%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : NUM571+3 : TPTP v8.1.2. Released v4.0.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n027.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 11:48:41 EDT 2023 % Result : Theorem 51.34s 7.96s % Output : Proof 71.72s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.13 % Problem : NUM571+3 : TPTP v8.1.2. Released v4.0.0. % 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.11/0.33 % Computer : n027.cluster.edu % 0.11/0.33 % Model : x86_64 x86_64 % 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.11/0.33 % Memory : 8042.1875MB % 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.11/0.33 % CPULimit : 300 % 0.11/0.33 % WCLimit : 300 % 0.11/0.33 % DateTime : Fri Aug 25 12:05:18 EDT 2023 % 0.11/0.33 % CPUTime : % 0.17/0.61 ________ _____ % 0.17/0.61 ___ __ \_________(_)________________________________ % 0.17/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.17/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.17/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.17/0.61 % 0.17/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.17/0.61 (2023-06-19) % 0.17/0.61 % 0.17/0.61 (c) Philipp Rümmer, 2009-2023 % 0.17/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.17/0.61 Amanda Stjerna. % 0.17/0.61 Free software under BSD-3-Clause. % 0.17/0.61 % 0.17/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.17/0.61 % 0.17/0.61 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.17/0.63 Running up to 7 provers in parallel. % 0.17/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.17/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.17/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.17/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.17/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.17/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.17/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 4.49/1.48 Prover 4: Preprocessing ... % 4.49/1.51 Prover 1: Preprocessing ... % 4.49/1.54 Prover 3: Preprocessing ... % 4.49/1.54 Prover 5: Preprocessing ... % 4.49/1.54 Prover 0: Preprocessing ... % 4.49/1.54 Prover 2: Preprocessing ... % 4.49/1.54 Prover 6: Preprocessing ... % 19.42/3.51 Prover 3: Constructing countermodel ... % 19.70/3.54 Prover 1: Constructing countermodel ... % 19.70/3.60 Prover 6: Proving ... % 20.62/3.69 Prover 5: Proving ... % 24.26/4.18 Prover 2: Proving ... % 30.82/5.09 Prover 4: Constructing countermodel ... % 36.53/5.80 Prover 0: Proving ... % 51.34/7.96 Prover 2: proved (7270ms) % 51.34/7.96 % 51.34/7.96 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 51.34/7.96 % 51.34/7.96 Prover 5: stopped % 51.34/7.96 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 51.34/7.96 Prover 3: stopped % 51.34/7.98 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 