%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : ANA139_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 : n009.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 6.91s 1.67s % Output : Proof 11.26s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : ANA139_1 : TPTP v8.2.0. Released v8.2.0. % 0.07/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.34 % Computer : n009.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 18:41:21 EDT 2023 % 0.13/0.34 % CPUTime : % 0.53/0.60 ________ _____ % 0.53/0.60 ___ __ \_________(_)________________________________ % 0.53/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.53/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.53/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.53/0.60 % 0.53/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.53/0.60 (2023-06-19) % 0.53/0.60 % 0.53/0.60 (c) Philipp Rümmer, 2009-2023 % 0.53/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.53/0.60 Amanda Stjerna. % 0.53/0.60 Free software under BSD-3-Clause. % 0.53/0.60 % 0.53/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.53/0.60 % 0.53/0.60 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.53/0.62 Running up to 7 provers in parallel. % 0.53/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.53/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.53/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.53/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.53/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.53/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.53/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 1.14/0.86 Prover 3: Warning: Problem contains reals, using incomplete axiomatisation % 1.14/0.86 Prover 4: Warning: Problem contains reals, using incomplete axiomatisation % 1.14/0.86 Prover 5: Warning: Problem contains reals, using incomplete axiomatisation % 1.14/0.86 Prover 0: Warning: Problem contains reals, using incomplete axiomatisation % 1.14/0.86 Prover 6: Warning: Problem contains reals, using incomplete axiomatisation % 1.14/0.86 Prover 1: Warning: Problem contains reals, using incomplete axiomatisation % 1.14/0.86 Prover 2: Warning: Problem contains reals, using incomplete axiomatisation % 1.86/0.99 Prover 1: Preprocessing ... % 1.86/0.99 Prover 4: Preprocessing ... % 2.55/1.03 Prover 3: Preprocessing ... % 2.55/1.03 Prover 5: Preprocessing ... % 2.55/1.03 Prover 0: Preprocessing ... % 2.55/1.03 Prover 2: Preprocessing ... % 2.55/1.03 Prover 6: Preprocessing ... % 4.82/1.45 Prover 6: Proving ... % 4.82/1.45 Prover 2: Proving ... % 4.82/1.45 Prover 5: Proving ... % 4.82/1.45 Prover 1: Constructing countermodel ... % 5.79/1.48 Prover 3: Constructing countermodel ... % 5.79/1.49 Prover 4: Constructing countermodel ... % 5.79/1.50 Prover 0: Proving ... % 