TSTP Solution File: NUM855+2 by Princess---230619

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Princess---230619
% Problem  : NUM855+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 : n014.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 11:50:27 EDT 2023

% Result   : Theorem 13.74s 2.65s
% Output   : Proof 16.66s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : NUM855+2 : TPTP v8.1.2. Released v4.1.0.
% 0.00/0.13  % Command  : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.35  % Computer : n014.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit : 300
% 0.13/0.35  % WCLimit  : 300
% 0.13/0.35  % DateTime : Fri Aug 25 15:07:33 EDT 2023
% 0.13/0.35  % CPUTime  : 
% 0.20/0.63  ________       _____
% 0.20/0.63  ___  __ \_________(_)________________________________
% 0.20/0.63  __  /_/ /_  ___/_  /__  __ \  ___/  _ \_  ___/_  ___/
% 0.20/0.63  _  ____/_  /   _  / _  / / / /__ /  __/(__  )_(__  )
% 0.20/0.63  /_/     /_/    /_/  /_/ /_/\___/ \___//____/ /____/
% 0.20/0.63  
% 0.20/0.63  A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.20/0.63  (2023-06-19)
% 0.20/0.63  
% 0.20/0.63  (c) Philipp Rümmer, 2009-2023
% 0.20/0.63  Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.20/0.63                Amanda Stjerna.
% 0.20/0.63  Free software under BSD-3-Clause.
% 0.20/0.63  
% 0.20/0.63  For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.20/0.63  
% 0.20/0.63  Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.20/0.65  Running up to 7 provers in parallel.
% 0.20/0.67  Prover 0: Options:  +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.20/0.67  Prover 2: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.20/0.67  Prover 1: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.20/0.67  Prover 3: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.20/0.67  Prover 4: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.20/0.67  Prover 5: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.20/0.67  Prover 6: Options:  -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 3.55/1.20  Prover 4: Preprocessing ...
% 3.55/1.20  Prover 1: Preprocessing ...
% 3.71/1.26  Prover 0: Preprocessing ...
% 3.71/1.27  Prover 6: Preprocessing ...
% 3.71/1.27  Prover 5: Preprocessing ...
% 3.71/1.27  Prover 2: Preprocessing ...
% 3.71/1.27  Prover 3: Preprocessing ...
% 8.89/2.03  Prover 1: Warning: ignoring some quantifiers
% 10.31/2.14  Prover 1: Constructing countermodel ...
% 10.31/2.16  Prover 6: Proving ...
% 10.31/2.16  Prover 3: Warning: ignoring some quantifiers
% 10.31/2.17  Prover 5: Proving ...
% 10.31/2.17  Prover 4: Warning: ignoring some quantifiers
% 10.31/2.20  Prover 3: Constructing countermodel ...
% 10.31/2.22  Prover 0: Proving ...
% 10.31/2.24  Prover 4: Constructing countermodel ...
% 11.26/2.40  Prover 2: Proving ...
% 13.74/2.64  Prover 3: proved (1967ms)
% 13.74/2.64  
% 13.74/2.65  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 13.74/2.65  
% 13.74/2.65  Prover 6: stopped
% 13.74/2.67  Prover 2: stopped
% 13.74/2.67  Prover 5: stopped
% 13.74/2.68  Prover 0: stopped
% 13.74/2.68  Prover 7: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 13.74/2.69  Prover 1: Found proof (size 45)
% 13.74/2.69  Prover 1: proved (1998ms)
% 13.74/2.69  Prover 8: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 13.74/2.69  Prover 10: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 13.74/2.69  Prover 11: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 13.74/2.69  Prover 13: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 13.74/2.69  Prover 4: stopped
% 14.25/2.78  Prover 7: Preprocessing ...
% 14.62/2.79  Prover 13: Preprocessing ...
% 14.62/2.79  Prover 11: Preprocessing ...
% 14.62/2.79  Prover 8: Preprocessing ...
% 14.62/2.81  Prover 10: Preprocessing ...
