TSTP Solution File: NUM840+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : NUM840+1 : TPTP v8.1.2. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n016.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 9.24s 2.21s
% Output : Proof 12.84s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : NUM840+1 : TPTP v8.1.2. Released v4.1.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.14/0.35 % Computer : n016.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Fri Aug 25 14:42:10 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.21/0.61 ________ _____
% 0.21/0.61 ___ __ \_________(_)________________________________
% 0.21/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.21/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.21/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.21/0.61
% 0.21/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.21/0.61 (2023-06-19)
% 0.21/0.61
% 0.21/0.61 (c) Philipp Rümmer, 2009-2023
% 0.21/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.21/0.61 Amanda Stjerna.
% 0.21/0.61 Free software under BSD-3-Clause.
% 0.21/0.61
% 0.21/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.21/0.61
% 0.21/0.61 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.21/0.62 Running up to 7 provers in parallel.
% 0.21/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.21/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.21/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.21/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.21/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.21/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 0.21/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 2.94/1.18 Prover 1: Preprocessing ...
% 2.94/1.18 Prover 4: Preprocessing ...
% 3.23/1.22 Prover 3: Preprocessing ...
% 3.23/1.22 Prover 5: Preprocessing ...
% 3.23/1.22 Prover 0: Preprocessing ...
% 3.23/1.22 Prover 6: Preprocessing ...
% 3.23/1.22 Prover 2: Preprocessing ...
% 6.44/1.70 Prover 1: Warning: ignoring some quantifiers
% 6.44/1.73 Prover 3: Warning: ignoring some quantifiers
% 7.04/1.73 Prover 5: Proving ...
% 7.04/1.73 Prover 6: Proving ...
% 7.04/1.74 Prover 1: Constructing countermodel ...
% 7.04/1.74 Prover 3: Constructing countermodel ...
% 7.04/1.76 Prover 4: Warning: ignoring some quantifiers
% 7.04/1.78 Prover 2: Proving ...
% 7.46/1.81 Prover 4: Constructing countermodel ...
% 7.46/1.85 Prover 0: Proving ...
% 9.24/2.21 Prover 0: proved (1587ms)
% 9.24/2.21
% 9.24/2.21 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 9.24/2.21
% 9.24/2.22 Prover 3: stopped
% 9.24/2.22 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 9.24/2.22 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 9.24/2.22 Prover 2: stopped
% 9.24/2.22 Prover 5: stopped
% 10.08/2.26 Prover 6: stopped
% 10.08/2.27 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 10.08/2.27 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 10.08/2.27 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 10.08/2.28 Prover 7: Preprocessing ...
% 10.08/2.31 Prover 8: Preprocessing ...
% 11.23/2.32 Prover 11: Preprocessing ...
% 11.23/2.32 Prover 13: Preprocessing ...
% 11.23/2.32 Prover 10: Preprocessing ...
% 11.36/2.38 Prover 4: Found proof (size 90)
% 11.36/2.39 Prover 4: proved (1754ms)
% 11.36/2.39 Prover 1: Found proof (size 84)
% 11.36/2.39 Prover 1: proved (1764ms)
% 11.36/2.40 Prover 11: stopped
% 11.36/2.40 Prover 7: Warning: ignoring some quantifiers
% 11.36/2.41 Prover 7: Constructing countermodel ...
% 11.99/2.42 Prover 10: Warning: ignoring some quantifiers
% 11.99/2.42 Prover 13: Warning: ignoring some quantifiers
% 11.99/2.42 Prover 7: stopped
% 11.99/2.43 Prover 10: Constructing countermodel ...
% 11.99/2.43 Prover 13: Constructing countermodel ...
% 11.99/2.43 Prover 10: stopped
% 11.99/2.43 Prover 13: stopped
% 11.99/2.44 Prover 8: Warning: ignoring some quantifiers
% 11.99/2.46 Prover 8: Constructing countermodel ...
