%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : NUM460+2 : TPTP v8.1.2. Released v4.0.0. % 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 11:47:53 EDT 2023 % Result : Theorem 9.90s 2.18s % Output : Proof 15.81s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.09/0.13 % Problem : NUM460+2 : TPTP v8.1.2. Released v4.0.0. % 0.09/0.14 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.15/0.36 % Computer : n011.cluster.edu % 0.15/0.36 % Model : x86_64 x86_64 % 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.15/0.36 % Memory : 8042.1875MB % 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64 % 0.15/0.36 % CPULimit : 300 % 0.15/0.36 % WCLimit : 300 % 0.15/0.36 % DateTime : Fri Aug 25 15:43:53 EDT 2023 % 0.15/0.36 % CPUTime : % 0.22/0.63 ________ _____ % 0.22/0.64 ___ __ \_________(_)________________________________ % 0.22/0.64 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.22/0.64 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.22/0.64 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.22/0.64 % 0.22/0.64 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.22/0.64 (2023-06-19) % 0.22/0.64 % 0.22/0.64 (c) Philipp Rümmer, 2009-2023 % 0.22/0.64 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.22/0.64 Amanda Stjerna. % 0.22/0.64 Free software under BSD-3-Clause. % 0.22/0.64 % 0.22/0.64 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.22/0.64 % 0.22/0.64 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.22/0.65 Running up to 7 provers in parallel. % 0.22/0.67 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.22/0.67 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.22/0.67 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.22/0.67 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.22/0.67 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.22/0.67 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 0.22/0.67 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 2.71/1.17 Prover 4: Preprocessing ... % 2.71/1.17 Prover 1: Preprocessing ... % 3.33/1.21 Prover 3: Preprocessing ... % 3.33/1.21 Prover 0: Preprocessing ... % 3.33/1.21 Prover 6: Preprocessing ... % 3.33/1.21 Prover 5: Preprocessing ... % 3.33/1.21 Prover 2: Preprocessing ... % 6.68/1.70 Prover 3: Constructing countermodel ... % 6.68/1.71 Prover 1: Constructing countermodel ... % 6.68/1.72 Prover 6: Proving ... % 7.39/1.79 Prover 5: Constructing countermodel ... % 7.51/1.94 Prover 2: Proving ... % 8.30/1.99 Prover 4: Constructing countermodel ... % 9.90/2.18 Prover 3: proved (1508ms) % 9.90/2.18 % 9.90/2.18 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 9.90/2.18 % 9.90/2.18 Prover 5: stopped % 9.90/2.18 Prover 2: stopped % 9.90/2.18 Prover 6: stopped % 10.17/2.20 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 10.17/2.20 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 