TSTP Solution File: SET921+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SET921+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n008.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 05:08:38 EDT 2022
% Result : Theorem 0.12s 0.38s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : SET921+1 : TPTP v8.1.0. Released v3.2.0.
% 0.06/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n008.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Sat Sep 3 08:37:25 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.33 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.33 Usage: tptp [options] [-file:]file
% 0.12/0.33 -h, -? prints this message.
% 0.12/0.33 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.33 -m, -model generate model.
% 0.12/0.33 -p, -proof generate proof.
% 0.12/0.33 -c, -core generate unsat core of named formulas.
% 0.12/0.33 -st, -statistics display statistics.
% 0.12/0.33 -t:timeout set timeout (in second).
% 0.12/0.33 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.33 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.33 -<param>:<value> configuration parameter and value.
% 0.12/0.33 -o:<output-file> file to place output in.
% 0.12/0.38 % SZS status Theorem
% 0.12/0.38 % SZS output start Proof
% 0.12/0.38 tff(tptp_fun_C_4_type, type, (
% 0.12/0.38 tptp_fun_C_4: $i)).
% 0.12/0.38 tff(tptp_fun_A_6_type, type, (
% 0.12/0.38 tptp_fun_A_6: $i)).
% 0.12/0.38 tff(in_type, type, (
% 0.12/0.38 in: ( $i * $i ) > $o)).
% 0.12/0.38 tff(singleton_type, type, (
% 0.12/0.38 singleton: $i > $i)).
% 0.12/0.38 tff(tptp_fun_C_0_type, type, (
% 0.12/0.38 tptp_fun_C_0: ( $i * $i ) > $i)).
% 0.12/0.38 tff(tptp_fun_B_5_type, type, (
% 0.12/0.38 tptp_fun_B_5: $i)).
% 0.12/0.38 tff(set_difference_type, type, (
% 0.12/0.38 set_difference: ( $i * $i ) > $i)).
% 0.12/0.38 tff(tptp_fun_D_1_type, type, (
% 0.12/0.38 tptp_fun_D_1: ( $i * $i * $i ) > $i)).
% 0.12/0.38 tff(1,assumption,(~(in(A!6, singleton(C!4)) <=> (A!6 = C!4))), introduced(assumption)).
% 0.12/0.38 tff(2,plain,
% 0.12/0.38 (^[A: $i, B: $i, C: $i] : refl((~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A)))))) <=> (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A)))))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(3,plain,
% 0.12/0.38 (![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A)))))) <=> ![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[2])).
% 0.12/0.38 tff(4,plain,
% 0.12/0.38 (![A: $i, B: $i] : ![C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A)))))) <=> ![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))))),
% 0.12/0.38 inference(pull_quant,[status(thm)],[])).
% 0.12/0.38 tff(5,plain,
% 0.12/0.38 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(pull_quant(((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A))) <=> ![C: $i] : ((~(B = singleton(A))) | (in(C, B) <=> (C = A)))), ((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) <=> (~![C: $i] : ((~(B = singleton(A))) | (in(C, B) <=> (C = A)))))), pull_quant((~![C: $i] : ((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) <=> ?[C: $i] : (~((~(B = singleton(A))) | (in(C, B) <=> (C = A))))), ((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) <=> ?[C: $i] : (~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))))), (((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))) <=> (?[C: $i] : (~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))))), pull_quant((?[C: $i] : (~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))) <=> ?[C: $i] : ((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A)))))), (((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))) <=> ?[C: $i] : ((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))))), ((~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A)))))) <=> (~?[C: $i] : ((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A)))))))), pull_quant((~?[C: $i] : ((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A)))))) <=> ![C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))))), ((~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A)))))) <=> ![C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(6,plain,
% 0.12/0.38 (![A: $i, B: $i] : (~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A)))))) <=> ![A: $i, B: $i] : ![C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[5])).
% 0.12/0.38 tff(7,plain,
% 0.12/0.38 (![A: $i, B: $i] : (~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A)))))) <=> ![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))))),
% 0.12/0.38 inference(transitivity,[status(thm)],[6, 4])).
% 0.12/0.38 tff(8,plain,
% 0.12/0.38 (![A: $i, B: $i] : (~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A)))))) <=> ![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))))),
% 0.12/0.38 inference(transitivity,[status(thm)],[7, 3])).
% 0.12/0.38 tff(9,plain,
% 0.12/0.38 (^[A: $i, B: $i] : rewrite((~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A)))))) <=> (~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A)))))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(10,plain,
% 0.12/0.38 (![A: $i, B: $i] : (~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A)))))) <=> ![A: $i, B: $i] : (~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[9])).
% 0.12/0.38 tff(11,plain,
% 0.12/0.38 (![A: $i, B: $i] : (~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A)))))) <=> ![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))))),
% 0.12/0.38 inference(transitivity,[status(thm)],[10, 8])).
% 0.12/0.38 tff(12,plain,
% 0.12/0.38 (^[A: $i, B: $i] : trans(monotonicity(rewrite(((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A))) <=> ((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))), ((((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A))) & ((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A)))) <=> (((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A))) & ((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A)))))), rewrite((((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A))) & ((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A)))) <=> (~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))))), ((((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A))) & ((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A)))) <=> (~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(13,plain,
% 0.12/0.38 (![A: $i, B: $i] : (((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A))) & ((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A)))) <=> ![A: $i, B: $i] : (~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))))),
% 0.19/0.38 inference(quant_intro,[status(thm)],[12])).
% 0.19/0.38 tff(14,plain,
% 0.19/0.38 (^[A: $i, B: $i] : rewrite((((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A))) & ((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A))))) <=> (((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A))) & ((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A)))))),
% 0.19/0.38 inference(bind,[status(th)],[])).
% 0.19/0.38 tff(15,plain,
% 0.19/0.38 (![A: $i, B: $i] : (((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A))) & ((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A))))) <=> ![A: $i, B: $i] : (((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A))) & ((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))),
% 0.19/0.38 inference(quant_intro,[status(thm)],[14])).
% 0.19/0.38 tff(16,plain,
% 0.19/0.38 (![A: $i, B: $i] : ((B = singleton(A)) <=> ![C: $i] : (in(C, B) <=> (C = A))) <=> ![A: $i, B: $i] : ((B = singleton(A)) <=> ![C: $i] : (in(C, B) <=> (C = A)))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(17,axiom,(![A: $i, B: $i] : ((B = singleton(A)) <=> ![C: $i] : (in(C, B) <=> (C = A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d1_tarski')).
