TSTP Solution File: SET983+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SET983+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n010.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 05:08:48 EDT 2022
% Result : Theorem 0.19s 0.39s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SET983+1 : TPTP v8.1.0. Released v3.2.0.
% 0.03/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n010.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Sat Sep 3 08:42:57 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 0.19/0.39 % SZS status Theorem
% 0.19/0.39 % SZS output start Proof
% 0.19/0.39 tff(in_type, type, (
% 0.19/0.39 in: ( $i * $i ) > $o)).
% 0.19/0.39 tff(set_intersection2_type, type, (
% 0.19/0.39 set_intersection2: ( $i * $i ) > $i)).
% 0.19/0.39 tff(cartesian_product2_type, type, (
% 0.19/0.39 cartesian_product2: ( $i * $i ) > $i)).
% 0.19/0.39 tff(tptp_fun_E_3_type, type, (
% 0.19/0.39 tptp_fun_E_3: $i)).
% 0.19/0.39 tff(tptp_fun_D_4_type, type, (
% 0.19/0.39 tptp_fun_D_4: $i)).
% 0.19/0.39 tff(tptp_fun_C_5_type, type, (
% 0.19/0.39 tptp_fun_C_5: $i)).
% 0.19/0.39 tff(tptp_fun_B_6_type, type, (
% 0.19/0.39 tptp_fun_B_6: $i)).
% 0.19/0.39 tff(tptp_fun_A_7_type, type, (
% 0.19/0.39 tptp_fun_A_7: $i)).
% 0.19/0.39 tff(tptp_fun_D_0_type, type, (
% 0.19/0.39 tptp_fun_D_0: ( $i * $i * $i ) > $i)).
% 0.19/0.39 tff(1,plain,
% 0.19/0.39 (^[A: $i, B: $i, C: $i, D: $i] : refl((cartesian_product2(set_intersection2(A, B), set_intersection2(C, D)) = set_intersection2(cartesian_product2(A, C), cartesian_product2(B, D))) <=> (cartesian_product2(set_intersection2(A, B), set_intersection2(C, D)) = set_intersection2(cartesian_product2(A, C), cartesian_product2(B, D))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(2,plain,
% 0.19/0.39 (![A: $i, B: $i, C: $i, D: $i] : (cartesian_product2(set_intersection2(A, B), set_intersection2(C, D)) = set_intersection2(cartesian_product2(A, C), cartesian_product2(B, D))) <=> ![A: $i, B: $i, C: $i, D: $i] : (cartesian_product2(set_intersection2(A, B), set_intersection2(C, D)) = set_intersection2(cartesian_product2(A, C), cartesian_product2(B, D)))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[1])).
% 0.19/0.39 tff(3,plain,
% 0.19/0.39 (![A: $i, B: $i, C: $i, D: $i] : (cartesian_product2(set_intersection2(A, B), set_intersection2(C, D)) = set_intersection2(cartesian_product2(A, C), cartesian_product2(B, D))) <=> ![A: $i, B: $i, C: $i, D: $i] : (cartesian_product2(set_intersection2(A, B), set_intersection2(C, D)) = set_intersection2(cartesian_product2(A, C), cartesian_product2(B, D)))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(4,axiom,(![A: $i, B: $i, C: $i, D: $i] : (cartesian_product2(set_intersection2(A, B), set_intersection2(C, D)) = set_intersection2(cartesian_product2(A, C), cartesian_product2(B, D)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t123_zfmisc_1')).
% 0.19/0.39 tff(5,plain,
% 0.19/0.39 (![A: $i, B: $i, C: $i, D: $i] : (cartesian_product2(set_intersection2(A, B), set_intersection2(C, D)) = set_intersection2(cartesian_product2(A, C), cartesian_product2(B, D)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.19/0.39 tff(6,plain,(
% 0.19/0.39 ![A: $i, B: $i, C: $i, D: $i] : (cartesian_product2(set_intersection2(A, B), set_intersection2(C, D)) = set_intersection2(cartesian_product2(A, C), cartesian_product2(B, D)))),
% 0.19/0.39 inference(skolemize,[status(sab)],[5])).
% 0.19/0.39 tff(7,plain,
% 0.19/0.39 (![A: $i, B: $i, C: $i, D: $i] : (cartesian_product2(set_intersection2(A, B), set_intersection2(C, D)) = set_intersection2(cartesian_product2(A, C), cartesian_product2(B, D)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.19/0.39 tff(8,plain,
% 0.19/0.39 ((~![A: $i, B: $i, C: $i, D: $i] : (cartesian_product2(set_intersection2(A, B), set_intersection2(C, D)) = set_intersection2(cartesian_product2(A, C), cartesian_product2(B, D)))) | (cartesian_product2(set_intersection2(B!6, D!4), set_intersection2(C!5, E!3)) = set_intersection2(cartesian_product2(B!6, C!5), cartesian_product2(D!4, E!3)))),
% 0.19/0.39 inference(quant_inst,[status(thm)],[])).
% 0.19/0.39 tff(9,plain,
% 0.19/0.39 (cartesian_product2(set_intersection2(B!6, D!4), set_intersection2(C!5, E!3)) = set_intersection2(cartesian_product2(B!6, C!5), cartesian_product2(D!4, E!3))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.19/0.39 tff(10,plain,
% 0.19/0.39 (set_intersection2(cartesian_product2(B!6, C!5), cartesian_product2(D!4, E!3)) = cartesian_product2(set_intersection2(B!6, D!4), set_intersection2(C!5, E!3))),
% 0.19/0.39 inference(symmetry,[status(thm)],[9])).
% 0.19/0.39 tff(11,plain,
% 0.19/0.39 (in(A!7, set_intersection2(cartesian_product2(B!6, C!5), cartesian_product2(D!4, E!3))) <=> in(A!7, cartesian_product2(set_intersection2(B!6, D!4), set_intersection2(C!5, E!3)))),
% 0.19/0.39 inference(monotonicity,[status(thm)],[10])).
% 0.19/0.39 tff(12,plain,
% 0.19/0.39 (in(A!7, cartesian_product2(set_intersection2(B!6, D!4), set_intersection2(C!5, E!3))) <=> in(A!7, set_intersection2(cartesian_product2(B!6, C!5), cartesian_product2(D!4, E!3)))),
% 0.19/0.39 inference(symmetry,[status(thm)],[11])).
% 0.19/0.39 tff(13,plain,
% 0.19/0.39 ((~in(A!7, cartesian_product2(set_intersection2(B!6, D!4), set_intersection2(C!5, E!3)))) <=> (~in(A!7, set_intersection2(cartesian_product2(B!6, C!5), cartesian_product2(D!4, E!3))))),
% 0.19/0.39 inference(monotonicity,[status(thm)],[12])).
