TSTP Solution File: SEU136+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SEU136+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n019.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 07:27:41 EDT 2022
% Result : Theorem 3.82s 2.59s
% Output : Proof 3.86s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEU136+1 : TPTP v8.1.0. Released v3.3.0.
% 0.00/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.11/0.33 % Computer : n019.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Sat Sep 3 09:40:05 EDT 2022
% 0.11/0.33 % CPUTime :
% 0.11/0.33 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.11/0.33 Usage: tptp [options] [-file:]file
% 0.11/0.33 -h, -? prints this message.
% 0.11/0.33 -smt2 print SMT-LIB2 benchmark.
% 0.11/0.33 -m, -model generate model.
% 0.11/0.33 -p, -proof generate proof.
% 0.11/0.33 -c, -core generate unsat core of named formulas.
% 0.11/0.33 -st, -statistics display statistics.
% 0.11/0.33 -t:timeout set timeout (in second).
% 0.11/0.33 -smt2status display status in smt2 format instead of SZS.
% 0.11/0.33 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.11/0.33 -<param>:<value> configuration parameter and value.
% 0.11/0.33 -o:<output-file> file to place output in.
% 3.82/2.59 % SZS status Theorem
% 3.82/2.59 % SZS output start Proof
% 3.82/2.59 tff(in_type, type, (
% 3.82/2.59 in: ( $i * $i ) > $o)).
% 3.82/2.59 tff(tptp_fun_B_5_type, type, (
% 3.82/2.59 tptp_fun_B_5: $i)).
% 3.82/2.59 tff(tptp_fun_D_2_type, type, (
% 3.82/2.59 tptp_fun_D_2: ( $i * $i * $i ) > $i)).
% 3.82/2.59 tff(set_union2_type, type, (
% 3.82/2.59 set_union2: ( $i * $i ) > $i)).
% 3.82/2.59 tff(tptp_fun_A_3_type, type, (
% 3.82/2.59 tptp_fun_A_3: $i)).
% 3.82/2.59 tff(tptp_fun_A_6_type, type, (
% 3.82/2.59 tptp_fun_A_6: $i)).
% 3.82/2.59 tff(set_difference_type, type, (
% 3.82/2.59 set_difference: ( $i * $i ) > $i)).
% 3.82/2.59 tff(empty_set_type, type, (
% 3.82/2.59 empty_set: $i)).
% 3.82/2.59 tff(empty_type, type, (
% 3.82/2.59 empty: $i > $o)).
% 3.82/2.59 tff(tptp_fun_D_0_type, type, (
% 3.82/2.59 tptp_fun_D_0: ( $i * $i * $i ) > $i)).
% 3.82/2.59 tff(1,assumption,(~in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(A!6, A!3)), B!5)), introduced(assumption)).
% 3.82/2.59 tff(2,assumption,(~in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(A!6, A!3)), set_difference(set_union2(A!6, B!5), B!5))), introduced(assumption)).
% 3.82/2.59 tff(3,plain,
% 3.82/2.59 (^[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))))))))),
% 3.82/2.59 inference(bind,[status(th)],[])).
% 3.82/2.59 tff(4,plain,
% 3.82/2.59 (![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)))))))),
% 3.82/2.59 inference(quant_intro,[status(thm)],[3])).
% 3.82/2.59 tff(5,plain,
% 3.82/2.59 (![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)))))))),
% 3.82/2.59 inference(pull_quant,[status(thm)],[])).
% 3.82/2.59 tff(6,plain,
% 3.82/2.59 (^[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)))))))))),
% 3.82/2.59 inference(bind,[status(th)],[])).
% 3.82/2.59 tff(7,plain,
% 3.82/2.59 (![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)))))))),
% 3.82/2.59 inference(quant_intro,[status(thm)],[6])).
% 3.82/2.59 tff(8,plain,
% 3.82/2.59 (![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)))))))),
% 3.82/2.59 inference(transitivity,[status(thm)],[7, 5])).
% 3.82/2.59 tff(9,plain,
% 3.82/2.59 (![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)))))))),
% 3.82/2.59 inference(transitivity,[status(thm)],[8, 4])).
% 3.82/2.59 tff(10,plain,
% 3.82/2.59 (^[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))))))))),
% 3.82/2.60 inference(bind,[status(th)],[])).
% 3.82/2.60 tff(11,plain,
% 3.82/2.60 (![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)))))))),
% 3.82/2.60 inference(quant_intro,[status(thm)],[10])).
% 3.82/2.60 tff(12,plain,
% 3.82/2.60 (![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)))))))),
% 3.82/2.60 inference(transitivity,[status(thm)],[11, 9])).
% 3.82/2.60 tff(13,plain,
% 3.82/2.60 (^[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)))))))))),
% 3.84/2.60 inference(bind,[status(th)],[])).
% 3.84/2.60 tff(14,plain,
% 3.84/2.60 (![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)))))))),
% 3.84/2.60 inference(quant_intro,[status(thm)],[13])).
% 3.84/2.60 tff(15,plain,
% 3.84/2.60 (^[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)))))))),
% 3.84/2.60 inference(bind,[status(th)],[])).
% 3.84/2.60 tff(16,plain,
% 3.84/2.60 (![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))))))),
% 3.84/2.60 inference(quant_intro,[status(thm)],[15])).
% 3.84/2.60 tff(17,plain,
% 3.84/2.60 (![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)))))),
% 3.84/2.60 inference(rewrite,[status(thm)],[])).
% 3.84/2.60 tff(18,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')).
% 3.84/2.60 tff(19,plain,
% 3.84/2.60 (![A: $i, B: $i, C: $i] : ((C = set_difference(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, A) & (~in(D, B)))))),
% 3.84/2.60 inference(modus_ponens,[status(thm)],[18, 17])).
% 3.84/2.60 tff(20,plain,(
% 3.84/2.60 ![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)))))))),
% 3.84/2.60 inference(skolemize,[status(sab)],[19])).
% 3.84/2.60 tff(21,plain,
% 3.84/2.60 (![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))))))),
% 3.84/2.60 inference(modus_ponens,[status(thm)],[20, 16])).
% 3.84/2.60 tff(22,plain,
% 3.84/2.60 (![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)))))))),
% 3.84/2.60 inference(modus_ponens,[status(thm)],[21, 14])).
% 3.84/2.60 tff(23,plain,
% 3.84/2.60 (![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)))))))),
% 3.84/2.60 inference(modus_ponens,[status(thm)],[22, 12])).
% 3.84/2.60 tff(24,plain,
% 3.84/2.60 (((~![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(set_union2(A!6, B!5), B!5) = set_difference(set_union2(B!5, A!6), B!5)) | (in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(B!5, A!6)), set_difference(set_union2(A!6, B!5), B!5)) <=> ((~in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(B!5, A!6)), set_union2(B!5, A!6))) | in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(B!5, A!6)), B!5))))) | (~((~(set_difference(set_union2(A!6, B!5), B!5) = set_difference(set_union2(B!5, A!6), B!5))) | (in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(A!6, A!3)), set_difference(set_union2(A!6, B!5), B!5)) <=> (~((~in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(A!6, A!3)), set_union2(B!5, A!6))) | in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(A!6, A!3)), B!5))))))))) <=> ((~![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(set_union2(A!6, B!5), B!5) = set_difference(set_union2(B!5, A!6), B!5)) | (in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(B!5, A!6)), set_difference(set_union2(A!6, B!5), B!5)) <=> ((~in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(B!5, A!6)), set_union2(B!5, A!6))) | in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(B!5, A!6)), B!5))))) | (~((~(set_difference(set_union2(A!6, B!5), B!5) = set_difference(set_union2(B!5, A!6), B!5))) | (in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(A!6, A!3)), set_difference(set_union2(A!6, B!5), B!5)) <=> (~((~in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(A!6, A!3)), set_union2(B!5, A!6))) | in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(A!6, A!3)), B!5)))))))))),
% 3.84/2.60 inference(rewrite,[status(thm)],[])).
% 3.84/2.60 tff(25,plain,
% 3.84/2.60 ((~((~((~(set_difference(set_union2(A!6, B!5), B!5) = set_difference(set_union2(B!5, A!6), B!5))) | (in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(A!6, A!3)), set_difference(set_union2(A!6, B!5), B!5)) <=> (~((~in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(A!6, A!3)), set_union2(B!5, A!6))) | in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(A!6, A!3)), B!5)))))) | (~((set_difference(set_union2(A!6, B!5), B!5) = set_difference(set_union2(B!5, A!6), B!5)) | (in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(B!5, A!6)), set_difference(set_union2(A!6, B!5), B!5)) <=> ((~in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(B!5, A!6)), set_union2(B!5, A!6))) | in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(B!5, A!6)), B!5))))))) <=> (~((~((set_difference(set_union2(A!6, B!5), B!5) = set_difference(set_union2(B!5, A!6), B!5)) | (in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(B!5, A!6)), set_difference(set_union2(A!6, B!5), B!5)) <=> ((~in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(B!5, A!6)), set_union2(B!5, A!6))) | in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(B!5, A!6)), B!5))))) | (~((~(set_difference(set_union2(A!6, B!5), B!5) = set_difference(set_union2(B!5, A!6), B!5))) | (in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(A!6, A!3)), set_difference(set_union2(A!6, B!5), B!5)) <=> (~((~in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(A!6, A!3)), set_union2(B!5, A!6))) | in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(A!6, A!3)), B!5))))))))),
% 3.84/2.60 inference(rewrite,[status(thm)],[])).
