TSTP Solution File: SET920+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SET920+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n028.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 05:08:38 EDT 2022
% Result : Theorem 0.15s 0.37s
% Output : Proof 0.15s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.10 % Problem : SET920+1 : TPTP v8.1.0. Released v3.2.0.
% 0.05/0.10 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.10/0.30 % Computer : n028.cluster.edu
% 0.10/0.30 % Model : x86_64 x86_64
% 0.10/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.30 % Memory : 8042.1875MB
% 0.10/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.30 % CPULimit : 300
% 0.10/0.30 % WCLimit : 300
% 0.10/0.30 % DateTime : Sat Sep 3 08:42:38 EDT 2022
% 0.10/0.31 % CPUTime :
% 0.10/0.31 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.10/0.31 Usage: tptp [options] [-file:]file
% 0.10/0.31 -h, -? prints this message.
% 0.10/0.31 -smt2 print SMT-LIB2 benchmark.
% 0.10/0.31 -m, -model generate model.
% 0.10/0.31 -p, -proof generate proof.
% 0.10/0.31 -c, -core generate unsat core of named formulas.
% 0.10/0.31 -st, -statistics display statistics.
% 0.10/0.31 -t:timeout set timeout (in second).
% 0.10/0.31 -smt2status display status in smt2 format instead of SZS.
% 0.10/0.31 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.10/0.31 -<param>:<value> configuration parameter and value.
% 0.10/0.31 -o:<output-file> file to place output in.
% 0.15/0.37 % SZS status Theorem
% 0.15/0.37 % SZS output start Proof
% 0.15/0.37 tff(in_type, type, (
% 0.15/0.37 in: ( $i * $i ) > $o)).
% 0.15/0.37 tff(tptp_fun_C_4_type, type, (
% 0.15/0.37 tptp_fun_C_4: $i)).
% 0.15/0.37 tff(tptp_fun_D_1_type, type, (
% 0.15/0.37 tptp_fun_D_1: ( $i * $i * $i ) > $i)).
% 0.15/0.37 tff(unordered_pair_type, type, (
% 0.15/0.37 unordered_pair: ( $i * $i ) > $i)).
% 0.15/0.37 tff(tptp_fun_B_5_type, type, (
% 0.15/0.37 tptp_fun_B_5: $i)).
% 0.15/0.37 tff(tptp_fun_A_6_type, type, (
% 0.15/0.37 tptp_fun_A_6: $i)).
% 0.15/0.37 tff(set_intersection2_type, type, (
% 0.15/0.37 set_intersection2: ( $i * $i ) > $i)).
% 0.15/0.37 tff(tptp_fun_D_0_type, type, (
% 0.15/0.37 tptp_fun_D_0: ( $i * $i * $i ) > $i)).
% 0.15/0.37 tff(1,plain,
% 0.15/0.37 ((~![A: $i, B: $i, C: $i] : ((~(set_intersection2(unordered_pair(A, B), C) = unordered_pair(A, B))) | in(A, C))) <=> (~![A: $i, B: $i, C: $i] : ((~(set_intersection2(unordered_pair(A, B), C) = unordered_pair(A, B))) | in(A, C)))),
% 0.15/0.37 inference(rewrite,[status(thm)],[])).
% 0.15/0.37 tff(2,plain,
% 0.15/0.37 ((~![A: $i, B: $i, C: $i] : ((set_intersection2(unordered_pair(A, B), C) = unordered_pair(A, B)) => in(A, C))) <=> (~![A: $i, B: $i, C: $i] : ((~(set_intersection2(unordered_pair(A, B), C) = unordered_pair(A, B))) | in(A, C)))),
% 0.15/0.37 inference(rewrite,[status(thm)],[])).
% 0.15/0.37 tff(3,axiom,(~![A: $i, B: $i, C: $i] : ((set_intersection2(unordered_pair(A, B), C) = unordered_pair(A, B)) => in(A, C))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t63_zfmisc_1')).
% 0.15/0.37 tff(4,plain,
% 0.15/0.37 (~![A: $i, B: $i, C: $i] : ((~(set_intersection2(unordered_pair(A, B), C) = unordered_pair(A, B))) | in(A, C))),
% 0.15/0.37 inference(modus_ponens,[status(thm)],[3, 2])).
% 0.15/0.37 tff(5,plain,
% 0.15/0.37 (~![A: $i, B: $i, C: $i] : ((~(set_intersection2(unordered_pair(A, B), C) = unordered_pair(A, B))) | in(A, C))),
% 0.15/0.37 inference(modus_ponens,[status(thm)],[4, 1])).
% 0.15/0.37 tff(6,plain,
% 0.15/0.37 (~![A: $i, B: $i, C: $i] : ((~(set_intersection2(unordered_pair(A, B), C) = unordered_pair(A, B))) | in(A, C))),
% 0.15/0.37 inference(modus_ponens,[status(thm)],[5, 1])).
% 0.15/0.37 tff(7,plain,
% 0.15/0.37 (~![A: $i, B: $i, C: $i] : ((~(set_intersection2(unordered_pair(A, B), C) = unordered_pair(A, B))) | in(A, C))),
% 0.15/0.37 inference(modus_ponens,[status(thm)],[6, 1])).
% 0.15/0.37 tff(8,plain,
% 0.15/0.37 (~![A: $i, B: $i, C: $i] : ((~(set_intersection2(unordered_pair(A, B), C) = unordered_pair(A, B))) | in(A, C))),
% 0.15/0.37 inference(modus_ponens,[status(thm)],[7, 1])).
