TSTP Solution File: GEO524+1 by Princess---230619
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : GEO524+1 : TPTP v8.1.2. Released v7.0.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n022.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 23:23:35 EDT 2023
% Result : Theorem 21.92s 3.70s
% Output : Proof 37.72s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GEO524+1 : TPTP v8.1.2. Released v7.0.0.
% 0.07/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.12/0.34 % Computer : n022.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Tue Aug 29 22:00:38 EDT 2023
% 0.12/0.35 % CPUTime :
% 0.66/0.65 ________ _____
% 0.66/0.65 ___ __ \_________(_)________________________________
% 0.66/0.65 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.66/0.65 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.66/0.65 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.66/0.65
% 0.66/0.65 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.66/0.65 (2023-06-19)
% 0.66/0.65
% 0.66/0.65 (c) Philipp Rümmer, 2009-2023
% 0.66/0.65 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.66/0.65 Amanda Stjerna.
% 0.66/0.65 Free software under BSD-3-Clause.
% 0.66/0.65
% 0.66/0.65 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.66/0.65
% 0.66/0.65 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.66/0.66 Running up to 7 provers in parallel.
% 0.66/0.67 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.66/0.67 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.66/0.67 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.66/0.67 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.66/0.67 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.66/0.67 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.66/0.68 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 9.32/1.95 Prover 4: Preprocessing ...
% 9.46/2.00 Prover 1: Preprocessing ...
% 9.46/2.00 Prover 2: Preprocessing ...
% 9.46/2.00 Prover 6: Preprocessing ...
% 9.46/2.00 Prover 3: Preprocessing ...
% 9.46/2.00 Prover 0: Preprocessing ...
% 9.46/2.00 Prover 5: Preprocessing ...
% 20.73/3.49 Prover 5: Proving ...
% 20.73/3.50 Prover 2: Proving ...
% 20.73/3.53 Prover 6: Proving ...
% 20.73/3.53 Prover 1: Warning: ignoring some quantifiers
% 21.92/3.64 Prover 3: Warning: ignoring some quantifiers
% 21.92/3.66 Prover 1: Constructing countermodel ...
% 21.92/3.70 Prover 2: proved (3025ms)
% 21.92/3.70
% 21.92/3.70 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 21.92/3.70
% 21.92/3.70 Prover 3: Constructing countermodel ...
% 21.92/3.70 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 21.92/3.70 Prover 5: stopped
% 21.92/3.71 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 21.92/3.71 Prover 6: stopped
% 21.92/3.71 Prover 3: stopped
% 21.92/3.71 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 21.92/3.71 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 25.76/4.16 Prover 8: Preprocessing ...
% 25.76/4.16 Prover 7: Preprocessing ...
% 25.76/4.16 Prover 10: Preprocessing ...
% 25.76/4.17 Prover 11: Preprocessing ...
% 29.67/4.67 Prover 7: Warning: ignoring some quantifiers
% 29.67/4.68 Prover 10: Warning: ignoring some quantifiers
% 30.52/4.76 Prover 10: Constructing countermodel ...
% 30.52/4.77 Prover 7: Constructing countermodel ...
% 30.91/4.85 Prover 4: Constructing countermodel ...
% 31.30/4.89 Prover 8: Warning: ignoring some quantifiers
% 31.96/4.95 Prover 0: Proving ...
% 31.96/4.95 Prover 0: stopped
% 31.96/4.97 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 31.96/4.98 Prover 8: Constructing countermodel ...
% 33.60/5.17 Prover 13: Preprocessing ...
% 35.06/5.36 Prover 7: Found proof (size 17)
% 35.06/5.36 Prover 7: proved (1658ms)
% 35.06/5.36 Prover 8: stopped
% 35.15/5.36 Prover 4: stopped
% 35.15/5.36 Prover 13: stopped
% 35.15/5.37 Prover 1: stopped
% 35.15/5.37 Prover 10: stopped
% 36.83/5.80 Prover 11: Constructing countermodel ...
