TSTP Solution File: SET916+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SET916+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n016.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 05:08:36 EDT 2022
% Result : Theorem 0.20s 0.40s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET916+1 : TPTP v8.1.0. Released v3.2.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n016.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sat Sep 3 08:55:22 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34 Usage: tptp [options] [-file:]file
% 0.13/0.34 -h, -? prints this message.
% 0.13/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.34 -m, -model generate model.
% 0.13/0.34 -p, -proof generate proof.
% 0.13/0.34 -c, -core generate unsat core of named formulas.
% 0.13/0.34 -st, -statistics display statistics.
% 0.13/0.34 -t:timeout set timeout (in second).
% 0.13/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34 -<param>:<value> configuration parameter and value.
% 0.13/0.34 -o:<output-file> file to place output in.
% 0.20/0.40 % SZS status Theorem
% 0.20/0.40 % SZS output start Proof
% 0.20/0.40 tff(in_type, type, (
% 0.20/0.40 in: ( $i * $i ) > $o)).
% 0.20/0.40 tff(tptp_fun_B_6_type, type, (
% 0.20/0.40 tptp_fun_B_6: $i)).
% 0.20/0.40 tff(tptp_fun_C_4_type, type, (
% 0.20/0.40 tptp_fun_C_4: ( $i * $i ) > $i)).
% 0.20/0.40 tff(unordered_pair_type, type, (
% 0.20/0.40 unordered_pair: ( $i * $i ) > $i)).
% 0.20/0.40 tff(tptp_fun_A_7_type, type, (
% 0.20/0.40 tptp_fun_A_7: $i)).
% 0.20/0.40 tff(tptp_fun_C_5_type, type, (
% 0.20/0.40 tptp_fun_C_5: $i)).
% 0.20/0.40 tff(disjoint_type, type, (
% 0.20/0.40 disjoint: ( $i * $i ) > $o)).
% 0.20/0.40 tff(set_intersection2_type, type, (
% 0.20/0.40 set_intersection2: ( $i * $i ) > $i)).
% 0.20/0.40 tff(tptp_fun_D_1_type, type, (
% 0.20/0.40 tptp_fun_D_1: ( $i * $i * $i ) > $i)).
% 0.20/0.40 tff(tptp_fun_D_0_type, type, (
% 0.20/0.40 tptp_fun_D_0: ( $i * $i * $i ) > $i)).
% 0.20/0.40 tff(1,assumption,(tptp_fun_C_4(unordered_pair(C!5, A!7), B!6) = C!5), introduced(assumption)).
% 0.20/0.40 tff(2,plain,
% 0.20/0.40 (in(tptp_fun_C_4(unordered_pair(C!5, A!7), B!6), B!6) <=> in(C!5, B!6)),
% 0.20/0.40 inference(monotonicity,[status(thm)],[1])).
% 0.20/0.40 tff(3,plain,
% 0.20/0.40 (in(C!5, B!6) <=> in(tptp_fun_C_4(unordered_pair(C!5, A!7), B!6), B!6)),
% 0.20/0.40 inference(symmetry,[status(thm)],[2])).
% 0.20/0.40 tff(4,plain,
% 0.20/0.40 ((~in(C!5, B!6)) <=> (~in(tptp_fun_C_4(unordered_pair(C!5, A!7), B!6), B!6))),
% 0.20/0.40 inference(monotonicity,[status(thm)],[3])).
% 0.20/0.40 tff(5,plain,
% 0.20/0.40 ((~(~((~in(A!7, B!6)) & (~in(C!5, B!6)) & (~disjoint(unordered_pair(A!7, C!5), B!6))))) <=> ((~in(A!7, B!6)) & (~in(C!5, B!6)) & (~disjoint(unordered_pair(A!7, C!5), B!6)))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(6,plain,
% 0.20/0.40 ((~![A: $i, B: $i, C: $i] : (~((~in(A, B)) & (~in(C, B)) & (~disjoint(unordered_pair(A, C), B))))) <=> (~![A: $i, B: $i, C: $i] : (~((~in(A, B)) & (~in(C, B)) & (~disjoint(unordered_pair(A, C), B)))))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(7,plain,
% 0.20/0.40 ((~![A: $i, B: $i, C: $i] : (~(((~in(A, B)) & (~in(C, B))) & (~disjoint(unordered_pair(A, C), B))))) <=> (~![A: $i, B: $i, C: $i] : (~((~in(A, B)) & (~in(C, B)) & (~disjoint(unordered_pair(A, C), B)))))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(8,axiom,(~![A: $i, B: $i, C: $i] : (~(((~in(A, B)) & (~in(C, B))) & (~disjoint(unordered_pair(A, C), B))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t57_zfmisc_1')).
% 0.20/0.40 tff(9,plain,
% 0.20/0.40 (~![A: $i, B: $i, C: $i] : (~((~in(A, B)) & (~in(C, B)) & (~disjoint(unordered_pair(A, C), B))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[8, 7])).
% 0.20/0.40 tff(10,plain,
% 0.20/0.40 (~![A: $i, B: $i, C: $i] : (~((~in(A, B)) & (~in(C, B)) & (~disjoint(unordered_pair(A, C), B))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[9, 6])).
% 0.20/0.40 tff(11,plain,
% 0.20/0.40 (~![A: $i, B: $i, C: $i] : (~((~in(A, B)) & (~in(C, B)) & (~disjoint(unordered_pair(A, C), B))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[10, 6])).
% 0.20/0.40 tff(12,plain,
% 0.20/0.40 (~![A: $i, B: $i, C: $i] : (~((~in(A, B)) & (~in(C, B)) & (~disjoint(unordered_pair(A, C), B))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[11, 6])).
% 0.20/0.40 tff(13,plain,
% 0.20/0.40 (~![A: $i, B: $i, C: $i] : (~((~in(A, B)) & (~in(C, B)) & (~disjoint(unordered_pair(A, C), B))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[12, 6])).
% 0.20/0.40 tff(14,plain,
% 0.20/0.40 (~![A: $i, B: $i, C: $i] : (~((~in(A, B)) & (~in(C, B)) & (~disjoint(unordered_pair(A, C), B))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[13, 6])).
% 0.20/0.40 tff(15,plain,
% 0.20/0.40 (~![A: $i, B: $i, C: $i] : (~((~in(A, B)) & (~in(C, B)) & (~disjoint(unordered_pair(A, C), B))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[14, 6])).
% 0.20/0.40 tff(16,plain,(
% 0.20/0.40 ~(~((~in(A!7, B!6)) & (~in(C!5, B!6)) & (~disjoint(unordered_pair(A!7, C!5), B!6))))),
% 0.20/0.40 inference(skolemize,[status(sab)],[15])).
% 0.20/0.40 tff(17,plain,
% 0.20/0.40 ((~in(A!7, B!6)) & (~in(C!5, B!6)) & (~disjoint(unordered_pair(A!7, C!5), B!6))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[16, 5])).
% 0.20/0.40 tff(18,plain,
% 0.20/0.40 (~in(C!5, B!6)),
% 0.20/0.40 inference(and_elim,[status(thm)],[17])).
% 0.20/0.40 tff(19,plain,
% 0.20/0.40 (~in(tptp_fun_C_4(unordered_pair(C!5, A!7), B!6), B!6)),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[18, 4])).
% 0.20/0.40 tff(20,plain,
% 0.20/0.40 (^[A: $i, B: $i, C: $i, D: $i] : refl((~((~((~(C = set_intersection2(A, B))) | (in(D, C) <=> (~((~in(D, A)) | (~in(D, B))))))) | (~((C = set_intersection2(A, B)) | (in(tptp_fun_D_1(C, B, A), C) <=> ((~in(tptp_fun_D_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B)))))))) <=> (~((~((~(C = set_intersection2(A, B))) | (in(D, C) <=> (~((~in(D, A)) | (~in(D, B))))))) | (~((C = set_intersection2(A, B)) | (in(tptp_fun_D_1(C, B, A), C) <=> ((~in(tptp_fun_D_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B)))))))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(21,plain,
% 0.20/0.40 (![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (in(D, C) <=> (~((~in(D, A)) | (~in(D, B))))))) | (~((C = set_intersection2(A, B)) | (in(tptp_fun_D_1(C, B, A), C) <=> ((~in(tptp_fun_D_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B)))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (in(D, C) <=> (~((~in(D, A)) | (~in(D, B))))))) | (~((C = set_intersection2(A, B)) | (in(tptp_fun_D_1(C, B, A), C) <=> ((~in(tptp_fun_D_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))))))))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[20])).
% 0.20/0.40 tff(22,plain,
% 0.20/0.40 (![A: $i, B: $i, C: $i] : ![D: $i] : (~((~((~(C = set_intersection2(A, B))) | (in(D, C) <=> (~((~in(D, A)) | (~in(D, B))))))) | (~((C = set_intersection2(A, B)) | (in(tptp_fun_D_1(C, B, A), C) <=> ((~in(tptp_fun_D_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B)))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (in(D, C) <=> (~((~in(D, A)) | (~in(D, B))))))) | (~((C = set_intersection2(A, B)) | (in(tptp_fun_D_1(C, B, A), C) <=> ((~in(tptp_fun_D_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))))))))),
% 0.20/0.40 inference(pull_quant,[status(thm)],[])).
