TSTP Solution File: GEO344+1 by Princess---230619
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- Process Solution
%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : GEO344+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 : n016.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 23:23:06 EDT 2023
% Result : Theorem 48.45s 6.98s
% Output : Proof 93.17s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : GEO344+1 : TPTP v8.1.2. Released v4.1.0.
% 0.10/0.12 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.12/0.33 % Computer : n016.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Wed Aug 30 00:07:16 EDT 2023
% 0.12/0.33 % CPUTime :
% 0.60/0.60 ________ _____
% 0.60/0.60 ___ __ \_________(_)________________________________
% 0.60/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.60/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.60/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.60/0.60
% 0.60/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.60/0.60 (2023-06-19)
% 0.60/0.60
% 0.60/0.60 (c) Philipp Rümmer, 2009-2023
% 0.60/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.60/0.60 Amanda Stjerna.
% 0.60/0.60 Free software under BSD-3-Clause.
% 0.60/0.60
% 0.60/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.60/0.60
% 0.60/0.60 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.65/0.61 Running up to 7 provers in parallel.
% 0.65/0.62 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.65/0.62 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.65/0.62 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.65/0.62 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.65/0.62 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.65/0.62 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.65/0.62 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 8.55/1.82 Prover 1: Preprocessing ...
% 8.60/1.85 Prover 3: Preprocessing ...
% 8.60/1.85 Prover 2: Preprocessing ...
% 8.60/1.85 Prover 4: Preprocessing ...
% 8.60/1.86 Prover 5: Preprocessing ...
% 8.60/1.86 Prover 6: Preprocessing ...
% 8.60/1.86 Prover 0: Preprocessing ...
% 21.90/3.63 Prover 1: Constructing countermodel ...
% 21.90/3.64 Prover 3: Constructing countermodel ...
% 23.09/3.74 Prover 6: Proving ...
% 26.37/4.24 Prover 2: Proving ...
% 26.37/4.25 Prover 5: Proving ...
% 36.67/5.49 Prover 4: Constructing countermodel ...
% 40.28/5.97 Prover 0: Proving ...
% 48.45/6.97 Prover 6: proved (6351ms)
% 48.45/6.97
% 48.45/6.98 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 48.45/6.98
% 48.45/6.98 Prover 3: stopped
% 48.45/6.98 Prover 5: stopped
% 48.45/6.98 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 48.45/6.99 Prover 2: stopped
% 48.45/6.99 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 48.45/6.99 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 48.45/6.99 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 48.45/7.04 Prover 0: stopped
% 48.45/7.04 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 52.60/7.54 Prover 10: Preprocessing ...
% 53.00/7.60 Prover 7: Preprocessing ...
% 53.00/7.60 Prover 11: Preprocessing ...
% 53.71/7.65 Prover 8: Preprocessing ...
% 54.09/7.73 Prover 13: Preprocessing ...
% 55.28/7.89 Prover 10: Warning: ignoring some quantifiers
% 55.69/7.92 Prover 10: Constructing countermodel ...
% 57.65/8.15 Prover 13: Warning: ignoring some quantifiers
% 57.65/8.18 Prover 13: Constructing countermodel ...
% 58.31/8.26 Prover 8: Warning: ignoring some quantifiers
% 58.71/8.31 Prover 8: Constructing countermodel ...
% 59.98/8.47 Prover 7: Warning: ignoring some quantifiers
% 60.68/8.54 Prover 7: Constructing countermodel ...
% 73.35/10.19 Prover 11: Constructing countermodel ...
% 84.60/11.66 Prover 13: stopped
% 84.60/11.68 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 86.25/11.89 Prover 16: Preprocessing ...
% 88.47/12.19 Prover 16: Warning: ignoring some quantifiers
% 88.47/12.20 Prover 16: Constructing countermodel ...
