%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : NUM855+1 : TPTP v8.1.2. Released v4.1.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n009.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 10.57s 2.12s % Output : Proof 12.45s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.06/0.12 % Problem : NUM855+1 : TPTP v8.1.2. Released v4.1.0. % 0.06/0.12 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.12/0.33 % Computer : n009.cluster.edu % 0.12/0.33 % Model : x86_64 x86_64 % 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.33 % Memory : 8042.1875MB % 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.33 % CPULimit : 300 % 0.12/0.33 % WCLimit : 300 % 0.12/0.33 % DateTime : Fri Aug 25 14:31:21 EDT 2023 % 0.12/0.33 % CPUTime : % 0.19/0.59 ________ _____ % 0.19/0.59 ___ __ \_________(_)________________________________ % 0.19/0.59 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.19/0.59 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.19/0.59 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.19/0.59 % 0.19/0.59 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.19/0.59 (2023-06-19) % 0.19/0.59 % 0.19/0.59 (c) Philipp Rümmer, 2009-2023 % 0.19/0.59 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.19/0.59 Amanda Stjerna. % 0.19/0.59 Free software under BSD-3-Clause. % 0.19/0.59 % 0.19/0.59 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.19/0.59 % 0.19/0.60 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.19/0.61 Running up to 7 provers in parallel. % 0.19/0.62 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.19/0.62 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.19/0.62 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.19/0.62 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.19/0.62 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.19/0.62 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.19/0.62 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 3.51/1.15 Prover 1: Preprocessing ... % 3.51/1.15 Prover 4: Preprocessing ... % 3.51/1.19 Prover 5: Preprocessing ... % 3.51/1.19 Prover 2: Preprocessing ... % 3.51/1.20 Prover 3: Preprocessing ... % 3.51/1.20 Prover 0: Preprocessing ... % 3.51/1.21 Prover 6: Preprocessing ... % 7.55/1.70 Prover 1: Warning: ignoring some quantifiers % 7.68/1.77 Prover 5: Proving ... % 7.68/1.78 Prover 1: Constructing countermodel ... % 7.68/1.79 Prover 6: Proving ... % 7.68/1.80 Prover 3: Warning: ignoring some quantifiers % 8.42/1.84 Prover 4: Warning: ignoring some quantifiers % 8.42/1.84 Prover 3: Constructing countermodel ... % 8.99/1.95 Prover 4: Constructing countermodel ... % 8.99/1.96 Prover 0: Proving ... % 9.58/2.00 Prover 2: Proving ... % 10.57/2.11 Prover 3: proved (1492ms) % 10.57/2.11 % 10.57/2.12 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 10.57/2.12 % 10.57/2.12 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 10.57/2.12 Prover 2: stopped % 10.57/2.12 Prover 5: stopped % 10.57/2.12 Prover 0: stopped % 10.57/2.12 Prover 6: stopped % 10.57/2.13 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 