TSTP Solution File: SEU254+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SEU254+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n002.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 07:28:31 EDT 2022
% Result : Theorem 0.19s 0.40s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU254+1 : TPTP v8.1.0. Released v3.3.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.34 % Computer : n002.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Sat Sep 3 11:19:47 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 0.19/0.40 % SZS status Theorem
% 0.19/0.40 % SZS output start Proof
% 0.19/0.40 tff(in_type, type, (
% 0.19/0.40 in: ( $i * $i ) > $o)).
% 0.19/0.40 tff(tptp_fun_A_10_type, type, (
% 0.19/0.40 tptp_fun_A_10: $i)).
% 0.19/0.40 tff(tptp_fun_D_1_type, type, (
% 0.19/0.40 tptp_fun_D_1: $i > $i)).
% 0.19/0.40 tff(relation_restriction_type, type, (
% 0.19/0.40 relation_restriction: ( $i * $i ) > $i)).
% 0.19/0.40 tff(tptp_fun_B_9_type, type, (
% 0.19/0.40 tptp_fun_B_9: $i)).
% 0.19/0.40 tff(tptp_fun_B_3_type, type, (
% 0.19/0.40 tptp_fun_B_3: $i > $i)).
% 0.19/0.40 tff(cartesian_product2_type, type, (
% 0.19/0.40 cartesian_product2: ( $i * $i ) > $i)).
% 0.19/0.40 tff(ordered_pair_type, type, (
% 0.19/0.40 ordered_pair: ( $i * $i ) > $i)).
% 0.19/0.40 tff(relation_type, type, (
% 0.19/0.40 relation: $i > $o)).
% 0.19/0.40 tff(transitive_type, type, (
% 0.19/0.40 transitive: $i > $o)).
% 0.19/0.40 tff(tptp_fun_C_2_type, type, (
% 0.19/0.40 tptp_fun_C_2: $i > $i)).
% 0.19/0.40 tff(1,plain,
% 0.19/0.40 (^[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))))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(2,plain,
% 0.19/0.40 (![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)))))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[1])).
% 0.19/0.40 tff(3,plain,
% 0.19/0.40 (^[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))))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(4,plain,
% 0.19/0.40 (![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)))))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[3])).
% 0.19/0.40 tff(5,plain,
% 0.19/0.40 (![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)))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(6,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')).
% 0.19/0.40 tff(7,plain,
% 0.19/0.40 (![A: $i, B: $i, C: $i, D: $i] : (in(ordered_pair(A, B), cartesian_product2(C, D)) <=> (in(A, C) & in(B, D)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.19/0.40 tff(8,plain,(
% 0.19/0.40 ![A: $i, B: $i, C: $i, D: $i] : (in(ordered_pair(A, B), cartesian_product2(C, D)) <=> (in(A, C) & in(B, D)))),
% 0.19/0.40 inference(skolemize,[status(sab)],[7])).
% 0.19/0.40 tff(9,plain,
% 0.19/0.40 (![A: $i, B: $i, C: $i, D: $i] : (in(ordered_pair(A, B), cartesian_product2(C, D)) <=> (~((~in(A, C)) | (~in(B, D)))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[8, 4])).
% 0.19/0.40 tff(10,plain,
% 0.19/0.40 (![A: $i, B: $i, C: $i, D: $i] : (in(ordered_pair(A, B), cartesian_product2(C, D)) <=> (~((~in(A, C)) | (~in(B, D)))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[9, 2])).
% 0.19/0.40 tff(11,plain,
% 0.19/0.40 ((~![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_3(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), cartesian_product2(A!10, A!10)) <=> (~((~in(tptp_fun_B_3(relation_restriction(B!9, A!10)), A!10)) | (~in(tptp_fun_D_1(relation_restriction(B!9, A!10)), A!10)))))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(12,plain,
% 0.19/0.40 (in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), cartesian_product2(A!10, A!10)) <=> (~((~in(tptp_fun_B_3(relation_restriction(B!9, A!10)), A!10)) | (~in(tptp_fun_D_1(relation_restriction(B!9, A!10)), A!10))))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[11, 10])).
% 0.19/0.40 tff(13,plain,
% 0.19/0.40 ((~(transitive(relation_restriction(B!9, A!10)) | (~relation(B!9)) | (~transitive(B!9)))) <=> (~(transitive(relation_restriction(B!9, A!10)) | (~relation(B!9)) | (~transitive(B!9))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(14,plain,
% 0.19/0.40 ((~![A: $i, B: $i] : (transitive(relation_restriction(B, A)) | (~relation(B)) | (~transitive(B)))) <=> (~![A: $i, B: $i] : (transitive(relation_restriction(B, A)) | (~relation(B)) | (~transitive(B))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(15,plain,
% 0.19/0.40 ((~![A: $i, B: $i] : (relation(B) => (transitive(B) => transitive(relation_restriction(B, A))))) <=> (~![A: $i, B: $i] : (transitive(relation_restriction(B, A)) | (~relation(B)) | (~transitive(B))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(16,axiom,(~![A: $i, B: $i] : (relation(B) => (transitive(B) => transitive(relation_restriction(B, A))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t24_wellord1')).
% 0.19/0.40 tff(17,plain,
% 0.19/0.40 (~![A: $i, B: $i] : (transitive(relation_restriction(B, A)) | (~relation(B)) | (~transitive(B)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[16, 15])).
% 0.19/0.40 tff(18,plain,
% 0.19/0.40 (~![A: $i, B: $i] : (transitive(relation_restriction(B, A)) | (~relation(B)) | (~transitive(B)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[17, 14])).
% 0.19/0.40 tff(19,plain,
% 0.19/0.40 (~![A: $i, B: $i] : (transitive(relation_restriction(B, A)) | (~relation(B)) | (~transitive(B)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[18, 14])).
% 0.19/0.40 tff(20,plain,
% 0.19/0.40 (~![A: $i, B: $i] : (transitive(relation_restriction(B, A)) | (~relation(B)) | (~transitive(B)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[19, 14])).
% 0.19/0.40 tff(21,plain,
% 0.19/0.40 (~![A: $i, B: $i] : (transitive(relation_restriction(B, A)) | (~relation(B)) | (~transitive(B)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[20, 14])).
% 0.19/0.40 tff(22,plain,
% 0.19/0.40 (~![A: $i, B: $i] : (transitive(relation_restriction(B, A)) | (~relation(B)) | (~transitive(B)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[21, 14])).
% 0.19/0.40 tff(23,plain,
% 0.19/0.40 (~![A: $i, B: $i] : (transitive(relation_restriction(B, A)) | (~relation(B)) | (~transitive(B)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[22, 14])).
% 0.19/0.40 tff(24,plain,(
% 0.19/0.40 ~(transitive(relation_restriction(B!9, A!10)) | (~relation(B!9)) | (~transitive(B!9)))),
% 0.19/0.40 inference(skolemize,[status(sab)],[23])).
% 0.19/0.40 tff(25,plain,
% 0.19/0.40 (~(transitive(relation_restriction(B!9, A!10)) | (~relation(B!9)) | (~transitive(B!9)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[24, 13])).
% 0.19/0.40 tff(26,plain,
% 0.19/0.40 (relation(B!9)),
% 0.19/0.40 inference(or_elim,[status(thm)],[25])).
% 0.19/0.40 tff(27,plain,
% 0.19/0.40 (^[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))))))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(28,plain,
% 0.19/0.40 (![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)))))))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[27])).
% 0.19/0.40 tff(29,plain,
% 0.19/0.40 (^[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))))))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(30,plain,
% 0.19/0.40 (![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)))))))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[29])).
% 0.19/0.40 tff(31,plain,
% 0.19/0.40 (![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)))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(32,plain,
% 0.19/0.40 (^[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))))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(33,plain,
% 0.19/0.40 (![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)))))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[32])).
% 0.19/0.40 tff(34,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')).
% 0.19/0.40 tff(35,plain,
% 0.19/0.40 (![A: $i, B: $i, C: $i] : ((~relation(C)) | (in(A, relation_restriction(C, B)) <=> (in(A, C) & in(A, cartesian_product2(B, B)))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[34, 33])).
% 0.19/0.40 tff(36,plain,
% 0.19/0.40 (![A: $i, B: $i, C: $i] : ((~relation(C)) | (in(A, relation_restriction(C, B)) <=> (in(A, C) & in(A, cartesian_product2(B, B)))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[35, 31])).
% 0.19/0.40 tff(37,plain,(
% 0.19/0.40 ![A: $i, B: $i, C: $i] : ((~relation(C)) | (in(A, relation_restriction(C, B)) <=> (in(A, C) & in(A, cartesian_product2(B, B)))))),
% 0.19/0.40 inference(skolemize,[status(sab)],[36])).
% 0.19/0.40 tff(38,plain,
% 0.19/0.40 (![A: $i, B: $i, C: $i] : ((~relation(C)) | (in(A, relation_restriction(C, B)) <=> (~((~in(A, C)) | (~in(A, cartesian_product2(B, B)))))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[37, 30])).
