TSTP Solution File: SEU125+1 by Princess---230619
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SEU125+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 17:42:37 EDT 2023
% Result : Theorem 6.17s 1.60s
% Output : Proof 8.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU125+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 18:07:06 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.20/0.60 ________ _____
% 0.20/0.60 ___ __ \_________(_)________________________________
% 0.20/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.20/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.20/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.20/0.60
% 0.20/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.20/0.60 (2023-06-19)
% 0.20/0.60
% 0.20/0.60 (c) Philipp Rümmer, 2009-2023
% 0.20/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.20/0.60 Amanda Stjerna.
% 0.20/0.60 Free software under BSD-3-Clause.
% 0.20/0.60
% 0.20/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.20/0.60
% 0.20/0.60 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.20/0.61 Running up to 7 provers in parallel.
% 0.20/0.62 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.20/0.62 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.20/0.62 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.20/0.62 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.20/0.62 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.20/0.62 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.20/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.12/1.03 Prover 4: Preprocessing ...
% 2.12/1.03 Prover 1: Preprocessing ...
% 2.63/1.08 Prover 6: Preprocessing ...
% 2.63/1.08 Prover 5: Preprocessing ...
% 2.63/1.08 Prover 0: Preprocessing ...
% 2.63/1.08 Prover 2: Preprocessing ...
% 2.63/1.08 Prover 3: Preprocessing ...
% 3.64/1.40 Prover 1: Warning: ignoring some quantifiers
% 3.64/1.40 Prover 4: Warning: ignoring some quantifiers
% 3.64/1.40 Prover 3: Warning: ignoring some quantifiers
% 3.64/1.41 Prover 2: Proving ...
% 3.64/1.41 Prover 5: Proving ...
% 4.65/1.42 Prover 6: Proving ...
% 4.65/1.42 Prover 4: Constructing countermodel ...
% 4.65/1.42 Prover 3: Constructing countermodel ...
% 4.65/1.42 Prover 1: Constructing countermodel ...
% 4.65/1.43 Prover 0: Proving ...
% 6.17/1.60 Prover 0: proved (985ms)
% 6.17/1.60
% 6.17/1.60 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.17/1.60
% 6.17/1.60 Prover 6: stopped
% 6.28/1.61 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 6.28/1.61 Prover 5: stopped
% 6.32/1.61 Prover 3: stopped
% 6.32/1.61 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 6.32/1.61 Prover 2: stopped
% 6.32/1.62 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 6.32/1.62 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 6.32/1.62 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 6.32/1.65 Prover 8: Preprocessing ...
% 6.32/1.65 Prover 7: Preprocessing ...
% 6.32/1.65 Prover 11: Preprocessing ...
% 6.32/1.65 Prover 13: Preprocessing ...
% 6.32/1.65 Prover 10: Preprocessing ...
% 6.32/1.70 Prover 10: Warning: ignoring some quantifiers
% 6.95/1.70 Prover 10: Constructing countermodel ...
% 6.95/1.71 Prover 7: Warning: ignoring some quantifiers
% 6.95/1.71 Prover 7: Constructing countermodel ...
% 6.95/1.72 Prover 8: Warning: ignoring some quantifiers
% 6.95/1.72 Prover 13: Warning: ignoring some quantifiers
% 6.95/1.72 Prover 13: Constructing countermodel ...
% 6.95/1.72 Prover 8: Constructing countermodel ...
% 6.95/1.72 Prover 1: gave up
% 6.95/1.74 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 6.95/1.76 Prover 16: Preprocessing ...
% 6.95/1.77 Prover 11: Warning: ignoring some quantifiers
% 6.95/1.77 Prover 11: Constructing countermodel ...
% 7.56/1.79 Prover 10: gave up
% 7.56/1.79 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085
% 7.56/1.80 Prover 13: gave up
% 7.56/1.80 Prover 4: Found proof (size 50)
% 7.56/1.80 Prover 4: proved (1182ms)
% 7.56/1.80 Prover 11: stopped
% 7.56/1.80 Prover 8: stopped
% 7.56/1.81 Prover 7: stopped
% 7.56/1.81 Prover 16: Warning: ignoring some quantifiers
% 7.56/1.82 Prover 19: Preprocessing ...
% 7.56/1.82 Prover 16: Constructing countermodel ...
% 7.56/1.82 Prover 16: stopped
% 7.56/1.87 Prover 19: Warning: ignoring some quantifiers
% 7.56/1.87 Prover 19: Constructing countermodel ...