% 11.99/2.47 Prover 8: stopped
% 11.99/2.47
% 11.99/2.47 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 11.99/2.47
% 11.99/2.48 % SZS output start Proof for theBenchmark
% 12.38/2.49 Assumptions after simplification:
% 12.38/2.49 ---------------------------------
% 12.38/2.49
% 12.38/2.49 (ass(cond(140, 0), 0))
% 12.38/2.51 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (less(v1, v0) = v2) |
% 12.38/2.51 ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ( ~ (v3 = 0) & greater(v0, v1) = v3))
% 12.38/2.51 & ! [v0: $i] : ! [v1: $i] : ( ~ (greater(v0, v1) = 0) | ~ $i(v1) | ~
% 12.38/2.51 $i(v0) | less(v1, v0) = 0)
% 12.38/2.51
% 12.38/2.51 (ass(cond(147, 0), 0))
% 12.38/2.51 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (greater(v1, v0) = v2)
% 12.38/2.51 | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ( ~ (v3 = 0) & less(v0, v1) = v3))
% 12.38/2.51 & ! [v0: $i] : ! [v1: $i] : ( ~ (less(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) |
% 12.38/2.51 greater(v1, v0) = 0)
% 12.38/2.51
% 12.38/2.51 (ass(cond(61, 0), 0))
% 12.38/2.52 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (vplus(v1, v0) = v2) | ~ $i(v1)
% 12.38/2.52 | ~ $i(v0) | (vplus(v0, v1) = v2 & $i(v2))) & ! [v0: $i] : ! [v1: $i] :
% 12.38/2.52 ! [v2: $i] : ( ~ (vplus(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | (vplus(v1, v0)
% 12.38/2.52 = v2 & $i(v2)))
% 12.38/2.52
% 12.38/2.52 (ass(cond(conjunct1(204), 0), 0))
% 12.38/2.52 $i(vd330) & $i(vd329) & $i(vd328) & ? [v0: $i] : ? [v1: $i] : ? [v2: any] :
% 12.38/2.52 ? [v3: any] : (greater(v0, v1) = v2 & greater(vd328, vd329) = v3 &
% 12.38/2.52 vplus(vd329, vd330) = v1 & vplus(vd328, vd330) = v0 & $i(v1) & $i(v0) & ( ~
% 12.38/2.52 (v2 = 0) | v3 = 0))
% 12.38/2.52
% 12.38/2.52 (ass(cond(conjunct1(conjunct2(204)), 0), 0))
% 12.38/2.52 $i(vd330) & $i(vd329) & $i(vd328) & ? [v0: $i] : ? [v1: $i] : (vplus(vd329,
% 12.38/2.52 vd330) = v1 & vplus(vd328, vd330) = v0 & $i(v1) & $i(v0) & ( ~ (v1 = v0) |
% 12.38/2.52 vd329 = vd328))
% 12.38/2.52
% 12.38/2.52 (ass(cond(goal(130), 0), 0))
% 12.38/2.52 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | v1 = v0 | ~ (greater(v0,
% 12.38/2.52 v1) = v2) | ~ $i(v1) | ~ $i(v0) | less(v0, v1) = 0) & ! [v0: $i] : !
% 12.38/2.52 [v1: $i] : ! [v2: int] : (v2 = 0 | v1 = v0 | ~ (less(v0, v1) = v2) | ~
% 12.38/2.52 $i(v1) | ~ $i(v0) | greater(v0, v1) = 0)
% 12.38/2.52
% 12.38/2.52 (ass(cond(goal(130), 0), 2))
% 12.38/2.52 ! [v0: $i] : ! [v1: $i] : ( ~ (greater(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0)
% 12.38/2.52 | ? [v2: int] : ( ~ (v2 = 0) & less(v0, v1) = v2)) & ! [v0: $i] : ! [v1:
% 12.38/2.52 $i] : ( ~ (less(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: int] : ( ~
% 12.38/2.53 (v2 = 0) & greater(v0, v1) = v2))
% 12.38/2.53
% 12.38/2.53 (ass(cond(goal(193), 0), 2))
% 12.38/2.53 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 12.38/2.53 int] : (v5 = 0 | ~ (greater(v3, v4) = v5) | ~ (vplus(v1, v2) = v4) | ~
% 12.38/2.53 (vplus(v0, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: int] : (
% 12.38/2.53 ~ (v6 = 0) & greater(v0, v1) = v6))
% 12.38/2.53
% 12.38/2.53 (holds(antec(conjunct2(conjunct2(204))), 335, 0))