% 15.05/2.86  Prover 7: stopped
% 15.15/2.89  Prover 10: stopped
% 15.15/2.90  Prover 11: stopped
% 15.15/2.91  Prover 13: stopped
% 15.15/3.01  Prover 8: Warning: ignoring some quantifiers
% 15.15/3.03  Prover 8: Constructing countermodel ...
% 15.65/3.05  Prover 8: stopped
% 15.65/3.05  
% 15.65/3.05  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 15.65/3.05  
% 16.09/3.06  % SZS output start Proof for theBenchmark
% 16.09/3.07  Assumptions after simplification:
% 16.09/3.07  ---------------------------------
% 16.09/3.07  
% 16.09/3.07    (ass(cond(270, 0), 0))
% 16.09/3.10     ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : ( ~ (vmul(v0, v1) = v2) |  ~ $i(v1)
% 16.09/3.10      |  ~ $i(v0) | (vmul(v1, v0) = v2 & $i(v2)))
% 16.09/3.10  
% 16.09/3.10    (ass(cond(33, 0), 0))
% 16.09/3.10     ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] :  ! [v4: $i] : ( ~
% 16.09/3.10      (vplus(v3, v2) = v4) |  ~ (vplus(v0, v1) = v3) |  ~ $i(v2) |  ~ $i(v1) |  ~
% 16.09/3.10      $i(v0) |  ? [v5: $i] : (vplus(v1, v2) = v5 & vplus(v0, v5) = v4 & $i(v5) &
% 16.09/3.10        $i(v4)))
% 16.09/3.10  
% 16.09/3.10    (def(cond(conseq(axiom(3)), 11), 1))
% 16.09/3.10     ! [v0: $i] :  ! [v1: $i] :  ! [v2: int] : (v2 = 0 |  ~ (greater(v1, v0) = v2)
% 16.09/3.10      |  ~ $i(v1) |  ~ $i(v0) |  ! [v3: $i] : ( ~ (vplus(v0, v3) = v1) |  ~
% 16.09/3.10        $i(v3))) &  ! [v0: $i] :  ! [v1: $i] : ( ~ (greater(v1, v0) = 0) |  ~
% 16.09/3.10      $i(v1) |  ~ $i(v0) |  ? [v2: $i] : (vplus(v0, v2) = v1 & $i(v2)))
% 16.09/3.10  
% 16.09/3.10    (holds(conjunct1(315), 514, 0))
% 16.09/3.11    $i(vd509) & $i(vd511) & $i(vd508) &  ? [v0: $i] :  ? [v1: $i] : (greater(v0,
% 16.09/3.11        v1) = 0 & vmul(vd509, vd511) = v1 & vmul(vd508, vd511) = v0 & $i(v1) &
% 16.09/3.11      $i(v0))
% 16.09/3.11  
% 16.09/3.11    (holds(conjunct2(315), 515, 0))
% 16.09/3.11    $i(vd509) & $i(vd511) &  ? [v0: $i] : (vmul(vd509, vd511) = v0 & vmul(vd511,
% 16.09/3.11        vd509) = v0 & $i(v0))
% 16.09/3.11  
% 16.09/3.11    (holds(conjunct2(315), 515, 1))
% 16.09/3.11    $i(vd512) & $i(vd509) & $i(vd511) &  ? [v0: $i] :  ? [v1: $i] : (greater(v0,
% 16.09/3.11        v1) = 0 & vmul(vd512, vd509) = v1 & vmul(vd511, vd509) = v0 & $i(v1) &
% 16.09/3.11      $i(v0))
% 16.09/3.11  
% 16.09/3.11    (holds(conjunct2(315), 515, 2))
% 16.09/3.11    $i(vd512) & $i(vd509) &  ? [v0: $i] : (vmul(vd512, vd509) = v0 & vmul(vd509,
% 16.09/3.11        vd512) = v0 & $i(v0))
% 16.09/3.11  
% 16.09/3.11    (holds(conseq_conjunct2(315), 516, 0))
% 16.09/3.11    $i(vd512) & $i(vd509) & $i(vd511) & $i(vd508) &  ? [v0: $i] :  ? [v1: $i] :  ?