% 0.19/0.38 tff(18,plain,
% 0.19/0.38 (![A: $i, B: $i] : ((B = singleton(A)) <=> ![C: $i] : (in(C, B) <=> (C = A)))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[17, 16])).
% 0.19/0.38 tff(19,plain,(
% 0.19/0.38 ![A: $i, B: $i] : (((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A))) & ((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))),
% 0.19/0.38 inference(skolemize,[status(sab)],[18])).
% 0.19/0.38 tff(20,plain,
% 0.19/0.38 (![A: $i, B: $i] : (((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A))) & ((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[19, 15])).
% 0.19/0.38 tff(21,plain,
% 0.19/0.38 (![A: $i, B: $i] : (~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[20, 13])).
% 0.19/0.38 tff(22,plain,
% 0.19/0.38 (![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[21, 11])).
% 0.19/0.38 tff(23,plain,
% 0.19/0.38 (((~![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))))) | (in(A!6, singleton(C!4)) <=> (A!6 = C!4))) <=> ((~![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(C!4)) <=> (A!6 = C!4)))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(24,plain,
% 0.19/0.38 ((~((~in(A!6, singleton(C!4))) <=> (A!6 = C!4))) <=> (in(A!6, singleton(C!4)) <=> (A!6 = C!4))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(25,plain,
% 0.19/0.38 ((((~in(A!6, singleton(C!4))) <=> (A!6 = C!4)) | $false) <=> ((~in(A!6, singleton(C!4))) <=> (A!6 = C!4))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(26,plain,
% 0.19/0.38 ((~$true) <=> $false),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(27,plain,
% 0.19/0.38 (($true | ((~in(tptp_fun_C_0(singleton(C!4), C!4), singleton(C!4))) <=> (tptp_fun_C_0(singleton(C!4), C!4) = C!4))) <=> $true),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(28,plain,
% 0.19/0.38 ((singleton(C!4) = singleton(C!4)) <=> $true),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(29,plain,
% 0.19/0.38 (((singleton(C!4) = singleton(C!4)) | ((~in(tptp_fun_C_0(singleton(C!4), C!4), singleton(C!4))) <=> (tptp_fun_C_0(singleton(C!4), C!4) = C!4))) <=> ($true | ((~in(tptp_fun_C_0(singleton(C!4), C!4), singleton(C!4))) <=> (tptp_fun_C_0(singleton(C!4), C!4) = C!4)))),
% 0.19/0.38 inference(monotonicity,[status(thm)],[28])).
% 0.19/0.39 tff(30,plain,
% 0.19/0.39 (((singleton(C!4) = singleton(C!4)) | ((~in(tptp_fun_C_0(singleton(C!4), C!4), singleton(C!4))) <=> (tptp_fun_C_0(singleton(C!4), C!4) = C!4))) <=> $true),
% 0.19/0.39 inference(transitivity,[status(thm)],[29, 27])).
% 0.19/0.39 tff(31,plain,
% 0.19/0.39 ((~((singleton(C!4) = singleton(C!4)) | ((~in(tptp_fun_C_0(singleton(C!4), C!4), singleton(C!4))) <=> (tptp_fun_C_0(singleton(C!4), C!4) = C!4)))) <=> (~$true)),
% 0.19/0.39 inference(monotonicity,[status(thm)],[30])).
% 0.19/0.39 tff(32,plain,
% 0.19/0.39 ((~((singleton(C!4) = singleton(C!4)) | ((~in(tptp_fun_C_0(singleton(C!4), C!4), singleton(C!4))) <=> (tptp_fun_C_0(singleton(C!4), C!4) = C!4)))) <=> $false),
% 0.19/0.39 inference(transitivity,[status(thm)],[31, 26])).
% 0.19/0.39 tff(33,plain,
% 0.19/0.39 ((~(in(A!6, singleton(C!4)) <=> (A!6 = C!4))) <=> ((~in(A!6, singleton(C!4))) <=> (A!6 = C!4))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(34,plain,
% 0.19/0.39 (($false | (in(A!6, singleton(C!4)) <=> (A!6 = C!4))) <=> (in(A!6, singleton(C!4)) <=> (A!6 = C!4))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(35,plain,
% 0.19/0.39 ((~(singleton(C!4) = singleton(C!4))) <=> (~$true)),
% 0.19/0.39 inference(monotonicity,[status(thm)],[28])).
% 0.19/0.39 tff(36,plain,
% 0.19/0.39 ((~(singleton(C!4) = singleton(C!4))) <=> $false),
% 0.19/0.39 inference(transitivity,[status(thm)],[35, 26])).
% 0.19/0.39 tff(37,plain,
% 0.19/0.39 (((~(singleton(C!4) = singleton(C!4))) | (in(A!6, singleton(C!4)) <=> (A!6 = C!4))) <=> ($false | (in(A!6, singleton(C!4)) <=> (A!6 = C!4)))),
% 0.19/0.39 inference(monotonicity,[status(thm)],[36])).
% 0.19/0.39 tff(38,plain,
% 0.19/0.39 (((~(singleton(C!4) = singleton(C!4))) | (in(A!6, singleton(C!4)) <=> (A!6 = C!4))) <=> (in(A!6, singleton(C!4)) <=> (A!6 = C!4))),
% 0.19/0.39 inference(transitivity,[status(thm)],[37, 34])).
% 0.19/0.39 tff(39,plain,
% 0.19/0.39 ((~((~(singleton(C!4) = singleton(C!4))) | (in(A!6, singleton(C!4)) <=> (A!6 = C!4)))) <=> (~(in(A!6, singleton(C!4)) <=> (A!6 = C!4)))),
% 0.19/0.39 inference(monotonicity,[status(thm)],[38])).
% 0.19/0.39 tff(40,plain,
% 0.19/0.39 ((~((~(singleton(C!4) = singleton(C!4))) | (in(A!6, singleton(C!4)) <=> (A!6 = C!4)))) <=> ((~in(A!6, singleton(C!4))) <=> (A!6 = C!4))),
% 0.19/0.39 inference(transitivity,[status(thm)],[39, 33])).
