TSTP Solution File: SEU252+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SEU252+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n008.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 07:28:30 EDT 2022
% Result : Theorem 0.13s 0.39s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SEU252+1 : TPTP v8.1.0. Released v3.3.0.
% 0.11/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.33 % Computer : n008.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Sat Sep 3 11:09:40 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.13/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34 Usage: tptp [options] [-file:]file
% 0.13/0.34 -h, -? prints this message.
% 0.13/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.34 -m, -model generate model.
% 0.13/0.34 -p, -proof generate proof.
% 0.13/0.34 -c, -core generate unsat core of named formulas.
% 0.13/0.34 -st, -statistics display statistics.
% 0.13/0.34 -t:timeout set timeout (in second).
% 0.13/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34 -<param>:<value> configuration parameter and value.
% 0.13/0.34 -o:<output-file> file to place output in.
% 0.13/0.39 % SZS status Theorem
% 0.13/0.39 % SZS output start Proof
% 0.13/0.39 tff(in_type, type, (
% 0.13/0.39 in: ( $i * $i ) > $o)).
% 0.13/0.39 tff(tptp_fun_A_8_type, type, (
% 0.13/0.39 tptp_fun_A_8: $i)).
% 0.13/0.39 tff(tptp_fun_B_1_type, type, (
% 0.13/0.39 tptp_fun_B_1: $i > $i)).
% 0.13/0.39 tff(relation_restriction_type, type, (
% 0.13/0.39 relation_restriction: ( $i * $i ) > $i)).
% 0.13/0.39 tff(tptp_fun_B_7_type, type, (
% 0.13/0.39 tptp_fun_B_7: $i)).
% 0.13/0.39 tff(cartesian_product2_type, type, (
% 0.13/0.39 cartesian_product2: ( $i * $i ) > $i)).
% 0.13/0.39 tff(ordered_pair_type, type, (
% 0.13/0.39 ordered_pair: ( $i * $i ) > $i)).
% 0.13/0.39 tff(relation_field_type, type, (
% 0.13/0.39 relation_field: $i > $i)).
% 0.13/0.39 tff(reflexive_type, type, (
% 0.13/0.39 reflexive: $i > $o)).
% 0.13/0.39 tff(relation_type, type, (
% 0.13/0.39 relation: $i > $o)).
% 0.13/0.39 tff(1,plain,
% 0.13/0.39 ((~(reflexive(relation_restriction(B!7, A!8)) | (~relation(B!7)) | (~reflexive(B!7)))) <=> (~(reflexive(relation_restriction(B!7, A!8)) | (~relation(B!7)) | (~reflexive(B!7))))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(2,plain,
% 0.13/0.39 ((~![A: $i, B: $i] : (reflexive(relation_restriction(B, A)) | (~relation(B)) | (~reflexive(B)))) <=> (~![A: $i, B: $i] : (reflexive(relation_restriction(B, A)) | (~relation(B)) | (~reflexive(B))))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(3,plain,
% 0.13/0.39 ((~![A: $i, B: $i] : (relation(B) => (reflexive(B) => reflexive(relation_restriction(B, A))))) <=> (~![A: $i, B: $i] : (reflexive(relation_restriction(B, A)) | (~relation(B)) | (~reflexive(B))))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(4,axiom,(~![A: $i, B: $i] : (relation(B) => (reflexive(B) => reflexive(relation_restriction(B, A))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t22_wellord1')).
% 0.13/0.39 tff(5,plain,
% 0.13/0.39 (~![A: $i, B: $i] : (reflexive(relation_restriction(B, A)) | (~relation(B)) | (~reflexive(B)))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.13/0.39 tff(6,plain,
% 0.13/0.39 (~![A: $i, B: $i] : (reflexive(relation_restriction(B, A)) | (~relation(B)) | (~reflexive(B)))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[5, 2])).
% 0.13/0.39 tff(7,plain,
% 0.13/0.39 (~![A: $i, B: $i] : (reflexive(relation_restriction(B, A)) | (~relation(B)) | (~reflexive(B)))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.13/0.39 tff(8,plain,
% 0.13/0.39 (~![A: $i, B: $i] : (reflexive(relation_restriction(B, A)) | (~relation(B)) | (~reflexive(B)))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[7, 2])).
% 0.13/0.39 tff(9,plain,
% 0.13/0.39 (~![A: $i, B: $i] : (reflexive(relation_restriction(B, A)) | (~relation(B)) | (~reflexive(B)))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[8, 2])).
% 0.13/0.39 tff(10,plain,
% 0.13/0.39 (~![A: $i, B: $i] : (reflexive(relation_restriction(B, A)) | (~relation(B)) | (~reflexive(B)))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[9, 2])).
% 0.13/0.39 tff(11,plain,
% 0.13/0.39 (~![A: $i, B: $i] : (reflexive(relation_restriction(B, A)) | (~relation(B)) | (~reflexive(B)))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[10, 2])).
% 0.13/0.39 tff(12,plain,(
% 0.13/0.39 ~(reflexive(relation_restriction(B!7, A!8)) | (~relation(B!7)) | (~reflexive(B!7)))),
% 0.13/0.39 inference(skolemize,[status(sab)],[11])).
% 0.13/0.39 tff(13,plain,
% 0.13/0.39 (~(reflexive(relation_restriction(B!7, A!8)) | (~relation(B!7)) | (~reflexive(B!7)))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[12, 1])).
% 0.13/0.39 tff(14,plain,
% 0.13/0.39 (relation(B!7)),
% 0.13/0.39 inference(or_elim,[status(thm)],[13])).
% 0.13/0.39 tff(15,plain,
% 0.13/0.39 (^[A: $i, B: $i] : refl(((~relation(A)) | relation(relation_restriction(A, B))) <=> ((~relation(A)) | relation(relation_restriction(A, B))))),
% 0.13/0.39 inference(bind,[status(th)],[])).
% 0.13/0.39 tff(16,plain,
% 0.13/0.39 (![A: $i, B: $i] : ((~relation(A)) | relation(relation_restriction(A, B))) <=> ![A: $i, B: $i] : ((~relation(A)) | relation(relation_restriction(A, B)))),
% 0.13/0.39 inference(quant_intro,[status(thm)],[15])).
% 0.13/0.39 tff(17,plain,
% 0.13/0.39 (![A: $i, B: $i] : ((~relation(A)) | relation(relation_restriction(A, B))) <=> ![A: $i, B: $i] : ((~relation(A)) | relation(relation_restriction(A, B)))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(18,plain,
% 0.13/0.39 (^[A: $i, B: $i] : rewrite((relation(A) => relation(relation_restriction(A, B))) <=> ((~relation(A)) | relation(relation_restriction(A, B))))),
% 0.13/0.39 inference(bind,[status(th)],[])).
% 0.13/0.39 tff(19,plain,
% 0.13/0.39 (![A: $i, B: $i] : (relation(A) => relation(relation_restriction(A, B))) <=> ![A: $i, B: $i] : ((~relation(A)) | relation(relation_restriction(A, B)))),
% 0.13/0.39 inference(quant_intro,[status(thm)],[18])).
% 0.13/0.39 tff(20,axiom,(![A: $i, B: $i] : (relation(A) => relation(relation_restriction(A, B)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_k2_wellord1')).
% 0.13/0.39 tff(21,plain,
% 0.13/0.39 (![A: $i, B: $i] : ((~relation(A)) | relation(relation_restriction(A, B)))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[20, 19])).
% 0.13/0.39 tff(22,plain,
% 0.13/0.39 (![A: $i, B: $i] : ((~relation(A)) | relation(relation_restriction(A, B)))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[21, 17])).
% 0.13/0.39 tff(23,plain,(
% 0.13/0.39 ![A: $i, B: $i] : ((~relation(A)) | relation(relation_restriction(A, B)))),
% 0.13/0.39 inference(skolemize,[status(sab)],[22])).
% 0.13/0.39 tff(24,plain,
% 0.13/0.39 (![A: $i, B: $i] : ((~relation(A)) | relation(relation_restriction(A, B)))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[23, 16])).
% 0.13/0.39 tff(25,plain,
% 0.13/0.39 (((~![A: $i, B: $i] : ((~relation(A)) | relation(relation_restriction(A, B)))) | ((~relation(B!7)) | relation(relation_restriction(B!7, A!8)))) <=> ((~![A: $i, B: $i] : ((~relation(A)) | relation(relation_restriction(A, B)))) | (~relation(B!7)) | relation(relation_restriction(B!7, A!8)))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(26,plain,
% 0.13/0.39 ((~![A: $i, B: $i] : ((~relation(A)) | relation(relation_restriction(A, B)))) | ((~relation(B!7)) | relation(relation_restriction(B!7, A!8)))),
% 0.13/0.39 inference(quant_inst,[status(thm)],[])).
% 0.13/0.39 tff(27,plain,
% 0.13/0.39 ((~![A: $i, B: $i] : ((~relation(A)) | relation(relation_restriction(A, B)))) | (~relation(B!7)) | relation(relation_restriction(B!7, A!8))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[26, 25])).
% 0.13/0.39 tff(28,plain,
% 0.13/0.39 (relation(relation_restriction(B!7, A!8))),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[27, 24, 14])).
