TSTP Solution File: SEU145+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SEU145+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n028.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 0.21s 0.39s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU145+1 : TPTP v8.1.0. Released v3.3.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.34 % Computer : n028.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Sat Sep 3 09:49:08 EDT 2022
% 0.14/0.34 % 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.
% 0.21/0.39 % SZS status Theorem
% 0.21/0.39 % SZS output start Proof
% 0.21/0.39 tff(in_type, type, (
% 0.21/0.39 in: ( $i * $i ) > $o)).
% 0.21/0.39 tff(tptp_fun_A_5_type, type, (
% 0.21/0.39 tptp_fun_A_5: $i)).
% 0.21/0.39 tff(tptp_fun_C_1_type, type, (
% 0.21/0.39 tptp_fun_C_1: ( $i * $i ) > $i)).
% 0.21/0.39 tff(set_difference_type, type, (
% 0.21/0.39 set_difference: ( $i * $i ) > $i)).
% 0.21/0.39 tff(singleton_type, type, (
% 0.21/0.39 singleton: $i > $i)).
% 0.21/0.39 tff(tptp_fun_C_3_type, type, (
% 0.21/0.39 tptp_fun_C_3: $i)).
% 0.21/0.39 tff(tptp_fun_B_4_type, type, (
% 0.21/0.39 tptp_fun_B_4: $i)).
% 0.21/0.39 tff(tptp_fun_C_0_type, type, (
% 0.21/0.39 tptp_fun_C_0: ( $i * $i ) > $i)).
% 0.21/0.39 tff(tptp_fun_D_2_type, type, (
% 0.21/0.39 tptp_fun_D_2: ( $i * $i * $i ) > $i)).
% 0.21/0.39 tff(subset_type, type, (
% 0.21/0.39 subset: ( $i * $i ) > $o)).
% 0.21/0.39 tff(1,plain,
% 0.21/0.39 (^[A: $i, B: $i, C: $i] : refl((~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A)))))) <=> (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A)))))))),
% 0.21/0.39 inference(bind,[status(th)],[])).
% 0.21/0.39 tff(2,plain,
% 0.21/0.39 (![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A)))))) <=> ![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))))),
% 0.21/0.39 inference(quant_intro,[status(thm)],[1])).
% 0.21/0.39 tff(3,plain,
% 0.21/0.39 (![A: $i, B: $i] : ![C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A)))))) <=> ![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))))),
% 0.21/0.39 inference(pull_quant,[status(thm)],[])).
% 0.21/0.39 tff(4,plain,
% 0.21/0.39 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(pull_quant(((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A))) <=> ![C: $i] : ((~(B = singleton(A))) | (in(C, B) <=> (C = A)))), ((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) <=> (~![C: $i] : ((~(B = singleton(A))) | (in(C, B) <=> (C = A)))))), pull_quant((~![C: $i] : ((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) <=> ?[C: $i] : (~((~(B = singleton(A))) | (in(C, B) <=> (C = A))))), ((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) <=> ?[C: $i] : (~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))))), (((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))) <=> (?[C: $i] : (~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))))), pull_quant((?[C: $i] : (~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))) <=> ?[C: $i] : ((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A)))))), (((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))) <=> ?[C: $i] : ((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))))), ((~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A)))))) <=> (~?[C: $i] : ((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A)))))))), pull_quant((~?[C: $i] : ((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A)))))) <=> ![C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))))), ((~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A)))))) <=> ![C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))))))),
% 0.21/0.40 inference(bind,[status(th)],[])).
% 0.21/0.40 tff(5,plain,
% 0.21/0.40 (![A: $i, B: $i] : (~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A)))))) <=> ![A: $i, B: $i] : ![C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))))),
% 0.21/0.40 inference(quant_intro,[status(thm)],[4])).
% 0.21/0.40 tff(6,plain,
% 0.21/0.40 (![A: $i, B: $i] : (~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A)))))) <=> ![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))))),
% 0.21/0.40 inference(transitivity,[status(thm)],[5, 3])).
% 0.21/0.40 tff(7,plain,
% 0.21/0.40 (![A: $i, B: $i] : (~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A)))))) <=> ![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))))),
% 0.21/0.40 inference(transitivity,[status(thm)],[6, 2])).
% 0.21/0.40 tff(8,plain,
% 0.21/0.40 (^[A: $i, B: $i] : rewrite((~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A)))))) <=> (~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A)))))))),
% 0.21/0.40 inference(bind,[status(th)],[])).
% 0.21/0.40 tff(9,plain,
% 0.21/0.40 (![A: $i, B: $i] : (~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A)))))) <=> ![A: $i, B: $i] : (~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))))),
% 0.21/0.40 inference(quant_intro,[status(thm)],[8])).
% 0.21/0.40 tff(10,plain,
% 0.21/0.40 (![A: $i, B: $i] : (~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A)))))) <=> ![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))))),
% 0.21/0.40 inference(transitivity,[status(thm)],[9, 7])).
% 0.21/0.40 tff(11,plain,
% 0.21/0.40 (^[A: $i, B: $i] : trans(monotonicity(rewrite(((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A))) <=> ((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))), ((((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A))) & ((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A)))) <=> (((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A))) & ((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A)))))), rewrite((((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A))) & ((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A)))) <=> (~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))))), ((((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A))) & ((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A)))) <=> (~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))))))),
% 0.21/0.40 inference(bind,[status(th)],[])).
% 0.21/0.40 tff(12,plain,
% 0.21/0.40 (![A: $i, B: $i] : (((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A))) & ((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A)))) <=> ![A: $i, B: $i] : (~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))))),
% 0.21/0.40 inference(quant_intro,[status(thm)],[11])).
% 0.21/0.40 tff(13,plain,
% 0.21/0.40 (^[A: $i, B: $i] : rewrite((((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A))) & ((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A))))) <=> (((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A))) & ((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A)))))),
% 0.21/0.40 inference(bind,[status(th)],[])).
% 0.21/0.40 tff(14,plain,
% 0.21/0.40 (![A: $i, B: $i] : (((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A))) & ((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A))))) <=> ![A: $i, B: $i] : (((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A))) & ((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))),
% 0.21/0.40 inference(quant_intro,[status(thm)],[13])).
% 0.21/0.40 tff(15,plain,
% 0.21/0.40 (![A: $i, B: $i] : ((B = singleton(A)) <=> ![C: $i] : (in(C, B) <=> (C = A))) <=> ![A: $i, B: $i] : ((B = singleton(A)) <=> ![C: $i] : (in(C, B) <=> (C = A)))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(16,axiom,(![A: $i, B: $i] : ((B = singleton(A)) <=> ![C: $i] : (in(C, B) <=> (C = A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d1_tarski')).
% 0.21/0.40 tff(17,plain,
% 0.21/0.40 (![A: $i, B: $i] : ((B = singleton(A)) <=> ![C: $i] : (in(C, B) <=> (C = A)))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[16, 15])).
% 0.21/0.40 tff(18,plain,(
% 0.21/0.40 ![A: $i, B: $i] : (((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A))) & ((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))),
% 0.21/0.40 inference(skolemize,[status(sab)],[17])).
% 0.21/0.40 tff(19,plain,
% 0.21/0.40 (![A: $i, B: $i] : (((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A))) & ((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[18, 14])).
% 0.21/0.40 tff(20,plain,
% 0.21/0.40 (![A: $i, B: $i] : (~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[19, 12])).
% 0.21/0.40 tff(21,plain,
% 0.21/0.40 (![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[20, 10])).
% 0.21/0.40 tff(22,plain,
% 0.21/0.40 (((~![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))))) | (in(tptp_fun_C_1(set_difference(B!4, singleton(C!3)), A!5), singleton(C!3)) <=> (tptp_fun_C_1(set_difference(B!4, singleton(C!3)), A!5) = C!3))) <=> ((~![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_1(set_difference(B!4, singleton(C!3)), A!5), singleton(C!3)) <=> (tptp_fun_C_1(set_difference(B!4, singleton(C!3)), A!5) = C!3)))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(23,plain,
% 0.21/0.40 ((~((~in(tptp_fun_C_1(set_difference(B!4, singleton(C!3)), A!5), singleton(C!3))) <=> (tptp_fun_C_1(set_difference(B!4, singleton(C!3)), A!5) = C!3))) <=> (in(tptp_fun_C_1(set_difference(B!4, singleton(C!3)), A!5), singleton(C!3)) <=> (tptp_fun_C_1(set_difference(B!4, singleton(C!3)), A!5) = C!3))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(24,plain,
% 0.21/0.40 ((((~in(tptp_fun_C_1(set_difference(B!4, singleton(C!3)), A!5), singleton(C!3))) <=> (tptp_fun_C_1(set_difference(B!4, singleton(C!3)), A!5) = C!3)) | $false) <=> ((~in(tptp_fun_C_1(set_difference(B!4, singleton(C!3)), A!5), singleton(C!3))) <=> (tptp_fun_C_1(set_difference(B!4, singleton(C!3)), A!5) = C!3))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(25,plain,
% 0.21/0.40 ((~$true) <=> $false),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(26,plain,
% 0.21/0.40 (($true | ((~in(tptp_fun_C_0(singleton(C!3), C!3), singleton(C!3))) <=> (tptp_fun_C_0(singleton(C!3), C!3) = C!3))) <=> $true),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(27,plain,
% 0.21/0.40 ((singleton(C!3) = singleton(C!3)) <=> $true),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(28,plain,
% 0.21/0.40 (((singleton(C!3) = singleton(C!3)) | ((~in(tptp_fun_C_0(singleton(C!3), C!3), singleton(C!3))) <=> (tptp_fun_C_0(singleton(C!3), C!3) = C!3))) <=> ($true | ((~in(tptp_fun_C_0(singleton(C!3), C!3), singleton(C!3))) <=> (tptp_fun_C_0(singleton(C!3), C!3) = C!3)))),
% 0.21/0.40 inference(monotonicity,[status(thm)],[27])).
% 0.21/0.40 tff(29,plain,
% 0.21/0.40 (((singleton(C!3) = singleton(C!3)) | ((~in(tptp_fun_C_0(singleton(C!3), C!3), singleton(C!3))) <=> (tptp_fun_C_0(singleton(C!3), C!3) = C!3))) <=> $true),
% 0.21/0.40 inference(transitivity,[status(thm)],[28, 26])).
