TSTP Solution File: SEU094+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SEU094+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 : n023.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 17:42:30 EDT 2023
% Result : Theorem 13.42s 2.67s
% Output : Proof 18.06s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SEU094+1 : TPTP v8.1.2. Released v3.2.0.
% 0.11/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.14/0.34 % Computer : n023.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Wed Aug 23 19:27:27 EDT 2023
% 0.14/0.34 % CPUTime :
% 0.67/0.65 ________ _____
% 0.67/0.65 ___ __ \_________(_)________________________________
% 0.67/0.65 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.67/0.65 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.67/0.65 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.67/0.65
% 0.67/0.65 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.67/0.65 (2023-06-19)
% 0.67/0.65
% 0.67/0.65 (c) Philipp Rümmer, 2009-2023
% 0.67/0.65 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.67/0.65 Amanda Stjerna.
% 0.67/0.65 Free software under BSD-3-Clause.
% 0.67/0.65
% 0.67/0.65 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.67/0.65
% 0.67/0.65 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.67/0.67 Running up to 7 provers in parallel.
% 0.67/0.69 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.67/0.69 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.67/0.69 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.67/0.69 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.67/0.69 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.67/0.69 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.67/0.69 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 3.32/1.20 Prover 1: Preprocessing ...
% 3.32/1.20 Prover 4: Preprocessing ...
% 3.51/1.24 Prover 5: Preprocessing ...
% 3.51/1.24 Prover 3: Preprocessing ...
% 3.51/1.24 Prover 6: Preprocessing ...
% 3.51/1.24 Prover 0: Preprocessing ...
% 3.51/1.24 Prover 2: Preprocessing ...
% 6.82/1.77 Prover 2: Proving ...
% 6.82/1.77 Prover 5: Proving ...
% 7.48/1.81 Prover 1: Warning: ignoring some quantifiers
% 7.61/1.86 Prover 1: Constructing countermodel ...
% 7.61/1.89 Prover 6: Proving ...
% 8.27/1.92 Prover 3: Warning: ignoring some quantifiers
% 8.27/1.93 Prover 3: Constructing countermodel ...
% 8.27/1.97 Prover 4: Warning: ignoring some quantifiers
% 8.85/2.01 Prover 4: Constructing countermodel ...
% 9.68/2.19 Prover 0: Proving ...
% 13.42/2.67 Prover 5: proved (1978ms)
% 13.42/2.67
% 13.42/2.67 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 13.42/2.67
% 13.42/2.67 Prover 0: stopped
% 13.42/2.67 Prover 6: stopped
% 13.42/2.67 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 13.42/2.67 Prover 2: stopped
% 13.42/2.69 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 13.42/2.69 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 13.42/2.69 Prover 3: stopped
% 14.08/2.70 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 14.08/2.70 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 14.08/2.76 Prover 11: Preprocessing ...
% 14.08/2.77 Prover 10: Preprocessing ...
% 14.08/2.78 Prover 7: Preprocessing ...
% 14.88/2.79 Prover 8: Preprocessing ...
% 14.88/2.80 Prover 13: Preprocessing ...
% 15.21/2.88 Prover 10: Warning: ignoring some quantifiers
% 15.21/2.89 Prover 10: Constructing countermodel ...
% 15.21/2.90 Prover 7: Warning: ignoring some quantifiers
% 15.21/2.90 Prover 7: Constructing countermodel ...
% 15.86/2.96 Prover 13: Warning: ignoring some quantifiers
% 15.86/2.98 Prover 13: Constructing countermodel ...
% 16.30/3.00 Prover 8: Warning: ignoring some quantifiers
% 16.30/3.02 Prover 8: Constructing countermodel ...
% 16.92/3.09 Prover 11: Warning: ignoring some quantifiers
% 17.23/3.13 Prover 11: Constructing countermodel ...