% 0.15/0.37 tff(9,plain,
% 0.15/0.37 (~![A: $i, B: $i, C: $i] : ((~(set_intersection2(unordered_pair(A, B), C) = unordered_pair(A, B))) | in(A, C))),
% 0.15/0.37 inference(modus_ponens,[status(thm)],[8, 1])).
% 0.15/0.37 tff(10,plain,
% 0.15/0.37 (~![A: $i, B: $i, C: $i] : ((~(set_intersection2(unordered_pair(A, B), C) = unordered_pair(A, B))) | in(A, C))),
% 0.15/0.37 inference(modus_ponens,[status(thm)],[9, 1])).
% 0.15/0.37 tff(11,plain,(
% 0.15/0.37 ~((~(set_intersection2(unordered_pair(A!6, B!5), C!4) = unordered_pair(A!6, B!5))) | in(A!6, C!4))),
% 0.15/0.37 inference(skolemize,[status(sab)],[10])).
% 0.15/0.37 tff(12,plain,
% 0.15/0.37 (~in(A!6, C!4)),
% 0.15/0.37 inference(or_elim,[status(thm)],[11])).
% 0.15/0.37 tff(13,plain,
% 0.15/0.37 (((~in(A!6, C!4)) | (~in(A!6, unordered_pair(A!6, B!5)))) | in(A!6, C!4)),
% 0.15/0.37 inference(tautology,[status(thm)],[])).
% 0.15/0.37 tff(14,plain,
% 0.15/0.37 ((~in(A!6, C!4)) | (~in(A!6, unordered_pair(A!6, B!5)))),
% 0.15/0.37 inference(unit_resolution,[status(thm)],[13, 12])).
% 0.15/0.37 tff(15,assumption,(~in(A!6, unordered_pair(A!6, B!5))), introduced(assumption)).
% 0.15/0.37 tff(16,plain,
% 0.15/0.37 (^[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))))))))),
% 0.15/0.37 inference(bind,[status(th)],[])).
% 0.15/0.37 tff(17,plain,
% 0.15/0.37 (![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)))))))),
% 0.15/0.37 inference(quant_intro,[status(thm)],[16])).
% 0.15/0.37 tff(18,plain,
% 0.15/0.37 (![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)))))))),
% 0.15/0.37 inference(pull_quant,[status(thm)],[])).
% 0.15/0.37 tff(19,plain,
% 0.15/0.37 (^[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)))))))))),
% 0.15/0.37 inference(bind,[status(th)],[])).
% 0.15/0.37 tff(20,plain,
% 0.15/0.37 (![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)))))))),
% 0.15/0.37 inference(quant_intro,[status(thm)],[19])).
% 0.15/0.37 tff(21,plain,
% 0.15/0.37 (![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)))))))),
% 0.15/0.37 inference(transitivity,[status(thm)],[20, 18])).
% 0.15/0.37 tff(22,plain,
% 0.15/0.37 (![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)))))))),
% 0.15/0.37 inference(transitivity,[status(thm)],[21, 17])).
% 0.15/0.37 tff(23,plain,
% 0.15/0.37 (^[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))))))))),
% 0.15/0.37 inference(bind,[status(th)],[])).
% 0.15/0.37 tff(24,plain,
% 0.15/0.37 (![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)))))))),
% 0.15/0.37 inference(quant_intro,[status(thm)],[23])).
% 0.15/0.37 tff(25,plain,
% 0.15/0.37 (![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)))))))),
% 0.15/0.37 inference(transitivity,[status(thm)],[24, 22])).
% 0.15/0.37 tff(26,plain,
% 0.15/0.37 (^[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)))))))))),
% 0.15/0.37 inference(bind,[status(th)],[])).
% 0.15/0.37 tff(27,plain,
% 0.15/0.37 (![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)))))))),
% 0.15/0.37 inference(quant_intro,[status(thm)],[26])).
% 0.15/0.37 tff(28,plain,
% 0.15/0.37 (^[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))))))),
% 0.15/0.37 inference(bind,[status(th)],[])).
% 0.15/0.37 tff(29,plain,
% 0.15/0.37 (![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)))))),
% 0.15/0.37 inference(quant_intro,[status(thm)],[28])).
% 0.15/0.37 tff(30,plain,
% 0.15/0.37 (![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))))),
% 0.15/0.37 inference(rewrite,[status(thm)],[])).
% 0.15/0.37 tff(31,plain,
% 0.15/0.37 (^[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)))))),
% 0.15/0.37 inference(bind,[status(th)],[])).
% 0.15/0.37 tff(32,plain,
% 0.15/0.37 (![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))))),
% 0.15/0.37 inference(quant_intro,[status(thm)],[31])).
% 0.15/0.37 tff(33,axiom,(![A: $i, B: $i, C: $i] : ((C = unordered_pair(A, B)) <=> ![D: $i] : (in(D, C) <=> ((D = A) | (D = B))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d2_tarski')).
% 0.15/0.37 tff(34,plain,
% 0.15/0.37 (![A: $i, B: $i, C: $i] : ((C = unordered_pair(A, B)) <=> ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))),
% 0.15/0.37 inference(modus_ponens,[status(thm)],[33, 32])).
% 0.15/0.37 tff(35,plain,
% 0.15/0.37 (![A: $i, B: $i, C: $i] : ((C = unordered_pair(A, B)) <=> ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))),
% 0.15/0.37 inference(modus_ponens,[status(thm)],[34, 30])).
