TSTP Solution File: SET908+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SET908+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n015.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 05:08:35 EDT 2022
% Result : Theorem 136.12s 86.62s
% Output : Proof 136.12s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : SET908+1 : TPTP v8.1.0. Released v3.2.0.
% 0.06/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.11/0.32 % Computer : n015.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Sat Sep 3 08:43:10 EDT 2022
% 0.11/0.32 % CPUTime :
% 0.11/0.33 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.11/0.33 Usage: tptp [options] [-file:]file
% 0.11/0.33 -h, -? prints this message.
% 0.11/0.33 -smt2 print SMT-LIB2 benchmark.
% 0.11/0.33 -m, -model generate model.
% 0.11/0.33 -p, -proof generate proof.
% 0.11/0.33 -c, -core generate unsat core of named formulas.
% 0.11/0.33 -st, -statistics display statistics.
% 0.11/0.33 -t:timeout set timeout (in second).
% 0.11/0.33 -smt2status display status in smt2 format instead of SZS.
% 0.11/0.33 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.11/0.33 -<param>:<value> configuration parameter and value.
% 0.11/0.33 -o:<output-file> file to place output in.
% 136.12/86.62 % SZS status Theorem
% 136.12/86.62 % SZS output start Proof
% 136.12/86.62 tff(set_union2_type, type, (
% 136.12/86.62 set_union2: ( $i * $i ) > $i)).
% 136.12/86.62 tff(tptp_fun_B_5_type, type, (
% 136.12/86.62 tptp_fun_B_5: $i)).
% 136.12/86.62 tff(singleton_type, type, (
% 136.12/86.62 singleton: $i > $i)).
% 136.12/86.62 tff(tptp_fun_A_6_type, type, (
% 136.12/86.62 tptp_fun_A_6: $i)).
% 136.12/86.62 tff(empty_set_type, type, (
% 136.12/86.62 empty_set: $i)).
% 136.12/86.62 tff(tptp_fun_C_0_type, type, (
% 136.12/86.62 tptp_fun_C_0: ( $i * $i ) > $i)).
% 136.12/86.62 tff(in_type, type, (
% 136.12/86.62 in: ( $i * $i ) > $o)).
% 136.12/86.62 tff(tptp_fun_B_1_type, type, (
% 136.12/86.62 tptp_fun_B_1: $i > $i)).
% 136.12/86.62 tff(tptp_fun_D_2_type, type, (
% 136.12/86.62 tptp_fun_D_2: ( $i * $i * $i ) > $i)).
% 136.12/86.62 tff(1,plain,
% 136.12/86.62 ((~(~(set_union2(singleton(A!6), B!5) = empty_set))) <=> (set_union2(singleton(A!6), B!5) = empty_set)),
% 136.12/86.62 inference(rewrite,[status(thm)],[])).
% 136.12/86.62 tff(2,plain,
% 136.12/86.62 ((~![A: $i, B: $i] : (~(set_union2(singleton(A), B) = empty_set))) <=> (~![A: $i, B: $i] : (~(set_union2(singleton(A), B) = empty_set)))),
% 136.12/86.62 inference(rewrite,[status(thm)],[])).
% 136.12/86.62 tff(3,axiom,(~![A: $i, B: $i] : (~(set_union2(singleton(A), B) = empty_set))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t49_zfmisc_1')).
% 136.12/86.62 tff(4,plain,
% 136.12/86.62 (~![A: $i, B: $i] : (~(set_union2(singleton(A), B) = empty_set))),
% 136.12/86.62 inference(modus_ponens,[status(thm)],[3, 2])).
% 136.12/86.62 tff(5,plain,
% 136.12/86.62 (~![A: $i, B: $i] : (~(set_union2(singleton(A), B) = empty_set))),
% 136.12/86.62 inference(modus_ponens,[status(thm)],[4, 2])).
% 136.12/86.62 tff(6,plain,
% 136.12/86.62 (~![A: $i, B: $i] : (~(set_union2(singleton(A), B) = empty_set))),
% 136.12/86.62 inference(modus_ponens,[status(thm)],[5, 2])).
% 136.12/86.62 tff(7,plain,
% 136.12/86.62 (~![A: $i, B: $i] : (~(set_union2(singleton(A), B) = empty_set))),
% 136.12/86.62 inference(modus_ponens,[status(thm)],[6, 2])).
% 136.12/86.62 tff(8,plain,
% 136.12/86.62 (~![A: $i, B: $i] : (~(set_union2(singleton(A), B) = empty_set))),
% 136.12/86.62 inference(modus_ponens,[status(thm)],[7, 2])).
% 136.12/86.62 tff(9,plain,
% 136.12/86.62 (~![A: $i, B: $i] : (~(set_union2(singleton(A), B) = empty_set))),
% 136.12/86.62 inference(modus_ponens,[status(thm)],[8, 2])).
% 136.12/86.62 tff(10,plain,
% 136.12/86.62 (~![A: $i, B: $i] : (~(set_union2(singleton(A), B) = empty_set))),
% 136.12/86.62 inference(modus_ponens,[status(thm)],[9, 2])).
% 136.12/86.62 tff(11,plain,(
% 136.12/86.62 ~(~(set_union2(singleton(A!6), B!5) = empty_set))),
% 136.12/86.62 inference(skolemize,[status(sab)],[10])).
% 136.12/86.62 tff(12,plain,
% 136.12/86.62 (set_union2(singleton(A!6), B!5) = empty_set),
% 136.12/86.62 inference(modus_ponens,[status(thm)],[11, 1])).
% 136.12/86.62 tff(13,plain,
% 136.12/86.62 (empty_set = set_union2(singleton(A!6), B!5)),
% 136.12/86.62 inference(symmetry,[status(thm)],[12])).
% 136.12/86.62 tff(14,plain,
% 136.12/86.62 (^[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)))))))),
% 136.12/86.62 inference(bind,[status(th)],[])).
% 136.12/86.62 tff(15,plain,
% 136.12/86.62 (![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))))))),
% 136.12/86.62 inference(quant_intro,[status(thm)],[14])).