6.91/1.67 Prover 5: proved (1041ms) % 6.91/1.67 % 6.91/1.67 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 6.91/1.67 % 6.91/1.67 Prover 3: stopped % 6.91/1.67 Prover 2: stopped % 6.91/1.68 Prover 0: stopped % 6.91/1.68 Prover 6: stopped % 6.91/1.68 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 6.91/1.68 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 6.91/1.68 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 6.91/1.68 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 6.91/1.68 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 6.91/1.68 Prover 8: Warning: Problem contains reals, using incomplete axiomatisation % 6.91/1.68 Prover 7: Warning: Problem contains reals, using incomplete axiomatisation % 6.91/1.68 Prover 10: Warning: Problem contains reals, using incomplete axiomatisation % 6.91/1.68 Prover 11: Warning: Problem contains reals, using incomplete axiomatisation % 6.91/1.68 Prover 13: Warning: Problem contains reals, using incomplete axiomatisation % 6.91/1.70 Prover 10: Preprocessing ... % 6.91/1.70 Prover 7: Preprocessing ... % 7.46/1.71 Prover 11: Preprocessing ... % 7.46/1.71 Prover 13: Preprocessing ... % 7.46/1.71 Prover 8: Preprocessing ... % 7.98/1.80 Prover 10: Warning: ignoring some quantifiers % 7.98/1.82 Prover 10: Constructing countermodel ... % 7.98/1.82 Prover 7: Warning: ignoring some quantifiers % 7.98/1.84 Prover 7: Constructing countermodel ... % 7.98/1.84 Prover 8: Warning: ignoring some quantifiers % 7.98/1.84 Prover 13: Warning: ignoring some quantifiers % 7.98/1.84 Prover 13: Constructing countermodel ... % 7.98/1.85 Prover 8: Constructing countermodel ... % 8.83/1.90 Prover 11: Constructing countermodel ... % 9.07/1.96 Prover 10: gave up % 9.07/1.98 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 9.07/1.98 Prover 16: Warning: Problem contains reals, using incomplete axiomatisation % 9.07/1.99 Prover 16: Preprocessing ... % 10.23/2.10 Prover 16: Warning: ignoring some quantifiers % 10.23/2.10 Prover 16: Constructing countermodel ... % 10.23/2.13 Prover 1: gave up % 10.23/2.14 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085 % 10.23/2.14 Prover 19: Warning: Problem contains reals, using incomplete axiomatisation % 10.23/2.15 Prover 19: Preprocessing ... % 10.83/2.18 Prover 13: gave up % 10.83/2.19 Prover 7: Found proof (size 28) % 10.83/2.19 Prover 7: proved (518ms) % 10.83/2.19 Prover 16: stopped % 10.83/2.19 Prover 11: stopped % 10.83/2.19 Prover 4: stopped % 10.83/2.19 Prover 8: stopped % 11.10/2.23 Prover 19: Warning: ignoring some quantifiers % 11.10/2.23 Prover 19: Constructing countermodel ... % 11.26/2.24 Prover 19: stopped % 11.26/2.24 % 11.26/2.24 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 11.26/2.24 % 11.26/2.24 % SZS output start Proof for theBenchmark % 11.26/2.24 