% 0.15/0.37 tff(36,plain,(
% 0.15/0.37 ![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))))))),
% 0.15/0.37 inference(skolemize,[status(sab)],[35])).
% 0.15/0.37 tff(37,plain,
% 0.15/0.37 (![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)))))),
% 0.15/0.37 inference(modus_ponens,[status(thm)],[36, 29])).
% 0.15/0.37 tff(38,plain,
% 0.15/0.37 (![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)))))))),
% 0.15/0.37 inference(modus_ponens,[status(thm)],[37, 27])).
% 0.15/0.37 tff(39,plain,
% 0.15/0.37 (![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)))))))),
% 0.15/0.37 inference(modus_ponens,[status(thm)],[38, 25])).
% 0.15/0.37 tff(40,plain,
% 0.15/0.37 (((~![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)))))))) | in(A!6, unordered_pair(A!6, B!5))) <=> ((~![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)))))))) | in(A!6, unordered_pair(A!6, B!5)))),
% 0.15/0.37 inference(rewrite,[status(thm)],[])).
% 0.15/0.37 tff(41,plain,
% 0.15/0.37 ((~(~in(A!6, unordered_pair(A!6, B!5)))) <=> in(A!6, unordered_pair(A!6, B!5))),
% 0.15/0.37 inference(rewrite,[status(thm)],[])).
% 0.15/0.37 tff(42,plain,
% 0.15/0.37 (((~in(A!6, unordered_pair(A!6, B!5))) | $false) <=> (~in(A!6, unordered_pair(A!6, B!5)))),
% 0.15/0.37 inference(rewrite,[status(thm)],[])).
% 0.15/0.37 tff(43,plain,
% 0.15/0.37 ((~$true) <=> $false),
% 0.15/0.37 inference(rewrite,[status(thm)],[])).
% 0.15/0.37 tff(44,plain,
% 0.15/0.37 (($true | ((~in(tptp_fun_D_0(unordered_pair(A!6, B!5), B!5, A!6), unordered_pair(A!6, B!5))) <=> ((tptp_fun_D_0(unordered_pair(A!6, B!5), B!5, A!6) = B!5) | (tptp_fun_D_0(unordered_pair(A!6, B!5), B!5, A!6) = A!6)))) <=> $true),
% 0.15/0.37 inference(rewrite,[status(thm)],[])).
% 0.15/0.37 tff(45,plain,
% 0.15/0.37 (((~in(tptp_fun_D_0(unordered_pair(A!6, B!5), B!5, A!6), unordered_pair(A!6, B!5))) <=> ((tptp_fun_D_0(unordered_pair(A!6, B!5), B!5, A!6) = B!5) | (tptp_fun_D_0(unordered_pair(A!6, B!5), B!5, A!6) = A!6))) <=> ((~in(tptp_fun_D_0(unordered_pair(A!6, B!5), B!5, A!6), unordered_pair(A!6, B!5))) <=> ((tptp_fun_D_0(unordered_pair(A!6, B!5), B!5, A!6) = B!5) | (tptp_fun_D_0(unordered_pair(A!6, B!5), B!5, A!6) = A!6)))),
% 0.15/0.37 inference(rewrite,[status(thm)],[])).
% 0.15/0.37 tff(46,plain,
% 0.15/0.37 ((unordered_pair(A!6, B!5) = unordered_pair(A!6, B!5)) <=> $true),
% 0.15/0.37 inference(rewrite,[status(thm)],[])).
% 0.15/0.37 tff(47,plain,
% 0.15/0.37 (((unordered_pair(A!6, B!5) = unordered_pair(A!6, B!5)) | ((~in(tptp_fun_D_0(unordered_pair(A!6, B!5), B!5, A!6), unordered_pair(A!6, B!5))) <=> ((tptp_fun_D_0(unordered_pair(A!6, B!5), B!5, A!6) = B!5) | (tptp_fun_D_0(unordered_pair(A!6, B!5), B!5, A!6) = A!6)))) <=> ($true | ((~in(tptp_fun_D_0(unordered_pair(A!6, B!5), B!5, A!6), unordered_pair(A!6, B!5))) <=> ((tptp_fun_D_0(unordered_pair(A!6, B!5), B!5, A!6) = B!5) | (tptp_fun_D_0(unordered_pair(A!6, B!5), B!5, A!6) = A!6))))),
% 0.15/0.37 inference(monotonicity,[status(thm)],[46, 45])).
% 0.15/0.37 tff(48,plain,
% 0.15/0.37 (((unordered_pair(A!6, B!5) = unordered_pair(A!6, B!5)) | ((~in(tptp_fun_D_0(unordered_pair(A!6, B!5), B!5, A!6), unordered_pair(A!6, B!5))) <=> ((tptp_fun_D_0(unordered_pair(A!6, B!5), B!5, A!6) = B!5) | (tptp_fun_D_0(unordered_pair(A!6, B!5), B!5, A!6) = A!6)))) <=> $true),
% 0.15/0.37 inference(transitivity,[status(thm)],[47, 44])).
% 0.15/0.37 tff(49,plain,
% 0.15/0.37 ((~((unordered_pair(A!6, B!5) = unordered_pair(A!6, B!5)) | ((~in(tptp_fun_D_0(unordered_pair(A!6, B!5), B!5, A!6), unordered_pair(A!6, B!5))) <=> ((tptp_fun_D_0(unordered_pair(A!6, B!5), B!5, A!6) = B!5) | (tptp_fun_D_0(unordered_pair(A!6, B!5), B!5, A!6) = A!6))))) <=> (~$true)),
% 0.15/0.38 inference(monotonicity,[status(thm)],[48])).