% 136.12/86.62 tff(16,plain,
% 136.12/86.62 (![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))))))),
% 136.12/86.62 inference(pull_quant,[status(thm)],[])).
% 136.12/86.62 tff(17,plain,
% 136.12/86.62 (^[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))))))))),
% 136.12/86.62 inference(bind,[status(th)],[])).
% 136.12/86.62 tff(18,plain,
% 136.12/86.62 (![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))))))),
% 136.12/86.62 inference(quant_intro,[status(thm)],[17])).
% 136.12/86.62 tff(19,plain,
% 136.12/86.62 (![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))))))),
% 136.12/86.62 inference(transitivity,[status(thm)],[18, 16])).
% 136.12/86.62 tff(20,plain,
% 136.12/86.62 (![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))))))),
% 136.12/86.62 inference(transitivity,[status(thm)],[19, 15])).
% 136.12/86.62 tff(21,plain,
% 136.12/86.62 (^[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)))))))),
% 136.12/86.62 inference(bind,[status(th)],[])).
% 136.12/86.62 tff(22,plain,
% 136.12/86.62 (![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))))))),
% 136.12/86.62 inference(quant_intro,[status(thm)],[21])).
% 136.12/86.62 tff(23,plain,
% 136.12/86.62 (![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))))))),
% 136.12/86.62 inference(transitivity,[status(thm)],[22, 20])).
% 136.12/86.62 tff(24,plain,
% 136.12/86.62 (^[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))))))))),
% 136.12/86.62 inference(bind,[status(th)],[])).
% 136.12/86.62 tff(25,plain,
% 136.12/86.62 (![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))))))),
% 136.12/86.62 inference(quant_intro,[status(thm)],[24])).
% 136.12/86.62 tff(26,plain,
% 136.12/86.62 (^[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)))))),
% 136.12/86.62 inference(bind,[status(th)],[])).
% 136.12/86.62 tff(27,plain,
% 136.12/86.62 (![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))))),
% 136.12/86.62 inference(quant_intro,[status(thm)],[26])).
% 136.12/86.62 tff(28,plain,
% 136.12/86.62 (![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)))),
% 136.12/86.62 inference(rewrite,[status(thm)],[])).
% 136.12/86.62 tff(29,axiom,(![A: $i, B: $i] : ((B = singleton(A)) <=> ![C: $i] : (in(C, B) <=> (C = A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d1_tarski')).
% 136.12/86.62 tff(30,plain,
% 136.12/86.62 (![A: $i, B: $i] : ((B = singleton(A)) <=> ![C: $i] : (in(C, B) <=> (C = A)))),
% 136.12/86.62 inference(modus_ponens,[status(thm)],[29, 28])).
% 136.12/86.62 tff(31,plain,(
% 136.12/86.62 ![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)))))),
% 136.12/86.62 inference(skolemize,[status(sab)],[30])).
% 136.12/86.62 tff(32,plain,
% 136.12/86.62 (![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))))),
% 136.12/86.62 inference(modus_ponens,[status(thm)],[31, 27])).
% 136.12/86.62 tff(33,plain,
% 136.12/86.62 (![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))))))),
% 136.12/86.62 inference(modus_ponens,[status(thm)],[32, 25])).
% 136.12/86.62 tff(34,plain,
% 136.12/86.62 (![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))))))),
% 136.12/86.62 inference(modus_ponens,[status(thm)],[33, 23])).
% 136.12/86.62 tff(35,plain,
% 136.12/86.62 ((~![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!6))) | (in(tptp_fun_C_0(empty_set, A!6), empty_set) <=> (tptp_fun_C_0(empty_set, A!6) = A!6)))) | (~((empty_set = singleton(A!6)) | ((~in(tptp_fun_C_0(empty_set, A!6), empty_set)) <=> (tptp_fun_C_0(empty_set, A!6) = A!6))))))),
% 136.12/86.62 inference(quant_inst,[status(thm)],[])).
% 136.12/86.62 tff(36,plain,
% 136.12/86.62 (~((~((~(empty_set = singleton(A!6))) | (in(tptp_fun_C_0(empty_set, A!6), empty_set) <=> (tptp_fun_C_0(empty_set, A!6) = A!6)))) | (~((empty_set = singleton(A!6)) | ((~in(tptp_fun_C_0(empty_set, A!6), empty_set)) <=> (tptp_fun_C_0(empty_set, A!6) = A!6)))))),
% 136.12/86.62 inference(unit_resolution,[status(thm)],[35, 34])).
% 136.12/86.62 tff(37,plain,
% 136.12/86.62 (((~((~(empty_set = singleton(A!6))) | (in(tptp_fun_C_0(empty_set, A!6), empty_set) <=> (tptp_fun_C_0(empty_set, A!6) = A!6)))) | (~((empty_set = singleton(A!6)) | ((~in(tptp_fun_C_0(empty_set, A!6), empty_set)) <=> (tptp_fun_C_0(empty_set, A!6) = A!6))))) | ((empty_set = singleton(A!6)) | ((~in(tptp_fun_C_0(empty_set, A!6), empty_set)) <=> (tptp_fun_C_0(empty_set, A!6) = A!6)))),
% 136.12/86.62 inference(tautology,[status(thm)],[])).
% 136.12/86.62 tff(38,plain,
% 136.12/86.62 ((empty_set = singleton(A!6)) | ((~in(tptp_fun_C_0(empty_set, A!6), empty_set)) <=> (tptp_fun_C_0(empty_set, A!6) = A!6))),
% 136.12/86.62 inference(unit_resolution,[status(thm)],[37, 36])).
% 136.12/86.62 tff(39,assumption,((~in(tptp_fun_C_0(empty_set, A!6), empty_set)) <=> (tptp_fun_C_0(empty_set, A!6) = A!6)), introduced(assumption)).
% 136.12/86.62 tff(40,plain,
% 136.12/86.62 (^[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))))))),
% 136.12/86.62 inference(bind,[status(th)],[])).
% 136.12/86.62 tff(41,plain,
% 136.12/86.62 (![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)))))),
% 136.12/86.62 inference(quant_intro,[status(thm)],[40])).
