TSTP Solution File: GEO274+1 by Princess---230619

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Princess---230619
% Problem  : GEO274+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 : n002.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 : Wed Aug 30 23:22:54 EDT 2023

% Result   : Theorem 31.80s 5.01s
% Output   : Proof 40.03s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12  % Problem  : GEO274+1 : TPTP v8.1.2. Released v4.1.0.
% 0.12/0.13  % Command  : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.34  % Computer : n002.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 : Tue Aug 29 23:21:50 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/sandbox2/benchmark/theBenchmark.p ...
% 0.20/0.62  Running up to 7 provers in parallel.
% 0.20/0.64  Prover 0: Options:  +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.20/0.64  Prover 2: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.20/0.64  Prover 1: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.20/0.64  Prover 3: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.20/0.64  Prover 5: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.20/0.64  Prover 4: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.20/0.64  Prover 6: Options:  -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 8.45/1.91  Prover 4: Preprocessing ...
% 8.45/2.01  Prover 1: Preprocessing ...
% 8.45/2.01  Prover 5: Preprocessing ...
% 8.45/2.01  Prover 6: Preprocessing ...
% 8.45/2.01  Prover 3: Preprocessing ...
% 8.45/2.01  Prover 0: Preprocessing ...
% 8.45/2.02  Prover 2: Preprocessing ...
% 21.26/3.58  Prover 3: Constructing countermodel ...
% 21.26/3.60  Prover 1: Constructing countermodel ...
% 21.92/3.64  Prover 6: Proving ...
% 22.76/3.89  Prover 2: Proving ...
% 24.88/4.05  Prover 5: Proving ...
% 31.80/5.01  Prover 3: proved (4361ms)
% 31.80/5.01  
% 31.80/5.01  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 31.80/5.01  
% 31.80/5.01  Prover 6: stopped
% 31.80/5.01  Prover 7: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 31.80/5.01  Prover 2: stopped
% 31.80/5.02  Prover 8: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 32.54/5.03  Prover 5: stopped
% 32.54/5.03  Prover 10: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 32.54/5.03  Prover 11: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 35.80/5.47  Prover 10: Preprocessing ...
% 35.80/5.47  Prover 8: Preprocessing ...
% 36.09/5.49  Prover 11: Preprocessing ...
% 36.09/5.49  Prover 7: Preprocessing ...
% 36.09/5.52  Prover 4: Constructing countermodel ...
% 36.44/5.57  Prover 1: Found proof (size 57)
% 36.44/5.57  Prover 1: proved (4943ms)
% 36.44/5.59  Prover 4: stopped
% 36.44/5.59  Prover 10: stopped
% 36.44/5.60  Prover 7: stopped
% 37.30/5.79  Prover 11: stopped
% 38.31/5.87  Prover 8: Warning: ignoring some quantifiers
% 38.56/5.89  Prover 8: Constructing countermodel ...
% 38.56/5.90  Prover 8: stopped
% 39.29/6.08  Prover 0: Proving ...
% 39.29/6.09  Prover 0: stopped
% 39.29/6.09  
% 39.29/6.09  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 39.29/6.09  
% 39.29/6.10  % SZS output start Proof for theBenchmark
% 39.29/6.13  Assumptions after simplification:
% 39.29/6.13  ---------------------------------
% 39.29/6.13  
% 39.29/6.13    (and(pred(s2(plural(the(227))), 0), and(pred(s1(plural(the(227))), 0), pred(the(227), 0))))
% 39.66/6.16    ron(vd1080, vd1092) = 0 & ron(vd1089, vd1092) = 0 & rline(vd1092) = 0 &
% 39.66/6.16    $i(vd1092) & $i(vd1080) & $i(vd1089)
% 39.66/6.16  
% 39.66/6.16    (holds(226, 1090, 0))
% 39.66/6.17    $i(vd1085) & $i(vd1080) & $i(vd1089) &  ? [v0: $i] : (vf(vd1089, vd1085) = v0
% 39.66/6.17      & vf(vd1089, vd1080) = v0 & $i(v0))
% 39.66/6.17  
% 39.66/6.17    (holds(226, 1090, 1))
% 39.66/6.17    $i(vd1085) & $i(vd1080) & $i(vd1089) &  ? [v0: $i] : (vf(vd1085, vd1080) = v0
