TSTP Solution File: NUM847+2 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : NUM847+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 : n022.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 11:50:22 EDT 2023
% Result : Theorem 6.41s 1.55s
% Output : Proof 9.14s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : NUM847+2 : TPTP v8.1.2. Released v4.1.0.
% 0.00/0.14 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.34 % Computer : n022.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 : Fri Aug 25 17:52:55 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.20/0.59 ________ _____
% 0.20/0.59 ___ __ \_________(_)________________________________
% 0.20/0.59 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.20/0.59 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.20/0.59 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.20/0.59
% 0.20/0.59 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.20/0.59 (2023-06-19)
% 0.20/0.59
% 0.20/0.59 (c) Philipp Rümmer, 2009-2023
% 0.20/0.59 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.20/0.59 Amanda Stjerna.
% 0.20/0.59 Free software under BSD-3-Clause.
% 0.20/0.59
% 0.20/0.59 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.20/0.59
% 0.20/0.59 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.20/0.60 Running up to 7 provers in parallel.
% 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 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 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
% 0.20/0.62 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.34/1.00 Prover 1: Preprocessing ...
% 2.34/1.01 Prover 4: Preprocessing ...
% 2.34/1.05 Prover 3: Preprocessing ...
% 2.34/1.05 Prover 6: Preprocessing ...
% 2.34/1.05 Prover 2: Preprocessing ...
% 2.34/1.05 Prover 5: Preprocessing ...
% 2.34/1.05 Prover 0: Preprocessing ...
% 4.44/1.32 Prover 1: Warning: ignoring some quantifiers
% 4.44/1.33 Prover 3: Warning: ignoring some quantifiers
% 4.44/1.35 Prover 3: Constructing countermodel ...
% 4.44/1.35 Prover 6: Proving ...
% 4.44/1.36 Prover 1: Constructing countermodel ...
% 5.11/1.37 Prover 4: Constructing countermodel ...
% 5.11/1.40 Prover 5: Proving ...
% 5.11/1.41 Prover 0: Proving ...
% 5.11/1.45 Prover 2: Proving ...
% 6.32/1.54 Prover 3: proved (929ms)
% 6.41/1.55
% 6.41/1.55 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.41/1.55
% 6.41/1.55 Prover 5: stopped
% 6.41/1.55 Prover 0: stopped
% 6.41/1.55 Prover 6: stopped
% 6.41/1.55 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 6.41/1.55 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 6.41/1.55 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 6.41/1.55 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 6.41/1.56 Prover 2: stopped
% 6.41/1.58 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 6.41/1.58 Prover 8: Preprocessing ...
% 6.41/1.58 Prover 10: Preprocessing ...
% 6.41/1.60 Prover 11: Preprocessing ...
% 6.41/1.60 Prover 13: Preprocessing ...
% 6.41/1.60 Prover 7: Preprocessing ...
% 7.24/1.68 Prover 10: Constructing countermodel ...
% 7.24/1.71 Prover 13: Warning: ignoring some quantifiers
% 7.24/1.71 Prover 13: Constructing countermodel ...
% 7.24/1.72 Prover 8: Warning: ignoring some quantifiers
% 7.24/1.73 Prover 8: Constructing countermodel ...
% 7.24/1.73 Prover 7: Constructing countermodel ...
% 7.24/1.74 Prover 11: Constructing countermodel ...
