TSTP Solution File: ARI216_1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : ARI216_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 : n003.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 17:47:19 EDT 2023
% Result : Theorem 7.36s 1.77s
% Output : Proof 7.85s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : ARI216_1 : TPTP v8.1.2. Released v5.0.0.
% 0.12/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.34 % Computer : n003.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 18:50:41 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.67/0.65 ________ _____
% 0.67/0.65 ___ __ \_________(_)________________________________
% 0.67/0.65 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.67/0.65 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.67/0.65 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.67/0.65
% 0.67/0.65 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.67/0.65 (2023-06-19)
% 0.67/0.65
% 0.67/0.65 (c) Philipp Rümmer, 2009-2023
% 0.67/0.65 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.67/0.65 Amanda Stjerna.
% 0.67/0.65 Free software under BSD-3-Clause.
% 0.67/0.65
% 0.67/0.65 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.67/0.65
% 0.67/0.65 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.67/0.66 Running up to 7 provers in parallel.
% 0.67/0.68 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.67/0.68 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.67/0.68 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.67/0.68 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.67/0.68 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.67/0.68 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.67/0.68 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 1.57/0.98 Prover 6: Warning: Problem contains rationals, using incomplete axiomatisation
% 1.57/0.98 Prover 2: Warning: Problem contains rationals, using incomplete axiomatisation
% 1.57/0.98 Prover 1: Warning: Problem contains rationals, using incomplete axiomatisation
% 1.57/0.98 Prover 3: Warning: Problem contains rationals, using incomplete axiomatisation
% 1.57/0.98 Prover 5: Warning: Problem contains rationals, using incomplete axiomatisation
% 1.57/0.98 Prover 4: Warning: Problem contains rationals, using incomplete axiomatisation
% 1.57/0.98 Prover 0: Warning: Problem contains rationals, using incomplete axiomatisation
% 2.47/1.08 Prover 1: Preprocessing ...
% 2.47/1.08 Prover 4: Preprocessing ...
% 2.47/1.13 Prover 0: Preprocessing ...
% 2.47/1.13 Prover 6: Preprocessing ...
% 2.47/1.13 Prover 5: Preprocessing ...
% 2.47/1.13 Prover 2: Preprocessing ...
% 2.47/1.14 Prover 3: Preprocessing ...
% 5.49/1.52 Prover 1: Constructing countermodel ...
% 5.49/1.55 Prover 6: Proving ...
% 6.57/1.64 Prover 4: Constructing countermodel ...
% 6.57/1.65 Prover 3: Constructing countermodel ...
% 6.57/1.65 Prover 0: Proving ...
% 6.57/1.65 Prover 2: Proving ...
% 6.57/1.73 Prover 5: Proving ...
% 7.36/1.76 Prover 4: Found proof (size 3)
% 7.36/1.76 Prover 1: Found proof (size 3)
% 7.36/1.76 Prover 4: proved (1088ms)
% 7.36/1.76 Prover 1: proved (1089ms)
% 7.36/1.76 Prover 0: proved (1094ms)
% 7.36/1.76 Prover 3: stopped
% 7.36/1.76 Prover 6: stopped
% 7.36/1.76 Prover 2: stopped
% 7.36/1.77 Prover 5: stopped
% 7.36/1.77
% 7.36/1.77 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 7.36/1.77
% 7.36/1.77 % SZS output start Proof for theBenchmark