% 91.59/12.59 Prover 1: Found proof (size 36)
% 92.12/12.61 Prover 1: proved (11973ms)
% 92.12/12.61 Prover 16: stopped
% 92.12/12.61 Prover 4: stopped
% 92.12/12.61 Prover 10: stopped
% 92.12/12.61 Prover 7: stopped
% 92.12/12.61 Prover 8: stopped
% 92.73/12.75 Prover 11: stopped
% 92.73/12.75
% 92.73/12.75 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 92.73/12.75
% 92.73/12.75 % SZS output start Proof for theBenchmark
% 92.73/12.76 Assumptions after simplification:
% 92.73/12.76 ---------------------------------
% 92.73/12.76
% 92.73/12.76 (and(pred(conjunct2(405), 5), and(pred(s2(plural(conjunct2(405))), 0), and(pred(s1(plural(conjunct2(405))), 0), and(pred(conjunct2(405), 1), and(pred(conjunct1(405), 9), and(pred(conjunct1(405), 8), and(pred(conjunct1(405), 7), and(qe(s3(plural(405))), and(qe(s2(plural(405))), qe(s1(plural(405)))))))))))))
% 92.73/12.78 vd1406 = vd1407 & ~ (vd1400 = vd1399) & ~ (vd1400 = vd1401) & ~ (vd1399 =
% 92.73/12.78 vd1401) & rpoint(vd1400) = 0 & rpoint(vd1399) = 0 & rpoint(vd1401) = 0 &
% 92.73/12.78 ron(vd1400, vd1407) = 0 & ron(vd1399, vd1407) = 0 & rline(vd1407) = 0 &
% 92.73/12.78 $i(vd1400) & $i(vd1407) & $i(vd1399) & $i(vd1401)
% 92.73/12.78
% 92.73/12.78 (and(pred(s2(plural(the(409))), 0), and(pred(s1(plural(the(409))), 0), pred(the(409), 0))))
% 92.73/12.78 ron(vd1401, vd1419) = 0 & ron(vd1409, vd1419) = 0 & rline(vd1419) = 0 &
% 92.73/12.78 $i(vd1419) & $i(vd1401) & $i(vd1409)
% 92.73/12.78
% 92.73/12.78 (holds(conjunct1(406), 1410, 0))
% 92.73/12.78 rS(vd1401, vd1409, vd1406) = 0 & $i(vd1406) & $i(vd1401) & $i(vd1409)
% 92.73/12.78
% 92.73/12.78 (holds(conjunct2(conjunct2(conjunct2(406))), 1413, 0))
% 92.73/12.78 ~ (vd1401 = vd1409) & $i(vd1401) & $i(vd1409)
% 92.73/12.79
% 92.73/12.79 (pred(406, 0))
% 92.73/12.79 rpoint(vd1409) = 0 & $i(vd1409)
% 92.73/12.79
% 92.73/12.79 (qu(cond(axiom(113), 0), imp(cond(axiom(113), 0))))
% 92.73/12.79 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 92.73/12.79 $i] : ! [v6: $i] : ( ~ (rS(v4, v6, v1) = 0) | ~ (rS(v4, v5, v2) = 0) | ~
% 92.73/12.79 (rpoint(v6) = 0) | ~ (rpoint(v5) = 0) | ~ (rpoint(v4) = 0) | ~
% 92.73/12.79 (rpoint(v3) = 0) | ~ (ron(v3, v0) = 0) | ~ (rline(v2) = 0) | ~ (rline(v1)
% 92.73/12.79 = 0) | ~ (rline(v0) = 0) | ~ $i(v6) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3)
% 92.73/12.79 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v7: any] : ? [v8: any] : ? [v9:
% 92.73/12.79 any] : ? [v10: any] : ? [v11: any] : ? [v12: any] : (rS(v5, v6, v0) =
% 92.73/12.79 v7 & ron(v6, v2) = v8 & ron(v5, v2) = v9 & ron(v4, v0) = v10 & ron(v3, v2)
% 92.73/12.79 = v11 & ron(v3, v1) = v12 & ( ~ (v12 = 0) | ~ (v11 = 0) | ~ (v10 = 0) |
% 92.73/12.79 ~ (v9 = 0) | ~ (v8 = 0) | ~ (v7 = 0))))
% 92.73/12.79
% 92.73/12.79 (qu(cond(axiom(73), 0), imp(cond(axiom(73), 0))))
% 92.73/12.79 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v2 | v1 = v0 |
% 92.73/12.79 ~ (rpoint(v1) = 0) | ~ (rpoint(v0) = 0) | ~ (ron(v1, v3) = 0) | ~
% 92.73/12.79 (ron(v0, v2) = 0) | ~ (rline(v3) = 0) | ~ (rline(v2) = 0) | ~ $i(v3) | ~
% 92.73/12.79 $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: any] : (ron(v1, v2)
% 92.73/12.79 = v4 & ron(v0, v3) = v5 & ( ~ (v5 = 0) | ~ (v4 = 0))))
% 92.73/12.79
% 92.73/12.79 (qu(theu(the(409), 1), imp(the(409))))
% 92.73/12.79 $i(vd1419) & $i(vd1401) & $i(vd1409) & ? [v0: $i] : ( ~ (v0 = vd1419) &
