TSTP Solution File: SEU132+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SEU132+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 : n018.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 17:42:40 EDT 2023
% Result : Theorem 6.08s 1.62s
% Output : Proof 7.42s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14 % Problem : SEU132+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.15 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.15/0.36 % Computer : n018.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Wed Aug 23 13:16:27 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.22/0.63 ________ _____
% 0.22/0.63 ___ __ \_________(_)________________________________
% 0.22/0.63 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.22/0.63 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.22/0.63 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.22/0.63
% 0.22/0.63 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.22/0.63 (2023-06-19)
% 0.22/0.63
% 0.22/0.63 (c) Philipp Rümmer, 2009-2023
% 0.22/0.63 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.22/0.63 Amanda Stjerna.
% 0.22/0.63 Free software under BSD-3-Clause.
% 0.22/0.63
% 0.22/0.63 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.22/0.63
% 0.22/0.63 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.22/0.64 Running up to 7 provers in parallel.
% 0.22/0.67 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.22/0.67 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.22/0.67 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.22/0.67 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.22/0.67 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.22/0.67 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.22/0.67 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 1.99/1.04 Prover 4: Preprocessing ...
% 1.99/1.04 Prover 1: Preprocessing ...
% 1.99/1.08 Prover 6: Preprocessing ...
% 1.99/1.08 Prover 0: Preprocessing ...
% 1.99/1.08 Prover 3: Preprocessing ...
% 1.99/1.08 Prover 5: Preprocessing ...
% 2.63/1.08 Prover 2: Preprocessing ...
% 3.98/1.32 Prover 1: Warning: ignoring some quantifiers
% 3.98/1.33 Prover 1: Constructing countermodel ...
% 3.98/1.34 Prover 3: Warning: ignoring some quantifiers
% 3.98/1.35 Prover 3: Constructing countermodel ...
% 3.98/1.35 Prover 2: Proving ...
% 3.98/1.35 Prover 5: Proving ...
% 3.98/1.36 Prover 6: Proving ...
% 3.98/1.37 Prover 4: Warning: ignoring some quantifiers
% 3.98/1.38 Prover 4: Constructing countermodel ...
% 4.67/1.40 Prover 0: Proving ...
% 6.08/1.62 Prover 0: proved (973ms)
% 6.08/1.62
% 6.08/1.62 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.08/1.62
% 6.08/1.62 Prover 3: stopped
% 6.08/1.62 Prover 5: stopped
% 6.08/1.62 Prover 2: stopped
% 6.08/1.62 Prover 6: stopped
% 6.08/1.62 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 6.08/1.62 Prover 1: gave up
% 6.08/1.62 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 6.08/1.62 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 6.08/1.63 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 6.08/1.63 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 6.08/1.63 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 6.08/1.66 Prover 7: Preprocessing ...
% 6.08/1.66 Prover 13: Preprocessing ...
% 6.08/1.67 Prover 16: Preprocessing ...
% 6.08/1.67 Prover 11: Preprocessing ...
% 6.08/1.68 Prover 8: Preprocessing ...
% 6.70/1.69 Prover 10: Preprocessing ...
% 6.70/1.69 Prover 4: Found proof (size 30)
% 6.70/1.69 Prover 4: proved (1029ms)
% 6.70/1.69 Prover 7: Warning: ignoring some quantifiers
% 6.70/1.70 Prover 7: Constructing countermodel ...
% 6.70/1.70 Prover 10: stopped
% 6.70/1.71 Prover 11: stopped
% 6.70/1.71 Prover 7: stopped
% 6.70/1.71 Prover 13: Warning: ignoring some quantifiers
% 6.70/1.72 Prover 13: Constructing countermodel ...
% 6.70/1.72 Prover 16: Warning: ignoring some quantifiers
% 6.70/1.73 Prover 13: stopped
% 6.70/1.73 Prover 16: Constructing countermodel ...
% 6.70/1.74 Prover 16: stopped
% 6.70/1.74 Prover 8: Warning: ignoring some quantifiers
% 6.70/1.75 Prover 8: Constructing countermodel ...