% 8.51/1.83 Prover 1: Found proof (size 77)
% 8.51/1.83 Prover 1: proved (1226ms)
% 8.51/1.83 Prover 10: stopped
% 8.51/1.83 Prover 8: stopped
% 8.51/1.83 Prover 7: stopped
% 8.51/1.84 Prover 11: stopped
% 8.51/1.84 Prover 13: stopped
% 8.58/1.85 Prover 4: stopped
% 8.58/1.85
% 8.58/1.85 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 8.58/1.85
% 8.58/1.87 % SZS output start Proof for theBenchmark
% 8.58/1.87 Assumptions after simplification:
% 8.58/1.87 ---------------------------------
% 8.58/1.87
% 8.58/1.87 (ass(cond(33, 0), 0))
% 8.58/1.90 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 8.58/1.90 (vplus(v3, v2) = v4) | ~ (vplus(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~
% 8.58/1.90 $i(v0) | ? [v5: $i] : (vplus(v1, v2) = v5 & vplus(v0, v5) = v4 & $i(v5) &
% 8.58/1.90 $i(v4)))
% 8.58/1.90
% 8.58/1.90 (holds(284, 438, 1))
% 8.58/1.90 $i(vd437) & $i(vd436) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 8.58/1.90 (vsucc(vd437) = v0 & vmul(vd436, v0) = v1 & vmul(vd436, vd437) = v2 &
% 8.58/1.90 vplus(v2, vd436) = v1 & $i(v2) & $i(v1) & $i(v0))
% 8.58/1.90
% 8.58/1.90 (holds(284, 438, 2))
% 8.58/1.90 $i(v1) & $i(vd437) & $i(vd436) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 8.58/1.90 (vmul(vd436, v1) = v2 & vmul(vd436, vd437) = v0 & vplus(v0, v2) = v1 &
% 8.58/1.90 vplus(v0, vd436) = v1 & $i(v2) & $i(v1) & $i(v0))
% 8.58/1.90
% 8.58/1.90 (holds(285, 440, 0))
% 8.58/1.90 $i(vd439) & $i(vd437) & $i(vd436) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 8.58/1.90 ? [v3: $i] : (vmul(vd436, v0) = v1 & vmul(vd436, vd439) = v3 & vmul(vd436,
% 8.58/1.90 vd437) = v2 & vplus(v2, v3) = v1 & vplus(vd437, vd439) = v0 & $i(v3) &
% 8.58/1.90 $i(v2) & $i(v1) & $i(v0))
% 8.58/1.90
% 8.58/1.90 (holds(286, 441, 0))
% 8.58/1.91 $i(vd439) & $i(vd437) & $i(vd436) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 8.58/1.91 ? [v3: $i] : ? [v4: $i] : (vsucc(v3) = v4 & vsucc(vd439) = v0 & vmul(vd436,
% 8.58/1.91 v4) = v2 & vmul(vd436, v1) = v2 & vplus(vd437, v0) = v1 & vplus(vd437,
% 8.58/1.91 vd439) = v3 & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 8.58/1.91
% 8.58/1.91 (holds(286, 441, 1))
% 8.87/1.91 $i(vd439) & $i(vd437) & $i(vd436) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 8.87/1.91 ? [v3: $i] : (vsucc(v0) = v1 & vmul(vd436, v1) = v2 & vmul(vd436, v0) = v3 &
% 8.87/1.91 vplus(v3, vd436) = v2 & vplus(vd437, vd439) = v0 & $i(v3) & $i(v2) & $i(v1)
% 8.87/1.91 & $i(v0))
% 8.87/1.91
% 8.87/1.91 (holds(286, 441, 2))
% 8.87/1.91 $i(vd439) & $i(vd437) & $i(vd436) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 8.87/1.91 ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : (vmul(vd436, v0) = v1 & vmul(vd436,
% 8.87/1.91 vd439) = v4 & vmul(vd436, vd437) = v3 & vplus(v5, vd436) = v2 & vplus(v3,
% 8.87/1.91 v4) = v5 & vplus(v1, vd436) = v2 & vplus(vd437, vd439) = v0 & $i(v5) &
% 8.87/1.91 $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 8.87/1.91
% 8.87/1.91 (holds(286, 441, 3))
% 8.87/1.91 $i(vd439) & $i(vd437) & $i(vd436) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 8.87/1.91 ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ( ~ (v5 = v3) & vmul(vd436, vd439) =
% 8.87/1.91 v1 & vmul(vd436, vd437) = v0 & vplus(v2, vd436) = v3 & vplus(v1, vd436) = v4
% 8.87/1.91 & vplus(v0, v4) = v5 & vplus(v0, v1) = v2 & $i(v5) & $i(v4) & $i(v3) &
% 8.87/1.91 $i(v2) & $i(v1) & $i(v0))
% 8.87/1.91
% 8.87/1.91 (function-axioms)
% 8.87/1.92 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 8.87/1.92 [v3: $i] : (v1 = v0 | ~ (geq(v3, v2) = v1) | ~ (geq(v3, v2) = v0)) & ! [v0:
% 8.87/1.92 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 8.87/1.92 : (v1 = v0 | ~ (greater(v3, v2) = v1) | ~ (greater(v3, v2) = v0)) & ! [v0:
% 8.87/1.92 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 8.87/1.92 : (v1 = v0 | ~ (less(v3, v2) = v1) | ~ (less(v3, v2) = v0)) & ! [v0:
% 8.87/1.92 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 8.87/1.92 : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = v0)) & ! [v0: $i] : !
