TSTP Solution File: SET573+3 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SET573+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 : n021.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 15:25:20 EDT 2023
% Result : Theorem 3.83s 1.24s
% Output : Proof 4.66s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SET573+3 : TPTP v8.1.2. Released v2.2.0.
% 0.00/0.14 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.16/0.35 % Computer : n021.cluster.edu
% 0.16/0.35 % Model : x86_64 x86_64
% 0.16/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.35 % Memory : 8042.1875MB
% 0.16/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.35 % CPULimit : 300
% 0.16/0.35 % WCLimit : 300
% 0.16/0.35 % DateTime : Sat Aug 26 10:59:11 EDT 2023
% 0.16/0.35 % CPUTime :
% 0.20/0.63 ________ _____
% 0.20/0.63 ___ __ \_________(_)________________________________
% 0.20/0.63 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.20/0.63 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.20/0.63 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.20/0.63
% 0.20/0.63 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.20/0.63 (2023-06-19)
% 0.20/0.63
% 0.20/0.63 (c) Philipp Rümmer, 2009-2023
% 0.20/0.63 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.20/0.63 Amanda Stjerna.
% 0.20/0.63 Free software under BSD-3-Clause.
% 0.20/0.63
% 0.20/0.63 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.20/0.63
% 0.20/0.63 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.20/0.64 Running up to 7 provers in parallel.
% 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 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 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 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 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 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 1.78/0.98 Prover 4: Preprocessing ...
% 1.78/0.98 Prover 1: Preprocessing ...
% 2.12/1.02 Prover 3: Preprocessing ...
% 2.12/1.02 Prover 6: Preprocessing ...
% 2.12/1.02 Prover 5: Preprocessing ...
% 2.12/1.02 Prover 2: Preprocessing ...
% 2.12/1.02 Prover 0: Preprocessing ...
% 2.65/1.10 Prover 5: Proving ...
% 2.65/1.10 Prover 2: Proving ...
% 2.65/1.11 Prover 6: Proving ...
% 3.00/1.13 Prover 1: Constructing countermodel ...
% 3.00/1.13 Prover 3: Constructing countermodel ...
% 3.22/1.16 Prover 0: Proving ...
% 3.22/1.16 Prover 4: Constructing countermodel ...
% 3.83/1.24 Prover 3: proved (591ms)
% 3.83/1.24
% 3.83/1.24 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.83/1.24
% 3.83/1.24 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 3.83/1.25 Prover 5: stopped
% 3.83/1.25 Prover 6: stopped
% 3.83/1.25 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 3.83/1.25 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 3.83/1.25 Prover 2: proved (604ms)
% 3.83/1.25 Prover 0: proved (603ms)
% 3.83/1.25
% 3.83/1.25 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.83/1.25
% 3.83/1.25
% 3.83/1.25 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.83/1.25
% 3.83/1.26 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 3.83/1.26 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 3.83/1.26 Prover 7: Preprocessing ...
% 3.83/1.27 Prover 10: Preprocessing ...
% 3.83/1.27 Prover 8: Preprocessing ...
% 4.18/1.28 Prover 7: Warning: ignoring some quantifiers
% 4.18/1.28 Prover 11: Preprocessing ...
% 4.18/1.28 Prover 13: Preprocessing ...
% 4.18/1.28 Prover 7: Constructing countermodel ...
% 4.18/1.29 Prover 10: Warning: ignoring some quantifiers
% 4.18/1.30 Prover 10: Constructing countermodel ...
% 4.18/1.30 Prover 13: Warning: ignoring some quantifiers
% 4.18/1.30 Prover 13: Constructing countermodel ...
% 4.18/1.31 Prover 4: Found proof (size 19)
% 4.18/1.31 Prover 8: Warning: ignoring some quantifiers
% 4.18/1.32 Prover 8: Constructing countermodel ...
% 4.18/1.32 Prover 1: Found proof (size 18)
% 4.18/1.32 Prover 1: proved (676ms)
% 4.18/1.32 Prover 4: proved (671ms)
% 4.18/1.32 Prover 8: stopped
% 4.18/1.32 Prover 13: stopped
% 4.18/1.32 Prover 10: stopped
% 4.18/1.33 Prover 7: stopped
% 4.18/1.34 Prover 11: Constructing countermodel ...