% 7.56/1.88 Prover 19: stopped
% 7.56/1.88
% 7.56/1.88 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 7.56/1.88
% 8.11/1.89 % SZS output start Proof for theBenchmark
% 8.11/1.89 Assumptions after simplification:
% 8.11/1.89 ---------------------------------
% 8.11/1.89
% 8.11/1.89 (commutativity_k2_xboole_0)
% 8.18/1.92 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (set_union2(v1, v0) = v2) | ~
% 8.18/1.92 $i(v1) | ~ $i(v0) | (set_union2(v0, v1) = v2 & $i(v2))) & ! [v0: $i] : !
% 8.18/1.92 [v1: $i] : ! [v2: $i] : ( ~ (set_union2(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0)
% 8.18/1.92 | (set_union2(v1, v0) = v2 & $i(v2)))
% 8.18/1.92
% 8.18/1.92 (d2_xboole_0)
% 8.18/1.94 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0
% 8.18/1.94 | ~ (set_union2(v0, v1) = v2) | ~ (in(v3, v2) = v4) | ~ $i(v3) | ~
% 8.18/1.94 $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ? [v6: int] : ( ~ (v6 = 0)
% 8.18/1.94 & ~ (v5 = 0) & in(v3, v1) = v6 & in(v3, v0) = v5)) & ! [v0: $i] : !
% 8.18/1.94 [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0 | ~
% 8.18/1.94 (set_union2(v0, v1) = v2) | ~ (in(v3, v1) = v4) | ~ $i(v3) | ~ $i(v2) |
% 8.18/1.94 ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : (in(v3, v2) = v5 &
% 8.18/1.94 in(v3, v0) = v6 & ( ~ (v5 = 0) | v6 = 0))) & ! [v0: $i] : ! [v1: $i] :
% 8.18/1.94 ! [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0 | ~ (set_union2(v0, v1) =
% 8.18/1.94 v2) | ~ (in(v3, v0) = v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0)
% 8.18/1.94 | ? [v5: any] : ? [v6: any] : (in(v3, v2) = v5 & in(v3, v1) = v6 & ( ~ (v5
% 8.18/1.94 = 0) | v6 = 0))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 8.18/1.94 $i] : ! [v4: any] : ( ~ (set_union2(v0, v1) = v2) | ~ (in(v3, v1) = v4) |
% 8.18/1.94 ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] :
% 8.18/1.94 (in(v3, v2) = v6 & in(v3, v0) = v5 & (v6 = 0 | ( ~ (v5 = 0) & ~ (v4 =
% 8.18/1.94 0))))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : !
% 8.18/1.94 [v4: any] : ( ~ (set_union2(v0, v1) = v2) | ~ (in(v3, v0) = v4) | ~ $i(v3) |
% 8.18/1.94 ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : (in(v3,
% 8.18/1.94 v2) = v6 & in(v3, v1) = v5 & (v6 = 0 | ( ~ (v5 = 0) & ~ (v4 = 0))))) &
% 8.18/1.94 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (set_union2(v0, v1)
% 8.18/1.94 = v2) | ~ (in(v3, v2) = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~
% 8.18/1.94 $i(v0) | ? [v4: any] : ? [v5: any] : (in(v3, v1) = v5 & in(v3, v0) = v4 &
% 8.18/1.94 (v5 = 0 | v4 = 0))) & ? [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 8.18/1.94 $i] : (v3 = v0 | ~ (set_union2(v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~
% 8.18/1.94 $i(v0) | ? [v4: $i] : ? [v5: any] : ? [v6: any] : ? [v7: any] : (in(v4,
% 8.18/1.94 v2) = v7 & in(v4, v1) = v6 & in(v4, v0) = v5 & $i(v4) & ( ~ (v5 = 0) | (
% 8.18/1.94 ~ (v7 = 0) & ~ (v6 = 0))) & (v7 = 0 | v6 = 0 | v5 = 0)))
% 8.18/1.94
% 8.18/1.94 (d3_tarski)
% 8.18/1.94 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~
% 8.18/1.94 (subset(v0, v1) = 0) | ~ (in(v2, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~
% 8.18/1.95 $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & in(v2, v0) = v4)) & ! [v0: $i] : !
