TSTP Solution File: SEU148+3 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SEU148+3 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n024.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 07:27:46 EDT 2022
% Result : Theorem 12.26s 8.16s
% Output : Proof 12.26s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : SEU148+3 : TPTP v8.1.0. Released v3.2.0.
% 0.11/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.34 % Computer : n024.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 09:44:03 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 12.26/8.16 % SZS status Theorem
% 12.26/8.16 % SZS output start Proof
% 12.26/8.16 tff(tptp_fun_A_4_type, type, (
% 12.26/8.16 tptp_fun_A_4: $i)).
% 12.26/8.16 tff(tptp_fun_C_0_type, type, (
% 12.26/8.16 tptp_fun_C_0: ( $i * $i ) > $i)).
% 12.26/8.16 tff(singleton_type, type, (
% 12.26/8.16 singleton: $i > $i)).
% 12.26/8.16 tff(tptp_fun_B_3_type, type, (
% 12.26/8.16 tptp_fun_B_3: $i)).
% 12.26/8.16 tff(in_type, type, (
% 12.26/8.16 in: ( $i * $i ) > $o)).
% 12.26/8.16 tff(subset_type, type, (
% 12.26/8.16 subset: ( $i * $i ) > $o)).
% 12.26/8.16 tff(empty_set_type, type, (
% 12.26/8.16 empty_set: $i)).
% 12.26/8.16 tff(1,assumption,(~in(B!3, singleton(B!3))), introduced(assumption)).
% 12.26/8.16 tff(2,plain,
% 12.26/8.16 (^[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)))))))),
% 12.26/8.16 inference(bind,[status(th)],[])).
% 12.26/8.16 tff(3,plain,
% 12.26/8.16 (![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))))))),
% 12.26/8.16 inference(quant_intro,[status(thm)],[2])).
% 12.26/8.16 tff(4,plain,
% 12.26/8.16 (![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))))))),
% 12.26/8.16 inference(pull_quant,[status(thm)],[])).
% 12.26/8.16 tff(5,plain,
% 12.26/8.16 (^[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))))))))),
% 12.26/8.16 inference(bind,[status(th)],[])).
% 12.26/8.16 tff(6,plain,
% 12.26/8.16 (![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))))))),
% 12.26/8.16 inference(quant_intro,[status(thm)],[5])).
% 12.26/8.16 tff(7,plain,
% 12.26/8.16 (![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))))))),
% 12.26/8.16 inference(transitivity,[status(thm)],[6, 4])).
% 12.26/8.16 tff(8,plain,
% 12.26/8.16 (![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))))))),
% 12.26/8.16 inference(transitivity,[status(thm)],[7, 3])).
% 12.26/8.16 tff(9,plain,
% 12.26/8.16 (^[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)))))))),
% 12.26/8.16 inference(bind,[status(th)],[])).
% 12.26/8.16 tff(10,plain,
% 12.26/8.16 (![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))))))),
% 12.26/8.16 inference(quant_intro,[status(thm)],[9])).
% 12.26/8.16 tff(11,plain,
% 12.26/8.16 (![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))))))),
% 12.26/8.16 inference(transitivity,[status(thm)],[10, 8])).
% 12.26/8.16 tff(12,plain,
% 12.26/8.16 (^[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))))))))),
% 12.26/8.16 inference(bind,[status(th)],[])).
% 12.26/8.16 tff(13,plain,
% 12.26/8.16 (![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))))))),
% 12.26/8.16 inference(quant_intro,[status(thm)],[12])).
% 12.26/8.16 tff(14,plain,
% 12.26/8.16 (^[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)))))),
% 12.26/8.16 inference(bind,[status(th)],[])).
% 12.26/8.16 tff(15,plain,
% 12.26/8.16 (![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))))),
% 12.26/8.16 inference(quant_intro,[status(thm)],[14])).
% 12.26/8.16 tff(16,plain,
% 12.26/8.16 (![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)))),
% 12.26/8.16 inference(rewrite,[status(thm)],[])).
% 12.26/8.16 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')).
