TSTP Solution File: SET941+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SET941+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n029.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 15:27:08 EDT 2023
% Result : Theorem 4.60s 1.45s
% Output : Proof 6.67s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SET941+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.35 % Computer : n029.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 : Sat Aug 26 09:08:25 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 ...
% 0.20/0.63 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 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 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 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
% 2.02/0.98 Prover 1: Preprocessing ...
% 2.02/0.98 Prover 4: Preprocessing ...
% 2.43/1.02 Prover 6: Preprocessing ...
% 2.43/1.02 Prover 2: Preprocessing ...
% 2.43/1.02 Prover 5: Preprocessing ...
% 2.43/1.02 Prover 0: Preprocessing ...
% 2.43/1.02 Prover 3: Preprocessing ...
% 3.82/1.22 Prover 1: Warning: ignoring some quantifiers
% 3.82/1.22 Prover 3: Warning: ignoring some quantifiers
% 3.82/1.23 Prover 5: Proving ...
% 3.82/1.24 Prover 2: Proving ...
% 3.82/1.24 Prover 1: Constructing countermodel ...
% 4.16/1.24 Prover 6: Proving ...
% 4.17/1.24 Prover 0: Proving ...
% 4.17/1.24 Prover 3: Constructing countermodel ...
% 4.17/1.25 Prover 4: Warning: ignoring some quantifiers
% 4.17/1.26 Prover 4: Constructing countermodel ...
% 4.60/1.44 Prover 0: proved (807ms)
% 4.60/1.45
% 4.60/1.45 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.60/1.45
% 4.60/1.45 Prover 5: stopped
% 4.60/1.46 Prover 3: stopped
% 4.60/1.46 Prover 2: stopped
% 4.60/1.46 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 4.60/1.46 Prover 6: stopped
% 4.60/1.46 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 4.60/1.46 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 4.60/1.46 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 4.60/1.46 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 5.61/1.48 Prover 4: Found proof (size 20)
% 5.61/1.48 Prover 4: proved (836ms)
% 5.61/1.48 Prover 1: stopped
% 5.61/1.48 Prover 10: Preprocessing ...
% 5.61/1.49 Prover 8: Preprocessing ...
% 5.61/1.49 Prover 7: Preprocessing ...
% 5.61/1.49 Prover 13: Preprocessing ...
% 5.61/1.50 Prover 11: Preprocessing ...
% 5.61/1.51 Prover 13: stopped
% 5.61/1.51 Prover 10: Warning: ignoring some quantifiers
% 5.61/1.51 Prover 7: Warning: ignoring some quantifiers
% 5.61/1.51 Prover 11: stopped
% 5.61/1.52 Prover 10: Constructing countermodel ...
% 5.61/1.52 Prover 7: Constructing countermodel ...
% 5.61/1.52 Prover 10: stopped
% 5.61/1.52 Prover 7: stopped
% 5.61/1.54 Prover 8: Warning: ignoring some quantifiers
% 5.61/1.55 Prover 8: Constructing countermodel ...
% 5.61/1.55 Prover 8: stopped
% 5.61/1.55
% 5.61/1.55 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.61/1.55
% 5.61/1.55 % SZS output start Proof for theBenchmark
% 5.61/1.56 Assumptions after simplification:
% 5.61/1.56 ---------------------------------
% 5.61/1.56
% 5.61/1.56 (d3_tarski)
% 6.35/1.59 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~
% 6.35/1.59 (subset(v0, v1) = 0) | ~ (in(v2, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~
% 6.35/1.59 $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & in(v2, v0) = v4)) & ! [v0: $i] : !
% 6.35/1.59 [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ~ $i(v1) | ~
% 6.35/1.59 $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) & in(v3, v1) = v4 &
% 6.35/1.59 in(v3, v0) = 0 & $i(v3))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 6.35/1.59 (subset(v0, v1) = 0) | ~ (in(v2, v0) = 0) | ~ $i(v2) | ~ $i(v1) | ~
% 6.35/1.59 $i(v0) | in(v2, v1) = 0)
% 6.35/1.59
% 6.35/1.59 (d4_tarski)
% 6.35/1.60 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : ! [v4: $i] : (v3 = 0
% 6.35/1.60 | ~ (union(v0) = v1) | ~ (in(v4, v0) = 0) | ~ (in(v2, v1) = v3) | ~
% 6.35/1.60 $i(v4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ( ~ (v5 = 0) &
% 6.35/1.60 in(v2, v4) = v5)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int]
% 6.35/1.60 : ! [v4: $i] : (v3 = 0 | ~ (union(v0) = v1) | ~ (in(v2, v4) = 0) | ~
% 6.35/1.60 (in(v2, v1) = v3) | ~ $i(v4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5:
% 6.35/1.60 int] : ( ~ (v5 = 0) & in(v4, v0) = v5)) & ! [v0: $i] : ! [v1: $i] : !
