TSTP Solution File: SET944+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SET944+1 : TPTP v8.1.2. Released v3.2.0.
% 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 15:27:09 EDT 2023
% Result : Theorem 7.05s 1.67s
% Output : Proof 8.89s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.01/0.12 % Problem : SET944+1 : TPTP v8.1.2. Released v3.2.0.
% 0.13/0.13 % 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
% 0.19/0.34 % CPULimit : 300
% 0.19/0.34 % WCLimit : 300
% 0.19/0.34 % DateTime : Sat Aug 26 10:56:41 EDT 2023
% 0.19/0.34 % CPUTime :
% 0.58/0.61 ________ _____
% 0.58/0.61 ___ __ \_________(_)________________________________
% 0.58/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.58/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.58/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.58/0.61
% 0.58/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.58/0.61 (2023-06-19)
% 0.58/0.61
% 0.58/0.61 (c) Philipp Rümmer, 2009-2023
% 0.58/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.58/0.61 Amanda Stjerna.
% 0.58/0.61 Free software under BSD-3-Clause.
% 0.58/0.61
% 0.58/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.58/0.61
% 0.58/0.61 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.58/0.62 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 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 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.71/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.71/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.71/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.11/0.97 Prover 4: Preprocessing ...
% 2.11/0.97 Prover 1: Preprocessing ...
% 2.52/1.02 Prover 6: Preprocessing ...
% 2.52/1.02 Prover 3: Preprocessing ...
% 2.52/1.02 Prover 0: Preprocessing ...
% 2.52/1.02 Prover 5: Preprocessing ...
% 2.52/1.02 Prover 2: Preprocessing ...
% 4.20/1.25 Prover 1: Warning: ignoring some quantifiers
% 4.20/1.26 Prover 5: Proving ...
% 4.20/1.26 Prover 6: Proving ...
% 4.20/1.27 Prover 3: Warning: ignoring some quantifiers
% 4.20/1.28 Prover 1: Constructing countermodel ...
% 4.20/1.28 Prover 2: Proving ...
% 4.20/1.28 Prover 3: Constructing countermodel ...
% 4.70/1.30 Prover 4: Warning: ignoring some quantifiers
% 4.70/1.32 Prover 4: Constructing countermodel ...
% 4.70/1.34 Prover 0: Proving ...
% 7.05/1.66 Prover 0: proved (1032ms)
% 7.05/1.66
% 7.05/1.67 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 7.05/1.67
% 7.05/1.67 Prover 3: stopped
% 7.05/1.67 Prover 2: stopped
% 7.05/1.67 Prover 6: stopped
% 7.05/1.67 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 7.05/1.67 Prover 5: stopped
% 7.55/1.67 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 7.55/1.67 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 7.55/1.68 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 7.55/1.68 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 7.55/1.69 Prover 8: Preprocessing ...
% 7.55/1.69 Prover 7: Preprocessing ...
% 7.55/1.70 Prover 13: Preprocessing ...
% 7.55/1.70 Prover 10: Preprocessing ...
% 7.55/1.71 Prover 11: Preprocessing ...
% 7.55/1.74 Prover 10: Warning: ignoring some quantifiers
% 7.55/1.75 Prover 10: Constructing countermodel ...
% 7.55/1.76 Prover 13: Warning: ignoring some quantifiers
% 7.55/1.76 Prover 8: Warning: ignoring some quantifiers
% 7.55/1.77 Prover 13: Constructing countermodel ...
% 7.55/1.77 Prover 4: Found proof (size 59)
% 7.55/1.77 Prover 4: proved (1135ms)
% 7.55/1.77 Prover 10: stopped
% 7.55/1.77 Prover 13: stopped
% 8.26/1.77 Prover 1: stopped
% 8.26/1.77 Prover 8: Constructing countermodel ...
% 8.26/1.77 Prover 8: stopped
% 8.26/1.78 Prover 7: Warning: ignoring some quantifiers
% 8.26/1.78 Prover 11: stopped
% 8.26/1.78 Prover 7: Constructing countermodel ...