% 12.26/8.16 tff(18,plain,
% 12.26/8.16 (![A: $i, B: $i] : ((B = singleton(A)) <=> ![C: $i] : (in(C, B) <=> (C = A)))),
% 12.26/8.16 inference(modus_ponens,[status(thm)],[17, 16])).
% 12.26/8.16 tff(19,plain,(
% 12.26/8.16 ![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)))))),
% 12.26/8.16 inference(skolemize,[status(sab)],[18])).
% 12.26/8.16 tff(20,plain,
% 12.26/8.16 (![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))))),
% 12.26/8.16 inference(modus_ponens,[status(thm)],[19, 15])).
% 12.26/8.16 tff(21,plain,
% 12.26/8.16 (![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))))))),
% 12.26/8.16 inference(modus_ponens,[status(thm)],[20, 13])).
% 12.26/8.16 tff(22,plain,
% 12.26/8.16 (![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))))))),
% 12.26/8.16 inference(modus_ponens,[status(thm)],[21, 11])).
% 12.26/8.16 tff(23,plain,
% 12.26/8.16 (((~![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)))),
% 12.26/8.16 inference(rewrite,[status(thm)],[])).
% 12.26/8.16 tff(24,plain,
% 12.26/8.16 ((~(~in(B!3, singleton(B!3)))) <=> in(B!3, singleton(B!3))),
% 12.26/8.16 inference(rewrite,[status(thm)],[])).
% 12.26/8.16 tff(25,plain,
% 12.26/8.16 (((~in(B!3, singleton(B!3))) | $false) <=> (~in(B!3, singleton(B!3)))),
% 12.26/8.16 inference(rewrite,[status(thm)],[])).
% 12.26/8.16 tff(26,plain,
% 12.26/8.16 ((~$true) <=> $false),
% 12.26/8.16 inference(rewrite,[status(thm)],[])).
% 12.26/8.16 tff(27,plain,
% 12.26/8.16 (($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),
% 12.26/8.16 inference(rewrite,[status(thm)],[])).
% 12.26/8.16 tff(28,plain,
% 12.26/8.16 ((singleton(B!3) = singleton(B!3)) <=> $true),
% 12.26/8.16 inference(rewrite,[status(thm)],[])).
% 12.26/8.16 tff(29,plain,
% 12.26/8.16 (((singleton(B!3) = singleton(B!3)) | ((~in(tptp_fun_C_0(singleton(B!3), B!3), singleton(B!3))) <=> (tptp_fun_C_0(singleton(B!3), B!3) = B!3))) <=> ($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)))),
% 12.26/8.16 inference(monotonicity,[status(thm)],[28])).
% 12.26/8.16 tff(30,plain,
% 12.26/8.16 (((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))) <=> $true),
% 12.26/8.16 inference(transitivity,[status(thm)],[29, 27])).
% 12.26/8.16 tff(31,plain,
% 12.26/8.16 ((~((singleton(B!3) = singleton(B!3)) | ((~in(tptp_fun_C_0(singleton(B!3), B!3), singleton(B!3))) <=> (tptp_fun_C_0(singleton(B!3), B!3) = B!3)))) <=> (~$true)),
% 12.26/8.16 inference(monotonicity,[status(thm)],[30])).
% 12.26/8.16 tff(32,plain,
% 12.26/8.16 ((~((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),
% 12.26/8.16 inference(transitivity,[status(thm)],[31, 26])).
% 12.26/8.16 tff(33,plain,
% 12.26/8.16 ((~((~(singleton(B!3) = singleton(B!3))) | (in(B!3, singleton(B!3)) <=> (B!3 = B!3)))) <=> (~in(B!3, singleton(B!3)))),
% 12.26/8.16 inference(rewrite,[status(thm)],[])).
% 12.26/8.16 tff(34,plain,
% 12.26/8.16 (((~((~(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)),
% 12.26/8.16 inference(monotonicity,[status(thm)],[33, 32])).
% 12.26/8.16 tff(35,plain,
% 12.26/8.16 (((~((~(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)))),
% 12.26/8.16 inference(transitivity,[status(thm)],[34, 25])).
