TSTP Solution File: SEU143+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SEU143+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n019.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 07:27:44 EDT 2022
% Result : Theorem 0.20s 0.40s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEU143+1 : TPTP v8.1.0. Released v3.3.0.
% 0.03/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n019.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sat Sep 3 09:42:35 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 0.20/0.40 % SZS status Theorem
% 0.20/0.40 % SZS output start Proof
% 0.20/0.40 tff(in_type, type, (
% 0.20/0.40 in: ( $i * $i ) > $o)).
% 0.20/0.40 tff(empty_set_type, type, (
% 0.20/0.40 empty_set: $i)).
% 0.20/0.40 tff(tptp_fun_A_2_type, type, (
% 0.20/0.40 tptp_fun_A_2: $i)).
% 0.20/0.40 tff(singleton_type, type, (
% 0.20/0.40 singleton: $i > $i)).
% 0.20/0.40 tff(tptp_fun_C_0_type, type, (
% 0.20/0.40 tptp_fun_C_0: ( $i * $i ) > $i)).
% 0.20/0.40 tff(tptp_fun_B_1_type, type, (
% 0.20/0.40 tptp_fun_B_1: $i > $i)).
% 0.20/0.40 tff(1,plain,
% 0.20/0.40 (^[A: $i, B: $i, C: $i] : refl((~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A)))))) <=> (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A)))))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(2,plain,
% 0.20/0.40 (![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A)))))) <=> ![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[1])).
% 0.20/0.40 tff(3,plain,
% 0.20/0.40 (![A: $i, B: $i] : ![C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A)))))) <=> ![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))))),
% 0.20/0.40 inference(pull_quant,[status(thm)],[])).
% 0.20/0.40 tff(4,plain,
% 0.20/0.40 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(pull_quant(((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A))) <=> ![C: $i] : ((~(B = singleton(A))) | (in(C, B) <=> (C = A)))), ((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) <=> (~![C: $i] : ((~(B = singleton(A))) | (in(C, B) <=> (C = A)))))), pull_quant((~![C: $i] : ((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) <=> ?[C: $i] : (~((~(B = singleton(A))) | (in(C, B) <=> (C = A))))), ((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) <=> ?[C: $i] : (~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))))), (((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))) <=> (?[C: $i] : (~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))))), pull_quant((?[C: $i] : (~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))) <=> ?[C: $i] : ((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A)))))), (((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))) <=> ?[C: $i] : ((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))))), ((~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A)))))) <=> (~?[C: $i] : ((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A)))))))), pull_quant((~?[C: $i] : ((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A)))))) <=> ![C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))))), ((~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A)))))) <=> ![C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(5,plain,
% 0.20/0.40 (![A: $i, B: $i] : (~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A)))))) <=> ![A: $i, B: $i] : ![C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[4])).
% 0.20/0.40 tff(6,plain,
% 0.20/0.40 (![A: $i, B: $i] : (~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A)))))) <=> ![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))))),
% 0.20/0.40 inference(transitivity,[status(thm)],[5, 3])).
% 0.20/0.40 tff(7,plain,
% 0.20/0.40 (![A: $i, B: $i] : (~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A)))))) <=> ![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))))),
% 0.20/0.40 inference(transitivity,[status(thm)],[6, 2])).
% 0.20/0.40 tff(8,plain,
% 0.20/0.40 (^[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)))))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(9,plain,
% 0.20/0.40 (![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))))))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[8])).
% 0.20/0.40 tff(10,plain,
% 0.20/0.40 (![A: $i, B: $i] : (~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A)))))) <=> ![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))))),
% 0.20/0.40 inference(transitivity,[status(thm)],[9, 7])).
% 0.20/0.40 tff(11,plain,
% 0.20/0.40 (^[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))))))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(12,plain,
% 0.20/0.40 (![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))))))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[11])).
% 0.20/0.40 tff(13,plain,
% 0.20/0.40 (^[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)))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(14,plain,
% 0.20/0.40 (![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))))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[13])).
