TSTP Solution File: SET881+1 by Princess---230619
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SET881+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 : 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 15:26:53 EDT 2023
% Result : Theorem 4.94s 1.47s
% Output : Proof 6.01s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : SET881+1 : TPTP v8.1.2. Released v3.2.0.
% 0.08/0.14 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.35 % Computer : n011.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Sat Aug 26 12:09:39 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.21/0.63 ________ _____
% 0.21/0.63 ___ __ \_________(_)________________________________
% 0.21/0.63 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.21/0.63 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.21/0.63 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.21/0.63
% 0.21/0.63 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.21/0.63 (2023-06-19)
% 0.21/0.63
% 0.21/0.63 (c) Philipp Rümmer, 2009-2023
% 0.21/0.63 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.21/0.63 Amanda Stjerna.
% 0.21/0.63 Free software under BSD-3-Clause.
% 0.21/0.63
% 0.21/0.63 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.21/0.63
% 0.21/0.63 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.21/0.65 Running up to 7 provers in parallel.
% 0.21/0.66 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.21/0.66 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.21/0.66 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.21/0.66 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.21/0.66 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.21/0.66 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.21/0.66 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 1.75/1.06 Prover 4: Preprocessing ...
% 1.75/1.06 Prover 1: Preprocessing ...
% 2.51/1.11 Prover 0: Preprocessing ...
% 2.51/1.11 Prover 2: Preprocessing ...
% 2.51/1.11 Prover 5: Preprocessing ...
% 2.51/1.11 Prover 3: Preprocessing ...
% 2.51/1.11 Prover 6: Preprocessing ...
% 3.85/1.30 Prover 3: Warning: ignoring some quantifiers
% 3.85/1.30 Prover 1: Warning: ignoring some quantifiers
% 3.85/1.31 Prover 6: Proving ...
% 3.85/1.31 Prover 3: Constructing countermodel ...
% 3.85/1.31 Prover 5: Proving ...
% 3.85/1.32 Prover 1: Constructing countermodel ...
% 3.85/1.32 Prover 4: Warning: ignoring some quantifiers
% 3.85/1.33 Prover 4: Constructing countermodel ...
% 3.85/1.34 Prover 2: Proving ...
% 3.85/1.35 Prover 0: Proving ...
% 4.94/1.47 Prover 3: proved (815ms)
% 4.94/1.47
% 4.94/1.47 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.94/1.47
% 4.94/1.47 Prover 6: stopped
% 4.94/1.47 Prover 5: stopped
% 4.94/1.47 Prover 0: stopped
% 5.13/1.48 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 5.13/1.48 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 5.13/1.48 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 5.13/1.48 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 5.13/1.49 Prover 2: proved (840ms)
% 5.13/1.49
% 5.13/1.49 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.13/1.49
% 5.13/1.49 Prover 11: Preprocessing ...
% 5.13/1.50 Prover 10: Preprocessing ...
% 5.13/1.50 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 5.13/1.50 Prover 7: Preprocessing ...
% 5.13/1.50 Prover 8: Preprocessing ...
% 5.13/1.51 Prover 13: Preprocessing ...
% 5.13/1.52 Prover 4: Found proof (size 17)
% 5.13/1.52 Prover 4: proved (868ms)
% 5.49/1.52 Prover 1: Found proof (size 18)
% 5.49/1.52 Prover 1: proved (871ms)
% 5.49/1.52 Prover 11: stopped
% 5.49/1.54 Prover 13: stopped
% 5.49/1.54 Prover 10: Warning: ignoring some quantifiers
% 5.49/1.54 Prover 10: Constructing countermodel ...
% 5.65/1.54 Prover 7: Warning: ignoring some quantifiers
% 5.65/1.55 Prover 10: stopped
% 5.65/1.55 Prover 7: Constructing countermodel ...
% 5.65/1.55 Prover 8: Warning: ignoring some quantifiers
% 5.65/1.55 Prover 7: stopped
% 5.65/1.56 Prover 8: Constructing countermodel ...
% 5.65/1.56 Prover 8: stopped
% 5.65/1.56
% 5.65/1.56 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.65/1.56
% 5.65/1.57 % SZS output start Proof for theBenchmark
% 5.65/1.57 Assumptions after simplification:
% 5.65/1.57 ---------------------------------
% 5.65/1.57
% 5.65/1.57 (commutativity_k2_tarski)
% 5.65/1.60 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (unordered_pair(v1, v0) = v2) |
% 5.65/1.60 ~ $i(v1) | ~ $i(v0) | (unordered_pair(v0, v1) = v2 & $i(v2))) & ! [v0: $i]
% 5.65/1.60 : ! [v1: $i] : ! [v2: $i] : ( ~ (unordered_pair(v0, v1) = v2) | ~ $i(v1) |
% 5.65/1.60 ~ $i(v0) | (unordered_pair(v1, v0) = v2 & $i(v2)))
% 5.65/1.60
% 5.65/1.60 (d2_tarski)
% 5.65/1.61 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v1 | v3 = v0 |
% 5.65/1.61 ~ (unordered_pair(v0, v1) = v2) | ~ (in(v3, v2) = 0) | ~ $i(v3) | ~
% 5.65/1.61 $i(v2) | ~ $i(v1) | ~ $i(v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 5.65/1.61 ! [v3: int] : (v3 = 0 | ~ (unordered_pair(v0, v1) = v2) | ~ (in(v1, v2) =
% 5.65/1.61 v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0)) & ! [v0: $i] : ! [v1: $i] : !
