TSTP Solution File: NUM914_1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : NUM914_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 : n018.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 11:50:41 EDT 2023
% Result : Theorem 6.77s 1.66s
% Output : Proof 7.80s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM914_1 : TPTP v8.1.2. Released v5.0.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.12/0.34 % Computer : n018.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Fri Aug 25 17:54:29 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.20/0.61 ________ _____
% 0.20/0.61 ___ __ \_________(_)________________________________
% 0.20/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.20/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.20/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.20/0.61
% 0.20/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.20/0.61 (2023-06-19)
% 0.20/0.61
% 0.20/0.61 (c) Philipp Rümmer, 2009-2023
% 0.20/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.20/0.61 Amanda Stjerna.
% 0.20/0.61 Free software under BSD-3-Clause.
% 0.20/0.61
% 0.20/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.20/0.61
% 0.20/0.61 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.20/0.62 Running up to 7 provers in parallel.
% 0.20/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.20/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.20/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.20/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.20/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.20/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.20/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 1.74/0.92 Prover 4: Warning: Problem contains reals, using incomplete axiomatisation
% 1.74/0.92 Prover 1: Warning: Problem contains reals, using incomplete axiomatisation
% 1.74/0.92 Prover 5: Warning: Problem contains reals, using incomplete axiomatisation
% 1.74/0.92 Prover 2: Warning: Problem contains reals, using incomplete axiomatisation
% 1.74/0.92 Prover 0: Warning: Problem contains reals, using incomplete axiomatisation
% 1.74/0.92 Prover 3: Warning: Problem contains reals, using incomplete axiomatisation
% 1.74/0.93 Prover 6: Warning: Problem contains reals, using incomplete axiomatisation
% 2.05/1.01 Prover 4: Preprocessing ...
% 2.05/1.01 Prover 1: Preprocessing ...
% 2.53/1.06 Prover 6: Preprocessing ...
% 2.53/1.06 Prover 5: Preprocessing ...
% 2.53/1.06 Prover 3: Preprocessing ...
% 2.53/1.06 Prover 2: Preprocessing ...
% 2.53/1.06 Prover 0: Preprocessing ...
% 4.87/1.47 Prover 1: Constructing countermodel ...
% 4.87/1.49 Prover 5: Proving ...
% 4.87/1.49 Prover 3: Constructing countermodel ...
% 4.87/1.49 Prover 6: Proving ...
% 4.87/1.55 Prover 2: Proving ...
% 4.87/1.56 Prover 4: Constructing countermodel ...
% 5.30/1.58 Prover 0: Proving ...
% 6.77/1.66 Prover 3: proved (1030ms)
% 6.77/1.66
% 6.77/1.66 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.77/1.66
% 6.77/1.66 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 6.77/1.66 Prover 0: stopped
% 6.77/1.66 Prover 2: stopped
% 6.77/1.66 Prover 6: stopped
% 6.77/1.67 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 6.77/1.67 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 6.77/1.67 Prover 7: Warning: Problem contains reals, using incomplete axiomatisation
% 6.77/1.67 Prover 5: stopped
% 6.89/1.67 Prover 10: Warning: Problem contains reals, using incomplete axiomatisation
% 6.89/1.67 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 6.89/1.67 Prover 8: Warning: Problem contains reals, using incomplete axiomatisation
% 6.89/1.68 Prover 11: Warning: Problem contains reals, using incomplete axiomatisation
% 6.89/1.68 Prover 7: Preprocessing ...
% 6.89/1.68 Prover 10: Preprocessing ...
% 6.89/1.68 Prover 8: Preprocessing ...
% 6.89/1.68 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 6.89/1.69 Prover 13: Warning: Problem contains reals, using incomplete axiomatisation
% 6.89/1.69 Prover 11: Preprocessing ...
% 6.89/1.69 Prover 1: Found proof (size 8)
% 6.89/1.69 Prover 1: proved (1065ms)
% 6.89/1.69 Prover 4: stopped
% 6.89/1.69 Prover 13: Preprocessing ...
% 6.89/1.71 Prover 10: stopped
% 6.89/1.71 Prover 7: stopped
% 7.21/1.73 Prover 13: stopped
% 7.21/1.73 Prover 11: stopped
% 7.39/1.76 Prover 8: Warning: ignoring some quantifiers
% 7.39/1.77 Prover 8: Constructing countermodel ...