% 0.19/0.39 tff(14,plain,
% 0.19/0.39 ((~![A: $i, B: $i, C: $i, D: $i, E: $i] : ((~(in(A, cartesian_product2(B, C)) & in(A, cartesian_product2(D, E)))) | in(A, cartesian_product2(set_intersection2(B, D), set_intersection2(C, E))))) <=> (~![A: $i, B: $i, C: $i, D: $i, E: $i] : ((~(in(A, cartesian_product2(B, C)) & in(A, cartesian_product2(D, E)))) | in(A, cartesian_product2(set_intersection2(B, D), set_intersection2(C, E)))))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(15,plain,
% 0.19/0.39 ((~![A: $i, B: $i, C: $i, D: $i, E: $i] : ((in(A, cartesian_product2(B, C)) & in(A, cartesian_product2(D, E))) => in(A, cartesian_product2(set_intersection2(B, D), set_intersection2(C, E))))) <=> (~![A: $i, B: $i, C: $i, D: $i, E: $i] : ((~(in(A, cartesian_product2(B, C)) & in(A, cartesian_product2(D, E)))) | in(A, cartesian_product2(set_intersection2(B, D), set_intersection2(C, E)))))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(16,axiom,(~![A: $i, B: $i, C: $i, D: $i, E: $i] : ((in(A, cartesian_product2(B, C)) & in(A, cartesian_product2(D, E))) => in(A, cartesian_product2(set_intersection2(B, D), set_intersection2(C, E))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t137_zfmisc_1')).
% 0.19/0.39 tff(17,plain,
% 0.19/0.39 (~![A: $i, B: $i, C: $i, D: $i, E: $i] : ((~(in(A, cartesian_product2(B, C)) & in(A, cartesian_product2(D, E)))) | in(A, cartesian_product2(set_intersection2(B, D), set_intersection2(C, E))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[16, 15])).
% 0.19/0.39 tff(18,plain,
% 0.19/0.39 (~![A: $i, B: $i, C: $i, D: $i, E: $i] : ((~(in(A, cartesian_product2(B, C)) & in(A, cartesian_product2(D, E)))) | in(A, cartesian_product2(set_intersection2(B, D), set_intersection2(C, E))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[17, 14])).
% 0.19/0.39 tff(19,plain,
% 0.19/0.39 (~![A: $i, B: $i, C: $i, D: $i, E: $i] : ((~(in(A, cartesian_product2(B, C)) & in(A, cartesian_product2(D, E)))) | in(A, cartesian_product2(set_intersection2(B, D), set_intersection2(C, E))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[18, 14])).
% 0.19/0.39 tff(20,plain,
% 0.19/0.39 (~![A: $i, B: $i, C: $i, D: $i, E: $i] : ((~(in(A, cartesian_product2(B, C)) & in(A, cartesian_product2(D, E)))) | in(A, cartesian_product2(set_intersection2(B, D), set_intersection2(C, E))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[19, 14])).
% 0.19/0.39 tff(21,plain,
% 0.19/0.39 (~![A: $i, B: $i, C: $i, D: $i, E: $i] : ((~(in(A, cartesian_product2(B, C)) & in(A, cartesian_product2(D, E)))) | in(A, cartesian_product2(set_intersection2(B, D), set_intersection2(C, E))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[20, 14])).
% 0.19/0.39 tff(22,plain,
% 0.19/0.39 (~![A: $i, B: $i, C: $i, D: $i, E: $i] : ((~(in(A, cartesian_product2(B, C)) & in(A, cartesian_product2(D, E)))) | in(A, cartesian_product2(set_intersection2(B, D), set_intersection2(C, E))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[21, 14])).
% 0.19/0.39 tff(23,plain,
% 0.19/0.39 (~![A: $i, B: $i, C: $i, D: $i, E: $i] : ((~(in(A, cartesian_product2(B, C)) & in(A, cartesian_product2(D, E)))) | in(A, cartesian_product2(set_intersection2(B, D), set_intersection2(C, E))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[22, 14])).
% 0.19/0.39 tff(24,plain,(
% 0.19/0.39 ~((~(in(A!7, cartesian_product2(B!6, C!5)) & in(A!7, cartesian_product2(D!4, E!3)))) | in(A!7, cartesian_product2(set_intersection2(B!6, D!4), set_intersection2(C!5, E!3))))),
% 0.19/0.39 inference(skolemize,[status(sab)],[23])).
% 0.19/0.39 tff(25,plain,
% 0.19/0.39 (~in(A!7, cartesian_product2(set_intersection2(B!6, D!4), set_intersection2(C!5, E!3)))),
% 0.19/0.39 inference(or_elim,[status(thm)],[24])).
% 0.19/0.39 tff(26,plain,
% 0.19/0.39 (~in(A!7, set_intersection2(cartesian_product2(B!6, C!5), cartesian_product2(D!4, E!3)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[25, 13])).
% 0.19/0.39 tff(27,plain,
% 0.19/0.39 (^[A: $i, B: $i, C: $i, D: $i] : refl((~((~((~(C = set_intersection2(A, B))) | (in(D, C) <=> (~((~in(D, A)) | (~in(D, B))))))) | (~((C = set_intersection2(A, B)) | (in(tptp_fun_D_0(C, B, A), C) <=> ((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B)))))))) <=> (~((~((~(C = set_intersection2(A, B))) | (in(D, C) <=> (~((~in(D, A)) | (~in(D, B))))))) | (~((C = set_intersection2(A, B)) | (in(tptp_fun_D_0(C, B, A), C) <=> ((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B)))))))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(28,plain,
% 0.19/0.39 (![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (in(D, C) <=> (~((~in(D, A)) | (~in(D, B))))))) | (~((C = set_intersection2(A, B)) | (in(tptp_fun_D_0(C, B, A), C) <=> ((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B)))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (in(D, C) <=> (~((~in(D, A)) | (~in(D, B))))))) | (~((C = set_intersection2(A, B)) | (in(tptp_fun_D_0(C, B, A), C) <=> ((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))))))))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[27])).
% 0.19/0.39 tff(29,plain,
% 0.19/0.39 (![A: $i, B: $i, C: $i] : ![D: $i] : (~((~((~(C = set_intersection2(A, B))) | (in(D, C) <=> (~((~in(D, A)) | (~in(D, B))))))) | (~((C = set_intersection2(A, B)) | (in(tptp_fun_D_0(C, B, A), C) <=> ((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B)))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (in(D, C) <=> (~((~in(D, A)) | (~in(D, B))))))) | (~((C = set_intersection2(A, B)) | (in(tptp_fun_D_0(C, B, A), C) <=> ((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))))))))),
% 0.19/0.39 inference(pull_quant,[status(thm)],[])).