% 8.26/1.79 Prover 7: stopped
% 8.26/1.79
% 8.26/1.79 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 8.26/1.79
% 8.38/1.80 % SZS output start Proof for theBenchmark
% 8.38/1.80 Assumptions after simplification:
% 8.38/1.80 ---------------------------------
% 8.38/1.80
% 8.38/1.80 (commutativity_k3_xboole_0)
% 8.53/1.83 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (set_intersection2(v1, v0) = v2)
% 8.53/1.83 | ~ $i(v1) | ~ $i(v0) | (set_intersection2(v0, v1) = v2 & $i(v2))) & !
% 8.53/1.83 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (set_intersection2(v0, v1) = v2) |
% 8.53/1.83 ~ $i(v1) | ~ $i(v0) | (set_intersection2(v1, v0) = v2 & $i(v2)))
% 8.53/1.83
% 8.53/1.83 (d3_tarski)
% 8.53/1.84 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~
% 8.53/1.84 (subset(v0, v1) = 0) | ~ (in(v2, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~
% 8.53/1.84 $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & in(v2, v0) = v4)) & ! [v0: $i] : !
% 8.53/1.84 [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ~ $i(v1) | ~
% 8.53/1.84 $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) & in(v3, v1) = v4 &
% 8.53/1.84 in(v3, v0) = 0 & $i(v3))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 8.53/1.84 (subset(v0, v1) = 0) | ~ (in(v2, v0) = 0) | ~ $i(v2) | ~ $i(v1) | ~
% 8.53/1.84 $i(v0) | in(v2, v1) = 0)
% 8.53/1.84
% 8.53/1.84 (d3_xboole_0)
% 8.53/1.85 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0
% 8.53/1.85 | ~ (set_intersection2(v0, v1) = v2) | ~ (in(v3, v2) = v4) | ~ $i(v3) |
% 8.53/1.85 ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : (in(v3, v1)
% 8.53/1.85 = v6 & in(v3, v0) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0)))) & ! [v0: $i] : !
% 8.53/1.85 [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: any] : ( ~
% 8.53/1.85 (set_intersection2(v0, v1) = v2) | ~ (in(v3, v1) = v4) | ~ $i(v3) | ~
% 8.53/1.85 $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : (in(v3, v2) =
% 8.53/1.85 v5 & in(v3, v0) = v6 & ( ~ (v5 = 0) | (v6 = 0 & v4 = 0)))) & ! [v0: $i] :
% 8.53/1.85 ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: any] : ( ~
% 8.53/1.85 (set_intersection2(v0, v1) = v2) | ~ (in(v3, v0) = v4) | ~ $i(v3) | ~
% 8.53/1.85 $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : (in(v3, v2) =
% 8.53/1.86 v5 & in(v3, v1) = v6 & ( ~ (v5 = 0) | (v6 = 0 & v4 = 0)))) & ! [v0: $i] :
% 8.53/1.86 ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (set_intersection2(v0, v1) = v2)
% 8.53/1.86 | ~ (in(v3, v2) = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 8.53/1.86 (in(v3, v1) = 0 & in(v3, v0) = 0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i]
% 8.53/1.86 : ! [v3: $i] : ( ~ (set_intersection2(v0, v1) = v2) | ~ (in(v3, v1) = 0) |
% 8.53/1.86 ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: any] :
% 8.53/1.86 (in(v3, v2) = v5 & in(v3, v0) = v4 & ( ~ (v4 = 0) | v5 = 0))) & ! [v0: $i]
% 8.53/1.86 : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (set_intersection2(v0, v1) =
% 8.53/1.86 v2) | ~ (in(v3, v0) = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0)
% 8.53/1.86 | ? [v4: any] : ? [v5: any] : (in(v3, v2) = v5 & in(v3, v1) = v4 & ( ~ (v4
% 8.53/1.86 = 0) | v5 = 0))) & ? [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 8.53/1.86 $i] : (v3 = v0 | ~ (set_intersection2(v1, v2) = v3) | ~ $i(v2) | ~ $i(v1)
% 8.53/1.86 | ~ $i(v0) | ? [v4: $i] : ? [v5: any] : ? [v6: any] : ? [v7: any] :
% 8.53/1.86 (in(v4, v2) = v7 & in(v4, v1) = v6 & in(v4, v0) = v5 & $i(v4) & ( ~ (v7 = 0)
% 8.53/1.86 | ~ (v6 = 0) | ~ (v5 = 0)) & (v5 = 0 | (v7 = 0 & v6 = 0))))
% 8.53/1.86
% 8.53/1.86 (d4_tarski)
% 8.53/1.87 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : ! [v4: $i] : (v3 = 0
% 8.53/1.87 | ~ (union(v0) = v1) | ~ (in(v4, v0) = 0) | ~ (in(v2, v1) = v3) | ~
% 8.53/1.87 $i(v4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ( ~ (v5 = 0) &
% 8.53/1.87 in(v2, v4) = v5)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int]
% 8.53/1.87 : ! [v4: $i] : (v3 = 0 | ~ (union(v0) = v1) | ~ (in(v2, v4) = 0) | ~
% 8.53/1.87 (in(v2, v1) = v3) | ~ $i(v4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5:
% 8.53/1.87 int] : ( ~ (v5 = 0) & in(v4, v0) = v5)) & ! [v0: $i] : ! [v1: $i] : !
