TSTP Solution File: COM012+3 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : COM012+3 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n015.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 18:44:15 EDT 2023
% Result : Theorem 4.64s 1.38s
% Output : Proof 7.30s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : COM012+3 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.34 % Computer : n015.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 13:46:11 EDT 2023
% 0.19/0.34 % CPUTime :
% 0.19/0.60 ________ _____
% 0.19/0.60 ___ __ \_________(_)________________________________
% 0.19/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.19/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.19/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.19/0.60
% 0.19/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.19/0.60 (2023-06-19)
% 0.19/0.60
% 0.19/0.60 (c) Philipp Rümmer, 2009-2023
% 0.19/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.19/0.60 Amanda Stjerna.
% 0.19/0.60 Free software under BSD-3-Clause.
% 0.19/0.60
% 0.19/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.19/0.60
% 0.19/0.60 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.19/0.61 Running up to 7 provers in parallel.
% 0.19/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.19/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.19/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.19/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.19/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.19/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.19/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.50/1.01 Prover 4: Preprocessing ...
% 2.50/1.01 Prover 1: Preprocessing ...
% 2.50/1.05 Prover 2: Preprocessing ...
% 2.50/1.05 Prover 0: Preprocessing ...
% 2.50/1.05 Prover 6: Preprocessing ...
% 2.50/1.05 Prover 5: Preprocessing ...
% 2.50/1.05 Prover 3: Preprocessing ...
% 3.87/1.21 Prover 5: Constructing countermodel ...
% 3.94/1.23 Prover 2: Constructing countermodel ...
% 3.94/1.28 Prover 1: Constructing countermodel ...
% 4.64/1.32 Prover 3: Constructing countermodel ...
% 4.64/1.33 Prover 6: Proving ...
% 4.64/1.37 Prover 2: proved (745ms)
% 4.64/1.38
% 4.64/1.38 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.64/1.38
% 4.64/1.38 Prover 5: stopped
% 4.64/1.39 Prover 3: stopped
% 4.64/1.40 Prover 6: stopped
% 4.64/1.41 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 4.64/1.41 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 4.64/1.41 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 4.64/1.41 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 4.64/1.42 Prover 8: Preprocessing ...
% 4.64/1.43 Prover 4: Constructing countermodel ...
% 4.64/1.45 Prover 7: Preprocessing ...
% 4.64/1.45 Prover 10: Preprocessing ...
% 4.64/1.48 Prover 11: Preprocessing ...
% 5.68/1.52 Prover 7: Constructing countermodel ...
% 5.68/1.52 Prover 10: Constructing countermodel ...
% 5.68/1.53 Prover 8: Warning: ignoring some quantifiers
% 5.68/1.54 Prover 0: Proving ...
% 5.68/1.54 Prover 8: Constructing countermodel ...
% 5.68/1.54 Prover 0: stopped
% 5.68/1.55 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 5.68/1.59 Prover 13: Preprocessing ...
% 6.70/1.63 Prover 13: Constructing countermodel ...
% 6.70/1.68 Prover 7: Found proof (size 16)
% 6.70/1.68 Prover 7: proved (297ms)
% 6.70/1.68 Prover 4: stopped