% 12.26/8.16 tff(36,plain,
% 12.26/8.16 ((~((~((~(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))))),
% 12.26/8.16 inference(monotonicity,[status(thm)],[35])).
% 12.26/8.16 tff(37,plain,
% 12.26/8.16 ((~((~((~(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))),
% 12.26/8.16 inference(transitivity,[status(thm)],[36, 24])).
% 12.26/8.16 tff(38,plain,
% 12.26/8.16 (((~![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)))),
% 12.26/8.16 inference(monotonicity,[status(thm)],[37])).
% 12.26/8.16 tff(39,plain,
% 12.26/8.16 (((~![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)))),
% 12.26/8.16 inference(transitivity,[status(thm)],[38, 23])).
% 12.26/8.16 tff(40,plain,
% 12.26/8.16 ((~![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))))))),
% 12.26/8.16 inference(quant_inst,[status(thm)],[])).
% 12.26/8.16 tff(41,plain,
% 12.26/8.16 ((~![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))))) | in(B!3, singleton(B!3))),
% 12.26/8.16 inference(modus_ponens,[status(thm)],[40, 39])).
% 12.26/8.16 tff(42,plain,
% 12.26/8.16 ($false),
% 12.26/8.16 inference(unit_resolution,[status(thm)],[41, 22, 1])).
% 12.26/8.16 tff(43,plain,(in(B!3, singleton(B!3))), inference(lemma,lemma(discharge,[]))).
% 12.26/8.16 tff(44,plain,
% 12.26/8.16 ((B!3 = A!4) <=> (A!4 = B!3)),
% 12.26/8.16 inference(commutativity,[status(thm)],[])).
% 12.26/8.16 tff(45,plain,
% 12.26/8.16 ((A!4 = B!3) <=> (B!3 = A!4)),
% 12.26/8.16 inference(symmetry,[status(thm)],[44])).
% 12.26/8.16 tff(46,plain,
% 12.26/8.16 ((~(A!4 = B!3)) <=> (~(B!3 = A!4))),
% 12.26/8.16 inference(monotonicity,[status(thm)],[45])).
% 12.26/8.16 tff(47,plain,
% 12.26/8.16 ((~![A: $i, B: $i] : ((~subset(singleton(A), singleton(B))) | (A = B))) <=> (~![A: $i, B: $i] : ((~subset(singleton(A), singleton(B))) | (A = B)))),
% 12.26/8.16 inference(rewrite,[status(thm)],[])).
% 12.26/8.16 tff(48,plain,
% 12.26/8.16 ((~![A: $i, B: $i] : (subset(singleton(A), singleton(B)) => (A = B))) <=> (~![A: $i, B: $i] : ((~subset(singleton(A), singleton(B))) | (A = B)))),
% 12.26/8.16 inference(rewrite,[status(thm)],[])).
% 12.26/8.16 tff(49,axiom,(~![A: $i, B: $i] : (subset(singleton(A), singleton(B)) => (A = B))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t6_zfmisc_1')).
% 12.26/8.16 tff(50,plain,
% 12.26/8.16 (~![A: $i, B: $i] : ((~subset(singleton(A), singleton(B))) | (A = B))),
% 12.26/8.16 inference(modus_ponens,[status(thm)],[49, 48])).
% 12.26/8.16 tff(51,plain,
% 12.26/8.16 (~![A: $i, B: $i] : ((~subset(singleton(A), singleton(B))) | (A = B))),
% 12.26/8.16 inference(modus_ponens,[status(thm)],[50, 47])).
% 12.26/8.16 tff(52,plain,
% 12.26/8.16 (~![A: $i, B: $i] : ((~subset(singleton(A), singleton(B))) | (A = B))),
% 12.26/8.16 inference(modus_ponens,[status(thm)],[51, 47])).
% 12.26/8.16 tff(53,plain,
% 12.26/8.16 (~![A: $i, B: $i] : ((~subset(singleton(A), singleton(B))) | (A = B))),
% 12.26/8.16 inference(modus_ponens,[status(thm)],[52, 47])).
