TSTP Solution File: SEU132+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SEU132+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n001.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 07:27:39 EDT 2022
% Result : Theorem 0.12s 0.40s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SEU132+1 : TPTP v8.1.0. Released v3.3.0.
% 0.12/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.34 % Computer : n001.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Sat Sep 3 09:56:40 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.35 Usage: tptp [options] [-file:]file
% 0.12/0.35 -h, -? prints this message.
% 0.12/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.35 -m, -model generate model.
% 0.12/0.35 -p, -proof generate proof.
% 0.12/0.35 -c, -core generate unsat core of named formulas.
% 0.12/0.35 -st, -statistics display statistics.
% 0.12/0.35 -t:timeout set timeout (in second).
% 0.12/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.35 -<param>:<value> configuration parameter and value.
% 0.12/0.35 -o:<output-file> file to place output in.
% 0.12/0.40 % SZS status Theorem
% 0.12/0.40 % SZS output start Proof
% 0.12/0.40 tff(in_type, type, (
% 0.12/0.40 in: ( $i * $i ) > $o)).
% 0.12/0.40 tff(tptp_fun_B_5_type, type, (
% 0.12/0.40 tptp_fun_B_5: $i)).
% 0.12/0.40 tff(tptp_fun_C_0_type, type, (
% 0.12/0.40 tptp_fun_C_0: ( $i * $i ) > $i)).
% 0.12/0.40 tff(set_difference_type, type, (
% 0.12/0.40 set_difference: ( $i * $i ) > $i)).
% 0.12/0.40 tff(tptp_fun_C_4_type, type, (
% 0.12/0.40 tptp_fun_C_4: $i)).
% 0.12/0.40 tff(tptp_fun_A_6_type, type, (
% 0.12/0.40 tptp_fun_A_6: $i)).
% 0.12/0.40 tff(tptp_fun_D_1_type, type, (
% 0.12/0.40 tptp_fun_D_1: ( $i * $i * $i ) > $i)).
% 0.12/0.40 tff(subset_type, type, (
% 0.12/0.40 subset: ( $i * $i ) > $o)).
% 0.12/0.40 tff(1,plain,
% 0.12/0.40 (^[A: $i, B: $i, C: $i, D: $i] : refl((~((~((~(C = set_difference(A, B))) | (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_1(C, B, A), C) <=> ((~in(tptp_fun_D_1(C, B, A), A)) | in(tptp_fun_D_1(C, B, A), B))))))) <=> (~((~((~(C = set_difference(A, B))) | (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_1(C, B, A), C) <=> ((~in(tptp_fun_D_1(C, B, A), A)) | in(tptp_fun_D_1(C, B, A), B))))))))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(2,plain,
% 0.12/0.40 (![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_difference(A, B))) | (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_1(C, B, A), C) <=> ((~in(tptp_fun_D_1(C, B, A), A)) | in(tptp_fun_D_1(C, B, A), B))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_difference(A, B))) | (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_1(C, B, A), C) <=> ((~in(tptp_fun_D_1(C, B, A), A)) | in(tptp_fun_D_1(C, B, A), B)))))))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[1])).
% 0.12/0.40 tff(3,plain,
% 0.12/0.40 (![A: $i, B: $i, C: $i] : ![D: $i] : (~((~((~(C = set_difference(A, B))) | (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_1(C, B, A), C) <=> ((~in(tptp_fun_D_1(C, B, A), A)) | in(tptp_fun_D_1(C, B, A), B))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_difference(A, B))) | (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_1(C, B, A), C) <=> ((~in(tptp_fun_D_1(C, B, A), A)) | in(tptp_fun_D_1(C, B, A), B)))))))),
% 0.12/0.40 inference(pull_quant,[status(thm)],[])).
% 0.12/0.40 tff(4,plain,
% 0.12/0.40 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(pull_quant(((~(C = set_difference(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, A)) | in(D, B))))) <=> ![D: $i] : ((~(C = set_difference(A, B))) | (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))), ((~((~(C = set_difference(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) <=> (~![D: $i] : ((~(C = set_difference(A, B))) | (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))))), pull_quant((~![D: $i] : ((~(C = set_difference(A, B))) | (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) <=> ?[D: $i] : (~((~(C = set_difference(A, B))) | (in(D, C) <=> (~((~in(D, A)) | in(D, B))))))), ((~((~(C = set_difference(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) <=> ?[D: $i] : (~((~(C = set_difference(A, B))) | (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))))), (((~((~(C = set_difference(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_1(C, B, A), C) <=> ((~in(tptp_fun_D_1(C, B, A), A)) | in(tptp_fun_D_1(C, B, A), B)))))) <=> (?[D: $i] : (~((~(C = set_difference(A, B))) | (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_1(C, B, A), C) <=> ((~in(tptp_fun_D_1(C, B, A), A)) | in(tptp_fun_D_1(C, B, A), B)))))))), pull_quant((?[D: $i] : (~((~(C = set_difference(A, B))) | (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_1(C, B, A), C) <=> ((~in(tptp_fun_D_1(C, B, A), A)) | in(tptp_fun_D_1(C, B, A), B)))))) <=> ?[D: $i] : ((~((~(C = set_difference(A, B))) | (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_1(C, B, A), C) <=> ((~in(tptp_fun_D_1(C, B, A), A)) | in(tptp_fun_D_1(C, B, A), B))))))), (((~((~(C = set_difference(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_1(C, B, A), C) <=> ((~in(tptp_fun_D_1(C, B, A), A)) | in(tptp_fun_D_1(C, B, A), B)))))) <=> ?[D: $i] : ((~((~(C = set_difference(A, B))) | (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_1(C, B, A), C) <=> ((~in(tptp_fun_D_1(C, B, A), A)) | in(tptp_fun_D_1(C, B, A), B)))))))), ((~((~((~(C = set_difference(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_1(C, B, A), C) <=> ((~in(tptp_fun_D_1(C, B, A), A)) | in(tptp_fun_D_1(C, B, A), B))))))) <=> (~?[D: $i] : ((~((~(C = set_difference(A, B))) | (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_1(C, B, A), C) <=> ((~in(tptp_fun_D_1(C, B, A), A)) | in(tptp_fun_D_1(C, B, A), B))))))))), pull_quant((~?[D: $i] : ((~((~(C = set_difference(A, B))) | (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_1(C, B, A), C) <=> ((~in(tptp_fun_D_1(C, B, A), A)) | in(tptp_fun_D_1(C, B, A), B))))))) <=> ![D: $i] : (~((~((~(C = set_difference(A, B))) | (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_1(C, B, A), C) <=> ((~in(tptp_fun_D_1(C, B, A), A)) | in(tptp_fun_D_1(C, B, A), B)))))))), ((~((~((~(C = set_difference(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_1(C, B, A), C) <=> ((~in(tptp_fun_D_1(C, B, A), A)) | in(tptp_fun_D_1(C, B, A), B))))))) <=> ![D: $i] : (~((~((~(C = set_difference(A, B))) | (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_1(C, B, A), C) <=> ((~in(tptp_fun_D_1(C, B, A), A)) | in(tptp_fun_D_1(C, B, A), B)))))))))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(5,plain,
% 0.12/0.40 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_difference(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_1(C, B, A), C) <=> ((~in(tptp_fun_D_1(C, B, A), A)) | in(tptp_fun_D_1(C, B, A), B))))))) <=> ![A: $i, B: $i, C: $i] : ![D: $i] : (~((~((~(C = set_difference(A, B))) | (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_1(C, B, A), C) <=> ((~in(tptp_fun_D_1(C, B, A), A)) | in(tptp_fun_D_1(C, B, A), B)))))))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[4])).
