TSTP Solution File: SEU129+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SEU129+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 07:27:38 EDT 2022
% Result : Theorem 0.14s 0.41s
% Output : Proof 0.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : SEU129+1 : TPTP v8.1.0. Released v3.3.0.
% 0.08/0.14 % 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 09:31:02 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.14/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.14/0.35 Usage: tptp [options] [-file:]file
% 0.14/0.35 -h, -? prints this message.
% 0.14/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.14/0.35 -m, -model generate model.
% 0.14/0.35 -p, -proof generate proof.
% 0.14/0.35 -c, -core generate unsat core of named formulas.
% 0.14/0.35 -st, -statistics display statistics.
% 0.14/0.35 -t:timeout set timeout (in second).
% 0.14/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.14/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.14/0.35 -<param>:<value> configuration parameter and value.
% 0.14/0.35 -o:<output-file> file to place output in.
% 0.14/0.41 % SZS status Theorem
% 0.14/0.41 % SZS output start Proof
% 0.14/0.41 tff(in_type, type, (
% 0.14/0.41 in: ( $i * $i ) > $o)).
% 0.14/0.41 tff(tptp_fun_B_5_type, type, (
% 0.14/0.41 tptp_fun_B_5: $i)).
% 0.14/0.41 tff(tptp_fun_C_0_type, type, (
% 0.14/0.41 tptp_fun_C_0: ( $i * $i ) > $i)).
% 0.14/0.41 tff(set_intersection2_type, type, (
% 0.14/0.41 set_intersection2: ( $i * $i ) > $i)).
% 0.14/0.41 tff(tptp_fun_C_4_type, type, (
% 0.14/0.41 tptp_fun_C_4: $i)).
% 0.14/0.41 tff(tptp_fun_A_6_type, type, (
% 0.14/0.41 tptp_fun_A_6: $i)).
% 0.14/0.41 tff(tptp_fun_D_1_type, type, (
% 0.14/0.41 tptp_fun_D_1: ( $i * $i * $i ) > $i)).
% 0.14/0.41 tff(subset_type, type, (
% 0.14/0.41 subset: ( $i * $i ) > $o)).
% 0.14/0.41 tff(1,plain,
% 0.14/0.41 (^[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)))))))))),
% 0.14/0.41 inference(bind,[status(th)],[])).
% 0.14/0.41 tff(2,plain,
% 0.14/0.41 (![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))))))))),
% 0.14/0.41 inference(quant_intro,[status(thm)],[1])).
% 0.14/0.41 tff(3,plain,
% 0.14/0.41 (![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))))))))),
% 0.14/0.41 inference(pull_quant,[status(thm)],[])).
% 0.14/0.41 tff(4,plain,
% 0.14/0.41 (^[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))))))))))),
% 0.14/0.41 inference(bind,[status(th)],[])).
% 0.14/0.41 tff(5,plain,
% 0.14/0.41 (![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))))))))),
% 0.14/0.41 inference(quant_intro,[status(thm)],[4])).
% 0.14/0.41 tff(6,plain,
% 0.14/0.41 (![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))))))))),
% 0.14/0.41 inference(transitivity,[status(thm)],[5, 3])).
% 0.14/0.41 tff(7,plain,
% 0.14/0.41 (![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))))))))),
% 0.14/0.41 inference(transitivity,[status(thm)],[6, 2])).
% 0.14/0.41 tff(8,plain,
% 0.14/0.41 (^[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)))))))))),
% 0.14/0.41 inference(bind,[status(th)],[])).
% 0.14/0.41 tff(9,plain,
% 0.14/0.41 (![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))))))))),
% 0.14/0.41 inference(quant_intro,[status(thm)],[8])).
% 0.14/0.41 tff(10,plain,
% 0.14/0.41 (![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))))))))),
% 0.14/0.41 inference(transitivity,[status(thm)],[9, 7])).
% 0.14/0.41 tff(11,plain,
% 0.14/0.41 (^[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))))))))))),
% 0.14/0.41 inference(bind,[status(th)],[])).
% 0.14/0.41 tff(12,plain,
% 0.14/0.41 (![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))))))))),
% 0.22/0.41 inference(quant_intro,[status(thm)],[11])).
% 0.22/0.41 tff(13,plain,
% 0.22/0.41 (^[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))))))),
% 0.22/0.41 inference(bind,[status(th)],[])).
% 0.22/0.41 tff(14,plain,
% 0.22/0.41 (![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)))))),
% 0.22/0.41 inference(quant_intro,[status(thm)],[13])).
% 0.22/0.41 tff(15,plain,
% 0.22/0.41 (![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))))),
% 0.22/0.41 inference(rewrite,[status(thm)],[])).
% 0.22/0.41 tff(16,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')).
% 0.22/0.41 tff(17,plain,
% 0.22/0.41 (![A: $i, B: $i, C: $i] : ((C = set_intersection2(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, A) & in(D, B))))),
% 0.22/0.41 inference(modus_ponens,[status(thm)],[16, 15])).
% 0.22/0.41 tff(18,plain,(
% 0.22/0.41 ![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))))))),
% 0.22/0.41 inference(skolemize,[status(sab)],[17])).
% 0.22/0.41 tff(19,plain,
% 0.22/0.41 (![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)))))),
% 0.22/0.41 inference(modus_ponens,[status(thm)],[18, 14])).
% 0.22/0.41 tff(20,plain,
% 0.22/0.41 (![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))))))))),
% 0.22/0.41 inference(modus_ponens,[status(thm)],[19, 12])).
% 0.22/0.41 tff(21,plain,
% 0.22/0.41 (![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))))))))),
% 0.22/0.41 inference(modus_ponens,[status(thm)],[20, 10])).
% 0.22/0.41 tff(22,plain,
% 0.22/0.41 (((~![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_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), set_intersection2(C!4, B!5))) <=> ((~in(tptp_fun_C_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), B!5)) | (~in(tptp_fun_C_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), C!4))))) <=> ((~![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_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), set_intersection2(C!4, B!5))) <=> ((~in(tptp_fun_C_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), B!5)) | (~in(tptp_fun_C_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), C!4)))))),
% 0.22/0.42 inference(rewrite,[status(thm)],[])).
% 0.22/0.42 tff(23,plain,
% 0.22/0.42 ((~(in(tptp_fun_C_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), set_intersection2(C!4, B!5)) <=> ((~in(tptp_fun_C_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), B!5)) | (~in(tptp_fun_C_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), C!4))))) <=> ((~in(tptp_fun_C_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), set_intersection2(C!4, B!5))) <=> ((~in(tptp_fun_C_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), B!5)) | (~in(tptp_fun_C_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), C!4))))),
% 0.22/0.42 inference(rewrite,[status(thm)],[])).
% 0.22/0.42 tff(24,plain,
% 0.22/0.42 (((in(tptp_fun_C_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), set_intersection2(C!4, B!5)) <=> ((~in(tptp_fun_C_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), B!5)) | (~in(tptp_fun_C_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), C!4)))) | $false) <=> (in(tptp_fun_C_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), set_intersection2(C!4, B!5)) <=> ((~in(tptp_fun_C_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), B!5)) | (~in(tptp_fun_C_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), C!4))))),
% 0.22/0.42 inference(rewrite,[status(thm)],[])).
% 0.22/0.42 tff(25,plain,
% 0.22/0.42 ((~$true) <=> $false),
% 0.22/0.42 inference(rewrite,[status(thm)],[])).
% 0.22/0.42 tff(26,plain,
% 0.22/0.42 (($true | (in(tptp_fun_D_1(set_intersection2(C!4, B!5), B!5, C!4), set_intersection2(C!4, B!5)) <=> ((~in(tptp_fun_D_1(set_intersection2(C!4, B!5), B!5, C!4), C!4)) | (~in(tptp_fun_D_1(set_intersection2(C!4, B!5), B!5, C!4), B!5))))) <=> $true),
% 0.22/0.42 inference(rewrite,[status(thm)],[])).
% 0.22/0.42 tff(27,plain,
% 0.22/0.42 ((in(tptp_fun_D_1(set_intersection2(C!4, B!5), B!5, C!4), set_intersection2(C!4, B!5)) <=> ((~in(tptp_fun_D_1(set_intersection2(C!4, B!5), B!5, C!4), C!4)) | (~in(tptp_fun_D_1(set_intersection2(C!4, B!5), B!5, C!4), B!5)))) <=> (in(tptp_fun_D_1(set_intersection2(C!4, B!5), B!5, C!4), set_intersection2(C!4, B!5)) <=> ((~in(tptp_fun_D_1(set_intersection2(C!4, B!5), B!5, C!4), C!4)) | (~in(tptp_fun_D_1(set_intersection2(C!4, B!5), B!5, C!4), B!5))))),
% 0.22/0.42 inference(rewrite,[status(thm)],[])).
