TSTP Solution File: SEU141+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SEU141+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n013.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 20 07:27:43 EDT 2022
% Result : Theorem 65.08s 40.67s
% Output : Proof 65.09s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : SEU141+1 : TPTP v8.1.0. Released v3.3.0.
% 0.13/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.35 % Computer : n013.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Sat Sep 3 09:35:02 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.21/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.21/0.35 Usage: tptp [options] [-file:]file
% 0.21/0.35 -h, -? prints this message.
% 0.21/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.21/0.35 -m, -model generate model.
% 0.21/0.35 -p, -proof generate proof.
% 0.21/0.35 -c, -core generate unsat core of named formulas.
% 0.21/0.35 -st, -statistics display statistics.
% 0.21/0.35 -t:timeout set timeout (in second).
% 0.21/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.21/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.21/0.35 -<param>:<value> configuration parameter and value.
% 0.21/0.35 -o:<output-file> file to place output in.
% 65.08/40.67 % SZS status Theorem
% 65.08/40.67 % SZS output start Proof
% 65.08/40.67 tff(in_type, type, (
% 65.08/40.67 in: ( $i * $i ) > $o)).
% 65.08/40.67 tff(empty_set_type, type, (
% 65.08/40.67 empty_set: $i)).
% 65.08/40.67 tff(tptp_fun_D_2_type, type, (
% 65.08/40.67 tptp_fun_D_2: ( $i * $i * $i ) > $i)).
% 65.08/40.67 tff(tptp_fun_A_7_type, type, (
% 65.08/40.67 tptp_fun_A_7: $i)).
% 65.08/40.67 tff(tptp_fun_B_6_type, type, (
% 65.08/40.67 tptp_fun_B_6: $i)).
% 65.08/40.67 tff(set_intersection2_type, type, (
% 65.08/40.67 set_intersection2: ( $i * $i ) > $i)).
% 65.08/40.67 tff(tptp_fun_D_1_type, type, (
% 65.08/40.67 tptp_fun_D_1: ( $i * $i * $i ) > $i)).
% 65.08/40.67 tff(disjoint_type, type, (
% 65.08/40.67 disjoint: ( $i * $i ) > $o)).
% 65.08/40.67 tff(tptp_fun_C_5_type, type, (
% 65.08/40.67 tptp_fun_C_5: ( $i * $i ) > $i)).
% 65.08/40.67 tff(set_difference_type, type, (
% 65.08/40.67 set_difference: ( $i * $i ) > $i)).
% 65.08/40.67 tff(empty_type, type, (
% 65.08/40.67 empty: $i > $o)).
% 65.08/40.67 tff(1,assumption,((~((empty_set = set_intersection2(A!7, B!6)) | (in(tptp_fun_D_1(empty_set, B!6, A!7), empty_set) <=> ((~in(tptp_fun_D_1(empty_set, B!6, A!7), A!7)) | (~in(tptp_fun_D_1(empty_set, B!6, A!7), B!6)))))) | (~((~(empty_set = set_intersection2(A!7, B!6))) | (in(tptp_fun_D_2(A!7, B!6, A!7), empty_set) <=> (~((~in(tptp_fun_D_2(A!7, B!6, A!7), A!7)) | (~in(tptp_fun_D_2(A!7, B!6, A!7), B!6)))))))), introduced(assumption)).
% 65.08/40.67 tff(2,plain,
% 65.08/40.67 (^[A: $i, B: $i, C: $i, D: $i] : refl((~((~((~(C = set_intersection2(A, B))) | (in(D, C) <=> (~((~in(D, B)) | (~in(D, A))))))) | (~((C = set_intersection2(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_intersection2(A, B))) | (in(D, C) <=> (~((~in(D, B)) | (~in(D, A))))))) | (~((C = set_intersection2(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)))))))))),
% 65.08/40.67 inference(bind,[status(th)],[])).
% 65.08/40.67 tff(3,plain,
% 65.08/40.67 (![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (in(D, C) <=> (~((~in(D, B)) | (~in(D, A))))))) | (~((C = set_intersection2(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_intersection2(A, B))) | (in(D, C) <=> (~((~in(D, B)) | (~in(D, A))))))) | (~((C = set_intersection2(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))))))))),
% 65.08/40.67 inference(quant_intro,[status(thm)],[2])).
% 65.08/40.67 tff(4,plain,
% 65.08/40.67 (![A: $i, B: $i, C: $i] : ![D: $i] : (~((~((~(C = set_intersection2(A, B))) | (in(D, C) <=> (~((~in(D, B)) | (~in(D, A))))))) | (~((C = set_intersection2(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_intersection2(A, B))) | (in(D, C) <=> (~((~in(D, B)) | (~in(D, A))))))) | (~((C = set_intersection2(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))))))))),
% 65.08/40.67 inference(pull_quant,[status(thm)],[])).
% 65.08/40.67 tff(5,plain,
% 65.08/40.67 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(pull_quant(((~(C = set_intersection2(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, B)) | (~in(D, A)))))) <=> ![D: $i] : ((~(C = set_intersection2(A, B))) | (in(D, C) <=> (~((~in(D, B)) | (~in(D, A))))))), ((~((~(C = set_intersection2(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, B)) | (~in(D, A))))))) <=> (~![D: $i] : ((~(C = set_intersection2(A, B))) | (in(D, C) <=> (~((~in(D, B)) | (~in(D, A))))))))), pull_quant((~![D: $i] : ((~(C = set_intersection2(A, B))) | (in(D, C) <=> (~((~in(D, B)) | (~in(D, A))))))) <=> ?[D: $i] : (~((~(C = set_intersection2(A, B))) | (in(D, C) <=> (~((~in(D, B)) | (~in(D, A)))))))), ((~((~(C = set_intersection2(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, B)) | (~in(D, A))))))) <=> ?[D: $i] : (~((~(C = set_intersection2(A, B))) | (in(D, C) <=> (~((~in(D, B)) | (~in(D, A))))))))), (((~((~(C = set_intersection2(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, B)) | (~in(D, A))))))) | (~((C = set_intersection2(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_intersection2(A, B))) | (in(D, C) <=> (~((~in(D, B)) | (~in(D, A))))))) | (~((C = set_intersection2(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_intersection2(A, B))) | (in(D, C) <=> (~((~in(D, B)) | (~in(D, A))))))) | (~((C = set_intersection2(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_intersection2(A, B))) | (in(D, C) <=> (~((~in(D, B)) | (~in(D, A))))))) | (~((C = set_intersection2(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_intersection2(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, B)) | (~in(D, A))))))) | (~((C = set_intersection2(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_intersection2(A, B))) | (in(D, C) <=> (~((~in(D, B)) | (~in(D, A))))))) | (~((C = set_intersection2(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_intersection2(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, B)) | (~in(D, A))))))) | (~((C = set_intersection2(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_intersection2(A, B))) | (in(D, C) <=> (~((~in(D, B)) | (~in(D, A))))))) | (~((C = set_intersection2(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_intersection2(A, B))) | (in(D, C) <=> (~((~in(D, B)) | (~in(D, A))))))) | (~((C = set_intersection2(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_intersection2(A, B))) | (in(D, C) <=> (~((~in(D, B)) | (~in(D, A))))))) | (~((C = set_intersection2(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_intersection2(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, B)) | (~in(D, A))))))) | (~((C = set_intersection2(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_intersection2(A, B))) | (in(D, C) <=> (~((~in(D, B)) | (~in(D, A))))))) | (~((C = set_intersection2(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))))))))))),
% 65.08/40.67 inference(bind,[status(th)],[])).
% 65.08/40.67 tff(6,plain,
% 65.08/40.67 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_intersection2(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, B)) | (~in(D, A))))))) | (~((C = set_intersection2(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_intersection2(A, B))) | (in(D, C) <=> (~((~in(D, B)) | (~in(D, A))))))) | (~((C = set_intersection2(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))))))))),
% 65.08/40.67 inference(quant_intro,[status(thm)],[5])).
% 65.08/40.67 tff(7,plain,
% 65.08/40.67 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_intersection2(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, B)) | (~in(D, A))))))) | (~((C = set_intersection2(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_intersection2(A, B))) | (in(D, C) <=> (~((~in(D, B)) | (~in(D, A))))))) | (~((C = set_intersection2(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))))))))),
% 65.08/40.67 inference(transitivity,[status(thm)],[6, 4])).
% 65.08/40.67 tff(8,plain,
% 65.08/40.67 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_intersection2(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, B)) | (~in(D, A))))))) | (~((C = set_intersection2(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_intersection2(A, B))) | (in(D, C) <=> (~((~in(D, B)) | (~in(D, A))))))) | (~((C = set_intersection2(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))))))))),
% 65.08/40.67 inference(transitivity,[status(thm)],[7, 3])).
% 65.08/40.67 tff(9,plain,
% 65.08/40.67 (^[A: $i, B: $i, C: $i] : rewrite((~((~((~(C = set_intersection2(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, B)) | (~in(D, A))))))) | (~((C = set_intersection2(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_intersection2(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, B)) | (~in(D, A))))))) | (~((C = set_intersection2(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)))))))))),
% 65.08/40.67 inference(bind,[status(th)],[])).
% 65.08/40.67 tff(10,plain,
% 65.08/40.67 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_intersection2(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, B)) | (~in(D, A))))))) | (~((C = set_intersection2(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_intersection2(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, B)) | (~in(D, A))))))) | (~((C = set_intersection2(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))))))))),
% 65.08/40.67 inference(quant_intro,[status(thm)],[9])).
% 65.08/40.67 tff(11,plain,
% 65.08/40.67 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_intersection2(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, B)) | (~in(D, A))))))) | (~((C = set_intersection2(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_intersection2(A, B))) | (in(D, C) <=> (~((~in(D, B)) | (~in(D, A))))))) | (~((C = set_intersection2(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))))))))),
% 65.08/40.67 inference(transitivity,[status(thm)],[10, 8])).
% 65.08/40.67 tff(12,plain,
% 65.08/40.67 (^[A: $i, B: $i, C: $i] : trans(monotonicity(rewrite(((~(C = set_intersection2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) & in(D, B)))) <=> ((~(C = set_intersection2(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, B)) | (~in(D, A))))))), rewrite(((C = set_intersection2(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_intersection2(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_intersection2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) & in(D, B)))) & ((C = set_intersection2(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_intersection2(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, B)) | (~in(D, A)))))) & ((C = set_intersection2(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_intersection2(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, B)) | (~in(D, A)))))) & ((C = set_intersection2(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_intersection2(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, B)) | (~in(D, A))))))) | (~((C = set_intersection2(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_intersection2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) & in(D, B)))) & ((C = set_intersection2(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_intersection2(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, B)) | (~in(D, A))))))) | (~((C = set_intersection2(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))))))))))),
% 65.08/40.67 inference(bind,[status(th)],[])).
% 65.08/40.67 tff(13,plain,
% 65.08/40.67 (![A: $i, B: $i, C: $i] : (((~(C = set_intersection2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) & in(D, B)))) & ((C = set_intersection2(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_intersection2(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, B)) | (~in(D, A))))))) | (~((C = set_intersection2(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))))))))),
% 65.08/40.67 inference(quant_intro,[status(thm)],[12])).
% 65.08/40.67 tff(14,plain,
% 65.08/40.67 (^[A: $i, B: $i, C: $i] : rewrite((((~(C = set_intersection2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) & in(D, B)))) & ((C = set_intersection2(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_intersection2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) & in(D, B)))) & ((C = set_intersection2(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))))))),
% 65.08/40.67 inference(bind,[status(th)],[])).
% 65.08/40.67 tff(15,plain,
% 65.08/40.67 (![A: $i, B: $i, C: $i] : (((~(C = set_intersection2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) & in(D, B)))) & ((C = set_intersection2(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_intersection2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) & in(D, B)))) & ((C = set_intersection2(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)))))),
% 65.08/40.67 inference(quant_intro,[status(thm)],[14])).
% 65.08/40.67 tff(16,plain,
% 65.08/40.67 (![A: $i, B: $i, C: $i] : ((C = set_intersection2(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, A) & in(D, B)))) <=> ![A: $i, B: $i, C: $i] : ((C = set_intersection2(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, A) & in(D, B))))),
% 65.08/40.67 inference(rewrite,[status(thm)],[])).
% 65.08/40.67 tff(17,axiom,(![A: $i, B: $i, C: $i] : ((C = set_intersection2(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, A) & in(D, B))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d3_xboole_0')).
% 65.08/40.67 tff(18,plain,
% 65.08/40.67 (![A: $i, B: $i, C: $i] : ((C = set_intersection2(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, A) & in(D, B))))),
% 65.08/40.67 inference(modus_ponens,[status(thm)],[17, 16])).
% 65.08/40.67 tff(19,plain,(
% 65.08/40.67 ![A: $i, B: $i, C: $i] : (((~(C = set_intersection2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) & in(D, B)))) & ((C = set_intersection2(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))))))),
% 65.08/40.67 inference(skolemize,[status(sab)],[18])).
% 65.08/40.67 tff(20,plain,
% 65.08/40.67 (![A: $i, B: $i, C: $i] : (((~(C = set_intersection2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) & in(D, B)))) & ((C = set_intersection2(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)))))),
% 65.08/40.67 inference(modus_ponens,[status(thm)],[19, 15])).
% 65.08/40.67 tff(21,plain,
% 65.08/40.67 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_intersection2(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, B)) | (~in(D, A))))))) | (~((C = set_intersection2(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))))))))),
% 65.08/40.67 inference(modus_ponens,[status(thm)],[20, 13])).
% 65.08/40.67 tff(22,plain,
% 65.08/40.67 (![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (in(D, C) <=> (~((~in(D, B)) | (~in(D, A))))))) | (~((C = set_intersection2(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))))))))),
% 65.08/40.67 inference(modus_ponens,[status(thm)],[21, 11])).