% 8.53/1.87 [v2: $i] : ( ~ (union(v0) = v1) | ~ (in(v2, v1) = 0) | ~ $i(v2) | ~ $i(v1)
% 8.53/1.87 | ~ $i(v0) | ? [v3: $i] : (in(v3, v0) = 0 & in(v2, v3) = 0 & $i(v3))) & ?
% 8.53/1.87 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v0 | ~ (union(v1) = v2) | ~
% 8.53/1.87 $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: any] : ? [v5: $i] : ? [v6: int]
% 8.53/1.87 : ? [v7: int] : (in(v3, v0) = v4 & $i(v5) & $i(v3) & ( ~ (v4 = 0) | ( !
% 8.53/1.87 [v8: $i] : ( ~ (in(v8, v1) = 0) | ~ $i(v8) | ? [v9: int] : ( ~ (v9 =
% 8.53/1.87 0) & in(v3, v8) = v9)) & ! [v8: $i] : ( ~ (in(v3, v8) = 0) | ~
% 8.53/1.87 $i(v8) | ? [v9: int] : ( ~ (v9 = 0) & in(v8, v1) = v9)))) & (v4 = 0
% 8.53/1.87 | (v7 = 0 & v6 = 0 & in(v5, v1) = 0 & in(v3, v5) = 0))))
% 8.53/1.87
% 8.53/1.87 (t97_zfmisc_1)
% 8.53/1.87 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5:
% 8.53/1.87 $i] : ? [v6: $i] : ? [v7: int] : ( ~ (v7 = 0) & union(v2) = v3 & union(v1)
% 8.53/1.87 = v5 & union(v0) = v4 & subset(v3, v6) = v7 & set_intersection2(v4, v5) = v6
% 8.53/1.87 & set_intersection2(v0, v1) = v2 & $i(v6) & $i(v5) & $i(v4) & $i(v3) &
% 8.53/1.87 $i(v2) & $i(v1) & $i(v0))
% 8.53/1.87
% 8.53/1.87 (function-axioms)
% 8.53/1.87 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 8.53/1.87 [v3: $i] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) &
% 8.53/1.87 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 8.53/1.87 (set_intersection2(v3, v2) = v1) | ~ (set_intersection2(v3, v2) = v0)) & !
