TSTP Solution File: SEU239+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SEU239+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n014.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 07:28:25 EDT 2022
% Result : Theorem 0.19s 0.37s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEU239+1 : TPTP v8.1.0. Released v3.3.0.
% 0.03/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n014.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 10:57:45 EDT 2022
% 0.12/0.34 % 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.
% 0.19/0.37 % SZS status Theorem
% 0.19/0.37 % SZS output start Proof
% 0.19/0.37 tff(in_type, type, (
% 0.19/0.37 in: ( $i * $i ) > $o)).
% 0.19/0.37 tff(relation_field_type, type, (
% 0.19/0.37 relation_field: $i > $i)).
% 0.19/0.37 tff(tptp_fun_A_2_type, type, (
% 0.19/0.37 tptp_fun_A_2: $i)).
% 0.19/0.37 tff(tptp_fun_C_0_type, type, (
% 0.19/0.37 tptp_fun_C_0: ( $i * $i ) > $i)).
% 0.19/0.37 tff(set_union2_type, type, (
% 0.19/0.37 set_union2: ( $i * $i ) > $i)).
% 0.19/0.37 tff(relation_rng_type, type, (
% 0.19/0.37 relation_rng: $i > $i)).
% 0.19/0.37 tff(relation_dom_type, type, (
% 0.19/0.37 relation_dom: $i > $i)).
% 0.19/0.37 tff(relation_type, type, (
% 0.19/0.37 relation: $i > $o)).
% 0.19/0.37 tff(ordered_pair_type, type, (
% 0.19/0.37 ordered_pair: ( $i * $i ) > $i)).
% 0.19/0.37 tff(tptp_fun_B_3_type, type, (
% 0.19/0.37 tptp_fun_B_3: $i)).
% 0.19/0.37 tff(reflexive_type, type, (
% 0.19/0.37 reflexive: $i > $o)).
% 0.19/0.37 tff(is_reflexive_in_type, type, (
% 0.19/0.37 is_reflexive_in: ( $i * $i ) > $o)).
% 0.19/0.37 tff(1,plain,
% 0.19/0.37 ((relation(A!2) & ((reflexive(A!2) | ![B: $i] : ((~in(B, relation_field(A!2))) | in(ordered_pair(B, B), A!2))) & ((~reflexive(A!2)) | (~((~in(B!3, relation_field(A!2))) | in(ordered_pair(B!3, B!3), A!2)))))) <=> (relation(A!2) & (reflexive(A!2) | ![B: $i] : ((~in(B, relation_field(A!2))) | in(ordered_pair(B, B), A!2))) & ((~reflexive(A!2)) | (~((~in(B!3, relation_field(A!2))) | in(ordered_pair(B!3, B!3), A!2)))))),
% 0.19/0.37 inference(rewrite,[status(thm)],[])).
% 0.19/0.37 tff(2,plain,
% 0.19/0.37 ((reflexive(A!2) | ![B: $i] : ((~in(B, relation_field(A!2))) | in(ordered_pair(B, B), A!2))) <=> (reflexive(A!2) | ![B: $i] : ((~in(B, relation_field(A!2))) | in(ordered_pair(B, B), A!2)))),
% 0.19/0.37 inference(rewrite,[status(thm)],[])).
% 0.19/0.37 tff(3,plain,
% 0.19/0.37 (((reflexive(A!2) | ![B: $i] : ((~in(B, relation_field(A!2))) | in(ordered_pair(B, B), A!2))) & ((~reflexive(A!2)) | (~((~in(B!3, relation_field(A!2))) | in(ordered_pair(B!3, B!3), A!2))))) <=> ((reflexive(A!2) | ![B: $i] : ((~in(B, relation_field(A!2))) | in(ordered_pair(B, B), A!2))) & ((~reflexive(A!2)) | (~((~in(B!3, relation_field(A!2))) | in(ordered_pair(B!3, B!3), A!2)))))),
% 0.19/0.37 inference(monotonicity,[status(thm)],[2])).
% 0.19/0.37 tff(4,plain,
% 0.19/0.37 ((~(~relation(A!2))) <=> relation(A!2)),
% 0.19/0.37 inference(rewrite,[status(thm)],[])).
% 0.19/0.37 tff(5,plain,
% 0.19/0.37 (((~(~relation(A!2))) & ((reflexive(A!2) | ![B: $i] : ((~in(B, relation_field(A!2))) | in(ordered_pair(B, B), A!2))) & ((~reflexive(A!2)) | (~((~in(B!3, relation_field(A!2))) | in(ordered_pair(B!3, B!3), A!2)))))) <=> (relation(A!2) & ((reflexive(A!2) | ![B: $i] : ((~in(B, relation_field(A!2))) | in(ordered_pair(B, B), A!2))) & ((~reflexive(A!2)) | (~((~in(B!3, relation_field(A!2))) | in(ordered_pair(B!3, B!3), A!2))))))),
% 0.19/0.37 inference(monotonicity,[status(thm)],[4, 3])).
% 0.19/0.37 tff(6,plain,
% 0.19/0.37 (((~(~relation(A!2))) & ((reflexive(A!2) | ![B: $i] : ((~in(B, relation_field(A!2))) | in(ordered_pair(B, B), A!2))) & ((~reflexive(A!2)) | (~((~in(B!3, relation_field(A!2))) | in(ordered_pair(B!3, B!3), A!2)))))) <=> (relation(A!2) & (reflexive(A!2) | ![B: $i] : ((~in(B, relation_field(A!2))) | in(ordered_pair(B, B), A!2))) & ((~reflexive(A!2)) | (~((~in(B!3, relation_field(A!2))) | in(ordered_pair(B!3, B!3), A!2)))))),
% 0.19/0.37 inference(transitivity,[status(thm)],[5, 1])).
% 0.19/0.37 tff(7,plain,
% 0.19/0.37 ((~![A: $i] : ((~relation(A)) | (reflexive(A) <=> ![B: $i] : ((~in(B, relation_field(A))) | in(ordered_pair(B, B), A))))) <=> (~![A: $i] : ((~relation(A)) | (reflexive(A) <=> ![B: $i] : ((~in(B, relation_field(A))) | in(ordered_pair(B, B), A)))))),
% 0.19/0.37 inference(rewrite,[status(thm)],[])).
% 0.19/0.37 tff(8,plain,
% 0.19/0.37 ((~![A: $i] : (relation(A) => (reflexive(A) <=> ![B: $i] : (in(B, relation_field(A)) => in(ordered_pair(B, B), A))))) <=> (~![A: $i] : ((~relation(A)) | (reflexive(A) <=> ![B: $i] : ((~in(B, relation_field(A))) | in(ordered_pair(B, B), A)))))),
% 0.19/0.37 inference(rewrite,[status(thm)],[])).
% 0.19/0.37 tff(9,axiom,(~![A: $i] : (relation(A) => (reflexive(A) <=> ![B: $i] : (in(B, relation_field(A)) => in(ordered_pair(B, B), A))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','l1_wellord1')).
% 0.19/0.37 tff(10,plain,
% 0.19/0.37 (~![A: $i] : ((~relation(A)) | (reflexive(A) <=> ![B: $i] : ((~in(B, relation_field(A))) | in(ordered_pair(B, B), A))))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[9, 8])).
% 0.19/0.37 tff(11,plain,
% 0.19/0.37 (~![A: $i] : ((~relation(A)) | (reflexive(A) <=> ![B: $i] : ((~in(B, relation_field(A))) | in(ordered_pair(B, B), A))))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[10, 7])).
