TSTP Solution File: SEU253+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SEU253+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 0.21s 0.42s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SEU253+1 : TPTP v8.1.0. Released v3.3.0.
% 0.11/0.13 % 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 11:19:02 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.35 Usage: tptp [options] [-file:]file
% 0.12/0.35 -h, -? prints this message.
% 0.12/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.35 -m, -model generate model.
% 0.12/0.35 -p, -proof generate proof.
% 0.12/0.35 -c, -core generate unsat core of named formulas.
% 0.12/0.35 -st, -statistics display statistics.
% 0.12/0.35 -t:timeout set timeout (in second).
% 0.12/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.35 -<param>:<value> configuration parameter and value.
% 0.12/0.35 -o:<output-file> file to place output in.
% 0.21/0.42 % SZS status Theorem
% 0.21/0.42 % SZS output start Proof
% 0.21/0.42 tff(in_type, type, (
% 0.21/0.42 in: ( $i * $i ) > $o)).
% 0.21/0.42 tff(tptp_fun_A_9_type, type, (
% 0.21/0.42 tptp_fun_A_9: $i)).
% 0.21/0.42 tff(tptp_fun_B_2_type, type, (
% 0.21/0.42 tptp_fun_B_2: $i > $i)).
% 0.21/0.42 tff(relation_restriction_type, type, (
% 0.21/0.42 relation_restriction: ( $i * $i ) > $i)).
% 0.21/0.42 tff(tptp_fun_B_8_type, type, (
% 0.21/0.42 tptp_fun_B_8: $i)).
% 0.21/0.42 tff(tptp_fun_C_1_type, type, (
% 0.21/0.42 tptp_fun_C_1: $i > $i)).
% 0.21/0.42 tff(cartesian_product2_type, type, (
% 0.21/0.42 cartesian_product2: ( $i * $i ) > $i)).
% 0.21/0.42 tff(ordered_pair_type, type, (
% 0.21/0.42 ordered_pair: ( $i * $i ) > $i)).
% 0.21/0.42 tff(relation_field_type, type, (
% 0.21/0.42 relation_field: $i > $i)).
% 0.21/0.42 tff(connected_type, type, (
% 0.21/0.42 connected: $i > $o)).
% 0.21/0.42 tff(relation_type, type, (
% 0.21/0.42 relation: $i > $o)).
% 0.21/0.42 tff(1,plain,
% 0.21/0.42 ((~(connected(relation_restriction(B!8, A!9)) | (~relation(B!8)) | (~connected(B!8)))) <=> (~(connected(relation_restriction(B!8, A!9)) | (~relation(B!8)) | (~connected(B!8))))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(2,plain,
% 0.21/0.42 ((~![A: $i, B: $i] : (connected(relation_restriction(B, A)) | (~relation(B)) | (~connected(B)))) <=> (~![A: $i, B: $i] : (connected(relation_restriction(B, A)) | (~relation(B)) | (~connected(B))))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(3,plain,
% 0.21/0.42 ((~![A: $i, B: $i] : (relation(B) => (connected(B) => connected(relation_restriction(B, A))))) <=> (~![A: $i, B: $i] : (connected(relation_restriction(B, A)) | (~relation(B)) | (~connected(B))))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(4,axiom,(~![A: $i, B: $i] : (relation(B) => (connected(B) => connected(relation_restriction(B, A))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t23_wellord1')).
% 0.21/0.42 tff(5,plain,
% 0.21/0.42 (~![A: $i, B: $i] : (connected(relation_restriction(B, A)) | (~relation(B)) | (~connected(B)))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.21/0.42 tff(6,plain,
% 0.21/0.42 (~![A: $i, B: $i] : (connected(relation_restriction(B, A)) | (~relation(B)) | (~connected(B)))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[5, 2])).
% 0.21/0.42 tff(7,plain,
% 0.21/0.42 (~![A: $i, B: $i] : (connected(relation_restriction(B, A)) | (~relation(B)) | (~connected(B)))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.21/0.42 tff(8,plain,
% 0.21/0.42 (~![A: $i, B: $i] : (connected(relation_restriction(B, A)) | (~relation(B)) | (~connected(B)))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[7, 2])).
% 0.21/0.42 tff(9,plain,
% 0.21/0.42 (~![A: $i, B: $i] : (connected(relation_restriction(B, A)) | (~relation(B)) | (~connected(B)))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[8, 2])).
% 0.21/0.42 tff(10,plain,
% 0.21/0.42 (~![A: $i, B: $i] : (connected(relation_restriction(B, A)) | (~relation(B)) | (~connected(B)))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[9, 2])).
% 0.21/0.42 tff(11,plain,
% 0.21/0.42 (~![A: $i, B: $i] : (connected(relation_restriction(B, A)) | (~relation(B)) | (~connected(B)))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[10, 2])).
% 0.21/0.42 tff(12,plain,(
% 0.21/0.42 ~(connected(relation_restriction(B!8, A!9)) | (~relation(B!8)) | (~connected(B!8)))),
% 0.21/0.42 inference(skolemize,[status(sab)],[11])).
% 0.21/0.42 tff(13,plain,
% 0.21/0.42 (~(connected(relation_restriction(B!8, A!9)) | (~relation(B!8)) | (~connected(B!8)))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[12, 1])).
% 0.21/0.42 tff(14,plain,
% 0.21/0.42 (relation(B!8)),
% 0.21/0.42 inference(or_elim,[status(thm)],[13])).
% 0.21/0.42 tff(15,plain,
% 0.21/0.42 (^[A: $i, B: $i] : refl(((~relation(A)) | relation(relation_restriction(A, B))) <=> ((~relation(A)) | relation(relation_restriction(A, B))))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(16,plain,
% 0.21/0.42 (![A: $i, B: $i] : ((~relation(A)) | relation(relation_restriction(A, B))) <=> ![A: $i, B: $i] : ((~relation(A)) | relation(relation_restriction(A, B)))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[15])).
% 0.21/0.42 tff(17,plain,
% 0.21/0.42 (![A: $i, B: $i] : ((~relation(A)) | relation(relation_restriction(A, B))) <=> ![A: $i, B: $i] : ((~relation(A)) | relation(relation_restriction(A, B)))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(18,plain,
% 0.21/0.42 (^[A: $i, B: $i] : rewrite((relation(A) => relation(relation_restriction(A, B))) <=> ((~relation(A)) | relation(relation_restriction(A, B))))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(19,plain,
% 0.21/0.42 (![A: $i, B: $i] : (relation(A) => relation(relation_restriction(A, B))) <=> ![A: $i, B: $i] : ((~relation(A)) | relation(relation_restriction(A, B)))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[18])).
% 0.21/0.42 tff(20,axiom,(![A: $i, B: $i] : (relation(A) => relation(relation_restriction(A, B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_k2_wellord1')).
% 0.21/0.42 tff(21,plain,
% 0.21/0.42 (![A: $i, B: $i] : ((~relation(A)) | relation(relation_restriction(A, B)))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[20, 19])).
% 0.21/0.42 tff(22,plain,
% 0.21/0.42 (![A: $i, B: $i] : ((~relation(A)) | relation(relation_restriction(A, B)))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[21, 17])).
% 0.21/0.42 tff(23,plain,(
% 0.21/0.42 ![A: $i, B: $i] : ((~relation(A)) | relation(relation_restriction(A, B)))),
% 0.21/0.42 inference(skolemize,[status(sab)],[22])).
% 0.21/0.42 tff(24,plain,
% 0.21/0.42 (![A: $i, B: $i] : ((~relation(A)) | relation(relation_restriction(A, B)))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[23, 16])).
% 0.21/0.42 tff(25,plain,
% 0.21/0.42 (((~![A: $i, B: $i] : ((~relation(A)) | relation(relation_restriction(A, B)))) | ((~relation(B!8)) | relation(relation_restriction(B!8, A!9)))) <=> ((~![A: $i, B: $i] : ((~relation(A)) | relation(relation_restriction(A, B)))) | (~relation(B!8)) | relation(relation_restriction(B!8, A!9)))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(26,plain,
% 0.21/0.42 ((~![A: $i, B: $i] : ((~relation(A)) | relation(relation_restriction(A, B)))) | ((~relation(B!8)) | relation(relation_restriction(B!8, A!9)))),
% 0.21/0.42 inference(quant_inst,[status(thm)],[])).
% 0.21/0.42 tff(27,plain,
% 0.21/0.42 ((~![A: $i, B: $i] : ((~relation(A)) | relation(relation_restriction(A, B)))) | (~relation(B!8)) | relation(relation_restriction(B!8, A!9))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[26, 25])).
% 0.21/0.42 tff(28,plain,
% 0.21/0.42 (relation(relation_restriction(B!8, A!9))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[27, 24, 14])).
% 0.21/0.42 tff(29,plain,
% 0.21/0.42 (^[A: $i] : rewrite(((~relation(A)) | (~((~((~connected(A)) | ![B: $i, C: $i] : (in(ordered_pair(C, B), A) | in(ordered_pair(B, C), A) | (B = C) | (~in(B, relation_field(A))) | (~in(C, relation_field(A)))))) | (~(connected(A) | (~((~in(tptp_fun_B_2(A), relation_field(A))) | (~in(tptp_fun_C_1(A), relation_field(A))) | (tptp_fun_B_2(A) = tptp_fun_C_1(A)) | in(ordered_pair(tptp_fun_B_2(A), tptp_fun_C_1(A)), A) | in(ordered_pair(tptp_fun_C_1(A), tptp_fun_B_2(A)), A)))))))) <=> ((~relation(A)) | (~((~(connected(A) | (~((~in(tptp_fun_B_2(A), relation_field(A))) | (~in(tptp_fun_C_1(A), relation_field(A))) | (tptp_fun_B_2(A) = tptp_fun_C_1(A)) | in(ordered_pair(tptp_fun_B_2(A), tptp_fun_C_1(A)), A) | in(ordered_pair(tptp_fun_C_1(A), tptp_fun_B_2(A)), A))))) | (~((~connected(A)) | ![B: $i, C: $i] : (in(ordered_pair(C, B), A) | in(ordered_pair(B, C), A) | (B = C) | (~in(B, relation_field(A))) | (~in(C, relation_field(A))))))))))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(30,plain,
% 0.21/0.42 (![A: $i] : ((~relation(A)) | (~((~((~connected(A)) | ![B: $i, C: $i] : (in(ordered_pair(C, B), A) | in(ordered_pair(B, C), A) | (B = C) | (~in(B, relation_field(A))) | (~in(C, relation_field(A)))))) | (~(connected(A) | (~((~in(tptp_fun_B_2(A), relation_field(A))) | (~in(tptp_fun_C_1(A), relation_field(A))) | (tptp_fun_B_2(A) = tptp_fun_C_1(A)) | in(ordered_pair(tptp_fun_B_2(A), tptp_fun_C_1(A)), A) | in(ordered_pair(tptp_fun_C_1(A), tptp_fun_B_2(A)), A)))))))) <=> ![A: $i] : ((~relation(A)) | (~((~(connected(A) | (~((~in(tptp_fun_B_2(A), relation_field(A))) | (~in(tptp_fun_C_1(A), relation_field(A))) | (tptp_fun_B_2(A) = tptp_fun_C_1(A)) | in(ordered_pair(tptp_fun_B_2(A), tptp_fun_C_1(A)), A) | in(ordered_pair(tptp_fun_C_1(A), tptp_fun_B_2(A)), A))))) | (~((~connected(A)) | ![B: $i, C: $i] : (in(ordered_pair(C, B), A) | in(ordered_pair(B, C), A) | (B = C) | (~in(B, relation_field(A))) | (~in(C, relation_field(A)))))))))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[29])).
% 0.21/0.42 tff(31,plain,
% 0.21/0.42 (^[A: $i] : refl(((~relation(A)) | (~((~((~connected(A)) | ![B: $i, C: $i] : (in(ordered_pair(C, B), A) | in(ordered_pair(B, C), A) | (B = C) | (~in(B, relation_field(A))) | (~in(C, relation_field(A)))))) | (~(connected(A) | (~((~in(tptp_fun_B_2(A), relation_field(A))) | (~in(tptp_fun_C_1(A), relation_field(A))) | (tptp_fun_B_2(A) = tptp_fun_C_1(A)) | in(ordered_pair(tptp_fun_B_2(A), tptp_fun_C_1(A)), A) | in(ordered_pair(tptp_fun_C_1(A), tptp_fun_B_2(A)), A)))))))) <=> ((~relation(A)) | (~((~((~connected(A)) | ![B: $i, C: $i] : (in(ordered_pair(C, B), A) | in(ordered_pair(B, C), A) | (B = C) | (~in(B, relation_field(A))) | (~in(C, relation_field(A)))))) | (~(connected(A) | (~((~in(tptp_fun_B_2(A), relation_field(A))) | (~in(tptp_fun_C_1(A), relation_field(A))) | (tptp_fun_B_2(A) = tptp_fun_C_1(A)) | in(ordered_pair(tptp_fun_B_2(A), tptp_fun_C_1(A)), A) | in(ordered_pair(tptp_fun_C_1(A), tptp_fun_B_2(A)), A)))))))))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(32,plain,
% 0.21/0.42 (![A: $i] : ((~relation(A)) | (~((~((~connected(A)) | ![B: $i, C: $i] : (in(ordered_pair(C, B), A) | in(ordered_pair(B, C), A) | (B = C) | (~in(B, relation_field(A))) | (~in(C, relation_field(A)))))) | (~(connected(A) | (~((~in(tptp_fun_B_2(A), relation_field(A))) | (~in(tptp_fun_C_1(A), relation_field(A))) | (tptp_fun_B_2(A) = tptp_fun_C_1(A)) | in(ordered_pair(tptp_fun_B_2(A), tptp_fun_C_1(A)), A) | in(ordered_pair(tptp_fun_C_1(A), tptp_fun_B_2(A)), A)))))))) <=> ![A: $i] : ((~relation(A)) | (~((~((~connected(A)) | ![B: $i, C: $i] : (in(ordered_pair(C, B), A) | in(ordered_pair(B, C), A) | (B = C) | (~in(B, relation_field(A))) | (~in(C, relation_field(A)))))) | (~(connected(A) | (~((~in(tptp_fun_B_2(A), relation_field(A))) | (~in(tptp_fun_C_1(A), relation_field(A))) | (tptp_fun_B_2(A) = tptp_fun_C_1(A)) | in(ordered_pair(tptp_fun_B_2(A), tptp_fun_C_1(A)), A) | in(ordered_pair(tptp_fun_C_1(A), tptp_fun_B_2(A)), A))))))))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[31])).
% 0.21/0.42 tff(33,plain,
% 0.21/0.42 (^[A: $i] : rewrite(((~relation(A)) | (~((~((~connected(A)) | ![B: $i, C: $i] : (in(ordered_pair(C, B), A) | in(ordered_pair(B, C), A) | (B = C) | (~in(B, relation_field(A))) | (~in(C, relation_field(A)))))) | (~(connected(A) | (~((~in(tptp_fun_B_2(A), relation_field(A))) | (~in(tptp_fun_C_1(A), relation_field(A))) | (tptp_fun_B_2(A) = tptp_fun_C_1(A)) | in(ordered_pair(tptp_fun_B_2(A), tptp_fun_C_1(A)), A) | in(ordered_pair(tptp_fun_C_1(A), tptp_fun_B_2(A)), A)))))))) <=> ((~relation(A)) | (~((~((~connected(A)) | ![B: $i, C: $i] : (in(ordered_pair(C, B), A) | in(ordered_pair(B, C), A) | (B = C) | (~in(B, relation_field(A))) | (~in(C, relation_field(A)))))) | (~(connected(A) | (~((~in(tptp_fun_B_2(A), relation_field(A))) | (~in(tptp_fun_C_1(A), relation_field(A))) | (tptp_fun_B_2(A) = tptp_fun_C_1(A)) | in(ordered_pair(tptp_fun_B_2(A), tptp_fun_C_1(A)), A) | in(ordered_pair(tptp_fun_C_1(A), tptp_fun_B_2(A)), A)))))))))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(34,plain,
% 0.21/0.42 (![A: $i] : ((~relation(A)) | (~((~((~connected(A)) | ![B: $i, C: $i] : (in(ordered_pair(C, B), A) | in(ordered_pair(B, C), A) | (B = C) | (~in(B, relation_field(A))) | (~in(C, relation_field(A)))))) | (~(connected(A) | (~((~in(tptp_fun_B_2(A), relation_field(A))) | (~in(tptp_fun_C_1(A), relation_field(A))) | (tptp_fun_B_2(A) = tptp_fun_C_1(A)) | in(ordered_pair(tptp_fun_B_2(A), tptp_fun_C_1(A)), A) | in(ordered_pair(tptp_fun_C_1(A), tptp_fun_B_2(A)), A)))))))) <=> ![A: $i] : ((~relation(A)) | (~((~((~connected(A)) | ![B: $i, C: $i] : (in(ordered_pair(C, B), A) | in(ordered_pair(B, C), A) | (B = C) | (~in(B, relation_field(A))) | (~in(C, relation_field(A)))))) | (~(connected(A) | (~((~in(tptp_fun_B_2(A), relation_field(A))) | (~in(tptp_fun_C_1(A), relation_field(A))) | (tptp_fun_B_2(A) = tptp_fun_C_1(A)) | in(ordered_pair(tptp_fun_B_2(A), tptp_fun_C_1(A)), A) | in(ordered_pair(tptp_fun_C_1(A), tptp_fun_B_2(A)), A))))))))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[33])).
