TSTP Solution File: COM022+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : COM022+1 : TPTP v8.1.2. Released v4.0.0.
% 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 : Wed Aug 30 18:44:18 EDT 2023
% Result : Theorem 21.96s 3.74s
% Output : Proof 39.08s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : COM022+1 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.17/0.34 % Computer : n014.cluster.edu
% 0.17/0.34 % Model : x86_64 x86_64
% 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.34 % Memory : 8042.1875MB
% 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.34 % CPULimit : 300
% 0.17/0.34 % WCLimit : 300
% 0.17/0.34 % DateTime : Tue Aug 29 13:28:45 EDT 2023
% 0.17/0.34 % CPUTime :
% 0.19/0.61 ________ _____
% 0.19/0.61 ___ __ \_________(_)________________________________
% 0.19/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.19/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.19/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.19/0.61
% 0.19/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.19/0.61 (2023-06-19)
% 0.19/0.61
% 0.19/0.61 (c) Philipp Rümmer, 2009-2023
% 0.19/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.19/0.61 Amanda Stjerna.
% 0.19/0.61 Free software under BSD-3-Clause.
% 0.19/0.61
% 0.19/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.19/0.61
% 0.19/0.61 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.19/0.62 Running up to 7 provers in parallel.
% 0.19/0.65 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.19/0.65 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.19/0.65 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.19/0.65 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.19/0.65 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.19/0.65 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.19/0.65 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.90/1.11 Prover 1: Preprocessing ...
% 2.90/1.11 Prover 4: Preprocessing ...
% 2.90/1.16 Prover 2: Preprocessing ...
% 2.90/1.16 Prover 0: Preprocessing ...
% 2.90/1.16 Prover 3: Preprocessing ...
% 2.90/1.16 Prover 6: Preprocessing ...
% 2.90/1.16 Prover 5: Preprocessing ...
% 5.49/1.51 Prover 5: Constructing countermodel ...
% 5.49/1.51 Prover 2: Constructing countermodel ...
% 6.15/1.61 Prover 1: Constructing countermodel ...
% 6.82/1.68 Prover 3: Constructing countermodel ...
% 6.82/1.70 Prover 6: Proving ...
% 9.37/2.04 Prover 4: Constructing countermodel ...
% 9.37/2.16 Prover 0: Proving ...
% 21.96/3.74 Prover 2: proved (3101ms)
% 21.96/3.74
% 21.96/3.74 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 21.96/3.74
% 21.96/3.74 Prover 5: stopped
% 21.96/3.74 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 21.96/3.74 Prover 6: stopped
% 21.96/3.74 Prover 0: stopped
% 21.96/3.75 Prover 3: stopped
% 21.96/3.75 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 22.23/3.77 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 22.23/3.77 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 22.23/3.77 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 22.23/3.81 Prover 7: Preprocessing ...
% 22.23/3.81 Prover 8: Preprocessing ...
% 22.23/3.82 Prover 10: Preprocessing ...
% 22.81/3.83 Prover 13: Preprocessing ...
% 22.81/3.84 Prover 11: Preprocessing ...
% 22.81/3.87 Prover 7: Constructing countermodel ...
% 22.81/3.88 Prover 10: Constructing countermodel ...
% 23.16/3.90 Prover 13: Constructing countermodel ...
% 23.16/3.91 Prover 8: Warning: ignoring some quantifiers
% 23.16/3.91 Prover 8: Constructing countermodel ...
% 25.41/4.24 Prover 11: Constructing countermodel ...
% 38.73/5.97 Prover 7: Found proof (size 32)
% 38.73/5.97 Prover 7: proved (2235ms)
% 38.73/5.97 Prover 1: stopped
% 38.73/5.97 Prover 13: stopped
% 38.73/5.98 Prover 8: stopped
% 38.73/5.98 Prover 10: stopped
% 38.73/5.98 Prover 4: stopped
% 38.73/5.98 Prover 11: stopped
% 38.73/5.98
% 38.73/5.98 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 38.73/5.98
% 38.73/5.98 % SZS output start Proof for theBenchmark
% 38.73/5.98 Assumptions after simplification:
% 38.73/5.98 ---------------------------------
% 38.73/5.99
% 38.73/5.99 (mNFRDef)
% 38.73/5.99 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ $i(v3) | ~ $i(v2)
% 38.73/5.99 | ~ $i(v1) | ~ $i(v0) | ~ aNormalFormOfIn0(v2, v0, v1) | ~
% 38.73/5.99 aReductOfIn0(v3, v2, v1) | ~ aRewritingSystem0(v1) | ~ aElement0(v0)) & !
