%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : COM224_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 : n024.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 20.50s 3.22s % Output : Proof 36.88s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.06 % Problem : COM224_1 : TPTP v9.3.0. Released v9.3.0. % 0.00/0.07 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.07/0.25 % Computer : n024.cluster.edu % 0.07/0.25 % Model : x86_64 x86_64 % 0.07/0.25 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.07/0.25 % Memory : 8042.1875MB % 0.07/0.25 % OS : Linux 3.10.0-693.el7.x86_64 % 0.07/0.25 % CPULimit : 300 % 0.07/0.25 % WCLimit : 300 % 0.07/0.25 % DateTime : Mon May 4 14:06:56 EDT 2026 % 0.07/0.25 % CPUTime : % 0.38/0.43 ________ _____ % 0.38/0.43 ___ __ \_________(_)________________________________ % 0.38/0.43 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.38/0.43 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.38/0.43 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.38/0.43 % 0.38/0.43 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.38/0.43 (2023-06-19) % 0.38/0.43 % 0.38/0.43 (c) Philipp Rümmer, 2009-2023 % 0.38/0.43 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.38/0.43 Amanda Stjerna. % 0.38/0.43 Free software under BSD-3-Clause. % 0.38/0.43 % 0.38/0.43 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.38/0.43 % 0.38/0.43 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.38/0.44 Running up to 7 provers in parallel. % 0.38/0.45 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.38/0.45 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.38/0.45 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.38/0.45 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.38/0.45 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.38/0.45 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.38/0.45 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 4.30/1.17 Prover 4: Preprocessing ... % 4.30/1.17 Prover 1: Preprocessing ... % 4.91/1.20 Prover 0: Preprocessing ... % 4.91/1.20 Prover 5: Preprocessing ... % 4.91/1.20 Prover 2: Preprocessing ... % 4.91/1.21 Prover 6: Preprocessing ... % 4.91/1.21 Prover 3: Preprocessing ... % 12.06/2.12 Prover 1: Warning: ignoring some quantifiers % 12.06/2.13 Prover 3: Warning: ignoring some quantifiers % 12.06/2.15 Prover 6: Proving ... % 12.06/2.17 Prover 3: Constructing countermodel ... % 12.06/2.17 Prover 1: Constructing countermodel ... % 12.06/2.19 Prover 5: Proving ... % 12.66/2.23 Prover 4: Warning: ignoring some quantifiers % 13.44/2.33 Prover 4: Constructing countermodel ... % 13.44/2.34 Prover 0: Proving ... % 14.99/2.51 Prover 2: Proving ... % 20.50/3.22 Prover 5: proved (2771ms) % 20.50/3.22 % 20.50/3.22 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 20.50/3.22 % 20.50/3.23 Prover 3: stopped % 20.50/3.23 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 20.50/3.23 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 