TSTP Solution File: NUM848+1 by Princess---230619
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : NUM848+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 : n017.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 11:50:23 EDT 2023
% Result : Theorem 9.79s 2.11s
% Output : Proof 13.38s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : NUM848+1 : TPTP v8.1.2. Released v4.1.0.
% 0.12/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.33 % Computer : n017.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Fri Aug 25 15:12:25 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.20/0.61 ________ _____
% 0.20/0.61 ___ __ \_________(_)________________________________
% 0.20/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.20/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.20/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.20/0.61
% 0.20/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.20/0.61 (2023-06-19)
% 0.20/0.61
% 0.20/0.61 (c) Philipp Rümmer, 2009-2023
% 0.20/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.20/0.61 Amanda Stjerna.
% 0.20/0.61 Free software under BSD-3-Clause.
% 0.20/0.61
% 0.20/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.20/0.61
% 0.20/0.61 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.20/0.62 Running up to 7 provers in parallel.
% 0.20/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.20/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.20/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.20/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.20/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.20/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.20/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 3.11/1.19 Prover 1: Preprocessing ...
% 3.11/1.19 Prover 4: Preprocessing ...
% 3.11/1.21 Prover 5: Preprocessing ...
% 3.11/1.21 Prover 2: Preprocessing ...
% 3.11/1.21 Prover 0: Preprocessing ...
% 3.11/1.21 Prover 6: Preprocessing ...
% 3.11/1.21 Prover 3: Preprocessing ...
% 7.88/1.83 Prover 1: Warning: ignoring some quantifiers
% 8.30/1.84 Prover 6: Proving ...
% 8.43/1.85 Prover 3: Warning: ignoring some quantifiers
% 8.43/1.86 Prover 5: Proving ...
% 8.43/1.88 Prover 3: Constructing countermodel ...
% 8.43/1.89 Prover 1: Constructing countermodel ...
% 8.43/1.91 Prover 4: Warning: ignoring some quantifiers
% 8.43/1.96 Prover 2: Proving ...
% 8.43/1.98 Prover 4: Constructing countermodel ...
% 8.43/1.99 Prover 0: Proving ...
% 9.79/2.11 Prover 3: proved (1480ms)
% 9.79/2.11
% 9.79/2.11 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 9.79/2.11
% 9.79/2.11 Prover 6: stopped
% 9.79/2.12 Prover 5: stopped
% 10.40/2.13 Prover 2: stopped
% 10.40/2.13 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 10.40/2.13 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 10.40/2.13 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 10.40/2.13 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 10.40/2.13 Prover 0: stopped
% 10.40/2.14 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 10.40/2.17 Prover 8: Preprocessing ...
% 10.40/2.18 Prover 11: Preprocessing ...
% 10.81/2.18 Prover 7: Preprocessing ...
% 10.81/2.19 Prover 13: Preprocessing ...
% 10.81/2.20 Prover 10: Preprocessing ...
% 12.08/2.36 Prover 13: Warning: ignoring some quantifiers
% 12.08/2.38 Prover 7: Warning: ignoring some quantifiers
% 12.08/2.38 Prover 10: Warning: ignoring some quantifiers
% 12.08/2.39 Prover 13: Constructing countermodel ...
% 12.08/2.39 Prover 7: Constructing countermodel ...
% 12.08/2.39 Prover 10: Constructing countermodel ...
% 12.08/2.42 Prover 8: Warning: ignoring some quantifiers
% 12.74/2.43 Prover 11: Warning: ignoring some quantifiers
% 12.74/2.44 Prover 1: Found proof (size 110)
% 12.74/2.44 Prover 1: proved (1817ms)
% 12.74/2.44 Prover 10: stopped
% 12.74/2.44 Prover 7: stopped
% 12.74/2.44 Prover 13: stopped
% 12.74/2.45 Prover 8: Constructing countermodel ...
% 12.74/2.45 Prover 4: stopped
% 12.74/2.46 Prover 8: stopped
% 12.74/2.46 Prover 11: Constructing countermodel ...