% 39.66/6.17      & vf(vd1089, vd1080) = v0 & $i(v0))
% 39.66/6.17  
% 39.66/6.17    (holds(conjunct1(225), 1087, 0))
% 39.66/6.17     ~ (vd1085 = vd1080) & $i(vd1085) & $i(vd1080)
% 39.66/6.17  
% 39.66/6.17    (pred(224, 5))
% 39.66/6.17     ~ (vd1081 = vd1080) & $i(vd1081) & $i(vd1080)
% 39.66/6.17  
% 39.66/6.17    (pred(225, 1))
% 39.66/6.17    rpoint(vd1086) = 0 & $i(vd1086)
% 39.66/6.17  
% 39.66/6.17    (pred(225, 4))
% 39.66/6.17    vd1086 = vd1085 & $i(vd1085)
% 39.66/6.17  
% 39.66/6.17    (pred(226, 0))
% 39.66/6.17    rpoint(vd1089) = 0 & $i(vd1089)
% 39.66/6.17  
% 39.66/6.17    (qe(s1(plural(224))))
% 39.66/6.17    rpoint(vd1080) = 0 & $i(vd1080)
% 39.66/6.17  
% 39.66/6.17    (qe(s2(plural(224))))
% 39.66/6.17    rpoint(vd1081) = 0 & $i(vd1081)
% 39.66/6.17  
% 39.66/6.17    (qu(cond(axiom(162), 0), imp(cond(axiom(162), 0))))
% 39.66/6.17    $i(v0) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : ( ~ (rpoint(v1) = 0) |  ~
% 39.66/6.18      (rpoint(v0) = 0) |  ~ (vf(v0, v1) = v2) |  ~ $i(v1) |  ~ $i(v0) | (( ~ (v2 =
% 39.66/6.18            v0) | v1 = v0) & ( ~ (v1 = v0) | v2 = v0)))
% 39.66/6.18  
% 39.66/6.18    (qu(cond(axiom(53), 0), imp(cond(axiom(53), 0))))
% 39.66/6.18     ! [v0: $i] :  ! [v1: $i] : (v1 = v0 |  ~ (rpoint(v1) = 0) |  ~ (rpoint(v0) =
% 39.66/6.18        0) |  ~ $i(v1) |  ~ $i(v0) |  ? [v2: $i] : (rcenter(v0, v2) = 0 &
% 39.66/6.18        rcircle(v2) = 0 & ron(v1, v2) = 0 & $i(v2)))
% 39.66/6.18  
% 39.66/6.18    (qu(cond(axiom(73), 0), imp(cond(axiom(73), 0))))
% 39.66/6.18     ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v3 = v2 | v1 = v0 | 
% 39.66/6.18      ~ (rpoint(v1) = 0) |  ~ (rpoint(v0) = 0) |  ~ (ron(v1, v3) = 0) |  ~
% 39.66/6.18      (ron(v0, v2) = 0) |  ~ (rline(v3) = 0) |  ~ (rline(v2) = 0) |  ~ $i(v3) |  ~
% 39.66/6.18      $i(v2) |  ~ $i(v1) |  ~ $i(v0) |  ? [v4: any] :  ? [v5: any] : (ron(v1, v2)
% 39.66/6.18        = v4 & ron(v0, v3) = v5 & ( ~ (v5 = 0) |  ~ (v4 = 0))))
% 39.66/6.18  
% 39.66/6.18    (qu(theu(the(227), 1), imp(the(227))))
% 39.66/6.18    $i(vd1092) & $i(vd1080) & $i(vd1089) &  ? [v0: $i] : ( ~ (v0 = vd1092) &
% 39.66/6.18      ron(vd1080, v0) = 0 & ron(vd1089, v0) = 0 & rline(v0) = 0 & $i(v0))
% 39.66/6.18  
% 39.66/6.18    (function-axioms)
% 39.82/6.19     ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] :  ! [v4: $i] :  ! [v5:
% 39.82/6.19      $i] : (v1 = v0 |  ~ (vskolem1052(v5, v4, v3, v2) = v1) |  ~ (vskolem1052(v5,
% 39.82/6.19          v4, v3, v2) = v0)) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3:
% 39.82/6.19      $i] :  ! [v4: $i] : (v1 = v0 |  ~ (vg(v4, v3, v2) = v1) |  ~ (vg(v4, v3, v2)
% 39.82/6.19        = v0)) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] :  ! [v4:
% 39.82/6.19      $i] : (v1 = v0 |  ~ (vtriangle(v4, v3, v2) = v1) |  ~ (vtriangle(v4, v3, v2)
% 39.82/6.19        = v0)) &  ! [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2:
% 39.82/6.20      $i] :  ! [v3: $i] :  ! [v4: $i] : (v1 = v0 |  ~ (rS(v4, v3, v2) = v1) |  ~
% 39.82/6.20      (rS(v4, v3, v2) = v0)) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3:
% 39.82/6.20      $i] :  ! [v4: $i] : (v1 = v0 |  ~ (vangle(v4, v3, v2) = v1) |  ~ (vangle(v4,
% 39.82/6.20          v3, v2) = v0)) &  ! [v0: MultipleValueBool] :  ! [v1: MultipleValueBool]
% 39.82/6.20    :  ! [v2: $i] :  ! [v3: $i] :  ! [v4: $i] : (v1 = v0 |  ~ (rR(v4, v3, v2) =
% 39.82/6.20        v1) |  ~ (rR(v4, v3, v2) = v0)) &  ! [v0: MultipleValueBool] :  ! [v1:
% 39.82/6.20      MultipleValueBool] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~ (rgeq(v3, v2)
% 39.82/6.20        = v1) |  ~ (rgeq(v3, v2) = v0)) &  ! [v0: MultipleValueBool] :  ! [v1:
% 39.82/6.20      MultipleValueBool] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~ (rcenter(v3,
% 39.82/6.20          v2) = v1) |  ~ (rcenter(v3, v2) = v0)) &  ! [v0: MultipleValueBool] :  !
