TSTP Solution File: NUM840+2 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : NUM840+2 : TPTP v8.1.2. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n027.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 11:50:19 EDT 2023
% Result : Theorem 8.49s 1.96s
% Output : Proof 11.78s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM840+2 : TPTP v8.1.2. Released v4.1.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.12/0.34 % Computer : n027.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Fri Aug 25 08:34:48 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.19/0.63 ________ _____
% 0.19/0.63 ___ __ \_________(_)________________________________
% 0.19/0.63 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.19/0.63 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.19/0.63 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.19/0.63
% 0.19/0.63 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.19/0.63 (2023-06-19)
% 0.19/0.63
% 0.19/0.63 (c) Philipp Rümmer, 2009-2023
% 0.19/0.63 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.19/0.63 Amanda Stjerna.
% 0.19/0.63 Free software under BSD-3-Clause.
% 0.19/0.63
% 0.19/0.63 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.19/0.63
% 0.19/0.63 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.19/0.64 Running up to 7 provers in parallel.
% 0.19/0.65 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.19/0.65 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.19/0.65 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.19/0.65 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.19/0.65 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.19/0.65 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 0.19/0.65 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 2.67/1.11 Prover 1: Preprocessing ...
% 2.67/1.11 Prover 4: Preprocessing ...
% 2.67/1.16 Prover 3: Preprocessing ...
% 2.67/1.16 Prover 5: Preprocessing ...
% 2.67/1.16 Prover 0: Preprocessing ...
% 2.67/1.16 Prover 2: Preprocessing ...
% 2.67/1.16 Prover 6: Preprocessing ...
% 6.31/1.66 Prover 4: Warning: ignoring some quantifiers
% 6.31/1.67 Prover 1: Warning: ignoring some quantifiers
% 6.56/1.68 Prover 5: Proving ...
% 6.56/1.71 Prover 4: Constructing countermodel ...
% 6.56/1.72 Prover 1: Constructing countermodel ...
% 6.56/1.72 Prover 3: Warning: ignoring some quantifiers
% 6.91/1.73 Prover 3: Constructing countermodel ...
% 7.03/1.75 Prover 6: Proving ...
% 7.03/1.78 Prover 0: Proving ...
% 7.03/1.80 Prover 2: Proving ...
% 8.49/1.96 Prover 3: proved (1308ms)
% 8.49/1.96
% 8.49/1.96 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 8.49/1.96
% 8.49/1.97 Prover 0: stopped
% 8.49/1.97 Prover 2: stopped
% 8.49/1.97 Prover 6: stopped
% 8.49/1.97 Prover 5: stopped
% 8.49/1.97 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 8.49/1.97 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 8.49/1.97 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 8.49/1.97 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 8.49/1.97 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 9.04/2.04 Prover 10: Preprocessing ...
% 9.04/2.04 Prover 7: Preprocessing ...
% 9.19/2.06 Prover 8: Preprocessing ...
% 9.19/2.08 Prover 13: Preprocessing ...
% 9.19/2.09 Prover 11: Preprocessing ...
% 9.19/2.18 Prover 10: Warning: ignoring some quantifiers
% 9.19/2.19 Prover 13: Warning: ignoring some quantifiers
% 9.19/2.20 Prover 10: Constructing countermodel ...
% 9.19/2.20 Prover 1: Found proof (size 65)
% 9.19/2.20 Prover 1: proved (1553ms)
% 9.19/2.20 Prover 4: stopped
% 9.19/2.21 Prover 13: Constructing countermodel ...
% 9.19/2.22 Prover 13: stopped
% 9.19/2.22 Prover 10: stopped
% 9.19/2.23 Prover 8: Warning: ignoring some quantifiers
% 9.19/2.25 Prover 8: Constructing countermodel ...
% 9.19/2.25 Prover 7: Warning: ignoring some quantifiers
% 9.19/2.26 Prover 8: stopped
% 9.19/2.27 Prover 7: Constructing countermodel ...
% 9.19/2.28 Prover 11: Warning: ignoring some quantifiers
% 9.19/2.28 Prover 7: stopped
% 10.66/2.30 Prover 11: Constructing countermodel ...
