TSTP Solution File: SET886+1 by Princess---230619
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SET886+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n019.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 15:26:55 EDT 2023
% Result : Theorem 3.95s 1.25s
% Output : Proof 3.95s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET886+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.12/0.34 % Computer : n019.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Sat Aug 26 16:14:43 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.19/0.56 ________ _____
% 0.19/0.56 ___ __ \_________(_)________________________________
% 0.19/0.56 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.19/0.56 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.19/0.56 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.19/0.56
% 0.19/0.56 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.19/0.56 (2023-06-19)
% 0.19/0.56
% 0.19/0.56 (c) Philipp Rümmer, 2009-2023
% 0.19/0.56 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.19/0.56 Amanda Stjerna.
% 0.19/0.56 Free software under BSD-3-Clause.
% 0.19/0.56
% 0.19/0.56 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.19/0.56
% 0.19/0.56 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.19/0.57 Running up to 7 provers in parallel.
% 0.19/0.59 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.19/0.59 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.19/0.59 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.19/0.59 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.19/0.59 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.19/0.59 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.19/0.59 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 1.85/0.96 Prover 4: Preprocessing ...
% 1.85/0.96 Prover 1: Preprocessing ...
% 1.85/1.00 Prover 2: Preprocessing ...
% 1.85/1.00 Prover 0: Preprocessing ...
% 1.85/1.00 Prover 6: Preprocessing ...
% 1.85/1.00 Prover 3: Preprocessing ...
% 1.85/1.00 Prover 5: Preprocessing ...
% 3.02/1.11 Prover 1: Warning: ignoring some quantifiers
% 3.02/1.11 Prover 6: Proving ...
% 3.02/1.12 Prover 3: Warning: ignoring some quantifiers
% 3.02/1.12 Prover 1: Constructing countermodel ...
% 3.02/1.12 Prover 3: Constructing countermodel ...
% 3.02/1.13 Prover 5: Proving ...
% 3.02/1.13 Prover 4: Constructing countermodel ...
% 3.02/1.13 Prover 0: Proving ...
% 3.02/1.14 Prover 2: Proving ...
% 3.95/1.25 Prover 3: proved (666ms)
% 3.95/1.25
% 3.95/1.25 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.95/1.25
% 3.95/1.25 Prover 6: stopped
% 3.95/1.25 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 3.95/1.25 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 3.95/1.26 Prover 5: proved (673ms)
% 3.95/1.26
% 3.95/1.26 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.95/1.26
% 3.95/1.26 Prover 2: proved (681ms)
% 3.95/1.26
% 3.95/1.26 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.95/1.26
% 3.95/1.26 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 3.95/1.26 Prover 0: proved (682ms)
% 3.95/1.26
% 3.95/1.26 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.95/1.26
% 3.95/1.26 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 3.95/1.26 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 3.95/1.27 Prover 7: Preprocessing ...
% 3.95/1.27 Prover 1: Found proof (size 16)
% 3.95/1.27 Prover 1: proved (691ms)
% 3.95/1.27 Prover 10: Preprocessing ...
% 3.95/1.28 Prover 4: stopped
% 3.95/1.28 Prover 13: Preprocessing ...
% 3.95/1.28 Prover 11: Preprocessing ...
% 3.95/1.28 Prover 8: Preprocessing ...
% 3.95/1.30 Prover 11: stopped
% 3.95/1.31 Prover 7: Warning: ignoring some quantifiers
% 3.95/1.31 Prover 7: Constructing countermodel ...
% 3.95/1.32 Prover 10: Warning: ignoring some quantifiers
% 3.95/1.32 Prover 8: Warning: ignoring some quantifiers
% 3.95/1.32 Prover 7: stopped
% 3.95/1.32 Prover 10: Constructing countermodel ...
% 3.95/1.32 Prover 13: Warning: ignoring some quantifiers
% 3.95/1.32 Prover 10: stopped
% 3.95/1.32 Prover 8: Constructing countermodel ...
% 3.95/1.33 Prover 13: Constructing countermodel ...