% 8.18/1.95 [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ~ $i(v1) | ~
% 8.18/1.95 $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) & in(v3, v1) = v4 &
% 8.18/1.95 in(v3, v0) = 0 & $i(v3))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 8.18/1.95 (subset(v0, v1) = 0) | ~ (in(v2, v0) = 0) | ~ $i(v2) | ~ $i(v1) | ~
% 8.18/1.95 $i(v0) | in(v2, v1) = 0)
% 8.18/1.95
% 8.18/1.95 (t8_xboole_1)
% 8.18/1.95 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: int] : ( ~ (v4
% 8.18/1.95 = 0) & subset(v3, v1) = v4 & subset(v2, v1) = 0 & subset(v0, v1) = 0 &
% 8.18/1.95 set_union2(v0, v2) = v3 & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 8.18/1.95
% 8.18/1.95 (function-axioms)
% 8.18/1.95 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 8.18/1.95 [v3: $i] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) &
% 8.18/1.95 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 8.18/1.95 (set_union2(v3, v2) = v1) | ~ (set_union2(v3, v2) = v0)) & ! [v0:
% 8.18/1.95 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 8.18/1.95 : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) & ! [v0:
% 8.18/1.95 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 |
% 8.18/1.95 ~ (empty(v2) = v1) | ~ (empty(v2) = v0))
% 8.18/1.95
% 8.18/1.95 Further assumptions not needed in the proof:
% 8.18/1.95 --------------------------------------------
% 8.18/1.95 antisymmetry_r2_hidden, dt_k1_xboole_0, dt_k2_xboole_0, fc1_xboole_0,
% 8.18/1.95 fc2_xboole_0, fc3_xboole_0, idempotence_k2_xboole_0, rc1_xboole_0, rc2_xboole_0,
% 8.18/1.95 reflexivity_r1_tarski, t1_boole, t6_boole, t7_boole, t8_boole
% 8.18/1.95
% 8.18/1.95 Those formulas are unsatisfiable:
% 8.18/1.95 ---------------------------------
% 8.18/1.95
% 8.18/1.95 Begin of proof
% 8.18/1.95 |
% 8.18/1.95 | ALPHA: (commutativity_k2_xboole_0) implies:
% 8.18/1.95 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (set_union2(v1, v0) = v2)
% 8.18/1.95 | | ~ $i(v1) | ~ $i(v0) | (set_union2(v0, v1) = v2 & $i(v2)))
% 8.18/1.95 |
% 8.18/1.95 | ALPHA: (d2_xboole_0) implies:
% 8.18/1.95 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 8.18/1.95 | (set_union2(v0, v1) = v2) | ~ (in(v3, v2) = 0) | ~ $i(v3) | ~
% 8.18/1.95 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: any] :
% 8.18/1.95 | (in(v3, v1) = v5 & in(v3, v0) = v4 & (v5 = 0 | v4 = 0)))
% 8.18/1.95 |
% 8.18/1.95 | ALPHA: (d3_tarski) implies:
% 8.18/1.96 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1)
% 8.18/1.96 | = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~
% 8.18/1.96 | (v4 = 0) & in(v3, v1) = v4 & in(v3, v0) = 0 & $i(v3)))
% 8.18/1.96 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~
% 8.18/1.96 | (subset(v0, v1) = 0) | ~ (in(v2, v1) = v3) | ~ $i(v2) | ~ $i(v1) |
% 8.18/1.96 | ~ $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & in(v2, v0) = v4))
% 8.18/1.96 |
% 8.18/1.96 | ALPHA: (function-axioms) implies:
% 8.18/1.96 | (5) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 8.18/1.96 | ! [v3: $i] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0))
% 8.18/1.96 |
% 8.18/1.96 | DELTA: instantiating (t8_xboole_1) with fresh symbols all_20_0, all_20_1,
% 8.18/1.96 | all_20_2, all_20_3, all_20_4 gives:
% 8.18/1.96 | (6) ~ (all_20_0 = 0) & subset(all_20_1, all_20_3) = all_20_0 &
% 8.18/1.96 | subset(all_20_2, all_20_3) = 0 & subset(all_20_4, all_20_3) = 0 &
% 8.18/1.96 | set_union2(all_20_4, all_20_2) = all_20_1 & $i(all_20_1) & $i(all_20_2)
% 8.18/1.96 | & $i(all_20_3) & $i(all_20_4)
% 8.18/1.96 |
% 8.18/1.96 | ALPHA: (6) implies:
% 8.18/1.96 | (7) ~ (all_20_0 = 0)
% 8.18/1.96 | (8) $i(all_20_4)
% 8.18/1.96 | (9) $i(all_20_3)
% 8.18/1.96 | (10) $i(all_20_2)
% 8.18/1.96 | (11) set_union2(all_20_4, all_20_2) = all_20_1
% 8.18/1.96 | (12) subset(all_20_4, all_20_3) = 0
% 8.18/1.96 | (13) subset(all_20_2, all_20_3) = 0
% 8.18/1.96 | (14) subset(all_20_1, all_20_3) = all_20_0
% 8.18/1.96 |
% 8.18/1.96 | GROUND_INST: instantiating (1) with all_20_2, all_20_4, all_20_1, simplifying
% 8.18/1.96 | with (8), (10), (11) gives:
% 8.18/1.96 | (15) set_union2(all_20_2, all_20_4) = all_20_1 & $i(all_20_1)
% 8.18/1.96 |
% 8.18/1.96 | ALPHA: (15) implies:
% 8.18/1.96 | (16) $i(all_20_1)
% 8.18/1.96 | (17) set_union2(all_20_2, all_20_4) = all_20_1
% 8.18/1.96 |
% 8.18/1.96 | GROUND_INST: instantiating (3) with all_20_1, all_20_3, all_20_0, simplifying
% 8.18/1.96 | with (9), (14), (16) gives:
% 8.18/1.96 | (18) all_20_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & in(v0,
% 8.18/1.96 | all_20_1) = 0 & in(v0, all_20_3) = v1 & $i(v0))
% 8.18/1.96 |
% 8.18/1.96 | BETA: splitting (18) gives:
% 8.18/1.96 |
% 8.18/1.97 | Case 1:
% 8.18/1.97 | |
% 8.18/1.97 | | (19) all_20_0 = 0
% 8.18/1.97 | |
% 8.18/1.97 | | REDUCE: (7), (19) imply:
% 8.18/1.97 | | (20) $false
% 8.18/1.97 | |
% 8.18/1.97 | | CLOSE: (20) is inconsistent.
% 8.18/1.97 | |
% 8.18/1.97 | Case 2:
% 8.18/1.97 | |
% 8.18/1.97 | | (21) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & in(v0, all_20_1) = 0 &
% 8.18/1.97 | | in(v0, all_20_3) = v1 & $i(v0))
% 8.18/1.97 | |
% 8.18/1.97 | | DELTA: instantiating (21) with fresh symbols all_38_0, all_38_1 gives:
% 8.18/1.97 | | (22) ~ (all_38_0 = 0) & in(all_38_1, all_20_1) = 0 & in(all_38_1,
% 8.18/1.97 | | all_20_3) = all_38_0 & $i(all_38_1)
% 8.18/1.97 | |
% 8.18/1.97 | | ALPHA: (22) implies:
% 8.18/1.97 | | (23) ~ (all_38_0 = 0)
% 8.18/1.97 | | (24) $i(all_38_1)
% 8.18/1.97 | | (25) in(all_38_1, all_20_3) = all_38_0
% 8.18/1.97 | | (26) in(all_38_1, all_20_1) = 0
% 8.18/1.97 | |
% 8.18/1.97 | | GROUND_INST: instantiating (4) with all_20_2, all_20_3, all_38_1, all_38_0,
% 8.18/1.97 | | simplifying with (9), (10), (13), (24), (25) gives:
% 8.18/1.97 | | (27) all_38_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & in(all_38_1, all_20_2)
% 8.18/1.97 | | = v0)
% 8.18/1.97 | |