% 8.53/1.87 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 8.53/1.87 $i] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) & ! [v0:
% 8.53/1.87 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 |
% 8.53/1.87 ~ (empty(v2) = v1) | ~ (empty(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 8.53/1.87 [v2: $i] : (v1 = v0 | ~ (union(v2) = v1) | ~ (union(v2) = v0))
% 8.53/1.87
% 8.53/1.87 Further assumptions not needed in the proof:
% 8.53/1.87 --------------------------------------------
% 8.53/1.87 antisymmetry_r2_hidden, idempotence_k3_xboole_0, rc1_xboole_0, rc2_xboole_0,
% 8.53/1.87 reflexivity_r1_tarski
% 8.53/1.87
% 8.53/1.87 Those formulas are unsatisfiable:
% 8.53/1.87 ---------------------------------
% 8.53/1.87
% 8.53/1.87 Begin of proof
% 8.53/1.88 |
% 8.53/1.88 | ALPHA: (commutativity_k3_xboole_0) implies:
% 8.53/1.88 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (set_intersection2(v1,
% 8.53/1.88 | v0) = v2) | ~ $i(v1) | ~ $i(v0) | (set_intersection2(v0, v1) =
% 8.53/1.88 | v2 & $i(v2)))
% 8.53/1.88 |
% 8.53/1.88 | ALPHA: (d3_tarski) implies:
% 8.53/1.88 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1)
% 8.53/1.88 | = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~
% 8.53/1.88 | (v4 = 0) & in(v3, v1) = v4 & in(v3, v0) = 0 & $i(v3)))
% 8.53/1.88 |
% 8.53/1.88 | ALPHA: (d3_xboole_0) implies:
% 8.53/1.88 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 8.53/1.88 | (set_intersection2(v0, v1) = v2) | ~ (in(v3, v2) = 0) | ~ $i(v3) |
% 8.53/1.88 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | (in(v3, v1) = 0 & in(v3, v0) = 0))
% 8.53/1.88 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] :
% 8.53/1.88 | (v4 = 0 | ~ (set_intersection2(v0, v1) = v2) | ~ (in(v3, v2) = v4) |
% 8.53/1.88 | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6:
% 8.53/1.88 | any] : (in(v3, v1) = v6 & in(v3, v0) = v5 & ( ~ (v6 = 0) | ~ (v5 =
% 8.53/1.88 | 0))))
% 8.53/1.88 |
% 8.53/1.88 | ALPHA: (d4_tarski) implies:
% 8.53/1.88 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (union(v0) = v1) | ~
% 8.53/1.88 | (in(v2, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] :
% 8.53/1.88 | (in(v3, v0) = 0 & in(v2, v3) = 0 & $i(v3)))
% 8.53/1.88 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : ! [v4: $i] :
% 8.53/1.88 | (v3 = 0 | ~ (union(v0) = v1) | ~ (in(v2, v4) = 0) | ~ (in(v2, v1) =
% 8.53/1.88 | v3) | ~ $i(v4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int]
% 8.53/1.88 | : ( ~ (v5 = 0) & in(v4, v0) = v5))
% 8.53/1.88 |
% 8.53/1.88 | ALPHA: (function-axioms) implies:
% 8.53/1.89 | (7) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 8.53/1.89 | ! [v3: $i] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0))
% 8.53/1.89 |
% 8.53/1.89 | DELTA: instantiating (t97_zfmisc_1) with fresh symbols all_14_0, all_14_1,
% 8.53/1.89 | all_14_2, all_14_3, all_14_4, all_14_5, all_14_6, all_14_7 gives:
% 8.53/1.89 | (8) ~ (all_14_0 = 0) & union(all_14_5) = all_14_4 & union(all_14_6) =
% 8.53/1.89 | all_14_2 & union(all_14_7) = all_14_3 & subset(all_14_4, all_14_1) =
% 8.53/1.89 | all_14_0 & set_intersection2(all_14_3, all_14_2) = all_14_1 &
% 8.53/1.89 | set_intersection2(all_14_7, all_14_6) = all_14_5 & $i(all_14_1) &
% 8.53/1.89 | $i(all_14_2) & $i(all_14_3) & $i(all_14_4) & $i(all_14_5) &
% 8.53/1.89 | $i(all_14_6) & $i(all_14_7)
% 8.53/1.89 |
% 8.53/1.89 | ALPHA: (8) implies:
% 8.53/1.89 | (9) ~ (all_14_0 = 0)
% 8.53/1.89 | (10) $i(all_14_7)
% 8.53/1.89 | (11) $i(all_14_6)
% 8.53/1.89 | (12) $i(all_14_4)
% 8.53/1.89 | (13) $i(all_14_3)
% 8.53/1.89 | (14) $i(all_14_2)
% 8.53/1.89 | (15) set_intersection2(all_14_7, all_14_6) = all_14_5
% 8.53/1.89 | (16) set_intersection2(all_14_3, all_14_2) = all_14_1
% 8.53/1.89 | (17) subset(all_14_4, all_14_1) = all_14_0
% 8.53/1.89 | (18) union(all_14_7) = all_14_3
% 8.53/1.89 | (19) union(all_14_6) = all_14_2
% 8.53/1.89 | (20) union(all_14_5) = all_14_4
% 8.53/1.89 |
% 8.53/1.89 | GROUND_INST: instantiating (1) with all_14_6, all_14_7, all_14_5, simplifying
% 8.53/1.89 | with (10), (11), (15) gives:
% 8.53/1.89 | (21) set_intersection2(all_14_6, all_14_7) = all_14_5 & $i(all_14_5)
% 8.53/1.89 |
% 8.53/1.89 | ALPHA: (21) implies:
% 8.53/1.89 | (22) $i(all_14_5)
% 8.53/1.89 |
% 8.53/1.89 | GROUND_INST: instantiating (1) with all_14_2, all_14_3, all_14_1, simplifying
% 8.53/1.89 | with (13), (14), (16) gives:
% 8.53/1.89 | (23) set_intersection2(all_14_2, all_14_3) = all_14_1 & $i(all_14_1)
% 8.53/1.89 |
% 8.53/1.89 | ALPHA: (23) implies:
% 8.53/1.89 | (24) $i(all_14_1)
% 8.53/1.89 | (25) set_intersection2(all_14_2, all_14_3) = all_14_1
% 8.53/1.89 |
% 8.53/1.89 | GROUND_INST: instantiating (2) with all_14_4, all_14_1, all_14_0, simplifying
% 8.53/1.89 | with (12), (17), (24) gives:
% 8.53/1.90 | (26) all_14_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & in(v0,
% 8.53/1.90 | all_14_1) = v1 & in(v0, all_14_4) = 0 & $i(v0))
% 8.53/1.90 |
% 8.53/1.90 | BETA: splitting (26) gives:
% 8.53/1.90 |
% 8.53/1.90 | Case 1:
% 8.53/1.90 | |
% 8.53/1.90 | | (27) all_14_0 = 0
% 8.53/1.90 | |
% 8.53/1.90 | | REDUCE: (9), (27) imply:
% 8.53/1.90 | | (28) $false
% 8.89/1.90 | |
% 8.89/1.90 | | CLOSE: (28) is inconsistent.
% 8.89/1.90 | |
% 8.89/1.90 | Case 2:
% 8.89/1.90 | |
% 8.89/1.90 | | (29) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & in(v0, all_14_1) = v1 &
% 8.89/1.90 | | in(v0, all_14_4) = 0 & $i(v0))
% 8.89/1.90 | |
% 8.89/1.90 | | DELTA: instantiating (29) with fresh symbols all_30_0, all_30_1 gives:
% 8.89/1.90 | | (30) ~ (all_30_0 = 0) & in(all_30_1, all_14_1) = all_30_0 & in(all_30_1,
% 8.89/1.90 | | all_14_4) = 0 & $i(all_30_1)
% 8.89/1.90 | |
% 8.89/1.90 | | ALPHA: (30) implies:
% 8.89/1.90 | | (31) ~ (all_30_0 = 0)
% 8.89/1.90 | | (32) $i(all_30_1)