% 65.08/40.67 tff(23,plain,
% 65.08/40.67 (((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (in(D, C) <=> (~((~in(D, B)) | (~in(D, A))))))) | (~((C = set_intersection2(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))))))))) | (~((~((empty_set = set_intersection2(A!7, B!6)) | (in(tptp_fun_D_1(empty_set, B!6, A!7), empty_set) <=> ((~in(tptp_fun_D_1(empty_set, B!6, A!7), A!7)) | (~in(tptp_fun_D_1(empty_set, B!6, A!7), B!6)))))) | (~((~(empty_set = set_intersection2(A!7, B!6))) | (in(tptp_fun_D_2(A!7, B!6, A!7), empty_set) <=> (~((~in(tptp_fun_D_2(A!7, B!6, A!7), A!7)) | (~in(tptp_fun_D_2(A!7, B!6, A!7), B!6)))))))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (in(D, C) <=> (~((~in(D, B)) | (~in(D, A))))))) | (~((C = set_intersection2(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))))))))) | (~((~((empty_set = set_intersection2(A!7, B!6)) | (in(tptp_fun_D_1(empty_set, B!6, A!7), empty_set) <=> ((~in(tptp_fun_D_1(empty_set, B!6, A!7), A!7)) | (~in(tptp_fun_D_1(empty_set, B!6, A!7), B!6)))))) | (~((~(empty_set = set_intersection2(A!7, B!6))) | (in(tptp_fun_D_2(A!7, B!6, A!7), empty_set) <=> (~((~in(tptp_fun_D_2(A!7, B!6, A!7), A!7)) | (~in(tptp_fun_D_2(A!7, B!6, A!7), B!6))))))))))),
% 65.08/40.67 inference(rewrite,[status(thm)],[])).
% 65.08/40.67 tff(24,plain,
% 65.08/40.67 ((~((~((~(empty_set = set_intersection2(A!7, B!6))) | (in(tptp_fun_D_2(A!7, B!6, A!7), empty_set) <=> (~((~in(tptp_fun_D_2(A!7, B!6, A!7), B!6)) | (~in(tptp_fun_D_2(A!7, B!6, A!7), A!7))))))) | (~((empty_set = set_intersection2(A!7, B!6)) | (in(tptp_fun_D_1(empty_set, B!6, A!7), empty_set) <=> ((~in(tptp_fun_D_1(empty_set, B!6, A!7), A!7)) | (~in(tptp_fun_D_1(empty_set, B!6, A!7), B!6)))))))) <=> (~((~((empty_set = set_intersection2(A!7, B!6)) | (in(tptp_fun_D_1(empty_set, B!6, A!7), empty_set) <=> ((~in(tptp_fun_D_1(empty_set, B!6, A!7), A!7)) | (~in(tptp_fun_D_1(empty_set, B!6, A!7), B!6)))))) | (~((~(empty_set = set_intersection2(A!7, B!6))) | (in(tptp_fun_D_2(A!7, B!6, A!7), empty_set) <=> (~((~in(tptp_fun_D_2(A!7, B!6, A!7), A!7)) | (~in(tptp_fun_D_2(A!7, B!6, A!7), B!6)))))))))),
% 65.08/40.67 inference(rewrite,[status(thm)],[])).
% 65.08/40.67 tff(25,plain,
% 65.08/40.67 (((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (in(D, C) <=> (~((~in(D, B)) | (~in(D, A))))))) | (~((C = set_intersection2(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))))))))) | (~((~((~(empty_set = set_intersection2(A!7, B!6))) | (in(tptp_fun_D_2(A!7, B!6, A!7), empty_set) <=> (~((~in(tptp_fun_D_2(A!7, B!6, A!7), B!6)) | (~in(tptp_fun_D_2(A!7, B!6, A!7), A!7))))))) | (~((empty_set = set_intersection2(A!7, B!6)) | (in(tptp_fun_D_1(empty_set, B!6, A!7), empty_set) <=> ((~in(tptp_fun_D_1(empty_set, B!6, A!7), A!7)) | (~in(tptp_fun_D_1(empty_set, B!6, A!7), B!6))))))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (in(D, C) <=> (~((~in(D, B)) | (~in(D, A))))))) | (~((C = set_intersection2(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))))))))) | (~((~((empty_set = set_intersection2(A!7, B!6)) | (in(tptp_fun_D_1(empty_set, B!6, A!7), empty_set) <=> ((~in(tptp_fun_D_1(empty_set, B!6, A!7), A!7)) | (~in(tptp_fun_D_1(empty_set, B!6, A!7), B!6)))))) | (~((~(empty_set = set_intersection2(A!7, B!6))) | (in(tptp_fun_D_2(A!7, B!6, A!7), empty_set) <=> (~((~in(tptp_fun_D_2(A!7, B!6, A!7), A!7)) | (~in(tptp_fun_D_2(A!7, B!6, A!7), B!6))))))))))),
% 65.08/40.67 inference(monotonicity,[status(thm)],[24])).
% 65.08/40.67 tff(26,plain,
% 65.08/40.67 (((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (in(D, C) <=> (~((~in(D, B)) | (~in(D, A))))))) | (~((C = set_intersection2(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))))))))) | (~((~((~(empty_set = set_intersection2(A!7, B!6))) | (in(tptp_fun_D_2(A!7, B!6, A!7), empty_set) <=> (~((~in(tptp_fun_D_2(A!7, B!6, A!7), B!6)) | (~in(tptp_fun_D_2(A!7, B!6, A!7), A!7))))))) | (~((empty_set = set_intersection2(A!7, B!6)) | (in(tptp_fun_D_1(empty_set, B!6, A!7), empty_set) <=> ((~in(tptp_fun_D_1(empty_set, B!6, A!7), A!7)) | (~in(tptp_fun_D_1(empty_set, B!6, A!7), B!6))))))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (in(D, C) <=> (~((~in(D, B)) | (~in(D, A))))))) | (~((C = set_intersection2(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))))))))) | (~((~((empty_set = set_intersection2(A!7, B!6)) | (in(tptp_fun_D_1(empty_set, B!6, A!7), empty_set) <=> ((~in(tptp_fun_D_1(empty_set, B!6, A!7), A!7)) | (~in(tptp_fun_D_1(empty_set, B!6, A!7), B!6)))))) | (~((~(empty_set = set_intersection2(A!7, B!6))) | (in(tptp_fun_D_2(A!7, B!6, A!7), empty_set) <=> (~((~in(tptp_fun_D_2(A!7, B!6, A!7), A!7)) | (~in(tptp_fun_D_2(A!7, B!6, A!7), B!6))))))))))),
% 65.08/40.67 inference(transitivity,[status(thm)],[25, 23])).
% 65.08/40.67 tff(27,plain,
% 65.08/40.67 ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (in(D, C) <=> (~((~in(D, B)) | (~in(D, A))))))) | (~((C = set_intersection2(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))))))))) | (~((~((~(empty_set = set_intersection2(A!7, B!6))) | (in(tptp_fun_D_2(A!7, B!6, A!7), empty_set) <=> (~((~in(tptp_fun_D_2(A!7, B!6, A!7), B!6)) | (~in(tptp_fun_D_2(A!7, B!6, A!7), A!7))))))) | (~((empty_set = set_intersection2(A!7, B!6)) | (in(tptp_fun_D_1(empty_set, B!6, A!7), empty_set) <=> ((~in(tptp_fun_D_1(empty_set, B!6, A!7), A!7)) | (~in(tptp_fun_D_1(empty_set, B!6, A!7), B!6))))))))),
% 65.08/40.67 inference(quant_inst,[status(thm)],[])).
% 65.08/40.67 tff(28,plain,
% 65.08/40.67 ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (in(D, C) <=> (~((~in(D, B)) | (~in(D, A))))))) | (~((C = set_intersection2(A, B)) | (in(tptp_fun_D_1(C, B, A), C) <=> ((~in(tptp_fun_D_1(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), B))))))))) | (~((~((empty_set = set_intersection2(A!7, B!6)) | (in(tptp_fun_D_1(empty_set, B!6, A!7), empty_set) <=> ((~in(tptp_fun_D_1(empty_set, B!6, A!7), A!7)) | (~in(tptp_fun_D_1(empty_set, B!6, A!7), B!6)))))) | (~((~(empty_set = set_intersection2(A!7, B!6))) | (in(tptp_fun_D_2(A!7, B!6, A!7), empty_set) <=> (~((~in(tptp_fun_D_2(A!7, B!6, A!7), A!7)) | (~in(tptp_fun_D_2(A!7, B!6, A!7), B!6)))))))))),
% 65.08/40.67 inference(modus_ponens,[status(thm)],[27, 26])).
% 65.08/40.67 tff(29,plain,
% 65.08/40.67 ($false),
% 65.08/40.67 inference(unit_resolution,[status(thm)],[28, 22, 1])).
% 65.08/40.67 tff(30,plain,(~((~((empty_set = set_intersection2(A!7, B!6)) | (in(tptp_fun_D_1(empty_set, B!6, A!7), empty_set) <=> ((~in(tptp_fun_D_1(empty_set, B!6, A!7), A!7)) | (~in(tptp_fun_D_1(empty_set, B!6, A!7), B!6)))))) | (~((~(empty_set = set_intersection2(A!7, B!6))) | (in(tptp_fun_D_2(A!7, B!6, A!7), empty_set) <=> (~((~in(tptp_fun_D_2(A!7, B!6, A!7), A!7)) | (~in(tptp_fun_D_2(A!7, B!6, A!7), B!6))))))))), inference(lemma,lemma(discharge,[]))).
% 65.08/40.67 tff(31,plain,
% 65.08/40.67 (((~((empty_set = set_intersection2(A!7, B!6)) | (in(tptp_fun_D_1(empty_set, B!6, A!7), empty_set) <=> ((~in(tptp_fun_D_1(empty_set, B!6, A!7), A!7)) | (~in(tptp_fun_D_1(empty_set, B!6, A!7), B!6)))))) | (~((~(empty_set = set_intersection2(A!7, B!6))) | (in(tptp_fun_D_2(A!7, B!6, A!7), empty_set) <=> (~((~in(tptp_fun_D_2(A!7, B!6, A!7), A!7)) | (~in(tptp_fun_D_2(A!7, B!6, A!7), B!6)))))))) | ((~(empty_set = set_intersection2(A!7, B!6))) | (in(tptp_fun_D_2(A!7, B!6, A!7), empty_set) <=> (~((~in(tptp_fun_D_2(A!7, B!6, A!7), A!7)) | (~in(tptp_fun_D_2(A!7, B!6, A!7), B!6))))))),
% 65.08/40.67 inference(tautology,[status(thm)],[])).
% 65.08/40.67 tff(32,plain,
% 65.08/40.67 ((~(empty_set = set_intersection2(A!7, B!6))) | (in(tptp_fun_D_2(A!7, B!6, A!7), empty_set) <=> (~((~in(tptp_fun_D_2(A!7, B!6, A!7), A!7)) | (~in(tptp_fun_D_2(A!7, B!6, A!7), B!6)))))),
% 65.08/40.67 inference(unit_resolution,[status(thm)],[31, 30])).
% 65.08/40.67 tff(33,plain,
% 65.08/40.67 (((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (in(D, C) <=> (~((~in(D, B)) | (~in(D, A))))))) | (~((C = set_intersection2(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_5(A!7, B!6), set_intersection2(B!6, A!7))) <=> ((~in(tptp_fun_C_5(A!7, B!6), A!7)) | (~in(tptp_fun_C_5(A!7, B!6), B!6))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (in(D, C) <=> (~((~in(D, B)) | (~in(D, A))))))) | (~((C = set_intersection2(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_5(A!7, B!6), set_intersection2(B!6, A!7))) <=> ((~in(tptp_fun_C_5(A!7, B!6), A!7)) | (~in(tptp_fun_C_5(A!7, B!6), B!6)))))),
% 65.09/40.67 inference(rewrite,[status(thm)],[])).
% 65.09/40.67 tff(34,plain,
% 65.09/40.67 ((~(in(tptp_fun_C_5(A!7, B!6), set_intersection2(B!6, A!7)) <=> ((~in(tptp_fun_C_5(A!7, B!6), A!7)) | (~in(tptp_fun_C_5(A!7, B!6), B!6))))) <=> ((~in(tptp_fun_C_5(A!7, B!6), set_intersection2(B!6, A!7))) <=> ((~in(tptp_fun_C_5(A!7, B!6), A!7)) | (~in(tptp_fun_C_5(A!7, B!6), B!6))))),
% 65.09/40.67 inference(rewrite,[status(thm)],[])).
% 65.09/40.67 tff(35,plain,
% 65.09/40.67 (((in(tptp_fun_C_5(A!7, B!6), set_intersection2(B!6, A!7)) <=> ((~in(tptp_fun_C_5(A!7, B!6), A!7)) | (~in(tptp_fun_C_5(A!7, B!6), B!6)))) | $false) <=> (in(tptp_fun_C_5(A!7, B!6), set_intersection2(B!6, A!7)) <=> ((~in(tptp_fun_C_5(A!7, B!6), A!7)) | (~in(tptp_fun_C_5(A!7, B!6), B!6))))),
% 65.09/40.67 inference(rewrite,[status(thm)],[])).
% 65.09/40.67 tff(36,plain,
% 65.09/40.67 ((~$true) <=> $false),
% 65.09/40.67 inference(rewrite,[status(thm)],[])).
% 65.09/40.67 tff(37,plain,
% 65.09/40.67 (($true | (in(tptp_fun_D_1(set_intersection2(B!6, A!7), A!7, B!6), set_intersection2(B!6, A!7)) <=> ((~in(tptp_fun_D_1(set_intersection2(B!6, A!7), A!7, B!6), B!6)) | (~in(tptp_fun_D_1(set_intersection2(B!6, A!7), A!7, B!6), A!7))))) <=> $true),
% 65.09/40.67 inference(rewrite,[status(thm)],[])).