% 3.95/1.33 Prover 8: stopped
% 3.95/1.33 Prover 13: stopped
% 3.95/1.33
% 3.95/1.33 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.95/1.33
% 3.95/1.33 % SZS output start Proof for theBenchmark
% 3.95/1.34 Assumptions after simplification:
% 3.95/1.34 ---------------------------------
% 3.95/1.34
% 3.95/1.34 (commutativity_k2_tarski)
% 3.95/1.37 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (unordered_pair(v0, v1) = v2) |
% 3.95/1.37 ~ $i(v1) | ~ $i(v0) | (unordered_pair(v1, v0) = v2 & $i(v2)))
% 3.95/1.37
% 3.95/1.37 (t26_zfmisc_1)
% 3.95/1.37 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v2 = v0
% 3.95/1.37 | ~ (singleton(v2) = v4) | ~ (subset(v3, v4) = 0) | ~ (unordered_pair(v0,
% 3.95/1.37 v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0))
% 3.95/1.37
% 3.95/1.37 (t27_zfmisc_1)
% 3.95/1.37 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ( ~ (v4
% 3.95/1.37 = v3) & singleton(v2) = v4 & subset(v3, v4) = 0 & unordered_pair(v0, v1) =
% 3.95/1.37 v3 & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 3.95/1.37
% 3.95/1.37 (t69_enumset1)
% 3.95/1.38 ! [v0: $i] : ! [v1: $i] : ( ~ (singleton(v0) = v1) | ~ $i(v0) |
% 3.95/1.38 (unordered_pair(v0, v0) = v1 & $i(v1)))
% 3.95/1.38
% 3.95/1.38 (function-axioms)
% 3.95/1.38 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 3.95/1.38 [v3: $i] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) &
% 3.95/1.38 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 3.95/1.38 (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) & ! [v0:
% 3.95/1.38 $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (singleton(v2) = v1) | ~
% 3.95/1.38 (singleton(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 3.95/1.38 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (empty(v2) = v1) | ~
% 3.95/1.38 (empty(v2) = v0))
% 3.95/1.38
% 3.95/1.38 Further assumptions not needed in the proof:
% 3.95/1.38 --------------------------------------------
% 3.95/1.38 rc1_xboole_0, rc2_xboole_0, reflexivity_r1_tarski
% 3.95/1.38
% 3.95/1.38 Those formulas are unsatisfiable:
% 3.95/1.38 ---------------------------------
% 3.95/1.38
% 3.95/1.38 Begin of proof
% 3.95/1.38 |
% 3.95/1.38 | ALPHA: (function-axioms) implies:
% 3.95/1.38 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 3.95/1.38 | (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0))
% 3.95/1.38 |
% 3.95/1.38 | DELTA: instantiating (t27_zfmisc_1) with fresh symbols all_12_0, all_12_1,
% 3.95/1.39 | all_12_2, all_12_3, all_12_4 gives:
% 3.95/1.39 | (2) ~ (all_12_0 = all_12_1) & singleton(all_12_2) = all_12_0 &
% 3.95/1.39 | subset(all_12_1, all_12_0) = 0 & unordered_pair(all_12_4, all_12_3) =
% 3.95/1.39 | all_12_1 & $i(all_12_0) & $i(all_12_1) & $i(all_12_2) & $i(all_12_3) &
% 3.95/1.39 | $i(all_12_4)
% 3.95/1.39 |
% 3.95/1.39 | ALPHA: (2) implies:
% 3.95/1.39 | (3) ~ (all_12_0 = all_12_1)
% 3.95/1.39 | (4) $i(all_12_4)
% 3.95/1.39 | (5) $i(all_12_3)
% 3.95/1.39 | (6) $i(all_12_2)
% 3.95/1.39 | (7) unordered_pair(all_12_4, all_12_3) = all_12_1
% 3.95/1.39 | (8) subset(all_12_1, all_12_0) = 0
% 3.95/1.39 | (9) singleton(all_12_2) = all_12_0
% 3.95/1.39 |
% 3.95/1.39 | GROUND_INST: instantiating (commutativity_k2_tarski) with all_12_4, all_12_3,
% 3.95/1.39 | all_12_1, simplifying with (4), (5), (7) gives:
% 3.95/1.39 | (10) unordered_pair(all_12_3, all_12_4) = all_12_1 & $i(all_12_1)
% 3.95/1.39 |
% 3.95/1.39 | ALPHA: (10) implies:
% 3.95/1.39 | (11) unordered_pair(all_12_3, all_12_4) = all_12_1
% 3.95/1.39 |
% 3.95/1.39 | GROUND_INST: instantiating (t26_zfmisc_1) with all_12_4, all_12_3, all_12_2,
% 3.95/1.39 | all_12_1, all_12_0, simplifying with (4), (5), (6), (7), (8), (9)
% 3.95/1.39 | gives:
% 3.95/1.39 | (12) all_12_2 = all_12_4
% 3.95/1.39 |
% 3.95/1.39 | GROUND_INST: instantiating (t69_enumset1) with all_12_2, all_12_0, simplifying
% 3.95/1.39 | with (6), (9) gives:
% 3.95/1.39 | (13) unordered_pair(all_12_2, all_12_2) = all_12_0 & $i(all_12_0)
% 3.95/1.39 |
% 3.95/1.39 | ALPHA: (13) implies:
% 3.95/1.39 | (14) unordered_pair(all_12_2, all_12_2) = all_12_0
% 3.95/1.39 |
% 3.95/1.39 | REDUCE: (9), (12) imply:
% 3.95/1.39 | (15) singleton(all_12_4) = all_12_0
% 3.95/1.39 |
% 3.95/1.39 | REDUCE: (12), (14) imply:
% 3.95/1.40 | (16) unordered_pair(all_12_4, all_12_4) = all_12_0
% 3.95/1.40 |
% 3.95/1.40 | GROUND_INST: instantiating (t26_zfmisc_1) with all_12_3, all_12_4, all_12_4,
% 3.95/1.40 | all_12_1, all_12_0, simplifying with (4), (5), (8), (11), (15)
% 3.95/1.40 | gives:
% 3.95/1.40 | (17) all_12_3 = all_12_4
% 3.95/1.40 |
% 3.95/1.40 | REDUCE: (7), (17) imply:
% 3.95/1.40 | (18) unordered_pair(all_12_4, all_12_4) = all_12_1
% 3.95/1.40 |
% 3.95/1.40 | GROUND_INST: instantiating (1) with all_12_0, all_12_1, all_12_4, all_12_4,
% 3.95/1.40 | simplifying with (16), (18) gives:
% 3.95/1.40 | (19) all_12_0 = all_12_1
% 3.95/1.40 |
% 3.95/1.40 | REDUCE: (3), (19) imply:
% 3.95/1.40 | (20) $false
% 3.95/1.40 |
% 3.95/1.40 | CLOSE: (20) is inconsistent.
% 3.95/1.40 |
% 3.95/1.40 End of proof
% 3.95/1.40 % SZS output end Proof for theBenchmark
% 3.95/1.40
% 3.95/1.40 839ms
%------------------------------------------------------------------------------