% 0.13/0.39 tff(29,plain,
% 0.13/0.39 (^[A: $i] : rewrite(((~relation(A)) | (~((~((~reflexive(A)) | ![B: $i] : ((~in(B, relation_field(A))) | in(ordered_pair(B, B), A)))) | (~(reflexive(A) | (~((~in(tptp_fun_B_1(A), relation_field(A))) | in(ordered_pair(tptp_fun_B_1(A), tptp_fun_B_1(A)), A)))))))) <=> ((~relation(A)) | (~((~(reflexive(A) | (~((~in(tptp_fun_B_1(A), relation_field(A))) | in(ordered_pair(tptp_fun_B_1(A), tptp_fun_B_1(A)), A))))) | (~((~reflexive(A)) | ![B: $i] : ((~in(B, relation_field(A))) | in(ordered_pair(B, B), A))))))))),
% 0.13/0.39 inference(bind,[status(th)],[])).
% 0.13/0.39 tff(30,plain,
% 0.13/0.39 (![A: $i] : ((~relation(A)) | (~((~((~reflexive(A)) | ![B: $i] : ((~in(B, relation_field(A))) | in(ordered_pair(B, B), A)))) | (~(reflexive(A) | (~((~in(tptp_fun_B_1(A), relation_field(A))) | in(ordered_pair(tptp_fun_B_1(A), tptp_fun_B_1(A)), A)))))))) <=> ![A: $i] : ((~relation(A)) | (~((~(reflexive(A) | (~((~in(tptp_fun_B_1(A), relation_field(A))) | in(ordered_pair(tptp_fun_B_1(A), tptp_fun_B_1(A)), A))))) | (~((~reflexive(A)) | ![B: $i] : ((~in(B, relation_field(A))) | in(ordered_pair(B, B), A)))))))),
% 0.13/0.39 inference(quant_intro,[status(thm)],[29])).
% 0.13/0.39 tff(31,plain,
% 0.13/0.39 (^[A: $i] : refl(((~relation(A)) | (~((~((~reflexive(A)) | ![B: $i] : ((~in(B, relation_field(A))) | in(ordered_pair(B, B), A)))) | (~(reflexive(A) | (~((~in(tptp_fun_B_1(A), relation_field(A))) | in(ordered_pair(tptp_fun_B_1(A), tptp_fun_B_1(A)), A)))))))) <=> ((~relation(A)) | (~((~((~reflexive(A)) | ![B: $i] : ((~in(B, relation_field(A))) | in(ordered_pair(B, B), A)))) | (~(reflexive(A) | (~((~in(tptp_fun_B_1(A), relation_field(A))) | in(ordered_pair(tptp_fun_B_1(A), tptp_fun_B_1(A)), A)))))))))),
% 0.13/0.39 inference(bind,[status(th)],[])).
% 0.13/0.39 tff(32,plain,
% 0.13/0.39 (![A: $i] : ((~relation(A)) | (~((~((~reflexive(A)) | ![B: $i] : ((~in(B, relation_field(A))) | in(ordered_pair(B, B), A)))) | (~(reflexive(A) | (~((~in(tptp_fun_B_1(A), relation_field(A))) | in(ordered_pair(tptp_fun_B_1(A), tptp_fun_B_1(A)), A)))))))) <=> ![A: $i] : ((~relation(A)) | (~((~((~reflexive(A)) | ![B: $i] : ((~in(B, relation_field(A))) | in(ordered_pair(B, B), A)))) | (~(reflexive(A) | (~((~in(tptp_fun_B_1(A), relation_field(A))) | in(ordered_pair(tptp_fun_B_1(A), tptp_fun_B_1(A)), A))))))))),
% 0.13/0.39 inference(quant_intro,[status(thm)],[31])).
% 0.13/0.39 tff(33,plain,
% 0.13/0.39 (^[A: $i] : rewrite(((~relation(A)) | (~((~((~reflexive(A)) | ![B: $i] : ((~in(B, relation_field(A))) | in(ordered_pair(B, B), A)))) | (~(reflexive(A) | (~((~in(tptp_fun_B_1(A), relation_field(A))) | in(ordered_pair(tptp_fun_B_1(A), tptp_fun_B_1(A)), A)))))))) <=> ((~relation(A)) | (~((~((~reflexive(A)) | ![B: $i] : ((~in(B, relation_field(A))) | in(ordered_pair(B, B), A)))) | (~(reflexive(A) | (~((~in(tptp_fun_B_1(A), relation_field(A))) | in(ordered_pair(tptp_fun_B_1(A), tptp_fun_B_1(A)), A)))))))))),
% 0.13/0.40 inference(bind,[status(th)],[])).
% 0.13/0.40 tff(34,plain,
% 0.13/0.40 (![A: $i] : ((~relation(A)) | (~((~((~reflexive(A)) | ![B: $i] : ((~in(B, relation_field(A))) | in(ordered_pair(B, B), A)))) | (~(reflexive(A) | (~((~in(tptp_fun_B_1(A), relation_field(A))) | in(ordered_pair(tptp_fun_B_1(A), tptp_fun_B_1(A)), A)))))))) <=> ![A: $i] : ((~relation(A)) | (~((~((~reflexive(A)) | ![B: $i] : ((~in(B, relation_field(A))) | in(ordered_pair(B, B), A)))) | (~(reflexive(A) | (~((~in(tptp_fun_B_1(A), relation_field(A))) | in(ordered_pair(tptp_fun_B_1(A), tptp_fun_B_1(A)), A))))))))),
% 0.13/0.40 inference(quant_intro,[status(thm)],[33])).
% 0.13/0.40 tff(35,plain,
% 0.13/0.40 (![A: $i] : ((~relation(A)) | (~((~((~reflexive(A)) | ![B: $i] : ((~in(B, relation_field(A))) | in(ordered_pair(B, B), A)))) | (~(reflexive(A) | (~((~in(tptp_fun_B_1(A), relation_field(A))) | in(ordered_pair(tptp_fun_B_1(A), tptp_fun_B_1(A)), A)))))))) <=> ![A: $i] : ((~relation(A)) | (~((~((~reflexive(A)) | ![B: $i] : ((~in(B, relation_field(A))) | in(ordered_pair(B, B), A)))) | (~(reflexive(A) | (~((~in(tptp_fun_B_1(A), relation_field(A))) | in(ordered_pair(tptp_fun_B_1(A), tptp_fun_B_1(A)), A))))))))),
% 0.13/0.40 inference(transitivity,[status(thm)],[34, 32])).
% 0.13/0.40 tff(36,plain,
% 0.13/0.40 (^[A: $i] : rewrite(((~relation(A)) | (((~reflexive(A)) | ![B: $i] : ((~in(B, relation_field(A))) | in(ordered_pair(B, B), A))) & (reflexive(A) | (~((~in(tptp_fun_B_1(A), relation_field(A))) | in(ordered_pair(tptp_fun_B_1(A), tptp_fun_B_1(A)), A)))))) <=> ((~relation(A)) | (~((~((~reflexive(A)) | ![B: $i] : ((~in(B, relation_field(A))) | in(ordered_pair(B, B), A)))) | (~(reflexive(A) | (~((~in(tptp_fun_B_1(A), relation_field(A))) | in(ordered_pair(tptp_fun_B_1(A), tptp_fun_B_1(A)), A)))))))))),
% 0.13/0.40 inference(bind,[status(th)],[])).
% 0.13/0.40 tff(37,plain,
% 0.13/0.40 (![A: $i] : ((~relation(A)) | (((~reflexive(A)) | ![B: $i] : ((~in(B, relation_field(A))) | in(ordered_pair(B, B), A))) & (reflexive(A) | (~((~in(tptp_fun_B_1(A), relation_field(A))) | in(ordered_pair(tptp_fun_B_1(A), tptp_fun_B_1(A)), A)))))) <=> ![A: $i] : ((~relation(A)) | (~((~((~reflexive(A)) | ![B: $i] : ((~in(B, relation_field(A))) | in(ordered_pair(B, B), A)))) | (~(reflexive(A) | (~((~in(tptp_fun_B_1(A), relation_field(A))) | in(ordered_pair(tptp_fun_B_1(A), tptp_fun_B_1(A)), A))))))))),
% 0.13/0.40 inference(quant_intro,[status(thm)],[36])).
% 0.13/0.40 tff(38,plain,
% 0.13/0.40 (![A: $i] : ((~relation(A)) | (reflexive(A) <=> ![B: $i] : ((~in(B, relation_field(A))) | in(ordered_pair(B, B), A)))) <=> ![A: $i] : ((~relation(A)) | (reflexive(A) <=> ![B: $i] : ((~in(B, relation_field(A))) | in(ordered_pair(B, B), A))))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(39,plain,
% 0.13/0.40 (^[A: $i] : trans(monotonicity(rewrite((reflexive(A) <=> ![B: $i] : (in(B, relation_field(A)) => in(ordered_pair(B, B), A))) <=> (reflexive(A) <=> ![B: $i] : ((~in(B, relation_field(A))) | in(ordered_pair(B, B), A)))), ((relation(A) => (reflexive(A) <=> ![B: $i] : (in(B, relation_field(A)) => in(ordered_pair(B, B), A)))) <=> (relation(A) => (reflexive(A) <=> ![B: $i] : ((~in(B, relation_field(A))) | in(ordered_pair(B, B), A)))))), rewrite((relation(A) => (reflexive(A) <=> ![B: $i] : ((~in(B, relation_field(A))) | in(ordered_pair(B, B), A)))) <=> ((~relation(A)) | (reflexive(A) <=> ![B: $i] : ((~in(B, relation_field(A))) | in(ordered_pair(B, B), A))))), ((relation(A) => (reflexive(A) <=> ![B: $i] : (in(B, relation_field(A)) => in(ordered_pair(B, B), A)))) <=> ((~relation(A)) | (reflexive(A) <=> ![B: $i] : ((~in(B, relation_field(A))) | in(ordered_pair(B, B), A))))))),
% 0.13/0.40 inference(bind,[status(th)],[])).