% 0.19/0.37 tff(12,plain,
% 0.19/0.37 (~![A: $i] : ((~relation(A)) | (reflexive(A) <=> ![B: $i] : ((~in(B, relation_field(A))) | in(ordered_pair(B, B), A))))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[11, 7])).
% 0.19/0.37 tff(13,plain,
% 0.19/0.37 (~![A: $i] : ((~relation(A)) | (reflexive(A) <=> ![B: $i] : ((~in(B, relation_field(A))) | in(ordered_pair(B, B), A))))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[12, 7])).
% 0.19/0.37 tff(14,plain,
% 0.19/0.37 (~![A: $i] : ((~relation(A)) | (reflexive(A) <=> ![B: $i] : ((~in(B, relation_field(A))) | in(ordered_pair(B, B), A))))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[13, 7])).
% 0.19/0.37 tff(15,plain,
% 0.19/0.37 (~![A: $i] : ((~relation(A)) | (reflexive(A) <=> ![B: $i] : ((~in(B, relation_field(A))) | in(ordered_pair(B, B), A))))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[14, 7])).
% 0.19/0.37 tff(16,plain,
% 0.19/0.37 (~![A: $i] : ((~relation(A)) | (reflexive(A) <=> ![B: $i] : ((~in(B, relation_field(A))) | in(ordered_pair(B, B), A))))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[15, 7])).
% 0.19/0.37 tff(17,plain,
% 0.19/0.37 (relation(A!2) & (reflexive(A!2) | ![B: $i] : ((~in(B, relation_field(A!2))) | in(ordered_pair(B, B), A!2))) & ((~reflexive(A!2)) | (~((~in(B!3, relation_field(A!2))) | in(ordered_pair(B!3, B!3), A!2))))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[16, 6])).
% 0.19/0.37 tff(18,plain,
% 0.19/0.37 (relation(A!2)),
% 0.19/0.37 inference(and_elim,[status(thm)],[17])).
% 0.19/0.37 tff(19,plain,
% 0.19/0.37 (^[A: $i] : refl(((~relation(A)) | (relation_field(A) = set_union2(relation_dom(A), relation_rng(A)))) <=> ((~relation(A)) | (relation_field(A) = set_union2(relation_dom(A), relation_rng(A)))))),
% 0.19/0.37 inference(bind,[status(th)],[])).
% 0.19/0.37 tff(20,plain,
% 0.19/0.37 (![A: $i] : ((~relation(A)) | (relation_field(A) = set_union2(relation_dom(A), relation_rng(A)))) <=> ![A: $i] : ((~relation(A)) | (relation_field(A) = set_union2(relation_dom(A), relation_rng(A))))),
% 0.19/0.37 inference(quant_intro,[status(thm)],[19])).
% 0.19/0.37 tff(21,plain,
% 0.19/0.37 (![A: $i] : ((~relation(A)) | (relation_field(A) = set_union2(relation_dom(A), relation_rng(A)))) <=> ![A: $i] : ((~relation(A)) | (relation_field(A) = set_union2(relation_dom(A), relation_rng(A))))),
% 0.19/0.37 inference(rewrite,[status(thm)],[])).
% 0.19/0.37 tff(22,plain,
% 0.19/0.37 (^[A: $i] : rewrite((relation(A) => (relation_field(A) = set_union2(relation_dom(A), relation_rng(A)))) <=> ((~relation(A)) | (relation_field(A) = set_union2(relation_dom(A), relation_rng(A)))))),
% 0.19/0.37 inference(bind,[status(th)],[])).
% 0.19/0.37 tff(23,plain,
% 0.19/0.37 (![A: $i] : (relation(A) => (relation_field(A) = set_union2(relation_dom(A), relation_rng(A)))) <=> ![A: $i] : ((~relation(A)) | (relation_field(A) = set_union2(relation_dom(A), relation_rng(A))))),
% 0.19/0.37 inference(quant_intro,[status(thm)],[22])).
% 0.19/0.37 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')).
% 0.19/0.37 tff(25,plain,
% 0.19/0.37 (![A: $i] : ((~relation(A)) | (relation_field(A) = set_union2(relation_dom(A), relation_rng(A))))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[24, 23])).
% 0.19/0.37 tff(26,plain,
% 0.19/0.37 (![A: $i] : ((~relation(A)) | (relation_field(A) = set_union2(relation_dom(A), relation_rng(A))))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[25, 21])).
% 0.19/0.37 tff(27,plain,(
% 0.19/0.37 ![A: $i] : ((~relation(A)) | (relation_field(A) = set_union2(relation_dom(A), relation_rng(A))))),
% 0.19/0.37 inference(skolemize,[status(sab)],[26])).
% 0.19/0.37 tff(28,plain,
% 0.19/0.37 (![A: $i] : ((~relation(A)) | (relation_field(A) = set_union2(relation_dom(A), relation_rng(A))))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[27, 20])).
% 0.19/0.37 tff(29,plain,
% 0.19/0.37 (((~![A: $i] : ((~relation(A)) | (relation_field(A) = set_union2(relation_dom(A), relation_rng(A))))) | ((~relation(A!2)) | (relation_field(A!2) = set_union2(relation_dom(A!2), relation_rng(A!2))))) <=> ((~![A: $i] : ((~relation(A)) | (relation_field(A) = set_union2(relation_dom(A), relation_rng(A))))) | (~relation(A!2)) | (relation_field(A!2) = set_union2(relation_dom(A!2), relation_rng(A!2))))),
% 0.19/0.37 inference(rewrite,[status(thm)],[])).
% 0.19/0.37 tff(30,plain,
% 0.19/0.37 ((~![A: $i] : ((~relation(A)) | (relation_field(A) = set_union2(relation_dom(A), relation_rng(A))))) | ((~relation(A!2)) | (relation_field(A!2) = set_union2(relation_dom(A!2), relation_rng(A!2))))),
% 0.19/0.37 inference(quant_inst,[status(thm)],[])).
% 0.19/0.37 tff(31,plain,
% 0.19/0.37 ((~![A: $i] : ((~relation(A)) | (relation_field(A) = set_union2(relation_dom(A), relation_rng(A))))) | (~relation(A!2)) | (relation_field(A!2) = set_union2(relation_dom(A!2), relation_rng(A!2)))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[30, 29])).
% 0.19/0.37 tff(32,plain,
% 0.19/0.37 (relation_field(A!2) = set_union2(relation_dom(A!2), relation_rng(A!2))),
% 0.19/0.37 inference(unit_resolution,[status(thm)],[31, 28, 18])).
% 0.19/0.37 tff(33,plain,
% 0.19/0.37 (in(tptp_fun_C_0(set_union2(relation_dom(A!2), relation_rng(A!2)), A!2), relation_field(A!2)) <=> in(tptp_fun_C_0(set_union2(relation_dom(A!2), relation_rng(A!2)), A!2), set_union2(relation_dom(A!2), relation_rng(A!2)))),
% 0.19/0.37 inference(monotonicity,[status(thm)],[32])).
% 0.19/0.37 tff(34,plain,
% 0.19/0.37 (in(tptp_fun_C_0(set_union2(relation_dom(A!2), relation_rng(A!2)), A!2), set_union2(relation_dom(A!2), relation_rng(A!2))) <=> in(tptp_fun_C_0(set_union2(relation_dom(A!2), relation_rng(A!2)), A!2), relation_field(A!2))),
% 0.19/0.37 inference(symmetry,[status(thm)],[33])).
% 0.19/0.37 tff(35,plain,
% 0.19/0.37 (set_union2(relation_dom(A!2), relation_rng(A!2)) = relation_field(A!2)),
% 0.19/0.37 inference(symmetry,[status(thm)],[32])).