% 12.74/2.48 Prover 11: stopped
% 12.74/2.48
% 12.74/2.48 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 12.74/2.48
% 13.06/2.52 % SZS output start Proof for theBenchmark
% 13.06/2.52 Assumptions after simplification:
% 13.06/2.52 ---------------------------------
% 13.06/2.52
% 13.06/2.52 (ass(cond(61, 0), 0))
% 13.06/2.55 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (vplus(v0, v1) = v2) | ~ $i(v1)
% 13.06/2.55 | ~ $i(v0) | (vplus(v1, v0) = v2 & $i(v2)))
% 13.06/2.55
% 13.06/2.55 (holds(284, 438, 1))
% 13.06/2.55 $i(vd437) & $i(vd436) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 13.06/2.55 (vsucc(vd437) = v0 & vmul(vd436, v0) = v1 & vmul(vd436, vd437) = v2 &
% 13.06/2.55 vplus(v2, vd436) = v1 & $i(v2) & $i(v1) & $i(v0))
% 13.06/2.55
% 13.06/2.55 (holds(284, 438, 2))
% 13.38/2.55 $i(v1) & $i(vd437) & $i(vd436) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 13.38/2.55 (vmul(vd436, v1) = v2 & vmul(vd436, vd437) = v0 & vplus(v0, v2) = v1 &
% 13.38/2.55 vplus(v0, vd436) = v1 & $i(v2) & $i(v1) & $i(v0))
% 13.38/2.55
% 13.38/2.55 (holds(285, 440, 0))
% 13.38/2.55 $i(vd439) & $i(vd437) & $i(vd436) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 13.38/2.55 ? [v3: $i] : (vmul(vd436, v0) = v1 & vmul(vd436, vd439) = v3 & vmul(vd436,
% 13.38/2.55 vd437) = v2 & vplus(v2, v3) = v1 & vplus(vd437, vd439) = v0 & $i(v3) &
% 13.38/2.55 $i(v2) & $i(v1) & $i(v0))
% 13.38/2.55
% 13.38/2.55 (holds(286, 441, 0))
% 13.38/2.56 $i(vd439) & $i(vd437) & $i(vd436) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 13.38/2.56 ? [v3: $i] : ? [v4: $i] : (vsucc(v3) = v4 & vsucc(vd439) = v0 & vmul(vd436,
% 13.38/2.56 v4) = v2 & vmul(vd436, v1) = v2 & vplus(vd437, v0) = v1 & vplus(vd437,
% 13.38/2.56 vd439) = v3 & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 13.38/2.56
% 13.38/2.56 (holds(286, 441, 1))
% 13.38/2.56 $i(vd439) & $i(vd437) & $i(vd436) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 13.38/2.56 ? [v3: $i] : (vsucc(v0) = v1 & vmul(vd436, v1) = v2 & vmul(vd436, v0) = v3 &
% 13.38/2.56 vplus(v3, vd436) = v2 & vplus(vd437, vd439) = v0 & $i(v3) & $i(v2) & $i(v1)
% 13.38/2.56 & $i(v0))
% 13.38/2.56
% 13.38/2.56 (holds(286, 441, 2))
% 13.38/2.56 $i(vd439) & $i(vd437) & $i(vd436) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 13.38/2.56 ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : (vmul(vd436, v0) = v1 & vmul(vd436,
% 13.38/2.56 vd439) = v4 & vmul(vd436, vd437) = v3 & vplus(v5, vd436) = v2 & vplus(v3,
% 13.38/2.56 v4) = v5 & vplus(v1, vd436) = v2 & vplus(vd437, vd439) = v0 & $i(v5) &
% 13.38/2.56 $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 13.38/2.56
% 13.38/2.56 (holds(286, 441, 3))
% 13.38/2.56 $i(vd439) & $i(vd437) & $i(vd436) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 13.38/2.56 ? [v3: $i] : ? [v4: $i] : (vmul(vd436, vd439) = v1 & vmul(vd436, vd437) = v0
% 13.38/2.56 & vplus(v2, vd436) = v3 & vplus(v1, vd436) = v4 & vplus(v0, v4) = v3 &
% 13.38/2.56 vplus(v0, v1) = v2 & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 13.38/2.56
% 13.38/2.56 (holds(286, 441, 4))
% 13.38/2.56 $i(vd439) & $i(vd437) & $i(vd436) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 13.38/2.56 ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ( ~ (v6 = v3) &
% 13.38/2.56 vsucc(vd439) = v4 & vmul(vd436, v4) = v5 & vmul(vd436, vd439) = v1 &
% 13.38/2.56 vmul(vd436, vd437) = v0 & vplus(v1, vd436) = v2 & vplus(v0, v5) = v6 &
% 13.38/2.56 vplus(v0, v2) = v3 & $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) &
% 13.38/2.56 $i(v0))
% 13.38/2.56
% 13.38/2.56 (qu(cond(conseq(axiom(3)), 32), and(holds(definiens(249), 399, 0), holds(definiens(249), 398, 0))))
% 13.38/2.57 $i(v1) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 13.38/2.57 (vsucc(v1) = v2) | ~ (vmul(v0, v2) = v3) | ~ $i(v1) | ~ $i(v0) | ? [v4:
% 13.38/2.57 $i] : (vmul(v0, v1) = v4 & vplus(v4, v0) = v3 & $i(v4) & $i(v3))) & ?
% 13.38/2.57 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v1 | ~ (vmul(v1, v1) = v2) | ~
% 13.38/2.57 $i(v1) | ~ $i(v0))
% 13.38/2.57
% 13.38/2.57 (function-axioms)
% 13.38/2.57 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 13.38/2.57 [v3: $i] : (v1 = v0 | ~ (geq(v3, v2) = v1) | ~ (geq(v3, v2) = v0)) & ! [v0:
% 13.38/2.57 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 13.38/2.57 : (v1 = v0 | ~ (greater(v3, v2) = v1) | ~ (greater(v3, v2) = v0)) & ! [v0:
% 13.38/2.57 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 13.38/2.57 : (v1 = v0 | ~ (less(v3, v2) = v1) | ~ (less(v3, v2) = v0)) & ! [v0:
% 13.38/2.57 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 13.38/2.57 : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = v0)) & ! [v0: $i] : !
