TSTP Solution File: SET882+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SET882+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n007.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 20 05:08:30 EDT 2022
% Result : Theorem 0.22s 0.40s
% Output : Proof 0.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SET882+1 : TPTP v8.1.0. Released v3.2.0.
% 0.04/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.35 % Computer : n007.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Sat Sep 3 08:12:19 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.14/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.14/0.35 Usage: tptp [options] [-file:]file
% 0.14/0.35 -h, -? prints this message.
% 0.14/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.14/0.35 -m, -model generate model.
% 0.14/0.35 -p, -proof generate proof.
% 0.14/0.35 -c, -core generate unsat core of named formulas.
% 0.14/0.35 -st, -statistics display statistics.
% 0.14/0.35 -t:timeout set timeout (in second).
% 0.14/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.14/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.14/0.35 -<param>:<value> configuration parameter and value.
% 0.14/0.35 -o:<output-file> file to place output in.
% 0.22/0.40 % SZS status Theorem
% 0.22/0.40 % SZS output start Proof
% 0.22/0.40 tff(tptp_fun_B_3_type, type, (
% 0.22/0.40 tptp_fun_B_3: $i)).
% 0.22/0.40 tff(tptp_fun_A_4_type, type, (
% 0.22/0.40 tptp_fun_A_4: $i)).
% 0.22/0.40 tff(in_type, type, (
% 0.22/0.40 in: ( $i * $i ) > $o)).
% 0.22/0.40 tff(singleton_type, type, (
% 0.22/0.40 singleton: $i > $i)).
% 0.22/0.40 tff(tptp_fun_C_0_type, type, (
% 0.22/0.40 tptp_fun_C_0: ( $i * $i ) > $i)).
% 0.22/0.40 tff(set_difference_type, type, (
% 0.22/0.40 set_difference: ( $i * $i ) > $i)).
% 0.22/0.40 tff(unordered_pair_type, type, (
% 0.22/0.40 unordered_pair: ( $i * $i ) > $i)).
% 0.22/0.40 tff(1,assumption,(~in(B!3, singleton(B!3))), introduced(assumption)).
% 0.22/0.40 tff(2,plain,
% 0.22/0.40 (^[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)))))))),
% 0.22/0.40 inference(bind,[status(th)],[])).
% 0.22/0.40 tff(3,plain,
% 0.22/0.40 (![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))))))),
% 0.22/0.40 inference(quant_intro,[status(thm)],[2])).
% 0.22/0.40 tff(4,plain,
% 0.22/0.40 (![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))))))),
% 0.22/0.40 inference(pull_quant,[status(thm)],[])).
% 0.22/0.40 tff(5,plain,
% 0.22/0.40 (^[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))))))))),
% 0.22/0.40 inference(bind,[status(th)],[])).
% 0.22/0.40 tff(6,plain,
% 0.22/0.40 (![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))))))),
% 0.22/0.40 inference(quant_intro,[status(thm)],[5])).
% 0.22/0.40 tff(7,plain,
% 0.22/0.40 (![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))))))),
% 0.22/0.40 inference(transitivity,[status(thm)],[6, 4])).
% 0.22/0.40 tff(8,plain,
% 0.22/0.40 (![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))))))),
% 0.22/0.40 inference(transitivity,[status(thm)],[7, 3])).
% 0.22/0.40 tff(9,plain,
% 0.22/0.40 (^[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)))))))),
% 0.22/0.40 inference(bind,[status(th)],[])).
% 0.22/0.40 tff(10,plain,
% 0.22/0.40 (![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))))))),
% 0.22/0.40 inference(quant_intro,[status(thm)],[9])).
% 0.22/0.40 tff(11,plain,
% 0.22/0.40 (![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))))))),
% 0.22/0.40 inference(transitivity,[status(thm)],[10, 8])).
% 0.22/0.40 tff(12,plain,
% 0.22/0.40 (^[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))))))))),
% 0.22/0.40 inference(bind,[status(th)],[])).
% 0.22/0.40 tff(13,plain,
% 0.22/0.40 (![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))))))),
% 0.22/0.40 inference(quant_intro,[status(thm)],[12])).
% 0.22/0.40 tff(14,plain,
% 0.22/0.40 (^[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)))))),
% 0.22/0.40 inference(bind,[status(th)],[])).
% 0.22/0.40 tff(15,plain,
% 0.22/0.40 (![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))))),
% 0.22/0.40 inference(quant_intro,[status(thm)],[14])).
% 0.22/0.40 tff(16,plain,
% 0.22/0.40 (![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)))),
% 0.22/0.40 inference(rewrite,[status(thm)],[])).
% 0.22/0.40 tff(17,axiom,(![A: $i, B: $i] : ((B = singleton(A)) <=> ![C: $i] : (in(C, B) <=> (C = A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d1_tarski')).