% 0.21/0.40 tff(30,plain,
% 0.21/0.40 ((~((singleton(C!3) = singleton(C!3)) | ((~in(tptp_fun_C_0(singleton(C!3), C!3), singleton(C!3))) <=> (tptp_fun_C_0(singleton(C!3), C!3) = C!3)))) <=> (~$true)),
% 0.21/0.40 inference(monotonicity,[status(thm)],[29])).
% 0.21/0.40 tff(31,plain,
% 0.21/0.40 ((~((singleton(C!3) = singleton(C!3)) | ((~in(tptp_fun_C_0(singleton(C!3), C!3), singleton(C!3))) <=> (tptp_fun_C_0(singleton(C!3), C!3) = C!3)))) <=> $false),
% 0.21/0.40 inference(transitivity,[status(thm)],[30, 25])).
% 0.21/0.40 tff(32,plain,
% 0.21/0.40 ((~(in(tptp_fun_C_1(set_difference(B!4, singleton(C!3)), A!5), singleton(C!3)) <=> (tptp_fun_C_1(set_difference(B!4, singleton(C!3)), A!5) = C!3))) <=> ((~in(tptp_fun_C_1(set_difference(B!4, singleton(C!3)), A!5), singleton(C!3))) <=> (tptp_fun_C_1(set_difference(B!4, singleton(C!3)), A!5) = C!3))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(33,plain,
% 0.21/0.40 (($false | (in(tptp_fun_C_1(set_difference(B!4, singleton(C!3)), A!5), singleton(C!3)) <=> (tptp_fun_C_1(set_difference(B!4, singleton(C!3)), A!5) = C!3))) <=> (in(tptp_fun_C_1(set_difference(B!4, singleton(C!3)), A!5), singleton(C!3)) <=> (tptp_fun_C_1(set_difference(B!4, singleton(C!3)), A!5) = C!3))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(34,plain,
% 0.21/0.40 ((~(singleton(C!3) = singleton(C!3))) <=> (~$true)),
% 0.21/0.40 inference(monotonicity,[status(thm)],[27])).
% 0.21/0.40 tff(35,plain,
% 0.21/0.40 ((~(singleton(C!3) = singleton(C!3))) <=> $false),
% 0.21/0.40 inference(transitivity,[status(thm)],[34, 25])).
% 0.21/0.40 tff(36,plain,
% 0.21/0.40 (((~(singleton(C!3) = singleton(C!3))) | (in(tptp_fun_C_1(set_difference(B!4, singleton(C!3)), A!5), singleton(C!3)) <=> (tptp_fun_C_1(set_difference(B!4, singleton(C!3)), A!5) = C!3))) <=> ($false | (in(tptp_fun_C_1(set_difference(B!4, singleton(C!3)), A!5), singleton(C!3)) <=> (tptp_fun_C_1(set_difference(B!4, singleton(C!3)), A!5) = C!3)))),
% 0.21/0.40 inference(monotonicity,[status(thm)],[35])).
% 0.21/0.40 tff(37,plain,
% 0.21/0.40 (((~(singleton(C!3) = singleton(C!3))) | (in(tptp_fun_C_1(set_difference(B!4, singleton(C!3)), A!5), singleton(C!3)) <=> (tptp_fun_C_1(set_difference(B!4, singleton(C!3)), A!5) = C!3))) <=> (in(tptp_fun_C_1(set_difference(B!4, singleton(C!3)), A!5), singleton(C!3)) <=> (tptp_fun_C_1(set_difference(B!4, singleton(C!3)), A!5) = C!3))),
% 0.21/0.40 inference(transitivity,[status(thm)],[36, 33])).
% 0.21/0.40 tff(38,plain,
% 0.21/0.40 ((~((~(singleton(C!3) = singleton(C!3))) | (in(tptp_fun_C_1(set_difference(B!4, singleton(C!3)), A!5), singleton(C!3)) <=> (tptp_fun_C_1(set_difference(B!4, singleton(C!3)), A!5) = C!3)))) <=> (~(in(tptp_fun_C_1(set_difference(B!4, singleton(C!3)), A!5), singleton(C!3)) <=> (tptp_fun_C_1(set_difference(B!4, singleton(C!3)), A!5) = C!3)))),
% 0.21/0.40 inference(monotonicity,[status(thm)],[37])).
% 0.21/0.40 tff(39,plain,
% 0.21/0.40 ((~((~(singleton(C!3) = singleton(C!3))) | (in(tptp_fun_C_1(set_difference(B!4, singleton(C!3)), A!5), singleton(C!3)) <=> (tptp_fun_C_1(set_difference(B!4, singleton(C!3)), A!5) = C!3)))) <=> ((~in(tptp_fun_C_1(set_difference(B!4, singleton(C!3)), A!5), singleton(C!3))) <=> (tptp_fun_C_1(set_difference(B!4, singleton(C!3)), A!5) = C!3))),
% 0.21/0.40 inference(transitivity,[status(thm)],[38, 32])).
% 0.21/0.40 tff(40,plain,
% 0.21/0.40 (((~((~(singleton(C!3) = singleton(C!3))) | (in(tptp_fun_C_1(set_difference(B!4, singleton(C!3)), A!5), singleton(C!3)) <=> (tptp_fun_C_1(set_difference(B!4, singleton(C!3)), A!5) = C!3)))) | (~((singleton(C!3) = singleton(C!3)) | ((~in(tptp_fun_C_0(singleton(C!3), C!3), singleton(C!3))) <=> (tptp_fun_C_0(singleton(C!3), C!3) = C!3))))) <=> (((~in(tptp_fun_C_1(set_difference(B!4, singleton(C!3)), A!5), singleton(C!3))) <=> (tptp_fun_C_1(set_difference(B!4, singleton(C!3)), A!5) = C!3)) | $false)),
% 0.21/0.40 inference(monotonicity,[status(thm)],[39, 31])).
% 0.21/0.40 tff(41,plain,
% 0.21/0.40 (((~((~(singleton(C!3) = singleton(C!3))) | (in(tptp_fun_C_1(set_difference(B!4, singleton(C!3)), A!5), singleton(C!3)) <=> (tptp_fun_C_1(set_difference(B!4, singleton(C!3)), A!5) = C!3)))) | (~((singleton(C!3) = singleton(C!3)) | ((~in(tptp_fun_C_0(singleton(C!3), C!3), singleton(C!3))) <=> (tptp_fun_C_0(singleton(C!3), C!3) = C!3))))) <=> ((~in(tptp_fun_C_1(set_difference(B!4, singleton(C!3)), A!5), singleton(C!3))) <=> (tptp_fun_C_1(set_difference(B!4, singleton(C!3)), A!5) = C!3))),
% 0.21/0.40 inference(transitivity,[status(thm)],[40, 24])).
% 0.21/0.40 tff(42,plain,
% 0.21/0.40 ((~((~((~(singleton(C!3) = singleton(C!3))) | (in(tptp_fun_C_1(set_difference(B!4, singleton(C!3)), A!5), singleton(C!3)) <=> (tptp_fun_C_1(set_difference(B!4, singleton(C!3)), A!5) = C!3)))) | (~((singleton(C!3) = singleton(C!3)) | ((~in(tptp_fun_C_0(singleton(C!3), C!3), singleton(C!3))) <=> (tptp_fun_C_0(singleton(C!3), C!3) = C!3)))))) <=> (~((~in(tptp_fun_C_1(set_difference(B!4, singleton(C!3)), A!5), singleton(C!3))) <=> (tptp_fun_C_1(set_difference(B!4, singleton(C!3)), A!5) = C!3)))),
% 0.21/0.40 inference(monotonicity,[status(thm)],[41])).
% 0.21/0.40 tff(43,plain,
% 0.21/0.40 ((~((~((~(singleton(C!3) = singleton(C!3))) | (in(tptp_fun_C_1(set_difference(B!4, singleton(C!3)), A!5), singleton(C!3)) <=> (tptp_fun_C_1(set_difference(B!4, singleton(C!3)), A!5) = C!3)))) | (~((singleton(C!3) = singleton(C!3)) | ((~in(tptp_fun_C_0(singleton(C!3), C!3), singleton(C!3))) <=> (tptp_fun_C_0(singleton(C!3), C!3) = C!3)))))) <=> (in(tptp_fun_C_1(set_difference(B!4, singleton(C!3)), A!5), singleton(C!3)) <=> (tptp_fun_C_1(set_difference(B!4, singleton(C!3)), A!5) = C!3))),
% 0.21/0.40 inference(transitivity,[status(thm)],[42, 23])).
% 0.21/0.40 tff(44,plain,
% 0.21/0.40 (((~![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))))) | (~((~((~(singleton(C!3) = singleton(C!3))) | (in(tptp_fun_C_1(set_difference(B!4, singleton(C!3)), A!5), singleton(C!3)) <=> (tptp_fun_C_1(set_difference(B!4, singleton(C!3)), A!5) = C!3)))) | (~((singleton(C!3) = singleton(C!3)) | ((~in(tptp_fun_C_0(singleton(C!3), C!3), singleton(C!3))) <=> (tptp_fun_C_0(singleton(C!3), C!3) = C!3))))))) <=> ((~![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_1(set_difference(B!4, singleton(C!3)), A!5), singleton(C!3)) <=> (tptp_fun_C_1(set_difference(B!4, singleton(C!3)), A!5) = C!3)))),
% 0.21/0.40 inference(monotonicity,[status(thm)],[43])).
% 0.21/0.40 tff(45,plain,
% 0.21/0.40 (((~![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))))) | (~((~((~(singleton(C!3) = singleton(C!3))) | (in(tptp_fun_C_1(set_difference(B!4, singleton(C!3)), A!5), singleton(C!3)) <=> (tptp_fun_C_1(set_difference(B!4, singleton(C!3)), A!5) = C!3)))) | (~((singleton(C!3) = singleton(C!3)) | ((~in(tptp_fun_C_0(singleton(C!3), C!3), singleton(C!3))) <=> (tptp_fun_C_0(singleton(C!3), C!3) = C!3))))))) <=> ((~![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_1(set_difference(B!4, singleton(C!3)), A!5), singleton(C!3)) <=> (tptp_fun_C_1(set_difference(B!4, singleton(C!3)), A!5) = C!3)))),
% 0.21/0.40 inference(transitivity,[status(thm)],[44, 22])).