% 0.19/0.39 tff(41,plain,
% 0.19/0.39 (((~((~(singleton(C!4) = singleton(C!4))) | (in(A!6, singleton(C!4)) <=> (A!6 = C!4)))) | (~((singleton(C!4) = singleton(C!4)) | ((~in(tptp_fun_C_0(singleton(C!4), C!4), singleton(C!4))) <=> (tptp_fun_C_0(singleton(C!4), C!4) = C!4))))) <=> (((~in(A!6, singleton(C!4))) <=> (A!6 = C!4)) | $false)),
% 0.19/0.39 inference(monotonicity,[status(thm)],[40, 32])).
% 0.19/0.39 tff(42,plain,
% 0.19/0.39 (((~((~(singleton(C!4) = singleton(C!4))) | (in(A!6, singleton(C!4)) <=> (A!6 = C!4)))) | (~((singleton(C!4) = singleton(C!4)) | ((~in(tptp_fun_C_0(singleton(C!4), C!4), singleton(C!4))) <=> (tptp_fun_C_0(singleton(C!4), C!4) = C!4))))) <=> ((~in(A!6, singleton(C!4))) <=> (A!6 = C!4))),
% 0.19/0.39 inference(transitivity,[status(thm)],[41, 25])).
% 0.19/0.39 tff(43,plain,
% 0.19/0.39 ((~((~((~(singleton(C!4) = singleton(C!4))) | (in(A!6, singleton(C!4)) <=> (A!6 = C!4)))) | (~((singleton(C!4) = singleton(C!4)) | ((~in(tptp_fun_C_0(singleton(C!4), C!4), singleton(C!4))) <=> (tptp_fun_C_0(singleton(C!4), C!4) = C!4)))))) <=> (~((~in(A!6, singleton(C!4))) <=> (A!6 = C!4)))),
% 0.19/0.39 inference(monotonicity,[status(thm)],[42])).
% 0.19/0.39 tff(44,plain,
% 0.19/0.39 ((~((~((~(singleton(C!4) = singleton(C!4))) | (in(A!6, singleton(C!4)) <=> (A!6 = C!4)))) | (~((singleton(C!4) = singleton(C!4)) | ((~in(tptp_fun_C_0(singleton(C!4), C!4), singleton(C!4))) <=> (tptp_fun_C_0(singleton(C!4), C!4) = C!4)))))) <=> (in(A!6, singleton(C!4)) <=> (A!6 = C!4))),
% 0.19/0.39 inference(transitivity,[status(thm)],[43, 24])).
% 0.19/0.39 tff(45,plain,
% 0.19/0.39 (((~![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))))) | (~((~((~(singleton(C!4) = singleton(C!4))) | (in(A!6, singleton(C!4)) <=> (A!6 = C!4)))) | (~((singleton(C!4) = singleton(C!4)) | ((~in(tptp_fun_C_0(singleton(C!4), C!4), singleton(C!4))) <=> (tptp_fun_C_0(singleton(C!4), C!4) = C!4))))))) <=> ((~![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(C!4)) <=> (A!6 = C!4)))),
% 0.19/0.39 inference(monotonicity,[status(thm)],[44])).
% 0.19/0.39 tff(46,plain,
% 0.19/0.39 (((~![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))))) | (~((~((~(singleton(C!4) = singleton(C!4))) | (in(A!6, singleton(C!4)) <=> (A!6 = C!4)))) | (~((singleton(C!4) = singleton(C!4)) | ((~in(tptp_fun_C_0(singleton(C!4), C!4), singleton(C!4))) <=> (tptp_fun_C_0(singleton(C!4), C!4) = C!4))))))) <=> ((~![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(C!4)) <=> (A!6 = C!4)))),
% 0.19/0.39 inference(transitivity,[status(thm)],[45, 23])).
% 0.19/0.39 tff(47,plain,
% 0.19/0.39 ((~![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))))) | (~((~((~(singleton(C!4) = singleton(C!4))) | (in(A!6, singleton(C!4)) <=> (A!6 = C!4)))) | (~((singleton(C!4) = singleton(C!4)) | ((~in(tptp_fun_C_0(singleton(C!4), C!4), singleton(C!4))) <=> (tptp_fun_C_0(singleton(C!4), C!4) = C!4))))))),
% 0.19/0.39 inference(quant_inst,[status(thm)],[])).
% 0.19/0.39 tff(48,plain,
% 0.19/0.39 ((~![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))))) | (in(A!6, singleton(C!4)) <=> (A!6 = C!4))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[47, 46])).
% 0.19/0.39 tff(49,plain,
% 0.19/0.39 ($false),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[48, 22, 1])).
% 0.19/0.39 tff(50,plain,(in(A!6, singleton(C!4)) <=> (A!6 = C!4)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.39 tff(51,assumption,(~in(A!6, set_difference(B!5, singleton(C!4)))), introduced(assumption)).
% 0.19/0.39 tff(52,plain,
% 0.19/0.39 (((~in(A!6, set_difference(B!5, singleton(C!4)))) <=> (~((~in(A!6, B!5)) | (A!6 = C!4)))) <=> (in(A!6, set_difference(B!5, singleton(C!4))) <=> ((~in(A!6, B!5)) | (A!6 = C!4)))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(53,plain,
% 0.19/0.39 ((in(A!6, B!5) & (~(A!6 = C!4))) <=> (~((~in(A!6, B!5)) | (A!6 = C!4)))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(54,plain,
% 0.19/0.39 (((~in(A!6, set_difference(B!5, singleton(C!4)))) <=> (in(A!6, B!5) & (~(A!6 = C!4)))) <=> ((~in(A!6, set_difference(B!5, singleton(C!4)))) <=> (~((~in(A!6, B!5)) | (A!6 = C!4))))),
% 0.19/0.39 inference(monotonicity,[status(thm)],[53])).
% 0.19/0.39 tff(55,plain,
% 0.19/0.39 (((~in(A!6, set_difference(B!5, singleton(C!4)))) <=> (in(A!6, B!5) & (~(A!6 = C!4)))) <=> (in(A!6, set_difference(B!5, singleton(C!4))) <=> ((~in(A!6, B!5)) | (A!6 = C!4)))),
% 0.19/0.39 inference(transitivity,[status(thm)],[54, 52])).