% 6.35/1.60 [v2: $i] : ( ~ (union(v0) = v1) | ~ (in(v2, v1) = 0) | ~ $i(v2) | ~ $i(v1)
% 6.35/1.60 | ~ $i(v0) | ? [v3: $i] : (in(v3, v0) = 0 & in(v2, v3) = 0 & $i(v3))) & ?
% 6.35/1.60 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v0 | ~ (union(v1) = v2) | ~
% 6.35/1.60 $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: any] : ? [v5: $i] : ? [v6: int]
% 6.35/1.60 : ? [v7: int] : (in(v3, v0) = v4 & $i(v5) & $i(v3) & ( ~ (v4 = 0) | ( !
% 6.35/1.60 [v8: $i] : ( ~ (in(v8, v1) = 0) | ~ $i(v8) | ? [v9: int] : ( ~ (v9 =
% 6.35/1.60 0) & in(v3, v8) = v9)) & ! [v8: $i] : ( ~ (in(v3, v8) = 0) | ~
% 6.35/1.60 $i(v8) | ? [v9: int] : ( ~ (v9 = 0) & in(v8, v1) = v9)))) & (v4 = 0
% 6.35/1.60 | (v7 = 0 & v6 = 0 & in(v5, v1) = 0 & in(v3, v5) = 0))))
% 6.35/1.60
% 6.35/1.60 (t94_zfmisc_1)
% 6.35/1.61 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) &
% 6.35/1.61 union(v0) = v2 & subset(v2, v1) = v3 & $i(v2) & $i(v1) & $i(v0) & ! [v4:
% 6.35/1.61 $i] : ! [v5: int] : (v5 = 0 | ~ (subset(v4, v1) = v5) | ~ $i(v4) | ?
% 6.35/1.61 [v6: int] : ( ~ (v6 = 0) & in(v4, v0) = v6)) & ! [v4: $i] : ( ~ (in(v4,
% 6.35/1.61 v0) = 0) | ~ $i(v4) | subset(v4, v1) = 0))
% 6.35/1.61
% 6.35/1.61 (function-axioms)
% 6.35/1.61 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 6.35/1.61 [v3: $i] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) &
% 6.35/1.61 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 6.35/1.61 $i] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) & ! [v0:
% 6.35/1.61 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 |
% 6.35/1.61 ~ (empty(v2) = v1) | ~ (empty(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 6.35/1.61 [v2: $i] : (v1 = v0 | ~ (union(v2) = v1) | ~ (union(v2) = v0))
% 6.35/1.61
% 6.35/1.61 Further assumptions not needed in the proof:
% 6.35/1.61 --------------------------------------------
% 6.35/1.61 antisymmetry_r2_hidden, rc1_xboole_0, rc2_xboole_0, reflexivity_r1_tarski
% 6.35/1.61
% 6.35/1.61 Those formulas are unsatisfiable:
% 6.35/1.61 ---------------------------------
% 6.35/1.61
% 6.35/1.61 Begin of proof
% 6.55/1.61 |
% 6.55/1.61 | ALPHA: (d3_tarski) implies:
% 6.55/1.62 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (subset(v0, v1) = 0) | ~
% 6.55/1.62 | (in(v2, v0) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | in(v2, v1) =
% 6.55/1.62 | 0)
% 6.55/1.62 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1)
% 6.55/1.62 | = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~
% 6.55/1.62 | (v4 = 0) & in(v3, v1) = v4 & in(v3, v0) = 0 & $i(v3)))
% 6.55/1.62 |
% 6.55/1.62 | ALPHA: (d4_tarski) implies:
% 6.55/1.62 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (union(v0) = v1) | ~
% 6.55/1.62 | (in(v2, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] :
% 6.55/1.62 | (in(v3, v0) = 0 & in(v2, v3) = 0 & $i(v3)))
% 6.55/1.62 |
% 6.55/1.62 | ALPHA: (function-axioms) implies:
% 6.55/1.62 | (4) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 6.55/1.62 | ! [v3: $i] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0))
% 6.55/1.62 |
% 6.55/1.62 | DELTA: instantiating (t94_zfmisc_1) with fresh symbols all_11_0, all_11_1,
% 6.55/1.62 | all_11_2, all_11_3 gives:
% 6.55/1.63 | (5) ~ (all_11_0 = 0) & union(all_11_3) = all_11_1 & subset(all_11_1,
% 6.55/1.63 | all_11_2) = all_11_0 & $i(all_11_1) & $i(all_11_2) & $i(all_11_3) &
% 6.55/1.63 | ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (subset(v0, all_11_2) = v1) |
% 6.55/1.63 | ~ $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & in(v0, all_11_3) = v2)) & !