% 3.84/2.60 tff(26,plain,
% 3.84/2.60 (((~![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(set_union2(A!6, B!5), B!5) = set_difference(set_union2(B!5, A!6), B!5))) | (in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(A!6, A!3)), set_difference(set_union2(A!6, B!5), B!5)) <=> (~((~in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(A!6, A!3)), set_union2(B!5, A!6))) | in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(A!6, A!3)), B!5)))))) | (~((set_difference(set_union2(A!6, B!5), B!5) = set_difference(set_union2(B!5, A!6), B!5)) | (in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(B!5, A!6)), set_difference(set_union2(A!6, B!5), B!5)) <=> ((~in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(B!5, A!6)), set_union2(B!5, A!6))) | in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(B!5, A!6)), B!5)))))))) <=> ((~![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(set_union2(A!6, B!5), B!5) = set_difference(set_union2(B!5, A!6), B!5)) | (in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(B!5, A!6)), set_difference(set_union2(A!6, B!5), B!5)) <=> ((~in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(B!5, A!6)), set_union2(B!5, A!6))) | in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(B!5, A!6)), B!5))))) | (~((~(set_difference(set_union2(A!6, B!5), B!5) = set_difference(set_union2(B!5, A!6), B!5))) | (in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(A!6, A!3)), set_difference(set_union2(A!6, B!5), B!5)) <=> (~((~in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(A!6, A!3)), set_union2(B!5, A!6))) | in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(A!6, A!3)), B!5)))))))))),
% 3.84/2.61 inference(monotonicity,[status(thm)],[25])).
% 3.84/2.61 tff(27,plain,
% 3.84/2.61 (((~![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(set_union2(A!6, B!5), B!5) = set_difference(set_union2(B!5, A!6), B!5))) | (in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(A!6, A!3)), set_difference(set_union2(A!6, B!5), B!5)) <=> (~((~in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(A!6, A!3)), set_union2(B!5, A!6))) | in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(A!6, A!3)), B!5)))))) | (~((set_difference(set_union2(A!6, B!5), B!5) = set_difference(set_union2(B!5, A!6), B!5)) | (in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(B!5, A!6)), set_difference(set_union2(A!6, B!5), B!5)) <=> ((~in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(B!5, A!6)), set_union2(B!5, A!6))) | in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(B!5, A!6)), B!5)))))))) <=> ((~![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(set_union2(A!6, B!5), B!5) = set_difference(set_union2(B!5, A!6), B!5)) | (in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(B!5, A!6)), set_difference(set_union2(A!6, B!5), B!5)) <=> ((~in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(B!5, A!6)), set_union2(B!5, A!6))) | in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(B!5, A!6)), B!5))))) | (~((~(set_difference(set_union2(A!6, B!5), B!5) = set_difference(set_union2(B!5, A!6), B!5))) | (in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(A!6, A!3)), set_difference(set_union2(A!6, B!5), B!5)) <=> (~((~in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(A!6, A!3)), set_union2(B!5, A!6))) | in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(A!6, A!3)), B!5)))))))))),
% 3.84/2.61 inference(transitivity,[status(thm)],[26, 24])).
% 3.84/2.61 tff(28,plain,
% 3.84/2.61 ((~![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(set_union2(A!6, B!5), B!5) = set_difference(set_union2(B!5, A!6), B!5))) | (in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(A!6, A!3)), set_difference(set_union2(A!6, B!5), B!5)) <=> (~((~in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(A!6, A!3)), set_union2(B!5, A!6))) | in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(A!6, A!3)), B!5)))))) | (~((set_difference(set_union2(A!6, B!5), B!5) = set_difference(set_union2(B!5, A!6), B!5)) | (in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(B!5, A!6)), set_difference(set_union2(A!6, B!5), B!5)) <=> ((~in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(B!5, A!6)), set_union2(B!5, A!6))) | in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(B!5, A!6)), B!5)))))))),
% 3.86/2.61 inference(quant_inst,[status(thm)],[])).
% 3.86/2.61 tff(29,plain,
% 3.86/2.61 ((~![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(set_union2(A!6, B!5), B!5) = set_difference(set_union2(B!5, A!6), B!5)) | (in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(B!5, A!6)), set_difference(set_union2(A!6, B!5), B!5)) <=> ((~in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(B!5, A!6)), set_union2(B!5, A!6))) | in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(B!5, A!6)), B!5))))) | (~((~(set_difference(set_union2(A!6, B!5), B!5) = set_difference(set_union2(B!5, A!6), B!5))) | (in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(A!6, A!3)), set_difference(set_union2(A!6, B!5), B!5)) <=> (~((~in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(A!6, A!3)), set_union2(B!5, A!6))) | in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(A!6, A!3)), B!5))))))))),
% 3.86/2.61 inference(modus_ponens,[status(thm)],[28, 27])).
% 3.86/2.61 tff(30,plain,
% 3.86/2.61 (~((~((set_difference(set_union2(A!6, B!5), B!5) = set_difference(set_union2(B!5, A!6), B!5)) | (in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(B!5, A!6)), set_difference(set_union2(A!6, B!5), B!5)) <=> ((~in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(B!5, A!6)), set_union2(B!5, A!6))) | in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(B!5, A!6)), B!5))))) | (~((~(set_difference(set_union2(A!6, B!5), B!5) = set_difference(set_union2(B!5, A!6), B!5))) | (in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(A!6, A!3)), set_difference(set_union2(A!6, B!5), B!5)) <=> (~((~in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(A!6, A!3)), set_union2(B!5, A!6))) | in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(A!6, A!3)), B!5)))))))),
% 3.86/2.61 inference(unit_resolution,[status(thm)],[29, 23])).
% 3.86/2.61 tff(31,plain,
% 3.86/2.61 (((~((set_difference(set_union2(A!6, B!5), B!5) = set_difference(set_union2(B!5, A!6), B!5)) | (in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(B!5, A!6)), set_difference(set_union2(A!6, B!5), B!5)) <=> ((~in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(B!5, A!6)), set_union2(B!5, A!6))) | in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(B!5, A!6)), B!5))))) | (~((~(set_difference(set_union2(A!6, B!5), B!5) = set_difference(set_union2(B!5, A!6), B!5))) | (in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(A!6, A!3)), set_difference(set_union2(A!6, B!5), B!5)) <=> (~((~in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(A!6, A!3)), set_union2(B!5, A!6))) | in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(A!6, A!3)), B!5))))))) | ((~(set_difference(set_union2(A!6, B!5), B!5) = set_difference(set_union2(B!5, A!6), B!5))) | (in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(A!6, A!3)), set_difference(set_union2(A!6, B!5), B!5)) <=> (~((~in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(A!6, A!3)), set_union2(B!5, A!6))) | in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(A!6, A!3)), B!5)))))),
% 3.86/2.61 inference(tautology,[status(thm)],[])).
% 3.86/2.61 tff(32,plain,
% 3.86/2.61 ((~(set_difference(set_union2(A!6, B!5), B!5) = set_difference(set_union2(B!5, A!6), B!5))) | (in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(A!6, A!3)), set_difference(set_union2(A!6, B!5), B!5)) <=> (~((~in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(A!6, A!3)), set_union2(B!5, A!6))) | in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(A!6, A!3)), B!5))))),
% 3.86/2.61 inference(unit_resolution,[status(thm)],[31, 30])).
% 3.86/2.61 tff(33,plain,
% 3.86/2.61 (^[A: $i, B: $i] : refl((set_union2(A, B) = set_union2(B, A)) <=> (set_union2(A, B) = set_union2(B, A)))),
% 3.86/2.61 inference(bind,[status(th)],[])).
% 3.86/2.61 tff(34,plain,
% 3.86/2.61 (![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A)) <=> ![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A))),
% 3.86/2.61 inference(quant_intro,[status(thm)],[33])).
% 3.86/2.61 tff(35,plain,
% 3.86/2.61 (![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A)) <=> ![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A))),
% 3.86/2.61 inference(rewrite,[status(thm)],[])).
% 3.86/2.61 tff(36,axiom,(![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','commutativity_k2_xboole_0')).
% 3.86/2.61 tff(37,plain,
% 3.86/2.61 (![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A))),
% 3.86/2.61 inference(modus_ponens,[status(thm)],[36, 35])).
% 3.86/2.61 tff(38,plain,(
% 3.86/2.61 ![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A))),
% 3.86/2.61 inference(skolemize,[status(sab)],[37])).
