TSTP Solution File: SET879+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SET879+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n009.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 05:08:29 EDT 2022
% Result : Theorem 0.12s 0.38s
% Output : Proof 0.12s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.11 % Problem : SET879+1 : TPTP v8.1.0. Released v3.2.0.
% 0.09/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n009.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Sat Sep 3 08:23:50 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.33 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.33 Usage: tptp [options] [-file:]file
% 0.12/0.33 -h, -? prints this message.
% 0.12/0.33 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.33 -m, -model generate model.
% 0.12/0.33 -p, -proof generate proof.
% 0.12/0.33 -c, -core generate unsat core of named formulas.
% 0.12/0.33 -st, -statistics display statistics.
% 0.12/0.33 -t:timeout set timeout (in second).
% 0.12/0.33 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.33 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.33 -<param>:<value> configuration parameter and value.
% 0.12/0.33 -o:<output-file> file to place output in.
% 0.12/0.38 % SZS status Theorem
% 0.12/0.38 % SZS output start Proof
% 0.12/0.38 tff(singleton_type, type, (
% 0.12/0.38 singleton: $i > $i)).
% 0.12/0.38 tff(tptp_fun_A_4_type, type, (
% 0.12/0.38 tptp_fun_A_4: $i)).
% 0.12/0.38 tff(set_difference_type, type, (
% 0.12/0.38 set_difference: ( $i * $i ) > $i)).
% 0.12/0.38 tff(tptp_fun_B_3_type, type, (
% 0.12/0.38 tptp_fun_B_3: $i)).
% 0.12/0.38 tff(in_type, type, (
% 0.12/0.38 in: ( $i * $i ) > $o)).
% 0.12/0.38 tff(tptp_fun_C_0_type, type, (
% 0.12/0.38 tptp_fun_C_0: ( $i * $i ) > $i)).
% 0.12/0.38 tff(1,assumption,(~(A!4 = B!3)), introduced(assumption)).
% 0.12/0.38 tff(2,plain,
% 0.12/0.38 ((~((set_difference(singleton(A!4), singleton(B!3)) = singleton(A!4)) <=> (~(A!4 = B!3)))) <=> ((set_difference(singleton(A!4), singleton(B!3)) = singleton(A!4)) <=> (A!4 = B!3))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(3,plain,
% 0.12/0.38 ((~![A: $i, B: $i] : ((set_difference(singleton(A), singleton(B)) = singleton(A)) <=> (~(A = B)))) <=> (~![A: $i, B: $i] : ((set_difference(singleton(A), singleton(B)) = singleton(A)) <=> (~(A = B))))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(4,axiom,(~![A: $i, B: $i] : ((set_difference(singleton(A), singleton(B)) = singleton(A)) <=> (~(A = B)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t20_zfmisc_1')).
% 0.12/0.38 tff(5,plain,
% 0.12/0.38 (~![A: $i, B: $i] : ((set_difference(singleton(A), singleton(B)) = singleton(A)) <=> (~(A = B)))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.12/0.38 tff(6,plain,
% 0.12/0.38 (~![A: $i, B: $i] : ((set_difference(singleton(A), singleton(B)) = singleton(A)) <=> (~(A = B)))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[5, 3])).
% 0.12/0.38 tff(7,plain,
% 0.12/0.38 (~![A: $i, B: $i] : ((set_difference(singleton(A), singleton(B)) = singleton(A)) <=> (~(A = B)))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[6, 3])).
% 0.12/0.38 tff(8,plain,
% 0.12/0.38 (~![A: $i, B: $i] : ((set_difference(singleton(A), singleton(B)) = singleton(A)) <=> (~(A = B)))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.12/0.38 tff(9,plain,
% 0.12/0.38 (~![A: $i, B: $i] : ((set_difference(singleton(A), singleton(B)) = singleton(A)) <=> (~(A = B)))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[8, 3])).
