TSTP Solution File: SEU135+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SEU135+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n015.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 20 07:27:40 EDT 2022
% Result : Theorem 0.21s 0.51s
% Output : Proof 0.47s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU135+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 : n015.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 09:47:55 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.
% 0.21/0.51 % SZS status Theorem
% 0.21/0.51 % SZS output start Proof
% 0.21/0.51 tff(in_type, type, (
% 0.21/0.51 in: ( $i * $i ) > $o)).
% 0.21/0.51 tff(tptp_fun_B_5_type, type, (
% 0.21/0.51 tptp_fun_B_5: $i)).
% 0.21/0.51 tff(tptp_fun_D_0_type, type, (
% 0.21/0.51 tptp_fun_D_0: ( $i * $i * $i ) > $i)).
% 0.21/0.51 tff(set_union2_type, type, (
% 0.21/0.51 set_union2: ( $i * $i ) > $i)).
% 0.21/0.51 tff(tptp_fun_A_3_type, type, (
% 0.21/0.51 tptp_fun_A_3: $i)).
% 0.21/0.51 tff(tptp_fun_A_6_type, type, (
% 0.21/0.51 tptp_fun_A_6: $i)).
% 0.21/0.51 tff(set_difference_type, type, (
% 0.21/0.51 set_difference: ( $i * $i ) > $i)).
% 0.21/0.51 tff(tptp_fun_D_2_type, type, (
% 0.21/0.51 tptp_fun_D_2: ( $i * $i * $i ) > $i)).
% 0.21/0.51 tff(empty_set_type, type, (
% 0.21/0.51 empty_set: $i)).
% 0.21/0.51 tff(empty_type, type, (
% 0.21/0.51 empty: $i > $o)).
% 0.21/0.51 tff(1,assumption,(~(in(tptp_fun_D_0(set_union2(set_difference(B!5, A!6), A!6), set_union2(A!6, A!3), B!5), set_union2(A!6, A!3)) | in(tptp_fun_D_0(set_union2(set_difference(B!5, A!6), A!6), set_union2(A!6, A!3), B!5), B!5))), introduced(assumption)).
% 0.21/0.51 tff(2,plain,
% 0.21/0.51 ((in(tptp_fun_D_0(set_union2(set_difference(B!5, A!6), A!6), set_union2(A!6, A!3), B!5), set_union2(A!6, A!3)) | in(tptp_fun_D_0(set_union2(set_difference(B!5, A!6), A!6), set_union2(A!6, A!3), B!5), B!5)) | (~in(tptp_fun_D_0(set_union2(set_difference(B!5, A!6), A!6), set_union2(A!6, A!3), B!5), set_union2(A!6, A!3)))),
% 0.21/0.51 inference(tautology,[status(thm)],[])).
% 0.21/0.51 tff(3,plain,
% 0.21/0.51 (~in(tptp_fun_D_0(set_union2(set_difference(B!5, A!6), A!6), set_union2(A!6, A!3), B!5), set_union2(A!6, A!3))),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[2, 1])).
% 0.21/0.51 tff(4,plain,
% 0.21/0.51 (^[A: $i, B: $i, C: $i, D: $i] : refl((~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A))))))) <=> (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A))))))))),
% 0.21/0.51 inference(bind,[status(th)],[])).
% 0.21/0.51 tff(5,plain,
% 0.21/0.51 (![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A)))))))),
% 0.21/0.51 inference(quant_intro,[status(thm)],[4])).
% 0.21/0.51 tff(6,plain,
% 0.21/0.51 (![A: $i, B: $i, C: $i] : ![D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A)))))))),
% 0.21/0.51 inference(pull_quant,[status(thm)],[])).
% 0.21/0.51 tff(7,plain,
% 0.21/0.51 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(pull_quant(((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A)))) <=> ![D: $i] : ((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))), ((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))) <=> (~![D: $i] : ((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))))), pull_quant((~![D: $i] : ((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) <=> ?[D: $i] : (~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A)))))), ((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))) <=> ?[D: $i] : (~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))))), (((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A)))))) <=> (?[D: $i] : (~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A)))))))), pull_quant((?[D: $i] : (~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A)))))) <=> ?[D: $i] : ((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A))))))), (((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A)))))) <=> ?[D: $i] : ((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A)))))))), ((~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A))))))) <=> (~?[D: $i] : ((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A))))))))), pull_quant((~?[D: $i] : ((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A))))))) <=> ![D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A)))))))), ((~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A))))))) <=> ![D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A)))))))))),
% 0.21/0.51 inference(bind,[status(th)],[])).
% 0.21/0.51 tff(8,plain,
% 0.21/0.51 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A))))))) <=> ![A: $i, B: $i, C: $i] : ![D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A)))))))),
% 0.21/0.51 inference(quant_intro,[status(thm)],[7])).
% 0.21/0.51 tff(9,plain,
% 0.21/0.51 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A)))))))),
% 0.21/0.51 inference(transitivity,[status(thm)],[8, 6])).
% 0.21/0.51 tff(10,plain,
% 0.21/0.51 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A)))))))),
% 0.21/0.51 inference(transitivity,[status(thm)],[9, 5])).
% 0.21/0.51 tff(11,plain,
% 0.21/0.51 (^[A: $i, B: $i, C: $i] : rewrite((~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A))))))) <=> (~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A))))))))),
% 0.21/0.51 inference(bind,[status(th)],[])).
% 0.21/0.51 tff(12,plain,
% 0.21/0.51 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A))))))) <=> ![A: $i, B: $i, C: $i] : (~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A)))))))),
% 0.21/0.51 inference(quant_intro,[status(thm)],[11])).
% 0.21/0.51 tff(13,plain,
% 0.21/0.51 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A)))))))),
% 0.21/0.51 inference(transitivity,[status(thm)],[12, 10])).
% 0.21/0.51 tff(14,plain,
% 0.21/0.51 (^[A: $i, B: $i, C: $i] : trans(monotonicity(rewrite(((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A)))) <=> ((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))), ((((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A)))) & ((C = set_union2(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A))))) <=> (((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A)))) & ((C = set_union2(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A))))))), rewrite((((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A)))) & ((C = set_union2(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A))))) <=> (~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A)))))))), ((((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A)))) & ((C = set_union2(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A))))) <=> (~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A)))))))))),
% 0.21/0.51 inference(bind,[status(th)],[])).
% 0.21/0.51 tff(15,plain,
% 0.21/0.51 (![A: $i, B: $i, C: $i] : (((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A)))) & ((C = set_union2(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A))))) <=> ![A: $i, B: $i, C: $i] : (~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A)))))))),
% 0.21/0.51 inference(quant_intro,[status(thm)],[14])).
% 0.21/0.51 tff(16,plain,
% 0.21/0.51 (^[A: $i, B: $i, C: $i] : rewrite((((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A)))) & ((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A)))))) <=> (((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A)))) & ((C = set_union2(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A))))))),
% 0.21/0.52 inference(bind,[status(th)],[])).
% 0.21/0.52 tff(17,plain,
% 0.21/0.52 (![A: $i, B: $i, C: $i] : (((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A)))) & ((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A)))))) <=> ![A: $i, B: $i, C: $i] : (((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A)))) & ((C = set_union2(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A)))))),
% 0.21/0.52 inference(quant_intro,[status(thm)],[16])).
% 0.21/0.52 tff(18,plain,
% 0.21/0.52 (![A: $i, B: $i, C: $i] : ((C = set_union2(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A)))) <=> ![A: $i, B: $i, C: $i] : ((C = set_union2(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))),
% 0.21/0.52 inference(rewrite,[status(thm)],[])).
% 0.21/0.52 tff(19,plain,
% 0.21/0.52 (^[A: $i, B: $i, C: $i] : rewrite(((C = set_union2(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B)))) <=> ((C = set_union2(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A)))))),
% 0.21/0.52 inference(bind,[status(th)],[])).
% 0.21/0.52 tff(20,plain,
% 0.21/0.52 (![A: $i, B: $i, C: $i] : ((C = set_union2(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B)))) <=> ![A: $i, B: $i, C: $i] : ((C = set_union2(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))),
% 0.21/0.52 inference(quant_intro,[status(thm)],[19])).
% 0.21/0.52 tff(21,axiom,(![A: $i, B: $i, C: $i] : ((C = set_union2(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d2_xboole_0')).
% 0.21/0.52 tff(22,plain,
% 0.21/0.52 (![A: $i, B: $i, C: $i] : ((C = set_union2(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[21, 20])).
% 0.21/0.52 tff(23,plain,
% 0.21/0.52 (![A: $i, B: $i, C: $i] : ((C = set_union2(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[22, 18])).
% 0.21/0.52 tff(24,plain,(
% 0.21/0.52 ![A: $i, B: $i, C: $i] : (((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A)))) & ((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A))))))),
% 0.21/0.52 inference(skolemize,[status(sab)],[23])).
% 0.21/0.52 tff(25,plain,
% 0.21/0.52 (![A: $i, B: $i, C: $i] : (((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A)))) & ((C = set_union2(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A)))))),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[24, 17])).
% 0.21/0.52 tff(26,plain,
% 0.21/0.52 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A)))))))),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[25, 15])).
% 0.21/0.52 tff(27,plain,
% 0.21/0.52 (![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A)))))))),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[26, 13])).
% 0.21/0.52 tff(28,plain,
% 0.21/0.52 ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A)))))))) | (~((~((~(set_union2(set_difference(B!5, A!6), A!6) = set_union2(B!5, set_union2(A!6, A!3)))) | (in(tptp_fun_D_2(set_union2(set_difference(B!5, A!6), A!6), A!6, B!5), set_union2(set_difference(B!5, A!6), A!6)) <=> (in(tptp_fun_D_2(set_union2(set_difference(B!5, A!6), A!6), A!6, B!5), set_union2(A!6, A!3)) | in(tptp_fun_D_2(set_union2(set_difference(B!5, A!6), A!6), A!6, B!5), B!5))))) | (~((set_union2(set_difference(B!5, A!6), A!6) = set_union2(B!5, set_union2(A!6, A!3))) | ((~in(tptp_fun_D_0(set_union2(set_difference(B!5, A!6), A!6), set_union2(A!6, A!3), B!5), set_union2(set_difference(B!5, A!6), A!6))) <=> (in(tptp_fun_D_0(set_union2(set_difference(B!5, A!6), A!6), set_union2(A!6, A!3), B!5), set_union2(A!6, A!3)) | in(tptp_fun_D_0(set_union2(set_difference(B!5, A!6), A!6), set_union2(A!6, A!3), B!5), B!5)))))))),
% 0.21/0.52 inference(quant_inst,[status(thm)],[])).
