TSTP Solution File: ARI298_1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : ARI298_1 : TPTP v8.1.2. Released v5.0.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n032.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 17:47:37 EDT 2023
% Result : Theorem 15.06s 2.91s
% Output : Proof 22.91s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : ARI298_1 : TPTP v8.1.2. Released v5.0.0.
% 0.06/0.12 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.11/0.32 % Computer : n032.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Tue Aug 29 18:49:02 EDT 2023
% 0.11/0.32 % CPUTime :
% 0.57/0.61 ________ _____
% 0.57/0.61 ___ __ \_________(_)________________________________
% 0.57/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.57/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.57/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.57/0.61
% 0.57/0.62 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.57/0.62 (2023-06-19)
% 0.57/0.62
% 0.57/0.62 (c) Philipp Rümmer, 2009-2023
% 0.57/0.62 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.57/0.62 Amanda Stjerna.
% 0.57/0.62 Free software under BSD-3-Clause.
% 0.57/0.62
% 0.57/0.62 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.57/0.62
% 0.57/0.62 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.57/0.63 Running up to 7 provers in parallel.
% 0.57/0.65 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.57/0.65 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.57/0.65 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.57/0.65 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.57/0.65 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.57/0.65 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.57/0.65 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 1.26/0.98 Prover 0: Warning: Problem contains rationals, using incomplete axiomatisation
% 1.26/0.98 Prover 1: Warning: Problem contains rationals, using incomplete axiomatisation
% 1.26/0.98 Prover 5: Warning: Problem contains rationals, using incomplete axiomatisation
% 1.26/0.98 Prover 6: Warning: Problem contains rationals, using incomplete axiomatisation
% 1.26/0.98 Prover 3: Warning: Problem contains rationals, using incomplete axiomatisation
% 1.26/0.98 Prover 4: Warning: Problem contains rationals, using incomplete axiomatisation
% 1.26/0.98 Prover 2: Warning: Problem contains rationals, using incomplete axiomatisation
% 2.21/1.14 Prover 4: Preprocessing ...
% 2.21/1.14 Prover 1: Preprocessing ...
% 2.83/1.23 Prover 0: Preprocessing ...
% 2.83/1.23 Prover 6: Preprocessing ...
% 4.92/1.50 Prover 3: Preprocessing ...
% 4.92/1.51 Prover 5: Preprocessing ...
% 4.92/1.51 Prover 2: Preprocessing ...
% 9.51/2.17 Prover 1: Constructing countermodel ...
% 9.51/2.18 Prover 6: Constructing countermodel ...
% 10.02/2.23 Prover 4: Constructing countermodel ...
% 10.02/2.25 Prover 0: Proving ...
% 15.06/2.91 Prover 6: proved (2260ms)
% 15.06/2.91
% 15.06/2.91 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 15.06/2.91
% 15.06/2.93 Prover 0: stopped
% 15.58/2.94 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 15.58/2.94 Prover 7: Warning: Problem contains rationals, using incomplete axiomatisation
% 15.58/2.94 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 15.58/2.94 Prover 8: Warning: Problem contains rationals, using incomplete axiomatisation
% 15.76/2.97 Prover 8: Preprocessing ...
% 15.76/2.97 Prover 1: Found proof (size 10)
% 15.76/2.97 Prover 1: proved (2332ms)
% 15.76/2.97 Prover 4: stopped
% 16.47/3.11 Prover 8: Warning: ignoring some quantifiers
% 16.47/3.12 Prover 8: Constructing countermodel ...
% 16.47/3.12 Prover 7: Preprocessing ...
% 17.06/3.14 Prover 8: stopped
% 19.30/3.47 Prover 7: stopped
% 21.30/3.78 Prover 3: Constructing countermodel ...
% 21.30/3.79 Prover 3: stopped
% 21.91/3.89 Prover 2: Proving ...
% 21.91/3.89 Prover 2: stopped
% 22.48/4.04 Prover 5: Proving ...