% 3.86/2.61 tff(39,plain,
% 3.86/2.61 (![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A))),
% 3.86/2.61 inference(modus_ponens,[status(thm)],[38, 34])).
% 3.86/2.61 tff(40,plain,
% 3.86/2.61 ((~![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A))) | (set_union2(A!6, B!5) = set_union2(B!5, A!6))),
% 3.86/2.61 inference(quant_inst,[status(thm)],[])).
% 3.86/2.61 tff(41,plain,
% 3.86/2.61 (set_union2(A!6, B!5) = set_union2(B!5, A!6)),
% 3.86/2.61 inference(unit_resolution,[status(thm)],[40, 39])).
% 3.86/2.61 tff(42,plain,
% 3.86/2.61 (set_union2(B!5, A!6) = set_union2(A!6, B!5)),
% 3.86/2.61 inference(symmetry,[status(thm)],[41])).
% 3.86/2.61 tff(43,plain,
% 3.86/2.61 (set_difference(set_union2(B!5, A!6), B!5) = set_difference(set_union2(A!6, B!5), B!5)),
% 3.86/2.61 inference(monotonicity,[status(thm)],[42])).
% 3.86/2.61 tff(44,plain,
% 3.86/2.61 (set_difference(set_union2(A!6, B!5), B!5) = set_difference(set_union2(B!5, A!6), B!5)),
% 3.86/2.61 inference(symmetry,[status(thm)],[43])).
% 3.86/2.61 tff(45,plain,
% 3.86/2.61 ((~((~(set_difference(set_union2(A!6, B!5), B!5) = set_difference(set_union2(B!5, A!6), B!5))) | (in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(A!6, A!3)), set_difference(set_union2(A!6, B!5), B!5)) <=> (~((~in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(A!6, A!3)), set_union2(B!5, A!6))) | in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(A!6, A!3)), B!5)))))) | (~(set_difference(set_union2(A!6, B!5), B!5) = set_difference(set_union2(B!5, A!6), B!5))) | (in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(A!6, A!3)), set_difference(set_union2(A!6, B!5), B!5)) <=> (~((~in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(A!6, A!3)), set_union2(B!5, A!6))) | in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(A!6, A!3)), B!5))))),
% 3.86/2.61 inference(tautology,[status(thm)],[])).
% 3.86/2.61 tff(46,plain,
% 3.86/2.61 ((~((~(set_difference(set_union2(A!6, B!5), B!5) = set_difference(set_union2(B!5, A!6), B!5))) | (in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(A!6, A!3)), set_difference(set_union2(A!6, B!5), B!5)) <=> (~((~in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(A!6, A!3)), set_union2(B!5, A!6))) | in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(A!6, A!3)), B!5)))))) | (in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(A!6, A!3)), set_difference(set_union2(A!6, B!5), B!5)) <=> (~((~in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(A!6, A!3)), set_union2(B!5, A!6))) | in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(A!6, A!3)), B!5))))),
% 3.86/2.62 inference(unit_resolution,[status(thm)],[45, 44])).
% 3.86/2.62 tff(47,plain,
% 3.86/2.62 (in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(A!6, A!3)), set_difference(set_union2(A!6, B!5), B!5)) <=> (~((~in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(A!6, A!3)), set_union2(B!5, A!6))) | in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(A!6, A!3)), B!5)))),
% 3.86/2.62 inference(unit_resolution,[status(thm)],[46, 32])).
% 3.86/2.62 tff(48,plain,
% 3.86/2.62 ((~(in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(A!6, A!3)), set_difference(set_union2(A!6, B!5), B!5)) <=> (~((~in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(A!6, A!3)), set_union2(B!5, A!6))) | in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(A!6, A!3)), B!5))))) | in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(A!6, A!3)), set_difference(set_union2(A!6, B!5), B!5)) | ((~in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(A!6, A!3)), set_union2(B!5, A!6))) | in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(A!6, A!3)), B!5))),
% 3.86/2.62 inference(tautology,[status(thm)],[])).
% 3.86/2.62 tff(49,plain,
% 3.86/2.62 (in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(A!6, A!3)), set_difference(set_union2(A!6, B!5), B!5)) | ((~in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(A!6, A!3)), set_union2(B!5, A!6))) | in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(A!6, A!3)), B!5))),
% 3.86/2.62 inference(unit_resolution,[status(thm)],[48, 47])).
% 3.86/2.62 tff(50,plain,
% 3.86/2.62 ((~in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(A!6, A!3)), set_union2(B!5, A!6))) | in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(A!6, A!3)), B!5)),
% 3.86/2.62 inference(unit_resolution,[status(thm)],[49, 2])).
% 3.86/2.62 tff(51,plain,
% 3.86/2.62 ((~((~in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(A!6, A!3)), set_union2(B!5, A!6))) | in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(A!6, A!3)), B!5))) | (~in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(A!6, A!3)), set_union2(B!5, A!6))) | in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(A!6, A!3)), B!5)),
% 3.86/2.62 inference(tautology,[status(thm)],[])).
% 3.86/2.62 tff(52,plain,
% 3.86/2.62 (~in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(A!6, A!3)), set_union2(B!5, A!6))),
% 3.86/2.62 inference(unit_resolution,[status(thm)],[51, 50, 1])).
% 3.86/2.62 tff(53,plain,
% 3.86/2.62 ((~![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(set_union2(A!6, B!5), B!5) = set_difference(set_union2(A!6, A!3), B!5))) | (in(tptp_fun_D_2(A!3, B!5, A!6), set_difference(set_union2(A!6, B!5), B!5)) <=> (~((~in(tptp_fun_D_2(A!3, B!5, A!6), set_union2(A!6, A!3))) | in(tptp_fun_D_2(A!3, B!5, A!6), B!5)))))) | (~((set_difference(set_union2(A!6, B!5), B!5) = set_difference(set_union2(A!6, A!3), B!5)) | (in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(A!6, A!3)), set_difference(set_union2(A!6, B!5), B!5)) <=> ((~in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(A!6, A!3)), set_union2(A!6, A!3))) | in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(A!6, A!3)), B!5)))))))),
% 3.86/2.62 inference(quant_inst,[status(thm)],[])).
% 3.86/2.62 tff(54,plain,
% 3.86/2.62 (~((~((~(set_difference(set_union2(A!6, B!5), B!5) = set_difference(set_union2(A!6, A!3), B!5))) | (in(tptp_fun_D_2(A!3, B!5, A!6), set_difference(set_union2(A!6, B!5), B!5)) <=> (~((~in(tptp_fun_D_2(A!3, B!5, A!6), set_union2(A!6, A!3))) | in(tptp_fun_D_2(A!3, B!5, A!6), B!5)))))) | (~((set_difference(set_union2(A!6, B!5), B!5) = set_difference(set_union2(A!6, A!3), B!5)) | (in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(A!6, A!3)), set_difference(set_union2(A!6, B!5), B!5)) <=> ((~in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(A!6, A!3)), set_union2(A!6, A!3))) | in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(A!6, A!3)), B!5))))))),
% 3.86/2.62 inference(unit_resolution,[status(thm)],[53, 23])).
% 3.86/2.62 tff(55,plain,
% 3.86/2.62 (((~((~(set_difference(set_union2(A!6, B!5), B!5) = set_difference(set_union2(A!6, A!3), B!5))) | (in(tptp_fun_D_2(A!3, B!5, A!6), set_difference(set_union2(A!6, B!5), B!5)) <=> (~((~in(tptp_fun_D_2(A!3, B!5, A!6), set_union2(A!6, A!3))) | in(tptp_fun_D_2(A!3, B!5, A!6), B!5)))))) | (~((set_difference(set_union2(A!6, B!5), B!5) = set_difference(set_union2(A!6, A!3), B!5)) | (in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(A!6, A!3)), set_difference(set_union2(A!6, B!5), B!5)) <=> ((~in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(A!6, A!3)), set_union2(A!6, A!3))) | in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(A!6, A!3)), B!5)))))) | ((set_difference(set_union2(A!6, B!5), B!5) = set_difference(set_union2(A!6, A!3), B!5)) | (in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(A!6, A!3)), set_difference(set_union2(A!6, B!5), B!5)) <=> ((~in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(A!6, A!3)), set_union2(A!6, A!3))) | in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(A!6, A!3)), B!5))))),
% 3.86/2.62 inference(tautology,[status(thm)],[])).
% 3.86/2.62 tff(56,plain,
% 3.86/2.62 ((set_difference(set_union2(A!6, B!5), B!5) = set_difference(set_union2(A!6, A!3), B!5)) | (in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(A!6, A!3)), set_difference(set_union2(A!6, B!5), B!5)) <=> ((~in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(A!6, A!3)), set_union2(A!6, A!3))) | in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(A!6, A!3)), B!5)))),
% 3.86/2.62 inference(unit_resolution,[status(thm)],[55, 54])).
