TSTP Solution File: ARI739_1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : ARI739_1 : TPTP v8.1.2. Released v7.0.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n020.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 17:48:58 EDT 2023
% Result : Theorem 11.26s 2.19s
% Output : Proof 12.71s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : ARI739_1 : TPTP v8.1.2. Released v7.0.0.
% 0.07/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.34 % Computer : n020.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
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Tue Aug 29 18:22:13 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.61/0.62 ________ _____
% 0.61/0.62 ___ __ \_________(_)________________________________
% 0.61/0.62 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.61/0.62 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.61/0.62 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.61/0.62
% 0.61/0.62 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.61/0.62 (2023-06-19)
% 0.61/0.62
% 0.61/0.62 (c) Philipp Rümmer, 2009-2023
% 0.61/0.62 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.61/0.62 Amanda Stjerna.
% 0.61/0.62 Free software under BSD-3-Clause.
% 0.61/0.62
% 0.61/0.62 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.61/0.62
% 0.61/0.62 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.61/0.63 Running up to 7 provers in parallel.
% 0.61/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.61/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.61/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.61/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.61/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.61/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.61/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 1.54/0.89 Prover 2: Warning: Problem contains reals, using incomplete axiomatisation
% 1.54/0.89 Prover 5: Warning: Problem contains reals, using incomplete axiomatisation
% 1.54/0.89 Prover 6: Warning: Problem contains reals, using incomplete axiomatisation
% 1.54/0.89 Prover 0: Warning: Problem contains reals, using incomplete axiomatisation
% 1.54/0.89 Prover 3: Warning: Problem contains reals, using incomplete axiomatisation
% 1.54/0.89 Prover 4: Warning: Problem contains reals, using incomplete axiomatisation
% 1.54/0.89 Prover 1: Warning: Problem contains reals, using incomplete axiomatisation
% 2.44/1.04 Prover 4: Preprocessing ...
% 2.44/1.04 Prover 1: Preprocessing ...
% 3.01/1.11 Prover 0: Preprocessing ...
% 3.01/1.11 Prover 6: Preprocessing ...
% 3.71/1.18 Prover 2: Preprocessing ...
% 3.71/1.18 Prover 5: Preprocessing ...
% 3.71/1.18 Prover 3: Preprocessing ...
% 6.75/1.63 Prover 6: Constructing countermodel ...
% 6.75/1.64 Prover 1: Constructing countermodel ...
% 7.37/1.67 Prover 4: Constructing countermodel ...
% 7.85/1.76 Prover 0: Proving ...
% 10.48/2.13 Prover 2: Proving ...
% 11.26/2.18 Prover 6: proved (1536ms)
% 11.26/2.18
% 11.26/2.19 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 11.26/2.19
% 11.26/2.19 Prover 0: stopped
% 11.26/2.19 Prover 1: Found proof (size 7)
% 11.26/2.19 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 11.26/2.19 Prover 1: proved (1549ms)
% 11.26/2.19 Prover 4: stopped
% 11.26/2.19 Prover 7: Warning: Problem contains reals, using incomplete axiomatisation
% 11.26/2.19 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 11.26/2.19 Prover 2: stopped
% 11.26/2.19 Prover 8: Warning: Problem contains reals, using incomplete axiomatisation
% 11.26/2.20 Prover 3: Constructing countermodel ...
% 11.26/2.20 Prover 3: stopped
% 11.26/2.21 Prover 8: Preprocessing ...
% 11.62/2.24 Prover 7: Preprocessing ...
% 11.78/2.30 Prover 8: Warning: ignoring some quantifiers
% 11.78/2.31 Prover 8: Constructing countermodel ...
% 11.78/2.32 Prover 8: stopped
% 12.27/2.35 Prover 7: stopped
% 12.27/2.39 Prover 5: Proving ...