% 0.15/0.38 tff(50,plain,
% 0.15/0.38 ((~((unordered_pair(A!6, B!5) = unordered_pair(A!6, B!5)) | ((~in(tptp_fun_D_0(unordered_pair(A!6, B!5), B!5, A!6), unordered_pair(A!6, B!5))) <=> ((tptp_fun_D_0(unordered_pair(A!6, B!5), B!5, A!6) = B!5) | (tptp_fun_D_0(unordered_pair(A!6, B!5), B!5, A!6) = A!6))))) <=> $false),
% 0.15/0.38 inference(transitivity,[status(thm)],[49, 43])).
% 0.15/0.38 tff(51,plain,
% 0.15/0.38 ((~((~(unordered_pair(A!6, B!5) = unordered_pair(A!6, B!5))) | (in(A!6, unordered_pair(A!6, B!5)) <=> ((A!6 = B!5) | (A!6 = A!6))))) <=> (~in(A!6, unordered_pair(A!6, B!5)))),
% 0.15/0.38 inference(rewrite,[status(thm)],[])).
% 0.15/0.38 tff(52,plain,
% 0.15/0.38 (((~((~(unordered_pair(A!6, B!5) = unordered_pair(A!6, B!5))) | (in(A!6, unordered_pair(A!6, B!5)) <=> ((A!6 = B!5) | (A!6 = A!6))))) | (~((unordered_pair(A!6, B!5) = unordered_pair(A!6, B!5)) | ((~in(tptp_fun_D_0(unordered_pair(A!6, B!5), B!5, A!6), unordered_pair(A!6, B!5))) <=> ((tptp_fun_D_0(unordered_pair(A!6, B!5), B!5, A!6) = B!5) | (tptp_fun_D_0(unordered_pair(A!6, B!5), B!5, A!6) = A!6)))))) <=> ((~in(A!6, unordered_pair(A!6, B!5))) | $false)),
% 0.15/0.38 inference(monotonicity,[status(thm)],[51, 50])).
% 0.15/0.38 tff(53,plain,
% 0.15/0.38 (((~((~(unordered_pair(A!6, B!5) = unordered_pair(A!6, B!5))) | (in(A!6, unordered_pair(A!6, B!5)) <=> ((A!6 = B!5) | (A!6 = A!6))))) | (~((unordered_pair(A!6, B!5) = unordered_pair(A!6, B!5)) | ((~in(tptp_fun_D_0(unordered_pair(A!6, B!5), B!5, A!6), unordered_pair(A!6, B!5))) <=> ((tptp_fun_D_0(unordered_pair(A!6, B!5), B!5, A!6) = B!5) | (tptp_fun_D_0(unordered_pair(A!6, B!5), B!5, A!6) = A!6)))))) <=> (~in(A!6, unordered_pair(A!6, B!5)))),
% 0.15/0.38 inference(transitivity,[status(thm)],[52, 42])).
% 0.15/0.38 tff(54,plain,
% 0.15/0.38 ((~((~((~(unordered_pair(A!6, B!5) = unordered_pair(A!6, B!5))) | (in(A!6, unordered_pair(A!6, B!5)) <=> ((A!6 = B!5) | (A!6 = A!6))))) | (~((unordered_pair(A!6, B!5) = unordered_pair(A!6, B!5)) | ((~in(tptp_fun_D_0(unordered_pair(A!6, B!5), B!5, A!6), unordered_pair(A!6, B!5))) <=> ((tptp_fun_D_0(unordered_pair(A!6, B!5), B!5, A!6) = B!5) | (tptp_fun_D_0(unordered_pair(A!6, B!5), B!5, A!6) = A!6))))))) <=> (~(~in(A!6, unordered_pair(A!6, B!5))))),
% 0.15/0.38 inference(monotonicity,[status(thm)],[53])).
% 0.15/0.38 tff(55,plain,
% 0.15/0.38 ((~((~((~(unordered_pair(A!6, B!5) = unordered_pair(A!6, B!5))) | (in(A!6, unordered_pair(A!6, B!5)) <=> ((A!6 = B!5) | (A!6 = A!6))))) | (~((unordered_pair(A!6, B!5) = unordered_pair(A!6, B!5)) | ((~in(tptp_fun_D_0(unordered_pair(A!6, B!5), B!5, A!6), unordered_pair(A!6, B!5))) <=> ((tptp_fun_D_0(unordered_pair(A!6, B!5), B!5, A!6) = B!5) | (tptp_fun_D_0(unordered_pair(A!6, B!5), B!5, A!6) = A!6))))))) <=> in(A!6, unordered_pair(A!6, B!5))),
% 0.15/0.38 inference(transitivity,[status(thm)],[54, 41])).
% 0.15/0.38 tff(56,plain,
% 0.15/0.38 (((~![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(A!6, B!5) = unordered_pair(A!6, B!5))) | (in(A!6, unordered_pair(A!6, B!5)) <=> ((A!6 = B!5) | (A!6 = A!6))))) | (~((unordered_pair(A!6, B!5) = unordered_pair(A!6, B!5)) | ((~in(tptp_fun_D_0(unordered_pair(A!6, B!5), B!5, A!6), unordered_pair(A!6, B!5))) <=> ((tptp_fun_D_0(unordered_pair(A!6, B!5), B!5, A!6) = B!5) | (tptp_fun_D_0(unordered_pair(A!6, B!5), B!5, A!6) = A!6)))))))) <=> ((~![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)))))))) | in(A!6, unordered_pair(A!6, B!5)))),
% 0.15/0.38 inference(monotonicity,[status(thm)],[55])).