% 8.87/1.92 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (vmul(v3, v2) = v1) | ~
% 8.87/1.92 (vmul(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i]
% 8.87/1.92 : (v1 = v0 | ~ (vplus(v3, v2) = v1) | ~ (vplus(v3, v2) = v0)) & ! [v0: $i]
% 8.87/1.92 : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (vskolem2(v2) = v1) | ~
% 8.87/1.92 (vskolem2(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 |
% 8.87/1.92 ~ (vsucc(v2) = v1) | ~ (vsucc(v2) = v0))
% 8.87/1.92
% 8.87/1.92 Further assumptions not needed in the proof:
% 8.87/1.92 --------------------------------------------
% 8.87/1.92 ass(cond(12, 0), 0), ass(cond(20, 0), 0), ass(cond(234, 0), 0), ass(cond(241,
% 8.87/1.92 0), 0), ass(cond(253, 0), 0), ass(cond(43, 0), 0), ass(cond(52, 0), 0),
% 8.87/1.92 ass(cond(61, 0), 0), holds(284, 438, 0), qu(cond(conseq(axiom(3)), 3),
% 8.87/1.92 and(holds(definiens(29), 45, 0), holds(definiens(29), 44, 0))),
% 8.87/1.92 qu(cond(conseq(axiom(3)), 32), and(holds(definiens(249), 399, 0),
% 8.87/1.92 holds(definiens(249), 398, 0)))
% 8.87/1.92
% 8.87/1.92 Those formulas are unsatisfiable:
% 8.87/1.92 ---------------------------------
% 8.87/1.92
% 8.87/1.92 Begin of proof
% 8.87/1.92 |
% 8.87/1.92 | ALPHA: (holds(286, 441, 2)) implies:
% 8.87/1.92 | (1) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 8.87/1.92 | ? [v5: $i] : (vmul(vd436, v0) = v1 & vmul(vd436, vd439) = v4 &
% 8.87/1.92 | vmul(vd436, vd437) = v3 & vplus(v5, vd436) = v2 & vplus(v3, v4) = v5
% 8.87/1.92 | & vplus(v1, vd436) = v2 & vplus(vd437, vd439) = v0 & $i(v5) & $i(v4)
% 8.87/1.92 | & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 8.87/1.92 |
% 8.87/1.92 | ALPHA: (holds(286, 441, 1)) implies:
% 8.87/1.93 | (2) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : (vsucc(v0) = v1
% 8.87/1.93 | & vmul(vd436, v1) = v2 & vmul(vd436, v0) = v3 & vplus(v3, vd436) = v2
% 8.87/1.93 | & vplus(vd437, vd439) = v0 & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 8.87/1.93 |
% 8.87/1.93 | ALPHA: (holds(286, 441, 0)) implies:
% 8.87/1.93 | (3) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 8.87/1.93 | (vsucc(v3) = v4 & vsucc(vd439) = v0 & vmul(vd436, v4) = v2 &
% 8.87/1.93 | vmul(vd436, v1) = v2 & vplus(vd437, v0) = v1 & vplus(vd437, vd439) =
% 8.87/1.93 | v3 & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 8.87/1.93 |
% 8.87/1.93 | ALPHA: (holds(285, 440, 0)) implies:
% 8.87/1.93 | (4) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : (vmul(vd436,
% 8.87/1.93 | v0) = v1 & vmul(vd436, vd439) = v3 & vmul(vd436, vd437) = v2 &
% 8.87/1.93 | vplus(v2, v3) = v1 & vplus(vd437, vd439) = v0 & $i(v3) & $i(v2) &
% 8.87/1.93 | $i(v1) & $i(v0))
% 8.87/1.93 |