% 0.21/0.42 tff(35,plain,
% 0.21/0.42 (![A: $i] : ((~relation(A)) | (~((~((~connected(A)) | ![B: $i, C: $i] : (in(ordered_pair(C, B), A) | in(ordered_pair(B, C), A) | (B = C) | (~in(B, relation_field(A))) | (~in(C, relation_field(A)))))) | (~(connected(A) | (~((~in(tptp_fun_B_2(A), relation_field(A))) | (~in(tptp_fun_C_1(A), relation_field(A))) | (tptp_fun_B_2(A) = tptp_fun_C_1(A)) | in(ordered_pair(tptp_fun_B_2(A), tptp_fun_C_1(A)), A) | in(ordered_pair(tptp_fun_C_1(A), tptp_fun_B_2(A)), A)))))))) <=> ![A: $i] : ((~relation(A)) | (~((~((~connected(A)) | ![B: $i, C: $i] : (in(ordered_pair(C, B), A) | in(ordered_pair(B, C), A) | (B = C) | (~in(B, relation_field(A))) | (~in(C, relation_field(A)))))) | (~(connected(A) | (~((~in(tptp_fun_B_2(A), relation_field(A))) | (~in(tptp_fun_C_1(A), relation_field(A))) | (tptp_fun_B_2(A) = tptp_fun_C_1(A)) | in(ordered_pair(tptp_fun_B_2(A), tptp_fun_C_1(A)), A) | in(ordered_pair(tptp_fun_C_1(A), tptp_fun_B_2(A)), A))))))))),
% 0.21/0.42 inference(transitivity,[status(thm)],[34, 32])).
% 0.21/0.42 tff(36,plain,
% 0.21/0.42 (^[A: $i] : rewrite(((~relation(A)) | (((~connected(A)) | ![B: $i, C: $i] : (~(in(B, relation_field(A)) & in(C, relation_field(A)) & (~(B = C)) & (~in(ordered_pair(B, C), A)) & (~in(ordered_pair(C, B), A))))) & (connected(A) | (in(tptp_fun_B_2(A), relation_field(A)) & in(tptp_fun_C_1(A), relation_field(A)) & (~(tptp_fun_B_2(A) = tptp_fun_C_1(A))) & (~in(ordered_pair(tptp_fun_B_2(A), tptp_fun_C_1(A)), A)) & (~in(ordered_pair(tptp_fun_C_1(A), tptp_fun_B_2(A)), A)))))) <=> ((~relation(A)) | (~((~((~connected(A)) | ![B: $i, C: $i] : (in(ordered_pair(C, B), A) | in(ordered_pair(B, C), A) | (B = C) | (~in(B, relation_field(A))) | (~in(C, relation_field(A)))))) | (~(connected(A) | (~((~in(tptp_fun_B_2(A), relation_field(A))) | (~in(tptp_fun_C_1(A), relation_field(A))) | (tptp_fun_B_2(A) = tptp_fun_C_1(A)) | in(ordered_pair(tptp_fun_B_2(A), tptp_fun_C_1(A)), A) | in(ordered_pair(tptp_fun_C_1(A), tptp_fun_B_2(A)), A)))))))))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(37,plain,
% 0.21/0.42 (![A: $i] : ((~relation(A)) | (((~connected(A)) | ![B: $i, C: $i] : (~(in(B, relation_field(A)) & in(C, relation_field(A)) & (~(B = C)) & (~in(ordered_pair(B, C), A)) & (~in(ordered_pair(C, B), A))))) & (connected(A) | (in(tptp_fun_B_2(A), relation_field(A)) & in(tptp_fun_C_1(A), relation_field(A)) & (~(tptp_fun_B_2(A) = tptp_fun_C_1(A))) & (~in(ordered_pair(tptp_fun_B_2(A), tptp_fun_C_1(A)), A)) & (~in(ordered_pair(tptp_fun_C_1(A), tptp_fun_B_2(A)), A)))))) <=> ![A: $i] : ((~relation(A)) | (~((~((~connected(A)) | ![B: $i, C: $i] : (in(ordered_pair(C, B), A) | in(ordered_pair(B, C), A) | (B = C) | (~in(B, relation_field(A))) | (~in(C, relation_field(A)))))) | (~(connected(A) | (~((~in(tptp_fun_B_2(A), relation_field(A))) | (~in(tptp_fun_C_1(A), relation_field(A))) | (tptp_fun_B_2(A) = tptp_fun_C_1(A)) | in(ordered_pair(tptp_fun_B_2(A), tptp_fun_C_1(A)), A) | in(ordered_pair(tptp_fun_C_1(A), tptp_fun_B_2(A)), A))))))))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[36])).
% 0.21/0.42 tff(38,plain,
% 0.21/0.42 (^[A: $i] : rewrite(((~relation(A)) | (((~connected(A)) | ![B: $i, C: $i] : (~(in(B, relation_field(A)) & in(C, relation_field(A)) & (~(B = C)) & (~in(ordered_pair(B, C), A)) & (~in(ordered_pair(C, B), A))))) & (connected(A) | (~(~(in(tptp_fun_B_2(A), relation_field(A)) & in(tptp_fun_C_1(A), relation_field(A)) & (~(tptp_fun_B_2(A) = tptp_fun_C_1(A))) & (~in(ordered_pair(tptp_fun_B_2(A), tptp_fun_C_1(A)), A)) & (~in(ordered_pair(tptp_fun_C_1(A), tptp_fun_B_2(A)), A)))))))) <=> ((~relation(A)) | (((~connected(A)) | ![B: $i, C: $i] : (~(in(B, relation_field(A)) & in(C, relation_field(A)) & (~(B = C)) & (~in(ordered_pair(B, C), A)) & (~in(ordered_pair(C, B), A))))) & (connected(A) | (in(tptp_fun_B_2(A), relation_field(A)) & in(tptp_fun_C_1(A), relation_field(A)) & (~(tptp_fun_B_2(A) = tptp_fun_C_1(A))) & (~in(ordered_pair(tptp_fun_B_2(A), tptp_fun_C_1(A)), A)) & (~in(ordered_pair(tptp_fun_C_1(A), tptp_fun_B_2(A)), A)))))))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(39,plain,
% 0.21/0.42 (![A: $i] : ((~relation(A)) | (((~connected(A)) | ![B: $i, C: $i] : (~(in(B, relation_field(A)) & in(C, relation_field(A)) & (~(B = C)) & (~in(ordered_pair(B, C), A)) & (~in(ordered_pair(C, B), A))))) & (connected(A) | (~(~(in(tptp_fun_B_2(A), relation_field(A)) & in(tptp_fun_C_1(A), relation_field(A)) & (~(tptp_fun_B_2(A) = tptp_fun_C_1(A))) & (~in(ordered_pair(tptp_fun_B_2(A), tptp_fun_C_1(A)), A)) & (~in(ordered_pair(tptp_fun_C_1(A), tptp_fun_B_2(A)), A)))))))) <=> ![A: $i] : ((~relation(A)) | (((~connected(A)) | ![B: $i, C: $i] : (~(in(B, relation_field(A)) & in(C, relation_field(A)) & (~(B = C)) & (~in(ordered_pair(B, C), A)) & (~in(ordered_pair(C, B), A))))) & (connected(A) | (in(tptp_fun_B_2(A), relation_field(A)) & in(tptp_fun_C_1(A), relation_field(A)) & (~(tptp_fun_B_2(A) = tptp_fun_C_1(A))) & (~in(ordered_pair(tptp_fun_B_2(A), tptp_fun_C_1(A)), A)) & (~in(ordered_pair(tptp_fun_C_1(A), tptp_fun_B_2(A)), A))))))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[38])).
% 0.21/0.42 tff(40,plain,
% 0.21/0.42 (![A: $i] : ((~relation(A)) | (connected(A) <=> ![B: $i, C: $i] : (~(in(B, relation_field(A)) & in(C, relation_field(A)) & (~(B = C)) & (~in(ordered_pair(B, C), A)) & (~in(ordered_pair(C, B), A)))))) <=> ![A: $i] : ((~relation(A)) | (connected(A) <=> ![B: $i, C: $i] : (~(in(B, relation_field(A)) & in(C, relation_field(A)) & (~(B = C)) & (~in(ordered_pair(B, C), A)) & (~in(ordered_pair(C, B), A))))))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(41,plain,
% 0.21/0.42 (^[A: $i] : trans(monotonicity(rewrite((connected(A) <=> ![B: $i, C: $i] : (~((((in(B, relation_field(A)) & in(C, relation_field(A))) & (~(B = C))) & (~in(ordered_pair(B, C), A))) & (~in(ordered_pair(C, B), A))))) <=> (connected(A) <=> ![B: $i, C: $i] : (~(in(B, relation_field(A)) & in(C, relation_field(A)) & (~(B = C)) & (~in(ordered_pair(B, C), A)) & (~in(ordered_pair(C, B), A)))))), ((relation(A) => (connected(A) <=> ![B: $i, C: $i] : (~((((in(B, relation_field(A)) & in(C, relation_field(A))) & (~(B = C))) & (~in(ordered_pair(B, C), A))) & (~in(ordered_pair(C, B), A)))))) <=> (relation(A) => (connected(A) <=> ![B: $i, C: $i] : (~(in(B, relation_field(A)) & in(C, relation_field(A)) & (~(B = C)) & (~in(ordered_pair(B, C), A)) & (~in(ordered_pair(C, B), A)))))))), rewrite((relation(A) => (connected(A) <=> ![B: $i, C: $i] : (~(in(B, relation_field(A)) & in(C, relation_field(A)) & (~(B = C)) & (~in(ordered_pair(B, C), A)) & (~in(ordered_pair(C, B), A)))))) <=> ((~relation(A)) | (connected(A) <=> ![B: $i, C: $i] : (~(in(B, relation_field(A)) & in(C, relation_field(A)) & (~(B = C)) & (~in(ordered_pair(B, C), A)) & (~in(ordered_pair(C, B), A))))))), ((relation(A) => (connected(A) <=> ![B: $i, C: $i] : (~((((in(B, relation_field(A)) & in(C, relation_field(A))) & (~(B = C))) & (~in(ordered_pair(B, C), A))) & (~in(ordered_pair(C, B), A)))))) <=> ((~relation(A)) | (connected(A) <=> ![B: $i, C: $i] : (~(in(B, relation_field(A)) & in(C, relation_field(A)) & (~(B = C)) & (~in(ordered_pair(B, C), A)) & (~in(ordered_pair(C, B), A))))))))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(42,plain,
% 0.21/0.42 (![A: $i] : (relation(A) => (connected(A) <=> ![B: $i, C: $i] : (~((((in(B, relation_field(A)) & in(C, relation_field(A))) & (~(B = C))) & (~in(ordered_pair(B, C), A))) & (~in(ordered_pair(C, B), A)))))) <=> ![A: $i] : ((~relation(A)) | (connected(A) <=> ![B: $i, C: $i] : (~(in(B, relation_field(A)) & in(C, relation_field(A)) & (~(B = C)) & (~in(ordered_pair(B, C), A)) & (~in(ordered_pair(C, B), A))))))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[41])).
% 0.21/0.42 tff(43,axiom,(![A: $i] : (relation(A) => (connected(A) <=> ![B: $i, C: $i] : (~((((in(B, relation_field(A)) & in(C, relation_field(A))) & (~(B = C))) & (~in(ordered_pair(B, C), A))) & (~in(ordered_pair(C, B), A))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','l4_wellord1')).
% 0.21/0.42 tff(44,plain,
% 0.21/0.42 (![A: $i] : ((~relation(A)) | (connected(A) <=> ![B: $i, C: $i] : (~(in(B, relation_field(A)) & in(C, relation_field(A)) & (~(B = C)) & (~in(ordered_pair(B, C), A)) & (~in(ordered_pair(C, B), A))))))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[43, 42])).
% 0.21/0.42 tff(45,plain,
% 0.21/0.42 (![A: $i] : ((~relation(A)) | (connected(A) <=> ![B: $i, C: $i] : (~(in(B, relation_field(A)) & in(C, relation_field(A)) & (~(B = C)) & (~in(ordered_pair(B, C), A)) & (~in(ordered_pair(C, B), A))))))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[44, 40])).
% 0.21/0.42 tff(46,plain,(
% 0.21/0.42 ![A: $i] : ((~relation(A)) | (((~connected(A)) | ![B: $i, C: $i] : (~(in(B, relation_field(A)) & in(C, relation_field(A)) & (~(B = C)) & (~in(ordered_pair(B, C), A)) & (~in(ordered_pair(C, B), A))))) & (connected(A) | (~(~(in(tptp_fun_B_2(A), relation_field(A)) & in(tptp_fun_C_1(A), relation_field(A)) & (~(tptp_fun_B_2(A) = tptp_fun_C_1(A))) & (~in(ordered_pair(tptp_fun_B_2(A), tptp_fun_C_1(A)), A)) & (~in(ordered_pair(tptp_fun_C_1(A), tptp_fun_B_2(A)), A))))))))),
% 0.21/0.42 inference(skolemize,[status(sab)],[45])).
% 0.21/0.42 tff(47,plain,
% 0.21/0.42 (![A: $i] : ((~relation(A)) | (((~connected(A)) | ![B: $i, C: $i] : (~(in(B, relation_field(A)) & in(C, relation_field(A)) & (~(B = C)) & (~in(ordered_pair(B, C), A)) & (~in(ordered_pair(C, B), A))))) & (connected(A) | (in(tptp_fun_B_2(A), relation_field(A)) & in(tptp_fun_C_1(A), relation_field(A)) & (~(tptp_fun_B_2(A) = tptp_fun_C_1(A))) & (~in(ordered_pair(tptp_fun_B_2(A), tptp_fun_C_1(A)), A)) & (~in(ordered_pair(tptp_fun_C_1(A), tptp_fun_B_2(A)), A))))))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[46, 39])).
% 0.21/0.42 tff(48,plain,
% 0.21/0.42 (![A: $i] : ((~relation(A)) | (~((~((~connected(A)) | ![B: $i, C: $i] : (in(ordered_pair(C, B), A) | in(ordered_pair(B, C), A) | (B = C) | (~in(B, relation_field(A))) | (~in(C, relation_field(A)))))) | (~(connected(A) | (~((~in(tptp_fun_B_2(A), relation_field(A))) | (~in(tptp_fun_C_1(A), relation_field(A))) | (tptp_fun_B_2(A) = tptp_fun_C_1(A)) | in(ordered_pair(tptp_fun_B_2(A), tptp_fun_C_1(A)), A) | in(ordered_pair(tptp_fun_C_1(A), tptp_fun_B_2(A)), A))))))))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[47, 37])).
% 0.21/0.42 tff(49,plain,
% 0.21/0.42 (![A: $i] : ((~relation(A)) | (~((~((~connected(A)) | ![B: $i, C: $i] : (in(ordered_pair(C, B), A) | in(ordered_pair(B, C), A) | (B = C) | (~in(B, relation_field(A))) | (~in(C, relation_field(A)))))) | (~(connected(A) | (~((~in(tptp_fun_B_2(A), relation_field(A))) | (~in(tptp_fun_C_1(A), relation_field(A))) | (tptp_fun_B_2(A) = tptp_fun_C_1(A)) | in(ordered_pair(tptp_fun_B_2(A), tptp_fun_C_1(A)), A) | in(ordered_pair(tptp_fun_C_1(A), tptp_fun_B_2(A)), A))))))))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[48, 35])).
% 0.21/0.42 tff(50,plain,
% 0.21/0.42 (![A: $i] : ((~relation(A)) | (~((~(connected(A) | (~((~in(tptp_fun_B_2(A), relation_field(A))) | (~in(tptp_fun_C_1(A), relation_field(A))) | (tptp_fun_B_2(A) = tptp_fun_C_1(A)) | in(ordered_pair(tptp_fun_B_2(A), tptp_fun_C_1(A)), A) | in(ordered_pair(tptp_fun_C_1(A), tptp_fun_B_2(A)), A))))) | (~((~connected(A)) | ![B: $i, C: $i] : (in(ordered_pair(C, B), A) | in(ordered_pair(B, C), A) | (B = C) | (~in(B, relation_field(A))) | (~in(C, relation_field(A)))))))))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[49, 30])).
