TSTP Solution File: SEU159+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SEU159+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n017.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 20 07:27:52 EDT 2022
% Result : Theorem 0.13s 0.40s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU159+1 : TPTP v8.1.0. Released v3.3.0.
% 0.12/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n017.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 09:10:39 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 0.13/0.40 % SZS status Theorem
% 0.13/0.40 % SZS output start Proof
% 0.13/0.40 tff(in_type, type, (
% 0.13/0.40 in: ( $i * $i ) > $o)).
% 0.13/0.40 tff(unordered_pair_type, type, (
% 0.13/0.40 unordered_pair: ( $i * $i ) > $i)).
% 0.13/0.40 tff(tptp_fun_A_4_type, type, (
% 0.13/0.40 tptp_fun_A_4: $i)).
% 0.13/0.40 tff(tptp_fun_B_3_type, type, (
% 0.13/0.40 tptp_fun_B_3: $i)).
% 0.13/0.40 tff(tptp_fun_C_2_type, type, (
% 0.13/0.40 tptp_fun_C_2: $i)).
% 0.13/0.40 tff(subset_type, type, (
% 0.13/0.40 subset: ( $i * $i ) > $o)).
% 0.13/0.40 tff(tptp_fun_C_1_type, type, (
% 0.13/0.40 tptp_fun_C_1: ( $i * $i ) > $i)).
% 0.13/0.40 tff(tptp_fun_D_0_type, type, (
% 0.13/0.40 tptp_fun_D_0: ( $i * $i * $i ) > $i)).
% 0.13/0.40 tff(1,plain,
% 0.13/0.40 (^[A: $i, B: $i] : refl((unordered_pair(A, B) = unordered_pair(B, A)) <=> (unordered_pair(A, B) = unordered_pair(B, A)))),
% 0.13/0.40 inference(bind,[status(th)],[])).
% 0.13/0.40 tff(2,plain,
% 0.13/0.40 (![A: $i, B: $i] : (unordered_pair(A, B) = unordered_pair(B, A)) <=> ![A: $i, B: $i] : (unordered_pair(A, B) = unordered_pair(B, A))),
% 0.13/0.40 inference(quant_intro,[status(thm)],[1])).
% 0.13/0.40 tff(3,plain,
% 0.13/0.40 (![A: $i, B: $i] : (unordered_pair(A, B) = unordered_pair(B, A)) <=> ![A: $i, B: $i] : (unordered_pair(A, B) = unordered_pair(B, A))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(4,axiom,(![A: $i, B: $i] : (unordered_pair(A, B) = unordered_pair(B, A))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','commutativity_k2_tarski')).
% 0.13/0.40 tff(5,plain,
% 0.13/0.40 (![A: $i, B: $i] : (unordered_pair(A, B) = unordered_pair(B, A))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.13/0.40 tff(6,plain,(
% 0.13/0.40 ![A: $i, B: $i] : (unordered_pair(A, B) = unordered_pair(B, A))),
% 0.13/0.40 inference(skolemize,[status(sab)],[5])).
% 0.13/0.40 tff(7,plain,
% 0.13/0.40 (![A: $i, B: $i] : (unordered_pair(A, B) = unordered_pair(B, A))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.13/0.40 tff(8,plain,
% 0.13/0.40 ((~![A: $i, B: $i] : (unordered_pair(A, B) = unordered_pair(B, A))) | (unordered_pair(A!4, B!3) = unordered_pair(B!3, A!4))),
% 0.13/0.40 inference(quant_inst,[status(thm)],[])).
% 0.13/0.40 tff(9,plain,
% 0.13/0.40 (unordered_pair(A!4, B!3) = unordered_pair(B!3, A!4)),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.13/0.40 tff(10,plain,
% 0.13/0.40 (unordered_pair(B!3, A!4) = unordered_pair(A!4, B!3)),
% 0.13/0.40 inference(symmetry,[status(thm)],[9])).
% 0.13/0.40 tff(11,plain,
% 0.13/0.40 (in(A!4, unordered_pair(B!3, A!4)) <=> in(A!4, unordered_pair(A!4, B!3))),
% 0.13/0.40 inference(monotonicity,[status(thm)],[10])).
% 0.13/0.40 tff(12,plain,
% 0.13/0.40 (in(A!4, unordered_pair(A!4, B!3)) <=> in(A!4, unordered_pair(B!3, A!4))),
% 0.13/0.40 inference(symmetry,[status(thm)],[11])).
% 0.13/0.40 tff(13,plain,
% 0.13/0.40 ((~in(A!4, unordered_pair(A!4, B!3))) <=> (~in(A!4, unordered_pair(B!3, A!4)))),
% 0.13/0.40 inference(monotonicity,[status(thm)],[12])).
% 0.13/0.40 tff(14,plain,
% 0.13/0.40 (^[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))))))))),
% 0.13/0.40 inference(bind,[status(th)],[])).
% 0.13/0.40 tff(15,plain,
% 0.13/0.40 (![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)))))))),
% 0.13/0.40 inference(quant_intro,[status(thm)],[14])).
% 0.13/0.40 tff(16,plain,
% 0.13/0.40 (![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)))))))),
% 0.13/0.40 inference(pull_quant,[status(thm)],[])).
% 0.13/0.40 tff(17,plain,
% 0.13/0.40 (^[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)))))))))),
% 0.13/0.40 inference(bind,[status(th)],[])).
% 0.13/0.40 tff(18,plain,
% 0.13/0.40 (![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)))))))),
% 0.13/0.40 inference(quant_intro,[status(thm)],[17])).
% 0.13/0.40 tff(19,plain,
% 0.13/0.40 (![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)))))))),
% 0.13/0.40 inference(transitivity,[status(thm)],[18, 16])).
% 0.13/0.40 tff(20,plain,
% 0.13/0.40 (![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)))))))),
% 0.13/0.40 inference(transitivity,[status(thm)],[19, 15])).
% 0.13/0.40 tff(21,plain,
% 0.13/0.40 (^[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))))))))),
% 0.13/0.40 inference(bind,[status(th)],[])).
% 0.13/0.40 tff(22,plain,
% 0.13/0.40 (![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)))))))),
% 0.13/0.40 inference(quant_intro,[status(thm)],[21])).
% 0.13/0.40 tff(23,plain,
% 0.13/0.40 (![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)))))))),
% 0.13/0.40 inference(transitivity,[status(thm)],[22, 20])).
% 0.13/0.40 tff(24,plain,
% 0.13/0.40 (^[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)))))))))),
% 0.13/0.40 inference(bind,[status(th)],[])).
% 0.13/0.40 tff(25,plain,
% 0.13/0.40 (![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)))))))),
% 0.13/0.40 inference(quant_intro,[status(thm)],[24])).
% 0.13/0.40 tff(26,plain,
% 0.13/0.40 (^[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))))))),
% 0.13/0.40 inference(bind,[status(th)],[])).
% 0.13/0.40 tff(27,plain,
% 0.13/0.40 (![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)))))),
% 0.13/0.40 inference(quant_intro,[status(thm)],[26])).
% 0.13/0.40 tff(28,plain,
% 0.13/0.40 (![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))))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(29,plain,
% 0.13/0.40 (^[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)))))),
% 0.13/0.40 inference(bind,[status(th)],[])).
% 0.13/0.40 tff(30,plain,
% 0.13/0.40 (![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))))),
% 0.13/0.40 inference(quant_intro,[status(thm)],[29])).
% 0.13/0.40 tff(31,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')).
% 0.13/0.40 tff(32,plain,
% 0.13/0.40 (![A: $i, B: $i, C: $i] : ((C = unordered_pair(A, B)) <=> ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[31, 30])).
% 0.13/0.40 tff(33,plain,
% 0.13/0.40 (![A: $i, B: $i, C: $i] : ((C = unordered_pair(A, B)) <=> ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[32, 28])).
% 0.13/0.40 tff(34,plain,(
% 0.13/0.40 ![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))))))),
% 0.13/0.40 inference(skolemize,[status(sab)],[33])).
% 0.13/0.40 tff(35,plain,
% 0.13/0.40 (![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)))))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[34, 27])).
