TSTP Solution File: SEU144+2 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SEU144+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n013.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 20 07:27:45 EDT 2022
% Result : Theorem 7.07s 4.77s
% Output : Proof 7.07s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : SEU144+2 : TPTP v8.1.0. Released v3.3.0.
% 0.12/0.14 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.35 % Computer : n013.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Sat Sep 3 09:36:17 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.14/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.14/0.35 Usage: tptp [options] [-file:]file
% 0.14/0.35 -h, -? prints this message.
% 0.14/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.14/0.35 -m, -model generate model.
% 0.14/0.35 -p, -proof generate proof.
% 0.14/0.35 -c, -core generate unsat core of named formulas.
% 0.14/0.35 -st, -statistics display statistics.
% 0.14/0.35 -t:timeout set timeout (in second).
% 0.14/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.14/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.14/0.35 -<param>:<value> configuration parameter and value.
% 0.14/0.35 -o:<output-file> file to place output in.
% 7.07/4.77 % SZS status Theorem
% 7.07/4.77 % SZS output start Proof
% 7.07/4.77 tff(in_type, type, (
% 7.07/4.77 in: ( $i * $i ) > $o)).
% 7.07/4.77 tff(tptp_fun_B_7_type, type, (
% 7.07/4.77 tptp_fun_B_7: $i)).
% 7.07/4.77 tff(tptp_fun_C_4_type, type, (
% 7.07/4.77 tptp_fun_C_4: ( $i * $i ) > $i)).
% 7.07/4.77 tff(singleton_type, type, (
% 7.07/4.77 singleton: $i > $i)).
% 7.07/4.77 tff(tptp_fun_A_8_type, type, (
% 7.07/4.77 tptp_fun_A_8: $i)).
% 7.07/4.77 tff(tptp_fun_C_0_type, type, (
% 7.07/4.77 tptp_fun_C_0: ( $i * $i ) > $i)).
% 7.07/4.77 tff(subset_type, type, (
% 7.07/4.77 subset: ( $i * $i ) > $o)).
% 7.07/4.77 tff(set_difference_type, type, (
% 7.07/4.77 set_difference: ( $i * $i ) > $i)).
% 7.07/4.77 tff(tptp_fun_C_12_type, type, (
% 7.07/4.77 tptp_fun_C_12: ( $i * $i ) > $i)).
% 7.07/4.77 tff(disjoint_type, type, (
% 7.07/4.77 disjoint: ( $i * $i ) > $o)).
% 7.07/4.77 tff(empty_set_type, type, (
% 7.07/4.77 empty_set: $i)).
% 7.07/4.77 tff(set_union2_type, type, (
% 7.07/4.77 set_union2: ( $i * $i ) > $i)).
% 7.07/4.77 tff(tptp_fun_D_3_type, type, (
% 7.07/4.77 tptp_fun_D_3: ( $i * $i * $i ) > $i)).
% 7.07/4.77 tff(1,plain,
% 7.07/4.77 (^[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)))))))),
% 7.07/4.77 inference(bind,[status(th)],[])).
% 7.07/4.77 tff(2,plain,
% 7.07/4.77 (![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))))))),
% 7.07/4.77 inference(quant_intro,[status(thm)],[1])).
% 7.07/4.77 tff(3,plain,
% 7.07/4.77 (![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))))))),
% 7.07/4.77 inference(pull_quant,[status(thm)],[])).
% 7.07/4.77 tff(4,plain,
% 7.07/4.77 (^[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))))))))),
% 7.07/4.77 inference(bind,[status(th)],[])).
% 7.07/4.77 tff(5,plain,
% 7.07/4.77 (![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))))))),
% 7.07/4.77 inference(quant_intro,[status(thm)],[4])).
% 7.07/4.77 tff(6,plain,
% 7.07/4.77 (![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))))))),
% 7.07/4.77 inference(transitivity,[status(thm)],[5, 3])).
% 7.07/4.77 tff(7,plain,
% 7.07/4.77 (![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))))))),
% 7.07/4.77 inference(transitivity,[status(thm)],[6, 2])).
% 7.07/4.77 tff(8,plain,
% 7.07/4.77 (^[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)))))))),
% 7.07/4.77 inference(bind,[status(th)],[])).
% 7.07/4.77 tff(9,plain,
% 7.07/4.77 (![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))))))),
% 7.07/4.77 inference(quant_intro,[status(thm)],[8])).
% 7.07/4.77 tff(10,plain,
% 7.07/4.77 (![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))))))),
% 7.07/4.77 inference(transitivity,[status(thm)],[9, 7])).
% 7.07/4.77 tff(11,plain,
% 7.07/4.77 (^[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))))))))),
% 7.07/4.77 inference(bind,[status(th)],[])).
% 7.07/4.77 tff(12,plain,
% 7.07/4.77 (![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))))))),
% 7.07/4.77 inference(quant_intro,[status(thm)],[11])).
% 7.07/4.77 tff(13,plain,
% 7.07/4.77 (^[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)))))),
% 7.07/4.77 inference(bind,[status(th)],[])).
% 7.07/4.77 tff(14,plain,
% 7.07/4.77 (![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))))),
% 7.07/4.77 inference(quant_intro,[status(thm)],[13])).
% 7.07/4.77 tff(15,plain,
% 7.07/4.77 (![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)))),
% 7.07/4.77 inference(rewrite,[status(thm)],[])).
% 7.07/4.77 tff(16,axiom,(![A: $i, B: $i] : ((B = singleton(A)) <=> ![C: $i] : (in(C, B) <=> (C = A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d1_tarski')).
% 7.07/4.77 tff(17,plain,
% 7.07/4.77 (![A: $i, B: $i] : ((B = singleton(A)) <=> ![C: $i] : (in(C, B) <=> (C = A)))),
% 7.07/4.77 inference(modus_ponens,[status(thm)],[16, 15])).
% 7.07/4.77 tff(18,plain,(
% 7.07/4.77 ![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)))))),
% 7.07/4.77 inference(skolemize,[status(sab)],[17])).
% 7.07/4.77 tff(19,plain,
% 7.07/4.77 (![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))))),
% 7.07/4.77 inference(modus_ponens,[status(thm)],[18, 14])).
% 7.07/4.77 tff(20,plain,
% 7.07/4.77 (![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))))))),
% 7.07/4.77 inference(modus_ponens,[status(thm)],[19, 12])).
% 7.07/4.77 tff(21,plain,
% 7.07/4.77 (![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))))))),
% 7.07/4.77 inference(modus_ponens,[status(thm)],[20, 10])).
% 7.07/4.77 tff(22,plain,
% 7.07/4.77 (((~![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_C_4(B!7, singleton(A!8)), singleton(A!8)) <=> (tptp_fun_C_4(B!7, singleton(A!8)) = A!8))) <=> ((~![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_C_4(B!7, singleton(A!8)), singleton(A!8)) <=> (tptp_fun_C_4(B!7, singleton(A!8)) = A!8)))),
% 7.07/4.77 inference(rewrite,[status(thm)],[])).
% 7.07/4.77 tff(23,plain,
% 7.07/4.77 ((~((~in(tptp_fun_C_4(B!7, singleton(A!8)), singleton(A!8))) <=> (tptp_fun_C_4(B!7, singleton(A!8)) = A!8))) <=> (in(tptp_fun_C_4(B!7, singleton(A!8)), singleton(A!8)) <=> (tptp_fun_C_4(B!7, singleton(A!8)) = A!8))),
% 7.07/4.77 inference(rewrite,[status(thm)],[])).
% 7.07/4.77 tff(24,plain,
% 7.07/4.77 ((((~in(tptp_fun_C_4(B!7, singleton(A!8)), singleton(A!8))) <=> (tptp_fun_C_4(B!7, singleton(A!8)) = A!8)) | $false) <=> ((~in(tptp_fun_C_4(B!7, singleton(A!8)), singleton(A!8))) <=> (tptp_fun_C_4(B!7, singleton(A!8)) = A!8))),
% 7.07/4.77 inference(rewrite,[status(thm)],[])).
% 7.07/4.77 tff(25,plain,
% 7.07/4.77 ((~$true) <=> $false),
% 7.07/4.77 inference(rewrite,[status(thm)],[])).
% 7.07/4.77 tff(26,plain,
% 7.07/4.77 (($true | ((~in(tptp_fun_C_0(singleton(A!8), A!8), singleton(A!8))) <=> (tptp_fun_C_0(singleton(A!8), A!8) = A!8))) <=> $true),
% 7.07/4.77 inference(rewrite,[status(thm)],[])).
% 7.07/4.77 tff(27,plain,
% 7.07/4.77 ((singleton(A!8) = singleton(A!8)) <=> $true),
% 7.07/4.77 inference(rewrite,[status(thm)],[])).
% 7.07/4.77 tff(28,plain,
% 7.07/4.77 (((singleton(A!8) = singleton(A!8)) | ((~in(tptp_fun_C_0(singleton(A!8), A!8), singleton(A!8))) <=> (tptp_fun_C_0(singleton(A!8), A!8) = A!8))) <=> ($true | ((~in(tptp_fun_C_0(singleton(A!8), A!8), singleton(A!8))) <=> (tptp_fun_C_0(singleton(A!8), A!8) = A!8)))),
% 7.07/4.77 inference(monotonicity,[status(thm)],[27])).
% 7.07/4.77 tff(29,plain,
% 7.07/4.77 (((singleton(A!8) = singleton(A!8)) | ((~in(tptp_fun_C_0(singleton(A!8), A!8), singleton(A!8))) <=> (tptp_fun_C_0(singleton(A!8), A!8) = A!8))) <=> $true),
% 7.07/4.77 inference(transitivity,[status(thm)],[28, 26])).
% 7.07/4.77 tff(30,plain,
% 7.07/4.77 ((~((singleton(A!8) = singleton(A!8)) | ((~in(tptp_fun_C_0(singleton(A!8), A!8), singleton(A!8))) <=> (tptp_fun_C_0(singleton(A!8), A!8) = A!8)))) <=> (~$true)),
% 7.07/4.77 inference(monotonicity,[status(thm)],[29])).
% 7.07/4.77 tff(31,plain,
% 7.07/4.77 ((~((singleton(A!8) = singleton(A!8)) | ((~in(tptp_fun_C_0(singleton(A!8), A!8), singleton(A!8))) <=> (tptp_fun_C_0(singleton(A!8), A!8) = A!8)))) <=> $false),
% 7.07/4.77 inference(transitivity,[status(thm)],[30, 25])).
% 7.07/4.77 tff(32,plain,
% 7.07/4.77 ((~(in(tptp_fun_C_4(B!7, singleton(A!8)), singleton(A!8)) <=> (tptp_fun_C_4(B!7, singleton(A!8)) = A!8))) <=> ((~in(tptp_fun_C_4(B!7, singleton(A!8)), singleton(A!8))) <=> (tptp_fun_C_4(B!7, singleton(A!8)) = A!8))),
% 7.07/4.77 inference(rewrite,[status(thm)],[])).
% 7.07/4.77 tff(33,plain,
% 7.07/4.77 (($false | (in(tptp_fun_C_4(B!7, singleton(A!8)), singleton(A!8)) <=> (tptp_fun_C_4(B!7, singleton(A!8)) = A!8))) <=> (in(tptp_fun_C_4(B!7, singleton(A!8)), singleton(A!8)) <=> (tptp_fun_C_4(B!7, singleton(A!8)) = A!8))),
% 7.07/4.77 inference(rewrite,[status(thm)],[])).
% 7.07/4.77 tff(34,plain,
% 7.07/4.77 ((~(singleton(A!8) = singleton(A!8))) <=> (~$true)),
% 7.07/4.77 inference(monotonicity,[status(thm)],[27])).
% 7.07/4.77 tff(35,plain,
% 7.07/4.77 ((~(singleton(A!8) = singleton(A!8))) <=> $false),
% 7.07/4.77 inference(transitivity,[status(thm)],[34, 25])).
% 7.07/4.77 tff(36,plain,
% 7.07/4.77 (((~(singleton(A!8) = singleton(A!8))) | (in(tptp_fun_C_4(B!7, singleton(A!8)), singleton(A!8)) <=> (tptp_fun_C_4(B!7, singleton(A!8)) = A!8))) <=> ($false | (in(tptp_fun_C_4(B!7, singleton(A!8)), singleton(A!8)) <=> (tptp_fun_C_4(B!7, singleton(A!8)) = A!8)))),
% 7.07/4.77 inference(monotonicity,[status(thm)],[35])).
% 7.07/4.77 tff(37,plain,
% 7.07/4.77 (((~(singleton(A!8) = singleton(A!8))) | (in(tptp_fun_C_4(B!7, singleton(A!8)), singleton(A!8)) <=> (tptp_fun_C_4(B!7, singleton(A!8)) = A!8))) <=> (in(tptp_fun_C_4(B!7, singleton(A!8)), singleton(A!8)) <=> (tptp_fun_C_4(B!7, singleton(A!8)) = A!8))),
% 7.07/4.77 inference(transitivity,[status(thm)],[36, 33])).
% 7.07/4.77 tff(38,plain,
% 7.07/4.77 ((~((~(singleton(A!8) = singleton(A!8))) | (in(tptp_fun_C_4(B!7, singleton(A!8)), singleton(A!8)) <=> (tptp_fun_C_4(B!7, singleton(A!8)) = A!8)))) <=> (~(in(tptp_fun_C_4(B!7, singleton(A!8)), singleton(A!8)) <=> (tptp_fun_C_4(B!7, singleton(A!8)) = A!8)))),
% 7.07/4.77 inference(monotonicity,[status(thm)],[37])).
% 7.07/4.77 tff(39,plain,
% 7.07/4.77 ((~((~(singleton(A!8) = singleton(A!8))) | (in(tptp_fun_C_4(B!7, singleton(A!8)), singleton(A!8)) <=> (tptp_fun_C_4(B!7, singleton(A!8)) = A!8)))) <=> ((~in(tptp_fun_C_4(B!7, singleton(A!8)), singleton(A!8))) <=> (tptp_fun_C_4(B!7, singleton(A!8)) = A!8))),
% 7.07/4.77 inference(transitivity,[status(thm)],[38, 32])).