% 0.19/0.37 tff(36,plain,
% 0.19/0.37 (is_reflexive_in(A!2, set_union2(relation_dom(A!2), relation_rng(A!2))) <=> is_reflexive_in(A!2, relation_field(A!2))),
% 0.19/0.37 inference(monotonicity,[status(thm)],[35])).
% 0.19/0.37 tff(37,plain,
% 0.19/0.37 (is_reflexive_in(A!2, relation_field(A!2)) <=> is_reflexive_in(A!2, set_union2(relation_dom(A!2), relation_rng(A!2)))),
% 0.19/0.37 inference(symmetry,[status(thm)],[36])).
% 0.19/0.37 tff(38,plain,
% 0.19/0.37 ((~is_reflexive_in(A!2, relation_field(A!2))) <=> (~is_reflexive_in(A!2, set_union2(relation_dom(A!2), relation_rng(A!2))))),
% 0.19/0.37 inference(monotonicity,[status(thm)],[37])).
% 0.19/0.37 tff(39,assumption,(~((~in(B!3, relation_field(A!2))) | in(ordered_pair(B!3, B!3), A!2))), introduced(assumption)).
% 0.19/0.37 tff(40,plain,
% 0.19/0.37 (((~in(B!3, relation_field(A!2))) | in(ordered_pair(B!3, B!3), A!2)) | (~in(ordered_pair(B!3, B!3), A!2))),
% 0.19/0.37 inference(tautology,[status(thm)],[])).
% 0.19/0.37 tff(41,plain,
% 0.19/0.37 (~in(ordered_pair(B!3, B!3), A!2)),
% 0.19/0.37 inference(unit_resolution,[status(thm)],[40, 39])).
% 0.19/0.37 tff(42,plain,
% 0.19/0.37 (((~in(B!3, relation_field(A!2))) | in(ordered_pair(B!3, B!3), A!2)) | in(B!3, relation_field(A!2))),
% 0.19/0.37 inference(tautology,[status(thm)],[])).
% 0.19/0.37 tff(43,plain,
% 0.19/0.37 (in(B!3, relation_field(A!2))),
% 0.19/0.37 inference(unit_resolution,[status(thm)],[42, 39])).
% 0.19/0.37 tff(44,plain,
% 0.19/0.37 ((~is_reflexive_in(A!2, set_union2(relation_dom(A!2), relation_rng(A!2)))) <=> (~is_reflexive_in(A!2, relation_field(A!2)))),
% 0.19/0.37 inference(monotonicity,[status(thm)],[36])).
% 0.19/0.37 tff(45,plain,
% 0.19/0.37 (in(B!3, set_union2(relation_dom(A!2), relation_rng(A!2))) <=> in(B!3, relation_field(A!2))),
% 0.19/0.37 inference(monotonicity,[status(thm)],[35])).
% 0.19/0.37 tff(46,plain,
% 0.19/0.37 (in(B!3, relation_field(A!2)) <=> in(B!3, set_union2(relation_dom(A!2), relation_rng(A!2)))),
% 0.19/0.37 inference(symmetry,[status(thm)],[45])).
% 0.19/0.37 tff(47,plain,
% 0.19/0.37 (in(B!3, set_union2(relation_dom(A!2), relation_rng(A!2)))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[43, 46])).
% 0.19/0.37 tff(48,assumption,(in(B!3, set_union2(relation_dom(A!2), relation_rng(A!2)))), introduced(assumption)).
% 0.19/0.37 tff(49,assumption,(![C: $i] : ((~in(C, set_union2(relation_dom(A!2), relation_rng(A!2)))) | in(ordered_pair(C, C), A!2))), introduced(assumption)).
% 0.19/0.37 tff(50,assumption,(~in(ordered_pair(B!3, B!3), A!2)), introduced(assumption)).
% 0.19/0.37 tff(51,plain,
% 0.19/0.37 (((~![C: $i] : ((~in(C, set_union2(relation_dom(A!2), relation_rng(A!2)))) | in(ordered_pair(C, C), A!2))) | ((~in(B!3, set_union2(relation_dom(A!2), relation_rng(A!2)))) | in(ordered_pair(B!3, B!3), A!2))) <=> ((~![C: $i] : ((~in(C, set_union2(relation_dom(A!2), relation_rng(A!2)))) | in(ordered_pair(C, C), A!2))) | (~in(B!3, set_union2(relation_dom(A!2), relation_rng(A!2)))) | in(ordered_pair(B!3, B!3), A!2))),
% 0.19/0.37 inference(rewrite,[status(thm)],[])).
% 0.19/0.37 tff(52,plain,
% 0.19/0.37 ((~![C: $i] : ((~in(C, set_union2(relation_dom(A!2), relation_rng(A!2)))) | in(ordered_pair(C, C), A!2))) | ((~in(B!3, set_union2(relation_dom(A!2), relation_rng(A!2)))) | in(ordered_pair(B!3, B!3), A!2))),
% 0.19/0.37 inference(quant_inst,[status(thm)],[])).
% 0.19/0.37 tff(53,plain,
% 0.19/0.37 ((~![C: $i] : ((~in(C, set_union2(relation_dom(A!2), relation_rng(A!2)))) | in(ordered_pair(C, C), A!2))) | (~in(B!3, set_union2(relation_dom(A!2), relation_rng(A!2)))) | in(ordered_pair(B!3, B!3), A!2)),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[52, 51])).
% 0.19/0.37 tff(54,plain,
% 0.19/0.37 ($false),
% 0.19/0.37 inference(unit_resolution,[status(thm)],[53, 50, 49, 48])).
% 0.19/0.37 tff(55,plain,((~![C: $i] : ((~in(C, set_union2(relation_dom(A!2), relation_rng(A!2)))) | in(ordered_pair(C, C), A!2))) | in(ordered_pair(B!3, B!3), A!2) | (~in(B!3, set_union2(relation_dom(A!2), relation_rng(A!2))))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.37 tff(56,plain,
% 0.19/0.37 (~![C: $i] : ((~in(C, set_union2(relation_dom(A!2), relation_rng(A!2)))) | in(ordered_pair(C, C), A!2))),
% 0.19/0.37 inference(unit_resolution,[status(thm)],[55, 41, 47])).
% 0.19/0.37 tff(57,plain,
% 0.19/0.37 (^[A: $i] : refl(((~relation(A)) | ![B: $i] : (~((~((~is_reflexive_in(A, B)) | ![C: $i] : ((~in(C, B)) | in(ordered_pair(C, C), A)))) | (~(is_reflexive_in(A, B) | (~((~in(tptp_fun_C_0(B, A), B)) | in(ordered_pair(tptp_fun_C_0(B, A), tptp_fun_C_0(B, A)), A)))))))) <=> ((~relation(A)) | ![B: $i] : (~((~((~is_reflexive_in(A, B)) | ![C: $i] : ((~in(C, B)) | in(ordered_pair(C, C), A)))) | (~(is_reflexive_in(A, B) | (~((~in(tptp_fun_C_0(B, A), B)) | in(ordered_pair(tptp_fun_C_0(B, A), tptp_fun_C_0(B, A)), A)))))))))),
% 0.19/0.37 inference(bind,[status(th)],[])).
% 0.19/0.37 tff(58,plain,
% 0.19/0.37 (![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~is_reflexive_in(A, B)) | ![C: $i] : ((~in(C, B)) | in(ordered_pair(C, C), A)))) | (~(is_reflexive_in(A, B) | (~((~in(tptp_fun_C_0(B, A), B)) | in(ordered_pair(tptp_fun_C_0(B, A), tptp_fun_C_0(B, A)), A)))))))) <=> ![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~is_reflexive_in(A, B)) | ![C: $i] : ((~in(C, B)) | in(ordered_pair(C, C), A)))) | (~(is_reflexive_in(A, B) | (~((~in(tptp_fun_C_0(B, A), B)) | in(ordered_pair(tptp_fun_C_0(B, A), tptp_fun_C_0(B, A)), A))))))))),
% 0.19/0.37 inference(quant_intro,[status(thm)],[57])).