% 0.22/0.40 tff(18,plain,
% 0.22/0.40 (![A: $i, B: $i] : ((B = singleton(A)) <=> ![C: $i] : (in(C, B) <=> (C = A)))),
% 0.22/0.40 inference(modus_ponens,[status(thm)],[17, 16])).
% 0.22/0.40 tff(19,plain,(
% 0.22/0.40 ![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)))))),
% 0.22/0.40 inference(skolemize,[status(sab)],[18])).
% 0.22/0.40 tff(20,plain,
% 0.22/0.40 (![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))))),
% 0.22/0.40 inference(modus_ponens,[status(thm)],[19, 15])).
% 0.22/0.40 tff(21,plain,
% 0.22/0.40 (![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))))))),
% 0.22/0.40 inference(modus_ponens,[status(thm)],[20, 13])).
% 0.22/0.40 tff(22,plain,
% 0.22/0.40 (![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))))))),
% 0.22/0.40 inference(modus_ponens,[status(thm)],[21, 11])).
% 0.22/0.40 tff(23,plain,
% 0.22/0.40 (((~![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(B!3, singleton(B!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(B!3, singleton(B!3)))),
% 0.22/0.40 inference(rewrite,[status(thm)],[])).
% 0.22/0.40 tff(24,plain,
% 0.22/0.40 ((~(~in(B!3, singleton(B!3)))) <=> in(B!3, singleton(B!3))),
% 0.22/0.40 inference(rewrite,[status(thm)],[])).
% 0.22/0.40 tff(25,plain,
% 0.22/0.40 (((~in(B!3, singleton(B!3))) | $false) <=> (~in(B!3, singleton(B!3)))),
% 0.22/0.40 inference(rewrite,[status(thm)],[])).
% 0.22/0.40 tff(26,plain,
% 0.22/0.40 ((~$true) <=> $false),
% 0.22/0.40 inference(rewrite,[status(thm)],[])).
% 0.22/0.40 tff(27,plain,
% 0.22/0.40 (($true | ((~in(tptp_fun_C_0(singleton(B!3), B!3), singleton(B!3))) <=> (tptp_fun_C_0(singleton(B!3), B!3) = B!3))) <=> $true),
% 0.22/0.40 inference(rewrite,[status(thm)],[])).
% 0.22/0.40 tff(28,plain,
% 0.22/0.40 ((singleton(B!3) = singleton(B!3)) <=> $true),
% 0.22/0.40 inference(rewrite,[status(thm)],[])).
% 0.22/0.40 tff(29,plain,
% 0.22/0.40 (((singleton(B!3) = singleton(B!3)) | ((~in(tptp_fun_C_0(singleton(B!3), B!3), singleton(B!3))) <=> (tptp_fun_C_0(singleton(B!3), B!3) = B!3))) <=> ($true | ((~in(tptp_fun_C_0(singleton(B!3), B!3), singleton(B!3))) <=> (tptp_fun_C_0(singleton(B!3), B!3) = B!3)))),
% 0.22/0.40 inference(monotonicity,[status(thm)],[28])).
% 0.22/0.40 tff(30,plain,
% 0.22/0.40 (((singleton(B!3) = singleton(B!3)) | ((~in(tptp_fun_C_0(singleton(B!3), B!3), singleton(B!3))) <=> (tptp_fun_C_0(singleton(B!3), B!3) = B!3))) <=> $true),
% 0.22/0.41 inference(transitivity,[status(thm)],[29, 27])).
% 0.22/0.41 tff(31,plain,
% 0.22/0.41 ((~((singleton(B!3) = singleton(B!3)) | ((~in(tptp_fun_C_0(singleton(B!3), B!3), singleton(B!3))) <=> (tptp_fun_C_0(singleton(B!3), B!3) = B!3)))) <=> (~$true)),
% 0.22/0.41 inference(monotonicity,[status(thm)],[30])).
% 0.22/0.41 tff(32,plain,
% 0.22/0.41 ((~((singleton(B!3) = singleton(B!3)) | ((~in(tptp_fun_C_0(singleton(B!3), B!3), singleton(B!3))) <=> (tptp_fun_C_0(singleton(B!3), B!3) = B!3)))) <=> $false),
% 0.22/0.41 inference(transitivity,[status(thm)],[31, 26])).
% 0.22/0.41 tff(33,plain,
% 0.22/0.41 ((~((~(singleton(B!3) = singleton(B!3))) | (in(B!3, singleton(B!3)) <=> (B!3 = B!3)))) <=> (~in(B!3, singleton(B!3)))),
% 0.22/0.41 inference(rewrite,[status(thm)],[])).
% 0.22/0.41 tff(34,plain,
% 0.22/0.41 (((~((~(singleton(B!3) = singleton(B!3))) | (in(B!3, singleton(B!3)) <=> (B!3 = B!3)))) | (~((singleton(B!3) = singleton(B!3)) | ((~in(tptp_fun_C_0(singleton(B!3), B!3), singleton(B!3))) <=> (tptp_fun_C_0(singleton(B!3), B!3) = B!3))))) <=> ((~in(B!3, singleton(B!3))) | $false)),
% 0.22/0.41 inference(monotonicity,[status(thm)],[33, 32])).