% 0.20/0.40 tff(15,plain,
% 0.20/0.40 (![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)))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(16,axiom,(![A: $i, B: $i] : ((B = singleton(A)) <=> ![C: $i] : (in(C, B) <=> (C = A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d1_tarski')).
% 0.20/0.40 tff(17,plain,
% 0.20/0.40 (![A: $i, B: $i] : ((B = singleton(A)) <=> ![C: $i] : (in(C, B) <=> (C = A)))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[16, 15])).
% 0.20/0.40 tff(18,plain,(
% 0.20/0.40 ![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)))))),
% 0.20/0.40 inference(skolemize,[status(sab)],[17])).
% 0.20/0.40 tff(19,plain,
% 0.20/0.40 (![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))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[18, 14])).
% 0.20/0.40 tff(20,plain,
% 0.20/0.40 (![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))))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[19, 12])).
% 0.20/0.40 tff(21,plain,
% 0.20/0.40 (![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))))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[20, 10])).
% 0.20/0.40 tff(22,plain,
% 0.20/0.40 (((~![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))))))) | (~((~((~(empty_set = singleton(A!2))) | in(A!2, empty_set))) | (~((empty_set = singleton(A!2)) | ((~in(tptp_fun_C_0(empty_set, A!2), empty_set)) <=> (tptp_fun_C_0(empty_set, A!2) = A!2))))))) <=> ((~![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))))))) | (~((~((~(empty_set = singleton(A!2))) | in(A!2, empty_set))) | (~((empty_set = singleton(A!2)) | ((~in(tptp_fun_C_0(empty_set, A!2), empty_set)) <=> (tptp_fun_C_0(empty_set, A!2) = A!2)))))))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(23,plain,
% 0.20/0.40 ((~((~((~(empty_set = singleton(A!2))) | (in(A!2, empty_set) <=> (A!2 = A!2)))) | (~((empty_set = singleton(A!2)) | ((~in(tptp_fun_C_0(empty_set, A!2), empty_set)) <=> (tptp_fun_C_0(empty_set, A!2) = A!2)))))) <=> (~((~((~(empty_set = singleton(A!2))) | in(A!2, empty_set))) | (~((empty_set = singleton(A!2)) | ((~in(tptp_fun_C_0(empty_set, A!2), empty_set)) <=> (tptp_fun_C_0(empty_set, A!2) = A!2))))))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(24,plain,
% 0.20/0.40 (((~![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))))))) | (~((~((~(empty_set = singleton(A!2))) | (in(A!2, empty_set) <=> (A!2 = A!2)))) | (~((empty_set = singleton(A!2)) | ((~in(tptp_fun_C_0(empty_set, A!2), empty_set)) <=> (tptp_fun_C_0(empty_set, A!2) = A!2))))))) <=> ((~![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))))))) | (~((~((~(empty_set = singleton(A!2))) | in(A!2, empty_set))) | (~((empty_set = singleton(A!2)) | ((~in(tptp_fun_C_0(empty_set, A!2), empty_set)) <=> (tptp_fun_C_0(empty_set, A!2) = A!2)))))))),
% 0.20/0.40 inference(monotonicity,[status(thm)],[23])).
% 0.20/0.40 tff(25,plain,
% 0.20/0.40 (((~![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))))))) | (~((~((~(empty_set = singleton(A!2))) | (in(A!2, empty_set) <=> (A!2 = A!2)))) | (~((empty_set = singleton(A!2)) | ((~in(tptp_fun_C_0(empty_set, A!2), empty_set)) <=> (tptp_fun_C_0(empty_set, A!2) = A!2))))))) <=> ((~![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))))))) | (~((~((~(empty_set = singleton(A!2))) | in(A!2, empty_set))) | (~((empty_set = singleton(A!2)) | ((~in(tptp_fun_C_0(empty_set, A!2), empty_set)) <=> (tptp_fun_C_0(empty_set, A!2) = A!2)))))))),
% 0.20/0.40 inference(transitivity,[status(thm)],[24, 22])).
