%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : ARI511_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 : n004.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 17:48:13 EDT 2023 % Result : Theorem 7.11s 1.70s % Output : Proof 7.35s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : ARI511_1 : TPTP v8.1.2. Released v5.0.0. % 0.07/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.35 % Computer : n004.cluster.edu % 0.13/0.35 % Model : x86_64 x86_64 % 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.35 % Memory : 8042.1875MB % 0.13/0.35 % 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 18:13:52 EDT 2023 % 0.13/0.35 % CPUTime : % 0.20/0.67 ________ _____ % 0.20/0.67 ___ __ \_________(_)________________________________ % 0.20/0.67 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.20/0.67 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.20/0.67 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.20/0.67 % 0.20/0.67 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.20/0.67 (2023-06-19) % 0.20/0.67 % 0.20/0.67 (c) Philipp Rümmer, 2009-2023 % 0.20/0.67 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.20/0.67 Amanda Stjerna. % 0.20/0.67 Free software under BSD-3-Clause. % 0.20/0.67 % 0.20/0.67 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.20/0.67 % 0.20/0.67 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.20/0.68 Running up to 7 provers in parallel. % 0.20/0.70 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.20/0.70 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.20/0.70 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.20/0.70 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.20/0.70 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.20/0.70 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 0.20/0.70 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 1.34/0.95 Prover 4: Warning: Problem contains rationals, using incomplete axiomatisation % 1.34/0.95 Prover 0: Warning: Problem contains rationals, using incomplete axiomatisation % 1.34/0.95 Prover 3: Warning: Problem contains rationals, using incomplete axiomatisation % 1.34/0.95 Prover 5: Warning: Problem contains rationals, using incomplete axiomatisation % 1.34/0.95 Prover 1: Warning: Problem contains rationals, using incomplete axiomatisation % 1.34/0.95 Prover 6: Warning: Problem contains rationals, using incomplete axiomatisation % 1.34/0.95 Prover 2: Warning: Problem contains rationals, using incomplete axiomatisation % 2.22/1.03 Prover 1: Preprocessing ... % 2.22/1.04 Prover 4: Preprocessing ... % 2.22/1.08 Prover 6: Preprocessing ... % 2.22/1.08 Prover 5: Preprocessing ... % 2.22/1.09 Prover 3: Preprocessing ... % 2.22/1.09 Prover 0: Preprocessing ... % 2.22/1.09 Prover 2: Preprocessing ... % 5.82/1.53 Prover 6: Proving ... % 5.82/1.55 Prover 1: Constructing countermodel ... % 5.82/1.57 Prover 4: Constructing countermodel ... % 5.82/1.57 Prover 3: Constructing countermodel ... % 6.37/1.60 Prover 0: Proving ... % 6.37/1.61 Prover 2: Proving ... % 6.37/1.66 Prover 5: Proving ... % 7.11/1.69 Prover 4: Found proof (size 3) % 7.11/1.69 Prover 1: Found proof (size 