TSTP Solution File: SEU144+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SEU144+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n001.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 07:27:44 EDT 2022
% Result : Theorem 0.13s 0.39s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU144+1 : TPTP v8.1.0. Released v3.3.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n001.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 10:01:10 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34 Usage: tptp [options] [-file:]file
% 0.13/0.34 -h, -? prints this message.
% 0.13/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.34 -m, -model generate model.
% 0.13/0.34 -p, -proof generate proof.
% 0.13/0.34 -c, -core generate unsat core of named formulas.
% 0.13/0.34 -st, -statistics display statistics.
% 0.13/0.34 -t:timeout set timeout (in second).
% 0.13/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34 -<param>:<value> configuration parameter and value.
% 0.13/0.34 -o:<output-file> file to place output in.
% 0.13/0.39 % SZS status Theorem
% 0.13/0.39 % SZS output start Proof
% 0.13/0.39 tff(in_type, type, (
% 0.13/0.39 in: ( $i * $i ) > $o)).
% 0.13/0.39 tff(tptp_fun_B_2_type, type, (
% 0.13/0.39 tptp_fun_B_2: $i)).
% 0.13/0.39 tff(tptp_fun_C_1_type, type, (
% 0.13/0.39 tptp_fun_C_1: ( $i * $i ) > $i)).
% 0.13/0.39 tff(singleton_type, type, (
% 0.13/0.39 singleton: $i > $i)).
% 0.13/0.39 tff(tptp_fun_A_3_type, type, (
% 0.13/0.39 tptp_fun_A_3: $i)).
% 0.13/0.39 tff(tptp_fun_C_0_type, type, (
% 0.13/0.39 tptp_fun_C_0: ( $i * $i ) > $i)).
% 0.13/0.39 tff(subset_type, type, (
% 0.13/0.39 subset: ( $i * $i ) > $o)).
% 0.13/0.39 tff(1,plain,
% 0.13/0.39 (^[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)))))))),
% 0.13/0.39 inference(bind,[status(th)],[])).
% 0.13/0.39 tff(2,plain,
% 0.13/0.39 (![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))))))),
% 0.13/0.39 inference(quant_intro,[status(thm)],[1])).
% 0.13/0.39 tff(3,plain,
% 0.13/0.39 (![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))))))),
% 0.13/0.39 inference(pull_quant,[status(thm)],[])).
% 0.13/0.39 tff(4,plain,
% 0.13/0.39 (^[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))))))))),
% 0.13/0.39 inference(bind,[status(th)],[])).
% 0.13/0.39 tff(5,plain,
% 0.13/0.39 (![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))))))),
% 0.13/0.39 inference(quant_intro,[status(thm)],[4])).
% 0.13/0.39 tff(6,plain,
% 0.13/0.39 (![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))))))),
% 0.13/0.39 inference(transitivity,[status(thm)],[5, 3])).
% 0.13/0.39 tff(7,plain,
% 0.13/0.39 (![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))))))),
% 0.13/0.39 inference(transitivity,[status(thm)],[6, 2])).
% 0.13/0.39 tff(8,plain,
% 0.13/0.39 (^[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)))))))),
% 0.13/0.39 inference(bind,[status(th)],[])).
% 0.13/0.39 tff(9,plain,
% 0.13/0.39 (![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))))))),
% 0.13/0.39 inference(quant_intro,[status(thm)],[8])).
% 0.13/0.39 tff(10,plain,
% 0.13/0.39 (![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))))))),
% 0.13/0.39 inference(transitivity,[status(thm)],[9, 7])).
% 0.13/0.39 tff(11,plain,
% 0.13/0.39 (^[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))))))))),
% 0.13/0.39 inference(bind,[status(th)],[])).
% 0.13/0.39 tff(12,plain,
% 0.13/0.39 (![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))))))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[11])).
% 0.20/0.39 tff(13,plain,
% 0.20/0.39 (^[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)))))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(14,plain,
% 0.20/0.39 (![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))))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[13])).
% 0.20/0.39 tff(15,plain,
% 0.20/0.39 (![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)))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(16,axiom,(![A: $i, B: $i] : ((B = singleton(A)) <=> ![C: $i] : (in(C, B) <=> (C = A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d1_tarski')).
% 0.20/0.39 tff(17,plain,
% 0.20/0.39 (![A: $i, B: $i] : ((B = singleton(A)) <=> ![C: $i] : (in(C, B) <=> (C = A)))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[16, 15])).
% 0.20/0.39 tff(18,plain,(
% 0.20/0.39 ![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)))))),
% 0.20/0.39 inference(skolemize,[status(sab)],[17])).
% 0.20/0.39 tff(19,plain,
% 0.20/0.39 (![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))))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[18, 14])).