% 7.07/4.77 tff(40,plain,
% 7.07/4.77 (((~((~(singleton(A!8) = singleton(A!8))) | (in(tptp_fun_C_4(B!7, singleton(A!8)), singleton(A!8)) <=> (tptp_fun_C_4(B!7, singleton(A!8)) = A!8)))) | (~((singleton(A!8) = singleton(A!8)) | ((~in(tptp_fun_C_0(singleton(A!8), A!8), singleton(A!8))) <=> (tptp_fun_C_0(singleton(A!8), A!8) = A!8))))) <=> (((~in(tptp_fun_C_4(B!7, singleton(A!8)), singleton(A!8))) <=> (tptp_fun_C_4(B!7, singleton(A!8)) = A!8)) | $false)),
% 7.07/4.77 inference(monotonicity,[status(thm)],[39, 31])).
% 7.07/4.77 tff(41,plain,
% 7.07/4.77 (((~((~(singleton(A!8) = singleton(A!8))) | (in(tptp_fun_C_4(B!7, singleton(A!8)), singleton(A!8)) <=> (tptp_fun_C_4(B!7, singleton(A!8)) = A!8)))) | (~((singleton(A!8) = singleton(A!8)) | ((~in(tptp_fun_C_0(singleton(A!8), A!8), singleton(A!8))) <=> (tptp_fun_C_0(singleton(A!8), A!8) = A!8))))) <=> ((~in(tptp_fun_C_4(B!7, singleton(A!8)), singleton(A!8))) <=> (tptp_fun_C_4(B!7, singleton(A!8)) = A!8))),
% 7.07/4.77 inference(transitivity,[status(thm)],[40, 24])).
% 7.07/4.77 tff(42,plain,
% 7.07/4.77 ((~((~((~(singleton(A!8) = singleton(A!8))) | (in(tptp_fun_C_4(B!7, singleton(A!8)), singleton(A!8)) <=> (tptp_fun_C_4(B!7, singleton(A!8)) = A!8)))) | (~((singleton(A!8) = singleton(A!8)) | ((~in(tptp_fun_C_0(singleton(A!8), A!8), singleton(A!8))) <=> (tptp_fun_C_0(singleton(A!8), A!8) = A!8)))))) <=> (~((~in(tptp_fun_C_4(B!7, singleton(A!8)), singleton(A!8))) <=> (tptp_fun_C_4(B!7, singleton(A!8)) = A!8)))),
% 7.07/4.77 inference(monotonicity,[status(thm)],[41])).
% 7.07/4.77 tff(43,plain,
% 7.07/4.77 ((~((~((~(singleton(A!8) = singleton(A!8))) | (in(tptp_fun_C_4(B!7, singleton(A!8)), singleton(A!8)) <=> (tptp_fun_C_4(B!7, singleton(A!8)) = A!8)))) | (~((singleton(A!8) = singleton(A!8)) | ((~in(tptp_fun_C_0(singleton(A!8), A!8), singleton(A!8))) <=> (tptp_fun_C_0(singleton(A!8), A!8) = A!8)))))) <=> (in(tptp_fun_C_4(B!7, singleton(A!8)), singleton(A!8)) <=> (tptp_fun_C_4(B!7, singleton(A!8)) = A!8))),
% 7.07/4.77 inference(transitivity,[status(thm)],[42, 23])).
% 7.07/4.77 tff(44,plain,
% 7.07/4.77 (((~![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!8) = singleton(A!8))) | (in(tptp_fun_C_4(B!7, singleton(A!8)), singleton(A!8)) <=> (tptp_fun_C_4(B!7, singleton(A!8)) = A!8)))) | (~((singleton(A!8) = singleton(A!8)) | ((~in(tptp_fun_C_0(singleton(A!8), A!8), singleton(A!8))) <=> (tptp_fun_C_0(singleton(A!8), A!8) = A!8))))))) <=> ((~![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_C_4(B!7, singleton(A!8)), singleton(A!8)) <=> (tptp_fun_C_4(B!7, singleton(A!8)) = A!8)))),
% 7.07/4.77 inference(monotonicity,[status(thm)],[43])).
% 7.07/4.77 tff(45,plain,
% 7.07/4.77 (((~![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!8) = singleton(A!8))) | (in(tptp_fun_C_4(B!7, singleton(A!8)), singleton(A!8)) <=> (tptp_fun_C_4(B!7, singleton(A!8)) = A!8)))) | (~((singleton(A!8) = singleton(A!8)) | ((~in(tptp_fun_C_0(singleton(A!8), A!8), singleton(A!8))) <=> (tptp_fun_C_0(singleton(A!8), A!8) = A!8))))))) <=> ((~![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_C_4(B!7, singleton(A!8)), singleton(A!8)) <=> (tptp_fun_C_4(B!7, singleton(A!8)) = A!8)))),
% 7.07/4.77 inference(transitivity,[status(thm)],[44, 22])).
% 7.07/4.77 tff(46,plain,
% 7.07/4.77 ((~![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!8) = singleton(A!8))) | (in(tptp_fun_C_4(B!7, singleton(A!8)), singleton(A!8)) <=> (tptp_fun_C_4(B!7, singleton(A!8)) = A!8)))) | (~((singleton(A!8) = singleton(A!8)) | ((~in(tptp_fun_C_0(singleton(A!8), A!8), singleton(A!8))) <=> (tptp_fun_C_0(singleton(A!8), A!8) = A!8))))))),
% 7.07/4.77 inference(quant_inst,[status(thm)],[])).
% 7.07/4.77 tff(47,plain,
% 7.07/4.77 ((~![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_C_4(B!7, singleton(A!8)), singleton(A!8)) <=> (tptp_fun_C_4(B!7, singleton(A!8)) = A!8))),
% 7.07/4.77 inference(modus_ponens,[status(thm)],[46, 45])).
% 7.07/4.77 tff(48,plain,
% 7.07/4.77 (in(tptp_fun_C_4(B!7, singleton(A!8)), singleton(A!8)) <=> (tptp_fun_C_4(B!7, singleton(A!8)) = A!8)),
% 7.07/4.77 inference(unit_resolution,[status(thm)],[47, 21])).
% 7.07/4.77 tff(49,assumption,(~in(A!8, B!7)), introduced(assumption)).
% 7.07/4.77 tff(50,plain,
% 7.07/4.77 (((~![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_C_12(singleton(A!8), singleton(A!8)), singleton(A!8)) <=> (tptp_fun_C_12(singleton(A!8), singleton(A!8)) = A!8))) <=> ((~![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_C_12(singleton(A!8), singleton(A!8)), singleton(A!8)) <=> (tptp_fun_C_12(singleton(A!8), singleton(A!8)) = A!8)))),
% 7.07/4.77 inference(rewrite,[status(thm)],[])).
% 7.07/4.77 tff(51,plain,
% 7.07/4.77 ((~((~in(tptp_fun_C_12(singleton(A!8), singleton(A!8)), singleton(A!8))) <=> (tptp_fun_C_12(singleton(A!8), singleton(A!8)) = A!8))) <=> (in(tptp_fun_C_12(singleton(A!8), singleton(A!8)), singleton(A!8)) <=> (tptp_fun_C_12(singleton(A!8), singleton(A!8)) = A!8))),
% 7.07/4.77 inference(rewrite,[status(thm)],[])).
% 7.07/4.77 tff(52,plain,
% 7.07/4.77 ((((~in(tptp_fun_C_12(singleton(A!8), singleton(A!8)), singleton(A!8))) <=> (tptp_fun_C_12(singleton(A!8), singleton(A!8)) = A!8)) | $false) <=> ((~in(tptp_fun_C_12(singleton(A!8), singleton(A!8)), singleton(A!8))) <=> (tptp_fun_C_12(singleton(A!8), singleton(A!8)) = A!8))),
% 7.07/4.77 inference(rewrite,[status(thm)],[])).
% 7.07/4.77 tff(53,plain,
% 7.07/4.77 ((~(in(tptp_fun_C_12(singleton(A!8), singleton(A!8)), singleton(A!8)) <=> (tptp_fun_C_12(singleton(A!8), singleton(A!8)) = A!8))) <=> ((~in(tptp_fun_C_12(singleton(A!8), singleton(A!8)), singleton(A!8))) <=> (tptp_fun_C_12(singleton(A!8), singleton(A!8)) = A!8))),
% 7.07/4.77 inference(rewrite,[status(thm)],[])).
% 7.07/4.77 tff(54,plain,
% 7.07/4.77 (($false | (in(tptp_fun_C_12(singleton(A!8), singleton(A!8)), singleton(A!8)) <=> (tptp_fun_C_12(singleton(A!8), singleton(A!8)) = A!8))) <=> (in(tptp_fun_C_12(singleton(A!8), singleton(A!8)), singleton(A!8)) <=> (tptp_fun_C_12(singleton(A!8), singleton(A!8)) = A!8))),
% 7.07/4.77 inference(rewrite,[status(thm)],[])).
% 7.07/4.77 tff(55,plain,
% 7.07/4.77 (((~(singleton(A!8) = singleton(A!8))) | (in(tptp_fun_C_12(singleton(A!8), singleton(A!8)), singleton(A!8)) <=> (tptp_fun_C_12(singleton(A!8), singleton(A!8)) = A!8))) <=> ($false | (in(tptp_fun_C_12(singleton(A!8), singleton(A!8)), singleton(A!8)) <=> (tptp_fun_C_12(singleton(A!8), singleton(A!8)) = A!8)))),
% 7.07/4.77 inference(monotonicity,[status(thm)],[35])).
% 7.07/4.77 tff(56,plain,
% 7.07/4.77 (((~(singleton(A!8) = singleton(A!8))) | (in(tptp_fun_C_12(singleton(A!8), singleton(A!8)), singleton(A!8)) <=> (tptp_fun_C_12(singleton(A!8), singleton(A!8)) = A!8))) <=> (in(tptp_fun_C_12(singleton(A!8), singleton(A!8)), singleton(A!8)) <=> (tptp_fun_C_12(singleton(A!8), singleton(A!8)) = A!8))),
% 7.07/4.77 inference(transitivity,[status(thm)],[55, 54])).
% 7.07/4.77 tff(57,plain,
% 7.07/4.77 ((~((~(singleton(A!8) = singleton(A!8))) | (in(tptp_fun_C_12(singleton(A!8), singleton(A!8)), singleton(A!8)) <=> (tptp_fun_C_12(singleton(A!8), singleton(A!8)) = A!8)))) <=> (~(in(tptp_fun_C_12(singleton(A!8), singleton(A!8)), singleton(A!8)) <=> (tptp_fun_C_12(singleton(A!8), singleton(A!8)) = A!8)))),
% 7.07/4.77 inference(monotonicity,[status(thm)],[56])).
% 7.07/4.77 tff(58,plain,
% 7.07/4.77 ((~((~(singleton(A!8) = singleton(A!8))) | (in(tptp_fun_C_12(singleton(A!8), singleton(A!8)), singleton(A!8)) <=> (tptp_fun_C_12(singleton(A!8), singleton(A!8)) = A!8)))) <=> ((~in(tptp_fun_C_12(singleton(A!8), singleton(A!8)), singleton(A!8))) <=> (tptp_fun_C_12(singleton(A!8), singleton(A!8)) = A!8))),
% 7.07/4.77 inference(transitivity,[status(thm)],[57, 53])).
% 7.07/4.77 tff(59,plain,
% 7.07/4.77 (((~((~(singleton(A!8) = singleton(A!8))) | (in(tptp_fun_C_12(singleton(A!8), singleton(A!8)), singleton(A!8)) <=> (tptp_fun_C_12(singleton(A!8), singleton(A!8)) = A!8)))) | (~((singleton(A!8) = singleton(A!8)) | ((~in(tptp_fun_C_0(singleton(A!8), A!8), singleton(A!8))) <=> (tptp_fun_C_0(singleton(A!8), A!8) = A!8))))) <=> (((~in(tptp_fun_C_12(singleton(A!8), singleton(A!8)), singleton(A!8))) <=> (tptp_fun_C_12(singleton(A!8), singleton(A!8)) = A!8)) | $false)),
% 7.07/4.77 inference(monotonicity,[status(thm)],[58, 31])).
% 7.07/4.77 tff(60,plain,
% 7.07/4.77 (((~((~(singleton(A!8) = singleton(A!8))) | (in(tptp_fun_C_12(singleton(A!8), singleton(A!8)), singleton(A!8)) <=> (tptp_fun_C_12(singleton(A!8), singleton(A!8)) = A!8)))) | (~((singleton(A!8) = singleton(A!8)) | ((~in(tptp_fun_C_0(singleton(A!8), A!8), singleton(A!8))) <=> (tptp_fun_C_0(singleton(A!8), A!8) = A!8))))) <=> ((~in(tptp_fun_C_12(singleton(A!8), singleton(A!8)), singleton(A!8))) <=> (tptp_fun_C_12(singleton(A!8), singleton(A!8)) = A!8))),
% 7.07/4.77 inference(transitivity,[status(thm)],[59, 52])).
% 7.07/4.77 tff(61,plain,
% 7.07/4.77 ((~((~((~(singleton(A!8) = singleton(A!8))) | (in(tptp_fun_C_12(singleton(A!8), singleton(A!8)), singleton(A!8)) <=> (tptp_fun_C_12(singleton(A!8), singleton(A!8)) = A!8)))) | (~((singleton(A!8) = singleton(A!8)) | ((~in(tptp_fun_C_0(singleton(A!8), A!8), singleton(A!8))) <=> (tptp_fun_C_0(singleton(A!8), A!8) = A!8)))))) <=> (~((~in(tptp_fun_C_12(singleton(A!8), singleton(A!8)), singleton(A!8))) <=> (tptp_fun_C_12(singleton(A!8), singleton(A!8)) = A!8)))),
% 7.07/4.77 inference(monotonicity,[status(thm)],[60])).
% 7.07/4.77 tff(62,plain,
% 7.07/4.77 ((~((~((~(singleton(A!8) = singleton(A!8))) | (in(tptp_fun_C_12(singleton(A!8), singleton(A!8)), singleton(A!8)) <=> (tptp_fun_C_12(singleton(A!8), singleton(A!8)) = A!8)))) | (~((singleton(A!8) = singleton(A!8)) | ((~in(tptp_fun_C_0(singleton(A!8), A!8), singleton(A!8))) <=> (tptp_fun_C_0(singleton(A!8), A!8) = A!8)))))) <=> (in(tptp_fun_C_12(singleton(A!8), singleton(A!8)), singleton(A!8)) <=> (tptp_fun_C_12(singleton(A!8), singleton(A!8)) = A!8))),
% 7.07/4.77 inference(transitivity,[status(thm)],[61, 51])).