% 13.38/2.57 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (vmul(v3, v2) = v1) | ~
% 13.38/2.57 (vmul(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i]
% 13.38/2.57 : (v1 = v0 | ~ (vplus(v3, v2) = v1) | ~ (vplus(v3, v2) = v0)) & ! [v0: $i]
% 13.38/2.57 : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (vskolem2(v2) = v1) | ~
% 13.38/2.57 (vskolem2(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 |
% 13.38/2.57 ~ (vsucc(v2) = v1) | ~ (vsucc(v2) = v0))
% 13.38/2.57
% 13.38/2.57 Further assumptions not needed in the proof:
% 13.38/2.57 --------------------------------------------
% 13.38/2.57 ass(cond(12, 0), 0), ass(cond(140, 0), 0), ass(cond(147, 0), 0), ass(cond(158,
% 13.38/2.57 0), 0), ass(cond(163, 0), 0), ass(cond(168, 0), 0), ass(cond(184, 0), 0),
% 13.38/2.57 ass(cond(189, 0), 0), ass(cond(20, 0), 0), ass(cond(209, 0), 0), ass(cond(223,
% 13.38/2.57 0), 0), ass(cond(228, 0), 0), ass(cond(234, 0), 0), ass(cond(241, 0), 0),
% 13.38/2.57 ass(cond(253, 0), 0), ass(cond(261, 0), 0), ass(cond(270, 0), 0), ass(cond(33,
% 13.38/2.57 0), 0), ass(cond(43, 0), 0), ass(cond(52, 0), 0), ass(cond(6, 0), 0),
% 13.38/2.57 ass(cond(73, 0), 0), ass(cond(81, 0), 0), ass(cond(goal(130), 0), 0),
% 13.38/2.57 ass(cond(goal(130), 0), 1), ass(cond(goal(130), 0), 2), ass(cond(goal(130), 0),
% 13.38/2.57 3), ass(cond(goal(177), 0), 0), ass(cond(goal(193), 0), 0),
% 13.38/2.57 ass(cond(goal(193), 0), 1), ass(cond(goal(193), 0), 2), ass(cond(goal(202), 0),
% 13.38/2.57 0), ass(cond(goal(202), 0), 1), ass(cond(goal(202), 0), 2),
% 13.38/2.57 ass(cond(goal(216), 0), 0), ass(cond(goal(88), 0), 0), ass(cond(goal(88), 0),
% 13.38/2.57 1), ass(cond(goal(88), 0), 2), ass(cond(goal(88), 0), 3),
% 13.38/2.57 def(cond(conseq(axiom(3)), 11), 1), def(cond(conseq(axiom(3)), 12), 1),
% 13.38/2.57 def(cond(conseq(axiom(3)), 16), 1), def(cond(conseq(axiom(3)), 17), 1),
% 13.38/2.57 holds(284, 438, 0), qu(antec(axiom(3)), imp(antec(axiom(3)))),
% 13.38/2.57 qu(cond(conseq(axiom(3)), 3), and(holds(definiens(29), 45, 0),
% 13.38/2.57 holds(definiens(29), 44, 0))), qu(restrictor(axiom(1)),
% 13.38/2.57 holds(scope(axiom(1)), 2, 0))
% 13.38/2.57
% 13.38/2.57 Those formulas are unsatisfiable:
% 13.38/2.57 ---------------------------------
% 13.38/2.57
% 13.38/2.57 Begin of proof
% 13.38/2.57 |
% 13.38/2.57 | ALPHA: (holds(286, 441, 3)) implies:
% 13.38/2.58 | (1) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 13.38/2.58 | (vmul(vd436, vd439) = v1 & vmul(vd436, vd437) = v0 & vplus(v2, vd436) =
% 13.38/2.58 | v3 & vplus(v1, vd436) = v4 & vplus(v0, v4) = v3 & vplus(v0, v1) = v2
% 13.38/2.58 | & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 13.38/2.58 |
% 13.38/2.58 | ALPHA: (holds(286, 441, 2)) implies:
% 13.38/2.58 | (2) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 13.38/2.58 | ? [v5: $i] : (vmul(vd436, v0) = v1 & vmul(vd436, vd439) = v4 &
% 13.38/2.58 | vmul(vd436, vd437) = v3 & vplus(v5, vd436) = v2 & vplus(v3, v4) = v5
% 13.38/2.58 | & vplus(v1, vd436) = v2 & vplus(vd437, vd439) = v0 & $i(v5) & $i(v4)
% 13.38/2.58 | & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 13.38/2.58 |
% 13.38/2.58 | ALPHA: (holds(286, 441, 1)) implies:
% 13.38/2.58 | (3) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : (vsucc(v0) = v1
% 13.38/2.58 | & vmul(vd436, v1) = v2 & vmul(vd436, v0) = v3 & vplus(v3, vd436) = v2
% 13.38/2.58 | & vplus(vd437, vd439) = v0 & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 13.38/2.58 |
% 13.38/2.58 | ALPHA: (holds(286, 441, 0)) implies:
% 13.38/2.58 | (4) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 13.38/2.58 | (vsucc(v3) = v4 & vsucc(vd439) = v0 & vmul(vd436, v4) = v2 &
% 13.38/2.58 | vmul(vd436, v1) = v2 & vplus(vd437, v0) = v1 & vplus(vd437, vd439) =