% 0.12/0.40 tff(6,plain,
% 0.12/0.40 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_difference(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_1(C, B, A), C) <=> ((~in(tptp_fun_D_1(C, B, A), A)) | in(tptp_fun_D_1(C, B, A), B))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_difference(A, B))) | (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_1(C, B, A), C) <=> ((~in(tptp_fun_D_1(C, B, A), A)) | in(tptp_fun_D_1(C, B, A), B)))))))),
% 0.12/0.40 inference(transitivity,[status(thm)],[5, 3])).
% 0.12/0.40 tff(7,plain,
% 0.12/0.40 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_difference(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_1(C, B, A), C) <=> ((~in(tptp_fun_D_1(C, B, A), A)) | in(tptp_fun_D_1(C, B, A), B))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_difference(A, B))) | (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_1(C, B, A), C) <=> ((~in(tptp_fun_D_1(C, B, A), A)) | in(tptp_fun_D_1(C, B, A), B)))))))),
% 0.12/0.40 inference(transitivity,[status(thm)],[6, 2])).
% 0.12/0.40 tff(8,plain,
% 0.12/0.40 (^[A: $i, B: $i, C: $i] : rewrite((~((~((~(C = set_difference(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_1(C, B, A), C) <=> ((~in(tptp_fun_D_1(C, B, A), A)) | in(tptp_fun_D_1(C, B, A), B))))))) <=> (~((~((~(C = set_difference(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_1(C, B, A), C) <=> ((~in(tptp_fun_D_1(C, B, A), A)) | in(tptp_fun_D_1(C, B, A), B))))))))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(9,plain,
% 0.12/0.40 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_difference(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_1(C, B, A), C) <=> ((~in(tptp_fun_D_1(C, B, A), A)) | in(tptp_fun_D_1(C, B, A), B))))))) <=> ![A: $i, B: $i, C: $i] : (~((~((~(C = set_difference(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_1(C, B, A), C) <=> ((~in(tptp_fun_D_1(C, B, A), A)) | in(tptp_fun_D_1(C, B, A), B)))))))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[8])).
% 0.12/0.40 tff(10,plain,
% 0.12/0.40 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_difference(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_1(C, B, A), C) <=> ((~in(tptp_fun_D_1(C, B, A), A)) | in(tptp_fun_D_1(C, B, A), B))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_difference(A, B))) | (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_1(C, B, A), C) <=> ((~in(tptp_fun_D_1(C, B, A), A)) | in(tptp_fun_D_1(C, B, A), B)))))))),
% 0.12/0.40 inference(transitivity,[status(thm)],[9, 7])).
% 0.12/0.40 tff(11,plain,
% 0.12/0.40 (^[A: $i, B: $i, C: $i] : trans(monotonicity(rewrite(((~(C = set_difference(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) & (~in(D, B))))) <=> ((~(C = set_difference(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))), rewrite(((C = set_difference(A, B)) | ((~in(tptp_fun_D_1(C, B, A), C)) <=> (in(tptp_fun_D_1(C, B, A), A) & (~in(tptp_fun_D_1(C, B, A), B))))) <=> ((C = set_difference(A, B)) | (in(tptp_fun_D_1(C, B, A), C) <=> ((~in(tptp_fun_D_1(C, B, A), A)) | in(tptp_fun_D_1(C, B, A), B))))), ((((~(C = set_difference(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) & (~in(D, B))))) & ((C = set_difference(A, B)) | ((~in(tptp_fun_D_1(C, B, A), C)) <=> (in(tptp_fun_D_1(C, B, A), A) & (~in(tptp_fun_D_1(C, B, A), B)))))) <=> (((~(C = set_difference(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, A)) | in(D, B))))) & ((C = set_difference(A, B)) | (in(tptp_fun_D_1(C, B, A), C) <=> ((~in(tptp_fun_D_1(C, B, A), A)) | in(tptp_fun_D_1(C, B, A), B))))))), rewrite((((~(C = set_difference(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, A)) | in(D, B))))) & ((C = set_difference(A, B)) | (in(tptp_fun_D_1(C, B, A), C) <=> ((~in(tptp_fun_D_1(C, B, A), A)) | in(tptp_fun_D_1(C, B, A), B))))) <=> (~((~((~(C = set_difference(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_1(C, B, A), C) <=> ((~in(tptp_fun_D_1(C, B, A), A)) | in(tptp_fun_D_1(C, B, A), B)))))))), ((((~(C = set_difference(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) & (~in(D, B))))) & ((C = set_difference(A, B)) | ((~in(tptp_fun_D_1(C, B, A), C)) <=> (in(tptp_fun_D_1(C, B, A), A) & (~in(tptp_fun_D_1(C, B, A), B)))))) <=> (~((~((~(C = set_difference(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_1(C, B, A), C) <=> ((~in(tptp_fun_D_1(C, B, A), A)) | in(tptp_fun_D_1(C, B, A), B)))))))))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(12,plain,
% 0.12/0.40 (![A: $i, B: $i, C: $i] : (((~(C = set_difference(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) & (~in(D, B))))) & ((C = set_difference(A, B)) | ((~in(tptp_fun_D_1(C, B, A), C)) <=> (in(tptp_fun_D_1(C, B, A), A) & (~in(tptp_fun_D_1(C, B, A), B)))))) <=> ![A: $i, B: $i, C: $i] : (~((~((~(C = set_difference(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_1(C, B, A), C) <=> ((~in(tptp_fun_D_1(C, B, A), A)) | in(tptp_fun_D_1(C, B, A), B)))))))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[11])).
% 0.12/0.40 tff(13,plain,
% 0.12/0.40 (^[A: $i, B: $i, C: $i] : rewrite((((~(C = set_difference(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) & (~in(D, B))))) & ((C = set_difference(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), A) & (~in(tptp_fun_D_1(C, B, A), B))))))) <=> (((~(C = set_difference(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) & (~in(D, B))))) & ((C = set_difference(A, B)) | ((~in(tptp_fun_D_1(C, B, A), C)) <=> (in(tptp_fun_D_1(C, B, A), A) & (~in(tptp_fun_D_1(C, B, A), B)))))))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(14,plain,
% 0.12/0.40 (![A: $i, B: $i, C: $i] : (((~(C = set_difference(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) & (~in(D, B))))) & ((C = set_difference(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), A) & (~in(tptp_fun_D_1(C, B, A), B))))))) <=> ![A: $i, B: $i, C: $i] : (((~(C = set_difference(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) & (~in(D, B))))) & ((C = set_difference(A, B)) | ((~in(tptp_fun_D_1(C, B, A), C)) <=> (in(tptp_fun_D_1(C, B, A), A) & (~in(tptp_fun_D_1(C, B, A), B))))))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[13])).
% 0.12/0.40 tff(15,plain,
% 0.12/0.40 (![A: $i, B: $i, C: $i] : ((C = set_difference(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, A) & (~in(D, B))))) <=> ![A: $i, B: $i, C: $i] : ((C = set_difference(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, A) & (~in(D, B)))))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(16,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/sandbox/benchmark/theBenchmark.p','d4_xboole_0')).
% 0.12/0.40 tff(17,plain,
% 0.12/0.40 (![A: $i, B: $i, C: $i] : ((C = set_difference(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, A) & (~in(D, B)))))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[16, 15])).
% 0.12/0.40 tff(18,plain,(
% 0.12/0.40 ![A: $i, B: $i, C: $i] : (((~(C = set_difference(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) & (~in(D, B))))) & ((C = set_difference(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), A) & (~in(tptp_fun_D_1(C, B, A), B)))))))),
% 0.12/0.40 inference(skolemize,[status(sab)],[17])).
% 0.12/0.40 tff(19,plain,
% 0.12/0.40 (![A: $i, B: $i, C: $i] : (((~(C = set_difference(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) & (~in(D, B))))) & ((C = set_difference(A, B)) | ((~in(tptp_fun_D_1(C, B, A), C)) <=> (in(tptp_fun_D_1(C, B, A), A) & (~in(tptp_fun_D_1(C, B, A), B))))))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[18, 14])).