% 0.19/0.37 tff(59,plain,
% 0.19/0.37 (^[A: $i] : rewrite(((~relation(A)) | ![B: $i] : (~((~((~is_reflexive_in(A, B)) | ![C: $i] : ((~in(C, B)) | in(ordered_pair(C, C), A)))) | (~(is_reflexive_in(A, B) | (~((~in(tptp_fun_C_0(B, A), B)) | in(ordered_pair(tptp_fun_C_0(B, A), tptp_fun_C_0(B, A)), A)))))))) <=> ((~relation(A)) | ![B: $i] : (~((~((~is_reflexive_in(A, B)) | ![C: $i] : ((~in(C, B)) | in(ordered_pair(C, C), A)))) | (~(is_reflexive_in(A, B) | (~((~in(tptp_fun_C_0(B, A), B)) | in(ordered_pair(tptp_fun_C_0(B, A), tptp_fun_C_0(B, A)), A)))))))))),
% 0.19/0.37 inference(bind,[status(th)],[])).
% 0.19/0.37 tff(60,plain,
% 0.19/0.37 (![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~is_reflexive_in(A, B)) | ![C: $i] : ((~in(C, B)) | in(ordered_pair(C, C), A)))) | (~(is_reflexive_in(A, B) | (~((~in(tptp_fun_C_0(B, A), B)) | in(ordered_pair(tptp_fun_C_0(B, A), tptp_fun_C_0(B, A)), A)))))))) <=> ![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~is_reflexive_in(A, B)) | ![C: $i] : ((~in(C, B)) | in(ordered_pair(C, C), A)))) | (~(is_reflexive_in(A, B) | (~((~in(tptp_fun_C_0(B, A), B)) | in(ordered_pair(tptp_fun_C_0(B, A), tptp_fun_C_0(B, A)), A))))))))),
% 0.19/0.37 inference(quant_intro,[status(thm)],[59])).
% 0.19/0.37 tff(61,plain,
% 0.19/0.37 (![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~is_reflexive_in(A, B)) | ![C: $i] : ((~in(C, B)) | in(ordered_pair(C, C), A)))) | (~(is_reflexive_in(A, B) | (~((~in(tptp_fun_C_0(B, A), B)) | in(ordered_pair(tptp_fun_C_0(B, A), tptp_fun_C_0(B, A)), A)))))))) <=> ![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~is_reflexive_in(A, B)) | ![C: $i] : ((~in(C, B)) | in(ordered_pair(C, C), A)))) | (~(is_reflexive_in(A, B) | (~((~in(tptp_fun_C_0(B, A), B)) | in(ordered_pair(tptp_fun_C_0(B, A), tptp_fun_C_0(B, A)), A))))))))),
% 0.19/0.37 inference(transitivity,[status(thm)],[60, 58])).
% 0.19/0.37 tff(62,plain,
% 0.19/0.37 (^[A: $i] : rewrite(((~relation(A)) | ![B: $i] : (((~is_reflexive_in(A, B)) | ![C: $i] : ((~in(C, B)) | in(ordered_pair(C, C), A))) & (is_reflexive_in(A, B) | (~((~in(tptp_fun_C_0(B, A), B)) | in(ordered_pair(tptp_fun_C_0(B, A), tptp_fun_C_0(B, A)), A)))))) <=> ((~relation(A)) | ![B: $i] : (~((~((~is_reflexive_in(A, B)) | ![C: $i] : ((~in(C, B)) | in(ordered_pair(C, C), A)))) | (~(is_reflexive_in(A, B) | (~((~in(tptp_fun_C_0(B, A), B)) | in(ordered_pair(tptp_fun_C_0(B, A), tptp_fun_C_0(B, A)), A)))))))))),
% 0.19/0.38 inference(bind,[status(th)],[])).
% 0.19/0.38 tff(63,plain,
% 0.19/0.38 (![A: $i] : ((~relation(A)) | ![B: $i] : (((~is_reflexive_in(A, B)) | ![C: $i] : ((~in(C, B)) | in(ordered_pair(C, C), A))) & (is_reflexive_in(A, B) | (~((~in(tptp_fun_C_0(B, A), B)) | in(ordered_pair(tptp_fun_C_0(B, A), tptp_fun_C_0(B, A)), A)))))) <=> ![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~is_reflexive_in(A, B)) | ![C: $i] : ((~in(C, B)) | in(ordered_pair(C, C), A)))) | (~(is_reflexive_in(A, B) | (~((~in(tptp_fun_C_0(B, A), B)) | in(ordered_pair(tptp_fun_C_0(B, A), tptp_fun_C_0(B, A)), A))))))))),
% 0.19/0.38 inference(quant_intro,[status(thm)],[62])).
% 0.19/0.38 tff(64,plain,
% 0.19/0.38 (![A: $i] : ((~relation(A)) | ![B: $i] : (is_reflexive_in(A, B) <=> ![C: $i] : ((~in(C, B)) | in(ordered_pair(C, C), A)))) <=> ![A: $i] : ((~relation(A)) | ![B: $i] : (is_reflexive_in(A, B) <=> ![C: $i] : ((~in(C, B)) | in(ordered_pair(C, C), A))))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(65,plain,
% 0.19/0.38 (^[A: $i] : trans(monotonicity(quant_intro(proof_bind(^[B: $i] : rewrite((is_reflexive_in(A, B) <=> ![C: $i] : (in(C, B) => in(ordered_pair(C, C), A))) <=> (is_reflexive_in(A, B) <=> ![C: $i] : ((~in(C, B)) | in(ordered_pair(C, C), A))))), (![B: $i] : (is_reflexive_in(A, B) <=> ![C: $i] : (in(C, B) => in(ordered_pair(C, C), A))) <=> ![B: $i] : (is_reflexive_in(A, B) <=> ![C: $i] : ((~in(C, B)) | in(ordered_pair(C, C), A))))), ((relation(A) => ![B: $i] : (is_reflexive_in(A, B) <=> ![C: $i] : (in(C, B) => in(ordered_pair(C, C), A)))) <=> (relation(A) => ![B: $i] : (is_reflexive_in(A, B) <=> ![C: $i] : ((~in(C, B)) | in(ordered_pair(C, C), A)))))), rewrite((relation(A) => ![B: $i] : (is_reflexive_in(A, B) <=> ![C: $i] : ((~in(C, B)) | in(ordered_pair(C, C), A)))) <=> ((~relation(A)) | ![B: $i] : (is_reflexive_in(A, B) <=> ![C: $i] : ((~in(C, B)) | in(ordered_pair(C, C), A))))), ((relation(A) => ![B: $i] : (is_reflexive_in(A, B) <=> ![C: $i] : (in(C, B) => in(ordered_pair(C, C), A)))) <=> ((~relation(A)) | ![B: $i] : (is_reflexive_in(A, B) <=> ![C: $i] : ((~in(C, B)) | in(ordered_pair(C, C), A))))))),
% 0.19/0.38 inference(bind,[status(th)],[])).
% 0.19/0.38 tff(66,plain,
% 0.19/0.38 (![A: $i] : (relation(A) => ![B: $i] : (is_reflexive_in(A, B) <=> ![C: $i] : (in(C, B) => in(ordered_pair(C, C), A)))) <=> ![A: $i] : ((~relation(A)) | ![B: $i] : (is_reflexive_in(A, B) <=> ![C: $i] : ((~in(C, B)) | in(ordered_pair(C, C), A))))),
% 0.19/0.38 inference(quant_intro,[status(thm)],[65])).