% 0.13/0.40 tff(36,plain,
% 0.13/0.40 (![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)))))))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[35, 25])).
% 0.13/0.41 tff(37,plain,
% 0.13/0.41 (![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)))))))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[36, 23])).
% 0.13/0.41 tff(38,plain,
% 0.13/0.41 ((~![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(B!3, A!4) = unordered_pair(A!4, B!3))) | (in(tptp_fun_C_1(C!2, unordered_pair(A!4, B!3)), unordered_pair(B!3, A!4)) <=> ((tptp_fun_C_1(C!2, unordered_pair(A!4, B!3)) = B!3) | (tptp_fun_C_1(C!2, unordered_pair(A!4, B!3)) = A!4))))) | (~((unordered_pair(B!3, A!4) = unordered_pair(A!4, B!3)) | ((~in(tptp_fun_D_0(unordered_pair(B!3, A!4), B!3, A!4), unordered_pair(B!3, A!4))) <=> ((tptp_fun_D_0(unordered_pair(B!3, A!4), B!3, A!4) = B!3) | (tptp_fun_D_0(unordered_pair(B!3, A!4), B!3, A!4) = A!4)))))))),
% 0.13/0.41 inference(quant_inst,[status(thm)],[])).
% 0.13/0.41 tff(39,plain,
% 0.13/0.41 (~((~((~(unordered_pair(B!3, A!4) = unordered_pair(A!4, B!3))) | (in(tptp_fun_C_1(C!2, unordered_pair(A!4, B!3)), unordered_pair(B!3, A!4)) <=> ((tptp_fun_C_1(C!2, unordered_pair(A!4, B!3)) = B!3) | (tptp_fun_C_1(C!2, unordered_pair(A!4, B!3)) = A!4))))) | (~((unordered_pair(B!3, A!4) = unordered_pair(A!4, B!3)) | ((~in(tptp_fun_D_0(unordered_pair(B!3, A!4), B!3, A!4), unordered_pair(B!3, A!4))) <=> ((tptp_fun_D_0(unordered_pair(B!3, A!4), B!3, A!4) = B!3) | (tptp_fun_D_0(unordered_pair(B!3, A!4), B!3, A!4) = A!4))))))),
% 0.13/0.41 inference(unit_resolution,[status(thm)],[38, 37])).
% 0.13/0.41 tff(40,plain,
% 0.13/0.41 (((~((~(unordered_pair(B!3, A!4) = unordered_pair(A!4, B!3))) | (in(tptp_fun_C_1(C!2, unordered_pair(A!4, B!3)), unordered_pair(B!3, A!4)) <=> ((tptp_fun_C_1(C!2, unordered_pair(A!4, B!3)) = B!3) | (tptp_fun_C_1(C!2, unordered_pair(A!4, B!3)) = A!4))))) | (~((unordered_pair(B!3, A!4) = unordered_pair(A!4, B!3)) | ((~in(tptp_fun_D_0(unordered_pair(B!3, A!4), B!3, A!4), unordered_pair(B!3, A!4))) <=> ((tptp_fun_D_0(unordered_pair(B!3, A!4), B!3, A!4) = B!3) | (tptp_fun_D_0(unordered_pair(B!3, A!4), B!3, A!4) = A!4)))))) | ((~(unordered_pair(B!3, A!4) = unordered_pair(A!4, B!3))) | (in(tptp_fun_C_1(C!2, unordered_pair(A!4, B!3)), unordered_pair(B!3, A!4)) <=> ((tptp_fun_C_1(C!2, unordered_pair(A!4, B!3)) = B!3) | (tptp_fun_C_1(C!2, unordered_pair(A!4, B!3)) = A!4))))),
% 0.13/0.41 inference(tautology,[status(thm)],[])).
% 0.13/0.41 tff(41,plain,
% 0.13/0.41 ((~(unordered_pair(B!3, A!4) = unordered_pair(A!4, B!3))) | (in(tptp_fun_C_1(C!2, unordered_pair(A!4, B!3)), unordered_pair(B!3, A!4)) <=> ((tptp_fun_C_1(C!2, unordered_pair(A!4, B!3)) = B!3) | (tptp_fun_C_1(C!2, unordered_pair(A!4, B!3)) = A!4)))),
% 0.13/0.41 inference(unit_resolution,[status(thm)],[40, 39])).
% 0.13/0.41 tff(42,plain,
% 0.13/0.41 ((~![A: $i, B: $i] : (unordered_pair(A, B) = unordered_pair(B, A))) | (unordered_pair(B!3, A!4) = unordered_pair(A!4, B!3))),
% 0.13/0.41 inference(quant_inst,[status(thm)],[])).
% 0.13/0.41 tff(43,plain,
% 0.13/0.41 (unordered_pair(B!3, A!4) = unordered_pair(A!4, B!3)),
% 0.13/0.41 inference(unit_resolution,[status(thm)],[42, 7])).
% 0.13/0.41 tff(44,plain,
% 0.13/0.41 ((~((~(unordered_pair(B!3, A!4) = unordered_pair(A!4, B!3))) | (in(tptp_fun_C_1(C!2, unordered_pair(A!4, B!3)), unordered_pair(B!3, A!4)) <=> ((tptp_fun_C_1(C!2, unordered_pair(A!4, B!3)) = B!3) | (tptp_fun_C_1(C!2, unordered_pair(A!4, B!3)) = A!4))))) | (~(unordered_pair(B!3, A!4) = unordered_pair(A!4, B!3))) | (in(tptp_fun_C_1(C!2, unordered_pair(A!4, B!3)), unordered_pair(B!3, A!4)) <=> ((tptp_fun_C_1(C!2, unordered_pair(A!4, B!3)) = B!3) | (tptp_fun_C_1(C!2, unordered_pair(A!4, B!3)) = A!4)))),
% 0.13/0.41 inference(tautology,[status(thm)],[])).
% 0.13/0.41 tff(45,plain,
% 0.13/0.41 ((~((~(unordered_pair(B!3, A!4) = unordered_pair(A!4, B!3))) | (in(tptp_fun_C_1(C!2, unordered_pair(A!4, B!3)), unordered_pair(B!3, A!4)) <=> ((tptp_fun_C_1(C!2, unordered_pair(A!4, B!3)) = B!3) | (tptp_fun_C_1(C!2, unordered_pair(A!4, B!3)) = A!4))))) | (in(tptp_fun_C_1(C!2, unordered_pair(A!4, B!3)), unordered_pair(B!3, A!4)) <=> ((tptp_fun_C_1(C!2, unordered_pair(A!4, B!3)) = B!3) | (tptp_fun_C_1(C!2, unordered_pair(A!4, B!3)) = A!4)))),
% 0.13/0.41 inference(unit_resolution,[status(thm)],[44, 43])).
% 0.13/0.41 tff(46,plain,
% 0.13/0.41 (in(tptp_fun_C_1(C!2, unordered_pair(A!4, B!3)), unordered_pair(B!3, A!4)) <=> ((tptp_fun_C_1(C!2, unordered_pair(A!4, B!3)) = B!3) | (tptp_fun_C_1(C!2, unordered_pair(A!4, B!3)) = A!4))),
% 0.13/0.41 inference(unit_resolution,[status(thm)],[45, 41])).
% 0.13/0.41 tff(47,plain,
% 0.13/0.41 (in(tptp_fun_C_1(C!2, unordered_pair(A!4, B!3)), unordered_pair(B!3, A!4)) <=> in(tptp_fun_C_1(C!2, unordered_pair(A!4, B!3)), unordered_pair(A!4, B!3))),
% 0.13/0.41 inference(monotonicity,[status(thm)],[10])).
% 0.13/0.41 tff(48,plain,
% 0.13/0.41 (in(tptp_fun_C_1(C!2, unordered_pair(A!4, B!3)), unordered_pair(A!4, B!3)) <=> in(tptp_fun_C_1(C!2, unordered_pair(A!4, B!3)), unordered_pair(B!3, A!4))),
% 0.13/0.41 inference(symmetry,[status(thm)],[47])).