% 0.12/0.40 tff(20,plain,
% 0.12/0.40 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_difference(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_1(C, B, A), C) <=> ((~in(tptp_fun_D_1(C, B, A), A)) | in(tptp_fun_D_1(C, B, A), B)))))))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[19, 12])).
% 0.12/0.40 tff(21,plain,
% 0.12/0.40 (![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_difference(A, B))) | (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_1(C, B, A), C) <=> ((~in(tptp_fun_D_1(C, B, A), A)) | in(tptp_fun_D_1(C, B, A), B)))))))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[20, 10])).
% 0.12/0.40 tff(22,plain,
% 0.12/0.40 (((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_difference(A, B))) | (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_1(C, B, A), C) <=> ((~in(tptp_fun_D_1(C, B, A), A)) | in(tptp_fun_D_1(C, B, A), B)))))))) | ((~in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), set_difference(B!5, C!4))) <=> ((~in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), B!5)) | in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), C!4)))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_difference(A, B))) | (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_1(C, B, A), C) <=> ((~in(tptp_fun_D_1(C, B, A), A)) | in(tptp_fun_D_1(C, B, A), B)))))))) | ((~in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), set_difference(B!5, C!4))) <=> ((~in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), B!5)) | in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), C!4))))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(23,plain,
% 0.12/0.40 ((~(in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), set_difference(B!5, C!4)) <=> ((~in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), B!5)) | in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), C!4)))) <=> ((~in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), set_difference(B!5, C!4))) <=> ((~in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), B!5)) | in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), C!4)))),
% 0.12/0.41 inference(rewrite,[status(thm)],[])).
% 0.12/0.41 tff(24,plain,
% 0.12/0.41 (((in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), set_difference(B!5, C!4)) <=> ((~in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), B!5)) | in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), C!4))) | $false) <=> (in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), set_difference(B!5, C!4)) <=> ((~in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), B!5)) | in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), C!4)))),
% 0.12/0.41 inference(rewrite,[status(thm)],[])).
% 0.12/0.41 tff(25,plain,
% 0.12/0.41 ((~$true) <=> $false),
% 0.12/0.41 inference(rewrite,[status(thm)],[])).
% 0.12/0.41 tff(26,plain,
% 0.12/0.41 (($true | (in(tptp_fun_D_1(set_difference(B!5, C!4), C!4, B!5), set_difference(B!5, C!4)) <=> ((~in(tptp_fun_D_1(set_difference(B!5, C!4), C!4, B!5), B!5)) | in(tptp_fun_D_1(set_difference(B!5, C!4), C!4, B!5), C!4)))) <=> $true),
% 0.12/0.41 inference(rewrite,[status(thm)],[])).
% 0.12/0.41 tff(27,plain,
% 0.12/0.41 ((set_difference(B!5, C!4) = set_difference(B!5, C!4)) <=> $true),
% 0.12/0.41 inference(rewrite,[status(thm)],[])).
% 0.12/0.41 tff(28,plain,
% 0.12/0.41 (((set_difference(B!5, C!4) = set_difference(B!5, C!4)) | (in(tptp_fun_D_1(set_difference(B!5, C!4), C!4, B!5), set_difference(B!5, C!4)) <=> ((~in(tptp_fun_D_1(set_difference(B!5, C!4), C!4, B!5), B!5)) | in(tptp_fun_D_1(set_difference(B!5, C!4), C!4, B!5), C!4)))) <=> ($true | (in(tptp_fun_D_1(set_difference(B!5, C!4), C!4, B!5), set_difference(B!5, C!4)) <=> ((~in(tptp_fun_D_1(set_difference(B!5, C!4), C!4, B!5), B!5)) | in(tptp_fun_D_1(set_difference(B!5, C!4), C!4, B!5), C!4))))),
% 0.12/0.41 inference(monotonicity,[status(thm)],[27])).
% 0.12/0.41 tff(29,plain,
% 0.12/0.41 (((set_difference(B!5, C!4) = set_difference(B!5, C!4)) | (in(tptp_fun_D_1(set_difference(B!5, C!4), C!4, B!5), set_difference(B!5, C!4)) <=> ((~in(tptp_fun_D_1(set_difference(B!5, C!4), C!4, B!5), B!5)) | in(tptp_fun_D_1(set_difference(B!5, C!4), C!4, B!5), C!4)))) <=> $true),
% 0.12/0.41 inference(transitivity,[status(thm)],[28, 26])).
% 0.12/0.41 tff(30,plain,
% 0.12/0.41 ((~((set_difference(B!5, C!4) = set_difference(B!5, C!4)) | (in(tptp_fun_D_1(set_difference(B!5, C!4), C!4, B!5), set_difference(B!5, C!4)) <=> ((~in(tptp_fun_D_1(set_difference(B!5, C!4), C!4, B!5), B!5)) | in(tptp_fun_D_1(set_difference(B!5, C!4), C!4, B!5), C!4))))) <=> (~$true)),
% 0.12/0.41 inference(monotonicity,[status(thm)],[29])).
% 0.12/0.41 tff(31,plain,
% 0.12/0.41 ((~((set_difference(B!5, C!4) = set_difference(B!5, C!4)) | (in(tptp_fun_D_1(set_difference(B!5, C!4), C!4, B!5), set_difference(B!5, C!4)) <=> ((~in(tptp_fun_D_1(set_difference(B!5, C!4), C!4, B!5), B!5)) | in(tptp_fun_D_1(set_difference(B!5, C!4), C!4, B!5), C!4))))) <=> $false),
% 0.12/0.41 inference(transitivity,[status(thm)],[30, 25])).
% 0.12/0.41 tff(32,plain,
% 0.12/0.41 ((~(in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), set_difference(B!5, C!4)) <=> (~((~in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), B!5)) | in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), C!4))))) <=> (in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), set_difference(B!5, C!4)) <=> ((~in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), B!5)) | in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), C!4)))),
% 0.12/0.41 inference(rewrite,[status(thm)],[])).
% 0.12/0.41 tff(33,plain,
% 0.12/0.41 (($false | (in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), set_difference(B!5, C!4)) <=> (~((~in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), B!5)) | in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), C!4))))) <=> (in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), set_difference(B!5, C!4)) <=> (~((~in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), B!5)) | in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), C!4))))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(34,plain,
% 0.21/0.41 ((~(set_difference(B!5, C!4) = set_difference(B!5, C!4))) <=> (~$true)),
% 0.21/0.41 inference(monotonicity,[status(thm)],[27])).
% 0.21/0.41 tff(35,plain,
% 0.21/0.41 ((~(set_difference(B!5, C!4) = set_difference(B!5, C!4))) <=> $false),
% 0.21/0.41 inference(transitivity,[status(thm)],[34, 25])).
% 0.21/0.41 tff(36,plain,
% 0.21/0.41 (((~(set_difference(B!5, C!4) = set_difference(B!5, C!4))) | (in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), set_difference(B!5, C!4)) <=> (~((~in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), B!5)) | in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), C!4))))) <=> ($false | (in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), set_difference(B!5, C!4)) <=> (~((~in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), B!5)) | in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), C!4)))))),
% 0.21/0.41 inference(monotonicity,[status(thm)],[35])).
% 0.21/0.41 tff(37,plain,
% 0.21/0.41 (((~(set_difference(B!5, C!4) = set_difference(B!5, C!4))) | (in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), set_difference(B!5, C!4)) <=> (~((~in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), B!5)) | in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), C!4))))) <=> (in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), set_difference(B!5, C!4)) <=> (~((~in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), B!5)) | in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), C!4))))),
% 0.21/0.41 inference(transitivity,[status(thm)],[36, 33])).