% 12.38/2.53 $i(vd330) & $i(vd329) & $i(vd328) & ? [v0: $i] : ? [v1: $i] : (vplus(vd329,
% 12.38/2.53 vd330) = v1 & vplus(vd328, vd330) = v0 & less(v0, v1) = 0 & $i(v1) &
% 12.38/2.53 $i(v0))
% 12.38/2.53
% 12.38/2.53 (holds(conseq(conjunct2(conjunct2(204))), 336, 0))
% 12.38/2.53 $i(vd329) & $i(vd328) & ? [v0: int] : ( ~ (v0 = 0) & less(vd328, vd329) = v0)
% 12.38/2.53
% 12.38/2.53 (function-axioms)
% 12.38/2.53 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 12.38/2.53 [v3: $i] : (v1 = v0 | ~ (geq(v3, v2) = v1) | ~ (geq(v3, v2) = v0)) & ! [v0:
% 12.38/2.53 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 12.38/2.53 : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = v0)) & ! [v0:
% 12.38/2.53 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 12.38/2.53 : (v1 = v0 | ~ (greater(v3, v2) = v1) | ~ (greater(v3, v2) = v0)) & ! [v0:
% 12.38/2.53 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (vplus(v3, v2)
% 12.38/2.53 = v1) | ~ (vplus(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 12.38/2.53 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (less(v3, v2)
% 12.38/2.53 = v1) | ~ (less(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i]
% 12.38/2.53 : (v1 = v0 | ~ (vskolem2(v2) = v1) | ~ (vskolem2(v2) = v0)) & ! [v0: $i] :
% 12.38/2.53 ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (vsucc(v2) = v1) | ~ (vsucc(v2) =
% 12.38/2.53 v0))
% 12.38/2.53
% 12.38/2.53 Further assumptions not needed in the proof:
% 12.38/2.53 --------------------------------------------
% 12.38/2.53 ass(cond(12, 0), 0), ass(cond(158, 0), 0), ass(cond(163, 0), 0), ass(cond(168,
% 12.38/2.53 0), 0), ass(cond(184, 0), 0), ass(cond(189, 0), 0), ass(cond(20, 0), 0),
% 12.38/2.53 ass(cond(33, 0), 0), ass(cond(43, 0), 0), ass(cond(52, 0), 0), ass(cond(6, 0),
% 12.38/2.53 0), ass(cond(73, 0), 0), ass(cond(81, 0), 0), ass(cond(goal(130), 0), 1),
% 12.38/2.53 ass(cond(goal(130), 0), 3), ass(cond(goal(177), 0), 0), ass(cond(goal(193), 0),
% 12.38/2.53 0), ass(cond(goal(193), 0), 1), ass(cond(goal(88), 0), 0), ass(cond(goal(88),
% 12.38/2.53 0), 1), ass(cond(goal(88), 0), 2), ass(cond(goal(88), 0), 3),
% 12.38/2.53 def(cond(conseq(axiom(3)), 11), 1), def(cond(conseq(axiom(3)), 12), 1),
% 12.38/2.53 def(cond(conseq(axiom(3)), 16), 1), def(cond(conseq(axiom(3)), 17), 1),
% 12.38/2.53 qu(antec(axiom(3)), imp(antec(axiom(3)))), qu(cond(conseq(axiom(3)), 3),
% 12.38/2.53 and(holds(definiens(29), 45, 0), holds(definiens(29), 44, 0))),
% 12.38/2.53 qu(restrictor(axiom(1)), holds(scope(axiom(1)), 2, 0))
% 12.38/2.53
% 12.38/2.53 Those formulas are unsatisfiable:
% 12.38/2.53 ---------------------------------
% 12.38/2.53
% 12.38/2.53 Begin of proof
% 12.38/2.53 |
% 12.38/2.53 | ALPHA: (holds(antec(conjunct2(conjunct2(204))), 335, 0)) implies:
% 12.38/2.54 | (1) ? [v0: $i] : ? [v1: $i] : (vplus(vd329, vd330) = v1 & vplus(vd328,
% 12.38/2.54 | vd330) = v0 & less(v0, v1) = 0 & $i(v1) & $i(v0))
% 12.38/2.54 |
% 12.38/2.54 | ALPHA: (ass(cond(conjunct1(conjunct2(204)), 0), 0)) implies:
% 12.38/2.54 | (2) ? [v0: $i] : ? [v1: $i] : (vplus(vd329, vd330) = v1 & vplus(vd328,
% 12.38/2.54 | vd330) = v0 & $i(v1) & $i(v0) & ( ~ (v1 = v0) | vd329 = vd328))
% 12.38/2.54 |