% 3.86/2.62 tff(57,plain,
% 3.86/2.62 (^[A: $i] : refl((set_union2(A, empty_set) = A) <=> (set_union2(A, empty_set) = A))),
% 3.86/2.62 inference(bind,[status(th)],[])).
% 3.86/2.62 tff(58,plain,
% 3.86/2.62 (![A: $i] : (set_union2(A, empty_set) = A) <=> ![A: $i] : (set_union2(A, empty_set) = A)),
% 3.86/2.62 inference(quant_intro,[status(thm)],[57])).
% 3.86/2.62 tff(59,plain,
% 3.86/2.62 (![A: $i] : (set_union2(A, empty_set) = A) <=> ![A: $i] : (set_union2(A, empty_set) = A)),
% 3.86/2.62 inference(rewrite,[status(thm)],[])).
% 3.86/2.62 tff(60,axiom,(![A: $i] : (set_union2(A, empty_set) = A)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t1_boole')).
% 3.86/2.62 tff(61,plain,
% 3.86/2.62 (![A: $i] : (set_union2(A, empty_set) = A)),
% 3.86/2.62 inference(modus_ponens,[status(thm)],[60, 59])).
% 3.86/2.62 tff(62,plain,(
% 3.86/2.62 ![A: $i] : (set_union2(A, empty_set) = A)),
% 3.86/2.62 inference(skolemize,[status(sab)],[61])).
% 3.86/2.62 tff(63,plain,
% 3.86/2.62 (![A: $i] : (set_union2(A, empty_set) = A)),
% 3.86/2.62 inference(modus_ponens,[status(thm)],[62, 58])).
% 3.86/2.62 tff(64,plain,
% 3.86/2.62 ((~![A: $i] : (set_union2(A, empty_set) = A)) | (set_union2(A!6, empty_set) = A!6)),
% 3.86/2.62 inference(quant_inst,[status(thm)],[])).
% 3.86/2.62 tff(65,plain,
% 3.86/2.62 (set_union2(A!6, empty_set) = A!6),
% 3.86/2.62 inference(unit_resolution,[status(thm)],[64, 63])).
% 3.86/2.62 tff(66,plain,
% 3.86/2.62 (^[A: $i, B: $i] : refl(((A = B) | (~empty(A)) | (~empty(B))) <=> ((A = B) | (~empty(A)) | (~empty(B))))),
% 3.86/2.62 inference(bind,[status(th)],[])).
% 3.86/2.62 tff(67,plain,
% 3.86/2.62 (![A: $i, B: $i] : ((A = B) | (~empty(A)) | (~empty(B))) <=> ![A: $i, B: $i] : ((A = B) | (~empty(A)) | (~empty(B)))),
% 3.86/2.62 inference(quant_intro,[status(thm)],[66])).
% 3.86/2.62 tff(68,plain,
% 3.86/2.62 (^[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)))))),
% 3.86/2.62 inference(bind,[status(th)],[])).
% 3.86/2.62 tff(69,plain,
% 3.86/2.62 (![A: $i, B: $i] : (~(empty(A) & (~(A = B)) & empty(B))) <=> ![A: $i, B: $i] : ((A = B) | (~empty(A)) | (~empty(B)))),
% 3.86/2.62 inference(quant_intro,[status(thm)],[68])).
% 3.86/2.62 tff(70,plain,
% 3.86/2.62 (![A: $i, B: $i] : (~(empty(A) & (~(A = B)) & empty(B))) <=> ![A: $i, B: $i] : (~(empty(A) & (~(A = B)) & empty(B)))),
% 3.86/2.62 inference(rewrite,[status(thm)],[])).
% 3.86/2.62 tff(71,plain,
% 3.86/2.62 (^[A: $i, B: $i] : rewrite((~((empty(A) & (~(A = B))) & empty(B))) <=> (~(empty(A) & (~(A = B)) & empty(B))))),
% 3.86/2.62 inference(bind,[status(th)],[])).
% 3.86/2.62 tff(72,plain,
% 3.86/2.62 (![A: $i, B: $i] : (~((empty(A) & (~(A = B))) & empty(B))) <=> ![A: $i, B: $i] : (~(empty(A) & (~(A = B)) & empty(B)))),
% 3.86/2.62 inference(quant_intro,[status(thm)],[71])).
% 3.86/2.62 tff(73,axiom,(![A: $i, B: $i] : (~((empty(A) & (~(A = B))) & empty(B)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t8_boole')).
% 3.86/2.62 tff(74,plain,
% 3.86/2.62 (![A: $i, B: $i] : (~(empty(A) & (~(A = B)) & empty(B)))),
% 3.86/2.62 inference(modus_ponens,[status(thm)],[73, 72])).
% 3.86/2.62 tff(75,plain,
% 3.86/2.62 (![A: $i, B: $i] : (~(empty(A) & (~(A = B)) & empty(B)))),
% 3.86/2.62 inference(modus_ponens,[status(thm)],[74, 70])).
% 3.86/2.62 tff(76,plain,(
% 3.86/2.62 ![A: $i, B: $i] : (~(empty(A) & (~(A = B)) & empty(B)))),
% 3.86/2.62 inference(skolemize,[status(sab)],[75])).
% 3.86/2.62 tff(77,plain,
% 3.86/2.62 (![A: $i, B: $i] : ((A = B) | (~empty(A)) | (~empty(B)))),
% 3.86/2.62 inference(modus_ponens,[status(thm)],[76, 69])).
% 3.86/2.62 tff(78,plain,
% 3.86/2.62 (![A: $i, B: $i] : ((A = B) | (~empty(A)) | (~empty(B)))),
% 3.86/2.62 inference(modus_ponens,[status(thm)],[77, 67])).
% 3.86/2.62 tff(79,plain,
% 3.86/2.62 (?[A: $i] : empty(A) <=> ?[A: $i] : empty(A)),
% 3.86/2.62 inference(rewrite,[status(thm)],[])).
% 3.86/2.62 tff(80,axiom,(?[A: $i] : empty(A)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','rc1_xboole_0')).
% 3.86/2.62 tff(81,plain,
% 3.86/2.62 (?[A: $i] : empty(A)),
% 3.86/2.62 inference(modus_ponens,[status(thm)],[80, 79])).
% 3.86/2.62 tff(82,plain,(
% 3.86/2.62 empty(A!3)),
% 3.86/2.62 inference(skolemize,[status(sab)],[81])).
% 3.86/2.62 tff(83,plain,
% 3.86/2.62 (empty(empty_set) <=> empty(empty_set)),
% 3.86/2.62 inference(rewrite,[status(thm)],[])).
% 3.86/2.62 tff(84,axiom,(empty(empty_set)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','fc1_xboole_0')).
% 3.86/2.62 tff(85,plain,
% 3.86/2.62 (empty(empty_set)),
% 3.86/2.62 inference(modus_ponens,[status(thm)],[84, 83])).
% 3.86/2.62 tff(86,plain,
% 3.86/2.62 (((~![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)))),
% 3.86/2.62 inference(rewrite,[status(thm)],[])).
% 3.86/2.62 tff(87,plain,
% 3.86/2.62 ((~![A: $i, B: $i] : ((A = B) | (~empty(A)) | (~empty(B)))) | ((empty_set = A!3) | (~empty(empty_set)) | (~empty(A!3)))),
% 3.86/2.62 inference(quant_inst,[status(thm)],[])).
% 3.86/2.62 tff(88,plain,
% 3.86/2.62 ((~![A: $i, B: $i] : ((A = B) | (~empty(A)) | (~empty(B)))) | (empty_set = A!3) | (~empty(empty_set)) | (~empty(A!3))),
% 3.86/2.62 inference(modus_ponens,[status(thm)],[87, 86])).
% 3.86/2.62 tff(89,plain,
% 3.86/2.62 (empty_set = A!3),
% 3.86/2.62 inference(unit_resolution,[status(thm)],[88, 85, 82, 78])).
% 3.86/2.62 tff(90,plain,
% 3.86/2.62 (set_union2(A!6, empty_set) = set_union2(A!6, A!3)),
% 3.86/2.62 inference(monotonicity,[status(thm)],[89])).
% 3.86/2.62 tff(91,plain,
% 3.86/2.62 (set_union2(A!6, A!3) = set_union2(A!6, empty_set)),
% 3.86/2.62 inference(symmetry,[status(thm)],[90])).
% 3.86/2.62 tff(92,plain,
% 3.86/2.62 (set_union2(A!6, A!3) = A!6),
% 3.86/2.62 inference(transitivity,[status(thm)],[91, 65])).
% 3.86/2.62 tff(93,plain,
% 3.86/2.62 (set_difference(set_union2(A!6, A!3), B!5) = set_difference(A!6, B!5)),
% 3.86/2.62 inference(monotonicity,[status(thm)],[92])).
% 3.86/2.62 tff(94,plain,
% 3.86/2.62 ((set_difference(set_union2(A!6, B!5), B!5) = set_difference(set_union2(A!6, A!3), B!5)) <=> (set_difference(set_union2(A!6, B!5), B!5) = set_difference(A!6, B!5))),
% 3.86/2.63 inference(monotonicity,[status(thm)],[93])).
