TSTP Solution File: SYN058+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SYN058+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 : n022.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 03:26:23 EDT 2023
% Result : Theorem 3.58s 1.19s
% Output : Proof 4.47s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYN058+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 : n022.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 20:57:39 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.60 ________ _____
% 0.19/0.60 ___ __ \_________(_)________________________________
% 0.19/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.19/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.19/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.19/0.60
% 0.19/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.19/0.60 (2023-06-19)
% 0.19/0.60
% 0.19/0.60 (c) Philipp Rümmer, 2009-2023
% 0.19/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.19/0.60 Amanda Stjerna.
% 0.19/0.60 Free software under BSD-3-Clause.
% 0.19/0.60
% 0.19/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.19/0.60
% 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 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 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 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
% 1.98/0.95 Prover 1: Preprocessing ...
% 1.98/0.95 Prover 4: Preprocessing ...
% 1.98/1.00 Prover 3: Preprocessing ...
% 1.98/1.00 Prover 5: Preprocessing ...
% 1.98/1.00 Prover 0: Preprocessing ...
% 1.98/1.00 Prover 2: Preprocessing ...
% 1.98/1.00 Prover 6: Preprocessing ...
% 2.56/1.06 Prover 2: Proving ...
% 2.56/1.07 Prover 5: Proving ...
% 2.56/1.08 Prover 1: Constructing countermodel ...
% 2.56/1.08 Prover 3: Constructing countermodel ...
% 3.03/1.10 Prover 6: Proving ...
% 3.03/1.10 Prover 4: Constructing countermodel ...
% 3.03/1.13 Prover 0: Proving ...
% 3.58/1.19 Prover 3: proved (555ms)
% 3.58/1.19
% 3.58/1.19 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.58/1.19
% 3.58/1.19 Prover 5: proved (551ms)
% 3.58/1.19
% 3.58/1.19 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.58/1.19
% 3.58/1.19 Prover 2: proved (555ms)
% 3.58/1.19
% 3.58/1.19 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.58/1.19
% 3.58/1.19 Prover 0: stopped
% 3.58/1.19 Prover 6: stopped
% 3.58/1.19 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 3.58/1.19 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 3.58/1.19 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 3.58/1.20 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 3.58/1.20 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 3.83/1.21 Prover 8: Preprocessing ...
% 3.83/1.21 Prover 13: Preprocessing ...
% 3.83/1.21 Prover 10: Preprocessing ...
% 3.83/1.22 Prover 11: Preprocessing ...
% 3.83/1.22 Prover 7: Preprocessing ...
% 4.06/1.24 Prover 4: Found proof (size 20)
% 4.06/1.24 Prover 10: Warning: ignoring some quantifiers
% 4.06/1.24 Prover 4: proved (605ms)
% 4.06/1.24 Prover 1: stopped
% 4.06/1.24 Prover 10: Constructing countermodel ...
% 4.06/1.24 Prover 10: stopped
% 4.06/1.24 Prover 13: Warning: ignoring some quantifiers
% 4.06/1.24 Prover 13: Constructing countermodel ...
% 4.06/1.24 Prover 11: stopped
% 4.06/1.24 Prover 13: stopped
% 4.06/1.24 Prover 7: Warning: ignoring some quantifiers
% 4.06/1.24 Prover 7: Constructing countermodel ...
% 4.06/1.25 Prover 7: stopped
% 4.06/1.25 Prover 8: Warning: ignoring some quantifiers
% 4.06/1.25 Prover 8: Constructing countermodel ...
% 4.06/1.26 Prover 8: stopped
% 4.06/1.26
% 4.06/1.26 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.06/1.26
% 4.06/1.26 % SZS output start Proof for theBenchmark
% 4.06/1.26 Assumptions after simplification:
% 4.06/1.26 ---------------------------------
% 4.06/1.26
% 4.06/1.26 (pel28)
% 4.06/1.30 ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & big_g(v0) = v1 & big_f(v0) = 0 &
% 4.06/1.30 big_p(v0) = 0 & $i(v0))
% 4.06/1.30
% 4.06/1.30 (pel28_1)
% 4.06/1.30 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (big_p(v0) = 0) | ~
% 4.06/1.30 (big_q(v1) = v2) | ~ $i(v1) | ~ $i(v0))
% 4.06/1.30
% 4.06/1.30 (pel28_2)
% 4.06/1.30 ? [v0: $i] : ? [v1: int] : ? [v2: int] : ? [v3: $i] : ? [v4: int] : ?