% 0.20/0.40 tff(23,plain,
% 0.20/0.40 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(pull_quant(((~(C = set_intersection2(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, A)) | (~in(D, B)))))) <=> ![D: $i] : ((~(C = set_intersection2(A, B))) | (in(D, C) <=> (~((~in(D, A)) | (~in(D, B))))))), ((~((~(C = set_intersection2(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, A)) | (~in(D, B))))))) <=> (~![D: $i] : ((~(C = set_intersection2(A, B))) | (in(D, C) <=> (~((~in(D, A)) | (~in(D, B))))))))), pull_quant((~![D: $i] : ((~(C = set_intersection2(A, B))) | (in(D, C) <=> (~((~in(D, A)) | (~in(D, B))))))) <=> ?[D: $i] : (~((~(C = set_intersection2(A, B))) | (in(D, C) <=> (~((~in(D, A)) | (~in(D, B)))))))), ((~((~(C = set_intersection2(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, A)) | (~in(D, B))))))) <=> ?[D: $i] : (~((~(C = set_intersection2(A, B))) | (in(D, C) <=> (~((~in(D, A)) | (~in(D, B))))))))), (((~((~(C = set_intersection2(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, A)) | (~in(D, B))))))) | (~((C = set_intersection2(A, B)) | (in(tptp_fun_D_1(C, B, A), C) <=> ((~in(tptp_fun_D_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))))))) <=> (?[D: $i] : (~((~(C = set_intersection2(A, B))) | (in(D, C) <=> (~((~in(D, A)) | (~in(D, B))))))) | (~((C = set_intersection2(A, B)) | (in(tptp_fun_D_1(C, B, A), C) <=> ((~in(tptp_fun_D_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))))))))), pull_quant((?[D: $i] : (~((~(C = set_intersection2(A, B))) | (in(D, C) <=> (~((~in(D, A)) | (~in(D, B))))))) | (~((C = set_intersection2(A, B)) | (in(tptp_fun_D_1(C, B, A), C) <=> ((~in(tptp_fun_D_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))))))) <=> ?[D: $i] : ((~((~(C = set_intersection2(A, B))) | (in(D, C) <=> (~((~in(D, A)) | (~in(D, B))))))) | (~((C = set_intersection2(A, B)) | (in(tptp_fun_D_1(C, B, A), C) <=> ((~in(tptp_fun_D_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B)))))))), (((~((~(C = set_intersection2(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, A)) | (~in(D, B))))))) | (~((C = set_intersection2(A, B)) | (in(tptp_fun_D_1(C, B, A), C) <=> ((~in(tptp_fun_D_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))))))) <=> ?[D: $i] : ((~((~(C = set_intersection2(A, B))) | (in(D, C) <=> (~((~in(D, A)) | (~in(D, B))))))) | (~((C = set_intersection2(A, B)) | (in(tptp_fun_D_1(C, B, A), C) <=> ((~in(tptp_fun_D_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))))))))), ((~((~((~(C = set_intersection2(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, A)) | (~in(D, B))))))) | (~((C = set_intersection2(A, B)) | (in(tptp_fun_D_1(C, B, A), C) <=> ((~in(tptp_fun_D_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B)))))))) <=> (~?[D: $i] : ((~((~(C = set_intersection2(A, B))) | (in(D, C) <=> (~((~in(D, A)) | (~in(D, B))))))) | (~((C = set_intersection2(A, B)) | (in(tptp_fun_D_1(C, B, A), C) <=> ((~in(tptp_fun_D_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B)))))))))), pull_quant((~?[D: $i] : ((~((~(C = set_intersection2(A, B))) | (in(D, C) <=> (~((~in(D, A)) | (~in(D, B))))))) | (~((C = set_intersection2(A, B)) | (in(tptp_fun_D_1(C, B, A), C) <=> ((~in(tptp_fun_D_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B)))))))) <=> ![D: $i] : (~((~((~(C = set_intersection2(A, B))) | (in(D, C) <=> (~((~in(D, A)) | (~in(D, B))))))) | (~((C = set_intersection2(A, B)) | (in(tptp_fun_D_1(C, B, A), C) <=> ((~in(tptp_fun_D_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))))))))), ((~((~((~(C = set_intersection2(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, A)) | (~in(D, B))))))) | (~((C = set_intersection2(A, B)) | (in(tptp_fun_D_1(C, B, A), C) <=> ((~in(tptp_fun_D_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B)))))))) <=> ![D: $i] : (~((~((~(C = set_intersection2(A, B))) | (in(D, C) <=> (~((~in(D, A)) | (~in(D, B))))))) | (~((C = set_intersection2(A, B)) | (in(tptp_fun_D_1(C, B, A), C) <=> ((~in(tptp_fun_D_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))))))))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(24,plain,
% 0.20/0.40 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_intersection2(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, A)) | (~in(D, B))))))) | (~((C = set_intersection2(A, B)) | (in(tptp_fun_D_1(C, B, A), C) <=> ((~in(tptp_fun_D_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B)))))))) <=> ![A: $i, B: $i, C: $i] : ![D: $i] : (~((~((~(C = set_intersection2(A, B))) | (in(D, C) <=> (~((~in(D, A)) | (~in(D, B))))))) | (~((C = set_intersection2(A, B)) | (in(tptp_fun_D_1(C, B, A), C) <=> ((~in(tptp_fun_D_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))))))))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[23])).
% 0.20/0.40 tff(25,plain,
% 0.20/0.40 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_intersection2(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, A)) | (~in(D, B))))))) | (~((C = set_intersection2(A, B)) | (in(tptp_fun_D_1(C, B, A), C) <=> ((~in(tptp_fun_D_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B)))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (in(D, C) <=> (~((~in(D, A)) | (~in(D, B))))))) | (~((C = set_intersection2(A, B)) | (in(tptp_fun_D_1(C, B, A), C) <=> ((~in(tptp_fun_D_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))))))))),
% 0.20/0.40 inference(transitivity,[status(thm)],[24, 22])).
% 0.20/0.40 tff(26,plain,
% 0.20/0.40 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_intersection2(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, A)) | (~in(D, B))))))) | (~((C = set_intersection2(A, B)) | (in(tptp_fun_D_1(C, B, A), C) <=> ((~in(tptp_fun_D_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B)))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (in(D, C) <=> (~((~in(D, A)) | (~in(D, B))))))) | (~((C = set_intersection2(A, B)) | (in(tptp_fun_D_1(C, B, A), C) <=> ((~in(tptp_fun_D_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))))))))),
% 0.20/0.40 inference(transitivity,[status(thm)],[25, 21])).
% 0.20/0.40 tff(27,plain,
% 0.20/0.40 (^[A: $i, B: $i, C: $i] : rewrite((~((~((~(C = set_intersection2(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, A)) | (~in(D, B))))))) | (~((C = set_intersection2(A, B)) | (in(tptp_fun_D_1(C, B, A), C) <=> ((~in(tptp_fun_D_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B)))))))) <=> (~((~((~(C = set_intersection2(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, A)) | (~in(D, B))))))) | (~((C = set_intersection2(A, B)) | (in(tptp_fun_D_1(C, B, A), C) <=> ((~in(tptp_fun_D_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B)))))))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(28,plain,
% 0.20/0.40 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_intersection2(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, A)) | (~in(D, B))))))) | (~((C = set_intersection2(A, B)) | (in(tptp_fun_D_1(C, B, A), C) <=> ((~in(tptp_fun_D_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B)))))))) <=> ![A: $i, B: $i, C: $i] : (~((~((~(C = set_intersection2(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, A)) | (~in(D, B))))))) | (~((C = set_intersection2(A, B)) | (in(tptp_fun_D_1(C, B, A), C) <=> ((~in(tptp_fun_D_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))))))))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[27])).
% 0.20/0.41 tff(29,plain,
% 0.20/0.41 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_intersection2(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, A)) | (~in(D, B))))))) | (~((C = set_intersection2(A, B)) | (in(tptp_fun_D_1(C, B, A), C) <=> ((~in(tptp_fun_D_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B)))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (in(D, C) <=> (~((~in(D, A)) | (~in(D, B))))))) | (~((C = set_intersection2(A, B)) | (in(tptp_fun_D_1(C, B, A), C) <=> ((~in(tptp_fun_D_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))))))))),
% 0.20/0.41 inference(transitivity,[status(thm)],[28, 26])).
% 0.20/0.41 tff(30,plain,
% 0.20/0.41 (^[A: $i, B: $i, C: $i] : trans(monotonicity(rewrite(((~(C = set_intersection2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) & in(D, B)))) <=> ((~(C = set_intersection2(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, A)) | (~in(D, B))))))), rewrite(((C = set_intersection2(A, B)) | ((~in(tptp_fun_D_1(C, B, A), C)) <=> (in(tptp_fun_D_1(C, B, A), A) & in(tptp_fun_D_1(C, B, A), B)))) <=> ((C = set_intersection2(A, B)) | (in(tptp_fun_D_1(C, B, A), C) <=> ((~in(tptp_fun_D_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B)))))), ((((~(C = set_intersection2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) & in(D, B)))) & ((C = set_intersection2(A, B)) | ((~in(tptp_fun_D_1(C, B, A), C)) <=> (in(tptp_fun_D_1(C, B, A), A) & in(tptp_fun_D_1(C, B, A), B))))) <=> (((~(C = set_intersection2(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, A)) | (~in(D, B)))))) & ((C = set_intersection2(A, B)) | (in(tptp_fun_D_1(C, B, A), C) <=> ((~in(tptp_fun_D_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B)))))))), rewrite((((~(C = set_intersection2(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, A)) | (~in(D, B)))))) & ((C = set_intersection2(A, B)) | (in(tptp_fun_D_1(C, B, A), C) <=> ((~in(tptp_fun_D_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B)))))) <=> (~((~((~(C = set_intersection2(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, A)) | (~in(D, B))))))) | (~((C = set_intersection2(A, B)) | (in(tptp_fun_D_1(C, B, A), C) <=> ((~in(tptp_fun_D_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))))))))), ((((~(C = set_intersection2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) & in(D, B)))) & ((C = set_intersection2(A, B)) | ((~in(tptp_fun_D_1(C, B, A), C)) <=> (in(tptp_fun_D_1(C, B, A), A) & in(tptp_fun_D_1(C, B, A), B))))) <=> (~((~((~(C = set_intersection2(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, A)) | (~in(D, B))))))) | (~((C = set_intersection2(A, B)) | (in(tptp_fun_D_1(C, B, A), C) <=> ((~in(tptp_fun_D_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))))))))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(31,plain,
% 0.20/0.41 (![A: $i, B: $i, C: $i] : (((~(C = set_intersection2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) & in(D, B)))) & ((C = set_intersection2(A, B)) | ((~in(tptp_fun_D_1(C, B, A), C)) <=> (in(tptp_fun_D_1(C, B, A), A) & in(tptp_fun_D_1(C, B, A), B))))) <=> ![A: $i, B: $i, C: $i] : (~((~((~(C = set_intersection2(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, A)) | (~in(D, B))))))) | (~((C = set_intersection2(A, B)) | (in(tptp_fun_D_1(C, B, A), C) <=> ((~in(tptp_fun_D_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))))))))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[30])).
% 0.20/0.41 tff(32,plain,
% 0.20/0.41 (^[A: $i, B: $i, C: $i] : rewrite((((~(C = set_intersection2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) & in(D, B)))) & ((C = set_intersection2(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), A) & in(tptp_fun_D_1(C, B, A), B)))))) <=> (((~(C = set_intersection2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) & in(D, B)))) & ((C = set_intersection2(A, B)) | ((~in(tptp_fun_D_1(C, B, A), C)) <=> (in(tptp_fun_D_1(C, B, A), A) & in(tptp_fun_D_1(C, B, A), B))))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(33,plain,
% 0.20/0.41 (![A: $i, B: $i, C: $i] : (((~(C = set_intersection2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) & in(D, B)))) & ((C = set_intersection2(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), A) & in(tptp_fun_D_1(C, B, A), B)))))) <=> ![A: $i, B: $i, C: $i] : (((~(C = set_intersection2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) & in(D, B)))) & ((C = set_intersection2(A, B)) | ((~in(tptp_fun_D_1(C, B, A), C)) <=> (in(tptp_fun_D_1(C, B, A), A) & in(tptp_fun_D_1(C, B, A), B)))))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[32])).
% 0.20/0.41 tff(34,plain,
% 0.20/0.41 (![A: $i, B: $i, C: $i] : ((C = set_intersection2(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, A) & in(D, B)))) <=> ![A: $i, B: $i, C: $i] : ((C = set_intersection2(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, A) & in(D, B))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(35,axiom,(![A: $i, B: $i, C: $i] : ((C = set_intersection2(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, A) & in(D, B))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d3_xboole_0')).
% 0.20/0.41 tff(36,plain,
% 0.20/0.41 (![A: $i, B: $i, C: $i] : ((C = set_intersection2(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, A) & in(D, B))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[35, 34])).
% 0.20/0.41 tff(37,plain,(
% 0.20/0.41 ![A: $i, B: $i, C: $i] : (((~(C = set_intersection2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) & in(D, B)))) & ((C = set_intersection2(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), A) & in(tptp_fun_D_1(C, B, A), B))))))),
% 0.20/0.41 inference(skolemize,[status(sab)],[36])).