% 22.48/4.04 Prover 5: stopped
% 22.48/4.04
% 22.48/4.04 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 22.48/4.04
% 22.48/4.05 % SZS output start Proof for theBenchmark
% 22.48/4.05 Assumptions after simplification:
% 22.48/4.05 ---------------------------------
% 22.48/4.05
% 22.48/4.05 (rat_product_problem_15)
% 22.91/4.09 ? [v0: $rat] : ( ~ (v0 = rat_2/5) & rat_$product(rat_5/8, v0) = rat_1/4)
% 22.91/4.09
% 22.91/4.09 (input)
% 22.91/4.14 ~ (rat_very_large = rat_very_small) & ~ (rat_very_large = rat_2/5) & ~
% 22.91/4.14 (rat_very_large = rat_1/4) & ~ (rat_very_large = rat_5/8) & ~
% 22.91/4.14 (rat_very_large = rat_0) & ~ (rat_very_small = rat_2/5) & ~ (rat_very_small
% 22.91/4.14 = rat_1/4) & ~ (rat_very_small = rat_5/8) & ~ (rat_very_small = rat_0) &
% 22.91/4.14 ~ (rat_2/5 = rat_1/4) & ~ (rat_2/5 = rat_5/8) & ~ (rat_2/5 = rat_0) & ~
% 22.91/4.14 (rat_1/4 = rat_5/8) & ~ (rat_1/4 = rat_0) & ~ (rat_5/8 = rat_0) &
% 22.91/4.14 rat_$is_int(rat_2/5) = 1 & rat_$is_int(rat_1/4) = 1 & rat_$is_int(rat_5/8) = 1
% 22.91/4.14 & rat_$is_int(rat_0) = 0 & rat_$is_rat(rat_2/5) = 0 & rat_$is_rat(rat_1/4) = 0
% 22.91/4.14 & rat_$is_rat(rat_5/8) = 0 & rat_$is_rat(rat_0) = 0 & rat_$floor(rat_2/5) =
% 22.91/4.14 rat_0 & rat_$floor(rat_1/4) = rat_0 & rat_$floor(rat_5/8) = rat_0 &
% 22.91/4.14 rat_$floor(rat_0) = rat_0 & rat_$ceiling(rat_0) = rat_0 &
% 22.91/4.14 rat_$truncate(rat_2/5) = rat_0 & rat_$truncate(rat_1/4) = rat_0 &
% 22.91/4.14 rat_$truncate(rat_5/8) = rat_0 & rat_$truncate(rat_0) = rat_0 &
% 22.91/4.14 rat_$round(rat_2/5) = rat_0 & rat_$round(rat_1/4) = rat_0 & rat_$round(rat_0)
% 22.91/4.14 = rat_0 & rat_$to_int(rat_2/5) = 0 & rat_$to_int(rat_1/4) = 0 &
% 22.91/4.14 rat_$to_int(rat_5/8) = 0 & rat_$to_int(rat_0) = 0 & rat_$to_rat(rat_2/5) =
% 22.91/4.14 rat_2/5 & rat_$to_rat(rat_1/4) = rat_1/4 & rat_$to_rat(rat_5/8) = rat_5/8 &
% 22.91/4.14 rat_$to_rat(rat_0) = rat_0 & rat_$to_real(rat_2/5) = real_2/5 &
% 22.91/4.14 rat_$to_real(rat_1/4) = real_1/4 & rat_$to_real(rat_5/8) = real_5/8 &
% 22.91/4.14 rat_$to_real(rat_0) = real_0 & int_$to_rat(0) = rat_0 & rat_$quotient(rat_1/4,
% 22.91/4.14 rat_2/5) = rat_5/8 & rat_$quotient(rat_1/4, rat_5/8) = rat_2/5 &
% 22.91/4.14 rat_$quotient(rat_0, rat_2/5) = rat_0 & rat_$quotient(rat_0, rat_1/4) = rat_0
% 22.91/4.14 & rat_$quotient(rat_0, rat_5/8) = rat_0 & rat_$difference(rat_2/5, rat_2/5) =