% 12.26/8.16 tff(54,plain,
% 12.26/8.16 (~![A: $i, B: $i] : ((~subset(singleton(A), singleton(B))) | (A = B))),
% 12.26/8.16 inference(modus_ponens,[status(thm)],[53, 47])).
% 12.26/8.16 tff(55,plain,
% 12.26/8.16 (~![A: $i, B: $i] : ((~subset(singleton(A), singleton(B))) | (A = B))),
% 12.26/8.16 inference(modus_ponens,[status(thm)],[54, 47])).
% 12.26/8.16 tff(56,plain,
% 12.26/8.16 (~![A: $i, B: $i] : ((~subset(singleton(A), singleton(B))) | (A = B))),
% 12.26/8.16 inference(modus_ponens,[status(thm)],[55, 47])).
% 12.26/8.16 tff(57,plain,(
% 12.26/8.16 ~((~subset(singleton(A!4), singleton(B!3))) | (A!4 = B!3))),
% 12.26/8.16 inference(skolemize,[status(sab)],[56])).
% 12.26/8.16 tff(58,plain,
% 12.26/8.16 (~(A!4 = B!3)),
% 12.26/8.16 inference(or_elim,[status(thm)],[57])).
% 12.26/8.16 tff(59,plain,
% 12.26/8.16 (~(B!3 = A!4)),
% 12.26/8.16 inference(modus_ponens,[status(thm)],[58, 46])).
% 12.26/8.16 tff(60,plain,
% 12.26/8.16 ((~(in(B!3, singleton(B!3)) <=> (B!3 = A!4))) | (~in(B!3, singleton(B!3))) | (B!3 = A!4)),
% 12.26/8.16 inference(tautology,[status(thm)],[])).
% 12.26/8.16 tff(61,plain,
% 12.26/8.16 (~(in(B!3, singleton(B!3)) <=> (B!3 = A!4))),
% 12.26/8.16 inference(unit_resolution,[status(thm)],[60, 59, 43])).
% 12.26/8.16 tff(62,plain,
% 12.26/8.16 (^[A: $i, B: $i] : refl((subset(A, singleton(B)) <=> ((A = empty_set) | (A = singleton(B)))) <=> (subset(A, singleton(B)) <=> ((A = empty_set) | (A = singleton(B)))))),
% 12.26/8.16 inference(bind,[status(th)],[])).
% 12.26/8.16 tff(63,plain,
% 12.26/8.16 (![A: $i, B: $i] : (subset(A, singleton(B)) <=> ((A = empty_set) | (A = singleton(B)))) <=> ![A: $i, B: $i] : (subset(A, singleton(B)) <=> ((A = empty_set) | (A = singleton(B))))),
% 12.26/8.16 inference(quant_intro,[status(thm)],[62])).
% 12.26/8.16 tff(64,plain,
% 12.26/8.16 (![A: $i, B: $i] : (subset(A, singleton(B)) <=> ((A = empty_set) | (A = singleton(B)))) <=> ![A: $i, B: $i] : (subset(A, singleton(B)) <=> ((A = empty_set) | (A = singleton(B))))),
% 12.26/8.16 inference(rewrite,[status(thm)],[])).
% 12.26/8.16 tff(65,axiom,(![A: $i, B: $i] : (subset(A, singleton(B)) <=> ((A = empty_set) | (A = singleton(B))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','l4_zfmisc_1')).
% 12.26/8.16 tff(66,plain,
% 12.26/8.16 (![A: $i, B: $i] : (subset(A, singleton(B)) <=> ((A = empty_set) | (A = singleton(B))))),
% 12.26/8.16 inference(modus_ponens,[status(thm)],[65, 64])).
% 12.26/8.16 tff(67,plain,(
% 12.26/8.16 ![A: $i, B: $i] : (subset(A, singleton(B)) <=> ((A = empty_set) | (A = singleton(B))))),
% 12.26/8.16 inference(skolemize,[status(sab)],[66])).
% 12.26/8.16 tff(68,plain,
% 12.26/8.16 (![A: $i, B: $i] : (subset(A, singleton(B)) <=> ((A = empty_set) | (A = singleton(B))))),
% 12.26/8.16 inference(modus_ponens,[status(thm)],[67, 63])).