% 0.15/0.38 tff(57,plain,
% 0.15/0.38 (((~![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(A!6, B!5) = unordered_pair(A!6, B!5))) | (in(A!6, unordered_pair(A!6, B!5)) <=> ((A!6 = B!5) | (A!6 = A!6))))) | (~((unordered_pair(A!6, B!5) = unordered_pair(A!6, B!5)) | ((~in(tptp_fun_D_0(unordered_pair(A!6, B!5), B!5, A!6), unordered_pair(A!6, B!5))) <=> ((tptp_fun_D_0(unordered_pair(A!6, B!5), B!5, A!6) = B!5) | (tptp_fun_D_0(unordered_pair(A!6, B!5), B!5, A!6) = A!6)))))))) <=> ((~![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)))))))) | in(A!6, unordered_pair(A!6, B!5)))),
% 0.15/0.38 inference(transitivity,[status(thm)],[56, 40])).
% 0.15/0.38 tff(58,plain,
% 0.15/0.38 ((~![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(A!6, B!5) = unordered_pair(A!6, B!5))) | (in(A!6, unordered_pair(A!6, B!5)) <=> ((A!6 = B!5) | (A!6 = A!6))))) | (~((unordered_pair(A!6, B!5) = unordered_pair(A!6, B!5)) | ((~in(tptp_fun_D_0(unordered_pair(A!6, B!5), B!5, A!6), unordered_pair(A!6, B!5))) <=> ((tptp_fun_D_0(unordered_pair(A!6, B!5), B!5, A!6) = B!5) | (tptp_fun_D_0(unordered_pair(A!6, B!5), B!5, A!6) = A!6)))))))),
% 0.15/0.38 inference(quant_inst,[status(thm)],[])).
% 0.15/0.38 tff(59,plain,
% 0.15/0.38 ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A)))))))) | in(A!6, unordered_pair(A!6, B!5))),
% 0.15/0.38 inference(modus_ponens,[status(thm)],[58, 57])).
% 0.15/0.38 tff(60,plain,
% 0.15/0.38 ($false),
% 0.15/0.38 inference(unit_resolution,[status(thm)],[59, 39, 15])).
% 0.15/0.38 tff(61,plain,(in(A!6, unordered_pair(A!6, B!5))), inference(lemma,lemma(discharge,[]))).
% 0.15/0.38 tff(62,plain,
% 0.15/0.38 ((~(in(A!6, unordered_pair(A!6, B!5)) <=> (~((~in(A!6, C!4)) | (~in(A!6, unordered_pair(A!6, B!5))))))) | (~in(A!6, unordered_pair(A!6, B!5))) | (~((~in(A!6, C!4)) | (~in(A!6, unordered_pair(A!6, B!5)))))),
% 0.15/0.38 inference(tautology,[status(thm)],[])).
% 0.15/0.38 tff(63,plain,
% 0.15/0.38 (~(in(A!6, unordered_pair(A!6, B!5)) <=> (~((~in(A!6, C!4)) | (~in(A!6, unordered_pair(A!6, B!5))))))),
% 0.15/0.38 inference(unit_resolution,[status(thm)],[62, 61, 14])).
% 0.15/0.38 tff(64,plain,
% 0.15/0.38 (set_intersection2(unordered_pair(A!6, B!5), C!4) = unordered_pair(A!6, B!5)),
% 0.15/0.38 inference(or_elim,[status(thm)],[11])).
% 0.15/0.38 tff(65,plain,
% 0.15/0.38 (unordered_pair(A!6, B!5) = set_intersection2(unordered_pair(A!6, B!5), C!4)),
% 0.15/0.38 inference(symmetry,[status(thm)],[64])).
% 0.15/0.38 tff(66,plain,
% 0.15/0.38 ((~((~(unordered_pair(A!6, B!5) = set_intersection2(unordered_pair(A!6, B!5), C!4))) | (in(A!6, unordered_pair(A!6, B!5)) <=> (~((~in(A!6, C!4)) | (~in(A!6, unordered_pair(A!6, B!5)))))))) | (~(unordered_pair(A!6, B!5) = set_intersection2(unordered_pair(A!6, B!5), C!4))) | (in(A!6, unordered_pair(A!6, B!5)) <=> (~((~in(A!6, C!4)) | (~in(A!6, unordered_pair(A!6, B!5))))))),
% 0.15/0.38 inference(tautology,[status(thm)],[])).
% 0.15/0.38 tff(67,plain,
% 0.15/0.38 (~((~(unordered_pair(A!6, B!5) = set_intersection2(unordered_pair(A!6, B!5), C!4))) | (in(A!6, unordered_pair(A!6, B!5)) <=> (~((~in(A!6, C!4)) | (~in(A!6, unordered_pair(A!6, B!5)))))))),
% 0.15/0.38 inference(unit_resolution,[status(thm)],[66, 65, 63])).