10.57/2.13 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 10.57/2.13 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 10.57/2.13 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 10.57/2.20 Prover 11: Preprocessing ... % 10.57/2.20 Prover 7: Preprocessing ... % 10.57/2.20 Prover 13: Preprocessing ... % 10.57/2.21 Prover 8: Preprocessing ... % 11.29/2.22 Prover 10: Preprocessing ... % 11.29/2.23 Prover 1: Found proof (size 45) % 11.29/2.23 Prover 1: proved (1614ms) % 11.29/2.23 Prover 4: stopped % 11.29/2.25 Prover 7: stopped % 11.29/2.27 Prover 10: stopped % 11.29/2.27 Prover 13: stopped % 11.29/2.28 Prover 11: stopped % 11.88/2.36 Prover 8: Warning: ignoring some quantifiers % 11.88/2.37 Prover 8: Constructing countermodel ... % 12.30/2.38 Prover 8: stopped % 12.30/2.38 % 12.30/2.38 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 12.30/2.38 % 12.30/2.40 % SZS output start Proof for theBenchmark % 12.38/2.40 Assumptions after simplification: % 12.38/2.40 --------------------------------- % 12.38/2.40 % 12.38/2.40 (ass(cond(270, 0), 0)) % 12.45/2.43 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (vmul(v0, v1) = v2) | ~ $i(v1) % 12.45/2.43 | ~ $i(v0) | (vmul(v1, v0) = v2 & $i(v2))) % 12.45/2.43 % 12.45/2.43 (ass(cond(33, 0), 0)) % 12.45/2.43 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 12.45/2.43 (vplus(v3, v2) = v4) | ~ (vplus(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ % 12.45/2.43 $i(v0) | ? [v5: $i] : (vplus(v1, v2) = v5 & vplus(v0, v5) = v4 & $i(v5) & % 12.45/2.43 $i(v4))) % 12.45/2.43 % 12.45/2.43 (def(cond(conseq(axiom(3)), 11), 1)) % 12.45/2.43 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (greater(v1, v0) = v2) % 12.45/2.43 | ~ $i(v1) | ~ $i(v0) | ! [v3: $i] : ( ~ (vplus(v0, v3) = v1) | ~ % 12.45/2.43 $i(v3))) & ! [v0: $i] : ! [v1: $i] : ( ~ (greater(v1, v0) = 0) | ~ % 12.45/2.43 $i(v1) | ~ $i(v0) | ? [v2: $i] : (vplus(v0, v2) = v1 & $i(v2))) % 12.45/2.43 % 12.45/2.43 (holds(conjunct1(315), 514, 0)) % 12.45/2.43 $i(vd509) & $i(vd511) & $i(vd508) & ? [v0: $i] : ? [v1: $i] : (greater(v0, % 12.45/2.43 v1) = 0 & vmul(vd509, vd511) = v1 & vmul(vd508, vd511) = v0 & $i(v1) & % 12.45/2.43 $i(v0)) % 12.45/2.43 % 12.45/2.43 (holds(conjunct2(315), 515, 0)) % 12.45/2.43 $i(vd509) & $i(vd511) & ? [v0: $i] : (vmul(vd509, vd511) = v0 & vmul(vd511, % 12.45/2.43 vd509) = v0 & $i(v0)) % 12.45/2.43 % 12.45/2.43 (holds(conjunct2(315), 515, 1)) % 12.45/2.43 $i(vd512) & $i(vd509) & $i(vd511) & ? [v0: $i] : ? [v1: $i] : (greater(v0, % 12.45/2.43 v1) = 0 & vmul(vd512, vd509) = v1 & vmul(vd511, vd509) = v0 & $i(v1) & % 12.45/2.43 $i(v0)) % 12.45/2.43 % 12.45/2.43 (holds(conjunct2(315), 515, 2)) % 12.45/2.44 $i(vd512) & $i(vd509) & ? [v0: $i] : (vmul(vd512, vd509) = v0 & vmul(vd509, % 12.45/2.44 vd512) = v0 & $i(v0)) % 12.45/2.44 % 12.45/2.44 (holds(conseq_conjunct2(315), 516, 0)) % 12.45/2.44 $i(vd512) & $i(vd509) & $i(vd511) & $i(vd508) & ? [v0: $i] : ? [v1: $i] : ? % 12.45/2.44 [v2: int] : ( ~ (v2 = 0) & greater(v0, v1) = v2 & vmul(vd509, vd512) = v1 & % 