% 8.18/1.97 | | GROUND_INST: instantiating (4) with all_20_4, all_20_3, all_38_1, all_38_0,
% 8.18/1.97 | | simplifying with (8), (9), (12), (24), (25) gives:
% 8.18/1.97 | | (28) all_38_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & in(all_38_1, all_20_4)
% 8.18/1.97 | | = v0)
% 8.18/1.97 | |
% 8.18/1.97 | | GROUND_INST: instantiating (2) with all_20_4, all_20_2, all_20_1, all_38_1,
% 8.18/1.97 | | simplifying with (8), (10), (11), (16), (24), (26) gives:
% 8.18/1.97 | | (29) ? [v0: any] : ? [v1: any] : (in(all_38_1, all_20_2) = v1 &
% 8.18/1.97 | | in(all_38_1, all_20_4) = v0 & (v1 = 0 | v0 = 0))
% 8.18/1.97 | |
% 8.18/1.97 | | GROUND_INST: instantiating (2) with all_20_2, all_20_4, all_20_1, all_38_1,
% 8.18/1.97 | | simplifying with (8), (10), (16), (17), (24), (26) gives:
% 8.18/1.98 | | (30) ? [v0: any] : ? [v1: any] : (in(all_38_1, all_20_2) = v0 &
% 8.18/1.98 | | in(all_38_1, all_20_4) = v1 & (v1 = 0 | v0 = 0))
% 8.18/1.98 | |
% 8.18/1.98 | | DELTA: instantiating (29) with fresh symbols all_55_0, all_55_1 gives:
% 8.18/1.98 | | (31) in(all_38_1, all_20_2) = all_55_0 & in(all_38_1, all_20_4) =
% 8.18/1.98 | | all_55_1 & (all_55_0 = 0 | all_55_1 = 0)
% 8.18/1.98 | |
% 8.18/1.98 | | ALPHA: (31) implies:
% 8.18/1.98 | | (32) in(all_38_1, all_20_4) = all_55_1
% 8.18/1.98 | | (33) in(all_38_1, all_20_2) = all_55_0
% 8.18/1.98 | |
% 8.18/1.98 | | DELTA: instantiating (30) with fresh symbols all_59_0, all_59_1 gives:
% 8.18/1.98 | | (34) in(all_38_1, all_20_2) = all_59_1 & in(all_38_1, all_20_4) =
% 8.18/1.98 | | all_59_0 & (all_59_0 = 0 | all_59_1 = 0)
% 8.18/1.98 | |
% 8.18/1.98 | | ALPHA: (34) implies:
% 8.18/1.98 | | (35) in(all_38_1, all_20_4) = all_59_0
% 8.18/1.98 | | (36) in(all_38_1, all_20_2) = all_59_1
% 8.18/1.98 | | (37) all_59_0 = 0 | all_59_1 = 0
% 8.18/1.98 | |
% 8.18/1.98 | | BETA: splitting (28) gives:
% 8.18/1.98 | |
% 8.18/1.98 | | Case 1:
% 8.18/1.98 | | |
% 8.18/1.98 | | | (38) all_38_0 = 0
% 8.18/1.98 | | |
% 8.18/1.98 | | | REDUCE: (23), (38) imply:
% 8.18/1.98 | | | (39) $false
% 8.18/1.98 | | |
% 8.18/1.98 | | | CLOSE: (39) is inconsistent.
% 8.18/1.98 | | |
% 8.18/1.98 | | Case 2:
% 8.18/1.98 | | |
% 8.18/1.98 | | | (40) ? [v0: int] : ( ~ (v0 = 0) & in(all_38_1, all_20_4) = v0)
% 8.18/1.98 | | |
% 8.18/1.98 | | | DELTA: instantiating (40) with fresh symbol all_65_0 gives:
% 8.18/1.98 | | | (41) ~ (all_65_0 = 0) & in(all_38_1, all_20_4) = all_65_0
% 8.18/1.98 | | |
% 8.18/1.98 | | | ALPHA: (41) implies:
% 8.18/1.98 | | | (42) ~ (all_65_0 = 0)
% 8.18/1.98 | | | (43) in(all_38_1, all_20_4) = all_65_0
% 8.18/1.98 | | |
% 8.18/1.98 | | | BETA: splitting (27) gives:
% 8.18/1.98 | | |
% 8.18/1.98 | | | Case 1:
% 8.18/1.98 | | | |
% 8.18/1.98 | | | | (44) all_38_0 = 0
% 8.18/1.98 | | | |
% 8.18/1.98 | | | | REDUCE: (23), (44) imply:
% 8.18/1.98 | | | | (45) $false
% 8.18/1.98 | | | |
% 8.18/1.98 | | | | CLOSE: (45) is inconsistent.
