%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : NUM912_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 : n011.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 6.15s 1.62s % Output : Proof 8.15s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.13 % Problem : NUM912_1 : TPTP v8.1.2. Released v5.0.0. % 0.07/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.15/0.35 % Computer : n011.cluster.edu % 0.15/0.35 % Model : x86_64 x86_64 % 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.15/0.35 % Memory : 8042.1875MB % 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.15/0.35 % CPULimit : 300 % 0.15/0.35 % WCLimit : 300 % 0.15/0.35 % DateTime : Fri Aug 25 17:00:53 EDT 2023 % 0.15/0.35 % CPUTime : % 0.21/0.61 ________ _____ % 0.21/0.61 ___ __ \_________(_)________________________________ % 0.21/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.21/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.21/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.21/0.61 % 0.21/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.21/0.61 (2023-06-19) % 0.21/0.61 % 0.21/0.61 (c) Philipp Rümmer, 2009-2023 % 0.21/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.21/0.61 Amanda Stjerna. % 0.21/0.61 Free software under BSD-3-Clause. % 0.21/0.61 % 0.21/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.21/0.61 % 0.21/0.61 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.21/0.63 Running up to 7 provers in parallel. % 0.21/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.21/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.21/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.21/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.21/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.21/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 0.21/0.65 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.21/0.90 Prover 5: Warning: Problem contains reals, using incomplete axiomatisation % 0.21/0.90 Prover 3: Warning: Problem contains reals, using incomplete axiomatisation % 0.21/0.90 Prover 2: Warning: Problem contains reals, using incomplete axiomatisation % 0.21/0.90 Prover 1: Warning: Problem contains reals, using incomplete axiomatisation % 0.21/0.90 Prover 0: Warning: Problem contains reals, using incomplete axiomatisation % 0.21/0.90 Prover 4: Warning: Problem contains reals, using incomplete axiomatisation % 0.21/0.90 Prover 6: Warning: Problem contains reals, using incomplete axiomatisation % 2.13/0.99 Prover 1: Preprocessing ... % 2.13/0.99 Prover 4: Preprocessing ... % 2.25/1.03 Prover 6: Preprocessing ... % 2.25/1.03 Prover 3: Preprocessing ... % 2.25/1.03 Prover 0: Preprocessing ... % 2.25/1.03 Prover 2: Preprocessing ... % 2.25/1.03 Prover 5: Preprocessing ... % 4.43/1.41 Prover 3: Constructing countermodel ... % 4.43/1.42 Prover 6: Constructing countermodel ... % 4.43/1.43 Prover 1: Constructing countermodel ... % 4.43/1.44 Prover 5: Proving ... % 4.43/1.45 Prover 2: Proving ... % 5.47/1.49 Prover 4: Constructing countermodel ... % 6.15/1.56 Prover 