%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : ARI357_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 17:47:45 EDT 2023 % Result : Theorem 9.62s 2.08s % Output : Proof 10.03s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.05/0.10 % Problem : ARI357_1 : TPTP v8.1.2. Released v5.0.0. % 0.05/0.11 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.10/0.31 % Computer : n003.cluster.edu % 0.10/0.31 % Model : x86_64 x86_64 % 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.10/0.31 % Memory : 8042.1875MB % 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64 % 0.10/0.31 % CPULimit : 300 % 0.10/0.31 % WCLimit : 300 % 0.10/0.31 % DateTime : Tue Aug 29 18:18:26 EDT 2023 % 0.10/0.31 % CPUTime : % 0.51/0.59 ________ _____ % 0.51/0.59 ___ __ \_________(_)________________________________ % 0.51/0.59 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.51/0.59 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.51/0.59 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.51/0.59 % 0.51/0.59 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.51/0.59 (2023-06-19) % 0.51/0.59 % 0.51/0.59 (c) Philipp Rümmer, 2009-2023 % 0.51/0.59 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.51/0.59 Amanda Stjerna. % 0.51/0.59 Free software under BSD-3-Clause. % 0.51/0.59 % 0.51/0.59 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.51/0.59 % 0.51/0.59 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.51/0.61 Running up to 7 provers in parallel. % 0.51/0.62 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.51/0.62 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.51/0.62 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.51/0.62 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.51/0.62 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.51/0.62 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.51/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 1.58/0.93 Prover 5: Warning: Problem contains reals, using incomplete axiomatisation % 1.58/0.93 Prover 1: Warning: Problem contains reals, using incomplete axiomatisation % 1.58/0.93 Prover 0: Warning: Problem contains reals, using incomplete axiomatisation % 1.58/0.93 Prover 4: Warning: Problem contains reals, using incomplete axiomatisation % 1.58/0.93 Prover 2: Warning: Problem contains reals, using incomplete axiomatisation % 1.58/0.93 Prover 3: Warning: Problem contains reals, using incomplete axiomatisation % 1.58/0.93 Prover 6: Warning: Problem contains reals, using incomplete axiomatisation % 2.04/1.04 Prover 1: Preprocessing ... % 2.04/1.05 Prover 4: Preprocessing ... % 2.52/1.10 Prover 0: Preprocessing ... % 2.52/1.10 Prover 3: Preprocessing ... % 2.52/1.10 Prover 2: Preprocessing ... % 2.52/1.10 Prover 5: Preprocessing ... % 2.52/1.10 Prover 6: Preprocessing ... % 7.15/1.73 Prover 1: Constructing countermodel ... % 7.15/1.78 Prover 6: Proving ... % 7.83/1.82 Prover 4: Constructing countermodel ... % 7.83/1.89 Prover 3: Constructing countermodel ... % 7.83/1.91 Prover 2: Proving ... % 7.83/1.93 Prover 0: Proving ... % 8.72/2.00 Prover 5: Proving ... % 9.62/2.07 Prover 4: Found proof (size 3) % 9.62/2.07 Prover 4: proved (1446ms) % 9.62/2.07 Prover 1: Found proof (size 3) % 9.62/2.07 Prover 1: proved (1456ms) % 9.62/2.07 Prover 3: stopped % 9.62/2.07 Prover 5: stopped % 9.62/2.07 Prover 2: stopped % 9.62/2.07 Prover 0: stopped % 9.62/2.08 Prover 6: stopped % 9.62/2.08 % 9.62/2.08 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 9.62/2.08 % 9.62/2.08 % SZS output start Proof for theBenchmark % 9.62/2.08 Assumptions after simplification: % 9.62/2.08 --------------------------------- % 9.62/2.08 % 9.62/2.08 (real_less_problem_13) % 9.87/2.13 ! [v0: $real] : ~ (real_$less(real_-32500, v0) = 0) % 9.87/2.13 % 9.87/2.13 (input) % 10.03/2.18 ~ (real_very_large = real_very_small) & ~ (real_very_large = real_-32500) & % 10.03/2.18 ~ (real_very_large = real_0) & ~ (real_very_small = real_-32500) & ~ % 10.03/2.18 (real_very_small = real_0) & ~ (real_-32500 = real_0) & % 10.03/2.18 real_$is_int(real_-32500) = 0 & real_$is_int(real_0) = 0 & % 10.03/2.18 real_$is_rat(real_-32500) = 0 & real_$is_rat(real_0) = 0 & % 10.03/2.18 real_$floor(real_-32500) = real_-32500 & real_$floor(real_0) = real_0 & % 10.03/2.18 real_$ceiling(real_-32500) = real_-32500 & real_$ceiling(real_0) = real_0 & % 10.03/2.18 real_$truncate(real_-32500) = real_-32500 & real_$truncate(real_0) = real_0 & % 10.03/2.18 real_$round(real_-32500) = real_-32500 & real_$round(real_0) = real_0 & % 10.03/2.18 real_$to_int(real_-32500) = -32500 & real_$to_int(real_0) = 0 & % 10.03/2.18 real_$to_rat(real_-32500) = rat_-32500 & real_$to_rat(real_0) = rat_0 & % 10.03/2.18 real_$to_real(real_-32500) = real_-32500 & real_$to_real(real_0) = real_0 & % 10.03/2.18 int_$to_real(-32500) = real_-32500 & int_$to_real(0) = real_0 & % 10.03/2.18 real_$quotient(real_0, real_-32500) = real_0 & real_$product(real_-32500, % 10.03/2.18 real_0) = real_0 & real_$product(real_0, real_-32500) = real_0 & % 10.03/2.18 real_$product(real_0, real_0) = real_0 & real_$difference(real_-32500, % 10.03/2.18 real_-32500) = real_0 & real_$difference(real_-32500, real_0) = real_-32500 % 10.03/2.18 & real_$difference(real_0, real_0) = real_0 & real_$uminus(real_0) = real_0 & % 10.03/2.18 real_$sum(real_-32500, real_0) = real_-32500 & real_$sum(real_0, real_-32500) % 10.03/2.18 = real_-32500 & real_$sum(real_0, real_0) = real_0 & % 10.03/2.18 real_$greatereq(real_very_small, real_very_large) = 1 & % 10.03/2.18 real_$greatereq(real_-32500, real_-32500) = 0 & real_$greatereq(real_-32500, % 10.03/2.18 real_0) = 1 & real_$greatereq(real_0, real_-32500) = 0 & % 10.03/2.18 real_$greatereq(real_0, real_0) = 0 & real_$lesseq(real_very_small, % 10.03/2.18 real_very_large) = 0 & real_$lesseq(real_-32500, real_-32500) = 0 & % 10.03/2.18 real_$lesseq(real_-32500, real_0) = 0 & real_$lesseq(real_0, real_-32500) = 1 % 10.03/2.18 & real_$lesseq(real_0, real_0) = 0 & real_$greater(real_very_large, % 10.03/2.18 real_-32500) = 0 & real_$greater(real_very_large, real_0) = 0 & % 10.03/2.18 real_$greater(real_very_small, real_very_large) = 1 & % 10.03/2.18 real_$greater(real_-32500, real_very_small) = 0 & real_$greater(real_-32500, % 10.03/2.18 real_-32500) = 1 & real_$greater(real_-32500, real_0) = 1 & % 10.03/2.18 real_$greater(real_0, real_very_small) = 0 & real_$greater(real_0, % 10.03/2.18 real_-32500) = 0 & real_$greater(real_0, real_0) = 1 & % 10.03/2.18 real_$less(real_very_small, real_very_large) = 0 & real_$less(real_very_small, % 10.03/2.18 real_-32500) = 0 & real_$less(real_very_small, real_0) = 0 & % 10.03/2.18 