TSTP Solution File: SEU133+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SEU133+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 : n016.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 17:42:41 EDT 2023
% Result : Theorem 5.70s 1.52s
% Output : Proof 6.57s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU133+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.12/0.34 % Computer : n016.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 : Wed Aug 23 17:02:22 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.19/0.61 ________ _____
% 0.19/0.61 ___ __ \_________(_)________________________________
% 0.19/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.19/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.19/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.19/0.61
% 0.19/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.19/0.61 (2023-06-19)
% 0.19/0.61
% 0.19/0.61 (c) Philipp Rümmer, 2009-2023
% 0.19/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.19/0.61 Amanda Stjerna.
% 0.19/0.61 Free software under BSD-3-Clause.
% 0.19/0.61
% 0.19/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.19/0.61
% 0.19/0.61 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.19/0.62 Running up to 7 provers in parallel.
% 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 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 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 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 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
% 2.23/1.01 Prover 1: Preprocessing ...
% 2.23/1.01 Prover 4: Preprocessing ...
% 2.23/1.05 Prover 3: Preprocessing ...
% 2.23/1.05 Prover 6: Preprocessing ...
% 2.23/1.05 Prover 5: Preprocessing ...
% 2.23/1.05 Prover 0: Preprocessing ...
% 2.23/1.05 Prover 2: Preprocessing ...
% 4.28/1.33 Prover 1: Warning: ignoring some quantifiers
% 4.28/1.33 Prover 4: Warning: ignoring some quantifiers
% 4.28/1.33 Prover 3: Warning: ignoring some quantifiers
% 4.28/1.33 Prover 6: Proving ...
% 4.28/1.34 Prover 2: Proving ...
% 4.28/1.34 Prover 5: Proving ...
% 4.28/1.34 Prover 1: Constructing countermodel ...
% 4.28/1.34 Prover 3: Constructing countermodel ...
% 4.28/1.35 Prover 4: Constructing countermodel ...
% 4.28/1.36 Prover 0: Proving ...
% 5.00/1.51 Prover 3: proved (878ms)
% 5.00/1.51
% 5.70/1.52 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.70/1.52
% 5.70/1.52 Prover 6: stopped
% 5.70/1.52 Prover 5: stopped
% 5.74/1.53 Prover 2: stopped
% 5.74/1.53 Prover 0: stopped
% 5.74/1.53 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 5.74/1.53 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 5.74/1.53 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 5.74/1.53 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 5.74/1.54 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 5.74/1.55 Prover 7: Preprocessing ...
% 5.74/1.55 Prover 8: Preprocessing ...
% 5.74/1.56 Prover 10: Preprocessing ...
% 5.74/1.57 Prover 11: Preprocessing ...
% 5.74/1.57 Prover 1: Found proof (size 23)
% 5.74/1.57 Prover 1: proved (944ms)
% 5.74/1.57 Prover 4: stopped
% 5.74/1.57 Prover 10: stopped
% 5.74/1.58 Prover 13: Preprocessing ...
% 5.74/1.59 Prover 7: stopped
% 5.74/1.60 Prover 13: stopped
% 6.22/1.61 Prover 11: stopped
% 6.22/1.63 Prover 8: Warning: ignoring some quantifiers
% 6.22/1.63 Prover 8: Constructing countermodel ...
