TSTP Solution File: SET027+4 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SET027+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 : n011.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 15:23:16 EDT 2023
% Result : Theorem 6.13s 1.63s
% Output : Proof 7.66s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET027+4 : TPTP v8.1.2. Released v2.2.0.
% 0.07/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.34 % Computer : n011.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 11:35:24 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.67 ________ _____
% 0.19/0.67 ___ __ \_________(_)________________________________
% 0.19/0.67 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.19/0.67 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.19/0.67 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.19/0.67
% 0.19/0.67 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.19/0.67 (2023-06-19)
% 0.19/0.67
% 0.19/0.67 (c) Philipp Rümmer, 2009-2023
% 0.19/0.67 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.19/0.67 Amanda Stjerna.
% 0.19/0.67 Free software under BSD-3-Clause.
% 0.19/0.67
% 0.19/0.67 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.19/0.67
% 0.19/0.67 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.19/0.68 Running up to 7 provers in parallel.
% 0.19/0.69 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.19/0.69 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.19/0.69 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.19/0.69 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.19/0.69 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.19/0.69 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.19/0.69 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.49/1.06 Prover 1: Preprocessing ...
% 2.49/1.06 Prover 4: Preprocessing ...
% 2.81/1.10 Prover 0: Preprocessing ...
% 2.81/1.10 Prover 2: Preprocessing ...
% 2.81/1.10 Prover 3: Preprocessing ...
% 2.81/1.10 Prover 5: Preprocessing ...
% 2.81/1.10 Prover 6: Preprocessing ...
% 5.14/1.49 Prover 6: Proving ...
% 5.14/1.49 Prover 5: Proving ...
% 5.65/1.51 Prover 1: Constructing countermodel ...
% 5.65/1.51 Prover 3: Constructing countermodel ...
% 5.65/1.51 Prover 2: Proving ...
% 5.65/1.52 Prover 4: Constructing countermodel ...
% 5.65/1.53 Prover 0: Proving ...
% 6.13/1.63 Prover 3: proved (937ms)
% 6.13/1.63
% 6.13/1.63 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.13/1.63
% 6.13/1.63 Prover 5: stopped
% 6.13/1.63 Prover 2: stopped
% 6.13/1.64 Prover 6: stopped
% 6.13/1.64 Prover 0: stopped
% 6.13/1.64 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 6.13/1.64 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 6.13/1.64 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 6.13/1.64 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 6.13/1.65 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 6.87/1.68 Prover 7: Preprocessing ...
% 6.87/1.68 Prover 13: Preprocessing ...
% 6.87/1.68 Prover 8: Preprocessing ...
% 6.87/1.68 Prover 10: Preprocessing ...
% 6.87/1.68 Prover 11: Preprocessing ...
% 6.87/1.69 Prover 1: Found proof (size 17)
% 6.87/1.69 Prover 1: proved (1000ms)
% 6.87/1.69 Prover 4: stopped
% 7.09/1.70 Prover 10: stopped
% 7.09/1.70 Prover 7: stopped
% 7.09/1.73 Prover 13: stopped
% 7.33/1.73 Prover 11: stopped
% 7.33/1.77 Prover 8: Warning: ignoring some quantifiers
% 7.33/1.78 Prover 8: Constructing countermodel ...
% 7.33/1.79 Prover 8: stopped
% 7.33/1.79
% 7.33/1.79 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 7.33/1.79
% 7.33/1.80 % SZS output start Proof for theBenchmark
% 7.33/1.80 Assumptions after simplification:
% 7.33/1.80 ---------------------------------
% 7.66/1.80
% 7.66/1.80 (subset)
% 7.66/1.83 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) = v2)
% 7.66/1.83 | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) &
% 7.66/1.83 member(v3, v1) = v4 & member(v3, v0) = 0 & $i(v3))) & ! [v0: $i] : !
