TSTP Solution File: SEU129+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SEU129+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 : n009.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 17:42:39 EDT 2023
% Result : Theorem 7.09s 1.70s
% Output : Proof 8.29s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU129+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.34 % Computer : n009.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Wed Aug 23 16:28:06 EDT 2023
% 0.13/0.34 % 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/sandbox/benchmark/theBenchmark.p ...
% 0.19/0.62 Running up to 7 provers in parallel.
% 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 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 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
% 1.73/0.98 Prover 1: Preprocessing ...
% 1.73/0.98 Prover 4: Preprocessing ...
% 2.41/1.02 Prover 2: Preprocessing ...
% 2.41/1.02 Prover 3: Preprocessing ...
% 2.41/1.02 Prover 6: Preprocessing ...
% 2.41/1.02 Prover 5: Preprocessing ...
% 2.41/1.02 Prover 0: Preprocessing ...
% 3.71/1.30 Prover 5: Proving ...
% 4.43/1.33 Prover 3: Warning: ignoring some quantifiers
% 4.43/1.33 Prover 1: Warning: ignoring some quantifiers
% 4.43/1.34 Prover 6: Proving ...
% 4.43/1.34 Prover 2: Proving ...
% 4.43/1.35 Prover 4: Warning: ignoring some quantifiers
% 4.43/1.35 Prover 3: Constructing countermodel ...
% 4.43/1.35 Prover 1: Constructing countermodel ...
% 4.43/1.36 Prover 4: Constructing countermodel ...
% 4.43/1.37 Prover 0: Proving ...
% 5.77/1.63 Prover 1: gave up
% 5.77/1.63 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 5.77/1.66 Prover 7: Preprocessing ...
% 7.09/1.70 Prover 0: proved (1071ms)
% 7.09/1.70
% 7.09/1.70 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 7.09/1.70
% 7.09/1.70 Prover 6: stopped
% 7.09/1.70 Prover 5: stopped
% 7.09/1.70 Prover 2: stopped
% 7.12/1.71 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 7.12/1.71 Prover 3: stopped
% 7.12/1.71 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 7.12/1.71 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 7.12/1.71 Prover 7: Warning: ignoring some quantifiers
% 7.12/1.71 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 7.12/1.71 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 7.12/1.73 Prover 7: Constructing countermodel ...
% 7.12/1.73 Prover 11: Preprocessing ...
% 7.12/1.74 Prover 8: Preprocessing ...
% 7.12/1.74 Prover 13: Preprocessing ...
% 7.12/1.74 Prover 10: Preprocessing ...
% 7.12/1.76 Prover 16: Preprocessing ...
% 7.12/1.78 Prover 4: Found proof (size 43)
% 7.12/1.78 Prover 4: proved (1145ms)
% 7.12/1.78 Prover 7: stopped
% 7.12/1.78 Prover 11: stopped
% 7.12/1.79 Prover 13: Warning: ignoring some quantifiers
% 7.12/1.79 Prover 16: stopped
% 7.12/1.79 Prover 13: Constructing countermodel ...
% 7.12/1.80 Prover 13: stopped
% 7.83/1.80 Prover 10: Warning: ignoring some quantifiers
% 7.83/1.81 Prover 10: Constructing countermodel ...
% 7.83/1.81 Prover 8: Warning: ignoring some quantifiers
% 7.83/1.81 Prover 10: stopped
% 7.83/1.82 Prover 8: Constructing countermodel ...
% 7.83/1.82 Prover 8: stopped
% 7.83/1.82
% 7.83/1.82 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 7.83/1.82
% 7.83/1.83 % SZS output start Proof for theBenchmark
% 7.83/1.83 Assumptions after simplification:
% 7.83/1.83 ---------------------------------
% 7.83/1.83
% 7.83/1.83 (commutativity_k3_xboole_0)
% 7.83/1.86 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (set_intersection2(v1, v0) = v2)
% 7.83/1.86 | ~ $i(v1) | ~ $i(v0) | (set_intersection2(v0, v1) = v2 & $i(v2))) & !
