TSTP Solution File: SYN068+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SYN068+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 : n031.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 03:26:27 EDT 2023
% Result : Theorem 3.51s 1.17s
% Output : Proof 4.13s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : SYN068+1 : TPTP v8.1.2. Released v2.0.0.
% 0.12/0.14 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.14/0.35 % Computer : n031.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Sat Aug 26 20:18:38 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.21/0.60 ________ _____
% 0.21/0.60 ___ __ \_________(_)________________________________
% 0.21/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.21/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.21/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.21/0.60
% 0.21/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.21/0.60 (2023-06-19)
% 0.21/0.60
% 0.21/0.60 (c) Philipp Rümmer, 2009-2023
% 0.21/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.21/0.60 Amanda Stjerna.
% 0.21/0.60 Free software under BSD-3-Clause.
% 0.21/0.60
% 0.21/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.21/0.60
% 0.21/0.60 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.21/0.61 Running up to 7 provers in parallel.
% 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 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 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 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 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 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
% 0.21/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 1.80/0.93 Prover 1: Preprocessing ...
% 1.80/0.93 Prover 4: Preprocessing ...
% 2.11/0.98 Prover 5: Preprocessing ...
% 2.11/0.98 Prover 3: Preprocessing ...
% 2.11/0.98 Prover 2: Preprocessing ...
% 2.11/0.98 Prover 6: Preprocessing ...
% 2.11/0.98 Prover 0: Preprocessing ...
% 2.69/1.06 Prover 5: Constructing countermodel ...
% 2.69/1.06 Prover 2: Constructing countermodel ...
% 2.69/1.08 Prover 1: Constructing countermodel ...
% 2.69/1.08 Prover 4: Constructing countermodel ...
% 2.69/1.08 Prover 3: Constructing countermodel ...
% 2.69/1.08 Prover 6: Proving ...
% 3.06/1.11 Prover 0: Proving ...
% 3.51/1.16 Prover 2: proved (537ms)
% 3.51/1.17
% 3.51/1.17 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.51/1.17
% 3.51/1.17 Prover 5: proved (537ms)
% 3.51/1.17
% 3.51/1.17 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.51/1.17
% 3.51/1.17 Prover 0: stopped
% 3.51/1.17 Prover 6: stopped
% 3.51/1.17 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 3.51/1.17 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 3.51/1.18 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 3.51/1.18 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 3.51/1.18 Prover 3: proved (557ms)
% 3.51/1.18
% 3.51/1.18 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.51/1.18
% 3.51/1.19 Prover 11: Preprocessing ...
% 3.51/1.19 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 3.51/1.19 Prover 10: Preprocessing ...
% 3.83/1.20 Prover 7: Preprocessing ...
% 3.83/1.20 Prover 13: Preprocessing ...
% 3.83/1.20 Prover 8: Preprocessing ...
% 3.83/1.20 Prover 10: Constructing countermodel ...
% 3.83/1.21 Prover 7: Constructing countermodel ...
% 3.83/1.22 Prover 13: Constructing countermodel ...
% 3.83/1.23 Prover 4: Found proof (size 14)
% 3.83/1.23 Prover 4: proved (611ms)
% 3.83/1.24 Prover 7: stopped
% 3.83/1.24 Prover 10: stopped
% 3.83/1.24 Prover 1: stopped
% 3.83/1.24 Prover 8: Warning: ignoring some quantifiers
% 3.83/1.24 Prover 11: Constructing countermodel ...
% 3.83/1.24 Prover 8: Constructing countermodel ...
% 3.83/1.24 Prover 13: stopped
% 3.83/1.24 Prover 11: stopped
% 4.13/1.25 Prover 8: stopped
% 4.13/1.25
% 4.13/1.25 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.13/1.25
% 4.13/1.25 % SZS output start Proof for theBenchmark
% 4.13/1.25 Assumptions after simplification:
% 4.13/1.25 ---------------------------------
% 4.13/1.25
% 4.13/1.25 (pel44)
% 4.13/1.28 ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (big_f(v0) = v1) | ~ $i(v0) | ?
% 4.13/1.28 [v2: int] : ( ~ (v2 = 0) & big_j(v0) = v2)) & ! [v0: $i] : ( ~ (big_j(v0) =
% 4.13/1.28 0) | ~ $i(v0) | big_f(v0) = 0)
% 4.13/1.28
% 4.13/1.28 (pel44_1)
% 4.13/1.29 ! [v0: $i] : ( ~ (big_f(v0) = 0) | ~ $i(v0) | ? [v1: $i] : ? [v2: int] : (
% 4.13/1.29 ~ (v2 = 0) & big_g(v1) = 0 & big_h(v0, v1) = v2 & $i(v1))) & ! [v0: $i] :
% 4.13/1.29 ( ~ (big_f(v0) = 0) | ~ $i(v0) | ? [v1: $i] : (big_g(v1) = 0 & big_h(v0, v1)
% 4.13/1.29 = 0 & $i(v1)))
% 4.13/1.29
% 4.13/1.29 (pel44_2)
% 4.13/1.29 ? [v0: $i] : (big_j(v0) = 0 & $i(v0) & ! [v1: $i] : ! [v2: int] : (v2 = 0 |
% 4.13/1.29 ~ (big_h(v0, v1) = v2) | ~ $i(v1) | ? [v3: int] : ( ~ (v3 = 0) &
% 4.13/1.29 big_g(v1) = v3)) & ! [v1: $i] : ( ~ (big_g(v1) = 0) | ~ $i(v1) |
% 4.13/1.29 big_h(v0, v1) = 0))
% 4.13/1.29
% 4.13/1.29 (function-axioms)
% 4.13/1.29 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 4.13/1.29 [v3: $i] : (v1 = v0 | ~ (big_h(v3, v2) = v1) | ~ (big_h(v3, v2) = v0)) & !
