TSTP Solution File: NUM907_1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : NUM907_1 : TPTP v8.1.2. Bugfixed v5.4.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n012.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 : Thu Aug 31 11:50:39 EDT 2023
% Result : Theorem 9.20s 2.07s
% Output : Proof 13.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : NUM907_1 : TPTP v8.1.2. Bugfixed v5.4.0.
% 0.14/0.14 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.14/0.35 % Computer : n012.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Fri Aug 25 08:41:56 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.21/0.62 ________ _____
% 0.21/0.63 ___ __ \_________(_)________________________________
% 0.21/0.63 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.21/0.63 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.21/0.63 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.21/0.63
% 0.21/0.63 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.21/0.63 (2023-06-19)
% 0.21/0.63
% 0.21/0.63 (c) Philipp Rümmer, 2009-2023
% 0.21/0.63 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.21/0.63 Amanda Stjerna.
% 0.21/0.63 Free software under BSD-3-Clause.
% 0.21/0.63
% 0.21/0.63 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.21/0.63
% 0.21/0.63 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.21/0.64 Running up to 7 provers in parallel.
% 0.21/0.66 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.21/0.66 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.21/0.66 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.21/0.66 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.21/0.66 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.21/0.66 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.21/0.66 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 1.61/0.91 Prover 6: Warning: Problem contains rationals, using incomplete axiomatisation
% 1.61/0.91 Prover 3: Warning: Problem contains rationals, using incomplete axiomatisation
% 1.61/0.91 Prover 5: Warning: Problem contains rationals, using incomplete axiomatisation
% 1.61/0.91 Prover 1: Warning: Problem contains rationals, using incomplete axiomatisation
% 1.61/0.91 Prover 2: Warning: Problem contains rationals, using incomplete axiomatisation
% 1.61/0.91 Prover 0: Warning: Problem contains rationals, using incomplete axiomatisation
% 1.61/0.91 Prover 4: Warning: Problem contains rationals, using incomplete axiomatisation
% 2.28/1.01 Prover 1: Preprocessing ...
% 2.28/1.01 Prover 4: Preprocessing ...
% 2.46/1.05 Prover 5: Preprocessing ...
% 2.46/1.05 Prover 3: Preprocessing ...
% 2.46/1.05 Prover 0: Preprocessing ...
% 2.46/1.05 Prover 6: Preprocessing ...
% 2.46/1.05 Prover 2: Preprocessing ...
% 4.02/1.46 Prover 5: Proving ...
% 4.02/1.47 Prover 6: Constructing countermodel ...
% 4.96/1.47 Prover 3: Constructing countermodel ...
% 4.96/1.48 Prover 1: Constructing countermodel ...
% 4.96/1.50 Prover 2: Proving ...
% 5.65/1.56 Prover 4: Constructing countermodel ...
% 5.65/1.56 Prover 0: Proving ...
% 6.28/1.68 Prover 1: gave up
% 6.28/1.69 Prover 3: gave up
% 6.28/1.69 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 6.28/1.69 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 6.28/1.69 Prover 8: Warning: Problem contains rationals, using incomplete axiomatisation
% 6.98/1.69 Prover 7: Warning: Problem contains rationals, using incomplete axiomatisation
% 6.98/1.70 Prover 8: Preprocessing ...
% 6.98/1.70 Prover 7: Preprocessing ...
% 6.98/1.71 Prover 6: gave up
% 6.98/1.73 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889
% 6.98/1.73 Prover 9: Warning: Problem contains rationals, using incomplete axiomatisation
% 6.98/1.74 Prover 9: Preprocessing ...
% 7.82/1.81 Prover 8: Warning: ignoring some quantifiers
% 7.82/1.81 Prover 8: Constructing countermodel ...
% 7.82/1.83 Prover 7: Warning: ignoring some quantifiers
% 7.82/1.84 Prover 7: Constructing countermodel ...
% 8.53/1.90 Prover 9: Constructing countermodel ...
% 8.53/1.98 Prover 8: gave up
% 8.53/1.98 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 8.53/1.98 Prover 10: Warning: Problem contains rationals, using incomplete axiomatisation
% 9.20/1.99 Prover 10: Preprocessing ...
% 9.20/2.07 Prover 0: proved (1425ms)
% 9.20/2.07 Prover 5: proved (1417ms)
% 9.20/2.07
% 9.20/2.07 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 9.20/2.07
% 9.20/2.08
% 9.20/2.08 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 9.20/2.08
% 9.20/2.09 Prover 2: stopped
% 9.96/2.09 Prover 9: stopped
% 9.96/2.11 Prover 10: Warning: ignoring some quantifiers
% 9.96/2.11 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 9.96/2.11 Prover 11: Warning: Problem contains rationals, using incomplete axiomatisation
% 9.96/2.11 Prover 10: Constructing countermodel ...
% 9.96/2.11 Prover 11: Preprocessing ...
% 9.96/2.11 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 9.96/2.11 Prover 16: Warning: Problem contains rationals, using incomplete axiomatisation
% 9.96/2.11 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 9.96/2.11 Prover 13: Warning: Problem contains rationals, using incomplete axiomatisation
% 9.96/2.11 Prover 16: Preprocessing ...
% 9.96/2.11 Prover 13: Preprocessing ...
% 9.96/2.11 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085
% 9.96/2.11 Prover 19: Warning: Problem contains rationals, using incomplete axiomatisation
% 9.96/2.11 Prover 19: Preprocessing ...
