TSTP Solution File: SEU125+2 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SEU125+2 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n019.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 17:42:37 EDT 2023
% Result : Theorem 9.58s 2.02s
% Output : Proof 12.00s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.15 % Problem : SEU125+2 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.15 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.37 % Computer : n019.cluster.edu
% 0.13/0.37 % Model : x86_64 x86_64
% 0.13/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.37 % Memory : 8042.1875MB
% 0.13/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.37 % CPULimit : 300
% 0.13/0.37 % WCLimit : 300
% 0.13/0.37 % DateTime : Wed Aug 23 13:28:28 EDT 2023
% 0.13/0.37 % CPUTime :
% 0.21/0.60 ________ _____
% 0.21/0.60 ___ __ \_________(_)________________________________
% 0.21/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.21/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.21/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.21/0.60
% 0.21/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.21/0.60 (2023-06-19)
% 0.21/0.60
% 0.21/0.60 (c) Philipp Rümmer, 2009-2023
% 0.21/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.21/0.60 Amanda Stjerna.
% 0.21/0.60 Free software under BSD-3-Clause.
% 0.21/0.60
% 0.21/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.21/0.60
% 0.21/0.60 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.21/0.61 Running up to 7 provers in parallel.
% 0.21/0.62 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.21/0.62 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.21/0.62 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.21/0.62 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.21/0.62 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.21/0.62 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.21/0.62 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.44/1.03 Prover 4: Preprocessing ...
% 2.44/1.05 Prover 1: Preprocessing ...
% 2.96/1.09 Prover 3: Preprocessing ...
% 2.96/1.09 Prover 0: Preprocessing ...
% 2.96/1.09 Prover 2: Preprocessing ...
% 2.96/1.09 Prover 6: Preprocessing ...
% 2.96/1.09 Prover 5: Preprocessing ...
% 5.18/1.45 Prover 5: Proving ...
% 5.18/1.48 Prover 1: Warning: ignoring some quantifiers
% 5.18/1.51 Prover 3: Warning: ignoring some quantifiers
% 5.18/1.52 Prover 2: Proving ...
% 5.18/1.53 Prover 3: Constructing countermodel ...
% 5.18/1.55 Prover 1: Constructing countermodel ...
% 5.18/1.56 Prover 4: Warning: ignoring some quantifiers
% 5.18/1.62 Prover 6: Proving ...
% 6.05/1.66 Prover 4: Constructing countermodel ...
% 7.44/1.72 Prover 0: Proving ...
% 9.58/2.02 Prover 0: proved (1403ms)
% 9.58/2.02
% 9.58/2.02 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 9.58/2.02
% 9.58/2.03 Prover 6: stopped
% 9.58/2.03 Prover 5: stopped
% 9.68/2.03 Prover 3: stopped
% 9.68/2.03 Prover 2: stopped
% 9.68/2.03 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 9.68/2.03 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 9.68/2.04 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 9.68/2.05 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 9.68/2.05 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 9.68/2.11 Prover 8: Preprocessing ...
% 9.68/2.11 Prover 13: Preprocessing ...
% 9.68/2.14 Prover 7: Preprocessing ...
% 9.68/2.14 Prover 10: Preprocessing ...
% 9.68/2.15 Prover 11: Preprocessing ...
% 9.68/2.23 Prover 10: Warning: ignoring some quantifiers
% 10.32/2.24 Prover 13: Warning: ignoring some quantifiers
% 10.32/2.24 Prover 10: Constructing countermodel ...
% 10.32/2.25 Prover 7: Warning: ignoring some quantifiers
% 10.32/2.26 Prover 7: Constructing countermodel ...
% 10.32/2.27 Prover 13: Constructing countermodel ...
% 10.32/2.27 Prover 8: Warning: ignoring some quantifiers
% 10.32/2.29 Prover 8: Constructing countermodel ...
