TSTP Solution File: SET631+3 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SET631+3 : TPTP v8.1.2. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n010.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 15:25:45 EDT 2023
% Result : Theorem 3.84s 1.34s
% Output : Proof 5.45s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SET631+3 : TPTP v8.1.2. Released v2.2.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.14/0.34 % Computer : n010.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Sat Aug 26 09:36:05 EDT 2023
% 0.14/0.34 % CPUTime :
% 0.21/0.62 ________ _____
% 0.21/0.62 ___ __ \_________(_)________________________________
% 0.21/0.62 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.21/0.62 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.21/0.62 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.21/0.62
% 0.21/0.62 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.21/0.62 (2023-06-19)
% 0.21/0.62
% 0.21/0.62 (c) Philipp Rümmer, 2009-2023
% 0.21/0.62 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.21/0.62 Amanda Stjerna.
% 0.21/0.62 Free software under BSD-3-Clause.
% 0.21/0.62
% 0.21/0.62 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.21/0.62
% 0.21/0.62 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.21/0.63 Running up to 7 provers in parallel.
% 0.21/0.65 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.21/0.65 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.21/0.65 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.21/0.65 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.21/0.65 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.21/0.65 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.21/0.65 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 1.86/1.01 Prover 1: Preprocessing ...
% 1.86/1.01 Prover 4: Preprocessing ...
% 2.26/1.05 Prover 0: Preprocessing ...
% 2.26/1.05 Prover 5: Preprocessing ...
% 2.26/1.05 Prover 3: Preprocessing ...
% 2.26/1.05 Prover 2: Preprocessing ...
% 2.26/1.05 Prover 6: Preprocessing ...
% 3.17/1.19 Prover 2: Proving ...
% 3.17/1.19 Prover 1: Constructing countermodel ...
% 3.17/1.20 Prover 5: Proving ...
% 3.17/1.20 Prover 6: Proving ...
% 3.17/1.21 Prover 3: Constructing countermodel ...
% 3.17/1.21 Prover 0: Proving ...
% 3.17/1.21 Prover 4: Constructing countermodel ...
% 3.84/1.34 Prover 3: proved (701ms)
% 3.84/1.34
% 3.84/1.34 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.84/1.34
% 3.84/1.35 Prover 5: stopped
% 3.84/1.35 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 3.84/1.35 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 3.84/1.35 Prover 0: proved (708ms)
% 3.84/1.35
% 3.84/1.35 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.84/1.35
% 3.84/1.35 Prover 2: stopped
% 3.84/1.35 Prover 6: stopped
% 3.84/1.38 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 3.84/1.38 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 3.84/1.38 Prover 8: Preprocessing ...
% 3.84/1.38 Prover 7: Preprocessing ...
% 3.84/1.38 Prover 10: Preprocessing ...
% 3.84/1.38 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 3.84/1.39 Prover 13: Preprocessing ...
% 3.84/1.41 Prover 1: Found proof (size 21)
% 3.84/1.41 Prover 1: proved (767ms)
% 3.84/1.41 Prover 4: stopped
% 3.84/1.42 Prover 7: Constructing countermodel ...
% 3.84/1.42 Prover 11: Preprocessing ...
% 3.84/1.42 Prover 8: Warning: ignoring some quantifiers
% 3.84/1.42 Prover 7: stopped
% 3.84/1.42 Prover 10: Constructing countermodel ...
% 3.84/1.43 Prover 8: Constructing countermodel ...
% 3.84/1.43 Prover 10: stopped
% 4.75/1.43 Prover 8: stopped
% 4.75/1.44 Prover 11: stopped
% 4.75/1.44 Prover 13: Warning: ignoring some quantifiers
% 4.75/1.45 Prover 13: Constructing countermodel ...
% 4.75/1.45 Prover 13: stopped
% 4.75/1.45
% 4.75/1.45 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.75/1.45
% 4.75/1.45 % SZS output start Proof for theBenchmark
% 4.75/1.46 Assumptions after simplification:
% 4.75/1.46 ---------------------------------
% 4.75/1.46
% 4.75/1.46 (difference_defn)
% 5.13/1.49 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0
% 5.13/1.49 | ~ (difference(v0, v1) = v3) | ~ (member(v2, v3) = v4) | ~ $i(v2) | ~
% 5.13/1.49 $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : (member(v2, v1) = v6 &
% 5.13/1.49 member(v2, v0) = v5 & ( ~ (v5 = 0) | v6 = 0))) & ! [v0: $i] : ! [v1: $i]
% 5.13/1.49 : ! [v2: $i] : ! [v3: $i] : ( ~ (difference(v0, v1) = v3) | ~ (member(v2,
% 5.13/1.49 v3) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: int] : ( ~ (v4 =
% 5.13/1.49 0) & member(v2, v1) = v4 & member(v2, v0) = 0))
% 5.13/1.49
% 5.13/1.49 (intersect_defn)
% 5.13/1.50 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (intersect(v0, v1) =
% 5.13/1.50 v2) | ~ $i(v1) | ~ $i(v0) | ! [v3: $i] : ( ~ (member(v3, v0) = 0) | ~
% 5.13/1.50 $i(v3) | ? [v4: int] : ( ~ (v4 = 0) & member(v3, v1) = v4))) & ! [v0:
% 5.13/1.50 $i] : ! [v1: $i] : ( ~ (intersect(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ?