% 16.09/3.11    [v2: int] : ( ~ (v2 = 0) & greater(v0, v1) = v2 & vmul(vd509, vd512) = v1 &
% 16.09/3.11      vmul(vd508, vd511) = v0 & $i(v1) & $i(v0))
% 16.09/3.11  
% 16.09/3.11    (function-axioms)
% 16.09/3.12     ! [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] :  !
% 16.09/3.12    [v3: $i] : (v1 = v0 |  ~ (geq(v3, v2) = v1) |  ~ (geq(v3, v2) = v0)) &  ! [v0:
% 16.09/3.12      MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] :  ! [v3: $i]
% 16.09/3.12    : (v1 = v0 |  ~ (leq(v3, v2) = v1) |  ~ (leq(v3, v2) = v0)) &  ! [v0: $i] :  !
% 16.09/3.12    [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~ (vplus(v3, v2) = v1) |  ~
% 16.09/3.12      (vplus(v3, v2) = v0)) &  ! [v0: MultipleValueBool] :  ! [v1:
% 16.09/3.12      MultipleValueBool] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~ (less(v3, v2)
% 16.09/3.12        = v1) |  ~ (less(v3, v2) = v0)) &  ! [v0: MultipleValueBool] :  ! [v1:
% 16.09/3.12      MultipleValueBool] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~ (greater(v3,
% 16.09/3.12          v2) = v1) |  ~ (greater(v3, v2) = v0)) &  ! [v0: $i] :  ! [v1: $i] :  !
% 16.09/3.12    [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~ (vmul(v3, v2) = v1) |  ~ (vmul(v3, v2)
% 16.09/3.12        = v0)) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : (v1 = v0 |  ~
% 16.09/3.12      (vskolem2(v2) = v1) |  ~ (vskolem2(v2) = v0)) &  ! [v0: $i] :  ! [v1: $i] : 
% 16.09/3.12    ! [v2: $i] : (v1 = v0 |  ~ (vsucc(v2) = v1) |  ~ (vsucc(v2) = v0))
% 16.09/3.12  
% 16.09/3.12  Further assumptions not needed in the proof:
% 16.09/3.12  --------------------------------------------
% 16.09/3.12  ass(cond(12, 0), 0), ass(cond(140, 0), 0), ass(cond(147, 0), 0), ass(cond(158,
% 16.09/3.12      0), 0), ass(cond(163, 0), 0), ass(cond(168, 0), 0), ass(cond(184, 0), 0),
% 16.09/3.12  ass(cond(189, 0), 0), ass(cond(20, 0), 0), ass(cond(209, 0), 0), ass(cond(223,
% 16.09/3.12      0), 0), ass(cond(228, 0), 0), ass(cond(234, 0), 0), ass(cond(241, 0), 0),
% 16.09/3.12  ass(cond(253, 0), 0), ass(cond(261, 0), 0), ass(cond(281, 0), 0), ass(cond(290,
% 16.09/3.12      0), 0), ass(cond(299, 0), 0), ass(cond(299, 0), 1), ass(cond(299, 0), 2),
% 16.09/3.12  ass(cond(43, 0), 0), ass(cond(52, 0), 0), ass(cond(6, 0), 0), ass(cond(61, 0),
% 16.09/3.12    0), ass(cond(73, 0), 0), ass(cond(81, 0), 0), ass(cond(conjunct1(307), 0), 0),
% 16.09/3.12  ass(cond(conjunct1(conjunct2(307)), 0), 0), ass(cond(conjunct2(conjunct2(307)),
% 16.09/3.12      0), 0), ass(cond(goal(130), 0), 0), ass(cond(goal(130), 0), 1),
% 16.09/3.12  ass(cond(goal(130), 0), 2), ass(cond(goal(130), 0), 3), ass(cond(goal(177), 0),
