%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : NUM855+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 : n014.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 11:50:27 EDT 2023 % Result : Theorem 13.74s 2.65s % Output : Proof 16.66s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.13 % Problem : NUM855+2 : TPTP v8.1.2. Released v4.1.0. % 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.35 % Computer : n014.cluster.edu % 0.13/0.35 % Model : x86_64 x86_64 % 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.35 % Memory : 8042.1875MB % 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.35 % CPULimit : 300 % 0.13/0.35 % WCLimit : 300 % 0.13/0.35 % DateTime : Fri Aug 25 15:07:33 EDT 2023 % 0.13/0.35 % CPUTime : % 0.20/0.63 ________ _____ % 0.20/0.63 ___ __ \_________(_)________________________________ % 0.20/0.63 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.20/0.63 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.20/0.63 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.20/0.63 % 0.20/0.63 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.20/0.63 (2023-06-19) % 0.20/0.63 % 0.20/0.63 (c) Philipp Rümmer, 2009-2023 % 0.20/0.63 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.20/0.63 Amanda Stjerna. % 0.20/0.63 Free software under BSD-3-Clause. % 0.20/0.63 % 0.20/0.63 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.20/0.63 % 0.20/0.63 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.20/0.65 Running up to 7 provers in parallel. % 0.20/0.67 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.20/0.67 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.20/0.67 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.20/0.67 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.20/0.67 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.20/0.67 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.20/0.67 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 3.55/1.20 Prover 4: Preprocessing ... % 3.55/1.20 Prover 1: Preprocessing ... % 3.71/1.26 Prover 0: Preprocessing ... % 3.71/1.27 Prover 6: Preprocessing ... % 3.71/1.27 Prover 5: Preprocessing ... % 3.71/1.27 Prover 2: Preprocessing ... % 3.71/1.27 Prover 3: Preprocessing ... % 8.89/2.03 Prover 1: Warning: ignoring some quantifiers % 10.31/2.14 Prover 1: Constructing countermodel ... % 10.31/2.16 Prover 6: Proving ... % 10.31/2.16 Prover 3: Warning: ignoring some quantifiers % 10.31/2.17 Prover 5: Proving ... % 10.31/2.17 Prover 4: Warning: ignoring some quantifiers % 10.31/2.20 Prover 3: Constructing countermodel ... % 10.31/2.22 Prover 0: Proving ... % 10.31/2.24 Prover 4: Constructing countermodel ... % 11.26/2.40 Prover 2: Proving ... % 13.74/2.64 Prover 3: proved (1967ms) % 13.74/2.64 % 13.74/2.65 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 13.74/2.65 % 13.74/2.65 Prover 6: stopped % 13.74/2.67 Prover 2: stopped % 13.74/2.67 Prover 5: stopped % 13.74/2.68 Prover 0: stopped % 13.74/2.68 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 13.74/2.69 Prover 1: Found proof (size 45) % 