TSTP Solution File: SEU142+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SEU142+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n004.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 07:27:43 EDT 2022
% Result : Theorem 0.19s 0.40s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : SEU142+1 : TPTP v8.1.0. Released v3.3.0.
% 0.11/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n004.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Sat Sep 3 09:35:34 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.33 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.33 Usage: tptp [options] [-file:]file
% 0.12/0.33 -h, -? prints this message.
% 0.12/0.33 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.33 -m, -model generate model.
% 0.12/0.33 -p, -proof generate proof.
% 0.12/0.33 -c, -core generate unsat core of named formulas.
% 0.12/0.33 -st, -statistics display statistics.
% 0.12/0.33 -t:timeout set timeout (in second).
% 0.12/0.33 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.33 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.33 -<param>:<value> configuration parameter and value.
% 0.12/0.33 -o:<output-file> file to place output in.
% 0.19/0.40 % SZS status Theorem
% 0.19/0.40 % SZS output start Proof
% 0.19/0.40 tff(tptp_fun_A_3_type, type, (
% 0.19/0.40 tptp_fun_A_3: $i)).
% 0.19/0.40 tff(tptp_fun_C_0_type, type, (
% 0.19/0.40 tptp_fun_C_0: ( $i * $i ) > $i)).
% 0.19/0.40 tff(unordered_pair_type, type, (
% 0.19/0.40 unordered_pair: ( $i * $i ) > $i)).
% 0.19/0.40 tff(in_type, type, (
% 0.19/0.40 in: ( $i * $i ) > $o)).
% 0.19/0.40 tff(singleton_type, type, (
% 0.19/0.40 singleton: $i > $i)).
% 0.19/0.40 tff(tptp_fun_D_1_type, type, (
% 0.19/0.40 tptp_fun_D_1: ( $i * $i * $i ) > $i)).
% 0.19/0.40 tff(1,plain,
% 0.19/0.40 (^[A: $i, B: $i, C: $i] : refl((~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A)))))) <=> (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A)))))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(2,plain,
% 0.19/0.40 (![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A)))))) <=> ![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[1])).
% 0.19/0.40 tff(3,plain,
% 0.19/0.40 (![A: $i, B: $i] : ![C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A)))))) <=> ![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))))),
% 0.19/0.40 inference(pull_quant,[status(thm)],[])).
% 0.19/0.40 tff(4,plain,
% 0.19/0.40 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(pull_quant(((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A))) <=> ![C: $i] : ((~(B = singleton(A))) | (in(C, B) <=> (C = A)))), ((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) <=> (~![C: $i] : ((~(B = singleton(A))) | (in(C, B) <=> (C = A)))))), pull_quant((~![C: $i] : ((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) <=> ?[C: $i] : (~((~(B = singleton(A))) | (in(C, B) <=> (C = A))))), ((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) <=> ?[C: $i] : (~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))))), (((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))) <=> (?[C: $i] : (~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))))), pull_quant((?[C: $i] : (~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))) <=> ?[C: $i] : ((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A)))))), (((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))) <=> ?[C: $i] : ((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))))), ((~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A)))))) <=> (~?[C: $i] : ((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A)))))))), pull_quant((~?[C: $i] : ((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A)))))) <=> ![C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))))), ((~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A)))))) <=> ![C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(5,plain,
% 0.19/0.41 (![A: $i, B: $i] : (~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A)))))) <=> ![A: $i, B: $i] : ![C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[4])).
% 0.19/0.41 tff(6,plain,
% 0.19/0.41 (![A: $i, B: $i] : (~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A)))))) <=> ![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))))),
% 0.19/0.41 inference(transitivity,[status(thm)],[5, 3])).
% 0.19/0.41 tff(7,plain,
% 0.19/0.41 (![A: $i, B: $i] : (~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A)))))) <=> ![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))))),
% 0.19/0.41 inference(transitivity,[status(thm)],[6, 2])).
% 0.19/0.41 tff(8,plain,
% 0.19/0.41 (^[A: $i, B: $i] : rewrite((~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A)))))) <=> (~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A)))))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(9,plain,
% 0.19/0.41 (![A: $i, B: $i] : (~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A)))))) <=> ![A: $i, B: $i] : (~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[8])).
% 0.19/0.41 tff(10,plain,
% 0.19/0.41 (![A: $i, B: $i] : (~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A)))))) <=> ![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))))),
% 0.19/0.41 inference(transitivity,[status(thm)],[9, 7])).
% 0.19/0.41 tff(11,plain,
% 0.19/0.41 (^[A: $i, B: $i] : trans(monotonicity(rewrite(((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A))) <=> ((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))), ((((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A))) & ((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A)))) <=> (((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A))) & ((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A)))))), rewrite((((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A))) & ((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A)))) <=> (~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))))), ((((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A))) & ((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A)))) <=> (~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(12,plain,
% 0.19/0.41 (![A: $i, B: $i] : (((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A))) & ((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A)))) <=> ![A: $i, B: $i] : (~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[11])).
% 0.19/0.41 tff(13,plain,
% 0.19/0.41 (^[A: $i, B: $i] : rewrite((((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A))) & ((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A))))) <=> (((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A))) & ((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A)))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(14,plain,
% 0.19/0.41 (![A: $i, B: $i] : (((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A))) & ((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A))))) <=> ![A: $i, B: $i] : (((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A))) & ((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[13])).
