TSTP Solution File: ARI445_1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : ARI445_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 : n011.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 17:48:04 EDT 2023
% Result : Theorem 12.16s 2.51s
% Output : Proof 12.55s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : ARI445_1 : TPTP v8.1.2. Released v5.0.0.
% 0.10/0.12 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.11/0.32 % Computer : n011.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
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Tue Aug 29 18:35:41 EDT 2023
% 0.11/0.33 % CPUTime :
% 0.17/0.62 ________ _____
% 0.17/0.62 ___ __ \_________(_)________________________________
% 0.17/0.62 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.17/0.62 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.17/0.62 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.17/0.62
% 0.17/0.62 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.17/0.62 (2023-06-19)
% 0.17/0.62
% 0.17/0.62 (c) Philipp Rümmer, 2009-2023
% 0.17/0.62 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.17/0.62 Amanda Stjerna.
% 0.17/0.62 Free software under BSD-3-Clause.
% 0.17/0.62
% 0.17/0.62 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.17/0.62
% 0.17/0.62 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.17/0.63 Running up to 7 provers in parallel.
% 0.17/0.65 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.17/0.65 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.17/0.65 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.17/0.65 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.17/0.65 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.17/0.65 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 0.17/0.65 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 1.29/0.97 Prover 0: Warning: Problem contains reals, using incomplete axiomatisation
% 1.29/0.97 Prover 2: Warning: Problem contains reals, using incomplete axiomatisation
% 1.29/0.97 Prover 1: Warning: Problem contains reals, using incomplete axiomatisation
% 1.29/0.97 Prover 3: Warning: Problem contains reals, using incomplete axiomatisation
% 1.29/0.97 Prover 6: Warning: Problem contains reals, using incomplete axiomatisation
% 1.29/0.97 Prover 5: Warning: Problem contains reals, using incomplete axiomatisation
% 1.29/0.97 Prover 4: Warning: Problem contains reals, using incomplete axiomatisation
% 2.23/1.10 Prover 4: Preprocessing ...
% 2.23/1.11 Prover 1: Preprocessing ...
% 2.87/1.19 Prover 0: Preprocessing ...
% 2.95/1.19 Prover 6: Preprocessing ...
% 3.08/1.24 Prover 5: Preprocessing ...
% 3.08/1.25 Prover 2: Preprocessing ...
% 3.08/1.26 Prover 3: Preprocessing ...
% 8.09/1.91 Prover 1: Constructing countermodel ...
% 8.09/1.96 Prover 6: Proving ...
% 8.09/1.98 Prover 0: Proving ...
% 8.09/1.99 Prover 4: Constructing countermodel ...
% 10.22/2.27 Prover 1: Found proof (size 3)
% 10.22/2.27 Prover 1: proved (1623ms)
% 10.22/2.27 Prover 6: stopped
% 10.22/2.28 Prover 4: stopped
% 10.22/2.28 Prover 0: proved (1638ms)
% 10.86/2.37 Prover 3: Constructing countermodel ...
% 10.86/2.38 Prover 3: stopped
% 11.73/2.42 Prover 2: Proving ...
% 11.73/2.42 Prover 2: stopped
% 12.16/2.50 Prover 5: Proving ...
