%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : COM226_1 : TPTP v9.3.0. Released v9.3.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n010.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 : Tue May 5 06:21:36 PM UTC 2026 % Result : Theorem 35.32s 5.34s % Output : Proof 48.43s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : COM226_1 : TPTP v9.3.0. Released v9.3.0. % 0.00/0.12 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.16/0.33 % Computer : n010.cluster.edu % 0.16/0.33 % Model : x86_64 x86_64 % 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.16/0.33 % Memory : 8042.1875MB % 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.16/0.33 % CPULimit : 300 % 0.16/0.33 % WCLimit : 300 % 0.16/0.33 % DateTime : Mon May 4 19:23:06 EDT 2026 % 0.16/0.33 % CPUTime : % 0.52/0.59 ________ _____ % 0.52/0.59 ___ __ \_________(_)________________________________ % 0.52/0.59 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.52/0.59 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.52/0.59 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.52/0.59 % 0.52/0.59 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.52/0.59 (2023-06-19) % 0.52/0.59 % 0.52/0.59 (c) Philipp Rümmer, 2009-2023 % 0.52/0.59 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.52/0.59 Amanda Stjerna. % 0.52/0.59 Free software under BSD-3-Clause. % 0.52/0.59 % 0.52/0.59 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.52/0.59 % 0.52/0.59 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.52/0.60 Running up to 7 provers in parallel. % 0.52/0.61 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.52/0.61 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.52/0.61 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.52/0.61 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.52/0.61 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.52/0.61 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.52/0.62 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 5.31/1.43 Prover 4: Preprocessing ... % 5.31/1.43 Prover 1: Preprocessing ... % 5.31/1.46 Prover 5: Preprocessing ... % 5.31/1.46 Prover 2: Preprocessing ... % 5.31/1.46 Prover 0: Preprocessing ... % 5.31/1.46 Prover 6: Preprocessing ... % 5.31/1.46 Prover 3: Preprocessing ... % 12.83/2.43 Prover 3: Warning: ignoring some quantifiers % 12.83/2.46 Prover 3: Constructing countermodel ... % 12.83/2.49 Prover 1: Warning: ignoring some quantifiers % 13.60/2.50 Prover 6: Proving ... % 13.60/2.54 Prover 1: Constructing countermodel ... % 14.30/2.62 Prover 5: Proving ... % 14.30/2.64 Prover 4: Warning: ignoring some quantifiers % 15.10/2.76 Prover 0: Proving ... % 15.10/2.78 Prover 4: Constructing countermodel ... % 16.57/3.00 Prover 2: Proving ... % 35.32/5.34 Prover 5: proved (4722ms) % 35.32/5.34 % 35.32/5.34 