% 0.19/0.39 tff(30,plain,
% 0.19/0.39 (^[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, A)) | (~in(D, B)))))) <=> ![D: $i] : ((~(C = set_intersection2(A, B))) | (in(D, C) <=> (~((~in(D, A)) | (~in(D, B))))))), ((~((~(C = set_intersection2(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, A)) | (~in(D, B))))))) <=> (~![D: $i] : ((~(C = set_intersection2(A, B))) | (in(D, C) <=> (~((~in(D, A)) | (~in(D, B))))))))), pull_quant((~![D: $i] : ((~(C = set_intersection2(A, B))) | (in(D, C) <=> (~((~in(D, A)) | (~in(D, B))))))) <=> ?[D: $i] : (~((~(C = set_intersection2(A, B))) | (in(D, C) <=> (~((~in(D, A)) | (~in(D, B)))))))), ((~((~(C = set_intersection2(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, A)) | (~in(D, B))))))) <=> ?[D: $i] : (~((~(C = set_intersection2(A, B))) | (in(D, C) <=> (~((~in(D, A)) | (~in(D, 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_0(C, B, A), C) <=> ((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))))))) <=> (?[D: $i] : (~((~(C = set_intersection2(A, B))) | (in(D, C) <=> (~((~in(D, A)) | (~in(D, B))))))) | (~((C = set_intersection2(A, B)) | (in(tptp_fun_D_0(C, B, A), C) <=> ((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))))))))), pull_quant((?[D: $i] : (~((~(C = set_intersection2(A, B))) | (in(D, C) <=> (~((~in(D, A)) | (~in(D, B))))))) | (~((C = set_intersection2(A, B)) | (in(tptp_fun_D_0(C, B, A), C) <=> ((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))))))) <=> ?[D: $i] : ((~((~(C = set_intersection2(A, B))) | (in(D, C) <=> (~((~in(D, A)) | (~in(D, B))))))) | (~((C = set_intersection2(A, B)) | (in(tptp_fun_D_0(C, B, A), C) <=> ((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(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_0(C, B, A), C) <=> ((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))))))) <=> ?[D: $i] : ((~((~(C = set_intersection2(A, B))) | (in(D, C) <=> (~((~in(D, A)) | (~in(D, B))))))) | (~((C = set_intersection2(A, B)) | (in(tptp_fun_D_0(C, B, A), C) <=> ((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(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_0(C, B, A), C) <=> ((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B)))))))) <=> (~?[D: $i] : ((~((~(C = set_intersection2(A, B))) | (in(D, C) <=> (~((~in(D, A)) | (~in(D, B))))))) | (~((C = set_intersection2(A, B)) | (in(tptp_fun_D_0(C, B, A), C) <=> ((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B)))))))))), pull_quant((~?[D: $i] : ((~((~(C = set_intersection2(A, B))) | (in(D, C) <=> (~((~in(D, A)) | (~in(D, B))))))) | (~((C = set_intersection2(A, B)) | (in(tptp_fun_D_0(C, B, A), C) <=> ((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B)))))))) <=> ![D: $i] : (~((~((~(C = set_intersection2(A, B))) | (in(D, C) <=> (~((~in(D, A)) | (~in(D, B))))))) | (~((C = set_intersection2(A, B)) | (in(tptp_fun_D_0(C, B, A), C) <=> ((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(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_0(C, B, A), C) <=> ((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B)))))))) <=> ![D: $i] : (~((~((~(C = set_intersection2(A, B))) | (in(D, C) <=> (~((~in(D, A)) | (~in(D, B))))))) | (~((C = set_intersection2(A, B)) | (in(tptp_fun_D_0(C, B, A), C) <=> ((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))))))))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(31,plain,
% 0.19/0.39 (![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_0(C, B, A), C) <=> ((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B)))))))) <=> ![A: $i, B: $i, C: $i] : ![D: $i] : (~((~((~(C = set_intersection2(A, B))) | (in(D, C) <=> (~((~in(D, A)) | (~in(D, B))))))) | (~((C = set_intersection2(A, B)) | (in(tptp_fun_D_0(C, B, A), C) <=> ((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))))))))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[30])).
% 0.19/0.39 tff(32,plain,
% 0.19/0.39 (![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_0(C, B, A), C) <=> ((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B)))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (in(D, C) <=> (~((~in(D, A)) | (~in(D, B))))))) | (~((C = set_intersection2(A, B)) | (in(tptp_fun_D_0(C, B, A), C) <=> ((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))))))))),
% 0.19/0.39 inference(transitivity,[status(thm)],[31, 29])).
% 0.19/0.39 tff(33,plain,
% 0.19/0.39 (![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_0(C, B, A), C) <=> ((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B)))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (in(D, C) <=> (~((~in(D, A)) | (~in(D, B))))))) | (~((C = set_intersection2(A, B)) | (in(tptp_fun_D_0(C, B, A), C) <=> ((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))))))))),
% 0.19/0.39 inference(transitivity,[status(thm)],[32, 28])).
% 0.19/0.39 tff(34,plain,
% 0.19/0.39 (^[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_0(C, B, A), C) <=> ((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(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_0(C, B, A), C) <=> ((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B)))))))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(35,plain,
% 0.19/0.39 (![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_0(C, B, A), C) <=> ((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(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_0(C, B, A), C) <=> ((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))))))))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[34])).
% 0.19/0.39 tff(36,plain,
% 0.19/0.39 (![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_0(C, B, A), C) <=> ((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B)))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (in(D, C) <=> (~((~in(D, A)) | (~in(D, B))))))) | (~((C = set_intersection2(A, B)) | (in(tptp_fun_D_0(C, B, A), C) <=> ((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))))))))),
% 0.19/0.39 inference(transitivity,[status(thm)],[35, 33])).
% 0.19/0.39 tff(37,plain,
% 0.19/0.39 (^[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, A)) | (~in(D, B))))))), rewrite(((C = set_intersection2(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> (in(tptp_fun_D_0(C, B, A), A) & in(tptp_fun_D_0(C, B, A), B)))) <=> ((C = set_intersection2(A, B)) | (in(tptp_fun_D_0(C, B, A), C) <=> ((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(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_0(C, B, A), C)) <=> (in(tptp_fun_D_0(C, B, A), A) & in(tptp_fun_D_0(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_0(C, B, A), C) <=> ((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B)))))))), 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_0(C, B, A), C) <=> ((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(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_0(C, B, A), C) <=> ((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(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_0(C, B, A), C)) <=> (in(tptp_fun_D_0(C, B, A), A) & in(tptp_fun_D_0(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_0(C, B, A), C) <=> ((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))))))))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(38,plain,
% 0.19/0.39 (![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_0(C, B, A), C)) <=> (in(tptp_fun_D_0(C, B, A), A) & in(tptp_fun_D_0(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_0(C, B, A), C) <=> ((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))))))))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[37])).
% 0.19/0.39 tff(39,plain,
% 0.19/0.39 (^[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_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), A) & in(tptp_fun_D_0(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_0(C, B, A), C)) <=> (in(tptp_fun_D_0(C, B, A), A) & in(tptp_fun_D_0(C, B, A), B))))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(40,plain,
% 0.19/0.40 (![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_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), A) & in(tptp_fun_D_0(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_0(C, B, A), C)) <=> (in(tptp_fun_D_0(C, B, A), A) & in(tptp_fun_D_0(C, B, A), B)))))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[39])).