% 13.38/2.58 | v3 & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 13.38/2.58 |
% 13.38/2.58 | ALPHA: (holds(285, 440, 0)) implies:
% 13.38/2.58 | (5) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : (vmul(vd436,
% 13.38/2.58 | v0) = v1 & vmul(vd436, vd439) = v3 & vmul(vd436, vd437) = v2 &
% 13.38/2.58 | vplus(v2, v3) = v1 & vplus(vd437, vd439) = v0 & $i(v3) & $i(v2) &
% 13.38/2.58 | $i(v1) & $i(v0))
% 13.38/2.58 |
% 13.38/2.58 | ALPHA: (holds(284, 438, 2)) implies:
% 13.38/2.58 | (6) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (vmul(vd436, v1) = v2 &
% 13.38/2.58 | vmul(vd436, vd437) = v0 & vplus(v0, v2) = v1 & vplus(v0, vd436) = v1
% 13.38/2.58 | & $i(v2) & $i(v1) & $i(v0))
% 13.38/2.58 |
% 13.38/2.58 | ALPHA: (holds(284, 438, 1)) implies:
% 13.38/2.58 | (7) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (vsucc(vd437) = v0 &
% 13.38/2.58 | vmul(vd436, v0) = v1 & vmul(vd436, vd437) = v2 & vplus(v2, vd436) =
% 13.38/2.58 | v1 & $i(v2) & $i(v1) & $i(v0))
% 13.38/2.58 |
% 13.38/2.58 | ALPHA: (qu(cond(conseq(axiom(3)), 32), and(holds(definiens(249), 399, 0),
% 13.38/2.58 | holds(definiens(249), 398, 0)))) implies:
% 13.38/2.58 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (vsucc(v1)
% 13.38/2.58 | = v2) | ~ (vmul(v0, v2) = v3) | ~ $i(v1) | ~ $i(v0) | ? [v4:
% 13.38/2.58 | $i] : (vmul(v0, v1) = v4 & vplus(v4, v0) = v3 & $i(v4) & $i(v3)))
% 13.38/2.58 |
% 13.38/2.58 | ALPHA: (holds(286, 441, 4)) implies:
% 13.38/2.58 | (9) $i(vd436)
% 13.38/2.58 | (10) $i(vd439)
% 13.38/2.59 | (11) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 13.38/2.59 | ? [v5: $i] : ? [v6: $i] : ( ~ (v6 = v3) & vsucc(vd439) = v4 &
% 13.38/2.59 | vmul(vd436, v4) = v5 & vmul(vd436, vd439) = v1 & vmul(vd436, vd437)
% 13.38/2.59 | = v0 & vplus(v1, vd436) = v2 & vplus(v0, v5) = v6 & vplus(v0, v2) =
% 13.38/2.59 | v3 & $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 13.38/2.59 |
% 13.38/2.59 | ALPHA: (function-axioms) implies:
% 13.38/2.59 | (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (vsucc(v2) =
% 13.38/2.59 | v1) | ~ (vsucc(v2) = v0))
% 13.38/2.59 | (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 13.38/2.59 | (vplus(v3, v2) = v1) | ~ (vplus(v3, v2) = v0))
% 13.38/2.59 | (14) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 13.38/2.59 | (vmul(v3, v2) = v1) | ~ (vmul(v3, v2) = v0))
% 13.38/2.59 |
% 13.38/2.59 | DELTA: instantiating (7) with fresh symbols all_53_0, all_53_1, all_53_2
% 13.38/2.59 | gives:
% 13.38/2.59 | (15) vsucc(vd437) = all_53_2 & vmul(vd436, all_53_2) = all_53_1 &
% 13.38/2.59 | vmul(vd436, vd437) = all_53_0 & vplus(all_53_0, vd436) = all_53_1 &
% 13.38/2.59 | $i(all_53_0) & $i(all_53_1) & $i(all_53_2)
% 13.38/2.59 |
% 13.38/2.59 | ALPHA: (15) implies:
% 13.38/2.59 | (16) vmul(vd436, vd437) = all_53_0
% 13.38/2.59 |
% 13.38/2.59 | DELTA: instantiating (6) with fresh symbols all_57_0, all_57_1, all_57_2
% 13.38/2.59 | gives:
% 13.38/2.59 | (17) vmul(vd436, v1) = all_57_0 & vmul(vd436, vd437) = all_57_2 &
% 13.38/2.59 | vplus(all_57_2, all_57_0) = all_57_1 & vplus(all_57_2, vd436) =
% 13.38/2.59 | all_57_1 & $i(all_57_0) & $i(all_57_1) & $i(all_57_2)
% 13.38/2.59 |
% 13.38/2.59 | ALPHA: (17) implies:
% 13.38/2.59 | (18) $i(all_57_2)
% 13.38/2.59 | (19) vmul(vd436, vd437) = all_57_2
% 13.38/2.59 |
% 13.38/2.59 | DELTA: instantiating (3) with fresh symbols all_61_0, all_61_1, all_61_2,
% 13.38/2.59 | all_61_3 gives:
% 13.38/2.59 | (20) vsucc(all_61_3) = all_61_2 & vmul(vd436, all_61_2) = all_61_1 &
% 13.38/2.59 | vmul(vd436, all_61_3) = all_61_0 & vplus(all_61_0, vd436) = all_61_1 &
% 13.38/2.59 | vplus(vd437, vd439) = all_61_3 & $i(all_61_0) & $i(all_61_1) &
% 13.38/2.59 | $i(all_61_2) & $i(all_61_3)
% 13.38/2.59 |
% 13.38/2.59 | ALPHA: (20) implies:
% 13.38/2.59 | (21) vplus(vd437, vd439) = all_61_3
% 13.38/2.59 | (22) vplus(all_61_0, vd436) = all_61_1