% 0.19/0.41 tff(15,plain,
% 0.19/0.41 (![A: $i, B: $i] : ((B = singleton(A)) <=> ![C: $i] : (in(C, B) <=> (C = A))) <=> ![A: $i, B: $i] : ((B = singleton(A)) <=> ![C: $i] : (in(C, B) <=> (C = A)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(16,axiom,(![A: $i, B: $i] : ((B = singleton(A)) <=> ![C: $i] : (in(C, B) <=> (C = A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d1_tarski')).
% 0.19/0.41 tff(17,plain,
% 0.19/0.41 (![A: $i, B: $i] : ((B = singleton(A)) <=> ![C: $i] : (in(C, B) <=> (C = A)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[16, 15])).
% 0.19/0.41 tff(18,plain,(
% 0.19/0.41 ![A: $i, B: $i] : (((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A))) & ((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))),
% 0.19/0.41 inference(skolemize,[status(sab)],[17])).
% 0.19/0.41 tff(19,plain,
% 0.19/0.41 (![A: $i, B: $i] : (((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A))) & ((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[18, 14])).
% 0.19/0.41 tff(20,plain,
% 0.19/0.41 (![A: $i, B: $i] : (~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[19, 12])).
% 0.19/0.41 tff(21,plain,
% 0.19/0.41 (![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[20, 10])).
% 0.19/0.41 tff(22,plain,
% 0.19/0.41 ((~![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))))) | (~((~((~(unordered_pair(A!3, A!3) = singleton(A!3))) | (in(tptp_fun_C_0(unordered_pair(A!3, A!3), A!3), unordered_pair(A!3, A!3)) <=> (tptp_fun_C_0(unordered_pair(A!3, A!3), A!3) = A!3)))) | (~((unordered_pair(A!3, A!3) = singleton(A!3)) | ((~in(tptp_fun_C_0(unordered_pair(A!3, A!3), A!3), unordered_pair(A!3, A!3))) <=> (tptp_fun_C_0(unordered_pair(A!3, A!3), A!3) = A!3))))))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(23,plain,
% 0.19/0.41 (~((~((~(unordered_pair(A!3, A!3) = singleton(A!3))) | (in(tptp_fun_C_0(unordered_pair(A!3, A!3), A!3), unordered_pair(A!3, A!3)) <=> (tptp_fun_C_0(unordered_pair(A!3, A!3), A!3) = A!3)))) | (~((unordered_pair(A!3, A!3) = singleton(A!3)) | ((~in(tptp_fun_C_0(unordered_pair(A!3, A!3), A!3), unordered_pair(A!3, A!3))) <=> (tptp_fun_C_0(unordered_pair(A!3, A!3), A!3) = A!3)))))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[22, 21])).
% 0.19/0.41 tff(24,plain,
% 0.19/0.41 (((~((~(unordered_pair(A!3, A!3) = singleton(A!3))) | (in(tptp_fun_C_0(unordered_pair(A!3, A!3), A!3), unordered_pair(A!3, A!3)) <=> (tptp_fun_C_0(unordered_pair(A!3, A!3), A!3) = A!3)))) | (~((unordered_pair(A!3, A!3) = singleton(A!3)) | ((~in(tptp_fun_C_0(unordered_pair(A!3, A!3), A!3), unordered_pair(A!3, A!3))) <=> (tptp_fun_C_0(unordered_pair(A!3, A!3), A!3) = A!3))))) | ((unordered_pair(A!3, A!3) = singleton(A!3)) | ((~in(tptp_fun_C_0(unordered_pair(A!3, A!3), A!3), unordered_pair(A!3, A!3))) <=> (tptp_fun_C_0(unordered_pair(A!3, A!3), A!3) = A!3)))),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(25,plain,
% 0.19/0.41 ((unordered_pair(A!3, A!3) = singleton(A!3)) | ((~in(tptp_fun_C_0(unordered_pair(A!3, A!3), A!3), unordered_pair(A!3, A!3))) <=> (tptp_fun_C_0(unordered_pair(A!3, A!3), A!3) = A!3))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[24, 23])).
% 0.19/0.41 tff(26,plain,
% 0.19/0.41 (^[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_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(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_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A))))))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(27,plain,
% 0.19/0.41 (![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_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(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_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A)))))))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[26])).
% 0.19/0.41 tff(28,plain,
% 0.19/0.41 (![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_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(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_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A)))))))),
% 0.19/0.41 inference(pull_quant,[status(thm)],[])).
% 0.19/0.41 tff(29,plain,
% 0.19/0.41 (^[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_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(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_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(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_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(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_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(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_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(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_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(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_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(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_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(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_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(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_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(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_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(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_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A)))))))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(30,plain,
% 0.19/0.41 (![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_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(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_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A)))))))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[29])).
% 0.19/0.41 tff(31,plain,
% 0.19/0.41 (![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_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(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_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A)))))))),
% 0.19/0.41 inference(transitivity,[status(thm)],[30, 28])).
% 0.19/0.41 tff(32,plain,
% 0.19/0.41 (![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_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(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_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A)))))))),
% 0.19/0.41 inference(transitivity,[status(thm)],[31, 27])).
% 0.19/0.41 tff(33,plain,
% 0.19/0.41 (^[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_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(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_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A))))))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(34,plain,
% 0.19/0.41 (![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_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(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_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A)))))))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[33])).
% 0.19/0.41 tff(35,plain,
% 0.19/0.41 (![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_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(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_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A)))))))),
% 0.19/0.41 inference(transitivity,[status(thm)],[34, 32])).