% 6.22/1.64 Prover 8: stopped
% 6.22/1.64
% 6.22/1.64 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.22/1.64
% 6.22/1.64 % SZS output start Proof for theBenchmark
% 6.22/1.65 Assumptions after simplification:
% 6.22/1.65 ---------------------------------
% 6.22/1.65
% 6.22/1.65 (d3_tarski)
% 6.22/1.67 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) = v2)
% 6.22/1.67 | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) & in(v3,
% 6.57/1.67 v1) = v4 & in(v3, v0) = 0 & $i(v3))) & ! [v0: $i] : ! [v1: $i] : ( ~
% 6.57/1.67 (subset(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ! [v2: $i] : ( ~ (in(v2, v0)
% 6.57/1.67 = 0) | ~ $i(v2) | in(v2, v1) = 0))
% 6.57/1.67
% 6.57/1.67 (d4_xboole_0)
% 6.57/1.68 ? [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v0 | ~
% 6.57/1.68 (set_difference(v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4:
% 6.57/1.68 $i] : ? [v5: any] : ? [v6: any] : ? [v7: any] : (in(v4, v2) = v7 &
% 6.57/1.68 in(v4, v1) = v6 & in(v4, v0) = v5 & $i(v4) & ( ~ (v6 = 0) | ~ (v5 = 0) |
% 6.57/1.68 v7 = 0) & (v5 = 0 | (v6 = 0 & ~ (v7 = 0))))) & ! [v0: $i] : ! [v1:
% 6.57/1.68 $i] : ! [v2: $i] : ( ~ (set_difference(v0, v1) = v2) | ~ $i(v2) | ~
% 6.57/1.68 $i(v1) | ~ $i(v0) | ( ! [v3: $i] : ! [v4: any] : ( ~ (in(v3, v0) = v4) |
% 6.57/1.68 ~ $i(v3) | ? [v5: any] : ? [v6: any] : (in(v3, v2) = v5 & in(v3, v1) =
% 6.57/1.68 v6 & ( ~ (v5 = 0) | (v4 = 0 & ~ (v6 = 0))))) & ! [v3: $i] : ( ~
% 6.57/1.68 (in(v3, v0) = 0) | ~ $i(v3) | ? [v4: any] : ? [v5: any] : (in(v3, v2)
% 6.57/1.68 = v5 & in(v3, v1) = v4 & (v5 = 0 | v4 = 0)))))
% 6.57/1.68
% 6.57/1.68 (t36_xboole_1)
% 6.57/1.68 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) &
% 6.57/1.68 set_difference(v0, v1) = v2 & subset(v2, v0) = v3 & $i(v2) & $i(v1) &
% 6.57/1.68 $i(v0))
% 6.57/1.68
% 6.57/1.68 (function-axioms)
% 6.57/1.69 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 6.57/1.69 (set_difference(v3, v2) = v1) | ~ (set_difference(v3, v2) = v0)) & ! [v0:
% 6.57/1.69 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 6.57/1.69 : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) & ! [v0:
% 6.57/1.69 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 6.57/1.69 : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) & ! [v0:
% 6.57/1.69 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 |
% 6.57/1.69 ~ (empty(v2) = v1) | ~ (empty(v2) = v0))
% 6.57/1.69
% 6.57/1.69 Further assumptions not needed in the proof:
% 6.57/1.69 --------------------------------------------
% 6.57/1.69 antisymmetry_r2_hidden, dt_k1_xboole_0, dt_k4_xboole_0, fc1_xboole_0,
% 6.57/1.69 rc1_xboole_0, rc2_xboole_0, reflexivity_r1_tarski, t3_boole, t4_boole, t6_boole,
% 6.57/1.69 t7_boole, t8_boole
% 6.57/1.69
% 6.57/1.69 Those formulas are unsatisfiable:
% 6.57/1.69 ---------------------------------
% 6.57/1.69
% 6.57/1.69 Begin of proof
% 6.57/1.69 |
% 6.57/1.69 | ALPHA: (d3_tarski) implies:
% 6.57/1.69 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1)