% 92.73/12.79 ron(vd1401, v0) = 0 & ron(vd1409, v0) = 0 & rline(v0) = 0 & $i(v0))
% 92.73/12.79
% 92.73/12.79 (function-axioms)
% 92.73/12.80 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 92.73/12.80 $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : (v1 = v0 | ~
% 92.73/12.80 (vskolem1120(v9, v8, v7, v6, v5, v4, v3, v2) = v1) | ~ (vskolem1120(v9, v8,
% 92.73/12.80 v7, v6, v5, v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i]
% 92.73/12.80 : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v1 = v0 | ~ (vskolem1052(v5, v4,
% 92.73/12.80 v3, v2) = v1) | ~ (vskolem1052(v5, v4, v3, v2) = v0)) & ! [v0: $i] :
% 92.73/12.80 ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v1 = v0
% 92.73/12.80 | ~ (vskolem1078(v5, v4, v3, v2) = v1) | ~ (vskolem1078(v5, v4, v3, v2) =
% 92.73/12.80 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i]
% 92.73/12.80 : (v1 = v0 | ~ (vtriangle(v4, v3, v2) = v1) | ~ (vtriangle(v4, v3, v2) =
% 92.73/12.80 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i]
% 92.73/12.80 : (v1 = v0 | ~ (vg(v4, v3, v2) = v1) | ~ (vg(v4, v3, v2) = v0)) & ! [v0:
% 92.73/12.80 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 92.73/12.80 : ! [v4: $i] : (v1 = v0 | ~ (rR(v4, v3, v2) = v1) | ~ (rR(v4, v3, v2) =
% 92.73/12.80 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i]
% 92.73/12.80 : (v1 = v0 | ~ (vangle(v4, v3, v2) = v1) | ~ (vangle(v4, v3, v2) = v0)) & !
% 92.73/12.80 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 92.73/12.80 $i] : ! [v4: $i] : (v1 = v0 | ~ (rS(v4, v3, v2) = v1) | ~ (rS(v4, v3, v2)
% 92.73/12.80 = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 92.73/12.80 $i] : ! [v3: $i] : (v1 = v0 | ~ (rgeq(v3, v2) = v1) | ~ (rgeq(v3, v2) =
% 92.73/12.80 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 92.73/12.80 $i] : ! [v3: $i] : (v1 = v0 | ~ (rleq(v3, v2) = v1) | ~ (rleq(v3, v2) =
% 92.73/12.80 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 92.73/12.80 $i] : ! [v3: $i] : (v1 = v0 | ~ (rintersect(v3, v2) = v1) | ~
% 92.73/12.80 (rintersect(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 92.73/12.80 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (rcenter(v3,
% 92.73/12.80 v2) = v1) | ~ (rcenter(v3, v2) = v0)) & ! [v0: MultipleValueBool] : !
% 92.73/12.80 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (rless(v3,
% 92.73/12.80 v2) = v1) | ~ (rless(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 92.73/12.80 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (vplus(v3, v2) = v1) | ~ (vplus(v3,
% 92.73/12.80 v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] :
% 92.73/12.80 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (rinside(v3, v2) = v1) | ~
% 92.73/12.80 (rinside(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 92.73/12.80 $i] : (v1 = v0 | ~ (vf(v3, v2) = v1) | ~ (vf(v3, v2) = v0)) & ! [v0:
% 92.73/12.80 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 92.73/12.80 : (v1 = v0 | ~ (ron(v3, v2) = v1) | ~ (ron(v3, v2) = v0)) & ! [v0:
% 92.73/12.80 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 |
% 92.73/12.80 ~ (rtriangle(v2) = v1) | ~ (rtriangle(v2) = v0)) & ! [v0:
% 92.73/12.80 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 |
% 92.73/12.80 ~ (rreal(v2) = v1) | ~ (rreal(v2) = v0)) & ! [v0: MultipleValueBool] : !