% 0.20/0.41 tff(38,plain,
% 0.20/0.41 (![A: $i, B: $i, C: $i] : (((~(C = set_intersection2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) & in(D, B)))) & ((C = set_intersection2(A, B)) | ((~in(tptp_fun_D_1(C, B, A), C)) <=> (in(tptp_fun_D_1(C, B, A), A) & in(tptp_fun_D_1(C, B, A), B)))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[37, 33])).
% 0.20/0.41 tff(39,plain,
% 0.20/0.41 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_intersection2(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, A)) | (~in(D, B))))))) | (~((C = set_intersection2(A, B)) | (in(tptp_fun_D_1(C, B, A), C) <=> ((~in(tptp_fun_D_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))))))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[38, 31])).
% 0.20/0.41 tff(40,plain,
% 0.20/0.41 (![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (in(D, C) <=> (~((~in(D, A)) | (~in(D, B))))))) | (~((C = set_intersection2(A, B)) | (in(tptp_fun_D_1(C, B, A), C) <=> ((~in(tptp_fun_D_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))))))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[39, 29])).
% 0.20/0.41 tff(41,plain,
% 0.20/0.41 (((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (in(D, C) <=> (~((~in(D, A)) | (~in(D, B))))))) | (~((C = set_intersection2(A, B)) | (in(tptp_fun_D_1(C, B, A), C) <=> ((~in(tptp_fun_D_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))))))))) | ((~in(tptp_fun_C_4(unordered_pair(C!5, A!7), B!6), set_intersection2(B!6, unordered_pair(C!5, A!7)))) <=> ((~in(tptp_fun_C_4(unordered_pair(C!5, A!7), B!6), B!6)) | (~in(tptp_fun_C_4(unordered_pair(C!5, A!7), B!6), unordered_pair(C!5, A!7)))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (in(D, C) <=> (~((~in(D, A)) | (~in(D, B))))))) | (~((C = set_intersection2(A, B)) | (in(tptp_fun_D_1(C, B, A), C) <=> ((~in(tptp_fun_D_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))))))))) | ((~in(tptp_fun_C_4(unordered_pair(C!5, A!7), B!6), set_intersection2(B!6, unordered_pair(C!5, A!7)))) <=> ((~in(tptp_fun_C_4(unordered_pair(C!5, A!7), B!6), B!6)) | (~in(tptp_fun_C_4(unordered_pair(C!5, A!7), B!6), unordered_pair(C!5, A!7))))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(42,plain,
% 0.20/0.41 ((~(in(tptp_fun_C_4(unordered_pair(C!5, A!7), B!6), set_intersection2(B!6, unordered_pair(C!5, A!7))) <=> ((~in(tptp_fun_C_4(unordered_pair(C!5, A!7), B!6), B!6)) | (~in(tptp_fun_C_4(unordered_pair(C!5, A!7), B!6), unordered_pair(C!5, A!7)))))) <=> ((~in(tptp_fun_C_4(unordered_pair(C!5, A!7), B!6), set_intersection2(B!6, unordered_pair(C!5, A!7)))) <=> ((~in(tptp_fun_C_4(unordered_pair(C!5, A!7), B!6), B!6)) | (~in(tptp_fun_C_4(unordered_pair(C!5, A!7), B!6), unordered_pair(C!5, A!7)))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(43,plain,
% 0.20/0.41 (((in(tptp_fun_C_4(unordered_pair(C!5, A!7), B!6), set_intersection2(B!6, unordered_pair(C!5, A!7))) <=> ((~in(tptp_fun_C_4(unordered_pair(C!5, A!7), B!6), B!6)) | (~in(tptp_fun_C_4(unordered_pair(C!5, A!7), B!6), unordered_pair(C!5, A!7))))) | $false) <=> (in(tptp_fun_C_4(unordered_pair(C!5, A!7), B!6), set_intersection2(B!6, unordered_pair(C!5, A!7))) <=> ((~in(tptp_fun_C_4(unordered_pair(C!5, A!7), B!6), B!6)) | (~in(tptp_fun_C_4(unordered_pair(C!5, A!7), B!6), unordered_pair(C!5, A!7)))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(44,plain,
% 0.20/0.41 ((~$true) <=> $false),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(45,plain,
% 0.20/0.41 (($true | (in(tptp_fun_D_1(set_intersection2(B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7), B!6), set_intersection2(B!6, unordered_pair(C!5, A!7))) <=> ((~in(tptp_fun_D_1(set_intersection2(B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7), B!6), B!6)) | (~in(tptp_fun_D_1(set_intersection2(B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7), B!6), unordered_pair(C!5, A!7)))))) <=> $true),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(46,plain,
% 0.20/0.41 ((set_intersection2(B!6, unordered_pair(C!5, A!7)) = set_intersection2(B!6, unordered_pair(C!5, A!7))) <=> $true),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(47,plain,
% 0.20/0.41 (((set_intersection2(B!6, unordered_pair(C!5, A!7)) = set_intersection2(B!6, unordered_pair(C!5, A!7))) | (in(tptp_fun_D_1(set_intersection2(B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7), B!6), set_intersection2(B!6, unordered_pair(C!5, A!7))) <=> ((~in(tptp_fun_D_1(set_intersection2(B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7), B!6), B!6)) | (~in(tptp_fun_D_1(set_intersection2(B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7), B!6), unordered_pair(C!5, A!7)))))) <=> ($true | (in(tptp_fun_D_1(set_intersection2(B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7), B!6), set_intersection2(B!6, unordered_pair(C!5, A!7))) <=> ((~in(tptp_fun_D_1(set_intersection2(B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7), B!6), B!6)) | (~in(tptp_fun_D_1(set_intersection2(B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7), B!6), unordered_pair(C!5, A!7))))))),
% 0.20/0.41 inference(monotonicity,[status(thm)],[46])).
% 0.20/0.41 tff(48,plain,
% 0.20/0.41 (((set_intersection2(B!6, unordered_pair(C!5, A!7)) = set_intersection2(B!6, unordered_pair(C!5, A!7))) | (in(tptp_fun_D_1(set_intersection2(B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7), B!6), set_intersection2(B!6, unordered_pair(C!5, A!7))) <=> ((~in(tptp_fun_D_1(set_intersection2(B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7), B!6), B!6)) | (~in(tptp_fun_D_1(set_intersection2(B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7), B!6), unordered_pair(C!5, A!7)))))) <=> $true),
% 0.20/0.41 inference(transitivity,[status(thm)],[47, 45])).
% 0.20/0.41 tff(49,plain,
% 0.20/0.41 ((~((set_intersection2(B!6, unordered_pair(C!5, A!7)) = set_intersection2(B!6, unordered_pair(C!5, A!7))) | (in(tptp_fun_D_1(set_intersection2(B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7), B!6), set_intersection2(B!6, unordered_pair(C!5, A!7))) <=> ((~in(tptp_fun_D_1(set_intersection2(B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7), B!6), B!6)) | (~in(tptp_fun_D_1(set_intersection2(B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7), B!6), unordered_pair(C!5, A!7))))))) <=> (~$true)),
% 0.20/0.41 inference(monotonicity,[status(thm)],[48])).
% 0.20/0.41 tff(50,plain,
% 0.20/0.41 ((~((set_intersection2(B!6, unordered_pair(C!5, A!7)) = set_intersection2(B!6, unordered_pair(C!5, A!7))) | (in(tptp_fun_D_1(set_intersection2(B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7), B!6), set_intersection2(B!6, unordered_pair(C!5, A!7))) <=> ((~in(tptp_fun_D_1(set_intersection2(B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7), B!6), B!6)) | (~in(tptp_fun_D_1(set_intersection2(B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7), B!6), unordered_pair(C!5, A!7))))))) <=> $false),
% 0.20/0.41 inference(transitivity,[status(thm)],[49, 44])).
% 0.20/0.41 tff(51,plain,
% 0.20/0.41 ((~(in(tptp_fun_C_4(unordered_pair(C!5, A!7), B!6), set_intersection2(B!6, unordered_pair(C!5, A!7))) <=> (~((~in(tptp_fun_C_4(unordered_pair(C!5, A!7), B!6), B!6)) | (~in(tptp_fun_C_4(unordered_pair(C!5, A!7), B!6), unordered_pair(C!5, A!7))))))) <=> (in(tptp_fun_C_4(unordered_pair(C!5, A!7), B!6), set_intersection2(B!6, unordered_pair(C!5, A!7))) <=> ((~in(tptp_fun_C_4(unordered_pair(C!5, A!7), B!6), B!6)) | (~in(tptp_fun_C_4(unordered_pair(C!5, A!7), B!6), unordered_pair(C!5, A!7)))))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(52,plain,
% 0.20/0.42 (($false | (in(tptp_fun_C_4(unordered_pair(C!5, A!7), B!6), set_intersection2(B!6, unordered_pair(C!5, A!7))) <=> (~((~in(tptp_fun_C_4(unordered_pair(C!5, A!7), B!6), B!6)) | (~in(tptp_fun_C_4(unordered_pair(C!5, A!7), B!6), unordered_pair(C!5, A!7))))))) <=> (in(tptp_fun_C_4(unordered_pair(C!5, A!7), B!6), set_intersection2(B!6, unordered_pair(C!5, A!7))) <=> (~((~in(tptp_fun_C_4(unordered_pair(C!5, A!7), B!6), B!6)) | (~in(tptp_fun_C_4(unordered_pair(C!5, A!7), B!6), unordered_pair(C!5, A!7))))))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(53,plain,
% 0.20/0.42 ((~(set_intersection2(B!6, unordered_pair(C!5, A!7)) = set_intersection2(B!6, unordered_pair(C!5, A!7)))) <=> (~$true)),
% 0.20/0.42 inference(monotonicity,[status(thm)],[46])).
% 0.20/0.42 tff(54,plain,
% 0.20/0.42 ((~(set_intersection2(B!6, unordered_pair(C!5, A!7)) = set_intersection2(B!6, unordered_pair(C!5, A!7)))) <=> $false),
% 0.20/0.42 inference(transitivity,[status(thm)],[53, 44])).
% 0.20/0.42 tff(55,plain,
% 0.20/0.42 (((~(set_intersection2(B!6, unordered_pair(C!5, A!7)) = set_intersection2(B!6, unordered_pair(C!5, A!7)))) | (in(tptp_fun_C_4(unordered_pair(C!5, A!7), B!6), set_intersection2(B!6, unordered_pair(C!5, A!7))) <=> (~((~in(tptp_fun_C_4(unordered_pair(C!5, A!7), B!6), B!6)) | (~in(tptp_fun_C_4(unordered_pair(C!5, A!7), B!6), unordered_pair(C!5, A!7))))))) <=> ($false | (in(tptp_fun_C_4(unordered_pair(C!5, A!7), B!6), set_intersection2(B!6, unordered_pair(C!5, A!7))) <=> (~((~in(tptp_fun_C_4(unordered_pair(C!5, A!7), B!6), B!6)) | (~in(tptp_fun_C_4(unordered_pair(C!5, A!7), B!6), unordered_pair(C!5, A!7)))))))),
% 0.20/0.42 inference(monotonicity,[status(thm)],[54])).