% 0.22/0.42 tff(28,plain,
% 0.22/0.42 ((set_intersection2(C!4, B!5) = set_intersection2(C!4, B!5)) <=> $true),
% 0.22/0.42 inference(rewrite,[status(thm)],[])).
% 0.22/0.42 tff(29,plain,
% 0.22/0.42 (((set_intersection2(C!4, B!5) = set_intersection2(C!4, B!5)) | (in(tptp_fun_D_1(set_intersection2(C!4, B!5), B!5, C!4), set_intersection2(C!4, B!5)) <=> ((~in(tptp_fun_D_1(set_intersection2(C!4, B!5), B!5, C!4), C!4)) | (~in(tptp_fun_D_1(set_intersection2(C!4, B!5), B!5, C!4), B!5))))) <=> ($true | (in(tptp_fun_D_1(set_intersection2(C!4, B!5), B!5, C!4), set_intersection2(C!4, B!5)) <=> ((~in(tptp_fun_D_1(set_intersection2(C!4, B!5), B!5, C!4), C!4)) | (~in(tptp_fun_D_1(set_intersection2(C!4, B!5), B!5, C!4), B!5)))))),
% 0.22/0.42 inference(monotonicity,[status(thm)],[28, 27])).
% 0.22/0.42 tff(30,plain,
% 0.22/0.42 (((set_intersection2(C!4, B!5) = set_intersection2(C!4, B!5)) | (in(tptp_fun_D_1(set_intersection2(C!4, B!5), B!5, C!4), set_intersection2(C!4, B!5)) <=> ((~in(tptp_fun_D_1(set_intersection2(C!4, B!5), B!5, C!4), C!4)) | (~in(tptp_fun_D_1(set_intersection2(C!4, B!5), B!5, C!4), B!5))))) <=> $true),
% 0.22/0.42 inference(transitivity,[status(thm)],[29, 26])).
% 0.22/0.42 tff(31,plain,
% 0.22/0.42 ((~((set_intersection2(C!4, B!5) = set_intersection2(C!4, B!5)) | (in(tptp_fun_D_1(set_intersection2(C!4, B!5), B!5, C!4), set_intersection2(C!4, B!5)) <=> ((~in(tptp_fun_D_1(set_intersection2(C!4, B!5), B!5, C!4), C!4)) | (~in(tptp_fun_D_1(set_intersection2(C!4, B!5), B!5, C!4), B!5)))))) <=> (~$true)),
% 0.22/0.42 inference(monotonicity,[status(thm)],[30])).
% 0.22/0.42 tff(32,plain,
% 0.22/0.42 ((~((set_intersection2(C!4, B!5) = set_intersection2(C!4, B!5)) | (in(tptp_fun_D_1(set_intersection2(C!4, B!5), B!5, C!4), set_intersection2(C!4, B!5)) <=> ((~in(tptp_fun_D_1(set_intersection2(C!4, B!5), B!5, C!4), C!4)) | (~in(tptp_fun_D_1(set_intersection2(C!4, B!5), B!5, C!4), B!5)))))) <=> $false),
% 0.22/0.42 inference(transitivity,[status(thm)],[31, 25])).
% 0.22/0.42 tff(33,plain,
% 0.22/0.42 ((~(in(tptp_fun_C_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), set_intersection2(C!4, B!5)) <=> (~((~in(tptp_fun_C_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), B!5)) | (~in(tptp_fun_C_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), C!4)))))) <=> (in(tptp_fun_C_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), set_intersection2(C!4, B!5)) <=> ((~in(tptp_fun_C_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), B!5)) | (~in(tptp_fun_C_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), C!4))))),
% 0.22/0.42 inference(rewrite,[status(thm)],[])).
% 0.22/0.42 tff(34,plain,
% 0.22/0.42 (($false | (in(tptp_fun_C_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), set_intersection2(C!4, B!5)) <=> (~((~in(tptp_fun_C_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), B!5)) | (~in(tptp_fun_C_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), C!4)))))) <=> (in(tptp_fun_C_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), set_intersection2(C!4, B!5)) <=> (~((~in(tptp_fun_C_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), B!5)) | (~in(tptp_fun_C_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), C!4)))))),
% 0.22/0.42 inference(rewrite,[status(thm)],[])).
% 0.22/0.42 tff(35,plain,
% 0.22/0.42 ((~(set_intersection2(C!4, B!5) = set_intersection2(C!4, B!5))) <=> (~$true)),
% 0.22/0.42 inference(monotonicity,[status(thm)],[28])).
% 0.22/0.42 tff(36,plain,
% 0.22/0.42 ((~(set_intersection2(C!4, B!5) = set_intersection2(C!4, B!5))) <=> $false),
% 0.22/0.42 inference(transitivity,[status(thm)],[35, 25])).
% 0.22/0.42 tff(37,plain,
% 0.22/0.42 (((~(set_intersection2(C!4, B!5) = set_intersection2(C!4, B!5))) | (in(tptp_fun_C_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), set_intersection2(C!4, B!5)) <=> (~((~in(tptp_fun_C_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), B!5)) | (~in(tptp_fun_C_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), C!4)))))) <=> ($false | (in(tptp_fun_C_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), set_intersection2(C!4, B!5)) <=> (~((~in(tptp_fun_C_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), B!5)) | (~in(tptp_fun_C_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), C!4))))))),
% 0.22/0.42 inference(monotonicity,[status(thm)],[36])).
% 0.22/0.42 tff(38,plain,
% 0.22/0.42 (((~(set_intersection2(C!4, B!5) = set_intersection2(C!4, B!5))) | (in(tptp_fun_C_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), set_intersection2(C!4, B!5)) <=> (~((~in(tptp_fun_C_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), B!5)) | (~in(tptp_fun_C_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), C!4)))))) <=> (in(tptp_fun_C_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), set_intersection2(C!4, B!5)) <=> (~((~in(tptp_fun_C_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), B!5)) | (~in(tptp_fun_C_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), C!4)))))),
% 0.22/0.42 inference(transitivity,[status(thm)],[37, 34])).
% 0.22/0.42 tff(39,plain,
% 0.22/0.42 ((~((~(set_intersection2(C!4, B!5) = set_intersection2(C!4, B!5))) | (in(tptp_fun_C_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), set_intersection2(C!4, B!5)) <=> (~((~in(tptp_fun_C_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), B!5)) | (~in(tptp_fun_C_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), C!4))))))) <=> (~(in(tptp_fun_C_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), set_intersection2(C!4, B!5)) <=> (~((~in(tptp_fun_C_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), B!5)) | (~in(tptp_fun_C_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), C!4))))))),
% 0.22/0.42 inference(monotonicity,[status(thm)],[38])).
% 0.22/0.42 tff(40,plain,
% 0.22/0.42 ((~((~(set_intersection2(C!4, B!5) = set_intersection2(C!4, B!5))) | (in(tptp_fun_C_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), set_intersection2(C!4, B!5)) <=> (~((~in(tptp_fun_C_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), B!5)) | (~in(tptp_fun_C_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), C!4))))))) <=> (in(tptp_fun_C_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), set_intersection2(C!4, B!5)) <=> ((~in(tptp_fun_C_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), B!5)) | (~in(tptp_fun_C_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), C!4))))),
% 0.22/0.42 inference(transitivity,[status(thm)],[39, 33])).
% 0.22/0.42 tff(41,plain,
% 0.22/0.42 (((~((~(set_intersection2(C!4, B!5) = set_intersection2(C!4, B!5))) | (in(tptp_fun_C_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), set_intersection2(C!4, B!5)) <=> (~((~in(tptp_fun_C_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), B!5)) | (~in(tptp_fun_C_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), C!4))))))) | (~((set_intersection2(C!4, B!5) = set_intersection2(C!4, B!5)) | (in(tptp_fun_D_1(set_intersection2(C!4, B!5), B!5, C!4), set_intersection2(C!4, B!5)) <=> ((~in(tptp_fun_D_1(set_intersection2(C!4, B!5), B!5, C!4), C!4)) | (~in(tptp_fun_D_1(set_intersection2(C!4, B!5), B!5, C!4), B!5))))))) <=> ((in(tptp_fun_C_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), set_intersection2(C!4, B!5)) <=> ((~in(tptp_fun_C_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), B!5)) | (~in(tptp_fun_C_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), C!4)))) | $false)),
% 0.22/0.42 inference(monotonicity,[status(thm)],[40, 32])).