% 22.91/4.14 rat_0 & rat_$difference(rat_2/5, rat_0) = rat_2/5 & rat_$difference(rat_1/4,
% 22.91/4.14 rat_1/4) = rat_0 & rat_$difference(rat_1/4, rat_0) = rat_1/4 &
% 22.91/4.14 rat_$difference(rat_5/8, rat_5/8) = rat_0 & rat_$difference(rat_5/8, rat_0) =
% 22.91/4.14 rat_5/8 & rat_$difference(rat_0, rat_0) = rat_0 & rat_$uminus(rat_0) = rat_0 &
% 22.91/4.14 rat_$sum(rat_2/5, rat_0) = rat_2/5 & rat_$sum(rat_1/4, rat_0) = rat_1/4 &
% 22.91/4.14 rat_$sum(rat_5/8, rat_0) = rat_5/8 & rat_$sum(rat_0, rat_2/5) = rat_2/5 &
% 22.91/4.14 rat_$sum(rat_0, rat_1/4) = rat_1/4 & rat_$sum(rat_0, rat_5/8) = rat_5/8 &
% 22.91/4.14 rat_$sum(rat_0, rat_0) = rat_0 & rat_$greatereq(rat_very_small,
% 22.91/4.14 rat_very_large) = 1 & rat_$greatereq(rat_2/5, rat_2/5) = 0 &
% 22.91/4.14 rat_$greatereq(rat_2/5, rat_1/4) = 0 & rat_$greatereq(rat_2/5, rat_5/8) = 1 &
% 22.91/4.14 rat_$greatereq(rat_2/5, rat_0) = 0 & rat_$greatereq(rat_1/4, rat_2/5) = 1 &
% 22.91/4.14 rat_$greatereq(rat_1/4, rat_1/4) = 0 & rat_$greatereq(rat_1/4, rat_5/8) = 1 &
% 22.91/4.14 rat_$greatereq(rat_1/4, rat_0) = 0 & rat_$greatereq(rat_5/8, rat_2/5) = 0 &
% 22.91/4.14 rat_$greatereq(rat_5/8, rat_1/4) = 0 & rat_$greatereq(rat_5/8, rat_5/8) = 0 &
% 22.91/4.14 rat_$greatereq(rat_5/8, rat_0) = 0 & rat_$greatereq(rat_0, rat_2/5) = 1 &
% 22.91/4.14 rat_$greatereq(rat_0, rat_1/4) = 1 & rat_$greatereq(rat_0, rat_5/8) = 1 &
% 22.91/4.14 rat_$greatereq(rat_0, rat_0) = 0 & rat_$lesseq(rat_very_small, rat_very_large)
% 22.91/4.14 = 0 & rat_$lesseq(rat_2/5, rat_2/5) = 0 & rat_$lesseq(rat_2/5, rat_1/4) = 1 &
% 22.91/4.14 rat_$lesseq(rat_2/5, rat_5/8) = 0 & rat_$lesseq(rat_2/5, rat_0) = 1 &
% 22.91/4.14 rat_$lesseq(rat_1/4, rat_2/5) = 0 & rat_$lesseq(rat_1/4, rat_1/4) = 0 &
% 22.91/4.14 rat_$lesseq(rat_1/4, rat_5/8) = 0 & rat_$lesseq(rat_1/4, rat_0) = 1 &
% 22.91/4.14 rat_$lesseq(rat_5/8, rat_2/5) = 1 & rat_$lesseq(rat_5/8, rat_1/4) = 1 &
% 22.91/4.14 rat_$lesseq(rat_5/8, rat_5/8) = 0 & rat_$lesseq(rat_5/8, rat_0) = 1 &
% 22.91/4.14 rat_$lesseq(rat_0, rat_2/5) = 0 & rat_$lesseq(rat_0, rat_1/4) = 0 &
% 22.91/4.14 rat_$lesseq(rat_0, rat_5/8) = 0 & rat_$lesseq(rat_0, rat_0) = 0 &
% 22.91/4.14 rat_$greater(rat_very_large, rat_2/5) = 0 & rat_$greater(rat_very_large,
% 22.91/4.14 rat_1/4) = 0 & rat_$greater(rat_very_large, rat_5/8) = 0 &
% 22.91/4.14 rat_$greater(rat_very_large, rat_0) = 0 & rat_$greater(rat_very_small,
