TSTP Solution File: SET873+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SET873+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n011.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 05:08:28 EDT 2022
% Result : Theorem 0.12s 0.39s
% Output : Proof 0.12s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SET873+1 : TPTP v8.1.0. Released v3.2.0.
% 0.12/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.34 % Computer : n011.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Sat Sep 3 08:23:13 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.35 Usage: tptp [options] [-file:]file
% 0.12/0.35 -h, -? prints this message.
% 0.12/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.35 -m, -model generate model.
% 0.12/0.35 -p, -proof generate proof.
% 0.12/0.35 -c, -core generate unsat core of named formulas.
% 0.12/0.35 -st, -statistics display statistics.
% 0.12/0.35 -t:timeout set timeout (in second).
% 0.12/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.35 -<param>:<value> configuration parameter and value.
% 0.12/0.35 -o:<output-file> file to place output in.
% 0.12/0.39 % SZS status Theorem
% 0.12/0.39 % SZS output start Proof
% 0.12/0.39 tff(tptp_fun_B_3_type, type, (
% 0.12/0.39 tptp_fun_B_3: $i)).
% 0.12/0.39 tff(tptp_fun_A_4_type, type, (
% 0.12/0.39 tptp_fun_A_4: $i)).
% 0.12/0.39 tff(in_type, type, (
% 0.12/0.39 in: ( $i * $i ) > $o)).
% 0.12/0.39 tff(singleton_type, type, (
% 0.12/0.39 singleton: $i > $i)).
% 0.12/0.39 tff(tptp_fun_C_0_type, type, (
% 0.12/0.39 tptp_fun_C_0: ( $i * $i ) > $i)).
% 0.12/0.39 tff(subset_type, type, (
% 0.12/0.39 subset: ( $i * $i ) > $o)).
% 0.12/0.39 tff(set_union2_type, type, (
% 0.12/0.39 set_union2: ( $i * $i ) > $i)).
% 0.12/0.39 tff(1,plain,
% 0.12/0.39 (^[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)))))))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(2,plain,
% 0.12/0.39 (![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))))))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[1])).
% 0.12/0.39 tff(3,plain,
% 0.12/0.39 (![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))))))),
% 0.12/0.39 inference(pull_quant,[status(thm)],[])).
% 0.12/0.39 tff(4,plain,
% 0.12/0.39 (^[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))))))))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(5,plain,
% 0.12/0.39 (![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))))))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[4])).
% 0.12/0.39 tff(6,plain,
% 0.12/0.39 (![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))))))),
% 0.12/0.39 inference(transitivity,[status(thm)],[5, 3])).
% 0.12/0.39 tff(7,plain,
% 0.12/0.39 (![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))))))),
% 0.12/0.39 inference(transitivity,[status(thm)],[6, 2])).
% 0.12/0.39 tff(8,plain,
% 0.12/0.39 (^[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)))))))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(9,plain,
% 0.12/0.39 (![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))))))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[8])).
% 0.12/0.39 tff(10,plain,
% 0.12/0.39 (![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))))))),
% 0.12/0.39 inference(transitivity,[status(thm)],[9, 7])).
% 0.12/0.39 tff(11,plain,
% 0.12/0.39 (^[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))))))))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(12,plain,
% 0.12/0.39 (![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))))))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[11])).
% 0.12/0.40 tff(13,plain,
% 0.12/0.40 (^[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)))))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(14,plain,
% 0.12/0.40 (![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))))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[13])).
% 0.12/0.40 tff(15,plain,
% 0.12/0.40 (![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)))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 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')).
% 0.12/0.40 tff(17,plain,
% 0.12/0.40 (![A: $i, B: $i] : ((B = singleton(A)) <=> ![C: $i] : (in(C, B) <=> (C = A)))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[16, 15])).
% 0.12/0.40 tff(18,plain,(
% 0.12/0.40 ![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)))))),
% 0.12/0.40 inference(skolemize,[status(sab)],[17])).
% 0.12/0.40 tff(19,plain,
% 0.12/0.40 (![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))))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[18, 14])).