% 0.13/0.41 tff(49,assumption,(~((~in(A!4, C!2)) | (~in(B!3, C!2)))), introduced(assumption)).
% 0.13/0.41 tff(50,plain,
% 0.13/0.41 (((~subset(unordered_pair(A!4, B!3), C!2)) <=> (~((~in(A!4, C!2)) | (~in(B!3, C!2))))) <=> (subset(unordered_pair(A!4, B!3), C!2) <=> ((~in(A!4, C!2)) | (~in(B!3, C!2))))),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(51,plain,
% 0.13/0.41 ((in(A!4, C!2) & in(B!3, C!2)) <=> (~((~in(A!4, C!2)) | (~in(B!3, C!2))))),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(52,plain,
% 0.13/0.41 (((~subset(unordered_pair(A!4, B!3), C!2)) <=> (in(A!4, C!2) & in(B!3, C!2))) <=> ((~subset(unordered_pair(A!4, B!3), C!2)) <=> (~((~in(A!4, C!2)) | (~in(B!3, C!2)))))),
% 0.13/0.41 inference(monotonicity,[status(thm)],[51])).
% 0.13/0.41 tff(53,plain,
% 0.13/0.41 (((~subset(unordered_pair(A!4, B!3), C!2)) <=> (in(A!4, C!2) & in(B!3, C!2))) <=> (subset(unordered_pair(A!4, B!3), C!2) <=> ((~in(A!4, C!2)) | (~in(B!3, C!2))))),
% 0.13/0.41 inference(transitivity,[status(thm)],[52, 50])).
% 0.13/0.41 tff(54,plain,
% 0.13/0.41 ((~(subset(unordered_pair(A!4, B!3), C!2) <=> (in(A!4, C!2) & in(B!3, C!2)))) <=> ((~subset(unordered_pair(A!4, B!3), C!2)) <=> (in(A!4, C!2) & in(B!3, C!2)))),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(55,plain,
% 0.13/0.41 ((~![A: $i, B: $i, C: $i] : (subset(unordered_pair(A, B), C) <=> (in(A, C) & in(B, C)))) <=> (~![A: $i, B: $i, C: $i] : (subset(unordered_pair(A, B), C) <=> (in(A, C) & in(B, C))))),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(56,axiom,(~![A: $i, B: $i, C: $i] : (subset(unordered_pair(A, B), C) <=> (in(A, C) & in(B, C)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t38_zfmisc_1')).
% 0.13/0.41 tff(57,plain,
% 0.13/0.41 (~![A: $i, B: $i, C: $i] : (subset(unordered_pair(A, B), C) <=> (in(A, C) & in(B, C)))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[56, 55])).
% 0.13/0.41 tff(58,plain,
% 0.13/0.41 (~![A: $i, B: $i, C: $i] : (subset(unordered_pair(A, B), C) <=> (in(A, C) & in(B, C)))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[57, 55])).
% 0.13/0.41 tff(59,plain,
% 0.13/0.41 (~![A: $i, B: $i, C: $i] : (subset(unordered_pair(A, B), C) <=> (in(A, C) & in(B, C)))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[58, 55])).
% 0.13/0.41 tff(60,plain,
% 0.13/0.41 (~![A: $i, B: $i, C: $i] : (subset(unordered_pair(A, B), C) <=> (in(A, C) & in(B, C)))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[59, 55])).
% 0.13/0.41 tff(61,plain,
% 0.13/0.41 (~![A: $i, B: $i, C: $i] : (subset(unordered_pair(A, B), C) <=> (in(A, C) & in(B, C)))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[60, 55])).
% 0.13/0.41 tff(62,plain,
% 0.13/0.41 (~![A: $i, B: $i, C: $i] : (subset(unordered_pair(A, B), C) <=> (in(A, C) & in(B, C)))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[61, 55])).
% 0.13/0.41 tff(63,plain,
% 0.13/0.41 (~![A: $i, B: $i, C: $i] : (subset(unordered_pair(A, B), C) <=> (in(A, C) & in(B, C)))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[62, 55])).
% 0.13/0.41 tff(64,plain,(
% 0.13/0.41 ~(subset(unordered_pair(A!4, B!3), C!2) <=> (in(A!4, C!2) & in(B!3, C!2)))),
% 0.13/0.41 inference(skolemize,[status(sab)],[63])).
% 0.13/0.41 tff(65,plain,
% 0.13/0.41 ((~subset(unordered_pair(A!4, B!3), C!2)) <=> (in(A!4, C!2) & in(B!3, C!2))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[64, 54])).
% 0.13/0.41 tff(66,plain,
% 0.13/0.41 (subset(unordered_pair(A!4, B!3), C!2) <=> ((~in(A!4, C!2)) | (~in(B!3, C!2)))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[65, 53])).
% 0.13/0.41 tff(67,plain,
% 0.13/0.41 ((~subset(unordered_pair(A!4, B!3), C!2)) | ((~in(A!4, C!2)) | (~in(B!3, C!2))) | (~(subset(unordered_pair(A!4, B!3), C!2) <=> ((~in(A!4, C!2)) | (~in(B!3, C!2)))))),
% 0.13/0.41 inference(tautology,[status(thm)],[])).
% 0.13/0.41 tff(68,plain,
% 0.13/0.41 ((~subset(unordered_pair(A!4, B!3), C!2)) | ((~in(A!4, C!2)) | (~in(B!3, C!2)))),
% 0.13/0.41 inference(unit_resolution,[status(thm)],[67, 66])).
% 0.13/0.41 tff(69,plain,
% 0.13/0.41 (~subset(unordered_pair(A!4, B!3), C!2)),
% 0.13/0.41 inference(unit_resolution,[status(thm)],[68, 49])).
% 0.13/0.41 tff(70,plain,
% 0.13/0.41 (^[A: $i, B: $i] : refl((~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_1(B, A), A)) | in(tptp_fun_C_1(B, A), B))))))) <=> (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_1(B, A), A)) | in(tptp_fun_C_1(B, A), B))))))))),
% 0.13/0.41 inference(bind,[status(th)],[])).
% 0.13/0.41 tff(71,plain,
% 0.13/0.41 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_1(B, A), A)) | in(tptp_fun_C_1(B, A), B))))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_1(B, A), A)) | in(tptp_fun_C_1(B, A), B)))))))),
% 0.13/0.41 inference(quant_intro,[status(thm)],[70])).
% 0.13/0.41 tff(72,plain,
% 0.13/0.41 (^[A: $i, B: $i] : rewrite((~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_1(B, A), A)) | in(tptp_fun_C_1(B, A), B))))))) <=> (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_1(B, A), A)) | in(tptp_fun_C_1(B, A), B))))))))),
% 0.13/0.41 inference(bind,[status(th)],[])).
% 0.13/0.41 tff(73,plain,
% 0.13/0.41 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_1(B, A), A)) | in(tptp_fun_C_1(B, A), B))))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_1(B, A), A)) | in(tptp_fun_C_1(B, A), B)))))))),
% 0.13/0.41 inference(quant_intro,[status(thm)],[72])).
% 0.13/0.41 tff(74,plain,
% 0.13/0.41 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_1(B, A), A)) | in(tptp_fun_C_1(B, A), B))))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_1(B, A), A)) | in(tptp_fun_C_1(B, A), B)))))))),
% 0.13/0.41 inference(transitivity,[status(thm)],[73, 71])).
% 0.13/0.41 tff(75,plain,
% 0.13/0.41 (^[A: $i, B: $i] : trans(monotonicity(rewrite(((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) <=> ((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))), rewrite((subset(A, B) | (~((~in(tptp_fun_C_1(B, A), A)) | in(tptp_fun_C_1(B, A), B)))) <=> (subset(A, B) | (~((~in(tptp_fun_C_1(B, A), A)) | in(tptp_fun_C_1(B, A), B))))), ((((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_1(B, A), A)) | in(tptp_fun_C_1(B, A), B))))) <=> (((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_1(B, A), A)) | in(tptp_fun_C_1(B, A), B))))))), rewrite((((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_1(B, A), A)) | in(tptp_fun_C_1(B, A), B))))) <=> (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_1(B, A), A)) | in(tptp_fun_C_1(B, A), B)))))))), ((((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_1(B, A), A)) | in(tptp_fun_C_1(B, A), B))))) <=> (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_1(B, A), A)) | in(tptp_fun_C_1(B, A), B)))))))))),
% 0.13/0.41 inference(bind,[status(th)],[])).