% 65.09/40.67 tff(38,plain,
% 65.09/40.67 ((in(tptp_fun_D_1(set_intersection2(B!6, A!7), A!7, B!6), set_intersection2(B!6, A!7)) <=> ((~in(tptp_fun_D_1(set_intersection2(B!6, A!7), A!7, B!6), B!6)) | (~in(tptp_fun_D_1(set_intersection2(B!6, A!7), A!7, B!6), A!7)))) <=> (in(tptp_fun_D_1(set_intersection2(B!6, A!7), A!7, B!6), set_intersection2(B!6, A!7)) <=> ((~in(tptp_fun_D_1(set_intersection2(B!6, A!7), A!7, B!6), B!6)) | (~in(tptp_fun_D_1(set_intersection2(B!6, A!7), A!7, B!6), A!7))))),
% 65.09/40.67 inference(rewrite,[status(thm)],[])).
% 65.09/40.67 tff(39,plain,
% 65.09/40.67 ((set_intersection2(B!6, A!7) = set_intersection2(B!6, A!7)) <=> $true),
% 65.09/40.67 inference(rewrite,[status(thm)],[])).
% 65.09/40.67 tff(40,plain,
% 65.09/40.67 (((set_intersection2(B!6, A!7) = set_intersection2(B!6, A!7)) | (in(tptp_fun_D_1(set_intersection2(B!6, A!7), A!7, B!6), set_intersection2(B!6, A!7)) <=> ((~in(tptp_fun_D_1(set_intersection2(B!6, A!7), A!7, B!6), B!6)) | (~in(tptp_fun_D_1(set_intersection2(B!6, A!7), A!7, B!6), A!7))))) <=> ($true | (in(tptp_fun_D_1(set_intersection2(B!6, A!7), A!7, B!6), set_intersection2(B!6, A!7)) <=> ((~in(tptp_fun_D_1(set_intersection2(B!6, A!7), A!7, B!6), B!6)) | (~in(tptp_fun_D_1(set_intersection2(B!6, A!7), A!7, B!6), A!7)))))),
% 65.09/40.67 inference(monotonicity,[status(thm)],[39, 38])).
% 65.09/40.67 tff(41,plain,
% 65.09/40.67 (((set_intersection2(B!6, A!7) = set_intersection2(B!6, A!7)) | (in(tptp_fun_D_1(set_intersection2(B!6, A!7), A!7, B!6), set_intersection2(B!6, A!7)) <=> ((~in(tptp_fun_D_1(set_intersection2(B!6, A!7), A!7, B!6), B!6)) | (~in(tptp_fun_D_1(set_intersection2(B!6, A!7), A!7, B!6), A!7))))) <=> $true),
% 65.09/40.67 inference(transitivity,[status(thm)],[40, 37])).
% 65.09/40.67 tff(42,plain,
% 65.09/40.67 ((~((set_intersection2(B!6, A!7) = set_intersection2(B!6, A!7)) | (in(tptp_fun_D_1(set_intersection2(B!6, A!7), A!7, B!6), set_intersection2(B!6, A!7)) <=> ((~in(tptp_fun_D_1(set_intersection2(B!6, A!7), A!7, B!6), B!6)) | (~in(tptp_fun_D_1(set_intersection2(B!6, A!7), A!7, B!6), A!7)))))) <=> (~$true)),
% 65.09/40.67 inference(monotonicity,[status(thm)],[41])).
% 65.09/40.67 tff(43,plain,
% 65.09/40.67 ((~((set_intersection2(B!6, A!7) = set_intersection2(B!6, A!7)) | (in(tptp_fun_D_1(set_intersection2(B!6, A!7), A!7, B!6), set_intersection2(B!6, A!7)) <=> ((~in(tptp_fun_D_1(set_intersection2(B!6, A!7), A!7, B!6), B!6)) | (~in(tptp_fun_D_1(set_intersection2(B!6, A!7), A!7, B!6), A!7)))))) <=> $false),
% 65.09/40.67 inference(transitivity,[status(thm)],[42, 36])).
% 65.09/40.67 tff(44,plain,
% 65.09/40.67 ((~(in(tptp_fun_C_5(A!7, B!6), set_intersection2(B!6, A!7)) <=> (~((~in(tptp_fun_C_5(A!7, B!6), A!7)) | (~in(tptp_fun_C_5(A!7, B!6), B!6)))))) <=> (in(tptp_fun_C_5(A!7, B!6), set_intersection2(B!6, A!7)) <=> ((~in(tptp_fun_C_5(A!7, B!6), A!7)) | (~in(tptp_fun_C_5(A!7, B!6), B!6))))),
% 65.09/40.68 inference(rewrite,[status(thm)],[])).
% 65.09/40.68 tff(45,plain,
% 65.09/40.68 (($false | (in(tptp_fun_C_5(A!7, B!6), set_intersection2(B!6, A!7)) <=> (~((~in(tptp_fun_C_5(A!7, B!6), A!7)) | (~in(tptp_fun_C_5(A!7, B!6), B!6)))))) <=> (in(tptp_fun_C_5(A!7, B!6), set_intersection2(B!6, A!7)) <=> (~((~in(tptp_fun_C_5(A!7, B!6), A!7)) | (~in(tptp_fun_C_5(A!7, B!6), B!6)))))),
% 65.09/40.68 inference(rewrite,[status(thm)],[])).
% 65.09/40.68 tff(46,plain,
% 65.09/40.68 ((~(set_intersection2(B!6, A!7) = set_intersection2(B!6, A!7))) <=> (~$true)),
% 65.09/40.68 inference(monotonicity,[status(thm)],[39])).
% 65.09/40.68 tff(47,plain,
% 65.09/40.68 ((~(set_intersection2(B!6, A!7) = set_intersection2(B!6, A!7))) <=> $false),
% 65.09/40.68 inference(transitivity,[status(thm)],[46, 36])).
% 65.09/40.68 tff(48,plain,
% 65.09/40.68 (((~(set_intersection2(B!6, A!7) = set_intersection2(B!6, A!7))) | (in(tptp_fun_C_5(A!7, B!6), set_intersection2(B!6, A!7)) <=> (~((~in(tptp_fun_C_5(A!7, B!6), A!7)) | (~in(tptp_fun_C_5(A!7, B!6), B!6)))))) <=> ($false | (in(tptp_fun_C_5(A!7, B!6), set_intersection2(B!6, A!7)) <=> (~((~in(tptp_fun_C_5(A!7, B!6), A!7)) | (~in(tptp_fun_C_5(A!7, B!6), B!6))))))),
% 65.09/40.68 inference(monotonicity,[status(thm)],[47])).
% 65.09/40.68 tff(49,plain,
% 65.09/40.68 (((~(set_intersection2(B!6, A!7) = set_intersection2(B!6, A!7))) | (in(tptp_fun_C_5(A!7, B!6), set_intersection2(B!6, A!7)) <=> (~((~in(tptp_fun_C_5(A!7, B!6), A!7)) | (~in(tptp_fun_C_5(A!7, B!6), B!6)))))) <=> (in(tptp_fun_C_5(A!7, B!6), set_intersection2(B!6, A!7)) <=> (~((~in(tptp_fun_C_5(A!7, B!6), A!7)) | (~in(tptp_fun_C_5(A!7, B!6), B!6)))))),
% 65.09/40.68 inference(transitivity,[status(thm)],[48, 45])).
% 65.09/40.68 tff(50,plain,
% 65.09/40.68 ((~((~(set_intersection2(B!6, A!7) = set_intersection2(B!6, A!7))) | (in(tptp_fun_C_5(A!7, B!6), set_intersection2(B!6, A!7)) <=> (~((~in(tptp_fun_C_5(A!7, B!6), A!7)) | (~in(tptp_fun_C_5(A!7, B!6), B!6))))))) <=> (~(in(tptp_fun_C_5(A!7, B!6), set_intersection2(B!6, A!7)) <=> (~((~in(tptp_fun_C_5(A!7, B!6), A!7)) | (~in(tptp_fun_C_5(A!7, B!6), B!6))))))),
% 65.09/40.68 inference(monotonicity,[status(thm)],[49])).
% 65.09/40.68 tff(51,plain,
% 65.09/40.68 ((~((~(set_intersection2(B!6, A!7) = set_intersection2(B!6, A!7))) | (in(tptp_fun_C_5(A!7, B!6), set_intersection2(B!6, A!7)) <=> (~((~in(tptp_fun_C_5(A!7, B!6), A!7)) | (~in(tptp_fun_C_5(A!7, B!6), B!6))))))) <=> (in(tptp_fun_C_5(A!7, B!6), set_intersection2(B!6, A!7)) <=> ((~in(tptp_fun_C_5(A!7, B!6), A!7)) | (~in(tptp_fun_C_5(A!7, B!6), B!6))))),
% 65.09/40.68 inference(transitivity,[status(thm)],[50, 44])).
% 65.09/40.68 tff(52,plain,
% 65.09/40.68 (((~((~(set_intersection2(B!6, A!7) = set_intersection2(B!6, A!7))) | (in(tptp_fun_C_5(A!7, B!6), set_intersection2(B!6, A!7)) <=> (~((~in(tptp_fun_C_5(A!7, B!6), A!7)) | (~in(tptp_fun_C_5(A!7, B!6), B!6))))))) | (~((set_intersection2(B!6, A!7) = set_intersection2(B!6, A!7)) | (in(tptp_fun_D_1(set_intersection2(B!6, A!7), A!7, B!6), set_intersection2(B!6, A!7)) <=> ((~in(tptp_fun_D_1(set_intersection2(B!6, A!7), A!7, B!6), B!6)) | (~in(tptp_fun_D_1(set_intersection2(B!6, A!7), A!7, B!6), A!7))))))) <=> ((in(tptp_fun_C_5(A!7, B!6), set_intersection2(B!6, A!7)) <=> ((~in(tptp_fun_C_5(A!7, B!6), A!7)) | (~in(tptp_fun_C_5(A!7, B!6), B!6)))) | $false)),
% 65.09/40.68 inference(monotonicity,[status(thm)],[51, 43])).
% 65.09/40.68 tff(53,plain,
% 65.09/40.68 (((~((~(set_intersection2(B!6, A!7) = set_intersection2(B!6, A!7))) | (in(tptp_fun_C_5(A!7, B!6), set_intersection2(B!6, A!7)) <=> (~((~in(tptp_fun_C_5(A!7, B!6), A!7)) | (~in(tptp_fun_C_5(A!7, B!6), B!6))))))) | (~((set_intersection2(B!6, A!7) = set_intersection2(B!6, A!7)) | (in(tptp_fun_D_1(set_intersection2(B!6, A!7), A!7, B!6), set_intersection2(B!6, A!7)) <=> ((~in(tptp_fun_D_1(set_intersection2(B!6, A!7), A!7, B!6), B!6)) | (~in(tptp_fun_D_1(set_intersection2(B!6, A!7), A!7, B!6), A!7))))))) <=> (in(tptp_fun_C_5(A!7, B!6), set_intersection2(B!6, A!7)) <=> ((~in(tptp_fun_C_5(A!7, B!6), A!7)) | (~in(tptp_fun_C_5(A!7, B!6), B!6))))),
% 65.09/40.68 inference(transitivity,[status(thm)],[52, 35])).
% 65.09/40.68 tff(54,plain,
% 65.09/40.68 ((~((~((~(set_intersection2(B!6, A!7) = set_intersection2(B!6, A!7))) | (in(tptp_fun_C_5(A!7, B!6), set_intersection2(B!6, A!7)) <=> (~((~in(tptp_fun_C_5(A!7, B!6), A!7)) | (~in(tptp_fun_C_5(A!7, B!6), B!6))))))) | (~((set_intersection2(B!6, A!7) = set_intersection2(B!6, A!7)) | (in(tptp_fun_D_1(set_intersection2(B!6, A!7), A!7, B!6), set_intersection2(B!6, A!7)) <=> ((~in(tptp_fun_D_1(set_intersection2(B!6, A!7), A!7, B!6), B!6)) | (~in(tptp_fun_D_1(set_intersection2(B!6, A!7), A!7, B!6), A!7)))))))) <=> (~(in(tptp_fun_C_5(A!7, B!6), set_intersection2(B!6, A!7)) <=> ((~in(tptp_fun_C_5(A!7, B!6), A!7)) | (~in(tptp_fun_C_5(A!7, B!6), B!6)))))),
% 65.09/40.68 inference(monotonicity,[status(thm)],[53])).
% 65.09/40.68 tff(55,plain,
% 65.09/40.68 ((~((~((~(set_intersection2(B!6, A!7) = set_intersection2(B!6, A!7))) | (in(tptp_fun_C_5(A!7, B!6), set_intersection2(B!6, A!7)) <=> (~((~in(tptp_fun_C_5(A!7, B!6), A!7)) | (~in(tptp_fun_C_5(A!7, B!6), B!6))))))) | (~((set_intersection2(B!6, A!7) = set_intersection2(B!6, A!7)) | (in(tptp_fun_D_1(set_intersection2(B!6, A!7), A!7, B!6), set_intersection2(B!6, A!7)) <=> ((~in(tptp_fun_D_1(set_intersection2(B!6, A!7), A!7, B!6), B!6)) | (~in(tptp_fun_D_1(set_intersection2(B!6, A!7), A!7, B!6), A!7)))))))) <=> ((~in(tptp_fun_C_5(A!7, B!6), set_intersection2(B!6, A!7))) <=> ((~in(tptp_fun_C_5(A!7, B!6), A!7)) | (~in(tptp_fun_C_5(A!7, B!6), B!6))))),
% 65.09/40.68 inference(transitivity,[status(thm)],[54, 34])).