% 0.21/0.52 tff(29,plain,
% 0.21/0.52 (~((~((~(set_union2(set_difference(B!5, A!6), A!6) = set_union2(B!5, set_union2(A!6, A!3)))) | (in(tptp_fun_D_2(set_union2(set_difference(B!5, A!6), A!6), A!6, B!5), set_union2(set_difference(B!5, A!6), A!6)) <=> (in(tptp_fun_D_2(set_union2(set_difference(B!5, A!6), A!6), A!6, B!5), set_union2(A!6, A!3)) | in(tptp_fun_D_2(set_union2(set_difference(B!5, A!6), A!6), A!6, B!5), B!5))))) | (~((set_union2(set_difference(B!5, A!6), A!6) = set_union2(B!5, set_union2(A!6, A!3))) | ((~in(tptp_fun_D_0(set_union2(set_difference(B!5, A!6), A!6), set_union2(A!6, A!3), B!5), set_union2(set_difference(B!5, A!6), A!6))) <=> (in(tptp_fun_D_0(set_union2(set_difference(B!5, A!6), A!6), set_union2(A!6, A!3), B!5), set_union2(A!6, A!3)) | in(tptp_fun_D_0(set_union2(set_difference(B!5, A!6), A!6), set_union2(A!6, A!3), B!5), B!5))))))),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[28, 27])).
% 0.21/0.52 tff(30,plain,
% 0.21/0.52 (((~((~(set_union2(set_difference(B!5, A!6), A!6) = set_union2(B!5, set_union2(A!6, A!3)))) | (in(tptp_fun_D_2(set_union2(set_difference(B!5, A!6), A!6), A!6, B!5), set_union2(set_difference(B!5, A!6), A!6)) <=> (in(tptp_fun_D_2(set_union2(set_difference(B!5, A!6), A!6), A!6, B!5), set_union2(A!6, A!3)) | in(tptp_fun_D_2(set_union2(set_difference(B!5, A!6), A!6), A!6, B!5), B!5))))) | (~((set_union2(set_difference(B!5, A!6), A!6) = set_union2(B!5, set_union2(A!6, A!3))) | ((~in(tptp_fun_D_0(set_union2(set_difference(B!5, A!6), A!6), set_union2(A!6, A!3), B!5), set_union2(set_difference(B!5, A!6), A!6))) <=> (in(tptp_fun_D_0(set_union2(set_difference(B!5, A!6), A!6), set_union2(A!6, A!3), B!5), set_union2(A!6, A!3)) | in(tptp_fun_D_0(set_union2(set_difference(B!5, A!6), A!6), set_union2(A!6, A!3), B!5), B!5)))))) | ((set_union2(set_difference(B!5, A!6), A!6) = set_union2(B!5, set_union2(A!6, A!3))) | ((~in(tptp_fun_D_0(set_union2(set_difference(B!5, A!6), A!6), set_union2(A!6, A!3), B!5), set_union2(set_difference(B!5, A!6), A!6))) <=> (in(tptp_fun_D_0(set_union2(set_difference(B!5, A!6), A!6), set_union2(A!6, A!3), B!5), set_union2(A!6, A!3)) | in(tptp_fun_D_0(set_union2(set_difference(B!5, A!6), A!6), set_union2(A!6, A!3), B!5), B!5))))),
% 0.21/0.52 inference(tautology,[status(thm)],[])).
% 0.21/0.52 tff(31,plain,
% 0.21/0.52 ((set_union2(set_difference(B!5, A!6), A!6) = set_union2(B!5, set_union2(A!6, A!3))) | ((~in(tptp_fun_D_0(set_union2(set_difference(B!5, A!6), A!6), set_union2(A!6, A!3), B!5), set_union2(set_difference(B!5, A!6), A!6))) <=> (in(tptp_fun_D_0(set_union2(set_difference(B!5, A!6), A!6), set_union2(A!6, A!3), B!5), set_union2(A!6, A!3)) | in(tptp_fun_D_0(set_union2(set_difference(B!5, A!6), A!6), set_union2(A!6, A!3), B!5), B!5)))),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[30, 29])).
% 0.21/0.52 tff(32,plain,
% 0.21/0.52 (^[A: $i, B: $i] : refl((set_union2(A, B) = set_union2(B, A)) <=> (set_union2(A, B) = set_union2(B, A)))),
% 0.21/0.52 inference(bind,[status(th)],[])).
% 0.21/0.52 tff(33,plain,
% 0.21/0.52 (![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A)) <=> ![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A))),
% 0.21/0.52 inference(quant_intro,[status(thm)],[32])).
% 0.21/0.52 tff(34,plain,
% 0.21/0.52 (![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A)) <=> ![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A))),
% 0.21/0.52 inference(rewrite,[status(thm)],[])).
% 0.21/0.52 tff(35,axiom,(![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','commutativity_k2_xboole_0')).
% 0.21/0.52 tff(36,plain,
% 0.21/0.52 (![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A))),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[35, 34])).
% 0.21/0.52 tff(37,plain,(
% 0.21/0.52 ![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A))),
% 0.21/0.52 inference(skolemize,[status(sab)],[36])).
% 0.21/0.52 tff(38,plain,
% 0.21/0.52 (![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A))),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[37, 33])).
% 0.21/0.52 tff(39,plain,
% 0.21/0.52 ((~![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A))) | (set_union2(A!6, B!5) = set_union2(B!5, A!6))),
% 0.21/0.52 inference(quant_inst,[status(thm)],[])).
% 0.21/0.52 tff(40,plain,
% 0.21/0.52 (set_union2(A!6, B!5) = set_union2(B!5, A!6)),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[39, 38])).
% 0.21/0.52 tff(41,plain,
% 0.21/0.52 (set_union2(B!5, A!6) = set_union2(A!6, B!5)),
% 0.21/0.52 inference(symmetry,[status(thm)],[40])).
% 0.21/0.52 tff(42,plain,
% 0.21/0.52 (^[A: $i] : refl((set_union2(A, empty_set) = A) <=> (set_union2(A, empty_set) = A))),
% 0.21/0.52 inference(bind,[status(th)],[])).
% 0.21/0.52 tff(43,plain,
% 0.21/0.52 (![A: $i] : (set_union2(A, empty_set) = A) <=> ![A: $i] : (set_union2(A, empty_set) = A)),
% 0.21/0.52 inference(quant_intro,[status(thm)],[42])).
% 0.21/0.52 tff(44,plain,
% 0.21/0.52 (![A: $i] : (set_union2(A, empty_set) = A) <=> ![A: $i] : (set_union2(A, empty_set) = A)),
% 0.21/0.52 inference(rewrite,[status(thm)],[])).
% 0.21/0.52 tff(45,axiom,(![A: $i] : (set_union2(A, empty_set) = A)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t1_boole')).
% 0.21/0.52 tff(46,plain,
% 0.21/0.52 (![A: $i] : (set_union2(A, empty_set) = A)),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[45, 44])).
% 0.21/0.52 tff(47,plain,(
% 0.21/0.52 ![A: $i] : (set_union2(A, empty_set) = A)),
% 0.21/0.52 inference(skolemize,[status(sab)],[46])).
% 0.21/0.52 tff(48,plain,
% 0.21/0.52 (![A: $i] : (set_union2(A, empty_set) = A)),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[47, 43])).
% 0.21/0.52 tff(49,plain,
% 0.21/0.52 ((~![A: $i] : (set_union2(A, empty_set) = A)) | (set_union2(A!6, empty_set) = A!6)),
% 0.21/0.52 inference(quant_inst,[status(thm)],[])).
% 0.21/0.52 tff(50,plain,
% 0.21/0.52 (set_union2(A!6, empty_set) = A!6),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[49, 48])).
% 0.21/0.52 tff(51,plain,
% 0.21/0.52 (^[A: $i, B: $i] : refl(((A = B) | (~empty(A)) | (~empty(B))) <=> ((A = B) | (~empty(A)) | (~empty(B))))),
% 0.21/0.52 inference(bind,[status(th)],[])).
% 0.21/0.52 tff(52,plain,
% 0.21/0.52 (![A: $i, B: $i] : ((A = B) | (~empty(A)) | (~empty(B))) <=> ![A: $i, B: $i] : ((A = B) | (~empty(A)) | (~empty(B)))),
% 0.21/0.52 inference(quant_intro,[status(thm)],[51])).
% 0.21/0.52 tff(53,plain,
% 0.21/0.52 (^[A: $i, B: $i] : trans(monotonicity(rewrite((empty(A) & (~(A = B)) & empty(B)) <=> (~((A = B) | (~empty(A)) | (~empty(B))))), ((~(empty(A) & (~(A = B)) & empty(B))) <=> (~(~((A = B) | (~empty(A)) | (~empty(B))))))), rewrite((~(~((A = B) | (~empty(A)) | (~empty(B))))) <=> ((A = B) | (~empty(A)) | (~empty(B)))), ((~(empty(A) & (~(A = B)) & empty(B))) <=> ((A = B) | (~empty(A)) | (~empty(B)))))),
% 0.21/0.52 inference(bind,[status(th)],[])).
% 0.21/0.52 tff(54,plain,
% 0.21/0.52 (![A: $i, B: $i] : (~(empty(A) & (~(A = B)) & empty(B))) <=> ![A: $i, B: $i] : ((A = B) | (~empty(A)) | (~empty(B)))),
% 0.21/0.52 inference(quant_intro,[status(thm)],[53])).
% 0.21/0.52 tff(55,plain,
% 0.21/0.52 (![A: $i, B: $i] : (~(empty(A) & (~(A = B)) & empty(B))) <=> ![A: $i, B: $i] : (~(empty(A) & (~(A = B)) & empty(B)))),
% 0.21/0.52 inference(rewrite,[status(thm)],[])).
% 0.21/0.52 tff(56,plain,
% 0.21/0.52 (^[A: $i, B: $i] : rewrite((~((empty(A) & (~(A = B))) & empty(B))) <=> (~(empty(A) & (~(A = B)) & empty(B))))),
% 0.21/0.52 inference(bind,[status(th)],[])).
% 0.21/0.52 tff(57,plain,
% 0.21/0.52 (![A: $i, B: $i] : (~((empty(A) & (~(A = B))) & empty(B))) <=> ![A: $i, B: $i] : (~(empty(A) & (~(A = B)) & empty(B)))),
% 0.21/0.52 inference(quant_intro,[status(thm)],[56])).
% 0.21/0.52 tff(58,axiom,(![A: $i, B: $i] : (~((empty(A) & (~(A = B))) & empty(B)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t8_boole')).
% 0.21/0.52 tff(59,plain,
% 0.21/0.52 (![A: $i, B: $i] : (~(empty(A) & (~(A = B)) & empty(B)))),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[58, 57])).
% 0.21/0.52 tff(60,plain,
% 0.21/0.52 (![A: $i, B: $i] : (~(empty(A) & (~(A = B)) & empty(B)))),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[59, 55])).
% 0.21/0.52 tff(61,plain,(
% 0.21/0.52 ![A: $i, B: $i] : (~(empty(A) & (~(A = B)) & empty(B)))),
% 0.21/0.52 inference(skolemize,[status(sab)],[60])).
% 0.21/0.52 tff(62,plain,
% 0.21/0.52 (![A: $i, B: $i] : ((A = B) | (~empty(A)) | (~empty(B)))),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[61, 54])).