% 0.22/0.42 tff(42,plain,
% 0.22/0.42 (((~((~(set_intersection2(C!4, B!5) = set_intersection2(C!4, B!5))) | (in(tptp_fun_C_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), set_intersection2(C!4, B!5)) <=> (~((~in(tptp_fun_C_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), B!5)) | (~in(tptp_fun_C_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), C!4))))))) | (~((set_intersection2(C!4, B!5) = set_intersection2(C!4, B!5)) | (in(tptp_fun_D_1(set_intersection2(C!4, B!5), B!5, C!4), set_intersection2(C!4, B!5)) <=> ((~in(tptp_fun_D_1(set_intersection2(C!4, B!5), B!5, C!4), C!4)) | (~in(tptp_fun_D_1(set_intersection2(C!4, B!5), B!5, C!4), B!5))))))) <=> (in(tptp_fun_C_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), set_intersection2(C!4, B!5)) <=> ((~in(tptp_fun_C_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), B!5)) | (~in(tptp_fun_C_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), C!4))))),
% 0.22/0.42 inference(transitivity,[status(thm)],[41, 24])).
% 0.22/0.42 tff(43,plain,
% 0.22/0.42 ((~((~((~(set_intersection2(C!4, B!5) = set_intersection2(C!4, B!5))) | (in(tptp_fun_C_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), set_intersection2(C!4, B!5)) <=> (~((~in(tptp_fun_C_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), B!5)) | (~in(tptp_fun_C_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), C!4))))))) | (~((set_intersection2(C!4, B!5) = set_intersection2(C!4, B!5)) | (in(tptp_fun_D_1(set_intersection2(C!4, B!5), B!5, C!4), set_intersection2(C!4, B!5)) <=> ((~in(tptp_fun_D_1(set_intersection2(C!4, B!5), B!5, C!4), C!4)) | (~in(tptp_fun_D_1(set_intersection2(C!4, B!5), B!5, C!4), B!5)))))))) <=> (~(in(tptp_fun_C_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), set_intersection2(C!4, B!5)) <=> ((~in(tptp_fun_C_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), B!5)) | (~in(tptp_fun_C_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), C!4)))))),
% 0.22/0.42 inference(monotonicity,[status(thm)],[42])).
% 0.22/0.42 tff(44,plain,
% 0.22/0.42 ((~((~((~(set_intersection2(C!4, B!5) = set_intersection2(C!4, B!5))) | (in(tptp_fun_C_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), set_intersection2(C!4, B!5)) <=> (~((~in(tptp_fun_C_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), B!5)) | (~in(tptp_fun_C_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), C!4))))))) | (~((set_intersection2(C!4, B!5) = set_intersection2(C!4, B!5)) | (in(tptp_fun_D_1(set_intersection2(C!4, B!5), B!5, C!4), set_intersection2(C!4, B!5)) <=> ((~in(tptp_fun_D_1(set_intersection2(C!4, B!5), B!5, C!4), C!4)) | (~in(tptp_fun_D_1(set_intersection2(C!4, B!5), B!5, C!4), B!5)))))))) <=> ((~in(tptp_fun_C_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), set_intersection2(C!4, B!5))) <=> ((~in(tptp_fun_C_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), B!5)) | (~in(tptp_fun_C_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), C!4))))),
% 0.22/0.43 inference(transitivity,[status(thm)],[43, 23])).
% 0.22/0.43 tff(45,plain,
% 0.22/0.43 (((~![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(C!4, B!5) = set_intersection2(C!4, B!5))) | (in(tptp_fun_C_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), set_intersection2(C!4, B!5)) <=> (~((~in(tptp_fun_C_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), B!5)) | (~in(tptp_fun_C_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), C!4))))))) | (~((set_intersection2(C!4, B!5) = set_intersection2(C!4, B!5)) | (in(tptp_fun_D_1(set_intersection2(C!4, B!5), B!5, C!4), set_intersection2(C!4, B!5)) <=> ((~in(tptp_fun_D_1(set_intersection2(C!4, B!5), B!5, C!4), C!4)) | (~in(tptp_fun_D_1(set_intersection2(C!4, B!5), B!5, C!4), B!5))))))))) <=> ((~![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_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), set_intersection2(C!4, B!5))) <=> ((~in(tptp_fun_C_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), B!5)) | (~in(tptp_fun_C_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), C!4)))))),
% 0.22/0.43 inference(monotonicity,[status(thm)],[44])).
% 0.22/0.43 tff(46,plain,
% 0.22/0.43 (((~![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(C!4, B!5) = set_intersection2(C!4, B!5))) | (in(tptp_fun_C_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), set_intersection2(C!4, B!5)) <=> (~((~in(tptp_fun_C_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), B!5)) | (~in(tptp_fun_C_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), C!4))))))) | (~((set_intersection2(C!4, B!5) = set_intersection2(C!4, B!5)) | (in(tptp_fun_D_1(set_intersection2(C!4, B!5), B!5, C!4), set_intersection2(C!4, B!5)) <=> ((~in(tptp_fun_D_1(set_intersection2(C!4, B!5), B!5, C!4), C!4)) | (~in(tptp_fun_D_1(set_intersection2(C!4, B!5), B!5, C!4), B!5))))))))) <=> ((~![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_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), set_intersection2(C!4, B!5))) <=> ((~in(tptp_fun_C_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), B!5)) | (~in(tptp_fun_C_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), C!4)))))),
% 0.22/0.43 inference(transitivity,[status(thm)],[45, 22])).
% 0.22/0.43 tff(47,plain,
% 0.22/0.43 ((~![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(C!4, B!5) = set_intersection2(C!4, B!5))) | (in(tptp_fun_C_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), set_intersection2(C!4, B!5)) <=> (~((~in(tptp_fun_C_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), B!5)) | (~in(tptp_fun_C_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), C!4))))))) | (~((set_intersection2(C!4, B!5) = set_intersection2(C!4, B!5)) | (in(tptp_fun_D_1(set_intersection2(C!4, B!5), B!5, C!4), set_intersection2(C!4, B!5)) <=> ((~in(tptp_fun_D_1(set_intersection2(C!4, B!5), B!5, C!4), C!4)) | (~in(tptp_fun_D_1(set_intersection2(C!4, B!5), B!5, C!4), B!5))))))))),
% 0.22/0.43 inference(quant_inst,[status(thm)],[])).
% 0.22/0.43 tff(48,plain,
% 0.22/0.43 ((~![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_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), set_intersection2(C!4, B!5))) <=> ((~in(tptp_fun_C_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), B!5)) | (~in(tptp_fun_C_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), C!4))))),
% 0.22/0.43 inference(modus_ponens,[status(thm)],[47, 46])).
% 0.22/0.43 tff(49,plain,
% 0.22/0.43 ((~in(tptp_fun_C_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), set_intersection2(C!4, B!5))) <=> ((~in(tptp_fun_C_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), B!5)) | (~in(tptp_fun_C_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), C!4)))),
% 0.22/0.43 inference(unit_resolution,[status(thm)],[48, 21])).
% 0.22/0.43 tff(50,plain,
% 0.22/0.43 (^[A: $i, B: $i] : refl((set_intersection2(A, B) = set_intersection2(B, A)) <=> (set_intersection2(A, B) = set_intersection2(B, A)))),
% 0.22/0.43 inference(bind,[status(th)],[])).
% 0.22/0.43 tff(51,plain,
% 0.22/0.43 (![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A)) <=> ![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))),
% 0.22/0.43 inference(quant_intro,[status(thm)],[50])).
% 0.22/0.43 tff(52,plain,
% 0.22/0.43 (![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A)) <=> ![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))),
% 0.22/0.43 inference(rewrite,[status(thm)],[])).
% 0.22/0.43 tff(53,axiom,(![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','commutativity_k3_xboole_0')).
% 0.22/0.43 tff(54,plain,
% 0.22/0.43 (![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))),
% 0.22/0.43 inference(modus_ponens,[status(thm)],[53, 52])).
% 0.22/0.43 tff(55,plain,(
% 0.22/0.43 ![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))),
% 0.22/0.43 inference(skolemize,[status(sab)],[54])).