% 0.22/0.41 tff(35,plain,
% 0.22/0.41 (((~((~(singleton(B!3) = singleton(B!3))) | (in(B!3, singleton(B!3)) <=> (B!3 = B!3)))) | (~((singleton(B!3) = singleton(B!3)) | ((~in(tptp_fun_C_0(singleton(B!3), B!3), singleton(B!3))) <=> (tptp_fun_C_0(singleton(B!3), B!3) = B!3))))) <=> (~in(B!3, singleton(B!3)))),
% 0.22/0.41 inference(transitivity,[status(thm)],[34, 25])).
% 0.22/0.41 tff(36,plain,
% 0.22/0.41 ((~((~((~(singleton(B!3) = singleton(B!3))) | (in(B!3, singleton(B!3)) <=> (B!3 = B!3)))) | (~((singleton(B!3) = singleton(B!3)) | ((~in(tptp_fun_C_0(singleton(B!3), B!3), singleton(B!3))) <=> (tptp_fun_C_0(singleton(B!3), B!3) = B!3)))))) <=> (~(~in(B!3, singleton(B!3))))),
% 0.22/0.41 inference(monotonicity,[status(thm)],[35])).
% 0.22/0.41 tff(37,plain,
% 0.22/0.41 ((~((~((~(singleton(B!3) = singleton(B!3))) | (in(B!3, singleton(B!3)) <=> (B!3 = B!3)))) | (~((singleton(B!3) = singleton(B!3)) | ((~in(tptp_fun_C_0(singleton(B!3), B!3), singleton(B!3))) <=> (tptp_fun_C_0(singleton(B!3), B!3) = B!3)))))) <=> in(B!3, singleton(B!3))),
% 0.22/0.41 inference(transitivity,[status(thm)],[36, 24])).
% 0.22/0.41 tff(38,plain,
% 0.22/0.41 (((~![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))))))) | (~((~((~(singleton(B!3) = singleton(B!3))) | (in(B!3, singleton(B!3)) <=> (B!3 = B!3)))) | (~((singleton(B!3) = singleton(B!3)) | ((~in(tptp_fun_C_0(singleton(B!3), B!3), singleton(B!3))) <=> (tptp_fun_C_0(singleton(B!3), B!3) = B!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(B!3, singleton(B!3)))),
% 0.22/0.41 inference(monotonicity,[status(thm)],[37])).
% 0.22/0.41 tff(39,plain,
% 0.22/0.41 (((~![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))))))) | (~((~((~(singleton(B!3) = singleton(B!3))) | (in(B!3, singleton(B!3)) <=> (B!3 = B!3)))) | (~((singleton(B!3) = singleton(B!3)) | ((~in(tptp_fun_C_0(singleton(B!3), B!3), singleton(B!3))) <=> (tptp_fun_C_0(singleton(B!3), B!3) = B!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(B!3, singleton(B!3)))),
% 0.22/0.41 inference(transitivity,[status(thm)],[38, 23])).
% 0.22/0.41 tff(40,plain,
% 0.22/0.41 ((~![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))))))) | (~((~((~(singleton(B!3) = singleton(B!3))) | (in(B!3, singleton(B!3)) <=> (B!3 = B!3)))) | (~((singleton(B!3) = singleton(B!3)) | ((~in(tptp_fun_C_0(singleton(B!3), B!3), singleton(B!3))) <=> (tptp_fun_C_0(singleton(B!3), B!3) = B!3))))))),
% 0.22/0.41 inference(quant_inst,[status(thm)],[])).
% 0.22/0.41 tff(41,plain,
% 0.22/0.41 ((~![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))))) | in(B!3, singleton(B!3))),
% 0.22/0.41 inference(modus_ponens,[status(thm)],[40, 39])).
% 0.22/0.41 tff(42,plain,
% 0.22/0.41 ($false),
% 0.22/0.41 inference(unit_resolution,[status(thm)],[41, 22, 1])).
% 0.22/0.41 tff(43,plain,(in(B!3, singleton(B!3))), inference(lemma,lemma(discharge,[]))).
% 0.22/0.41 tff(44,plain,
% 0.22/0.41 (((A!4 = B!3) | in(B!3, singleton(B!3))) | (~in(B!3, singleton(B!3)))),
% 0.22/0.41 inference(tautology,[status(thm)],[])).
% 0.22/0.41 tff(45,plain,
% 0.22/0.41 ((A!4 = B!3) | in(B!3, singleton(B!3))),
% 0.22/0.41 inference(unit_resolution,[status(thm)],[44, 43])).