% 0.21/0.42 tff(51,plain,
% 0.21/0.42 (((~![A: $i] : ((~relation(A)) | (~((~(connected(A) | (~((~in(tptp_fun_B_2(A), relation_field(A))) | (~in(tptp_fun_C_1(A), relation_field(A))) | (tptp_fun_B_2(A) = tptp_fun_C_1(A)) | in(ordered_pair(tptp_fun_B_2(A), tptp_fun_C_1(A)), A) | in(ordered_pair(tptp_fun_C_1(A), tptp_fun_B_2(A)), A))))) | (~((~connected(A)) | ![B: $i, C: $i] : (in(ordered_pair(C, B), A) | in(ordered_pair(B, C), A) | (B = C) | (~in(B, relation_field(A))) | (~in(C, relation_field(A)))))))))) | ((~relation(relation_restriction(B!8, A!9))) | (~((~(connected(relation_restriction(B!8, A!9)) | (~((~in(tptp_fun_B_2(relation_restriction(B!8, A!9)), relation_field(relation_restriction(B!8, A!9)))) | (~in(tptp_fun_C_1(relation_restriction(B!8, A!9)), relation_field(relation_restriction(B!8, A!9)))) | (tptp_fun_B_2(relation_restriction(B!8, A!9)) = tptp_fun_C_1(relation_restriction(B!8, A!9))) | in(ordered_pair(tptp_fun_B_2(relation_restriction(B!8, A!9)), tptp_fun_C_1(relation_restriction(B!8, A!9))), relation_restriction(B!8, A!9)) | in(ordered_pair(tptp_fun_C_1(relation_restriction(B!8, A!9)), tptp_fun_B_2(relation_restriction(B!8, A!9))), relation_restriction(B!8, A!9)))))) | (~((~connected(relation_restriction(B!8, A!9))) | ![B: $i, C: $i] : ((B = C) | in(ordered_pair(C, B), relation_restriction(B!8, A!9)) | in(ordered_pair(B, C), relation_restriction(B!8, A!9)) | (~in(B, relation_field(relation_restriction(B!8, A!9)))) | (~in(C, relation_field(relation_restriction(B!8, A!9))))))))))) <=> ((~![A: $i] : ((~relation(A)) | (~((~(connected(A) | (~((~in(tptp_fun_B_2(A), relation_field(A))) | (~in(tptp_fun_C_1(A), relation_field(A))) | (tptp_fun_B_2(A) = tptp_fun_C_1(A)) | in(ordered_pair(tptp_fun_B_2(A), tptp_fun_C_1(A)), A) | in(ordered_pair(tptp_fun_C_1(A), tptp_fun_B_2(A)), A))))) | (~((~connected(A)) | ![B: $i, C: $i] : (in(ordered_pair(C, B), A) | in(ordered_pair(B, C), A) | (B = C) | (~in(B, relation_field(A))) | (~in(C, relation_field(A)))))))))) | (~relation(relation_restriction(B!8, A!9))) | (~((~(connected(relation_restriction(B!8, A!9)) | (~((~in(tptp_fun_B_2(relation_restriction(B!8, A!9)), relation_field(relation_restriction(B!8, A!9)))) | (~in(tptp_fun_C_1(relation_restriction(B!8, A!9)), relation_field(relation_restriction(B!8, A!9)))) | (tptp_fun_B_2(relation_restriction(B!8, A!9)) = tptp_fun_C_1(relation_restriction(B!8, A!9))) | in(ordered_pair(tptp_fun_B_2(relation_restriction(B!8, A!9)), tptp_fun_C_1(relation_restriction(B!8, A!9))), relation_restriction(B!8, A!9)) | in(ordered_pair(tptp_fun_C_1(relation_restriction(B!8, A!9)), tptp_fun_B_2(relation_restriction(B!8, A!9))), relation_restriction(B!8, A!9)))))) | (~((~connected(relation_restriction(B!8, A!9))) | ![B: $i, C: $i] : ((B = C) | in(ordered_pair(C, B), relation_restriction(B!8, A!9)) | in(ordered_pair(B, C), relation_restriction(B!8, A!9)) | (~in(B, relation_field(relation_restriction(B!8, A!9)))) | (~in(C, relation_field(relation_restriction(B!8, A!9))))))))))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(52,plain,
% 0.21/0.43 (((~relation(relation_restriction(B!8, A!9))) | (~((~(connected(relation_restriction(B!8, A!9)) | (~((~in(tptp_fun_B_2(relation_restriction(B!8, A!9)), relation_field(relation_restriction(B!8, A!9)))) | (~in(tptp_fun_C_1(relation_restriction(B!8, A!9)), relation_field(relation_restriction(B!8, A!9)))) | (tptp_fun_B_2(relation_restriction(B!8, A!9)) = tptp_fun_C_1(relation_restriction(B!8, A!9))) | in(ordered_pair(tptp_fun_B_2(relation_restriction(B!8, A!9)), tptp_fun_C_1(relation_restriction(B!8, A!9))), relation_restriction(B!8, A!9)) | in(ordered_pair(tptp_fun_C_1(relation_restriction(B!8, A!9)), tptp_fun_B_2(relation_restriction(B!8, A!9))), relation_restriction(B!8, A!9)))))) | (~((~connected(relation_restriction(B!8, A!9))) | ![B: $i, C: $i] : (in(ordered_pair(C, B), relation_restriction(B!8, A!9)) | in(ordered_pair(B, C), relation_restriction(B!8, A!9)) | (B = C) | (~in(B, relation_field(relation_restriction(B!8, A!9)))) | (~in(C, relation_field(relation_restriction(B!8, A!9)))))))))) <=> ((~relation(relation_restriction(B!8, A!9))) | (~((~(connected(relation_restriction(B!8, A!9)) | (~((~in(tptp_fun_B_2(relation_restriction(B!8, A!9)), relation_field(relation_restriction(B!8, A!9)))) | (~in(tptp_fun_C_1(relation_restriction(B!8, A!9)), relation_field(relation_restriction(B!8, A!9)))) | (tptp_fun_B_2(relation_restriction(B!8, A!9)) = tptp_fun_C_1(relation_restriction(B!8, A!9))) | in(ordered_pair(tptp_fun_B_2(relation_restriction(B!8, A!9)), tptp_fun_C_1(relation_restriction(B!8, A!9))), relation_restriction(B!8, A!9)) | in(ordered_pair(tptp_fun_C_1(relation_restriction(B!8, A!9)), tptp_fun_B_2(relation_restriction(B!8, A!9))), relation_restriction(B!8, A!9)))))) | (~((~connected(relation_restriction(B!8, A!9))) | ![B: $i, C: $i] : ((B = C) | in(ordered_pair(C, B), relation_restriction(B!8, A!9)) | in(ordered_pair(B, C), relation_restriction(B!8, A!9)) | (~in(B, relation_field(relation_restriction(B!8, A!9)))) | (~in(C, relation_field(relation_restriction(B!8, A!9))))))))))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(53,plain,
% 0.21/0.43 (((~![A: $i] : ((~relation(A)) | (~((~(connected(A) | (~((~in(tptp_fun_B_2(A), relation_field(A))) | (~in(tptp_fun_C_1(A), relation_field(A))) | (tptp_fun_B_2(A) = tptp_fun_C_1(A)) | in(ordered_pair(tptp_fun_B_2(A), tptp_fun_C_1(A)), A) | in(ordered_pair(tptp_fun_C_1(A), tptp_fun_B_2(A)), A))))) | (~((~connected(A)) | ![B: $i, C: $i] : (in(ordered_pair(C, B), A) | in(ordered_pair(B, C), A) | (B = C) | (~in(B, relation_field(A))) | (~in(C, relation_field(A)))))))))) | ((~relation(relation_restriction(B!8, A!9))) | (~((~(connected(relation_restriction(B!8, A!9)) | (~((~in(tptp_fun_B_2(relation_restriction(B!8, A!9)), relation_field(relation_restriction(B!8, A!9)))) | (~in(tptp_fun_C_1(relation_restriction(B!8, A!9)), relation_field(relation_restriction(B!8, A!9)))) | (tptp_fun_B_2(relation_restriction(B!8, A!9)) = tptp_fun_C_1(relation_restriction(B!8, A!9))) | in(ordered_pair(tptp_fun_B_2(relation_restriction(B!8, A!9)), tptp_fun_C_1(relation_restriction(B!8, A!9))), relation_restriction(B!8, A!9)) | in(ordered_pair(tptp_fun_C_1(relation_restriction(B!8, A!9)), tptp_fun_B_2(relation_restriction(B!8, A!9))), relation_restriction(B!8, A!9)))))) | (~((~connected(relation_restriction(B!8, A!9))) | ![B: $i, C: $i] : (in(ordered_pair(C, B), relation_restriction(B!8, A!9)) | in(ordered_pair(B, C), relation_restriction(B!8, A!9)) | (B = C) | (~in(B, relation_field(relation_restriction(B!8, A!9)))) | (~in(C, relation_field(relation_restriction(B!8, A!9))))))))))) <=> ((~![A: $i] : ((~relation(A)) | (~((~(connected(A) | (~((~in(tptp_fun_B_2(A), relation_field(A))) | (~in(tptp_fun_C_1(A), relation_field(A))) | (tptp_fun_B_2(A) = tptp_fun_C_1(A)) | in(ordered_pair(tptp_fun_B_2(A), tptp_fun_C_1(A)), A) | in(ordered_pair(tptp_fun_C_1(A), tptp_fun_B_2(A)), A))))) | (~((~connected(A)) | ![B: $i, C: $i] : (in(ordered_pair(C, B), A) | in(ordered_pair(B, C), A) | (B = C) | (~in(B, relation_field(A))) | (~in(C, relation_field(A)))))))))) | ((~relation(relation_restriction(B!8, A!9))) | (~((~(connected(relation_restriction(B!8, A!9)) | (~((~in(tptp_fun_B_2(relation_restriction(B!8, A!9)), relation_field(relation_restriction(B!8, A!9)))) | (~in(tptp_fun_C_1(relation_restriction(B!8, A!9)), relation_field(relation_restriction(B!8, A!9)))) | (tptp_fun_B_2(relation_restriction(B!8, A!9)) = tptp_fun_C_1(relation_restriction(B!8, A!9))) | in(ordered_pair(tptp_fun_B_2(relation_restriction(B!8, A!9)), tptp_fun_C_1(relation_restriction(B!8, A!9))), relation_restriction(B!8, A!9)) | in(ordered_pair(tptp_fun_C_1(relation_restriction(B!8, A!9)), tptp_fun_B_2(relation_restriction(B!8, A!9))), relation_restriction(B!8, A!9)))))) | (~((~connected(relation_restriction(B!8, A!9))) | ![B: $i, C: $i] : ((B = C) | in(ordered_pair(C, B), relation_restriction(B!8, A!9)) | in(ordered_pair(B, C), relation_restriction(B!8, A!9)) | (~in(B, relation_field(relation_restriction(B!8, A!9)))) | (~in(C, relation_field(relation_restriction(B!8, A!9)))))))))))),
% 0.21/0.43 inference(monotonicity,[status(thm)],[52])).
% 0.21/0.43 tff(54,plain,
% 0.21/0.43 (((~![A: $i] : ((~relation(A)) | (~((~(connected(A) | (~((~in(tptp_fun_B_2(A), relation_field(A))) | (~in(tptp_fun_C_1(A), relation_field(A))) | (tptp_fun_B_2(A) = tptp_fun_C_1(A)) | in(ordered_pair(tptp_fun_B_2(A), tptp_fun_C_1(A)), A) | in(ordered_pair(tptp_fun_C_1(A), tptp_fun_B_2(A)), A))))) | (~((~connected(A)) | ![B: $i, C: $i] : (in(ordered_pair(C, B), A) | in(ordered_pair(B, C), A) | (B = C) | (~in(B, relation_field(A))) | (~in(C, relation_field(A)))))))))) | ((~relation(relation_restriction(B!8, A!9))) | (~((~(connected(relation_restriction(B!8, A!9)) | (~((~in(tptp_fun_B_2(relation_restriction(B!8, A!9)), relation_field(relation_restriction(B!8, A!9)))) | (~in(tptp_fun_C_1(relation_restriction(B!8, A!9)), relation_field(relation_restriction(B!8, A!9)))) | (tptp_fun_B_2(relation_restriction(B!8, A!9)) = tptp_fun_C_1(relation_restriction(B!8, A!9))) | in(ordered_pair(tptp_fun_B_2(relation_restriction(B!8, A!9)), tptp_fun_C_1(relation_restriction(B!8, A!9))), relation_restriction(B!8, A!9)) | in(ordered_pair(tptp_fun_C_1(relation_restriction(B!8, A!9)), tptp_fun_B_2(relation_restriction(B!8, A!9))), relation_restriction(B!8, A!9)))))) | (~((~connected(relation_restriction(B!8, A!9))) | ![B: $i, C: $i] : (in(ordered_pair(C, B), relation_restriction(B!8, A!9)) | in(ordered_pair(B, C), relation_restriction(B!8, A!9)) | (B = C) | (~in(B, relation_field(relation_restriction(B!8, A!9)))) | (~in(C, relation_field(relation_restriction(B!8, A!9))))))))))) <=> ((~![A: $i] : ((~relation(A)) | (~((~(connected(A) | (~((~in(tptp_fun_B_2(A), relation_field(A))) | (~in(tptp_fun_C_1(A), relation_field(A))) | (tptp_fun_B_2(A) = tptp_fun_C_1(A)) | in(ordered_pair(tptp_fun_B_2(A), tptp_fun_C_1(A)), A) | in(ordered_pair(tptp_fun_C_1(A), tptp_fun_B_2(A)), A))))) | (~((~connected(A)) | ![B: $i, C: $i] : (in(ordered_pair(C, B), A) | in(ordered_pair(B, C), A) | (B = C) | (~in(B, relation_field(A))) | (~in(C, relation_field(A)))))))))) | (~relation(relation_restriction(B!8, A!9))) | (~((~(connected(relation_restriction(B!8, A!9)) | (~((~in(tptp_fun_B_2(relation_restriction(B!8, A!9)), relation_field(relation_restriction(B!8, A!9)))) | (~in(tptp_fun_C_1(relation_restriction(B!8, A!9)), relation_field(relation_restriction(B!8, A!9)))) | (tptp_fun_B_2(relation_restriction(B!8, A!9)) = tptp_fun_C_1(relation_restriction(B!8, A!9))) | in(ordered_pair(tptp_fun_B_2(relation_restriction(B!8, A!9)), tptp_fun_C_1(relation_restriction(B!8, A!9))), relation_restriction(B!8, A!9)) | in(ordered_pair(tptp_fun_C_1(relation_restriction(B!8, A!9)), tptp_fun_B_2(relation_restriction(B!8, A!9))), relation_restriction(B!8, A!9)))))) | (~((~connected(relation_restriction(B!8, A!9))) | ![B: $i, C: $i] : ((B = C) | in(ordered_pair(C, B), relation_restriction(B!8, A!9)) | in(ordered_pair(B, C), relation_restriction(B!8, A!9)) | (~in(B, relation_field(relation_restriction(B!8, A!9)))) | (~in(C, relation_field(relation_restriction(B!8, A!9))))))))))),
% 0.21/0.43 inference(transitivity,[status(thm)],[53, 51])).
% 0.21/0.43 tff(55,plain,
% 0.21/0.43 ((~![A: $i] : ((~relation(A)) | (~((~(connected(A) | (~((~in(tptp_fun_B_2(A), relation_field(A))) | (~in(tptp_fun_C_1(A), relation_field(A))) | (tptp_fun_B_2(A) = tptp_fun_C_1(A)) | in(ordered_pair(tptp_fun_B_2(A), tptp_fun_C_1(A)), A) | in(ordered_pair(tptp_fun_C_1(A), tptp_fun_B_2(A)), A))))) | (~((~connected(A)) | ![B: $i, C: $i] : (in(ordered_pair(C, B), A) | in(ordered_pair(B, C), A) | (B = C) | (~in(B, relation_field(A))) | (~in(C, relation_field(A)))))))))) | ((~relation(relation_restriction(B!8, A!9))) | (~((~(connected(relation_restriction(B!8, A!9)) | (~((~in(tptp_fun_B_2(relation_restriction(B!8, A!9)), relation_field(relation_restriction(B!8, A!9)))) | (~in(tptp_fun_C_1(relation_restriction(B!8, A!9)), relation_field(relation_restriction(B!8, A!9)))) | (tptp_fun_B_2(relation_restriction(B!8, A!9)) = tptp_fun_C_1(relation_restriction(B!8, A!9))) | in(ordered_pair(tptp_fun_B_2(relation_restriction(B!8, A!9)), tptp_fun_C_1(relation_restriction(B!8, A!9))), relation_restriction(B!8, A!9)) | in(ordered_pair(tptp_fun_C_1(relation_restriction(B!8, A!9)), tptp_fun_B_2(relation_restriction(B!8, A!9))), relation_restriction(B!8, A!9)))))) | (~((~connected(relation_restriction(B!8, A!9))) | ![B: $i, C: $i] : (in(ordered_pair(C, B), relation_restriction(B!8, A!9)) | in(ordered_pair(B, C), relation_restriction(B!8, A!9)) | (B = C) | (~in(B, relation_field(relation_restriction(B!8, A!9)))) | (~in(C, relation_field(relation_restriction(B!8, A!9))))))))))),
% 0.21/0.43 inference(quant_inst,[status(thm)],[])).