% 0.19/0.40 tff(39,plain,
% 0.19/0.40 (![A: $i, B: $i, C: $i] : ((~relation(C)) | (in(A, relation_restriction(C, B)) <=> (~((~in(A, C)) | (~in(A, cartesian_product2(B, B)))))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[38, 28])).
% 0.19/0.40 tff(40,plain,
% 0.19/0.40 (((~![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!9)) | (in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), relation_restriction(B!9, A!10)) <=> (~((~in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), B!9)) | (~in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), cartesian_product2(A!10, A!10)))))))) <=> ((~![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!9)) | (in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), relation_restriction(B!9, A!10)) <=> (~((~in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), B!9)) | (~in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), cartesian_product2(A!10, A!10)))))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(41,plain,
% 0.19/0.40 ((~![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!9)) | (in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), relation_restriction(B!9, A!10)) <=> (~((~in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), B!9)) | (~in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), cartesian_product2(A!10, A!10)))))))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(42,plain,
% 0.19/0.40 ((~![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!9)) | (in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), relation_restriction(B!9, A!10)) <=> (~((~in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), B!9)) | (~in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), cartesian_product2(A!10, A!10))))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[41, 40])).
% 0.19/0.40 tff(43,plain,
% 0.19/0.40 (in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), relation_restriction(B!9, A!10)) <=> (~((~in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), B!9)) | (~in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), cartesian_product2(A!10, A!10)))))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[42, 39, 26])).
% 0.19/0.40 tff(44,plain,
% 0.19/0.40 (^[A: $i, B: $i] : refl(((~relation(A)) | relation(relation_restriction(A, B))) <=> ((~relation(A)) | relation(relation_restriction(A, B))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(45,plain,
% 0.19/0.40 (![A: $i, B: $i] : ((~relation(A)) | relation(relation_restriction(A, B))) <=> ![A: $i, B: $i] : ((~relation(A)) | relation(relation_restriction(A, B)))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[44])).
% 0.19/0.40 tff(46,plain,
% 0.19/0.40 (![A: $i, B: $i] : ((~relation(A)) | relation(relation_restriction(A, B))) <=> ![A: $i, B: $i] : ((~relation(A)) | relation(relation_restriction(A, B)))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(47,plain,
% 0.19/0.40 (^[A: $i, B: $i] : rewrite((relation(A) => relation(relation_restriction(A, B))) <=> ((~relation(A)) | relation(relation_restriction(A, B))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(48,plain,
% 0.19/0.40 (![A: $i, B: $i] : (relation(A) => relation(relation_restriction(A, B))) <=> ![A: $i, B: $i] : ((~relation(A)) | relation(relation_restriction(A, B)))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[47])).
% 0.19/0.40 tff(49,axiom,(![A: $i, B: $i] : (relation(A) => relation(relation_restriction(A, B)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_k2_wellord1')).
% 0.19/0.40 tff(50,plain,
% 0.19/0.40 (![A: $i, B: $i] : ((~relation(A)) | relation(relation_restriction(A, B)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[49, 48])).
% 0.19/0.40 tff(51,plain,
% 0.19/0.40 (![A: $i, B: $i] : ((~relation(A)) | relation(relation_restriction(A, B)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[50, 46])).
% 0.19/0.40 tff(52,plain,(
% 0.19/0.40 ![A: $i, B: $i] : ((~relation(A)) | relation(relation_restriction(A, B)))),
% 0.19/0.40 inference(skolemize,[status(sab)],[51])).
% 0.19/0.40 tff(53,plain,
% 0.19/0.40 (![A: $i, B: $i] : ((~relation(A)) | relation(relation_restriction(A, B)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[52, 45])).
% 0.19/0.40 tff(54,plain,
% 0.19/0.40 (((~![A: $i, B: $i] : ((~relation(A)) | relation(relation_restriction(A, B)))) | ((~relation(B!9)) | relation(relation_restriction(B!9, A!10)))) <=> ((~![A: $i, B: $i] : ((~relation(A)) | relation(relation_restriction(A, B)))) | (~relation(B!9)) | relation(relation_restriction(B!9, A!10)))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(55,plain,
% 0.19/0.40 ((~![A: $i, B: $i] : ((~relation(A)) | relation(relation_restriction(A, B)))) | ((~relation(B!9)) | relation(relation_restriction(B!9, A!10)))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(56,plain,
% 0.19/0.40 ((~![A: $i, B: $i] : ((~relation(A)) | relation(relation_restriction(A, B)))) | (~relation(B!9)) | relation(relation_restriction(B!9, A!10))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[55, 54])).
% 0.19/0.40 tff(57,plain,
% 0.19/0.40 (relation(relation_restriction(B!9, A!10))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[56, 53, 26])).
% 0.19/0.40 tff(58,plain,
% 0.19/0.40 (^[A: $i] : refl(((~relation(A)) | (~((~((~transitive(A)) | ![B: $i, C: $i, D: $i] : (in(ordered_pair(B, D), A) | (~in(ordered_pair(B, C), A)) | (~in(ordered_pair(C, D), A))))) | (~(transitive(A) | (~(in(ordered_pair(tptp_fun_B_3(A), tptp_fun_D_1(A)), A) | (~in(ordered_pair(tptp_fun_B_3(A), tptp_fun_C_2(A)), A)) | (~in(ordered_pair(tptp_fun_C_2(A), tptp_fun_D_1(A)), A))))))))) <=> ((~relation(A)) | (~((~((~transitive(A)) | ![B: $i, C: $i, D: $i] : (in(ordered_pair(B, D), A) | (~in(ordered_pair(B, C), A)) | (~in(ordered_pair(C, D), A))))) | (~(transitive(A) | (~(in(ordered_pair(tptp_fun_B_3(A), tptp_fun_D_1(A)), A) | (~in(ordered_pair(tptp_fun_B_3(A), tptp_fun_C_2(A)), A)) | (~in(ordered_pair(tptp_fun_C_2(A), tptp_fun_D_1(A)), A))))))))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(59,plain,
% 0.19/0.40 (![A: $i] : ((~relation(A)) | (~((~((~transitive(A)) | ![B: $i, C: $i, D: $i] : (in(ordered_pair(B, D), A) | (~in(ordered_pair(B, C), A)) | (~in(ordered_pair(C, D), A))))) | (~(transitive(A) | (~(in(ordered_pair(tptp_fun_B_3(A), tptp_fun_D_1(A)), A) | (~in(ordered_pair(tptp_fun_B_3(A), tptp_fun_C_2(A)), A)) | (~in(ordered_pair(tptp_fun_C_2(A), tptp_fun_D_1(A)), A))))))))) <=> ![A: $i] : ((~relation(A)) | (~((~((~transitive(A)) | ![B: $i, C: $i, D: $i] : (in(ordered_pair(B, D), A) | (~in(ordered_pair(B, C), A)) | (~in(ordered_pair(C, D), A))))) | (~(transitive(A) | (~(in(ordered_pair(tptp_fun_B_3(A), tptp_fun_D_1(A)), A) | (~in(ordered_pair(tptp_fun_B_3(A), tptp_fun_C_2(A)), A)) | (~in(ordered_pair(tptp_fun_C_2(A), tptp_fun_D_1(A)), A)))))))))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[58])).
% 0.19/0.40 tff(60,plain,
% 0.19/0.40 (^[A: $i] : rewrite(((~relation(A)) | (~((~((~transitive(A)) | ![B: $i, C: $i, D: $i] : (in(ordered_pair(B, D), A) | (~in(ordered_pair(B, C), A)) | (~in(ordered_pair(C, D), A))))) | (~(transitive(A) | (~(in(ordered_pair(tptp_fun_B_3(A), tptp_fun_D_1(A)), A) | (~in(ordered_pair(tptp_fun_B_3(A), tptp_fun_C_2(A)), A)) | (~in(ordered_pair(tptp_fun_C_2(A), tptp_fun_D_1(A)), A))))))))) <=> ((~relation(A)) | (~((~((~transitive(A)) | ![B: $i, C: $i, D: $i] : (in(ordered_pair(B, D), A) | (~in(ordered_pair(B, C), A)) | (~in(ordered_pair(C, D), A))))) | (~(transitive(A) | (~(in(ordered_pair(tptp_fun_B_3(A), tptp_fun_D_1(A)), A) | (~in(ordered_pair(tptp_fun_B_3(A), tptp_fun_C_2(A)), A)) | (~in(ordered_pair(tptp_fun_C_2(A), tptp_fun_D_1(A)), A))))))))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(61,plain,
% 0.19/0.40 (![A: $i] : ((~relation(A)) | (~((~((~transitive(A)) | ![B: $i, C: $i, D: $i] : (in(ordered_pair(B, D), A) | (~in(ordered_pair(B, C), A)) | (~in(ordered_pair(C, D), A))))) | (~(transitive(A) | (~(in(ordered_pair(tptp_fun_B_3(A), tptp_fun_D_1(A)), A) | (~in(ordered_pair(tptp_fun_B_3(A), tptp_fun_C_2(A)), A)) | (~in(ordered_pair(tptp_fun_C_2(A), tptp_fun_D_1(A)), A))))))))) <=> ![A: $i] : ((~relation(A)) | (~((~((~transitive(A)) | ![B: $i, C: $i, D: $i] : (in(ordered_pair(B, D), A) | (~in(ordered_pair(B, C), A)) | (~in(ordered_pair(C, D), A))))) | (~(transitive(A) | (~(in(ordered_pair(tptp_fun_B_3(A), tptp_fun_D_1(A)), A) | (~in(ordered_pair(tptp_fun_B_3(A), tptp_fun_C_2(A)), A)) | (~in(ordered_pair(tptp_fun_C_2(A), tptp_fun_D_1(A)), A)))))))))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[60])).
