%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : ARI744_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 : n022.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 17:49:00 EDT 2023 % Result : Theorem 11.90s 2.35s % Output : Proof 13.62s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : ARI744_1 : TPTP v8.1.2. Released v7.0.0. % 0.03/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.34 % Computer : n022.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 : Tue Aug 29 17:47:38 EDT 2023 % 0.13/0.34 % CPUTime : % 0.73/0.67 ________ _____ % 0.73/0.67 ___ __ \_________(_)________________________________ % 0.73/0.67 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.73/0.67 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.73/0.67 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.73/0.67 % 0.73/0.67 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.73/0.67 (2023-06-19) % 0.73/0.67 % 0.73/0.67 (c) Philipp Rümmer, 2009-2023 % 0.73/0.67 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.73/0.67 Amanda Stjerna. % 0.73/0.67 Free software under BSD-3-Clause. % 0.73/0.67 % 0.73/0.67 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.73/0.67 % 0.73/0.67 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.73/0.69 Running up to 7 provers in parallel. % 0.73/0.70 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.73/0.70 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.73/0.70 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.73/0.70 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.73/0.70 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.73/0.70 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.73/0.70 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 1.64/0.94 Prover 0: Warning: Problem contains reals, using incomplete axiomatisation % 1.64/0.94 Prover 5: Warning: Problem contains reals, using incomplete axiomatisation % 1.64/0.94 Prover 1: Warning: Problem contains reals, using incomplete axiomatisation % 1.64/0.94 Prover 2: Warning: Problem contains reals, using incomplete axiomatisation % 1.64/0.94 Prover 3: Warning: Problem contains reals, using incomplete axiomatisation % 1.64/0.94 Prover 6: Warning: Problem contains reals, using incomplete axiomatisation % 1.64/0.94 Prover 4: Warning: Problem contains reals, using incomplete axiomatisation % 2.65/1.10 Prover 4: Preprocessing ... % 2.65/1.10 Prover 1: Preprocessing ... % 3.15/1.17 Prover 6: Preprocessing ... % 3.15/1.17 Prover 0: Preprocessing ... % 3.39/1.19 Prover 5: Preprocessing ... % 3.39/1.19 Prover 2: Preprocessing ... % 3.39/1.20 Prover 3: Preprocessing ... % 7.23/1.75 Prover 1: Constructing countermodel ... % 7.83/1.76 Prover 6: Constructing countermodel ... % 7.83/1.77 Prover 4: Constructing countermodel ... % 8.47/1.86 Prover 0: Proving ... % 10.07/2.06 Prover 3: Constructing countermodel ... % 