% 0.21/0.43 tff(56,plain,
% 0.21/0.43 ((~![A: $i] : ((~relation(A)) | (~((~(connected(A) | (~((~in(tptp_fun_B_2(A), relation_field(A))) | (~in(tptp_fun_C_1(A), relation_field(A))) | (tptp_fun_B_2(A) = tptp_fun_C_1(A)) | in(ordered_pair(tptp_fun_B_2(A), tptp_fun_C_1(A)), A) | in(ordered_pair(tptp_fun_C_1(A), tptp_fun_B_2(A)), A))))) | (~((~connected(A)) | ![B: $i, C: $i] : (in(ordered_pair(C, B), A) | in(ordered_pair(B, C), A) | (B = C) | (~in(B, relation_field(A))) | (~in(C, relation_field(A)))))))))) | (~relation(relation_restriction(B!8, A!9))) | (~((~(connected(relation_restriction(B!8, A!9)) | (~((~in(tptp_fun_B_2(relation_restriction(B!8, A!9)), relation_field(relation_restriction(B!8, A!9)))) | (~in(tptp_fun_C_1(relation_restriction(B!8, A!9)), relation_field(relation_restriction(B!8, A!9)))) | (tptp_fun_B_2(relation_restriction(B!8, A!9)) = tptp_fun_C_1(relation_restriction(B!8, A!9))) | in(ordered_pair(tptp_fun_B_2(relation_restriction(B!8, A!9)), tptp_fun_C_1(relation_restriction(B!8, A!9))), relation_restriction(B!8, A!9)) | in(ordered_pair(tptp_fun_C_1(relation_restriction(B!8, A!9)), tptp_fun_B_2(relation_restriction(B!8, A!9))), relation_restriction(B!8, A!9)))))) | (~((~connected(relation_restriction(B!8, A!9))) | ![B: $i, C: $i] : ((B = C) | in(ordered_pair(C, B), relation_restriction(B!8, A!9)) | in(ordered_pair(B, C), relation_restriction(B!8, A!9)) | (~in(B, relation_field(relation_restriction(B!8, A!9)))) | (~in(C, relation_field(relation_restriction(B!8, A!9)))))))))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[55, 54])).
% 0.21/0.44 tff(57,plain,
% 0.21/0.44 (~((~(connected(relation_restriction(B!8, A!9)) | (~((~in(tptp_fun_B_2(relation_restriction(B!8, A!9)), relation_field(relation_restriction(B!8, A!9)))) | (~in(tptp_fun_C_1(relation_restriction(B!8, A!9)), relation_field(relation_restriction(B!8, A!9)))) | (tptp_fun_B_2(relation_restriction(B!8, A!9)) = tptp_fun_C_1(relation_restriction(B!8, A!9))) | in(ordered_pair(tptp_fun_B_2(relation_restriction(B!8, A!9)), tptp_fun_C_1(relation_restriction(B!8, A!9))), relation_restriction(B!8, A!9)) | in(ordered_pair(tptp_fun_C_1(relation_restriction(B!8, A!9)), tptp_fun_B_2(relation_restriction(B!8, A!9))), relation_restriction(B!8, A!9)))))) | (~((~connected(relation_restriction(B!8, A!9))) | ![B: $i, C: $i] : ((B = C) | in(ordered_pair(C, B), relation_restriction(B!8, A!9)) | in(ordered_pair(B, C), relation_restriction(B!8, A!9)) | (~in(B, relation_field(relation_restriction(B!8, A!9)))) | (~in(C, relation_field(relation_restriction(B!8, A!9))))))))),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[56, 50, 28])).
% 0.21/0.44 tff(58,plain,
% 0.21/0.44 (((~(connected(relation_restriction(B!8, A!9)) | (~((~in(tptp_fun_B_2(relation_restriction(B!8, A!9)), relation_field(relation_restriction(B!8, A!9)))) | (~in(tptp_fun_C_1(relation_restriction(B!8, A!9)), relation_field(relation_restriction(B!8, A!9)))) | (tptp_fun_B_2(relation_restriction(B!8, A!9)) = tptp_fun_C_1(relation_restriction(B!8, A!9))) | in(ordered_pair(tptp_fun_B_2(relation_restriction(B!8, A!9)), tptp_fun_C_1(relation_restriction(B!8, A!9))), relation_restriction(B!8, A!9)) | in(ordered_pair(tptp_fun_C_1(relation_restriction(B!8, A!9)), tptp_fun_B_2(relation_restriction(B!8, A!9))), relation_restriction(B!8, A!9)))))) | (~((~connected(relation_restriction(B!8, A!9))) | ![B: $i, C: $i] : ((B = C) | in(ordered_pair(C, B), relation_restriction(B!8, A!9)) | in(ordered_pair(B, C), relation_restriction(B!8, A!9)) | (~in(B, relation_field(relation_restriction(B!8, A!9)))) | (~in(C, relation_field(relation_restriction(B!8, A!9)))))))) | (connected(relation_restriction(B!8, A!9)) | (~((~in(tptp_fun_B_2(relation_restriction(B!8, A!9)), relation_field(relation_restriction(B!8, A!9)))) | (~in(tptp_fun_C_1(relation_restriction(B!8, A!9)), relation_field(relation_restriction(B!8, A!9)))) | (tptp_fun_B_2(relation_restriction(B!8, A!9)) = tptp_fun_C_1(relation_restriction(B!8, A!9))) | in(ordered_pair(tptp_fun_B_2(relation_restriction(B!8, A!9)), tptp_fun_C_1(relation_restriction(B!8, A!9))), relation_restriction(B!8, A!9)) | in(ordered_pair(tptp_fun_C_1(relation_restriction(B!8, A!9)), tptp_fun_B_2(relation_restriction(B!8, A!9))), relation_restriction(B!8, A!9)))))),
% 0.21/0.44 inference(tautology,[status(thm)],[])).
% 0.21/0.44 tff(59,plain,
% 0.21/0.44 (connected(relation_restriction(B!8, A!9)) | (~((~in(tptp_fun_B_2(relation_restriction(B!8, A!9)), relation_field(relation_restriction(B!8, A!9)))) | (~in(tptp_fun_C_1(relation_restriction(B!8, A!9)), relation_field(relation_restriction(B!8, A!9)))) | (tptp_fun_B_2(relation_restriction(B!8, A!9)) = tptp_fun_C_1(relation_restriction(B!8, A!9))) | in(ordered_pair(tptp_fun_B_2(relation_restriction(B!8, A!9)), tptp_fun_C_1(relation_restriction(B!8, A!9))), relation_restriction(B!8, A!9)) | in(ordered_pair(tptp_fun_C_1(relation_restriction(B!8, A!9)), tptp_fun_B_2(relation_restriction(B!8, A!9))), relation_restriction(B!8, A!9))))),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[58, 57])).
% 0.21/0.44 tff(60,plain,
% 0.21/0.44 (~connected(relation_restriction(B!8, A!9))),
% 0.21/0.44 inference(or_elim,[status(thm)],[13])).
% 0.21/0.44 tff(61,plain,
% 0.21/0.44 ((~(connected(relation_restriction(B!8, A!9)) | (~((~in(tptp_fun_B_2(relation_restriction(B!8, A!9)), relation_field(relation_restriction(B!8, A!9)))) | (~in(tptp_fun_C_1(relation_restriction(B!8, A!9)), relation_field(relation_restriction(B!8, A!9)))) | (tptp_fun_B_2(relation_restriction(B!8, A!9)) = tptp_fun_C_1(relation_restriction(B!8, A!9))) | in(ordered_pair(tptp_fun_B_2(relation_restriction(B!8, A!9)), tptp_fun_C_1(relation_restriction(B!8, A!9))), relation_restriction(B!8, A!9)) | in(ordered_pair(tptp_fun_C_1(relation_restriction(B!8, A!9)), tptp_fun_B_2(relation_restriction(B!8, A!9))), relation_restriction(B!8, A!9)))))) | connected(relation_restriction(B!8, A!9)) | (~((~in(tptp_fun_B_2(relation_restriction(B!8, A!9)), relation_field(relation_restriction(B!8, A!9)))) | (~in(tptp_fun_C_1(relation_restriction(B!8, A!9)), relation_field(relation_restriction(B!8, A!9)))) | (tptp_fun_B_2(relation_restriction(B!8, A!9)) = tptp_fun_C_1(relation_restriction(B!8, A!9))) | in(ordered_pair(tptp_fun_B_2(relation_restriction(B!8, A!9)), tptp_fun_C_1(relation_restriction(B!8, A!9))), relation_restriction(B!8, A!9)) | in(ordered_pair(tptp_fun_C_1(relation_restriction(B!8, A!9)), tptp_fun_B_2(relation_restriction(B!8, A!9))), relation_restriction(B!8, A!9))))),
% 0.21/0.44 inference(tautology,[status(thm)],[])).
% 0.21/0.44 tff(62,plain,
% 0.21/0.44 ((~(connected(relation_restriction(B!8, A!9)) | (~((~in(tptp_fun_B_2(relation_restriction(B!8, A!9)), relation_field(relation_restriction(B!8, A!9)))) | (~in(tptp_fun_C_1(relation_restriction(B!8, A!9)), relation_field(relation_restriction(B!8, A!9)))) | (tptp_fun_B_2(relation_restriction(B!8, A!9)) = tptp_fun_C_1(relation_restriction(B!8, A!9))) | in(ordered_pair(tptp_fun_B_2(relation_restriction(B!8, A!9)), tptp_fun_C_1(relation_restriction(B!8, A!9))), relation_restriction(B!8, A!9)) | in(ordered_pair(tptp_fun_C_1(relation_restriction(B!8, A!9)), tptp_fun_B_2(relation_restriction(B!8, A!9))), relation_restriction(B!8, A!9)))))) | (~((~in(tptp_fun_B_2(relation_restriction(B!8, A!9)), relation_field(relation_restriction(B!8, A!9)))) | (~in(tptp_fun_C_1(relation_restriction(B!8, A!9)), relation_field(relation_restriction(B!8, A!9)))) | (tptp_fun_B_2(relation_restriction(B!8, A!9)) = tptp_fun_C_1(relation_restriction(B!8, A!9))) | in(ordered_pair(tptp_fun_B_2(relation_restriction(B!8, A!9)), tptp_fun_C_1(relation_restriction(B!8, A!9))), relation_restriction(B!8, A!9)) | in(ordered_pair(tptp_fun_C_1(relation_restriction(B!8, A!9)), tptp_fun_B_2(relation_restriction(B!8, A!9))), relation_restriction(B!8, A!9))))),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[61, 60])).
% 0.21/0.44 tff(63,plain,
% 0.21/0.44 (~((~in(tptp_fun_B_2(relation_restriction(B!8, A!9)), relation_field(relation_restriction(B!8, A!9)))) | (~in(tptp_fun_C_1(relation_restriction(B!8, A!9)), relation_field(relation_restriction(B!8, A!9)))) | (tptp_fun_B_2(relation_restriction(B!8, A!9)) = tptp_fun_C_1(relation_restriction(B!8, A!9))) | in(ordered_pair(tptp_fun_B_2(relation_restriction(B!8, A!9)), tptp_fun_C_1(relation_restriction(B!8, A!9))), relation_restriction(B!8, A!9)) | in(ordered_pair(tptp_fun_C_1(relation_restriction(B!8, A!9)), tptp_fun_B_2(relation_restriction(B!8, A!9))), relation_restriction(B!8, A!9)))),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[62, 59])).
% 0.21/0.44 tff(64,plain,
% 0.21/0.44 (((~in(tptp_fun_B_2(relation_restriction(B!8, A!9)), relation_field(relation_restriction(B!8, A!9)))) | (~in(tptp_fun_C_1(relation_restriction(B!8, A!9)), relation_field(relation_restriction(B!8, A!9)))) | (tptp_fun_B_2(relation_restriction(B!8, A!9)) = tptp_fun_C_1(relation_restriction(B!8, A!9))) | in(ordered_pair(tptp_fun_B_2(relation_restriction(B!8, A!9)), tptp_fun_C_1(relation_restriction(B!8, A!9))), relation_restriction(B!8, A!9)) | in(ordered_pair(tptp_fun_C_1(relation_restriction(B!8, A!9)), tptp_fun_B_2(relation_restriction(B!8, A!9))), relation_restriction(B!8, A!9))) | in(tptp_fun_B_2(relation_restriction(B!8, A!9)), relation_field(relation_restriction(B!8, A!9)))),
% 0.21/0.44 inference(tautology,[status(thm)],[])).
% 0.21/0.44 tff(65,plain,
% 0.21/0.44 (in(tptp_fun_B_2(relation_restriction(B!8, A!9)), relation_field(relation_restriction(B!8, A!9)))),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[64, 63])).
% 0.21/0.44 tff(66,plain,
% 0.21/0.44 (^[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))))))),
% 0.21/0.44 inference(bind,[status(th)],[])).
% 0.21/0.44 tff(67,plain,
% 0.21/0.44 (![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)))))),
% 0.21/0.44 inference(quant_intro,[status(thm)],[66])).
% 0.21/0.44 tff(68,plain,
% 0.21/0.44 (^[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)))))))),
% 0.21/0.44 inference(bind,[status(th)],[])).
% 0.21/0.44 tff(69,plain,
% 0.21/0.44 (![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)))))),
% 0.21/0.44 inference(quant_intro,[status(thm)],[68])).
% 0.21/0.44 tff(70,plain,
% 0.21/0.44 (![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)))))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(71,plain,
% 0.21/0.44 (^[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)))))))),
% 0.21/0.44 inference(bind,[status(th)],[])).
% 0.21/0.44 tff(72,plain,
% 0.21/0.44 (![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)))))),
% 0.21/0.44 inference(quant_intro,[status(thm)],[71])).
% 0.21/0.44 tff(73,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')).
% 0.21/0.44 tff(74,plain,
% 0.21/0.44 (![A: $i, B: $i, C: $i] : ((in(A, relation_field(C)) & in(A, B)) | (~relation(C)) | (~in(A, relation_field(relation_restriction(C, B)))))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[73, 72])).
% 0.21/0.44 tff(75,plain,
% 0.21/0.44 (![A: $i, B: $i, C: $i] : ((in(A, relation_field(C)) & in(A, B)) | (~relation(C)) | (~in(A, relation_field(relation_restriction(C, B)))))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[74, 70])).
% 0.21/0.44 tff(76,plain,(
% 0.21/0.44 ![A: $i, B: $i, C: $i] : ((in(A, relation_field(C)) & in(A, B)) | (~relation(C)) | (~in(A, relation_field(relation_restriction(C, B)))))),
% 0.21/0.44 inference(skolemize,[status(sab)],[75])).
% 0.21/0.44 tff(77,plain,
% 0.21/0.44 (![A: $i, B: $i, C: $i] : ((~relation(C)) | (~in(A, relation_field(relation_restriction(C, B)))) | (~((~in(A, relation_field(C))) | (~in(A, B)))))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[76, 69])).
% 0.21/0.44 tff(78,plain,
% 0.21/0.44 (![A: $i, B: $i, C: $i] : ((~relation(C)) | (~in(A, relation_field(relation_restriction(C, B)))) | (~((~in(A, relation_field(C))) | (~in(A, B)))))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[77, 67])).
% 0.21/0.44 tff(79,plain,
% 0.21/0.44 (((~![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!8)) | (~in(tptp_fun_B_2(relation_restriction(B!8, A!9)), relation_field(relation_restriction(B!8, A!9)))) | (~((~in(tptp_fun_B_2(relation_restriction(B!8, A!9)), relation_field(B!8))) | (~in(tptp_fun_B_2(relation_restriction(B!8, A!9)), A!9)))))) <=> ((~![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!8)) | (~in(tptp_fun_B_2(relation_restriction(B!8, A!9)), relation_field(relation_restriction(B!8, A!9)))) | (~((~in(tptp_fun_B_2(relation_restriction(B!8, A!9)), relation_field(B!8))) | (~in(tptp_fun_B_2(relation_restriction(B!8, A!9)), A!9)))))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(80,plain,
% 0.21/0.44 ((~![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!8)) | (~in(tptp_fun_B_2(relation_restriction(B!8, A!9)), relation_field(relation_restriction(B!8, A!9)))) | (~((~in(tptp_fun_B_2(relation_restriction(B!8, A!9)), relation_field(B!8))) | (~in(tptp_fun_B_2(relation_restriction(B!8, A!9)), A!9)))))),
% 0.21/0.44 inference(quant_inst,[status(thm)],[])).
% 0.21/0.44 tff(81,plain,
% 0.21/0.44 ((~![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!8)) | (~in(tptp_fun_B_2(relation_restriction(B!8, A!9)), relation_field(relation_restriction(B!8, A!9)))) | (~((~in(tptp_fun_B_2(relation_restriction(B!8, A!9)), relation_field(B!8))) | (~in(tptp_fun_B_2(relation_restriction(B!8, A!9)), A!9))))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[80, 79])).
% 0.21/0.44 tff(82,plain,
% 0.21/0.44 (~((~in(tptp_fun_B_2(relation_restriction(B!8, A!9)), relation_field(B!8))) | (~in(tptp_fun_B_2(relation_restriction(B!8, A!9)), A!9)))),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[81, 78, 14, 65])).
% 0.21/0.44 tff(83,plain,
% 0.21/0.44 (((~in(tptp_fun_B_2(relation_restriction(B!8, A!9)), relation_field(B!8))) | (~in(tptp_fun_B_2(relation_restriction(B!8, A!9)), A!9))) | in(tptp_fun_B_2(relation_restriction(B!8, A!9)), A!9)),
% 0.21/0.44 inference(tautology,[status(thm)],[])).