% 0.15/0.38 tff(68,plain,
% 0.15/0.38 (((~((~(unordered_pair(A!6, B!5) = set_intersection2(unordered_pair(A!6, B!5), C!4))) | (in(A!6, unordered_pair(A!6, B!5)) <=> (~((~in(A!6, C!4)) | (~in(A!6, unordered_pair(A!6, B!5)))))))) | (~((unordered_pair(A!6, B!5) = set_intersection2(unordered_pair(A!6, B!5), C!4)) | (in(tptp_fun_D_1(unordered_pair(A!6, B!5), C!4, unordered_pair(A!6, B!5)), unordered_pair(A!6, B!5)) <=> ((~in(tptp_fun_D_1(unordered_pair(A!6, B!5), C!4, unordered_pair(A!6, B!5)), unordered_pair(A!6, B!5))) | (~in(tptp_fun_D_1(unordered_pair(A!6, B!5), C!4, unordered_pair(A!6, B!5)), C!4))))))) | ((~(unordered_pair(A!6, B!5) = set_intersection2(unordered_pair(A!6, B!5), C!4))) | (in(A!6, unordered_pair(A!6, B!5)) <=> (~((~in(A!6, C!4)) | (~in(A!6, unordered_pair(A!6, B!5)))))))),
% 0.15/0.38 inference(tautology,[status(thm)],[])).
% 0.15/0.38 tff(69,plain,
% 0.15/0.38 ((~((~(unordered_pair(A!6, B!5) = set_intersection2(unordered_pair(A!6, B!5), C!4))) | (in(A!6, unordered_pair(A!6, B!5)) <=> (~((~in(A!6, C!4)) | (~in(A!6, unordered_pair(A!6, B!5)))))))) | (~((unordered_pair(A!6, B!5) = set_intersection2(unordered_pair(A!6, B!5), C!4)) | (in(tptp_fun_D_1(unordered_pair(A!6, B!5), C!4, unordered_pair(A!6, B!5)), unordered_pair(A!6, B!5)) <=> ((~in(tptp_fun_D_1(unordered_pair(A!6, B!5), C!4, unordered_pair(A!6, B!5)), unordered_pair(A!6, B!5))) | (~in(tptp_fun_D_1(unordered_pair(A!6, B!5), C!4, unordered_pair(A!6, B!5)), C!4))))))),
% 0.15/0.38 inference(unit_resolution,[status(thm)],[68, 67])).
% 0.15/0.38 tff(70,plain,
% 0.15/0.38 (^[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)))))))))),
% 0.15/0.38 inference(bind,[status(th)],[])).
% 0.15/0.38 tff(71,plain,
% 0.15/0.38 (![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))))))))),
% 0.15/0.38 inference(quant_intro,[status(thm)],[70])).
% 0.15/0.38 tff(72,plain,
% 0.15/0.38 (![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))))))))),
% 0.15/0.38 inference(pull_quant,[status(thm)],[])).
% 0.15/0.38 tff(73,plain,
% 0.15/0.38 (^[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))))))))))),
% 0.15/0.39 inference(bind,[status(th)],[])).
% 0.15/0.39 tff(74,plain,
% 0.15/0.39 (![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))))))))),
% 0.15/0.39 inference(quant_intro,[status(thm)],[73])).
% 0.15/0.39 tff(75,plain,
% 0.15/0.39 (![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))))))))),
% 0.15/0.39 inference(transitivity,[status(thm)],[74, 72])).
% 0.15/0.39 tff(76,plain,
% 0.15/0.39 (![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))))))))),
% 0.15/0.39 inference(transitivity,[status(thm)],[75, 71])).
% 0.15/0.39 tff(77,plain,
% 0.15/0.39 (^[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)))))))))),
% 0.15/0.39 inference(bind,[status(th)],[])).
% 0.15/0.39 tff(78,plain,
% 0.15/0.39 (![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))))))))),
% 0.15/0.39 inference(quant_intro,[status(thm)],[77])).
% 0.15/0.39 tff(79,plain,
% 0.15/0.39 (![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))))))))),
% 0.15/0.39 inference(transitivity,[status(thm)],[78, 76])).
% 0.15/0.39 tff(80,plain,
% 0.15/0.39 (^[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))))))))))),
% 0.15/0.39 inference(bind,[status(th)],[])).
% 0.15/0.39 tff(81,plain,
% 0.15/0.39 (![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))))))))),
% 0.15/0.39 inference(quant_intro,[status(thm)],[80])).
% 0.15/0.39 tff(82,plain,
% 0.15/0.39 (^[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))))))),
% 0.15/0.39 inference(bind,[status(th)],[])).
% 0.15/0.39 tff(83,plain,
% 0.15/0.39 (![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)))))),
% 0.15/0.39 inference(quant_intro,[status(thm)],[82])).
% 0.15/0.39 tff(84,plain,
% 0.15/0.39 (![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))))),
% 0.15/0.39 inference(rewrite,[status(thm)],[])).
% 0.15/0.39 tff(85,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/sandbox/benchmark/theBenchmark.p','d3_xboole_0')).
% 0.15/0.39 tff(86,plain,
% 0.15/0.39 (![A: $i, B: $i, C: $i] : ((C = set_intersection2(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, A) & in(D, B))))),
% 0.15/0.39 inference(modus_ponens,[status(thm)],[85, 84])).
% 0.15/0.39 tff(87,plain,(
% 0.15/0.39 ![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))))))),
% 0.15/0.39 inference(skolemize,[status(sab)],[86])).
% 0.15/0.39 tff(88,plain,
% 0.15/0.39 (![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)))))),
% 0.15/0.39 inference(modus_ponens,[status(thm)],[87, 83])).
% 0.15/0.39 tff(89,plain,
% 0.15/0.39 (![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))))))))),
% 0.15/0.39 inference(modus_ponens,[status(thm)],[88, 81])).