% 11.56/2.31 Prover 4: Found proof (size 41)
% 11.56/2.31 Prover 4: proved (1688ms)
% 11.56/2.31 Prover 8: stopped
% 11.56/2.31 Prover 1: stopped
% 11.56/2.31 Prover 13: stopped
% 11.56/2.31 Prover 7: stopped
% 11.56/2.31 Prover 10: stopped
% 11.56/2.33 Prover 11: Warning: ignoring some quantifiers
% 11.56/2.35 Prover 11: Constructing countermodel ...
% 11.56/2.36 Prover 11: stopped
% 11.56/2.36
% 11.56/2.36 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 11.56/2.36
% 11.56/2.36 % SZS output start Proof for theBenchmark
% 11.56/2.37 Assumptions after simplification:
% 11.56/2.37 ---------------------------------
% 11.56/2.37
% 11.56/2.37 (commutativity_k2_xboole_0)
% 11.56/2.39 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (set_union2(v1, v0) = v2) | ~
% 11.56/2.39 $i(v1) | ~ $i(v0) | (set_union2(v0, v1) = v2 & $i(v2))) & ! [v0: $i] : !
% 11.56/2.39 [v1: $i] : ! [v2: $i] : ( ~ (set_union2(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0)
% 11.56/2.39 | (set_union2(v1, v0) = v2 & $i(v2)))
% 11.56/2.39
% 11.56/2.39 (d2_xboole_0)
% 12.00/2.41 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0
% 12.00/2.41 | ~ (set_union2(v0, v1) = v2) | ~ (in(v3, v2) = v4) | ~ $i(v3) | ~
% 12.00/2.41 $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ? [v6: int] : ( ~ (v6 = 0)
% 12.00/2.41 & ~ (v5 = 0) & in(v3, v1) = v6 & in(v3, v0) = v5)) & ! [v0: $i] : !
% 12.00/2.41 [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0 | ~
% 12.00/2.41 (set_union2(v0, v1) = v2) | ~ (in(v3, v1) = v4) | ~ $i(v3) | ~ $i(v2) |
% 12.00/2.41 ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : (in(v3, v2) = v5 &
% 12.00/2.41 in(v3, v0) = v6 & ( ~ (v5 = 0) | v6 = 0))) & ! [v0: $i] : ! [v1: $i] :
% 12.00/2.41 ! [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0 | ~ (set_union2(v0, v1) =
% 12.00/2.41 v2) | ~ (in(v3, v0) = v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0)
% 12.00/2.41 | ? [v5: any] : ? [v6: any] : (in(v3, v2) = v5 & in(v3, v1) = v6 & ( ~ (v5
% 12.00/2.41 = 0) | v6 = 0))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 12.00/2.41 $i] : ! [v4: any] : ( ~ (set_union2(v0, v1) = v2) | ~ (in(v3, v1) = v4) |
% 12.00/2.41 ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] :
% 12.00/2.41 (in(v3, v2) = v6 & in(v3, v0) = v5 & (v6 = 0 | ( ~ (v5 = 0) & ~ (v4 =
% 12.00/2.41 0))))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : !
% 12.00/2.41 [v4: any] : ( ~ (set_union2(v0, v1) = v2) | ~ (in(v3, v0) = v4) | ~ $i(v3) |
% 12.00/2.41 ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : (in(v3,
% 12.00/2.41 v2) = v6 & in(v3, v1) = v5 & (v6 = 0 | ( ~ (v5 = 0) & ~ (v4 = 0))))) &
% 12.00/2.41 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (set_union2(v0, v1)
% 12.00/2.41 = v2) | ~ (in(v3, v2) = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~
% 12.00/2.41 $i(v0) | ? [v4: any] : ? [v5: any] : (in(v3, v1) = v5 & in(v3, v0) = v4 &
% 12.00/2.41 (v5 = 0 | v4 = 0))) & ? [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 12.00/2.41 $i] : (v3 = v0 | ~ (set_union2(v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~
% 12.00/2.41 $i(v0) | ? [v4: $i] : ? [v5: any] : ? [v6: any] : ? [v7: any] : (in(v4,
% 12.00/2.41 v2) = v7 & in(v4, v1) = v6 & in(v4, v0) = v5 & $i(v4) & ( ~ (v5 = 0) | (
% 12.00/2.41 ~ (v7 = 0) & ~ (v6 = 0))) & (v7 = 0 | v6 = 0 | v5 = 0)))
% 12.00/2.41
% 12.00/2.41 (d3_tarski)
% 12.00/2.41 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~
% 12.00/2.41 (subset(v0, v1) = 0) | ~ (in(v2, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~
% 12.00/2.41 $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & in(v2, v0) = v4)) & ! [v0: $i] : !