% 0.20/0.39 tff(20,plain,
% 0.20/0.39 (![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))))))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[19, 12])).
% 0.20/0.39 tff(21,plain,
% 0.20/0.39 (![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))))))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[20, 10])).
% 0.20/0.39 tff(22,plain,
% 0.20/0.39 (((~![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))))))) | (in(tptp_fun_C_1(B!2, singleton(A!3)), singleton(A!3)) <=> (tptp_fun_C_1(B!2, singleton(A!3)) = A!3))) <=> ((~![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))))))) | (in(tptp_fun_C_1(B!2, singleton(A!3)), singleton(A!3)) <=> (tptp_fun_C_1(B!2, singleton(A!3)) = A!3)))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(23,plain,
% 0.20/0.39 ((~((~in(tptp_fun_C_1(B!2, singleton(A!3)), singleton(A!3))) <=> (tptp_fun_C_1(B!2, singleton(A!3)) = A!3))) <=> (in(tptp_fun_C_1(B!2, singleton(A!3)), singleton(A!3)) <=> (tptp_fun_C_1(B!2, singleton(A!3)) = A!3))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(24,plain,
% 0.20/0.39 ((((~in(tptp_fun_C_1(B!2, singleton(A!3)), singleton(A!3))) <=> (tptp_fun_C_1(B!2, singleton(A!3)) = A!3)) | $false) <=> ((~in(tptp_fun_C_1(B!2, singleton(A!3)), singleton(A!3))) <=> (tptp_fun_C_1(B!2, singleton(A!3)) = A!3))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(25,plain,
% 0.20/0.39 ((~$true) <=> $false),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(26,plain,
% 0.20/0.39 (($true | ((~in(tptp_fun_C_0(singleton(A!3), A!3), singleton(A!3))) <=> (tptp_fun_C_0(singleton(A!3), A!3) = A!3))) <=> $true),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(27,plain,
% 0.20/0.39 ((singleton(A!3) = singleton(A!3)) <=> $true),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(28,plain,
% 0.20/0.39 (((singleton(A!3) = singleton(A!3)) | ((~in(tptp_fun_C_0(singleton(A!3), A!3), singleton(A!3))) <=> (tptp_fun_C_0(singleton(A!3), A!3) = A!3))) <=> ($true | ((~in(tptp_fun_C_0(singleton(A!3), A!3), singleton(A!3))) <=> (tptp_fun_C_0(singleton(A!3), A!3) = A!3)))),
% 0.20/0.40 inference(monotonicity,[status(thm)],[27])).
% 0.20/0.40 tff(29,plain,
% 0.20/0.40 (((singleton(A!3) = singleton(A!3)) | ((~in(tptp_fun_C_0(singleton(A!3), A!3), singleton(A!3))) <=> (tptp_fun_C_0(singleton(A!3), A!3) = A!3))) <=> $true),
% 0.20/0.40 inference(transitivity,[status(thm)],[28, 26])).
% 0.20/0.40 tff(30,plain,
% 0.20/0.40 ((~((singleton(A!3) = singleton(A!3)) | ((~in(tptp_fun_C_0(singleton(A!3), A!3), singleton(A!3))) <=> (tptp_fun_C_0(singleton(A!3), A!3) = A!3)))) <=> (~$true)),
% 0.20/0.40 inference(monotonicity,[status(thm)],[29])).
% 0.20/0.40 tff(31,plain,
% 0.20/0.40 ((~((singleton(A!3) = singleton(A!3)) | ((~in(tptp_fun_C_0(singleton(A!3), A!3), singleton(A!3))) <=> (tptp_fun_C_0(singleton(A!3), A!3) = A!3)))) <=> $false),
% 0.20/0.40 inference(transitivity,[status(thm)],[30, 25])).
% 0.20/0.40 tff(32,plain,
% 0.20/0.40 ((~(in(tptp_fun_C_1(B!2, singleton(A!3)), singleton(A!3)) <=> (tptp_fun_C_1(B!2, singleton(A!3)) = A!3))) <=> ((~in(tptp_fun_C_1(B!2, singleton(A!3)), singleton(A!3))) <=> (tptp_fun_C_1(B!2, singleton(A!3)) = A!3))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(33,plain,
% 0.20/0.40 (($false | (in(tptp_fun_C_1(B!2, singleton(A!3)), singleton(A!3)) <=> (tptp_fun_C_1(B!2, singleton(A!3)) = A!3))) <=> (in(tptp_fun_C_1(B!2, singleton(A!3)), singleton(A!3)) <=> (tptp_fun_C_1(B!2, singleton(A!3)) = A!3))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(34,plain,
% 0.20/0.40 ((~(singleton(A!3) = singleton(A!3))) <=> (~$true)),
% 0.20/0.40 inference(monotonicity,[status(thm)],[27])).