% 136.12/86.62 tff(42,plain,
% 136.12/86.62 (![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)))))),
% 136.12/86.62 inference(pull_quant,[status(thm)],[])).
% 136.12/86.62 tff(43,plain,
% 136.12/86.62 (^[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)))))))),
% 136.12/86.63 inference(bind,[status(th)],[])).
% 136.12/86.63 tff(44,plain,
% 136.12/86.63 (![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)))))),
% 136.12/86.63 inference(quant_intro,[status(thm)],[43])).
% 136.12/86.63 tff(45,plain,
% 136.12/86.63 (![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)))))),
% 136.12/86.63 inference(transitivity,[status(thm)],[44, 42])).
% 136.12/86.63 tff(46,plain,
% 136.12/86.63 (![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)))))),
% 136.12/86.63 inference(transitivity,[status(thm)],[45, 41])).
% 136.12/86.63 tff(47,plain,
% 136.12/86.63 (^[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))))))),
% 136.12/86.63 inference(bind,[status(th)],[])).
% 136.12/86.63 tff(48,plain,
% 136.12/86.63 (![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)))))),
% 136.12/86.63 inference(quant_intro,[status(thm)],[47])).
% 136.12/86.63 tff(49,plain,
% 136.12/86.63 (![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)))))),
% 136.12/86.63 inference(transitivity,[status(thm)],[48, 46])).
% 136.12/86.63 tff(50,plain,
% 136.12/86.63 (^[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)))))))),
% 136.12/86.63 inference(bind,[status(th)],[])).
% 136.12/86.63 tff(51,plain,
% 136.12/86.63 (![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)))))),
% 136.12/86.63 inference(quant_intro,[status(thm)],[50])).
% 136.12/86.63 tff(52,plain,
% 136.12/86.63 (^[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))))),
% 136.12/86.63 inference(bind,[status(th)],[])).
% 136.12/86.63 tff(53,plain,
% 136.12/86.63 (![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)))),
% 136.12/86.63 inference(quant_intro,[status(thm)],[52])).
% 136.12/86.63 tff(54,plain,
% 136.12/86.63 (![A: $i] : ((A = empty_set) <=> ![B: $i] : (~in(B, A))) <=> ![A: $i] : ((A = empty_set) <=> ![B: $i] : (~in(B, A)))),
% 136.12/86.63 inference(rewrite,[status(thm)],[])).
% 136.12/86.63 tff(55,axiom,(![A: $i] : ((A = empty_set) <=> ![B: $i] : (~in(B, A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d1_xboole_0')).
% 136.12/86.63 tff(56,plain,
% 136.12/86.63 (![A: $i] : ((A = empty_set) <=> ![B: $i] : (~in(B, A)))),
% 136.12/86.63 inference(modus_ponens,[status(thm)],[55, 54])).
% 136.12/86.63 tff(57,plain,(
% 136.12/86.63 ![A: $i] : (((~(A = empty_set)) | ![B: $i] : (~in(B, A))) & ((A = empty_set) | (~(~in(tptp_fun_B_1(A), A)))))),
% 136.12/86.63 inference(skolemize,[status(sab)],[56])).
% 136.12/86.63 tff(58,plain,
% 136.12/86.63 (![A: $i] : (((~(A = empty_set)) | ![B: $i] : (~in(B, A))) & ((A = empty_set) | in(tptp_fun_B_1(A), A)))),
% 136.12/86.63 inference(modus_ponens,[status(thm)],[57, 53])).
% 136.12/86.63 tff(59,plain,
% 136.12/86.63 (![A: $i] : (~((~((~(A = empty_set)) | ![B: $i] : (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_1(A), A)))))),
% 136.12/86.63 inference(modus_ponens,[status(thm)],[58, 51])).
% 136.12/86.63 tff(60,plain,
% 136.12/86.63 (![A: $i, B: $i] : (~((~((~(A = empty_set)) | (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_1(A), A)))))),
% 136.12/86.63 inference(modus_ponens,[status(thm)],[59, 49])).
% 136.12/86.63 tff(61,plain,
% 136.12/86.63 (((~![A: $i, B: $i] : (~((~((~(A = empty_set)) | (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_1(A), A)))))) | (~in(tptp_fun_C_0(empty_set, A!6), empty_set))) <=> ((~![A: $i, B: $i] : (~((~((~(A = empty_set)) | (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_1(A), A)))))) | (~in(tptp_fun_C_0(empty_set, A!6), empty_set)))),
% 136.12/86.63 inference(rewrite,[status(thm)],[])).
% 136.12/86.63 tff(62,plain,
% 136.12/86.63 ((~((~((~(empty_set = empty_set)) | (~in(tptp_fun_C_0(empty_set, A!6), empty_set)))) | (~((empty_set = empty_set) | in(tptp_fun_B_1(empty_set), empty_set))))) <=> (~in(tptp_fun_C_0(empty_set, A!6), empty_set))),
% 136.12/86.63 inference(rewrite,[status(thm)],[])).
% 136.12/86.63 tff(63,plain,
% 136.12/86.63 (((~![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(tptp_fun_C_0(empty_set, A!6), 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(tptp_fun_C_0(empty_set, A!6), empty_set)))),
% 136.12/86.63 inference(monotonicity,[status(thm)],[62])).
% 136.12/86.63 tff(64,plain,
% 136.12/86.63 (((~![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(tptp_fun_C_0(empty_set, A!6), 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(tptp_fun_C_0(empty_set, A!6), empty_set)))),
% 136.12/86.63 inference(transitivity,[status(thm)],[63, 61])).
% 136.12/86.63 tff(65,plain,
% 136.12/86.63 ((~![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(tptp_fun_C_0(empty_set, A!6), empty_set)))) | (~((empty_set = empty_set) | in(tptp_fun_B_1(empty_set), empty_set)))))),
% 136.12/86.63 inference(quant_inst,[status(thm)],[])).
% 136.12/86.63 tff(66,plain,
% 136.12/86.63 ((~![A: $i, B: $i] : (~((~((~(A = empty_set)) | (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_1(A), A)))))) | (~in(tptp_fun_C_0(empty_set, A!6), empty_set))),
% 136.12/86.63 inference(modus_ponens,[status(thm)],[65, 64])).
