TSTP Solution File: SEU128+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SEU128+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 : n023.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 17:42:38 EDT 2023
% Result : Theorem 5.71s 1.52s
% Output : Proof 6.81s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : SEU128+1 : TPTP v8.1.2. Released v3.3.0.
% 0.10/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.34 % Computer : n023.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 19:14:57 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.19/0.60 ________ _____
% 0.19/0.60 ___ __ \_________(_)________________________________
% 0.19/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.19/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.19/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.19/0.60
% 0.19/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.19/0.60 (2023-06-19)
% 0.19/0.60
% 0.19/0.60 (c) Philipp Rümmer, 2009-2023
% 0.19/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.19/0.60 Amanda Stjerna.
% 0.19/0.60 Free software under BSD-3-Clause.
% 0.19/0.60
% 0.19/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.19/0.60
% 0.19/0.60 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.62/0.61 Running up to 7 provers in parallel.
% 0.71/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.71/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.71/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.71/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.71/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.71/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.71/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 1.88/1.00 Prover 4: Preprocessing ...
% 1.88/1.00 Prover 1: Preprocessing ...
% 2.38/1.05 Prover 3: Preprocessing ...
% 2.38/1.05 Prover 0: Preprocessing ...
% 2.38/1.05 Prover 5: Preprocessing ...
% 2.38/1.05 Prover 6: Preprocessing ...
% 2.38/1.06 Prover 2: Preprocessing ...
% 3.94/1.29 Prover 5: Proving ...
% 4.40/1.31 Prover 1: Warning: ignoring some quantifiers
% 4.40/1.32 Prover 2: Proving ...
% 4.40/1.32 Prover 3: Warning: ignoring some quantifiers
% 4.40/1.32 Prover 6: Proving ...
% 4.40/1.33 Prover 3: Constructing countermodel ...
% 4.40/1.33 Prover 4: Warning: ignoring some quantifiers
% 4.40/1.34 Prover 1: Constructing countermodel ...
% 4.40/1.35 Prover 4: Constructing countermodel ...
% 4.40/1.35 Prover 0: Proving ...
% 5.71/1.52 Prover 0: proved (903ms)
% 5.71/1.52
% 5.71/1.52 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.71/1.52
% 5.71/1.53 Prover 3: stopped
% 5.71/1.53 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 5.71/1.53 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 5.71/1.53 Prover 5: stopped
% 5.71/1.53 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 5.71/1.53 Prover 2: stopped
% 6.08/1.54 Prover 6: stopped
% 6.08/1.54 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 6.08/1.54 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 6.08/1.56 Prover 7: Preprocessing ...
% 6.08/1.56 Prover 10: Preprocessing ...
% 6.08/1.57 Prover 13: Preprocessing ...
% 6.08/1.57 Prover 4: Found proof (size 30)
% 6.08/1.57 Prover 11: Preprocessing ...
% 6.08/1.57 Prover 4: proved (944ms)
% 6.08/1.57 Prover 1: stopped
% 6.08/1.57 Prover 8: Preprocessing ...
% 6.08/1.59 Prover 10: stopped
% 6.08/1.59 Prover 7: stopped
% 6.08/1.59 Prover 13: stopped
% 6.08/1.59 Prover 11: stopped
% 6.51/1.63 Prover 8: Warning: ignoring some quantifiers
% 6.51/1.64 Prover 8: Constructing countermodel ...
% 6.51/1.65 Prover 8: stopped
% 6.51/1.65
% 6.51/1.65 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.51/1.65
% 6.51/1.66 % SZS output start Proof for theBenchmark
% 6.51/1.66 Assumptions after simplification:
% 6.51/1.66 ---------------------------------
% 6.51/1.66
% 6.51/1.66 (commutativity_k3_xboole_0)
% 6.81/1.69 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (set_intersection2(v1, v0) = v2)
% 6.81/1.69 | ~ $i(v1) | ~ $i(v0) | (set_intersection2(v0, v1) = v2 & $i(v2))) & !