% 0.21/0.40 tff(46,plain,
% 0.21/0.40 ((~![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> (tptp_fun_C_0(B, A) = A))))))) | (~((~((~(singleton(C!3) = singleton(C!3))) | (in(tptp_fun_C_1(set_difference(B!4, singleton(C!3)), A!5), singleton(C!3)) <=> (tptp_fun_C_1(set_difference(B!4, singleton(C!3)), A!5) = C!3)))) | (~((singleton(C!3) = singleton(C!3)) | ((~in(tptp_fun_C_0(singleton(C!3), C!3), singleton(C!3))) <=> (tptp_fun_C_0(singleton(C!3), C!3) = C!3))))))),
% 0.21/0.41 inference(quant_inst,[status(thm)],[])).
% 0.21/0.41 tff(47,plain,
% 0.21/0.41 ((~![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_1(set_difference(B!4, singleton(C!3)), A!5), singleton(C!3)) <=> (tptp_fun_C_1(set_difference(B!4, singleton(C!3)), A!5) = C!3))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[46, 45])).
% 0.21/0.41 tff(48,plain,
% 0.21/0.41 (in(tptp_fun_C_1(set_difference(B!4, singleton(C!3)), A!5), singleton(C!3)) <=> (tptp_fun_C_1(set_difference(B!4, singleton(C!3)), A!5) = C!3)),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[47, 21])).
% 0.21/0.41 tff(49,plain,
% 0.21/0.41 (^[A: $i, B: $i, C: $i, D: $i] : refl((~((~((~(C = set_difference(A, B))) | (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_2(C, B, A), C) <=> ((~in(tptp_fun_D_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B))))))) <=> (~((~((~(C = set_difference(A, B))) | (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_2(C, B, A), C) <=> ((~in(tptp_fun_D_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B))))))))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(50,plain,
% 0.21/0.41 (![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_difference(A, B))) | (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_2(C, B, A), C) <=> ((~in(tptp_fun_D_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_difference(A, B))) | (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_2(C, B, A), C) <=> ((~in(tptp_fun_D_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B)))))))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[49])).
% 0.21/0.41 tff(51,plain,
% 0.21/0.41 (![A: $i, B: $i, C: $i] : ![D: $i] : (~((~((~(C = set_difference(A, B))) | (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_2(C, B, A), C) <=> ((~in(tptp_fun_D_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_difference(A, B))) | (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_2(C, B, A), C) <=> ((~in(tptp_fun_D_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B)))))))),
% 0.21/0.41 inference(pull_quant,[status(thm)],[])).
% 0.21/0.41 tff(52,plain,
% 0.21/0.41 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(pull_quant(((~(C = set_difference(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, A)) | in(D, B))))) <=> ![D: $i] : ((~(C = set_difference(A, B))) | (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))), ((~((~(C = set_difference(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) <=> (~![D: $i] : ((~(C = set_difference(A, B))) | (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))))), pull_quant((~![D: $i] : ((~(C = set_difference(A, B))) | (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) <=> ?[D: $i] : (~((~(C = set_difference(A, B))) | (in(D, C) <=> (~((~in(D, A)) | in(D, B))))))), ((~((~(C = set_difference(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) <=> ?[D: $i] : (~((~(C = set_difference(A, B))) | (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))))), (((~((~(C = set_difference(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_2(C, B, A), C) <=> ((~in(tptp_fun_D_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B)))))) <=> (?[D: $i] : (~((~(C = set_difference(A, B))) | (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_2(C, B, A), C) <=> ((~in(tptp_fun_D_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B)))))))), pull_quant((?[D: $i] : (~((~(C = set_difference(A, B))) | (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_2(C, B, A), C) <=> ((~in(tptp_fun_D_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B)))))) <=> ?[D: $i] : ((~((~(C = set_difference(A, B))) | (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_2(C, B, A), C) <=> ((~in(tptp_fun_D_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B))))))), (((~((~(C = set_difference(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_2(C, B, A), C) <=> ((~in(tptp_fun_D_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B)))))) <=> ?[D: $i] : ((~((~(C = set_difference(A, B))) | (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_2(C, B, A), C) <=> ((~in(tptp_fun_D_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B)))))))), ((~((~((~(C = set_difference(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_2(C, B, A), C) <=> ((~in(tptp_fun_D_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B))))))) <=> (~?[D: $i] : ((~((~(C = set_difference(A, B))) | (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_2(C, B, A), C) <=> ((~in(tptp_fun_D_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B))))))))), pull_quant((~?[D: $i] : ((~((~(C = set_difference(A, B))) | (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_2(C, B, A), C) <=> ((~in(tptp_fun_D_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B))))))) <=> ![D: $i] : (~((~((~(C = set_difference(A, B))) | (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_2(C, B, A), C) <=> ((~in(tptp_fun_D_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B)))))))), ((~((~((~(C = set_difference(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_2(C, B, A), C) <=> ((~in(tptp_fun_D_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B))))))) <=> ![D: $i] : (~((~((~(C = set_difference(A, B))) | (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_2(C, B, A), C) <=> ((~in(tptp_fun_D_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B)))))))))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(53,plain,
% 0.21/0.41 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_difference(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_2(C, B, A), C) <=> ((~in(tptp_fun_D_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B))))))) <=> ![A: $i, B: $i, C: $i] : ![D: $i] : (~((~((~(C = set_difference(A, B))) | (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_2(C, B, A), C) <=> ((~in(tptp_fun_D_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B)))))))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[52])).
% 0.21/0.41 tff(54,plain,
% 0.21/0.41 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_difference(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_2(C, B, A), C) <=> ((~in(tptp_fun_D_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_difference(A, B))) | (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_2(C, B, A), C) <=> ((~in(tptp_fun_D_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B)))))))),
% 0.21/0.41 inference(transitivity,[status(thm)],[53, 51])).
% 0.21/0.41 tff(55,plain,
% 0.21/0.41 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_difference(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_2(C, B, A), C) <=> ((~in(tptp_fun_D_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_difference(A, B))) | (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_2(C, B, A), C) <=> ((~in(tptp_fun_D_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B)))))))),
% 0.21/0.41 inference(transitivity,[status(thm)],[54, 50])).
% 0.21/0.41 tff(56,plain,
% 0.21/0.41 (^[A: $i, B: $i, C: $i] : rewrite((~((~((~(C = set_difference(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_2(C, B, A), C) <=> ((~in(tptp_fun_D_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B))))))) <=> (~((~((~(C = set_difference(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_2(C, B, A), C) <=> ((~in(tptp_fun_D_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B))))))))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(57,plain,
% 0.21/0.41 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_difference(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_2(C, B, A), C) <=> ((~in(tptp_fun_D_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B))))))) <=> ![A: $i, B: $i, C: $i] : (~((~((~(C = set_difference(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_2(C, B, A), C) <=> ((~in(tptp_fun_D_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B)))))))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[56])).
% 0.21/0.41 tff(58,plain,
% 0.21/0.41 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_difference(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_2(C, B, A), C) <=> ((~in(tptp_fun_D_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_difference(A, B))) | (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_2(C, B, A), C) <=> ((~in(tptp_fun_D_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B)))))))),
% 0.21/0.41 inference(transitivity,[status(thm)],[57, 55])).
% 0.21/0.41 tff(59,plain,
% 0.21/0.41 (^[A: $i, B: $i, C: $i] : trans(monotonicity(rewrite(((~(C = set_difference(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) & (~in(D, B))))) <=> ((~(C = set_difference(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))), rewrite(((C = set_difference(A, B)) | ((~in(tptp_fun_D_2(C, B, A), C)) <=> (in(tptp_fun_D_2(C, B, A), A) & (~in(tptp_fun_D_2(C, B, A), B))))) <=> ((C = set_difference(A, B)) | (in(tptp_fun_D_2(C, B, A), C) <=> ((~in(tptp_fun_D_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B))))), ((((~(C = set_difference(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) & (~in(D, B))))) & ((C = set_difference(A, B)) | ((~in(tptp_fun_D_2(C, B, A), C)) <=> (in(tptp_fun_D_2(C, B, A), A) & (~in(tptp_fun_D_2(C, B, A), B)))))) <=> (((~(C = set_difference(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, A)) | in(D, B))))) & ((C = set_difference(A, B)) | (in(tptp_fun_D_2(C, B, A), C) <=> ((~in(tptp_fun_D_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B))))))), rewrite((((~(C = set_difference(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, A)) | in(D, B))))) & ((C = set_difference(A, B)) | (in(tptp_fun_D_2(C, B, A), C) <=> ((~in(tptp_fun_D_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B))))) <=> (~((~((~(C = set_difference(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_2(C, B, A), C) <=> ((~in(tptp_fun_D_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B)))))))), ((((~(C = set_difference(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) & (~in(D, B))))) & ((C = set_difference(A, B)) | ((~in(tptp_fun_D_2(C, B, A), C)) <=> (in(tptp_fun_D_2(C, B, A), A) & (~in(tptp_fun_D_2(C, B, A), B)))))) <=> (~((~((~(C = set_difference(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_2(C, B, A), C) <=> ((~in(tptp_fun_D_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B)))))))))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(60,plain,
% 0.21/0.41 (![A: $i, B: $i, C: $i] : (((~(C = set_difference(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) & (~in(D, B))))) & ((C = set_difference(A, B)) | ((~in(tptp_fun_D_2(C, B, A), C)) <=> (in(tptp_fun_D_2(C, B, A), A) & (~in(tptp_fun_D_2(C, B, A), B)))))) <=> ![A: $i, B: $i, C: $i] : (~((~((~(C = set_difference(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_2(C, B, A), C) <=> ((~in(tptp_fun_D_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B)))))))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[59])).
