TSTP Solution File: SEU090+1 by Princess---230619
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SEU090+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 : n022.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 16.21s 2.94s
% Output : Proof 16.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU090+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.34 % Computer : n022.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 : Wed Aug 23 15:34:11 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.20/0.66 ________ _____
% 0.20/0.66 ___ __ \_________(_)________________________________
% 0.20/0.66 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.20/0.66 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.20/0.66 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.20/0.66
% 0.20/0.66 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.20/0.66 (2023-06-19)
% 0.20/0.66
% 0.20/0.66 (c) Philipp Rümmer, 2009-2023
% 0.20/0.66 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.20/0.66 Amanda Stjerna.
% 0.20/0.66 Free software under BSD-3-Clause.
% 0.20/0.66
% 0.20/0.66 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.20/0.66
% 0.20/0.66 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.20/0.67 Running up to 7 provers in parallel.
% 0.20/0.69 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.20/0.69 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.20/0.69 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.20/0.69 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.20/0.69 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.20/0.69 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.20/0.69 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 3.37/1.27 Prover 4: Preprocessing ...
% 3.37/1.27 Prover 1: Preprocessing ...
% 3.37/1.31 Prover 3: Preprocessing ...
% 3.37/1.31 Prover 6: Preprocessing ...
% 3.37/1.31 Prover 5: Preprocessing ...
% 3.37/1.31 Prover 0: Preprocessing ...
% 3.37/1.31 Prover 2: Preprocessing ...
% 7.11/1.76 Prover 5: Proving ...
% 7.11/1.77 Prover 2: Proving ...
% 8.17/1.87 Prover 1: Warning: ignoring some quantifiers
% 8.17/1.91 Prover 1: Constructing countermodel ...
% 8.17/1.91 Prover 3: Warning: ignoring some quantifiers
% 8.17/1.93 Prover 6: Proving ...
% 8.17/1.96 Prover 3: Constructing countermodel ...
% 8.17/1.99 Prover 4: Warning: ignoring some quantifiers
% 8.17/2.02 Prover 4: Constructing countermodel ...
% 9.53/2.08 Prover 0: Proving ...
% 12.57/2.48 Prover 3: gave up
% 12.57/2.48 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 13.16/2.55 Prover 7: Preprocessing ...
% 13.61/2.65 Prover 7: Warning: ignoring some quantifiers
% 13.61/2.67 Prover 7: Constructing countermodel ...
% 16.21/2.94 Prover 7: Found proof (size 9)
% 16.21/2.94 Prover 7: proved (461ms)
% 16.21/2.94 Prover 1: stopped
% 16.21/2.94 Prover 5: stopped
% 16.21/2.94 Prover 2: stopped
% 16.21/2.94 Prover 0: stopped
% 16.21/2.94 Prover 6: stopped
% 16.21/2.94 Prover 4: stopped
% 16.21/2.94
% 16.21/2.94 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 16.21/2.94
% 16.21/2.95 % SZS output start Proof for theBenchmark
% 16.21/2.95 Assumptions after simplification:
% 16.21/2.95 ---------------------------------
% 16.21/2.95
% 16.21/2.95 (d4_zfmisc_1)
% 16.21/2.98 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 16.21/2.98 $i] : ( ~ (cartesian_product3(v0, v1, v2) = v4) | ~ (cartesian_product2(v4,
% 16.21/2.98 v3) = v5) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 16.21/2.98 (cartesian_product4(v0, v1, v2, v3) = v5 & $i(v5))) & ! [v0: $i] : ! [v1:
% 16.21/2.98 $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (cartesian_product4(v0,
% 16.21/2.98 v1, v2, v3) = v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ?
