TSTP Solution File: SYN317+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SYN317+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 : n016.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 03:27:07 EDT 2023
% Result : Theorem 3.31s 1.21s
% Output : Proof 4.07s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYN317+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 : n016.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 21:26:42 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.20/0.61 ________ _____
% 0.20/0.61 ___ __ \_________(_)________________________________
% 0.20/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.20/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.20/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.20/0.61
% 0.20/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.20/0.61 (2023-06-19)
% 0.20/0.61
% 0.20/0.61 (c) Philipp Rümmer, 2009-2023
% 0.20/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.20/0.61 Amanda Stjerna.
% 0.20/0.61 Free software under BSD-3-Clause.
% 0.20/0.61
% 0.20/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.20/0.61
% 0.20/0.61 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.20/0.63 Running up to 7 provers in parallel.
% 0.20/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.20/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.20/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.20/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.20/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.20/0.65 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.20/0.65 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 1.89/0.99 Prover 1: Preprocessing ...
% 1.89/0.99 Prover 4: Preprocessing ...
% 2.19/1.04 Prover 3: Preprocessing ...
% 2.19/1.04 Prover 2: Preprocessing ...
% 2.19/1.04 Prover 5: Preprocessing ...
% 2.19/1.04 Prover 0: Preprocessing ...
% 2.19/1.04 Prover 6: Preprocessing ...
% 2.38/1.10 Prover 2: Proving ...
% 2.38/1.10 Prover 5: Proving ...
% 2.38/1.10 Prover 4: Constructing countermodel ...
% 2.38/1.10 Prover 0: Proving ...
% 2.38/1.10 Prover 1: Warning: ignoring some quantifiers
% 2.38/1.10 Prover 6: Proving ...
% 2.38/1.10 Prover 3: Warning: ignoring some quantifiers
% 2.38/1.10 Prover 1: Constructing countermodel ...
% 2.38/1.11 Prover 3: Constructing countermodel ...
% 3.31/1.21 Prover 0: proved (574ms)
% 3.31/1.21
% 3.31/1.21 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.31/1.21
% 3.31/1.21 Prover 3: stopped
% 3.31/1.21 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 3.31/1.21 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 3.31/1.22 Prover 2: stopped
% 3.31/1.22 Prover 5: stopped
% 3.31/1.22 Prover 6: stopped
% 3.31/1.22 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 3.31/1.22 Prover 7: Preprocessing ...
% 3.31/1.22 Prover 8: Preprocessing ...
% 3.31/1.22 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 3.31/1.22 Prover 10: Preprocessing ...
% 3.31/1.23 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 3.31/1.23 Prover 13: Preprocessing ...
% 3.31/1.23 Prover 11: Preprocessing ...
% 3.31/1.24 Prover 4: Found proof (size 19)
% 3.31/1.24 Prover 4: proved (598ms)
% 3.31/1.24 Prover 1: stopped
% 3.31/1.24 Prover 7: Warning: ignoring some quantifiers
% 3.31/1.24 Prover 10: Warning: ignoring some quantifiers
% 3.31/1.24 Prover 7: Constructing countermodel ...
% 3.79/1.24 Prover 10: Constructing countermodel ...
% 3.79/1.25 Prover 7: stopped
% 3.79/1.25 Prover 10: stopped
% 3.79/1.25 Prover 13: Warning: ignoring some quantifiers
% 3.79/1.25 Prover 13: Constructing countermodel ...
% 3.79/1.25 Prover 13: stopped
% 3.79/1.25 Prover 8: Warning: ignoring some quantifiers
% 3.79/1.25 Prover 8: Constructing countermodel ...
% 3.79/1.25 Prover 8: stopped
% 3.88/1.27 Prover 11: Constructing countermodel ...
% 3.88/1.27 Prover 11: stopped
% 3.88/1.27
% 3.88/1.27 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.88/1.27
% 3.88/1.27 % SZS output start Proof for theBenchmark
% 3.88/1.28 Assumptions after simplification:
% 3.88/1.28 ---------------------------------
% 3.88/1.28
% 3.88/1.28 (church_46_2_3)
% 3.88/1.31 ? [v0: $i] : ? [v1: $i] : ? [v2: any] : ? [v3: any] : ? [v4: $i] : ?