% 136.12/86.63 tff(67,plain,
% 136.12/86.63 (~in(tptp_fun_C_0(empty_set, A!6), empty_set)),
% 136.12/86.63 inference(unit_resolution,[status(thm)],[66, 60])).
% 136.12/86.63 tff(68,plain,
% 136.12/86.63 ((~((~in(tptp_fun_C_0(empty_set, A!6), empty_set)) <=> (tptp_fun_C_0(empty_set, A!6) = A!6))) | in(tptp_fun_C_0(empty_set, A!6), empty_set) | (tptp_fun_C_0(empty_set, A!6) = A!6)),
% 136.12/86.63 inference(tautology,[status(thm)],[])).
% 136.12/86.63 tff(69,plain,
% 136.12/86.63 (tptp_fun_C_0(empty_set, A!6) = A!6),
% 136.12/86.63 inference(unit_resolution,[status(thm)],[68, 67, 39])).
% 136.12/86.63 tff(70,plain,
% 136.12/86.63 (in(tptp_fun_C_0(empty_set, A!6), empty_set) <=> in(A!6, empty_set)),
% 136.12/86.63 inference(monotonicity,[status(thm)],[69])).
% 136.12/86.63 tff(71,plain,
% 136.12/86.63 (in(A!6, empty_set) <=> in(tptp_fun_C_0(empty_set, A!6), empty_set)),
% 136.12/86.63 inference(symmetry,[status(thm)],[70])).
% 136.12/86.63 tff(72,assumption,((~((~(empty_set = set_union2(singleton(A!6), B!5))) | (in(A!6, empty_set) <=> (in(A!6, B!5) | in(A!6, singleton(A!6)))))) | (~((empty_set = set_union2(singleton(A!6), B!5)) | ((~in(tptp_fun_D_2(empty_set, B!5, singleton(A!6)), empty_set)) <=> (in(tptp_fun_D_2(empty_set, B!5, singleton(A!6)), B!5) | in(tptp_fun_D_2(empty_set, B!5, singleton(A!6)), singleton(A!6))))))), introduced(assumption)).
% 136.12/86.63 tff(73,plain,
% 136.12/86.63 (^[A: $i, B: $i, C: $i, D: $i] : refl((~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_2(C, B, A), C)) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A))))))) <=> (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_2(C, B, A), C)) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A))))))))),
% 136.12/86.63 inference(bind,[status(th)],[])).
% 136.12/86.63 tff(74,plain,
% 136.12/86.63 (![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_2(C, B, A), C)) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_2(C, B, A), C)) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A)))))))),
% 136.12/86.63 inference(quant_intro,[status(thm)],[73])).
% 136.12/86.63 tff(75,plain,
% 136.12/86.63 (![A: $i, B: $i, C: $i] : ![D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_2(C, B, A), C)) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_2(C, B, A), C)) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A)))))))),
% 136.12/86.63 inference(pull_quant,[status(thm)],[])).
% 136.12/86.63 tff(76,plain,
% 136.12/86.63 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(pull_quant(((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A)))) <=> ![D: $i] : ((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))), ((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))) <=> (~![D: $i] : ((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))))), pull_quant((~![D: $i] : ((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) <=> ?[D: $i] : (~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A)))))), ((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))) <=> ?[D: $i] : (~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))))), (((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_2(C, B, A), C)) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A)))))) <=> (?[D: $i] : (~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_2(C, B, A), C)) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A)))))))), pull_quant((?[D: $i] : (~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_2(C, B, A), C)) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A)))))) <=> ?[D: $i] : ((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_2(C, B, A), C)) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A))))))), (((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_2(C, B, A), C)) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A)))))) <=> ?[D: $i] : ((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_2(C, B, A), C)) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A)))))))), ((~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_2(C, B, A), C)) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A))))))) <=> (~?[D: $i] : ((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_2(C, B, A), C)) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A))))))))), pull_quant((~?[D: $i] : ((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_2(C, B, A), C)) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A))))))) <=> ![D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_2(C, B, A), C)) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A)))))))), ((~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_2(C, B, A), C)) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A))))))) <=> ![D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_2(C, B, A), C)) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A)))))))))),
% 136.12/86.63 inference(bind,[status(th)],[])).
% 136.12/86.63 tff(77,plain,
% 136.12/86.63 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_2(C, B, A), C)) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A))))))) <=> ![A: $i, B: $i, C: $i] : ![D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_2(C, B, A), C)) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A)))))))),
% 136.12/86.63 inference(quant_intro,[status(thm)],[76])).
% 136.12/86.63 tff(78,plain,
% 136.12/86.63 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_2(C, B, A), C)) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_2(C, B, A), C)) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A)))))))),
% 136.12/86.63 inference(transitivity,[status(thm)],[77, 75])).
% 136.12/86.63 tff(79,plain,
% 136.12/86.63 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_2(C, B, A), C)) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_2(C, B, A), C)) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A)))))))),
% 136.12/86.63 inference(transitivity,[status(thm)],[78, 74])).
% 136.12/86.63 tff(80,plain,
% 136.12/86.63 (^[A: $i, B: $i, C: $i] : rewrite((~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_2(C, B, A), C)) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A))))))) <=> (~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_2(C, B, A), C)) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A))))))))),
% 136.12/86.63 inference(bind,[status(th)],[])).
% 136.12/86.63 tff(81,plain,
% 136.12/86.63 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_2(C, B, A), C)) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A))))))) <=> ![A: $i, B: $i, C: $i] : (~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_2(C, B, A), C)) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A)))))))),
% 136.12/86.63 inference(quant_intro,[status(thm)],[80])).
% 136.12/86.63 tff(82,plain,
% 136.12/86.63 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_2(C, B, A), C)) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_2(C, B, A), C)) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A)))))))),
% 136.12/86.63 inference(transitivity,[status(thm)],[81, 79])).