% 0.21/0.41 tff(61,plain,
% 0.21/0.41 (^[A: $i, B: $i, C: $i] : rewrite((((~(C = set_difference(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) & (~in(D, B))))) & ((C = set_difference(A, B)) | (~(in(tptp_fun_D_2(C, B, A), C) <=> (in(tptp_fun_D_2(C, B, A), A) & (~in(tptp_fun_D_2(C, B, A), B))))))) <=> (((~(C = set_difference(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) & (~in(D, B))))) & ((C = set_difference(A, B)) | ((~in(tptp_fun_D_2(C, B, A), C)) <=> (in(tptp_fun_D_2(C, B, A), A) & (~in(tptp_fun_D_2(C, B, A), B)))))))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(62,plain,
% 0.21/0.41 (![A: $i, B: $i, C: $i] : (((~(C = set_difference(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) & (~in(D, B))))) & ((C = set_difference(A, B)) | (~(in(tptp_fun_D_2(C, B, A), C) <=> (in(tptp_fun_D_2(C, B, A), A) & (~in(tptp_fun_D_2(C, B, A), B))))))) <=> ![A: $i, B: $i, C: $i] : (((~(C = set_difference(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) & (~in(D, B))))) & ((C = set_difference(A, B)) | ((~in(tptp_fun_D_2(C, B, A), C)) <=> (in(tptp_fun_D_2(C, B, A), A) & (~in(tptp_fun_D_2(C, B, A), B))))))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[61])).
% 0.21/0.41 tff(63,plain,
% 0.21/0.41 (![A: $i, B: $i, C: $i] : ((C = set_difference(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, A) & (~in(D, B))))) <=> ![A: $i, B: $i, C: $i] : ((C = set_difference(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, A) & (~in(D, B)))))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(64,axiom,(![A: $i, B: $i, C: $i] : ((C = set_difference(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, A) & (~in(D, B)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d4_xboole_0')).
% 0.21/0.41 tff(65,plain,
% 0.21/0.41 (![A: $i, B: $i, C: $i] : ((C = set_difference(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, A) & (~in(D, B)))))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[64, 63])).
% 0.21/0.41 tff(66,plain,(
% 0.21/0.41 ![A: $i, B: $i, C: $i] : (((~(C = set_difference(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) & (~in(D, B))))) & ((C = set_difference(A, B)) | (~(in(tptp_fun_D_2(C, B, A), C) <=> (in(tptp_fun_D_2(C, B, A), A) & (~in(tptp_fun_D_2(C, B, A), B)))))))),
% 0.21/0.41 inference(skolemize,[status(sab)],[65])).
% 0.21/0.41 tff(67,plain,
% 0.21/0.41 (![A: $i, B: $i, C: $i] : (((~(C = set_difference(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) & (~in(D, B))))) & ((C = set_difference(A, B)) | ((~in(tptp_fun_D_2(C, B, A), C)) <=> (in(tptp_fun_D_2(C, B, A), A) & (~in(tptp_fun_D_2(C, B, A), B))))))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[66, 62])).
% 0.21/0.41 tff(68,plain,
% 0.21/0.41 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_difference(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_2(C, B, A), C) <=> ((~in(tptp_fun_D_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B)))))))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[67, 60])).
% 0.21/0.41 tff(69,plain,
% 0.21/0.41 (![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_difference(A, B))) | (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_2(C, B, A), C) <=> ((~in(tptp_fun_D_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B)))))))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[68, 58])).
% 0.21/0.41 tff(70,plain,
% 0.21/0.41 (((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_difference(A, B))) | (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_2(C, B, A), C) <=> ((~in(tptp_fun_D_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B)))))))) | ((~in(tptp_fun_C_1(set_difference(B!4, singleton(C!3)), A!5), set_difference(B!4, singleton(C!3)))) <=> ((~in(tptp_fun_C_1(set_difference(B!4, singleton(C!3)), A!5), B!4)) | in(tptp_fun_C_1(set_difference(B!4, singleton(C!3)), A!5), singleton(C!3))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_difference(A, B))) | (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_2(C, B, A), C) <=> ((~in(tptp_fun_D_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B)))))))) | ((~in(tptp_fun_C_1(set_difference(B!4, singleton(C!3)), A!5), set_difference(B!4, singleton(C!3)))) <=> ((~in(tptp_fun_C_1(set_difference(B!4, singleton(C!3)), A!5), B!4)) | in(tptp_fun_C_1(set_difference(B!4, singleton(C!3)), A!5), singleton(C!3)))))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(71,plain,
% 0.21/0.42 ((~(in(tptp_fun_C_1(set_difference(B!4, singleton(C!3)), A!5), set_difference(B!4, singleton(C!3))) <=> ((~in(tptp_fun_C_1(set_difference(B!4, singleton(C!3)), A!5), B!4)) | in(tptp_fun_C_1(set_difference(B!4, singleton(C!3)), A!5), singleton(C!3))))) <=> ((~in(tptp_fun_C_1(set_difference(B!4, singleton(C!3)), A!5), set_difference(B!4, singleton(C!3)))) <=> ((~in(tptp_fun_C_1(set_difference(B!4, singleton(C!3)), A!5), B!4)) | in(tptp_fun_C_1(set_difference(B!4, singleton(C!3)), A!5), singleton(C!3))))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(72,plain,
% 0.21/0.42 (((in(tptp_fun_C_1(set_difference(B!4, singleton(C!3)), A!5), set_difference(B!4, singleton(C!3))) <=> ((~in(tptp_fun_C_1(set_difference(B!4, singleton(C!3)), A!5), B!4)) | in(tptp_fun_C_1(set_difference(B!4, singleton(C!3)), A!5), singleton(C!3)))) | $false) <=> (in(tptp_fun_C_1(set_difference(B!4, singleton(C!3)), A!5), set_difference(B!4, singleton(C!3))) <=> ((~in(tptp_fun_C_1(set_difference(B!4, singleton(C!3)), A!5), B!4)) | in(tptp_fun_C_1(set_difference(B!4, singleton(C!3)), A!5), singleton(C!3))))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(73,plain,
% 0.21/0.42 (($true | (in(tptp_fun_D_2(set_difference(B!4, singleton(C!3)), singleton(C!3), B!4), set_difference(B!4, singleton(C!3))) <=> ((~in(tptp_fun_D_2(set_difference(B!4, singleton(C!3)), singleton(C!3), B!4), B!4)) | in(tptp_fun_D_2(set_difference(B!4, singleton(C!3)), singleton(C!3), B!4), singleton(C!3))))) <=> $true),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(74,plain,
% 0.21/0.42 ((set_difference(B!4, singleton(C!3)) = set_difference(B!4, singleton(C!3))) <=> $true),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(75,plain,
% 0.21/0.42 (((set_difference(B!4, singleton(C!3)) = set_difference(B!4, singleton(C!3))) | (in(tptp_fun_D_2(set_difference(B!4, singleton(C!3)), singleton(C!3), B!4), set_difference(B!4, singleton(C!3))) <=> ((~in(tptp_fun_D_2(set_difference(B!4, singleton(C!3)), singleton(C!3), B!4), B!4)) | in(tptp_fun_D_2(set_difference(B!4, singleton(C!3)), singleton(C!3), B!4), singleton(C!3))))) <=> ($true | (in(tptp_fun_D_2(set_difference(B!4, singleton(C!3)), singleton(C!3), B!4), set_difference(B!4, singleton(C!3))) <=> ((~in(tptp_fun_D_2(set_difference(B!4, singleton(C!3)), singleton(C!3), B!4), B!4)) | in(tptp_fun_D_2(set_difference(B!4, singleton(C!3)), singleton(C!3), B!4), singleton(C!3)))))),
% 0.21/0.42 inference(monotonicity,[status(thm)],[74])).
% 0.21/0.42 tff(76,plain,
% 0.21/0.42 (((set_difference(B!4, singleton(C!3)) = set_difference(B!4, singleton(C!3))) | (in(tptp_fun_D_2(set_difference(B!4, singleton(C!3)), singleton(C!3), B!4), set_difference(B!4, singleton(C!3))) <=> ((~in(tptp_fun_D_2(set_difference(B!4, singleton(C!3)), singleton(C!3), B!4), B!4)) | in(tptp_fun_D_2(set_difference(B!4, singleton(C!3)), singleton(C!3), B!4), singleton(C!3))))) <=> $true),
% 0.21/0.42 inference(transitivity,[status(thm)],[75, 73])).
% 0.21/0.42 tff(77,plain,
% 0.21/0.42 ((~((set_difference(B!4, singleton(C!3)) = set_difference(B!4, singleton(C!3))) | (in(tptp_fun_D_2(set_difference(B!4, singleton(C!3)), singleton(C!3), B!4), set_difference(B!4, singleton(C!3))) <=> ((~in(tptp_fun_D_2(set_difference(B!4, singleton(C!3)), singleton(C!3), B!4), B!4)) | in(tptp_fun_D_2(set_difference(B!4, singleton(C!3)), singleton(C!3), B!4), singleton(C!3)))))) <=> (~$true)),
% 0.21/0.42 inference(monotonicity,[status(thm)],[76])).
% 0.21/0.42 tff(78,plain,
% 0.21/0.42 ((~((set_difference(B!4, singleton(C!3)) = set_difference(B!4, singleton(C!3))) | (in(tptp_fun_D_2(set_difference(B!4, singleton(C!3)), singleton(C!3), B!4), set_difference(B!4, singleton(C!3))) <=> ((~in(tptp_fun_D_2(set_difference(B!4, singleton(C!3)), singleton(C!3), B!4), B!4)) | in(tptp_fun_D_2(set_difference(B!4, singleton(C!3)), singleton(C!3), B!4), singleton(C!3)))))) <=> $false),
% 0.21/0.42 inference(transitivity,[status(thm)],[77, 25])).