% 92.73/12.80 [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (rcircle(v2) = v1) | ~
% 92.73/12.80 (rcircle(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 92.73/12.80 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (rpoint(v2) = v1) | ~
% 92.73/12.80 (rpoint(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool]
% 92.73/12.80 : ! [v2: $i] : (v1 = v0 | ~ (rline(v2) = v1) | ~ (rline(v2) = v0))
% 92.73/12.80
% 92.73/12.80 Further assumptions not needed in the proof:
% 92.73/12.80 --------------------------------------------
% 92.73/12.80 ass(cond(156, 0), 0), ass(cond(goal(206), 0), 0), ass(cond(goal(206), 0), 1),
% 92.73/12.80 ass(cond(goal(206), 0), 2), ass(cond(goal(219), 0), 0), ass(cond(goal(219), 0),
% 92.73/12.80 1), ass(cond(goal(238), 0), 0), ass(cond(goal(238), 0), 1),
% 92.73/12.80 ass(cond(goal(238), 0), 2), ass(cond(goal(264), 0), 0), ass(cond(goal(264), 0),
% 92.73/12.80 1), ass(cond(goal(264), 0), 2), ass(cond(goal(340), 0), 0),
% 92.73/12.80 ass(cond(goal(340), 0), 1), ass(cond(goal(382), 0), 0), holds(407, 1414, 0),
% 92.73/12.80 holds(conjunct1(conjunct2(406)), 1411, 0),
% 92.73/12.80 holds(conjunct1(conjunct2(conjunct2(406))), 1412, 0), pred(axiom(137), 1),
% 92.73/12.80 pred(axiom(137), 2), pred(axiom(5), 0), qu(cond(axiom(1), 0), imp(cond(axiom(1),
% 92.73/12.80 0))), qu(cond(axiom(101), 0), imp(cond(axiom(101), 0))),
% 92.73/12.80 qu(cond(axiom(103), 0), imp(cond(axiom(103), 0))), qu(cond(axiom(105), 0),
% 92.73/12.80 imp(cond(axiom(105), 0))), qu(cond(axiom(107), 0), imp(cond(axiom(107), 0))),
% 92.73/12.80 qu(cond(axiom(109), 0), imp(cond(axiom(109), 0))), qu(cond(axiom(11), 0),
% 92.73/12.80 imp(cond(axiom(11), 0))), qu(cond(axiom(111), 0), imp(cond(axiom(111), 0))),
% 92.73/12.80 qu(cond(axiom(115), 0), imp(cond(axiom(115), 0))), qu(cond(axiom(117), 0),
% 92.73/12.80 imp(cond(axiom(117), 0))), qu(cond(axiom(119), 0), imp(cond(axiom(119), 0))),
% 92.73/12.80 qu(cond(axiom(121), 0), imp(cond(axiom(121), 0))), qu(cond(axiom(123), 0),
% 92.73/12.80 imp(cond(axiom(123), 0))), qu(cond(axiom(125), 0), imp(cond(axiom(125), 0))),
% 92.73/12.80 qu(cond(axiom(127), 0), imp(cond(axiom(127), 0))), qu(cond(axiom(129), 0),
% 92.73/12.80 imp(cond(axiom(129), 0))), qu(cond(axiom(13), 0), imp(cond(axiom(13), 0))),
% 92.73/12.80 qu(cond(axiom(131), 0), imp(cond(axiom(131), 0))), qu(cond(axiom(133), 0),
% 92.73/12.80 imp(cond(axiom(133), 0))), qu(cond(axiom(135), 0), imp(cond(axiom(135), 0))),
% 92.73/12.80 qu(cond(axiom(139), 0), imp(cond(axiom(139), 0))), qu(cond(axiom(141), 0),
% 92.73/12.80 imp(cond(axiom(141), 0))), qu(cond(axiom(143), 0), imp(cond(axiom(143), 0))),
% 92.73/12.80 qu(cond(axiom(145), 0), imp(cond(axiom(145), 0))), qu(cond(axiom(147), 0),
% 92.73/12.80 imp(cond(axiom(147), 0))), qu(cond(axiom(149), 0), imp(cond(axiom(149), 0))),
% 92.73/12.80 qu(cond(axiom(15), 0), imp(cond(axiom(15), 0))), qu(cond(axiom(151), 0),
% 92.73/12.80 imp(cond(axiom(151), 0))), qu(cond(axiom(153), 0), imp(cond(axiom(153), 0))),