10.17/2.20 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 10.17/2.20 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 10.50/2.25 Prover 10: Preprocessing ... % 10.50/2.26 Prover 0: Proving ... % 10.50/2.26 Prover 0: stopped % 10.50/2.26 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 10.50/2.26 Prover 11: Preprocessing ... % 10.50/2.27 Prover 8: Preprocessing ... % 10.50/2.28 Prover 7: Preprocessing ... % 10.95/2.33 Prover 13: Preprocessing ... % 11.40/2.39 Prover 10: Constructing countermodel ... % 11.40/2.45 Prover 8: Warning: ignoring some quantifiers % 12.10/2.46 Prover 8: Constructing countermodel ... % 12.10/2.48 Prover 7: Constructing countermodel ... % 12.40/2.52 Prover 13: Constructing countermodel ... % 12.88/2.66 Prover 11: Constructing countermodel ... % 15.07/2.87 Prover 10: Found proof (size 44) % 15.07/2.87 Prover 10: proved (690ms) % 15.07/2.88 Prover 11: stopped % 15.07/2.88 Prover 13: stopped % 15.07/2.88 Prover 7: stopped % 15.07/2.88 Prover 8: stopped % 15.07/2.88 Prover 4: stopped % 15.07/2.88 Prover 1: Found proof (size 123) % 15.07/2.88 Prover 1: proved (2213ms) % 15.07/2.88 % 15.07/2.88 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 15.07/2.88 % 15.07/2.90 % SZS output start Proof for theBenchmark % 15.07/2.90 Assumptions after simplification: % 15.07/2.90 --------------------------------- % 15.07/2.90 % 15.07/2.90 (mAddAsso) % 15.58/2.94 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 15.58/2.94 (sdtpldt0(v3, v2) = v4) | ~ (sdtpldt0(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) % 15.58/2.94 | ~ $i(v0) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ % 15.58/2.94 aNaturalNumber0(v0) | ? [v5: $i] : (sdtpldt0(v1, v2) = v5 & sdtpldt0(v0, % 15.58/2.94 v5) = v4 & $i(v5) & $i(v4))) % 15.58/2.94 % 15.58/2.94 (mAddCanc) % 15.58/2.94 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v2 = v1 % 15.58/2.95 | ~ (sdtpldt0(v0, v2) = v4) | ~ (sdtpldt0(v0, v1) = v3) | ~ $i(v2) | ~ % 15.58/2.95 $i(v1) | ~ $i(v0) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ % 15.58/2.95 aNaturalNumber0(v0) | ? [v5: $i] : ? [v6: $i] : ( ~ (v6 = v5) & % 15.58/2.95 sdtpldt0(v2, v0) = v6 & sdtpldt0(v1, v0) = v5 & $i(v6) & $i(v5))) & ! % 15.58/2.95 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v2 = v1 | ~ % 15.58/2.95 (sdtpldt0(v0, v2) = v3) | ~ (sdtpldt0(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) % 15.58/2.95 | ~ $i(v0) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ % 15.58/2.95 aNaturalNumber0(v0)) % 15.58/2.95 % 15.58/2.95 (mAddComm) % 15.58/2.95 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtpldt0(v0, v1) = v2) | ~ % 15.58/2.95 $i(v1) | ~ $i(v0) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | % 15.58/2.95 (sdtpldt0(v1, v0) = v2 & $i(v2))) % 15.58/2.95 % 15.58/2.95 (mDefLE) % 15.58/2.95 