%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SEU090+1 : TPTP v9.0.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n007.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 05:26:53 AM UTC 2025
% Result : Theorem 0.21s 0.40s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : SEU090+1 : TPTP v9.0.0. Released v3.2.0.
% 0.03/0.13 % Command : run_E %s %d THM
% 0.13/0.34 % Computer : n007.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Fri Jun 20 06:04:50 EDT 2025
% 0.13/0.34 % CPUTime :
% 0.21/0.40 % SZS status Theorem
% 0.21/0.40 % SZS output start Proof
% 0.21/0.40 tff(finite_type, type, (
% 0.21/0.40 finite: $i > $o)).
% 0.21/0.40 tff(cartesian_product2_type, type, (
% 0.21/0.40 cartesian_product2: ( $i * $i ) > $i)).
% 0.21/0.40 tff(tptp_fun_D_26_type, type, (
% 0.21/0.40 tptp_fun_D_26: $i)).
% 0.21/0.40 tff(cartesian_product3_type, type, (
% 0.21/0.40 cartesian_product3: ( $i * $i * $i ) > $i)).
% 0.21/0.40 tff(tptp_fun_C_27_type, type, (
% 0.21/0.40 tptp_fun_C_27: $i)).
% 0.21/0.40 tff(tptp_fun_B_28_type, type, (
% 0.21/0.40 tptp_fun_B_28: $i)).
% 0.21/0.40 tff(tptp_fun_A_29_type, type, (
% 0.21/0.40 tptp_fun_A_29: $i)).
% 0.21/0.40 tff(cartesian_product4_type, type, (
% 0.21/0.40 cartesian_product4: ( $i * $i * $i * $i ) > $i)).
% 0.21/0.40 tff(1,plain,
% 0.21/0.40 (^[A: $i, B: $i, C: $i, D: $i] : refl((cartesian_product4(A, B, C, D) = cartesian_product2(cartesian_product3(A, B, C), D)) <=> (cartesian_product4(A, B, C, D) = cartesian_product2(cartesian_product3(A, B, C), D)))),
% 0.21/0.40 inference(bind,[status(th)],[])).
% 0.21/0.40 tff(2,plain,
% 0.21/0.40 (![A: $i, B: $i, C: $i, D: $i] : (cartesian_product4(A, B, C, D) = cartesian_product2(cartesian_product3(A, B, C), D)) <=> ![A: $i, B: $i, C: $i, D: $i] : (cartesian_product4(A, B, C, D) = cartesian_product2(cartesian_product3(A, B, C), D))),
% 0.21/0.40 inference(quant_intro,[status(thm)],[1])).
% 0.21/0.40 tff(3,plain,
% 0.21/0.40 (![A: $i, B: $i, C: $i, D: $i] : (cartesian_product4(A, B, C, D) = cartesian_product2(cartesian_product3(A, B, C), D)) <=> ![A: $i, B: $i, C: $i, D: $i] : (cartesian_product4(A, B, C, D) = cartesian_product2(cartesian_product3(A, B, C), D))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(4,axiom,(![A: $i, B: $i, C: $i, D: $i] : (cartesian_product4(A, B, C, D) = cartesian_product2(cartesian_product3(A, B, C), D))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d4_zfmisc_1')).
% 0.21/0.40 tff(5,plain,
% 0.21/0.40 (![A: $i, B: $i, C: $i, D: $i] : (cartesian_product4(A, B, C, D) = cartesian_product2(cartesian_product3(A, B, C), D))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.21/0.40 tff(6,plain,(
% 0.21/0.40 ![A: $i, B: $i, C: $i, D: $i] : (cartesian_product4(A, B, C, D) = cartesian_product2(cartesian_product3(A, B, C), D))),
% 0.21/0.40 inference(skolemize,[status(sab)],[5])).