% 38.73/5.99 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~
% 38.73/5.99 aNormalFormOfIn0(v2, v0, v1) | ~ aRewritingSystem0(v1) | ~ aElement0(v0) |
% 38.73/5.99 sdtmndtasgtdt0(v0, v1, v2)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 38.73/5.99 $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ aNormalFormOfIn0(v2, v0, v1) | ~
% 38.73/5.99 aRewritingSystem0(v1) | ~ aElement0(v0) | aElement0(v2)) & ! [v0: $i] : !
% 38.73/5.99 [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~
% 38.73/5.99 sdtmndtasgtdt0(v0, v1, v2) | ~ aRewritingSystem0(v1) | ~ aElement0(v2) |
% 38.73/5.99 ~ aElement0(v0) | aNormalFormOfIn0(v2, v0, v1) | ? [v3: $i] : ($i(v3) &
% 38.73/5.99 aReductOfIn0(v3, v2, v1)))
% 38.73/5.99
% 38.73/5.99 (mTCRDef)
% 38.73/6.00 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v0 | ~ $i(v2) | ~ $i(v1) |
% 38.73/6.00 ~ $i(v0) | ~ sdtmndtasgtdt0(v0, v1, v2) | ~ aRewritingSystem0(v1) | ~
% 38.73/6.00 aElement0(v2) | ~ aElement0(v0) | sdtmndtplgtdt0(v0, v1, v2)) & ! [v0: $i]
% 38.73/6.00 : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~
% 38.73/6.00 sdtmndtplgtdt0(v0, v1, v2) | ~ aRewritingSystem0(v1) | ~ aElement0(v2) |
% 38.73/6.00 ~ aElement0(v0) | sdtmndtasgtdt0(v0, v1, v2)) & ! [v0: $i] : ! [v1: $i] :
% 38.73/6.00 ( ~ $i(v1) | ~ $i(v0) | ~ aRewritingSystem0(v1) | ~ aElement0(v0) |
% 38.73/6.00 sdtmndtasgtdt0(v0, v1, v0))
% 38.73/6.00
% 38.73/6.00 (m__)
% 38.73/6.00 $i(xc) & $i(xb) & $i(xa) & $i(xR) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 38.73/6.00 ? [v3: $i] : ($i(v3) & $i(v2) & $i(v1) & $i(v0) & sdtmndtasgtdt0(xa, xR, xc) &
% 38.73/6.00 sdtmndtasgtdt0(xa, xR, xb) & ! [v4: $i] : ( ~ $i(v4) | ~
% 38.73/6.00 sdtmndtasgtdt0(xc, xR, v4) | ~ sdtmndtasgtdt0(xb, xR, v4) | ~
% 38.73/6.00 aElement0(v4)) & ( ~ sdtmndtplgtdt0(xa, xR, xc) | ~ sdtmndtplgtdt0(xa,
% 38.73/6.00 xR, xb) | (aNormalFormOfIn0(v3, v2, xR) & sdtmndtasgtdt0(v1, xR, v2) &
% 38.73/6.00 sdtmndtasgtdt0(v1, xR, xc) & sdtmndtasgtdt0(v0, xR, v2) &
% 38.73/6.00 sdtmndtasgtdt0(v0, xR, xb) & sdtmndtasgtdt0(xc, xR, v3) &
% 38.73/6.00 sdtmndtasgtdt0(xb, xR, v3) & aReductOfIn0(v1, xa, xR) & aReductOfIn0(v0,
% 38.73/6.00 xa, xR) & aElement0(v2) & aElement0(v1) & aElement0(v0))))
% 38.73/6.00
% 38.73/6.00 (m__656)
% 38.73/6.00 $i(xR) & aRewritingSystem0(xR)
% 38.73/6.00
% 38.73/6.00 (m__731)
% 38.73/6.00 $i(xc) & $i(xb) & $i(xa) & aElement0(xc) & aElement0(xb) & aElement0(xa)
% 38.73/6.00