% 0.20/0.42 tff(56,plain,
% 0.20/0.42 (((~(set_intersection2(B!6, unordered_pair(C!5, A!7)) = set_intersection2(B!6, unordered_pair(C!5, A!7)))) | (in(tptp_fun_C_4(unordered_pair(C!5, A!7), B!6), set_intersection2(B!6, unordered_pair(C!5, A!7))) <=> (~((~in(tptp_fun_C_4(unordered_pair(C!5, A!7), B!6), B!6)) | (~in(tptp_fun_C_4(unordered_pair(C!5, A!7), B!6), unordered_pair(C!5, A!7))))))) <=> (in(tptp_fun_C_4(unordered_pair(C!5, A!7), B!6), set_intersection2(B!6, unordered_pair(C!5, A!7))) <=> (~((~in(tptp_fun_C_4(unordered_pair(C!5, A!7), B!6), B!6)) | (~in(tptp_fun_C_4(unordered_pair(C!5, A!7), B!6), unordered_pair(C!5, A!7))))))),
% 0.20/0.42 inference(transitivity,[status(thm)],[55, 52])).
% 0.20/0.42 tff(57,plain,
% 0.20/0.42 ((~((~(set_intersection2(B!6, unordered_pair(C!5, A!7)) = set_intersection2(B!6, unordered_pair(C!5, A!7)))) | (in(tptp_fun_C_4(unordered_pair(C!5, A!7), B!6), set_intersection2(B!6, unordered_pair(C!5, A!7))) <=> (~((~in(tptp_fun_C_4(unordered_pair(C!5, A!7), B!6), B!6)) | (~in(tptp_fun_C_4(unordered_pair(C!5, A!7), B!6), unordered_pair(C!5, A!7)))))))) <=> (~(in(tptp_fun_C_4(unordered_pair(C!5, A!7), B!6), set_intersection2(B!6, unordered_pair(C!5, A!7))) <=> (~((~in(tptp_fun_C_4(unordered_pair(C!5, A!7), B!6), B!6)) | (~in(tptp_fun_C_4(unordered_pair(C!5, A!7), B!6), unordered_pair(C!5, A!7)))))))),
% 0.20/0.42 inference(monotonicity,[status(thm)],[56])).
% 0.20/0.42 tff(58,plain,
% 0.20/0.42 ((~((~(set_intersection2(B!6, unordered_pair(C!5, A!7)) = set_intersection2(B!6, unordered_pair(C!5, A!7)))) | (in(tptp_fun_C_4(unordered_pair(C!5, A!7), B!6), set_intersection2(B!6, unordered_pair(C!5, A!7))) <=> (~((~in(tptp_fun_C_4(unordered_pair(C!5, A!7), B!6), B!6)) | (~in(tptp_fun_C_4(unordered_pair(C!5, A!7), B!6), unordered_pair(C!5, A!7)))))))) <=> (in(tptp_fun_C_4(unordered_pair(C!5, A!7), B!6), set_intersection2(B!6, unordered_pair(C!5, A!7))) <=> ((~in(tptp_fun_C_4(unordered_pair(C!5, A!7), B!6), B!6)) | (~in(tptp_fun_C_4(unordered_pair(C!5, A!7), B!6), unordered_pair(C!5, A!7)))))),
% 0.20/0.42 inference(transitivity,[status(thm)],[57, 51])).
% 0.20/0.42 tff(59,plain,
% 0.20/0.42 (((~((~(set_intersection2(B!6, unordered_pair(C!5, A!7)) = set_intersection2(B!6, unordered_pair(C!5, A!7)))) | (in(tptp_fun_C_4(unordered_pair(C!5, A!7), B!6), set_intersection2(B!6, unordered_pair(C!5, A!7))) <=> (~((~in(tptp_fun_C_4(unordered_pair(C!5, A!7), B!6), B!6)) | (~in(tptp_fun_C_4(unordered_pair(C!5, A!7), B!6), unordered_pair(C!5, A!7)))))))) | (~((set_intersection2(B!6, unordered_pair(C!5, A!7)) = set_intersection2(B!6, unordered_pair(C!5, A!7))) | (in(tptp_fun_D_1(set_intersection2(B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7), B!6), set_intersection2(B!6, unordered_pair(C!5, A!7))) <=> ((~in(tptp_fun_D_1(set_intersection2(B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7), B!6), B!6)) | (~in(tptp_fun_D_1(set_intersection2(B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7), B!6), unordered_pair(C!5, A!7)))))))) <=> ((in(tptp_fun_C_4(unordered_pair(C!5, A!7), B!6), set_intersection2(B!6, unordered_pair(C!5, A!7))) <=> ((~in(tptp_fun_C_4(unordered_pair(C!5, A!7), B!6), B!6)) | (~in(tptp_fun_C_4(unordered_pair(C!5, A!7), B!6), unordered_pair(C!5, A!7))))) | $false)),
% 0.20/0.42 inference(monotonicity,[status(thm)],[58, 50])).
% 0.20/0.42 tff(60,plain,
% 0.20/0.42 (((~((~(set_intersection2(B!6, unordered_pair(C!5, A!7)) = set_intersection2(B!6, unordered_pair(C!5, A!7)))) | (in(tptp_fun_C_4(unordered_pair(C!5, A!7), B!6), set_intersection2(B!6, unordered_pair(C!5, A!7))) <=> (~((~in(tptp_fun_C_4(unordered_pair(C!5, A!7), B!6), B!6)) | (~in(tptp_fun_C_4(unordered_pair(C!5, A!7), B!6), unordered_pair(C!5, A!7)))))))) | (~((set_intersection2(B!6, unordered_pair(C!5, A!7)) = set_intersection2(B!6, unordered_pair(C!5, A!7))) | (in(tptp_fun_D_1(set_intersection2(B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7), B!6), set_intersection2(B!6, unordered_pair(C!5, A!7))) <=> ((~in(tptp_fun_D_1(set_intersection2(B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7), B!6), B!6)) | (~in(tptp_fun_D_1(set_intersection2(B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7), B!6), unordered_pair(C!5, A!7)))))))) <=> (in(tptp_fun_C_4(unordered_pair(C!5, A!7), B!6), set_intersection2(B!6, unordered_pair(C!5, A!7))) <=> ((~in(tptp_fun_C_4(unordered_pair(C!5, A!7), B!6), B!6)) | (~in(tptp_fun_C_4(unordered_pair(C!5, A!7), B!6), unordered_pair(C!5, A!7)))))),
% 0.20/0.42 inference(transitivity,[status(thm)],[59, 43])).
% 0.20/0.42 tff(61,plain,
% 0.20/0.42 ((~((~((~(set_intersection2(B!6, unordered_pair(C!5, A!7)) = set_intersection2(B!6, unordered_pair(C!5, A!7)))) | (in(tptp_fun_C_4(unordered_pair(C!5, A!7), B!6), set_intersection2(B!6, unordered_pair(C!5, A!7))) <=> (~((~in(tptp_fun_C_4(unordered_pair(C!5, A!7), B!6), B!6)) | (~in(tptp_fun_C_4(unordered_pair(C!5, A!7), B!6), unordered_pair(C!5, A!7)))))))) | (~((set_intersection2(B!6, unordered_pair(C!5, A!7)) = set_intersection2(B!6, unordered_pair(C!5, A!7))) | (in(tptp_fun_D_1(set_intersection2(B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7), B!6), set_intersection2(B!6, unordered_pair(C!5, A!7))) <=> ((~in(tptp_fun_D_1(set_intersection2(B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7), B!6), B!6)) | (~in(tptp_fun_D_1(set_intersection2(B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7), B!6), unordered_pair(C!5, A!7))))))))) <=> (~(in(tptp_fun_C_4(unordered_pair(C!5, A!7), B!6), set_intersection2(B!6, unordered_pair(C!5, A!7))) <=> ((~in(tptp_fun_C_4(unordered_pair(C!5, A!7), B!6), B!6)) | (~in(tptp_fun_C_4(unordered_pair(C!5, A!7), B!6), unordered_pair(C!5, A!7))))))),
% 0.20/0.42 inference(monotonicity,[status(thm)],[60])).
% 0.20/0.42 tff(62,plain,
% 0.20/0.42 ((~((~((~(set_intersection2(B!6, unordered_pair(C!5, A!7)) = set_intersection2(B!6, unordered_pair(C!5, A!7)))) | (in(tptp_fun_C_4(unordered_pair(C!5, A!7), B!6), set_intersection2(B!6, unordered_pair(C!5, A!7))) <=> (~((~in(tptp_fun_C_4(unordered_pair(C!5, A!7), B!6), B!6)) | (~in(tptp_fun_C_4(unordered_pair(C!5, A!7), B!6), unordered_pair(C!5, A!7)))))))) | (~((set_intersection2(B!6, unordered_pair(C!5, A!7)) = set_intersection2(B!6, unordered_pair(C!5, A!7))) | (in(tptp_fun_D_1(set_intersection2(B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7), B!6), set_intersection2(B!6, unordered_pair(C!5, A!7))) <=> ((~in(tptp_fun_D_1(set_intersection2(B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7), B!6), B!6)) | (~in(tptp_fun_D_1(set_intersection2(B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7), B!6), unordered_pair(C!5, A!7))))))))) <=> ((~in(tptp_fun_C_4(unordered_pair(C!5, A!7), B!6), set_intersection2(B!6, unordered_pair(C!5, A!7)))) <=> ((~in(tptp_fun_C_4(unordered_pair(C!5, A!7), B!6), B!6)) | (~in(tptp_fun_C_4(unordered_pair(C!5, A!7), B!6), unordered_pair(C!5, A!7)))))),
% 0.20/0.43 inference(transitivity,[status(thm)],[61, 42])).
% 0.20/0.43 tff(63,plain,
% 0.20/0.43 (((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (in(D, C) <=> (~((~in(D, A)) | (~in(D, B))))))) | (~((C = set_intersection2(A, B)) | (in(tptp_fun_D_1(C, B, A), C) <=> ((~in(tptp_fun_D_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))))))))) | (~((~((~(set_intersection2(B!6, unordered_pair(C!5, A!7)) = set_intersection2(B!6, unordered_pair(C!5, A!7)))) | (in(tptp_fun_C_4(unordered_pair(C!5, A!7), B!6), set_intersection2(B!6, unordered_pair(C!5, A!7))) <=> (~((~in(tptp_fun_C_4(unordered_pair(C!5, A!7), B!6), B!6)) | (~in(tptp_fun_C_4(unordered_pair(C!5, A!7), B!6), unordered_pair(C!5, A!7)))))))) | (~((set_intersection2(B!6, unordered_pair(C!5, A!7)) = set_intersection2(B!6, unordered_pair(C!5, A!7))) | (in(tptp_fun_D_1(set_intersection2(B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7), B!6), set_intersection2(B!6, unordered_pair(C!5, A!7))) <=> ((~in(tptp_fun_D_1(set_intersection2(B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7), B!6), B!6)) | (~in(tptp_fun_D_1(set_intersection2(B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7), B!6), unordered_pair(C!5, A!7)))))))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (in(D, C) <=> (~((~in(D, A)) | (~in(D, B))))))) | (~((C = set_intersection2(A, B)) | (in(tptp_fun_D_1(C, B, A), C) <=> ((~in(tptp_fun_D_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))))))))) | ((~in(tptp_fun_C_4(unordered_pair(C!5, A!7), B!6), set_intersection2(B!6, unordered_pair(C!5, A!7)))) <=> ((~in(tptp_fun_C_4(unordered_pair(C!5, A!7), B!6), B!6)) | (~in(tptp_fun_C_4(unordered_pair(C!5, A!7), B!6), unordered_pair(C!5, A!7))))))),
% 0.20/0.43 inference(monotonicity,[status(thm)],[62])).
