TSTP Solution File: KRS178+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : KRS178+1 : TPTP v8.1.2. Bugfixed v5.4.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n005.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 05:51:33 EDT 2023
% Result : Theorem 5.56s 1.46s
% Output : Proof 7.43s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : KRS178+1 : TPTP v8.1.2. Bugfixed v5.4.0.
% 0.07/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.34 % Computer : n005.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 : Mon Aug 28 02:06:53 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.61 ________ _____
% 0.19/0.61 ___ __ \_________(_)________________________________
% 0.19/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.19/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.19/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.19/0.61
% 0.19/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.19/0.61 (2023-06-19)
% 0.19/0.61
% 0.19/0.61 (c) Philipp Rümmer, 2009-2023
% 0.19/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.19/0.61 Amanda Stjerna.
% 0.19/0.61 Free software under BSD-3-Clause.
% 0.19/0.61
% 0.19/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.19/0.61
% 0.19/0.61 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.19/0.62 Running up to 7 provers in parallel.
% 0.19/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.19/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.19/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.19/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.19/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.19/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.19/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.58/1.01 Prover 1: Preprocessing ...
% 2.58/1.01 Prover 4: Preprocessing ...
% 2.62/1.06 Prover 3: Preprocessing ...
% 2.62/1.06 Prover 6: Preprocessing ...
% 2.62/1.06 Prover 2: Preprocessing ...
% 2.62/1.06 Prover 5: Preprocessing ...
% 2.62/1.06 Prover 0: Preprocessing ...
% 4.60/1.31 Prover 2: Proving ...
% 4.60/1.31 Prover 5: Proving ...
% 4.98/1.36 Prover 6: Proving ...
% 4.98/1.36 Prover 3: Constructing countermodel ...
% 5.26/1.39 Prover 4: Constructing countermodel ...
% 5.44/1.40 Prover 1: Constructing countermodel ...
% 5.44/1.42 Prover 0: Proving ...
% 5.56/1.46 Prover 3: proved (833ms)
% 5.56/1.46
% 5.56/1.46 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.56/1.46
% 5.56/1.47 Prover 0: stopped
% 5.56/1.47 Prover 6: stopped
% 5.56/1.47 Prover 5: stopped
% 5.56/1.47 Prover 2: stopped
% 5.56/1.47 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 5.56/1.47 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 5.56/1.47 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 5.56/1.47 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 5.56/1.48 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 5.56/1.51 Prover 10: Preprocessing ...
% 6.26/1.52 Prover 8: Preprocessing ...
% 6.26/1.52 Prover 13: Preprocessing ...
% 6.26/1.52 Prover 7: Preprocessing ...
% 6.26/1.52 Prover 11: Preprocessing ...
% 6.26/1.57 Prover 7: Warning: ignoring some quantifiers
% 6.26/1.57 Prover 10: Warning: ignoring some quantifiers
% 6.26/1.57 Prover 13: Warning: ignoring some quantifiers
% 6.26/1.58 Prover 1: Found proof (size 13)
% 6.26/1.58 Prover 1: proved (951ms)
% 6.26/1.58 Prover 7: Constructing countermodel ...
% 6.26/1.58 Prover 10: Constructing countermodel ...
% 6.26/1.58 Prover 10: stopped
% 6.26/1.59 Prover 4: stopped
% 6.26/1.59 Prover 13: Constructing countermodel ...
% 6.26/1.59 Prover 7: stopped
% 6.84/1.59 Prover 13: stopped
% 6.84/1.63 Prover 8: Warning: ignoring some quantifiers
% 6.84/1.64 Prover 8: Constructing countermodel ...
% 6.84/1.65 Prover 11: Constructing countermodel ...