% 0.22/0.41 tff(46,plain,
% 0.22/0.41 (^[A: $i, B: $i, C: $i] : refl(((set_difference(unordered_pair(A, B), C) = singleton(A)) <=> (~(in(A, C) | (~(in(B, C) | (A = B)))))) <=> ((set_difference(unordered_pair(A, B), C) = singleton(A)) <=> (~(in(A, C) | (~(in(B, C) | (A = B)))))))),
% 0.22/0.41 inference(bind,[status(th)],[])).
% 0.22/0.41 tff(47,plain,
% 0.22/0.41 (![A: $i, B: $i, C: $i] : ((set_difference(unordered_pair(A, B), C) = singleton(A)) <=> (~(in(A, C) | (~(in(B, C) | (A = B)))))) <=> ![A: $i, B: $i, C: $i] : ((set_difference(unordered_pair(A, B), C) = singleton(A)) <=> (~(in(A, C) | (~(in(B, C) | (A = B))))))),
% 0.22/0.41 inference(quant_intro,[status(thm)],[46])).
% 0.22/0.41 tff(48,plain,
% 0.22/0.41 (^[A: $i, B: $i, C: $i] : rewrite(((set_difference(unordered_pair(A, B), C) = singleton(A)) <=> ((~in(A, C)) & (in(B, C) | (A = B)))) <=> ((set_difference(unordered_pair(A, B), C) = singleton(A)) <=> (~(in(A, C) | (~(in(B, C) | (A = B)))))))),
% 0.22/0.41 inference(bind,[status(th)],[])).
% 0.22/0.41 tff(49,plain,
% 0.22/0.41 (![A: $i, B: $i, C: $i] : ((set_difference(unordered_pair(A, B), C) = singleton(A)) <=> ((~in(A, C)) & (in(B, C) | (A = B)))) <=> ![A: $i, B: $i, C: $i] : ((set_difference(unordered_pair(A, B), C) = singleton(A)) <=> (~(in(A, C) | (~(in(B, C) | (A = B))))))),
% 0.22/0.41 inference(quant_intro,[status(thm)],[48])).
% 0.22/0.41 tff(50,plain,
% 0.22/0.41 (![A: $i, B: $i, C: $i] : ((set_difference(unordered_pair(A, B), C) = singleton(A)) <=> ((~in(A, C)) & (in(B, C) | (A = B)))) <=> ![A: $i, B: $i, C: $i] : ((set_difference(unordered_pair(A, B), C) = singleton(A)) <=> ((~in(A, C)) & (in(B, C) | (A = B))))),
% 0.22/0.41 inference(rewrite,[status(thm)],[])).
% 0.22/0.41 tff(51,axiom,(![A: $i, B: $i, C: $i] : ((set_difference(unordered_pair(A, B), C) = singleton(A)) <=> ((~in(A, C)) & (in(B, C) | (A = B))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','l39_zfmisc_1')).
% 0.22/0.41 tff(52,plain,
% 0.22/0.41 (![A: $i, B: $i, C: $i] : ((set_difference(unordered_pair(A, B), C) = singleton(A)) <=> ((~in(A, C)) & (in(B, C) | (A = B))))),
% 0.22/0.41 inference(modus_ponens,[status(thm)],[51, 50])).
% 0.22/0.41 tff(53,plain,(
% 0.22/0.41 ![A: $i, B: $i, C: $i] : ((set_difference(unordered_pair(A, B), C) = singleton(A)) <=> ((~in(A, C)) & (in(B, C) | (A = B))))),
% 0.22/0.41 inference(skolemize,[status(sab)],[52])).
% 0.22/0.41 tff(54,plain,
% 0.22/0.41 (![A: $i, B: $i, C: $i] : ((set_difference(unordered_pair(A, B), C) = singleton(A)) <=> (~(in(A, C) | (~(in(B, C) | (A = B))))))),
% 0.22/0.41 inference(modus_ponens,[status(thm)],[53, 49])).
% 0.22/0.41 tff(55,plain,
% 0.22/0.41 (![A: $i, B: $i, C: $i] : ((set_difference(unordered_pair(A, B), C) = singleton(A)) <=> (~(in(A, C) | (~(in(B, C) | (A = B))))))),
% 0.22/0.41 inference(modus_ponens,[status(thm)],[54, 47])).
% 0.22/0.41 tff(56,plain,
% 0.22/0.41 (((~![A: $i, B: $i, C: $i] : ((set_difference(unordered_pair(A, B), C) = singleton(A)) <=> (~(in(A, C) | (~(in(B, C) | (A = B))))))) | ((set_difference(unordered_pair(A!4, B!3), singleton(B!3)) = singleton(A!4)) <=> (~(in(A!4, singleton(B!3)) | (~((A!4 = B!3) | in(B!3, singleton(B!3)))))))) <=> ((~![A: $i, B: $i, C: $i] : ((set_difference(unordered_pair(A, B), C) = singleton(A)) <=> (~(in(A, C) | (~(in(B, C) | (A = B))))))) | ((set_difference(unordered_pair(A!4, B!3), singleton(B!3)) = singleton(A!4)) <=> (~(in(A!4, singleton(B!3)) | (~((A!4 = B!3) | in(B!3, singleton(B!3))))))))),
% 0.22/0.41 inference(rewrite,[status(thm)],[])).