% 0.20/0.43 tff(64,plain,
% 0.20/0.43 (((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (in(D, C) <=> (~((~in(D, A)) | (~in(D, B))))))) | (~((C = set_intersection2(A, B)) | (in(tptp_fun_D_1(C, B, A), C) <=> ((~in(tptp_fun_D_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))))))))) | (~((~((~(set_intersection2(B!6, unordered_pair(C!5, A!7)) = set_intersection2(B!6, unordered_pair(C!5, A!7)))) | (in(tptp_fun_C_4(unordered_pair(C!5, A!7), B!6), set_intersection2(B!6, unordered_pair(C!5, A!7))) <=> (~((~in(tptp_fun_C_4(unordered_pair(C!5, A!7), B!6), B!6)) | (~in(tptp_fun_C_4(unordered_pair(C!5, A!7), B!6), unordered_pair(C!5, A!7)))))))) | (~((set_intersection2(B!6, unordered_pair(C!5, A!7)) = set_intersection2(B!6, unordered_pair(C!5, A!7))) | (in(tptp_fun_D_1(set_intersection2(B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7), B!6), set_intersection2(B!6, unordered_pair(C!5, A!7))) <=> ((~in(tptp_fun_D_1(set_intersection2(B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7), B!6), B!6)) | (~in(tptp_fun_D_1(set_intersection2(B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7), B!6), unordered_pair(C!5, A!7)))))))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (in(D, C) <=> (~((~in(D, A)) | (~in(D, B))))))) | (~((C = set_intersection2(A, B)) | (in(tptp_fun_D_1(C, B, A), C) <=> ((~in(tptp_fun_D_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))))))))) | ((~in(tptp_fun_C_4(unordered_pair(C!5, A!7), B!6), set_intersection2(B!6, unordered_pair(C!5, A!7)))) <=> ((~in(tptp_fun_C_4(unordered_pair(C!5, A!7), B!6), B!6)) | (~in(tptp_fun_C_4(unordered_pair(C!5, A!7), B!6), unordered_pair(C!5, A!7))))))),
% 0.20/0.43 inference(transitivity,[status(thm)],[63, 41])).
% 0.20/0.43 tff(65,plain,
% 0.20/0.43 ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (in(D, C) <=> (~((~in(D, A)) | (~in(D, B))))))) | (~((C = set_intersection2(A, B)) | (in(tptp_fun_D_1(C, B, A), C) <=> ((~in(tptp_fun_D_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))))))))) | (~((~((~(set_intersection2(B!6, unordered_pair(C!5, A!7)) = set_intersection2(B!6, unordered_pair(C!5, A!7)))) | (in(tptp_fun_C_4(unordered_pair(C!5, A!7), B!6), set_intersection2(B!6, unordered_pair(C!5, A!7))) <=> (~((~in(tptp_fun_C_4(unordered_pair(C!5, A!7), B!6), B!6)) | (~in(tptp_fun_C_4(unordered_pair(C!5, A!7), B!6), unordered_pair(C!5, A!7)))))))) | (~((set_intersection2(B!6, unordered_pair(C!5, A!7)) = set_intersection2(B!6, unordered_pair(C!5, A!7))) | (in(tptp_fun_D_1(set_intersection2(B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7), B!6), set_intersection2(B!6, unordered_pair(C!5, A!7))) <=> ((~in(tptp_fun_D_1(set_intersection2(B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7), B!6), B!6)) | (~in(tptp_fun_D_1(set_intersection2(B!6, unordered_pair(C!5, A!7)), unordered_pair(C!5, A!7), B!6), unordered_pair(C!5, A!7)))))))))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(66,plain,
% 0.20/0.43 ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (in(D, C) <=> (~((~in(D, A)) | (~in(D, B))))))) | (~((C = set_intersection2(A, B)) | (in(tptp_fun_D_1(C, B, A), C) <=> ((~in(tptp_fun_D_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))))))))) | ((~in(tptp_fun_C_4(unordered_pair(C!5, A!7), B!6), set_intersection2(B!6, unordered_pair(C!5, A!7)))) <=> ((~in(tptp_fun_C_4(unordered_pair(C!5, A!7), B!6), B!6)) | (~in(tptp_fun_C_4(unordered_pair(C!5, A!7), B!6), unordered_pair(C!5, A!7)))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[65, 64])).
% 0.20/0.43 tff(67,plain,
% 0.20/0.43 ((~in(tptp_fun_C_4(unordered_pair(C!5, A!7), B!6), set_intersection2(B!6, unordered_pair(C!5, A!7)))) <=> ((~in(tptp_fun_C_4(unordered_pair(C!5, A!7), B!6), B!6)) | (~in(tptp_fun_C_4(unordered_pair(C!5, A!7), B!6), unordered_pair(C!5, A!7))))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[66, 40])).
% 0.20/0.43 tff(68,plain,
% 0.20/0.43 (^[A: $i, B: $i] : rewrite((~((~(disjoint(A, B) | in(tptp_fun_C_4(B, A), set_intersection2(A, B)))) | (~(![C: $i] : (~in(C, set_intersection2(A, B))) | (~disjoint(A, B)))))) <=> (~((~(disjoint(A, B) | in(tptp_fun_C_4(B, A), set_intersection2(A, B)))) | (~((~disjoint(A, B)) | ![C: $i] : (~in(C, set_intersection2(A, B))))))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(69,plain,
% 0.20/0.43 (![A: $i, B: $i] : (~((~(disjoint(A, B) | in(tptp_fun_C_4(B, A), set_intersection2(A, B)))) | (~(![C: $i] : (~in(C, set_intersection2(A, B))) | (~disjoint(A, B)))))) <=> ![A: $i, B: $i] : (~((~(disjoint(A, B) | in(tptp_fun_C_4(B, A), set_intersection2(A, B)))) | (~((~disjoint(A, B)) | ![C: $i] : (~in(C, set_intersection2(A, B)))))))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[68])).
% 0.20/0.43 tff(70,plain,
% 0.20/0.43 (^[A: $i, B: $i] : refl((~((~(disjoint(A, B) | in(tptp_fun_C_4(B, A), set_intersection2(A, B)))) | (~(![C: $i] : (~in(C, set_intersection2(A, B))) | (~disjoint(A, B)))))) <=> (~((~(disjoint(A, B) | in(tptp_fun_C_4(B, A), set_intersection2(A, B)))) | (~(![C: $i] : (~in(C, set_intersection2(A, B))) | (~disjoint(A, B)))))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(71,plain,
% 0.20/0.43 (![A: $i, B: $i] : (~((~(disjoint(A, B) | in(tptp_fun_C_4(B, A), set_intersection2(A, B)))) | (~(![C: $i] : (~in(C, set_intersection2(A, B))) | (~disjoint(A, B)))))) <=> ![A: $i, B: $i] : (~((~(disjoint(A, B) | in(tptp_fun_C_4(B, A), set_intersection2(A, B)))) | (~(![C: $i] : (~in(C, set_intersection2(A, B))) | (~disjoint(A, B))))))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[70])).
% 0.20/0.43 tff(72,plain,
% 0.20/0.43 (^[A: $i, B: $i] : rewrite((~((~(disjoint(A, B) | in(tptp_fun_C_4(B, A), set_intersection2(A, B)))) | (~(![C: $i] : (~in(C, set_intersection2(A, B))) | (~disjoint(A, B)))))) <=> (~((~(disjoint(A, B) | in(tptp_fun_C_4(B, A), set_intersection2(A, B)))) | (~(![C: $i] : (~in(C, set_intersection2(A, B))) | (~disjoint(A, B)))))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(73,plain,
% 0.20/0.43 (![A: $i, B: $i] : (~((~(disjoint(A, B) | in(tptp_fun_C_4(B, A), set_intersection2(A, B)))) | (~(![C: $i] : (~in(C, set_intersection2(A, B))) | (~disjoint(A, B)))))) <=> ![A: $i, B: $i] : (~((~(disjoint(A, B) | in(tptp_fun_C_4(B, A), set_intersection2(A, B)))) | (~(![C: $i] : (~in(C, set_intersection2(A, B))) | (~disjoint(A, B))))))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[72])).
% 0.20/0.43 tff(74,plain,
% 0.20/0.43 (![A: $i, B: $i] : (~((~(disjoint(A, B) | in(tptp_fun_C_4(B, A), set_intersection2(A, B)))) | (~(![C: $i] : (~in(C, set_intersection2(A, B))) | (~disjoint(A, B)))))) <=> ![A: $i, B: $i] : (~((~(disjoint(A, B) | in(tptp_fun_C_4(B, A), set_intersection2(A, B)))) | (~(![C: $i] : (~in(C, set_intersection2(A, B))) | (~disjoint(A, B))))))),
% 0.20/0.43 inference(transitivity,[status(thm)],[73, 71])).
% 0.20/0.43 tff(75,plain,
% 0.20/0.43 (^[A: $i, B: $i] : trans(monotonicity(rewrite((![C: $i] : (~in(C, set_intersection2(A, B))) | (~disjoint(A, B))) <=> (![C: $i] : (~in(C, set_intersection2(A, B))) | (~disjoint(A, B)))), (((disjoint(A, B) | in(tptp_fun_C_4(B, A), set_intersection2(A, B))) & (![C: $i] : (~in(C, set_intersection2(A, B))) | (~disjoint(A, B)))) <=> ((disjoint(A, B) | in(tptp_fun_C_4(B, A), set_intersection2(A, B))) & (![C: $i] : (~in(C, set_intersection2(A, B))) | (~disjoint(A, B)))))), rewrite(((disjoint(A, B) | in(tptp_fun_C_4(B, A), set_intersection2(A, B))) & (![C: $i] : (~in(C, set_intersection2(A, B))) | (~disjoint(A, B)))) <=> (~((~(disjoint(A, B) | in(tptp_fun_C_4(B, A), set_intersection2(A, B)))) | (~(![C: $i] : (~in(C, set_intersection2(A, B))) | (~disjoint(A, B))))))), (((disjoint(A, B) | in(tptp_fun_C_4(B, A), set_intersection2(A, B))) & (![C: $i] : (~in(C, set_intersection2(A, B))) | (~disjoint(A, B)))) <=> (~((~(disjoint(A, B) | in(tptp_fun_C_4(B, A), set_intersection2(A, B)))) | (~(![C: $i] : (~in(C, set_intersection2(A, B))) | (~disjoint(A, B))))))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(76,plain,
% 0.20/0.43 (![A: $i, B: $i] : ((disjoint(A, B) | in(tptp_fun_C_4(B, A), set_intersection2(A, B))) & (![C: $i] : (~in(C, set_intersection2(A, B))) | (~disjoint(A, B)))) <=> ![A: $i, B: $i] : (~((~(disjoint(A, B) | in(tptp_fun_C_4(B, A), set_intersection2(A, B)))) | (~(![C: $i] : (~in(C, set_intersection2(A, B))) | (~disjoint(A, B))))))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[75])).