% 7.83/1.86 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (set_intersection2(v0, v1) = v2) |
% 7.83/1.86 ~ $i(v1) | ~ $i(v0) | (set_intersection2(v1, v0) = v2 & $i(v2)))
% 7.83/1.86
% 7.83/1.86 (d3_tarski)
% 7.83/1.86 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~
% 7.83/1.86 (subset(v0, v1) = 0) | ~ (in(v2, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~
% 7.83/1.86 $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & in(v2, v0) = v4)) & ! [v0: $i] : !
% 7.83/1.86 [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ~ $i(v1) | ~
% 7.83/1.86 $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) & in(v3, v1) = v4 &
% 7.83/1.86 in(v3, v0) = 0 & $i(v3))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 7.83/1.86 (subset(v0, v1) = 0) | ~ (in(v2, v0) = 0) | ~ $i(v2) | ~ $i(v1) | ~
% 7.83/1.86 $i(v0) | in(v2, v1) = 0)
% 7.83/1.86
% 7.83/1.86 (d3_xboole_0)
% 7.83/1.87 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0
% 7.83/1.87 | ~ (set_intersection2(v0, v1) = v2) | ~ (in(v3, v2) = v4) | ~ $i(v3) |
% 7.83/1.87 ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : (in(v3, v1)
% 7.83/1.87 = v6 & in(v3, v0) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0)))) & ! [v0: $i] : !
% 7.83/1.87 [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: any] : ( ~
% 7.83/1.87 (set_intersection2(v0, v1) = v2) | ~ (in(v3, v1) = v4) | ~ $i(v3) | ~
% 7.83/1.87 $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : (in(v3, v2) =
% 7.83/1.87 v5 & in(v3, v0) = v6 & ( ~ (v5 = 0) | (v6 = 0 & v4 = 0)))) & ! [v0: $i] :
% 7.83/1.87 ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: any] : ( ~
% 7.83/1.87 (set_intersection2(v0, v1) = v2) | ~ (in(v3, v0) = v4) | ~ $i(v3) | ~
% 7.83/1.87 $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : (in(v3, v2) =
% 7.83/1.87 v5 & in(v3, v1) = v6 & ( ~ (v5 = 0) | (v6 = 0 & v4 = 0)))) & ! [v0: $i] :
% 7.83/1.87 ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (set_intersection2(v0, v1) = v2)
% 7.83/1.87 | ~ (in(v3, v2) = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 7.83/1.87 (in(v3, v1) = 0 & in(v3, v0) = 0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i]
% 7.83/1.87 : ! [v3: $i] : ( ~ (set_intersection2(v0, v1) = v2) | ~ (in(v3, v1) = 0) |
% 7.83/1.87 ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: any] :
% 7.83/1.87 (in(v3, v2) = v5 & in(v3, v0) = v4 & ( ~ (v4 = 0) | v5 = 0))) & ! [v0: $i]
% 7.83/1.87 : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (set_intersection2(v0, v1) =
% 7.83/1.87 v2) | ~ (in(v3, v0) = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0)
% 7.83/1.87 | ? [v4: any] : ? [v5: any] : (in(v3, v2) = v5 & in(v3, v1) = v4 & ( ~ (v4
% 7.83/1.87 = 0) | v5 = 0))) & ? [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 7.83/1.87 $i] : (v3 = v0 | ~ (set_intersection2(v1, v2) = v3) | ~ $i(v2) | ~ $i(v1)
% 7.83/1.87 | ~ $i(v0) | ? [v4: $i] : ? [v5: any] : ? [v6: any] : ? [v7: any] :
% 7.83/1.87 (in(v4, v2) = v7 & in(v4, v1) = v6 & in(v4, v0) = v5 & $i(v4) & ( ~ (v7 = 0)
% 7.83/1.87 | ~ (v6 = 0) | ~ (v5 = 0)) & (v5 = 0 | (v7 = 0 & v6 = 0))))
% 7.83/1.88
% 7.83/1.88 (t26_xboole_1)
% 7.83/1.88 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5:
% 7.83/1.88 int] : ( ~ (v5 = 0) & subset(v3, v4) = v5 & subset(v0, v1) = 0 &
% 7.83/1.88 set_intersection2(v1, v2) = v4 & set_intersection2(v0, v2) = v3 & $i(v4) &
% 7.83/1.88 $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 7.83/1.88
% 7.83/1.88 (function-axioms)
% 7.83/1.88 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 7.83/1.88 [v3: $i] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) &
% 7.83/1.88 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 7.83/1.88 (set_intersection2(v3, v2) = v1) | ~ (set_intersection2(v3, v2) = v0)) & !
