%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SEU252+1 : TPTP v9.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n003.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:27:24 AM UTC 2025
% Result : Theorem 0.13s 0.39s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SEU252+1 : TPTP v9.0.0. Released v3.3.0.
% 0.07/0.13 % Command : run_E %s %d THM
% 0.13/0.35 % Computer : n003.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Fri Jun 20 06:29:39 EDT 2025
% 0.13/0.35 % CPUTime :
% 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(cartesian_product2_type, type, (
% 0.13/0.39 cartesian_product2: ( $i * $i ) > $i)).
% 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(ordered_pair_type, type, (
% 0.13/0.39 ordered_pair: ( $i * $i ) > $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(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/sandbox/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 ~(reflexive(relation_restriction(B!7, A!8)) | (~relation(B!7)) | (~reflexive(B!7)))),
% 0.13/0.39 inference(skolemize,[status(sab)],[8])).
% 0.13/0.39 tff(10,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)],[9, 1])).
% 0.13/0.39 tff(11,plain,
% 0.13/0.39 (relation(B!7)),
% 0.13/0.39 inference(or_elim,[status(thm)],[10])).
% 0.13/0.39 tff(12,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(13,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)],[12])).
% 0.13/0.39 tff(14,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(15,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(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,axiom,(![A: $i, B: $i] : (relation(A) => relation(relation_restriction(A, B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_k2_wellord1')).
% 0.13/0.39 tff(18,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)],[17, 16])).
% 0.13/0.39 tff(19,plain,
% 0.13/0.39 (![A: $i, B: $i] : ((~relation(A)) | relation(relation_restriction(A, B)))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[18, 14])).
% 0.13/0.40 tff(20,plain,(
% 0.13/0.40 ![A: $i, B: $i] : ((~relation(A)) | relation(relation_restriction(A, B)))),
% 0.13/0.40 inference(skolemize,[status(sab)],[19])).
% 0.13/0.40 tff(21,plain,
% 0.13/0.40 (![A: $i, B: $i] : ((~relation(A)) | relation(relation_restriction(A, B)))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[20, 13])).
% 0.13/0.40 tff(22,plain,
% 0.13/0.40 (((~![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)))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(23,plain,
% 0.13/0.40 ((~![A: $i, B: $i] : ((~relation(A)) | relation(relation_restriction(A, B)))) | ((~relation(B!7)) | relation(relation_restriction(B!7, A!8)))),
% 0.13/0.40 inference(quant_inst,[status(thm)],[])).
% 0.13/0.40 tff(24,plain,
% 0.13/0.40 ((~![A: $i, B: $i] : ((~relation(A)) | relation(relation_restriction(A, B)))) | (~relation(B!7)) | relation(relation_restriction(B!7, A!8))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[23, 22])).
% 0.13/0.40 tff(25,plain,
% 0.13/0.40 (relation(relation_restriction(B!7, A!8))),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[24, 21, 11])).
% 0.13/0.40 tff(26,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) | (~((~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(bind,[status(th)],[])).
% 0.13/0.40 tff(27,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) | (~((~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(quant_intro,[status(thm)],[26])).
% 0.13/0.40 tff(28,plain,
% 0.13/0.40 (^[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)))))))))),
% 0.13/0.40 inference(bind,[status(th)],[])).
% 0.13/0.40 tff(29,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)],[28])).
% 0.13/0.40 tff(30,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(31,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)],[30])).
% 0.13/0.40 tff(32,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)],[31, 29])).
% 0.13/0.40 tff(33,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(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)))) <=> ![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(36,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(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)))) <=> ![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)],[36])).
% 0.13/0.40 tff(38,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')).
% 0.13/0.40 tff(39,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)],[38, 37])).
% 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))))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[39, 35])).
% 0.13/0.40 tff(41,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)],[40])).
% 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)))) | (~(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)],[41, 34])).
% 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)))) | (~(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)],[42, 32])).