% 0.21/0.40 tff(7,plain,
% 0.21/0.40 (![A: $i, B: $i, C: $i, D: $i] : (cartesian_product4(A, B, C, D) = cartesian_product2(cartesian_product3(A, B, C), D))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.21/0.40 tff(8,plain,
% 0.21/0.40 ((~![A: $i, B: $i, C: $i, D: $i] : (cartesian_product4(A, B, C, D) = cartesian_product2(cartesian_product3(A, B, C), D))) | (cartesian_product4(A!29, B!28, C!27, D!26) = cartesian_product2(cartesian_product3(A!29, B!28, C!27), D!26))),
% 0.21/0.40 inference(quant_inst,[status(thm)],[])).
% 0.21/0.40 tff(9,plain,
% 0.21/0.40 (cartesian_product4(A!29, B!28, C!27, D!26) = cartesian_product2(cartesian_product3(A!29, B!28, C!27), D!26)),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.21/0.40 tff(10,plain,
% 0.21/0.40 (cartesian_product2(cartesian_product3(A!29, B!28, C!27), D!26) = cartesian_product4(A!29, B!28, C!27, D!26)),
% 0.21/0.40 inference(symmetry,[status(thm)],[9])).
% 0.21/0.40 tff(11,plain,
% 0.21/0.40 (finite(cartesian_product2(cartesian_product3(A!29, B!28, C!27), D!26)) <=> finite(cartesian_product4(A!29, B!28, C!27, D!26))),
% 0.21/0.40 inference(monotonicity,[status(thm)],[10])).
% 0.21/0.40 tff(12,plain,
% 0.21/0.40 (finite(cartesian_product4(A!29, B!28, C!27, D!26)) <=> finite(cartesian_product2(cartesian_product3(A!29, B!28, C!27), D!26))),
% 0.21/0.40 inference(symmetry,[status(thm)],[11])).
% 0.21/0.40 tff(13,plain,
% 0.21/0.40 ((~finite(cartesian_product4(A!29, B!28, C!27, D!26))) <=> (~finite(cartesian_product2(cartesian_product3(A!29, B!28, C!27), D!26)))),
% 0.21/0.40 inference(monotonicity,[status(thm)],[12])).
% 0.21/0.40 tff(14,plain,
% 0.21/0.40 ((~![A: $i, B: $i, C: $i, D: $i] : (finite(cartesian_product4(A, B, C, D)) | (~(finite(A) & finite(B) & finite(C) & finite(D))))) <=> (~![A: $i, B: $i, C: $i, D: $i] : (finite(cartesian_product4(A, B, C, D)) | (~(finite(A) & finite(B) & finite(C) & finite(D)))))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(15,plain,
% 0.21/0.40 ((~![A: $i, B: $i, C: $i, D: $i] : ((((finite(A) & finite(B)) & finite(C)) & finite(D)) => finite(cartesian_product4(A, B, C, D)))) <=> (~![A: $i, B: $i, C: $i, D: $i] : (finite(cartesian_product4(A, B, C, D)) | (~(finite(A) & finite(B) & finite(C) & finite(D)))))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(16,axiom,(~![A: $i, B: $i, C: $i, D: $i] : ((((finite(A) & finite(B)) & finite(C)) & finite(D)) => finite(cartesian_product4(A, B, C, D)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t21_finset_1')).
% 0.21/0.40 tff(17,plain,
% 0.21/0.40 (~![A: $i, B: $i, C: $i, D: $i] : (finite(cartesian_product4(A, B, C, D)) | (~(finite(A) & finite(B) & finite(C) & finite(D))))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[16, 15])).
% 0.21/0.40 tff(18,plain,
% 0.21/0.40 (~![A: $i, B: $i, C: $i, D: $i] : (finite(cartesian_product4(A, B, C, D)) | (~(finite(A) & finite(B) & finite(C) & finite(D))))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[17, 14])).
% 0.21/0.40 tff(19,plain,
% 0.21/0.40 (~![A: $i, B: $i, C: $i, D: $i] : (finite(cartesian_product4(A, B, C, D)) | (~(finite(A) & finite(B) & finite(C) & finite(D))))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[18, 14])).