% 9.96/2.14 Prover 10: gave up
% 9.96/2.21 Prover 16: Warning: ignoring some quantifiers
% 9.96/2.21 Prover 16: Constructing countermodel ...
% 9.96/2.21 Prover 11: Constructing countermodel ...
% 9.96/2.21 Prover 13: Warning: ignoring some quantifiers
% 9.96/2.22 Prover 13: Constructing countermodel ...
% 11.01/2.26 Prover 19: Warning: ignoring some quantifiers
% 11.01/2.27 Prover 19: Constructing countermodel ...
% 11.55/2.36 Prover 13: gave up
% 11.93/2.42 Prover 19: gave up
% 12.83/2.50 Prover 11: Found proof (size 59)
% 12.83/2.50 Prover 11: proved (420ms)
% 12.83/2.50 Prover 16: gave up
% 12.83/2.50 Prover 7: stopped
% 12.83/2.50 Prover 4: stopped
% 12.83/2.50
% 12.83/2.50 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 12.83/2.50
% 12.83/2.50 % SZS output start Proof for theBenchmark
% 12.83/2.51 Assumptions after simplification:
% 12.83/2.51 ---------------------------------
% 12.83/2.51
% 12.83/2.51 (rat_combined_problem_2)
% 13.13/2.53 ? [v0: $rat] : ? [v1: $rat] : ? [v2: $rat] : ? [v3: $rat] : ? [v4: $rat]
% 13.13/2.53 : ? [v5: $rat] : (rat_$sum(v0, v1) = v3 & ((v5 = v1 & v4 = v0 & ~ (v3 = v2)
% 13.13/2.53 & rat_$difference(v2, v1) = v0 & rat_$difference(v2, v0) = v1) | (v3 =
% 13.13/2.53 v2 & (( ~ (v5 = v1) & rat_$difference(v2, v0) = v5) | ( ~ (v4 = v0) &
% 13.13/2.53 rat_$difference(v2, v1) = v4)))))
% 13.13/2.53
% 13.13/2.53 (input)
% 13.21/2.55 ~ (rat_very_large = rat_very_small) & ~ (rat_very_large = rat_0) & ~
% 13.21/2.55 (rat_very_small = rat_0) & rat_$is_int(rat_0) = 0 & rat_$is_rat(rat_0) = 0 &
% 13.21/2.55 rat_$floor(rat_0) = rat_0 & rat_$ceiling(rat_0) = rat_0 & rat_$truncate(rat_0)
% 13.21/2.55 = rat_0 & rat_$round(rat_0) = rat_0 & rat_$to_int(rat_0) = 0 &
% 13.21/2.55 rat_$to_rat(rat_0) = rat_0 & rat_$to_real(rat_0) = real_0 & int_$to_rat(0) =
% 13.21/2.55 rat_0 & rat_$product(rat_0, rat_0) = rat_0 & rat_$uminus(rat_0) = rat_0 &
% 13.21/2.55 rat_$greatereq(rat_very_small, rat_very_large) = 1 & rat_$greatereq(rat_0,
% 13.21/2.55 rat_0) = 0 & rat_$lesseq(rat_very_small, rat_very_large) = 0 &
% 13.21/2.55 rat_$lesseq(rat_0, rat_0) = 0 & rat_$greater(rat_very_large, rat_0) = 0 &
% 13.21/2.55 rat_$greater(rat_very_small, rat_very_large) = 1 & rat_$greater(rat_0,
% 13.21/2.55 rat_very_small) = 0 & rat_$greater(rat_0, rat_0) = 1 &
% 13.21/2.55 rat_$less(rat_very_small, rat_very_large) = 0 & rat_$less(rat_very_small,
% 13.21/2.55 rat_0) = 0 & rat_$less(rat_0, rat_very_large) = 0 & rat_$less(rat_0, rat_0)
% 13.21/2.55 = 1 & rat_$sum(rat_0, rat_0) = rat_0 & rat_$difference(rat_0, rat_0) = rat_0 &
% 13.21/2.55 ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : ! [v3: $rat] : ! [v4: $rat]
% 13.21/2.55 : ( ~ (rat_$sum(v3, v0) = v4) | ~ (rat_$sum(v2, v1) = v3) | ? [v5: $rat] :
% 13.21/2.55 (rat_$sum(v2, v5) = v4 & rat_$sum(v1, v0) = v5)) & ! [v0: $rat] : ! [v1:
% 13.21/2.55 $rat] : ! [v2: $rat] : ! [v3: $rat] : ! [v4: $rat] : ( ~ (rat_$sum(v2,
% 13.21/2.55 v3) = v4) | ~ (rat_$sum(v1, v0) = v3) | ? [v5: $rat] : (rat_$sum(v5,
% 13.21/2.55 v0) = v4 & rat_$sum(v2, v1) = v5)) & ! [v0: $rat] : ! [v1: $rat] : !