% 6.81/1.69 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (set_intersection2(v0, v1) = v2) |
% 6.81/1.69 ~ $i(v1) | ~ $i(v0) | (set_intersection2(v1, v0) = v2 & $i(v2)))
% 6.81/1.69
% 6.81/1.69 (d3_tarski)
% 6.81/1.70 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~
% 6.81/1.70 (subset(v0, v1) = 0) | ~ (in(v2, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~
% 6.81/1.70 $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & in(v2, v0) = v4)) & ! [v0: $i] : !
% 6.81/1.70 [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ~ $i(v1) | ~
% 6.81/1.70 $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) & in(v3, v1) = v4 &
% 6.81/1.70 in(v3, v0) = 0 & $i(v3))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 6.81/1.70 (subset(v0, v1) = 0) | ~ (in(v2, v0) = 0) | ~ $i(v2) | ~ $i(v1) | ~
% 6.81/1.70 $i(v0) | in(v2, v1) = 0)
% 6.81/1.70
% 6.81/1.70 (d3_xboole_0)
% 6.81/1.71 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0
% 6.81/1.71 | ~ (set_intersection2(v0, v1) = v2) | ~ (in(v3, v2) = v4) | ~ $i(v3) |
% 6.81/1.71 ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : (in(v3, v1)
% 6.81/1.71 = v6 & in(v3, v0) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0)))) & ! [v0: $i] : !
% 6.81/1.71 [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: any] : ( ~
% 6.81/1.71 (set_intersection2(v0, v1) = v2) | ~ (in(v3, v1) = v4) | ~ $i(v3) | ~
% 6.81/1.71 $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : (in(v3, v2) =
% 6.81/1.71 v5 & in(v3, v0) = v6 & ( ~ (v5 = 0) | (v6 = 0 & v4 = 0)))) & ! [v0: $i] :
% 6.81/1.71 ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: any] : ( ~
% 6.81/1.71 (set_intersection2(v0, v1) = v2) | ~ (in(v3, v0) = v4) | ~ $i(v3) | ~
% 6.81/1.71 $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : (in(v3, v2) =
% 6.81/1.71 v5 & in(v3, v1) = v6 & ( ~ (v5 = 0) | (v6 = 0 & v4 = 0)))) & ! [v0: $i] :
% 6.81/1.71 ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (set_intersection2(v0, v1) = v2)
% 6.81/1.71 | ~ (in(v3, v2) = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 6.81/1.71 (in(v3, v1) = 0 & in(v3, v0) = 0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i]
% 6.81/1.71 : ! [v3: $i] : ( ~ (set_intersection2(v0, v1) = v2) | ~ (in(v3, v1) = 0) |
% 6.81/1.71 ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: any] :
% 6.81/1.71 (in(v3, v2) = v5 & in(v3, v0) = v4 & ( ~ (v4 = 0) | v5 = 0))) & ! [v0: $i]
% 6.81/1.71 : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (set_intersection2(v0, v1) =
% 6.81/1.71 v2) | ~ (in(v3, v0) = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0)
% 6.81/1.71 | ? [v4: any] : ? [v5: any] : (in(v3, v2) = v5 & in(v3, v1) = v4 & ( ~ (v4
% 6.81/1.71 = 0) | v5 = 0))) & ? [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 6.81/1.71 $i] : (v3 = v0 | ~ (set_intersection2(v1, v2) = v3) | ~ $i(v2) | ~ $i(v1)
% 6.81/1.71 | ~ $i(v0) | ? [v4: $i] : ? [v5: any] : ? [v6: any] : ? [v7: any] :
% 6.81/1.71 (in(v4, v2) = v7 & in(v4, v1) = v6 & in(v4, v0) = v5 & $i(v4) & ( ~ (v7 = 0)
% 6.81/1.72 | ~ (v6 = 0) | ~ (v5 = 0)) & (v5 = 0 | (v7 = 0 & v6 = 0))))
% 6.81/1.72
% 6.81/1.72 (t19_xboole_1)
% 6.81/1.72 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: int] : ( ~ (v4
% 6.81/1.72 = 0) & subset(v0, v3) = v4 & subset(v0, v2) = 0 & subset(v0, v1) = 0 &
% 6.81/1.72 set_intersection2(v1, v2) = v3 & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 6.81/1.72
% 6.81/1.72 (function-axioms)
% 6.81/1.72 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 6.81/1.72 [v3: $i] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) &
% 6.81/1.72 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 6.81/1.72 (set_intersection2(v3, v2) = v1) | ~ (set_intersection2(v3, v2) = v0)) & !
