%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SET983+1 : TPTP v9.0.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n006.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 : Sat Jun 21 05:26:45 AM UTC 2025
% Result : Theorem 0.19s 0.37s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET983+1 : TPTP v9.0.0. Released v3.2.0.
% 0.00/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n006.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 : Fri Jun 20 05:54:20 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.19/0.37 % SZS status Theorem
% 0.19/0.37 % SZS output start Proof
% 0.19/0.37 tff(in_type, type, (
% 0.19/0.37 in: ( $i * $i ) > $o)).
% 0.19/0.37 tff(set_intersection2_type, type, (
% 0.19/0.37 set_intersection2: ( $i * $i ) > $i)).
% 0.19/0.37 tff(cartesian_product2_type, type, (
% 0.19/0.37 cartesian_product2: ( $i * $i ) > $i)).
% 0.19/0.37 tff(tptp_fun_E_3_type, type, (
% 0.19/0.37 tptp_fun_E_3: $i)).
% 0.19/0.37 tff(tptp_fun_D_4_type, type, (
% 0.19/0.37 tptp_fun_D_4: $i)).
% 0.19/0.37 tff(tptp_fun_C_5_type, type, (
% 0.19/0.37 tptp_fun_C_5: $i)).
% 0.19/0.37 tff(tptp_fun_B_6_type, type, (
% 0.19/0.37 tptp_fun_B_6: $i)).
% 0.19/0.37 tff(tptp_fun_A_7_type, type, (
% 0.19/0.37 tptp_fun_A_7: $i)).
% 0.19/0.37 tff(tptp_fun_D_0_type, type, (
% 0.19/0.37 tptp_fun_D_0: ( $i * $i * $i ) > $i)).
% 0.19/0.37 tff(1,plain,
% 0.19/0.37 (^[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))))),
% 0.19/0.37 inference(bind,[status(th)],[])).
% 0.19/0.37 tff(2,plain,
% 0.19/0.37 (![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)))),
% 0.19/0.37 inference(quant_intro,[status(thm)],[1])).
% 0.19/0.37 tff(3,plain,
% 0.19/0.37 (![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)))),
% 0.19/0.37 inference(rewrite,[status(thm)],[])).
% 0.19/0.37 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')).
% 0.19/0.37 tff(5,plain,
% 0.19/0.37 (![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)))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.19/0.37 tff(6,plain,(
% 0.19/0.37 ![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)))),
% 0.19/0.37 inference(skolemize,[status(sab)],[5])).
% 0.19/0.37 tff(7,plain,
% 0.19/0.37 (![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)))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.19/0.37 tff(8,plain,
% 0.19/0.37 ((~![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)))),
% 0.19/0.37 inference(quant_inst,[status(thm)],[])).
% 0.19/0.37 tff(9,plain,
% 0.19/0.37 (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))),
% 0.19/0.37 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.19/0.37 tff(10,plain,
% 0.19/0.37 (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))),
% 0.19/0.37 inference(symmetry,[status(thm)],[9])).
% 0.19/0.37 tff(11,plain,
% 0.19/0.37 (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)))),
% 0.19/0.37 inference(monotonicity,[status(thm)],[10])).
% 0.19/0.37 tff(12,plain,
% 0.19/0.37 (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)))),
% 0.19/0.37 inference(symmetry,[status(thm)],[11])).
% 0.19/0.37 tff(13,plain,
% 0.19/0.37 ((~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))))),
% 0.19/0.37 inference(monotonicity,[status(thm)],[12])).
% 0.19/0.37 tff(14,plain,
% 0.19/0.37 ((~![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)))))),
% 0.19/0.37 inference(rewrite,[status(thm)],[])).
% 0.19/0.37 tff(15,plain,
% 0.19/0.37 ((~![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)))))),
% 0.19/0.37 inference(rewrite,[status(thm)],[])).
% 0.19/0.37 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')).
% 0.19/0.37 tff(17,plain,
% 0.19/0.37 (~![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))))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[16, 15])).
% 0.19/0.37 tff(18,plain,
% 0.19/0.37 (~![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))))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[17, 14])).
