TSTP Solution File: SYN924+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SYN924+1 : TPTP v8.1.2. Released v3.1.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n007.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 03:29:14 EDT 2023
% Result : Theorem 3.22s 1.19s
% Output : Proof 3.81s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SYN924+1 : TPTP v8.1.2. Released v3.1.0.
% 0.07/0.14 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.14/0.35 % Computer : n007.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 17:18:26 EDT 2023
% 0.14/0.35 % 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 ...
% 0.21/0.63 Running up to 7 provers in parallel.
% 0.21/0.65 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.21/0.65 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.21/0.65 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.21/0.65 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.21/0.65 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.21/0.65 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.21/0.65 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 1.97/1.00 Prover 1: Preprocessing ...
% 1.97/1.00 Prover 4: Preprocessing ...
% 1.97/1.04 Prover 6: Preprocessing ...
% 1.97/1.04 Prover 2: Preprocessing ...
% 1.97/1.04 Prover 3: Preprocessing ...
% 1.97/1.04 Prover 5: Preprocessing ...
% 1.97/1.04 Prover 0: Preprocessing ...
% 2.71/1.10 Prover 2: Constructing countermodel ...
% 2.71/1.10 Prover 5: Constructing countermodel ...
% 2.71/1.10 Prover 1: Constructing countermodel ...
% 2.71/1.10 Prover 4: Constructing countermodel ...
% 2.71/1.10 Prover 3: Constructing countermodel ...
% 2.71/1.11 Prover 0: Proving ...
% 2.71/1.11 Prover 6: Proving ...
% 3.22/1.19 Prover 2: proved (547ms)
% 3.22/1.19
% 3.22/1.19 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.22/1.19
% 3.22/1.19 Prover 5: proved (542ms)
% 3.22/1.19
% 3.22/1.19 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.22/1.19
% 3.22/1.19 Prover 3: stopped
% 3.22/1.19 Prover 0: stopped
% 3.22/1.19 Prover 6: stopped
% 3.22/1.22 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 3.22/1.22 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 3.22/1.22 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 3.22/1.22 Prover 8: Preprocessing ...
% 3.22/1.22 Prover 10: Preprocessing ...
% 3.22/1.22 Prover 7: Preprocessing ...
% 3.22/1.22 Prover 10: Constructing countermodel ...
% 3.22/1.22 Prover 7: Constructing countermodel ...
% 3.22/1.22 Prover 1: Found proof (size 20)
% 3.22/1.22 Prover 1: proved (575ms)
% 3.22/1.22 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 3.22/1.22 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 3.22/1.22 Prover 7: stopped
% 3.22/1.22 Prover 10: stopped
% 3.22/1.22 Prover 4: Found proof (size 18)
% 3.22/1.22 Prover 4: proved (576ms)
% 3.22/1.22 Prover 8: Warning: ignoring some quantifiers
% 3.22/1.22 Prover 11: Preprocessing ...
% 3.22/1.22 Prover 13: Preprocessing ...
% 3.22/1.23 Prover 8: Constructing countermodel ...
% 3.22/1.23 Prover 8: stopped
% 3.22/1.23 Prover 13: Constructing countermodel ...
% 3.22/1.23 Prover 13: stopped
% 3.22/1.25 Prover 11: Constructing countermodel ...
% 3.22/1.25 Prover 11: stopped
% 3.22/1.25
% 3.22/1.25 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.22/1.25
% 3.22/1.26 % SZS output start Proof for theBenchmark
% 3.22/1.26 Assumptions after simplification:
% 3.22/1.26 ---------------------------------
% 3.22/1.26
% 3.22/1.26 (prove_this)
% 3.81/1.30 ! [v0: $i] : ( ~ (p(v0) = 0) | ~ $i(v0)) & ! [v0: $i] : ( ~ (q(v0) = 0) |
% 3.81/1.30 ~ $i(v0)) & ( ? [v0: $i] : ? [v1: any] : ? [v2: any] : (p(v0) = v1 & q(v0)
% 3.81/1.30 = v2 & $i(v0) & (v2 = 0 | v1 = 0)) | ? [v0: $i] : (p(v0) = 0 & $i(v0)) |
% 3.81/1.30 ? [v0: $i] : (q(v0) = 0 & $i(v0)))
% 3.81/1.30
% 3.81/1.30 Those formulas are unsatisfiable:
% 3.81/1.30 ---------------------------------
% 3.81/1.30
% 3.81/1.30 Begin of proof
% 3.81/1.30 |
% 3.81/1.30 | ALPHA: (prove_this) implies:
% 3.81/1.30 | (1) ? [v0: $i] : ? [v1: any] : ? [v2: any] : (p(v0) = v1 & q(v0) = v2 &
% 3.81/1.30 | $i(v0) & (v2 = 0 | v1 = 0)) | ? [v0: $i] : (p(v0) = 0 & $i(v0)) | ?