% 0.21/0.52 tff(63,plain,
% 0.21/0.52 (![A: $i, B: $i] : ((A = B) | (~empty(A)) | (~empty(B)))),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[62, 52])).
% 0.21/0.52 tff(64,plain,
% 0.21/0.52 (?[A: $i] : empty(A) <=> ?[A: $i] : empty(A)),
% 0.21/0.52 inference(rewrite,[status(thm)],[])).
% 0.21/0.52 tff(65,axiom,(?[A: $i] : empty(A)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','rc1_xboole_0')).
% 0.21/0.52 tff(66,plain,
% 0.21/0.52 (?[A: $i] : empty(A)),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[65, 64])).
% 0.21/0.52 tff(67,plain,(
% 0.21/0.52 empty(A!3)),
% 0.21/0.52 inference(skolemize,[status(sab)],[66])).
% 0.21/0.52 tff(68,plain,
% 0.21/0.52 (empty(empty_set) <=> empty(empty_set)),
% 0.21/0.52 inference(rewrite,[status(thm)],[])).
% 0.21/0.52 tff(69,axiom,(empty(empty_set)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','fc1_xboole_0')).
% 0.21/0.52 tff(70,plain,
% 0.21/0.52 (empty(empty_set)),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[69, 68])).
% 0.21/0.52 tff(71,plain,
% 0.21/0.52 (((~![A: $i, B: $i] : ((A = B) | (~empty(A)) | (~empty(B)))) | ((empty_set = A!3) | (~empty(empty_set)) | (~empty(A!3)))) <=> ((~![A: $i, B: $i] : ((A = B) | (~empty(A)) | (~empty(B)))) | (empty_set = A!3) | (~empty(empty_set)) | (~empty(A!3)))),
% 0.21/0.52 inference(rewrite,[status(thm)],[])).
% 0.21/0.52 tff(72,plain,
% 0.21/0.52 ((~![A: $i, B: $i] : ((A = B) | (~empty(A)) | (~empty(B)))) | ((empty_set = A!3) | (~empty(empty_set)) | (~empty(A!3)))),
% 0.21/0.52 inference(quant_inst,[status(thm)],[])).
% 0.21/0.52 tff(73,plain,
% 0.21/0.52 ((~![A: $i, B: $i] : ((A = B) | (~empty(A)) | (~empty(B)))) | (empty_set = A!3) | (~empty(empty_set)) | (~empty(A!3))),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[72, 71])).
% 0.21/0.52 tff(74,plain,
% 0.21/0.52 (empty_set = A!3),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[73, 70, 67, 63])).
% 0.21/0.52 tff(75,plain,
% 0.21/0.52 (set_union2(A!6, empty_set) = set_union2(A!6, A!3)),
% 0.21/0.52 inference(monotonicity,[status(thm)],[74])).
% 0.21/0.52 tff(76,plain,
% 0.21/0.52 (set_union2(A!6, A!3) = set_union2(A!6, empty_set)),
% 0.21/0.52 inference(symmetry,[status(thm)],[75])).
% 0.21/0.52 tff(77,plain,
% 0.21/0.52 (set_union2(A!6, A!3) = A!6),
% 0.21/0.52 inference(transitivity,[status(thm)],[76, 50])).
% 0.21/0.52 tff(78,plain,
% 0.21/0.52 (set_union2(B!5, set_union2(A!6, A!3)) = set_union2(B!5, A!6)),
% 0.21/0.52 inference(monotonicity,[status(thm)],[77])).
% 0.21/0.52 tff(79,plain,
% 0.21/0.52 (set_union2(B!5, set_union2(A!6, A!3)) = set_union2(A!6, B!5)),
% 0.21/0.52 inference(transitivity,[status(thm)],[78, 41])).
% 0.21/0.52 tff(80,plain,
% 0.21/0.52 ((~![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A))) | (set_union2(A!6, set_difference(B!5, A!6)) = set_union2(set_difference(B!5, A!6), A!6))),
% 0.21/0.52 inference(quant_inst,[status(thm)],[])).
% 0.21/0.52 tff(81,plain,
% 0.21/0.52 (set_union2(A!6, set_difference(B!5, A!6)) = set_union2(set_difference(B!5, A!6), A!6)),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[80, 38])).
% 0.21/0.52 tff(82,plain,
% 0.21/0.52 (set_union2(set_difference(B!5, A!6), A!6) = set_union2(A!6, set_difference(B!5, A!6))),
% 0.21/0.52 inference(symmetry,[status(thm)],[81])).
% 0.21/0.52 tff(83,plain,
% 0.21/0.52 ((set_union2(set_difference(B!5, A!6), A!6) = set_union2(B!5, set_union2(A!6, A!3))) <=> (set_union2(A!6, set_difference(B!5, A!6)) = set_union2(A!6, B!5))),
% 0.21/0.52 inference(monotonicity,[status(thm)],[82, 79])).
% 0.21/0.52 tff(84,plain,
% 0.21/0.52 ((set_union2(A!6, set_difference(B!5, A!6)) = set_union2(A!6, B!5)) <=> (set_union2(set_difference(B!5, A!6), A!6) = set_union2(B!5, set_union2(A!6, A!3)))),
% 0.21/0.52 inference(symmetry,[status(thm)],[83])).
% 0.21/0.52 tff(85,plain,
% 0.21/0.52 ((~(set_union2(A!6, set_difference(B!5, A!6)) = set_union2(A!6, B!5))) <=> (~(set_union2(set_difference(B!5, A!6), A!6) = set_union2(B!5, set_union2(A!6, A!3))))),
% 0.21/0.52 inference(monotonicity,[status(thm)],[84])).
% 0.21/0.52 tff(86,plain,
% 0.21/0.52 ((~![A: $i, B: $i] : (set_union2(A, set_difference(B, A)) = set_union2(A, B))) <=> (~![A: $i, B: $i] : (set_union2(A, set_difference(B, A)) = set_union2(A, B)))),
% 0.21/0.52 inference(rewrite,[status(thm)],[])).
% 0.21/0.52 tff(87,axiom,(~![A: $i, B: $i] : (set_union2(A, set_difference(B, A)) = set_union2(A, B))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t39_xboole_1')).
% 0.21/0.52 tff(88,plain,
% 0.21/0.52 (~![A: $i, B: $i] : (set_union2(A, set_difference(B, A)) = set_union2(A, B))),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[87, 86])).
% 0.21/0.52 tff(89,plain,
% 0.21/0.52 (~![A: $i, B: $i] : (set_union2(A, set_difference(B, A)) = set_union2(A, B))),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[88, 86])).
% 0.21/0.52 tff(90,plain,
% 0.21/0.52 (~![A: $i, B: $i] : (set_union2(A, set_difference(B, A)) = set_union2(A, B))),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[89, 86])).
% 0.21/0.52 tff(91,plain,
% 0.21/0.52 (~![A: $i, B: $i] : (set_union2(A, set_difference(B, A)) = set_union2(A, B))),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[90, 86])).
% 0.21/0.52 tff(92,plain,
% 0.21/0.52 (~![A: $i, B: $i] : (set_union2(A, set_difference(B, A)) = set_union2(A, B))),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[91, 86])).
% 0.21/0.52 tff(93,plain,
% 0.21/0.52 (~![A: $i, B: $i] : (set_union2(A, set_difference(B, A)) = set_union2(A, B))),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[92, 86])).
% 0.21/0.52 tff(94,plain,
% 0.21/0.52 (~![A: $i, B: $i] : (set_union2(A, set_difference(B, A)) = set_union2(A, B))),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[93, 86])).
% 0.21/0.52 tff(95,plain,(
% 0.21/0.52 ~(set_union2(A!6, set_difference(B!5, A!6)) = set_union2(A!6, B!5))),
% 0.21/0.52 inference(skolemize,[status(sab)],[94])).
% 0.21/0.52 tff(96,plain,
% 0.21/0.52 (~(set_union2(set_difference(B!5, A!6), A!6) = set_union2(B!5, set_union2(A!6, A!3)))),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[95, 85])).
% 0.21/0.52 tff(97,plain,
% 0.21/0.52 ((~((set_union2(set_difference(B!5, A!6), A!6) = set_union2(B!5, set_union2(A!6, A!3))) | ((~in(tptp_fun_D_0(set_union2(set_difference(B!5, A!6), A!6), set_union2(A!6, A!3), B!5), set_union2(set_difference(B!5, A!6), A!6))) <=> (in(tptp_fun_D_0(set_union2(set_difference(B!5, A!6), A!6), set_union2(A!6, A!3), B!5), set_union2(A!6, A!3)) | in(tptp_fun_D_0(set_union2(set_difference(B!5, A!6), A!6), set_union2(A!6, A!3), B!5), B!5))))) | (set_union2(set_difference(B!5, A!6), A!6) = set_union2(B!5, set_union2(A!6, A!3))) | ((~in(tptp_fun_D_0(set_union2(set_difference(B!5, A!6), A!6), set_union2(A!6, A!3), B!5), set_union2(set_difference(B!5, A!6), A!6))) <=> (in(tptp_fun_D_0(set_union2(set_difference(B!5, A!6), A!6), set_union2(A!6, A!3), B!5), set_union2(A!6, A!3)) | in(tptp_fun_D_0(set_union2(set_difference(B!5, A!6), A!6), set_union2(A!6, A!3), B!5), B!5)))),
% 0.21/0.52 inference(tautology,[status(thm)],[])).
% 0.21/0.52 tff(98,plain,
% 0.21/0.52 ((~in(tptp_fun_D_0(set_union2(set_difference(B!5, A!6), A!6), set_union2(A!6, A!3), B!5), set_union2(set_difference(B!5, A!6), A!6))) <=> (in(tptp_fun_D_0(set_union2(set_difference(B!5, A!6), A!6), set_union2(A!6, A!3), B!5), set_union2(A!6, A!3)) | in(tptp_fun_D_0(set_union2(set_difference(B!5, A!6), A!6), set_union2(A!6, A!3), B!5), B!5))),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[97, 96, 31])).
% 0.21/0.52 tff(99,plain,
% 0.21/0.52 ((~((~in(tptp_fun_D_0(set_union2(set_difference(B!5, A!6), A!6), set_union2(A!6, A!3), B!5), set_union2(set_difference(B!5, A!6), A!6))) <=> (in(tptp_fun_D_0(set_union2(set_difference(B!5, A!6), A!6), set_union2(A!6, A!3), B!5), set_union2(A!6, A!3)) | in(tptp_fun_D_0(set_union2(set_difference(B!5, A!6), A!6), set_union2(A!6, A!3), B!5), B!5)))) | in(tptp_fun_D_0(set_union2(set_difference(B!5, A!6), A!6), set_union2(A!6, A!3), B!5), set_union2(set_difference(B!5, A!6), A!6)) | (in(tptp_fun_D_0(set_union2(set_difference(B!5, A!6), A!6), set_union2(A!6, A!3), B!5), set_union2(A!6, A!3)) | in(tptp_fun_D_0(set_union2(set_difference(B!5, A!6), A!6), set_union2(A!6, A!3), B!5), B!5))),
% 0.21/0.52 inference(tautology,[status(thm)],[])).