% 5.13/1.50 [v2: $i] : (member(v2, v1) = 0 & member(v2, v0) = 0 & $i(v2)))
% 5.13/1.50
% 5.13/1.50 (prove_th113)
% 5.13/1.50 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: int] : ( ~ (v4
% 5.13/1.50 = 0) & intersect(v0, v3) = 0 & intersect(v0, v1) = v4 & difference(v1, v2)
% 5.13/1.50 = v3 & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 5.13/1.50
% 5.13/1.50 (function-axioms)
% 5.13/1.50 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 5.13/1.50 [v3: $i] : (v1 = v0 | ~ (intersect(v3, v2) = v1) | ~ (intersect(v3, v2) =
% 5.13/1.50 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 |
% 5.13/1.50 ~ (difference(v3, v2) = v1) | ~ (difference(v3, v2) = v0)) & ! [v0:
% 5.13/1.50 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 5.13/1.50 : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2) = v0))
% 5.13/1.50
% 5.13/1.50 Further assumptions not needed in the proof:
% 5.13/1.50 --------------------------------------------
% 5.13/1.50 symmetry_of_intersect
% 5.13/1.50
% 5.13/1.50 Those formulas are unsatisfiable:
% 5.13/1.50 ---------------------------------
% 5.13/1.50
% 5.13/1.50 Begin of proof
% 5.13/1.50 |
% 5.13/1.50 | ALPHA: (difference_defn) implies:
% 5.13/1.51 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 5.13/1.51 | (difference(v0, v1) = v3) | ~ (member(v2, v3) = 0) | ~ $i(v2) | ~
% 5.13/1.51 | $i(v1) | ~ $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & member(v2, v1) =
% 5.13/1.51 | v4 & member(v2, v0) = 0))
% 5.13/1.51 |
% 5.13/1.51 | ALPHA: (intersect_defn) implies:
% 5.13/1.51 | (2) ! [v0: $i] : ! [v1: $i] : ( ~ (intersect(v0, v1) = 0) | ~ $i(v1) |
% 5.13/1.51 | ~ $i(v0) | ? [v2: $i] : (member(v2, v1) = 0 & member(v2, v0) = 0 &
% 5.13/1.51 | $i(v2)))
% 5.13/1.51 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (intersect(v0,
% 5.13/1.51 | v1) = v2) | ~ $i(v1) | ~ $i(v0) | ! [v3: $i] : ( ~ (member(v3,
% 5.13/1.51 | v0) = 0) | ~ $i(v3) | ? [v4: int] : ( ~ (v4 = 0) & member(v3,
% 5.13/1.51 | v1) = v4)))
% 5.13/1.51 |
% 5.13/1.51 | ALPHA: (function-axioms) implies:
% 5.13/1.51 | (4) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 5.13/1.51 | ! [v3: $i] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2)
% 5.13/1.51 | = v0))
% 5.13/1.51 |
% 5.13/1.51 | DELTA: instantiating (prove_th113) with fresh symbols all_6_0, all_6_1,
% 5.13/1.51 | all_6_2, all_6_3, all_6_4 gives:
% 5.13/1.52 | (5) ~ (all_6_0 = 0) & intersect(all_6_4, all_6_1) = 0 & intersect(all_6_4,
% 5.13/1.52 | all_6_3) = all_6_0 & difference(all_6_3, all_6_2) = all_6_1 &
% 5.13/1.52 | $i(all_6_1) & $i(all_6_2) & $i(all_6_3) & $i(all_6_4)
% 5.13/1.52 |
% 5.13/1.52 | ALPHA: (5) implies:
% 5.13/1.52 | (6) ~ (all_6_0 = 0)
% 5.13/1.52 | (7) $i(all_6_4)
% 5.13/1.52 | (8) $i(all_6_3)
% 5.13/1.52 | (9) $i(all_6_2)
% 5.13/1.52 | (10) $i(all_6_1)
% 5.13/1.52 | (11) difference(all_6_3, all_6_2) = all_6_1
% 5.13/1.52 | (12) intersect(all_6_4, all_6_3) = all_6_0
% 5.13/1.52 | (13) intersect(all_6_4, all_6_1) = 0
% 5.13/1.52 |
% 5.13/1.52 | GROUND_INST: instantiating (3) with all_6_4, all_6_3, all_6_0, simplifying