13.74/2.69 Prover 1: proved (1998ms) % 13.74/2.69 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 13.74/2.69 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 13.74/2.69 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 13.74/2.69 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 13.74/2.69 Prover 4: stopped % 14.25/2.78 Prover 7: Preprocessing ... % 14.62/2.79 Prover 13: Preprocessing ... % 14.62/2.79 Prover 11: Preprocessing ... % 14.62/2.79 Prover 8: Preprocessing ... % 14.62/2.81 Prover 10: Preprocessing ... % 15.05/2.86 Prover 7: stopped % 15.15/2.89 Prover 10: stopped % 15.15/2.90 Prover 11: stopped % 15.15/2.91 Prover 13: stopped % 15.15/3.01 Prover 8: Warning: ignoring some quantifiers % 15.15/3.03 Prover 8: Constructing countermodel ... % 15.65/3.05 Prover 8: stopped % 15.65/3.05 % 15.65/3.05 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 15.65/3.05 % 16.09/3.06 % SZS output start Proof for theBenchmark % 16.09/3.07 Assumptions after simplification: % 16.09/3.07 --------------------------------- % 16.09/3.07 % 16.09/3.07 (ass(cond(270, 0), 0)) % 16.09/3.10 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (vmul(v0, v1) = v2) | ~ $i(v1) % 16.09/3.10 | ~ $i(v0) | (vmul(v1, v0) = v2 & $i(v2))) % 16.09/3.10 % 16.09/3.10 (ass(cond(33, 0), 0)) % 16.09/3.10 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 16.09/3.10 (vplus(v3, v2) = v4) | ~ (vplus(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ % 16.09/3.10 $i(v0) | ? [v5: $i] : (vplus(v1, v2) = v5 & vplus(v0, v5) = v4 & $i(v5) & % 16.09/3.10 $i(v4))) % 16.09/3.10 % 16.09/3.10 (def(cond(conseq(axiom(3)), 11), 1)) % 16.09/3.10 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (greater(v1, v0) = v2) % 16.09/3.10 | ~ $i(v1) | ~ $i(v0) | ! [v3: $i] : ( ~ (vplus(v0, v3) = v1) | ~ % 16.09/3.10 $i(v3))) & ! [v0: $i] : ! [v1: $i] : ( ~ (greater(v1, v0) = 0) | ~ % 16.09/3.10 $i(v1) | ~ $i(v0) | ? [v2: $i] : (vplus(v0, v2) = v1 & $i(v2))) % 16.09/3.10 % 16.09/3.10 (holds(conjunct1(315), 514, 0)) % 16.09/3.11 $i(vd509) & $i(vd511) & $i(vd508) & ? [v0: $i] : ? [v1: $i] : (greater(v0, % 16.09/3.11 v1) = 0 & vmul(vd509, vd511) = v1 & vmul(vd508, vd511) = v0 & $i(v1) & % 16.09/3.11 $i(v0)) % 16.09/3.11 % 16.09/3.11 (holds(conjunct2(315), 515, 0)) % 16.09/3.11 $i(vd509) & $i(vd511) & ? [v0: $i] : (vmul(vd509, vd511) = v0 & vmul(vd511, % 16.09/3.11 vd509) = v0 & $i(v0)) % 16.09/3.11 % 16.09/3.11 (holds(conjunct2(315), 515, 1)) % 16.09/3.11 $i(vd512) & $i(vd509) & $i(vd511) & ? [v0: $i] : ? [v1: $i] : (greater(v0, % 16.09/3.11 v1) = 0 & vmul(vd512, vd509) = v1 & vmul(vd511, vd509) = v0 & $i(v1) & % 16.09/3.11 $i(v0)) % 16.09/3.11 % 16.09/3.11 (holds(conjunct2(315), 515, 2)) % 16.09/3.11 $i(vd512) & $i(vd509) & ? [v0: $i] : (vmul(vd512, vd509) = v0 & vmul(vd509, % 16.09/3.11 vd512) = v0 & $i(v0)) % 16.09/3.11 % 16.09/3.11 (holds(conseq_conjunct2(315), 516, 0)) % 16.09/3.11 $i(vd512) & $i(vd509) & $i(vd511) & $i(vd508) & ? [v0: $i] : ? [v1: $i] : ? % 16.09/3.11 [v2: int] : ( ~ (v2 = 0) & greater(v0, v1) = v2 & vmul(vd509, vd512) = v1 & % 