% 8.89/1.90 | | (33) in(all_30_1, all_14_4) = 0
% 8.89/1.90 | | (34) in(all_30_1, all_14_1) = all_30_0
% 8.89/1.90 | |
% 8.89/1.90 | | GROUND_INST: instantiating (5) with all_14_5, all_14_4, all_30_1,
% 8.89/1.90 | | simplifying with (12), (20), (22), (32), (33) gives:
% 8.89/1.90 | | (35) ? [v0: $i] : (in(v0, all_14_5) = 0 & in(all_30_1, v0) = 0 & $i(v0))
% 8.89/1.90 | |
% 8.89/1.90 | | GROUND_INST: instantiating (4) with all_14_3, all_14_2, all_14_1, all_30_1,
% 8.89/1.90 | | all_30_0, simplifying with (13), (14), (16), (24), (32), (34)
% 8.89/1.90 | | gives:
% 8.89/1.90 | | (36) all_30_0 = 0 | ? [v0: any] : ? [v1: any] : (in(all_30_1, all_14_2)
% 8.89/1.90 | | = v1 & in(all_30_1, all_14_3) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 8.89/1.90 | |
% 8.89/1.90 | | GROUND_INST: instantiating (4) with all_14_2, all_14_3, all_14_1, all_30_1,
% 8.89/1.90 | | all_30_0, simplifying with (13), (14), (24), (25), (32), (34)
% 8.89/1.90 | | gives:
% 8.89/1.91 | | (37) all_30_0 = 0 | ? [v0: any] : ? [v1: any] : (in(all_30_1, all_14_2)
% 8.89/1.91 | | = v0 & in(all_30_1, all_14_3) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 8.89/1.91 | |
% 8.89/1.91 | | DELTA: instantiating (35) with fresh symbol all_39_0 gives:
% 8.89/1.91 | | (38) in(all_39_0, all_14_5) = 0 & in(all_30_1, all_39_0) = 0 &
% 8.89/1.91 | | $i(all_39_0)
% 8.89/1.91 | |
% 8.89/1.91 | | ALPHA: (38) implies:
% 8.89/1.91 | | (39) $i(all_39_0)
% 8.89/1.91 | | (40) in(all_30_1, all_39_0) = 0
% 8.89/1.91 | | (41) in(all_39_0, all_14_5) = 0
% 8.89/1.91 | |
% 8.89/1.91 | | BETA: splitting (36) gives:
% 8.89/1.91 | |
% 8.89/1.91 | | Case 1:
% 8.89/1.91 | | |
% 8.89/1.91 | | | (42) all_30_0 = 0
% 8.89/1.91 | | |
% 8.89/1.91 | | | REDUCE: (31), (42) imply:
% 8.89/1.91 | | | (43) $false
% 8.89/1.91 | | |
% 8.89/1.91 | | | CLOSE: (43) is inconsistent.
% 8.89/1.91 | | |
% 8.89/1.91 | | Case 2:
% 8.89/1.91 | | |
% 8.89/1.91 | | | (44) ? [v0: any] : ? [v1: any] : (in(all_30_1, all_14_2) = v1 &
% 8.89/1.91 | | | in(all_30_1, all_14_3) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 8.89/1.91 | | |
% 8.89/1.91 | | | DELTA: instantiating (44) with fresh symbols all_45_0, all_45_1 gives:
% 8.89/1.91 | | | (45) in(all_30_1, all_14_2) = all_45_0 & in(all_30_1, all_14_3) =
% 8.89/1.91 | | | all_45_1 & ( ~ (all_45_0 = 0) | ~ (all_45_1 = 0))
% 8.89/1.91 | | |
% 8.89/1.91 | | | ALPHA: (45) implies:
% 8.89/1.91 | | | (46) in(all_30_1, all_14_3) = all_45_1
% 8.89/1.91 | | | (47) in(all_30_1, all_14_2) = all_45_0
% 8.89/1.91 | | | (48) ~ (all_45_0 = 0) | ~ (all_45_1 = 0)
% 8.89/1.91 | | |
% 8.89/1.91 | | | BETA: splitting (37) gives:
% 8.89/1.91 | | |
% 8.89/1.91 | | | Case 1:
% 8.89/1.91 | | | |
% 8.89/1.91 | | | | (49) all_30_0 = 0
% 8.89/1.91 | | | |
% 8.89/1.91 | | | | REDUCE: (31), (49) imply:
% 8.89/1.91 | | | | (50) $false
% 8.89/1.91 | | | |
% 8.89/1.91 | | | | CLOSE: (50) is inconsistent.