% 7.83/1.88 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 7.83/1.88 $i] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) & ! [v0:
% 7.83/1.88 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 |
% 7.83/1.88 ~ (empty(v2) = v1) | ~ (empty(v2) = v0))
% 7.83/1.88
% 7.83/1.88 Further assumptions not needed in the proof:
% 7.83/1.88 --------------------------------------------
% 7.83/1.88 antisymmetry_r2_hidden, dt_k1_xboole_0, dt_k3_xboole_0, fc1_xboole_0,
% 7.83/1.88 idempotence_k3_xboole_0, rc1_xboole_0, rc2_xboole_0, reflexivity_r1_tarski,
% 7.83/1.88 t2_boole, t6_boole, t7_boole, t8_boole
% 7.83/1.88
% 7.83/1.88 Those formulas are unsatisfiable:
% 7.83/1.88 ---------------------------------
% 7.83/1.88
% 7.83/1.88 Begin of proof
% 7.83/1.88 |
% 7.83/1.88 | ALPHA: (commutativity_k3_xboole_0) implies:
% 7.83/1.88 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (set_intersection2(v1,
% 7.83/1.88 | v0) = v2) | ~ $i(v1) | ~ $i(v0) | (set_intersection2(v0, v1) =
% 7.83/1.88 | v2 & $i(v2)))
% 7.83/1.88 |
% 7.83/1.88 | ALPHA: (d3_tarski) implies:
% 7.83/1.88 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (subset(v0, v1) = 0) | ~
% 7.83/1.88 | (in(v2, v0) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | in(v2, v1) =
% 7.83/1.88 | 0)
% 7.83/1.88 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1)
% 7.83/1.88 | = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~
% 7.83/1.88 | (v4 = 0) & in(v3, v1) = v4 & in(v3, v0) = 0 & $i(v3)))
% 7.83/1.88 |
% 7.83/1.88 | ALPHA: (d3_xboole_0) implies:
% 7.83/1.89 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 7.83/1.89 | (set_intersection2(v0, v1) = v2) | ~ (in(v3, v2) = 0) | ~ $i(v3) |
% 7.83/1.89 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | (in(v3, v1) = 0 & in(v3, v0) = 0))
% 7.83/1.89 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] :
% 7.83/1.89 | (v4 = 0 | ~ (set_intersection2(v0, v1) = v2) | ~ (in(v3, v2) = v4) |
% 7.83/1.89 | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6:
% 7.83/1.89 | any] : (in(v3, v1) = v6 & in(v3, v0) = v5 & ( ~ (v6 = 0) | ~ (v5 =
% 7.83/1.89 | 0))))
% 7.83/1.89 |
% 7.83/1.89 | ALPHA: (function-axioms) implies:
% 7.83/1.89 | (6) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 7.83/1.89 | ! [v3: $i] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0))
% 7.83/1.89 |
% 7.83/1.89 | DELTA: instantiating (t26_xboole_1) with fresh symbols all_18_0, all_18_1,
% 7.83/1.89 | all_18_2, all_18_3, all_18_4, all_18_5 gives:
% 7.83/1.89 | (7) ~ (all_18_0 = 0) & subset(all_18_2, all_18_1) = all_18_0 &
% 7.83/1.89 | subset(all_18_5, all_18_4) = 0 & set_intersection2(all_18_4, all_18_3)