% 12.27/2.39 Prover 5: stopped
% 12.27/2.39
% 12.27/2.39 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 12.27/2.39
% 12.27/2.39 % SZS output start Proof for theBenchmark
% 12.27/2.40 Assumptions after simplification:
% 12.27/2.40 ---------------------------------
% 12.27/2.40
% 12.27/2.40 (log_e)
% 12.71/2.44 ? [v0: $real] : ? [v1: $real] : ( ~ (v1 = real_1) & log(v0) = v1 &
% 12.71/2.44 exp(real_1) = v0)
% 12.71/2.44
% 12.71/2.44 (log_exp)
% 12.71/2.44 ! [v0: $real] : ! [v1: $real] : ( ~ (exp(v0) = v1) | log(v1) = v0)
% 12.71/2.44
% 12.71/2.44 (function-axioms)
% 12.71/2.46 ! [v0: $real] : ! [v1: $real] : ! [v2: $real] : ! [v3: $real] : (v1 = v0 |
% 12.71/2.46 ~ (real_$difference(v3, v2) = v1) | ~ (real_$difference(v3, v2) = v0)) &
% 12.71/2.46 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $real] : !
% 12.71/2.46 [v3: $real] : (v1 = v0 | ~ (real_$greatereq(v3, v2) = v1) | ~
% 12.71/2.46 (real_$greatereq(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 12.71/2.46 MultipleValueBool] : ! [v2: $real] : ! [v3: $real] : (v1 = v0 | ~
% 12.71/2.46 (real_$lesseq(v3, v2) = v1) | ~ (real_$lesseq(v3, v2) = v0)) & ! [v0:
% 12.71/2.46 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $real] : ! [v3:
% 12.71/2.46 $real] : (v1 = v0 | ~ (real_$greater(v3, v2) = v1) | ~ (real_$greater(v3,
% 12.71/2.46 v2) = v0)) & ! [v0: $real] : ! [v1: $real] : ! [v2: $real] : ! [v3:
% 12.71/2.46 $real] : (v1 = v0 | ~ (real_$quotient(v3, v2) = v1) | ~
% 12.71/2.46 (real_$quotient(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 12.71/2.46 MultipleValueBool] : ! [v2: $real] : ! [v3: $real] : (v1 = v0 | ~
% 12.71/2.46 (real_$less(v3, v2) = v1) | ~ (real_$less(v3, v2) = v0)) & ! [v0: $real] :
% 12.71/2.46 ! [v1: $real] : ! [v2: $real] : ! [v3: $real] : (v1 = v0 | ~
% 12.71/2.46 (real_$product(v3, v2) = v1) | ~ (real_$product(v3, v2) = v0)) & ! [v0:
% 12.71/2.46 $real] : ! [v1: $real] : ! [v2: $real] : ! [v3: $real] : (v1 = v0 | ~
% 12.71/2.46 (real_$sum(v3, v2) = v1) | ~ (real_$sum(v3, v2) = v0)) & ! [v0:
% 12.71/2.46 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $real] : (v1 = v0
% 12.71/2.46 | ~ (real_$is_int(v2) = v1) | ~ (real_$is_int(v2) = v0)) & ! [v0:
% 12.71/2.46 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $real] : (v1 = v0
% 12.71/2.46 | ~ (real_$is_rat(v2) = v1) | ~ (real_$is_rat(v2) = v0)) & ! [v0: $real]
% 12.71/2.46 : ! [v1: $real] : ! [v2: $real] : (v1 = v0 | ~ (real_$floor(v2) = v1) | ~
% 12.71/2.46 (real_$floor(v2) = v0)) & ! [v0: $real] : ! [v1: $real] : ! [v2: $real] :
% 12.71/2.46 (v1 = v0 | ~ (real_$ceiling(v2) = v1) | ~ (real_$ceiling(v2) = v0)) & !
% 12.71/2.46 [v0: $real] : ! [v1: $real] : ! [v2: $real] : (v1 = v0 | ~
% 12.71/2.46 (real_$truncate(v2) = v1) | ~ (real_$truncate(v2) = v0)) & ! [v0: $real] :
% 12.71/2.46 ! [v1: $real] : ! [v2: $real] : (v1 = v0 | ~ (real_$round(v2) = v1) | ~
% 12.71/2.46 (real_$round(v2) = v0)) & ! [v0: int] : ! [v1: int] : ! [v2: $real] : (v1
% 12.71/2.46 = v0 | ~ (real_$to_int(v2) = v1) | ~ (real_$to_int(v2) = v0)) & ! [v0:
% 12.71/2.46 $rat] : ! [v1: $rat] : ! [v2: $real] : (v1 = v0 | ~ (real_$to_rat(v2) =
% 12.71/2.46 v1) | ~ (real_$to_rat(v2) = v0)) & ! [v0: $real] : ! [v1: $real] : !
