TSTP Solution File: SET986+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SET986+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n009.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 20 05:08:49 EDT 2022
% Result : Theorem 0.16s 0.36s
% Output : Proof 0.16s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.10 % Problem : SET986+1 : TPTP v8.1.0. Released v3.2.0.
% 0.09/0.11 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.10/0.30 % Computer : n009.cluster.edu
% 0.10/0.30 % Model : x86_64 x86_64
% 0.10/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.30 % Memory : 8042.1875MB
% 0.10/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.30 % CPULimit : 300
% 0.10/0.30 % WCLimit : 300
% 0.10/0.30 % DateTime : Sat Sep 3 08:48:20 EDT 2022
% 0.10/0.31 % CPUTime :
% 0.10/0.31 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.10/0.31 Usage: tptp [options] [-file:]file
% 0.10/0.31 -h, -? prints this message.
% 0.10/0.31 -smt2 print SMT-LIB2 benchmark.
% 0.10/0.31 -m, -model generate model.
% 0.10/0.31 -p, -proof generate proof.
% 0.10/0.31 -c, -core generate unsat core of named formulas.
% 0.10/0.31 -st, -statistics display statistics.
% 0.10/0.31 -t:timeout set timeout (in second).
% 0.10/0.31 -smt2status display status in smt2 format instead of SZS.
% 0.10/0.31 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.10/0.31 -<param>:<value> configuration parameter and value.
% 0.10/0.31 -o:<output-file> file to place output in.
% 0.16/0.36 % SZS status Theorem
% 0.16/0.36 % SZS output start Proof
% 0.16/0.36 tff(tptp_fun_A_7_type, type, (
% 0.16/0.36 tptp_fun_A_7: $i)).
% 0.16/0.36 tff(tptp_fun_D_1_type, type, (
% 0.16/0.36 tptp_fun_D_1: ( $i * $i * $i ) > $i)).
% 0.16/0.36 tff(singleton_type, type, (
% 0.16/0.36 singleton: $i > $i)).
% 0.16/0.36 tff(set_difference_type, type, (
% 0.16/0.36 set_difference: ( $i * $i ) > $i)).
% 0.16/0.36 tff(tptp_fun_B_6_type, type, (
% 0.16/0.36 tptp_fun_B_6: $i)).
% 0.16/0.36 tff(in_type, type, (
% 0.16/0.36 in: ( $i * $i ) > $o)).
% 0.16/0.36 tff(tptp_fun_C_0_type, type, (
% 0.16/0.36 tptp_fun_C_0: ( $i * $i ) > $i)).
% 0.16/0.36 tff(set_union2_type, type, (
% 0.16/0.36 set_union2: ( $i * $i ) > $i)).
% 0.16/0.36 tff(1,assumption,(~(in(tptp_fun_D_1(B!6, set_difference(B!6, singleton(A!7)), singleton(A!7)), singleton(A!7)) <=> (tptp_fun_D_1(B!6, set_difference(B!6, singleton(A!7)), singleton(A!7)) = A!7))), introduced(assumption)).
% 0.16/0.36 tff(2,plain,
% 0.16/0.36 (^[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)))))))),
% 0.16/0.36 inference(bind,[status(th)],[])).
% 0.16/0.36 tff(3,plain,
% 0.16/0.36 (![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))))))),
% 0.16/0.36 inference(quant_intro,[status(thm)],[2])).
% 0.16/0.36 tff(4,plain,
% 0.16/0.36 (![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))))))),
% 0.16/0.36 inference(pull_quant,[status(thm)],[])).
% 0.16/0.36 tff(5,plain,
% 0.16/0.36 (^[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))))))))),
% 0.16/0.36 inference(bind,[status(th)],[])).
% 0.16/0.36 tff(6,plain,
% 0.16/0.36 (![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))))))),
% 0.16/0.36 inference(quant_intro,[status(thm)],[5])).
% 0.16/0.36 tff(7,plain,
% 0.16/0.36 (![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))))))),
% 0.16/0.36 inference(transitivity,[status(thm)],[6, 4])).
% 0.16/0.36 tff(8,plain,
% 0.16/0.36 (![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))))))),
% 0.16/0.36 inference(transitivity,[status(thm)],[7, 3])).
% 0.16/0.36 tff(9,plain,
% 0.16/0.36 (^[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)))))))),
% 0.16/0.36 inference(bind,[status(th)],[])).
% 0.16/0.36 tff(10,plain,
% 0.16/0.36 (![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))))))),
% 0.16/0.36 inference(quant_intro,[status(thm)],[9])).
% 0.16/0.36 tff(11,plain,
% 0.16/0.36 (![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))))))),
% 0.16/0.36 inference(transitivity,[status(thm)],[10, 8])).
% 0.16/0.36 tff(12,plain,
% 0.16/0.36 (^[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))))))))),
% 0.16/0.36 inference(bind,[status(th)],[])).
% 0.16/0.37 tff(13,plain,
% 0.16/0.37 (![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))))))),
% 0.16/0.37 inference(quant_intro,[status(thm)],[12])).
% 0.16/0.37 tff(14,plain,
% 0.16/0.37 (^[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)))))),
% 0.16/0.37 inference(bind,[status(th)],[])).
% 0.16/0.37 tff(15,plain,
% 0.16/0.37 (![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))))),
% 0.16/0.37 inference(quant_intro,[status(thm)],[14])).
% 0.16/0.37 tff(16,plain,
% 0.16/0.37 (![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)))),
% 0.16/0.37 inference(rewrite,[status(thm)],[])).
% 0.16/0.37 tff(17,axiom,(![A: $i, B: $i] : ((B = singleton(A)) <=> ![C: $i] : (in(C, B) <=> (C = A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d1_tarski')).
% 0.16/0.37 tff(18,plain,
% 0.16/0.37 (![A: $i, B: $i] : ((B = singleton(A)) <=> ![C: $i] : (in(C, B) <=> (C = A)))),
% 0.16/0.37 inference(modus_ponens,[status(thm)],[17, 16])).
% 0.16/0.37 tff(19,plain,(
% 0.16/0.37 ![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)))))),
% 0.16/0.37 inference(skolemize,[status(sab)],[18])).
% 0.16/0.37 tff(20,plain,
% 0.16/0.37 (![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))))),
% 0.16/0.37 inference(modus_ponens,[status(thm)],[19, 15])).
% 0.16/0.37 tff(21,plain,
% 0.16/0.37 (![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))))))),
% 0.16/0.37 inference(modus_ponens,[status(thm)],[20, 13])).
% 0.16/0.37 tff(22,plain,
% 0.16/0.37 (![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))))))),
% 0.16/0.37 inference(modus_ponens,[status(thm)],[21, 11])).
% 0.16/0.37 tff(23,plain,
% 0.16/0.37 (((~![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(tptp_fun_D_1(B!6, set_difference(B!6, singleton(A!7)), singleton(A!7)), singleton(A!7)) <=> (tptp_fun_D_1(B!6, set_difference(B!6, singleton(A!7)), singleton(A!7)) = A!7))) <=> ((~![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(tptp_fun_D_1(B!6, set_difference(B!6, singleton(A!7)), singleton(A!7)), singleton(A!7)) <=> (tptp_fun_D_1(B!6, set_difference(B!6, singleton(A!7)), singleton(A!7)) = A!7)))),
% 0.16/0.37 inference(rewrite,[status(thm)],[])).
% 0.16/0.37 tff(24,plain,
% 0.16/0.37 ((~((~in(tptp_fun_D_1(B!6, set_difference(B!6, singleton(A!7)), singleton(A!7)), singleton(A!7))) <=> (tptp_fun_D_1(B!6, set_difference(B!6, singleton(A!7)), singleton(A!7)) = A!7))) <=> (in(tptp_fun_D_1(B!6, set_difference(B!6, singleton(A!7)), singleton(A!7)), singleton(A!7)) <=> (tptp_fun_D_1(B!6, set_difference(B!6, singleton(A!7)), singleton(A!7)) = A!7))),
% 0.16/0.37 inference(rewrite,[status(thm)],[])).
% 0.16/0.37 tff(25,plain,
% 0.16/0.37 ((((~in(tptp_fun_D_1(B!6, set_difference(B!6, singleton(A!7)), singleton(A!7)), singleton(A!7))) <=> (tptp_fun_D_1(B!6, set_difference(B!6, singleton(A!7)), singleton(A!7)) = A!7)) | $false) <=> ((~in(tptp_fun_D_1(B!6, set_difference(B!6, singleton(A!7)), singleton(A!7)), singleton(A!7))) <=> (tptp_fun_D_1(B!6, set_difference(B!6, singleton(A!7)), singleton(A!7)) = A!7))),
% 0.16/0.37 inference(rewrite,[status(thm)],[])).