% 12.38/2.54 | ALPHA: (ass(cond(conjunct1(204), 0), 0)) implies:
% 12.38/2.54 | (3) $i(vd330)
% 12.38/2.54 | (4) ? [v0: $i] : ? [v1: $i] : ? [v2: any] : ? [v3: any] : (greater(v0,
% 12.38/2.54 | v1) = v2 & greater(vd328, vd329) = v3 & vplus(vd329, vd330) = v1 &
% 12.38/2.54 | vplus(vd328, vd330) = v0 & $i(v1) & $i(v0) & ( ~ (v2 = 0) | v3 = 0))
% 12.38/2.54 |
% 12.38/2.54 | ALPHA: (ass(cond(147, 0), 0)) implies:
% 12.38/2.54 | (5) ! [v0: $i] : ! [v1: $i] : ( ~ (less(v0, v1) = 0) | ~ $i(v1) | ~
% 12.38/2.54 | $i(v0) | greater(v1, v0) = 0)
% 12.38/2.54 |
% 12.38/2.54 | ALPHA: (ass(cond(140, 0), 0)) implies:
% 12.38/2.54 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (less(v1, v0) =
% 12.38/2.54 | v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ( ~ (v3 = 0) &
% 12.38/2.54 | greater(v0, v1) = v3))
% 12.38/2.54 |
% 12.38/2.54 | ALPHA: (ass(cond(goal(130), 0), 0)) implies:
% 12.38/2.54 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | v1 = v0 | ~
% 12.38/2.54 | (less(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | greater(v0, v1) = 0)
% 12.38/2.54 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | v1 = v0 | ~
% 12.38/2.54 | (greater(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | less(v0, v1) = 0)
% 12.38/2.54 |
% 12.38/2.54 | ALPHA: (ass(cond(goal(130), 0), 2)) implies:
% 12.38/2.54 | (9) ! [v0: $i] : ! [v1: $i] : ( ~ (less(v0, v1) = 0) | ~ $i(v1) | ~
% 12.38/2.54 | $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & greater(v0, v1) = v2))
% 12.38/2.54 |
% 12.38/2.54 | ALPHA: (ass(cond(61, 0), 0)) implies:
% 12.38/2.54 | (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (vplus(v1, v0) = v2) |
% 12.38/2.54 | ~ $i(v1) | ~ $i(v0) | (vplus(v0, v1) = v2 & $i(v2)))
% 12.38/2.54 |
% 12.38/2.54 | ALPHA: (holds(conseq(conjunct2(conjunct2(204))), 336, 0)) implies:
% 12.38/2.55 | (11) $i(vd328)
% 12.38/2.55 | (12) $i(vd329)
% 12.38/2.55 | (13) ? [v0: int] : ( ~ (v0 = 0) & less(vd328, vd329) = v0)
% 12.38/2.55 |
% 12.38/2.55 | ALPHA: (function-axioms) implies:
% 12.38/2.55 | (14) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 12.38/2.55 | : ! [v3: $i] : (v1 = v0 | ~ (less(v3, v2) = v1) | ~ (less(v3, v2) =
% 12.38/2.55 | v0))
% 12.38/2.55 | (15) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 12.38/2.55 | (vplus(v3, v2) = v1) | ~ (vplus(v3, v2) = v0))
% 12.38/2.55 | (16) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 12.38/2.55 | : ! [v3: $i] : (v1 = v0 | ~ (greater(v3, v2) = v1) | ~ (greater(v3,
% 12.38/2.55 | v2) = v0))
% 12.38/2.55 |
% 12.38/2.55 | DELTA: instantiating (13) with fresh symbol all_36_0 gives:
% 12.38/2.55 | (17) ~ (all_36_0 = 0) & less(vd328, vd329) = all_36_0
% 12.38/2.55 |
% 12.38/2.55 | ALPHA: (17) implies:
% 12.38/2.55 | (18) ~ (all_36_0 = 0)
% 12.38/2.55 | (19) less(vd328, vd329) = all_36_0
% 12.38/2.55 |
% 12.38/2.55 | DELTA: instantiating (1) with fresh symbols all_38_0, all_38_1 gives:
% 12.38/2.55 | (20) vplus(vd329, vd330) = all_38_0 & vplus(vd328, vd330) = all_38_1 &
% 12.38/2.55 | less(all_38_1, all_38_0) = 0 & $i(all_38_0) & $i(all_38_1)
% 12.38/2.55 |
% 12.38/2.55 | ALPHA: (20) implies:
% 12.38/2.55 | (21) less(all_38_1, all_38_0) = 0
% 12.38/2.55 | (22) vplus(vd328, vd330) = all_38_1
