TSTP Solution File: SET704+4 by Princess---230619
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SET704+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 : n002.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 15:26:03 EDT 2023
% Result : Theorem 7.05s 1.65s
% Output : Proof 8.81s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.11 % Problem : SET704+4 : TPTP v8.1.2. Released v2.2.0.
% 0.08/0.11 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.08/0.30 % Computer : n002.cluster.edu
% 0.08/0.30 % Model : x86_64 x86_64
% 0.08/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.30 % Memory : 8042.1875MB
% 0.08/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.08/0.30 % CPULimit : 300
% 0.08/0.30 % WCLimit : 300
% 0.08/0.30 % DateTime : Sat Aug 26 12:51:33 EDT 2023
% 0.08/0.30 % CPUTime :
% 0.13/0.52 ________ _____
% 0.13/0.52 ___ __ \_________(_)________________________________
% 0.13/0.52 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.13/0.52 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.13/0.52 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.13/0.52
% 0.13/0.52 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.13/0.52 (2023-06-19)
% 0.13/0.52
% 0.13/0.52 (c) Philipp Rümmer, 2009-2023
% 0.13/0.52 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.13/0.52 Amanda Stjerna.
% 0.13/0.52 Free software under BSD-3-Clause.
% 0.13/0.52
% 0.13/0.52 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.13/0.52
% 0.13/0.53 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.13/0.54 Running up to 7 provers in parallel.
% 0.13/0.55 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.13/0.55 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.13/0.55 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.13/0.55 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.13/0.55 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.13/0.55 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.13/0.56 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.31/0.98 Prover 4: Preprocessing ...
% 2.31/0.98 Prover 1: Preprocessing ...
% 2.31/1.02 Prover 6: Preprocessing ...
% 2.31/1.02 Prover 3: Preprocessing ...
% 2.31/1.03 Prover 5: Preprocessing ...
% 2.31/1.03 Prover 2: Preprocessing ...
% 2.31/1.03 Prover 0: Preprocessing ...
% 5.78/1.49 Prover 3: Constructing countermodel ...
% 5.78/1.49 Prover 6: Proving ...
% 5.78/1.50 Prover 1: Constructing countermodel ...
% 5.78/1.50 Prover 5: Proving ...
% 5.78/1.52 Prover 2: Proving ...
% 6.31/1.55 Prover 4: Constructing countermodel ...
% 6.55/1.58 Prover 0: Proving ...
% 6.94/1.65 Prover 3: proved (1099ms)
% 7.05/1.65
% 7.05/1.65 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 7.05/1.65
% 7.05/1.65 Prover 2: stopped
% 7.05/1.66 Prover 5: stopped
% 7.05/1.66 Prover 0: stopped
% 7.05/1.67 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 7.05/1.67 Prover 6: stopped
% 7.05/1.67 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 7.05/1.67 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 7.05/1.67 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 7.05/1.68 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 7.05/1.69 Prover 8: Preprocessing ...
% 7.05/1.69 Prover 7: Preprocessing ...
% 7.49/1.73 Prover 10: Preprocessing ...
% 7.49/1.73 Prover 11: Preprocessing ...
% 7.49/1.73 Prover 13: Preprocessing ...
% 7.49/1.75 Prover 1: Found proof (size 21)
% 7.49/1.75 Prover 1: proved (1201ms)
% 7.49/1.75 Prover 4: stopped
% 7.49/1.76 Prover 10: stopped
% 7.83/1.77 Prover 11: stopped
% 7.83/1.79 Prover 7: Warning: ignoring some quantifiers
% 7.83/1.79 Prover 13: stopped
% 7.83/1.80 Prover 7: Constructing countermodel ...
% 7.83/1.82 Prover 7: stopped
% 8.29/1.85 Prover 8: Warning: ignoring some quantifiers
% 8.29/1.86 Prover 8: Constructing countermodel ...
% 8.29/1.87 Prover 8: stopped
% 8.29/1.87
% 8.29/1.87 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 8.29/1.87
% 8.29/1.88 % SZS output start Proof for theBenchmark
% 8.29/1.88 Assumptions after simplification:
% 8.29/1.88 ---------------------------------
% 8.29/1.88
% 8.29/1.88 (product)
% 8.29/1.92 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~
% 8.29/1.92 (product(v1) = v2) | ~ (member(v0, v2) = v3) | ~ $i(v1) | ~ $i(v0) | ?
% 8.29/1.92 [v4: $i] : ? [v5: int] : ( ~ (v5 = 0) & member(v4, v1) = 0 & member(v0, v4)
% 8.29/1.92 = v5 & $i(v4))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 8.29/1.92 (product(v1) = v2) | ~ (member(v0, v2) = 0) | ~ $i(v1) | ~ $i(v0) | !
% 8.29/1.92 [v3: $i] : ! [v4: int] : (v4 = 0 | ~ (member(v0, v3) = v4) | ~ $i(v3) |
% 8.29/1.92 ? [v5: int] : ( ~ (v5 = 0) & member(v3, v1) = v5)))
% 8.29/1.92
% 8.29/1.92 (subset)
% 8.29/1.93 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) = v2)
% 8.29/1.93 | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) &
% 8.29/1.93 member(v3, v1) = v4 & member(v3, v0) = 0 & $i(v3))) & ! [v0: $i] : !
