TSTP Solution File: NUM844+2 by Princess---230619
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : NUM844+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 : n012.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 11:50:21 EDT 2023
% Result : Theorem 5.75s 1.64s
% Output : Proof 9.32s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14 % Problem : NUM844+2 : TPTP v8.1.2. Released v4.1.0.
% 0.00/0.14 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.14/0.35 % Computer : n012.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 07:58:41 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.21/0.62 ________ _____
% 0.21/0.62 ___ __ \_________(_)________________________________
% 0.21/0.62 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.21/0.62 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.21/0.62 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.21/0.62
% 0.21/0.62 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.21/0.62 (2023-06-19)
% 0.21/0.62
% 0.21/0.62 (c) Philipp Rümmer, 2009-2023
% 0.21/0.62 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.21/0.62 Amanda Stjerna.
% 0.21/0.62 Free software under BSD-3-Clause.
% 0.21/0.62
% 0.21/0.62 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.21/0.62
% 0.21/0.62 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.21/0.63 Running up to 7 provers in parallel.
% 0.21/0.66 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.21/0.66 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.21/0.66 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.21/0.66 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.21/0.66 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.21/0.66 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.21/0.66 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.49/1.09 Prover 1: Preprocessing ...
% 2.49/1.09 Prover 4: Preprocessing ...
% 2.49/1.13 Prover 0: Preprocessing ...
% 2.49/1.13 Prover 6: Preprocessing ...
% 2.49/1.13 Prover 5: Preprocessing ...
% 2.49/1.13 Prover 3: Preprocessing ...
% 2.49/1.14 Prover 2: Preprocessing ...
% 4.39/1.39 Prover 3: Warning: ignoring some quantifiers
% 4.39/1.40 Prover 1: Warning: ignoring some quantifiers
% 4.92/1.42 Prover 3: Constructing countermodel ...
% 4.92/1.42 Prover 1: Constructing countermodel ...
% 4.92/1.45 Prover 6: Proving ...
% 4.92/1.45 Prover 4: Constructing countermodel ...
% 4.92/1.45 Prover 5: Proving ...
% 4.92/1.47 Prover 0: Proving ...
% 4.92/1.48 Prover 2: Proving ...
% 5.75/1.64 Prover 3: proved (990ms)
% 5.75/1.64
% 5.75/1.64 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.75/1.64
% 5.75/1.65 Prover 0: stopped
% 5.75/1.65 Prover 5: stopped
% 5.75/1.65 Prover 6: stopped
% 5.75/1.66 Prover 2: stopped
% 5.75/1.66 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 5.75/1.66 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 5.75/1.66 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 5.75/1.66 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 5.75/1.66 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 6.86/1.68 Prover 8: Preprocessing ...
% 6.86/1.70 Prover 7: Preprocessing ...
% 6.86/1.70 Prover 10: Preprocessing ...
% 6.86/1.71 Prover 13: Preprocessing ...
% 7.06/1.71 Prover 11: Preprocessing ...
% 7.22/1.81 Prover 13: Warning: ignoring some quantifiers
% 7.91/1.82 Prover 7: Constructing countermodel ...
% 7.91/1.82 Prover 10: Constructing countermodel ...
% 7.91/1.83 Prover 13: Constructing countermodel ...
% 7.91/1.83 Prover 8: Warning: ignoring some quantifiers
% 7.91/1.84 Prover 11: Constructing countermodel ...
% 7.91/1.84 Prover 8: Constructing countermodel ...