% 4.06/1.30 [v5: int] : ($i(v3) & $i(v0) & ((v2 = 0 & v1 = 0 & big_s(v0) = 0 & big_q(v0) =
% 4.06/1.30 0) | ( ~ (v5 = 0) & ~ (v4 = 0) & big_r(v3) = v5 & big_q(v3) = v4)))
% 4.06/1.30
% 4.06/1.30 (pel28_3)
% 4.06/1.31 ! [v0: $i] : ( ~ (big_s(v0) = 0) | ~ $i(v0)) | ( ! [v0: $i] : ! [v1: int] :
% 4.06/1.31 (v1 = 0 | ~ (big_g(v0) = v1) | ~ $i(v0) | ? [v2: int] : ( ~ (v2 = 0) &
% 4.06/1.31 big_f(v0) = v2)) & ! [v0: $i] : ( ~ (big_f(v0) = 0) | ~ $i(v0) |
% 4.06/1.31 big_g(v0) = 0))
% 4.06/1.31
% 4.06/1.31 (function-axioms)
% 4.06/1.31 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 =
% 4.06/1.31 v0 | ~ (big_g(v2) = v1) | ~ (big_g(v2) = v0)) & ! [v0: MultipleValueBool]
% 4.06/1.31 : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (big_f(v2) = v1) |
% 4.06/1.31 ~ (big_f(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 4.06/1.31 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (big_s(v2) = v1) | ~
% 4.06/1.31 (big_s(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool]
% 4.06/1.31 : ! [v2: $i] : (v1 = v0 | ~ (big_r(v2) = v1) | ~ (big_r(v2) = v0)) & !
% 4.06/1.31 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0
% 4.06/1.31 | ~ (big_p(v2) = v1) | ~ (big_p(v2) = v0)) & ! [v0: MultipleValueBool] :
% 4.06/1.31 ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (big_q(v2) = v1) | ~
% 4.06/1.31 (big_q(v2) = v0))
% 4.06/1.31
% 4.06/1.31 Those formulas are unsatisfiable:
% 4.06/1.31 ---------------------------------
% 4.06/1.31
% 4.06/1.31 Begin of proof
% 4.06/1.32 |
% 4.06/1.32 | ALPHA: (function-axioms) implies:
% 4.06/1.32 | (1) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 4.06/1.32 | (v1 = v0 | ~ (big_g(v2) = v1) | ~ (big_g(v2) = v0))
% 4.06/1.32 |
% 4.06/1.32 | DELTA: instantiating (pel28) with fresh symbols all_4_0, all_4_1 gives:
% 4.06/1.32 | (2) ~ (all_4_0 = 0) & big_g(all_4_1) = all_4_0 & big_f(all_4_1) = 0 &
% 4.06/1.32 | big_p(all_4_1) = 0 & $i(all_4_1)
% 4.06/1.32 |
% 4.06/1.32 | ALPHA: (2) implies:
% 4.06/1.32 | (3) ~ (all_4_0 = 0)
% 4.06/1.32 | (4) $i(all_4_1)
% 4.06/1.32 | (5) big_p(all_4_1) = 0
% 4.06/1.32 | (6) big_f(all_4_1) = 0
% 4.06/1.32 | (7) big_g(all_4_1) = all_4_0
% 4.06/1.32 |
% 4.06/1.32 | DELTA: instantiating (pel28_2) with fresh symbols all_6_0, all_6_1, all_6_2,
% 4.06/1.32 | all_6_3, all_6_4, all_6_5 gives:
% 4.06/1.32 | (8) $i(all_6_2) & $i(all_6_5) & ((all_6_3 = 0 & all_6_4 = 0 &
% 4.06/1.32 | big_s(all_6_5) = 0 & big_q(all_6_5) = 0) | ( ~ (all_6_0 = 0) & ~
% 4.06/1.32 | (all_6_1 = 0) & big_r(all_6_2) = all_6_0 & big_q(all_6_2) =
% 4.06/1.32 | all_6_1))
% 4.06/1.32 |
% 4.06/1.32 | ALPHA: (8) implies:
% 4.06/1.32 | (9) $i(all_6_5)
% 4.06/1.32 | (10) $i(all_6_2)
% 4.06/1.33 | (11) (all_6_3 = 0 & all_6_4 = 0 & big_s(all_6_5) = 0 & big_q(all_6_5) = 0)