% 13.21/2.55 [v2: $rat] : ! [v3: int] : (v3 = 0 | ~ (rat_$lesseq(v2, v1) = 0) | ~
% 13.21/2.55 (rat_$lesseq(v2, v0) = v3) | ? [v4: int] : ( ~ (v4 = 0) & rat_$lesseq(v1,
% 13.21/2.55 v0) = v4)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : ! [v3:
% 13.21/2.55 int] : (v3 = 0 | ~ (rat_$lesseq(v2, v1) = 0) | ~ (rat_$less(v2, v0) = v3)
% 13.21/2.55 | ? [v4: int] : ( ~ (v4 = 0) & rat_$less(v1, v0) = v4)) & ! [v0: $rat] :
% 13.21/2.55 ! [v1: $rat] : ! [v2: $rat] : ! [v3: int] : (v3 = 0 | ~ (rat_$lesseq(v2,
% 13.21/2.55 v0) = v3) | ~ (rat_$lesseq(v1, v0) = 0) | ? [v4: int] : ( ~ (v4 = 0) &
% 13.21/2.55 rat_$lesseq(v2, v1) = v4)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat]
% 13.21/2.55 : ! [v3: int] : (v3 = 0 | ~ (rat_$lesseq(v1, v0) = 0) | ~ (rat_$less(v2,
% 13.21/2.55 v0) = v3) | ? [v4: int] : ( ~ (v4 = 0) & rat_$less(v2, v1) = v4)) & !
% 13.21/2.55 [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : ! [v3: int] : (v3 = 0 | ~
% 13.21/2.55 (rat_$less(v2, v1) = 0) | ~ (rat_$less(v2, v0) = v3) | ? [v4: int] : ( ~
% 13.21/2.55 (v4 = 0) & rat_$lesseq(v1, v0) = v4)) & ! [v0: $rat] : ! [v1: $rat] : !
% 13.21/2.55 [v2: $rat] : ! [v3: int] : (v3 = 0 | ~ (rat_$less(v2, v0) = v3) | ~
% 13.21/2.55 (rat_$less(v1, v0) = 0) | ? [v4: int] : ( ~ (v4 = 0) & rat_$lesseq(v2, v1)
% 13.21/2.55 = v4)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : ! [v3: $rat] : (
% 13.21/2.55 ~ (rat_$uminus(v0) = v2) | ~ (rat_$sum(v1, v2) = v3) | rat_$difference(v1,
% 13.21/2.55 v0) = v3) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: int] : (v2 = 0 | v1 =
% 13.21/2.55 v0 | ~ (rat_$less(v1, v0) = v2) | ? [v3: int] : ( ~ (v3 = 0) &
% 13.21/2.55 rat_$lesseq(v1, v0) = v3)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: int]
% 13.21/2.55 : (v2 = 0 | ~ (rat_$greatereq(v0, v1) = v2) | ? [v3: int] : ( ~ (v3 = 0) &
% 13.21/2.55 rat_$lesseq(v1, v0) = v3)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: int]
% 13.21/2.55 : (v2 = 0 | ~ (rat_$lesseq(v1, v0) = v2) | ? [v3: int] : ( ~ (v3 = 0) &
% 13.21/2.55 rat_$greatereq(v0, v1) = v3)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2:
% 13.21/2.55 int] : (v2 = 0 | ~ (rat_$lesseq(v1, v0) = v2) | ? [v3: int] : ( ~ (v3 = 0)
% 13.21/2.55 & rat_$less(v1, v0) = v3)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: int]
% 13.21/2.55 : (v2 = 0 | ~ (rat_$greater(v0, v1) = v2) | ? [v3: int] : ( ~ (v3 = 0) &
% 13.21/2.55 rat_$less(v1, v0) = v3)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: int] :
% 13.21/2.55 (v2 = 0 | ~ (rat_$less(v1, v0) = v2) | ? [v3: int] : ( ~ (v3 = 0) &
% 13.21/2.55 rat_$greater(v0, v1) = v3)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2:
% 13.21/2.55 $rat] : (v0 = rat_0 | ~ (rat_$product(v1, v0) = v2) | rat_$quotient(v2, v0)
% 13.21/2.55 = v1) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : ( ~
% 13.21/2.55 (rat_$product(v1, v0) = v2) | rat_$product(v0, v1) = v2) & ! [v0: $rat] :
% 13.21/2.55 ! [v1: $rat] : ! [v2: $rat] : ( ~ (rat_$product(v0, v1) = v2) |
% 13.21/2.55 rat_$product(v1, v0) = v2) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] :
% 13.21/2.55 ( ~ (rat_$lesseq(v2, v1) = 0) | ~ (rat_$lesseq(v1, v0) = 0) | rat_$lesseq(v2,
% 13.21/2.55 v0) = 0) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : ( ~
% 13.21/2.55 (rat_$lesseq(v2, v1) = 0) | ~ (rat_$less(v1, v0) = 0) | rat_$less(v2, v0) =
% 13.21/2.55 0) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : ( ~ (rat_$lesseq(v1,
% 13.21/2.55 v0) = 0) | ~ (rat_$less(v2, v1) = 0) | rat_$less(v2, v0) = 0) & ! [v0:
% 13.21/2.55 $rat] : ! [v1: $rat] : ! [v2: $rat] : ( ~ (rat_$sum(v1, v0) = v2) |
% 13.21/2.55 rat_$sum(v0, v1) = v2) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : ( ~
% 13.21/2.55 (rat_$sum(v0, v1) = v2) | rat_$sum(v1, v0) = v2) & ! [v0: $rat] : ! [v1:
% 13.21/2.55 $rat] : ! [v2: $rat] : ( ~ (rat_$difference(v1, v0) = v2) | ? [v3: $rat] :
% 13.21/2.55 (rat_$uminus(v0) = v3 & rat_$sum(v1, v3) = v2)) & ! [v0: $rat] : ! [v1:
% 13.21/2.55 $rat] : (v1 = v0 | ~ (rat_$lesseq(v1, v0) = 0) | rat_$less(v1, v0) = 0) &
% 13.21/2.55 ! [v0: $rat] : ! [v1: $rat] : (v1 = v0 | ~ (rat_$sum(v0, rat_0) = v1)) & !