% 12.16/2.51 Prover 5: stopped
% 12.16/2.51
% 12.16/2.51 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 12.16/2.51
% 12.16/2.51 % SZS output start Proof for theBenchmark
% 12.16/2.51 Assumptions after simplification:
% 12.16/2.51 ---------------------------------
% 12.16/2.51
% 12.16/2.51 (real_product_problem_10)
% 12.16/2.56 ! [v0: $real] : ~ (real_$product(real_11/2, v0) = real_121/4)
% 12.16/2.56
% 12.16/2.56 (input)
% 12.55/2.61 ~ (real_very_large = real_very_small) & ~ (real_very_large = real_121/4) &
% 12.55/2.61 ~ (real_very_large = real_11/2) & ~ (real_very_large = real_0) & ~
% 12.55/2.61 (real_very_small = real_121/4) & ~ (real_very_small = real_11/2) & ~
% 12.55/2.61 (real_very_small = real_0) & ~ (real_121/4 = real_11/2) & ~ (real_121/4 =
% 12.55/2.61 real_0) & ~ (real_11/2 = real_0) & real_$is_int(real_121/4) = 1 &
% 12.55/2.61 real_$is_int(real_11/2) = 1 & real_$is_int(real_0) = 0 &
% 12.55/2.61 real_$is_rat(real_121/4) = 0 & real_$is_rat(real_11/2) = 0 &
% 12.55/2.61 real_$is_rat(real_0) = 0 & real_$floor(real_0) = real_0 &
% 12.55/2.61 real_$ceiling(real_0) = real_0 & real_$truncate(real_0) = real_0 &
% 12.55/2.61 real_$round(real_0) = real_0 & real_$to_int(real_121/4) = 30 &
% 12.55/2.61 real_$to_int(real_11/2) = 5 & real_$to_int(real_0) = 0 &
% 12.55/2.61 real_$to_rat(real_121/4) = rat_121/4 & real_$to_rat(real_11/2) = rat_11/2 &
% 12.55/2.61 real_$to_rat(real_0) = rat_0 & real_$to_real(real_121/4) = real_121/4 &
% 12.55/2.61 real_$to_real(real_11/2) = real_11/2 & real_$to_real(real_0) = real_0 &
% 12.55/2.61 int_$to_real(0) = real_0 & real_$quotient(real_121/4, real_11/2) = real_11/2 &
% 12.55/2.61 real_$quotient(real_0, real_121/4) = real_0 & real_$quotient(real_0,
% 12.55/2.61 real_11/2) = real_0 & real_$difference(real_121/4, real_121/4) = real_0 &
% 12.55/2.61 real_$difference(real_121/4, real_0) = real_121/4 &
% 12.55/2.61 real_$difference(real_11/2, real_11/2) = real_0 & real_$difference(real_11/2,
% 12.55/2.61 real_0) = real_11/2 & real_$difference(real_0, real_0) = real_0 &
% 12.55/2.61 real_$uminus(real_0) = real_0 & real_$sum(real_121/4, real_0) = real_121/4 &
% 12.55/2.61 real_$sum(real_11/2, real_0) = real_11/2 & real_$sum(real_0, real_121/4) =
% 12.55/2.61 real_121/4 & real_$sum(real_0, real_11/2) = real_11/2 & real_$sum(real_0,
% 12.55/2.62 real_0) = real_0 & real_$greatereq(real_very_small, real_very_large) = 1 &
% 12.55/2.62 real_$greatereq(real_121/4, real_121/4) = 0 & real_$greatereq(real_121/4,
% 12.55/2.62 real_11/2) = 0 & real_$greatereq(real_121/4, real_0) = 0 &
% 12.55/2.62 real_$greatereq(real_11/2, real_121/4) = 1 & real_$greatereq(real_11/2,
% 12.55/2.62 real_11/2) = 0 & real_$greatereq(real_11/2, real_0) = 0 &
% 12.55/2.62 real_$greatereq(real_0, real_121/4) = 1 & real_$greatereq(real_0, real_11/2) =
% 12.55/2.62 1 & real_$greatereq(real_0, real_0) = 0 & real_$lesseq(real_very_small,
% 12.55/2.62 real_very_large) = 0 & real_$lesseq(real_121/4, real_121/4) = 0 &
% 12.55/2.62 real_$lesseq(real_121/4, real_11/2) = 1 & real_$lesseq(real_121/4, real_0) = 1
% 12.55/2.62 & real_$lesseq(real_11/2, real_121/4) = 0 & real_$lesseq(real_11/2, real_11/2)
% 12.55/2.62 = 0 & real_$lesseq(real_11/2, real_0) = 1 & real_$lesseq(real_0, real_121/4) =
% 12.55/2.62 0 & real_$lesseq(real_0, real_11/2) = 0 & real_$lesseq(real_0, real_0) = 0 &
% 12.55/2.62 real_$greater(real_very_large, real_121/4) = 0 &