51.34/7.98 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 51.34/8.01 Prover 0: stopped % 51.34/8.01 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 54.44/8.20 Prover 6: stopped % 54.44/8.21 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 55.34/8.33 Prover 7: Preprocessing ... % 55.82/8.35 Prover 11: Preprocessing ... % 56.03/8.38 Prover 10: Preprocessing ... % 56.03/8.40 Prover 8: Preprocessing ... % 56.83/8.49 Prover 13: Preprocessing ... % 58.08/8.78 Prover 8: Warning: ignoring some quantifiers % 58.08/8.80 Prover 8: Constructing countermodel ... % 58.08/8.80 Prover 7: Constructing countermodel ... % 58.08/8.85 Prover 10: Constructing countermodel ... % 62.57/9.24 Prover 13: Warning: ignoring some quantifiers % 62.79/9.27 Prover 13: Constructing countermodel ... % 69.81/10.29 Prover 10: Found proof (size 38) % 69.81/10.29 Prover 10: proved (2310ms) % 69.81/10.29 Prover 7: stopped % 69.81/10.29 Prover 1: stopped % 69.81/10.29 Prover 8: stopped % 69.81/10.31 Prover 4: stopped % 69.81/10.31 Prover 13: stopped % 70.94/10.39 Prover 11: Constructing countermodel ... % 70.94/10.43 Prover 11: stopped % 70.94/10.43 % 70.94/10.43 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 70.94/10.43 % 70.94/10.43 % SZS output start Proof for theBenchmark % 70.94/10.44 Assumptions after simplification: % 70.94/10.44 --------------------------------- % 70.94/10.44 % 70.94/10.44 (m__) % 71.42/10.48 $i(xi) & $i(xN) & $i(szNzAzT0) & ? [v0: $i] : ? [v1: $i] : (sdtlpdtrp0(xN, % 71.42/10.48 xi) = v0 & $i(v1) & $i(v0) & ( ~ isCountable0(v0) | ( ~ aSubsetOf0(v0, % 71.42/10.48 szNzAzT0) & ( ~ aSet0(v0) | (aElementOf0(v1, v0) & ~ aElementOf0(v1, % 71.42/10.48 szNzAzT0)))))) % 71.42/10.48 % 71.42/10.48 (m__3435) % 71.42/10.48 $i(xS) & $i(szNzAzT0) & aSubsetOf0(xS, szNzAzT0) & isCountable0(xS) & % 71.42/10.48 aSet0(xS) & ! [v0: $i] : ( ~ $i(v0) | ~ aElementOf0(v0, xS) | % 71.42/10.48 aElementOf0(v0, szNzAzT0)) % 71.42/10.48 % 71.42/10.48 (m__3623) % 71.42/10.50 sdtlpdtrp0(xN, sz00) = xS & szDzozmdt0(xN) = szNzAzT0 & $i(xN) & $i(xS) & % 71.42/10.50 $i(sz00) & $i(szNzAzT0) & aFunction0(xN) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 71.42/10.50 $i] : ! [v3: $i] : ! [v4: $i] : (v4 = v2 | ~ (sdtlpdtrp0(xN, v0) = v1) | % 71.42/10.50 ~ (szmzizndt0(v1) = v2) | ~ (sdtmndt0(v1, v2) = v3) | ~ $i(v4) | ~ $i(v0) % 71.42/10.50 | ~ aSubsetOf0(v1, szNzAzT0) | ~ isCountable0(v1) | ~ aElementOf0(v4, v1) % 71.42/10.50 | ~ aElementOf0(v0, szNzAzT0) | ~ aElement0(v4) | aElementOf0(v4, v3)) & % 71.42/10.50 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v4 = v2 % 71.42/10.50 | ~ (sdtlpdtrp0(xN, v0) = v1) | ~ (szmzizndt0(v1) = v2) | ~ (sdtmndt0(v1, % 71.42/10.50 v2) = v3) | ~ $i(v4) | ~ $i(v0) | ~ isCountable0(v1) | ~ % 71.42/10.50 aElementOf0(v4, v1) | ~ aElementOf0(v0, szNzAzT0) | ~ aElement0(v4) | ~ % 71.42/10.50 aSet0(v1) | aElementOf0(v4, v3) | ? [v5: $i] : ($i(v5) & aElementOf0(v5, % 71.42/10.50 v1) & ~ aElementOf0(v5, szNzAzT0))) & ! [v0: $i] : ! [v1: $i] : ! % 71.42/10.50 [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (sdtlpdtrp0(xN, v0) = v1) | ~ % 71.42/10.50 (szmzizndt0(v1) = v2) | ~ (sdtmndt0(v1, v2) = v3) | ~ $i(v4) | ~ $i(v0) | % 71.42/10.50 ~ aSubsetOf0(v1, szNzAzT0) | ~ isCountable0(v1) | ~ aElementOf0(v4, v3) | % 71.42/10.50 ~ aElementOf0(v0, szNzAzT0) | aElementOf0(v4, v1)) & ! [v0: $i] : ! [v1: % 71.42/10.50 $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (sdtlpdtrp0(xN, v0) = % 71.42/10.50 v1) | ~ (szmzizndt0(v1) = v2) | ~ (sdtmndt0(v1, v2) = v3) | ~ $i(v4) | % 71.42/10.50 ~ $i(v0) | ~ aSubsetOf0(v1, szNzAzT0) | ~ isCountable0(v1) | ~ % 71.42/10.50 aElementOf0(v4, v3) | ~ aElementOf0(v0, szNzAzT0) | aElement0(v4)) & ! % 71.42/10.50 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 71.42/10.50 (sdtlpdtrp0(xN, v0) = v1) | ~ (szmzizndt0(v1) = v2) | ~ (sdtmndt0(v1, v2) % 71.42/10.50 = v3) | ~ $i(v4) | ~ $i(v0) | ~ aSubsetOf0(v1, szNzAzT0) | ~ % 71.42/10.50 isCountable0(v1) | ~ aElementOf0(v4, v1) | ~ aElementOf0(v0, szNzAzT0) | % 71.42/10.50 sdtlseqdt0(v2, v4)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] % 71.42/10.51 : ! [v4: $i] : ( ~ (sdtlpdtrp0(xN, v0) = v1) | ~ (szmzizndt0(v1) = v2) | ~ % 71.42/10.51 (sdtmndt0(v1, v2) = v3) | ~ $i(v4) | ~ $i(v0) | ~ isCountable0(v1) | ~ % 71.42/10.51 aElementOf0(v4, v3) | ~ aElementOf0(v0, szNzAzT0) | ~ aSet0(v1) | % 71.42/10.51 aElementOf0(v4, v1) | ? [v5: $i] : ($i(v5) & aElementOf0(v5, v1) & ~ % 71.42/10.51 aElementOf0(v5, szNzAzT0))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 71.42/10.51 [v3: $i] : ! [v4: $i] : ( ~ (sdtlpdtrp0(xN, v0) = v1) | ~ (szmzizndt0(v1) = % 71.42/10.51 v2) | ~ (sdtmndt0(v1, v2) = v3) | ~ $i(v4) | ~ $i(v0) | ~ % 71.42/10.51 isCountable0(v1) | ~ aElementOf0(v4, v3) | ~ aElementOf0(v0, szNzAzT0) | % 71.42/10.51 ~ aSet0(v1) | aElement0(v4) | ? [v5: $i] : ($i(v5) & aElementOf0(v5, v1) & % 71.42/10.51 ~ aElementOf0(v5, szNzAzT0))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 71.42/10.51 ! [v3: $i] : ! [v4: $i] : ( ~ (sdtlpdtrp0(xN, v0) = v1) | ~ (szmzizndt0(v1) % 71.42/10.51 = v2) | ~ (sdtmndt0(v1, v2) = v3) | ~ $i(v4) | ~ $i(v0) | ~ % 71.42/10.51 isCountable0(v1) | ~ aElementOf0(v4, v1) | ~ aElementOf0(v0, szNzAzT0) | % 71.42/10.51 ~ aSet0(v1) | sdtlseqdt0(v2, v4) | ? [v5: $i] : ($i(v5) & aElementOf0(v5, % 71.42/10.51 v1) & ~ aElementOf0(v5, szNzAzT0))) & ! [v0: $i] : ! [v1: $i] : ! % 71.42/10.51 [v2: $i] : ! [v3: $i] : ( ~ (sdtlpdtrp0(xN, v0) = v1) | ~ (szmzizndt0(v1) = % 71.42/10.51 v2) | ~ (sdtmndt0(v1, v2) = v3) | ~ $i(v2) | ~ $i(v0) | ~ % 71.42/10.51 aSubsetOf0(v1, szNzAzT0) | ~ isCountable0(v1) | ~ aElementOf0(v2, v3) | ~ % 71.42/10.51 