% 7.39/1.78 Prover 8: stopped
% 7.39/1.78
% 7.39/1.78 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 7.39/1.78
% 7.39/1.78 % SZS output start Proof for theBenchmark
% 7.39/1.78 Assumptions after simplification:
% 7.39/1.78 ---------------------------------
% 7.39/1.78
% 7.39/1.78 (real_combined_problem_2)
% 7.39/1.81 ! [v0: $real] : ! [v1: $real] : ! [v2: $real] : ! [v3: $real] : ! [v4:
% 7.39/1.81 $real] : ( ~ (real_$difference(v2, v1) = v3) | ~ (real_$difference(v2, v0)
% 7.39/1.81 = v4) | real_$sum(v0, v1) = v2 | (v4 = v1 & v3 = v0)) & ! [v0: $real] :
% 7.39/1.81 ! [v1: $real] : ! [v2: $real] : ( ~ (real_$difference(v2, v1) = v0) | ~
% 7.39/1.81 (real_$difference(v2, v0) = v1) | ? [v3: $real] : ( ~ (v3 = v2) &
% 7.39/1.81 real_$sum(v0, v1) = v3))
% 7.39/1.81
% 7.39/1.81 (input)
% 7.80/1.83 ~ (real_very_large = real_very_small) & ~ (real_very_large = real_0) & ~
% 7.80/1.83 (real_very_small = real_0) & real_$is_int(real_0) = 0 & real_$is_rat(real_0) =
% 7.80/1.83 0 & real_$floor(real_0) = real_0 & real_$ceiling(real_0) = real_0 &
% 7.80/1.83 real_$truncate(real_0) = real_0 & real_$round(real_0) = real_0 &
% 7.80/1.83 real_$to_int(real_0) = 0 & real_$to_rat(real_0) = rat_0 &
% 7.80/1.83 real_$to_real(real_0) = real_0 & int_$to_real(0) = real_0 &
% 7.80/1.83 real_$product(real_0, real_0) = real_0 & real_$uminus(real_0) = real_0 &
% 7.80/1.83 real_$greatereq(real_very_small, real_very_large) = 1 &
% 7.80/1.83 real_$greatereq(real_0, real_0) = 0 & real_$lesseq(real_very_small,
% 7.80/1.83 real_very_large) = 0 & real_$lesseq(real_0, real_0) = 0 &
% 7.80/1.83 real_$greater(real_very_large, real_0) = 0 & real_$greater(real_very_small,
% 7.80/1.83 real_very_large) = 1 & real_$greater(real_0, real_very_small) = 0 &
% 7.80/1.83 real_$greater(real_0, real_0) = 1 & real_$less(real_very_small,
% 7.80/1.83 real_very_large) = 0 & real_$less(real_very_small, real_0) = 0 &
% 7.80/1.83 real_$less(real_0, real_very_large) = 0 & real_$less(real_0, real_0) = 1 &
% 7.80/1.83 real_$difference(real_0, real_0) = real_0 & real_$sum(real_0, real_0) = real_0
% 7.80/1.83 & ! [v0: $real] : ! [v1: $real] : ! [v2: $real] : ! [v3: $real] : ! [v4:
% 7.80/1.83 $real] : ( ~ (real_$sum(v3, v0) = v4) | ~ (real_$sum(v2, v1) = v3) | ?
% 7.80/1.83 [v5: $real] : (real_$sum(v2, v5) = v4 & real_$sum(v1, v0) = v5)) & ! [v0:
% 7.80/1.83 $real] : ! [v1: $real] : ! [v2: $real] : ! [v3: $real] : (v3 = v1 | v0 =
% 7.80/1.83 real_0 | ~ (real_$quotient(v2, v0) = v3) | ~ (real_$product(v1, v0) = v2))
% 7.80/1.83 & ! [v0: $real] : ! [v1: $real] : ! [v2: $real] : ! [v3: int] : (v3 = 0 |
% 7.80/1.83 ~ (real_$lesseq(v2, v0) = v3) | ~ (real_$lesseq(v1, v0) = 0) | ? [v4: int]
% 7.80/1.83 : ( ~ (v4 = 0) & real_$lesseq(v2, v1) = v4)) & ! [v0: $real] : ! [v1:
% 7.80/1.83 $real] : ! [v2: $real] : ! [v3: int] : (v3 = 0 | ~ (real_$lesseq(v1, v0)
% 7.80/1.83 = 0) | ~ (real_$less(v2, v0) = v3) | ? [v4: int] : ( ~ (v4 = 0) &
% 7.80/1.83 real_$less(v2, v1) = v4)) & ! [v0: $real] : ! [v1: $real] : ! [v2:
% 7.80/1.83 $real] : ! [v3: $real] : ( ~ (real_$uminus(v0) = v2) | ~ (real_$sum(v1,
% 7.80/1.83 v2) = v3) | real_$difference(v1, v0) = v3) & ! [v0: $real] : ! [v1:
% 7.80/1.83 $real] : ! [v2: $real] : (v2 = real_0 | ~ (real_$uminus(v0) = v1) | ~
% 7.80/1.83 (real_$sum(v0, v1) = v2)) & ! [v0: $real] : ! [v1: $real] : ! [v2: int] :
% 7.80/1.83 (v2 = 0 | ~ (real_$greatereq(v0, v1) = v2) | ? [v3: int] : ( ~ (v3 = 0) &
% 7.80/1.83 real_$lesseq(v1, v0) = v3)) & ! [v0: $real] : ! [v1: $real] : ! [v2:
% 7.80/1.83 int] : (v2 = 0 | ~ (real_$lesseq(v1, v0) = v2) | ( ~ (v1 = v0) & ? [v3:
% 7.80/1.83 int] : ( ~ (v3 = 0) & real_$less(v1, v0) = v3))) & ! [v0: $real] : !