% 8.18/1.98 | | | |
% 8.18/1.98 | | | Case 2:
% 8.18/1.98 | | | |
% 8.18/1.98 | | | | (46) ? [v0: int] : ( ~ (v0 = 0) & in(all_38_1, all_20_2) = v0)
% 8.18/1.98 | | | |
% 8.18/1.98 | | | | DELTA: instantiating (46) with fresh symbol all_71_0 gives:
% 8.18/1.98 | | | | (47) ~ (all_71_0 = 0) & in(all_38_1, all_20_2) = all_71_0
% 8.18/1.98 | | | |
% 8.18/1.98 | | | | ALPHA: (47) implies:
% 8.18/1.98 | | | | (48) ~ (all_71_0 = 0)
% 8.18/1.98 | | | | (49) in(all_38_1, all_20_2) = all_71_0
% 8.18/1.98 | | | |
% 8.18/1.98 | | | | GROUND_INST: instantiating (5) with all_59_0, all_65_0, all_20_4,
% 8.18/1.98 | | | | all_38_1, simplifying with (35), (43) gives:
% 8.18/1.98 | | | | (50) all_65_0 = all_59_0
% 8.18/1.98 | | | |
% 8.18/1.98 | | | | GROUND_INST: instantiating (5) with all_55_1, all_65_0, all_20_4,
% 8.18/1.98 | | | | all_38_1, simplifying with (32), (43) gives:
% 8.18/1.98 | | | | (51) all_65_0 = all_55_1
% 8.18/1.98 | | | |
% 8.18/1.98 | | | | GROUND_INST: instantiating (5) with all_59_1, all_71_0, all_20_2,
% 8.18/1.98 | | | | all_38_1, simplifying with (36), (49) gives:
% 8.18/1.98 | | | | (52) all_71_0 = all_59_1
% 8.18/1.98 | | | |
% 8.18/1.98 | | | | GROUND_INST: instantiating (5) with all_55_0, all_71_0, all_20_2,
% 8.18/1.98 | | | | all_38_1, simplifying with (33), (49) gives:
% 8.18/1.98 | | | | (53) all_71_0 = all_55_0
% 8.18/1.98 | | | |
% 8.18/1.98 | | | | COMBINE_EQS: (52), (53) imply:
% 8.18/1.98 | | | | (54) all_59_1 = all_55_0
% 8.18/1.98 | | | |
% 8.18/1.98 | | | | SIMP: (54) implies:
% 8.18/1.99 | | | | (55) all_59_1 = all_55_0
% 8.18/1.99 | | | |
% 8.18/1.99 | | | | COMBINE_EQS: (50), (51) imply:
% 8.18/1.99 | | | | (56) all_59_0 = all_55_1
% 8.18/1.99 | | | |
% 8.18/1.99 | | | | REDUCE: (48), (53) imply:
% 8.18/1.99 | | | | (57) ~ (all_55_0 = 0)
% 8.18/1.99 | | | |
% 8.18/1.99 | | | | REDUCE: (42), (51) imply:
% 8.18/1.99 | | | | (58) ~ (all_55_1 = 0)
% 8.18/1.99 | | | |
% 8.18/1.99 | | | | BETA: splitting (37) gives:
% 8.18/1.99 | | | |
% 8.18/1.99 | | | | Case 1:
% 8.18/1.99 | | | | |
% 8.18/1.99 | | | | | (59) all_59_0 = 0
% 8.18/1.99 | | | | |
% 8.18/1.99 | | | | | COMBINE_EQS: (56), (59) imply:
% 8.18/1.99 | | | | | (60) all_55_1 = 0
% 8.18/1.99 | | | | |
% 8.18/1.99 | | | | | SIMP: (60) implies:
% 8.18/1.99 | | | | | (61) all_55_1 = 0
% 8.18/1.99 | | | | |
% 8.18/1.99 | | | | | REDUCE: (58), (61) imply:
% 8.18/1.99 | | | | | (62) $false
% 8.18/1.99 | | | | |
% 8.18/1.99 | | | | | CLOSE: (62) is inconsistent.
% 8.18/1.99 | | | | |
% 8.18/1.99 | | | | Case 2:
% 8.18/1.99 | | | | |
% 8.18/1.99 | | | | | (63) all_59_1 = 0
% 8.18/1.99 | | | | |
% 8.18/1.99 | | | | | COMBINE_EQS: (55), (63) imply:
% 8.18/1.99 | | | | | (64) all_55_0 = 0
% 8.18/1.99 | | | | |
% 8.18/1.99 | | | | | REDUCE: (57), (64) imply:
% 8.18/1.99 | | | | | (65) $false
% 8.18/1.99 | | | | |
% 8.18/1.99 | | | | | CLOSE: (65) is inconsistent.
% 8.18/1.99 | | | | |
% 8.18/1.99 | | | | End of split
% 8.18/1.99 | | | |
% 8.18/1.99 | | | End of split
% 8.18/1.99 | | |
% 8.18/1.99 | | End of split
% 8.18/1.99 | |
% 8.18/1.99 | End of split
% 8.18/1.99 |
% 8.18/1.99 End of proof
% 8.18/1.99 % SZS output end Proof for theBenchmark
% 8.18/1.99
% 8.18/1.99 1389ms
%------------------------------------------------------------------------------