% 8.44/1.96 Prover 1: Found proof (size 104)
% 8.44/1.96 Prover 1: proved (1315ms)
% 8.44/1.96 Prover 10: stopped
% 8.44/1.96 Prover 7: stopped
% 8.44/1.96 Prover 8: stopped
% 8.44/1.96 Prover 13: stopped
% 8.44/1.96 Prover 4: stopped
% 8.44/1.96 Prover 11: stopped
% 8.44/1.96
% 8.44/1.96 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 8.44/1.96
% 9.10/1.99 % SZS output start Proof for theBenchmark
% 9.10/2.00 Assumptions after simplification:
% 9.10/2.00 ---------------------------------
% 9.10/2.00
% 9.10/2.00 (ass(cond(61, 0), 0))
% 9.23/2.02 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (vplus(v0, v1) = v2) | ~ $i(v1)
% 9.23/2.02 | ~ $i(v0) | (vplus(v1, v0) = v2 & $i(v2)))
% 9.23/2.02
% 9.23/2.02 (holds(264, 412, 0))
% 9.23/2.02 $i(v1) & $i(vd411) & ? [v0: $i] : (vmul(v0, v1) = v0 & vsucc(vd411) = v0 &
% 9.23/2.02 $i(v0))
% 9.23/2.02
% 9.23/2.02 (holds(264, 412, 1))
% 9.23/2.02 $i(v1) & $i(vd411) & ? [v0: $i] : ? [v1: $i] : (vmul(vd411, v1) = v1 &
% 9.23/2.02 vsucc(v1) = v0 & vsucc(vd411) = v0 & $i(v1) & $i(v0))
% 9.23/2.02
% 9.23/2.02 (holds(264, 412, 2))
% 9.23/2.02 $i(v1) & $i(vd411) & ? [v0: $i] : ? [v1: $i] : (vmul(vd411, v1) = v0 &
% 9.23/2.02 vsucc(v0) = v1 & vplus(v0, v1) = v1 & $i(v1) & $i(v0))
% 9.23/2.02
% 9.23/2.02 (holds(265, 414, 0))
% 9.32/2.03 $i(vd413) & $i(vd411) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (vmul(v0,
% 9.32/2.03 vd413) = v1 & vmul(vd411, vd413) = v2 & vsucc(vd411) = v0 & vplus(v2,
% 9.32/2.03 vd413) = v1 & $i(v2) & $i(v1) & $i(v0))
% 9.32/2.03
% 9.32/2.03 (holds(266, 415, 0))
% 9.32/2.03 $i(vd413) & $i(vd411) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i]
% 9.32/2.03 : (vmul(v0, v1) = v2 & vmul(v0, vd413) = v3 & vsucc(vd413) = v1 & vsucc(vd411)
% 9.32/2.03 = v0 & vplus(v3, v0) = v2 & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 9.32/2.03
% 9.32/2.03 (holds(266, 415, 1))
% 9.32/2.03 $i(vd413) & $i(vd411) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i]
% 9.32/2.03 : ? [v4: $i] : (vmul(v0, vd413) = v1 & vmul(vd411, vd413) = v3 & vsucc(vd411)
% 9.32/2.03 = v0 & vplus(v4, v0) = v2 & vplus(v3, vd413) = v4 & vplus(v1, v0) = v2 &
% 9.32/2.03 $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 9.32/2.03
% 9.32/2.03 (holds(266, 415, 2))
% 9.32/2.03 $i(vd413) & $i(vd411) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i]
% 9.32/2.03 : ? [v4: $i] : (vmul(vd411, vd413) = v0 & vsucc(vd411) = v2 & vplus(v1, v2) =
% 9.32/2.03 v3 & vplus(v0, v4) = v3 & vplus(v0, vd413) = v1 & vplus(vd413, v2) = v4 &
% 9.32/2.03 $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 9.32/2.03
% 9.32/2.03 (holds(266, 415, 3))
% 9.32/2.04 $i(vd413) & $i(vd411) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i]
% 9.32/2.04 : ? [v4: $i] : ? [v5: $i] : ( ~ (v5 = v3) & vmul(vd411, vd413) = v0 &
% 9.32/2.04 vsucc(vd411) = v1 & vplus(v1, vd413) = v4 & vplus(v0, v4) = v5 & vplus(v0,
% 9.32/2.04 v2) = v3 & vplus(vd413, v1) = v2 & $i(v5) & $i(v4) & $i(v3) & $i(v2) &
% 9.32/2.04 $i(v1) & $i(v0))
% 9.32/2.04
% 9.32/2.04 (function-axioms)
% 9.32/2.04 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 9.32/2.04 [v3: $i] : (v1 = v0 | ~ (geq(v3, v2) = v1) | ~ (geq(v3, v2) = v0)) & ! [v0:
% 9.32/2.04 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 9.32/2.04 : (v1 = v0 | ~ (greater(v3, v2) = v1) | ~ (greater(v3, v2) = v0)) & ! [v0:
% 9.32/2.04 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 9.32/2.04 : (v1 = v0 | ~ (less(v3, v2) = v1) | ~ (less(v3, v2) = v0)) & ! [v0:
% 9.32/2.04 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 9.32/2.04 : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = v0)) & ! [v0: $i] : !