% 0.21/0.41 tff(38,plain,
% 0.21/0.41 ((~((~(set_difference(B!5, C!4) = set_difference(B!5, C!4))) | (in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), set_difference(B!5, C!4)) <=> (~((~in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), B!5)) | in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), C!4)))))) <=> (~(in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), set_difference(B!5, C!4)) <=> (~((~in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), B!5)) | in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), C!4)))))),
% 0.21/0.41 inference(monotonicity,[status(thm)],[37])).
% 0.21/0.41 tff(39,plain,
% 0.21/0.41 ((~((~(set_difference(B!5, C!4) = set_difference(B!5, C!4))) | (in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), set_difference(B!5, C!4)) <=> (~((~in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), B!5)) | in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), C!4)))))) <=> (in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), set_difference(B!5, C!4)) <=> ((~in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), B!5)) | in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), C!4)))),
% 0.21/0.41 inference(transitivity,[status(thm)],[38, 32])).
% 0.21/0.41 tff(40,plain,
% 0.21/0.41 (((~((~(set_difference(B!5, C!4) = set_difference(B!5, C!4))) | (in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), set_difference(B!5, C!4)) <=> (~((~in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), B!5)) | in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), C!4)))))) | (~((set_difference(B!5, C!4) = set_difference(B!5, C!4)) | (in(tptp_fun_D_1(set_difference(B!5, C!4), C!4, B!5), set_difference(B!5, C!4)) <=> ((~in(tptp_fun_D_1(set_difference(B!5, C!4), C!4, B!5), B!5)) | in(tptp_fun_D_1(set_difference(B!5, C!4), C!4, B!5), C!4)))))) <=> ((in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), set_difference(B!5, C!4)) <=> ((~in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), B!5)) | in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), C!4))) | $false)),
% 0.21/0.41 inference(monotonicity,[status(thm)],[39, 31])).
% 0.21/0.41 tff(41,plain,
% 0.21/0.41 (((~((~(set_difference(B!5, C!4) = set_difference(B!5, C!4))) | (in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), set_difference(B!5, C!4)) <=> (~((~in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), B!5)) | in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), C!4)))))) | (~((set_difference(B!5, C!4) = set_difference(B!5, C!4)) | (in(tptp_fun_D_1(set_difference(B!5, C!4), C!4, B!5), set_difference(B!5, C!4)) <=> ((~in(tptp_fun_D_1(set_difference(B!5, C!4), C!4, B!5), B!5)) | in(tptp_fun_D_1(set_difference(B!5, C!4), C!4, B!5), C!4)))))) <=> (in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), set_difference(B!5, C!4)) <=> ((~in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), B!5)) | in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), C!4)))),
% 0.21/0.42 inference(transitivity,[status(thm)],[40, 24])).
% 0.21/0.42 tff(42,plain,
% 0.21/0.42 ((~((~((~(set_difference(B!5, C!4) = set_difference(B!5, C!4))) | (in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), set_difference(B!5, C!4)) <=> (~((~in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), B!5)) | in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), C!4)))))) | (~((set_difference(B!5, C!4) = set_difference(B!5, C!4)) | (in(tptp_fun_D_1(set_difference(B!5, C!4), C!4, B!5), set_difference(B!5, C!4)) <=> ((~in(tptp_fun_D_1(set_difference(B!5, C!4), C!4, B!5), B!5)) | in(tptp_fun_D_1(set_difference(B!5, C!4), C!4, B!5), C!4))))))) <=> (~(in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), set_difference(B!5, C!4)) <=> ((~in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), B!5)) | in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), C!4))))),
% 0.21/0.42 inference(monotonicity,[status(thm)],[41])).
% 0.21/0.42 tff(43,plain,
% 0.21/0.42 ((~((~((~(set_difference(B!5, C!4) = set_difference(B!5, C!4))) | (in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), set_difference(B!5, C!4)) <=> (~((~in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), B!5)) | in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), C!4)))))) | (~((set_difference(B!5, C!4) = set_difference(B!5, C!4)) | (in(tptp_fun_D_1(set_difference(B!5, C!4), C!4, B!5), set_difference(B!5, C!4)) <=> ((~in(tptp_fun_D_1(set_difference(B!5, C!4), C!4, B!5), B!5)) | in(tptp_fun_D_1(set_difference(B!5, C!4), C!4, B!5), C!4))))))) <=> ((~in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), set_difference(B!5, C!4))) <=> ((~in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), B!5)) | in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), C!4)))),
% 0.21/0.42 inference(transitivity,[status(thm)],[42, 23])).
% 0.21/0.42 tff(44,plain,
% 0.21/0.42 (((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_difference(A, B))) | (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_1(C, B, A), C) <=> ((~in(tptp_fun_D_1(C, B, A), A)) | in(tptp_fun_D_1(C, B, A), B)))))))) | (~((~((~(set_difference(B!5, C!4) = set_difference(B!5, C!4))) | (in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), set_difference(B!5, C!4)) <=> (~((~in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), B!5)) | in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), C!4)))))) | (~((set_difference(B!5, C!4) = set_difference(B!5, C!4)) | (in(tptp_fun_D_1(set_difference(B!5, C!4), C!4, B!5), set_difference(B!5, C!4)) <=> ((~in(tptp_fun_D_1(set_difference(B!5, C!4), C!4, B!5), B!5)) | in(tptp_fun_D_1(set_difference(B!5, C!4), C!4, B!5), C!4)))))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_difference(A, B))) | (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_1(C, B, A), C) <=> ((~in(tptp_fun_D_1(C, B, A), A)) | in(tptp_fun_D_1(C, B, A), B)))))))) | ((~in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), set_difference(B!5, C!4))) <=> ((~in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), B!5)) | in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), C!4))))),
% 0.21/0.42 inference(monotonicity,[status(thm)],[43])).
% 0.21/0.42 tff(45,plain,
% 0.21/0.42 (((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_difference(A, B))) | (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_1(C, B, A), C) <=> ((~in(tptp_fun_D_1(C, B, A), A)) | in(tptp_fun_D_1(C, B, A), B)))))))) | (~((~((~(set_difference(B!5, C!4) = set_difference(B!5, C!4))) | (in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), set_difference(B!5, C!4)) <=> (~((~in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), B!5)) | in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), C!4)))))) | (~((set_difference(B!5, C!4) = set_difference(B!5, C!4)) | (in(tptp_fun_D_1(set_difference(B!5, C!4), C!4, B!5), set_difference(B!5, C!4)) <=> ((~in(tptp_fun_D_1(set_difference(B!5, C!4), C!4, B!5), B!5)) | in(tptp_fun_D_1(set_difference(B!5, C!4), C!4, B!5), C!4)))))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_difference(A, B))) | (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_1(C, B, A), C) <=> ((~in(tptp_fun_D_1(C, B, A), A)) | in(tptp_fun_D_1(C, B, A), B)))))))) | ((~in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), set_difference(B!5, C!4))) <=> ((~in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), B!5)) | in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), C!4))))),
% 0.21/0.42 inference(transitivity,[status(thm)],[44, 22])).
% 0.21/0.42 tff(46,plain,
% 0.21/0.42 ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_difference(A, B))) | (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_1(C, B, A), C) <=> ((~in(tptp_fun_D_1(C, B, A), A)) | in(tptp_fun_D_1(C, B, A), B)))))))) | (~((~((~(set_difference(B!5, C!4) = set_difference(B!5, C!4))) | (in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), set_difference(B!5, C!4)) <=> (~((~in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), B!5)) | in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), C!4)))))) | (~((set_difference(B!5, C!4) = set_difference(B!5, C!4)) | (in(tptp_fun_D_1(set_difference(B!5, C!4), C!4, B!5), set_difference(B!5, C!4)) <=> ((~in(tptp_fun_D_1(set_difference(B!5, C!4), C!4, B!5), B!5)) | in(tptp_fun_D_1(set_difference(B!5, C!4), C!4, B!5), C!4)))))))),
% 0.21/0.42 inference(quant_inst,[status(thm)],[])).