% 0.19/0.40 tff(41,plain,
% 0.19/0.40 (![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))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(42,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')).
% 0.19/0.40 tff(43,plain,
% 0.19/0.40 (![A: $i, B: $i, C: $i] : ((C = set_intersection2(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, A) & in(D, B))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[42, 41])).
% 0.19/0.40 tff(44,plain,(
% 0.19/0.40 ![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_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), A) & in(tptp_fun_D_0(C, B, A), B))))))),
% 0.19/0.40 inference(skolemize,[status(sab)],[43])).
% 0.19/0.40 tff(45,plain,
% 0.19/0.40 (![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_0(C, B, A), C)) <=> (in(tptp_fun_D_0(C, B, A), A) & in(tptp_fun_D_0(C, B, A), B)))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[44, 40])).
% 0.19/0.40 tff(46,plain,
% 0.19/0.40 (![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_0(C, B, A), C) <=> ((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))))))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[45, 38])).
% 0.19/0.40 tff(47,plain,
% 0.19/0.40 (![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (in(D, C) <=> (~((~in(D, A)) | (~in(D, B))))))) | (~((C = set_intersection2(A, B)) | (in(tptp_fun_D_0(C, B, A), C) <=> ((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))))))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[46, 36])).
% 0.19/0.40 tff(48,plain,
% 0.19/0.40 (((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (in(D, C) <=> (~((~in(D, A)) | (~in(D, B))))))) | (~((C = set_intersection2(A, B)) | (in(tptp_fun_D_0(C, B, A), C) <=> ((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))))))))) | ((~in(A!7, set_intersection2(cartesian_product2(B!6, C!5), cartesian_product2(D!4, E!3)))) <=> ((~in(A!7, cartesian_product2(B!6, C!5))) | (~in(A!7, cartesian_product2(D!4, E!3)))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (in(D, C) <=> (~((~in(D, A)) | (~in(D, B))))))) | (~((C = set_intersection2(A, B)) | (in(tptp_fun_D_0(C, B, A), C) <=> ((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))))))))) | ((~in(A!7, set_intersection2(cartesian_product2(B!6, C!5), cartesian_product2(D!4, E!3)))) <=> ((~in(A!7, cartesian_product2(B!6, C!5))) | (~in(A!7, cartesian_product2(D!4, E!3))))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(49,plain,
% 0.19/0.40 ((~(in(A!7, set_intersection2(cartesian_product2(B!6, C!5), cartesian_product2(D!4, E!3))) <=> ((~in(A!7, cartesian_product2(B!6, C!5))) | (~in(A!7, cartesian_product2(D!4, E!3)))))) <=> ((~in(A!7, set_intersection2(cartesian_product2(B!6, C!5), cartesian_product2(D!4, E!3)))) <=> ((~in(A!7, cartesian_product2(B!6, C!5))) | (~in(A!7, cartesian_product2(D!4, E!3)))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(50,plain,
% 0.19/0.40 (((in(A!7, set_intersection2(cartesian_product2(B!6, C!5), cartesian_product2(D!4, E!3))) <=> ((~in(A!7, cartesian_product2(B!6, C!5))) | (~in(A!7, cartesian_product2(D!4, E!3))))) | $false) <=> (in(A!7, set_intersection2(cartesian_product2(B!6, C!5), cartesian_product2(D!4, E!3))) <=> ((~in(A!7, cartesian_product2(B!6, C!5))) | (~in(A!7, cartesian_product2(D!4, E!3)))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(51,plain,
% 0.19/0.40 ((~$true) <=> $false),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(52,plain,
% 0.19/0.40 (($true | (in(tptp_fun_D_0(set_intersection2(cartesian_product2(B!6, C!5), cartesian_product2(D!4, E!3)), cartesian_product2(D!4, E!3), cartesian_product2(B!6, C!5)), set_intersection2(cartesian_product2(B!6, C!5), cartesian_product2(D!4, E!3))) <=> ((~in(tptp_fun_D_0(set_intersection2(cartesian_product2(B!6, C!5), cartesian_product2(D!4, E!3)), cartesian_product2(D!4, E!3), cartesian_product2(B!6, C!5)), cartesian_product2(B!6, C!5))) | (~in(tptp_fun_D_0(set_intersection2(cartesian_product2(B!6, C!5), cartesian_product2(D!4, E!3)), cartesian_product2(D!4, E!3), cartesian_product2(B!6, C!5)), cartesian_product2(D!4, E!3)))))) <=> $true),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(53,plain,
% 0.19/0.40 ((set_intersection2(cartesian_product2(B!6, C!5), cartesian_product2(D!4, E!3)) = set_intersection2(cartesian_product2(B!6, C!5), cartesian_product2(D!4, E!3))) <=> $true),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(54,plain,
% 0.19/0.40 (((set_intersection2(cartesian_product2(B!6, C!5), cartesian_product2(D!4, E!3)) = set_intersection2(cartesian_product2(B!6, C!5), cartesian_product2(D!4, E!3))) | (in(tptp_fun_D_0(set_intersection2(cartesian_product2(B!6, C!5), cartesian_product2(D!4, E!3)), cartesian_product2(D!4, E!3), cartesian_product2(B!6, C!5)), set_intersection2(cartesian_product2(B!6, C!5), cartesian_product2(D!4, E!3))) <=> ((~in(tptp_fun_D_0(set_intersection2(cartesian_product2(B!6, C!5), cartesian_product2(D!4, E!3)), cartesian_product2(D!4, E!3), cartesian_product2(B!6, C!5)), cartesian_product2(B!6, C!5))) | (~in(tptp_fun_D_0(set_intersection2(cartesian_product2(B!6, C!5), cartesian_product2(D!4, E!3)), cartesian_product2(D!4, E!3), cartesian_product2(B!6, C!5)), cartesian_product2(D!4, E!3)))))) <=> ($true | (in(tptp_fun_D_0(set_intersection2(cartesian_product2(B!6, C!5), cartesian_product2(D!4, E!3)), cartesian_product2(D!4, E!3), cartesian_product2(B!6, C!5)), set_intersection2(cartesian_product2(B!6, C!5), cartesian_product2(D!4, E!3))) <=> ((~in(tptp_fun_D_0(set_intersection2(cartesian_product2(B!6, C!5), cartesian_product2(D!4, E!3)), cartesian_product2(D!4, E!3), cartesian_product2(B!6, C!5)), cartesian_product2(B!6, C!5))) | (~in(tptp_fun_D_0(set_intersection2(cartesian_product2(B!6, C!5), cartesian_product2(D!4, E!3)), cartesian_product2(D!4, E!3), cartesian_product2(B!6, C!5)), cartesian_product2(D!4, E!3))))))),
% 0.19/0.40 inference(monotonicity,[status(thm)],[53])).