% 7.80/1.83 [v1: $real] : ! [v2: int] : (v2 = 0 | ~ (real_$greater(v0, v1) = v2) | ?
% 7.80/1.83 [v3: int] : ( ~ (v3 = 0) & real_$less(v1, v0) = v3)) & ! [v0: $real] : !
% 7.80/1.83 [v1: $real] : ! [v2: $real] : ( ~ (real_$product(v0, v1) = v2) |
% 7.80/1.83 real_$product(v1, v0) = v2) & ! [v0: $real] : ! [v1: $real] : ! [v2:
% 7.80/1.83 $real] : ( ~ (real_$lesseq(v2, v1) = 0) | ~ (real_$less(v1, v0) = 0) |
% 7.80/1.83 real_$less(v2, v0) = 0) & ! [v0: $real] : ! [v1: $real] : ! [v2: $real] :
% 7.80/1.83 ( ~ (real_$sum(v0, v1) = v2) | real_$sum(v1, v0) = v2) & ! [v0: $real] : !
% 7.80/1.83 [v1: $real] : (v1 = v0 | ~ (real_$lesseq(v1, v0) = 0) | real_$less(v1, v0) =
% 7.80/1.83 0) & ! [v0: $real] : ! [v1: $real] : (v1 = v0 | ~ (real_$sum(v0, real_0)
% 7.80/1.83 = v1)) & ! [v0: $real] : ! [v1: $real] : ( ~ (real_$uminus(v0) = v1) |
% 7.80/1.83 real_$uminus(v1) = v0) & ! [v0: $real] : ! [v1: $real] : ( ~
% 7.80/1.83 (real_$greatereq(v0, v1) = 0) | real_$lesseq(v1, v0) = 0) & ! [v0: $real] :
% 7.80/1.83 ! [v1: $real] : ( ~ (real_$greater(v0, v1) = 0) | real_$less(v1, v0) = 0) &
% 7.80/1.83 ! [v0: $real] : (v0 = real_0 | ~ (real_$uminus(v0) = v0))
% 7.80/1.83
% 7.80/1.83 Those formulas are unsatisfiable:
% 7.80/1.83 ---------------------------------
% 7.80/1.83
% 7.80/1.83 Begin of proof
% 7.80/1.83 |
% 7.80/1.83 | ALPHA: (real_combined_problem_2) implies:
% 7.80/1.84 | (1) ! [v0: $real] : ! [v1: $real] : ! [v2: $real] : ( ~
% 7.80/1.84 | (real_$difference(v2, v1) = v0) | ~ (real_$difference(v2, v0) = v1)
% 7.80/1.84 | | ? [v3: $real] : ( ~ (v3 = v2) & real_$sum(v0, v1) = v3))
% 7.80/1.84 |
% 7.80/1.84 | ALPHA: (input) implies:
% 7.80/1.84 | (2) real_$difference(real_0, real_0) = real_0
% 7.80/1.84 | (3) ! [v0: $real] : ! [v1: $real] : (v1 = v0 | ~ (real_$sum(v0, real_0)
% 7.80/1.84 | = v1))
% 7.80/1.84 |
% 7.80/1.84 | GROUND_INST: instantiating (1) with real_0, real_0, real_0, simplifying with
% 7.80/1.84 | (2) gives:
% 7.80/1.84 | (4) ? [v0: $real] : ( ~ (v0 = real_0) & real_$sum(real_0, real_0) = v0)
% 7.80/1.84 |
% 7.80/1.84 | DELTA: instantiating (4) with fresh symbol all_15_0 gives:
% 7.80/1.84 | (5) ~ (all_15_0 = real_0) & real_$sum(real_0, real_0) = all_15_0
% 7.80/1.84 |
% 7.80/1.84 | ALPHA: (5) implies:
% 7.80/1.84 | (6) ~ (all_15_0 = real_0)
% 7.80/1.84 | (7) real_$sum(real_0, real_0) = all_15_0
% 7.80/1.84 |
% 7.80/1.84 | GROUND_INST: instantiating (3) with real_0, all_15_0, simplifying with (7)
% 7.80/1.84 | gives:
% 7.80/1.84 | (8) all_15_0 = real_0
% 7.80/1.84 |
% 7.80/1.84 | REDUCE: (6), (8) imply:
% 7.80/1.84 | (9) $false
% 7.80/1.84 |
% 7.80/1.84 | CLOSE: (9) is inconsistent.
% 7.80/1.84 |
% 7.80/1.84 End of proof
% 7.80/1.84 % SZS output end Proof for theBenchmark
% 7.80/1.84
% 7.80/1.84 1236ms
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