% 12.38/2.55 | (23) vplus(vd329, vd330) = all_38_0
% 12.38/2.55 |
% 12.38/2.55 | DELTA: instantiating (2) with fresh symbols all_40_0, all_40_1 gives:
% 12.38/2.55 | (24) vplus(vd329, vd330) = all_40_0 & vplus(vd328, vd330) = all_40_1 &
% 12.38/2.55 | $i(all_40_0) & $i(all_40_1) & ( ~ (all_40_0 = all_40_1) | vd329 =
% 12.38/2.55 | vd328)
% 12.38/2.55 |
% 12.38/2.55 | ALPHA: (24) implies:
% 12.38/2.55 | (25) $i(all_40_1)
% 12.38/2.55 | (26) $i(all_40_0)
% 12.38/2.55 | (27) vplus(vd328, vd330) = all_40_1
% 12.38/2.55 | (28) vplus(vd329, vd330) = all_40_0
% 12.38/2.55 |
% 12.38/2.55 | DELTA: instantiating (4) with fresh symbols all_42_0, all_42_1, all_42_2,
% 12.38/2.55 | all_42_3 gives:
% 12.38/2.55 | (29) greater(all_42_3, all_42_2) = all_42_1 & greater(vd328, vd329) =
% 12.38/2.55 | all_42_0 & vplus(vd329, vd330) = all_42_2 & vplus(vd328, vd330) =
% 12.38/2.55 | all_42_3 & $i(all_42_2) & $i(all_42_3) & ( ~ (all_42_1 = 0) | all_42_0
% 12.38/2.55 | = 0)
% 12.38/2.55 |
% 12.38/2.55 | ALPHA: (29) implies:
% 12.38/2.55 | (30) vplus(vd328, vd330) = all_42_3
% 12.38/2.55 | (31) vplus(vd329, vd330) = all_42_2
% 12.38/2.55 | (32) greater(vd328, vd329) = all_42_0
% 12.38/2.55 | (33) greater(all_42_3, all_42_2) = all_42_1
% 12.38/2.55 |
% 12.38/2.56 | GROUND_INST: instantiating (15) with all_40_1, all_42_3, vd330, vd328,
% 12.38/2.56 | simplifying with (27), (30) gives:
% 12.38/2.56 | (34) all_42_3 = all_40_1
% 12.38/2.56 |
% 12.38/2.56 | GROUND_INST: instantiating (15) with all_38_1, all_42_3, vd330, vd328,
% 12.38/2.56 | simplifying with (22), (30) gives:
% 12.38/2.56 | (35) all_42_3 = all_38_1
% 12.38/2.56 |
% 12.38/2.56 | GROUND_INST: instantiating (15) with all_40_0, all_42_2, vd330, vd329,
% 12.38/2.56 | simplifying with (28), (31) gives:
% 12.38/2.56 | (36) all_42_2 = all_40_0
% 12.38/2.56 |
% 12.38/2.56 | GROUND_INST: instantiating (15) with all_38_0, all_42_2, vd330, vd329,
% 12.38/2.56 | simplifying with (23), (31) gives:
% 12.38/2.56 | (37) all_42_2 = all_38_0
% 12.38/2.56 |
% 12.38/2.56 | COMBINE_EQS: (36), (37) imply:
% 12.38/2.56 | (38) all_40_0 = all_38_0
% 12.38/2.56 |
% 12.38/2.56 | SIMP: (38) implies:
% 12.38/2.56 | (39) all_40_0 = all_38_0
% 12.38/2.56 |
% 12.38/2.56 | COMBINE_EQS: (34), (35) imply:
% 12.38/2.56 | (40) all_40_1 = all_38_1
% 12.38/2.56 |
% 12.38/2.56 | SIMP: (40) implies:
% 12.38/2.56 | (41) all_40_1 = all_38_1
% 12.38/2.56 |
% 12.38/2.56 | REDUCE: (33), (35), (37) imply:
% 12.38/2.56 | (42) greater(all_38_1, all_38_0) = all_42_1
% 12.38/2.56 |
% 12.38/2.56 | REDUCE: (26), (39) imply:
% 12.38/2.56 | (43) $i(all_38_0)
% 12.38/2.56 |
% 12.38/2.56 | REDUCE: (25), (41) imply:
% 12.38/2.56 | (44) $i(all_38_1)
% 12.38/2.56 |
% 12.38/2.56 | GROUND_INST: instantiating (7) with vd328, vd329, all_36_0, simplifying with
% 12.38/2.56 | (11), (12), (19) gives:
% 12.38/2.56 | (45) all_36_0 = 0 | vd329 = vd328 | greater(vd328, vd329) = 0
% 12.38/2.56 |
% 12.38/2.56 | GROUND_INST: instantiating (6) with vd329, vd328, all_36_0, simplifying with
% 12.38/2.56 | (11), (12), (19) gives:
% 12.38/2.56 | (46) all_36_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & greater(vd329, vd328) =
% 12.38/2.56 | v0)
% 12.38/2.56 |