% 0.13/0.40 tff(40,plain,
% 0.13/0.40 (![A: $i] : (relation(A) => (reflexive(A) <=> ![B: $i] : (in(B, relation_field(A)) => in(ordered_pair(B, B), A)))) <=> ![A: $i] : ((~relation(A)) | (reflexive(A) <=> ![B: $i] : ((~in(B, relation_field(A))) | in(ordered_pair(B, B), A))))),
% 0.13/0.40 inference(quant_intro,[status(thm)],[39])).
% 0.13/0.40 tff(41,axiom,(![A: $i] : (relation(A) => (reflexive(A) <=> ![B: $i] : (in(B, relation_field(A)) => in(ordered_pair(B, B), A))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','l1_wellord1')).
% 0.13/0.40 tff(42,plain,
% 0.13/0.40 (![A: $i] : ((~relation(A)) | (reflexive(A) <=> ![B: $i] : ((~in(B, relation_field(A))) | in(ordered_pair(B, B), A))))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[41, 40])).
% 0.13/0.40 tff(43,plain,
% 0.13/0.40 (![A: $i] : ((~relation(A)) | (reflexive(A) <=> ![B: $i] : ((~in(B, relation_field(A))) | in(ordered_pair(B, B), A))))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[42, 38])).
% 0.13/0.40 tff(44,plain,(
% 0.13/0.40 ![A: $i] : ((~relation(A)) | (((~reflexive(A)) | ![B: $i] : ((~in(B, relation_field(A))) | in(ordered_pair(B, B), A))) & (reflexive(A) | (~((~in(tptp_fun_B_1(A), relation_field(A))) | in(ordered_pair(tptp_fun_B_1(A), tptp_fun_B_1(A)), A))))))),
% 0.13/0.40 inference(skolemize,[status(sab)],[43])).
% 0.13/0.40 tff(45,plain,
% 0.13/0.40 (![A: $i] : ((~relation(A)) | (~((~((~reflexive(A)) | ![B: $i] : ((~in(B, relation_field(A))) | in(ordered_pair(B, B), A)))) | (~(reflexive(A) | (~((~in(tptp_fun_B_1(A), relation_field(A))) | in(ordered_pair(tptp_fun_B_1(A), tptp_fun_B_1(A)), A))))))))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[44, 37])).
% 0.13/0.40 tff(46,plain,
% 0.13/0.40 (![A: $i] : ((~relation(A)) | (~((~((~reflexive(A)) | ![B: $i] : ((~in(B, relation_field(A))) | in(ordered_pair(B, B), A)))) | (~(reflexive(A) | (~((~in(tptp_fun_B_1(A), relation_field(A))) | in(ordered_pair(tptp_fun_B_1(A), tptp_fun_B_1(A)), A))))))))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[45, 35])).
% 0.13/0.40 tff(47,plain,
% 0.13/0.40 (![A: $i] : ((~relation(A)) | (~((~(reflexive(A) | (~((~in(tptp_fun_B_1(A), relation_field(A))) | in(ordered_pair(tptp_fun_B_1(A), tptp_fun_B_1(A)), A))))) | (~((~reflexive(A)) | ![B: $i] : ((~in(B, relation_field(A))) | in(ordered_pair(B, B), A)))))))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[46, 30])).
% 0.13/0.40 tff(48,plain,
% 0.13/0.40 (((~![A: $i] : ((~relation(A)) | (~((~(reflexive(A) | (~((~in(tptp_fun_B_1(A), relation_field(A))) | in(ordered_pair(tptp_fun_B_1(A), tptp_fun_B_1(A)), A))))) | (~((~reflexive(A)) | ![B: $i] : ((~in(B, relation_field(A))) | in(ordered_pair(B, B), A)))))))) | ((~relation(relation_restriction(B!7, A!8))) | (~((~(reflexive(relation_restriction(B!7, A!8)) | (~((~in(tptp_fun_B_1(relation_restriction(B!7, A!8)), relation_field(relation_restriction(B!7, A!8)))) | in(ordered_pair(tptp_fun_B_1(relation_restriction(B!7, A!8)), tptp_fun_B_1(relation_restriction(B!7, A!8))), relation_restriction(B!7, A!8)))))) | (~((~reflexive(relation_restriction(B!7, A!8))) | ![B: $i] : ((~in(B, relation_field(relation_restriction(B!7, A!8)))) | in(ordered_pair(B, B), relation_restriction(B!7, A!8))))))))) <=> ((~![A: $i] : ((~relation(A)) | (~((~(reflexive(A) | (~((~in(tptp_fun_B_1(A), relation_field(A))) | in(ordered_pair(tptp_fun_B_1(A), tptp_fun_B_1(A)), A))))) | (~((~reflexive(A)) | ![B: $i] : ((~in(B, relation_field(A))) | in(ordered_pair(B, B), A)))))))) | (~relation(relation_restriction(B!7, A!8))) | (~((~(reflexive(relation_restriction(B!7, A!8)) | (~((~in(tptp_fun_B_1(relation_restriction(B!7, A!8)), relation_field(relation_restriction(B!7, A!8)))) | in(ordered_pair(tptp_fun_B_1(relation_restriction(B!7, A!8)), tptp_fun_B_1(relation_restriction(B!7, A!8))), relation_restriction(B!7, A!8)))))) | (~((~reflexive(relation_restriction(B!7, A!8))) | ![B: $i] : ((~in(B, relation_field(relation_restriction(B!7, A!8)))) | in(ordered_pair(B, B), relation_restriction(B!7, A!8))))))))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(49,plain,
% 0.13/0.40 ((~![A: $i] : ((~relation(A)) | (~((~(reflexive(A) | (~((~in(tptp_fun_B_1(A), relation_field(A))) | in(ordered_pair(tptp_fun_B_1(A), tptp_fun_B_1(A)), A))))) | (~((~reflexive(A)) | ![B: $i] : ((~in(B, relation_field(A))) | in(ordered_pair(B, B), A)))))))) | ((~relation(relation_restriction(B!7, A!8))) | (~((~(reflexive(relation_restriction(B!7, A!8)) | (~((~in(tptp_fun_B_1(relation_restriction(B!7, A!8)), relation_field(relation_restriction(B!7, A!8)))) | in(ordered_pair(tptp_fun_B_1(relation_restriction(B!7, A!8)), tptp_fun_B_1(relation_restriction(B!7, A!8))), relation_restriction(B!7, A!8)))))) | (~((~reflexive(relation_restriction(B!7, A!8))) | ![B: $i] : ((~in(B, relation_field(relation_restriction(B!7, A!8)))) | in(ordered_pair(B, B), relation_restriction(B!7, A!8))))))))),
% 0.13/0.40 inference(quant_inst,[status(thm)],[])).
% 0.13/0.40 tff(50,plain,
% 0.13/0.40 ((~![A: $i] : ((~relation(A)) | (~((~(reflexive(A) | (~((~in(tptp_fun_B_1(A), relation_field(A))) | in(ordered_pair(tptp_fun_B_1(A), tptp_fun_B_1(A)), A))))) | (~((~reflexive(A)) | ![B: $i] : ((~in(B, relation_field(A))) | in(ordered_pair(B, B), A)))))))) | (~relation(relation_restriction(B!7, A!8))) | (~((~(reflexive(relation_restriction(B!7, A!8)) | (~((~in(tptp_fun_B_1(relation_restriction(B!7, A!8)), relation_field(relation_restriction(B!7, A!8)))) | in(ordered_pair(tptp_fun_B_1(relation_restriction(B!7, A!8)), tptp_fun_B_1(relation_restriction(B!7, A!8))), relation_restriction(B!7, A!8)))))) | (~((~reflexive(relation_restriction(B!7, A!8))) | ![B: $i] : ((~in(B, relation_field(relation_restriction(B!7, A!8)))) | in(ordered_pair(B, B), relation_restriction(B!7, A!8)))))))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[49, 48])).
% 0.13/0.40 tff(51,plain,
% 0.13/0.40 (~((~(reflexive(relation_restriction(B!7, A!8)) | (~((~in(tptp_fun_B_1(relation_restriction(B!7, A!8)), relation_field(relation_restriction(B!7, A!8)))) | in(ordered_pair(tptp_fun_B_1(relation_restriction(B!7, A!8)), tptp_fun_B_1(relation_restriction(B!7, A!8))), relation_restriction(B!7, A!8)))))) | (~((~reflexive(relation_restriction(B!7, A!8))) | ![B: $i] : ((~in(B, relation_field(relation_restriction(B!7, A!8)))) | in(ordered_pair(B, B), relation_restriction(B!7, A!8))))))),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[50, 47, 28])).
% 0.13/0.40 tff(52,plain,
% 0.13/0.40 (((~(reflexive(relation_restriction(B!7, A!8)) | (~((~in(tptp_fun_B_1(relation_restriction(B!7, A!8)), relation_field(relation_restriction(B!7, A!8)))) | in(ordered_pair(tptp_fun_B_1(relation_restriction(B!7, A!8)), tptp_fun_B_1(relation_restriction(B!7, A!8))), relation_restriction(B!7, A!8)))))) | (~((~reflexive(relation_restriction(B!7, A!8))) | ![B: $i] : ((~in(B, relation_field(relation_restriction(B!7, A!8)))) | in(ordered_pair(B, B), relation_restriction(B!7, A!8)))))) | (reflexive(relation_restriction(B!7, A!8)) | (~((~in(tptp_fun_B_1(relation_restriction(B!7, A!8)), relation_field(relation_restriction(B!7, A!8)))) | in(ordered_pair(tptp_fun_B_1(relation_restriction(B!7, A!8)), tptp_fun_B_1(relation_restriction(B!7, A!8))), relation_restriction(B!7, A!8)))))),
% 0.13/0.40 inference(tautology,[status(thm)],[])).