% 9.32/2.04 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (vmul(v3, v2) = v1) | ~
% 9.32/2.04 (vmul(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i]
% 9.32/2.04 : (v1 = v0 | ~ (vplus(v3, v2) = v1) | ~ (vplus(v3, v2) = v0)) & ! [v0: $i]
% 9.32/2.04 : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (vskolem2(v2) = v1) | ~
% 9.32/2.04 (vskolem2(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 |
% 9.32/2.04 ~ (vsucc(v2) = v1) | ~ (vsucc(v2) = v0))
% 9.32/2.04
% 9.32/2.04 Further assumptions not needed in the proof:
% 9.32/2.04 --------------------------------------------
% 9.32/2.04 ass(cond(12, 0), 0), ass(cond(20, 0), 0), ass(cond(234, 0), 0), ass(cond(241,
% 9.32/2.04 0), 0), ass(cond(253, 0), 0), ass(cond(33, 0), 0), ass(cond(43, 0), 0),
% 9.32/2.04 ass(cond(52, 0), 0), ass(cond(6, 0), 0), qu(cond(conseq(axiom(3)), 3),
% 9.32/2.04 and(holds(definiens(29), 45, 0), holds(definiens(29), 44, 0))),
% 9.32/2.04 qu(cond(conseq(axiom(3)), 32), and(holds(definiens(249), 399, 0),
% 9.32/2.04 holds(definiens(249), 398, 0)))
% 9.32/2.04
% 9.32/2.04 Those formulas are unsatisfiable:
% 9.32/2.04 ---------------------------------
% 9.32/2.04
% 9.32/2.04 Begin of proof
% 9.32/2.04 |
% 9.32/2.04 | ALPHA: (holds(266, 415, 2)) implies:
% 9.32/2.05 | (1) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 9.32/2.05 | (vmul(vd411, vd413) = v0 & vsucc(vd411) = v2 & vplus(v1, v2) = v3 &
% 9.32/2.05 | vplus(v0, v4) = v3 & vplus(v0, vd413) = v1 & vplus(vd413, v2) = v4 &
% 9.32/2.05 | $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 9.32/2.05 |
% 9.32/2.05 | ALPHA: (holds(266, 415, 1)) implies:
% 9.32/2.05 | (2) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 9.32/2.05 | (vmul(v0, vd413) = v1 & vmul(vd411, vd413) = v3 & vsucc(vd411) = v0 &
% 9.32/2.05 | vplus(v4, v0) = v2 & vplus(v3, vd413) = v4 & vplus(v1, v0) = v2 &
% 9.32/2.05 | $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 9.32/2.05 |
% 9.32/2.05 | ALPHA: (holds(266, 415, 0)) implies:
% 9.32/2.05 | (3) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : (vmul(v0, v1) =
% 9.32/2.05 | v2 & vmul(v0, vd413) = v3 & vsucc(vd413) = v1 & vsucc(vd411) = v0 &
% 9.32/2.05 | vplus(v3, v0) = v2 & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 9.32/2.05 |
% 9.32/2.05 | ALPHA: (holds(265, 414, 0)) implies:
% 9.32/2.05 | (4) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (vmul(v0, vd413) = v1 &
% 9.32/2.05 | vmul(vd411, vd413) = v2 & vsucc(vd411) = v0 & vplus(v2, vd413) = v1 &
% 9.32/2.05 | $i(v2) & $i(v1) & $i(v0))
% 9.32/2.05 |
% 9.32/2.05 | ALPHA: (holds(264, 412, 2)) implies:
% 9.32/2.05 | (5) ? [v0: $i] : ? [v1: $i] : (vmul(vd411, v1) = v0 & vsucc(v0) = v1 &
% 9.32/2.05 | vplus(v0, v1) = v1 & $i(v1) & $i(v0))
% 9.32/2.05 |
% 9.32/2.05 | ALPHA: (holds(264, 412, 1)) implies:
% 9.32/2.05 | (6) ? [v0: $i] : ? [v1: $i] : (vmul(vd411, v1) = v1 & vsucc(v1) = v0 &
% 9.32/2.05 | vsucc(vd411) = v0 & $i(v1) & $i(v0))
% 9.32/2.05 |
% 9.32/2.05 | ALPHA: (holds(264, 412, 0)) implies:
% 9.32/2.05 | (7) ? [v0: $i] : (vmul(v0, v1) = v0 & vsucc(vd411) = v0 & $i(v0))
% 9.32/2.05 |
% 9.32/2.05 | ALPHA: (holds(266, 415, 3)) implies:
% 9.32/2.05 | (8) $i(vd413)