% 12.55/2.62 real_$greater(real_very_large, real_11/2) = 0 & real_$greater(real_very_large,
% 12.55/2.62 real_0) = 0 & real_$greater(real_very_small, real_very_large) = 1 &
% 12.55/2.62 real_$greater(real_121/4, real_very_small) = 0 & real_$greater(real_121/4,
% 12.55/2.62 real_121/4) = 1 & real_$greater(real_121/4, real_11/2) = 0 &
% 12.55/2.62 real_$greater(real_121/4, real_0) = 0 & real_$greater(real_11/2,
% 12.55/2.62 real_very_small) = 0 & real_$greater(real_11/2, real_121/4) = 1 &
% 12.55/2.62 real_$greater(real_11/2, real_11/2) = 1 & real_$greater(real_11/2, real_0) = 0
% 12.55/2.62 & real_$greater(real_0, real_very_small) = 0 & real_$greater(real_0,
% 12.55/2.62 real_121/4) = 1 & real_$greater(real_0, real_11/2) = 1 &
% 12.55/2.62 real_$greater(real_0, real_0) = 1 & real_$less(real_very_small,
% 12.55/2.62 real_very_large) = 0 & real_$less(real_very_small, real_121/4) = 0 &
% 12.55/2.62 real_$less(real_very_small, real_11/2) = 0 & real_$less(real_very_small,
% 12.55/2.62 real_0) = 0 & real_$less(real_121/4, real_very_large) = 0 &
% 12.55/2.62 real_$less(real_121/4, real_121/4) = 1 & real_$less(real_121/4, real_11/2) = 1
% 12.55/2.62 & real_$less(real_121/4, real_0) = 1 & real_$less(real_11/2, real_very_large)
% 12.55/2.62 = 0 & real_$less(real_11/2, real_121/4) = 0 & real_$less(real_11/2, real_11/2)
% 12.55/2.62 = 1 & real_$less(real_11/2, real_0) = 1 & real_$less(real_0, real_very_large)
% 12.55/2.62 = 0 & real_$less(real_0, real_121/4) = 0 & real_$less(real_0, real_11/2) = 0 &
% 12.55/2.62 real_$less(real_0, real_0) = 1 & real_$product(real_121/4, real_0) = real_0 &
% 12.55/2.62 real_$product(real_11/2, real_11/2) = real_121/4 & real_$product(real_11/2,
% 12.55/2.62 real_0) = real_0 & real_$product(real_0, real_121/4) = real_0 &
% 12.55/2.62 real_$product(real_0, real_11/2) = real_0 & real_$product(real_0, real_0) =
% 12.55/2.62 real_0 & ! [v0: $real] : ! [v1: $real] : ! [v2: $real] : ! [v3: $real] :
% 12.55/2.62 ! [v4: $real] : ( ~ (real_$sum(v3, v0) = v4) | ~ (real_$sum(v2, v1) = v3) |
% 12.55/2.62 ? [v5: $real] : (real_$sum(v2, v5) = v4 & real_$sum(v1, v0) = v5)) & ! [v0:
% 12.55/2.62 $real] : ! [v1: $real] : ! [v2: $real] : ! [v3: $real] : (v3 = v1 | v0 =
% 12.55/2.62 real_0 | ~ (real_$quotient(v2, v0) = v3) | ~ (real_$product(v1, v0) = v2))
% 12.55/2.62 & ! [v0: $real] : ! [v1: $real] : ! [v2: $real] : ! [v3: int] : (v3 = 0 |
% 12.55/2.62 ~ (real_$lesseq(v2, v0) = v3) | ~ (real_$lesseq(v1, v0) = 0) | ? [v4: int]
% 12.55/2.62 : ( ~ (v4 = 0) & real_$lesseq(v2, v1) = v4)) & ! [v0: $real] : ! [v1:
% 12.55/2.62 $real] : ! [v2: $real] : ! [v3: int] : (v3 = 0 | ~ (real_$lesseq(v1, v0)
% 12.55/2.62 = 0) | ~ (real_$less(v2, v0) = v3) | ? [v4: int] : ( ~ (v4 = 0) &
% 12.55/2.62 real_$less(v2, v1) = v4)) & ! [v0: $real] : ! [v1: $real] : ! [v2:
% 12.55/2.62 $real] : ! [v3: $real] : ( ~ (real_$uminus(v0) = v2) | ~ (real_$sum(v1,
% 12.55/2.62 v2) = v3) | real_$difference(v1, v0) = v3) & ! [v0: $real] : ! [v1:
% 12.55/2.62 $real] : ! [v2: $real] : (v2 = real_0 | ~ (real_$uminus(v0) = v1) | ~
% 12.55/2.62 (real_$sum(v0, v1) = v2)) & ! [v0: $real] : ! [v1: $real] : ! [v2: int] :
% 12.55/2.62 (v2 = 0 | ~ (real_$greatereq(v0, v1) = v2) | ? [v3: int] : ( ~ (v3 = 0) &
% 12.55/2.62 real_$lesseq(v1, v0) = v3)) & ! [v0: $real] : ! [v1: $real] : ! [v2:
% 12.55/2.62 int] : (v2 = 0 | ~ (real_$lesseq(v1, v0) = v2) | ( ~ (v1 = v0) & ? [v3:
% 12.55/2.62 int] : ( ~ (v3 = 0) & real_$less(v1, v0) = v3))) & ! [v0: $real] : !