% 0.21/0.42 tff(79,plain,
% 0.21/0.42 ((~(in(tptp_fun_C_1(set_difference(B!4, singleton(C!3)), A!5), set_difference(B!4, singleton(C!3))) <=> (~((~in(tptp_fun_C_1(set_difference(B!4, singleton(C!3)), A!5), B!4)) | in(tptp_fun_C_1(set_difference(B!4, singleton(C!3)), A!5), singleton(C!3)))))) <=> (in(tptp_fun_C_1(set_difference(B!4, singleton(C!3)), A!5), set_difference(B!4, singleton(C!3))) <=> ((~in(tptp_fun_C_1(set_difference(B!4, singleton(C!3)), A!5), B!4)) | in(tptp_fun_C_1(set_difference(B!4, singleton(C!3)), A!5), singleton(C!3))))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(80,plain,
% 0.21/0.42 (($false | (in(tptp_fun_C_1(set_difference(B!4, singleton(C!3)), A!5), set_difference(B!4, singleton(C!3))) <=> (~((~in(tptp_fun_C_1(set_difference(B!4, singleton(C!3)), A!5), B!4)) | in(tptp_fun_C_1(set_difference(B!4, singleton(C!3)), A!5), singleton(C!3)))))) <=> (in(tptp_fun_C_1(set_difference(B!4, singleton(C!3)), A!5), set_difference(B!4, singleton(C!3))) <=> (~((~in(tptp_fun_C_1(set_difference(B!4, singleton(C!3)), A!5), B!4)) | in(tptp_fun_C_1(set_difference(B!4, singleton(C!3)), A!5), singleton(C!3)))))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(81,plain,
% 0.21/0.42 ((~(set_difference(B!4, singleton(C!3)) = set_difference(B!4, singleton(C!3)))) <=> (~$true)),
% 0.21/0.42 inference(monotonicity,[status(thm)],[74])).
% 0.21/0.42 tff(82,plain,
% 0.21/0.42 ((~(set_difference(B!4, singleton(C!3)) = set_difference(B!4, singleton(C!3)))) <=> $false),
% 0.21/0.42 inference(transitivity,[status(thm)],[81, 25])).
% 0.21/0.42 tff(83,plain,
% 0.21/0.42 (((~(set_difference(B!4, singleton(C!3)) = set_difference(B!4, singleton(C!3)))) | (in(tptp_fun_C_1(set_difference(B!4, singleton(C!3)), A!5), set_difference(B!4, singleton(C!3))) <=> (~((~in(tptp_fun_C_1(set_difference(B!4, singleton(C!3)), A!5), B!4)) | in(tptp_fun_C_1(set_difference(B!4, singleton(C!3)), A!5), singleton(C!3)))))) <=> ($false | (in(tptp_fun_C_1(set_difference(B!4, singleton(C!3)), A!5), set_difference(B!4, singleton(C!3))) <=> (~((~in(tptp_fun_C_1(set_difference(B!4, singleton(C!3)), A!5), B!4)) | in(tptp_fun_C_1(set_difference(B!4, singleton(C!3)), A!5), singleton(C!3))))))),
% 0.21/0.42 inference(monotonicity,[status(thm)],[82])).
% 0.21/0.42 tff(84,plain,
% 0.21/0.42 (((~(set_difference(B!4, singleton(C!3)) = set_difference(B!4, singleton(C!3)))) | (in(tptp_fun_C_1(set_difference(B!4, singleton(C!3)), A!5), set_difference(B!4, singleton(C!3))) <=> (~((~in(tptp_fun_C_1(set_difference(B!4, singleton(C!3)), A!5), B!4)) | in(tptp_fun_C_1(set_difference(B!4, singleton(C!3)), A!5), singleton(C!3)))))) <=> (in(tptp_fun_C_1(set_difference(B!4, singleton(C!3)), A!5), set_difference(B!4, singleton(C!3))) <=> (~((~in(tptp_fun_C_1(set_difference(B!4, singleton(C!3)), A!5), B!4)) | in(tptp_fun_C_1(set_difference(B!4, singleton(C!3)), A!5), singleton(C!3)))))),
% 0.21/0.42 inference(transitivity,[status(thm)],[83, 80])).
% 0.21/0.42 tff(85,plain,
% 0.21/0.42 ((~((~(set_difference(B!4, singleton(C!3)) = set_difference(B!4, singleton(C!3)))) | (in(tptp_fun_C_1(set_difference(B!4, singleton(C!3)), A!5), set_difference(B!4, singleton(C!3))) <=> (~((~in(tptp_fun_C_1(set_difference(B!4, singleton(C!3)), A!5), B!4)) | in(tptp_fun_C_1(set_difference(B!4, singleton(C!3)), A!5), singleton(C!3))))))) <=> (~(in(tptp_fun_C_1(set_difference(B!4, singleton(C!3)), A!5), set_difference(B!4, singleton(C!3))) <=> (~((~in(tptp_fun_C_1(set_difference(B!4, singleton(C!3)), A!5), B!4)) | in(tptp_fun_C_1(set_difference(B!4, singleton(C!3)), A!5), singleton(C!3))))))),
% 0.21/0.42 inference(monotonicity,[status(thm)],[84])).
% 0.21/0.42 tff(86,plain,
% 0.21/0.42 ((~((~(set_difference(B!4, singleton(C!3)) = set_difference(B!4, singleton(C!3)))) | (in(tptp_fun_C_1(set_difference(B!4, singleton(C!3)), A!5), set_difference(B!4, singleton(C!3))) <=> (~((~in(tptp_fun_C_1(set_difference(B!4, singleton(C!3)), A!5), B!4)) | in(tptp_fun_C_1(set_difference(B!4, singleton(C!3)), A!5), singleton(C!3))))))) <=> (in(tptp_fun_C_1(set_difference(B!4, singleton(C!3)), A!5), set_difference(B!4, singleton(C!3))) <=> ((~in(tptp_fun_C_1(set_difference(B!4, singleton(C!3)), A!5), B!4)) | in(tptp_fun_C_1(set_difference(B!4, singleton(C!3)), A!5), singleton(C!3))))),
% 0.21/0.42 inference(transitivity,[status(thm)],[85, 79])).
% 0.21/0.42 tff(87,plain,
% 0.21/0.42 (((~((~(set_difference(B!4, singleton(C!3)) = set_difference(B!4, singleton(C!3)))) | (in(tptp_fun_C_1(set_difference(B!4, singleton(C!3)), A!5), set_difference(B!4, singleton(C!3))) <=> (~((~in(tptp_fun_C_1(set_difference(B!4, singleton(C!3)), A!5), B!4)) | in(tptp_fun_C_1(set_difference(B!4, singleton(C!3)), A!5), singleton(C!3))))))) | (~((set_difference(B!4, singleton(C!3)) = set_difference(B!4, singleton(C!3))) | (in(tptp_fun_D_2(set_difference(B!4, singleton(C!3)), singleton(C!3), B!4), set_difference(B!4, singleton(C!3))) <=> ((~in(tptp_fun_D_2(set_difference(B!4, singleton(C!3)), singleton(C!3), B!4), B!4)) | in(tptp_fun_D_2(set_difference(B!4, singleton(C!3)), singleton(C!3), B!4), singleton(C!3))))))) <=> ((in(tptp_fun_C_1(set_difference(B!4, singleton(C!3)), A!5), set_difference(B!4, singleton(C!3))) <=> ((~in(tptp_fun_C_1(set_difference(B!4, singleton(C!3)), A!5), B!4)) | in(tptp_fun_C_1(set_difference(B!4, singleton(C!3)), A!5), singleton(C!3)))) | $false)),
% 0.21/0.42 inference(monotonicity,[status(thm)],[86, 78])).
% 0.21/0.42 tff(88,plain,
% 0.21/0.42 (((~((~(set_difference(B!4, singleton(C!3)) = set_difference(B!4, singleton(C!3)))) | (in(tptp_fun_C_1(set_difference(B!4, singleton(C!3)), A!5), set_difference(B!4, singleton(C!3))) <=> (~((~in(tptp_fun_C_1(set_difference(B!4, singleton(C!3)), A!5), B!4)) | in(tptp_fun_C_1(set_difference(B!4, singleton(C!3)), A!5), singleton(C!3))))))) | (~((set_difference(B!4, singleton(C!3)) = set_difference(B!4, singleton(C!3))) | (in(tptp_fun_D_2(set_difference(B!4, singleton(C!3)), singleton(C!3), B!4), set_difference(B!4, singleton(C!3))) <=> ((~in(tptp_fun_D_2(set_difference(B!4, singleton(C!3)), singleton(C!3), B!4), B!4)) | in(tptp_fun_D_2(set_difference(B!4, singleton(C!3)), singleton(C!3), B!4), singleton(C!3))))))) <=> (in(tptp_fun_C_1(set_difference(B!4, singleton(C!3)), A!5), set_difference(B!4, singleton(C!3))) <=> ((~in(tptp_fun_C_1(set_difference(B!4, singleton(C!3)), A!5), B!4)) | in(tptp_fun_C_1(set_difference(B!4, singleton(C!3)), A!5), singleton(C!3))))),
% 0.21/0.42 inference(transitivity,[status(thm)],[87, 72])).
% 0.21/0.42 tff(89,plain,
% 0.21/0.42 ((~((~((~(set_difference(B!4, singleton(C!3)) = set_difference(B!4, singleton(C!3)))) | (in(tptp_fun_C_1(set_difference(B!4, singleton(C!3)), A!5), set_difference(B!4, singleton(C!3))) <=> (~((~in(tptp_fun_C_1(set_difference(B!4, singleton(C!3)), A!5), B!4)) | in(tptp_fun_C_1(set_difference(B!4, singleton(C!3)), A!5), singleton(C!3))))))) | (~((set_difference(B!4, singleton(C!3)) = set_difference(B!4, singleton(C!3))) | (in(tptp_fun_D_2(set_difference(B!4, singleton(C!3)), singleton(C!3), B!4), set_difference(B!4, singleton(C!3))) <=> ((~in(tptp_fun_D_2(set_difference(B!4, singleton(C!3)), singleton(C!3), B!4), B!4)) | in(tptp_fun_D_2(set_difference(B!4, singleton(C!3)), singleton(C!3), B!4), singleton(C!3)))))))) <=> (~(in(tptp_fun_C_1(set_difference(B!4, singleton(C!3)), A!5), set_difference(B!4, singleton(C!3))) <=> ((~in(tptp_fun_C_1(set_difference(B!4, singleton(C!3)), A!5), B!4)) | in(tptp_fun_C_1(set_difference(B!4, singleton(C!3)), A!5), singleton(C!3)))))),
% 0.21/0.42 inference(monotonicity,[status(thm)],[88])).