% 38.73/6.00 Further assumptions not needed in the proof:
% 38.73/6.00 --------------------------------------------
% 38.73/6.00 mCRDef, mElmSort, mReduct, mRelSort, mTCDef, mTCRTrans, mTCTrans, mTCbr,
% 38.73/6.00 mTermNF, mTermin, mWCRDef, mWFOrd, m__656_01, m__715
% 38.73/6.00
% 38.73/6.00 Those formulas are unsatisfiable:
% 38.73/6.00 ---------------------------------
% 38.73/6.00
% 38.73/6.00 Begin of proof
% 38.73/6.00 |
% 38.73/6.00 | ALPHA: (m__) implies:
% 39.08/6.00 | (1) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ($i(v3) &
% 39.08/6.00 | $i(v2) & $i(v1) & $i(v0) & sdtmndtasgtdt0(xa, xR, xc) &
% 39.08/6.00 | sdtmndtasgtdt0(xa, xR, xb) & ! [v4: $i] : ( ~ $i(v4) | ~
% 39.08/6.00 | sdtmndtasgtdt0(xc, xR, v4) | ~ sdtmndtasgtdt0(xb, xR, v4) | ~
% 39.08/6.00 | aElement0(v4)) & ( ~ sdtmndtplgtdt0(xa, xR, xc) | ~
% 39.08/6.00 | sdtmndtplgtdt0(xa, xR, xb) | (aNormalFormOfIn0(v3, v2, xR) &
% 39.08/6.00 | sdtmndtasgtdt0(v1, xR, v2) & sdtmndtasgtdt0(v1, xR, xc) &
% 39.08/6.00 | sdtmndtasgtdt0(v0, xR, v2) & sdtmndtasgtdt0(v0, xR, xb) &
% 39.08/6.00 | sdtmndtasgtdt0(xc, xR, v3) & sdtmndtasgtdt0(xb, xR, v3) &
% 39.08/6.00 | aReductOfIn0(v1, xa, xR) & aReductOfIn0(v0, xa, xR) &
% 39.08/6.00 | aElement0(v2) & aElement0(v1) & aElement0(v0))))
% 39.08/6.00 |
% 39.08/6.00 | ALPHA: (m__731) implies:
% 39.08/6.00 | (2) aElement0(xa)
% 39.08/6.00 | (3) aElement0(xb)
% 39.08/6.00 | (4) aElement0(xc)
% 39.08/6.00 | (5) $i(xa)
% 39.08/6.00 | (6) $i(xb)
% 39.08/6.00 | (7) $i(xc)
% 39.08/6.00 |
% 39.08/6.00 | ALPHA: (m__656) implies:
% 39.08/6.01 | (8) aRewritingSystem0(xR)
% 39.08/6.01 | (9) $i(xR)
% 39.08/6.01 |
% 39.08/6.01 | ALPHA: (mNFRDef) implies:
% 39.08/6.01 | (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~
% 39.08/6.01 | $i(v0) | ~ aNormalFormOfIn0(v2, v0, v1) | ~ aRewritingSystem0(v1)
% 39.08/6.01 | | ~ aElement0(v0) | aElement0(v2))
% 39.08/6.01 |
% 39.08/6.01 | ALPHA: (mTCRDef) implies:
% 39.08/6.01 | (11) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~
% 39.08/6.01 | aRewritingSystem0(v1) | ~ aElement0(v0) | sdtmndtasgtdt0(v0, v1,
% 39.08/6.01 | v0))
% 39.08/6.01 | (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v0 | ~ $i(v2) | ~
% 39.08/6.01 | $i(v1) | ~ $i(v0) | ~ sdtmndtasgtdt0(v0, v1, v2) | ~
% 39.08/6.01 | aRewritingSystem0(v1) | ~ aElement0(v2) | ~ aElement0(v0) |
% 39.08/6.01 | sdtmndtplgtdt0(v0, v1, v2))
% 39.08/6.01 |
% 39.08/6.01 | DELTA: instantiating (1) with fresh symbols all_14_0, all_14_1, all_14_2,