% 0.21/0.52 tff(100,plain,
% 0.21/0.52 (in(tptp_fun_D_0(set_union2(set_difference(B!5, A!6), A!6), set_union2(A!6, A!3), B!5), set_union2(set_difference(B!5, A!6), A!6)) | (in(tptp_fun_D_0(set_union2(set_difference(B!5, A!6), A!6), set_union2(A!6, A!3), B!5), set_union2(A!6, A!3)) | in(tptp_fun_D_0(set_union2(set_difference(B!5, A!6), A!6), set_union2(A!6, A!3), B!5), B!5))),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[99, 98])).
% 0.21/0.52 tff(101,plain,
% 0.21/0.52 (in(tptp_fun_D_0(set_union2(set_difference(B!5, A!6), A!6), set_union2(A!6, A!3), B!5), set_union2(set_difference(B!5, A!6), A!6))),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[100, 1])).
% 0.21/0.52 tff(102,plain,
% 0.21/0.52 ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A)))))))) | (~((~((~(set_union2(set_difference(B!5, A!6), A!6) = set_union2(set_union2(A!6, A!3), set_difference(B!5, A!6)))) | (in(tptp_fun_D_0(set_union2(set_difference(B!5, A!6), A!6), set_union2(A!6, A!3), B!5), set_union2(set_difference(B!5, A!6), A!6)) <=> (in(tptp_fun_D_0(set_union2(set_difference(B!5, A!6), A!6), set_union2(A!6, A!3), B!5), set_difference(B!5, A!6)) | in(tptp_fun_D_0(set_union2(set_difference(B!5, A!6), A!6), set_union2(A!6, A!3), B!5), set_union2(A!6, A!3)))))) | (~((set_union2(set_difference(B!5, A!6), A!6) = set_union2(set_union2(A!6, A!3), set_difference(B!5, A!6))) | ((~in(tptp_fun_D_0(set_union2(set_difference(B!5, A!6), A!6), set_difference(B!5, A!6), set_union2(A!6, A!3)), set_union2(set_difference(B!5, A!6), A!6))) <=> (in(tptp_fun_D_0(set_union2(set_difference(B!5, A!6), A!6), set_difference(B!5, A!6), set_union2(A!6, A!3)), set_difference(B!5, A!6)) | in(tptp_fun_D_0(set_union2(set_difference(B!5, A!6), A!6), set_difference(B!5, A!6), set_union2(A!6, A!3)), set_union2(A!6, A!3))))))))),
% 0.21/0.53 inference(quant_inst,[status(thm)],[])).
% 0.21/0.53 tff(103,plain,
% 0.21/0.53 (~((~((~(set_union2(set_difference(B!5, A!6), A!6) = set_union2(set_union2(A!6, A!3), set_difference(B!5, A!6)))) | (in(tptp_fun_D_0(set_union2(set_difference(B!5, A!6), A!6), set_union2(A!6, A!3), B!5), set_union2(set_difference(B!5, A!6), A!6)) <=> (in(tptp_fun_D_0(set_union2(set_difference(B!5, A!6), A!6), set_union2(A!6, A!3), B!5), set_difference(B!5, A!6)) | in(tptp_fun_D_0(set_union2(set_difference(B!5, A!6), A!6), set_union2(A!6, A!3), B!5), set_union2(A!6, A!3)))))) | (~((set_union2(set_difference(B!5, A!6), A!6) = set_union2(set_union2(A!6, A!3), set_difference(B!5, A!6))) | ((~in(tptp_fun_D_0(set_union2(set_difference(B!5, A!6), A!6), set_difference(B!5, A!6), set_union2(A!6, A!3)), set_union2(set_difference(B!5, A!6), A!6))) <=> (in(tptp_fun_D_0(set_union2(set_difference(B!5, A!6), A!6), set_difference(B!5, A!6), set_union2(A!6, A!3)), set_difference(B!5, A!6)) | in(tptp_fun_D_0(set_union2(set_difference(B!5, A!6), A!6), set_difference(B!5, A!6), set_union2(A!6, A!3)), set_union2(A!6, A!3)))))))),
% 0.21/0.53 inference(unit_resolution,[status(thm)],[102, 27])).
% 0.21/0.53 tff(104,plain,
% 0.21/0.53 (((~((~(set_union2(set_difference(B!5, A!6), A!6) = set_union2(set_union2(A!6, A!3), set_difference(B!5, A!6)))) | (in(tptp_fun_D_0(set_union2(set_difference(B!5, A!6), A!6), set_union2(A!6, A!3), B!5), set_union2(set_difference(B!5, A!6), A!6)) <=> (in(tptp_fun_D_0(set_union2(set_difference(B!5, A!6), A!6), set_union2(A!6, A!3), B!5), set_difference(B!5, A!6)) | in(tptp_fun_D_0(set_union2(set_difference(B!5, A!6), A!6), set_union2(A!6, A!3), B!5), set_union2(A!6, A!3)))))) | (~((set_union2(set_difference(B!5, A!6), A!6) = set_union2(set_union2(A!6, A!3), set_difference(B!5, A!6))) | ((~in(tptp_fun_D_0(set_union2(set_difference(B!5, A!6), A!6), set_difference(B!5, A!6), set_union2(A!6, A!3)), set_union2(set_difference(B!5, A!6), A!6))) <=> (in(tptp_fun_D_0(set_union2(set_difference(B!5, A!6), A!6), set_difference(B!5, A!6), set_union2(A!6, A!3)), set_difference(B!5, A!6)) | in(tptp_fun_D_0(set_union2(set_difference(B!5, A!6), A!6), set_difference(B!5, A!6), set_union2(A!6, A!3)), set_union2(A!6, A!3))))))) | ((~(set_union2(set_difference(B!5, A!6), A!6) = set_union2(set_union2(A!6, A!3), set_difference(B!5, A!6)))) | (in(tptp_fun_D_0(set_union2(set_difference(B!5, A!6), A!6), set_union2(A!6, A!3), B!5), set_union2(set_difference(B!5, A!6), A!6)) <=> (in(tptp_fun_D_0(set_union2(set_difference(B!5, A!6), A!6), set_union2(A!6, A!3), B!5), set_difference(B!5, A!6)) | in(tptp_fun_D_0(set_union2(set_difference(B!5, A!6), A!6), set_union2(A!6, A!3), B!5), set_union2(A!6, A!3)))))),
% 0.21/0.53 inference(tautology,[status(thm)],[])).
% 0.21/0.53 tff(105,plain,
% 0.21/0.53 ((~(set_union2(set_difference(B!5, A!6), A!6) = set_union2(set_union2(A!6, A!3), set_difference(B!5, A!6)))) | (in(tptp_fun_D_0(set_union2(set_difference(B!5, A!6), A!6), set_union2(A!6, A!3), B!5), set_union2(set_difference(B!5, A!6), A!6)) <=> (in(tptp_fun_D_0(set_union2(set_difference(B!5, A!6), A!6), set_union2(A!6, A!3), B!5), set_difference(B!5, A!6)) | in(tptp_fun_D_0(set_union2(set_difference(B!5, A!6), A!6), set_union2(A!6, A!3), B!5), set_union2(A!6, A!3))))),
% 0.21/0.53 inference(unit_resolution,[status(thm)],[104, 103])).
% 0.21/0.53 tff(106,plain,
% 0.21/0.53 (set_union2(set_union2(A!6, A!3), set_difference(B!5, A!6)) = set_union2(A!6, set_difference(B!5, A!6))),
% 0.21/0.53 inference(monotonicity,[status(thm)],[77])).
% 0.21/0.53 tff(107,plain,
% 0.21/0.53 (set_union2(A!6, set_difference(B!5, A!6)) = set_union2(set_union2(A!6, A!3), set_difference(B!5, A!6))),
% 0.21/0.53 inference(symmetry,[status(thm)],[106])).
% 0.21/0.53 tff(108,plain,
% 0.21/0.53 (set_union2(set_difference(B!5, A!6), A!6) = set_union2(set_union2(A!6, A!3), set_difference(B!5, A!6))),
% 0.21/0.53 inference(transitivity,[status(thm)],[82, 107])).
% 0.21/0.53 tff(109,assumption,(~(set_union2(set_difference(B!5, A!6), A!6) = set_union2(set_union2(A!6, A!3), set_difference(B!5, A!6)))), introduced(assumption)).
% 0.21/0.53 tff(110,plain,
% 0.21/0.53 ($false),
% 0.21/0.53 inference(unit_resolution,[status(thm)],[109, 108])).
% 0.21/0.53 tff(111,plain,(set_union2(set_difference(B!5, A!6), A!6) = set_union2(set_union2(A!6, A!3), set_difference(B!5, A!6))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.53 tff(112,plain,
% 0.21/0.53 ((~((~(set_union2(set_difference(B!5, A!6), A!6) = set_union2(set_union2(A!6, A!3), set_difference(B!5, A!6)))) | (in(tptp_fun_D_0(set_union2(set_difference(B!5, A!6), A!6), set_union2(A!6, A!3), B!5), set_union2(set_difference(B!5, A!6), A!6)) <=> (in(tptp_fun_D_0(set_union2(set_difference(B!5, A!6), A!6), set_union2(A!6, A!3), B!5), set_difference(B!5, A!6)) | in(tptp_fun_D_0(set_union2(set_difference(B!5, A!6), A!6), set_union2(A!6, A!3), B!5), set_union2(A!6, A!3)))))) | (~(set_union2(set_difference(B!5, A!6), A!6) = set_union2(set_union2(A!6, A!3), set_difference(B!5, A!6)))) | (in(tptp_fun_D_0(set_union2(set_difference(B!5, A!6), A!6), set_union2(A!6, A!3), B!5), set_union2(set_difference(B!5, A!6), A!6)) <=> (in(tptp_fun_D_0(set_union2(set_difference(B!5, A!6), A!6), set_union2(A!6, A!3), B!5), set_difference(B!5, A!6)) | in(tptp_fun_D_0(set_union2(set_difference(B!5, A!6), A!6), set_union2(A!6, A!3), B!5), set_union2(A!6, A!3))))),
% 0.21/0.53 inference(tautology,[status(thm)],[])).