% 22.91/4.14 rat_very_large) = 1 & rat_$greater(rat_2/5, rat_very_small) = 0 &
% 22.91/4.14 rat_$greater(rat_2/5, rat_2/5) = 1 & rat_$greater(rat_2/5, rat_1/4) = 0 &
% 22.91/4.14 rat_$greater(rat_2/5, rat_5/8) = 1 & rat_$greater(rat_2/5, rat_0) = 0 &
% 22.91/4.14 rat_$greater(rat_1/4, rat_very_small) = 0 & rat_$greater(rat_1/4, rat_2/5) = 1
% 22.91/4.14 & rat_$greater(rat_1/4, rat_1/4) = 1 & rat_$greater(rat_1/4, rat_5/8) = 1 &
% 22.91/4.14 rat_$greater(rat_1/4, rat_0) = 0 & rat_$greater(rat_5/8, rat_very_small) = 0 &
% 22.91/4.14 rat_$greater(rat_5/8, rat_2/5) = 0 & rat_$greater(rat_5/8, rat_1/4) = 0 &
% 22.91/4.14 rat_$greater(rat_5/8, rat_5/8) = 1 & rat_$greater(rat_5/8, rat_0) = 0 &
% 22.91/4.14 rat_$greater(rat_0, rat_very_small) = 0 & rat_$greater(rat_0, rat_2/5) = 1 &
% 22.91/4.14 rat_$greater(rat_0, rat_1/4) = 1 & rat_$greater(rat_0, rat_5/8) = 1 &
% 22.91/4.14 rat_$greater(rat_0, rat_0) = 1 & rat_$less(rat_very_small, rat_very_large) = 0
% 22.91/4.15 & rat_$less(rat_very_small, rat_2/5) = 0 & rat_$less(rat_very_small, rat_1/4)
% 22.91/4.15 = 0 & rat_$less(rat_very_small, rat_5/8) = 0 & rat_$less(rat_very_small,
% 22.91/4.15 rat_0) = 0 & rat_$less(rat_2/5, rat_very_large) = 0 & rat_$less(rat_2/5,
% 22.91/4.15 rat_2/5) = 1 & rat_$less(rat_2/5, rat_1/4) = 1 & rat_$less(rat_2/5, rat_5/8)
% 22.91/4.15 = 0 & rat_$less(rat_2/5, rat_0) = 1 & rat_$less(rat_1/4, rat_very_large) = 0 &
% 22.91/4.15 rat_$less(rat_1/4, rat_2/5) = 0 & rat_$less(rat_1/4, rat_1/4) = 1 &
% 22.91/4.15 rat_$less(rat_1/4, rat_5/8) = 0 & rat_$less(rat_1/4, rat_0) = 1 &
% 22.91/4.15 rat_$less(rat_5/8, rat_very_large) = 0 & rat_$less(rat_5/8, rat_2/5) = 1 &
% 22.91/4.15 rat_$less(rat_5/8, rat_1/4) = 1 & rat_$less(rat_5/8, rat_5/8) = 1 &
% 22.91/4.15 rat_$less(rat_5/8, rat_0) = 1 & rat_$less(rat_0, rat_very_large) = 0 &
% 22.91/4.15 rat_$less(rat_0, rat_2/5) = 0 & rat_$less(rat_0, rat_1/4) = 0 &
% 22.91/4.15 rat_$less(rat_0, rat_5/8) = 0 & rat_$less(rat_0, rat_0) = 1 &
% 22.91/4.15 rat_$product(rat_2/5, rat_5/8) = rat_1/4 & rat_$product(rat_2/5, rat_0) =
% 22.91/4.15 rat_0 & rat_$product(rat_1/4, rat_0) = rat_0 & rat_$product(rat_5/8, rat_2/5)
% 22.91/4.15 = rat_1/4 & rat_$product(rat_5/8, rat_0) = rat_0 & rat_$product(rat_0,
% 22.91/4.15 rat_2/5) = rat_0 & rat_$product(rat_0, rat_1/4) = rat_0 &
% 22.91/4.15 rat_$product(rat_0, rat_5/8) = rat_0 & rat_$product(rat_0, rat_0) = rat_0 & !