% 6.70/1.68 Prover 1: stopped
% 6.70/1.68 Prover 8: stopped
% 6.70/1.68 Prover 10: Found proof (size 16)
% 6.70/1.68 Prover 10: proved (279ms)
% 6.70/1.68 Prover 13: stopped
% 7.30/1.71 Prover 11: Constructing countermodel ...
% 7.30/1.72 Prover 11: stopped
% 7.30/1.72
% 7.30/1.72 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 7.30/1.72
% 7.30/1.73 % SZS output start Proof for theBenchmark
% 7.30/1.73 Assumptions after simplification:
% 7.30/1.73 ---------------------------------
% 7.30/1.73
% 7.30/1.73 (mTCTrans)
% 7.30/1.74 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ $i(v3) | ~ $i(v2)
% 7.30/1.74 | ~ $i(v1) | ~ $i(v0) | ~ sdtmndtplgtdt0(v2, v1, v3) | ~
% 7.30/1.74 sdtmndtplgtdt0(v0, v1, v2) | ~ aRewritingSystem0(v1) | ~ aElement0(v3) |
% 7.30/1.74 ~ aElement0(v2) | ~ aElement0(v0) | sdtmndtplgtdt0(v0, v1, v3))
% 7.30/1.74
% 7.30/1.74 (m__)
% 7.30/1.74 $i(xz) & $i(xy) & $i(xR) & $i(xx) & ? [v0: $i] : ? [v1: $i] : ( ~ (xz = xx)
% 7.30/1.74 & $i(v1) & $i(v0) & sdtmndtasgtdt0(xy, xR, xz) & sdtmndtasgtdt0(xx, xR, xy)
% 7.30/1.74 & ~ sdtmndtasgtdt0(xx, xR, xz) & ~ sdtmndtplgtdt0(xx, xR, xz) & ~
% 7.30/1.74 aReductOfIn0(xz, xx, xR) & ! [v2: $i] : ( ~ $i(v2) | ~ sdtmndtplgtdt0(v2,
% 7.30/1.74 xR, xz) | ~ aReductOfIn0(v2, xx, xR) | ~ aElement0(v2)) & (xz = xy |
% 7.30/1.74 (sdtmndtplgtdt0(xy, xR, xz) & (aReductOfIn0(xz, xy, xR) |
% 7.30/1.74 (sdtmndtplgtdt0(v0, xR, xz) & aReductOfIn0(v0, xy, xR) &
% 7.30/1.74 aElement0(v0))))) & (xy = xx | (sdtmndtplgtdt0(xx, xR, xy) &
% 7.30/1.74 (aReductOfIn0(xy, xx, xR) | (sdtmndtplgtdt0(v1, xR, xy) &
% 7.30/1.74 aReductOfIn0(v1, xx, xR) & aElement0(v1))))))
% 7.30/1.74
% 7.30/1.74 (m__349)
% 7.30/1.74 $i(xz) & $i(xy) & $i(xR) & $i(xx) & aRewritingSystem0(xR) & aElement0(xz) &
% 7.30/1.74 aElement0(xy) & aElement0(xx)
% 7.30/1.74
% 7.30/1.74 Further assumptions not needed in the proof:
% 7.30/1.74 --------------------------------------------
% 7.30/1.74 mElmSort, mReduct, mRelSort, mTCDef, mTCRDef, mTCbr, mWFOrd
% 7.30/1.74
% 7.30/1.74 Those formulas are unsatisfiable:
% 7.30/1.74 ---------------------------------
% 7.30/1.74
% 7.30/1.74 Begin of proof
% 7.30/1.74 |
% 7.30/1.75 | ALPHA: (m__) implies:
% 7.30/1.75 | (1) ? [v0: $i] : ? [v1: $i] : ( ~ (xz = xx) & $i(v1) & $i(v0) &
% 7.30/1.75 | sdtmndtasgtdt0(xy, xR, xz) & sdtmndtasgtdt0(xx, xR, xy) & ~
% 7.30/1.75 | sdtmndtasgtdt0(xx, xR, xz) & ~ sdtmndtplgtdt0(xx, xR, xz) & ~
% 7.30/1.75 | aReductOfIn0(xz, xx, xR) & ! [v2: $i] : ( ~ $i(v2) | ~
% 7.30/1.75 | sdtmndtplgtdt0(v2, xR, xz) | ~ aReductOfIn0(v2, xx, xR) | ~
% 7.30/1.75 | aElement0(v2)) & (xz = xy | (sdtmndtplgtdt0(xy, xR, xz) &
% 7.30/1.75 | (aReductOfIn0(xz, xy, xR) | (sdtmndtplgtdt0(v0, xR, xz) &
% 7.30/1.75 | aReductOfIn0(v0, xy, xR) & aElement0(v0))))) & (xy = xx |
% 7.30/1.75 | (sdtmndtplgtdt0(xx, xR, xy) & (aReductOfIn0(xy, xx, xR) |
% 7.30/1.75 | (sdtmndtplgtdt0(v1, xR, xy) & aReductOfIn0(v1, xx, xR) &
% 7.30/1.75 | aElement0(v1))))))
% 7.30/1.75 |
% 7.30/1.75 | ALPHA: (m__349) implies:
% 7.30/1.75 | (2) aElement0(xx)
% 7.30/1.75 | (3) aElement0(xy)
% 7.30/1.75 | (4) aElement0(xz)
% 7.30/1.75 | (5) aRewritingSystem0(xR)
% 7.30/1.75 | (6) $i(xx)
% 7.30/1.75 | (7) $i(xR)
% 7.30/1.75 | (8) $i(xy)
% 7.30/1.75 | (9) $i(xz)
% 7.30/1.75 |
% 7.30/1.75 | DELTA: instantiating (1) with fresh symbols all_7_0, all_7_1 gives:
% 7.30/1.75 | (10) ~ (xz = xx) & $i(all_7_0) & $i(all_7_1) & sdtmndtasgtdt0(xy, xR, xz)