% 39.82/6.20    [v1: MultipleValueBool] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 39.82/6.20      (rintersect(v3, v2) = v1) |  ~ (rintersect(v3, v2) = v0)) &  ! [v0:
% 39.82/6.20      MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] :  ! [v3: $i]
% 39.82/6.20    : (v1 = v0 |  ~ (rless(v3, v2) = v1) |  ~ (rless(v3, v2) = v0)) &  ! [v0:
% 39.82/6.20      MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] :  ! [v3: $i]
% 39.82/6.20    : (v1 = v0 |  ~ (rinside(v3, v2) = v1) |  ~ (rinside(v3, v2) = v0)) &  ! [v0:
% 39.82/6.20      $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~ (vplus(v3, v2)
% 39.82/6.20        = v1) |  ~ (vplus(v3, v2) = v0)) &  ! [v0: MultipleValueBool] :  ! [v1:
% 39.82/6.20      MultipleValueBool] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~ (rleq(v3, v2)
% 39.82/6.20        = v1) |  ~ (rleq(v3, v2) = v0)) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i]
% 39.82/6.20    :  ! [v3: $i] : (v1 = v0 |  ~ (vf(v3, v2) = v1) |  ~ (vf(v3, v2) = v0)) &  !
% 39.82/6.20    [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] :  ! [v3:
% 39.82/6.20      $i] : (v1 = v0 |  ~ (ron(v3, v2) = v1) |  ~ (ron(v3, v2) = v0)) &  ! [v0:
% 39.82/6.20      MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] : (v1 = v0 | 
% 39.82/6.20      ~ (rtriangle(v2) = v1) |  ~ (rtriangle(v2) = v0)) &  ! [v0:
% 39.82/6.20      MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] : (v1 = v0 | 
% 39.82/6.20      ~ (rcircle(v2) = v1) |  ~ (rcircle(v2) = v0)) &  ! [v0: MultipleValueBool] :
% 39.82/6.20     ! [v1: MultipleValueBool] :  ! [v2: $i] : (v1 = v0 |  ~ (rreal(v2) = v1) |  ~
% 39.82/6.20      (rreal(v2) = v0)) &  ! [v0: MultipleValueBool] :  ! [v1: MultipleValueBool]
% 39.82/6.20    :  ! [v2: $i] : (v1 = v0 |  ~ (rpoint(v2) = v1) |  ~ (rpoint(v2) = v0)) &  !
% 39.82/6.20    [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] : (v1 = v0
% 39.82/6.20      |  ~ (rline(v2) = v1) |  ~ (rline(v2) = v0))
% 39.82/6.20  
% 39.82/6.20  Further assumptions not needed in the proof:
% 39.82/6.20  --------------------------------------------
% 39.82/6.20  ass(cond(156, 0), 0), ass(cond(goal(206), 0), 0), ass(cond(goal(206), 0), 1),
% 39.82/6.20  ass(cond(goal(206), 0), 2), holds(conjunct2(225), 1088, 0), pred(axiom(137), 1),
% 39.82/6.20  pred(axiom(137), 2), pred(axiom(5), 0), qu(cond(axiom(1), 0), imp(cond(axiom(1),
% 39.82/6.20        0))), qu(cond(axiom(101), 0), imp(cond(axiom(101), 0))),
% 39.82/6.20  qu(cond(axiom(103), 0), imp(cond(axiom(103), 0))), qu(cond(axiom(105), 0),
% 39.82/6.20    imp(cond(axiom(105), 0))), qu(cond(axiom(107), 0), imp(cond(axiom(107), 0))),
% 39.82/6.20  qu(cond(axiom(109), 0), imp(cond(axiom(109), 0))), qu(cond(axiom(11), 0),
% 39.82/6.20    imp(cond(axiom(11), 0))), qu(cond(axiom(111), 0), imp(cond(axiom(111), 0))),
% 39.82/6.20  qu(cond(axiom(113), 0), imp(cond(axiom(113), 0))), qu(cond(axiom(115), 0),
% 39.82/6.20    imp(cond(axiom(115), 0))), qu(cond(axiom(117), 0), imp(cond(axiom(117), 0))),
% 39.82/6.20  qu(cond(axiom(119), 0), imp(cond(axiom(119), 0))), qu(cond(axiom(121), 0),
% 39.82/6.20    imp(cond(axiom(121), 0))), qu(cond(axiom(123), 0), imp(cond(axiom(123), 0))),