% 3.86/2.63 tff(95,plain,
% 3.86/2.63 ((set_difference(set_union2(A!6, B!5), B!5) = set_difference(A!6, B!5)) <=> (set_difference(set_union2(A!6, B!5), B!5) = set_difference(set_union2(A!6, A!3), B!5))),
% 3.86/2.63 inference(symmetry,[status(thm)],[94])).
% 3.86/2.63 tff(96,plain,
% 3.86/2.63 ((~(set_difference(set_union2(A!6, B!5), B!5) = set_difference(A!6, B!5))) <=> (~(set_difference(set_union2(A!6, B!5), B!5) = set_difference(set_union2(A!6, A!3), B!5)))),
% 3.86/2.63 inference(monotonicity,[status(thm)],[95])).
% 3.86/2.63 tff(97,plain,
% 3.86/2.63 ((~![A: $i, B: $i] : (set_difference(set_union2(A, B), B) = set_difference(A, B))) <=> (~![A: $i, B: $i] : (set_difference(set_union2(A, B), B) = set_difference(A, B)))),
% 3.86/2.63 inference(rewrite,[status(thm)],[])).
% 3.86/2.63 tff(98,axiom,(~![A: $i, B: $i] : (set_difference(set_union2(A, B), B) = set_difference(A, B))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t40_xboole_1')).
% 3.86/2.63 tff(99,plain,
% 3.86/2.63 (~![A: $i, B: $i] : (set_difference(set_union2(A, B), B) = set_difference(A, B))),
% 3.86/2.63 inference(modus_ponens,[status(thm)],[98, 97])).
% 3.86/2.63 tff(100,plain,
% 3.86/2.63 (~![A: $i, B: $i] : (set_difference(set_union2(A, B), B) = set_difference(A, B))),
% 3.86/2.63 inference(modus_ponens,[status(thm)],[99, 97])).
% 3.86/2.63 tff(101,plain,
% 3.86/2.63 (~![A: $i, B: $i] : (set_difference(set_union2(A, B), B) = set_difference(A, B))),
% 3.86/2.63 inference(modus_ponens,[status(thm)],[100, 97])).
% 3.86/2.63 tff(102,plain,
% 3.86/2.63 (~![A: $i, B: $i] : (set_difference(set_union2(A, B), B) = set_difference(A, B))),
% 3.86/2.63 inference(modus_ponens,[status(thm)],[101, 97])).
% 3.86/2.63 tff(103,plain,
% 3.86/2.63 (~![A: $i, B: $i] : (set_difference(set_union2(A, B), B) = set_difference(A, B))),
% 3.86/2.63 inference(modus_ponens,[status(thm)],[102, 97])).
% 3.86/2.63 tff(104,plain,
% 3.86/2.63 (~![A: $i, B: $i] : (set_difference(set_union2(A, B), B) = set_difference(A, B))),
% 3.86/2.63 inference(modus_ponens,[status(thm)],[103, 97])).
% 3.86/2.63 tff(105,plain,
% 3.86/2.63 (~![A: $i, B: $i] : (set_difference(set_union2(A, B), B) = set_difference(A, B))),
% 3.86/2.63 inference(modus_ponens,[status(thm)],[104, 97])).
% 3.86/2.63 tff(106,plain,(
% 3.86/2.63 ~(set_difference(set_union2(A!6, B!5), B!5) = set_difference(A!6, B!5))),
% 3.86/2.63 inference(skolemize,[status(sab)],[105])).
% 3.86/2.63 tff(107,plain,
% 3.86/2.63 (~(set_difference(set_union2(A!6, B!5), B!5) = set_difference(set_union2(A!6, A!3), B!5))),
% 3.86/2.63 inference(modus_ponens,[status(thm)],[106, 96])).
% 3.86/2.63 tff(108,plain,
% 3.86/2.63 ((~((set_difference(set_union2(A!6, B!5), B!5) = set_difference(set_union2(A!6, A!3), B!5)) | (in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(A!6, A!3)), set_difference(set_union2(A!6, B!5), B!5)) <=> ((~in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(A!6, A!3)), set_union2(A!6, A!3))) | in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(A!6, A!3)), B!5))))) | (set_difference(set_union2(A!6, B!5), B!5) = set_difference(set_union2(A!6, A!3), B!5)) | (in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(A!6, A!3)), set_difference(set_union2(A!6, B!5), B!5)) <=> ((~in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(A!6, A!3)), set_union2(A!6, A!3))) | in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(A!6, A!3)), B!5)))),
% 3.86/2.63 inference(tautology,[status(thm)],[])).
% 3.86/2.63 tff(109,plain,
% 3.86/2.63 (in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(A!6, A!3)), set_difference(set_union2(A!6, B!5), B!5)) <=> ((~in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(A!6, A!3)), set_union2(A!6, A!3))) | in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(A!6, A!3)), B!5))),
% 3.86/2.63 inference(unit_resolution,[status(thm)],[108, 107, 56])).
% 3.86/2.63 tff(110,plain,
% 3.86/2.63 ((~(in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(A!6, A!3)), set_difference(set_union2(A!6, B!5), B!5)) <=> ((~in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(A!6, A!3)), set_union2(A!6, A!3))) | in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(A!6, A!3)), B!5)))) | in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(A!6, A!3)), set_difference(set_union2(A!6, B!5), B!5)) | (~((~in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(A!6, A!3)), set_union2(A!6, A!3))) | in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(A!6, A!3)), B!5)))),
% 3.86/2.63 inference(tautology,[status(thm)],[])).
% 3.86/2.63 tff(111,plain,
% 3.86/2.63 (in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(A!6, A!3)), set_difference(set_union2(A!6, B!5), B!5)) | (~((~in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(A!6, A!3)), set_union2(A!6, A!3))) | in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(A!6, A!3)), B!5)))),
% 3.86/2.63 inference(unit_resolution,[status(thm)],[110, 109])).
% 3.86/2.63 tff(112,plain,
% 3.86/2.63 (~((~in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(A!6, A!3)), set_union2(A!6, A!3))) | in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(A!6, A!3)), B!5))),
% 3.86/2.63 inference(unit_resolution,[status(thm)],[111, 2])).
% 3.86/2.63 tff(113,plain,
% 3.86/2.63 (((~in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(A!6, A!3)), set_union2(A!6, A!3))) | in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(A!6, A!3)), B!5)) | in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(A!6, A!3)), set_union2(A!6, A!3))),
% 3.86/2.63 inference(tautology,[status(thm)],[])).
% 3.86/2.63 tff(114,plain,
% 3.86/2.63 (in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(A!6, A!3)), set_union2(A!6, A!3))),
% 3.86/2.63 inference(unit_resolution,[status(thm)],[113, 112])).
% 3.86/2.63 tff(115,plain,
% 3.86/2.63 ((in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(A!6, A!3)), B!5) | in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(A!6, A!3)), set_union2(A!6, A!3))) | (~in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(A!6, A!3)), set_union2(A!6, A!3)))),
% 3.86/2.63 inference(tautology,[status(thm)],[])).
% 3.86/2.63 tff(116,plain,
% 3.86/2.63 (in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(A!6, A!3)), B!5) | in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(A!6, A!3)), set_union2(A!6, A!3))),
% 3.86/2.63 inference(unit_resolution,[status(thm)],[115, 114])).
% 3.86/2.63 tff(117,assumption,((~((set_union2(B!5, A!6) = set_union2(set_union2(A!6, A!3), B!5)) | ((~in(tptp_fun_D_0(set_union2(B!5, A!6), B!5, set_union2(A!6, A!3)), set_union2(B!5, A!6))) <=> (in(tptp_fun_D_0(set_union2(B!5, A!6), B!5, set_union2(A!6, A!3)), B!5) | in(tptp_fun_D_0(set_union2(B!5, A!6), B!5, set_union2(A!6, A!3)), set_union2(A!6, A!3)))))) | (~((~(set_union2(B!5, A!6) = set_union2(set_union2(A!6, A!3), B!5))) | (in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(A!6, A!3)), set_union2(B!5, A!6)) <=> (in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(A!6, A!3)), B!5) | in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(A!6, A!3)), set_union2(A!6, A!3))))))), introduced(assumption)).
% 3.86/2.63 tff(118,plain,
% 3.86/2.63 (^[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))))))))),
% 3.86/2.63 inference(bind,[status(th)],[])).
% 3.86/2.63 tff(119,plain,
% 3.86/2.63 (![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)))))))),
% 3.86/2.63 inference(quant_intro,[status(thm)],[118])).
% 3.86/2.63 tff(120,plain,
% 3.86/2.63 (![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)))))))),
% 3.86/2.63 inference(pull_quant,[status(thm)],[])).
% 3.86/2.63 tff(121,plain,
% 3.86/2.63 (^[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)))))))))),
% 3.86/2.63 inference(bind,[status(th)],[])).