% 6.55/1.63 | [v0: $i] : ( ~ (in(v0, all_11_3) = 0) | ~ $i(v0) | subset(v0,
% 6.55/1.63 | all_11_2) = 0)
% 6.55/1.63 |
% 6.55/1.63 | ALPHA: (5) implies:
% 6.55/1.63 | (6) ~ (all_11_0 = 0)
% 6.55/1.63 | (7) $i(all_11_3)
% 6.55/1.63 | (8) $i(all_11_2)
% 6.55/1.63 | (9) $i(all_11_1)
% 6.55/1.63 | (10) subset(all_11_1, all_11_2) = all_11_0
% 6.55/1.63 | (11) union(all_11_3) = all_11_1
% 6.55/1.63 | (12) ! [v0: $i] : ( ~ (in(v0, all_11_3) = 0) | ~ $i(v0) | subset(v0,
% 6.55/1.63 | all_11_2) = 0)
% 6.55/1.63 |
% 6.55/1.63 | GROUND_INST: instantiating (2) with all_11_1, all_11_2, all_11_0, simplifying
% 6.55/1.63 | with (8), (9), (10) gives:
% 6.55/1.63 | (13) all_11_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & in(v0,
% 6.55/1.63 | all_11_1) = 0 & in(v0, all_11_2) = v1 & $i(v0))
% 6.55/1.63 |
% 6.55/1.63 | BETA: splitting (13) gives:
% 6.55/1.63 |
% 6.55/1.63 | Case 1:
% 6.55/1.63 | |
% 6.55/1.63 | | (14) all_11_0 = 0
% 6.55/1.63 | |
% 6.55/1.63 | | REDUCE: (6), (14) imply:
% 6.55/1.63 | | (15) $false
% 6.55/1.63 | |
% 6.55/1.63 | | CLOSE: (15) is inconsistent.
% 6.55/1.63 | |
% 6.55/1.63 | Case 2:
% 6.55/1.63 | |
% 6.55/1.63 | | (16) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & in(v0, all_11_1) = 0 &
% 6.55/1.63 | | in(v0, all_11_2) = v1 & $i(v0))
% 6.55/1.63 | |
% 6.55/1.63 | | DELTA: instantiating (16) with fresh symbols all_23_0, all_23_1 gives:
% 6.55/1.64 | | (17) ~ (all_23_0 = 0) & in(all_23_1, all_11_1) = 0 & in(all_23_1,
% 6.55/1.64 | | all_11_2) = all_23_0 & $i(all_23_1)
% 6.55/1.64 | |
% 6.55/1.64 | | ALPHA: (17) implies:
% 6.55/1.64 | | (18) ~ (all_23_0 = 0)
% 6.55/1.64 | | (19) $i(all_23_1)
% 6.55/1.64 | | (20) in(all_23_1, all_11_2) = all_23_0
% 6.55/1.64 | | (21) in(all_23_1, all_11_1) = 0
% 6.55/1.64 | |
% 6.55/1.64 | | GROUND_INST: instantiating (3) with all_11_3, all_11_1, all_23_1,
% 6.55/1.64 | | simplifying with (7), (9), (11), (19), (21) gives:
% 6.67/1.64 | | (22) ? [v0: $i] : (in(v0, all_11_3) = 0 & in(all_23_1, v0) = 0 & $i(v0))
% 6.67/1.64 | |
% 6.67/1.64 | | DELTA: instantiating (22) with fresh symbol all_38_0 gives:
% 6.67/1.64 | | (23) in(all_38_0, all_11_3) = 0 & in(all_23_1, all_38_0) = 0 &
% 6.67/1.64 | | $i(all_38_0)
% 6.67/1.64 | |
% 6.67/1.64 | | ALPHA: (23) implies:
% 6.67/1.64 | | (24) $i(all_38_0)
% 6.67/1.64 | | (25) in(all_23_1, all_38_0) = 0
% 6.67/1.64 | | (26) in(all_38_0, all_11_3) = 0
% 6.67/1.64 | |
% 6.67/1.64 | | GROUND_INST: instantiating (12) with all_38_0, simplifying with (24), (26)
% 6.67/1.64 | | gives:
% 6.67/1.64 | | (27) subset(all_38_0, all_11_2) = 0
% 6.67/1.64 | |
% 6.67/1.64 | | GROUND_INST: instantiating (1) with all_38_0, all_11_2, all_23_1,
% 6.67/1.64 | | simplifying with (8), (19), (24), (25), (27) gives:
% 6.67/1.64 | | (28) in(all_23_1, all_11_2) = 0
% 6.67/1.64 | |
% 6.67/1.64 | | GROUND_INST: instantiating (4) with all_23_0, 0, all_11_2, all_23_1,
% 6.67/1.64 | | simplifying with (20), (28) gives:
% 6.67/1.64 | | (29) all_23_0 = 0
% 6.67/1.64 | |
% 6.67/1.64 | | REDUCE: (18), (29) imply:
% 6.67/1.64 | | (30) $false
% 6.67/1.64 | |
% 6.67/1.64 | | CLOSE: (30) is inconsistent.
% 6.67/1.64 | |
% 6.67/1.64 | End of split
% 6.67/1.64 |
% 6.67/1.64 End of proof
% 6.67/1.64 % SZS output end Proof for theBenchmark
% 6.67/1.64
% 6.67/1.64 1023ms
%------------------------------------------------------------------------------