% 9.32/2.05 | (9) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 9.32/2.05 | ? [v5: $i] : ( ~ (v5 = v3) & vmul(vd411, vd413) = v0 & vsucc(vd411) =
% 9.32/2.05 | v1 & vplus(v1, vd413) = v4 & vplus(v0, v4) = v5 & vplus(v0, v2) = v3
% 9.32/2.06 | & vplus(vd413, v1) = v2 & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1)
% 9.32/2.06 | & $i(v0))
% 9.32/2.06 |
% 9.32/2.06 | ALPHA: (function-axioms) implies:
% 9.32/2.06 | (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (vsucc(v2) =
% 9.32/2.06 | v1) | ~ (vsucc(v2) = v0))
% 9.32/2.06 | (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 9.32/2.06 | (vplus(v3, v2) = v1) | ~ (vplus(v3, v2) = v0))
% 9.32/2.06 | (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 9.32/2.06 | (vmul(v3, v2) = v1) | ~ (vmul(v3, v2) = v0))
% 9.32/2.06 |
% 9.32/2.06 | DELTA: instantiating (7) with fresh symbol all_16_0 gives:
% 9.32/2.06 | (13) vmul(all_16_0, v1) = all_16_0 & vsucc(vd411) = all_16_0 & $i(all_16_0)
% 9.32/2.06 |
% 9.32/2.06 | ALPHA: (13) implies:
% 9.32/2.06 | (14) vsucc(vd411) = all_16_0
% 9.32/2.06 |
% 9.32/2.06 | DELTA: instantiating (6) with fresh symbols all_20_0, all_20_1 gives:
% 9.32/2.06 | (15) vmul(vd411, v1) = all_20_0 & vsucc(all_20_0) = all_20_1 & vsucc(vd411)
% 9.32/2.06 | = all_20_1 & $i(all_20_0) & $i(all_20_1)
% 9.32/2.06 |
% 9.32/2.06 | ALPHA: (15) implies:
% 9.32/2.06 | (16) vsucc(vd411) = all_20_1
% 9.32/2.06 | (17) vsucc(all_20_0) = all_20_1
% 9.32/2.06 | (18) vmul(vd411, v1) = all_20_0
% 9.32/2.06 |
% 9.32/2.06 | DELTA: instantiating (5) with fresh symbols all_22_0, all_22_1 gives:
% 9.32/2.06 | (19) vmul(vd411, v1) = all_22_1 & vsucc(all_22_1) = all_22_0 &
% 9.32/2.06 | vplus(all_22_1, v1) = all_22_0 & $i(all_22_0) & $i(all_22_1)
% 9.32/2.06 |
% 9.32/2.06 | ALPHA: (19) implies:
% 9.32/2.06 | (20) $i(all_22_0)
% 9.32/2.06 | (21) vsucc(all_22_1) = all_22_0
% 9.32/2.06 | (22) vmul(vd411, v1) = all_22_1
% 9.32/2.06 |
% 9.32/2.06 | DELTA: instantiating (4) with fresh symbols all_26_0, all_26_1, all_26_2
% 9.32/2.06 | gives:
% 9.32/2.06 | (23) vmul(all_26_2, vd413) = all_26_1 & vmul(vd411, vd413) = all_26_0 &
% 9.32/2.06 | vsucc(vd411) = all_26_2 & vplus(all_26_0, vd413) = all_26_1 &
% 9.32/2.06 | $i(all_26_0) & $i(all_26_1) & $i(all_26_2)
% 9.32/2.06 |
% 9.32/2.06 | ALPHA: (23) implies:
% 9.32/2.06 | (24) vplus(all_26_0, vd413) = all_26_1
% 9.32/2.06 | (25) vsucc(vd411) = all_26_2
% 9.32/2.06 | (26) vmul(vd411, vd413) = all_26_0
% 9.32/2.06 | (27) vmul(all_26_2, vd413) = all_26_1
% 9.32/2.06 |
% 9.32/2.06 | DELTA: instantiating (3) with fresh symbols all_28_0, all_28_1, all_28_2,
% 9.32/2.06 | all_28_3 gives:
% 9.32/2.06 | (28) vmul(all_28_3, all_28_2) = all_28_1 & vmul(all_28_3, vd413) = all_28_0
% 9.32/2.06 | & vsucc(vd413) = all_28_2 & vsucc(vd411) = all_28_3 & vplus(all_28_0,
% 9.32/2.06 | all_28_3) = all_28_1 & $i(all_28_0) & $i(all_28_1) & $i(all_28_2) &
% 9.32/2.06 | $i(all_28_3)
% 9.32/2.06 |
% 9.32/2.06 | ALPHA: (28) implies:
% 9.32/2.07 | (29) vplus(all_28_0, all_28_3) = all_28_1
% 9.32/2.07 | (30) vsucc(vd411) = all_28_3
% 9.32/2.07 | (31) vmul(all_28_3, vd413) = all_28_0
% 9.32/2.07 |
% 9.32/2.07 | DELTA: instantiating (1) with fresh symbols all_30_0, all_30_1, all_30_2,