% 13.21/2.55 [v0: $rat] : ! [v1: int] : (v1 = 0 | ~ (rat_$lesseq(v0, v0) = v1)) & ! [v0:
% 13.21/2.55 $rat] : ! [v1: $rat] : ( ~ (rat_$uminus(v0) = v1) | rat_$uminus(v1) = v0) &
% 13.21/2.55 ! [v0: $rat] : ! [v1: $rat] : ( ~ (rat_$uminus(v0) = v1) | rat_$sum(v0, v1)
% 13.21/2.55 = rat_0) & ! [v0: $rat] : ! [v1: $rat] : ( ~ (rat_$greatereq(v0, v1) = 0)
% 13.21/2.55 | rat_$lesseq(v1, v0) = 0) & ! [v0: $rat] : ! [v1: $rat] : ( ~
% 13.21/2.55 (rat_$lesseq(v1, v0) = 0) | rat_$greatereq(v0, v1) = 0) & ! [v0: $rat] : !
% 13.21/2.56 [v1: $rat] : ( ~ (rat_$greater(v0, v1) = 0) | rat_$less(v1, v0) = 0) & ! [v0:
% 13.21/2.56 $rat] : ! [v1: $rat] : ( ~ (rat_$less(v1, v0) = 0) | rat_$lesseq(v1, v0) =
% 13.21/2.56 0) & ! [v0: $rat] : ! [v1: $rat] : ( ~ (rat_$less(v1, v0) = 0) |
% 13.21/2.56 rat_$greater(v0, v1) = 0) & ! [v0: $rat] : ! [v1: MultipleValueBool] : ( ~
% 13.21/2.56 (rat_$less(v0, v0) = v1) | rat_$lesseq(v0, v0) = 0) & ! [v0: $rat] : (v0 =
% 13.21/2.56 rat_0 | ~ (rat_$uminus(v0) = v0))
% 13.21/2.56
% 13.21/2.56 (function-axioms)
% 13.21/2.56 ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : ! [v3: $rat] : (v1 = v0 | ~
% 13.21/2.56 (rat_$quotient(v3, v2) = v1) | ~ (rat_$quotient(v3, v2) = v0)) & ! [v0:
% 13.21/2.56 $rat] : ! [v1: $rat] : ! [v2: $rat] : ! [v3: $rat] : (v1 = v0 | ~
% 13.21/2.56 (rat_$product(v3, v2) = v1) | ~ (rat_$product(v3, v2) = v0)) & ! [v0:
% 13.21/2.56 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $rat] : ! [v3:
% 13.21/2.56 $rat] : (v1 = v0 | ~ (rat_$greatereq(v3, v2) = v1) | ~ (rat_$greatereq(v3,
% 13.21/2.56 v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] :
% 13.21/2.56 ! [v2: $rat] : ! [v3: $rat] : (v1 = v0 | ~ (rat_$lesseq(v3, v2) = v1) | ~
% 13.21/2.56 (rat_$lesseq(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 13.21/2.56 MultipleValueBool] : ! [v2: $rat] : ! [v3: $rat] : (v1 = v0 | ~
% 13.21/2.56 (rat_$greater(v3, v2) = v1) | ~ (rat_$greater(v3, v2) = v0)) & ! [v0:
% 13.21/2.56 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $rat] : ! [v3:
% 13.21/2.56 $rat] : (v1 = v0 | ~ (rat_$less(v3, v2) = v1) | ~ (rat_$less(v3, v2) =
% 13.21/2.56 v0)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : ! [v3: $rat] : (v1
% 13.21/2.56 = v0 | ~ (rat_$sum(v3, v2) = v1) | ~ (rat_$sum(v3, v2) = v0)) & ! [v0:
% 13.21/2.56 $rat] : ! [v1: $rat] : ! [v2: $rat] : ! [v3: $rat] : (v1 = v0 | ~
% 13.21/2.56 (rat_$difference(v3, v2) = v1) | ~ (rat_$difference(v3, v2) = v0)) & !
% 13.21/2.56 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $rat] : (v1 =
% 13.21/2.56 v0 | ~ (rat_$is_int(v2) = v1) | ~ (rat_$is_int(v2) = v0)) & ! [v0:
% 13.21/2.56 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $rat] : (v1 = v0 |
% 13.21/2.56 ~ (rat_$is_rat(v2) = v1) | ~ (rat_$is_rat(v2) = v0)) & ! [v0: $rat] : !
% 13.21/2.56 [v1: $rat] : ! [v2: $rat] : (v1 = v0 | ~ (rat_$floor(v2) = v1) | ~
% 13.21/2.56 (rat_$floor(v2) = v0)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : (v1
% 13.21/2.56 = v0 | ~ (rat_$ceiling(v2) = v1) | ~ (rat_$ceiling(v2) = v0)) & ! [v0:
% 13.21/2.56 $rat] : ! [v1: $rat] : ! [v2: $rat] : (v1 = v0 | ~ (rat_$truncate(v2) =
% 13.21/2.56 v1) | ~ (rat_$truncate(v2) = v0)) & ! [v0: $rat] : ! [v1: $rat] : !