% 0.19/0.38 tff(67,axiom,(![A: $i] : (relation(A) => ![B: $i] : (is_reflexive_in(A, B) <=> ![C: $i] : (in(C, B) => in(ordered_pair(C, C), A))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d1_relat_2')).
% 0.19/0.38 tff(68,plain,
% 0.19/0.38 (![A: $i] : ((~relation(A)) | ![B: $i] : (is_reflexive_in(A, B) <=> ![C: $i] : ((~in(C, B)) | in(ordered_pair(C, C), A))))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[67, 66])).
% 0.19/0.38 tff(69,plain,
% 0.19/0.38 (![A: $i] : ((~relation(A)) | ![B: $i] : (is_reflexive_in(A, B) <=> ![C: $i] : ((~in(C, B)) | in(ordered_pair(C, C), A))))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[68, 64])).
% 0.19/0.38 tff(70,plain,(
% 0.19/0.38 ![A: $i] : ((~relation(A)) | ![B: $i] : (((~is_reflexive_in(A, B)) | ![C: $i] : ((~in(C, B)) | in(ordered_pair(C, C), A))) & (is_reflexive_in(A, B) | (~((~in(tptp_fun_C_0(B, A), B)) | in(ordered_pair(tptp_fun_C_0(B, A), tptp_fun_C_0(B, A)), A))))))),
% 0.19/0.38 inference(skolemize,[status(sab)],[69])).
% 0.19/0.38 tff(71,plain,
% 0.19/0.38 (![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~is_reflexive_in(A, B)) | ![C: $i] : ((~in(C, B)) | in(ordered_pair(C, C), A)))) | (~(is_reflexive_in(A, B) | (~((~in(tptp_fun_C_0(B, A), B)) | in(ordered_pair(tptp_fun_C_0(B, A), tptp_fun_C_0(B, A)), A))))))))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[70, 63])).
% 0.19/0.38 tff(72,plain,
% 0.19/0.38 (![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~is_reflexive_in(A, B)) | ![C: $i] : ((~in(C, B)) | in(ordered_pair(C, C), A)))) | (~(is_reflexive_in(A, B) | (~((~in(tptp_fun_C_0(B, A), B)) | in(ordered_pair(tptp_fun_C_0(B, A), tptp_fun_C_0(B, A)), A))))))))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[71, 61])).
% 0.19/0.38 tff(73,plain,
% 0.19/0.38 (((~![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~is_reflexive_in(A, B)) | ![C: $i] : ((~in(C, B)) | in(ordered_pair(C, C), A)))) | (~(is_reflexive_in(A, B) | (~((~in(tptp_fun_C_0(B, A), B)) | in(ordered_pair(tptp_fun_C_0(B, A), tptp_fun_C_0(B, A)), A))))))))) | ((~relation(A!2)) | ![B: $i] : (~((~((~is_reflexive_in(A!2, B)) | ![C: $i] : ((~in(C, B)) | in(ordered_pair(C, C), A!2)))) | (~(is_reflexive_in(A!2, B) | (~((~in(tptp_fun_C_0(B, A!2), B)) | in(ordered_pair(tptp_fun_C_0(B, A!2), tptp_fun_C_0(B, A!2)), A!2))))))))) <=> ((~![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~is_reflexive_in(A, B)) | ![C: $i] : ((~in(C, B)) | in(ordered_pair(C, C), A)))) | (~(is_reflexive_in(A, B) | (~((~in(tptp_fun_C_0(B, A), B)) | in(ordered_pair(tptp_fun_C_0(B, A), tptp_fun_C_0(B, A)), A))))))))) | (~relation(A!2)) | ![B: $i] : (~((~((~is_reflexive_in(A!2, B)) | ![C: $i] : ((~in(C, B)) | in(ordered_pair(C, C), A!2)))) | (~(is_reflexive_in(A!2, B) | (~((~in(tptp_fun_C_0(B, A!2), B)) | in(ordered_pair(tptp_fun_C_0(B, A!2), tptp_fun_C_0(B, A!2)), A!2))))))))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(74,plain,
% 0.19/0.38 ((~![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~is_reflexive_in(A, B)) | ![C: $i] : ((~in(C, B)) | in(ordered_pair(C, C), A)))) | (~(is_reflexive_in(A, B) | (~((~in(tptp_fun_C_0(B, A), B)) | in(ordered_pair(tptp_fun_C_0(B, A), tptp_fun_C_0(B, A)), A))))))))) | ((~relation(A!2)) | ![B: $i] : (~((~((~is_reflexive_in(A!2, B)) | ![C: $i] : ((~in(C, B)) | in(ordered_pair(C, C), A!2)))) | (~(is_reflexive_in(A!2, B) | (~((~in(tptp_fun_C_0(B, A!2), B)) | in(ordered_pair(tptp_fun_C_0(B, A!2), tptp_fun_C_0(B, A!2)), A!2))))))))),
% 0.19/0.38 inference(quant_inst,[status(thm)],[])).
% 0.19/0.38 tff(75,plain,
% 0.19/0.38 ((~![A: $i] : ((~relation(A)) | ![B: $i] : (~((~((~is_reflexive_in(A, B)) | ![C: $i] : ((~in(C, B)) | in(ordered_pair(C, C), A)))) | (~(is_reflexive_in(A, B) | (~((~in(tptp_fun_C_0(B, A), B)) | in(ordered_pair(tptp_fun_C_0(B, A), tptp_fun_C_0(B, A)), A))))))))) | (~relation(A!2)) | ![B: $i] : (~((~((~is_reflexive_in(A!2, B)) | ![C: $i] : ((~in(C, B)) | in(ordered_pair(C, C), A!2)))) | (~(is_reflexive_in(A!2, B) | (~((~in(tptp_fun_C_0(B, A!2), B)) | in(ordered_pair(tptp_fun_C_0(B, A!2), tptp_fun_C_0(B, A!2)), A!2)))))))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[74, 73])).
% 0.19/0.38 tff(76,plain,
% 0.19/0.38 (![B: $i] : (~((~((~is_reflexive_in(A!2, B)) | ![C: $i] : ((~in(C, B)) | in(ordered_pair(C, C), A!2)))) | (~(is_reflexive_in(A!2, B) | (~((~in(tptp_fun_C_0(B, A!2), B)) | in(ordered_pair(tptp_fun_C_0(B, A!2), tptp_fun_C_0(B, A!2)), A!2)))))))),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[75, 72, 18])).
% 0.19/0.38 tff(77,plain,
% 0.19/0.38 ((~![B: $i] : (~((~((~is_reflexive_in(A!2, B)) | ![C: $i] : ((~in(C, B)) | in(ordered_pair(C, C), A!2)))) | (~(is_reflexive_in(A!2, B) | (~((~in(tptp_fun_C_0(B, A!2), B)) | in(ordered_pair(tptp_fun_C_0(B, A!2), tptp_fun_C_0(B, A!2)), A!2)))))))) | (~((~((~is_reflexive_in(A!2, set_union2(relation_dom(A!2), relation_rng(A!2)))) | ![C: $i] : ((~in(C, set_union2(relation_dom(A!2), relation_rng(A!2)))) | in(ordered_pair(C, C), A!2)))) | (~(is_reflexive_in(A!2, set_union2(relation_dom(A!2), relation_rng(A!2))) | (~((~in(tptp_fun_C_0(set_union2(relation_dom(A!2), relation_rng(A!2)), A!2), set_union2(relation_dom(A!2), relation_rng(A!2)))) | in(ordered_pair(tptp_fun_C_0(set_union2(relation_dom(A!2), relation_rng(A!2)), A!2), tptp_fun_C_0(set_union2(relation_dom(A!2), relation_rng(A!2)), A!2)), A!2)))))))),
% 0.19/0.38 inference(quant_inst,[status(thm)],[])).