% 0.19/0.40 tff(62,plain,
% 0.19/0.40 (![A: $i] : ((~relation(A)) | (~((~((~transitive(A)) | ![B: $i, C: $i, D: $i] : (in(ordered_pair(B, D), A) | (~in(ordered_pair(B, C), A)) | (~in(ordered_pair(C, D), A))))) | (~(transitive(A) | (~(in(ordered_pair(tptp_fun_B_3(A), tptp_fun_D_1(A)), A) | (~in(ordered_pair(tptp_fun_B_3(A), tptp_fun_C_2(A)), A)) | (~in(ordered_pair(tptp_fun_C_2(A), tptp_fun_D_1(A)), A))))))))) <=> ![A: $i] : ((~relation(A)) | (~((~((~transitive(A)) | ![B: $i, C: $i, D: $i] : (in(ordered_pair(B, D), A) | (~in(ordered_pair(B, C), A)) | (~in(ordered_pair(C, D), A))))) | (~(transitive(A) | (~(in(ordered_pair(tptp_fun_B_3(A), tptp_fun_D_1(A)), A) | (~in(ordered_pair(tptp_fun_B_3(A), tptp_fun_C_2(A)), A)) | (~in(ordered_pair(tptp_fun_C_2(A), tptp_fun_D_1(A)), A)))))))))),
% 0.19/0.40 inference(transitivity,[status(thm)],[61, 59])).
% 0.19/0.40 tff(63,plain,
% 0.19/0.40 (^[A: $i] : rewrite(((~relation(A)) | (((~transitive(A)) | ![B: $i, C: $i, D: $i] : ((~(in(ordered_pair(B, C), A) & in(ordered_pair(C, D), A))) | in(ordered_pair(B, D), A))) & (transitive(A) | (~((~(in(ordered_pair(tptp_fun_B_3(A), tptp_fun_C_2(A)), A) & in(ordered_pair(tptp_fun_C_2(A), tptp_fun_D_1(A)), A))) | in(ordered_pair(tptp_fun_B_3(A), tptp_fun_D_1(A)), A)))))) <=> ((~relation(A)) | (~((~((~transitive(A)) | ![B: $i, C: $i, D: $i] : (in(ordered_pair(B, D), A) | (~in(ordered_pair(B, C), A)) | (~in(ordered_pair(C, D), A))))) | (~(transitive(A) | (~(in(ordered_pair(tptp_fun_B_3(A), tptp_fun_D_1(A)), A) | (~in(ordered_pair(tptp_fun_B_3(A), tptp_fun_C_2(A)), A)) | (~in(ordered_pair(tptp_fun_C_2(A), tptp_fun_D_1(A)), A))))))))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(64,plain,
% 0.19/0.41 (![A: $i] : ((~relation(A)) | (((~transitive(A)) | ![B: $i, C: $i, D: $i] : ((~(in(ordered_pair(B, C), A) & in(ordered_pair(C, D), A))) | in(ordered_pair(B, D), A))) & (transitive(A) | (~((~(in(ordered_pair(tptp_fun_B_3(A), tptp_fun_C_2(A)), A) & in(ordered_pair(tptp_fun_C_2(A), tptp_fun_D_1(A)), A))) | in(ordered_pair(tptp_fun_B_3(A), tptp_fun_D_1(A)), A)))))) <=> ![A: $i] : ((~relation(A)) | (~((~((~transitive(A)) | ![B: $i, C: $i, D: $i] : (in(ordered_pair(B, D), A) | (~in(ordered_pair(B, C), A)) | (~in(ordered_pair(C, D), A))))) | (~(transitive(A) | (~(in(ordered_pair(tptp_fun_B_3(A), tptp_fun_D_1(A)), A) | (~in(ordered_pair(tptp_fun_B_3(A), tptp_fun_C_2(A)), A)) | (~in(ordered_pair(tptp_fun_C_2(A), tptp_fun_D_1(A)), A)))))))))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[63])).
% 0.19/0.41 tff(65,plain,
% 0.19/0.41 (![A: $i] : ((~relation(A)) | (transitive(A) <=> ![B: $i, C: $i, D: $i] : ((~(in(ordered_pair(B, C), A) & in(ordered_pair(C, D), A))) | in(ordered_pair(B, D), A)))) <=> ![A: $i] : ((~relation(A)) | (transitive(A) <=> ![B: $i, C: $i, D: $i] : ((~(in(ordered_pair(B, C), A) & in(ordered_pair(C, D), A))) | in(ordered_pair(B, D), A))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(66,plain,
% 0.19/0.41 (^[A: $i] : trans(monotonicity(rewrite((transitive(A) <=> ![B: $i, C: $i, D: $i] : ((in(ordered_pair(B, C), A) & in(ordered_pair(C, D), A)) => in(ordered_pair(B, D), A))) <=> (transitive(A) <=> ![B: $i, C: $i, D: $i] : ((~(in(ordered_pair(B, C), A) & in(ordered_pair(C, D), A))) | in(ordered_pair(B, D), A)))), ((relation(A) => (transitive(A) <=> ![B: $i, C: $i, D: $i] : ((in(ordered_pair(B, C), A) & in(ordered_pair(C, D), A)) => in(ordered_pair(B, D), A)))) <=> (relation(A) => (transitive(A) <=> ![B: $i, C: $i, D: $i] : ((~(in(ordered_pair(B, C), A) & in(ordered_pair(C, D), A))) | in(ordered_pair(B, D), A)))))), rewrite((relation(A) => (transitive(A) <=> ![B: $i, C: $i, D: $i] : ((~(in(ordered_pair(B, C), A) & in(ordered_pair(C, D), A))) | in(ordered_pair(B, D), A)))) <=> ((~relation(A)) | (transitive(A) <=> ![B: $i, C: $i, D: $i] : ((~(in(ordered_pair(B, C), A) & in(ordered_pair(C, D), A))) | in(ordered_pair(B, D), A))))), ((relation(A) => (transitive(A) <=> ![B: $i, C: $i, D: $i] : ((in(ordered_pair(B, C), A) & in(ordered_pair(C, D), A)) => in(ordered_pair(B, D), A)))) <=> ((~relation(A)) | (transitive(A) <=> ![B: $i, C: $i, D: $i] : ((~(in(ordered_pair(B, C), A) & in(ordered_pair(C, D), A))) | in(ordered_pair(B, D), A))))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(67,plain,
% 0.19/0.41 (![A: $i] : (relation(A) => (transitive(A) <=> ![B: $i, C: $i, D: $i] : ((in(ordered_pair(B, C), A) & in(ordered_pair(C, D), A)) => in(ordered_pair(B, D), A)))) <=> ![A: $i] : ((~relation(A)) | (transitive(A) <=> ![B: $i, C: $i, D: $i] : ((~(in(ordered_pair(B, C), A) & in(ordered_pair(C, D), A))) | in(ordered_pair(B, D), A))))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[66])).
% 0.19/0.41 tff(68,axiom,(![A: $i] : (relation(A) => (transitive(A) <=> ![B: $i, C: $i, D: $i] : ((in(ordered_pair(B, C), A) & in(ordered_pair(C, D), A)) => in(ordered_pair(B, D), A))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','l2_wellord1')).
% 0.19/0.41 tff(69,plain,
% 0.19/0.41 (![A: $i] : ((~relation(A)) | (transitive(A) <=> ![B: $i, C: $i, D: $i] : ((~(in(ordered_pair(B, C), A) & in(ordered_pair(C, D), A))) | in(ordered_pair(B, D), A))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[68, 67])).
% 0.19/0.41 tff(70,plain,
% 0.19/0.41 (![A: $i] : ((~relation(A)) | (transitive(A) <=> ![B: $i, C: $i, D: $i] : ((~(in(ordered_pair(B, C), A) & in(ordered_pair(C, D), A))) | in(ordered_pair(B, D), A))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[69, 65])).
% 0.19/0.41 tff(71,plain,(
% 0.19/0.41 ![A: $i] : ((~relation(A)) | (((~transitive(A)) | ![B: $i, C: $i, D: $i] : ((~(in(ordered_pair(B, C), A) & in(ordered_pair(C, D), A))) | in(ordered_pair(B, D), A))) & (transitive(A) | (~((~(in(ordered_pair(tptp_fun_B_3(A), tptp_fun_C_2(A)), A) & in(ordered_pair(tptp_fun_C_2(A), tptp_fun_D_1(A)), A))) | in(ordered_pair(tptp_fun_B_3(A), tptp_fun_D_1(A)), A))))))),
% 0.19/0.41 inference(skolemize,[status(sab)],[70])).
