%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : NUM622+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 : n029.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 11:49:02 EDT 2023 % Result : Theorem 46.74s 7.04s % Output : Proof 73.66s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.13 % Problem : NUM622+3 : TPTP v8.1.2. Released v4.0.0. % 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.18/0.35 % Computer : n029.cluster.edu % 0.18/0.35 % Model : x86_64 x86_64 % 0.18/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.18/0.35 % Memory : 8042.1875MB % 0.18/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.18/0.35 % CPULimit : 300 % 0.18/0.35 % WCLimit : 300 % 0.18/0.35 % DateTime : Fri Aug 25 11:03:24 EDT 2023 % 0.18/0.35 % CPUTime : % 0.21/0.61 ________ _____ % 0.21/0.61 ___ __ \_________(_)________________________________ % 0.21/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.21/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.21/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.21/0.61 % 0.21/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.21/0.61 (2023-06-19) % 0.21/0.61 % 0.21/0.61 (c) Philipp Rümmer, 2009-2023 % 0.21/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.21/0.61 Amanda Stjerna. % 0.21/0.61 Free software under BSD-3-Clause. % 0.21/0.61 % 0.21/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.21/0.61 % 0.21/0.61 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.21/0.62 Running up to 7 provers in parallel. % 0.21/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.21/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.21/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.21/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.21/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.21/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.21/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 6.08/1.72 Prover 4: Preprocessing ... % 6.08/1.72 Prover 1: Preprocessing ... % 6.08/1.75 Prover 6: Preprocessing ... % 6.08/1.75 Prover 2: Preprocessing ... % 6.08/1.75 Prover 3: Preprocessing ... % 6.08/1.75 Prover 5: Preprocessing ... % 6.08/1.75 Prover 0: Preprocessing ... % 20.05/3.54 Prover 6: Proving ... % 20.68/3.55 Prover 1: Constructing countermodel ... % 20.92/3.62 Prover 3: Constructing countermodel ... % 25.60/4.27 Prover 5: Proving ... % 46.74/7.04 Prover 6: proved (6403ms) % 46.74/7.04 % 46.74/7.04 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 46.74/7.04 % 47.13/7.06 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 47.13/7.06 Prover 5: stopped % 47.13/7.06 Prover 3: stopped % 47.13/7.08 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 47.13/7.08 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 48.95/7.31 Prover 7: Preprocessing ... % 48.95/7.32 Prover 8: Preprocessing ... % 48.95/7.34 Prover 10: Preprocessing ... % 49.36/7.52 Prover 4: Constructing countermodel ... % 53.09/7.89 Prover 8: Warning: ignoring some quantifiers % 53.09/7.91 Prover 8: Constructing countermodel ... % 54.78/8.22 Prover 10: Constructing countermodel ... % 54.78/8.24 Prover 2: Proving ... % 56.06/8.28 Prover 2: stopped % 56.06/8.28 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 57.07/8.38 Prover 7: Constructing countermodel ... % 58.23/8.57 Prover 11: Preprocessing ... % 60.77/8.93 Prover 0: Proving ... % 60.77/8.96 Prover 0: stopped % 60.77/8.96 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 63.05/9.18 Prover 13: Preprocessing ... % 65.10/9.49 Prover 10: Found proof (size 69) % 65.10/9.49 Prover 10: proved (2411ms) % 65.10/9.49 Prover 7: stopped % 65.10/9.49 Prover 4: stopped % 65.10/9.49 Prover 8: stopped % 65.10/9.49 Prover 1: stopped % 67.35/9.88 Prover 13: Warning: ignoring some quantifiers % 67.68/9.96 Prover 13: Constructing countermodel ... % 68.04/9.98 Prover 13: stopped % 72.63/11.13 Prover 11: Constructing countermodel ... % 72.63/11.15 Prover 11: stopped % 72.63/11.15 % 72.63/11.15 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 