% 3.88/1.31 [v5: any] : ? [v6: any] : ($i(v4) & $i(v1) & $i(v0) & ((big_f(v4) = v5 &
% 3.88/1.31 big_g(v4) = v6 & ! [v7: $i] : ! [v8: int] : (v8 = 0 | ~ (big_f(v7) =
% 3.88/1.31 v8) | ~ $i(v7)) & ! [v7: $i] : ( ~ (big_g(v7) = 0) | ~ $i(v7)) &
% 3.88/1.31 ( ~ (v5 = 0) | v6 = 0)) | (big_f(v0) = v2 & big_g(v1) = v3 & ! [v7: $i]
% 3.88/1.31 : ! [v8: int] : (v8 = 0 | ~ (big_f(v7) = v8) | ~ $i(v7)) & ! [v7:
% 3.88/1.31 $i] : ( ~ (big_g(v7) = 0) | ~ $i(v7)) & ( ~ (v2 = 0) | v3 = 0))))
% 3.88/1.31
% 3.88/1.31 Those formulas are unsatisfiable:
% 3.88/1.31 ---------------------------------
% 3.88/1.31
% 3.88/1.31 Begin of proof
% 3.88/1.31 |
% 3.88/1.31 | DELTA: instantiating (church_46_2_3) with fresh symbols all_3_0, all_3_1,
% 3.88/1.31 | all_3_2, all_3_3, all_3_4, all_3_5, all_3_6 gives:
% 4.07/1.32 | (1) $i(all_3_2) & $i(all_3_5) & $i(all_3_6) & ((big_f(all_3_2) = all_3_1 &
% 4.07/1.32 | big_g(all_3_2) = all_3_0 & ! [v0: $i] : ! [v1: int] : (v1 = 0 |
% 4.07/1.32 | ~ (big_f(v0) = v1) | ~ $i(v0)) & ! [v0: $i] : ( ~ (big_g(v0) =
% 4.07/1.32 | 0) | ~ $i(v0)) & ( ~ (all_3_1 = 0) | all_3_0 = 0)) |
% 4.07/1.32 | (big_f(all_3_6) = all_3_4 & big_g(all_3_5) = all_3_3 & ! [v0: $i] :
% 4.07/1.32 | ! [v1: int] : (v1 = 0 | ~ (big_f(v0) = v1) | ~ $i(v0)) & ! [v0:
% 4.07/1.32 | $i] : ( ~ (big_g(v0) = 0) | ~ $i(v0)) & ( ~ (all_3_4 = 0) |
% 4.07/1.32 | all_3_3 = 0)))
% 4.07/1.32 |
% 4.07/1.32 | ALPHA: (1) implies:
% 4.07/1.32 | (2) $i(all_3_6)
% 4.07/1.32 | (3) $i(all_3_5)
% 4.07/1.32 | (4) $i(all_3_2)
% 4.07/1.32 | (5) (big_f(all_3_2) = all_3_1 & big_g(all_3_2) = all_3_0 & ! [v0: $i] : !
% 4.07/1.32 | [v1: int] : (v1 = 0 | ~ (big_f(v0) = v1) | ~ $i(v0)) & ! [v0: $i]
% 4.07/1.32 | : ( ~ (big_g(v0) = 0) | ~ $i(v0)) & ( ~ (all_3_1 = 0) | all_3_0 =
% 4.07/1.32 | 0)) | (big_f(all_3_6) = all_3_4 & big_g(all_3_5) = all_3_3 & !
% 4.07/1.32 | [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (big_f(v0) = v1) | ~ $i(v0))
% 4.07/1.32 | & ! [v0: $i] : ( ~ (big_g(v0) = 0) | ~ $i(v0)) & ( ~ (all_3_4 = 0)
% 4.07/1.32 | | all_3_3 = 0))
% 4.07/1.32 |
% 4.07/1.32 | BETA: splitting (5) gives:
% 4.07/1.32 |
% 4.07/1.32 | Case 1:
% 4.07/1.32 | |
% 4.07/1.32 | | (6) big_f(all_3_2) = all_3_1 & big_g(all_3_2) = all_3_0 & ! [v0: $i] :
% 4.07/1.32 | | ! [v1: int] : (v1 = 0 | ~ (big_f(v0) = v1) | ~ $i(v0)) & ! [v0:
% 4.07/1.32 | | $i] : ( ~ (big_g(v0) = 0) | ~ $i(v0)) & ( ~ (all_3_1 = 0) |
% 4.07/1.32 | | all_3_0 = 0)
% 4.07/1.33 | |
% 4.07/1.33 | | ALPHA: (6) implies:
% 4.07/1.33 | | (7) big_g(all_3_2) = all_3_0
% 4.07/1.33 | | (8) big_f(all_3_2) = all_3_1
% 4.07/1.33 | | (9) ~ (all_3_1 = 0) | all_3_0 = 0
% 4.07/1.33 | | (10) ! [v0: $i] : ( ~ (big_g(v0) = 0) | ~ $i(v0))
% 4.07/1.33 | | (11) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (big_f(v0) = v1) | ~
% 4.07/1.33 | | $i(v0))
% 4.07/1.33 | |
% 4.07/1.33 | | GROUND_INST: instantiating (11) with all_3_2, all_3_1, simplifying with (4),
% 4.07/1.33 | | (8) gives:
% 4.07/1.33 | | (12) all_3_1 = 0
% 4.07/1.33 | |
% 4.07/1.33 | | BETA: splitting (9) gives:
% 4.07/1.33 | |
% 4.07/1.33 | | Case 1:
% 4.07/1.33 | | |
% 4.07/1.33 | | | (13) ~ (all_3_1 = 0)
% 4.07/1.33 | | |
% 4.07/1.33 | | | REDUCE: (12), (13) imply:
% 4.07/1.33 | | | (14) $false
% 4.07/1.33 | | |
% 4.07/1.33 | | | CLOSE: (14) is inconsistent.