% 8.87/1.93 | ALPHA: (holds(284, 438, 2)) implies:
% 8.87/1.93 | (5) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (vmul(vd436, v1) = v2 &
% 8.87/1.93 | vmul(vd436, vd437) = v0 & vplus(v0, v2) = v1 & vplus(v0, vd436) = v1
% 8.87/1.93 | & $i(v2) & $i(v1) & $i(v0))
% 8.87/1.93 |
% 8.87/1.93 | ALPHA: (holds(284, 438, 1)) implies:
% 8.87/1.93 | (6) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (vsucc(vd437) = v0 &
% 8.87/1.93 | vmul(vd436, v0) = v1 & vmul(vd436, vd437) = v2 & vplus(v2, vd436) =
% 8.87/1.93 | v1 & $i(v2) & $i(v1) & $i(v0))
% 8.87/1.93 |
% 8.87/1.93 | ALPHA: (holds(286, 441, 3)) implies:
% 8.87/1.93 | (7) $i(vd436)
% 8.87/1.93 | (8) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 8.87/1.93 | ? [v5: $i] : ( ~ (v5 = v3) & vmul(vd436, vd439) = v1 & vmul(vd436,
% 8.87/1.93 | vd437) = v0 & vplus(v2, vd436) = v3 & vplus(v1, vd436) = v4 &
% 8.87/1.93 | vplus(v0, v4) = v5 & vplus(v0, v1) = v2 & $i(v5) & $i(v4) & $i(v3) &
% 8.87/1.93 | $i(v2) & $i(v1) & $i(v0))
% 8.87/1.93 |
% 8.87/1.93 | ALPHA: (function-axioms) implies:
% 8.87/1.93 | (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 8.87/1.93 | (vplus(v3, v2) = v1) | ~ (vplus(v3, v2) = v0))
% 8.87/1.93 | (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 8.87/1.93 | (vmul(v3, v2) = v1) | ~ (vmul(v3, v2) = v0))
% 8.87/1.93 |
% 8.87/1.94 | DELTA: instantiating (6) with fresh symbols all_19_0, all_19_1, all_19_2
% 8.87/1.94 | gives:
% 8.87/1.94 | (11) vsucc(vd437) = all_19_2 & vmul(vd436, all_19_2) = all_19_1 &
% 8.87/1.94 | vmul(vd436, vd437) = all_19_0 & vplus(all_19_0, vd436) = all_19_1 &
% 8.87/1.94 | $i(all_19_0) & $i(all_19_1) & $i(all_19_2)
% 8.87/1.94 |
% 8.87/1.94 | ALPHA: (11) implies:
% 8.87/1.94 | (12) vmul(vd436, vd437) = all_19_0
% 8.87/1.94 |
% 8.87/1.94 | DELTA: instantiating (5) with fresh symbols all_23_0, all_23_1, all_23_2
% 8.87/1.94 | gives:
% 8.87/1.94 | (13) vmul(vd436, v1) = all_23_0 & vmul(vd436, vd437) = all_23_2 &
% 8.87/1.94 | vplus(all_23_2, all_23_0) = all_23_1 & vplus(all_23_2, vd436) =
% 8.87/1.94 | all_23_1 & $i(all_23_0) & $i(all_23_1) & $i(all_23_2)
% 8.87/1.94 |
% 8.87/1.94 | ALPHA: (13) implies:
% 8.87/1.94 | (14) $i(all_23_2)
% 8.87/1.94 | (15) vmul(vd436, vd437) = all_23_2
% 8.87/1.94 |
% 8.87/1.94 | DELTA: instantiating (2) with fresh symbols all_25_0, all_25_1, all_25_2,
% 8.87/1.94 | all_25_3 gives:
% 8.87/1.94 | (16) vsucc(all_25_3) = all_25_2 & vmul(vd436, all_25_2) = all_25_1 &
% 8.87/1.94 | vmul(vd436, all_25_3) = all_25_0 & vplus(all_25_0, vd436) = all_25_1 &
% 8.87/1.94 | vplus(vd437, vd439) = all_25_3 & $i(all_25_0) & $i(all_25_1) &
% 8.87/1.94 | $i(all_25_2) & $i(all_25_3)
% 8.87/1.94 |
% 8.87/1.94 | ALPHA: (16) implies:
% 8.87/1.94 | (17) vplus(vd437, vd439) = all_25_3
% 8.87/1.94 | (18) vplus(all_25_0, vd436) = all_25_1
% 8.87/1.94 | (19) vmul(vd436, all_25_3) = all_25_0
% 8.87/1.94 |
% 8.87/1.94 | DELTA: instantiating (4) with fresh symbols all_27_0, all_27_1, all_27_2,
% 8.87/1.94 | all_27_3 gives:
% 8.87/1.94 | (20) vmul(vd436, all_27_3) = all_27_2 & vmul(vd436, vd439) = all_27_0 &
% 8.87/1.94 | vmul(vd436, vd437) = all_27_1 & vplus(all_27_1, all_27_0) = all_27_2 &
% 8.87/1.94 | vplus(vd437, vd439) = all_27_3 & $i(all_27_0) & $i(all_27_1) &
% 8.87/1.94 | $i(all_27_2) & $i(all_27_3)
% 8.87/1.94 |
% 8.87/1.94 | ALPHA: (20) implies:
% 8.87/1.94 | (21) vplus(vd437, vd439) = all_27_3
% 8.87/1.94 | (22) vplus(all_27_1, all_27_0) = all_27_2
% 8.87/1.94 | (23) vmul(vd436, vd437) = all_27_1
% 8.87/1.94 | (24) vmul(vd436, vd439) = all_27_0
% 8.87/1.94 | (25) vmul(vd436, all_27_3) = all_27_2
% 8.87/1.94 |
% 8.87/1.94 | DELTA: instantiating (3) with fresh symbols all_29_0, all_29_1, all_29_2,
% 8.87/1.94 | all_29_3, all_29_4 gives:
% 8.87/1.94 | (26) vsucc(all_29_1) = all_29_0 & vsucc(vd439) = all_29_4 & vmul(vd436,
% 8.87/1.94 | all_29_0) = all_29_2 & vmul(vd436, all_29_3) = all_29_2 &
% 8.87/1.94 | vplus(vd437, all_29_4) = all_29_3 & vplus(vd437, vd439) = all_29_1 &
% 8.87/1.94 | $i(all_29_0) & $i(all_29_1) & $i(all_29_2) & $i(all_29_3) &
% 8.87/1.94 | $i(all_29_4)
% 8.87/1.94 |
% 8.87/1.94 | ALPHA: (26) implies:
% 8.87/1.94 | (27) vplus(vd437, vd439) = all_29_1
% 8.87/1.94 |
% 8.87/1.94 | DELTA: instantiating (8) with fresh symbols all_31_0, all_31_1, all_31_2,
% 8.87/1.94 | all_31_3, all_31_4, all_31_5 gives:
% 8.87/1.95 | (28) ~ (all_31_0 = all_31_2) & vmul(vd436, vd439) = all_31_4 & vmul(vd436,
% 8.87/1.95 | vd437) = all_31_5 & vplus(all_31_3, vd436) = all_31_2 &
% 8.87/1.95 | vplus(all_31_4, vd436) = all_31_1 & vplus(all_31_5, all_31_1) =
% 8.87/1.95 | all_31_0 & vplus(all_31_5, all_31_4) = all_31_3 & $i(all_31_0) &
% 8.87/1.95 | $i(all_31_1) & $i(all_31_2) & $i(all_31_3) & $i(all_31_4) &
% 8.87/1.95 | $i(all_31_5)
% 8.87/1.95 |
% 8.87/1.95 | ALPHA: (28) implies:
% 8.87/1.95 | (29) ~ (all_31_0 = all_31_2)
% 8.87/1.95 | (30) $i(all_31_4)
% 8.87/1.95 | (31) vplus(all_31_5, all_31_4) = all_31_3
% 8.87/1.95 | (32) vplus(all_31_5, all_31_1) = all_31_0
% 8.87/1.95 | (33) vplus(all_31_4, vd436) = all_31_1
% 8.87/1.95 | (34) vplus(all_31_3, vd436) = all_31_2
% 8.87/1.95 | (35) vmul(vd436, vd437) = all_31_5
% 8.87/1.95 | (36) vmul(vd436, vd439) = all_31_4
% 8.87/1.95 |
% 8.87/1.95 | DELTA: instantiating (1) with fresh symbols all_33_0, all_33_1, all_33_2,
% 8.87/1.95 | all_33_3, all_33_4, all_33_5 gives:
% 8.87/1.95 | (37) vmul(vd436, all_33_5) = all_33_4 & vmul(vd436, vd439) = all_33_1 &