16.09/3.11 vmul(vd508, vd511) = v0 & $i(v1) & $i(v0)) % 16.09/3.11 % 16.09/3.11 (function-axioms) % 16.09/3.12 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 16.09/3.12 [v3: $i] : (v1 = v0 | ~ (geq(v3, v2) = v1) | ~ (geq(v3, v2) = v0)) & ! [v0: % 16.09/3.12 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 16.09/3.12 : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = v0)) & ! [v0: $i] : ! % 16.09/3.12 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (vplus(v3, v2) = v1) | ~ % 16.09/3.12 (vplus(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 16.09/3.12 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (less(v3, v2) % 16.09/3.12 = v1) | ~ (less(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 16.09/3.12 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (greater(v3, % 16.09/3.12 v2) = v1) | ~ (greater(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 16.09/3.12 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (vmul(v3, v2) = v1) | ~ (vmul(v3, v2) % 16.09/3.12 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 16.09/3.12 (vskolem2(v2) = v1) | ~ (vskolem2(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : % 16.09/3.12 ! [v2: $i] : (v1 = v0 | ~ (vsucc(v2) = v1) | ~ (vsucc(v2) = v0)) % 16.09/3.12 % 16.09/3.12 Further assumptions not needed in the proof: % 16.09/3.12 -------------------------------------------- % 16.09/3.12 ass(cond(12, 0), 0), ass(cond(140, 0), 0), ass(cond(147, 0), 0), ass(cond(158, % 16.09/3.12 0), 0), ass(cond(163, 0), 0), ass(cond(168, 0), 0), ass(cond(184, 0), 0), % 16.09/3.12 ass(cond(189, 0), 0), ass(cond(20, 0), 0), ass(cond(209, 0), 0), ass(cond(223, % 16.09/3.12 0), 0), ass(cond(228, 0), 0), ass(cond(234, 0), 0), ass(cond(241, 0), 0), % 16.09/3.12 ass(cond(253, 0), 0), ass(cond(261, 0), 0), ass(cond(281, 0), 0), ass(cond(290, % 16.09/3.12 0), 0), ass(cond(299, 0), 0), ass(cond(299, 0), 1), ass(cond(299, 0), 2), % 16.09/3.12 ass(cond(43, 0), 0), ass(cond(52, 0), 0), ass(cond(6, 0), 0), ass(cond(61, 0), % 16.09/3.12 0), ass(cond(73, 0), 0), ass(cond(81, 0), 0), ass(cond(conjunct1(307), 0), 0), % 16.09/3.12 ass(cond(conjunct1(conjunct2(307)), 0), 0), ass(cond(conjunct2(conjunct2(307)), % 16.09/3.12 0), 0), ass(cond(goal(130), 0), 0), ass(cond(goal(130), 0), 1), % 16.09/3.12 ass(cond(goal(130), 0), 2), ass(cond(goal(130), 0), 3), ass(cond(goal(177), 0), % 16.09/3.12 0), ass(cond(goal(193), 0), 0), ass(cond(goal(193), 0), 1), % 16.09/3.12 ass(cond(goal(193), 0), 2), ass(cond(goal(202), 0), 0), ass(cond(goal(202), 0), % 16.09/3.12 1), ass(cond(goal(202), 0), 2), ass(cond(goal(216), 0), 0), ass(cond(goal(88), % 16.09/3.12 0), 0), ass(cond(goal(88), 0), 1), ass(cond(goal(88), 0), 2), % 16.09/3.12 ass(cond(goal(88), 0), 3), def(cond(conseq(axiom(3)), 12), 1), % 16.09/3.12 def(cond(conseq(axiom(3)), 16), 1), def(cond(conseq(axiom(3)), 17), 1), % 16.09/3.12 holds(conjunct1(314), 510, 0), holds(conjunct2(314), 513, 0), % 16.09/3.12 qu(antec(axiom(3)), imp(antec(axiom(3)))), qu(cond(conseq(axiom(3)), 3), % 16.09/3.12 and(holds(definiens(29), 45, 