% 0.13/0.40 tff(53,plain,
% 0.13/0.40 (reflexive(relation_restriction(B!7, A!8)) | (~((~in(tptp_fun_B_1(relation_restriction(B!7, A!8)), relation_field(relation_restriction(B!7, A!8)))) | in(ordered_pair(tptp_fun_B_1(relation_restriction(B!7, A!8)), tptp_fun_B_1(relation_restriction(B!7, A!8))), relation_restriction(B!7, A!8))))),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[52, 51])).
% 0.13/0.40 tff(54,plain,
% 0.13/0.40 (~reflexive(relation_restriction(B!7, A!8))),
% 0.13/0.40 inference(or_elim,[status(thm)],[13])).
% 0.13/0.40 tff(55,plain,
% 0.13/0.40 ((~(reflexive(relation_restriction(B!7, A!8)) | (~((~in(tptp_fun_B_1(relation_restriction(B!7, A!8)), relation_field(relation_restriction(B!7, A!8)))) | in(ordered_pair(tptp_fun_B_1(relation_restriction(B!7, A!8)), tptp_fun_B_1(relation_restriction(B!7, A!8))), relation_restriction(B!7, A!8)))))) | reflexive(relation_restriction(B!7, A!8)) | (~((~in(tptp_fun_B_1(relation_restriction(B!7, A!8)), relation_field(relation_restriction(B!7, A!8)))) | in(ordered_pair(tptp_fun_B_1(relation_restriction(B!7, A!8)), tptp_fun_B_1(relation_restriction(B!7, A!8))), relation_restriction(B!7, A!8))))),
% 0.13/0.40 inference(tautology,[status(thm)],[])).
% 0.13/0.40 tff(56,plain,
% 0.13/0.40 ((~(reflexive(relation_restriction(B!7, A!8)) | (~((~in(tptp_fun_B_1(relation_restriction(B!7, A!8)), relation_field(relation_restriction(B!7, A!8)))) | in(ordered_pair(tptp_fun_B_1(relation_restriction(B!7, A!8)), tptp_fun_B_1(relation_restriction(B!7, A!8))), relation_restriction(B!7, A!8)))))) | (~((~in(tptp_fun_B_1(relation_restriction(B!7, A!8)), relation_field(relation_restriction(B!7, A!8)))) | in(ordered_pair(tptp_fun_B_1(relation_restriction(B!7, A!8)), tptp_fun_B_1(relation_restriction(B!7, A!8))), relation_restriction(B!7, A!8))))),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[55, 54])).
% 0.13/0.40 tff(57,plain,
% 0.13/0.40 (~((~in(tptp_fun_B_1(relation_restriction(B!7, A!8)), relation_field(relation_restriction(B!7, A!8)))) | in(ordered_pair(tptp_fun_B_1(relation_restriction(B!7, A!8)), tptp_fun_B_1(relation_restriction(B!7, A!8))), relation_restriction(B!7, A!8)))),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[56, 53])).
% 0.13/0.40 tff(58,plain,
% 0.13/0.40 (((~in(tptp_fun_B_1(relation_restriction(B!7, A!8)), relation_field(relation_restriction(B!7, A!8)))) | in(ordered_pair(tptp_fun_B_1(relation_restriction(B!7, A!8)), tptp_fun_B_1(relation_restriction(B!7, A!8))), relation_restriction(B!7, A!8))) | in(tptp_fun_B_1(relation_restriction(B!7, A!8)), relation_field(relation_restriction(B!7, A!8)))),
% 0.13/0.40 inference(tautology,[status(thm)],[])).
% 0.13/0.40 tff(59,plain,
% 0.13/0.40 (in(tptp_fun_B_1(relation_restriction(B!7, A!8)), relation_field(relation_restriction(B!7, A!8)))),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[58, 57])).
% 0.13/0.40 tff(60,plain,
% 0.13/0.40 (^[A: $i, B: $i, C: $i] : refl(((~relation(C)) | (~in(A, relation_field(relation_restriction(C, B)))) | (~((~in(A, relation_field(C))) | (~in(A, B))))) <=> ((~relation(C)) | (~in(A, relation_field(relation_restriction(C, B)))) | (~((~in(A, relation_field(C))) | (~in(A, B))))))),
% 0.13/0.40 inference(bind,[status(th)],[])).
% 0.13/0.40 tff(61,plain,
% 0.13/0.40 (![A: $i, B: $i, C: $i] : ((~relation(C)) | (~in(A, relation_field(relation_restriction(C, B)))) | (~((~in(A, relation_field(C))) | (~in(A, B))))) <=> ![A: $i, B: $i, C: $i] : ((~relation(C)) | (~in(A, relation_field(relation_restriction(C, B)))) | (~((~in(A, relation_field(C))) | (~in(A, B)))))),
% 0.13/0.40 inference(quant_intro,[status(thm)],[60])).
% 0.13/0.40 tff(62,plain,
% 0.13/0.40 (^[A: $i, B: $i, C: $i] : trans(monotonicity(rewrite((in(A, relation_field(C)) & in(A, B)) <=> (~((~in(A, relation_field(C))) | (~in(A, B))))), (((in(A, relation_field(C)) & in(A, B)) | (~relation(C)) | (~in(A, relation_field(relation_restriction(C, B))))) <=> ((~((~in(A, relation_field(C))) | (~in(A, B)))) | (~relation(C)) | (~in(A, relation_field(relation_restriction(C, B))))))), rewrite(((~((~in(A, relation_field(C))) | (~in(A, B)))) | (~relation(C)) | (~in(A, relation_field(relation_restriction(C, B))))) <=> ((~relation(C)) | (~in(A, relation_field(relation_restriction(C, B)))) | (~((~in(A, relation_field(C))) | (~in(A, B)))))), (((in(A, relation_field(C)) & in(A, B)) | (~relation(C)) | (~in(A, relation_field(relation_restriction(C, B))))) <=> ((~relation(C)) | (~in(A, relation_field(relation_restriction(C, B)))) | (~((~in(A, relation_field(C))) | (~in(A, B)))))))),
% 0.13/0.40 inference(bind,[status(th)],[])).
% 0.13/0.40 tff(63,plain,
% 0.13/0.40 (![A: $i, B: $i, C: $i] : ((in(A, relation_field(C)) & in(A, B)) | (~relation(C)) | (~in(A, relation_field(relation_restriction(C, B))))) <=> ![A: $i, B: $i, C: $i] : ((~relation(C)) | (~in(A, relation_field(relation_restriction(C, B)))) | (~((~in(A, relation_field(C))) | (~in(A, B)))))),
% 0.13/0.40 inference(quant_intro,[status(thm)],[62])).
% 0.13/0.40 tff(64,plain,
% 0.13/0.40 (![A: $i, B: $i, C: $i] : ((in(A, relation_field(C)) & in(A, B)) | (~relation(C)) | (~in(A, relation_field(relation_restriction(C, B))))) <=> ![A: $i, B: $i, C: $i] : ((in(A, relation_field(C)) & in(A, B)) | (~relation(C)) | (~in(A, relation_field(relation_restriction(C, B)))))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(65,plain,
% 0.13/0.40 (^[A: $i, B: $i, C: $i] : trans(monotonicity(rewrite((in(A, relation_field(relation_restriction(C, B))) => (in(A, relation_field(C)) & in(A, B))) <=> ((~in(A, relation_field(relation_restriction(C, B)))) | (in(A, relation_field(C)) & in(A, B)))), ((relation(C) => (in(A, relation_field(relation_restriction(C, B))) => (in(A, relation_field(C)) & in(A, B)))) <=> (relation(C) => ((~in(A, relation_field(relation_restriction(C, B)))) | (in(A, relation_field(C)) & in(A, B)))))), rewrite((relation(C) => ((~in(A, relation_field(relation_restriction(C, B)))) | (in(A, relation_field(C)) & in(A, B)))) <=> ((in(A, relation_field(C)) & in(A, B)) | (~relation(C)) | (~in(A, relation_field(relation_restriction(C, B)))))), ((relation(C) => (in(A, relation_field(relation_restriction(C, B))) => (in(A, relation_field(C)) & in(A, B)))) <=> ((in(A, relation_field(C)) & in(A, B)) | (~relation(C)) | (~in(A, relation_field(relation_restriction(C, B)))))))),
% 0.13/0.40 inference(bind,[status(th)],[])).
% 0.13/0.40 tff(66,plain,
% 0.13/0.40 (![A: $i, B: $i, C: $i] : (relation(C) => (in(A, relation_field(relation_restriction(C, B))) => (in(A, relation_field(C)) & in(A, B)))) <=> ![A: $i, B: $i, C: $i] : ((in(A, relation_field(C)) & in(A, B)) | (~relation(C)) | (~in(A, relation_field(relation_restriction(C, B)))))),
% 0.13/0.40 inference(quant_intro,[status(thm)],[65])).
% 0.13/0.40 tff(67,axiom,(![A: $i, B: $i, C: $i] : (relation(C) => (in(A, relation_field(relation_restriction(C, B))) => (in(A, relation_field(C)) & in(A, B))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t19_wellord1')).