72.63/11.15 % 72.63/11.17 % SZS output start Proof for theBenchmark % 72.95/11.18 Assumptions after simplification: % 72.95/11.18 --------------------------------- % 72.95/11.18 % 72.95/11.18 (mCountNFin_01) % 72.95/11.18 $i(slcrc0) & ( ~ isCountable0(slcrc0) | ~ aSet0(slcrc0)) % 72.95/11.18 % 72.95/11.18 (mDefEmp) % 72.95/11.19 $i(slcrc0) & aSet0(slcrc0) & ! [v0: $i] : (v0 = slcrc0 | ~ $i(v0) | ~ % 72.95/11.19 aSet0(v0) | ? [v1: $i] : ($i(v1) & aElementOf0(v1, v0))) & ! [v0: $i] : ( % 72.95/11.19 ~ $i(v0) | ~ aElementOf0(v0, slcrc0)) % 72.95/11.19 % 72.95/11.19 (mDefSub) % 72.95/11.19 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 72.95/11.19 ~ aSubsetOf0(v1, v0) | ~ aElementOf0(v2, v1) | ~ aSet0(v0) | % 72.95/11.19 aElementOf0(v2, v0)) & ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | % 72.95/11.19 ~ aSubsetOf0(v1, v0) | ~ aSet0(v0) | aSet0(v1)) & ! [v0: $i] : ! [v1: $i] % 72.95/11.19 : ( ~ $i(v1) | ~ $i(v0) | ~ aSet0(v1) | ~ aSet0(v0) | aSubsetOf0(v1, v0) | % 72.95/11.19 ? [v2: $i] : ($i(v2) & aElementOf0(v2, v1) & ~ aElementOf0(v2, v0))) % 72.95/11.20 % 72.95/11.20 (m__) % 72.95/11.24 $i(xm) & $i(xp) & $i(xN) & ? [v0: $i] : (sdtlpdtrp0(xN, xm) = v0 & $i(v0) & % 72.95/11.24 ~ aElementOf0(xp, v0)) % 72.95/11.24 % 72.95/11.24 (m__3671) % 72.95/11.24 $i(xN) & $i(szNzAzT0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 72.95/11.24 (sdtlpdtrp0(xN, v0) = v1) | ~ $i(v2) | ~ $i(v0) | ~ aElementOf0(v2, v1) | % 72.95/11.24 ~ aElementOf0(v0, szNzAzT0) | aElementOf0(v2, szNzAzT0)) & ! [v0: $i] : ! % 72.95/11.24 [v1: $i] : ( ~ (sdtlpdtrp0(xN, v0) = v1) | ~ $i(v0) | ~ aElementOf0(v0, % 72.95/11.24 szNzAzT0) | aSubsetOf0(v1, szNzAzT0)) & ! [v0: $i] : ! [v1: $i] : ( ~ % 72.95/11.24 (sdtlpdtrp0(xN, v0) = v1) | ~ $i(v0) | ~ aElementOf0(v0, szNzAzT0) | % 72.95/11.24 isCountable0(v1)) & ! [v0: $i] : ! [v1: $i] : ( ~ (sdtlpdtrp0(xN, v0) = % 72.95/11.24 v1) | ~ $i(v0) | ~ aElementOf0(v0, szNzAzT0) | aSet0(v1)) % 72.95/11.24 % 72.95/11.24 (m__4660) % 72.95/11.24 szDzozmdt0(xe) = szNzAzT0 & $i(xe) & $i(xN) & $i(szNzAzT0) & aFunction0(xe) & % 72.95/11.24 ! [v0: $i] : ! [v1: $i] : ( ~ (sdtlpdtrp0(xe, v0) = v1) | ~ $i(v0) | ~ % 72.95/11.24 aElementOf0(v0, szNzAzT0) | ? [v2: $i] : (sdtlpdtrp0(xN, v0) = v2 & % 72.95/11.24 szmzizndt0(v2) = v1 & $i(v2) & $i(v1) & aElementOf0(v1, v2) & ! [v3: $i] % 72.95/11.24 : ( ~ $i(v3) | ~ aElementOf0(v3, v2) | sdtlseqdt0(v1, v3)))) % 72.95/11.24 % 72.95/11.24 (m__4730) % 72.95/11.25 szDzozmdt0(xd) = szNzAzT0 & $i(xd) & $i(xC) & $i(xN) & $i(xk) & $i(szNzAzT0) & % 72.95/11.25 aFunction0(xd) & ! [v0: $i] : ! [v1: $i] : ( ~ (sdtlpdtrp0(xC, v0) = v1) | % 72.95/11.25 ~ $i(v0) | ~ aElementOf0(v0, szNzAzT0) | ? [v2: $i] : ? [v3: $i] : ? % 72.95/11.25 [v4: $i] : ? [v5: $i] : (sdtlpdtrp0(xd, v0) = v5 & sdtlpdtrp0(xN, v2) = v3 % 72.95/11.25 & slbdtsldtrb0(v3, xk) = v4 & szszuzczcdt0(v0) = v2 & $i(v5) & $i(v4) & % 72.95/11.25 $i(v3) & $i(v2) & ! [v6: $i] : ! [v7: $i] : (v7 = v5 | ~ % 72.95/11.25 (sdtlpdtrp0(v1, v6) = v7) | ~ $i(v6) | ~ aSubsetOf0(v6, v3) | ~ % 72.95/11.25 aSet0(v6) | ? [v8: $i] : ( ~ (v8 = xk) & sbrdtbr0(v6) = v8 & $i(v8))) & % 72.95/11.25 ! [v6: $i] : ! [v7: $i] : (v7 = v5 | ~ (sdtlpdtrp0(v1, v6) = v7) | ~ % 72.95/11.25 $i(v6) | ~ aElementOf0(v6, v4) | ~ aSet0(v6)) & ! [v6: $i] : ! [v7: % 72.95/11.25 $i] : (v7 = v5 | ~ (sdtlpdtrp0(v1, v6) = v7) | ~ $i(v6) | ~ aSet0(v6) % 72.95/11.25 | ? [v8: $i] : ? [v9: $i] : ($i(v9) & (( ~ (v8 = xk) & sbrdtbr0(v6) = % 72.95/11.25 v8 & $i(v8)) | (aElementOf0(v9, v6) & ~ aElementOf0(v9, v3))))))) % 72.95/11.25 % 72.95/11.25 (m__4758) % 72.95/11.26 $i(xd) & $i(xT) & ? [v0: $i] : ? [v1: $i] : (sdtlcdtrc0(xd, v0) = v1 & % 72.95/11.26 szDzozmdt0(xd) = v0 & $i(v1) & $i(v0) & aSubsetOf0(v1, xT) & aSet0(v1) & ! % 72.95/11.26 [v2: $i] : ! [v3: $i] : ( ~ (sdtlpdtrp0(xd, v3) = v2) | ~ $i(v3) | ~ % 72.95/11.26 $i(v2) | ~ aElementOf0(v3, v0) | aElementOf0(v2, v1)) & ! [v2: $i] : ( ~ % 72.95/11.26 $i(v2) | ~ aElementOf0(v2, v1) | aElementOf0(v2, xT)) & ! [v2: $i] : ( ~ % 72.95/11.26 $i(v2) | ~ aElementOf0(v2, v1) | ? [v3: $i] : (sdtlpdtrp0(xd, v3) = v2 & % 72.95/11.26 $i(v3) & aElementOf0(v3, v0)))) % 72.95/11.26 % 72.95/11.26 (m__4854) % 72.95/11.26 $i(xd) & $i(xT) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (szDzizrdt0(xd) = % 72.95/11.26 v0 & sdtlbdtrb0(xd, v0) = v1 & szDzozmdt0(xd) = v2 & $i(v2) & $i(v1) & % 72.95/11.26 $i(v0) & aElementOf0(v0, xT) & aSet0(v1) & ! [v3: $i] : ! [v4: $i] : (v4 = % 72.95/11.26 v0 | ~ (sdtlpdtrp0(xd, v3) = v4) | ~ $i(v3) | ~ aElementOf0(v3, v1)) & % 72.95/11.26 ! [v3: $i] : ! [v4: $i] : ( ~ (sdtlpdtrp0(xd, v3) = v4) | ~ $i(v3) | ~ % 72.95/11.26 aElementOf0(v3, v1) | aElementOf0(v3, v2)) & ! [v3: $i] : ( ~ % 72.95/11.26 (sdtlpdtrp0(xd, v3) = v0) | ~ $i(v3) | ~ aElementOf0(v3, v2) | % 72.95/11.26 aElementOf0(v3, v1))) % 72.95/11.26 % 72.95/11.26 (m__4891) % 72.95/11.27 $i(xO) & $i(xd) & $i(xe) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 72.95/11.27 (szDzizrdt0(xd) = v0 & sdtlcdtrc0(xe, v1) = xO & sdtlbdtrb0(xd, v0) = v1 & % 72.95/11.27 szDzozmdt0(xd) = v2 & $i(v2) & $i(v1) & $i(v0) & aSet0(v1) & aSet0(xO) & ! % 72.95/11.27 [v3: $i] : ! [v4: $i] : (v4 = v0 | ~ (sdtlpdtrp0(xd, v3) = v4) | ~ $i(v3) % 72.95/11.27 | ~ aElementOf0(v3, v1)) & ! [v3: $i] : ! [v4: $i] : ( ~ % 72.95/11.27 (sdtlpdtrp0(xd, v3) = v4) | ~ $i(v3) | ~ aElementOf0(v3, v1) | % 72.95/11.27 aElementOf0(v3, v2)) & ! [v3: $i] : ! [v4: $i] : ( ~ (sdtlpdtrp0(xe, v4) % 72.95/11.27 = v3) | ~ $i(v4) | ~ $i(v3) | ~ aElementOf0(v4, v1) | aElementOf0(v3, % 72.95/11.27 xO)) & ! [v3: $i] : ( ~ (sdtlpdtrp0(xd, v3) = v0) | ~ $i(v3) | ~ % 72.95/11.27 aElementOf0(v3, v2) | aElementOf0(v3, v1)) & ! [v3: $i] : ( ~ $i(v3) | ~ % 72.95/11.27 aElementOf0(v3, xO) | ? [v4: $i] : (sdtlpdtrp0(xe, v4) = v3 & $i(v4) & % 72.95/11.27 aElementOf0(v4, v1)))) % 72.95/11.27 % 72.95/11.27 (m__5309) % 72.95/11.27 $i(xn) & $i(xp) & $i(xd) & $i(xe) & $i(szNzAzT0) & ? [v0: $i] : ? [v1: $i] : % 72.95/11.27 ? [v2: $i] : (szDzizrdt0(xd) = v1 & sdtlbdtrb0(xd, v1) = v2 & sdtlpdtrp0(xd, % 73.38/11.27 xn) = v1 & sdtlpdtrp0(xe, xn) = xp & szDzozmdt0(xd) = v0 & $i(v2) & $i(v1) % 73.38/11.27 & $i(v0) & aElementOf0(xn, v2) & aElementOf0(xn, v0) & aElementOf0(xn, % 73.38/11.27 szNzAzT0)) % 73.38/11.27 % 73.38/11.27 (m__5389) % 73.38/11.27 sdtlpdtrp0(xe, xm) = xx & $i(xm) & $i(xx) & $i(xe) & $i(szNzAzT0) & % 73.38/11.27 aElementOf0(xm, szNzAzT0) % 73.38/11.27 % 73.38/11.27 (m__5401) % 73.38/11.27 $i(xm) & $i(xx) & $i(xN) & ? [v0: $i] : (sdtlpdtrp0(xN, xm) = v0 & $i(v0) & % 73.38/11.27 ! [v1: $i] : ( ~ $i(v1) | ~ aElementOf0(v1, v0) | sdtlseqdt0(xx, v1))) % 73.38/11.27 % 73.38/11.27 (m__5442) % 73.38/11.27 $i(xm) & $i(xn) & $i(xN) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: % 73.38/11.27 $i] : (sdtlpdtrp0(xN, v1) = v2 & sdtlpdtrp0(xN, xm) = v0 & szszuzczcdt0(xn) % 73.38/11.27 = v1 & $i(v3) & $i(v2) & $i(v1) & $i(v0) & aElementOf0(v3, v0) & ~ % 73.38/11.27 aSubsetOf0(v0, v2) & ~ aElementOf0(v3, v2)) % 73.38/11.27 % 73.38/11.27 (m__5461) % 73.38/11.28 $i(xm) & $i(xn) & $i(xN) & ? [v0: $i] : ? [v1: $i] : (sdtlpdtrp0(xN, xm) = % 73.38/11.28 v1 & sdtlpdtrp0(xN, xn) = v0 & $i(v1) & $i(v0) & aSubsetOf0(v0, v1) & ! % 73.38/11.28 [v2: $i] : ( ~ $i(v2) | ~ aElementOf0(v2, v0) | aElementOf0(v2, v1))) % 73.38/11.28 % 73.38/11.28 (function-axioms) % 73.38/11.28 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 73.38/11.28 (sdtexdt0(v3, v2) = v1) | ~ (sdtexdt0(v3, v2) = v0)) & ! [v0: $i] : ! % 73.38/11.28 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtlcdtrc0(v3, v2) = v1) % 73.38/11.28 | ~ (sdtlcdtrc0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 73.38/11.28 ! [v3: $i] : (v1 = v0 | ~ (sdtlbdtrb0(v3, v2) = v1) | ~ (sdtlbdtrb0(v3, v2) % 73.38/11.28 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 % 73.38/11.28 | ~ (sdtlpdtrp0(v3, v2) = v1) | ~ (sdtlpdtrp0(v3, v2) = v0)) & ! [v0: $i] % 73.38/11.28 : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (slbdtsldtrb0(v3, % 73.38/11.28 v2) = v1) | ~ (slbdtsldtrb0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] % 73.38/11.28 : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtmndt0(v3, v2) = v1) | ~ % 73.38/11.28 (sdtmndt0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 73.38/11.28 $i] : (v1 = v0 | ~ (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0)) & % 73.38/11.28 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (szDzizrdt0(v2) = v1) | % 73.38/11.28 ~ (szDzizrdt0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = % 73.38/11.28 v0 | ~ (szDzozmdt0(v2) = v1) | ~ (szDzozmdt0(v2) = v0)) & ! [v0: $i] : ! % 73.38/11.28 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (slbdtrb0(v2) = v1) | ~ (slbdtrb0(v2) % 73.38/11.28 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 73.38/11.28 (szmzazxdt0(v2) = v1) | ~ (szmzazxdt0(v2) = v0)) & ! [v0: $i] : ! [v1: % 73.38/11.28 $i] : ! [v2: $i] : (v1 = v0 | ~ (szmzizndt0(v2) = v1) | ~ (szmzizndt0(v2) % 73.38/11.28 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 73.38/11.28 (sbrdtbr0(v2) = v1) | ~ (sbrdtbr0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : % 73.38/11.28 ! [v2: $i] : (v1 = v0 | ~ (szszuzczcdt0(v2) = v1) | ~ (szszuzczcdt0(v2) = % 73.38/11.28 v0)) % 73.38/11.28 % 73.38/11.28 Further assumptions not needed in the proof: % 73.38/11.28 -------------------------------------------- % 73.38/11.29 mCConsSet, mCDiffSet, mCardCons, mCardDiff, mCardEmpty, mCardNum, mCardS, % 73.38/11.29 mCardSeg, mCardSub, mCardSubEx, mCntRel, mConsDiff, mCountNFin, mDefCons, % 73.38/11.29 mDefDiff, mDefMax, mDefMin, mDefPtt, mDefRst, mDefSImg, mDefSeg, mDefSel, % 73.38/11.29 mDiffCons, mDirichlet, mDomSet, mEOfElem, mElmSort, mEmpFin, mFConsSet, % 73.38/11.29 mFDiffSet, mFinRel, mFinSubSeg, mFunSort, mIH, mIHSort, mImgCount, mImgElm, % 73.38/11.29 mImgRng, mLessASymm, mLessRefl, mLessRel, mLessSucc, mLessTotal, mLessTrans, % 73.38/11.29 mMinMin, mNATSet, mNatExtra, mNatNSucc, mNoScLessZr, mPttSet, mSegFin, mSegLess, % 73.38/11.29 mSegSucc, mSegZero, mSelCSet, mSelExtra, mSelFSet, mSelNSet, mSelSub, mSetSort, % 73.38/11.29 mSubASymm, mSubFSet, mSubRefl, mSubTrans, mSuccEquSucc, mSuccLess, mSuccNum, % 73.38/11.29 mZeroLess, mZeroNum, m__3291, m__3398, m__3418, m__3435, m__3453, m__3462, % 73.38/11.29 m__3520, m__3533, m__3623, m__3754, m__3821, m__3965, m__4151, m__4182, m__4331, % 73.38/11.29 m__4411, m__4618, m__4908, m__4982, m__4998, m__5078, m__5093, m__5106, m__5116, % 73.38/11.29 m__5147, m__5164, m__5173, m__5182, m__5195, m__5208, m__5217, m__5270, m__5321, % 73.38/11.29 m__5348, m__5365 % 73.38/11.29 % 73.38/11.29 Those formulas are unsatisfiable: % 73.38/11.29 --------------------------------- % 73.38/11.29 % 73.38/11.29 Begin of proof % 73.38/11.29 | % 73.38/11.29 | ALPHA: (mDefEmp) implies: % 73.38/11.29 | (1) aSet0(slcrc0) % 73.38/11.29 | % 73.38/11.29 | ALPHA: (mCountNFin_01) implies: % 73.38/11.29 | (2) ~ isCountable0(slcrc0) | ~ aSet0(slcrc0) % 73.38/11.29 | % 73.38/11.29 | ALPHA: (mDefSub) implies: % 73.38/11.29 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ % 73.38/11.29 | $i(v0) | ~ aSubsetOf0(v1, v0) | ~ aElementOf0(v2, v1) | ~ % 73.38/11.29 | aSet0(v0) | aElementOf0(v2, v0)) % 73.38/11.29 | % 73.38/11.29 | ALPHA: (m__3671) implies: % 73.49/11.29 | (4) ! [v0: $i] : ! [v1: $i] : ( ~ (sdtlpdtrp0(xN, v0) = v1) | ~ $i(v0) | % 73.49/11.29 | ~ aElementOf0(v0, szNzAzT0) | aSet0(v1)) % 73.49/11.29 | % 73.49/11.29 | ALPHA: (m__4660) implies: % 73.49/11.29 | (5) ! [v0: $i] : ! [v1: $i] : ( ~ (sdtlpdtrp0(xe, v0) = v1) | ~ $i(v0) | % 73.49/11.29 | ~ aElementOf0(v0, szNzAzT0) | ? [v2: $i] : (sdtlpdtrp0(xN, v0) = v2 % 73.49/11.29 | & szmzizndt0(v2) = v1 & $i(v2) & $i(v1) & aElementOf0(v1, v2) & ! % 73.49/11.29 | [v3: $i] : ( ~ $i(v3) | ~ aElementOf0(v3, v2) | sdtlseqdt0(v1, % 73.49/11.29 | v3)))) % 73.49/11.29 | % 73.49/11.29 | ALPHA: (m__4730) implies: % 73.49/11.29 | (6) szDzozmdt0(xd) = szNzAzT0 % 73.49/11.29 | % 73.49/11.29 | ALPHA: (m__4758) implies: % 73.49/11.29 | (7) ? [v0: $i] : ? [v1: $i] : (sdtlcdtrc0(xd, v0) = v1 & szDzozmdt0(xd) = % 73.49/11.29 | v0 & $i(v1) & $i(v0) & aSubsetOf0(v1, xT) & aSet0(v1) & ! [v2: $i] : % 73.49/11.29 | ! [v3: $i] : ( ~ (sdtlpdtrp0(xd, v3) = v2) | ~ $i(v3) | ~ $i(v2) | % 73.49/11.29 | ~ aElementOf0(v3, v0) | aElementOf0(v2, v1)) & ! [v2: $i] : ( ~ % 73.49/11.29 | $i(v2) | ~ aElementOf0(v2, v1) | aElementOf0(v2, xT)) & ! [v2: % 73.49/11.29 | $i] : ( ~ $i(v2) | ~ aElementOf0(v2, v1) | ? [v3: $i] : % 73.49/11.29 | (sdtlpdtrp0(xd, v3) = v2 & $i(v3) & aElementOf0(v3, v0)))) % 73.49/11.29 | % 73.49/11.29 | ALPHA: (m__4854) implies: % 73.49/11.30 | (8) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (szDzizrdt0(xd) = v0 & % 73.49/11.30 | sdtlbdtrb0(xd, v0) = v1 & szDzozmdt0(xd) = v2 & $i(v2) & $i(v1) & % 73.49/11.30 | $i(v0) & aElementOf0(v0, xT) & aSet0(v1) & ! [v3: $i] : ! [v4: $i] % 73.49/11.30 | : (v4 = v0 | ~ (sdtlpdtrp0(xd, v3) = v4) | ~ $i(v3) | ~ % 73.49/11.30 | aElementOf0(v3, v1)) & ! [v3: $i] : ! [v4: $i] : ( ~ % 73.49/11.30 | (sdtlpdtrp0(xd, v3) = v4) | ~ $i(v3) | ~ aElementOf0(v3, v1) | % 73.49/11.30 | aElementOf0(v3, v2)) & ! [v3: $i] : ( ~ (sdtlpdtrp0(xd, v3) = v0) % 73.49/11.30 | | ~ $i(v3) | ~ aElementOf0(v3, v2) | aElementOf0(v3, v1))) % 73.49/11.30 | % 73.49/11.30 | ALPHA: (m__4891) implies: % 73.49/11.30 | (9) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (szDzizrdt0(xd) = v0 & % 73.49/11.30 | sdtlcdtrc0(xe, v1) = xO & sdtlbdtrb0(xd, v0) = v1 & szDzozmdt0(xd) = % 73.49/11.30 | v2 & $i(v2) & $i(v1) & $i(v0) & aSet0(v1) & aSet0(xO) & ! [v3: $i] : % 73.49/11.30 | ! [v4: $i] : (v4 = v0 | ~ (sdtlpdtrp0(xd, v3) = v4) | ~ $i(v3) | % 73.49/11.30 | ~ aElementOf0(v3, v1)) & ! [v3: $i] : ! [v4: $i] : ( ~ % 73.49/11.30 | (sdtlpdtrp0(xd, v3) = v4) | ~ $i(v3) | ~ aElementOf0(v3, v1) | % 73.49/11.30 | aElementOf0(v3, v2)) & ! [v3: $i] : ! [v4: $i] : ( ~ % 73.49/11.30 | (sdtlpdtrp0(xe, v4) = v3) | ~ $i(v4) | ~ $i(v3) | ~ % 73.49/11.30 | aElementOf0(v4, v1) | aElementOf0(v3, xO)) & ! [v3: $i] : ( ~ % 73.49/11.30 | (sdtlpdtrp0(xd, v3) = v0) | ~ $i(v3) | ~ aElementOf0(v3, v2) | % 73.49/11.30 | aElementOf0(v3, v1)) & ! [v3: $i] : ( ~ $i(v3) | ~ % 73.49/11.30 | aElementOf0(v3, xO) | ? [v4: $i] : (sdtlpdtrp0(xe, v4) = v3 & % 73.49/11.30 | $i(v4) & aElementOf0(v4, v1)))) % 73.49/11.30 | % 73.49/11.30 | ALPHA: (m__5309) implies: % 73.49/11.30 | (10) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (szDzizrdt0(xd) = v1 & % 73.49/11.30 | sdtlbdtrb0(xd, v1) = v2 & sdtlpdtrp0(xd, xn) = v1 & sdtlpdtrp0(xe, % 73.49/11.30 | xn) = xp & szDzozmdt0(xd) = v0 & $i(v2) & $i(v1) & $i(v0) & % 73.49/11.30 | aElementOf0(xn, v2) & aElementOf0(xn, v0) & aElementOf0(xn, % 73.49/11.30 | szNzAzT0)) % 73.49/11.30 | % 73.49/11.30 | ALPHA: (m__5389) implies: % 73.49/11.30 | (11) aElementOf0(xm, szNzAzT0) % 73.49/11.30 | (12) sdtlpdtrp0(xe, xm) = xx % 73.49/11.30 | % 73.49/11.30 | ALPHA: (m__5401) implies: % 73.49/11.31 | (13) ? [v0: $i] : (sdtlpdtrp0(xN, xm) = v0 & $i(v0) & ! [v1: $i] : ( ~ % 73.49/11.31 | $i(v1) | ~ aElementOf0(v1, v0) | sdtlseqdt0(xx, v1))) % 73.49/11.31 | % 73.49/11.31 | ALPHA: (m__5442) implies: % 73.49/11.31 | (14) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : % 73.49/11.31 | (sdtlpdtrp0(xN, v1) = v2 & sdtlpdtrp0(xN, xm) = v0 & szszuzczcdt0(xn) % 73.49/11.31 | = v1 & $i(v3) & $i(v2) & $i(v1) & $i(v0) & aElementOf0(v3, v0) & ~ % 73.49/11.31 | aSubsetOf0(v0, v2) & ~ aElementOf0(v3, v2)) % 73.49/11.31 | % 73.49/11.31 | ALPHA: (m__5461) implies: % 73.49/11.31 | (15) $i(xn) % 73.49/11.31 | (16) ? [v0: $i] : ? [v1: $i] : (sdtlpdtrp0(xN, xm) = v1 & sdtlpdtrp0(xN, % 73.49/11.31 | xn) = v0 & $i(v1) & $i(v0) & aSubsetOf0(v0, v1) & ! [v2: $i] : ( % 73.49/11.31 | ~ $i(v2) | ~ aElementOf0(v2, v0) | aElementOf0(v2, v1))) % 73.49/11.31 | % 73.49/11.31 | ALPHA: (m__) implies: % 73.49/11.31 | (17) $i(xm) % 73.49/11.31 | (18) ? [v0: $i] : (sdtlpdtrp0(xN, xm) = v0 & $i(v0) & ~ aElementOf0(xp, % 73.49/11.31 | v0)) % 73.49/11.31 | % 73.49/11.31 | ALPHA: (function-axioms) implies: % 73.49/11.31 | (19) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 