% 6.57/1.69 | = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~
% 6.57/1.69 | (v4 = 0) & in(v3, v1) = v4 & in(v3, v0) = 0 & $i(v3)))
% 6.57/1.69 |
% 6.57/1.69 | ALPHA: (d4_xboole_0) implies:
% 6.57/1.69 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (set_difference(v0, v1) =
% 6.57/1.69 | v2) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ( ! [v3: $i] : ! [v4:
% 6.57/1.69 | any] : ( ~ (in(v3, v0) = v4) | ~ $i(v3) | ? [v5: any] : ? [v6:
% 6.57/1.69 | any] : (in(v3, v2) = v5 & in(v3, v1) = v6 & ( ~ (v5 = 0) | (v4
% 6.57/1.69 | = 0 & ~ (v6 = 0))))) & ! [v3: $i] : ( ~ (in(v3, v0) = 0)
% 6.57/1.69 | | ~ $i(v3) | ? [v4: any] : ? [v5: any] : (in(v3, v2) = v5 &
% 6.57/1.69 | in(v3, v1) = v4 & (v5 = 0 | v4 = 0)))))
% 6.57/1.69 |
% 6.57/1.69 | ALPHA: (function-axioms) implies:
% 6.57/1.69 | (3) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 6.57/1.69 | ! [v3: $i] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0))
% 6.57/1.69 |
% 6.57/1.70 | DELTA: instantiating (t36_xboole_1) with fresh symbols all_18_0, all_18_1,
% 6.57/1.70 | all_18_2, all_18_3 gives:
% 6.57/1.70 | (4) ~ (all_18_0 = 0) & set_difference(all_18_3, all_18_2) = all_18_1 &
% 6.57/1.70 | subset(all_18_1, all_18_3) = all_18_0 & $i(all_18_1) & $i(all_18_2) &
% 6.57/1.70 | $i(all_18_3)
% 6.57/1.70 |
% 6.57/1.70 | ALPHA: (4) implies:
% 6.57/1.70 | (5) ~ (all_18_0 = 0)
% 6.57/1.70 | (6) $i(all_18_3)
% 6.57/1.70 | (7) $i(all_18_2)
% 6.57/1.70 | (8) $i(all_18_1)
% 6.57/1.70 | (9) subset(all_18_1, all_18_3) = all_18_0
% 6.57/1.70 | (10) set_difference(all_18_3, all_18_2) = all_18_1
% 6.57/1.70 |
% 6.57/1.70 | GROUND_INST: instantiating (1) with all_18_1, all_18_3, all_18_0, simplifying
% 6.57/1.70 | with (6), (8), (9) gives:
% 6.57/1.70 | (11) all_18_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & in(v0,
% 6.57/1.70 | all_18_1) = 0 & in(v0, all_18_3) = v1 & $i(v0))
% 6.57/1.70 |
% 6.57/1.70 | GROUND_INST: instantiating (2) with all_18_3, all_18_2, all_18_1, simplifying
% 6.57/1.70 | with (6), (7), (8), (10) gives:
% 6.57/1.70 | (12) ! [v0: $i] : ! [v1: any] : ( ~ (in(v0, all_18_3) = v1) | ~ $i(v0) |
% 6.57/1.70 | ? [v2: any] : ? [v3: any] : (in(v0, all_18_1) = v2 & in(v0,
% 6.57/1.70 | all_18_2) = v3 & ( ~ (v2 = 0) | (v1 = 0 & ~ (v3 = 0))))) & !
% 6.57/1.70 | [v0: $i] : ( ~ (in(v0, all_18_3) = 0) | ~ $i(v0) | ? [v1: any] : ?
% 6.57/1.70 | [v2: any] : (in(v0, all_18_1) = v2 & in(v0, all_18_2) = v1 & (v2 = 0
% 6.57/1.70 | | v1 = 0)))
% 6.57/1.70 |
% 6.57/1.70 | ALPHA: (12) implies:
% 6.57/1.70 | (13) ! [v0: $i] : ! [v1: any] : ( ~ (in(v0, all_18_3) = v1) | ~ $i(v0) |
% 6.57/1.70 | ? [v2: any] : ? [v3: any] : (in(v0, all_18_1) = v2 & in(v0,
% 6.57/1.70 | all_18_2) = v3 & ( ~ (v2 = 0) | (v1 = 0 & ~ (v3 = 0)))))
% 6.57/1.70 |
% 6.57/1.70 | BETA: splitting (11) gives:
% 6.57/1.70 |
% 6.57/1.70 | Case 1:
% 6.57/1.70 | |
% 6.57/1.70 | | (14) all_18_0 = 0
% 6.57/1.70 | |
% 6.57/1.70 | | REDUCE: (5), (14) imply:
% 6.57/1.70 | | (15) $false
% 6.57/1.71 | |
% 6.57/1.71 | | CLOSE: (15) is inconsistent.