12.45/2.44 vmul(vd508, vd511) = v0 & $i(v1) & $i(v0)) % 12.45/2.44 % 12.45/2.44 (function-axioms) % 12.45/2.44 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 12.45/2.44 [v3: $i] : (v1 = v0 | ~ (geq(v3, v2) = v1) | ~ (geq(v3, v2) = v0)) & ! [v0: % 12.45/2.44 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 12.45/2.44 : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = v0)) & ! [v0: $i] : ! % 12.45/2.44 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (vplus(v3, v2) = v1) | ~ % 12.45/2.44 (vplus(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 12.45/2.44 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (less(v3, v2) % 12.45/2.44 = v1) | ~ (less(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 12.45/2.44 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (greater(v3, % 12.45/2.44 v2) = v1) | ~ (greater(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 12.45/2.44 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (vmul(v3, v2) = v1) | ~ (vmul(v3, v2) % 12.45/2.44 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 12.45/2.44 (vskolem2(v2) = v1) | ~ (vskolem2(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : % 12.45/2.44 ! [v2: $i] : (v1 = v0 | ~ (vsucc(v2) = v1) | ~ (vsucc(v2) = v0)) % 12.45/2.44 % 12.45/2.44 Further assumptions not needed in the proof: % 12.45/2.44 -------------------------------------------- % 12.45/2.44 ass(cond(12, 0), 0), ass(cond(140, 0), 0), ass(cond(147, 0), 0), ass(cond(158, % 12.45/2.44 0), 0), ass(cond(163, 0), 0), ass(cond(168, 0), 0), ass(cond(184, 0), 0), % 12.45/2.44 ass(cond(189, 0), 0), ass(cond(20, 0), 0), ass(cond(209, 0), 0), ass(cond(223, % 12.45/2.44 0), 0), ass(cond(228, 0), 0), ass(cond(234, 0), 0), ass(cond(241, 0), 0), % 12.45/2.44 ass(cond(253, 0), 0), ass(cond(261, 0), 0), ass(cond(281, 0), 0), ass(cond(290, % 12.45/2.44 0), 0), ass(cond(299, 0), 0), ass(cond(299, 0), 1), ass(cond(299, 0), 2), % 12.45/2.44 ass(cond(43, 0), 0), ass(cond(52, 0), 0), ass(cond(6, 0), 0), ass(cond(61, 0), % 12.45/2.44 0), ass(cond(73, 0), 0), ass(cond(81, 0), 0), ass(cond(conjunct1(307), 0), 0), % 12.45/2.44 ass(cond(conjunct1(conjunct2(307)), 0), 0), ass(cond(conjunct2(conjunct2(307)), % 12.45/2.44 0), 0), ass(cond(goal(130), 0), 0), ass(cond(goal(130), 0), 1), % 12.45/2.44 ass(cond(goal(130), 0), 2), ass(cond(goal(130), 0), 3), ass(cond(goal(177), 0), % 12.45/2.44 0), ass(cond(goal(193), 0), 0), ass(cond(goal(193), 0), 1), % 12.45/2.44 ass(cond(goal(193), 0), 2), ass(cond(goal(202), 0), 0), ass(cond(goal(202), 0), % 12.45/2.44 1), ass(cond(goal(202), 0), 2), ass(cond(goal(216), 0), 0), ass(cond(goal(88), % 12.45/2.44 0), 0), ass(cond(goal(88), 0), 1), ass(cond(goal(88), 0), 2), % 12.45/2.44 ass(cond(goal(88), 0), 3), def(cond(conseq(axiom(3)), 12), 1), % 12.45/2.44 def(cond(conseq(axiom(3)), 16), 1), def(cond(conseq(axiom(3)), 17), 1), % 12.45/2.44 holds(conjunct1(314), 510, 0), holds(conjunct2(314), 513, 0), % 12.45/2.44 qu(antec(axiom(3)), imp(antec(axiom(3)))), qu(cond(conseq(axiom(3)), 3), % 12.45/2.44 and(holds(definiens(29), 45, 