aElementOf0(v0, szNzAzT0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 71.42/10.51 [v3: $i] : ( ~ (sdtlpdtrp0(xN, v0) = v1) | ~ (szmzizndt0(v1) = v2) | ~ % 71.42/10.51 (sdtmndt0(v1, v2) = v3) | ~ $i(v2) | ~ $i(v0) | ~ isCountable0(v1) | ~ % 71.42/10.51 aElementOf0(v2, v3) | ~ aElementOf0(v0, szNzAzT0) | ~ aSet0(v1) | ? [v4: % 71.42/10.51 $i] : ($i(v4) & aElementOf0(v4, v1) & ~ aElementOf0(v4, szNzAzT0))) & ! % 71.42/10.51 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (sdtlpdtrp0(xN, v0) = % 71.42/10.51 v1) | ~ (szmzizndt0(v1) = v2) | ~ (sdtmndt0(v1, v2) = v3) | ~ $i(v0) | % 71.42/10.51 ~ aSubsetOf0(v1, szNzAzT0) | ~ isCountable0(v1) | ~ aElementOf0(v0, % 71.42/10.51 szNzAzT0) | aElementOf0(v2, v1)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] % 71.42/10.51 : ! [v3: $i] : ( ~ (sdtlpdtrp0(xN, v0) = v1) | ~ (szmzizndt0(v1) = v2) | ~ % 71.42/10.51 (sdtmndt0(v1, v2) = v3) | ~ $i(v0) | ~ aSubsetOf0(v1, szNzAzT0) | ~ % 71.42/10.51 isCountable0(v1) | ~ aElementOf0(v0, szNzAzT0) | aSet0(v3)) & ! [v0: $i] : % 71.42/10.51 ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (sdtlpdtrp0(xN, v0) = v1) | ~ % 71.42/10.51 (szmzizndt0(v1) = v2) | ~ (sdtmndt0(v1, v2) = v3) | ~ $i(v0) | ~ % 71.42/10.51 aSubsetOf0(v1, szNzAzT0) | ~ isCountable0(v1) | ~ aElementOf0(v0, % 71.42/10.51 szNzAzT0) | ? [v4: $i] : ? [v5: $i] : (sdtlpdtrp0(xN, v4) = v5 & % 71.42/10.51 szszuzczcdt0(v0) = v4 & $i(v5) & $i(v4) & aSubsetOf0(v5, v3) & % 71.42/10.51 isCountable0(v5) & aSet0(v5) & ! [v6: $i] : ( ~ $i(v6) | ~ % 71.42/10.51 aElementOf0(v6, v5) | aElementOf0(v6, v3)))) & ! [v0: $i] : ! [v1: $i] % 71.42/10.51 : ! [v2: $i] : ! [v3: $i] : ( ~ (sdtlpdtrp0(xN, v0) = v1) | ~ % 71.42/10.51 (szmzizndt0(v1) = v2) | ~ (sdtmndt0(v1, v2) = v3) | ~ $i(v0) | ~ % 71.42/10.51 isCountable0(v1) | ~ aElementOf0(v0, szNzAzT0) | ~ aSet0(v1) | % 71.42/10.51 aElementOf0(v2, v1) | ? [v4: $i] : ($i(v4) & aElementOf0(v4, v1) & ~ % 71.42/10.51 aElementOf0(v4, szNzAzT0))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 71.42/10.51 [v3: $i] : ( ~ (sdtlpdtrp0(xN, v0) = v1) | ~ (szmzizndt0(v1) = v2) | ~ % 71.42/10.51 (sdtmndt0(v1, v2) = v3) | ~ $i(v0) | ~ isCountable0(v1) | ~ % 71.42/10.51 aElementOf0(v0, szNzAzT0) | ~ aSet0(v1) | aSet0(v3) | ? [v4: $i] : ($i(v4) % 71.42/10.51 & aElementOf0(v4, v1) & ~ aElementOf0(v4, szNzAzT0))) & ! [v0: $i] : ! % 71.42/10.51 [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (sdtlpdtrp0(xN, v0) = v1) | ~ % 71.42/10.51 (szmzizndt0(v1) = v2) | ~ (sdtmndt0(v1, v2) = v3) | ~ $i(v0) | ~ % 71.42/10.51 isCountable0(v1) | ~ aElementOf0(v0, szNzAzT0) | ~ aSet0(v1) | ? [v4: $i] % 71.42/10.51 : ? [v5: $i] : ? [v6: $i] : ($i(v6) & ((sdtlpdtrp0(xN, v4) = v5 & % 71.42/10.51 szszuzczcdt0(v0) = v4 & $i(v5) & $i(v4) & aSubsetOf0(v5, v3) & % 71.42/10.51 isCountable0(v5) & aSet0(v5) & ! [v7: $i] : ( ~ $i(v7) | ~ % 71.42/10.51 aElementOf0(v7, v5) | aElementOf0(v7, v3))) | (aElementOf0(v6, v1) & % 71.42/10.51 ~ aElementOf0(v6, szNzAzT0))))) % 71.42/10.51 % 71.42/10.51 (m__3702_02) % 71.42/10.51 $i(xi) & $i(xN) & $i(sz00) & $i(szNzAzT0) & ? [v0: $i] : ? [v1: $i] : ? % 71.42/10.51 [v2: $i] : ($i(v1) & (xi = sz00 | (v2 = xi & sdtlpdtrp0(xN, xi) = v0 & % 71.42/10.51 szszuzczcdt0(v1) = xi & $i(v0) & aSubsetOf0(v0, szNzAzT0) & % 71.42/10.51 isCountable0(v0) & aElementOf0(v1, szNzAzT0) & aSet0(v0) & ! [v3: $i] : % 71.42/10.51 ( ~ $i(v3) | ~ aElementOf0(v3, v0) | aElementOf0(v3, szNzAzT0))))) % 71.42/10.51 % 71.42/10.51 (function-axioms) % 71.42/10.51 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 71.42/10.51 (sdtexdt0(v3, v2) = v1) | ~ (sdtexdt0(v3, v2) = v0)) & ! [v0: $i] : ! % 71.42/10.51 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtlcdtrc0(v3, v2) = v1) % 71.42/10.51 | ~ (sdtlcdtrc0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 71.42/10.51 ! [v3: $i] : (v1 = v0 | ~ (sdtlbdtrb0(v3, v2) = v1) | ~ (sdtlbdtrb0(v3, v2) % 71.42/10.51 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 % 71.42/10.51 | ~ (sdtlpdtrp0(v3, v2) = v1) | ~ (sdtlpdtrp0(v3, v2) = v0)) & ! [v0: $i] % 71.42/10.51 : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (slbdtsldtrb0(v3, % 71.42/10.51 v2) = v1) | ~ (slbdtsldtrb0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] % 71.42/10.51 : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtmndt0(v3, v2) = v1) | ~ % 71.42/10.51 (sdtmndt0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 71.42/10.51 $i] : (v1 = v0 | ~ (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0)) & % 71.42/10.51 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (szDzizrdt0(v2) = v1) | % 71.42/10.51 ~ (szDzizrdt0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = % 71.42/10.51 v0 | ~ (szDzozmdt0(v2) = v1) | ~ (szDzozmdt0(v2) = v0)) & ! [v0: $i] : ! % 71.42/10.51 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (slbdtrb0(v2) = v1) | ~ (slbdtrb0(v2) % 71.42/10.51 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 71.42/10.51 (szmzazxdt0(v2) = v1) | ~ (szmzazxdt0(v2) = v0)) & ! [v0: $i] : ! [v1: % 71.42/10.51 $i] : ! [v2: $i] : (v1 = v0 | ~ (szmzizndt0(v2) = v1) | ~ (szmzizndt0(v2) % 71.42/10.51 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 71.42/10.51 (sbrdtbr0(v2) = v1) | ~ (sbrdtbr0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : % 71.42/10.51 ! [v2: $i] : (v1 = v0 | ~ (szszuzczcdt0(v2) = v1) | ~ (szszuzczcdt0(v2) = % 71.42/10.51 v0)) % 71.42/10.51 % 71.42/10.51 Further assumptions not needed in the proof: % 71.42/10.51 -------------------------------------------- % 71.42/10.52 mCConsSet, mCDiffSet, mCardCons, mCardDiff, mCardEmpty, mCardNum, mCardS, % 71.42/10.52 mCardSeg, mCardSub, mCardSubEx, mCntRel, mConsDiff, mCountNFin, mCountNFin_01, % 