% 5.65/1.61 [v2: $i] : ! [v3: int] : (v3 = 0 | ~ (unordered_pair(v0, v1) = v2) | ~
% 5.65/1.61 (in(v0, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0)) & ? [v0: $i] : !
% 5.65/1.61 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v0 | ~ (unordered_pair(v1, v2) =
% 5.65/1.61 v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: $i] : ? [v5: any] :
% 5.65/1.61 (in(v4, v0) = v5 & $i(v4) & ( ~ (v5 = 0) | ( ~ (v4 = v2) & ~ (v4 = v1))) &
% 5.65/1.61 (v5 = 0 | v4 = v2 | v4 = v1)))
% 5.65/1.61
% 5.65/1.61 (l36_zfmisc_1)
% 5.65/1.61 $i(empty_set) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 =
% 5.65/1.61 empty_set | ~ (singleton(v0) = v2) | ~ (set_difference(v2, v1) = v3) | ~
% 5.65/1.61 $i(v1) | ~ $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & in(v0, v1) = v4)) & !
% 5.65/1.61 [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (in(v0, v1) = v2) | ~
% 5.65/1.61 $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] : ( ~ (v4 = empty_set) &
% 5.65/1.61 singleton(v0) = v3 & set_difference(v3, v1) = v4 & $i(v4) & $i(v3))) & !
% 5.65/1.61 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (singleton(v0) = v2) | ~
% 5.65/1.61 (set_difference(v2, v1) = empty_set) | ~ $i(v1) | ~ $i(v0) | in(v0, v1) =
% 5.65/1.61 0) & ! [v0: $i] : ! [v1: $i] : ( ~ (in(v0, v1) = 0) | ~ $i(v1) | ~
% 5.65/1.61 $i(v0) | ? [v2: $i] : (singleton(v0) = v2 & set_difference(v2, v1) =
% 5.65/1.61 empty_set & $i(v2)))
% 5.65/1.61
% 5.65/1.61 (t22_zfmisc_1)
% 5.65/1.62 $i(empty_set) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ?
% 5.65/1.62 [v4: $i] : ( ~ (v4 = empty_set) & singleton(v0) = v2 & set_difference(v2, v3)
% 5.65/1.62 = v4 & unordered_pair(v0, v1) = v3 & $i(v4) & $i(v3) & $i(v2) & $i(v1) &
% 5.65/1.62 $i(v0))
% 5.65/1.62
% 5.65/1.62 Further assumptions not needed in the proof:
% 5.65/1.62 --------------------------------------------
% 5.65/1.62 antisymmetry_r2_hidden, fc1_xboole_0, rc1_xboole_0, rc2_xboole_0
% 5.65/1.62
% 5.65/1.62 Those formulas are unsatisfiable:
% 5.65/1.62 ---------------------------------
% 5.65/1.62
% 5.65/1.62 Begin of proof
% 5.65/1.62 |
% 5.65/1.62 | ALPHA: (commutativity_k2_tarski) implies:
% 6.01/1.62 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (unordered_pair(v1, v0) =
% 6.01/1.62 | v2) | ~ $i(v1) | ~ $i(v0) | (unordered_pair(v0, v1) = v2 &
% 6.01/1.62 | $i(v2)))
% 6.01/1.62 |
% 6.01/1.62 | ALPHA: (d2_tarski) implies:
% 6.01/1.62 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~
% 6.01/1.62 | (unordered_pair(v0, v1) = v2) | ~ (in(v1, v2) = v3) | ~ $i(v2) | ~
% 6.01/1.62 | $i(v1) | ~ $i(v0))
% 6.01/1.62 |
% 6.01/1.62 | ALPHA: (l36_zfmisc_1) implies:
% 6.01/1.62 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = empty_set
% 6.01/1.62 | | ~ (singleton(v0) = v2) | ~ (set_difference(v2, v1) = v3) | ~
% 6.01/1.62 | $i(v1) | ~ $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & in(v0, v1) = v4))
% 6.01/1.62 |
% 6.01/1.62 | ALPHA: (t22_zfmisc_1) implies:
% 6.01/1.63 | (4) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : (
% 6.01/1.63 | ~ (v4 = empty_set) & singleton(v0) = v2 & set_difference(v2, v3) = v4
% 6.01/1.63 | & unordered_pair(v0, v1) = v3 & $i(v4) & $i(v3) & $i(v2) & $i(v1) &
% 6.01/1.63 | $i(v0))
% 6.01/1.63 |
% 6.01/1.63 | DELTA: instantiating (4) with fresh symbols all_12_0, all_12_1, all_12_2,
% 6.01/1.63 | all_12_3, all_12_4 gives:
% 6.01/1.63 | (5) ~ (all_12_0 = empty_set) & singleton(all_12_4) = all_12_2 &
% 6.01/1.63 | set_difference(all_12_2, all_12_1) = all_12_0 &
% 6.01/1.63 | unordered_pair(all_12_4, all_12_3) = all_12_1 & $i(all_12_0) &
% 6.01/1.63 | $i(all_12_1) & $i(all_12_2) & $i(all_12_3) & $i(all_12_4)
% 6.01/1.63 |
% 6.01/1.63 | ALPHA: (5) implies:
% 6.01/1.63 | (6) ~ (all_12_0 = empty_set)
% 6.01/1.63 | (7) $i(all_12_4)
% 6.01/1.63 | (8) $i(all_12_3)
% 6.01/1.63 | (9) unordered_pair(all_12_4, all_12_3) = all_12_1
% 6.01/1.63 | (10) set_difference(all_12_2, all_12_1) = all_12_0
% 6.01/1.63 | (11) singleton(all_12_4) = all_12_2
% 6.01/1.63 |
% 6.01/1.63 | GROUND_INST: instantiating (1) with all_12_3, all_12_4, all_12_1, simplifying
% 6.01/1.63 | with (7), (8), (9) gives:
% 6.01/1.63 | (12) unordered_pair(all_12_3, all_12_4) = all_12_1 & $i(all_12_1)
% 6.01/1.63 |
% 6.01/1.63 | ALPHA: (12) implies:
% 6.01/1.63 | (13) $i(all_12_1)
% 6.01/1.63 | (14) unordered_pair(all_12_3, all_12_4) = all_12_1
% 6.01/1.63 |
% 6.01/1.63 | GROUND_INST: instantiating (3) with all_12_4, all_12_1, all_12_2, all_12_0,
% 6.01/1.63 | simplifying with (7), (10), (11), (13) gives:
% 6.01/1.64 | (15) all_12_0 = empty_set | ? [v0: int] : ( ~ (v0 = 0) & in(all_12_4,
% 6.01/1.64 | all_12_1) = v0)
% 6.01/1.64 |
% 6.01/1.64 | BETA: splitting (15) gives:
% 6.01/1.64 |
% 6.01/1.64 | Case 1:
% 6.01/1.64 | |
% 6.01/1.64 | | (16) all_12_0 = empty_set
% 6.01/1.64 | |
% 6.01/1.64 | | REDUCE: (6), (16) imply:
% 6.01/1.64 | | (17) $false
% 6.01/1.64 | |
% 6.01/1.64 | | CLOSE: (17) is inconsistent.
% 6.01/1.64 | |
% 6.01/1.64 | Case 2:
% 6.01/1.64 | |
% 6.01/1.64 | | (18) ? [v0: int] : ( ~ (v0 = 0) & in(all_12_4, all_12_1) = v0)
% 6.01/1.64 | |
% 6.01/1.64 | | DELTA: instantiating (18) with fresh symbol all_26_0 gives:
% 6.01/1.64 | | (19) ~ (all_26_0 = 0) & in(all_12_4, all_12_1) = all_26_0
% 6.01/1.64 | |
% 6.01/1.64 | | ALPHA: (19) implies:
% 6.01/1.64 | | (20) ~ (all_26_0 = 0)
% 6.01/1.64 | | (21) in(all_12_4, all_12_1) = all_26_0
% 6.01/1.64 | |
% 6.01/1.64 | | GROUND_INST: instantiating (2) with all_12_3, all_12_4, all_12_1, all_26_0,
% 6.01/1.64 | | simplifying with (7), (8), (13), (14), (21) gives:
% 6.01/1.64 | | (22) all_26_0 = 0
% 6.01/1.64 | |
% 6.01/1.64 | | REDUCE: (20), (22) imply:
% 6.01/1.64 | | (23) $false
% 6.01/1.64 | |
% 6.01/1.64 | | CLOSE: (23) is inconsistent.
% 6.01/1.64 | |
% 6.01/1.64 | End of split
% 6.01/1.64 |
% 6.01/1.64 End of proof
% 6.01/1.64 % SZS output end Proof for theBenchmark
% 6.01/1.64
% 6.01/1.64 1006ms
%------------------------------------------------------------------------------