% 9.32/2.07 | all_30_3, all_30_4 gives:
% 9.32/2.07 | (32) vmul(vd411, vd413) = all_30_4 & vsucc(vd411) = all_30_2 &
% 9.32/2.07 | vplus(all_30_3, all_30_2) = all_30_1 & vplus(all_30_4, all_30_0) =
% 9.32/2.07 | all_30_1 & vplus(all_30_4, vd413) = all_30_3 & vplus(vd413, all_30_2)
% 9.32/2.07 | = all_30_0 & $i(all_30_0) & $i(all_30_1) & $i(all_30_2) & $i(all_30_3)
% 9.32/2.07 | & $i(all_30_4)
% 9.32/2.07 |
% 9.32/2.07 | ALPHA: (32) implies:
% 9.32/2.07 | (33) $i(all_30_4)
% 9.32/2.07 | (34) vplus(vd413, all_30_2) = all_30_0
% 9.32/2.07 | (35) vplus(all_30_4, vd413) = all_30_3
% 9.32/2.07 | (36) vplus(all_30_4, all_30_0) = all_30_1
% 9.32/2.07 | (37) vplus(all_30_3, all_30_2) = all_30_1
% 9.32/2.07 | (38) vsucc(vd411) = all_30_2
% 9.32/2.07 | (39) vmul(vd411, vd413) = all_30_4
% 9.32/2.07 |
% 9.32/2.07 | DELTA: instantiating (2) with fresh symbols all_32_0, all_32_1, all_32_2,
% 9.32/2.07 | all_32_3, all_32_4 gives:
% 9.32/2.07 | (40) vmul(all_32_4, vd413) = all_32_3 & vmul(vd411, vd413) = all_32_1 &
% 9.32/2.07 | vsucc(vd411) = all_32_4 & vplus(all_32_0, all_32_4) = all_32_2 &
% 9.32/2.07 | vplus(all_32_1, vd413) = all_32_0 & vplus(all_32_3, all_32_4) =
% 9.32/2.07 | all_32_2 & $i(all_32_0) & $i(all_32_1) & $i(all_32_2) & $i(all_32_3) &
% 9.32/2.07 | $i(all_32_4)
% 9.32/2.07 |
% 9.32/2.07 | ALPHA: (40) implies:
% 9.32/2.07 | (41) vplus(all_32_3, all_32_4) = all_32_2
% 9.32/2.07 | (42) vplus(all_32_1, vd413) = all_32_0
% 9.32/2.07 | (43) vsucc(vd411) = all_32_4
% 9.32/2.07 | (44) vmul(vd411, vd413) = all_32_1
% 9.32/2.07 | (45) vmul(all_32_4, vd413) = all_32_3
% 9.32/2.07 |
% 9.32/2.07 | DELTA: instantiating (9) with fresh symbols all_34_0, all_34_1, all_34_2,
% 9.32/2.07 | all_34_3, all_34_4, all_34_5 gives:
% 9.32/2.07 | (46) ~ (all_34_0 = all_34_2) & vmul(vd411, vd413) = all_34_5 &
% 9.32/2.07 | vsucc(vd411) = all_34_4 & vplus(all_34_4, vd413) = all_34_1 &
% 9.32/2.07 | vplus(all_34_5, all_34_1) = all_34_0 & vplus(all_34_5, all_34_3) =
% 9.32/2.07 | all_34_2 & vplus(vd413, all_34_4) = all_34_3 & $i(all_34_0) &
% 9.32/2.07 | $i(all_34_1) & $i(all_34_2) & $i(all_34_3) & $i(all_34_4) &
% 9.32/2.07 | $i(all_34_5)
% 9.32/2.07 |
% 9.32/2.07 | ALPHA: (46) implies:
% 9.32/2.07 | (47) ~ (all_34_0 = all_34_2)
% 9.32/2.07 | (48) vplus(vd413, all_34_4) = all_34_3
% 9.32/2.07 | (49) vplus(all_34_5, all_34_3) = all_34_2
% 9.32/2.07 | (50) vplus(all_34_5, all_34_1) = all_34_0
% 9.32/2.07 | (51) vplus(all_34_4, vd413) = all_34_1
% 9.32/2.07 | (52) vsucc(vd411) = all_34_4
% 9.32/2.07 | (53) vmul(vd411, vd413) = all_34_5
% 9.32/2.07 |
% 9.32/2.07 | GROUND_INST: instantiating (10) with all_28_3, all_30_2, vd411, simplifying
% 9.32/2.07 | with (30), (38) gives:
% 9.32/2.07 | (54) all_30_2 = all_28_3
% 9.32/2.07 |
% 9.32/2.07 | GROUND_INST: instantiating (10) with all_28_3, all_32_4, vd411, simplifying
% 9.32/2.07 | with (30), (43) gives:
% 9.32/2.07 | (55) all_32_4 = all_28_3
% 9.32/2.07 |
% 9.32/2.07 | GROUND_INST: instantiating (10) with all_26_2, all_32_4, vd411, simplifying
% 9.32/2.07 | with (25), (43) gives:
% 9.32/2.07 | (56) all_32_4 = all_26_2
% 9.32/2.07 |
% 9.32/2.07 | GROUND_INST: instantiating (10) with all_20_1, all_32_4, vd411, simplifying