% 0.12/0.40 tff(20,plain,
% 0.12/0.40 (![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))))))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[19, 12])).
% 0.12/0.40 tff(21,plain,
% 0.12/0.40 (![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))))))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[20, 10])).
% 0.12/0.40 tff(22,plain,
% 0.12/0.40 (((~![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(A!4)) <=> (B!3 = A!4))) <=> ((~![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(A!4)) <=> (B!3 = A!4)))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(23,plain,
% 0.12/0.40 ((~((~in(B!3, singleton(A!4))) <=> (B!3 = A!4))) <=> (in(B!3, singleton(A!4)) <=> (B!3 = A!4))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(24,plain,
% 0.12/0.40 ((((~in(B!3, singleton(A!4))) <=> (B!3 = A!4)) | $false) <=> ((~in(B!3, singleton(A!4))) <=> (B!3 = A!4))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(25,plain,
% 0.12/0.40 ((~$true) <=> $false),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(26,plain,
% 0.12/0.40 (($true | ((~in(tptp_fun_C_0(singleton(A!4), A!4), singleton(A!4))) <=> (tptp_fun_C_0(singleton(A!4), A!4) = A!4))) <=> $true),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(27,plain,
% 0.12/0.40 ((singleton(A!4) = singleton(A!4)) <=> $true),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(28,plain,
% 0.12/0.40 (((singleton(A!4) = singleton(A!4)) | ((~in(tptp_fun_C_0(singleton(A!4), A!4), singleton(A!4))) <=> (tptp_fun_C_0(singleton(A!4), A!4) = A!4))) <=> ($true | ((~in(tptp_fun_C_0(singleton(A!4), A!4), singleton(A!4))) <=> (tptp_fun_C_0(singleton(A!4), A!4) = A!4)))),
% 0.12/0.40 inference(monotonicity,[status(thm)],[27])).
% 0.12/0.40 tff(29,plain,
% 0.12/0.40 (((singleton(A!4) = singleton(A!4)) | ((~in(tptp_fun_C_0(singleton(A!4), A!4), singleton(A!4))) <=> (tptp_fun_C_0(singleton(A!4), A!4) = A!4))) <=> $true),
% 0.12/0.40 inference(transitivity,[status(thm)],[28, 26])).
% 0.12/0.40 tff(30,plain,
% 0.12/0.40 ((~((singleton(A!4) = singleton(A!4)) | ((~in(tptp_fun_C_0(singleton(A!4), A!4), singleton(A!4))) <=> (tptp_fun_C_0(singleton(A!4), A!4) = A!4)))) <=> (~$true)),
% 0.12/0.40 inference(monotonicity,[status(thm)],[29])).
% 0.12/0.40 tff(31,plain,
% 0.12/0.40 ((~((singleton(A!4) = singleton(A!4)) | ((~in(tptp_fun_C_0(singleton(A!4), A!4), singleton(A!4))) <=> (tptp_fun_C_0(singleton(A!4), A!4) = A!4)))) <=> $false),
% 0.12/0.40 inference(transitivity,[status(thm)],[30, 25])).
% 0.12/0.40 tff(32,plain,
% 0.12/0.40 ((~(in(B!3, singleton(A!4)) <=> (B!3 = A!4))) <=> ((~in(B!3, singleton(A!4))) <=> (B!3 = A!4))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(33,plain,
% 0.12/0.40 (($false | (in(B!3, singleton(A!4)) <=> (B!3 = A!4))) <=> (in(B!3, singleton(A!4)) <=> (B!3 = A!4))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(34,plain,
% 0.12/0.40 ((~(singleton(A!4) = singleton(A!4))) <=> (~$true)),
% 0.12/0.40 inference(monotonicity,[status(thm)],[27])).
% 0.12/0.40 tff(35,plain,
% 0.12/0.40 ((~(singleton(A!4) = singleton(A!4))) <=> $false),
% 0.12/0.40 inference(transitivity,[status(thm)],[34, 25])).
