_0(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4)), A!4))) | in(ordered_pair(tptp_fun_D_1(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), tptp_fun_E_0(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4)), A!4)),
% 0.19/0.46 inference(tautology,[status(thm)],[])).
% 0.19/0.46 tff(169,plain,
% 0.19/0.46 (in(ordered_pair(tptp_fun_D_1(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), tptp_fun_E_0(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4)), A!4)),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[168, 167])).
% 0.19/0.46 tff(170,plain,
% 0.19/0.46 ((in(ordered_pair(tptp_fun_C_2(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), tptp_fun_E_0(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4)), A!4) | (~in(tptp_fun_C_2(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(tptp_fun_D_1(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(tptp_fun_E_0(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(ordered_pair(tptp_fun_C_2(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), tptp_fun_D_1(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4)), A!4)) | (~in(ordered_pair(tptp_fun_D_1(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), tptp_fun_E_0(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4)), A!4))) | in(ordered_pair(tptp_fun_C_2(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), tptp_fun_D_1(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4)), A!4)),
% 0.19/0.46 inference(tautology,[status(thm)],[])).
% 0.19/0.46 tff(171,plain,
% 0.19/0.46 (in(ordered_pair(tptp_fun_C_2(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), tptp_fun_D_1(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4)), A!4)),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[170, 167])).
% 0.19/0.46 tff(172,plain,
% 0.19/0.46 ((in(ordered_pair(tptp_fun_C_2(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), tptp_fun_E_0(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4)), A!4) | (~in(tptp_fun_C_2(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(tptp_fun_D_1(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(tptp_fun_E_0(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), set_union2(relation_dom(A!4), relation_rng(A!4)))) | (~in(ordered_pair(tptp_fun_C_2(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), tptp_fun_D_1(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4)), A!4)) | (~in(ordered_pair(tptp_fun_D_1(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), tptp_fun_E_0(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4)), A!4))) | (~in(ordered_pair(tptp_fun_C_2(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), tptp_fun_E_0(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4)), A!4))),
% 0.19/0.46 inference(tautology,[status(thm)],[])).
% 0.19/0.46 tff(173,plain,
% 0.19/0.46 (~in(ordered_pair(tptp_fun_C_2(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), tptp_fun_E_0(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4)), A!4)),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[172, 167])).
% 0.19/0.46 tff(174,plain,
% 0.19/0.46 (![B: $i, C: $i, D: $i] : (in(ordered_pair(B, D), A!4) | (~in(ordered_pair(B, C), A!4)) | (~in(ordered_pair(C, D), A!4)))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[148, 158])).
% 0.19/0.46 tff(175,plain,
% 0.19/0.46 (((~![B: $i, C: $i, D: $i] : (in(ordered_pair(B, D), A!4) | (~in(ordered_pair(B, C), A!4)) | (~in(ordered_pair(C, D), A!4)))) | (in(ordered_pair(tptp_fun_C_2(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), tptp_fun_E_0(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4)), A!4) | (~in(ordered_pair(tptp_fun_C_2(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), tptp_fun_D_1(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4)), A!4)) | (~in(ordered_pair(tptp_fun_D_1(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), tptp_fun_E_0(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4)), A!4)))) <=> ((~![B: $i, C: $i, D: $i] : (in(ordered_pair(B, D), A!4) | (~in(ordered_pair(B, C), A!4)) | (~in(ordered_pair(C, D), A!4)))) | in(ordered_pair(tptp_fun_C_2(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), tptp_fun_E_0(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4)), A!4) | (~in(ordered_pair(tptp_fun_C_2(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), tptp_fun_D_1(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4)), A!4)) | (~in(ordered_pair(tptp_fun_D_1(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), tptp_fun_E_0(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4)), A!4)))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(176,plain,
% 0.19/0.46 ((~![B: $i, C: $i, D: $i] : (in(ordered_pair(B, D), A!4) | (~in(ordered_pair(B, C), A!4)) | (~in(ordered_pair(C, D), A!4)))) | (in(ordered_pair(tptp_fun_C_2(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), tptp_fun_E_0(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4)), A!4) | (~in(ordered_pair(tptp_fun_C_2(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), tptp_fun_D_1(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4)), A!4)) | (~in(ordered_pair(tptp_fun_D_1(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), tptp_fun_E_0(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4)), A!4)))),
% 0.19/0.46 inference(quant_inst,[status(thm)],[])).
% 0.19/0.46 tff(177,plain,
% 0.19/0.46 ((~![B: $i, C: $i, D: $i] : (in(ordered_pair(B, D), A!4) | (~in(ordered_pair(B, C), A!4)) | (~in(ordered_pair(C, D), A!4)))) | in(ordered_pair(tptp_fun_C_2(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), tptp_fun_E_0(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4)), A!4) | (~in(ordered_pair(tptp_fun_C_2(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), tptp_fun_D_1(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4)), A!4)) | (~in(ordered_pair(tptp_fun_D_1(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4), tptp_fun_E_0(set_union2(relation_dom(A!4), relation_rng(A!4)), A!4)), A!4))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[176, 175])).
% 0.19/0.46 tff(178,plain,
% 0.19/0.46 ($false),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[177, 174, 173, 171, 169])).
% 0.19/0.46 % SZS output end Proof
%------------------------------------------------------------------------------