% 0.13/0.40 tff(44,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)],[43, 27])).
% 0.13/0.40 tff(45,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(46,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(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)))))))) | (~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)],[46, 45])).
% 0.13/0.40 tff(48,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)],[47, 44, 25])).
% 0.13/0.40 tff(49,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(50,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)],[49, 48])).
% 0.13/0.40 tff(51,plain,
% 0.13/0.40 (~reflexive(relation_restriction(B!7, A!8))),
% 0.13/0.40 inference(or_elim,[status(thm)],[10])).
% 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)) | (~((~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)))))) | (~((~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 (~((~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)],[53, 50])).
% 0.13/0.40 tff(55,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(56,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)],[55, 54])).
% 0.13/0.40 tff(57,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(58,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)],[57])).
% 0.13/0.40 tff(59,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(60,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)],[59])).
% 0.13/0.40 tff(61,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)))))),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(62,plain,
% 0.13/0.41 (^[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)))))))),
% 0.13/0.41 inference(bind,[status(th)],[])).
% 0.13/0.41 tff(63,plain,
% 0.13/0.41 (![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)))))),
% 0.13/0.41 inference(quant_intro,[status(thm)],[62])).
% 0.13/0.41 tff(64,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/sandbox/benchmark/theBenchmark.p','t19_wellord1')).
% 0.13/0.41 tff(65,plain,
% 0.13/0.41 (![A: $i, B: $i, C: $i] : ((in(A, relation_field(C)) & in(A, B)) | (~relation(C)) | (~in(A, relation_field(relation_restriction(C, B)))))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[64, 63])).
% 0.13/0.41 tff(66,plain,
% 0.13/0.41 (![A: $i, B: $i, C: $i] : ((in(A, relation_field(C)) & in(A, B)) | (~relation(C)) | (~in(A, relation_field(relation_restriction(C, B)))))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[65, 61])).
% 0.13/0.41 tff(67,plain,(
% 0.13/0.41 ![A: $i, B: $i, C: $i] : ((in(A, relation_field(C)) & in(A, B)) | (~relation(C)) | (~in(A, relation_field(relation_restriction(C, B)))))),
% 0.13/0.41 inference(skolemize,[status(sab)],[66])).
% 0.13/0.41 tff(68,plain,
% 0.13/0.41 (![A: $i, B: $i, C: $i] : ((~relation(C)) | (~in(A, relation_field(relation_restriction(C, B)))) | (~((~in(A, relation_field(C))) | (~in(A, B)))))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[67, 60])).
% 0.13/0.41 tff(69,plain,
% 0.13/0.41 (![A: $i, B: $i, C: $i] : ((~relation(C)) | (~in(A, relation_field(relation_restriction(C, B)))) | (~((~in(A, relation_field(C))) | (~in(A, B)))))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[68, 58])).
% 0.13/0.41 tff(70,plain,
% 0.13/0.41 (((~![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)))))),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(71,plain,
% 0.13/0.41 ((~![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)))))),
% 0.13/0.41 inference(quant_inst,[status(thm)],[])).
% 0.13/0.41 tff(72,plain,
% 0.13/0.41 ((~![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))))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[71, 70])).
% 0.13/0.41 tff(73,plain,
% 0.13/0.41 (~((~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)))),
% 0.13/0.41 inference(unit_resolution,[status(thm)],[72, 69, 11, 56])).
% 0.13/0.41 tff(74,plain,
% 0.13/0.41 (((~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)),
% 0.13/0.41 inference(tautology,[status(thm)],[])).
% 0.13/0.41 tff(75,plain,
% 0.13/0.41 (in(tptp_fun_B_1(relation_restriction(B!7, A!8)), A!8)),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[74, 73])).