% 0.21/0.53 tff(113,plain,
% 0.21/0.53 ((~((~(set_union2(set_difference(B!5, A!6), A!6) = set_union2(set_union2(A!6, A!3), set_difference(B!5, A!6)))) | (in(tptp_fun_D_0(set_union2(set_difference(B!5, A!6), A!6), set_union2(A!6, A!3), B!5), set_union2(set_difference(B!5, A!6), A!6)) <=> (in(tptp_fun_D_0(set_union2(set_difference(B!5, A!6), A!6), set_union2(A!6, A!3), B!5), set_difference(B!5, A!6)) | in(tptp_fun_D_0(set_union2(set_difference(B!5, A!6), A!6), set_union2(A!6, A!3), B!5), set_union2(A!6, A!3)))))) | (in(tptp_fun_D_0(set_union2(set_difference(B!5, A!6), A!6), set_union2(A!6, A!3), B!5), set_union2(set_difference(B!5, A!6), A!6)) <=> (in(tptp_fun_D_0(set_union2(set_difference(B!5, A!6), A!6), set_union2(A!6, A!3), B!5), set_difference(B!5, A!6)) | in(tptp_fun_D_0(set_union2(set_difference(B!5, A!6), A!6), set_union2(A!6, A!3), B!5), set_union2(A!6, A!3))))),
% 0.21/0.53 inference(unit_resolution,[status(thm)],[112, 111])).
% 0.21/0.53 tff(114,plain,
% 0.21/0.53 (in(tptp_fun_D_0(set_union2(set_difference(B!5, A!6), A!6), set_union2(A!6, A!3), B!5), set_union2(set_difference(B!5, A!6), A!6)) <=> (in(tptp_fun_D_0(set_union2(set_difference(B!5, A!6), A!6), set_union2(A!6, A!3), B!5), set_difference(B!5, A!6)) | in(tptp_fun_D_0(set_union2(set_difference(B!5, A!6), A!6), set_union2(A!6, A!3), B!5), set_union2(A!6, A!3)))),
% 0.21/0.53 inference(unit_resolution,[status(thm)],[113, 105])).
% 0.21/0.53 tff(115,plain,
% 0.21/0.53 ((~(in(tptp_fun_D_0(set_union2(set_difference(B!5, A!6), A!6), set_union2(A!6, A!3), B!5), set_union2(set_difference(B!5, A!6), A!6)) <=> (in(tptp_fun_D_0(set_union2(set_difference(B!5, A!6), A!6), set_union2(A!6, A!3), B!5), set_difference(B!5, A!6)) | in(tptp_fun_D_0(set_union2(set_difference(B!5, A!6), A!6), set_union2(A!6, A!3), B!5), set_union2(A!6, A!3))))) | (~in(tptp_fun_D_0(set_union2(set_difference(B!5, A!6), A!6), set_union2(A!6, A!3), B!5), set_union2(set_difference(B!5, A!6), A!6))) | (in(tptp_fun_D_0(set_union2(set_difference(B!5, A!6), A!6), set_union2(A!6, A!3), B!5), set_difference(B!5, A!6)) | in(tptp_fun_D_0(set_union2(set_difference(B!5, A!6), A!6), set_union2(A!6, A!3), B!5), set_union2(A!6, A!3)))),
% 0.21/0.53 inference(tautology,[status(thm)],[])).
% 0.21/0.53 tff(116,plain,
% 0.21/0.53 ((~in(tptp_fun_D_0(set_union2(set_difference(B!5, A!6), A!6), set_union2(A!6, A!3), B!5), set_union2(set_difference(B!5, A!6), A!6))) | (in(tptp_fun_D_0(set_union2(set_difference(B!5, A!6), A!6), set_union2(A!6, A!3), B!5), set_difference(B!5, A!6)) | in(tptp_fun_D_0(set_union2(set_difference(B!5, A!6), A!6), set_union2(A!6, A!3), B!5), set_union2(A!6, A!3)))),
% 0.21/0.53 inference(unit_resolution,[status(thm)],[115, 114])).
% 0.21/0.53 tff(117,plain,
% 0.21/0.53 (in(tptp_fun_D_0(set_union2(set_difference(B!5, A!6), A!6), set_union2(A!6, A!3), B!5), set_difference(B!5, A!6)) | in(tptp_fun_D_0(set_union2(set_difference(B!5, A!6), A!6), set_union2(A!6, A!3), B!5), set_union2(A!6, A!3))),
% 0.21/0.53 inference(unit_resolution,[status(thm)],[116, 101])).
% 0.21/0.53 tff(118,assumption,((~((set_difference(B!5, A!6) = set_difference(B!5, set_union2(A!6, A!3))) | (in(tptp_fun_D_2(set_difference(B!5, A!6), set_union2(A!6, A!3), B!5), set_difference(B!5, A!6)) <=> ((~in(tptp_fun_D_2(set_difference(B!5, A!6), set_union2(A!6, A!3), B!5), B!5)) | in(tptp_fun_D_2(set_difference(B!5, A!6), set_union2(A!6, A!3), B!5), set_union2(A!6, A!3)))))) | (~((~(set_difference(B!5, A!6) = set_difference(B!5, set_union2(A!6, A!3)))) | (in(tptp_fun_D_0(set_union2(set_difference(B!5, A!6), A!6), set_union2(A!6, A!3), B!5), set_difference(B!5, A!6)) <=> (~((~in(tptp_fun_D_0(set_union2(set_difference(B!5, A!6), A!6), set_union2(A!6, A!3), B!5), B!5)) | in(tptp_fun_D_0(set_union2(set_difference(B!5, A!6), A!6), set_union2(A!6, A!3), B!5), set_union2(A!6, A!3)))))))), introduced(assumption)).
% 0.21/0.53 tff(119,plain,
% 0.21/0.53 (^[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))))))))),
% 0.21/0.53 inference(bind,[status(th)],[])).
% 0.21/0.53 tff(120,plain,
% 0.21/0.53 (![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)))))))),
% 0.21/0.53 inference(quant_intro,[status(thm)],[119])).
% 0.21/0.53 tff(121,plain,
% 0.21/0.53 (![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)))))))),
% 0.21/0.53 inference(pull_quant,[status(thm)],[])).
% 0.21/0.53 tff(122,plain,
% 0.21/0.53 (^[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)))))))))),
% 0.21/0.53 inference(bind,[status(th)],[])).
% 0.21/0.53 tff(123,plain,
% 0.21/0.53 (![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)))))))),
% 0.21/0.53 inference(quant_intro,[status(thm)],[122])).
% 0.21/0.53 tff(124,plain,
% 0.21/0.53 (![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)))))))),
% 0.21/0.53 inference(transitivity,[status(thm)],[123, 121])).
% 0.21/0.53 tff(125,plain,
% 0.21/0.53 (![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)))))))),
% 0.21/0.53 inference(transitivity,[status(thm)],[124, 120])).
% 0.21/0.53 tff(126,plain,
% 0.21/0.53 (^[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))))))))),
% 0.21/0.53 inference(bind,[status(th)],[])).
% 0.21/0.53 tff(127,plain,
% 0.21/0.53 (![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)))))))),
% 0.21/0.53 inference(quant_intro,[status(thm)],[126])).
% 0.21/0.53 tff(128,plain,
% 0.21/0.53 (![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)))))))),
% 0.21/0.53 inference(transitivity,[status(thm)],[127, 125])).
% 0.21/0.53 tff(129,plain,
% 0.21/0.53 (^[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)))))))))),
% 0.21/0.53 inference(bind,[status(th)],[])).
% 0.21/0.53 tff(130,plain,
% 0.21/0.53 (![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)))))))),
% 0.21/0.53 inference(quant_intro,[status(thm)],[129])).
% 0.21/0.53 tff(131,plain,
% 0.21/0.53 (^[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)))))))),
% 0.21/0.53 inference(bind,[status(th)],[])).
% 0.21/0.53 tff(132,plain,
% 0.21/0.53 (![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))))))),
% 0.21/0.53 inference(quant_intro,[status(thm)],[131])).
% 0.21/0.53 tff(133,plain,
% 0.21/0.53 (![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)))))),
% 0.21/0.53 inference(rewrite,[status(thm)],[])).
% 0.21/0.53 tff(134,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')).
% 0.21/0.53 tff(135,plain,
% 0.21/0.53 (![A: $i, B: $i, C: $i] : ((C = set_difference(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, A) & (~in(D, B)))))),
% 0.21/0.53 inference(modus_ponens,[status(thm)],[134, 133])).
% 0.21/0.53 tff(136,plain,(
% 0.21/0.53 ![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)))))))),
% 0.21/0.53 inference(skolemize,[status(sab)],[135])).
% 0.21/0.53 tff(137,plain,
% 0.21/0.53 (![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))))))),
% 0.21/0.53 inference(modus_ponens,[status(thm)],[136, 132])).
% 0.21/0.53 tff(138,plain,
% 0.21/0.53 (![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)))))))),
% 0.21/0.53 inference(modus_ponens,[status(thm)],[137, 130])).
% 0.21/0.53 tff(139,plain,
% 0.21/0.53 (![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)))))))),
% 0.21/0.53 inference(modus_ponens,[status(thm)],[138, 128])).
% 0.21/0.53 tff(140,plain,
% 0.21/0.53 (((~![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!5, A!6) = set_difference(B!5, set_union2(A!6, A!3))) | (in(tptp_fun_D_2(set_difference(B!5, A!6), set_union2(A!6, A!3), B!5), set_difference(B!5, A!6)) <=> ((~in(tptp_fun_D_2(set_difference(B!5, A!6), set_union2(A!6, A!3), B!5), B!5)) | in(tptp_fun_D_2(set_difference(B!5, A!6), set_union2(A!6, A!3), B!5), set_union2(A!6, A!3)))))) | (~((~(set_difference(B!5, A!6) = set_difference(B!5, set_union2(A!6, A!3)))) | (in(tptp_fun_D_0(set_union2(set_difference(B!5, A!6), A!6), set_union2(A!6, A!3), B!5), set_difference(B!5, A!6)) <=> (~((~in(tptp_fun_D_0(set_union2(set_difference(B!5, A!6), A!6), set_union2(A!6, A!3), B!5), B!5)) | in(tptp_fun_D_0(set_union2(set_difference(B!5, A!6), A!6), set_union2(A!6, A!3), B!5), set_union2(A!6, A!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)))))))) | (~((~((set_difference(B!5, A!6) = set_difference(B!5, set_union2(A!6, A!3))) | (in(tptp_fun_D_2(set_difference(B!5, A!6), set_union2(A!6, A!3), B!5), set_difference(B!5, A!6)) <=> ((~in(tptp_fun_D_2(set_difference(B!5, A!6), set_union2(A!6, A!3), B!5), B!5)) | in(tptp_fun_D_2(set_difference(B!5, A!6), set_union2(A!6, A!3), B!5), set_union2(A!6, A!3)))))) | (~((~(set_difference(B!5, A!6) = set_difference(B!5, set_union2(A!6, A!3)))) | (in(tptp_fun_D_0(set_union2(set_difference(B!5, A!6), A!6), set_union2(A!6, A!3), B!5), set_difference(B!5, A!6)) <=> (~((~in(tptp_fun_D_0(set_union2(set_difference(B!5, A!6), A!6), set_union2(A!6, A!3), B!5), B!5)) | in(tptp_fun_D_0(set_union2(set_difference(B!5, A!6), A!6), set_union2(A!6, A!3), B!5), set_union2(A!6, A!3))))))))))),
% 0.21/0.54 inference(rewrite,[status(thm)],[])).