% 0.19/0.41 tff(72,plain,
% 0.19/0.41 (![A: $i] : ((~relation(A)) | (~((~((~transitive(A)) | ![B: $i, C: $i, D: $i] : (in(ordered_pair(B, D), A) | (~in(ordered_pair(B, C), A)) | (~in(ordered_pair(C, D), A))))) | (~(transitive(A) | (~(in(ordered_pair(tptp_fun_B_3(A), tptp_fun_D_1(A)), A) | (~in(ordered_pair(tptp_fun_B_3(A), tptp_fun_C_2(A)), A)) | (~in(ordered_pair(tptp_fun_C_2(A), tptp_fun_D_1(A)), A)))))))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[71, 64])).
% 0.19/0.41 tff(73,plain,
% 0.19/0.41 (![A: $i] : ((~relation(A)) | (~((~((~transitive(A)) | ![B: $i, C: $i, D: $i] : (in(ordered_pair(B, D), A) | (~in(ordered_pair(B, C), A)) | (~in(ordered_pair(C, D), A))))) | (~(transitive(A) | (~(in(ordered_pair(tptp_fun_B_3(A), tptp_fun_D_1(A)), A) | (~in(ordered_pair(tptp_fun_B_3(A), tptp_fun_C_2(A)), A)) | (~in(ordered_pair(tptp_fun_C_2(A), tptp_fun_D_1(A)), A)))))))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[72, 62])).
% 0.19/0.41 tff(74,plain,
% 0.19/0.41 (((~![A: $i] : ((~relation(A)) | (~((~((~transitive(A)) | ![B: $i, C: $i, D: $i] : (in(ordered_pair(B, D), A) | (~in(ordered_pair(B, C), A)) | (~in(ordered_pair(C, D), A))))) | (~(transitive(A) | (~(in(ordered_pair(tptp_fun_B_3(A), tptp_fun_D_1(A)), A) | (~in(ordered_pair(tptp_fun_B_3(A), tptp_fun_C_2(A)), A)) | (~in(ordered_pair(tptp_fun_C_2(A), tptp_fun_D_1(A)), A)))))))))) | ((~relation(relation_restriction(B!9, A!10))) | (~((~((~transitive(relation_restriction(B!9, A!10))) | ![B: $i, C: $i, D: $i] : (in(ordered_pair(B, D), relation_restriction(B!9, A!10)) | (~in(ordered_pair(B, C), relation_restriction(B!9, A!10))) | (~in(ordered_pair(C, D), relation_restriction(B!9, A!10)))))) | (~(transitive(relation_restriction(B!9, A!10)) | (~(in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), relation_restriction(B!9, A!10)) | (~in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_C_2(relation_restriction(B!9, A!10))), relation_restriction(B!9, A!10))) | (~in(ordered_pair(tptp_fun_C_2(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), relation_restriction(B!9, A!10))))))))))) <=> ((~![A: $i] : ((~relation(A)) | (~((~((~transitive(A)) | ![B: $i, C: $i, D: $i] : (in(ordered_pair(B, D), A) | (~in(ordered_pair(B, C), A)) | (~in(ordered_pair(C, D), A))))) | (~(transitive(A) | (~(in(ordered_pair(tptp_fun_B_3(A), tptp_fun_D_1(A)), A) | (~in(ordered_pair(tptp_fun_B_3(A), tptp_fun_C_2(A)), A)) | (~in(ordered_pair(tptp_fun_C_2(A), tptp_fun_D_1(A)), A)))))))))) | (~relation(relation_restriction(B!9, A!10))) | (~((~((~transitive(relation_restriction(B!9, A!10))) | ![B: $i, C: $i, D: $i] : (in(ordered_pair(B, D), relation_restriction(B!9, A!10)) | (~in(ordered_pair(B, C), relation_restriction(B!9, A!10))) | (~in(ordered_pair(C, D), relation_restriction(B!9, A!10)))))) | (~(transitive(relation_restriction(B!9, A!10)) | (~(in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), relation_restriction(B!9, A!10)) | (~in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_C_2(relation_restriction(B!9, A!10))), relation_restriction(B!9, A!10))) | (~in(ordered_pair(tptp_fun_C_2(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), relation_restriction(B!9, A!10))))))))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(75,plain,
% 0.19/0.41 ((~![A: $i] : ((~relation(A)) | (~((~((~transitive(A)) | ![B: $i, C: $i, D: $i] : (in(ordered_pair(B, D), A) | (~in(ordered_pair(B, C), A)) | (~in(ordered_pair(C, D), A))))) | (~(transitive(A) | (~(in(ordered_pair(tptp_fun_B_3(A), tptp_fun_D_1(A)), A) | (~in(ordered_pair(tptp_fun_B_3(A), tptp_fun_C_2(A)), A)) | (~in(ordered_pair(tptp_fun_C_2(A), tptp_fun_D_1(A)), A)))))))))) | ((~relation(relation_restriction(B!9, A!10))) | (~((~((~transitive(relation_restriction(B!9, A!10))) | ![B: $i, C: $i, D: $i] : (in(ordered_pair(B, D), relation_restriction(B!9, A!10)) | (~in(ordered_pair(B, C), relation_restriction(B!9, A!10))) | (~in(ordered_pair(C, D), relation_restriction(B!9, A!10)))))) | (~(transitive(relation_restriction(B!9, A!10)) | (~(in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), relation_restriction(B!9, A!10)) | (~in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_C_2(relation_restriction(B!9, A!10))), relation_restriction(B!9, A!10))) | (~in(ordered_pair(tptp_fun_C_2(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), relation_restriction(B!9, A!10))))))))))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(76,plain,
% 0.19/0.41 ((~![A: $i] : ((~relation(A)) | (~((~((~transitive(A)) | ![B: $i, C: $i, D: $i] : (in(ordered_pair(B, D), A) | (~in(ordered_pair(B, C), A)) | (~in(ordered_pair(C, D), A))))) | (~(transitive(A) | (~(in(ordered_pair(tptp_fun_B_3(A), tptp_fun_D_1(A)), A) | (~in(ordered_pair(tptp_fun_B_3(A), tptp_fun_C_2(A)), A)) | (~in(ordered_pair(tptp_fun_C_2(A), tptp_fun_D_1(A)), A)))))))))) | (~relation(relation_restriction(B!9, A!10))) | (~((~((~transitive(relation_restriction(B!9, A!10))) | ![B: $i, C: $i, D: $i] : (in(ordered_pair(B, D), relation_restriction(B!9, A!10)) | (~in(ordered_pair(B, C), relation_restriction(B!9, A!10))) | (~in(ordered_pair(C, D), relation_restriction(B!9, A!10)))))) | (~(transitive(relation_restriction(B!9, A!10)) | (~(in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), relation_restriction(B!9, A!10)) | (~in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_C_2(relation_restriction(B!9, A!10))), relation_restriction(B!9, A!10))) | (~in(ordered_pair(tptp_fun_C_2(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), relation_restriction(B!9, A!10)))))))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[75, 74])).
% 0.19/0.41 tff(77,plain,
% 0.19/0.41 (~((~((~transitive(relation_restriction(B!9, A!10))) | ![B: $i, C: $i, D: $i] : (in(ordered_pair(B, D), relation_restriction(B!9, A!10)) | (~in(ordered_pair(B, C), relation_restriction(B!9, A!10))) | (~in(ordered_pair(C, D), relation_restriction(B!9, A!10)))))) | (~(transitive(relation_restriction(B!9, A!10)) | (~(in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), relation_restriction(B!9, A!10)) | (~in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_C_2(relation_restriction(B!9, A!10))), relation_restriction(B!9, A!10))) | (~in(ordered_pair(tptp_fun_C_2(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), relation_restriction(B!9, A!10))))))))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[76, 73, 57])).
% 0.19/0.41 tff(78,plain,
% 0.19/0.41 (((~((~transitive(relation_restriction(B!9, A!10))) | ![B: $i, C: $i, D: $i] : (in(ordered_pair(B, D), relation_restriction(B!9, A!10)) | (~in(ordered_pair(B, C), relation_restriction(B!9, A!10))) | (~in(ordered_pair(C, D), relation_restriction(B!9, A!10)))))) | (~(transitive(relation_restriction(B!9, A!10)) | (~(in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), relation_restriction(B!9, A!10)) | (~in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_C_2(relation_restriction(B!9, A!10))), relation_restriction(B!9, A!10))) | (~in(ordered_pair(tptp_fun_C_2(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), relation_restriction(B!9, A!10)))))))) | (transitive(relation_restriction(B!9, A!10)) | (~(in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), relation_restriction(B!9, A!10)) | (~in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_C_2(relation_restriction(B!9, A!10))), relation_restriction(B!9, A!10))) | (~in(ordered_pair(tptp_fun_C_2(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), relation_restriction(B!9, A!10))))))),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(79,plain,
% 0.19/0.41 (transitive(relation_restriction(B!9, A!10)) | (~(in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), relation_restriction(B!9, A!10)) | (~in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_C_2(relation_restriction(B!9, A!10))), relation_restriction(B!9, A!10))) | (~in(ordered_pair(tptp_fun_C_2(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), relation_restriction(B!9, A!10)))))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[78, 77])).
