%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SEU089+1 : TPTP v9.0.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n009.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 0.19s 0.39s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU089+1 : TPTP v9.0.0. Released v3.2.0.
% 0.00/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n009.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Fri Jun 20 06:03:18 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.19/0.39 % SZS status Theorem
% 0.19/0.39 % SZS output start Proof
% 0.19/0.39 tff(finite_type, type, (
% 0.19/0.39 finite: $i > $o)).
% 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_C_26_type, type, (
% 0.19/0.39 tptp_fun_C_26: $i)).
% 0.19/0.39 tff(tptp_fun_B_27_type, type, (
% 0.19/0.39 tptp_fun_B_27: $i)).
% 0.19/0.39 tff(tptp_fun_A_28_type, type, (
% 0.19/0.39 tptp_fun_A_28: $i)).
% 0.19/0.39 tff(cartesian_product3_type, type, (
% 0.19/0.39 cartesian_product3: ( $i * $i * $i ) > $i)).
% 0.19/0.39 tff(1,plain,
% 0.19/0.39 (^[A: $i, B: $i, C: $i] : refl((cartesian_product3(A, B, C) = cartesian_product2(cartesian_product2(A, B), C)) <=> (cartesian_product3(A, B, C) = cartesian_product2(cartesian_product2(A, B), C)))),
% 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] : (cartesian_product3(A, B, C) = cartesian_product2(cartesian_product2(A, B), C)) <=> ![A: $i, B: $i, C: $i] : (cartesian_product3(A, B, C) = cartesian_product2(cartesian_product2(A, B), C))),
% 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] : (cartesian_product3(A, B, C) = cartesian_product2(cartesian_product2(A, B), C)) <=> ![A: $i, B: $i, C: $i] : (cartesian_product3(A, B, C) = cartesian_product2(cartesian_product2(A, B), C))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(4,axiom,(![A: $i, B: $i, C: $i] : (cartesian_product3(A, B, C) = cartesian_product2(cartesian_product2(A, B), C))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d3_zfmisc_1')).
% 0.19/0.39 tff(5,plain,
% 0.19/0.39 (![A: $i, B: $i, C: $i] : (cartesian_product3(A, B, C) = cartesian_product2(cartesian_product2(A, B), C))),
% 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] : (cartesian_product3(A, B, C) = cartesian_product2(cartesian_product2(A, B), C))),
% 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] : (cartesian_product3(A, B, C) = cartesian_product2(cartesian_product2(A, B), C))),
% 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] : (cartesian_product3(A, B, C) = cartesian_product2(cartesian_product2(A, B), C))) | (cartesian_product3(A!28, B!27, C!26) = cartesian_product2(cartesian_product2(A!28, B!27), C!26))),
% 0.19/0.39 inference(quant_inst,[status(thm)],[])).
% 0.19/0.39 tff(9,plain,
% 0.19/0.39 (cartesian_product3(A!28, B!27, C!26) = cartesian_product2(cartesian_product2(A!28, B!27), C!26)),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.19/0.39 tff(10,plain,
% 0.19/0.39 (cartesian_product2(cartesian_product2(A!28, B!27), C!26) = cartesian_product3(A!28, B!27, C!26)),
% 0.19/0.39 inference(symmetry,[status(thm)],[9])).
% 0.19/0.39 tff(11,plain,
% 0.19/0.39 (finite(cartesian_product2(cartesian_product2(A!28, B!27), C!26)) <=> finite(cartesian_product3(A!28, B!27, C!26))),
% 0.19/0.39 inference(monotonicity,[status(thm)],[10])).
% 0.19/0.39 tff(12,plain,
% 0.19/0.39 (finite(cartesian_product3(A!28, B!27, C!26)) <=> finite(cartesian_product2(cartesian_product2(A!28, B!27), C!26))),
% 0.19/0.39 inference(symmetry,[status(thm)],[11])).