% 0.21/0.40 tff(20,plain,
% 0.21/0.40 (~![A: $i, B: $i, C: $i, D: $i] : (finite(cartesian_product4(A, B, C, D)) | (~(finite(A) & finite(B) & finite(C) & finite(D))))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[19, 14])).
% 0.21/0.40 tff(21,plain,(
% 0.21/0.40 ~(finite(cartesian_product4(A!29, B!28, C!27, D!26)) | (~(finite(A!29) & finite(B!28) & finite(C!27) & finite(D!26))))),
% 0.21/0.40 inference(skolemize,[status(sab)],[20])).
% 0.21/0.40 tff(22,plain,
% 0.21/0.40 (~finite(cartesian_product4(A!29, B!28, C!27, D!26))),
% 0.21/0.40 inference(or_elim,[status(thm)],[21])).
% 0.21/0.40 tff(23,plain,
% 0.21/0.40 (~finite(cartesian_product2(cartesian_product3(A!29, B!28, C!27), D!26))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[22, 13])).
% 0.21/0.40 tff(24,plain,
% 0.21/0.40 (finite(A!29) & finite(B!28) & finite(C!27) & finite(D!26)),
% 0.21/0.40 inference(or_elim,[status(thm)],[21])).
% 0.21/0.40 tff(25,plain,
% 0.21/0.40 (finite(C!27)),
% 0.21/0.40 inference(and_elim,[status(thm)],[24])).
% 0.21/0.40 tff(26,plain,
% 0.21/0.40 (finite(B!28)),
% 0.21/0.40 inference(and_elim,[status(thm)],[24])).
% 0.21/0.40 tff(27,plain,
% 0.21/0.40 (finite(A!29)),
% 0.21/0.40 inference(and_elim,[status(thm)],[24])).
% 0.21/0.40 tff(28,plain,
% 0.21/0.40 (^[A: $i, B: $i, C: $i] : refl((finite(cartesian_product3(A, B, C)) | (~finite(C)) | (~finite(B)) | (~finite(A))) <=> (finite(cartesian_product3(A, B, C)) | (~finite(C)) | (~finite(B)) | (~finite(A))))),
% 0.21/0.40 inference(bind,[status(th)],[])).
% 0.21/0.40 tff(29,plain,
% 0.21/0.40 (![A: $i, B: $i, C: $i] : (finite(cartesian_product3(A, B, C)) | (~finite(C)) | (~finite(B)) | (~finite(A))) <=> ![A: $i, B: $i, C: $i] : (finite(cartesian_product3(A, B, C)) | (~finite(C)) | (~finite(B)) | (~finite(A)))),
% 0.21/0.40 inference(quant_intro,[status(thm)],[28])).
% 0.21/0.40 tff(30,plain,
% 0.21/0.40 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(rewrite((finite(A) & finite(B) & finite(C)) <=> (~((~finite(C)) | (~finite(B)) | (~finite(A))))), ((~(finite(A) & finite(B) & finite(C))) <=> (~(~((~finite(C)) | (~finite(B)) | (~finite(A))))))), rewrite((~(~((~finite(C)) | (~finite(B)) | (~finite(A))))) <=> ((~finite(C)) | (~finite(B)) | (~finite(A)))), ((~(finite(A) & finite(B) & finite(C))) <=> ((~finite(C)) | (~finite(B)) | (~finite(A))))), ((finite(cartesian_product3(A, B, C)) | (~(finite(A) & finite(B) & finite(C)))) <=> (finite(cartesian_product3(A, B, C)) | ((~finite(C)) | (~finite(B)) | (~finite(A)))))), rewrite((finite(cartesian_product3(A, B, C)) | ((~finite(C)) | (~finite(B)) | (~finite(A)))) <=> (finite(cartesian_product3(A, B, C)) | (~finite(C)) | (~finite(B)) | (~finite(A)))), ((finite(cartesian_product3(A, B, C)) | (~(finite(A) & finite(B) & finite(C)))) <=> (finite(cartesian_product3(A, B, C)) | (~finite(C)) | (~finite(B)) | (~finite(A)))))),
% 0.21/0.40 inference(bind,[status(th)],[])).