% 8.29/1.93 [v1: $i] : ( ~ (subset(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ! [v2: $i] : (
% 8.29/1.93 ~ (member(v2, v0) = 0) | ~ $i(v2) | member(v2, v1) = 0))
% 8.29/1.93
% 8.29/1.93 (thI42)
% 8.29/1.93 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) &
% 8.29/1.93 product(v0) = v2 & subset(v2, v1) = v3 & member(v1, v0) = 0 & $i(v2) &
% 8.29/1.93 $i(v1) & $i(v0))
% 8.29/1.93
% 8.29/1.93 (function-axioms)
% 8.29/1.94 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 8.29/1.94 (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) & ! [v0:
% 8.29/1.94 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 8.29/1.94 (difference(v3, v2) = v1) | ~ (difference(v3, v2) = v0)) & ! [v0: $i] : !
% 8.29/1.94 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (union(v3, v2) = v1) | ~
% 8.29/1.94 (union(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 8.29/1.94 $i] : (v1 = v0 | ~ (intersection(v3, v2) = v1) | ~ (intersection(v3, v2) =
% 8.29/1.94 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 8.29/1.94 $i] : ! [v3: $i] : (v1 = v0 | ~ (equal_set(v3, v2) = v1) | ~
% 8.29/1.94 (equal_set(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 8.29/1.94 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (subset(v3,
% 8.29/1.94 v2) = v1) | ~ (subset(v3, v2) = v0)) & ! [v0: MultipleValueBool] : !
% 8.29/1.94 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 8.29/1.94 (member(v3, v2) = v1) | ~ (member(v3, v2) = v0)) & ! [v0: $i] : ! [v1:
% 8.29/1.94 $i] : ! [v2: $i] : (v1 = v0 | ~ (product(v2) = v1) | ~ (product(v2) =
% 8.29/1.94 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (sum(v2) =
% 8.29/1.94 v1) | ~ (sum(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 =
% 8.29/1.94 v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) & ! [v0: $i] : !
% 8.29/1.94 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (power_set(v2) = v1) | ~
% 8.29/1.94 (power_set(v2) = v0))
% 8.29/1.94
% 8.29/1.94 Further assumptions not needed in the proof:
% 8.29/1.94 --------------------------------------------
% 8.29/1.95 difference, empty_set, equal_set, intersection, power_set, singleton, sum,
% 8.29/1.95 union, unordered_pair
% 8.29/1.95
% 8.29/1.95 Those formulas are unsatisfiable:
% 8.29/1.95 ---------------------------------
% 8.29/1.95
% 8.29/1.95 Begin of proof
% 8.29/1.95 |
% 8.29/1.95 | ALPHA: (subset) implies:
% 8.29/1.95 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1)
% 8.29/1.95 | = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~
% 8.29/1.95 | (v4 = 0) & member(v3, v1) = v4 & member(v3, v0) = 0 & $i(v3)))
% 8.29/1.95 |
% 8.29/1.95 | ALPHA: (product) implies:
% 8.29/1.95 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (product(v1) = v2) | ~
% 8.29/1.96 | (member(v0, v2) = 0) | ~ $i(v1) | ~ $i(v0) | ! [v3: $i] : ! [v4:
% 8.29/1.96 | int] : (v4 = 0 | ~ (member(v0, v3) = v4) | ~ $i(v3) | ? [v5:
% 8.29/1.96 | int] : ( ~ (v5 = 0) & member(v3, v1) = v5)))
% 8.29/1.96 |
% 8.29/1.96 | ALPHA: (function-axioms) implies:
% 8.29/1.96 | (3) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 8.29/1.96 | ! [v3: $i] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2)
% 8.29/1.96 | = v0))
% 8.29/1.96 |
% 8.29/1.96 | DELTA: instantiating (thI42) with fresh symbols all_15_0, all_15_1, all_15_2,
% 8.29/1.96 | all_15_3 gives:
% 8.29/1.96 | (4) ~ (all_15_0 = 0) & product(all_15_3) = all_15_1 & subset(all_15_1,
% 8.29/1.96 | all_15_2) = all_15_0 & member(all_15_2, all_15_3) = 0 & $i(all_15_1)
% 8.29/1.96 | & $i(all_15_2) & $i(all_15_3)
% 8.29/1.96 |
% 8.29/1.96 | ALPHA: (4) implies:
% 8.81/1.96 | (5) ~ (all_15_0 = 0)
% 8.81/1.96 | (6) $i(all_15_3)
% 8.81/1.96 | (7) $i(all_15_2)
% 8.81/1.96 | (8) $i(all_15_1)
% 8.81/1.96 | (9) member(all_15_2, all_15_3) = 0
% 8.81/1.96 | (10) subset(all_15_1, all_15_2) = all_15_0
% 8.81/1.96 | (11) product(all_15_3) = all_15_1
% 8.81/1.96 |
% 8.81/1.96 | GROUND_INST: instantiating (1) with all_15_1, all_15_2, all_15_0, simplifying
% 8.81/1.96 | with (7), (8), (10) gives:
% 8.81/1.97 | (12) all_15_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & member(v0,
% 8.81/1.97 | all_15_1) = 0 & member(v0, all_15_2) = v1 & $i(v0))
% 8.81/1.97 |
% 8.81/1.97 | BETA: splitting (12) gives:
% 8.81/1.97 |
% 8.81/1.97 | Case 1:
% 8.81/1.97 | |
% 8.81/1.97 | | (13) all_15_0 = 0
% 8.81/1.97 | |
% 8.81/1.97 | | REDUCE: (5), (13) imply:
% 8.81/1.97 | | (14) $false
% 8.81/1.97 | |
% 8.81/1.97 | | CLOSE: (14) is inconsistent.
