TSTP Solution File: SEU155+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SEU155+1 : TPTP v8.1.2. Released v3.3.0.
% 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 17:42:50 EDT 2023
% Result : Theorem 4.61s 1.37s
% Output : Proof 5.42s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SEU155+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.35 % Computer : n019.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 : Thu Aug 24 01:10:13 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.19/0.62 ________ _____
% 0.19/0.62 ___ __ \_________(_)________________________________
% 0.19/0.62 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.19/0.62 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.19/0.62 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.19/0.62
% 0.19/0.62 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.19/0.62 (2023-06-19)
% 0.19/0.62
% 0.19/0.62 (c) Philipp Rümmer, 2009-2023
% 0.19/0.62 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.19/0.62 Amanda Stjerna.
% 0.19/0.62 Free software under BSD-3-Clause.
% 0.19/0.62
% 0.19/0.62 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.19/0.62
% 0.19/0.62 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.19/0.63 Running up to 7 provers in parallel.
% 0.19/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.19/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.19/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.19/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.19/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.19/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.19/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.13/0.97 Prover 4: Preprocessing ...
% 2.13/0.98 Prover 1: Preprocessing ...
% 2.37/1.02 Prover 6: Preprocessing ...
% 2.37/1.02 Prover 3: Preprocessing ...
% 2.37/1.02 Prover 5: Preprocessing ...
% 2.37/1.02 Prover 0: Preprocessing ...
% 2.37/1.02 Prover 2: Preprocessing ...
% 3.57/1.19 Prover 1: Warning: ignoring some quantifiers
% 3.57/1.20 Prover 5: Proving ...
% 3.57/1.20 Prover 2: Proving ...
% 3.57/1.20 Prover 6: Proving ...
% 3.57/1.20 Prover 3: Warning: ignoring some quantifiers
% 3.57/1.21 Prover 4: Warning: ignoring some quantifiers
% 3.57/1.22 Prover 1: Constructing countermodel ...
% 3.57/1.22 Prover 0: Proving ...
% 3.57/1.22 Prover 3: Constructing countermodel ...
% 3.57/1.22 Prover 4: Constructing countermodel ...
% 4.61/1.36 Prover 3: proved (722ms)
% 4.61/1.37
% 4.61/1.37 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.61/1.37
% 4.61/1.37 Prover 5: stopped
% 4.61/1.37 Prover 6: stopped
% 4.61/1.38 Prover 2: stopped
% 4.61/1.39 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 4.61/1.39 Prover 0: proved (732ms)
% 4.61/1.39
% 4.61/1.39 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.61/1.39
% 4.61/1.39 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 4.61/1.39 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 4.61/1.39 Prover 7: Preprocessing ...
% 4.61/1.39 Prover 10: Preprocessing ...
% 4.61/1.39 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 4.61/1.39 Prover 8: Preprocessing ...
% 4.61/1.39 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 4.61/1.40 Prover 13: Preprocessing ...
% 4.61/1.40 Prover 11: Preprocessing ...
% 4.61/1.41 Prover 10: Warning: ignoring some quantifiers
% 4.61/1.42 Prover 7: Warning: ignoring some quantifiers
% 4.61/1.42 Prover 4: Found proof (size 21)
% 4.61/1.42 Prover 4: proved (783ms)
% 4.61/1.42 Prover 1: stopped
% 4.61/1.42 Prover 13: stopped
% 4.61/1.43 Prover 7: Constructing countermodel ...
% 4.61/1.43 Prover 7: stopped
% 4.61/1.43 Prover 11: stopped
% 4.61/1.43 Prover 10: Constructing countermodel ...
% 4.61/1.44 Prover 10: stopped
% 4.61/1.45 Prover 8: Warning: ignoring some quantifiers
% 4.61/1.46 Prover 8: Constructing countermodel ...
% 4.61/1.46 Prover 8: stopped
% 4.61/1.46
% 4.61/1.46 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.61/1.46
% 4.61/1.46 % SZS output start Proof for theBenchmark
% 4.61/1.47 Assumptions after simplification:
% 4.61/1.47 ---------------------------------
% 4.61/1.47
% 4.61/1.47 (d3_tarski)
% 4.61/1.50 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~
% 4.61/1.50 (subset(v0, v1) = 0) | ~ (in(v2, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~
% 4.61/1.50 $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & in(v2, v0) = v4)) & ! [v0: $i] : !