% 7.07/4.77 tff(63,plain,
% 7.07/4.77 (((~![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!8) = singleton(A!8))) | (in(tptp_fun_C_12(singleton(A!8), singleton(A!8)), singleton(A!8)) <=> (tptp_fun_C_12(singleton(A!8), singleton(A!8)) = A!8)))) | (~((singleton(A!8) = singleton(A!8)) | ((~in(tptp_fun_C_0(singleton(A!8), A!8), singleton(A!8))) <=> (tptp_fun_C_0(singleton(A!8), A!8) = A!8))))))) <=> ((~![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_C_12(singleton(A!8), singleton(A!8)), singleton(A!8)) <=> (tptp_fun_C_12(singleton(A!8), singleton(A!8)) = A!8)))),
% 7.07/4.77 inference(monotonicity,[status(thm)],[62])).
% 7.07/4.77 tff(64,plain,
% 7.07/4.77 (((~![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!8) = singleton(A!8))) | (in(tptp_fun_C_12(singleton(A!8), singleton(A!8)), singleton(A!8)) <=> (tptp_fun_C_12(singleton(A!8), singleton(A!8)) = A!8)))) | (~((singleton(A!8) = singleton(A!8)) | ((~in(tptp_fun_C_0(singleton(A!8), A!8), singleton(A!8))) <=> (tptp_fun_C_0(singleton(A!8), A!8) = A!8))))))) <=> ((~![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_C_12(singleton(A!8), singleton(A!8)), singleton(A!8)) <=> (tptp_fun_C_12(singleton(A!8), singleton(A!8)) = A!8)))),
% 7.07/4.77 inference(transitivity,[status(thm)],[63, 50])).
% 7.07/4.77 tff(65,plain,
% 7.07/4.77 ((~![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!8) = singleton(A!8))) | (in(tptp_fun_C_12(singleton(A!8), singleton(A!8)), singleton(A!8)) <=> (tptp_fun_C_12(singleton(A!8), singleton(A!8)) = A!8)))) | (~((singleton(A!8) = singleton(A!8)) | ((~in(tptp_fun_C_0(singleton(A!8), A!8), singleton(A!8))) <=> (tptp_fun_C_0(singleton(A!8), A!8) = A!8))))))),
% 7.07/4.77 inference(quant_inst,[status(thm)],[])).
% 7.07/4.77 tff(66,plain,
% 7.07/4.77 ((~![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_C_12(singleton(A!8), singleton(A!8)), singleton(A!8)) <=> (tptp_fun_C_12(singleton(A!8), singleton(A!8)) = A!8))),
% 7.07/4.77 inference(modus_ponens,[status(thm)],[65, 64])).
% 7.07/4.77 tff(67,plain,
% 7.07/4.77 (in(tptp_fun_C_12(singleton(A!8), singleton(A!8)), singleton(A!8)) <=> (tptp_fun_C_12(singleton(A!8), singleton(A!8)) = A!8)),
% 7.07/4.77 inference(unit_resolution,[status(thm)],[66, 21])).
% 7.07/4.77 tff(68,plain,
% 7.07/4.77 (^[A: $i, B: $i] : refl((~((~(disjoint(A, B) | (~((~in(tptp_fun_C_12(B, A), A)) | (~in(tptp_fun_C_12(B, A), B)))))) | (~((~disjoint(A, B)) | ![C: $i] : ((~in(C, B)) | (~in(C, A))))))) <=> (~((~(disjoint(A, B) | (~((~in(tptp_fun_C_12(B, A), A)) | (~in(tptp_fun_C_12(B, A), B)))))) | (~((~disjoint(A, B)) | ![C: $i] : ((~in(C, B)) | (~in(C, A))))))))),
% 7.07/4.77 inference(bind,[status(th)],[])).
% 7.07/4.77 tff(69,plain,
% 7.07/4.77 (![A: $i, B: $i] : (~((~(disjoint(A, B) | (~((~in(tptp_fun_C_12(B, A), A)) | (~in(tptp_fun_C_12(B, A), B)))))) | (~((~disjoint(A, B)) | ![C: $i] : ((~in(C, B)) | (~in(C, A))))))) <=> ![A: $i, B: $i] : (~((~(disjoint(A, B) | (~((~in(tptp_fun_C_12(B, A), A)) | (~in(tptp_fun_C_12(B, A), B)))))) | (~((~disjoint(A, B)) | ![C: $i] : ((~in(C, B)) | (~in(C, A)))))))),
% 7.07/4.77 inference(quant_intro,[status(thm)],[68])).
% 7.07/4.77 tff(70,plain,
% 7.07/4.77 (^[A: $i, B: $i] : rewrite((~((~(disjoint(A, B) | (~((~in(tptp_fun_C_12(B, A), A)) | (~in(tptp_fun_C_12(B, A), B)))))) | (~((~disjoint(A, B)) | ![C: $i] : ((~in(C, B)) | (~in(C, A))))))) <=> (~((~(disjoint(A, B) | (~((~in(tptp_fun_C_12(B, A), A)) | (~in(tptp_fun_C_12(B, A), B)))))) | (~((~disjoint(A, B)) | ![C: $i] : ((~in(C, B)) | (~in(C, A))))))))),
% 7.07/4.77 inference(bind,[status(th)],[])).
% 7.07/4.77 tff(71,plain,
% 7.07/4.77 (![A: $i, B: $i] : (~((~(disjoint(A, B) | (~((~in(tptp_fun_C_12(B, A), A)) | (~in(tptp_fun_C_12(B, A), B)))))) | (~((~disjoint(A, B)) | ![C: $i] : ((~in(C, B)) | (~in(C, A))))))) <=> ![A: $i, B: $i] : (~((~(disjoint(A, B) | (~((~in(tptp_fun_C_12(B, A), A)) | (~in(tptp_fun_C_12(B, A), B)))))) | (~((~disjoint(A, B)) | ![C: $i] : ((~in(C, B)) | (~in(C, A)))))))),
% 7.07/4.77 inference(quant_intro,[status(thm)],[70])).
% 7.07/4.77 tff(72,plain,
% 7.07/4.77 (![A: $i, B: $i] : (~((~(disjoint(A, B) | (~((~in(tptp_fun_C_12(B, A), A)) | (~in(tptp_fun_C_12(B, A), B)))))) | (~((~disjoint(A, B)) | ![C: $i] : ((~in(C, B)) | (~in(C, A))))))) <=> ![A: $i, B: $i] : (~((~(disjoint(A, B) | (~((~in(tptp_fun_C_12(B, A), A)) | (~in(tptp_fun_C_12(B, A), B)))))) | (~((~disjoint(A, B)) | ![C: $i] : ((~in(C, B)) | (~in(C, A)))))))),
% 7.07/4.77 inference(transitivity,[status(thm)],[71, 69])).
% 7.07/4.77 tff(73,plain,
% 7.07/4.77 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite((in(tptp_fun_C_12(B, A), A) & in(tptp_fun_C_12(B, A), B)) <=> (~((~in(tptp_fun_C_12(B, A), A)) | (~in(tptp_fun_C_12(B, A), B))))), ((disjoint(A, B) | (in(tptp_fun_C_12(B, A), A) & in(tptp_fun_C_12(B, A), B))) <=> (disjoint(A, B) | (~((~in(tptp_fun_C_12(B, A), A)) | (~in(tptp_fun_C_12(B, A), B))))))), rewrite((disjoint(A, B) | (~((~in(tptp_fun_C_12(B, A), A)) | (~in(tptp_fun_C_12(B, A), B))))) <=> (disjoint(A, B) | (~((~in(tptp_fun_C_12(B, A), A)) | (~in(tptp_fun_C_12(B, A), B)))))), ((disjoint(A, B) | (in(tptp_fun_C_12(B, A), A) & in(tptp_fun_C_12(B, A), B))) <=> (disjoint(A, B) | (~((~in(tptp_fun_C_12(B, A), A)) | (~in(tptp_fun_C_12(B, A), B))))))), trans(monotonicity(quant_intro(proof_bind(^[C: $i] : trans(monotonicity(rewrite((in(C, A) & in(C, B)) <=> (~((~in(C, B)) | (~in(C, A))))), ((~(in(C, A) & in(C, B))) <=> (~(~((~in(C, B)) | (~in(C, A))))))), rewrite((~(~((~in(C, B)) | (~in(C, A))))) <=> ((~in(C, B)) | (~in(C, A)))), ((~(in(C, A) & in(C, B))) <=> ((~in(C, B)) | (~in(C, A)))))), (![C: $i] : (~(in(C, A) & in(C, B))) <=> ![C: $i] : ((~in(C, B)) | (~in(C, A))))), ((![C: $i] : (~(in(C, A) & in(C, B))) | (~disjoint(A, B))) <=> (![C: $i] : ((~in(C, B)) | (~in(C, A))) | (~disjoint(A, B))))), rewrite((![C: $i] : ((~in(C, B)) | (~in(C, A))) | (~disjoint(A, B))) <=> ((~disjoint(A, B)) | ![C: $i] : ((~in(C, B)) | (~in(C, A))))), ((![C: $i] : (~(in(C, A) & in(C, B))) | (~disjoint(A, B))) <=> ((~disjoint(A, B)) | ![C: $i] : ((~in(C, B)) | (~in(C, A)))))), (((disjoint(A, B) | (in(tptp_fun_C_12(B, A), A) & in(tptp_fun_C_12(B, A), B))) & (![C: $i] : (~(in(C, A) & in(C, B))) | (~disjoint(A, B)))) <=> ((disjoint(A, B) | (~((~in(tptp_fun_C_12(B, A), A)) | (~in(tptp_fun_C_12(B, A), B))))) & ((~disjoint(A, B)) | ![C: $i] : ((~in(C, B)) | (~in(C, A))))))), rewrite(((disjoint(A, B) | (~((~in(tptp_fun_C_12(B, A), A)) | (~in(tptp_fun_C_12(B, A), B))))) & ((~disjoint(A, B)) | ![C: $i] : ((~in(C, B)) | (~in(C, A))))) <=> (~((~(disjoint(A, B) | (~((~in(tptp_fun_C_12(B, A), A)) | (~in(tptp_fun_C_12(B, A), B)))))) | (~((~disjoint(A, B)) | ![C: $i] : ((~in(C, B)) | (~in(C, A)))))))), (((disjoint(A, B) | (in(tptp_fun_C_12(B, A), A) & in(tptp_fun_C_12(B, A), B))) & (![C: $i] : (~(in(C, A) & in(C, B))) | (~disjoint(A, B)))) <=> (~((~(disjoint(A, B) | (~((~in(tptp_fun_C_12(B, A), A)) | (~in(tptp_fun_C_12(B, A), B)))))) | (~((~disjoint(A, B)) | ![C: $i] : ((~in(C, B)) | (~in(C, A)))))))))),
% 7.07/4.77 inference(bind,[status(th)],[])).
% 7.07/4.77 tff(74,plain,
% 7.07/4.77 (![A: $i, B: $i] : ((disjoint(A, B) | (in(tptp_fun_C_12(B, A), A) & in(tptp_fun_C_12(B, A), B))) & (![C: $i] : (~(in(C, A) & in(C, B))) | (~disjoint(A, B)))) <=> ![A: $i, B: $i] : (~((~(disjoint(A, B) | (~((~in(tptp_fun_C_12(B, A), A)) | (~in(tptp_fun_C_12(B, A), B)))))) | (~((~disjoint(A, B)) | ![C: $i] : ((~in(C, B)) | (~in(C, A)))))))),
% 7.07/4.77 inference(quant_intro,[status(thm)],[73])).
% 7.07/4.77 tff(75,plain,
% 7.07/4.77 (^[A: $i, B: $i] : rewrite((((~(~disjoint(A, B))) | (~(~(in(tptp_fun_C_12(B, A), A) & in(tptp_fun_C_12(B, A), B))))) & (![C: $i] : (~(in(C, A) & in(C, B))) | (~disjoint(A, B)))) <=> ((disjoint(A, B) | (in(tptp_fun_C_12(B, A), A) & in(tptp_fun_C_12(B, A), B))) & (![C: $i] : (~(in(C, A) & in(C, B))) | (~disjoint(A, B)))))),
% 7.07/4.77 inference(bind,[status(th)],[])).
% 7.07/4.77 tff(76,plain,
% 7.07/4.77 (![A: $i, B: $i] : (((~(~disjoint(A, B))) | (~(~(in(tptp_fun_C_12(B, A), A) & in(tptp_fun_C_12(B, A), B))))) & (![C: $i] : (~(in(C, A) & in(C, B))) | (~disjoint(A, B)))) <=> ![A: $i, B: $i] : ((disjoint(A, B) | (in(tptp_fun_C_12(B, A), A) & in(tptp_fun_C_12(B, A), B))) & (![C: $i] : (~(in(C, A) & in(C, B))) | (~disjoint(A, B))))),
% 7.07/4.77 inference(quant_intro,[status(thm)],[75])).
% 7.07/4.77 tff(77,plain,
% 7.07/4.77 (![A: $i, B: $i] : ((~((~disjoint(A, B)) & ![C: $i] : (~(in(C, A) & in(C, B))))) & (~(?[C: $i] : (in(C, A) & in(C, B)) & disjoint(A, B)))) <=> ![A: $i, B: $i] : ((~((~disjoint(A, B)) & ![C: $i] : (~(in(C, A) & in(C, B))))) & (~(?[C: $i] : (in(C, A) & in(C, B)) & disjoint(A, B))))),
% 7.07/4.77 inference(rewrite,[status(thm)],[])).
% 7.07/4.77 tff(78,axiom,(![A: $i, B: $i] : ((~((~disjoint(A, B)) & ![C: $i] : (~(in(C, A) & in(C, B))))) & (~(?[C: $i] : (in(C, A) & in(C, B)) & disjoint(A, B))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t3_xboole_0')).
% 7.07/4.77 tff(79,plain,
% 7.07/4.77 (![A: $i, B: $i] : ((~((~disjoint(A, B)) & ![C: $i] : (~(in(C, A) & in(C, B))))) & (~(?[C: $i] : (in(C, A) & in(C, B)) & disjoint(A, B))))),
% 7.07/4.77 inference(modus_ponens,[status(thm)],[78, 77])).
% 7.07/4.77 tff(80,plain,(
% 7.07/4.77 ![A: $i, B: $i] : (((~(~disjoint(A, B))) | (~(~(in(tptp_fun_C_12(B, A), A) & in(tptp_fun_C_12(B, A), B))))) & (![C: $i] : (~(in(C, A) & in(C, B))) | (~disjoint(A, B))))),
% 7.07/4.77 inference(skolemize,[status(sab)],[79])).