% 136.12/86.63 tff(83,plain,
% 136.12/86.63 (^[A: $i, B: $i, C: $i] : trans(monotonicity(rewrite(((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A)))) <=> ((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))), ((((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A)))) & ((C = set_union2(A, B)) | ((~in(tptp_fun_D_2(C, B, A), C)) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A))))) <=> (((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A)))) & ((C = set_union2(A, B)) | ((~in(tptp_fun_D_2(C, B, A), C)) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A))))))), rewrite((((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A)))) & ((C = set_union2(A, B)) | ((~in(tptp_fun_D_2(C, B, A), C)) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A))))) <=> (~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_2(C, B, A), C)) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A)))))))), ((((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A)))) & ((C = set_union2(A, B)) | ((~in(tptp_fun_D_2(C, B, A), C)) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A))))) <=> (~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_2(C, B, A), C)) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A)))))))))),
% 136.12/86.63 inference(bind,[status(th)],[])).
% 136.12/86.63 tff(84,plain,
% 136.12/86.63 (![A: $i, B: $i, C: $i] : (((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A)))) & ((C = set_union2(A, B)) | ((~in(tptp_fun_D_2(C, B, A), C)) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A))))) <=> ![A: $i, B: $i, C: $i] : (~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_2(C, B, A), C)) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A)))))))),
% 136.12/86.63 inference(quant_intro,[status(thm)],[83])).
% 136.12/86.63 tff(85,plain,
% 136.12/86.63 (^[A: $i, B: $i, C: $i] : rewrite((((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A)))) & ((C = set_union2(A, B)) | (~(in(tptp_fun_D_2(C, B, A), C) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A)))))) <=> (((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A)))) & ((C = set_union2(A, B)) | ((~in(tptp_fun_D_2(C, B, A), C)) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A))))))),
% 136.12/86.63 inference(bind,[status(th)],[])).
% 136.12/86.63 tff(86,plain,
% 136.12/86.63 (![A: $i, B: $i, C: $i] : (((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A)))) & ((C = set_union2(A, B)) | (~(in(tptp_fun_D_2(C, B, A), C) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A)))))) <=> ![A: $i, B: $i, C: $i] : (((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A)))) & ((C = set_union2(A, B)) | ((~in(tptp_fun_D_2(C, B, A), C)) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A)))))),
% 136.12/86.63 inference(quant_intro,[status(thm)],[85])).
% 136.12/86.63 tff(87,plain,
% 136.12/86.63 (![A: $i, B: $i, C: $i] : ((C = set_union2(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A)))) <=> ![A: $i, B: $i, C: $i] : ((C = set_union2(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))),
% 136.12/86.63 inference(rewrite,[status(thm)],[])).
% 136.12/86.63 tff(88,plain,
% 136.12/86.63 (^[A: $i, B: $i, C: $i] : rewrite(((C = set_union2(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B)))) <=> ((C = set_union2(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A)))))),
% 136.12/86.63 inference(bind,[status(th)],[])).
% 136.12/86.63 tff(89,plain,
% 136.12/86.63 (![A: $i, B: $i, C: $i] : ((C = set_union2(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B)))) <=> ![A: $i, B: $i, C: $i] : ((C = set_union2(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))),
% 136.12/86.63 inference(quant_intro,[status(thm)],[88])).
% 136.12/86.63 tff(90,axiom,(![A: $i, B: $i, C: $i] : ((C = set_union2(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d2_xboole_0')).
% 136.12/86.63 tff(91,plain,
% 136.12/86.63 (![A: $i, B: $i, C: $i] : ((C = set_union2(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))),
% 136.12/86.63 inference(modus_ponens,[status(thm)],[90, 89])).
% 136.12/86.63 tff(92,plain,
% 136.12/86.63 (![A: $i, B: $i, C: $i] : ((C = set_union2(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))),
% 136.12/86.63 inference(modus_ponens,[status(thm)],[91, 87])).
% 136.12/86.63 tff(93,plain,(
% 136.12/86.63 ![A: $i, B: $i, C: $i] : (((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A)))) & ((C = set_union2(A, B)) | (~(in(tptp_fun_D_2(C, B, A), C) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A))))))),
% 136.12/86.63 inference(skolemize,[status(sab)],[92])).
% 136.12/86.63 tff(94,plain,
% 136.12/86.63 (![A: $i, B: $i, C: $i] : (((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A)))) & ((C = set_union2(A, B)) | ((~in(tptp_fun_D_2(C, B, A), C)) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A)))))),
% 136.12/86.63 inference(modus_ponens,[status(thm)],[93, 86])).
% 136.12/86.63 tff(95,plain,
% 136.12/86.63 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_2(C, B, A), C)) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A)))))))),
% 136.12/86.63 inference(modus_ponens,[status(thm)],[94, 84])).
% 136.12/86.63 tff(96,plain,
% 136.12/86.63 (![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_2(C, B, A), C)) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A)))))))),
% 136.12/86.63 inference(modus_ponens,[status(thm)],[95, 82])).
% 136.12/86.63 tff(97,plain,
% 136.12/86.63 ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_2(C, B, A), C)) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A)))))))) | (~((~((~(empty_set = set_union2(singleton(A!6), B!5))) | (in(A!6, empty_set) <=> (in(A!6, B!5) | in(A!6, singleton(A!6)))))) | (~((empty_set = set_union2(singleton(A!6), B!5)) | ((~in(tptp_fun_D_2(empty_set, B!5, singleton(A!6)), empty_set)) <=> (in(tptp_fun_D_2(empty_set, B!5, singleton(A!6)), B!5) | in(tptp_fun_D_2(empty_set, B!5, singleton(A!6)), singleton(A!6))))))))),
% 136.12/86.63 inference(quant_inst,[status(thm)],[])).
% 136.12/86.63 tff(98,plain,
% 136.12/86.63 ($false),
% 136.12/86.63 inference(unit_resolution,[status(thm)],[97, 96, 72])).
% 136.12/86.63 tff(99,plain,(~((~((~(empty_set = set_union2(singleton(A!6), B!5))) | (in(A!6, empty_set) <=> (in(A!6, B!5) | in(A!6, singleton(A!6)))))) | (~((empty_set = set_union2(singleton(A!6), B!5)) | ((~in(tptp_fun_D_2(empty_set, B!5, singleton(A!6)), empty_set)) <=> (in(tptp_fun_D_2(empty_set, B!5, singleton(A!6)), B!5) | in(tptp_fun_D_2(empty_set, B!5, singleton(A!6)), singleton(A!6)))))))), inference(lemma,lemma(discharge,[]))).