% 4.13/1.29 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0
% 4.13/1.29 | ~ (big_j(v2) = v1) | ~ (big_j(v2) = v0)) & ! [v0: MultipleValueBool] :
% 4.13/1.29 ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (big_f(v2) = v1) | ~
% 4.13/1.29 (big_f(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool]
% 4.13/1.29 : ! [v2: $i] : (v1 = v0 | ~ (big_g(v2) = v1) | ~ (big_g(v2) = v0))
% 4.13/1.29
% 4.13/1.29 Those formulas are unsatisfiable:
% 4.13/1.29 ---------------------------------
% 4.13/1.29
% 4.13/1.29 Begin of proof
% 4.13/1.29 |
% 4.13/1.29 | ALPHA: (pel44_1) implies:
% 4.13/1.30 | (1) ! [v0: $i] : ( ~ (big_f(v0) = 0) | ~ $i(v0) | ? [v1: $i] : ? [v2:
% 4.13/1.30 | int] : ( ~ (v2 = 0) & big_g(v1) = 0 & big_h(v0, v1) = v2 & $i(v1)))
% 4.13/1.30 |
% 4.13/1.30 | ALPHA: (pel44) implies:
% 4.13/1.30 | (2) ! [v0: $i] : ( ~ (big_j(v0) = 0) | ~ $i(v0) | big_f(v0) = 0)
% 4.13/1.30 |
% 4.13/1.30 | ALPHA: (function-axioms) implies:
% 4.13/1.30 | (3) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 4.13/1.30 | ! [v3: $i] : (v1 = v0 | ~ (big_h(v3, v2) = v1) | ~ (big_h(v3, v2) =
% 4.13/1.30 | v0))
% 4.13/1.30 |
% 4.13/1.30 | DELTA: instantiating (pel44_2) with fresh symbol all_5_0 gives:
% 4.13/1.30 | (4) big_j(all_5_0) = 0 & $i(all_5_0) & ! [v0: $i] : ! [v1: int] : (v1 = 0
% 4.13/1.30 | | ~ (big_h(all_5_0, v0) = v1) | ~ $i(v0) | ? [v2: int] : ( ~ (v2 =
% 4.13/1.30 | 0) & big_g(v0) = v2)) & ! [v0: $i] : ( ~ (big_g(v0) = 0) | ~
% 4.13/1.30 | $i(v0) | big_h(all_5_0, v0) = 0)
% 4.13/1.30 |
% 4.13/1.30 | ALPHA: (4) implies:
% 4.13/1.30 | (5) $i(all_5_0)
% 4.13/1.30 | (6) big_j(all_5_0) = 0
% 4.13/1.30 | (7) ! [v0: $i] : ( ~ (big_g(v0) = 0) | ~ $i(v0) | big_h(all_5_0, v0) = 0)
% 4.13/1.30 |
% 4.13/1.30 | GROUND_INST: instantiating (2) with all_5_0, simplifying with (5), (6) gives:
% 4.13/1.31 | (8) big_f(all_5_0) = 0
% 4.13/1.31 |
% 4.13/1.31 | GROUND_INST: instantiating (1) with all_5_0, simplifying with (5), (8) gives:
% 4.13/1.31 | (9) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & big_g(v0) = 0 &
% 4.13/1.31 | big_h(all_5_0, v0) = v1 & $i(v0))
% 4.13/1.31 |
% 4.13/1.31 | DELTA: instantiating (9) with fresh symbols all_21_0, all_21_1 gives:
% 4.13/1.31 | (10) ~ (all_21_0 = 0) & big_g(all_21_1) = 0 & big_h(all_5_0, all_21_1) =
% 4.13/1.31 | all_21_0 & $i(all_21_1)
% 4.13/1.31 |
% 4.13/1.31 | ALPHA: (10) implies:
% 4.13/1.31 | (11) ~ (all_21_0 = 0)
% 4.13/1.31 | (12) $i(all_21_1)
% 4.13/1.31 | (13) big_h(all_5_0, all_21_1) = all_21_0
% 4.13/1.31 | (14) big_g(all_21_1) = 0
% 4.13/1.31 |
% 4.13/1.31 | GROUND_INST: instantiating (7) with all_21_1, simplifying with (12), (14)
% 4.13/1.31 | gives:
% 4.13/1.31 | (15) big_h(all_5_0, all_21_1) = 0
% 4.13/1.31 |
% 4.13/1.31 | GROUND_INST: instantiating (3) with all_21_0, 0, all_21_1, all_5_0,
% 4.13/1.31 | simplifying with (13), (15) gives:
% 4.13/1.31 | (16) all_21_0 = 0
% 4.13/1.31 |
% 4.13/1.31 | REDUCE: (11), (16) imply:
% 4.13/1.31 | (17) $false
% 4.13/1.31 |
% 4.13/1.31 | CLOSE: (17) is inconsistent.
% 4.13/1.31 |
% 4.13/1.31 End of proof
% 4.13/1.31 % SZS output end Proof for theBenchmark
% 4.13/1.31
% 4.13/1.31 710ms
%------------------------------------------------------------------------------