%------------------------------------------------------------------------------ % 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 %------------------------------------------------------------------------------