% 65.09/40.68 tff(56,plain,
% 65.09/40.68 (((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (in(D, C) <=> (~((~in(D, B)) | (~in(D, A))))))) | (~((C = set_intersection2(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_intersection2(B!6, A!7) = set_intersection2(B!6, A!7))) | (in(tptp_fun_C_5(A!7, B!6), set_intersection2(B!6, A!7)) <=> (~((~in(tptp_fun_C_5(A!7, B!6), A!7)) | (~in(tptp_fun_C_5(A!7, B!6), B!6))))))) | (~((set_intersection2(B!6, A!7) = set_intersection2(B!6, A!7)) | (in(tptp_fun_D_1(set_intersection2(B!6, A!7), A!7, B!6), set_intersection2(B!6, A!7)) <=> ((~in(tptp_fun_D_1(set_intersection2(B!6, A!7), A!7, B!6), B!6)) | (~in(tptp_fun_D_1(set_intersection2(B!6, A!7), A!7, B!6), A!7))))))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (in(D, C) <=> (~((~in(D, B)) | (~in(D, A))))))) | (~((C = set_intersection2(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_5(A!7, B!6), set_intersection2(B!6, A!7))) <=> ((~in(tptp_fun_C_5(A!7, B!6), A!7)) | (~in(tptp_fun_C_5(A!7, B!6), B!6)))))),
% 65.09/40.68 inference(monotonicity,[status(thm)],[55])).
% 65.09/40.68 tff(57,plain,
% 65.09/40.68 (((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (in(D, C) <=> (~((~in(D, B)) | (~in(D, A))))))) | (~((C = set_intersection2(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_intersection2(B!6, A!7) = set_intersection2(B!6, A!7))) | (in(tptp_fun_C_5(A!7, B!6), set_intersection2(B!6, A!7)) <=> (~((~in(tptp_fun_C_5(A!7, B!6), A!7)) | (~in(tptp_fun_C_5(A!7, B!6), B!6))))))) | (~((set_intersection2(B!6, A!7) = set_intersection2(B!6, A!7)) | (in(tptp_fun_D_1(set_intersection2(B!6, A!7), A!7, B!6), set_intersection2(B!6, A!7)) <=> ((~in(tptp_fun_D_1(set_intersection2(B!6, A!7), A!7, B!6), B!6)) | (~in(tptp_fun_D_1(set_intersection2(B!6, A!7), A!7, B!6), A!7))))))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (in(D, C) <=> (~((~in(D, B)) | (~in(D, A))))))) | (~((C = set_intersection2(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_5(A!7, B!6), set_intersection2(B!6, A!7))) <=> ((~in(tptp_fun_C_5(A!7, B!6), A!7)) | (~in(tptp_fun_C_5(A!7, B!6), B!6)))))),
% 65.09/40.68 inference(transitivity,[status(thm)],[56, 33])).
% 65.09/40.68 tff(58,plain,
% 65.09/40.68 ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (in(D, C) <=> (~((~in(D, B)) | (~in(D, A))))))) | (~((C = set_intersection2(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_intersection2(B!6, A!7) = set_intersection2(B!6, A!7))) | (in(tptp_fun_C_5(A!7, B!6), set_intersection2(B!6, A!7)) <=> (~((~in(tptp_fun_C_5(A!7, B!6), A!7)) | (~in(tptp_fun_C_5(A!7, B!6), B!6))))))) | (~((set_intersection2(B!6, A!7) = set_intersection2(B!6, A!7)) | (in(tptp_fun_D_1(set_intersection2(B!6, A!7), A!7, B!6), set_intersection2(B!6, A!7)) <=> ((~in(tptp_fun_D_1(set_intersection2(B!6, A!7), A!7, B!6), B!6)) | (~in(tptp_fun_D_1(set_intersection2(B!6, A!7), A!7, B!6), A!7))))))))),
% 65.09/40.68 inference(quant_inst,[status(thm)],[])).
% 65.09/40.68 tff(59,plain,
% 65.09/40.68 ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (in(D, C) <=> (~((~in(D, B)) | (~in(D, A))))))) | (~((C = set_intersection2(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_5(A!7, B!6), set_intersection2(B!6, A!7))) <=> ((~in(tptp_fun_C_5(A!7, B!6), A!7)) | (~in(tptp_fun_C_5(A!7, B!6), B!6))))),
% 65.09/40.68 inference(modus_ponens,[status(thm)],[58, 57])).
% 65.09/40.68 tff(60,plain,
% 65.09/40.68 ((~in(tptp_fun_C_5(A!7, B!6), set_intersection2(B!6, A!7))) <=> ((~in(tptp_fun_C_5(A!7, B!6), A!7)) | (~in(tptp_fun_C_5(A!7, B!6), B!6)))),
% 65.09/40.68 inference(unit_resolution,[status(thm)],[59, 22])).
% 65.09/40.68 tff(61,assumption,(~disjoint(A!7, B!6)), introduced(assumption)).
% 65.09/40.68 tff(62,plain,
% 65.09/40.68 (^[A: $i, B: $i] : refl(((~disjoint(A, B)) | disjoint(B, A)) <=> ((~disjoint(A, B)) | disjoint(B, A)))),
% 65.09/40.68 inference(bind,[status(th)],[])).
% 65.09/40.68 tff(63,plain,
% 65.09/40.68 (![A: $i, B: $i] : ((~disjoint(A, B)) | disjoint(B, A)) <=> ![A: $i, B: $i] : ((~disjoint(A, B)) | disjoint(B, A))),
% 65.09/40.68 inference(quant_intro,[status(thm)],[62])).
% 65.09/40.68 tff(64,plain,
% 65.09/40.68 (![A: $i, B: $i] : ((~disjoint(A, B)) | disjoint(B, A)) <=> ![A: $i, B: $i] : ((~disjoint(A, B)) | disjoint(B, A))),
% 65.09/40.68 inference(rewrite,[status(thm)],[])).
% 65.09/40.68 tff(65,plain,
% 65.09/40.68 (^[A: $i, B: $i] : rewrite((disjoint(A, B) => disjoint(B, A)) <=> ((~disjoint(A, B)) | disjoint(B, A)))),
% 65.09/40.68 inference(bind,[status(th)],[])).
% 65.09/40.68 tff(66,plain,
% 65.09/40.68 (![A: $i, B: $i] : (disjoint(A, B) => disjoint(B, A)) <=> ![A: $i, B: $i] : ((~disjoint(A, B)) | disjoint(B, A))),
% 65.09/40.68 inference(quant_intro,[status(thm)],[65])).
% 65.09/40.68 tff(67,axiom,(![A: $i, B: $i] : (disjoint(A, B) => disjoint(B, A))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','symmetry_r1_xboole_0')).
% 65.09/40.68 tff(68,plain,
% 65.09/40.68 (![A: $i, B: $i] : ((~disjoint(A, B)) | disjoint(B, A))),
% 65.09/40.68 inference(modus_ponens,[status(thm)],[67, 66])).
% 65.09/40.68 tff(69,plain,
% 65.09/40.68 (![A: $i, B: $i] : ((~disjoint(A, B)) | disjoint(B, A))),
% 65.09/40.68 inference(modus_ponens,[status(thm)],[68, 64])).
% 65.09/40.68 tff(70,plain,(
% 65.09/40.68 ![A: $i, B: $i] : ((~disjoint(A, B)) | disjoint(B, A))),
% 65.09/40.68 inference(skolemize,[status(sab)],[69])).
% 65.09/40.68 tff(71,plain,
% 65.09/40.68 (![A: $i, B: $i] : ((~disjoint(A, B)) | disjoint(B, A))),
% 65.09/40.68 inference(modus_ponens,[status(thm)],[70, 63])).
% 65.09/40.68 tff(72,plain,
% 65.09/40.68 (((~![A: $i, B: $i] : ((~disjoint(A, B)) | disjoint(B, A))) | ((~disjoint(B!6, A!7)) | disjoint(A!7, B!6))) <=> ((~![A: $i, B: $i] : ((~disjoint(A, B)) | disjoint(B, A))) | (~disjoint(B!6, A!7)) | disjoint(A!7, B!6))),
% 65.09/40.68 inference(rewrite,[status(thm)],[])).
% 65.09/40.68 tff(73,plain,
% 65.09/40.68 ((~![A: $i, B: $i] : ((~disjoint(A, B)) | disjoint(B, A))) | ((~disjoint(B!6, A!7)) | disjoint(A!7, B!6))),
% 65.09/40.68 inference(quant_inst,[status(thm)],[])).
% 65.09/40.68 tff(74,plain,
% 65.09/40.68 ((~![A: $i, B: $i] : ((~disjoint(A, B)) | disjoint(B, A))) | (~disjoint(B!6, A!7)) | disjoint(A!7, B!6)),
% 65.09/40.68 inference(modus_ponens,[status(thm)],[73, 72])).
% 65.09/40.68 tff(75,plain,
% 65.09/40.68 ((~disjoint(B!6, A!7)) | disjoint(A!7, B!6)),
% 65.09/40.68 inference(unit_resolution,[status(thm)],[74, 71])).
% 65.09/40.68 tff(76,plain,
% 65.09/40.68 (~disjoint(B!6, A!7)),
% 65.09/40.68 inference(unit_resolution,[status(thm)],[75, 61])).
% 65.09/40.68 tff(77,plain,
% 65.09/40.68 (^[A: $i, B: $i] : rewrite((~((~(disjoint(A, B) | in(tptp_fun_C_5(B, A), set_intersection2(A, B)))) | (~(![C: $i] : (~in(C, set_intersection2(A, B))) | (~disjoint(A, B)))))) <=> (~((~(disjoint(A, B) | in(tptp_fun_C_5(B, A), set_intersection2(A, B)))) | (~((~disjoint(A, B)) | ![C: $i] : (~in(C, set_intersection2(A, B))))))))),
% 65.09/40.68 inference(bind,[status(th)],[])).
% 65.09/40.68 tff(78,plain,
% 65.09/40.68 (![A: $i, B: $i] : (~((~(disjoint(A, B) | in(tptp_fun_C_5(B, A), set_intersection2(A, B)))) | (~(![C: $i] : (~in(C, set_intersection2(A, B))) | (~disjoint(A, B)))))) <=> ![A: $i, B: $i] : (~((~(disjoint(A, B) | in(tptp_fun_C_5(B, A), set_intersection2(A, B)))) | (~((~disjoint(A, B)) | ![C: $i] : (~in(C, set_intersection2(A, B)))))))),
% 65.09/40.68 inference(quant_intro,[status(thm)],[77])).
% 65.09/40.68 tff(79,plain,
% 65.09/40.68 (^[A: $i, B: $i] : refl((~((~(disjoint(A, B) | in(tptp_fun_C_5(B, A), set_intersection2(A, B)))) | (~(![C: $i] : (~in(C, set_intersection2(A, B))) | (~disjoint(A, B)))))) <=> (~((~(disjoint(A, B) | in(tptp_fun_C_5(B, A), set_intersection2(A, B)))) | (~(![C: $i] : (~in(C, set_intersection2(A, B))) | (~disjoint(A, B)))))))),
% 65.09/40.68 inference(bind,[status(th)],[])).
% 65.09/40.68 tff(80,plain,
% 65.09/40.68 (![A: $i, B: $i] : (~((~(disjoint(A, B) | in(tptp_fun_C_5(B, A), set_intersection2(A, B)))) | (~(![C: $i] : (~in(C, set_intersection2(A, B))) | (~disjoint(A, B)))))) <=> ![A: $i, B: $i] : (~((~(disjoint(A, B) | in(tptp_fun_C_5(B, A), set_intersection2(A, B)))) | (~(![C: $i] : (~in(C, set_intersection2(A, B))) | (~disjoint(A, B))))))),
% 65.09/40.68 inference(quant_intro,[status(thm)],[79])).
% 65.09/40.68 tff(81,plain,
% 65.09/40.68 (^[A: $i, B: $i] : rewrite((~((~(disjoint(A, B) | in(tptp_fun_C_5(B, A), set_intersection2(A, B)))) | (~(![C: $i] : (~in(C, set_intersection2(A, B))) | (~disjoint(A, B)))))) <=> (~((~(disjoint(A, B) | in(tptp_fun_C_5(B, A), set_intersection2(A, B)))) | (~(![C: $i] : (~in(C, set_intersection2(A, B))) | (~disjoint(A, B)))))))),
% 65.09/40.68 inference(bind,[status(th)],[])).
% 65.09/40.68 tff(82,plain,
% 65.09/40.68 (![A: $i, B: $i] : (~((~(disjoint(A, B) | in(tptp_fun_C_5(B, A), set_intersection2(A, B)))) | (~(![C: $i] : (~in(C, set_intersection2(A, B))) | (~disjoint(A, B)))))) <=> ![A: $i, B: $i] : (~((~(disjoint(A, B) | in(tptp_fun_C_5(B, A), set_intersection2(A, B)))) | (~(![C: $i] : (~in(C, set_intersection2(A, B))) | (~disjoint(A, B))))))),
% 65.09/40.68 inference(quant_intro,[status(thm)],[81])).
% 65.09/40.68 tff(83,plain,
% 65.09/40.68 (![A: $i, B: $i] : (~((~(disjoint(A, B) | in(tptp_fun_C_5(B, A), set_intersection2(A, B)))) | (~(![C: $i] : (~in(C, set_intersection2(A, B))) | (~disjoint(A, B)))))) <=> ![A: $i, B: $i] : (~((~(disjoint(A, B) | in(tptp_fun_C_5(B, A), set_intersection2(A, B)))) | (~(![C: $i] : (~in(C, set_intersection2(A, B))) | (~disjoint(A, B))))))),
% 65.09/40.68 inference(transitivity,[status(thm)],[82, 80])).