% 0.21/0.42 tff(47,plain,
% 0.21/0.42 ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_difference(A, B))) | (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_1(C, B, A), C) <=> ((~in(tptp_fun_D_1(C, B, A), A)) | in(tptp_fun_D_1(C, B, A), B)))))))) | ((~in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), set_difference(B!5, C!4))) <=> ((~in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), B!5)) | in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), C!4)))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[46, 45])).
% 0.21/0.42 tff(48,plain,
% 0.21/0.42 ((~in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), set_difference(B!5, C!4))) <=> ((~in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), B!5)) | in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), C!4))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[47, 21])).
% 0.21/0.42 tff(49,plain,
% 0.21/0.42 (^[A: $i, B: $i] : refl((~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B))))))) <=> (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B))))))))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(50,plain,
% 0.21/0.42 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B))))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B)))))))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[49])).
% 0.21/0.42 tff(51,plain,
% 0.21/0.42 (^[A: $i, B: $i] : rewrite((~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B))))))) <=> (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B))))))))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(52,plain,
% 0.21/0.42 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B))))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B)))))))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[51])).
% 0.21/0.42 tff(53,plain,
% 0.21/0.42 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B))))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B)))))))),
% 0.21/0.42 inference(transitivity,[status(thm)],[52, 50])).
% 0.21/0.42 tff(54,plain,
% 0.21/0.42 (^[A: $i, B: $i] : trans(monotonicity(rewrite(((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) <=> ((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))), rewrite((subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B)))) <=> (subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B))))), ((((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B))))) <=> (((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B))))))), rewrite((((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B))))) <=> (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B)))))))), ((((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B))))) <=> (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B)))))))))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(55,plain,
% 0.21/0.42 (![A: $i, B: $i] : (((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B)))))))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[54])).
% 0.21/0.42 tff(56,plain,
% 0.21/0.42 (![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B))) <=> ![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B)))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(57,plain,
% 0.21/0.42 (^[A: $i, B: $i] : rewrite((subset(A, B) <=> ![C: $i] : (in(C, A) => in(C, B))) <=> (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B))))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(58,plain,
% 0.21/0.42 (![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : (in(C, A) => in(C, B))) <=> ![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B)))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[57])).
% 0.21/0.42 tff(59,axiom,(![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : (in(C, A) => in(C, B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d3_tarski')).
% 0.21/0.42 tff(60,plain,
% 0.21/0.42 (![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B)))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[59, 58])).
% 0.21/0.42 tff(61,plain,
% 0.21/0.42 (![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B)))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[60, 56])).
% 0.21/0.42 tff(62,plain,(
% 0.21/0.42 ![A: $i, B: $i] : (((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B)))))),
% 0.21/0.43 inference(skolemize,[status(sab)],[61])).
% 0.21/0.43 tff(63,plain,
% 0.21/0.43 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B)))))))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[62, 55])).
% 0.21/0.43 tff(64,plain,
% 0.21/0.43 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B)))))))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[63, 53])).
% 0.21/0.43 tff(65,plain,
% 0.21/0.43 ((~![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B)))))))) | (~((~((~subset(set_difference(A!6, C!4), set_difference(B!5, C!4))) | ![C: $i] : ((~in(C, set_difference(A!6, C!4))) | in(C, set_difference(B!5, C!4))))) | (~(subset(set_difference(A!6, C!4), set_difference(B!5, C!4)) | (~((~in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), set_difference(A!6, C!4))) | in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), set_difference(B!5, C!4))))))))),
% 0.21/0.43 inference(quant_inst,[status(thm)],[])).
% 0.21/0.43 tff(66,plain,
% 0.21/0.43 (~((~((~subset(set_difference(A!6, C!4), set_difference(B!5, C!4))) | ![C: $i] : ((~in(C, set_difference(A!6, C!4))) | in(C, set_difference(B!5, C!4))))) | (~(subset(set_difference(A!6, C!4), set_difference(B!5, C!4)) | (~((~in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), set_difference(A!6, C!4))) | in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), set_difference(B!5, C!4)))))))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[65, 64])).
% 0.21/0.43 tff(67,plain,
% 0.21/0.43 (((~((~subset(set_difference(A!6, C!4), set_difference(B!5, C!4))) | ![C: $i] : ((~in(C, set_difference(A!6, C!4))) | in(C, set_difference(B!5, C!4))))) | (~(subset(set_difference(A!6, C!4), set_difference(B!5, C!4)) | (~((~in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), set_difference(A!6, C!4))) | in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), set_difference(B!5, C!4))))))) | (subset(set_difference(A!6, C!4), set_difference(B!5, C!4)) | (~((~in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), set_difference(A!6, C!4))) | in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), set_difference(B!5, C!4)))))),
% 0.21/0.43 inference(tautology,[status(thm)],[])).
% 0.21/0.43 tff(68,plain,
% 0.21/0.43 (subset(set_difference(A!6, C!4), set_difference(B!5, C!4)) | (~((~in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), set_difference(A!6, C!4))) | in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), set_difference(B!5, C!4))))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[67, 66])).
% 0.21/0.43 tff(69,plain,
% 0.21/0.43 ((~![A: $i, B: $i, C: $i] : ((~subset(A, B)) | subset(set_difference(A, C), set_difference(B, C)))) <=> (~![A: $i, B: $i, C: $i] : ((~subset(A, B)) | subset(set_difference(A, C), set_difference(B, C))))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(70,plain,
% 0.21/0.43 ((~![A: $i, B: $i, C: $i] : (subset(A, B) => subset(set_difference(A, C), set_difference(B, C)))) <=> (~![A: $i, B: $i, C: $i] : ((~subset(A, B)) | subset(set_difference(A, C), set_difference(B, C))))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(71,axiom,(~![A: $i, B: $i, C: $i] : (subset(A, B) => subset(set_difference(A, C), set_difference(B, C)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t33_xboole_1')).
% 0.21/0.43 tff(72,plain,
% 0.21/0.43 (~![A: $i, B: $i, C: $i] : ((~subset(A, B)) | subset(set_difference(A, C), set_difference(B, C)))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[71, 70])).
% 0.21/0.43 tff(73,plain,
% 0.21/0.43 (~![A: $i, B: $i, C: $i] : ((~subset(A, B)) | subset(set_difference(A, C), set_difference(B, C)))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[72, 69])).
% 0.21/0.43 tff(74,plain,
% 0.21/0.43 (~![A: $i, B: $i, C: $i] : ((~subset(A, B)) | subset(set_difference(A, C), set_difference(B, C)))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[73, 69])).
% 0.21/0.43 tff(75,plain,
% 0.21/0.43 (~![A: $i, B: $i, C: $i] : ((~subset(A, B)) | subset(set_difference(A, C), set_difference(B, C)))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[74, 69])).
% 0.21/0.43 tff(76,plain,
% 0.21/0.43 (~![A: $i, B: $i, C: $i] : ((~subset(A, B)) | subset(set_difference(A, C), set_difference(B, C)))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[75, 69])).
% 0.21/0.43 tff(77,plain,
% 0.21/0.43 (~![A: $i, B: $i, C: $i] : ((~subset(A, B)) | subset(set_difference(A, C), set_difference(B, C)))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[76, 69])).
% 0.21/0.43 tff(78,plain,
% 0.21/0.43 (~![A: $i, B: $i, C: $i] : ((~subset(A, B)) | subset(set_difference(A, C), set_difference(B, C)))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[77, 69])).
% 0.21/0.43 tff(79,plain,(
% 0.21/0.43 ~((~subset(A!6, B!5)) | subset(set_difference(A!6, C!4), set_difference(B!5, C!4)))),
% 0.21/0.43 inference(skolemize,[status(sab)],[78])).