% 7.36/1.77 Assumptions after simplification:
% 7.36/1.77 ---------------------------------
% 7.36/1.77
% 7.36/1.77 (rat_lesseq_problem_14)
% 7.36/1.80 ! [v0: $rat] : ~ (rat_$lesseq(rat_-7/16, v0) = 0)
% 7.36/1.80
% 7.36/1.80 (input)
% 7.85/1.83 ~ (rat_very_large = rat_very_small) & ~ (rat_very_large = rat_-7/16) & ~
% 7.85/1.83 (rat_very_large = rat_0) & ~ (rat_very_small = rat_-7/16) & ~
% 7.85/1.83 (rat_very_small = rat_0) & ~ (rat_-7/16 = rat_0) & rat_$is_int(rat_-7/16) = 1
% 7.85/1.83 & rat_$is_int(rat_0) = 0 & rat_$is_rat(rat_-7/16) = 0 & rat_$is_rat(rat_0) = 0
% 7.85/1.83 & rat_$floor(rat_0) = rat_0 & rat_$ceiling(rat_-7/16) = rat_0 &
% 7.85/1.83 rat_$ceiling(rat_0) = rat_0 & rat_$truncate(rat_-7/16) = rat_0 &
% 7.85/1.83 rat_$truncate(rat_0) = rat_0 & rat_$round(rat_-7/16) = rat_0 &
% 7.85/1.83 rat_$round(rat_0) = rat_0 & rat_$to_int(rat_-7/16) = -1 & rat_$to_int(rat_0) =
% 7.85/1.83 0 & rat_$to_rat(rat_-7/16) = rat_-7/16 & rat_$to_rat(rat_0) = rat_0 &
% 7.85/1.83 rat_$to_real(rat_-7/16) = real_-7/16 & rat_$to_real(rat_0) = real_0 &
% 7.85/1.83 int_$to_rat(0) = rat_0 & rat_$quotient(rat_0, rat_-7/16) = rat_0 &
% 7.85/1.83 rat_$product(rat_-7/16, rat_0) = rat_0 & rat_$product(rat_0, rat_-7/16) =
% 7.85/1.83 rat_0 & rat_$product(rat_0, rat_0) = rat_0 & rat_$difference(rat_-7/16,
% 7.85/1.83 rat_-7/16) = rat_0 & rat_$difference(rat_-7/16, rat_0) = rat_-7/16 &
% 7.85/1.83 rat_$difference(rat_0, rat_0) = rat_0 & rat_$uminus(rat_0) = rat_0 &
% 7.85/1.83 rat_$sum(rat_-7/16, rat_0) = rat_-7/16 & rat_$sum(rat_0, rat_-7/16) =
% 7.85/1.83 rat_-7/16 & rat_$sum(rat_0, rat_0) = rat_0 & rat_$greatereq(rat_very_small,
% 7.85/1.83 rat_very_large) = 1 & rat_$greatereq(rat_-7/16, rat_-7/16) = 0 &
% 7.85/1.83 rat_$greatereq(rat_-7/16, rat_0) = 1 & rat_$greatereq(rat_0, rat_-7/16) = 0 &
% 7.85/1.83 rat_$greatereq(rat_0, rat_0) = 0 & rat_$greater(rat_very_large, rat_-7/16) = 0
% 7.85/1.83 & rat_$greater(rat_very_large, rat_0) = 0 & rat_$greater(rat_very_small,
% 7.85/1.83 rat_very_large) = 1 & rat_$greater(rat_-7/16, rat_very_small) = 0 &
% 7.85/1.83 rat_$greater(rat_-7/16, rat_-7/16) = 1 & rat_$greater(rat_-7/16, rat_0) = 1 &
% 7.85/1.83 rat_$greater(rat_0, rat_very_small) = 0 & rat_$greater(rat_0, rat_-7/16) = 0 &
% 7.85/1.83 rat_$greater(rat_0, rat_0) = 1 & rat_$less(rat_very_small, rat_very_large) = 0
% 7.85/1.83 & rat_$less(rat_very_small, rat_-7/16) = 0 & rat_$less(rat_very_small, rat_0)
% 7.85/1.83 = 0 & rat_$less(rat_-7/16, rat_very_large) = 0 & rat_$less(rat_-7/16,
% 7.85/1.83 rat_-7/16) = 1 & rat_$less(rat_-7/16, rat_0) = 0 & rat_$less(rat_0,
% 7.85/1.83 rat_very_large) = 0 & rat_$less(rat_0, rat_-7/16) = 1 & rat_$less(rat_0,
% 7.85/1.83 rat_0) = 1 & rat_$lesseq(rat_very_small, rat_very_large) = 0 &
% 7.85/1.83 rat_$lesseq(rat_-7/16, rat_-7/16) = 0 & rat_$lesseq(rat_-7/16, rat_0) = 0 &
% 7.85/1.83 rat_$lesseq(rat_0, rat_-7/16) = 1 & rat_$lesseq(rat_0, rat_0) = 0 & ! [v0:
% 7.85/1.83 $rat] : ! [v1: $rat] : ! [v2: $rat] : ! [v3: $rat] : ! [v4: $rat] : ( ~
% 7.85/1.83 (rat_$sum(v3, v0) = v4) | ~ (rat_$sum(v2, v1) = v3) | ? [v5: $rat] :
% 7.85/1.83 (rat_$sum(v2, v5) = v4 & rat_$sum(v1, v0) = v5)) & ! [v0: $rat] : ! [v1:
% 7.85/1.83 $rat] : ! [v2: $rat] : ! [v3: $rat] : ! [v4: $rat] : ( ~ (rat_$sum(v2,
% 7.85/1.83 v3) = v4) | ~ (rat_$sum(v1, v0) = v3) | ? [v5: $rat] : (rat_$sum(v5,
% 7.85/1.83 v0) = v4 & rat_$sum(v2, v1) = v5)) & ! [v0: $rat] : ! [v1: $rat] : !