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 35.32/5.34 % 35.32/5.34 Prover 2: stopped % 35.32/5.35 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 35.32/5.35 Prover 0: stopped % 35.32/5.35 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 35.32/5.36 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 36.11/5.40 Prover 3: stopped % 36.11/5.41 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 36.11/5.48 Prover 6: stopped % 36.11/5.48 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 37.61/5.62 Prover 11: Preprocessing ... % 37.61/5.63 Prover 10: Preprocessing ... % 37.61/5.66 Prover 8: Preprocessing ... % 37.61/5.68 Prover 7: Preprocessing ... % 38.40/5.72 Prover 13: Preprocessing ... % 39.91/5.94 Prover 8: Warning: ignoring some quantifiers % 39.91/5.96 Prover 8: Constructing countermodel ... % 39.91/5.99 Prover 10: Warning: ignoring some quantifiers % 39.91/6.00 Prover 10: Constructing countermodel ... % 40.84/6.02 Prover 11: Warning: ignoring some quantifiers % 40.84/6.03 Prover 11: Constructing countermodel ... % 42.30/6.20 Prover 7: Warning: ignoring some quantifiers % 42.30/6.21 Prover 7: Constructing countermodel ... % 42.30/6.26 Prover 13: Warning: ignoring some quantifiers % 42.30/6.28 Prover 13: Constructing countermodel ... % 47.68/6.97 Prover 10: Found proof (size 44) % 47.68/6.97 Prover 10: proved (1610ms) % 47.68/6.97 Prover 13: stopped % 47.68/6.97 Prover 8: stopped % 47.68/6.97 Prover 11: stopped % 47.68/6.98 Prover 7: stopped % 47.68/6.98 Prover 1: stopped % 47.68/6.98 Prover 4: stopped % 47.68/6.98 % 47.68/6.98 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 47.68/6.98 % 47.68/6.98 % SZS output start Proof for theBenchmark % 47.68/6.99 Assumptions after simplification: % 47.68/6.99 --------------------------------- % 47.68/6.99 % 47.68/6.99 (EQ-someTerm) % 48.43/7.03 ! [v0: vTerm] : ! [v1: vTerm] : ! [v2: vOptTerm] : (v1 = v0 | ~ % 48.43/7.03 (vsomeTerm(v1) = v2) | ~ (vsomeTerm(v0) = v2) | ~ vTerm(v1) | ~ % 48.43/7.03 vTerm(v0)) % 48.43/7.03 % 48.43/7.03 (Preservation-Succ-IH0) % 48.43/7.03 vTerm(vt1) & ? [v0: vOptTerm] : (vreduce(vt1) = v0 & vOptTerm(v0) & ! [v1: % 48.43/7.03 vTy] : ! [v2: vTerm] : ( ~ (vsomeTerm(v2) = v0) | ~ vTy(v1) | ~ % 48.43/7.03 vTerm(v2) | ~ vptchecksimple(vt1, v1) | vptchecksimple(v2, v1))) % 48.43/7.03 % 48.43/7.03 (Preservation-Succ-isSomeTerm-True) % 48.43/7.03 vTerm(vt1) & ? [v0: vOptTerm] : ? [v1: vTerm] : ? [v2: vOptTerm] : ? [v3: % 48.43/7.03 vTy] : ? [v4: vTerm] : (vreduce(v1) = v2 & vreduce(vt1) = v0 & % 48.43/7.03 vsomeTerm(v4) = v2 & vSucc(vt1) = v1 & vTy(v3) & vOptTerm(v2) & vOptTerm(v0) % 48.43/7.03 & vTerm(v4) & vTerm(v1) & vptchecksimple(v1, v3) & visSomeTerm(v0) & ~ % 48.43/7.03 vptchecksimple(v4, v3)) % 48.43/7.03 % 48.43/7.03 (TSucc) % 48.43/7.03 vTy(vNat) & ! [v0: vTerm] : ! [v1: vTerm] : ( ~ (vSucc(v0) = v1) | ~ % 48.43/7.03 vTerm(v0) | ~ vptchecksimple(v0, vNat) | vptchecksimple(v1, vNat)) % 48.43/7.03 % 48.43/7.03 (TSucc_inv1) % 48.43/7.03 vTy(vNat) & ! [v0: vTerm] : ! [v1: vTy] : ! [v2: vTerm] : (v1 = vNat | ~ % 48.43/7.03 (vSucc(v0) = v2) | ~ vTy(v1) | ~ vTerm(v0) | ~ vptchecksimple(v2, v1)) % 48.43/7.03 % 48.43/7.03 (TSucc_inv2) % 48.43/7.03 vTy(vNat) & ! [v0: vTerm] : ! [v1: vTerm] : ( ~ (vSucc(v0) = v1) | ~ % 48.43/7.03 vTerm(v0) | ~ vptchecksimple(v1, vNat) | vptchecksimple(v0, vNat)) % 48.43/7.03 % 48.43/7.03 (getTerm-0) % 48.43/7.03 ! [v0: vTerm] : ! [v1: vOptTerm] : ( ~ (vsomeTerm(v0) = v1) | ~ vTerm(v0) | % 48.43/7.03 vgetTerm(v1) = v0) % 48.43/7.03 % 48.43/7.03 (isSomeTerm-true-INV) % 48.43/7.03 ! [v0: vOptTerm] : ( ~ vOptTerm(v0) | ~ visSomeTerm(v0) | ? [v1: vTerm] : % 48.43/7.03 (vsomeTerm(v1) = v0 & vTerm(v1))) % 48.43/7.03 % 48.43/7.04 (reduce-4) % 48.43/7.04 ! [v0: vTerm] : ! [v1: vTerm] : ( ~ (vSucc(v0) = v1) | ~ vTerm(v0) | ? % 48.43/7.04 [v2: vOptTerm] : ? [v3: vOptTerm] : ? [v4: vTerm] : ? [v5: vTerm] : ? % 48.43/7.04 [v6: vOptTerm] : (vreduce(v0) = v2 & vOptTerm(v2) & ( ~ visSomeTerm(v2) | % 48.43/7.04 (v6 = v3 & vreduce(v1) = v3 & vgetTerm(v2) = v4 & vsomeTerm(v5) = v3 & % 48.43/7.04 vSucc(v4) = v5 & vOptTerm(v3) & vTerm(v5) & vTerm(v4))))) % 48.43/7.04 % 48.43/7.04 (function-axioms) % 48.43/7.04 ! [v0: vTerm] : ! [v1: vTerm] : ! [v2: vTerm] : ! [v3: vTerm] : ! [v4: % 48.43/7.04 vTerm] : (v1 = v0 | ~ (vIfelse(v4, v3, v2) = v1) | ~ (vIfelse(v4, v3, v2) % 48.43/7.04 = v0)) & ! [v0: vTerm] : ! [v1: vTerm] : ! [v2: vTerm] : ! [v3: vTerm] % 48.43/7.04 : (v1 = v0 | ~ (vplusop(v3, v2) = v1) | ~ (vplusop(v3, v2) = v0)) & ! [v0: % 48.43/7.04 vTerm] : ! [v1: vTerm] : ! [v2: vTerm] : ! [v3: vTerm] : (v1 = v0 | ~ % 48.43/7.04 (vPlus(v3, v2) = v1) | ~ (vPlus(v3, v2) = v0)) & ! [v0: vOptTerm] : ! % 48.43/7.04 [v1: vOptTerm] : ! [v2: vTerm] : (v1 = v0 | ~ (vreduce(v2) = v1) | ~ % 48.43/7.04 (vreduce(v2) = v0)) & ! [v0: vTerm] : ! [v1: vTerm] : ! [v2: vOptTerm] : % 48.43/7.04 (v1 = v0 | ~ (vgetTerm(v2) = v1) | ~ (vgetTerm(v2) = v0)) & ! [v0: % 48.43/7.04 vOptTerm] : ! [v1: vOptTerm] : ! [v2: vTerm] : (v1 = v0 | ~ % 48.43/7.04 (vsomeTerm(v2) = v1) | ~ (vsomeTerm(v2) = v0)) & ! [v0: vTerm] : ! [v1: % 48.43/7.04 vTerm] : ! [v2: vTerm] : (v1 = v0 | ~ (vIszero(v2) = v1) | ~ (vIszero(v2) % 48.43/7.04 = v0)) & ! [v0: vTerm] : ! [v1: vTerm] : ! [v2: vTerm] : (v1 = v0 | ~ % 48.43/7.04 (vPred(v2) = v1) | ~ (vPred(v2) = v0)) & ! [v0: vTerm] : ! [v1: vTerm] : % 48.43/7.04 ! [v2: vTerm] : (v1 = v0 | ~ (vSucc(v2) = v1) | ~ (vSucc(v2) = v0)) % 48.43/7.04 % 48.43/7.04 Further assumptions not needed in the proof: % 48.43/7.04 -------------------------------------------- % 48.43/7.04 DIFF-B-Nat, DIFF-False-Ifelse, DIFF-False-Iszero, DIFF-False-Plus, % 48.43/7.04 