% 0.20/0.40 tff(26,plain,
% 0.20/0.40 ((~![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))))))) | (~((~((~(empty_set = singleton(A!2))) | (in(A!2, empty_set) <=> (A!2 = A!2)))) | (~((empty_set = singleton(A!2)) | ((~in(tptp_fun_C_0(empty_set, A!2), empty_set)) <=> (tptp_fun_C_0(empty_set, A!2) = A!2))))))),
% 0.20/0.40 inference(quant_inst,[status(thm)],[])).
% 0.20/0.40 tff(27,plain,
% 0.20/0.40 ((~![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))))))) | (~((~((~(empty_set = singleton(A!2))) | in(A!2, empty_set))) | (~((empty_set = singleton(A!2)) | ((~in(tptp_fun_C_0(empty_set, A!2), empty_set)) <=> (tptp_fun_C_0(empty_set, A!2) = A!2))))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[26, 25])).
% 0.20/0.40 tff(28,plain,
% 0.20/0.40 (~((~((~(empty_set = singleton(A!2))) | in(A!2, empty_set))) | (~((empty_set = singleton(A!2)) | ((~in(tptp_fun_C_0(empty_set, A!2), empty_set)) <=> (tptp_fun_C_0(empty_set, A!2) = A!2)))))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[27, 21])).
% 0.20/0.40 tff(29,plain,
% 0.20/0.40 (((~((~(empty_set = singleton(A!2))) | in(A!2, empty_set))) | (~((empty_set = singleton(A!2)) | ((~in(tptp_fun_C_0(empty_set, A!2), empty_set)) <=> (tptp_fun_C_0(empty_set, A!2) = A!2))))) | ((~(empty_set = singleton(A!2))) | in(A!2, empty_set))),
% 0.20/0.40 inference(tautology,[status(thm)],[])).
% 0.20/0.40 tff(30,plain,
% 0.20/0.40 ((~(empty_set = singleton(A!2))) | in(A!2, empty_set)),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[29, 28])).
% 0.20/0.40 tff(31,plain,
% 0.20/0.40 ((~(~(singleton(A!2) = empty_set))) <=> (singleton(A!2) = empty_set)),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(32,plain,
% 0.20/0.40 ((~![A: $i] : (~(singleton(A) = empty_set))) <=> (~![A: $i] : (~(singleton(A) = empty_set)))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(33,axiom,(~![A: $i] : (~(singleton(A) = empty_set))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','l1_zfmisc_1')).
% 0.20/0.40 tff(34,plain,
% 0.20/0.40 (~![A: $i] : (~(singleton(A) = empty_set))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[33, 32])).
% 0.20/0.40 tff(35,plain,
% 0.20/0.40 (~![A: $i] : (~(singleton(A) = empty_set))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[34, 32])).
% 0.20/0.40 tff(36,plain,
% 0.20/0.40 (~![A: $i] : (~(singleton(A) = empty_set))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[35, 32])).
% 0.20/0.40 tff(37,plain,
% 0.20/0.40 (~![A: $i] : (~(singleton(A) = empty_set))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[36, 32])).
% 0.20/0.40 tff(38,plain,
% 0.20/0.40 (~![A: $i] : (~(singleton(A) = empty_set))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[37, 32])).
% 0.20/0.40 tff(39,plain,
% 0.20/0.40 (~![A: $i] : (~(singleton(A) = empty_set))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[38, 32])).
% 0.20/0.40 tff(40,plain,
% 0.20/0.40 (~![A: $i] : (~(singleton(A) = empty_set))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[39, 32])).
% 0.20/0.40 tff(41,plain,(
% 0.20/0.40 ~(~(singleton(A!2) = empty_set))),
% 0.20/0.40 inference(skolemize,[status(sab)],[40])).
% 0.20/0.41 tff(42,plain,
% 0.20/0.41 (singleton(A!2) = empty_set),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[41, 31])).
% 0.20/0.41 tff(43,plain,
% 0.20/0.41 (empty_set = singleton(A!2)),
% 0.20/0.41 inference(symmetry,[status(thm)],[42])).