% 6.57/1.71 | |
% 6.57/1.71 | Case 2:
% 6.57/1.71 | |
% 6.57/1.71 | | (16) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & in(v0, all_18_1) = 0 &
% 6.57/1.71 | | in(v0, all_18_3) = v1 & $i(v0))
% 6.57/1.71 | |
% 6.57/1.71 | | DELTA: instantiating (16) with fresh symbols all_33_0, all_33_1 gives:
% 6.57/1.71 | | (17) ~ (all_33_0 = 0) & in(all_33_1, all_18_1) = 0 & in(all_33_1,
% 6.57/1.71 | | all_18_3) = all_33_0 & $i(all_33_1)
% 6.57/1.71 | |
% 6.57/1.71 | | ALPHA: (17) implies:
% 6.57/1.71 | | (18) ~ (all_33_0 = 0)
% 6.57/1.71 | | (19) $i(all_33_1)
% 6.57/1.71 | | (20) in(all_33_1, all_18_3) = all_33_0
% 6.57/1.71 | | (21) in(all_33_1, all_18_1) = 0
% 6.57/1.71 | |
% 6.57/1.71 | | GROUND_INST: instantiating (13) with all_33_1, all_33_0, simplifying with
% 6.57/1.71 | | (19), (20) gives:
% 6.57/1.71 | | (22) ? [v0: any] : ? [v1: any] : (in(all_33_1, all_18_1) = v0 &
% 6.57/1.71 | | in(all_33_1, all_18_2) = v1 & ( ~ (v0 = 0) | (all_33_0 = 0 & ~
% 6.57/1.71 | | (v1 = 0))))
% 6.57/1.71 | |
% 6.57/1.71 | | DELTA: instantiating (22) with fresh symbols all_44_0, all_44_1 gives:
% 6.57/1.71 | | (23) in(all_33_1, all_18_1) = all_44_1 & in(all_33_1, all_18_2) =
% 6.57/1.71 | | all_44_0 & ( ~ (all_44_1 = 0) | (all_33_0 = 0 & ~ (all_44_0 = 0)))
% 6.57/1.71 | |
% 6.57/1.71 | | ALPHA: (23) implies:
% 6.57/1.71 | | (24) in(all_33_1, all_18_1) = all_44_1
% 6.57/1.71 | | (25) ~ (all_44_1 = 0) | (all_33_0 = 0 & ~ (all_44_0 = 0))
% 6.57/1.71 | |
% 6.57/1.71 | | BETA: splitting (25) gives:
% 6.57/1.71 | |
% 6.57/1.71 | | Case 1:
% 6.57/1.71 | | |
% 6.57/1.71 | | | (26) ~ (all_44_1 = 0)
% 6.57/1.71 | | |
% 6.57/1.71 | | | GROUND_INST: instantiating (3) with 0, all_44_1, all_18_1, all_33_1,
% 6.57/1.71 | | | simplifying with (21), (24) gives:
% 6.57/1.71 | | | (27) all_44_1 = 0
% 6.57/1.71 | | |
% 6.57/1.71 | | | REDUCE: (26), (27) imply:
% 6.57/1.71 | | | (28) $false
% 6.57/1.71 | | |
% 6.57/1.71 | | | CLOSE: (28) is inconsistent.
% 6.57/1.71 | | |
% 6.57/1.71 | | Case 2:
% 6.57/1.71 | | |
% 6.57/1.71 | | | (29) all_33_0 = 0 & ~ (all_44_0 = 0)
% 6.57/1.71 | | |
% 6.57/1.71 | | | ALPHA: (29) implies:
% 6.57/1.71 | | | (30) all_33_0 = 0
% 6.57/1.71 | | |
% 6.57/1.71 | | | REDUCE: (18), (30) imply:
% 6.57/1.71 | | | (31) $false
% 6.57/1.71 | | |
% 6.57/1.71 | | | CLOSE: (31) is inconsistent.
% 6.57/1.71 | | |
% 6.57/1.71 | | End of split
% 6.57/1.71 | |
% 6.57/1.71 | End of split
% 6.57/1.71 |
% 6.57/1.71 End of proof
% 6.57/1.71 % SZS output end Proof for theBenchmark
% 6.57/1.71
% 6.57/1.71 1105ms
%------------------------------------------------------------------------------