% 0.13/0.41 tff(76,plain,
% 0.13/0.41 (![A: $i, B: $i] : (((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_1(B, A), A)) | in(tptp_fun_C_1(B, A), B))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_1(B, A), A)) | in(tptp_fun_C_1(B, A), B)))))))),
% 0.13/0.42 inference(quant_intro,[status(thm)],[75])).
% 0.13/0.42 tff(77,plain,
% 0.13/0.42 (![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B))) <=> ![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B)))),
% 0.13/0.42 inference(rewrite,[status(thm)],[])).
% 0.13/0.42 tff(78,plain,
% 0.13/0.42 (^[A: $i, B: $i] : rewrite((subset(A, B) <=> ![C: $i] : (in(C, A) => in(C, B))) <=> (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B))))),
% 0.13/0.42 inference(bind,[status(th)],[])).
% 0.13/0.42 tff(79,plain,
% 0.13/0.42 (![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : (in(C, A) => in(C, B))) <=> ![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B)))),
% 0.13/0.42 inference(quant_intro,[status(thm)],[78])).
% 0.13/0.42 tff(80,axiom,(![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : (in(C, A) => in(C, B)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d3_tarski')).
% 0.13/0.42 tff(81,plain,
% 0.13/0.42 (![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B)))),
% 0.13/0.42 inference(modus_ponens,[status(thm)],[80, 79])).
% 0.13/0.42 tff(82,plain,
% 0.13/0.42 (![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B)))),
% 0.13/0.42 inference(modus_ponens,[status(thm)],[81, 77])).
% 0.13/0.42 tff(83,plain,(
% 0.13/0.42 ![A: $i, B: $i] : (((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_1(B, A), A)) | in(tptp_fun_C_1(B, A), B)))))),
% 0.13/0.42 inference(skolemize,[status(sab)],[82])).
% 0.13/0.42 tff(84,plain,
% 0.13/0.42 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_1(B, A), A)) | in(tptp_fun_C_1(B, A), B)))))))),
% 0.13/0.42 inference(modus_ponens,[status(thm)],[83, 76])).
% 0.13/0.42 tff(85,plain,
% 0.13/0.42 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_1(B, A), A)) | in(tptp_fun_C_1(B, A), B)))))))),
% 0.13/0.42 inference(modus_ponens,[status(thm)],[84, 74])).
% 0.13/0.42 tff(86,plain,
% 0.13/0.42 ((~![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_1(B, A), A)) | in(tptp_fun_C_1(B, A), B)))))))) | (~((~((~subset(unordered_pair(A!4, B!3), C!2)) | ![C: $i] : ((~in(C, unordered_pair(A!4, B!3))) | in(C, C!2)))) | (~(subset(unordered_pair(A!4, B!3), C!2) | (~((~in(tptp_fun_C_1(C!2, unordered_pair(A!4, B!3)), unordered_pair(A!4, B!3))) | in(tptp_fun_C_1(C!2, unordered_pair(A!4, B!3)), C!2)))))))),
% 0.13/0.42 inference(quant_inst,[status(thm)],[])).
% 0.13/0.42 tff(87,plain,
% 0.13/0.42 (~((~((~subset(unordered_pair(A!4, B!3), C!2)) | ![C: $i] : ((~in(C, unordered_pair(A!4, B!3))) | in(C, C!2)))) | (~(subset(unordered_pair(A!4, B!3), C!2) | (~((~in(tptp_fun_C_1(C!2, unordered_pair(A!4, B!3)), unordered_pair(A!4, B!3))) | in(tptp_fun_C_1(C!2, unordered_pair(A!4, B!3)), C!2))))))),
% 0.13/0.42 inference(unit_resolution,[status(thm)],[86, 85])).
% 0.13/0.42 tff(88,plain,
% 0.13/0.42 (((~((~subset(unordered_pair(A!4, B!3), C!2)) | ![C: $i] : ((~in(C, unordered_pair(A!4, B!3))) | in(C, C!2)))) | (~(subset(unordered_pair(A!4, B!3), C!2) | (~((~in(tptp_fun_C_1(C!2, unordered_pair(A!4, B!3)), unordered_pair(A!4, B!3))) | in(tptp_fun_C_1(C!2, unordered_pair(A!4, B!3)), C!2)))))) | (subset(unordered_pair(A!4, B!3), C!2) | (~((~in(tptp_fun_C_1(C!2, unordered_pair(A!4, B!3)), unordered_pair(A!4, B!3))) | in(tptp_fun_C_1(C!2, unordered_pair(A!4, B!3)), C!2))))),
% 0.13/0.42 inference(tautology,[status(thm)],[])).
% 0.13/0.42 tff(89,plain,
% 0.13/0.42 (subset(unordered_pair(A!4, B!3), C!2) | (~((~in(tptp_fun_C_1(C!2, unordered_pair(A!4, B!3)), unordered_pair(A!4, B!3))) | in(tptp_fun_C_1(C!2, unordered_pair(A!4, B!3)), C!2)))),
% 0.13/0.42 inference(unit_resolution,[status(thm)],[88, 87])).
% 0.13/0.42 tff(90,plain,
% 0.13/0.42 ((~(subset(unordered_pair(A!4, B!3), C!2) | (~((~in(tptp_fun_C_1(C!2, unordered_pair(A!4, B!3)), unordered_pair(A!4, B!3))) | in(tptp_fun_C_1(C!2, unordered_pair(A!4, B!3)), C!2))))) | subset(unordered_pair(A!4, B!3), C!2) | (~((~in(tptp_fun_C_1(C!2, unordered_pair(A!4, B!3)), unordered_pair(A!4, B!3))) | in(tptp_fun_C_1(C!2, unordered_pair(A!4, B!3)), C!2)))),
% 0.13/0.42 inference(tautology,[status(thm)],[])).
% 0.13/0.42 tff(91,plain,
% 0.13/0.42 (subset(unordered_pair(A!4, B!3), C!2) | (~((~in(tptp_fun_C_1(C!2, unordered_pair(A!4, B!3)), unordered_pair(A!4, B!3))) | in(tptp_fun_C_1(C!2, unordered_pair(A!4, B!3)), C!2)))),
% 0.13/0.42 inference(unit_resolution,[status(thm)],[90, 89])).
% 0.13/0.42 tff(92,plain,
% 0.13/0.42 (~((~in(tptp_fun_C_1(C!2, unordered_pair(A!4, B!3)), unordered_pair(A!4, B!3))) | in(tptp_fun_C_1(C!2, unordered_pair(A!4, B!3)), C!2))),
% 0.13/0.42 inference(unit_resolution,[status(thm)],[91, 69])).
% 0.13/0.42 tff(93,plain,
% 0.13/0.42 (((~in(tptp_fun_C_1(C!2, unordered_pair(A!4, B!3)), unordered_pair(A!4, B!3))) | in(tptp_fun_C_1(C!2, unordered_pair(A!4, B!3)), C!2)) | in(tptp_fun_C_1(C!2, unordered_pair(A!4, B!3)), unordered_pair(A!4, B!3))),
% 0.13/0.42 inference(tautology,[status(thm)],[])).
% 0.13/0.42 tff(94,plain,
% 0.13/0.42 (in(tptp_fun_C_1(C!2, unordered_pair(A!4, B!3)), unordered_pair(A!4, B!3))),
% 0.13/0.42 inference(unit_resolution,[status(thm)],[93, 92])).
% 0.13/0.42 tff(95,plain,
% 0.13/0.42 (in(tptp_fun_C_1(C!2, unordered_pair(A!4, B!3)), unordered_pair(B!3, A!4))),
% 0.13/0.42 inference(modus_ponens,[status(thm)],[94, 48])).