% 0.19/0.39 tff(56,plain,
% 0.19/0.39 ((~(in(A!6, set_difference(B!5, singleton(C!4))) <=> (in(A!6, B!5) & (~(A!6 = C!4))))) <=> ((~in(A!6, set_difference(B!5, singleton(C!4)))) <=> (in(A!6, B!5) & (~(A!6 = C!4))))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(57,plain,
% 0.19/0.39 ((~![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)))))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(58,axiom,(~![A: $i, B: $i, C: $i] : (in(A, set_difference(B, singleton(C))) <=> (in(A, B) & (~(A = C))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t64_zfmisc_1')).
% 0.19/0.39 tff(59,plain,
% 0.19/0.39 (~![A: $i, B: $i, C: $i] : (in(A, set_difference(B, singleton(C))) <=> (in(A, B) & (~(A = C))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[58, 57])).
% 0.19/0.39 tff(60,plain,
% 0.19/0.39 (~![A: $i, B: $i, C: $i] : (in(A, set_difference(B, singleton(C))) <=> (in(A, B) & (~(A = C))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[59, 57])).
% 0.19/0.39 tff(61,plain,
% 0.19/0.39 (~![A: $i, B: $i, C: $i] : (in(A, set_difference(B, singleton(C))) <=> (in(A, B) & (~(A = C))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[60, 57])).
% 0.19/0.39 tff(62,plain,
% 0.19/0.39 (~![A: $i, B: $i, C: $i] : (in(A, set_difference(B, singleton(C))) <=> (in(A, B) & (~(A = C))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[61, 57])).
% 0.19/0.39 tff(63,plain,
% 0.19/0.39 (~![A: $i, B: $i, C: $i] : (in(A, set_difference(B, singleton(C))) <=> (in(A, B) & (~(A = C))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[62, 57])).
% 0.19/0.39 tff(64,plain,
% 0.19/0.39 (~![A: $i, B: $i, C: $i] : (in(A, set_difference(B, singleton(C))) <=> (in(A, B) & (~(A = C))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[63, 57])).
% 0.19/0.39 tff(65,plain,
% 0.19/0.39 (~![A: $i, B: $i, C: $i] : (in(A, set_difference(B, singleton(C))) <=> (in(A, B) & (~(A = C))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[64, 57])).
% 0.19/0.39 tff(66,plain,(
% 0.19/0.39 ~(in(A!6, set_difference(B!5, singleton(C!4))) <=> (in(A!6, B!5) & (~(A!6 = C!4))))),
% 0.19/0.39 inference(skolemize,[status(sab)],[65])).
% 0.19/0.39 tff(67,plain,
% 0.19/0.39 ((~in(A!6, set_difference(B!5, singleton(C!4)))) <=> (in(A!6, B!5) & (~(A!6 = C!4)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[66, 56])).
% 0.19/0.39 tff(68,plain,
% 0.19/0.39 (in(A!6, set_difference(B!5, singleton(C!4))) <=> ((~in(A!6, B!5)) | (A!6 = C!4))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[67, 55])).
% 0.19/0.39 tff(69,plain,
% 0.19/0.39 (in(A!6, set_difference(B!5, singleton(C!4))) | (~((~in(A!6, B!5)) | (A!6 = C!4))) | (~(in(A!6, set_difference(B!5, singleton(C!4))) <=> ((~in(A!6, B!5)) | (A!6 = C!4))))),
% 0.19/0.39 inference(tautology,[status(thm)],[])).
% 0.19/0.39 tff(70,plain,
% 0.19/0.39 (in(A!6, set_difference(B!5, singleton(C!4))) | (~((~in(A!6, B!5)) | (A!6 = C!4)))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[69, 68])).
% 0.19/0.39 tff(71,plain,
% 0.19/0.39 (~((~in(A!6, B!5)) | (A!6 = C!4))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[70, 51])).
% 0.19/0.39 tff(72,plain,
% 0.19/0.39 (((~in(A!6, B!5)) | (A!6 = C!4)) | (~(A!6 = C!4))),
% 0.19/0.39 inference(tautology,[status(thm)],[])).
% 0.19/0.39 tff(73,plain,
% 0.19/0.39 (~(A!6 = C!4)),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[72, 71])).
% 0.19/0.39 tff(74,plain,
% 0.19/0.39 (((~in(A!6, B!5)) | (A!6 = C!4)) | in(A!6, B!5)),
% 0.19/0.39 inference(tautology,[status(thm)],[])).
% 0.19/0.39 tff(75,plain,
% 0.19/0.39 (in(A!6, B!5)),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[74, 71])).
% 0.19/0.39 tff(76,plain,
% 0.19/0.39 (^[A: $i, B: $i, C: $i, D: $i] : refl((~((~((~(C = set_difference(A, B))) | (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(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_difference(A, B))) | (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(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))))))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(77,plain,
% 0.19/0.39 (![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_difference(A, B))) | (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(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_difference(A, B))) | (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(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)))))))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[76])).
% 0.19/0.39 tff(78,plain,
% 0.19/0.39 (![A: $i, B: $i, C: $i] : ![D: $i] : (~((~((~(C = set_difference(A, B))) | (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(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_difference(A, B))) | (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(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)))))))),
% 0.19/0.39 inference(pull_quant,[status(thm)],[])).
% 0.19/0.39 tff(79,plain,
% 0.19/0.39 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(pull_quant(((~(C = set_difference(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, A)) | in(D, B))))) <=> ![D: $i] : ((~(C = set_difference(A, B))) | (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))), ((~((~(C = set_difference(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) <=> (~![D: $i] : ((~(C = set_difference(A, B))) | (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))))), pull_quant((~![D: $i] : ((~(C = set_difference(A, B))) | (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) <=> ?[D: $i] : (~((~(C = set_difference(A, B))) | (in(D, C) <=> (~((~in(D, A)) | in(D, B))))))), ((~((~(C = set_difference(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) <=> ?[D: $i] : (~((~(C = set_difference(A, B))) | (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))))), (((~((~(C = set_difference(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(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_difference(A, B))) | (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(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_difference(A, B))) | (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(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_difference(A, B))) | (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(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_difference(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(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_difference(A, B))) | (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(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_difference(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(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_difference(A, B))) | (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(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_difference(A, B))) | (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(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_difference(A, B))) | (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(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_difference(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(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_difference(A, B))) | (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(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)))))))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(80,plain,
% 0.19/0.39 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_difference(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(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_difference(A, B))) | (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(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)))))))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[79])).