0), holds(definiens(29), 44, 0))), % 16.09/3.12 qu(cond(conseq(axiom(3)), 32), and(holds(definiens(249), 399, 0), % 16.09/3.12 holds(definiens(249), 398, 0))), qu(restrictor(axiom(1)), % 16.09/3.12 holds(scope(axiom(1)), 2, 0)) % 16.09/3.12 % 16.09/3.12 Those formulas are unsatisfiable: % 16.09/3.12 --------------------------------- % 16.09/3.12 % 16.09/3.12 Begin of proof % 16.09/3.13 | % 16.09/3.13 | ALPHA: (holds(conjunct2(315), 515, 2)) implies: % 16.09/3.13 | (1) ? [v0: $i] : (vmul(vd512, vd509) = v0 & vmul(vd509, vd512) = v0 & % 16.09/3.13 | $i(v0)) % 16.09/3.13 | % 16.09/3.13 | ALPHA: (holds(conjunct2(315), 515, 1)) implies: % 16.09/3.13 | (2) ? [v0: $i] : ? [v1: $i] : (greater(v0, v1) = 0 & vmul(vd512, vd509) = % 16.09/3.13 | v1 & vmul(vd511, vd509) = v0 & $i(v1) & $i(v0)) % 16.09/3.13 | % 16.09/3.13 | ALPHA: (holds(conjunct2(315), 515, 0)) implies: % 16.09/3.13 | (3) ? [v0: $i] : (vmul(vd509, vd511) = v0 & vmul(vd511, vd509) = v0 & % 16.09/3.13 | $i(v0)) % 16.09/3.13 | % 16.09/3.13 | ALPHA: (holds(conjunct1(315), 514, 0)) implies: % 16.09/3.13 | (4) ? [v0: $i] : ? [v1: $i] : (greater(v0, v1) = 0 & vmul(vd509, vd511) = % 16.09/3.13 | v1 & vmul(vd508, vd511) = v0 & $i(v1) & $i(v0)) % 16.09/3.14 | % 16.09/3.14 | ALPHA: (def(cond(conseq(axiom(3)), 11), 1)) implies: % 16.09/3.14 | (5) ! [v0: $i] : ! [v1: $i] : ( ~ (greater(v1, v0) = 0) | ~ $i(v1) | ~ % 16.49/3.14 | $i(v0) | ? [v2: $i] : (vplus(v0, v2) = v1 & $i(v2))) % 16.49/3.14 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (greater(v1, % 16.49/3.14 | v0) = v2) | ~ $i(v1) | ~ $i(v0) | ! [v3: $i] : ( ~ (vplus(v0, % 16.49/3.14 | v3) = v1) | ~ $i(v3))) % 16.49/3.14 | % 16.49/3.14 | ALPHA: (holds(conseq_conjunct2(315), 516, 0)) implies: % 16.49/3.15 | (7) $i(vd508) % 16.49/3.15 | (8) $i(vd511) % 16.49/3.15 | (9) ? [v0: $i] : ? [v1: $i] : ? [v2: int] : ( ~ (v2 = 0) & greater(v0, % 16.49/3.15 | v1) = v2 & vmul(vd509, vd512) = v1 & vmul(vd508, vd511) = v0 & % 16.49/3.15 | $i(v1) & $i(v0)) % 16.49/3.15 | % 16.49/3.15 | ALPHA: (function-axioms) implies: % 16.49/3.15 | (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 16.49/3.15 | (vmul(v3, v2) = v1) | ~ (vmul(v3, v2) = v0)) % 16.49/3.15 | % 16.49/3.15 | DELTA: instantiating (1) with fresh symbol all_54_0 gives: % 16.49/3.15 | (11) vmul(vd512, vd509) = all_54_0 & vmul(vd509, vd512) = all_54_0 & % 16.49/3.15 | $i(all_54_0) % 16.49/3.15 | % 16.49/3.15 | ALPHA: (11) implies: % 16.49/3.15 | (12) vmul(vd509, vd512) = all_54_0 % 16.49/3.15 | (13) vmul(vd512, vd509) = all_54_0 % 16.49/3.15 | % 16.49/3.15 | DELTA: instantiating (3) with fresh symbol all_56_0 gives: % 16.49/3.15 | (14) vmul(vd509, vd511) = all_56_0 & vmul(vd511, vd509) = all_56_0 & % 16.49/3.15 | $i(all_56_0) % 16.49/3.15 | % 16.49/3.15 | ALPHA: (14) implies: % 16.49/3.16 | (15) vmul(vd511, vd509) = all_56_0 % 16.49/3.16 | (16) vmul(vd509, vd511) = all_56_0 % 16.49/3.16 | % 16.49/3.16 | DELTA: instantiating (2) with fresh symbols all_63_0, all_63_1 gives: % 16.49/3.16 | (17) greater(all_63_1, all_63_0) = 0 & vmul(vd512, vd509) = all_63_0 & % 16.49/3.16 | vmul(vd511, vd509) = all_63_1 & $i(all_63_0) & $i(all_63_1) % 16.49/3.16 | % 16.49/3.16 | ALPHA: (17) implies: % 16.49/3.16 | (18) $i(all_63_1) % 16.49/3.16 | (19) $i(all_63_0) % 16.49/3.16 | (20) vmul(vd511, vd509) = all_63_1 % 16.49/3.16 | (21) vmul(vd512, vd509) = all_63_0 % 16.49/3.16 | (22) greater(all_63_1, all_63_0) = 0 % 16.49/3.16 | % 16.49/3.16 | DELTA: instantiating (4) with fresh symbols all_65_0, all_65_1 gives: % 16.49/3.16 | (23) greater(all_65_1, all_65_0) = 0 & vmul(vd509, vd511) = all_65_0 & % 16.49/3.16 | vmul(vd508, vd511) = all_65_1 & $i(all_65_0) & $i(all_65_1) % 16.49/3.16 | % 16.49/3.16 | ALPHA: (23) implies: % 16.49/3.16 | (24) vmul(vd508, vd511) = all_65_1 % 16.49/3.16 | (25) vmul(vd509, vd511) = all_65_0 % 16.49/3.16 | (26) greater(all_65_1, all_65_0) = 0 % 16.49/3.16 | % 16.49/3.16 | DELTA: instantiating (9) with fresh symbols all_68_0, all_68_1, all_68_2 % 16.49/3.16 | gives: % 16.49/3.16 | (27) ~ (all_68_0 = 0) & greater(all_68_2, all_68_1) = all_68_0 & % 16.49/3.16 | vmul(vd509, vd512) = all_68_1 & vmul(vd508, vd511) = all_68_2 & % 16.49/3.16 | $i(all_68_1) & $i(all_68_2) % 16.49/3.16 | % 16.49/3.16 | ALPHA: (27) implies: % 16.49/3.16 | (28) ~ (all_68_0 = 0) % 16.49/3.16 | (29) vmul(vd508, vd511) = all_68_2 % 16.49/3.16 | (30) vmul(vd509, vd512) = all_68_1 % 16.49/3.16 | (31) greater(all_68_2, all_68_1) = all_68_0 % 16.49/3.16 | % 16.49/3.17 | GROUND_INST: instantiating (10) with all_65_1, all_68_2, vd511, vd508, % 16.49/3.17 | simplifying with (24), (29) gives: % 16.49/3.17 | (32) all_68_2 = all_65_1 % 16.49/3.17 | % 16.49/3.17 | GROUND_INST: instantiating (10) with all_56_0, all_63_1, vd509, vd511, % 16.49/3.17 | simplifying with (15), (20) gives: % 16.49/3.17 | (33) all_63_1 = all_56_0 % 16.49/3.17 | % 16.49/3.17 | GROUND_INST: instantiating (10) with all_56_0, all_65_0, vd511, vd509, % 16.49/3.17 | simplifying with (16), (25) gives: % 16.49/3.17 | (34) all_65_0 = all_56_0 % 16.49/3.17 | % 16.49/3.17 | GROUND_INST: instantiating (10) with all_54_0, all_68_1, vd512, vd509, % 16.49/3.17 | simplifying with (12), (30) gives: % 16.49/3.17 | (35) all_68_1 = all_54_0 % 16.49/3.17 | % 16.49/3.17 | GROUND_INST: instantiating (10) with all_54_0, all_63_0, vd509, vd512, % 16.49/3.17 | simplifying with (13), (21) gives: % 16.49/3.17 | (36) all_63_0 = all_54_0 % 16.49/3.17 | % 16.49/3.17 | REDUCE: (31), (32), (35) imply: % 16.49/3.17 | (37) greater(all_65_1, all_54_0) = all_68_0 % 16.49/3.17 | % 16.49/3.17 | REDUCE: (26), (34) imply: % 16.49/3.17 | (38) greater(all_65_1, all_56_0) = 0 % 16.49/3.17 | % 16.49/3.17 | REDUCE: (22), (33), (36) imply: % 16.49/3.17 | (39) greater(all_56_0, all_54_0) = 0 % 16.49/3.17 | % 16.49/3.17 | REDUCE: (19), (36) imply: % 16.49/3.17 | (40) $i(all_54_0) % 16.49/3.17 | % 16.49/3.17 | REDUCE: (18), (33) imply: % 16.49/3.17 | (41) $i(all_56_0) % 16.49/3.17 | % 16.49/3.17 | GROUND_INST: instantiating (ass(cond(270, 0), 0)) with vd508, vd511, all_65_1, % 16.49/3.17 | simplifying with (7), (8), (24) gives: % 16.49/3.17 | (42) vmul(vd511, vd508) = all_65_1 & $i(all_65_1) % 