TSTP Solution File: SYN061+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SYN061+1 : TPTP v8.1.2. Released v2.0.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n004.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 : Fri Sep 1 03:26:24 EDT 2023
% Result : Theorem 3.49s 1.17s
% Output : Proof 4.35s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYN061+1 : TPTP v8.1.2. Released v2.0.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.34 % Computer : n004.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 : Sat Aug 26 18:31:07 EDT 2023
% 0.20/0.34 % CPUTime :
% 0.20/0.60 ________ _____
% 0.20/0.60 ___ __ \_________(_)________________________________
% 0.20/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.20/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.20/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.20/0.60
% 0.20/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.20/0.60 (2023-06-19)
% 0.20/0.60
% 0.20/0.60 (c) Philipp Rümmer, 2009-2023
% 0.20/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.20/0.60 Amanda Stjerna.
% 0.20/0.60 Free software under BSD-3-Clause.
% 0.20/0.60
% 0.20/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.20/0.60
% 0.20/0.60 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.20/0.61 Running up to 7 provers in parallel.
% 0.20/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.20/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.20/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.20/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.20/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.20/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.20/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 1.53/0.93 Prover 1: Preprocessing ...
% 1.53/0.93 Prover 4: Preprocessing ...
% 2.10/0.98 Prover 2: Preprocessing ...
% 2.10/0.98 Prover 6: Preprocessing ...
% 2.10/0.98 Prover 3: Preprocessing ...
% 2.10/0.98 Prover 0: Preprocessing ...
% 2.10/0.98 Prover 5: Preprocessing ...
% 2.61/1.05 Prover 2: Proving ...
% 2.61/1.05 Prover 5: Proving ...
% 2.61/1.07 Prover 1: Constructing countermodel ...
% 2.61/1.07 Prover 6: Proving ...
% 2.61/1.07 Prover 4: Constructing countermodel ...
% 2.61/1.08 Prover 3: Constructing countermodel ...
% 2.61/1.10 Prover 0: Proving ...
% 3.08/1.13 Prover 3: gave up
% 3.08/1.13 Prover 1: gave up
% 3.08/1.14 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 3.08/1.14 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 3.08/1.15 Prover 7: Preprocessing ...
% 3.08/1.16 Prover 8: Preprocessing ...
% 3.49/1.17 Prover 2: proved (548ms)
% 3.49/1.17
% 3.49/1.17 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.49/1.17
% 3.49/1.17 Prover 0: stopped
% 3.49/1.18 Prover 5: stopped
% 3.49/1.18 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 3.49/1.18 Prover 6: stopped
% 3.49/1.18 Prover 7: Warning: ignoring some quantifiers
% 3.49/1.18 Prover 10: Preprocessing ...
% 3.49/1.18 Prover 7: Constructing countermodel ...
% 3.49/1.18 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 3.49/1.19 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 3.49/1.19 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 3.49/1.20 Prover 16: Preprocessing ...
% 3.49/1.21 Prover 11: Preprocessing ...
% 3.49/1.21 Prover 13: Preprocessing ...
% 3.49/1.21 Prover 8: Warning: ignoring some quantifiers
% 3.49/1.22 Prover 16: Warning: ignoring some quantifiers
% 3.49/1.22 Prover 10: Warning: ignoring some quantifiers
% 3.49/1.22 Prover 16: Constructing countermodel ...
% 3.49/1.23 Prover 10: Constructing countermodel ...
% 3.49/1.23 Prover 13: Warning: ignoring some quantifiers
% 3.49/1.23 Prover 7: gave up
% 3.49/1.23 Prover 13: Constructing countermodel ...
% 3.49/1.23 Prover 8: Constructing countermodel ...
% 3.49/1.23 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085
% 3.49/1.24 Prover 10: gave up
% 3.49/1.24 Prover 19: Preprocessing ...
% 3.49/1.24 Prover 13: gave up
% 3.49/1.25 Prover 4: Found proof (size 20)
% 3.49/1.25 Prover 4: proved (623ms)
% 3.49/1.25 Prover 8: stopped
% 3.49/1.25 Prover 16: stopped
% 3.49/1.25 Prover 11: Constructing countermodel ...
% 4.19/1.26 Prover 11: stopped
% 4.19/1.27 Prover 19: Warning: ignoring some quantifiers
% 4.19/1.28 Prover 19: Constructing countermodel ...
