TSTP Solution File: SYN060+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SYN060+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 : n018.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 2.94s 1.15s
% Output : Proof 4.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYN060+1 : TPTP v8.1.2. Released v2.0.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.17/0.34 % Computer : n018.cluster.edu
% 0.17/0.34 % Model : x86_64 x86_64
% 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.34 % Memory : 8042.1875MB
% 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.34 % CPULimit : 300
% 0.17/0.34 % WCLimit : 300
% 0.17/0.34 % DateTime : Sat Aug 26 21:24:00 EDT 2023
% 0.17/0.34 % 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 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 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 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
% 1.84/0.94 Prover 4: Preprocessing ...
% 1.84/0.94 Prover 1: Preprocessing ...
% 1.84/0.98 Prover 2: Preprocessing ...
% 1.84/0.98 Prover 0: Preprocessing ...
% 1.84/0.98 Prover 6: Preprocessing ...
% 1.84/0.98 Prover 5: Preprocessing ...
% 1.84/0.98 Prover 3: Preprocessing ...
% 2.36/1.05 Prover 2: Proving ...
% 2.36/1.05 Prover 3: Constructing countermodel ...
% 2.36/1.06 Prover 5: Proving ...
% 2.36/1.06 Prover 1: Constructing countermodel ...
% 2.36/1.06 Prover 6: Constructing countermodel ...
% 2.94/1.09 Prover 4: Constructing countermodel ...
% 2.94/1.10 Prover 0: Proving ...
% 2.94/1.15 Prover 3: proved (510ms)
% 2.94/1.15 Prover 6: proved (508ms)
% 2.94/1.15
% 2.94/1.15 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.94/1.15
% 2.94/1.16
% 2.94/1.16 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.94/1.16
% 2.94/1.16 Prover 0: stopped
% 2.94/1.16 Prover 5: stopped
% 2.94/1.17 Prover 2: stopped
% 2.94/1.17 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 2.94/1.17 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 2.94/1.17 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 2.94/1.17 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 2.94/1.17 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 3.59/1.18 Prover 10: Preprocessing ...
% 3.59/1.19 Prover 7: Preprocessing ...
% 3.59/1.19 Prover 11: Preprocessing ...
% 3.59/1.19 Prover 13: Preprocessing ...
% 3.68/1.20 Prover 8: Preprocessing ...
% 3.68/1.20 Prover 7: Warning: ignoring some quantifiers
% 3.68/1.21 Prover 7: Constructing countermodel ...
% 3.68/1.21 Prover 13: Warning: ignoring some quantifiers
% 3.68/1.21 Prover 13: Constructing countermodel ...
% 3.79/1.21 Prover 10: Warning: ignoring some quantifiers
% 3.80/1.21 Prover 10: Constructing countermodel ...
% 3.80/1.23 Prover 8: Warning: ignoring some quantifiers
% 3.80/1.23 Prover 1: Found proof (size 19)
% 3.80/1.23 Prover 1: proved (604ms)
% 3.80/1.23 Prover 7: stopped
% 3.80/1.23 Prover 4: stopped
% 3.80/1.24 Prover 10: stopped
% 3.80/1.24 Prover 8: Constructing countermodel ...
% 3.80/1.24 Prover 13: stopped
% 3.80/1.24 Prover 8: stopped
% 3.80/1.27 Prover 11: Constructing countermodel ...
% 3.80/1.28 Prover 11: stopped
% 3.80/1.28
% 3.80/1.28 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.80/1.28
% 3.80/1.28 % SZS output start Proof for theBenchmark
% 3.80/1.29 Assumptions after simplification:
% 3.80/1.29 ---------------------------------
% 3.80/1.29
% 3.80/1.29 (pel30)
% 4.22/1.32 ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & big_i(v0) = v1 & $i(v0))
% 4.22/1.32
% 4.22/1.32 (pel30_1)
% 4.22/1.32 ! [v0: $i] : ( ~ (big_h(v0) = 0) | ~ $i(v0) | ? [v1: int] : ? [v2: int] :
% 4.22/1.32 ( ~ (v2 = 0) & ~ (v1 = 0) & big_f(v0) = v1 & big_g(v0) = v2))
% 4.22/1.32
% 4.22/1.32 (pel30_2)
% 4.22/1.32 ! [v0: $i] : ! [v1: any] : ( ~ (big_i(v0) = v1) | ~ $i(v0) | ? [v2: any] :
% 4.22/1.32 ? [v3: any] : ? [v4: any] : (big_h(v0) = v4 & big_f(v0) = v3 & big_g(v0) =
% 4.22/1.32 v2 & ((v4 = 0 & v3 = 0) | (v2 = 0 & v1 = 0))))
% 4.22/1.32
% 4.22/1.32 (function-axioms)
% 4.22/1.33 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 =