% 0.19/0.37 tff(19,plain,
% 0.19/0.37 (~![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))))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[18, 14])).
% 0.19/0.37 tff(20,plain,
% 0.19/0.37 (~![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))))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[19, 14])).
% 0.19/0.37 tff(21,plain,(
% 0.19/0.37 ~((~(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))))),
% 0.19/0.37 inference(skolemize,[status(sab)],[20])).
% 0.19/0.37 tff(22,plain,
% 0.19/0.37 (~in(A!7, cartesian_product2(set_intersection2(B!6, D!4), set_intersection2(C!5, E!3)))),
% 0.19/0.37 inference(or_elim,[status(thm)],[21])).
% 0.19/0.37 tff(23,plain,
% 0.19/0.37 (~in(A!7, set_intersection2(cartesian_product2(B!6, C!5), cartesian_product2(D!4, E!3)))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[22, 13])).
% 0.19/0.37 tff(24,plain,
% 0.19/0.37 (^[A: $i, B: $i, C: $i, D: $i] : refl((~((~((~(C = set_intersection2(A, B))) | (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))) <=> in(tptp_fun_D_0(C, B, A), C)))))) <=> (~((~((~(C = set_intersection2(A, B))) | (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))) <=> in(tptp_fun_D_0(C, B, A), C)))))))),
% 0.19/0.37 inference(bind,[status(th)],[])).
% 0.19/0.37 tff(25,plain,
% 0.19/0.37 (![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))) <=> in(tptp_fun_D_0(C, B, A), C)))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))) <=> in(tptp_fun_D_0(C, B, A), C))))))),
% 0.19/0.37 inference(quant_intro,[status(thm)],[24])).
% 0.19/0.37 tff(26,plain,
% 0.19/0.37 (![A: $i, B: $i, C: $i] : ![D: $i] : (~((~((~(C = set_intersection2(A, B))) | (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))) <=> in(tptp_fun_D_0(C, B, A), C)))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))) <=> in(tptp_fun_D_0(C, B, A), C))))))),
% 0.19/0.37 inference(pull_quant,[status(thm)],[])).
% 0.19/0.37 tff(27,plain,
% 0.19/0.37 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(pull_quant(((~(C = set_intersection2(A, B))) | ![D: $i] : (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C)))) <=> ![D: $i] : ((~(C = set_intersection2(A, B))) | (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))), ((~((~(C = set_intersection2(A, B))) | ![D: $i] : (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) <=> (~![D: $i] : ((~(C = set_intersection2(A, B))) | (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))))), pull_quant((~![D: $i] : ((~(C = set_intersection2(A, B))) | (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) <=> ?[D: $i] : (~((~(C = set_intersection2(A, B))) | (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C)))))), ((~((~(C = set_intersection2(A, B))) | ![D: $i] : (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) <=> ?[D: $i] : (~((~(C = set_intersection2(A, B))) | (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))))), (((~((~(C = set_intersection2(A, B))) | ![D: $i] : (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))) <=> in(tptp_fun_D_0(C, B, A), C))))) <=> (?[D: $i] : (~((~(C = set_intersection2(A, B))) | (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))) <=> in(tptp_fun_D_0(C, B, A), C))))))), pull_quant((?[D: $i] : (~((~(C = set_intersection2(A, B))) | (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))) <=> in(tptp_fun_D_0(C, B, A), C))))) <=> ?[D: $i] : ((~((~(C = set_intersection2(A, B))) | (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))) <=> in(tptp_fun_D_0(C, B, A), C)))))), (((~((~(C = set_intersection2(A, B))) | ![D: $i] : (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))) <=> in(tptp_fun_D_0(C, B, A), C))))) <=> ?[D: $i] : ((~((~(C = set_intersection2(A, B))) | (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))) <=> in(tptp_fun_D_0(C, B, A), C))))))), ((~((~((~(C = set_intersection2(A, B))) | ![D: $i] : (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))) <=> in(tptp_fun_D_0(C, B, A), C)))))) <=> (~?[D: $i] : ((~((~(C = set_intersection2(A, B))) | (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))) <=> in(tptp_fun_D_0(C, B, A), C)))))))), pull_quant((~?[D: $i] : ((~((~(C = set_intersection2(A, B))) | (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))) <=> in(tptp_fun_D_0(C, B, A), C)))))) <=> ![D: $i] : (~((~((~(C = set_intersection2(A, B))) | (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))) <=> in(tptp_fun_D_0(C, B, A), C))))))), ((~((~((~(C = set_intersection2(A, B))) | ![D: $i] : (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))) <=> in(tptp_fun_D_0(C, B, A), C)))))) <=> ![D: $i] : (~((~((~(C = set_intersection2(A, B))) | (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))) <=> in(tptp_fun_D_0(C, B, A), C))))))))),
% 0.19/0.38 inference(bind,[status(th)],[])).