% 8.87/1.95 | vmul(vd436, vd437) = all_33_2 & vplus(all_33_0, vd436) = all_33_3 &
% 8.87/1.95 | vplus(all_33_2, all_33_1) = all_33_0 & vplus(all_33_4, vd436) =
% 8.87/1.95 | all_33_3 & vplus(vd437, vd439) = all_33_5 & $i(all_33_0) &
% 8.87/1.95 | $i(all_33_1) & $i(all_33_2) & $i(all_33_3) & $i(all_33_4) &
% 8.87/1.95 | $i(all_33_5)
% 8.87/1.95 |
% 8.87/1.95 | ALPHA: (37) implies:
% 8.87/1.95 | (38) vplus(vd437, vd439) = all_33_5
% 8.87/1.95 | (39) vplus(all_33_4, vd436) = all_33_3
% 8.87/1.95 | (40) vplus(all_33_2, all_33_1) = all_33_0
% 8.87/1.95 | (41) vmul(vd436, vd437) = all_33_2
% 8.87/1.95 | (42) vmul(vd436, vd439) = all_33_1
% 8.87/1.95 | (43) vmul(vd436, all_33_5) = all_33_4
% 8.87/1.95 |
% 8.87/1.95 | GROUND_INST: instantiating (9) with all_27_3, all_29_1, vd439, vd437,
% 8.87/1.95 | simplifying with (21), (27) gives:
% 8.87/1.95 | (44) all_29_1 = all_27_3
% 8.87/1.95 |
% 8.87/1.95 | GROUND_INST: instantiating (9) with all_29_1, all_33_5, vd439, vd437,
% 8.87/1.95 | simplifying with (27), (38) gives:
% 8.87/1.95 | (45) all_33_5 = all_29_1
% 8.87/1.95 |
% 8.87/1.95 | GROUND_INST: instantiating (9) with all_25_3, all_33_5, vd439, vd437,
% 8.87/1.95 | simplifying with (17), (38) gives:
% 8.87/1.95 | (46) all_33_5 = all_25_3
% 8.87/1.95 |
% 8.87/1.95 | GROUND_INST: instantiating (10) with all_23_2, all_27_1, vd437, vd436,
% 8.87/1.95 | simplifying with (15), (23) gives:
% 8.87/1.95 | (47) all_27_1 = all_23_2
% 8.87/1.95 |
% 8.87/1.95 | GROUND_INST: instantiating (10) with all_27_1, all_31_5, vd437, vd436,
% 8.87/1.95 | simplifying with (23), (35) gives:
% 8.87/1.95 | (48) all_31_5 = all_27_1
% 8.87/1.95 |
% 8.87/1.95 | GROUND_INST: instantiating (10) with all_31_5, all_33_2, vd437, vd436,
% 8.87/1.95 | simplifying with (35), (41) gives:
% 8.87/1.95 | (49) all_33_2 = all_31_5
% 8.87/1.95 |
% 8.87/1.95 | GROUND_INST: instantiating (10) with all_19_0, all_33_2, vd437, vd436,
% 8.87/1.95 | simplifying with (12), (41) gives:
% 8.87/1.95 | (50) all_33_2 = all_19_0
% 8.87/1.95 |
% 8.87/1.95 | GROUND_INST: instantiating (10) with all_31_4, all_33_1, vd439, vd436,
% 8.87/1.95 | simplifying with (36), (42) gives:
% 8.87/1.96 | (51) all_33_1 = all_31_4
% 8.87/1.96 |
% 8.87/1.96 | GROUND_INST: instantiating (10) with all_27_0, all_33_1, vd439, vd436,
% 8.87/1.96 | simplifying with (24), (42) gives:
% 8.87/1.96 | (52) all_33_1 = all_27_0
% 8.87/1.96 |
% 8.87/1.96 | COMBINE_EQS: (51), (52) imply:
% 8.87/1.96 | (53) all_31_4 = all_27_0
% 8.87/1.96 |
% 8.87/1.96 | SIMP: (53) implies:
% 8.87/1.96 | (54) all_31_4 = all_27_0
% 8.87/1.96 |
% 8.87/1.96 | COMBINE_EQS: (49), (50) imply:
% 8.87/1.96 | (55) all_31_5 = all_19_0
% 8.87/1.96 |
% 8.87/1.96 | SIMP: (55) implies:
% 8.87/1.96 | (56) all_31_5 = all_19_0
% 8.87/1.96 |
% 8.87/1.96 | COMBINE_EQS: (45), (46) imply:
% 8.87/1.96 | (57) all_29_1 = all_25_3
% 8.87/1.96 |
% 8.87/1.96 | SIMP: (57) implies:
% 8.87/1.96 | (58) all_29_1 = all_25_3
% 8.87/1.96 |
% 8.87/1.96 | COMBINE_EQS: (48), (56) imply:
% 8.87/1.96 | (59) all_27_1 = all_19_0
% 8.87/1.96 |
% 8.87/1.96 | SIMP: (59) implies:
% 8.87/1.96 | (60) all_27_1 = all_19_0
% 8.87/1.96 |
% 8.87/1.96 | COMBINE_EQS: (44), (58) imply:
% 8.87/1.96 | (61) all_27_3 = all_25_3
% 8.87/1.96 |
% 8.87/1.96 | SIMP: (61) implies:
% 8.87/1.96 | (62) all_27_3 = all_25_3
% 8.87/1.96 |
% 8.87/1.96 | COMBINE_EQS: (47), (60) imply:
% 8.87/1.96 | (63) all_23_2 = all_19_0
% 8.87/1.96 |
% 8.87/1.96 | SIMP: (63) implies:
% 8.87/1.96 | (64) all_23_2 = all_19_0
% 8.87/1.96 |
% 8.87/1.96 | REDUCE: (43), (46) imply:
% 8.87/1.96 | (65) vmul(vd436, all_25_3) = all_33_4
% 8.87/1.96 |
% 8.87/1.96 | REDUCE: (25), (62) imply:
% 8.87/1.96 | (66) vmul(vd436, all_25_3) = all_27_2
% 8.87/1.96 |
% 8.87/1.96 | REDUCE: (40), (50), (52) imply:
% 8.87/1.96 | (67) vplus(all_19_0, all_27_0) = all_33_0
% 8.87/1.96 |
% 8.87/1.96 | REDUCE: (33), (54) imply:
% 8.87/1.96 | (68) vplus(all_27_0, vd436) = all_31_1
% 8.87/1.96 |
% 8.87/1.96 | REDUCE: (32), (56) imply:
% 9.14/1.96 | (69) vplus(all_19_0, all_31_1) = all_31_0
% 9.14/1.96 |
% 9.14/1.96 | REDUCE: (31), (54), (56) imply:
% 9.14/1.96 | (70) vplus(all_19_0, all_27_0) = all_31_3
% 9.14/1.96 |
% 9.14/1.96 | REDUCE: (22), (60) imply:
% 9.14/1.96 | (71) vplus(all_19_0, all_27_0) = all_27_2
% 9.14/1.96 |
% 9.14/1.96 | REDUCE: (30), (54) imply:
% 9.14/1.96 | (72) $i(all_27_0)
% 9.14/1.96 |
% 9.14/1.96 | REDUCE: (14), (64) imply:
% 9.14/1.96 | (73) $i(all_19_0)
% 9.14/1.96 |
% 9.14/1.96 | GROUND_INST: instantiating (9) with all_31_3, all_33_0, all_27_0, all_19_0,
% 9.14/1.96 | simplifying with (67), (70) gives:
% 9.14/1.96 | (74) all_33_0 = all_31_3
% 9.14/1.96 |
% 9.14/1.96 | GROUND_INST: instantiating (9) with all_27_2, all_33_0, all_27_0, all_19_0,
% 9.14/1.96 | simplifying with (67), (71) gives:
% 9.14/1.96 | (75) all_33_0 = all_27_2
% 9.14/1.96 |
% 9.14/1.96 | GROUND_INST: instantiating (10) with all_25_0, all_33_4, all_25_3, vd436,
% 9.14/1.96 | simplifying with (19), (65) gives:
% 9.14/1.96 | (76) all_33_4 = all_25_0
% 9.14/1.96 |
% 9.14/1.96 | GROUND_INST: instantiating (10) with all_27_2, all_33_4, all_25_3, vd436,
% 9.14/1.96 | simplifying with (65), (66) gives:
% 9.14/1.96 | (77) all_33_4 = all_27_2
% 9.14/1.96 |
% 9.14/1.96 | COMBINE_EQS: (74), (75) imply:
% 9.14/1.96 | (78) all_31_3 = all_27_2
% 9.14/1.96 |
% 9.14/1.96 | SIMP: (78) implies:
% 9.14/1.96 | (79) all_31_3 = all_27_2
% 9.14/1.96 |