% 0.16/0.37 tff(26,plain,
% 0.16/0.37 ((~$true) <=> $false),
% 0.16/0.37 inference(rewrite,[status(thm)],[])).
% 0.16/0.37 tff(27,plain,
% 0.16/0.37 (($true | ((~in(tptp_fun_C_0(singleton(A!7), A!7), singleton(A!7))) <=> (tptp_fun_C_0(singleton(A!7), A!7) = A!7))) <=> $true),
% 0.16/0.37 inference(rewrite,[status(thm)],[])).
% 0.16/0.37 tff(28,plain,
% 0.16/0.37 ((singleton(A!7) = singleton(A!7)) <=> $true),
% 0.16/0.37 inference(rewrite,[status(thm)],[])).
% 0.16/0.37 tff(29,plain,
% 0.16/0.37 (((singleton(A!7) = singleton(A!7)) | ((~in(tptp_fun_C_0(singleton(A!7), A!7), singleton(A!7))) <=> (tptp_fun_C_0(singleton(A!7), A!7) = A!7))) <=> ($true | ((~in(tptp_fun_C_0(singleton(A!7), A!7), singleton(A!7))) <=> (tptp_fun_C_0(singleton(A!7), A!7) = A!7)))),
% 0.16/0.37 inference(monotonicity,[status(thm)],[28])).
% 0.16/0.37 tff(30,plain,
% 0.16/0.37 (((singleton(A!7) = singleton(A!7)) | ((~in(tptp_fun_C_0(singleton(A!7), A!7), singleton(A!7))) <=> (tptp_fun_C_0(singleton(A!7), A!7) = A!7))) <=> $true),
% 0.16/0.37 inference(transitivity,[status(thm)],[29, 27])).
% 0.16/0.37 tff(31,plain,
% 0.16/0.37 ((~((singleton(A!7) = singleton(A!7)) | ((~in(tptp_fun_C_0(singleton(A!7), A!7), singleton(A!7))) <=> (tptp_fun_C_0(singleton(A!7), A!7) = A!7)))) <=> (~$true)),
% 0.16/0.37 inference(monotonicity,[status(thm)],[30])).
% 0.16/0.37 tff(32,plain,
% 0.16/0.37 ((~((singleton(A!7) = singleton(A!7)) | ((~in(tptp_fun_C_0(singleton(A!7), A!7), singleton(A!7))) <=> (tptp_fun_C_0(singleton(A!7), A!7) = A!7)))) <=> $false),
% 0.16/0.37 inference(transitivity,[status(thm)],[31, 26])).
% 0.16/0.37 tff(33,plain,
% 0.16/0.37 ((~(in(tptp_fun_D_1(B!6, set_difference(B!6, singleton(A!7)), singleton(A!7)), singleton(A!7)) <=> (tptp_fun_D_1(B!6, set_difference(B!6, singleton(A!7)), singleton(A!7)) = A!7))) <=> ((~in(tptp_fun_D_1(B!6, set_difference(B!6, singleton(A!7)), singleton(A!7)), singleton(A!7))) <=> (tptp_fun_D_1(B!6, set_difference(B!6, singleton(A!7)), singleton(A!7)) = A!7))),
% 0.16/0.37 inference(rewrite,[status(thm)],[])).
% 0.16/0.37 tff(34,plain,
% 0.16/0.37 (($false | (in(tptp_fun_D_1(B!6, set_difference(B!6, singleton(A!7)), singleton(A!7)), singleton(A!7)) <=> (tptp_fun_D_1(B!6, set_difference(B!6, singleton(A!7)), singleton(A!7)) = A!7))) <=> (in(tptp_fun_D_1(B!6, set_difference(B!6, singleton(A!7)), singleton(A!7)), singleton(A!7)) <=> (tptp_fun_D_1(B!6, set_difference(B!6, singleton(A!7)), singleton(A!7)) = A!7))),
% 0.16/0.37 inference(rewrite,[status(thm)],[])).
% 0.16/0.37 tff(35,plain,
% 0.16/0.37 ((~(singleton(A!7) = singleton(A!7))) <=> (~$true)),
% 0.16/0.37 inference(monotonicity,[status(thm)],[28])).
% 0.16/0.37 tff(36,plain,
% 0.16/0.37 ((~(singleton(A!7) = singleton(A!7))) <=> $false),
% 0.16/0.37 inference(transitivity,[status(thm)],[35, 26])).
% 0.16/0.37 tff(37,plain,
% 0.16/0.37 (((~(singleton(A!7) = singleton(A!7))) | (in(tptp_fun_D_1(B!6, set_difference(B!6, singleton(A!7)), singleton(A!7)), singleton(A!7)) <=> (tptp_fun_D_1(B!6, set_difference(B!6, singleton(A!7)), singleton(A!7)) = A!7))) <=> ($false | (in(tptp_fun_D_1(B!6, set_difference(B!6, singleton(A!7)), singleton(A!7)), singleton(A!7)) <=> (tptp_fun_D_1(B!6, set_difference(B!6, singleton(A!7)), singleton(A!7)) = A!7)))),
% 0.16/0.37 inference(monotonicity,[status(thm)],[36])).
% 0.16/0.37 tff(38,plain,
% 0.16/0.37 (((~(singleton(A!7) = singleton(A!7))) | (in(tptp_fun_D_1(B!6, set_difference(B!6, singleton(A!7)), singleton(A!7)), singleton(A!7)) <=> (tptp_fun_D_1(B!6, set_difference(B!6, singleton(A!7)), singleton(A!7)) = A!7))) <=> (in(tptp_fun_D_1(B!6, set_difference(B!6, singleton(A!7)), singleton(A!7)), singleton(A!7)) <=> (tptp_fun_D_1(B!6, set_difference(B!6, singleton(A!7)), singleton(A!7)) = A!7))),
% 0.16/0.37 inference(transitivity,[status(thm)],[37, 34])).
% 0.16/0.37 tff(39,plain,
% 0.16/0.37 ((~((~(singleton(A!7) = singleton(A!7))) | (in(tptp_fun_D_1(B!6, set_difference(B!6, singleton(A!7)), singleton(A!7)), singleton(A!7)) <=> (tptp_fun_D_1(B!6, set_difference(B!6, singleton(A!7)), singleton(A!7)) = A!7)))) <=> (~(in(tptp_fun_D_1(B!6, set_difference(B!6, singleton(A!7)), singleton(A!7)), singleton(A!7)) <=> (tptp_fun_D_1(B!6, set_difference(B!6, singleton(A!7)), singleton(A!7)) = A!7)))),
% 0.16/0.37 inference(monotonicity,[status(thm)],[38])).
% 0.16/0.37 tff(40,plain,
% 0.16/0.37 ((~((~(singleton(A!7) = singleton(A!7))) | (in(tptp_fun_D_1(B!6, set_difference(B!6, singleton(A!7)), singleton(A!7)), singleton(A!7)) <=> (tptp_fun_D_1(B!6, set_difference(B!6, singleton(A!7)), singleton(A!7)) = A!7)))) <=> ((~in(tptp_fun_D_1(B!6, set_difference(B!6, singleton(A!7)), singleton(A!7)), singleton(A!7))) <=> (tptp_fun_D_1(B!6, set_difference(B!6, singleton(A!7)), singleton(A!7)) = A!7))),
% 0.16/0.37 inference(transitivity,[status(thm)],[39, 33])).
% 0.16/0.37 tff(41,plain,
% 0.16/0.37 (((~((~(singleton(A!7) = singleton(A!7))) | (in(tptp_fun_D_1(B!6, set_difference(B!6, singleton(A!7)), singleton(A!7)), singleton(A!7)) <=> (tptp_fun_D_1(B!6, set_difference(B!6, singleton(A!7)), singleton(A!7)) = A!7)))) | (~((singleton(A!7) = singleton(A!7)) | ((~in(tptp_fun_C_0(singleton(A!7), A!7), singleton(A!7))) <=> (tptp_fun_C_0(singleton(A!7), A!7) = A!7))))) <=> (((~in(tptp_fun_D_1(B!6, set_difference(B!6, singleton(A!7)), singleton(A!7)), singleton(A!7))) <=> (tptp_fun_D_1(B!6, set_difference(B!6, singleton(A!7)), singleton(A!7)) = A!7)) | $false)),
% 0.16/0.37 inference(monotonicity,[status(thm)],[40, 32])).