% 0.21/0.43 tff(80,plain,
% 0.21/0.43 (~subset(set_difference(A!6, C!4), set_difference(B!5, C!4))),
% 0.21/0.43 inference(or_elim,[status(thm)],[79])).
% 0.21/0.43 tff(81,plain,
% 0.21/0.43 ((~(subset(set_difference(A!6, C!4), set_difference(B!5, C!4)) | (~((~in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), set_difference(A!6, C!4))) | in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), set_difference(B!5, C!4)))))) | subset(set_difference(A!6, C!4), set_difference(B!5, C!4)) | (~((~in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), set_difference(A!6, C!4))) | in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), set_difference(B!5, C!4))))),
% 0.21/0.43 inference(tautology,[status(thm)],[])).
% 0.21/0.43 tff(82,plain,
% 0.21/0.43 ((~(subset(set_difference(A!6, C!4), set_difference(B!5, C!4)) | (~((~in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), set_difference(A!6, C!4))) | in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), set_difference(B!5, C!4)))))) | (~((~in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), set_difference(A!6, C!4))) | in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), set_difference(B!5, C!4))))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[81, 80])).
% 0.21/0.43 tff(83,plain,
% 0.21/0.43 (~((~in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), set_difference(A!6, C!4))) | in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), set_difference(B!5, C!4)))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[82, 68])).
% 0.21/0.43 tff(84,plain,
% 0.21/0.43 (((~in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), set_difference(A!6, C!4))) | in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), set_difference(B!5, C!4))) | (~in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), set_difference(B!5, C!4)))),
% 0.21/0.43 inference(tautology,[status(thm)],[])).
% 0.21/0.43 tff(85,plain,
% 0.21/0.43 (~in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), set_difference(B!5, C!4))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[84, 83])).
% 0.21/0.43 tff(86,plain,
% 0.21/0.43 ((~((~in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), set_difference(B!5, C!4))) <=> ((~in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), B!5)) | in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), C!4)))) | in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), set_difference(B!5, C!4)) | ((~in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), B!5)) | in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), C!4))),
% 0.21/0.43 inference(tautology,[status(thm)],[])).
% 0.21/0.43 tff(87,plain,
% 0.21/0.43 ((~((~in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), set_difference(B!5, C!4))) <=> ((~in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), B!5)) | in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), C!4)))) | ((~in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), B!5)) | in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), C!4))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[86, 85])).
% 0.21/0.43 tff(88,plain,
% 0.21/0.43 ((~in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), B!5)) | in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), C!4)),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[87, 48])).
% 0.21/0.43 tff(89,plain,
% 0.21/0.43 (((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_difference(A, B))) | (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_1(C, B, A), C) <=> ((~in(tptp_fun_D_1(C, B, A), A)) | in(tptp_fun_D_1(C, B, A), B)))))))) | ((~in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), set_difference(A!6, C!4))) <=> ((~in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), A!6)) | in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), C!4)))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_difference(A, B))) | (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_1(C, B, A), C) <=> ((~in(tptp_fun_D_1(C, B, A), A)) | in(tptp_fun_D_1(C, B, A), B)))))))) | ((~in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), set_difference(A!6, C!4))) <=> ((~in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), A!6)) | in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), C!4))))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(90,plain,
% 0.21/0.43 ((~(in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), set_difference(A!6, C!4)) <=> ((~in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), A!6)) | in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), C!4)))) <=> ((~in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), set_difference(A!6, C!4))) <=> ((~in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), A!6)) | in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), C!4)))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(91,plain,
% 0.21/0.43 (((in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), set_difference(A!6, C!4)) <=> ((~in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), A!6)) | in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), C!4))) | $false) <=> (in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), set_difference(A!6, C!4)) <=> ((~in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), A!6)) | in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), C!4)))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(92,plain,
% 0.21/0.43 (($true | (in(tptp_fun_D_1(set_difference(A!6, C!4), C!4, A!6), set_difference(A!6, C!4)) <=> ((~in(tptp_fun_D_1(set_difference(A!6, C!4), C!4, A!6), A!6)) | in(tptp_fun_D_1(set_difference(A!6, C!4), C!4, A!6), C!4)))) <=> $true),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(93,plain,
% 0.21/0.43 ((set_difference(A!6, C!4) = set_difference(A!6, C!4)) <=> $true),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(94,plain,
% 0.21/0.43 (((set_difference(A!6, C!4) = set_difference(A!6, C!4)) | (in(tptp_fun_D_1(set_difference(A!6, C!4), C!4, A!6), set_difference(A!6, C!4)) <=> ((~in(tptp_fun_D_1(set_difference(A!6, C!4), C!4, A!6), A!6)) | in(tptp_fun_D_1(set_difference(A!6, C!4), C!4, A!6), C!4)))) <=> ($true | (in(tptp_fun_D_1(set_difference(A!6, C!4), C!4, A!6), set_difference(A!6, C!4)) <=> ((~in(tptp_fun_D_1(set_difference(A!6, C!4), C!4, A!6), A!6)) | in(tptp_fun_D_1(set_difference(A!6, C!4), C!4, A!6), C!4))))),
% 0.21/0.43 inference(monotonicity,[status(thm)],[93])).
% 0.21/0.43 tff(95,plain,
% 0.21/0.43 (((set_difference(A!6, C!4) = set_difference(A!6, C!4)) | (in(tptp_fun_D_1(set_difference(A!6, C!4), C!4, A!6), set_difference(A!6, C!4)) <=> ((~in(tptp_fun_D_1(set_difference(A!6, C!4), C!4, A!6), A!6)) | in(tptp_fun_D_1(set_difference(A!6, C!4), C!4, A!6), C!4)))) <=> $true),
% 0.21/0.43 inference(transitivity,[status(thm)],[94, 92])).
% 0.21/0.43 tff(96,plain,
% 0.21/0.43 ((~((set_difference(A!6, C!4) = set_difference(A!6, C!4)) | (in(tptp_fun_D_1(set_difference(A!6, C!4), C!4, A!6), set_difference(A!6, C!4)) <=> ((~in(tptp_fun_D_1(set_difference(A!6, C!4), C!4, A!6), A!6)) | in(tptp_fun_D_1(set_difference(A!6, C!4), C!4, A!6), C!4))))) <=> (~$true)),
% 0.21/0.43 inference(monotonicity,[status(thm)],[95])).
% 0.21/0.43 tff(97,plain,
% 0.21/0.44 ((~((set_difference(A!6, C!4) = set_difference(A!6, C!4)) | (in(tptp_fun_D_1(set_difference(A!6, C!4), C!4, A!6), set_difference(A!6, C!4)) <=> ((~in(tptp_fun_D_1(set_difference(A!6, C!4), C!4, A!6), A!6)) | in(tptp_fun_D_1(set_difference(A!6, C!4), C!4, A!6), C!4))))) <=> $false),
% 0.21/0.44 inference(transitivity,[status(thm)],[96, 25])).
% 0.21/0.44 tff(98,plain,
% 0.21/0.44 ((~(in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), set_difference(A!6, C!4)) <=> (~((~in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), A!6)) | in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), C!4))))) <=> (in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), set_difference(A!6, C!4)) <=> ((~in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), A!6)) | in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), C!4)))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(99,plain,
% 0.21/0.44 (($false | (in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), set_difference(A!6, C!4)) <=> (~((~in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), A!6)) | in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), C!4))))) <=> (in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), set_difference(A!6, C!4)) <=> (~((~in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), A!6)) | in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), C!4))))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(100,plain,
% 0.21/0.44 ((~(set_difference(A!6, C!4) = set_difference(A!6, C!4))) <=> (~$true)),
% 0.21/0.44 inference(monotonicity,[status(thm)],[93])).
% 0.21/0.44 tff(101,plain,
% 0.21/0.44 ((~(set_difference(A!6, C!4) = set_difference(A!6, C!4))) <=> $false),
% 0.21/0.44 inference(transitivity,[status(thm)],[100, 25])).