% 0.21/0.44 tff(84,plain,
% 0.21/0.44 (in(tptp_fun_B_2(relation_restriction(B!8, A!9)), A!9)),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[83, 82])).
% 0.21/0.44 tff(85,plain,
% 0.21/0.44 (((~in(tptp_fun_B_2(relation_restriction(B!8, A!9)), relation_field(relation_restriction(B!8, A!9)))) | (~in(tptp_fun_C_1(relation_restriction(B!8, A!9)), relation_field(relation_restriction(B!8, A!9)))) | (tptp_fun_B_2(relation_restriction(B!8, A!9)) = tptp_fun_C_1(relation_restriction(B!8, A!9))) | in(ordered_pair(tptp_fun_B_2(relation_restriction(B!8, A!9)), tptp_fun_C_1(relation_restriction(B!8, A!9))), relation_restriction(B!8, A!9)) | in(ordered_pair(tptp_fun_C_1(relation_restriction(B!8, A!9)), tptp_fun_B_2(relation_restriction(B!8, A!9))), relation_restriction(B!8, A!9))) | in(tptp_fun_C_1(relation_restriction(B!8, A!9)), relation_field(relation_restriction(B!8, A!9)))),
% 0.21/0.44 inference(tautology,[status(thm)],[])).
% 0.21/0.44 tff(86,plain,
% 0.21/0.44 (in(tptp_fun_C_1(relation_restriction(B!8, A!9)), relation_field(relation_restriction(B!8, A!9)))),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[85, 63])).
% 0.21/0.45 tff(87,plain,
% 0.21/0.45 (((~![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!8)) | (~in(tptp_fun_C_1(relation_restriction(B!8, A!9)), relation_field(relation_restriction(B!8, A!9)))) | (~((~in(tptp_fun_C_1(relation_restriction(B!8, A!9)), relation_field(B!8))) | (~in(tptp_fun_C_1(relation_restriction(B!8, A!9)), A!9)))))) <=> ((~![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!8)) | (~in(tptp_fun_C_1(relation_restriction(B!8, A!9)), relation_field(relation_restriction(B!8, A!9)))) | (~((~in(tptp_fun_C_1(relation_restriction(B!8, A!9)), relation_field(B!8))) | (~in(tptp_fun_C_1(relation_restriction(B!8, A!9)), A!9)))))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(88,plain,
% 0.21/0.45 ((~![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!8)) | (~in(tptp_fun_C_1(relation_restriction(B!8, A!9)), relation_field(relation_restriction(B!8, A!9)))) | (~((~in(tptp_fun_C_1(relation_restriction(B!8, A!9)), relation_field(B!8))) | (~in(tptp_fun_C_1(relation_restriction(B!8, A!9)), A!9)))))),
% 0.21/0.45 inference(quant_inst,[status(thm)],[])).
% 0.21/0.45 tff(89,plain,
% 0.21/0.45 ((~![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!8)) | (~in(tptp_fun_C_1(relation_restriction(B!8, A!9)), relation_field(relation_restriction(B!8, A!9)))) | (~((~in(tptp_fun_C_1(relation_restriction(B!8, A!9)), relation_field(B!8))) | (~in(tptp_fun_C_1(relation_restriction(B!8, A!9)), A!9))))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[88, 87])).
% 0.21/0.45 tff(90,plain,
% 0.21/0.45 (~((~in(tptp_fun_C_1(relation_restriction(B!8, A!9)), relation_field(B!8))) | (~in(tptp_fun_C_1(relation_restriction(B!8, A!9)), A!9)))),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[89, 78, 14, 86])).
% 0.21/0.45 tff(91,plain,
% 0.21/0.45 (((~in(tptp_fun_C_1(relation_restriction(B!8, A!9)), relation_field(B!8))) | (~in(tptp_fun_C_1(relation_restriction(B!8, A!9)), A!9))) | in(tptp_fun_C_1(relation_restriction(B!8, A!9)), A!9)),
% 0.21/0.45 inference(tautology,[status(thm)],[])).
% 0.21/0.45 tff(92,plain,
% 0.21/0.45 (in(tptp_fun_C_1(relation_restriction(B!8, A!9)), A!9)),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[91, 90])).
% 0.21/0.45 tff(93,plain,
% 0.21/0.45 ((~((~in(tptp_fun_C_1(relation_restriction(B!8, A!9)), A!9)) | (~in(tptp_fun_B_2(relation_restriction(B!8, A!9)), A!9)))) | (~in(tptp_fun_C_1(relation_restriction(B!8, A!9)), A!9)) | (~in(tptp_fun_B_2(relation_restriction(B!8, A!9)), A!9))),
% 0.21/0.45 inference(tautology,[status(thm)],[])).
% 0.21/0.45 tff(94,plain,
% 0.21/0.45 (~((~in(tptp_fun_C_1(relation_restriction(B!8, A!9)), A!9)) | (~in(tptp_fun_B_2(relation_restriction(B!8, A!9)), A!9)))),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[93, 92, 84])).
% 0.21/0.45 tff(95,assumption,(~(in(ordered_pair(tptp_fun_C_1(relation_restriction(B!8, A!9)), tptp_fun_B_2(relation_restriction(B!8, A!9))), cartesian_product2(A!9, A!9)) <=> (~((~in(tptp_fun_B_2(relation_restriction(B!8, A!9)), A!9)) | (~in(tptp_fun_C_1(relation_restriction(B!8, A!9)), A!9)))))), introduced(assumption)).
% 0.21/0.45 tff(96,plain,
% 0.21/0.45 (^[A: $i, B: $i, C: $i, D: $i] : refl((in(ordered_pair(A, B), cartesian_product2(C, D)) <=> (~((~in(B, D)) | (~in(A, C))))) <=> (in(ordered_pair(A, B), cartesian_product2(C, D)) <=> (~((~in(B, D)) | (~in(A, C))))))),
% 0.21/0.45 inference(bind,[status(th)],[])).
% 0.21/0.45 tff(97,plain,
% 0.21/0.45 (![A: $i, B: $i, C: $i, D: $i] : (in(ordered_pair(A, B), cartesian_product2(C, D)) <=> (~((~in(B, D)) | (~in(A, C))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (in(ordered_pair(A, B), cartesian_product2(C, D)) <=> (~((~in(B, D)) | (~in(A, C)))))),
% 0.21/0.45 inference(quant_intro,[status(thm)],[96])).
% 0.21/0.45 tff(98,plain,
% 0.21/0.45 (^[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(B, D)) | (~in(A, C))))))),
% 0.21/0.45 inference(bind,[status(th)],[])).
% 0.21/0.45 tff(99,plain,
% 0.21/0.45 (![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(B, D)) | (~in(A, C)))))),
% 0.21/0.45 inference(quant_intro,[status(thm)],[98])).
% 0.21/0.45 tff(100,plain,
% 0.21/0.45 (![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)))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(101,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')).
% 0.21/0.45 tff(102,plain,
% 0.21/0.45 (![A: $i, B: $i, C: $i, D: $i] : (in(ordered_pair(A, B), cartesian_product2(C, D)) <=> (in(A, C) & in(B, D)))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[101, 100])).
% 0.21/0.45 tff(103,plain,(
% 0.21/0.45 ![A: $i, B: $i, C: $i, D: $i] : (in(ordered_pair(A, B), cartesian_product2(C, D)) <=> (in(A, C) & in(B, D)))),
% 0.21/0.45 inference(skolemize,[status(sab)],[102])).
% 0.21/0.45 tff(104,plain,
% 0.21/0.45 (![A: $i, B: $i, C: $i, D: $i] : (in(ordered_pair(A, B), cartesian_product2(C, D)) <=> (~((~in(B, D)) | (~in(A, C)))))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[103, 99])).
% 0.21/0.45 tff(105,plain,
% 0.21/0.45 (![A: $i, B: $i, C: $i, D: $i] : (in(ordered_pair(A, B), cartesian_product2(C, D)) <=> (~((~in(B, D)) | (~in(A, C)))))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[104, 97])).
% 0.21/0.45 tff(106,plain,
% 0.21/0.45 ((~![A: $i, B: $i, C: $i, D: $i] : (in(ordered_pair(A, B), cartesian_product2(C, D)) <=> (~((~in(B, D)) | (~in(A, C)))))) | (in(ordered_pair(tptp_fun_C_1(relation_restriction(B!8, A!9)), tptp_fun_B_2(relation_restriction(B!8, A!9))), cartesian_product2(A!9, A!9)) <=> (~((~in(tptp_fun_B_2(relation_restriction(B!8, A!9)), A!9)) | (~in(tptp_fun_C_1(relation_restriction(B!8, A!9)), A!9)))))),
% 0.21/0.45 inference(quant_inst,[status(thm)],[])).
% 0.21/0.45 tff(107,plain,
% 0.21/0.45 ($false),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[106, 105, 95])).
% 0.21/0.45 tff(108,plain,(in(ordered_pair(tptp_fun_C_1(relation_restriction(B!8, A!9)), tptp_fun_B_2(relation_restriction(B!8, A!9))), cartesian_product2(A!9, A!9)) <=> (~((~in(tptp_fun_B_2(relation_restriction(B!8, A!9)), A!9)) | (~in(tptp_fun_C_1(relation_restriction(B!8, A!9)), A!9))))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.45 tff(109,plain,
% 0.21/0.45 ((~((~in(tptp_fun_B_2(relation_restriction(B!8, A!9)), A!9)) | (~in(tptp_fun_C_1(relation_restriction(B!8, A!9)), A!9)))) | (~in(tptp_fun_B_2(relation_restriction(B!8, A!9)), A!9)) | (~in(tptp_fun_C_1(relation_restriction(B!8, A!9)), A!9))),
% 0.21/0.45 inference(tautology,[status(thm)],[])).
% 0.21/0.45 tff(110,plain,
% 0.21/0.45 (~((~in(tptp_fun_B_2(relation_restriction(B!8, A!9)), A!9)) | (~in(tptp_fun_C_1(relation_restriction(B!8, A!9)), A!9)))),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[109, 92, 84])).
% 0.21/0.45 tff(111,plain,
% 0.21/0.45 ((~(in(ordered_pair(tptp_fun_C_1(relation_restriction(B!8, A!9)), tptp_fun_B_2(relation_restriction(B!8, A!9))), cartesian_product2(A!9, A!9)) <=> (~((~in(tptp_fun_B_2(relation_restriction(B!8, A!9)), A!9)) | (~in(tptp_fun_C_1(relation_restriction(B!8, A!9)), A!9)))))) | in(ordered_pair(tptp_fun_C_1(relation_restriction(B!8, A!9)), tptp_fun_B_2(relation_restriction(B!8, A!9))), cartesian_product2(A!9, A!9)) | ((~in(tptp_fun_B_2(relation_restriction(B!8, A!9)), A!9)) | (~in(tptp_fun_C_1(relation_restriction(B!8, A!9)), A!9)))),
% 0.21/0.45 inference(tautology,[status(thm)],[])).
% 0.21/0.45 tff(112,plain,
% 0.21/0.45 ((~(in(ordered_pair(tptp_fun_C_1(relation_restriction(B!8, A!9)), tptp_fun_B_2(relation_restriction(B!8, A!9))), cartesian_product2(A!9, A!9)) <=> (~((~in(tptp_fun_B_2(relation_restriction(B!8, A!9)), A!9)) | (~in(tptp_fun_C_1(relation_restriction(B!8, A!9)), A!9)))))) | in(ordered_pair(tptp_fun_C_1(relation_restriction(B!8, A!9)), tptp_fun_B_2(relation_restriction(B!8, A!9))), cartesian_product2(A!9, A!9))),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[111, 110])).
% 0.21/0.45 tff(113,plain,
% 0.21/0.45 (in(ordered_pair(tptp_fun_C_1(relation_restriction(B!8, A!9)), tptp_fun_B_2(relation_restriction(B!8, A!9))), cartesian_product2(A!9, A!9))),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[112, 108])).
% 0.21/0.45 tff(114,plain,
% 0.21/0.45 (^[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))))))))),
% 0.21/0.45 inference(bind,[status(th)],[])).
% 0.21/0.45 tff(115,plain,
% 0.21/0.45 (![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)))))))),
% 0.21/0.45 inference(quant_intro,[status(thm)],[114])).
% 0.21/0.45 tff(116,plain,
% 0.21/0.45 (^[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))))))))),
% 0.21/0.45 inference(bind,[status(th)],[])).
% 0.21/0.45 tff(117,plain,
% 0.21/0.45 (![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)))))))),
% 0.21/0.45 inference(quant_intro,[status(thm)],[116])).
% 0.21/0.45 tff(118,plain,
% 0.21/0.45 (![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)))))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(119,plain,
% 0.21/0.45 (^[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))))))),
% 0.21/0.45 inference(bind,[status(th)],[])).
% 0.21/0.45 tff(120,plain,
% 0.21/0.45 (![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)))))),
% 0.21/0.45 inference(quant_intro,[status(thm)],[119])).
% 0.21/0.45 tff(121,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')).
% 0.21/0.45 tff(122,plain,
% 0.21/0.45 (![A: $i, B: $i, C: $i] : ((~relation(C)) | (in(A, relation_restriction(C, B)) <=> (in(A, C) & in(A, cartesian_product2(B, B)))))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[121, 120])).
% 0.21/0.45 tff(123,plain,
% 0.21/0.45 (![A: $i, B: $i, C: $i] : ((~relation(C)) | (in(A, relation_restriction(C, B)) <=> (in(A, C) & in(A, cartesian_product2(B, B)))))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[122, 118])).
% 0.21/0.45 tff(124,plain,(
% 0.21/0.45 ![A: $i, B: $i, C: $i] : ((~relation(C)) | (in(A, relation_restriction(C, B)) <=> (in(A, C) & in(A, cartesian_product2(B, B)))))),
% 0.21/0.45 inference(skolemize,[status(sab)],[123])).
% 0.21/0.45 tff(125,plain,
% 0.21/0.45 (![A: $i, B: $i, C: $i] : ((~relation(C)) | (in(A, relation_restriction(C, B)) <=> (~((~in(A, C)) | (~in(A, cartesian_product2(B, B)))))))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[124, 117])).
% 0.21/0.45 tff(126,plain,
% 0.21/0.45 (![A: $i, B: $i, C: $i] : ((~relation(C)) | (in(A, relation_restriction(C, B)) <=> (~((~in(A, C)) | (~in(A, cartesian_product2(B, B)))))))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[125, 115])).
% 0.21/0.45 tff(127,plain,
% 0.21/0.45 (((~![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!8)) | (in(ordered_pair(tptp_fun_C_1(relation_restriction(B!8, A!9)), tptp_fun_B_2(relation_restriction(B!8, A!9))), relation_restriction(B!8, A!9)) <=> (~((~in(ordered_pair(tptp_fun_C_1(relation_restriction(B!8, A!9)), tptp_fun_B_2(relation_restriction(B!8, A!9))), B!8)) | (~in(ordered_pair(tptp_fun_C_1(relation_restriction(B!8, A!9)), tptp_fun_B_2(relation_restriction(B!8, A!9))), cartesian_product2(A!9, A!9)))))))) <=> ((~![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!8)) | (in(ordered_pair(tptp_fun_C_1(relation_restriction(B!8, A!9)), tptp_fun_B_2(relation_restriction(B!8, A!9))), relation_restriction(B!8, A!9)) <=> (~((~in(ordered_pair(tptp_fun_C_1(relation_restriction(B!8, A!9)), tptp_fun_B_2(relation_restriction(B!8, A!9))), B!8)) | (~in(ordered_pair(tptp_fun_C_1(relation_restriction(B!8, A!9)), tptp_fun_B_2(relation_restriction(B!8, A!9))), cartesian_product2(A!9, A!9)))))))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(128,plain,
% 0.21/0.45 ((~![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!8)) | (in(ordered_pair(tptp_fun_C_1(relation_restriction(B!8, A!9)), tptp_fun_B_2(relation_restriction(B!8, A!9))), relation_restriction(B!8, A!9)) <=> (~((~in(ordered_pair(tptp_fun_C_1(relation_restriction(B!8, A!9)), tptp_fun_B_2(relation_restriction(B!8, A!9))), B!8)) | (~in(ordered_pair(tptp_fun_C_1(relation_restriction(B!8, A!9)), tptp_fun_B_2(relation_restriction(B!8, A!9))), cartesian_product2(A!9, A!9)))))))),
% 0.21/0.45 inference(quant_inst,[status(thm)],[])).
% 0.21/0.45 tff(129,plain,
% 0.21/0.45 ((~![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!8)) | (in(ordered_pair(tptp_fun_C_1(relation_restriction(B!8, A!9)), tptp_fun_B_2(relation_restriction(B!8, A!9))), relation_restriction(B!8, A!9)) <=> (~((~in(ordered_pair(tptp_fun_C_1(relation_restriction(B!8, A!9)), tptp_fun_B_2(relation_restriction(B!8, A!9))), B!8)) | (~in(ordered_pair(tptp_fun_C_1(relation_restriction(B!8, A!9)), tptp_fun_B_2(relation_restriction(B!8, A!9))), cartesian_product2(A!9, A!9))))))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[128, 127])).