% 0.16/0.37 tff(42,plain,
% 0.16/0.37 (((~((~(singleton(A!7) = singleton(A!7))) | (in(tptp_fun_D_1(B!6, set_difference(B!6, singleton(A!7)), singleton(A!7)), singleton(A!7)) <=> (tptp_fun_D_1(B!6, set_difference(B!6, singleton(A!7)), singleton(A!7)) = A!7)))) | (~((singleton(A!7) = singleton(A!7)) | ((~in(tptp_fun_C_0(singleton(A!7), A!7), singleton(A!7))) <=> (tptp_fun_C_0(singleton(A!7), A!7) = A!7))))) <=> ((~in(tptp_fun_D_1(B!6, set_difference(B!6, singleton(A!7)), singleton(A!7)), singleton(A!7))) <=> (tptp_fun_D_1(B!6, set_difference(B!6, singleton(A!7)), singleton(A!7)) = A!7))),
% 0.16/0.37 inference(transitivity,[status(thm)],[41, 25])).
% 0.16/0.37 tff(43,plain,
% 0.16/0.37 ((~((~((~(singleton(A!7) = singleton(A!7))) | (in(tptp_fun_D_1(B!6, set_difference(B!6, singleton(A!7)), singleton(A!7)), singleton(A!7)) <=> (tptp_fun_D_1(B!6, set_difference(B!6, singleton(A!7)), singleton(A!7)) = A!7)))) | (~((singleton(A!7) = singleton(A!7)) | ((~in(tptp_fun_C_0(singleton(A!7), A!7), singleton(A!7))) <=> (tptp_fun_C_0(singleton(A!7), A!7) = A!7)))))) <=> (~((~in(tptp_fun_D_1(B!6, set_difference(B!6, singleton(A!7)), singleton(A!7)), singleton(A!7))) <=> (tptp_fun_D_1(B!6, set_difference(B!6, singleton(A!7)), singleton(A!7)) = A!7)))),
% 0.16/0.37 inference(monotonicity,[status(thm)],[42])).
% 0.16/0.37 tff(44,plain,
% 0.16/0.37 ((~((~((~(singleton(A!7) = singleton(A!7))) | (in(tptp_fun_D_1(B!6, set_difference(B!6, singleton(A!7)), singleton(A!7)), singleton(A!7)) <=> (tptp_fun_D_1(B!6, set_difference(B!6, singleton(A!7)), singleton(A!7)) = A!7)))) | (~((singleton(A!7) = singleton(A!7)) | ((~in(tptp_fun_C_0(singleton(A!7), A!7), singleton(A!7))) <=> (tptp_fun_C_0(singleton(A!7), A!7) = A!7)))))) <=> (in(tptp_fun_D_1(B!6, set_difference(B!6, singleton(A!7)), singleton(A!7)), singleton(A!7)) <=> (tptp_fun_D_1(B!6, set_difference(B!6, singleton(A!7)), singleton(A!7)) = A!7))),
% 0.16/0.37 inference(transitivity,[status(thm)],[43, 24])).
% 0.16/0.37 tff(45,plain,
% 0.16/0.37 (((~![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!7) = singleton(A!7))) | (in(tptp_fun_D_1(B!6, set_difference(B!6, singleton(A!7)), singleton(A!7)), singleton(A!7)) <=> (tptp_fun_D_1(B!6, set_difference(B!6, singleton(A!7)), singleton(A!7)) = A!7)))) | (~((singleton(A!7) = singleton(A!7)) | ((~in(tptp_fun_C_0(singleton(A!7), A!7), singleton(A!7))) <=> (tptp_fun_C_0(singleton(A!7), A!7) = A!7))))))) <=> ((~![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(tptp_fun_D_1(B!6, set_difference(B!6, singleton(A!7)), singleton(A!7)), singleton(A!7)) <=> (tptp_fun_D_1(B!6, set_difference(B!6, singleton(A!7)), singleton(A!7)) = A!7)))),
% 0.16/0.37 inference(monotonicity,[status(thm)],[44])).
% 0.16/0.37 tff(46,plain,
% 0.16/0.37 (((~![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!7) = singleton(A!7))) | (in(tptp_fun_D_1(B!6, set_difference(B!6, singleton(A!7)), singleton(A!7)), singleton(A!7)) <=> (tptp_fun_D_1(B!6, set_difference(B!6, singleton(A!7)), singleton(A!7)) = A!7)))) | (~((singleton(A!7) = singleton(A!7)) | ((~in(tptp_fun_C_0(singleton(A!7), A!7), singleton(A!7))) <=> (tptp_fun_C_0(singleton(A!7), A!7) = A!7))))))) <=> ((~![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(tptp_fun_D_1(B!6, set_difference(B!6, singleton(A!7)), singleton(A!7)), singleton(A!7)) <=> (tptp_fun_D_1(B!6, set_difference(B!6, singleton(A!7)), singleton(A!7)) = A!7)))),
% 0.16/0.37 inference(transitivity,[status(thm)],[45, 23])).
% 0.16/0.37 tff(47,plain,
% 0.16/0.37 ((~![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!7) = singleton(A!7))) | (in(tptp_fun_D_1(B!6, set_difference(B!6, singleton(A!7)), singleton(A!7)), singleton(A!7)) <=> (tptp_fun_D_1(B!6, set_difference(B!6, singleton(A!7)), singleton(A!7)) = A!7)))) | (~((singleton(A!7) = singleton(A!7)) | ((~in(tptp_fun_C_0(singleton(A!7), A!7), singleton(A!7))) <=> (tptp_fun_C_0(singleton(A!7), A!7) = A!7))))))),
% 0.16/0.37 inference(quant_inst,[status(thm)],[])).
% 0.16/0.37 tff(48,plain,
% 0.16/0.37 ((~![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))))) | (in(tptp_fun_D_1(B!6, set_difference(B!6, singleton(A!7)), singleton(A!7)), singleton(A!7)) <=> (tptp_fun_D_1(B!6, set_difference(B!6, singleton(A!7)), singleton(A!7)) = A!7))),
% 0.16/0.37 inference(modus_ponens,[status(thm)],[47, 46])).
% 0.16/0.37 tff(49,plain,
% 0.16/0.37 ($false),
% 0.16/0.37 inference(unit_resolution,[status(thm)],[48, 22, 1])).
% 0.16/0.37 tff(50,plain,(in(tptp_fun_D_1(B!6, set_difference(B!6, singleton(A!7)), singleton(A!7)), singleton(A!7)) <=> (tptp_fun_D_1(B!6, set_difference(B!6, singleton(A!7)), singleton(A!7)) = A!7)), inference(lemma,lemma(discharge,[]))).
% 0.16/0.37 tff(51,assumption,(~in(tptp_fun_D_1(B!6, set_difference(B!6, singleton(A!7)), singleton(A!7)), B!6)), introduced(assumption)).
% 0.16/0.37 tff(52,plain,
% 0.16/0.37 (((~in(tptp_fun_D_1(B!6, set_difference(B!6, singleton(A!7)), singleton(A!7)), B!6)) | (tptp_fun_D_1(B!6, set_difference(B!6, singleton(A!7)), singleton(A!7)) = A!7)) | in(tptp_fun_D_1(B!6, set_difference(B!6, singleton(A!7)), singleton(A!7)), B!6)),
% 0.16/0.37 inference(tautology,[status(thm)],[])).
% 0.16/0.37 tff(53,plain,
% 0.16/0.37 ((~in(tptp_fun_D_1(B!6, set_difference(B!6, singleton(A!7)), singleton(A!7)), B!6)) | (tptp_fun_D_1(B!6, set_difference(B!6, singleton(A!7)), singleton(A!7)) = A!7)),
% 0.16/0.37 inference(unit_resolution,[status(thm)],[52, 51])).
% 0.16/0.37 tff(54,assumption,(~in(tptp_fun_D_1(B!6, set_difference(B!6, singleton(A!7)), singleton(A!7)), singleton(A!7))), introduced(assumption)).
% 0.16/0.37 tff(55,plain,
% 0.16/0.37 (^[A: $i, B: $i, C: $i, D: $i] : refl((~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_1(C, B, A), C)) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B))))))) <=> (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_1(C, B, A), C)) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B))))))))),
% 0.16/0.37 inference(bind,[status(th)],[])).
% 0.16/0.37 tff(56,plain,
% 0.16/0.37 (![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_1(C, B, A), C)) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_1(C, B, A), C)) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B)))))))),
% 0.16/0.37 inference(quant_intro,[status(thm)],[55])).
% 0.16/0.37 tff(57,plain,
% 0.16/0.37 (![A: $i, B: $i, C: $i] : ![D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_1(C, B, A), C)) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_1(C, B, A), C)) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B)))))))),
% 0.16/0.37 inference(pull_quant,[status(thm)],[])).