% 0.21/0.42 tff(90,plain,
% 0.21/0.42 ((~((~((~(set_difference(B!4, singleton(C!3)) = set_difference(B!4, singleton(C!3)))) | (in(tptp_fun_C_1(set_difference(B!4, singleton(C!3)), A!5), set_difference(B!4, singleton(C!3))) <=> (~((~in(tptp_fun_C_1(set_difference(B!4, singleton(C!3)), A!5), B!4)) | in(tptp_fun_C_1(set_difference(B!4, singleton(C!3)), A!5), singleton(C!3))))))) | (~((set_difference(B!4, singleton(C!3)) = set_difference(B!4, singleton(C!3))) | (in(tptp_fun_D_2(set_difference(B!4, singleton(C!3)), singleton(C!3), B!4), set_difference(B!4, singleton(C!3))) <=> ((~in(tptp_fun_D_2(set_difference(B!4, singleton(C!3)), singleton(C!3), B!4), B!4)) | in(tptp_fun_D_2(set_difference(B!4, singleton(C!3)), singleton(C!3), B!4), singleton(C!3)))))))) <=> ((~in(tptp_fun_C_1(set_difference(B!4, singleton(C!3)), A!5), set_difference(B!4, singleton(C!3)))) <=> ((~in(tptp_fun_C_1(set_difference(B!4, singleton(C!3)), A!5), B!4)) | in(tptp_fun_C_1(set_difference(B!4, singleton(C!3)), A!5), singleton(C!3))))),
% 0.21/0.43 inference(transitivity,[status(thm)],[89, 71])).
% 0.21/0.43 tff(91,plain,
% 0.21/0.43 (((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_difference(A, B))) | (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_2(C, B, A), C) <=> ((~in(tptp_fun_D_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B)))))))) | (~((~((~(set_difference(B!4, singleton(C!3)) = set_difference(B!4, singleton(C!3)))) | (in(tptp_fun_C_1(set_difference(B!4, singleton(C!3)), A!5), set_difference(B!4, singleton(C!3))) <=> (~((~in(tptp_fun_C_1(set_difference(B!4, singleton(C!3)), A!5), B!4)) | in(tptp_fun_C_1(set_difference(B!4, singleton(C!3)), A!5), singleton(C!3))))))) | (~((set_difference(B!4, singleton(C!3)) = set_difference(B!4, singleton(C!3))) | (in(tptp_fun_D_2(set_difference(B!4, singleton(C!3)), singleton(C!3), B!4), set_difference(B!4, singleton(C!3))) <=> ((~in(tptp_fun_D_2(set_difference(B!4, singleton(C!3)), singleton(C!3), B!4), B!4)) | in(tptp_fun_D_2(set_difference(B!4, singleton(C!3)), singleton(C!3), B!4), singleton(C!3))))))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_difference(A, B))) | (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_2(C, B, A), C) <=> ((~in(tptp_fun_D_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B)))))))) | ((~in(tptp_fun_C_1(set_difference(B!4, singleton(C!3)), A!5), set_difference(B!4, singleton(C!3)))) <=> ((~in(tptp_fun_C_1(set_difference(B!4, singleton(C!3)), A!5), B!4)) | in(tptp_fun_C_1(set_difference(B!4, singleton(C!3)), A!5), singleton(C!3)))))),
% 0.21/0.43 inference(monotonicity,[status(thm)],[90])).
% 0.21/0.43 tff(92,plain,
% 0.21/0.43 (((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_difference(A, B))) | (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_2(C, B, A), C) <=> ((~in(tptp_fun_D_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B)))))))) | (~((~((~(set_difference(B!4, singleton(C!3)) = set_difference(B!4, singleton(C!3)))) | (in(tptp_fun_C_1(set_difference(B!4, singleton(C!3)), A!5), set_difference(B!4, singleton(C!3))) <=> (~((~in(tptp_fun_C_1(set_difference(B!4, singleton(C!3)), A!5), B!4)) | in(tptp_fun_C_1(set_difference(B!4, singleton(C!3)), A!5), singleton(C!3))))))) | (~((set_difference(B!4, singleton(C!3)) = set_difference(B!4, singleton(C!3))) | (in(tptp_fun_D_2(set_difference(B!4, singleton(C!3)), singleton(C!3), B!4), set_difference(B!4, singleton(C!3))) <=> ((~in(tptp_fun_D_2(set_difference(B!4, singleton(C!3)), singleton(C!3), B!4), B!4)) | in(tptp_fun_D_2(set_difference(B!4, singleton(C!3)), singleton(C!3), B!4), singleton(C!3))))))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_difference(A, B))) | (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_2(C, B, A), C) <=> ((~in(tptp_fun_D_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B)))))))) | ((~in(tptp_fun_C_1(set_difference(B!4, singleton(C!3)), A!5), set_difference(B!4, singleton(C!3)))) <=> ((~in(tptp_fun_C_1(set_difference(B!4, singleton(C!3)), A!5), B!4)) | in(tptp_fun_C_1(set_difference(B!4, singleton(C!3)), A!5), singleton(C!3)))))),
% 0.21/0.43 inference(transitivity,[status(thm)],[91, 70])).
% 0.21/0.43 tff(93,plain,
% 0.21/0.43 ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_difference(A, B))) | (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_2(C, B, A), C) <=> ((~in(tptp_fun_D_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B)))))))) | (~((~((~(set_difference(B!4, singleton(C!3)) = set_difference(B!4, singleton(C!3)))) | (in(tptp_fun_C_1(set_difference(B!4, singleton(C!3)), A!5), set_difference(B!4, singleton(C!3))) <=> (~((~in(tptp_fun_C_1(set_difference(B!4, singleton(C!3)), A!5), B!4)) | in(tptp_fun_C_1(set_difference(B!4, singleton(C!3)), A!5), singleton(C!3))))))) | (~((set_difference(B!4, singleton(C!3)) = set_difference(B!4, singleton(C!3))) | (in(tptp_fun_D_2(set_difference(B!4, singleton(C!3)), singleton(C!3), B!4), set_difference(B!4, singleton(C!3))) <=> ((~in(tptp_fun_D_2(set_difference(B!4, singleton(C!3)), singleton(C!3), B!4), B!4)) | in(tptp_fun_D_2(set_difference(B!4, singleton(C!3)), singleton(C!3), B!4), singleton(C!3))))))))),
% 0.21/0.43 inference(quant_inst,[status(thm)],[])).
% 0.21/0.43 tff(94,plain,
% 0.21/0.43 ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_difference(A, B))) | (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_2(C, B, A), C) <=> ((~in(tptp_fun_D_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B)))))))) | ((~in(tptp_fun_C_1(set_difference(B!4, singleton(C!3)), A!5), set_difference(B!4, singleton(C!3)))) <=> ((~in(tptp_fun_C_1(set_difference(B!4, singleton(C!3)), A!5), B!4)) | in(tptp_fun_C_1(set_difference(B!4, singleton(C!3)), A!5), singleton(C!3))))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[93, 92])).
% 0.21/0.43 tff(95,plain,
% 0.21/0.43 ((~in(tptp_fun_C_1(set_difference(B!4, singleton(C!3)), A!5), set_difference(B!4, singleton(C!3)))) <=> ((~in(tptp_fun_C_1(set_difference(B!4, singleton(C!3)), A!5), B!4)) | in(tptp_fun_C_1(set_difference(B!4, singleton(C!3)), A!5), singleton(C!3)))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[94, 69])).
% 0.21/0.43 tff(96,plain,
% 0.21/0.43 (^[A: $i, B: $i] : refl((~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_1(B, A), A)) | in(tptp_fun_C_1(B, A), B))))))) <=> (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_1(B, A), A)) | in(tptp_fun_C_1(B, A), B))))))))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(97,plain,
% 0.21/0.43 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_1(B, A), A)) | in(tptp_fun_C_1(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_1(B, A), A)) | in(tptp_fun_C_1(B, A), B)))))))),
% 0.21/0.43 inference(quant_intro,[status(thm)],[96])).
% 0.21/0.43 tff(98,plain,
% 0.21/0.43 (^[A: $i, B: $i] : rewrite((~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_1(B, A), A)) | in(tptp_fun_C_1(B, A), B))))))) <=> (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_1(B, A), A)) | in(tptp_fun_C_1(B, A), B))))))))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(99,plain,
% 0.21/0.43 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_1(B, A), A)) | in(tptp_fun_C_1(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_1(B, A), A)) | in(tptp_fun_C_1(B, A), B)))))))),
% 0.21/0.43 inference(quant_intro,[status(thm)],[98])).
% 0.21/0.43 tff(100,plain,
% 0.21/0.43 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_1(B, A), A)) | in(tptp_fun_C_1(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_1(B, A), A)) | in(tptp_fun_C_1(B, A), B)))))))),
% 0.21/0.43 inference(transitivity,[status(thm)],[99, 97])).
% 0.21/0.43 tff(101,plain,
% 0.21/0.43 (^[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_1(B, A), A)) | in(tptp_fun_C_1(B, A), B)))) <=> (subset(A, B) | (~((~in(tptp_fun_C_1(B, A), A)) | in(tptp_fun_C_1(B, A), B))))), ((((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_1(B, A), A)) | in(tptp_fun_C_1(B, A), B))))) <=> (((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_1(B, A), A)) | in(tptp_fun_C_1(B, A), B))))))), rewrite((((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_1(B, A), A)) | in(tptp_fun_C_1(B, A), B))))) <=> (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_1(B, A), A)) | in(tptp_fun_C_1(B, A), B)))))))), ((((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_1(B, A), A)) | in(tptp_fun_C_1(B, A), B))))) <=> (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_1(B, A), A)) | in(tptp_fun_C_1(B, A), B)))))))))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(102,plain,
% 0.21/0.43 (![A: $i, B: $i] : (((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_1(B, A), A)) | in(tptp_fun_C_1(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_1(B, A), A)) | in(tptp_fun_C_1(B, A), B)))))))),
% 0.21/0.43 inference(quant_intro,[status(thm)],[101])).
% 0.21/0.43 tff(103,plain,
% 0.21/0.43 (![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)))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(104,plain,
% 0.21/0.43 (^[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))))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(105,plain,
% 0.21/0.43 (![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)))),
% 0.21/0.43 inference(quant_intro,[status(thm)],[104])).