% 0.13/0.40 tff(68,plain,
% 0.13/0.40 (![A: $i, B: $i, C: $i] : ((in(A, relation_field(C)) & in(A, B)) | (~relation(C)) | (~in(A, relation_field(relation_restriction(C, B)))))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[67, 66])).
% 0.13/0.40 tff(69,plain,
% 0.13/0.40 (![A: $i, B: $i, C: $i] : ((in(A, relation_field(C)) & in(A, B)) | (~relation(C)) | (~in(A, relation_field(relation_restriction(C, B)))))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[68, 64])).
% 0.13/0.40 tff(70,plain,(
% 0.13/0.40 ![A: $i, B: $i, C: $i] : ((in(A, relation_field(C)) & in(A, B)) | (~relation(C)) | (~in(A, relation_field(relation_restriction(C, B)))))),
% 0.13/0.40 inference(skolemize,[status(sab)],[69])).
% 0.13/0.40 tff(71,plain,
% 0.13/0.40 (![A: $i, B: $i, C: $i] : ((~relation(C)) | (~in(A, relation_field(relation_restriction(C, B)))) | (~((~in(A, relation_field(C))) | (~in(A, B)))))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[70, 63])).
% 0.13/0.40 tff(72,plain,
% 0.13/0.40 (![A: $i, B: $i, C: $i] : ((~relation(C)) | (~in(A, relation_field(relation_restriction(C, B)))) | (~((~in(A, relation_field(C))) | (~in(A, B)))))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[71, 61])).
% 0.13/0.40 tff(73,plain,
% 0.13/0.40 (((~![A: $i, B: $i, C: $i] : ((~relation(C)) | (~in(A, relation_field(relation_restriction(C, B)))) | (~((~in(A, relation_field(C))) | (~in(A, B)))))) | ((~relation(B!7)) | (~in(tptp_fun_B_1(relation_restriction(B!7, A!8)), relation_field(relation_restriction(B!7, A!8)))) | (~((~in(tptp_fun_B_1(relation_restriction(B!7, A!8)), relation_field(B!7))) | (~in(tptp_fun_B_1(relation_restriction(B!7, A!8)), A!8)))))) <=> ((~![A: $i, B: $i, C: $i] : ((~relation(C)) | (~in(A, relation_field(relation_restriction(C, B)))) | (~((~in(A, relation_field(C))) | (~in(A, B)))))) | (~relation(B!7)) | (~in(tptp_fun_B_1(relation_restriction(B!7, A!8)), relation_field(relation_restriction(B!7, A!8)))) | (~((~in(tptp_fun_B_1(relation_restriction(B!7, A!8)), relation_field(B!7))) | (~in(tptp_fun_B_1(relation_restriction(B!7, A!8)), A!8)))))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(74,plain,
% 0.13/0.40 ((~![A: $i, B: $i, C: $i] : ((~relation(C)) | (~in(A, relation_field(relation_restriction(C, B)))) | (~((~in(A, relation_field(C))) | (~in(A, B)))))) | ((~relation(B!7)) | (~in(tptp_fun_B_1(relation_restriction(B!7, A!8)), relation_field(relation_restriction(B!7, A!8)))) | (~((~in(tptp_fun_B_1(relation_restriction(B!7, A!8)), relation_field(B!7))) | (~in(tptp_fun_B_1(relation_restriction(B!7, A!8)), A!8)))))),
% 0.13/0.40 inference(quant_inst,[status(thm)],[])).
% 0.13/0.40 tff(75,plain,
% 0.13/0.40 ((~![A: $i, B: $i, C: $i] : ((~relation(C)) | (~in(A, relation_field(relation_restriction(C, B)))) | (~((~in(A, relation_field(C))) | (~in(A, B)))))) | (~relation(B!7)) | (~in(tptp_fun_B_1(relation_restriction(B!7, A!8)), relation_field(relation_restriction(B!7, A!8)))) | (~((~in(tptp_fun_B_1(relation_restriction(B!7, A!8)), relation_field(B!7))) | (~in(tptp_fun_B_1(relation_restriction(B!7, A!8)), A!8))))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[74, 73])).
% 0.13/0.40 tff(76,plain,
% 0.13/0.40 (~((~in(tptp_fun_B_1(relation_restriction(B!7, A!8)), relation_field(B!7))) | (~in(tptp_fun_B_1(relation_restriction(B!7, A!8)), A!8)))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[75, 72, 14, 59])).
% 0.20/0.41 tff(77,plain,
% 0.20/0.41 (((~in(tptp_fun_B_1(relation_restriction(B!7, A!8)), relation_field(B!7))) | (~in(tptp_fun_B_1(relation_restriction(B!7, A!8)), A!8))) | in(tptp_fun_B_1(relation_restriction(B!7, A!8)), A!8)),
% 0.20/0.41 inference(tautology,[status(thm)],[])).
% 0.20/0.41 tff(78,plain,
% 0.20/0.41 (in(tptp_fun_B_1(relation_restriction(B!7, A!8)), A!8)),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[77, 76])).
% 0.20/0.41 tff(79,plain,
% 0.20/0.41 (^[A: $i, B: $i, C: $i] : refl(((~relation(C)) | (in(A, relation_restriction(C, B)) <=> (~((~in(A, C)) | (~in(A, cartesian_product2(B, B))))))) <=> ((~relation(C)) | (in(A, relation_restriction(C, B)) <=> (~((~in(A, C)) | (~in(A, cartesian_product2(B, B))))))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(80,plain,
% 0.20/0.41 (![A: $i, B: $i, C: $i] : ((~relation(C)) | (in(A, relation_restriction(C, B)) <=> (~((~in(A, C)) | (~in(A, cartesian_product2(B, B))))))) <=> ![A: $i, B: $i, C: $i] : ((~relation(C)) | (in(A, relation_restriction(C, B)) <=> (~((~in(A, C)) | (~in(A, cartesian_product2(B, B)))))))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[79])).
% 0.20/0.41 tff(81,plain,
% 0.20/0.41 (^[A: $i, B: $i, C: $i] : rewrite(((~relation(C)) | (in(A, relation_restriction(C, B)) <=> (in(A, C) & in(A, cartesian_product2(B, B))))) <=> ((~relation(C)) | (in(A, relation_restriction(C, B)) <=> (~((~in(A, C)) | (~in(A, cartesian_product2(B, B))))))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(82,plain,
% 0.20/0.41 (![A: $i, B: $i, C: $i] : ((~relation(C)) | (in(A, relation_restriction(C, B)) <=> (in(A, C) & in(A, cartesian_product2(B, B))))) <=> ![A: $i, B: $i, C: $i] : ((~relation(C)) | (in(A, relation_restriction(C, B)) <=> (~((~in(A, C)) | (~in(A, cartesian_product2(B, B)))))))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[81])).
% 0.20/0.41 tff(83,plain,
% 0.20/0.41 (![A: $i, B: $i, C: $i] : ((~relation(C)) | (in(A, relation_restriction(C, B)) <=> (in(A, C) & in(A, cartesian_product2(B, B))))) <=> ![A: $i, B: $i, C: $i] : ((~relation(C)) | (in(A, relation_restriction(C, B)) <=> (in(A, C) & in(A, cartesian_product2(B, B)))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(84,plain,
% 0.20/0.41 (^[A: $i, B: $i, C: $i] : rewrite((relation(C) => (in(A, relation_restriction(C, B)) <=> (in(A, C) & in(A, cartesian_product2(B, B))))) <=> ((~relation(C)) | (in(A, relation_restriction(C, B)) <=> (in(A, C) & in(A, cartesian_product2(B, B))))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(85,plain,
% 0.20/0.41 (![A: $i, B: $i, C: $i] : (relation(C) => (in(A, relation_restriction(C, B)) <=> (in(A, C) & in(A, cartesian_product2(B, B))))) <=> ![A: $i, B: $i, C: $i] : ((~relation(C)) | (in(A, relation_restriction(C, B)) <=> (in(A, C) & in(A, cartesian_product2(B, B)))))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[84])).
% 0.20/0.41 tff(86,axiom,(![A: $i, B: $i, C: $i] : (relation(C) => (in(A, relation_restriction(C, B)) <=> (in(A, C) & in(A, cartesian_product2(B, B)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t16_wellord1')).
% 0.20/0.41 tff(87,plain,
% 0.20/0.41 (![A: $i, B: $i, C: $i] : ((~relation(C)) | (in(A, relation_restriction(C, B)) <=> (in(A, C) & in(A, cartesian_product2(B, B)))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[86, 85])).
% 0.20/0.41 tff(88,plain,
% 0.20/0.41 (![A: $i, B: $i, C: $i] : ((~relation(C)) | (in(A, relation_restriction(C, B)) <=> (in(A, C) & in(A, cartesian_product2(B, B)))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[87, 83])).
% 0.20/0.41 tff(89,plain,(
% 0.20/0.41 ![A: $i, B: $i, C: $i] : ((~relation(C)) | (in(A, relation_restriction(C, B)) <=> (in(A, C) & in(A, cartesian_product2(B, B)))))),
% 0.20/0.41 inference(skolemize,[status(sab)],[88])).
% 0.20/0.41 tff(90,plain,
% 0.20/0.41 (![A: $i, B: $i, C: $i] : ((~relation(C)) | (in(A, relation_restriction(C, B)) <=> (~((~in(A, C)) | (~in(A, cartesian_product2(B, B)))))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[89, 82])).