% 0.20/0.40 tff(35,plain,
% 0.20/0.40 ((~(singleton(A!3) = singleton(A!3))) <=> $false),
% 0.20/0.40 inference(transitivity,[status(thm)],[34, 25])).
% 0.20/0.40 tff(36,plain,
% 0.20/0.40 (((~(singleton(A!3) = singleton(A!3))) | (in(tptp_fun_C_1(B!2, singleton(A!3)), singleton(A!3)) <=> (tptp_fun_C_1(B!2, singleton(A!3)) = A!3))) <=> ($false | (in(tptp_fun_C_1(B!2, singleton(A!3)), singleton(A!3)) <=> (tptp_fun_C_1(B!2, singleton(A!3)) = A!3)))),
% 0.20/0.40 inference(monotonicity,[status(thm)],[35])).
% 0.20/0.40 tff(37,plain,
% 0.20/0.40 (((~(singleton(A!3) = singleton(A!3))) | (in(tptp_fun_C_1(B!2, singleton(A!3)), singleton(A!3)) <=> (tptp_fun_C_1(B!2, singleton(A!3)) = A!3))) <=> (in(tptp_fun_C_1(B!2, singleton(A!3)), singleton(A!3)) <=> (tptp_fun_C_1(B!2, singleton(A!3)) = A!3))),
% 0.20/0.40 inference(transitivity,[status(thm)],[36, 33])).
% 0.20/0.40 tff(38,plain,
% 0.20/0.40 ((~((~(singleton(A!3) = singleton(A!3))) | (in(tptp_fun_C_1(B!2, singleton(A!3)), singleton(A!3)) <=> (tptp_fun_C_1(B!2, singleton(A!3)) = A!3)))) <=> (~(in(tptp_fun_C_1(B!2, singleton(A!3)), singleton(A!3)) <=> (tptp_fun_C_1(B!2, singleton(A!3)) = A!3)))),
% 0.20/0.40 inference(monotonicity,[status(thm)],[37])).
% 0.20/0.40 tff(39,plain,
% 0.20/0.40 ((~((~(singleton(A!3) = singleton(A!3))) | (in(tptp_fun_C_1(B!2, singleton(A!3)), singleton(A!3)) <=> (tptp_fun_C_1(B!2, singleton(A!3)) = A!3)))) <=> ((~in(tptp_fun_C_1(B!2, singleton(A!3)), singleton(A!3))) <=> (tptp_fun_C_1(B!2, singleton(A!3)) = A!3))),
% 0.20/0.40 inference(transitivity,[status(thm)],[38, 32])).
% 0.20/0.40 tff(40,plain,
% 0.20/0.40 (((~((~(singleton(A!3) = singleton(A!3))) | (in(tptp_fun_C_1(B!2, singleton(A!3)), singleton(A!3)) <=> (tptp_fun_C_1(B!2, singleton(A!3)) = A!3)))) | (~((singleton(A!3) = singleton(A!3)) | ((~in(tptp_fun_C_0(singleton(A!3), A!3), singleton(A!3))) <=> (tptp_fun_C_0(singleton(A!3), A!3) = A!3))))) <=> (((~in(tptp_fun_C_1(B!2, singleton(A!3)), singleton(A!3))) <=> (tptp_fun_C_1(B!2, singleton(A!3)) = A!3)) | $false)),
% 0.20/0.40 inference(monotonicity,[status(thm)],[39, 31])).
% 0.20/0.40 tff(41,plain,
% 0.20/0.40 (((~((~(singleton(A!3) = singleton(A!3))) | (in(tptp_fun_C_1(B!2, singleton(A!3)), singleton(A!3)) <=> (tptp_fun_C_1(B!2, singleton(A!3)) = A!3)))) | (~((singleton(A!3) = singleton(A!3)) | ((~in(tptp_fun_C_0(singleton(A!3), A!3), singleton(A!3))) <=> (tptp_fun_C_0(singleton(A!3), A!3) = A!3))))) <=> ((~in(tptp_fun_C_1(B!2, singleton(A!3)), singleton(A!3))) <=> (tptp_fun_C_1(B!2, singleton(A!3)) = A!3))),
% 0.20/0.40 inference(transitivity,[status(thm)],[40, 24])).
% 0.20/0.40 tff(42,plain,
% 0.20/0.40 ((~((~((~(singleton(A!3) = singleton(A!3))) | (in(tptp_fun_C_1(B!2, singleton(A!3)), singleton(A!3)) <=> (tptp_fun_C_1(B!2, singleton(A!3)) = A!3)))) | (~((singleton(A!3) = singleton(A!3)) | ((~in(tptp_fun_C_0(singleton(A!3), A!3), singleton(A!3))) <=> (tptp_fun_C_0(singleton(A!3), A!3) = A!3)))))) <=> (~((~in(tptp_fun_C_1(B!2, singleton(A!3)), singleton(A!3))) <=> (tptp_fun_C_1(B!2, singleton(A!3)) = A!3)))),
% 0.20/0.40 inference(monotonicity,[status(thm)],[41])).