% 0.19/0.38 tff(28,plain,
% 0.19/0.38 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_intersection2(A, B))) | ![D: $i] : (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))) <=> in(tptp_fun_D_0(C, B, A), C)))))) <=> ![A: $i, B: $i, C: $i] : ![D: $i] : (~((~((~(C = set_intersection2(A, B))) | (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))) <=> in(tptp_fun_D_0(C, B, A), C))))))),
% 0.19/0.38 inference(quant_intro,[status(thm)],[27])).
% 0.19/0.38 tff(29,plain,
% 0.19/0.38 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_intersection2(A, B))) | ![D: $i] : (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))) <=> in(tptp_fun_D_0(C, B, A), C)))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))) <=> in(tptp_fun_D_0(C, B, A), C))))))),
% 0.19/0.38 inference(transitivity,[status(thm)],[28, 26])).
% 0.19/0.38 tff(30,plain,
% 0.19/0.38 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_intersection2(A, B))) | ![D: $i] : (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))) <=> in(tptp_fun_D_0(C, B, A), C)))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))) <=> in(tptp_fun_D_0(C, B, A), C))))))),
% 0.19/0.38 inference(transitivity,[status(thm)],[29, 25])).
% 0.19/0.38 tff(31,plain,
% 0.19/0.38 (^[A: $i, B: $i, C: $i] : rewrite((~((~((~(C = set_intersection2(A, B))) | ![D: $i] : (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))) <=> in(tptp_fun_D_0(C, B, A), C)))))) <=> (~((~((~(C = set_intersection2(A, B))) | ![D: $i] : (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))) <=> in(tptp_fun_D_0(C, B, A), C)))))))),
% 0.19/0.38 inference(bind,[status(th)],[])).
% 0.19/0.38 tff(32,plain,
% 0.19/0.38 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_intersection2(A, B))) | ![D: $i] : (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))) <=> in(tptp_fun_D_0(C, B, A), C)))))) <=> ![A: $i, B: $i, C: $i] : (~((~((~(C = set_intersection2(A, B))) | ![D: $i] : (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))) <=> in(tptp_fun_D_0(C, B, A), C))))))),
% 0.19/0.38 inference(quant_intro,[status(thm)],[31])).
% 0.19/0.38 tff(33,plain,
% 0.19/0.38 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_intersection2(A, B))) | ![D: $i] : (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))) <=> in(tptp_fun_D_0(C, B, A), C)))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))) <=> in(tptp_fun_D_0(C, B, A), C))))))),
% 0.19/0.38 inference(transitivity,[status(thm)],[32, 30])).
% 0.19/0.38 tff(34,plain,
% 0.19/0.38 (^[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, A)) | (~in(D, B))) <=> in(D, C))))), 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), A)) | (~in(tptp_fun_D_0(C, B, A), B))) <=> in(tptp_fun_D_0(C, B, A), C)))), ((((~(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, A)) | (~in(D, B))) <=> in(D, C)))) & ((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))) <=> in(tptp_fun_D_0(C, B, A), C)))))), rewrite((((~(C = set_intersection2(A, B))) | ![D: $i] : (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C)))) & ((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))) <=> in(tptp_fun_D_0(C, B, A), C)))) <=> (~((~((~(C = set_intersection2(A, B))) | ![D: $i] : (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))) <=> in(tptp_fun_D_0(C, B, A), C))))))), ((((~(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, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))) <=> in(tptp_fun_D_0(C, B, A), C))))))))),
% 0.19/0.38 inference(bind,[status(th)],[])).