% 13.38/2.59 | (23) vmul(vd436, all_61_3) = all_61_0
% 13.38/2.59 |
% 13.38/2.59 | DELTA: instantiating (5) with fresh symbols all_63_0, all_63_1, all_63_2,
% 13.38/2.59 | all_63_3 gives:
% 13.38/2.59 | (24) vmul(vd436, all_63_3) = all_63_2 & vmul(vd436, vd439) = all_63_0 &
% 13.38/2.59 | vmul(vd436, vd437) = all_63_1 & vplus(all_63_1, all_63_0) = all_63_2 &
% 13.38/2.59 | vplus(vd437, vd439) = all_63_3 & $i(all_63_0) & $i(all_63_1) &
% 13.38/2.59 | $i(all_63_2) & $i(all_63_3)
% 13.38/2.59 |
% 13.38/2.59 | ALPHA: (24) implies:
% 13.38/2.59 | (25) vplus(vd437, vd439) = all_63_3
% 13.38/2.59 | (26) vplus(all_63_1, all_63_0) = all_63_2
% 13.38/2.59 | (27) vmul(vd436, vd437) = all_63_1
% 13.38/2.59 | (28) vmul(vd436, vd439) = all_63_0
% 13.38/2.59 | (29) vmul(vd436, all_63_3) = all_63_2
% 13.38/2.59 |
% 13.38/2.59 | DELTA: instantiating (4) with fresh symbols all_65_0, all_65_1, all_65_2,
% 13.38/2.59 | all_65_3, all_65_4 gives:
% 13.38/2.59 | (30) vsucc(all_65_1) = all_65_0 & vsucc(vd439) = all_65_4 & vmul(vd436,
% 13.38/2.59 | all_65_0) = all_65_2 & vmul(vd436, all_65_3) = all_65_2 &
% 13.38/2.59 | vplus(vd437, all_65_4) = all_65_3 & vplus(vd437, vd439) = all_65_1 &
% 13.38/2.59 | $i(all_65_0) & $i(all_65_1) & $i(all_65_2) & $i(all_65_3) &
% 13.38/2.59 | $i(all_65_4)
% 13.38/2.59 |
% 13.38/2.59 | ALPHA: (30) implies:
% 13.38/2.60 | (31) vplus(vd437, vd439) = all_65_1
% 13.38/2.60 | (32) vsucc(vd439) = all_65_4
% 13.38/2.60 |
% 13.38/2.60 | DELTA: instantiating (1) with fresh symbols all_67_0, all_67_1, all_67_2,
% 13.38/2.60 | all_67_3, all_67_4 gives:
% 13.38/2.60 | (33) vmul(vd436, vd439) = all_67_3 & vmul(vd436, vd437) = all_67_4 &
% 13.38/2.60 | vplus(all_67_2, vd436) = all_67_1 & vplus(all_67_3, vd436) = all_67_0
% 13.38/2.60 | & vplus(all_67_4, all_67_0) = all_67_1 & vplus(all_67_4, all_67_3) =
% 13.38/2.60 | all_67_2 & $i(all_67_0) & $i(all_67_1) & $i(all_67_2) & $i(all_67_3) &
% 13.38/2.60 | $i(all_67_4)
% 13.38/2.60 |
% 13.38/2.60 | ALPHA: (33) implies:
% 13.38/2.60 | (34) vplus(all_67_4, all_67_3) = all_67_2
% 13.38/2.60 | (35) vplus(all_67_4, all_67_0) = all_67_1
% 13.38/2.60 | (36) vplus(all_67_3, vd436) = all_67_0
% 13.38/2.60 | (37) vplus(all_67_2, vd436) = all_67_1
% 13.38/2.60 | (38) vmul(vd436, vd437) = all_67_4
% 13.38/2.60 | (39) vmul(vd436, vd439) = all_67_3
% 13.38/2.60 |
% 13.38/2.60 | DELTA: instantiating (2) with fresh symbols all_69_0, all_69_1, all_69_2,
% 13.38/2.60 | all_69_3, all_69_4, all_69_5 gives:
% 13.38/2.60 | (40) vmul(vd436, all_69_5) = all_69_4 & vmul(vd436, vd439) = all_69_1 &
% 13.38/2.60 | vmul(vd436, vd437) = all_69_2 & vplus(all_69_0, vd436) = all_69_3 &
% 13.38/2.60 | vplus(all_69_2, all_69_1) = all_69_0 & vplus(all_69_4, vd436) =
% 13.38/2.60 | all_69_3 & vplus(vd437, vd439) = all_69_5 & $i(all_69_0) &
% 13.38/2.60 | $i(all_69_1) & $i(all_69_2) & $i(all_69_3) & $i(all_69_4) &
% 13.38/2.60 | $i(all_69_5)
% 13.38/2.60 |
% 13.38/2.60 | ALPHA: (40) implies:
% 13.38/2.60 | (41) vplus(vd437, vd439) = all_69_5
% 13.38/2.60 | (42) vplus(all_69_4, vd436) = all_69_3
% 13.38/2.60 | (43) vplus(all_69_2, all_69_1) = all_69_0
% 13.38/2.60 | (44) vmul(vd436, vd437) = all_69_2
% 13.38/2.60 | (45) vmul(vd436, vd439) = all_69_1
% 13.38/2.60 | (46) vmul(vd436, all_69_5) = all_69_4
% 13.38/2.60 |
% 13.38/2.60 | DELTA: instantiating (11) with fresh symbols all_71_0, all_71_1, all_71_2,
% 13.38/2.60 | all_71_3, all_71_4, all_71_5, all_71_6 gives:
% 13.38/2.60 | (47) ~ (all_71_0 = all_71_3) & vsucc(vd439) = all_71_2 & vmul(vd436,
% 13.38/2.60 | all_71_2) = all_71_1 & vmul(vd436, vd439) = all_71_5 & vmul(vd436,
% 13.38/2.60 | vd437) = all_71_6 & vplus(all_71_5, vd436) = all_71_4 &
% 13.38/2.60 | vplus(all_71_6, all_71_1) = all_71_0 & vplus(all_71_6, all_71_4) =