3) % 7.11/1.70 Prover 4: proved (998ms) % 7.11/1.70 Prover 2: stopped % 7.11/1.70 Prover 5: stopped % 7.11/1.70 Prover 6: stopped % 7.11/1.70 Prover 3: stopped % 7.11/1.70 Prover 1: proved (999ms) % 7.11/1.70 Prover 0: proved (1004ms) % 7.11/1.70 % 7.11/1.70 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 7.11/1.70 % 7.11/1.70 % SZS output start Proof for theBenchmark % 7.11/1.70 Assumptions after simplification: % 7.11/1.70 --------------------------------- % 7.11/1.71 % 7.11/1.71 (mixed_types_problem_16) % 7.35/1.73 ! [v0: $rat] : ~ (rat_$less(rat_5/19, v0) = 0) % 7.35/1.73 % 7.35/1.73 (input) % 7.35/1.76 ~ (rat_very_large = rat_very_small) & ~ (rat_very_large = rat_5/19) & ~ % 7.35/1.76 (rat_very_large = rat_0) & ~ (rat_very_small = rat_5/19) & ~ (rat_very_small % 7.35/1.76 = rat_0) & ~ (rat_5/19 = rat_0) & rat_$is_int(rat_5/19) = 1 & % 7.35/1.76 rat_$is_int(rat_0) = 0 & rat_$is_rat(rat_5/19) = 0 & rat_$is_rat(rat_0) = 0 & % 7.35/1.76 rat_$floor(rat_5/19) = rat_0 & rat_$floor(rat_0) = rat_0 & rat_$ceiling(rat_0) % 7.35/1.76 = rat_0 & rat_$truncate(rat_5/19) = rat_0 & rat_$truncate(rat_0) = rat_0 & % 7.35/1.76 rat_$round(rat_5/19) = rat_0 & rat_$round(rat_0) = rat_0 & % 7.35/1.76 rat_$to_int(rat_5/19) = 0 & rat_$to_int(rat_0) = 0 & rat_$to_rat(rat_5/19) = % 7.35/1.76 rat_5/19 & rat_$to_rat(rat_0) = rat_0 & rat_$to_real(rat_5/19) = real_5/19 & % 7.35/1.76 rat_$to_real(rat_0) = real_0 & int_$to_rat(0) = rat_0 & rat_$quotient(rat_0, % 7.35/1.76 rat_5/19) = rat_0 & rat_$product(rat_5/19, rat_0) = rat_0 & % 7.35/1.76 rat_$product(rat_0, rat_5/19) = rat_0 & rat_$product(rat_0, rat_0) = rat_0 & % 7.35/1.76 rat_$difference(rat_5/19, rat_5/19) = rat_0 & rat_$difference(rat_5/19, rat_0) % 7.35/1.76 = rat_5/19 & rat_$difference(rat_0, rat_0) = rat_0 & rat_$uminus(rat_0) = % 7.35/1.76 rat_0 & rat_$sum(rat_5/19, rat_0) = rat_5/19 & rat_$sum(rat_0, rat_5/19) = % 7.35/1.76 rat_5/19 & rat_$sum(rat_0, rat_0) = rat_0 & rat_$greatereq(rat_very_small, % 7.35/1.76 rat_very_large) = 1 & rat_$greatereq(rat_5/19, rat_5/19) = 0 & % 7.35/1.76 rat_$greatereq(rat_5/19, rat_0) = 0 & rat_$greatereq(rat_0, rat_5/19) = 1 & % 7.35/1.76 rat_$greatereq(rat_0, rat_0) = 0 & rat_$lesseq(rat_very_small, rat_very_large) % 7.35/1.76 = 0 & rat_$lesseq(rat_5/19, rat_5/19) = 0 & rat_$lesseq(rat_5/19, rat_0) = 1 & % 7.35/1.76 rat_$lesseq(rat_0, rat_5/19) = 0 & rat_$lesseq(rat_0, rat_0) = 0 & % 7.35/1.76 rat_$greater(rat_very_large, rat_5/19) = 0 & rat_$greater(rat_very_large, % 7.35/1.76 rat_0) = 0 & rat_$greater(rat_very_small, rat_very_large) = 1 & % 7.35/1.76 rat_$greater(rat_5/19, rat_very_small) = 0 & rat_$greater(rat_5/19, rat_5/19) % 7.35/1.76 = 1 & rat_$greater(rat_5/19, rat_0) = 0 & rat_$greater(rat_0, rat_very_small) % 7.35/1.76 = 0 & rat_$greater(rat_0, rat_5/19) = 1 & rat_$greater(rat_0, rat_0) = 1 & % 7.35/1.76 rat_$less(rat_very_small, rat_very_large) = 0 & rat_$less(rat_very_small, % 7.35/1.76 rat_5/19) = 0 & rat_$less(rat_very_small, rat_0) = 0 & rat_$less(rat_5/19, % 7.35/1.76 rat_very_large) = 0 & rat_$less(rat_5/19, rat_5/19) = 1 & % 7.35/1.76 rat_$less(rat_5/19, rat_0) = 1 & rat_$less(rat_0, rat_very_large) = 0 & % 