% 7.83/1.89 | = all_18_1 & set_intersection2(all_18_5, all_18_3) = all_18_2 &
% 7.83/1.89 | $i(all_18_1) & $i(all_18_2) & $i(all_18_3) & $i(all_18_4) &
% 7.83/1.89 | $i(all_18_5)
% 7.83/1.89 |
% 7.83/1.89 | ALPHA: (7) implies:
% 7.83/1.89 | (8) ~ (all_18_0 = 0)
% 7.83/1.89 | (9) $i(all_18_5)
% 7.83/1.89 | (10) $i(all_18_4)
% 7.83/1.89 | (11) $i(all_18_3)
% 7.83/1.89 | (12) set_intersection2(all_18_5, all_18_3) = all_18_2
% 7.83/1.89 | (13) set_intersection2(all_18_4, all_18_3) = all_18_1
% 7.83/1.89 | (14) subset(all_18_5, all_18_4) = 0
% 7.83/1.89 | (15) subset(all_18_2, all_18_1) = all_18_0
% 7.83/1.89 |
% 7.83/1.89 | GROUND_INST: instantiating (1) with all_18_3, all_18_5, all_18_2, simplifying
% 7.83/1.89 | with (9), (11), (12) gives:
% 7.83/1.89 | (16) set_intersection2(all_18_3, all_18_5) = all_18_2 & $i(all_18_2)
% 7.83/1.89 |
% 7.83/1.89 | ALPHA: (16) implies:
% 7.83/1.89 | (17) $i(all_18_2)
% 7.83/1.89 | (18) set_intersection2(all_18_3, all_18_5) = all_18_2
% 7.83/1.89 |
% 7.83/1.89 | GROUND_INST: instantiating (1) with all_18_3, all_18_4, all_18_1, simplifying
% 7.83/1.89 | with (10), (11), (13) gives:
% 8.29/1.89 | (19) set_intersection2(all_18_3, all_18_4) = all_18_1 & $i(all_18_1)
% 8.29/1.89 |
% 8.29/1.89 | ALPHA: (19) implies:
% 8.29/1.89 | (20) $i(all_18_1)
% 8.29/1.89 | (21) set_intersection2(all_18_3, all_18_4) = all_18_1
% 8.29/1.89 |
% 8.29/1.89 | GROUND_INST: instantiating (3) with all_18_2, all_18_1, all_18_0, simplifying
% 8.29/1.89 | with (15), (17), (20) gives:
% 8.29/1.90 | (22) all_18_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & in(v0,
% 8.29/1.90 | all_18_1) = v1 & in(v0, all_18_2) = 0 & $i(v0))
% 8.29/1.90 |
% 8.29/1.90 | BETA: splitting (22) gives:
% 8.29/1.90 |
% 8.29/1.90 | Case 1:
% 8.29/1.90 | |
% 8.29/1.90 | | (23) all_18_0 = 0
% 8.29/1.90 | |
% 8.29/1.90 | | REDUCE: (8), (23) imply:
% 8.29/1.90 | | (24) $false
% 8.29/1.90 | |
% 8.29/1.90 | | CLOSE: (24) is inconsistent.
% 8.29/1.90 | |
% 8.29/1.90 | Case 2:
% 8.29/1.90 | |
% 8.29/1.90 | | (25) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & in(v0, all_18_1) = v1 &
% 8.29/1.90 | | in(v0, all_18_2) = 0 & $i(v0))
% 8.29/1.90 | |
% 8.29/1.90 | | DELTA: instantiating (25) with fresh symbols all_32_0, all_32_1 gives:
% 8.29/1.90 | | (26) ~ (all_32_0 = 0) & in(all_32_1, all_18_1) = all_32_0 & in(all_32_1,
% 8.29/1.90 | | all_18_2) = 0 & $i(all_32_1)
% 8.29/1.90 | |
% 8.29/1.90 | | ALPHA: (26) implies:
% 8.29/1.90 | | (27) ~ (all_32_0 = 0)
% 8.29/1.90 | | (28) $i(all_32_1)
% 8.29/1.90 | | (29) in(all_32_1, all_18_2) = 0