% 12.00/2.41 [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ~ $i(v1) | ~
% 12.00/2.41 $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) & in(v3, v1) = v4 &
% 12.00/2.41 in(v3, v0) = 0 & $i(v3))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 12.00/2.41 (subset(v0, v1) = 0) | ~ (in(v2, v0) = 0) | ~ $i(v2) | ~ $i(v1) | ~
% 12.00/2.41 $i(v0) | in(v2, v1) = 0)
% 12.00/2.41
% 12.00/2.41 (t8_xboole_1)
% 12.00/2.41 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: int] : ( ~ (v4
% 12.00/2.41 = 0) & subset(v3, v1) = v4 & subset(v2, v1) = 0 & subset(v0, v1) = 0 &
% 12.00/2.41 set_union2(v0, v2) = v3 & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 12.00/2.41
% 12.00/2.41 (function-axioms)
% 12.00/2.42 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 12.00/2.42 [v3: $i] : (v1 = v0 | ~ (disjoint(v3, v2) = v1) | ~ (disjoint(v3, v2) = v0))
% 12.00/2.42 & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 12.00/2.42 [v3: $i] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) &
% 12.00/2.42 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 12.00/2.42 (set_intersection2(v3, v2) = v1) | ~ (set_intersection2(v3, v2) = v0)) & !
% 12.00/2.42 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 12.00/2.42 (set_union2(v3, v2) = v1) | ~ (set_union2(v3, v2) = v0)) & ! [v0:
% 12.00/2.42 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 12.00/2.42 : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) & ! [v0:
% 12.00/2.42 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 |
% 12.00/2.42 ~ (empty(v2) = v1) | ~ (empty(v2) = v0))
% 12.00/2.42
% 12.00/2.42 Further assumptions not needed in the proof:
% 12.00/2.42 --------------------------------------------
% 12.00/2.42 antisymmetry_r2_hidden, commutativity_k3_xboole_0, d10_xboole_0, d1_xboole_0,
% 12.00/2.42 d3_xboole_0, d7_xboole_0, dt_k1_xboole_0, dt_k2_xboole_0, dt_k3_xboole_0,
% 12.00/2.42 fc1_xboole_0, fc2_xboole_0, fc3_xboole_0, idempotence_k2_xboole_0,
% 12.00/2.42 idempotence_k3_xboole_0, rc1_xboole_0, rc2_xboole_0, reflexivity_r1_tarski,
% 12.00/2.42 symmetry_r1_xboole_0, t1_boole, t1_xboole_1, t2_xboole_1, t3_xboole_0,
% 12.00/2.42 t3_xboole_1, t4_xboole_0, t6_boole, t7_boole, t7_xboole_1, t8_boole
% 12.00/2.42
% 12.00/2.42 Those formulas are unsatisfiable:
% 12.00/2.42 ---------------------------------
% 12.00/2.42
% 12.00/2.42 Begin of proof
% 12.00/2.42 |
% 12.00/2.42 | ALPHA: (commutativity_k2_xboole_0) implies:
% 12.00/2.42 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (set_union2(v1, v0) = v2)
% 12.00/2.42 | | ~ $i(v1) | ~ $i(v0) | (set_union2(v0, v1) = v2 & $i(v2)))
% 12.00/2.42 |
% 12.00/2.42 | ALPHA: (d2_xboole_0) implies:
% 12.00/2.42 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 12.00/2.42 | (set_union2(v0, v1) = v2) | ~ (in(v3, v2) = 0) | ~ $i(v3) | ~