% 0.19/0.41 tff(36,plain,
% 0.19/0.41 (^[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_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(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_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(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_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(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_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(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_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(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_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A)))))))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(37,plain,
% 0.19/0.41 (![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_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(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_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A)))))))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[36])).
% 0.19/0.41 tff(38,plain,
% 0.19/0.41 (^[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_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(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_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A))))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(39,plain,
% 0.19/0.41 (![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_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(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_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A)))))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[38])).
% 0.19/0.41 tff(40,plain,
% 0.19/0.41 (![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))))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(41,plain,
% 0.19/0.42 (^[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)))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(42,plain,
% 0.19/0.42 (![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))))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[41])).
% 0.19/0.42 tff(43,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')).
% 0.19/0.42 tff(44,plain,
% 0.19/0.42 (![A: $i, B: $i, C: $i] : ((C = unordered_pair(A, B)) <=> ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[43, 42])).
% 0.19/0.42 tff(45,plain,
% 0.19/0.42 (![A: $i, B: $i, C: $i] : ((C = unordered_pair(A, B)) <=> ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[44, 40])).
% 0.19/0.42 tff(46,plain,(
% 0.19/0.42 ![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_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A))))))),
% 0.19/0.42 inference(skolemize,[status(sab)],[45])).
% 0.19/0.42 tff(47,plain,
% 0.19/0.42 (![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_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A)))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[46, 39])).
% 0.19/0.42 tff(48,plain,
% 0.19/0.42 (![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_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A)))))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[47, 37])).
% 0.19/0.42 tff(49,plain,
% 0.19/0.42 (![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_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A)))))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[48, 35])).
% 0.19/0.42 tff(50,plain,
% 0.19/0.42 (((~![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_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A)))))))) | (in(tptp_fun_C_0(unordered_pair(A!3, A!3), A!3), unordered_pair(A!3, A!3)) <=> (tptp_fun_C_0(unordered_pair(A!3, A!3), A!3) = A!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_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A)))))))) | (in(tptp_fun_C_0(unordered_pair(A!3, A!3), A!3), unordered_pair(A!3, A!3)) <=> (tptp_fun_C_0(unordered_pair(A!3, A!3), A!3) = A!3)))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(51,plain,
% 0.19/0.42 ((~((~in(tptp_fun_C_0(unordered_pair(A!3, A!3), A!3), unordered_pair(A!3, A!3))) <=> (tptp_fun_C_0(unordered_pair(A!3, A!3), A!3) = A!3))) <=> (in(tptp_fun_C_0(unordered_pair(A!3, A!3), A!3), unordered_pair(A!3, A!3)) <=> (tptp_fun_C_0(unordered_pair(A!3, A!3), A!3) = A!3))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(52,plain,
% 0.19/0.42 ((((~in(tptp_fun_C_0(unordered_pair(A!3, A!3), A!3), unordered_pair(A!3, A!3))) <=> (tptp_fun_C_0(unordered_pair(A!3, A!3), A!3) = A!3)) | $false) <=> ((~in(tptp_fun_C_0(unordered_pair(A!3, A!3), A!3), unordered_pair(A!3, A!3))) <=> (tptp_fun_C_0(unordered_pair(A!3, A!3), A!3) = A!3))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(53,plain,
% 0.19/0.42 ((~$true) <=> $false),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(54,plain,
% 0.19/0.42 (($true | ((~in(tptp_fun_D_1(unordered_pair(A!3, A!3), A!3, A!3), unordered_pair(A!3, A!3))) <=> (tptp_fun_D_1(unordered_pair(A!3, A!3), A!3, A!3) = A!3))) <=> $true),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(55,plain,
% 0.19/0.42 (((~in(tptp_fun_D_1(unordered_pair(A!3, A!3), A!3, A!3), unordered_pair(A!3, A!3))) <=> ((tptp_fun_D_1(unordered_pair(A!3, A!3), A!3, A!3) = A!3) | (tptp_fun_D_1(unordered_pair(A!3, A!3), A!3, A!3) = A!3))) <=> ((~in(tptp_fun_D_1(unordered_pair(A!3, A!3), A!3, A!3), unordered_pair(A!3, A!3))) <=> (tptp_fun_D_1(unordered_pair(A!3, A!3), A!3, A!3) = A!3))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(56,plain,
% 0.19/0.42 ((unordered_pair(A!3, A!3) = unordered_pair(A!3, A!3)) <=> $true),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(57,plain,
% 0.19/0.42 (((unordered_pair(A!3, A!3) = unordered_pair(A!3, A!3)) | ((~in(tptp_fun_D_1(unordered_pair(A!3, A!3), A!3, A!3), unordered_pair(A!3, A!3))) <=> ((tptp_fun_D_1(unordered_pair(A!3, A!3), A!3, A!3) = A!3) | (tptp_fun_D_1(unordered_pair(A!3, A!3), A!3, A!3) = A!3)))) <=> ($true | ((~in(tptp_fun_D_1(unordered_pair(A!3, A!3), A!3, A!3), unordered_pair(A!3, A!3))) <=> (tptp_fun_D_1(unordered_pair(A!3, A!3), A!3, A!3) = A!3)))),
% 0.19/0.42 inference(monotonicity,[status(thm)],[56, 55])).