% 6.84/1.65 Prover 8: stopped
% 6.84/1.65 Prover 11: stopped
% 6.84/1.65
% 6.84/1.65 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.84/1.65
% 6.84/1.66 % SZS output start Proof for theBenchmark
% 6.84/1.66 Assumptions after simplification:
% 6.84/1.66 ---------------------------------
% 6.84/1.66
% 6.84/1.66 (isa)
% 7.31/1.69 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (isa(v0, v1) = v2) |
% 7.31/1.69 ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] : ? [v5: int] : ( ~ (v5 =
% 7.31/1.69 0) & status(v3, v4, v1) = v5 & status(v3, v4, v0) = 0 & $i(v4) &
% 7.31/1.69 $i(v3))) & ! [v0: $i] : ! [v1: $i] : ( ~ (isa(v0, v1) = 0) | ~ $i(v1) |
% 7.31/1.69 ~ $i(v0) | ! [v2: $i] : ! [v3: $i] : ( ~ (status(v2, v3, v0) = 0) | ~
% 7.31/1.69 $i(v3) | ~ $i(v2) | status(v2, v3, v1) = 0))
% 7.31/1.69
% 7.31/1.69 (isa_reflexive)
% 7.31/1.69 ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & isa(v0, v0) = v1 & $i(v0))
% 7.31/1.69
% 7.31/1.69 (function-axioms)
% 7.31/1.70 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 7.31/1.70 [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (status(v4, v3, v2) = v1) | ~
% 7.31/1.70 (status(v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 7.31/1.70 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (model(v3,
% 7.31/1.70 v2) = v1) | ~ (model(v3, v2) = v0)) & ! [v0: MultipleValueBool] : !
% 7.31/1.70 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (xora(v3,
% 7.31/1.70 v2) = v1) | ~ (xora(v3, v2) = v0)) & ! [v0: MultipleValueBool] : !
% 7.31/1.70 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 7.31/1.70 (nevera(v3, v2) = v1) | ~ (nevera(v3, v2) = v0)) & ! [v0:
% 7.31/1.70 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 7.31/1.70 : (v1 = v0 | ~ (nota(v3, v2) = v1) | ~ (nota(v3, v2) = v0)) & ! [v0:
% 7.31/1.70 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 7.31/1.70 : (v1 = v0 | ~ (isa(v3, v2) = v1) | ~ (isa(v3, v2) = v0)) & ! [v0:
% 7.31/1.70 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 7.31/1.70 : (v1 = v0 | ~ (mighta(v3, v2) = v1) | ~ (mighta(v3, v2) = v0)) & ! [v0:
% 7.31/1.70 $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (not(v2) = v1) | ~ (not(v2)
% 7.31/1.70 = v0))
% 7.31/1.70
% 7.31/1.70 Further assumptions not needed in the proof:
% 7.31/1.70 --------------------------------------------
% 7.43/1.70 completeness, contradiction, mighta, mixed_pair, nevera, non_thm_spt, not, nota,
% 7.43/1.70 sat_non_taut_pair, satisfiable, tautology, xora
% 7.43/1.70
% 7.43/1.70 Those formulas are unsatisfiable:
% 7.43/1.70 ---------------------------------
% 7.43/1.70
% 7.43/1.70 Begin of proof
% 7.43/1.70 |
% 7.43/1.70 | ALPHA: (isa) implies:
% 7.43/1.70 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (isa(v0, v1) =
% 7.43/1.70 | v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] : ? [v5:
% 7.43/1.70 | int] : ( ~ (v5 = 0) & status(v3, v4, v1) = v5 & status(v3, v4, v0)
% 7.43/1.70 | = 0 & $i(v4) & $i(v3)))
% 7.43/1.70 |
% 7.43/1.70 | ALPHA: (function-axioms) implies:
% 7.43/1.71 | (2) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 7.43/1.71 | ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (status(v4, v3, v2) = v1) |
% 7.43/1.71 | ~ (status(v4, v3, v2) = v0))
% 7.43/1.71 |
% 7.43/1.71 | DELTA: instantiating (isa_reflexive) with fresh symbols all_10_0, all_10_1
% 7.43/1.71 | gives:
% 7.43/1.71 | (3) ~ (all_10_0 = 0) & isa(all_10_1, all_10_1) = all_10_0 & $i(all_10_1)
% 7.43/1.71 |
% 7.43/1.71 | ALPHA: (3) implies:
% 7.43/1.71 | (4) ~ (all_10_0 = 0)
% 7.43/1.71 | (5) $i(all_10_1)
% 7.43/1.71 | (6) isa(all_10_1, all_10_1) = all_10_0
% 7.43/1.71 |
% 7.43/1.71 | GROUND_INST: instantiating (1) with all_10_1, all_10_1, all_10_0, simplifying
% 7.43/1.71 | with (5), (6) gives:
% 7.43/1.71 | (7) all_10_0 = 0 | ? [v0: $i] : ? [v1: $i] : ? [v2: int] : ( ~ (v2 = 0)
% 7.43/1.71 | & status(v0, v1, all_10_1) = v2 & status(v0, v1, all_10_1) = 0 &
% 7.43/1.71 | $i(v1) & $i(v0))
% 7.43/1.71 |
% 7.43/1.71 | BETA: splitting (7) gives:
% 7.43/1.71 |
% 7.43/1.71 | Case 1:
% 7.43/1.71 | |
% 7.43/1.71 | | (8) all_10_0 = 0
% 7.43/1.71 | |
% 7.43/1.71 | | REDUCE: (4), (8) imply:
% 7.43/1.71 | | (9) $false
% 7.43/1.71 | |
% 7.43/1.71 | | CLOSE: (9) is inconsistent.
% 7.43/1.71 | |
% 7.43/1.71 | Case 2:
% 7.43/1.71 | |
% 7.43/1.71 | | (10) ? [v0: $i] : ? [v1: $i] : ? [v2: int] : ( ~ (v2 = 0) & status(v0,
% 7.43/1.71 | | v1, all_10_1) = v2 & status(v0, v1, all_10_1) = 0 & $i(v1) &
% 7.43/1.71 | | $i(v0))
% 7.43/1.71 | |
% 7.43/1.71 | | DELTA: instantiating (10) with fresh symbols all_53_0, all_53_1, all_53_2
% 7.43/1.71 | | gives:
% 7.43/1.72 | | (11) ~ (all_53_0 = 0) & status(all_53_2, all_53_1, all_10_1) = all_53_0
% 7.43/1.72 | | & status(all_53_2, all_53_1, all_10_1) = 0 & $i(all_53_1) &
% 7.43/1.72 | | $i(all_53_2)
% 7.43/1.72 | |
% 7.43/1.72 | | ALPHA: (11) implies:
% 7.43/1.72 | | (12) ~ (all_53_0 = 0)
% 7.43/1.72 | | (13) status(all_53_2, all_53_1, all_10_1) = 0
% 7.43/1.72 | | (14) status(all_53_2, all_53_1, all_10_1) = all_53_0
% 7.43/1.72 | |
% 7.43/1.72 | | GROUND_INST: instantiating (2) with 0, all_53_0, all_10_1, all_53_1,
% 7.43/1.72 | | all_53_2, simplifying with (13), (14) gives:
% 7.43/1.72 | | (15) all_53_0 = 0
% 7.43/1.72 | |
% 7.43/1.72 | | REDUCE: (12), (15) imply:
% 7.43/1.72 | | (16) $false
% 7.43/1.72 | |
% 7.43/1.72 | | CLOSE: (16) is inconsistent.
% 7.43/1.72 | |
% 7.43/1.72 | End of split
% 7.43/1.72 |
% 7.43/1.72 End of proof
% 7.43/1.72 % SZS output end Proof for theBenchmark
% 7.43/1.72
% 7.43/1.72 1111ms
%------------------------------------------------------------------------------