% 0.19/0.39 tff(81,plain,
% 0.19/0.39 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_difference(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(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_difference(A, B))) | (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(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)))))))),
% 0.19/0.39 inference(transitivity,[status(thm)],[80, 78])).
% 0.19/0.39 tff(82,plain,
% 0.19/0.39 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_difference(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(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_difference(A, B))) | (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(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)))))))),
% 0.19/0.39 inference(transitivity,[status(thm)],[81, 77])).
% 0.19/0.39 tff(83,plain,
% 0.19/0.39 (^[A: $i, B: $i, C: $i] : rewrite((~((~((~(C = set_difference(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(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_difference(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(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))))))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(84,plain,
% 0.19/0.39 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_difference(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(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_difference(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(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)))))))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[83])).
% 0.19/0.39 tff(85,plain,
% 0.19/0.39 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_difference(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(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_difference(A, B))) | (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(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)))))))),
% 0.19/0.39 inference(transitivity,[status(thm)],[84, 82])).
% 0.19/0.39 tff(86,plain,
% 0.19/0.39 (^[A: $i, B: $i, C: $i] : trans(monotonicity(rewrite(((~(C = set_difference(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) & (~in(D, B))))) <=> ((~(C = set_difference(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))), rewrite(((C = set_difference(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_difference(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_difference(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) & (~in(D, B))))) & ((C = set_difference(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_difference(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, A)) | in(D, B))))) & ((C = set_difference(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_difference(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, A)) | in(D, B))))) & ((C = set_difference(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_difference(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(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_difference(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) & (~in(D, B))))) & ((C = set_difference(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_difference(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(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)))))))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(87,plain,
% 0.19/0.40 (![A: $i, B: $i, C: $i] : (((~(C = set_difference(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) & (~in(D, B))))) & ((C = set_difference(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_difference(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(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)))))))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[86])).
% 0.19/0.40 tff(88,plain,
% 0.19/0.40 (^[A: $i, B: $i, C: $i] : rewrite((((~(C = set_difference(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) & (~in(D, B))))) & ((C = set_difference(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_difference(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) & (~in(D, B))))) & ((C = set_difference(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)))))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(89,plain,
% 0.19/0.40 (![A: $i, B: $i, C: $i] : (((~(C = set_difference(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) & (~in(D, B))))) & ((C = set_difference(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_difference(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) & (~in(D, B))))) & ((C = set_difference(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))))))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[88])).
% 0.19/0.40 tff(90,plain,
% 0.19/0.40 (![A: $i, B: $i, C: $i] : ((C = set_difference(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, A) & (~in(D, B))))) <=> ![A: $i, B: $i, C: $i] : ((C = set_difference(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, A) & (~in(D, B)))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(91,axiom,(![A: $i, B: $i, C: $i] : ((C = set_difference(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, A) & (~in(D, B)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d4_xboole_0')).
% 0.19/0.40 tff(92,plain,
% 0.19/0.40 (![A: $i, B: $i, C: $i] : ((C = set_difference(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, A) & (~in(D, B)))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[91, 90])).
% 0.19/0.40 tff(93,plain,(
% 0.19/0.40 ![A: $i, B: $i, C: $i] : (((~(C = set_difference(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) & (~in(D, B))))) & ((C = set_difference(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)))))))),
% 0.19/0.40 inference(skolemize,[status(sab)],[92])).
% 0.19/0.40 tff(94,plain,
% 0.19/0.40 (![A: $i, B: $i, C: $i] : (((~(C = set_difference(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) & (~in(D, B))))) & ((C = set_difference(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))))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[93, 89])).
% 0.19/0.40 tff(95,plain,
% 0.19/0.40 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_difference(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(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)))))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[94, 87])).
% 0.19/0.40 tff(96,plain,
% 0.19/0.40 (![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_difference(A, B))) | (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(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)))))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[95, 85])).
% 0.19/0.40 tff(97,plain,
% 0.19/0.40 (((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_difference(A, B))) | (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(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)))))))) | ((~in(A!6, set_difference(B!5, singleton(C!4)))) <=> ((~in(A!6, B!5)) | in(A!6, singleton(C!4))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_difference(A, B))) | (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(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)))))))) | ((~in(A!6, set_difference(B!5, singleton(C!4)))) <=> ((~in(A!6, B!5)) | in(A!6, singleton(C!4)))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(98,plain,
% 0.19/0.40 ((~(in(A!6, set_difference(B!5, singleton(C!4))) <=> ((~in(A!6, B!5)) | in(A!6, singleton(C!4))))) <=> ((~in(A!6, set_difference(B!5, singleton(C!4)))) <=> ((~in(A!6, B!5)) | in(A!6, singleton(C!4))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(99,plain,
% 0.19/0.40 (((in(A!6, set_difference(B!5, singleton(C!4))) <=> ((~in(A!6, B!5)) | in(A!6, singleton(C!4)))) | $false) <=> (in(A!6, set_difference(B!5, singleton(C!4))) <=> ((~in(A!6, B!5)) | in(A!6, singleton(C!4))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(100,plain,
% 0.19/0.40 (($true | (in(tptp_fun_D_1(set_difference(B!5, singleton(C!4)), singleton(C!4), B!5), set_difference(B!5, singleton(C!4))) <=> ((~in(tptp_fun_D_1(set_difference(B!5, singleton(C!4)), singleton(C!4), B!5), B!5)) | in(tptp_fun_D_1(set_difference(B!5, singleton(C!4)), singleton(C!4), B!5), singleton(C!4))))) <=> $true),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(101,plain,
% 0.19/0.40 ((set_difference(B!5, singleton(C!4)) = set_difference(B!5, singleton(C!4))) <=> $true),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(102,plain,
% 0.19/0.40 (((set_difference(B!5, singleton(C!4)) = set_difference(B!5, singleton(C!4))) | (in(tptp_fun_D_1(set_difference(B!5, singleton(C!4)), singleton(C!4), B!5), set_difference(B!5, singleton(C!4))) <=> ((~in(tptp_fun_D_1(set_difference(B!5, singleton(C!4)), singleton(C!4), B!5), B!5)) | in(tptp_fun_D_1(set_difference(B!5, singleton(C!4)), singleton(C!4), B!5), singleton(C!4))))) <=> ($true | (in(tptp_fun_D_1(set_difference(B!5, singleton(C!4)), singleton(C!4), B!5), set_difference(B!5, singleton(C!4))) <=> ((~in(tptp_fun_D_1(set_difference(B!5, singleton(C!4)), singleton(C!4), B!5), B!5)) | in(tptp_fun_D_1(set_difference(B!5, singleton(C!4)), singleton(C!4), B!5), singleton(C!4)))))),
% 0.19/0.40 inference(monotonicity,[status(thm)],[101])).