% 0.21/0.45 tff(130,plain,
% 0.21/0.45 (in(ordered_pair(tptp_fun_C_1(relation_restriction(B!8, A!9)), tptp_fun_B_2(relation_restriction(B!8, A!9))), relation_restriction(B!8, A!9)) <=> (~((~in(ordered_pair(tptp_fun_C_1(relation_restriction(B!8, A!9)), tptp_fun_B_2(relation_restriction(B!8, A!9))), B!8)) | (~in(ordered_pair(tptp_fun_C_1(relation_restriction(B!8, A!9)), tptp_fun_B_2(relation_restriction(B!8, A!9))), cartesian_product2(A!9, A!9)))))),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[129, 126, 14])).
% 0.21/0.45 tff(131,plain,
% 0.21/0.45 (((~in(tptp_fun_B_2(relation_restriction(B!8, A!9)), relation_field(relation_restriction(B!8, A!9)))) | (~in(tptp_fun_C_1(relation_restriction(B!8, A!9)), relation_field(relation_restriction(B!8, A!9)))) | (tptp_fun_B_2(relation_restriction(B!8, A!9)) = tptp_fun_C_1(relation_restriction(B!8, A!9))) | in(ordered_pair(tptp_fun_B_2(relation_restriction(B!8, A!9)), tptp_fun_C_1(relation_restriction(B!8, A!9))), relation_restriction(B!8, A!9)) | in(ordered_pair(tptp_fun_C_1(relation_restriction(B!8, A!9)), tptp_fun_B_2(relation_restriction(B!8, A!9))), relation_restriction(B!8, A!9))) | (~in(ordered_pair(tptp_fun_C_1(relation_restriction(B!8, A!9)), tptp_fun_B_2(relation_restriction(B!8, A!9))), relation_restriction(B!8, A!9)))),
% 0.21/0.45 inference(tautology,[status(thm)],[])).
% 0.21/0.45 tff(132,plain,
% 0.21/0.45 (~in(ordered_pair(tptp_fun_C_1(relation_restriction(B!8, A!9)), tptp_fun_B_2(relation_restriction(B!8, A!9))), relation_restriction(B!8, A!9))),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[131, 63])).
% 0.21/0.45 tff(133,plain,
% 0.21/0.45 ((~(in(ordered_pair(tptp_fun_C_1(relation_restriction(B!8, A!9)), tptp_fun_B_2(relation_restriction(B!8, A!9))), relation_restriction(B!8, A!9)) <=> (~((~in(ordered_pair(tptp_fun_C_1(relation_restriction(B!8, A!9)), tptp_fun_B_2(relation_restriction(B!8, A!9))), B!8)) | (~in(ordered_pair(tptp_fun_C_1(relation_restriction(B!8, A!9)), tptp_fun_B_2(relation_restriction(B!8, A!9))), cartesian_product2(A!9, A!9))))))) | in(ordered_pair(tptp_fun_C_1(relation_restriction(B!8, A!9)), tptp_fun_B_2(relation_restriction(B!8, A!9))), relation_restriction(B!8, A!9)) | ((~in(ordered_pair(tptp_fun_C_1(relation_restriction(B!8, A!9)), tptp_fun_B_2(relation_restriction(B!8, A!9))), B!8)) | (~in(ordered_pair(tptp_fun_C_1(relation_restriction(B!8, A!9)), tptp_fun_B_2(relation_restriction(B!8, A!9))), cartesian_product2(A!9, A!9))))),
% 0.21/0.46 inference(tautology,[status(thm)],[])).
% 0.21/0.46 tff(134,plain,
% 0.21/0.46 ((~(in(ordered_pair(tptp_fun_C_1(relation_restriction(B!8, A!9)), tptp_fun_B_2(relation_restriction(B!8, A!9))), relation_restriction(B!8, A!9)) <=> (~((~in(ordered_pair(tptp_fun_C_1(relation_restriction(B!8, A!9)), tptp_fun_B_2(relation_restriction(B!8, A!9))), B!8)) | (~in(ordered_pair(tptp_fun_C_1(relation_restriction(B!8, A!9)), tptp_fun_B_2(relation_restriction(B!8, A!9))), cartesian_product2(A!9, A!9))))))) | ((~in(ordered_pair(tptp_fun_C_1(relation_restriction(B!8, A!9)), tptp_fun_B_2(relation_restriction(B!8, A!9))), B!8)) | (~in(ordered_pair(tptp_fun_C_1(relation_restriction(B!8, A!9)), tptp_fun_B_2(relation_restriction(B!8, A!9))), cartesian_product2(A!9, A!9))))),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[133, 132])).
% 0.21/0.46 tff(135,plain,
% 0.21/0.46 ((~in(ordered_pair(tptp_fun_C_1(relation_restriction(B!8, A!9)), tptp_fun_B_2(relation_restriction(B!8, A!9))), B!8)) | (~in(ordered_pair(tptp_fun_C_1(relation_restriction(B!8, A!9)), tptp_fun_B_2(relation_restriction(B!8, A!9))), cartesian_product2(A!9, A!9)))),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[134, 130])).
% 0.21/0.46 tff(136,plain,
% 0.21/0.46 ((~((~in(ordered_pair(tptp_fun_C_1(relation_restriction(B!8, A!9)), tptp_fun_B_2(relation_restriction(B!8, A!9))), B!8)) | (~in(ordered_pair(tptp_fun_C_1(relation_restriction(B!8, A!9)), tptp_fun_B_2(relation_restriction(B!8, A!9))), cartesian_product2(A!9, A!9))))) | (~in(ordered_pair(tptp_fun_C_1(relation_restriction(B!8, A!9)), tptp_fun_B_2(relation_restriction(B!8, A!9))), B!8)) | (~in(ordered_pair(tptp_fun_C_1(relation_restriction(B!8, A!9)), tptp_fun_B_2(relation_restriction(B!8, A!9))), cartesian_product2(A!9, A!9)))),
% 0.21/0.46 inference(tautology,[status(thm)],[])).
% 0.21/0.46 tff(137,plain,
% 0.21/0.46 ((~in(ordered_pair(tptp_fun_C_1(relation_restriction(B!8, A!9)), tptp_fun_B_2(relation_restriction(B!8, A!9))), B!8)) | (~in(ordered_pair(tptp_fun_C_1(relation_restriction(B!8, A!9)), tptp_fun_B_2(relation_restriction(B!8, A!9))), cartesian_product2(A!9, A!9)))),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[136, 135])).
% 0.21/0.46 tff(138,plain,
% 0.21/0.46 (~in(ordered_pair(tptp_fun_C_1(relation_restriction(B!8, A!9)), tptp_fun_B_2(relation_restriction(B!8, A!9))), B!8)),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[137, 113])).
% 0.21/0.46 tff(139,plain,
% 0.21/0.46 ((tptp_fun_C_1(relation_restriction(B!8, A!9)) = tptp_fun_B_2(relation_restriction(B!8, A!9))) <=> (tptp_fun_B_2(relation_restriction(B!8, A!9)) = tptp_fun_C_1(relation_restriction(B!8, A!9)))),
% 0.21/0.46 inference(commutativity,[status(thm)],[])).
% 0.21/0.46 tff(140,plain,
% 0.21/0.46 ((tptp_fun_B_2(relation_restriction(B!8, A!9)) = tptp_fun_C_1(relation_restriction(B!8, A!9))) <=> (tptp_fun_C_1(relation_restriction(B!8, A!9)) = tptp_fun_B_2(relation_restriction(B!8, A!9)))),
% 0.21/0.46 inference(symmetry,[status(thm)],[139])).
% 0.21/0.46 tff(141,plain,
% 0.21/0.46 ((~(tptp_fun_B_2(relation_restriction(B!8, A!9)) = tptp_fun_C_1(relation_restriction(B!8, A!9)))) <=> (~(tptp_fun_C_1(relation_restriction(B!8, A!9)) = tptp_fun_B_2(relation_restriction(B!8, A!9))))),
% 0.21/0.46 inference(monotonicity,[status(thm)],[140])).
% 0.21/0.46 tff(142,plain,
% 0.21/0.46 (((~in(tptp_fun_B_2(relation_restriction(B!8, A!9)), relation_field(relation_restriction(B!8, A!9)))) | (~in(tptp_fun_C_1(relation_restriction(B!8, A!9)), relation_field(relation_restriction(B!8, A!9)))) | (tptp_fun_B_2(relation_restriction(B!8, A!9)) = tptp_fun_C_1(relation_restriction(B!8, A!9))) | in(ordered_pair(tptp_fun_B_2(relation_restriction(B!8, A!9)), tptp_fun_C_1(relation_restriction(B!8, A!9))), relation_restriction(B!8, A!9)) | in(ordered_pair(tptp_fun_C_1(relation_restriction(B!8, A!9)), tptp_fun_B_2(relation_restriction(B!8, A!9))), relation_restriction(B!8, A!9))) | (~(tptp_fun_B_2(relation_restriction(B!8, A!9)) = tptp_fun_C_1(relation_restriction(B!8, A!9))))),
% 0.21/0.46 inference(tautology,[status(thm)],[])).
% 0.21/0.46 tff(143,plain,
% 0.21/0.46 (~(tptp_fun_B_2(relation_restriction(B!8, A!9)) = tptp_fun_C_1(relation_restriction(B!8, A!9)))),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[142, 63])).
% 0.21/0.46 tff(144,plain,
% 0.21/0.46 (~(tptp_fun_C_1(relation_restriction(B!8, A!9)) = tptp_fun_B_2(relation_restriction(B!8, A!9)))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[143, 141])).
% 0.21/0.46 tff(145,plain,
% 0.21/0.46 (((~in(tptp_fun_B_2(relation_restriction(B!8, A!9)), relation_field(B!8))) | (~in(tptp_fun_B_2(relation_restriction(B!8, A!9)), A!9))) | in(tptp_fun_B_2(relation_restriction(B!8, A!9)), relation_field(B!8))),
% 0.21/0.46 inference(tautology,[status(thm)],[])).
% 0.21/0.46 tff(146,plain,
% 0.21/0.46 (in(tptp_fun_B_2(relation_restriction(B!8, A!9)), relation_field(B!8))),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[145, 82])).
% 0.21/0.46 tff(147,plain,
% 0.21/0.46 (((~in(tptp_fun_C_1(relation_restriction(B!8, A!9)), relation_field(B!8))) | (~in(tptp_fun_C_1(relation_restriction(B!8, A!9)), A!9))) | in(tptp_fun_C_1(relation_restriction(B!8, A!9)), relation_field(B!8))),
% 0.21/0.46 inference(tautology,[status(thm)],[])).
% 0.21/0.46 tff(148,plain,
% 0.21/0.46 (in(tptp_fun_C_1(relation_restriction(B!8, A!9)), relation_field(B!8))),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[147, 90])).
% 0.21/0.46 tff(149,plain,
% 0.21/0.46 (((~![A: $i] : ((~relation(A)) | (~((~(connected(A) | (~((~in(tptp_fun_B_2(A), relation_field(A))) | (~in(tptp_fun_C_1(A), relation_field(A))) | (tptp_fun_B_2(A) = tptp_fun_C_1(A)) | in(ordered_pair(tptp_fun_B_2(A), tptp_fun_C_1(A)), A) | in(ordered_pair(tptp_fun_C_1(A), tptp_fun_B_2(A)), A))))) | (~((~connected(A)) | ![B: $i, C: $i] : (in(ordered_pair(C, B), A) | in(ordered_pair(B, C), A) | (B = C) | (~in(B, relation_field(A))) | (~in(C, relation_field(A)))))))))) | ((~relation(B!8)) | (~((~(connected(B!8) | (~((~in(tptp_fun_B_2(B!8), relation_field(B!8))) | (~in(tptp_fun_C_1(B!8), relation_field(B!8))) | (tptp_fun_B_2(B!8) = tptp_fun_C_1(B!8)) | in(ordered_pair(tptp_fun_B_2(B!8), tptp_fun_C_1(B!8)), B!8) | in(ordered_pair(tptp_fun_C_1(B!8), tptp_fun_B_2(B!8)), B!8))))) | (~((~connected(B!8)) | ![B: $i, C: $i] : ((B = C) | in(ordered_pair(C, B), B!8) | in(ordered_pair(B, C), B!8) | (~in(B, relation_field(B!8))) | (~in(C, relation_field(B!8)))))))))) <=> ((~![A: $i] : ((~relation(A)) | (~((~(connected(A) | (~((~in(tptp_fun_B_2(A), relation_field(A))) | (~in(tptp_fun_C_1(A), relation_field(A))) | (tptp_fun_B_2(A) = tptp_fun_C_1(A)) | in(ordered_pair(tptp_fun_B_2(A), tptp_fun_C_1(A)), A) | in(ordered_pair(tptp_fun_C_1(A), tptp_fun_B_2(A)), A))))) | (~((~connected(A)) | ![B: $i, C: $i] : (in(ordered_pair(C, B), A) | in(ordered_pair(B, C), A) | (B = C) | (~in(B, relation_field(A))) | (~in(C, relation_field(A)))))))))) | (~relation(B!8)) | (~((~(connected(B!8) | (~((~in(tptp_fun_B_2(B!8), relation_field(B!8))) | (~in(tptp_fun_C_1(B!8), relation_field(B!8))) | (tptp_fun_B_2(B!8) = tptp_fun_C_1(B!8)) | in(ordered_pair(tptp_fun_B_2(B!8), tptp_fun_C_1(B!8)), B!8) | in(ordered_pair(tptp_fun_C_1(B!8), tptp_fun_B_2(B!8)), B!8))))) | (~((~connected(B!8)) | ![B: $i, C: $i] : ((B = C) | in(ordered_pair(C, B), B!8) | in(ordered_pair(B, C), B!8) | (~in(B, relation_field(B!8))) | (~in(C, relation_field(B!8)))))))))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(150,plain,
% 0.21/0.46 (((~relation(B!8)) | (~((~(connected(B!8) | (~((~in(tptp_fun_B_2(B!8), relation_field(B!8))) | (~in(tptp_fun_C_1(B!8), relation_field(B!8))) | (tptp_fun_B_2(B!8) = tptp_fun_C_1(B!8)) | in(ordered_pair(tptp_fun_B_2(B!8), tptp_fun_C_1(B!8)), B!8) | in(ordered_pair(tptp_fun_C_1(B!8), tptp_fun_B_2(B!8)), B!8))))) | (~((~connected(B!8)) | ![B: $i, C: $i] : (in(ordered_pair(C, B), B!8) | in(ordered_pair(B, C), B!8) | (B = C) | (~in(B, relation_field(B!8))) | (~in(C, relation_field(B!8))))))))) <=> ((~relation(B!8)) | (~((~(connected(B!8) | (~((~in(tptp_fun_B_2(B!8), relation_field(B!8))) | (~in(tptp_fun_C_1(B!8), relation_field(B!8))) | (tptp_fun_B_2(B!8) = tptp_fun_C_1(B!8)) | in(ordered_pair(tptp_fun_B_2(B!8), tptp_fun_C_1(B!8)), B!8) | in(ordered_pair(tptp_fun_C_1(B!8), tptp_fun_B_2(B!8)), B!8))))) | (~((~connected(B!8)) | ![B: $i, C: $i] : ((B = C) | in(ordered_pair(C, B), B!8) | in(ordered_pair(B, C), B!8) | (~in(B, relation_field(B!8))) | (~in(C, relation_field(B!8)))))))))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(151,plain,
% 0.21/0.46 (((~![A: $i] : ((~relation(A)) | (~((~(connected(A) | (~((~in(tptp_fun_B_2(A), relation_field(A))) | (~in(tptp_fun_C_1(A), relation_field(A))) | (tptp_fun_B_2(A) = tptp_fun_C_1(A)) | in(ordered_pair(tptp_fun_B_2(A), tptp_fun_C_1(A)), A) | in(ordered_pair(tptp_fun_C_1(A), tptp_fun_B_2(A)), A))))) | (~((~connected(A)) | ![B: $i, C: $i] : (in(ordered_pair(C, B), A) | in(ordered_pair(B, C), A) | (B = C) | (~in(B, relation_field(A))) | (~in(C, relation_field(A)))))))))) | ((~relation(B!8)) | (~((~(connected(B!8) | (~((~in(tptp_fun_B_2(B!8), relation_field(B!8))) | (~in(tptp_fun_C_1(B!8), relation_field(B!8))) | (tptp_fun_B_2(B!8) = tptp_fun_C_1(B!8)) | in(ordered_pair(tptp_fun_B_2(B!8), tptp_fun_C_1(B!8)), B!8) | in(ordered_pair(tptp_fun_C_1(B!8), tptp_fun_B_2(B!8)), B!8))))) | (~((~connected(B!8)) | ![B: $i, C: $i] : (in(ordered_pair(C, B), B!8) | in(ordered_pair(B, C), B!8) | (B = C) | (~in(B, relation_field(B!8))) | (~in(C, relation_field(B!8)))))))))) <=> ((~![A: $i] : ((~relation(A)) | (~((~(connected(A) | (~((~in(tptp_fun_B_2(A), relation_field(A))) | (~in(tptp_fun_C_1(A), relation_field(A))) | (tptp_fun_B_2(A) = tptp_fun_C_1(A)) | in(ordered_pair(tptp_fun_B_2(A), tptp_fun_C_1(A)), A) | in(ordered_pair(tptp_fun_C_1(A), tptp_fun_B_2(A)), A))))) | (~((~connected(A)) | ![B: $i, C: $i] : (in(ordered_pair(C, B), A) | in(ordered_pair(B, C), A) | (B = C) | (~in(B, relation_field(A))) | (~in(C, relation_field(A)))))))))) | ((~relation(B!8)) | (~((~(connected(B!8) | (~((~in(tptp_fun_B_2(B!8), relation_field(B!8))) | (~in(tptp_fun_C_1(B!8), relation_field(B!8))) | (tptp_fun_B_2(B!8) = tptp_fun_C_1(B!8)) | in(ordered_pair(tptp_fun_B_2(B!8), tptp_fun_C_1(B!8)), B!8) | in(ordered_pair(tptp_fun_C_1(B!8), tptp_fun_B_2(B!8)), B!8))))) | (~((~connected(B!8)) | ![B: $i, C: $i] : ((B = C) | in(ordered_pair(C, B), B!8) | in(ordered_pair(B, C), B!8) | (~in(B, relation_field(B!8))) | (~in(C, relation_field(B!8))))))))))),
% 0.21/0.46 inference(monotonicity,[status(thm)],[150])).