% 0.19/0.40 tff(55,plain,
% 0.19/0.40 (((set_intersection2(cartesian_product2(B!6, C!5), cartesian_product2(D!4, E!3)) = set_intersection2(cartesian_product2(B!6, C!5), cartesian_product2(D!4, E!3))) | (in(tptp_fun_D_0(set_intersection2(cartesian_product2(B!6, C!5), cartesian_product2(D!4, E!3)), cartesian_product2(D!4, E!3), cartesian_product2(B!6, C!5)), set_intersection2(cartesian_product2(B!6, C!5), cartesian_product2(D!4, E!3))) <=> ((~in(tptp_fun_D_0(set_intersection2(cartesian_product2(B!6, C!5), cartesian_product2(D!4, E!3)), cartesian_product2(D!4, E!3), cartesian_product2(B!6, C!5)), cartesian_product2(B!6, C!5))) | (~in(tptp_fun_D_0(set_intersection2(cartesian_product2(B!6, C!5), cartesian_product2(D!4, E!3)), cartesian_product2(D!4, E!3), cartesian_product2(B!6, C!5)), cartesian_product2(D!4, E!3)))))) <=> $true),
% 0.19/0.40 inference(transitivity,[status(thm)],[54, 52])).
% 0.19/0.40 tff(56,plain,
% 0.19/0.40 ((~((set_intersection2(cartesian_product2(B!6, C!5), cartesian_product2(D!4, E!3)) = set_intersection2(cartesian_product2(B!6, C!5), cartesian_product2(D!4, E!3))) | (in(tptp_fun_D_0(set_intersection2(cartesian_product2(B!6, C!5), cartesian_product2(D!4, E!3)), cartesian_product2(D!4, E!3), cartesian_product2(B!6, C!5)), set_intersection2(cartesian_product2(B!6, C!5), cartesian_product2(D!4, E!3))) <=> ((~in(tptp_fun_D_0(set_intersection2(cartesian_product2(B!6, C!5), cartesian_product2(D!4, E!3)), cartesian_product2(D!4, E!3), cartesian_product2(B!6, C!5)), cartesian_product2(B!6, C!5))) | (~in(tptp_fun_D_0(set_intersection2(cartesian_product2(B!6, C!5), cartesian_product2(D!4, E!3)), cartesian_product2(D!4, E!3), cartesian_product2(B!6, C!5)), cartesian_product2(D!4, E!3))))))) <=> (~$true)),
% 0.19/0.40 inference(monotonicity,[status(thm)],[55])).
% 0.19/0.40 tff(57,plain,
% 0.19/0.40 ((~((set_intersection2(cartesian_product2(B!6, C!5), cartesian_product2(D!4, E!3)) = set_intersection2(cartesian_product2(B!6, C!5), cartesian_product2(D!4, E!3))) | (in(tptp_fun_D_0(set_intersection2(cartesian_product2(B!6, C!5), cartesian_product2(D!4, E!3)), cartesian_product2(D!4, E!3), cartesian_product2(B!6, C!5)), set_intersection2(cartesian_product2(B!6, C!5), cartesian_product2(D!4, E!3))) <=> ((~in(tptp_fun_D_0(set_intersection2(cartesian_product2(B!6, C!5), cartesian_product2(D!4, E!3)), cartesian_product2(D!4, E!3), cartesian_product2(B!6, C!5)), cartesian_product2(B!6, C!5))) | (~in(tptp_fun_D_0(set_intersection2(cartesian_product2(B!6, C!5), cartesian_product2(D!4, E!3)), cartesian_product2(D!4, E!3), cartesian_product2(B!6, C!5)), cartesian_product2(D!4, E!3))))))) <=> $false),
% 0.19/0.40 inference(transitivity,[status(thm)],[56, 51])).
% 0.19/0.40 tff(58,plain,
% 0.19/0.40 ((~(in(A!7, set_intersection2(cartesian_product2(B!6, C!5), cartesian_product2(D!4, E!3))) <=> (~((~in(A!7, cartesian_product2(B!6, C!5))) | (~in(A!7, cartesian_product2(D!4, E!3))))))) <=> (in(A!7, set_intersection2(cartesian_product2(B!6, C!5), cartesian_product2(D!4, E!3))) <=> ((~in(A!7, cartesian_product2(B!6, C!5))) | (~in(A!7, cartesian_product2(D!4, E!3)))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(59,plain,
% 0.19/0.40 (($false | (in(A!7, set_intersection2(cartesian_product2(B!6, C!5), cartesian_product2(D!4, E!3))) <=> (~((~in(A!7, cartesian_product2(B!6, C!5))) | (~in(A!7, cartesian_product2(D!4, E!3))))))) <=> (in(A!7, set_intersection2(cartesian_product2(B!6, C!5), cartesian_product2(D!4, E!3))) <=> (~((~in(A!7, cartesian_product2(B!6, C!5))) | (~in(A!7, cartesian_product2(D!4, E!3))))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(60,plain,
% 0.19/0.40 ((~(set_intersection2(cartesian_product2(B!6, C!5), cartesian_product2(D!4, E!3)) = set_intersection2(cartesian_product2(B!6, C!5), cartesian_product2(D!4, E!3)))) <=> (~$true)),
% 0.19/0.40 inference(monotonicity,[status(thm)],[53])).
% 0.19/0.40 tff(61,plain,
% 0.19/0.40 ((~(set_intersection2(cartesian_product2(B!6, C!5), cartesian_product2(D!4, E!3)) = set_intersection2(cartesian_product2(B!6, C!5), cartesian_product2(D!4, E!3)))) <=> $false),
% 0.19/0.40 inference(transitivity,[status(thm)],[60, 51])).
% 0.19/0.40 tff(62,plain,
% 0.19/0.40 (((~(set_intersection2(cartesian_product2(B!6, C!5), cartesian_product2(D!4, E!3)) = set_intersection2(cartesian_product2(B!6, C!5), cartesian_product2(D!4, E!3)))) | (in(A!7, set_intersection2(cartesian_product2(B!6, C!5), cartesian_product2(D!4, E!3))) <=> (~((~in(A!7, cartesian_product2(B!6, C!5))) | (~in(A!7, cartesian_product2(D!4, E!3))))))) <=> ($false | (in(A!7, set_intersection2(cartesian_product2(B!6, C!5), cartesian_product2(D!4, E!3))) <=> (~((~in(A!7, cartesian_product2(B!6, C!5))) | (~in(A!7, cartesian_product2(D!4, E!3)))))))),
% 0.19/0.40 inference(monotonicity,[status(thm)],[61])).