% 0.19/0.42 tff(58,plain,
% 0.19/0.42 (((unordered_pair(A!3, A!3) = unordered_pair(A!3, A!3)) | ((~in(tptp_fun_D_1(unordered_pair(A!3, A!3), A!3, A!3), unordered_pair(A!3, A!3))) <=> ((tptp_fun_D_1(unordered_pair(A!3, A!3), A!3, A!3) = A!3) | (tptp_fun_D_1(unordered_pair(A!3, A!3), A!3, A!3) = A!3)))) <=> $true),
% 0.19/0.42 inference(transitivity,[status(thm)],[57, 54])).
% 0.19/0.42 tff(59,plain,
% 0.19/0.42 ((~((unordered_pair(A!3, A!3) = unordered_pair(A!3, A!3)) | ((~in(tptp_fun_D_1(unordered_pair(A!3, A!3), A!3, A!3), unordered_pair(A!3, A!3))) <=> ((tptp_fun_D_1(unordered_pair(A!3, A!3), A!3, A!3) = A!3) | (tptp_fun_D_1(unordered_pair(A!3, A!3), A!3, A!3) = A!3))))) <=> (~$true)),
% 0.19/0.42 inference(monotonicity,[status(thm)],[58])).
% 0.19/0.42 tff(60,plain,
% 0.19/0.42 ((~((unordered_pair(A!3, A!3) = unordered_pair(A!3, A!3)) | ((~in(tptp_fun_D_1(unordered_pair(A!3, A!3), A!3, A!3), unordered_pair(A!3, A!3))) <=> ((tptp_fun_D_1(unordered_pair(A!3, A!3), A!3, A!3) = A!3) | (tptp_fun_D_1(unordered_pair(A!3, A!3), A!3, A!3) = A!3))))) <=> $false),
% 0.19/0.42 inference(transitivity,[status(thm)],[59, 53])).
% 0.19/0.42 tff(61,plain,
% 0.19/0.42 ((~(in(tptp_fun_C_0(unordered_pair(A!3, A!3), A!3), unordered_pair(A!3, A!3)) <=> (tptp_fun_C_0(unordered_pair(A!3, A!3), A!3) = A!3))) <=> ((~in(tptp_fun_C_0(unordered_pair(A!3, A!3), A!3), unordered_pair(A!3, A!3))) <=> (tptp_fun_C_0(unordered_pair(A!3, A!3), A!3) = A!3))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(62,plain,
% 0.19/0.42 (($false | (in(tptp_fun_C_0(unordered_pair(A!3, A!3), A!3), unordered_pair(A!3, A!3)) <=> (tptp_fun_C_0(unordered_pair(A!3, A!3), A!3) = A!3))) <=> (in(tptp_fun_C_0(unordered_pair(A!3, A!3), A!3), unordered_pair(A!3, A!3)) <=> (tptp_fun_C_0(unordered_pair(A!3, A!3), A!3) = A!3))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(63,plain,
% 0.19/0.42 ((in(tptp_fun_C_0(unordered_pair(A!3, A!3), A!3), unordered_pair(A!3, A!3)) <=> ((tptp_fun_C_0(unordered_pair(A!3, A!3), A!3) = A!3) | (tptp_fun_C_0(unordered_pair(A!3, A!3), A!3) = A!3))) <=> (in(tptp_fun_C_0(unordered_pair(A!3, A!3), A!3), unordered_pair(A!3, A!3)) <=> (tptp_fun_C_0(unordered_pair(A!3, A!3), A!3) = A!3))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(64,plain,
% 0.19/0.42 ((~(unordered_pair(A!3, A!3) = unordered_pair(A!3, A!3))) <=> (~$true)),
% 0.19/0.42 inference(monotonicity,[status(thm)],[56])).
% 0.19/0.42 tff(65,plain,
% 0.19/0.42 ((~(unordered_pair(A!3, A!3) = unordered_pair(A!3, A!3))) <=> $false),
% 0.19/0.42 inference(transitivity,[status(thm)],[64, 53])).
% 0.19/0.42 tff(66,plain,
% 0.19/0.42 (((~(unordered_pair(A!3, A!3) = unordered_pair(A!3, A!3))) | (in(tptp_fun_C_0(unordered_pair(A!3, A!3), A!3), unordered_pair(A!3, A!3)) <=> ((tptp_fun_C_0(unordered_pair(A!3, A!3), A!3) = A!3) | (tptp_fun_C_0(unordered_pair(A!3, A!3), A!3) = A!3)))) <=> ($false | (in(tptp_fun_C_0(unordered_pair(A!3, A!3), A!3), unordered_pair(A!3, A!3)) <=> (tptp_fun_C_0(unordered_pair(A!3, A!3), A!3) = A!3)))),
% 0.19/0.42 inference(monotonicity,[status(thm)],[65, 63])).
% 0.19/0.42 tff(67,plain,
% 0.19/0.42 (((~(unordered_pair(A!3, A!3) = unordered_pair(A!3, A!3))) | (in(tptp_fun_C_0(unordered_pair(A!3, A!3), A!3), unordered_pair(A!3, A!3)) <=> ((tptp_fun_C_0(unordered_pair(A!3, A!3), A!3) = A!3) | (tptp_fun_C_0(unordered_pair(A!3, A!3), A!3) = A!3)))) <=> (in(tptp_fun_C_0(unordered_pair(A!3, A!3), A!3), unordered_pair(A!3, A!3)) <=> (tptp_fun_C_0(unordered_pair(A!3, A!3), A!3) = A!3))),
% 0.19/0.43 inference(transitivity,[status(thm)],[66, 62])).