% 0.21/0.41 tff(76,plain,
% 0.21/0.41 (^[A: $i, B: $i, C: $i] : refl(((~relation(C)) | (~(((~in(A, C)) | (~in(A, cartesian_product2(B, B)))) <=> in(A, relation_restriction(C, B))))) <=> ((~relation(C)) | (~(((~in(A, C)) | (~in(A, cartesian_product2(B, B)))) <=> in(A, relation_restriction(C, B))))))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(77,plain,
% 0.21/0.41 (![A: $i, B: $i, C: $i] : ((~relation(C)) | (~(((~in(A, C)) | (~in(A, cartesian_product2(B, B)))) <=> in(A, relation_restriction(C, B))))) <=> ![A: $i, B: $i, C: $i] : ((~relation(C)) | (~(((~in(A, C)) | (~in(A, cartesian_product2(B, B)))) <=> in(A, relation_restriction(C, B)))))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[76])).
% 0.21/0.41 tff(78,plain,
% 0.21/0.41 (^[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, C)) | (~in(A, cartesian_product2(B, B)))) <=> in(A, relation_restriction(C, B))))))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(79,plain,
% 0.21/0.41 (![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, C)) | (~in(A, cartesian_product2(B, B)))) <=> in(A, relation_restriction(C, B)))))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[78])).
% 0.21/0.41 tff(80,plain,
% 0.21/0.41 (![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)))))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(81,plain,
% 0.21/0.41 (^[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))))))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(82,plain,
% 0.21/0.41 (![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)))))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[81])).
% 0.21/0.41 tff(83,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/sandbox/benchmark/theBenchmark.p','t16_wellord1')).
% 0.21/0.41 tff(84,plain,
% 0.21/0.41 (![A: $i, B: $i, C: $i] : ((~relation(C)) | (in(A, relation_restriction(C, B)) <=> (in(A, C) & in(A, cartesian_product2(B, B)))))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[83, 82])).
% 0.21/0.41 tff(85,plain,
% 0.21/0.41 (![A: $i, B: $i, C: $i] : ((~relation(C)) | (in(A, relation_restriction(C, B)) <=> (in(A, C) & in(A, cartesian_product2(B, B)))))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[84, 80])).
% 0.21/0.41 tff(86,plain,(
% 0.21/0.41 ![A: $i, B: $i, C: $i] : ((~relation(C)) | (in(A, relation_restriction(C, B)) <=> (in(A, C) & in(A, cartesian_product2(B, B)))))),
% 0.21/0.41 inference(skolemize,[status(sab)],[85])).
% 0.21/0.41 tff(87,plain,
% 0.21/0.41 (![A: $i, B: $i, C: $i] : ((~relation(C)) | (~(((~in(A, C)) | (~in(A, cartesian_product2(B, B)))) <=> in(A, relation_restriction(C, B)))))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[86, 79])).
% 0.21/0.41 tff(88,plain,
% 0.21/0.41 (![A: $i, B: $i, C: $i] : ((~relation(C)) | (~(((~in(A, C)) | (~in(A, cartesian_product2(B, B)))) <=> in(A, relation_restriction(C, B)))))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[87, 77])).
% 0.21/0.41 tff(89,plain,
% 0.21/0.41 (((~![A: $i, B: $i, C: $i] : ((~relation(C)) | (~(((~in(A, C)) | (~in(A, cartesian_product2(B, B)))) <=> in(A, relation_restriction(C, 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))), 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)))))) <=> ((~![A: $i, B: $i, C: $i] : ((~relation(C)) | (~(((~in(A, C)) | (~in(A, cartesian_product2(B, B)))) <=> in(A, relation_restriction(C, 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))), 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)))))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(90,plain,
% 0.21/0.41 ((~![A: $i, B: $i, C: $i] : ((~relation(C)) | (~(((~in(A, C)) | (~in(A, cartesian_product2(B, B)))) <=> in(A, relation_restriction(C, 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))), 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)))))),
% 0.21/0.41 inference(quant_inst,[status(thm)],[])).