% 0.19/0.40 tff(63,plain,
% 0.19/0.40 (((~(set_intersection2(cartesian_product2(B!6, C!5), cartesian_product2(D!4, E!3)) = set_intersection2(cartesian_product2(B!6, C!5), cartesian_product2(D!4, E!3)))) | (in(A!7, set_intersection2(cartesian_product2(B!6, C!5), cartesian_product2(D!4, E!3))) <=> (~((~in(A!7, cartesian_product2(B!6, C!5))) | (~in(A!7, cartesian_product2(D!4, E!3))))))) <=> (in(A!7, set_intersection2(cartesian_product2(B!6, C!5), cartesian_product2(D!4, E!3))) <=> (~((~in(A!7, cartesian_product2(B!6, C!5))) | (~in(A!7, cartesian_product2(D!4, E!3))))))),
% 0.19/0.40 inference(transitivity,[status(thm)],[62, 59])).
% 0.19/0.40 tff(64,plain,
% 0.19/0.40 ((~((~(set_intersection2(cartesian_product2(B!6, C!5), cartesian_product2(D!4, E!3)) = set_intersection2(cartesian_product2(B!6, C!5), cartesian_product2(D!4, E!3)))) | (in(A!7, set_intersection2(cartesian_product2(B!6, C!5), cartesian_product2(D!4, E!3))) <=> (~((~in(A!7, cartesian_product2(B!6, C!5))) | (~in(A!7, cartesian_product2(D!4, E!3)))))))) <=> (~(in(A!7, set_intersection2(cartesian_product2(B!6, C!5), cartesian_product2(D!4, E!3))) <=> (~((~in(A!7, cartesian_product2(B!6, C!5))) | (~in(A!7, cartesian_product2(D!4, E!3)))))))),
% 0.19/0.41 inference(monotonicity,[status(thm)],[63])).
% 0.19/0.41 tff(65,plain,
% 0.19/0.41 ((~((~(set_intersection2(cartesian_product2(B!6, C!5), cartesian_product2(D!4, E!3)) = set_intersection2(cartesian_product2(B!6, C!5), cartesian_product2(D!4, E!3)))) | (in(A!7, set_intersection2(cartesian_product2(B!6, C!5), cartesian_product2(D!4, E!3))) <=> (~((~in(A!7, cartesian_product2(B!6, C!5))) | (~in(A!7, cartesian_product2(D!4, E!3)))))))) <=> (in(A!7, set_intersection2(cartesian_product2(B!6, C!5), cartesian_product2(D!4, E!3))) <=> ((~in(A!7, cartesian_product2(B!6, C!5))) | (~in(A!7, cartesian_product2(D!4, E!3)))))),
% 0.19/0.41 inference(transitivity,[status(thm)],[64, 58])).
% 0.19/0.41 tff(66,plain,
% 0.19/0.41 (((~((~(set_intersection2(cartesian_product2(B!6, C!5), cartesian_product2(D!4, E!3)) = set_intersection2(cartesian_product2(B!6, C!5), cartesian_product2(D!4, E!3)))) | (in(A!7, set_intersection2(cartesian_product2(B!6, C!5), cartesian_product2(D!4, E!3))) <=> (~((~in(A!7, cartesian_product2(B!6, C!5))) | (~in(A!7, cartesian_product2(D!4, E!3)))))))) | (~((set_intersection2(cartesian_product2(B!6, C!5), cartesian_product2(D!4, E!3)) = set_intersection2(cartesian_product2(B!6, C!5), cartesian_product2(D!4, E!3))) | (in(tptp_fun_D_0(set_intersection2(cartesian_product2(B!6, C!5), cartesian_product2(D!4, E!3)), cartesian_product2(D!4, E!3), cartesian_product2(B!6, C!5)), set_intersection2(cartesian_product2(B!6, C!5), cartesian_product2(D!4, E!3))) <=> ((~in(tptp_fun_D_0(set_intersection2(cartesian_product2(B!6, C!5), cartesian_product2(D!4, E!3)), cartesian_product2(D!4, E!3), cartesian_product2(B!6, C!5)), cartesian_product2(B!6, C!5))) | (~in(tptp_fun_D_0(set_intersection2(cartesian_product2(B!6, C!5), cartesian_product2(D!4, E!3)), cartesian_product2(D!4, E!3), cartesian_product2(B!6, C!5)), cartesian_product2(D!4, E!3)))))))) <=> ((in(A!7, set_intersection2(cartesian_product2(B!6, C!5), cartesian_product2(D!4, E!3))) <=> ((~in(A!7, cartesian_product2(B!6, C!5))) | (~in(A!7, cartesian_product2(D!4, E!3))))) | $false)),
% 0.19/0.41 inference(monotonicity,[status(thm)],[65, 57])).
% 0.19/0.41 tff(67,plain,
% 0.19/0.41 (((~((~(set_intersection2(cartesian_product2(B!6, C!5), cartesian_product2(D!4, E!3)) = set_intersection2(cartesian_product2(B!6, C!5), cartesian_product2(D!4, E!3)))) | (in(A!7, set_intersection2(cartesian_product2(B!6, C!5), cartesian_product2(D!4, E!3))) <=> (~((~in(A!7, cartesian_product2(B!6, C!5))) | (~in(A!7, cartesian_product2(D!4, E!3)))))))) | (~((set_intersection2(cartesian_product2(B!6, C!5), cartesian_product2(D!4, E!3)) = set_intersection2(cartesian_product2(B!6, C!5), cartesian_product2(D!4, E!3))) | (in(tptp_fun_D_0(set_intersection2(cartesian_product2(B!6, C!5), cartesian_product2(D!4, E!3)), cartesian_product2(D!4, E!3), cartesian_product2(B!6, C!5)), set_intersection2(cartesian_product2(B!6, C!5), cartesian_product2(D!4, E!3))) <=> ((~in(tptp_fun_D_0(set_intersection2(cartesian_product2(B!6, C!5), cartesian_product2(D!4, E!3)), cartesian_product2(D!4, E!3), cartesian_product2(B!6, C!5)), cartesian_product2(B!6, C!5))) | (~in(tptp_fun_D_0(set_intersection2(cartesian_product2(B!6, C!5), cartesian_product2(D!4, E!3)), cartesian_product2(D!4, E!3), cartesian_product2(B!6, C!5)), cartesian_product2(D!4, E!3)))))))) <=> (in(A!7, set_intersection2(cartesian_product2(B!6, C!5), cartesian_product2(D!4, E!3))) <=> ((~in(A!7, cartesian_product2(B!6, C!5))) | (~in(A!7, cartesian_product2(D!4, E!3)))))),
% 0.19/0.41 inference(transitivity,[status(thm)],[66, 50])).