% 7.66/1.83 [v1: $i] : ( ~ (subset(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ! [v2: $i] : (
% 7.66/1.83 ~ (member(v2, v0) = 0) | ~ $i(v2) | member(v2, v1) = 0))
% 7.66/1.83
% 7.66/1.83 (thI03)
% 7.66/1.83 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) &
% 7.66/1.83 subset(v1, v2) = 0 & subset(v0, v2) = v3 & subset(v0, v1) = 0 & $i(v2) &
% 7.66/1.83 $i(v1) & $i(v0))
% 7.66/1.83
% 7.66/1.83 (function-axioms)
% 7.66/1.84 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 7.66/1.84 (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) & ! [v0:
% 7.66/1.84 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 7.66/1.84 (difference(v3, v2) = v1) | ~ (difference(v3, v2) = v0)) & ! [v0: $i] : !
% 7.66/1.84 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (union(v3, v2) = v1) | ~
% 7.66/1.84 (union(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 7.66/1.84 $i] : (v1 = v0 | ~ (intersection(v3, v2) = v1) | ~ (intersection(v3, v2) =
% 7.66/1.84 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 7.66/1.84 $i] : ! [v3: $i] : (v1 = v0 | ~ (equal_set(v3, v2) = v1) | ~
% 7.66/1.84 (equal_set(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 7.66/1.84 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (subset(v3,
% 7.66/1.84 v2) = v1) | ~ (subset(v3, v2) = v0)) & ! [v0: MultipleValueBool] : !
% 7.66/1.84 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 7.66/1.84 (member(v3, v2) = v1) | ~ (member(v3, v2) = v0)) & ! [v0: $i] : ! [v1:
% 7.66/1.84 $i] : ! [v2: $i] : (v1 = v0 | ~ (product(v2) = v1) | ~ (product(v2) =
% 7.66/1.84 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (sum(v2) =
% 7.66/1.84 v1) | ~ (sum(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 =
% 7.66/1.84 v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) & ! [v0: $i] : !
% 7.66/1.84 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (power_set(v2) = v1) | ~
% 7.66/1.84 (power_set(v2) = v0))
% 7.66/1.84
% 7.66/1.84 Further assumptions not needed in the proof:
% 7.66/1.84 --------------------------------------------
% 7.66/1.84 difference, empty_set, equal_set, intersection, power_set, product, singleton,
% 7.66/1.84 sum, union, unordered_pair
% 7.66/1.84
% 7.66/1.84 Those formulas are unsatisfiable:
% 7.66/1.84 ---------------------------------
% 7.66/1.84
% 7.66/1.84 Begin of proof
% 7.66/1.84 |
% 7.66/1.84 | ALPHA: (subset) implies:
% 7.66/1.85 | (1) ! [v0: $i] : ! [v1: $i] : ( ~ (subset(v0, v1) = 0) | ~ $i(v1) | ~
% 7.66/1.85 | $i(v0) | ! [v2: $i] : ( ~ (member(v2, v0) = 0) | ~ $i(v2) |
% 7.66/1.85 | member(v2, v1) = 0))
% 7.66/1.85 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1)
% 7.66/1.85 | = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~
% 7.66/1.85 | (v4 = 0) & member(v3, v1) = v4 & member(v3, v0) = 0 & $i(v3)))
% 7.66/1.85 |
% 7.66/1.85 | ALPHA: (function-axioms) implies:
% 7.66/1.85 | (3) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 7.66/1.85 | ! [v3: $i] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2)
% 7.66/1.85 | = v0))
% 7.66/1.85 |
% 7.66/1.85 | DELTA: instantiating (thI03) with fresh symbols all_15_0, all_15_1, all_15_2,
% 7.66/1.85 | all_15_3 gives:
% 7.66/1.85 | (4) ~ (all_15_0 = 0) & subset(all_15_2, all_15_1) = 0 & subset(all_15_3,