% 0.22/0.43 tff(56,plain,
% 0.22/0.43 (![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))),
% 0.22/0.43 inference(modus_ponens,[status(thm)],[55, 51])).
% 0.22/0.43 tff(57,plain,
% 0.22/0.43 ((~![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))) | (set_intersection2(B!5, C!4) = set_intersection2(C!4, B!5))),
% 0.22/0.43 inference(quant_inst,[status(thm)],[])).
% 0.22/0.43 tff(58,plain,
% 0.22/0.43 (set_intersection2(B!5, C!4) = set_intersection2(C!4, B!5)),
% 0.22/0.43 inference(unit_resolution,[status(thm)],[57, 56])).
% 0.22/0.43 tff(59,plain,
% 0.22/0.43 (set_intersection2(C!4, B!5) = set_intersection2(B!5, C!4)),
% 0.22/0.43 inference(symmetry,[status(thm)],[58])).
% 0.22/0.43 tff(60,plain,
% 0.22/0.43 (in(tptp_fun_C_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), set_intersection2(C!4, B!5)) <=> in(tptp_fun_C_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), set_intersection2(B!5, C!4))),
% 0.22/0.43 inference(monotonicity,[status(thm)],[59])).
% 0.22/0.43 tff(61,plain,
% 0.22/0.43 (in(tptp_fun_C_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), set_intersection2(B!5, C!4)) <=> in(tptp_fun_C_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), set_intersection2(C!4, B!5))),
% 0.22/0.43 inference(symmetry,[status(thm)],[60])).
% 0.22/0.43 tff(62,plain,
% 0.22/0.43 ((~in(tptp_fun_C_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), set_intersection2(B!5, C!4))) <=> (~in(tptp_fun_C_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), set_intersection2(C!4, B!5)))),
% 0.22/0.43 inference(monotonicity,[status(thm)],[61])).
% 0.22/0.43 tff(63,plain,
% 0.22/0.43 (^[A: $i, B: $i] : refl((~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B))))))) <=> (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B))))))))),
% 0.22/0.43 inference(bind,[status(th)],[])).
% 0.22/0.43 tff(64,plain,
% 0.22/0.43 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B))))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B)))))))),
% 0.22/0.43 inference(quant_intro,[status(thm)],[63])).
% 0.22/0.43 tff(65,plain,
% 0.22/0.43 (^[A: $i, B: $i] : rewrite((~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B))))))) <=> (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B))))))))),
% 0.22/0.43 inference(bind,[status(th)],[])).
% 0.22/0.43 tff(66,plain,
% 0.22/0.43 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B))))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B)))))))),
% 0.22/0.43 inference(quant_intro,[status(thm)],[65])).
% 0.22/0.43 tff(67,plain,
% 0.22/0.43 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B))))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B)))))))),
% 0.22/0.43 inference(transitivity,[status(thm)],[66, 64])).
% 0.22/0.43 tff(68,plain,
% 0.22/0.43 (^[A: $i, B: $i] : trans(monotonicity(rewrite(((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) <=> ((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))), rewrite((subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B)))) <=> (subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B))))), ((((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B))))) <=> (((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B))))))), rewrite((((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B))))) <=> (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B)))))))), ((((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B))))) <=> (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B)))))))))),
% 0.22/0.43 inference(bind,[status(th)],[])).
% 0.22/0.43 tff(69,plain,
% 0.22/0.43 (![A: $i, B: $i] : (((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B)))))))),
% 0.22/0.43 inference(quant_intro,[status(thm)],[68])).
% 0.22/0.43 tff(70,plain,
% 0.22/0.43 (![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B))) <=> ![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B)))),
% 0.22/0.43 inference(rewrite,[status(thm)],[])).
% 0.22/0.43 tff(71,plain,
% 0.22/0.43 (^[A: $i, B: $i] : rewrite((subset(A, B) <=> ![C: $i] : (in(C, A) => in(C, B))) <=> (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B))))),
% 0.22/0.43 inference(bind,[status(th)],[])).
% 0.22/0.43 tff(72,plain,
% 0.22/0.43 (![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : (in(C, A) => in(C, B))) <=> ![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B)))),
% 0.22/0.44 inference(quant_intro,[status(thm)],[71])).
% 0.22/0.44 tff(73,axiom,(![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : (in(C, A) => in(C, B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d3_tarski')).
% 0.22/0.44 tff(74,plain,
% 0.22/0.44 (![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B)))),
% 0.22/0.44 inference(modus_ponens,[status(thm)],[73, 72])).
% 0.22/0.44 tff(75,plain,
% 0.22/0.44 (![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B)))),
% 0.22/0.44 inference(modus_ponens,[status(thm)],[74, 70])).
% 0.22/0.44 tff(76,plain,(
% 0.22/0.44 ![A: $i, B: $i] : (((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B)))))),
% 0.22/0.44 inference(skolemize,[status(sab)],[75])).
% 0.22/0.44 tff(77,plain,
% 0.22/0.44 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B)))))))),
% 0.22/0.44 inference(modus_ponens,[status(thm)],[76, 69])).
% 0.22/0.44 tff(78,plain,
% 0.22/0.44 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B)))))))),
% 0.22/0.44 inference(modus_ponens,[status(thm)],[77, 67])).
% 0.22/0.44 tff(79,plain,
% 0.22/0.44 ((~![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B)))))))) | (~((~((~subset(set_intersection2(A!6, C!4), set_intersection2(B!5, C!4))) | ![C: $i] : ((~in(C, set_intersection2(A!6, C!4))) | in(C, set_intersection2(B!5, C!4))))) | (~(subset(set_intersection2(A!6, C!4), set_intersection2(B!5, C!4)) | (~((~in(tptp_fun_C_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), set_intersection2(A!6, C!4))) | in(tptp_fun_C_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), set_intersection2(B!5, C!4))))))))),
% 0.22/0.44 inference(quant_inst,[status(thm)],[])).
% 0.22/0.44 tff(80,plain,
% 0.22/0.44 (~((~((~subset(set_intersection2(A!6, C!4), set_intersection2(B!5, C!4))) | ![C: $i] : ((~in(C, set_intersection2(A!6, C!4))) | in(C, set_intersection2(B!5, C!4))))) | (~(subset(set_intersection2(A!6, C!4), set_intersection2(B!5, C!4)) | (~((~in(tptp_fun_C_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), set_intersection2(A!6, C!4))) | in(tptp_fun_C_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), set_intersection2(B!5, C!4)))))))),
% 0.22/0.44 inference(unit_resolution,[status(thm)],[79, 78])).
% 0.22/0.44 tff(81,plain,
% 0.22/0.44 (((~((~subset(set_intersection2(A!6, C!4), set_intersection2(B!5, C!4))) | ![C: $i] : ((~in(C, set_intersection2(A!6, C!4))) | in(C, set_intersection2(B!5, C!4))))) | (~(subset(set_intersection2(A!6, C!4), set_intersection2(B!5, C!4)) | (~((~in(tptp_fun_C_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), set_intersection2(A!6, C!4))) | in(tptp_fun_C_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), set_intersection2(B!5, C!4))))))) | (subset(set_intersection2(A!6, C!4), set_intersection2(B!5, C!4)) | (~((~in(tptp_fun_C_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), set_intersection2(A!6, C!4))) | in(tptp_fun_C_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), set_intersection2(B!5, C!4)))))),
% 0.22/0.44 inference(tautology,[status(thm)],[])).
% 0.22/0.44 tff(82,plain,
% 0.22/0.44 (subset(set_intersection2(A!6, C!4), set_intersection2(B!5, C!4)) | (~((~in(tptp_fun_C_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), set_intersection2(A!6, C!4))) | in(tptp_fun_C_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), set_intersection2(B!5, C!4))))),
% 0.22/0.44 inference(unit_resolution,[status(thm)],[81, 80])).
% 0.22/0.44 tff(83,plain,
% 0.22/0.44 ((~![A: $i, B: $i, C: $i] : ((~subset(A, B)) | subset(set_intersection2(A, C), set_intersection2(B, C)))) <=> (~![A: $i, B: $i, C: $i] : ((~subset(A, B)) | subset(set_intersection2(A, C), set_intersection2(B, C))))),
% 0.22/0.44 inference(rewrite,[status(thm)],[])).