% 0.12/0.38 tff(10,plain,
% 0.12/0.38 (~![A: $i, B: $i] : ((set_difference(singleton(A), singleton(B)) = singleton(A)) <=> (~(A = B)))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[9, 3])).
% 0.12/0.38 tff(11,plain,
% 0.12/0.38 (~![A: $i, B: $i] : ((set_difference(singleton(A), singleton(B)) = singleton(A)) <=> (~(A = B)))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[10, 3])).
% 0.12/0.38 tff(12,plain,(
% 0.12/0.38 ~((set_difference(singleton(A!4), singleton(B!3)) = singleton(A!4)) <=> (~(A!4 = B!3)))),
% 0.12/0.38 inference(skolemize,[status(sab)],[11])).
% 0.12/0.38 tff(13,plain,
% 0.12/0.38 ((set_difference(singleton(A!4), singleton(B!3)) = singleton(A!4)) <=> (A!4 = B!3)),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[12, 2])).
% 0.12/0.38 tff(14,plain,
% 0.12/0.38 ((~(set_difference(singleton(A!4), singleton(B!3)) = singleton(A!4))) | (A!4 = B!3) | (~((set_difference(singleton(A!4), singleton(B!3)) = singleton(A!4)) <=> (A!4 = B!3)))),
% 0.12/0.38 inference(tautology,[status(thm)],[])).
% 0.12/0.38 tff(15,plain,
% 0.12/0.38 ((~(set_difference(singleton(A!4), singleton(B!3)) = singleton(A!4))) | (A!4 = B!3)),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[14, 13])).
% 0.12/0.38 tff(16,plain,
% 0.12/0.38 (~(set_difference(singleton(A!4), singleton(B!3)) = singleton(A!4))),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[15, 1])).
% 0.12/0.38 tff(17,plain,
% 0.12/0.38 (^[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)))))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(18,plain,
% 0.12/0.38 (![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))))))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[17])).
% 0.12/0.38 tff(19,plain,
% 0.12/0.38 (![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))))))),
% 0.12/0.38 inference(pull_quant,[status(thm)],[])).
% 0.12/0.38 tff(20,plain,
% 0.12/0.38 (^[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))))))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(21,plain,
% 0.12/0.38 (![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))))))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[20])).
% 0.12/0.38 tff(22,plain,
% 0.12/0.38 (![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))))))),
% 0.12/0.38 inference(transitivity,[status(thm)],[21, 19])).
% 0.12/0.38 tff(23,plain,
% 0.12/0.38 (![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))))))),
% 0.12/0.38 inference(transitivity,[status(thm)],[22, 18])).
% 0.12/0.38 tff(24,plain,
% 0.12/0.38 (^[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)))))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(25,plain,
% 0.12/0.38 (![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))))))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[24])).
% 0.12/0.38 tff(26,plain,
% 0.12/0.38 (![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))))))),
% 0.12/0.38 inference(transitivity,[status(thm)],[25, 23])).
% 0.12/0.38 tff(27,plain,
% 0.12/0.38 (^[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))))))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(28,plain,
% 0.12/0.38 (![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))))))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[27])).
% 0.12/0.38 tff(29,plain,
% 0.12/0.38 (^[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)))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(30,plain,
% 0.12/0.38 (![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))))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[29])).
% 0.12/0.38 tff(31,plain,
% 0.12/0.38 (![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)))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(32,axiom,(![A: $i, B: $i] : ((B = singleton(A)) <=> ![C: $i] : (in(C, B) <=> (C = A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d1_tarski')).
% 0.12/0.38 tff(33,plain,
% 0.12/0.38 (![A: $i, B: $i] : ((B = singleton(A)) <=> ![C: $i] : (in(C, B) <=> (C = A)))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[32, 31])).
% 0.12/0.38 tff(34,plain,(
% 0.12/0.38 ![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)))))),
% 0.12/0.38 inference(skolemize,[status(sab)],[33])).