% 0.21/0.41 tff(91,plain,
% 0.21/0.41 ((~![A: $i, B: $i, C: $i] : ((~relation(C)) | (~(((~in(A, C)) | (~in(A, cartesian_product2(B, B)))) <=> in(A, relation_restriction(C, 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))), 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))))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[90, 89])).
% 0.21/0.41 tff(92,plain,
% 0.21/0.41 (~(((~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)))) <=> 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)))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[91, 88, 11])).
% 0.21/0.41 tff(93,plain,
% 0.21/0.41 (((~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)))),
% 0.21/0.41 inference(tautology,[status(thm)],[])).
% 0.21/0.41 tff(94,plain,
% 0.21/0.41 (~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))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[93, 54])).
% 0.21/0.41 tff(95,plain,
% 0.21/0.41 ((((~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)))) <=> 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))),
% 0.21/0.41 inference(tautology,[status(thm)],[])).
% 0.21/0.41 tff(96,plain,
% 0.21/0.41 ((((~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)))) <=> 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))))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[95, 94])).
% 0.21/0.41 tff(97,plain,
% 0.21/0.41 ((~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)))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[96, 92])).
% 0.21/0.42 tff(98,plain,
% 0.21/0.42 (((~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))),
% 0.21/0.42 inference(tautology,[status(thm)],[])).
% 0.21/0.42 tff(99,plain,
% 0.21/0.42 (in(tptp_fun_B_1(relation_restriction(B!7, A!8)), relation_field(B!7))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[98, 73])).
% 0.21/0.42 tff(100,plain,
% 0.21/0.42 (((~![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)))))))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(101,plain,
% 0.21/0.42 ((~![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)))))))),
% 0.21/0.42 inference(quant_inst,[status(thm)],[])).
% 0.21/0.42 tff(102,plain,
% 0.21/0.42 ((~![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))))))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[101, 100])).
% 0.21/0.42 tff(103,plain,
% 0.21/0.42 (~((~(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)))))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[102, 44, 11])).
% 0.21/0.42 tff(104,plain,
% 0.21/0.42 (((~(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)))),
% 0.21/0.42 inference(tautology,[status(thm)],[])).
% 0.21/0.42 tff(105,plain,
% 0.21/0.42 ((~reflexive(B!7)) | ![B: $i] : ((~in(B, relation_field(B!7))) | in(ordered_pair(B, B), B!7))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[104, 103])).
% 0.21/0.42 tff(106,plain,
% 0.21/0.42 (reflexive(B!7)),
% 0.21/0.42 inference(or_elim,[status(thm)],[10])).
% 0.21/0.42 tff(107,plain,
% 0.21/0.42 ((~((~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))),
% 0.21/0.42 inference(tautology,[status(thm)],[])).
% 0.21/0.42 tff(108,plain,
% 0.21/0.42 ((~((~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))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[107, 106])).
% 0.21/0.42 tff(109,plain,
% 0.21/0.42 (![B: $i] : ((~in(B, relation_field(B!7))) | in(ordered_pair(B, B), B!7))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[108, 105])).
% 0.21/0.42 tff(110,plain,
% 0.21/0.42 (((~![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))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(111,plain,
% 0.21/0.42 ((~![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))),
% 0.21/0.42 inference(quant_inst,[status(thm)],[])).
% 0.21/0.42 tff(112,plain,
% 0.21/0.42 ((~![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)),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[111, 110])).
% 0.21/0.42 tff(113,plain,
% 0.21/0.42 ((~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)),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[112, 109])).
% 0.21/0.42 tff(114,plain,
% 0.21/0.42 (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)),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[113, 99])).
% 0.21/0.42 tff(115,plain,
% 0.21/0.42 ((~((~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)))),
% 0.21/0.42 inference(tautology,[status(thm)],[])).
% 0.21/0.42 tff(116,plain,
% 0.21/0.42 (~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))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[115, 114, 97])).