% 16.09/3.12    0), ass(cond(goal(193), 0), 0), ass(cond(goal(193), 0), 1),
% 16.09/3.12  ass(cond(goal(193), 0), 2), ass(cond(goal(202), 0), 0), ass(cond(goal(202), 0),
% 16.09/3.12    1), ass(cond(goal(202), 0), 2), ass(cond(goal(216), 0), 0), ass(cond(goal(88),
% 16.09/3.12      0), 0), ass(cond(goal(88), 0), 1), ass(cond(goal(88), 0), 2),
% 16.09/3.12  ass(cond(goal(88), 0), 3), def(cond(conseq(axiom(3)), 12), 1),
% 16.09/3.12  def(cond(conseq(axiom(3)), 16), 1), def(cond(conseq(axiom(3)), 17), 1),
% 16.09/3.12  holds(conjunct1(314), 510, 0), holds(conjunct2(314), 513, 0),
% 16.09/3.12  qu(antec(axiom(3)), imp(antec(axiom(3)))), qu(cond(conseq(axiom(3)), 3),
% 16.09/3.12    and(holds(definiens(29), 45, 0), holds(definiens(29), 44, 0))),
% 16.09/3.12  qu(cond(conseq(axiom(3)), 32), and(holds(definiens(249), 399, 0),
% 16.09/3.12      holds(definiens(249), 398, 0))), qu(restrictor(axiom(1)),
% 16.09/3.12    holds(scope(axiom(1)), 2, 0))
% 16.09/3.12  
% 16.09/3.12  Those formulas are unsatisfiable:
% 16.09/3.12  ---------------------------------
% 16.09/3.12  
% 16.09/3.12  Begin of proof
% 16.09/3.13  | 
% 16.09/3.13  | ALPHA: (holds(conjunct2(315), 515, 2)) implies:
% 16.09/3.13  |   (1)   ? [v0: $i] : (vmul(vd512, vd509) = v0 & vmul(vd509, vd512) = v0 &
% 16.09/3.13  |          $i(v0))
% 16.09/3.13  | 
% 16.09/3.13  | ALPHA: (holds(conjunct2(315), 515, 1)) implies:
% 16.09/3.13  |   (2)   ? [v0: $i] :  ? [v1: $i] : (greater(v0, v1) = 0 & vmul(vd512, vd509) =
% 16.09/3.13  |          v1 & vmul(vd511, vd509) = v0 & $i(v1) & $i(v0))
% 16.09/3.13  | 
% 16.09/3.13  | ALPHA: (holds(conjunct2(315), 515, 0)) implies:
% 16.09/3.13  |   (3)   ? [v0: $i] : (vmul(vd509, vd511) = v0 & vmul(vd511, vd509) = v0 &
% 16.09/3.13  |          $i(v0))
% 16.09/3.13  | 
% 16.09/3.13  | ALPHA: (holds(conjunct1(315), 514, 0)) implies:
% 16.09/3.13  |   (4)   ? [v0: $i] :  ? [v1: $i] : (greater(v0, v1) = 0 & vmul(vd509, vd511) =
% 16.09/3.13  |          v1 & vmul(vd508, vd511) = v0 & $i(v1) & $i(v0))
% 16.09/3.14  | 
% 16.09/3.14  | ALPHA: (def(cond(conseq(axiom(3)), 11), 1)) implies:
% 16.09/3.14  |   (5)   ! [v0: $i] :  ! [v1: $i] : ( ~ (greater(v1, v0) = 0) |  ~ $i(v1) |  ~
% 16.49/3.14  |          $i(v0) |  ? [v2: $i] : (vplus(v0, v2) = v1 & $i(v2)))
% 16.49/3.14  |   (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: int] : (v2 = 0 |  ~ (greater(v1,
% 16.49/3.14  |              v0) = v2) |  ~ $i(v1) |  ~ $i(v0) |  ! [v3: $i] : ( ~ (vplus(v0,
% 16.49/3.14  |                v3) = v1) |  ~ $i(v3)))
% 16.49/3.14  | 
% 16.49/3.14  | ALPHA: (holds(conseq_conjunct2(315), 516, 0)) implies:
% 16.49/3.15  |   (7)  $i(vd508)
% 16.49/3.15  |   (8)  $i(vd511)