% 0.21/0.43 tff(106,axiom,(![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : (in(C, A) => in(C, B)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d3_tarski')).
% 0.21/0.43 tff(107,plain,
% 0.21/0.43 (![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B)))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[106, 105])).
% 0.21/0.43 tff(108,plain,
% 0.21/0.43 (![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B)))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[107, 103])).
% 0.21/0.43 tff(109,plain,(
% 0.21/0.43 ![A: $i, B: $i] : (((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_1(B, A), A)) | in(tptp_fun_C_1(B, A), B)))))),
% 0.21/0.43 inference(skolemize,[status(sab)],[108])).
% 0.21/0.43 tff(110,plain,
% 0.21/0.43 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_1(B, A), A)) | in(tptp_fun_C_1(B, A), B)))))))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[109, 102])).
% 0.21/0.43 tff(111,plain,
% 0.21/0.43 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_1(B, A), A)) | in(tptp_fun_C_1(B, A), B)))))))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[110, 100])).
% 0.21/0.43 tff(112,plain,
% 0.21/0.43 ((~![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_1(B, A), A)) | in(tptp_fun_C_1(B, A), B)))))))) | (~((~((~subset(A!5, set_difference(B!4, singleton(C!3)))) | ![C: $i] : ((~in(C, A!5)) | in(C, set_difference(B!4, singleton(C!3)))))) | (~(subset(A!5, set_difference(B!4, singleton(C!3))) | (~((~in(tptp_fun_C_1(set_difference(B!4, singleton(C!3)), A!5), A!5)) | in(tptp_fun_C_1(set_difference(B!4, singleton(C!3)), A!5), set_difference(B!4, singleton(C!3)))))))))),
% 0.21/0.43 inference(quant_inst,[status(thm)],[])).
% 0.21/0.43 tff(113,plain,
% 0.21/0.43 (~((~((~subset(A!5, set_difference(B!4, singleton(C!3)))) | ![C: $i] : ((~in(C, A!5)) | in(C, set_difference(B!4, singleton(C!3)))))) | (~(subset(A!5, set_difference(B!4, singleton(C!3))) | (~((~in(tptp_fun_C_1(set_difference(B!4, singleton(C!3)), A!5), A!5)) | in(tptp_fun_C_1(set_difference(B!4, singleton(C!3)), A!5), set_difference(B!4, singleton(C!3))))))))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[112, 111])).
% 0.21/0.43 tff(114,plain,
% 0.21/0.43 (((~((~subset(A!5, set_difference(B!4, singleton(C!3)))) | ![C: $i] : ((~in(C, A!5)) | in(C, set_difference(B!4, singleton(C!3)))))) | (~(subset(A!5, set_difference(B!4, singleton(C!3))) | (~((~in(tptp_fun_C_1(set_difference(B!4, singleton(C!3)), A!5), A!5)) | in(tptp_fun_C_1(set_difference(B!4, singleton(C!3)), A!5), set_difference(B!4, singleton(C!3)))))))) | (subset(A!5, set_difference(B!4, singleton(C!3))) | (~((~in(tptp_fun_C_1(set_difference(B!4, singleton(C!3)), A!5), A!5)) | in(tptp_fun_C_1(set_difference(B!4, singleton(C!3)), A!5), set_difference(B!4, singleton(C!3))))))),
% 0.21/0.44 inference(tautology,[status(thm)],[])).
% 0.21/0.44 tff(115,plain,
% 0.21/0.44 (subset(A!5, set_difference(B!4, singleton(C!3))) | (~((~in(tptp_fun_C_1(set_difference(B!4, singleton(C!3)), A!5), A!5)) | in(tptp_fun_C_1(set_difference(B!4, singleton(C!3)), A!5), set_difference(B!4, singleton(C!3)))))),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[114, 113])).
% 0.21/0.44 tff(116,plain,
% 0.21/0.44 ((~(in(C!3, A!5) | subset(A!5, set_difference(B!4, singleton(C!3))) | (~subset(A!5, B!4)))) <=> (~(in(C!3, A!5) | subset(A!5, set_difference(B!4, singleton(C!3))) | (~subset(A!5, B!4))))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(117,plain,
% 0.21/0.44 ((~![A: $i, B: $i, C: $i] : (in(C, A) | subset(A, set_difference(B, singleton(C))) | (~subset(A, B)))) <=> (~![A: $i, B: $i, C: $i] : (in(C, A) | subset(A, set_difference(B, singleton(C))) | (~subset(A, B))))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(118,plain,
% 0.21/0.44 ((~![A: $i, B: $i, C: $i] : (subset(A, B) => (in(C, A) | subset(A, set_difference(B, singleton(C)))))) <=> (~![A: $i, B: $i, C: $i] : (in(C, A) | subset(A, set_difference(B, singleton(C))) | (~subset(A, B))))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(119,axiom,(~![A: $i, B: $i, C: $i] : (subset(A, B) => (in(C, A) | subset(A, set_difference(B, singleton(C)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','l3_zfmisc_1')).
% 0.21/0.44 tff(120,plain,
% 0.21/0.44 (~![A: $i, B: $i, C: $i] : (in(C, A) | subset(A, set_difference(B, singleton(C))) | (~subset(A, B)))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[119, 118])).
% 0.21/0.44 tff(121,plain,
% 0.21/0.44 (~![A: $i, B: $i, C: $i] : (in(C, A) | subset(A, set_difference(B, singleton(C))) | (~subset(A, B)))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[120, 117])).
% 0.21/0.44 tff(122,plain,
% 0.21/0.44 (~![A: $i, B: $i, C: $i] : (in(C, A) | subset(A, set_difference(B, singleton(C))) | (~subset(A, B)))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[121, 117])).
% 0.21/0.44 tff(123,plain,
% 0.21/0.44 (~![A: $i, B: $i, C: $i] : (in(C, A) | subset(A, set_difference(B, singleton(C))) | (~subset(A, B)))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[122, 117])).
% 0.21/0.44 tff(124,plain,
% 0.21/0.44 (~![A: $i, B: $i, C: $i] : (in(C, A) | subset(A, set_difference(B, singleton(C))) | (~subset(A, B)))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[123, 117])).
% 0.21/0.44 tff(125,plain,
% 0.21/0.44 (~![A: $i, B: $i, C: $i] : (in(C, A) | subset(A, set_difference(B, singleton(C))) | (~subset(A, B)))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[124, 117])).
% 0.21/0.44 tff(126,plain,
% 0.21/0.44 (~![A: $i, B: $i, C: $i] : (in(C, A) | subset(A, set_difference(B, singleton(C))) | (~subset(A, B)))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[125, 117])).
% 0.21/0.44 tff(127,plain,(
% 0.21/0.44 ~(in(C!3, A!5) | subset(A!5, set_difference(B!4, singleton(C!3))) | (~subset(A!5, B!4)))),
% 0.21/0.44 inference(skolemize,[status(sab)],[126])).
% 0.21/0.44 tff(128,plain,
% 0.21/0.44 (~(in(C!3, A!5) | subset(A!5, set_difference(B!4, singleton(C!3))) | (~subset(A!5, B!4)))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[127, 116])).
% 0.21/0.44 tff(129,plain,
% 0.21/0.44 (~subset(A!5, set_difference(B!4, singleton(C!3)))),
% 0.21/0.44 inference(or_elim,[status(thm)],[128])).
% 0.21/0.44 tff(130,plain,
% 0.21/0.44 ((~(subset(A!5, set_difference(B!4, singleton(C!3))) | (~((~in(tptp_fun_C_1(set_difference(B!4, singleton(C!3)), A!5), A!5)) | in(tptp_fun_C_1(set_difference(B!4, singleton(C!3)), A!5), set_difference(B!4, singleton(C!3))))))) | subset(A!5, set_difference(B!4, singleton(C!3))) | (~((~in(tptp_fun_C_1(set_difference(B!4, singleton(C!3)), A!5), A!5)) | in(tptp_fun_C_1(set_difference(B!4, singleton(C!3)), A!5), set_difference(B!4, singleton(C!3)))))),
% 0.21/0.44 inference(tautology,[status(thm)],[])).
% 0.21/0.44 tff(131,plain,
% 0.21/0.44 ((~(subset(A!5, set_difference(B!4, singleton(C!3))) | (~((~in(tptp_fun_C_1(set_difference(B!4, singleton(C!3)), A!5), A!5)) | in(tptp_fun_C_1(set_difference(B!4, singleton(C!3)), A!5), set_difference(B!4, singleton(C!3))))))) | (~((~in(tptp_fun_C_1(set_difference(B!4, singleton(C!3)), A!5), A!5)) | in(tptp_fun_C_1(set_difference(B!4, singleton(C!3)), A!5), set_difference(B!4, singleton(C!3)))))),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[130, 129])).
% 0.21/0.44 tff(132,plain,
% 0.21/0.44 (~((~in(tptp_fun_C_1(set_difference(B!4, singleton(C!3)), A!5), A!5)) | in(tptp_fun_C_1(set_difference(B!4, singleton(C!3)), A!5), set_difference(B!4, singleton(C!3))))),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[131, 115])).
% 0.21/0.44 tff(133,plain,
% 0.21/0.44 (((~in(tptp_fun_C_1(set_difference(B!4, singleton(C!3)), A!5), A!5)) | in(tptp_fun_C_1(set_difference(B!4, singleton(C!3)), A!5), set_difference(B!4, singleton(C!3)))) | (~in(tptp_fun_C_1(set_difference(B!4, singleton(C!3)), A!5), set_difference(B!4, singleton(C!3))))),
% 0.21/0.44 inference(tautology,[status(thm)],[])).
% 0.21/0.44 tff(134,plain,
% 0.21/0.44 (~in(tptp_fun_C_1(set_difference(B!4, singleton(C!3)), A!5), set_difference(B!4, singleton(C!3)))),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[133, 132])).