% 0.20/0.40 tff(43,plain,
% 0.20/0.40 ((~((~((~(singleton(A!3) = singleton(A!3))) | (in(tptp_fun_C_1(B!2, singleton(A!3)), singleton(A!3)) <=> (tptp_fun_C_1(B!2, singleton(A!3)) = A!3)))) | (~((singleton(A!3) = singleton(A!3)) | ((~in(tptp_fun_C_0(singleton(A!3), A!3), singleton(A!3))) <=> (tptp_fun_C_0(singleton(A!3), A!3) = A!3)))))) <=> (in(tptp_fun_C_1(B!2, singleton(A!3)), singleton(A!3)) <=> (tptp_fun_C_1(B!2, singleton(A!3)) = A!3))),
% 0.20/0.40 inference(transitivity,[status(thm)],[42, 23])).
% 0.20/0.40 tff(44,plain,
% 0.20/0.40 (((~![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))))))) | (~((~((~(singleton(A!3) = singleton(A!3))) | (in(tptp_fun_C_1(B!2, singleton(A!3)), singleton(A!3)) <=> (tptp_fun_C_1(B!2, singleton(A!3)) = A!3)))) | (~((singleton(A!3) = singleton(A!3)) | ((~in(tptp_fun_C_0(singleton(A!3), A!3), singleton(A!3))) <=> (tptp_fun_C_0(singleton(A!3), A!3) = A!3))))))) <=> ((~![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))))))) | (in(tptp_fun_C_1(B!2, singleton(A!3)), singleton(A!3)) <=> (tptp_fun_C_1(B!2, singleton(A!3)) = A!3)))),
% 0.20/0.40 inference(monotonicity,[status(thm)],[43])).
% 0.20/0.40 tff(45,plain,
% 0.20/0.40 (((~![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))))))) | (~((~((~(singleton(A!3) = singleton(A!3))) | (in(tptp_fun_C_1(B!2, singleton(A!3)), singleton(A!3)) <=> (tptp_fun_C_1(B!2, singleton(A!3)) = A!3)))) | (~((singleton(A!3) = singleton(A!3)) | ((~in(tptp_fun_C_0(singleton(A!3), A!3), singleton(A!3))) <=> (tptp_fun_C_0(singleton(A!3), A!3) = A!3))))))) <=> ((~![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))))))) | (in(tptp_fun_C_1(B!2, singleton(A!3)), singleton(A!3)) <=> (tptp_fun_C_1(B!2, singleton(A!3)) = A!3)))),
% 0.20/0.40 inference(transitivity,[status(thm)],[44, 22])).
% 0.20/0.40 tff(46,plain,
% 0.20/0.40 ((~![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))))))) | (~((~((~(singleton(A!3) = singleton(A!3))) | (in(tptp_fun_C_1(B!2, singleton(A!3)), singleton(A!3)) <=> (tptp_fun_C_1(B!2, singleton(A!3)) = A!3)))) | (~((singleton(A!3) = singleton(A!3)) | ((~in(tptp_fun_C_0(singleton(A!3), A!3), singleton(A!3))) <=> (tptp_fun_C_0(singleton(A!3), A!3) = A!3))))))),
% 0.20/0.40 inference(quant_inst,[status(thm)],[])).
% 0.20/0.40 tff(47,plain,
% 0.20/0.40 ((~![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))))))) | (in(tptp_fun_C_1(B!2, singleton(A!3)), singleton(A!3)) <=> (tptp_fun_C_1(B!2, singleton(A!3)) = A!3))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[46, 45])).
% 0.20/0.40 tff(48,plain,
% 0.20/0.40 (in(tptp_fun_C_1(B!2, singleton(A!3)), singleton(A!3)) <=> (tptp_fun_C_1(B!2, singleton(A!3)) = A!3)),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[47, 21])).
% 0.20/0.40 tff(49,assumption,(~in(A!3, singleton(A!3))), introduced(assumption)).