20.50/3.23 Prover 0: stopped % 20.50/3.23 Prover 2: stopped % 20.50/3.23 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 20.50/3.23 Prover 6: stopped % 20.50/3.23 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 20.50/3.23 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 22.05/3.48 Prover 8: Preprocessing ... % 22.05/3.49 Prover 13: Preprocessing ... % 22.05/3.49 Prover 10: Preprocessing ... % 22.05/3.49 Prover 11: Preprocessing ... % 22.84/3.51 Prover 7: Preprocessing ... % 24.42/3.75 Prover 8: Warning: ignoring some quantifiers % 24.42/3.79 Prover 8: Constructing countermodel ... % 25.21/3.87 Prover 10: Warning: ignoring some quantifiers % 26.00/3.90 Prover 10: Constructing countermodel ... % 26.00/3.91 Prover 7: Warning: ignoring some quantifiers % 26.00/3.93 Prover 11: Warning: ignoring some quantifiers % 26.00/3.94 Prover 13: Warning: ignoring some quantifiers % 26.00/3.94 Prover 11: Constructing countermodel ... % 26.00/3.95 Prover 7: Constructing countermodel ... % 26.00/3.95 Prover 13: Constructing countermodel ... % 36.28/5.24 Prover 7: Found proof (size 26) % 36.28/5.24 Prover 7: proved (2014ms) % 36.28/5.24 Prover 8: stopped % 36.28/5.24 Prover 1: stopped % 36.28/5.24 Prover 13: stopped % 36.28/5.24 Prover 4: stopped % 36.28/5.24 Prover 11: stopped % 36.28/5.25 Prover 10: stopped % 36.28/5.25 % 36.28/5.25 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 36.28/5.25 % 36.28/5.25 % SZS output start Proof for theBenchmark % 36.28/5.26 Assumptions after simplification: % 36.28/5.26 --------------------------------- % 36.28/5.26 % 36.28/5.26 (EQ-someTerm) % 36.28/5.28 ! [v0: vTerm] : ! [v1: vTerm] : ! [v2: vOptTerm] : (v1 = v0 | ~ % 36.28/5.28 (vsomeTerm(v1) = v2) | ~ (vsomeTerm(v0) = v2) | ~ vTerm(v1) | ~ % 36.28/5.28 vTerm(v0)) % 36.28/5.28 % 36.28/5.28 (Preservation-Pred-Succ-isNV-True) % 36.28/5.29 vTerm(vt1) & vTerm(vZero) & ? [v0: vTerm] : ? [v1: vOptTerm] : ? [v2: % 36.28/5.29 vTerm] : ? [v3: vTy] : ? [v4: vTerm] : ( ~ (vt1 = vZero) & vreduce(v0) = % 36.28/5.29 v1 & vsomeTerm(v4) = v1 & vPred(vt1) = v0 & vSucc(v2) = vt1 & vTy(v3) & % 36.28/5.29 vOptTerm(v1) & vTerm(v4) & vTerm(v2) & vTerm(v0) & vptchecksimple(v0, v3) & % 36.28/5.29 visNV(v2) & ~ vptchecksimple(v4, v3)) % 36.28/5.29 % 36.28/5.29 (TPred_inv2) % 36.28/5.29 vTy(vNat) & ! [v0: vTerm] : ! [v1: vTy] : ! [v2: vTerm] : (v1 = vNat | ~ % 36.28/5.29 (vPred(v0) = v2) | ~ vTy(v1) | ~ vTerm(v0) | ~ vptchecksimple(v2, v1)) % 36.28/5.29 % 36.28/5.29 (isNVisNat) % 36.28/5.29 vTy(vNat) & ! [v0: vTerm] : ( ~ vTerm(v0) | ~ visNV(v0) | vptchecksimple(v0, % 36.28/5.29 vNat)) % 36.28/5.29 % 36.28/5.29 (reduce-7) % 36.28/5.29 ! [v0: vTerm] : ! [v1: vOptTerm] : ( ~ (vsomeTerm(v0) = v1) | ~ vTerm(v0) | % 36.28/5.29 ~ visNV(v0) | ? [v2: vTerm] : ? [v3: vTerm] : (vreduce(v3) = v1 & % 36.28/5.29 vPred(v2) = v3 & vSucc(v0) = v2 & vOptTerm(v1) & vTerm(v3) & vTerm(v2))) & % 36.28/5.29 ! [v0: vTerm] : ! [v1: vTerm] : ( ~ (vSucc(v0) = v1) | ~ vTerm(v0) | ~ % 36.28/5.29 