% 0.12/0.40 tff(36,plain,
% 0.12/0.40 (((~(singleton(A!4) = singleton(A!4))) | (in(B!3, singleton(A!4)) <=> (B!3 = A!4))) <=> ($false | (in(B!3, singleton(A!4)) <=> (B!3 = A!4)))),
% 0.12/0.40 inference(monotonicity,[status(thm)],[35])).
% 0.12/0.40 tff(37,plain,
% 0.12/0.40 (((~(singleton(A!4) = singleton(A!4))) | (in(B!3, singleton(A!4)) <=> (B!3 = A!4))) <=> (in(B!3, singleton(A!4)) <=> (B!3 = A!4))),
% 0.12/0.40 inference(transitivity,[status(thm)],[36, 33])).
% 0.12/0.40 tff(38,plain,
% 0.12/0.40 ((~((~(singleton(A!4) = singleton(A!4))) | (in(B!3, singleton(A!4)) <=> (B!3 = A!4)))) <=> (~(in(B!3, singleton(A!4)) <=> (B!3 = A!4)))),
% 0.12/0.40 inference(monotonicity,[status(thm)],[37])).
% 0.12/0.40 tff(39,plain,
% 0.12/0.40 ((~((~(singleton(A!4) = singleton(A!4))) | (in(B!3, singleton(A!4)) <=> (B!3 = A!4)))) <=> ((~in(B!3, singleton(A!4))) <=> (B!3 = A!4))),
% 0.12/0.40 inference(transitivity,[status(thm)],[38, 32])).
% 0.12/0.40 tff(40,plain,
% 0.12/0.40 (((~((~(singleton(A!4) = singleton(A!4))) | (in(B!3, singleton(A!4)) <=> (B!3 = A!4)))) | (~((singleton(A!4) = singleton(A!4)) | ((~in(tptp_fun_C_0(singleton(A!4), A!4), singleton(A!4))) <=> (tptp_fun_C_0(singleton(A!4), A!4) = A!4))))) <=> (((~in(B!3, singleton(A!4))) <=> (B!3 = A!4)) | $false)),
% 0.12/0.40 inference(monotonicity,[status(thm)],[39, 31])).
% 0.12/0.40 tff(41,plain,
% 0.12/0.40 (((~((~(singleton(A!4) = singleton(A!4))) | (in(B!3, singleton(A!4)) <=> (B!3 = A!4)))) | (~((singleton(A!4) = singleton(A!4)) | ((~in(tptp_fun_C_0(singleton(A!4), A!4), singleton(A!4))) <=> (tptp_fun_C_0(singleton(A!4), A!4) = A!4))))) <=> ((~in(B!3, singleton(A!4))) <=> (B!3 = A!4))),
% 0.12/0.40 inference(transitivity,[status(thm)],[40, 24])).
% 0.12/0.40 tff(42,plain,
% 0.12/0.40 ((~((~((~(singleton(A!4) = singleton(A!4))) | (in(B!3, singleton(A!4)) <=> (B!3 = A!4)))) | (~((singleton(A!4) = singleton(A!4)) | ((~in(tptp_fun_C_0(singleton(A!4), A!4), singleton(A!4))) <=> (tptp_fun_C_0(singleton(A!4), A!4) = A!4)))))) <=> (~((~in(B!3, singleton(A!4))) <=> (B!3 = A!4)))),
% 0.12/0.40 inference(monotonicity,[status(thm)],[41])).
% 0.12/0.40 tff(43,plain,
% 0.12/0.40 ((~((~((~(singleton(A!4) = singleton(A!4))) | (in(B!3, singleton(A!4)) <=> (B!3 = A!4)))) | (~((singleton(A!4) = singleton(A!4)) | ((~in(tptp_fun_C_0(singleton(A!4), A!4), singleton(A!4))) <=> (tptp_fun_C_0(singleton(A!4), A!4) = A!4)))))) <=> (in(B!3, singleton(A!4)) <=> (B!3 = A!4))),
% 0.12/0.40 inference(transitivity,[status(thm)],[42, 23])).