% 8.29/1.90 | | (30) in(all_32_1, all_18_1) = all_32_0
% 8.29/1.90 | |
% 8.29/1.90 | | GROUND_INST: instantiating (5) with all_18_4, all_18_3, all_18_1, all_32_1,
% 8.29/1.90 | | all_32_0, simplifying with (10), (11), (13), (20), (28), (30)
% 8.29/1.90 | | gives:
% 8.29/1.90 | | (31) all_32_0 = 0 | ? [v0: any] : ? [v1: any] : (in(all_32_1, all_18_3)
% 8.29/1.90 | | = v1 & in(all_32_1, all_18_4) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 8.29/1.90 | |
% 8.29/1.90 | | GROUND_INST: instantiating (4) with all_18_3, all_18_5, all_18_2, all_32_1,
% 8.29/1.90 | | simplifying with (9), (11), (17), (18), (28), (29) gives:
% 8.29/1.90 | | (32) in(all_32_1, all_18_3) = 0 & in(all_32_1, all_18_5) = 0
% 8.29/1.90 | |
% 8.29/1.90 | | ALPHA: (32) implies:
% 8.29/1.90 | | (33) in(all_32_1, all_18_5) = 0
% 8.29/1.90 | | (34) in(all_32_1, all_18_3) = 0
% 8.29/1.90 | |
% 8.29/1.90 | | GROUND_INST: instantiating (5) with all_18_3, all_18_4, all_18_1, all_32_1,
% 8.29/1.90 | | all_32_0, simplifying with (10), (11), (20), (21), (28), (30)
% 8.29/1.90 | | gives:
% 8.29/1.90 | | (35) all_32_0 = 0 | ? [v0: any] : ? [v1: any] : (in(all_32_1, all_18_3)
% 8.29/1.91 | | = v0 & in(all_32_1, all_18_4) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 8.29/1.91 | |
% 8.29/1.91 | | BETA: splitting (31) gives:
% 8.29/1.91 | |
% 8.29/1.91 | | Case 1:
% 8.29/1.91 | | |
% 8.29/1.91 | | | (36) all_32_0 = 0
% 8.29/1.91 | | |
% 8.29/1.91 | | | REDUCE: (27), (36) imply:
% 8.29/1.91 | | | (37) $false
% 8.29/1.91 | | |
% 8.29/1.91 | | | CLOSE: (37) is inconsistent.
% 8.29/1.91 | | |
% 8.29/1.91 | | Case 2:
% 8.29/1.91 | | |
% 8.29/1.91 | | | (38) ? [v0: any] : ? [v1: any] : (in(all_32_1, all_18_3) = v1 &
% 8.29/1.91 | | | in(all_32_1, all_18_4) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 8.29/1.91 | | |
% 8.29/1.91 | | | DELTA: instantiating (38) with fresh symbols all_48_0, all_48_1 gives:
% 8.29/1.91 | | | (39) in(all_32_1, all_18_3) = all_48_0 & in(all_32_1, all_18_4) =
% 8.29/1.91 | | | all_48_1 & ( ~ (all_48_0 = 0) | ~ (all_48_1 = 0))
% 8.29/1.91 | | |
% 8.29/1.91 | | | ALPHA: (39) implies:
% 8.29/1.91 | | | (40) in(all_32_1, all_18_4) = all_48_1
% 8.29/1.91 | | | (41) in(all_32_1, all_18_3) = all_48_0
% 8.29/1.91 | | | (42) ~ (all_48_0 = 0) | ~ (all_48_1 = 0)
% 8.29/1.91 | | |
% 8.29/1.91 | | | BETA: splitting (35) gives:
% 8.29/1.91 | | |
% 8.29/1.91 | | | Case 1:
% 8.29/1.91 | | | |
% 8.29/1.91 | | | | (43) all_32_0 = 0
% 8.29/1.91 | | | |
% 8.29/1.91 | | | | REDUCE: (27), (43) imply:
% 8.29/1.91 | | | | (44) $false
% 8.29/1.91 | | | |
% 8.29/1.91 | | | | CLOSE: (44) is inconsistent.