% 0.19/0.40 tff(103,plain,
% 0.19/0.40 (((set_difference(B!5, singleton(C!4)) = set_difference(B!5, singleton(C!4))) | (in(tptp_fun_D_1(set_difference(B!5, singleton(C!4)), singleton(C!4), B!5), set_difference(B!5, singleton(C!4))) <=> ((~in(tptp_fun_D_1(set_difference(B!5, singleton(C!4)), singleton(C!4), B!5), B!5)) | in(tptp_fun_D_1(set_difference(B!5, singleton(C!4)), singleton(C!4), B!5), singleton(C!4))))) <=> $true),
% 0.19/0.40 inference(transitivity,[status(thm)],[102, 100])).
% 0.19/0.40 tff(104,plain,
% 0.19/0.40 ((~((set_difference(B!5, singleton(C!4)) = set_difference(B!5, singleton(C!4))) | (in(tptp_fun_D_1(set_difference(B!5, singleton(C!4)), singleton(C!4), B!5), set_difference(B!5, singleton(C!4))) <=> ((~in(tptp_fun_D_1(set_difference(B!5, singleton(C!4)), singleton(C!4), B!5), B!5)) | in(tptp_fun_D_1(set_difference(B!5, singleton(C!4)), singleton(C!4), B!5), singleton(C!4)))))) <=> (~$true)),
% 0.19/0.40 inference(monotonicity,[status(thm)],[103])).
% 0.19/0.40 tff(105,plain,
% 0.19/0.40 ((~((set_difference(B!5, singleton(C!4)) = set_difference(B!5, singleton(C!4))) | (in(tptp_fun_D_1(set_difference(B!5, singleton(C!4)), singleton(C!4), B!5), set_difference(B!5, singleton(C!4))) <=> ((~in(tptp_fun_D_1(set_difference(B!5, singleton(C!4)), singleton(C!4), B!5), B!5)) | in(tptp_fun_D_1(set_difference(B!5, singleton(C!4)), singleton(C!4), B!5), singleton(C!4)))))) <=> $false),
% 0.19/0.40 inference(transitivity,[status(thm)],[104, 26])).
% 0.19/0.40 tff(106,plain,
% 0.19/0.40 ((~(in(A!6, set_difference(B!5, singleton(C!4))) <=> (~((~in(A!6, B!5)) | in(A!6, singleton(C!4)))))) <=> (in(A!6, set_difference(B!5, singleton(C!4))) <=> ((~in(A!6, B!5)) | in(A!6, singleton(C!4))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(107,plain,
% 0.19/0.40 (($false | (in(A!6, set_difference(B!5, singleton(C!4))) <=> (~((~in(A!6, B!5)) | in(A!6, singleton(C!4)))))) <=> (in(A!6, set_difference(B!5, singleton(C!4))) <=> (~((~in(A!6, B!5)) | in(A!6, singleton(C!4)))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(108,plain,
% 0.19/0.40 ((~(set_difference(B!5, singleton(C!4)) = set_difference(B!5, singleton(C!4)))) <=> (~$true)),
% 0.19/0.40 inference(monotonicity,[status(thm)],[101])).
% 0.19/0.40 tff(109,plain,
% 0.19/0.40 ((~(set_difference(B!5, singleton(C!4)) = set_difference(B!5, singleton(C!4)))) <=> $false),
% 0.19/0.40 inference(transitivity,[status(thm)],[108, 26])).
% 0.19/0.40 tff(110,plain,
% 0.19/0.40 (((~(set_difference(B!5, singleton(C!4)) = set_difference(B!5, singleton(C!4)))) | (in(A!6, set_difference(B!5, singleton(C!4))) <=> (~((~in(A!6, B!5)) | in(A!6, singleton(C!4)))))) <=> ($false | (in(A!6, set_difference(B!5, singleton(C!4))) <=> (~((~in(A!6, B!5)) | in(A!6, singleton(C!4))))))),
% 0.19/0.40 inference(monotonicity,[status(thm)],[109])).
% 0.19/0.40 tff(111,plain,
% 0.19/0.40 (((~(set_difference(B!5, singleton(C!4)) = set_difference(B!5, singleton(C!4)))) | (in(A!6, set_difference(B!5, singleton(C!4))) <=> (~((~in(A!6, B!5)) | in(A!6, singleton(C!4)))))) <=> (in(A!6, set_difference(B!5, singleton(C!4))) <=> (~((~in(A!6, B!5)) | in(A!6, singleton(C!4)))))),
% 0.19/0.40 inference(transitivity,[status(thm)],[110, 107])).
% 0.19/0.40 tff(112,plain,
% 0.19/0.40 ((~((~(set_difference(B!5, singleton(C!4)) = set_difference(B!5, singleton(C!4)))) | (in(A!6, set_difference(B!5, singleton(C!4))) <=> (~((~in(A!6, B!5)) | in(A!6, singleton(C!4))))))) <=> (~(in(A!6, set_difference(B!5, singleton(C!4))) <=> (~((~in(A!6, B!5)) | in(A!6, singleton(C!4))))))),
% 0.19/0.40 inference(monotonicity,[status(thm)],[111])).
% 0.19/0.40 tff(113,plain,
% 0.19/0.40 ((~((~(set_difference(B!5, singleton(C!4)) = set_difference(B!5, singleton(C!4)))) | (in(A!6, set_difference(B!5, singleton(C!4))) <=> (~((~in(A!6, B!5)) | in(A!6, singleton(C!4))))))) <=> (in(A!6, set_difference(B!5, singleton(C!4))) <=> ((~in(A!6, B!5)) | in(A!6, singleton(C!4))))),
% 0.19/0.40 inference(transitivity,[status(thm)],[112, 106])).