% 7.07/4.77 tff(81,plain,
% 7.07/4.77 (![A: $i, B: $i] : ((disjoint(A, B) | (in(tptp_fun_C_12(B, A), A) & in(tptp_fun_C_12(B, A), B))) & (![C: $i] : (~(in(C, A) & in(C, B))) | (~disjoint(A, B))))),
% 7.07/4.78 inference(modus_ponens,[status(thm)],[80, 76])).
% 7.07/4.78 tff(82,plain,
% 7.07/4.78 (![A: $i, B: $i] : (~((~(disjoint(A, B) | (~((~in(tptp_fun_C_12(B, A), A)) | (~in(tptp_fun_C_12(B, A), B)))))) | (~((~disjoint(A, B)) | ![C: $i] : ((~in(C, B)) | (~in(C, A)))))))),
% 7.07/4.78 inference(modus_ponens,[status(thm)],[81, 74])).
% 7.07/4.78 tff(83,plain,
% 7.07/4.78 (![A: $i, B: $i] : (~((~(disjoint(A, B) | (~((~in(tptp_fun_C_12(B, A), A)) | (~in(tptp_fun_C_12(B, A), B)))))) | (~((~disjoint(A, B)) | ![C: $i] : ((~in(C, B)) | (~in(C, A)))))))),
% 7.07/4.78 inference(modus_ponens,[status(thm)],[82, 72])).
% 7.07/4.78 tff(84,plain,
% 7.07/4.78 (((~![A: $i, B: $i] : (~((~(disjoint(A, B) | (~((~in(tptp_fun_C_12(B, A), A)) | (~in(tptp_fun_C_12(B, A), B)))))) | (~((~disjoint(A, B)) | ![C: $i] : ((~in(C, B)) | (~in(C, A)))))))) | (~((~(disjoint(singleton(A!8), singleton(A!8)) | in(tptp_fun_C_12(singleton(A!8), singleton(A!8)), singleton(A!8)))) | (~((~disjoint(singleton(A!8), singleton(A!8))) | ![C: $i] : (~in(C, singleton(A!8)))))))) <=> ((~![A: $i, B: $i] : (~((~(disjoint(A, B) | (~((~in(tptp_fun_C_12(B, A), A)) | (~in(tptp_fun_C_12(B, A), B)))))) | (~((~disjoint(A, B)) | ![C: $i] : ((~in(C, B)) | (~in(C, A)))))))) | (~((~(disjoint(singleton(A!8), singleton(A!8)) | in(tptp_fun_C_12(singleton(A!8), singleton(A!8)), singleton(A!8)))) | (~((~disjoint(singleton(A!8), singleton(A!8))) | ![C: $i] : (~in(C, singleton(A!8))))))))),
% 7.07/4.78 inference(rewrite,[status(thm)],[])).
% 7.07/4.78 tff(85,plain,
% 7.07/4.78 ((~((~(disjoint(singleton(A!8), singleton(A!8)) | (~((~in(tptp_fun_C_12(singleton(A!8), singleton(A!8)), singleton(A!8))) | (~in(tptp_fun_C_12(singleton(A!8), singleton(A!8)), singleton(A!8))))))) | (~((~disjoint(singleton(A!8), singleton(A!8))) | ![C: $i] : ((~in(C, singleton(A!8))) | (~in(C, singleton(A!8)))))))) <=> (~((~(disjoint(singleton(A!8), singleton(A!8)) | in(tptp_fun_C_12(singleton(A!8), singleton(A!8)), singleton(A!8)))) | (~((~disjoint(singleton(A!8), singleton(A!8))) | ![C: $i] : (~in(C, singleton(A!8)))))))),
% 7.07/4.78 inference(rewrite,[status(thm)],[])).
% 7.07/4.78 tff(86,plain,
% 7.07/4.78 (((~![A: $i, B: $i] : (~((~(disjoint(A, B) | (~((~in(tptp_fun_C_12(B, A), A)) | (~in(tptp_fun_C_12(B, A), B)))))) | (~((~disjoint(A, B)) | ![C: $i] : ((~in(C, B)) | (~in(C, A)))))))) | (~((~(disjoint(singleton(A!8), singleton(A!8)) | (~((~in(tptp_fun_C_12(singleton(A!8), singleton(A!8)), singleton(A!8))) | (~in(tptp_fun_C_12(singleton(A!8), singleton(A!8)), singleton(A!8))))))) | (~((~disjoint(singleton(A!8), singleton(A!8))) | ![C: $i] : ((~in(C, singleton(A!8))) | (~in(C, singleton(A!8))))))))) <=> ((~![A: $i, B: $i] : (~((~(disjoint(A, B) | (~((~in(tptp_fun_C_12(B, A), A)) | (~in(tptp_fun_C_12(B, A), B)))))) | (~((~disjoint(A, B)) | ![C: $i] : ((~in(C, B)) | (~in(C, A)))))))) | (~((~(disjoint(singleton(A!8), singleton(A!8)) | in(tptp_fun_C_12(singleton(A!8), singleton(A!8)), singleton(A!8)))) | (~((~disjoint(singleton(A!8), singleton(A!8))) | ![C: $i] : (~in(C, singleton(A!8))))))))),
% 7.07/4.78 inference(monotonicity,[status(thm)],[85])).
% 7.07/4.78 tff(87,plain,
% 7.07/4.78 (((~![A: $i, B: $i] : (~((~(disjoint(A, B) | (~((~in(tptp_fun_C_12(B, A), A)) | (~in(tptp_fun_C_12(B, A), B)))))) | (~((~disjoint(A, B)) | ![C: $i] : ((~in(C, B)) | (~in(C, A)))))))) | (~((~(disjoint(singleton(A!8), singleton(A!8)) | (~((~in(tptp_fun_C_12(singleton(A!8), singleton(A!8)), singleton(A!8))) | (~in(tptp_fun_C_12(singleton(A!8), singleton(A!8)), singleton(A!8))))))) | (~((~disjoint(singleton(A!8), singleton(A!8))) | ![C: $i] : ((~in(C, singleton(A!8))) | (~in(C, singleton(A!8))))))))) <=> ((~![A: $i, B: $i] : (~((~(disjoint(A, B) | (~((~in(tptp_fun_C_12(B, A), A)) | (~in(tptp_fun_C_12(B, A), B)))))) | (~((~disjoint(A, B)) | ![C: $i] : ((~in(C, B)) | (~in(C, A)))))))) | (~((~(disjoint(singleton(A!8), singleton(A!8)) | in(tptp_fun_C_12(singleton(A!8), singleton(A!8)), singleton(A!8)))) | (~((~disjoint(singleton(A!8), singleton(A!8))) | ![C: $i] : (~in(C, singleton(A!8))))))))),
% 7.07/4.78 inference(transitivity,[status(thm)],[86, 84])).
% 7.07/4.78 tff(88,plain,
% 7.07/4.78 ((~![A: $i, B: $i] : (~((~(disjoint(A, B) | (~((~in(tptp_fun_C_12(B, A), A)) | (~in(tptp_fun_C_12(B, A), B)))))) | (~((~disjoint(A, B)) | ![C: $i] : ((~in(C, B)) | (~in(C, A)))))))) | (~((~(disjoint(singleton(A!8), singleton(A!8)) | (~((~in(tptp_fun_C_12(singleton(A!8), singleton(A!8)), singleton(A!8))) | (~in(tptp_fun_C_12(singleton(A!8), singleton(A!8)), singleton(A!8))))))) | (~((~disjoint(singleton(A!8), singleton(A!8))) | ![C: $i] : ((~in(C, singleton(A!8))) | (~in(C, singleton(A!8))))))))),
% 7.07/4.78 inference(quant_inst,[status(thm)],[])).
% 7.07/4.78 tff(89,plain,
% 7.07/4.78 ((~![A: $i, B: $i] : (~((~(disjoint(A, B) | (~((~in(tptp_fun_C_12(B, A), A)) | (~in(tptp_fun_C_12(B, A), B)))))) | (~((~disjoint(A, B)) | ![C: $i] : ((~in(C, B)) | (~in(C, A)))))))) | (~((~(disjoint(singleton(A!8), singleton(A!8)) | in(tptp_fun_C_12(singleton(A!8), singleton(A!8)), singleton(A!8)))) | (~((~disjoint(singleton(A!8), singleton(A!8))) | ![C: $i] : (~in(C, singleton(A!8)))))))),
% 7.07/4.78 inference(modus_ponens,[status(thm)],[88, 87])).
% 7.07/4.78 tff(90,plain,
% 7.07/4.78 (~((~(disjoint(singleton(A!8), singleton(A!8)) | in(tptp_fun_C_12(singleton(A!8), singleton(A!8)), singleton(A!8)))) | (~((~disjoint(singleton(A!8), singleton(A!8))) | ![C: $i] : (~in(C, singleton(A!8))))))),
% 7.07/4.78 inference(unit_resolution,[status(thm)],[89, 83])).
% 7.07/4.78 tff(91,plain,
% 7.07/4.78 (((~(disjoint(singleton(A!8), singleton(A!8)) | in(tptp_fun_C_12(singleton(A!8), singleton(A!8)), singleton(A!8)))) | (~((~disjoint(singleton(A!8), singleton(A!8))) | ![C: $i] : (~in(C, singleton(A!8)))))) | (disjoint(singleton(A!8), singleton(A!8)) | in(tptp_fun_C_12(singleton(A!8), singleton(A!8)), singleton(A!8)))),
% 7.07/4.78 inference(tautology,[status(thm)],[])).
% 7.07/4.78 tff(92,plain,
% 7.07/4.78 (disjoint(singleton(A!8), singleton(A!8)) | in(tptp_fun_C_12(singleton(A!8), singleton(A!8)), singleton(A!8))),
% 7.07/4.78 inference(unit_resolution,[status(thm)],[91, 90])).
% 7.07/4.78 tff(93,plain,
% 7.07/4.78 (^[A: $i, B: $i] : refl((disjoint(A, B) <=> (set_difference(A, B) = A)) <=> (disjoint(A, B) <=> (set_difference(A, B) = A)))),
% 7.07/4.78 inference(bind,[status(th)],[])).
% 7.07/4.78 tff(94,plain,
% 7.07/4.78 (![A: $i, B: $i] : (disjoint(A, B) <=> (set_difference(A, B) = A)) <=> ![A: $i, B: $i] : (disjoint(A, B) <=> (set_difference(A, B) = A))),
% 7.07/4.78 inference(quant_intro,[status(thm)],[93])).
% 7.07/4.78 tff(95,plain,
% 7.07/4.78 (![A: $i, B: $i] : (disjoint(A, B) <=> (set_difference(A, B) = A)) <=> ![A: $i, B: $i] : (disjoint(A, B) <=> (set_difference(A, B) = A))),
% 7.07/4.78 inference(rewrite,[status(thm)],[])).
% 7.07/4.78 tff(96,axiom,(![A: $i, B: $i] : (disjoint(A, B) <=> (set_difference(A, B) = A))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t83_xboole_1')).
% 7.07/4.78 tff(97,plain,
% 7.07/4.78 (![A: $i, B: $i] : (disjoint(A, B) <=> (set_difference(A, B) = A))),
% 7.07/4.78 inference(modus_ponens,[status(thm)],[96, 95])).
% 7.07/4.78 tff(98,plain,(
% 7.07/4.78 ![A: $i, B: $i] : (disjoint(A, B) <=> (set_difference(A, B) = A))),
% 7.07/4.78 inference(skolemize,[status(sab)],[97])).
% 7.07/4.78 tff(99,plain,
% 7.07/4.78 (![A: $i, B: $i] : (disjoint(A, B) <=> (set_difference(A, B) = A))),
% 7.07/4.78 inference(modus_ponens,[status(thm)],[98, 94])).
% 7.07/4.78 tff(100,plain,
% 7.07/4.78 ((~![A: $i, B: $i] : (disjoint(A, B) <=> (set_difference(A, B) = A))) | (disjoint(singleton(A!8), singleton(A!8)) <=> (set_difference(singleton(A!8), singleton(A!8)) = singleton(A!8)))),
% 7.07/4.78 inference(quant_inst,[status(thm)],[])).
% 7.07/4.78 tff(101,plain,
% 7.07/4.78 (disjoint(singleton(A!8), singleton(A!8)) <=> (set_difference(singleton(A!8), singleton(A!8)) = singleton(A!8))),
% 7.07/4.78 inference(unit_resolution,[status(thm)],[100, 99])).
% 7.07/4.78 tff(102,plain,
% 7.07/4.78 ((empty_set = singleton(A!8)) <=> (singleton(A!8) = empty_set)),
% 7.07/4.78 inference(commutativity,[status(thm)],[])).
% 7.07/4.78 tff(103,plain,
% 7.07/4.78 (^[A: $i, B: $i] : refl(((set_difference(A, B) = empty_set) <=> subset(A, B)) <=> ((set_difference(A, B) = empty_set) <=> subset(A, B)))),
% 7.07/4.78 inference(bind,[status(th)],[])).
% 7.07/4.78 tff(104,plain,
% 7.07/4.78 (![A: $i, B: $i] : ((set_difference(A, B) = empty_set) <=> subset(A, B)) <=> ![A: $i, B: $i] : ((set_difference(A, B) = empty_set) <=> subset(A, B))),
% 7.07/4.78 inference(quant_intro,[status(thm)],[103])).
% 7.07/4.78 tff(105,plain,
% 7.07/4.78 (![A: $i, B: $i] : ((set_difference(A, B) = empty_set) <=> subset(A, B)) <=> ![A: $i, B: $i] : ((set_difference(A, B) = empty_set) <=> subset(A, B))),
% 7.07/4.78 inference(rewrite,[status(thm)],[])).
% 7.07/4.78 tff(106,axiom,(![A: $i, B: $i] : ((set_difference(A, B) = empty_set) <=> subset(A, B))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','l32_xboole_1')).
% 7.07/4.78 tff(107,plain,
% 7.07/4.78 (![A: $i, B: $i] : ((set_difference(A, B) = empty_set) <=> subset(A, B))),
% 7.07/4.78 inference(modus_ponens,[status(thm)],[106, 105])).
% 7.07/4.78 tff(108,plain,(
% 7.07/4.78 ![A: $i, B: $i] : ((set_difference(A, B) = empty_set) <=> subset(A, B))),
% 7.07/4.78 inference(skolemize,[status(sab)],[107])).