% 0.20/0.43 tff(77,plain,
% 0.20/0.43 (^[A: $i, B: $i] : rewrite((((~(~disjoint(A, B))) | (~(~in(tptp_fun_C_4(B, A), set_intersection2(A, B))))) & (![C: $i] : (~in(C, set_intersection2(A, B))) | (~disjoint(A, B)))) <=> ((disjoint(A, B) | in(tptp_fun_C_4(B, A), set_intersection2(A, B))) & (![C: $i] : (~in(C, set_intersection2(A, B))) | (~disjoint(A, B)))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(78,plain,
% 0.20/0.43 (![A: $i, B: $i] : (((~(~disjoint(A, B))) | (~(~in(tptp_fun_C_4(B, A), set_intersection2(A, B))))) & (![C: $i] : (~in(C, set_intersection2(A, B))) | (~disjoint(A, B)))) <=> ![A: $i, B: $i] : ((disjoint(A, B) | in(tptp_fun_C_4(B, A), set_intersection2(A, B))) & (![C: $i] : (~in(C, set_intersection2(A, B))) | (~disjoint(A, B))))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[77])).
% 0.20/0.43 tff(79,plain,
% 0.20/0.43 (![A: $i, B: $i] : ((~((~disjoint(A, B)) & ![C: $i] : (~in(C, set_intersection2(A, B))))) & (~(?[C: $i] : in(C, set_intersection2(A, B)) & disjoint(A, B)))) <=> ![A: $i, B: $i] : ((~((~disjoint(A, B)) & ![C: $i] : (~in(C, set_intersection2(A, B))))) & (~(?[C: $i] : in(C, set_intersection2(A, B)) & disjoint(A, B))))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(80,axiom,(![A: $i, B: $i] : ((~((~disjoint(A, B)) & ![C: $i] : (~in(C, set_intersection2(A, B))))) & (~(?[C: $i] : in(C, set_intersection2(A, B)) & disjoint(A, B))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t4_xboole_0')).
% 0.20/0.43 tff(81,plain,
% 0.20/0.43 (![A: $i, B: $i] : ((~((~disjoint(A, B)) & ![C: $i] : (~in(C, set_intersection2(A, B))))) & (~(?[C: $i] : in(C, set_intersection2(A, B)) & disjoint(A, B))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[80, 79])).
% 0.20/0.43 tff(82,plain,(
% 0.20/0.43 ![A: $i, B: $i] : (((~(~disjoint(A, B))) | (~(~in(tptp_fun_C_4(B, A), set_intersection2(A, B))))) & (![C: $i] : (~in(C, set_intersection2(A, B))) | (~disjoint(A, B))))),
% 0.20/0.43 inference(skolemize,[status(sab)],[81])).
% 0.20/0.43 tff(83,plain,
% 0.20/0.43 (![A: $i, B: $i] : ((disjoint(A, B) | in(tptp_fun_C_4(B, A), set_intersection2(A, B))) & (![C: $i] : (~in(C, set_intersection2(A, B))) | (~disjoint(A, B))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[82, 78])).
% 0.20/0.43 tff(84,plain,
% 0.20/0.43 (![A: $i, B: $i] : (~((~(disjoint(A, B) | in(tptp_fun_C_4(B, A), set_intersection2(A, B)))) | (~(![C: $i] : (~in(C, set_intersection2(A, B))) | (~disjoint(A, B))))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[83, 76])).
% 0.20/0.43 tff(85,plain,
% 0.20/0.43 (![A: $i, B: $i] : (~((~(disjoint(A, B) | in(tptp_fun_C_4(B, A), set_intersection2(A, B)))) | (~(![C: $i] : (~in(C, set_intersection2(A, B))) | (~disjoint(A, B))))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[84, 74])).
% 0.20/0.43 tff(86,plain,
% 0.20/0.43 (![A: $i, B: $i] : (~((~(disjoint(A, B) | in(tptp_fun_C_4(B, A), set_intersection2(A, B)))) | (~((~disjoint(A, B)) | ![C: $i] : (~in(C, set_intersection2(A, B)))))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[85, 69])).
% 0.20/0.43 tff(87,plain,
% 0.20/0.43 ((~![A: $i, B: $i] : (~((~(disjoint(A, B) | in(tptp_fun_C_4(B, A), set_intersection2(A, B)))) | (~((~disjoint(A, B)) | ![C: $i] : (~in(C, set_intersection2(A, B)))))))) | (~((~(disjoint(B!6, unordered_pair(C!5, A!7)) | in(tptp_fun_C_4(unordered_pair(C!5, A!7), B!6), set_intersection2(B!6, unordered_pair(C!5, A!7))))) | (~((~disjoint(B!6, unordered_pair(C!5, A!7))) | ![C: $i] : (~in(C, set_intersection2(B!6, unordered_pair(C!5, A!7))))))))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(88,plain,
% 0.20/0.43 (~((~(disjoint(B!6, unordered_pair(C!5, A!7)) | in(tptp_fun_C_4(unordered_pair(C!5, A!7), B!6), set_intersection2(B!6, unordered_pair(C!5, A!7))))) | (~((~disjoint(B!6, unordered_pair(C!5, A!7))) | ![C: $i] : (~in(C, set_intersection2(B!6, unordered_pair(C!5, A!7)))))))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[87, 86])).
% 0.20/0.43 tff(89,plain,
% 0.20/0.43 (((~(disjoint(B!6, unordered_pair(C!5, A!7)) | in(tptp_fun_C_4(unordered_pair(C!5, A!7), B!6), set_intersection2(B!6, unordered_pair(C!5, A!7))))) | (~((~disjoint(B!6, unordered_pair(C!5, A!7))) | ![C: $i] : (~in(C, set_intersection2(B!6, unordered_pair(C!5, A!7))))))) | (disjoint(B!6, unordered_pair(C!5, A!7)) | in(tptp_fun_C_4(unordered_pair(C!5, A!7), B!6), set_intersection2(B!6, unordered_pair(C!5, A!7))))),
% 0.20/0.43 inference(tautology,[status(thm)],[])).
% 0.20/0.43 tff(90,plain,
% 0.20/0.43 (disjoint(B!6, unordered_pair(C!5, A!7)) | in(tptp_fun_C_4(unordered_pair(C!5, A!7), B!6), set_intersection2(B!6, unordered_pair(C!5, A!7)))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[89, 88])).
% 0.20/0.43 tff(91,plain,
% 0.20/0.43 (^[A: $i, B: $i] : refl((unordered_pair(A, B) = unordered_pair(B, A)) <=> (unordered_pair(A, B) = unordered_pair(B, A)))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(92,plain,
% 0.20/0.43 (![A: $i, B: $i] : (unordered_pair(A, B) = unordered_pair(B, A)) <=> ![A: $i, B: $i] : (unordered_pair(A, B) = unordered_pair(B, A))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[91])).
% 0.20/0.43 tff(93,plain,
% 0.20/0.43 (![A: $i, B: $i] : (unordered_pair(A, B) = unordered_pair(B, A)) <=> ![A: $i, B: $i] : (unordered_pair(A, B) = unordered_pair(B, A))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(94,axiom,(![A: $i, B: $i] : (unordered_pair(A, B) = unordered_pair(B, A))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','commutativity_k2_tarski')).
% 0.20/0.43 tff(95,plain,
% 0.20/0.43 (![A: $i, B: $i] : (unordered_pair(A, B) = unordered_pair(B, A))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[94, 93])).
% 0.20/0.43 tff(96,plain,(
% 0.20/0.43 ![A: $i, B: $i] : (unordered_pair(A, B) = unordered_pair(B, A))),
% 0.20/0.43 inference(skolemize,[status(sab)],[95])).
% 0.20/0.43 tff(97,plain,
% 0.20/0.43 (![A: $i, B: $i] : (unordered_pair(A, B) = unordered_pair(B, A))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[96, 92])).
% 0.20/0.43 tff(98,plain,
% 0.20/0.43 ((~![A: $i, B: $i] : (unordered_pair(A, B) = unordered_pair(B, A))) | (unordered_pair(A!7, C!5) = unordered_pair(C!5, A!7))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(99,plain,
% 0.20/0.43 (unordered_pair(A!7, C!5) = unordered_pair(C!5, A!7)),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[98, 97])).
% 0.20/0.44 tff(100,plain,
% 0.20/0.44 (unordered_pair(C!5, A!7) = unordered_pair(A!7, C!5)),
% 0.20/0.44 inference(symmetry,[status(thm)],[99])).
% 0.20/0.44 tff(101,plain,
% 0.20/0.44 (disjoint(B!6, unordered_pair(C!5, A!7)) <=> disjoint(B!6, unordered_pair(A!7, C!5))),
% 0.20/0.44 inference(monotonicity,[status(thm)],[100])).
% 0.20/0.44 tff(102,plain,
% 0.20/0.44 (disjoint(B!6, unordered_pair(A!7, C!5)) <=> disjoint(B!6, unordered_pair(C!5, A!7))),
% 0.20/0.44 inference(symmetry,[status(thm)],[101])).
% 0.20/0.44 tff(103,plain,
% 0.20/0.44 ((~disjoint(B!6, unordered_pair(A!7, C!5))) <=> (~disjoint(B!6, unordered_pair(C!5, A!7)))),
% 0.20/0.44 inference(monotonicity,[status(thm)],[102])).
% 0.20/0.44 tff(104,plain,
% 0.20/0.44 (~disjoint(unordered_pair(A!7, C!5), B!6)),
% 0.20/0.44 inference(and_elim,[status(thm)],[17])).
% 0.20/0.44 tff(105,plain,
% 0.20/0.44 (^[A: $i, B: $i] : refl(((~disjoint(A, B)) | disjoint(B, A)) <=> ((~disjoint(A, B)) | disjoint(B, A)))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(106,plain,
% 0.20/0.44 (![A: $i, B: $i] : ((~disjoint(A, B)) | disjoint(B, A)) <=> ![A: $i, B: $i] : ((~disjoint(A, B)) | disjoint(B, A))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[105])).
% 0.20/0.44 tff(107,plain,
% 0.20/0.44 (![A: $i, B: $i] : ((~disjoint(A, B)) | disjoint(B, A)) <=> ![A: $i, B: $i] : ((~disjoint(A, B)) | disjoint(B, A))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(108,plain,
% 0.20/0.44 (^[A: $i, B: $i] : rewrite((disjoint(A, B) => disjoint(B, A)) <=> ((~disjoint(A, B)) | disjoint(B, A)))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(109,plain,
% 0.20/0.44 (![A: $i, B: $i] : (disjoint(A, B) => disjoint(B, A)) <=> ![A: $i, B: $i] : ((~disjoint(A, B)) | disjoint(B, A))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[108])).
% 0.20/0.44 tff(110,axiom,(![A: $i, B: $i] : (disjoint(A, B) => disjoint(B, A))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','symmetry_r1_xboole_0')).
% 0.20/0.44 tff(111,plain,
% 0.20/0.44 (![A: $i, B: $i] : ((~disjoint(A, B)) | disjoint(B, A))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[110, 109])).
% 0.20/0.44 tff(112,plain,
% 0.20/0.44 (![A: $i, B: $i] : ((~disjoint(A, B)) | disjoint(B, A))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[111, 107])).