% 12.38/2.56 | GROUND_INST: instantiating (5) with all_38_1, all_38_0, simplifying with (21),
% 12.38/2.56 | (43), (44) gives:
% 12.38/2.56 | (47) greater(all_38_0, all_38_1) = 0
% 12.38/2.56 |
% 12.38/2.56 | GROUND_INST: instantiating (9) with all_38_1, all_38_0, simplifying with (21),
% 12.38/2.56 | (43), (44) gives:
% 12.38/2.56 | (48) ? [v0: int] : ( ~ (v0 = 0) & greater(all_38_1, all_38_0) = v0)
% 12.38/2.56 |
% 12.38/2.56 | GROUND_INST: instantiating (10) with vd330, vd328, all_38_1, simplifying with
% 12.38/2.56 | (3), (11), (22) gives:
% 12.38/2.56 | (49) vplus(vd330, vd328) = all_38_1 & $i(all_38_1)
% 12.38/2.56 |
% 12.38/2.56 | ALPHA: (49) implies:
% 12.38/2.56 | (50) vplus(vd330, vd328) = all_38_1
% 12.38/2.56 |
% 12.38/2.56 | GROUND_INST: instantiating (10) with vd330, vd329, all_38_0, simplifying with
% 12.38/2.56 | (3), (12), (23) gives:
% 12.38/2.56 | (51) vplus(vd330, vd329) = all_38_0 & $i(all_38_0)
% 12.38/2.56 |
% 12.38/2.56 | ALPHA: (51) implies:
% 12.38/2.56 | (52) vplus(vd330, vd329) = all_38_0
% 12.38/2.56 |
% 12.38/2.56 | GROUND_INST: instantiating (8) with vd328, vd329, all_42_0, simplifying with
% 12.38/2.56 | (11), (12), (32) gives:
% 12.38/2.56 | (53) all_42_0 = 0 | vd329 = vd328 | less(vd328, vd329) = 0
% 12.38/2.56 |
% 12.38/2.56 | GROUND_INST: instantiating (ass(cond(goal(193), 0), 2)) with vd328, vd329,
% 12.38/2.57 | vd330, all_38_1, all_38_0, all_42_1, simplifying with (3), (11),
% 12.38/2.57 | (12), (22), (23), (42) gives:
% 12.78/2.57 | (54) all_42_1 = 0 | ? [v0: int] : ( ~ (v0 = 0) & greater(vd328, vd329) =
% 12.78/2.57 | v0)
% 12.78/2.57 |
% 12.78/2.57 | DELTA: instantiating (48) with fresh symbol all_57_0 gives:
% 12.78/2.57 | (55) ~ (all_57_0 = 0) & greater(all_38_1, all_38_0) = all_57_0
% 12.78/2.57 |
% 12.78/2.57 | ALPHA: (55) implies:
% 12.78/2.57 | (56) ~ (all_57_0 = 0)
% 12.78/2.57 | (57) greater(all_38_1, all_38_0) = all_57_0
% 12.78/2.57 |
% 12.78/2.57 | BETA: splitting (46) gives:
% 12.78/2.57 |
% 12.78/2.57 | Case 1:
% 12.78/2.57 | |
% 12.78/2.57 | | (58) all_36_0 = 0
% 12.78/2.57 | |
% 12.78/2.57 | | REDUCE: (18), (58) imply:
% 12.78/2.57 | | (59) $false
% 12.78/2.57 | |
% 12.78/2.57 | | CLOSE: (59) is inconsistent.
% 12.78/2.57 | |
% 12.78/2.57 | Case 2:
% 12.78/2.57 | |
% 12.78/2.57 | | (60) ? [v0: int] : ( ~ (v0 = 0) & greater(vd329, vd328) = v0)
% 12.78/2.57 | |
% 12.78/2.57 | | DELTA: instantiating (60) with fresh symbol all_73_0 gives:
% 12.78/2.57 | | (61) ~ (all_73_0 = 0) & greater(vd329, vd328) = all_73_0
% 12.78/2.57 | |
% 12.78/2.57 | | ALPHA: (61) implies:
% 12.78/2.57 | | (62) greater(vd329, vd328) = all_73_0
% 12.78/2.57 | |
% 12.78/2.57 | | GROUND_INST: instantiating (16) with all_42_1, all_57_0, all_38_0, all_38_1,
% 12.78/2.57 | | simplifying with (42), (57) gives:
% 12.78/2.57 | | (63) all_57_0 = all_42_1
% 12.78/2.57 | |
% 12.78/2.57 | | REDUCE: (56), (63) imply:
% 12.78/2.57 | | (64) ~ (all_42_1 = 0)
% 12.78/2.57 | |
% 12.78/2.57 | | BETA: splitting (54) gives:
% 12.78/2.57 | |
% 12.78/2.57 | | Case 1:
% 12.78/2.57 | | |
% 12.78/2.57 | | | (65) all_42_1 = 0
% 12.78/2.57 | | |
% 12.78/2.57 | | | REDUCE: (64), (65) imply:
% 12.78/2.57 | | | (66) $false
% 12.78/2.57 | | |
% 12.78/2.57 | | | CLOSE: (66) is inconsistent.