% 0.19/0.38 tff(78,plain,
% 0.19/0.38 (~((~((~is_reflexive_in(A!2, set_union2(relation_dom(A!2), relation_rng(A!2)))) | ![C: $i] : ((~in(C, set_union2(relation_dom(A!2), relation_rng(A!2)))) | in(ordered_pair(C, C), A!2)))) | (~(is_reflexive_in(A!2, set_union2(relation_dom(A!2), relation_rng(A!2))) | (~((~in(tptp_fun_C_0(set_union2(relation_dom(A!2), relation_rng(A!2)), A!2), set_union2(relation_dom(A!2), relation_rng(A!2)))) | in(ordered_pair(tptp_fun_C_0(set_union2(relation_dom(A!2), relation_rng(A!2)), A!2), tptp_fun_C_0(set_union2(relation_dom(A!2), relation_rng(A!2)), A!2)), A!2))))))),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[77, 76])).
% 0.19/0.38 tff(79,plain,
% 0.19/0.38 (((~((~is_reflexive_in(A!2, set_union2(relation_dom(A!2), relation_rng(A!2)))) | ![C: $i] : ((~in(C, set_union2(relation_dom(A!2), relation_rng(A!2)))) | in(ordered_pair(C, C), A!2)))) | (~(is_reflexive_in(A!2, set_union2(relation_dom(A!2), relation_rng(A!2))) | (~((~in(tptp_fun_C_0(set_union2(relation_dom(A!2), relation_rng(A!2)), A!2), set_union2(relation_dom(A!2), relation_rng(A!2)))) | in(ordered_pair(tptp_fun_C_0(set_union2(relation_dom(A!2), relation_rng(A!2)), A!2), tptp_fun_C_0(set_union2(relation_dom(A!2), relation_rng(A!2)), A!2)), A!2)))))) | ((~is_reflexive_in(A!2, set_union2(relation_dom(A!2), relation_rng(A!2)))) | ![C: $i] : ((~in(C, set_union2(relation_dom(A!2), relation_rng(A!2)))) | in(ordered_pair(C, C), A!2)))),
% 0.19/0.38 inference(tautology,[status(thm)],[])).
% 0.19/0.38 tff(80,plain,
% 0.19/0.38 ((~is_reflexive_in(A!2, set_union2(relation_dom(A!2), relation_rng(A!2)))) | ![C: $i] : ((~in(C, set_union2(relation_dom(A!2), relation_rng(A!2)))) | in(ordered_pair(C, C), A!2))),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[79, 78])).
% 0.19/0.38 tff(81,plain,
% 0.19/0.38 ((~((~is_reflexive_in(A!2, set_union2(relation_dom(A!2), relation_rng(A!2)))) | ![C: $i] : ((~in(C, set_union2(relation_dom(A!2), relation_rng(A!2)))) | in(ordered_pair(C, C), A!2)))) | (~is_reflexive_in(A!2, set_union2(relation_dom(A!2), relation_rng(A!2)))) | ![C: $i] : ((~in(C, set_union2(relation_dom(A!2), relation_rng(A!2)))) | in(ordered_pair(C, C), A!2))),
% 0.19/0.38 inference(tautology,[status(thm)],[])).
% 0.19/0.38 tff(82,plain,
% 0.19/0.38 ((~is_reflexive_in(A!2, set_union2(relation_dom(A!2), relation_rng(A!2)))) | ![C: $i] : ((~in(C, set_union2(relation_dom(A!2), relation_rng(A!2)))) | in(ordered_pair(C, C), A!2))),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[81, 80])).
% 0.19/0.38 tff(83,plain,
% 0.19/0.38 (~is_reflexive_in(A!2, set_union2(relation_dom(A!2), relation_rng(A!2)))),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[82, 56])).
% 0.19/0.38 tff(84,plain,
% 0.19/0.38 (~is_reflexive_in(A!2, relation_field(A!2))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[83, 44])).
% 0.19/0.38 tff(85,plain,
% 0.19/0.38 (^[A: $i] : refl(((~relation(A)) | (reflexive(A) <=> is_reflexive_in(A, relation_field(A)))) <=> ((~relation(A)) | (reflexive(A) <=> is_reflexive_in(A, relation_field(A)))))),
% 0.19/0.38 inference(bind,[status(th)],[])).
% 0.19/0.38 tff(86,plain,
% 0.19/0.38 (![A: $i] : ((~relation(A)) | (reflexive(A) <=> is_reflexive_in(A, relation_field(A)))) <=> ![A: $i] : ((~relation(A)) | (reflexive(A) <=> is_reflexive_in(A, relation_field(A))))),
% 0.19/0.38 inference(quant_intro,[status(thm)],[85])).
% 0.19/0.38 tff(87,plain,
% 0.19/0.38 (![A: $i] : ((~relation(A)) | (reflexive(A) <=> is_reflexive_in(A, relation_field(A)))) <=> ![A: $i] : ((~relation(A)) | (reflexive(A) <=> is_reflexive_in(A, relation_field(A))))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(88,plain,
% 0.19/0.38 (^[A: $i] : rewrite((relation(A) => (reflexive(A) <=> is_reflexive_in(A, relation_field(A)))) <=> ((~relation(A)) | (reflexive(A) <=> is_reflexive_in(A, relation_field(A)))))),
% 0.19/0.38 inference(bind,[status(th)],[])).
% 0.19/0.38 tff(89,plain,
% 0.19/0.38 (![A: $i] : (relation(A) => (reflexive(A) <=> is_reflexive_in(A, relation_field(A)))) <=> ![A: $i] : ((~relation(A)) | (reflexive(A) <=> is_reflexive_in(A, relation_field(A))))),
% 0.19/0.38 inference(quant_intro,[status(thm)],[88])).
% 0.19/0.38 tff(90,axiom,(![A: $i] : (relation(A) => (reflexive(A) <=> is_reflexive_in(A, relation_field(A))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d9_relat_2')).
% 0.19/0.38 tff(91,plain,
% 0.19/0.38 (![A: $i] : ((~relation(A)) | (reflexive(A) <=> is_reflexive_in(A, relation_field(A))))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[90, 89])).
% 0.19/0.38 tff(92,plain,
% 0.19/0.38 (![A: $i] : ((~relation(A)) | (reflexive(A) <=> is_reflexive_in(A, relation_field(A))))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[91, 87])).
% 0.19/0.38 tff(93,plain,(
% 0.19/0.38 ![A: $i] : ((~relation(A)) | (reflexive(A) <=> is_reflexive_in(A, relation_field(A))))),
% 0.19/0.38 inference(skolemize,[status(sab)],[92])).
% 0.19/0.38 tff(94,plain,
% 0.19/0.38 (![A: $i] : ((~relation(A)) | (reflexive(A) <=> is_reflexive_in(A, relation_field(A))))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[93, 86])).