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtpldt0(v0, v2) = v1) | ~ % 15.58/2.95 $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ aNaturalNumber0(v2) | ~ % 15.58/2.95 aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtlseqdt0(v0, v1)) & ! [v0: % 15.58/2.95 $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ sdtlseqdt0(v0, v1) | ~ % 15.58/2.95 aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v2: $i] : (sdtpldt0(v0, % 15.58/2.95 v2) = v1 & $i(v2) & aNaturalNumber0(v2))) % 15.58/2.95 % 15.58/2.95 (mSortsB) % 15.58/2.95 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtpldt0(v0, v1) = v2) | ~ % 15.58/2.95 $i(v1) | ~ $i(v0) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | % 15.58/2.95 aNaturalNumber0(v2)) % 15.58/2.95 % 15.58/2.95 (m__) % 15.58/2.95 $i(xl) & $i(xn) & $i(xm) & ? [v0: $i] : ? [v1: $i] : (sdtpldt0(xn, v0) = xl % 15.58/2.95 & sdtpldt0(xm, v1) = xn & $i(v1) & $i(v0) & sdtlseqdt0(xn, xl) & % 15.58/2.95 sdtlseqdt0(xm, xn) & aNaturalNumber0(v1) & aNaturalNumber0(v0) & ~ % 15.58/2.95 sdtlseqdt0(xm, xl) & ! [v2: $i] : ( ~ (sdtpldt0(xm, v2) = xl) | ~ $i(v2) | % 15.58/2.95 ~ aNaturalNumber0(v2))) % 15.58/2.95 % 15.58/2.95 (m__773) % 15.58/2.95 $i(xl) & $i(xn) & $i(xm) & aNaturalNumber0(xl) & aNaturalNumber0(xn) & % 15.58/2.95 aNaturalNumber0(xm) % 15.58/2.95 % 15.58/2.95 (function-axioms) % 15.58/2.96 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 15.58/2.96 (sdtmndt0(v3, v2) = v1) | ~ (sdtmndt0(v3, v2) = v0)) & ! [v0: $i] : ! % 15.58/2.96 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtasdt0(v3, v2) = v1) | % 15.58/2.96 ~ (sdtasdt0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 15.58/2.96 [v3: $i] : (v1 = v0 | ~ (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0)) % 15.58/2.96 % 15.58/2.96 Further assumptions not needed in the proof: % 15.58/2.96 -------------------------------------------- % 15.58/2.96 mAMDistr, mDefDiff, mLEAsym, mLERefl, mMulAsso, mMulCanc, mMulComm, mNatSort, % 15.58/2.96 mSortsB_02, mSortsC, mSortsC_01, mZeroAdd, mZeroMul, m_AddZero, m_MulUnit, % 15.58/2.96 m_MulZero % 15.58/2.96 % 15.58/2.96 Those formulas are unsatisfiable: % 15.58/2.96 --------------------------------- % 15.58/2.96 % 15.58/2.96 Begin of proof % 15.58/2.96 | % 15.58/2.96 | ALPHA: (mAddCanc) implies: % 15.58/2.96 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v2 = v1 | ~ % 15.58/2.96 | (sdtpldt0(v0, v2) = v3) | ~ (sdtpldt0(v0, v1) = v3) | ~ $i(v2) | ~ % 15.58/2.96 | $i(v1) | ~ $i(v0) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) % 15.58/2.96 | | ~ aNaturalNumber0(v0)) % 15.58/2.96 | % 15.58/2.96 | ALPHA: (mDefLE) implies: % 15.58/2.96 | (2) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ sdtlseqdt0(v0, % 15.58/2.96 | v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v2: $i] % 15.58/2.96 | : (sdtpldt0(v0, v2) = v1 & $i(v2) & aNaturalNumber0(v2))) % 