TSTP Solution File: NUN073+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : NUN073+1 : TPTP v8.1.2. Released v7.3.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n004.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 : Thu Aug 31 12:51:02 EDT 2023
% Result : Theorem 7.60s 1.79s
% Output : Proof 9.78s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : NUN073+1 : TPTP v8.1.2. Released v7.3.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.35 % Computer : n004.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Sun Aug 27 09:28:52 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.62 ________ _____
% 0.20/0.62 ___ __ \_________(_)________________________________
% 0.20/0.62 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.20/0.62 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.20/0.62 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.20/0.62
% 0.20/0.62 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.20/0.62 (2023-06-19)
% 0.20/0.62
% 0.20/0.62 (c) Philipp Rümmer, 2009-2023
% 0.20/0.62 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.20/0.62 Amanda Stjerna.
% 0.20/0.62 Free software under BSD-3-Clause.
% 0.20/0.62
% 0.20/0.62 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.20/0.62
% 0.20/0.62 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.20/0.64 Running up to 7 provers in parallel.
% 0.20/0.65 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.20/0.65 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.20/0.65 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.20/0.65 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.20/0.65 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
% 3.05/1.12 Prover 4: Preprocessing ...
% 3.05/1.12 Prover 1: Preprocessing ...
% 3.05/1.16 Prover 6: Preprocessing ...
% 3.05/1.16 Prover 3: Preprocessing ...
% 3.05/1.16 Prover 2: Preprocessing ...
% 3.05/1.16 Prover 5: Preprocessing ...
% 3.05/1.17 Prover 0: Preprocessing ...
% 4.71/1.42 Prover 2: Proving ...
% 5.43/1.43 Prover 5: Proving ...
% 5.43/1.50 Prover 1: Warning: ignoring some quantifiers
% 5.43/1.50 Prover 6: Proving ...
% 5.43/1.53 Prover 3: Warning: ignoring some quantifiers
% 5.43/1.53 Prover 1: Constructing countermodel ...
% 5.43/1.55 Prover 4: Warning: ignoring some quantifiers
% 5.43/1.57 Prover 3: Constructing countermodel ...
% 6.15/1.61 Prover 4: Constructing countermodel ...
% 7.01/1.69 Prover 0: Proving ...
% 7.60/1.79 Prover 2: proved (1140ms)
% 7.60/1.79
% 7.60/1.79 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 7.60/1.79
% 7.60/1.79 Prover 3: stopped
% 7.60/1.79 Prover 5: stopped
% 7.60/1.79 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 7.60/1.79 Prover 6: stopped
% 7.60/1.80 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 7.60/1.80 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 7.60/1.80 Prover 0: stopped
% 7.60/1.81 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 7.60/1.81 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 8.36/1.87 Prover 8: Preprocessing ...
% 8.36/1.88 Prover 13: Preprocessing ...
% 8.36/1.89 Prover 7: Preprocessing ...
% 8.36/1.89 Prover 10: Preprocessing ...
% 8.80/1.91 Prover 11: Preprocessing ...
% 8.80/1.92 Prover 1: Found proof (size 28)
% 8.80/1.92 Prover 1: proved (1272ms)
% 8.80/1.92 Prover 4: stopped
% 8.80/1.94 Prover 13: Warning: ignoring some quantifiers
% 8.80/1.94 Prover 13: Constructing countermodel ...
% 8.80/1.95 Prover 10: Warning: ignoring some quantifiers
% 8.80/1.95 Prover 10: Constructing countermodel ...
% 8.80/1.96 Prover 13: stopped
% 9.25/1.96 Prover 10: stopped
% 9.25/1.96 Prover 7: Warning: ignoring some quantifiers
% 9.25/1.97 Prover 7: Constructing countermodel ...
% 9.25/1.97 Prover 7: stopped
% 9.25/1.98 Prover 11: stopped
% 9.25/1.98 Prover 8: Warning: ignoring some quantifiers
% 9.25/1.99 Prover 8: Constructing countermodel ...