10.82/2.17 Prover 2: Proving ... % 11.90/2.35 Prover 6: proved (1647ms) % 11.90/2.35 % 11.90/2.35 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 11.90/2.35 % 11.90/2.35 Prover 2: stopped % 11.90/2.35 Prover 0: stopped % 12.41/2.36 Prover 3: stopped % 12.41/2.36 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 12.41/2.36 Prover 8: Warning: Problem contains reals, using incomplete axiomatisation % 12.41/2.36 Prover 1: Found proof (size 22) % 12.41/2.36 Prover 1: proved (1661ms) % 12.41/2.36 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 12.41/2.36 Prover 10: Warning: Problem contains reals, using incomplete axiomatisation % 12.41/2.36 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 12.41/2.36 Prover 4: stopped % 12.41/2.36 Prover 7: Warning: Problem contains reals, using incomplete axiomatisation % 12.48/2.37 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 12.48/2.37 Prover 11: Warning: Problem contains reals, using incomplete axiomatisation % 12.48/2.37 Prover 8: Preprocessing ... % 12.48/2.40 Prover 5: Proving ... % 12.48/2.40 Prover 5: stopped % 12.48/2.41 Prover 7: Preprocessing ... % 12.82/2.41 Prover 11: Preprocessing ... % 12.82/2.42 Prover 10: Preprocessing ... % 13.08/2.46 Prover 8: Warning: ignoring some quantifiers % 13.08/2.46 Prover 7: stopped % 13.08/2.47 Prover 8: Constructing countermodel ... % 13.08/2.47 Prover 10: stopped % 13.08/2.48 Prover 8: stopped % 13.08/2.49 Prover 11: stopped % 13.08/2.49 % 13.08/2.49 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 13.08/2.49 % 13.08/2.50 % SZS output start Proof for theBenchmark % 13.08/2.50 Assumptions after simplification: % 13.08/2.50 --------------------------------- % 13.08/2.50 % 13.08/2.50 (sqrt_four) % 13.08/2.52 ? [v0: $real] : ( ~ (v0 = real_2) & sqrt(real_4) = v0) % 13.08/2.52 % 13.08/2.52 (sqrt_positive) % 13.08/2.52 ! [v0: $real] : ( ~ (real_$lesseq(real_0, v0) = 0) | ? [v1: $real] : % 13.08/2.52 (sqrt(v0) = v1 & real_$lesseq(real_0, v1) = 0)) % 13.08/2.52 % 13.08/2.52 (sqrt_square) % 13.08/2.52 ! [v0: $real] : ( ~ (real_$lesseq(real_0, v0) = 0) | ? [v1: $real] : % 13.08/2.52 (sqrt(v0) = v1 & sqr(v1) = v0)) % 13.08/2.52 % 13.08/2.52 (square_sqrt) % 13.08/2.52 ! [v0: $real] : ( ~ (real_$lesseq(real_0, v0) = 0) | ? [v1: $real] : % 13.08/2.52 (sqrt(v1) = v0 & real_$product(v0, v0) = v1)) % 13.08/2.52 % 13.08/2.52 (input) % 13.62/2.55 ~ (real_very_large = real_very_small) & ~ (real_very_large = real_2) & ~ % 13.62/2.55 (real_very_large = real_4) & ~ (real_very_large = real_1) & ~ % 13.62/2.55 (real_very_large = real_0) & ~ (real_very_small = real_2) & ~ % 13.62/2.55 (real_very_small = real_4) & ~ (real_very_small = real_1) & ~ % 13.62/2.55 (real_very_small = real_0) & ~ (real_2 = real_4) & ~ (real_2 = real_1) & ~ % 13.62/2.55 (real_2 = real_0) & ~ (real_4 = real_1) & ~ (real_4 = real_0) & ~ (real_1 = % 13.62/2.55 