% 0.20/0.40 tff(50,plain,
% 0.20/0.40 (((~![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))))))) | in(A!3, singleton(A!3))) <=> ((~![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))))))) | in(A!3, singleton(A!3)))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(51,plain,
% 0.20/0.40 ((~(~in(A!3, singleton(A!3)))) <=> in(A!3, singleton(A!3))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(52,plain,
% 0.20/0.40 (((~in(A!3, singleton(A!3))) | $false) <=> (~in(A!3, singleton(A!3)))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(53,plain,
% 0.20/0.40 ((~((~(singleton(A!3) = singleton(A!3))) | (in(A!3, singleton(A!3)) <=> (A!3 = A!3)))) <=> (~in(A!3, singleton(A!3)))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(54,plain,
% 0.20/0.40 (((~((~(singleton(A!3) = singleton(A!3))) | (in(A!3, singleton(A!3)) <=> (A!3 = A!3)))) | (~((singleton(A!3) = singleton(A!3)) | ((~in(tptp_fun_C_0(singleton(A!3), A!3), singleton(A!3))) <=> (tptp_fun_C_0(singleton(A!3), A!3) = A!3))))) <=> ((~in(A!3, singleton(A!3))) | $false)),
% 0.20/0.40 inference(monotonicity,[status(thm)],[53, 31])).
% 0.20/0.40 tff(55,plain,
% 0.20/0.40 (((~((~(singleton(A!3) = singleton(A!3))) | (in(A!3, singleton(A!3)) <=> (A!3 = A!3)))) | (~((singleton(A!3) = singleton(A!3)) | ((~in(tptp_fun_C_0(singleton(A!3), A!3), singleton(A!3))) <=> (tptp_fun_C_0(singleton(A!3), A!3) = A!3))))) <=> (~in(A!3, singleton(A!3)))),
% 0.20/0.40 inference(transitivity,[status(thm)],[54, 52])).
% 0.20/0.40 tff(56,plain,
% 0.20/0.40 ((~((~((~(singleton(A!3) = singleton(A!3))) | (in(A!3, singleton(A!3)) <=> (A!3 = A!3)))) | (~((singleton(A!3) = singleton(A!3)) | ((~in(tptp_fun_C_0(singleton(A!3), A!3), singleton(A!3))) <=> (tptp_fun_C_0(singleton(A!3), A!3) = A!3)))))) <=> (~(~in(A!3, singleton(A!3))))),
% 0.20/0.40 inference(monotonicity,[status(thm)],[55])).
% 0.20/0.40 tff(57,plain,
% 0.20/0.40 ((~((~((~(singleton(A!3) = singleton(A!3))) | (in(A!3, singleton(A!3)) <=> (A!3 = A!3)))) | (~((singleton(A!3) = singleton(A!3)) | ((~in(tptp_fun_C_0(singleton(A!3), A!3), singleton(A!3))) <=> (tptp_fun_C_0(singleton(A!3), A!3) = A!3)))))) <=> in(A!3, singleton(A!3))),
% 0.20/0.40 inference(transitivity,[status(thm)],[56, 51])).
% 0.20/0.40 tff(58,plain,
% 0.20/0.40 (((~![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))))))) | (~((~((~(singleton(A!3) = singleton(A!3))) | (in(A!3, singleton(A!3)) <=> (A!3 = A!3)))) | (~((singleton(A!3) = singleton(A!3)) | ((~in(tptp_fun_C_0(singleton(A!3), A!3), singleton(A!3))) <=> (tptp_fun_C_0(singleton(A!3), A!3) = A!3))))))) <=> ((~![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))))))) | in(A!3, singleton(A!3)))),
% 0.20/0.40 inference(monotonicity,[status(thm)],[57])).
% 0.20/0.40 tff(59,plain,
% 0.20/0.40 (((~![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))))))) | (~((~((~(singleton(A!3) = singleton(A!3))) | (in(A!3, singleton(A!3)) <=> (A!3 = A!3)))) | (~((singleton(A!3) = singleton(A!3)) | ((~in(tptp_fun_C_0(singleton(A!3), A!3), singleton(A!3))) <=> (tptp_fun_C_0(singleton(A!3), A!3) = A!3))))))) <=> ((~![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))))))) | in(A!3, singleton(A!3)))),
% 0.20/0.40 inference(transitivity,[status(thm)],[58, 50])).
% 0.20/0.40 tff(60,plain,
% 0.20/0.40 ((~![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))))))) | (~((~((~(singleton(A!3) = singleton(A!3))) | (in(A!3, singleton(A!3)) <=> (A!3 = A!3)))) | (~((singleton(A!3) = singleton(A!3)) | ((~in(tptp_fun_C_0(singleton(A!3), A!3), singleton(A!3))) <=> (tptp_fun_C_0(singleton(A!3), A!3) = A!3))))))),
% 0.20/0.40 inference(quant_inst,[status(thm)],[])).
% 0.20/0.40 tff(61,plain,
% 0.20/0.40 ((~![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))))) | in(A!3, singleton(A!3))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[60, 59])).
% 0.20/0.40 tff(62,plain,
% 0.20/0.40 ($false),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[61, 21, 49])).
% 0.20/0.40 tff(63,plain,(in(A!3, singleton(A!3))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.41 tff(64,assumption,(~in(A!3, B!2)), introduced(assumption)).
