%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : ANA140_1 : TPTP v8.2.0. Released v8.2.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n013.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 17:20:27 EDT 2023 % Result : Theorem 6.85s 1.69s % Output : Proof 8.78s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : ANA140_1 : TPTP v8.2.0. Released v8.2.0. % 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.34 % Computer : n013.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 % 0.13/0.34 % CPULimit : 300 % 0.13/0.34 % WCLimit : 300 % 0.13/0.34 % DateTime : Fri Aug 25 18:33:32 EDT 2023 % 0.13/0.34 % CPUTime : % 0.19/0.65 ________ _____ % 0.19/0.65 ___ __ \_________(_)________________________________ % 0.19/0.65 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.19/0.65 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.19/0.65 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.19/0.65 % 0.19/0.65 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.19/0.65 (2023-06-19) % 0.19/0.65 % 0.19/0.65 (c) Philipp Rümmer, 2009-2023 % 0.19/0.65 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.19/0.65 Amanda Stjerna. % 0.19/0.65 Free software under BSD-3-Clause. % 0.19/0.65 % 0.19/0.65 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.19/0.65 % 0.19/0.65 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.19/0.66 Running up to 7 provers in parallel. % 0.19/0.68 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.19/0.68 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.19/0.68 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.19/0.68 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.19/0.68 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.19/0.68 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.19/0.68 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 1.42/0.92 Prover 6: Warning: Problem contains reals, using incomplete axiomatisation % 1.42/0.92 Prover 2: Warning: Problem contains reals, using incomplete axiomatisation % 1.42/0.92 Prover 1: Warning: Problem contains reals, using incomplete axiomatisation % 1.42/0.92 Prover 4: Warning: Problem contains reals, using incomplete axiomatisation % 1.42/0.92 Prover 5: Warning: Problem contains reals, using incomplete axiomatisation % 1.42/0.92 Prover 3: Warning: Problem contains reals, using incomplete axiomatisation % 1.42/0.92 Prover 0: Warning: Problem contains reals, using incomplete axiomatisation % 2.23/1.05 Prover 4: Preprocessing ... % 2.23/1.06 Prover 1: Preprocessing ... % 2.60/1.10 Prover 0: Preprocessing ... % 2.60/1.10 Prover 6: Preprocessing ... % 2.60/1.10 Prover 5: Preprocessing ... % 2.60/1.10 Prover 2: Preprocessing ... % 2.60/1.10 Prover 