Assumptions after simplification: % 11.26/2.24 --------------------------------- % 11.26/2.25 % 11.26/2.25 (formula_1) % 11.26/2.27 ? [v0: $real] : ? [v1: $real] : ? [v2: $real] : (real_$difference(c, c) = % 11.26/2.27 v0 & real_$uminus(v0) = v1 & real_$less(real_0, v2) & ! [v3: $real] : ( ~ % 11.26/2.27 real_$less(real_0, v3) | ? [v4: $real] : ? [v5: $real] : ? [v6: $real] % 11.26/2.27 : ( ~ (v4 = a) & real_$difference(v4, a) = v5 & ( ~ real_$greatereq(v5, % 11.26/2.27 real_0) | real_$less(v5, v3)) & (real_$greatereq(v5, real_0) | % 11.26/2.27 (real_$uminus(v5) = v6 & real_$less(v6, v3))) & ((real_$greatereq(v0, % 11.26/2.27 real_0) & ~ real_$less(v0, v2)) | ( ~ real_$greatereq(v0, real_0) % 11.26/2.27 & ~ real_$less(v1, v2)))))) % 11.26/2.27 % 11.26/2.27 (input) % 11.26/2.29 ~ (real_very_large = real_very_small) & ~ (real_very_large = real_0) & ~ % 11.26/2.29 (real_very_small = real_0) & real_$floor(real_0) = real_0 & % 11.26/2.29 real_$ceiling(real_0) = real_0 & real_$truncate(real_0) = real_0 & % 11.26/2.29 real_$round(real_0) = real_0 & real_$to_int(real_0) = 0 & real_$to_rat(real_0) % 11.26/2.29 = rat_0 & real_$to_real(real_0) = real_0 & int_$to_real(0) = real_0 & % 11.26/2.29 real_$product(real_0, real_0) = real_0 & real_$sum(real_0, real_0) = real_0 & % 11.26/2.29 real_$difference(real_0, real_0) = real_0 & real_$uminus(real_0) = real_0 & % 11.26/2.29 real_$is_rat(real_0) & real_$is_int(real_0) & real_$greatereq(real_0, real_0) % 11.26/2.29 & real_$greater(real_very_large, real_0) & real_$greater(real_0, % 11.26/2.29 real_very_small) & real_$lesseq(real_very_small, real_very_large) & % 11.26/2.29 real_$lesseq(real_0, real_0) & real_$less(real_very_small, real_very_large) & % 11.26/2.29 real_$less(real_very_small, real_0) & real_$less(real_0, real_very_large) & ~ % 11.26/2.29 real_$greatereq(real_very_small, real_very_large) & ~ % 11.26/2.29 real_$greater(real_very_small, real_very_large) & ~ real_$greater(real_0, % 11.26/2.29 real_0) & ~ real_$less(real_0, real_0) & ! [v0: $real] : ! [v1: $real] : % 11.26/2.29 ! [v2: $real] : ! [v3: $real] : ! [v4: $real] : ( ~ (real_$sum(v3, v0) = v4) % 11.26/2.29 | ~ (real_$sum(v2, v1) = v3) | ? [v5: $real] : (real_$sum(v2, v5) = v4 & % 11.26/2.29 real_$sum(v1, v0) = v5)) & ! [v0: $real] : ! [v1: $real] : ! [v2: % 11.26/2.29 $real] : ! [v3: $real] : ! [v4: $real] : ( ~ (real_$sum(v2, v3) = v4) | ~ % 11.26/2.29 (real_$sum(v1, v0) = v3) | ? [v5: $real] : (real_$sum(v5, v0) = v4 & % 11.26/2.29 real_$sum(v2, v1) = v5)) & ! [v0: $real] : ! [v1: $real] : ! [v2: % 11.26/2.29 $real] : ! [v3: $real] : ( ~ (real_$sum(v1, v2) = v3) | ~ % 11.26/2.29 (real_$uminus(v0) = v2) | real_$difference(v1, v0) = v3) & ! [v0: $real] : % 11.26/2.29 ! [v1: $real] : ! [v2: $real] : (v0 = real_0 | ~ (real_$product(v1, v0) = % 11.26/2.29 