% 0.22/0.41 tff(57,plain,
% 0.22/0.41 (((set_difference(unordered_pair(A!4, B!3), singleton(B!3)) = singleton(A!4)) <=> (~(in(A!4, singleton(B!3)) | (~(in(B!3, singleton(B!3)) | (A!4 = B!3)))))) <=> ((set_difference(unordered_pair(A!4, B!3), singleton(B!3)) = singleton(A!4)) <=> (~(in(A!4, singleton(B!3)) | (~((A!4 = B!3) | in(B!3, singleton(B!3)))))))),
% 0.22/0.41 inference(rewrite,[status(thm)],[])).
% 0.22/0.41 tff(58,plain,
% 0.22/0.41 (((~![A: $i, B: $i, C: $i] : ((set_difference(unordered_pair(A, B), C) = singleton(A)) <=> (~(in(A, C) | (~(in(B, C) | (A = B))))))) | ((set_difference(unordered_pair(A!4, B!3), singleton(B!3)) = singleton(A!4)) <=> (~(in(A!4, singleton(B!3)) | (~(in(B!3, singleton(B!3)) | (A!4 = B!3))))))) <=> ((~![A: $i, B: $i, C: $i] : ((set_difference(unordered_pair(A, B), C) = singleton(A)) <=> (~(in(A, C) | (~(in(B, C) | (A = B))))))) | ((set_difference(unordered_pair(A!4, B!3), singleton(B!3)) = singleton(A!4)) <=> (~(in(A!4, singleton(B!3)) | (~((A!4 = B!3) | in(B!3, singleton(B!3))))))))),
% 0.22/0.41 inference(monotonicity,[status(thm)],[57])).
% 0.22/0.41 tff(59,plain,
% 0.22/0.41 (((~![A: $i, B: $i, C: $i] : ((set_difference(unordered_pair(A, B), C) = singleton(A)) <=> (~(in(A, C) | (~(in(B, C) | (A = B))))))) | ((set_difference(unordered_pair(A!4, B!3), singleton(B!3)) = singleton(A!4)) <=> (~(in(A!4, singleton(B!3)) | (~(in(B!3, singleton(B!3)) | (A!4 = B!3))))))) <=> ((~![A: $i, B: $i, C: $i] : ((set_difference(unordered_pair(A, B), C) = singleton(A)) <=> (~(in(A, C) | (~(in(B, C) | (A = B))))))) | ((set_difference(unordered_pair(A!4, B!3), singleton(B!3)) = singleton(A!4)) <=> (~(in(A!4, singleton(B!3)) | (~((A!4 = B!3) | in(B!3, singleton(B!3))))))))),
% 0.22/0.41 inference(transitivity,[status(thm)],[58, 56])).
% 0.22/0.41 tff(60,plain,
% 0.22/0.41 ((~![A: $i, B: $i, C: $i] : ((set_difference(unordered_pair(A, B), C) = singleton(A)) <=> (~(in(A, C) | (~(in(B, C) | (A = B))))))) | ((set_difference(unordered_pair(A!4, B!3), singleton(B!3)) = singleton(A!4)) <=> (~(in(A!4, singleton(B!3)) | (~(in(B!3, singleton(B!3)) | (A!4 = B!3))))))),
% 0.22/0.41 inference(quant_inst,[status(thm)],[])).
% 0.22/0.41 tff(61,plain,
% 0.22/0.41 ((~![A: $i, B: $i, C: $i] : ((set_difference(unordered_pair(A, B), C) = singleton(A)) <=> (~(in(A, C) | (~(in(B, C) | (A = B))))))) | ((set_difference(unordered_pair(A!4, B!3), singleton(B!3)) = singleton(A!4)) <=> (~(in(A!4, singleton(B!3)) | (~((A!4 = B!3) | in(B!3, singleton(B!3)))))))),
% 0.22/0.41 inference(modus_ponens,[status(thm)],[60, 59])).
% 0.22/0.41 tff(62,plain,
% 0.22/0.41 ((set_difference(unordered_pair(A!4, B!3), singleton(B!3)) = singleton(A!4)) <=> (~(in(A!4, singleton(B!3)) | (~((A!4 = B!3) | in(B!3, singleton(B!3))))))),
% 0.22/0.41 inference(unit_resolution,[status(thm)],[61, 55])).
% 0.22/0.41 tff(63,plain,
% 0.22/0.41 ((~![A: $i, B: $i] : ((A = B) | (set_difference(unordered_pair(A, B), singleton(B)) = singleton(A)))) <=> (~![A: $i, B: $i] : ((A = B) | (set_difference(unordered_pair(A, B), singleton(B)) = singleton(A))))),
% 0.22/0.41 inference(rewrite,[status(thm)],[])).