% 8.89/1.91 | | | |
% 8.89/1.91 | | | Case 2:
% 8.89/1.91 | | | |
% 8.89/1.91 | | | | (51) ? [v0: any] : ? [v1: any] : (in(all_30_1, all_14_2) = v0 &
% 8.89/1.91 | | | | in(all_30_1, all_14_3) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 8.89/1.91 | | | |
% 8.89/1.91 | | | | DELTA: instantiating (51) with fresh symbols all_50_0, all_50_1 gives:
% 8.89/1.91 | | | | (52) in(all_30_1, all_14_2) = all_50_1 & in(all_30_1, all_14_3) =
% 8.89/1.91 | | | | all_50_0 & ( ~ (all_50_0 = 0) | ~ (all_50_1 = 0))
% 8.89/1.91 | | | |
% 8.89/1.91 | | | | ALPHA: (52) implies:
% 8.89/1.91 | | | | (53) in(all_30_1, all_14_3) = all_50_0
% 8.89/1.91 | | | | (54) in(all_30_1, all_14_2) = all_50_1
% 8.89/1.91 | | | |
% 8.89/1.91 | | | | GROUND_INST: instantiating (7) with all_45_1, all_50_0, all_14_3,
% 8.89/1.91 | | | | all_30_1, simplifying with (46), (53) gives:
% 8.89/1.91 | | | | (55) all_50_0 = all_45_1
% 8.89/1.91 | | | |
% 8.89/1.92 | | | | GROUND_INST: instantiating (7) with all_45_0, all_50_1, all_14_2,
% 8.89/1.92 | | | | all_30_1, simplifying with (47), (54) gives:
% 8.89/1.92 | | | | (56) all_50_1 = all_45_0
% 8.89/1.92 | | | |
% 8.89/1.92 | | | | GROUND_INST: instantiating (6) with all_14_6, all_14_2, all_30_1,
% 8.89/1.92 | | | | all_45_0, all_39_0, simplifying with (11), (14), (19),
% 8.89/1.92 | | | | (32), (39), (40), (47) gives:
% 8.89/1.92 | | | | (57) all_45_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & in(all_39_0,
% 8.89/1.92 | | | | all_14_6) = v0)
% 8.89/1.92 | | | |
% 8.89/1.92 | | | | GROUND_INST: instantiating (6) with all_14_7, all_14_3, all_30_1,
% 8.89/1.92 | | | | all_45_1, all_39_0, simplifying with (10), (13), (18),
% 8.89/1.92 | | | | (32), (39), (40), (46) gives:
% 8.89/1.92 | | | | (58) all_45_1 = 0 | ? [v0: int] : ( ~ (v0 = 0) & in(all_39_0,
% 8.89/1.92 | | | | all_14_7) = v0)
% 8.89/1.92 | | | |
% 8.89/1.92 | | | | GROUND_INST: instantiating (3) with all_14_7, all_14_6, all_14_5,
% 8.89/1.92 | | | | all_39_0, simplifying with (10), (11), (15), (22), (39),
% 8.89/1.92 | | | | (41) gives:
% 8.89/1.92 | | | | (59) in(all_39_0, all_14_6) = 0 & in(all_39_0, all_14_7) = 0
% 8.89/1.92 | | | |
% 8.89/1.92 | | | | ALPHA: (59) implies:
% 8.89/1.92 | | | | (60) in(all_39_0, all_14_7) = 0
% 8.89/1.92 | | | | (61) in(all_39_0, all_14_6) = 0
% 8.89/1.92 | | | |
% 8.89/1.92 | | | | BETA: splitting (58) gives:
% 8.89/1.92 | | | |
% 8.89/1.92 | | | | Case 1:
% 8.89/1.92 | | | | |
% 8.89/1.92 | | | | | (62) all_45_1 = 0
% 8.89/1.92 | | | | |
% 8.89/1.92 | | | | | BETA: splitting (57) gives:
% 8.89/1.92 | | | | |
% 8.89/1.92 | | | | | Case 1:
% 8.89/1.92 | | | | | |
% 8.89/1.92 | | | | | | (63) all_45_0 = 0
% 8.89/1.92 | | | | | |
% 8.89/1.92 | | | | | | BETA: splitting (48) gives:
% 8.89/1.92 | | | | | |
% 8.89/1.92 | | | | | | Case 1:
% 8.89/1.92 | | | | | | |
% 8.89/1.92 | | | | | | | (64) ~ (all_45_0 = 0)
% 8.89/1.92 | | | | | | |
% 8.89/1.92 | | | | | | | REDUCE: (63), (64) imply:
% 8.89/1.92 | | | | | | | (65) $false
% 8.89/1.92 | | | | | | |
% 8.89/1.92 | | | | | | | CLOSE: (65) is inconsistent.
