TSTP Solution File: SET875+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SET875+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n025.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 0.39s
% Output : Proof 0.12s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET875+1 : TPTP v8.1.0. Released v3.2.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.34 % Computer : n025.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 08:35:03 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(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_B_3_type, type, (
% 0.12/0.39 tptp_fun_B_3: $i)).
% 0.12/0.39 tff(disjoint_type, type, (
% 0.12/0.39 disjoint: ( $i * $i ) > $o)).
% 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(tptp_fun_C_0_type, type, (
% 0.12/0.39 tptp_fun_C_0: ( $i * $i ) > $i)).
% 0.12/0.39 tff(1,plain,
% 0.12/0.39 ((~(~(disjoint(singleton(A!4), singleton(B!3)) & (A!4 = B!3)))) <=> (disjoint(singleton(A!4), singleton(B!3)) & (A!4 = B!3))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(2,plain,
% 0.12/0.39 ((~![A: $i, B: $i] : (~(disjoint(singleton(A), singleton(B)) & (A = B)))) <=> (~![A: $i, B: $i] : (~(disjoint(singleton(A), singleton(B)) & (A = B))))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(3,axiom,(~![A: $i, B: $i] : (~(disjoint(singleton(A), singleton(B)) & (A = B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t16_zfmisc_1')).
% 0.12/0.39 tff(4,plain,
% 0.12/0.39 (~![A: $i, B: $i] : (~(disjoint(singleton(A), singleton(B)) & (A = B)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[3, 2])).
% 0.12/0.39 tff(5,plain,
% 0.12/0.39 (~![A: $i, B: $i] : (~(disjoint(singleton(A), singleton(B)) & (A = B)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[4, 2])).
% 0.12/0.39 tff(6,plain,
% 0.12/0.39 (~![A: $i, B: $i] : (~(disjoint(singleton(A), singleton(B)) & (A = B)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[5, 2])).
% 0.12/0.39 tff(7,plain,
% 0.12/0.39 (~![A: $i, B: $i] : (~(disjoint(singleton(A), singleton(B)) & (A = B)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.12/0.39 tff(8,plain,
% 0.12/0.39 (~![A: $i, B: $i] : (~(disjoint(singleton(A), singleton(B)) & (A = B)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[7, 2])).
% 0.12/0.39 tff(9,plain,
% 0.12/0.39 (~![A: $i, B: $i] : (~(disjoint(singleton(A), singleton(B)) & (A = B)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[8, 2])).
% 0.12/0.39 tff(10,plain,
% 0.12/0.39 (~![A: $i, B: $i] : (~(disjoint(singleton(A), singleton(B)) & (A = B)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[9, 2])).
% 0.12/0.39 tff(11,plain,(
% 0.12/0.39 ~(~(disjoint(singleton(A!4), singleton(B!3)) & (A!4 = B!3)))),
% 0.12/0.39 inference(skolemize,[status(sab)],[10])).
% 0.12/0.39 tff(12,plain,
% 0.12/0.39 (disjoint(singleton(A!4), singleton(B!3)) & (A!4 = B!3)),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[11, 1])).
% 0.12/0.39 tff(13,plain,
% 0.12/0.39 (A!4 = B!3),
% 0.12/0.39 inference(and_elim,[status(thm)],[12])).
% 0.12/0.39 tff(14,plain,
% 0.12/0.39 (singleton(A!4) = singleton(B!3)),
% 0.12/0.39 inference(monotonicity,[status(thm)],[13])).
% 0.12/0.39 tff(15,plain,
% 0.12/0.39 (singleton(B!3) = singleton(A!4)),
% 0.12/0.39 inference(symmetry,[status(thm)],[14])).
% 0.12/0.39 tff(16,plain,
% 0.12/0.39 (disjoint(singleton(B!3), singleton(B!3)) <=> disjoint(singleton(A!4), singleton(B!3))),
% 0.12/0.39 inference(monotonicity,[status(thm)],[15])).
% 0.12/0.39 tff(17,plain,
% 0.12/0.39 (disjoint(singleton(A!4), singleton(B!3)) <=> disjoint(singleton(B!3), singleton(B!3))),
% 0.12/0.39 inference(symmetry,[status(thm)],[16])).
% 0.12/0.39 tff(18,plain,
% 0.12/0.39 (disjoint(singleton(A!4), singleton(B!3))),
% 0.12/0.39 inference(and_elim,[status(thm)],[12])).