% 4.06/1.33 | | ( ~ (all_6_0 = 0) & ~ (all_6_1 = 0) & big_r(all_6_2) = all_6_0 &
% 4.06/1.33 | big_q(all_6_2) = all_6_1)
% 4.06/1.33 |
% 4.06/1.33 | BETA: splitting (pel28_3) gives:
% 4.06/1.33 |
% 4.06/1.33 | Case 1:
% 4.06/1.33 | |
% 4.06/1.33 | | (12) ! [v0: $i] : ( ~ (big_s(v0) = 0) | ~ $i(v0))
% 4.06/1.33 | |
% 4.06/1.33 | | BETA: splitting (11) gives:
% 4.06/1.33 | |
% 4.06/1.33 | | Case 1:
% 4.06/1.33 | | |
% 4.47/1.33 | | | (13) all_6_3 = 0 & all_6_4 = 0 & big_s(all_6_5) = 0 & big_q(all_6_5) =
% 4.47/1.33 | | | 0
% 4.47/1.33 | | |
% 4.47/1.33 | | | ALPHA: (13) implies:
% 4.47/1.33 | | | (14) big_s(all_6_5) = 0
% 4.47/1.33 | | |
% 4.47/1.33 | | | GROUND_INST: instantiating (12) with all_6_5, simplifying with (9), (14)
% 4.47/1.33 | | | gives:
% 4.47/1.33 | | | (15) $false
% 4.47/1.33 | | |
% 4.47/1.33 | | | CLOSE: (15) is inconsistent.
% 4.47/1.33 | | |
% 4.47/1.33 | | Case 2:
% 4.47/1.33 | | |
% 4.47/1.33 | | | (16) ~ (all_6_0 = 0) & ~ (all_6_1 = 0) & big_r(all_6_2) = all_6_0 &
% 4.47/1.33 | | | big_q(all_6_2) = all_6_1
% 4.47/1.33 | | |
% 4.47/1.33 | | | ALPHA: (16) implies:
% 4.47/1.33 | | | (17) ~ (all_6_1 = 0)
% 4.47/1.33 | | | (18) big_q(all_6_2) = all_6_1
% 4.47/1.33 | | |
% 4.47/1.33 | | | GROUND_INST: instantiating (pel28_1) with all_4_1, all_6_2, all_6_1,
% 4.47/1.33 | | | simplifying with (4), (5), (10), (18) gives:
% 4.47/1.33 | | | (19) all_6_1 = 0
% 4.47/1.33 | | |
% 4.47/1.33 | | | REDUCE: (17), (19) imply:
% 4.47/1.33 | | | (20) $false
% 4.47/1.33 | | |
% 4.47/1.33 | | | CLOSE: (20) is inconsistent.
% 4.47/1.33 | | |
% 4.47/1.33 | | End of split
% 4.47/1.33 | |
% 4.47/1.33 | Case 2:
% 4.47/1.33 | |
% 4.47/1.34 | | (21) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (big_g(v0) = v1) | ~
% 4.47/1.34 | | $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & big_f(v0) = v2)) & ! [v0:
% 4.47/1.34 | | $i] : ( ~ (big_f(v0) = 0) | ~ $i(v0) | big_g(v0) = 0)
% 4.47/1.34 | |
% 4.47/1.34 | | ALPHA: (21) implies:
% 4.47/1.34 | | (22) ! [v0: $i] : ( ~ (big_f(v0) = 0) | ~ $i(v0) | big_g(v0) = 0)
% 4.47/1.34 | |
% 4.47/1.34 | | GROUND_INST: instantiating (22) with all_4_1, simplifying with (4), (6)
% 4.47/1.34 | | gives:
% 4.47/1.34 | | (23) big_g(all_4_1) = 0
% 4.47/1.34 | |
% 4.47/1.34 | | GROUND_INST: instantiating (1) with all_4_0, 0, all_4_1, simplifying with
% 4.47/1.34 | | (7), (23) gives:
% 4.47/1.34 | | (24) all_4_0 = 0
% 4.47/1.34 | |
% 4.47/1.34 | | REDUCE: (3), (24) imply:
% 4.47/1.34 | | (25) $false
% 4.47/1.34 | |
% 4.47/1.34 | | CLOSE: (25) is inconsistent.
% 4.47/1.34 | |
% 4.47/1.34 | End of split
% 4.47/1.34 |
% 4.47/1.34 End of proof
% 4.47/1.34 % SZS output end Proof for theBenchmark
% 4.47/1.34
% 4.47/1.34 734ms
%------------------------------------------------------------------------------