% 12.26/8.16 tff(69,plain,
% 12.26/8.16 ((~![A: $i, B: $i] : (subset(A, singleton(B)) <=> ((A = empty_set) | (A = singleton(B))))) | (subset(singleton(A!4), singleton(B!3)) <=> ((singleton(A!4) = empty_set) | (singleton(A!4) = singleton(B!3))))),
% 12.26/8.16 inference(quant_inst,[status(thm)],[])).
% 12.26/8.16 tff(70,plain,
% 12.26/8.16 (subset(singleton(A!4), singleton(B!3)) <=> ((singleton(A!4) = empty_set) | (singleton(A!4) = singleton(B!3)))),
% 12.26/8.16 inference(unit_resolution,[status(thm)],[69, 68])).
% 12.26/8.16 tff(71,plain,
% 12.26/8.16 (subset(singleton(A!4), singleton(B!3))),
% 12.26/8.16 inference(or_elim,[status(thm)],[57])).
% 12.26/8.16 tff(72,plain,
% 12.26/8.16 ((~(subset(singleton(A!4), singleton(B!3)) <=> ((singleton(A!4) = empty_set) | (singleton(A!4) = singleton(B!3))))) | (~subset(singleton(A!4), singleton(B!3))) | ((singleton(A!4) = empty_set) | (singleton(A!4) = singleton(B!3)))),
% 12.26/8.16 inference(tautology,[status(thm)],[])).
% 12.26/8.16 tff(73,plain,
% 12.26/8.16 ((~(subset(singleton(A!4), singleton(B!3)) <=> ((singleton(A!4) = empty_set) | (singleton(A!4) = singleton(B!3))))) | ((singleton(A!4) = empty_set) | (singleton(A!4) = singleton(B!3)))),
% 12.26/8.16 inference(unit_resolution,[status(thm)],[72, 71])).
% 12.26/8.16 tff(74,plain,
% 12.26/8.16 ((singleton(A!4) = empty_set) | (singleton(A!4) = singleton(B!3))),
% 12.26/8.16 inference(unit_resolution,[status(thm)],[73, 70])).
% 12.26/8.16 tff(75,plain,
% 12.26/8.16 (^[A: $i] : refl((~(singleton(A) = empty_set)) <=> (~(singleton(A) = empty_set)))),
% 12.26/8.16 inference(bind,[status(th)],[])).
% 12.26/8.16 tff(76,plain,
% 12.26/8.16 (![A: $i] : (~(singleton(A) = empty_set)) <=> ![A: $i] : (~(singleton(A) = empty_set))),
% 12.26/8.16 inference(quant_intro,[status(thm)],[75])).
% 12.26/8.16 tff(77,plain,
% 12.26/8.16 (![A: $i] : (~(singleton(A) = empty_set)) <=> ![A: $i] : (~(singleton(A) = empty_set))),
% 12.26/8.16 inference(rewrite,[status(thm)],[])).
% 12.26/8.16 tff(78,axiom,(![A: $i] : (~(singleton(A) = empty_set))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','l1_zfmisc_1')).
% 12.26/8.16 tff(79,plain,
% 12.26/8.16 (![A: $i] : (~(singleton(A) = empty_set))),
% 12.26/8.16 inference(modus_ponens,[status(thm)],[78, 77])).
% 12.26/8.16 tff(80,plain,(
% 12.26/8.16 ![A: $i] : (~(singleton(A) = empty_set))),
% 12.26/8.16 inference(skolemize,[status(sab)],[79])).
% 12.26/8.16 tff(81,plain,
% 12.26/8.16 (![A: $i] : (~(singleton(A) = empty_set))),
% 12.26/8.16 inference(modus_ponens,[status(thm)],[80, 76])).
% 12.26/8.16 tff(82,plain,
% 12.26/8.16 ((~![A: $i] : (~(singleton(A) = empty_set))) | (~(singleton(A!4) = empty_set))),
% 12.26/8.16 inference(quant_inst,[status(thm)],[])).