% 10.66/2.31 Prover 11: stopped
% 10.66/2.31
% 10.66/2.31 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 10.66/2.31
% 10.66/2.34 % SZS output start Proof for theBenchmark
% 10.66/2.34 Assumptions after simplification:
% 10.66/2.34 ---------------------------------
% 10.66/2.34
% 10.66/2.34 (ass(cond(147, 0), 0))
% 11.14/2.37 ! [v0: $i] : ! [v1: $i] : ( ~ (less(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) |
% 11.14/2.37 greater(v1, v0) = 0)
% 11.14/2.37
% 11.14/2.37 (ass(cond(61, 0), 0))
% 11.14/2.38 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (vplus(v0, v1) = v2) | ~ $i(v1)
% 11.14/2.38 | ~ $i(v0) | (vplus(v1, v0) = v2 & $i(v2)))
% 11.14/2.38
% 11.14/2.38 (ass(cond(conjunct1(204), 0), 0))
% 11.14/2.38 $i(vd330) & $i(vd329) & $i(vd328) & ? [v0: $i] : ? [v1: $i] : ? [v2: any] :
% 11.14/2.38 ? [v3: any] : (greater(v0, v1) = v2 & greater(vd328, vd329) = v3 &
% 11.14/2.38 vplus(vd329, vd330) = v1 & vplus(vd328, vd330) = v0 & $i(v1) & $i(v0) & ( ~
% 11.14/2.38 (v2 = 0) | v3 = 0))
% 11.14/2.38
% 11.14/2.38 (ass(cond(conjunct1(conjunct2(204)), 0), 0))
% 11.14/2.39 $i(vd330) & $i(vd329) & $i(vd328) & ? [v0: $i] : ? [v1: $i] : (vplus(vd329,
% 11.14/2.39 vd330) = v1 & vplus(vd328, vd330) = v0 & $i(v1) & $i(v0) & ( ~ (v1 = v0) |
% 11.14/2.39 vd329 = vd328))
% 11.14/2.39
% 11.14/2.39 (ass(cond(goal(130), 0), 0))
% 11.14/2.39 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | v1 = v0 | ~ (less(v0,
% 11.14/2.39 v1) = v2) | ~ $i(v1) | ~ $i(v0) | greater(v0, v1) = 0)
% 11.14/2.39
% 11.14/2.39 (ass(cond(goal(130), 0), 2))
% 11.14/2.39 ! [v0: $i] : ! [v1: $i] : ( ~ (less(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) |
% 11.14/2.39 ? [v2: int] : ( ~ (v2 = 0) & greater(v0, v1) = v2))
% 11.14/2.39
% 11.14/2.39 (ass(cond(goal(193), 0), 2))
% 11.14/2.40 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 11.14/2.40 int] : (v5 = 0 | ~ (greater(v3, v4) = v5) | ~ (vplus(v1, v2) = v4) | ~
% 11.14/2.40 (vplus(v0, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: int] : (
% 11.14/2.40 ~ (v6 = 0) & greater(v0, v1) = v6))
% 11.14/2.40
% 11.14/2.40 (holds(antec(conjunct2(conjunct2(204))), 335, 0))
% 11.14/2.40 $i(vd330) & $i(vd329) & $i(vd328) & ? [v0: $i] : ? [v1: $i] : (vplus(vd329,
% 11.14/2.40 vd330) = v1 & vplus(vd328, vd330) = v0 & less(v0, v1) = 0 & $i(v1) &
% 11.14/2.40 $i(v0))
% 11.14/2.40
% 11.14/2.40 (holds(conseq(conjunct2(conjunct2(204))), 336, 0))
% 11.14/2.40 $i(vd329) & $i(vd328) & ? [v0: int] : ( ~ (v0 = 0) & less(vd328, vd329) = v0)
% 11.14/2.40
% 11.14/2.40 (function-axioms)
% 11.14/2.41 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 11.14/2.41 [v3: $i] : (v1 = v0 | ~ (greater(v3, v2) = v1) | ~ (greater(v3, v2) = v0)) &
% 11.14/2.41 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 11.14/2.41 (vplus(v3, v2) = v1) | ~ (vplus(v3, v2) = v0)) & ! [v0: MultipleValueBool]