% 9.14/1.96 | COMBINE_EQS: (76), (77) imply:
% 9.14/1.96 | (80) all_27_2 = all_25_0
% 9.14/1.96 |
% 9.14/1.96 | SIMP: (80) implies:
% 9.14/1.96 | (81) all_27_2 = all_25_0
% 9.14/1.96 |
% 9.14/1.96 | COMBINE_EQS: (79), (81) imply:
% 9.14/1.96 | (82) all_31_3 = all_25_0
% 9.14/1.96 |
% 9.14/1.96 | REDUCE: (39), (76) imply:
% 9.14/1.96 | (83) vplus(all_25_0, vd436) = all_33_3
% 9.14/1.96 |
% 9.14/1.96 | REDUCE: (34), (82) imply:
% 9.14/1.96 | (84) vplus(all_25_0, vd436) = all_31_2
% 9.14/1.96 |
% 9.14/1.96 | REDUCE: (71), (81) imply:
% 9.14/1.97 | (85) vplus(all_19_0, all_27_0) = all_25_0
% 9.14/1.97 |
% 9.14/1.97 | GROUND_INST: instantiating (9) with all_25_1, all_33_3, vd436, all_25_0,
% 9.14/1.97 | simplifying with (18), (83) gives:
% 9.14/1.97 | (86) all_33_3 = all_25_1
% 9.14/1.97 |
% 9.14/1.97 | GROUND_INST: instantiating (9) with all_31_2, all_33_3, vd436, all_25_0,
% 9.14/1.97 | simplifying with (83), (84) gives:
% 9.14/1.97 | (87) all_33_3 = all_31_2
% 9.14/1.97 |
% 9.14/1.97 | COMBINE_EQS: (86), (87) imply:
% 9.14/1.97 | (88) all_31_2 = all_25_1
% 9.14/1.97 |
% 9.14/1.97 | REDUCE: (29), (88) imply:
% 9.14/1.97 | (89) ~ (all_31_0 = all_25_1)
% 9.14/1.97 |
% 9.14/1.97 | GROUND_INST: instantiating (ass(cond(33, 0), 0)) with all_19_0, all_27_0,
% 9.14/1.97 | vd436, all_25_0, all_25_1, simplifying with (7), (18), (72),
% 9.14/1.97 | (73), (85) gives:
% 9.14/1.97 | (90) ? [v0: $i] : (vplus(all_27_0, vd436) = v0 & vplus(all_19_0, v0) =
% 9.14/1.97 | all_25_1 & $i(v0) & $i(all_25_1))
% 9.14/1.97 |
% 9.14/1.97 | DELTA: instantiating (90) with fresh symbol all_53_0 gives:
% 9.14/1.97 | (91) vplus(all_27_0, vd436) = all_53_0 & vplus(all_19_0, all_53_0) =
% 9.14/1.97 | all_25_1 & $i(all_53_0) & $i(all_25_1)
% 9.14/1.97 |
% 9.14/1.97 | ALPHA: (91) implies:
% 9.14/1.97 | (92) vplus(all_19_0, all_53_0) = all_25_1
% 9.14/1.97 | (93) vplus(all_27_0, vd436) = all_53_0
% 9.14/1.97 |
% 9.14/1.97 | GROUND_INST: instantiating (9) with all_31_1, all_53_0, vd436, all_27_0,
% 9.14/1.97 | simplifying with (68), (93) gives:
% 9.14/1.97 | (94) all_53_0 = all_31_1
% 9.14/1.97 |
% 9.14/1.97 | REDUCE: (92), (94) imply:
% 9.14/1.97 | (95) vplus(all_19_0, all_31_1) = all_25_1
% 9.14/1.97 |
% 9.14/1.97 | GROUND_INST: instantiating (9) with all_31_0, all_25_1, all_31_1, all_19_0,
% 9.14/1.97 | simplifying with (69), (95) gives:
% 9.14/1.97 | (96) all_31_0 = all_25_1
% 9.14/1.97 |
% 9.14/1.97 | REDUCE: (89), (96) imply:
% 9.14/1.97 | (97) $false
% 9.14/1.97 |
% 9.14/1.97 | CLOSE: (97) is inconsistent.
% 9.14/1.97 |
% 9.14/1.97 End of proof
% 9.14/1.97 % SZS output end Proof for theBenchmark
% 9.14/1.97
% 9.14/1.97 1383ms
%------------------------------------------------------------------------------