% 6.70/1.75 Prover 8: stopped
% 6.70/1.75
% 6.70/1.75 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.70/1.75
% 6.70/1.75 % SZS output start Proof for theBenchmark
% 6.70/1.76 Assumptions after simplification:
% 6.70/1.76 ---------------------------------
% 6.70/1.76
% 6.70/1.76 (d3_tarski)
% 7.26/1.79 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~
% 7.26/1.79 (subset(v0, v1) = 0) | ~ (in(v2, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~
% 7.26/1.79 $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & in(v2, v0) = v4)) & ! [v0: $i] : !
% 7.26/1.79 [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ~ $i(v1) | ~
% 7.26/1.79 $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) & in(v3, v1) = v4 &
% 7.26/1.79 in(v3, v0) = 0 & $i(v3))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 7.26/1.79 (subset(v0, v1) = 0) | ~ (in(v2, v0) = 0) | ~ $i(v2) | ~ $i(v1) | ~
% 7.26/1.79 $i(v0) | in(v2, v1) = 0)
% 7.26/1.79
% 7.26/1.79 (d4_xboole_0)
% 7.31/1.81 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0
% 7.31/1.81 | ~ (set_difference(v0, v1) = v2) | ~ (in(v3, v2) = v4) | ~ $i(v3) | ~
% 7.31/1.81 $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : (in(v3, v1) =
% 7.31/1.81 v6 & in(v3, v0) = v5 & ( ~ (v5 = 0) | v6 = 0))) & ! [v0: $i] : ! [v1:
% 7.31/1.81 $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0 | ~
% 7.31/1.81 (set_difference(v0, v1) = v2) | ~ (in(v3, v1) = v4) | ~ $i(v3) | ~ $i(v2)
% 7.31/1.81 | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : (in(v3, v2) = v6 &
% 7.31/1.81 in(v3, v0) = v5 & ( ~ (v5 = 0) | v6 = 0))) & ! [v0: $i] : ! [v1: $i] :
% 7.31/1.81 ! [v2: $i] : ! [v3: $i] : ! [v4: any] : ( ~ (set_difference(v0, v1) = v2) |
% 7.31/1.81 ~ (in(v3, v1) = v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ?
% 7.31/1.81 [v5: any] : ? [v6: any] : (in(v3, v2) = v5 & in(v3, v0) = v6 & ( ~ (v5 = 0)
% 7.31/1.81 | (v6 = 0 & ~ (v4 = 0))))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 7.31/1.81 ! [v3: $i] : ! [v4: any] : ( ~ (set_difference(v0, v1) = v2) | ~ (in(v3, v0)
% 7.31/1.81 = v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ?
% 7.31/1.81 [v6: any] : (in(v3, v2) = v5 & in(v3, v1) = v6 & ( ~ (v5 = 0) | (v4 = 0 & ~
% 7.31/1.81 (v6 = 0))))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] :
% 7.31/1.81 ( ~ (set_difference(v0, v1) = v2) | ~ (in(v3, v2) = 0) | ~ $i(v3) | ~
% 7.31/1.81 $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & in(v3, v1) =
% 7.31/1.81 v4 & in(v3, v0) = 0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 7.31/1.81 $i] : ( ~ (set_difference(v0, v1) = v2) | ~ (in(v3, v0) = 0) | ~ $i(v3) |
% 7.31/1.81 ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: any] : (in(v3, v2)
% 7.39/1.81 = v5 & in(v3, v1) = v4 & (v5 = 0 | v4 = 0))) & ? [v0: $i] : ! [v1: $i] :
% 7.39/1.81 ! [v2: $i] : ! [v3: $i] : (v3 = v0 | ~ (set_difference(v1, v2) = v3) | ~
% 7.39/1.81 $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: $i] : ? [v5: any] : ? [v6: any] :
% 7.39/1.81 ? [v7: any] : (in(v4, v2) = v7 & in(v4, v1) = v6 & in(v4, v0) = v5 & $i(v4)
% 7.39/1.81 & ( ~ (v6 = 0) | ~ (v5 = 0) | v7 = 0) & (v5 = 0 | (v6 = 0 & ~ (v7 =
% 7.39/1.81 0)))))
% 7.39/1.81
% 7.39/1.81 (t33_xboole_1)
% 7.39/1.81 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5:
% 7.39/1.81 int] : ( ~ (v5 = 0) & set_difference(v1, v2) = v4 & set_difference(v0, v2) =
% 7.39/1.81 v3 & subset(v3, v4) = v5 & subset(v0, v1) = 0 & $i(v4) & $i(v3) & $i(v2) &
% 7.39/1.81 $i(v1) & $i(v0))
% 7.39/1.81
% 7.39/1.81 (function-axioms)
% 7.39/1.81 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 7.39/1.81 (set_difference(v3, v2) = v1) | ~ (set_difference(v3, v2) = v0)) & ! [v0:
% 7.39/1.81 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 7.39/1.81 : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) & ! [v0:
% 7.39/1.81 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 7.39/1.81 : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) & ! [v0:
% 7.39/1.81 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 |
% 7.39/1.81 ~ (empty(v2) = v1) | ~ (empty(v2) = v0))
% 7.39/1.81
% 7.39/1.81 Further assumptions not needed in the proof:
% 7.39/1.81 --------------------------------------------
% 7.39/1.81 antisymmetry_r2_hidden, dt_k1_xboole_0, dt_k4_xboole_0, fc1_xboole_0,
% 7.39/1.81 rc1_xboole_0, rc2_xboole_0, reflexivity_r1_tarski, t3_boole, t4_boole, t6_boole,
% 7.39/1.81 t7_boole, t8_boole
% 7.39/1.81
% 7.39/1.81 Those formulas are unsatisfiable:
% 7.39/1.81 ---------------------------------
% 7.39/1.81
% 7.39/1.81 Begin of proof
% 7.42/1.81 |
% 7.42/1.81 | ALPHA: (d3_tarski) implies:
% 7.42/1.82 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (subset(v0, v1) = 0) | ~
% 7.42/1.82 | (in(v2, v0) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | in(v2, v1) =
% 7.42/1.82 | 0)
% 7.42/1.82 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1)
% 7.42/1.82 | = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~
% 7.42/1.82 | (v4 = 0) & in(v3, v1) = v4 & in(v3, v0) = 0 & $i(v3)))
% 7.42/1.82 |
% 7.42/1.82 | ALPHA: (d4_xboole_0) implies:
% 7.42/1.82 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 7.42/1.82 | (set_difference(v0, v1) = v2) | ~ (in(v3, v2) = 0) | ~ $i(v3) | ~
% 7.42/1.82 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & in(v3,
% 7.42/1.82 | v1) = v4 & in(v3, v0) = 0))
% 7.42/1.82 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] :
% 7.42/1.82 | (v4 = 0 | ~ (set_difference(v0, v1) = v2) | ~ (in(v3, v2) = v4) | ~
% 7.42/1.82 | $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6:
% 7.42/1.82 | any] : (in(v3, v1) = v6 & in(v3, v0) = v5 & ( ~ (v5 = 0) | v6 =
% 7.42/1.82 | 0)))
% 7.42/1.82 |
% 7.42/1.82 | ALPHA: (function-axioms) implies:
% 7.42/1.82 | (5) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 7.42/1.82 | ! [v3: $i] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0))
% 7.42/1.82 |
% 7.42/1.82 | DELTA: instantiating (t33_xboole_1) with fresh symbols all_17_0, all_17_1,
% 7.42/1.82 | all_17_2, all_17_3, all_17_4, all_17_5 gives:
% 7.42/1.82 | (6) ~ (all_17_0 = 0) & set_difference(all_17_4, all_17_3) = all_17_1 &
% 7.42/1.82 | set_difference(all_17_5, all_17_3) = all_17_2 & subset(all_17_2,
% 7.42/1.82 | all_17_1) = all_17_0 & subset(all_17_5, all_17_4) = 0 & $i(all_17_1)
% 7.42/1.82 | & $i(all_17_2) & $i(all_17_3) & $i(all_17_4) & $i(all_17_5)
% 7.42/1.82 |
% 7.42/1.82 | ALPHA: (6) implies:
% 7.42/1.82 | (7) ~ (all_17_0 = 0)
% 7.42/1.82 | (8) $i(all_17_5)
% 7.42/1.82 | (9) $i(all_17_4)
% 7.42/1.82 | (10) $i(all_17_3)
% 7.42/1.82 | (11) $i(all_17_2)
% 7.42/1.82 | (12) $i(all_17_1)
% 7.42/1.82 | (13) subset(all_17_5, all_17_4) = 0
% 7.42/1.82 | (14) subset(all_17_2, all_17_1) = all_17_0
% 7.42/1.82 | (15) set_difference(all_17_5, all_17_3) = all_17_2
% 7.42/1.82 | (16) set_difference(all_17_4, all_17_3) = all_17_1
% 7.42/1.83 |
% 7.42/1.83 | GROUND_INST: instantiating (2) with all_17_2, all_17_1, all_17_0, simplifying
% 7.42/1.83 | with (11), (12), (14) gives:
% 7.42/1.83 | (17) all_17_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & in(v0,
% 7.42/1.83 | all_17_1) = v1 & in(v0, all_17_2) = 0 & $i(v0))
% 7.42/1.83 |
% 7.42/1.83 | BETA: splitting (17) gives:
% 7.42/1.83 |
% 7.42/1.83 | Case 1:
% 7.42/1.83 | |
% 7.42/1.83 | | (18) all_17_0 = 0
% 7.42/1.83 | |
% 7.42/1.83 | | REDUCE: (7), (18) imply:
% 7.42/1.83 | | (19) $false
% 7.42/1.83 | |
% 7.42/1.83 | | CLOSE: (19) is inconsistent.