% 0.19/0.42 tff(80,plain,
% 0.19/0.42 (~transitive(relation_restriction(B!9, A!10))),
% 0.19/0.42 inference(or_elim,[status(thm)],[25])).
% 0.19/0.42 tff(81,plain,
% 0.19/0.42 ((~(transitive(relation_restriction(B!9, A!10)) | (~(in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), relation_restriction(B!9, A!10)) | (~in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_C_2(relation_restriction(B!9, A!10))), relation_restriction(B!9, A!10))) | (~in(ordered_pair(tptp_fun_C_2(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), relation_restriction(B!9, A!10))))))) | transitive(relation_restriction(B!9, A!10)) | (~(in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), relation_restriction(B!9, A!10)) | (~in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_C_2(relation_restriction(B!9, A!10))), relation_restriction(B!9, A!10))) | (~in(ordered_pair(tptp_fun_C_2(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), relation_restriction(B!9, A!10)))))),
% 0.19/0.42 inference(tautology,[status(thm)],[])).
% 0.19/0.42 tff(82,plain,
% 0.19/0.42 ((~(transitive(relation_restriction(B!9, A!10)) | (~(in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), relation_restriction(B!9, A!10)) | (~in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_C_2(relation_restriction(B!9, A!10))), relation_restriction(B!9, A!10))) | (~in(ordered_pair(tptp_fun_C_2(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), relation_restriction(B!9, A!10))))))) | (~(in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), relation_restriction(B!9, A!10)) | (~in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_C_2(relation_restriction(B!9, A!10))), relation_restriction(B!9, A!10))) | (~in(ordered_pair(tptp_fun_C_2(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), relation_restriction(B!9, A!10)))))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[81, 80])).
% 0.19/0.42 tff(83,plain,
% 0.19/0.42 (~(in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), relation_restriction(B!9, A!10)) | (~in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_C_2(relation_restriction(B!9, A!10))), relation_restriction(B!9, A!10))) | (~in(ordered_pair(tptp_fun_C_2(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), relation_restriction(B!9, A!10))))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[82, 79])).
% 0.19/0.42 tff(84,plain,
% 0.19/0.42 ((in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), relation_restriction(B!9, A!10)) | (~in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_C_2(relation_restriction(B!9, A!10))), relation_restriction(B!9, A!10))) | (~in(ordered_pair(tptp_fun_C_2(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), relation_restriction(B!9, A!10)))) | (~in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), relation_restriction(B!9, A!10)))),
% 0.19/0.42 inference(tautology,[status(thm)],[])).
% 0.19/0.42 tff(85,plain,
% 0.19/0.42 (~in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), relation_restriction(B!9, A!10))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[84, 83])).
% 0.19/0.42 tff(86,plain,
% 0.19/0.42 ((~(in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), relation_restriction(B!9, A!10)) <=> (~((~in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), B!9)) | (~in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), cartesian_product2(A!10, A!10))))))) | in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), relation_restriction(B!9, A!10)) | ((~in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), B!9)) | (~in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), cartesian_product2(A!10, A!10))))),
% 0.19/0.42 inference(tautology,[status(thm)],[])).
% 0.19/0.42 tff(87,plain,
% 0.19/0.42 ((~(in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), relation_restriction(B!9, A!10)) <=> (~((~in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), B!9)) | (~in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), cartesian_product2(A!10, A!10))))))) | ((~in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), B!9)) | (~in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), cartesian_product2(A!10, A!10))))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[86, 85])).
% 0.19/0.42 tff(88,plain,
% 0.19/0.42 ((~in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), B!9)) | (~in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), cartesian_product2(A!10, A!10)))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[87, 43])).
% 0.19/0.42 tff(89,plain,
% 0.19/0.42 (((~![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!9)) | (in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_C_2(relation_restriction(B!9, A!10))), relation_restriction(B!9, A!10)) <=> (~((~in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_C_2(relation_restriction(B!9, A!10))), B!9)) | (~in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_C_2(relation_restriction(B!9, A!10))), cartesian_product2(A!10, A!10)))))))) <=> ((~![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!9)) | (in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_C_2(relation_restriction(B!9, A!10))), relation_restriction(B!9, A!10)) <=> (~((~in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_C_2(relation_restriction(B!9, A!10))), B!9)) | (~in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_C_2(relation_restriction(B!9, A!10))), cartesian_product2(A!10, A!10)))))))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(90,plain,
% 0.19/0.42 ((~![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!9)) | (in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_C_2(relation_restriction(B!9, A!10))), relation_restriction(B!9, A!10)) <=> (~((~in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_C_2(relation_restriction(B!9, A!10))), B!9)) | (~in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_C_2(relation_restriction(B!9, A!10))), cartesian_product2(A!10, A!10)))))))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(91,plain,
% 0.19/0.42 ((~![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!9)) | (in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_C_2(relation_restriction(B!9, A!10))), relation_restriction(B!9, A!10)) <=> (~((~in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_C_2(relation_restriction(B!9, A!10))), B!9)) | (~in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_C_2(relation_restriction(B!9, A!10))), cartesian_product2(A!10, A!10))))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[90, 89])).
% 0.19/0.42 tff(92,plain,
% 0.19/0.42 (in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_C_2(relation_restriction(B!9, A!10))), relation_restriction(B!9, A!10)) <=> (~((~in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_C_2(relation_restriction(B!9, A!10))), B!9)) | (~in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_C_2(relation_restriction(B!9, A!10))), cartesian_product2(A!10, A!10)))))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[91, 39, 26])).
% 0.19/0.42 tff(93,plain,
% 0.19/0.42 ((in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), relation_restriction(B!9, A!10)) | (~in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_C_2(relation_restriction(B!9, A!10))), relation_restriction(B!9, A!10))) | (~in(ordered_pair(tptp_fun_C_2(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), relation_restriction(B!9, A!10)))) | in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_C_2(relation_restriction(B!9, A!10))), relation_restriction(B!9, A!10))),
% 0.19/0.42 inference(tautology,[status(thm)],[])).
% 0.19/0.42 tff(94,plain,
% 0.19/0.42 (in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_C_2(relation_restriction(B!9, A!10))), relation_restriction(B!9, A!10))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[93, 83])).
% 0.19/0.42 tff(95,plain,
% 0.19/0.42 ((~(in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_C_2(relation_restriction(B!9, A!10))), relation_restriction(B!9, A!10)) <=> (~((~in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_C_2(relation_restriction(B!9, A!10))), B!9)) | (~in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_C_2(relation_restriction(B!9, A!10))), cartesian_product2(A!10, A!10))))))) | (~in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_C_2(relation_restriction(B!9, A!10))), relation_restriction(B!9, A!10))) | (~((~in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_C_2(relation_restriction(B!9, A!10))), B!9)) | (~in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_C_2(relation_restriction(B!9, A!10))), cartesian_product2(A!10, A!10)))))),
% 0.19/0.42 inference(tautology,[status(thm)],[])).
% 0.19/0.42 tff(96,plain,
% 0.19/0.42 ((~(in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_C_2(relation_restriction(B!9, A!10))), relation_restriction(B!9, A!10)) <=> (~((~in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_C_2(relation_restriction(B!9, A!10))), B!9)) | (~in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_C_2(relation_restriction(B!9, A!10))), cartesian_product2(A!10, A!10))))))) | (~((~in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_C_2(relation_restriction(B!9, A!10))), B!9)) | (~in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_C_2(relation_restriction(B!9, A!10))), cartesian_product2(A!10, A!10)))))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[95, 94])).
% 0.19/0.42 tff(97,plain,
% 0.19/0.42 (~((~in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_C_2(relation_restriction(B!9, A!10))), B!9)) | (~in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_C_2(relation_restriction(B!9, A!10))), cartesian_product2(A!10, A!10))))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[96, 92])).
% 0.19/0.42 tff(98,plain,
% 0.19/0.42 (((~in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_C_2(relation_restriction(B!9, A!10))), B!9)) | (~in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_C_2(relation_restriction(B!9, A!10))), cartesian_product2(A!10, A!10)))) | in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_C_2(relation_restriction(B!9, A!10))), B!9)),
% 0.19/0.42 inference(tautology,[status(thm)],[])).
% 0.19/0.42 tff(99,plain,
% 0.19/0.42 (in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_C_2(relation_restriction(B!9, A!10))), B!9)),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[98, 97])).
% 0.19/0.42 tff(100,plain,
% 0.19/0.42 (((~![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!9)) | (in(ordered_pair(tptp_fun_C_2(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), relation_restriction(B!9, A!10)) <=> (~((~in(ordered_pair(tptp_fun_C_2(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), B!9)) | (~in(ordered_pair(tptp_fun_C_2(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), cartesian_product2(A!10, A!10)))))))) <=> ((~![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!9)) | (in(ordered_pair(tptp_fun_C_2(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), relation_restriction(B!9, A!10)) <=> (~((~in(ordered_pair(tptp_fun_C_2(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), B!9)) | (~in(ordered_pair(tptp_fun_C_2(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), cartesian_product2(A!10, A!10)))))))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(101,plain,
% 0.19/0.42 ((~![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!9)) | (in(ordered_pair(tptp_fun_C_2(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), relation_restriction(B!9, A!10)) <=> (~((~in(ordered_pair(tptp_fun_C_2(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), B!9)) | (~in(ordered_pair(tptp_fun_C_2(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), cartesian_product2(A!10, A!10)))))))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(102,plain,
% 0.19/0.42 ((~![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!9)) | (in(ordered_pair(tptp_fun_C_2(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), relation_restriction(B!9, A!10)) <=> (~((~in(ordered_pair(tptp_fun_C_2(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), B!9)) | (~in(ordered_pair(tptp_fun_C_2(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), cartesian_product2(A!10, A!10))))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[101, 100])).