% 0.22/0.41 tff(64,plain,
% 0.22/0.41 ((~![A: $i, B: $i] : ((~(A = B)) => (set_difference(unordered_pair(A, B), singleton(B)) = singleton(A)))) <=> (~![A: $i, B: $i] : ((A = B) | (set_difference(unordered_pair(A, B), singleton(B)) = singleton(A))))),
% 0.22/0.41 inference(rewrite,[status(thm)],[])).
% 0.22/0.41 tff(65,axiom,(~![A: $i, B: $i] : ((~(A = B)) => (set_difference(unordered_pair(A, B), singleton(B)) = singleton(A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t23_zfmisc_1')).
% 0.22/0.41 tff(66,plain,
% 0.22/0.41 (~![A: $i, B: $i] : ((A = B) | (set_difference(unordered_pair(A, B), singleton(B)) = singleton(A)))),
% 0.22/0.41 inference(modus_ponens,[status(thm)],[65, 64])).
% 0.22/0.41 tff(67,plain,
% 0.22/0.41 (~![A: $i, B: $i] : ((A = B) | (set_difference(unordered_pair(A, B), singleton(B)) = singleton(A)))),
% 0.22/0.41 inference(modus_ponens,[status(thm)],[66, 63])).
% 0.22/0.41 tff(68,plain,
% 0.22/0.41 (~![A: $i, B: $i] : ((A = B) | (set_difference(unordered_pair(A, B), singleton(B)) = singleton(A)))),
% 0.22/0.41 inference(modus_ponens,[status(thm)],[67, 63])).
% 0.22/0.41 tff(69,plain,
% 0.22/0.41 (~![A: $i, B: $i] : ((A = B) | (set_difference(unordered_pair(A, B), singleton(B)) = singleton(A)))),
% 0.22/0.41 inference(modus_ponens,[status(thm)],[68, 63])).
% 0.22/0.41 tff(70,plain,
% 0.22/0.41 (~![A: $i, B: $i] : ((A = B) | (set_difference(unordered_pair(A, B), singleton(B)) = singleton(A)))),
% 0.22/0.41 inference(modus_ponens,[status(thm)],[69, 63])).
% 0.22/0.41 tff(71,plain,
% 0.22/0.41 (~![A: $i, B: $i] : ((A = B) | (set_difference(unordered_pair(A, B), singleton(B)) = singleton(A)))),
% 0.22/0.41 inference(modus_ponens,[status(thm)],[70, 63])).
% 0.22/0.41 tff(72,plain,
% 0.22/0.41 (~![A: $i, B: $i] : ((A = B) | (set_difference(unordered_pair(A, B), singleton(B)) = singleton(A)))),
% 0.22/0.41 inference(modus_ponens,[status(thm)],[71, 63])).
% 0.22/0.41 tff(73,plain,(
% 0.22/0.41 ~((A!4 = B!3) | (set_difference(unordered_pair(A!4, B!3), singleton(B!3)) = singleton(A!4)))),
% 0.22/0.41 inference(skolemize,[status(sab)],[72])).
% 0.22/0.41 tff(74,plain,
% 0.22/0.41 (~(set_difference(unordered_pair(A!4, B!3), singleton(B!3)) = singleton(A!4))),
% 0.22/0.41 inference(or_elim,[status(thm)],[73])).
% 0.22/0.41 tff(75,plain,
% 0.22/0.41 ((~((set_difference(unordered_pair(A!4, B!3), singleton(B!3)) = singleton(A!4)) <=> (~(in(A!4, singleton(B!3)) | (~((A!4 = B!3) | in(B!3, singleton(B!3)))))))) | (set_difference(unordered_pair(A!4, B!3), singleton(B!3)) = singleton(A!4)) | (in(A!4, singleton(B!3)) | (~((A!4 = B!3) | in(B!3, singleton(B!3)))))),
% 0.22/0.41 inference(tautology,[status(thm)],[])).
% 0.22/0.41 tff(76,plain,
% 0.22/0.41 ((~((set_difference(unordered_pair(A!4, B!3), singleton(B!3)) = singleton(A!4)) <=> (~(in(A!4, singleton(B!3)) | (~((A!4 = B!3) | in(B!3, singleton(B!3)))))))) | (in(A!4, singleton(B!3)) | (~((A!4 = B!3) | in(B!3, singleton(B!3)))))),
% 0.22/0.41 inference(unit_resolution,[status(thm)],[75, 74])).
% 0.22/0.41 tff(77,plain,
% 0.22/0.41 (in(A!4, singleton(B!3)) | (~((A!4 = B!3) | in(B!3, singleton(B!3))))),
% 0.22/0.41 inference(unit_resolution,[status(thm)],[76, 62])).