% 9.25/1.99 Prover 8: stopped
% 9.25/1.99
% 9.25/1.99 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 9.25/1.99
% 9.25/2.00 % SZS output start Proof for theBenchmark
% 9.25/2.00 Assumptions after simplification:
% 9.25/2.00 ---------------------------------
% 9.25/2.00
% 9.25/2.00 (axiom_3a)
% 9.25/2.03 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (id(v0, v1) = v2) | ~
% 9.25/2.03 $i(v1) | ~ $i(v0) | ! [v3: $i] : ( ~ (r2(v1, v3) = 0) | ~ $i(v3) | !
% 9.25/2.03 [v4: $i] : ( ~ (r2(v0, v4) = 0) | ~ $i(v4) | ? [v5: int] : ( ~ (v5 = 0)
% 9.25/2.03 & id(v4, v3) = v5))))
% 9.25/2.03
% 9.25/2.03 (axiom_7a)
% 9.25/2.03 ! [v0: $i] : ! [v1: $i] : ( ~ (r2(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | !
% 9.25/2.03 [v2: $i] : ( ~ (r1(v2) = 0) | ~ $i(v2) | ? [v3: int] : ( ~ (v3 = 0) &
% 9.25/2.03 id(v2, v1) = v3)))
% 9.25/2.03
% 9.25/2.03 (oneunidtwo)
% 9.25/2.03 ? [v0: $i] : ($i(v0) & ? [v1: $i] : (r2(v1, v0) = 0 & $i(v1) & ? [v2: $i] :
% 9.25/2.03 (r2(v2, v1) = 0 & r1(v2) = 0 & $i(v2))) & ? [v1: $i] : (id(v1, v0) = 0 &
% 9.25/2.03 $i(v1) & ? [v2: $i] : (r2(v2, v1) = 0 & r1(v2) = 0 & $i(v2))))
% 9.25/2.03
% 9.25/2.03 (function-axioms)
% 9.25/2.04 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 9.25/2.04 [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (r4(v4, v3, v2) = v1) | ~ (r4(v4, v3,
% 9.25/2.04 v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] :
% 9.25/2.04 ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (r3(v4, v3, v2) = v1) |
% 9.25/2.04 ~ (r3(v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 9.25/2.04 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (r2(v3, v2) =
% 9.25/2.04 v1) | ~ (r2(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 9.25/2.04 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (id(v3, v2) =
% 9.25/2.04 v1) | ~ (id(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 9.25/2.04 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (r1(v2) = v1) | ~ (r1(v2)
% 9.25/2.04 = v0))
% 9.25/2.04
% 9.25/2.04 Further assumptions not needed in the proof:
% 9.25/2.04 --------------------------------------------
% 9.25/2.04 axiom_1, axiom_10, axiom_11, axiom_1a, axiom_2, axiom_2a, axiom_3, axiom_4,
% 9.25/2.04 axiom_4a, axiom_5, axiom_5a, axiom_6, axiom_6a, axiom_7, axiom_8, axiom_9
% 9.25/2.04
% 9.25/2.04 Those formulas are unsatisfiable:
% 9.25/2.04 ---------------------------------
% 9.25/2.04
% 9.25/2.04 Begin of proof
% 9.25/2.04 |
% 9.25/2.04 | ALPHA: (function-axioms) implies:
% 9.25/2.04 | (1) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 9.25/2.04 | ! [v3: $i] : (v1 = v0 | ~ (id(v3, v2) = v1) | ~ (id(v3, v2) = v0))