% 0.19/0.42 tff(103,plain,
% 0.19/0.42 (in(ordered_pair(tptp_fun_C_2(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), relation_restriction(B!9, A!10)) <=> (~((~in(ordered_pair(tptp_fun_C_2(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), B!9)) | (~in(ordered_pair(tptp_fun_C_2(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), cartesian_product2(A!10, A!10)))))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[102, 39, 26])).
% 0.19/0.42 tff(104,plain,
% 0.19/0.42 ((in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), relation_restriction(B!9, A!10)) | (~in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_C_2(relation_restriction(B!9, A!10))), relation_restriction(B!9, A!10))) | (~in(ordered_pair(tptp_fun_C_2(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), relation_restriction(B!9, A!10)))) | in(ordered_pair(tptp_fun_C_2(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), relation_restriction(B!9, A!10))),
% 0.19/0.43 inference(tautology,[status(thm)],[])).
% 0.19/0.43 tff(105,plain,
% 0.19/0.43 (in(ordered_pair(tptp_fun_C_2(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), relation_restriction(B!9, A!10))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[104, 83])).
% 0.19/0.43 tff(106,plain,
% 0.19/0.43 ((~(in(ordered_pair(tptp_fun_C_2(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), relation_restriction(B!9, A!10)) <=> (~((~in(ordered_pair(tptp_fun_C_2(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), B!9)) | (~in(ordered_pair(tptp_fun_C_2(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), cartesian_product2(A!10, A!10))))))) | (~in(ordered_pair(tptp_fun_C_2(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), relation_restriction(B!9, A!10))) | (~((~in(ordered_pair(tptp_fun_C_2(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), B!9)) | (~in(ordered_pair(tptp_fun_C_2(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), cartesian_product2(A!10, A!10)))))),
% 0.19/0.43 inference(tautology,[status(thm)],[])).
% 0.19/0.43 tff(107,plain,
% 0.19/0.43 ((~(in(ordered_pair(tptp_fun_C_2(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), relation_restriction(B!9, A!10)) <=> (~((~in(ordered_pair(tptp_fun_C_2(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), B!9)) | (~in(ordered_pair(tptp_fun_C_2(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), cartesian_product2(A!10, A!10))))))) | (~((~in(ordered_pair(tptp_fun_C_2(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), B!9)) | (~in(ordered_pair(tptp_fun_C_2(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), cartesian_product2(A!10, A!10)))))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[106, 105])).
% 0.19/0.43 tff(108,plain,
% 0.19/0.43 (~((~in(ordered_pair(tptp_fun_C_2(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), B!9)) | (~in(ordered_pair(tptp_fun_C_2(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), cartesian_product2(A!10, A!10))))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[107, 103])).
% 0.19/0.43 tff(109,plain,
% 0.19/0.43 (((~in(ordered_pair(tptp_fun_C_2(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), B!9)) | (~in(ordered_pair(tptp_fun_C_2(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), cartesian_product2(A!10, A!10)))) | in(ordered_pair(tptp_fun_C_2(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), B!9)),
% 0.19/0.43 inference(tautology,[status(thm)],[])).
% 0.19/0.43 tff(110,plain,
% 0.19/0.43 (in(ordered_pair(tptp_fun_C_2(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), B!9)),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[109, 108])).
% 0.19/0.43 tff(111,plain,
% 0.19/0.43 (((~![A: $i] : ((~relation(A)) | (~((~((~transitive(A)) | ![B: $i, C: $i, D: $i] : (in(ordered_pair(B, D), A) | (~in(ordered_pair(B, C), A)) | (~in(ordered_pair(C, D), A))))) | (~(transitive(A) | (~(in(ordered_pair(tptp_fun_B_3(A), tptp_fun_D_1(A)), A) | (~in(ordered_pair(tptp_fun_B_3(A), tptp_fun_C_2(A)), A)) | (~in(ordered_pair(tptp_fun_C_2(A), tptp_fun_D_1(A)), A)))))))))) | ((~relation(B!9)) | (~((~((~transitive(B!9)) | ![B: $i, C: $i, D: $i] : (in(ordered_pair(B, D), B!9) | (~in(ordered_pair(B, C), B!9)) | (~in(ordered_pair(C, D), B!9))))) | (~(transitive(B!9) | (~(in(ordered_pair(tptp_fun_B_3(B!9), tptp_fun_D_1(B!9)), B!9) | (~in(ordered_pair(tptp_fun_B_3(B!9), tptp_fun_C_2(B!9)), B!9)) | (~in(ordered_pair(tptp_fun_C_2(B!9), tptp_fun_D_1(B!9)), B!9)))))))))) <=> ((~![A: $i] : ((~relation(A)) | (~((~((~transitive(A)) | ![B: $i, C: $i, D: $i] : (in(ordered_pair(B, D), A) | (~in(ordered_pair(B, C), A)) | (~in(ordered_pair(C, D), A))))) | (~(transitive(A) | (~(in(ordered_pair(tptp_fun_B_3(A), tptp_fun_D_1(A)), A) | (~in(ordered_pair(tptp_fun_B_3(A), tptp_fun_C_2(A)), A)) | (~in(ordered_pair(tptp_fun_C_2(A), tptp_fun_D_1(A)), A)))))))))) | (~relation(B!9)) | (~((~((~transitive(B!9)) | ![B: $i, C: $i, D: $i] : (in(ordered_pair(B, D), B!9) | (~in(ordered_pair(B, C), B!9)) | (~in(ordered_pair(C, D), B!9))))) | (~(transitive(B!9) | (~(in(ordered_pair(tptp_fun_B_3(B!9), tptp_fun_D_1(B!9)), B!9) | (~in(ordered_pair(tptp_fun_B_3(B!9), tptp_fun_C_2(B!9)), B!9)) | (~in(ordered_pair(tptp_fun_C_2(B!9), tptp_fun_D_1(B!9)), B!9)))))))))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(112,plain,
% 0.19/0.43 ((~![A: $i] : ((~relation(A)) | (~((~((~transitive(A)) | ![B: $i, C: $i, D: $i] : (in(ordered_pair(B, D), A) | (~in(ordered_pair(B, C), A)) | (~in(ordered_pair(C, D), A))))) | (~(transitive(A) | (~(in(ordered_pair(tptp_fun_B_3(A), tptp_fun_D_1(A)), A) | (~in(ordered_pair(tptp_fun_B_3(A), tptp_fun_C_2(A)), A)) | (~in(ordered_pair(tptp_fun_C_2(A), tptp_fun_D_1(A)), A)))))))))) | ((~relation(B!9)) | (~((~((~transitive(B!9)) | ![B: $i, C: $i, D: $i] : (in(ordered_pair(B, D), B!9) | (~in(ordered_pair(B, C), B!9)) | (~in(ordered_pair(C, D), B!9))))) | (~(transitive(B!9) | (~(in(ordered_pair(tptp_fun_B_3(B!9), tptp_fun_D_1(B!9)), B!9) | (~in(ordered_pair(tptp_fun_B_3(B!9), tptp_fun_C_2(B!9)), B!9)) | (~in(ordered_pair(tptp_fun_C_2(B!9), tptp_fun_D_1(B!9)), B!9)))))))))),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(113,plain,
% 0.19/0.43 ((~![A: $i] : ((~relation(A)) | (~((~((~transitive(A)) | ![B: $i, C: $i, D: $i] : (in(ordered_pair(B, D), A) | (~in(ordered_pair(B, C), A)) | (~in(ordered_pair(C, D), A))))) | (~(transitive(A) | (~(in(ordered_pair(tptp_fun_B_3(A), tptp_fun_D_1(A)), A) | (~in(ordered_pair(tptp_fun_B_3(A), tptp_fun_C_2(A)), A)) | (~in(ordered_pair(tptp_fun_C_2(A), tptp_fun_D_1(A)), A)))))))))) | (~relation(B!9)) | (~((~((~transitive(B!9)) | ![B: $i, C: $i, D: $i] : (in(ordered_pair(B, D), B!9) | (~in(ordered_pair(B, C), B!9)) | (~in(ordered_pair(C, D), B!9))))) | (~(transitive(B!9) | (~(in(ordered_pair(tptp_fun_B_3(B!9), tptp_fun_D_1(B!9)), B!9) | (~in(ordered_pair(tptp_fun_B_3(B!9), tptp_fun_C_2(B!9)), B!9)) | (~in(ordered_pair(tptp_fun_C_2(B!9), tptp_fun_D_1(B!9)), B!9))))))))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[112, 111])).