% 3.86/2.63 tff(122,plain,
% 3.86/2.63 (![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)))))))),
% 3.86/2.63 inference(quant_intro,[status(thm)],[121])).
% 3.86/2.63 tff(123,plain,
% 3.86/2.63 (![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)))))))),
% 3.86/2.63 inference(transitivity,[status(thm)],[122, 120])).
% 3.86/2.63 tff(124,plain,
% 3.86/2.63 (![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)))))))),
% 3.86/2.63 inference(transitivity,[status(thm)],[123, 119])).
% 3.86/2.63 tff(125,plain,
% 3.86/2.63 (^[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))))))))),
% 3.86/2.63 inference(bind,[status(th)],[])).
% 3.86/2.63 tff(126,plain,
% 3.86/2.63 (![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)))))))),
% 3.86/2.63 inference(quant_intro,[status(thm)],[125])).
% 3.86/2.63 tff(127,plain,
% 3.86/2.63 (![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)))))))),
% 3.86/2.63 inference(transitivity,[status(thm)],[126, 124])).
% 3.86/2.63 tff(128,plain,
% 3.86/2.63 (^[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)))))))))),
% 3.86/2.64 inference(bind,[status(th)],[])).
% 3.86/2.64 tff(129,plain,
% 3.86/2.64 (![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)))))))),
% 3.86/2.64 inference(quant_intro,[status(thm)],[128])).
% 3.86/2.64 tff(130,plain,
% 3.86/2.64 (^[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))))))),
% 3.86/2.64 inference(bind,[status(th)],[])).
% 3.86/2.64 tff(131,plain,
% 3.86/2.64 (![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)))))),
% 3.86/2.64 inference(quant_intro,[status(thm)],[130])).
% 3.86/2.64 tff(132,plain,
% 3.86/2.64 (![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))))),
% 3.86/2.64 inference(rewrite,[status(thm)],[])).
% 3.86/2.64 tff(133,plain,
% 3.86/2.64 (^[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)))))),
% 3.86/2.64 inference(bind,[status(th)],[])).
% 3.86/2.64 tff(134,plain,
% 3.86/2.64 (![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))))),
% 3.86/2.64 inference(quant_intro,[status(thm)],[133])).
% 3.86/2.64 tff(135,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')).
% 3.86/2.64 tff(136,plain,
% 3.86/2.64 (![A: $i, B: $i, C: $i] : ((C = set_union2(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))),
% 3.86/2.64 inference(modus_ponens,[status(thm)],[135, 134])).
% 3.86/2.64 tff(137,plain,
% 3.86/2.64 (![A: $i, B: $i, C: $i] : ((C = set_union2(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))),
% 3.86/2.64 inference(modus_ponens,[status(thm)],[136, 132])).
% 3.86/2.64 tff(138,plain,(
% 3.86/2.64 ![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))))))),
% 3.86/2.64 inference(skolemize,[status(sab)],[137])).
% 3.86/2.64 tff(139,plain,
% 3.86/2.64 (![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)))))),
% 3.86/2.64 inference(modus_ponens,[status(thm)],[138, 131])).
% 3.86/2.64 tff(140,plain,
% 3.86/2.64 (![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)))))))),
% 3.86/2.64 inference(modus_ponens,[status(thm)],[139, 129])).
% 3.86/2.64 tff(141,plain,
% 3.86/2.64 (![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)))))))),
% 3.86/2.64 inference(modus_ponens,[status(thm)],[140, 127])).
% 3.86/2.64 tff(142,plain,
% 3.86/2.64 (((~![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(B!5, A!6) = set_union2(set_union2(A!6, A!3), B!5)) | ((~in(tptp_fun_D_0(set_union2(B!5, A!6), B!5, set_union2(A!6, A!3)), set_union2(B!5, A!6))) <=> (in(tptp_fun_D_0(set_union2(B!5, A!6), B!5, set_union2(A!6, A!3)), B!5) | in(tptp_fun_D_0(set_union2(B!5, A!6), B!5, set_union2(A!6, A!3)), set_union2(A!6, A!3)))))) | (~((~(set_union2(B!5, A!6) = set_union2(set_union2(A!6, A!3), B!5))) | (in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(A!6, A!3)), set_union2(B!5, A!6)) <=> (in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(A!6, A!3)), B!5) | in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(A!6, A!3)), set_union2(A!6, A!3))))))))) <=> ((~![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(B!5, A!6) = set_union2(set_union2(A!6, A!3), B!5)) | ((~in(tptp_fun_D_0(set_union2(B!5, A!6), B!5, set_union2(A!6, A!3)), set_union2(B!5, A!6))) <=> (in(tptp_fun_D_0(set_union2(B!5, A!6), B!5, set_union2(A!6, A!3)), B!5) | in(tptp_fun_D_0(set_union2(B!5, A!6), B!5, set_union2(A!6, A!3)), set_union2(A!6, A!3)))))) | (~((~(set_union2(B!5, A!6) = set_union2(set_union2(A!6, A!3), B!5))) | (in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(A!6, A!3)), set_union2(B!5, A!6)) <=> (in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(A!6, A!3)), B!5) | in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(A!6, A!3)), set_union2(A!6, A!3)))))))))),
% 3.86/2.64 inference(rewrite,[status(thm)],[])).
% 3.86/2.64 tff(143,plain,
% 3.86/2.64 ((~((~((~(set_union2(B!5, A!6) = set_union2(set_union2(A!6, A!3), B!5))) | (in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(A!6, A!3)), set_union2(B!5, A!6)) <=> (in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(A!6, A!3)), B!5) | in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(A!6, A!3)), set_union2(A!6, A!3)))))) | (~((set_union2(B!5, A!6) = set_union2(set_union2(A!6, A!3), B!5)) | ((~in(tptp_fun_D_0(set_union2(B!5, A!6), B!5, set_union2(A!6, A!3)), set_union2(B!5, A!6))) <=> (in(tptp_fun_D_0(set_union2(B!5, A!6), B!5, set_union2(A!6, A!3)), B!5) | in(tptp_fun_D_0(set_union2(B!5, A!6), B!5, set_union2(A!6, A!3)), set_union2(A!6, A!3)))))))) <=> (~((~((set_union2(B!5, A!6) = set_union2(set_union2(A!6, A!3), B!5)) | ((~in(tptp_fun_D_0(set_union2(B!5, A!6), B!5, set_union2(A!6, A!3)), set_union2(B!5, A!6))) <=> (in(tptp_fun_D_0(set_union2(B!5, A!6), B!5, set_union2(A!6, A!3)), B!5) | in(tptp_fun_D_0(set_union2(B!5, A!6), B!5, set_union2(A!6, A!3)), set_union2(A!6, A!3)))))) | (~((~(set_union2(B!5, A!6) = set_union2(set_union2(A!6, A!3), B!5))) | (in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(A!6, A!3)), set_union2(B!5, A!6)) <=> (in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(A!6, A!3)), B!5) | in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(A!6, A!3)), set_union2(A!6, A!3))))))))),
% 3.86/2.64 inference(rewrite,[status(thm)],[])).
% 3.86/2.64 tff(144,plain,
% 3.86/2.64 (((~![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(B!5, A!6) = set_union2(set_union2(A!6, A!3), B!5))) | (in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(A!6, A!3)), set_union2(B!5, A!6)) <=> (in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(A!6, A!3)), B!5) | in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(A!6, A!3)), set_union2(A!6, A!3)))))) | (~((set_union2(B!5, A!6) = set_union2(set_union2(A!6, A!3), B!5)) | ((~in(tptp_fun_D_0(set_union2(B!5, A!6), B!5, set_union2(A!6, A!3)), set_union2(B!5, A!6))) <=> (in(tptp_fun_D_0(set_union2(B!5, A!6), B!5, set_union2(A!6, A!3)), B!5) | in(tptp_fun_D_0(set_union2(B!5, A!6), B!5, set_union2(A!6, A!3)), set_union2(A!6, A!3))))))))) <=> ((~![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(B!5, A!6) = set_union2(set_union2(A!6, A!3), B!5)) | ((~in(tptp_fun_D_0(set_union2(B!5, A!6), B!5, set_union2(A!6, A!3)), set_union2(B!5, A!6))) <=> (in(tptp_fun_D_0(set_union2(B!5, A!6), B!5, set_union2(A!6, A!3)), B!5) | in(tptp_fun_D_0(set_union2(B!5, A!6), B!5, set_union2(A!6, A!3)), set_union2(A!6, A!3)))))) | (~((~(set_union2(B!5, A!6) = set_union2(set_union2(A!6, A!3), B!5))) | (in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(A!6, A!3)), set_union2(B!5, A!6)) <=> (in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(A!6, A!3)), B!5) | in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(A!6, A!3)), set_union2(A!6, A!3)))))))))),
% 3.86/2.64 inference(monotonicity,[status(thm)],[143])).