% 0.19/0.38 tff(35,plain,
% 0.19/0.38 (![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, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))) <=> in(tptp_fun_D_0(C, B, A), C))))))),
% 0.19/0.38 inference(quant_intro,[status(thm)],[34])).
% 0.19/0.38 tff(36,plain,
% 0.19/0.38 (![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))))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(37,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')).
% 0.19/0.38 tff(38,plain,
% 0.19/0.38 (![A: $i, B: $i, C: $i] : ((C = set_intersection2(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, A) & in(D, B))))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[37, 36])).
% 0.19/0.38 tff(39,plain,(
% 0.19/0.38 ![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))))))),
% 0.19/0.38 inference(skolemize,[status(sab)],[38])).
% 0.19/0.38 tff(40,plain,
% 0.19/0.38 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_intersection2(A, B))) | ![D: $i] : (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))) <=> in(tptp_fun_D_0(C, B, A), C))))))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[39, 35])).
% 0.19/0.38 tff(41,plain,
% 0.19/0.38 (![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))) <=> in(tptp_fun_D_0(C, B, A), C))))))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[40, 33])).
% 0.19/0.38 tff(42,plain,
% 0.19/0.38 (((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))) <=> in(tptp_fun_D_0(C, B, A), C))))))) | (~(((~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)))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))) <=> in(tptp_fun_D_0(C, B, A), C))))))) | (~(((~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))))))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(43,plain,
% 0.19/0.38 ((~(((~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)))) <=> in(A!7, set_intersection2(cartesian_product2(B!6, C!5), cartesian_product2(D!4, E!3)))))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(44,plain,
% 0.19/0.38 (((((~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)))) | $false) <=> (((~in(A!7, cartesian_product2(B!6, C!5))) | (~in(A!7, cartesian_product2(D!4, E!3)))) <=> in(A!7, set_intersection2(cartesian_product2(B!6, C!5), cartesian_product2(D!4, E!3))))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(45,plain,
% 0.19/0.38 ((~$true) <=> $false),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(46,plain,
% 0.19/0.38 (($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)), 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(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))))) <=> $true),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(47,plain,
% 0.19/0.38 ((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))) <=> $true),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(48,plain,
% 0.19/0.38 (((set_intersection2(cartesian_product2(B!6, C!5), cartesian_product2(D!4, E!3)) = set_intersection2(cartesian_product2(B!6, C!5), cartesian_product2(D!4, E!3))) | (((~in(tptp_fun_D_0(set_intersection2(cartesian_product2(B!6, C!5), cartesian_product2(D!4, E!3)), cartesian_product2(D!4, E!3), cartesian_product2(B!6, C!5)), cartesian_product2(B!6, C!5))) | (~in(tptp_fun_D_0(set_intersection2(cartesian_product2(B!6, C!5), cartesian_product2(D!4, E!3)), cartesian_product2(D!4, E!3), cartesian_product2(B!6, C!5)), cartesian_product2(D!4, E!3)))) <=> in(tptp_fun_D_0(set_intersection2(cartesian_product2(B!6, C!5), cartesian_product2(D!4, E!3)), cartesian_product2(D!4, E!3), cartesian_product2(B!6, C!5)), set_intersection2(cartesian_product2(B!6, C!5), cartesian_product2(D!4, E!3))))) <=> ($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)), 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(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)))))),
% 0.19/0.38 inference(monotonicity,[status(thm)],[47])).
% 0.19/0.38 tff(49,plain,
% 0.19/0.38 (((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)), 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(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))))) <=> $true),
% 0.19/0.38 inference(transitivity,[status(thm)],[48, 46])).