% 0.19/0.39 tff(13,plain,
% 0.19/0.39 ((~finite(cartesian_product3(A!28, B!27, C!26))) <=> (~finite(cartesian_product2(cartesian_product2(A!28, B!27), C!26)))),
% 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] : (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)))))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(15,plain,
% 0.19/0.39 ((~![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)))))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(16,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','t20_finset_1')).
% 0.19/0.39 tff(17,plain,
% 0.19/0.39 (~![A: $i, B: $i, C: $i] : (finite(cartesian_product3(A, B, C)) | (~(finite(A) & finite(B) & finite(C))))),
% 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] : (finite(cartesian_product3(A, B, C)) | (~(finite(A) & finite(B) & finite(C))))),
% 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] : (finite(cartesian_product3(A, B, C)) | (~(finite(A) & finite(B) & finite(C))))),
% 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] : (finite(cartesian_product3(A, B, C)) | (~(finite(A) & finite(B) & finite(C))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[19, 14])).
% 0.19/0.39 tff(21,plain,(
% 0.19/0.39 ~(finite(cartesian_product3(A!28, B!27, C!26)) | (~(finite(A!28) & finite(B!27) & finite(C!26))))),
% 0.19/0.39 inference(skolemize,[status(sab)],[20])).
% 0.19/0.39 tff(22,plain,
% 0.19/0.39 (~finite(cartesian_product3(A!28, B!27, C!26))),
% 0.19/0.39 inference(or_elim,[status(thm)],[21])).
% 0.19/0.39 tff(23,plain,
% 0.19/0.39 (~finite(cartesian_product2(cartesian_product2(A!28, B!27), C!26))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[22, 13])).
% 0.19/0.39 tff(24,plain,
% 0.19/0.39 (finite(A!28) & finite(B!27) & finite(C!26)),
% 0.19/0.39 inference(or_elim,[status(thm)],[21])).
% 0.19/0.39 tff(25,plain,
% 0.19/0.39 (finite(B!27)),
% 0.19/0.39 inference(and_elim,[status(thm)],[24])).
% 0.19/0.39 tff(26,plain,
% 0.19/0.39 (finite(A!28)),
% 0.19/0.39 inference(and_elim,[status(thm)],[24])).
% 0.19/0.39 tff(27,plain,
% 0.19/0.39 (^[A: $i, B: $i] : refl((finite(cartesian_product2(A, B)) | (~finite(B)) | (~finite(A))) <=> (finite(cartesian_product2(A, B)) | (~finite(B)) | (~finite(A))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(28,plain,
% 0.19/0.39 (![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)))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[27])).
% 0.19/0.39 tff(29,plain,
% 0.19/0.39 (^[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)))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(30,plain,
% 0.19/0.39 (![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)))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[29])).
% 0.19/0.39 tff(31,plain,
% 0.19/0.39 (![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))))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(32,plain,
% 0.19/0.39 (^[A: $i, B: $i] : rewrite(((finite(A) & finite(B)) => finite(cartesian_product2(A, B))) <=> (finite(cartesian_product2(A, B)) | (~(finite(A) & finite(B)))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(33,plain,
% 0.19/0.39 (![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))))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[32])).
% 0.19/0.39 tff(34,axiom,(![A: $i, B: $i] : ((finite(A) & finite(B)) => finite(cartesian_product2(A, B)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','fc14_finset_1')).
% 0.19/0.39 tff(35,plain,
% 0.19/0.39 (![A: $i, B: $i] : (finite(cartesian_product2(A, B)) | (~(finite(A) & finite(B))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[34, 33])).
% 0.19/0.39 tff(36,plain,
% 0.19/0.39 (![A: $i, B: $i] : (finite(cartesian_product2(A, B)) | (~(finite(A) & finite(B))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[35, 31])).