% 0.15/0.39 tff(90,plain,
% 0.15/0.39 (![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))))))))),
% 0.15/0.39 inference(modus_ponens,[status(thm)],[89, 79])).
% 0.15/0.39 tff(91,plain,
% 0.15/0.39 (((~![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))))))))) | (~((~((~(unordered_pair(A!6, B!5) = set_intersection2(unordered_pair(A!6, B!5), C!4))) | (in(A!6, unordered_pair(A!6, B!5)) <=> (~((~in(A!6, C!4)) | (~in(A!6, unordered_pair(A!6, B!5)))))))) | (~((unordered_pair(A!6, B!5) = set_intersection2(unordered_pair(A!6, B!5), C!4)) | (in(tptp_fun_D_1(unordered_pair(A!6, B!5), C!4, unordered_pair(A!6, B!5)), unordered_pair(A!6, B!5)) <=> ((~in(tptp_fun_D_1(unordered_pair(A!6, B!5), C!4, unordered_pair(A!6, B!5)), unordered_pair(A!6, B!5))) | (~in(tptp_fun_D_1(unordered_pair(A!6, B!5), C!4, unordered_pair(A!6, B!5)), C!4))))))))) <=> ((~![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))))))))) | (~((~((~(unordered_pair(A!6, B!5) = set_intersection2(unordered_pair(A!6, B!5), C!4))) | (in(A!6, unordered_pair(A!6, B!5)) <=> (~((~in(A!6, C!4)) | (~in(A!6, unordered_pair(A!6, B!5)))))))) | (~((unordered_pair(A!6, B!5) = set_intersection2(unordered_pair(A!6, B!5), C!4)) | (in(tptp_fun_D_1(unordered_pair(A!6, B!5), C!4, unordered_pair(A!6, B!5)), unordered_pair(A!6, B!5)) <=> ((~in(tptp_fun_D_1(unordered_pair(A!6, B!5), C!4, unordered_pair(A!6, B!5)), unordered_pair(A!6, B!5))) | (~in(tptp_fun_D_1(unordered_pair(A!6, B!5), C!4, unordered_pair(A!6, B!5)), C!4)))))))))),
% 0.15/0.39 inference(rewrite,[status(thm)],[])).
% 0.15/0.39 tff(92,plain,
% 0.15/0.39 ((~((~((~(unordered_pair(A!6, B!5) = set_intersection2(unordered_pair(A!6, B!5), C!4))) | (in(A!6, unordered_pair(A!6, B!5)) <=> (~((~in(A!6, unordered_pair(A!6, B!5))) | (~in(A!6, C!4))))))) | (~((unordered_pair(A!6, B!5) = set_intersection2(unordered_pair(A!6, B!5), C!4)) | (in(tptp_fun_D_1(unordered_pair(A!6, B!5), C!4, unordered_pair(A!6, B!5)), unordered_pair(A!6, B!5)) <=> ((~in(tptp_fun_D_1(unordered_pair(A!6, B!5), C!4, unordered_pair(A!6, B!5)), unordered_pair(A!6, B!5))) | (~in(tptp_fun_D_1(unordered_pair(A!6, B!5), C!4, unordered_pair(A!6, B!5)), C!4)))))))) <=> (~((~((~(unordered_pair(A!6, B!5) = set_intersection2(unordered_pair(A!6, B!5), C!4))) | (in(A!6, unordered_pair(A!6, B!5)) <=> (~((~in(A!6, C!4)) | (~in(A!6, unordered_pair(A!6, B!5)))))))) | (~((unordered_pair(A!6, B!5) = set_intersection2(unordered_pair(A!6, B!5), C!4)) | (in(tptp_fun_D_1(unordered_pair(A!6, B!5), C!4, unordered_pair(A!6, B!5)), unordered_pair(A!6, B!5)) <=> ((~in(tptp_fun_D_1(unordered_pair(A!6, B!5), C!4, unordered_pair(A!6, B!5)), unordered_pair(A!6, B!5))) | (~in(tptp_fun_D_1(unordered_pair(A!6, B!5), C!4, unordered_pair(A!6, B!5)), C!4))))))))),
% 0.15/0.39 inference(rewrite,[status(thm)],[])).
% 0.15/0.39 tff(93,plain,
% 0.15/0.39 (((~![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))))))))) | (~((~((~(unordered_pair(A!6, B!5) = set_intersection2(unordered_pair(A!6, B!5), C!4))) | (in(A!6, unordered_pair(A!6, B!5)) <=> (~((~in(A!6, unordered_pair(A!6, B!5))) | (~in(A!6, C!4))))))) | (~((unordered_pair(A!6, B!5) = set_intersection2(unordered_pair(A!6, B!5), C!4)) | (in(tptp_fun_D_1(unordered_pair(A!6, B!5), C!4, unordered_pair(A!6, B!5)), unordered_pair(A!6, B!5)) <=> ((~in(tptp_fun_D_1(unordered_pair(A!6, B!5), C!4, unordered_pair(A!6, B!5)), unordered_pair(A!6, B!5))) | (~in(tptp_fun_D_1(unordered_pair(A!6, B!5), C!4, unordered_pair(A!6, B!5)), C!4))))))))) <=> ((~![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))))))))) | (~((~((~(unordered_pair(A!6, B!5) = set_intersection2(unordered_pair(A!6, B!5), C!4))) | (in(A!6, unordered_pair(A!6, B!5)) <=> (~((~in(A!6, C!4)) | (~in(A!6, unordered_pair(A!6, B!5)))))))) | (~((unordered_pair(A!6, B!5) = set_intersection2(unordered_pair(A!6, B!5), C!4)) | (in(tptp_fun_D_1(unordered_pair(A!6, B!5), C!4, unordered_pair(A!6, B!5)), unordered_pair(A!6, B!5)) <=> ((~in(tptp_fun_D_1(unordered_pair(A!6, B!5), C!4, unordered_pair(A!6, B!5)), unordered_pair(A!6, B!5))) | (~in(tptp_fun_D_1(unordered_pair(A!6, B!5), C!4, unordered_pair(A!6, B!5)), C!4)))))))))),
% 0.15/0.40 inference(monotonicity,[status(thm)],[92])).