% 12.00/2.42 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: any] :
% 12.00/2.42 | (in(v3, v1) = v5 & in(v3, v0) = v4 & (v5 = 0 | v4 = 0)))
% 12.00/2.42 |
% 12.00/2.42 | ALPHA: (d3_tarski) implies:
% 12.00/2.42 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1)
% 12.00/2.42 | = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~
% 12.00/2.42 | (v4 = 0) & in(v3, v1) = v4 & in(v3, v0) = 0 & $i(v3)))
% 12.00/2.42 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~
% 12.00/2.42 | (subset(v0, v1) = 0) | ~ (in(v2, v1) = v3) | ~ $i(v2) | ~ $i(v1) |
% 12.00/2.42 | ~ $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & in(v2, v0) = v4))
% 12.00/2.42 |
% 12.00/2.42 | ALPHA: (function-axioms) implies:
% 12.00/2.42 | (5) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 12.00/2.42 | ! [v3: $i] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0))
% 12.00/2.42 |
% 12.00/2.42 | DELTA: instantiating (t8_xboole_1) with fresh symbols all_34_0, all_34_1,
% 12.00/2.42 | all_34_2, all_34_3, all_34_4 gives:
% 12.00/2.43 | (6) ~ (all_34_0 = 0) & subset(all_34_1, all_34_3) = all_34_0 &
% 12.00/2.43 | subset(all_34_2, all_34_3) = 0 & subset(all_34_4, all_34_3) = 0 &
% 12.00/2.43 | set_union2(all_34_4, all_34_2) = all_34_1 & $i(all_34_1) & $i(all_34_2)
% 12.00/2.43 | & $i(all_34_3) & $i(all_34_4)
% 12.00/2.43 |
% 12.00/2.43 | ALPHA: (6) implies:
% 12.00/2.43 | (7) ~ (all_34_0 = 0)
% 12.00/2.43 | (8) $i(all_34_4)
% 12.00/2.43 | (9) $i(all_34_3)
% 12.00/2.43 | (10) $i(all_34_2)
% 12.00/2.43 | (11) set_union2(all_34_4, all_34_2) = all_34_1
% 12.00/2.43 | (12) subset(all_34_4, all_34_3) = 0
% 12.00/2.43 | (13) subset(all_34_2, all_34_3) = 0
% 12.00/2.43 | (14) subset(all_34_1, all_34_3) = all_34_0
% 12.00/2.43 |
% 12.00/2.43 | GROUND_INST: instantiating (1) with all_34_2, all_34_4, all_34_1, simplifying
% 12.00/2.43 | with (8), (10), (11) gives:
% 12.00/2.43 | (15) set_union2(all_34_2, all_34_4) = all_34_1 & $i(all_34_1)
% 12.00/2.43 |
% 12.00/2.43 | ALPHA: (15) implies:
% 12.00/2.43 | (16) $i(all_34_1)
% 12.00/2.43 | (17) set_union2(all_34_2, all_34_4) = all_34_1
% 12.00/2.43 |
% 12.00/2.43 | GROUND_INST: instantiating (3) with all_34_1, all_34_3, all_34_0, simplifying
% 12.00/2.43 | with (9), (14), (16) gives:
% 12.00/2.43 | (18) all_34_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & in(v0,
% 12.00/2.43 | all_34_1) = 0 & in(v0, all_34_3) = v1 & $i(v0))
% 12.00/2.43 |
% 12.00/2.43 | BETA: splitting (18) gives:
% 12.00/2.43 |
% 12.00/2.43 | Case 1:
% 12.00/2.43 | |
% 12.00/2.43 | | (19) all_34_0 = 0
% 12.00/2.43 | |
% 12.00/2.43 | | REDUCE: (7), (19) imply:
% 12.00/2.43 | | (20) $false
% 12.00/2.43 | |
% 12.00/2.43 | | CLOSE: (20) is inconsistent.