% 9.25/2.04 |
% 9.25/2.04 | DELTA: instantiating (oneunidtwo) with fresh symbol all_23_0 gives:
% 9.25/2.04 | (2) $i(all_23_0) & ? [v0: $i] : (r2(v0, all_23_0) = 0 & $i(v0) & ? [v1:
% 9.25/2.04 | $i] : (r2(v1, v0) = 0 & r1(v1) = 0 & $i(v1))) & ? [v0: $i] :
% 9.25/2.04 | (id(v0, all_23_0) = 0 & $i(v0) & ? [v1: $i] : (r2(v1, v0) = 0 & r1(v1)
% 9.25/2.04 | = 0 & $i(v1)))
% 9.25/2.04 |
% 9.25/2.04 | ALPHA: (2) implies:
% 9.25/2.04 | (3) $i(all_23_0)
% 9.25/2.05 | (4) ? [v0: $i] : (id(v0, all_23_0) = 0 & $i(v0) & ? [v1: $i] : (r2(v1,
% 9.25/2.05 | v0) = 0 & r1(v1) = 0 & $i(v1)))
% 9.25/2.05 | (5) ? [v0: $i] : (r2(v0, all_23_0) = 0 & $i(v0) & ? [v1: $i] : (r2(v1,
% 9.25/2.05 | v0) = 0 & r1(v1) = 0 & $i(v1)))
% 9.25/2.05 |
% 9.25/2.05 | DELTA: instantiating (4) with fresh symbol all_25_0 gives:
% 9.25/2.05 | (6) id(all_25_0, all_23_0) = 0 & $i(all_25_0) & ? [v0: $i] : (r2(v0,
% 9.25/2.05 | all_25_0) = 0 & r1(v0) = 0 & $i(v0))
% 9.25/2.05 |
% 9.25/2.05 | ALPHA: (6) implies:
% 9.25/2.05 | (7) $i(all_25_0)
% 9.25/2.05 | (8) id(all_25_0, all_23_0) = 0
% 9.25/2.05 | (9) ? [v0: $i] : (r2(v0, all_25_0) = 0 & r1(v0) = 0 & $i(v0))
% 9.25/2.05 |
% 9.25/2.05 | DELTA: instantiating (5) with fresh symbol all_27_0 gives:
% 9.25/2.05 | (10) r2(all_27_0, all_23_0) = 0 & $i(all_27_0) & ? [v0: $i] : (r2(v0,
% 9.25/2.05 | all_27_0) = 0 & r1(v0) = 0 & $i(v0))
% 9.25/2.05 |
% 9.25/2.05 | ALPHA: (10) implies:
% 9.25/2.05 | (11) $i(all_27_0)
% 9.25/2.05 | (12) r2(all_27_0, all_23_0) = 0
% 9.25/2.05 | (13) ? [v0: $i] : (r2(v0, all_27_0) = 0 & r1(v0) = 0 & $i(v0))
% 9.25/2.05 |
% 9.25/2.05 | DELTA: instantiating (9) with fresh symbol all_29_0 gives:
% 9.25/2.05 | (14) r2(all_29_0, all_25_0) = 0 & r1(all_29_0) = 0 & $i(all_29_0)
% 9.25/2.05 |
% 9.25/2.05 | ALPHA: (14) implies:
% 9.25/2.05 | (15) $i(all_29_0)
% 9.25/2.05 | (16) r1(all_29_0) = 0
% 9.25/2.05 | (17) r2(all_29_0, all_25_0) = 0
% 9.25/2.05 |
% 9.25/2.05 | DELTA: instantiating (13) with fresh symbol all_31_0 gives:
% 9.25/2.05 | (18) r2(all_31_0, all_27_0) = 0 & r1(all_31_0) = 0 & $i(all_31_0)
% 9.25/2.05 |
% 9.25/2.05 | ALPHA: (18) implies:
% 9.25/2.05 | (19) $i(all_31_0)
% 9.25/2.05 | (20) r2(all_31_0, all_27_0) = 0
% 9.25/2.05 |
% 9.25/2.05 | GROUND_INST: instantiating (axiom_7a) with all_31_0, all_27_0, simplifying
% 9.25/2.05 | with (11), (19), (20) gives:
% 9.25/2.05 | (21) ! [v0: $i] : ( ~ (r1(v0) = 0) | ~ $i(v0) | ? [v1: int] : ( ~ (v1 =
% 9.25/2.05 | 0) & id(v0, all_27_0) = v1))
% 9.25/2.05 |
% 9.25/2.05 | GROUND_INST: instantiating (21) with all_29_0, simplifying with (15), (16)
% 9.25/2.05 | gives:
% 9.25/2.05 | (22) ? [v0: int] : ( ~ (v0 = 0) & id(all_29_0, all_27_0) = v0)
% 9.25/2.05 |
% 9.25/2.05 | DELTA: instantiating (22) with fresh symbol all_44_0 gives:
% 9.25/2.05 | (23) ~ (all_44_0 = 0) & id(all_29_0, all_27_0) = all_44_0
% 9.25/2.05 |
% 9.25/2.06 | ALPHA: (23) implies:
% 9.25/2.06 | (24) ~ (all_44_0 = 0)
% 9.25/2.06 | (25) id(all_29_0, all_27_0) = all_44_0
% 9.25/2.06 |
% 9.25/2.06 | GROUND_INST: instantiating (axiom_3a) with all_29_0, all_27_0, all_44_0,
% 9.25/2.06 | simplifying with (11), (15), (25) gives:
% 9.25/2.06 | (26) all_44_0 = 0 | ! [v0: $i] : ( ~ (r2(all_27_0, v0) = 0) | ~ $i(v0) |
% 9.25/2.06 | ! [v1: $i] : ( ~ (r2(all_29_0, v1) = 0) | ~ $i(v1) | ? [v2: int] :
% 9.25/2.06 | ( ~ (v2 = 0) & id(v1, v0) = v2)))
% 9.25/2.06 |
% 9.25/2.06 | BETA: splitting (26) gives:
% 9.25/2.06 |
% 9.25/2.06 | Case 1:
% 9.25/2.06 | |
% 9.25/2.06 | | (27) all_44_0 = 0
% 9.25/2.06 | |
% 9.25/2.06 | | REDUCE: (24), (27) imply:
% 9.25/2.06 | | (28) $false
% 9.78/2.06 | |
% 9.78/2.06 | | CLOSE: (28) is inconsistent.
% 9.78/2.06 | |
% 9.78/2.06 | Case 2:
% 9.78/2.06 | |
% 9.78/2.06 | | (29) ! [v0: $i] : ( ~ (r2(all_27_0, v0) = 0) | ~ $i(v0) | ! [v1: $i] :
% 9.78/2.06 | | ( ~ (r2(all_29_0, v1) = 0) | ~ $i(v1) | ? [v2: int] : ( ~ (v2 =
% 9.78/2.06 | | 0) & id(v1, v0) = v2)))
% 9.78/2.06 | |
% 9.78/2.06 | | GROUND_INST: instantiating (29) with all_23_0, simplifying with (3), (12)
% 9.78/2.06 | | gives:
% 9.78/2.06 | | (30) ! [v0: $i] : ( ~ (r2(all_29_0, v0) = 0) | ~ $i(v0) | ? [v1: int]
% 9.78/2.06 | | : ( ~ (v1 = 0) & id(v0, all_23_0) = v1))
% 9.78/2.06 | |
% 9.78/2.06 | | GROUND_INST: instantiating (30) with all_25_0, simplifying with (7), (17)
% 9.78/2.06 | | gives:
% 9.78/2.06 | | (31) ? [v0: int] : ( ~ (v0 = 0) & id(all_25_0, all_23_0) = v0)
% 9.78/2.06 | |
% 9.78/2.06 | | DELTA: instantiating (31) with fresh symbol all_89_0 gives:
% 9.78/2.06 | | (32) ~ (all_89_0 = 0) & id(all_25_0, all_23_0) = all_89_0
% 9.78/2.06 | |
% 9.78/2.06 | | ALPHA: (32) implies:
% 9.78/2.06 | | (33) ~ (all_89_0 = 0)
% 9.78/2.06 | | (34) id(all_25_0, all_23_0) = all_89_0
% 9.78/2.06 | |
% 9.78/2.06 | | GROUND_INST: instantiating (1) with 0, all_89_0, all_23_0, all_25_0,
% 9.78/2.06 | | simplifying with (8), (34) gives:
% 9.78/2.06 | | (35) all_89_0 = 0
% 9.78/2.06 | |
% 9.78/2.06 | | REDUCE: (33), (35) imply:
% 9.78/2.06 | | (36) $false
% 9.78/2.06 | |
% 9.78/2.06 | | CLOSE: (36) is inconsistent.
% 9.78/2.06 | |
% 9.78/2.06 | End of split
% 9.78/2.06 |
% 9.78/2.06 End of proof
% 9.78/2.06 % SZS output end Proof for theBenchmark
% 9.78/2.06
% 9.78/2.06 1439ms
%------------------------------------------------------------------------------