% 12.78/2.57 | | |
% 12.78/2.57 | | Case 2:
% 12.78/2.57 | | |
% 12.78/2.57 | | | (67) ? [v0: int] : ( ~ (v0 = 0) & greater(vd328, vd329) = v0)
% 12.78/2.57 | | |
% 12.78/2.57 | | | DELTA: instantiating (67) with fresh symbol all_93_0 gives:
% 12.78/2.57 | | | (68) ~ (all_93_0 = 0) & greater(vd328, vd329) = all_93_0
% 12.78/2.57 | | |
% 12.78/2.57 | | | ALPHA: (68) implies:
% 12.78/2.57 | | | (69) ~ (all_93_0 = 0)
% 12.78/2.57 | | | (70) greater(vd328, vd329) = all_93_0
% 12.78/2.57 | | |
% 12.78/2.57 | | | GROUND_INST: instantiating (16) with all_42_0, all_93_0, vd329, vd328,
% 12.78/2.57 | | | simplifying with (32), (70) gives:
% 12.78/2.57 | | | (71) all_93_0 = all_42_0
% 12.78/2.57 | | |
% 12.78/2.57 | | | REDUCE: (69), (71) imply:
% 12.78/2.57 | | | (72) ~ (all_42_0 = 0)
% 12.78/2.57 | | |
% 12.78/2.57 | | | BETA: splitting (45) gives:
% 12.78/2.57 | | |
% 12.78/2.57 | | | Case 1:
% 12.78/2.57 | | | |
% 12.78/2.57 | | | | (73) greater(vd328, vd329) = 0
% 12.78/2.57 | | | |
% 12.78/2.57 | | | | BETA: splitting (53) gives:
% 12.78/2.57 | | | |
% 12.78/2.57 | | | | Case 1:
% 12.78/2.57 | | | | |
% 12.78/2.57 | | | | | (74) less(vd328, vd329) = 0
% 12.78/2.57 | | | | |
% 12.78/2.57 | | | | | GROUND_INST: instantiating (14) with all_36_0, 0, vd329, vd328,
% 12.78/2.57 | | | | | simplifying with (19), (74) gives:
% 12.78/2.57 | | | | | (75) all_36_0 = 0
% 12.78/2.57 | | | | |
% 12.78/2.57 | | | | | REDUCE: (18), (75) imply:
% 12.78/2.57 | | | | | (76) $false
% 12.78/2.57 | | | | |
% 12.78/2.57 | | | | | CLOSE: (76) is inconsistent.
% 12.78/2.57 | | | | |
% 12.78/2.57 | | | | Case 2:
% 12.78/2.57 | | | | |
% 12.78/2.57 | | | | | (77) all_42_0 = 0 | vd329 = vd328
% 12.78/2.57 | | | | |
% 12.78/2.57 | | | | | BETA: splitting (77) gives:
% 12.78/2.57 | | | | |
% 12.78/2.57 | | | | | Case 1:
% 12.78/2.57 | | | | | |
% 12.78/2.57 | | | | | | (78) vd329 = vd328
% 12.78/2.57 | | | | | |
% 12.78/2.57 | | | | | | REDUCE: (62), (78) imply:
% 12.78/2.57 | | | | | | (79) greater(vd328, vd328) = all_73_0
% 12.78/2.57 | | | | | |
% 12.78/2.58 | | | | | | REDUCE: (32), (78) imply:
% 12.78/2.58 | | | | | | (80) greater(vd328, vd328) = all_42_0
% 12.78/2.58 | | | | | |
% 12.78/2.58 | | | | | | REDUCE: (73), (78) imply:
% 12.78/2.58 | | | | | | (81) greater(vd328, vd328) = 0
% 12.78/2.58 | | | | | |
% 12.78/2.58 | | | | | | GROUND_INST: instantiating (16) with all_42_0, all_73_0, vd328,
% 12.78/2.58 | | | | | | vd328, simplifying with (79), (80) gives:
% 12.78/2.58 | | | | | | (82) all_73_0 = all_42_0
% 12.78/2.58 | | | | | |
% 12.78/2.58 | | | | | | GROUND_INST: instantiating (16) with 0, all_73_0, vd328, vd328,
% 12.78/2.58 | | | | | | simplifying with (79), (81) gives:
% 12.78/2.58 | | | | | | (83) all_73_0 = 0
% 12.78/2.58 | | | | | |
% 12.78/2.58 | | | | | | COMBINE_EQS: (82), (83) imply:
% 12.78/2.58 | | | | | | (84) all_42_0 = 0
% 12.78/2.58 | | | | | |
% 12.78/2.58 | | | | | | REDUCE: (72), (84) imply:
% 12.78/2.58 | | | | | | (85) $false
% 12.78/2.58 | | | | | |
% 12.78/2.58 | | | | | | CLOSE: (85) is inconsistent.