% 65.09/40.68 tff(84,plain,
% 65.09/40.68 (^[A: $i, B: $i] : trans(monotonicity(rewrite((![C: $i] : (~in(C, set_intersection2(A, B))) | (~disjoint(A, B))) <=> (![C: $i] : (~in(C, set_intersection2(A, B))) | (~disjoint(A, B)))), (((disjoint(A, B) | in(tptp_fun_C_5(B, A), set_intersection2(A, B))) & (![C: $i] : (~in(C, set_intersection2(A, B))) | (~disjoint(A, B)))) <=> ((disjoint(A, B) | in(tptp_fun_C_5(B, A), set_intersection2(A, B))) & (![C: $i] : (~in(C, set_intersection2(A, B))) | (~disjoint(A, B)))))), rewrite(((disjoint(A, B) | in(tptp_fun_C_5(B, A), set_intersection2(A, B))) & (![C: $i] : (~in(C, set_intersection2(A, B))) | (~disjoint(A, B)))) <=> (~((~(disjoint(A, B) | in(tptp_fun_C_5(B, A), set_intersection2(A, B)))) | (~(![C: $i] : (~in(C, set_intersection2(A, B))) | (~disjoint(A, B))))))), (((disjoint(A, B) | in(tptp_fun_C_5(B, A), set_intersection2(A, B))) & (![C: $i] : (~in(C, set_intersection2(A, B))) | (~disjoint(A, B)))) <=> (~((~(disjoint(A, B) | in(tptp_fun_C_5(B, A), set_intersection2(A, B)))) | (~(![C: $i] : (~in(C, set_intersection2(A, B))) | (~disjoint(A, B))))))))),
% 65.09/40.68 inference(bind,[status(th)],[])).
% 65.09/40.68 tff(85,plain,
% 65.09/40.68 (![A: $i, B: $i] : ((disjoint(A, B) | in(tptp_fun_C_5(B, A), set_intersection2(A, B))) & (![C: $i] : (~in(C, set_intersection2(A, B))) | (~disjoint(A, B)))) <=> ![A: $i, B: $i] : (~((~(disjoint(A, B) | in(tptp_fun_C_5(B, A), set_intersection2(A, B)))) | (~(![C: $i] : (~in(C, set_intersection2(A, B))) | (~disjoint(A, B))))))),
% 65.09/40.68 inference(quant_intro,[status(thm)],[84])).
% 65.09/40.68 tff(86,plain,
% 65.09/40.68 (^[A: $i, B: $i] : rewrite((((~(~disjoint(A, B))) | (~(~in(tptp_fun_C_5(B, A), set_intersection2(A, B))))) & (![C: $i] : (~in(C, set_intersection2(A, B))) | (~disjoint(A, B)))) <=> ((disjoint(A, B) | in(tptp_fun_C_5(B, A), set_intersection2(A, B))) & (![C: $i] : (~in(C, set_intersection2(A, B))) | (~disjoint(A, B)))))),
% 65.09/40.68 inference(bind,[status(th)],[])).
% 65.09/40.68 tff(87,plain,
% 65.09/40.68 (![A: $i, B: $i] : (((~(~disjoint(A, B))) | (~(~in(tptp_fun_C_5(B, A), set_intersection2(A, B))))) & (![C: $i] : (~in(C, set_intersection2(A, B))) | (~disjoint(A, B)))) <=> ![A: $i, B: $i] : ((disjoint(A, B) | in(tptp_fun_C_5(B, A), set_intersection2(A, B))) & (![C: $i] : (~in(C, set_intersection2(A, B))) | (~disjoint(A, B))))),
% 65.09/40.68 inference(quant_intro,[status(thm)],[86])).
% 65.09/40.68 tff(88,plain,
% 65.09/40.68 (![A: $i, B: $i] : ((~((~disjoint(A, B)) & ![C: $i] : (~in(C, set_intersection2(A, B))))) & (~(?[C: $i] : in(C, set_intersection2(A, B)) & disjoint(A, B)))) <=> ![A: $i, B: $i] : ((~((~disjoint(A, B)) & ![C: $i] : (~in(C, set_intersection2(A, B))))) & (~(?[C: $i] : in(C, set_intersection2(A, B)) & disjoint(A, B))))),
% 65.09/40.68 inference(rewrite,[status(thm)],[])).
% 65.09/40.68 tff(89,axiom,(![A: $i, B: $i] : ((~((~disjoint(A, B)) & ![C: $i] : (~in(C, set_intersection2(A, B))))) & (~(?[C: $i] : in(C, set_intersection2(A, B)) & disjoint(A, B))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t4_xboole_0')).
% 65.09/40.68 tff(90,plain,
% 65.09/40.68 (![A: $i, B: $i] : ((~((~disjoint(A, B)) & ![C: $i] : (~in(C, set_intersection2(A, B))))) & (~(?[C: $i] : in(C, set_intersection2(A, B)) & disjoint(A, B))))),
% 65.09/40.68 inference(modus_ponens,[status(thm)],[89, 88])).
% 65.09/40.68 tff(91,plain,(
% 65.09/40.68 ![A: $i, B: $i] : (((~(~disjoint(A, B))) | (~(~in(tptp_fun_C_5(B, A), set_intersection2(A, B))))) & (![C: $i] : (~in(C, set_intersection2(A, B))) | (~disjoint(A, B))))),
% 65.09/40.68 inference(skolemize,[status(sab)],[90])).
% 65.09/40.68 tff(92,plain,
% 65.09/40.68 (![A: $i, B: $i] : ((disjoint(A, B) | in(tptp_fun_C_5(B, A), set_intersection2(A, B))) & (![C: $i] : (~in(C, set_intersection2(A, B))) | (~disjoint(A, B))))),
% 65.09/40.68 inference(modus_ponens,[status(thm)],[91, 87])).
% 65.09/40.68 tff(93,plain,
% 65.09/40.68 (![A: $i, B: $i] : (~((~(disjoint(A, B) | in(tptp_fun_C_5(B, A), set_intersection2(A, B)))) | (~(![C: $i] : (~in(C, set_intersection2(A, B))) | (~disjoint(A, B))))))),
% 65.09/40.68 inference(modus_ponens,[status(thm)],[92, 85])).
% 65.09/40.68 tff(94,plain,
% 65.09/40.68 (![A: $i, B: $i] : (~((~(disjoint(A, B) | in(tptp_fun_C_5(B, A), set_intersection2(A, B)))) | (~(![C: $i] : (~in(C, set_intersection2(A, B))) | (~disjoint(A, B))))))),
% 65.09/40.68 inference(modus_ponens,[status(thm)],[93, 83])).
% 65.09/40.68 tff(95,plain,
% 65.09/40.68 (![A: $i, B: $i] : (~((~(disjoint(A, B) | in(tptp_fun_C_5(B, A), set_intersection2(A, B)))) | (~((~disjoint(A, B)) | ![C: $i] : (~in(C, set_intersection2(A, B)))))))),
% 65.09/40.68 inference(modus_ponens,[status(thm)],[94, 78])).
% 65.09/40.68 tff(96,plain,
% 65.09/40.68 ((~![A: $i, B: $i] : (~((~(disjoint(A, B) | in(tptp_fun_C_5(B, A), set_intersection2(A, B)))) | (~((~disjoint(A, B)) | ![C: $i] : (~in(C, set_intersection2(A, B)))))))) | (~((~(disjoint(B!6, A!7) | in(tptp_fun_C_5(A!7, B!6), set_intersection2(B!6, A!7)))) | (~((~disjoint(B!6, A!7)) | ![C: $i] : (~in(C, set_intersection2(B!6, A!7)))))))),
% 65.09/40.68 inference(quant_inst,[status(thm)],[])).
% 65.09/40.68 tff(97,plain,
% 65.09/40.68 (~((~(disjoint(B!6, A!7) | in(tptp_fun_C_5(A!7, B!6), set_intersection2(B!6, A!7)))) | (~((~disjoint(B!6, A!7)) | ![C: $i] : (~in(C, set_intersection2(B!6, A!7))))))),
% 65.09/40.68 inference(unit_resolution,[status(thm)],[96, 95])).
% 65.09/40.68 tff(98,plain,
% 65.09/40.68 (((~(disjoint(B!6, A!7) | in(tptp_fun_C_5(A!7, B!6), set_intersection2(B!6, A!7)))) | (~((~disjoint(B!6, A!7)) | ![C: $i] : (~in(C, set_intersection2(B!6, A!7)))))) | (disjoint(B!6, A!7) | in(tptp_fun_C_5(A!7, B!6), set_intersection2(B!6, A!7)))),
% 65.09/40.68 inference(tautology,[status(thm)],[])).
% 65.09/40.68 tff(99,plain,
% 65.09/40.68 (disjoint(B!6, A!7) | in(tptp_fun_C_5(A!7, B!6), set_intersection2(B!6, A!7))),
% 65.09/40.68 inference(unit_resolution,[status(thm)],[98, 97])).
% 65.09/40.68 tff(100,plain,
% 65.09/40.68 ((~(disjoint(B!6, A!7) | in(tptp_fun_C_5(A!7, B!6), set_intersection2(B!6, A!7)))) | disjoint(B!6, A!7) | in(tptp_fun_C_5(A!7, B!6), set_intersection2(B!6, A!7))),
% 65.09/40.68 inference(tautology,[status(thm)],[])).
% 65.09/40.68 tff(101,plain,
% 65.09/40.68 (disjoint(B!6, A!7) | in(tptp_fun_C_5(A!7, B!6), set_intersection2(B!6, A!7))),
% 65.09/40.68 inference(unit_resolution,[status(thm)],[100, 99])).
% 65.09/40.68 tff(102,plain,
% 65.09/40.68 (in(tptp_fun_C_5(A!7, B!6), set_intersection2(B!6, A!7))),
% 65.09/40.68 inference(unit_resolution,[status(thm)],[101, 76])).
% 65.09/40.68 tff(103,plain,
% 65.09/40.68 ((~((~in(tptp_fun_C_5(A!7, B!6), set_intersection2(B!6, A!7))) <=> ((~in(tptp_fun_C_5(A!7, B!6), A!7)) | (~in(tptp_fun_C_5(A!7, B!6), B!6))))) | (~in(tptp_fun_C_5(A!7, B!6), set_intersection2(B!6, A!7))) | (~((~in(tptp_fun_C_5(A!7, B!6), A!7)) | (~in(tptp_fun_C_5(A!7, B!6), B!6))))),
% 65.09/40.68 inference(tautology,[status(thm)],[])).
% 65.09/40.68 tff(104,plain,
% 65.09/40.68 ((~((~in(tptp_fun_C_5(A!7, B!6), set_intersection2(B!6, A!7))) <=> ((~in(tptp_fun_C_5(A!7, B!6), A!7)) | (~in(tptp_fun_C_5(A!7, B!6), B!6))))) | (~((~in(tptp_fun_C_5(A!7, B!6), A!7)) | (~in(tptp_fun_C_5(A!7, B!6), B!6))))),
% 65.09/40.68 inference(unit_resolution,[status(thm)],[103, 102])).
% 65.09/40.68 tff(105,plain,
% 65.09/40.68 (~((~in(tptp_fun_C_5(A!7, B!6), A!7)) | (~in(tptp_fun_C_5(A!7, B!6), B!6)))),
% 65.09/40.68 inference(unit_resolution,[status(thm)],[104, 60])).
% 65.09/40.68 tff(106,plain,
% 65.09/40.68 (((~in(tptp_fun_C_5(A!7, B!6), A!7)) | (~in(tptp_fun_C_5(A!7, B!6), B!6))) | in(tptp_fun_C_5(A!7, B!6), B!6)),
% 65.09/40.68 inference(tautology,[status(thm)],[])).
% 65.09/40.68 tff(107,plain,
% 65.09/40.68 (in(tptp_fun_C_5(A!7, B!6), B!6)),
% 65.09/40.68 inference(unit_resolution,[status(thm)],[106, 105])).
% 65.09/40.68 tff(108,plain,
% 65.09/40.68 ((A!7 = set_difference(A!7, B!6)) <=> (set_difference(A!7, B!6) = A!7)),
% 65.09/40.68 inference(commutativity,[status(thm)],[])).
% 65.09/40.68 tff(109,plain,
% 65.09/40.68 ((set_difference(A!7, B!6) = A!7) <=> (A!7 = set_difference(A!7, B!6))),
% 65.09/40.68 inference(symmetry,[status(thm)],[108])).
% 65.09/40.68 tff(110,plain,
% 65.09/40.68 ((~(disjoint(A!7, B!6) <=> (set_difference(A!7, B!6) = A!7))) <=> ((~disjoint(A!7, B!6)) <=> (set_difference(A!7, B!6) = A!7))),
% 65.09/40.68 inference(rewrite,[status(thm)],[])).
% 65.09/40.68 tff(111,plain,
% 65.09/40.68 ((~![A: $i, B: $i] : (disjoint(A, B) <=> (set_difference(A, B) = A))) <=> (~![A: $i, B: $i] : (disjoint(A, B) <=> (set_difference(A, B) = A)))),
% 65.09/40.68 inference(rewrite,[status(thm)],[])).
% 65.09/40.68 tff(112,axiom,(~![A: $i, B: $i] : (disjoint(A, B) <=> (set_difference(A, B) = A))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t83_xboole_1')).
% 65.09/40.68 tff(113,plain,
% 65.09/40.68 (~![A: $i, B: $i] : (disjoint(A, B) <=> (set_difference(A, B) = A))),
% 65.09/40.68 inference(modus_ponens,[status(thm)],[112, 111])).
% 65.09/40.68 tff(114,plain,
% 65.09/40.68 (~![A: $i, B: $i] : (disjoint(A, B) <=> (set_difference(A, B) = A))),
% 65.09/40.68 inference(modus_ponens,[status(thm)],[113, 111])).