% 0.12/0.39 tff(19,plain,
% 0.12/0.39 (disjoint(singleton(B!3), singleton(B!3))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[18, 17])).
% 0.12/0.39 tff(20,plain,
% 0.12/0.39 (^[A: $i, B: $i] : refl(((~in(A, B)) | (~disjoint(singleton(A), B))) <=> ((~in(A, B)) | (~disjoint(singleton(A), B))))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(21,plain,
% 0.12/0.39 (![A: $i, B: $i] : ((~in(A, B)) | (~disjoint(singleton(A), B))) <=> ![A: $i, B: $i] : ((~in(A, B)) | (~disjoint(singleton(A), B)))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[20])).
% 0.12/0.39 tff(22,plain,
% 0.12/0.39 (^[A: $i, B: $i] : trans(monotonicity(rewrite((disjoint(singleton(A), B) & in(A, B)) <=> (~((~in(A, B)) | (~disjoint(singleton(A), B))))), ((~(disjoint(singleton(A), B) & in(A, B))) <=> (~(~((~in(A, B)) | (~disjoint(singleton(A), B))))))), rewrite((~(~((~in(A, B)) | (~disjoint(singleton(A), B))))) <=> ((~in(A, B)) | (~disjoint(singleton(A), B)))), ((~(disjoint(singleton(A), B) & in(A, B))) <=> ((~in(A, B)) | (~disjoint(singleton(A), B)))))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(23,plain,
% 0.12/0.39 (![A: $i, B: $i] : (~(disjoint(singleton(A), B) & in(A, B))) <=> ![A: $i, B: $i] : ((~in(A, B)) | (~disjoint(singleton(A), B)))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[22])).
% 0.12/0.39 tff(24,plain,
% 0.12/0.39 (![A: $i, B: $i] : (~(disjoint(singleton(A), B) & in(A, B))) <=> ![A: $i, B: $i] : (~(disjoint(singleton(A), B) & in(A, B)))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(25,axiom,(![A: $i, B: $i] : (~(disjoint(singleton(A), B) & in(A, B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','l25_zfmisc_1')).
% 0.12/0.39 tff(26,plain,
% 0.12/0.39 (![A: $i, B: $i] : (~(disjoint(singleton(A), B) & in(A, B)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[25, 24])).
% 0.12/0.39 tff(27,plain,(
% 0.12/0.39 ![A: $i, B: $i] : (~(disjoint(singleton(A), B) & in(A, B)))),
% 0.12/0.39 inference(skolemize,[status(sab)],[26])).
% 0.12/0.39 tff(28,plain,
% 0.12/0.39 (![A: $i, B: $i] : ((~in(A, B)) | (~disjoint(singleton(A), B)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[27, 23])).
% 0.12/0.39 tff(29,plain,
% 0.12/0.39 (![A: $i, B: $i] : ((~in(A, B)) | (~disjoint(singleton(A), B)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[28, 21])).
% 0.12/0.39 tff(30,plain,
% 0.12/0.39 (((~![A: $i, B: $i] : ((~in(A, B)) | (~disjoint(singleton(A), B)))) | ((~in(B!3, singleton(B!3))) | (~disjoint(singleton(B!3), singleton(B!3))))) <=> ((~![A: $i, B: $i] : ((~in(A, B)) | (~disjoint(singleton(A), B)))) | (~in(B!3, singleton(B!3))) | (~disjoint(singleton(B!3), singleton(B!3))))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(31,plain,
% 0.12/0.39 ((~![A: $i, B: $i] : ((~in(A, B)) | (~disjoint(singleton(A), B)))) | ((~in(B!3, singleton(B!3))) | (~disjoint(singleton(B!3), singleton(B!3))))),
% 0.12/0.39 inference(quant_inst,[status(thm)],[])).
% 0.12/0.39 tff(32,plain,
% 0.12/0.39 ((~![A: $i, B: $i] : ((~in(A, B)) | (~disjoint(singleton(A), B)))) | (~in(B!3, singleton(B!3))) | (~disjoint(singleton(B!3), singleton(B!3)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[31, 30])).
% 0.12/0.39 tff(33,plain,
% 0.12/0.39 ((~in(B!3, singleton(B!3))) | (~disjoint(singleton(B!3), singleton(B!3)))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[32, 29])).