% 0.21/0.44 tff(102,plain,
% 0.21/0.44 (((~(set_difference(A!6, C!4) = set_difference(A!6, C!4))) | (in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), set_difference(A!6, C!4)) <=> (~((~in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), A!6)) | in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), C!4))))) <=> ($false | (in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), set_difference(A!6, C!4)) <=> (~((~in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), A!6)) | in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), C!4)))))),
% 0.21/0.44 inference(monotonicity,[status(thm)],[101])).
% 0.21/0.44 tff(103,plain,
% 0.21/0.44 (((~(set_difference(A!6, C!4) = set_difference(A!6, C!4))) | (in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), set_difference(A!6, C!4)) <=> (~((~in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), A!6)) | in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), C!4))))) <=> (in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), set_difference(A!6, C!4)) <=> (~((~in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), A!6)) | in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), C!4))))),
% 0.21/0.44 inference(transitivity,[status(thm)],[102, 99])).
% 0.21/0.44 tff(104,plain,
% 0.21/0.44 ((~((~(set_difference(A!6, C!4) = set_difference(A!6, C!4))) | (in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), set_difference(A!6, C!4)) <=> (~((~in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), A!6)) | in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), C!4)))))) <=> (~(in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), set_difference(A!6, C!4)) <=> (~((~in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), A!6)) | in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), C!4)))))),
% 0.21/0.44 inference(monotonicity,[status(thm)],[103])).
% 0.21/0.44 tff(105,plain,
% 0.21/0.44 ((~((~(set_difference(A!6, C!4) = set_difference(A!6, C!4))) | (in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), set_difference(A!6, C!4)) <=> (~((~in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), A!6)) | in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), C!4)))))) <=> (in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), set_difference(A!6, C!4)) <=> ((~in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), A!6)) | in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), C!4)))),
% 0.21/0.44 inference(transitivity,[status(thm)],[104, 98])).
% 0.21/0.44 tff(106,plain,
% 0.21/0.44 (((~((~(set_difference(A!6, C!4) = set_difference(A!6, C!4))) | (in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), set_difference(A!6, C!4)) <=> (~((~in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), A!6)) | in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), C!4)))))) | (~((set_difference(A!6, C!4) = set_difference(A!6, C!4)) | (in(tptp_fun_D_1(set_difference(A!6, C!4), C!4, A!6), set_difference(A!6, C!4)) <=> ((~in(tptp_fun_D_1(set_difference(A!6, C!4), C!4, A!6), A!6)) | in(tptp_fun_D_1(set_difference(A!6, C!4), C!4, A!6), C!4)))))) <=> ((in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), set_difference(A!6, C!4)) <=> ((~in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), A!6)) | in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), C!4))) | $false)),
% 0.21/0.44 inference(monotonicity,[status(thm)],[105, 97])).
% 0.21/0.44 tff(107,plain,
% 0.21/0.44 (((~((~(set_difference(A!6, C!4) = set_difference(A!6, C!4))) | (in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), set_difference(A!6, C!4)) <=> (~((~in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), A!6)) | in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), C!4)))))) | (~((set_difference(A!6, C!4) = set_difference(A!6, C!4)) | (in(tptp_fun_D_1(set_difference(A!6, C!4), C!4, A!6), set_difference(A!6, C!4)) <=> ((~in(tptp_fun_D_1(set_difference(A!6, C!4), C!4, A!6), A!6)) | in(tptp_fun_D_1(set_difference(A!6, C!4), C!4, A!6), C!4)))))) <=> (in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), set_difference(A!6, C!4)) <=> ((~in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), A!6)) | in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), C!4)))),
% 0.21/0.44 inference(transitivity,[status(thm)],[106, 91])).
% 0.21/0.44 tff(108,plain,
% 0.21/0.44 ((~((~((~(set_difference(A!6, C!4) = set_difference(A!6, C!4))) | (in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), set_difference(A!6, C!4)) <=> (~((~in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), A!6)) | in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), C!4)))))) | (~((set_difference(A!6, C!4) = set_difference(A!6, C!4)) | (in(tptp_fun_D_1(set_difference(A!6, C!4), C!4, A!6), set_difference(A!6, C!4)) <=> ((~in(tptp_fun_D_1(set_difference(A!6, C!4), C!4, A!6), A!6)) | in(tptp_fun_D_1(set_difference(A!6, C!4), C!4, A!6), C!4))))))) <=> (~(in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), set_difference(A!6, C!4)) <=> ((~in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), A!6)) | in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), C!4))))),
% 0.21/0.44 inference(monotonicity,[status(thm)],[107])).
% 0.21/0.44 tff(109,plain,
% 0.21/0.44 ((~((~((~(set_difference(A!6, C!4) = set_difference(A!6, C!4))) | (in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), set_difference(A!6, C!4)) <=> (~((~in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), A!6)) | in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), C!4)))))) | (~((set_difference(A!6, C!4) = set_difference(A!6, C!4)) | (in(tptp_fun_D_1(set_difference(A!6, C!4), C!4, A!6), set_difference(A!6, C!4)) <=> ((~in(tptp_fun_D_1(set_difference(A!6, C!4), C!4, A!6), A!6)) | in(tptp_fun_D_1(set_difference(A!6, C!4), C!4, A!6), C!4))))))) <=> ((~in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), set_difference(A!6, C!4))) <=> ((~in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), A!6)) | in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), C!4)))),
% 0.21/0.44 inference(transitivity,[status(thm)],[108, 90])).
% 0.21/0.45 tff(110,plain,
% 0.21/0.45 (((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_difference(A, B))) | (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_1(C, B, A), C) <=> ((~in(tptp_fun_D_1(C, B, A), A)) | in(tptp_fun_D_1(C, B, A), B)))))))) | (~((~((~(set_difference(A!6, C!4) = set_difference(A!6, C!4))) | (in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), set_difference(A!6, C!4)) <=> (~((~in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), A!6)) | in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), C!4)))))) | (~((set_difference(A!6, C!4) = set_difference(A!6, C!4)) | (in(tptp_fun_D_1(set_difference(A!6, C!4), C!4, A!6), set_difference(A!6, C!4)) <=> ((~in(tptp_fun_D_1(set_difference(A!6, C!4), C!4, A!6), A!6)) | in(tptp_fun_D_1(set_difference(A!6, C!4), C!4, A!6), C!4)))))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_difference(A, B))) | (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_1(C, B, A), C) <=> ((~in(tptp_fun_D_1(C, B, A), A)) | in(tptp_fun_D_1(C, B, A), B)))))))) | ((~in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), set_difference(A!6, C!4))) <=> ((~in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), A!6)) | in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), C!4))))),
% 0.21/0.45 inference(monotonicity,[status(thm)],[109])).
% 0.21/0.45 tff(111,plain,
% 0.21/0.45 (((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_difference(A, B))) | (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_1(C, B, A), C) <=> ((~in(tptp_fun_D_1(C, B, A), A)) | in(tptp_fun_D_1(C, B, A), B)))))))) | (~((~((~(set_difference(A!6, C!4) = set_difference(A!6, C!4))) | (in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), set_difference(A!6, C!4)) <=> (~((~in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), A!6)) | in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), C!4)))))) | (~((set_difference(A!6, C!4) = set_difference(A!6, C!4)) | (in(tptp_fun_D_1(set_difference(A!6, C!4), C!4, A!6), set_difference(A!6, C!4)) <=> ((~in(tptp_fun_D_1(set_difference(A!6, C!4), C!4, A!6), A!6)) | in(tptp_fun_D_1(set_difference(A!6, C!4), C!4, A!6), C!4)))))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_difference(A, B))) | (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_1(C, B, A), C) <=> ((~in(tptp_fun_D_1(C, B, A), A)) | in(tptp_fun_D_1(C, B, A), B)))))))) | ((~in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), set_difference(A!6, C!4))) <=> ((~in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), A!6)) | in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), C!4))))),
% 0.21/0.45 inference(transitivity,[status(thm)],[110, 89])).