% 0.19/0.38 tff(50,plain,
% 0.19/0.38 ((~((set_intersection2(cartesian_product2(B!6, C!5), cartesian_product2(D!4, E!3)) = set_intersection2(cartesian_product2(B!6, C!5), cartesian_product2(D!4, E!3))) | (((~in(tptp_fun_D_0(set_intersection2(cartesian_product2(B!6, C!5), cartesian_product2(D!4, E!3)), cartesian_product2(D!4, E!3), cartesian_product2(B!6, C!5)), cartesian_product2(B!6, C!5))) | (~in(tptp_fun_D_0(set_intersection2(cartesian_product2(B!6, C!5), cartesian_product2(D!4, E!3)), cartesian_product2(D!4, E!3), cartesian_product2(B!6, C!5)), cartesian_product2(D!4, E!3)))) <=> in(tptp_fun_D_0(set_intersection2(cartesian_product2(B!6, C!5), cartesian_product2(D!4, E!3)), cartesian_product2(D!4, E!3), cartesian_product2(B!6, C!5)), set_intersection2(cartesian_product2(B!6, C!5), cartesian_product2(D!4, E!3)))))) <=> (~$true)),
% 0.19/0.38 inference(monotonicity,[status(thm)],[49])).
% 0.19/0.38 tff(51,plain,
% 0.19/0.38 ((~((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)), 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(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)))))) <=> $false),
% 0.19/0.38 inference(transitivity,[status(thm)],[50, 45])).
% 0.19/0.38 tff(52,plain,
% 0.19/0.38 ((~(~(((~in(A!7, cartesian_product2(B!6, C!5))) | (~in(A!7, cartesian_product2(D!4, E!3)))) <=> in(A!7, set_intersection2(cartesian_product2(B!6, C!5), cartesian_product2(D!4, E!3)))))) <=> (((~in(A!7, cartesian_product2(B!6, C!5))) | (~in(A!7, cartesian_product2(D!4, E!3)))) <=> in(A!7, set_intersection2(cartesian_product2(B!6, C!5), cartesian_product2(D!4, E!3))))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(53,plain,
% 0.19/0.38 (($false | (~(((~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)))) <=> in(A!7, set_intersection2(cartesian_product2(B!6, C!5), cartesian_product2(D!4, E!3)))))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(54,plain,
% 0.19/0.39 ((~(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)),
% 0.19/0.39 inference(monotonicity,[status(thm)],[47])).
% 0.19/0.39 tff(55,plain,
% 0.19/0.39 ((~(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)))) <=> $false),
% 0.19/0.39 inference(transitivity,[status(thm)],[54, 45])).
% 0.19/0.39 tff(56,plain,
% 0.19/0.39 (((~(set_intersection2(cartesian_product2(B!6, C!5), cartesian_product2(D!4, E!3)) = set_intersection2(cartesian_product2(B!6, C!5), cartesian_product2(D!4, E!3)))) | (~(((~in(A!7, cartesian_product2(B!6, C!5))) | (~in(A!7, cartesian_product2(D!4, E!3)))) <=> in(A!7, set_intersection2(cartesian_product2(B!6, C!5), cartesian_product2(D!4, E!3)))))) <=> ($false | (~(((~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))))))),
% 0.19/0.39 inference(monotonicity,[status(thm)],[55, 43])).
% 0.19/0.39 tff(57,plain,
% 0.19/0.39 (((~(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, 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)))) <=> in(A!7, set_intersection2(cartesian_product2(B!6, C!5), cartesian_product2(D!4, E!3)))))),
% 0.19/0.39 inference(transitivity,[status(thm)],[56, 53])).
% 0.19/0.39 tff(58,plain,
% 0.19/0.39 ((~((~(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, 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)))) <=> 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)],[57])).
% 0.19/0.39 tff(59,plain,
% 0.19/0.39 ((~((~(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, 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)))) <=> in(A!7, set_intersection2(cartesian_product2(B!6, C!5), cartesian_product2(D!4, E!3))))),
% 0.19/0.39 inference(transitivity,[status(thm)],[58, 52])).
% 0.19/0.39 tff(60,plain,
% 0.19/0.39 (((~((~(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, 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))))))) | (~((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)), 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(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(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)))) | $false)),
% 0.19/0.39 inference(monotonicity,[status(thm)],[59, 51])).