% 0.19/0.38 tff(95,plain,
% 0.19/0.38 (((~![A: $i] : ((~relation(A)) | (reflexive(A) <=> is_reflexive_in(A, relation_field(A))))) | ((~relation(A!2)) | (reflexive(A!2) <=> is_reflexive_in(A!2, relation_field(A!2))))) <=> ((~![A: $i] : ((~relation(A)) | (reflexive(A) <=> is_reflexive_in(A, relation_field(A))))) | (~relation(A!2)) | (reflexive(A!2) <=> is_reflexive_in(A!2, relation_field(A!2))))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(96,plain,
% 0.19/0.38 ((~![A: $i] : ((~relation(A)) | (reflexive(A) <=> is_reflexive_in(A, relation_field(A))))) | ((~relation(A!2)) | (reflexive(A!2) <=> is_reflexive_in(A!2, relation_field(A!2))))),
% 0.19/0.38 inference(quant_inst,[status(thm)],[])).
% 0.19/0.38 tff(97,plain,
% 0.19/0.38 ((~![A: $i] : ((~relation(A)) | (reflexive(A) <=> is_reflexive_in(A, relation_field(A))))) | (~relation(A!2)) | (reflexive(A!2) <=> is_reflexive_in(A!2, relation_field(A!2)))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[96, 95])).
% 0.19/0.38 tff(98,plain,
% 0.19/0.38 (reflexive(A!2) <=> is_reflexive_in(A!2, relation_field(A!2))),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[97, 94, 18])).
% 0.19/0.38 tff(99,plain,
% 0.19/0.38 ((~(reflexive(A!2) <=> is_reflexive_in(A!2, relation_field(A!2)))) | (~reflexive(A!2)) | is_reflexive_in(A!2, relation_field(A!2))),
% 0.19/0.38 inference(tautology,[status(thm)],[])).
% 0.19/0.38 tff(100,plain,
% 0.19/0.38 ((~reflexive(A!2)) | is_reflexive_in(A!2, relation_field(A!2))),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[99, 98])).
% 0.19/0.38 tff(101,plain,
% 0.19/0.38 (~reflexive(A!2)),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[100, 84])).
% 0.19/0.38 tff(102,plain,
% 0.19/0.38 ((reflexive(A!2) | ![B: $i] : ((~in(B, relation_field(A!2))) | in(ordered_pair(B, B), A!2))) <=> (reflexive(A!2) | ![B: $i] : ((~in(B, relation_field(A!2))) | in(ordered_pair(B, B), A!2)))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(103,plain,
% 0.19/0.38 (reflexive(A!2) | ![B: $i] : ((~in(B, relation_field(A!2))) | in(ordered_pair(B, B), A!2))),
% 0.19/0.38 inference(and_elim,[status(thm)],[17])).
% 0.19/0.38 tff(104,plain,
% 0.19/0.38 (reflexive(A!2) | ![B: $i] : ((~in(B, relation_field(A!2))) | in(ordered_pair(B, B), A!2))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[103, 102])).
% 0.19/0.38 tff(105,plain,
% 0.19/0.38 (![B: $i] : ((~in(B, relation_field(A!2))) | in(ordered_pair(B, B), A!2))),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[104, 101])).
% 0.19/0.38 tff(106,plain,
% 0.19/0.38 (((~![B: $i] : ((~in(B, relation_field(A!2))) | in(ordered_pair(B, B), A!2))) | ((~in(B!3, relation_field(A!2))) | in(ordered_pair(B!3, B!3), A!2))) <=> ((~![B: $i] : ((~in(B, relation_field(A!2))) | in(ordered_pair(B, B), A!2))) | (~in(B!3, relation_field(A!2))) | in(ordered_pair(B!3, B!3), A!2))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(107,plain,
% 0.19/0.38 ((~![B: $i] : ((~in(B, relation_field(A!2))) | in(ordered_pair(B, B), A!2))) | ((~in(B!3, relation_field(A!2))) | in(ordered_pair(B!3, B!3), A!2))),
% 0.19/0.38 inference(quant_inst,[status(thm)],[])).
% 0.19/0.38 tff(108,plain,
% 0.19/0.38 ((~![B: $i] : ((~in(B, relation_field(A!2))) | in(ordered_pair(B, B), A!2))) | (~in(B!3, relation_field(A!2))) | in(ordered_pair(B!3, B!3), A!2)),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[107, 106])).
% 0.19/0.38 tff(109,plain,
% 0.19/0.38 ($false),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[108, 105, 43, 41])).
% 0.19/0.38 tff(110,plain,((~in(B!3, relation_field(A!2))) | in(ordered_pair(B!3, B!3), A!2)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.38 tff(111,plain,
% 0.19/0.38 ((~reflexive(A!2)) | (~((~in(B!3, relation_field(A!2))) | in(ordered_pair(B!3, B!3), A!2)))),
% 0.19/0.38 inference(and_elim,[status(thm)],[17])).
% 0.19/0.38 tff(112,plain,
% 0.19/0.38 (~reflexive(A!2)),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[111, 110])).
% 0.19/0.38 tff(113,plain,
% 0.19/0.38 ((~(reflexive(A!2) <=> is_reflexive_in(A!2, relation_field(A!2)))) | reflexive(A!2) | (~is_reflexive_in(A!2, relation_field(A!2)))),
% 0.19/0.38 inference(tautology,[status(thm)],[])).
% 0.19/0.38 tff(114,plain,
% 0.19/0.38 (reflexive(A!2) | (~is_reflexive_in(A!2, relation_field(A!2)))),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[113, 98])).
% 0.19/0.38 tff(115,plain,
% 0.19/0.38 (~is_reflexive_in(A!2, relation_field(A!2))),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[114, 112])).
% 0.19/0.38 tff(116,plain,
% 0.19/0.38 (~is_reflexive_in(A!2, set_union2(relation_dom(A!2), relation_rng(A!2)))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[115, 38])).
% 0.19/0.38 tff(117,plain,
% 0.19/0.38 (((~((~is_reflexive_in(A!2, set_union2(relation_dom(A!2), relation_rng(A!2)))) | ![C: $i] : ((~in(C, set_union2(relation_dom(A!2), relation_rng(A!2)))) | in(ordered_pair(C, C), A!2)))) | (~(is_reflexive_in(A!2, set_union2(relation_dom(A!2), relation_rng(A!2))) | (~((~in(tptp_fun_C_0(set_union2(relation_dom(A!2), relation_rng(A!2)), A!2), set_union2(relation_dom(A!2), relation_rng(A!2)))) | in(ordered_pair(tptp_fun_C_0(set_union2(relation_dom(A!2), relation_rng(A!2)), A!2), tptp_fun_C_0(set_union2(relation_dom(A!2), relation_rng(A!2)), A!2)), A!2)))))) | (is_reflexive_in(A!2, set_union2(relation_dom(A!2), relation_rng(A!2))) | (~((~in(tptp_fun_C_0(set_union2(relation_dom(A!2), relation_rng(A!2)), A!2), set_union2(relation_dom(A!2), relation_rng(A!2)))) | in(ordered_pair(tptp_fun_C_0(set_union2(relation_dom(A!2), relation_rng(A!2)), A!2), tptp_fun_C_0(set_union2(relation_dom(A!2), relation_rng(A!2)), A!2)), A!2))))),
% 0.19/0.38 inference(tautology,[status(thm)],[])).
% 0.19/0.38 tff(118,plain,
% 0.19/0.38 (is_reflexive_in(A!2, set_union2(relation_dom(A!2), relation_rng(A!2))) | (~((~in(tptp_fun_C_0(set_union2(relation_dom(A!2), relation_rng(A!2)), A!2), set_union2(relation_dom(A!2), relation_rng(A!2)))) | in(ordered_pair(tptp_fun_C_0(set_union2(relation_dom(A!2), relation_rng(A!2)), A!2), tptp_fun_C_0(set_union2(relation_dom(A!2), relation_rng(A!2)), A!2)), A!2)))),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[117, 78])).