real_0) & real_$is_int(real_2) = 0 & real_$is_int(real_4) = 0 & % 13.62/2.55 real_$is_int(real_1) = 0 & real_$is_int(real_0) = 0 & real_$is_rat(real_2) = 0 % 13.62/2.55 & real_$is_rat(real_4) = 0 & real_$is_rat(real_1) = 0 & real_$is_rat(real_0) = % 13.62/2.55 0 & real_$floor(real_2) = real_2 & real_$floor(real_4) = real_4 & % 13.62/2.55 real_$floor(real_1) = real_1 & real_$floor(real_0) = real_0 & % 13.62/2.55 real_$ceiling(real_2) = real_2 & real_$ceiling(real_4) = real_4 & % 13.62/2.55 real_$ceiling(real_1) = real_1 & real_$ceiling(real_0) = real_0 & % 13.62/2.55 real_$truncate(real_2) = real_2 & real_$truncate(real_4) = real_4 & % 13.62/2.55 real_$truncate(real_1) = real_1 & real_$truncate(real_0) = real_0 & % 13.62/2.55 real_$round(real_2) = real_2 & real_$round(real_4) = real_4 & % 13.62/2.55 real_$round(real_1) = real_1 & real_$round(real_0) = real_0 & % 13.62/2.55 real_$to_int(real_2) = 2 & real_$to_int(real_4) = 4 & real_$to_int(real_1) = 1 % 13.62/2.55 & real_$to_int(real_0) = 0 & real_$to_rat(real_2) = rat_2 & % 13.62/2.55 real_$to_rat(real_4) = rat_4 & real_$to_rat(real_1) = rat_1 & % 13.62/2.55 real_$to_rat(real_0) = rat_0 & real_$to_real(real_2) = real_2 & % 13.62/2.55 real_$to_real(real_4) = real_4 & real_$to_real(real_1) = real_1 & % 13.62/2.55 real_$to_real(real_0) = real_0 & int_$to_real(4) = real_4 & int_$to_real(2) = % 13.62/2.55 real_2 & int_$to_real(1) = real_1 & int_$to_real(0) = real_0 & % 13.62/2.55 real_$quotient(real_2, real_2) = real_1 & real_$quotient(real_2, real_1) = % 13.62/2.55 real_2 & real_$quotient(real_4, real_2) = real_2 & real_$quotient(real_4, % 13.62/2.55 real_4) = real_1 & real_$quotient(real_4, real_1) = real_4 & % 13.62/2.55 real_$quotient(real_1, real_1) = real_1 & real_$quotient(real_0, real_2) = % 13.62/2.55 real_0 & real_$quotient(real_0, real_4) = real_0 & real_$quotient(real_0, % 13.62/2.55 real_1) = real_0 & real_$difference(real_2, real_2) = real_0 & % 13.62/2.55 real_$difference(real_2, real_1) = real_1 & real_$difference(real_2, real_0) = % 13.62/2.55 real_2 & real_$difference(real_4, real_2) = real_2 & real_$difference(real_4, % 13.62/2.55 real_4) = real_0 & real_$difference(real_4, real_0) = real_4 & % 13.62/2.55 real_$difference(real_1, real_1) = real_0 & real_$difference(real_1, real_0) = % 13.62/2.55 real_1 & real_$difference(real_0, real_0) = real_0 & real_$uminus(real_0) = % 13.62/2.55 real_0 & real_$sum(real_2, real_2) = real_4 & real_$sum(real_2, real_0) = % 13.62/2.55 real_2 & real_$sum(real_4, real_0) = real_4 & real_$sum(real_1, real_1) = % 13.62/2.55 real_2 & real_$sum(real_1, real_0) = real_1 & real_$sum(real_0, real_2) = % 13.62/2.55 real_2 & real_$sum(real_0, real_4) = real_4 & real_$sum(real_0, real_1) = % 13.62/2.55 real_1 & real_$sum(real_0, real_0) = real_0 & real_$greatereq(real_very_small, % 13.62/2.55 real_very_large) = 1 & real_$greatereq(real_2, real_2) = 