TSTP Solution File: SEU089+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SEU089+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n027.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 : Thu Aug 31 17:42:29 EDT 2023
% Result : Theorem 9.68s 2.25s
% Output : Proof 16.01s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU089+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.33 % Computer : n027.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.20/0.33 % CPULimit : 300
% 0.20/0.34 % WCLimit : 300
% 0.20/0.34 % DateTime : Wed Aug 23 14:49:01 EDT 2023
% 0.20/0.34 % CPUTime :
% 0.20/0.63 ________ _____
% 0.20/0.63 ___ __ \_________(_)________________________________
% 0.20/0.63 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.20/0.63 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.20/0.63 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.20/0.63
% 0.20/0.63 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.20/0.63 (2023-06-19)
% 0.20/0.63
% 0.20/0.63 (c) Philipp Rümmer, 2009-2023
% 0.20/0.63 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.20/0.63 Amanda Stjerna.
% 0.20/0.63 Free software under BSD-3-Clause.
% 0.20/0.63
% 0.20/0.63 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.20/0.63
% 0.20/0.63 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.20/0.64 Running up to 7 provers in parallel.
% 0.20/0.66 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.20/0.66 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.20/0.66 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.20/0.66 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.20/0.66 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.20/0.66 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.20/0.66 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.92/1.16 Prover 4: Preprocessing ...
% 2.92/1.16 Prover 1: Preprocessing ...
% 3.54/1.19 Prover 5: Preprocessing ...
% 3.54/1.19 Prover 3: Preprocessing ...
% 3.54/1.19 Prover 6: Preprocessing ...
% 3.54/1.19 Prover 2: Preprocessing ...
% 3.54/1.19 Prover 0: Preprocessing ...
% 6.91/1.69 Prover 5: Proving ...
% 7.24/1.72 Prover 2: Proving ...
% 7.49/1.76 Prover 1: Warning: ignoring some quantifiers
% 7.49/1.80 Prover 3: Warning: ignoring some quantifiers
% 7.49/1.81 Prover 4: Warning: ignoring some quantifiers
% 7.49/1.81 Prover 1: Constructing countermodel ...
% 8.18/1.83 Prover 3: Constructing countermodel ...
% 8.18/1.86 Prover 6: Proving ...
% 8.56/1.90 Prover 4: Constructing countermodel ...
% 9.06/2.00 Prover 0: Proving ...
% 9.68/2.25 Prover 5: proved (1596ms)
% 9.68/2.25
% 9.68/2.25 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 9.68/2.25
% 9.68/2.25 Prover 3: stopped
% 9.68/2.25 Prover 2: stopped
% 9.68/2.25 Prover 0: stopped
% 9.68/2.26 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 9.68/2.26 Prover 6: stopped
% 9.68/2.26 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 9.68/2.26 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 9.68/2.26 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 9.68/2.26 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 11.02/2.33 Prover 7: Preprocessing ...
% 11.74/2.35 Prover 13: Preprocessing ...
% 11.74/2.35 Prover 11: Preprocessing ...
% 11.74/2.36 Prover 10: Preprocessing ...
% 11.74/2.37 Prover 8: Preprocessing ...
% 12.28/2.42 Prover 13: Warning: ignoring some quantifiers
% 12.28/2.43 Prover 7: Warning: ignoring some quantifiers
% 12.28/2.43 Prover 13: Constructing countermodel ...
% 12.28/2.45 Prover 7: Constructing countermodel ...
% 12.85/2.47 Prover 10: Warning: ignoring some quantifiers
% 12.85/2.48 Prover 10: Constructing countermodel ...
% 13.31/2.56 Prover 8: Warning: ignoring some quantifiers
% 13.31/2.57 Prover 8: Constructing countermodel ...
% 14.01/2.68 Prover 11: Warning: ignoring some quantifiers
% 14.52/2.70 Prover 10: gave up
% 14.52/2.70 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 14.52/2.71 Prover 11: Constructing countermodel ...
% 14.52/2.73 Prover 13: gave up
% 14.52/2.73 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085
% 14.52/2.74 Prover 16: Preprocessing ...
% 15.11/2.77 Prover 19: Preprocessing ...