% 136.12/86.63 tff(100,plain,
% 136.12/86.63 (((~((~(empty_set = set_union2(singleton(A!6), B!5))) | (in(A!6, empty_set) <=> (in(A!6, B!5) | in(A!6, singleton(A!6)))))) | (~((empty_set = set_union2(singleton(A!6), B!5)) | ((~in(tptp_fun_D_2(empty_set, B!5, singleton(A!6)), empty_set)) <=> (in(tptp_fun_D_2(empty_set, B!5, singleton(A!6)), B!5) | in(tptp_fun_D_2(empty_set, B!5, singleton(A!6)), singleton(A!6))))))) | ((~(empty_set = set_union2(singleton(A!6), B!5))) | (in(A!6, empty_set) <=> (in(A!6, B!5) | in(A!6, singleton(A!6)))))),
% 136.12/86.63 inference(tautology,[status(thm)],[])).
% 136.12/86.63 tff(101,plain,
% 136.12/86.63 ((~(empty_set = set_union2(singleton(A!6), B!5))) | (in(A!6, empty_set) <=> (in(A!6, B!5) | in(A!6, singleton(A!6))))),
% 136.12/86.63 inference(unit_resolution,[status(thm)],[100, 99])).
% 136.12/86.63 tff(102,plain,
% 136.12/86.63 ((~((~(empty_set = set_union2(singleton(A!6), B!5))) | (in(A!6, empty_set) <=> (in(A!6, B!5) | in(A!6, singleton(A!6)))))) | (~(empty_set = set_union2(singleton(A!6), B!5))) | (in(A!6, empty_set) <=> (in(A!6, B!5) | in(A!6, singleton(A!6))))),
% 136.12/86.63 inference(tautology,[status(thm)],[])).
% 136.12/86.63 tff(103,plain,
% 136.12/86.63 ((~((~(empty_set = set_union2(singleton(A!6), B!5))) | (in(A!6, empty_set) <=> (in(A!6, B!5) | in(A!6, singleton(A!6)))))) | (in(A!6, empty_set) <=> (in(A!6, B!5) | in(A!6, singleton(A!6))))),
% 136.12/86.63 inference(unit_resolution,[status(thm)],[102, 13])).
% 136.12/86.63 tff(104,plain,
% 136.12/86.63 (in(A!6, empty_set) <=> (in(A!6, B!5) | in(A!6, singleton(A!6)))),
% 136.12/86.63 inference(unit_resolution,[status(thm)],[103, 101])).
% 136.12/86.63 tff(105,assumption,(~in(A!6, singleton(A!6))), introduced(assumption)).
% 136.12/86.63 tff(106,plain,
% 136.12/86.63 (((~![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!6, singleton(A!6))) <=> ((~![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!6, singleton(A!6)))),
% 136.12/86.63 inference(rewrite,[status(thm)],[])).
% 136.12/86.63 tff(107,plain,
% 136.12/86.63 ((~(~in(A!6, singleton(A!6)))) <=> in(A!6, singleton(A!6))),
% 136.12/86.63 inference(rewrite,[status(thm)],[])).
% 136.12/86.63 tff(108,plain,
% 136.12/86.63 (((~in(A!6, singleton(A!6))) | $false) <=> (~in(A!6, singleton(A!6)))),
% 136.12/86.63 inference(rewrite,[status(thm)],[])).
% 136.12/86.63 tff(109,plain,
% 136.12/86.63 ((~$true) <=> $false),
% 136.12/86.63 inference(rewrite,[status(thm)],[])).
% 136.12/86.63 tff(110,plain,
% 136.12/86.63 (($true | ((~in(tptp_fun_C_0(singleton(A!6), A!6), singleton(A!6))) <=> (tptp_fun_C_0(singleton(A!6), A!6) = A!6))) <=> $true),
% 136.12/86.63 inference(rewrite,[status(thm)],[])).
% 136.12/86.63 tff(111,plain,
% 136.12/86.63 ((singleton(A!6) = singleton(A!6)) <=> $true),
% 136.12/86.63 inference(rewrite,[status(thm)],[])).
% 136.12/86.63 tff(112,plain,
% 136.12/86.63 (((singleton(A!6) = singleton(A!6)) | ((~in(tptp_fun_C_0(singleton(A!6), A!6), singleton(A!6))) <=> (tptp_fun_C_0(singleton(A!6), A!6) = A!6))) <=> ($true | ((~in(tptp_fun_C_0(singleton(A!6), A!6), singleton(A!6))) <=> (tptp_fun_C_0(singleton(A!6), A!6) = A!6)))),
% 136.12/86.63 inference(monotonicity,[status(thm)],[111])).
% 136.12/86.63 tff(113,plain,
% 136.12/86.63 (((singleton(A!6) = singleton(A!6)) | ((~in(tptp_fun_C_0(singleton(A!6), A!6), singleton(A!6))) <=> (tptp_fun_C_0(singleton(A!6), A!6) = A!6))) <=> $true),
% 136.12/86.63 inference(transitivity,[status(thm)],[112, 110])).
% 136.12/86.63 tff(114,plain,
% 136.12/86.63 ((~((singleton(A!6) = singleton(A!6)) | ((~in(tptp_fun_C_0(singleton(A!6), A!6), singleton(A!6))) <=> (tptp_fun_C_0(singleton(A!6), A!6) = A!6)))) <=> (~$true)),
% 136.12/86.63 inference(monotonicity,[status(thm)],[113])).
% 136.12/86.63 tff(115,plain,
% 136.12/86.63 ((~((singleton(A!6) = singleton(A!6)) | ((~in(tptp_fun_C_0(singleton(A!6), A!6), singleton(A!6))) <=> (tptp_fun_C_0(singleton(A!6), A!6) = A!6)))) <=> $false),
% 136.12/86.63 inference(transitivity,[status(thm)],[114, 109])).