% 0.16/0.37 tff(58,plain,
% 0.16/0.37 (^[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, A) | in(D, B)))) <=> ![D: $i] : ((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, A) | in(D, B))))), ((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B))))) <=> (~![D: $i] : ((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, A) | in(D, B))))))), pull_quant((~![D: $i] : ((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, A) | in(D, B))))) <=> ?[D: $i] : (~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, A) | in(D, B)))))), ((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B))))) <=> ?[D: $i] : (~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, A) | in(D, B))))))), (((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_1(C, B, A), C)) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B)))))) <=> (?[D: $i] : (~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_1(C, B, A), C)) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B)))))))), pull_quant((?[D: $i] : (~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_1(C, B, A), C)) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B)))))) <=> ?[D: $i] : ((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_1(C, B, A), C)) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B))))))), (((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_1(C, B, A), C)) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B)))))) <=> ?[D: $i] : ((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_1(C, B, A), C)) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B)))))))), ((~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_1(C, B, A), C)) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B))))))) <=> (~?[D: $i] : ((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_1(C, B, A), C)) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B))))))))), pull_quant((~?[D: $i] : ((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_1(C, B, A), C)) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B))))))) <=> ![D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_1(C, B, A), C)) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B)))))))), ((~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_1(C, B, A), C)) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B))))))) <=> ![D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_1(C, B, A), C)) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B)))))))))),
% 0.16/0.38 inference(bind,[status(th)],[])).
% 0.16/0.38 tff(59,plain,
% 0.16/0.38 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_1(C, B, A), C)) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B))))))) <=> ![A: $i, B: $i, C: $i] : ![D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_1(C, B, A), C)) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B)))))))),
% 0.16/0.38 inference(quant_intro,[status(thm)],[58])).
% 0.16/0.38 tff(60,plain,
% 0.16/0.38 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_1(C, B, A), C)) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_1(C, B, A), C)) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B)))))))),
% 0.16/0.38 inference(transitivity,[status(thm)],[59, 57])).
% 0.16/0.38 tff(61,plain,
% 0.16/0.38 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_1(C, B, A), C)) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_1(C, B, A), C)) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B)))))))),
% 0.16/0.38 inference(transitivity,[status(thm)],[60, 56])).
% 0.16/0.38 tff(62,plain,
% 0.16/0.38 (^[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)) | ((~in(tptp_fun_D_1(C, B, A), C)) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B))))))) <=> (~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_1(C, B, A), C)) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B))))))))),
% 0.16/0.38 inference(bind,[status(th)],[])).
% 0.16/0.38 tff(63,plain,
% 0.16/0.38 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_1(C, B, A), C)) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B))))))) <=> ![A: $i, B: $i, C: $i] : (~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_1(C, B, A), C)) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B)))))))),
% 0.16/0.38 inference(quant_intro,[status(thm)],[62])).
% 0.16/0.38 tff(64,plain,
% 0.16/0.38 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_1(C, B, A), C)) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_1(C, B, A), C)) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B)))))))),
% 0.16/0.38 inference(transitivity,[status(thm)],[63, 61])).
% 0.16/0.38 tff(65,plain,
% 0.16/0.38 (^[A: $i, B: $i, C: $i] : trans(monotonicity(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, A) | in(D, B))))), monotonicity(rewrite(((~in(tptp_fun_D_1(C, B, A), C)) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B))) <=> ((~in(tptp_fun_D_1(C, B, A), C)) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B)))), (((C = set_union2(A, B)) | ((~in(tptp_fun_D_1(C, B, A), C)) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B)))) <=> ((C = set_union2(A, B)) | ((~in(tptp_fun_D_1(C, B, A), C)) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B)))))), ((((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B)))) & ((C = set_union2(A, B)) | ((~in(tptp_fun_D_1(C, B, A), C)) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B))))) <=> (((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B)))) & ((C = set_union2(A, B)) | ((~in(tptp_fun_D_1(C, B, A), C)) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B))))))), rewrite((((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B)))) & ((C = set_union2(A, B)) | ((~in(tptp_fun_D_1(C, B, A), C)) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B))))) <=> (~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_1(C, B, A), C)) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B)))))))), ((((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B)))) & ((C = set_union2(A, B)) | ((~in(tptp_fun_D_1(C, B, A), C)) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B))))) <=> (~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_1(C, B, A), C)) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B)))))))))),
% 0.16/0.38 inference(bind,[status(th)],[])).
% 0.16/0.38 tff(66,plain,
% 0.16/0.38 (![A: $i, B: $i, C: $i] : (((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B)))) & ((C = set_union2(A, B)) | ((~in(tptp_fun_D_1(C, B, A), C)) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B))))) <=> ![A: $i, B: $i, C: $i] : (~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_1(C, B, A), C)) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B)))))))),
% 0.16/0.38 inference(quant_intro,[status(thm)],[65])).
% 0.16/0.38 tff(67,plain,
% 0.16/0.38 (^[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)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B)))))) <=> (((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B)))) & ((C = set_union2(A, B)) | ((~in(tptp_fun_D_1(C, B, A), C)) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B))))))),
% 0.16/0.38 inference(bind,[status(th)],[])).
% 0.16/0.38 tff(68,plain,
% 0.16/0.38 (![A: $i, B: $i, C: $i] : (((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B)))) & ((C = set_union2(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B)))))) <=> ![A: $i, B: $i, C: $i] : (((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B)))) & ((C = set_union2(A, B)) | ((~in(tptp_fun_D_1(C, B, A), C)) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B)))))),
% 0.16/0.38 inference(quant_intro,[status(thm)],[67])).
% 0.16/0.38 tff(69,plain,
% 0.16/0.38 (![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, A) | in(D, B))))),
% 0.16/0.38 inference(rewrite,[status(thm)],[])).
% 0.16/0.38 tff(70,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/sandbox/benchmark/theBenchmark.p','d2_xboole_0')).
% 0.16/0.38 tff(71,plain,
% 0.16/0.38 (![A: $i, B: $i, C: $i] : ((C = set_union2(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B))))),
% 0.16/0.38 inference(modus_ponens,[status(thm)],[70, 69])).
% 0.16/0.38 tff(72,plain,(
% 0.16/0.38 ![A: $i, B: $i, C: $i] : (((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B)))) & ((C = set_union2(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B))))))),
% 0.16/0.38 inference(skolemize,[status(sab)],[71])).
% 0.16/0.38 tff(73,plain,
% 0.16/0.38 (![A: $i, B: $i, C: $i] : (((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B)))) & ((C = set_union2(A, B)) | ((~in(tptp_fun_D_1(C, B, A), C)) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B)))))),
% 0.16/0.38 inference(modus_ponens,[status(thm)],[72, 68])).
% 0.16/0.38 tff(74,plain,
% 0.16/0.38 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_1(C, B, A), C)) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B)))))))),
% 0.16/0.38 inference(modus_ponens,[status(thm)],[73, 66])).
% 0.16/0.38 tff(75,plain,
% 0.16/0.38 (![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_1(C, B, A), C)) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B)))))))),
% 0.16/0.38 inference(modus_ponens,[status(thm)],[74, 64])).
% 0.16/0.38 tff(76,plain,
% 0.16/0.38 ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_1(C, B, A), C)) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B)))))))) | (~((~((~(B!6 = set_union2(singleton(A!7), set_difference(B!6, singleton(A!7))))) | (in(A!7, B!6) <=> (in(A!7, singleton(A!7)) | in(A!7, set_difference(B!6, singleton(A!7))))))) | (~((B!6 = set_union2(singleton(A!7), set_difference(B!6, singleton(A!7)))) | ((~in(tptp_fun_D_1(B!6, set_difference(B!6, singleton(A!7)), singleton(A!7)), B!6)) <=> (in(tptp_fun_D_1(B!6, set_difference(B!6, singleton(A!7)), singleton(A!7)), singleton(A!7)) | in(tptp_fun_D_1(B!6, set_difference(B!6, singleton(A!7)), singleton(A!7)), set_difference(B!6, singleton(A!7)))))))))),
% 0.16/0.38 inference(quant_inst,[status(thm)],[])).
% 0.16/0.38 tff(77,plain,
% 0.16/0.38 (~((~((~(B!6 = set_union2(singleton(A!7), set_difference(B!6, singleton(A!7))))) | (in(A!7, B!6) <=> (in(A!7, singleton(A!7)) | in(A!7, set_difference(B!6, singleton(A!7))))))) | (~((B!6 = set_union2(singleton(A!7), set_difference(B!6, singleton(A!7)))) | ((~in(tptp_fun_D_1(B!6, set_difference(B!6, singleton(A!7)), singleton(A!7)), B!6)) <=> (in(tptp_fun_D_1(B!6, set_difference(B!6, singleton(A!7)), singleton(A!7)), singleton(A!7)) | in(tptp_fun_D_1(B!6, set_difference(B!6, singleton(A!7)), singleton(A!7)), set_difference(B!6, singleton(A!7))))))))),
% 0.16/0.38 inference(unit_resolution,[status(thm)],[76, 75])).