71.42/10.52 mDefCons, mDefDiff, mDefEmp, mDefMax, mDefMin, mDefPtt, mDefRst, mDefSImg, % 71.42/10.52 mDefSeg, mDefSel, mDefSub, mDiffCons, mDirichlet, mDomSet, mEOfElem, mElmSort, % 71.42/10.52 mEmpFin, mFConsSet, mFDiffSet, mFinRel, mFinSubSeg, mFunSort, mIH, mIHSort, % 71.42/10.52 mImgCount, mImgElm, mImgRng, mLessASymm, mLessRefl, mLessRel, mLessSucc, % 71.42/10.52 mLessTotal, mLessTrans, mMinMin, mNATSet, mNatExtra, mNatNSucc, mNoScLessZr, % 71.42/10.52 mPttSet, mSegFin, mSegLess, mSegSucc, mSegZero, mSelCSet, mSelExtra, mSelFSet, % 71.42/10.52 mSelNSet, mSelSub, mSetSort, mSubASymm, mSubFSet, mSubRefl, mSubTrans, % 71.42/10.52 mSuccEquSucc, mSuccLess, mSuccNum, mZeroLess, mZeroNum, m__3291, m__3398, % 71.42/10.52 m__3418, m__3453, m__3462, m__3520, m__3533, m__3671, m__3702 % 71.42/10.52 % 71.42/10.52 Those formulas are unsatisfiable: % 71.42/10.52 --------------------------------- % 71.42/10.52 % 71.42/10.52 Begin of proof % 71.42/10.52 | % 71.42/10.52 | ALPHA: (m__3435) implies: % 71.42/10.52 | (1) isCountable0(xS) % 71.42/10.52 | (2) aSubsetOf0(xS, szNzAzT0) % 71.42/10.52 | % 71.42/10.52 | ALPHA: (m__3623) implies: % 71.42/10.52 | (3) sdtlpdtrp0(xN, sz00) = xS % 71.42/10.52 | % 71.42/10.52 | ALPHA: (m__3702_02) implies: % 71.42/10.52 | (4) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ($i(v1) & (xi = sz00 | (v2 = % 71.42/10.52 | xi & sdtlpdtrp0(xN, xi) = v0 & szszuzczcdt0(v1) = xi & $i(v0) & % 71.42/10.52 | aSubsetOf0(v0, szNzAzT0) & isCountable0(v0) & aElementOf0(v1, % 71.42/10.52 | szNzAzT0) & aSet0(v0) & ! [v3: $i] : ( ~ $i(v3) | ~ % 71.42/10.52 | aElementOf0(v3, v0) | aElementOf0(v3, szNzAzT0))))) % 71.42/10.52 | % 71.42/10.52 | ALPHA: (m__) implies: % 71.42/10.52 | (5) ? [v0: $i] : ? [v1: $i] : (sdtlpdtrp0(xN, xi) = v0 & $i(v1) & $i(v0) % 71.42/10.52 | & ( ~ isCountable0(v0) | ( ~ aSubsetOf0(v0, szNzAzT0) & ( ~ aSet0(v0) % 71.42/10.52 | | (aElementOf0(v1, v0) & ~ aElementOf0(v1, szNzAzT0)))))) % 71.42/10.52 | % 71.42/10.52 | ALPHA: (function-axioms) implies: % 71.42/10.52 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 71.42/10.52 | (sdtlpdtrp0(v3, v2) = v1) | ~ (sdtlpdtrp0(v3, v2) = v0)) % 71.42/10.52 | % 71.42/10.52 | DELTA: instantiating (5) with fresh symbols all_68_0, all_68_1 gives: % 71.42/10.52 | (7) sdtlpdtrp0(xN, xi) = all_68_1 & $i(all_68_0) & $i(all_68_1) & ( ~ % 71.42/10.52 | isCountable0(all_68_1) | ( ~ aSubsetOf0(all_68_1, szNzAzT0) & ( ~ % 71.42/10.52 | aSet0(all_68_1) | (aElementOf0(all_68_0, all_68_1) & ~ % 71.42/10.52 | aElementOf0(all_68_0, szNzAzT0))))) % 71.42/10.52 | % 71.42/10.52 | ALPHA: (7) implies: % 71.42/10.52 | (8) sdtlpdtrp0(xN, xi) = all_68_1 % 71.42/10.52 | (9) ~ isCountable0(all_68_1) | ( ~ aSubsetOf0(all_68_1, szNzAzT0) & ( ~ % 71.42/10.52 | aSet0(all_68_1) | (aElementOf0(all_68_0, all_68_1) & ~ % 71.42/10.52 | aElementOf0(all_68_0, szNzAzT0)))) % 71.42/10.52 | % 71.42/10.52 | DELTA: instantiating (4) with fresh symbols all_70_0, all_70_1, all_70_2 % 71.42/10.52 | gives: % 71.42/10.52 | (10) $i(all_70_1) & (xi = sz00 | (all_70_0 = xi & sdtlpdtrp0(xN, xi) = % 71.42/10.52 | all_70_2 & szszuzczcdt0(all_70_1) = xi & $i(all_70_2) & % 71.42/10.52 | aSubsetOf0(all_70_2, szNzAzT0) & isCountable0(all_70_2) & % 71.42/10.53 | aElementOf0(all_70_1, szNzAzT0) & aSet0(all_70_2) & ! [v0: $i] : % 71.42/10.53 | ( ~ $i(v0) | ~ aElementOf0(v0, all_70_2) | aElementOf0(v0, % 71.42/10.53 | szNzAzT0)))) % 71.42/10.53 | % 71.42/10.53 | ALPHA: (10) implies: % 71.64/10.53 | (11) xi = sz00 | (all_70_0 = xi & sdtlpdtrp0(xN, xi) = all_70_2 & % 71.64/10.53 | szszuzczcdt0(all_70_1) = xi & $i(all_70_2) & aSubsetOf0(all_70_2, % 71.64/10.53 | szNzAzT0) & isCountable0(all_70_2) & aElementOf0(all_70_1, % 71.64/10.53 | szNzAzT0) & aSet0(all_70_2) & ! [v0: $i] : ( ~ $i(v0) | ~ % 71.64/10.53 | aElementOf0(v0, all_70_2) | aElementOf0(v0, szNzAzT0))) % 71.64/10.53 | % 71.64/10.53 | BETA: splitting (9) gives: % 71.64/10.53 | % 71.64/10.53 | Case 1: % 71.64/10.53 | | % 71.64/10.53 | | (12) ~ isCountable0(all_68_1) % 71.64/10.53 | | % 71.64/10.53 | | BETA: splitting (11) gives: % 71.64/10.53 | | % 71.64/10.53 | | Case 1: % 71.64/10.53 | | | % 71.64/10.53 | | | (13) xi = sz00 % 71.64/10.53 | | | % 71.64/10.53 | | | REDUCE: (8), (13) imply: % 71.64/10.53 | | | (14) sdtlpdtrp0(xN, sz00) = all_68_1 % 71.64/10.53 | | | % 71.64/10.53 | | | GROUND_INST: instantiating (6) with xS, all_68_1, sz00, xN, simplifying % 71.64/10.53 | | | with (3), (14) gives: % 71.64/10.53 | | | (15) all_68_1 = xS % 71.64/10.53 | | | % 71.64/10.53 | | | REDUCE: (12), (15) imply: % 71.64/10.53 | | | (16) ~ isCountable0(xS) % 71.64/10.53 | | | % 71.64/10.53 | | | PRED_UNIFY: (1), (16) imply: % 71.64/10.53 | | | (17) $false % 71.64/10.53 | | | % 71.64/10.53 | | | CLOSE: (17) is inconsistent. % 71.64/10.53 | | | % 71.64/10.53 | | Case 2: % 71.64/10.53 | | | % 71.64/10.53 | | | (18) all_70_0 = xi & sdtlpdtrp0(xN, xi) = all_70_2 & % 71.64/10.53 | | | szszuzczcdt0(all_70_1) = xi & $i(all_70_2) & aSubsetOf0(all_70_2, % 71.64/10.53 | | | szNzAzT0) & isCountable0(all_70_2) & aElementOf0(all_70_1, % 71.64/10.53 | | | szNzAzT0) & aSet0(all_70_2) & ! [v0: $i] : ( ~ $i(v0) | ~ % 71.64/10.53 | | | aElementOf0(v0, all_70_2) | aElementOf0(v0, szNzAzT0)) % 71.64/10.53 | | | % 71.64/10.53 | | | ALPHA: (18) implies: % 71.64/10.53 | | | (19) isCountable0(all_70_2) % 71.64/10.53 | | | (20) sdtlpdtrp0(xN, xi) = all_70_2 % 71.64/10.53 | | | % 71.64/10.53 | | | GROUND_INST: instantiating (6) with all_68_1, all_70_2, xi, xN, % 71.64/10.53 | | | simplifying with (8), (20) gives: % 71.64/10.54 | | | (21) all_70_2 = all_68_1 % 71.64/10.54 | | | % 71.64/10.54 | | | REDUCE: (19), (21) imply: % 71.64/10.54 | | | (22) isCountable0(all_68_1) % 71.64/10.54 | | | % 71.64/10.54 | | | PRED_UNIFY: (12), (22) imply: % 71.64/10.54 | | | (23) $false % 71.64/10.54 | | | % 71.64/10.54 | | | CLOSE: (23) is inconsistent. % 71.64/10.54 | | | % 71.64/10.54 | | End of split % 71.64/10.54 | | % 71.64/10.54 | Case 2: % 71.64/10.54 | | % 71.64/10.54 | | (24) ~ aSubsetOf0(all_68_1, szNzAzT0) & ( ~ aSet0(all_68_1) | % 71.64/10.54 | | (aElementOf0(all_68_0, all_68_1) & ~ aElementOf0(all_68_0, % 71.64/10.54 | | szNzAzT0))) % 71.64/10.54 | | % 71.64/10.54 | | ALPHA: (24) implies: % 71.64/10.54 | | (25) ~ aSubsetOf0(all_68_1, szNzAzT0) % 71.64/10.54 | | % 71.64/10.54 | | BETA: splitting (11) gives: % 71.64/10.54 | | % 71.64/10.54 | | Case 1: % 71.64/10.54 | | | % 71.64/10.54 | | | (26) xi = sz00 % 71.64/10.54 | | | % 71.64/10.54 | | | REDUCE: (8), (26) imply: % 71.64/10.54 | | | (27) sdtlpdtrp0(xN, sz00) = all_68_1 % 71.64/10.54 | | | % 71.64/10.54 | | | GROUND_INST: instantiating (6) with xS, all_68_1, sz00, xN, simplifying % 71.64/10.54 | | | with (3), (27) gives: % 71.64/10.54 | | | (28) all_68_1 = xS % 71.64/10.54 | | | % 71.64/10.54 | | | REDUCE: (25), (28) imply: % 71.64/10.54 | | | (29) ~ aSubsetOf0(xS, szNzAzT0) % 71.64/10.54 | | | % 71.64/10.54 | | | PRED_UNIFY: (2), (29) imply: % 71.64/10.54 | | | (30) $false % 71.64/10.54 | | | % 71.64/10.54 | | | CLOSE: (30) is inconsistent. % 71.64/10.54 | | | % 71.64/10.54 | | Case 2: % 71.64/10.54 | | | % 71.72/10.54 | | | (31) all_70_0 = xi & sdtlpdtrp0(xN, xi) = all_70_2 & % 71.72/10.54 | | | szszuzczcdt0(all_70_1) = xi & $i(all_70_2) & aSubsetOf0(all_70_2, % 71.72/10.54 | | | szNzAzT0) & isCountable0(all_70_2) & aElementOf0(all_70_1, % 71.72/10.54 | | | szNzAzT0) & aSet0(all_70_2) & ! [v0: $i] : ( ~ $i(v0) | ~ % 71.72/10.54 | | | aElementOf0(v0, all_70_2) | aElementOf0(v0, szNzAzT0)) % 71.72/10.54 | | | % 71.72/10.54 | | | ALPHA: (31) implies: % 71.72/10.54 | | | (32) aSubsetOf0(all_70_2, szNzAzT0) % 71.72/10.54 | | | (33) sdtlpdtrp0(xN, xi) = all_70_2 % 71.72/10.54 | | | % 71.72/10.54 | | | GROUND_INST: instantiating (6) with all_68_1, all_70_2, xi, xN, % 71.72/10.54 | | | simplifying with (8), (33) gives: % 71.72/10.54 | | | (34) all_70_2 = all_68_1 % 71.72/10.55 | | | % 71.72/10.55 | | | REDUCE: (32), (34) imply: % 71.72/10.55 | | | (35) aSubsetOf0(all_68_1, szNzAzT0) % 71.72/10.55 | | | % 71.72/10.55 | | | PRED_UNIFY: (25), (35) imply: % 71.72/10.55 | | | (36) $false % 71.72/10.55 | | | % 71.72/10.55 | | | CLOSE: (36) is inconsistent. % 71.72/10.55 | | | % 71.72/10.55 | | End of split % 71.72/10.55 | | % 71.72/10.55 | End of split % 71.72/10.55 | % 71.72/10.55 End of proof % 71.72/10.55 % SZS output end Proof for theBenchmark % 71.72/10.55 % 71.72/10.55 9932ms %------------------------------------------------------------------------------