% 65.09/40.68 tff(115,plain,
% 65.09/40.68 (~![A: $i, B: $i] : (disjoint(A, B) <=> (set_difference(A, B) = A))),
% 65.09/40.68 inference(modus_ponens,[status(thm)],[114, 111])).
% 65.09/40.68 tff(116,plain,
% 65.09/40.68 (~![A: $i, B: $i] : (disjoint(A, B) <=> (set_difference(A, B) = A))),
% 65.09/40.68 inference(modus_ponens,[status(thm)],[115, 111])).
% 65.09/40.68 tff(117,plain,
% 65.09/40.68 (~![A: $i, B: $i] : (disjoint(A, B) <=> (set_difference(A, B) = A))),
% 65.09/40.68 inference(modus_ponens,[status(thm)],[116, 111])).
% 65.09/40.68 tff(118,plain,
% 65.09/40.68 (~![A: $i, B: $i] : (disjoint(A, B) <=> (set_difference(A, B) = A))),
% 65.09/40.68 inference(modus_ponens,[status(thm)],[117, 111])).
% 65.09/40.68 tff(119,plain,
% 65.09/40.68 (~![A: $i, B: $i] : (disjoint(A, B) <=> (set_difference(A, B) = A))),
% 65.09/40.68 inference(modus_ponens,[status(thm)],[118, 111])).
% 65.09/40.68 tff(120,plain,(
% 65.09/40.68 ~(disjoint(A!7, B!6) <=> (set_difference(A!7, B!6) = A!7))),
% 65.09/40.68 inference(skolemize,[status(sab)],[119])).
% 65.09/40.68 tff(121,plain,
% 65.09/40.68 ((~disjoint(A!7, B!6)) <=> (set_difference(A!7, B!6) = A!7)),
% 65.09/40.68 inference(modus_ponens,[status(thm)],[120, 110])).
% 65.09/40.68 tff(122,plain,
% 65.09/40.68 (disjoint(A!7, B!6) | (set_difference(A!7, B!6) = A!7) | (~((~disjoint(A!7, B!6)) <=> (set_difference(A!7, B!6) = A!7)))),
% 65.09/40.68 inference(tautology,[status(thm)],[])).
% 65.09/40.68 tff(123,plain,
% 65.09/40.68 (disjoint(A!7, B!6) | (set_difference(A!7, B!6) = A!7)),
% 65.09/40.68 inference(unit_resolution,[status(thm)],[122, 121])).
% 65.09/40.68 tff(124,plain,
% 65.09/40.68 (set_difference(A!7, B!6) = A!7),
% 65.09/40.68 inference(unit_resolution,[status(thm)],[123, 61])).
% 65.09/40.68 tff(125,plain,
% 65.09/40.68 (A!7 = set_difference(A!7, B!6)),
% 65.09/40.68 inference(modus_ponens,[status(thm)],[124, 109])).
% 65.09/40.68 tff(126,assumption,((~((A!7 = set_difference(A!7, B!6)) | (in(tptp_fun_D_2(A!7, B!6, A!7), A!7) <=> ((~in(tptp_fun_D_2(A!7, B!6, A!7), A!7)) | in(tptp_fun_D_2(A!7, B!6, A!7), B!6))))) | (~((~(A!7 = set_difference(A!7, B!6))) | (in(tptp_fun_C_5(A!7, B!6), A!7) <=> (~((~in(tptp_fun_C_5(A!7, B!6), A!7)) | in(tptp_fun_C_5(A!7, B!6), B!6))))))), introduced(assumption)).
% 65.09/40.68 tff(127,plain,
% 65.09/40.68 (^[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))))))))),
% 65.09/40.68 inference(bind,[status(th)],[])).
% 65.09/40.68 tff(128,plain,
% 65.09/40.68 (![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)))))))),
% 65.09/40.68 inference(quant_intro,[status(thm)],[127])).
% 65.09/40.68 tff(129,plain,
% 65.09/40.68 (![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)))))))),
% 65.09/40.68 inference(pull_quant,[status(thm)],[])).
% 65.09/40.68 tff(130,plain,
% 65.09/40.68 (^[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)))))))))),
% 65.09/40.68 inference(bind,[status(th)],[])).
% 65.09/40.68 tff(131,plain,
% 65.09/40.68 (![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)))))))),
% 65.09/40.68 inference(quant_intro,[status(thm)],[130])).
% 65.09/40.68 tff(132,plain,
% 65.09/40.68 (![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)))))))),
% 65.09/40.68 inference(transitivity,[status(thm)],[131, 129])).
% 65.09/40.68 tff(133,plain,
% 65.09/40.68 (![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)))))))),
% 65.09/40.68 inference(transitivity,[status(thm)],[132, 128])).
% 65.09/40.68 tff(134,plain,
% 65.09/40.68 (^[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))))))))),
% 65.09/40.68 inference(bind,[status(th)],[])).
% 65.09/40.68 tff(135,plain,
% 65.09/40.68 (![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)))))))),
% 65.09/40.68 inference(quant_intro,[status(thm)],[134])).
% 65.09/40.68 tff(136,plain,
% 65.09/40.68 (![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)))))))),
% 65.09/40.68 inference(transitivity,[status(thm)],[135, 133])).
% 65.09/40.68 tff(137,plain,
% 65.09/40.68 (^[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)))))))))),
% 65.09/40.68 inference(bind,[status(th)],[])).
% 65.09/40.68 tff(138,plain,
% 65.09/40.68 (![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)))))))),
% 65.09/40.68 inference(quant_intro,[status(thm)],[137])).
% 65.09/40.68 tff(139,plain,
% 65.09/40.68 (^[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)))))))),
% 65.09/40.68 inference(bind,[status(th)],[])).
% 65.09/40.68 tff(140,plain,
% 65.09/40.68 (![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))))))),
% 65.09/40.69 inference(quant_intro,[status(thm)],[139])).
% 65.09/40.69 tff(141,plain,
% 65.09/40.69 (![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)))))),
% 65.09/40.69 inference(rewrite,[status(thm)],[])).
% 65.09/40.69 tff(142,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')).
% 65.09/40.69 tff(143,plain,
% 65.09/40.69 (![A: $i, B: $i, C: $i] : ((C = set_difference(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, A) & (~in(D, B)))))),
% 65.09/40.69 inference(modus_ponens,[status(thm)],[142, 141])).
% 65.09/40.69 tff(144,plain,(
% 65.09/40.69 ![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)))))))),
% 65.09/40.69 inference(skolemize,[status(sab)],[143])).
% 65.09/40.69 tff(145,plain,
% 65.09/40.69 (![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))))))),
% 65.09/40.69 inference(modus_ponens,[status(thm)],[144, 140])).
% 65.09/40.69 tff(146,plain,
% 65.09/40.69 (![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)))))))),
% 65.09/40.69 inference(modus_ponens,[status(thm)],[145, 138])).
% 65.09/40.69 tff(147,plain,
% 65.09/40.69 (![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)))))))),
% 65.09/40.69 inference(modus_ponens,[status(thm)],[146, 136])).
% 65.09/40.69 tff(148,plain,
% 65.09/40.69 (((~![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!7 = set_difference(A!7, B!6)) | (in(tptp_fun_D_2(A!7, B!6, A!7), A!7) <=> ((~in(tptp_fun_D_2(A!7, B!6, A!7), A!7)) | in(tptp_fun_D_2(A!7, B!6, A!7), B!6))))) | (~((~(A!7 = set_difference(A!7, B!6))) | (in(tptp_fun_C_5(A!7, B!6), A!7) <=> (~((~in(tptp_fun_C_5(A!7, B!6), A!7)) | in(tptp_fun_C_5(A!7, B!6), B!6))))))))) <=> ((~![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!7 = set_difference(A!7, B!6)) | (in(tptp_fun_D_2(A!7, B!6, A!7), A!7) <=> ((~in(tptp_fun_D_2(A!7, B!6, A!7), A!7)) | in(tptp_fun_D_2(A!7, B!6, A!7), B!6))))) | (~((~(A!7 = set_difference(A!7, B!6))) | (in(tptp_fun_C_5(A!7, B!6), A!7) <=> (~((~in(tptp_fun_C_5(A!7, B!6), A!7)) | in(tptp_fun_C_5(A!7, B!6), B!6)))))))))),
% 65.09/40.69 inference(rewrite,[status(thm)],[])).
% 65.09/40.69 tff(149,plain,
% 65.09/40.69 ((~((~((~(A!7 = set_difference(A!7, B!6))) | (in(tptp_fun_C_5(A!7, B!6), A!7) <=> (~((~in(tptp_fun_C_5(A!7, B!6), A!7)) | in(tptp_fun_C_5(A!7, B!6), B!6)))))) | (~((A!7 = set_difference(A!7, B!6)) | (in(tptp_fun_D_2(A!7, B!6, A!7), A!7) <=> ((~in(tptp_fun_D_2(A!7, B!6, A!7), A!7)) | in(tptp_fun_D_2(A!7, B!6, A!7), B!6))))))) <=> (~((~((A!7 = set_difference(A!7, B!6)) | (in(tptp_fun_D_2(A!7, B!6, A!7), A!7) <=> ((~in(tptp_fun_D_2(A!7, B!6, A!7), A!7)) | in(tptp_fun_D_2(A!7, B!6, A!7), B!6))))) | (~((~(A!7 = set_difference(A!7, B!6))) | (in(tptp_fun_C_5(A!7, B!6), A!7) <=> (~((~in(tptp_fun_C_5(A!7, B!6), A!7)) | in(tptp_fun_C_5(A!7, B!6), B!6))))))))),
% 65.09/40.69 inference(rewrite,[status(thm)],[])).
% 65.09/40.69 tff(150,plain,
% 65.09/40.69 (((~![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!7 = set_difference(A!7, B!6))) | (in(tptp_fun_C_5(A!7, B!6), A!7) <=> (~((~in(tptp_fun_C_5(A!7, B!6), A!7)) | in(tptp_fun_C_5(A!7, B!6), B!6)))))) | (~((A!7 = set_difference(A!7, B!6)) | (in(tptp_fun_D_2(A!7, B!6, A!7), A!7) <=> ((~in(tptp_fun_D_2(A!7, B!6, A!7), A!7)) | in(tptp_fun_D_2(A!7, B!6, A!7), B!6)))))))) <=> ((~![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!7 = set_difference(A!7, B!6)) | (in(tptp_fun_D_2(A!7, B!6, A!7), A!7) <=> ((~in(tptp_fun_D_2(A!7, B!6, A!7), A!7)) | in(tptp_fun_D_2(A!7, B!6, A!7), B!6))))) | (~((~(A!7 = set_difference(A!7, B!6))) | (in(tptp_fun_C_5(A!7, B!6), A!7) <=> (~((~in(tptp_fun_C_5(A!7, B!6), A!7)) | in(tptp_fun_C_5(A!7, B!6), B!6)))))))))),
% 65.09/40.69 inference(monotonicity,[status(thm)],[149])).
% 65.09/40.69 tff(151,plain,
% 65.09/40.69 (((~![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!7 = set_difference(A!7, B!6))) | (in(tptp_fun_C_5(A!7, B!6), A!7) <=> (~((~in(tptp_fun_C_5(A!7, B!6), A!7)) | in(tptp_fun_C_5(A!7, B!6), B!6)))))) | (~((A!7 = set_difference(A!7, B!6)) | (in(tptp_fun_D_2(A!7, B!6, A!7), A!7) <=> ((~in(tptp_fun_D_2(A!7, B!6, A!7), A!7)) | in(tptp_fun_D_2(A!7, B!6, A!7), B!6)))))))) <=> ((~![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!7 = set_difference(A!7, B!6)) | (in(tptp_fun_D_2(A!7, B!6, A!7), A!7) <=> ((~in(tptp_fun_D_2(A!7, B!6, A!7), A!7)) | in(tptp_fun_D_2(A!7, B!6, A!7), B!6))))) | (~((~(A!7 = set_difference(A!7, B!6))) | (in(tptp_fun_C_5(A!7, B!6), A!7) <=> (~((~in(tptp_fun_C_5(A!7, B!6), A!7)) | in(tptp_fun_C_5(A!7, B!6), B!6)))))))))),
% 65.09/40.69 inference(transitivity,[status(thm)],[150, 148])).
% 65.09/40.69 tff(152,plain,
% 65.09/40.69 ((~![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!7 = set_difference(A!7, B!6))) | (in(tptp_fun_C_5(A!7, B!6), A!7) <=> (~((~in(tptp_fun_C_5(A!7, B!6), A!7)) | in(tptp_fun_C_5(A!7, B!6), B!6)))))) | (~((A!7 = set_difference(A!7, B!6)) | (in(tptp_fun_D_2(A!7, B!6, A!7), A!7) <=> ((~in(tptp_fun_D_2(A!7, B!6, A!7), A!7)) | in(tptp_fun_D_2(A!7, B!6, A!7), B!6)))))))),
% 65.09/40.69 inference(quant_inst,[status(thm)],[])).
% 65.09/40.69 tff(153,plain,
% 65.09/40.69 ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_difference(A, B))) | (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_2(C, B, A), C) <=> ((~in(tptp_fun_D_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B)))))))) | (~((~((A!7 = set_difference(A!7, B!6)) | (in(tptp_fun_D_2(A!7, B!6, A!7), A!7) <=> ((~in(tptp_fun_D_2(A!7, B!6, A!7), A!7)) | in(tptp_fun_D_2(A!7, B!6, A!7), B!6))))) | (~((~(A!7 = set_difference(A!7, B!6))) | (in(tptp_fun_C_5(A!7, B!6), A!7) <=> (~((~in(tptp_fun_C_5(A!7, B!6), A!7)) | in(tptp_fun_C_5(A!7, B!6), B!6))))))))),
% 65.09/40.69 inference(modus_ponens,[status(thm)],[152, 151])).