% 8.89/1.92 | | | | | | |
% 8.89/1.92 | | | | | | Case 2:
% 8.89/1.92 | | | | | | |
% 8.89/1.92 | | | | | | | (66) ~ (all_45_1 = 0)
% 8.89/1.92 | | | | | | |
% 8.89/1.92 | | | | | | | REDUCE: (62), (66) imply:
% 8.89/1.92 | | | | | | | (67) $false
% 8.89/1.92 | | | | | | |
% 8.89/1.92 | | | | | | | CLOSE: (67) is inconsistent.
% 8.89/1.92 | | | | | | |
% 8.89/1.92 | | | | | | End of split
% 8.89/1.92 | | | | | |
% 8.89/1.92 | | | | | Case 2:
% 8.89/1.92 | | | | | |
% 8.89/1.92 | | | | | | (68) ? [v0: int] : ( ~ (v0 = 0) & in(all_39_0, all_14_6) = v0)
% 8.89/1.92 | | | | | |
% 8.89/1.92 | | | | | | DELTA: instantiating (68) with fresh symbol all_74_0 gives:
% 8.89/1.92 | | | | | | (69) ~ (all_74_0 = 0) & in(all_39_0, all_14_6) = all_74_0
% 8.89/1.92 | | | | | |
% 8.89/1.92 | | | | | | ALPHA: (69) implies:
% 8.89/1.92 | | | | | | (70) ~ (all_74_0 = 0)
% 8.89/1.92 | | | | | | (71) in(all_39_0, all_14_6) = all_74_0
% 8.89/1.92 | | | | | |
% 8.89/1.92 | | | | | | GROUND_INST: instantiating (7) with 0, all_74_0, all_14_6, all_39_0,
% 8.89/1.92 | | | | | | simplifying with (61), (71) gives:
% 8.89/1.92 | | | | | | (72) all_74_0 = 0
% 8.89/1.92 | | | | | |
% 8.89/1.92 | | | | | | REDUCE: (70), (72) imply:
% 8.89/1.92 | | | | | | (73) $false
% 8.89/1.92 | | | | | |
% 8.89/1.92 | | | | | | CLOSE: (73) is inconsistent.
% 8.89/1.93 | | | | | |
% 8.89/1.93 | | | | | End of split
% 8.89/1.93 | | | | |
% 8.89/1.93 | | | | Case 2:
% 8.89/1.93 | | | | |
% 8.89/1.93 | | | | | (74) ? [v0: int] : ( ~ (v0 = 0) & in(all_39_0, all_14_7) = v0)
% 8.89/1.93 | | | | |
% 8.89/1.93 | | | | | DELTA: instantiating (74) with fresh symbol all_70_0 gives:
% 8.89/1.93 | | | | | (75) ~ (all_70_0 = 0) & in(all_39_0, all_14_7) = all_70_0
% 8.89/1.93 | | | | |
% 8.89/1.93 | | | | | ALPHA: (75) implies:
% 8.89/1.93 | | | | | (76) ~ (all_70_0 = 0)
% 8.89/1.93 | | | | | (77) in(all_39_0, all_14_7) = all_70_0
% 8.89/1.93 | | | | |
% 8.89/1.93 | | | | | GROUND_INST: instantiating (7) with 0, all_70_0, all_14_7, all_39_0,
% 8.89/1.93 | | | | | simplifying with (60), (77) gives:
% 8.89/1.93 | | | | | (78) all_70_0 = 0
% 8.89/1.93 | | | | |
% 8.89/1.93 | | | | | REDUCE: (76), (78) imply:
% 8.89/1.93 | | | | | (79) $false
% 8.89/1.93 | | | | |
% 8.89/1.93 | | | | | CLOSE: (79) is inconsistent.
% 8.89/1.93 | | | | |
% 8.89/1.93 | | | | End of split
% 8.89/1.93 | | | |
% 8.89/1.93 | | | End of split
% 8.89/1.93 | | |
% 8.89/1.93 | | End of split
% 8.89/1.93 | |
% 8.89/1.93 | End of split
% 8.89/1.93 |
% 8.89/1.93 End of proof
% 8.89/1.93 % SZS output end Proof for theBenchmark
% 8.89/1.93
% 8.89/1.93 1317ms
%------------------------------------------------------------------------------