real_$less(real_-32500, real_very_large) = 0 & real_$less(real_-32500, % 10.03/2.18 real_-32500) = 1 & real_$less(real_-32500, real_0) = 0 & real_$less(real_0, % 10.03/2.18 real_very_large) = 0 & real_$less(real_0, real_-32500) = 1 & % 10.03/2.18 real_$less(real_0, real_0) = 1 & ! [v0: $real] : ! [v1: $real] : ! [v2: % 10.03/2.18 $real] : ! [v3: $real] : ! [v4: $real] : ( ~ (real_$sum(v3, v0) = v4) | ~ % 10.03/2.18 (real_$sum(v2, v1) = v3) | ? [v5: $real] : (real_$sum(v2, v5) = v4 & % 10.03/2.18 real_$sum(v1, v0) = v5)) & ! [v0: $real] : ! [v1: $real] : ! [v2: % 10.03/2.18 $real] : ! [v3: $real] : ! [v4: $real] : ( ~ (real_$sum(v2, v3) = v4) | ~ % 10.03/2.18 (real_$sum(v1, v0) = v3) | ? [v5: $real] : (real_$sum(v5, v0) = v4 & % 10.03/2.18 real_$sum(v2, v1) = v5)) & ! [v0: $real] : ! [v1: $real] : ! [v2: % 10.03/2.18 $real] : ! [v3: int] : (v3 = 0 | ~ (real_$lesseq(v2, v1) = 0) | ~ % 10.03/2.18 (real_$lesseq(v2, v0) = v3) | ? [v4: int] : ( ~ (v4 = 0) & real_$lesseq(v1, % 10.03/2.18 v0) = v4)) & ! [v0: $real] : ! [v1: $real] : ! [v2: $real] : ! [v3: % 10.03/2.18 int] : (v3 = 0 | ~ (real_$lesseq(v2, v1) = 0) | ~ (real_$less(v2, v0) = % 10.03/2.18 v3) | ? [v4: int] : ( ~ (v4 = 0) & real_$less(v1, v0) = v4)) & ! [v0: % 10.03/2.18 $real] : ! [v1: $real] : ! [v2: $real] : ! [v3: int] : (v3 = 0 | ~ % 10.03/2.18 (real_$lesseq(v2, v0) = v3) | ~ (real_$lesseq(v1, v0) = 0) | ? [v4: int] : % 10.03/2.18 ( ~ (v4 = 0) & real_$lesseq(v2, v1) = v4)) & ! [v0: $real] : ! [v1: $real] % 10.03/2.18 : ! [v2: $real] : ! [v3: int] : (v3 = 0 | ~ (real_$lesseq(v1, v0) = 0) | ~ % 10.03/2.18 (real_$less(v2, v0) = v3) | ? [v4: int] : ( ~ (v4 = 0) & real_$less(v2, v1) % 10.03/2.18 = v4)) & ! [v0: $real] : ! [v1: $real] : ! [v2: $real] : ! [v3: int] : % 10.03/2.18 (v3 = 0 | ~ (real_$less(v2, v1) = 0) | ~ (real_$less(v2, v0) = v3) | ? [v4: % 10.03/2.18 int] : ( ~ (v4 = 0) & real_$lesseq(v1, v0) = v4)) & ! [v0: $real] : ! % 10.03/2.18 [v1: $real] : ! [v2: $real] : ! [v3: int] : (v3 = 0 | ~ (real_$less(v2, v0) % 10.03/2.18 = v3) | ~ (real_$less(v1, v0) = 0) | ? [v4: int] : ( ~ (v4 = 0) & % 10.03/2.18 real_$lesseq(v2, v1) = v4)) & ! [v0: $real] : ! [v1: $real] : ! [v2: % 10.03/2.18 $real] : ! [v3: $real] : ( ~ (real_$uminus(v0) = v2) | ~ (real_$sum(v1, % 10.03/2.18 v2) = v3) | real_$difference(v1, v0) = v3) & ! [v0: $real] : ! [v1: % 10.03/2.18 $real] : ! [v2: int] : (v2 = 0 | v1 = v0 | ~ (real_$less(v1, v0) = v2) | % 10.03/2.18 ? [v3: int] : ( ~ (v3 = 0) & real_$lesseq(v1, v0) = v3)) & ! [v0: $real] : % 10.03/2.18 ! [v1: $real] : ! [v2: int] : (v2 = 0 | ~ (real_$greatereq(v0, v1) = v2) | % 10.03/2.18 ? [v3: int] : ( ~ (v3 = 0) & real_$lesseq(v1, v0) = v3)) & ! [v0: $real] : % 10.03/2.19 ! [v1: $real] : ! [v2: int] : (v2 = 0 | ~ (real_$lesseq(v1, v0) = v2) | ? % 10.03/2.19 [v3: int] : ( ~ (v3 = 0) & real_$greatereq(v0, v1) = v3)) & ! [v0: $real] : % 10.03/2.19 ! [v1: $real] : ! [v2: int] : (v2 = 0 | ~ (real_$lesseq(v1, v0) = v2) | ? % 10.03/2.19 [v3: int] : ( ~ (v3 = 0) & real_$less(v1, v0) = v3)) & ! [v0: $real] : ! % 10.03/2.19 [v1: $real] : ! [v2: int] : (v2 = 0 | ~ (real_$greater(v0, v1) = v2) | ? % 10.03/2.19 [v3: int] : ( ~ (v3 = 0) & real_$less(v1, v0) = v3)) & ! [v0: $real] : ! % 10.03/2.19 [v1: $real] : ! [v2: int] : (v2 = 0 | ~ (real_$less(v1, v0) = v2) | ? [v3: % 10.03/2.19 int] : ( ~ (v3 = 0) & real_$greater(v0, v1) = v3)) & ! [v0: $real] : ! % 10.03/2.19 [v1: $real] : ! [v2: $real] : (v0 = real_0 | ~ (real_$product(v1, v0) = v2) % 10.03/2.19 | real_$quotient(v2, v0) = v1) & ! [v0: $real] : ! [v1: $real] : ! [v2: % 10.03/2.19 $real] : ( ~ (real_$product(v1, v0) = v2) | real_$product(v0, v1) = v2) & ! % 10.03/2.19 [v0: $real] : ! [v1: $real] : ! [v2: $real] : ( ~ (real_$product(v0, v1) = % 10.03/2.19 v2) | real_$product(v1, v0) = v2) & ! [v0: $real] : ! [v1: $real] : ! % 10.03/2.19 [v2: $real] : ( ~ (real_$difference(v1, v0) = v2) | ? [v3: $real] : % 10.03/2.19 (real_$uminus(v0) = v3 & real_$sum(v1, v3) = v2)) & ! [v0: $real] : ! [v1: % 10.03/2.19 $real] : ! [v2: $real] : ( ~ (real_$sum(v1, v0) = v2) | real_$sum(v0, v1) = % 10.03/2.19 v2) & ! [v0: $real] : ! [v1: $real] : ! [v2: $real] : ( ~ (real_$sum(v0, % 10.03/2.19 v1) = v2) | real_$sum(v1, v0) = v2) & ! [v0: $real] : ! [v1: $real] : % 10.03/2.19 ! [v2: $real] : ( ~ (real_$lesseq(v2, v1) = 0) | ~ (real_$lesseq(v1, v0) = 0) % 10.03/2.19 | real_$lesseq(v2, v0) = 0) & ! [v0: $real] : ! [v1: $real] : ! [v2: % 10.03/2.19 $real] : ( ~ (real_$lesseq(v2, v1) = 0) | ~ (real_$less(v1, v0) = 0) | % 10.03/2.19 real_$less(v2, v0) = 0) & ! [v0: $real] : ! [v1: $real] : ! [v2: $real] : % 10.03/2.19 ( ~ (real_$lesseq(v1, v0) = 0) | ~ (real_$less(v2, v1) = 0) | real_$less(v2, % 10.03/2.19 v0) = 0) & ! [v0: $real] : ! [v1: $real] : (v1 = v0 | ~ (real_$sum(v0, % 10.03/2.19 real_0) = v1)) & ! [v0: $real] : ! [v1: $real] : (v1 = v0 | ~ % 10.03/2.19 (real_$lesseq(v1, v0) = 0) | real_$less(v1, v0) = 0) & ! [v0: $real] : ! % 10.03/2.19 [v1: int] : (v1 = 0 | ~ (real_$lesseq(v0, v0) = v1)) & ! [v0: $real] : ! % 10.03/2.19 [v1: $real] : ( ~ (real_$uminus(v0) = v1) | real_$uminus(v1) = v0) & ! [v0: % 10.03/2.19 $real] : ! [v1: $real] : ( ~ (real_$uminus(v0) = v1) | real_$sum(v0, v1) = % 10.03/2.19 real_0) & ! [v0: $real] : ! [v1: $real] : ( ~ (real_$greatereq(v0, v1) = % 10.03/2.19 0) | real_$lesseq(v1, v0) = 0) & ! [v0: $real] : ! [v1: $real] : ( ~ % 10.03/2.19 (real_$lesseq(v1, v0) = 0) | real_$greatereq(v0, v1) = 0) & ! [v0: $real] : % 10.03/2.19 ! [v1: $real] : ( ~ (real_$greater(v0, v1) = 0) | real_$less(v1, v0) = 0) & % 10.03/2.19 ! [v0: $real] : ! [v1: $real] : ( ~ (real_$less(v1, v0) = 0) | % 10.03/2.19 real_$lesseq(v1, v0) = 0) & ! [v0: $real] : ! [v1: $real] : ( ~ % 10.03/2.19 (real_$less(v1, v0) = 0) | real_$greater(v0, v1) = 0) & ! [v0: $real] : ! % 10.03/2.19 [v1: MultipleValueBool] : ( ~ (real_$less(v0, v0) = v1) | real_$lesseq(v0, v0) % 10.03/2.19 = 0) & ! [v0: $real] : (v0 = real_0 | ~ (real_$uminus(v0) = v0)) % 10.03/2.19 % 10.03/2.19 Those formulas are unsatisfiable: % 10.03/2.19 --------------------------------- % 10.03/2.19 % 10.03/2.19 Begin of proof % 10.03/2.19 | % 10.03/2.19 | ALPHA: (input) implies: % 10.03/2.20 | (1) real_$less(real_-32500, real_very_large) = 0 % 10.03/2.20 | % 10.03/2.20 | GROUND_INST: instantiating (real_less_problem_13) with real_very_large, % 10.03/2.20 | simplifying with (1) gives: % 10.03/2.20 | (2) $false % 10.03/2.20 | % 10.03/2.20 | CLOSE: (2) is inconsistent. % 10.03/2.20 | % 10.03/2.20 End of proof % 10.03/2.20 % SZS output end Proof for theBenchmark % 10.03/2.20 % 10.03/2.20 1609ms %------------------------------------------------------------------------------