% 0.12/0.38 tff(35,plain,
% 0.12/0.38 (![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))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[34, 30])).
% 0.12/0.38 tff(36,plain,
% 0.12/0.38 (![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))))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[35, 28])).
% 0.12/0.38 tff(37,plain,
% 0.12/0.38 (![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))))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[36, 26])).
% 0.12/0.38 tff(38,plain,
% 0.12/0.38 (((~![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)))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(39,plain,
% 0.12/0.38 ((~((~in(A!4, singleton(B!3))) <=> (A!4 = B!3))) <=> (in(A!4, singleton(B!3)) <=> (A!4 = B!3))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(40,plain,
% 0.12/0.38 ((((~in(A!4, singleton(B!3))) <=> (A!4 = B!3)) | $false) <=> ((~in(A!4, singleton(B!3))) <=> (A!4 = B!3))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(41,plain,
% 0.12/0.38 ((~$true) <=> $false),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(42,plain,
% 0.12/0.38 (($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),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(43,plain,
% 0.12/0.38 ((singleton(B!3) = singleton(B!3)) <=> $true),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(44,plain,
% 0.12/0.38 (((singleton(B!3) = singleton(B!3)) | ((~in(tptp_fun_C_0(singleton(B!3), B!3), singleton(B!3))) <=> (tptp_fun_C_0(singleton(B!3), B!3) = B!3))) <=> ($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)))),
% 0.12/0.38 inference(monotonicity,[status(thm)],[43])).
% 0.12/0.38 tff(45,plain,
% 0.12/0.38 (((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))) <=> $true),
% 0.12/0.38 inference(transitivity,[status(thm)],[44, 42])).
% 0.12/0.38 tff(46,plain,
% 0.12/0.38 ((~((singleton(B!3) = singleton(B!3)) | ((~in(tptp_fun_C_0(singleton(B!3), B!3), singleton(B!3))) <=> (tptp_fun_C_0(singleton(B!3), B!3) = B!3)))) <=> (~$true)),
% 0.12/0.38 inference(monotonicity,[status(thm)],[45])).
% 0.12/0.38 tff(47,plain,
% 0.12/0.38 ((~((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)))) <=> $false),
% 0.12/0.38 inference(transitivity,[status(thm)],[46, 41])).
% 0.12/0.38 tff(48,plain,
% 0.12/0.38 ((~(in(A!4, singleton(B!3)) <=> (A!4 = B!3))) <=> ((~in(A!4, singleton(B!3))) <=> (A!4 = B!3))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(49,plain,
% 0.12/0.38 (($false | (in(A!4, singleton(B!3)) <=> (A!4 = B!3))) <=> (in(A!4, singleton(B!3)) <=> (A!4 = B!3))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(50,plain,
% 0.12/0.38 ((~(singleton(B!3) = singleton(B!3))) <=> (~$true)),
% 0.12/0.38 inference(monotonicity,[status(thm)],[43])).
% 0.12/0.38 tff(51,plain,
% 0.12/0.38 ((~(singleton(B!3) = singleton(B!3))) <=> $false),
% 0.12/0.38 inference(transitivity,[status(thm)],[50, 41])).
% 0.12/0.38 tff(52,plain,
% 0.12/0.38 (((~(singleton(B!3) = singleton(B!3))) | (in(A!4, singleton(B!3)) <=> (A!4 = B!3))) <=> ($false | (in(A!4, singleton(B!3)) <=> (A!4 = B!3)))),
% 0.12/0.38 inference(monotonicity,[status(thm)],[51])).
% 0.12/0.38 tff(53,plain,
% 0.12/0.38 (((~(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))),
% 0.12/0.39 inference(transitivity,[status(thm)],[52, 49])).
% 0.12/0.39 tff(54,plain,
% 0.12/0.39 ((~((~(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)))),
% 0.12/0.39 inference(monotonicity,[status(thm)],[53])).