% 0.19/0.41 tff(68,plain,
% 0.19/0.41 ((~((~((~(set_intersection2(cartesian_product2(B!6, C!5), cartesian_product2(D!4, E!3)) = set_intersection2(cartesian_product2(B!6, C!5), cartesian_product2(D!4, E!3)))) | (in(A!7, set_intersection2(cartesian_product2(B!6, C!5), cartesian_product2(D!4, E!3))) <=> (~((~in(A!7, cartesian_product2(B!6, C!5))) | (~in(A!7, cartesian_product2(D!4, E!3)))))))) | (~((set_intersection2(cartesian_product2(B!6, C!5), cartesian_product2(D!4, E!3)) = set_intersection2(cartesian_product2(B!6, C!5), cartesian_product2(D!4, E!3))) | (in(tptp_fun_D_0(set_intersection2(cartesian_product2(B!6, C!5), cartesian_product2(D!4, E!3)), cartesian_product2(D!4, E!3), cartesian_product2(B!6, C!5)), set_intersection2(cartesian_product2(B!6, C!5), cartesian_product2(D!4, E!3))) <=> ((~in(tptp_fun_D_0(set_intersection2(cartesian_product2(B!6, C!5), cartesian_product2(D!4, E!3)), cartesian_product2(D!4, E!3), cartesian_product2(B!6, C!5)), cartesian_product2(B!6, C!5))) | (~in(tptp_fun_D_0(set_intersection2(cartesian_product2(B!6, C!5), cartesian_product2(D!4, E!3)), cartesian_product2(D!4, E!3), cartesian_product2(B!6, C!5)), cartesian_product2(D!4, E!3))))))))) <=> (~(in(A!7, set_intersection2(cartesian_product2(B!6, C!5), cartesian_product2(D!4, E!3))) <=> ((~in(A!7, cartesian_product2(B!6, C!5))) | (~in(A!7, cartesian_product2(D!4, E!3))))))),
% 0.19/0.41 inference(monotonicity,[status(thm)],[67])).
% 0.19/0.41 tff(69,plain,
% 0.19/0.41 ((~((~((~(set_intersection2(cartesian_product2(B!6, C!5), cartesian_product2(D!4, E!3)) = set_intersection2(cartesian_product2(B!6, C!5), cartesian_product2(D!4, E!3)))) | (in(A!7, set_intersection2(cartesian_product2(B!6, C!5), cartesian_product2(D!4, E!3))) <=> (~((~in(A!7, cartesian_product2(B!6, C!5))) | (~in(A!7, cartesian_product2(D!4, E!3)))))))) | (~((set_intersection2(cartesian_product2(B!6, C!5), cartesian_product2(D!4, E!3)) = set_intersection2(cartesian_product2(B!6, C!5), cartesian_product2(D!4, E!3))) | (in(tptp_fun_D_0(set_intersection2(cartesian_product2(B!6, C!5), cartesian_product2(D!4, E!3)), cartesian_product2(D!4, E!3), cartesian_product2(B!6, C!5)), set_intersection2(cartesian_product2(B!6, C!5), cartesian_product2(D!4, E!3))) <=> ((~in(tptp_fun_D_0(set_intersection2(cartesian_product2(B!6, C!5), cartesian_product2(D!4, E!3)), cartesian_product2(D!4, E!3), cartesian_product2(B!6, C!5)), cartesian_product2(B!6, C!5))) | (~in(tptp_fun_D_0(set_intersection2(cartesian_product2(B!6, C!5), cartesian_product2(D!4, E!3)), cartesian_product2(D!4, E!3), cartesian_product2(B!6, C!5)), cartesian_product2(D!4, E!3))))))))) <=> ((~in(A!7, set_intersection2(cartesian_product2(B!6, C!5), cartesian_product2(D!4, E!3)))) <=> ((~in(A!7, cartesian_product2(B!6, C!5))) | (~in(A!7, cartesian_product2(D!4, E!3)))))),
% 0.19/0.41 inference(transitivity,[status(thm)],[68, 49])).
% 0.19/0.41 tff(70,plain,
% 0.19/0.41 (((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (in(D, C) <=> (~((~in(D, A)) | (~in(D, B))))))) | (~((C = set_intersection2(A, B)) | (in(tptp_fun_D_0(C, B, A), C) <=> ((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))))))))) | (~((~((~(set_intersection2(cartesian_product2(B!6, C!5), cartesian_product2(D!4, E!3)) = set_intersection2(cartesian_product2(B!6, C!5), cartesian_product2(D!4, E!3)))) | (in(A!7, set_intersection2(cartesian_product2(B!6, C!5), cartesian_product2(D!4, E!3))) <=> (~((~in(A!7, cartesian_product2(B!6, C!5))) | (~in(A!7, cartesian_product2(D!4, E!3)))))))) | (~((set_intersection2(cartesian_product2(B!6, C!5), cartesian_product2(D!4, E!3)) = set_intersection2(cartesian_product2(B!6, C!5), cartesian_product2(D!4, E!3))) | (in(tptp_fun_D_0(set_intersection2(cartesian_product2(B!6, C!5), cartesian_product2(D!4, E!3)), cartesian_product2(D!4, E!3), cartesian_product2(B!6, C!5)), set_intersection2(cartesian_product2(B!6, C!5), cartesian_product2(D!4, E!3))) <=> ((~in(tptp_fun_D_0(set_intersection2(cartesian_product2(B!6, C!5), cartesian_product2(D!4, E!3)), cartesian_product2(D!4, E!3), cartesian_product2(B!6, C!5)), cartesian_product2(B!6, C!5))) | (~in(tptp_fun_D_0(set_intersection2(cartesian_product2(B!6, C!5), cartesian_product2(D!4, E!3)), cartesian_product2(D!4, E!3), cartesian_product2(B!6, C!5)), cartesian_product2(D!4, E!3)))))))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (in(D, C) <=> (~((~in(D, A)) | (~in(D, B))))))) | (~((C = set_intersection2(A, B)) | (in(tptp_fun_D_0(C, B, A), C) <=> ((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))))))))) | ((~in(A!7, set_intersection2(cartesian_product2(B!6, C!5), cartesian_product2(D!4, E!3)))) <=> ((~in(A!7, cartesian_product2(B!6, C!5))) | (~in(A!7, cartesian_product2(D!4, E!3))))))),
% 0.19/0.42 inference(monotonicity,[status(thm)],[69])).