% 39.82/6.20  qu(cond(axiom(125), 0), imp(cond(axiom(125), 0))), qu(cond(axiom(127), 0),
% 39.82/6.20    imp(cond(axiom(127), 0))), qu(cond(axiom(129), 0), imp(cond(axiom(129), 0))),
% 39.82/6.20  qu(cond(axiom(13), 0), imp(cond(axiom(13), 0))), qu(cond(axiom(131), 0),
% 39.82/6.20    imp(cond(axiom(131), 0))), qu(cond(axiom(133), 0), imp(cond(axiom(133), 0))),
% 39.82/6.20  qu(cond(axiom(135), 0), imp(cond(axiom(135), 0))), qu(cond(axiom(139), 0),
% 39.82/6.20    imp(cond(axiom(139), 0))), qu(cond(axiom(141), 0), imp(cond(axiom(141), 0))),
% 39.82/6.20  qu(cond(axiom(143), 0), imp(cond(axiom(143), 0))), qu(cond(axiom(145), 0),
% 39.82/6.20    imp(cond(axiom(145), 0))), qu(cond(axiom(147), 0), imp(cond(axiom(147), 0))),
% 39.82/6.20  qu(cond(axiom(149), 0), imp(cond(axiom(149), 0))), qu(cond(axiom(15), 0),
% 39.82/6.20    imp(cond(axiom(15), 0))), qu(cond(axiom(151), 0), imp(cond(axiom(151), 0))),
% 39.82/6.20  qu(cond(axiom(153), 0), imp(cond(axiom(153), 0))), qu(cond(axiom(160), 0),
% 39.82/6.20    imp(cond(axiom(160), 0))), qu(cond(axiom(164), 0), imp(cond(axiom(164), 0))),
% 39.82/6.20  qu(cond(axiom(166), 0), imp(cond(axiom(166), 0))), qu(cond(axiom(168), 0),
% 39.82/6.20    imp(cond(axiom(168), 0))), qu(cond(axiom(17), 0), imp(cond(axiom(17), 0))),
% 39.82/6.20  qu(cond(axiom(170), 0), imp(cond(axiom(170), 0))), qu(cond(axiom(172), 0),
% 39.82/6.20    imp(cond(axiom(172), 0))), qu(cond(axiom(174), 0), imp(cond(axiom(174), 0))),
% 39.82/6.20  qu(cond(axiom(176), 0), imp(cond(axiom(176), 0))), qu(cond(axiom(178), 0),
% 39.82/6.20    imp(cond(axiom(178), 0))), qu(cond(axiom(180), 0), imp(cond(axiom(180), 0))),
% 39.82/6.20  qu(cond(axiom(182), 0), imp(cond(axiom(182), 0))), qu(cond(axiom(184), 0),
% 39.82/6.20    imp(cond(axiom(184), 0))), qu(cond(axiom(186), 0), imp(cond(axiom(186), 0))),
% 39.82/6.20  qu(cond(axiom(188), 0), imp(cond(axiom(188), 0))), qu(cond(axiom(19), 0),
% 39.82/6.20    imp(cond(axiom(19), 0))), qu(cond(axiom(190), 0), imp(cond(axiom(190), 0))),
% 39.82/6.20  qu(cond(axiom(192), 0), imp(cond(axiom(192), 0))), qu(cond(axiom(194), 0),
% 39.82/6.20    imp(cond(axiom(194), 0))), qu(cond(axiom(196), 0), imp(cond(axiom(196), 0))),
% 39.82/6.20  qu(cond(axiom(198), 0), imp(cond(axiom(198), 0))), qu(cond(axiom(200), 0),
% 39.82/6.20    imp(cond(axiom(200), 0))), qu(cond(axiom(202), 0), imp(cond(axiom(202), 0))),
% 39.82/6.20  qu(cond(axiom(204), 0), imp(cond(axiom(204), 0))), qu(cond(axiom(21), 0),
% 39.82/6.20    imp(cond(axiom(21), 0))), qu(cond(axiom(23), 0), imp(cond(axiom(23), 0))),
% 39.82/6.20  qu(cond(axiom(25), 0), imp(cond(axiom(25), 0))), qu(cond(axiom(27), 0),
% 39.82/6.20    imp(cond(axiom(27), 0))), qu(cond(axiom(29), 0), imp(cond(axiom(29), 0))),
% 39.82/6.20  qu(cond(axiom(3), 0), imp(cond(axiom(3), 0))), qu(cond(axiom(31), 0),
% 39.82/6.20    imp(cond(axiom(31), 0))), qu(cond(axiom(33), 0), imp(cond(axiom(33), 0))),
% 39.82/6.20  qu(cond(axiom(35), 0), imp(cond(axiom(35), 0))), qu(cond(axiom(37), 0),
% 39.82/6.20    imp(cond(axiom(37), 0))), qu(cond(axiom(39), 0), imp(cond(axiom(39), 0))),