% 0.12/0.40 tff(44,plain,
% 0.12/0.40 (((~![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!4) = singleton(A!4))) | (in(B!3, singleton(A!4)) <=> (B!3 = A!4)))) | (~((singleton(A!4) = singleton(A!4)) | ((~in(tptp_fun_C_0(singleton(A!4), A!4), singleton(A!4))) <=> (tptp_fun_C_0(singleton(A!4), A!4) = A!4))))))) <=> ((~![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(A!4)) <=> (B!3 = A!4)))),
% 0.12/0.40 inference(monotonicity,[status(thm)],[43])).
% 0.12/0.40 tff(45,plain,
% 0.12/0.40 (((~![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!4) = singleton(A!4))) | (in(B!3, singleton(A!4)) <=> (B!3 = A!4)))) | (~((singleton(A!4) = singleton(A!4)) | ((~in(tptp_fun_C_0(singleton(A!4), A!4), singleton(A!4))) <=> (tptp_fun_C_0(singleton(A!4), A!4) = A!4))))))) <=> ((~![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(A!4)) <=> (B!3 = A!4)))),
% 0.12/0.40 inference(transitivity,[status(thm)],[44, 22])).
% 0.12/0.40 tff(46,plain,
% 0.12/0.40 ((~![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!4) = singleton(A!4))) | (in(B!3, singleton(A!4)) <=> (B!3 = A!4)))) | (~((singleton(A!4) = singleton(A!4)) | ((~in(tptp_fun_C_0(singleton(A!4), A!4), singleton(A!4))) <=> (tptp_fun_C_0(singleton(A!4), A!4) = A!4))))))),
% 0.12/0.40 inference(quant_inst,[status(thm)],[])).
% 0.12/0.40 tff(47,plain,
% 0.12/0.40 ((~![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(A!4)) <=> (B!3 = A!4))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[46, 45])).
% 0.12/0.40 tff(48,plain,
% 0.12/0.40 (in(B!3, singleton(A!4)) <=> (B!3 = A!4)),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[47, 21])).
% 0.12/0.40 tff(49,plain,
% 0.12/0.40 (^[A: $i, B: $i] : refl((set_union2(A, B) = set_union2(B, A)) <=> (set_union2(A, B) = set_union2(B, A)))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(50,plain,
% 0.12/0.40 (![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A)) <=> ![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[49])).
% 0.12/0.40 tff(51,plain,
% 0.12/0.40 (![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A)) <=> ![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(52,axiom,(![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','commutativity_k2_xboole_0')).
% 0.12/0.40 tff(53,plain,
% 0.12/0.40 (![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[52, 51])).
% 0.12/0.40 tff(54,plain,(
% 0.12/0.40 ![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A))),
% 0.12/0.40 inference(skolemize,[status(sab)],[53])).
% 0.12/0.40 tff(55,plain,
% 0.12/0.40 (![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[54, 50])).
% 0.12/0.40 tff(56,plain,
% 0.12/0.40 ((~![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A))) | (set_union2(singleton(A!4), singleton(B!3)) = set_union2(singleton(B!3), singleton(A!4)))),
% 0.12/0.40 inference(quant_inst,[status(thm)],[])).
% 0.12/0.40 tff(57,plain,
% 0.12/0.40 (set_union2(singleton(A!4), singleton(B!3)) = set_union2(singleton(B!3), singleton(A!4))),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[56, 55])).
% 0.12/0.40 tff(58,plain,
% 0.12/0.40 ((~![A: $i, B: $i] : ((~(set_union2(singleton(A), singleton(B)) = singleton(A))) | (A = B))) <=> (~![A: $i, B: $i] : ((~(set_union2(singleton(A), singleton(B)) = singleton(A))) | (A = B)))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(59,plain,
% 0.12/0.40 ((~![A: $i, B: $i] : ((set_union2(singleton(A), singleton(B)) = singleton(A)) => (A = B))) <=> (~![A: $i, B: $i] : ((~(set_union2(singleton(A), singleton(B)) = singleton(A))) | (A = B)))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(60,axiom,(~![A: $i, B: $i] : ((set_union2(singleton(A), singleton(B)) = singleton(A)) => (A = B))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t13_zfmisc_1')).