% 0.19/0.43 tff(68,plain,
% 0.19/0.43 ((~((~(unordered_pair(A!3, A!3) = unordered_pair(A!3, A!3))) | (in(tptp_fun_C_0(unordered_pair(A!3, A!3), A!3), unordered_pair(A!3, A!3)) <=> ((tptp_fun_C_0(unordered_pair(A!3, A!3), A!3) = A!3) | (tptp_fun_C_0(unordered_pair(A!3, A!3), A!3) = A!3))))) <=> (~(in(tptp_fun_C_0(unordered_pair(A!3, A!3), A!3), unordered_pair(A!3, A!3)) <=> (tptp_fun_C_0(unordered_pair(A!3, A!3), A!3) = A!3)))),
% 0.19/0.43 inference(monotonicity,[status(thm)],[67])).
% 0.19/0.43 tff(69,plain,
% 0.19/0.43 ((~((~(unordered_pair(A!3, A!3) = unordered_pair(A!3, A!3))) | (in(tptp_fun_C_0(unordered_pair(A!3, A!3), A!3), unordered_pair(A!3, A!3)) <=> ((tptp_fun_C_0(unordered_pair(A!3, A!3), A!3) = A!3) | (tptp_fun_C_0(unordered_pair(A!3, A!3), A!3) = A!3))))) <=> ((~in(tptp_fun_C_0(unordered_pair(A!3, A!3), A!3), unordered_pair(A!3, A!3))) <=> (tptp_fun_C_0(unordered_pair(A!3, A!3), A!3) = A!3))),
% 0.19/0.43 inference(transitivity,[status(thm)],[68, 61])).
% 0.19/0.43 tff(70,plain,
% 0.19/0.43 (((~((~(unordered_pair(A!3, A!3) = unordered_pair(A!3, A!3))) | (in(tptp_fun_C_0(unordered_pair(A!3, A!3), A!3), unordered_pair(A!3, A!3)) <=> ((tptp_fun_C_0(unordered_pair(A!3, A!3), A!3) = A!3) | (tptp_fun_C_0(unordered_pair(A!3, A!3), A!3) = A!3))))) | (~((unordered_pair(A!3, A!3) = unordered_pair(A!3, A!3)) | ((~in(tptp_fun_D_1(unordered_pair(A!3, A!3), A!3, A!3), unordered_pair(A!3, A!3))) <=> ((tptp_fun_D_1(unordered_pair(A!3, A!3), A!3, A!3) = A!3) | (tptp_fun_D_1(unordered_pair(A!3, A!3), A!3, A!3) = A!3)))))) <=> (((~in(tptp_fun_C_0(unordered_pair(A!3, A!3), A!3), unordered_pair(A!3, A!3))) <=> (tptp_fun_C_0(unordered_pair(A!3, A!3), A!3) = A!3)) | $false)),
% 0.19/0.43 inference(monotonicity,[status(thm)],[69, 60])).
% 0.19/0.43 tff(71,plain,
% 0.19/0.43 (((~((~(unordered_pair(A!3, A!3) = unordered_pair(A!3, A!3))) | (in(tptp_fun_C_0(unordered_pair(A!3, A!3), A!3), unordered_pair(A!3, A!3)) <=> ((tptp_fun_C_0(unordered_pair(A!3, A!3), A!3) = A!3) | (tptp_fun_C_0(unordered_pair(A!3, A!3), A!3) = A!3))))) | (~((unordered_pair(A!3, A!3) = unordered_pair(A!3, A!3)) | ((~in(tptp_fun_D_1(unordered_pair(A!3, A!3), A!3, A!3), unordered_pair(A!3, A!3))) <=> ((tptp_fun_D_1(unordered_pair(A!3, A!3), A!3, A!3) = A!3) | (tptp_fun_D_1(unordered_pair(A!3, A!3), A!3, A!3) = A!3)))))) <=> ((~in(tptp_fun_C_0(unordered_pair(A!3, A!3), A!3), unordered_pair(A!3, A!3))) <=> (tptp_fun_C_0(unordered_pair(A!3, A!3), A!3) = A!3))),
% 0.19/0.43 inference(transitivity,[status(thm)],[70, 52])).
% 0.19/0.43 tff(72,plain,
% 0.19/0.43 ((~((~((~(unordered_pair(A!3, A!3) = unordered_pair(A!3, A!3))) | (in(tptp_fun_C_0(unordered_pair(A!3, A!3), A!3), unordered_pair(A!3, A!3)) <=> ((tptp_fun_C_0(unordered_pair(A!3, A!3), A!3) = A!3) | (tptp_fun_C_0(unordered_pair(A!3, A!3), A!3) = A!3))))) | (~((unordered_pair(A!3, A!3) = unordered_pair(A!3, A!3)) | ((~in(tptp_fun_D_1(unordered_pair(A!3, A!3), A!3, A!3), unordered_pair(A!3, A!3))) <=> ((tptp_fun_D_1(unordered_pair(A!3, A!3), A!3, A!3) = A!3) | (tptp_fun_D_1(unordered_pair(A!3, A!3), A!3, A!3) = A!3))))))) <=> (~((~in(tptp_fun_C_0(unordered_pair(A!3, A!3), A!3), unordered_pair(A!3, A!3))) <=> (tptp_fun_C_0(unordered_pair(A!3, A!3), A!3) = A!3)))),
% 0.19/0.43 inference(monotonicity,[status(thm)],[71])).