% 39.82/6.20  qu(cond(axiom(41), 0), imp(cond(axiom(41), 0))), qu(cond(axiom(43), 0),
% 39.82/6.20    imp(cond(axiom(43), 0))), qu(cond(axiom(45), 0), imp(cond(axiom(45), 0))),
% 39.82/6.20  qu(cond(axiom(47), 0), imp(cond(axiom(47), 0))), qu(cond(axiom(49), 0),
% 39.82/6.20    imp(cond(axiom(49), 0))), qu(cond(axiom(51), 0), imp(cond(axiom(51), 0))),
% 39.82/6.20  qu(cond(axiom(55), 0), imp(cond(axiom(55), 0))), qu(cond(axiom(57), 0),
% 39.82/6.20    imp(cond(axiom(57), 0))), qu(cond(axiom(59), 0), imp(cond(axiom(59), 0))),
% 39.82/6.20  qu(cond(axiom(61), 0), imp(cond(axiom(61), 0))), qu(cond(axiom(63), 0),
% 39.82/6.20    imp(cond(axiom(63), 0))), qu(cond(axiom(65), 0), imp(cond(axiom(65), 0))),
% 39.82/6.20  qu(cond(axiom(67), 0), imp(cond(axiom(67), 0))), qu(cond(axiom(69), 0),
% 39.82/6.20    imp(cond(axiom(69), 0))), qu(cond(axiom(7), 0), imp(cond(axiom(7), 0))),
% 39.82/6.20  qu(cond(axiom(71), 0), imp(cond(axiom(71), 0))), qu(cond(axiom(75), 0),
% 39.82/6.20    imp(cond(axiom(75), 0))), qu(cond(axiom(77), 0), imp(cond(axiom(77), 0))),
% 39.82/6.20  qu(cond(axiom(79), 0), imp(cond(axiom(79), 0))), qu(cond(axiom(81), 0),
% 39.82/6.20    imp(cond(axiom(81), 0))), qu(cond(axiom(83), 0), imp(cond(axiom(83), 0))),
% 39.82/6.20  qu(cond(axiom(85), 0), imp(cond(axiom(85), 0))), qu(cond(axiom(87), 0),
% 39.82/6.20    imp(cond(axiom(87), 0))), qu(cond(axiom(89), 0), imp(cond(axiom(89), 0))),
% 39.82/6.20  qu(cond(axiom(9), 0), imp(cond(axiom(9), 0))), qu(cond(axiom(91), 0),
% 39.82/6.20    imp(cond(axiom(91), 0))), qu(cond(axiom(93), 0), imp(cond(axiom(93), 0))),
% 39.82/6.20  qu(cond(axiom(95), 0), imp(cond(axiom(95), 0))), qu(cond(axiom(97), 0),
% 39.82/6.20    imp(cond(axiom(97), 0))), qu(cond(axiom(99), 0), imp(cond(axiom(99), 0)))
% 39.82/6.20  
% 39.82/6.20  Those formulas are unsatisfiable:
% 39.82/6.20  ---------------------------------
% 39.82/6.20  
% 39.82/6.20  Begin of proof
% 39.82/6.20  | 
% 39.82/6.20  | ALPHA: (and(pred(s2(plural(the(227))), 0), and(pred(s1(plural(the(227))), 0),
% 39.82/6.20  |              pred(the(227), 0)))) implies:
% 39.82/6.20  |   (1)  rline(vd1092) = 0
% 39.82/6.20  |   (2)  ron(vd1089, vd1092) = 0
% 39.82/6.20  |   (3)  ron(vd1080, vd1092) = 0
% 39.82/6.21  | 
% 39.82/6.21  | ALPHA: (holds(226, 1090, 1)) implies:
% 39.82/6.21  |   (4)   ? [v0: $i] : (vf(vd1085, vd1080) = v0 & vf(vd1089, vd1080) = v0 &
% 39.82/6.21  |          $i(v0))
% 39.82/6.21  | 
% 39.82/6.21  | ALPHA: (holds(226, 1090, 0)) implies:
% 39.82/6.21  |   (5)   ? [v0: $i] : (vf(vd1089, vd1085) = v0 & vf(vd1089, vd1080) = v0 &
% 39.82/6.21  |          $i(v0))
% 39.82/6.21  | 
% 39.82/6.21  | ALPHA: (pred(226, 0)) implies:
% 39.82/6.21  |   (6)  rpoint(vd1089) = 0
% 39.82/6.21  | 
% 39.82/6.21  | ALPHA: (pred(225, 4)) implies:
% 39.82/6.21  |   (7)  vd1086 = vd1085
% 39.82/6.21  | 
% 39.82/6.21  | ALPHA: (holds(conjunct1(225), 1087, 0)) implies:
% 39.82/6.21  |   (8)   ~ (vd1085 = vd1080)
% 39.82/6.21  | 
% 39.82/6.21  | ALPHA: (pred(225, 1)) implies:
% 39.82/6.21  |   (9)  $i(vd1086)
% 39.82/6.21  |   (10)  rpoint(vd1086) = 0
% 39.82/6.21  | 
% 39.82/6.21  | ALPHA: (qe(s1(plural(224)))) implies:
% 39.82/6.21  |   (11)  rpoint(vd1080) = 0
% 39.82/6.21  | 
% 39.82/6.21  | ALPHA: (qu(cond(axiom(162), 0), imp(cond(axiom(162), 0)))) implies:
% 39.82/6.21  |   (12)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : ( ~ (rpoint(v1) = 0) |  ~
% 39.82/6.21  |           (rpoint(v0) = 0) |  ~ (vf(v0, v1) = v2) |  ~ $i(v1) |  ~ $i(v0) | ((
% 39.82/6.21  |               ~ (v2 = v0) | v1 = v0) & ( ~ (v1 = v0) | v2 = v0)))
% 39.82/6.21  | 
% 39.82/6.21  | ALPHA: (pred(224, 5)) implies:
% 39.82/6.21  |   (13)   ~ (vd1081 = vd1080)
% 39.82/6.21  | 
% 39.82/6.21  | ALPHA: (qe(s2(plural(224)))) implies:
% 39.82/6.21  |   (14)  $i(vd1081)
% 39.82/6.21  |   (15)  rpoint(vd1081) = 0
% 39.82/6.21  | 
% 39.82/6.21  | ALPHA: (qu(theu(the(227), 1), imp(the(227)))) implies:
% 39.82/6.21  |   (16)  $i(vd1089)
% 39.82/6.21  |   (17)  $i(vd1080)
% 39.82/6.21  |   (18)  $i(vd1092)
% 39.82/6.21  |   (19)   ? [v0: $i] : ( ~ (v0 = vd1092) & ron(vd1080, v0) = 0 & ron(vd1089,
% 39.82/6.21  |             v0) = 0 & rline(v0) = 0 & $i(v0))
% 39.82/6.21  | 
% 39.82/6.21  | ALPHA: (function-axioms) implies:
% 39.82/6.21  |   (20)   ! [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i]
% 39.82/6.21  |         :  ! [v3: $i] : (v1 = v0 |  ~ (ron(v3, v2) = v1) |  ~ (ron(v3, v2) =
% 39.82/6.21  |             v0))
% 39.82/6.21  |   (21)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 39.82/6.21  |           (vf(v3, v2) = v1) |  ~ (vf(v3, v2) = v0))
% 39.82/6.21  | 
% 39.82/6.22  | DELTA: instantiating (4) with fresh symbol all_104_0 gives:
% 39.82/6.22  |   (22)  vf(vd1085, vd1080) = all_104_0 & vf(vd1089, vd1080) = all_104_0 &
% 39.82/6.22  |         $i(all_104_0)
% 39.82/6.22  | 
% 39.82/6.22  | ALPHA: (22) implies:
% 39.82/6.22  |   (23)  vf(vd1089, vd1080) = all_104_0
% 39.82/6.22  |   (24)  vf(vd1085, vd1080) = all_104_0
% 39.82/6.22  | 
% 39.82/6.22  | DELTA: instantiating (5) with fresh symbol all_106_0 gives:
% 39.82/6.22  |   (25)  vf(vd1089, vd1085) = all_106_0 & vf(vd1089, vd1080) = all_106_0 &
% 39.82/6.22  |         $i(all_106_0)
% 39.82/6.22  | 
% 39.82/6.22  | ALPHA: (25) implies:
% 39.82/6.22  |   (26)  vf(vd1089, vd1080) = all_106_0
% 39.82/6.22  | 
% 39.82/6.22  | DELTA: instantiating (19) with fresh symbol all_108_0 gives:
% 39.82/6.22  |   (27)   ~ (all_108_0 = vd1092) & ron(vd1080, all_108_0) = 0 & ron(vd1089,
% 39.82/6.22  |           all_108_0) = 0 & rline(all_108_0) = 0 & $i(all_108_0)
% 39.82/6.22  | 
% 39.82/6.22  | ALPHA: (27) implies:
% 39.82/6.22  |   (28)   ~ (all_108_0 = vd1092)
% 39.82/6.22  |   (29)  $i(all_108_0)
% 39.82/6.22  |   (30)  rline(all_108_0) = 0
% 39.82/6.22  |   (31)  ron(vd1089, all_108_0) = 0
% 39.82/6.22  |   (32)  ron(vd1080, all_108_0) = 0
% 39.82/6.22  | 
% 39.82/6.22  | REDUCE: (7), (10) imply:
% 39.82/6.22  |   (33)  rpoint(vd1085) = 0
% 39.82/6.22  | 
% 39.82/6.22  | REDUCE: (7), (9) imply:
% 39.82/6.22  |   (34)  $i(vd1085)
% 39.82/6.22  | 
% 39.82/6.22  | GROUND_INST: instantiating (21) with all_104_0, all_106_0, vd1080, vd1089,
% 39.82/6.22  |              simplifying with (23), (26) gives:
% 39.82/6.22  |   (35)  all_106_0 = all_104_0
% 39.82/6.22  | 