% 0.21/0.40 tff(31,plain,
% 0.21/0.40 (![A: $i, B: $i, C: $i] : (finite(cartesian_product3(A, B, C)) | (~(finite(A) & finite(B) & finite(C)))) <=> ![A: $i, B: $i, C: $i] : (finite(cartesian_product3(A, B, C)) | (~finite(C)) | (~finite(B)) | (~finite(A)))),
% 0.21/0.40 inference(quant_intro,[status(thm)],[30])).
% 0.21/0.40 tff(32,plain,
% 0.21/0.40 (![A: $i, B: $i, C: $i] : (finite(cartesian_product3(A, B, C)) | (~(finite(A) & finite(B) & finite(C)))) <=> ![A: $i, B: $i, C: $i] : (finite(cartesian_product3(A, B, C)) | (~(finite(A) & finite(B) & finite(C))))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(33,plain,
% 0.21/0.40 (^[A: $i, B: $i, C: $i] : trans(monotonicity(rewrite(((finite(A) & finite(B)) & finite(C)) <=> (finite(A) & finite(B) & finite(C))), ((((finite(A) & finite(B)) & finite(C)) => finite(cartesian_product3(A, B, C))) <=> ((finite(A) & finite(B) & finite(C)) => finite(cartesian_product3(A, B, C))))), rewrite(((finite(A) & finite(B) & finite(C)) => finite(cartesian_product3(A, B, C))) <=> (finite(cartesian_product3(A, B, C)) | (~(finite(A) & finite(B) & finite(C))))), ((((finite(A) & finite(B)) & finite(C)) => finite(cartesian_product3(A, B, C))) <=> (finite(cartesian_product3(A, B, C)) | (~(finite(A) & finite(B) & finite(C))))))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(34,plain,
% 0.21/0.41 (![A: $i, B: $i, C: $i] : (((finite(A) & finite(B)) & finite(C)) => finite(cartesian_product3(A, B, C))) <=> ![A: $i, B: $i, C: $i] : (finite(cartesian_product3(A, B, C)) | (~(finite(A) & finite(B) & finite(C))))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[33])).
% 0.21/0.41 tff(35,axiom,(![A: $i, B: $i, C: $i] : (((finite(A) & finite(B)) & finite(C)) => finite(cartesian_product3(A, B, C)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','fc15_finset_1')).
% 0.21/0.41 tff(36,plain,
% 0.21/0.41 (![A: $i, B: $i, C: $i] : (finite(cartesian_product3(A, B, C)) | (~(finite(A) & finite(B) & finite(C))))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[35, 34])).
% 0.21/0.41 tff(37,plain,
% 0.21/0.41 (![A: $i, B: $i, C: $i] : (finite(cartesian_product3(A, B, C)) | (~(finite(A) & finite(B) & finite(C))))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[36, 32])).
% 0.21/0.41 tff(38,plain,(
% 0.21/0.41 ![A: $i, B: $i, C: $i] : (finite(cartesian_product3(A, B, C)) | (~(finite(A) & finite(B) & finite(C))))),
% 0.21/0.41 inference(skolemize,[status(sab)],[37])).
% 0.21/0.41 tff(39,plain,
% 0.21/0.41 (![A: $i, B: $i, C: $i] : (finite(cartesian_product3(A, B, C)) | (~finite(C)) | (~finite(B)) | (~finite(A)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[38, 31])).
% 0.21/0.41 tff(40,plain,
% 0.21/0.41 (![A: $i, B: $i, C: $i] : (finite(cartesian_product3(A, B, C)) | (~finite(C)) | (~finite(B)) | (~finite(A)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[39, 29])).