% 6.81/1.72 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 6.81/1.72 $i] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) & ! [v0:
% 6.81/1.72 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 |
% 6.81/1.72 ~ (empty(v2) = v1) | ~ (empty(v2) = v0))
% 6.81/1.72
% 6.81/1.72 Further assumptions not needed in the proof:
% 6.81/1.72 --------------------------------------------
% 6.81/1.72 antisymmetry_r2_hidden, dt_k1_xboole_0, dt_k3_xboole_0, fc1_xboole_0,
% 6.81/1.72 idempotence_k3_xboole_0, rc1_xboole_0, rc2_xboole_0, reflexivity_r1_tarski,
% 6.81/1.72 t2_boole, t6_boole, t7_boole, t8_boole
% 6.81/1.72
% 6.81/1.72 Those formulas are unsatisfiable:
% 6.81/1.72 ---------------------------------
% 6.81/1.72
% 6.81/1.72 Begin of proof
% 6.81/1.72 |
% 6.81/1.72 | ALPHA: (commutativity_k3_xboole_0) implies:
% 6.81/1.72 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (set_intersection2(v1,
% 6.81/1.72 | v0) = v2) | ~ $i(v1) | ~ $i(v0) | (set_intersection2(v0, v1) =
% 6.81/1.72 | v2 & $i(v2)))
% 6.81/1.72 |
% 6.81/1.72 | ALPHA: (d3_tarski) implies:
% 6.81/1.72 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (subset(v0, v1) = 0) | ~
% 6.81/1.72 | (in(v2, v0) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | in(v2, v1) =
% 6.81/1.72 | 0)
% 6.81/1.72 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1)
% 6.81/1.72 | = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~
% 6.81/1.72 | (v4 = 0) & in(v3, v1) = v4 & in(v3, v0) = 0 & $i(v3)))
% 6.81/1.72 |
% 6.81/1.72 | ALPHA: (d3_xboole_0) implies:
% 6.81/1.73 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] :
% 6.81/1.73 | (v4 = 0 | ~ (set_intersection2(v0, v1) = v2) | ~ (in(v3, v2) = v4) |
% 6.81/1.73 | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6:
% 6.81/1.73 | any] : (in(v3, v1) = v6 & in(v3, v0) = v5 & ( ~ (v6 = 0) | ~ (v5 =
% 6.81/1.73 | 0))))
% 6.81/1.73 |
% 6.81/1.73 | ALPHA: (function-axioms) implies:
% 6.81/1.73 | (5) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 6.81/1.73 | ! [v3: $i] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0))
% 6.81/1.73 |
% 6.81/1.73 | DELTA: instantiating (t19_xboole_1) with fresh symbols all_18_0, all_18_1,
% 6.81/1.73 | all_18_2, all_18_3, all_18_4 gives:
% 6.81/1.73 | (6) ~ (all_18_0 = 0) & subset(all_18_4, all_18_1) = all_18_0 &
% 6.81/1.73 | subset(all_18_4, all_18_2) = 0 & subset(all_18_4, all_18_3) = 0 &
% 6.81/1.73 | set_intersection2(all_18_3, all_18_2) = all_18_1 & $i(all_18_1) &
% 6.81/1.73 | $i(all_18_2) & $i(all_18_3) & $i(all_18_4)
% 6.81/1.73 |
% 6.81/1.73 | ALPHA: (6) implies:
% 6.81/1.73 | (7) ~ (all_18_0 = 0)
% 6.81/1.73 | (8) $i(all_18_4)
% 6.81/1.73 | (9) $i(all_18_3)
% 6.81/1.73 | (10) $i(all_18_2)
% 6.81/1.73 | (11) set_intersection2(all_18_3, all_18_2) = all_18_1
% 6.81/1.73 | (12) subset(all_18_4, all_18_3) = 0