% 0.21/0.45 tff(112,plain,
% 0.21/0.45 ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_difference(A, B))) | (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_1(C, B, A), C) <=> ((~in(tptp_fun_D_1(C, B, A), A)) | in(tptp_fun_D_1(C, B, A), B)))))))) | (~((~((~(set_difference(A!6, C!4) = set_difference(A!6, C!4))) | (in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), set_difference(A!6, C!4)) <=> (~((~in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), A!6)) | in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), C!4)))))) | (~((set_difference(A!6, C!4) = set_difference(A!6, C!4)) | (in(tptp_fun_D_1(set_difference(A!6, C!4), C!4, A!6), set_difference(A!6, C!4)) <=> ((~in(tptp_fun_D_1(set_difference(A!6, C!4), C!4, A!6), A!6)) | in(tptp_fun_D_1(set_difference(A!6, C!4), C!4, A!6), C!4)))))))),
% 0.21/0.45 inference(quant_inst,[status(thm)],[])).
% 0.21/0.45 tff(113,plain,
% 0.21/0.45 ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_difference(A, B))) | (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_1(C, B, A), C) <=> ((~in(tptp_fun_D_1(C, B, A), A)) | in(tptp_fun_D_1(C, B, A), B)))))))) | ((~in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), set_difference(A!6, C!4))) <=> ((~in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), A!6)) | in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), C!4)))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[112, 111])).
% 0.21/0.45 tff(114,plain,
% 0.21/0.45 ((~in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), set_difference(A!6, C!4))) <=> ((~in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), A!6)) | in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), C!4))),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[113, 21])).
% 0.21/0.45 tff(115,plain,
% 0.21/0.45 (((~in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), set_difference(A!6, C!4))) | in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), set_difference(B!5, C!4))) | in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), set_difference(A!6, C!4))),
% 0.21/0.45 inference(tautology,[status(thm)],[])).
% 0.21/0.45 tff(116,plain,
% 0.21/0.45 (in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), set_difference(A!6, C!4))),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[115, 83])).
% 0.21/0.45 tff(117,plain,
% 0.21/0.45 ((~((~in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), set_difference(A!6, C!4))) <=> ((~in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), A!6)) | in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), C!4)))) | (~in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), set_difference(A!6, C!4))) | (~((~in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), A!6)) | in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), C!4)))),
% 0.21/0.45 inference(tautology,[status(thm)],[])).
% 0.21/0.45 tff(118,plain,
% 0.21/0.45 ((~((~in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), set_difference(A!6, C!4))) <=> ((~in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), A!6)) | in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), C!4)))) | (~((~in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), A!6)) | in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), C!4)))),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[117, 116])).
% 0.21/0.45 tff(119,plain,
% 0.21/0.45 (~((~in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), A!6)) | in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), C!4))),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[118, 114])).
% 0.21/0.45 tff(120,plain,
% 0.21/0.45 (((~in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), A!6)) | in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), C!4)) | (~in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), C!4))),
% 0.21/0.45 inference(tautology,[status(thm)],[])).
% 0.21/0.45 tff(121,plain,
% 0.21/0.45 (~in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), C!4)),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[120, 119])).
% 0.21/0.45 tff(122,plain,
% 0.21/0.45 ((~((~in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), B!5)) | in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), C!4))) | (~in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), B!5)) | in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), C!4)),
% 0.21/0.45 inference(tautology,[status(thm)],[])).
% 0.21/0.45 tff(123,plain,
% 0.21/0.45 (~in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), B!5)),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[122, 121, 88])).
% 0.21/0.45 tff(124,plain,
% 0.21/0.45 (((~in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), A!6)) | in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), C!4)) | in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), A!6)),
% 0.21/0.45 inference(tautology,[status(thm)],[])).
% 0.21/0.45 tff(125,plain,
% 0.21/0.45 (in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), A!6)),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[124, 119])).
% 0.21/0.45 tff(126,plain,
% 0.21/0.45 ((~![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B)))))))) | (~((~((~subset(A!6, B!5)) | ![C: $i] : ((~in(C, A!6)) | in(C, B!5)))) | (~(subset(A!6, B!5) | (~((~in(tptp_fun_C_0(B!5, A!6), A!6)) | in(tptp_fun_C_0(B!5, A!6), B!5)))))))),
% 0.21/0.46 inference(quant_inst,[status(thm)],[])).
% 0.21/0.46 tff(127,plain,
% 0.21/0.46 (~((~((~subset(A!6, B!5)) | ![C: $i] : ((~in(C, A!6)) | in(C, B!5)))) | (~(subset(A!6, B!5) | (~((~in(tptp_fun_C_0(B!5, A!6), A!6)) | in(tptp_fun_C_0(B!5, A!6), B!5))))))),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[126, 64])).
% 0.21/0.46 tff(128,plain,
% 0.21/0.46 (((~((~subset(A!6, B!5)) | ![C: $i] : ((~in(C, A!6)) | in(C, B!5)))) | (~(subset(A!6, B!5) | (~((~in(tptp_fun_C_0(B!5, A!6), A!6)) | in(tptp_fun_C_0(B!5, A!6), B!5)))))) | ((~subset(A!6, B!5)) | ![C: $i] : ((~in(C, A!6)) | in(C, B!5)))),
% 0.21/0.46 inference(tautology,[status(thm)],[])).
% 0.21/0.46 tff(129,plain,
% 0.21/0.46 ((~subset(A!6, B!5)) | ![C: $i] : ((~in(C, A!6)) | in(C, B!5))),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[128, 127])).
% 0.21/0.46 tff(130,plain,
% 0.21/0.46 (subset(A!6, B!5)),
% 0.21/0.46 inference(or_elim,[status(thm)],[79])).
% 0.21/0.46 tff(131,plain,
% 0.21/0.46 ((~((~subset(A!6, B!5)) | ![C: $i] : ((~in(C, A!6)) | in(C, B!5)))) | (~subset(A!6, B!5)) | ![C: $i] : ((~in(C, A!6)) | in(C, B!5))),
% 0.21/0.46 inference(tautology,[status(thm)],[])).
% 0.21/0.46 tff(132,plain,
% 0.21/0.46 ((~((~subset(A!6, B!5)) | ![C: $i] : ((~in(C, A!6)) | in(C, B!5)))) | ![C: $i] : ((~in(C, A!6)) | in(C, B!5))),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[131, 130])).
% 0.21/0.46 tff(133,plain,
% 0.21/0.46 (![C: $i] : ((~in(C, A!6)) | in(C, B!5))),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[132, 129])).
% 0.21/0.46 tff(134,plain,
% 0.21/0.46 (((~![C: $i] : ((~in(C, A!6)) | in(C, B!5))) | ((~in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), A!6)) | in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), B!5))) <=> ((~![C: $i] : ((~in(C, A!6)) | in(C, B!5))) | (~in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), A!6)) | in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), B!5))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(135,plain,
% 0.21/0.46 ((~![C: $i] : ((~in(C, A!6)) | in(C, B!5))) | ((~in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), A!6)) | in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), B!5))),
% 0.21/0.46 inference(quant_inst,[status(thm)],[])).
% 0.21/0.46 tff(136,plain,
% 0.21/0.46 ((~![C: $i] : ((~in(C, A!6)) | in(C, B!5))) | (~in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), A!6)) | in(tptp_fun_C_0(set_difference(B!5, C!4), set_difference(A!6, C!4)), B!5)),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[135, 134])).
% 0.21/0.46 tff(137,plain,
% 0.21/0.46 ($false),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[136, 133, 125, 123])).
% 0.21/0.46 % SZS output end Proof
%------------------------------------------------------------------------------