% 0.12/0.40 tff(61,plain,
% 0.12/0.40 (~![A: $i, B: $i] : ((~(set_union2(singleton(A), singleton(B)) = singleton(A))) | (A = B))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[60, 59])).
% 0.12/0.40 tff(62,plain,
% 0.12/0.40 (~![A: $i, B: $i] : ((~(set_union2(singleton(A), singleton(B)) = singleton(A))) | (A = B))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[61, 58])).
% 0.12/0.40 tff(63,plain,
% 0.12/0.40 (~![A: $i, B: $i] : ((~(set_union2(singleton(A), singleton(B)) = singleton(A))) | (A = B))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[62, 58])).
% 0.12/0.40 tff(64,plain,
% 0.12/0.40 (~![A: $i, B: $i] : ((~(set_union2(singleton(A), singleton(B)) = singleton(A))) | (A = B))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[63, 58])).
% 0.12/0.40 tff(65,plain,
% 0.12/0.40 (~![A: $i, B: $i] : ((~(set_union2(singleton(A), singleton(B)) = singleton(A))) | (A = B))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[64, 58])).
% 0.12/0.40 tff(66,plain,
% 0.12/0.40 (~![A: $i, B: $i] : ((~(set_union2(singleton(A), singleton(B)) = singleton(A))) | (A = B))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[65, 58])).
% 0.12/0.40 tff(67,plain,
% 0.12/0.40 (~![A: $i, B: $i] : ((~(set_union2(singleton(A), singleton(B)) = singleton(A))) | (A = B))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[66, 58])).
% 0.12/0.40 tff(68,plain,(
% 0.12/0.40 ~((~(set_union2(singleton(A!4), singleton(B!3)) = singleton(A!4))) | (A!4 = B!3))),
% 0.12/0.40 inference(skolemize,[status(sab)],[67])).
% 0.12/0.40 tff(69,plain,
% 0.12/0.40 (set_union2(singleton(A!4), singleton(B!3)) = singleton(A!4)),
% 0.12/0.40 inference(or_elim,[status(thm)],[68])).
% 0.12/0.40 tff(70,plain,
% 0.12/0.40 (singleton(A!4) = set_union2(singleton(A!4), singleton(B!3))),
% 0.12/0.40 inference(symmetry,[status(thm)],[69])).
% 0.12/0.40 tff(71,plain,
% 0.12/0.40 (singleton(A!4) = set_union2(singleton(B!3), singleton(A!4))),
% 0.12/0.40 inference(transitivity,[status(thm)],[70, 57])).
% 0.12/0.40 tff(72,plain,
% 0.12/0.40 (subset(singleton(A!4), singleton(A!4)) <=> subset(set_union2(singleton(B!3), singleton(A!4)), singleton(A!4))),
% 0.12/0.40 inference(monotonicity,[status(thm)],[71])).
% 0.12/0.40 tff(73,plain,
% 0.12/0.40 (subset(set_union2(singleton(B!3), singleton(A!4)), singleton(A!4)) <=> subset(singleton(A!4), singleton(A!4))),
% 0.12/0.40 inference(symmetry,[status(thm)],[72])).
% 0.12/0.40 tff(74,plain,
% 0.12/0.40 ((~subset(set_union2(singleton(B!3), singleton(A!4)), singleton(A!4))) <=> (~subset(singleton(A!4), singleton(A!4)))),
% 0.12/0.40 inference(monotonicity,[status(thm)],[73])).
% 0.12/0.40 tff(75,assumption,(~subset(set_union2(singleton(B!3), singleton(A!4)), singleton(A!4))), introduced(assumption)).
% 0.12/0.40 tff(76,plain,
% 0.12/0.40 (~subset(singleton(A!4), singleton(A!4))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[75, 74])).
% 0.12/0.40 tff(77,plain,
% 0.12/0.40 (^[A: $i] : refl(subset(A, A) <=> subset(A, A))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(78,plain,
% 0.12/0.40 (![A: $i] : subset(A, A) <=> ![A: $i] : subset(A, A)),
% 0.12/0.40 inference(quant_intro,[status(thm)],[77])).