0), holds(definiens(29), 44, 0))), % 12.45/2.44 qu(cond(conseq(axiom(3)), 32), and(holds(definiens(249), 399, 0), % 12.45/2.44 holds(definiens(249), 398, 0))), qu(restrictor(axiom(1)), % 12.45/2.44 holds(scope(axiom(1)), 2, 0)) % 12.45/2.44 % 12.45/2.44 Those formulas are unsatisfiable: % 12.45/2.44 --------------------------------- % 12.45/2.44 % 12.45/2.44 Begin of proof % 12.45/2.44 | % 12.45/2.44 | ALPHA: (holds(conjunct2(315), 515, 2)) implies: % 12.45/2.44 | (1) ? [v0: $i] : (vmul(vd512, vd509) = v0 & vmul(vd509, vd512) = v0 & % 12.45/2.44 | $i(v0)) % 12.45/2.44 | % 12.45/2.44 | ALPHA: (holds(conjunct2(315), 515, 1)) implies: % 12.45/2.45 | (2) ? [v0: $i] : ? [v1: $i] : (greater(v0, v1) = 0 & vmul(vd512, vd509) = % 12.45/2.45 | v1 & vmul(vd511, vd509) = v0 & $i(v1) & $i(v0)) % 12.45/2.45 | % 12.45/2.45 | ALPHA: (holds(conjunct2(315), 515, 0)) implies: % 12.45/2.45 | (3) ? [v0: $i] : (vmul(vd509, vd511) = v0 & vmul(vd511, vd509) = v0 & % 12.45/2.45 | $i(v0)) % 12.45/2.45 | % 12.45/2.45 | ALPHA: (holds(conjunct1(315), 514, 0)) implies: % 12.45/2.45 | (4) ? [v0: $i] : ? [v1: $i] : (greater(v0, v1) = 0 & vmul(vd509, vd511) = % 12.45/2.45 | v1 & vmul(vd508, vd511) = v0 & $i(v1) & $i(v0)) % 12.45/2.45 | % 12.45/2.45 | ALPHA: (def(cond(conseq(axiom(3)), 11), 1)) implies: % 12.45/2.45 | (5) ! [v0: $i] : ! [v1: $i] : ( ~ (greater(v1, v0) = 0) | ~ $i(v1) | ~ % 12.45/2.45 | $i(v0) | ? [v2: $i] : (vplus(v0, v2) = v1 & $i(v2))) % 12.45/2.45 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (greater(v1, % 12.45/2.45 | v0) = v2) | ~ $i(v1) | ~ $i(v0) | ! [v3: $i] : ( ~ (vplus(v0, % 12.45/2.45 | v3) = v1) | ~ $i(v3))) % 12.45/2.45 | % 12.45/2.45 | ALPHA: (holds(conseq_conjunct2(315), 516, 0)) implies: % 12.45/2.45 | (7) $i(vd508) % 12.45/2.45 | (8) $i(vd511) % 12.45/2.45 | (9) ? [v0: $i] : ? [v1: $i] : ? [v2: int] : ( ~ (v2 = 0) & greater(v0, % 12.45/2.45 | v1) = v2 & vmul(vd509, vd512) = v1 & vmul(vd508, vd511) = v0 & % 12.45/2.45 | $i(v1) & $i(v0)) % 12.45/2.45 | % 12.45/2.45 | ALPHA: (function-axioms) implies: % 12.45/2.45 | (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 12.45/2.45 | (vmul(v3, v2) = v1) | ~ (vmul(v3, v2) = v0)) % 12.45/2.45 | % 12.45/2.45 | DELTA: instantiating (1) with fresh symbol all_54_0 gives: % 12.45/2.45 | (11) vmul(vd512, vd509) = all_54_0 & vmul(vd509, vd512) = all_54_0 & % 12.45/2.45 | $i(all_54_0) % 12.45/2.45 | % 12.45/2.45 | ALPHA: (11) implies: % 12.45/2.45 | (12) vmul(vd509, vd512) = all_54_0 % 12.45/2.45 | (13) vmul(vd512, vd509) = all_54_0 % 12.45/2.45 | % 12.45/2.45 | DELTA: instantiating (3) with fresh symbol all_56_0 gives: % 12.45/2.45 | (14) vmul(vd509, vd511) = all_56_0 & vmul(vd511, vd509) = all_56_0 & % 12.45/2.45 | $i(all_56_0) % 12.45/2.45 | % 12.45/2.45 | ALPHA: (14) implies: % 12.45/2.45 | (15) vmul(vd511, vd509) = all_56_0 % 12.45/2.45 | (16) vmul(vd509, vd511) = all_56_0 % 12.45/2.45 | % 12.45/2.45 | DELTA: instantiating (2) with fresh symbols all_63_0, all_63_1 gives: % 12.45/2.45 | (17) greater(all_63_1, all_63_0) = 0 & vmul(vd512, vd509) = all_63_0 & % 12.45/2.45 | vmul(vd511, vd509) = all_63_1 & $i(all_63_0) & $i(all_63_1) % 12.45/2.45 | % 12.45/2.45 | ALPHA: (17) implies: % 12.45/2.45 | (18) $i(all_63_1) % 12.45/2.45 | (19) $i(all_63_0) % 12.45/2.45 | (20) vmul(vd511, vd509) = all_63_1 % 12.45/2.45 | (21) vmul(vd512, vd509) = all_63_0 % 12.45/2.46 | (22) greater(all_63_1, all_63_0) = 0 % 12.45/2.46 | % 12.45/2.46 | DELTA: instantiating (4) with fresh symbols all_65_0, all_65_1 gives: % 12.45/2.46 | (23) greater(all_65_1, all_65_0) = 0 & vmul(vd509, vd511) = all_65_0 & % 12.45/2.46 | vmul(vd508, vd511) = all_65_1 & $i(all_65_0) & $i(all_65_1) % 12.45/2.46 | % 12.45/2.46 | ALPHA: (23) implies: % 12.45/2.46 | (24) vmul(vd508, vd511) = all_65_1 % 12.45/2.46 | (25) vmul(vd509, vd511) = all_65_0 % 12.45/2.46 | (26) greater(all_65_1, all_65_0) = 0 % 12.45/2.46 | % 12.45/2.46 | DELTA: instantiating (9) with fresh symbols all_68_0, all_68_1, all_68_2 % 12.45/2.46 | gives: % 12.45/2.46 | (27) ~ (all_68_0 = 0) & greater(all_68_2, all_68_1) = all_68_0 & % 12.45/2.46 | vmul(vd509, vd512) = all_68_1 & vmul(vd508, vd511) = all_68_2 & % 12.45/2.46 | $i(all_68_1) & $i(all_68_2) % 12.45/2.46 | % 12.45/2.46 | ALPHA: (27) implies: % 12.45/2.46 | (28) ~ (all_68_0 = 0) % 12.45/2.46 | (29) vmul(vd508, vd511) = all_68_2 % 12.45/2.46 | (30) vmul(vd509, vd512) = all_68_1 % 12.45/2.46 | (31) greater(all_68_2, all_68_1) = all_68_0 % 12.45/2.46 | % 12.45/2.46 | GROUND_INST: instantiating (10) with all_65_1, all_68_2, vd511, vd508, % 12.45/2.46 | simplifying with (24), (29) gives: % 12.45/2.46 | (32) all_68_2 = all_65_1 % 12.45/2.46 | % 12.45/2.46 | GROUND_INST: instantiating (10) with all_56_0, all_63_1, vd509, vd511, % 12.45/2.46 | simplifying with (15), (20) gives: % 12.45/2.46 | (33) all_63_1 = all_56_0 % 12.45/2.46 | % 12.45/2.46 | GROUND_INST: instantiating (10) with all_56_0, all_65_0, vd511, vd509, % 12.45/2.46 | simplifying with (16), (25) gives: % 12.45/2.46 | (34) all_65_0 = all_56_0 % 12.45/2.46 | % 12.45/2.46 | GROUND_INST: instantiating (10) with all_54_0, all_68_1, vd512, vd509, % 12.45/2.46 | simplifying with (12), (30) gives: % 12.45/2.46 | (35) all_68_1 = all_54_0 % 12.45/2.46 | % 12.45/2.46 | GROUND_INST: instantiating (10) with all_54_0, all_63_0, vd509, vd512, % 12.45/2.46 | simplifying with (13), (21) gives: % 12.45/2.46 | (36) all_63_0 = all_54_0 % 12.45/2.46 | % 12.45/2.46 | REDUCE: (31), (32), (35) imply: % 12.45/2.46 | (37) greater(all_65_1, all_54_0) = all_68_0 % 12.45/2.46 | % 12.45/2.46 | REDUCE: (26), (34) imply: % 12.45/2.46 | (38) greater(all_65_1, all_56_0) = 0 % 12.45/2.46 | % 12.45/2.46 | REDUCE: (22), (33), (36) imply: % 12.45/2.46 | (39) greater(all_56_0, all_54_0) = 0 % 12.45/2.46 | % 12.45/2.46 | REDUCE: (19), (36) imply: % 12.45/2.46 | (40) $i(all_54_0) % 12.45/2.46 | % 12.45/2.46 | REDUCE: (18), (33) imply: % 12.45/2.46 | (41) $i(all_56_0) % 12.45/2.46 | % 12.45/2.46 | GROUND_INST: instantiating (ass(cond(270, 0), 0)) with vd508, vd511, all_65_1, % 12.45/2.46 | simplifying with (7), (8), (24) gives: % 12.45/2.46 | (42) vmul(vd511, vd508) = all_65_1 & $i(all_65_1) % 