% 0.19/0.40 tff(114,plain,
% 0.19/0.40 (((~((~(set_difference(B!5, singleton(C!4)) = set_difference(B!5, singleton(C!4)))) | (in(A!6, set_difference(B!5, singleton(C!4))) <=> (~((~in(A!6, B!5)) | in(A!6, singleton(C!4))))))) | (~((set_difference(B!5, singleton(C!4)) = set_difference(B!5, singleton(C!4))) | (in(tptp_fun_D_1(set_difference(B!5, singleton(C!4)), singleton(C!4), B!5), set_difference(B!5, singleton(C!4))) <=> ((~in(tptp_fun_D_1(set_difference(B!5, singleton(C!4)), singleton(C!4), B!5), B!5)) | in(tptp_fun_D_1(set_difference(B!5, singleton(C!4)), singleton(C!4), B!5), singleton(C!4))))))) <=> ((in(A!6, set_difference(B!5, singleton(C!4))) <=> ((~in(A!6, B!5)) | in(A!6, singleton(C!4)))) | $false)),
% 0.19/0.40 inference(monotonicity,[status(thm)],[113, 105])).
% 0.19/0.40 tff(115,plain,
% 0.19/0.40 (((~((~(set_difference(B!5, singleton(C!4)) = set_difference(B!5, singleton(C!4)))) | (in(A!6, set_difference(B!5, singleton(C!4))) <=> (~((~in(A!6, B!5)) | in(A!6, singleton(C!4))))))) | (~((set_difference(B!5, singleton(C!4)) = set_difference(B!5, singleton(C!4))) | (in(tptp_fun_D_1(set_difference(B!5, singleton(C!4)), singleton(C!4), B!5), set_difference(B!5, singleton(C!4))) <=> ((~in(tptp_fun_D_1(set_difference(B!5, singleton(C!4)), singleton(C!4), B!5), B!5)) | in(tptp_fun_D_1(set_difference(B!5, singleton(C!4)), singleton(C!4), B!5), singleton(C!4))))))) <=> (in(A!6, set_difference(B!5, singleton(C!4))) <=> ((~in(A!6, B!5)) | in(A!6, singleton(C!4))))),
% 0.19/0.40 inference(transitivity,[status(thm)],[114, 99])).
% 0.19/0.40 tff(116,plain,
% 0.19/0.40 ((~((~((~(set_difference(B!5, singleton(C!4)) = set_difference(B!5, singleton(C!4)))) | (in(A!6, set_difference(B!5, singleton(C!4))) <=> (~((~in(A!6, B!5)) | in(A!6, singleton(C!4))))))) | (~((set_difference(B!5, singleton(C!4)) = set_difference(B!5, singleton(C!4))) | (in(tptp_fun_D_1(set_difference(B!5, singleton(C!4)), singleton(C!4), B!5), set_difference(B!5, singleton(C!4))) <=> ((~in(tptp_fun_D_1(set_difference(B!5, singleton(C!4)), singleton(C!4), B!5), B!5)) | in(tptp_fun_D_1(set_difference(B!5, singleton(C!4)), singleton(C!4), B!5), singleton(C!4)))))))) <=> (~(in(A!6, set_difference(B!5, singleton(C!4))) <=> ((~in(A!6, B!5)) | in(A!6, singleton(C!4)))))),
% 0.19/0.41 inference(monotonicity,[status(thm)],[115])).
% 0.19/0.41 tff(117,plain,
% 0.19/0.41 ((~((~((~(set_difference(B!5, singleton(C!4)) = set_difference(B!5, singleton(C!4)))) | (in(A!6, set_difference(B!5, singleton(C!4))) <=> (~((~in(A!6, B!5)) | in(A!6, singleton(C!4))))))) | (~((set_difference(B!5, singleton(C!4)) = set_difference(B!5, singleton(C!4))) | (in(tptp_fun_D_1(set_difference(B!5, singleton(C!4)), singleton(C!4), B!5), set_difference(B!5, singleton(C!4))) <=> ((~in(tptp_fun_D_1(set_difference(B!5, singleton(C!4)), singleton(C!4), B!5), B!5)) | in(tptp_fun_D_1(set_difference(B!5, singleton(C!4)), singleton(C!4), B!5), singleton(C!4)))))))) <=> ((~in(A!6, set_difference(B!5, singleton(C!4)))) <=> ((~in(A!6, B!5)) | in(A!6, singleton(C!4))))),
% 0.19/0.41 inference(transitivity,[status(thm)],[116, 98])).
% 0.19/0.41 tff(118,plain,
% 0.19/0.41 (((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_difference(A, B))) | (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(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)))))))) | (~((~((~(set_difference(B!5, singleton(C!4)) = set_difference(B!5, singleton(C!4)))) | (in(A!6, set_difference(B!5, singleton(C!4))) <=> (~((~in(A!6, B!5)) | in(A!6, singleton(C!4))))))) | (~((set_difference(B!5, singleton(C!4)) = set_difference(B!5, singleton(C!4))) | (in(tptp_fun_D_1(set_difference(B!5, singleton(C!4)), singleton(C!4), B!5), set_difference(B!5, singleton(C!4))) <=> ((~in(tptp_fun_D_1(set_difference(B!5, singleton(C!4)), singleton(C!4), B!5), B!5)) | in(tptp_fun_D_1(set_difference(B!5, singleton(C!4)), singleton(C!4), B!5), singleton(C!4))))))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_difference(A, B))) | (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(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)))))))) | ((~in(A!6, set_difference(B!5, singleton(C!4)))) <=> ((~in(A!6, B!5)) | in(A!6, singleton(C!4)))))),
% 0.19/0.41 inference(monotonicity,[status(thm)],[117])).
% 0.19/0.41 tff(119,plain,
% 0.19/0.41 (((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_difference(A, B))) | (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(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)))))))) | (~((~((~(set_difference(B!5, singleton(C!4)) = set_difference(B!5, singleton(C!4)))) | (in(A!6, set_difference(B!5, singleton(C!4))) <=> (~((~in(A!6, B!5)) | in(A!6, singleton(C!4))))))) | (~((set_difference(B!5, singleton(C!4)) = set_difference(B!5, singleton(C!4))) | (in(tptp_fun_D_1(set_difference(B!5, singleton(C!4)), singleton(C!4), B!5), set_difference(B!5, singleton(C!4))) <=> ((~in(tptp_fun_D_1(set_difference(B!5, singleton(C!4)), singleton(C!4), B!5), B!5)) | in(tptp_fun_D_1(set_difference(B!5, singleton(C!4)), singleton(C!4), B!5), singleton(C!4))))))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_difference(A, B))) | (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(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)))))))) | ((~in(A!6, set_difference(B!5, singleton(C!4)))) <=> ((~in(A!6, B!5)) | in(A!6, singleton(C!4)))))),
% 0.19/0.41 inference(transitivity,[status(thm)],[118, 97])).