% 0.22/0.41 tff(78,plain,
% 0.22/0.41 ((~(in(A!4, singleton(B!3)) | (~((A!4 = B!3) | in(B!3, singleton(B!3)))))) | in(A!4, singleton(B!3)) | (~((A!4 = B!3) | in(B!3, singleton(B!3))))),
% 0.22/0.41 inference(tautology,[status(thm)],[])).
% 0.22/0.41 tff(79,plain,
% 0.22/0.41 (in(A!4, singleton(B!3)) | (~((A!4 = B!3) | in(B!3, singleton(B!3))))),
% 0.22/0.41 inference(unit_resolution,[status(thm)],[78, 77])).
% 0.22/0.41 tff(80,plain,
% 0.22/0.41 (in(A!4, singleton(B!3))),
% 0.22/0.41 inference(unit_resolution,[status(thm)],[79, 45])).
% 0.22/0.41 tff(81,plain,
% 0.22/0.41 (~(A!4 = B!3)),
% 0.22/0.41 inference(or_elim,[status(thm)],[73])).
% 0.22/0.41 tff(82,plain,
% 0.22/0.41 ((~(in(A!4, singleton(B!3)) <=> (A!4 = B!3))) | (~in(A!4, singleton(B!3))) | (A!4 = B!3)),
% 0.22/0.41 inference(tautology,[status(thm)],[])).
% 0.22/0.41 tff(83,plain,
% 0.22/0.41 (~(in(A!4, singleton(B!3)) <=> (A!4 = B!3))),
% 0.22/0.41 inference(unit_resolution,[status(thm)],[82, 81, 80])).
% 0.22/0.41 tff(84,plain,
% 0.22/0.41 (((~![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))))))) | (in(A!4, singleton(B!3)) <=> (A!4 = B!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!4, singleton(B!3)) <=> (A!4 = B!3)))),
% 0.22/0.41 inference(rewrite,[status(thm)],[])).
% 0.22/0.41 tff(85,plain,
% 0.22/0.41 ((~((~in(A!4, singleton(B!3))) <=> (A!4 = B!3))) <=> (in(A!4, singleton(B!3)) <=> (A!4 = B!3))),
% 0.22/0.41 inference(rewrite,[status(thm)],[])).
% 0.22/0.41 tff(86,plain,
% 0.22/0.41 ((((~in(A!4, singleton(B!3))) <=> (A!4 = B!3)) | $false) <=> ((~in(A!4, singleton(B!3))) <=> (A!4 = B!3))),
% 0.22/0.41 inference(rewrite,[status(thm)],[])).
% 0.22/0.41 tff(87,plain,
% 0.22/0.41 ((~(in(A!4, singleton(B!3)) <=> (A!4 = B!3))) <=> ((~in(A!4, singleton(B!3))) <=> (A!4 = B!3))),
% 0.22/0.41 inference(rewrite,[status(thm)],[])).
% 0.22/0.41 tff(88,plain,
% 0.22/0.41 (($false | (in(A!4, singleton(B!3)) <=> (A!4 = B!3))) <=> (in(A!4, singleton(B!3)) <=> (A!4 = B!3))),
% 0.22/0.41 inference(rewrite,[status(thm)],[])).
% 0.22/0.41 tff(89,plain,
% 0.22/0.41 ((~(singleton(B!3) = singleton(B!3))) <=> (~$true)),
% 0.22/0.41 inference(monotonicity,[status(thm)],[28])).
% 0.22/0.41 tff(90,plain,
% 0.22/0.41 ((~(singleton(B!3) = singleton(B!3))) <=> $false),
% 0.22/0.41 inference(transitivity,[status(thm)],[89, 26])).
% 0.22/0.41 tff(91,plain,
% 0.22/0.41 (((~(singleton(B!3) = singleton(B!3))) | (in(A!4, singleton(B!3)) <=> (A!4 = B!3))) <=> ($false | (in(A!4, singleton(B!3)) <=> (A!4 = B!3)))),
% 0.22/0.41 inference(monotonicity,[status(thm)],[90])).
% 0.22/0.41 tff(92,plain,
% 0.22/0.41 (((~(singleton(B!3) = singleton(B!3))) | (in(A!4, singleton(B!3)) <=> (A!4 = B!3))) <=> (in(A!4, singleton(B!3)) <=> (A!4 = B!3))),
% 0.22/0.41 inference(transitivity,[status(thm)],[91, 88])).
% 0.22/0.41 tff(93,plain,
% 0.22/0.41 ((~((~(singleton(B!3) = singleton(B!3))) | (in(A!4, singleton(B!3)) <=> (A!4 = B!3)))) <=> (~(in(A!4, singleton(B!3)) <=> (A!4 = B!3)))),
% 0.22/0.41 inference(monotonicity,[status(thm)],[92])).
% 0.22/0.42 tff(94,plain,
% 0.22/0.42 ((~((~(singleton(B!3) = singleton(B!3))) | (in(A!4, singleton(B!3)) <=> (A!4 = B!3)))) <=> ((~in(A!4, singleton(B!3))) <=> (A!4 = B!3))),
% 0.22/0.42 inference(transitivity,[status(thm)],[93, 87])).