% 0.20/0.41 tff(65,plain,
% 0.20/0.41 ((~(subset(singleton(A!3), B!2) <=> in(A!3, B!2))) <=> ((~subset(singleton(A!3), B!2)) <=> in(A!3, B!2))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(66,plain,
% 0.20/0.41 ((~![A: $i, B: $i] : (subset(singleton(A), B) <=> in(A, B))) <=> (~![A: $i, B: $i] : (subset(singleton(A), B) <=> in(A, B)))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(67,axiom,(~![A: $i, B: $i] : (subset(singleton(A), B) <=> in(A, B))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','l2_zfmisc_1')).
% 0.20/0.41 tff(68,plain,
% 0.20/0.41 (~![A: $i, B: $i] : (subset(singleton(A), B) <=> in(A, B))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[67, 66])).
% 0.20/0.41 tff(69,plain,
% 0.20/0.41 (~![A: $i, B: $i] : (subset(singleton(A), B) <=> in(A, B))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[68, 66])).
% 0.20/0.41 tff(70,plain,
% 0.20/0.41 (~![A: $i, B: $i] : (subset(singleton(A), B) <=> in(A, B))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[69, 66])).
% 0.20/0.41 tff(71,plain,
% 0.20/0.41 (~![A: $i, B: $i] : (subset(singleton(A), B) <=> in(A, B))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[70, 66])).
% 0.20/0.41 tff(72,plain,
% 0.20/0.41 (~![A: $i, B: $i] : (subset(singleton(A), B) <=> in(A, B))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[71, 66])).
% 0.20/0.41 tff(73,plain,
% 0.20/0.41 (~![A: $i, B: $i] : (subset(singleton(A), B) <=> in(A, B))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[72, 66])).
% 0.20/0.41 tff(74,plain,
% 0.20/0.41 (~![A: $i, B: $i] : (subset(singleton(A), B) <=> in(A, B))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[73, 66])).
% 0.20/0.41 tff(75,plain,(
% 0.20/0.41 ~(subset(singleton(A!3), B!2) <=> in(A!3, B!2))),
% 0.20/0.41 inference(skolemize,[status(sab)],[74])).
% 0.20/0.41 tff(76,plain,
% 0.20/0.41 ((~subset(singleton(A!3), B!2)) <=> in(A!3, B!2)),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[75, 65])).
% 0.20/0.41 tff(77,plain,
% 0.20/0.41 (subset(singleton(A!3), B!2) | in(A!3, B!2) | (~((~subset(singleton(A!3), B!2)) <=> in(A!3, B!2)))),
% 0.20/0.41 inference(tautology,[status(thm)],[])).
% 0.20/0.41 tff(78,plain,
% 0.20/0.41 (subset(singleton(A!3), B!2) | in(A!3, B!2)),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[77, 76])).
% 0.20/0.41 tff(79,plain,
% 0.20/0.41 (subset(singleton(A!3), B!2)),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[78, 64])).
% 0.20/0.41 tff(80,plain,
% 0.20/0.41 (^[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))))))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(81,plain,
% 0.20/0.41 (![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)))))))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[80])).
% 0.20/0.41 tff(82,plain,
% 0.20/0.41 (^[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))))))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(83,plain,
% 0.20/0.41 (![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)))))))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[82])).
% 0.20/0.41 tff(84,plain,
% 0.20/0.41 (![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)))))))),
% 0.20/0.41 inference(transitivity,[status(thm)],[83, 81])).
% 0.20/0.41 tff(85,plain,
% 0.20/0.41 (^[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)))))))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(86,plain,
% 0.20/0.41 (![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)))))))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[85])).
% 0.20/0.41 tff(87,plain,
% 0.20/0.41 (![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)))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(88,plain,
% 0.20/0.41 (^[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))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(89,plain,
% 0.20/0.41 (![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)))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[88])).
% 0.20/0.41 tff(90,axiom,(![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : (in(C, A) => in(C, B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d3_tarski')).
% 0.20/0.41 tff(91,plain,
% 0.20/0.41 (![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[90, 89])).
% 0.20/0.41 tff(92,plain,
% 0.20/0.41 (![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[91, 87])).
% 0.20/0.41 tff(93,plain,(
% 0.20/0.41 ![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)))))),
% 0.20/0.41 inference(skolemize,[status(sab)],[92])).
% 0.20/0.41 tff(94,plain,
% 0.20/0.41 (![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)))))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[93, 86])).
% 0.20/0.41 tff(95,plain,
% 0.20/0.41 (![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)))))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[94, 84])).