DIFF-False-Pred, DIFF-False-Succ, DIFF-False-Zero, DIFF-Ifelse-Iszero, % 48.43/7.04 DIFF-Ifelse-Plus, DIFF-Ifelse-Pred, DIFF-Ifelse-Succ, DIFF-Ifelse-Zero, % 48.43/7.04 DIFF-Iszero-Plus, DIFF-Pred-Iszero, DIFF-Pred-Plus, DIFF-Succ-Iszero, % 48.43/7.04 DIFF-Succ-Plus, DIFF-Succ-Pred, DIFF-True-False, DIFF-True-Ifelse, % 48.43/7.04 DIFF-True-Iszero, DIFF-True-Plus, DIFF-True-Pred, DIFF-True-Succ, % 48.43/7.04 DIFF-True-Zero, DIFF-Zero-Iszero, DIFF-Zero-Plus, DIFF-Zero-Pred, % 48.43/7.04 DIFF-Zero-Succ, DIFF-noTerm-someTerm, EQ-Ifelse, EQ-Iszero, EQ-Plus, EQ-Pred, % 48.43/7.04 EQ-Succ, TPlus, TPlus_inv0, TPlus_inv1, TPlus_inv2, TPred, TPred_inv1, % 48.43/7.04 TPred_inv2, TZero, TZero_inv, Tfalse, Tif, Tif_inv1, Tif_inv2, Tif_inv3, % 48.43/7.04 Tiszero, Tiszero_inv1, Tiszero_inv2, Ttrue, dom-OptTerm, dom-Term, dom-Ty, % 48.43/7.04 isNV-0, isNV-1, isNV-2, isNV-false-INV, isNV-true-INV, isSomeTerm-0, % 48.43/7.04 isSomeTerm-1, isSomeTerm-false-INV, isValue-0, isValue-1, isValue-2, % 48.43/7.04 isValue-false-INV, isValue-true-INV, plusop-0, plusop-1, plusop-2, plusop-INV, % 48.43/7.04 reduce-0, reduce-1, reduce-10, reduce-11, reduce-12, reduce-13, reduce-14, % 48.43/7.04 reduce-15, reduce-16, reduce-17, reduce-18, reduce-19, reduce-2, reduce-20, % 48.43/7.04 reduce-21, reduce-22, reduce-23, reduce-3, reduce-5, reduce-6, reduce-7, % 48.43/7.04 reduce-8, reduce-9, reduce-INV % 48.43/7.04 % 48.43/7.04 Those formulas are unsatisfiable: % 48.43/7.04 --------------------------------- % 48.43/7.04 % 48.43/7.04 Begin of proof % 48.43/7.04 | % 48.43/7.04 | ALPHA: (TSucc) implies: % 48.43/7.04 | (1) ! [v0: vTerm] : ! [v1: vTerm] : ( ~ (vSucc(v0) = v1) | ~ vTerm(v0) | % 48.43/7.04 | ~ vptchecksimple(v0, vNat) | vptchecksimple(v1, vNat)) % 48.43/7.04 | % 48.43/7.04 | ALPHA: (TSucc_inv1) implies: % 48.43/7.04 | (2) ! [v0: vTerm] : ! [v1: vTy] : ! [v2: vTerm] : (v1 = vNat | ~ % 48.43/7.04 | (vSucc(v0) = v2) | ~ vTy(v1) | ~ vTerm(v0) | ~ vptchecksimple(v2, % 48.43/7.04 | v1)) % 48.43/7.04 | % 48.43/7.04 | ALPHA: (TSucc_inv2) implies: % 48.43/7.05 | (3) ! [v0: vTerm] : ! [v1: vTerm] : ( ~ (vSucc(v0) = v1) | ~ vTerm(v0) | % 48.43/7.05 | ~ vptchecksimple(v1, vNat) | vptchecksimple(v0, vNat)) % 48.43/7.05 | % 48.43/7.05 | ALPHA: (Preservation-Succ-IH0) implies: % 48.43/7.05 | (4) ? [v0: vOptTerm] : (vreduce(vt1) = v0 & vOptTerm(v0) & ! [v1: vTy] : % 48.43/7.05 | ! [v2: vTerm] : ( ~ (vsomeTerm(v2) = v0) | ~ vTy(v1) | ~ vTerm(v2) % 48.43/7.05 | | ~ vptchecksimple(vt1, v1) | vptchecksimple(v2, v1))) % 48.43/7.05 | % 48.43/7.05 | ALPHA: (Preservation-Succ-isSomeTerm-True) implies: % 48.43/7.05 | (5) vTerm(vt1) % 48.43/7.05 | (6) ? [v0: vOptTerm] : ? [v1: vTerm] : ? [v2: vOptTerm] : ? [v3: vTy] : % 48.43/7.05 | ? [v4: vTerm] : (vreduce(v1) = v2 & vreduce(vt1) = v0 & vsomeTerm(v4) % 48.43/7.05 | = v2 & vSucc(vt1) = v1 & vTy(v3) & vOptTerm(v2) & vOptTerm(v0) & % 48.43/7.05 | vTerm(v4) & vTerm(v1) & vptchecksimple(v1, v3) & visSomeTerm(v0) & ~ % 48.43/7.05 | vptchecksimple(v4, v3)) % 48.43/7.05 | % 48.43/7.05 | ALPHA: (function-axioms) implies: % 48.43/7.05 | (7) ! [v0: vTerm] : ! [v1: vTerm] : ! [v2: vOptTerm] : (v1 = v0 | ~ % 48.43/7.05 | (vgetTerm(v2) = v1) | ~ (vgetTerm(v2) = v0)) % 48.43/7.05 | (8) ! [v0: vOptTerm] : ! [v1: vOptTerm] : ! [v2: vTerm] : (v1 = v0 | ~ % 48.43/7.05 | (vreduce(v2) = v1) | ~ (vreduce(v2) = v0)) % 48.43/7.05 | % 48.43/7.05 | DELTA: instantiating (4) with fresh symbol all_100_0 gives: % 48.43/7.05 | (9) vreduce(vt1) = all_100_0 & vOptTerm(all_100_0) & ! [v0: vTy] : ! [v1: % 48.43/7.05 | vTerm] : ( ~ (vsomeTerm(v1) = all_100_0) | ~ vTy(v0) | ~ vTerm(v1) % 48.43/7.05 | | ~ vptchecksimple(vt1, v0) | vptchecksimple(v1, v0)) % 48.43/7.05 | % 48.43/7.05 | ALPHA: (9) implies: % 48.43/7.05 | (10) vreduce(vt1) = all_100_0 % 48.43/7.05 | (11) ! [v0: vTy] : ! [v1: vTerm] : ( ~ (vsomeTerm(v1) = all_100_0) | ~ % 48.43/7.05 | vTy(v0) | ~ vTerm(v1) | ~ vptchecksimple(vt1, v0) | % 48.43/7.05 | vptchecksimple(v1, v0)) % 48.43/7.05 | % 48.43/7.05 | DELTA: instantiating (6) with fresh symbols all_107_0, all_107_1, all_107_2, % 48.43/7.05 | all_107_3, all_107_4 gives: % 48.43/7.05 | (12) vreduce(all_107_3) = all_107_2 & vreduce(vt1) = all_107_4 & % 48.43/7.05 | vsomeTerm(all_107_0) = all_107_2 & vSucc(vt1) = all_107_3 & % 48.43/7.05 | vTy(all_107_1) & vOptTerm(all_107_2) & vOptTerm(all_107_4) & % 48.43/7.05 | vTerm(all_107_0) & vTerm(all_107_3) & vptchecksimple(all_107_3, % 48.43/7.05 | all_107_1) & visSomeTerm(all_107_4) & ~ vptchecksimple(all_107_0, % 48.43/7.05 | all_107_1) % 48.43/7.05 | % 48.43/7.05 | ALPHA: (12) implies: % 48.43/7.05 | (13) ~ vptchecksimple(all_107_0, all_107_1) % 48.43/7.05 | (14) visSomeTerm(all_107_4) % 48.43/7.05 | (15) vptchecksimple(all_107_3, all_107_1) % 48.43/7.05 | (16) vTerm(all_107_0) % 48.43/7.05 | (17) vOptTerm(all_107_4) % 48.43/7.05 | (18) vTy(all_107_1) % 48.43/7.05 | (19) vSucc(vt1) = all_107_3 % 48.43/7.05 | (20) vsomeTerm(all_107_0) = all_107_2 % 48.43/7.05 | (21) vreduce(vt1) = all_107_4 % 48.43/7.05 | (22) vreduce(all_107_3) = all_107_2 % 48.43/7.05 | % 48.43/7.06 | GROUND_INST: instantiating (8) with all_100_0, all_107_4, vt1, simplifying % 48.43/7.06 | with (10), (21) gives: % 48.43/7.06 | (23) all_107_4 = all_100_0 % 48.43/7.06 | % 48.43/7.06 | REDUCE: (17), (23) imply: % 48.43/7.06 | (24) vOptTerm(all_100_0) % 48.43/7.06 | % 48.43/7.06 | REDUCE: (14), (23) imply: % 48.43/7.06 | (25) visSomeTerm(all_100_0) % 48.43/7.06 | % 48.43/7.06 | GROUND_INST: instantiating (isSomeTerm-true-INV) with all_100_0, simplifying % 48.43/7.06 | with (24), (25) gives: % 48.43/7.06 | (26) ? [v0: vTerm] : (vsomeTerm(v0) = all_100_0 & vTerm(v0)) % 48.43/7.06 | % 48.43/7.06 | GROUND_INST: instantiating (2) with vt1, all_107_1, all_107_3, simplifying % 48.43/7.06 | with (5), (15), (18), (19) gives: % 48.43/7.06 | (27) all_107_1 = vNat % 48.43/7.06 | % 48.43/7.06 | GROUND_INST: instantiating (reduce-4) with vt1, all_107_3, simplifying with % 48.43/7.06 | (5), (19) gives: % 48.43/7.06 | (28) ? [v0: vOptTerm] : ? [v1: vOptTerm] : ? [v2: vTerm] : ? [v3: % 48.43/7.06 | vTerm] : ? [v4: vOptTerm] : (vreduce(vt1) = v0 & vOptTerm(v0) & ( ~ % 48.43/7.06 | visSomeTerm(v0) | (v4 = v1 & vreduce(all_107_3) = v1 & % 48.43/7.06 | vgetTerm(v0) = v2 & vsomeTerm(v3) = v1 & vSucc(v2) = v3 & % 48.43/7.06 | vOptTerm(v1) & vTerm(v3) & vTerm(v2)))) % 48.43/7.06 | % 48.43/7.06 | DELTA: instantiating (26) with fresh symbol all_126_0 gives: % 48.43/7.06 | (29) vsomeTerm(all_126_0) = all_100_0 & vTerm(all_126_0) % 48.43/7.06 | % 48.43/7.06 | ALPHA: (29) implies: % 48.43/7.06 | (30) vTerm(all_126_0) % 48.43/7.06 | (31) vsomeTerm(all_126_0) = all_100_0 % 48.43/7.06 | % 48.43/7.06 | DELTA: instantiating (28) with fresh symbols all_131_0, all_131_1, all_131_2, % 48.43/7.06 | all_131_3, all_131_4 gives: % 48.43/7.06 | (32) vreduce(vt1) = all_131_4 & vOptTerm(all_131_4) & ( ~ % 48.43/7.06 | visSomeTerm(all_131_4) | (all_131_0 = all_131_3 & vreduce(all_107_3) % 48.43/7.06 | = all_131_3 & vgetTerm(all_131_4) = all_131_2 & % 48.43/7.06 | vsomeTerm(all_131_1) = all_131_3 & vSucc(all_131_2) = all_131_1 & % 48.43/7.06 | vOptTerm(all_131_3) & vTerm(all_131_1) & vTerm(all_131_2))) % 48.43/7.06 | % 48.43/7.06 | ALPHA: (32) implies: % 48.43/7.06 | (33) vreduce(vt1) = all_131_4 % 48.43/7.06 | (34) ~ visSomeTerm(all_131_4) | (all_131_0 = all_131_3 & % 48.43/7.06 | vreduce(all_107_3) = all_131_3 & vgetTerm(all_131_4) = all_131_2 & % 48.43/7.06 | vsomeTerm(all_131_1) = all_131_3 & vSucc(all_131_2) = all_131_1 & % 48.43/7.06 | vOptTerm(all_131_3) & vTerm(all_131_1) & vTerm(all_131_2)) % 48.43/7.06 | % 48.43/7.06 | REDUCE: (18), (27) imply: % 48.43/7.06 | (35) vTy(vNat) % 48.43/7.06 | % 48.43/7.06 | REDUCE: (15), (27) imply: % 48.43/7.06 | (36) vptchecksimple(all_107_3, vNat) % 48.43/7.06 | % 48.43/7.06 | REDUCE: (13), (27) imply: % 48.43/7.06 | (37) ~ vptchecksimple(all_107_0, vNat) % 48.43/7.06 | % 48.43/7.06 | GROUND_INST: instantiating (8) with all_100_0, all_131_4, vt1, simplifying % 48.43/7.06 | with (10), (33) gives: % 48.43/7.06 | (38) all_131_4 = all_100_0 % 48.43/7.06 | % 48.43/7.06 | BETA: splitting (34) gives: % 48.43/7.06 | % 48.43/7.06 | Case 1: % 48.43/7.06 | | % 48.43/7.06 | | (39) ~ visSomeTerm(all_131_4) % 48.43/7.06 | | % 48.43/7.06 | | REDUCE: (38), (39) imply: % 48.43/7.06 | | (40) ~ visSomeTerm(all_100_0) % 48.43/7.06 | | % 48.43/7.06 | | PRED_UNIFY: (25), (40) imply: % 48.43/7.06 | | (41) $false % 48.43/7.06 | | % 48.43/7.06 | | CLOSE: (41) is inconsistent. % 48.43/7.06 | | % 48.43/7.06 | Case 2: % 48.43/7.06 | | % 48.43/7.07 | | (42) all_131_0 = all_131_3 & vreduce(all_107_3) = all_131_3 & % 48.43/7.07 | | vgetTerm(all_131_4) = all_131_2 & vsomeTerm(all_131_1) = all_131_3 & % 48.43/7.07 | | vSucc(all_131_2) = all_131_1 & vOptTerm(all_131_3) & % 48.43/7.07 | | vTerm(all_131_1) & vTerm(all_131_2) % 48.43/7.07 | | % 48.43/7.07 | | ALPHA: (42) implies: % 48.43/7.07 | | (43) vTerm(all_131_2) % 48.43/7.07 | | (44) vTerm(all_131_1) % 48.43/7.07 | | (45) vSucc(all_131_2) = all_131_1 % 48.43/7.07 | | (46) vsomeTerm(all_131_1) = all_131_3 % 48.43/7.07 | | (47) vgetTerm(all_131_4) = all_131_2 % 48.43/7.07 | | (48) vreduce(all_107_3) = all_131_3 % 48.43/7.07 | | % 48.43/7.07 | | REDUCE: (38), (47) imply: % 48.43/7.07 | | (49) vgetTerm(all_100_0) = all_131_2 % 48.43/7.07 | | % 48.43/7.07 | | GROUND_INST: instantiating (8) with all_107_2, all_131_3, all_107_3, % 48.43/7.07 | | simplifying with (22), (48) gives: % 48.43/7.07 | | (50) all_131_3 = all_107_2 % 48.43/7.07 | | % 48.43/7.07 | | REDUCE: (46), (50) imply: % 48.43/7.07 | | (51) vsomeTerm(all_131_1) = all_107_2 % 48.43/7.07 | | % 48.43/7.07 | | GROUND_INST: instantiating (3) with vt1, all_107_3, simplifying with (5), % 48.43/7.07 | | (19), (36) gives: % 48.43/7.07 | | (52) vptchecksimple(vt1, vNat) % 48.43/7.07 | | % 48.43/7.07 | | GROUND_INST: instantiating (getTerm-0) with all_126_0, all_100_0, % 48.43/7.07 | | simplifying with (30), (31) gives: % 48.43/7.07 | | (53) vgetTerm(all_100_0) = all_126_0 % 48.43/7.07 | | % 48.43/7.07 | | GROUND_INST: instantiating (EQ-someTerm) with all_107_0, all_131_1, % 48.43/7.07 | | all_107_2, simplifying with (16), (20), (44), (51) gives: % 48.43/7.07 | | (54) all_131_1 = all_107_0 % 48.43/7.07 | | % 48.43/7.07 | | REDUCE: (45), (54) imply: % 48.43/7.07 | | (55) vSucc(all_131_2) = all_107_0 % 48.43/7.07 | | % 48.43/7.07 | | GROUND_INST: instantiating (7) with all_131_2, all_126_0, all_100_0, % 48.43/7.07 | | simplifying with (49), (53) gives: % 48.43/7.07 | | (56) all_131_2 = all_126_0 % 48.43/7.07 | | % 48.43/7.07 | | REDUCE: (55), (56) imply: % 48.43/7.07 | | (57) vSucc(all_126_0) = all_107_0 % 48.43/7.07 | | % 48.43/7.07 | | GROUND_INST: instantiating (11) with vNat, all_126_0, simplifying with (30), % 48.43/7.07 | | (31), (35), (52) gives: % 48.43/7.07 | | (58) vptchecksimple(all_126_0, vNat) % 48.43/7.07 | | % 48.43/7.07 | | GROUND_INST: instantiating (1) with all_126_0, all_107_0, simplifying with % 48.43/7.07 | | (30), (37), (57), (58) gives: % 48.43/7.07 | | (59) $false % 48.43/7.07 | | % 48.43/7.07 | | CLOSE: (59) is inconsistent. % 48.43/7.07 | | % 48.43/7.07 | End of split % 48.43/7.07 | % 48.43/7.07 End of proof % 48.43/7.07 % SZS output end Proof for theBenchmark % 48.43/7.07 % 48.43/7.07 6481ms %------------------------------------------------------------------------------