15.58/2.96 | % 15.58/2.96 | ALPHA: (m__773) implies: % 15.58/2.96 | (3) aNaturalNumber0(xm) % 15.58/2.96 | (4) aNaturalNumber0(xn) % 15.58/2.96 | (5) aNaturalNumber0(xl) % 15.58/2.96 | % 15.58/2.96 | ALPHA: (m__) implies: % 15.58/2.96 | (6) $i(xm) % 15.58/2.96 | (7) $i(xn) % 15.58/2.96 | (8) $i(xl) % 15.58/2.96 | (9) ? [v0: $i] : ? [v1: $i] : (sdtpldt0(xn, v0) = xl & sdtpldt0(xm, v1) = % 15.58/2.96 | xn & $i(v1) & $i(v0) & sdtlseqdt0(xn, xl) & sdtlseqdt0(xm, xn) & % 15.58/2.96 | aNaturalNumber0(v1) & aNaturalNumber0(v0) & ~ sdtlseqdt0(xm, xl) & % 15.58/2.96 | ! [v2: $i] : ( ~ (sdtpldt0(xm, v2) = xl) | ~ $i(v2) | ~ % 15.58/2.96 | aNaturalNumber0(v2))) % 15.58/2.96 | % 15.58/2.96 | ALPHA: (function-axioms) implies: % 15.58/2.96 | (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 15.58/2.96 | (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0)) % 15.58/2.96 | % 15.58/2.96 | DELTA: instantiating (9) with fresh symbols all_22_0, all_22_1 gives: % 15.58/2.96 | (11) sdtpldt0(xn, all_22_1) = xl & sdtpldt0(xm, all_22_0) = xn & % 15.58/2.96 | $i(all_22_0) & $i(all_22_1) & sdtlseqdt0(xn, xl) & sdtlseqdt0(xm, xn) % 15.58/2.96 | & aNaturalNumber0(all_22_0) & aNaturalNumber0(all_22_1) & ~ % 15.58/2.96 | sdtlseqdt0(xm, xl) & ! [v0: $i] : ( ~ (sdtpldt0(xm, v0) = xl) | ~ % 15.58/2.96 | $i(v0) | ~ aNaturalNumber0(v0)) % 15.58/2.96 | % 15.58/2.97 | ALPHA: (11) implies: % 15.58/2.97 | (12) aNaturalNumber0(all_22_1) % 15.58/2.97 | (13) aNaturalNumber0(all_22_0) % 15.58/2.97 | (14) sdtlseqdt0(xm, xn) % 15.58/2.97 | (15) sdtlseqdt0(xn, xl) % 15.58/2.97 | (16) $i(all_22_1) % 15.58/2.97 | (17) $i(all_22_0) % 15.58/2.97 | (18) sdtpldt0(xm, all_22_0) = xn % 15.58/2.97 | (19) sdtpldt0(xn, all_22_1) = xl % 15.58/2.97 | (20) ! [v0: $i] : ( ~ (sdtpldt0(xm, v0) = xl) | ~ $i(v0) | ~ % 15.58/2.97 | aNaturalNumber0(v0)) % 15.58/2.97 | % 15.58/2.97 | GROUND_INST: instantiating (2) with xm, xn, simplifying with (3), (4), (6), % 15.58/2.97 | (7), (14) gives: % 15.58/2.97 | (21) ? [v0: $i] : (sdtpldt0(xm, v0) = xn & $i(v0) & aNaturalNumber0(v0)) % 15.58/2.97 | % 15.58/2.97 | GROUND_INST: instantiating (2) with xn, xl, simplifying with (4), (5), (7), % 15.58/2.97 | (8), (15) gives: % 15.58/2.97 | (22) ? [v0: $i] : (sdtpldt0(xn, v0) = xl & $i(v0) & aNaturalNumber0(v0)) % 15.58/2.97 | % 15.58/2.97 | GROUND_INST: instantiating (mAddAsso) with xm, all_22_0, all_22_1, xn, xl, % 15.58/2.97 | simplifying with (3), (6), (12), (13), (16), (17), (18), (19) % 15.58/2.97 | gives: % 15.58/2.97 | (23) ? [v0: $i] : (sdtpldt0(all_22_0, all_22_1) = v0 & sdtpldt0(xm, v0) = % 15.58/2.97 | xl & $i(v0) & $i(xl)) % 15.58/2.97 | % 15.58/2.97 | DELTA: instantiating (22) with fresh symbol all_31_0 gives: % 15.58/2.97 | (24) sdtpldt0(xn, all_31_0) = xl & $i(all_31_0) & aNaturalNumber0(all_31_0) % 15.58/2.97 | % 15.58/2.97 | ALPHA: (24) implies: % 15.58/2.97 | (25) aNaturalNumber0(all_31_0) % 15.58/2.97 | (26) $i(all_31_0) % 15.58/2.97 | (27) sdtpldt0(xn, all_31_0) = xl % 15.58/2.97 | % 15.58/2.97 | DELTA: instantiating (21) with fresh symbol all_33_0 gives: % 15.58/2.97 | (28) sdtpldt0(xm, all_33_0) = xn & $i(all_33_0) & aNaturalNumber0(all_33_0) % 15.58/2.97 | % 15.58/2.97 | ALPHA: (28) implies: % 15.58/2.97 | (29) aNaturalNumber0(all_33_0) % 15.58/2.97 | (30) $i(all_33_0) % 15.58/2.97 | (31) sdtpldt0(xm, all_33_0) = xn % 15.58/2.97 | % 15.58/2.97 | DELTA: instantiating (23) with fresh symbol all_35_0 gives: % 15.58/2.97 | (32) sdtpldt0(all_22_0, all_22_1) = all_35_0 & sdtpldt0(xm, all_35_0) = xl % 15.58/2.97 | & $i(all_35_0) & $i(xl) % 15.58/2.97 | % 15.58/2.97 | ALPHA: (32) implies: % 15.58/2.97 | (33) sdtpldt0(all_22_0, all_22_1) = all_35_0 % 15.58/2.97 | % 15.58/2.97 | GROUND_INST: instantiating (mAddAsso) with xm, all_33_0, all_22_1, xn, xl, % 15.58/2.97 | simplifying with (3), (6), (12), (16), (19), (29), (30), (31) % 15.58/2.97 | gives: % 15.58/2.97 | (34) ? [v0: $i] : (sdtpldt0(all_33_0, all_22_1) = v0 & sdtpldt0(xm, v0) = % 15.58/2.97 | xl & $i(v0) & $i(xl)) % 15.58/2.97 | % 15.58/2.98 | GROUND_INST: instantiating (1) with xm, all_33_0, all_22_0, xn, simplifying % 15.58/2.98 | with (3), (6), (13), (17), (18), (29), (30), (31) gives: % 15.58/2.98 | (35) all_33_0 = all_22_0 % 15.58/2.98 | % 15.58/2.98 | GROUND_INST: instantiating (mAddComm) with xm, all_33_0, xn, simplifying with % 15.58/2.98 | (3), (6), (29), (30), (31) gives: % 15.58/2.98 | (36) sdtpldt0(all_33_0, xm) = xn & $i(xn) % 15.58/2.98 | % 15.58/2.98 | GROUND_INST: instantiating (1) with xn, all_31_0, all_22_1, xl, simplifying % 15.58/2.98 | with (4), (7), (12), (16), (19), (25), (26), (27) gives: % 15.58/2.98 | (37) all_31_0 = all_22_1 % 15.58/2.98 | % 15.58/2.98 | GROUND_INST: instantiating (mAddAsso) with xm, all_22_0, all_31_0, xn, xl, % 15.58/2.98 | simplifying with (3), (6), (13), (17), (18), (25), (26), (27) % 15.58/2.98 | gives: % 15.58/2.98 | (38) ? [v0: $i] : (sdtpldt0(all_22_0, all_31_0) = v0 & sdtpldt0(xm, v0) = % 15.58/2.98 | xl & $i(v0) & $i(xl)) % 15.58/2.98 | % 15.58/2.98 | GROUND_INST: instantiating (mAddAsso) with xm, all_33_0, all_31_0, xn, xl, % 15.58/2.98 | simplifying with (3), (6), (25), (26), (27), (29), (30), (31) % 15.58/2.98 | gives: % 15.58/2.98 | (39) ? [v0: $i] : (sdtpldt0(all_33_0, all_31_0) = v0 & sdtpldt0(xm, v0) = % 15.58/2.98 | xl & $i(v0) & $i(xl)) % 15.58/2.98 | % 15.58/2.98 | GROUND_INST: instantiating (mSortsB) with all_22_0, all_22_1, all_35_0, % 15.58/2.98 | simplifying with (12), (13), (16), (17), (33) gives: % 15.58/2.98 | (40) aNaturalNumber0(all_35_0) % 15.58/2.98 | % 15.58/2.98 | DELTA: instantiating (38) with fresh symbol all_57_0 gives: % 15.58/2.98 | (41) sdtpldt0(all_22_0, all_31_0) = all_57_0 & sdtpldt0(xm, all_57_0) = xl % 15.58/2.98 | & $i(all_57_0) & $i(xl) % 15.58/2.98 | % 15.58/2.98 | ALPHA: (41) implies: % 15.58/2.98 | (42) $i(all_57_0) % 15.58/2.98 | (43) sdtpldt0(xm, all_57_0) = xl % 15.58/2.98 | (44) sdtpldt0(all_22_0, all_31_0) = all_57_0 % 15.58/2.98 | % 15.58/2.98 | DELTA: instantiating (34) with fresh symbol all_59_0 gives: % 15.58/2.98 | (45) sdtpldt0(all_33_0, all_22_1) = all_59_0 & sdtpldt0(xm, all_59_0) = xl % 15.58/2.98 | & $i(all_59_0) & $i(xl) % 15.58/2.98 | % 15.58/2.98 | ALPHA: (45) implies: % 15.58/2.98 | (46) sdtpldt0(all_33_0, all_22_1) = all_59_0 % 15.58/2.98 | % 15.58/2.98 | DELTA: instantiating (39) with fresh symbol all_63_0 gives: % 15.58/2.98 | (47) sdtpldt0(all_33_0, all_31_0) = all_63_0 & sdtpldt0(xm, all_63_0) = xl % 15.58/2.98 | & $i(all_63_0) & $i(xl) % 15.58/2.98 | % 15.58/2.98 | ALPHA: (47) implies: % 15.58/2.98 | (48) sdtpldt0(all_33_0, all_31_0) = all_63_0 % 15.58/2.98 | % 15.58/2.98 | REDUCE: (35), (37), (48) imply: % 15.58/2.98 | (49) sdtpldt0(all_22_0, all_22_1) = all_63_0 % 15.58/2.98 | % 15.58/2.98 | REDUCE: (35), (46) imply: % 15.58/2.98 | (50) sdtpldt0(all_22_0, all_22_1) = all_59_0 % 15.58/2.98 | % 15.58/2.98 | REDUCE: (37), (44) imply: % 15.58/2.98 | (51) sdtpldt0(all_22_0, all_22_1) = all_57_0 % 15.58/2.98 | % 15.58/2.98 | GROUND_INST: instantiating (10) with all_57_0, all_59_0, all_22_1, all_22_0, % 15.58/2.98 | simplifying with (50), (51) gives: % 15.58/2.98 | (52) all_59_0 = all_57_0 % 15.58/2.98 | % 15.58/2.99 | GROUND_INST: instantiating (10) with all_35_0, all_63_0, all_22_1, all_22_0, % 15.58/2.99 | simplifying with (33), (49) gives: % 15.81/2.99 | (53) all_63_0 = all_35_0 % 15.81/2.99 | % 15.81/2.99 | GROUND_INST: instantiating (10) with all_59_0, all_63_0, all_22_1, all_22_0, % 15.81/2.99 | simplifying with (49), (50) gives: % 15.81/2.99 | (54) all_63_0 = all_59_0 % 15.81/2.99 | % 15.81/2.99 | COMBINE_EQS: (53), (54) imply: % 15.81/2.99 | (55) all_59_0 = all_35_0 % 15.81/2.99 | % 15.81/2.99 | SIMP: (55) implies: % 15.81/2.99 | (56) all_59_0 = all_35_0 % 15.81/2.99 | % 15.81/2.99 | COMBINE_EQS: (52), (56) imply: % 15.81/2.99 | (57) all_57_0 = all_35_0 % 15.81/2.99 | % 15.81/2.99 | SIMP: (57) implies: % 15.81/2.99 | (58) all_57_0 = all_35_0 % 15.81/2.99 | % 15.81/2.99 | REDUCE: (43), (58) imply: % 15.81/2.99 | (59) sdtpldt0(xm, all_35_0) = xl % 15.81/2.99 | % 15.81/2.99 | REDUCE: (42), (58) imply: % 15.81/2.99 | (60) $i(all_35_0) % 15.81/2.99 | % 15.81/2.99 | GROUND_INST: instantiating (20) with all_35_0, simplifying with (40), (59), % 15.81/2.99 | (60) gives: % 15.81/2.99 | (61) $false % 15.81/2.99 | % 15.81/2.99 | CLOSE: (61) is inconsistent. % 15.81/2.99 | % 15.81/2.99 End of proof % 15.81/2.99 % SZS output end Proof for theBenchmark % 15.81/2.99 % 15.81/2.99 2353ms %------------------------------------------------------------------------------