% 0.21/0.46 tff(152,plain,
% 0.21/0.46 (((~![A: $i] : ((~relation(A)) | (~((~(connected(A) | (~((~in(tptp_fun_B_2(A), relation_field(A))) | (~in(tptp_fun_C_1(A), relation_field(A))) | (tptp_fun_B_2(A) = tptp_fun_C_1(A)) | in(ordered_pair(tptp_fun_B_2(A), tptp_fun_C_1(A)), A) | in(ordered_pair(tptp_fun_C_1(A), tptp_fun_B_2(A)), A))))) | (~((~connected(A)) | ![B: $i, C: $i] : (in(ordered_pair(C, B), A) | in(ordered_pair(B, C), A) | (B = C) | (~in(B, relation_field(A))) | (~in(C, relation_field(A)))))))))) | ((~relation(B!8)) | (~((~(connected(B!8) | (~((~in(tptp_fun_B_2(B!8), relation_field(B!8))) | (~in(tptp_fun_C_1(B!8), relation_field(B!8))) | (tptp_fun_B_2(B!8) = tptp_fun_C_1(B!8)) | in(ordered_pair(tptp_fun_B_2(B!8), tptp_fun_C_1(B!8)), B!8) | in(ordered_pair(tptp_fun_C_1(B!8), tptp_fun_B_2(B!8)), B!8))))) | (~((~connected(B!8)) | ![B: $i, C: $i] : (in(ordered_pair(C, B), B!8) | in(ordered_pair(B, C), B!8) | (B = C) | (~in(B, relation_field(B!8))) | (~in(C, relation_field(B!8)))))))))) <=> ((~![A: $i] : ((~relation(A)) | (~((~(connected(A) | (~((~in(tptp_fun_B_2(A), relation_field(A))) | (~in(tptp_fun_C_1(A), relation_field(A))) | (tptp_fun_B_2(A) = tptp_fun_C_1(A)) | in(ordered_pair(tptp_fun_B_2(A), tptp_fun_C_1(A)), A) | in(ordered_pair(tptp_fun_C_1(A), tptp_fun_B_2(A)), A))))) | (~((~connected(A)) | ![B: $i, C: $i] : (in(ordered_pair(C, B), A) | in(ordered_pair(B, C), A) | (B = C) | (~in(B, relation_field(A))) | (~in(C, relation_field(A)))))))))) | (~relation(B!8)) | (~((~(connected(B!8) | (~((~in(tptp_fun_B_2(B!8), relation_field(B!8))) | (~in(tptp_fun_C_1(B!8), relation_field(B!8))) | (tptp_fun_B_2(B!8) = tptp_fun_C_1(B!8)) | in(ordered_pair(tptp_fun_B_2(B!8), tptp_fun_C_1(B!8)), B!8) | in(ordered_pair(tptp_fun_C_1(B!8), tptp_fun_B_2(B!8)), B!8))))) | (~((~connected(B!8)) | ![B: $i, C: $i] : ((B = C) | in(ordered_pair(C, B), B!8) | in(ordered_pair(B, C), B!8) | (~in(B, relation_field(B!8))) | (~in(C, relation_field(B!8)))))))))),
% 0.21/0.46 inference(transitivity,[status(thm)],[151, 149])).
% 0.21/0.46 tff(153,plain,
% 0.21/0.46 ((~![A: $i] : ((~relation(A)) | (~((~(connected(A) | (~((~in(tptp_fun_B_2(A), relation_field(A))) | (~in(tptp_fun_C_1(A), relation_field(A))) | (tptp_fun_B_2(A) = tptp_fun_C_1(A)) | in(ordered_pair(tptp_fun_B_2(A), tptp_fun_C_1(A)), A) | in(ordered_pair(tptp_fun_C_1(A), tptp_fun_B_2(A)), A))))) | (~((~connected(A)) | ![B: $i, C: $i] : (in(ordered_pair(C, B), A) | in(ordered_pair(B, C), A) | (B = C) | (~in(B, relation_field(A))) | (~in(C, relation_field(A)))))))))) | ((~relation(B!8)) | (~((~(connected(B!8) | (~((~in(tptp_fun_B_2(B!8), relation_field(B!8))) | (~in(tptp_fun_C_1(B!8), relation_field(B!8))) | (tptp_fun_B_2(B!8) = tptp_fun_C_1(B!8)) | in(ordered_pair(tptp_fun_B_2(B!8), tptp_fun_C_1(B!8)), B!8) | in(ordered_pair(tptp_fun_C_1(B!8), tptp_fun_B_2(B!8)), B!8))))) | (~((~connected(B!8)) | ![B: $i, C: $i] : (in(ordered_pair(C, B), B!8) | in(ordered_pair(B, C), B!8) | (B = C) | (~in(B, relation_field(B!8))) | (~in(C, relation_field(B!8)))))))))),
% 0.21/0.46 inference(quant_inst,[status(thm)],[])).
% 0.21/0.46 tff(154,plain,
% 0.21/0.46 ((~![A: $i] : ((~relation(A)) | (~((~(connected(A) | (~((~in(tptp_fun_B_2(A), relation_field(A))) | (~in(tptp_fun_C_1(A), relation_field(A))) | (tptp_fun_B_2(A) = tptp_fun_C_1(A)) | in(ordered_pair(tptp_fun_B_2(A), tptp_fun_C_1(A)), A) | in(ordered_pair(tptp_fun_C_1(A), tptp_fun_B_2(A)), A))))) | (~((~connected(A)) | ![B: $i, C: $i] : (in(ordered_pair(C, B), A) | in(ordered_pair(B, C), A) | (B = C) | (~in(B, relation_field(A))) | (~in(C, relation_field(A)))))))))) | (~relation(B!8)) | (~((~(connected(B!8) | (~((~in(tptp_fun_B_2(B!8), relation_field(B!8))) | (~in(tptp_fun_C_1(B!8), relation_field(B!8))) | (tptp_fun_B_2(B!8) = tptp_fun_C_1(B!8)) | in(ordered_pair(tptp_fun_B_2(B!8), tptp_fun_C_1(B!8)), B!8) | in(ordered_pair(tptp_fun_C_1(B!8), tptp_fun_B_2(B!8)), B!8))))) | (~((~connected(B!8)) | ![B: $i, C: $i] : ((B = C) | in(ordered_pair(C, B), B!8) | in(ordered_pair(B, C), B!8) | (~in(B, relation_field(B!8))) | (~in(C, relation_field(B!8))))))))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[153, 152])).
% 0.21/0.46 tff(155,plain,
% 0.21/0.46 (~((~(connected(B!8) | (~((~in(tptp_fun_B_2(B!8), relation_field(B!8))) | (~in(tptp_fun_C_1(B!8), relation_field(B!8))) | (tptp_fun_B_2(B!8) = tptp_fun_C_1(B!8)) | in(ordered_pair(tptp_fun_B_2(B!8), tptp_fun_C_1(B!8)), B!8) | in(ordered_pair(tptp_fun_C_1(B!8), tptp_fun_B_2(B!8)), B!8))))) | (~((~connected(B!8)) | ![B: $i, C: $i] : ((B = C) | in(ordered_pair(C, B), B!8) | in(ordered_pair(B, C), B!8) | (~in(B, relation_field(B!8))) | (~in(C, relation_field(B!8)))))))),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[154, 50, 14])).
% 0.21/0.46 tff(156,plain,
% 0.21/0.46 (((~(connected(B!8) | (~((~in(tptp_fun_B_2(B!8), relation_field(B!8))) | (~in(tptp_fun_C_1(B!8), relation_field(B!8))) | (tptp_fun_B_2(B!8) = tptp_fun_C_1(B!8)) | in(ordered_pair(tptp_fun_B_2(B!8), tptp_fun_C_1(B!8)), B!8) | in(ordered_pair(tptp_fun_C_1(B!8), tptp_fun_B_2(B!8)), B!8))))) | (~((~connected(B!8)) | ![B: $i, C: $i] : ((B = C) | in(ordered_pair(C, B), B!8) | in(ordered_pair(B, C), B!8) | (~in(B, relation_field(B!8))) | (~in(C, relation_field(B!8))))))) | ((~connected(B!8)) | ![B: $i, C: $i] : ((B = C) | in(ordered_pair(C, B), B!8) | in(ordered_pair(B, C), B!8) | (~in(B, relation_field(B!8))) | (~in(C, relation_field(B!8)))))),
% 0.21/0.46 inference(tautology,[status(thm)],[])).
% 0.21/0.46 tff(157,plain,
% 0.21/0.46 ((~connected(B!8)) | ![B: $i, C: $i] : ((B = C) | in(ordered_pair(C, B), B!8) | in(ordered_pair(B, C), B!8) | (~in(B, relation_field(B!8))) | (~in(C, relation_field(B!8))))),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[156, 155])).
% 0.21/0.46 tff(158,plain,
% 0.21/0.46 (connected(B!8)),
% 0.21/0.46 inference(or_elim,[status(thm)],[13])).
% 0.21/0.46 tff(159,plain,
% 0.21/0.46 ((~((~connected(B!8)) | ![B: $i, C: $i] : ((B = C) | in(ordered_pair(C, B), B!8) | in(ordered_pair(B, C), B!8) | (~in(B, relation_field(B!8))) | (~in(C, relation_field(B!8)))))) | (~connected(B!8)) | ![B: $i, C: $i] : ((B = C) | in(ordered_pair(C, B), B!8) | in(ordered_pair(B, C), B!8) | (~in(B, relation_field(B!8))) | (~in(C, relation_field(B!8))))),
% 0.21/0.46 inference(tautology,[status(thm)],[])).
% 0.21/0.46 tff(160,plain,
% 0.21/0.46 ((~((~connected(B!8)) | ![B: $i, C: $i] : ((B = C) | in(ordered_pair(C, B), B!8) | in(ordered_pair(B, C), B!8) | (~in(B, relation_field(B!8))) | (~in(C, relation_field(B!8)))))) | ![B: $i, C: $i] : ((B = C) | in(ordered_pair(C, B), B!8) | in(ordered_pair(B, C), B!8) | (~in(B, relation_field(B!8))) | (~in(C, relation_field(B!8))))),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[159, 158])).
% 0.21/0.46 tff(161,plain,
% 0.21/0.46 (![B: $i, C: $i] : ((B = C) | in(ordered_pair(C, B), B!8) | in(ordered_pair(B, C), B!8) | (~in(B, relation_field(B!8))) | (~in(C, relation_field(B!8))))),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[160, 157])).
% 0.21/0.46 tff(162,plain,
% 0.21/0.46 (((~![B: $i, C: $i] : ((B = C) | in(ordered_pair(C, B), B!8) | in(ordered_pair(B, C), B!8) | (~in(B, relation_field(B!8))) | (~in(C, relation_field(B!8))))) | (in(ordered_pair(tptp_fun_C_1(relation_restriction(B!8, A!9)), tptp_fun_B_2(relation_restriction(B!8, A!9))), B!8) | in(ordered_pair(tptp_fun_B_2(relation_restriction(B!8, A!9)), tptp_fun_C_1(relation_restriction(B!8, A!9))), B!8) | (~in(tptp_fun_C_1(relation_restriction(B!8, A!9)), relation_field(B!8))) | (~in(tptp_fun_B_2(relation_restriction(B!8, A!9)), relation_field(B!8))) | (tptp_fun_C_1(relation_restriction(B!8, A!9)) = tptp_fun_B_2(relation_restriction(B!8, A!9))))) <=> ((~![B: $i, C: $i] : ((B = C) | in(ordered_pair(C, B), B!8) | in(ordered_pair(B, C), B!8) | (~in(B, relation_field(B!8))) | (~in(C, relation_field(B!8))))) | in(ordered_pair(tptp_fun_C_1(relation_restriction(B!8, A!9)), tptp_fun_B_2(relation_restriction(B!8, A!9))), B!8) | in(ordered_pair(tptp_fun_B_2(relation_restriction(B!8, A!9)), tptp_fun_C_1(relation_restriction(B!8, A!9))), B!8) | (~in(tptp_fun_C_1(relation_restriction(B!8, A!9)), relation_field(B!8))) | (~in(tptp_fun_B_2(relation_restriction(B!8, A!9)), relation_field(B!8))) | (tptp_fun_C_1(relation_restriction(B!8, A!9)) = tptp_fun_B_2(relation_restriction(B!8, A!9))))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(163,plain,
% 0.21/0.46 (((tptp_fun_C_1(relation_restriction(B!8, A!9)) = tptp_fun_B_2(relation_restriction(B!8, A!9))) | in(ordered_pair(tptp_fun_B_2(relation_restriction(B!8, A!9)), tptp_fun_C_1(relation_restriction(B!8, A!9))), B!8) | in(ordered_pair(tptp_fun_C_1(relation_restriction(B!8, A!9)), tptp_fun_B_2(relation_restriction(B!8, A!9))), B!8) | (~in(tptp_fun_C_1(relation_restriction(B!8, A!9)), relation_field(B!8))) | (~in(tptp_fun_B_2(relation_restriction(B!8, A!9)), relation_field(B!8)))) <=> (in(ordered_pair(tptp_fun_C_1(relation_restriction(B!8, A!9)), tptp_fun_B_2(relation_restriction(B!8, A!9))), B!8) | in(ordered_pair(tptp_fun_B_2(relation_restriction(B!8, A!9)), tptp_fun_C_1(relation_restriction(B!8, A!9))), B!8) | (~in(tptp_fun_C_1(relation_restriction(B!8, A!9)), relation_field(B!8))) | (~in(tptp_fun_B_2(relation_restriction(B!8, A!9)), relation_field(B!8))) | (tptp_fun_C_1(relation_restriction(B!8, A!9)) = tptp_fun_B_2(relation_restriction(B!8, A!9))))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(164,plain,
% 0.21/0.46 (((~![B: $i, C: $i] : ((B = C) | in(ordered_pair(C, B), B!8) | in(ordered_pair(B, C), B!8) | (~in(B, relation_field(B!8))) | (~in(C, relation_field(B!8))))) | ((tptp_fun_C_1(relation_restriction(B!8, A!9)) = tptp_fun_B_2(relation_restriction(B!8, A!9))) | in(ordered_pair(tptp_fun_B_2(relation_restriction(B!8, A!9)), tptp_fun_C_1(relation_restriction(B!8, A!9))), B!8) | in(ordered_pair(tptp_fun_C_1(relation_restriction(B!8, A!9)), tptp_fun_B_2(relation_restriction(B!8, A!9))), B!8) | (~in(tptp_fun_C_1(relation_restriction(B!8, A!9)), relation_field(B!8))) | (~in(tptp_fun_B_2(relation_restriction(B!8, A!9)), relation_field(B!8))))) <=> ((~![B: $i, C: $i] : ((B = C) | in(ordered_pair(C, B), B!8) | in(ordered_pair(B, C), B!8) | (~in(B, relation_field(B!8))) | (~in(C, relation_field(B!8))))) | (in(ordered_pair(tptp_fun_C_1(relation_restriction(B!8, A!9)), tptp_fun_B_2(relation_restriction(B!8, A!9))), B!8) | in(ordered_pair(tptp_fun_B_2(relation_restriction(B!8, A!9)), tptp_fun_C_1(relation_restriction(B!8, A!9))), B!8) | (~in(tptp_fun_C_1(relation_restriction(B!8, A!9)), relation_field(B!8))) | (~in(tptp_fun_B_2(relation_restriction(B!8, A!9)), relation_field(B!8))) | (tptp_fun_C_1(relation_restriction(B!8, A!9)) = tptp_fun_B_2(relation_restriction(B!8, A!9)))))),
% 0.21/0.47 inference(monotonicity,[status(thm)],[163])).