% 0.12/0.39 tff(55,plain,
% 0.12/0.39 ((~((~(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))),
% 0.12/0.39 inference(transitivity,[status(thm)],[54, 48])).
% 0.12/0.39 tff(56,plain,
% 0.12/0.39 (((~((~(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)),
% 0.12/0.39 inference(monotonicity,[status(thm)],[55, 47])).
% 0.12/0.39 tff(57,plain,
% 0.12/0.39 (((~((~(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))),
% 0.12/0.39 inference(transitivity,[status(thm)],[56, 40])).
% 0.12/0.39 tff(58,plain,
% 0.12/0.39 ((~((~((~(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)))),
% 0.12/0.39 inference(monotonicity,[status(thm)],[57])).
% 0.12/0.39 tff(59,plain,
% 0.12/0.39 ((~((~((~(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))),
% 0.12/0.39 inference(transitivity,[status(thm)],[58, 39])).
% 0.12/0.39 tff(60,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))))))) | (~((~((~(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)))),
% 0.12/0.39 inference(monotonicity,[status(thm)],[59])).
% 0.12/0.39 tff(61,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))))))) | (~((~((~(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)))),
% 0.12/0.39 inference(transitivity,[status(thm)],[60, 38])).
% 0.12/0.39 tff(62,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))))))) | (~((~((~(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))))))),
% 0.12/0.39 inference(quant_inst,[status(thm)],[])).
% 0.12/0.39 tff(63,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))))))) | (in(A!4, singleton(B!3)) <=> (A!4 = B!3))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[62, 61])).
% 0.12/0.39 tff(64,plain,
% 0.12/0.39 (in(A!4, singleton(B!3)) <=> (A!4 = B!3)),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[63, 37])).
% 0.12/0.39 tff(65,plain,
% 0.12/0.39 ((~(in(A!4, singleton(B!3)) <=> (A!4 = B!3))) | (~in(A!4, singleton(B!3))) | (A!4 = B!3)),
% 0.12/0.39 inference(tautology,[status(thm)],[])).
% 0.12/0.39 tff(66,plain,
% 0.12/0.39 ((~in(A!4, singleton(B!3))) | (A!4 = B!3)),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[65, 64])).
% 0.12/0.39 tff(67,plain,
% 0.12/0.39 (~in(A!4, singleton(B!3))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[66, 1])).
% 0.12/0.39 tff(68,plain,
% 0.12/0.39 (^[A: $i, B: $i] : refl(((set_difference(singleton(A), B) = singleton(A)) <=> (~in(A, B))) <=> ((set_difference(singleton(A), B) = singleton(A)) <=> (~in(A, B))))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(69,plain,
% 0.12/0.39 (![A: $i, B: $i] : ((set_difference(singleton(A), B) = singleton(A)) <=> (~in(A, B))) <=> ![A: $i, B: $i] : ((set_difference(singleton(A), B) = singleton(A)) <=> (~in(A, B)))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[68])).
% 0.12/0.39 tff(70,plain,
% 0.12/0.39 (![A: $i, B: $i] : ((set_difference(singleton(A), B) = singleton(A)) <=> (~in(A, B))) <=> ![A: $i, B: $i] : ((set_difference(singleton(A), B) = singleton(A)) <=> (~in(A, B)))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(71,axiom,(![A: $i, B: $i] : ((set_difference(singleton(A), B) = singleton(A)) <=> (~in(A, B)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','l34_zfmisc_1')).
% 0.12/0.39 tff(72,plain,
% 0.12/0.39 (![A: $i, B: $i] : ((set_difference(singleton(A), B) = singleton(A)) <=> (~in(A, B)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[71, 70])).
% 0.12/0.39 tff(73,plain,(
% 0.12/0.39 ![A: $i, B: $i] : ((set_difference(singleton(A), B) = singleton(A)) <=> (~in(A, B)))),
% 0.12/0.39 inference(skolemize,[status(sab)],[72])).