% 0.19/0.43 tff(114,plain,
% 0.19/0.43 (~((~((~transitive(B!9)) | ![B: $i, C: $i, D: $i] : (in(ordered_pair(B, D), B!9) | (~in(ordered_pair(B, C), B!9)) | (~in(ordered_pair(C, D), B!9))))) | (~(transitive(B!9) | (~(in(ordered_pair(tptp_fun_B_3(B!9), tptp_fun_D_1(B!9)), B!9) | (~in(ordered_pair(tptp_fun_B_3(B!9), tptp_fun_C_2(B!9)), B!9)) | (~in(ordered_pair(tptp_fun_C_2(B!9), tptp_fun_D_1(B!9)), B!9)))))))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[113, 73, 26])).
% 0.19/0.43 tff(115,plain,
% 0.19/0.43 (((~((~transitive(B!9)) | ![B: $i, C: $i, D: $i] : (in(ordered_pair(B, D), B!9) | (~in(ordered_pair(B, C), B!9)) | (~in(ordered_pair(C, D), B!9))))) | (~(transitive(B!9) | (~(in(ordered_pair(tptp_fun_B_3(B!9), tptp_fun_D_1(B!9)), B!9) | (~in(ordered_pair(tptp_fun_B_3(B!9), tptp_fun_C_2(B!9)), B!9)) | (~in(ordered_pair(tptp_fun_C_2(B!9), tptp_fun_D_1(B!9)), B!9))))))) | ((~transitive(B!9)) | ![B: $i, C: $i, D: $i] : (in(ordered_pair(B, D), B!9) | (~in(ordered_pair(B, C), B!9)) | (~in(ordered_pair(C, D), B!9))))),
% 0.19/0.43 inference(tautology,[status(thm)],[])).
% 0.19/0.43 tff(116,plain,
% 0.19/0.43 ((~transitive(B!9)) | ![B: $i, C: $i, D: $i] : (in(ordered_pair(B, D), B!9) | (~in(ordered_pair(B, C), B!9)) | (~in(ordered_pair(C, D), B!9)))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[115, 114])).
% 0.19/0.43 tff(117,plain,
% 0.19/0.43 (transitive(B!9)),
% 0.19/0.43 inference(or_elim,[status(thm)],[25])).
% 0.19/0.43 tff(118,plain,
% 0.19/0.43 ((~((~transitive(B!9)) | ![B: $i, C: $i, D: $i] : (in(ordered_pair(B, D), B!9) | (~in(ordered_pair(B, C), B!9)) | (~in(ordered_pair(C, D), B!9))))) | (~transitive(B!9)) | ![B: $i, C: $i, D: $i] : (in(ordered_pair(B, D), B!9) | (~in(ordered_pair(B, C), B!9)) | (~in(ordered_pair(C, D), B!9)))),
% 0.19/0.43 inference(tautology,[status(thm)],[])).
% 0.19/0.43 tff(119,plain,
% 0.19/0.43 ((~((~transitive(B!9)) | ![B: $i, C: $i, D: $i] : (in(ordered_pair(B, D), B!9) | (~in(ordered_pair(B, C), B!9)) | (~in(ordered_pair(C, D), B!9))))) | ![B: $i, C: $i, D: $i] : (in(ordered_pair(B, D), B!9) | (~in(ordered_pair(B, C), B!9)) | (~in(ordered_pair(C, D), B!9)))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[118, 117])).
% 0.19/0.43 tff(120,plain,
% 0.19/0.43 (![B: $i, C: $i, D: $i] : (in(ordered_pair(B, D), B!9) | (~in(ordered_pair(B, C), B!9)) | (~in(ordered_pair(C, D), B!9)))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[119, 116])).
% 0.19/0.43 tff(121,plain,
% 0.19/0.43 (((~![B: $i, C: $i, D: $i] : (in(ordered_pair(B, D), B!9) | (~in(ordered_pair(B, C), B!9)) | (~in(ordered_pair(C, D), B!9)))) | (in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), B!9) | (~in(ordered_pair(tptp_fun_C_2(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), B!9)) | (~in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_C_2(relation_restriction(B!9, A!10))), B!9)))) <=> ((~![B: $i, C: $i, D: $i] : (in(ordered_pair(B, D), B!9) | (~in(ordered_pair(B, C), B!9)) | (~in(ordered_pair(C, D), B!9)))) | in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), B!9) | (~in(ordered_pair(tptp_fun_C_2(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), B!9)) | (~in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_C_2(relation_restriction(B!9, A!10))), B!9)))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(122,plain,
% 0.19/0.43 ((in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), B!9) | (~in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_C_2(relation_restriction(B!9, A!10))), B!9)) | (~in(ordered_pair(tptp_fun_C_2(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), B!9))) <=> (in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), B!9) | (~in(ordered_pair(tptp_fun_C_2(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), B!9)) | (~in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_C_2(relation_restriction(B!9, A!10))), B!9)))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(123,plain,
% 0.19/0.43 (((~![B: $i, C: $i, D: $i] : (in(ordered_pair(B, D), B!9) | (~in(ordered_pair(B, C), B!9)) | (~in(ordered_pair(C, D), B!9)))) | (in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), B!9) | (~in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_C_2(relation_restriction(B!9, A!10))), B!9)) | (~in(ordered_pair(tptp_fun_C_2(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), B!9)))) <=> ((~![B: $i, C: $i, D: $i] : (in(ordered_pair(B, D), B!9) | (~in(ordered_pair(B, C), B!9)) | (~in(ordered_pair(C, D), B!9)))) | (in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), B!9) | (~in(ordered_pair(tptp_fun_C_2(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), B!9)) | (~in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_C_2(relation_restriction(B!9, A!10))), B!9))))),
% 0.19/0.43 inference(monotonicity,[status(thm)],[122])).
% 0.19/0.43 tff(124,plain,
% 0.19/0.43 (((~![B: $i, C: $i, D: $i] : (in(ordered_pair(B, D), B!9) | (~in(ordered_pair(B, C), B!9)) | (~in(ordered_pair(C, D), B!9)))) | (in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), B!9) | (~in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_C_2(relation_restriction(B!9, A!10))), B!9)) | (~in(ordered_pair(tptp_fun_C_2(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), B!9)))) <=> ((~![B: $i, C: $i, D: $i] : (in(ordered_pair(B, D), B!9) | (~in(ordered_pair(B, C), B!9)) | (~in(ordered_pair(C, D), B!9)))) | in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), B!9) | (~in(ordered_pair(tptp_fun_C_2(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), B!9)) | (~in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_C_2(relation_restriction(B!9, A!10))), B!9)))),
% 0.19/0.44 inference(transitivity,[status(thm)],[123, 121])).
% 0.19/0.44 tff(125,plain,
% 0.19/0.44 ((~![B: $i, C: $i, D: $i] : (in(ordered_pair(B, D), B!9) | (~in(ordered_pair(B, C), B!9)) | (~in(ordered_pair(C, D), B!9)))) | (in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), B!9) | (~in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_C_2(relation_restriction(B!9, A!10))), B!9)) | (~in(ordered_pair(tptp_fun_C_2(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), B!9)))),
% 0.19/0.44 inference(quant_inst,[status(thm)],[])).
% 0.19/0.44 tff(126,plain,
% 0.19/0.44 ((~![B: $i, C: $i, D: $i] : (in(ordered_pair(B, D), B!9) | (~in(ordered_pair(B, C), B!9)) | (~in(ordered_pair(C, D), B!9)))) | in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), B!9) | (~in(ordered_pair(tptp_fun_C_2(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), B!9)) | (~in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_C_2(relation_restriction(B!9, A!10))), B!9))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[125, 124])).
% 0.19/0.44 tff(127,plain,
% 0.19/0.44 (in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), B!9) | (~in(ordered_pair(tptp_fun_C_2(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), B!9)) | (~in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_C_2(relation_restriction(B!9, A!10))), B!9))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[126, 120])).
% 0.19/0.44 tff(128,plain,
% 0.19/0.44 (in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), B!9)),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[127, 110, 99])).
% 0.19/0.44 tff(129,plain,
% 0.19/0.44 ((~((~in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), B!9)) | (~in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), cartesian_product2(A!10, A!10))))) | (~in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), B!9)) | (~in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), cartesian_product2(A!10, A!10)))),
% 0.19/0.44 inference(tautology,[status(thm)],[])).
% 0.19/0.44 tff(130,plain,
% 0.19/0.44 (~in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), cartesian_product2(A!10, A!10))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[129, 128, 88])).
% 0.19/0.44 tff(131,plain,
% 0.19/0.44 ((~(in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), cartesian_product2(A!10, A!10)) <=> (~((~in(tptp_fun_B_3(relation_restriction(B!9, A!10)), A!10)) | (~in(tptp_fun_D_1(relation_restriction(B!9, A!10)), A!10)))))) | in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), cartesian_product2(A!10, A!10)) | ((~in(tptp_fun_B_3(relation_restriction(B!9, A!10)), A!10)) | (~in(tptp_fun_D_1(relation_restriction(B!9, A!10)), A!10)))),
% 0.19/0.44 inference(tautology,[status(thm)],[])).