% 0.21/0.47 tff(165,plain,
% 0.21/0.47 (((~![B: $i, C: $i] : ((B = C) | in(ordered_pair(C, B), B!8) | in(ordered_pair(B, C), B!8) | (~in(B, relation_field(B!8))) | (~in(C, relation_field(B!8))))) | ((tptp_fun_C_1(relation_restriction(B!8, A!9)) = tptp_fun_B_2(relation_restriction(B!8, A!9))) | in(ordered_pair(tptp_fun_B_2(relation_restriction(B!8, A!9)), tptp_fun_C_1(relation_restriction(B!8, A!9))), B!8) | in(ordered_pair(tptp_fun_C_1(relation_restriction(B!8, A!9)), tptp_fun_B_2(relation_restriction(B!8, A!9))), B!8) | (~in(tptp_fun_C_1(relation_restriction(B!8, A!9)), relation_field(B!8))) | (~in(tptp_fun_B_2(relation_restriction(B!8, A!9)), relation_field(B!8))))) <=> ((~![B: $i, C: $i] : ((B = C) | in(ordered_pair(C, B), B!8) | in(ordered_pair(B, C), B!8) | (~in(B, relation_field(B!8))) | (~in(C, relation_field(B!8))))) | in(ordered_pair(tptp_fun_C_1(relation_restriction(B!8, A!9)), tptp_fun_B_2(relation_restriction(B!8, A!9))), B!8) | in(ordered_pair(tptp_fun_B_2(relation_restriction(B!8, A!9)), tptp_fun_C_1(relation_restriction(B!8, A!9))), B!8) | (~in(tptp_fun_C_1(relation_restriction(B!8, A!9)), relation_field(B!8))) | (~in(tptp_fun_B_2(relation_restriction(B!8, A!9)), relation_field(B!8))) | (tptp_fun_C_1(relation_restriction(B!8, A!9)) = tptp_fun_B_2(relation_restriction(B!8, A!9))))),
% 0.21/0.47 inference(transitivity,[status(thm)],[164, 162])).
% 0.21/0.47 tff(166,plain,
% 0.21/0.47 ((~![B: $i, C: $i] : ((B = C) | in(ordered_pair(C, B), B!8) | in(ordered_pair(B, C), B!8) | (~in(B, relation_field(B!8))) | (~in(C, relation_field(B!8))))) | ((tptp_fun_C_1(relation_restriction(B!8, A!9)) = tptp_fun_B_2(relation_restriction(B!8, A!9))) | in(ordered_pair(tptp_fun_B_2(relation_restriction(B!8, A!9)), tptp_fun_C_1(relation_restriction(B!8, A!9))), B!8) | in(ordered_pair(tptp_fun_C_1(relation_restriction(B!8, A!9)), tptp_fun_B_2(relation_restriction(B!8, A!9))), B!8) | (~in(tptp_fun_C_1(relation_restriction(B!8, A!9)), relation_field(B!8))) | (~in(tptp_fun_B_2(relation_restriction(B!8, A!9)), relation_field(B!8))))),
% 0.21/0.47 inference(quant_inst,[status(thm)],[])).
% 0.21/0.47 tff(167,plain,
% 0.21/0.47 ((~![B: $i, C: $i] : ((B = C) | in(ordered_pair(C, B), B!8) | in(ordered_pair(B, C), B!8) | (~in(B, relation_field(B!8))) | (~in(C, relation_field(B!8))))) | in(ordered_pair(tptp_fun_C_1(relation_restriction(B!8, A!9)), tptp_fun_B_2(relation_restriction(B!8, A!9))), B!8) | in(ordered_pair(tptp_fun_B_2(relation_restriction(B!8, A!9)), tptp_fun_C_1(relation_restriction(B!8, A!9))), B!8) | (~in(tptp_fun_C_1(relation_restriction(B!8, A!9)), relation_field(B!8))) | (~in(tptp_fun_B_2(relation_restriction(B!8, A!9)), relation_field(B!8))) | (tptp_fun_C_1(relation_restriction(B!8, A!9)) = tptp_fun_B_2(relation_restriction(B!8, A!9)))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[166, 165])).
% 0.21/0.47 tff(168,plain,
% 0.21/0.47 (in(ordered_pair(tptp_fun_C_1(relation_restriction(B!8, A!9)), tptp_fun_B_2(relation_restriction(B!8, A!9))), B!8) | in(ordered_pair(tptp_fun_B_2(relation_restriction(B!8, A!9)), tptp_fun_C_1(relation_restriction(B!8, A!9))), B!8) | (~in(tptp_fun_C_1(relation_restriction(B!8, A!9)), relation_field(B!8))) | (~in(tptp_fun_B_2(relation_restriction(B!8, A!9)), relation_field(B!8))) | (tptp_fun_C_1(relation_restriction(B!8, A!9)) = tptp_fun_B_2(relation_restriction(B!8, A!9)))),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[167, 161])).
% 0.21/0.47 tff(169,plain,
% 0.21/0.47 (in(ordered_pair(tptp_fun_C_1(relation_restriction(B!8, A!9)), tptp_fun_B_2(relation_restriction(B!8, A!9))), B!8) | in(ordered_pair(tptp_fun_B_2(relation_restriction(B!8, A!9)), tptp_fun_C_1(relation_restriction(B!8, A!9))), B!8)),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[168, 148, 146, 144])).
% 0.21/0.47 tff(170,plain,
% 0.21/0.47 (in(ordered_pair(tptp_fun_B_2(relation_restriction(B!8, A!9)), tptp_fun_C_1(relation_restriction(B!8, A!9))), B!8)),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[169, 138])).
% 0.21/0.47 tff(171,plain,
% 0.21/0.47 (((~![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!8)) | (in(ordered_pair(tptp_fun_B_2(relation_restriction(B!8, A!9)), tptp_fun_C_1(relation_restriction(B!8, A!9))), relation_restriction(B!8, A!9)) <=> (~((~in(ordered_pair(tptp_fun_B_2(relation_restriction(B!8, A!9)), tptp_fun_C_1(relation_restriction(B!8, A!9))), B!8)) | (~in(ordered_pair(tptp_fun_B_2(relation_restriction(B!8, A!9)), tptp_fun_C_1(relation_restriction(B!8, A!9))), cartesian_product2(A!9, A!9)))))))) <=> ((~![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!8)) | (in(ordered_pair(tptp_fun_B_2(relation_restriction(B!8, A!9)), tptp_fun_C_1(relation_restriction(B!8, A!9))), relation_restriction(B!8, A!9)) <=> (~((~in(ordered_pair(tptp_fun_B_2(relation_restriction(B!8, A!9)), tptp_fun_C_1(relation_restriction(B!8, A!9))), B!8)) | (~in(ordered_pair(tptp_fun_B_2(relation_restriction(B!8, A!9)), tptp_fun_C_1(relation_restriction(B!8, A!9))), cartesian_product2(A!9, A!9)))))))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(172,plain,
% 0.21/0.47 ((~![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!8)) | (in(ordered_pair(tptp_fun_B_2(relation_restriction(B!8, A!9)), tptp_fun_C_1(relation_restriction(B!8, A!9))), relation_restriction(B!8, A!9)) <=> (~((~in(ordered_pair(tptp_fun_B_2(relation_restriction(B!8, A!9)), tptp_fun_C_1(relation_restriction(B!8, A!9))), B!8)) | (~in(ordered_pair(tptp_fun_B_2(relation_restriction(B!8, A!9)), tptp_fun_C_1(relation_restriction(B!8, A!9))), cartesian_product2(A!9, A!9)))))))),
% 0.21/0.47 inference(quant_inst,[status(thm)],[])).
% 0.21/0.47 tff(173,plain,
% 0.21/0.47 ((~![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!8)) | (in(ordered_pair(tptp_fun_B_2(relation_restriction(B!8, A!9)), tptp_fun_C_1(relation_restriction(B!8, A!9))), relation_restriction(B!8, A!9)) <=> (~((~in(ordered_pair(tptp_fun_B_2(relation_restriction(B!8, A!9)), tptp_fun_C_1(relation_restriction(B!8, A!9))), B!8)) | (~in(ordered_pair(tptp_fun_B_2(relation_restriction(B!8, A!9)), tptp_fun_C_1(relation_restriction(B!8, A!9))), cartesian_product2(A!9, A!9))))))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[172, 171])).
% 0.21/0.47 tff(174,plain,
% 0.21/0.47 (in(ordered_pair(tptp_fun_B_2(relation_restriction(B!8, A!9)), tptp_fun_C_1(relation_restriction(B!8, A!9))), relation_restriction(B!8, A!9)) <=> (~((~in(ordered_pair(tptp_fun_B_2(relation_restriction(B!8, A!9)), tptp_fun_C_1(relation_restriction(B!8, A!9))), B!8)) | (~in(ordered_pair(tptp_fun_B_2(relation_restriction(B!8, A!9)), tptp_fun_C_1(relation_restriction(B!8, A!9))), cartesian_product2(A!9, A!9)))))),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[173, 126, 14])).
% 0.21/0.47 tff(175,plain,
% 0.21/0.47 (((~in(tptp_fun_B_2(relation_restriction(B!8, A!9)), relation_field(relation_restriction(B!8, A!9)))) | (~in(tptp_fun_C_1(relation_restriction(B!8, A!9)), relation_field(relation_restriction(B!8, A!9)))) | (tptp_fun_B_2(relation_restriction(B!8, A!9)) = tptp_fun_C_1(relation_restriction(B!8, A!9))) | in(ordered_pair(tptp_fun_B_2(relation_restriction(B!8, A!9)), tptp_fun_C_1(relation_restriction(B!8, A!9))), relation_restriction(B!8, A!9)) | in(ordered_pair(tptp_fun_C_1(relation_restriction(B!8, A!9)), tptp_fun_B_2(relation_restriction(B!8, A!9))), relation_restriction(B!8, A!9))) | (~in(ordered_pair(tptp_fun_B_2(relation_restriction(B!8, A!9)), tptp_fun_C_1(relation_restriction(B!8, A!9))), relation_restriction(B!8, A!9)))),
% 0.21/0.47 inference(tautology,[status(thm)],[])).
% 0.21/0.47 tff(176,plain,
% 0.21/0.47 (~in(ordered_pair(tptp_fun_B_2(relation_restriction(B!8, A!9)), tptp_fun_C_1(relation_restriction(B!8, A!9))), relation_restriction(B!8, A!9))),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[175, 63])).
% 0.21/0.47 tff(177,plain,
% 0.21/0.47 ((~(in(ordered_pair(tptp_fun_B_2(relation_restriction(B!8, A!9)), tptp_fun_C_1(relation_restriction(B!8, A!9))), relation_restriction(B!8, A!9)) <=> (~((~in(ordered_pair(tptp_fun_B_2(relation_restriction(B!8, A!9)), tptp_fun_C_1(relation_restriction(B!8, A!9))), B!8)) | (~in(ordered_pair(tptp_fun_B_2(relation_restriction(B!8, A!9)), tptp_fun_C_1(relation_restriction(B!8, A!9))), cartesian_product2(A!9, A!9))))))) | in(ordered_pair(tptp_fun_B_2(relation_restriction(B!8, A!9)), tptp_fun_C_1(relation_restriction(B!8, A!9))), relation_restriction(B!8, A!9)) | ((~in(ordered_pair(tptp_fun_B_2(relation_restriction(B!8, A!9)), tptp_fun_C_1(relation_restriction(B!8, A!9))), B!8)) | (~in(ordered_pair(tptp_fun_B_2(relation_restriction(B!8, A!9)), tptp_fun_C_1(relation_restriction(B!8, A!9))), cartesian_product2(A!9, A!9))))),
% 0.21/0.47 inference(tautology,[status(thm)],[])).
% 0.21/0.47 tff(178,plain,
% 0.21/0.47 ((~(in(ordered_pair(tptp_fun_B_2(relation_restriction(B!8, A!9)), tptp_fun_C_1(relation_restriction(B!8, A!9))), relation_restriction(B!8, A!9)) <=> (~((~in(ordered_pair(tptp_fun_B_2(relation_restriction(B!8, A!9)), tptp_fun_C_1(relation_restriction(B!8, A!9))), B!8)) | (~in(ordered_pair(tptp_fun_B_2(relation_restriction(B!8, A!9)), tptp_fun_C_1(relation_restriction(B!8, A!9))), cartesian_product2(A!9, A!9))))))) | ((~in(ordered_pair(tptp_fun_B_2(relation_restriction(B!8, A!9)), tptp_fun_C_1(relation_restriction(B!8, A!9))), B!8)) | (~in(ordered_pair(tptp_fun_B_2(relation_restriction(B!8, A!9)), tptp_fun_C_1(relation_restriction(B!8, A!9))), cartesian_product2(A!9, A!9))))),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[177, 176])).
% 0.21/0.47 tff(179,plain,
% 0.21/0.47 ((~in(ordered_pair(tptp_fun_B_2(relation_restriction(B!8, A!9)), tptp_fun_C_1(relation_restriction(B!8, A!9))), B!8)) | (~in(ordered_pair(tptp_fun_B_2(relation_restriction(B!8, A!9)), tptp_fun_C_1(relation_restriction(B!8, A!9))), cartesian_product2(A!9, A!9)))),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[178, 174])).
% 0.21/0.47 tff(180,plain,
% 0.21/0.47 ((~((~in(ordered_pair(tptp_fun_B_2(relation_restriction(B!8, A!9)), tptp_fun_C_1(relation_restriction(B!8, A!9))), B!8)) | (~in(ordered_pair(tptp_fun_B_2(relation_restriction(B!8, A!9)), tptp_fun_C_1(relation_restriction(B!8, A!9))), cartesian_product2(A!9, A!9))))) | (~in(ordered_pair(tptp_fun_B_2(relation_restriction(B!8, A!9)), tptp_fun_C_1(relation_restriction(B!8, A!9))), B!8)) | (~in(ordered_pair(tptp_fun_B_2(relation_restriction(B!8, A!9)), tptp_fun_C_1(relation_restriction(B!8, A!9))), cartesian_product2(A!9, A!9)))),
% 0.21/0.47 inference(tautology,[status(thm)],[])).
% 0.21/0.47 tff(181,plain,
% 0.21/0.47 ((~in(ordered_pair(tptp_fun_B_2(relation_restriction(B!8, A!9)), tptp_fun_C_1(relation_restriction(B!8, A!9))), B!8)) | (~in(ordered_pair(tptp_fun_B_2(relation_restriction(B!8, A!9)), tptp_fun_C_1(relation_restriction(B!8, A!9))), cartesian_product2(A!9, A!9)))),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[180, 179])).
% 0.21/0.47 tff(182,plain,
% 0.21/0.47 (~in(ordered_pair(tptp_fun_B_2(relation_restriction(B!8, A!9)), tptp_fun_C_1(relation_restriction(B!8, A!9))), cartesian_product2(A!9, A!9))),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[181, 170])).
% 0.21/0.47 tff(183,plain,
% 0.21/0.47 ((~(in(ordered_pair(tptp_fun_B_2(relation_restriction(B!8, A!9)), tptp_fun_C_1(relation_restriction(B!8, A!9))), cartesian_product2(A!9, A!9)) <=> (~((~in(tptp_fun_C_1(relation_restriction(B!8, A!9)), A!9)) | (~in(tptp_fun_B_2(relation_restriction(B!8, A!9)), A!9)))))) | in(ordered_pair(tptp_fun_B_2(relation_restriction(B!8, A!9)), tptp_fun_C_1(relation_restriction(B!8, A!9))), cartesian_product2(A!9, A!9)) | ((~in(tptp_fun_C_1(relation_restriction(B!8, A!9)), A!9)) | (~in(tptp_fun_B_2(relation_restriction(B!8, A!9)), A!9)))),
% 0.21/0.47 inference(tautology,[status(thm)],[])).
% 0.21/0.47 tff(184,plain,
% 0.21/0.47 (~(in(ordered_pair(tptp_fun_B_2(relation_restriction(B!8, A!9)), tptp_fun_C_1(relation_restriction(B!8, A!9))), cartesian_product2(A!9, A!9)) <=> (~((~in(tptp_fun_C_1(relation_restriction(B!8, A!9)), A!9)) | (~in(tptp_fun_B_2(relation_restriction(B!8, A!9)), A!9)))))),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[183, 182, 94])).
% 0.21/0.47 tff(185,plain,
% 0.21/0.47 ((~![A: $i, B: $i, C: $i, D: $i] : (in(ordered_pair(A, B), cartesian_product2(C, D)) <=> (~((~in(B, D)) | (~in(A, C)))))) | (in(ordered_pair(tptp_fun_B_2(relation_restriction(B!8, A!9)), tptp_fun_C_1(relation_restriction(B!8, A!9))), cartesian_product2(A!9, A!9)) <=> (~((~in(tptp_fun_C_1(relation_restriction(B!8, A!9)), A!9)) | (~in(tptp_fun_B_2(relation_restriction(B!8, A!9)), A!9)))))),
% 0.21/0.47 inference(quant_inst,[status(thm)],[])).
% 0.21/0.47 tff(186,plain,
% 0.21/0.47 ($false),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[185, 105, 184])).
% 0.21/0.47 % SZS output end Proof
%------------------------------------------------------------------------------