% 7.42/1.83 | |
% 7.42/1.83 | Case 2:
% 7.42/1.83 | |
% 7.42/1.83 | | (20) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & in(v0, all_17_1) = v1 &
% 7.42/1.83 | | in(v0, all_17_2) = 0 & $i(v0))
% 7.42/1.83 | |
% 7.42/1.83 | | DELTA: instantiating (20) with fresh symbols all_31_0, all_31_1 gives:
% 7.42/1.83 | | (21) ~ (all_31_0 = 0) & in(all_31_1, all_17_1) = all_31_0 & in(all_31_1,
% 7.42/1.83 | | all_17_2) = 0 & $i(all_31_1)
% 7.42/1.83 | |
% 7.42/1.83 | | ALPHA: (21) implies:
% 7.42/1.83 | | (22) ~ (all_31_0 = 0)
% 7.42/1.83 | | (23) $i(all_31_1)
% 7.42/1.83 | | (24) in(all_31_1, all_17_2) = 0
% 7.42/1.83 | | (25) in(all_31_1, all_17_1) = all_31_0
% 7.42/1.83 | |
% 7.42/1.83 | | GROUND_INST: instantiating (3) with all_17_5, all_17_3, all_17_2, all_31_1,
% 7.42/1.83 | | simplifying with (8), (10), (11), (15), (23), (24) gives:
% 7.42/1.83 | | (26) ? [v0: int] : ( ~ (v0 = 0) & in(all_31_1, all_17_3) = v0 &
% 7.42/1.83 | | in(all_31_1, all_17_5) = 0)
% 7.42/1.83 | |
% 7.42/1.83 | | GROUND_INST: instantiating (4) with all_17_4, all_17_3, all_17_1, all_31_1,
% 7.42/1.83 | | all_31_0, simplifying with (9), (10), (12), (16), (23), (25)
% 7.42/1.83 | | gives:
% 7.42/1.83 | | (27) all_31_0 = 0 | ? [v0: any] : ? [v1: any] : (in(all_31_1, all_17_3)
% 7.42/1.83 | | = v1 & in(all_31_1, all_17_4) = v0 & ( ~ (v0 = 0) | v1 = 0))
% 7.42/1.83 | |
% 7.42/1.83 | | DELTA: instantiating (26) with fresh symbol all_42_0 gives:
% 7.42/1.84 | | (28) ~ (all_42_0 = 0) & in(all_31_1, all_17_3) = all_42_0 & in(all_31_1,
% 7.42/1.84 | | all_17_5) = 0
% 7.42/1.84 | |
% 7.42/1.84 | | ALPHA: (28) implies:
% 7.42/1.84 | | (29) ~ (all_42_0 = 0)
% 7.42/1.84 | | (30) in(all_31_1, all_17_5) = 0
% 7.42/1.84 | | (31) in(all_31_1, all_17_3) = all_42_0
% 7.42/1.84 | |
% 7.42/1.84 | | BETA: splitting (27) gives:
% 7.42/1.84 | |
% 7.42/1.84 | | Case 1:
% 7.42/1.84 | | |
% 7.42/1.84 | | | (32) all_31_0 = 0
% 7.42/1.84 | | |
% 7.42/1.84 | | | REDUCE: (22), (32) imply:
% 7.42/1.84 | | | (33) $false
% 7.42/1.84 | | |
% 7.42/1.84 | | | CLOSE: (33) is inconsistent.