% 0.21/0.42 tff(117,plain,
% 0.21/0.42 ((~(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)) | 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))),
% 0.21/0.42 inference(tautology,[status(thm)],[])).
% 0.21/0.42 tff(118,plain,
% 0.21/0.42 (~(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)))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[117, 116, 75])).
% 0.21/0.42 tff(119,plain,
% 0.21/0.42 (^[A: $i, B: $i, C: $i, D: $i] : refl((~(((~in(A, C)) | (~in(B, D))) <=> in(ordered_pair(A, B), cartesian_product2(C, D)))) <=> (~(((~in(A, C)) | (~in(B, D))) <=> in(ordered_pair(A, B), cartesian_product2(C, D)))))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(120,plain,
% 0.21/0.42 (![A: $i, B: $i, C: $i, D: $i] : (~(((~in(A, C)) | (~in(B, D))) <=> in(ordered_pair(A, B), cartesian_product2(C, D)))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~(((~in(A, C)) | (~in(B, D))) <=> in(ordered_pair(A, B), cartesian_product2(C, D))))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[119])).
% 0.21/0.42 tff(121,plain,
% 0.21/0.42 (^[A: $i, B: $i, C: $i, D: $i] : trans(trans(monotonicity(rewrite((in(A, C) & in(B, D)) <=> (~((~in(A, C)) | (~in(B, D))))), ((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))))))), rewrite((in(ordered_pair(A, B), cartesian_product2(C, D)) <=> (~((~in(A, C)) | (~in(B, D))))) <=> (~(((~in(A, C)) | (~in(B, D))) <=> in(ordered_pair(A, B), cartesian_product2(C, D))))), ((in(ordered_pair(A, B), cartesian_product2(C, D)) <=> (in(A, C) & in(B, D))) <=> (~(((~in(A, C)) | (~in(B, D))) <=> in(ordered_pair(A, B), cartesian_product2(C, D)))))), rewrite((~(((~in(A, C)) | (~in(B, D))) <=> 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(ordered_pair(A, B), cartesian_product2(C, D)) <=> (in(A, C) & in(B, D))) <=> (~(((~in(A, C)) | (~in(B, D))) <=> in(ordered_pair(A, B), cartesian_product2(C, D))))))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(122,plain,
% 0.21/0.42 (![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(A, C)) | (~in(B, D))) <=> in(ordered_pair(A, B), cartesian_product2(C, D))))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[121])).
% 0.21/0.42 tff(123,plain,
% 0.21/0.42 (![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)))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(124,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/sandbox/benchmark/theBenchmark.p','t106_zfmisc_1')).
% 0.21/0.42 tff(125,plain,
% 0.21/0.42 (![A: $i, B: $i, C: $i, D: $i] : (in(ordered_pair(A, B), cartesian_product2(C, D)) <=> (in(A, C) & in(B, D)))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[124, 123])).
% 0.21/0.42 tff(126,plain,(
% 0.21/0.42 ![A: $i, B: $i, C: $i, D: $i] : (in(ordered_pair(A, B), cartesian_product2(C, D)) <=> (in(A, C) & in(B, D)))),
% 0.21/0.42 inference(skolemize,[status(sab)],[125])).
% 0.21/0.42 tff(127,plain,
% 0.21/0.42 (![A: $i, B: $i, C: $i, D: $i] : (~(((~in(A, C)) | (~in(B, D))) <=> in(ordered_pair(A, B), cartesian_product2(C, D))))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[126, 122])).
% 0.21/0.42 tff(128,plain,
% 0.21/0.42 (![A: $i, B: $i, C: $i, D: $i] : (~(((~in(A, C)) | (~in(B, D))) <=> in(ordered_pair(A, B), cartesian_product2(C, D))))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[127, 120])).