% 15.11/2.80 Prover 16: Warning: ignoring some quantifiers
% 15.11/2.80 Prover 7: Found proof (size 9)
% 15.11/2.80 Prover 7: proved (551ms)
% 15.11/2.80 Prover 8: stopped
% 15.11/2.80 Prover 1: stopped
% 15.11/2.80 Prover 4: stopped
% 15.11/2.81 Prover 11: stopped
% 15.11/2.81 Prover 16: Constructing countermodel ...
% 15.11/2.82 Prover 16: stopped
% 15.11/2.89 Prover 19: Warning: ignoring some quantifiers
% 15.11/2.89 Prover 19: Constructing countermodel ...
% 15.11/2.90 Prover 19: stopped
% 15.11/2.90
% 15.11/2.90 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 15.11/2.90
% 15.63/2.90 % SZS output start Proof for theBenchmark
% 15.63/2.91 Assumptions after simplification:
% 15.63/2.91 ---------------------------------
% 15.63/2.91
% 15.63/2.91 (d3_zfmisc_1)
% 15.63/2.93 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 15.63/2.93 (cartesian_product2(v3, v2) = v4) | ~ (cartesian_product2(v0, v1) = v3) |
% 15.63/2.93 ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | (cartesian_product3(v0, v1, v2) = v4 &
% 15.63/2.93 $i(v4))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 15.63/2.93 (cartesian_product3(v0, v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 15.63/2.93 ? [v4: $i] : (cartesian_product2(v4, v2) = v3 & cartesian_product2(v0, v1) =
% 16.01/2.93 v4 & $i(v4) & $i(v3)))
% 16.01/2.93
% 16.01/2.93 (fc14_finset_1)
% 16.01/2.93 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (cartesian_product2(v0, v1) =
% 16.01/2.93 v2) | ~ $i(v1) | ~ $i(v0) | ~ finite(v1) | ~ finite(v0) | finite(v2))
% 16.01/2.93
% 16.01/2.93 (t19_finset_1)
% 16.01/2.94 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (cartesian_product2(v0, v1) =
% 16.01/2.94 v2) | ~ $i(v1) | ~ $i(v0) | ~ finite(v1) | ~ finite(v0) | finite(v2))
% 16.01/2.94
% 16.01/2.94 (t20_finset_1)
% 16.01/2.94 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] :
% 16.01/2.94 (cartesian_product3(v0, v1, v2) = v3 & $i(v3) & $i(v2) & $i(v1) & $i(v0) &
% 16.01/2.94 finite(v2) & finite(v1) & finite(v0) & ~ finite(v3))
% 16.01/2.94
% 16.01/2.94 Further assumptions not needed in the proof:
% 16.01/2.94 --------------------------------------------
% 16.01/2.94 antisymmetry_r2_hidden, cc1_arytm_3, cc1_finset_1, cc1_funct_1, cc1_ordinal1,
% 16.01/2.94 cc1_relat_1, cc1_relset_1, cc2_arytm_3, cc2_finset_1, cc2_funct_1, cc2_ordinal1,
% 16.01/2.94 cc3_ordinal1, cc4_arytm_3, existence_m1_subset_1, fc12_relat_1, fc1_subset_1,
% 16.01/2.94 fc1_xboole_0, fc2_ordinal1, fc4_relat_1, fc4_subset_1, fc5_subset_1,
% 16.01/2.94 fc8_arytm_3, rc1_arytm_3, rc1_finset_1, rc1_funcop_1, rc1_funct_1, rc1_ordinal1,
% 16.01/2.94 rc1_ordinal2, rc1_relat_1, rc1_subset_1, rc1_xboole_0, rc2_arytm_3,
% 16.01/2.94 rc2_finset_1, rc2_funct_1, rc2_ordinal1, rc2_ordinal2, rc2_relat_1,
% 16.01/2.94 rc2_subset_1, rc2_xboole_0, rc3_arytm_3, rc3_finset_1, rc3_funct_1,
% 16.01/2.94 rc3_ordinal1, rc3_relat_1, rc4_funct_1, rc4_ordinal1, rc5_funct_1,