% 0.20/0.41 tff(91,plain,
% 0.20/0.41 (![A: $i, B: $i, C: $i] : ((~relation(C)) | (in(A, relation_restriction(C, B)) <=> (~((~in(A, C)) | (~in(A, cartesian_product2(B, B)))))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[90, 80])).
% 0.20/0.41 tff(92,plain,
% 0.20/0.41 (((~![A: $i, B: $i, C: $i] : ((~relation(C)) | (in(A, relation_restriction(C, B)) <=> (~((~in(A, C)) | (~in(A, cartesian_product2(B, B)))))))) | ((~relation(B!7)) | (in(ordered_pair(tptp_fun_B_1(relation_restriction(B!7, A!8)), tptp_fun_B_1(relation_restriction(B!7, A!8))), relation_restriction(B!7, A!8)) <=> (~((~in(ordered_pair(tptp_fun_B_1(relation_restriction(B!7, A!8)), tptp_fun_B_1(relation_restriction(B!7, A!8))), B!7)) | (~in(ordered_pair(tptp_fun_B_1(relation_restriction(B!7, A!8)), tptp_fun_B_1(relation_restriction(B!7, A!8))), cartesian_product2(A!8, A!8)))))))) <=> ((~![A: $i, B: $i, C: $i] : ((~relation(C)) | (in(A, relation_restriction(C, B)) <=> (~((~in(A, C)) | (~in(A, cartesian_product2(B, B)))))))) | (~relation(B!7)) | (in(ordered_pair(tptp_fun_B_1(relation_restriction(B!7, A!8)), tptp_fun_B_1(relation_restriction(B!7, A!8))), relation_restriction(B!7, A!8)) <=> (~((~in(ordered_pair(tptp_fun_B_1(relation_restriction(B!7, A!8)), tptp_fun_B_1(relation_restriction(B!7, A!8))), B!7)) | (~in(ordered_pair(tptp_fun_B_1(relation_restriction(B!7, A!8)), tptp_fun_B_1(relation_restriction(B!7, A!8))), cartesian_product2(A!8, A!8)))))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(93,plain,
% 0.20/0.41 ((~![A: $i, B: $i, C: $i] : ((~relation(C)) | (in(A, relation_restriction(C, B)) <=> (~((~in(A, C)) | (~in(A, cartesian_product2(B, B)))))))) | ((~relation(B!7)) | (in(ordered_pair(tptp_fun_B_1(relation_restriction(B!7, A!8)), tptp_fun_B_1(relation_restriction(B!7, A!8))), relation_restriction(B!7, A!8)) <=> (~((~in(ordered_pair(tptp_fun_B_1(relation_restriction(B!7, A!8)), tptp_fun_B_1(relation_restriction(B!7, A!8))), B!7)) | (~in(ordered_pair(tptp_fun_B_1(relation_restriction(B!7, A!8)), tptp_fun_B_1(relation_restriction(B!7, A!8))), cartesian_product2(A!8, A!8)))))))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(94,plain,
% 0.20/0.41 ((~![A: $i, B: $i, C: $i] : ((~relation(C)) | (in(A, relation_restriction(C, B)) <=> (~((~in(A, C)) | (~in(A, cartesian_product2(B, B)))))))) | (~relation(B!7)) | (in(ordered_pair(tptp_fun_B_1(relation_restriction(B!7, A!8)), tptp_fun_B_1(relation_restriction(B!7, A!8))), relation_restriction(B!7, A!8)) <=> (~((~in(ordered_pair(tptp_fun_B_1(relation_restriction(B!7, A!8)), tptp_fun_B_1(relation_restriction(B!7, A!8))), B!7)) | (~in(ordered_pair(tptp_fun_B_1(relation_restriction(B!7, A!8)), tptp_fun_B_1(relation_restriction(B!7, A!8))), cartesian_product2(A!8, A!8))))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[93, 92])).
% 0.20/0.41 tff(95,plain,
% 0.20/0.41 (in(ordered_pair(tptp_fun_B_1(relation_restriction(B!7, A!8)), tptp_fun_B_1(relation_restriction(B!7, A!8))), relation_restriction(B!7, A!8)) <=> (~((~in(ordered_pair(tptp_fun_B_1(relation_restriction(B!7, A!8)), tptp_fun_B_1(relation_restriction(B!7, A!8))), B!7)) | (~in(ordered_pair(tptp_fun_B_1(relation_restriction(B!7, A!8)), tptp_fun_B_1(relation_restriction(B!7, A!8))), cartesian_product2(A!8, A!8)))))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[94, 91, 14])).
% 0.20/0.41 tff(96,plain,
% 0.20/0.41 (((~in(tptp_fun_B_1(relation_restriction(B!7, A!8)), relation_field(relation_restriction(B!7, A!8)))) | in(ordered_pair(tptp_fun_B_1(relation_restriction(B!7, A!8)), tptp_fun_B_1(relation_restriction(B!7, A!8))), relation_restriction(B!7, A!8))) | (~in(ordered_pair(tptp_fun_B_1(relation_restriction(B!7, A!8)), tptp_fun_B_1(relation_restriction(B!7, A!8))), relation_restriction(B!7, A!8)))),
% 0.20/0.41 inference(tautology,[status(thm)],[])).
% 0.20/0.41 tff(97,plain,
% 0.20/0.41 (~in(ordered_pair(tptp_fun_B_1(relation_restriction(B!7, A!8)), tptp_fun_B_1(relation_restriction(B!7, A!8))), relation_restriction(B!7, A!8))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[96, 57])).
% 0.20/0.41 tff(98,plain,
% 0.20/0.41 ((~(in(ordered_pair(tptp_fun_B_1(relation_restriction(B!7, A!8)), tptp_fun_B_1(relation_restriction(B!7, A!8))), relation_restriction(B!7, A!8)) <=> (~((~in(ordered_pair(tptp_fun_B_1(relation_restriction(B!7, A!8)), tptp_fun_B_1(relation_restriction(B!7, A!8))), B!7)) | (~in(ordered_pair(tptp_fun_B_1(relation_restriction(B!7, A!8)), tptp_fun_B_1(relation_restriction(B!7, A!8))), cartesian_product2(A!8, A!8))))))) | in(ordered_pair(tptp_fun_B_1(relation_restriction(B!7, A!8)), tptp_fun_B_1(relation_restriction(B!7, A!8))), relation_restriction(B!7, A!8)) | ((~in(ordered_pair(tptp_fun_B_1(relation_restriction(B!7, A!8)), tptp_fun_B_1(relation_restriction(B!7, A!8))), B!7)) | (~in(ordered_pair(tptp_fun_B_1(relation_restriction(B!7, A!8)), tptp_fun_B_1(relation_restriction(B!7, A!8))), cartesian_product2(A!8, A!8))))),
% 0.20/0.41 inference(tautology,[status(thm)],[])).
% 0.20/0.41 tff(99,plain,
% 0.20/0.41 ((~(in(ordered_pair(tptp_fun_B_1(relation_restriction(B!7, A!8)), tptp_fun_B_1(relation_restriction(B!7, A!8))), relation_restriction(B!7, A!8)) <=> (~((~in(ordered_pair(tptp_fun_B_1(relation_restriction(B!7, A!8)), tptp_fun_B_1(relation_restriction(B!7, A!8))), B!7)) | (~in(ordered_pair(tptp_fun_B_1(relation_restriction(B!7, A!8)), tptp_fun_B_1(relation_restriction(B!7, A!8))), cartesian_product2(A!8, A!8))))))) | ((~in(ordered_pair(tptp_fun_B_1(relation_restriction(B!7, A!8)), tptp_fun_B_1(relation_restriction(B!7, A!8))), B!7)) | (~in(ordered_pair(tptp_fun_B_1(relation_restriction(B!7, A!8)), tptp_fun_B_1(relation_restriction(B!7, A!8))), cartesian_product2(A!8, A!8))))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[98, 97])).
% 0.20/0.41 tff(100,plain,
% 0.20/0.41 ((~in(ordered_pair(tptp_fun_B_1(relation_restriction(B!7, A!8)), tptp_fun_B_1(relation_restriction(B!7, A!8))), B!7)) | (~in(ordered_pair(tptp_fun_B_1(relation_restriction(B!7, A!8)), tptp_fun_B_1(relation_restriction(B!7, A!8))), cartesian_product2(A!8, A!8)))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[99, 95])).
% 0.20/0.41 tff(101,plain,
% 0.20/0.41 (((~in(tptp_fun_B_1(relation_restriction(B!7, A!8)), relation_field(B!7))) | (~in(tptp_fun_B_1(relation_restriction(B!7, A!8)), A!8))) | in(tptp_fun_B_1(relation_restriction(B!7, A!8)), relation_field(B!7))),
% 0.20/0.41 inference(tautology,[status(thm)],[])).
% 0.20/0.41 tff(102,plain,
% 0.20/0.41 (in(tptp_fun_B_1(relation_restriction(B!7, A!8)), relation_field(B!7))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[101, 76])).