% 12.26/8.16 tff(83,plain,
% 12.26/8.16 (~(singleton(A!4) = empty_set)),
% 12.26/8.16 inference(unit_resolution,[status(thm)],[82, 81])).
% 12.26/8.16 tff(84,plain,
% 12.26/8.16 ((~((singleton(A!4) = empty_set) | (singleton(A!4) = singleton(B!3)))) | (singleton(A!4) = empty_set) | (singleton(A!4) = singleton(B!3))),
% 12.26/8.16 inference(tautology,[status(thm)],[])).
% 12.26/8.16 tff(85,plain,
% 12.26/8.16 ((~((singleton(A!4) = empty_set) | (singleton(A!4) = singleton(B!3)))) | (singleton(A!4) = singleton(B!3))),
% 12.26/8.16 inference(unit_resolution,[status(thm)],[84, 83])).
% 12.26/8.16 tff(86,plain,
% 12.26/8.16 (singleton(A!4) = singleton(B!3)),
% 12.26/8.16 inference(unit_resolution,[status(thm)],[85, 74])).
% 12.26/8.16 tff(87,plain,
% 12.26/8.16 (singleton(B!3) = singleton(A!4)),
% 12.26/8.16 inference(symmetry,[status(thm)],[86])).
% 12.26/8.16 tff(88,plain,
% 12.26/8.16 ((~((~(singleton(B!3) = singleton(A!4))) | (in(B!3, singleton(B!3)) <=> (B!3 = A!4)))) | (~(singleton(B!3) = singleton(A!4))) | (in(B!3, singleton(B!3)) <=> (B!3 = A!4))),
% 12.26/8.16 inference(tautology,[status(thm)],[])).
% 12.26/8.16 tff(89,plain,
% 12.26/8.16 (~((~(singleton(B!3) = singleton(A!4))) | (in(B!3, singleton(B!3)) <=> (B!3 = A!4)))),
% 12.26/8.16 inference(unit_resolution,[status(thm)],[88, 87, 61])).
% 12.26/8.16 tff(90,plain,
% 12.26/8.16 (((~((~(singleton(B!3) = singleton(A!4))) | (in(B!3, singleton(B!3)) <=> (B!3 = A!4)))) | (~((singleton(B!3) = singleton(A!4)) | ((~in(tptp_fun_C_0(singleton(B!3), A!4), singleton(B!3))) <=> (tptp_fun_C_0(singleton(B!3), A!4) = A!4))))) | ((~(singleton(B!3) = singleton(A!4))) | (in(B!3, singleton(B!3)) <=> (B!3 = A!4)))),
% 12.26/8.16 inference(tautology,[status(thm)],[])).
% 12.26/8.16 tff(91,plain,
% 12.26/8.16 ((~((~(singleton(B!3) = singleton(A!4))) | (in(B!3, singleton(B!3)) <=> (B!3 = A!4)))) | (~((singleton(B!3) = singleton(A!4)) | ((~in(tptp_fun_C_0(singleton(B!3), A!4), singleton(B!3))) <=> (tptp_fun_C_0(singleton(B!3), A!4) = A!4))))),
% 12.26/8.16 inference(unit_resolution,[status(thm)],[90, 89])).
% 12.26/8.16 tff(92,plain,
% 12.26/8.16 ((~![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))))) | (~((~((~(singleton(B!3) = singleton(A!4))) | (in(B!3, singleton(B!3)) <=> (B!3 = A!4)))) | (~((singleton(B!3) = singleton(A!4)) | ((~in(tptp_fun_C_0(singleton(B!3), A!4), singleton(B!3))) <=> (tptp_fun_C_0(singleton(B!3), A!4) = A!4))))))),
% 12.26/8.16 inference(quant_inst,[status(thm)],[])).
% 12.26/8.16 tff(93,plain,
% 12.26/8.16 ($false),
% 12.26/8.16 inference(unit_resolution,[status(thm)],[92, 22, 91])).
% 12.26/8.16 % SZS output end Proof
%------------------------------------------------------------------------------