% 0.13/0.42 tff(96,plain,
% 0.13/0.42 ((~(in(tptp_fun_C_1(C!2, unordered_pair(A!4, B!3)), unordered_pair(B!3, A!4)) <=> ((tptp_fun_C_1(C!2, unordered_pair(A!4, B!3)) = B!3) | (tptp_fun_C_1(C!2, unordered_pair(A!4, B!3)) = A!4)))) | (~in(tptp_fun_C_1(C!2, unordered_pair(A!4, B!3)), unordered_pair(B!3, A!4))) | ((tptp_fun_C_1(C!2, unordered_pair(A!4, B!3)) = B!3) | (tptp_fun_C_1(C!2, unordered_pair(A!4, B!3)) = A!4))),
% 0.13/0.42 inference(tautology,[status(thm)],[])).
% 0.13/0.42 tff(97,plain,
% 0.13/0.42 ((tptp_fun_C_1(C!2, unordered_pair(A!4, B!3)) = B!3) | (tptp_fun_C_1(C!2, unordered_pair(A!4, B!3)) = A!4)),
% 0.13/0.42 inference(unit_resolution,[status(thm)],[96, 95, 46])).
% 0.13/0.42 tff(98,plain,
% 0.13/0.42 (((~in(A!4, C!2)) | (~in(B!3, C!2))) | in(B!3, C!2)),
% 0.13/0.42 inference(tautology,[status(thm)],[])).
% 0.13/0.42 tff(99,plain,
% 0.13/0.42 (in(B!3, C!2)),
% 0.13/0.42 inference(unit_resolution,[status(thm)],[98, 49])).
% 0.13/0.42 tff(100,plain,
% 0.13/0.42 (((~in(tptp_fun_C_1(C!2, unordered_pair(A!4, B!3)), unordered_pair(A!4, B!3))) | in(tptp_fun_C_1(C!2, unordered_pair(A!4, B!3)), C!2)) | (~in(tptp_fun_C_1(C!2, unordered_pair(A!4, B!3)), C!2))),
% 0.13/0.42 inference(tautology,[status(thm)],[])).
% 0.13/0.42 tff(101,plain,
% 0.13/0.42 (~in(tptp_fun_C_1(C!2, unordered_pair(A!4, B!3)), C!2)),
% 0.13/0.42 inference(unit_resolution,[status(thm)],[100, 92])).
% 0.13/0.42 tff(102,assumption,(tptp_fun_C_1(C!2, unordered_pair(A!4, B!3)) = B!3), introduced(assumption)).
% 0.13/0.42 tff(103,plain,
% 0.13/0.42 (in(tptp_fun_C_1(C!2, unordered_pair(A!4, B!3)), C!2) <=> in(B!3, C!2)),
% 0.13/0.42 inference(monotonicity,[status(thm)],[102])).
% 0.13/0.42 tff(104,plain,
% 0.13/0.42 (in(B!3, C!2) <=> in(tptp_fun_C_1(C!2, unordered_pair(A!4, B!3)), C!2)),
% 0.13/0.42 inference(symmetry,[status(thm)],[103])).
% 0.13/0.42 tff(105,assumption,(in(B!3, C!2)), introduced(assumption)).
% 0.13/0.42 tff(106,plain,
% 0.13/0.42 (in(tptp_fun_C_1(C!2, unordered_pair(A!4, B!3)), C!2)),
% 0.13/0.42 inference(modus_ponens,[status(thm)],[105, 104])).
% 0.13/0.42 tff(107,assumption,(~in(tptp_fun_C_1(C!2, unordered_pair(A!4, B!3)), C!2)), introduced(assumption)).
% 0.13/0.42 tff(108,plain,
% 0.13/0.42 ($false),
% 0.13/0.42 inference(unit_resolution,[status(thm)],[107, 106])).
% 0.13/0.42 tff(109,plain,((~(tptp_fun_C_1(C!2, unordered_pair(A!4, B!3)) = B!3)) | in(tptp_fun_C_1(C!2, unordered_pair(A!4, B!3)), C!2) | (~in(B!3, C!2))), inference(lemma,lemma(discharge,[]))).
% 0.13/0.42 tff(110,plain,
% 0.13/0.42 (~(tptp_fun_C_1(C!2, unordered_pair(A!4, B!3)) = B!3)),
% 0.13/0.42 inference(unit_resolution,[status(thm)],[109, 101, 99])).
% 0.13/0.42 tff(111,plain,
% 0.13/0.42 ((~((tptp_fun_C_1(C!2, unordered_pair(A!4, B!3)) = B!3) | (tptp_fun_C_1(C!2, unordered_pair(A!4, B!3)) = A!4))) | (tptp_fun_C_1(C!2, unordered_pair(A!4, B!3)) = B!3) | (tptp_fun_C_1(C!2, unordered_pair(A!4, B!3)) = A!4)),
% 0.13/0.42 inference(tautology,[status(thm)],[])).
% 0.13/0.42 tff(112,plain,
% 0.13/0.42 (tptp_fun_C_1(C!2, unordered_pair(A!4, B!3)) = A!4),
% 0.13/0.42 inference(unit_resolution,[status(thm)],[111, 110, 97])).
% 0.13/0.42 tff(113,plain,
% 0.13/0.42 (in(tptp_fun_C_1(C!2, unordered_pair(A!4, B!3)), C!2) <=> in(A!4, C!2)),
% 0.13/0.42 inference(monotonicity,[status(thm)],[112])).
% 0.13/0.42 tff(114,plain,
% 0.13/0.42 (in(A!4, C!2) <=> in(tptp_fun_C_1(C!2, unordered_pair(A!4, B!3)), C!2)),
% 0.13/0.42 inference(symmetry,[status(thm)],[113])).
% 0.13/0.42 tff(115,plain,
% 0.13/0.42 (((~in(A!4, C!2)) | (~in(B!3, C!2))) | in(A!4, C!2)),
% 0.13/0.42 inference(tautology,[status(thm)],[])).
% 0.13/0.42 tff(116,plain,
% 0.13/0.42 (in(A!4, C!2)),
% 0.13/0.42 inference(unit_resolution,[status(thm)],[115, 49])).
% 0.13/0.42 tff(117,plain,
% 0.13/0.42 (in(tptp_fun_C_1(C!2, unordered_pair(A!4, B!3)), C!2)),
% 0.13/0.42 inference(modus_ponens,[status(thm)],[116, 114])).
% 0.13/0.42 tff(118,plain,
% 0.13/0.42 ($false),
% 0.13/0.42 inference(unit_resolution,[status(thm)],[101, 117])).
% 0.13/0.42 tff(119,plain,((~in(A!4, C!2)) | (~in(B!3, C!2))), inference(lemma,lemma(discharge,[]))).
% 0.13/0.42 tff(120,plain,
% 0.13/0.42 (subset(unordered_pair(A!4, B!3), C!2) | (~((~in(A!4, C!2)) | (~in(B!3, C!2)))) | (~(subset(unordered_pair(A!4, B!3), C!2) <=> ((~in(A!4, C!2)) | (~in(B!3, C!2)))))),
% 0.13/0.42 inference(tautology,[status(thm)],[])).
% 0.13/0.42 tff(121,plain,
% 0.13/0.42 (subset(unordered_pair(A!4, B!3), C!2) | (~((~in(A!4, C!2)) | (~in(B!3, C!2))))),
% 0.13/0.42 inference(unit_resolution,[status(thm)],[120, 66])).
% 0.13/0.42 tff(122,plain,
% 0.13/0.42 (subset(unordered_pair(A!4, B!3), C!2)),
% 0.13/0.42 inference(unit_resolution,[status(thm)],[121, 119])).
% 0.13/0.42 tff(123,plain,
% 0.13/0.42 (((~((~subset(unordered_pair(A!4, B!3), C!2)) | ![C: $i] : ((~in(C, unordered_pair(A!4, B!3))) | in(C, C!2)))) | (~(subset(unordered_pair(A!4, B!3), C!2) | (~((~in(tptp_fun_C_1(C!2, unordered_pair(A!4, B!3)), unordered_pair(A!4, B!3))) | in(tptp_fun_C_1(C!2, unordered_pair(A!4, B!3)), C!2)))))) | ((~subset(unordered_pair(A!4, B!3), C!2)) | ![C: $i] : ((~in(C, unordered_pair(A!4, B!3))) | in(C, C!2)))),
% 0.13/0.42 inference(tautology,[status(thm)],[])).