% 7.66/1.85 | all_15_1) = all_15_0 & subset(all_15_3, all_15_2) = 0 & $i(all_15_1)
% 7.66/1.85 | & $i(all_15_2) & $i(all_15_3)
% 7.66/1.85 |
% 7.66/1.85 | ALPHA: (4) implies:
% 7.66/1.85 | (5) ~ (all_15_0 = 0)
% 7.66/1.85 | (6) $i(all_15_3)
% 7.66/1.85 | (7) $i(all_15_2)
% 7.66/1.85 | (8) $i(all_15_1)
% 7.66/1.85 | (9) subset(all_15_3, all_15_2) = 0
% 7.66/1.85 | (10) subset(all_15_3, all_15_1) = all_15_0
% 7.66/1.85 | (11) subset(all_15_2, all_15_1) = 0
% 7.66/1.85 |
% 7.66/1.85 | GROUND_INST: instantiating (1) with all_15_3, all_15_2, simplifying with (6),
% 7.66/1.85 | (7), (9) gives:
% 7.66/1.85 | (12) ! [v0: $i] : ( ~ (member(v0, all_15_3) = 0) | ~ $i(v0) | member(v0,
% 7.66/1.85 | all_15_2) = 0)
% 7.66/1.85 |
% 7.66/1.85 | GROUND_INST: instantiating (2) with all_15_3, all_15_1, all_15_0, simplifying
% 7.66/1.85 | with (6), (8), (10) gives:
% 7.66/1.85 | (13) all_15_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & member(v0,
% 7.66/1.85 | all_15_1) = v1 & member(v0, all_15_3) = 0 & $i(v0))
% 7.66/1.86 |
% 7.66/1.86 | GROUND_INST: instantiating (1) with all_15_2, all_15_1, simplifying with (7),
% 7.66/1.86 | (8), (11) gives:
% 7.66/1.86 | (14) ! [v0: $i] : ( ~ (member(v0, all_15_2) = 0) | ~ $i(v0) | member(v0,
% 7.66/1.86 | all_15_1) = 0)
% 7.66/1.86 |
% 7.66/1.86 | BETA: splitting (13) gives:
% 7.66/1.86 |
% 7.66/1.86 | Case 1:
% 7.66/1.86 | |
% 7.66/1.86 | | (15) all_15_0 = 0
% 7.66/1.86 | |
% 7.66/1.86 | | REDUCE: (5), (15) imply:
% 7.66/1.86 | | (16) $false
% 7.66/1.86 | |
% 7.66/1.86 | | CLOSE: (16) is inconsistent.
% 7.66/1.86 | |
% 7.66/1.86 | Case 2:
% 7.66/1.86 | |
% 7.66/1.86 | | (17) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & member(v0, all_15_1) =
% 7.66/1.86 | | v1 & member(v0, all_15_3) = 0 & $i(v0))
% 7.66/1.86 | |
% 7.66/1.86 | | DELTA: instantiating (17) with fresh symbols all_27_0, all_27_1 gives:
% 7.66/1.86 | | (18) ~ (all_27_0 = 0) & member(all_27_1, all_15_1) = all_27_0 &
% 7.66/1.86 | | member(all_27_1, all_15_3) = 0 & $i(all_27_1)
% 7.66/1.86 | |
% 7.66/1.86 | | ALPHA: (18) implies:
% 7.66/1.86 | | (19) ~ (all_27_0 = 0)
% 7.66/1.86 | | (20) $i(all_27_1)
% 7.66/1.86 | | (21) member(all_27_1, all_15_3) = 0
% 7.66/1.86 | | (22) member(all_27_1, all_15_1) = all_27_0
% 7.66/1.86 | |
% 7.66/1.86 | | GROUND_INST: instantiating (12) with all_27_1, simplifying with (20), (21)
% 7.66/1.86 | | gives:
% 7.66/1.86 | | (23) member(all_27_1, all_15_2) = 0
% 7.66/1.86 | |
% 7.66/1.86 | | GROUND_INST: instantiating (14) with all_27_1, simplifying with (20), (23)
% 7.66/1.86 | | gives:
% 7.66/1.86 | | (24) member(all_27_1, all_15_1) = 0
% 7.66/1.86 | |
% 7.66/1.86 | | GROUND_INST: instantiating (3) with all_27_0, 0, all_15_1, all_27_1,
% 7.66/1.86 | | simplifying with (22), (24) gives:
% 7.66/1.86 | | (25) all_27_0 = 0
% 7.66/1.86 | |
% 7.66/1.86 | | REDUCE: (19), (25) imply:
% 7.66/1.86 | | (26) $false
% 7.66/1.86 | |
% 7.66/1.86 | | CLOSE: (26) is inconsistent.
% 7.66/1.86 | |
% 7.66/1.86 | End of split
% 7.66/1.86 |
% 7.66/1.86 End of proof
% 7.66/1.86 % SZS output end Proof for theBenchmark
% 7.66/1.86
% 7.66/1.86 1193ms
%------------------------------------------------------------------------------