0: Proving ... % 6.15/1.62 Prover 3: proved (972ms) % 6.15/1.62 % 6.15/1.62 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 6.15/1.62 % 6.15/1.62 Prover 0: stopped % 6.15/1.62 Prover 2: stopped % 6.15/1.64 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 6.15/1.64 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 6.15/1.64 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 6.15/1.64 Prover 7: Warning: Problem contains reals, using incomplete axiomatisation % 6.15/1.64 Prover 8: Warning: Problem contains reals, using incomplete axiomatisation % 6.15/1.64 Prover 10: Warning: Problem contains reals, using incomplete axiomatisation % 6.15/1.64 Prover 5: proved (986ms) % 6.15/1.64 % 6.15/1.64 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 6.15/1.64 % 6.15/1.64 Prover 6: stopped % 6.85/1.65 Prover 8: Preprocessing ... % 6.85/1.65 Prover 7: Preprocessing ... % 6.85/1.65 Prover 10: Preprocessing ... % 6.85/1.65 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 6.85/1.65 Prover 11: Warning: Problem contains reals, using incomplete axiomatisation % 6.85/1.65 Prover 11: Preprocessing ... % 6.85/1.65 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 6.85/1.66 Prover 13: Warning: Problem contains reals, using incomplete axiomatisation % 6.85/1.66 Prover 13: Preprocessing ... % 7.20/1.71 Prover 1: Found proof (size 15) % 7.20/1.71 Prover 1: proved (1072ms) % 7.20/1.71 Prover 4: stopped % 7.20/1.72 Prover 7: Warning: ignoring some quantifiers % 7.20/1.72 Prover 10: Warning: ignoring some quantifiers % 7.20/1.73 Prover 7: Constructing countermodel ... % 7.20/1.73 Prover 10: Constructing countermodel ... % 7.20/1.73 Prover 7: stopped % 7.20/1.74 Prover 10: stopped % 7.57/1.75 Prover 13: Warning: ignoring some quantifiers % 7.57/1.76 Prover 8: Warning: ignoring some quantifiers % 7.57/1.76 Prover 13: Constructing countermodel ... % 7.57/1.76 Prover 13: stopped % 7.57/1.77 Prover 8: Constructing countermodel ... % 7.57/1.78 Prover 8: stopped % 7.89/1.80 Prover 11: Constructing countermodel ... % 7.89/1.81 Prover 11: stopped % 7.89/1.81 % 7.89/1.81 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 7.89/1.81 % 7.89/1.82 % SZS output start Proof for theBenchmark % 7.89/1.82 Assumptions after simplification: % 7.89/1.82 --------------------------------- % 7.89/1.82 % 7.89/1.82 (real_uminus_problem_9) % 7.89/1.85 ? [v0: $real] : ? [v1: $real] : (real_$uminus(v0) = v1 & ((v1 = v0 & ~ (v0 % 7.89/1.85 = real_0)) | (v0 = real_0 & ~ (v1 = real_0)))) % 7.89/1.85 % 7.89/1.85 (input) % 8.15/1.87 ~ (real_very_large = real_very_small) & ~ (real_very_large = real_0) & ~ % 8.15/1.87 (real_very_small = real_0) & real_$is_int(real_0) = 0 & real_$is_rat(real_0) = % 8.15/1.87 0 & real_$floor(real_0) = real_0 & real_$ceiling(real_0) = real_0 & % 8.15/1.87 real_$truncate(real_0) = real_0 & real_$round(real_0) = real_0 & % 8.15/1.87 real_$to_int(real_0) = 0 & real_$to_rat(real_0) = rat_0 & % 8.15/1.87 real_$to_real(real_0) = real_0 & int_$to_real(0) = real_0 & % 8.15/1.87 real_$product(real_0, real_0) = real_0 & real_$difference(real_0, real_0) = % 8.15/1.87 real_0 & real_$sum(real_0, real_0) = real_0 & real_$greatereq(real_very_small, % 8.15/1.87 real_very_large) = 1 & real_$greatereq(real_0, real_0) = 0 & % 8.15/1.87 real_$lesseq(real_very_small, real_very_large) = 0 & real_$lesseq(real_0, % 8.15/1.87 real_0) = 0 & real_$greater(real_very_large, real_0) = 0 & % 8.15/1.87 real_$greater(real_very_small, real_very_large) = 1 & real_$greater(real_0, % 8.15/1.87 real_very_small) = 0 & real_$greater(real_0, real_0) = 1 & % 8.15/1.87 real_$less(real_very_small, real_very_large) = 0 & real_$less(real_very_small, % 8.15/1.87 real_0) = 0 & real_$less(real_0, real_very_large) = 0 & real_$less(real_0, % 8.15/1.87 real_0) = 1 & real_$uminus(real_0) = real_0 & ! [v0: $real] : ! [v1: % 8.15/1.87 $real] : ! [v2: $real] : ! [v3: $real] : ! [v4: $real] : ( ~ % 8.15/1.87 (real_$sum(v3, v0) = v4) | ~ (real_$sum(v2, v1) = v3) | ? [v5: $real] : % 8.15/1.87 (real_$sum(v2, v5) = v4 & real_$sum(v1, v0) = v5)) & ! [v0: $real] : ! % 8.15/1.87 [v1: $real] : ! [v2: $real] : ! [v3: $real] : (v3 = v1 | v0 = real_0 | ~ % 8.15/1.87 (real_$quotient(v2, v0) = v3) | ~ (real_$product(v1, v0) = v2)) & ! [v0: % 8.15/1.87 $real] : ! [v1: $real] : ! [v2: $real] : ! [v3: int] : (v3 = 0 | ~ % 8.15/1.87 (real_$lesseq(v2, v0) = v3) | ~ (real_$lesseq(v1, v0) = 0) | ? [v4: int] : % 8.15/1.87 ( ~ (v4 = 0) & real_$lesseq(v2, v1) = v4)) & ! [v0: $real] : ! [v1: $real] % 8.15/1.87 : ! [v2: $real] : ! [v3: int] : (v3 = 0 | ~ (real_$lesseq(v1, v0) = 0) | ~ % 8.15/1.87 (real_$less(v2, v0) = v3) | ? [v4: int] : ( ~ (v4 = 0) & real_$less(v2, v1) % 8.15/1.87 = v4)) & ! [v0: $real] : ! [v1: $real] : ! [v2: $real] : ! [v3: $real] % 8.15/1.87 : ( ~ (real_$sum(v1, v2) = v3) | ~ (real_$uminus(v0) = v2) | % 8.15/1.87 real_$difference(v1, v0) = v3) & ! [v0: $real] : ! [v1: $real] : ! [v2: % 8.15/1.87 $real] : (v2 = real_0 | ~ (real_$sum(v0, v1) = v2) | ~ (real_$uminus(v0) = % 8.15/1.87 v1)) & ! [v0: $real] : ! [v1: $real] : ! [v2: int] : (v2 = 0 | ~ % 8.15/1.87 (real_$greatereq(v0, v1) = v2) | ? [v3: int] : ( ~ (v3 = 0) & % 8.15/1.87 real_$lesseq(v1, v0) = v3)) & ! [v0: $real] : ! [v1: $real] : ! [v2: % 8.15/1.87 int] : (v2 = 0 | ~ (real_$lesseq(v1, v0) = v2) | ( ~ (v1 = v0) & ? [v3: % 8.15/1.87 int] : ( ~ (v3 = 0) & real_$less(v1, v0) = v3))) & ! [v0: $real] : ! % 8.15/1.87 [v1: $real] : ! [v2: int] : (v2 = 0 | ~ (real_$greater(v0, v1) = v2) | ? % 8.15/1.87 [v3: int] : ( ~ (v3 = 0) & real_$less(v1, v0) = v3)) & ! [v0: $real] : ! % 8.15/1.87 [v1: $real] : ! [v2: $real] : ( ~ (real_$product(v0, v1) = v2) | % 8.15/1.87 real_$product(v1, v0) = v2) & ! [v0: $real] : ! [v1: $real] : ! [v2: % 8.15/1.87 $real] : ( ~ (real_$sum(v0, v1) = v2) | real_$sum(v1, v0) = v2) & ! [v0: % 8.15/1.87 $real] : ! [v1: $real] : ! [v2: $real] : ( ~ (real_$lesseq(v2, v1) = 0) | % 8.15/1.87 ~ (real_$less(v1, v0) = 0) | real_$less(v2, v0) = 0) & ! [v0: $real] : ! % 8.15/1.87 [v1: $real] : (v1 = v0 | ~ (real_$sum(v0, real_0) = v1)) & ! [v0: $real] : % 8.15/1.87 ! [v1: $real] : (v1 = v0 | ~ (real_$lesseq(v1, v0) = 0) | real_$less(v1, v0) % 8.15/1.87 = 0) & ! [v0: $real] : ! [v1: $real] : ( ~ (real_$greatereq(v0, v1) = 0) | % 8.15/1.87 real_$lesseq(v1, v0) = 0) & ! [v0: $real] : ! [v1: $real] : ( ~ % 8.15/1.87 (real_$greater(v0, v1) = 0) | real_$less(v1, v0) = 0) & ! [v0: $real] : ! % 8.15/1.87 [v1: $real] : ( ~ (real_$uminus(v0) = v1) | real_$uminus(v1) = v0) & ! [v0: % 8.15/1.87 $real] : (v0 = real_0 | ~ (real_$uminus(v0) = v0)) % 8.15/1.87 % 8.15/1.87 (function-axioms) % 8.15/1.88 ! [v0: $real] : ! [v1: $real] : ! [v2: $real] : ! [v3: $real] : (v1 = v0 | % 8.15/1.88 ~ (real_$quotient(v3, v2) = v1) | ~ (real_$quotient(v3, v2) = v0)) & ! % 8.15/1.88 [v0: $real] : ! [v1: $real] : ! [v2: $real] : ! [v3: $real] : (v1 = v0 | ~ % 8.15/1.88 (real_$product(v3, v2) = v1) | ~ (real_$product(v3, v2) = v0)) & ! [v0: % 8.15/1.88 $real] : ! [v1: $real] : ! [v2: $real] : ! [v3: $real] : (v1 = v0 | ~ % 8.15/1.88 (real_$difference(v3, v2) = v1) | ~ (real_$difference(v3, v2) = v0)) & ! % 8.15/1.88 [v0: $real] : ! [v1: $real] : ! [v2: $real] : ! [v3: $real] : (v1 = v0 | ~ % 8.15/1.88 (real_$sum(v3, v2) = v1) | ~ (real_$sum(v3, v2) = v0)) & ! [v0: % 8.15/1.88 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $real] : ! [v3: % 8.15/1.88 $real] : (v1 = v0 | ~ (real_$greatereq(v3, v2) = v1) | ~ % 8.15/1.88 (real_$greatereq(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 8.15/1.88 MultipleValueBool] : ! [v2: $real] : ! [v3: $real] : (v1 = v0 | ~ % 8.15/1.88 (real_$lesseq(v3, v2) = v1) | ~ (real_$lesseq(v3, v2) = v0)) & ! [v0: % 8.15/1.88 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $real] : ! [v3: % 8.15/1.88 $real] : (v1 = v0 | ~ (real_$greater(v3, v2) = v1) | ~ (real_$greater(v3, % 8.15/1.88 v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : % 8.15/1.88 ! [v2: $real] : ! [v3: $real] : (v1 = v0 | ~ (real_$less(v3, v2) = v1) | ~ % 8.15/1.88 (real_$less(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 8.15/1.88 MultipleValueBool] : ! [v2: $real] : (v1 = v0 | ~ (real_$is_int(v2) = v1) % 8.15/1.88 | ~ (real_$is_int(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 8.15/1.88 MultipleValueBool] : ! [v2: $real] : (v1 = v0 | ~ (real_$is_rat(v2) = v1) % 8.15/1.88 | ~ (real_$is_rat(v2) = v0)) & ! [v0: $real] : ! [v1: $real] : ! [v2: % 8.15/1.88 $real] : (v1 = v0 | ~ (real_$floor(v2) = v1) | ~ (real_$floor(v2) = v0)) & % 8.15/1.88 ! [v0: $real] : ! [v1: $real] : ! [v2: $real] : (v1 = v0 | ~ % 8.15/1.88 (real_$ceiling(v2) = v1) | ~ (real_$ceiling(v2) = v0)) & ! [v0: $real] : % 8.15/1.88 ! [v1: $real] : ! [v2: $real] : (v1 = v0 | ~ (real_$truncate(v2) = v1) | ~ % 8.15/1.88 (real_$truncate(v2) = v0)) & ! [v0: $real] : ! [v1: $real] : ! [v2: % 8.15/1.88 $real] : (v1 = v0 | ~ (real_$round(v2) = v1) | ~ (real_$round(v2) = v0)) & % 8.15/1.88 ! [v0: int] : ! [v1: int] : ! [v2: $real] : (v1 = v0 | ~ (real_$to_int(v2) % 8.15/1.88 = v1) | ~ (real_$to_int(v2) = v0)) & ! [v0: $rat] : ! [v1: $rat] : ! % 8.15/1.88 [v2: $real] : (v1 = v0 | ~ (real_$to_rat(v2) = v1) | ~ (real_$to_rat(v2) = % 8.15/1.88 