% 0.13/0.42 tff(124,plain,
% 0.13/0.42 ((~subset(unordered_pair(A!4, B!3), C!2)) | ![C: $i] : ((~in(C, unordered_pair(A!4, B!3))) | in(C, C!2))),
% 0.13/0.42 inference(unit_resolution,[status(thm)],[123, 87])).
% 0.13/0.42 tff(125,plain,
% 0.13/0.42 ((~((~subset(unordered_pair(A!4, B!3), C!2)) | ![C: $i] : ((~in(C, unordered_pair(A!4, B!3))) | in(C, C!2)))) | (~subset(unordered_pair(A!4, B!3), C!2)) | ![C: $i] : ((~in(C, unordered_pair(A!4, B!3))) | in(C, C!2))),
% 0.13/0.42 inference(tautology,[status(thm)],[])).
% 0.13/0.42 tff(126,plain,
% 0.13/0.42 ((~subset(unordered_pair(A!4, B!3), C!2)) | ![C: $i] : ((~in(C, unordered_pair(A!4, B!3))) | in(C, C!2))),
% 0.13/0.42 inference(unit_resolution,[status(thm)],[125, 124])).
% 0.13/0.42 tff(127,plain,
% 0.13/0.42 (![C: $i] : ((~in(C, unordered_pair(A!4, B!3))) | in(C, C!2))),
% 0.13/0.42 inference(unit_resolution,[status(thm)],[126, 122])).
% 0.13/0.42 tff(128,plain,
% 0.13/0.42 (in(B!3, unordered_pair(B!3, A!4)) <=> in(B!3, unordered_pair(A!4, B!3))),
% 0.13/0.42 inference(monotonicity,[status(thm)],[10])).
% 0.13/0.42 tff(129,plain,
% 0.13/0.42 (in(B!3, unordered_pair(A!4, B!3)) <=> in(B!3, unordered_pair(B!3, A!4))),
% 0.13/0.42 inference(symmetry,[status(thm)],[128])).
% 0.13/0.42 tff(130,plain,
% 0.13/0.42 ((~in(B!3, unordered_pair(A!4, B!3))) <=> (~in(B!3, unordered_pair(B!3, A!4)))),
% 0.13/0.42 inference(monotonicity,[status(thm)],[129])).
% 0.13/0.42 tff(131,assumption,(~in(B!3, unordered_pair(A!4, B!3))), introduced(assumption)).
% 0.13/0.42 tff(132,plain,
% 0.13/0.42 (~in(B!3, unordered_pair(B!3, A!4))),
% 0.13/0.42 inference(modus_ponens,[status(thm)],[131, 130])).
% 0.13/0.42 tff(133,plain,
% 0.13/0.42 (((~![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(B!3, unordered_pair(B!3, A!4))) <=> ((~![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(B!3, unordered_pair(B!3, A!4)))),
% 0.13/0.42 inference(rewrite,[status(thm)],[])).
% 0.13/0.42 tff(134,plain,
% 0.13/0.42 ((~(~in(B!3, unordered_pair(B!3, A!4)))) <=> in(B!3, unordered_pair(B!3, A!4))),
% 0.13/0.42 inference(rewrite,[status(thm)],[])).
% 0.13/0.42 tff(135,plain,
% 0.13/0.42 (((~in(B!3, unordered_pair(B!3, A!4))) | $false) <=> (~in(B!3, unordered_pair(B!3, A!4)))),
% 0.13/0.42 inference(rewrite,[status(thm)],[])).
% 0.13/0.42 tff(136,plain,
% 0.13/0.42 ((~$true) <=> $false),
% 0.13/0.42 inference(rewrite,[status(thm)],[])).
% 0.13/0.42 tff(137,plain,
% 0.13/0.42 (($true | ((~in(tptp_fun_D_0(unordered_pair(B!3, A!4), A!4, B!3), unordered_pair(B!3, A!4))) <=> ((tptp_fun_D_0(unordered_pair(B!3, A!4), A!4, B!3) = A!4) | (tptp_fun_D_0(unordered_pair(B!3, A!4), A!4, B!3) = B!3)))) <=> $true),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(138,plain,
% 0.20/0.43 ((unordered_pair(B!3, A!4) = unordered_pair(B!3, A!4)) <=> $true),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(139,plain,
% 0.20/0.43 (((unordered_pair(B!3, A!4) = unordered_pair(B!3, A!4)) | ((~in(tptp_fun_D_0(unordered_pair(B!3, A!4), A!4, B!3), unordered_pair(B!3, A!4))) <=> ((tptp_fun_D_0(unordered_pair(B!3, A!4), A!4, B!3) = A!4) | (tptp_fun_D_0(unordered_pair(B!3, A!4), A!4, B!3) = B!3)))) <=> ($true | ((~in(tptp_fun_D_0(unordered_pair(B!3, A!4), A!4, B!3), unordered_pair(B!3, A!4))) <=> ((tptp_fun_D_0(unordered_pair(B!3, A!4), A!4, B!3) = A!4) | (tptp_fun_D_0(unordered_pair(B!3, A!4), A!4, B!3) = B!3))))),
% 0.20/0.43 inference(monotonicity,[status(thm)],[138])).
% 0.20/0.43 tff(140,plain,
% 0.20/0.43 (((unordered_pair(B!3, A!4) = unordered_pair(B!3, A!4)) | ((~in(tptp_fun_D_0(unordered_pair(B!3, A!4), A!4, B!3), unordered_pair(B!3, A!4))) <=> ((tptp_fun_D_0(unordered_pair(B!3, A!4), A!4, B!3) = A!4) | (tptp_fun_D_0(unordered_pair(B!3, A!4), A!4, B!3) = B!3)))) <=> $true),
% 0.20/0.43 inference(transitivity,[status(thm)],[139, 137])).
% 0.20/0.43 tff(141,plain,
% 0.20/0.43 ((~((unordered_pair(B!3, A!4) = unordered_pair(B!3, A!4)) | ((~in(tptp_fun_D_0(unordered_pair(B!3, A!4), A!4, B!3), unordered_pair(B!3, A!4))) <=> ((tptp_fun_D_0(unordered_pair(B!3, A!4), A!4, B!3) = A!4) | (tptp_fun_D_0(unordered_pair(B!3, A!4), A!4, B!3) = B!3))))) <=> (~$true)),
% 0.20/0.43 inference(monotonicity,[status(thm)],[140])).
% 0.20/0.43 tff(142,plain,
% 0.20/0.43 ((~((unordered_pair(B!3, A!4) = unordered_pair(B!3, A!4)) | ((~in(tptp_fun_D_0(unordered_pair(B!3, A!4), A!4, B!3), unordered_pair(B!3, A!4))) <=> ((tptp_fun_D_0(unordered_pair(B!3, A!4), A!4, B!3) = A!4) | (tptp_fun_D_0(unordered_pair(B!3, A!4), A!4, B!3) = B!3))))) <=> $false),
% 0.20/0.43 inference(transitivity,[status(thm)],[141, 136])).
% 0.20/0.43 tff(143,plain,
% 0.20/0.43 ((~((~(unordered_pair(B!3, A!4) = unordered_pair(B!3, A!4))) | (in(B!3, unordered_pair(B!3, A!4)) <=> ((B!3 = A!4) | (B!3 = B!3))))) <=> (~in(B!3, unordered_pair(B!3, A!4)))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(144,plain,
% 0.20/0.43 (((~((~(unordered_pair(B!3, A!4) = unordered_pair(B!3, A!4))) | (in(B!3, unordered_pair(B!3, A!4)) <=> ((B!3 = A!4) | (B!3 = B!3))))) | (~((unordered_pair(B!3, A!4) = unordered_pair(B!3, A!4)) | ((~in(tptp_fun_D_0(unordered_pair(B!3, A!4), A!4, B!3), unordered_pair(B!3, A!4))) <=> ((tptp_fun_D_0(unordered_pair(B!3, A!4), A!4, B!3) = A!4) | (tptp_fun_D_0(unordered_pair(B!3, A!4), A!4, B!3) = B!3)))))) <=> ((~in(B!3, unordered_pair(B!3, A!4))) | $false)),
% 0.20/0.43 inference(monotonicity,[status(thm)],[143, 142])).