% 92.73/12.80 qu(cond(axiom(160), 0), imp(cond(axiom(160), 0))), qu(cond(axiom(162), 0),
% 92.73/12.80 imp(cond(axiom(162), 0))), qu(cond(axiom(164), 0), imp(cond(axiom(164), 0))),
% 92.73/12.80 qu(cond(axiom(166), 0), imp(cond(axiom(166), 0))), qu(cond(axiom(168), 0),
% 92.73/12.80 imp(cond(axiom(168), 0))), qu(cond(axiom(17), 0), imp(cond(axiom(17), 0))),
% 92.73/12.80 qu(cond(axiom(170), 0), imp(cond(axiom(170), 0))), qu(cond(axiom(172), 0),
% 92.73/12.80 imp(cond(axiom(172), 0))), qu(cond(axiom(174), 0), imp(cond(axiom(174), 0))),
% 92.73/12.80 qu(cond(axiom(176), 0), imp(cond(axiom(176), 0))), qu(cond(axiom(178), 0),
% 92.73/12.80 imp(cond(axiom(178), 0))), qu(cond(axiom(180), 0), imp(cond(axiom(180), 0))),
% 92.73/12.80 qu(cond(axiom(182), 0), imp(cond(axiom(182), 0))), qu(cond(axiom(184), 0),
% 92.73/12.80 imp(cond(axiom(184), 0))), qu(cond(axiom(186), 0), imp(cond(axiom(186), 0))),
% 92.73/12.80 qu(cond(axiom(188), 0), imp(cond(axiom(188), 0))), qu(cond(axiom(19), 0),
% 92.73/12.80 imp(cond(axiom(19), 0))), qu(cond(axiom(190), 0), imp(cond(axiom(190), 0))),
% 92.73/12.80 qu(cond(axiom(192), 0), imp(cond(axiom(192), 0))), qu(cond(axiom(194), 0),
% 92.73/12.80 imp(cond(axiom(194), 0))), qu(cond(axiom(196), 0), imp(cond(axiom(196), 0))),
% 92.73/12.80 qu(cond(axiom(198), 0), imp(cond(axiom(198), 0))), qu(cond(axiom(200), 0),
% 92.73/12.80 imp(cond(axiom(200), 0))), qu(cond(axiom(202), 0), imp(cond(axiom(202), 0))),
% 92.73/12.80 qu(cond(axiom(204), 0), imp(cond(axiom(204), 0))), qu(cond(axiom(21), 0),
% 92.73/12.80 imp(cond(axiom(21), 0))), qu(cond(axiom(23), 0), imp(cond(axiom(23), 0))),
% 92.73/12.80 qu(cond(axiom(25), 0), imp(cond(axiom(25), 0))), qu(cond(axiom(27), 0),
% 92.73/12.80 imp(cond(axiom(27), 0))), qu(cond(axiom(29), 0), imp(cond(axiom(29), 0))),
% 92.73/12.80 qu(cond(axiom(3), 0), imp(cond(axiom(3), 0))), qu(cond(axiom(31), 0),
% 92.73/12.80 imp(cond(axiom(31), 0))), qu(cond(axiom(33), 0), imp(cond(axiom(33), 0))),
% 92.73/12.80 qu(cond(axiom(35), 0), imp(cond(axiom(35), 0))), qu(cond(axiom(37), 0),
% 92.73/12.80 imp(cond(axiom(37), 0))), qu(cond(axiom(39), 0), imp(cond(axiom(39), 0))),
% 92.73/12.80 qu(cond(axiom(41), 0), imp(cond(axiom(41), 0))), qu(cond(axiom(43), 0),
% 92.73/12.80 imp(cond(axiom(43), 0))), qu(cond(axiom(45), 0), imp(cond(axiom(45), 0))),
% 92.73/12.80 qu(cond(axiom(47), 0), imp(cond(axiom(47), 0))), qu(cond(axiom(49), 0),
% 92.73/12.80 imp(cond(axiom(49), 0))), qu(cond(axiom(51), 0), imp(cond(axiom(51), 0))),
% 92.73/12.80 qu(cond(axiom(53), 0), imp(cond(axiom(53), 0))), qu(cond(axiom(55), 0),
% 92.73/12.80 imp(cond(axiom(55), 0))), qu(cond(axiom(57), 0), imp(cond(axiom(57), 0))),
% 92.73/12.81 qu(cond(axiom(59), 0), imp(cond(axiom(59), 0))), qu(cond(axiom(61), 0),
% 92.73/12.81 imp(cond(axiom(61), 0))), qu(cond(axiom(63), 0), imp(cond(axiom(63), 0))),
% 92.73/12.81 qu(cond(axiom(65), 0), imp(cond(axiom(65), 0))), qu(cond(axiom(67), 0),
% 92.73/12.81 imp(cond(axiom(67), 0))), qu(cond(axiom(69), 0), imp(cond(axiom(69), 0))),