% 6.81/1.73 | (13) subset(all_18_4, all_18_2) = 0
% 6.81/1.73 | (14) subset(all_18_4, all_18_1) = all_18_0
% 6.81/1.73 |
% 6.81/1.73 | GROUND_INST: instantiating (1) with all_18_2, all_18_3, all_18_1, simplifying
% 6.81/1.73 | with (9), (10), (11) gives:
% 6.81/1.73 | (15) set_intersection2(all_18_2, all_18_3) = all_18_1 & $i(all_18_1)
% 6.81/1.73 |
% 6.81/1.73 | ALPHA: (15) implies:
% 6.81/1.73 | (16) $i(all_18_1)
% 6.81/1.73 |
% 6.81/1.73 | GROUND_INST: instantiating (3) with all_18_4, all_18_1, all_18_0, simplifying
% 6.81/1.73 | with (8), (14), (16) gives:
% 6.81/1.73 | (17) all_18_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & in(v0,
% 6.81/1.73 | all_18_1) = v1 & in(v0, all_18_4) = 0 & $i(v0))
% 6.81/1.73 |
% 6.81/1.73 | BETA: splitting (17) gives:
% 6.81/1.73 |
% 6.81/1.73 | Case 1:
% 6.81/1.73 | |
% 6.81/1.73 | | (18) all_18_0 = 0
% 6.81/1.73 | |
% 6.81/1.73 | | REDUCE: (7), (18) imply:
% 6.81/1.73 | | (19) $false
% 6.81/1.74 | |
% 6.81/1.74 | | CLOSE: (19) is inconsistent.
% 6.81/1.74 | |
% 6.81/1.74 | Case 2:
% 6.81/1.74 | |
% 6.81/1.74 | | (20) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & in(v0, all_18_1) = v1 &
% 6.81/1.74 | | in(v0, all_18_4) = 0 & $i(v0))
% 6.81/1.74 | |
% 6.81/1.74 | | DELTA: instantiating (20) with fresh symbols all_32_0, all_32_1 gives:
% 6.81/1.74 | | (21) ~ (all_32_0 = 0) & in(all_32_1, all_18_1) = all_32_0 & in(all_32_1,
% 6.81/1.74 | | all_18_4) = 0 & $i(all_32_1)
% 6.81/1.74 | |
% 6.81/1.74 | | ALPHA: (21) implies:
% 6.81/1.74 | | (22) ~ (all_32_0 = 0)
% 6.81/1.74 | | (23) $i(all_32_1)
% 6.81/1.74 | | (24) in(all_32_1, all_18_4) = 0
% 6.81/1.74 | | (25) in(all_32_1, all_18_1) = all_32_0
% 6.81/1.74 | |
% 6.81/1.74 | | GROUND_INST: instantiating (2) with all_18_4, all_18_2, all_32_1,
% 6.81/1.74 | | simplifying with (8), (10), (13), (23), (24) gives:
% 6.81/1.74 | | (26) in(all_32_1, all_18_2) = 0
% 6.81/1.74 | |
% 6.81/1.74 | | GROUND_INST: instantiating (2) with all_18_4, all_18_3, all_32_1,
% 6.81/1.74 | | simplifying with (8), (9), (12), (23), (24) gives:
% 6.81/1.74 | | (27) in(all_32_1, all_18_3) = 0
% 6.81/1.74 | |
% 6.81/1.74 | | GROUND_INST: instantiating (4) with all_18_3, all_18_2, all_18_1, all_32_1,
% 6.81/1.74 | | all_32_0, simplifying with (9), (10), (11), (16), (23), (25)
% 6.81/1.74 | | gives:
% 6.81/1.74 | | (28) all_32_0 = 0 | ? [v0: any] : ? [v1: any] : (in(all_32_1, all_18_2)
% 6.81/1.74 | | = v1 & in(all_32_1, all_18_3) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 6.81/1.74 | |
% 6.81/1.74 | | BETA: splitting (28) gives:
% 6.81/1.74 | |
% 6.81/1.74 | | Case 1:
% 6.81/1.74 | | |
% 6.81/1.74 | | | (29) all_32_0 = 0
% 6.81/1.74 | | |
% 6.81/1.74 | | | REDUCE: (22), (29) imply:
% 6.81/1.74 | | | (30) $false
% 6.81/1.74 | | |
% 6.81/1.74 | | | CLOSE: (30) is inconsistent.