% 0.15/0.40 tff(94,plain,
% 0.15/0.40 (((~![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))))))))) | (~((~((~(unordered_pair(A!6, B!5) = set_intersection2(unordered_pair(A!6, B!5), C!4))) | (in(A!6, unordered_pair(A!6, B!5)) <=> (~((~in(A!6, unordered_pair(A!6, B!5))) | (~in(A!6, C!4))))))) | (~((unordered_pair(A!6, B!5) = set_intersection2(unordered_pair(A!6, B!5), C!4)) | (in(tptp_fun_D_1(unordered_pair(A!6, B!5), C!4, unordered_pair(A!6, B!5)), unordered_pair(A!6, B!5)) <=> ((~in(tptp_fun_D_1(unordered_pair(A!6, B!5), C!4, unordered_pair(A!6, B!5)), unordered_pair(A!6, B!5))) | (~in(tptp_fun_D_1(unordered_pair(A!6, B!5), C!4, unordered_pair(A!6, B!5)), C!4))))))))) <=> ((~![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))))))))) | (~((~((~(unordered_pair(A!6, B!5) = set_intersection2(unordered_pair(A!6, B!5), C!4))) | (in(A!6, unordered_pair(A!6, B!5)) <=> (~((~in(A!6, C!4)) | (~in(A!6, unordered_pair(A!6, B!5)))))))) | (~((unordered_pair(A!6, B!5) = set_intersection2(unordered_pair(A!6, B!5), C!4)) | (in(tptp_fun_D_1(unordered_pair(A!6, B!5), C!4, unordered_pair(A!6, B!5)), unordered_pair(A!6, B!5)) <=> ((~in(tptp_fun_D_1(unordered_pair(A!6, B!5), C!4, unordered_pair(A!6, B!5)), unordered_pair(A!6, B!5))) | (~in(tptp_fun_D_1(unordered_pair(A!6, B!5), C!4, unordered_pair(A!6, B!5)), C!4)))))))))),
% 0.15/0.40 inference(transitivity,[status(thm)],[93, 91])).
% 0.15/0.40 tff(95,plain,
% 0.15/0.40 ((~![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))))))))) | (~((~((~(unordered_pair(A!6, B!5) = set_intersection2(unordered_pair(A!6, B!5), C!4))) | (in(A!6, unordered_pair(A!6, B!5)) <=> (~((~in(A!6, unordered_pair(A!6, B!5))) | (~in(A!6, C!4))))))) | (~((unordered_pair(A!6, B!5) = set_intersection2(unordered_pair(A!6, B!5), C!4)) | (in(tptp_fun_D_1(unordered_pair(A!6, B!5), C!4, unordered_pair(A!6, B!5)), unordered_pair(A!6, B!5)) <=> ((~in(tptp_fun_D_1(unordered_pair(A!6, B!5), C!4, unordered_pair(A!6, B!5)), unordered_pair(A!6, B!5))) | (~in(tptp_fun_D_1(unordered_pair(A!6, B!5), C!4, unordered_pair(A!6, B!5)), C!4))))))))),
% 0.15/0.40 inference(quant_inst,[status(thm)],[])).
% 0.15/0.40 tff(96,plain,
% 0.15/0.40 ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (in(D, C) <=> (~((~in(D, A)) | (~in(D, B))))))) | (~((C = set_intersection2(A, B)) | (in(tptp_fun_D_1(C, B, A), C) <=> ((~in(tptp_fun_D_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))))))))) | (~((~((~(unordered_pair(A!6, B!5) = set_intersection2(unordered_pair(A!6, B!5), C!4))) | (in(A!6, unordered_pair(A!6, B!5)) <=> (~((~in(A!6, C!4)) | (~in(A!6, unordered_pair(A!6, B!5)))))))) | (~((unordered_pair(A!6, B!5) = set_intersection2(unordered_pair(A!6, B!5), C!4)) | (in(tptp_fun_D_1(unordered_pair(A!6, B!5), C!4, unordered_pair(A!6, B!5)), unordered_pair(A!6, B!5)) <=> ((~in(tptp_fun_D_1(unordered_pair(A!6, B!5), C!4, unordered_pair(A!6, B!5)), unordered_pair(A!6, B!5))) | (~in(tptp_fun_D_1(unordered_pair(A!6, B!5), C!4, unordered_pair(A!6, B!5)), C!4))))))))),
% 0.15/0.40 inference(modus_ponens,[status(thm)],[95, 94])).
% 0.15/0.40 tff(97,plain,
% 0.15/0.40 ($false),
% 0.15/0.40 inference(unit_resolution,[status(thm)],[96, 90, 69])).
% 0.15/0.40 % SZS output end Proof
%------------------------------------------------------------------------------