% 12.00/2.43 | |
% 12.00/2.43 | Case 2:
% 12.00/2.43 | |
% 12.00/2.43 | | (21) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & in(v0, all_34_1) = 0 &
% 12.00/2.43 | | in(v0, all_34_3) = v1 & $i(v0))
% 12.00/2.43 | |
% 12.00/2.43 | | DELTA: instantiating (21) with fresh symbols all_54_0, all_54_1 gives:
% 12.00/2.43 | | (22) ~ (all_54_0 = 0) & in(all_54_1, all_34_1) = 0 & in(all_54_1,
% 12.00/2.43 | | all_34_3) = all_54_0 & $i(all_54_1)
% 12.00/2.43 | |
% 12.00/2.43 | | ALPHA: (22) implies:
% 12.00/2.43 | | (23) ~ (all_54_0 = 0)
% 12.00/2.43 | | (24) $i(all_54_1)
% 12.00/2.43 | | (25) in(all_54_1, all_34_3) = all_54_0
% 12.00/2.43 | | (26) in(all_54_1, all_34_1) = 0
% 12.00/2.43 | |
% 12.00/2.43 | | GROUND_INST: instantiating (4) with all_34_2, all_34_3, all_54_1, all_54_0,
% 12.00/2.43 | | simplifying with (9), (10), (13), (24), (25) gives:
% 12.00/2.43 | | (27) all_54_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & in(all_54_1, all_34_2)
% 12.00/2.43 | | = v0)
% 12.00/2.44 | |
% 12.00/2.44 | | GROUND_INST: instantiating (4) with all_34_4, all_34_3, all_54_1, all_54_0,
% 12.00/2.44 | | simplifying with (8), (9), (12), (24), (25) gives:
% 12.00/2.44 | | (28) all_54_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & in(all_54_1, all_34_4)
% 12.00/2.44 | | = v0)
% 12.00/2.44 | |
% 12.00/2.44 | | GROUND_INST: instantiating (2) with all_34_2, all_34_4, all_34_1, all_54_1,
% 12.00/2.44 | | simplifying with (8), (10), (16), (17), (24), (26) gives:
% 12.00/2.44 | | (29) ? [v0: any] : ? [v1: any] : (in(all_54_1, all_34_2) = v0 &
% 12.00/2.44 | | in(all_54_1, all_34_4) = v1 & (v1 = 0 | v0 = 0))
% 12.00/2.44 | |
% 12.00/2.44 | | DELTA: instantiating (29) with fresh symbols all_82_0, all_82_1 gives:
% 12.00/2.44 | | (30) in(all_54_1, all_34_2) = all_82_1 & in(all_54_1, all_34_4) =
% 12.00/2.44 | | all_82_0 & (all_82_0 = 0 | all_82_1 = 0)
% 12.00/2.44 | |
% 12.00/2.44 | | ALPHA: (30) implies:
% 12.00/2.44 | | (31) in(all_54_1, all_34_4) = all_82_0
% 12.00/2.44 | | (32) in(all_54_1, all_34_2) = all_82_1
% 12.00/2.44 | | (33) all_82_0 = 0 | all_82_1 = 0
% 12.00/2.44 | |
% 12.00/2.44 | | BETA: splitting (28) gives:
% 12.00/2.44 | |
% 12.00/2.44 | | Case 1:
% 12.00/2.44 | | |
% 12.00/2.44 | | | (34) all_54_0 = 0
% 12.00/2.44 | | |
% 12.00/2.44 | | | REDUCE: (23), (34) imply:
% 12.00/2.44 | | | (35) $false
% 12.00/2.44 | | |
% 12.00/2.44 | | | CLOSE: (35) is inconsistent.
% 12.00/2.44 | | |
% 12.00/2.44 | | Case 2:
% 12.00/2.44 | | |
% 12.00/2.44 | | | (36) ? [v0: int] : ( ~ (v0 = 0) & in(all_54_1, all_34_4) = v0)
% 12.00/2.44 | | |
% 12.00/2.44 | | | DELTA: instantiating (36) with fresh symbol all_92_0 gives:
% 12.00/2.44 | | | (37) ~ (all_92_0 = 0) & in(all_54_1, all_34_4) = all_92_0
% 12.00/2.44 | | |
% 12.00/2.44 | | | ALPHA: (37) implies:
% 12.00/2.44 | | | (38) ~ (all_92_0 = 0)
% 12.00/2.44 | | | (39) in(all_54_1, all_34_4) = all_92_0
% 12.00/2.44 | | |
% 12.00/2.44 | | | BETA: splitting (27) gives:
% 12.00/2.44 | | |
% 12.00/2.44 | | | Case 1:
% 12.00/2.44 | | | |
% 12.00/2.44 | | | | (40) all_54_0 = 0
% 12.00/2.44 | | | |
% 12.00/2.44 | | | | REDUCE: (23), (40) imply:
% 12.00/2.44 | | | | (41) $false
% 12.00/2.44 | | | |
% 12.00/2.44 | | | | CLOSE: (41) is inconsistent.