% 3.86/2.64 tff(145,plain,
% 3.86/2.64 (((~![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(B!5, A!6) = set_union2(set_union2(A!6, A!3), B!5))) | (in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(A!6, A!3)), set_union2(B!5, A!6)) <=> (in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(A!6, A!3)), B!5) | in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(A!6, A!3)), set_union2(A!6, A!3)))))) | (~((set_union2(B!5, A!6) = set_union2(set_union2(A!6, A!3), B!5)) | ((~in(tptp_fun_D_0(set_union2(B!5, A!6), B!5, set_union2(A!6, A!3)), set_union2(B!5, A!6))) <=> (in(tptp_fun_D_0(set_union2(B!5, A!6), B!5, set_union2(A!6, A!3)), B!5) | in(tptp_fun_D_0(set_union2(B!5, A!6), B!5, set_union2(A!6, A!3)), set_union2(A!6, A!3))))))))) <=> ((~![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(B!5, A!6) = set_union2(set_union2(A!6, A!3), B!5)) | ((~in(tptp_fun_D_0(set_union2(B!5, A!6), B!5, set_union2(A!6, A!3)), set_union2(B!5, A!6))) <=> (in(tptp_fun_D_0(set_union2(B!5, A!6), B!5, set_union2(A!6, A!3)), B!5) | in(tptp_fun_D_0(set_union2(B!5, A!6), B!5, set_union2(A!6, A!3)), set_union2(A!6, A!3)))))) | (~((~(set_union2(B!5, A!6) = set_union2(set_union2(A!6, A!3), B!5))) | (in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(A!6, A!3)), set_union2(B!5, A!6)) <=> (in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(A!6, A!3)), B!5) | in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(A!6, A!3)), set_union2(A!6, A!3)))))))))),
% 3.86/2.65 inference(transitivity,[status(thm)],[144, 142])).
% 3.86/2.65 tff(146,plain,
% 3.86/2.65 ((~![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(B!5, A!6) = set_union2(set_union2(A!6, A!3), B!5))) | (in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(A!6, A!3)), set_union2(B!5, A!6)) <=> (in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(A!6, A!3)), B!5) | in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(A!6, A!3)), set_union2(A!6, A!3)))))) | (~((set_union2(B!5, A!6) = set_union2(set_union2(A!6, A!3), B!5)) | ((~in(tptp_fun_D_0(set_union2(B!5, A!6), B!5, set_union2(A!6, A!3)), set_union2(B!5, A!6))) <=> (in(tptp_fun_D_0(set_union2(B!5, A!6), B!5, set_union2(A!6, A!3)), B!5) | in(tptp_fun_D_0(set_union2(B!5, A!6), B!5, set_union2(A!6, A!3)), set_union2(A!6, A!3))))))))),
% 3.86/2.65 inference(quant_inst,[status(thm)],[])).
% 3.86/2.65 tff(147,plain,
% 3.86/2.65 ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A)))))))) | (~((~((set_union2(B!5, A!6) = set_union2(set_union2(A!6, A!3), B!5)) | ((~in(tptp_fun_D_0(set_union2(B!5, A!6), B!5, set_union2(A!6, A!3)), set_union2(B!5, A!6))) <=> (in(tptp_fun_D_0(set_union2(B!5, A!6), B!5, set_union2(A!6, A!3)), B!5) | in(tptp_fun_D_0(set_union2(B!5, A!6), B!5, set_union2(A!6, A!3)), set_union2(A!6, A!3)))))) | (~((~(set_union2(B!5, A!6) = set_union2(set_union2(A!6, A!3), B!5))) | (in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(A!6, A!3)), set_union2(B!5, A!6)) <=> (in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(A!6, A!3)), B!5) | in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(A!6, A!3)), set_union2(A!6, A!3))))))))),
% 3.86/2.65 inference(modus_ponens,[status(thm)],[146, 145])).
% 3.86/2.65 tff(148,plain,
% 3.86/2.65 ($false),
% 3.86/2.65 inference(unit_resolution,[status(thm)],[147, 141, 117])).
% 3.86/2.65 tff(149,plain,(~((~((set_union2(B!5, A!6) = set_union2(set_union2(A!6, A!3), B!5)) | ((~in(tptp_fun_D_0(set_union2(B!5, A!6), B!5, set_union2(A!6, A!3)), set_union2(B!5, A!6))) <=> (in(tptp_fun_D_0(set_union2(B!5, A!6), B!5, set_union2(A!6, A!3)), B!5) | in(tptp_fun_D_0(set_union2(B!5, A!6), B!5, set_union2(A!6, A!3)), set_union2(A!6, A!3)))))) | (~((~(set_union2(B!5, A!6) = set_union2(set_union2(A!6, A!3), B!5))) | (in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(A!6, A!3)), set_union2(B!5, A!6)) <=> (in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(A!6, A!3)), B!5) | in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(A!6, A!3)), set_union2(A!6, A!3)))))))), inference(lemma,lemma(discharge,[]))).
% 3.86/2.65 tff(150,plain,
% 3.86/2.65 (((~((set_union2(B!5, A!6) = set_union2(set_union2(A!6, A!3), B!5)) | ((~in(tptp_fun_D_0(set_union2(B!5, A!6), B!5, set_union2(A!6, A!3)), set_union2(B!5, A!6))) <=> (in(tptp_fun_D_0(set_union2(B!5, A!6), B!5, set_union2(A!6, A!3)), B!5) | in(tptp_fun_D_0(set_union2(B!5, A!6), B!5, set_union2(A!6, A!3)), set_union2(A!6, A!3)))))) | (~((~(set_union2(B!5, A!6) = set_union2(set_union2(A!6, A!3), B!5))) | (in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(A!6, A!3)), set_union2(B!5, A!6)) <=> (in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(A!6, A!3)), B!5) | in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(A!6, A!3)), set_union2(A!6, A!3))))))) | ((~(set_union2(B!5, A!6) = set_union2(set_union2(A!6, A!3), B!5))) | (in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(A!6, A!3)), set_union2(B!5, A!6)) <=> (in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(A!6, A!3)), B!5) | in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(A!6, A!3)), set_union2(A!6, A!3)))))),
% 3.86/2.65 inference(tautology,[status(thm)],[])).
% 3.86/2.65 tff(151,plain,
% 3.86/2.65 ((~(set_union2(B!5, A!6) = set_union2(set_union2(A!6, A!3), B!5))) | (in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(A!6, A!3)), set_union2(B!5, A!6)) <=> (in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(A!6, A!3)), B!5) | in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(A!6, A!3)), set_union2(A!6, A!3))))),
% 3.86/2.65 inference(unit_resolution,[status(thm)],[150, 149])).
% 3.86/2.65 tff(152,plain,
% 3.86/2.65 (set_union2(set_union2(A!6, A!3), B!5) = set_union2(A!6, B!5)),
% 3.86/2.65 inference(monotonicity,[status(thm)],[92])).
% 3.86/2.65 tff(153,plain,
% 3.86/2.65 (set_union2(A!6, B!5) = set_union2(set_union2(A!6, A!3), B!5)),
% 3.86/2.65 inference(symmetry,[status(thm)],[152])).
% 3.86/2.65 tff(154,plain,
% 3.86/2.65 (set_union2(B!5, A!6) = set_union2(set_union2(A!6, A!3), B!5)),
% 3.86/2.65 inference(transitivity,[status(thm)],[42, 153])).
% 3.86/2.65 tff(155,plain,
% 3.86/2.65 ((~((~(set_union2(B!5, A!6) = set_union2(set_union2(A!6, A!3), B!5))) | (in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(A!6, A!3)), set_union2(B!5, A!6)) <=> (in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(A!6, A!3)), B!5) | in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(A!6, A!3)), set_union2(A!6, A!3)))))) | (~(set_union2(B!5, A!6) = set_union2(set_union2(A!6, A!3), B!5))) | (in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(A!6, A!3)), set_union2(B!5, A!6)) <=> (in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(A!6, A!3)), B!5) | in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(A!6, A!3)), set_union2(A!6, A!3))))),
% 3.86/2.65 inference(tautology,[status(thm)],[])).
% 3.86/2.65 tff(156,plain,
% 3.86/2.65 ((~((~(set_union2(B!5, A!6) = set_union2(set_union2(A!6, A!3), B!5))) | (in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(A!6, A!3)), set_union2(B!5, A!6)) <=> (in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(A!6, A!3)), B!5) | in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(A!6, A!3)), set_union2(A!6, A!3)))))) | (in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(A!6, A!3)), set_union2(B!5, A!6)) <=> (in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(A!6, A!3)), B!5) | in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(A!6, A!3)), set_union2(A!6, A!3))))),
% 3.86/2.65 inference(unit_resolution,[status(thm)],[155, 154])).
% 3.86/2.65 tff(157,plain,
% 3.86/2.65 (in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(A!6, A!3)), set_union2(B!5, A!6)) <=> (in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(A!6, A!3)), B!5) | in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(A!6, A!3)), set_union2(A!6, A!3)))),
% 3.86/2.65 inference(unit_resolution,[status(thm)],[156, 151])).