7.35/1.76 rat_$less(rat_0, rat_5/19) = 0 & rat_$less(rat_0, rat_0) = 1 & ! [v0: $rat] : % 7.35/1.76 ! [v1: $rat] : ! [v2: $rat] : ! [v3: $rat] : ! [v4: $rat] : ( ~ % 7.35/1.76 (rat_$sum(v3, v0) = v4) | ~ (rat_$sum(v2, v1) = v3) | ? [v5: $rat] : % 7.35/1.76 (rat_$sum(v2, v5) = v4 & rat_$sum(v1, v0) = v5)) & ! [v0: $rat] : ! [v1: % 7.35/1.76 $rat] : ! [v2: $rat] : ! [v3: $rat] : ! [v4: $rat] : ( ~ (rat_$sum(v2, % 7.35/1.76 v3) = v4) | ~ (rat_$sum(v1, v0) = v3) | ? [v5: $rat] : (rat_$sum(v5, % 7.35/1.76 v0) = v4 & rat_$sum(v2, v1) = v5)) & ! [v0: $rat] : ! [v1: $rat] : ! % 7.35/1.76 [v2: $rat] : ! [v3: int] : (v3 = 0 | ~ (rat_$lesseq(v2, v1) = 0) | ~ % 7.35/1.76 (rat_$lesseq(v2, v0) = v3) | ? [v4: int] : ( ~ (v4 = 0) & rat_$lesseq(v1, % 7.35/1.76 v0) = v4)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : ! [v3: % 7.35/1.76 int] : (v3 = 0 | ~ (rat_$lesseq(v2, v1) = 0) | ~ (rat_$less(v2, v0) = v3) % 7.35/1.76 | ? [v4: int] : ( ~ (v4 = 0) & rat_$less(v1, v0) = v4)) & ! [v0: $rat] : % 7.35/1.76 ! [v1: $rat] : ! [v2: $rat] : ! [v3: int] : (v3 = 0 | ~ (rat_$lesseq(v2, % 7.35/1.76 v0) = v3) | ~ (rat_$lesseq(v1, v0) = 0) | ? [v4: int] : ( ~ (v4 = 0) & % 7.35/1.76 rat_$lesseq(v2, v1) = v4)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] % 7.35/1.76 : ! [v3: int] : (v3 = 0 | ~ (rat_$lesseq(v1, v0) = 0) | ~ (rat_$less(v2, % 7.35/1.76 v0) = v3) | ? [v4: int] : ( ~ (v4 = 0) & rat_$less(v2, v1) = v4)) & ! % 7.35/1.77 [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : ! [v3: int] : (v3 = 0 | ~ % 7.35/1.77 (rat_$less(v2, v1) = 0) | ~ (rat_$less(v2, v0) = v3) | ? [v4: int] : ( ~ % 7.35/1.77 (v4 = 0) & rat_$lesseq(v1, v0) = v4)) & ! [v0: $rat] : ! [v1: $rat] : ! % 7.35/1.77 [v2: $rat] : ! [v3: int] : (v3 = 0 | ~ (rat_$less(v2, v0) = v3) | ~ % 7.35/1.77 (rat_$less(v1, v0) = 0) | ? [v4: int] : ( ~ (v4 = 0) & rat_$lesseq(v2, v1) % 7.35/1.77 = v4)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : ! [v3: $rat] : ( % 7.35/1.77 ~ (rat_$uminus(v0) = v2) | ~ (rat_$sum(v1, v2) = v3) | rat_$difference(v1, % 7.35/1.77 v0) = v3) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: int] : (v2 = 0 | v1 = % 7.35/1.77 v0 | ~ (rat_$less(v1, v0) = v2) | ? [v3: int] : ( ~ (v3 = 0) & % 7.35/1.77 rat_$lesseq(v1, v0) = v3)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: int] % 7.35/1.77 : (v2 = 0 | ~ (rat_$greatereq(v0, v1) = v2) | ? [v3: int] : ( ~ (v3 = 0) & % 7.35/1.77 rat_$lesseq(v1, v0) = v3)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: int] % 7.35/1.77 : (v2 = 0 | ~ (rat_$lesseq(v1, v0) = v2) | ? [v3: int] : ( ~ (v3 = 0) & % 7.35/1.77 rat_$greatereq(v0, v1) = v3)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: % 7.35/1.77 int] : (v2 = 0 | ~ (rat_$lesseq(v1, v0) = v2) | ? [v3: int] : ( ~ (v3 = 0) % 7.35/1.77 & rat_$less(v1, v0) = v3)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: int] % 7.35/1.77 : (v2 = 0 | ~ (rat_$greater(v0, v1) = v2) | ? [v3: int] : ( ~ (v3 = 0) & % 7.35/1.77 rat_$less(v1, v0) = v3)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: int] : % 7.35/1.77 (v2 = 0 | ~ (rat_$less(v1, v0) = v2) | ? [v3: int] : ( ~ (v3 = 0) & % 7.35/1.77 