% 7.07/4.78 tff(109,plain,
% 7.07/4.78 (![A: $i, B: $i] : ((set_difference(A, B) = empty_set) <=> subset(A, B))),
% 7.07/4.78 inference(modus_ponens,[status(thm)],[108, 104])).
% 7.07/4.78 tff(110,plain,
% 7.07/4.78 ((~![A: $i, B: $i] : ((set_difference(A, B) = empty_set) <=> subset(A, B))) | ((set_difference(set_difference(singleton(A!8), B!7), singleton(A!8)) = empty_set) <=> subset(set_difference(singleton(A!8), B!7), singleton(A!8)))),
% 7.07/4.78 inference(quant_inst,[status(thm)],[])).
% 7.07/4.78 tff(111,plain,
% 7.07/4.78 ((set_difference(set_difference(singleton(A!8), B!7), singleton(A!8)) = empty_set) <=> subset(set_difference(singleton(A!8), B!7), singleton(A!8))),
% 7.07/4.78 inference(unit_resolution,[status(thm)],[110, 109])).
% 7.07/4.78 tff(112,plain,
% 7.07/4.78 (^[A: $i, B: $i] : refl(subset(set_difference(A, B), A) <=> subset(set_difference(A, B), A))),
% 7.07/4.78 inference(bind,[status(th)],[])).
% 7.07/4.78 tff(113,plain,
% 7.07/4.78 (![A: $i, B: $i] : subset(set_difference(A, B), A) <=> ![A: $i, B: $i] : subset(set_difference(A, B), A)),
% 7.07/4.78 inference(quant_intro,[status(thm)],[112])).
% 7.07/4.78 tff(114,plain,
% 7.07/4.78 (![A: $i, B: $i] : subset(set_difference(A, B), A) <=> ![A: $i, B: $i] : subset(set_difference(A, B), A)),
% 7.07/4.78 inference(rewrite,[status(thm)],[])).
% 7.07/4.78 tff(115,axiom,(![A: $i, B: $i] : subset(set_difference(A, B), A)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t36_xboole_1')).
% 7.07/4.78 tff(116,plain,
% 7.07/4.78 (![A: $i, B: $i] : subset(set_difference(A, B), A)),
% 7.07/4.78 inference(modus_ponens,[status(thm)],[115, 114])).
% 7.07/4.78 tff(117,plain,(
% 7.07/4.78 ![A: $i, B: $i] : subset(set_difference(A, B), A)),
% 7.07/4.78 inference(skolemize,[status(sab)],[116])).
% 7.07/4.78 tff(118,plain,
% 7.07/4.78 (![A: $i, B: $i] : subset(set_difference(A, B), A)),
% 7.07/4.78 inference(modus_ponens,[status(thm)],[117, 113])).
% 7.07/4.78 tff(119,plain,
% 7.07/4.78 ((~![A: $i, B: $i] : subset(set_difference(A, B), A)) | subset(set_difference(singleton(A!8), B!7), singleton(A!8))),
% 7.07/4.78 inference(quant_inst,[status(thm)],[])).
% 7.07/4.78 tff(120,plain,
% 7.07/4.78 (subset(set_difference(singleton(A!8), B!7), singleton(A!8))),
% 7.07/4.78 inference(unit_resolution,[status(thm)],[119, 118])).
% 7.07/4.78 tff(121,plain,
% 7.07/4.78 ((~((set_difference(set_difference(singleton(A!8), B!7), singleton(A!8)) = empty_set) <=> subset(set_difference(singleton(A!8), B!7), singleton(A!8)))) | (set_difference(set_difference(singleton(A!8), B!7), singleton(A!8)) = empty_set) | (~subset(set_difference(singleton(A!8), B!7), singleton(A!8)))),
% 7.07/4.78 inference(tautology,[status(thm)],[])).
% 7.07/4.78 tff(122,plain,
% 7.07/4.78 ((~((set_difference(set_difference(singleton(A!8), B!7), singleton(A!8)) = empty_set) <=> subset(set_difference(singleton(A!8), B!7), singleton(A!8)))) | (set_difference(set_difference(singleton(A!8), B!7), singleton(A!8)) = empty_set)),
% 7.07/4.78 inference(unit_resolution,[status(thm)],[121, 120])).
% 7.07/4.78 tff(123,plain,
% 7.07/4.78 (set_difference(set_difference(singleton(A!8), B!7), singleton(A!8)) = empty_set),
% 7.07/4.78 inference(unit_resolution,[status(thm)],[122, 111])).
% 7.07/4.78 tff(124,plain,
% 7.07/4.78 (^[A: $i, B: $i] : refl((set_difference(set_union2(A, B), B) = set_difference(A, B)) <=> (set_difference(set_union2(A, B), B) = set_difference(A, B)))),
% 7.07/4.78 inference(bind,[status(th)],[])).
% 7.07/4.78 tff(125,plain,
% 7.07/4.78 (![A: $i, B: $i] : (set_difference(set_union2(A, B), B) = set_difference(A, B)) <=> ![A: $i, B: $i] : (set_difference(set_union2(A, B), B) = set_difference(A, B))),
% 7.07/4.78 inference(quant_intro,[status(thm)],[124])).
% 7.07/4.78 tff(126,plain,
% 7.07/4.78 (![A: $i, B: $i] : (set_difference(set_union2(A, B), B) = set_difference(A, B)) <=> ![A: $i, B: $i] : (set_difference(set_union2(A, B), B) = set_difference(A, B))),
% 7.07/4.78 inference(rewrite,[status(thm)],[])).
% 7.07/4.78 tff(127,axiom,(![A: $i, B: $i] : (set_difference(set_union2(A, B), B) = set_difference(A, B))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t40_xboole_1')).
% 7.07/4.78 tff(128,plain,
% 7.07/4.78 (![A: $i, B: $i] : (set_difference(set_union2(A, B), B) = set_difference(A, B))),
% 7.07/4.78 inference(modus_ponens,[status(thm)],[127, 126])).
% 7.07/4.78 tff(129,plain,(
% 7.07/4.78 ![A: $i, B: $i] : (set_difference(set_union2(A, B), B) = set_difference(A, B))),
% 7.07/4.78 inference(skolemize,[status(sab)],[128])).
% 7.07/4.78 tff(130,plain,
% 7.07/4.78 (![A: $i, B: $i] : (set_difference(set_union2(A, B), B) = set_difference(A, B))),
% 7.07/4.78 inference(modus_ponens,[status(thm)],[129, 125])).
% 7.07/4.78 tff(131,plain,
% 7.07/4.78 ((~![A: $i, B: $i] : (set_difference(set_union2(A, B), B) = set_difference(A, B))) | (set_difference(set_union2(set_difference(singleton(A!8), B!7), singleton(A!8)), singleton(A!8)) = set_difference(set_difference(singleton(A!8), B!7), singleton(A!8)))),
% 7.07/4.78 inference(quant_inst,[status(thm)],[])).
% 7.07/4.78 tff(132,plain,
% 7.07/4.78 (set_difference(set_union2(set_difference(singleton(A!8), B!7), singleton(A!8)), singleton(A!8)) = set_difference(set_difference(singleton(A!8), B!7), singleton(A!8))),
% 7.07/4.78 inference(unit_resolution,[status(thm)],[131, 130])).
% 7.07/4.78 tff(133,plain,
% 7.07/4.78 (^[A: $i, B: $i] : refl(((~subset(A, B)) | (set_union2(A, B) = B)) <=> ((~subset(A, B)) | (set_union2(A, B) = B)))),
% 7.07/4.78 inference(bind,[status(th)],[])).
% 7.07/4.78 tff(134,plain,
% 7.07/4.78 (![A: $i, B: $i] : ((~subset(A, B)) | (set_union2(A, B) = B)) <=> ![A: $i, B: $i] : ((~subset(A, B)) | (set_union2(A, B) = B))),
% 7.07/4.78 inference(quant_intro,[status(thm)],[133])).
% 7.07/4.78 tff(135,plain,
% 7.07/4.78 (![A: $i, B: $i] : ((~subset(A, B)) | (set_union2(A, B) = B)) <=> ![A: $i, B: $i] : ((~subset(A, B)) | (set_union2(A, B) = B))),
% 7.07/4.78 inference(rewrite,[status(thm)],[])).
% 7.07/4.78 tff(136,plain,
% 7.07/4.78 (^[A: $i, B: $i] : rewrite((subset(A, B) => (set_union2(A, B) = B)) <=> ((~subset(A, B)) | (set_union2(A, B) = B)))),
% 7.07/4.78 inference(bind,[status(th)],[])).
% 7.07/4.78 tff(137,plain,
% 7.07/4.78 (![A: $i, B: $i] : (subset(A, B) => (set_union2(A, B) = B)) <=> ![A: $i, B: $i] : ((~subset(A, B)) | (set_union2(A, B) = B))),
% 7.07/4.78 inference(quant_intro,[status(thm)],[136])).
% 7.07/4.78 tff(138,axiom,(![A: $i, B: $i] : (subset(A, B) => (set_union2(A, B) = B))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t12_xboole_1')).
% 7.07/4.78 tff(139,plain,
% 7.07/4.78 (![A: $i, B: $i] : ((~subset(A, B)) | (set_union2(A, B) = B))),
% 7.07/4.78 inference(modus_ponens,[status(thm)],[138, 137])).
% 7.07/4.78 tff(140,plain,
% 7.07/4.78 (![A: $i, B: $i] : ((~subset(A, B)) | (set_union2(A, B) = B))),
% 7.07/4.78 inference(modus_ponens,[status(thm)],[139, 135])).
% 7.07/4.78 tff(141,plain,(
% 7.07/4.78 ![A: $i, B: $i] : ((~subset(A, B)) | (set_union2(A, B) = B))),
% 7.07/4.78 inference(skolemize,[status(sab)],[140])).
% 7.07/4.78 tff(142,plain,
% 7.07/4.78 (![A: $i, B: $i] : ((~subset(A, B)) | (set_union2(A, B) = B))),
% 7.07/4.78 inference(modus_ponens,[status(thm)],[141, 134])).
% 7.07/4.78 tff(143,plain,
% 7.07/4.78 (((~![A: $i, B: $i] : ((~subset(A, B)) | (set_union2(A, B) = B))) | ((~subset(set_difference(singleton(A!8), B!7), singleton(A!8))) | (set_union2(set_difference(singleton(A!8), B!7), singleton(A!8)) = singleton(A!8)))) <=> ((~![A: $i, B: $i] : ((~subset(A, B)) | (set_union2(A, B) = B))) | (~subset(set_difference(singleton(A!8), B!7), singleton(A!8))) | (set_union2(set_difference(singleton(A!8), B!7), singleton(A!8)) = singleton(A!8)))),
% 7.07/4.78 inference(rewrite,[status(thm)],[])).
% 7.07/4.78 tff(144,plain,
% 7.07/4.78 ((~![A: $i, B: $i] : ((~subset(A, B)) | (set_union2(A, B) = B))) | ((~subset(set_difference(singleton(A!8), B!7), singleton(A!8))) | (set_union2(set_difference(singleton(A!8), B!7), singleton(A!8)) = singleton(A!8)))),
% 7.07/4.78 inference(quant_inst,[status(thm)],[])).
% 7.07/4.78 tff(145,plain,
% 7.07/4.78 ((~![A: $i, B: $i] : ((~subset(A, B)) | (set_union2(A, B) = B))) | (~subset(set_difference(singleton(A!8), B!7), singleton(A!8))) | (set_union2(set_difference(singleton(A!8), B!7), singleton(A!8)) = singleton(A!8))),
% 7.07/4.78 inference(modus_ponens,[status(thm)],[144, 143])).
% 7.07/4.78 tff(146,plain,
% 7.07/4.78 (set_union2(set_difference(singleton(A!8), B!7), singleton(A!8)) = singleton(A!8)),
% 7.07/4.78 inference(unit_resolution,[status(thm)],[145, 142, 120])).
% 7.07/4.78 tff(147,plain,
% 7.07/4.78 (singleton(A!8) = set_union2(set_difference(singleton(A!8), B!7), singleton(A!8))),
% 7.07/4.78 inference(symmetry,[status(thm)],[146])).
% 7.07/4.78 tff(148,plain,
% 7.07/4.78 (set_difference(singleton(A!8), singleton(A!8)) = set_difference(set_union2(set_difference(singleton(A!8), B!7), singleton(A!8)), singleton(A!8))),
% 7.07/4.78 inference(monotonicity,[status(thm)],[147])).
% 7.07/4.78 tff(149,plain,
% 7.07/4.78 (set_difference(singleton(A!8), singleton(A!8)) = empty_set),
% 7.07/4.78 inference(transitivity,[status(thm)],[148, 132, 123])).
% 7.07/4.78 tff(150,plain,
% 7.07/4.78 ((set_difference(singleton(A!8), singleton(A!8)) = singleton(A!8)) <=> (empty_set = singleton(A!8))),
% 7.07/4.78 inference(monotonicity,[status(thm)],[149])).
% 7.07/4.78 tff(151,plain,
% 7.07/4.78 ((set_difference(singleton(A!8), singleton(A!8)) = singleton(A!8)) <=> (singleton(A!8) = empty_set)),
% 7.07/4.78 inference(transitivity,[status(thm)],[150, 102])).
% 7.07/4.78 tff(152,plain,
% 7.07/4.78 ((singleton(A!8) = empty_set) <=> (set_difference(singleton(A!8), singleton(A!8)) = singleton(A!8))),
% 7.07/4.78 inference(symmetry,[status(thm)],[151])).
% 7.07/4.78 tff(153,plain,
% 7.07/4.78 ((~(singleton(A!8) = empty_set)) <=> (~(set_difference(singleton(A!8), singleton(A!8)) = singleton(A!8)))),
% 7.07/4.78 inference(monotonicity,[status(thm)],[152])).
% 7.07/4.78 tff(154,plain,
% 7.07/4.78 (^[A: $i] : refl((~(singleton(A) = empty_set)) <=> (~(singleton(A) = empty_set)))),
% 7.07/4.78 inference(bind,[status(th)],[])).
% 7.07/4.78 tff(155,plain,
% 7.07/4.78 (![A: $i] : (~(singleton(A) = empty_set)) <=> ![A: $i] : (~(singleton(A) = empty_set))),
% 7.07/4.78 inference(quant_intro,[status(thm)],[154])).