% 4.59/1.35 Prover 11: stopped
% 4.59/1.35
% 4.59/1.35 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.59/1.35
% 4.59/1.35 % SZS output start Proof for theBenchmark
% 4.59/1.35 Assumptions after simplification:
% 4.59/1.35 ---------------------------------
% 4.59/1.35
% 4.59/1.35 (disjoint_defn)
% 4.66/1.38 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (disjoint(v0, v1) =
% 4.66/1.38 v2) | ~ $i(v1) | ~ $i(v0) | intersect(v0, v1) = 0) & ! [v0: $i] : !
% 4.66/1.38 [v1: $i] : ( ~ (disjoint(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: int] :
% 4.66/1.38 ( ~ (v2 = 0) & intersect(v0, v1) = v2))
% 4.66/1.38
% 4.66/1.38 (intersect_defn)
% 4.66/1.39 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (intersect(v0, v1) =
% 4.66/1.39 v2) | ~ $i(v1) | ~ $i(v0) | ! [v3: $i] : ( ~ (member(v3, v0) = 0) | ~
% 4.66/1.39 $i(v3) | ? [v4: int] : ( ~ (v4 = 0) & member(v3, v1) = v4))) & ! [v0:
% 4.66/1.39 $i] : ! [v1: $i] : ( ~ (intersect(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ?
% 4.66/1.39 [v2: $i] : (member(v2, v1) = 0 & member(v2, v0) = 0 & $i(v2)))
% 4.66/1.39
% 4.66/1.39 (prove_th12)
% 4.66/1.39 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (disjoint(v1, v2) = 0 & member(v0,
% 4.66/1.39 v2) = 0 & member(v0, v1) = 0 & $i(v2) & $i(v1) & $i(v0))
% 4.66/1.39
% 4.66/1.39 (function-axioms)
% 4.66/1.39 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 4.66/1.39 [v3: $i] : (v1 = v0 | ~ (disjoint(v3, v2) = v1) | ~ (disjoint(v3, v2) = v0))
% 4.66/1.39 & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 4.66/1.39 [v3: $i] : (v1 = v0 | ~ (intersect(v3, v2) = v1) | ~ (intersect(v3, v2) =
% 4.66/1.39 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 4.66/1.39 $i] : ! [v3: $i] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2)
% 4.66/1.39 = v0))
% 4.66/1.39
% 4.66/1.39 Further assumptions not needed in the proof:
% 4.66/1.39 --------------------------------------------
% 4.66/1.39 symmetry_of_intersect
% 4.66/1.39
% 4.66/1.39 Those formulas are unsatisfiable:
% 4.66/1.39 ---------------------------------
% 4.66/1.39
% 4.66/1.39 Begin of proof
% 4.66/1.39 |
% 4.66/1.39 | ALPHA: (intersect_defn) implies:
% 4.66/1.40 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (intersect(v0,
% 4.66/1.40 | v1) = v2) | ~ $i(v1) | ~ $i(v0) | ! [v3: $i] : ( ~ (member(v3,
% 4.66/1.40 | v0) = 0) | ~ $i(v3) | ? [v4: int] : ( ~ (v4 = 0) & member(v3,
% 4.66/1.40 | v1) = v4)))
% 4.66/1.40 |
% 4.66/1.40 | ALPHA: (disjoint_defn) implies:
% 4.66/1.40 | (2) ! [v0: $i] : ! [v1: $i] : ( ~ (disjoint(v0, v1) = 0) | ~ $i(v1) | ~
% 4.66/1.40 | $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & intersect(v0, v1) = v2))
% 4.66/1.40 |
% 4.66/1.40 | ALPHA: (function-axioms) implies:
% 4.66/1.40 | (3) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 4.66/1.40 | ! [v3: $i] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2)
% 4.66/1.40 | = v0))
% 4.66/1.40 |