% 13.21/2.56 [v2: $rat] : (v1 = v0 | ~ (rat_$round(v2) = v1) | ~ (rat_$round(v2) = v0)) &
% 13.21/2.56 ! [v0: int] : ! [v1: int] : ! [v2: $rat] : (v1 = v0 | ~ (rat_$to_int(v2) =
% 13.21/2.56 v1) | ~ (rat_$to_int(v2) = v0)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2:
% 13.21/2.56 $rat] : (v1 = v0 | ~ (rat_$to_rat(v2) = v1) | ~ (rat_$to_rat(v2) = v0)) &
% 13.21/2.56 ! [v0: $real] : ! [v1: $real] : ! [v2: $rat] : (v1 = v0 | ~
% 13.21/2.56 (rat_$to_real(v2) = v1) | ~ (rat_$to_real(v2) = v0)) & ! [v0: $rat] : !
% 13.21/2.56 [v1: $rat] : ! [v2: int] : (v1 = v0 | ~ (int_$to_rat(v2) = v1) | ~
% 13.21/2.56 (int_$to_rat(v2) = v0)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] :
% 13.21/2.56 (v1 = v0 | ~ (rat_$uminus(v2) = v1) | ~ (rat_$uminus(v2) = v0))
% 13.21/2.56
% 13.21/2.56 Those formulas are unsatisfiable:
% 13.21/2.56 ---------------------------------
% 13.21/2.56
% 13.21/2.56 Begin of proof
% 13.21/2.56 |
% 13.21/2.56 | ALPHA: (function-axioms) implies:
% 13.21/2.57 | (1) ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : ! [v3: $rat] : (v1 =
% 13.21/2.57 | v0 | ~ (rat_$sum(v3, v2) = v1) | ~ (rat_$sum(v3, v2) = v0))
% 13.21/2.57 |
% 13.21/2.57 | ALPHA: (input) implies:
% 13.21/2.57 | (2) ! [v0: $rat] : ! [v1: $rat] : ( ~ (rat_$uminus(v0) = v1) |
% 13.21/2.57 | rat_$sum(v0, v1) = rat_0)
% 13.21/2.57 | (3) ! [v0: $rat] : ! [v1: $rat] : (v1 = v0 | ~ (rat_$sum(v0, rat_0) =
% 13.21/2.57 | v1))
% 13.21/2.57 | (4) ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : ( ~
% 13.21/2.57 | (rat_$difference(v1, v0) = v2) | ? [v3: $rat] : (rat_$uminus(v0) =
% 13.21/2.57 | v3 & rat_$sum(v1, v3) = v2))
% 13.21/2.57 | (5) ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : ( ~ (rat_$sum(v1, v0) =
% 13.21/2.57 | v2) | rat_$sum(v0, v1) = v2)
% 13.21/2.57 | (6) ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : ! [v3: $rat] : ! [v4:
% 13.21/2.57 | $rat] : ( ~ (rat_$sum(v2, v3) = v4) | ~ (rat_$sum(v1, v0) = v3) | ?
% 13.21/2.57 | [v5: $rat] : (rat_$sum(v5, v0) = v4 & rat_$sum(v2, v1) = v5))
% 13.21/2.57 | (7) ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : ! [v3: $rat] : ! [v4:
% 13.21/2.57 | $rat] : ( ~ (rat_$sum(v3, v0) = v4) | ~ (rat_$sum(v2, v1) = v3) | ?
% 13.21/2.57 | [v5: $rat] : (rat_$sum(v2, v5) = v4 & rat_$sum(v1, v0) = v5))
% 13.21/2.57 |
% 13.21/2.57 | DELTA: instantiating (rat_combined_problem_2) with fresh symbols all_5_0,
% 13.21/2.57 | all_5_1, all_5_2, all_5_3, all_5_4, all_5_5 gives:
% 13.21/2.57 | (8) rat_$sum(all_5_5, all_5_4) = all_5_2 & ((all_5_0 = all_5_4 & all_5_1 =
% 13.21/2.57 | all_5_5 & ~ (all_5_2 = all_5_3) & rat_$difference(all_5_3,
% 13.21/2.57 | all_5_4) = all_5_5 & rat_$difference(all_5_3, all_5_5) = all_5_4)
% 13.21/2.57 | | (all_5_2 = all_5_3 & (( ~ (all_5_0 = all_5_4) &
% 13.21/2.57 | rat_$difference(all_5_3, all_5_5) = all_5_0) | ( ~ (all_5_1 =
% 13.21/2.57 | all_5_5) & rat_$difference(all_5_3, all_5_4) = all_5_1))))
% 13.21/2.57 |
% 13.21/2.57 | ALPHA: (8) implies:
% 13.21/2.57 | (9) rat_$sum(all_5_5, all_5_4) = all_5_2
% 13.21/2.57 | (10) (all_5_0 = all_5_4 & all_5_1 = all_5_5 & ~ (all_5_2 = all_5_3) &
% 13.21/2.57 | rat_$difference(all_5_3, all_5_4) = all_5_5 &
% 13.21/2.57 | rat_$difference(all_5_3, all_5_5) = all_5_4) | (all_5_2 = all_5_3 &
% 13.21/2.57 | (( ~ (all_5_0 = all_5_4) & rat_$difference(all_5_3, all_5_5) =
% 13.21/2.57 | all_5_0) | ( ~ (all_5_1 = all_5_5) & rat_$difference(all_5_3,
% 13.21/2.57 | all_5_4) = all_5_1)))
% 13.21/2.57 |
% 13.21/2.57 | GROUND_INST: instantiating (5) with all_5_4, all_5_5, all_5_2, simplifying
% 13.21/2.57 | with (9) gives:
% 13.21/2.57 | (11) rat_$sum(all_5_4, all_5_5) = all_5_2
% 13.21/2.57 |
% 13.21/2.57 | BETA: splitting (10) gives:
% 13.21/2.57 |
% 13.21/2.57 | Case 1:
% 13.21/2.57 | |
% 13.21/2.58 | | (12) all_5_0 = all_5_4 & all_5_1 = all_5_5 & ~ (all_5_2 = all_5_3) &