% 0.20/0.44 tff(113,plain,(
% 0.20/0.44 ![A: $i, B: $i] : ((~disjoint(A, B)) | disjoint(B, A))),
% 0.20/0.44 inference(skolemize,[status(sab)],[112])).
% 0.20/0.44 tff(114,plain,
% 0.20/0.44 (![A: $i, B: $i] : ((~disjoint(A, B)) | disjoint(B, A))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[113, 106])).
% 0.20/0.44 tff(115,plain,
% 0.20/0.44 (((~![A: $i, B: $i] : ((~disjoint(A, B)) | disjoint(B, A))) | ((~disjoint(B!6, unordered_pair(A!7, C!5))) | disjoint(unordered_pair(A!7, C!5), B!6))) <=> ((~![A: $i, B: $i] : ((~disjoint(A, B)) | disjoint(B, A))) | (~disjoint(B!6, unordered_pair(A!7, C!5))) | disjoint(unordered_pair(A!7, C!5), B!6))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(116,plain,
% 0.20/0.44 ((~![A: $i, B: $i] : ((~disjoint(A, B)) | disjoint(B, A))) | ((~disjoint(B!6, unordered_pair(A!7, C!5))) | disjoint(unordered_pair(A!7, C!5), B!6))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(117,plain,
% 0.20/0.44 ((~![A: $i, B: $i] : ((~disjoint(A, B)) | disjoint(B, A))) | (~disjoint(B!6, unordered_pair(A!7, C!5))) | disjoint(unordered_pair(A!7, C!5), B!6)),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[116, 115])).
% 0.20/0.44 tff(118,plain,
% 0.20/0.44 (~disjoint(B!6, unordered_pair(A!7, C!5))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[117, 114, 104])).
% 0.20/0.44 tff(119,plain,
% 0.20/0.44 (~disjoint(B!6, unordered_pair(C!5, A!7))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[118, 103])).
% 0.20/0.44 tff(120,plain,
% 0.20/0.44 ((~(disjoint(B!6, unordered_pair(C!5, A!7)) | in(tptp_fun_C_4(unordered_pair(C!5, A!7), B!6), set_intersection2(B!6, unordered_pair(C!5, A!7))))) | disjoint(B!6, unordered_pair(C!5, A!7)) | in(tptp_fun_C_4(unordered_pair(C!5, A!7), B!6), set_intersection2(B!6, unordered_pair(C!5, A!7)))),
% 0.20/0.44 inference(tautology,[status(thm)],[])).
% 0.20/0.44 tff(121,plain,
% 0.20/0.44 (in(tptp_fun_C_4(unordered_pair(C!5, A!7), B!6), set_intersection2(B!6, unordered_pair(C!5, A!7)))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[120, 119, 90])).
% 0.20/0.44 tff(122,plain,
% 0.20/0.44 ((~((~in(tptp_fun_C_4(unordered_pair(C!5, A!7), B!6), set_intersection2(B!6, unordered_pair(C!5, A!7)))) <=> ((~in(tptp_fun_C_4(unordered_pair(C!5, A!7), B!6), B!6)) | (~in(tptp_fun_C_4(unordered_pair(C!5, A!7), B!6), unordered_pair(C!5, A!7)))))) | (~in(tptp_fun_C_4(unordered_pair(C!5, A!7), B!6), set_intersection2(B!6, unordered_pair(C!5, A!7)))) | (~((~in(tptp_fun_C_4(unordered_pair(C!5, A!7), B!6), B!6)) | (~in(tptp_fun_C_4(unordered_pair(C!5, A!7), B!6), unordered_pair(C!5, A!7)))))),
% 0.20/0.44 inference(tautology,[status(thm)],[])).
% 0.20/0.44 tff(123,plain,
% 0.20/0.44 ((~((~in(tptp_fun_C_4(unordered_pair(C!5, A!7), B!6), set_intersection2(B!6, unordered_pair(C!5, A!7)))) <=> ((~in(tptp_fun_C_4(unordered_pair(C!5, A!7), B!6), B!6)) | (~in(tptp_fun_C_4(unordered_pair(C!5, A!7), B!6), unordered_pair(C!5, A!7)))))) | (~((~in(tptp_fun_C_4(unordered_pair(C!5, A!7), B!6), B!6)) | (~in(tptp_fun_C_4(unordered_pair(C!5, A!7), B!6), unordered_pair(C!5, A!7)))))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[122, 121])).
% 0.20/0.44 tff(124,plain,
% 0.20/0.44 (~((~in(tptp_fun_C_4(unordered_pair(C!5, A!7), B!6), B!6)) | (~in(tptp_fun_C_4(unordered_pair(C!5, A!7), B!6), unordered_pair(C!5, A!7))))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[123, 67])).
% 0.20/0.44 tff(125,plain,
% 0.20/0.44 (((~in(tptp_fun_C_4(unordered_pair(C!5, A!7), B!6), B!6)) | (~in(tptp_fun_C_4(unordered_pair(C!5, A!7), B!6), unordered_pair(C!5, A!7)))) | in(tptp_fun_C_4(unordered_pair(C!5, A!7), B!6), B!6)),
% 0.20/0.44 inference(tautology,[status(thm)],[])).
% 0.20/0.44 tff(126,plain,
% 0.20/0.44 (in(tptp_fun_C_4(unordered_pair(C!5, A!7), B!6), B!6)),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[125, 124])).
% 0.20/0.44 tff(127,plain,
% 0.20/0.44 ($false),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[126, 19])).
% 0.20/0.44 tff(128,plain,(~(tptp_fun_C_4(unordered_pair(C!5, A!7), B!6) = C!5)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.44 tff(129,plain,
% 0.20/0.44 (^[A: $i, B: $i, C: $i, D: $i] : refl((~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A))))))) <=> (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A))))))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(130,plain,
% 0.20/0.44 (![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A)))))))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[129])).
% 0.20/0.44 tff(131,plain,
% 0.20/0.44 (![A: $i, B: $i, C: $i] : ![D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A)))))))),
% 0.20/0.44 inference(pull_quant,[status(thm)],[])).
% 0.20/0.44 tff(132,plain,
% 0.20/0.44 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(pull_quant(((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A)))) <=> ![D: $i] : ((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))), ((~((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))) <=> (~![D: $i] : ((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))))), pull_quant((~![D: $i] : ((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) <=> ?[D: $i] : (~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A)))))), ((~((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))) <=> ?[D: $i] : (~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))))), (((~((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A)))))) <=> (?[D: $i] : (~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A)))))))), pull_quant((?[D: $i] : (~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A)))))) <=> ?[D: $i] : ((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A))))))), (((~((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A)))))) <=> ?[D: $i] : ((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A)))))))), ((~((~((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A))))))) <=> (~?[D: $i] : ((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A))))))))), pull_quant((~?[D: $i] : ((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A))))))) <=> ![D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A)))))))), ((~((~((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A))))))) <=> ![D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A)))))))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(133,plain,
% 0.20/0.44 (![A: $i, B: $i, C: $i] : (~((~((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A))))))) <=> ![A: $i, B: $i, C: $i] : ![D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A)))))))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[132])).
% 0.20/0.44 tff(134,plain,
% 0.20/0.44 (![A: $i, B: $i, C: $i] : (~((~((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A)))))))),
% 0.20/0.44 inference(transitivity,[status(thm)],[133, 131])).
% 0.20/0.44 tff(135,plain,
% 0.20/0.44 (![A: $i, B: $i, C: $i] : (~((~((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A)))))))),
% 0.20/0.44 inference(transitivity,[status(thm)],[134, 130])).
% 0.20/0.44 tff(136,plain,
% 0.20/0.44 (^[A: $i, B: $i, C: $i] : rewrite((~((~((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A))))))) <=> (~((~((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A))))))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(137,plain,
% 0.20/0.44 (![A: $i, B: $i, C: $i] : (~((~((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A))))))) <=> ![A: $i, B: $i, C: $i] : (~((~((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A)))))))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[136])).
% 0.20/0.44 tff(138,plain,
% 0.20/0.44 (![A: $i, B: $i, C: $i] : (~((~((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A)))))))),
% 0.20/0.44 inference(transitivity,[status(thm)],[137, 135])).
% 0.20/0.44 tff(139,plain,
% 0.20/0.44 (^[A: $i, B: $i, C: $i] : trans(monotonicity(rewrite(((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A)))) <=> ((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))), ((((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A)))) & ((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A))))) <=> (((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A)))) & ((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A))))))), rewrite((((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A)))) & ((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A))))) <=> (~((~((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A)))))))), ((((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A)))) & ((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A))))) <=> (~((~((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A)))))))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(140,plain,
% 0.20/0.44 (![A: $i, B: $i, C: $i] : (((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A)))) & ((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A))))) <=> ![A: $i, B: $i, C: $i] : (~((~((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A)))))))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[139])).
% 0.20/0.44 tff(141,plain,
% 0.20/0.44 (^[A: $i, B: $i, C: $i] : rewrite((((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A)))) & ((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A)))))) <=> (((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A)))) & ((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A))))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(142,plain,
% 0.20/0.44 (![A: $i, B: $i, C: $i] : (((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A)))) & ((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A)))))) <=> ![A: $i, B: $i, C: $i] : (((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A)))) & ((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A)))))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[141])).
% 0.20/0.44 tff(143,plain,
% 0.20/0.44 (![A: $i, B: $i, C: $i] : ((C = unordered_pair(A, B)) <=> ![D: $i] : (in(D, C) <=> ((D = B) | (D = A)))) <=> ![A: $i, B: $i, C: $i] : ((C = unordered_pair(A, B)) <=> ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(144,plain,
% 0.20/0.44 (^[A: $i, B: $i, C: $i] : rewrite(((C = unordered_pair(A, B)) <=> ![D: $i] : (in(D, C) <=> ((D = A) | (D = B)))) <=> ((C = unordered_pair(A, B)) <=> ![D: $i] : (in(D, C) <=> ((D = B) | (D = A)))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(145,plain,
% 0.20/0.44 (![A: $i, B: $i, C: $i] : ((C = unordered_pair(A, B)) <=> ![D: $i] : (in(D, C) <=> ((D = A) | (D = B)))) <=> ![A: $i, B: $i, C: $i] : ((C = unordered_pair(A, B)) <=> ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[144])).
% 0.20/0.44 tff(146,axiom,(![A: $i, B: $i, C: $i] : ((C = unordered_pair(A, B)) <=> ![D: $i] : (in(D, C) <=> ((D = A) | (D = B))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d2_tarski')).
% 0.20/0.44 tff(147,plain,
% 0.20/0.44 (![A: $i, B: $i, C: $i] : ((C = unordered_pair(A, B)) <=> ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[146, 145])).
% 0.20/0.44 tff(148,plain,
% 0.20/0.44 (![A: $i, B: $i, C: $i] : ((C = unordered_pair(A, B)) <=> ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[147, 143])).
% 0.20/0.44 tff(149,plain,(
% 0.20/0.44 ![A: $i, B: $i, C: $i] : (((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A)))) & ((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A))))))),
% 0.20/0.44 inference(skolemize,[status(sab)],[148])).
% 0.20/0.44 tff(150,plain,
% 0.20/0.44 (![A: $i, B: $i, C: $i] : (((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A)))) & ((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A)))))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[149, 142])).
% 0.20/0.44 tff(151,plain,
% 0.20/0.44 (![A: $i, B: $i, C: $i] : (~((~((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A)))))))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[150, 140])).