% 5.13/1.52 | with (7), (8), (12) gives:
% 5.13/1.52 | (14) all_6_0 = 0 | ! [v0: $i] : ( ~ (member(v0, all_6_4) = 0) | ~ $i(v0)
% 5.13/1.52 | | ? [v1: int] : ( ~ (v1 = 0) & member(v0, all_6_3) = v1))
% 5.13/1.52 |
% 5.13/1.52 | GROUND_INST: instantiating (2) with all_6_4, all_6_1, simplifying with (7),
% 5.13/1.52 | (10), (13) gives:
% 5.13/1.52 | (15) ? [v0: $i] : (member(v0, all_6_1) = 0 & member(v0, all_6_4) = 0 &
% 5.13/1.52 | $i(v0))
% 5.13/1.52 |
% 5.13/1.52 | DELTA: instantiating (15) with fresh symbol all_14_0 gives:
% 5.13/1.52 | (16) member(all_14_0, all_6_1) = 0 & member(all_14_0, all_6_4) = 0 &
% 5.13/1.52 | $i(all_14_0)
% 5.13/1.52 |
% 5.13/1.52 | ALPHA: (16) implies:
% 5.13/1.52 | (17) $i(all_14_0)
% 5.13/1.52 | (18) member(all_14_0, all_6_4) = 0
% 5.13/1.52 | (19) member(all_14_0, all_6_1) = 0
% 5.13/1.52 |
% 5.13/1.52 | BETA: splitting (14) gives:
% 5.13/1.52 |
% 5.13/1.52 | Case 1:
% 5.13/1.52 | |
% 5.13/1.53 | | (20) all_6_0 = 0
% 5.13/1.53 | |
% 5.13/1.53 | | REDUCE: (6), (20) imply:
% 5.13/1.53 | | (21) $false
% 5.13/1.53 | |
% 5.13/1.53 | | CLOSE: (21) is inconsistent.
% 5.13/1.53 | |
% 5.13/1.53 | Case 2:
% 5.13/1.53 | |
% 5.13/1.53 | | (22) ! [v0: $i] : ( ~ (member(v0, all_6_4) = 0) | ~ $i(v0) | ? [v1:
% 5.13/1.53 | | int] : ( ~ (v1 = 0) & member(v0, all_6_3) = v1))
% 5.13/1.53 | |
% 5.13/1.53 | | GROUND_INST: instantiating (22) with all_14_0, simplifying with (17), (18)
% 5.13/1.53 | | gives:
% 5.13/1.53 | | (23) ? [v0: int] : ( ~ (v0 = 0) & member(all_14_0, all_6_3) = v0)
% 5.13/1.53 | |
% 5.13/1.53 | | GROUND_INST: instantiating (1) with all_6_3, all_6_2, all_14_0, all_6_1,
% 5.13/1.53 | | simplifying with (8), (9), (11), (17), (19) gives:
% 5.13/1.53 | | (24) ? [v0: int] : ( ~ (v0 = 0) & member(all_14_0, all_6_2) = v0 &
% 5.13/1.53 | | member(all_14_0, all_6_3) = 0)
% 5.13/1.53 | |
% 5.13/1.53 | | DELTA: instantiating (23) with fresh symbol all_26_0 gives:
% 5.45/1.53 | | (25) ~ (all_26_0 = 0) & member(all_14_0, all_6_3) = all_26_0
% 5.45/1.53 | |
% 5.45/1.53 | | ALPHA: (25) implies:
% 5.45/1.53 | | (26) ~ (all_26_0 = 0)
% 5.45/1.53 | | (27) member(all_14_0, all_6_3) = all_26_0
% 5.45/1.53 | |
% 5.45/1.53 | | DELTA: instantiating (24) with fresh symbol all_30_0 gives:
% 5.45/1.53 | | (28) ~ (all_30_0 = 0) & member(all_14_0, all_6_2) = all_30_0 &
% 5.45/1.53 | | member(all_14_0, all_6_3) = 0
% 5.45/1.53 | |
% 5.45/1.53 | | ALPHA: (28) implies:
% 5.45/1.53 | | (29) member(all_14_0, all_6_3) = 0
% 5.45/1.53 | |
% 5.45/1.53 | | GROUND_INST: instantiating (4) with 0, all_26_0, all_6_3, all_14_0,
% 5.45/1.53 | | simplifying with (27), (29) gives:
% 5.45/1.53 | | (30) all_26_0 = 0
% 5.45/1.53 | |
% 5.45/1.53 | | REDUCE: (26), (30) imply:
% 5.45/1.53 | | (31) $false
% 5.45/1.53 | |
% 5.45/1.53 | | CLOSE: (31) is inconsistent.
% 5.45/1.53 | |
% 5.45/1.53 | End of split
% 5.45/1.53 |
% 5.45/1.53 End of proof
% 5.45/1.53 % SZS output end Proof for theBenchmark
% 5.45/1.53
% 5.45/1.53 912ms
%------------------------------------------------------------------------------