% 16.49/3.15  |   (9)   ? [v0: $i] :  ? [v1: $i] :  ? [v2: int] : ( ~ (v2 = 0) & greater(v0,
% 16.49/3.15  |            v1) = v2 & vmul(vd509, vd512) = v1 & vmul(vd508, vd511) = v0 &
% 16.49/3.15  |          $i(v1) & $i(v0))
% 16.49/3.15  | 
% 16.49/3.15  | ALPHA: (function-axioms) implies:
% 16.49/3.15  |   (10)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 16.49/3.15  |           (vmul(v3, v2) = v1) |  ~ (vmul(v3, v2) = v0))
% 16.49/3.15  | 
% 16.49/3.15  | DELTA: instantiating (1) with fresh symbol all_54_0 gives:
% 16.49/3.15  |   (11)  vmul(vd512, vd509) = all_54_0 & vmul(vd509, vd512) = all_54_0 &
% 16.49/3.15  |         $i(all_54_0)
% 16.49/3.15  | 
% 16.49/3.15  | ALPHA: (11) implies:
% 16.49/3.15  |   (12)  vmul(vd509, vd512) = all_54_0
% 16.49/3.15  |   (13)  vmul(vd512, vd509) = all_54_0
% 16.49/3.15  | 
% 16.49/3.15  | DELTA: instantiating (3) with fresh symbol all_56_0 gives:
% 16.49/3.15  |   (14)  vmul(vd509, vd511) = all_56_0 & vmul(vd511, vd509) = all_56_0 &
% 16.49/3.15  |         $i(all_56_0)
% 16.49/3.15  | 
% 16.49/3.15  | ALPHA: (14) implies:
% 16.49/3.16  |   (15)  vmul(vd511, vd509) = all_56_0
% 16.49/3.16  |   (16)  vmul(vd509, vd511) = all_56_0
% 16.49/3.16  | 
% 16.49/3.16  | DELTA: instantiating (2) with fresh symbols all_63_0, all_63_1 gives:
% 16.49/3.16  |   (17)  greater(all_63_1, all_63_0) = 0 & vmul(vd512, vd509) = all_63_0 &
% 16.49/3.16  |         vmul(vd511, vd509) = all_63_1 & $i(all_63_0) & $i(all_63_1)
% 16.49/3.16  | 
% 16.49/3.16  | ALPHA: (17) implies:
% 16.49/3.16  |   (18)  $i(all_63_1)
% 16.49/3.16  |   (19)  $i(all_63_0)
% 16.49/3.16  |   (20)  vmul(vd511, vd509) = all_63_1
% 16.49/3.16  |   (21)  vmul(vd512, vd509) = all_63_0
% 16.49/3.16  |   (22)  greater(all_63_1, all_63_0) = 0
% 16.49/3.16  | 
% 16.49/3.16  | DELTA: instantiating (4) with fresh symbols all_65_0, all_65_1 gives:
% 16.49/3.16  |   (23)  greater(all_65_1, all_65_0) = 0 & vmul(vd509, vd511) = all_65_0 &
% 16.49/3.16  |         vmul(vd508, vd511) = all_65_1 & $i(all_65_0) & $i(all_65_1)
% 16.49/3.16  | 
% 16.49/3.16  | ALPHA: (23) implies:
% 16.49/3.16  |   (24)  vmul(vd508, vd511) = all_65_1
% 16.49/3.16  |   (25)  vmul(vd509, vd511) = all_65_0
% 16.49/3.16  |   (26)  greater(all_65_1, all_65_0) = 0
% 16.49/3.16  | 
% 16.49/3.16  | DELTA: instantiating (9) with fresh symbols all_68_0, all_68_1, all_68_2
% 16.49/3.16  |        gives:
% 16.49/3.16  |   (27)   ~ (all_68_0 = 0) & greater(all_68_2, all_68_1) = all_68_0 &
% 16.49/3.16  |         vmul(vd509, vd512) = all_68_1 & vmul(vd508, vd511) = all_68_2 &
% 16.49/3.16  |         $i(all_68_1) & $i(all_68_2)
% 16.49/3.16  | 
% 16.49/3.16  | ALPHA: (27) implies:
% 16.49/3.16  |   (28)   ~ (all_68_0 = 0)