% 22.91/4.15 [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : ! [v3: $rat] : ! [v4: $rat] : (
% 22.91/4.15 ~ (rat_$sum(v3, v0) = v4) | ~ (rat_$sum(v2, v1) = v3) | ? [v5: $rat] :
% 22.91/4.15 (rat_$sum(v2, v5) = v4 & rat_$sum(v1, v0) = v5)) & ! [v0: $rat] : ! [v1:
% 22.91/4.15 $rat] : ! [v2: $rat] : ! [v3: $rat] : (v3 = v1 | v0 = rat_0 | ~
% 22.91/4.15 (rat_$quotient(v2, v0) = v3) | ~ (rat_$product(v1, v0) = v2)) & ! [v0:
% 22.91/4.15 $rat] : ! [v1: $rat] : ! [v2: $rat] : ! [v3: int] : (v3 = 0 | ~
% 22.91/4.15 (rat_$lesseq(v2, v0) = v3) | ~ (rat_$lesseq(v1, v0) = 0) | ? [v4: int] : (
% 22.91/4.15 ~ (v4 = 0) & rat_$lesseq(v2, v1) = v4)) & ! [v0: $rat] : ! [v1: $rat] :
% 22.91/4.15 ! [v2: $rat] : ! [v3: int] : (v3 = 0 | ~ (rat_$lesseq(v1, v0) = 0) | ~
% 22.91/4.15 (rat_$less(v2, v0) = v3) | ? [v4: int] : ( ~ (v4 = 0) & rat_$less(v2, v1) =
% 22.91/4.15 v4)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : ! [v3: $rat] : ( ~
% 22.91/4.15 (rat_$uminus(v0) = v2) | ~ (rat_$sum(v1, v2) = v3) | rat_$difference(v1,
% 22.91/4.15 v0) = v3) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : (v2 = rat_0 |
% 22.91/4.15 ~ (rat_$uminus(v0) = v1) | ~ (rat_$sum(v0, v1) = v2)) & ! [v0: $rat] : !
% 22.91/4.15 [v1: $rat] : ! [v2: int] : (v2 = 0 | ~ (rat_$greatereq(v0, v1) = v2) | ?
% 22.91/4.15 [v3: int] : ( ~ (v3 = 0) & rat_$lesseq(v1, v0) = v3)) & ! [v0: $rat] : !
% 22.91/4.15 [v1: $rat] : ! [v2: int] : (v2 = 0 | ~ (rat_$lesseq(v1, v0) = v2) | ( ~ (v1
% 22.91/4.15 = v0) & ? [v3: int] : ( ~ (v3 = 0) & rat_$less(v1, v0) = v3))) & !
% 22.91/4.15 [v0: $rat] : ! [v1: $rat] : ! [v2: int] : (v2 = 0 | ~ (rat_$greater(v0, v1)
% 22.91/4.15 = v2) | ? [v3: int] : ( ~ (v3 = 0) & rat_$less(v1, v0) = v3)) & ! [v0:
% 22.91/4.15 $rat] : ! [v1: $rat] : ! [v2: $rat] : ( ~ (rat_$sum(v0, v1) = v2) |
% 22.91/4.15 rat_$sum(v1, v0) = v2) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : ( ~
% 22.91/4.15 (rat_$lesseq(v2, v1) = 0) | ~ (rat_$less(v1, v0) = 0) | rat_$less(v2, v0) =
% 22.91/4.15 0) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : ( ~ (rat_$product(v0,
% 22.91/4.15 v1) = v2) | rat_$product(v1, v0) = v2) & ! [v0: $rat] : ! [v1: $rat] :
% 22.91/4.15 (v1 = v0 | ~ (rat_$sum(v0, rat_0) = v1)) & ! [v0: $rat] : ! [v1: $rat] :
% 22.91/4.15 (v1 = v0 | ~ (rat_$lesseq(v1, v0) = 0) | rat_$less(v1, v0) = 0) & ! [v0:
% 22.91/4.15 $rat] : ! [v1: $rat] : ( ~ (rat_$uminus(v0) = v1) | rat_$uminus(v1) = v0) &