% 0.21/0.44 tff(135,plain,
% 0.21/0.44 ((~((~in(tptp_fun_C_1(set_difference(B!4, singleton(C!3)), A!5), set_difference(B!4, singleton(C!3)))) <=> ((~in(tptp_fun_C_1(set_difference(B!4, singleton(C!3)), A!5), B!4)) | in(tptp_fun_C_1(set_difference(B!4, singleton(C!3)), A!5), singleton(C!3))))) | in(tptp_fun_C_1(set_difference(B!4, singleton(C!3)), A!5), set_difference(B!4, singleton(C!3))) | ((~in(tptp_fun_C_1(set_difference(B!4, singleton(C!3)), A!5), B!4)) | in(tptp_fun_C_1(set_difference(B!4, singleton(C!3)), A!5), singleton(C!3)))),
% 0.21/0.44 inference(tautology,[status(thm)],[])).
% 0.21/0.44 tff(136,plain,
% 0.21/0.44 ((~((~in(tptp_fun_C_1(set_difference(B!4, singleton(C!3)), A!5), set_difference(B!4, singleton(C!3)))) <=> ((~in(tptp_fun_C_1(set_difference(B!4, singleton(C!3)), A!5), B!4)) | in(tptp_fun_C_1(set_difference(B!4, singleton(C!3)), A!5), singleton(C!3))))) | ((~in(tptp_fun_C_1(set_difference(B!4, singleton(C!3)), A!5), B!4)) | in(tptp_fun_C_1(set_difference(B!4, singleton(C!3)), A!5), singleton(C!3)))),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[135, 134])).
% 0.21/0.44 tff(137,plain,
% 0.21/0.44 ((~in(tptp_fun_C_1(set_difference(B!4, singleton(C!3)), A!5), B!4)) | in(tptp_fun_C_1(set_difference(B!4, singleton(C!3)), A!5), singleton(C!3))),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[136, 95])).
% 0.21/0.44 tff(138,plain,
% 0.21/0.44 ((~![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_1(B, A), A)) | in(tptp_fun_C_1(B, A), B)))))))) | (~((~((~subset(A!5, B!4)) | ![C: $i] : ((~in(C, A!5)) | in(C, B!4)))) | (~(subset(A!5, B!4) | (~((~in(tptp_fun_C_1(B!4, A!5), A!5)) | in(tptp_fun_C_1(B!4, A!5), B!4)))))))),
% 0.21/0.44 inference(quant_inst,[status(thm)],[])).
% 0.21/0.44 tff(139,plain,
% 0.21/0.44 (~((~((~subset(A!5, B!4)) | ![C: $i] : ((~in(C, A!5)) | in(C, B!4)))) | (~(subset(A!5, B!4) | (~((~in(tptp_fun_C_1(B!4, A!5), A!5)) | in(tptp_fun_C_1(B!4, A!5), B!4))))))),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[138, 111])).
% 0.21/0.44 tff(140,plain,
% 0.21/0.44 (((~((~subset(A!5, B!4)) | ![C: $i] : ((~in(C, A!5)) | in(C, B!4)))) | (~(subset(A!5, B!4) | (~((~in(tptp_fun_C_1(B!4, A!5), A!5)) | in(tptp_fun_C_1(B!4, A!5), B!4)))))) | ((~subset(A!5, B!4)) | ![C: $i] : ((~in(C, A!5)) | in(C, B!4)))),
% 0.21/0.44 inference(tautology,[status(thm)],[])).
% 0.21/0.44 tff(141,plain,
% 0.21/0.44 ((~subset(A!5, B!4)) | ![C: $i] : ((~in(C, A!5)) | in(C, B!4))),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[140, 139])).
% 0.21/0.44 tff(142,plain,
% 0.21/0.44 (subset(A!5, B!4)),
% 0.21/0.44 inference(or_elim,[status(thm)],[128])).
% 0.21/0.44 tff(143,plain,
% 0.21/0.44 ((~((~subset(A!5, B!4)) | ![C: $i] : ((~in(C, A!5)) | in(C, B!4)))) | (~subset(A!5, B!4)) | ![C: $i] : ((~in(C, A!5)) | in(C, B!4))),
% 0.21/0.44 inference(tautology,[status(thm)],[])).
% 0.21/0.44 tff(144,plain,
% 0.21/0.44 ((~((~subset(A!5, B!4)) | ![C: $i] : ((~in(C, A!5)) | in(C, B!4)))) | ![C: $i] : ((~in(C, A!5)) | in(C, B!4))),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[143, 142])).
% 0.21/0.44 tff(145,plain,
% 0.21/0.44 (![C: $i] : ((~in(C, A!5)) | in(C, B!4))),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[144, 141])).
% 0.21/0.44 tff(146,plain,
% 0.21/0.44 (((~in(tptp_fun_C_1(set_difference(B!4, singleton(C!3)), A!5), A!5)) | in(tptp_fun_C_1(set_difference(B!4, singleton(C!3)), A!5), set_difference(B!4, singleton(C!3)))) | in(tptp_fun_C_1(set_difference(B!4, singleton(C!3)), A!5), A!5)),
% 0.21/0.44 inference(tautology,[status(thm)],[])).
% 0.21/0.44 tff(147,plain,
% 0.21/0.44 (in(tptp_fun_C_1(set_difference(B!4, singleton(C!3)), A!5), A!5)),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[146, 132])).
% 0.21/0.44 tff(148,plain,
% 0.21/0.44 (((~![C: $i] : ((~in(C, A!5)) | in(C, B!4))) | ((~in(tptp_fun_C_1(set_difference(B!4, singleton(C!3)), A!5), A!5)) | in(tptp_fun_C_1(set_difference(B!4, singleton(C!3)), A!5), B!4))) <=> ((~![C: $i] : ((~in(C, A!5)) | in(C, B!4))) | (~in(tptp_fun_C_1(set_difference(B!4, singleton(C!3)), A!5), A!5)) | in(tptp_fun_C_1(set_difference(B!4, singleton(C!3)), A!5), B!4))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(149,plain,
% 0.21/0.44 ((~![C: $i] : ((~in(C, A!5)) | in(C, B!4))) | ((~in(tptp_fun_C_1(set_difference(B!4, singleton(C!3)), A!5), A!5)) | in(tptp_fun_C_1(set_difference(B!4, singleton(C!3)), A!5), B!4))),
% 0.21/0.44 inference(quant_inst,[status(thm)],[])).
% 0.21/0.44 tff(150,plain,
% 0.21/0.44 ((~![C: $i] : ((~in(C, A!5)) | in(C, B!4))) | (~in(tptp_fun_C_1(set_difference(B!4, singleton(C!3)), A!5), A!5)) | in(tptp_fun_C_1(set_difference(B!4, singleton(C!3)), A!5), B!4)),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[149, 148])).
% 0.21/0.44 tff(151,plain,
% 0.21/0.44 (in(tptp_fun_C_1(set_difference(B!4, singleton(C!3)), A!5), B!4)),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[150, 147, 145])).
% 0.21/0.44 tff(152,plain,
% 0.21/0.44 ((~((~in(tptp_fun_C_1(set_difference(B!4, singleton(C!3)), A!5), B!4)) | in(tptp_fun_C_1(set_difference(B!4, singleton(C!3)), A!5), singleton(C!3)))) | (~in(tptp_fun_C_1(set_difference(B!4, singleton(C!3)), A!5), B!4)) | in(tptp_fun_C_1(set_difference(B!4, singleton(C!3)), A!5), singleton(C!3))),
% 0.21/0.44 inference(tautology,[status(thm)],[])).
% 0.21/0.44 tff(153,plain,
% 0.21/0.44 (in(tptp_fun_C_1(set_difference(B!4, singleton(C!3)), A!5), singleton(C!3))),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[152, 151, 137])).
% 0.21/0.44 tff(154,plain,
% 0.21/0.44 ((~(in(tptp_fun_C_1(set_difference(B!4, singleton(C!3)), A!5), singleton(C!3)) <=> (tptp_fun_C_1(set_difference(B!4, singleton(C!3)), A!5) = C!3))) | (~in(tptp_fun_C_1(set_difference(B!4, singleton(C!3)), A!5), singleton(C!3))) | (tptp_fun_C_1(set_difference(B!4, singleton(C!3)), A!5) = C!3)),
% 0.21/0.44 inference(tautology,[status(thm)],[])).
% 0.21/0.44 tff(155,plain,
% 0.21/0.44 ((~(in(tptp_fun_C_1(set_difference(B!4, singleton(C!3)), A!5), singleton(C!3)) <=> (tptp_fun_C_1(set_difference(B!4, singleton(C!3)), A!5) = C!3))) | (tptp_fun_C_1(set_difference(B!4, singleton(C!3)), A!5) = C!3)),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[154, 153])).
% 0.21/0.44 tff(156,plain,
% 0.21/0.44 (tptp_fun_C_1(set_difference(B!4, singleton(C!3)), A!5) = C!3),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[155, 48])).
% 0.21/0.44 tff(157,plain,
% 0.21/0.44 (in(tptp_fun_C_1(set_difference(B!4, singleton(C!3)), A!5), A!5) <=> in(C!3, A!5)),
% 0.21/0.44 inference(monotonicity,[status(thm)],[156])).
% 0.21/0.44 tff(158,plain,
% 0.21/0.44 (in(C!3, A!5) <=> in(tptp_fun_C_1(set_difference(B!4, singleton(C!3)), A!5), A!5)),
% 0.21/0.44 inference(symmetry,[status(thm)],[157])).
% 0.21/0.44 tff(159,plain,
% 0.21/0.44 ((~in(C!3, A!5)) <=> (~in(tptp_fun_C_1(set_difference(B!4, singleton(C!3)), A!5), A!5))),
% 0.21/0.44 inference(monotonicity,[status(thm)],[158])).
% 0.21/0.44 tff(160,plain,
% 0.21/0.44 (~in(C!3, A!5)),
% 0.21/0.44 inference(or_elim,[status(thm)],[128])).
% 0.21/0.44 tff(161,plain,
% 0.21/0.44 (~in(tptp_fun_C_1(set_difference(B!4, singleton(C!3)), A!5), A!5)),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[160, 159])).
% 0.21/0.44 tff(162,plain,
% 0.21/0.44 ($false),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[147, 161])).
% 0.21/0.44 % SZS output end Proof
%------------------------------------------------------------------------------