% 4.61/1.50 [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ~ $i(v1) | ~
% 4.61/1.50 $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) & in(v3, v1) = v4 &
% 4.61/1.50 in(v3, v0) = 0 & $i(v3))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 4.61/1.50 (subset(v0, v1) = 0) | ~ (in(v2, v0) = 0) | ~ $i(v2) | ~ $i(v1) | ~
% 4.61/1.50 $i(v0) | in(v2, v1) = 0)
% 4.61/1.50
% 4.61/1.50 (d4_tarski)
% 4.61/1.51 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : ! [v4: $i] : (v3 = 0
% 4.61/1.51 | ~ (union(v0) = v1) | ~ (in(v4, v0) = 0) | ~ (in(v2, v1) = v3) | ~
% 4.61/1.51 $i(v4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ( ~ (v5 = 0) &
% 4.61/1.51 in(v2, v4) = v5)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int]
% 4.61/1.51 : ! [v4: $i] : (v3 = 0 | ~ (union(v0) = v1) | ~ (in(v2, v4) = 0) | ~
% 4.61/1.51 (in(v2, v1) = v3) | ~ $i(v4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5:
% 4.61/1.51 int] : ( ~ (v5 = 0) & in(v4, v0) = v5)) & ! [v0: $i] : ! [v1: $i] : !
% 4.61/1.51 [v2: $i] : ( ~ (union(v0) = v1) | ~ (in(v2, v1) = 0) | ~ $i(v2) | ~ $i(v1)
% 4.61/1.51 | ~ $i(v0) | ? [v3: $i] : (in(v3, v0) = 0 & in(v2, v3) = 0 & $i(v3))) & ?
% 4.61/1.51 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v0 | ~ (union(v1) = v2) | ~
% 4.61/1.51 $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: any] : ? [v5: $i] : ? [v6: int]
% 4.61/1.51 : ? [v7: int] : (in(v3, v0) = v4 & $i(v5) & $i(v3) & ( ~ (v4 = 0) | ( !
% 4.61/1.51 [v8: $i] : ( ~ (in(v8, v1) = 0) | ~ $i(v8) | ? [v9: int] : ( ~ (v9 =
% 4.61/1.51 0) & in(v3, v8) = v9)) & ! [v8: $i] : ( ~ (in(v3, v8) = 0) | ~
% 4.61/1.51 $i(v8) | ? [v9: int] : ( ~ (v9 = 0) & in(v8, v1) = v9)))) & (v4 = 0
% 4.61/1.51 | (v7 = 0 & v6 = 0 & in(v5, v1) = 0 & in(v3, v5) = 0))))
% 4.61/1.51
% 4.61/1.51 (l50_zfmisc_1)
% 4.61/1.51 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) &
% 4.61/1.51 union(v1) = v2 & subset(v0, v2) = v3 & in(v0, v1) = 0 & $i(v2) & $i(v1) &
% 4.61/1.51 $i(v0))
% 4.61/1.52
% 4.61/1.52 (function-axioms)
% 4.61/1.52 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 4.61/1.52 [v3: $i] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) &
% 4.61/1.52 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 4.61/1.52 $i] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) & ! [v0: $i]
% 4.61/1.52 : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (union(v2) = v1) | ~ (union(v2) =
% 4.61/1.52 v0))
% 4.61/1.52
% 4.61/1.52 Further assumptions not needed in the proof:
% 4.61/1.52 --------------------------------------------
% 4.61/1.52 antisymmetry_r2_hidden, dt_k3_tarski, reflexivity_r1_tarski
% 4.61/1.52
% 4.61/1.52 Those formulas are unsatisfiable:
% 4.61/1.52 ---------------------------------
% 4.61/1.52
% 4.61/1.52 Begin of proof
% 4.61/1.52 |
% 4.61/1.52 | ALPHA: (d3_tarski) implies:
% 4.61/1.52 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1)
% 4.61/1.52 | = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~
% 4.61/1.52 | (v4 = 0) & in(v3, v1) = v4 & in(v3, v0) = 0 & $i(v3)))
% 4.61/1.52 |
% 4.61/1.52 | ALPHA: (d4_tarski) implies:
% 4.61/1.53 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : ! [v4: $i] :
% 4.61/1.53 | (v3 = 0 | ~ (union(v0) = v1) | ~ (in(v2, v4) = 0) | ~ (in(v2, v1) =
% 4.61/1.53 | v3) | ~ $i(v4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int]
% 4.61/1.53 | : ( ~ (v5 = 0) & in(v4, v0) = v5))
% 4.61/1.53 |
% 4.61/1.53 | ALPHA: (function-axioms) implies:
% 4.61/1.53 | (3) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 4.61/1.53 | ! [v3: $i] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0))
% 4.61/1.53 |
% 4.61/1.53 | DELTA: instantiating (l50_zfmisc_1) with fresh symbols all_7_0, all_7_1,
% 4.61/1.53 | all_7_2, all_7_3 gives:
% 5.42/1.53 | (4) ~ (all_7_0 = 0) & union(all_7_2) = all_7_1 & subset(all_7_3, all_7_1)
% 5.42/1.53 | = all_7_0 & in(all_7_3, all_7_2) = 0 & $i(all_7_1) & $i(all_7_2) &
% 5.42/1.53 | $i(all_7_3)
% 5.42/1.53 |
% 5.42/1.53 | ALPHA: (4) implies:
% 5.42/1.53 | (5) ~ (all_7_0 = 0)
% 5.42/1.53 | (6) $i(all_7_3)
% 5.42/1.53 | (7) $i(all_7_2)
% 5.42/1.53 | (8) $i(all_7_1)
% 5.42/1.53 | (9) in(all_7_3, all_7_2) = 0
% 5.42/1.53 | (10) subset(all_7_3, all_7_1) = all_7_0
% 5.42/1.53 | (11) union(all_7_2) = all_7_1
% 5.42/1.53 |
% 5.42/1.53 | GROUND_INST: instantiating (1) with all_7_3, all_7_1, all_7_0, simplifying
% 5.42/1.53 | with (6), (8), (10) gives:
% 5.42/1.53 | (12) all_7_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & in(v0,
% 5.42/1.53 | all_7_1) = v1 & in(v0, all_7_3) = 0 & $i(v0))
% 5.42/1.53 |
% 5.42/1.53 | BETA: splitting (12) gives:
% 5.42/1.53 |
% 5.42/1.54 | Case 1:
% 5.42/1.54 | |
% 5.42/1.54 | | (13) all_7_0 = 0
% 5.42/1.54 | |
% 5.42/1.54 | | REDUCE: (5), (13) imply:
% 5.42/1.54 | | (14) $false
% 5.42/1.54 | |
% 5.42/1.54 | | CLOSE: (14) is inconsistent.