% 11.14/2.41 : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 11.14/2.41 (less(v3, v2) = v1) | ~ (less(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] :
% 11.14/2.41 ! [v2: $i] : (v1 = v0 | ~ (vsucc(v2) = v1) | ~ (vsucc(v2) = v0))
% 11.14/2.41
% 11.14/2.41 Further assumptions not needed in the proof:
% 11.14/2.41 --------------------------------------------
% 11.14/2.41 ass(cond(140, 0), 0), ass(cond(33, 0), 0), ass(cond(43, 0), 0), ass(cond(52, 0),
% 11.14/2.41 0), ass(cond(73, 0), 0), ass(cond(81, 0), 0), ass(cond(goal(130), 0), 1),
% 11.14/2.41 ass(cond(goal(130), 0), 3), ass(cond(goal(193), 0), 0), ass(cond(goal(193), 0),
% 11.14/2.41 1), ass(cond(goal(88), 0), 0), ass(cond(goal(88), 0), 1), ass(cond(goal(88),
% 11.14/2.41 0), 2), ass(cond(goal(88), 0), 3), def(cond(conseq(axiom(3)), 11), 1),
% 11.14/2.41 def(cond(conseq(axiom(3)), 12), 1), qu(cond(conseq(axiom(3)), 3),
% 11.14/2.41 and(holds(definiens(29), 45, 0), holds(definiens(29), 44, 0)))
% 11.14/2.41
% 11.14/2.41 Those formulas are unsatisfiable:
% 11.14/2.41 ---------------------------------
% 11.14/2.41
% 11.14/2.41 Begin of proof
% 11.14/2.41 |
% 11.14/2.41 | ALPHA: (holds(antec(conjunct2(conjunct2(204))), 335, 0)) implies:
% 11.14/2.42 | (1) ? [v0: $i] : ? [v1: $i] : (vplus(vd329, vd330) = v1 & vplus(vd328,
% 11.14/2.42 | vd330) = v0 & less(v0, v1) = 0 & $i(v1) & $i(v0))
% 11.14/2.42 |
% 11.14/2.42 | ALPHA: (ass(cond(conjunct1(conjunct2(204)), 0), 0)) implies:
% 11.14/2.42 | (2) ? [v0: $i] : ? [v1: $i] : (vplus(vd329, vd330) = v1 & vplus(vd328,
% 11.14/2.42 | vd330) = v0 & $i(v1) & $i(v0) & ( ~ (v1 = v0) | vd329 = vd328))
% 11.14/2.42 |
% 11.14/2.42 | ALPHA: (ass(cond(conjunct1(204), 0), 0)) implies:
% 11.14/2.42 | (3) $i(vd330)
% 11.14/2.42 | (4) ? [v0: $i] : ? [v1: $i] : ? [v2: any] : ? [v3: any] : (greater(v0,
% 11.14/2.42 | v1) = v2 & greater(vd328, vd329) = v3 & vplus(vd329, vd330) = v1 &
% 11.14/2.42 | vplus(vd328, vd330) = v0 & $i(v1) & $i(v0) & ( ~ (v2 = 0) | v3 = 0))
% 11.14/2.42 |
% 11.14/2.42 | ALPHA: (holds(conseq(conjunct2(conjunct2(204))), 336, 0)) implies:
% 11.14/2.43 | (5) $i(vd328)
% 11.14/2.43 | (6) $i(vd329)
% 11.14/2.43 | (7) ? [v0: int] : ( ~ (v0 = 0) & less(vd328, vd329) = v0)
% 11.14/2.43 |
% 11.14/2.43 | ALPHA: (function-axioms) implies:
% 11.53/2.43 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 11.53/2.43 | (vplus(v3, v2) = v1) | ~ (vplus(v3, v2) = v0))
% 11.53/2.43 | (9) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 11.53/2.43 | ! [v3: $i] : (v1 = v0 | ~ (greater(v3, v2) = v1) | ~ (greater(v3,
% 11.53/2.43 | v2) = v0))
% 11.53/2.43 |
% 11.53/2.43 | DELTA: instantiating (7) with fresh symbol all_20_0 gives:
% 11.53/2.43 | (10) ~ (all_20_0 = 0) & less(vd328, vd329) = all_20_0
% 11.53/2.43 |
% 11.53/2.43 | ALPHA: (10) implies:
% 11.53/2.43 | (11) ~ (all_20_0 = 0)
% 11.53/2.43 | (12) less(vd328, vd329) = all_20_0
% 11.53/2.43 |
% 11.53/2.43 | DELTA: instantiating (1) with fresh symbols all_24_0, all_24_1 gives:
% 11.53/2.43 | (13) vplus(vd329, vd330) = all_24_0 & vplus(vd328, vd330) = all_24_1 &
% 11.53/2.43 | less(all_24_1, all_24_0) = 0 & $i(all_24_0) & $i(all_24_1)
% 11.53/2.43 |
% 11.53/2.43 | ALPHA: (13) implies:
% 11.53/2.44 | (14) less(all_24_1, all_24_0) = 0
% 11.53/2.44 | (15) vplus(vd328, vd330) = all_24_1
% 11.53/2.44 | (16) vplus(vd329, vd330) = all_24_0
% 11.53/2.44 |
% 11.53/2.44 | DELTA: instantiating (2) with fresh symbols all_28_0, all_28_1 gives:
% 11.53/2.44 | (17) vplus(vd329, vd330) = all_28_0 & vplus(vd328, vd330) = all_28_1 &
% 11.53/2.44 | $i(all_28_0) & $i(all_28_1) & ( ~ (all_28_0 = all_28_1) | vd329 =
% 11.53/2.44 | vd328)
% 11.53/2.44 |
% 11.53/2.44 | ALPHA: (17) implies:
% 11.53/2.44 | (18) $i(all_28_1)
% 11.53/2.44 | (19) $i(all_28_0)
% 11.53/2.44 | (20) vplus(vd328, vd330) = all_28_1
% 11.53/2.44 | (21) vplus(vd329, vd330) = all_28_0
% 11.53/2.44 |
% 11.53/2.44 | DELTA: instantiating (4) with fresh symbols all_33_0, all_33_1, all_33_2,
% 11.53/2.44 | all_33_3 gives:
% 11.53/2.44 | (22) greater(all_33_3, all_33_2) = all_33_1 & greater(vd328, vd329) =
% 11.53/2.44 | all_33_0 & vplus(vd329, vd330) = all_33_2 & vplus(vd328, vd330) =
% 11.53/2.44 | all_33_3 & $i(all_33_2) & $i(all_33_3) & ( ~ (all_33_1 = 0) | all_33_0
% 11.53/2.44 | = 0)
% 11.53/2.44 |
% 11.53/2.44 | ALPHA: (22) implies:
% 11.53/2.44 | (23) vplus(vd328, vd330) = all_33_3
% 11.53/2.44 | (24) vplus(vd329, vd330) = all_33_2
% 11.53/2.44 | (25) greater(vd328, vd329) = all_33_0
% 11.53/2.44 | (26) greater(all_33_3, all_33_2) = all_33_1
% 11.53/2.44 |
% 11.53/2.44 | GROUND_INST: instantiating (8) with all_28_1, all_33_3, vd330, vd328,
% 11.53/2.44 | simplifying with (20), (23) gives:
% 11.53/2.44 | (27) all_33_3 = all_28_1
% 11.53/2.44 |
% 11.53/2.44 | GROUND_INST: instantiating (8) with all_24_1, all_33_3, vd330, vd328,
% 11.53/2.44 | simplifying with (15), (23) gives:
% 11.53/2.45 | (28) all_33_3 = all_24_1
% 11.53/2.45 |
% 11.53/2.45 | GROUND_INST: instantiating (8) with all_28_0, all_33_2, vd330, vd329,
% 11.53/2.45 | simplifying with (21), (24) gives:
% 11.53/2.45 | (29) all_33_2 = all_28_0
% 11.53/2.45 |
% 11.53/2.45 | GROUND_INST: instantiating (8) with all_24_0, all_33_2, vd330, vd329,
% 11.53/2.45 | simplifying with (16), (24) gives:
% 11.53/2.45 | (30) all_33_2 = all_24_0
% 11.53/2.45 |
% 11.53/2.45 | COMBINE_EQS: (29), (30) imply:
% 11.53/2.45 | (31) all_28_0 = all_24_0
% 11.53/2.45 |
% 11.53/2.45 | SIMP: (31) implies:
% 11.53/2.45 | (32) all_28_0 = all_24_0
% 11.53/2.45 |
% 11.53/2.45 | COMBINE_EQS: (27), (28) imply:
% 11.53/2.45 | (33) all_28_1 = all_24_1
% 11.53/2.45 |
% 11.53/2.45 | REDUCE: (26), (28), (30) imply:
% 11.53/2.45 | (34) greater(all_24_1, all_24_0) = all_33_1
% 11.53/2.45 |
% 11.53/2.45 | REDUCE: (19), (32) imply:
% 11.53/2.45 | (35) $i(all_24_0)
% 11.53/2.45 |
% 11.53/2.45 | REDUCE: (18), (33) imply:
% 11.53/2.45 | (36) $i(all_24_1)
% 11.53/2.45 |
% 11.53/2.45 | GROUND_INST: instantiating (ass(cond(goal(130), 0), 0)) with vd328, vd329,
% 11.53/2.45 | all_20_0, simplifying with (5), (6), (12) gives:
% 11.53/2.45 | (37) all_20_0 = 0 | vd329 = vd328 | greater(vd328, vd329) = 0
% 11.53/2.45 |
% 11.53/2.45 | GROUND_INST: instantiating (ass(cond(147, 0), 0)) with all_24_1, all_24_0,
% 11.53/2.45 | simplifying with (14), (35), (36) gives:
% 11.53/2.45 | (38) greater(all_24_0, all_24_1) = 0
% 11.53/2.45 |
% 11.53/2.45 | GROUND_INST: instantiating (ass(cond(goal(130), 0), 2)) with all_24_1,
% 11.53/2.45 | all_24_0, simplifying with (14), (35), (36) gives:
% 11.53/2.45 | (39) ? [v0: int] : ( ~ (v0 = 0) & greater(all_24_1, all_24_0) = v0)
% 11.53/2.45 |
% 11.53/2.45 | GROUND_INST: instantiating (ass(cond(61, 0), 0)) with vd328, vd330, all_24_1,
% 11.53/2.45 | simplifying with (3), (5), (15) gives:
% 11.53/2.45 | (40) vplus(vd330, vd328) = all_24_1 & $i(all_24_1)
% 11.53/2.46 |
% 11.53/2.46 | ALPHA: (40) implies:
% 11.53/2.46 | (41) vplus(vd330, vd328) = all_24_1
% 11.53/2.46 |
% 11.53/2.46 | GROUND_INST: instantiating (ass(cond(61, 0), 0)) with vd329, vd330, all_24_0,
% 11.53/2.46 | simplifying with (3), (6), (16) gives:
% 11.53/2.46 | (42) vplus(vd330, vd329) = all_24_0 & $i(all_24_0)
% 11.53/2.46 |
% 11.53/2.46 | ALPHA: (42) implies:
% 11.53/2.46 | (43) vplus(vd330, vd329) = all_24_0
% 11.53/2.46 |
% 11.53/2.46 | GROUND_INST: instantiating (ass(cond(goal(193), 0), 2)) with vd328, vd329,
% 11.53/2.46 | vd330, all_24_1, all_24_0, all_33_1, simplifying with (3), (5),
% 11.53/2.46 | (6), (15), (16), (34) gives:
% 11.53/2.46 | (44) all_33_1 = 0 | ? [v0: int] : ( ~ (v0 = 0) & greater(vd328, vd329) =
% 11.53/2.46 | v0)
% 11.53/2.46 |
% 11.53/2.46 | DELTA: instantiating (39) with fresh symbol all_45_0 gives:
% 11.53/2.46 | (45) ~ (all_45_0 = 0) & greater(all_24_1, all_24_0) = all_45_0
% 11.53/2.46 |
% 11.53/2.46 | ALPHA: (45) implies:
% 11.53/2.46 | (46) ~ (all_45_0 = 0)
% 11.53/2.46 | (47) greater(all_24_1, all_24_0) = all_45_0
% 11.53/2.46 |
% 11.53/2.46 | GROUND_INST: instantiating (9) with all_33_1, all_45_0, all_24_0, all_24_1,
% 11.53/2.46 | simplifying with (34), (47) gives:
% 11.53/2.46 | (48) all_45_0 = all_33_1
% 11.53/2.46 |
% 11.53/2.46 | REDUCE: (46), (48) imply:
% 11.53/2.46 | (49) ~ (all_33_1 = 0)
% 11.53/2.46 |
% 11.53/2.46 | BETA: splitting (44) gives:
% 11.53/2.46 |
% 11.53/2.46 | Case 1:
% 11.53/2.46 | |
% 11.53/2.46 | | (50) all_33_1 = 0
% 11.53/2.46 | |
% 11.53/2.46 | | REDUCE: (49), (50) imply:
% 11.53/2.46 | | (51) $false
% 11.53/2.47 | |
% 11.53/2.47 | | CLOSE: (51) is inconsistent.