% 0.19/0.43 tff(73,plain,
% 0.19/0.43 ((~((~((~(unordered_pair(A!3, A!3) = unordered_pair(A!3, A!3))) | (in(tptp_fun_C_0(unordered_pair(A!3, A!3), A!3), unordered_pair(A!3, A!3)) <=> ((tptp_fun_C_0(unordered_pair(A!3, A!3), A!3) = A!3) | (tptp_fun_C_0(unordered_pair(A!3, A!3), A!3) = A!3))))) | (~((unordered_pair(A!3, A!3) = unordered_pair(A!3, A!3)) | ((~in(tptp_fun_D_1(unordered_pair(A!3, A!3), A!3, A!3), unordered_pair(A!3, A!3))) <=> ((tptp_fun_D_1(unordered_pair(A!3, A!3), A!3, A!3) = A!3) | (tptp_fun_D_1(unordered_pair(A!3, A!3), A!3, A!3) = A!3))))))) <=> (in(tptp_fun_C_0(unordered_pair(A!3, A!3), A!3), unordered_pair(A!3, A!3)) <=> (tptp_fun_C_0(unordered_pair(A!3, A!3), A!3) = A!3))),
% 0.19/0.43 inference(transitivity,[status(thm)],[72, 51])).
% 0.19/0.43 tff(74,plain,
% 0.19/0.43 (((~![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_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A)))))))) | (~((~((~(unordered_pair(A!3, A!3) = unordered_pair(A!3, A!3))) | (in(tptp_fun_C_0(unordered_pair(A!3, A!3), A!3), unordered_pair(A!3, A!3)) <=> ((tptp_fun_C_0(unordered_pair(A!3, A!3), A!3) = A!3) | (tptp_fun_C_0(unordered_pair(A!3, A!3), A!3) = A!3))))) | (~((unordered_pair(A!3, A!3) = unordered_pair(A!3, A!3)) | ((~in(tptp_fun_D_1(unordered_pair(A!3, A!3), A!3, A!3), unordered_pair(A!3, A!3))) <=> ((tptp_fun_D_1(unordered_pair(A!3, A!3), A!3, A!3) = A!3) | (tptp_fun_D_1(unordered_pair(A!3, A!3), A!3, A!3) = A!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_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A)))))))) | (in(tptp_fun_C_0(unordered_pair(A!3, A!3), A!3), unordered_pair(A!3, A!3)) <=> (tptp_fun_C_0(unordered_pair(A!3, A!3), A!3) = A!3)))),
% 0.19/0.43 inference(monotonicity,[status(thm)],[73])).
% 0.19/0.43 tff(75,plain,
% 0.19/0.43 (((~![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_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A)))))))) | (~((~((~(unordered_pair(A!3, A!3) = unordered_pair(A!3, A!3))) | (in(tptp_fun_C_0(unordered_pair(A!3, A!3), A!3), unordered_pair(A!3, A!3)) <=> ((tptp_fun_C_0(unordered_pair(A!3, A!3), A!3) = A!3) | (tptp_fun_C_0(unordered_pair(A!3, A!3), A!3) = A!3))))) | (~((unordered_pair(A!3, A!3) = unordered_pair(A!3, A!3)) | ((~in(tptp_fun_D_1(unordered_pair(A!3, A!3), A!3, A!3), unordered_pair(A!3, A!3))) <=> ((tptp_fun_D_1(unordered_pair(A!3, A!3), A!3, A!3) = A!3) | (tptp_fun_D_1(unordered_pair(A!3, A!3), A!3, A!3) = A!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_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A)))))))) | (in(tptp_fun_C_0(unordered_pair(A!3, A!3), A!3), unordered_pair(A!3, A!3)) <=> (tptp_fun_C_0(unordered_pair(A!3, A!3), A!3) = A!3)))),
% 0.19/0.43 inference(transitivity,[status(thm)],[74, 50])).
% 0.19/0.43 tff(76,plain,
% 0.19/0.43 ((~![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_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A)))))))) | (~((~((~(unordered_pair(A!3, A!3) = unordered_pair(A!3, A!3))) | (in(tptp_fun_C_0(unordered_pair(A!3, A!3), A!3), unordered_pair(A!3, A!3)) <=> ((tptp_fun_C_0(unordered_pair(A!3, A!3), A!3) = A!3) | (tptp_fun_C_0(unordered_pair(A!3, A!3), A!3) = A!3))))) | (~((unordered_pair(A!3, A!3) = unordered_pair(A!3, A!3)) | ((~in(tptp_fun_D_1(unordered_pair(A!3, A!3), A!3, A!3), unordered_pair(A!3, A!3))) <=> ((tptp_fun_D_1(unordered_pair(A!3, A!3), A!3, A!3) = A!3) | (tptp_fun_D_1(unordered_pair(A!3, A!3), A!3, A!3) = A!3)))))))),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(77,plain,
% 0.19/0.43 ((~![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_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A)))))))) | (in(tptp_fun_C_0(unordered_pair(A!3, A!3), A!3), unordered_pair(A!3, A!3)) <=> (tptp_fun_C_0(unordered_pair(A!3, A!3), A!3) = A!3))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[76, 75])).
% 0.19/0.43 tff(78,plain,
% 0.19/0.43 (in(tptp_fun_C_0(unordered_pair(A!3, A!3), A!3), unordered_pair(A!3, A!3)) <=> (tptp_fun_C_0(unordered_pair(A!3, A!3), A!3) = A!3)),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[77, 49])).
% 0.19/0.43 tff(79,assumption,(in(tptp_fun_C_0(unordered_pair(A!3, A!3), A!3), unordered_pair(A!3, A!3))), introduced(assumption)).