% 7.85/1.83 [v2: $rat] : ! [v3: int] : (v3 = 0 | ~ (rat_$less(v2, v1) = 0) | ~
% 7.85/1.83 (rat_$less(v2, v0) = v3) | ? [v4: int] : ( ~ (v4 = 0) & rat_$lesseq(v1, v0)
% 7.85/1.83 = v4)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : ! [v3: int] :
% 7.85/1.83 (v3 = 0 | ~ (rat_$less(v2, v0) = v3) | ~ (rat_$less(v1, v0) = 0) | ? [v4:
% 7.85/1.83 int] : ( ~ (v4 = 0) & rat_$lesseq(v2, v1) = v4)) & ! [v0: $rat] : ! [v1:
% 7.85/1.83 $rat] : ! [v2: $rat] : ! [v3: int] : (v3 = 0 | ~ (rat_$less(v2, v0) = v3)
% 7.85/1.83 | ~ (rat_$lesseq(v2, v1) = 0) | ? [v4: int] : ( ~ (v4 = 0) & rat_$less(v1,
% 7.85/1.83 v0) = v4)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : ! [v3:
% 7.85/1.83 int] : (v3 = 0 | ~ (rat_$less(v2, v0) = v3) | ~ (rat_$lesseq(v1, v0) = 0)
% 7.85/1.83 | ? [v4: int] : ( ~ (v4 = 0) & rat_$less(v2, v1) = v4)) & ! [v0: $rat] :
% 7.85/1.83 ! [v1: $rat] : ! [v2: $rat] : ! [v3: int] : (v3 = 0 | ~ (rat_$lesseq(v2,
% 7.85/1.83 v1) = 0) | ~ (rat_$lesseq(v2, v0) = v3) | ? [v4: int] : ( ~ (v4 = 0) &
% 7.85/1.83 rat_$lesseq(v1, v0) = v4)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat]
% 7.85/1.83 : ! [v3: int] : (v3 = 0 | ~ (rat_$lesseq(v2, v0) = v3) | ~ (rat_$lesseq(v1,
% 7.85/1.83 v0) = 0) | ? [v4: int] : ( ~ (v4 = 0) & rat_$lesseq(v2, v1) = v4)) & !
% 7.85/1.83 [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : ! [v3: $rat] : ( ~
% 7.85/1.83 (rat_$uminus(v0) = v2) | ~ (rat_$sum(v1, v2) = v3) | rat_$difference(v1,
% 7.85/1.83 v0) = v3) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: int] : (v2 = 0 | v1 =
% 7.85/1.83 v0 | ~ (rat_$less(v1, v0) = v2) | ? [v3: int] : ( ~ (v3 = 0) &
% 7.85/1.83 rat_$lesseq(v1, v0) = v3)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: int]
% 7.85/1.83 : (v2 = 0 | ~ (rat_$greatereq(v0, v1) = v2) | ? [v3: int] : ( ~ (v3 = 0) &
% 7.85/1.83 rat_$lesseq(v1, v0) = v3)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: int]
% 7.85/1.83 : (v2 = 0 | ~ (rat_$greater(v0, v1) = v2) | ? [v3: int] : ( ~ (v3 = 0) &
% 7.85/1.83 rat_$less(v1, v0) = v3)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: int] :
% 7.85/1.83 (v2 = 0 | ~ (rat_$less(v1, v0) = v2) | ? [v3: int] : ( ~ (v3 = 0) &
% 7.85/1.83 rat_$greater(v0, v1) = v3)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: int]
% 7.85/1.83 : (v2 = 0 | ~ (rat_$lesseq(v1, v0) = v2) | ? [v3: int] : ( ~ (v3 = 0) &
% 7.85/1.83 rat_$greatereq(v0, v1) = v3)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2:
% 7.85/1.83 int] : (v2 = 0 | ~ (rat_$lesseq(v1, v0) = v2) | ? [v3: int] : ( ~ (v3 = 0)
% 7.85/1.83 & rat_$less(v1, v0) = v3)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat]
% 7.85/1.83 : (v0 = rat_0 | ~ (rat_$product(v1, v0) = v2) | rat_$quotient(v2, v0) = v1) &
% 7.85/1.83 ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : ( ~ (rat_$product(v1, v0) =
% 7.85/1.83 v2) | rat_$product(v0, v1) = v2) & ! [v0: $rat] : ! [v1: $rat] : ! [v2:
% 7.85/1.83 $rat] : ( ~ (rat_$product(v0, v1) = v2) | rat_$product(v1, v0) = v2) & !