% 12.55/2.62 [v1: $real] : ! [v2: int] : (v2 = 0 | ~ (real_$greater(v0, v1) = v2) | ?
% 12.55/2.62 [v3: int] : ( ~ (v3 = 0) & real_$less(v1, v0) = v3)) & ! [v0: $real] : !
% 12.55/2.62 [v1: $real] : ! [v2: $real] : ( ~ (real_$sum(v0, v1) = v2) | real_$sum(v1,
% 12.55/2.62 v0) = v2) & ! [v0: $real] : ! [v1: $real] : ! [v2: $real] : ( ~
% 12.55/2.62 (real_$lesseq(v2, v1) = 0) | ~ (real_$less(v1, v0) = 0) | real_$less(v2,
% 12.55/2.62 v0) = 0) & ! [v0: $real] : ! [v1: $real] : ! [v2: $real] : ( ~
% 12.55/2.62 (real_$product(v0, v1) = v2) | real_$product(v1, v0) = v2) & ! [v0: $real]
% 12.55/2.62 : ! [v1: $real] : (v1 = v0 | ~ (real_$sum(v0, real_0) = v1)) & ! [v0:
% 12.55/2.62 $real] : ! [v1: $real] : (v1 = v0 | ~ (real_$lesseq(v1, v0) = 0) |
% 12.55/2.62 real_$less(v1, v0) = 0) & ! [v0: $real] : ! [v1: $real] : ( ~
% 12.55/2.62 (real_$uminus(v0) = v1) | real_$uminus(v1) = v0) & ! [v0: $real] : ! [v1:
% 12.55/2.62 $real] : ( ~ (real_$greatereq(v0, v1) = 0) | real_$lesseq(v1, v0) = 0) & !
% 12.55/2.62 [v0: $real] : ! [v1: $real] : ( ~ (real_$greater(v0, v1) = 0) |
% 12.55/2.62 real_$less(v1, v0) = 0) & ! [v0: $real] : (v0 = real_0 | ~
% 12.55/2.62 (real_$uminus(v0) = v0))
% 12.55/2.62
% 12.55/2.62 Those formulas are unsatisfiable:
% 12.55/2.62 ---------------------------------
% 12.55/2.62
% 12.55/2.62 Begin of proof
% 12.55/2.62 |
% 12.55/2.62 | ALPHA: (input) implies:
% 12.55/2.63 | (1) real_$product(real_11/2, real_11/2) = real_121/4
% 12.55/2.63 |
% 12.55/2.63 | GROUND_INST: instantiating (real_product_problem_10) with real_11/2,
% 12.55/2.63 | simplifying with (1) gives:
% 12.55/2.63 | (2) $false
% 12.55/2.63 |
% 12.55/2.63 | CLOSE: (2) is inconsistent.
% 12.55/2.63 |
% 12.55/2.63 End of proof
% 12.55/2.63 % SZS output end Proof for theBenchmark
% 12.55/2.63
% 12.55/2.63 2012ms
%------------------------------------------------------------------------------