% 0.19/0.41 tff(120,plain,
% 0.19/0.41 ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_difference(A, B))) | (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(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)))))))) | (~((~((~(set_difference(B!5, singleton(C!4)) = set_difference(B!5, singleton(C!4)))) | (in(A!6, set_difference(B!5, singleton(C!4))) <=> (~((~in(A!6, B!5)) | in(A!6, singleton(C!4))))))) | (~((set_difference(B!5, singleton(C!4)) = set_difference(B!5, singleton(C!4))) | (in(tptp_fun_D_1(set_difference(B!5, singleton(C!4)), singleton(C!4), B!5), set_difference(B!5, singleton(C!4))) <=> ((~in(tptp_fun_D_1(set_difference(B!5, singleton(C!4)), singleton(C!4), B!5), B!5)) | in(tptp_fun_D_1(set_difference(B!5, singleton(C!4)), singleton(C!4), B!5), singleton(C!4))))))))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(121,plain,
% 0.19/0.41 ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_difference(A, B))) | (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_1(C, B, A), C) <=> ((~in(tptp_fun_D_1(C, B, A), A)) | in(tptp_fun_D_1(C, B, A), B)))))))) | ((~in(A!6, set_difference(B!5, singleton(C!4)))) <=> ((~in(A!6, B!5)) | in(A!6, singleton(C!4))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[120, 119])).
% 0.19/0.41 tff(122,plain,
% 0.19/0.41 ((~in(A!6, set_difference(B!5, singleton(C!4)))) <=> ((~in(A!6, B!5)) | in(A!6, singleton(C!4)))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[121, 96])).
% 0.19/0.41 tff(123,plain,
% 0.19/0.41 ((~((~in(A!6, set_difference(B!5, singleton(C!4)))) <=> ((~in(A!6, B!5)) | in(A!6, singleton(C!4))))) | in(A!6, set_difference(B!5, singleton(C!4))) | ((~in(A!6, B!5)) | in(A!6, singleton(C!4)))),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(124,plain,
% 0.19/0.41 (in(A!6, set_difference(B!5, singleton(C!4))) | ((~in(A!6, B!5)) | in(A!6, singleton(C!4)))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[123, 122])).
% 0.19/0.41 tff(125,plain,
% 0.19/0.41 ((~in(A!6, B!5)) | in(A!6, singleton(C!4))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[124, 51])).
% 0.19/0.41 tff(126,plain,
% 0.19/0.41 ((~((~in(A!6, B!5)) | in(A!6, singleton(C!4)))) | (~in(A!6, B!5)) | in(A!6, singleton(C!4))),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(127,plain,
% 0.19/0.41 (in(A!6, singleton(C!4))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[126, 125, 75])).
% 0.19/0.41 tff(128,plain,
% 0.19/0.41 ((~(in(A!6, singleton(C!4)) <=> (A!6 = C!4))) | (~in(A!6, singleton(C!4))) | (A!6 = C!4)),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(129,plain,
% 0.19/0.41 ($false),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[128, 127, 73, 50])).
% 0.19/0.41 tff(130,plain,(in(A!6, set_difference(B!5, singleton(C!4)))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.41 tff(131,plain,
% 0.19/0.41 ((~((~in(A!6, set_difference(B!5, singleton(C!4)))) <=> ((~in(A!6, B!5)) | in(A!6, singleton(C!4))))) | (~in(A!6, set_difference(B!5, singleton(C!4)))) | (~((~in(A!6, B!5)) | in(A!6, singleton(C!4))))),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(132,plain,
% 0.19/0.41 ((~in(A!6, set_difference(B!5, singleton(C!4)))) | (~((~in(A!6, B!5)) | in(A!6, singleton(C!4))))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[131, 122])).
% 0.19/0.41 tff(133,plain,
% 0.19/0.41 (~((~in(A!6, B!5)) | in(A!6, singleton(C!4)))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[132, 130])).
% 0.19/0.41 tff(134,plain,
% 0.19/0.41 (((~in(A!6, B!5)) | in(A!6, singleton(C!4))) | (~in(A!6, singleton(C!4)))),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(135,plain,
% 0.19/0.41 (~in(A!6, singleton(C!4))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[134, 133])).
% 0.19/0.41 tff(136,plain,
% 0.19/0.41 ((~in(A!6, set_difference(B!5, singleton(C!4)))) | ((~in(A!6, B!5)) | (A!6 = C!4)) | (~(in(A!6, set_difference(B!5, singleton(C!4))) <=> ((~in(A!6, B!5)) | (A!6 = C!4))))),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(137,plain,
% 0.19/0.41 ((~in(A!6, set_difference(B!5, singleton(C!4)))) | ((~in(A!6, B!5)) | (A!6 = C!4))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[136, 68])).
% 0.19/0.41 tff(138,plain,
% 0.19/0.41 ((~in(A!6, B!5)) | (A!6 = C!4)),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[137, 130])).
% 0.19/0.41 tff(139,plain,
% 0.19/0.41 (((~in(A!6, B!5)) | in(A!6, singleton(C!4))) | in(A!6, B!5)),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(140,plain,
% 0.19/0.41 (in(A!6, B!5)),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[139, 133])).
% 0.19/0.41 tff(141,plain,
% 0.19/0.41 ((~((~in(A!6, B!5)) | (A!6 = C!4))) | (~in(A!6, B!5)) | (A!6 = C!4)),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(142,plain,
% 0.19/0.41 (A!6 = C!4),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[141, 140, 138])).
% 0.19/0.41 tff(143,plain,
% 0.19/0.41 ((~(in(A!6, singleton(C!4)) <=> (A!6 = C!4))) | in(A!6, singleton(C!4)) | (~(A!6 = C!4))),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(144,plain,
% 0.19/0.41 ($false),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[143, 142, 135, 50])).
% 0.19/0.41 % SZS output end Proof
%------------------------------------------------------------------------------