% 9.32/2.07 | with (16), (43) gives:
% 9.32/2.07 | (57) all_32_4 = all_20_1
% 9.32/2.07 |
% 9.32/2.07 | GROUND_INST: instantiating (10) with all_30_2, all_34_4, vd411, simplifying
% 9.32/2.07 | with (38), (52) gives:
% 9.32/2.08 | (58) all_34_4 = all_30_2
% 9.32/2.08 |
% 9.32/2.08 | GROUND_INST: instantiating (10) with all_16_0, all_34_4, vd411, simplifying
% 9.32/2.08 | with (14), (52) gives:
% 9.32/2.08 | (59) all_34_4 = all_16_0
% 9.32/2.08 |
% 9.32/2.08 | GROUND_INST: instantiating (12) with all_30_4, all_32_1, vd413, vd411,
% 9.32/2.08 | simplifying with (39), (44) gives:
% 9.32/2.08 | (60) all_32_1 = all_30_4
% 9.32/2.08 |
% 9.32/2.08 | GROUND_INST: instantiating (12) with all_32_1, all_34_5, vd413, vd411,
% 9.32/2.08 | simplifying with (44), (53) gives:
% 9.32/2.08 | (61) all_34_5 = all_32_1
% 9.32/2.08 |
% 9.32/2.08 | GROUND_INST: instantiating (12) with all_26_0, all_34_5, vd413, vd411,
% 9.32/2.08 | simplifying with (26), (53) gives:
% 9.32/2.08 | (62) all_34_5 = all_26_0
% 9.32/2.08 |
% 9.32/2.08 | GROUND_INST: instantiating (12) with all_20_0, all_22_1, v1, vd411,
% 9.32/2.08 | simplifying with (18), (22) gives:
% 9.32/2.08 | (63) all_22_1 = all_20_0
% 9.32/2.08 |
% 9.32/2.08 | COMBINE_EQS: (58), (59) imply:
% 9.32/2.08 | (64) all_30_2 = all_16_0
% 9.32/2.08 |
% 9.32/2.08 | SIMP: (64) implies:
% 9.32/2.08 | (65) all_30_2 = all_16_0
% 9.32/2.08 |
% 9.32/2.08 | COMBINE_EQS: (61), (62) imply:
% 9.32/2.08 | (66) all_32_1 = all_26_0
% 9.32/2.08 |
% 9.32/2.08 | SIMP: (66) implies:
% 9.32/2.08 | (67) all_32_1 = all_26_0
% 9.32/2.08 |
% 9.32/2.08 | COMBINE_EQS: (60), (67) imply:
% 9.32/2.08 | (68) all_30_4 = all_26_0
% 9.32/2.08 |
% 9.32/2.08 | COMBINE_EQS: (55), (56) imply:
% 9.32/2.08 | (69) all_28_3 = all_26_2
% 9.32/2.08 |
% 9.32/2.08 | SIMP: (69) implies:
% 9.32/2.08 | (70) all_28_3 = all_26_2
% 9.32/2.08 |
% 9.32/2.08 | COMBINE_EQS: (56), (57) imply:
% 9.32/2.08 | (71) all_26_2 = all_20_1
% 9.32/2.08 |
% 9.32/2.08 | COMBINE_EQS: (54), (65) imply:
% 9.32/2.08 | (72) all_28_3 = all_16_0
% 9.32/2.08 |
% 9.32/2.08 | SIMP: (72) implies:
% 9.32/2.08 | (73) all_28_3 = all_16_0
% 9.32/2.08 |
% 9.32/2.08 | COMBINE_EQS: (70), (73) imply:
% 9.32/2.08 | (74) all_26_2 = all_16_0
% 9.32/2.08 |
% 9.32/2.08 | SIMP: (74) implies:
% 9.32/2.08 | (75) all_26_2 = all_16_0
% 9.32/2.08 |
% 9.32/2.08 | COMBINE_EQS: (71), (75) imply:
% 9.32/2.08 | (76) all_20_1 = all_16_0
% 9.32/2.08 |
% 9.32/2.08 | COMBINE_EQS: (56), (75) imply:
% 9.32/2.08 | (77) all_32_4 = all_16_0
% 9.32/2.08 |
% 9.32/2.08 | REDUCE: (45), (77) imply:
% 9.32/2.08 | (78) vmul(all_16_0, vd413) = all_32_3
% 9.32/2.08 |
% 9.32/2.08 | REDUCE: (31), (73) imply:
% 9.32/2.08 | (79) vmul(all_16_0, vd413) = all_28_0
% 9.32/2.08 |
% 9.32/2.08 | REDUCE: (27), (75) imply:
% 9.32/2.08 | (80) vmul(all_16_0, vd413) = all_26_1
% 9.32/2.08 |
% 9.32/2.08 | REDUCE: (21), (63) imply:
% 9.32/2.08 | (81) vsucc(all_20_0) = all_22_0
% 9.32/2.08 |
% 9.32/2.08 | REDUCE: (17), (76) imply:
% 9.32/2.08 | (82) vsucc(all_20_0) = all_16_0
% 9.32/2.08 |
% 9.32/2.08 | REDUCE: (51), (59) imply:
% 9.32/2.08 | (83) vplus(all_16_0, vd413) = all_34_1
% 9.32/2.08 |
% 9.32/2.08 | REDUCE: (50), (62) imply:
% 9.32/2.08 | (84) vplus(all_26_0, all_34_1) = all_34_0
% 9.32/2.08 |
% 9.32/2.08 | REDUCE: (49), (62) imply:
% 9.32/2.08 | (85) vplus(all_26_0, all_34_3) = all_34_2
% 9.32/2.08 |
% 9.32/2.08 | REDUCE: (42), (67) imply:
% 9.32/2.08 | (86) vplus(all_26_0, vd413) = all_32_0
% 9.32/2.08 |
% 9.32/2.08 | REDUCE: (41), (77) imply:
% 9.32/2.08 | (87) vplus(all_32_3, all_16_0) = all_32_2
% 9.32/2.08 |
% 9.32/2.08 | REDUCE: (37), (65) imply:
% 9.32/2.08 | (88) vplus(all_30_3, all_16_0) = all_30_1
% 9.32/2.08 |
% 9.32/2.08 | REDUCE: (36), (68) imply:
% 9.32/2.08 | (89) vplus(all_26_0, all_30_0) = all_30_1
% 9.32/2.08 |
% 9.32/2.08 | REDUCE: (35), (68) imply:
% 9.32/2.08 | (90) vplus(all_26_0, vd413) = all_30_3
% 9.32/2.08 |
% 9.32/2.08 | REDUCE: (29), (73) imply:
% 9.32/2.09 | (91) vplus(all_28_0, all_16_0) = all_28_1
% 9.32/2.09 |
% 9.32/2.09 | REDUCE: (48), (59) imply:
% 9.32/2.09 | (92) vplus(vd413, all_16_0) = all_34_3
% 9.32/2.09 |
% 9.32/2.09 | REDUCE: (34), (65) imply:
% 9.32/2.09 | (93) vplus(vd413, all_16_0) = all_30_0
% 9.32/2.09 |
% 9.32/2.09 | REDUCE: (33), (68) imply:
% 9.32/2.09 | (94) $i(all_26_0)
% 9.32/2.09 |
% 9.32/2.09 | GROUND_INST: instantiating (11) with all_30_0, all_34_3, all_16_0, vd413,
% 9.32/2.09 | simplifying with (92), (93) gives:
% 9.32/2.09 | (95) all_34_3 = all_30_0
% 9.32/2.09 |
% 9.32/2.09 | GROUND_INST: instantiating (11) with all_26_1, all_32_0, vd413, all_26_0,
% 9.32/2.09 | simplifying with (24), (86) gives:
% 9.32/2.09 | (96) all_32_0 = all_26_1
% 9.32/2.09 |
% 9.32/2.09 | GROUND_INST: instantiating (11) with all_30_3, all_32_0, vd413, all_26_0,
% 9.32/2.09 | simplifying with (86), (90) gives:
% 9.32/2.09 | (97) all_32_0 = all_30_3
% 9.32/2.09 |
% 9.32/2.09 | GROUND_INST: instantiating (10) with all_16_0, all_22_0, all_20_0, simplifying
% 9.32/2.09 | with (81), (82) gives:
% 9.32/2.09 | (98) all_22_0 = all_16_0
% 9.32/2.09 |
% 9.32/2.09 | GROUND_INST: instantiating (12) with all_28_0, all_32_3, vd413, all_16_0,
% 9.32/2.09 | simplifying with (78), (79) gives:
% 9.32/2.09 | (99) all_32_3 = all_28_0
% 9.32/2.09 |
% 9.32/2.09 | GROUND_INST: instantiating (12) with all_26_1, all_32_3, vd413, all_16_0,
% 9.32/2.09 | simplifying with (78), (80) gives:
% 9.32/2.09 | (100) all_32_3 = all_26_1
% 9.32/2.09 |
% 9.32/2.09 | COMBINE_EQS: (96), (97) imply:
% 9.32/2.09 | (101) all_30_3 = all_26_1
% 9.32/2.09 |
% 9.32/2.09 | COMBINE_EQS: (99), (100) imply:
% 9.32/2.09 | (102) all_28_0 = all_26_1
% 9.32/2.09 |
% 9.32/2.09 | SIMP: (102) implies:
% 9.32/2.09 | (103) all_28_0 = all_26_1
% 9.32/2.09 |
% 9.32/2.09 | REDUCE: (87), (100) imply:
% 9.32/2.09 | (104) vplus(all_26_1, all_16_0) = all_32_2
% 9.32/2.09 |
% 9.32/2.09 | REDUCE: (88), (101) imply:
% 9.32/2.09 | (105) vplus(all_26_1, all_16_0) = all_30_1
% 9.32/2.09 |
% 9.32/2.09 | REDUCE: (91), (103) imply:
% 9.32/2.09 | (106) vplus(all_26_1, all_16_0) = all_28_1
% 9.32/2.09 |
% 9.32/2.09 | REDUCE: (85), (95) imply:
% 9.32/2.09 | (107) vplus(all_26_0, all_30_0) = all_34_2
% 9.32/2.09 |
% 9.32/2.09 | REDUCE: (20), (98) imply:
% 9.32/2.09 | (108) $i(all_16_0)
% 9.32/2.09 |
% 9.32/2.09 | GROUND_INST: instantiating (11) with all_30_1, all_32_2, all_16_0, all_26_1,