% 13.21/2.58 | | rat_$difference(all_5_3, all_5_4) = all_5_5 &
% 13.21/2.58 | | rat_$difference(all_5_3, all_5_5) = all_5_4
% 13.21/2.58 | |
% 13.21/2.58 | | ALPHA: (12) implies:
% 13.21/2.58 | | (13) ~ (all_5_2 = all_5_3)
% 13.21/2.58 | | (14) rat_$difference(all_5_3, all_5_4) = all_5_5
% 13.21/2.58 | |
% 13.21/2.58 | | GROUND_INST: instantiating (4) with all_5_4, all_5_3, all_5_5, simplifying
% 13.21/2.58 | | with (14) gives:
% 13.21/2.58 | | (15) ? [v0: $rat] : (rat_$uminus(all_5_4) = v0 & rat_$sum(all_5_3, v0) =
% 13.21/2.58 | | all_5_5)
% 13.21/2.58 | |
% 13.21/2.58 | | DELTA: instantiating (15) with fresh symbol all_65_0 gives:
% 13.21/2.58 | | (16) rat_$uminus(all_5_4) = all_65_0 & rat_$sum(all_5_3, all_65_0) =
% 13.21/2.58 | | all_5_5
% 13.21/2.58 | |
% 13.21/2.58 | | ALPHA: (16) implies:
% 13.21/2.58 | | (17) rat_$sum(all_5_3, all_65_0) = all_5_5
% 13.21/2.58 | | (18) rat_$uminus(all_5_4) = all_65_0
% 13.21/2.58 | |
% 13.21/2.58 | | GROUND_INST: instantiating (7) with all_5_4, all_65_0, all_5_3, all_5_5,
% 13.21/2.58 | | all_5_2, simplifying with (9), (17) gives:
% 13.21/2.58 | | (19) ? [v0: $rat] : (rat_$sum(all_65_0, all_5_4) = v0 &
% 13.21/2.58 | | rat_$sum(all_5_3, v0) = all_5_2)
% 13.21/2.58 | |
% 13.21/2.58 | | GROUND_INST: instantiating (5) with all_65_0, all_5_3, all_5_5, simplifying
% 13.21/2.58 | | with (17) gives:
% 13.21/2.58 | | (20) rat_$sum(all_65_0, all_5_3) = all_5_5
% 13.21/2.58 | |
% 13.21/2.58 | | GROUND_INST: instantiating (2) with all_5_4, all_65_0, simplifying with (18)
% 13.21/2.58 | | gives:
% 13.21/2.58 | | (21) rat_$sum(all_5_4, all_65_0) = rat_0
% 13.21/2.58 | |
% 13.21/2.58 | | DELTA: instantiating (19) with fresh symbol all_77_0 gives:
% 13.21/2.58 | | (22) rat_$sum(all_65_0, all_5_4) = all_77_0 & rat_$sum(all_5_3, all_77_0)
% 13.21/2.58 | | = all_5_2
% 13.21/2.58 | |
% 13.21/2.58 | | ALPHA: (22) implies:
% 13.21/2.58 | | (23) rat_$sum(all_5_3, all_77_0) = all_5_2
% 13.21/2.58 | | (24) rat_$sum(all_65_0, all_5_4) = all_77_0
% 13.21/2.58 | |
% 13.21/2.58 | | GROUND_INST: instantiating (5) with all_5_4, all_65_0, all_77_0, simplifying
% 13.21/2.58 | | with (24) gives:
% 13.21/2.58 | | (25) rat_$sum(all_5_4, all_65_0) = all_77_0
% 13.21/2.58 | |
% 13.21/2.58 | | GROUND_INST: instantiating (6) with all_5_3, all_65_0, all_5_4, all_5_5,
% 13.21/2.58 | | all_5_2, simplifying with (11), (20) gives:
% 13.21/2.58 | | (26) ? [v0: $rat] : (rat_$sum(v0, all_5_3) = all_5_2 & rat_$sum(all_5_4,
% 13.21/2.58 | | all_65_0) = v0)
% 13.21/2.58 | |
% 13.21/2.58 | | DELTA: instantiating (26) with fresh symbol all_105_0 gives:
% 13.21/2.58 | | (27) rat_$sum(all_105_0, all_5_3) = all_5_2 & rat_$sum(all_5_4, all_65_0)
% 13.21/2.58 | | = all_105_0
% 13.21/2.58 | |
% 13.21/2.58 | | ALPHA: (27) implies:
% 13.21/2.58 | | (28) rat_$sum(all_5_4, all_65_0) = all_105_0
% 13.21/2.58 | |
% 13.21/2.58 | | GROUND_INST: instantiating (1) with rat_0, all_105_0, all_65_0, all_5_4,
% 13.21/2.58 | | simplifying with (21), (28) gives:
% 13.21/2.58 | | (29) all_105_0 = rat_0
% 13.21/2.58 | |
% 13.21/2.58 | | GROUND_INST: instantiating (1) with all_77_0, all_105_0, all_65_0, all_5_4,
% 13.21/2.58 | | simplifying with (25), (28) gives:
% 13.21/2.58 | | (30) all_105_0 = all_77_0
% 13.21/2.58 | |
% 13.21/2.58 | | COMBINE_EQS: (29), (30) imply:
% 13.21/2.58 | | (31) all_77_0 = rat_0
% 13.21/2.58 | |
% 13.21/2.58 | | REDUCE: (23), (31) imply:
% 13.21/2.58 | | (32) rat_$sum(all_5_3, rat_0) = all_5_2
% 13.21/2.58 | |
% 13.21/2.58 | | GROUND_INST: instantiating (3) with all_5_3, all_5_2, simplifying with (32)
% 13.21/2.58 | | gives:
% 13.21/2.58 | | (33) all_5_2 = all_5_3
% 13.21/2.58 | |
% 13.21/2.58 | | REDUCE: (13), (33) imply:
% 13.21/2.58 | | (34) $false
% 13.21/2.58 | |
% 13.21/2.58 | | CLOSE: (34) is inconsistent.