% 0.20/0.41 tff(103,plain,
% 0.20/0.41 (((~![A: $i] : ((~relation(A)) | (~((~(reflexive(A) | (~((~in(tptp_fun_B_1(A), relation_field(A))) | in(ordered_pair(tptp_fun_B_1(A), tptp_fun_B_1(A)), A))))) | (~((~reflexive(A)) | ![B: $i] : ((~in(B, relation_field(A))) | in(ordered_pair(B, B), A)))))))) | ((~relation(B!7)) | (~((~(reflexive(B!7) | (~((~in(tptp_fun_B_1(B!7), relation_field(B!7))) | in(ordered_pair(tptp_fun_B_1(B!7), tptp_fun_B_1(B!7)), B!7))))) | (~((~reflexive(B!7)) | ![B: $i] : ((~in(B, relation_field(B!7))) | in(ordered_pair(B, B), B!7)))))))) <=> ((~![A: $i] : ((~relation(A)) | (~((~(reflexive(A) | (~((~in(tptp_fun_B_1(A), relation_field(A))) | in(ordered_pair(tptp_fun_B_1(A), tptp_fun_B_1(A)), A))))) | (~((~reflexive(A)) | ![B: $i] : ((~in(B, relation_field(A))) | in(ordered_pair(B, B), A)))))))) | (~relation(B!7)) | (~((~(reflexive(B!7) | (~((~in(tptp_fun_B_1(B!7), relation_field(B!7))) | in(ordered_pair(tptp_fun_B_1(B!7), tptp_fun_B_1(B!7)), B!7))))) | (~((~reflexive(B!7)) | ![B: $i] : ((~in(B, relation_field(B!7))) | in(ordered_pair(B, B), B!7)))))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(104,plain,
% 0.20/0.41 ((~![A: $i] : ((~relation(A)) | (~((~(reflexive(A) | (~((~in(tptp_fun_B_1(A), relation_field(A))) | in(ordered_pair(tptp_fun_B_1(A), tptp_fun_B_1(A)), A))))) | (~((~reflexive(A)) | ![B: $i] : ((~in(B, relation_field(A))) | in(ordered_pair(B, B), A)))))))) | ((~relation(B!7)) | (~((~(reflexive(B!7) | (~((~in(tptp_fun_B_1(B!7), relation_field(B!7))) | in(ordered_pair(tptp_fun_B_1(B!7), tptp_fun_B_1(B!7)), B!7))))) | (~((~reflexive(B!7)) | ![B: $i] : ((~in(B, relation_field(B!7))) | in(ordered_pair(B, B), B!7)))))))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(105,plain,
% 0.20/0.41 ((~![A: $i] : ((~relation(A)) | (~((~(reflexive(A) | (~((~in(tptp_fun_B_1(A), relation_field(A))) | in(ordered_pair(tptp_fun_B_1(A), tptp_fun_B_1(A)), A))))) | (~((~reflexive(A)) | ![B: $i] : ((~in(B, relation_field(A))) | in(ordered_pair(B, B), A)))))))) | (~relation(B!7)) | (~((~(reflexive(B!7) | (~((~in(tptp_fun_B_1(B!7), relation_field(B!7))) | in(ordered_pair(tptp_fun_B_1(B!7), tptp_fun_B_1(B!7)), B!7))))) | (~((~reflexive(B!7)) | ![B: $i] : ((~in(B, relation_field(B!7))) | in(ordered_pair(B, B), B!7))))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[104, 103])).
% 0.20/0.42 tff(106,plain,
% 0.20/0.42 (~((~(reflexive(B!7) | (~((~in(tptp_fun_B_1(B!7), relation_field(B!7))) | in(ordered_pair(tptp_fun_B_1(B!7), tptp_fun_B_1(B!7)), B!7))))) | (~((~reflexive(B!7)) | ![B: $i] : ((~in(B, relation_field(B!7))) | in(ordered_pair(B, B), B!7)))))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[105, 47, 14])).
% 0.20/0.42 tff(107,plain,
% 0.20/0.42 (((~(reflexive(B!7) | (~((~in(tptp_fun_B_1(B!7), relation_field(B!7))) | in(ordered_pair(tptp_fun_B_1(B!7), tptp_fun_B_1(B!7)), B!7))))) | (~((~reflexive(B!7)) | ![B: $i] : ((~in(B, relation_field(B!7))) | in(ordered_pair(B, B), B!7))))) | ((~reflexive(B!7)) | ![B: $i] : ((~in(B, relation_field(B!7))) | in(ordered_pair(B, B), B!7)))),
% 0.20/0.42 inference(tautology,[status(thm)],[])).
% 0.20/0.42 tff(108,plain,
% 0.20/0.42 ((~reflexive(B!7)) | ![B: $i] : ((~in(B, relation_field(B!7))) | in(ordered_pair(B, B), B!7))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[107, 106])).
% 0.20/0.42 tff(109,plain,
% 0.20/0.42 (reflexive(B!7)),
% 0.20/0.42 inference(or_elim,[status(thm)],[13])).
% 0.20/0.42 tff(110,plain,
% 0.20/0.42 ((~((~reflexive(B!7)) | ![B: $i] : ((~in(B, relation_field(B!7))) | in(ordered_pair(B, B), B!7)))) | (~reflexive(B!7)) | ![B: $i] : ((~in(B, relation_field(B!7))) | in(ordered_pair(B, B), B!7))),
% 0.20/0.42 inference(tautology,[status(thm)],[])).
% 0.20/0.42 tff(111,plain,
% 0.20/0.42 ((~((~reflexive(B!7)) | ![B: $i] : ((~in(B, relation_field(B!7))) | in(ordered_pair(B, B), B!7)))) | ![B: $i] : ((~in(B, relation_field(B!7))) | in(ordered_pair(B, B), B!7))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[110, 109])).
% 0.20/0.42 tff(112,plain,
% 0.20/0.42 (![B: $i] : ((~in(B, relation_field(B!7))) | in(ordered_pair(B, B), B!7))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[111, 108])).
% 0.20/0.42 tff(113,plain,
% 0.20/0.42 (((~![B: $i] : ((~in(B, relation_field(B!7))) | in(ordered_pair(B, B), B!7))) | ((~in(tptp_fun_B_1(relation_restriction(B!7, A!8)), relation_field(B!7))) | in(ordered_pair(tptp_fun_B_1(relation_restriction(B!7, A!8)), tptp_fun_B_1(relation_restriction(B!7, A!8))), B!7))) <=> ((~![B: $i] : ((~in(B, relation_field(B!7))) | in(ordered_pair(B, B), B!7))) | (~in(tptp_fun_B_1(relation_restriction(B!7, A!8)), relation_field(B!7))) | in(ordered_pair(tptp_fun_B_1(relation_restriction(B!7, A!8)), tptp_fun_B_1(relation_restriction(B!7, A!8))), B!7))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(114,plain,
% 0.20/0.42 ((~![B: $i] : ((~in(B, relation_field(B!7))) | in(ordered_pair(B, B), B!7))) | ((~in(tptp_fun_B_1(relation_restriction(B!7, A!8)), relation_field(B!7))) | in(ordered_pair(tptp_fun_B_1(relation_restriction(B!7, A!8)), tptp_fun_B_1(relation_restriction(B!7, A!8))), B!7))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(115,plain,
% 0.20/0.42 ((~![B: $i] : ((~in(B, relation_field(B!7))) | in(ordered_pair(B, B), B!7))) | (~in(tptp_fun_B_1(relation_restriction(B!7, A!8)), relation_field(B!7))) | in(ordered_pair(tptp_fun_B_1(relation_restriction(B!7, A!8)), tptp_fun_B_1(relation_restriction(B!7, A!8))), B!7)),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[114, 113])).
% 0.20/0.42 tff(116,plain,
% 0.20/0.42 ((~in(tptp_fun_B_1(relation_restriction(B!7, A!8)), relation_field(B!7))) | in(ordered_pair(tptp_fun_B_1(relation_restriction(B!7, A!8)), tptp_fun_B_1(relation_restriction(B!7, A!8))), B!7)),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[115, 112])).
% 0.20/0.42 tff(117,plain,
% 0.20/0.42 (in(ordered_pair(tptp_fun_B_1(relation_restriction(B!7, A!8)), tptp_fun_B_1(relation_restriction(B!7, A!8))), B!7)),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[116, 102])).
% 0.20/0.42 tff(118,plain,
% 0.20/0.42 ((~((~in(ordered_pair(tptp_fun_B_1(relation_restriction(B!7, A!8)), tptp_fun_B_1(relation_restriction(B!7, A!8))), B!7)) | (~in(ordered_pair(tptp_fun_B_1(relation_restriction(B!7, A!8)), tptp_fun_B_1(relation_restriction(B!7, A!8))), cartesian_product2(A!8, A!8))))) | (~in(ordered_pair(tptp_fun_B_1(relation_restriction(B!7, A!8)), tptp_fun_B_1(relation_restriction(B!7, A!8))), B!7)) | (~in(ordered_pair(tptp_fun_B_1(relation_restriction(B!7, A!8)), tptp_fun_B_1(relation_restriction(B!7, A!8))), cartesian_product2(A!8, A!8)))),
% 0.20/0.42 inference(tautology,[status(thm)],[])).
% 0.20/0.42 tff(119,plain,
% 0.20/0.42 (~in(ordered_pair(tptp_fun_B_1(relation_restriction(B!7, A!8)), tptp_fun_B_1(relation_restriction(B!7, A!8))), cartesian_product2(A!8, A!8))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[118, 117, 100])).
% 0.20/0.42 tff(120,plain,
% 0.20/0.42 ((~(in(ordered_pair(tptp_fun_B_1(relation_restriction(B!7, A!8)), tptp_fun_B_1(relation_restriction(B!7, A!8))), cartesian_product2(A!8, A!8)) <=> in(tptp_fun_B_1(relation_restriction(B!7, A!8)), A!8))) | in(ordered_pair(tptp_fun_B_1(relation_restriction(B!7, A!8)), tptp_fun_B_1(relation_restriction(B!7, A!8))), cartesian_product2(A!8, A!8)) | (~in(tptp_fun_B_1(relation_restriction(B!7, A!8)), A!8))),
% 0.20/0.42 inference(tautology,[status(thm)],[])).