0 & % 13.62/2.55 real_$greatereq(real_2, real_4) = 1 & real_$greatereq(real_2, real_1) = 0 & % 13.62/2.55 real_$greatereq(real_2, real_0) = 0 & real_$greatereq(real_4, real_2) = 0 & % 13.62/2.55 real_$greatereq(real_4, real_4) = 0 & real_$greatereq(real_4, real_1) = 0 & % 13.62/2.55 real_$greatereq(real_4, real_0) = 0 & real_$greatereq(real_1, real_2) = 1 & % 13.62/2.55 real_$greatereq(real_1, real_4) = 1 & real_$greatereq(real_1, real_1) = 0 & % 13.62/2.55 real_$greatereq(real_1, real_0) = 0 & real_$greatereq(real_0, real_2) = 1 & % 13.62/2.55 real_$greatereq(real_0, real_4) = 1 & real_$greatereq(real_0, real_1) = 1 & % 13.62/2.55 real_$greatereq(real_0, real_0) = 0 & real_$greater(real_very_large, real_2) = % 13.62/2.55 0 & real_$greater(real_very_large, real_4) = 0 & % 13.62/2.55 real_$greater(real_very_large, real_1) = 0 & real_$greater(real_very_large, % 13.62/2.55 real_0) = 0 & real_$greater(real_very_small, real_very_large) = 1 & % 13.62/2.55 real_$greater(real_2, real_very_small) = 0 & real_$greater(real_2, real_2) = 1 % 13.62/2.55 & real_$greater(real_2, real_4) = 1 & real_$greater(real_2, real_1) = 0 & % 13.62/2.55 real_$greater(real_2, real_0) = 0 & real_$greater(real_4, real_very_small) = 0 % 13.62/2.55 & real_$greater(real_4, real_2) = 0 & real_$greater(real_4, real_4) = 1 & % 13.62/2.55 real_$greater(real_4, real_1) = 0 & real_$greater(real_4, real_0) = 0 & % 13.62/2.55 real_$greater(real_1, real_very_small) = 0 & real_$greater(real_1, real_2) = 1 % 13.62/2.55 & real_$greater(real_1, real_4) = 1 & real_$greater(real_1, real_1) = 1 & % 13.62/2.55 real_$greater(real_1, real_0) = 0 & real_$greater(real_0, real_very_small) = 0 % 13.62/2.55 & real_$greater(real_0, real_2) = 1 & real_$greater(real_0, real_4) = 1 & % 13.62/2.55 real_$greater(real_0, real_1) = 1 & real_$greater(real_0, real_0) = 1 & % 13.62/2.55 real_$less(real_very_small, real_very_large) = 0 & real_$less(real_very_small, % 13.62/2.55 real_2) = 0 & real_$less(real_very_small, real_4) = 0 & % 13.62/2.55 real_$less(real_very_small, real_1) = 0 & real_$less(real_very_small, real_0) % 13.62/2.55 = 0 & real_$less(real_2, real_very_large) = 0 & real_$less(real_2, real_2) = 1 % 13.62/2.55 & real_$less(real_2, real_4) = 0 & real_$less(real_2, real_1) = 1 & % 13.62/2.55 real_$less(real_2, real_0) = 1 & real_$less(real_4, real_very_large) = 0 & % 13.62/2.55 real_$less(real_4, real_2) = 1 & real_$less(real_4, real_4) = 1 & % 13.62/2.55 real_$less(real_4, real_1) = 1 & real_$less(real_4, real_0) = 1 & % 13.62/2.55 real_$less(real_1, real_very_large) = 0 & real_$less(real_1, real_2) = 0 & % 13.62/2.55 real_$less(real_1, real_4) = 0 & real_$less(real_1, real_1) = 1 & % 13.62/2.55 real_$less(real_1, real_0) = 1 & real_$less(real_0, real_very_large) = 0 & % 13.62/2.55 real_$less(real_0, real_2) = 0 & real_$less(real_0, real_4) = 0 & % 13.62/2.55 real_$less(real_0, real_1) = 