visNV(v0) | ? [v2: vTerm] : ? [v3: vOptTerm] : (vreduce(v2) = v3 & % 36.28/5.29 vsomeTerm(v0) = v3 & vPred(v1) = v2 & vOptTerm(v3) & vTerm(v2))) % 36.28/5.29 % 36.28/5.29 (function-axioms) % 36.28/5.30 ! [v0: vTerm] : ! [v1: vTerm] : ! [v2: vTerm] : ! [v3: vTerm] : ! [v4: % 36.28/5.30 vTerm] : (v1 = v0 | ~ (vIfelse(v4, v3, v2) = v1) | ~ (vIfelse(v4, v3, v2) % 36.28/5.30 = v0)) & ! [v0: vTerm] : ! [v1: vTerm] : ! [v2: vTerm] : ! [v3: vTerm] % 36.28/5.30 : (v1 = v0 | ~ (vplusop(v3, v2) = v1) | ~ (vplusop(v3, v2) = v0)) & ! [v0: % 36.28/5.30 vTerm] : ! [v1: vTerm] : ! [v2: vTerm] : ! [v3: vTerm] : (v1 = v0 | ~ % 36.28/5.30 (vPlus(v3, v2) = v1) | ~ (vPlus(v3, v2) = v0)) & ! [v0: vOptTerm] : ! % 36.28/5.30 [v1: vOptTerm] : ! [v2: vTerm] : (v1 = v0 | ~ (vreduce(v2) = v1) | ~ % 36.28/5.30 (vreduce(v2) = v0)) & ! [v0: vTerm] : ! [v1: vTerm] : ! [v2: vOptTerm] : % 36.28/5.30 (v1 = v0 | ~ (vgetTerm(v2) = v1) | ~ (vgetTerm(v2) = v0)) & ! [v0: % 36.28/5.30 vOptTerm] : ! [v1: vOptTerm] : ! [v2: vTerm] : (v1 = v0 | ~ % 36.28/5.30 (vsomeTerm(v2) = v1) | ~ (vsomeTerm(v2) = v0)) & ! [v0: vTerm] : ! [v1: % 36.28/5.30 vTerm] : ! [v2: vTerm] : (v1 = v0 | ~ (vIszero(v2) = v1) | ~ (vIszero(v2) % 36.28/5.30 = v0)) & ! [v0: vTerm] : ! [v1: vTerm] : ! [v2: vTerm] : (v1 = v0 | ~ % 36.28/5.30 (vPred(v2) = v1) | ~ (vPred(v2) = v0)) & ! [v0: vTerm] : ! [v1: vTerm] : % 36.28/5.30 ! [v2: vTerm] : (v1 = v0 | ~ (vSucc(v2) = v1) | ~ (vSucc(v2) = v0)) % 36.28/5.30 % 36.28/5.30 Further assumptions not needed in the proof: % 36.28/5.30 -------------------------------------------- % 36.88/5.30 DIFF-B-Nat, DIFF-False-Ifelse, DIFF-False-Iszero, DIFF-False-Plus, % 36.88/5.30 DIFF-False-Pred, DIFF-False-Succ, DIFF-False-Zero, DIFF-Ifelse-Iszero, % 36.88/5.30 DIFF-Ifelse-Plus, DIFF-Ifelse-Pred, DIFF-Ifelse-Succ, DIFF-Ifelse-Zero, % 36.88/5.30 DIFF-Iszero-Plus, DIFF-Pred-Iszero, DIFF-Pred-Plus, DIFF-Succ-Iszero, % 36.88/5.30 DIFF-Succ-Plus, DIFF-Succ-Pred, DIFF-True-False, DIFF-True-Ifelse, % 36.88/5.30 DIFF-True-Iszero, DIFF-True-Plus, DIFF-True-Pred, DIFF-True-Succ, % 36.88/5.30 DIFF-True-Zero, DIFF-Zero-Iszero, DIFF-Zero-Plus, DIFF-Zero-Pred, % 36.88/5.30 DIFF-Zero-Succ, DIFF-noTerm-someTerm, EQ-Ifelse, EQ-Iszero, EQ-Plus, EQ-Pred, % 36.88/5.30 EQ-Succ, Preservation-Pred-IH0, TPlus, TPlus_inv0, TPlus_inv1, TPlus_inv2, % 36.88/5.30 TPred, TPred_inv1, TSucc, TSucc_inv1, TSucc_inv2, TZero, TZero_inv, Tfalse, Tif, % 36.88/5.30 Tif_inv1, Tif_inv2, Tif_inv3, Tiszero, Tiszero_inv1, Tiszero_inv2, Ttrue, % 36.88/5.30 dom-OptTerm, dom-Term, dom-Ty, getTerm-0, isNV-0, isNV-1, isNV-2, % 36.88/5.30 isNV-false-INV, isNV-true-INV, isSomeTerm-0, isSomeTerm-1, isSomeTerm-false-INV, % 36.88/5.30 isSomeTerm-true-INV, isValue-0, isValue-1, isValue-2, isValue-false-INV, % 36.88/5.30 isValue-true-INV, plusop-0, plusop-1, plusop-2, plusop-INV, reduce-0, reduce-1, % 36.88/5.30 reduce-10, reduce-11, reduce-12, reduce-13, reduce-14, reduce-15, reduce-16, % 36.88/5.30 