% 0.19/0.42 tff(71,plain,
% 0.19/0.42 (((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (in(D, C) <=> (~((~in(D, A)) | (~in(D, B))))))) | (~((C = set_intersection2(A, B)) | (in(tptp_fun_D_0(C, B, A), C) <=> ((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))))))))) | (~((~((~(set_intersection2(cartesian_product2(B!6, C!5), cartesian_product2(D!4, E!3)) = set_intersection2(cartesian_product2(B!6, C!5), cartesian_product2(D!4, E!3)))) | (in(A!7, set_intersection2(cartesian_product2(B!6, C!5), cartesian_product2(D!4, E!3))) <=> (~((~in(A!7, cartesian_product2(B!6, C!5))) | (~in(A!7, cartesian_product2(D!4, E!3)))))))) | (~((set_intersection2(cartesian_product2(B!6, C!5), cartesian_product2(D!4, E!3)) = set_intersection2(cartesian_product2(B!6, C!5), cartesian_product2(D!4, E!3))) | (in(tptp_fun_D_0(set_intersection2(cartesian_product2(B!6, C!5), cartesian_product2(D!4, E!3)), cartesian_product2(D!4, E!3), cartesian_product2(B!6, C!5)), set_intersection2(cartesian_product2(B!6, C!5), cartesian_product2(D!4, E!3))) <=> ((~in(tptp_fun_D_0(set_intersection2(cartesian_product2(B!6, C!5), cartesian_product2(D!4, E!3)), cartesian_product2(D!4, E!3), cartesian_product2(B!6, C!5)), cartesian_product2(B!6, C!5))) | (~in(tptp_fun_D_0(set_intersection2(cartesian_product2(B!6, C!5), cartesian_product2(D!4, E!3)), cartesian_product2(D!4, E!3), cartesian_product2(B!6, C!5)), cartesian_product2(D!4, E!3)))))))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (in(D, C) <=> (~((~in(D, A)) | (~in(D, B))))))) | (~((C = set_intersection2(A, B)) | (in(tptp_fun_D_0(C, B, A), C) <=> ((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))))))))) | ((~in(A!7, set_intersection2(cartesian_product2(B!6, C!5), cartesian_product2(D!4, E!3)))) <=> ((~in(A!7, cartesian_product2(B!6, C!5))) | (~in(A!7, cartesian_product2(D!4, E!3))))))),
% 0.19/0.42 inference(transitivity,[status(thm)],[70, 48])).
% 0.19/0.42 tff(72,plain,
% 0.19/0.42 ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (in(D, C) <=> (~((~in(D, A)) | (~in(D, B))))))) | (~((C = set_intersection2(A, B)) | (in(tptp_fun_D_0(C, B, A), C) <=> ((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))))))))) | (~((~((~(set_intersection2(cartesian_product2(B!6, C!5), cartesian_product2(D!4, E!3)) = set_intersection2(cartesian_product2(B!6, C!5), cartesian_product2(D!4, E!3)))) | (in(A!7, set_intersection2(cartesian_product2(B!6, C!5), cartesian_product2(D!4, E!3))) <=> (~((~in(A!7, cartesian_product2(B!6, C!5))) | (~in(A!7, cartesian_product2(D!4, E!3)))))))) | (~((set_intersection2(cartesian_product2(B!6, C!5), cartesian_product2(D!4, E!3)) = set_intersection2(cartesian_product2(B!6, C!5), cartesian_product2(D!4, E!3))) | (in(tptp_fun_D_0(set_intersection2(cartesian_product2(B!6, C!5), cartesian_product2(D!4, E!3)), cartesian_product2(D!4, E!3), cartesian_product2(B!6, C!5)), set_intersection2(cartesian_product2(B!6, C!5), cartesian_product2(D!4, E!3))) <=> ((~in(tptp_fun_D_0(set_intersection2(cartesian_product2(B!6, C!5), cartesian_product2(D!4, E!3)), cartesian_product2(D!4, E!3), cartesian_product2(B!6, C!5)), cartesian_product2(B!6, C!5))) | (~in(tptp_fun_D_0(set_intersection2(cartesian_product2(B!6, C!5), cartesian_product2(D!4, E!3)), cartesian_product2(D!4, E!3), cartesian_product2(B!6, C!5)), cartesian_product2(D!4, E!3)))))))))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(73,plain,
% 0.19/0.42 ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (in(D, C) <=> (~((~in(D, A)) | (~in(D, B))))))) | (~((C = set_intersection2(A, B)) | (in(tptp_fun_D_0(C, B, A), C) <=> ((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))))))))) | ((~in(A!7, set_intersection2(cartesian_product2(B!6, C!5), cartesian_product2(D!4, E!3)))) <=> ((~in(A!7, cartesian_product2(B!6, C!5))) | (~in(A!7, cartesian_product2(D!4, E!3)))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[72, 71])).
% 0.19/0.42 tff(74,plain,
% 0.19/0.42 ((~in(A!7, set_intersection2(cartesian_product2(B!6, C!5), cartesian_product2(D!4, E!3)))) <=> ((~in(A!7, cartesian_product2(B!6, C!5))) | (~in(A!7, cartesian_product2(D!4, E!3))))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[73, 47])).
% 0.19/0.42 tff(75,plain,
% 0.19/0.42 (in(A!7, cartesian_product2(B!6, C!5)) & in(A!7, cartesian_product2(D!4, E!3))),
% 0.19/0.42 inference(or_elim,[status(thm)],[24])).
% 0.19/0.42 tff(76,plain,
% 0.19/0.42 (in(A!7, cartesian_product2(D!4, E!3))),
% 0.19/0.42 inference(and_elim,[status(thm)],[75])).
% 0.19/0.42 tff(77,plain,
% 0.19/0.42 (in(A!7, cartesian_product2(B!6, C!5))),
% 0.19/0.42 inference(and_elim,[status(thm)],[75])).
% 0.19/0.42 tff(78,plain,
% 0.19/0.42 ((~((~in(A!7, cartesian_product2(B!6, C!5))) | (~in(A!7, cartesian_product2(D!4, E!3))))) | (~in(A!7, cartesian_product2(B!6, C!5))) | (~in(A!7, cartesian_product2(D!4, E!3)))),
% 0.19/0.42 inference(tautology,[status(thm)],[])).
% 0.19/0.42 tff(79,plain,
% 0.19/0.42 (~((~in(A!7, cartesian_product2(B!6, C!5))) | (~in(A!7, cartesian_product2(D!4, E!3))))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[78, 77, 76])).
% 0.19/0.42 tff(80,plain,
% 0.19/0.42 ((~((~in(A!7, set_intersection2(cartesian_product2(B!6, C!5), cartesian_product2(D!4, E!3)))) <=> ((~in(A!7, cartesian_product2(B!6, C!5))) | (~in(A!7, cartesian_product2(D!4, E!3)))))) | in(A!7, set_intersection2(cartesian_product2(B!6, C!5), cartesian_product2(D!4, E!3))) | ((~in(A!7, cartesian_product2(B!6, C!5))) | (~in(A!7, cartesian_product2(D!4, E!3))))),
% 0.19/0.42 inference(tautology,[status(thm)],[])).
% 0.19/0.42 tff(81,plain,
% 0.19/0.42 ((~((~in(A!7, set_intersection2(cartesian_product2(B!6, C!5), cartesian_product2(D!4, E!3)))) <=> ((~in(A!7, cartesian_product2(B!6, C!5))) | (~in(A!7, cartesian_product2(D!4, E!3)))))) | in(A!7, set_intersection2(cartesian_product2(B!6, C!5), cartesian_product2(D!4, E!3)))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[80, 79])).
% 0.19/0.42 tff(82,plain,
% 0.19/0.42 (in(A!7, set_intersection2(cartesian_product2(B!6, C!5), cartesian_product2(D!4, E!3)))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[81, 74])).
% 0.19/0.42 tff(83,plain,
% 0.19/0.42 ($false),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[82, 26])).
% 0.19/0.42 % SZS output end Proof
%------------------------------------------------------------------------------