% 16.49/3.16  |   (29)  vmul(vd508, vd511) = all_68_2
% 16.49/3.16  |   (30)  vmul(vd509, vd512) = all_68_1
% 16.49/3.16  |   (31)  greater(all_68_2, all_68_1) = all_68_0
% 16.49/3.16  | 
% 16.49/3.17  | GROUND_INST: instantiating (10) with all_65_1, all_68_2, vd511, vd508,
% 16.49/3.17  |              simplifying with (24), (29) gives:
% 16.49/3.17  |   (32)  all_68_2 = all_65_1
% 16.49/3.17  | 
% 16.49/3.17  | GROUND_INST: instantiating (10) with all_56_0, all_63_1, vd509, vd511,
% 16.49/3.17  |              simplifying with (15), (20) gives:
% 16.49/3.17  |   (33)  all_63_1 = all_56_0
% 16.49/3.17  | 
% 16.49/3.17  | GROUND_INST: instantiating (10) with all_56_0, all_65_0, vd511, vd509,
% 16.49/3.17  |              simplifying with (16), (25) gives:
% 16.49/3.17  |   (34)  all_65_0 = all_56_0
% 16.49/3.17  | 
% 16.49/3.17  | GROUND_INST: instantiating (10) with all_54_0, all_68_1, vd512, vd509,
% 16.49/3.17  |              simplifying with (12), (30) gives:
% 16.49/3.17  |   (35)  all_68_1 = all_54_0
% 16.49/3.17  | 
% 16.49/3.17  | GROUND_INST: instantiating (10) with all_54_0, all_63_0, vd509, vd512,
% 16.49/3.17  |              simplifying with (13), (21) gives:
% 16.49/3.17  |   (36)  all_63_0 = all_54_0
% 16.49/3.17  | 
% 16.49/3.17  | REDUCE: (31), (32), (35) imply:
% 16.49/3.17  |   (37)  greater(all_65_1, all_54_0) = all_68_0
% 16.49/3.17  | 
% 16.49/3.17  | REDUCE: (26), (34) imply:
% 16.49/3.17  |   (38)  greater(all_65_1, all_56_0) = 0
% 16.49/3.17  | 
% 16.49/3.17  | REDUCE: (22), (33), (36) imply:
% 16.49/3.17  |   (39)  greater(all_56_0, all_54_0) = 0
% 16.49/3.17  | 
% 16.49/3.17  | REDUCE: (19), (36) imply:
% 16.49/3.17  |   (40)  $i(all_54_0)
% 16.49/3.17  | 
% 16.49/3.17  | REDUCE: (18), (33) imply:
% 16.49/3.17  |   (41)  $i(all_56_0)
% 16.49/3.17  | 
% 16.49/3.17  | GROUND_INST: instantiating (ass(cond(270, 0), 0)) with vd508, vd511, all_65_1,
% 16.49/3.17  |              simplifying with (7), (8), (24) gives:
% 16.49/3.17  |   (42)  vmul(vd511, vd508) = all_65_1 & $i(all_65_1)
% 16.49/3.17  | 
% 16.49/3.17  | ALPHA: (42) implies:
% 16.49/3.17  |   (43)  $i(all_65_1)
% 16.49/3.17  | 
% 16.49/3.17  | GROUND_INST: instantiating (5) with all_54_0, all_56_0, simplifying with (39),
% 16.49/3.17  |              (40), (41) gives:
% 16.49/3.18  |   (44)   ? [v0: $i] : (vplus(all_54_0, v0) = all_56_0 & $i(v0))
% 16.49/3.18  | 
% 16.49/3.18  | GROUND_INST: instantiating (6) with all_54_0, all_65_1, all_68_0, simplifying
% 16.49/3.18  |              with (37), (40), (43) gives:
% 16.49/3.18  |   (45)  all_68_0 = 0 |  ! [v0: $i] : ( ~ (vplus(all_54_0, v0) = all_65_1) |  ~
% 16.49/3.18  |           $i(v0))
% 16.49/3.18  | 