% 0.16/0.38 tff(78,plain,
% 0.16/0.38 (((~((~(B!6 = set_union2(singleton(A!7), set_difference(B!6, singleton(A!7))))) | (in(A!7, B!6) <=> (in(A!7, singleton(A!7)) | in(A!7, set_difference(B!6, singleton(A!7))))))) | (~((B!6 = set_union2(singleton(A!7), set_difference(B!6, singleton(A!7)))) | ((~in(tptp_fun_D_1(B!6, set_difference(B!6, singleton(A!7)), singleton(A!7)), B!6)) <=> (in(tptp_fun_D_1(B!6, set_difference(B!6, singleton(A!7)), singleton(A!7)), singleton(A!7)) | in(tptp_fun_D_1(B!6, set_difference(B!6, singleton(A!7)), singleton(A!7)), set_difference(B!6, singleton(A!7)))))))) | ((B!6 = set_union2(singleton(A!7), set_difference(B!6, singleton(A!7)))) | ((~in(tptp_fun_D_1(B!6, set_difference(B!6, singleton(A!7)), singleton(A!7)), B!6)) <=> (in(tptp_fun_D_1(B!6, set_difference(B!6, singleton(A!7)), singleton(A!7)), singleton(A!7)) | in(tptp_fun_D_1(B!6, set_difference(B!6, singleton(A!7)), singleton(A!7)), set_difference(B!6, singleton(A!7))))))),
% 0.16/0.38 inference(tautology,[status(thm)],[])).
% 0.16/0.38 tff(79,plain,
% 0.16/0.38 ((B!6 = set_union2(singleton(A!7), set_difference(B!6, singleton(A!7)))) | ((~in(tptp_fun_D_1(B!6, set_difference(B!6, singleton(A!7)), singleton(A!7)), B!6)) <=> (in(tptp_fun_D_1(B!6, set_difference(B!6, singleton(A!7)), singleton(A!7)), singleton(A!7)) | in(tptp_fun_D_1(B!6, set_difference(B!6, singleton(A!7)), singleton(A!7)), set_difference(B!6, singleton(A!7)))))),
% 0.16/0.38 inference(unit_resolution,[status(thm)],[78, 77])).
% 0.16/0.38 tff(80,plain,
% 0.16/0.38 ((B!6 = set_union2(set_difference(B!6, singleton(A!7)), singleton(A!7))) <=> (set_union2(set_difference(B!6, singleton(A!7)), singleton(A!7)) = B!6)),
% 0.16/0.38 inference(commutativity,[status(thm)],[])).
% 0.16/0.38 tff(81,plain,
% 0.16/0.38 (^[A: $i, B: $i] : refl((set_union2(A, B) = set_union2(B, A)) <=> (set_union2(A, B) = set_union2(B, A)))),
% 0.16/0.38 inference(bind,[status(th)],[])).
% 0.16/0.38 tff(82,plain,
% 0.16/0.38 (![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A)) <=> ![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A))),
% 0.16/0.38 inference(quant_intro,[status(thm)],[81])).
% 0.16/0.38 tff(83,plain,
% 0.16/0.38 (![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A)) <=> ![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A))),
% 0.16/0.38 inference(rewrite,[status(thm)],[])).
% 0.16/0.38 tff(84,axiom,(![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','commutativity_k2_xboole_0')).
% 0.16/0.38 tff(85,plain,
% 0.16/0.38 (![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A))),
% 0.16/0.38 inference(modus_ponens,[status(thm)],[84, 83])).
% 0.16/0.38 tff(86,plain,(
% 0.16/0.38 ![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A))),
% 0.16/0.38 inference(skolemize,[status(sab)],[85])).
% 0.16/0.38 tff(87,plain,
% 0.16/0.38 (![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A))),
% 0.16/0.38 inference(modus_ponens,[status(thm)],[86, 82])).
% 0.16/0.38 tff(88,plain,
% 0.16/0.38 ((~![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A))) | (set_union2(set_difference(B!6, singleton(A!7)), singleton(A!7)) = set_union2(singleton(A!7), set_difference(B!6, singleton(A!7))))),
% 0.16/0.38 inference(quant_inst,[status(thm)],[])).
% 0.16/0.38 tff(89,plain,
% 0.16/0.38 (set_union2(set_difference(B!6, singleton(A!7)), singleton(A!7)) = set_union2(singleton(A!7), set_difference(B!6, singleton(A!7)))),
% 0.16/0.38 inference(unit_resolution,[status(thm)],[88, 87])).
% 0.16/0.38 tff(90,plain,
% 0.16/0.38 (set_union2(singleton(A!7), set_difference(B!6, singleton(A!7))) = set_union2(set_difference(B!6, singleton(A!7)), singleton(A!7))),
% 0.16/0.38 inference(symmetry,[status(thm)],[89])).
% 0.16/0.38 tff(91,plain,
% 0.16/0.38 ((B!6 = set_union2(singleton(A!7), set_difference(B!6, singleton(A!7)))) <=> (B!6 = set_union2(set_difference(B!6, singleton(A!7)), singleton(A!7)))),
% 0.16/0.38 inference(monotonicity,[status(thm)],[90])).
% 0.16/0.38 tff(92,plain,
% 0.16/0.38 ((B!6 = set_union2(singleton(A!7), set_difference(B!6, singleton(A!7)))) <=> (set_union2(set_difference(B!6, singleton(A!7)), singleton(A!7)) = B!6)),
% 0.16/0.38 inference(transitivity,[status(thm)],[91, 80])).
% 0.16/0.38 tff(93,plain,
% 0.16/0.38 ((set_union2(set_difference(B!6, singleton(A!7)), singleton(A!7)) = B!6) <=> (B!6 = set_union2(singleton(A!7), set_difference(B!6, singleton(A!7))))),
% 0.16/0.38 inference(symmetry,[status(thm)],[92])).
% 0.16/0.38 tff(94,plain,
% 0.16/0.38 ((~(set_union2(set_difference(B!6, singleton(A!7)), singleton(A!7)) = B!6)) <=> (~(B!6 = set_union2(singleton(A!7), set_difference(B!6, singleton(A!7)))))),
% 0.16/0.38 inference(monotonicity,[status(thm)],[93])).
% 0.16/0.38 tff(95,plain,
% 0.16/0.38 ((~![A: $i, B: $i] : ((~in(A, B)) | (set_union2(set_difference(B, singleton(A)), singleton(A)) = B))) <=> (~![A: $i, B: $i] : ((~in(A, B)) | (set_union2(set_difference(B, singleton(A)), singleton(A)) = B)))),
% 0.16/0.38 inference(rewrite,[status(thm)],[])).
% 0.16/0.38 tff(96,plain,
% 0.16/0.38 ((~![A: $i, B: $i] : (in(A, B) => (set_union2(set_difference(B, singleton(A)), singleton(A)) = B))) <=> (~![A: $i, B: $i] : ((~in(A, B)) | (set_union2(set_difference(B, singleton(A)), singleton(A)) = B)))),
% 0.16/0.38 inference(rewrite,[status(thm)],[])).
% 0.16/0.38 tff(97,axiom,(~![A: $i, B: $i] : (in(A, B) => (set_union2(set_difference(B, singleton(A)), singleton(A)) = B))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t140_zfmisc_1')).
% 0.16/0.38 tff(98,plain,
% 0.16/0.38 (~![A: $i, B: $i] : ((~in(A, B)) | (set_union2(set_difference(B, singleton(A)), singleton(A)) = B))),
% 0.16/0.38 inference(modus_ponens,[status(thm)],[97, 96])).
% 0.16/0.38 tff(99,plain,
% 0.16/0.38 (~![A: $i, B: $i] : ((~in(A, B)) | (set_union2(set_difference(B, singleton(A)), singleton(A)) = B))),
% 0.16/0.38 inference(modus_ponens,[status(thm)],[98, 95])).
% 0.16/0.38 tff(100,plain,
% 0.16/0.38 (~![A: $i, B: $i] : ((~in(A, B)) | (set_union2(set_difference(B, singleton(A)), singleton(A)) = B))),
% 0.16/0.38 inference(modus_ponens,[status(thm)],[99, 95])).
% 0.16/0.38 tff(101,plain,
% 0.16/0.38 (~![A: $i, B: $i] : ((~in(A, B)) | (set_union2(set_difference(B, singleton(A)), singleton(A)) = B))),
% 0.16/0.38 inference(modus_ponens,[status(thm)],[100, 95])).