% 0.20/0.41 tff(44,plain,
% 0.20/0.41 ((~((~(empty_set = singleton(A!2))) | in(A!2, empty_set))) | (~(empty_set = singleton(A!2))) | in(A!2, empty_set)),
% 0.20/0.41 inference(tautology,[status(thm)],[])).
% 0.20/0.41 tff(45,plain,
% 0.20/0.41 ((~((~(empty_set = singleton(A!2))) | in(A!2, empty_set))) | in(A!2, empty_set)),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[44, 43])).
% 0.20/0.41 tff(46,plain,
% 0.20/0.41 (in(A!2, empty_set)),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[45, 30])).
% 0.20/0.41 tff(47,plain,
% 0.20/0.41 (^[A: $i, B: $i] : refl((~((~((~(A = empty_set)) | (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_1(A), A))))) <=> (~((~((~(A = empty_set)) | (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_1(A), A))))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(48,plain,
% 0.20/0.41 (![A: $i, B: $i] : (~((~((~(A = empty_set)) | (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_1(A), A))))) <=> ![A: $i, B: $i] : (~((~((~(A = empty_set)) | (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_1(A), A)))))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[47])).
% 0.20/0.41 tff(49,plain,
% 0.20/0.41 (![A: $i] : ![B: $i] : (~((~((~(A = empty_set)) | (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_1(A), A))))) <=> ![A: $i, B: $i] : (~((~((~(A = empty_set)) | (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_1(A), A)))))),
% 0.20/0.41 inference(pull_quant,[status(thm)],[])).
% 0.20/0.41 tff(50,plain,
% 0.20/0.41 (^[A: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(pull_quant(((~(A = empty_set)) | ![B: $i] : (~in(B, A))) <=> ![B: $i] : ((~(A = empty_set)) | (~in(B, A)))), ((~((~(A = empty_set)) | ![B: $i] : (~in(B, A)))) <=> (~![B: $i] : ((~(A = empty_set)) | (~in(B, A)))))), pull_quant((~![B: $i] : ((~(A = empty_set)) | (~in(B, A)))) <=> ?[B: $i] : (~((~(A = empty_set)) | (~in(B, A))))), ((~((~(A = empty_set)) | ![B: $i] : (~in(B, A)))) <=> ?[B: $i] : (~((~(A = empty_set)) | (~in(B, A)))))), (((~((~(A = empty_set)) | ![B: $i] : (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_1(A), A)))) <=> (?[B: $i] : (~((~(A = empty_set)) | (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_1(A), A)))))), pull_quant((?[B: $i] : (~((~(A = empty_set)) | (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_1(A), A)))) <=> ?[B: $i] : ((~((~(A = empty_set)) | (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_1(A), A))))), (((~((~(A = empty_set)) | ![B: $i] : (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_1(A), A)))) <=> ?[B: $i] : ((~((~(A = empty_set)) | (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_1(A), A)))))), ((~((~((~(A = empty_set)) | ![B: $i] : (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_1(A), A))))) <=> (~?[B: $i] : ((~((~(A = empty_set)) | (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_1(A), A))))))), pull_quant((~?[B: $i] : ((~((~(A = empty_set)) | (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_1(A), A))))) <=> ![B: $i] : (~((~((~(A = empty_set)) | (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_1(A), A)))))), ((~((~((~(A = empty_set)) | ![B: $i] : (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_1(A), A))))) <=> ![B: $i] : (~((~((~(A = empty_set)) | (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_1(A), A)))))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(51,plain,
% 0.20/0.41 (![A: $i] : (~((~((~(A = empty_set)) | ![B: $i] : (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_1(A), A))))) <=> ![A: $i] : ![B: $i] : (~((~((~(A = empty_set)) | (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_1(A), A)))))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[50])).
