TSTP Solution File: SET767+4 by Princess---230619
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SET767+4 : TPTP v8.1.2. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n025.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 15:26:21 EDT 2023
% Result : Theorem 8.16s 1.85s
% Output : Proof 9.89s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET767+4 : TPTP v8.1.2. Released v2.2.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.33 % Computer : n025.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Sat Aug 26 08:47:53 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
% 0.19/0.60 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.19/0.62 Running up to 7 provers in parallel.
% 0.19/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.19/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.19/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.19/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.19/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.19/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.19/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.77/1.07 Prover 1: Preprocessing ...
% 2.77/1.08 Prover 4: Preprocessing ...
% 3.02/1.13 Prover 6: Preprocessing ...
% 3.02/1.13 Prover 0: Preprocessing ...
% 3.02/1.13 Prover 5: Preprocessing ...
% 3.02/1.13 Prover 2: Preprocessing ...
% 3.02/1.13 Prover 3: Preprocessing ...
% 6.85/1.67 Prover 5: Proving ...
% 6.85/1.68 Prover 2: Proving ...
% 6.85/1.69 Prover 6: Proving ...
% 6.85/1.73 Prover 3: Constructing countermodel ...
% 6.85/1.74 Prover 1: Constructing countermodel ...
% 8.16/1.85 Prover 3: proved (1219ms)
% 8.16/1.85
% 8.16/1.85 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 8.16/1.85
% 8.16/1.86 Prover 2: stopped
% 8.16/1.86 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 8.16/1.86 Prover 5: stopped
% 8.16/1.87 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 8.16/1.87 Prover 6: stopped
% 8.16/1.89 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 8.55/1.91 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 8.55/1.91 Prover 1: Found proof (size 16)
% 8.55/1.91 Prover 1: proved (1286ms)
% 8.55/1.91 Prover 8: Preprocessing ...
% 8.55/1.94 Prover 7: Preprocessing ...
% 8.55/1.94 Prover 11: Preprocessing ...
% 8.55/1.95 Prover 10: Preprocessing ...
% 8.95/1.98 Prover 7: stopped
% 8.95/1.98 Prover 10: stopped
% 8.95/1.99 Prover 0: Proving ...
% 8.95/1.99 Prover 0: stopped
% 8.95/1.99 Prover 4: Constructing countermodel ...
% 8.95/2.01 Prover 4: stopped
% 8.95/2.01 Prover 11: stopped
% 8.95/2.07 Prover 8: Warning: ignoring some quantifiers
% 8.95/2.08 Prover 8: Constructing countermodel ...
% 8.95/2.09 Prover 8: stopped
% 8.95/2.09
% 8.95/2.09 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 8.95/2.09
% 8.95/2.10 % SZS output start Proof for theBenchmark
% 8.95/2.10 Assumptions after simplification:
% 8.95/2.10 ---------------------------------
% 8.95/2.10
% 8.95/2.10 (equivalence_class)
% 8.95/2.13 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 8.95/2.13 int] : (v5 = 0 | ~ (equivalence_class(v2, v1, v0) = v4) | ~ (member(v3,
% 8.95/2.13 v4) = v5) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: any]
% 8.95/2.13 : ? [v7: any] : (apply(v0, v2, v3) = v7 & member(v3, v1) = v6 & ( ~ (v7 =
% 8.95/2.13 0) | ~ (v6 = 0)))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 8.95/2.13 [v3: $i] : ! [v4: $i] : ( ~ (equivalence_class(v2, v1, v0) = v4) | ~
% 8.95/2.13 (member(v3, v4) = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 8.95/2.13 (apply(v0, v2, v3) = 0 & member(v3, v1) = 0))
% 8.95/2.13
% 8.95/2.13 (subset)
% 8.95/2.14 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) = v2)
% 8.95/2.14 | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) &
% 8.95/2.14 member(v3, v1) = v4 & member(v3, v0) = 0 & $i(v3))) & ! [v0: $i] : !