% 17.48/3.18 Prover 10: Found proof (size 24)
% 17.48/3.19 Prover 10: proved (510ms)
% 17.48/3.19 Prover 13: stopped
% 17.48/3.19 Prover 7: stopped
% 17.48/3.19 Prover 1: stopped
% 17.48/3.19 Prover 8: stopped
% 17.48/3.19 Prover 11: stopped
% 17.48/3.19 Prover 4: stopped
% 17.48/3.19
% 17.48/3.19 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 17.48/3.19
% 17.48/3.20 % SZS output start Proof for theBenchmark
% 17.48/3.20 Assumptions after simplification:
% 17.48/3.20 ---------------------------------
% 17.48/3.20
% 17.48/3.20 (l22_finset_1)
% 17.48/3.23 ! [v0: $i] : ! [v1: $i] : ( ~ (union(v0) = v1) | ~ $i(v0) | ~ finite(v0) |
% 17.48/3.23 finite(v1) | ? [v2: $i] : ($i(v2) & in(v2, v0) & ~ finite(v2)))
% 18.06/3.23
% 18.06/3.23 (t100_zfmisc_1)
% 18.06/3.23 ! [v0: $i] : ! [v1: $i] : ( ~ (union(v0) = v1) | ~ $i(v0) | ? [v2: $i] :
% 18.06/3.23 (powerset(v1) = v2 & $i(v2) & subset(v0, v2)))
% 18.06/3.23
% 18.06/3.23 (t13_finset_1)
% 18.06/3.23 ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ subset(v0, v1) | ~
% 18.06/3.23 finite(v1) | finite(v0))
% 18.06/3.23
% 18.06/3.23 (t24_finset_1)
% 18.06/3.23 ! [v0: $i] : ! [v1: $i] : ( ~ (powerset(v0) = v1) | ~ $i(v0) | ~
% 18.06/3.23 finite(v1) | finite(v0)) & ! [v0: $i] : ! [v1: $i] : ( ~ (powerset(v0) =
% 18.06/3.23 v1) | ~ $i(v0) | ~ finite(v0) | finite(v1))
% 18.06/3.23
% 18.06/3.23 (t25_finset_1)
% 18.06/3.23 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (union(v0) = v1 & $i(v2) & $i(v1) &
% 18.06/3.23 $i(v0) & ((finite(v1) & ( ~ finite(v0) | (in(v2, v0) & ~ finite(v2)))) |
% 18.06/3.23 (finite(v0) & ~ finite(v1) & ! [v3: $i] : ( ~ $i(v3) | ~ in(v3, v0) |
% 18.06/3.23 finite(v3)))))
% 18.06/3.23
% 18.06/3.23 (t92_zfmisc_1)
% 18.06/3.23 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (union(v1) = v2) | ~ $i(v1) |
% 18.06/3.23 ~ $i(v0) | ~ in(v0, v1) | subset(v0, v2))
% 18.06/3.23
% 18.06/3.23 Further assumptions not needed in the proof:
% 18.06/3.23 --------------------------------------------
% 18.06/3.23 antisymmetry_r2_hidden, cc1_arytm_3, cc1_finset_1, cc1_funct_1, cc1_ordinal1,
% 18.06/3.23 cc1_relat_1, cc2_arytm_3, cc2_finset_1, cc2_funct_1, cc2_ordinal1, cc3_ordinal1,
% 18.06/3.23 cc4_arytm_3, existence_m1_subset_1, fc12_relat_1, fc1_subset_1, fc1_xboole_0,
% 18.06/3.23 fc2_ordinal1, fc4_ordinal1, fc4_relat_1, fc8_arytm_3, rc1_arytm_3, rc1_finset_1,
% 18.06/3.23 rc1_funcop_1, rc1_funct_1, rc1_ordinal1, rc1_ordinal2, rc1_relat_1,
% 18.06/3.23 rc1_subset_1, rc1_xboole_0, rc2_arytm_3, rc2_finset_1, rc2_funct_1,
% 18.06/3.23 rc2_ordinal1, rc2_ordinal2, rc2_relat_1, rc2_subset_1, rc2_xboole_0,
% 18.06/3.24 rc3_arytm_3, rc3_finset_1, rc3_funct_1, rc3_ordinal1, rc3_relat_1, rc4_funct_1,
% 18.06/3.24 rc4_ordinal1, rc5_funct_1, reflexivity_r1_tarski, t1_subset, t2_subset,
% 18.06/3.24 t3_subset, t4_subset, t5_subset, t6_boole, t7_boole, t8_boole
% 18.06/3.24
% 18.06/3.24 Those formulas are unsatisfiable:
% 18.06/3.24 ---------------------------------
% 18.06/3.24
% 18.06/3.24 Begin of proof
% 18.06/3.24 |
% 18.06/3.24 | ALPHA: (t24_finset_1) implies:
% 18.06/3.24 | (1) ! [v0: $i] : ! [v1: $i] : ( ~ (powerset(v0) = v1) | ~ $i(v0) | ~
% 18.06/3.24 | finite(v0) | finite(v1))
% 18.06/3.24 |
% 18.06/3.24 | DELTA: instantiating (t25_finset_1) with fresh symbols all_79_0, all_79_1,
% 18.06/3.24 | all_79_2 gives:
% 18.06/3.24 | (2) union(all_79_2) = all_79_1 & $i(all_79_0) & $i(all_79_1) & $i(all_79_2)
% 18.06/3.24 | & ((finite(all_79_1) & ( ~ finite(all_79_2) | (in(all_79_0, all_79_2) &
% 18.06/3.24 | ~ finite(all_79_0)))) | (finite(all_79_2) & ~
% 18.06/3.24 | finite(all_79_1) & ! [v0: $i] : ( ~ $i(v0) | ~ in(v0, all_79_2) |
% 18.06/3.24 | finite(v0))))
% 18.06/3.24 |
% 18.06/3.24 | ALPHA: (2) implies:
% 18.06/3.24 | (3) $i(all_79_2)
% 18.06/3.24 | (4) $i(all_79_1)
% 18.06/3.24 | (5) $i(all_79_0)
% 18.06/3.24 | (6) union(all_79_2) = all_79_1
% 18.06/3.24 | (7) (finite(all_79_1) & ( ~ finite(all_79_2) | (in(all_79_0, all_79_2) & ~
% 18.06/3.24 | finite(all_79_0)))) | (finite(all_79_2) & ~ finite(all_79_1) &
% 18.06/3.24 | ! [v0: $i] : ( ~ $i(v0) | ~ in(v0, all_79_2) | finite(v0)))
% 18.06/3.24 |
% 18.06/3.24 | GROUND_INST: instantiating (t100_zfmisc_1) with all_79_2, all_79_1,
% 18.06/3.24 | simplifying with (3), (6) gives:
% 18.06/3.24 | (8) ? [v0: $i] : (powerset(all_79_1) = v0 & $i(v0) & subset(all_79_2, v0))
% 18.06/3.24 |
% 18.06/3.24 | DELTA: instantiating (8) with fresh symbol all_87_0 gives:
% 18.06/3.24 | (9) powerset(all_79_1) = all_87_0 & $i(all_87_0) & subset(all_79_2,
% 18.06/3.24 | all_87_0)
% 18.06/3.24 |
% 18.06/3.24 | ALPHA: (9) implies:
% 18.06/3.24 | (10) subset(all_79_2, all_87_0)
% 18.06/3.24 | (11) $i(all_87_0)
% 18.06/3.24 | (12) powerset(all_79_1) = all_87_0
% 18.06/3.25 |
% 18.06/3.25 | BETA: splitting (7) gives:
% 18.06/3.25 |
% 18.06/3.25 | Case 1:
% 18.06/3.25 | |
% 18.06/3.25 | | (13) finite(all_79_1) & ( ~ finite(all_79_2) | (in(all_79_0, all_79_2) &
% 18.06/3.25 | | ~ finite(all_79_0)))
% 18.06/3.25 | |
% 18.06/3.25 | | ALPHA: (13) implies:
% 18.06/3.25 | | (14) finite(all_79_1)
% 18.06/3.25 | | (15) ~ finite(all_79_2) | (in(all_79_0, all_79_2) & ~ finite(all_79_0))
% 18.06/3.25 | |
% 18.06/3.25 | | GROUND_INST: instantiating (1) with all_79_1, all_87_0, simplifying with
% 18.06/3.25 | | (4), (12), (14) gives:
% 18.06/3.25 | | (16) finite(all_87_0)
% 18.06/3.25 | |
% 18.06/3.25 | | GROUND_INST: instantiating (t13_finset_1) with all_79_2, all_87_0,
% 18.06/3.25 | | simplifying with (3), (10), (11), (16) gives:
% 18.06/3.25 | | (17) finite(all_79_2)
% 18.06/3.25 | |
% 18.06/3.25 | | BETA: splitting (15) gives:
% 18.06/3.25 | |
% 18.06/3.25 | | Case 1:
% 18.06/3.25 | | |
% 18.06/3.25 | | | (18) ~ finite(all_79_2)
% 18.06/3.25 | | |
% 18.06/3.25 | | | PRED_UNIFY: (17), (18) imply:
% 18.06/3.25 | | | (19) $false
% 18.06/3.25 | | |
% 18.06/3.25 | | | CLOSE: (19) is inconsistent.