reduce-17, reduce-18, reduce-19, reduce-2, reduce-20, reduce-21, reduce-22, % 36.88/5.30 reduce-23, reduce-3, reduce-4, reduce-5, reduce-6, reduce-8, reduce-9, % 36.88/5.30 reduce-INV % 36.88/5.30 % 36.88/5.30 Those formulas are unsatisfiable: % 36.88/5.30 --------------------------------- % 36.88/5.30 % 36.88/5.30 Begin of proof % 36.88/5.30 | % 36.88/5.30 | ALPHA: (reduce-7) implies: % 36.88/5.30 | (1) ! [v0: vTerm] : ! [v1: vTerm] : ( ~ (vSucc(v0) = v1) | ~ vTerm(v0) | % 36.88/5.30 | ~ visNV(v0) | ? [v2: vTerm] : ? [v3: vOptTerm] : (vreduce(v2) = v3 % 36.88/5.30 | & vsomeTerm(v0) = v3 & vPred(v1) = v2 & vOptTerm(v3) & vTerm(v2))) % 36.88/5.30 | % 36.88/5.30 | ALPHA: (TPred_inv2) implies: % 36.88/5.30 | (2) ! [v0: vTerm] : ! [v1: vTy] : ! [v2: vTerm] : (v1 = vNat | ~ % 36.88/5.30 | (vPred(v0) = v2) | ~ vTy(v1) | ~ vTerm(v0) | ~ vptchecksimple(v2, % 36.88/5.30 | v1)) % 36.88/5.30 | % 36.88/5.30 | ALPHA: (isNVisNat) implies: % 36.88/5.30 | (3) ! [v0: vTerm] : ( ~ vTerm(v0) | ~ visNV(v0) | vptchecksimple(v0, % 36.88/5.30 | vNat)) % 36.88/5.30 | % 36.88/5.30 | ALPHA: (Preservation-Pred-Succ-isNV-True) implies: % 36.88/5.30 | (4) vTerm(vt1) % 36.88/5.30 | (5) ? [v0: vTerm] : ? [v1: vOptTerm] : ? [v2: vTerm] : ? [v3: vTy] : ? % 36.88/5.30 | [v4: vTerm] : ( ~ (vt1 = vZero) & vreduce(v0) = v1 & vsomeTerm(v4) = v1 % 36.88/5.30 | & vPred(vt1) = v0 & vSucc(v2) = vt1 & vTy(v3) & vOptTerm(v1) & % 36.88/5.30 | vTerm(v4) & vTerm(v2) & vTerm(v0) & vptchecksimple(v0, v3) & % 36.88/5.30 | visNV(v2) & ~ vptchecksimple(v4, v3)) % 36.88/5.30 | % 36.88/5.30 | ALPHA: (function-axioms) implies: % 36.88/5.30 | (6) ! [v0: vTerm] : ! [v1: vTerm] : ! [v2: vTerm] : (v1 = v0 | ~ % 36.88/5.30 | (vPred(v2) = v1) | ~ (vPred(v2) = v0)) % 36.88/5.30 | (7) ! [v0: vOptTerm] : ! [v1: vOptTerm] : ! [v2: vTerm] : (v1 = v0 | ~ % 36.88/5.30 | (vreduce(v2) = v1) | ~ (vreduce(v2) = v0)) % 36.88/5.30 | % 36.88/5.31 | DELTA: instantiating (5) with fresh symbols all_108_0, all_108_1, all_108_2, % 36.88/5.31 | all_108_3, all_108_4 gives: % 36.88/5.31 | (8) ~ (vt1 = vZero) & vreduce(all_108_4) = all_108_3 & % 36.88/5.31 | vsomeTerm(all_108_0) = all_108_3 & vPred(vt1) = all_108_4 & % 36.88/5.31 | vSucc(all_108_2) = vt1 & vTy(all_108_1) & vOptTerm(all_108_3) & % 36.88/5.31 | vTerm(all_108_0) & vTerm(all_108_2) & vTerm(all_108_4) & % 36.88/5.31 | vptchecksimple(all_108_4, all_108_1) & visNV(all_108_2) & ~ % 36.88/5.31 | vptchecksimple(all_108_0, all_108_1) % 36.88/5.31 | % 36.88/5.31 | ALPHA: (8) implies: % 36.88/5.31 | (9) ~ vptchecksimple(all_108_0, all_108_1) % 36.88/5.31 | (10) visNV(all_108_2) % 36.88/5.31 | (11) vptchecksimple(all_108_4, all_108_1) % 36.88/5.31 | (12) vTerm(all_108_2) % 36.88/5.31 | (13) vTerm(all_108_0) % 36.88/5.31 | (14) vTy(all_108_1) % 36.88/5.31 | (15) vSucc(all_108_2) = vt1 % 36.88/5.31 | (16) vPred(vt1) = all_108_4 % 36.88/5.31 | (17) vsomeTerm(all_108_0) = all_108_3 % 36.88/5.31 | (18) vreduce(all_108_4) = all_108_3 % 36.88/5.31 | % 36.88/5.31 | GROUND_INST: instantiating (3) with