% 0.22/0.44 tff(84,plain,
% 0.22/0.44 ((~![A: $i, B: $i, C: $i] : (subset(A, B) => subset(set_intersection2(A, C), set_intersection2(B, C)))) <=> (~![A: $i, B: $i, C: $i] : ((~subset(A, B)) | subset(set_intersection2(A, C), set_intersection2(B, C))))),
% 0.22/0.44 inference(rewrite,[status(thm)],[])).
% 0.22/0.44 tff(85,axiom,(~![A: $i, B: $i, C: $i] : (subset(A, B) => subset(set_intersection2(A, C), set_intersection2(B, C)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t26_xboole_1')).
% 0.22/0.44 tff(86,plain,
% 0.22/0.44 (~![A: $i, B: $i, C: $i] : ((~subset(A, B)) | subset(set_intersection2(A, C), set_intersection2(B, C)))),
% 0.22/0.44 inference(modus_ponens,[status(thm)],[85, 84])).
% 0.22/0.44 tff(87,plain,
% 0.22/0.44 (~![A: $i, B: $i, C: $i] : ((~subset(A, B)) | subset(set_intersection2(A, C), set_intersection2(B, C)))),
% 0.22/0.44 inference(modus_ponens,[status(thm)],[86, 83])).
% 0.22/0.44 tff(88,plain,
% 0.22/0.44 (~![A: $i, B: $i, C: $i] : ((~subset(A, B)) | subset(set_intersection2(A, C), set_intersection2(B, C)))),
% 0.22/0.44 inference(modus_ponens,[status(thm)],[87, 83])).
% 0.22/0.44 tff(89,plain,
% 0.22/0.44 (~![A: $i, B: $i, C: $i] : ((~subset(A, B)) | subset(set_intersection2(A, C), set_intersection2(B, C)))),
% 0.22/0.44 inference(modus_ponens,[status(thm)],[88, 83])).
% 0.22/0.44 tff(90,plain,
% 0.22/0.44 (~![A: $i, B: $i, C: $i] : ((~subset(A, B)) | subset(set_intersection2(A, C), set_intersection2(B, C)))),
% 0.22/0.44 inference(modus_ponens,[status(thm)],[89, 83])).
% 0.22/0.44 tff(91,plain,
% 0.22/0.44 (~![A: $i, B: $i, C: $i] : ((~subset(A, B)) | subset(set_intersection2(A, C), set_intersection2(B, C)))),
% 0.22/0.44 inference(modus_ponens,[status(thm)],[90, 83])).
% 0.22/0.44 tff(92,plain,
% 0.22/0.44 (~![A: $i, B: $i, C: $i] : ((~subset(A, B)) | subset(set_intersection2(A, C), set_intersection2(B, C)))),
% 0.22/0.44 inference(modus_ponens,[status(thm)],[91, 83])).
% 0.22/0.44 tff(93,plain,(
% 0.22/0.44 ~((~subset(A!6, B!5)) | subset(set_intersection2(A!6, C!4), set_intersection2(B!5, C!4)))),
% 0.22/0.44 inference(skolemize,[status(sab)],[92])).
% 0.22/0.44 tff(94,plain,
% 0.22/0.44 (~subset(set_intersection2(A!6, C!4), set_intersection2(B!5, C!4))),
% 0.22/0.44 inference(or_elim,[status(thm)],[93])).
% 0.22/0.44 tff(95,plain,
% 0.22/0.44 ((~(subset(set_intersection2(A!6, C!4), set_intersection2(B!5, C!4)) | (~((~in(tptp_fun_C_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), set_intersection2(A!6, C!4))) | in(tptp_fun_C_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), set_intersection2(B!5, C!4)))))) | subset(set_intersection2(A!6, C!4), set_intersection2(B!5, C!4)) | (~((~in(tptp_fun_C_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), set_intersection2(A!6, C!4))) | in(tptp_fun_C_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), set_intersection2(B!5, C!4))))),
% 0.22/0.44 inference(tautology,[status(thm)],[])).
% 0.22/0.44 tff(96,plain,
% 0.22/0.44 ((~(subset(set_intersection2(A!6, C!4), set_intersection2(B!5, C!4)) | (~((~in(tptp_fun_C_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), set_intersection2(A!6, C!4))) | in(tptp_fun_C_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), set_intersection2(B!5, C!4)))))) | (~((~in(tptp_fun_C_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), set_intersection2(A!6, C!4))) | in(tptp_fun_C_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), set_intersection2(B!5, C!4))))),
% 0.22/0.44 inference(unit_resolution,[status(thm)],[95, 94])).
% 0.22/0.44 tff(97,plain,
% 0.22/0.44 (~((~in(tptp_fun_C_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), set_intersection2(A!6, C!4))) | in(tptp_fun_C_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), set_intersection2(B!5, C!4)))),
% 0.22/0.44 inference(unit_resolution,[status(thm)],[96, 82])).
% 0.22/0.44 tff(98,plain,
% 0.22/0.44 (((~in(tptp_fun_C_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), set_intersection2(A!6, C!4))) | in(tptp_fun_C_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), set_intersection2(B!5, C!4))) | (~in(tptp_fun_C_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), set_intersection2(B!5, C!4)))),
% 0.22/0.44 inference(tautology,[status(thm)],[])).
% 0.22/0.44 tff(99,plain,
% 0.22/0.44 (~in(tptp_fun_C_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), set_intersection2(B!5, C!4))),
% 0.22/0.44 inference(unit_resolution,[status(thm)],[98, 97])).
% 0.22/0.44 tff(100,plain,
% 0.22/0.44 (~in(tptp_fun_C_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), set_intersection2(C!4, B!5))),
% 0.22/0.44 inference(modus_ponens,[status(thm)],[99, 62])).
% 0.22/0.44 tff(101,plain,
% 0.22/0.44 ((~((~in(tptp_fun_C_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), set_intersection2(C!4, B!5))) <=> ((~in(tptp_fun_C_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), B!5)) | (~in(tptp_fun_C_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), C!4))))) | in(tptp_fun_C_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), set_intersection2(C!4, B!5)) | ((~in(tptp_fun_C_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), B!5)) | (~in(tptp_fun_C_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), C!4)))),
% 0.22/0.44 inference(tautology,[status(thm)],[])).
% 0.22/0.44 tff(102,plain,
% 0.22/0.44 ((~in(tptp_fun_C_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), B!5)) | (~in(tptp_fun_C_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), C!4))),
% 0.22/0.44 inference(unit_resolution,[status(thm)],[101, 100, 49])).
% 0.22/0.44 tff(103,plain,
% 0.22/0.44 (((~![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_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), set_intersection2(C!4, A!6))) <=> ((~in(tptp_fun_C_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), A!6)) | (~in(tptp_fun_C_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), C!4))))) <=> ((~![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_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), set_intersection2(C!4, A!6))) <=> ((~in(tptp_fun_C_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), A!6)) | (~in(tptp_fun_C_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), C!4)))))),
% 0.22/0.44 inference(rewrite,[status(thm)],[])).
% 0.22/0.44 tff(104,plain,
% 0.22/0.44 ((~(in(tptp_fun_C_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), set_intersection2(C!4, A!6)) <=> ((~in(tptp_fun_C_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), A!6)) | (~in(tptp_fun_C_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), C!4))))) <=> ((~in(tptp_fun_C_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), set_intersection2(C!4, A!6))) <=> ((~in(tptp_fun_C_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), A!6)) | (~in(tptp_fun_C_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), C!4))))),
% 0.22/0.44 inference(rewrite,[status(thm)],[])).
% 0.22/0.44 tff(105,plain,
% 0.22/0.44 (((in(tptp_fun_C_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), set_intersection2(C!4, A!6)) <=> ((~in(tptp_fun_C_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), A!6)) | (~in(tptp_fun_C_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), C!4)))) | $false) <=> (in(tptp_fun_C_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), set_intersection2(C!4, A!6)) <=> ((~in(tptp_fun_C_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), A!6)) | (~in(tptp_fun_C_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), C!4))))),
% 0.22/0.44 inference(rewrite,[status(thm)],[])).
% 0.22/0.44 tff(106,plain,
% 0.22/0.44 (($true | (in(tptp_fun_D_1(set_intersection2(C!4, A!6), A!6, C!4), set_intersection2(C!4, A!6)) <=> ((~in(tptp_fun_D_1(set_intersection2(C!4, A!6), A!6, C!4), C!4)) | (~in(tptp_fun_D_1(set_intersection2(C!4, A!6), A!6, C!4), A!6))))) <=> $true),
% 0.22/0.44 inference(rewrite,[status(thm)],[])).