v2) | real_$quotient(v2, v0) = v1) & ! [v0: $real] : ! [v1: $real] : ! % 11.26/2.29 [v2: $real] : ( ~ (real_$product(v1, v0) = v2) | real_$product(v0, v1) = v2) & % 11.26/2.29 ! [v0: $real] : ! [v1: $real] : ! [v2: $real] : ( ~ (real_$product(v0, v1) % 11.26/2.29 = v2) | real_$product(v1, v0) = v2) & ! [v0: $real] : ! [v1: $real] : ! % 11.26/2.29 [v2: $real] : ( ~ (real_$sum(v1, v0) = v2) | real_$sum(v0, v1) = v2) & ! [v0: % 11.26/2.29 $real] : ! [v1: $real] : ! [v2: $real] : ( ~ (real_$sum(v0, v1) = v2) | % 11.26/2.29 real_$sum(v1, v0) = v2) & ! [v0: $real] : ! [v1: $real] : ! [v2: $real] : % 11.26/2.29 ( ~ (real_$difference(v1, v0) = v2) | ? [v3: $real] : (real_$sum(v1, v3) = v2 % 11.26/2.29 & real_$uminus(v0) = v3)) & ! [v0: $real] : ! [v1: $real] : ! [v2: % 11.26/2.29 $real] : ( ~ real_$lesseq(v2, v1) | ~ real_$lesseq(v1, v0) | % 11.26/2.29 real_$lesseq(v2, v0)) & ! [v0: $real] : ! [v1: $real] : ! [v2: $real] : ( % 11.26/2.29 ~ real_$lesseq(v2, v1) | ~ real_$less(v1, v0) | real_$less(v2, v0)) & ! % 11.26/2.29 [v0: $real] : ! [v1: $real] : ! [v2: $real] : ( ~ real_$lesseq(v1, v0) | ~ % 11.26/2.29 real_$less(v2, v1) | real_$less(v2, v0)) & ! [v0: $real] : ! [v1: $real] : % 11.26/2.29 (v1 = v0 | ~ (real_$sum(v0, real_0) = v1)) & ! [v0: $real] : ! [v1: $real] % 11.26/2.29 : (v1 = v0 | ~ real_$lesseq(v1, v0) | real_$less(v1, v0)) & ! [v0: $real] : % 11.26/2.29 ! [v1: $real] : ( ~ (real_$uminus(v0) = v1) | real_$sum(v0, v1) = real_0) & ! % 11.26/2.29 [v0: $real] : ! [v1: $real] : ( ~ (real_$uminus(v0) = v1) | real_$uminus(v1) % 11.26/2.29 = v0) & ! [v0: $real] : ! [v1: $real] : ( ~ real_$greatereq(v0, v1) | % 11.26/2.29 real_$lesseq(v1, v0)) & ! [v0: $real] : ! [v1: $real] : ( ~ % 11.26/2.29 real_$greater(v0, v1) | real_$less(v1, v0)) & ! [v0: $real] : ! [v1: % 11.26/2.29 $real] : ( ~ real_$lesseq(v1, v0) | real_$greatereq(v0, v1)) & ! [v0: % 11.26/2.29 $real] : ! [v1: $real] : ( ~ real_$less(v1, v0) | real_$greater(v0, v1)) & % 11.26/2.29 ! [v0: $real] : ! [v1: $real] : ( ~ real_$less(v1, v0) | real_$lesseq(v1, % 11.26/2.29 v0)) & ! [v0: $real] : (v0 = real_0 | ~ (real_$uminus(v0) = v0)) & ? % 11.26/2.29 [v0: $real] : real_$lesseq(v0, v0) % 11.26/2.29 % 11.26/2.29 (function-axioms) % 11.26/2.30 ! [v0: $real] : ! [v1: $real] : ! [v2: $real] : ! [v3: $real] : (v1 = v0 | % 11.26/2.30 ~ (real_$quotient(v3, v2) = v1) | ~ (real_$quotient(v3, v2) = v0)) & ! % 11.26/2.30 [v0: $real] : ! [v1: $real] : ! [v2: $real] : ! [v3: $real] : (v1 = v0 | ~ % 11.26/2.30 (real_$product(v3, v2) = v1) | ~ (real_$product(v3, v2) = v0)) & ! [v0: % 11.26/2.30 $real] : ! [v1: $real] : ! [v2: $real] : ! [v3: $real] : (v1 = v0 | ~ % 11.26/2.30 (real_$sum(v3, v2) = v1) | ~ (real_$sum(v3, v2) = v0)) & ! [v0: $real] : % 11.26/2.30 ! [v1: $real] : ! [v2: $real] : ! [v3: $real] : (v1 = v0 | ~ % 11.26/2.30 (real_$difference(v3, v2) = v1) | ~ (real_$difference(v3, v2) = v0)) & ! % 11.26/2.30 [v0: $real] : ! [v1: $real] : ! [v2: $real] : (v1 = v0 | ~ (real_$floor(v2) % 11.26/2.30 = v1) | ~ (real_$floor(v2) = v0)) & ! [v0: $real] : ! [v1: $real] : ! % 11.26/2.30 [v2: $real] : (v1 = v0 | ~ (real_$ceiling(v2) = v1) | ~ (real_$ceiling(v2) = % 11.26/2.30 v0)) & ! [v0: $real] : ! [v1: $real] : ! [v2: $real] : (v1 = v0 | ~ % 11.26/2.30 (real_$truncate(v2) = v1) | ~ (real_$truncate(v2) = v0)) & ! [v0: $real] : % 11.26/2.30 ! [v1: $real] : ! [v2: $real] : (v1 = v0 | ~ (real_$round(v2) = v1) | ~ % 11.26/2.30 (real_$round(v2) = v0)) & ! [v0: int] : ! [v1: int] : ! [v2: $real] : (v1 % 11.26/2.30 = v0 | ~ (real_$to_int(v2) = v1) | ~ (real_$to_int(v2) = v0)) & ! [v0: % 11.26/2.30 $rat] : ! [v1: $rat] : ! [v2: $real] : (v1 = v0 | ~ (real_$to_rat(v2) = % 11.26/2.30 v1) | ~ (real_$to_rat(v2) = v0)) & ! [v0: $real] : ! [v1: $real] : ! % 11.26/2.30 [v2: $real] : (v1 = v0 | ~ (real_$to_real(v2) = v1) | ~ (real_$to_real(v2) = % 11.26/2.30 v0)) & ! [v0: $real] : ! [v1: $real] : ! [v2: int] : (v1 = v0 | ~ % 11.26/2.30 (int_$to_real(v2) = v1) | ~ (int_$to_real(v2) = v0)) & ! [v0: $real] : ! % 11.26/2.30 [v1: $real] : ! [v2: $real] : (v1 = v0 | ~ (real_$uminus(v2) = v1) | ~ % 11.26/2.30 (real_$uminus(v2) = v0)) % 11.26/2.30 % 11.26/2.30 Those formulas are unsatisfiable: % 11.26/2.30 --------------------------------- % 11.26/2.30 % 11.26/2.30 Begin of proof % 11.26/2.30 | % 11.26/2.30 | ALPHA: (function-axioms) implies: % 11.26/2.30 | (1) ! [v0: $real] : ! [v1: $real] : ! [v2: $real] : ! [v3: $real] : (v1 % 11.26/2.30 | = v0 | ~ (real_$sum(v3, v2) = v1) | ~ (real_$sum(v3, v2) = v0)) % 11.26/2.30 | % 11.26/2.30 | ALPHA: (input) implies: % 11.26/2.30 | (2) real_$greatereq(real_0, real_0) % 11.26/2.30 | (3) real_$sum(real_0, real_0) = real_0 % 11.26/2.30 | (4) ! [v0: $real] : ! [v1: $real] : ( ~ (real_$uminus(v0) = v1) | % 11.26/2.30 | real_$sum(v0, v1) = real_0) % 11.26/2.30 | (5) ! [v0: $real] : ! [v1: $real] : ! [v2: $real] : ( ~ % 11.26/2.30 | (real_$difference(v1, v0) = v2) | ? [v3: $real] : (real_$sum(v1, v3) % 11.26/2.30 | = v2 & real_$uminus(v0) = v3)) % 11.26/2.30 | (6) ! [v0: $real] : ! [v1: $real] : ! [v2: $real] : ! [v3: $real] : ! % 11.26/2.30 | [v4: $real] : ( ~ (real_$sum(v3, v0) = v4) | ~ (real_$sum(v2, v1) = % 11.26/2.30 | v3) | ? [v5: $real] : (real_$sum(v2, v5) = v4 & real_$sum(v1, v0) % 11.26/2.30 | = v5)) % 11.26/2.30 | % 11.26/2.30 | DELTA: instantiating (formula_1) with fresh symbols all_7_0, all_7_1, all_7_2 % 11.26/2.30 | gives: % 11.26/2.30 | (7) real_$difference(c, c) = all_7_2 & real_$uminus(all_7_2) = all_7_1 & % 11.26/2.30 | real_$less(real_0, all_7_0) & ! [v0: $real] : ( ~ real_$less(real_0, % 11.26/2.30 | v0) | ? [v1: $real] : ? [v2: $real] : ? [v3: $real] : ( ~ (v1 = % 11.26/2.30 | a) & real_$difference(v1, a) = v2 & ( ~ real_$greatereq(v2, % 11.26/2.30 | real_0) | real_$less(v2, v0)) & (real_$greatereq(v2, real_0) | % 11.26/2.30 | (real_$uminus(v2) = v3 & real_$less(v3, v0))) & % 11.26/2.30 | ((real_$greatereq(all_7_2, real_0) & ~ real_$less(all_7_2, % 11.26/2.30 | all_7_0)) | ( ~ real_$greatereq(all_7_2, real_0) & ~ % 11.26/2.30 | real_$less(all_7_1, all_7_0))))) % 11.26/2.30 | % 11.26/2.30 | ALPHA: (7) implies: % 11.26/2.31 | (8) real_$less(real_0, all_7_0) % 11.26/2.31 | (9) real_$difference(c, c) = all_7_2 % 11.26/2.31 | (10) ! [v0: $real] : ( ~ real_$less(real_0, v0) | ? [v1: $real] : ? [v2: % 11.26/2.31 | $real] : ? [v3: $real] : ( ~ (v1 = a) & real_$difference(v1, a) = % 11.26/2.31 | v2 & ( ~ real_$greatereq(v2, real_0) | real_$less(v2, v0)) & % 11.26/2.31 | (real_$greatereq(v2, real_0) | (real_$uminus(v2) = v3 & % 11.26/2.31 | real_$less(v3, v0))) & ((real_$greatereq(all_7_2, real_0) & ~ % 11.26/2.31 | real_$less(all_7_2, all_7_0)) | ( ~ real_$greatereq(all_7_2, % 11.26/2.31 | real_0) & ~ real_$less(all_7_1, all_7_0))))) % 11.26/2.31 | % 11.26/2.31 | GROUND_INST: instantiating (10) with all_7_0, simplifying with (8) gives: % 11.26/2.31 | (11) ? [v0: $real] : ? [v1: $real] : ? [v2: $real] : ( ~ (v0 = a) & % 11.26/2.31 | real_$difference(v0, a) = v1 & ( ~ real_$greatereq(v1, real_0) | % 11.26/2.31 | real_$less(v1, all_7_0)) & (real_$greatereq(v1, real_0) | % 11.26/2.31 | (real_$uminus(v1) = v2 & real_$less(v2, all_7_0))) & % 11.26/2.31 | ((real_$greatereq(all_7_2, real_0) & ~ real_$less(all_7_2, % 11.26/2.31 | all_7_0)) | ( ~ real_$greatereq(all_7_2, real_0) & ~ % 11.26/2.31 | real_$less(all_7_1, all_7_0)))) % 11.26/2.31 | % 11.26/2.31 | GROUND_INST: instantiating (5) with c, c, all_7_2, simplifying with (9) gives: % 11.26/2.31 | (12) ? [v0: $real] : (real_$sum(c, v0) = all_7_2 & real_$uminus(c) = v0) % 11.26/2.31 | % 11.26/2.31 | DELTA: instantiating (12) with fresh symbol all_20_0 gives: % 11.26/2.31 | (13) real_$sum(c, all_20_0) = all_7_2 & real_$uminus(c) = all_20_0 % 11.26/2.31 | % 11.26/2.31 | ALPHA: (13) implies: % 11.26/2.31 | (14) real_$uminus(c) = all_20_0 % 11.26/2.31 | (15) real_$sum(c, all_20_0) = all_7_2 % 11.26/2.31 | % 11.26/2.31 | DELTA: instantiating (11) with fresh symbols all_24_0, all_24_1, all_24_2 % 11.26/2.31 | gives: % 11.26/2.31 | (16) ~ (all_24_2 = a) & real_$difference(all_24_2, a) = all_24_1 & ( ~ % 11.26/2.31 | real_$greatereq(all_24_1, real_0) | real_$less(all_24_1, all_7_0)) & % 11.26/2.31 | (real_$greatereq(all_24_1, real_0) | (real_$uminus(all_24_1) = % 11.26/2.31 | all_24_0 & real_$less(all_24_0, all_7_0))) & % 11.26/2.31 | ((real_$greatereq(all_7_2, real_0) & ~ real_$less(all_7_2, all_7_0)) % 11.26/2.31 | | ( ~ real_$greatereq(all_7_2, real_0) & ~ real_$less(all_7_1, % 11.26/2.31 | all_7_0))) % 11.26/2.31 | % 11.26/2.31 | ALPHA: (16) implies: % 11.26/2.31 | (17) (real_$greatereq(all_7_2, real_0) & ~ real_$less(all_7_2, all_7_0)) | % 11.26/2.31 | ( ~ real_$greatereq(all_7_2, real_0) & ~ real_$less(all_7_1, % 11.26/2.31 | all_7_0)) % 11.26/2.31 | % 11.26/2.31 | GROUND_INST: instantiating (4) with c, all_20_0, simplifying with (14) gives: % 11.26/2.31 | (18) real_$sum(c, all_20_0) = real_0 % 11.26/2.31 | % 11.26/2.31 | GROUND_INST: instantiating (6) with real_0, all_20_0, c, real_0, real_0, % 11.26/2.31 | simplifying with (3) gives: % 11.26/2.31 | (19) ~ (real_$sum(c, all_20_0) = real_0) | ? [v0: $real] : % 11.26/2.31 | (real_$sum(all_20_0, real_0) = v0 & real_$sum(c, v0) = real_0) % 11.26/2.31 | % 11.26/2.31 | BETA: splitting (19) gives: % 11.26/2.31 | % 11.26/2.31 | Case 1: % 11.26/2.31 | | % 11.26/2.31 | | (20) ~ (real_$sum(c, all_20_0) = real_0) % 11.26/2.31 | | % 11.26/2.31 | | PRED_UNIFY: (18), (20) imply: % 11.26/2.31 | | (21) $false % 11.26/2.32 | | % 11.26/2.32 | | CLOSE: (21) is inconsistent. % 11.26/2.32 | | % 11.26/2.32 | Case 2: % 11.26/2.32 | | % 11.26/2.32 | | % 11.26/2.32 | | GROUND_INST: instantiating (1) with all_7_2, real_0, all_20_0, c, % 11.26/2.32 | | simplifying with (15), (18) gives: % 11.26/2.32 | | (22) all_7_2 = real_0 % 11.26/2.32 | | % 11.26/2.32 | | BETA: splitting (17) gives: % 11.26/2.32 | | % 11.26/2.32 | | Case 1: % 11.26/2.32 | | | % 11.26/2.32 | | | (23) real_$greatereq(all_7_2, real_0) & ~ real_$less(all_7_2, all_7_0) % 11.26/2.32 | | | % 11.26/2.32 | | | ALPHA: (23) implies: % 11.26/2.32 | | | (24) ~ real_$less(all_7_2, all_7_0) % 11.26/2.32 | | | % 11.26/2.32 | | | REDUCE: (22), (24) imply: % 11.26/2.32 | | | (25) ~ real_$less(real_0, all_7_0) % 11.26/2.32 | | | % 11.26/2.32 | | | PRED_UNIFY: (8), (25) imply: % 11.26/2.32 | | | (26) $false % 11.26/2.32 | | | % 11.26/2.32 | | | CLOSE: (26) is inconsistent. % 11.26/2.32 | | | % 11.26/2.32 | | Case 2: % 11.26/2.32 | | | % 11.26/2.32 | | | (27) ~ real_$greatereq(all_7_2, real_0) & ~ real_$less(all_7_1, % 11.26/2.32 | | | all_7_0) % 11.26/2.32 | | | % 11.26/2.32 | | | ALPHA: (27) implies: % 11.26/2.32 | | | (28) ~ real_$greatereq(all_7_2, real_0) % 11.26/2.32 | | | % 11.26/2.32 | | | REDUCE: (22), (28) imply: % 11.26/2.32 | | | (29) ~ real_$greatereq(real_0, real_0) % 11.26/2.32 | | | % 11.26/2.32 | | | PRED_UNIFY: (2), (29) imply: % 11.26/2.32 | | | (30) $false % 11.26/2.32 | | | % 11.26/2.32 | | | CLOSE: (30) is inconsistent. % 11.26/2.32 | | | % 11.26/2.32 | | End of split % 11.26/2.32 | | % 11.26/2.32 | End of split % 11.26/2.32 | % 11.26/2.32 End of proof % 11.26/2.32 % SZS output end Proof for theBenchmark % 11.26/2.32 % 11.26/2.32 1715ms %------------------------------------------------------------------------------