rat_$greater(v0, v1) = v3)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: % 7.35/1.77 $rat] : (v0 = rat_0 | ~ (rat_$product(v1, v0) = v2) | rat_$quotient(v2, v0) % 7.35/1.77 = v1) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : ( ~ % 7.35/1.77 (rat_$product(v1, v0) = v2) | rat_$product(v0, v1) = v2) & ! [v0: $rat] : % 7.35/1.77 ! [v1: $rat] : ! [v2: $rat] : ( ~ (rat_$product(v0, v1) = v2) | % 7.35/1.77 rat_$product(v1, v0) = v2) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : % 7.35/1.77 ( ~ (rat_$difference(v1, v0) = v2) | ? [v3: $rat] : (rat_$uminus(v0) = v3 & % 7.35/1.77 rat_$sum(v1, v3) = v2)) & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : % 7.35/1.77 ( ~ (rat_$sum(v1, v0) = v2) | rat_$sum(v0, v1) = v2) & ! [v0: $rat] : ! [v1: % 7.35/1.77 $rat] : ! [v2: $rat] : ( ~ (rat_$sum(v0, v1) = v2) | rat_$sum(v1, v0) = v2) % 7.35/1.77 & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $rat] : ( ~ (rat_$lesseq(v2, v1) = % 7.35/1.77 0) | ~ (rat_$lesseq(v1, v0) = 0) | rat_$lesseq(v2, v0) = 0) & ! [v0: % 7.35/1.77 $rat] : ! [v1: $rat] : ! [v2: $rat] : ( ~ (rat_$lesseq(v2, v1) = 0) | ~ % 7.35/1.77 (rat_$less(v1, v0) = 0) | rat_$less(v2, v0) = 0) & ! [v0: $rat] : ! [v1: % 7.35/1.77 $rat] : ! [v2: $rat] : ( ~ (rat_$lesseq(v1, v0) = 0) | ~ (rat_$less(v2, % 7.35/1.77 v1) = 0) | rat_$less(v2, v0) = 0) & ! [v0: $rat] : ! [v1: $rat] : (v1 % 7.35/1.77 = v0 | ~ (rat_$sum(v0, rat_0) = v1)) & ! [v0: $rat] : ! [v1: $rat] : (v1 % 7.35/1.77 = v0 | ~ (rat_$lesseq(v1, v0) = 0) | rat_$less(v1, v0) = 0) & ! [v0: $rat] % 7.35/1.77 : ! [v1: int] : (v1 = 0 | ~ (rat_$lesseq(v0, v0) = v1)) & ! [v0: $rat] : ! % 7.35/1.77 [v1: $rat] : ( ~ (rat_$uminus(v0) = v1) | rat_$uminus(v1) = v0) & ! [v0: % 7.35/1.77 $rat] : ! [v1: $rat] : ( ~ (rat_$uminus(v0) = v1) | rat_$sum(v0, v1) = % 7.35/1.77 rat_0) & ! [v0: $rat] : ! [v1: $rat] : ( ~ (rat_$greatereq(v0, v1) = 0) | % 7.35/1.77 rat_$lesseq(v1, v0) = 0) & ! [v0: $rat] : ! [v1: $rat] : ( ~ % 7.35/1.77 (rat_$lesseq(v1, v0) = 0) | rat_$greatereq(v0, v1) = 0) & ! [v0: $rat] : ! % 7.35/1.77 [v1: $rat] : ( ~ (rat_$greater(v0, v1) = 0) | rat_$less(v1, v0) = 0) & ! [v0: % 7.35/1.77 $rat] : ! [v1: $rat] : ( ~ (rat_$less(v1, v0) = 0) | rat_$lesseq(v1, v0) = % 7.35/1.77 0) & ! [v0: $rat] : ! [v1: $rat] : ( ~ (rat_$less(v1, v0) = 0) | % 7.35/1.77 rat_$greater(v0, v1) = 0) & ! [v0: $rat] : ! [v1: MultipleValueBool] : ( ~ % 7.35/1.77 (rat_$less(v0, v0) = v1) | rat_$lesseq(v0, v0) = 0) & ! [v0: $rat] : (v0 = % 7.35/1.77 rat_0 | ~ (rat_$uminus(v0) = v0)) % 7.35/1.77 % 7.35/1.77 Those formulas are unsatisfiable: % 7.35/1.77 --------------------------------- % 7.35/1.77 % 7.35/1.77 Begin of proof % 7.35/1.77 | % 7.35/1.77 | ALPHA: (input) implies: % 7.35/1.77 | (1) rat_$less(rat_5/19, rat_very_large) = 0 % 7.35/1.77 | % 7.35/1.77 | GROUND_INST: instantiating (mixed_types_problem_16) with rat_very_large, % 7.35/1.77 | simplifying with (1) gives: % 7.35/1.77 | (2) $false % 7.35/1.77 | % 7.35/1.77 | CLOSE: (2) is inconsistent. % 7.35/1.77 | % 7.35/1.77 End of proof % 7.35/1.77 % SZS output end Proof for theBenchmark % 7.35/1.77 % 7.35/1.77 1103ms %------------------------------------------------------------------------------