% 11.53/2.47 | |
% 11.53/2.47 | Case 2:
% 11.53/2.47 | |
% 11.53/2.47 | | (52) ? [v0: int] : ( ~ (v0 = 0) & greater(vd328, vd329) = v0)
% 11.53/2.47 | |
% 11.53/2.47 | | DELTA: instantiating (52) with fresh symbol all_71_0 gives:
% 11.53/2.47 | | (53) ~ (all_71_0 = 0) & greater(vd328, vd329) = all_71_0
% 11.53/2.47 | |
% 11.53/2.47 | | ALPHA: (53) implies:
% 11.53/2.47 | | (54) ~ (all_71_0 = 0)
% 11.53/2.47 | | (55) greater(vd328, vd329) = all_71_0
% 11.53/2.47 | |
% 11.53/2.47 | | GROUND_INST: instantiating (9) with all_33_0, all_71_0, vd329, vd328,
% 11.53/2.47 | | simplifying with (25), (55) gives:
% 11.53/2.47 | | (56) all_71_0 = all_33_0
% 11.53/2.47 | |
% 11.53/2.47 | | REDUCE: (54), (56) imply:
% 11.53/2.47 | | (57) ~ (all_33_0 = 0)
% 11.53/2.47 | |
% 11.53/2.47 | | BETA: splitting (37) gives:
% 11.53/2.47 | |
% 11.53/2.47 | | Case 1:
% 11.53/2.47 | | |
% 11.53/2.47 | | | (58) greater(vd328, vd329) = 0
% 11.53/2.47 | | |
% 11.53/2.47 | | | GROUND_INST: instantiating (9) with all_33_0, 0, vd329, vd328, simplifying
% 11.53/2.47 | | | with (25), (58) gives:
% 11.53/2.47 | | | (59) all_33_0 = 0
% 11.53/2.47 | | |
% 11.53/2.47 | | | REDUCE: (57), (59) imply:
% 11.53/2.47 | | | (60) $false
% 11.53/2.47 | | |
% 11.53/2.47 | | | CLOSE: (60) is inconsistent.
% 11.53/2.47 | | |
% 11.53/2.47 | | Case 2:
% 11.53/2.47 | | |
% 11.53/2.47 | | | (61) all_20_0 = 0 | vd329 = vd328
% 11.53/2.47 | | |
% 11.53/2.47 | | | BETA: splitting (61) gives:
% 11.53/2.47 | | |
% 11.53/2.47 | | | Case 1:
% 11.53/2.47 | | | |
% 11.53/2.47 | | | | (62) vd329 = vd328
% 11.53/2.47 | | | |
% 11.53/2.47 | | | | REDUCE: (43), (62) imply:
% 11.53/2.47 | | | | (63) vplus(vd330, vd328) = all_24_0
% 11.53/2.47 | | | |
% 11.53/2.47 | | | | GROUND_INST: instantiating (8) with all_24_1, all_24_0, vd328, vd330,
% 11.53/2.47 | | | | simplifying with (41), (63) gives:
% 11.53/2.48 | | | | (64) all_24_0 = all_24_1
% 11.53/2.48 | | | |
% 11.53/2.48 | | | | REDUCE: (38), (64) imply:
% 11.53/2.48 | | | | (65) greater(all_24_1, all_24_1) = 0
% 11.53/2.48 | | | |
% 11.53/2.48 | | | | REDUCE: (34), (64) imply:
% 11.53/2.48 | | | | (66) greater(all_24_1, all_24_1) = all_33_1
% 11.53/2.48 | | | |
% 11.53/2.48 | | | | GROUND_INST: instantiating (9) with 0, all_33_1, all_24_1, all_24_1,
% 11.53/2.48 | | | | simplifying with (65), (66) gives:
% 11.53/2.48 | | | | (67) all_33_1 = 0
% 11.53/2.48 | | | |
% 11.53/2.48 | | | | REDUCE: (49), (67) imply:
% 11.53/2.48 | | | | (68) $false
% 11.53/2.48 | | | |
% 11.53/2.48 | | | | CLOSE: (68) is inconsistent.
% 11.53/2.48 | | | |
% 11.53/2.48 | | | Case 2:
% 11.53/2.48 | | | |
% 11.53/2.48 | | | | (69) all_20_0 = 0
% 11.53/2.48 | | | |
% 11.53/2.48 | | | | REDUCE: (11), (69) imply:
% 11.78/2.48 | | | | (70) $false
% 11.78/2.48 | | | |
% 11.78/2.48 | | | | CLOSE: (70) is inconsistent.
% 11.78/2.48 | | | |
% 11.78/2.48 | | | End of split
% 11.78/2.48 | | |
% 11.78/2.48 | | End of split
% 11.78/2.48 | |
% 11.78/2.48 | End of split
% 11.78/2.48 |
% 11.78/2.48 End of proof
% 11.78/2.48 % SZS output end Proof for theBenchmark
% 11.78/2.48
% 11.78/2.48 1852ms
%------------------------------------------------------------------------------