% 136.12/86.63 tff(116,plain,
% 136.12/86.63 ((~((~(singleton(A!6) = singleton(A!6))) | (in(A!6, singleton(A!6)) <=> (A!6 = A!6)))) <=> (~in(A!6, singleton(A!6)))),
% 136.12/86.63 inference(rewrite,[status(thm)],[])).
% 136.12/86.63 tff(117,plain,
% 136.12/86.63 (((~((~(singleton(A!6) = singleton(A!6))) | (in(A!6, singleton(A!6)) <=> (A!6 = A!6)))) | (~((singleton(A!6) = singleton(A!6)) | ((~in(tptp_fun_C_0(singleton(A!6), A!6), singleton(A!6))) <=> (tptp_fun_C_0(singleton(A!6), A!6) = A!6))))) <=> ((~in(A!6, singleton(A!6))) | $false)),
% 136.12/86.63 inference(monotonicity,[status(thm)],[116, 115])).
% 136.12/86.63 tff(118,plain,
% 136.12/86.63 (((~((~(singleton(A!6) = singleton(A!6))) | (in(A!6, singleton(A!6)) <=> (A!6 = A!6)))) | (~((singleton(A!6) = singleton(A!6)) | ((~in(tptp_fun_C_0(singleton(A!6), A!6), singleton(A!6))) <=> (tptp_fun_C_0(singleton(A!6), A!6) = A!6))))) <=> (~in(A!6, singleton(A!6)))),
% 136.12/86.63 inference(transitivity,[status(thm)],[117, 108])).
% 136.12/86.63 tff(119,plain,
% 136.12/86.63 ((~((~((~(singleton(A!6) = singleton(A!6))) | (in(A!6, singleton(A!6)) <=> (A!6 = A!6)))) | (~((singleton(A!6) = singleton(A!6)) | ((~in(tptp_fun_C_0(singleton(A!6), A!6), singleton(A!6))) <=> (tptp_fun_C_0(singleton(A!6), A!6) = A!6)))))) <=> (~(~in(A!6, singleton(A!6))))),
% 136.12/86.63 inference(monotonicity,[status(thm)],[118])).
% 136.12/86.63 tff(120,plain,
% 136.12/86.63 ((~((~((~(singleton(A!6) = singleton(A!6))) | (in(A!6, singleton(A!6)) <=> (A!6 = A!6)))) | (~((singleton(A!6) = singleton(A!6)) | ((~in(tptp_fun_C_0(singleton(A!6), A!6), singleton(A!6))) <=> (tptp_fun_C_0(singleton(A!6), A!6) = A!6)))))) <=> in(A!6, singleton(A!6))),
% 136.12/86.63 inference(transitivity,[status(thm)],[119, 107])).
% 136.12/86.63 tff(121,plain,
% 136.12/86.63 (((~![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))))) | (~((~((~(singleton(A!6) = singleton(A!6))) | (in(A!6, singleton(A!6)) <=> (A!6 = A!6)))) | (~((singleton(A!6) = singleton(A!6)) | ((~in(tptp_fun_C_0(singleton(A!6), A!6), singleton(A!6))) <=> (tptp_fun_C_0(singleton(A!6), A!6) = A!6))))))) <=> ((~![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!6, singleton(A!6)))),
% 136.12/86.63 inference(monotonicity,[status(thm)],[120])).
% 136.12/86.63 tff(122,plain,
% 136.12/86.63 (((~![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))))) | (~((~((~(singleton(A!6) = singleton(A!6))) | (in(A!6, singleton(A!6)) <=> (A!6 = A!6)))) | (~((singleton(A!6) = singleton(A!6)) | ((~in(tptp_fun_C_0(singleton(A!6), A!6), singleton(A!6))) <=> (tptp_fun_C_0(singleton(A!6), A!6) = A!6))))))) <=> ((~![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!6, singleton(A!6)))),
% 136.12/86.63 inference(transitivity,[status(thm)],[121, 106])).
% 136.12/86.63 tff(123,plain,
% 136.12/86.63 ((~![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))))) | (~((~((~(singleton(A!6) = singleton(A!6))) | (in(A!6, singleton(A!6)) <=> (A!6 = A!6)))) | (~((singleton(A!6) = singleton(A!6)) | ((~in(tptp_fun_C_0(singleton(A!6), A!6), singleton(A!6))) <=> (tptp_fun_C_0(singleton(A!6), A!6) = A!6))))))),
% 136.12/86.63 inference(quant_inst,[status(thm)],[])).
% 136.12/86.63 tff(124,plain,
% 136.12/86.63 ((~![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))))) | in(A!6, singleton(A!6))),
% 136.12/86.63 inference(modus_ponens,[status(thm)],[123, 122])).
% 136.12/86.63 tff(125,plain,
% 136.12/86.63 ($false),
% 136.12/86.63 inference(unit_resolution,[status(thm)],[124, 34, 105])).
% 136.12/86.63 tff(126,plain,(in(A!6, singleton(A!6))), inference(lemma,lemma(discharge,[]))).
% 136.12/86.63 tff(127,plain,
% 136.12/86.63 ((in(A!6, B!5) | in(A!6, singleton(A!6))) | (~in(A!6, singleton(A!6)))),
% 136.12/86.63 inference(tautology,[status(thm)],[])).
% 136.12/86.63 tff(128,plain,
% 136.12/86.63 (in(A!6, B!5) | in(A!6, singleton(A!6))),
% 136.12/86.63 inference(unit_resolution,[status(thm)],[127, 126])).
% 136.12/86.63 tff(129,plain,
% 136.12/86.63 ((~(in(A!6, empty_set) <=> (in(A!6, B!5) | in(A!6, singleton(A!6))))) | in(A!6, empty_set) | (~(in(A!6, B!5) | in(A!6, singleton(A!6))))),
% 136.12/86.63 inference(tautology,[status(thm)],[])).