% 8.29/1.91 | | | |
% 8.29/1.91 | | | Case 2:
% 8.29/1.91 | | | |
% 8.29/1.91 | | | | (45) ? [v0: any] : ? [v1: any] : (in(all_32_1, all_18_3) = v0 &
% 8.29/1.91 | | | | in(all_32_1, all_18_4) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 8.29/1.91 | | | |
% 8.29/1.91 | | | | DELTA: instantiating (45) with fresh symbols all_53_0, all_53_1 gives:
% 8.29/1.91 | | | | (46) in(all_32_1, all_18_3) = all_53_1 & in(all_32_1, all_18_4) =
% 8.29/1.91 | | | | all_53_0 & ( ~ (all_53_0 = 0) | ~ (all_53_1 = 0))
% 8.29/1.91 | | | |
% 8.29/1.91 | | | | ALPHA: (46) implies:
% 8.29/1.91 | | | | (47) in(all_32_1, all_18_4) = all_53_0
% 8.29/1.91 | | | | (48) in(all_32_1, all_18_3) = all_53_1
% 8.29/1.91 | | | |
% 8.29/1.91 | | | | GROUND_INST: instantiating (6) with all_48_1, all_53_0, all_18_4,
% 8.29/1.91 | | | | all_32_1, simplifying with (40), (47) gives:
% 8.29/1.91 | | | | (49) all_53_0 = all_48_1
% 8.29/1.91 | | | |
% 8.29/1.91 | | | | GROUND_INST: instantiating (6) with all_48_0, all_53_1, all_18_3,
% 8.29/1.91 | | | | all_32_1, simplifying with (41), (48) gives:
% 8.29/1.91 | | | | (50) all_53_1 = all_48_0
% 8.29/1.91 | | | |
% 8.29/1.91 | | | | GROUND_INST: instantiating (6) with 0, all_53_1, all_18_3, all_32_1,
% 8.29/1.91 | | | | simplifying with (34), (48) gives:
% 8.29/1.91 | | | | (51) all_53_1 = 0
% 8.29/1.91 | | | |
% 8.29/1.91 | | | | COMBINE_EQS: (50), (51) imply:
% 8.29/1.91 | | | | (52) all_48_0 = 0
% 8.29/1.91 | | | |
% 8.29/1.91 | | | | BETA: splitting (42) gives:
% 8.29/1.91 | | | |
% 8.29/1.91 | | | | Case 1:
% 8.29/1.91 | | | | |
% 8.29/1.91 | | | | | (53) ~ (all_48_0 = 0)
% 8.29/1.91 | | | | |
% 8.29/1.91 | | | | | REDUCE: (52), (53) imply:
% 8.29/1.91 | | | | | (54) $false
% 8.29/1.91 | | | | |
% 8.29/1.91 | | | | | CLOSE: (54) is inconsistent.
% 8.29/1.91 | | | | |
% 8.29/1.91 | | | | Case 2:
% 8.29/1.91 | | | | |
% 8.29/1.91 | | | | | (55) ~ (all_48_1 = 0)
% 8.29/1.91 | | | | |
% 8.29/1.91 | | | | | GROUND_INST: instantiating (2) with all_18_5, all_18_4, all_32_1,
% 8.29/1.91 | | | | | simplifying with (9), (10), (14), (28), (33) gives:
% 8.29/1.91 | | | | | (56) in(all_32_1, all_18_4) = 0
% 8.29/1.91 | | | | |
% 8.29/1.91 | | | | | GROUND_INST: instantiating (6) with all_48_1, 0, all_18_4, all_32_1,
% 8.29/1.91 | | | | | simplifying with (40), (56) gives:
% 8.29/1.91 | | | | | (57) all_48_1 = 0
% 8.29/1.91 | | | | |
% 8.29/1.91 | | | | | REDUCE: (55), (57) imply:
% 8.29/1.91 | | | | | (58) $false
% 8.29/1.91 | | | | |
% 8.29/1.91 | | | | | CLOSE: (58) is inconsistent.
% 8.29/1.91 | | | | |
% 8.29/1.91 | | | | End of split
% 8.29/1.91 | | | |
% 8.29/1.91 | | | End of split
% 8.29/1.91 | | |
% 8.29/1.91 | | End of split
% 8.29/1.91 | |
% 8.29/1.91 | End of split
% 8.29/1.91 |
% 8.29/1.91 End of proof
% 8.29/1.91 % SZS output end Proof for theBenchmark
% 8.29/1.91
% 8.29/1.91 1305ms
%------------------------------------------------------------------------------