TSTP Solution File: NUM531+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : NUM531+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n013.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 11:48:25 EDT 2023
% Result : Theorem 3.78s 1.21s
% Output : Proof 4.52s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM531+1 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.34 % Computer : n013.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 : Fri Aug 25 15:16:47 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.21/0.61 ________ _____
% 0.21/0.61 ___ __ \_________(_)________________________________
% 0.21/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.21/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.21/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.21/0.61
% 0.21/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.21/0.61 (2023-06-19)
% 0.21/0.61
% 0.21/0.61 (c) Philipp Rümmer, 2009-2023
% 0.21/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.21/0.61 Amanda Stjerna.
% 0.21/0.61 Free software under BSD-3-Clause.
% 0.21/0.61
% 0.21/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.21/0.61
% 0.21/0.61 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.21/0.62 Running up to 7 provers in parallel.
% 0.21/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.21/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.21/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.21/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.21/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.21/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.21/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 1.83/0.97 Prover 1: Preprocessing ...
% 1.83/0.97 Prover 4: Preprocessing ...
% 1.83/1.02 Prover 3: Preprocessing ...
% 1.83/1.02 Prover 2: Preprocessing ...
% 1.83/1.02 Prover 0: Preprocessing ...
% 1.83/1.02 Prover 5: Preprocessing ...
% 1.83/1.02 Prover 6: Preprocessing ...
% 3.00/1.12 Prover 5: Constructing countermodel ...
% 3.00/1.12 Prover 2: Constructing countermodel ...
% 3.00/1.13 Prover 1: Constructing countermodel ...
% 3.00/1.14 Prover 3: Constructing countermodel ...
% 3.00/1.15 Prover 4: Constructing countermodel ...
% 3.57/1.17 Prover 6: Proving ...
% 3.60/1.18 Prover 0: Proving ...
% 3.78/1.21 Prover 2: proved (572ms)
% 3.78/1.21
% 3.78/1.21 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.78/1.21
% 3.78/1.21 Prover 5: stopped
% 3.90/1.22 Prover 0: stopped
% 3.90/1.22 Prover 6: stopped
% 3.90/1.23 Prover 3: stopped
% 3.90/1.23 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 3.90/1.23 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 3.90/1.23 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 3.90/1.23 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 3.90/1.23 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 3.90/1.24 Prover 7: Preprocessing ...
% 3.90/1.26 Prover 11: Preprocessing ...
% 3.90/1.26 Prover 13: Preprocessing ...
% 3.90/1.26 Prover 10: Preprocessing ...
% 3.90/1.27 Prover 1: Found proof (size 13)
% 3.90/1.27 Prover 8: Preprocessing ...
% 3.90/1.27 Prover 1: proved (639ms)
% 3.90/1.27 Prover 4: stopped
% 3.90/1.27 Prover 7: Constructing countermodel ...
% 3.90/1.27 Prover 7: stopped
% 3.90/1.28 Prover 11: stopped
% 3.90/1.29 Prover 10: Constructing countermodel ...
% 3.90/1.29 Prover 10: stopped
% 3.90/1.29 Prover 13: Constructing countermodel ...
% 3.90/1.30 Prover 13: stopped
% 3.90/1.31 Prover 8: Warning: ignoring some quantifiers
% 3.90/1.31 Prover 8: Constructing countermodel ...
% 4.52/1.32 Prover 8: stopped
% 4.52/1.32
% 4.52/1.32 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.52/1.32
% 4.52/1.32 % SZS output start Proof for theBenchmark
% 4.52/1.33 Assumptions after simplification:
% 4.52/1.33 ---------------------------------
% 4.52/1.33
% 4.52/1.33 (mCountNFin)
% 4.52/1.36 ! [v0: $i] : ( ~ (isFinite0(v0) = 0) | ~ $i(v0) | ? [v1: any] : ? [v2:
% 4.52/1.36 any] : (isCountable0(v0) = v2 & aSet0(v0) = v1 & ( ~ (v2 = 0) | ~ (v1 =
% 4.52/1.36 0))))
% 4.52/1.36
% 4.52/1.36 (mEmpFin)
% 4.52/1.36 isFinite0(slcrc0) = 0 & $i(slcrc0)
% 4.52/1.36
% 4.52/1.36 (m__)
% 4.52/1.36 isCountable0(slcrc0) = 0 & aSet0(slcrc0) = 0 & $i(slcrc0)
% 4.52/1.36
% 4.52/1.36 (function-axioms)
% 4.52/1.36 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 4.52/1.36 [v3: $i] : (v1 = v0 | ~ (aElementOf0(v3, v2) = v1) | ~ (aElementOf0(v3, v2)
% 4.52/1.36 = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 4.52/1.36 $i] : (v1 = v0 | ~ (isCountable0(v2) = v1) | ~ (isCountable0(v2) = v0)) &
% 4.52/1.36 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 =
% 4.52/1.36 v0 | ~ (isFinite0(v2) = v1) | ~ (isFinite0(v2) = v0)) & ! [v0:
% 4.52/1.36 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 |
% 4.52/1.36 ~ (aSet0(v2) = v1) | ~ (aSet0(v2) = v0)) & ! [v0: MultipleValueBool] : !