% 18.06/3.25 | | |
% 18.06/3.25 | | Case 2:
% 18.06/3.25 | | |
% 18.06/3.25 | | | (20) in(all_79_0, all_79_2) & ~ finite(all_79_0)
% 18.06/3.25 | | |
% 18.06/3.25 | | | ALPHA: (20) implies:
% 18.06/3.25 | | | (21) ~ finite(all_79_0)
% 18.06/3.25 | | | (22) in(all_79_0, all_79_2)
% 18.06/3.25 | | |
% 18.06/3.25 | | | GROUND_INST: instantiating (t92_zfmisc_1) with all_79_0, all_79_2,
% 18.06/3.25 | | | all_79_1, simplifying with (3), (5), (6), (22) gives:
% 18.06/3.25 | | | (23) subset(all_79_0, all_79_1)
% 18.06/3.25 | | |
% 18.06/3.25 | | | GROUND_INST: instantiating (t13_finset_1) with all_79_0, all_79_1,
% 18.06/3.25 | | | simplifying with (4), (5), (14), (21), (23) gives:
% 18.06/3.25 | | | (24) $false
% 18.06/3.25 | | |
% 18.06/3.25 | | | CLOSE: (24) is inconsistent.
% 18.06/3.25 | | |
% 18.06/3.25 | | End of split
% 18.06/3.25 | |
% 18.06/3.25 | Case 2:
% 18.06/3.25 | |
% 18.06/3.25 | | (25) finite(all_79_2) & ~ finite(all_79_1) & ! [v0: $i] : ( ~ $i(v0) |
% 18.06/3.25 | | ~ in(v0, all_79_2) | finite(v0))
% 18.06/3.25 | |
% 18.06/3.25 | | ALPHA: (25) implies:
% 18.06/3.25 | | (26) ~ finite(all_79_1)
% 18.06/3.25 | | (27) finite(all_79_2)
% 18.06/3.25 | | (28) ! [v0: $i] : ( ~ $i(v0) | ~ in(v0, all_79_2) | finite(v0))
% 18.06/3.25 | |
% 18.06/3.25 | | GROUND_INST: instantiating (l22_finset_1) with all_79_2, all_79_1,
% 18.06/3.25 | | simplifying with (3), (6), (26), (27) gives:
% 18.06/3.25 | | (29) ? [v0: $i] : ($i(v0) & in(v0, all_79_2) & ~ finite(v0))
% 18.06/3.25 | |
% 18.06/3.25 | | DELTA: instantiating (29) with fresh symbol all_131_0 gives:
% 18.06/3.25 | | (30) $i(all_131_0) & in(all_131_0, all_79_2) & ~ finite(all_131_0)
% 18.06/3.25 | |
% 18.06/3.25 | | ALPHA: (30) implies:
% 18.06/3.25 | | (31) ~ finite(all_131_0)
% 18.06/3.25 | | (32) in(all_131_0, all_79_2)
% 18.06/3.25 | | (33) $i(all_131_0)
% 18.06/3.25 | |
% 18.06/3.25 | | GROUND_INST: instantiating (28) with all_131_0, simplifying with (31), (32),
% 18.06/3.25 | | (33) gives:
% 18.06/3.25 | | (34) $false
% 18.06/3.25 | |
% 18.06/3.25 | | CLOSE: (34) is inconsistent.
% 18.06/3.25 | |
% 18.06/3.25 | End of split
% 18.06/3.25 |
% 18.06/3.25 End of proof
% 18.06/3.26 % SZS output end Proof for theBenchmark
% 18.06/3.26
% 18.06/3.26 2601ms
%------------------------------------------------------------------------------