% 8.95/2.14 [v1: $i] : ( ~ (subset(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ! [v2: $i] : (
% 8.95/2.14 ~ (member(v2, v0) = 0) | ~ $i(v2) | member(v2, v1) = 0))
% 8.95/2.14
% 8.95/2.14 (thIII03)
% 8.95/2.14 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: int] : ( ~ (v4
% 8.95/2.14 = 0) & equivalence_class(v2, v0, v1) = v3 & equivalence(v1, v0) = 0 &
% 8.95/2.14 subset(v3, v0) = v4 & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 8.95/2.14
% 8.95/2.14 (function-axioms)
% 9.89/2.15 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0
% 9.89/2.15 | ~ (equivalence_class(v4, v3, v2) = v1) | ~ (equivalence_class(v4, v3,
% 9.89/2.15 v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] :
% 9.89/2.15 ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (apply(v4, v3, v2) =
% 9.89/2.15 v1) | ~ (apply(v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 9.89/2.15 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 9.89/2.15 (pre_order(v3, v2) = v1) | ~ (pre_order(v3, v2) = v0)) & ! [v0:
% 9.89/2.15 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 9.89/2.15 : (v1 = v0 | ~ (equivalence(v3, v2) = v1) | ~ (equivalence(v3, v2) = v0)) &
% 9.89/2.15 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 9.89/2.15 $i] : (v1 = v0 | ~ (partition(v3, v2) = v1) | ~ (partition(v3, v2) = v0))
% 9.89/2.15 & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 9.89/2.15 [v3: $i] : (v1 = v0 | ~ (disjoint(v3, v2) = v1) | ~ (disjoint(v3, v2) = v0))
% 9.89/2.15 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 9.89/2.15 (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) & ! [v0:
% 9.89/2.15 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 9.89/2.15 (difference(v3, v2) = v1) | ~ (difference(v3, v2) = v0)) & ! [v0: $i] : !
% 9.89/2.15 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (union(v3, v2) = v1) | ~
% 9.89/2.15 (union(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 9.89/2.15 $i] : (v1 = v0 | ~ (intersection(v3, v2) = v1) | ~ (intersection(v3, v2) =
% 9.89/2.15 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 9.89/2.15 $i] : ! [v3: $i] : (v1 = v0 | ~ (equal_set(v3, v2) = v1) | ~
% 9.89/2.15 (equal_set(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 9.89/2.15 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (subset(v3,
% 9.89/2.15 v2) = v1) | ~ (subset(v3, v2) = v0)) & ! [v0: MultipleValueBool] : !
% 9.89/2.15 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 9.89/2.15 (member(v3, v2) = v1) | ~ (member(v3, v2) = v0)) & ! [v0: $i] : ! [v1:
% 9.89/2.15 $i] : ! [v2: $i] : (v1 = v0 | ~ (product(v2) = v1) | ~ (product(v2) =
% 9.89/2.15 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (sum(v2) =
% 9.89/2.15 v1) | ~ (sum(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 =
% 9.89/2.15 v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) & ! [v0: $i] : !
% 9.89/2.15 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (power_set(v2) = v1) | ~
% 9.89/2.15 (power_set(v2) = v0))
% 9.89/2.15
% 9.89/2.15 Further assumptions not needed in the proof:
% 9.89/2.15 --------------------------------------------
% 9.89/2.15 difference, disjoint, empty_set, equal_set, equivalence, intersection,
% 9.89/2.15 partition, power_set, pre_order, product, singleton, sum, union, unordered_pair
% 9.89/2.15
% 9.89/2.15 Those formulas are unsatisfiable:
% 9.89/2.15 ---------------------------------
% 9.89/2.15
% 9.89/2.15 Begin of proof
% 9.89/2.15 |
% 9.89/2.15 | ALPHA: (subset) implies:
% 9.89/2.15 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1)
% 9.89/2.15 | = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~
% 9.89/2.15 | (v4 = 0) & member(v3, v1) = v4 & member(v3, v0) = 0 & $i(v3)))