% 4.22/1.33 v0 | ~ (big_i(v2) = v1) | ~ (big_i(v2) = v0)) & ! [v0: MultipleValueBool]
% 4.22/1.33 : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (big_h(v2) = v1) |
% 4.22/1.33 ~ (big_h(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 4.22/1.33 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (big_f(v2) = v1) | ~
% 4.22/1.33 (big_f(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool]
% 4.22/1.33 : ! [v2: $i] : (v1 = v0 | ~ (big_g(v2) = v1) | ~ (big_g(v2) = v0))
% 4.22/1.33
% 4.22/1.33 Those formulas are unsatisfiable:
% 4.22/1.33 ---------------------------------
% 4.22/1.33
% 4.22/1.33 Begin of proof
% 4.22/1.33 |
% 4.22/1.33 | ALPHA: (function-axioms) implies:
% 4.22/1.33 | (1) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 4.22/1.33 | (v1 = v0 | ~ (big_f(v2) = v1) | ~ (big_f(v2) = v0))
% 4.22/1.33 |
% 4.22/1.33 | DELTA: instantiating (pel30) with fresh symbols all_5_0, all_5_1 gives:
% 4.22/1.33 | (2) ~ (all_5_0 = 0) & big_i(all_5_1) = all_5_0 & $i(all_5_1)
% 4.22/1.33 |
% 4.22/1.33 | ALPHA: (2) implies:
% 4.22/1.33 | (3) ~ (all_5_0 = 0)
% 4.22/1.33 | (4) $i(all_5_1)
% 4.22/1.33 | (5) big_i(all_5_1) = all_5_0
% 4.22/1.33 |
% 4.22/1.33 | GROUND_INST: instantiating (pel30_2) with all_5_1, all_5_0, simplifying with
% 4.22/1.33 | (4), (5) gives:
% 4.22/1.34 | (6) ? [v0: any] : ? [v1: any] : ? [v2: any] : (big_h(all_5_1) = v2 &
% 4.22/1.34 | big_f(all_5_1) = v1 & big_g(all_5_1) = v0 & ((v2 = 0 & v1 = 0) | (v0
% 4.22/1.34 | = 0 & all_5_0 = 0)))
% 4.22/1.34 |
% 4.22/1.34 | DELTA: instantiating (6) with fresh symbols all_12_0, all_12_1, all_12_2
% 4.22/1.34 | gives:
% 4.22/1.34 | (7) big_h(all_5_1) = all_12_0 & big_f(all_5_1) = all_12_1 & big_g(all_5_1)
% 4.22/1.34 | = all_12_2 & ((all_12_0 = 0 & all_12_1 = 0) | (all_12_2 = 0 & all_5_0 =
% 4.22/1.34 | 0))
% 4.22/1.34 |
% 4.22/1.34 | ALPHA: (7) implies:
% 4.22/1.34 | (8) big_f(all_5_1) = all_12_1
% 4.22/1.34 | (9) big_h(all_5_1) = all_12_0
% 4.22/1.34 | (10) (all_12_0 = 0 & all_12_1 = 0) | (all_12_2 = 0 & all_5_0 = 0)
% 4.22/1.34 |
% 4.22/1.34 | BETA: splitting (10) gives:
% 4.22/1.34 |
% 4.22/1.34 | Case 1:
% 4.22/1.34 | |
% 4.22/1.34 | | (11) all_12_0 = 0 & all_12_1 = 0
% 4.22/1.34 | |
% 4.22/1.34 | | ALPHA: (11) implies:
% 4.22/1.34 | | (12) all_12_1 = 0
% 4.22/1.34 | | (13) all_12_0 = 0
% 4.22/1.34 | |
% 4.22/1.34 | | REDUCE: (9), (13) imply:
% 4.22/1.34 | | (14) big_h(all_5_1) = 0
% 4.22/1.34 | |
% 4.22/1.34 | | REDUCE: (8), (12) imply:
% 4.22/1.34 | | (15) big_f(all_5_1) = 0
% 4.22/1.34 | |
% 4.22/1.34 | | GROUND_INST: instantiating (pel30_1) with all_5_1, simplifying with (4),
% 4.22/1.34 | | (14) gives:
% 4.22/1.34 | | (16) ? [v0: int] : ? [v1: int] : ( ~ (v1 = 0) & ~ (v0 = 0) &
% 4.22/1.34 | | big_f(all_5_1) = v0 & big_g(all_5_1) = v1)
% 4.22/1.34 | |
% 4.22/1.34 | | DELTA: instantiating (16) with fresh symbols all_23_0, all_23_1 gives:
% 4.22/1.34 | | (17) ~ (all_23_0 = 0) & ~ (all_23_1 = 0) & big_f(all_5_1) = all_23_1 &
% 4.22/1.34 | | big_g(all_5_1) = all_23_0
% 4.22/1.34 | |
% 4.22/1.34 | | ALPHA: (17) implies:
% 4.22/1.34 | | (18) ~ (all_23_1 = 0)
% 4.22/1.34 | | (19) big_f(all_5_1) = all_23_1
% 4.22/1.34 | |
% 4.22/1.34 | | GROUND_INST: instantiating (1) with 0, all_23_1, all_5_1, simplifying with
% 4.22/1.34 | | (15), (19) gives:
% 4.22/1.34 | | (20) all_23_1 = 0
% 4.22/1.34 | |
% 4.22/1.34 | | REDUCE: (18), (20) imply:
% 4.22/1.34 | | (21) $false
% 4.22/1.34 | |
% 4.22/1.34 | | CLOSE: (21) is inconsistent.
% 4.22/1.34 | |
% 4.22/1.35 | Case 2:
% 4.22/1.35 | |
% 4.22/1.35 | | (22) all_12_2 = 0 & all_5_0 = 0
% 4.22/1.35 | |
% 4.22/1.35 | | ALPHA: (22) implies:
% 4.22/1.35 | | (23) all_5_0 = 0
% 4.22/1.35 | |
% 4.22/1.35 | | REDUCE: (3), (23) imply:
% 4.22/1.35 | | (24) $false
% 4.22/1.35 | |
% 4.22/1.35 | | CLOSE: (24) is inconsistent.
% 4.22/1.35 | |
% 4.22/1.35 | End of split
% 4.22/1.35 |
% 4.22/1.35 End of proof
% 4.22/1.35 % SZS output end Proof for theBenchmark
% 4.22/1.35
% 4.22/1.35 734ms
%------------------------------------------------------------------------------