% 0.22/0.44 tff(107,plain,
% 0.22/0.44 ((in(tptp_fun_D_1(set_intersection2(C!4, A!6), A!6, C!4), set_intersection2(C!4, A!6)) <=> ((~in(tptp_fun_D_1(set_intersection2(C!4, A!6), A!6, C!4), C!4)) | (~in(tptp_fun_D_1(set_intersection2(C!4, A!6), A!6, C!4), A!6)))) <=> (in(tptp_fun_D_1(set_intersection2(C!4, A!6), A!6, C!4), set_intersection2(C!4, A!6)) <=> ((~in(tptp_fun_D_1(set_intersection2(C!4, A!6), A!6, C!4), C!4)) | (~in(tptp_fun_D_1(set_intersection2(C!4, A!6), A!6, C!4), A!6))))),
% 0.22/0.45 inference(rewrite,[status(thm)],[])).
% 0.22/0.45 tff(108,plain,
% 0.22/0.45 ((set_intersection2(C!4, A!6) = set_intersection2(C!4, A!6)) <=> $true),
% 0.22/0.45 inference(rewrite,[status(thm)],[])).
% 0.22/0.45 tff(109,plain,
% 0.22/0.45 (((set_intersection2(C!4, A!6) = set_intersection2(C!4, A!6)) | (in(tptp_fun_D_1(set_intersection2(C!4, A!6), A!6, C!4), set_intersection2(C!4, A!6)) <=> ((~in(tptp_fun_D_1(set_intersection2(C!4, A!6), A!6, C!4), C!4)) | (~in(tptp_fun_D_1(set_intersection2(C!4, A!6), A!6, C!4), A!6))))) <=> ($true | (in(tptp_fun_D_1(set_intersection2(C!4, A!6), A!6, C!4), set_intersection2(C!4, A!6)) <=> ((~in(tptp_fun_D_1(set_intersection2(C!4, A!6), A!6, C!4), C!4)) | (~in(tptp_fun_D_1(set_intersection2(C!4, A!6), A!6, C!4), A!6)))))),
% 0.22/0.45 inference(monotonicity,[status(thm)],[108, 107])).
% 0.22/0.45 tff(110,plain,
% 0.22/0.45 (((set_intersection2(C!4, A!6) = set_intersection2(C!4, A!6)) | (in(tptp_fun_D_1(set_intersection2(C!4, A!6), A!6, C!4), set_intersection2(C!4, A!6)) <=> ((~in(tptp_fun_D_1(set_intersection2(C!4, A!6), A!6, C!4), C!4)) | (~in(tptp_fun_D_1(set_intersection2(C!4, A!6), A!6, C!4), A!6))))) <=> $true),
% 0.22/0.45 inference(transitivity,[status(thm)],[109, 106])).
% 0.22/0.45 tff(111,plain,
% 0.22/0.45 ((~((set_intersection2(C!4, A!6) = set_intersection2(C!4, A!6)) | (in(tptp_fun_D_1(set_intersection2(C!4, A!6), A!6, C!4), set_intersection2(C!4, A!6)) <=> ((~in(tptp_fun_D_1(set_intersection2(C!4, A!6), A!6, C!4), C!4)) | (~in(tptp_fun_D_1(set_intersection2(C!4, A!6), A!6, C!4), A!6)))))) <=> (~$true)),
% 0.22/0.45 inference(monotonicity,[status(thm)],[110])).
% 0.22/0.45 tff(112,plain,
% 0.22/0.45 ((~((set_intersection2(C!4, A!6) = set_intersection2(C!4, A!6)) | (in(tptp_fun_D_1(set_intersection2(C!4, A!6), A!6, C!4), set_intersection2(C!4, A!6)) <=> ((~in(tptp_fun_D_1(set_intersection2(C!4, A!6), A!6, C!4), C!4)) | (~in(tptp_fun_D_1(set_intersection2(C!4, A!6), A!6, C!4), A!6)))))) <=> $false),
% 0.22/0.45 inference(transitivity,[status(thm)],[111, 25])).
% 0.22/0.45 tff(113,plain,
% 0.22/0.45 ((~(in(tptp_fun_C_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), set_intersection2(C!4, A!6)) <=> (~((~in(tptp_fun_C_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), A!6)) | (~in(tptp_fun_C_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), C!4)))))) <=> (in(tptp_fun_C_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), set_intersection2(C!4, A!6)) <=> ((~in(tptp_fun_C_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), A!6)) | (~in(tptp_fun_C_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), C!4))))),
% 0.22/0.45 inference(rewrite,[status(thm)],[])).
% 0.22/0.45 tff(114,plain,
% 0.22/0.45 (($false | (in(tptp_fun_C_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), set_intersection2(C!4, A!6)) <=> (~((~in(tptp_fun_C_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), A!6)) | (~in(tptp_fun_C_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), C!4)))))) <=> (in(tptp_fun_C_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), set_intersection2(C!4, A!6)) <=> (~((~in(tptp_fun_C_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), A!6)) | (~in(tptp_fun_C_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), C!4)))))),
% 0.22/0.45 inference(rewrite,[status(thm)],[])).
% 0.22/0.45 tff(115,plain,
% 0.22/0.45 ((~(set_intersection2(C!4, A!6) = set_intersection2(C!4, A!6))) <=> (~$true)),
% 0.22/0.45 inference(monotonicity,[status(thm)],[108])).
% 0.22/0.45 tff(116,plain,
% 0.22/0.45 ((~(set_intersection2(C!4, A!6) = set_intersection2(C!4, A!6))) <=> $false),
% 0.22/0.45 inference(transitivity,[status(thm)],[115, 25])).
% 0.22/0.45 tff(117,plain,
% 0.22/0.45 (((~(set_intersection2(C!4, A!6) = set_intersection2(C!4, A!6))) | (in(tptp_fun_C_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), set_intersection2(C!4, A!6)) <=> (~((~in(tptp_fun_C_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), A!6)) | (~in(tptp_fun_C_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), C!4)))))) <=> ($false | (in(tptp_fun_C_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), set_intersection2(C!4, A!6)) <=> (~((~in(tptp_fun_C_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), A!6)) | (~in(tptp_fun_C_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), C!4))))))),
% 0.22/0.45 inference(monotonicity,[status(thm)],[116])).
% 0.22/0.45 tff(118,plain,
% 0.22/0.45 (((~(set_intersection2(C!4, A!6) = set_intersection2(C!4, A!6))) | (in(tptp_fun_C_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), set_intersection2(C!4, A!6)) <=> (~((~in(tptp_fun_C_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), A!6)) | (~in(tptp_fun_C_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), C!4)))))) <=> (in(tptp_fun_C_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), set_intersection2(C!4, A!6)) <=> (~((~in(tptp_fun_C_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), A!6)) | (~in(tptp_fun_C_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), C!4)))))),
% 0.22/0.45 inference(transitivity,[status(thm)],[117, 114])).
% 0.22/0.45 tff(119,plain,
% 0.22/0.45 ((~((~(set_intersection2(C!4, A!6) = set_intersection2(C!4, A!6))) | (in(tptp_fun_C_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), set_intersection2(C!4, A!6)) <=> (~((~in(tptp_fun_C_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), A!6)) | (~in(tptp_fun_C_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), C!4))))))) <=> (~(in(tptp_fun_C_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), set_intersection2(C!4, A!6)) <=> (~((~in(tptp_fun_C_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), A!6)) | (~in(tptp_fun_C_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), C!4))))))),
% 0.22/0.45 inference(monotonicity,[status(thm)],[118])).
% 0.22/0.45 tff(120,plain,
% 0.22/0.45 ((~((~(set_intersection2(C!4, A!6) = set_intersection2(C!4, A!6))) | (in(tptp_fun_C_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), set_intersection2(C!4, A!6)) <=> (~((~in(tptp_fun_C_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), A!6)) | (~in(tptp_fun_C_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), C!4))))))) <=> (in(tptp_fun_C_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), set_intersection2(C!4, A!6)) <=> ((~in(tptp_fun_C_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), A!6)) | (~in(tptp_fun_C_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), C!4))))),
% 0.22/0.45 inference(transitivity,[status(thm)],[119, 113])).