% 6.81/1.74 | | |
% 6.81/1.74 | | Case 2:
% 6.81/1.74 | | |
% 6.81/1.74 | | | (31) ? [v0: any] : ? [v1: any] : (in(all_32_1, all_18_2) = v1 &
% 6.81/1.74 | | | in(all_32_1, all_18_3) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 6.81/1.74 | | |
% 6.81/1.74 | | | DELTA: instantiating (31) with fresh symbols all_48_0, all_48_1 gives:
% 6.81/1.74 | | | (32) in(all_32_1, all_18_2) = all_48_0 & in(all_32_1, all_18_3) =
% 6.81/1.74 | | | all_48_1 & ( ~ (all_48_0 = 0) | ~ (all_48_1 = 0))
% 6.81/1.74 | | |
% 6.81/1.74 | | | ALPHA: (32) implies:
% 6.81/1.74 | | | (33) in(all_32_1, all_18_3) = all_48_1
% 6.81/1.74 | | | (34) in(all_32_1, all_18_2) = all_48_0
% 6.81/1.74 | | | (35) ~ (all_48_0 = 0) | ~ (all_48_1 = 0)
% 6.81/1.74 | | |
% 6.81/1.74 | | | GROUND_INST: instantiating (5) with 0, all_48_1, all_18_3, all_32_1,
% 6.81/1.74 | | | simplifying with (27), (33) gives:
% 6.81/1.74 | | | (36) all_48_1 = 0
% 6.81/1.74 | | |
% 6.81/1.75 | | | GROUND_INST: instantiating (5) with 0, all_48_0, all_18_2, all_32_1,
% 6.81/1.75 | | | simplifying with (26), (34) gives:
% 6.81/1.75 | | | (37) all_48_0 = 0
% 6.81/1.75 | | |
% 6.81/1.75 | | | BETA: splitting (35) gives:
% 6.81/1.75 | | |
% 6.81/1.75 | | | Case 1:
% 6.81/1.75 | | | |
% 6.81/1.75 | | | | (38) ~ (all_48_0 = 0)
% 6.81/1.75 | | | |
% 6.81/1.75 | | | | REDUCE: (37), (38) imply:
% 6.81/1.75 | | | | (39) $false
% 6.81/1.75 | | | |
% 6.81/1.75 | | | | CLOSE: (39) is inconsistent.
% 6.81/1.75 | | | |
% 6.81/1.75 | | | Case 2:
% 6.81/1.75 | | | |
% 6.81/1.75 | | | | (40) ~ (all_48_1 = 0)
% 6.81/1.75 | | | |
% 6.81/1.75 | | | | REDUCE: (36), (40) imply:
% 6.81/1.75 | | | | (41) $false
% 6.81/1.75 | | | |
% 6.81/1.75 | | | | CLOSE: (41) is inconsistent.
% 6.81/1.75 | | | |
% 6.81/1.75 | | | End of split
% 6.81/1.75 | | |
% 6.81/1.75 | | End of split
% 6.81/1.75 | |
% 6.81/1.75 | End of split
% 6.81/1.75 |
% 6.81/1.75 End of proof
% 6.81/1.75 % SZS output end Proof for theBenchmark
% 6.81/1.75
% 6.81/1.75 1146ms
%------------------------------------------------------------------------------