% 0.16/0.38 tff(102,plain,
% 0.16/0.38 (~![A: $i, B: $i] : ((~in(A, B)) | (set_union2(set_difference(B, singleton(A)), singleton(A)) = B))),
% 0.16/0.38 inference(modus_ponens,[status(thm)],[101, 95])).
% 0.16/0.38 tff(103,plain,
% 0.16/0.38 (~![A: $i, B: $i] : ((~in(A, B)) | (set_union2(set_difference(B, singleton(A)), singleton(A)) = B))),
% 0.16/0.38 inference(modus_ponens,[status(thm)],[102, 95])).
% 0.16/0.38 tff(104,plain,
% 0.16/0.38 (~![A: $i, B: $i] : ((~in(A, B)) | (set_union2(set_difference(B, singleton(A)), singleton(A)) = B))),
% 0.16/0.38 inference(modus_ponens,[status(thm)],[103, 95])).
% 0.16/0.38 tff(105,plain,(
% 0.16/0.38 ~((~in(A!7, B!6)) | (set_union2(set_difference(B!6, singleton(A!7)), singleton(A!7)) = B!6))),
% 0.16/0.38 inference(skolemize,[status(sab)],[104])).
% 0.16/0.38 tff(106,plain,
% 0.16/0.38 (~(set_union2(set_difference(B!6, singleton(A!7)), singleton(A!7)) = B!6)),
% 0.16/0.38 inference(or_elim,[status(thm)],[105])).
% 0.16/0.38 tff(107,plain,
% 0.16/0.38 (~(B!6 = set_union2(singleton(A!7), set_difference(B!6, singleton(A!7))))),
% 0.16/0.38 inference(modus_ponens,[status(thm)],[106, 94])).
% 0.16/0.38 tff(108,plain,
% 0.16/0.38 ((~((B!6 = set_union2(singleton(A!7), set_difference(B!6, singleton(A!7)))) | ((~in(tptp_fun_D_1(B!6, set_difference(B!6, singleton(A!7)), singleton(A!7)), B!6)) <=> (in(tptp_fun_D_1(B!6, set_difference(B!6, singleton(A!7)), singleton(A!7)), singleton(A!7)) | in(tptp_fun_D_1(B!6, set_difference(B!6, singleton(A!7)), singleton(A!7)), set_difference(B!6, singleton(A!7))))))) | (B!6 = set_union2(singleton(A!7), set_difference(B!6, singleton(A!7)))) | ((~in(tptp_fun_D_1(B!6, set_difference(B!6, singleton(A!7)), singleton(A!7)), B!6)) <=> (in(tptp_fun_D_1(B!6, set_difference(B!6, singleton(A!7)), singleton(A!7)), singleton(A!7)) | in(tptp_fun_D_1(B!6, set_difference(B!6, singleton(A!7)), singleton(A!7)), set_difference(B!6, singleton(A!7)))))),
% 0.16/0.38 inference(tautology,[status(thm)],[])).
% 0.16/0.38 tff(109,plain,
% 0.16/0.38 ((~in(tptp_fun_D_1(B!6, set_difference(B!6, singleton(A!7)), singleton(A!7)), B!6)) <=> (in(tptp_fun_D_1(B!6, set_difference(B!6, singleton(A!7)), singleton(A!7)), singleton(A!7)) | in(tptp_fun_D_1(B!6, set_difference(B!6, singleton(A!7)), singleton(A!7)), set_difference(B!6, singleton(A!7))))),
% 0.16/0.38 inference(unit_resolution,[status(thm)],[108, 107, 79])).
% 0.16/0.38 tff(110,plain,
% 0.16/0.38 ((~((~in(tptp_fun_D_1(B!6, set_difference(B!6, singleton(A!7)), singleton(A!7)), B!6)) <=> (in(tptp_fun_D_1(B!6, set_difference(B!6, singleton(A!7)), singleton(A!7)), singleton(A!7)) | in(tptp_fun_D_1(B!6, set_difference(B!6, singleton(A!7)), singleton(A!7)), set_difference(B!6, singleton(A!7)))))) | in(tptp_fun_D_1(B!6, set_difference(B!6, singleton(A!7)), singleton(A!7)), B!6) | (in(tptp_fun_D_1(B!6, set_difference(B!6, singleton(A!7)), singleton(A!7)), singleton(A!7)) | in(tptp_fun_D_1(B!6, set_difference(B!6, singleton(A!7)), singleton(A!7)), set_difference(B!6, singleton(A!7))))),
% 0.16/0.38 inference(tautology,[status(thm)],[])).
% 0.16/0.38 tff(111,plain,
% 0.16/0.38 (in(tptp_fun_D_1(B!6, set_difference(B!6, singleton(A!7)), singleton(A!7)), B!6) | (in(tptp_fun_D_1(B!6, set_difference(B!6, singleton(A!7)), singleton(A!7)), singleton(A!7)) | in(tptp_fun_D_1(B!6, set_difference(B!6, singleton(A!7)), singleton(A!7)), set_difference(B!6, singleton(A!7))))),
% 0.16/0.38 inference(unit_resolution,[status(thm)],[110, 109])).
% 0.16/0.38 tff(112,plain,
% 0.16/0.38 (in(tptp_fun_D_1(B!6, set_difference(B!6, singleton(A!7)), singleton(A!7)), singleton(A!7)) | in(tptp_fun_D_1(B!6, set_difference(B!6, singleton(A!7)), singleton(A!7)), set_difference(B!6, singleton(A!7)))),
% 0.16/0.38 inference(unit_resolution,[status(thm)],[111, 51])).
% 0.16/0.38 tff(113,plain,
% 0.16/0.38 ((~(in(tptp_fun_D_1(B!6, set_difference(B!6, singleton(A!7)), singleton(A!7)), singleton(A!7)) | in(tptp_fun_D_1(B!6, set_difference(B!6, singleton(A!7)), singleton(A!7)), set_difference(B!6, singleton(A!7))))) | in(tptp_fun_D_1(B!6, set_difference(B!6, singleton(A!7)), singleton(A!7)), singleton(A!7)) | in(tptp_fun_D_1(B!6, set_difference(B!6, singleton(A!7)), singleton(A!7)), set_difference(B!6, singleton(A!7)))),
% 0.16/0.38 inference(tautology,[status(thm)],[])).
% 0.16/0.38 tff(114,plain,
% 0.16/0.38 (in(tptp_fun_D_1(B!6, set_difference(B!6, singleton(A!7)), singleton(A!7)), set_difference(B!6, singleton(A!7)))),
% 0.16/0.38 inference(unit_resolution,[status(thm)],[113, 112, 54])).
% 0.16/0.38 tff(115,assumption,(~(in(tptp_fun_D_1(B!6, set_difference(B!6, singleton(A!7)), singleton(A!7)), set_difference(B!6, singleton(A!7))) <=> (~((~in(tptp_fun_D_1(B!6, set_difference(B!6, singleton(A!7)), singleton(A!7)), B!6)) | (tptp_fun_D_1(B!6, set_difference(B!6, singleton(A!7)), singleton(A!7)) = A!7))))), introduced(assumption)).
% 0.16/0.39 tff(116,plain,
% 0.16/0.39 (^[A: $i, B: $i, C: $i] : refl((in(A, set_difference(B, singleton(C))) <=> (~((~in(A, B)) | (A = C)))) <=> (in(A, set_difference(B, singleton(C))) <=> (~((~in(A, B)) | (A = C)))))),
% 0.16/0.39 inference(bind,[status(th)],[])).
% 0.16/0.39 tff(117,plain,
% 0.16/0.39 (![A: $i, B: $i, C: $i] : (in(A, set_difference(B, singleton(C))) <=> (~((~in(A, B)) | (A = C)))) <=> ![A: $i, B: $i, C: $i] : (in(A, set_difference(B, singleton(C))) <=> (~((~in(A, B)) | (A = C))))),
% 0.16/0.39 inference(quant_intro,[status(thm)],[116])).
% 0.16/0.39 tff(118,plain,
% 0.16/0.39 (^[A: $i, B: $i, C: $i] : rewrite((in(A, set_difference(B, singleton(C))) <=> (in(A, B) & (~(A = C)))) <=> (in(A, set_difference(B, singleton(C))) <=> (~((~in(A, B)) | (A = C)))))),
% 0.16/0.39 inference(bind,[status(th)],[])).
% 0.16/0.39 tff(119,plain,
% 0.16/0.39 (![A: $i, B: $i, C: $i] : (in(A, set_difference(B, singleton(C))) <=> (in(A, B) & (~(A = C)))) <=> ![A: $i, B: $i, C: $i] : (in(A, set_difference(B, singleton(C))) <=> (~((~in(A, B)) | (A = C))))),
% 0.16/0.39 inference(quant_intro,[status(thm)],[118])).