% 39.08/6.01 | all_14_3 gives:
% 39.08/6.01 | (13) $i(all_14_0) & $i(all_14_1) & $i(all_14_2) & $i(all_14_3) &
% 39.08/6.01 | sdtmndtasgtdt0(xa, xR, xc) & sdtmndtasgtdt0(xa, xR, xb) & ! [v0: $i]
% 39.08/6.01 | : ( ~ $i(v0) | ~ sdtmndtasgtdt0(xc, xR, v0) | ~ sdtmndtasgtdt0(xb,
% 39.08/6.01 | xR, v0) | ~ aElement0(v0)) & ( ~ sdtmndtplgtdt0(xa, xR, xc) | ~
% 39.08/6.01 | sdtmndtplgtdt0(xa, xR, xb) | (aNormalFormOfIn0(all_14_0, all_14_1,
% 39.08/6.01 | xR) & sdtmndtasgtdt0(all_14_2, xR, all_14_1) &
% 39.08/6.01 | sdtmndtasgtdt0(all_14_2, xR, xc) & sdtmndtasgtdt0(all_14_3, xR,
% 39.08/6.01 | all_14_1) & sdtmndtasgtdt0(all_14_3, xR, xb) &
% 39.08/6.01 | sdtmndtasgtdt0(xc, xR, all_14_0) & sdtmndtasgtdt0(xb, xR,
% 39.08/6.01 | all_14_0) & aReductOfIn0(all_14_2, xa, xR) &
% 39.08/6.01 | aReductOfIn0(all_14_3, xa, xR) & aElement0(all_14_1) &
% 39.08/6.01 | aElement0(all_14_2) & aElement0(all_14_3)))
% 39.08/6.01 |
% 39.08/6.01 | ALPHA: (13) implies:
% 39.08/6.01 | (14) sdtmndtasgtdt0(xa, xR, xb)
% 39.08/6.01 | (15) sdtmndtasgtdt0(xa, xR, xc)
% 39.08/6.01 | (16) $i(all_14_1)
% 39.08/6.01 | (17) $i(all_14_0)
% 39.08/6.01 | (18) ~ sdtmndtplgtdt0(xa, xR, xc) | ~ sdtmndtplgtdt0(xa, xR, xb) |
% 39.08/6.01 | (aNormalFormOfIn0(all_14_0, all_14_1, xR) & sdtmndtasgtdt0(all_14_2,
% 39.08/6.01 | xR, all_14_1) & sdtmndtasgtdt0(all_14_2, xR, xc) &
% 39.08/6.01 | sdtmndtasgtdt0(all_14_3, xR, all_14_1) & sdtmndtasgtdt0(all_14_3,
% 39.08/6.01 | xR, xb) & sdtmndtasgtdt0(xc, xR, all_14_0) & sdtmndtasgtdt0(xb,
% 39.08/6.01 | xR, all_14_0) & aReductOfIn0(all_14_2, xa, xR) &
% 39.08/6.01 | aReductOfIn0(all_14_3, xa, xR) & aElement0(all_14_1) &
% 39.08/6.01 | aElement0(all_14_2) & aElement0(all_14_3))
% 39.08/6.01 | (19) ! [v0: $i] : ( ~ $i(v0) | ~ sdtmndtasgtdt0(xc, xR, v0) | ~
% 39.08/6.01 | sdtmndtasgtdt0(xb, xR, v0) | ~ aElement0(v0))
% 39.08/6.01 |
% 39.08/6.01 | GROUND_INST: instantiating (11) with xc, xR, simplifying with (4), (7), (8),
% 39.08/6.01 | (9) gives:
% 39.08/6.01 | (20) sdtmndtasgtdt0(xc, xR, xc)
% 39.08/6.01 |
% 39.08/6.01 | GROUND_INST: instantiating (11) with xb, xR, simplifying with (3), (6), (8),
% 39.08/6.01 | (9) gives:
% 39.08/6.01 | (21) sdtmndtasgtdt0(xb, xR, xb)
% 39.08/6.01 |
% 39.08/6.01 | GROUND_INST: instantiating (12) with xa, xR, xb, simplifying with (2), (3),
% 39.08/6.01 | (5), (6), (8), (9), (14) gives:
% 39.08/6.01 | (22) xb = xa | sdtmndtplgtdt0(xa, xR, xb)
% 39.08/6.01 |