% 7.30/1.75 | & sdtmndtasgtdt0(xx, xR, xy) & ~ sdtmndtasgtdt0(xx, xR, xz) & ~
% 7.30/1.75 | sdtmndtplgtdt0(xx, xR, xz) & ~ aReductOfIn0(xz, xx, xR) & ! [v0: $i]
% 7.30/1.75 | : ( ~ $i(v0) | ~ sdtmndtplgtdt0(v0, xR, xz) | ~ aReductOfIn0(v0, xx,
% 7.30/1.75 | xR) | ~ aElement0(v0)) & (xz = xy | (sdtmndtplgtdt0(xy, xR, xz) &
% 7.30/1.75 | (aReductOfIn0(xz, xy, xR) | (sdtmndtplgtdt0(all_7_1, xR, xz) &
% 7.30/1.75 | aReductOfIn0(all_7_1, xy, xR) & aElement0(all_7_1))))) & (xy =
% 7.30/1.75 | xx | (sdtmndtplgtdt0(xx, xR, xy) & (aReductOfIn0(xy, xx, xR) |
% 7.30/1.75 | (sdtmndtplgtdt0(all_7_0, xR, xy) & aReductOfIn0(all_7_0, xx, xR)
% 7.30/1.75 | & aElement0(all_7_0)))))
% 7.30/1.76 |
% 7.30/1.76 | ALPHA: (10) implies:
% 7.30/1.76 | (11) ~ sdtmndtplgtdt0(xx, xR, xz)
% 7.30/1.76 | (12) ~ sdtmndtasgtdt0(xx, xR, xz)
% 7.30/1.76 | (13) sdtmndtasgtdt0(xx, xR, xy)
% 7.30/1.76 | (14) sdtmndtasgtdt0(xy, xR, xz)
% 7.30/1.76 | (15) xy = xx | (sdtmndtplgtdt0(xx, xR, xy) & (aReductOfIn0(xy, xx, xR) |
% 7.30/1.76 | (sdtmndtplgtdt0(all_7_0, xR, xy) & aReductOfIn0(all_7_0, xx, xR) &
% 7.30/1.76 | aElement0(all_7_0))))
% 7.30/1.76 | (16) xz = xy | (sdtmndtplgtdt0(xy, xR, xz) & (aReductOfIn0(xz, xy, xR) |
% 7.30/1.76 | (sdtmndtplgtdt0(all_7_1, xR, xz) & aReductOfIn0(all_7_1, xy, xR) &
% 7.30/1.76 | aElement0(all_7_1))))
% 7.30/1.76 |
% 7.30/1.76 | PRED_UNIFY: (12), (14) imply:
% 7.30/1.76 | (17) ~ (xy = xx)
% 7.30/1.76 |
% 7.30/1.76 | PRED_UNIFY: (12), (13) imply:
% 7.30/1.76 | (18) ~ (xz = xy)
% 7.30/1.76 |
% 7.30/1.76 | BETA: splitting (15) gives:
% 7.30/1.76 |
% 7.30/1.76 | Case 1:
% 7.30/1.76 | |
% 7.30/1.76 | | (19) xy = xx
% 7.30/1.76 | |
% 7.30/1.76 | | REDUCE: (17), (19) imply:
% 7.30/1.76 | | (20) $false
% 7.30/1.76 | |
% 7.30/1.76 | | CLOSE: (20) is inconsistent.
% 7.30/1.76 | |
% 7.30/1.76 | Case 2:
% 7.30/1.76 | |
% 7.30/1.76 | | (21) sdtmndtplgtdt0(xx, xR, xy) & (aReductOfIn0(xy, xx, xR) |
% 7.30/1.76 | | (sdtmndtplgtdt0(all_7_0, xR, xy) & aReductOfIn0(all_7_0, xx, xR) &
% 7.30/1.76 | | aElement0(all_7_0)))
% 7.30/1.76 | |
% 7.30/1.76 | | ALPHA: (21) implies:
% 7.30/1.76 | | (22) sdtmndtplgtdt0(xx, xR, xy)
% 7.30/1.76 | |
% 7.30/1.76 | | BETA: splitting (16) gives:
% 7.30/1.76 | |
% 7.30/1.76 | | Case 1:
% 7.30/1.76 | | |
% 7.30/1.76 | | | (23) xz = xy
% 7.30/1.76 | | |
% 7.30/1.76 | | | REDUCE: (18), (23) imply:
% 7.30/1.76 | | | (24) $false
% 7.30/1.76 | | |
% 7.30/1.76 | | | CLOSE: (24) is inconsistent.
% 7.30/1.76 | | |
% 7.30/1.76 | | Case 2:
% 7.30/1.76 | | |
% 7.30/1.76 | | | (25) sdtmndtplgtdt0(xy, xR, xz) & (aReductOfIn0(xz, xy, xR) |
% 7.30/1.76 | | | (sdtmndtplgtdt0(all_7_1, xR, xz) & aReductOfIn0(all_7_1, xy, xR)
% 7.30/1.76 | | | & aElement0(all_7_1)))
% 7.30/1.76 | | |
% 7.30/1.76 | | | ALPHA: (25) implies:
% 7.30/1.76 | | | (26) sdtmndtplgtdt0(xy, xR, xz)
% 7.30/1.76 | | |
% 7.30/1.77 | | | GROUND_INST: instantiating (mTCTrans) with xx, xR, xy, xz, simplifying
% 7.30/1.77 | | | with (2), (3), (4), (5), (6), (7), (8), (9), (11), (22), (26)
% 7.30/1.77 | | | gives:
% 7.30/1.77 | | | (27) $false
% 7.30/1.77 | | |
% 7.30/1.77 | | | CLOSE: (27) is inconsistent.
% 7.30/1.77 | | |
% 7.30/1.77 | | End of split
% 7.30/1.77 | |
% 7.30/1.77 | End of split
% 7.30/1.77 |
% 7.30/1.77 End of proof
% 7.30/1.77 % SZS output end Proof for theBenchmark
% 7.30/1.77
% 7.30/1.77 1163ms
%------------------------------------------------------------------------------