% 7.07/4.78 tff(156,plain,
% 7.07/4.78 (![A: $i] : (~(singleton(A) = empty_set)) <=> ![A: $i] : (~(singleton(A) = empty_set))),
% 7.07/4.78 inference(rewrite,[status(thm)],[])).
% 7.07/4.78 tff(157,axiom,(![A: $i] : (~(singleton(A) = empty_set))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','l1_zfmisc_1')).
% 7.07/4.78 tff(158,plain,
% 7.07/4.78 (![A: $i] : (~(singleton(A) = empty_set))),
% 7.07/4.78 inference(modus_ponens,[status(thm)],[157, 156])).
% 7.07/4.78 tff(159,plain,(
% 7.07/4.78 ![A: $i] : (~(singleton(A) = empty_set))),
% 7.07/4.78 inference(skolemize,[status(sab)],[158])).
% 7.07/4.78 tff(160,plain,
% 7.07/4.78 (![A: $i] : (~(singleton(A) = empty_set))),
% 7.07/4.78 inference(modus_ponens,[status(thm)],[159, 155])).
% 7.07/4.78 tff(161,plain,
% 7.07/4.78 ((~![A: $i] : (~(singleton(A) = empty_set))) | (~(singleton(A!8) = empty_set))),
% 7.07/4.78 inference(quant_inst,[status(thm)],[])).
% 7.07/4.78 tff(162,plain,
% 7.07/4.78 (~(singleton(A!8) = empty_set)),
% 7.07/4.78 inference(unit_resolution,[status(thm)],[161, 160])).
% 7.07/4.78 tff(163,plain,
% 7.07/4.78 (~(set_difference(singleton(A!8), singleton(A!8)) = singleton(A!8))),
% 7.07/4.78 inference(modus_ponens,[status(thm)],[162, 153])).
% 7.07/4.78 tff(164,plain,
% 7.07/4.78 ((~(disjoint(singleton(A!8), singleton(A!8)) <=> (set_difference(singleton(A!8), singleton(A!8)) = singleton(A!8)))) | (~disjoint(singleton(A!8), singleton(A!8))) | (set_difference(singleton(A!8), singleton(A!8)) = singleton(A!8))),
% 7.07/4.78 inference(tautology,[status(thm)],[])).
% 7.07/4.78 tff(165,plain,
% 7.07/4.78 (~disjoint(singleton(A!8), singleton(A!8))),
% 7.07/4.78 inference(unit_resolution,[status(thm)],[164, 163, 101])).
% 7.07/4.78 tff(166,plain,
% 7.07/4.78 ((~(disjoint(singleton(A!8), singleton(A!8)) | in(tptp_fun_C_12(singleton(A!8), singleton(A!8)), singleton(A!8)))) | disjoint(singleton(A!8), singleton(A!8)) | in(tptp_fun_C_12(singleton(A!8), singleton(A!8)), singleton(A!8))),
% 7.07/4.78 inference(tautology,[status(thm)],[])).
% 7.07/4.78 tff(167,plain,
% 7.07/4.78 (in(tptp_fun_C_12(singleton(A!8), singleton(A!8)), singleton(A!8))),
% 7.07/4.78 inference(unit_resolution,[status(thm)],[166, 165, 92])).
% 7.07/4.78 tff(168,plain,
% 7.07/4.78 ((~(in(tptp_fun_C_12(singleton(A!8), singleton(A!8)), singleton(A!8)) <=> (tptp_fun_C_12(singleton(A!8), singleton(A!8)) = A!8))) | (~in(tptp_fun_C_12(singleton(A!8), singleton(A!8)), singleton(A!8))) | (tptp_fun_C_12(singleton(A!8), singleton(A!8)) = A!8)),
% 7.07/4.78 inference(tautology,[status(thm)],[])).
% 7.07/4.78 tff(169,plain,
% 7.07/4.78 ((~(in(tptp_fun_C_12(singleton(A!8), singleton(A!8)), singleton(A!8)) <=> (tptp_fun_C_12(singleton(A!8), singleton(A!8)) = A!8))) | (tptp_fun_C_12(singleton(A!8), singleton(A!8)) = A!8)),
% 7.07/4.78 inference(unit_resolution,[status(thm)],[168, 167])).
% 7.07/4.78 tff(170,plain,
% 7.07/4.78 (tptp_fun_C_12(singleton(A!8), singleton(A!8)) = A!8),
% 7.07/4.78 inference(unit_resolution,[status(thm)],[169, 67])).
% 7.07/4.78 tff(171,plain,
% 7.07/4.78 (in(tptp_fun_C_12(singleton(A!8), singleton(A!8)), singleton(A!8)) <=> in(A!8, singleton(A!8))),
% 7.07/4.78 inference(monotonicity,[status(thm)],[170])).
% 7.07/4.78 tff(172,plain,
% 7.07/4.78 (in(A!8, singleton(A!8))),
% 7.07/4.78 inference(modus_ponens,[status(thm)],[167, 171])).
% 7.07/4.78 tff(173,plain,
% 7.07/4.78 ((in(A!8, singleton(A!8)) | in(A!8, set_difference(B!7, singleton(A!8)))) | (~in(A!8, singleton(A!8)))),
% 7.07/4.78 inference(tautology,[status(thm)],[])).
% 7.07/4.78 tff(174,plain,
% 7.07/4.78 (in(A!8, singleton(A!8)) | in(A!8, set_difference(B!7, singleton(A!8)))),
% 7.07/4.78 inference(unit_resolution,[status(thm)],[173, 172])).
% 7.07/4.78 tff(175,plain,
% 7.07/4.78 ((~(in(A!8, B!7) <=> (in(A!8, singleton(A!8)) | in(A!8, set_difference(B!7, singleton(A!8)))))) | in(A!8, B!7) | (~(in(A!8, singleton(A!8)) | in(A!8, set_difference(B!7, singleton(A!8)))))),
% 7.07/4.78 inference(tautology,[status(thm)],[])).
% 7.07/4.78 tff(176,plain,
% 7.07/4.78 ((~(in(A!8, B!7) <=> (in(A!8, singleton(A!8)) | in(A!8, set_difference(B!7, singleton(A!8)))))) | in(A!8, B!7)),
% 7.07/4.78 inference(unit_resolution,[status(thm)],[175, 174])).
% 7.07/4.78 tff(177,plain,
% 7.07/4.78 (~(in(A!8, B!7) <=> (in(A!8, singleton(A!8)) | in(A!8, set_difference(B!7, singleton(A!8)))))),
% 7.07/4.78 inference(unit_resolution,[status(thm)],[176, 49])).
% 7.07/4.78 tff(178,plain,
% 7.07/4.78 ((~(subset(singleton(A!8), B!7) <=> in(A!8, B!7))) <=> ((~subset(singleton(A!8), B!7)) <=> in(A!8, B!7))),
% 7.07/4.78 inference(rewrite,[status(thm)],[])).
% 7.07/4.78 tff(179,plain,
% 7.07/4.78 ((~![A: $i, B: $i] : (subset(singleton(A), B) <=> in(A, B))) <=> (~![A: $i, B: $i] : (subset(singleton(A), B) <=> in(A, B)))),
% 7.07/4.78 inference(rewrite,[status(thm)],[])).
% 7.07/4.78 tff(180,axiom,(~![A: $i, B: $i] : (subset(singleton(A), B) <=> in(A, B))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','l2_zfmisc_1')).
% 7.07/4.78 tff(181,plain,
% 7.07/4.78 (~![A: $i, B: $i] : (subset(singleton(A), B) <=> in(A, B))),
% 7.07/4.78 inference(modus_ponens,[status(thm)],[180, 179])).
% 7.07/4.78 tff(182,plain,
% 7.07/4.78 (~![A: $i, B: $i] : (subset(singleton(A), B) <=> in(A, B))),
% 7.07/4.78 inference(modus_ponens,[status(thm)],[181, 179])).
% 7.07/4.78 tff(183,plain,
% 7.07/4.78 (~![A: $i, B: $i] : (subset(singleton(A), B) <=> in(A, B))),
% 7.07/4.78 inference(modus_ponens,[status(thm)],[182, 179])).
% 7.07/4.78 tff(184,plain,
% 7.07/4.78 (~![A: $i, B: $i] : (subset(singleton(A), B) <=> in(A, B))),
% 7.07/4.78 inference(modus_ponens,[status(thm)],[183, 179])).
% 7.07/4.78 tff(185,plain,
% 7.07/4.78 (~![A: $i, B: $i] : (subset(singleton(A), B) <=> in(A, B))),
% 7.07/4.78 inference(modus_ponens,[status(thm)],[184, 179])).
% 7.07/4.78 tff(186,plain,
% 7.07/4.78 (~![A: $i, B: $i] : (subset(singleton(A), B) <=> in(A, B))),
% 7.07/4.78 inference(modus_ponens,[status(thm)],[185, 179])).
% 7.07/4.78 tff(187,plain,
% 7.07/4.78 (~![A: $i, B: $i] : (subset(singleton(A), B) <=> in(A, B))),
% 7.07/4.78 inference(modus_ponens,[status(thm)],[186, 179])).
% 7.07/4.78 tff(188,plain,(
% 7.07/4.78 ~(subset(singleton(A!8), B!7) <=> in(A!8, B!7))),
% 7.07/4.78 inference(skolemize,[status(sab)],[187])).
% 7.07/4.78 tff(189,plain,
% 7.07/4.78 ((~subset(singleton(A!8), B!7)) <=> in(A!8, B!7)),
% 7.07/4.78 inference(modus_ponens,[status(thm)],[188, 178])).
% 7.07/4.78 tff(190,plain,
% 7.07/4.78 (subset(singleton(A!8), B!7) | in(A!8, B!7) | (~((~subset(singleton(A!8), B!7)) <=> in(A!8, B!7)))),
% 7.07/4.78 inference(tautology,[status(thm)],[])).
% 7.07/4.78 tff(191,plain,
% 7.07/4.78 (subset(singleton(A!8), B!7) | in(A!8, B!7)),
% 7.07/4.78 inference(unit_resolution,[status(thm)],[190, 189])).
% 7.07/4.78 tff(192,plain,
% 7.07/4.78 (subset(singleton(A!8), B!7)),
% 7.07/4.78 inference(unit_resolution,[status(thm)],[191, 49])).
% 7.07/4.78 tff(193,plain,
% 7.07/4.78 (^[A: $i, B: $i] : refl(((~subset(A, B)) | (B = set_union2(A, set_difference(B, A)))) <=> ((~subset(A, B)) | (B = set_union2(A, set_difference(B, A)))))),
% 7.07/4.78 inference(bind,[status(th)],[])).
% 7.07/4.78 tff(194,plain,
% 7.07/4.78 (![A: $i, B: $i] : ((~subset(A, B)) | (B = set_union2(A, set_difference(B, A)))) <=> ![A: $i, B: $i] : ((~subset(A, B)) | (B = set_union2(A, set_difference(B, A))))),
% 7.07/4.78 inference(quant_intro,[status(thm)],[193])).
% 7.07/4.78 tff(195,plain,
% 7.07/4.78 (![A: $i, B: $i] : ((~subset(A, B)) | (B = set_union2(A, set_difference(B, A)))) <=> ![A: $i, B: $i] : ((~subset(A, B)) | (B = set_union2(A, set_difference(B, A))))),
% 7.07/4.78 inference(rewrite,[status(thm)],[])).
% 7.07/4.78 tff(196,plain,
% 7.07/4.78 (^[A: $i, B: $i] : rewrite((subset(A, B) => (B = set_union2(A, set_difference(B, A)))) <=> ((~subset(A, B)) | (B = set_union2(A, set_difference(B, A)))))),
% 7.07/4.78 inference(bind,[status(th)],[])).
% 7.07/4.78 tff(197,plain,
% 7.07/4.78 (![A: $i, B: $i] : (subset(A, B) => (B = set_union2(A, set_difference(B, A)))) <=> ![A: $i, B: $i] : ((~subset(A, B)) | (B = set_union2(A, set_difference(B, A))))),
% 7.07/4.78 inference(quant_intro,[status(thm)],[196])).
% 7.07/4.78 tff(198,axiom,(![A: $i, B: $i] : (subset(A, B) => (B = set_union2(A, set_difference(B, A))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t45_xboole_1')).
% 7.07/4.78 tff(199,plain,
% 7.07/4.78 (![A: $i, B: $i] : ((~subset(A, B)) | (B = set_union2(A, set_difference(B, A))))),
% 7.07/4.78 inference(modus_ponens,[status(thm)],[198, 197])).
% 7.07/4.78 tff(200,plain,
% 7.07/4.78 (![A: $i, B: $i] : ((~subset(A, B)) | (B = set_union2(A, set_difference(B, A))))),
% 7.07/4.78 inference(modus_ponens,[status(thm)],[199, 195])).
% 7.07/4.78 tff(201,plain,(
% 7.07/4.78 ![A: $i, B: $i] : ((~subset(A, B)) | (B = set_union2(A, set_difference(B, A))))),
% 7.07/4.78 inference(skolemize,[status(sab)],[200])).
% 7.07/4.78 tff(202,plain,
% 7.07/4.78 (![A: $i, B: $i] : ((~subset(A, B)) | (B = set_union2(A, set_difference(B, A))))),
% 7.07/4.78 inference(modus_ponens,[status(thm)],[201, 194])).
% 7.07/4.78 tff(203,plain,
% 7.07/4.78 (((~![A: $i, B: $i] : ((~subset(A, B)) | (B = set_union2(A, set_difference(B, A))))) | ((~subset(singleton(A!8), B!7)) | (B!7 = set_union2(singleton(A!8), set_difference(B!7, singleton(A!8)))))) <=> ((~![A: $i, B: $i] : ((~subset(A, B)) | (B = set_union2(A, set_difference(B, A))))) | (~subset(singleton(A!8), B!7)) | (B!7 = set_union2(singleton(A!8), set_difference(B!7, singleton(A!8)))))),
% 7.07/4.78 inference(rewrite,[status(thm)],[])).
% 7.07/4.78 tff(204,plain,
% 7.07/4.78 ((~![A: $i, B: $i] : ((~subset(A, B)) | (B = set_union2(A, set_difference(B, A))))) | ((~subset(singleton(A!8), B!7)) | (B!7 = set_union2(singleton(A!8), set_difference(B!7, singleton(A!8)))))),
% 7.07/4.78 inference(quant_inst,[status(thm)],[])).