% 4.07/1.33 | | |
% 4.07/1.33 | | Case 2:
% 4.07/1.33 | | |
% 4.07/1.33 | | | (15) all_3_0 = 0
% 4.07/1.33 | | |
% 4.07/1.33 | | | REDUCE: (7), (15) imply:
% 4.07/1.33 | | | (16) big_g(all_3_2) = 0
% 4.07/1.33 | | |
% 4.07/1.33 | | | GROUND_INST: instantiating (10) with all_3_2, simplifying with (4), (16)
% 4.07/1.33 | | | gives:
% 4.07/1.33 | | | (17) $false
% 4.07/1.33 | | |
% 4.07/1.33 | | | CLOSE: (17) is inconsistent.
% 4.07/1.33 | | |
% 4.07/1.33 | | End of split
% 4.07/1.33 | |
% 4.07/1.33 | Case 2:
% 4.07/1.33 | |
% 4.07/1.33 | | (18) big_f(all_3_6) = all_3_4 & big_g(all_3_5) = all_3_3 & ! [v0: $i] :
% 4.07/1.33 | | ! [v1: int] : (v1 = 0 | ~ (big_f(v0) = v1) | ~ $i(v0)) & ! [v0:
% 4.07/1.33 | | $i] : ( ~ (big_g(v0) = 0) | ~ $i(v0)) & ( ~ (all_3_4 = 0) |
% 4.07/1.33 | | all_3_3 = 0)
% 4.07/1.33 | |
% 4.07/1.33 | | ALPHA: (18) implies:
% 4.07/1.33 | | (19) big_g(all_3_5) = all_3_3
% 4.07/1.33 | | (20) big_f(all_3_6) = all_3_4
% 4.07/1.33 | | (21) ~ (all_3_4 = 0) | all_3_3 = 0
% 4.07/1.34 | | (22) ! [v0: $i] : ( ~ (big_g(v0) = 0) | ~ $i(v0))
% 4.07/1.34 | | (23) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (big_f(v0) = v1) | ~
% 4.07/1.34 | | $i(v0))
% 4.07/1.34 | |
% 4.07/1.34 | | GROUND_INST: instantiating (23) with all_3_6, all_3_4, simplifying with (2),
% 4.07/1.34 | | (20) gives:
% 4.07/1.34 | | (24) all_3_4 = 0
% 4.07/1.34 | |
% 4.07/1.34 | | BETA: splitting (21) gives:
% 4.07/1.34 | |
% 4.07/1.34 | | Case 1:
% 4.07/1.34 | | |
% 4.07/1.34 | | | (25) ~ (all_3_4 = 0)
% 4.07/1.34 | | |
% 4.07/1.34 | | | REDUCE: (24), (25) imply:
% 4.07/1.34 | | | (26) $false
% 4.07/1.34 | | |
% 4.07/1.34 | | | CLOSE: (26) is inconsistent.
% 4.07/1.34 | | |
% 4.07/1.34 | | Case 2:
% 4.07/1.34 | | |
% 4.07/1.34 | | | (27) all_3_3 = 0
% 4.07/1.34 | | |
% 4.07/1.34 | | | REDUCE: (19), (27) imply:
% 4.07/1.34 | | | (28) big_g(all_3_5) = 0
% 4.07/1.34 | | |
% 4.07/1.34 | | | GROUND_INST: instantiating (22) with all_3_5, simplifying with (3), (28)
% 4.07/1.34 | | | gives:
% 4.07/1.34 | | | (29) $false
% 4.07/1.34 | | |
% 4.07/1.34 | | | CLOSE: (29) is inconsistent.
% 4.07/1.34 | | |
% 4.07/1.34 | | End of split
% 4.07/1.34 | |
% 4.07/1.34 | End of split
% 4.07/1.34 |
% 4.07/1.34 End of proof
% 4.07/1.34 % SZS output end Proof for theBenchmark
% 4.07/1.34
% 4.07/1.34 729ms
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