% 0.12/0.39 tff(34,plain,
% 0.12/0.39 (~in(B!3, singleton(B!3))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[33, 19])).
% 0.12/0.39 tff(35,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(36,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)],[35])).
% 0.12/0.39 tff(37,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(38,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(39,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)],[38])).
% 0.12/0.39 tff(40,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)],[39, 37])).
% 0.12/0.39 tff(41,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)],[40, 36])).
% 0.12/0.39 tff(42,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(43,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)],[42])).
% 0.12/0.39 tff(44,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)],[43, 41])).
% 0.12/0.40 tff(45,plain,
% 0.12/0.40 (^[A: $i, B: $i] : trans(monotonicity(rewrite(((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A))) <=> ((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))), ((((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A))) & ((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A)))) <=> (((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A))) & ((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A)))))), rewrite((((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A))) & ((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A)))) <=> (~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))))), ((((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A))) & ((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A)))) <=> (~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))))))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(46,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)],[45])).
% 0.12/0.40 tff(47,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(48,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)],[47])).
% 0.12/0.40 tff(49,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(50,axiom,(![A: $i, B: $i] : ((B = singleton(A)) <=> ![C: $i] : (in(C, B) <=> (C = A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d1_tarski')).
% 0.12/0.40 tff(51,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)],[50, 49])).
% 0.12/0.40 tff(52,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)],[51])).
% 0.12/0.40 tff(53,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)],[52, 48])).
% 0.12/0.40 tff(54,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)],[53, 46])).
% 0.12/0.40 tff(55,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)],[54, 44])).
% 0.12/0.40 tff(56,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(B!3))) <=> ((~![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))))) | in(B!3, singleton(B!3)))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(57,plain,
% 0.12/0.40 ((~(~in(B!3, singleton(B!3)))) <=> in(B!3, singleton(B!3))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(58,plain,
% 0.12/0.40 (((~in(B!3, singleton(B!3))) | $false) <=> (~in(B!3, singleton(B!3)))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(59,plain,
% 0.12/0.40 ((~$true) <=> $false),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(60,plain,
% 0.12/0.40 (($true | ((~in(tptp_fun_C_0(singleton(B!3), B!3), singleton(B!3))) <=> (tptp_fun_C_0(singleton(B!3), B!3) = B!3))) <=> $true),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(61,plain,
% 0.12/0.40 ((singleton(B!3) = singleton(B!3)) <=> $true),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(62,plain,
% 0.12/0.40 (((singleton(B!3) = singleton(B!3)) | ((~in(tptp_fun_C_0(singleton(B!3), B!3), singleton(B!3))) <=> (tptp_fun_C_0(singleton(B!3), B!3) = B!3))) <=> ($true | ((~in(tptp_fun_C_0(singleton(B!3), B!3), singleton(B!3))) <=> (tptp_fun_C_0(singleton(B!3), B!3) = B!3)))),
% 0.12/0.40 inference(monotonicity,[status(thm)],[61])).
% 0.12/0.40 tff(63,plain,
% 0.12/0.40 (((singleton(B!3) = singleton(B!3)) | ((~in(tptp_fun_C_0(singleton(B!3), B!3), singleton(B!3))) <=> (tptp_fun_C_0(singleton(B!3), B!3) = B!3))) <=> $true),
% 0.12/0.40 inference(transitivity,[status(thm)],[62, 60])).
% 0.12/0.40 tff(64,plain,
% 0.12/0.40 ((~((singleton(B!3) = singleton(B!3)) | ((~in(tptp_fun_C_0(singleton(B!3), B!3), singleton(B!3))) <=> (tptp_fun_C_0(singleton(B!3), B!3) = B!3)))) <=> (~$true)),
% 0.12/0.40 inference(monotonicity,[status(thm)],[63])).
% 0.12/0.40 tff(65,plain,
% 0.12/0.40 ((~((singleton(B!3) = singleton(B!3)) | ((~in(tptp_fun_C_0(singleton(B!3), B!3), singleton(B!3))) <=> (tptp_fun_C_0(singleton(B!3), B!3) = B!3)))) <=> $false),
% 0.12/0.40 inference(transitivity,[status(thm)],[64, 59])).