% 7.07/4.78 tff(205,plain,
% 7.07/4.78 ((~![A: $i, B: $i] : ((~subset(A, B)) | (B = set_union2(A, set_difference(B, A))))) | (~subset(singleton(A!8), B!7)) | (B!7 = set_union2(singleton(A!8), set_difference(B!7, singleton(A!8))))),
% 7.07/4.78 inference(modus_ponens,[status(thm)],[204, 203])).
% 7.07/4.78 tff(206,plain,
% 7.07/4.78 ((~subset(singleton(A!8), B!7)) | (B!7 = set_union2(singleton(A!8), set_difference(B!7, singleton(A!8))))),
% 7.07/4.78 inference(unit_resolution,[status(thm)],[205, 202])).
% 7.07/4.78 tff(207,plain,
% 7.07/4.78 (B!7 = set_union2(singleton(A!8), set_difference(B!7, singleton(A!8)))),
% 7.07/4.78 inference(unit_resolution,[status(thm)],[206, 192])).
% 7.07/4.78 tff(208,plain,
% 7.07/4.78 (^[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_3(C, B, A), C)) <=> (in(tptp_fun_D_3(C, B, A), A) | in(tptp_fun_D_3(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_3(C, B, A), C)) <=> (in(tptp_fun_D_3(C, B, A), A) | in(tptp_fun_D_3(C, B, A), B))))))))),
% 7.07/4.78 inference(bind,[status(th)],[])).
% 7.07/4.78 tff(209,plain,
% 7.07/4.78 (![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_3(C, B, A), C)) <=> (in(tptp_fun_D_3(C, B, A), A) | in(tptp_fun_D_3(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_3(C, B, A), C)) <=> (in(tptp_fun_D_3(C, B, A), A) | in(tptp_fun_D_3(C, B, A), B)))))))),
% 7.07/4.78 inference(quant_intro,[status(thm)],[208])).
% 7.07/4.78 tff(210,plain,
% 7.07/4.78 (![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_3(C, B, A), C)) <=> (in(tptp_fun_D_3(C, B, A), A) | in(tptp_fun_D_3(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_3(C, B, A), C)) <=> (in(tptp_fun_D_3(C, B, A), A) | in(tptp_fun_D_3(C, B, A), B)))))))),
% 7.07/4.78 inference(pull_quant,[status(thm)],[])).
% 7.07/4.78 tff(211,plain,
% 7.07/4.78 (^[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_3(C, B, A), C)) <=> (in(tptp_fun_D_3(C, B, A), A) | in(tptp_fun_D_3(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_3(C, B, A), C)) <=> (in(tptp_fun_D_3(C, B, A), A) | in(tptp_fun_D_3(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_3(C, B, A), C)) <=> (in(tptp_fun_D_3(C, B, A), A) | in(tptp_fun_D_3(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_3(C, B, A), C)) <=> (in(tptp_fun_D_3(C, B, A), A) | in(tptp_fun_D_3(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_3(C, B, A), C)) <=> (in(tptp_fun_D_3(C, B, A), A) | in(tptp_fun_D_3(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_3(C, B, A), C)) <=> (in(tptp_fun_D_3(C, B, A), A) | in(tptp_fun_D_3(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_3(C, B, A), C)) <=> (in(tptp_fun_D_3(C, B, A), A) | in(tptp_fun_D_3(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_3(C, B, A), C)) <=> (in(tptp_fun_D_3(C, B, A), A) | in(tptp_fun_D_3(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_3(C, B, A), C)) <=> (in(tptp_fun_D_3(C, B, A), A) | in(tptp_fun_D_3(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_3(C, B, A), C)) <=> (in(tptp_fun_D_3(C, B, A), A) | in(tptp_fun_D_3(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_3(C, B, A), C)) <=> (in(tptp_fun_D_3(C, B, A), A) | in(tptp_fun_D_3(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_3(C, B, A), C)) <=> (in(tptp_fun_D_3(C, B, A), A) | in(tptp_fun_D_3(C, B, A), B)))))))))),
% 7.07/4.78 inference(bind,[status(th)],[])).
% 7.07/4.78 tff(212,plain,
% 7.07/4.78 (![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_3(C, B, A), C)) <=> (in(tptp_fun_D_3(C, B, A), A) | in(tptp_fun_D_3(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_3(C, B, A), C)) <=> (in(tptp_fun_D_3(C, B, A), A) | in(tptp_fun_D_3(C, B, A), B)))))))),
% 7.07/4.78 inference(quant_intro,[status(thm)],[211])).
% 7.07/4.78 tff(213,plain,
% 7.07/4.78 (![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_3(C, B, A), C)) <=> (in(tptp_fun_D_3(C, B, A), A) | in(tptp_fun_D_3(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_3(C, B, A), C)) <=> (in(tptp_fun_D_3(C, B, A), A) | in(tptp_fun_D_3(C, B, A), B)))))))),
% 7.07/4.78 inference(transitivity,[status(thm)],[212, 210])).
% 7.07/4.78 tff(214,plain,
% 7.07/4.78 (![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_3(C, B, A), C)) <=> (in(tptp_fun_D_3(C, B, A), A) | in(tptp_fun_D_3(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_3(C, B, A), C)) <=> (in(tptp_fun_D_3(C, B, A), A) | in(tptp_fun_D_3(C, B, A), B)))))))),
% 7.07/4.78 inference(transitivity,[status(thm)],[213, 209])).
% 7.07/4.78 tff(215,plain,
% 7.07/4.78 (^[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_3(C, B, A), C)) <=> (in(tptp_fun_D_3(C, B, A), A) | in(tptp_fun_D_3(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_3(C, B, A), C)) <=> (in(tptp_fun_D_3(C, B, A), A) | in(tptp_fun_D_3(C, B, A), B))))))))),
% 7.07/4.78 inference(bind,[status(th)],[])).
% 7.07/4.78 tff(216,plain,
% 7.07/4.78 (![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_3(C, B, A), C)) <=> (in(tptp_fun_D_3(C, B, A), A) | in(tptp_fun_D_3(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_3(C, B, A), C)) <=> (in(tptp_fun_D_3(C, B, A), A) | in(tptp_fun_D_3(C, B, A), B)))))))),
% 7.07/4.78 inference(quant_intro,[status(thm)],[215])).
% 7.07/4.78 tff(217,plain,
% 7.07/4.78 (![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_3(C, B, A), C)) <=> (in(tptp_fun_D_3(C, B, A), A) | in(tptp_fun_D_3(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_3(C, B, A), C)) <=> (in(tptp_fun_D_3(C, B, A), A) | in(tptp_fun_D_3(C, B, A), B)))))))),
% 7.07/4.78 inference(transitivity,[status(thm)],[216, 214])).
% 7.07/4.78 tff(218,plain,
% 7.07/4.78 (^[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_3(C, B, A), C)) <=> (in(tptp_fun_D_3(C, B, A), A) | in(tptp_fun_D_3(C, B, A), B))) <=> ((~in(tptp_fun_D_3(C, B, A), C)) <=> (in(tptp_fun_D_3(C, B, A), A) | in(tptp_fun_D_3(C, B, A), B)))), (((C = set_union2(A, B)) | ((~in(tptp_fun_D_3(C, B, A), C)) <=> (in(tptp_fun_D_3(C, B, A), A) | in(tptp_fun_D_3(C, B, A), B)))) <=> ((C = set_union2(A, B)) | ((~in(tptp_fun_D_3(C, B, A), C)) <=> (in(tptp_fun_D_3(C, B, A), A) | in(tptp_fun_D_3(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_3(C, B, A), C)) <=> (in(tptp_fun_D_3(C, B, A), A) | in(tptp_fun_D_3(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_3(C, B, A), C)) <=> (in(tptp_fun_D_3(C, B, A), A) | in(tptp_fun_D_3(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_3(C, B, A), C)) <=> (in(tptp_fun_D_3(C, B, A), A) | in(tptp_fun_D_3(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_3(C, B, A), C)) <=> (in(tptp_fun_D_3(C, B, A), A) | in(tptp_fun_D_3(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_3(C, B, A), C)) <=> (in(tptp_fun_D_3(C, B, A), A) | in(tptp_fun_D_3(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_3(C, B, A), C)) <=> (in(tptp_fun_D_3(C, B, A), A) | in(tptp_fun_D_3(C, B, A), B)))))))))),
% 7.07/4.78 inference(bind,[status(th)],[])).
% 7.07/4.78 tff(219,plain,
% 7.07/4.78 (![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_3(C, B, A), C)) <=> (in(tptp_fun_D_3(C, B, A), A) | in(tptp_fun_D_3(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_3(C, B, A), C)) <=> (in(tptp_fun_D_3(C, B, A), A) | in(tptp_fun_D_3(C, B, A), B)))))))),
% 7.07/4.78 inference(quant_intro,[status(thm)],[218])).
% 7.07/4.78 tff(220,plain,
% 7.07/4.78 (^[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_3(C, B, A), C) <=> (in(tptp_fun_D_3(C, B, A), A) | in(tptp_fun_D_3(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_3(C, B, A), C)) <=> (in(tptp_fun_D_3(C, B, A), A) | in(tptp_fun_D_3(C, B, A), B))))))),
% 7.07/4.78 inference(bind,[status(th)],[])).
% 7.07/4.78 tff(221,plain,
% 7.07/4.78 (![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_3(C, B, A), C) <=> (in(tptp_fun_D_3(C, B, A), A) | in(tptp_fun_D_3(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_3(C, B, A), C)) <=> (in(tptp_fun_D_3(C, B, A), A) | in(tptp_fun_D_3(C, B, A), B)))))),
% 7.07/4.78 inference(quant_intro,[status(thm)],[220])).
% 7.07/4.78 tff(222,plain,
% 7.07/4.78 (![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))))),
% 7.07/4.78 inference(rewrite,[status(thm)],[])).
% 7.07/4.78 tff(223,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')).
% 7.07/4.78 tff(224,plain,
% 7.07/4.78 (![A: $i, B: $i, C: $i] : ((C = set_union2(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B))))),
% 7.07/4.78 inference(modus_ponens,[status(thm)],[223, 222])).
% 7.07/4.78 tff(225,plain,(
% 7.07/4.78 ![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_3(C, B, A), C) <=> (in(tptp_fun_D_3(C, B, A), A) | in(tptp_fun_D_3(C, B, A), B))))))),
% 7.07/4.78 inference(skolemize,[status(sab)],[224])).
% 7.07/4.78 tff(226,plain,
% 7.07/4.78 (![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_3(C, B, A), C)) <=> (in(tptp_fun_D_3(C, B, A), A) | in(tptp_fun_D_3(C, B, A), B)))))),
% 7.07/4.78 inference(modus_ponens,[status(thm)],[225, 221])).
% 7.07/4.78 tff(227,plain,
% 7.07/4.78 (![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_3(C, B, A), C)) <=> (in(tptp_fun_D_3(C, B, A), A) | in(tptp_fun_D_3(C, B, A), B)))))))),
% 7.07/4.78 inference(modus_ponens,[status(thm)],[226, 219])).
% 7.07/4.78 tff(228,plain,
% 7.07/4.78 (![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_3(C, B, A), C)) <=> (in(tptp_fun_D_3(C, B, A), A) | in(tptp_fun_D_3(C, B, A), B)))))))),
% 7.07/4.78 inference(modus_ponens,[status(thm)],[227, 217])).
% 7.07/4.78 tff(229,plain,
% 7.07/4.78 ((~![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_3(C, B, A), C)) <=> (in(tptp_fun_D_3(C, B, A), A) | in(tptp_fun_D_3(C, B, A), B)))))))) | (~((~((~(B!7 = set_union2(singleton(A!8), set_difference(B!7, singleton(A!8))))) | (in(A!8, B!7) <=> (in(A!8, singleton(A!8)) | in(A!8, set_difference(B!7, singleton(A!8))))))) | (~((B!7 = set_union2(singleton(A!8), set_difference(B!7, singleton(A!8)))) | ((~in(tptp_fun_D_3(B!7, set_difference(B!7, singleton(A!8)), singleton(A!8)), B!7)) <=> (in(tptp_fun_D_3(B!7, set_difference(B!7, singleton(A!8)), singleton(A!8)), singleton(A!8)) | in(tptp_fun_D_3(B!7, set_difference(B!7, singleton(A!8)), singleton(A!8)), set_difference(B!7, singleton(A!8)))))))))),
% 7.07/4.78 inference(quant_inst,[status(thm)],[])).
% 7.07/4.78 tff(230,plain,
% 7.07/4.78 (~((~((~(B!7 = set_union2(singleton(A!8), set_difference(B!7, singleton(A!8))))) | (in(A!8, B!7) <=> (in(A!8, singleton(A!8)) | in(A!8, set_difference(B!7, singleton(A!8))))))) | (~((B!7 = set_union2(singleton(A!8), set_difference(B!7, singleton(A!8)))) | ((~in(tptp_fun_D_3(B!7, set_difference(B!7, singleton(A!8)), singleton(A!8)), B!7)) <=> (in(tptp_fun_D_3(B!7, set_difference(B!7, singleton(A!8)), singleton(A!8)), singleton(A!8)) | in(tptp_fun_D_3(B!7, set_difference(B!7, singleton(A!8)), singleton(A!8)), set_difference(B!7, singleton(A!8))))))))),
% 7.07/4.79 inference(unit_resolution,[status(thm)],[229, 228])).
% 7.07/4.79 tff(231,plain,
% 7.07/4.79 (((~((~(B!7 = set_union2(singleton(A!8), set_difference(B!7, singleton(A!8))))) | (in(A!8, B!7) <=> (in(A!8, singleton(A!8)) | in(A!8, set_difference(B!7, singleton(A!8))))))) | (~((B!7 = set_union2(singleton(A!8), set_difference(B!7, singleton(A!8)))) | ((~in(tptp_fun_D_3(B!7, set_difference(B!7, singleton(A!8)), singleton(A!8)), B!7)) <=> (in(tptp_fun_D_3(B!7, set_difference(B!7, singleton(A!8)), singleton(A!8)), singleton(A!8)) | in(tptp_fun_D_3(B!7, set_difference(B!7, singleton(A!8)), singleton(A!8)), set_difference(B!7, singleton(A!8)))))))) | ((~(B!7 = set_union2(singleton(A!8), set_difference(B!7, singleton(A!8))))) | (in(A!8, B!7) <=> (in(A!8, singleton(A!8)) | in(A!8, set_difference(B!7, singleton(A!8))))))),
% 7.07/4.79 inference(tautology,[status(thm)],[])).