% 0.21/0.54 tff(141,plain,
% 0.21/0.54 ((~((~((~(set_difference(B!5, A!6) = set_difference(B!5, set_union2(A!6, A!3)))) | (in(tptp_fun_D_0(set_union2(set_difference(B!5, A!6), A!6), set_union2(A!6, A!3), B!5), set_difference(B!5, A!6)) <=> (~((~in(tptp_fun_D_0(set_union2(set_difference(B!5, A!6), A!6), set_union2(A!6, A!3), B!5), B!5)) | in(tptp_fun_D_0(set_union2(set_difference(B!5, A!6), A!6), set_union2(A!6, A!3), B!5), set_union2(A!6, A!3))))))) | (~((set_difference(B!5, A!6) = set_difference(B!5, set_union2(A!6, A!3))) | (in(tptp_fun_D_2(set_difference(B!5, A!6), set_union2(A!6, A!3), B!5), set_difference(B!5, A!6)) <=> ((~in(tptp_fun_D_2(set_difference(B!5, A!6), set_union2(A!6, A!3), B!5), B!5)) | in(tptp_fun_D_2(set_difference(B!5, A!6), set_union2(A!6, A!3), B!5), set_union2(A!6, A!3)))))))) <=> (~((~((set_difference(B!5, A!6) = set_difference(B!5, set_union2(A!6, A!3))) | (in(tptp_fun_D_2(set_difference(B!5, A!6), set_union2(A!6, A!3), B!5), set_difference(B!5, A!6)) <=> ((~in(tptp_fun_D_2(set_difference(B!5, A!6), set_union2(A!6, A!3), B!5), B!5)) | in(tptp_fun_D_2(set_difference(B!5, A!6), set_union2(A!6, A!3), B!5), set_union2(A!6, A!3)))))) | (~((~(set_difference(B!5, A!6) = set_difference(B!5, set_union2(A!6, A!3)))) | (in(tptp_fun_D_0(set_union2(set_difference(B!5, A!6), A!6), set_union2(A!6, A!3), B!5), set_difference(B!5, A!6)) <=> (~((~in(tptp_fun_D_0(set_union2(set_difference(B!5, A!6), A!6), set_union2(A!6, A!3), B!5), B!5)) | in(tptp_fun_D_0(set_union2(set_difference(B!5, A!6), A!6), set_union2(A!6, A!3), B!5), set_union2(A!6, A!3)))))))))),
% 0.21/0.54 inference(rewrite,[status(thm)],[])).
% 0.21/0.54 tff(142,plain,
% 0.21/0.54 (((~![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!5, A!6) = set_difference(B!5, set_union2(A!6, A!3)))) | (in(tptp_fun_D_0(set_union2(set_difference(B!5, A!6), A!6), set_union2(A!6, A!3), B!5), set_difference(B!5, A!6)) <=> (~((~in(tptp_fun_D_0(set_union2(set_difference(B!5, A!6), A!6), set_union2(A!6, A!3), B!5), B!5)) | in(tptp_fun_D_0(set_union2(set_difference(B!5, A!6), A!6), set_union2(A!6, A!3), B!5), set_union2(A!6, A!3))))))) | (~((set_difference(B!5, A!6) = set_difference(B!5, set_union2(A!6, A!3))) | (in(tptp_fun_D_2(set_difference(B!5, A!6), set_union2(A!6, A!3), B!5), set_difference(B!5, A!6)) <=> ((~in(tptp_fun_D_2(set_difference(B!5, A!6), set_union2(A!6, A!3), B!5), B!5)) | in(tptp_fun_D_2(set_difference(B!5, A!6), set_union2(A!6, A!3), B!5), set_union2(A!6, A!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)))))))) | (~((~((set_difference(B!5, A!6) = set_difference(B!5, set_union2(A!6, A!3))) | (in(tptp_fun_D_2(set_difference(B!5, A!6), set_union2(A!6, A!3), B!5), set_difference(B!5, A!6)) <=> ((~in(tptp_fun_D_2(set_difference(B!5, A!6), set_union2(A!6, A!3), B!5), B!5)) | in(tptp_fun_D_2(set_difference(B!5, A!6), set_union2(A!6, A!3), B!5), set_union2(A!6, A!3)))))) | (~((~(set_difference(B!5, A!6) = set_difference(B!5, set_union2(A!6, A!3)))) | (in(tptp_fun_D_0(set_union2(set_difference(B!5, A!6), A!6), set_union2(A!6, A!3), B!5), set_difference(B!5, A!6)) <=> (~((~in(tptp_fun_D_0(set_union2(set_difference(B!5, A!6), A!6), set_union2(A!6, A!3), B!5), B!5)) | in(tptp_fun_D_0(set_union2(set_difference(B!5, A!6), A!6), set_union2(A!6, A!3), B!5), set_union2(A!6, A!3))))))))))),
% 0.47/0.54 inference(monotonicity,[status(thm)],[141])).
% 0.47/0.54 tff(143,plain,
% 0.47/0.54 (((~![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!5, A!6) = set_difference(B!5, set_union2(A!6, A!3)))) | (in(tptp_fun_D_0(set_union2(set_difference(B!5, A!6), A!6), set_union2(A!6, A!3), B!5), set_difference(B!5, A!6)) <=> (~((~in(tptp_fun_D_0(set_union2(set_difference(B!5, A!6), A!6), set_union2(A!6, A!3), B!5), B!5)) | in(tptp_fun_D_0(set_union2(set_difference(B!5, A!6), A!6), set_union2(A!6, A!3), B!5), set_union2(A!6, A!3))))))) | (~((set_difference(B!5, A!6) = set_difference(B!5, set_union2(A!6, A!3))) | (in(tptp_fun_D_2(set_difference(B!5, A!6), set_union2(A!6, A!3), B!5), set_difference(B!5, A!6)) <=> ((~in(tptp_fun_D_2(set_difference(B!5, A!6), set_union2(A!6, A!3), B!5), B!5)) | in(tptp_fun_D_2(set_difference(B!5, A!6), set_union2(A!6, A!3), B!5), set_union2(A!6, A!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)))))))) | (~((~((set_difference(B!5, A!6) = set_difference(B!5, set_union2(A!6, A!3))) | (in(tptp_fun_D_2(set_difference(B!5, A!6), set_union2(A!6, A!3), B!5), set_difference(B!5, A!6)) <=> ((~in(tptp_fun_D_2(set_difference(B!5, A!6), set_union2(A!6, A!3), B!5), B!5)) | in(tptp_fun_D_2(set_difference(B!5, A!6), set_union2(A!6, A!3), B!5), set_union2(A!6, A!3)))))) | (~((~(set_difference(B!5, A!6) = set_difference(B!5, set_union2(A!6, A!3)))) | (in(tptp_fun_D_0(set_union2(set_difference(B!5, A!6), A!6), set_union2(A!6, A!3), B!5), set_difference(B!5, A!6)) <=> (~((~in(tptp_fun_D_0(set_union2(set_difference(B!5, A!6), A!6), set_union2(A!6, A!3), B!5), B!5)) | in(tptp_fun_D_0(set_union2(set_difference(B!5, A!6), A!6), set_union2(A!6, A!3), B!5), set_union2(A!6, A!3))))))))))),
% 0.47/0.54 inference(transitivity,[status(thm)],[142, 140])).
% 0.47/0.54 tff(144,plain,
% 0.47/0.54 ((~![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!5, A!6) = set_difference(B!5, set_union2(A!6, A!3)))) | (in(tptp_fun_D_0(set_union2(set_difference(B!5, A!6), A!6), set_union2(A!6, A!3), B!5), set_difference(B!5, A!6)) <=> (~((~in(tptp_fun_D_0(set_union2(set_difference(B!5, A!6), A!6), set_union2(A!6, A!3), B!5), B!5)) | in(tptp_fun_D_0(set_union2(set_difference(B!5, A!6), A!6), set_union2(A!6, A!3), B!5), set_union2(A!6, A!3))))))) | (~((set_difference(B!5, A!6) = set_difference(B!5, set_union2(A!6, A!3))) | (in(tptp_fun_D_2(set_difference(B!5, A!6), set_union2(A!6, A!3), B!5), set_difference(B!5, A!6)) <=> ((~in(tptp_fun_D_2(set_difference(B!5, A!6), set_union2(A!6, A!3), B!5), B!5)) | in(tptp_fun_D_2(set_difference(B!5, A!6), set_union2(A!6, A!3), B!5), set_union2(A!6, A!3))))))))),
% 0.47/0.54 inference(quant_inst,[status(thm)],[])).
% 0.47/0.54 tff(145,plain,
% 0.47/0.54 ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_difference(A, B))) | (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_2(C, B, A), C) <=> ((~in(tptp_fun_D_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B)))))))) | (~((~((set_difference(B!5, A!6) = set_difference(B!5, set_union2(A!6, A!3))) | (in(tptp_fun_D_2(set_difference(B!5, A!6), set_union2(A!6, A!3), B!5), set_difference(B!5, A!6)) <=> ((~in(tptp_fun_D_2(set_difference(B!5, A!6), set_union2(A!6, A!3), B!5), B!5)) | in(tptp_fun_D_2(set_difference(B!5, A!6), set_union2(A!6, A!3), B!5), set_union2(A!6, A!3)))))) | (~((~(set_difference(B!5, A!6) = set_difference(B!5, set_union2(A!6, A!3)))) | (in(tptp_fun_D_0(set_union2(set_difference(B!5, A!6), A!6), set_union2(A!6, A!3), B!5), set_difference(B!5, A!6)) <=> (~((~in(tptp_fun_D_0(set_union2(set_difference(B!5, A!6), A!6), set_union2(A!6, A!3), B!5), B!5)) | in(tptp_fun_D_0(set_union2(set_difference(B!5, A!6), A!6), set_union2(A!6, A!3), B!5), set_union2(A!6, A!3)))))))))),
% 0.47/0.54 inference(modus_ponens,[status(thm)],[144, 143])).
% 0.47/0.54 tff(146,plain,
% 0.47/0.54 ($false),
% 0.47/0.54 inference(unit_resolution,[status(thm)],[145, 139, 118])).
% 0.47/0.54 tff(147,plain,(~((~((set_difference(B!5, A!6) = set_difference(B!5, set_union2(A!6, A!3))) | (in(tptp_fun_D_2(set_difference(B!5, A!6), set_union2(A!6, A!3), B!5), set_difference(B!5, A!6)) <=> ((~in(tptp_fun_D_2(set_difference(B!5, A!6), set_union2(A!6, A!3), B!5), B!5)) | in(tptp_fun_D_2(set_difference(B!5, A!6), set_union2(A!6, A!3), B!5), set_union2(A!6, A!3)))))) | (~((~(set_difference(B!5, A!6) = set_difference(B!5, set_union2(A!6, A!3)))) | (in(tptp_fun_D_0(set_union2(set_difference(B!5, A!6), A!6), set_union2(A!6, A!3), B!5), set_difference(B!5, A!6)) <=> (~((~in(tptp_fun_D_0(set_union2(set_difference(B!5, A!6), A!6), set_union2(A!6, A!3), B!5), B!5)) | in(tptp_fun_D_0(set_union2(set_difference(B!5, A!6), A!6), set_union2(A!6, A!3), B!5), set_union2(A!6, A!3))))))))), inference(lemma,lemma(discharge,[]))).