% 5.42/1.54 | |
% 5.42/1.54 | Case 2:
% 5.42/1.54 | |
% 5.42/1.54 | | (15) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & in(v0, all_7_1) = v1 &
% 5.42/1.54 | | in(v0, all_7_3) = 0 & $i(v0))
% 5.42/1.54 | |
% 5.42/1.54 | | DELTA: instantiating (15) with fresh symbols all_22_0, all_22_1 gives:
% 5.42/1.54 | | (16) ~ (all_22_0 = 0) & in(all_22_1, all_7_1) = all_22_0 & in(all_22_1,
% 5.42/1.54 | | all_7_3) = 0 & $i(all_22_1)
% 5.42/1.54 | |
% 5.42/1.54 | | ALPHA: (16) implies:
% 5.42/1.54 | | (17) ~ (all_22_0 = 0)
% 5.42/1.54 | | (18) $i(all_22_1)
% 5.42/1.54 | | (19) in(all_22_1, all_7_3) = 0
% 5.42/1.54 | | (20) in(all_22_1, all_7_1) = all_22_0
% 5.42/1.54 | |
% 5.42/1.54 | | GROUND_INST: instantiating (2) with all_7_2, all_7_1, all_22_1, all_22_0,
% 5.42/1.54 | | all_7_3, simplifying with (6), (7), (8), (11), (18), (19), (20)
% 5.42/1.54 | | gives:
% 5.42/1.54 | | (21) all_22_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & in(all_7_3, all_7_2) =
% 5.42/1.54 | | v0)
% 5.42/1.54 | |
% 5.42/1.54 | | BETA: splitting (21) gives:
% 5.42/1.54 | |
% 5.42/1.54 | | Case 1:
% 5.42/1.54 | | |
% 5.42/1.54 | | | (22) all_22_0 = 0
% 5.42/1.54 | | |
% 5.42/1.54 | | | REDUCE: (17), (22) imply:
% 5.42/1.54 | | | (23) $false
% 5.42/1.54 | | |
% 5.42/1.54 | | | CLOSE: (23) is inconsistent.
% 5.42/1.54 | | |
% 5.42/1.54 | | Case 2:
% 5.42/1.54 | | |
% 5.42/1.54 | | | (24) ? [v0: int] : ( ~ (v0 = 0) & in(all_7_3, all_7_2) = v0)
% 5.42/1.54 | | |
% 5.42/1.54 | | | DELTA: instantiating (24) with fresh symbol all_35_0 gives:
% 5.42/1.54 | | | (25) ~ (all_35_0 = 0) & in(all_7_3, all_7_2) = all_35_0
% 5.42/1.54 | | |
% 5.42/1.54 | | | ALPHA: (25) implies:
% 5.42/1.54 | | | (26) ~ (all_35_0 = 0)
% 5.42/1.54 | | | (27) in(all_7_3, all_7_2) = all_35_0
% 5.42/1.54 | | |
% 5.42/1.54 | | | GROUND_INST: instantiating (3) with 0, all_35_0, all_7_2, all_7_3,
% 5.42/1.54 | | | simplifying with (9), (27) gives:
% 5.42/1.54 | | | (28) all_35_0 = 0
% 5.42/1.54 | | |
% 5.42/1.54 | | | REDUCE: (26), (28) imply:
% 5.42/1.54 | | | (29) $false
% 5.42/1.54 | | |
% 5.42/1.54 | | | CLOSE: (29) is inconsistent.
% 5.42/1.54 | | |
% 5.42/1.54 | | End of split
% 5.42/1.54 | |
% 5.42/1.54 | End of split
% 5.42/1.54 |
% 5.42/1.54 End of proof
% 5.42/1.54 % SZS output end Proof for theBenchmark
% 5.42/1.54
% 5.42/1.54 926ms
%------------------------------------------------------------------------------