% 0.21/0.41 tff(41,plain,
% 0.21/0.41 (((~![A: $i, B: $i, C: $i] : (finite(cartesian_product3(A, B, C)) | (~finite(C)) | (~finite(B)) | (~finite(A)))) | ((~finite(A!29)) | (~finite(B!28)) | (~finite(C!27)) | finite(cartesian_product3(A!29, B!28, C!27)))) <=> ((~![A: $i, B: $i, C: $i] : (finite(cartesian_product3(A, B, C)) | (~finite(C)) | (~finite(B)) | (~finite(A)))) | (~finite(A!29)) | (~finite(B!28)) | (~finite(C!27)) | finite(cartesian_product3(A!29, B!28, C!27)))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(42,plain,
% 0.21/0.41 ((finite(cartesian_product3(A!29, B!28, C!27)) | (~finite(C!27)) | (~finite(B!28)) | (~finite(A!29))) <=> ((~finite(A!29)) | (~finite(B!28)) | (~finite(C!27)) | finite(cartesian_product3(A!29, B!28, C!27)))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(43,plain,
% 0.21/0.41 (((~![A: $i, B: $i, C: $i] : (finite(cartesian_product3(A, B, C)) | (~finite(C)) | (~finite(B)) | (~finite(A)))) | (finite(cartesian_product3(A!29, B!28, C!27)) | (~finite(C!27)) | (~finite(B!28)) | (~finite(A!29)))) <=> ((~![A: $i, B: $i, C: $i] : (finite(cartesian_product3(A, B, C)) | (~finite(C)) | (~finite(B)) | (~finite(A)))) | ((~finite(A!29)) | (~finite(B!28)) | (~finite(C!27)) | finite(cartesian_product3(A!29, B!28, C!27))))),
% 0.21/0.41 inference(monotonicity,[status(thm)],[42])).
% 0.21/0.41 tff(44,plain,
% 0.21/0.41 (((~![A: $i, B: $i, C: $i] : (finite(cartesian_product3(A, B, C)) | (~finite(C)) | (~finite(B)) | (~finite(A)))) | (finite(cartesian_product3(A!29, B!28, C!27)) | (~finite(C!27)) | (~finite(B!28)) | (~finite(A!29)))) <=> ((~![A: $i, B: $i, C: $i] : (finite(cartesian_product3(A, B, C)) | (~finite(C)) | (~finite(B)) | (~finite(A)))) | (~finite(A!29)) | (~finite(B!28)) | (~finite(C!27)) | finite(cartesian_product3(A!29, B!28, C!27)))),
% 0.21/0.41 inference(transitivity,[status(thm)],[43, 41])).
% 0.21/0.41 tff(45,plain,
% 0.21/0.41 ((~![A: $i, B: $i, C: $i] : (finite(cartesian_product3(A, B, C)) | (~finite(C)) | (~finite(B)) | (~finite(A)))) | (finite(cartesian_product3(A!29, B!28, C!27)) | (~finite(C!27)) | (~finite(B!28)) | (~finite(A!29)))),
% 0.21/0.41 inference(quant_inst,[status(thm)],[])).
% 0.21/0.41 tff(46,plain,
% 0.21/0.41 ((~![A: $i, B: $i, C: $i] : (finite(cartesian_product3(A, B, C)) | (~finite(C)) | (~finite(B)) | (~finite(A)))) | (~finite(A!29)) | (~finite(B!28)) | (~finite(C!27)) | finite(cartesian_product3(A!29, B!28, C!27))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[45, 44])).
% 0.21/0.41 tff(47,plain,
% 0.21/0.41 (finite(cartesian_product3(A!29, B!28, C!27))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[46, 40, 27, 26, 25])).
% 0.21/0.41 tff(48,plain,
% 0.21/0.41 (finite(D!26)),
% 0.21/0.41 inference(and_elim,[status(thm)],[24])).
% 0.21/0.41 tff(49,plain,
% 0.21/0.41 (^[A: $i, B: $i] : refl((finite(cartesian_product2(A, B)) | (~finite(B)) | (~finite(A))) <=> (finite(cartesian_product2(A, B)) | (~finite(B)) | (~finite(A))))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(50,plain,
% 0.21/0.41 (![A: $i, B: $i] : (finite(cartesian_product2(A, B)) | (~finite(B)) | (~finite(A))) <=> ![A: $i, B: $i] : (finite(cartesian_product2(A, B)) | (~finite(B)) | (~finite(A)))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[49])).