73.49/11.31 | (szDzozmdt0(v2) = v1) | ~ (szDzozmdt0(v2) = v0)) % 73.49/11.31 | (20) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 73.49/11.31 | (sdtlpdtrp0(v3, v2) = v1) | ~ (sdtlpdtrp0(v3, v2) = v0)) % 73.49/11.31 | % 73.49/11.31 | DELTA: instantiating (18) with fresh symbol all_82_0 gives: % 73.49/11.31 | (21) sdtlpdtrp0(xN, xm) = all_82_0 & $i(all_82_0) & ~ aElementOf0(xp, % 73.49/11.31 | all_82_0) % 73.49/11.31 | % 73.49/11.31 | ALPHA: (21) implies: % 73.49/11.31 | (22) ~ aElementOf0(xp, all_82_0) % 73.49/11.31 | (23) sdtlpdtrp0(xN, xm) = all_82_0 % 73.49/11.31 | % 73.49/11.31 | DELTA: instantiating (13) with fresh symbol all_88_0 gives: % 73.49/11.31 | (24) sdtlpdtrp0(xN, xm) = all_88_0 & $i(all_88_0) & ! [v0: $i] : ( ~ % 73.49/11.31 | $i(v0) | ~ aElementOf0(v0, all_88_0) | sdtlseqdt0(xx, v0)) % 73.49/11.31 | % 73.49/11.31 | ALPHA: (24) implies: % 73.49/11.31 | (25) sdtlpdtrp0(xN, xm) = all_88_0 % 73.49/11.31 | % 73.49/11.31 | DELTA: instantiating (16) with fresh symbols all_103_0, all_103_1 gives: % 73.49/11.31 | (26) sdtlpdtrp0(xN, xm) = all_103_0 & sdtlpdtrp0(xN, xn) = all_103_1 & % 73.49/11.31 | $i(all_103_0) & $i(all_103_1) & aSubsetOf0(all_103_1, all_103_0) & ! % 73.49/11.31 | [v0: $i] : ( ~ $i(v0) | ~ aElementOf0(v0, all_103_1) | % 73.49/11.31 | aElementOf0(v0, all_103_0)) % 73.49/11.31 | % 73.49/11.31 | ALPHA: (26) implies: % 73.49/11.31 | (27) aSubsetOf0(all_103_1, all_103_0) % 73.49/11.32 | (28) sdtlpdtrp0(xN, xn) = all_103_1 % 73.49/11.32 | (29) sdtlpdtrp0(xN, xm) = all_103_0 % 73.49/11.32 | % 73.49/11.32 | DELTA: instantiating (14) with fresh symbols all_109_0, all_109_1, all_109_2, % 73.49/11.32 | all_109_3 gives: % 73.49/11.32 | (30) sdtlpdtrp0(xN, all_109_2) = all_109_1 & sdtlpdtrp0(xN, xm) = all_109_3 % 73.49/11.32 | & szszuzczcdt0(xn) = all_109_2 & $i(all_109_0) & $i(all_109_1) & % 73.49/11.32 | $i(all_109_2) & $i(all_109_3) & aElementOf0(all_109_0, all_109_3) & ~ % 73.49/11.32 | aSubsetOf0(all_109_3, all_109_1) & ~ aElementOf0(all_109_0, % 73.49/11.32 | all_109_1) % 73.49/11.32 | % 73.49/11.32 | ALPHA: (30) implies: % 73.49/11.32 | (31) sdtlpdtrp0(xN, xm) = all_109_3 % 73.49/11.32 | % 73.49/11.32 | DELTA: instantiating (10) with fresh symbols all_111_0, all_111_1, all_111_2 % 73.49/11.32 | gives: % 73.49/11.32 | (32) szDzizrdt0(xd) = all_111_1 & sdtlbdtrb0(xd, all_111_1) = all_111_0 & % 73.49/11.32 | sdtlpdtrp0(xd, xn) = all_111_1 & sdtlpdtrp0(xe, xn) = xp & % 73.49/11.32 | szDzozmdt0(xd) = all_111_2 & $i(all_111_0) & $i(all_111_1) & % 73.49/11.32 | $i(all_111_2) & aElementOf0(xn, all_111_0) & aElementOf0(xn, % 73.49/11.32 | all_111_2) & aElementOf0(xn, szNzAzT0) % 73.49/11.32 | % 73.49/11.32 | ALPHA: (32) implies: % 73.49/11.32 | (33) aElementOf0(xn, all_111_2) % 73.49/11.32 | (34) szDzozmdt0(xd) = all_111_2 % 73.49/11.32 | (35) sdtlpdtrp0(xe, xn) = xp % 73.49/11.32 | % 73.49/11.32 | DELTA: instantiating (7) with fresh symbols all_113_0, all_113_1 gives: % 73.62/11.32 | (36) sdtlcdtrc0(xd, all_113_1) = all_113_0 & szDzozmdt0(xd) = all_113_1 & % 73.62/11.32 | $i(all_113_0) & $i(all_113_1) & aSubsetOf0(all_113_0, xT) & % 73.62/11.32 | aSet0(all_113_0) & ! [v0: $i] : ! [v1: $i] : ( ~ (sdtlpdtrp0(xd, v1) % 73.62/11.32 | = v0) | ~ $i(v1) | ~ $i(v0) | ~ aElementOf0(v1, all_113_1) | % 73.62/11.32 | aElementOf0(v0, all_113_0)) & ! [v0: $i] : ( ~ $i(v0) | ~ % 73.62/11.32 | aElementOf0(v0, all_113_0) | aElementOf0(v0, xT)) & ! [v0: $i] : ( % 73.62/11.32 | ~ $i(v0) | ~ aElementOf0(v0, all_113_0) | ? [v1: $i] : % 73.62/11.32 | (sdtlpdtrp0(xd, v1) = v0 & $i(v1) & aElementOf0(v1, all_113_1))) % 73.62/11.32 | % 73.62/11.32 | ALPHA: (36) implies: % 73.62/11.32 | (37) szDzozmdt0(xd) = all_113_1 % 73.62/11.32 | % 73.62/11.32 | DELTA: instantiating (8) with fresh symbols all_119_0, all_119_1, all_119_2 % 73.62/11.32 | gives: % 73.62/11.32 | (38) szDzizrdt0(xd) = all_119_2 & sdtlbdtrb0(xd, all_119_2) = all_119_1 & % 73.62/11.32 | szDzozmdt0(xd) = all_119_0 & $i(all_119_0) & $i(all_119_1) & % 73.62/11.32 | $i(all_119_2) & aElementOf0(all_119_2, xT) & aSet0(all_119_1) & ! % 73.62/11.32 | [v0: $i] : ! [v1: int] : (v1 = all_119_2 | ~ (sdtlpdtrp0(xd, v0) = % 73.62/11.32 | v1) | ~ $i(v0) | ~ aElementOf0(v0, all_119_1)) & ! [v0: $i] : % 73.62/11.32 | ! [v1: $i] : ( ~ (sdtlpdtrp0(xd, v0) = v1) | ~ $i(v0) | ~ % 73.62/11.32 | aElementOf0(v0, all_119_1) | aElementOf0(v0, all_119_0)) & ! [v0: % 73.62/11.32 | $i] : ( ~ (sdtlpdtrp0(xd, v0) = all_119_2) | ~ $i(v0) | ~ % 73.62/11.32 | aElementOf0(v0, all_119_0) | aElementOf0(v0, all_119_1)) % 73.62/11.32 | % 73.62/11.32 | ALPHA: (38) implies: % 73.62/11.32 | (39) szDzozmdt0(xd) = all_119_0 % 73.62/11.32 | % 73.62/11.32 | DELTA: instantiating (9) with fresh symbols all_125_0, all_125_1, all_125_2 % 73.62/11.32 | gives: % 73.62/11.33 | (40) szDzizrdt0(xd) = all_125_2 & sdtlcdtrc0(xe, all_125_1) = xO & % 73.62/11.33 | sdtlbdtrb0(xd, all_125_2) = all_125_1 & szDzozmdt0(xd) = all_125_0 & % 73.62/11.33 | $i(all_125_0) & $i(all_125_1) & $i(all_125_2) & aSet0(all_125_1) & % 73.62/11.33 | aSet0(xO) & ! [v0: $i] : ! [v1: int] : (v1 = all_125_2 | ~ % 73.62/11.33 | (sdtlpdtrp0(xd, v0) = v1) | ~ $i(v0) | ~ aElementOf0(v0, % 73.62/11.33 | all_125_1)) & ! [v0: $i] : ! [v1: $i] : ( ~ (sdtlpdtrp0(xd, v0) % 73.62/11.33 | = v1) | ~ $i(v0) | ~ aElementOf0(v0, all_125_1) | % 73.66/11.33 | aElementOf0(v0, all_125_0)) & ! [v0: $i] : ! [v1: $i] : ( ~ % 73.66/11.33 | (sdtlpdtrp0(xe, v1) = v0) | ~ $i(v1) | ~ $i(v0) | ~ % 73.66/11.33 | aElementOf0(v1, all_125_1) | aElementOf0(v0, xO)) & ! [v0: $i] : ( % 73.66/11.33 | ~ (sdtlpdtrp0(xd, v0) = all_125_2) | ~ $i(v0) | ~ aElementOf0(v0, % 73.66/11.33 | all_125_0) | aElementOf0(v0, all_125_1)) & ! [v0: $i] : ( ~ % 73.66/11.33 | $i(v0) | ~ aElementOf0(v0, xO) | ? [v1: $i] : (sdtlpdtrp0(xe, v1) % 73.66/11.33 | = v0 & $i(v1) & aElementOf0(v1, all_125_1))) % 73.66/11.33 | % 73.66/11.33 | ALPHA: (40) implies: % 73.66/11.33 | (41) szDzozmdt0(xd) = all_125_0 % 73.66/11.33 | % 73.66/11.33 | BETA: splitting (2) gives: % 73.66/11.33 | % 73.66/11.33 | Case 1: % 73.66/11.33 | | % 73.66/11.33 | | (42) ~ aSet0(slcrc0) % 73.66/11.33 | | % 73.66/11.33 | | PRED_UNIFY: (1), (42) imply: % 73.66/11.33 | | (43) $false % 73.66/11.33 | | % 73.66/11.33 | | CLOSE: (43) is inconsistent. % 73.66/11.33 | | % 73.66/11.33 | Case 2: % 73.66/11.33 | | % 73.66/11.33 | | % 73.66/11.33 | | GROUND_INST: instantiating (19) with all_113_1, all_119_0, xd, simplifying % 73.66/11.33 | | with (37), (39) gives: % 73.66/11.33 | | (44) all_119_0 = all_113_1 % 73.66/11.33 | | % 73.66/11.33 | | GROUND_INST: instantiating (19) with all_111_2, all_119_0, xd, simplifying % 73.66/11.33 | | with (34), (39) gives: % 73.66/11.33 | | (45) all_119_0 = all_111_2 % 73.66/11.33 | | % 73.66/11.33 | | GROUND_INST: instantiating (19) with all_113_1, all_125_0, xd, simplifying % 73.66/11.33 | | with (37), (41) gives: % 73.66/11.33 | | (46) all_125_0 = all_113_1 % 73.66/11.33 | | % 73.66/11.33 | | GROUND_INST: instantiating (19) with szNzAzT0, all_125_0, xd, simplifying % 73.66/11.33 | | with (6), (41) gives: % 73.66/11.33 | | (47) all_125_0 = szNzAzT0 % 73.66/11.33 | | % 73.66/11.33 | | GROUND_INST: instantiating (20) with all_88_0, all_103_0, xm, xN, % 73.66/11.33 | | simplifying with (25), (29) gives: % 73.66/11.33 | | (48) all_103_0 = all_88_0 % 73.66/11.33 | | % 73.66/11.33 | | GROUND_INST: instantiating (20) with all_103_0, all_109_3, xm, xN, % 73.66/11.33 | | simplifying with (29), (31) gives: % 73.66/11.33 | | (49) all_109_3 = all_103_0 % 73.66/11.33 | | % 73.66/11.33 | | GROUND_INST: instantiating (20) with all_82_0, all_109_3, xm, xN, % 73.66/11.33 | | simplifying with (23), (31) gives: % 73.66/11.33 | | (50) all_109_3 = all_82_0 % 73.66/11.33 | | % 73.66/11.33 | | COMBINE_EQS: (46), (47) imply: % 73.66/11.33 | | (51) all_113_1 = szNzAzT0 % 73.66/11.33 | | % 73.66/11.33 | | SIMP: (51) implies: % 73.66/11.33 | | (52) all_113_1 = szNzAzT0 % 73.66/11.33 | | % 73.66/11.33 | | COMBINE_EQS: (44), (45) imply: % 73.66/11.33 | | (53) all_113_1 = all_111_2 % 73.66/11.33 | | % 73.66/11.33 | | SIMP: (53) implies: % 73.66/11.33 | | (54) all_113_1 = all_111_2 % 73.66/11.33 | | % 73.66/11.33 | | COMBINE_EQS: (52), (54) imply: % 73.66/11.33 | | (55) all_111_2 = szNzAzT0 % 73.66/11.33 | | % 73.66/11.33 | | COMBINE_EQS: (49), (50) imply: % 73.66/11.33 | | (56) all_103_0 = all_82_0 % 73.66/11.33 | | % 73.66/11.33 | | SIMP: (56) implies: % 73.66/11.33 | | (57) all_103_0 = all_82_0 % 73.66/11.33 | | % 73.66/11.33 | | COMBINE_EQS: (48), (57) imply: % 73.66/11.33 | | (58) all_88_0 = all_82_0 % 73.66/11.33 | | % 73.66/11.33 | | REDUCE: (27), (57) imply: % 73.66/11.33 | | (59) aSubsetOf0(all_103_1, all_82_0) % 73.66/11.33 | | % 73.66/11.33 | | REDUCE: (33), (55) imply: % 73.66/11.33 | | (60) aElementOf0(xn, szNzAzT0) % 73.66/11.33 | | % 73.66/11.33 | | GROUND_INST: instantiating (4) with xm, all_82_0, simplifying with (11), % 73.66/11.33 | | (17), (23) gives: % 73.66/11.33 | | (61) aSet0(all_82_0) % 73.66/11.33 | | % 73.66/11.34 | | GROUND_INST: instantiating (5) with xn, xp, simplifying with (15), (35), % 73.66/11.34 | | (60) gives: % 73.66/11.34 | | (62) ? [v0: $i] : (sdtlpdtrp0(xN, xn) = v0 & szmzizndt0(v0) = xp & % 73.66/11.34 | | $i(v0) & $i(xp) & aElementOf0(xp, v0) & ! [v1: $i] : ( ~ $i(v1) | % 73.66/11.34 | | ~ aElementOf0(v1, v0) | sdtlseqdt0(xp, v1))) % 73.66/11.34 | | % 73.66/11.34 | | GROUND_INST: instantiating (5) with xm, xx, simplifying with (11), (12), % 73.66/11.34 | | (17) gives: % 73.66/11.34 | | (63) ? [v0: $i] : (sdtlpdtrp0(xN, xm) = v0 & szmzizndt0(v0) = xx & % 73.66/11.34 | | $i(v0) & $i(xx) & aElementOf0(xx, v0) & ! [v1: $i] : ( ~ $i(v1) | % 73.66/11.34 | | ~ aElementOf0(v1, v0) | sdtlseqdt0(xx, v1))) % 73.66/11.34 | | % 73.66/11.34 | | DELTA: instantiating (62) with fresh symbol all_154_0 gives: % 73.66/11.34 | | (64) sdtlpdtrp0(xN, xn) = all_154_0 & szmzizndt0(all_154_0) = xp & % 73.66/11.34 | | $i(all_154_0) & $i(xp) & aElementOf0(xp, all_154_0) & ! [v0: $i] : % 73.66/11.34 | | ( ~ $i(v0) | ~ aElementOf0(v0, all_154_0) | sdtlseqdt0(xp, v0)) % 73.66/11.34 | | % 73.66/11.34 | | ALPHA: (64) implies: % 73.66/11.34 | | (65) aElementOf0(xp, all_154_0) % 73.66/11.34 | | (66) $i(xp) % 73.66/11.34 | | (67) $i(all_154_0) % 73.66/11.34 | | (68) sdtlpdtrp0(xN, xn) = all_154_0 % 73.66/11.34 | | % 73.66/11.34 | | DELTA: instantiating (63) with fresh symbol all_157_0 gives: % 73.66/11.34 | | (69) sdtlpdtrp0(xN, xm) = all_157_0 & szmzizndt0(all_157_0) = xx & % 73.66/11.34 | | $i(all_157_0) & $i(xx) & aElementOf0(xx, all_157_0) & ! [v0: $i] : % 73.66/11.34 | | ( ~ $i(v0) | ~ aElementOf0(v0, all_157_0) | sdtlseqdt0(xx, v0)) % 73.66/11.34 | | % 73.66/11.34 | | ALPHA: (69) implies: % 73.66/11.34 | | (70) $i(all_157_0) % 73.66/11.34 | | (71) sdtlpdtrp0(xN, xm) = all_157_0 % 73.66/11.34 | | % 73.66/11.34 | | GROUND_INST: instantiating (20) with all_103_1, all_154_0, xn, xN, % 73.66/11.34 | | simplifying with (28), (68) gives: % 73.66/11.34 | | (72) all_154_0 = all_103_1 % 73.66/11.34 | | % 73.66/11.34 | | GROUND_INST: instantiating (20) with all_82_0, all_157_0, xm, xN, % 73.66/11.34 | | simplifying with (23), (71) gives: % 73.66/11.34 | | (73) all_157_0 = all_82_0 % 73.66/11.34 | | % 73.66/11.34 | | REDUCE: (70), (73) imply: % 73.66/11.34 | | (74) $i(all_82_0) % 73.66/11.34 | | % 73.66/11.34 | | REDUCE: (67), (72) imply: % 73.66/11.34 | | (75) $i(all_103_1) % 73.66/11.34 | | % 73.66/11.34 | | REDUCE: (65), (72) imply: % 73.66/11.34 | | (76) aElementOf0(xp, all_103_1) % 73.66/11.34 | | % 73.66/11.34 | | GROUND_INST: instantiating (3) with all_82_0, all_103_1, xp, simplifying % 73.66/11.34 | | with (22), (59), (61), (66), (74), (75), (76) gives: % 73.66/11.34 | | (77) $false % 73.66/11.34 | | % 73.66/11.34 | | CLOSE: (77) is inconsistent. % 73.66/11.34 | | % 73.66/11.34 | End of split % 73.66/11.34 | % 73.66/11.34 End of proof % 73.66/11.34 % SZS output end Proof for theBenchmark % 73.66/11.34 % 73.66/11.34 10733ms %------------------------------------------------------------------------------