% 16.21/2.98 [v5: $i] : (cartesian_product3(v0, v1, v2) = v5 & cartesian_product2(v5, v3)
% 16.21/2.98 = v4 & $i(v5) & $i(v4)))
% 16.21/2.98
% 16.21/2.98 (fc14_finset_1)
% 16.21/2.98 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (cartesian_product2(v0, v1) =
% 16.21/2.98 v2) | ~ $i(v1) | ~ $i(v0) | ~ finite(v1) | ~ finite(v0) | finite(v2))
% 16.21/2.98
% 16.21/2.98 (fc15_finset_1)
% 16.21/2.98 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 16.21/2.98 (cartesian_product3(v0, v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 16.21/2.98 ~ finite(v2) | ~ finite(v1) | ~ finite(v0) | finite(v3))
% 16.21/2.98
% 16.21/2.98 (t19_finset_1)
% 16.21/2.98 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (cartesian_product2(v0, v1) =
% 16.21/2.98 v2) | ~ $i(v1) | ~ $i(v0) | ~ finite(v1) | ~ finite(v0) | finite(v2))
% 16.21/2.98
% 16.21/2.98 (t20_finset_1)
% 16.21/2.98 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 16.21/2.98 (cartesian_product3(v0, v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 16.21/2.98 ~ finite(v2) | ~ finite(v1) | ~ finite(v0) | finite(v3))
% 16.21/2.98
% 16.21/2.98 (t21_finset_1)
% 16.21/2.99 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 16.21/2.99 (cartesian_product4(v0, v1, v2, v3) = v4 & $i(v4) & $i(v3) & $i(v2) & $i(v1) &
% 16.21/2.99 $i(v0) & finite(v3) & finite(v2) & finite(v1) & finite(v0) & ~ finite(v4))
% 16.21/2.99
% 16.21/2.99 Further assumptions not needed in the proof:
% 16.21/2.99 --------------------------------------------
% 16.21/2.99 antisymmetry_r2_hidden, cc1_arytm_3, cc1_finset_1, cc1_funct_1, cc1_ordinal1,
% 16.21/2.99 cc1_relat_1, cc1_relset_1, cc2_arytm_3, cc2_finset_1, cc2_funct_1, cc2_ordinal1,
% 16.21/2.99 cc3_ordinal1, cc4_arytm_3, existence_m1_subset_1, fc12_relat_1, fc1_subset_1,
% 16.21/2.99 fc1_xboole_0, fc2_ordinal1, fc4_relat_1, fc4_subset_1, fc5_subset_1,
% 16.21/2.99 fc6_subset_1, fc8_arytm_3, rc1_arytm_3, rc1_finset_1, rc1_funcop_1, rc1_funct_1,
% 16.21/2.99 rc1_ordinal1, rc1_ordinal2, rc1_relat_1, rc1_subset_1, rc1_xboole_0,
% 16.21/2.99 rc2_arytm_3, rc2_finset_1, rc2_funct_1, rc2_ordinal1, rc2_ordinal2, rc2_relat_1,
% 16.21/2.99 rc2_subset_1, rc2_xboole_0, rc3_arytm_3, rc3_finset_1, rc3_funct_1,
% 16.21/2.99 rc3_ordinal1, rc3_relat_1, rc4_funct_1, rc4_ordinal1, rc5_funct_1,
% 16.21/2.99 reflexivity_r1_tarski, t1_subset, t2_subset, t3_subset, t4_subset, t5_subset,
% 16.21/2.99 t6_boole, t7_boole, t8_boole
% 16.21/2.99
% 16.21/2.99 Those formulas are unsatisfiable:
% 16.21/2.99 ---------------------------------
% 16.21/2.99
% 16.21/2.99 Begin of proof
% 16.21/2.99 |
% 16.21/2.99 | ALPHA: (d4_zfmisc_1) implies:
% 16.21/2.99 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (
% 16.21/2.99 | ~ (cartesian_product4(v0, v1, v2, v3) = v4) | ~ $i(v3) | ~ $i(v2) |
% 16.21/2.99 | ~ $i(v1) | ~ $i(v0) | ? [v5: $i] : (cartesian_product3(v0, v1, v2)
% 16.21/2.99 | = v5 & cartesian_product2(v5, v3) = v4 & $i(v5) & $i(v4)))
% 16.21/2.99 |
% 16.21/2.99 | DELTA: instantiating (t21_finset_1) with fresh symbols all_82_0, all_82_1,
% 16.21/2.99 | all_82_2, all_82_3, all_82_4 gives:
% 16.21/2.99 | (2) cartesian_product4(all_82_4, all_82_3, all_82_2, all_82_1) = all_82_0 &
% 16.21/2.99 | $i(all_82_0) & $i(all_82_1) & $i(all_82_2) & $i(all_82_3) &
% 16.21/2.99 | $i(all_82_4) & finite(all_82_1) & finite(all_82_2) & finite(all_82_3) &
% 16.21/2.99 | finite(all_82_4) & ~ finite(all_82_0)
% 16.21/2.99 |
% 16.21/2.99 | ALPHA: (2) implies:
% 16.21/2.99 | (3) ~ finite(all_82_0)
% 16.21/2.99 | (4) finite(all_82_4)
% 16.21/2.99 | (5) finite(all_82_3)
% 16.21/2.99 | (6) finite(all_82_2)
% 16.21/2.99 | (7) finite(all_82_1)
% 16.21/2.99 | (8) $i(all_82_4)
% 16.21/2.99 | (9) $i(all_82_3)
% 16.21/2.99 | (10) $i(all_82_2)
% 16.21/2.99 | (11) $i(all_82_1)
% 16.21/2.99 | (12) cartesian_product4(all_82_4, all_82_3, all_82_2, all_82_1) = all_82_0
% 16.21/2.99 |
% 16.21/2.99 | GROUND_INST: instantiating (1) with all_82_4, all_82_3, all_82_2, all_82_1,
% 16.21/2.99 | all_82_0, simplifying with (8), (9), (10), (11), (12) gives:
% 16.21/3.00 | (13) ? [v0: $i] : (cartesian_product3(all_82_4, all_82_3, all_82_2) = v0 &
% 16.21/3.00 | cartesian_product2(v0, all_82_1) = all_82_0 & $i(v0) & $i(all_82_0))
% 16.21/3.00 |
% 16.21/3.00 | DELTA: instantiating (13) with fresh symbol all_94_0 gives:
% 16.21/3.00 | (14) cartesian_product3(all_82_4, all_82_3, all_82_2) = all_94_0 &
% 16.21/3.00 | cartesian_product2(all_94_0, all_82_1) = all_82_0 & $i(all_94_0) &
% 16.21/3.00 | $i(all_82_0)
% 16.21/3.00 |
% 16.21/3.00 | ALPHA: (14) implies:
% 16.21/3.00 | (15) $i(all_94_0)
% 16.21/3.00 | (16) cartesian_product2(all_94_0, all_82_1) = all_82_0
% 16.21/3.00 | (17) cartesian_product3(all_82_4, all_82_3, all_82_2) = all_94_0
% 16.21/3.00 |
% 16.21/3.00 | GROUND_INST: instantiating (t20_finset_1) with all_82_4, all_82_3, all_82_2,
% 16.21/3.00 | all_94_0, simplifying with (4), (5), (6), (8), (9), (10), (17)
% 16.21/3.00 | gives:
% 16.21/3.00 | (18) finite(all_94_0)
% 16.21/3.00 |
% 16.21/3.00 | GROUND_INST: instantiating (t19_finset_1) with all_94_0, all_82_1, all_82_0,
% 16.21/3.00 | simplifying with (3), (7), (11), (15), (16), (18) gives:
% 16.21/3.00 | (19) $false
% 16.21/3.00 |
% 16.21/3.00 | CLOSE: (19) is inconsistent.
% 16.21/3.00 |
% 16.21/3.00 End of proof
% 16.21/3.00 % SZS output end Proof for theBenchmark
% 16.21/3.00
% 16.21/3.00 2339ms
%------------------------------------------------------------------------------