% 0.19/0.38 tff(119,plain,
% 0.19/0.38 ((~(is_reflexive_in(A!2, set_union2(relation_dom(A!2), relation_rng(A!2))) | (~((~in(tptp_fun_C_0(set_union2(relation_dom(A!2), relation_rng(A!2)), A!2), set_union2(relation_dom(A!2), relation_rng(A!2)))) | in(ordered_pair(tptp_fun_C_0(set_union2(relation_dom(A!2), relation_rng(A!2)), A!2), tptp_fun_C_0(set_union2(relation_dom(A!2), relation_rng(A!2)), A!2)), A!2))))) | is_reflexive_in(A!2, set_union2(relation_dom(A!2), relation_rng(A!2))) | (~((~in(tptp_fun_C_0(set_union2(relation_dom(A!2), relation_rng(A!2)), A!2), set_union2(relation_dom(A!2), relation_rng(A!2)))) | in(ordered_pair(tptp_fun_C_0(set_union2(relation_dom(A!2), relation_rng(A!2)), A!2), tptp_fun_C_0(set_union2(relation_dom(A!2), relation_rng(A!2)), A!2)), A!2)))),
% 0.19/0.38 inference(tautology,[status(thm)],[])).
% 0.19/0.38 tff(120,plain,
% 0.19/0.38 (is_reflexive_in(A!2, set_union2(relation_dom(A!2), relation_rng(A!2))) | (~((~in(tptp_fun_C_0(set_union2(relation_dom(A!2), relation_rng(A!2)), A!2), set_union2(relation_dom(A!2), relation_rng(A!2)))) | in(ordered_pair(tptp_fun_C_0(set_union2(relation_dom(A!2), relation_rng(A!2)), A!2), tptp_fun_C_0(set_union2(relation_dom(A!2), relation_rng(A!2)), A!2)), A!2)))),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[119, 118])).
% 0.19/0.38 tff(121,plain,
% 0.19/0.38 (~((~in(tptp_fun_C_0(set_union2(relation_dom(A!2), relation_rng(A!2)), A!2), set_union2(relation_dom(A!2), relation_rng(A!2)))) | in(ordered_pair(tptp_fun_C_0(set_union2(relation_dom(A!2), relation_rng(A!2)), A!2), tptp_fun_C_0(set_union2(relation_dom(A!2), relation_rng(A!2)), A!2)), A!2))),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[120, 116])).
% 0.19/0.38 tff(122,plain,
% 0.19/0.38 (((~in(tptp_fun_C_0(set_union2(relation_dom(A!2), relation_rng(A!2)), A!2), set_union2(relation_dom(A!2), relation_rng(A!2)))) | in(ordered_pair(tptp_fun_C_0(set_union2(relation_dom(A!2), relation_rng(A!2)), A!2), tptp_fun_C_0(set_union2(relation_dom(A!2), relation_rng(A!2)), A!2)), A!2)) | in(tptp_fun_C_0(set_union2(relation_dom(A!2), relation_rng(A!2)), A!2), set_union2(relation_dom(A!2), relation_rng(A!2)))),
% 0.19/0.38 inference(tautology,[status(thm)],[])).
% 0.19/0.38 tff(123,plain,
% 0.19/0.38 (in(tptp_fun_C_0(set_union2(relation_dom(A!2), relation_rng(A!2)), A!2), set_union2(relation_dom(A!2), relation_rng(A!2)))),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[122, 121])).
% 0.19/0.38 tff(124,plain,
% 0.19/0.38 (in(tptp_fun_C_0(set_union2(relation_dom(A!2), relation_rng(A!2)), A!2), relation_field(A!2))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[123, 34])).
% 0.19/0.38 tff(125,plain,
% 0.19/0.38 (((~in(tptp_fun_C_0(set_union2(relation_dom(A!2), relation_rng(A!2)), A!2), set_union2(relation_dom(A!2), relation_rng(A!2)))) | in(ordered_pair(tptp_fun_C_0(set_union2(relation_dom(A!2), relation_rng(A!2)), A!2), tptp_fun_C_0(set_union2(relation_dom(A!2), relation_rng(A!2)), A!2)), A!2)) | (~in(ordered_pair(tptp_fun_C_0(set_union2(relation_dom(A!2), relation_rng(A!2)), A!2), tptp_fun_C_0(set_union2(relation_dom(A!2), relation_rng(A!2)), A!2)), A!2))),
% 0.19/0.38 inference(tautology,[status(thm)],[])).
% 0.19/0.38 tff(126,plain,
% 0.19/0.38 (~in(ordered_pair(tptp_fun_C_0(set_union2(relation_dom(A!2), relation_rng(A!2)), A!2), tptp_fun_C_0(set_union2(relation_dom(A!2), relation_rng(A!2)), A!2)), A!2)),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[125, 121])).
% 0.19/0.38 tff(127,plain,
% 0.19/0.38 (![B: $i] : ((~in(B, relation_field(A!2))) | in(ordered_pair(B, B), A!2))),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[104, 112])).
% 0.19/0.38 tff(128,plain,
% 0.19/0.38 (((~![B: $i] : ((~in(B, relation_field(A!2))) | in(ordered_pair(B, B), A!2))) | ((~in(tptp_fun_C_0(set_union2(relation_dom(A!2), relation_rng(A!2)), A!2), relation_field(A!2))) | in(ordered_pair(tptp_fun_C_0(set_union2(relation_dom(A!2), relation_rng(A!2)), A!2), tptp_fun_C_0(set_union2(relation_dom(A!2), relation_rng(A!2)), A!2)), A!2))) <=> ((~![B: $i] : ((~in(B, relation_field(A!2))) | in(ordered_pair(B, B), A!2))) | (~in(tptp_fun_C_0(set_union2(relation_dom(A!2), relation_rng(A!2)), A!2), relation_field(A!2))) | in(ordered_pair(tptp_fun_C_0(set_union2(relation_dom(A!2), relation_rng(A!2)), A!2), tptp_fun_C_0(set_union2(relation_dom(A!2), relation_rng(A!2)), A!2)), A!2))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(129,plain,
% 0.19/0.38 ((~![B: $i] : ((~in(B, relation_field(A!2))) | in(ordered_pair(B, B), A!2))) | ((~in(tptp_fun_C_0(set_union2(relation_dom(A!2), relation_rng(A!2)), A!2), relation_field(A!2))) | in(ordered_pair(tptp_fun_C_0(set_union2(relation_dom(A!2), relation_rng(A!2)), A!2), tptp_fun_C_0(set_union2(relation_dom(A!2), relation_rng(A!2)), A!2)), A!2))),
% 0.19/0.38 inference(quant_inst,[status(thm)],[])).
% 0.19/0.38 tff(130,plain,
% 0.19/0.38 ((~![B: $i] : ((~in(B, relation_field(A!2))) | in(ordered_pair(B, B), A!2))) | (~in(tptp_fun_C_0(set_union2(relation_dom(A!2), relation_rng(A!2)), A!2), relation_field(A!2))) | in(ordered_pair(tptp_fun_C_0(set_union2(relation_dom(A!2), relation_rng(A!2)), A!2), tptp_fun_C_0(set_union2(relation_dom(A!2), relation_rng(A!2)), A!2)), A!2)),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[129, 128])).
% 0.19/0.38 tff(131,plain,
% 0.19/0.38 (~in(tptp_fun_C_0(set_union2(relation_dom(A!2), relation_rng(A!2)), A!2), relation_field(A!2))),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[130, 127, 126])).
% 0.19/0.38 tff(132,plain,
% 0.19/0.38 ($false),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[131, 124])).
% 0.19/0.38 % SZS output end Proof
%------------------------------------------------------------------------------