% 0.12/0.40 tff(79,plain,
% 0.12/0.40 (![A: $i] : subset(A, A) <=> ![A: $i] : subset(A, A)),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(80,plain,
% 0.12/0.40 (![A: $i, B: $i] : subset(A, A) <=> ![A: $i] : subset(A, A)),
% 0.12/0.40 inference(elim_unused_vars,[status(thm)],[])).
% 0.12/0.40 tff(81,axiom,(![A: $i, B: $i] : subset(A, A)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','reflexivity_r1_tarski')).
% 0.12/0.40 tff(82,plain,
% 0.12/0.40 (![A: $i] : subset(A, A)),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[81, 80])).
% 0.12/0.40 tff(83,plain,
% 0.12/0.40 (![A: $i] : subset(A, A)),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[82, 79])).
% 0.12/0.40 tff(84,plain,(
% 0.12/0.40 ![A: $i] : subset(A, A)),
% 0.12/0.40 inference(skolemize,[status(sab)],[83])).
% 0.12/0.40 tff(85,plain,
% 0.12/0.40 (![A: $i] : subset(A, A)),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[84, 78])).
% 0.12/0.40 tff(86,plain,
% 0.12/0.40 ((~![A: $i] : subset(A, A)) | subset(singleton(A!4), singleton(A!4))),
% 0.12/0.40 inference(quant_inst,[status(thm)],[])).
% 0.12/0.40 tff(87,plain,
% 0.12/0.40 (subset(singleton(A!4), singleton(A!4))),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[86, 85])).
% 0.12/0.40 tff(88,plain,
% 0.12/0.40 ($false),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[87, 76])).
% 0.12/0.40 tff(89,plain,(subset(set_union2(singleton(B!3), singleton(A!4)), singleton(A!4))), inference(lemma,lemma(discharge,[]))).
% 0.12/0.40 tff(90,plain,
% 0.12/0.40 (^[A: $i, B: $i] : refl(((~subset(set_union2(singleton(A), B), B)) | in(A, B)) <=> ((~subset(set_union2(singleton(A), B), B)) | in(A, B)))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(91,plain,
% 0.12/0.40 (![A: $i, B: $i] : ((~subset(set_union2(singleton(A), B), B)) | in(A, B)) <=> ![A: $i, B: $i] : ((~subset(set_union2(singleton(A), B), B)) | in(A, B))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[90])).
% 0.12/0.40 tff(92,plain,
% 0.12/0.40 (![A: $i, B: $i] : ((~subset(set_union2(singleton(A), B), B)) | in(A, B)) <=> ![A: $i, B: $i] : ((~subset(set_union2(singleton(A), B), B)) | in(A, B))),
% 0.12/0.41 inference(rewrite,[status(thm)],[])).
% 0.12/0.41 tff(93,plain,
% 0.12/0.41 (^[A: $i, B: $i] : rewrite((subset(set_union2(singleton(A), B), B) => in(A, B)) <=> ((~subset(set_union2(singleton(A), B), B)) | in(A, B)))),
% 0.12/0.41 inference(bind,[status(th)],[])).
% 0.12/0.41 tff(94,plain,
% 0.12/0.41 (![A: $i, B: $i] : (subset(set_union2(singleton(A), B), B) => in(A, B)) <=> ![A: $i, B: $i] : ((~subset(set_union2(singleton(A), B), B)) | in(A, B))),
% 0.12/0.41 inference(quant_intro,[status(thm)],[93])).
% 0.12/0.41 tff(95,axiom,(![A: $i, B: $i] : (subset(set_union2(singleton(A), B), B) => in(A, B))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','l21_zfmisc_1')).
% 0.12/0.41 tff(96,plain,
% 0.12/0.41 (![A: $i, B: $i] : ((~subset(set_union2(singleton(A), B), B)) | in(A, B))),
% 0.12/0.41 inference(modus_ponens,[status(thm)],[95, 94])).