% 37.11/5.86 Prover 11: stopped
% 37.11/5.86
% 37.11/5.86 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 37.11/5.86
% 37.11/5.87 % SZS output start Proof for theBenchmark
% 37.29/5.89 Assumptions after simplification:
% 37.29/5.89 ---------------------------------
% 37.29/5.89
% 37.29/5.89 (aSatz10_5)
% 37.29/5.93 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 37.29/5.93 (reflect(v0, v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | reflect(v0,
% 37.29/5.93 v1, v3) = v2)
% 37.29/5.93
% 37.29/5.93 (aSatz10_7)
% 37.29/5.93 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ( ~ (v3
% 37.29/5.93 = v2) & ~ (v1 = v0) & reflect(v0, v1, v3) = v4 & reflect(v0, v1, v2) = v4
% 37.29/5.94 & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 37.29/5.94
% 37.29/5.94 (function-axioms)
% 37.57/5.96 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 37.57/5.96 $i] : ! [v6: $i] : ! [v7: $i] : (v1 = v0 | ~ (crossbar(v7, v6, v5, v4,
% 37.57/5.96 v3, v2) = v1) | ~ (crossbar(v7, v6, v5, v4, v3, v2) = v0)) & ! [v0:
% 37.57/5.96 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] :
% 37.57/5.96 ! [v6: $i] : (v1 = v0 | ~ (g811(v6, v5, v4, v3, v2) = v1) | ~ (g811(v6, v5,
% 37.57/5.96 v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 37.57/5.96 $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : (v1 = v0 | ~ (f811(v6, v5,
% 37.57/5.96 v4, v3, v2) = v1) | ~ (f811(v6, v5, v4, v3, v2) = v0)) & ! [v0: $i] :
% 37.57/5.96 ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6:
% 37.57/5.96 $i] : (v1 = v0 | ~ (op(v6, v5, v4, v3, v2) = v1) | ~ (op(v6, v5, v4, v3,
% 37.57/5.96 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : !
% 37.57/5.96 [v4: $i] : ! [v5: $i] : ! [v6: $i] : (v1 = v0 | ~ (midpointAux(v6, v5, v4,
% 37.57/5.96 v3, v2) = v1) | ~ (midpointAux(v6, v5, v4, v3, v2) = v0)) & ! [v0: $i]
% 37.57/5.96 : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : !
% 37.57/5.96 [v6: $i] : (v1 = v0 | ~ (g813(v6, v5, v4, v3, v2) = v1) | ~ (g813(v6, v5,
% 37.57/5.96 v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 37.57/5.96 $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : (v1 = v0 | ~ (f813(v6, v5,
% 37.57/5.96 v4, v3, v2) = v1) | ~ (f813(v6, v5, v4, v3, v2) = v0)) & ! [v0: $i] :
% 37.57/5.96 ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6:
% 37.57/5.96 $i] : (v1 = v0 | ~ (insert5(v6, v5, v4, v3, v2) = v1) | ~ (insert5(v6, v5,
% 37.57/5.96 v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 37.57/5.96 $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : (v1 = v0 | ~ (ip(v6, v5,
% 37.57/5.96 v4, v3, v2) = v1) | ~ (ip(v6, v5, v4, v3, v2) = v0)) & ! [v0: $i] : !
% 37.57/5.96 [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v1 = v0 |
% 37.57/5.96 ~ (ss3(v5, v4, v3, v2) = v1) | ~ (ss3(v5, v4, v3, v2) = v0)) & ! [v0: $i]
% 37.57/5.96 : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v1 =
% 37.57/5.96 v0 | ~ (ss2(v5, v4, v3, v2) = v1) | ~ (ss2(v5, v4, v3, v2) = v0)) & !
% 37.57/5.96 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i]
% 37.57/5.96 : (v1 = v0 | ~ (ss1(v5, v4, v3, v2) = v1) | ~ (ss1(v5, v4, v3, v2) = v0)) &
% 37.57/5.96 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 37.57/5.96 $i] : (v1 = v0 | ~ (il(v5, v4, v3, v2) = v1) | ~ (il(v5, v4, v3, v2) =
% 37.57/5.96 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i]
% 37.57/5.96 : ! [v5: $i] : (v1 = v0 | ~ (ins(v5, v4, v3, v2) = v1) | ~ (ins(v5, v4, v3,
% 37.57/5.96 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : !
% 37.57/5.96 [v4: $i] : ! [v5: $i] : (v1 = v0 | ~ (insert(v5, v4, v3, v2) = v1) | ~
% 37.57/5.96 (insert(v5, v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 37.57/5.96 ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v1 = v0 | ~ (ext(v5, v4, v3, v2) =
% 37.57/5.96 v1) | ~ (ext(v5, v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 37.57/5.96 $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (reflect(v4, v3, v2) = v1) |
% 37.57/5.96 ~ (reflect(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 37.57/5.96 ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (erectAux(v4, v3, v2) = v1) | ~
% 37.57/5.96 (erectAux(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 37.57/5.96 [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (erect(v4, v3, v2) = v1) | ~
% 37.57/5.96 (erect(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 37.57/5.96 [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (erectAux21a(v4, v3, v2) = v1) | ~
% 37.57/5.96 (erectAux21a(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 37.57/5.96 ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (erect21a(v4, v3, v2) = v1) | ~
% 37.57/5.96 (erect21a(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 37.57/5.96 [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (foot(v4, v3, v2) = v1) | ~ (foot(v4,
% 37.57/5.96 v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] :
% 37.57/5.96 ! [v4: $i] : (v1 = v0 | ~ (isomidpoint(v4, v3, v2) = v1) | ~
% 37.57/5.96 (isomidpoint(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 37.57/5.96 ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (c63(v4, v3, v2) = v1) | ~ (c63(v4,
% 37.57/5.96 v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] :
% 37.57/5.96 (v1 = v0 | ~ (midpoint(v3, v2) = v1) | ~ (midpoint(v3, v2) = v0)) & ! [v0:
% 37.57/5.96 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (s(v3, v2) =
% 37.57/5.96 v1) | ~ (s(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 37.57/5.96 [v3: $i] : (v1 = v0 | ~ (pointOffLine(v3, v2) = v1) | ~ (pointOffLine(v3,
% 37.57/5.96 v2) = v0))
% 37.57/5.96
% 37.57/5.96 Further assumptions not needed in the proof:
% 37.57/5.96 --------------------------------------------
% 37.57/5.96 aA1, aA2, aA3, aA4, aA5, aA6, aA7, aA8, aExtCol2, aExtPerp, aExtPerp2,
% 37.57/5.96 aExtPerp3, aExtPerp4, aExtPerp5, aExtPerp6, aExtSameSide1, aExtSameSide2,
% 37.57/5.96 aLemma9_13a, aLemma9_13b, aLemma9_13c, aLemma9_13d, aLemma9_13e, aLemma9_13f,
% 37.57/5.96 aLemma9_13f_case1, aLemma9_13f_case2, aLemma9_13g, aNarbouxLemma1, aSatz10_2a,
% 37.57/5.96 aSatz10_2b, aSatz10_4, aSatz10_6, aSatz2_1, aSatz2_11, aSatz2_12, aSatz2_13,
% 37.57/5.96 aSatz2_14, aSatz2_15, aSatz2_2, aSatz2_3, aSatz2_4, aSatz2_5, aSatz2_8,