% 0.16/0.39 tff(120,plain,
% 0.16/0.39 (![A: $i, B: $i, C: $i] : (in(A, set_difference(B, singleton(C))) <=> (in(A, B) & (~(A = C)))) <=> ![A: $i, B: $i, C: $i] : (in(A, set_difference(B, singleton(C))) <=> (in(A, B) & (~(A = C))))),
% 0.16/0.39 inference(rewrite,[status(thm)],[])).
% 0.16/0.39 tff(121,axiom,(![A: $i, B: $i, C: $i] : (in(A, set_difference(B, singleton(C))) <=> (in(A, B) & (~(A = C))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t64_zfmisc_1')).
% 0.16/0.39 tff(122,plain,
% 0.16/0.39 (![A: $i, B: $i, C: $i] : (in(A, set_difference(B, singleton(C))) <=> (in(A, B) & (~(A = C))))),
% 0.16/0.39 inference(modus_ponens,[status(thm)],[121, 120])).
% 0.16/0.39 tff(123,plain,(
% 0.16/0.39 ![A: $i, B: $i, C: $i] : (in(A, set_difference(B, singleton(C))) <=> (in(A, B) & (~(A = C))))),
% 0.16/0.39 inference(skolemize,[status(sab)],[122])).
% 0.16/0.39 tff(124,plain,
% 0.16/0.39 (![A: $i, B: $i, C: $i] : (in(A, set_difference(B, singleton(C))) <=> (~((~in(A, B)) | (A = C))))),
% 0.16/0.39 inference(modus_ponens,[status(thm)],[123, 119])).
% 0.16/0.39 tff(125,plain,
% 0.16/0.39 (![A: $i, B: $i, C: $i] : (in(A, set_difference(B, singleton(C))) <=> (~((~in(A, B)) | (A = C))))),
% 0.16/0.39 inference(modus_ponens,[status(thm)],[124, 117])).
% 0.16/0.39 tff(126,plain,
% 0.16/0.39 ((~![A: $i, B: $i, C: $i] : (in(A, set_difference(B, singleton(C))) <=> (~((~in(A, B)) | (A = C))))) | (in(tptp_fun_D_1(B!6, set_difference(B!6, singleton(A!7)), singleton(A!7)), set_difference(B!6, singleton(A!7))) <=> (~((~in(tptp_fun_D_1(B!6, set_difference(B!6, singleton(A!7)), singleton(A!7)), B!6)) | (tptp_fun_D_1(B!6, set_difference(B!6, singleton(A!7)), singleton(A!7)) = A!7))))),
% 0.16/0.39 inference(quant_inst,[status(thm)],[])).
% 0.16/0.39 tff(127,plain,
% 0.16/0.39 ($false),
% 0.16/0.39 inference(unit_resolution,[status(thm)],[126, 125, 115])).
% 0.16/0.39 tff(128,plain,(in(tptp_fun_D_1(B!6, set_difference(B!6, singleton(A!7)), singleton(A!7)), set_difference(B!6, singleton(A!7))) <=> (~((~in(tptp_fun_D_1(B!6, set_difference(B!6, singleton(A!7)), singleton(A!7)), B!6)) | (tptp_fun_D_1(B!6, set_difference(B!6, singleton(A!7)), singleton(A!7)) = A!7)))), inference(lemma,lemma(discharge,[]))).
% 0.16/0.39 tff(129,plain,
% 0.16/0.39 ((~(in(tptp_fun_D_1(B!6, set_difference(B!6, singleton(A!7)), singleton(A!7)), set_difference(B!6, singleton(A!7))) <=> (~((~in(tptp_fun_D_1(B!6, set_difference(B!6, singleton(A!7)), singleton(A!7)), B!6)) | (tptp_fun_D_1(B!6, set_difference(B!6, singleton(A!7)), singleton(A!7)) = A!7))))) | (~in(tptp_fun_D_1(B!6, set_difference(B!6, singleton(A!7)), singleton(A!7)), set_difference(B!6, singleton(A!7)))) | (~((~in(tptp_fun_D_1(B!6, set_difference(B!6, singleton(A!7)), singleton(A!7)), B!6)) | (tptp_fun_D_1(B!6, set_difference(B!6, singleton(A!7)), singleton(A!7)) = A!7)))),
% 0.16/0.39 inference(tautology,[status(thm)],[])).
% 0.16/0.39 tff(130,plain,
% 0.16/0.39 ((~in(tptp_fun_D_1(B!6, set_difference(B!6, singleton(A!7)), singleton(A!7)), set_difference(B!6, singleton(A!7)))) | (~((~in(tptp_fun_D_1(B!6, set_difference(B!6, singleton(A!7)), singleton(A!7)), B!6)) | (tptp_fun_D_1(B!6, set_difference(B!6, singleton(A!7)), singleton(A!7)) = A!7)))),
% 0.16/0.39 inference(unit_resolution,[status(thm)],[129, 128])).
% 0.16/0.39 tff(131,plain,
% 0.16/0.39 ($false),
% 0.16/0.39 inference(unit_resolution,[status(thm)],[130, 114, 53])).
% 0.16/0.39 tff(132,plain,(in(tptp_fun_D_1(B!6, set_difference(B!6, singleton(A!7)), singleton(A!7)), B!6) | in(tptp_fun_D_1(B!6, set_difference(B!6, singleton(A!7)), singleton(A!7)), singleton(A!7))), inference(lemma,lemma(discharge,[]))).
% 0.16/0.39 tff(133,plain,
% 0.16/0.39 (in(tptp_fun_D_1(B!6, set_difference(B!6, singleton(A!7)), singleton(A!7)), singleton(A!7))),
% 0.16/0.39 inference(unit_resolution,[status(thm)],[132, 51])).
% 0.16/0.39 tff(134,plain,
% 0.16/0.39 ((~(in(tptp_fun_D_1(B!6, set_difference(B!6, singleton(A!7)), singleton(A!7)), singleton(A!7)) <=> (tptp_fun_D_1(B!6, set_difference(B!6, singleton(A!7)), singleton(A!7)) = A!7))) | (~in(tptp_fun_D_1(B!6, set_difference(B!6, singleton(A!7)), singleton(A!7)), singleton(A!7))) | (tptp_fun_D_1(B!6, set_difference(B!6, singleton(A!7)), singleton(A!7)) = A!7)),
% 0.16/0.39 inference(tautology,[status(thm)],[])).
% 0.16/0.39 tff(135,plain,
% 0.16/0.39 (tptp_fun_D_1(B!6, set_difference(B!6, singleton(A!7)), singleton(A!7)) = A!7),
% 0.16/0.39 inference(unit_resolution,[status(thm)],[134, 133, 50])).
% 0.16/0.39 tff(136,plain,
% 0.16/0.39 (in(tptp_fun_D_1(B!6, set_difference(B!6, singleton(A!7)), singleton(A!7)), B!6) <=> in(A!7, B!6)),
% 0.16/0.39 inference(monotonicity,[status(thm)],[135])).
% 0.16/0.39 tff(137,plain,
% 0.16/0.39 (in(A!7, B!6) <=> in(tptp_fun_D_1(B!6, set_difference(B!6, singleton(A!7)), singleton(A!7)), B!6)),
% 0.16/0.39 inference(symmetry,[status(thm)],[136])).
% 0.16/0.39 tff(138,plain,
% 0.16/0.39 (in(A!7, B!6)),
% 0.16/0.39 inference(or_elim,[status(thm)],[105])).
% 0.16/0.39 tff(139,plain,
% 0.16/0.39 (in(tptp_fun_D_1(B!6, set_difference(B!6, singleton(A!7)), singleton(A!7)), B!6)),
% 0.16/0.39 inference(modus_ponens,[status(thm)],[138, 137])).
% 0.16/0.39 tff(140,plain,
% 0.16/0.39 ($false),
% 0.16/0.39 inference(unit_resolution,[status(thm)],[51, 139])).
% 0.16/0.39 tff(141,plain,(in(tptp_fun_D_1(B!6, set_difference(B!6, singleton(A!7)), singleton(A!7)), B!6)), inference(lemma,lemma(discharge,[]))).
% 0.16/0.39 tff(142,assumption,(~(tptp_fun_D_1(B!6, set_difference(B!6, singleton(A!7)), singleton(A!7)) = A!7)), introduced(assumption)).
% 0.16/0.39 tff(143,assumption,(in(tptp_fun_D_1(B!6, set_difference(B!6, singleton(A!7)), singleton(A!7)), B!6)), introduced(assumption)).