% 0.22/0.42 tff(95,plain,
% 0.22/0.42 (((~((~(singleton(B!3) = singleton(B!3))) | (in(A!4, singleton(B!3)) <=> (A!4 = B!3)))) | (~((singleton(B!3) = singleton(B!3)) | ((~in(tptp_fun_C_0(singleton(B!3), B!3), singleton(B!3))) <=> (tptp_fun_C_0(singleton(B!3), B!3) = B!3))))) <=> (((~in(A!4, singleton(B!3))) <=> (A!4 = B!3)) | $false)),
% 0.22/0.42 inference(monotonicity,[status(thm)],[94, 32])).
% 0.22/0.42 tff(96,plain,
% 0.22/0.42 (((~((~(singleton(B!3) = singleton(B!3))) | (in(A!4, singleton(B!3)) <=> (A!4 = B!3)))) | (~((singleton(B!3) = singleton(B!3)) | ((~in(tptp_fun_C_0(singleton(B!3), B!3), singleton(B!3))) <=> (tptp_fun_C_0(singleton(B!3), B!3) = B!3))))) <=> ((~in(A!4, singleton(B!3))) <=> (A!4 = B!3))),
% 0.22/0.42 inference(transitivity,[status(thm)],[95, 86])).
% 0.22/0.42 tff(97,plain,
% 0.22/0.42 ((~((~((~(singleton(B!3) = singleton(B!3))) | (in(A!4, singleton(B!3)) <=> (A!4 = B!3)))) | (~((singleton(B!3) = singleton(B!3)) | ((~in(tptp_fun_C_0(singleton(B!3), B!3), singleton(B!3))) <=> (tptp_fun_C_0(singleton(B!3), B!3) = B!3)))))) <=> (~((~in(A!4, singleton(B!3))) <=> (A!4 = B!3)))),
% 0.22/0.42 inference(monotonicity,[status(thm)],[96])).
% 0.22/0.42 tff(98,plain,
% 0.22/0.42 ((~((~((~(singleton(B!3) = singleton(B!3))) | (in(A!4, singleton(B!3)) <=> (A!4 = B!3)))) | (~((singleton(B!3) = singleton(B!3)) | ((~in(tptp_fun_C_0(singleton(B!3), B!3), singleton(B!3))) <=> (tptp_fun_C_0(singleton(B!3), B!3) = B!3)))))) <=> (in(A!4, singleton(B!3)) <=> (A!4 = B!3))),
% 0.22/0.42 inference(transitivity,[status(thm)],[97, 85])).
% 0.22/0.42 tff(99,plain,
% 0.22/0.42 (((~![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(B!3) = singleton(B!3))) | (in(A!4, singleton(B!3)) <=> (A!4 = B!3)))) | (~((singleton(B!3) = singleton(B!3)) | ((~in(tptp_fun_C_0(singleton(B!3), B!3), singleton(B!3))) <=> (tptp_fun_C_0(singleton(B!3), B!3) = B!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!4, singleton(B!3)) <=> (A!4 = B!3)))),
% 0.22/0.42 inference(monotonicity,[status(thm)],[98])).
% 0.22/0.42 tff(100,plain,
% 0.22/0.42 (((~![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(B!3) = singleton(B!3))) | (in(A!4, singleton(B!3)) <=> (A!4 = B!3)))) | (~((singleton(B!3) = singleton(B!3)) | ((~in(tptp_fun_C_0(singleton(B!3), B!3), singleton(B!3))) <=> (tptp_fun_C_0(singleton(B!3), B!3) = B!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!4, singleton(B!3)) <=> (A!4 = B!3)))),
% 0.22/0.42 inference(transitivity,[status(thm)],[99, 84])).
% 0.22/0.42 tff(101,plain,
% 0.22/0.42 ((~![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(B!3) = singleton(B!3))) | (in(A!4, singleton(B!3)) <=> (A!4 = B!3)))) | (~((singleton(B!3) = singleton(B!3)) | ((~in(tptp_fun_C_0(singleton(B!3), B!3), singleton(B!3))) <=> (tptp_fun_C_0(singleton(B!3), B!3) = B!3))))))),
% 0.22/0.42 inference(quant_inst,[status(thm)],[])).
% 0.22/0.42 tff(102,plain,
% 0.22/0.42 ((~![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))))) | (in(A!4, singleton(B!3)) <=> (A!4 = B!3))),
% 0.22/0.42 inference(modus_ponens,[status(thm)],[101, 100])).
% 0.22/0.42 tff(103,plain,
% 0.22/0.42 ($false),
% 0.22/0.42 inference(unit_resolution,[status(thm)],[102, 22, 83])).
% 0.22/0.42 % SZS output end Proof
%------------------------------------------------------------------------------