% 13.21/2.58 | |
% 13.21/2.59 | Case 2:
% 13.21/2.59 | |
% 13.21/2.59 | | (35) all_5_2 = all_5_3 & (( ~ (all_5_0 = all_5_4) &
% 13.21/2.59 | | rat_$difference(all_5_3, all_5_5) = all_5_0) | ( ~ (all_5_1 =
% 13.21/2.59 | | all_5_5) & rat_$difference(all_5_3, all_5_4) = all_5_1))
% 13.21/2.59 | |
% 13.21/2.59 | | ALPHA: (35) implies:
% 13.21/2.59 | | (36) all_5_2 = all_5_3
% 13.21/2.59 | | (37) ( ~ (all_5_0 = all_5_4) & rat_$difference(all_5_3, all_5_5) =
% 13.21/2.59 | | all_5_0) | ( ~ (all_5_1 = all_5_5) & rat_$difference(all_5_3,
% 13.21/2.59 | | all_5_4) = all_5_1)
% 13.21/2.59 | |
% 13.21/2.59 | | REDUCE: (11), (36) imply:
% 13.21/2.59 | | (38) rat_$sum(all_5_4, all_5_5) = all_5_3
% 13.21/2.59 | |
% 13.21/2.59 | | REDUCE: (9), (36) imply:
% 13.21/2.59 | | (39) rat_$sum(all_5_5, all_5_4) = all_5_3
% 13.21/2.59 | |
% 13.21/2.59 | | BETA: splitting (37) gives:
% 13.21/2.59 | |
% 13.21/2.59 | | Case 1:
% 13.21/2.59 | | |
% 13.21/2.59 | | | (40) ~ (all_5_0 = all_5_4) & rat_$difference(all_5_3, all_5_5) =
% 13.21/2.59 | | | all_5_0
% 13.21/2.59 | | |
% 13.21/2.59 | | | ALPHA: (40) implies:
% 13.21/2.59 | | | (41) ~ (all_5_0 = all_5_4)
% 13.21/2.59 | | | (42) rat_$difference(all_5_3, all_5_5) = all_5_0
% 13.21/2.59 | | |
% 13.21/2.59 | | | GROUND_INST: instantiating (4) with all_5_5, all_5_3, all_5_0, simplifying
% 13.21/2.59 | | | with (42) gives:
% 13.21/2.59 | | | (43) ? [v0: $rat] : (rat_$uminus(all_5_5) = v0 & rat_$sum(all_5_3, v0)
% 13.21/2.59 | | | = all_5_0)
% 13.21/2.59 | | |
% 13.21/2.59 | | | DELTA: instantiating (43) with fresh symbol all_72_0 gives:
% 13.21/2.59 | | | (44) rat_$uminus(all_5_5) = all_72_0 & rat_$sum(all_5_3, all_72_0) =
% 13.21/2.59 | | | all_5_0
% 13.21/2.59 | | |
% 13.21/2.59 | | | ALPHA: (44) implies:
% 13.21/2.59 | | | (45) rat_$sum(all_5_3, all_72_0) = all_5_0
% 13.21/2.59 | | | (46) rat_$uminus(all_5_5) = all_72_0
% 13.21/2.59 | | |
% 13.21/2.59 | | | GROUND_INST: instantiating (7) with all_72_0, all_5_5, all_5_4, all_5_3,
% 13.21/2.59 | | | all_5_0, simplifying with (38), (45) gives:
% 13.21/2.59 | | | (47) ? [v0: $rat] : (rat_$sum(all_5_4, v0) = all_5_0 &
% 13.21/2.59 | | | rat_$sum(all_5_5, all_72_0) = v0)
% 13.21/2.59 | | |
% 13.21/2.59 | | | GROUND_INST: instantiating (2) with all_5_5, all_72_0, simplifying with
% 13.21/2.59 | | | (46) gives:
% 13.21/2.59 | | | (48) rat_$sum(all_5_5, all_72_0) = rat_0
% 13.21/2.59 | | |
% 13.21/2.59 | | | DELTA: instantiating (47) with fresh symbol all_82_0 gives:
% 13.21/2.59 | | | (49) rat_$sum(all_5_4, all_82_0) = all_5_0 & rat_$sum(all_5_5,
% 13.21/2.59 | | | all_72_0) = all_82_0
% 13.21/2.59 | | |
% 13.21/2.59 | | | ALPHA: (49) implies:
% 13.21/2.59 | | | (50) rat_$sum(all_5_5, all_72_0) = all_82_0
% 13.21/2.59 | | | (51) rat_$sum(all_5_4, all_82_0) = all_5_0
% 13.21/2.59 | | |
% 13.21/2.59 | | | GROUND_INST: instantiating (1) with rat_0, all_82_0, all_72_0, all_5_5,
% 13.21/2.59 | | | simplifying with (48), (50) gives:
% 13.21/2.59 | | | (52) all_82_0 = rat_0
% 13.21/2.59 | | |
% 13.21/2.59 | | | REDUCE: (51), (52) imply:
% 13.21/2.59 | | | (53) rat_$sum(all_5_4, rat_0) = all_5_0
% 13.21/2.59 | | |
% 13.21/2.59 | | | GROUND_INST: instantiating (3) with all_5_4, all_5_0, simplifying with
% 13.21/2.59 | | | (53) gives:
% 13.21/2.59 | | | (54) all_5_0 = all_5_4
% 13.21/2.59 | | |
% 13.21/2.59 | | | REDUCE: (41), (54) imply:
% 13.21/2.59 | | | (55) $false
% 13.21/2.59 | | |
% 13.21/2.59 | | | CLOSE: (55) is inconsistent.