% 7.07/4.79 tff(232,plain,
% 7.07/4.79 ((~(B!7 = set_union2(singleton(A!8), set_difference(B!7, singleton(A!8))))) | (in(A!8, B!7) <=> (in(A!8, singleton(A!8)) | in(A!8, set_difference(B!7, singleton(A!8)))))),
% 7.07/4.79 inference(unit_resolution,[status(thm)],[231, 230])).
% 7.07/4.79 tff(233,plain,
% 7.07/4.79 ((~((~(B!7 = set_union2(singleton(A!8), set_difference(B!7, singleton(A!8))))) | (in(A!8, B!7) <=> (in(A!8, singleton(A!8)) | in(A!8, set_difference(B!7, singleton(A!8))))))) | (~(B!7 = set_union2(singleton(A!8), set_difference(B!7, singleton(A!8))))) | (in(A!8, B!7) <=> (in(A!8, singleton(A!8)) | in(A!8, set_difference(B!7, singleton(A!8)))))),
% 7.07/4.79 inference(tautology,[status(thm)],[])).
% 7.07/4.79 tff(234,plain,
% 7.07/4.79 ((~(B!7 = set_union2(singleton(A!8), set_difference(B!7, singleton(A!8))))) | (in(A!8, B!7) <=> (in(A!8, singleton(A!8)) | in(A!8, set_difference(B!7, singleton(A!8)))))),
% 7.07/4.79 inference(unit_resolution,[status(thm)],[233, 232])).
% 7.07/4.79 tff(235,plain,
% 7.07/4.79 ($false),
% 7.07/4.79 inference(unit_resolution,[status(thm)],[234, 207, 177])).
% 7.07/4.79 tff(236,plain,(in(A!8, B!7)), inference(lemma,lemma(discharge,[]))).
% 7.07/4.79 tff(237,plain,
% 7.07/4.79 ((~subset(singleton(A!8), B!7)) | (~in(A!8, B!7)) | (~((~subset(singleton(A!8), B!7)) <=> in(A!8, B!7)))),
% 7.07/4.79 inference(tautology,[status(thm)],[])).
% 7.07/4.79 tff(238,plain,
% 7.07/4.79 ((~subset(singleton(A!8), B!7)) | (~in(A!8, B!7))),
% 7.07/4.79 inference(unit_resolution,[status(thm)],[237, 189])).
% 7.07/4.79 tff(239,plain,
% 7.07/4.79 (~subset(singleton(A!8), B!7)),
% 7.07/4.79 inference(unit_resolution,[status(thm)],[238, 236])).
% 7.07/4.79 tff(240,plain,
% 7.07/4.79 (^[A: $i, B: $i] : refl((~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_4(B, A), A)) | in(tptp_fun_C_4(B, A), B))))))) <=> (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_4(B, A), A)) | in(tptp_fun_C_4(B, A), B))))))))),
% 7.07/4.79 inference(bind,[status(th)],[])).
% 7.07/4.79 tff(241,plain,
% 7.07/4.79 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_4(B, A), A)) | in(tptp_fun_C_4(B, A), B))))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_4(B, A), A)) | in(tptp_fun_C_4(B, A), B)))))))),
% 7.07/4.79 inference(quant_intro,[status(thm)],[240])).
% 7.07/4.79 tff(242,plain,
% 7.07/4.79 (^[A: $i, B: $i] : rewrite((~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_4(B, A), A)) | in(tptp_fun_C_4(B, A), B))))))) <=> (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_4(B, A), A)) | in(tptp_fun_C_4(B, A), B))))))))),
% 7.07/4.79 inference(bind,[status(th)],[])).
% 7.07/4.79 tff(243,plain,
% 7.07/4.79 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_4(B, A), A)) | in(tptp_fun_C_4(B, A), B))))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_4(B, A), A)) | in(tptp_fun_C_4(B, A), B)))))))),
% 7.07/4.79 inference(quant_intro,[status(thm)],[242])).
% 7.07/4.79 tff(244,plain,
% 7.07/4.79 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_4(B, A), A)) | in(tptp_fun_C_4(B, A), B))))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_4(B, A), A)) | in(tptp_fun_C_4(B, A), B)))))))),
% 7.07/4.79 inference(transitivity,[status(thm)],[243, 241])).
% 7.07/4.79 tff(245,plain,
% 7.07/4.79 (^[A: $i, B: $i] : trans(monotonicity(rewrite(((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) <=> ((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))), rewrite((subset(A, B) | (~((~in(tptp_fun_C_4(B, A), A)) | in(tptp_fun_C_4(B, A), B)))) <=> (subset(A, B) | (~((~in(tptp_fun_C_4(B, A), A)) | in(tptp_fun_C_4(B, A), B))))), ((((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_4(B, A), A)) | in(tptp_fun_C_4(B, A), B))))) <=> (((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_4(B, A), A)) | in(tptp_fun_C_4(B, A), B))))))), rewrite((((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_4(B, A), A)) | in(tptp_fun_C_4(B, A), B))))) <=> (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_4(B, A), A)) | in(tptp_fun_C_4(B, A), B)))))))), ((((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_4(B, A), A)) | in(tptp_fun_C_4(B, A), B))))) <=> (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_4(B, A), A)) | in(tptp_fun_C_4(B, A), B)))))))))),
% 7.07/4.79 inference(bind,[status(th)],[])).
% 7.07/4.79 tff(246,plain,
% 7.07/4.79 (![A: $i, B: $i] : (((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_4(B, A), A)) | in(tptp_fun_C_4(B, A), B))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_4(B, A), A)) | in(tptp_fun_C_4(B, A), B)))))))),
% 7.07/4.79 inference(quant_intro,[status(thm)],[245])).
% 7.07/4.79 tff(247,plain,
% 7.07/4.79 (![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B))) <=> ![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B)))),
% 7.07/4.79 inference(rewrite,[status(thm)],[])).
% 7.07/4.79 tff(248,plain,
% 7.07/4.79 (^[A: $i, B: $i] : rewrite((subset(A, B) <=> ![C: $i] : (in(C, A) => in(C, B))) <=> (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B))))),
% 7.07/4.79 inference(bind,[status(th)],[])).
% 7.07/4.79 tff(249,plain,
% 7.07/4.79 (![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : (in(C, A) => in(C, B))) <=> ![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B)))),
% 7.07/4.79 inference(quant_intro,[status(thm)],[248])).
% 7.07/4.79 tff(250,axiom,(![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : (in(C, A) => in(C, B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d3_tarski')).
% 7.07/4.79 tff(251,plain,
% 7.07/4.79 (![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B)))),
% 7.07/4.79 inference(modus_ponens,[status(thm)],[250, 249])).
% 7.07/4.79 tff(252,plain,
% 7.07/4.79 (![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B)))),
% 7.07/4.79 inference(modus_ponens,[status(thm)],[251, 247])).
% 7.07/4.79 tff(253,plain,(
% 7.07/4.79 ![A: $i, B: $i] : (((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_4(B, A), A)) | in(tptp_fun_C_4(B, A), B)))))),
% 7.07/4.79 inference(skolemize,[status(sab)],[252])).
% 7.07/4.79 tff(254,plain,
% 7.07/4.79 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_4(B, A), A)) | in(tptp_fun_C_4(B, A), B)))))))),
% 7.07/4.79 inference(modus_ponens,[status(thm)],[253, 246])).
% 7.07/4.79 tff(255,plain,
% 7.07/4.79 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_4(B, A), A)) | in(tptp_fun_C_4(B, A), B)))))))),
% 7.07/4.79 inference(modus_ponens,[status(thm)],[254, 244])).
% 7.07/4.80 tff(256,plain,
% 7.07/4.80 ((~![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_4(B, A), A)) | in(tptp_fun_C_4(B, A), B)))))))) | (~((~((~subset(singleton(A!8), B!7)) | ![C: $i] : ((~in(C, singleton(A!8))) | in(C, B!7)))) | (~(subset(singleton(A!8), B!7) | (~((~in(tptp_fun_C_4(B!7, singleton(A!8)), singleton(A!8))) | in(tptp_fun_C_4(B!7, singleton(A!8)), B!7)))))))),
% 7.07/4.80 inference(quant_inst,[status(thm)],[])).
% 7.07/4.80 tff(257,plain,
% 7.07/4.80 (~((~((~subset(singleton(A!8), B!7)) | ![C: $i] : ((~in(C, singleton(A!8))) | in(C, B!7)))) | (~(subset(singleton(A!8), B!7) | (~((~in(tptp_fun_C_4(B!7, singleton(A!8)), singleton(A!8))) | in(tptp_fun_C_4(B!7, singleton(A!8)), B!7))))))),
% 7.07/4.80 inference(unit_resolution,[status(thm)],[256, 255])).
% 7.07/4.80 tff(258,plain,
% 7.07/4.80 (((~((~subset(singleton(A!8), B!7)) | ![C: $i] : ((~in(C, singleton(A!8))) | in(C, B!7)))) | (~(subset(singleton(A!8), B!7) | (~((~in(tptp_fun_C_4(B!7, singleton(A!8)), singleton(A!8))) | in(tptp_fun_C_4(B!7, singleton(A!8)), B!7)))))) | (subset(singleton(A!8), B!7) | (~((~in(tptp_fun_C_4(B!7, singleton(A!8)), singleton(A!8))) | in(tptp_fun_C_4(B!7, singleton(A!8)), B!7))))),
% 7.07/4.80 inference(tautology,[status(thm)],[])).
% 7.07/4.80 tff(259,plain,
% 7.07/4.80 (subset(singleton(A!8), B!7) | (~((~in(tptp_fun_C_4(B!7, singleton(A!8)), singleton(A!8))) | in(tptp_fun_C_4(B!7, singleton(A!8)), B!7)))),
% 7.07/4.80 inference(unit_resolution,[status(thm)],[258, 257])).
% 7.07/4.80 tff(260,plain,
% 7.07/4.80 ((~(subset(singleton(A!8), B!7) | (~((~in(tptp_fun_C_4(B!7, singleton(A!8)), singleton(A!8))) | in(tptp_fun_C_4(B!7, singleton(A!8)), B!7))))) | subset(singleton(A!8), B!7) | (~((~in(tptp_fun_C_4(B!7, singleton(A!8)), singleton(A!8))) | in(tptp_fun_C_4(B!7, singleton(A!8)), B!7)))),
% 7.07/4.80 inference(tautology,[status(thm)],[])).
% 7.07/4.80 tff(261,plain,
% 7.07/4.80 (subset(singleton(A!8), B!7) | (~((~in(tptp_fun_C_4(B!7, singleton(A!8)), singleton(A!8))) | in(tptp_fun_C_4(B!7, singleton(A!8)), B!7)))),
% 7.07/4.80 inference(unit_resolution,[status(thm)],[260, 259])).
% 7.07/4.80 tff(262,plain,
% 7.07/4.80 (~((~in(tptp_fun_C_4(B!7, singleton(A!8)), singleton(A!8))) | in(tptp_fun_C_4(B!7, singleton(A!8)), B!7))),
% 7.07/4.80 inference(unit_resolution,[status(thm)],[261, 239])).
% 7.07/4.80 tff(263,plain,
% 7.07/4.80 (((~in(tptp_fun_C_4(B!7, singleton(A!8)), singleton(A!8))) | in(tptp_fun_C_4(B!7, singleton(A!8)), B!7)) | in(tptp_fun_C_4(B!7, singleton(A!8)), singleton(A!8))),
% 7.07/4.80 inference(tautology,[status(thm)],[])).
% 7.07/4.80 tff(264,plain,
% 7.07/4.80 (in(tptp_fun_C_4(B!7, singleton(A!8)), singleton(A!8))),
% 7.07/4.80 inference(unit_resolution,[status(thm)],[263, 262])).
% 7.07/4.80 tff(265,plain,
% 7.07/4.80 ((~(in(tptp_fun_C_4(B!7, singleton(A!8)), singleton(A!8)) <=> (tptp_fun_C_4(B!7, singleton(A!8)) = A!8))) | (~in(tptp_fun_C_4(B!7, singleton(A!8)), singleton(A!8))) | (tptp_fun_C_4(B!7, singleton(A!8)) = A!8)),
% 7.07/4.80 inference(tautology,[status(thm)],[])).
% 7.07/4.80 tff(266,plain,
% 7.07/4.80 ((~(in(tptp_fun_C_4(B!7, singleton(A!8)), singleton(A!8)) <=> (tptp_fun_C_4(B!7, singleton(A!8)) = A!8))) | (tptp_fun_C_4(B!7, singleton(A!8)) = A!8)),
% 7.07/4.80 inference(unit_resolution,[status(thm)],[265, 264])).
% 7.07/4.80 tff(267,plain,
% 7.07/4.80 (tptp_fun_C_4(B!7, singleton(A!8)) = A!8),
% 7.07/4.80 inference(unit_resolution,[status(thm)],[266, 48])).
% 7.07/4.80 tff(268,plain,
% 7.07/4.80 (in(tptp_fun_C_4(B!7, singleton(A!8)), B!7) <=> in(A!8, B!7)),
% 7.07/4.80 inference(monotonicity,[status(thm)],[267])).
% 7.07/4.80 tff(269,plain,
% 7.07/4.80 (in(A!8, B!7) <=> in(tptp_fun_C_4(B!7, singleton(A!8)), B!7)),
% 7.07/4.80 inference(symmetry,[status(thm)],[268])).
% 7.07/4.80 tff(270,plain,
% 7.07/4.80 (in(tptp_fun_C_4(B!7, singleton(A!8)), B!7)),
% 7.07/4.80 inference(modus_ponens,[status(thm)],[236, 269])).
% 7.07/4.80 tff(271,plain,
% 7.07/4.80 (((~in(tptp_fun_C_4(B!7, singleton(A!8)), singleton(A!8))) | in(tptp_fun_C_4(B!7, singleton(A!8)), B!7)) | (~in(tptp_fun_C_4(B!7, singleton(A!8)), B!7))),
% 7.07/4.80 inference(tautology,[status(thm)],[])).
% 7.07/4.80 tff(272,plain,
% 7.07/4.80 (~in(tptp_fun_C_4(B!7, singleton(A!8)), B!7)),
% 7.07/4.80 inference(unit_resolution,[status(thm)],[271, 262])).
% 7.07/4.80 tff(273,plain,
% 7.07/4.80 ($false),
% 7.07/4.80 inference(unit_resolution,[status(thm)],[272, 270])).
% 7.07/4.80 % SZS output end Proof
%------------------------------------------------------------------------------