% 4.19/1.28 Prover 19: stopped
% 4.19/1.28
% 4.19/1.28 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.19/1.28
% 4.19/1.29 % SZS output start Proof for theBenchmark
% 4.19/1.29 Assumptions after simplification:
% 4.19/1.29 ---------------------------------
% 4.19/1.29
% 4.19/1.29 (pel31)
% 4.35/1.32 ! [v0: $i] : ( ~ (big_j(v0) = 0) | ~ $i(v0) | ? [v1: int] : ( ~ (v1 = 0) &
% 4.35/1.32 big_i(v0) = v1)) & ! [v0: $i] : ( ~ (big_i(v0) = 0) | ~ $i(v0) | ? [v1:
% 4.35/1.32 int] : ( ~ (v1 = 0) & big_j(v0) = v1))
% 4.35/1.32
% 4.35/1.32 (pel31_1)
% 4.35/1.33 ! [v0: $i] : ! [v1: any] : ( ~ (big_g(v0) = v1) | ~ $i(v0) | ? [v2: any] :
% 4.35/1.33 ? [v3: any] : (big_f(v0) = v2 & big_h(v0) = v3 & ( ~ (v2 = 0) | ( ~ (v3 =
% 4.35/1.33 0) & ~ (v1 = 0))))) & ! [v0: $i] : ! [v1: any] : ( ~ (big_h(v0) =
% 4.35/1.33 v1) | ~ $i(v0) | ? [v2: any] : ? [v3: any] : (big_g(v0) = v3 &
% 4.35/1.33 big_f(v0) = v2 & ( ~ (v2 = 0) | ( ~ (v3 = 0) & ~ (v1 = 0))))) & ! [v0:
% 4.35/1.33 $i] : ( ~ (big_f(v0) = 0) | ~ $i(v0) | ? [v1: int] : ? [v2: int] : ( ~
% 4.35/1.33 (v2 = 0) & ~ (v1 = 0) & big_g(v0) = v1 & big_h(v0) = v2))
% 4.35/1.33
% 4.35/1.33 (pel31_2)
% 4.35/1.33 ? [v0: $i] : (big_i(v0) = 0 & big_f(v0) = 0 & $i(v0))
% 4.35/1.33
% 4.35/1.33 (pel31_3)
% 4.35/1.33 ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (big_j(v0) = v1) | ~ $i(v0) |
% 4.35/1.33 big_h(v0) = 0) & ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (big_h(v0) = v1)
% 4.35/1.33 | ~ $i(v0) | big_j(v0) = 0)
% 4.35/1.33
% 4.35/1.33 (function-axioms)
% 4.35/1.33 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 =
% 4.35/1.33 v0 | ~ (big_j(v2) = v1) | ~ (big_j(v2) = v0)) & ! [v0: MultipleValueBool]
% 4.35/1.33 : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (big_i(v2) = v1) |
% 4.35/1.33 ~ (big_i(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 4.35/1.33 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (big_g(v2) = v1) | ~
% 4.35/1.33 (big_g(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool]
% 4.35/1.33 : ! [v2: $i] : (v1 = v0 | ~ (big_f(v2) = v1) | ~ (big_f(v2) = v0)) & !
% 4.35/1.33 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0
% 4.35/1.33 | ~ (big_h(v2) = v1) | ~ (big_h(v2) = v0))
% 4.35/1.33
% 4.35/1.33 Those formulas are unsatisfiable:
% 4.35/1.33 ---------------------------------
% 4.35/1.33
% 4.35/1.33 Begin of proof
% 4.35/1.34 |
% 4.35/1.34 | ALPHA: (pel31_1) implies:
% 4.35/1.34 | (1) ! [v0: $i] : ( ~ (big_f(v0) = 0) | ~ $i(v0) | ? [v1: int] : ? [v2:
% 4.35/1.34 | int] : ( ~ (v2 = 0) & ~ (v1 = 0) & big_g(v0) = v1 & big_h(v0) =
% 4.35/1.34 | v2))
% 4.35/1.34 |
% 4.35/1.34 | ALPHA: (pel31_3) implies:
% 4.35/1.34 | (2) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (big_h(v0) = v1) | ~ $i(v0)
% 4.35/1.34 | | big_j(v0) = 0)
% 4.35/1.34 |
% 4.35/1.34 | ALPHA: (pel31) implies:
% 4.35/1.34 | (3) ! [v0: $i] : ( ~ (big_i(v0) = 0) | ~ $i(v0) | ? [v1: int] : ( ~ (v1
% 4.35/1.34 | = 0) & big_j(v0) = v1))
% 4.35/1.34 |
% 4.35/1.34 | ALPHA: (function-axioms) implies:
% 4.35/1.34 | (4) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 4.35/1.34 | (v1 = v0 | ~ (big_j(v2) = v1) | ~ (big_j(v2) = v0))
% 4.35/1.34 |
% 4.35/1.34 | DELTA: instantiating (pel31_2) with fresh symbol all_6_0 gives:
% 4.35/1.34 | (5) big_i(all_6_0) = 0 & big_f(all_6_0) = 0 & $i(all_6_0)
% 4.35/1.34 |
% 4.35/1.34 | ALPHA: (5) implies:
% 4.35/1.34 | (6) $i(all_6_0)
% 4.35/1.34 | (7) big_f(all_6_0) = 0
% 4.35/1.34 | (8) big_i(all_6_0) = 0
% 4.35/1.34 |
% 4.35/1.35 | GROUND_INST: instantiating (1) with all_6_0, simplifying with (6), (7) gives:
% 4.35/1.35 | (9) ? [v0: int] : ? [v1: int] : ( ~ (v1 = 0) & ~ (v0 = 0) &
% 4.35/1.35 | big_g(all_6_0) = v0 & big_h(all_6_0) = v1)
% 4.35/1.35 |
% 4.35/1.35 | GROUND_INST: instantiating (3) with all_6_0, simplifying with (6), (8) gives:
% 4.35/1.35 | (10) ? [v0: int] : ( ~ (v0 = 0) & big_j(all_6_0) = v0)
% 4.35/1.35 |
% 4.35/1.35 | DELTA: instantiating (10) with fresh symbol all_13_0 gives:
% 4.35/1.35 | (11) ~ (all_13_0 = 0) & big_j(all_6_0) = all_13_0
% 4.35/1.35 |
% 4.35/1.35 | ALPHA: (11) implies:
% 4.35/1.35 | (12) ~ (all_13_0 = 0)
% 4.35/1.35 | (13) big_j(all_6_0) = all_13_0
% 4.35/1.35 |
% 4.35/1.35 | DELTA: instantiating (9) with fresh symbols all_15_0, all_15_1 gives:
% 4.35/1.35 | (14) ~ (all_15_0 = 0) & ~ (all_15_1 = 0) & big_g(all_6_0) = all_15_1 &
% 4.35/1.35 | big_h(all_6_0) = all_15_0
% 4.35/1.35 |
% 4.35/1.35 | ALPHA: (14) implies:
% 4.35/1.35 | (15) ~ (all_15_0 = 0)
% 4.35/1.35 | (16) big_h(all_6_0) = all_15_0
% 4.35/1.35 |
% 4.35/1.35 | GROUND_INST: instantiating (2) with all_6_0, all_15_0, simplifying with (6),
% 4.35/1.35 | (16) gives:
% 4.35/1.35 | (17) all_15_0 = 0 | big_j(all_6_0) = 0
% 4.35/1.35 |
% 4.35/1.35 | BETA: splitting (17) gives:
% 4.35/1.35 |
% 4.35/1.35 | Case 1:
% 4.35/1.35 | |
% 4.35/1.35 | | (18) big_j(all_6_0) = 0
% 4.35/1.35 | |
% 4.35/1.35 | | GROUND_INST: instantiating (4) with all_13_0, 0, all_6_0, simplifying with
% 4.35/1.35 | | (13), (18) gives:
% 4.35/1.35 | | (19) all_13_0 = 0
% 4.35/1.35 | |
% 4.35/1.35 | | REDUCE: (12), (19) imply:
% 4.35/1.35 | | (20) $false
% 4.35/1.35 | |
% 4.35/1.35 | | CLOSE: (20) is inconsistent.
% 4.35/1.35 | |
% 4.35/1.35 | Case 2:
% 4.35/1.35 | |
% 4.35/1.35 | | (21) all_15_0 = 0
% 4.35/1.35 | |
% 4.35/1.35 | | REDUCE: (15), (21) imply:
% 4.35/1.35 | | (22) $false
% 4.35/1.35 | |
% 4.35/1.35 | | CLOSE: (22) is inconsistent.
% 4.35/1.35 | |
% 4.35/1.35 | End of split
% 4.35/1.35 |
% 4.35/1.35 End of proof
% 4.35/1.35 % SZS output end Proof for theBenchmark
% 4.35/1.36
% 4.35/1.36 753ms
%------------------------------------------------------------------------------