% 12.71/2.46 [v2: $real] : (v1 = v0 | ~ (real_$to_real(v2) = v1) | ~ (real_$to_real(v2) =
% 12.71/2.46 v0)) & ! [v0: $real] : ! [v1: $real] : ! [v2: int] : (v1 = v0 | ~
% 12.71/2.46 (int_$to_real(v2) = v1) | ~ (int_$to_real(v2) = v0)) & ! [v0: $real] : !
% 12.71/2.46 [v1: $real] : ! [v2: $real] : (v1 = v0 | ~ (real_$uminus(v2) = v1) | ~
% 12.71/2.46 (real_$uminus(v2) = v0)) & ! [v0: $real] : ! [v1: $real] : ! [v2: $real]
% 12.71/2.46 : (v1 = v0 | ~ (log10(v2) = v1) | ~ (log10(v2) = v0)) & ! [v0: $real] : !
% 12.71/2.46 [v1: $real] : ! [v2: $real] : (v1 = v0 | ~ (log2(v2) = v1) | ~ (log2(v2) =
% 12.71/2.46 v0)) & ! [v0: $real] : ! [v1: $real] : ! [v2: $real] : (v1 = v0 | ~
% 12.71/2.46 (log(v2) = v1) | ~ (log(v2) = v0)) & ! [v0: $real] : ! [v1: $real] : !
% 12.71/2.46 [v2: $real] : (v1 = v0 | ~ (exp(v2) = v1) | ~ (exp(v2) = v0))
% 12.71/2.46
% 12.71/2.46 Further assumptions not needed in the proof:
% 12.71/2.46 --------------------------------------------
% 12.71/2.46 exp_log, exp_sum, exp_zero, log10_def, log2_def, log_mul, log_one
% 12.71/2.46
% 12.71/2.46 Those formulas are unsatisfiable:
% 12.71/2.46 ---------------------------------
% 12.71/2.46
% 12.71/2.46 Begin of proof
% 12.71/2.46 |
% 12.71/2.46 | ALPHA: (function-axioms) implies:
% 12.71/2.46 | (1) ! [v0: $real] : ! [v1: $real] : ! [v2: $real] : (v1 = v0 | ~
% 12.71/2.46 | (log(v2) = v1) | ~ (log(v2) = v0))
% 12.71/2.46 |
% 12.71/2.46 | DELTA: instantiating (log_e) with fresh symbols all_9_0, all_9_1 gives:
% 12.71/2.46 | (2) ~ (all_9_0 = real_1) & log(all_9_1) = all_9_0 & exp(real_1) = all_9_1
% 12.71/2.46 |
% 12.71/2.46 | ALPHA: (2) implies:
% 12.71/2.47 | (3) ~ (all_9_0 = real_1)
% 12.71/2.47 | (4) exp(real_1) = all_9_1
% 12.71/2.47 | (5) log(all_9_1) = all_9_0
% 12.71/2.47 |
% 12.71/2.47 | GROUND_INST: instantiating (log_exp) with real_1, all_9_1, simplifying with
% 12.71/2.47 | (4) gives:
% 12.71/2.47 | (6) log(all_9_1) = real_1
% 12.71/2.47 |
% 12.71/2.47 | GROUND_INST: instantiating (1) with all_9_0, real_1, all_9_1, simplifying with
% 12.71/2.47 | (5), (6) gives:
% 12.71/2.47 | (7) all_9_0 = real_1
% 12.71/2.47 |
% 12.71/2.47 | REDUCE: (3), (7) imply:
% 12.71/2.47 | (8) $false
% 12.71/2.47 |
% 12.71/2.47 | CLOSE: (8) is inconsistent.
% 12.71/2.47 |
% 12.71/2.47 End of proof
% 12.71/2.47 % SZS output end Proof for theBenchmark
% 12.71/2.47
% 12.71/2.47 1849ms
%------------------------------------------------------------------------------