% 39.08/6.01 | GROUND_INST: instantiating (12) with xa, xR, xc, simplifying with (2), (4),
% 39.08/6.01 | (5), (7), (8), (9), (15) gives:
% 39.08/6.01 | (23) xc = xa | sdtmndtplgtdt0(xa, xR, xc)
% 39.08/6.01 |
% 39.08/6.02 | GROUND_INST: instantiating (19) with xb, simplifying with (3), (6), (21)
% 39.08/6.02 | gives:
% 39.08/6.02 | (24) ~ sdtmndtasgtdt0(xc, xR, xb)
% 39.08/6.02 |
% 39.08/6.02 | GROUND_INST: instantiating (19) with xc, simplifying with (4), (7), (20)
% 39.08/6.02 | gives:
% 39.08/6.02 | (25) ~ sdtmndtasgtdt0(xb, xR, xc)
% 39.08/6.02 |
% 39.08/6.02 | PRED_UNIFY: (15), (25) imply:
% 39.08/6.02 | (26) ~ (xb = xa)
% 39.08/6.02 |
% 39.08/6.02 | PRED_UNIFY: (14), (24) imply:
% 39.08/6.02 | (27) ~ (xc = xa)
% 39.08/6.02 |
% 39.08/6.02 | BETA: splitting (23) gives:
% 39.08/6.02 |
% 39.08/6.02 | Case 1:
% 39.08/6.02 | |
% 39.08/6.02 | | (28) sdtmndtplgtdt0(xa, xR, xc)
% 39.08/6.02 | |
% 39.08/6.02 | | BETA: splitting (22) gives:
% 39.08/6.02 | |
% 39.08/6.02 | | Case 1:
% 39.08/6.02 | | |
% 39.08/6.02 | | | (29) sdtmndtplgtdt0(xa, xR, xb)
% 39.08/6.02 | | |
% 39.08/6.02 | | | BETA: splitting (18) gives:
% 39.08/6.02 | | |
% 39.08/6.02 | | | Case 1:
% 39.08/6.02 | | | |
% 39.08/6.02 | | | | (30) ~ sdtmndtplgtdt0(xa, xR, xc)
% 39.08/6.02 | | | |
% 39.08/6.02 | | | | PRED_UNIFY: (28), (30) imply:
% 39.08/6.02 | | | | (31) $false
% 39.08/6.02 | | | |
% 39.08/6.02 | | | | CLOSE: (31) is inconsistent.
% 39.08/6.02 | | | |
% 39.08/6.02 | | | Case 2:
% 39.08/6.02 | | | |
% 39.08/6.02 | | | | (32) ~ sdtmndtplgtdt0(xa, xR, xb) | (aNormalFormOfIn0(all_14_0,
% 39.08/6.02 | | | | all_14_1, xR) & sdtmndtasgtdt0(all_14_2, xR, all_14_1) &
% 39.08/6.02 | | | | sdtmndtasgtdt0(all_14_2, xR, xc) & sdtmndtasgtdt0(all_14_3,
% 39.08/6.02 | | | | xR, all_14_1) & sdtmndtasgtdt0(all_14_3, xR, xb) &
% 39.08/6.02 | | | | sdtmndtasgtdt0(xc, xR, all_14_0) & sdtmndtasgtdt0(xb, xR,
% 39.08/6.02 | | | | all_14_0) & aReductOfIn0(all_14_2, xa, xR) &
% 39.08/6.02 | | | | aReductOfIn0(all_14_3, xa, xR) & aElement0(all_14_1) &
% 39.08/6.02 | | | | aElement0(all_14_2) & aElement0(all_14_3))
% 39.08/6.02 | | | |
% 39.08/6.02 | | | | BETA: splitting (32) gives:
% 39.08/6.02 | | | |
% 39.08/6.02 | | | | Case 1:
% 39.08/6.02 | | | | |
% 39.08/6.02 | | | | | (33) ~ sdtmndtplgtdt0(xa, xR, xb)
% 39.08/6.02 | | | | |
% 39.08/6.02 | | | | | PRED_UNIFY: (29), (33) imply:
% 39.08/6.02 | | | | | (34) $false
% 39.08/6.02 | | | | |
% 39.08/6.02 | | | | | CLOSE: (34) is inconsistent.