3: Preprocessing ... % 5.45/1.48 Prover 5: Proving ... % 5.45/1.49 Prover 6: Proving ... % 5.45/1.49 Prover 3: Constructing countermodel ... % 5.45/1.49 Prover 1: Constructing countermodel ... % 5.45/1.51 Prover 2: Proving ... % 5.45/1.53 Prover 4: Constructing countermodel ... % 6.09/1.56 Prover 0: Proving ... % 6.85/1.69 Prover 3: proved (1014ms) % 6.85/1.69 % 6.85/1.69 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 6.85/1.69 % 6.85/1.69 Prover 2: stopped % 6.85/1.69 Prover 0: stopped % 6.85/1.70 Prover 5: stopped % 6.85/1.70 Prover 6: stopped % 6.85/1.70 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 6.85/1.70 Prover 7: Warning: Problem contains reals, using incomplete axiomatisation % 6.85/1.70 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 6.85/1.70 Prover 8: Warning: Problem contains reals, using incomplete axiomatisation % 6.85/1.70 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 6.85/1.70 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 6.85/1.70 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 6.85/1.70 Prover 10: Warning: Problem contains reals, using incomplete axiomatisation % 6.85/1.70 Prover 13: Warning: Problem contains reals, using incomplete axiomatisation % 6.85/1.70 Prover 11: Warning: Problem contains reals, using incomplete axiomatisation % 7.32/1.72 Prover 7: Preprocessing ... % 7.32/1.72 Prover 8: Preprocessing ... % 7.32/1.72 Prover 13: Preprocessing ... % 7.32/1.72 Prover 10: Preprocessing ... % 7.32/1.72 Prover 11: Preprocessing ... % 7.70/1.79 Prover 13: Warning: ignoring some quantifiers % 7.70/1.80 Prover 13: Constructing countermodel ... % 7.70/1.80 Prover 10: Warning: ignoring some quantifiers % 7.70/1.81 Prover 10: Constructing countermodel ... % 7.70/1.82 Prover 1: Found proof (size 38) % 7.70/1.82 Prover 1: proved (1148ms) % 7.70/1.82 Prover 13: stopped % 7.70/1.82 Prover 4: stopped % 7.70/1.82 Prover 7: Warning: ignoring some quantifiers % 7.70/1.82 Prover 10: stopped % 7.70/1.83 Prover 7: Constructing countermodel ... % 7.70/1.83 Prover 7: stopped % 7.70/1.84 Prover 8: Warning: ignoring some quantifiers % 8.34/1.85 Prover 8: Constructing countermodel ... % 8.34/1.86 Prover 8: stopped % 8.52/1.89 Prover 11: Constructing countermodel ... % 8.52/1.90 Prover 11: stopped % 8.52/1.90 % 8.52/1.90 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 8.52/1.90 % 8.52/1.91 % SZS output start Proof for theBenchmark % 8.52/1.91 Assumptions after simplification: % 8.52/1.91 --------------------------------- % 8.52/1.91 % 8.52/1.91 (formula_1) % 8.78/1.94 ? [v0: $real] : (real_$less(real_0, v0) = 0 & ! [v1: $real] : ( ~ % 8.78/1.94 (real_$less(real_0, v1) = 0) | ? [v2: $real] : ? [v3: $real] : ? [v4: % 8.78/1.94 any] : ? [v5: any] : ? [v6: $real] : ? [v7: any] : ? [v8: any] : ? % 8.78/1.94 [v9: any] : ( ~ (v2 = a) & real_$difference(v2, a) = v3 & % 8.78/1.94 real_$greatereq(v3, real_0) = v4 & real_$uminus(v3) = v6 & % 8.78/1.94 real_$less(v6, v1) = v7 & real_$less(v6, v0) = v9 & real_$less(v3, v1) = % 8.78/1.94 v5 & real_$less(v3, v0) = v8 & ( ~ (v4 = 0) | v5 = 0) & (v7 = 0 | v4 = % 8.78/1.94 0) & ((v4 = 0 & ~ (v8 = 0)) | ( ~ (v9 = 0) & ~ (v4 = 0)))))) % 8.78/1.94 % 8.78/1.94 (function-axioms) % 8.78/1.95 ! [v0: $real] : ! [v1: $real] : ! [v2: $real] : ! [v3: $real] : (v1 = v0 | % 8.78/1.95 ~ (real_$quotient(v3, v2) = v1) | ~ (real_$quotient(v3, v2) = v0)) & ! % 8.78/1.95 [v0: $real] : ! [v1: $real] : ! [v2: $real] : ! [v3: $real] : (v1 = v0 | ~ % 8.78/1.95 (real_$product(v3, v2) = v1) | ~ (real_$product(v3, v2) = v0)) & ! [v0: % 8.78/1.95 $real] : ! [v1: $real] : ! [v2: $real] : ! [v3: $real] : (v1 = v0 | ~ % 8.78/1.95 (real_$sum(v3, v2) = v1) | ~ (real_$sum(v3, v2) = v0)) & ! [v0: % 8.78/1.95 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $real] : ! [v3: % 8.78/1.95 $real] : (v1 = v0 | ~ (real_$lesseq(v3, v2) = v1) | ~ (real_$lesseq(v3, % 8.78/1.95 v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : % 8.78/1.95 ! [v2: $real] : ! [v3: $real] : (v1 = v0 | ~ (real_$greater(v3, v2) = v1) | % 8.78/1.95 ~ (real_$greater(v3, v2) = v0)) & ! [v0: $real] : ! [v1: $real] : ! [v2: % 8.78/1.95 $real] : ! [v3: $real] : (v1 = v0 | ~ (real_$difference(v3, v2) = v1) | ~ % 8.78/1.95 (real_$difference(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 8.78/1.95 MultipleValueBool] : ! [v2: $real] : ! [v3: $real] : (v1 = v0 | ~ % 8.78/1.95 (real_$greatereq(v3, v2) = v1) | ~ (real_$greatereq(v3, v2) = v0)) & ! % 8.78/1.95 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $real] : ! % 8.78/1.95 [v3: $real] : (v1 = v0 | ~ (real_$less(v3, v2) = v1) | ~ (real_$less(v3, v2) % 8.78/1.95 = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 8.78/1.95 $real] : (v1 = v0 | ~ (real_$is_int(v2) = v1) | ~ (real_$is_int(v2) = v0)) % 8.78/1.95 & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $real] : % 8.78/1.95 (v1 = v0 | ~ (real_$is_rat(v2) = v1) | ~ (real_$is_rat(v2) = v0)) & ! [v0: % 8.78/1.95 $real] : ! [v1: $real] : ! [v2: $real] : (v1 = v0 | ~ (real_$floor(v2) = % 8.78/1.95 v1) | ~ (real_$floor(v2) = v0)) & ! [v0: $real] : ! [v1: $real] : ! % 8.78/1.95 [v2: $real] : (v1 = v0 | ~ (real_$ceiling(v2) = v1) | ~ (real_$ceiling(v2) = % 8.78/1.95 v0)) & ! [v0: $real] : ! [v1: $real] : ! [v2: $real] : (v1 = v0 | ~ % 8.78/1.95 (real_$truncate(v2) = v1) | ~ (real_$truncate(v2) = v0)) & ! [v0: $real] : % 8.78/1.95 ! [v1: $real] : ! [v2: $real] : (v1 = v0 | ~ (real_$round(v2) = v1) | ~ % 8.78/1.95 (real_$round(v2) = v0)) & ! [v0: int] : ! [v1: int] : ! [v2: $real] : (v1 % 8.78/1.95 = v0 | ~ (real_$to_int(v2) = v1) | ~ (real_$to_int(v2) = v0)) & ! [v0: % 8.78/1.95 $rat] : ! [v1: $rat] : ! [v2: $real] : (v1 = v0 | ~ (real_$to_rat(v2) = % 8.78/1.95 v1) | ~ (real_$to_rat(v2) = v0)) & ! [v0: $real] : ! [v1: $real] : ! % 8.78/1.95 [v2: $real] : (v1 = v0 | ~ (real_$to_real(v2) = v1) | ~ (real_$to_real(v2) = % 8.78/1.95 v0)) & ! [v0: $real] : ! [v1: $real] : ! [v2: int] : (v1 = v0 | ~ % 8.78/1.95 (int_$to_real(v2) = v1) | ~ (int_$to_real(v2) = v0)) & ! [v0: $real] : ! % 8.78/1.95 [v1: $real] : ! [v2: $real] : (v1 = v0 | ~ (real_$uminus(v2) = v1) | ~ % 8.78/1.95 (real_$uminus(v2) = v0)) % 8.78/1.95 % 8.78/1.95 Those formulas are unsatisfiable: % 8.78/1.95 --------------------------------- % 8.78/1.95 % 8.78/1.95 Begin of proof % 8.78/1.96 | % 8.78/1.96 | ALPHA: (function-axioms) implies: % 8.78/1.96 | (1) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 8.78/1.96 | $real] : ! [v3: $real] : (v1 = v0 | ~ (real_$less(v3, v2) = v1) | % 8.78/1.96 | ~ (real_$less(v3, v2) = v0)) % 8.78/1.96 | % 8.78/1.96 | DELTA: instantiating (formula_1) with fresh symbol all_5_0 gives: % 8.78/1.96 | (2) real_$less(real_0, all_5_0) = 0 & ! [v0: $real] : ( ~ % 8.78/1.96 | (real_$less(real_0, v0) = 0) | ? [v1: $real] : ? [v2: $real] : ? % 8.78/1.96 | [v3: any] : ? [v4: any] : ? [v5: $real] : ? [v6: any] : ? [v7: % 8.78/1.96 | any] : ? [v8: any] : ( ~ (v1 = a) & real_$difference(v1, a) = v2 & % 8.78/1.96 | real_$greatereq(v2, real_0) = v3 & real_$uminus(v2) = v5 & % 8.78/1.96 | real_$less(v5, v0) = v6 & real_$less(v5, all_5_0) = v8 & % 8.78/1.96 | real_$less(v2, v0) = v4 & real_$less(v2, all_5_0) = v7 & ( ~ (v3 = % 8.78/1.96 | 0) | v4 = 0) & (v6 = 0 | v3 = 0) & ((v3 = 0 & ~ (v7 = 0)) | ( % 8.78/1.96 | ~ (v8 = 0) & ~ (v3 = 0))))) % 8.78/1.96 | % 8.78/1.96 | ALPHA: (2) implies: % 8.78/1.96 | (3) real_$less(real_0, all_5_0) = 0 % 8.78/1.97 | (4) ! [v0: $real] : ( ~ (real_$less(real_0, v0) = 0) | ? [v1: $real] : ? % 8.78/1.97 | [v2: $real] : ? [v3: any] : ? [v4: any] : ? [v5: $real] : ? [v6: % 8.78/1.97 | any] : ? [v7: any] : ? [v8: any] : ( ~ (v1 = a) & % 8.78/1.97 | real_$difference(v1, a) = v2 & real_$greatereq(v2, real_0) = v3 & % 8.78/1.97 | real_$uminus(v2) = v5 & real_$less(v5, v0) = v6 & real_$less(v5, % 8.78/1.97 | all_5_0) = v8 & real_$less(v2, v0) = v4 & real_$less(v2, all_5_0) % 8.78/1.97 | = v7 & ( ~ (v3 = 0) | v4 = 0) & (v6 = 0 | v3 = 0) & ((v3 = 0 & ~ % 8.78/1.97 | (v7 = 0)) | ( ~ (v8 = 0) & ~ (v3 = 0))))) % 8.78/1.97 | % 8.78/1.97 | GROUND_INST: instantiating (4) with all_5_0, simplifying with (3) gives: % 8.78/1.97 | (5) ? [v0: $real] : ? [v1: $real] : ? [v2: any] : ? [v3: any] : ? [v4: % 8.78/1.97 | $real] : ? [v5: any] : ? [v6: any] : ? [v7: any] : ( ~ (v0 = a) & % 8.78/1.97 | real_$difference(v0, a) = v1 & real_$greatereq(v1, real_0) = v2 & % 8.78/1.97 | real_$uminus(v1) = v4 & real_$less(v4, all_5_0) = v7 & real_$less(v4, % 8.78/1.97 | all_5_0) = v5 & real_$less(v1, all_5_0) = v6 & real_$less(v1, % 8.78/1.97 | all_5_0) = v3 & ( ~ (v2 = 0) | v3 = 0) & (v5 = 0 | v2 = 0) & ((v2 = % 8.78/1.97 | 0 & ~ (v6 = 0)) | ( ~ (v7 = 0) & ~ (v2 = 0)))) % 8.78/1.97 | % 8.78/1.97 | DELTA: instantiating (5) with fresh symbols all_17_0, all_17_1, all_17_2, % 8.78/1.97 | all_17_3, all_17_4, all_17_5, all_17_6, all_17_7 gives: % 8.78/1.97 | (6) ~ (all_17_7 = a) & real_$difference(all_17_7, a) = all_17_6 & % 8.78/1.97 | real_$greatereq(all_17_6, real_0) = all_17_5 & real_$uminus(all_17_6) = % 8.78/1.97 | all_17_3 & real_$less(all_17_3, all_5_0) = all_17_0 & % 8.78/1.97 | real_$less(all_17_3, all_5_0) = all_17_2 & real_$less(all_17_6, % 8.78/1.97 | all_5_0) = all_17_1 & real_$less(all_17_6, all_5_0) = all_17_4 & ( ~ % 8.78/1.97 | (all_17_5 = 0) | all_17_4 = 0) & (all_17_2 = 0 | all_17_5 = 0) & % 8.78/1.97 | ((all_17_5 = 0 & ~ (all_17_1 = 0)) | ( ~ (all_17_0 = 0) & ~ (all_17_5 % 8.78/1.97 | = 0))) % 8.78/1.97 | % 8.78/1.97 | ALPHA: (6) implies: % 8.78/1.97 | (7) real_$less(all_17_6, all_5_0) = all_17_4 % 8.78/1.97 | (8) real_$less(all_17_6, all_5_0) = all_17_1 % 8.78/1.97 | (9) real_$less(all_17_3, all_5_0) = all_17_2 % 8.78/1.97 | (10) real_$less(all_17_3, all_5_0) = all_17_0 % 8.78/1.97 | (11) (all_17_5 = 0 & ~ (all_17_1 = 0)) | ( ~ (all_17_0 = 0) & ~ (all_17_5 % 8.78/1.97 | = 0)) % 8.78/1.97 | (12) all_17_2 = 0 | all_17_5 = 0 % 8.78/1.97 | (13) ~ (all_17_5 = 0) | all_17_4 = 0 % 8.78/1.97 | % 8.78/1.97 | GROUND_INST: instantiating (1) with all_17_4, all_17_1, all_5_0, all_17_6, % 8.78/1.97 | simplifying with (7), (8) gives: % 8.78/1.97 | (14) all_17_1 = all_17_4 % 8.78/1.97 | % 8.78/1.97 | GROUND_INST: instantiating (1) with all_17_2, all_17_0, all_5_0, all_17_3, % 8.78/1.97 | simplifying with (9), (10) gives: % 8.78/1.97 | (15) all_17_0 = all_17_2 % 8.78/1.97 | % 8.78/1.97 | BETA: splitting (12) gives: % 8.78/1.97 | % 8.78/1.97 | Case 1: % 8.78/1.97 | | % 8.78/1.97 | | (16) all_17_2 = 0 % 8.78/1.97 | | % 8.78/1.97 | | COMBINE_EQS: (15), (16) imply: % 8.78/1.97 | | (17) all_17_0 = 0 % 8.78/1.97 | | % 8.78/1.97 | | BETA: splitting (11) gives: % 8.78/1.97 | | % 8.78/1.97 | | Case 1: % 8.78/1.97 | | | % 8.78/1.97 | | | (18) all_17_5 = 0 & ~ (all_17_1 = 0) % 8.78/1.97 | | | % 8.78/1.97 | | | ALPHA: (18) implies: % 8.78/1.97 | | | (19) all_17_5 = 0 % 8.78/1.97 | | | % 8.78/1.98 | | | REF_CLOSE: (11), (13), (14), (19) are