% 0.19/0.44 tff(132,plain,
% 0.19/0.44 ((~(in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), cartesian_product2(A!10, A!10)) <=> (~((~in(tptp_fun_B_3(relation_restriction(B!9, A!10)), A!10)) | (~in(tptp_fun_D_1(relation_restriction(B!9, A!10)), A!10)))))) | ((~in(tptp_fun_B_3(relation_restriction(B!9, A!10)), A!10)) | (~in(tptp_fun_D_1(relation_restriction(B!9, A!10)), A!10)))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[131, 130])).
% 0.19/0.44 tff(133,plain,
% 0.19/0.44 ((~in(tptp_fun_B_3(relation_restriction(B!9, A!10)), A!10)) | (~in(tptp_fun_D_1(relation_restriction(B!9, A!10)), A!10))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[132, 12])).
% 0.19/0.44 tff(134,plain,
% 0.19/0.44 ((~![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_C_2(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), cartesian_product2(A!10, A!10)) <=> (~((~in(tptp_fun_C_2(relation_restriction(B!9, A!10)), A!10)) | (~in(tptp_fun_D_1(relation_restriction(B!9, A!10)), A!10)))))),
% 0.19/0.44 inference(quant_inst,[status(thm)],[])).
% 0.19/0.44 tff(135,plain,
% 0.19/0.44 (in(ordered_pair(tptp_fun_C_2(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), cartesian_product2(A!10, A!10)) <=> (~((~in(tptp_fun_C_2(relation_restriction(B!9, A!10)), A!10)) | (~in(tptp_fun_D_1(relation_restriction(B!9, A!10)), A!10))))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[134, 10])).
% 0.19/0.44 tff(136,plain,
% 0.19/0.44 (((~in(ordered_pair(tptp_fun_C_2(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), B!9)) | (~in(ordered_pair(tptp_fun_C_2(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), cartesian_product2(A!10, A!10)))) | in(ordered_pair(tptp_fun_C_2(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), cartesian_product2(A!10, A!10))),
% 0.19/0.44 inference(tautology,[status(thm)],[])).
% 0.19/0.44 tff(137,plain,
% 0.19/0.44 (in(ordered_pair(tptp_fun_C_2(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), cartesian_product2(A!10, A!10))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[136, 108])).
% 0.19/0.44 tff(138,plain,
% 0.19/0.44 ((~(in(ordered_pair(tptp_fun_C_2(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), cartesian_product2(A!10, A!10)) <=> (~((~in(tptp_fun_C_2(relation_restriction(B!9, A!10)), A!10)) | (~in(tptp_fun_D_1(relation_restriction(B!9, A!10)), A!10)))))) | (~in(ordered_pair(tptp_fun_C_2(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), cartesian_product2(A!10, A!10))) | (~((~in(tptp_fun_C_2(relation_restriction(B!9, A!10)), A!10)) | (~in(tptp_fun_D_1(relation_restriction(B!9, A!10)), A!10))))),
% 0.19/0.44 inference(tautology,[status(thm)],[])).
% 0.19/0.44 tff(139,plain,
% 0.19/0.44 ((~(in(ordered_pair(tptp_fun_C_2(relation_restriction(B!9, A!10)), tptp_fun_D_1(relation_restriction(B!9, A!10))), cartesian_product2(A!10, A!10)) <=> (~((~in(tptp_fun_C_2(relation_restriction(B!9, A!10)), A!10)) | (~in(tptp_fun_D_1(relation_restriction(B!9, A!10)), A!10)))))) | (~((~in(tptp_fun_C_2(relation_restriction(B!9, A!10)), A!10)) | (~in(tptp_fun_D_1(relation_restriction(B!9, A!10)), A!10))))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[138, 137])).
% 0.19/0.44 tff(140,plain,
% 0.19/0.44 (~((~in(tptp_fun_C_2(relation_restriction(B!9, A!10)), A!10)) | (~in(tptp_fun_D_1(relation_restriction(B!9, A!10)), A!10)))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[139, 135])).
% 0.19/0.44 tff(141,plain,
% 0.19/0.44 (((~in(tptp_fun_C_2(relation_restriction(B!9, A!10)), A!10)) | (~in(tptp_fun_D_1(relation_restriction(B!9, A!10)), A!10))) | in(tptp_fun_D_1(relation_restriction(B!9, A!10)), A!10)),
% 0.19/0.44 inference(tautology,[status(thm)],[])).
% 0.19/0.44 tff(142,plain,
% 0.19/0.44 (in(tptp_fun_D_1(relation_restriction(B!9, A!10)), A!10)),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[141, 140])).
% 0.19/0.44 tff(143,plain,
% 0.19/0.44 ((~![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_3(relation_restriction(B!9, A!10)), tptp_fun_C_2(relation_restriction(B!9, A!10))), cartesian_product2(A!10, A!10)) <=> (~((~in(tptp_fun_B_3(relation_restriction(B!9, A!10)), A!10)) | (~in(tptp_fun_C_2(relation_restriction(B!9, A!10)), A!10)))))),
% 0.19/0.44 inference(quant_inst,[status(thm)],[])).
% 0.19/0.44 tff(144,plain,
% 0.19/0.44 (in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_C_2(relation_restriction(B!9, A!10))), cartesian_product2(A!10, A!10)) <=> (~((~in(tptp_fun_B_3(relation_restriction(B!9, A!10)), A!10)) | (~in(tptp_fun_C_2(relation_restriction(B!9, A!10)), A!10))))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[143, 10])).
% 0.19/0.44 tff(145,plain,
% 0.19/0.44 (((~in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_C_2(relation_restriction(B!9, A!10))), B!9)) | (~in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_C_2(relation_restriction(B!9, A!10))), cartesian_product2(A!10, A!10)))) | in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_C_2(relation_restriction(B!9, A!10))), cartesian_product2(A!10, A!10))),
% 0.19/0.45 inference(tautology,[status(thm)],[])).
% 0.19/0.45 tff(146,plain,
% 0.19/0.45 (in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_C_2(relation_restriction(B!9, A!10))), cartesian_product2(A!10, A!10))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[145, 97])).
% 0.19/0.45 tff(147,plain,
% 0.19/0.45 ((~(in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_C_2(relation_restriction(B!9, A!10))), cartesian_product2(A!10, A!10)) <=> (~((~in(tptp_fun_B_3(relation_restriction(B!9, A!10)), A!10)) | (~in(tptp_fun_C_2(relation_restriction(B!9, A!10)), A!10)))))) | (~in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_C_2(relation_restriction(B!9, A!10))), cartesian_product2(A!10, A!10))) | (~((~in(tptp_fun_B_3(relation_restriction(B!9, A!10)), A!10)) | (~in(tptp_fun_C_2(relation_restriction(B!9, A!10)), A!10))))),
% 0.19/0.45 inference(tautology,[status(thm)],[])).
% 0.19/0.45 tff(148,plain,
% 0.19/0.45 ((~(in(ordered_pair(tptp_fun_B_3(relation_restriction(B!9, A!10)), tptp_fun_C_2(relation_restriction(B!9, A!10))), cartesian_product2(A!10, A!10)) <=> (~((~in(tptp_fun_B_3(relation_restriction(B!9, A!10)), A!10)) | (~in(tptp_fun_C_2(relation_restriction(B!9, A!10)), A!10)))))) | (~((~in(tptp_fun_B_3(relation_restriction(B!9, A!10)), A!10)) | (~in(tptp_fun_C_2(relation_restriction(B!9, A!10)), A!10))))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[147, 146])).
% 0.19/0.45 tff(149,plain,
% 0.19/0.45 (~((~in(tptp_fun_B_3(relation_restriction(B!9, A!10)), A!10)) | (~in(tptp_fun_C_2(relation_restriction(B!9, A!10)), A!10)))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[148, 144])).
% 0.19/0.45 tff(150,plain,
% 0.19/0.45 (((~in(tptp_fun_B_3(relation_restriction(B!9, A!10)), A!10)) | (~in(tptp_fun_C_2(relation_restriction(B!9, A!10)), A!10))) | in(tptp_fun_B_3(relation_restriction(B!9, A!10)), A!10)),
% 0.19/0.45 inference(tautology,[status(thm)],[])).
% 0.19/0.45 tff(151,plain,
% 0.19/0.45 (in(tptp_fun_B_3(relation_restriction(B!9, A!10)), A!10)),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[150, 149])).
% 0.19/0.45 tff(152,plain,
% 0.19/0.45 ((~((~in(tptp_fun_B_3(relation_restriction(B!9, A!10)), A!10)) | (~in(tptp_fun_D_1(relation_restriction(B!9, A!10)), A!10)))) | (~in(tptp_fun_B_3(relation_restriction(B!9, A!10)), A!10)) | (~in(tptp_fun_D_1(relation_restriction(B!9, A!10)), A!10))),
% 0.19/0.45 inference(tautology,[status(thm)],[])).
% 0.19/0.45 tff(153,plain,
% 0.19/0.45 ($false),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[152, 151, 142, 133])).
% 0.19/0.45 % SZS output end Proof
%------------------------------------------------------------------------------