% 0.12/0.39 tff(74,plain,
% 0.12/0.39 (![A: $i, B: $i] : ((set_difference(singleton(A), B) = singleton(A)) <=> (~in(A, B)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[73, 69])).
% 0.12/0.39 tff(75,plain,
% 0.12/0.39 ((~![A: $i, B: $i] : ((set_difference(singleton(A), B) = singleton(A)) <=> (~in(A, B)))) | ((set_difference(singleton(A!4), singleton(B!3)) = singleton(A!4)) <=> (~in(A!4, singleton(B!3))))),
% 0.12/0.39 inference(quant_inst,[status(thm)],[])).
% 0.12/0.39 tff(76,plain,
% 0.12/0.39 ((set_difference(singleton(A!4), singleton(B!3)) = singleton(A!4)) <=> (~in(A!4, singleton(B!3)))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[75, 74])).
% 0.12/0.39 tff(77,plain,
% 0.12/0.39 ((~((set_difference(singleton(A!4), singleton(B!3)) = singleton(A!4)) <=> (~in(A!4, singleton(B!3))))) | (set_difference(singleton(A!4), singleton(B!3)) = singleton(A!4)) | in(A!4, singleton(B!3))),
% 0.12/0.39 inference(tautology,[status(thm)],[])).
% 0.12/0.39 tff(78,plain,
% 0.12/0.39 ((set_difference(singleton(A!4), singleton(B!3)) = singleton(A!4)) | in(A!4, singleton(B!3))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[77, 76])).
% 0.12/0.39 tff(79,plain,
% 0.12/0.39 ($false),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[78, 67, 16])).
% 0.12/0.39 tff(80,plain,(A!4 = B!3), inference(lemma,lemma(discharge,[]))).
% 0.12/0.39 tff(81,plain,
% 0.12/0.39 ((set_difference(singleton(A!4), singleton(B!3)) = singleton(A!4)) | (~(A!4 = B!3)) | (~((set_difference(singleton(A!4), singleton(B!3)) = singleton(A!4)) <=> (A!4 = B!3)))),
% 0.12/0.39 inference(tautology,[status(thm)],[])).
% 0.12/0.39 tff(82,plain,
% 0.12/0.39 ((set_difference(singleton(A!4), singleton(B!3)) = singleton(A!4)) | (~(A!4 = B!3))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[81, 13])).
% 0.12/0.39 tff(83,plain,
% 0.12/0.39 (set_difference(singleton(A!4), singleton(B!3)) = singleton(A!4)),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[82, 80])).
% 0.12/0.39 tff(84,plain,
% 0.12/0.39 ((~(in(A!4, singleton(B!3)) <=> (A!4 = B!3))) | in(A!4, singleton(B!3)) | (~(A!4 = B!3))),
% 0.12/0.39 inference(tautology,[status(thm)],[])).
% 0.12/0.39 tff(85,plain,
% 0.12/0.39 (in(A!4, singleton(B!3)) | (~(A!4 = B!3))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[84, 64])).
% 0.12/0.39 tff(86,plain,
% 0.12/0.39 (in(A!4, singleton(B!3))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[85, 80])).
% 0.12/0.39 tff(87,plain,
% 0.12/0.39 ((~((set_difference(singleton(A!4), singleton(B!3)) = singleton(A!4)) <=> (~in(A!4, singleton(B!3))))) | (~(set_difference(singleton(A!4), singleton(B!3)) = singleton(A!4))) | (~in(A!4, singleton(B!3)))),
% 0.12/0.39 inference(tautology,[status(thm)],[])).
% 0.12/0.39 tff(88,plain,
% 0.12/0.39 ((~(set_difference(singleton(A!4), singleton(B!3)) = singleton(A!4))) | (~in(A!4, singleton(B!3)))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[87, 76])).
% 0.12/0.39 tff(89,plain,
% 0.12/0.39 ($false),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[88, 86, 83])).
% 0.12/0.39 % SZS output end Proof
%------------------------------------------------------------------------------