% 3.81/1.30 | [v0: $i] : (q(v0) = 0 & $i(v0))
% 3.81/1.30 | (2) ! [v0: $i] : ( ~ (q(v0) = 0) | ~ $i(v0))
% 3.81/1.30 | (3) ! [v0: $i] : ( ~ (p(v0) = 0) | ~ $i(v0))
% 3.81/1.30 |
% 3.81/1.30 | BETA: splitting (1) gives:
% 3.81/1.30 |
% 3.81/1.30 | Case 1:
% 3.81/1.30 | |
% 3.81/1.30 | | (4) ? [v0: $i] : ? [v1: any] : ? [v2: any] : (p(v0) = v1 & q(v0) = v2
% 3.81/1.30 | | & $i(v0) & (v2 = 0 | v1 = 0))
% 3.81/1.30 | |
% 3.81/1.30 | | DELTA: instantiating (4) with fresh symbols all_10_0, all_10_1, all_10_2
% 3.81/1.30 | | gives:
% 3.81/1.31 | | (5) p(all_10_2) = all_10_1 & q(all_10_2) = all_10_0 & $i(all_10_2) &
% 3.81/1.31 | | (all_10_0 = 0 | all_10_1 = 0)
% 3.81/1.31 | |
% 3.81/1.31 | | ALPHA: (5) implies:
% 3.81/1.31 | | (6) $i(all_10_2)
% 3.81/1.31 | | (7) q(all_10_2) = all_10_0
% 3.81/1.31 | | (8) p(all_10_2) = all_10_1
% 3.81/1.31 | | (9) all_10_0 = 0 | all_10_1 = 0
% 3.81/1.31 | |
% 3.81/1.31 | | BETA: splitting (9) gives:
% 3.81/1.31 | |
% 3.81/1.31 | | Case 1:
% 3.81/1.31 | | |
% 3.81/1.31 | | | (10) all_10_0 = 0
% 3.81/1.31 | | |
% 3.81/1.31 | | | REDUCE: (7), (10) imply:
% 3.81/1.31 | | | (11) q(all_10_2) = 0
% 3.81/1.31 | | |
% 3.81/1.31 | | | GROUND_INST: instantiating (2) with all_10_2, simplifying with (6), (11)
% 3.81/1.31 | | | gives:
% 3.81/1.31 | | | (12) $false
% 3.81/1.31 | | |
% 3.81/1.31 | | | CLOSE: (12) is inconsistent.
% 3.81/1.31 | | |
% 3.81/1.31 | | Case 2:
% 3.81/1.31 | | |
% 3.81/1.31 | | | (13) all_10_1 = 0
% 3.81/1.31 | | |
% 3.81/1.31 | | | REDUCE: (8), (13) imply:
% 3.81/1.31 | | | (14) p(all_10_2) = 0
% 3.81/1.31 | | |
% 3.81/1.31 | | | GROUND_INST: instantiating (3) with all_10_2, simplifying with (6), (14)
% 3.81/1.31 | | | gives:
% 3.81/1.31 | | | (15) $false
% 3.81/1.31 | | |
% 3.81/1.31 | | | CLOSE: (15) is inconsistent.
% 3.81/1.31 | | |
% 3.81/1.31 | | End of split
% 3.81/1.31 | |
% 3.81/1.31 | Case 2:
% 3.81/1.31 | |
% 3.81/1.31 | | (16) ? [v0: $i] : (p(v0) = 0 & $i(v0)) | ? [v0: $i] : (q(v0) = 0 &
% 3.81/1.31 | | $i(v0))
% 3.81/1.31 | |
% 3.81/1.31 | | BETA: splitting (16) gives:
% 3.81/1.31 | |
% 3.81/1.31 | | Case 1:
% 3.81/1.31 | | |
% 3.81/1.31 | | | (17) ? [v0: $i] : (p(v0) = 0 & $i(v0))
% 3.81/1.31 | | |
% 3.81/1.31 | | | DELTA: instantiating (17) with fresh symbol all_10_0 gives:
% 3.81/1.32 | | | (18) p(all_10_0) = 0 & $i(all_10_0)
% 3.81/1.32 | | |
% 3.81/1.32 | | | ALPHA: (18) implies:
% 3.81/1.32 | | | (19) $i(all_10_0)
% 3.81/1.32 | | | (20) p(all_10_0) = 0
% 3.81/1.32 | | |
% 3.81/1.32 | | | GROUND_INST: instantiating (3) with all_10_0, simplifying with (19), (20)
% 3.81/1.32 | | | gives:
% 3.81/1.32 | | | (21) $false
% 3.81/1.32 | | |
% 3.81/1.32 | | | CLOSE: (21) is inconsistent.
% 3.81/1.32 | | |
% 3.81/1.32 | | Case 2:
% 3.81/1.32 | | |
% 3.81/1.32 | | | (22) ? [v0: $i] : (q(v0) = 0 & $i(v0))
% 3.81/1.32 | | |
% 3.81/1.32 | | | DELTA: instantiating (22) with fresh symbol all_10_0 gives:
% 3.81/1.32 | | | (23) q(all_10_0) = 0 & $i(all_10_0)
% 3.81/1.32 | | |
% 3.81/1.32 | | | ALPHA: (23) implies:
% 3.81/1.32 | | | (24) $i(all_10_0)
% 3.81/1.32 | | | (25) q(all_10_0) = 0
% 3.81/1.32 | | |
% 3.81/1.32 | | | GROUND_INST: instantiating (2) with all_10_0, simplifying with (24), (25)
% 3.81/1.32 | | | gives:
% 3.81/1.32 | | | (26) $false
% 3.81/1.32 | | |
% 3.81/1.32 | | | CLOSE: (26) is inconsistent.
% 3.81/1.32 | | |
% 3.81/1.32 | | End of split
% 3.81/1.32 | |
% 3.81/1.32 | End of split
% 3.81/1.32 |
% 3.81/1.32 End of proof
% 3.81/1.32 % SZS output end Proof for theBenchmark
% 3.81/1.32
% 3.81/1.32 706ms
%------------------------------------------------------------------------------