12.45/2.46 | % 12.45/2.46 | ALPHA: (42) implies: % 12.45/2.46 | (43) $i(all_65_1) % 12.45/2.46 | % 12.45/2.46 | GROUND_INST: instantiating (5) with all_54_0, all_56_0, simplifying with (39), % 12.45/2.46 | (40), (41) gives: % 12.45/2.46 | (44) ? [v0: $i] : (vplus(all_54_0, v0) = all_56_0 & $i(v0)) % 12.45/2.46 | % 12.45/2.46 | GROUND_INST: instantiating (6) with all_54_0, all_65_1, all_68_0, simplifying % 12.45/2.46 | with (37), (40), (43) gives: % 12.45/2.47 | (45) all_68_0 = 0 | ! [v0: $i] : ( ~ (vplus(all_54_0, v0) = all_65_1) | ~ % 12.45/2.47 | $i(v0)) % 12.45/2.47 | % 12.45/2.47 | GROUND_INST: instantiating (5) with all_56_0, all_65_1, simplifying with (38), % 12.45/2.47 | (41), (43) gives: % 12.45/2.47 | (46) ? [v0: $i] : (vplus(all_56_0, v0) = all_65_1 & $i(v0)) % 12.45/2.47 | % 12.45/2.47 | DELTA: instantiating (44) with fresh symbol all_82_0 gives: % 12.45/2.47 | (47) vplus(all_54_0, all_82_0) = all_56_0 & $i(all_82_0) % 12.45/2.47 | % 12.45/2.47 | ALPHA: (47) implies: % 12.45/2.47 | (48) $i(all_82_0) % 12.45/2.47 | (49) vplus(all_54_0, all_82_0) = all_56_0 % 12.45/2.47 | % 12.45/2.47 | DELTA: instantiating (46) with fresh symbol all_86_0 gives: % 12.45/2.47 | (50) vplus(all_56_0, all_86_0) = all_65_1 & $i(all_86_0) % 12.45/2.47 | % 12.45/2.47 | ALPHA: (50) implies: % 12.45/2.47 | (51) $i(all_86_0) % 12.45/2.47 | (52) vplus(all_56_0, all_86_0) = all_65_1 % 12.45/2.47 | % 12.45/2.47 | BETA: splitting (45) gives: % 12.45/2.47 | % 12.45/2.47 | Case 1: % 12.45/2.47 | | % 12.45/2.47 | | (53) all_68_0 = 0 % 12.45/2.47 | | % 12.45/2.47 | | REDUCE: (28), (53) imply: % 12.45/2.47 | | (54) $false % 12.45/2.47 | | % 12.45/2.47 | | CLOSE: (54) is inconsistent. % 12.45/2.47 | | % 12.45/2.47 | Case 2: % 12.45/2.47 | | % 12.45/2.47 | | (55) ! [v0: $i] : ( ~ (vplus(all_54_0, v0) = all_65_1) | ~ $i(v0)) % 12.45/2.47 | | % 12.45/2.47 | | GROUND_INST: instantiating (ass(cond(33, 0), 0)) with all_54_0, all_82_0, % 12.45/2.47 | | all_86_0, all_56_0, all_65_1, simplifying with (40), (48), % 12.45/2.47 | | (49), (51), (52) gives: % 12.45/2.47 | | (56) ? [v0: $i] : (vplus(all_82_0, all_86_0) = v0 & vplus(all_54_0, v0) % 12.45/2.47 | | = all_65_1 & $i(v0) & $i(all_65_1)) % 12.45/2.47 | | % 12.45/2.47 | | DELTA: instantiating (56) with fresh symbol all_101_0 gives: % 12.45/2.47 | | (57) vplus(all_82_0, all_86_0) = all_101_0 & vplus(all_54_0, all_101_0) = % 12.45/2.47 | | all_65_1 & $i(all_101_0) & $i(all_65_1) % 12.45/2.47 | | % 12.45/2.47 | | ALPHA: (57) implies: % 12.45/2.47 | | (58) $i(all_101_0) % 12.45/2.47 | | (59) vplus(all_54_0, all_101_0) = all_65_1 % 12.45/2.47 | | % 12.45/2.47 | | GROUND_INST: instantiating (55) with all_101_0, simplifying with (58), (59) % 12.45/2.47 | | gives: % 12.45/2.47 | | (60) $false % 12.45/2.47 | | % 12.45/2.47 | | CLOSE: (60) is inconsistent. % 12.45/2.47 | | % 12.45/2.47 | End of split % 12.45/2.47 | % 12.45/2.47 End of proof % 12.45/2.47 % SZS output end Proof for theBenchmark % 12.45/2.47 % 12.45/2.47 1876ms %------------------------------------------------------------------------------