0 & real_$less(real_0, real_0) = 1 & % 13.62/2.55 real_$lesseq(real_very_small, real_very_large) = 0 & real_$lesseq(real_2, % 13.62/2.55 real_2) = 0 & real_$lesseq(real_2, real_4) = 0 & real_$lesseq(real_2, % 13.62/2.55 real_1) = 1 & real_$lesseq(real_2, real_0) = 1 & real_$lesseq(real_4, % 13.62/2.55 real_2) = 1 & real_$lesseq(real_4, real_4) = 0 & real_$lesseq(real_4, % 13.62/2.55 real_1) = 1 & real_$lesseq(real_4, real_0) = 1 & real_$lesseq(real_1, % 13.62/2.55 real_2) = 0 & real_$lesseq(real_1, real_4) = 0 & real_$lesseq(real_1, % 13.62/2.55 real_1) = 0 & real_$lesseq(real_1, real_0) = 1 & real_$lesseq(real_0, % 13.62/2.55 real_2) = 0 & real_$lesseq(real_0, real_4) = 0 & real_$lesseq(real_0, % 13.62/2.55 real_1) = 0 & real_$lesseq(real_0, real_0) = 0 & real_$product(real_2, % 13.62/2.55 real_2) = real_4 & real_$product(real_2, real_1) = real_2 & % 13.62/2.55 real_$product(real_2, real_0) = real_0 & real_$product(real_4, real_1) = % 13.62/2.55 real_4 & real_$product(real_4, real_0) = real_0 & real_$product(real_1, % 13.62/2.55 real_2) = real_2 & real_$product(real_1, real_4) = real_4 & % 13.62/2.55 real_$product(real_1, real_1) = real_1 & real_$product(real_1, real_0) = % 13.62/2.55 real_0 & real_$product(real_0, real_2) = real_0 & real_$product(real_0, % 13.62/2.55 real_4) = real_0 & real_$product(real_0, real_1) = real_0 & % 13.62/2.55 real_$product(real_0, real_0) = real_0 & ! [v0: $real] : ! [v1: $real] : ! % 13.62/2.55 [v2: $real] : ! [v3: $real] : ! [v4: $real] : ( ~ (real_$sum(v3, v0) = v4) | % 13.62/2.55 ~ (real_$sum(v2, v1) = v3) | ? [v5: $real] : (real_$sum(v2, v5) = v4 & % 13.62/2.55 real_$sum(v1, v0) = v5)) & ! [v0: $real] : ! [v1: $real] : ! [v2: % 13.62/2.55 $real] : ! [v3: $real] : (v3 = v1 | v0 = real_0 | ~ (real_$quotient(v2, % 13.62/2.56 v0) = v3) | ~ (real_$product(v1, v0) = v2)) & ! [v0: $real] : ! [v1: % 13.62/2.56 $real] : ! [v2: $real] : ! [v3: int] : (v3 = 0 | ~ (real_$less(v2, v0) = % 13.62/2.56 v3) | ~ (real_$lesseq(v1, v0) = 0) | ? [v4: int] : ( ~ (v4 = 0) & % 13.62/2.56 real_$less(v2, v1) = v4)) & ! [v0: $real] : ! [v1: $real] : ! [v2: % 13.62/2.56 $real] : ! [v3: int] : (v3 = 0 | ~ (real_$lesseq(v2, v0) = v3) | ~ % 13.62/2.56 (real_$lesseq(v1, v0) = 0) | ? [v4: int] : ( ~ (v4 = 0) & real_$lesseq(v2, % 13.62/2.56 v1) = v4)) & ! [v0: $real] : ! [v1: $real] : ! [v2: $real] : ! [v3: % 13.62/2.56 $real] : ( ~ (real_$uminus(v0) = v2) | ~ (real_$sum(v1, v2) = v3) | % 13.62/2.56 real_$difference(v1, v0) = v3) & ! [v0: $real] : ! [v1: $real] : ! [v2: % 13.62/2.56 $real] : (v2 = real_0 | ~ (real_$uminus(v0) = v1) | ~ (real_$sum(v0, v1) = % 13.62/2.56 v2)) & ! [v0: $real] : ! [v1: $real] : ! [v2: int] : (v2 = 0 | ~ % 13.62/2.56 (real_$greatereq(v0, v1) = v2) | ? [v3: int] : ( ~ (v3 = 0) & % 13.62/2.56 real_$lesseq(v1, v0) = v3)) & ! [v0: $real] : ! [v1: $real] : ! [v2: % 13.62/2.56 int] : (v2 = 0 | ~ (real_$greater(v0, v1) = v2) | ? [v3: int] : ( ~ (v3 = % 13.62/2.56 0) & real_$less(v1, v0) = v3)) & ! [v0: $real] : ! [v1: $real] : ! % 13.62/2.56 [v2: int] : (v2 = 0 | ~ (real_$lesseq(v1, v0) = v2) | ( ~ (v1 = v0) & ? [v3: % 13.62/2.56 int] : ( ~ (v3 = 0) & real_$less(v1, v0) = v3))) & ! [v0: $real] : ! % 13.62/2.56 [v1: $real] : ! [v2: $real] : ( ~ (real_$sum(v0, v1) = v2) | real_$sum(v1, % 13.62/2.56 v0) = v2) & ! [v0: $real] : ! [v1: $real] : ! [v2: $real] : ( ~ % 13.62/2.56 (real_$less(v1, v0) = 0) | ~ (real_$lesseq(v2, v1) = 0) | real_$less(v2, % 13.62/2.56 v0) = 0) & ! [v0: $real] : ! [v1: $real] : ! [v2: $real] : ( ~ % 13.62/2.56 (real_$product(v0, v1) = v2) | real_$product(v1, v0) = v2) & ! [v0: $real] % 13.62/2.56 : ! [v1: $real] : (v1 = v0 | ~ (real_$sum(v0, real_0) = v1)) & ! [v0: % 13.62/2.56 $real] : ! [v1: $real] : (v1 = v0 | ~ (real_$lesseq(v1, v0) = 0) | % 13.62/2.56 real_$less(v1, v0) = 0) & ! [v0: $real] : ! [v1: $real] : ( ~ % 13.62/2.56 (real_$uminus(v0) = v1) | real_$uminus(v1) = v0) & ! [v0: $real] : ! [v1: % 13.62/2.56 $real] : ( ~ (real_$greatereq(v0, v1) = 0) | real_$lesseq(v1, v0) = 0) & ! % 13.62/2.56 [v0: $real] : ! [v1: $real] : ( ~ (real_$greater(v0, v1) = 0) | % 13.62/2.56 real_$less(v1, v0) = 0) & ! [v0: $real] : (v0 = real_0 | ~ % 13.62/2.56 (real_$uminus(v0) = v0)) % 13.62/2.56 % 13.62/2.56 (function-axioms) % 13.62/2.56 ! [v0: $real] : ! [v1: $real] : ! [v2: $real] : ! [v3: $real] : (v1 = v0 | % 13.62/2.56 ~ (real_$quotient(v3, v2) = v1) | ~ (real_$quotient(v3, v2) = v0)) & ! % 13.62/2.56 [v0: $real] : ! [v1: $real] : ! [v2: $real] : ! [v3: $real] : (v1 = v0 | ~ % 13.62/2.56 (real_$difference(v3, v2) = v1) | ~ (real_$difference(v3, v2) = v0)) & ! % 13.62/2.56 [v0: $real] : ! [v1: $real] : ! [v2: $real] : ! [v3: $real] : (v1 = v0 | ~ % 13.62/2.56 (real_$sum(v3, v2) = v1) | ~ (real_$sum(v3, v2) = v0)) & ! [v0: % 13.62/2.56 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $real] : ! [v3: % 13.62/2.56 $real] : (v1 = v0 | ~ (real_$greatereq(v3, v2) = v1) | ~ % 13.62/2.56 (real_$greatereq(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 13.62/2.56 MultipleValueBool] : ! [v2: $real] : ! [v3: $real] : (v1 = v0 | ~ % 13.62/2.56 (real_$greater(v3, v2) = v1) | ~ (real_$greater(v3, v2) = v0)) & ! [v0: % 13.62/2.56 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $real] : ! [v3: % 13.62/2.56 $real] : (v1 = v0 | ~ (real_$less(v3, v2) = v1) | ~ (real_$less(v3, v2) = % 13.62/2.56 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 13.62/2.56 $real] : ! [v3: $real] : (v1 = v0 | ~ (real_$lesseq(v3, v2) = v1) | ~ % 13.62/2.56 (real_$lesseq(v3, v2) = v0)) & ! [v0: $real] : ! [v1: $real] : ! [v2: % 13.62/2.56 $real] : ! [v3: $real] : (v1 = v0 | ~ (real_$product(v3, v2) = v1) | ~ % 13.62/2.56 (real_$product(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 13.62/2.56 MultipleValueBool] : ! [v2: $real] : (v1 = v0 | ~ (real_$is_int(v2) = v1) % 13.62/2.56 | ~ (real_$is_int(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 13.62/2.56 MultipleValueBool] : ! [v2: $real] : (v1 = v0 | ~ (real_$is_rat(v2) = v1) % 13.62/2.56 | ~ (real_$is_rat(v2) = v0)) & ! [v0: $real] : ! [v1: $real] : ! [v2: % 13.62/2.56 $real] : (v1 = v0 | ~ (real_$floor(v2) = v1) | ~ (real_$floor(v2) = v0)) & % 13.62/2.57 ! [v0: $real] : ! [v1: $real] : ! [v2: $real] : (v1 = v0 | ~ % 13.62/2.57 (real_$ceiling(v2) = v1) | ~ (real_$ceiling(v2) = v0)) & ! [v0: $real] : % 13.62/2.57 ! [v1: $real] : ! [v2: $real] : (v1 = v0 | ~ (real_$truncate(v2) = v1) | ~ % 13.62/2.57 (real_$truncate(v2) = v0)) & ! [v0: $real] : ! [v1: $real] : ! [v2: % 13.62/2.57 $real] : (v1 = v0 | ~ (real_$round(v2) = v1) | ~ (real_$round(v2) = v0)) & % 13.62/2.57 ! [v0: int] : ! [v1: int] : ! [v2: $real] : (v1 = v0 | ~ (real_$to_int(v2) % 13.62/2.57 = v1) | ~ (real_$to_int(v2) = v0)) & ! [v0: $rat] : ! [v1: $rat] : ! % 13.62/2.57 [v2: $real] : (v1 = v0 | ~ (real_$to_rat(v2) = v1) | ~ (real_$to_rat(v2) = % 13.62/2.57 v0)) & ! [v0: $real] : ! [v1: $real] : ! [v2: $real] : (v1 = v0 | ~ % 13.62/2.57 (real_$to_real(v2) = v1) | ~ (real_$to_real(v2) = v0)) & ! [v0: $real] : % 13.62/2.57 ! [v1: $real] : ! [v2: int] : (v1 = v0 | ~ (int_$to_real(v2) = v1) | ~ % 13.62/2.57 (int_$to_real(v2) = v0)) & ! [v0: $real] : ! [v1: $real] : ! [v2: $real] % 13.62/2.57 : (v1 = v0 | ~ (real_$uminus(v2) = v1) | ~ (real_$uminus(v2) = v0)) & ! % 13.62/2.57 [v0: $real] : ! [v1: $real] : ! [v2: $real] : (v1 = v0 | ~ (sqrt(v2) = v1) % 13.62/2.57 | ~ (sqrt(v2) = v0)) & ! [v0: $real] : ! [v1: $real] : ! [v2: $real] : % 13.62/2.57 (v1 = v0 | ~ (sqr(v2) = v1) | ~ (sqr(v2) = v0)) % 13.62/2.57 % 13.62/2.57 Further assumptions not needed in the proof: % 13.62/2.57 -------------------------------------------- % 13.62/2.57 sqr_def, sqrt_le, sqrt_mul, sqrt_one, sqrt_zero % 13.62/2.57 % 13.62/2.57 Those formulas are unsatisfiable: % 13.62/2.57 --------------------------------- % 13.62/2.57 % 13.62/2.57 Begin of proof % 13.62/2.57 | % 13.62/2.57 | ALPHA: (function-axioms) implies: % 13.62/2.57 | (1) ! [v0: $real] : ! [v1: $real] : ! [v2: $real] : (v1 = v0 | ~ % 13.62/2.57 | (sqrt(v2) = v1) | ~ (sqrt(v2) = v0)) % 13.62/2.57 | (2) ! [v0: $real] : ! [v1: $real] : ! [v2: $real] : ! [v3: $real] : (v1 % 13.62/2.57 | = v0 | ~ (real_$product(v3, v2) = v1) | ~ (real_$product(v3, v2) = % 13.62/2.57 | v0)) % 13.62/2.57 | % 13.62/2.57 | ALPHA: (input) implies: % 13.62/2.57 | (3) real_$product(real_2, real_2) = real_4 % 13.62/2.57 | (4) real_$lesseq(real_0, real_4) = 0 % 13.62/2.57 | (5) real_$lesseq(real_0, real_2) = 0 % 13.62/2.57 | % 13.62/2.57 | DELTA: instantiating (sqrt_four) with fresh symbol all_11_0 gives: % 13.62/2.57 | (6) ~ (all_11_0 = real_2) & sqrt(real_4) = all_11_0 % 13.62/2.57 | % 13.62/2.57 | ALPHA: (6) implies: % 13.62/2.57 | (7) ~ (all_11_0 = real_2) % 13.62/2.57 | (8) sqrt(real_4) = all_11_0 % 13.62/2.57 | % 13.62/2.57 | GROUND_INST: instantiating (sqrt_positive) with real_4, simplifying with (4) % 13.62/2.57 | gives: % 13.62/2.57 | (9) ? [v0: $real] : (sqrt(real_4) = v0 & real_$lesseq(real_0, v0) = 0) % 13.62/2.57 | % 13.62/2.57 | GROUND_INST: instantiating (sqrt_square) with real_4, simplifying with (4) % 13.62/2.58 | gives: % 13.62/2.58 | (10) ? [v0: $real] : (sqrt(real_4) = v0 & sqr(v0) = real_4) % 13.62/2.58 | % 13.62/2.58 | GROUND_INST: instantiating (square_sqrt) with real_2, simplifying with (5) % 13.62/2.58 | gives: % 13.62/2.58 | (11) ? [v0: $real] : (sqrt(v0) = real_2 & real_$product(real_2, real_2) = % 13.62/2.58 | v0) % 13.62/2.58 | % 13.62/2.58 | DELTA: instantiating (11) with fresh symbol all_24_0 gives: % 13.62/2.58 | (12) sqrt(all_24_0) = real_2 & real_$product(real_2, real_2) = all_24_0 % 13.62/2.58 | % 13.62/2.58 | ALPHA: (12) implies: % 13.62/2.58 | (13) real_$product(real_2, real_2) = all_24_0 % 13.62/2.58 | (14) sqrt(all_24_0) = real_2 % 13.62/2.58 | % 13.62/2.58 | DELTA: instantiating (9) with fresh symbol all_28_0 gives: % 13.62/2.58 | (15) sqrt(real_4) = all_28_0 & real_$lesseq(real_0, all_28_0) = 0 % 13.62/2.58 | % 13.62/2.58 | ALPHA: (15) implies: % 13.62/2.58 | (16) sqrt(real_4) = all_28_0 % 13.62/2.58 | % 13.62/2.58 | DELTA: instantiating (10) with fresh symbol all_38_0 gives: % 13.62/2.58 | (17) sqrt(real_4) = all_38_0 & sqr(all_38_0) = real_4 % 13.62/2.58 | % 13.62/2.58 | ALPHA: (17) implies: % 13.62/2.58 | (18) sqrt(real_4) = all_38_0 % 13.62/2.58 | % 13.62/2.58 | GROUND_INST: instantiating (2) with real_4, all_24_0, real_2, real_2, % 13.62/2.58 | simplifying with (3), (13) gives: % 13.62/2.58 | (19) all_24_0 = real_4 % 13.62/2.58 | % 13.62/2.58 | GROUND_INST: instantiating (1) with all_11_0, all_38_0, real_4, simplifying % 13.62/2.58 | with (8), (18) gives: % 13.62/2.58 | (20) all_38_0 = all_11_0 % 13.62/2.58 | % 13.62/2.58 | GROUND_INST: instantiating (1) with all_28_0, all_38_0, real_4, simplifying % 13.62/2.58 | with (16), (18) gives: % 13.62/2.58 | (21) all_38_0 = all_28_0 % 13.62/2.58 | % 13.62/2.58 | COMBINE_EQS: (20), (21) imply: % 13.62/2.58 | (22) all_28_0 = all_11_0 % 13.62/2.58 | % 13.62/2.58 | REDUCE: (14), (19) imply: % 13.62/2.58 | (23) sqrt(real_4) = real_2 % 13.62/2.58 | % 13.62/2.58 | GROUND_INST: instantiating (1) with all_11_0, real_2, real_4, simplifying with % 13.62/2.58 | (8), (23) gives: % 13.62/2.58 | (24) all_11_0 = real_2 % 13.62/2.58 | % 13.62/2.58 | REDUCE: (7), (24) imply: % 13.62/2.58 | (25) $false % 13.62/2.58 | % 13.62/2.58 | CLOSE: (25) is inconsistent. % 13.62/2.58 | % 13.62/2.58 End of proof % 13.62/2.58 % SZS output end Proof for theBenchmark % 13.62/2.58 % 13.62/2.58 1908ms %------------------------------------------------------------------------------