% 37.57/5.96 aSatz3_1, aSatz3_13a, aSatz3_13b, aSatz3_13c, aSatz3_14a, aSatz3_14b, aSatz3_17,
% 37.57/5.96 aSatz3_2, aSatz3_3, aSatz3_4, aSatz3_5a, aSatz3_5b, aSatz3_6a, aSatz3_6b,
% 37.57/5.96 aSatz3_7a, aSatz3_7b, aSatz4_11a, aSatz4_11b, aSatz4_11c, aSatz4_11d,
% 37.57/5.96 aSatz4_11e, aSatz4_12, aSatz4_12b, aSatz4_13, aSatz4_14, aSatz4_16, aSatz4_17,
% 37.57/5.96 aSatz4_18, aSatz4_19, aSatz4_2, aSatz4_3, aSatz4_5, aSatz4_6, aSatz5_1,
% 37.57/5.96 aSatz5_10, aSatz5_11, aSatz5_12a1, aSatz5_12a2, aSatz5_12b, aSatz5_2, aSatz5_3,
% 37.57/5.96 aSatz5_5a, aSatz5_5b, aSatz5_6, aSatz5_7, aSatz5_8, aSatz5_9, aSatz6_11a,
% 37.57/5.96 aSatz6_11b, aSatz6_13a, aSatz6_13b, aSatz6_15a, aSatz6_15b, aSatz6_15c,
% 37.57/5.96 aSatz6_15d, aSatz6_16a, aSatz6_16b, aSatz6_17a, aSatz6_17b, aSatz6_18,
% 37.57/5.96 aSatz6_21, aSatz6_25, aSatz6_28, aSatz6_2a, aSatz6_2b, aSatz6_3a, aSatz6_3b,
% 37.57/5.96 aSatz6_4a, aSatz6_4b, aSatz6_5, aSatz6_6, aSatz6_7, aSatz7_10a, aSatz7_10b,
% 37.57/5.96 aSatz7_13, aSatz7_15a, aSatz7_15b, aSatz7_16a, aSatz7_16b, aSatz7_17, aSatz7_18,
% 37.57/5.96 aSatz7_19, aSatz7_2, aSatz7_20, aSatz7_21, aSatz7_22, aSatz7_22a, aSatz7_22b,
% 37.57/5.96 aSatz7_25, aSatz7_3a, aSatz7_3b, aSatz7_4a, aSatz7_4b, aSatz7_6, aSatz7_7,
% 37.57/5.96 aSatz7_8, aSatz7_9, aSatz8_10, aSatz8_12a, aSatz8_12b, aSatz8_13a, aSatz8_13b,
% 37.57/5.96 aSatz8_14a, aSatz8_14b, aSatz8_14c, aSatz8_15, aSatz8_16a, aSatz8_16b,
% 37.57/5.96 aSatz8_18, aSatz8_18a, aSatz8_2, aSatz8_20a, aSatz8_20b, aSatz8_21, aSatz8_21a,
% 37.57/5.96 aSatz8_22, aSatz8_22b, aSatz8_24, aSatz8_24a, aSatz8_24b, aSatz8_3, aSatz8_4,
% 37.57/5.96 aSatz8_5, aSatz8_6, aSatz8_7, aSatz8_8, aSatz8_9, aSatz9_13, aSatz9_16,
% 37.57/5.96 aSatz9_19b, aSatz9_2, aSatz9_3, aSatz9_3a, aSatz9_4, aSatz9_4a, aSatz9_4a2,
% 37.57/5.96 aSatz9_4b, aSatz9_4c, aSatz9_5, aSatz9_6, aSatz9_8, aSatz9_9, aSideReflect,
% 37.57/5.96 aext1, aperp1, d_Defn2_10, d_Defn4_1, d_Defn4_10, d_Defn4_15, d_Defn4_4,
% 37.57/5.96 d_Defn5_4, d_Defn6_1, d_Defn7_1, d_Defn7_23, d_Defn8_1, d_Defn8_11a,
% 37.57/5.96 d_Defn8_11b, d_Defn9_1, d_Defn9_7, d_insert
% 37.57/5.96
% 37.57/5.96 Those formulas are unsatisfiable:
% 37.57/5.96 ---------------------------------
% 37.57/5.96
% 37.57/5.96 Begin of proof
% 37.57/5.96 |
% 37.57/5.96 | ALPHA: (function-axioms) implies:
% 37.57/5.97 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 37.57/5.97 | (v1 = v0 | ~ (reflect(v4, v3, v2) = v1) | ~ (reflect(v4, v3, v2) =
% 37.57/5.97 | v0))
% 37.57/5.97 |
% 37.57/5.97 | DELTA: instantiating (aSatz10_7) with fresh symbols all_200_0, all_200_1,
% 37.57/5.97 | all_200_2, all_200_3, all_200_4 gives:
% 37.57/5.97 | (2) ~ (all_200_1 = all_200_2) & ~ (all_200_3 = all_200_4) &
% 37.57/5.97 | reflect(all_200_4, all_200_3, all_200_1) = all_200_0 &