% 0.20/0.42 tff(121,plain,
% 0.20/0.42 (~(in(ordered_pair(tptp_fun_B_1(relation_restriction(B!7, A!8)), tptp_fun_B_1(relation_restriction(B!7, A!8))), cartesian_product2(A!8, A!8)) <=> in(tptp_fun_B_1(relation_restriction(B!7, A!8)), A!8))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[120, 119, 78])).
% 0.20/0.42 tff(122,plain,
% 0.20/0.42 (^[A: $i, B: $i, C: $i, D: $i] : refl((in(ordered_pair(A, B), cartesian_product2(C, D)) <=> (~((~in(A, C)) | (~in(B, D))))) <=> (in(ordered_pair(A, B), cartesian_product2(C, D)) <=> (~((~in(A, C)) | (~in(B, D))))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(123,plain,
% 0.20/0.42 (![A: $i, B: $i, C: $i, D: $i] : (in(ordered_pair(A, B), cartesian_product2(C, D)) <=> (~((~in(A, C)) | (~in(B, D))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (in(ordered_pair(A, B), cartesian_product2(C, D)) <=> (~((~in(A, C)) | (~in(B, D)))))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[122])).
% 0.20/0.42 tff(124,plain,
% 0.20/0.42 (^[A: $i, B: $i, C: $i, D: $i] : rewrite((in(ordered_pair(A, B), cartesian_product2(C, D)) <=> (in(A, C) & in(B, D))) <=> (in(ordered_pair(A, B), cartesian_product2(C, D)) <=> (~((~in(A, C)) | (~in(B, D))))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(125,plain,
% 0.20/0.42 (![A: $i, B: $i, C: $i, D: $i] : (in(ordered_pair(A, B), cartesian_product2(C, D)) <=> (in(A, C) & in(B, D))) <=> ![A: $i, B: $i, C: $i, D: $i] : (in(ordered_pair(A, B), cartesian_product2(C, D)) <=> (~((~in(A, C)) | (~in(B, D)))))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[124])).
% 0.20/0.42 tff(126,plain,
% 0.20/0.42 (![A: $i, B: $i, C: $i, D: $i] : (in(ordered_pair(A, B), cartesian_product2(C, D)) <=> (in(A, C) & in(B, D))) <=> ![A: $i, B: $i, C: $i, D: $i] : (in(ordered_pair(A, B), cartesian_product2(C, D)) <=> (in(A, C) & in(B, D)))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(127,axiom,(![A: $i, B: $i, C: $i, D: $i] : (in(ordered_pair(A, B), cartesian_product2(C, D)) <=> (in(A, C) & in(B, D)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t106_zfmisc_1')).
% 0.20/0.42 tff(128,plain,
% 0.20/0.42 (![A: $i, B: $i, C: $i, D: $i] : (in(ordered_pair(A, B), cartesian_product2(C, D)) <=> (in(A, C) & in(B, D)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[127, 126])).
% 0.20/0.42 tff(129,plain,(
% 0.20/0.42 ![A: $i, B: $i, C: $i, D: $i] : (in(ordered_pair(A, B), cartesian_product2(C, D)) <=> (in(A, C) & in(B, D)))),
% 0.20/0.42 inference(skolemize,[status(sab)],[128])).
% 0.20/0.42 tff(130,plain,
% 0.20/0.42 (![A: $i, B: $i, C: $i, D: $i] : (in(ordered_pair(A, B), cartesian_product2(C, D)) <=> (~((~in(A, C)) | (~in(B, D)))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[129, 125])).
% 0.20/0.42 tff(131,plain,
% 0.20/0.42 (![A: $i, B: $i, C: $i, D: $i] : (in(ordered_pair(A, B), cartesian_product2(C, D)) <=> (~((~in(A, C)) | (~in(B, D)))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[130, 123])).
% 0.20/0.42 tff(132,plain,
% 0.20/0.42 (((~![A: $i, B: $i, C: $i, D: $i] : (in(ordered_pair(A, B), cartesian_product2(C, D)) <=> (~((~in(A, C)) | (~in(B, D)))))) | (in(ordered_pair(tptp_fun_B_1(relation_restriction(B!7, A!8)), tptp_fun_B_1(relation_restriction(B!7, A!8))), cartesian_product2(A!8, A!8)) <=> in(tptp_fun_B_1(relation_restriction(B!7, A!8)), A!8))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (in(ordered_pair(A, B), cartesian_product2(C, D)) <=> (~((~in(A, C)) | (~in(B, D)))))) | (in(ordered_pair(tptp_fun_B_1(relation_restriction(B!7, A!8)), tptp_fun_B_1(relation_restriction(B!7, A!8))), cartesian_product2(A!8, A!8)) <=> in(tptp_fun_B_1(relation_restriction(B!7, A!8)), A!8)))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(133,plain,
% 0.20/0.42 ((in(ordered_pair(tptp_fun_B_1(relation_restriction(B!7, A!8)), tptp_fun_B_1(relation_restriction(B!7, A!8))), cartesian_product2(A!8, A!8)) <=> (~((~in(tptp_fun_B_1(relation_restriction(B!7, A!8)), A!8)) | (~in(tptp_fun_B_1(relation_restriction(B!7, A!8)), A!8))))) <=> (in(ordered_pair(tptp_fun_B_1(relation_restriction(B!7, A!8)), tptp_fun_B_1(relation_restriction(B!7, A!8))), cartesian_product2(A!8, A!8)) <=> in(tptp_fun_B_1(relation_restriction(B!7, A!8)), A!8))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(134,plain,
% 0.20/0.42 (((~![A: $i, B: $i, C: $i, D: $i] : (in(ordered_pair(A, B), cartesian_product2(C, D)) <=> (~((~in(A, C)) | (~in(B, D)))))) | (in(ordered_pair(tptp_fun_B_1(relation_restriction(B!7, A!8)), tptp_fun_B_1(relation_restriction(B!7, A!8))), cartesian_product2(A!8, A!8)) <=> (~((~in(tptp_fun_B_1(relation_restriction(B!7, A!8)), A!8)) | (~in(tptp_fun_B_1(relation_restriction(B!7, A!8)), A!8)))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (in(ordered_pair(A, B), cartesian_product2(C, D)) <=> (~((~in(A, C)) | (~in(B, D)))))) | (in(ordered_pair(tptp_fun_B_1(relation_restriction(B!7, A!8)), tptp_fun_B_1(relation_restriction(B!7, A!8))), cartesian_product2(A!8, A!8)) <=> in(tptp_fun_B_1(relation_restriction(B!7, A!8)), A!8)))),
% 0.20/0.42 inference(monotonicity,[status(thm)],[133])).
% 0.20/0.42 tff(135,plain,
% 0.20/0.42 (((~![A: $i, B: $i, C: $i, D: $i] : (in(ordered_pair(A, B), cartesian_product2(C, D)) <=> (~((~in(A, C)) | (~in(B, D)))))) | (in(ordered_pair(tptp_fun_B_1(relation_restriction(B!7, A!8)), tptp_fun_B_1(relation_restriction(B!7, A!8))), cartesian_product2(A!8, A!8)) <=> (~((~in(tptp_fun_B_1(relation_restriction(B!7, A!8)), A!8)) | (~in(tptp_fun_B_1(relation_restriction(B!7, A!8)), A!8)))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (in(ordered_pair(A, B), cartesian_product2(C, D)) <=> (~((~in(A, C)) | (~in(B, D)))))) | (in(ordered_pair(tptp_fun_B_1(relation_restriction(B!7, A!8)), tptp_fun_B_1(relation_restriction(B!7, A!8))), cartesian_product2(A!8, A!8)) <=> in(tptp_fun_B_1(relation_restriction(B!7, A!8)), A!8)))),
% 0.20/0.42 inference(transitivity,[status(thm)],[134, 132])).
% 0.20/0.42 tff(136,plain,
% 0.20/0.42 ((~![A: $i, B: $i, C: $i, D: $i] : (in(ordered_pair(A, B), cartesian_product2(C, D)) <=> (~((~in(A, C)) | (~in(B, D)))))) | (in(ordered_pair(tptp_fun_B_1(relation_restriction(B!7, A!8)), tptp_fun_B_1(relation_restriction(B!7, A!8))), cartesian_product2(A!8, A!8)) <=> (~((~in(tptp_fun_B_1(relation_restriction(B!7, A!8)), A!8)) | (~in(tptp_fun_B_1(relation_restriction(B!7, A!8)), A!8)))))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(137,plain,
% 0.20/0.42 ((~![A: $i, B: $i, C: $i, D: $i] : (in(ordered_pair(A, B), cartesian_product2(C, D)) <=> (~((~in(A, C)) | (~in(B, D)))))) | (in(ordered_pair(tptp_fun_B_1(relation_restriction(B!7, A!8)), tptp_fun_B_1(relation_restriction(B!7, A!8))), cartesian_product2(A!8, A!8)) <=> in(tptp_fun_B_1(relation_restriction(B!7, A!8)), A!8))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[136, 135])).
% 0.20/0.42 tff(138,plain,
% 0.20/0.42 ($false),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[137, 131, 121])).
% 0.20/0.42 % SZS output end Proof
%------------------------------------------------------------------------------