% 0.21/0.41 tff(51,plain,
% 0.21/0.41 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite((finite(A) & finite(B)) <=> (~((~finite(B)) | (~finite(A))))), ((~(finite(A) & finite(B))) <=> (~(~((~finite(B)) | (~finite(A))))))), rewrite((~(~((~finite(B)) | (~finite(A))))) <=> ((~finite(B)) | (~finite(A)))), ((~(finite(A) & finite(B))) <=> ((~finite(B)) | (~finite(A))))), ((finite(cartesian_product2(A, B)) | (~(finite(A) & finite(B)))) <=> (finite(cartesian_product2(A, B)) | ((~finite(B)) | (~finite(A)))))), rewrite((finite(cartesian_product2(A, B)) | ((~finite(B)) | (~finite(A)))) <=> (finite(cartesian_product2(A, B)) | (~finite(B)) | (~finite(A)))), ((finite(cartesian_product2(A, B)) | (~(finite(A) & finite(B)))) <=> (finite(cartesian_product2(A, B)) | (~finite(B)) | (~finite(A)))))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(52,plain,
% 0.21/0.41 (![A: $i, B: $i] : (finite(cartesian_product2(A, B)) | (~(finite(A) & finite(B)))) <=> ![A: $i, B: $i] : (finite(cartesian_product2(A, B)) | (~finite(B)) | (~finite(A)))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[51])).
% 0.21/0.41 tff(53,plain,
% 0.21/0.41 (![A: $i, B: $i] : (finite(cartesian_product2(A, B)) | (~(finite(A) & finite(B)))) <=> ![A: $i, B: $i] : (finite(cartesian_product2(A, B)) | (~(finite(A) & finite(B))))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(54,plain,
% 0.21/0.41 (^[A: $i, B: $i] : rewrite(((finite(A) & finite(B)) => finite(cartesian_product2(A, B))) <=> (finite(cartesian_product2(A, B)) | (~(finite(A) & finite(B)))))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(55,plain,
% 0.21/0.41 (![A: $i, B: $i] : ((finite(A) & finite(B)) => finite(cartesian_product2(A, B))) <=> ![A: $i, B: $i] : (finite(cartesian_product2(A, B)) | (~(finite(A) & finite(B))))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[54])).
% 0.21/0.41 tff(56,axiom,(![A: $i, B: $i] : ((finite(A) & finite(B)) => finite(cartesian_product2(A, B)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','fc14_finset_1')).
% 0.21/0.41 tff(57,plain,
% 0.21/0.41 (![A: $i, B: $i] : (finite(cartesian_product2(A, B)) | (~(finite(A) & finite(B))))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[56, 55])).
% 0.21/0.41 tff(58,plain,
% 0.21/0.41 (![A: $i, B: $i] : (finite(cartesian_product2(A, B)) | (~(finite(A) & finite(B))))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[57, 53])).
% 0.21/0.41 tff(59,plain,(
% 0.21/0.41 ![A: $i, B: $i] : (finite(cartesian_product2(A, B)) | (~(finite(A) & finite(B))))),
% 0.21/0.41 inference(skolemize,[status(sab)],[58])).
% 0.21/0.41 tff(60,plain,
% 0.21/0.41 (![A: $i, B: $i] : (finite(cartesian_product2(A, B)) | (~finite(B)) | (~finite(A)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[59, 52])).
% 0.21/0.41 tff(61,plain,
% 0.21/0.41 (![A: $i, B: $i] : (finite(cartesian_product2(A, B)) | (~finite(B)) | (~finite(A)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[60, 50])).