% 7.85/1.83 [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : ( ~ (rat_$difference(v1, v0) =
% 7.85/1.83 v2) | ? [v3: $rat] : (rat_$uminus(v0) = v3 & rat_$sum(v1, v3) = v2)) & !
% 7.85/1.83 [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : ( ~ (rat_$sum(v1, v0) = v2) |
% 7.85/1.83 rat_$sum(v0, v1) = v2) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : ( ~
% 7.85/1.83 (rat_$sum(v0, v1) = v2) | rat_$sum(v1, v0) = v2) & ! [v0: $rat] : ! [v1:
% 7.85/1.83 $rat] : ! [v2: $rat] : ( ~ (rat_$less(v2, v1) = 0) | ~ (rat_$lesseq(v1,
% 7.85/1.83 v0) = 0) | rat_$less(v2, v0) = 0) & ! [v0: $rat] : ! [v1: $rat] : !
% 7.85/1.83 [v2: $rat] : ( ~ (rat_$less(v1, v0) = 0) | ~ (rat_$lesseq(v2, v1) = 0) |
% 7.85/1.83 rat_$less(v2, v0) = 0) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : ( ~
% 7.85/1.83 (rat_$lesseq(v2, v1) = 0) | ~ (rat_$lesseq(v1, v0) = 0) | rat_$lesseq(v2,
% 7.85/1.83 v0) = 0) & ! [v0: $rat] : ! [v1: $rat] : (v1 = v0 | ~ (rat_$sum(v0,
% 7.85/1.83 rat_0) = v1)) & ! [v0: $rat] : ! [v1: $rat] : (v1 = v0 | ~
% 7.85/1.84 (rat_$lesseq(v1, v0) = 0) | rat_$less(v1, v0) = 0) & ! [v0: $rat] : ! [v1:
% 7.85/1.84 int] : (v1 = 0 | ~ (rat_$lesseq(v0, v0) = v1)) & ! [v0: $rat] : ! [v1:
% 7.85/1.84 $rat] : ( ~ (rat_$uminus(v0) = v1) | rat_$uminus(v1) = v0) & ! [v0: $rat] :
% 7.85/1.84 ! [v1: $rat] : ( ~ (rat_$uminus(v0) = v1) | rat_$sum(v0, v1) = rat_0) & !
% 7.85/1.84 [v0: $rat] : ! [v1: $rat] : ( ~ (rat_$greatereq(v0, v1) = 0) |
% 7.85/1.84 rat_$lesseq(v1, v0) = 0) & ! [v0: $rat] : ! [v1: $rat] : ( ~
% 7.85/1.84 (rat_$greater(v0, v1) = 0) | rat_$less(v1, v0) = 0) & ! [v0: $rat] : !
% 7.85/1.84 [v1: $rat] : ( ~ (rat_$less(v1, v0) = 0) | rat_$greater(v0, v1) = 0) & ! [v0:
% 7.85/1.84 $rat] : ! [v1: $rat] : ( ~ (rat_$less(v1, v0) = 0) | rat_$lesseq(v1, v0) =
% 7.85/1.84 0) & ! [v0: $rat] : ! [v1: MultipleValueBool] : ( ~ (rat_$less(v0, v0) =
% 7.85/1.84 v1) | rat_$lesseq(v0, v0) = 0) & ! [v0: $rat] : ! [v1: $rat] : ( ~
% 7.85/1.84 (rat_$lesseq(v1, v0) = 0) | rat_$greatereq(v0, v1) = 0) & ! [v0: $rat] :
% 7.85/1.84 (v0 = rat_0 | ~ (rat_$uminus(v0) = v0))
% 7.85/1.84
% 7.85/1.84 Those formulas are unsatisfiable:
% 7.85/1.84 ---------------------------------
% 7.85/1.84
% 7.85/1.84 Begin of proof
% 7.85/1.84 |
% 7.85/1.84 | ALPHA: (input) implies:
% 7.85/1.84 | (1) rat_$lesseq(rat_-7/16, rat_-7/16) = 0
% 7.85/1.84 |
% 7.85/1.84 | GROUND_INST: instantiating (rat_lesseq_problem_14) with rat_-7/16, simplifying
% 7.85/1.84 | with (1) gives:
% 7.85/1.84 | (2) $false
% 7.85/1.84 |
% 7.85/1.84 | CLOSE: (2) is inconsistent.
% 7.85/1.84 |
% 7.85/1.84 End of proof
% 7.85/1.84 % SZS output end Proof for theBenchmark
% 7.85/1.84
% 7.85/1.84 1192ms
%------------------------------------------------------------------------------