% 9.89/2.15 |
% 9.89/2.15 | ALPHA: (equivalence_class) implies:
% 9.89/2.15 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (
% 9.89/2.15 | ~ (equivalence_class(v2, v1, v0) = v4) | ~ (member(v3, v4) = 0) | ~
% 9.89/2.15 | $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | (apply(v0, v2, v3) = 0 &
% 9.89/2.15 | member(v3, v1) = 0))
% 9.89/2.15 |
% 9.89/2.15 | ALPHA: (function-axioms) implies:
% 9.89/2.15 | (3) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 9.89/2.15 | ! [v3: $i] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2)
% 9.89/2.15 | = v0))
% 9.89/2.15 |
% 9.89/2.15 | DELTA: instantiating (thIII03) with fresh symbols all_20_0, all_20_1,
% 9.89/2.15 | all_20_2, all_20_3, all_20_4 gives:
% 9.89/2.16 | (4) ~ (all_20_0 = 0) & equivalence_class(all_20_2, all_20_4, all_20_3) =
% 9.89/2.16 | all_20_1 & equivalence(all_20_3, all_20_4) = 0 & subset(all_20_1,
% 9.89/2.16 | all_20_4) = all_20_0 & $i(all_20_1) & $i(all_20_2) & $i(all_20_3) &
% 9.89/2.16 | $i(all_20_4)
% 9.89/2.16 |
% 9.89/2.16 | ALPHA: (4) implies:
% 9.89/2.16 | (5) ~ (all_20_0 = 0)
% 9.89/2.16 | (6) $i(all_20_4)
% 9.89/2.16 | (7) $i(all_20_3)
% 9.89/2.16 | (8) $i(all_20_2)
% 9.89/2.16 | (9) $i(all_20_1)
% 9.89/2.16 | (10) subset(all_20_1, all_20_4) = all_20_0
% 9.89/2.16 | (11) equivalence_class(all_20_2, all_20_4, all_20_3) = all_20_1
% 9.89/2.16 |
% 9.89/2.16 | GROUND_INST: instantiating (1) with all_20_1, all_20_4, all_20_0, simplifying
% 9.89/2.16 | with (6), (9), (10) gives:
% 9.89/2.16 | (12) all_20_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & member(v0,
% 9.89/2.16 | all_20_1) = 0 & member(v0, all_20_4) = v1 & $i(v0))
% 9.89/2.16 |
% 9.89/2.16 | BETA: splitting (12) gives:
% 9.89/2.16 |
% 9.89/2.16 | Case 1:
% 9.89/2.16 | |
% 9.89/2.16 | | (13) all_20_0 = 0
% 9.89/2.16 | |
% 9.89/2.16 | | REDUCE: (5), (13) imply:
% 9.89/2.16 | | (14) $false
% 9.89/2.16 | |
% 9.89/2.16 | | CLOSE: (14) is inconsistent.
% 9.89/2.16 | |
% 9.89/2.16 | Case 2:
% 9.89/2.16 | |
% 9.89/2.16 | | (15) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & member(v0, all_20_1) = 0
% 9.89/2.16 | | & member(v0, all_20_4) = v1 & $i(v0))
% 9.89/2.16 | |
% 9.89/2.16 | | DELTA: instantiating (15) with fresh symbols all_32_0, all_32_1 gives:
% 9.89/2.16 | | (16) ~ (all_32_0 = 0) & member(all_32_1, all_20_1) = 0 &
% 9.89/2.16 | | member(all_32_1, all_20_4) = all_32_0 & $i(all_32_1)
% 9.89/2.16 | |
% 9.89/2.16 | | ALPHA: (16) implies:
% 9.89/2.16 | | (17) ~ (all_32_0 = 0)
% 9.89/2.16 | | (18) $i(all_32_1)
% 9.89/2.16 | | (19) member(all_32_1, all_20_4) = all_32_0
% 9.89/2.16 | | (20) member(all_32_1, all_20_1) = 0
% 9.89/2.16 | |
% 9.89/2.16 | | GROUND_INST: instantiating (2) with all_20_3, all_20_4, all_20_2, all_32_1,
% 9.89/2.16 | | all_20_1, simplifying with (6), (7), (8), (11), (18), (20)
% 9.89/2.16 | | gives:
% 9.89/2.16 | | (21) apply(all_20_3, all_20_2, all_32_1) = 0 & member(all_32_1, all_20_4)
% 9.89/2.16 | | = 0
% 9.89/2.16 | |
% 9.89/2.16 | | ALPHA: (21) implies:
% 9.89/2.16 | | (22) member(all_32_1, all_20_4) = 0
% 9.89/2.16 | |
% 9.89/2.16 | | GROUND_INST: instantiating (3) with all_32_0, 0, all_20_4, all_32_1,
% 9.89/2.16 | | simplifying with (19), (22) gives:
% 9.89/2.16 | | (23) all_32_0 = 0
% 9.89/2.16 | |
% 9.89/2.17 | | REDUCE: (17), (23) imply:
% 9.89/2.17 | | (24) $false
% 9.89/2.17 | |
% 9.89/2.17 | | CLOSE: (24) is inconsistent.
% 9.89/2.17 | |
% 9.89/2.17 | End of split
% 9.89/2.17 |
% 9.89/2.17 End of proof
% 9.89/2.17 % SZS output end Proof for theBenchmark
% 9.89/2.17
% 9.89/2.17 1561ms
%------------------------------------------------------------------------------