% 39.82/6.22  | GROUND_INST: instantiating (qu(cond(axiom(73), 0), imp(cond(axiom(73), 0))))
% 39.82/6.22  |              with vd1080, vd1089, vd1092, all_108_0, simplifying with (1),
% 39.82/6.22  |              (3), (6), (11), (16), (17), (18), (29), (30), (31) gives:
% 39.82/6.22  |   (36)  all_108_0 = vd1092 | vd1080 = vd1089 |  ? [v0: any] :  ? [v1: any] :
% 39.82/6.22  |         (ron(vd1080, all_108_0) = v1 & ron(vd1089, vd1092) = v0 & ( ~ (v1 = 0)
% 39.82/6.22  |             |  ~ (v0 = 0)))
% 39.82/6.22  | 
% 39.82/6.22  | GROUND_INST: instantiating (12) with vd1089, vd1080, all_104_0, simplifying
% 39.82/6.22  |              with (6), (11), (16), (17), (23) gives:
% 39.82/6.23  |   (37)  ( ~ (all_104_0 = v0) | vd1080 = vd1089) & ( ~ (vd1080 = vd1089) |
% 39.82/6.23  |           all_104_0 = v0)
% 39.82/6.23  | 
% 39.82/6.23  | ALPHA: (37) implies:
% 39.82/6.23  |   (38)   ~ (vd1080 = vd1089) | all_104_0 = v0
% 39.82/6.23  | 
% 39.82/6.23  | GROUND_INST: instantiating (12) with vd1085, vd1080, all_104_0, simplifying
% 39.82/6.23  |              with (11), (17), (24), (33), (34) gives:
% 39.82/6.23  |   (39)  ( ~ (all_104_0 = v0) | vd1085 = vd1080) & ( ~ (vd1085 = vd1080) |
% 39.82/6.23  |           all_104_0 = v0)
% 39.82/6.23  | 
% 39.82/6.23  | ALPHA: (39) implies:
% 39.82/6.23  |   (40)   ~ (all_104_0 = v0) | vd1085 = vd1080
% 39.82/6.23  | 
% 39.82/6.23  | GROUND_INST: instantiating (qu(cond(axiom(53), 0), imp(cond(axiom(53), 0))))
% 39.82/6.23  |              with vd1081, vd1080, simplifying with (11), (14), (15), (17)
% 39.82/6.23  |              gives:
% 39.82/6.23  |   (41)  vd1081 = vd1080 |  ? [v0: $i] : (rcenter(vd1081, v0) = 0 & rcircle(v0)
% 39.82/6.23  |           = 0 & ron(vd1080, v0) = 0 & $i(v0))
% 39.82/6.23  | 
% 39.82/6.23  | BETA: splitting (40) gives:
% 39.82/6.23  | 
% 39.82/6.23  | Case 1:
% 39.82/6.23  | | 
% 39.82/6.23  | |   (42)   ~ (all_104_0 = v0)
% 39.82/6.23  | | 
% 39.82/6.23  | | BETA: splitting (38) gives:
% 39.82/6.23  | | 
% 39.82/6.23  | | Case 1:
% 39.82/6.23  | | | 
% 39.82/6.23  | | |   (43)   ~ (vd1080 = vd1089)
% 39.82/6.23  | | | 
% 39.82/6.23  | | | BETA: splitting (36) gives:
% 39.82/6.23  | | | 
% 39.82/6.23  | | | Case 1:
% 39.82/6.23  | | | | 
% 39.82/6.23  | | | |   (44)  vd1080 = vd1089
% 39.82/6.23  | | | | 
% 39.82/6.23  | | | | REDUCE: (43), (44) imply:
% 39.82/6.23  | | | |   (45)  $false
% 40.03/6.23  | | | | 
% 40.03/6.23  | | | | CLOSE: (45) is inconsistent.
% 40.03/6.23  | | | | 
% 40.03/6.23  | | | Case 2:
% 40.03/6.23  | | | | 
% 40.03/6.23  | | | |   (46)  all_108_0 = vd1092 |  ? [v0: any] :  ? [v1: any] : (ron(vd1080,
% 40.03/6.23  | | | |             all_108_0) = v1 & ron(vd1089, vd1092) = v0 & ( ~ (v1 = 0) | 
% 40.03/6.23  | | | |             ~ (v0 = 0)))
% 40.03/6.23  | | | | 
% 40.03/6.23  | | | | BETA: splitting (46) gives:
% 40.03/6.23  | | | | 
% 40.03/6.23  | | | | Case 1:
% 40.03/6.23  | | | | | 
% 40.03/6.23  | | | | |   (47)  all_108_0 = vd1092
% 40.03/6.23  | | | | | 
% 40.03/6.23  | | | | | REDUCE: (28), (47) imply:
% 40.03/6.23  | | | | |   (48)  $false
% 40.03/6.23  | | | | | 
% 40.03/6.23  | | | | | CLOSE: (48) is inconsistent.