% 92.73/12.81 qu(cond(axiom(7), 0), imp(cond(axiom(7), 0))), qu(cond(axiom(71), 0),
% 92.73/12.81 imp(cond(axiom(71), 0))), qu(cond(axiom(75), 0), imp(cond(axiom(75), 0))),
% 92.73/12.81 qu(cond(axiom(77), 0), imp(cond(axiom(77), 0))), qu(cond(axiom(79), 0),
% 92.73/12.81 imp(cond(axiom(79), 0))), qu(cond(axiom(81), 0), imp(cond(axiom(81), 0))),
% 92.73/12.81 qu(cond(axiom(83), 0), imp(cond(axiom(83), 0))), qu(cond(axiom(85), 0),
% 92.73/12.81 imp(cond(axiom(85), 0))), qu(cond(axiom(87), 0), imp(cond(axiom(87), 0))),
% 92.73/12.81 qu(cond(axiom(89), 0), imp(cond(axiom(89), 0))), qu(cond(axiom(9), 0),
% 92.73/12.81 imp(cond(axiom(9), 0))), qu(cond(axiom(91), 0), imp(cond(axiom(91), 0))),
% 92.73/12.81 qu(cond(axiom(93), 0), imp(cond(axiom(93), 0))), qu(cond(axiom(95), 0),
% 92.73/12.81 imp(cond(axiom(95), 0))), qu(cond(axiom(97), 0), imp(cond(axiom(97), 0))),
% 92.73/12.81 qu(cond(axiom(99), 0), imp(cond(axiom(99), 0))), replace(pred(408, 2)),
% 92.73/12.81 replace(qu(theu(the(408), 1), imp(the(408)))),
% 92.73/12.81 replace(replace(and(pred(s2(plural(the(408))), 0),
% 92.73/12.81 and(pred(s1(plural(the(408))), 0), pred(the(408), 0)))))
% 92.73/12.81
% 92.73/12.81 Those formulas are unsatisfiable:
% 92.73/12.81 ---------------------------------
% 92.73/12.81
% 92.73/12.81 Begin of proof
% 92.73/12.81 |
% 92.73/12.81 | ALPHA: (and(pred(s2(plural(the(409))), 0), and(pred(s1(plural(the(409))), 0),
% 92.73/12.81 | pred(the(409), 0)))) implies:
% 92.73/12.81 | (1) rline(vd1419) = 0
% 92.73/12.81 | (2) ron(vd1409, vd1419) = 0
% 92.73/12.81 | (3) ron(vd1401, vd1419) = 0
% 92.73/12.81 |
% 92.73/12.81 | ALPHA: (holds(conjunct2(conjunct2(conjunct2(406))), 1413, 0)) implies:
% 92.73/12.81 | (4) ~ (vd1401 = vd1409)
% 92.73/12.81 |
% 92.73/12.81 | ALPHA: (pred(406, 0)) implies:
% 92.73/12.81 | (5) rpoint(vd1409) = 0
% 92.73/12.81 |
% 92.73/12.81 | ALPHA: (and(pred(conjunct2(405), 5), and(pred(s2(plural(conjunct2(405))), 0),
% 92.73/12.81 | and(pred(s1(plural(conjunct2(405))), 0), and(pred(conjunct2(405),
% 92.73/12.81 | 1), and(pred(conjunct1(405), 9), and(pred(conjunct1(405),
% 92.73/12.81 | 8), and(pred(conjunct1(405), 7),
% 92.73/12.81 | and(qe(s3(plural(405))), and(qe(s2(plural(405))),
% 92.73/12.81 | qe(s1(plural(405))))))))))))) implies:
% 92.73/12.81 | (6) vd1406 = vd1407
% 92.73/12.81 | (7) rline(vd1407) = 0
% 92.73/12.81 | (8) rpoint(vd1401) = 0
% 92.73/12.81 |
% 92.73/12.81 | ALPHA: (holds(conjunct1(406), 1410, 0)) implies:
% 92.73/12.81 | (9) $i(vd1406)
% 92.73/12.81 | (10) rS(vd1401, vd1409, vd1406) = 0
% 92.73/12.81 |
% 92.73/12.81 | ALPHA: (qu(theu(the(409), 1), imp(the(409)))) implies:
% 92.73/12.81 | (11) $i(vd1409)
% 92.73/12.81 | (12) $i(vd1401)
% 92.73/12.81 | (13) $i(vd1419)
% 92.73/12.81 | (14) ? [v0: $i] : ( ~ (v0 = vd1419) & ron(vd1401, v0) = 0 & ron(vd1409,
% 92.73/12.81 | v0) = 0 & rline(v0) = 0 & $i(v0))
% 92.73/12.81 |
% 92.73/12.81 | ALPHA: (function-axioms) implies:
% 92.73/12.81 | (15) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 92.73/12.81 | : ! [v3: $i] : (v1 = v0 | ~ (ron(v3, v2) = v1) | ~ (ron(v3, v2) =