% 0.20/0.41 tff(96,plain,
% 0.20/0.41 ((~![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)))))))) | (~((~((~subset(singleton(A!3), B!2)) | ![C: $i] : ((~in(C, singleton(A!3))) | in(C, B!2)))) | (~(subset(singleton(A!3), B!2) | (~((~in(tptp_fun_C_1(B!2, singleton(A!3)), singleton(A!3))) | in(tptp_fun_C_1(B!2, singleton(A!3)), B!2)))))))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(97,plain,
% 0.20/0.41 (~((~((~subset(singleton(A!3), B!2)) | ![C: $i] : ((~in(C, singleton(A!3))) | in(C, B!2)))) | (~(subset(singleton(A!3), B!2) | (~((~in(tptp_fun_C_1(B!2, singleton(A!3)), singleton(A!3))) | in(tptp_fun_C_1(B!2, singleton(A!3)), B!2))))))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[96, 95])).
% 0.20/0.41 tff(98,plain,
% 0.20/0.41 (((~((~subset(singleton(A!3), B!2)) | ![C: $i] : ((~in(C, singleton(A!3))) | in(C, B!2)))) | (~(subset(singleton(A!3), B!2) | (~((~in(tptp_fun_C_1(B!2, singleton(A!3)), singleton(A!3))) | in(tptp_fun_C_1(B!2, singleton(A!3)), B!2)))))) | ((~subset(singleton(A!3), B!2)) | ![C: $i] : ((~in(C, singleton(A!3))) | in(C, B!2)))),
% 0.20/0.41 inference(tautology,[status(thm)],[])).
% 0.20/0.41 tff(99,plain,
% 0.20/0.41 ((~subset(singleton(A!3), B!2)) | ![C: $i] : ((~in(C, singleton(A!3))) | in(C, B!2))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[98, 97])).
% 0.20/0.41 tff(100,plain,
% 0.20/0.41 ((~((~subset(singleton(A!3), B!2)) | ![C: $i] : ((~in(C, singleton(A!3))) | in(C, B!2)))) | (~subset(singleton(A!3), B!2)) | ![C: $i] : ((~in(C, singleton(A!3))) | in(C, B!2))),
% 0.20/0.41 inference(tautology,[status(thm)],[])).
% 0.20/0.41 tff(101,plain,
% 0.20/0.41 ((~subset(singleton(A!3), B!2)) | ![C: $i] : ((~in(C, singleton(A!3))) | in(C, B!2))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[100, 99])).
% 0.20/0.41 tff(102,plain,
% 0.20/0.41 (![C: $i] : ((~in(C, singleton(A!3))) | in(C, B!2))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[101, 79])).
% 0.20/0.41 tff(103,plain,
% 0.20/0.41 (((~![C: $i] : ((~in(C, singleton(A!3))) | in(C, B!2))) | ((~in(A!3, singleton(A!3))) | in(A!3, B!2))) <=> ((~![C: $i] : ((~in(C, singleton(A!3))) | in(C, B!2))) | (~in(A!3, singleton(A!3))) | in(A!3, B!2))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(104,plain,
% 0.20/0.41 ((~![C: $i] : ((~in(C, singleton(A!3))) | in(C, B!2))) | ((~in(A!3, singleton(A!3))) | in(A!3, B!2))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(105,plain,
% 0.20/0.41 ((~![C: $i] : ((~in(C, singleton(A!3))) | in(C, B!2))) | (~in(A!3, singleton(A!3))) | in(A!3, B!2)),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[104, 103])).
% 0.20/0.41 tff(106,plain,
% 0.20/0.41 ($false),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[105, 64, 102, 63])).
% 0.20/0.41 tff(107,plain,(in(A!3, B!2)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.41 tff(108,plain,
% 0.20/0.41 ((~subset(singleton(A!3), B!2)) | (~in(A!3, B!2)) | (~((~subset(singleton(A!3), B!2)) <=> in(A!3, B!2)))),
% 0.20/0.41 inference(tautology,[status(thm)],[])).
% 0.20/0.41 tff(109,plain,
% 0.20/0.41 ((~subset(singleton(A!3), B!2)) | (~in(A!3, B!2))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[108, 76])).
% 0.20/0.41 tff(110,plain,
% 0.20/0.41 (~subset(singleton(A!3), B!2)),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[109, 107])).
% 0.20/0.41 tff(111,plain,
% 0.20/0.41 (((~((~subset(singleton(A!3), B!2)) | ![C: $i] : ((~in(C, singleton(A!3))) | in(C, B!2)))) | (~(subset(singleton(A!3), B!2) | (~((~in(tptp_fun_C_1(B!2, singleton(A!3)), singleton(A!3))) | in(tptp_fun_C_1(B!2, singleton(A!3)), B!2)))))) | (subset(singleton(A!3), B!2) | (~((~in(tptp_fun_C_1(B!2, singleton(A!3)), singleton(A!3))) | in(tptp_fun_C_1(B!2, singleton(A!3)), B!2))))),
% 0.20/0.41 inference(tautology,[status(thm)],[])).