% 0.12/0.41 tff(97,plain,
% 0.12/0.41 (![A: $i, B: $i] : ((~subset(set_union2(singleton(A), B), B)) | in(A, B))),
% 0.12/0.41 inference(modus_ponens,[status(thm)],[96, 92])).
% 0.12/0.41 tff(98,plain,(
% 0.12/0.41 ![A: $i, B: $i] : ((~subset(set_union2(singleton(A), B), B)) | in(A, B))),
% 0.12/0.41 inference(skolemize,[status(sab)],[97])).
% 0.12/0.41 tff(99,plain,
% 0.12/0.41 (![A: $i, B: $i] : ((~subset(set_union2(singleton(A), B), B)) | in(A, B))),
% 0.12/0.41 inference(modus_ponens,[status(thm)],[98, 91])).
% 0.12/0.41 tff(100,plain,
% 0.12/0.41 (((~![A: $i, B: $i] : ((~subset(set_union2(singleton(A), B), B)) | in(A, B))) | ((~subset(set_union2(singleton(B!3), singleton(A!4)), singleton(A!4))) | in(B!3, singleton(A!4)))) <=> ((~![A: $i, B: $i] : ((~subset(set_union2(singleton(A), B), B)) | in(A, B))) | (~subset(set_union2(singleton(B!3), singleton(A!4)), singleton(A!4))) | in(B!3, singleton(A!4)))),
% 0.12/0.41 inference(rewrite,[status(thm)],[])).
% 0.12/0.41 tff(101,plain,
% 0.12/0.41 ((~![A: $i, B: $i] : ((~subset(set_union2(singleton(A), B), B)) | in(A, B))) | ((~subset(set_union2(singleton(B!3), singleton(A!4)), singleton(A!4))) | in(B!3, singleton(A!4)))),
% 0.12/0.41 inference(quant_inst,[status(thm)],[])).
% 0.12/0.41 tff(102,plain,
% 0.12/0.41 ((~![A: $i, B: $i] : ((~subset(set_union2(singleton(A), B), B)) | in(A, B))) | (~subset(set_union2(singleton(B!3), singleton(A!4)), singleton(A!4))) | in(B!3, singleton(A!4))),
% 0.12/0.41 inference(modus_ponens,[status(thm)],[101, 100])).
% 0.12/0.41 tff(103,plain,
% 0.12/0.41 ((~subset(set_union2(singleton(B!3), singleton(A!4)), singleton(A!4))) | in(B!3, singleton(A!4))),
% 0.12/0.41 inference(unit_resolution,[status(thm)],[102, 99])).
% 0.12/0.41 tff(104,plain,
% 0.12/0.41 (in(B!3, singleton(A!4))),
% 0.12/0.41 inference(unit_resolution,[status(thm)],[103, 89])).
% 0.12/0.41 tff(105,plain,
% 0.12/0.41 ((~(in(B!3, singleton(A!4)) <=> (B!3 = A!4))) | (~in(B!3, singleton(A!4))) | (B!3 = A!4)),
% 0.12/0.41 inference(tautology,[status(thm)],[])).
% 0.12/0.41 tff(106,plain,
% 0.12/0.41 ((~(in(B!3, singleton(A!4)) <=> (B!3 = A!4))) | (B!3 = A!4)),
% 0.12/0.41 inference(unit_resolution,[status(thm)],[105, 104])).
% 0.12/0.41 tff(107,plain,
% 0.12/0.41 (B!3 = A!4),
% 0.12/0.41 inference(unit_resolution,[status(thm)],[106, 48])).
% 0.12/0.41 tff(108,plain,
% 0.12/0.41 (A!4 = B!3),
% 0.12/0.41 inference(symmetry,[status(thm)],[107])).
% 0.12/0.41 tff(109,plain,
% 0.12/0.41 (~(A!4 = B!3)),
% 0.12/0.41 inference(or_elim,[status(thm)],[68])).
% 0.12/0.41 tff(110,plain,
% 0.12/0.41 ($false),
% 0.12/0.41 inference(unit_resolution,[status(thm)],[109, 108])).
% 0.12/0.41 % SZS output end Proof
%------------------------------------------------------------------------------