% 13.21/2.59 | | |
% 13.21/2.59 | | Case 2:
% 13.21/2.59 | | |
% 13.21/2.59 | | | (56) ~ (all_5_1 = all_5_5) & rat_$difference(all_5_3, all_5_4) =
% 13.21/2.59 | | | all_5_1
% 13.21/2.59 | | |
% 13.21/2.59 | | | ALPHA: (56) implies:
% 13.21/2.59 | | | (57) ~ (all_5_1 = all_5_5)
% 13.21/2.59 | | | (58) rat_$difference(all_5_3, all_5_4) = all_5_1
% 13.21/2.59 | | |
% 13.21/2.59 | | | GROUND_INST: instantiating (4) with all_5_4, all_5_3, all_5_1, simplifying
% 13.21/2.59 | | | with (58) gives:
% 13.21/2.60 | | | (59) ? [v0: $rat] : (rat_$uminus(all_5_4) = v0 & rat_$sum(all_5_3, v0)
% 13.21/2.60 | | | = all_5_1)
% 13.21/2.60 | | |
% 13.21/2.60 | | | DELTA: instantiating (59) with fresh symbol all_72_0 gives:
% 13.21/2.60 | | | (60) rat_$uminus(all_5_4) = all_72_0 & rat_$sum(all_5_3, all_72_0) =
% 13.21/2.60 | | | all_5_1
% 13.21/2.60 | | |
% 13.21/2.60 | | | ALPHA: (60) implies:
% 13.21/2.60 | | | (61) rat_$sum(all_5_3, all_72_0) = all_5_1
% 13.21/2.60 | | | (62) rat_$uminus(all_5_4) = all_72_0
% 13.21/2.60 | | |
% 13.21/2.60 | | | GROUND_INST: instantiating (7) with all_72_0, all_5_4, all_5_5, all_5_3,
% 13.21/2.60 | | | all_5_1, simplifying with (39), (61) gives:
% 13.21/2.60 | | | (63) ? [v0: $rat] : (rat_$sum(all_5_4, all_72_0) = v0 &
% 13.21/2.60 | | | rat_$sum(all_5_5, v0) = all_5_1)
% 13.21/2.60 | | |
% 13.21/2.60 | | | GROUND_INST: instantiating (2) with all_5_4, all_72_0, simplifying with
% 13.21/2.60 | | | (62) gives:
% 13.21/2.60 | | | (64) rat_$sum(all_5_4, all_72_0) = rat_0
% 13.21/2.60 | | |
% 13.21/2.60 | | | DELTA: instantiating (63) with fresh symbol all_80_0 gives:
% 13.21/2.60 | | | (65) rat_$sum(all_5_4, all_72_0) = all_80_0 & rat_$sum(all_5_5,
% 13.21/2.60 | | | all_80_0) = all_5_1
% 13.21/2.60 | | |
% 13.21/2.60 | | | ALPHA: (65) implies:
% 13.21/2.60 | | | (66) rat_$sum(all_5_5, all_80_0) = all_5_1
% 13.21/2.60 | | | (67) rat_$sum(all_5_4, all_72_0) = all_80_0
% 13.21/2.60 | | |
% 13.21/2.60 | | | GROUND_INST: instantiating (1) with rat_0, all_80_0, all_72_0, all_5_4,
% 13.21/2.60 | | | simplifying with (64), (67) gives:
% 13.21/2.60 | | | (68) all_80_0 = rat_0
% 13.21/2.60 | | |
% 13.21/2.60 | | | REDUCE: (66), (68) imply:
% 13.21/2.60 | | | (69) rat_$sum(all_5_5, rat_0) = all_5_1
% 13.21/2.60 | | |
% 13.21/2.60 | | | GROUND_INST: instantiating (3) with all_5_5, all_5_1, simplifying with
% 13.21/2.60 | | | (69) gives:
% 13.21/2.60 | | | (70) all_5_1 = all_5_5
% 13.21/2.60 | | |
% 13.21/2.60 | | | REDUCE: (57), (70) imply:
% 13.21/2.60 | | | (71) $false
% 13.21/2.60 | | |
% 13.21/2.60 | | | CLOSE: (71) is inconsistent.
% 13.21/2.60 | | |
% 13.21/2.60 | | End of split
% 13.21/2.60 | |
% 13.21/2.60 | End of split
% 13.21/2.60 |
% 13.21/2.60 End of proof
% 13.21/2.60 % SZS output end Proof for theBenchmark
% 13.21/2.60
% 13.21/2.60 1973ms
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