% 37.57/5.97 | reflect(all_200_4, all_200_3, all_200_2) = all_200_0 & $i(all_200_0) &
% 37.57/5.97 | $i(all_200_1) & $i(all_200_2) & $i(all_200_3) & $i(all_200_4)
% 37.57/5.97 |
% 37.57/5.97 | ALPHA: (2) implies:
% 37.57/5.97 | (3) ~ (all_200_3 = all_200_4)
% 37.57/5.97 | (4) ~ (all_200_1 = all_200_2)
% 37.57/5.97 | (5) $i(all_200_4)
% 37.57/5.97 | (6) $i(all_200_3)
% 37.57/5.97 | (7) $i(all_200_2)
% 37.57/5.97 | (8) $i(all_200_1)
% 37.57/5.97 | (9) reflect(all_200_4, all_200_3, all_200_2) = all_200_0
% 37.57/5.97 | (10) reflect(all_200_4, all_200_3, all_200_1) = all_200_0
% 37.57/5.97 |
% 37.57/5.97 | GROUND_INST: instantiating (aSatz10_5) with all_200_4, all_200_3, all_200_2,
% 37.57/5.97 | all_200_0, simplifying with (5), (6), (7), (9) gives:
% 37.57/5.97 | (11) all_200_3 = all_200_4 | reflect(all_200_4, all_200_3, all_200_0) =
% 37.57/5.97 | all_200_2
% 37.57/5.97 |
% 37.57/5.97 | GROUND_INST: instantiating (aSatz10_5) with all_200_4, all_200_3, all_200_1,
% 37.57/5.97 | all_200_0, simplifying with (5), (6), (8), (10) gives:
% 37.57/5.97 | (12) all_200_3 = all_200_4 | reflect(all_200_4, all_200_3, all_200_0) =
% 37.57/5.97 | all_200_1
% 37.57/5.97 |
% 37.57/5.97 | BETA: splitting (12) gives:
% 37.57/5.97 |
% 37.57/5.97 | Case 1:
% 37.57/5.97 | |
% 37.57/5.97 | | (13) reflect(all_200_4, all_200_3, all_200_0) = all_200_1
% 37.57/5.97 | |
% 37.72/5.97 | | BETA: splitting (11) gives:
% 37.72/5.97 | |
% 37.72/5.97 | | Case 1:
% 37.72/5.97 | | |
% 37.72/5.97 | | | (14) reflect(all_200_4, all_200_3, all_200_0) = all_200_2
% 37.72/5.97 | | |
% 37.72/5.97 | | | GROUND_INST: instantiating (1) with all_200_2, all_200_1, all_200_0,
% 37.72/5.97 | | | all_200_3, all_200_4, simplifying with (13), (14) gives:
% 37.72/5.97 | | | (15) all_200_1 = all_200_2
% 37.72/5.97 | | |
% 37.72/5.97 | | | REDUCE: (4), (15) imply:
% 37.72/5.97 | | | (16) $false
% 37.72/5.97 | | |
% 37.72/5.97 | | | CLOSE: (16) is inconsistent.
% 37.72/5.97 | | |
% 37.72/5.97 | | Case 2:
% 37.72/5.97 | | |
% 37.72/5.97 | | | (17) all_200_3 = all_200_4
% 37.72/5.97 | | |
% 37.72/5.97 | | | REDUCE: (3), (17) imply:
% 37.72/5.97 | | | (18) $false
% 37.72/5.97 | | |
% 37.72/5.97 | | | CLOSE: (18) is inconsistent.
% 37.72/5.97 | | |
% 37.72/5.97 | | End of split
% 37.72/5.97 | |
% 37.72/5.97 | Case 2:
% 37.72/5.97 | |
% 37.72/5.97 | | (19) all_200_3 = all_200_4
% 37.72/5.97 | |
% 37.72/5.97 | | REDUCE: (3), (19) imply:
% 37.72/5.97 | | (20) $false
% 37.72/5.97 | |
% 37.72/5.97 | | CLOSE: (20) is inconsistent.
% 37.72/5.97 | |
% 37.72/5.97 | End of split
% 37.72/5.97 |
% 37.72/5.97 End of proof
% 37.72/5.97 % SZS output end Proof for theBenchmark
% 37.72/5.98
% 37.72/5.98 5321ms
%------------------------------------------------------------------------------