% 92.73/12.81 | v0))
% 92.73/12.81 |
% 92.73/12.81 | DELTA: instantiating (14) with fresh symbol all_122_0 gives:
% 92.73/12.81 | (16) ~ (all_122_0 = vd1419) & ron(vd1401, all_122_0) = 0 & ron(vd1409,
% 92.73/12.81 | all_122_0) = 0 & rline(all_122_0) = 0 & $i(all_122_0)
% 92.73/12.81 |
% 92.73/12.81 | ALPHA: (16) implies:
% 92.73/12.81 | (17) ~ (all_122_0 = vd1419)
% 92.73/12.81 | (18) $i(all_122_0)
% 92.73/12.81 | (19) rline(all_122_0) = 0
% 92.73/12.81 | (20) ron(vd1409, all_122_0) = 0
% 92.73/12.81 | (21) ron(vd1401, all_122_0) = 0
% 92.73/12.81 |
% 92.73/12.81 | REDUCE: (6), (10) imply:
% 92.73/12.81 | (22) rS(vd1401, vd1409, vd1407) = 0
% 92.73/12.81 |
% 92.73/12.81 | REDUCE: (6), (9) imply:
% 92.73/12.81 | (23) $i(vd1407)
% 92.73/12.81 |
% 92.73/12.82 | GROUND_INST: instantiating (qu(cond(axiom(73), 0), imp(cond(axiom(73), 0))))
% 92.73/12.82 | with vd1401, vd1409, vd1419, all_122_0, simplifying with (1),
% 92.73/12.82 | (3), (5), (8), (11), (12), (13), (18), (19), (20) gives:
% 92.73/12.82 | (24) all_122_0 = vd1419 | vd1401 = vd1409 | ? [v0: any] : ? [v1: any] :
% 92.73/12.82 | (ron(vd1401, all_122_0) = v1 & ron(vd1409, vd1419) = v0 & ( ~ (v1 = 0)
% 92.73/12.82 | | ~ (v0 = 0)))
% 92.73/12.82 |
% 92.73/12.82 | GROUND_INST: instantiating (qu(cond(axiom(113), 0), imp(cond(axiom(113), 0))))
% 92.73/12.82 | with all_122_0, vd1407, vd1407, vd1401, vd1401, vd1409, vd1409,
% 92.73/12.82 | simplifying with (5), (7), (8), (11), (12), (18), (19), (21),
% 92.73/12.82 | (22), (23) gives:
% 92.73/12.82 | (25) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] : ? [v4:
% 92.73/12.82 | any] : ? [v5: any] : (rS(vd1409, vd1409, all_122_0) = v0 &
% 92.73/12.82 | ron(vd1401, all_122_0) = v3 & ron(vd1401, vd1407) = v5 & ron(vd1401,
% 92.73/12.82 | vd1407) = v4 & ron(vd1409, vd1407) = v2 & ron(vd1409, vd1407) = v1
% 92.73/12.82 | & ( ~ (v5 = 0) | ~ (v4 = 0) | ~ (v3 = 0) | ~ (v2 = 0) | ~ (v1 =
% 92.73/12.82 | 0) | ~ (v0 = 0)))
% 92.73/12.82 |
% 92.73/12.82 | DELTA: instantiating (25) with fresh symbols all_238_0, all_238_1, all_238_2,
% 92.73/12.82 | all_238_3, all_238_4, all_238_5 gives:
% 93.17/12.82 | (26) rS(vd1409, vd1409, all_122_0) = all_238_5 & ron(vd1401, all_122_0) =
% 93.17/12.82 | all_238_2 & ron(vd1401, vd1407) = all_238_0 & ron(vd1401, vd1407) =
% 93.17/12.82 | all_238_1 & ron(vd1409, vd1407) = all_238_3 & ron(vd1409, vd1407) =
% 93.17/12.82 | all_238_4 & ( ~ (all_238_0 = 0) | ~ (all_238_1 = 0) | ~ (all_238_2 =
% 93.17/12.82 | 0) | ~ (all_238_3 = 0) | ~ (all_238_4 = 0) | ~ (all_238_5 = 0))
% 93.17/12.82 |
% 93.17/12.82 | ALPHA: (26) implies:
% 93.17/12.82 | (27) ron(vd1401, all_122_0) = all_238_2
% 93.17/12.82 |
% 93.17/12.82 | BETA: splitting (24) gives:
% 93.17/12.82 |
% 93.17/12.82 | Case 1:
% 93.17/12.82 | |
% 93.17/12.82 | | (28) vd1401 = vd1409
% 93.17/12.82 | |
% 93.17/12.82 | | REDUCE: (4), (28) imply:
% 93.17/12.82 | | (29) $false
% 93.17/12.82 | |
% 93.17/12.82 | | CLOSE: (29) is inconsistent.