% 0.22/0.45 tff(121,plain,
% 0.22/0.45 (((~((~(set_intersection2(C!4, A!6) = set_intersection2(C!4, A!6))) | (in(tptp_fun_C_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), set_intersection2(C!4, A!6)) <=> (~((~in(tptp_fun_C_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), A!6)) | (~in(tptp_fun_C_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), C!4))))))) | (~((set_intersection2(C!4, A!6) = set_intersection2(C!4, A!6)) | (in(tptp_fun_D_1(set_intersection2(C!4, A!6), A!6, C!4), set_intersection2(C!4, A!6)) <=> ((~in(tptp_fun_D_1(set_intersection2(C!4, A!6), A!6, C!4), C!4)) | (~in(tptp_fun_D_1(set_intersection2(C!4, A!6), A!6, C!4), A!6))))))) <=> ((in(tptp_fun_C_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), set_intersection2(C!4, A!6)) <=> ((~in(tptp_fun_C_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), A!6)) | (~in(tptp_fun_C_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), C!4)))) | $false)),
% 0.22/0.45 inference(monotonicity,[status(thm)],[120, 112])).
% 0.22/0.45 tff(122,plain,
% 0.22/0.45 (((~((~(set_intersection2(C!4, A!6) = set_intersection2(C!4, A!6))) | (in(tptp_fun_C_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), set_intersection2(C!4, A!6)) <=> (~((~in(tptp_fun_C_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), A!6)) | (~in(tptp_fun_C_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), C!4))))))) | (~((set_intersection2(C!4, A!6) = set_intersection2(C!4, A!6)) | (in(tptp_fun_D_1(set_intersection2(C!4, A!6), A!6, C!4), set_intersection2(C!4, A!6)) <=> ((~in(tptp_fun_D_1(set_intersection2(C!4, A!6), A!6, C!4), C!4)) | (~in(tptp_fun_D_1(set_intersection2(C!4, A!6), A!6, C!4), A!6))))))) <=> (in(tptp_fun_C_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), set_intersection2(C!4, A!6)) <=> ((~in(tptp_fun_C_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), A!6)) | (~in(tptp_fun_C_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), C!4))))),
% 0.22/0.46 inference(transitivity,[status(thm)],[121, 105])).
% 0.22/0.46 tff(123,plain,
% 0.22/0.46 ((~((~((~(set_intersection2(C!4, A!6) = set_intersection2(C!4, A!6))) | (in(tptp_fun_C_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), set_intersection2(C!4, A!6)) <=> (~((~in(tptp_fun_C_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), A!6)) | (~in(tptp_fun_C_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), C!4))))))) | (~((set_intersection2(C!4, A!6) = set_intersection2(C!4, A!6)) | (in(tptp_fun_D_1(set_intersection2(C!4, A!6), A!6, C!4), set_intersection2(C!4, A!6)) <=> ((~in(tptp_fun_D_1(set_intersection2(C!4, A!6), A!6, C!4), C!4)) | (~in(tptp_fun_D_1(set_intersection2(C!4, A!6), A!6, C!4), A!6)))))))) <=> (~(in(tptp_fun_C_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), set_intersection2(C!4, A!6)) <=> ((~in(tptp_fun_C_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), A!6)) | (~in(tptp_fun_C_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), C!4)))))),
% 0.22/0.46 inference(monotonicity,[status(thm)],[122])).
% 0.22/0.46 tff(124,plain,
% 0.22/0.46 ((~((~((~(set_intersection2(C!4, A!6) = set_intersection2(C!4, A!6))) | (in(tptp_fun_C_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), set_intersection2(C!4, A!6)) <=> (~((~in(tptp_fun_C_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), A!6)) | (~in(tptp_fun_C_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), C!4))))))) | (~((set_intersection2(C!4, A!6) = set_intersection2(C!4, A!6)) | (in(tptp_fun_D_1(set_intersection2(C!4, A!6), A!6, C!4), set_intersection2(C!4, A!6)) <=> ((~in(tptp_fun_D_1(set_intersection2(C!4, A!6), A!6, C!4), C!4)) | (~in(tptp_fun_D_1(set_intersection2(C!4, A!6), A!6, C!4), A!6)))))))) <=> ((~in(tptp_fun_C_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), set_intersection2(C!4, A!6))) <=> ((~in(tptp_fun_C_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), A!6)) | (~in(tptp_fun_C_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), C!4))))),
% 0.22/0.46 inference(transitivity,[status(thm)],[123, 104])).
% 0.22/0.46 tff(125,plain,
% 0.22/0.46 (((~![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(C!4, A!6) = set_intersection2(C!4, A!6))) | (in(tptp_fun_C_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), set_intersection2(C!4, A!6)) <=> (~((~in(tptp_fun_C_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), A!6)) | (~in(tptp_fun_C_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), C!4))))))) | (~((set_intersection2(C!4, A!6) = set_intersection2(C!4, A!6)) | (in(tptp_fun_D_1(set_intersection2(C!4, A!6), A!6, C!4), set_intersection2(C!4, A!6)) <=> ((~in(tptp_fun_D_1(set_intersection2(C!4, A!6), A!6, C!4), C!4)) | (~in(tptp_fun_D_1(set_intersection2(C!4, A!6), A!6, C!4), A!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_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), set_intersection2(C!4, A!6))) <=> ((~in(tptp_fun_C_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), A!6)) | (~in(tptp_fun_C_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), C!4)))))),
% 0.22/0.46 inference(monotonicity,[status(thm)],[124])).
% 0.22/0.46 tff(126,plain,
% 0.22/0.46 (((~![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(C!4, A!6) = set_intersection2(C!4, A!6))) | (in(tptp_fun_C_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), set_intersection2(C!4, A!6)) <=> (~((~in(tptp_fun_C_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), A!6)) | (~in(tptp_fun_C_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), C!4))))))) | (~((set_intersection2(C!4, A!6) = set_intersection2(C!4, A!6)) | (in(tptp_fun_D_1(set_intersection2(C!4, A!6), A!6, C!4), set_intersection2(C!4, A!6)) <=> ((~in(tptp_fun_D_1(set_intersection2(C!4, A!6), A!6, C!4), C!4)) | (~in(tptp_fun_D_1(set_intersection2(C!4, A!6), A!6, C!4), A!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_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), set_intersection2(C!4, A!6))) <=> ((~in(tptp_fun_C_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), A!6)) | (~in(tptp_fun_C_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), C!4)))))),
% 0.22/0.46 inference(transitivity,[status(thm)],[125, 103])).
% 0.22/0.46 tff(127,plain,
% 0.22/0.46 ((~![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(C!4, A!6) = set_intersection2(C!4, A!6))) | (in(tptp_fun_C_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), set_intersection2(C!4, A!6)) <=> (~((~in(tptp_fun_C_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), A!6)) | (~in(tptp_fun_C_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), C!4))))))) | (~((set_intersection2(C!4, A!6) = set_intersection2(C!4, A!6)) | (in(tptp_fun_D_1(set_intersection2(C!4, A!6), A!6, C!4), set_intersection2(C!4, A!6)) <=> ((~in(tptp_fun_D_1(set_intersection2(C!4, A!6), A!6, C!4), C!4)) | (~in(tptp_fun_D_1(set_intersection2(C!4, A!6), A!6, C!4), A!6))))))))),
% 0.22/0.46 inference(quant_inst,[status(thm)],[])).
% 0.22/0.46 tff(128,plain,
% 0.22/0.46 ((~![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_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), set_intersection2(C!4, A!6))) <=> ((~in(tptp_fun_C_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), A!6)) | (~in(tptp_fun_C_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), C!4))))),
% 0.22/0.46 inference(modus_ponens,[status(thm)],[127, 126])).
% 0.22/0.46 tff(129,plain,
% 0.22/0.46 ((~in(tptp_fun_C_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), set_intersection2(C!4, A!6))) <=> ((~in(tptp_fun_C_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), A!6)) | (~in(tptp_fun_C_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), C!4)))),
% 0.22/0.46 inference(unit_resolution,[status(thm)],[128, 21])).
% 0.22/0.46 tff(130,plain,
% 0.22/0.46 ((~![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))) | (set_intersection2(A!6, C!4) = set_intersection2(C!4, A!6))),
% 0.22/0.46 inference(quant_inst,[status(thm)],[])).
% 0.22/0.46 tff(131,plain,
% 0.22/0.46 (set_intersection2(A!6, C!4) = set_intersection2(C!4, A!6)),
% 0.22/0.46 inference(unit_resolution,[status(thm)],[130, 56])).
% 0.22/0.46 tff(132,plain,
% 0.22/0.46 (set_intersection2(C!4, A!6) = set_intersection2(A!6, C!4)),
% 0.22/0.46 inference(symmetry,[status(thm)],[131])).