% 0.20/0.41 tff(52,plain,
% 0.20/0.41 (![A: $i] : (~((~((~(A = empty_set)) | ![B: $i] : (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_1(A), A))))) <=> ![A: $i, B: $i] : (~((~((~(A = empty_set)) | (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_1(A), A)))))),
% 0.20/0.41 inference(transitivity,[status(thm)],[51, 49])).
% 0.20/0.41 tff(53,plain,
% 0.20/0.41 (![A: $i] : (~((~((~(A = empty_set)) | ![B: $i] : (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_1(A), A))))) <=> ![A: $i, B: $i] : (~((~((~(A = empty_set)) | (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_1(A), A)))))),
% 0.20/0.41 inference(transitivity,[status(thm)],[52, 48])).
% 0.20/0.41 tff(54,plain,
% 0.20/0.41 (^[A: $i] : rewrite((~((~((~(A = empty_set)) | ![B: $i] : (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_1(A), A))))) <=> (~((~((~(A = empty_set)) | ![B: $i] : (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_1(A), A))))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(55,plain,
% 0.20/0.41 (![A: $i] : (~((~((~(A = empty_set)) | ![B: $i] : (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_1(A), A))))) <=> ![A: $i] : (~((~((~(A = empty_set)) | ![B: $i] : (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_1(A), A)))))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[54])).
% 0.20/0.41 tff(56,plain,
% 0.20/0.41 (![A: $i] : (~((~((~(A = empty_set)) | ![B: $i] : (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_1(A), A))))) <=> ![A: $i, B: $i] : (~((~((~(A = empty_set)) | (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_1(A), A)))))),
% 0.20/0.41 inference(transitivity,[status(thm)],[55, 53])).
% 0.20/0.41 tff(57,plain,
% 0.20/0.41 (^[A: $i] : trans(monotonicity(rewrite(((~(A = empty_set)) | ![B: $i] : (~in(B, A))) <=> ((~(A = empty_set)) | ![B: $i] : (~in(B, A)))), ((((~(A = empty_set)) | ![B: $i] : (~in(B, A))) & ((A = empty_set) | in(tptp_fun_B_1(A), A))) <=> (((~(A = empty_set)) | ![B: $i] : (~in(B, A))) & ((A = empty_set) | in(tptp_fun_B_1(A), A))))), rewrite((((~(A = empty_set)) | ![B: $i] : (~in(B, A))) & ((A = empty_set) | in(tptp_fun_B_1(A), A))) <=> (~((~((~(A = empty_set)) | ![B: $i] : (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_1(A), A)))))), ((((~(A = empty_set)) | ![B: $i] : (~in(B, A))) & ((A = empty_set) | in(tptp_fun_B_1(A), A))) <=> (~((~((~(A = empty_set)) | ![B: $i] : (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_1(A), A)))))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(58,plain,
% 0.20/0.41 (![A: $i] : (((~(A = empty_set)) | ![B: $i] : (~in(B, A))) & ((A = empty_set) | in(tptp_fun_B_1(A), A))) <=> ![A: $i] : (~((~((~(A = empty_set)) | ![B: $i] : (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_1(A), A)))))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[57])).
% 0.20/0.41 tff(59,plain,
% 0.20/0.41 (^[A: $i] : rewrite((((~(A = empty_set)) | ![B: $i] : (~in(B, A))) & ((A = empty_set) | (~(~in(tptp_fun_B_1(A), A))))) <=> (((~(A = empty_set)) | ![B: $i] : (~in(B, A))) & ((A = empty_set) | in(tptp_fun_B_1(A), A))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(60,plain,
% 0.20/0.41 (![A: $i] : (((~(A = empty_set)) | ![B: $i] : (~in(B, A))) & ((A = empty_set) | (~(~in(tptp_fun_B_1(A), A))))) <=> ![A: $i] : (((~(A = empty_set)) | ![B: $i] : (~in(B, A))) & ((A = empty_set) | in(tptp_fun_B_1(A), A)))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[59])).
% 0.20/0.41 tff(61,plain,
% 0.20/0.41 (![A: $i] : ((A = empty_set) <=> ![B: $i] : (~in(B, A))) <=> ![A: $i] : ((A = empty_set) <=> ![B: $i] : (~in(B, A)))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(62,axiom,(![A: $i] : ((A = empty_set) <=> ![B: $i] : (~in(B, A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d1_xboole_0')).
