%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : NUM853+2 : TPTP v8.1.2. Released v4.1.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n006.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 11:50:26 EDT 2023 % Result : Theorem 9.73s 2.10s % Output : Proof 13.89s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : NUM853+2 : TPTP v8.1.2. Released v4.1.0. % 0.00/0.12 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.12/0.34 % Computer : n006.cluster.edu % 0.12/0.34 % Model : x86_64 x86_64 % 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.34 % Memory : 8042.1875MB % 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.34 % CPULimit : 300 % 0.12/0.34 % WCLimit : 300 % 0.12/0.34 % DateTime : Fri Aug 25 16:49:37 EDT 2023 % 0.12/0.34 % CPUTime : % 0.18/0.62 ________ _____ % 0.18/0.62 ___ __ \_________(_)________________________________ % 0.18/0.62 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.18/0.62 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.18/0.62 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.18/0.62 % 0.18/0.62 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.18/0.62 (2023-06-19) % 0.18/0.62 % 0.18/0.62 (c) Philipp Rümmer, 2009-2023 % 0.18/0.62 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.18/0.62 Amanda Stjerna. % 0.18/0.62 Free software under BSD-3-Clause. % 0.18/0.62 % 0.18/0.62 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.18/0.62 % 0.18/0.62 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.18/0.63 Running up to 7 provers in parallel. % 0.18/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.18/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.18/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.18/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.18/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.18/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 0.18/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 3.06/1.15 Prover 4: Preprocessing ... % 3.06/1.15 Prover 1: Preprocessing ... % 3.06/1.19 Prover 5: Preprocessing ... % 3.06/1.19 Prover 6: Preprocessing ... % 3.06/1.19 Prover 0: Preprocessing ... % 3.06/1.19 Prover 2: Preprocessing ... % 3.55/1.20 Prover 3: Preprocessing ... % 6.41/1.61 Prover 1: Warning: ignoring some quantifiers % 6.41/1.66 Prover 6: Proving ... % 6.41/1.67 Prover 3: Warning: ignoring some quantifiers % 7.02/1.67 Prover 1: Constructing countermodel ... % 7.02/1.67 Prover 5: Proving ... % 7.08/1.69 Prover 3: Constructing countermodel ... % 7.08/1.70 Prover 4: Warning: ignoring some quantifiers % 7.28/1.71 Prover 0: Proving ... % 7.43/1.73 Prover 4: Constructing countermodel ... % 7.43/1.80 Prover 2: Proving ... % 8.68/1.89 Prover 3: gave up % 8.68/1.90 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 8.68/1.96 Prover 1: gave up % 8.68/1.96 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 9.30/1.97 Prover 7: Preprocessing ... % 9.30/2.03 Prover 8: Preprocessing ... % 9.73/2.10 Prover 0: proved (1461ms) % 9.73/2.10 % 9.73/2.10 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 9.73/2.10 % 9.73/2.10 Prover 5: stopped % 9.73/2.10 Prover 6: stopped % 10.17/2.12 Prover 2: stopped % 10.17/2.12 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 10.17/2.12 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 10.17/2.12 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 10.28/2.14 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 10.28/2.15 Prover 10: Preprocessing ... % 10.28/2.15 Prover 13: Preprocessing ... % 10.28/2.17 Prover 11: Preprocessing ... % 10.28/2.17 Prover 16: Preprocessing ... % 10.28/2.18 Prover 7: Warning: ignoring some quantifiers % 10.28/2.19 Prover 7: Constructing countermodel ... % 10.28/2.22 Prover 8: Warning: ignoring some quantifiers % 11.01/2.23 Prover 8: Constructing countermodel ... % 11.01/2.24 Prover 10: Warning: ignoring some quantifiers % 11.01/2.25 Prover 10: Constructing countermodel ... % 11.01/2.26 Prover 16: Warning: ignoring some quantifiers % 11.01/2.27 Prover 13: Warning: ignoring some quantifiers % 11.01/2.29 Prover 16: Constructing countermodel ... % 11.54/2.30 Prover 13: Constructing countermodel ... % 11.54/2.34 Prover 11: Warning: ignoring some quantifiers % 11.54/2.35 Prover 11: Constructing countermodel ... % 12.58/2.43 Prover 8: gave up % 12.58/2.43 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085 % 12.58/2.46 Prover 19: Preprocessing ... % 13.33/2.55 Prover 19: Warning: ignoring some quantifiers % 13.33/2.56 Prover 19: Constructing countermodel ... % 13.89/2.64 Prover 4: Found proof (size 41) % 13.89/2.64 Prover 4: proved (2002ms) % 13.89/2.64 Prover 7: stopped % 13.89/2.64 Prover 10: stopped % 13.89/2.64 Prover 16: stopped % 13.89/2.64 Prover 13: stopped % 13.89/2.64 Prover 11: stopped % 13.89/2.65 Prover 19: stopped % 13.89/2.65 % 13.89/2.65 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 13.89/2.65 % 13.89/2.65 % SZS output start Proof for theBenchmark % 13.89/2.66 Assumptions after simplification: % 13.89/2.66 --------------------------------- % 13.89/2.66 % 13.89/2.66 (ass(cond(140, 0), 0)) % 13.89/2.68 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (less(v1, v0) = v2) | % 13.89/2.68 ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ( ~ (v3 = 0) & greater(v0, v1) = v3)) % 13.89/2.68 & ! [v0: $i] : ! [v1: $i] : ( ~ (greater(v0, v1) = 0) | ~ $i(v1) | ~ % 13.89/2.68 $i(v0) | less(v1, v0) = 0) % 13.89/2.68 % 13.89/2.68 (ass(cond(270, 0), 0)) % 13.89/2.68 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (vmul(v1, v0) = v2) | ~ $i(v1) % 13.89/2.68 | ~ $i(v0) | (vmul(v0, v1) = v2 & $i(v2))) & ! [v0: $i] : ! [v1: $i] : ! % 13.89/2.68 [v2: $i] : ( ~ (vmul(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | (vmul(v1, v0) = % 13.89/2.68 v2 & $i(v2))) % 13.89/2.68 % 13.89/2.68 (ass(cond(299, 0), 0)) % 13.89/2.68 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 13.89/2.68 int] : (v5 = 0 | ~ (less(v3, v4) = v5) | ~ (vmul(v2, v0) = v4) | ~ % 13.89/2.68 (vmul(v1, v0) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: int] : ( ~ % 13.89/2.68 (v6 = 0) & less(v1, v2) = v6)) % 13.89/2.68 % 13.89/2.68 (ass(cond(goal(130), 0), 0)) % 13.89/2.68 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | v1 = v0 | ~ (less(v0, % 13.89/2.68 v1) = v2) | ~ $i(v1) | ~ $i(v0) | greater(v0, v1) = 0) & ! [v0: $i] : % 13.89/2.68 ! [v1: $i] : ! [v2: int] : (v2 = 0 | v1 = v0 | ~ (greater(v0, v1) = v2) | % 13.89/2.68 ~ $i(v1) | ~ $i(v0) | less(v0, v1) = 0) % 13.89/2.68 % 13.89/2.68 (ass(cond(goal(130), 0), 2)) % 13.89/2.69 ! [v0: $i] : ! [v1: $i] : ( ~ (less(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | % 13.89/2.69 ? [v2: int] : ( ~ (v2 = 0) & greater(v0, v1) = v2)) & ! [v0: $i] : ! [v1: % 13.89/2.69 $i] : ( ~ (greater(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: int] : ( ~ % 13.89/2.69 (v2 = 0) & less(v0, v1) = v2)) % 13.89/2.69 % 13.89/2.69 (holds(antec(307), 489, 0)) % 13.89/2.69 $i(vd487) & $i(vd488) & $i(vd486) & ? [v0: $i] : ? [v1: $i] : (vmul(vd488, % 13.89/2.69 vd487) = v1 & vmul(vd486, vd487) = v0 & greater(v0, v1) = 0 & $i(v1) & % 13.89/2.69 $i(v0)) % 13.89/2.69 % 13.89/2.69 (holds(conseq(307), 490, 0)) % 13.89/2.69 $i(vd488) & $i(vd486) & ? [v0: int] : ( ~ (v0 = 0) & greater(vd486, vd488) = % 13.89/2.69 v0) % 13.89/2.69 % 13.89/2.69 (function-axioms) % 13.89/2.69 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 13.89/2.69 [v3: $i] : (v1 = v0 | ~ (geq(v3, v2) = v1) | ~ (geq(v3, v2) = v0)) & ! [v0: % 13.89/2.69 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 13.89/2.69 : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = v0)) & ! [v0: $i] : ! % 13.89/2.69 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (vplus(v3, v2) = v1) | ~ % 13.89/2.69 (vplus(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 13.89/2.69 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (less(v3, v2) % 13.89/2.69 = v1) | ~ (less(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] % 13.89/2.69 : ! [v3: $i] : (v1 = v0 | ~ (vmul(v3, v2) = v1) | ~ (vmul(v3, v2) = v0)) & % 13.89/2.69 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 13.89/2.69 $i] : (v1 = v0 | ~ (greater(v3, v2) = v1) | ~ (greater(v3, v2) = v0)) & ! % 13.89/2.69 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (vskolem2(v2) = v1) | ~ % 13.89/2.69 (vskolem2(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | % 13.89/2.69 ~ (vsucc(v2) = v1) | ~ (vsucc(v2) = v0)) % 13.89/2.69 % 13.89/2.69 Further assumptions not needed in the proof: % 13.89/2.69 -------------------------------------------- % 13.89/2.69 ass(cond(12, 0), 0), ass(cond(147, 0), 0), ass(cond(20, 0), 0), ass(cond(223, % 13.89/2.69 0), 0), ass(cond(228, 0), 0), ass(cond(234, 0), 0), ass(cond(241, 0), 0), % 13.89/2.69 ass(cond(253, 0), 0), ass(cond(261, 0), 0), ass(cond(281, 0), 0), ass(cond(290, % 13.89/2.69 0), 0), ass(cond(299, 0), 1), ass(cond(299, 0), 2), ass(cond(33, 0), 0), % 13.89/2.69 ass(cond(43, 0), 0), ass(cond(52, 0), 0), ass(cond(6, 0), 0), ass(cond(61, 0), % 13.89/2.69 0), ass(cond(73, 0), 0), ass(cond(81, 0), 0), ass(cond(goal(130), 0), 1), % 13.89/2.69 ass(cond(goal(130), 0), 3), ass(cond(goal(88), 0), 0), ass(cond(goal(88), 0), % 13.89/2.69 1), ass(cond(goal(88), 0), 2), ass(cond(goal(88), 0), 3), % 13.89/2.69 def(cond(conseq(axiom(3)), 11), 1), def(cond(conseq(axiom(3)), 12), 1), % 13.89/2.69 qu(cond(conseq(axiom(3)), 3), and(holds(definiens(29), 45, 0), % 13.89/2.69 holds(definiens(29), 44, 0))), qu(cond(conseq(axiom(3)), 32), % 13.89/2.69 and(holds(definiens(249), 399, 0), holds(definiens(249), 398, 0))) % 13.89/2.69 % 13.89/2.69 Those formulas are unsatisfiable: % 13.89/2.69 --------------------------------- % 13.89/2.69 % 13.89/2.69 Begin of proof % 13.89/2.69 | % 13.89/2.69 | ALPHA: (holds(antec(307), 489, 0)) implies: % 13.89/2.69 | (1) $i(vd487) % 13.89/2.70 | (2) ? [v0: $i] : ? [v1: $i] : (vmul(vd488, vd487) = v1 & vmul(vd486, % 13.89/2.70 | vd487) = v0 & greater(v0, v1) = 0 & $i(v1) & $i(v0)) % 13.89/2.70 | % 13.89/2.70 | ALPHA: (ass(cond(270, 0), 0)) implies: % 13.89/2.70 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (vmul(v1, v0) = v2) | ~ % 13.89/2.70 | $i(v1) | ~ $i(v0) | (vmul(v0, v1) = v2 & $i(v2))) % 13.89/2.70 | % 13.89/2.70 | ALPHA: (ass(cond(140, 0), 0)) implies: % 13.89/2.70 | (4) ! [v0: $i] : ! [v1: $i] : ( ~ (greater(v0, v1) = 0) | ~ $i(v1) | ~ % 13.89/2.70 | $i(v0) | less(v1, v0) = 0) % 13.89/2.70 | % 13.89/2.70 | ALPHA: (ass(cond(goal(130), 0), 0)) implies: % 13.89/2.70 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | v1 = v0 | ~ % 13.89/2.70 | (greater(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | less(v0, v1) = 0) % 13.89/2.70 | % 13.89/2.70 | ALPHA: (ass(cond(goal(130), 0), 2)) implies: % 13.89/2.70 | (6) ! [v0: $i] : ! [v1: $i] : ( ~ (greater(v0, v1) = 0) | ~ $i(v1) | ~ % 13.89/2.70 | $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & less(v0, v1) = v2)) % 13.89/2.70 | % 13.89/2.70 | ALPHA: (holds(conseq(307), 490, 0)) implies: % 13.89/2.70 | (7) $i(vd486) % 13.89/2.70 | (8) $i(vd488) % 13.89/2.70 | (9) ? [v0: int] : ( ~ (v0 = 0) & greater(vd486, vd488) = v0) % 13.89/2.70 | % 13.89/2.70 | ALPHA: (function-axioms) implies: % 13.89/2.70 | (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 13.89/2.70 | (vmul(v3, v2) = v1) | ~ (vmul(v3, v2) = v0)) % 13.89/2.70 | (11) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 13.89/2.70 | : ! [v3: $i] : (v1 = v0 | ~ (less(v3, v2) = v1) | ~ (less(v3, v2) = % 13.89/2.70 | v0)) % 13.89/2.70 | % 13.89/2.70 | DELTA: instantiating (9) with fresh symbol all_36_0 gives: % 13.89/2.70 | (12) ~ (all_36_0 = 0) & greater(vd486, vd488) = all_36_0 % 13.89/2.70 | % 13.89/2.70 | ALPHA: (12) implies: % 13.89/2.70 | (13) ~ (all_36_0 = 0) % 13.89/2.70 | (14) greater(vd486, vd488) = all_36_0 % 13.89/2.70 | % 13.89/2.70 | DELTA: instantiating (2) with fresh symbols all_38_0, all_38_1 gives: % 13.89/2.70 | (15) vmul(vd488, vd487) = all_38_0 & vmul(vd486, vd487) = all_38_1 & % 13.89/2.70 | greater(all_38_1, all_38_0) = 0 & $i(all_38_0) & $i(all_38_1) % 13.89/2.70 | % 13.89/2.70 | ALPHA: (15) implies: % 13.89/2.70 | (16) $i(all_38_1) % 13.89/2.70 | (17) $i(all_38_0) % 13.89/2.70 | (18) greater(all_38_1, all_38_0) = 0 % 13.89/2.70 | (19) vmul(vd486, vd487) = all_38_1 % 13.89/2.70 | (20) vmul(vd488, vd487) = all_38_0 % 13.89/2.70 | % 13.89/2.70 | GROUND_INST: instantiating (5) with vd486, vd488, all_36_0, simplifying with % 13.89/2.70 | (7), (8), (14) gives: % 13.89/2.70 | (21) all_36_0 = 0 | vd488 = vd486 | less(vd486, vd488) = 0 % 13.89/2.70 | % 13.89/2.70 | GROUND_INST: instantiating (4) with all_38_1, all_38_0, simplifying with (16), % 13.89/2.70 | (17), (18) gives: % 13.89/2.70 | (22) less(all_38_0, all_38_1) = 0 % 13.89/2.70 | % 13.89/2.70 | GROUND_INST: instantiating (6) with all_38_1, all_38_0, simplifying with (16), % 13.89/2.70 | (17), (18) gives: % 13.89/2.71 | (23) ? [v0: int] : ( ~ (v0 = 0) & less(all_38_1, all_38_0) = v0) % 13.89/2.71 | % 13.89/2.71 | GROUND_INST: instantiating (3) with vd487, vd486, all_38_1, simplifying with % 13.89/2.71 | (1), (7), (19) gives: % 13.89/2.71 | (24) vmul(vd487, vd486) = all_38_1 & $i(all_38_1) % 13.89/2.71 | % 13.89/2.71 | ALPHA: (24) implies: % 13.89/2.71 | (25) vmul(vd487, vd486) = all_38_1 % 13.89/2.71 | % 13.89/2.71 | GROUND_INST: instantiating (3) with vd487, vd488, all_38_0, simplifying with % 13.89/2.71 | (1), (8), (20) gives: % 13.89/2.71 | (26) vmul(vd487, vd488) = all_38_0 & $i(all_38_0) % 13.89/2.71 | % 13.89/2.71 | ALPHA: (26) implies: % 13.89/2.71 | (27) vmul(vd487, vd488) = all_38_0 % 13.89/2.71 | % 13.89/2.71 | DELTA: instantiating (23) with fresh symbol all_51_0 gives: % 13.89/2.71 | (28) ~ (all_51_0 = 0) & less(all_38_1, all_38_0) = all_51_0 % 13.89/2.71 | % 13.89/2.71 | ALPHA: (28) implies: % 13.89/2.71 | (29) ~ (all_51_0 = 0) % 13.89/2.71 | (30) less(all_38_1, all_38_0) = all_51_0 % 13.89/2.71 | % 13.89/2.71 | GROUND_INST: instantiating (ass(cond(299, 0), 0)) with vd487, vd486, vd488, % 13.89/2.71 | all_38_1, all_38_0, all_51_0, simplifying with (1), (7), (8), % 13.89/2.71 | (19), (20), (30) gives: % 13.89/2.71 | (31) all_51_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & less(vd486, vd488) = v0) % 13.89/2.71 | % 13.89/2.71 | BETA: splitting (31) gives: % 13.89/2.71 | % 13.89/2.71 | Case 1: % 13.89/2.71 | | % 13.89/2.71 | | (32) all_51_0 = 0 % 13.89/2.71 | | % 13.89/2.71 | | REDUCE: (29), (32) imply: % 13.89/2.71 | | (33) $false % 13.89/2.71 | | % 13.89/2.71 | | CLOSE: (33) is inconsistent. % 13.89/2.71 | | % 13.89/2.71 | Case 2: % 13.89/2.71 | | % 13.89/2.71 | | (34) ? [v0: int] : ( ~ (v0 = 0) & less(vd486, vd488) = v0) % 13.89/2.71 | | % 13.89/2.71 | | DELTA: instantiating (34) with fresh symbol all_139_0 gives: % 13.89/2.71 | | (35) ~ (all_139_0 = 0) & less(vd486, vd488) = all_139_0 % 13.89/2.71 | | % 13.89/2.71 | | ALPHA: (35) implies: % 13.89/2.71 | | (36) ~ (all_139_0 = 0) % 13.89/2.71 | | (37) less(vd486, vd488) = all_139_0 % 13.89/2.71 | | % 13.89/2.71 | | BETA: splitting (21) gives: % 13.89/2.71 | | % 13.89/2.71 | | Case 1: % 13.89/2.71 | | | % 13.89/2.71 | | | (38) less(vd486, vd488) = 0 % 13.89/2.71 | | | % 13.89/2.71 | | | GROUND_INST: instantiating (11) with 0, all_139_0, vd488, vd486, % 13.89/2.71 | | | simplifying with (37), (38) gives: % 13.89/2.71 | | | (39) all_139_0 = 0 % 13.89/2.71 | | | % 13.89/2.71 | | | REDUCE: (36), (39) imply: % 13.89/2.71 | | | (40) $false % 13.89/2.71 | | | % 13.89/2.71 | | | CLOSE: (40) is inconsistent. % 13.89/2.71 | | | % 13.89/2.71 | | Case 2: % 13.89/2.71 | | | % 13.89/2.71 | | | (41) all_36_0 = 0 | vd488 = vd486 % 13.89/2.71 | | | % 13.89/2.71 | | | BETA: splitting (41) gives: % 13.89/2.71 | | | % 13.89/2.71 | | | Case 1: % 13.89/2.71 | | | | % 13.89/2.71 | | | | (42) all_36_0 = 0 % 13.89/2.71 | | | | % 13.89/2.71 | | | | REDUCE: (13), (42) imply: % 13.89/2.71 | | | | (43) $false % 13.89/2.71 | | | | % 13.89/2.71 | | | | CLOSE: (43) is inconsistent. % 13.89/2.71 | | | | % 13.89/2.71 | | | Case 2: % 13.89/2.71 | | | | % 13.89/2.71 | | | | (44) vd488 = vd486 % 13.89/2.71 | | | | % 13.89/2.71 | | | | REDUCE: (27), (44) imply: % 13.89/2.71 | | | | (45) vmul(vd487, vd486) = all_38_0 % 13.89/2.71 | | | | % 13.89/2.71 | | | | GROUND_INST: instantiating (10) with all_38_1, all_38_0, vd486, vd487, % 13.89/2.71 | | | | simplifying with (25), (45) gives: % 13.89/2.71 | | | | (46) all_38_0 = all_38_1 % 13.89/2.71 | | | | % 13.89/2.71 | | | | REDUCE: (22), (46) imply: % 13.89/2.71 | | | | (47) less(all_38_1, all_38_1) = 0 % 13.89/2.71 | | | | % 13.89/2.71 | | | | REDUCE: (30), (46) imply: % 13.89/2.71 | | | | (48) less(all_38_1, all_38_1) = all_51_0 % 13.89/2.71 | | | | % 13.89/2.72 | | | | GROUND_INST: instantiating (11) with 0, all_51_0, all_38_1, all_38_1, % 13.89/2.72 | | | | simplifying with (47), (48) gives: % 13.89/2.72 | | | | (49) all_51_0 = 0 % 13.89/2.72 | | | | % 13.89/2.72 | | | | REDUCE: (29), (49) imply: % 13.89/2.72 | | | | (50) $false % 13.89/2.72 | | | | % 13.89/2.72 | | | | CLOSE: (50) is inconsistent. % 13.89/2.72 | | | | % 13.89/2.72 | | | End of split % 13.89/2.72 | | | % 13.89/2.72 | | End of split % 13.89/2.72 | | % 13.89/2.72 | End of split % 13.89/2.72 | % 13.89/2.72 End of proof % 13.89/2.72 % SZS output end Proof for theBenchmark % 13.89/2.72 % 13.89/2.72 2098ms %------------------------------------------------------------------------------