% 65.09/40.69 tff(154,plain,
% 65.09/40.69 ($false),
% 65.09/40.69 inference(unit_resolution,[status(thm)],[153, 147, 126])).
% 65.09/40.69 tff(155,plain,(~((~((A!7 = set_difference(A!7, B!6)) | (in(tptp_fun_D_2(A!7, B!6, A!7), A!7) <=> ((~in(tptp_fun_D_2(A!7, B!6, A!7), A!7)) | in(tptp_fun_D_2(A!7, B!6, A!7), B!6))))) | (~((~(A!7 = set_difference(A!7, B!6))) | (in(tptp_fun_C_5(A!7, B!6), A!7) <=> (~((~in(tptp_fun_C_5(A!7, B!6), A!7)) | in(tptp_fun_C_5(A!7, B!6), B!6)))))))), inference(lemma,lemma(discharge,[]))).
% 65.09/40.69 tff(156,plain,
% 65.09/40.69 (((~((A!7 = set_difference(A!7, B!6)) | (in(tptp_fun_D_2(A!7, B!6, A!7), A!7) <=> ((~in(tptp_fun_D_2(A!7, B!6, A!7), A!7)) | in(tptp_fun_D_2(A!7, B!6, A!7), B!6))))) | (~((~(A!7 = set_difference(A!7, B!6))) | (in(tptp_fun_C_5(A!7, B!6), A!7) <=> (~((~in(tptp_fun_C_5(A!7, B!6), A!7)) | in(tptp_fun_C_5(A!7, B!6), B!6))))))) | ((~(A!7 = set_difference(A!7, B!6))) | (in(tptp_fun_C_5(A!7, B!6), A!7) <=> (~((~in(tptp_fun_C_5(A!7, B!6), A!7)) | in(tptp_fun_C_5(A!7, B!6), B!6)))))),
% 65.09/40.69 inference(tautology,[status(thm)],[])).
% 65.09/40.69 tff(157,plain,
% 65.09/40.69 ((~(A!7 = set_difference(A!7, B!6))) | (in(tptp_fun_C_5(A!7, B!6), A!7) <=> (~((~in(tptp_fun_C_5(A!7, B!6), A!7)) | in(tptp_fun_C_5(A!7, B!6), B!6))))),
% 65.09/40.69 inference(unit_resolution,[status(thm)],[156, 155])).
% 65.09/40.69 tff(158,plain,
% 65.09/40.69 ((~((~(A!7 = set_difference(A!7, B!6))) | (in(tptp_fun_C_5(A!7, B!6), A!7) <=> (~((~in(tptp_fun_C_5(A!7, B!6), A!7)) | in(tptp_fun_C_5(A!7, B!6), B!6)))))) | (~(A!7 = set_difference(A!7, B!6))) | (in(tptp_fun_C_5(A!7, B!6), A!7) <=> (~((~in(tptp_fun_C_5(A!7, B!6), A!7)) | in(tptp_fun_C_5(A!7, B!6), B!6))))),
% 65.09/40.69 inference(tautology,[status(thm)],[])).
% 65.09/40.69 tff(159,plain,
% 65.09/40.69 ((~(A!7 = set_difference(A!7, B!6))) | (in(tptp_fun_C_5(A!7, B!6), A!7) <=> (~((~in(tptp_fun_C_5(A!7, B!6), A!7)) | in(tptp_fun_C_5(A!7, B!6), B!6))))),
% 65.09/40.69 inference(unit_resolution,[status(thm)],[158, 157])).
% 65.09/40.69 tff(160,plain,
% 65.09/40.69 (in(tptp_fun_C_5(A!7, B!6), A!7) <=> (~((~in(tptp_fun_C_5(A!7, B!6), A!7)) | in(tptp_fun_C_5(A!7, B!6), B!6)))),
% 65.09/40.69 inference(unit_resolution,[status(thm)],[159, 125])).
% 65.09/40.69 tff(161,plain,
% 65.09/40.69 (((~in(tptp_fun_C_5(A!7, B!6), A!7)) | (~in(tptp_fun_C_5(A!7, B!6), B!6))) | in(tptp_fun_C_5(A!7, B!6), A!7)),
% 65.09/40.69 inference(tautology,[status(thm)],[])).
% 65.09/40.69 tff(162,plain,
% 65.09/40.69 (in(tptp_fun_C_5(A!7, B!6), A!7)),
% 65.09/40.69 inference(unit_resolution,[status(thm)],[161, 105])).
% 65.09/40.69 tff(163,plain,
% 65.09/40.69 ((~(in(tptp_fun_C_5(A!7, B!6), A!7) <=> (~((~in(tptp_fun_C_5(A!7, B!6), A!7)) | in(tptp_fun_C_5(A!7, B!6), B!6))))) | (~in(tptp_fun_C_5(A!7, B!6), A!7)) | (~((~in(tptp_fun_C_5(A!7, B!6), A!7)) | in(tptp_fun_C_5(A!7, B!6), B!6)))),
% 65.09/40.69 inference(tautology,[status(thm)],[])).
% 65.09/40.69 tff(164,plain,
% 65.09/40.69 (~((~in(tptp_fun_C_5(A!7, B!6), A!7)) | in(tptp_fun_C_5(A!7, B!6), B!6))),
% 65.09/40.69 inference(unit_resolution,[status(thm)],[163, 162, 160])).
% 65.09/40.69 tff(165,plain,
% 65.09/40.69 (((~in(tptp_fun_C_5(A!7, B!6), A!7)) | in(tptp_fun_C_5(A!7, B!6), B!6)) | (~in(tptp_fun_C_5(A!7, B!6), B!6))),
% 65.09/40.69 inference(tautology,[status(thm)],[])).
% 65.09/40.69 tff(166,plain,
% 65.09/40.69 ($false),
% 65.09/40.69 inference(unit_resolution,[status(thm)],[165, 164, 107])).
% 65.09/40.69 tff(167,plain,(disjoint(A!7, B!6)), inference(lemma,lemma(discharge,[]))).
% 65.09/40.69 tff(168,plain,
% 65.09/40.69 (^[A: $i, B: $i] : refl((disjoint(A, B) <=> (set_intersection2(A, B) = empty_set)) <=> (disjoint(A, B) <=> (set_intersection2(A, B) = empty_set)))),
% 65.09/40.69 inference(bind,[status(th)],[])).
% 65.09/40.69 tff(169,plain,
% 65.09/40.69 (![A: $i, B: $i] : (disjoint(A, B) <=> (set_intersection2(A, B) = empty_set)) <=> ![A: $i, B: $i] : (disjoint(A, B) <=> (set_intersection2(A, B) = empty_set))),
% 65.09/40.69 inference(quant_intro,[status(thm)],[168])).
% 65.09/40.69 tff(170,plain,
% 65.09/40.69 (![A: $i, B: $i] : (disjoint(A, B) <=> (set_intersection2(A, B) = empty_set)) <=> ![A: $i, B: $i] : (disjoint(A, B) <=> (set_intersection2(A, B) = empty_set))),
% 65.09/40.69 inference(rewrite,[status(thm)],[])).
% 65.09/40.69 tff(171,axiom,(![A: $i, B: $i] : (disjoint(A, B) <=> (set_intersection2(A, B) = empty_set))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d7_xboole_0')).
% 65.09/40.69 tff(172,plain,
% 65.09/40.69 (![A: $i, B: $i] : (disjoint(A, B) <=> (set_intersection2(A, B) = empty_set))),
% 65.09/40.69 inference(modus_ponens,[status(thm)],[171, 170])).
% 65.09/40.69 tff(173,plain,(
% 65.09/40.69 ![A: $i, B: $i] : (disjoint(A, B) <=> (set_intersection2(A, B) = empty_set))),
% 65.09/40.69 inference(skolemize,[status(sab)],[172])).
% 65.09/40.69 tff(174,plain,
% 65.09/40.69 (![A: $i, B: $i] : (disjoint(A, B) <=> (set_intersection2(A, B) = empty_set))),
% 65.09/40.69 inference(modus_ponens,[status(thm)],[173, 169])).
% 65.09/40.69 tff(175,plain,
% 65.09/40.69 ((~![A: $i, B: $i] : (disjoint(A, B) <=> (set_intersection2(A, B) = empty_set))) | (disjoint(A!7, B!6) <=> (set_intersection2(A!7, B!6) = empty_set))),
% 65.09/40.69 inference(quant_inst,[status(thm)],[])).
% 65.09/40.69 tff(176,plain,
% 65.09/40.69 (disjoint(A!7, B!6) <=> (set_intersection2(A!7, B!6) = empty_set)),
% 65.09/40.69 inference(unit_resolution,[status(thm)],[175, 174])).
% 65.09/40.69 tff(177,plain,
% 65.09/40.69 ((~(disjoint(A!7, B!6) <=> (set_intersection2(A!7, B!6) = empty_set))) | (~disjoint(A!7, B!6)) | (set_intersection2(A!7, B!6) = empty_set)),
% 65.09/40.69 inference(tautology,[status(thm)],[])).
% 65.09/40.69 tff(178,plain,
% 65.09/40.69 ((~disjoint(A!7, B!6)) | (set_intersection2(A!7, B!6) = empty_set)),
% 65.09/40.69 inference(unit_resolution,[status(thm)],[177, 176])).
% 65.09/40.69 tff(179,plain,
% 65.09/40.69 (set_intersection2(A!7, B!6) = empty_set),
% 65.09/40.69 inference(unit_resolution,[status(thm)],[178, 167])).
% 65.09/40.69 tff(180,plain,
% 65.09/40.69 (empty_set = set_intersection2(A!7, B!6)),
% 65.09/40.69 inference(symmetry,[status(thm)],[179])).
% 65.09/40.69 tff(181,plain,
% 65.09/40.69 ((~((~(empty_set = set_intersection2(A!7, B!6))) | (in(tptp_fun_D_2(A!7, B!6, A!7), empty_set) <=> (~((~in(tptp_fun_D_2(A!7, B!6, A!7), A!7)) | (~in(tptp_fun_D_2(A!7, B!6, A!7), B!6))))))) | (~(empty_set = set_intersection2(A!7, B!6))) | (in(tptp_fun_D_2(A!7, B!6, A!7), empty_set) <=> (~((~in(tptp_fun_D_2(A!7, B!6, A!7), A!7)) | (~in(tptp_fun_D_2(A!7, B!6, A!7), B!6)))))),
% 65.09/40.69 inference(tautology,[status(thm)],[])).
% 65.09/40.69 tff(182,plain,
% 65.09/40.69 ((~((~(empty_set = set_intersection2(A!7, B!6))) | (in(tptp_fun_D_2(A!7, B!6, A!7), empty_set) <=> (~((~in(tptp_fun_D_2(A!7, B!6, A!7), A!7)) | (~in(tptp_fun_D_2(A!7, B!6, A!7), B!6))))))) | (in(tptp_fun_D_2(A!7, B!6, A!7), empty_set) <=> (~((~in(tptp_fun_D_2(A!7, B!6, A!7), A!7)) | (~in(tptp_fun_D_2(A!7, B!6, A!7), B!6)))))),
% 65.09/40.69 inference(unit_resolution,[status(thm)],[181, 180])).
% 65.09/40.69 tff(183,plain,
% 65.09/40.69 (in(tptp_fun_D_2(A!7, B!6, A!7), empty_set) <=> (~((~in(tptp_fun_D_2(A!7, B!6, A!7), A!7)) | (~in(tptp_fun_D_2(A!7, B!6, A!7), B!6))))),
% 65.09/40.69 inference(unit_resolution,[status(thm)],[182, 32])).
% 65.09/40.69 tff(184,plain,
% 65.09/40.69 ((~(set_difference(A!7, B!6) = A!7)) <=> (~(A!7 = set_difference(A!7, B!6)))),
% 65.09/40.69 inference(monotonicity,[status(thm)],[109])).
% 65.09/40.69 tff(185,plain,
% 65.09/40.69 ((~disjoint(A!7, B!6)) | (~(set_difference(A!7, B!6) = A!7)) | (~((~disjoint(A!7, B!6)) <=> (set_difference(A!7, B!6) = A!7)))),
% 65.09/40.69 inference(tautology,[status(thm)],[])).
% 65.09/40.69 tff(186,plain,
% 65.09/40.69 ((~disjoint(A!7, B!6)) | (~(set_difference(A!7, B!6) = A!7))),
% 65.09/40.69 inference(unit_resolution,[status(thm)],[185, 121])).
% 65.09/40.69 tff(187,plain,
% 65.09/40.69 (~(set_difference(A!7, B!6) = A!7)),
% 65.09/40.69 inference(unit_resolution,[status(thm)],[186, 167])).
% 65.09/40.69 tff(188,plain,
% 65.09/40.69 (~(A!7 = set_difference(A!7, B!6))),
% 65.09/40.69 inference(modus_ponens,[status(thm)],[187, 184])).
% 65.09/40.69 tff(189,plain,
% 65.09/40.69 ((~![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!7 = set_difference(A!7, B!6))) | (in(A!7, A!7) <=> (~((~in(A!7, A!7)) | in(A!7, B!6)))))) | (~((A!7 = set_difference(A!7, B!6)) | (in(tptp_fun_D_2(A!7, B!6, A!7), A!7) <=> ((~in(tptp_fun_D_2(A!7, B!6, A!7), A!7)) | in(tptp_fun_D_2(A!7, B!6, A!7), B!6)))))))),
% 65.09/40.69 inference(quant_inst,[status(thm)],[])).
% 65.09/40.69 tff(190,plain,
% 65.09/40.69 (~((~((~(A!7 = set_difference(A!7, B!6))) | (in(A!7, A!7) <=> (~((~in(A!7, A!7)) | in(A!7, B!6)))))) | (~((A!7 = set_difference(A!7, B!6)) | (in(tptp_fun_D_2(A!7, B!6, A!7), A!7) <=> ((~in(tptp_fun_D_2(A!7, B!6, A!7), A!7)) | in(tptp_fun_D_2(A!7, B!6, A!7), B!6))))))),
% 65.09/40.69 inference(unit_resolution,[status(thm)],[189, 147])).