% 0.20/0.41 tff(63,plain,
% 0.20/0.41 (![A: $i] : ((A = empty_set) <=> ![B: $i] : (~in(B, A)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[62, 61])).
% 0.20/0.41 tff(64,plain,(
% 0.20/0.41 ![A: $i] : (((~(A = empty_set)) | ![B: $i] : (~in(B, A))) & ((A = empty_set) | (~(~in(tptp_fun_B_1(A), A)))))),
% 0.20/0.41 inference(skolemize,[status(sab)],[63])).
% 0.20/0.41 tff(65,plain,
% 0.20/0.41 (![A: $i] : (((~(A = empty_set)) | ![B: $i] : (~in(B, A))) & ((A = empty_set) | in(tptp_fun_B_1(A), A)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[64, 60])).
% 0.20/0.41 tff(66,plain,
% 0.20/0.41 (![A: $i] : (~((~((~(A = empty_set)) | ![B: $i] : (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_1(A), A)))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[65, 58])).
% 0.20/0.41 tff(67,plain,
% 0.20/0.41 (![A: $i, B: $i] : (~((~((~(A = empty_set)) | (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_1(A), A)))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[66, 56])).
% 0.20/0.41 tff(68,plain,
% 0.20/0.41 (((~![A: $i, B: $i] : (~((~((~(A = empty_set)) | (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_1(A), A)))))) | (~in(A!2, empty_set))) <=> ((~![A: $i, B: $i] : (~((~((~(A = empty_set)) | (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_1(A), A)))))) | (~in(A!2, empty_set)))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(69,plain,
% 0.20/0.41 ((~((~((~(empty_set = empty_set)) | (~in(A!2, empty_set)))) | (~((empty_set = empty_set) | in(tptp_fun_B_1(empty_set), empty_set))))) <=> (~in(A!2, empty_set))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(70,plain,
% 0.20/0.41 (((~![A: $i, B: $i] : (~((~((~(A = empty_set)) | (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_1(A), A)))))) | (~((~((~(empty_set = empty_set)) | (~in(A!2, empty_set)))) | (~((empty_set = empty_set) | in(tptp_fun_B_1(empty_set), empty_set)))))) <=> ((~![A: $i, B: $i] : (~((~((~(A = empty_set)) | (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_1(A), A)))))) | (~in(A!2, empty_set)))),
% 0.20/0.41 inference(monotonicity,[status(thm)],[69])).
% 0.20/0.41 tff(71,plain,
% 0.20/0.41 (((~![A: $i, B: $i] : (~((~((~(A = empty_set)) | (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_1(A), A)))))) | (~((~((~(empty_set = empty_set)) | (~in(A!2, empty_set)))) | (~((empty_set = empty_set) | in(tptp_fun_B_1(empty_set), empty_set)))))) <=> ((~![A: $i, B: $i] : (~((~((~(A = empty_set)) | (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_1(A), A)))))) | (~in(A!2, empty_set)))),
% 0.20/0.41 inference(transitivity,[status(thm)],[70, 68])).
% 0.20/0.41 tff(72,plain,
% 0.20/0.41 ((~![A: $i, B: $i] : (~((~((~(A = empty_set)) | (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_1(A), A)))))) | (~((~((~(empty_set = empty_set)) | (~in(A!2, empty_set)))) | (~((empty_set = empty_set) | in(tptp_fun_B_1(empty_set), empty_set)))))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(73,plain,
% 0.20/0.41 ((~![A: $i, B: $i] : (~((~((~(A = empty_set)) | (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_1(A), A)))))) | (~in(A!2, empty_set))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[72, 71])).
% 0.20/0.41 tff(74,plain,
% 0.20/0.41 ($false),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[73, 67, 46])).
% 0.20/0.41 % SZS output end Proof
%------------------------------------------------------------------------------