% 0.12/0.40 tff(66,plain,
% 0.12/0.40 ((~((~(singleton(B!3) = singleton(B!3))) | (in(B!3, singleton(B!3)) <=> (B!3 = B!3)))) <=> (~in(B!3, singleton(B!3)))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(67,plain,
% 0.12/0.40 (((~((~(singleton(B!3) = singleton(B!3))) | (in(B!3, singleton(B!3)) <=> (B!3 = B!3)))) | (~((singleton(B!3) = singleton(B!3)) | ((~in(tptp_fun_C_0(singleton(B!3), B!3), singleton(B!3))) <=> (tptp_fun_C_0(singleton(B!3), B!3) = B!3))))) <=> ((~in(B!3, singleton(B!3))) | $false)),
% 0.12/0.40 inference(monotonicity,[status(thm)],[66, 65])).
% 0.12/0.40 tff(68,plain,
% 0.12/0.40 (((~((~(singleton(B!3) = singleton(B!3))) | (in(B!3, singleton(B!3)) <=> (B!3 = B!3)))) | (~((singleton(B!3) = singleton(B!3)) | ((~in(tptp_fun_C_0(singleton(B!3), B!3), singleton(B!3))) <=> (tptp_fun_C_0(singleton(B!3), B!3) = B!3))))) <=> (~in(B!3, singleton(B!3)))),
% 0.12/0.40 inference(transitivity,[status(thm)],[67, 58])).
% 0.12/0.40 tff(69,plain,
% 0.12/0.40 ((~((~((~(singleton(B!3) = singleton(B!3))) | (in(B!3, singleton(B!3)) <=> (B!3 = B!3)))) | (~((singleton(B!3) = singleton(B!3)) | ((~in(tptp_fun_C_0(singleton(B!3), B!3), singleton(B!3))) <=> (tptp_fun_C_0(singleton(B!3), B!3) = B!3)))))) <=> (~(~in(B!3, singleton(B!3))))),
% 0.12/0.40 inference(monotonicity,[status(thm)],[68])).
% 0.12/0.40 tff(70,plain,
% 0.12/0.40 ((~((~((~(singleton(B!3) = singleton(B!3))) | (in(B!3, singleton(B!3)) <=> (B!3 = B!3)))) | (~((singleton(B!3) = singleton(B!3)) | ((~in(tptp_fun_C_0(singleton(B!3), B!3), singleton(B!3))) <=> (tptp_fun_C_0(singleton(B!3), B!3) = B!3)))))) <=> in(B!3, singleton(B!3))),
% 0.12/0.40 inference(transitivity,[status(thm)],[69, 57])).
% 0.12/0.40 tff(71,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(B!3) = singleton(B!3))) | (in(B!3, singleton(B!3)) <=> (B!3 = B!3)))) | (~((singleton(B!3) = singleton(B!3)) | ((~in(tptp_fun_C_0(singleton(B!3), B!3), singleton(B!3))) <=> (tptp_fun_C_0(singleton(B!3), B!3) = B!3))))))) <=> ((~![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))))) | in(B!3, singleton(B!3)))),
% 0.12/0.40 inference(monotonicity,[status(thm)],[70])).
% 0.12/0.40 tff(72,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(B!3) = singleton(B!3))) | (in(B!3, singleton(B!3)) <=> (B!3 = B!3)))) | (~((singleton(B!3) = singleton(B!3)) | ((~in(tptp_fun_C_0(singleton(B!3), B!3), singleton(B!3))) <=> (tptp_fun_C_0(singleton(B!3), B!3) = B!3))))))) <=> ((~![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))))) | in(B!3, singleton(B!3)))),
% 0.12/0.40 inference(transitivity,[status(thm)],[71, 56])).
% 0.12/0.40 tff(73,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(B!3) = singleton(B!3))) | (in(B!3, singleton(B!3)) <=> (B!3 = B!3)))) | (~((singleton(B!3) = singleton(B!3)) | ((~in(tptp_fun_C_0(singleton(B!3), B!3), singleton(B!3))) <=> (tptp_fun_C_0(singleton(B!3), B!3) = B!3))))))),
% 0.12/0.40 inference(quant_inst,[status(thm)],[])).
% 0.12/0.40 tff(74,plain,
% 0.12/0.40 ((~![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))))) | in(B!3, singleton(B!3))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[73, 72])).
% 0.12/0.40 tff(75,plain,
% 0.12/0.40 ($false),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[74, 55, 34])).
% 0.12/0.40 % SZS output end Proof
%------------------------------------------------------------------------------