% 0.20/0.43 tff(145,plain,
% 0.20/0.43 (((~((~(unordered_pair(B!3, A!4) = unordered_pair(B!3, A!4))) | (in(B!3, unordered_pair(B!3, A!4)) <=> ((B!3 = A!4) | (B!3 = B!3))))) | (~((unordered_pair(B!3, A!4) = unordered_pair(B!3, A!4)) | ((~in(tptp_fun_D_0(unordered_pair(B!3, A!4), A!4, B!3), unordered_pair(B!3, A!4))) <=> ((tptp_fun_D_0(unordered_pair(B!3, A!4), A!4, B!3) = A!4) | (tptp_fun_D_0(unordered_pair(B!3, A!4), A!4, B!3) = B!3)))))) <=> (~in(B!3, unordered_pair(B!3, A!4)))),
% 0.20/0.43 inference(transitivity,[status(thm)],[144, 135])).
% 0.20/0.43 tff(146,plain,
% 0.20/0.43 ((~((~((~(unordered_pair(B!3, A!4) = unordered_pair(B!3, A!4))) | (in(B!3, unordered_pair(B!3, A!4)) <=> ((B!3 = A!4) | (B!3 = B!3))))) | (~((unordered_pair(B!3, A!4) = unordered_pair(B!3, A!4)) | ((~in(tptp_fun_D_0(unordered_pair(B!3, A!4), A!4, B!3), unordered_pair(B!3, A!4))) <=> ((tptp_fun_D_0(unordered_pair(B!3, A!4), A!4, B!3) = A!4) | (tptp_fun_D_0(unordered_pair(B!3, A!4), A!4, B!3) = B!3))))))) <=> (~(~in(B!3, unordered_pair(B!3, A!4))))),
% 0.20/0.43 inference(monotonicity,[status(thm)],[145])).
% 0.20/0.43 tff(147,plain,
% 0.20/0.43 ((~((~((~(unordered_pair(B!3, A!4) = unordered_pair(B!3, A!4))) | (in(B!3, unordered_pair(B!3, A!4)) <=> ((B!3 = A!4) | (B!3 = B!3))))) | (~((unordered_pair(B!3, A!4) = unordered_pair(B!3, A!4)) | ((~in(tptp_fun_D_0(unordered_pair(B!3, A!4), A!4, B!3), unordered_pair(B!3, A!4))) <=> ((tptp_fun_D_0(unordered_pair(B!3, A!4), A!4, B!3) = A!4) | (tptp_fun_D_0(unordered_pair(B!3, A!4), A!4, B!3) = B!3))))))) <=> in(B!3, unordered_pair(B!3, A!4))),
% 0.20/0.43 inference(transitivity,[status(thm)],[146, 134])).
% 0.20/0.43 tff(148,plain,
% 0.20/0.43 (((~![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(B!3, A!4) = unordered_pair(B!3, A!4))) | (in(B!3, unordered_pair(B!3, A!4)) <=> ((B!3 = A!4) | (B!3 = B!3))))) | (~((unordered_pair(B!3, A!4) = unordered_pair(B!3, A!4)) | ((~in(tptp_fun_D_0(unordered_pair(B!3, A!4), A!4, B!3), unordered_pair(B!3, A!4))) <=> ((tptp_fun_D_0(unordered_pair(B!3, A!4), A!4, B!3) = A!4) | (tptp_fun_D_0(unordered_pair(B!3, A!4), A!4, B!3) = B!3)))))))) <=> ((~![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(B!3, unordered_pair(B!3, A!4)))),
% 0.20/0.43 inference(monotonicity,[status(thm)],[147])).
% 0.20/0.43 tff(149,plain,
% 0.20/0.43 (((~![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(B!3, A!4) = unordered_pair(B!3, A!4))) | (in(B!3, unordered_pair(B!3, A!4)) <=> ((B!3 = A!4) | (B!3 = B!3))))) | (~((unordered_pair(B!3, A!4) = unordered_pair(B!3, A!4)) | ((~in(tptp_fun_D_0(unordered_pair(B!3, A!4), A!4, B!3), unordered_pair(B!3, A!4))) <=> ((tptp_fun_D_0(unordered_pair(B!3, A!4), A!4, B!3) = A!4) | (tptp_fun_D_0(unordered_pair(B!3, A!4), A!4, B!3) = B!3)))))))) <=> ((~![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(B!3, unordered_pair(B!3, A!4)))),
% 0.20/0.43 inference(transitivity,[status(thm)],[148, 133])).
% 0.20/0.43 tff(150,plain,
% 0.20/0.43 ((~![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(B!3, A!4) = unordered_pair(B!3, A!4))) | (in(B!3, unordered_pair(B!3, A!4)) <=> ((B!3 = A!4) | (B!3 = B!3))))) | (~((unordered_pair(B!3, A!4) = unordered_pair(B!3, A!4)) | ((~in(tptp_fun_D_0(unordered_pair(B!3, A!4), A!4, B!3), unordered_pair(B!3, A!4))) <=> ((tptp_fun_D_0(unordered_pair(B!3, A!4), A!4, B!3) = A!4) | (tptp_fun_D_0(unordered_pair(B!3, A!4), A!4, B!3) = B!3)))))))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(151,plain,
% 0.20/0.43 ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A)))))))) | in(B!3, unordered_pair(B!3, A!4))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[150, 149])).
% 0.20/0.43 tff(152,plain,
% 0.20/0.43 (in(B!3, unordered_pair(B!3, A!4))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[151, 37])).
% 0.20/0.43 tff(153,plain,
% 0.20/0.43 ($false),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[152, 132])).
% 0.20/0.43 tff(154,plain,(in(B!3, unordered_pair(A!4, B!3))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.43 tff(155,plain,
% 0.20/0.43 (((~![C: $i] : ((~in(C, unordered_pair(A!4, B!3))) | in(C, C!2))) | ((~in(B!3, unordered_pair(A!4, B!3))) | in(B!3, C!2))) <=> ((~![C: $i] : ((~in(C, unordered_pair(A!4, B!3))) | in(C, C!2))) | (~in(B!3, unordered_pair(A!4, B!3))) | in(B!3, C!2))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(156,plain,
% 0.20/0.43 ((~![C: $i] : ((~in(C, unordered_pair(A!4, B!3))) | in(C, C!2))) | ((~in(B!3, unordered_pair(A!4, B!3))) | in(B!3, C!2))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(157,plain,
% 0.20/0.43 ((~![C: $i] : ((~in(C, unordered_pair(A!4, B!3))) | in(C, C!2))) | (~in(B!3, unordered_pair(A!4, B!3))) | in(B!3, C!2)),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[156, 155])).
% 0.20/0.44 tff(158,plain,
% 0.20/0.44 (in(B!3, C!2)),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[157, 127, 154])).
% 0.20/0.44 tff(159,plain,
% 0.20/0.44 ((~((~in(A!4, C!2)) | (~in(B!3, C!2)))) | (~in(A!4, C!2)) | (~in(B!3, C!2))),
% 0.20/0.44 inference(tautology,[status(thm)],[])).
% 0.20/0.44 tff(160,plain,
% 0.20/0.44 ((~in(A!4, C!2)) | (~in(B!3, C!2))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[159, 119])).
% 0.20/0.44 tff(161,plain,
% 0.20/0.44 (~in(A!4, C!2)),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[160, 158])).