% 4.66/1.40 | DELTA: instantiating (prove_th12) with fresh symbols all_6_0, all_6_1, all_6_2
% 4.66/1.40 | gives:
% 4.66/1.40 | (4) disjoint(all_6_1, all_6_0) = 0 & member(all_6_2, all_6_0) = 0 &
% 4.66/1.40 | member(all_6_2, all_6_1) = 0 & $i(all_6_0) & $i(all_6_1) & $i(all_6_2)
% 4.66/1.40 |
% 4.66/1.40 | ALPHA: (4) implies:
% 4.66/1.40 | (5) $i(all_6_2)
% 4.66/1.40 | (6) $i(all_6_1)
% 4.66/1.40 | (7) $i(all_6_0)
% 4.66/1.40 | (8) member(all_6_2, all_6_1) = 0
% 4.66/1.40 | (9) member(all_6_2, all_6_0) = 0
% 4.66/1.40 | (10) disjoint(all_6_1, all_6_0) = 0
% 4.66/1.40 |
% 4.66/1.40 | GROUND_INST: instantiating (2) with all_6_1, all_6_0, simplifying with (6),
% 4.66/1.40 | (7), (10) gives:
% 4.66/1.40 | (11) ? [v0: int] : ( ~ (v0 = 0) & intersect(all_6_1, all_6_0) = v0)
% 4.66/1.40 |
% 4.66/1.40 | DELTA: instantiating (11) with fresh symbol all_13_0 gives:
% 4.66/1.41 | (12) ~ (all_13_0 = 0) & intersect(all_6_1, all_6_0) = all_13_0
% 4.66/1.41 |
% 4.66/1.41 | ALPHA: (12) implies:
% 4.66/1.41 | (13) ~ (all_13_0 = 0)
% 4.66/1.41 | (14) intersect(all_6_1, all_6_0) = all_13_0
% 4.66/1.41 |
% 4.66/1.41 | GROUND_INST: instantiating (1) with all_6_1, all_6_0, all_13_0, simplifying
% 4.66/1.41 | with (6), (7), (14) gives:
% 4.66/1.41 | (15) all_13_0 = 0 | ! [v0: $i] : ( ~ (member(v0, all_6_1) = 0) | ~ $i(v0)
% 4.66/1.41 | | ? [v1: int] : ( ~ (v1 = 0) & member(v0, all_6_0) = v1))
% 4.66/1.41 |
% 4.66/1.41 | BETA: splitting (15) gives:
% 4.66/1.41 |
% 4.66/1.41 | Case 1:
% 4.66/1.41 | |
% 4.66/1.41 | | (16) all_13_0 = 0
% 4.66/1.41 | |
% 4.66/1.41 | | REDUCE: (13), (16) imply:
% 4.66/1.41 | | (17) $false
% 4.66/1.41 | |
% 4.66/1.41 | | CLOSE: (17) is inconsistent.
% 4.66/1.41 | |
% 4.66/1.41 | Case 2:
% 4.66/1.41 | |
% 4.66/1.41 | | (18) ! [v0: $i] : ( ~ (member(v0, all_6_1) = 0) | ~ $i(v0) | ? [v1:
% 4.66/1.41 | | int] : ( ~ (v1 = 0) & member(v0, all_6_0) = v1))
% 4.66/1.41 | |
% 4.66/1.41 | | GROUND_INST: instantiating (18) with all_6_2, simplifying with (5), (8)
% 4.66/1.41 | | gives:
% 4.66/1.41 | | (19) ? [v0: int] : ( ~ (v0 = 0) & member(all_6_2, all_6_0) = v0)
% 4.66/1.41 | |
% 4.66/1.41 | | DELTA: instantiating (19) with fresh symbol all_23_0 gives:
% 4.66/1.41 | | (20) ~ (all_23_0 = 0) & member(all_6_2, all_6_0) = all_23_0
% 4.66/1.41 | |
% 4.66/1.41 | | ALPHA: (20) implies:
% 4.66/1.41 | | (21) ~ (all_23_0 = 0)
% 4.66/1.41 | | (22) member(all_6_2, all_6_0) = all_23_0
% 4.66/1.41 | |
% 4.66/1.41 | | GROUND_INST: instantiating (3) with 0, all_23_0, all_6_0, all_6_2,
% 4.66/1.41 | | simplifying with (9), (22) gives:
% 4.66/1.41 | | (23) all_23_0 = 0
% 4.66/1.41 | |
% 4.66/1.41 | | REDUCE: (21), (23) imply:
% 4.66/1.41 | | (24) $false
% 4.66/1.41 | |
% 4.66/1.41 | | CLOSE: (24) is inconsistent.
% 4.66/1.41 | |
% 4.66/1.41 | End of split
% 4.66/1.41 |
% 4.66/1.41 End of proof
% 4.66/1.41 % SZS output end Proof for theBenchmark
% 4.66/1.41
% 4.66/1.41 787ms
%------------------------------------------------------------------------------