% 39.08/6.02 | | | | |
% 39.08/6.02 | | | | Case 2:
% 39.08/6.02 | | | | |
% 39.08/6.02 | | | | | (35) aNormalFormOfIn0(all_14_0, all_14_1, xR) &
% 39.08/6.02 | | | | | sdtmndtasgtdt0(all_14_2, xR, all_14_1) &
% 39.08/6.02 | | | | | sdtmndtasgtdt0(all_14_2, xR, xc) & sdtmndtasgtdt0(all_14_3,
% 39.08/6.02 | | | | | xR, all_14_1) & sdtmndtasgtdt0(all_14_3, xR, xb) &
% 39.08/6.02 | | | | | sdtmndtasgtdt0(xc, xR, all_14_0) & sdtmndtasgtdt0(xb, xR,
% 39.08/6.02 | | | | | all_14_0) & aReductOfIn0(all_14_2, xa, xR) &
% 39.08/6.02 | | | | | aReductOfIn0(all_14_3, xa, xR) & aElement0(all_14_1) &
% 39.08/6.02 | | | | | aElement0(all_14_2) & aElement0(all_14_3)
% 39.08/6.02 | | | | |
% 39.08/6.02 | | | | | ALPHA: (35) implies:
% 39.08/6.02 | | | | | (36) aElement0(all_14_1)
% 39.08/6.02 | | | | | (37) sdtmndtasgtdt0(xb, xR, all_14_0)
% 39.08/6.02 | | | | | (38) sdtmndtasgtdt0(xc, xR, all_14_0)
% 39.08/6.02 | | | | | (39) aNormalFormOfIn0(all_14_0, all_14_1, xR)
% 39.08/6.02 | | | | |
% 39.08/6.02 | | | | | GROUND_INST: instantiating (10) with all_14_1, xR, all_14_0,
% 39.08/6.02 | | | | | simplifying with (8), (9), (16), (17), (36), (39) gives:
% 39.08/6.02 | | | | | (40) aElement0(all_14_0)
% 39.08/6.02 | | | | |
% 39.08/6.02 | | | | | GROUND_INST: instantiating (19) with all_14_0, simplifying with (17),
% 39.08/6.02 | | | | | (37), (38), (40) gives:
% 39.08/6.02 | | | | | (41) $false
% 39.08/6.02 | | | | |
% 39.08/6.02 | | | | | CLOSE: (41) is inconsistent.
% 39.08/6.02 | | | | |
% 39.08/6.02 | | | | End of split
% 39.08/6.02 | | | |
% 39.08/6.02 | | | End of split
% 39.08/6.02 | | |
% 39.08/6.02 | | Case 2:
% 39.08/6.02 | | |
% 39.08/6.02 | | | (42) xb = xa
% 39.08/6.02 | | |
% 39.08/6.02 | | | REDUCE: (26), (42) imply:
% 39.08/6.02 | | | (43) $false
% 39.08/6.02 | | |
% 39.08/6.02 | | | CLOSE: (43) is inconsistent.
% 39.08/6.02 | | |
% 39.08/6.02 | | End of split
% 39.08/6.02 | |
% 39.08/6.02 | Case 2:
% 39.08/6.02 | |
% 39.08/6.02 | | (44) xc = xa
% 39.08/6.02 | |
% 39.08/6.02 | | REDUCE: (27), (44) imply:
% 39.08/6.02 | | (45) $false
% 39.08/6.02 | |
% 39.08/6.02 | | CLOSE: (45) is inconsistent.
% 39.08/6.02 | |
% 39.08/6.02 | End of split
% 39.08/6.02 |
% 39.08/6.02 End of proof
% 39.08/6.02 % SZS output end Proof for theBenchmark
% 39.08/6.02
% 39.08/6.02 5416ms
%------------------------------------------------------------------------------