% 0.20/0.44 tff(162,plain,
% 0.20/0.44 (((~![C: $i] : ((~in(C, unordered_pair(A!4, B!3))) | in(C, C!2))) | ((~in(A!4, unordered_pair(A!4, B!3))) | in(A!4, C!2))) <=> ((~![C: $i] : ((~in(C, unordered_pair(A!4, B!3))) | in(C, C!2))) | (~in(A!4, unordered_pair(A!4, B!3))) | in(A!4, C!2))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(163,plain,
% 0.20/0.44 ((~![C: $i] : ((~in(C, unordered_pair(A!4, B!3))) | in(C, C!2))) | ((~in(A!4, unordered_pair(A!4, B!3))) | in(A!4, C!2))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(164,plain,
% 0.20/0.44 ((~![C: $i] : ((~in(C, unordered_pair(A!4, B!3))) | in(C, C!2))) | (~in(A!4, unordered_pair(A!4, B!3))) | in(A!4, C!2)),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[163, 162])).
% 0.20/0.44 tff(165,plain,
% 0.20/0.44 (~in(A!4, unordered_pair(A!4, B!3))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[164, 161, 127])).
% 0.20/0.44 tff(166,plain,
% 0.20/0.44 (~in(A!4, unordered_pair(B!3, A!4))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[165, 13])).
% 0.20/0.44 tff(167,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)))))))) | in(A!4, unordered_pair(B!3, A!4))) <=> ((~![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!4, unordered_pair(B!3, A!4)))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(168,plain,
% 0.20/0.44 ((~(~in(A!4, unordered_pair(B!3, A!4)))) <=> in(A!4, unordered_pair(B!3, A!4))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(169,plain,
% 0.20/0.44 (((~in(A!4, unordered_pair(B!3, A!4))) | $false) <=> (~in(A!4, unordered_pair(B!3, A!4)))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(170,plain,
% 0.20/0.44 ((~((~(unordered_pair(B!3, A!4) = unordered_pair(B!3, A!4))) | (in(A!4, unordered_pair(B!3, A!4)) <=> ((A!4 = A!4) | (A!4 = B!3))))) <=> (~in(A!4, unordered_pair(B!3, A!4)))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(171,plain,
% 0.20/0.44 (((~((~(unordered_pair(B!3, A!4) = unordered_pair(B!3, A!4))) | (in(A!4, unordered_pair(B!3, A!4)) <=> ((A!4 = A!4) | (A!4 = B!3))))) | (~((unordered_pair(B!3, A!4) = unordered_pair(B!3, A!4)) | ((~in(tptp_fun_D_0(unordered_pair(B!3, A!4), A!4, B!3), unordered_pair(B!3, A!4))) <=> ((tptp_fun_D_0(unordered_pair(B!3, A!4), A!4, B!3) = A!4) | (tptp_fun_D_0(unordered_pair(B!3, A!4), A!4, B!3) = B!3)))))) <=> ((~in(A!4, unordered_pair(B!3, A!4))) | $false)),
% 0.20/0.44 inference(monotonicity,[status(thm)],[170, 142])).
% 0.20/0.44 tff(172,plain,
% 0.20/0.44 (((~((~(unordered_pair(B!3, A!4) = unordered_pair(B!3, A!4))) | (in(A!4, unordered_pair(B!3, A!4)) <=> ((A!4 = A!4) | (A!4 = B!3))))) | (~((unordered_pair(B!3, A!4) = unordered_pair(B!3, A!4)) | ((~in(tptp_fun_D_0(unordered_pair(B!3, A!4), A!4, B!3), unordered_pair(B!3, A!4))) <=> ((tptp_fun_D_0(unordered_pair(B!3, A!4), A!4, B!3) = A!4) | (tptp_fun_D_0(unordered_pair(B!3, A!4), A!4, B!3) = B!3)))))) <=> (~in(A!4, unordered_pair(B!3, A!4)))),
% 0.20/0.44 inference(transitivity,[status(thm)],[171, 169])).
% 0.20/0.44 tff(173,plain,
% 0.20/0.44 ((~((~((~(unordered_pair(B!3, A!4) = unordered_pair(B!3, A!4))) | (in(A!4, unordered_pair(B!3, A!4)) <=> ((A!4 = A!4) | (A!4 = B!3))))) | (~((unordered_pair(B!3, A!4) = unordered_pair(B!3, A!4)) | ((~in(tptp_fun_D_0(unordered_pair(B!3, A!4), A!4, B!3), unordered_pair(B!3, A!4))) <=> ((tptp_fun_D_0(unordered_pair(B!3, A!4), A!4, B!3) = A!4) | (tptp_fun_D_0(unordered_pair(B!3, A!4), A!4, B!3) = B!3))))))) <=> (~(~in(A!4, unordered_pair(B!3, A!4))))),
% 0.20/0.44 inference(monotonicity,[status(thm)],[172])).
% 0.20/0.44 tff(174,plain,
% 0.20/0.44 ((~((~((~(unordered_pair(B!3, A!4) = unordered_pair(B!3, A!4))) | (in(A!4, unordered_pair(B!3, A!4)) <=> ((A!4 = A!4) | (A!4 = B!3))))) | (~((unordered_pair(B!3, A!4) = unordered_pair(B!3, A!4)) | ((~in(tptp_fun_D_0(unordered_pair(B!3, A!4), A!4, B!3), unordered_pair(B!3, A!4))) <=> ((tptp_fun_D_0(unordered_pair(B!3, A!4), A!4, B!3) = A!4) | (tptp_fun_D_0(unordered_pair(B!3, A!4), A!4, B!3) = B!3))))))) <=> in(A!4, unordered_pair(B!3, A!4))),
% 0.20/0.44 inference(transitivity,[status(thm)],[173, 168])).
% 0.20/0.44 tff(175,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(B!3, A!4) = unordered_pair(B!3, A!4))) | (in(A!4, unordered_pair(B!3, A!4)) <=> ((A!4 = A!4) | (A!4 = B!3))))) | (~((unordered_pair(B!3, A!4) = unordered_pair(B!3, A!4)) | ((~in(tptp_fun_D_0(unordered_pair(B!3, A!4), A!4, B!3), unordered_pair(B!3, A!4))) <=> ((tptp_fun_D_0(unordered_pair(B!3, A!4), A!4, B!3) = A!4) | (tptp_fun_D_0(unordered_pair(B!3, A!4), A!4, B!3) = B!3)))))))) <=> ((~![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!4, unordered_pair(B!3, A!4)))),
% 0.20/0.44 inference(monotonicity,[status(thm)],[174])).
% 0.20/0.44 tff(176,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(B!3, A!4) = unordered_pair(B!3, A!4))) | (in(A!4, unordered_pair(B!3, A!4)) <=> ((A!4 = A!4) | (A!4 = B!3))))) | (~((unordered_pair(B!3, A!4) = unordered_pair(B!3, A!4)) | ((~in(tptp_fun_D_0(unordered_pair(B!3, A!4), A!4, B!3), unordered_pair(B!3, A!4))) <=> ((tptp_fun_D_0(unordered_pair(B!3, A!4), A!4, B!3) = A!4) | (tptp_fun_D_0(unordered_pair(B!3, A!4), A!4, B!3) = B!3)))))))) <=> ((~![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!4, unordered_pair(B!3, A!4)))),
% 0.20/0.44 inference(transitivity,[status(thm)],[175, 167])).
% 0.20/0.44 tff(177,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(B!3, A!4) = unordered_pair(B!3, A!4))) | (in(A!4, unordered_pair(B!3, A!4)) <=> ((A!4 = A!4) | (A!4 = B!3))))) | (~((unordered_pair(B!3, A!4) = unordered_pair(B!3, A!4)) | ((~in(tptp_fun_D_0(unordered_pair(B!3, A!4), A!4, B!3), unordered_pair(B!3, A!4))) <=> ((tptp_fun_D_0(unordered_pair(B!3, A!4), A!4, B!3) = A!4) | (tptp_fun_D_0(unordered_pair(B!3, A!4), A!4, B!3) = B!3)))))))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(178,plain,
% 0.20/0.44 ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A)))))))) | in(A!4, unordered_pair(B!3, A!4))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[177, 176])).
% 0.20/0.44 tff(179,plain,
% 0.20/0.44 (in(A!4, unordered_pair(B!3, A!4))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[178, 37])).
% 0.20/0.44 tff(180,plain,
% 0.20/0.44 ($false),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[179, 166])).
% 0.20/0.44 % SZS output end Proof
%------------------------------------------------------------------------------