% 8.81/1.97 | |
% 8.81/1.97 | Case 2:
% 8.81/1.97 | |
% 8.81/1.97 | | (15) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & member(v0, all_15_1) = 0
% 8.81/1.97 | | & member(v0, all_15_2) = v1 & $i(v0))
% 8.81/1.97 | |
% 8.81/1.97 | | DELTA: instantiating (15) with fresh symbols all_24_0, all_24_1 gives:
% 8.81/1.97 | | (16) ~ (all_24_0 = 0) & member(all_24_1, all_15_1) = 0 &
% 8.81/1.97 | | member(all_24_1, all_15_2) = all_24_0 & $i(all_24_1)
% 8.81/1.97 | |
% 8.81/1.97 | | ALPHA: (16) implies:
% 8.81/1.97 | | (17) ~ (all_24_0 = 0)
% 8.81/1.97 | | (18) $i(all_24_1)
% 8.81/1.97 | | (19) member(all_24_1, all_15_2) = all_24_0
% 8.81/1.97 | | (20) member(all_24_1, all_15_1) = 0
% 8.81/1.97 | |
% 8.81/1.97 | | GROUND_INST: instantiating (2) with all_24_1, all_15_3, all_15_1,
% 8.81/1.97 | | simplifying with (6), (11), (18), (20) gives:
% 8.81/1.97 | | (21) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (member(all_24_1, v0) =
% 8.81/1.97 | | v1) | ~ $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & member(v0,
% 8.81/1.97 | | all_15_3) = v2))
% 8.81/1.97 | |
% 8.81/1.97 | | GROUND_INST: instantiating (21) with all_15_2, all_24_0, simplifying with
% 8.81/1.97 | | (7), (19) gives:
% 8.81/1.97 | | (22) all_24_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & member(all_15_2,
% 8.81/1.97 | | all_15_3) = v0)
% 8.81/1.97 | |
% 8.81/1.97 | | BETA: splitting (22) gives:
% 8.81/1.97 | |
% 8.81/1.97 | | Case 1:
% 8.81/1.97 | | |
% 8.81/1.97 | | | (23) all_24_0 = 0
% 8.81/1.98 | | |
% 8.81/1.98 | | | REDUCE: (17), (23) imply:
% 8.81/1.98 | | | (24) $false
% 8.81/1.98 | | |
% 8.81/1.98 | | | CLOSE: (24) is inconsistent.
% 8.81/1.98 | | |
% 8.81/1.98 | | Case 2:
% 8.81/1.98 | | |
% 8.81/1.98 | | | (25) ? [v0: int] : ( ~ (v0 = 0) & member(all_15_2, all_15_3) = v0)
% 8.81/1.98 | | |
% 8.81/1.98 | | | DELTA: instantiating (25) with fresh symbol all_36_0 gives:
% 8.81/1.98 | | | (26) ~ (all_36_0 = 0) & member(all_15_2, all_15_3) = all_36_0
% 8.81/1.98 | | |
% 8.81/1.98 | | | ALPHA: (26) implies:
% 8.81/1.98 | | | (27) ~ (all_36_0 = 0)
% 8.81/1.98 | | | (28) member(all_15_2, all_15_3) = all_36_0
% 8.81/1.98 | | |
% 8.81/1.98 | | | GROUND_INST: instantiating (3) with 0, all_36_0, all_15_3, all_15_2,
% 8.81/1.98 | | | simplifying with (9), (28) gives:
% 8.81/1.98 | | | (29) all_36_0 = 0
% 8.81/1.98 | | |
% 8.81/1.98 | | | REDUCE: (27), (29) imply:
% 8.81/1.98 | | | (30) $false
% 8.81/1.98 | | |
% 8.81/1.98 | | | CLOSE: (30) is inconsistent.
% 8.81/1.98 | | |
% 8.81/1.98 | | End of split
% 8.81/1.98 | |
% 8.81/1.98 | End of split
% 8.81/1.98 |
% 8.81/1.98 End of proof
% 8.81/1.98 % SZS output end Proof for theBenchmark
% 8.81/1.98
% 8.81/1.98 1454ms
%------------------------------------------------------------------------------