% 0.16/0.39 tff(144,plain,
% 0.16/0.39 ((~((~in(tptp_fun_D_1(B!6, set_difference(B!6, singleton(A!7)), singleton(A!7)), B!6)) | (tptp_fun_D_1(B!6, set_difference(B!6, singleton(A!7)), singleton(A!7)) = A!7))) | (~in(tptp_fun_D_1(B!6, set_difference(B!6, singleton(A!7)), singleton(A!7)), B!6)) | (tptp_fun_D_1(B!6, set_difference(B!6, singleton(A!7)), singleton(A!7)) = A!7)),
% 0.16/0.39 inference(tautology,[status(thm)],[])).
% 0.16/0.39 tff(145,plain,
% 0.16/0.39 (~((~in(tptp_fun_D_1(B!6, set_difference(B!6, singleton(A!7)), singleton(A!7)), B!6)) | (tptp_fun_D_1(B!6, set_difference(B!6, singleton(A!7)), singleton(A!7)) = A!7))),
% 0.16/0.39 inference(unit_resolution,[status(thm)],[144, 143, 142])).
% 0.16/0.39 tff(146,plain,
% 0.16/0.39 ((~((~in(tptp_fun_D_1(B!6, set_difference(B!6, singleton(A!7)), singleton(A!7)), B!6)) <=> (in(tptp_fun_D_1(B!6, set_difference(B!6, singleton(A!7)), singleton(A!7)), singleton(A!7)) | in(tptp_fun_D_1(B!6, set_difference(B!6, singleton(A!7)), singleton(A!7)), set_difference(B!6, singleton(A!7)))))) | (~in(tptp_fun_D_1(B!6, set_difference(B!6, singleton(A!7)), singleton(A!7)), B!6)) | (~(in(tptp_fun_D_1(B!6, set_difference(B!6, singleton(A!7)), singleton(A!7)), singleton(A!7)) | in(tptp_fun_D_1(B!6, set_difference(B!6, singleton(A!7)), singleton(A!7)), set_difference(B!6, singleton(A!7)))))),
% 0.16/0.39 inference(tautology,[status(thm)],[])).
% 0.16/0.39 tff(147,plain,
% 0.16/0.39 ((~in(tptp_fun_D_1(B!6, set_difference(B!6, singleton(A!7)), singleton(A!7)), B!6)) | (~(in(tptp_fun_D_1(B!6, set_difference(B!6, singleton(A!7)), singleton(A!7)), singleton(A!7)) | in(tptp_fun_D_1(B!6, set_difference(B!6, singleton(A!7)), singleton(A!7)), set_difference(B!6, singleton(A!7)))))),
% 0.16/0.39 inference(unit_resolution,[status(thm)],[146, 109])).
% 0.16/0.39 tff(148,plain,
% 0.16/0.39 (~(in(tptp_fun_D_1(B!6, set_difference(B!6, singleton(A!7)), singleton(A!7)), singleton(A!7)) | in(tptp_fun_D_1(B!6, set_difference(B!6, singleton(A!7)), singleton(A!7)), set_difference(B!6, singleton(A!7))))),
% 0.16/0.39 inference(unit_resolution,[status(thm)],[147, 143])).
% 0.16/0.39 tff(149,plain,
% 0.16/0.39 ((in(tptp_fun_D_1(B!6, set_difference(B!6, singleton(A!7)), singleton(A!7)), singleton(A!7)) | in(tptp_fun_D_1(B!6, set_difference(B!6, singleton(A!7)), singleton(A!7)), set_difference(B!6, singleton(A!7)))) | (~in(tptp_fun_D_1(B!6, set_difference(B!6, singleton(A!7)), singleton(A!7)), set_difference(B!6, singleton(A!7))))),
% 0.16/0.39 inference(tautology,[status(thm)],[])).
% 0.16/0.39 tff(150,plain,
% 0.16/0.39 (~in(tptp_fun_D_1(B!6, set_difference(B!6, singleton(A!7)), singleton(A!7)), set_difference(B!6, singleton(A!7)))),
% 0.16/0.39 inference(unit_resolution,[status(thm)],[149, 148])).
% 0.16/0.39 tff(151,plain,
% 0.16/0.39 ((~(in(tptp_fun_D_1(B!6, set_difference(B!6, singleton(A!7)), singleton(A!7)), set_difference(B!6, singleton(A!7))) <=> (~((~in(tptp_fun_D_1(B!6, set_difference(B!6, singleton(A!7)), singleton(A!7)), B!6)) | (tptp_fun_D_1(B!6, set_difference(B!6, singleton(A!7)), singleton(A!7)) = A!7))))) | in(tptp_fun_D_1(B!6, set_difference(B!6, singleton(A!7)), singleton(A!7)), set_difference(B!6, singleton(A!7))) | ((~in(tptp_fun_D_1(B!6, set_difference(B!6, singleton(A!7)), singleton(A!7)), B!6)) | (tptp_fun_D_1(B!6, set_difference(B!6, singleton(A!7)), singleton(A!7)) = A!7))),
% 0.16/0.39 inference(tautology,[status(thm)],[])).
% 0.16/0.39 tff(152,plain,
% 0.16/0.39 (in(tptp_fun_D_1(B!6, set_difference(B!6, singleton(A!7)), singleton(A!7)), set_difference(B!6, singleton(A!7))) | ((~in(tptp_fun_D_1(B!6, set_difference(B!6, singleton(A!7)), singleton(A!7)), B!6)) | (tptp_fun_D_1(B!6, set_difference(B!6, singleton(A!7)), singleton(A!7)) = A!7))),
% 0.16/0.39 inference(unit_resolution,[status(thm)],[151, 128])).
% 0.16/0.39 tff(153,plain,
% 0.16/0.39 ($false),
% 0.16/0.39 inference(unit_resolution,[status(thm)],[152, 150, 145])).
% 0.16/0.39 tff(154,plain,((~in(tptp_fun_D_1(B!6, set_difference(B!6, singleton(A!7)), singleton(A!7)), B!6)) | (tptp_fun_D_1(B!6, set_difference(B!6, singleton(A!7)), singleton(A!7)) = A!7)), inference(lemma,lemma(discharge,[]))).
% 0.16/0.39 tff(155,plain,
% 0.16/0.39 (tptp_fun_D_1(B!6, set_difference(B!6, singleton(A!7)), singleton(A!7)) = A!7),
% 0.16/0.39 inference(unit_resolution,[status(thm)],[154, 141])).
% 0.16/0.39 tff(156,plain,
% 0.16/0.39 (~(in(tptp_fun_D_1(B!6, set_difference(B!6, singleton(A!7)), singleton(A!7)), singleton(A!7)) | in(tptp_fun_D_1(B!6, set_difference(B!6, singleton(A!7)), singleton(A!7)), set_difference(B!6, singleton(A!7))))),
% 0.16/0.39 inference(unit_resolution,[status(thm)],[147, 141])).
% 0.16/0.39 tff(157,plain,
% 0.16/0.39 ((in(tptp_fun_D_1(B!6, set_difference(B!6, singleton(A!7)), singleton(A!7)), singleton(A!7)) | in(tptp_fun_D_1(B!6, set_difference(B!6, singleton(A!7)), singleton(A!7)), set_difference(B!6, singleton(A!7)))) | (~in(tptp_fun_D_1(B!6, set_difference(B!6, singleton(A!7)), singleton(A!7)), singleton(A!7)))),
% 0.16/0.39 inference(tautology,[status(thm)],[])).
% 0.16/0.39 tff(158,plain,
% 0.16/0.39 (~in(tptp_fun_D_1(B!6, set_difference(B!6, singleton(A!7)), singleton(A!7)), singleton(A!7))),
% 0.16/0.39 inference(unit_resolution,[status(thm)],[157, 156])).
% 0.16/0.39 tff(159,plain,
% 0.16/0.39 ((~(in(tptp_fun_D_1(B!6, set_difference(B!6, singleton(A!7)), singleton(A!7)), singleton(A!7)) <=> (tptp_fun_D_1(B!6, set_difference(B!6, singleton(A!7)), singleton(A!7)) = A!7))) | in(tptp_fun_D_1(B!6, set_difference(B!6, singleton(A!7)), singleton(A!7)), singleton(A!7)) | (~(tptp_fun_D_1(B!6, set_difference(B!6, singleton(A!7)), singleton(A!7)) = A!7))),
% 0.16/0.39 inference(tautology,[status(thm)],[])).
% 0.16/0.39 tff(160,plain,
% 0.16/0.39 ($false),
% 0.16/0.39 inference(unit_resolution,[status(thm)],[159, 158, 155, 50])).
% 0.16/0.39 % SZS output end Proof
%------------------------------------------------------------------------------