% 136.12/86.63 tff(130,plain,
% 136.12/86.63 ((~(in(A!6, empty_set) <=> (in(A!6, B!5) | in(A!6, singleton(A!6))))) | in(A!6, empty_set)),
% 136.12/86.63 inference(unit_resolution,[status(thm)],[129, 128])).
% 136.12/86.63 tff(131,plain,
% 136.12/86.63 (in(A!6, empty_set)),
% 136.12/86.63 inference(unit_resolution,[status(thm)],[130, 104])).
% 136.12/86.63 tff(132,plain,
% 136.12/86.63 (in(tptp_fun_C_0(empty_set, A!6), empty_set)),
% 136.12/86.63 inference(modus_ponens,[status(thm)],[131, 71])).
% 136.12/86.63 tff(133,plain,
% 136.12/86.63 ($false),
% 136.12/86.63 inference(unit_resolution,[status(thm)],[67, 132])).
% 136.12/86.63 tff(134,plain,(~((~in(tptp_fun_C_0(empty_set, A!6), empty_set)) <=> (tptp_fun_C_0(empty_set, A!6) = A!6))), inference(lemma,lemma(discharge,[]))).
% 136.12/86.63 tff(135,plain,
% 136.12/86.63 ((~((empty_set = singleton(A!6)) | ((~in(tptp_fun_C_0(empty_set, A!6), empty_set)) <=> (tptp_fun_C_0(empty_set, A!6) = A!6)))) | (empty_set = singleton(A!6)) | ((~in(tptp_fun_C_0(empty_set, A!6), empty_set)) <=> (tptp_fun_C_0(empty_set, A!6) = A!6))),
% 136.12/86.64 inference(tautology,[status(thm)],[])).
% 136.12/86.64 tff(136,plain,
% 136.12/86.64 ((~((empty_set = singleton(A!6)) | ((~in(tptp_fun_C_0(empty_set, A!6), empty_set)) <=> (tptp_fun_C_0(empty_set, A!6) = A!6)))) | (empty_set = singleton(A!6))),
% 136.12/86.64 inference(unit_resolution,[status(thm)],[135, 134])).
% 136.12/86.64 tff(137,plain,
% 136.12/86.64 (empty_set = singleton(A!6)),
% 136.12/86.64 inference(unit_resolution,[status(thm)],[136, 38])).
% 136.12/86.64 tff(138,plain,
% 136.12/86.64 (singleton(A!6) = empty_set),
% 136.12/86.64 inference(symmetry,[status(thm)],[137])).
% 136.12/86.64 tff(139,plain,
% 136.12/86.64 (singleton(A!6) = set_union2(singleton(A!6), B!5)),
% 136.12/86.64 inference(transitivity,[status(thm)],[138, 13])).
% 136.12/86.64 tff(140,plain,
% 136.12/86.64 ((singleton(A!6) = empty_set) <=> (singleton(A!6) = set_union2(singleton(A!6), B!5))),
% 136.12/86.64 inference(monotonicity,[status(thm)],[13])).
% 136.12/86.64 tff(141,plain,
% 136.12/86.64 ((~(singleton(A!6) = empty_set)) <=> (~(singleton(A!6) = set_union2(singleton(A!6), B!5)))),
% 136.12/86.64 inference(monotonicity,[status(thm)],[140])).
% 136.12/86.64 tff(142,plain,
% 136.12/86.64 ((~![A: $i, B: $i] : (~((~((~(A = empty_set)) | (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_1(A), A)))))) | (~((~((~(singleton(A!6) = empty_set)) | (~in(A!6, singleton(A!6))))) | (~((singleton(A!6) = empty_set) | in(tptp_fun_B_1(singleton(A!6)), singleton(A!6))))))),
% 136.12/86.64 inference(quant_inst,[status(thm)],[])).
% 136.12/86.64 tff(143,plain,
% 136.12/86.64 (~((~((~(singleton(A!6) = empty_set)) | (~in(A!6, singleton(A!6))))) | (~((singleton(A!6) = empty_set) | in(tptp_fun_B_1(singleton(A!6)), singleton(A!6)))))),
% 136.12/86.64 inference(unit_resolution,[status(thm)],[142, 60])).
% 136.12/86.64 tff(144,plain,
% 136.12/86.64 (((~((~(singleton(A!6) = empty_set)) | (~in(A!6, singleton(A!6))))) | (~((singleton(A!6) = empty_set) | in(tptp_fun_B_1(singleton(A!6)), singleton(A!6))))) | ((~(singleton(A!6) = empty_set)) | (~in(A!6, singleton(A!6))))),
% 136.12/86.64 inference(tautology,[status(thm)],[])).
% 136.12/86.64 tff(145,plain,
% 136.12/86.64 ((~(singleton(A!6) = empty_set)) | (~in(A!6, singleton(A!6)))),
% 136.12/86.64 inference(unit_resolution,[status(thm)],[144, 143])).
% 136.12/86.64 tff(146,plain,
% 136.12/86.64 ((~((~(singleton(A!6) = empty_set)) | (~in(A!6, singleton(A!6))))) | (~(singleton(A!6) = empty_set)) | (~in(A!6, singleton(A!6)))),
% 136.12/86.64 inference(tautology,[status(thm)],[])).
% 136.12/86.64 tff(147,plain,
% 136.12/86.64 ((~((~(singleton(A!6) = empty_set)) | (~in(A!6, singleton(A!6))))) | (~(singleton(A!6) = empty_set))),
% 136.12/86.64 inference(unit_resolution,[status(thm)],[146, 126])).
% 136.12/86.64 tff(148,plain,
% 136.12/86.64 (~(singleton(A!6) = empty_set)),
% 136.12/86.64 inference(unit_resolution,[status(thm)],[147, 145])).
% 136.12/86.64 tff(149,plain,
% 136.12/86.64 (~(singleton(A!6) = set_union2(singleton(A!6), B!5))),
% 136.12/86.64 inference(modus_ponens,[status(thm)],[148, 141])).
% 136.12/86.64 tff(150,plain,
% 136.12/86.64 ($false),
% 136.12/86.64 inference(unit_resolution,[status(thm)],[149, 139])).
% 136.12/86.64 % SZS output end Proof
%------------------------------------------------------------------------------