% 3.86/2.65 tff(158,plain,
% 3.86/2.65 ((~(in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(A!6, A!3)), set_union2(B!5, A!6)) <=> (in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(A!6, A!3)), B!5) | in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(A!6, A!3)), set_union2(A!6, A!3))))) | in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(A!6, A!3)), set_union2(B!5, A!6)) | (~(in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(A!6, A!3)), B!5) | in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(A!6, A!3)), set_union2(A!6, A!3))))),
% 3.86/2.65 inference(tautology,[status(thm)],[])).
% 3.86/2.66 tff(159,plain,
% 3.86/2.66 (in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(A!6, A!3)), set_union2(B!5, A!6)) | (~(in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(A!6, A!3)), B!5) | in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(A!6, A!3)), set_union2(A!6, A!3))))),
% 3.86/2.66 inference(unit_resolution,[status(thm)],[158, 157])).
% 3.86/2.66 tff(160,plain,
% 3.86/2.66 ($false),
% 3.86/2.66 inference(unit_resolution,[status(thm)],[159, 116, 52])).
% 3.86/2.66 tff(161,plain,(in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(A!6, A!3)), set_difference(set_union2(A!6, B!5), B!5)) | in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(A!6, A!3)), B!5)), inference(lemma,lemma(discharge,[]))).
% 3.86/2.66 tff(162,plain,
% 3.86/2.66 (in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(A!6, A!3)), set_difference(set_union2(A!6, B!5), B!5))),
% 3.86/2.66 inference(unit_resolution,[status(thm)],[161, 1])).
% 3.86/2.66 tff(163,plain,
% 3.86/2.66 ((~(in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(A!6, A!3)), set_difference(set_union2(A!6, B!5), B!5)) <=> (~((~in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(A!6, A!3)), set_union2(B!5, A!6))) | in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(A!6, A!3)), B!5))))) | (~in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(A!6, A!3)), set_difference(set_union2(A!6, B!5), B!5))) | (~((~in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(A!6, A!3)), set_union2(B!5, A!6))) | in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(A!6, A!3)), B!5)))),
% 3.86/2.66 inference(tautology,[status(thm)],[])).
% 3.86/2.66 tff(164,plain,
% 3.86/2.66 ((~in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(A!6, A!3)), set_difference(set_union2(A!6, B!5), B!5))) | (~((~in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(A!6, A!3)), set_union2(B!5, A!6))) | in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(A!6, A!3)), B!5)))),
% 3.86/2.66 inference(unit_resolution,[status(thm)],[163, 47])).
% 3.86/2.66 tff(165,plain,
% 3.86/2.66 (~((~in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(A!6, A!3)), set_union2(B!5, A!6))) | in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(A!6, A!3)), B!5))),
% 3.86/2.66 inference(unit_resolution,[status(thm)],[164, 162])).
% 3.86/2.66 tff(166,plain,
% 3.86/2.66 (((~in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(A!6, A!3)), set_union2(B!5, A!6))) | in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(A!6, A!3)), B!5)) | in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(A!6, A!3)), set_union2(B!5, A!6))),
% 3.86/2.66 inference(tautology,[status(thm)],[])).
% 3.86/2.66 tff(167,plain,
% 3.86/2.66 (in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(A!6, A!3)), set_union2(B!5, A!6))),
% 3.86/2.66 inference(unit_resolution,[status(thm)],[166, 165])).
% 3.86/2.66 tff(168,plain,
% 3.86/2.66 ((~(in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(A!6, A!3)), set_difference(set_union2(A!6, B!5), B!5)) <=> ((~in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(A!6, A!3)), set_union2(A!6, A!3))) | in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(A!6, A!3)), B!5)))) | (~in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(A!6, A!3)), set_difference(set_union2(A!6, B!5), B!5))) | ((~in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(A!6, A!3)), set_union2(A!6, A!3))) | in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(A!6, A!3)), B!5))),
% 3.86/2.66 inference(tautology,[status(thm)],[])).
% 3.86/2.66 tff(169,plain,
% 3.86/2.66 ((~in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(A!6, A!3)), set_difference(set_union2(A!6, B!5), B!5))) | ((~in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(A!6, A!3)), set_union2(A!6, A!3))) | in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(A!6, A!3)), B!5))),
% 3.86/2.66 inference(unit_resolution,[status(thm)],[168, 109])).
% 3.86/2.66 tff(170,plain,
% 3.86/2.66 ((~in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(A!6, A!3)), set_union2(A!6, A!3))) | in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(A!6, A!3)), B!5)),
% 3.86/2.66 inference(unit_resolution,[status(thm)],[169, 162])).
% 3.86/2.66 tff(171,plain,
% 3.86/2.66 ((~((~in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(A!6, A!3)), set_union2(A!6, A!3))) | in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(A!6, A!3)), B!5))) | (~in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(A!6, A!3)), set_union2(A!6, A!3))) | in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(A!6, A!3)), B!5)),
% 3.86/2.66 inference(tautology,[status(thm)],[])).
% 3.86/2.66 tff(172,plain,
% 3.86/2.66 (~in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(A!6, A!3)), set_union2(A!6, A!3))),
% 3.86/2.66 inference(unit_resolution,[status(thm)],[171, 170, 1])).
% 3.86/2.66 tff(173,plain,
% 3.86/2.66 ((~(in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(A!6, A!3)), B!5) | in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(A!6, A!3)), set_union2(A!6, A!3)))) | in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(A!6, A!3)), B!5) | in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(A!6, A!3)), set_union2(A!6, A!3))),
% 3.86/2.66 inference(tautology,[status(thm)],[])).
% 3.86/2.66 tff(174,plain,
% 3.86/2.66 (~(in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(A!6, A!3)), B!5) | in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(A!6, A!3)), set_union2(A!6, A!3)))),
% 3.86/2.66 inference(unit_resolution,[status(thm)],[173, 172, 1])).
% 3.86/2.66 tff(175,plain,
% 3.86/2.66 ((~(in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(A!6, A!3)), set_union2(B!5, A!6)) <=> (in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(A!6, A!3)), B!5) | in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(A!6, A!3)), set_union2(A!6, A!3))))) | (~in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(A!6, A!3)), set_union2(B!5, A!6))) | (in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(A!6, A!3)), B!5) | in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(A!6, A!3)), set_union2(A!6, A!3)))),
% 3.86/2.66 inference(tautology,[status(thm)],[])).
% 3.86/2.66 tff(176,plain,
% 3.86/2.66 ((~in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(A!6, A!3)), set_union2(B!5, A!6))) | (in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(A!6, A!3)), B!5) | in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(A!6, A!3)), set_union2(A!6, A!3)))),
% 3.86/2.66 inference(unit_resolution,[status(thm)],[175, 157])).
% 3.86/2.66 tff(177,plain,
% 3.86/2.66 ($false),
% 3.86/2.66 inference(unit_resolution,[status(thm)],[176, 174, 167])).
% 3.86/2.66 tff(178,plain,(in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(A!6, A!3)), B!5)), inference(lemma,lemma(discharge,[]))).
% 3.86/2.66 tff(179,plain,
% 3.86/2.66 (((~in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(A!6, A!3)), set_union2(B!5, A!6))) | in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(A!6, A!3)), B!5)) | (~in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(A!6, A!3)), B!5))),
% 3.86/2.66 inference(tautology,[status(thm)],[])).
% 3.86/2.66 tff(180,plain,
% 3.86/2.66 ((~in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(A!6, A!3)), set_union2(B!5, A!6))) | in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(A!6, A!3)), B!5)),
% 3.86/2.66 inference(unit_resolution,[status(thm)],[179, 178])).
% 3.86/2.66 tff(181,plain,
% 3.86/2.66 (((~in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(A!6, A!3)), set_union2(A!6, A!3))) | in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(A!6, A!3)), B!5)) | (~in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(A!6, A!3)), B!5))),
% 3.86/2.66 inference(tautology,[status(thm)],[])).
% 3.86/2.66 tff(182,plain,
% 3.86/2.66 ((~in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(A!6, A!3)), set_union2(A!6, A!3))) | in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(A!6, A!3)), B!5)),
% 3.86/2.66 inference(unit_resolution,[status(thm)],[181, 178])).
% 3.86/2.66 tff(183,plain,
% 3.86/2.66 (in(tptp_fun_D_2(set_difference(set_union2(A!6, B!5), B!5), B!5, set_union2(A!6, A!3)), set_difference(set_union2(A!6, B!5), B!5))),
% 3.86/2.66 inference(unit_resolution,[status(thm)],[111, 182])).
% 3.86/2.66 tff(184,plain,
% 3.86/2.66 ($false),
% 3.86/2.66 inference(unit_resolution,[status(thm)],[164, 183, 180])).
% 3.86/2.66 % SZS output end Proof
%------------------------------------------------------------------------------