% 0.19/0.43 tff(80,plain,
% 0.19/0.43 ((~![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))))) | (~((~((~(unordered_pair(A!3, A!3) = singleton(A!3))) | (in(tptp_fun_D_1(unordered_pair(A!3, A!3), unordered_pair(A!3, A!3), singleton(A!3)), unordered_pair(A!3, A!3)) <=> (tptp_fun_D_1(unordered_pair(A!3, A!3), unordered_pair(A!3, A!3), singleton(A!3)) = A!3)))) | (~((unordered_pair(A!3, A!3) = singleton(A!3)) | ((~in(tptp_fun_C_0(unordered_pair(A!3, A!3), A!3), unordered_pair(A!3, A!3))) <=> (tptp_fun_C_0(unordered_pair(A!3, A!3), A!3) = A!3))))))),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(81,plain,
% 0.19/0.43 (~((~((~(unordered_pair(A!3, A!3) = singleton(A!3))) | (in(tptp_fun_D_1(unordered_pair(A!3, A!3), unordered_pair(A!3, A!3), singleton(A!3)), unordered_pair(A!3, A!3)) <=> (tptp_fun_D_1(unordered_pair(A!3, A!3), unordered_pair(A!3, A!3), singleton(A!3)) = A!3)))) | (~((unordered_pair(A!3, A!3) = singleton(A!3)) | ((~in(tptp_fun_C_0(unordered_pair(A!3, A!3), A!3), unordered_pair(A!3, A!3))) <=> (tptp_fun_C_0(unordered_pair(A!3, A!3), A!3) = A!3)))))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[80, 21])).
% 0.19/0.43 tff(82,plain,
% 0.19/0.43 (((~((~(unordered_pair(A!3, A!3) = singleton(A!3))) | (in(tptp_fun_D_1(unordered_pair(A!3, A!3), unordered_pair(A!3, A!3), singleton(A!3)), unordered_pair(A!3, A!3)) <=> (tptp_fun_D_1(unordered_pair(A!3, A!3), unordered_pair(A!3, A!3), singleton(A!3)) = A!3)))) | (~((unordered_pair(A!3, A!3) = singleton(A!3)) | ((~in(tptp_fun_C_0(unordered_pair(A!3, A!3), A!3), unordered_pair(A!3, A!3))) <=> (tptp_fun_C_0(unordered_pair(A!3, A!3), A!3) = A!3))))) | ((unordered_pair(A!3, A!3) = singleton(A!3)) | ((~in(tptp_fun_C_0(unordered_pair(A!3, A!3), A!3), unordered_pair(A!3, A!3))) <=> (tptp_fun_C_0(unordered_pair(A!3, A!3), A!3) = A!3)))),
% 0.19/0.43 inference(tautology,[status(thm)],[])).
% 0.19/0.43 tff(83,plain,
% 0.19/0.43 ((unordered_pair(A!3, A!3) = singleton(A!3)) | ((~in(tptp_fun_C_0(unordered_pair(A!3, A!3), A!3), unordered_pair(A!3, A!3))) <=> (tptp_fun_C_0(unordered_pair(A!3, A!3), A!3) = A!3))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[82, 81])).
% 0.19/0.43 tff(84,plain,
% 0.19/0.43 ((~![A: $i] : (unordered_pair(A, A) = singleton(A))) <=> (~![A: $i] : (unordered_pair(A, A) = singleton(A)))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(85,axiom,(~![A: $i] : (unordered_pair(A, A) = singleton(A))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t69_enumset1')).
% 0.19/0.43 tff(86,plain,
% 0.19/0.43 (~![A: $i] : (unordered_pair(A, A) = singleton(A))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[85, 84])).
% 0.19/0.43 tff(87,plain,
% 0.19/0.43 (~![A: $i] : (unordered_pair(A, A) = singleton(A))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[86, 84])).
% 0.19/0.43 tff(88,plain,
% 0.19/0.43 (~![A: $i] : (unordered_pair(A, A) = singleton(A))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[87, 84])).
% 0.19/0.43 tff(89,plain,
% 0.19/0.43 (~![A: $i] : (unordered_pair(A, A) = singleton(A))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[88, 84])).
% 0.19/0.43 tff(90,plain,
% 0.19/0.43 (~![A: $i] : (unordered_pair(A, A) = singleton(A))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[89, 84])).
% 0.19/0.43 tff(91,plain,
% 0.19/0.43 (~![A: $i] : (unordered_pair(A, A) = singleton(A))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[90, 84])).
% 0.19/0.43 tff(92,plain,
% 0.19/0.43 (~![A: $i] : (unordered_pair(A, A) = singleton(A))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[91, 84])).
% 0.19/0.43 tff(93,plain,(
% 0.19/0.43 ~(unordered_pair(A!3, A!3) = singleton(A!3))),
% 0.19/0.43 inference(skolemize,[status(sab)],[92])).
% 0.19/0.43 tff(94,plain,
% 0.19/0.43 ((~((unordered_pair(A!3, A!3) = singleton(A!3)) | ((~in(tptp_fun_C_0(unordered_pair(A!3, A!3), A!3), unordered_pair(A!3, A!3))) <=> (tptp_fun_C_0(unordered_pair(A!3, A!3), A!3) = A!3)))) | (unordered_pair(A!3, A!3) = singleton(A!3)) | ((~in(tptp_fun_C_0(unordered_pair(A!3, A!3), A!3), unordered_pair(A!3, A!3))) <=> (tptp_fun_C_0(unordered_pair(A!3, A!3), A!3) = A!3))),
% 0.19/0.43 inference(tautology,[status(thm)],[])).