16.49/3.17 | % 16.49/3.17 | ALPHA: (42) implies: % 16.49/3.17 | (43) $i(all_65_1) % 16.49/3.17 | % 16.49/3.17 | GROUND_INST: instantiating (5) with all_54_0, all_56_0, simplifying with (39), % 16.49/3.17 | (40), (41) gives: % 16.49/3.18 | (44) ? [v0: $i] : (vplus(all_54_0, v0) = all_56_0 & $i(v0)) % 16.49/3.18 | % 16.49/3.18 | GROUND_INST: instantiating (6) with all_54_0, all_65_1, all_68_0, simplifying % 16.49/3.18 | with (37), (40), (43) gives: % 16.49/3.18 | (45) all_68_0 = 0 | ! [v0: $i] : ( ~ (vplus(all_54_0, v0) = all_65_1) | ~ % 16.49/3.18 | $i(v0)) % 16.49/3.18 | % 16.49/3.18 | GROUND_INST: instantiating (5) with all_56_0, all_65_1, simplifying with (38), % 16.49/3.18 | (41), (43) gives: % 16.49/3.18 | (46) ? [v0: $i] : (vplus(all_56_0, v0) = all_65_1 & $i(v0)) % 16.49/3.18 | % 16.49/3.18 | DELTA: instantiating (44) with fresh symbol all_82_0 gives: % 16.49/3.18 | (47) vplus(all_54_0, all_82_0) = all_56_0 & $i(all_82_0) % 16.49/3.18 | % 16.49/3.18 | ALPHA: (47) implies: % 16.66/3.18 | (48) $i(all_82_0) % 16.66/3.18 | (49) vplus(all_54_0, all_82_0) = all_56_0 % 16.66/3.18 | % 16.66/3.18 | DELTA: instantiating (46) with fresh symbol all_86_0 gives: % 16.66/3.18 | (50) vplus(all_56_0, all_86_0) = all_65_1 & $i(all_86_0) % 16.66/3.18 | % 16.66/3.18 | ALPHA: (50) implies: % 16.66/3.18 | (51) $i(all_86_0) % 16.66/3.18 | (52) vplus(all_56_0, all_86_0) = all_65_1 % 16.66/3.18 | % 16.66/3.18 | BETA: splitting (45) gives: % 16.66/3.18 | % 16.66/3.18 | Case 1: % 16.66/3.18 | | % 16.66/3.18 | | (53) all_68_0 = 0 % 16.66/3.18 | | % 16.66/3.18 | | REDUCE: (28), (53) imply: % 16.66/3.18 | | (54) $false % 16.66/3.18 | | % 16.66/3.18 | | CLOSE: (54) is inconsistent. % 16.66/3.18 | | % 16.66/3.18 | Case 2: % 16.66/3.18 | | % 16.66/3.18 | | (55) ! [v0: $i] : ( ~ (vplus(all_54_0, v0) = all_65_1) | ~ $i(v0)) % 16.66/3.18 | | % 16.66/3.19 | | GROUND_INST: instantiating (ass(cond(33, 0), 0)) with all_54_0, all_82_0, % 16.66/3.19 | | all_86_0, all_56_0, all_65_1, simplifying with (40), (48), % 16.66/3.19 | | (49), (51), (52) gives: % 16.66/3.19 | | (56) ? [v0: $i] : (vplus(all_82_0, all_86_0) = v0 & vplus(all_54_0, v0) % 16.66/3.19 | | = all_65_1 & $i(v0) & $i(all_65_1)) % 16.66/3.19 | | % 16.66/3.19 | | DELTA: instantiating (56) with fresh symbol all_101_0 gives: % 16.66/3.19 | | (57) vplus(all_82_0, all_86_0) = all_101_0 & vplus(all_54_0, all_101_0) = % 16.66/3.19 | | all_65_1 & $i(all_101_0) & $i(all_65_1) % 16.66/3.19 | | % 16.66/3.19 | | ALPHA: (57) implies: % 16.66/3.19 | | (58) $i(all_101_0) % 16.66/3.19 | | (59) vplus(all_54_0, all_101_0) = all_65_1 % 16.66/3.19 | | % 16.66/3.19 | | GROUND_INST: instantiating (55) with all_101_0, simplifying with (58), (59) % 16.66/3.19 | | gives: % 16.66/3.19 | | (60) $false % 16.66/3.19 | | % 16.66/3.19 | | CLOSE: (60) is inconsistent. % 16.66/3.19 | | % 16.66/3.19 | End of split % 16.66/3.19 | % 16.66/3.19 End of proof % 16.66/3.19 % SZS output end Proof for theBenchmark % 16.66/3.19 % 16.66/3.19 2559ms %------------------------------------------------------------------------------