% 0.21/0.41 tff(62,plain,
% 0.21/0.41 (((~![A: $i, B: $i] : (finite(cartesian_product2(A, B)) | (~finite(B)) | (~finite(A)))) | ((~finite(D!26)) | finite(cartesian_product2(cartesian_product3(A!29, B!28, C!27), D!26)) | (~finite(cartesian_product3(A!29, B!28, C!27))))) <=> ((~![A: $i, B: $i] : (finite(cartesian_product2(A, B)) | (~finite(B)) | (~finite(A)))) | (~finite(D!26)) | finite(cartesian_product2(cartesian_product3(A!29, B!28, C!27), D!26)) | (~finite(cartesian_product3(A!29, B!28, C!27))))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(63,plain,
% 0.21/0.41 ((finite(cartesian_product2(cartesian_product3(A!29, B!28, C!27), D!26)) | (~finite(D!26)) | (~finite(cartesian_product3(A!29, B!28, C!27)))) <=> ((~finite(D!26)) | finite(cartesian_product2(cartesian_product3(A!29, B!28, C!27), D!26)) | (~finite(cartesian_product3(A!29, B!28, C!27))))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(64,plain,
% 0.21/0.41 (((~![A: $i, B: $i] : (finite(cartesian_product2(A, B)) | (~finite(B)) | (~finite(A)))) | (finite(cartesian_product2(cartesian_product3(A!29, B!28, C!27), D!26)) | (~finite(D!26)) | (~finite(cartesian_product3(A!29, B!28, C!27))))) <=> ((~![A: $i, B: $i] : (finite(cartesian_product2(A, B)) | (~finite(B)) | (~finite(A)))) | ((~finite(D!26)) | finite(cartesian_product2(cartesian_product3(A!29, B!28, C!27), D!26)) | (~finite(cartesian_product3(A!29, B!28, C!27)))))),
% 0.21/0.41 inference(monotonicity,[status(thm)],[63])).
% 0.21/0.41 tff(65,plain,
% 0.21/0.41 (((~![A: $i, B: $i] : (finite(cartesian_product2(A, B)) | (~finite(B)) | (~finite(A)))) | (finite(cartesian_product2(cartesian_product3(A!29, B!28, C!27), D!26)) | (~finite(D!26)) | (~finite(cartesian_product3(A!29, B!28, C!27))))) <=> ((~![A: $i, B: $i] : (finite(cartesian_product2(A, B)) | (~finite(B)) | (~finite(A)))) | (~finite(D!26)) | finite(cartesian_product2(cartesian_product3(A!29, B!28, C!27), D!26)) | (~finite(cartesian_product3(A!29, B!28, C!27))))),
% 0.21/0.41 inference(transitivity,[status(thm)],[64, 62])).
% 0.21/0.41 tff(66,plain,
% 0.21/0.41 ((~![A: $i, B: $i] : (finite(cartesian_product2(A, B)) | (~finite(B)) | (~finite(A)))) | (finite(cartesian_product2(cartesian_product3(A!29, B!28, C!27), D!26)) | (~finite(D!26)) | (~finite(cartesian_product3(A!29, B!28, C!27))))),
% 0.21/0.41 inference(quant_inst,[status(thm)],[])).
% 0.21/0.41 tff(67,plain,
% 0.21/0.41 ((~![A: $i, B: $i] : (finite(cartesian_product2(A, B)) | (~finite(B)) | (~finite(A)))) | (~finite(D!26)) | finite(cartesian_product2(cartesian_product3(A!29, B!28, C!27), D!26)) | (~finite(cartesian_product3(A!29, B!28, C!27)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[66, 65])).
% 0.21/0.41 tff(68,plain,
% 0.21/0.41 (finite(cartesian_product2(cartesian_product3(A!29, B!28, C!27), D!26)) | (~finite(cartesian_product3(A!29, B!28, C!27)))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[67, 61, 48])).
% 0.21/0.41 tff(69,plain,
% 0.21/0.41 (finite(cartesian_product2(cartesian_product3(A!29, B!28, C!27), D!26))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[68, 47])).
% 0.21/0.41 tff(70,plain,
% 0.21/0.41 ($false),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[69, 23])).
% 0.21/0.41 % SZS output end Proof
% 0.21/0.42 % E exiting
%------------------------------------------------------------------------------