% 9.32/2.09 | simplifying with (104), (105) gives:
% 9.32/2.09 | (109) all_32_2 = all_30_1
% 9.32/2.09 |
% 9.32/2.09 | GROUND_INST: instantiating (11) with all_28_1, all_32_2, all_16_0, all_26_1,
% 9.32/2.09 | simplifying with (104), (106) gives:
% 9.32/2.09 | (110) all_32_2 = all_28_1
% 9.32/2.09 |
% 9.32/2.09 | GROUND_INST: instantiating (11) with all_30_1, all_34_2, all_30_0, all_26_0,
% 9.32/2.09 | simplifying with (89), (107) gives:
% 9.32/2.09 | (111) all_34_2 = all_30_1
% 9.32/2.09 |
% 9.32/2.09 | COMBINE_EQS: (109), (110) imply:
% 9.32/2.09 | (112) all_30_1 = all_28_1
% 9.32/2.09 |
% 9.32/2.09 | SIMP: (112) implies:
% 9.32/2.09 | (113) all_30_1 = all_28_1
% 9.32/2.09 |
% 9.32/2.09 | COMBINE_EQS: (111), (113) imply:
% 9.32/2.09 | (114) all_34_2 = all_28_1
% 9.32/2.09 |
% 9.32/2.09 | REDUCE: (47), (114) imply:
% 9.32/2.09 | (115) ~ (all_34_0 = all_28_1)
% 9.32/2.09 |
% 9.32/2.09 | REDUCE: (89), (113) imply:
% 9.32/2.09 | (116) vplus(all_26_0, all_30_0) = all_28_1
% 9.32/2.09 |
% 9.32/2.09 | GROUND_INST: instantiating (ass(cond(61, 0), 0)) with vd413, all_16_0,
% 9.32/2.09 | all_30_0, simplifying with (8), (93), (108) gives:
% 9.32/2.09 | (117) vplus(all_16_0, vd413) = all_30_0 & $i(all_30_0)
% 9.32/2.09 |
% 9.32/2.09 | ALPHA: (117) implies:
% 9.32/2.09 | (118) $i(all_30_0)
% 9.32/2.09 | (119) vplus(all_16_0, vd413) = all_30_0
% 9.32/2.09 |
% 9.32/2.09 | GROUND_INST: instantiating (ass(cond(61, 0), 0)) with all_16_0, vd413,
% 9.32/2.09 | all_34_1, simplifying with (8), (83), (108) gives:
% 9.32/2.10 | (120) vplus(vd413, all_16_0) = all_34_1 & $i(all_34_1)
% 9.32/2.10 |
% 9.32/2.10 | ALPHA: (120) implies:
% 9.32/2.10 | (121) $i(all_34_1)
% 9.32/2.10 |
% 9.32/2.10 | GROUND_INST: instantiating (ass(cond(61, 0), 0)) with all_26_0, all_30_0,
% 9.32/2.10 | all_28_1, simplifying with (94), (116), (118) gives:
% 9.32/2.10 | (122) vplus(all_30_0, all_26_0) = all_28_1 & $i(all_28_1)
% 9.32/2.10 |
% 9.32/2.10 | ALPHA: (122) implies:
% 9.32/2.10 | (123) vplus(all_30_0, all_26_0) = all_28_1
% 9.32/2.10 |
% 9.32/2.10 | GROUND_INST: instantiating (ass(cond(61, 0), 0)) with all_26_0, all_34_1,
% 9.32/2.10 | all_34_0, simplifying with (84), (94), (121) gives:
% 9.32/2.10 | (124) vplus(all_34_1, all_26_0) = all_34_0 & $i(all_34_0)
% 9.32/2.10 |
% 9.32/2.10 | ALPHA: (124) implies:
% 9.32/2.10 | (125) vplus(all_34_1, all_26_0) = all_34_0
% 9.32/2.10 |
% 9.32/2.10 | GROUND_INST: instantiating (11) with all_34_1, all_30_0, vd413, all_16_0,
% 9.32/2.10 | simplifying with (83), (119) gives:
% 9.32/2.10 | (126) all_34_1 = all_30_0
% 9.32/2.10 |
% 9.32/2.10 | REDUCE: (125), (126) imply:
% 9.32/2.10 | (127) vplus(all_30_0, all_26_0) = all_34_0
% 9.32/2.10 |
% 9.32/2.10 | GROUND_INST: instantiating (11) with all_28_1, all_34_0, all_26_0, all_30_0,
% 9.32/2.10 | simplifying with (123), (127) gives:
% 9.32/2.10 | (128) all_34_0 = all_28_1
% 9.32/2.10 |
% 9.32/2.10 | REDUCE: (115), (128) imply:
% 9.32/2.10 | (129) $false
% 9.32/2.10 |
% 9.32/2.10 | CLOSE: (129) is inconsistent.
% 9.32/2.10 |
% 9.32/2.10 End of proof
% 9.32/2.10 % SZS output end Proof for theBenchmark
% 9.32/2.10
% 9.32/2.10 1478ms
%------------------------------------------------------------------------------