v0)) & ! [v0: $real] : ! [v1: $real] : ! [v2: $real] : (v1 = v0 | ~ % 8.15/1.88 (real_$to_real(v2) = v1) | ~ (real_$to_real(v2) = v0)) & ! [v0: $real] : % 8.15/1.88 ! [v1: $real] : ! [v2: int] : (v1 = v0 | ~ (int_$to_real(v2) = v1) | ~ % 8.15/1.88 (int_$to_real(v2) = v0)) & ! [v0: $real] : ! [v1: $real] : ! [v2: $real] % 8.15/1.88 : (v1 = v0 | ~ (real_$uminus(v2) = v1) | ~ (real_$uminus(v2) = v0)) % 8.15/1.88 % 8.15/1.88 Those formulas are unsatisfiable: % 8.15/1.88 --------------------------------- % 8.15/1.88 % 8.15/1.88 Begin of proof % 8.15/1.88 | % 8.15/1.88 | ALPHA: (function-axioms) implies: % 8.15/1.89 | (1) ! [v0: $real] : ! [v1: $real] : ! [v2: $real] : (v1 = v0 | ~ % 8.15/1.89 | (real_$uminus(v2) = v1) | ~ (real_$uminus(v2) = v0)) % 8.15/1.89 | % 8.15/1.89 | ALPHA: (input) implies: % 8.15/1.89 | (2) real_$uminus(real_0) = real_0 % 8.15/1.89 | (3) ! [v0: $real] : (v0 = real_0 | ~ (real_$uminus(v0) = v0)) % 8.15/1.89 | % 8.15/1.89 | DELTA: instantiating (real_uminus_problem_9) with fresh symbols all_5_0, % 8.15/1.89 | all_5_1 gives: % 8.15/1.89 | (4) real_$uminus(all_5_1) = all_5_0 & ((all_5_0 = all_5_1 & ~ (all_5_1 = % 8.15/1.89 | real_0)) | (all_5_1 = real_0 & ~ (all_5_0 = real_0))) % 8.15/1.89 | % 8.15/1.89 | ALPHA: (4) implies: % 8.15/1.89 | (5) real_$uminus(all_5_1) = all_5_0 % 8.15/1.89 | (6) (all_5_0 = all_5_1 & ~ (all_5_1 = real_0)) | (all_5_1 = real_0 & ~ % 8.15/1.89 | (all_5_0 = real_0)) % 8.15/1.89 | % 8.15/1.89 | BETA: splitting (6) gives: % 8.15/1.89 | % 8.15/1.89 | Case 1: % 8.15/1.89 | | % 8.15/1.89 | | (7) all_5_0 = all_5_1 & ~ (all_5_1 = real_0) % 8.15/1.89 | | % 8.15/1.89 | | ALPHA: (7) implies: % 8.15/1.89 | | (8) all_5_0 = all_5_1 % 8.15/1.89 | | (9) ~ (all_5_1 = real_0) % 8.15/1.89 | | % 8.15/1.89 | | REDUCE: (5), (8) imply: % 8.15/1.89 | | (10) real_$uminus(all_5_1) = all_5_1 % 8.15/1.89 | | % 8.15/1.89 | | GROUND_INST: instantiating (3) with all_5_1, simplifying with (10) gives: % 8.15/1.89 | | (11) all_5_1 = real_0 % 8.15/1.89 | | % 8.15/1.89 | | REDUCE: (9), (11) imply: % 8.15/1.89 | | (12) $false % 8.15/1.89 | | % 8.15/1.89 | | CLOSE: (12) is inconsistent. % 8.15/1.89 | | % 8.15/1.89 | Case 2: % 8.15/1.89 | | % 8.15/1.89 | | (13) all_5_1 = real_0 & ~ (all_5_0 = real_0) % 8.15/1.89 | | % 8.15/1.89 | | ALPHA: (13) implies: % 8.15/1.89 | | (14) all_5_1 = real_0 % 8.15/1.89 | | (15) ~ (all_5_0 = real_0) % 8.15/1.89 | | % 8.15/1.89 | | REDUCE: (5), (14) imply: % 8.15/1.89 | | (16) real_$uminus(real_0) = all_5_0 % 8.15/1.89 | | % 8.15/1.89 | | GROUND_INST: instantiating (1) with real_0, all_5_0, real_0, simplifying % 8.15/1.89 | | with (2), (16) gives: % 8.15/1.89 | | (17) all_5_0 = real_0 % 8.15/1.89 | | % 8.15/1.89 | | REDUCE: (15), (17) imply: % 8.15/1.89 | | (18) $false % 8.15/1.89 | | % 8.15/1.89 | | CLOSE: (18) is inconsistent. % 8.15/1.89 | | % 8.15/1.89 | End of split % 8.15/1.89 | % 8.15/1.89 End of proof % 8.15/1.89 % SZS output end Proof for theBenchmark % 8.15/1.90 % 8.15/1.90 1281ms %------------------------------------------------------------------------------