% 7.42/1.84 | | |
% 7.42/1.84 | | Case 2:
% 7.42/1.84 | | |
% 7.42/1.84 | | | (34) ? [v0: any] : ? [v1: any] : (in(all_31_1, all_17_3) = v1 &
% 7.42/1.84 | | | in(all_31_1, all_17_4) = v0 & ( ~ (v0 = 0) | v1 = 0))
% 7.42/1.84 | | |
% 7.42/1.84 | | | DELTA: instantiating (34) with fresh symbols all_48_0, all_48_1 gives:
% 7.42/1.84 | | | (35) in(all_31_1, all_17_3) = all_48_0 & in(all_31_1, all_17_4) =
% 7.42/1.84 | | | all_48_1 & ( ~ (all_48_1 = 0) | all_48_0 = 0)
% 7.42/1.84 | | |
% 7.42/1.84 | | | ALPHA: (35) implies:
% 7.42/1.84 | | | (36) in(all_31_1, all_17_4) = all_48_1
% 7.42/1.84 | | | (37) in(all_31_1, all_17_3) = all_48_0
% 7.42/1.84 | | | (38) ~ (all_48_1 = 0) | all_48_0 = 0
% 7.42/1.84 | | |
% 7.42/1.84 | | | GROUND_INST: instantiating (5) with all_42_0, all_48_0, all_17_3,
% 7.42/1.84 | | | all_31_1, simplifying with (31), (37) gives:
% 7.42/1.84 | | | (39) all_48_0 = all_42_0
% 7.42/1.84 | | |
% 7.42/1.84 | | | BETA: splitting (38) gives:
% 7.42/1.84 | | |
% 7.42/1.84 | | | Case 1:
% 7.42/1.84 | | | |
% 7.42/1.84 | | | | (40) ~ (all_48_1 = 0)
% 7.42/1.84 | | | |
% 7.42/1.84 | | | | GROUND_INST: instantiating (1) with all_17_5, all_17_4, all_31_1,
% 7.42/1.84 | | | | simplifying with (8), (9), (13), (23), (30) gives:
% 7.42/1.84 | | | | (41) in(all_31_1, all_17_4) = 0
% 7.42/1.84 | | | |
% 7.42/1.84 | | | | GROUND_INST: instantiating (5) with all_48_1, 0, all_17_4, all_31_1,
% 7.42/1.84 | | | | simplifying with (36), (41) gives:
% 7.42/1.84 | | | | (42) all_48_1 = 0
% 7.42/1.84 | | | |
% 7.42/1.84 | | | | REDUCE: (40), (42) imply:
% 7.42/1.84 | | | | (43) $false
% 7.42/1.84 | | | |
% 7.42/1.84 | | | | CLOSE: (43) is inconsistent.
% 7.42/1.84 | | | |
% 7.42/1.84 | | | Case 2:
% 7.42/1.84 | | | |
% 7.42/1.84 | | | | (44) all_48_0 = 0
% 7.42/1.84 | | | |
% 7.42/1.84 | | | | COMBINE_EQS: (39), (44) imply:
% 7.42/1.84 | | | | (45) all_42_0 = 0
% 7.42/1.84 | | | |
% 7.42/1.84 | | | | REDUCE: (29), (45) imply:
% 7.42/1.84 | | | | (46) $false
% 7.42/1.84 | | | |
% 7.42/1.84 | | | | CLOSE: (46) is inconsistent.
% 7.42/1.84 | | | |
% 7.42/1.84 | | | End of split
% 7.42/1.84 | | |
% 7.42/1.84 | | End of split
% 7.42/1.84 | |
% 7.42/1.84 | End of split
% 7.42/1.84 |
% 7.42/1.84 End of proof
% 7.42/1.84 % SZS output end Proof for theBenchmark
% 7.42/1.84
% 7.42/1.84 1214ms
%------------------------------------------------------------------------------