% 16.01/2.94 reflexivity_r1_tarski, t1_subset, t2_subset, t3_subset, t4_subset, t5_subset,
% 16.01/2.94 t6_boole, t7_boole, t8_boole
% 16.01/2.94
% 16.01/2.94 Those formulas are unsatisfiable:
% 16.01/2.94 ---------------------------------
% 16.01/2.94
% 16.01/2.94 Begin of proof
% 16.01/2.94 |
% 16.01/2.94 | ALPHA: (d3_zfmisc_1) implies:
% 16.01/2.94 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 16.01/2.94 | (cartesian_product3(v0, v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~
% 16.01/2.94 | $i(v0) | ? [v4: $i] : (cartesian_product2(v4, v2) = v3 &
% 16.01/2.94 | cartesian_product2(v0, v1) = v4 & $i(v4) & $i(v3)))
% 16.01/2.94 |
% 16.01/2.94 | DELTA: instantiating (t20_finset_1) with fresh symbols all_79_0, all_79_1,
% 16.01/2.94 | all_79_2, all_79_3 gives:
% 16.01/2.94 | (2) cartesian_product3(all_79_3, all_79_2, all_79_1) = all_79_0 &
% 16.01/2.94 | $i(all_79_0) & $i(all_79_1) & $i(all_79_2) & $i(all_79_3) &
% 16.01/2.94 | finite(all_79_1) & finite(all_79_2) & finite(all_79_3) & ~
% 16.01/2.94 | finite(all_79_0)
% 16.01/2.94 |
% 16.01/2.94 | ALPHA: (2) implies:
% 16.01/2.94 | (3) ~ finite(all_79_0)
% 16.01/2.94 | (4) finite(all_79_3)
% 16.01/2.94 | (5) finite(all_79_2)
% 16.01/2.94 | (6) finite(all_79_1)
% 16.01/2.94 | (7) $i(all_79_3)
% 16.01/2.94 | (8) $i(all_79_2)
% 16.01/2.94 | (9) $i(all_79_1)
% 16.01/2.94 | (10) cartesian_product3(all_79_3, all_79_2, all_79_1) = all_79_0
% 16.01/2.94 |
% 16.01/2.95 | GROUND_INST: instantiating (1) with all_79_3, all_79_2, all_79_1, all_79_0,
% 16.01/2.95 | simplifying with (7), (8), (9), (10) gives:
% 16.01/2.95 | (11) ? [v0: $i] : (cartesian_product2(v0, all_79_1) = all_79_0 &
% 16.01/2.95 | cartesian_product2(all_79_3, all_79_2) = v0 & $i(v0) & $i(all_79_0))
% 16.01/2.95 |
% 16.01/2.95 | DELTA: instantiating (11) with fresh symbol all_91_0 gives:
% 16.01/2.95 | (12) cartesian_product2(all_91_0, all_79_1) = all_79_0 &
% 16.01/2.95 | cartesian_product2(all_79_3, all_79_2) = all_91_0 & $i(all_91_0) &
% 16.01/2.95 | $i(all_79_0)
% 16.01/2.95 |
% 16.01/2.95 | ALPHA: (12) implies:
% 16.01/2.95 | (13) $i(all_91_0)
% 16.01/2.95 | (14) cartesian_product2(all_79_3, all_79_2) = all_91_0
% 16.01/2.95 | (15) cartesian_product2(all_91_0, all_79_1) = all_79_0
% 16.01/2.95 |
% 16.01/2.95 | GROUND_INST: instantiating (t19_finset_1) with all_79_3, all_79_2, all_91_0,
% 16.01/2.95 | simplifying with (4), (5), (7), (8), (14) gives:
% 16.01/2.95 | (16) finite(all_91_0)
% 16.01/2.95 |
% 16.01/2.95 | GROUND_INST: instantiating (t19_finset_1) with all_91_0, all_79_1, all_79_0,
% 16.01/2.95 | simplifying with (3), (6), (9), (13), (15), (16) gives:
% 16.01/2.95 | (17) $false
% 16.01/2.95 |
% 16.01/2.95 | CLOSE: (17) is inconsistent.
% 16.01/2.95 |
% 16.01/2.95 End of proof
% 16.01/2.95 % SZS output end Proof for theBenchmark
% 16.01/2.95
% 16.01/2.95 2321ms
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