% 93.17/12.82 | |
% 93.17/12.82 | Case 2:
% 93.17/12.82 | |
% 93.17/12.82 | | (30) all_122_0 = vd1419 | ? [v0: any] : ? [v1: any] : (ron(vd1401,
% 93.17/12.82 | | all_122_0) = v1 & ron(vd1409, vd1419) = v0 & ( ~ (v1 = 0) | ~
% 93.17/12.82 | | (v0 = 0)))
% 93.17/12.82 | |
% 93.17/12.82 | | BETA: splitting (30) gives:
% 93.17/12.82 | |
% 93.17/12.82 | | Case 1:
% 93.17/12.82 | | |
% 93.17/12.82 | | | (31) all_122_0 = vd1419
% 93.17/12.82 | | |
% 93.17/12.82 | | | REDUCE: (17), (31) imply:
% 93.17/12.82 | | | (32) $false
% 93.17/12.82 | | |
% 93.17/12.82 | | | CLOSE: (32) is inconsistent.
% 93.17/12.82 | | |
% 93.17/12.82 | | Case 2:
% 93.17/12.82 | | |
% 93.17/12.82 | | | (33) ? [v0: any] : ? [v1: any] : (ron(vd1401, all_122_0) = v1 &
% 93.17/12.82 | | | ron(vd1409, vd1419) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 93.17/12.82 | | |
% 93.17/12.82 | | | DELTA: instantiating (33) with fresh symbols all_401_0, all_401_1 gives:
% 93.17/12.82 | | | (34) ron(vd1401, all_122_0) = all_401_0 & ron(vd1409, vd1419) =
% 93.17/12.82 | | | all_401_1 & ( ~ (all_401_0 = 0) | ~ (all_401_1 = 0))
% 93.17/12.82 | | |
% 93.17/12.82 | | | ALPHA: (34) implies:
% 93.17/12.82 | | | (35) ron(vd1409, vd1419) = all_401_1
% 93.17/12.82 | | | (36) ron(vd1401, all_122_0) = all_401_0
% 93.17/12.82 | | | (37) ~ (all_401_0 = 0) | ~ (all_401_1 = 0)
% 93.17/12.82 | | |
% 93.17/12.82 | | | GROUND_INST: instantiating (15) with 0, all_401_1, vd1419, vd1409,
% 93.17/12.82 | | | simplifying with (2), (35) gives:
% 93.17/12.82 | | | (38) all_401_1 = 0
% 93.17/12.82 | | |
% 93.17/12.82 | | | GROUND_INST: instantiating (15) with 0, all_401_0, all_122_0, vd1401,
% 93.17/12.82 | | | simplifying with (21), (36) gives:
% 93.17/12.82 | | | (39) all_401_0 = 0
% 93.17/12.82 | | |
% 93.17/12.83 | | | GROUND_INST: instantiating (15) with all_238_2, all_401_0, all_122_0,
% 93.17/12.83 | | | vd1401, simplifying with (27), (36) gives:
% 93.17/12.83 | | | (40) all_401_0 = all_238_2
% 93.17/12.83 | | |
% 93.17/12.83 | | | COMBINE_EQS: (39), (40) imply:
% 93.17/12.83 | | | (41) all_238_2 = 0
% 93.17/12.83 | | |
% 93.17/12.83 | | | BETA: splitting (37) gives:
% 93.17/12.83 | | |
% 93.17/12.83 | | | Case 1:
% 93.17/12.83 | | | |
% 93.17/12.83 | | | | (42) ~ (all_401_0 = 0)
% 93.17/12.83 | | | |
% 93.17/12.83 | | | | REDUCE: (39), (42) imply:
% 93.17/12.83 | | | | (43) $false
% 93.17/12.83 | | | |
% 93.17/12.83 | | | | CLOSE: (43) is inconsistent.
% 93.17/12.83 | | | |
% 93.17/12.83 | | | Case 2:
% 93.17/12.83 | | | |
% 93.17/12.83 | | | | (44) ~ (all_401_1 = 0)
% 93.17/12.83 | | | |
% 93.17/12.83 | | | | REDUCE: (38), (44) imply:
% 93.17/12.83 | | | | (45) $false
% 93.17/12.83 | | | |
% 93.17/12.83 | | | | CLOSE: (45) is inconsistent.
% 93.17/12.83 | | | |
% 93.17/12.83 | | | End of split
% 93.17/12.83 | | |
% 93.17/12.83 | | End of split
% 93.17/12.83 | |
% 93.17/12.83 | End of split
% 93.17/12.83 |
% 93.17/12.83 End of proof
% 93.17/12.83 % SZS output end Proof for theBenchmark
% 93.17/12.83
% 93.17/12.83 12230ms
%------------------------------------------------------------------------------