% 12.78/2.58 | | | | | |
% 12.78/2.58 | | | | | Case 2:
% 12.78/2.58 | | | | | |
% 12.78/2.58 | | | | | | (86) all_42_0 = 0
% 12.78/2.58 | | | | | |
% 12.78/2.58 | | | | | | REDUCE: (72), (86) imply:
% 12.78/2.58 | | | | | | (87) $false
% 12.78/2.58 | | | | | |
% 12.78/2.58 | | | | | | CLOSE: (87) is inconsistent.
% 12.78/2.58 | | | | | |
% 12.78/2.58 | | | | | End of split
% 12.78/2.58 | | | | |
% 12.78/2.58 | | | | End of split
% 12.78/2.58 | | | |
% 12.78/2.58 | | | Case 2:
% 12.78/2.58 | | | |
% 12.78/2.58 | | | | (88) all_36_0 = 0 | vd329 = vd328
% 12.78/2.58 | | | |
% 12.78/2.58 | | | | BETA: splitting (88) gives:
% 12.78/2.58 | | | |
% 12.78/2.58 | | | | Case 1:
% 12.78/2.58 | | | | |
% 12.84/2.58 | | | | | (89) vd329 = vd328
% 12.84/2.58 | | | | |
% 12.84/2.58 | | | | | REDUCE: (52), (89) imply:
% 12.84/2.58 | | | | | (90) vplus(vd330, vd328) = all_38_0
% 12.84/2.58 | | | | |
% 12.84/2.58 | | | | | GROUND_INST: instantiating (15) with all_38_1, all_38_0, vd328, vd330,
% 12.84/2.58 | | | | | simplifying with (50), (90) gives:
% 12.84/2.58 | | | | | (91) all_38_0 = all_38_1
% 12.84/2.58 | | | | |
% 12.84/2.58 | | | | | REDUCE: (47), (91) imply:
% 12.84/2.58 | | | | | (92) greater(all_38_1, all_38_1) = 0
% 12.84/2.58 | | | | |
% 12.84/2.58 | | | | | REDUCE: (42), (91) imply:
% 12.84/2.58 | | | | | (93) greater(all_38_1, all_38_1) = all_42_1
% 12.84/2.58 | | | | |
% 12.84/2.58 | | | | | GROUND_INST: instantiating (16) with 0, all_42_1, all_38_1, all_38_1,
% 12.84/2.58 | | | | | simplifying with (92), (93) gives:
% 12.84/2.58 | | | | | (94) all_42_1 = 0
% 12.84/2.58 | | | | |
% 12.84/2.58 | | | | | REDUCE: (64), (94) imply:
% 12.84/2.58 | | | | | (95) $false
% 12.84/2.58 | | | | |
% 12.84/2.58 | | | | | CLOSE: (95) is inconsistent.
% 12.84/2.58 | | | | |
% 12.84/2.58 | | | | Case 2:
% 12.84/2.58 | | | | |
% 12.84/2.58 | | | | | (96) all_36_0 = 0
% 12.84/2.58 | | | | |
% 12.84/2.58 | | | | | REDUCE: (18), (96) imply:
% 12.84/2.58 | | | | | (97) $false
% 12.84/2.58 | | | | |
% 12.84/2.58 | | | | | CLOSE: (97) is inconsistent.
% 12.84/2.58 | | | | |
% 12.84/2.58 | | | | End of split
% 12.84/2.58 | | | |
% 12.84/2.58 | | | End of split
% 12.84/2.58 | | |
% 12.84/2.58 | | End of split
% 12.84/2.58 | |
% 12.84/2.58 | End of split
% 12.84/2.58 |
% 12.84/2.58 End of proof
% 12.84/2.58 % SZS output end Proof for theBenchmark
% 12.84/2.58
% 12.84/2.58 1974ms
%------------------------------------------------------------------------------