% 0.20/0.41 tff(112,plain,
% 0.20/0.41 (subset(singleton(A!3), B!2) | (~((~in(tptp_fun_C_1(B!2, singleton(A!3)), singleton(A!3))) | in(tptp_fun_C_1(B!2, singleton(A!3)), B!2)))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[111, 97])).
% 0.20/0.41 tff(113,plain,
% 0.20/0.41 ((~(subset(singleton(A!3), B!2) | (~((~in(tptp_fun_C_1(B!2, singleton(A!3)), singleton(A!3))) | in(tptp_fun_C_1(B!2, singleton(A!3)), B!2))))) | subset(singleton(A!3), B!2) | (~((~in(tptp_fun_C_1(B!2, singleton(A!3)), singleton(A!3))) | in(tptp_fun_C_1(B!2, singleton(A!3)), B!2)))),
% 0.20/0.41 inference(tautology,[status(thm)],[])).
% 0.20/0.41 tff(114,plain,
% 0.20/0.41 (subset(singleton(A!3), B!2) | (~((~in(tptp_fun_C_1(B!2, singleton(A!3)), singleton(A!3))) | in(tptp_fun_C_1(B!2, singleton(A!3)), B!2)))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[113, 112])).
% 0.20/0.41 tff(115,plain,
% 0.20/0.41 (~((~in(tptp_fun_C_1(B!2, singleton(A!3)), singleton(A!3))) | in(tptp_fun_C_1(B!2, singleton(A!3)), B!2))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[114, 110])).
% 0.20/0.41 tff(116,plain,
% 0.20/0.41 (((~in(tptp_fun_C_1(B!2, singleton(A!3)), singleton(A!3))) | in(tptp_fun_C_1(B!2, singleton(A!3)), B!2)) | in(tptp_fun_C_1(B!2, singleton(A!3)), singleton(A!3))),
% 0.20/0.41 inference(tautology,[status(thm)],[])).
% 0.20/0.41 tff(117,plain,
% 0.20/0.41 (in(tptp_fun_C_1(B!2, singleton(A!3)), singleton(A!3))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[116, 115])).
% 0.20/0.41 tff(118,plain,
% 0.20/0.41 ((~(in(tptp_fun_C_1(B!2, singleton(A!3)), singleton(A!3)) <=> (tptp_fun_C_1(B!2, singleton(A!3)) = A!3))) | (~in(tptp_fun_C_1(B!2, singleton(A!3)), singleton(A!3))) | (tptp_fun_C_1(B!2, singleton(A!3)) = A!3)),
% 0.20/0.41 inference(tautology,[status(thm)],[])).
% 0.20/0.41 tff(119,plain,
% 0.20/0.41 ((~(in(tptp_fun_C_1(B!2, singleton(A!3)), singleton(A!3)) <=> (tptp_fun_C_1(B!2, singleton(A!3)) = A!3))) | (tptp_fun_C_1(B!2, singleton(A!3)) = A!3)),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[118, 117])).
% 0.20/0.41 tff(120,plain,
% 0.20/0.41 (tptp_fun_C_1(B!2, singleton(A!3)) = A!3),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[119, 48])).
% 0.20/0.41 tff(121,plain,
% 0.20/0.41 (in(tptp_fun_C_1(B!2, singleton(A!3)), B!2) <=> in(A!3, B!2)),
% 0.20/0.41 inference(monotonicity,[status(thm)],[120])).
% 0.20/0.41 tff(122,plain,
% 0.20/0.41 (in(A!3, B!2) <=> in(tptp_fun_C_1(B!2, singleton(A!3)), B!2)),
% 0.20/0.41 inference(symmetry,[status(thm)],[121])).
% 0.20/0.41 tff(123,plain,
% 0.20/0.41 (in(tptp_fun_C_1(B!2, singleton(A!3)), B!2)),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[107, 122])).
% 0.20/0.41 tff(124,plain,
% 0.20/0.41 (((~in(tptp_fun_C_1(B!2, singleton(A!3)), singleton(A!3))) | in(tptp_fun_C_1(B!2, singleton(A!3)), B!2)) | (~in(tptp_fun_C_1(B!2, singleton(A!3)), B!2))),
% 0.20/0.41 inference(tautology,[status(thm)],[])).
% 0.20/0.41 tff(125,plain,
% 0.20/0.41 (~in(tptp_fun_C_1(B!2, singleton(A!3)), B!2)),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[124, 115])).
% 0.20/0.41 tff(126,plain,
% 0.20/0.41 ($false),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[125, 123])).
% 0.20/0.41 % SZS output end Proof
%------------------------------------------------------------------------------