% 13.38/2.60 | all_71_3 & $i(all_71_0) & $i(all_71_1) & $i(all_71_2) & $i(all_71_3) &
% 13.38/2.60 | $i(all_71_4) & $i(all_71_5) & $i(all_71_6)
% 13.38/2.60 |
% 13.38/2.60 | ALPHA: (47) implies:
% 13.38/2.60 | (48) ~ (all_71_0 = all_71_3)
% 13.38/2.60 | (49) $i(all_71_4)
% 13.38/2.60 | (50) $i(all_71_1)
% 13.38/2.60 | (51) vplus(all_71_6, all_71_4) = all_71_3
% 13.38/2.60 | (52) vplus(all_71_6, all_71_1) = all_71_0
% 13.38/2.60 | (53) vplus(all_71_5, vd436) = all_71_4
% 13.38/2.60 | (54) vmul(vd436, vd437) = all_71_6
% 13.38/2.60 | (55) vmul(vd436, vd439) = all_71_5
% 13.38/2.60 | (56) vmul(vd436, all_71_2) = all_71_1
% 13.38/2.60 | (57) vsucc(vd439) = all_71_2
% 13.38/2.60 |
% 13.38/2.60 | GROUND_INST: instantiating (13) with all_65_1, all_69_5, vd439, vd437,
% 13.38/2.60 | simplifying with (31), (41) gives:
% 13.38/2.60 | (58) all_69_5 = all_65_1
% 13.38/2.60 |
% 13.38/2.60 | GROUND_INST: instantiating (13) with all_63_3, all_69_5, vd439, vd437,
% 13.38/2.60 | simplifying with (25), (41) gives:
% 13.38/2.60 | (59) all_69_5 = all_63_3
% 13.38/2.60 |
% 13.38/2.60 | GROUND_INST: instantiating (13) with all_61_3, all_69_5, vd439, vd437,
% 13.38/2.60 | simplifying with (21), (41) gives:
% 13.38/2.61 | (60) all_69_5 = all_61_3
% 13.38/2.61 |
% 13.38/2.61 | GROUND_INST: instantiating (14) with all_67_4, all_69_2, vd437, vd436,
% 13.38/2.61 | simplifying with (38), (44) gives:
% 13.38/2.61 | (61) all_69_2 = all_67_4
% 13.38/2.61 |
% 13.38/2.61 | GROUND_INST: instantiating (14) with all_63_1, all_69_2, vd437, vd436,
% 13.38/2.61 | simplifying with (27), (44) gives:
% 13.38/2.61 | (62) all_69_2 = all_63_1
% 13.38/2.61 |
% 13.38/2.61 | GROUND_INST: instantiating (14) with all_53_0, all_69_2, vd437, vd436,
% 13.38/2.61 | simplifying with (16), (44) gives:
% 13.38/2.61 | (63) all_69_2 = all_53_0
% 13.38/2.61 |
% 13.38/2.61 | GROUND_INST: instantiating (14) with all_67_4, all_71_6, vd437, vd436,
% 13.38/2.61 | simplifying with (38), (54) gives:
% 13.38/2.61 | (64) all_71_6 = all_67_4
% 13.38/2.61 |
% 13.38/2.61 | GROUND_INST: instantiating (14) with all_57_2, all_71_6, vd437, vd436,
% 13.38/2.61 | simplifying with (19), (54) gives:
% 13.38/2.61 | (65) all_71_6 = all_57_2
% 13.38/2.61 |
% 13.38/2.61 | GROUND_INST: instantiating (14) with all_69_1, all_71_5, vd439, vd436,
% 13.38/2.61 | simplifying with (45), (55) gives:
% 13.38/2.61 | (66) all_71_5 = all_69_1
% 13.38/2.61 |
% 13.38/2.61 | GROUND_INST: instantiating (14) with all_67_3, all_71_5, vd439, vd436,
% 13.38/2.61 | simplifying with (39), (55) gives:
% 13.38/2.61 | (67) all_71_5 = all_67_3
% 13.38/2.61 |
% 13.38/2.61 | GROUND_INST: instantiating (14) with all_63_0, all_71_5, vd439, vd436,
% 13.38/2.61 | simplifying with (28), (55) gives:
% 13.38/2.61 | (68) all_71_5 = all_63_0
% 13.38/2.61 |
% 13.38/2.61 | GROUND_INST: instantiating (12) with all_65_4, all_71_2, vd439, simplifying
% 13.38/2.61 | with (32), (57) gives:
% 13.38/2.61 | (69) all_71_2 = all_65_4
% 13.38/2.61 |
% 13.38/2.61 | COMBINE_EQS: (66), (68) imply:
% 13.38/2.61 | (70) all_69_1 = all_63_0
% 13.38/2.61 |
% 13.38/2.61 | COMBINE_EQS: (66), (67) imply:
% 13.38/2.61 | (71) all_69_1 = all_67_3
% 13.38/2.61 |
% 13.38/2.61 | COMBINE_EQS: (64), (65) imply:
% 13.38/2.61 | (72) all_67_4 = all_57_2
% 13.38/2.61 |
% 13.38/2.61 | SIMP: (72) implies:
% 13.38/2.61 | (73) all_67_4 = all_57_2
% 13.38/2.61 |
% 13.38/2.61 | COMBINE_EQS: (70), (71) imply:
% 13.38/2.61 | (74) all_67_3 = all_63_0
% 13.38/2.61 |
% 13.38/2.61 | SIMP: (74) implies:
% 13.38/2.61 | (75) all_67_3 = all_63_0
% 13.38/2.61 |
% 13.38/2.61 | COMBINE_EQS: (62), (63) imply:
% 13.38/2.61 | (76) all_63_1 = all_53_0
% 13.38/2.61 |
% 13.38/2.61 | COMBINE_EQS: (61), (62) imply:
% 13.38/2.61 | (77) all_67_4 = all_63_1
% 13.38/2.61 |
% 13.38/2.61 | SIMP: (77) implies:
% 13.38/2.61 | (78) all_67_4 = all_63_1