all_108_2, simplifying with (10), (12) % 36.88/5.31 | gives: % 36.88/5.31 | (19) vptchecksimple(all_108_2, vNat) % 36.88/5.31 | % 36.88/5.31 | GROUND_INST: instantiating (1) with all_108_2, vt1, simplifying with (10), % 36.88/5.31 | (12), (15) gives: % 36.88/5.31 | (20) ? [v0: vTerm] : ? [v1: vOptTerm] : (vreduce(v0) = v1 & % 36.88/5.31 | vsomeTerm(all_108_2) = v1 & vPred(vt1) = v0 & vOptTerm(v1) & % 36.88/5.31 | vTerm(v0)) % 36.88/5.31 | % 36.88/5.31 | GROUND_INST: instantiating (2) with vt1, all_108_1, all_108_4, simplifying % 36.88/5.31 | with (4), (11), (14), (16) gives: % 36.88/5.31 | (21) all_108_1 = vNat % 36.88/5.31 | % 36.88/5.31 | DELTA: instantiating (20) with fresh symbols all_129_0, all_129_1 gives: % 36.88/5.31 | (22) vreduce(all_129_1) = all_129_0 & vsomeTerm(all_108_2) = all_129_0 & % 36.88/5.31 | vPred(vt1) = all_129_1 & vOptTerm(all_129_0) & vTerm(all_129_1) % 36.88/5.31 | % 36.88/5.31 | ALPHA: (22) implies: % 36.88/5.31 | (23) vPred(vt1) = all_129_1 % 36.88/5.31 | (24) vsomeTerm(all_108_2) = all_129_0 % 36.88/5.31 | (25) vreduce(all_129_1) = all_129_0 % 36.88/5.31 | % 36.88/5.31 | REDUCE: (9), (21) imply: % 36.88/5.31 | (26) ~ vptchecksimple(all_108_0, vNat) % 36.88/5.31 | % 36.88/5.31 | GROUND_INST: instantiating (6) with all_108_4, all_129_1, vt1, simplifying % 36.88/5.31 | with (16), (23) gives: % 36.88/5.31 | (27) all_129_1 = all_108_4 % 36.88/5.31 | % 36.88/5.31 | GROUND_INST: instantiating (7) with all_108_3, all_129_0, all_108_4, % 36.88/5.31 | simplifying with (18) gives: % 36.88/5.31 | (28) all_129_0 = all_108_3 | ~ (vreduce(all_108_4) = all_129_0) % 36.88/5.31 | % 36.88/5.31 | PRED_UNIFY: (19), (26) imply: % 36.88/5.31 | (29) ~ (all_108_0 = all_108_2) % 36.88/5.31 | % 36.88/5.31 | REDUCE: (25), (27) imply: % 36.88/5.31 | (30) vreduce(all_108_4) = all_129_0 % 36.88/5.31 | % 36.88/5.31 | BETA: splitting (28) gives: % 36.88/5.31 | % 36.88/5.31 | Case 1: % 36.88/5.31 | | % 36.88/5.31 | | (31) ~ (vreduce(all_108_4) = all_129_0) % 36.88/5.31 | | % 36.88/5.31 | | PRED_UNIFY: (30), (31) imply: % 36.88/5.31 | | (32) $false % 36.88/5.31 | | % 36.88/5.31 | | CLOSE: (32) is inconsistent. % 36.88/5.31 | | % 36.88/5.31 | Case 2: % 36.88/5.31 | | % 36.88/5.31 | | (33) all_129_0 = all_108_3 % 36.88/5.31 | | % 36.88/5.31 | | REDUCE: (24), (33) imply: % 36.88/5.31 | | (34) vsomeTerm(all_108_2) = all_108_3 % 36.88/5.31 | | % 36.88/5.31 | | GROUND_INST: instantiating (EQ-someTerm) with all_108_0, all_108_2, % 36.88/5.31 | | all_108_3, simplifying with (12), (13), (17), (34) gives: % 36.88/5.31 | | (35) all_108_0 = all_108_2 % 36.88/5.31 | | % 36.88/5.31 | | REDUCE: (29), (35) imply: % 36.88/5.32 | | (36) $false % 36.88/5.32 | | % 36.88/5.32 | | CLOSE: (36) is inconsistent. % 36.88/5.32 | | % 36.88/5.32 | End of split % 36.88/5.32 | % 36.88/5.32 End of proof % 36.88/5.32 % SZS output end Proof for theBenchmark % 36.88/5.32 % 36.88/5.32 4883ms %------------------------------------------------------------------------------