% 65.09/40.69 tff(191,plain,
% 65.09/40.69 (((~((~(A!7 = set_difference(A!7, B!6))) | (in(A!7, A!7) <=> (~((~in(A!7, A!7)) | in(A!7, B!6)))))) | (~((A!7 = set_difference(A!7, B!6)) | (in(tptp_fun_D_2(A!7, B!6, A!7), A!7) <=> ((~in(tptp_fun_D_2(A!7, B!6, A!7), A!7)) | in(tptp_fun_D_2(A!7, B!6, A!7), B!6)))))) | ((A!7 = set_difference(A!7, B!6)) | (in(tptp_fun_D_2(A!7, B!6, A!7), A!7) <=> ((~in(tptp_fun_D_2(A!7, B!6, A!7), A!7)) | in(tptp_fun_D_2(A!7, B!6, A!7), B!6))))),
% 65.09/40.69 inference(tautology,[status(thm)],[])).
% 65.09/40.69 tff(192,plain,
% 65.09/40.69 ((A!7 = set_difference(A!7, B!6)) | (in(tptp_fun_D_2(A!7, B!6, A!7), A!7) <=> ((~in(tptp_fun_D_2(A!7, B!6, A!7), A!7)) | in(tptp_fun_D_2(A!7, B!6, A!7), B!6)))),
% 65.09/40.69 inference(unit_resolution,[status(thm)],[191, 190])).
% 65.09/40.69 tff(193,plain,
% 65.09/40.69 ((~((A!7 = set_difference(A!7, B!6)) | (in(tptp_fun_D_2(A!7, B!6, A!7), A!7) <=> ((~in(tptp_fun_D_2(A!7, B!6, A!7), A!7)) | in(tptp_fun_D_2(A!7, B!6, A!7), B!6))))) | (A!7 = set_difference(A!7, B!6)) | (in(tptp_fun_D_2(A!7, B!6, A!7), A!7) <=> ((~in(tptp_fun_D_2(A!7, B!6, A!7), A!7)) | in(tptp_fun_D_2(A!7, B!6, A!7), B!6)))),
% 65.09/40.69 inference(tautology,[status(thm)],[])).
% 65.09/40.69 tff(194,plain,
% 65.09/40.69 ((A!7 = set_difference(A!7, B!6)) | (in(tptp_fun_D_2(A!7, B!6, A!7), A!7) <=> ((~in(tptp_fun_D_2(A!7, B!6, A!7), A!7)) | in(tptp_fun_D_2(A!7, B!6, A!7), B!6)))),
% 65.09/40.69 inference(unit_resolution,[status(thm)],[193, 192])).
% 65.09/40.69 tff(195,plain,
% 65.09/40.69 (in(tptp_fun_D_2(A!7, B!6, A!7), A!7) <=> ((~in(tptp_fun_D_2(A!7, B!6, A!7), A!7)) | in(tptp_fun_D_2(A!7, B!6, A!7), B!6))),
% 65.09/40.69 inference(unit_resolution,[status(thm)],[194, 188])).
% 65.09/40.69 tff(196,assumption,(~((~in(tptp_fun_D_2(A!7, B!6, A!7), A!7)) | in(tptp_fun_D_2(A!7, B!6, A!7), B!6))), introduced(assumption)).
% 65.09/40.69 tff(197,plain,
% 65.09/40.69 (((~in(tptp_fun_D_2(A!7, B!6, A!7), A!7)) | in(tptp_fun_D_2(A!7, B!6, A!7), B!6)) | in(tptp_fun_D_2(A!7, B!6, A!7), A!7)),
% 65.09/40.69 inference(tautology,[status(thm)],[])).
% 65.09/40.69 tff(198,plain,
% 65.09/40.69 (in(tptp_fun_D_2(A!7, B!6, A!7), A!7)),
% 65.09/40.69 inference(unit_resolution,[status(thm)],[197, 196])).
% 65.09/40.69 tff(199,plain,
% 65.09/40.69 ((~(in(tptp_fun_D_2(A!7, B!6, A!7), A!7) <=> ((~in(tptp_fun_D_2(A!7, B!6, A!7), A!7)) | in(tptp_fun_D_2(A!7, B!6, A!7), B!6)))) | (~in(tptp_fun_D_2(A!7, B!6, A!7), A!7)) | ((~in(tptp_fun_D_2(A!7, B!6, A!7), A!7)) | in(tptp_fun_D_2(A!7, B!6, A!7), B!6))),
% 65.09/40.69 inference(tautology,[status(thm)],[])).
% 65.09/40.69 tff(200,plain,
% 65.09/40.69 ($false),
% 65.09/40.69 inference(unit_resolution,[status(thm)],[199, 198, 196, 195])).
% 65.09/40.69 tff(201,plain,((~in(tptp_fun_D_2(A!7, B!6, A!7), A!7)) | in(tptp_fun_D_2(A!7, B!6, A!7), B!6)), inference(lemma,lemma(discharge,[]))).
% 65.09/40.69 tff(202,plain,
% 65.09/40.69 ((~(in(tptp_fun_D_2(A!7, B!6, A!7), A!7) <=> ((~in(tptp_fun_D_2(A!7, B!6, A!7), A!7)) | in(tptp_fun_D_2(A!7, B!6, A!7), B!6)))) | in(tptp_fun_D_2(A!7, B!6, A!7), A!7) | (~((~in(tptp_fun_D_2(A!7, B!6, A!7), A!7)) | in(tptp_fun_D_2(A!7, B!6, A!7), B!6)))),
% 65.09/40.69 inference(tautology,[status(thm)],[])).
% 65.09/40.69 tff(203,plain,
% 65.09/40.69 (in(tptp_fun_D_2(A!7, B!6, A!7), A!7)),
% 65.09/40.69 inference(unit_resolution,[status(thm)],[202, 201, 195])).
% 65.09/40.69 tff(204,plain,
% 65.09/40.69 ((~((~in(tptp_fun_D_2(A!7, B!6, A!7), A!7)) | in(tptp_fun_D_2(A!7, B!6, A!7), B!6))) | (~in(tptp_fun_D_2(A!7, B!6, A!7), A!7)) | in(tptp_fun_D_2(A!7, B!6, A!7), B!6)),
% 65.09/40.69 inference(tautology,[status(thm)],[])).
% 65.09/40.69 tff(205,plain,
% 65.09/40.69 (in(tptp_fun_D_2(A!7, B!6, A!7), B!6)),
% 65.09/40.69 inference(unit_resolution,[status(thm)],[204, 203, 201])).
% 65.09/40.69 tff(206,plain,
% 65.09/40.69 ((~((~in(tptp_fun_D_2(A!7, B!6, A!7), A!7)) | (~in(tptp_fun_D_2(A!7, B!6, A!7), B!6)))) | (~in(tptp_fun_D_2(A!7, B!6, A!7), A!7)) | (~in(tptp_fun_D_2(A!7, B!6, A!7), B!6))),
% 65.09/40.69 inference(tautology,[status(thm)],[])).
% 65.09/40.69 tff(207,plain,
% 65.09/40.69 (~((~in(tptp_fun_D_2(A!7, B!6, A!7), A!7)) | (~in(tptp_fun_D_2(A!7, B!6, A!7), B!6)))),
% 65.09/40.69 inference(unit_resolution,[status(thm)],[206, 205, 203])).
% 65.09/40.69 tff(208,plain,
% 65.09/40.69 ((~(in(tptp_fun_D_2(A!7, B!6, A!7), empty_set) <=> (~((~in(tptp_fun_D_2(A!7, B!6, A!7), A!7)) | (~in(tptp_fun_D_2(A!7, B!6, A!7), B!6)))))) | in(tptp_fun_D_2(A!7, B!6, A!7), empty_set) | ((~in(tptp_fun_D_2(A!7, B!6, A!7), A!7)) | (~in(tptp_fun_D_2(A!7, B!6, A!7), B!6)))),
% 65.09/40.69 inference(tautology,[status(thm)],[])).
% 65.09/40.69 tff(209,plain,
% 65.09/40.69 ((~(in(tptp_fun_D_2(A!7, B!6, A!7), empty_set) <=> (~((~in(tptp_fun_D_2(A!7, B!6, A!7), A!7)) | (~in(tptp_fun_D_2(A!7, B!6, A!7), B!6)))))) | in(tptp_fun_D_2(A!7, B!6, A!7), empty_set)),
% 65.09/40.70 inference(unit_resolution,[status(thm)],[208, 207])).
% 65.09/40.70 tff(210,plain,
% 65.09/40.70 (in(tptp_fun_D_2(A!7, B!6, A!7), empty_set)),
% 65.09/40.70 inference(unit_resolution,[status(thm)],[209, 183])).
% 65.09/40.70 tff(211,plain,
% 65.09/40.70 (^[A: $i, B: $i] : refl(((~empty(B)) | (~in(A, B))) <=> ((~empty(B)) | (~in(A, B))))),
% 65.09/40.70 inference(bind,[status(th)],[])).
% 65.09/40.70 tff(212,plain,
% 65.09/40.70 (![A: $i, B: $i] : ((~empty(B)) | (~in(A, B))) <=> ![A: $i, B: $i] : ((~empty(B)) | (~in(A, B)))),
% 65.09/40.70 inference(quant_intro,[status(thm)],[211])).
% 65.09/40.70 tff(213,plain,
% 65.09/40.70 (^[A: $i, B: $i] : trans(monotonicity(rewrite((in(A, B) & empty(B)) <=> (~((~empty(B)) | (~in(A, B))))), ((~(in(A, B) & empty(B))) <=> (~(~((~empty(B)) | (~in(A, B))))))), rewrite((~(~((~empty(B)) | (~in(A, B))))) <=> ((~empty(B)) | (~in(A, B)))), ((~(in(A, B) & empty(B))) <=> ((~empty(B)) | (~in(A, B)))))),
% 65.09/40.70 inference(bind,[status(th)],[])).
% 65.09/40.70 tff(214,plain,
% 65.09/40.70 (![A: $i, B: $i] : (~(in(A, B) & empty(B))) <=> ![A: $i, B: $i] : ((~empty(B)) | (~in(A, B)))),
% 65.09/40.70 inference(quant_intro,[status(thm)],[213])).
% 65.09/40.70 tff(215,plain,
% 65.09/40.70 (![A: $i, B: $i] : (~(in(A, B) & empty(B))) <=> ![A: $i, B: $i] : (~(in(A, B) & empty(B)))),
% 65.09/40.70 inference(rewrite,[status(thm)],[])).
% 65.09/40.70 tff(216,axiom,(![A: $i, B: $i] : (~(in(A, B) & empty(B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t7_boole')).
% 65.09/40.70 tff(217,plain,
% 65.09/40.70 (![A: $i, B: $i] : (~(in(A, B) & empty(B)))),
% 65.09/40.70 inference(modus_ponens,[status(thm)],[216, 215])).
% 65.09/40.70 tff(218,plain,(
% 65.09/40.70 ![A: $i, B: $i] : (~(in(A, B) & empty(B)))),
% 65.09/40.70 inference(skolemize,[status(sab)],[217])).
% 65.09/40.70 tff(219,plain,
% 65.09/40.70 (![A: $i, B: $i] : ((~empty(B)) | (~in(A, B)))),
% 65.09/40.70 inference(modus_ponens,[status(thm)],[218, 214])).
% 65.09/40.70 tff(220,plain,
% 65.09/40.70 (![A: $i, B: $i] : ((~empty(B)) | (~in(A, B)))),
% 65.09/40.70 inference(modus_ponens,[status(thm)],[219, 212])).
% 65.09/40.70 tff(221,plain,
% 65.09/40.70 (empty(empty_set) <=> empty(empty_set)),
% 65.09/40.70 inference(rewrite,[status(thm)],[])).
% 65.09/40.70 tff(222,axiom,(empty(empty_set)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','fc1_xboole_0')).
% 65.09/40.70 tff(223,plain,
% 65.09/40.70 (empty(empty_set)),
% 65.09/40.70 inference(modus_ponens,[status(thm)],[222, 221])).
% 65.09/40.70 tff(224,plain,
% 65.09/40.70 (((~![A: $i, B: $i] : ((~empty(B)) | (~in(A, B)))) | ((~empty(empty_set)) | (~in(tptp_fun_D_2(A!7, B!6, A!7), empty_set)))) <=> ((~![A: $i, B: $i] : ((~empty(B)) | (~in(A, B)))) | (~empty(empty_set)) | (~in(tptp_fun_D_2(A!7, B!6, A!7), empty_set)))),
% 65.09/40.70 inference(rewrite,[status(thm)],[])).
% 65.09/40.70 tff(225,plain,
% 65.09/40.70 ((~![A: $i, B: $i] : ((~empty(B)) | (~in(A, B)))) | ((~empty(empty_set)) | (~in(tptp_fun_D_2(A!7, B!6, A!7), empty_set)))),
% 65.09/40.70 inference(quant_inst,[status(thm)],[])).
% 65.09/40.70 tff(226,plain,
% 65.09/40.70 ((~![A: $i, B: $i] : ((~empty(B)) | (~in(A, B)))) | (~empty(empty_set)) | (~in(tptp_fun_D_2(A!7, B!6, A!7), empty_set))),
% 65.09/40.70 inference(modus_ponens,[status(thm)],[225, 224])).
% 65.09/40.70 tff(227,plain,
% 65.09/40.70 ($false),
% 65.09/40.70 inference(unit_resolution,[status(thm)],[226, 223, 220, 210])).
% 65.09/40.70 % SZS output end Proof
%------------------------------------------------------------------------------