% 0.19/0.39 tff(37,plain,(
% 0.19/0.39 ![A: $i, B: $i] : (finite(cartesian_product2(A, B)) | (~(finite(A) & finite(B))))),
% 0.19/0.39 inference(skolemize,[status(sab)],[36])).
% 0.19/0.39 tff(38,plain,
% 0.19/0.39 (![A: $i, B: $i] : (finite(cartesian_product2(A, B)) | (~finite(B)) | (~finite(A)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[37, 30])).
% 0.19/0.39 tff(39,plain,
% 0.19/0.39 (![A: $i, B: $i] : (finite(cartesian_product2(A, B)) | (~finite(B)) | (~finite(A)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[38, 28])).
% 0.19/0.39 tff(40,plain,
% 0.19/0.39 (((~![A: $i, B: $i] : (finite(cartesian_product2(A, B)) | (~finite(B)) | (~finite(A)))) | ((~finite(A!28)) | (~finite(B!27)) | finite(cartesian_product2(A!28, B!27)))) <=> ((~![A: $i, B: $i] : (finite(cartesian_product2(A, B)) | (~finite(B)) | (~finite(A)))) | (~finite(A!28)) | (~finite(B!27)) | finite(cartesian_product2(A!28, B!27)))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(41,plain,
% 0.19/0.39 ((finite(cartesian_product2(A!28, B!27)) | (~finite(B!27)) | (~finite(A!28))) <=> ((~finite(A!28)) | (~finite(B!27)) | finite(cartesian_product2(A!28, B!27)))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(42,plain,
% 0.19/0.39 (((~![A: $i, B: $i] : (finite(cartesian_product2(A, B)) | (~finite(B)) | (~finite(A)))) | (finite(cartesian_product2(A!28, B!27)) | (~finite(B!27)) | (~finite(A!28)))) <=> ((~![A: $i, B: $i] : (finite(cartesian_product2(A, B)) | (~finite(B)) | (~finite(A)))) | ((~finite(A!28)) | (~finite(B!27)) | finite(cartesian_product2(A!28, B!27))))),
% 0.19/0.39 inference(monotonicity,[status(thm)],[41])).
% 0.19/0.39 tff(43,plain,
% 0.19/0.39 (((~![A: $i, B: $i] : (finite(cartesian_product2(A, B)) | (~finite(B)) | (~finite(A)))) | (finite(cartesian_product2(A!28, B!27)) | (~finite(B!27)) | (~finite(A!28)))) <=> ((~![A: $i, B: $i] : (finite(cartesian_product2(A, B)) | (~finite(B)) | (~finite(A)))) | (~finite(A!28)) | (~finite(B!27)) | finite(cartesian_product2(A!28, B!27)))),
% 0.19/0.39 inference(transitivity,[status(thm)],[42, 40])).
% 0.19/0.39 tff(44,plain,
% 0.19/0.39 ((~![A: $i, B: $i] : (finite(cartesian_product2(A, B)) | (~finite(B)) | (~finite(A)))) | (finite(cartesian_product2(A!28, B!27)) | (~finite(B!27)) | (~finite(A!28)))),
% 0.19/0.39 inference(quant_inst,[status(thm)],[])).
% 0.19/0.39 tff(45,plain,
% 0.19/0.39 ((~![A: $i, B: $i] : (finite(cartesian_product2(A, B)) | (~finite(B)) | (~finite(A)))) | (~finite(A!28)) | (~finite(B!27)) | finite(cartesian_product2(A!28, B!27))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[44, 43])).
% 0.19/0.39 tff(46,plain,
% 0.19/0.39 (finite(cartesian_product2(A!28, B!27))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[45, 39, 26, 25])).
% 0.19/0.39 tff(47,plain,
% 0.19/0.39 (finite(C!26)),
% 0.19/0.39 inference(and_elim,[status(thm)],[24])).