% 0.21/0.42 tff(129,plain,
% 0.21/0.42 (((~![A: $i, B: $i, C: $i, D: $i] : (~(((~in(A, C)) | (~in(B, D))) <=> in(ordered_pair(A, B), cartesian_product2(C, D))))) | (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)))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (~(((~in(A, C)) | (~in(B, D))) <=> in(ordered_pair(A, B), cartesian_product2(C, D))))) | (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))))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(130,plain,
% 0.21/0.42 ((~(~(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) <=> 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)))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(131,plain,
% 0.21/0.42 ((~(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) <=> 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))))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(132,plain,
% 0.21/0.42 (((~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) <=> 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))))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(133,plain,
% 0.21/0.42 (((~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(tptp_fun_B_1(relation_restriction(B!7, A!8)), A!8))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(134,plain,
% 0.21/0.42 ((((~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)) <=> 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)))),
% 0.21/0.42 inference(monotonicity,[status(thm)],[133])).
% 0.21/0.42 tff(135,plain,
% 0.21/0.42 ((((~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) <=> 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))))),
% 0.21/0.42 inference(transitivity,[status(thm)],[134, 132])).
% 0.21/0.42 tff(136,plain,
% 0.21/0.42 ((((~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) <=> 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))))),
% 0.21/0.42 inference(transitivity,[status(thm)],[135, 131])).
% 0.21/0.42 tff(137,plain,
% 0.21/0.42 ((~(((~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) <=> 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)))))),
% 0.21/0.43 inference(monotonicity,[status(thm)],[136])).
% 0.21/0.43 tff(138,plain,
% 0.21/0.43 ((~(((~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) <=> 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)))),
% 0.21/0.43 inference(transitivity,[status(thm)],[137, 130])).
% 0.21/0.43 tff(139,plain,
% 0.21/0.43 (((~![A: $i, B: $i, C: $i, D: $i] : (~(((~in(A, C)) | (~in(B, D))) <=> in(ordered_pair(A, B), cartesian_product2(C, D))))) | (~(((~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))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (~(((~in(A, C)) | (~in(B, D))) <=> in(ordered_pair(A, B), cartesian_product2(C, D))))) | (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))))),
% 0.21/0.43 inference(monotonicity,[status(thm)],[138])).
% 0.21/0.43 tff(140,plain,
% 0.21/0.43 (((~![A: $i, B: $i, C: $i, D: $i] : (~(((~in(A, C)) | (~in(B, D))) <=> in(ordered_pair(A, B), cartesian_product2(C, D))))) | (~(((~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))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (~(((~in(A, C)) | (~in(B, D))) <=> in(ordered_pair(A, B), cartesian_product2(C, D))))) | (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))))),
% 0.21/0.43 inference(transitivity,[status(thm)],[139, 129])).
% 0.21/0.43 tff(141,plain,
% 0.21/0.43 ((~![A: $i, B: $i, C: $i, D: $i] : (~(((~in(A, C)) | (~in(B, D))) <=> in(ordered_pair(A, B), cartesian_product2(C, D))))) | (~(((~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))))),
% 0.21/0.43 inference(quant_inst,[status(thm)],[])).
% 0.21/0.43 tff(142,plain,
% 0.21/0.43 ((~![A: $i, B: $i, C: $i, D: $i] : (~(((~in(A, C)) | (~in(B, D))) <=> in(ordered_pair(A, B), cartesian_product2(C, D))))) | (in(tptp_fun_B_1(relation_restriction(B!7, A!8)), A!8) <=> in(ordered_pair(tptp_fun_B_1(relation_restriction(B!7, A!8)), tptp_fun_B_1(relation_restriction(B!7, A!8))), cartesian_product2(A!8, A!8)))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[141, 140])).
% 0.21/0.43 tff(143,plain,
% 0.21/0.43 ($false),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[142, 128, 118])).
% 0.21/0.43 % SZS output end Proof
% 0.21/0.43 % E exiting
%------------------------------------------------------------------------------