% 4.52/1.36 [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (aElement0(v2) = v1) |
% 4.52/1.36 ~ (aElement0(v2) = v0))
% 4.52/1.36
% 4.52/1.36 Further assumptions not needed in the proof:
% 4.52/1.36 --------------------------------------------
% 4.52/1.36 mCntRel, mDefEmp, mEOfElem, mElmSort, mFinRel, mSetSort
% 4.52/1.36
% 4.52/1.36 Those formulas are unsatisfiable:
% 4.52/1.36 ---------------------------------
% 4.52/1.36
% 4.52/1.36 Begin of proof
% 4.52/1.36 |
% 4.52/1.37 | ALPHA: (mEmpFin) implies:
% 4.52/1.37 | (1) isFinite0(slcrc0) = 0
% 4.52/1.37 |
% 4.52/1.37 | ALPHA: (m__) implies:
% 4.52/1.37 | (2) $i(slcrc0)
% 4.52/1.37 | (3) aSet0(slcrc0) = 0
% 4.52/1.37 | (4) isCountable0(slcrc0) = 0
% 4.52/1.37 |
% 4.52/1.37 | ALPHA: (function-axioms) implies:
% 4.52/1.37 | (5) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 4.52/1.37 | (v1 = v0 | ~ (aSet0(v2) = v1) | ~ (aSet0(v2) = v0))
% 4.52/1.37 | (6) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 4.52/1.37 | (v1 = v0 | ~ (isCountable0(v2) = v1) | ~ (isCountable0(v2) = v0))
% 4.52/1.37 |
% 4.52/1.37 | GROUND_INST: instantiating (mCountNFin) with slcrc0, simplifying with (1), (2)
% 4.52/1.37 | gives:
% 4.52/1.37 | (7) ? [v0: any] : ? [v1: any] : (isCountable0(slcrc0) = v1 &
% 4.52/1.37 | aSet0(slcrc0) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 4.52/1.37 |
% 4.52/1.37 | DELTA: instantiating (7) with fresh symbols all_14_0, all_14_1 gives:
% 4.52/1.37 | (8) isCountable0(slcrc0) = all_14_0 & aSet0(slcrc0) = all_14_1 & ( ~
% 4.52/1.37 | (all_14_0 = 0) | ~ (all_14_1 = 0))
% 4.52/1.37 |
% 4.52/1.37 | ALPHA: (8) implies:
% 4.52/1.38 | (9) aSet0(slcrc0) = all_14_1
% 4.52/1.38 | (10) isCountable0(slcrc0) = all_14_0
% 4.52/1.38 | (11) ~ (all_14_0 = 0) | ~ (all_14_1 = 0)
% 4.52/1.38 |
% 4.52/1.38 | GROUND_INST: instantiating (5) with 0, all_14_1, slcrc0, simplifying with (3),
% 4.52/1.38 | (9) gives:
% 4.52/1.38 | (12) all_14_1 = 0
% 4.52/1.38 |
% 4.52/1.38 | GROUND_INST: instantiating (6) with 0, all_14_0, slcrc0, simplifying with (4),
% 4.52/1.38 | (10) gives:
% 4.52/1.38 | (13) all_14_0 = 0
% 4.52/1.38 |
% 4.52/1.38 | BETA: splitting (11) gives:
% 4.52/1.38 |
% 4.52/1.38 | Case 1:
% 4.52/1.38 | |
% 4.52/1.38 | | (14) ~ (all_14_0 = 0)
% 4.52/1.38 | |
% 4.52/1.38 | | REDUCE: (13), (14) imply:
% 4.52/1.38 | | (15) $false
% 4.52/1.38 | |
% 4.52/1.38 | | CLOSE: (15) is inconsistent.
% 4.52/1.38 | |
% 4.52/1.38 | Case 2:
% 4.52/1.38 | |
% 4.52/1.38 | | (16) ~ (all_14_1 = 0)
% 4.52/1.38 | |
% 4.52/1.38 | | REDUCE: (12), (16) imply:
% 4.52/1.38 | | (17) $false
% 4.52/1.38 | |
% 4.52/1.38 | | CLOSE: (17) is inconsistent.
% 4.52/1.38 | |
% 4.52/1.38 | End of split
% 4.52/1.38 |
% 4.52/1.38 End of proof
% 4.52/1.38 % SZS output end Proof for theBenchmark
% 4.52/1.38
% 4.52/1.38 770ms
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