% 22.91/4.15 ! [v0: $rat] : ! [v1: $rat] : ( ~ (rat_$greatereq(v0, v1) = 0) |
% 22.91/4.15 rat_$lesseq(v1, v0) = 0) & ! [v0: $rat] : ! [v1: $rat] : ( ~
% 22.91/4.15 (rat_$greater(v0, v1) = 0) | rat_$less(v1, v0) = 0) & ! [v0: $rat] : (v0 =
% 22.91/4.15 rat_0 | ~ (rat_$uminus(v0) = v0))
% 22.91/4.15
% 22.91/4.15 Those formulas are unsatisfiable:
% 22.91/4.15 ---------------------------------
% 22.91/4.15
% 22.91/4.15 Begin of proof
% 22.91/4.15 |
% 22.91/4.15 | ALPHA: (input) implies:
% 22.91/4.16 | (1) ~ (rat_5/8 = rat_0)
% 22.91/4.16 | (2) rat_$quotient(rat_1/4, rat_5/8) = rat_2/5
% 22.91/4.16 | (3) ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : ( ~ (rat_$product(v0,
% 22.91/4.16 | v1) = v2) | rat_$product(v1, v0) = v2)
% 22.91/4.16 | (4) ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : ! [v3: $rat] : (v3 =
% 22.91/4.16 | v1 | v0 = rat_0 | ~ (rat_$quotient(v2, v0) = v3) | ~
% 22.91/4.16 | (rat_$product(v1, v0) = v2))
% 22.91/4.16 |
% 22.91/4.16 | DELTA: instantiating (rat_product_problem_15) with fresh symbol all_5_0 gives:
% 22.91/4.16 | (5) ~ (all_5_0 = rat_2/5) & rat_$product(rat_5/8, all_5_0) = rat_1/4
% 22.91/4.16 |
% 22.91/4.16 | ALPHA: (5) implies:
% 22.91/4.16 | (6) ~ (all_5_0 = rat_2/5)
% 22.91/4.16 | (7) rat_$product(rat_5/8, all_5_0) = rat_1/4
% 22.91/4.16 |
% 22.91/4.16 | GROUND_INST: instantiating (3) with rat_5/8, all_5_0, rat_1/4, simplifying
% 22.91/4.16 | with (7) gives:
% 22.91/4.16 | (8) rat_$product(all_5_0, rat_5/8) = rat_1/4
% 22.91/4.16 |
% 22.91/4.17 | GROUND_INST: instantiating (4) with rat_5/8, all_5_0, rat_1/4, rat_2/5,
% 22.91/4.17 | simplifying with (2), (8) gives:
% 22.91/4.17 | (9) all_5_0 = rat_2/5 | rat_5/8 = rat_0
% 22.91/4.17 |
% 22.91/4.17 | BETA: splitting (9) gives:
% 22.91/4.17 |
% 22.91/4.17 | Case 1:
% 22.91/4.17 | |
% 22.91/4.17 | | (10) rat_5/8 = rat_0
% 22.91/4.17 | |
% 22.91/4.17 | | REDUCE: (1), (10) imply:
% 22.91/4.17 | | (11) $false
% 22.91/4.17 | |
% 22.91/4.17 | | CLOSE: (11) is inconsistent.
% 22.91/4.17 | |
% 22.91/4.17 | Case 2:
% 22.91/4.17 | |
% 22.91/4.17 | | (12) all_5_0 = rat_2/5
% 22.91/4.17 | |
% 22.91/4.17 | | REDUCE: (6), (12) imply:
% 22.91/4.17 | | (13) $false
% 22.91/4.17 | |
% 22.91/4.17 | | CLOSE: (13) is inconsistent.
% 22.91/4.17 | |
% 22.91/4.17 | End of split
% 22.91/4.17 |
% 22.91/4.17 End of proof
% 22.91/4.17 % SZS output end Proof for theBenchmark
% 22.91/4.17
% 22.91/4.17 3552ms
%------------------------------------------------------------------------------