% 0.19/0.43 tff(95,plain,
% 0.19/0.43 ((~((unordered_pair(A!3, A!3) = singleton(A!3)) | ((~in(tptp_fun_C_0(unordered_pair(A!3, A!3), A!3), unordered_pair(A!3, A!3))) <=> (tptp_fun_C_0(unordered_pair(A!3, A!3), A!3) = A!3)))) | ((~in(tptp_fun_C_0(unordered_pair(A!3, A!3), A!3), unordered_pair(A!3, A!3))) <=> (tptp_fun_C_0(unordered_pair(A!3, A!3), A!3) = A!3))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[94, 93])).
% 0.19/0.44 tff(96,plain,
% 0.19/0.44 ((~in(tptp_fun_C_0(unordered_pair(A!3, A!3), A!3), unordered_pair(A!3, A!3))) <=> (tptp_fun_C_0(unordered_pair(A!3, A!3), A!3) = A!3)),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[95, 83])).
% 0.19/0.44 tff(97,plain,
% 0.19/0.44 ((~((~in(tptp_fun_C_0(unordered_pair(A!3, A!3), A!3), unordered_pair(A!3, A!3))) <=> (tptp_fun_C_0(unordered_pair(A!3, A!3), A!3) = A!3))) | (~in(tptp_fun_C_0(unordered_pair(A!3, A!3), A!3), unordered_pair(A!3, A!3))) | (~(tptp_fun_C_0(unordered_pair(A!3, A!3), A!3) = A!3))),
% 0.19/0.44 inference(tautology,[status(thm)],[])).
% 0.19/0.44 tff(98,plain,
% 0.19/0.44 (~(tptp_fun_C_0(unordered_pair(A!3, A!3), A!3) = A!3)),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[97, 79, 96])).
% 0.19/0.44 tff(99,plain,
% 0.19/0.44 ((~(in(tptp_fun_C_0(unordered_pair(A!3, A!3), A!3), unordered_pair(A!3, A!3)) <=> (tptp_fun_C_0(unordered_pair(A!3, A!3), A!3) = A!3))) | (~in(tptp_fun_C_0(unordered_pair(A!3, A!3), A!3), unordered_pair(A!3, A!3))) | (tptp_fun_C_0(unordered_pair(A!3, A!3), A!3) = A!3)),
% 0.19/0.44 inference(tautology,[status(thm)],[])).
% 0.19/0.44 tff(100,plain,
% 0.19/0.44 ($false),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[99, 98, 79, 78])).
% 0.19/0.44 tff(101,plain,(~in(tptp_fun_C_0(unordered_pair(A!3, A!3), A!3), unordered_pair(A!3, A!3))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.44 tff(102,plain,
% 0.19/0.44 ((~(in(tptp_fun_C_0(unordered_pair(A!3, A!3), A!3), unordered_pair(A!3, A!3)) <=> (tptp_fun_C_0(unordered_pair(A!3, A!3), A!3) = A!3))) | in(tptp_fun_C_0(unordered_pair(A!3, A!3), A!3), unordered_pair(A!3, A!3)) | (~(tptp_fun_C_0(unordered_pair(A!3, A!3), A!3) = A!3))),
% 0.19/0.44 inference(tautology,[status(thm)],[])).
% 0.19/0.44 tff(103,plain,
% 0.19/0.44 ((~(in(tptp_fun_C_0(unordered_pair(A!3, A!3), A!3), unordered_pair(A!3, A!3)) <=> (tptp_fun_C_0(unordered_pair(A!3, A!3), A!3) = A!3))) | (~(tptp_fun_C_0(unordered_pair(A!3, A!3), A!3) = A!3))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[102, 101])).
% 0.19/0.44 tff(104,plain,
% 0.19/0.44 (~(tptp_fun_C_0(unordered_pair(A!3, A!3), A!3) = A!3)),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[103, 78])).
% 0.19/0.44 tff(105,plain,
% 0.19/0.44 ((~((~in(tptp_fun_C_0(unordered_pair(A!3, A!3), A!3), unordered_pair(A!3, A!3))) <=> (tptp_fun_C_0(unordered_pair(A!3, A!3), A!3) = A!3))) | in(tptp_fun_C_0(unordered_pair(A!3, A!3), A!3), unordered_pair(A!3, A!3)) | (tptp_fun_C_0(unordered_pair(A!3, A!3), A!3) = A!3)),
% 0.19/0.44 inference(tautology,[status(thm)],[])).
% 0.19/0.44 tff(106,plain,
% 0.19/0.44 ((~((~in(tptp_fun_C_0(unordered_pair(A!3, A!3), A!3), unordered_pair(A!3, A!3))) <=> (tptp_fun_C_0(unordered_pair(A!3, A!3), A!3) = A!3))) | (tptp_fun_C_0(unordered_pair(A!3, A!3), A!3) = A!3)),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[105, 101])).
% 0.19/0.44 tff(107,plain,
% 0.19/0.44 (~((~in(tptp_fun_C_0(unordered_pair(A!3, A!3), A!3), unordered_pair(A!3, A!3))) <=> (tptp_fun_C_0(unordered_pair(A!3, A!3), A!3) = A!3))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[106, 104])).
% 0.19/0.44 tff(108,plain,
% 0.19/0.44 ($false),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[95, 107, 25])).
% 0.19/0.44 % SZS output end Proof
%------------------------------------------------------------------------------