% 12.00/2.44 | | | |
% 12.00/2.44 | | | Case 2:
% 12.00/2.44 | | | |
% 12.00/2.44 | | | | (42) ? [v0: int] : ( ~ (v0 = 0) & in(all_54_1, all_34_2) = v0)
% 12.00/2.44 | | | |
% 12.00/2.44 | | | | DELTA: instantiating (42) with fresh symbol all_103_0 gives:
% 12.00/2.44 | | | | (43) ~ (all_103_0 = 0) & in(all_54_1, all_34_2) = all_103_0
% 12.00/2.44 | | | |
% 12.00/2.44 | | | | ALPHA: (43) implies:
% 12.00/2.44 | | | | (44) ~ (all_103_0 = 0)
% 12.00/2.44 | | | | (45) in(all_54_1, all_34_2) = all_103_0
% 12.00/2.44 | | | |
% 12.00/2.44 | | | | GROUND_INST: instantiating (5) with all_82_0, all_92_0, all_34_4,
% 12.00/2.44 | | | | all_54_1, simplifying with (31), (39) gives:
% 12.00/2.44 | | | | (46) all_92_0 = all_82_0
% 12.00/2.44 | | | |
% 12.00/2.44 | | | | GROUND_INST: instantiating (5) with all_82_1, all_103_0, all_34_2,
% 12.00/2.44 | | | | all_54_1, simplifying with (32), (45) gives:
% 12.00/2.44 | | | | (47) all_103_0 = all_82_1
% 12.00/2.44 | | | |
% 12.00/2.44 | | | | REDUCE: (44), (47) imply:
% 12.00/2.44 | | | | (48) ~ (all_82_1 = 0)
% 12.00/2.44 | | | |
% 12.00/2.44 | | | | REDUCE: (38), (46) imply:
% 12.00/2.44 | | | | (49) ~ (all_82_0 = 0)
% 12.00/2.44 | | | |
% 12.00/2.44 | | | | BETA: splitting (33) gives:
% 12.00/2.44 | | | |
% 12.00/2.44 | | | | Case 1:
% 12.00/2.44 | | | | |
% 12.00/2.44 | | | | | (50) all_82_0 = 0
% 12.00/2.44 | | | | |
% 12.00/2.44 | | | | | REDUCE: (49), (50) imply:
% 12.00/2.44 | | | | | (51) $false
% 12.00/2.44 | | | | |
% 12.00/2.44 | | | | | CLOSE: (51) is inconsistent.
% 12.00/2.44 | | | | |
% 12.00/2.44 | | | | Case 2:
% 12.00/2.44 | | | | |
% 12.00/2.44 | | | | | (52) all_82_1 = 0
% 12.00/2.44 | | | | |
% 12.00/2.44 | | | | | REDUCE: (48), (52) imply:
% 12.00/2.44 | | | | | (53) $false
% 12.00/2.44 | | | | |
% 12.00/2.44 | | | | | CLOSE: (53) is inconsistent.
% 12.00/2.44 | | | | |
% 12.00/2.44 | | | | End of split
% 12.00/2.44 | | | |
% 12.00/2.45 | | | End of split
% 12.00/2.45 | | |
% 12.00/2.45 | | End of split
% 12.00/2.45 | |
% 12.00/2.45 | End of split
% 12.00/2.45 |
% 12.00/2.45 End of proof
% 12.00/2.45 % SZS output end Proof for theBenchmark
% 12.00/2.45
% 12.00/2.45 1845ms
%------------------------------------------------------------------------------