% 0.20/0.44 tff(152,plain,
% 0.20/0.44 (![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A)))))))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[151, 138])).
% 0.20/0.44 tff(153,plain,
% 0.20/0.44 ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A)))))))) | (~((~((~(unordered_pair(C!5, A!7) = unordered_pair(A!7, C!5))) | (in(tptp_fun_C_4(unordered_pair(C!5, A!7), B!6), unordered_pair(C!5, A!7)) <=> ((tptp_fun_C_4(unordered_pair(C!5, A!7), B!6) = C!5) | (tptp_fun_C_4(unordered_pair(C!5, A!7), B!6) = A!7))))) | (~((unordered_pair(C!5, A!7) = unordered_pair(A!7, C!5)) | ((~in(tptp_fun_D_0(unordered_pair(C!5, A!7), C!5, A!7), unordered_pair(C!5, A!7))) <=> ((tptp_fun_D_0(unordered_pair(C!5, A!7), C!5, A!7) = C!5) | (tptp_fun_D_0(unordered_pair(C!5, A!7), C!5, A!7) = A!7)))))))),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(154,plain,
% 0.20/0.45 (~((~((~(unordered_pair(C!5, A!7) = unordered_pair(A!7, C!5))) | (in(tptp_fun_C_4(unordered_pair(C!5, A!7), B!6), unordered_pair(C!5, A!7)) <=> ((tptp_fun_C_4(unordered_pair(C!5, A!7), B!6) = C!5) | (tptp_fun_C_4(unordered_pair(C!5, A!7), B!6) = A!7))))) | (~((unordered_pair(C!5, A!7) = unordered_pair(A!7, C!5)) | ((~in(tptp_fun_D_0(unordered_pair(C!5, A!7), C!5, A!7), unordered_pair(C!5, A!7))) <=> ((tptp_fun_D_0(unordered_pair(C!5, A!7), C!5, A!7) = C!5) | (tptp_fun_D_0(unordered_pair(C!5, A!7), C!5, A!7) = A!7))))))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[153, 152])).
% 0.20/0.45 tff(155,plain,
% 0.20/0.45 (((~((~(unordered_pair(C!5, A!7) = unordered_pair(A!7, C!5))) | (in(tptp_fun_C_4(unordered_pair(C!5, A!7), B!6), unordered_pair(C!5, A!7)) <=> ((tptp_fun_C_4(unordered_pair(C!5, A!7), B!6) = C!5) | (tptp_fun_C_4(unordered_pair(C!5, A!7), B!6) = A!7))))) | (~((unordered_pair(C!5, A!7) = unordered_pair(A!7, C!5)) | ((~in(tptp_fun_D_0(unordered_pair(C!5, A!7), C!5, A!7), unordered_pair(C!5, A!7))) <=> ((tptp_fun_D_0(unordered_pair(C!5, A!7), C!5, A!7) = C!5) | (tptp_fun_D_0(unordered_pair(C!5, A!7), C!5, A!7) = A!7)))))) | ((~(unordered_pair(C!5, A!7) = unordered_pair(A!7, C!5))) | (in(tptp_fun_C_4(unordered_pair(C!5, A!7), B!6), unordered_pair(C!5, A!7)) <=> ((tptp_fun_C_4(unordered_pair(C!5, A!7), B!6) = C!5) | (tptp_fun_C_4(unordered_pair(C!5, A!7), B!6) = A!7))))),
% 0.20/0.45 inference(tautology,[status(thm)],[])).
% 0.20/0.45 tff(156,plain,
% 0.20/0.45 ((~(unordered_pair(C!5, A!7) = unordered_pair(A!7, C!5))) | (in(tptp_fun_C_4(unordered_pair(C!5, A!7), B!6), unordered_pair(C!5, A!7)) <=> ((tptp_fun_C_4(unordered_pair(C!5, A!7), B!6) = C!5) | (tptp_fun_C_4(unordered_pair(C!5, A!7), B!6) = A!7)))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[155, 154])).
% 0.20/0.45 tff(157,plain,
% 0.20/0.45 ((~![A: $i, B: $i] : (unordered_pair(A, B) = unordered_pair(B, A))) | (unordered_pair(C!5, A!7) = unordered_pair(A!7, C!5))),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(158,plain,
% 0.20/0.45 (unordered_pair(C!5, A!7) = unordered_pair(A!7, C!5)),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[157, 97])).
% 0.20/0.45 tff(159,plain,
% 0.20/0.45 ((~((~(unordered_pair(C!5, A!7) = unordered_pair(A!7, C!5))) | (in(tptp_fun_C_4(unordered_pair(C!5, A!7), B!6), unordered_pair(C!5, A!7)) <=> ((tptp_fun_C_4(unordered_pair(C!5, A!7), B!6) = C!5) | (tptp_fun_C_4(unordered_pair(C!5, A!7), B!6) = A!7))))) | (~(unordered_pair(C!5, A!7) = unordered_pair(A!7, C!5))) | (in(tptp_fun_C_4(unordered_pair(C!5, A!7), B!6), unordered_pair(C!5, A!7)) <=> ((tptp_fun_C_4(unordered_pair(C!5, A!7), B!6) = C!5) | (tptp_fun_C_4(unordered_pair(C!5, A!7), B!6) = A!7)))),
% 0.20/0.45 inference(tautology,[status(thm)],[])).
% 0.20/0.45 tff(160,plain,
% 0.20/0.45 ((~((~(unordered_pair(C!5, A!7) = unordered_pair(A!7, C!5))) | (in(tptp_fun_C_4(unordered_pair(C!5, A!7), B!6), unordered_pair(C!5, A!7)) <=> ((tptp_fun_C_4(unordered_pair(C!5, A!7), B!6) = C!5) | (tptp_fun_C_4(unordered_pair(C!5, A!7), B!6) = A!7))))) | (in(tptp_fun_C_4(unordered_pair(C!5, A!7), B!6), unordered_pair(C!5, A!7)) <=> ((tptp_fun_C_4(unordered_pair(C!5, A!7), B!6) = C!5) | (tptp_fun_C_4(unordered_pair(C!5, A!7), B!6) = A!7)))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[159, 158])).
% 0.20/0.45 tff(161,plain,
% 0.20/0.45 (in(tptp_fun_C_4(unordered_pair(C!5, A!7), B!6), unordered_pair(C!5, A!7)) <=> ((tptp_fun_C_4(unordered_pair(C!5, A!7), B!6) = C!5) | (tptp_fun_C_4(unordered_pair(C!5, A!7), B!6) = A!7))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[160, 156])).
% 0.20/0.45 tff(162,plain,
% 0.20/0.45 (((~in(tptp_fun_C_4(unordered_pair(C!5, A!7), B!6), B!6)) | (~in(tptp_fun_C_4(unordered_pair(C!5, A!7), B!6), unordered_pair(C!5, A!7)))) | in(tptp_fun_C_4(unordered_pair(C!5, A!7), B!6), unordered_pair(C!5, A!7))),
% 0.20/0.45 inference(tautology,[status(thm)],[])).
% 0.20/0.45 tff(163,plain,
% 0.20/0.45 (in(tptp_fun_C_4(unordered_pair(C!5, A!7), B!6), unordered_pair(C!5, A!7))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[162, 124])).
% 0.20/0.45 tff(164,plain,
% 0.20/0.45 ((~(in(tptp_fun_C_4(unordered_pair(C!5, A!7), B!6), unordered_pair(C!5, A!7)) <=> ((tptp_fun_C_4(unordered_pair(C!5, A!7), B!6) = C!5) | (tptp_fun_C_4(unordered_pair(C!5, A!7), B!6) = A!7)))) | (~in(tptp_fun_C_4(unordered_pair(C!5, A!7), B!6), unordered_pair(C!5, A!7))) | ((tptp_fun_C_4(unordered_pair(C!5, A!7), B!6) = C!5) | (tptp_fun_C_4(unordered_pair(C!5, A!7), B!6) = A!7))),
% 0.20/0.45 inference(tautology,[status(thm)],[])).
% 0.20/0.45 tff(165,plain,
% 0.20/0.45 ((~(in(tptp_fun_C_4(unordered_pair(C!5, A!7), B!6), unordered_pair(C!5, A!7)) <=> ((tptp_fun_C_4(unordered_pair(C!5, A!7), B!6) = C!5) | (tptp_fun_C_4(unordered_pair(C!5, A!7), B!6) = A!7)))) | ((tptp_fun_C_4(unordered_pair(C!5, A!7), B!6) = C!5) | (tptp_fun_C_4(unordered_pair(C!5, A!7), B!6) = A!7))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[164, 163])).
% 0.20/0.45 tff(166,plain,
% 0.20/0.45 ((tptp_fun_C_4(unordered_pair(C!5, A!7), B!6) = C!5) | (tptp_fun_C_4(unordered_pair(C!5, A!7), B!6) = A!7)),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[165, 161])).
% 0.20/0.45 tff(167,plain,
% 0.20/0.45 ((~((tptp_fun_C_4(unordered_pair(C!5, A!7), B!6) = C!5) | (tptp_fun_C_4(unordered_pair(C!5, A!7), B!6) = A!7))) | (tptp_fun_C_4(unordered_pair(C!5, A!7), B!6) = C!5) | (tptp_fun_C_4(unordered_pair(C!5, A!7), B!6) = A!7)),
% 0.20/0.45 inference(tautology,[status(thm)],[])).
% 0.20/0.45 tff(168,plain,
% 0.20/0.45 ((tptp_fun_C_4(unordered_pair(C!5, A!7), B!6) = C!5) | (tptp_fun_C_4(unordered_pair(C!5, A!7), B!6) = A!7)),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[167, 166])).
% 0.20/0.45 tff(169,plain,
% 0.20/0.45 (tptp_fun_C_4(unordered_pair(C!5, A!7), B!6) = A!7),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[168, 128])).
% 0.20/0.45 tff(170,plain,
% 0.20/0.45 (in(tptp_fun_C_4(unordered_pair(C!5, A!7), B!6), B!6) <=> in(A!7, B!6)),
% 0.20/0.45 inference(monotonicity,[status(thm)],[169])).
% 0.20/0.45 tff(171,plain,
% 0.20/0.45 (in(A!7, B!6) <=> in(tptp_fun_C_4(unordered_pair(C!5, A!7), B!6), B!6)),
% 0.20/0.45 inference(symmetry,[status(thm)],[170])).
% 0.20/0.45 tff(172,plain,
% 0.20/0.45 ((~in(A!7, B!6)) <=> (~in(tptp_fun_C_4(unordered_pair(C!5, A!7), B!6), B!6))),
% 0.20/0.45 inference(monotonicity,[status(thm)],[171])).
% 0.20/0.45 tff(173,plain,
% 0.20/0.45 (~in(A!7, B!6)),
% 0.20/0.45 inference(and_elim,[status(thm)],[17])).
% 0.20/0.45 tff(174,plain,
% 0.20/0.45 (~in(tptp_fun_C_4(unordered_pair(C!5, A!7), B!6), B!6)),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[173, 172])).
% 0.20/0.45 tff(175,plain,
% 0.20/0.45 ($false),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[126, 174])).
% 0.20/0.45 % SZS output end Proof
%------------------------------------------------------------------------------