% 0.47/0.54 tff(148,plain,
% 0.47/0.54 (((~((set_difference(B!5, A!6) = set_difference(B!5, set_union2(A!6, A!3))) | (in(tptp_fun_D_2(set_difference(B!5, A!6), set_union2(A!6, A!3), B!5), set_difference(B!5, A!6)) <=> ((~in(tptp_fun_D_2(set_difference(B!5, A!6), set_union2(A!6, A!3), B!5), B!5)) | in(tptp_fun_D_2(set_difference(B!5, A!6), set_union2(A!6, A!3), B!5), set_union2(A!6, A!3)))))) | (~((~(set_difference(B!5, A!6) = set_difference(B!5, set_union2(A!6, A!3)))) | (in(tptp_fun_D_0(set_union2(set_difference(B!5, A!6), A!6), set_union2(A!6, A!3), B!5), set_difference(B!5, A!6)) <=> (~((~in(tptp_fun_D_0(set_union2(set_difference(B!5, A!6), A!6), set_union2(A!6, A!3), B!5), B!5)) | in(tptp_fun_D_0(set_union2(set_difference(B!5, A!6), A!6), set_union2(A!6, A!3), B!5), set_union2(A!6, A!3)))))))) | ((~(set_difference(B!5, A!6) = set_difference(B!5, set_union2(A!6, A!3)))) | (in(tptp_fun_D_0(set_union2(set_difference(B!5, A!6), A!6), set_union2(A!6, A!3), B!5), set_difference(B!5, A!6)) <=> (~((~in(tptp_fun_D_0(set_union2(set_difference(B!5, A!6), A!6), set_union2(A!6, A!3), B!5), B!5)) | in(tptp_fun_D_0(set_union2(set_difference(B!5, A!6), A!6), set_union2(A!6, A!3), B!5), set_union2(A!6, A!3))))))),
% 0.47/0.54 inference(tautology,[status(thm)],[])).
% 0.47/0.54 tff(149,plain,
% 0.47/0.54 ((~(set_difference(B!5, A!6) = set_difference(B!5, set_union2(A!6, A!3)))) | (in(tptp_fun_D_0(set_union2(set_difference(B!5, A!6), A!6), set_union2(A!6, A!3), B!5), set_difference(B!5, A!6)) <=> (~((~in(tptp_fun_D_0(set_union2(set_difference(B!5, A!6), A!6), set_union2(A!6, A!3), B!5), B!5)) | in(tptp_fun_D_0(set_union2(set_difference(B!5, A!6), A!6), set_union2(A!6, A!3), B!5), set_union2(A!6, A!3)))))),
% 0.47/0.54 inference(unit_resolution,[status(thm)],[148, 147])).
% 0.47/0.54 tff(150,plain,
% 0.47/0.54 (set_difference(B!5, set_union2(A!6, A!3)) = set_difference(B!5, A!6)),
% 0.47/0.54 inference(monotonicity,[status(thm)],[77])).
% 0.47/0.54 tff(151,plain,
% 0.47/0.54 (set_difference(B!5, A!6) = set_difference(B!5, set_union2(A!6, A!3))),
% 0.47/0.54 inference(symmetry,[status(thm)],[150])).
% 0.47/0.54 tff(152,plain,
% 0.47/0.54 ((~((~(set_difference(B!5, A!6) = set_difference(B!5, set_union2(A!6, A!3)))) | (in(tptp_fun_D_0(set_union2(set_difference(B!5, A!6), A!6), set_union2(A!6, A!3), B!5), set_difference(B!5, A!6)) <=> (~((~in(tptp_fun_D_0(set_union2(set_difference(B!5, A!6), A!6), set_union2(A!6, A!3), B!5), B!5)) | in(tptp_fun_D_0(set_union2(set_difference(B!5, A!6), A!6), set_union2(A!6, A!3), B!5), set_union2(A!6, A!3))))))) | (~(set_difference(B!5, A!6) = set_difference(B!5, set_union2(A!6, A!3)))) | (in(tptp_fun_D_0(set_union2(set_difference(B!5, A!6), A!6), set_union2(A!6, A!3), B!5), set_difference(B!5, A!6)) <=> (~((~in(tptp_fun_D_0(set_union2(set_difference(B!5, A!6), A!6), set_union2(A!6, A!3), B!5), B!5)) | in(tptp_fun_D_0(set_union2(set_difference(B!5, A!6), A!6), set_union2(A!6, A!3), B!5), set_union2(A!6, A!3)))))),
% 0.47/0.54 inference(tautology,[status(thm)],[])).
% 0.47/0.54 tff(153,plain,
% 0.47/0.54 ((~((~(set_difference(B!5, A!6) = set_difference(B!5, set_union2(A!6, A!3)))) | (in(tptp_fun_D_0(set_union2(set_difference(B!5, A!6), A!6), set_union2(A!6, A!3), B!5), set_difference(B!5, A!6)) <=> (~((~in(tptp_fun_D_0(set_union2(set_difference(B!5, A!6), A!6), set_union2(A!6, A!3), B!5), B!5)) | in(tptp_fun_D_0(set_union2(set_difference(B!5, A!6), A!6), set_union2(A!6, A!3), B!5), set_union2(A!6, A!3))))))) | (in(tptp_fun_D_0(set_union2(set_difference(B!5, A!6), A!6), set_union2(A!6, A!3), B!5), set_difference(B!5, A!6)) <=> (~((~in(tptp_fun_D_0(set_union2(set_difference(B!5, A!6), A!6), set_union2(A!6, A!3), B!5), B!5)) | in(tptp_fun_D_0(set_union2(set_difference(B!5, A!6), A!6), set_union2(A!6, A!3), B!5), set_union2(A!6, A!3)))))),
% 0.47/0.54 inference(unit_resolution,[status(thm)],[152, 151])).
% 0.47/0.54 tff(154,plain,
% 0.47/0.54 (in(tptp_fun_D_0(set_union2(set_difference(B!5, A!6), A!6), set_union2(A!6, A!3), B!5), set_difference(B!5, A!6)) <=> (~((~in(tptp_fun_D_0(set_union2(set_difference(B!5, A!6), A!6), set_union2(A!6, A!3), B!5), B!5)) | in(tptp_fun_D_0(set_union2(set_difference(B!5, A!6), A!6), set_union2(A!6, A!3), B!5), set_union2(A!6, A!3))))),
% 0.47/0.54 inference(unit_resolution,[status(thm)],[153, 149])).
% 0.47/0.54 tff(155,plain,
% 0.47/0.54 ((in(tptp_fun_D_0(set_union2(set_difference(B!5, A!6), A!6), set_union2(A!6, A!3), B!5), set_union2(A!6, A!3)) | in(tptp_fun_D_0(set_union2(set_difference(B!5, A!6), A!6), set_union2(A!6, A!3), B!5), B!5)) | (~in(tptp_fun_D_0(set_union2(set_difference(B!5, A!6), A!6), set_union2(A!6, A!3), B!5), B!5))),
% 0.47/0.54 inference(tautology,[status(thm)],[])).
% 0.47/0.54 tff(156,plain,
% 0.47/0.54 (~in(tptp_fun_D_0(set_union2(set_difference(B!5, A!6), A!6), set_union2(A!6, A!3), B!5), B!5)),
% 0.47/0.54 inference(unit_resolution,[status(thm)],[155, 1])).
% 0.47/0.54 tff(157,plain,
% 0.47/0.54 (((~in(tptp_fun_D_0(set_union2(set_difference(B!5, A!6), A!6), set_union2(A!6, A!3), B!5), B!5)) | in(tptp_fun_D_0(set_union2(set_difference(B!5, A!6), A!6), set_union2(A!6, A!3), B!5), set_union2(A!6, A!3))) | in(tptp_fun_D_0(set_union2(set_difference(B!5, A!6), A!6), set_union2(A!6, A!3), B!5), B!5)),
% 0.47/0.54 inference(tautology,[status(thm)],[])).
% 0.47/0.54 tff(158,plain,
% 0.47/0.54 ((~in(tptp_fun_D_0(set_union2(set_difference(B!5, A!6), A!6), set_union2(A!6, A!3), B!5), B!5)) | in(tptp_fun_D_0(set_union2(set_difference(B!5, A!6), A!6), set_union2(A!6, A!3), B!5), set_union2(A!6, A!3))),
% 0.47/0.54 inference(unit_resolution,[status(thm)],[157, 156])).
% 0.47/0.54 tff(159,plain,
% 0.47/0.54 ((~(in(tptp_fun_D_0(set_union2(set_difference(B!5, A!6), A!6), set_union2(A!6, A!3), B!5), set_difference(B!5, A!6)) <=> (~((~in(tptp_fun_D_0(set_union2(set_difference(B!5, A!6), A!6), set_union2(A!6, A!3), B!5), B!5)) | in(tptp_fun_D_0(set_union2(set_difference(B!5, A!6), A!6), set_union2(A!6, A!3), B!5), set_union2(A!6, A!3)))))) | (~in(tptp_fun_D_0(set_union2(set_difference(B!5, A!6), A!6), set_union2(A!6, A!3), B!5), set_difference(B!5, A!6))) | (~((~in(tptp_fun_D_0(set_union2(set_difference(B!5, A!6), A!6), set_union2(A!6, A!3), B!5), B!5)) | in(tptp_fun_D_0(set_union2(set_difference(B!5, A!6), A!6), set_union2(A!6, A!3), B!5), set_union2(A!6, A!3))))),
% 0.47/0.55 inference(tautology,[status(thm)],[])).
% 0.47/0.55 tff(160,plain,
% 0.47/0.55 (~in(tptp_fun_D_0(set_union2(set_difference(B!5, A!6), A!6), set_union2(A!6, A!3), B!5), set_difference(B!5, A!6))),
% 0.47/0.55 inference(unit_resolution,[status(thm)],[159, 158, 154])).
% 0.47/0.55 tff(161,plain,
% 0.47/0.55 ((~(in(tptp_fun_D_0(set_union2(set_difference(B!5, A!6), A!6), set_union2(A!6, A!3), B!5), set_difference(B!5, A!6)) | in(tptp_fun_D_0(set_union2(set_difference(B!5, A!6), A!6), set_union2(A!6, A!3), B!5), set_union2(A!6, A!3)))) | in(tptp_fun_D_0(set_union2(set_difference(B!5, A!6), A!6), set_union2(A!6, A!3), B!5), set_difference(B!5, A!6)) | in(tptp_fun_D_0(set_union2(set_difference(B!5, A!6), A!6), set_union2(A!6, A!3), B!5), set_union2(A!6, A!3))),
% 0.47/0.55 inference(tautology,[status(thm)],[])).