% 0.19/0.39 tff(61,plain,
% 0.19/0.39 (((~((~(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, 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))))))) | (~((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)), 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(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(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))))),
% 0.19/0.39 inference(transitivity,[status(thm)],[60, 44])).
% 0.19/0.39 tff(62,plain,
% 0.19/0.39 ((~((~((~(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, 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))))))) | (~((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)), 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(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(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)))))),
% 0.19/0.39 inference(monotonicity,[status(thm)],[61])).
% 0.19/0.39 tff(63,plain,
% 0.19/0.39 ((~((~((~(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, 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))))))) | (~((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)), 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(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(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)))))),
% 0.19/0.39 inference(transitivity,[status(thm)],[62, 43])).
% 0.19/0.39 tff(64,plain,
% 0.19/0.39 (((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))) <=> in(tptp_fun_D_0(C, B, A), C))))))) | (~((~((~(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, 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))))))) | (~((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)), 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(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))))))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))) <=> in(tptp_fun_D_0(C, B, A), C))))))) | (~(((~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))))))),
% 0.19/0.39 inference(monotonicity,[status(thm)],[63])).
% 0.19/0.39 tff(65,plain,
% 0.19/0.39 (((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))) <=> in(tptp_fun_D_0(C, B, A), C))))))) | (~((~((~(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, 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))))))) | (~((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)), 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(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))))))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))) <=> in(tptp_fun_D_0(C, B, A), C))))))) | (~(((~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))))))),
% 0.19/0.40 inference(transitivity,[status(thm)],[64, 42])).
% 0.19/0.40 tff(66,plain,
% 0.19/0.40 ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))) <=> in(tptp_fun_D_0(C, B, A), C))))))) | (~((~((~(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, 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))))))) | (~((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)), 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(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))))))))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(67,plain,
% 0.19/0.40 ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_intersection2(A, B))) | (~(((~in(D, A)) | (~in(D, B))) <=> in(D, C))))) | (~((C = set_intersection2(A, B)) | (((~in(tptp_fun_D_0(C, B, A), A)) | (~in(tptp_fun_D_0(C, B, A), B))) <=> in(tptp_fun_D_0(C, B, A), C))))))) | (~(((~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)))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[66, 65])).
% 0.19/0.40 tff(68,plain,
% 0.19/0.40 (~(((~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))))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[67, 41])).
% 0.19/0.40 tff(69,plain,
% 0.19/0.40 (in(A!7, cartesian_product2(B!6, C!5)) & in(A!7, cartesian_product2(D!4, E!3))),
% 0.19/0.40 inference(or_elim,[status(thm)],[21])).
% 0.19/0.40 tff(70,plain,
% 0.19/0.40 (in(A!7, cartesian_product2(D!4, E!3))),
% 0.19/0.40 inference(and_elim,[status(thm)],[69])).
% 0.19/0.40 tff(71,plain,
% 0.19/0.40 (in(A!7, cartesian_product2(B!6, C!5))),
% 0.19/0.40 inference(and_elim,[status(thm)],[69])).
% 0.19/0.40 tff(72,plain,
% 0.19/0.40 ((~((~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)))),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(73,plain,
% 0.19/0.40 (~((~in(A!7, cartesian_product2(B!6, C!5))) | (~in(A!7, cartesian_product2(D!4, E!3))))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[72, 71, 70])).
% 0.19/0.40 tff(74,plain,
% 0.19/0.40 ((((~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)))) | in(A!7, set_intersection2(cartesian_product2(B!6, C!5), cartesian_product2(D!4, E!3)))),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(75,plain,
% 0.19/0.40 ((((~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, set_intersection2(cartesian_product2(B!6, C!5), cartesian_product2(D!4, E!3)))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[74, 73])).
% 0.19/0.40 tff(76,plain,
% 0.19/0.40 (in(A!7, set_intersection2(cartesian_product2(B!6, C!5), cartesian_product2(D!4, E!3)))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[75, 68])).
% 0.19/0.40 tff(77,plain,
% 0.19/0.40 ($false),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[76, 23])).
% 0.19/0.40 % SZS output end Proof
% 0.19/0.40 % E exiting
%------------------------------------------------------------------------------