% 13.38/2.61 |
% 13.38/2.61 | COMBINE_EQS: (58), (60) imply:
% 13.38/2.61 | (79) all_65_1 = all_61_3
% 13.38/2.61 |
% 13.38/2.61 | COMBINE_EQS: (58), (59) imply:
% 13.38/2.61 | (80) all_65_1 = all_63_3
% 13.38/2.61 |
% 13.38/2.61 | COMBINE_EQS: (73), (78) imply:
% 13.38/2.61 | (81) all_63_1 = all_57_2
% 13.38/2.61 |
% 13.38/2.61 | SIMP: (81) implies:
% 13.38/2.61 | (82) all_63_1 = all_57_2
% 13.38/2.61 |
% 13.38/2.61 | COMBINE_EQS: (79), (80) imply:
% 13.38/2.61 | (83) all_63_3 = all_61_3
% 13.38/2.61 |
% 13.38/2.61 | COMBINE_EQS: (76), (82) imply:
% 13.38/2.61 | (84) all_57_2 = all_53_0
% 13.38/2.61 |
% 13.38/2.61 | SIMP: (84) implies:
% 13.38/2.61 | (85) all_57_2 = all_53_0
% 13.38/2.61 |
% 13.38/2.61 | COMBINE_EQS: (73), (85) imply:
% 13.38/2.61 | (86) all_67_4 = all_53_0
% 13.38/2.61 |
% 13.38/2.61 | COMBINE_EQS: (65), (85) imply:
% 13.38/2.61 | (87) all_71_6 = all_53_0
% 13.38/2.61 |
% 13.38/2.61 | REDUCE: (56), (69) imply:
% 13.38/2.61 | (88) vmul(vd436, all_65_4) = all_71_1
% 13.38/2.61 |
% 13.38/2.61 | REDUCE: (46), (60) imply:
% 13.38/2.61 | (89) vmul(vd436, all_61_3) = all_69_4
% 13.38/2.61 |
% 13.38/2.61 | REDUCE: (29), (83) imply:
% 13.38/2.61 | (90) vmul(vd436, all_61_3) = all_63_2
% 13.38/2.61 |
% 13.38/2.61 | REDUCE: (53), (68) imply:
% 13.38/2.61 | (91) vplus(all_63_0, vd436) = all_71_4
% 13.38/2.61 |
% 13.38/2.61 | REDUCE: (52), (87) imply:
% 13.38/2.61 | (92) vplus(all_53_0, all_71_1) = all_71_0
% 13.38/2.61 |
% 13.38/2.61 | REDUCE: (51), (87) imply:
% 13.38/2.61 | (93) vplus(all_53_0, all_71_4) = all_71_3
% 13.38/2.61 |
% 13.38/2.61 | REDUCE: (43), (63), (70) imply:
% 13.38/2.62 | (94) vplus(all_53_0, all_63_0) = all_69_0
% 13.38/2.62 |
% 13.38/2.62 | REDUCE: (36), (75) imply:
% 13.38/2.62 | (95) vplus(all_63_0, vd436) = all_67_0
% 13.38/2.62 |
% 13.38/2.62 | REDUCE: (35), (86) imply:
% 13.38/2.62 | (96) vplus(all_53_0, all_67_0) = all_67_1
% 13.38/2.62 |
% 13.38/2.62 | REDUCE: (34), (75), (86) imply:
% 13.38/2.62 | (97) vplus(all_53_0, all_63_0) = all_67_2
% 13.38/2.62 |
% 13.38/2.62 | REDUCE: (26), (76) imply:
% 13.38/2.62 | (98) vplus(all_53_0, all_63_0) = all_63_2
% 13.38/2.62 |
% 13.38/2.62 | REDUCE: (18), (85) imply:
% 13.38/2.62 | (99) $i(all_53_0)
% 13.38/2.62 |
% 13.38/2.62 | GROUND_INST: instantiating (13) with all_67_2, all_69_0, all_63_0, all_53_0,
% 13.38/2.62 | simplifying with (94), (97) gives:
% 13.38/2.62 | (100) all_69_0 = all_67_2
% 13.38/2.62 |
% 13.38/2.62 | GROUND_INST: instantiating (13) with all_63_2, all_69_0, all_63_0, all_53_0,
% 13.38/2.62 | simplifying with (94), (98) gives:
% 13.38/2.62 | (101) all_69_0 = all_63_2
% 13.38/2.62 |
% 13.38/2.62 | GROUND_INST: instantiating (13) with all_67_0, all_71_4, vd436, all_63_0,
% 13.38/2.62 | simplifying with (91), (95) gives:
% 13.38/2.62 | (102) all_71_4 = all_67_0
% 13.38/2.62 |
% 13.38/2.62 | GROUND_INST: instantiating (14) with all_61_0, all_69_4, all_61_3, vd436,
% 13.38/2.62 | simplifying with (23), (89) gives:
% 13.38/2.62 | (103) all_69_4 = all_61_0
% 13.38/2.62 |
% 13.38/2.62 | GROUND_INST: instantiating (14) with all_63_2, all_69_4, all_61_3, vd436,
% 13.38/2.62 | simplifying with (89), (90) gives:
% 13.38/2.62 | (104) all_69_4 = all_63_2
% 13.38/2.62 |
% 13.38/2.62 | COMBINE_EQS: (100), (101) imply:
% 13.38/2.62 | (105) all_67_2 = all_63_2
% 13.38/2.62 |
% 13.38/2.62 | SIMP: (105) implies:
% 13.38/2.62 | (106) all_67_2 = all_63_2
% 13.38/2.62 |
% 13.38/2.62 | COMBINE_EQS: (103), (104) imply:
% 13.38/2.62 | (107) all_63_2 = all_61_0
% 13.38/2.62 |
% 13.38/2.62 | COMBINE_EQS: (106), (107) imply:
% 13.38/2.62 | (108) all_67_2 = all_61_0
% 13.38/2.62 |
% 13.38/2.62 | REDUCE: (42), (103) imply:
% 13.38/2.62 | (109) vplus(all_61_0, vd436) = all_69_3
% 13.38/2.62 |
% 13.38/2.62 | REDUCE: (37), (108) imply:
% 13.38/2.62 | (110) vplus(all_61_0, vd436) = all_67_1
% 13.38/2.62 |
% 13.38/2.62 | REDUCE: (93), (102) imply:
% 13.38/2.62 | (111) vplus(all_53_0, all_67_0) = all_71_3
% 13.38/2.62 |
% 13.38/2.62 | REDUCE: (49), (102) imply:
% 13.38/2.62 | (112) $i(all_67_0)
% 13.38/2.62 |
% 13.38/2.62 | GROUND_INST: instantiating (13) with all_67_1, all_71_3, all_67_0, all_53_0,
% 13.38/2.62 | simplifying with (96), (111) gives:
% 13.38/2.62 | (113) all_71_3 = all_67_1
% 13.38/2.62 |
% 13.38/2.62 | GROUND_INST: instantiating (13) with all_61_1, all_69_3, vd436, all_61_0,
% 13.38/2.62 | simplifying with (22), (109) gives:
% 13.38/2.62 | (114) all_69_3 = all_61_1
% 13.38/2.62 |
% 13.38/2.62 | GROUND_INST: instantiating (13) with all_67_1, all_69_3, vd436, all_61_0,
% 13.38/2.62 | simplifying with (109), (110) gives:
% 13.38/2.62 | (115) all_69_3 = all_67_1
% 13.38/2.62 |
% 13.38/2.62 | COMBINE_EQS: (114), (115) imply:
% 13.38/2.62 | (116) all_67_1 = all_61_1
% 13.38/2.62 |
% 13.38/2.62 | COMBINE_EQS: (113), (116) imply:
% 13.38/2.62 | (117) all_71_3 = all_61_1
% 13.38/2.62 |
% 13.38/2.62 | REDUCE: (48), (117) imply:
% 13.38/2.62 | (118) ~ (all_71_0 = all_61_1)
% 13.38/2.62 |
% 13.38/2.62 | REDUCE: (96), (116) imply:
% 13.38/2.62 | (119) vplus(all_53_0, all_67_0) = all_61_1
% 13.38/2.62 |
% 13.38/2.62 | GROUND_INST: instantiating (ass(cond(61, 0), 0)) with all_53_0, all_67_0,
% 13.38/2.62 | all_61_1, simplifying with (99), (112), (119) gives:
% 13.38/2.62 | (120) vplus(all_67_0, all_53_0) = all_61_1 & $i(all_61_1)
% 13.38/2.62 |
% 13.38/2.62 | ALPHA: (120) implies:
% 13.38/2.62 | (121) vplus(all_67_0, all_53_0) = all_61_1
% 13.38/2.62 |
% 13.38/2.62 | GROUND_INST: instantiating (ass(cond(61, 0), 0)) with all_53_0, all_71_1,
% 13.38/2.62 | all_71_0, simplifying with (50), (92), (99) gives:
% 13.38/2.62 | (122) vplus(all_71_1, all_53_0) = all_71_0 & $i(all_71_0)
% 13.38/2.62 |
% 13.38/2.62 | ALPHA: (122) implies:
% 13.38/2.63 | (123) vplus(all_71_1, all_53_0) = all_71_0
% 13.38/2.63 |
% 13.38/2.63 | GROUND_INST: instantiating (8) with vd436, vd439, all_65_4, all_71_1,
% 13.38/2.63 | simplifying with (9), (10), (32), (88) gives:
% 13.38/2.63 | (124) ? [v0: $i] : (vmul(vd436, vd439) = v0 & vplus(v0, vd436) = all_71_1
% 13.38/2.63 | & $i(v0) & $i(all_71_1))
% 13.38/2.63 |
% 13.38/2.63 | DELTA: instantiating (124) with fresh symbol all_91_0 gives:
% 13.38/2.63 | (125) vmul(vd436, vd439) = all_91_0 & vplus(all_91_0, vd436) = all_71_1 &
% 13.38/2.63 | $i(all_91_0) & $i(all_71_1)
% 13.38/2.63 |
% 13.38/2.63 | ALPHA: (125) implies:
% 13.38/2.63 | (126) vplus(all_91_0, vd436) = all_71_1
% 13.38/2.63 | (127) vmul(vd436, vd439) = all_91_0
% 13.38/2.63 |
% 13.38/2.63 | GROUND_INST: instantiating (14) with all_63_0, all_91_0, vd439, vd436,
% 13.38/2.63 | simplifying with (28), (127) gives:
% 13.38/2.63 | (128) all_91_0 = all_63_0
% 13.38/2.63 |
% 13.38/2.63 | REDUCE: (126), (128) imply:
% 13.38/2.63 | (129) vplus(all_63_0, vd436) = all_71_1
% 13.38/2.63 |
% 13.38/2.63 | GROUND_INST: instantiating (13) with all_67_0, all_71_1, vd436, all_63_0,
% 13.38/2.63 | simplifying with (95), (129) gives:
% 13.38/2.63 | (130) all_71_1 = all_67_0
% 13.38/2.63 |
% 13.38/2.63 | REDUCE: (123), (130) imply:
% 13.38/2.63 | (131) vplus(all_67_0, all_53_0) = all_71_0
% 13.38/2.63 |
% 13.38/2.63 | GROUND_INST: instantiating (13) with all_61_1, all_71_0, all_53_0, all_67_0,
% 13.38/2.63 | simplifying with (121), (131) gives:
% 13.38/2.63 | (132) all_71_0 = all_61_1
% 13.38/2.63 |
% 13.38/2.63 | REDUCE: (118), (132) imply:
% 13.38/2.63 | (133) $false
% 13.38/2.63 |
% 13.38/2.63 | CLOSE: (133) is inconsistent.
% 13.38/2.63 |
% 13.38/2.63 End of proof
% 13.38/2.63 % SZS output end Proof for theBenchmark
% 13.73/2.63
% 13.73/2.63 2023ms
%------------------------------------------------------------------------------