% 0.47/0.55 tff(162,plain,
% 0.47/0.55 ($false),
% 0.47/0.55 inference(unit_resolution,[status(thm)],[161, 160, 117, 3])).
% 0.47/0.55 tff(163,plain,(in(tptp_fun_D_0(set_union2(set_difference(B!5, A!6), A!6), set_union2(A!6, A!3), B!5), set_union2(A!6, A!3)) | in(tptp_fun_D_0(set_union2(set_difference(B!5, A!6), A!6), set_union2(A!6, A!3), B!5), B!5)), inference(lemma,lemma(discharge,[]))).
% 0.47/0.55 tff(164,plain,
% 0.47/0.55 ((~((~in(tptp_fun_D_0(set_union2(set_difference(B!5, A!6), A!6), set_union2(A!6, A!3), B!5), set_union2(set_difference(B!5, A!6), A!6))) <=> (in(tptp_fun_D_0(set_union2(set_difference(B!5, A!6), A!6), set_union2(A!6, A!3), B!5), set_union2(A!6, A!3)) | in(tptp_fun_D_0(set_union2(set_difference(B!5, A!6), A!6), set_union2(A!6, A!3), B!5), B!5)))) | (~in(tptp_fun_D_0(set_union2(set_difference(B!5, A!6), A!6), set_union2(A!6, A!3), B!5), set_union2(set_difference(B!5, A!6), A!6))) | (~(in(tptp_fun_D_0(set_union2(set_difference(B!5, A!6), A!6), set_union2(A!6, A!3), B!5), set_union2(A!6, A!3)) | in(tptp_fun_D_0(set_union2(set_difference(B!5, A!6), A!6), set_union2(A!6, A!3), B!5), B!5)))),
% 0.47/0.55 inference(tautology,[status(thm)],[])).
% 0.47/0.55 tff(165,plain,
% 0.47/0.55 ((~in(tptp_fun_D_0(set_union2(set_difference(B!5, A!6), A!6), set_union2(A!6, A!3), B!5), set_union2(set_difference(B!5, A!6), A!6))) | (~(in(tptp_fun_D_0(set_union2(set_difference(B!5, A!6), A!6), set_union2(A!6, A!3), B!5), set_union2(A!6, A!3)) | in(tptp_fun_D_0(set_union2(set_difference(B!5, A!6), A!6), set_union2(A!6, A!3), B!5), B!5)))),
% 0.47/0.55 inference(unit_resolution,[status(thm)],[164, 98])).
% 0.47/0.55 tff(166,plain,
% 0.47/0.55 (~in(tptp_fun_D_0(set_union2(set_difference(B!5, A!6), A!6), set_union2(A!6, A!3), B!5), set_union2(set_difference(B!5, A!6), A!6))),
% 0.47/0.55 inference(unit_resolution,[status(thm)],[165, 163])).
% 0.47/0.55 tff(167,plain,
% 0.47/0.55 ((~(in(tptp_fun_D_0(set_union2(set_difference(B!5, A!6), A!6), set_union2(A!6, A!3), B!5), set_union2(set_difference(B!5, A!6), A!6)) <=> (in(tptp_fun_D_0(set_union2(set_difference(B!5, A!6), A!6), set_union2(A!6, A!3), B!5), set_difference(B!5, A!6)) | in(tptp_fun_D_0(set_union2(set_difference(B!5, A!6), A!6), set_union2(A!6, A!3), B!5), set_union2(A!6, A!3))))) | in(tptp_fun_D_0(set_union2(set_difference(B!5, A!6), A!6), set_union2(A!6, A!3), B!5), set_union2(set_difference(B!5, A!6), A!6)) | (~(in(tptp_fun_D_0(set_union2(set_difference(B!5, A!6), A!6), set_union2(A!6, A!3), B!5), set_difference(B!5, A!6)) | in(tptp_fun_D_0(set_union2(set_difference(B!5, A!6), A!6), set_union2(A!6, A!3), B!5), set_union2(A!6, A!3))))),
% 0.47/0.55 inference(tautology,[status(thm)],[])).
% 0.47/0.55 tff(168,plain,
% 0.47/0.55 (in(tptp_fun_D_0(set_union2(set_difference(B!5, A!6), A!6), set_union2(A!6, A!3), B!5), set_union2(set_difference(B!5, A!6), A!6)) | (~(in(tptp_fun_D_0(set_union2(set_difference(B!5, A!6), A!6), set_union2(A!6, A!3), B!5), set_difference(B!5, A!6)) | in(tptp_fun_D_0(set_union2(set_difference(B!5, A!6), A!6), set_union2(A!6, A!3), B!5), set_union2(A!6, A!3))))),
% 0.47/0.55 inference(unit_resolution,[status(thm)],[167, 114])).
% 0.47/0.55 tff(169,plain,
% 0.47/0.55 (~(in(tptp_fun_D_0(set_union2(set_difference(B!5, A!6), A!6), set_union2(A!6, A!3), B!5), set_difference(B!5, A!6)) | in(tptp_fun_D_0(set_union2(set_difference(B!5, A!6), A!6), set_union2(A!6, A!3), B!5), set_union2(A!6, A!3)))),
% 0.47/0.55 inference(unit_resolution,[status(thm)],[168, 166])).
% 0.47/0.55 tff(170,plain,
% 0.47/0.55 ((in(tptp_fun_D_0(set_union2(set_difference(B!5, A!6), A!6), set_union2(A!6, A!3), B!5), set_difference(B!5, A!6)) | in(tptp_fun_D_0(set_union2(set_difference(B!5, A!6), A!6), set_union2(A!6, A!3), B!5), set_union2(A!6, A!3))) | (~in(tptp_fun_D_0(set_union2(set_difference(B!5, A!6), A!6), set_union2(A!6, A!3), B!5), set_union2(A!6, A!3)))),
% 0.47/0.55 inference(tautology,[status(thm)],[])).
% 0.47/0.55 tff(171,plain,
% 0.47/0.55 (~in(tptp_fun_D_0(set_union2(set_difference(B!5, A!6), A!6), set_union2(A!6, A!3), B!5), set_union2(A!6, A!3))),
% 0.47/0.55 inference(unit_resolution,[status(thm)],[170, 169])).
% 0.47/0.55 tff(172,plain,
% 0.47/0.55 ((in(tptp_fun_D_0(set_union2(set_difference(B!5, A!6), A!6), set_union2(A!6, A!3), B!5), set_difference(B!5, A!6)) | in(tptp_fun_D_0(set_union2(set_difference(B!5, A!6), A!6), set_union2(A!6, A!3), B!5), set_union2(A!6, A!3))) | (~in(tptp_fun_D_0(set_union2(set_difference(B!5, A!6), A!6), set_union2(A!6, A!3), B!5), set_difference(B!5, A!6)))),
% 0.47/0.55 inference(tautology,[status(thm)],[])).
% 0.47/0.55 tff(173,plain,
% 0.47/0.55 (~in(tptp_fun_D_0(set_union2(set_difference(B!5, A!6), A!6), set_union2(A!6, A!3), B!5), set_difference(B!5, A!6))),
% 0.47/0.55 inference(unit_resolution,[status(thm)],[172, 169])).
% 0.47/0.55 tff(174,plain,
% 0.47/0.55 ((~(in(tptp_fun_D_0(set_union2(set_difference(B!5, A!6), A!6), set_union2(A!6, A!3), B!5), set_difference(B!5, A!6)) <=> (~((~in(tptp_fun_D_0(set_union2(set_difference(B!5, A!6), A!6), set_union2(A!6, A!3), B!5), B!5)) | in(tptp_fun_D_0(set_union2(set_difference(B!5, A!6), A!6), set_union2(A!6, A!3), B!5), set_union2(A!6, A!3)))))) | in(tptp_fun_D_0(set_union2(set_difference(B!5, A!6), A!6), set_union2(A!6, A!3), B!5), set_difference(B!5, A!6)) | ((~in(tptp_fun_D_0(set_union2(set_difference(B!5, A!6), A!6), set_union2(A!6, A!3), B!5), B!5)) | in(tptp_fun_D_0(set_union2(set_difference(B!5, A!6), A!6), set_union2(A!6, A!3), B!5), set_union2(A!6, A!3)))),
% 0.47/0.55 inference(tautology,[status(thm)],[])).
% 0.47/0.55 tff(175,plain,
% 0.47/0.55 ((~in(tptp_fun_D_0(set_union2(set_difference(B!5, A!6), A!6), set_union2(A!6, A!3), B!5), B!5)) | in(tptp_fun_D_0(set_union2(set_difference(B!5, A!6), A!6), set_union2(A!6, A!3), B!5), set_union2(A!6, A!3))),
% 0.47/0.55 inference(unit_resolution,[status(thm)],[174, 173, 154])).
% 0.47/0.55 tff(176,plain,
% 0.47/0.55 ((~((~in(tptp_fun_D_0(set_union2(set_difference(B!5, A!6), A!6), set_union2(A!6, A!3), B!5), B!5)) | in(tptp_fun_D_0(set_union2(set_difference(B!5, A!6), A!6), set_union2(A!6, A!3), B!5), set_union2(A!6, A!3)))) | (~in(tptp_fun_D_0(set_union2(set_difference(B!5, A!6), A!6), set_union2(A!6, A!3), B!5), B!5)) | in(tptp_fun_D_0(set_union2(set_difference(B!5, A!6), A!6), set_union2(A!6, A!3), B!5), set_union2(A!6, A!3))),
% 0.47/0.55 inference(tautology,[status(thm)],[])).
% 0.47/0.55 tff(177,plain,
% 0.47/0.55 (~in(tptp_fun_D_0(set_union2(set_difference(B!5, A!6), A!6), set_union2(A!6, A!3), B!5), B!5)),
% 0.47/0.55 inference(unit_resolution,[status(thm)],[176, 171, 175])).
% 0.47/0.55 tff(178,plain,
% 0.47/0.55 ((~(in(tptp_fun_D_0(set_union2(set_difference(B!5, A!6), A!6), set_union2(A!6, A!3), B!5), set_union2(A!6, A!3)) | in(tptp_fun_D_0(set_union2(set_difference(B!5, A!6), A!6), set_union2(A!6, A!3), B!5), B!5))) | in(tptp_fun_D_0(set_union2(set_difference(B!5, A!6), A!6), set_union2(A!6, A!3), B!5), set_union2(A!6, A!3)) | in(tptp_fun_D_0(set_union2(set_difference(B!5, A!6), A!6), set_union2(A!6, A!3), B!5), B!5)),
% 0.47/0.55 inference(tautology,[status(thm)],[])).
% 0.47/0.55 tff(179,plain,
% 0.47/0.55 ($false),
% 0.47/0.55 inference(unit_resolution,[status(thm)],[178, 177, 171, 163])).
% 0.47/0.55 % SZS output end Proof
%------------------------------------------------------------------------------