% 0.22/0.46 tff(133,plain,
% 0.22/0.46 (in(tptp_fun_C_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), set_intersection2(C!4, A!6)) <=> in(tptp_fun_C_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), set_intersection2(A!6, C!4))),
% 0.22/0.46 inference(monotonicity,[status(thm)],[132])).
% 0.22/0.46 tff(134,plain,
% 0.22/0.46 (in(tptp_fun_C_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), set_intersection2(A!6, C!4)) <=> in(tptp_fun_C_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), set_intersection2(C!4, A!6))),
% 0.22/0.46 inference(symmetry,[status(thm)],[133])).
% 0.22/0.46 tff(135,plain,
% 0.22/0.46 (((~in(tptp_fun_C_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), set_intersection2(A!6, C!4))) | in(tptp_fun_C_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), set_intersection2(B!5, C!4))) | in(tptp_fun_C_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), set_intersection2(A!6, C!4))),
% 0.22/0.46 inference(tautology,[status(thm)],[])).
% 0.22/0.46 tff(136,plain,
% 0.22/0.46 (in(tptp_fun_C_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), set_intersection2(A!6, C!4))),
% 0.22/0.46 inference(unit_resolution,[status(thm)],[135, 97])).
% 0.22/0.46 tff(137,plain,
% 0.22/0.46 (in(tptp_fun_C_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), set_intersection2(C!4, A!6))),
% 0.22/0.46 inference(modus_ponens,[status(thm)],[136, 134])).
% 0.22/0.46 tff(138,plain,
% 0.22/0.46 ((~((~in(tptp_fun_C_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), set_intersection2(C!4, A!6))) <=> ((~in(tptp_fun_C_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), A!6)) | (~in(tptp_fun_C_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), C!4))))) | (~in(tptp_fun_C_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), set_intersection2(C!4, A!6))) | (~((~in(tptp_fun_C_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), A!6)) | (~in(tptp_fun_C_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), C!4))))),
% 0.22/0.46 inference(tautology,[status(thm)],[])).
% 0.22/0.46 tff(139,plain,
% 0.22/0.46 (~((~in(tptp_fun_C_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), A!6)) | (~in(tptp_fun_C_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), C!4)))),
% 0.22/0.46 inference(unit_resolution,[status(thm)],[138, 137, 129])).
% 0.22/0.46 tff(140,plain,
% 0.22/0.46 (((~in(tptp_fun_C_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), A!6)) | (~in(tptp_fun_C_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), C!4))) | in(tptp_fun_C_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), C!4)),
% 0.22/0.46 inference(tautology,[status(thm)],[])).
% 0.22/0.46 tff(141,plain,
% 0.22/0.46 (in(tptp_fun_C_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), C!4)),
% 0.22/0.46 inference(unit_resolution,[status(thm)],[140, 139])).
% 0.22/0.46 tff(142,plain,
% 0.22/0.46 ((~((~in(tptp_fun_C_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), B!5)) | (~in(tptp_fun_C_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), C!4)))) | (~in(tptp_fun_C_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), B!5)) | (~in(tptp_fun_C_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), C!4))),
% 0.22/0.46 inference(tautology,[status(thm)],[])).
% 0.22/0.46 tff(143,plain,
% 0.22/0.46 (~in(tptp_fun_C_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), B!5)),
% 0.22/0.46 inference(unit_resolution,[status(thm)],[142, 141, 102])).
% 0.22/0.46 tff(144,plain,
% 0.22/0.46 (((~in(tptp_fun_C_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), A!6)) | (~in(tptp_fun_C_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), C!4))) | in(tptp_fun_C_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), A!6)),
% 0.22/0.46 inference(tautology,[status(thm)],[])).
% 0.22/0.46 tff(145,plain,
% 0.22/0.46 (in(tptp_fun_C_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), A!6)),
% 0.22/0.46 inference(unit_resolution,[status(thm)],[144, 139])).
% 0.22/0.46 tff(146,plain,
% 0.22/0.46 ((~![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B)))))))) | (~((~((~subset(A!6, B!5)) | ![C: $i] : ((~in(C, A!6)) | in(C, B!5)))) | (~(subset(A!6, B!5) | (~((~in(tptp_fun_C_0(B!5, A!6), A!6)) | in(tptp_fun_C_0(B!5, A!6), B!5)))))))),
% 0.22/0.46 inference(quant_inst,[status(thm)],[])).
% 0.22/0.46 tff(147,plain,
% 0.22/0.46 (~((~((~subset(A!6, B!5)) | ![C: $i] : ((~in(C, A!6)) | in(C, B!5)))) | (~(subset(A!6, B!5) | (~((~in(tptp_fun_C_0(B!5, A!6), A!6)) | in(tptp_fun_C_0(B!5, A!6), B!5))))))),
% 0.22/0.46 inference(unit_resolution,[status(thm)],[146, 78])).
% 0.22/0.46 tff(148,plain,
% 0.22/0.46 (((~((~subset(A!6, B!5)) | ![C: $i] : ((~in(C, A!6)) | in(C, B!5)))) | (~(subset(A!6, B!5) | (~((~in(tptp_fun_C_0(B!5, A!6), A!6)) | in(tptp_fun_C_0(B!5, A!6), B!5)))))) | ((~subset(A!6, B!5)) | ![C: $i] : ((~in(C, A!6)) | in(C, B!5)))),
% 0.22/0.47 inference(tautology,[status(thm)],[])).
% 0.22/0.47 tff(149,plain,
% 0.22/0.47 ((~subset(A!6, B!5)) | ![C: $i] : ((~in(C, A!6)) | in(C, B!5))),
% 0.22/0.47 inference(unit_resolution,[status(thm)],[148, 147])).
% 0.22/0.47 tff(150,plain,
% 0.22/0.47 (subset(A!6, B!5)),
% 0.22/0.47 inference(or_elim,[status(thm)],[93])).
% 0.22/0.47 tff(151,plain,
% 0.22/0.47 ((~((~subset(A!6, B!5)) | ![C: $i] : ((~in(C, A!6)) | in(C, B!5)))) | (~subset(A!6, B!5)) | ![C: $i] : ((~in(C, A!6)) | in(C, B!5))),
% 0.22/0.47 inference(tautology,[status(thm)],[])).
% 0.22/0.47 tff(152,plain,
% 0.22/0.47 ((~((~subset(A!6, B!5)) | ![C: $i] : ((~in(C, A!6)) | in(C, B!5)))) | ![C: $i] : ((~in(C, A!6)) | in(C, B!5))),
% 0.22/0.47 inference(unit_resolution,[status(thm)],[151, 150])).
% 0.22/0.47 tff(153,plain,
% 0.22/0.47 (![C: $i] : ((~in(C, A!6)) | in(C, B!5))),
% 0.22/0.47 inference(unit_resolution,[status(thm)],[152, 149])).
% 0.22/0.47 tff(154,plain,
% 0.22/0.47 (((~![C: $i] : ((~in(C, A!6)) | in(C, B!5))) | ((~in(tptp_fun_C_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), A!6)) | in(tptp_fun_C_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), B!5))) <=> ((~![C: $i] : ((~in(C, A!6)) | in(C, B!5))) | (~in(tptp_fun_C_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), A!6)) | in(tptp_fun_C_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), B!5))),
% 0.22/0.47 inference(rewrite,[status(thm)],[])).
% 0.22/0.47 tff(155,plain,
% 0.22/0.47 ((~![C: $i] : ((~in(C, A!6)) | in(C, B!5))) | ((~in(tptp_fun_C_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), A!6)) | in(tptp_fun_C_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), B!5))),
% 0.22/0.47 inference(quant_inst,[status(thm)],[])).
% 0.22/0.47 tff(156,plain,
% 0.22/0.47 ((~![C: $i] : ((~in(C, A!6)) | in(C, B!5))) | (~in(tptp_fun_C_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), A!6)) | in(tptp_fun_C_0(set_intersection2(B!5, C!4), set_intersection2(A!6, C!4)), B!5)),
% 0.22/0.47 inference(modus_ponens,[status(thm)],[155, 154])).
% 0.22/0.47 tff(157,plain,
% 0.22/0.47 ($false),
% 0.22/0.47 inference(unit_resolution,[status(thm)],[156, 153, 145, 143])).
% 0.22/0.47 % SZS output end Proof
%------------------------------------------------------------------------------