% 0.19/0.39 tff(48,plain,
% 0.19/0.39 (((~![A: $i, B: $i] : (finite(cartesian_product2(A, B)) | (~finite(B)) | (~finite(A)))) | ((~finite(C!26)) | finite(cartesian_product2(cartesian_product2(A!28, B!27), C!26)) | (~finite(cartesian_product2(A!28, B!27))))) <=> ((~![A: $i, B: $i] : (finite(cartesian_product2(A, B)) | (~finite(B)) | (~finite(A)))) | (~finite(C!26)) | finite(cartesian_product2(cartesian_product2(A!28, B!27), C!26)) | (~finite(cartesian_product2(A!28, B!27))))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(49,plain,
% 0.19/0.39 ((finite(cartesian_product2(cartesian_product2(A!28, B!27), C!26)) | (~finite(C!26)) | (~finite(cartesian_product2(A!28, B!27)))) <=> ((~finite(C!26)) | finite(cartesian_product2(cartesian_product2(A!28, B!27), C!26)) | (~finite(cartesian_product2(A!28, B!27))))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(50,plain,
% 0.19/0.39 (((~![A: $i, B: $i] : (finite(cartesian_product2(A, B)) | (~finite(B)) | (~finite(A)))) | (finite(cartesian_product2(cartesian_product2(A!28, B!27), C!26)) | (~finite(C!26)) | (~finite(cartesian_product2(A!28, B!27))))) <=> ((~![A: $i, B: $i] : (finite(cartesian_product2(A, B)) | (~finite(B)) | (~finite(A)))) | ((~finite(C!26)) | finite(cartesian_product2(cartesian_product2(A!28, B!27), C!26)) | (~finite(cartesian_product2(A!28, B!27)))))),
% 0.19/0.39 inference(monotonicity,[status(thm)],[49])).
% 0.19/0.39 tff(51,plain,
% 0.19/0.39 (((~![A: $i, B: $i] : (finite(cartesian_product2(A, B)) | (~finite(B)) | (~finite(A)))) | (finite(cartesian_product2(cartesian_product2(A!28, B!27), C!26)) | (~finite(C!26)) | (~finite(cartesian_product2(A!28, B!27))))) <=> ((~![A: $i, B: $i] : (finite(cartesian_product2(A, B)) | (~finite(B)) | (~finite(A)))) | (~finite(C!26)) | finite(cartesian_product2(cartesian_product2(A!28, B!27), C!26)) | (~finite(cartesian_product2(A!28, B!27))))),
% 0.19/0.40 inference(transitivity,[status(thm)],[50, 48])).
% 0.19/0.40 tff(52,plain,
% 0.19/0.40 ((~![A: $i, B: $i] : (finite(cartesian_product2(A, B)) | (~finite(B)) | (~finite(A)))) | (finite(cartesian_product2(cartesian_product2(A!28, B!27), C!26)) | (~finite(C!26)) | (~finite(cartesian_product2(A!28, B!27))))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(53,plain,
% 0.19/0.40 ((~![A: $i, B: $i] : (finite(cartesian_product2(A, B)) | (~finite(B)) | (~finite(A)))) | (~finite(C!26)) | finite(cartesian_product2(cartesian_product2(A!28, B!27), C!26)) | (~finite(cartesian_product2(A!28, B!27)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[52, 51])).
% 0.19/0.40 tff(54,plain,
% 0.19/0.40 (finite(cartesian_product2(cartesian_product2(A!28, B!27), C!26)) | (~finite(cartesian_product2(A!28, B!27)))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[53, 39, 47])).
% 0.19/0.40 tff(55,plain,
% 0.19/0.40 (finite(cartesian_product2(cartesian_product2(A!28, B!27), C!26))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[54, 46])).
% 0.19/0.40 tff(56,plain,
% 0.19/0.40 ($false),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[55, 23])).
% 0.19/0.40 % SZS output end Proof
% 0.19/0.40 % E exiting
%------------------------------------------------------------------------------