% 16.49/3.18  | GROUND_INST: instantiating (5) with all_56_0, all_65_1, simplifying with (38),
% 16.49/3.18  |              (41), (43) gives:
% 16.49/3.18  |   (46)   ? [v0: $i] : (vplus(all_56_0, v0) = all_65_1 & $i(v0))
% 16.49/3.18  | 
% 16.49/3.18  | DELTA: instantiating (44) with fresh symbol all_82_0 gives:
% 16.49/3.18  |   (47)  vplus(all_54_0, all_82_0) = all_56_0 & $i(all_82_0)
% 16.49/3.18  | 
% 16.49/3.18  | ALPHA: (47) implies:
% 16.66/3.18  |   (48)  $i(all_82_0)
% 16.66/3.18  |   (49)  vplus(all_54_0, all_82_0) = all_56_0
% 16.66/3.18  | 
% 16.66/3.18  | DELTA: instantiating (46) with fresh symbol all_86_0 gives:
% 16.66/3.18  |   (50)  vplus(all_56_0, all_86_0) = all_65_1 & $i(all_86_0)
% 16.66/3.18  | 
% 16.66/3.18  | ALPHA: (50) implies:
% 16.66/3.18  |   (51)  $i(all_86_0)
% 16.66/3.18  |   (52)  vplus(all_56_0, all_86_0) = all_65_1
% 16.66/3.18  | 
% 16.66/3.18  | BETA: splitting (45) gives:
% 16.66/3.18  | 
% 16.66/3.18  | Case 1:
% 16.66/3.18  | | 
% 16.66/3.18  | |   (53)  all_68_0 = 0
% 16.66/3.18  | | 
% 16.66/3.18  | | REDUCE: (28), (53) imply:
% 16.66/3.18  | |   (54)  $false
% 16.66/3.18  | | 
% 16.66/3.18  | | CLOSE: (54) is inconsistent.
% 16.66/3.18  | | 
% 16.66/3.18  | Case 2:
% 16.66/3.18  | | 
% 16.66/3.18  | |   (55)   ! [v0: $i] : ( ~ (vplus(all_54_0, v0) = all_65_1) |  ~ $i(v0))
% 16.66/3.18  | | 
% 16.66/3.19  | | GROUND_INST: instantiating (ass(cond(33, 0), 0)) with all_54_0, all_82_0,
% 16.66/3.19  | |              all_86_0, all_56_0, all_65_1, simplifying with (40), (48),
% 16.66/3.19  | |              (49), (51), (52) gives:
% 16.66/3.19  | |   (56)   ? [v0: $i] : (vplus(all_82_0, all_86_0) = v0 & vplus(all_54_0, v0)
% 16.66/3.19  | |           = all_65_1 & $i(v0) & $i(all_65_1))
% 16.66/3.19  | | 
% 16.66/3.19  | | DELTA: instantiating (56) with fresh symbol all_101_0 gives:
% 16.66/3.19  | |   (57)  vplus(all_82_0, all_86_0) = all_101_0 & vplus(all_54_0, all_101_0) =
% 16.66/3.19  | |         all_65_1 & $i(all_101_0) & $i(all_65_1)
% 16.66/3.19  | | 
% 16.66/3.19  | | ALPHA: (57) implies:
% 16.66/3.19  | |   (58)  $i(all_101_0)
% 16.66/3.19  | |   (59)  vplus(all_54_0, all_101_0) = all_65_1
% 16.66/3.19  | | 
% 16.66/3.19  | | GROUND_INST: instantiating (55) with all_101_0, simplifying with (58), (59)
% 16.66/3.19  | |              gives:
% 16.66/3.19  | |   (60)  $false
% 16.66/3.19  | | 
% 16.66/3.19  | | CLOSE: (60) is inconsistent.
% 16.66/3.19  | | 
% 16.66/3.19  | End of split
% 16.66/3.19  | 
% 16.66/3.19  End of proof
% 16.66/3.19  % SZS output end Proof for theBenchmark
% 16.66/3.19  
% 16.66/3.19  2559ms
%------------------------------------------------------------------------------