inconsistent by sub-proof #1. % 8.78/1.98 | | | % 8.78/1.98 | | Case 2: % 8.78/1.98 | | | % 8.78/1.98 | | | (20) ~ (all_17_0 = 0) & ~ (all_17_5 = 0) % 8.78/1.98 | | | % 8.78/1.98 | | | ALPHA: (20) implies: % 8.78/1.98 | | | (21) ~ (all_17_0 = 0) % 8.78/1.98 | | | % 8.78/1.98 | | | REDUCE: (17), (21) imply: % 8.78/1.98 | | | (22) $false % 8.78/1.98 | | | % 8.78/1.98 | | | CLOSE: (22) is inconsistent. % 8.78/1.98 | | | % 8.78/1.98 | | End of split % 8.78/1.98 | | % 8.78/1.98 | Case 2: % 8.78/1.98 | | % 8.78/1.98 | | (23) all_17_5 = 0 % 8.78/1.98 | | % 8.78/1.98 | | REF_CLOSE: (11), (13), (14), (23) are inconsistent by sub-proof #1. % 8.78/1.98 | | % 8.78/1.98 | End of split % 8.78/1.98 | % 8.78/1.98 End of proof % 8.78/1.98 % 8.78/1.98 Sub-proof #1 shows that the following formulas are inconsistent: % 8.78/1.98 ---------------------------------------------------------------- % 8.78/1.98 (1) ~ (all_17_5 = 0) | all_17_4 = 0 % 8.78/1.98 (2) all_17_5 = 0 % 8.78/1.98 (3) all_17_1 = all_17_4 % 8.78/1.98 (4) (all_17_5 = 0 & ~ (all_17_1 = 0)) | ( ~ (all_17_0 = 0) & ~ (all_17_5 = % 8.78/1.98 0)) % 8.78/1.98 % 8.78/1.98 Begin of proof % 8.78/1.98 | % 8.78/1.98 | BETA: splitting (1) gives: % 8.78/1.98 | % 8.78/1.98 | Case 1: % 8.78/1.98 | | % 8.78/1.98 | | (5) ~ (all_17_5 = 0) % 8.78/1.98 | | % 8.78/1.98 | | REDUCE: (2), (5) imply: % 8.78/1.98 | | (6) $false % 8.78/1.98 | | % 8.78/1.98 | | CLOSE: (6) is inconsistent. % 8.78/1.98 | | % 8.78/1.98 | Case 2: % 8.78/1.98 | | % 8.78/1.98 | | (7) all_17_4 = 0 % 8.78/1.98 | | % 8.78/1.98 | | COMBINE_EQS: (3), (7) imply: % 8.78/1.98 | | (8) all_17_1 = 0 % 8.78/1.98 | | % 8.78/1.98 | | BETA: splitting (4) gives: % 8.78/1.98 | | % 8.78/1.98 | | Case 1: % 8.78/1.98 | | | % 8.78/1.98 | | | (9) all_17_5 = 0 & ~ (all_17_1 = 0) % 8.78/1.98 | | | % 8.78/1.98 | | | ALPHA: (9) implies: % 8.78/1.98 | | | (10) ~ (all_17_1 = 0) % 8.78/1.98 | | | % 8.78/1.98 | | | REDUCE: (8), (10) imply: % 8.78/1.98 | | | (11) $false % 8.78/1.98 | | | % 8.78/1.98 | | | CLOSE: (11) is inconsistent. % 8.78/1.98 | | | % 8.78/1.98 | | Case 2: % 8.78/1.98 | | | % 8.78/1.98 | | | (12) ~ (all_17_0 = 0) & ~ (all_17_5 = 0) % 8.78/1.98 | | | % 8.78/1.98 | | | ALPHA: (12) implies: % 8.78/1.98 | | | (13) ~ (all_17_5 = 0) % 8.78/1.98 | | | % 8.78/1.98 | | | REDUCE: (2), (13) imply: % 8.78/1.98 | | | (14) $false % 8.78/1.98 | | | % 8.78/1.98 | | | CLOSE: (14) is inconsistent. % 8.78/1.98 | | | % 8.78/1.98 | | End of split % 8.78/1.98 | | % 8.78/1.98 | End of split % 8.78/1.98 | % 8.78/1.98 End of proof % 8.78/1.98 % SZS output end Proof for theBenchmark % 8.78/1.98 % 8.78/1.98 1330ms %------------------------------------------------------------------------------