% 40.03/6.23  | | | | | 
% 40.03/6.23  | | | | Case 2:
% 40.03/6.23  | | | | | 
% 40.03/6.23  | | | | |   (49)   ? [v0: any] :  ? [v1: any] : (ron(vd1080, all_108_0) = v1 &
% 40.03/6.23  | | | | |           ron(vd1089, vd1092) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0)))
% 40.03/6.23  | | | | | 
% 40.03/6.23  | | | | | DELTA: instantiating (49) with fresh symbols all_251_0, all_251_1
% 40.03/6.23  | | | | |        gives:
% 40.03/6.23  | | | | |   (50)  ron(vd1080, all_108_0) = all_251_0 & ron(vd1089, vd1092) =
% 40.03/6.23  | | | | |         all_251_1 & ( ~ (all_251_0 = 0) |  ~ (all_251_1 = 0))
% 40.03/6.23  | | | | | 
% 40.03/6.23  | | | | | ALPHA: (50) implies:
% 40.03/6.23  | | | | |   (51)  ron(vd1089, vd1092) = all_251_1
% 40.03/6.23  | | | | |   (52)  ron(vd1080, all_108_0) = all_251_0
% 40.03/6.23  | | | | |   (53)   ~ (all_251_0 = 0) |  ~ (all_251_1 = 0)
% 40.03/6.23  | | | | | 
% 40.03/6.23  | | | | | BETA: splitting (41) gives:
% 40.03/6.23  | | | | | 
% 40.03/6.23  | | | | | Case 1:
% 40.03/6.23  | | | | | | 
% 40.03/6.23  | | | | | |   (54)  vd1081 = vd1080
% 40.03/6.23  | | | | | | 
% 40.03/6.23  | | | | | | REDUCE: (13), (54) imply:
% 40.03/6.23  | | | | | |   (55)  $false
% 40.03/6.23  | | | | | | 
% 40.03/6.23  | | | | | | CLOSE: (55) is inconsistent.
% 40.03/6.23  | | | | | | 
% 40.03/6.23  | | | | | Case 2:
% 40.03/6.23  | | | | | | 
% 40.03/6.23  | | | | | | 
% 40.03/6.23  | | | | | | GROUND_INST: instantiating (20) with 0, all_251_1, vd1092, vd1089,
% 40.03/6.23  | | | | | |              simplifying with (2), (51) gives:
% 40.03/6.23  | | | | | |   (56)  all_251_1 = 0
% 40.03/6.23  | | | | | | 
% 40.03/6.23  | | | | | | GROUND_INST: instantiating (20) with 0, all_251_0, all_108_0,
% 40.03/6.23  | | | | | |              vd1080, simplifying with (32), (52) gives:
% 40.03/6.23  | | | | | |   (57)  all_251_0 = 0
% 40.03/6.23  | | | | | | 
% 40.03/6.23  | | | | | | BETA: splitting (53) gives:
% 40.03/6.23  | | | | | | 
% 40.03/6.23  | | | | | | Case 1:
% 40.03/6.23  | | | | | | | 
% 40.03/6.23  | | | | | | |   (58)   ~ (all_251_0 = 0)
% 40.03/6.23  | | | | | | | 
% 40.03/6.23  | | | | | | | REDUCE: (57), (58) imply:
% 40.03/6.23  | | | | | | |   (59)  $false
% 40.03/6.23  | | | | | | | 
% 40.03/6.23  | | | | | | | CLOSE: (59) is inconsistent.
% 40.03/6.23  | | | | | | | 
% 40.03/6.23  | | | | | | Case 2:
% 40.03/6.23  | | | | | | | 
% 40.03/6.23  | | | | | | |   (60)   ~ (all_251_1 = 0)
% 40.03/6.23  | | | | | | | 
% 40.03/6.24  | | | | | | | REDUCE: (56), (60) imply:
% 40.03/6.24  | | | | | | |   (61)  $false
% 40.03/6.24  | | | | | | | 
% 40.03/6.24  | | | | | | | CLOSE: (61) is inconsistent.
% 40.03/6.24  | | | | | | | 
% 40.03/6.24  | | | | | | End of split
% 40.03/6.24  | | | | | | 
% 40.03/6.24  | | | | | End of split
% 40.03/6.24  | | | | | 
% 40.03/6.24  | | | | End of split
% 40.03/6.24  | | | | 
% 40.03/6.24  | | | End of split
% 40.03/6.24  | | | 
% 40.03/6.24  | | Case 2:
% 40.03/6.24  | | | 
% 40.03/6.24  | | |   (62)  all_104_0 = v0
% 40.03/6.24  | | | 
% 40.03/6.24  | | | REDUCE: (42), (62) imply:
% 40.03/6.24  | | |   (63)  $false
% 40.03/6.24  | | | 
% 40.03/6.24  | | | CLOSE: (63) is inconsistent.
% 40.03/6.24  | | | 
% 40.03/6.24  | | End of split
% 40.03/6.24  | | 
% 40.03/6.24  | Case 2:
% 40.03/6.24  | | 
% 40.03/6.24  | |   (64)  vd1085 = vd1080
% 40.03/6.24  | | 
% 40.03/6.24  | | REDUCE: (8), (64) imply:
% 40.03/6.24  | |   (65)  $false
% 40.03/6.24  | | 
% 40.03/6.24  | | CLOSE: (65) is inconsistent.
% 40.03/6.24  | | 
% 40.03/6.24  | End of split
% 40.03/6.24  | 
% 40.03/6.24  End of proof
% 40.03/6.24  % SZS output end Proof for theBenchmark
% 40.03/6.24  
% 40.03/6.24  5626ms
%------------------------------------------------------------------------------