%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : NUM856+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 11:50:27 EDT 2023 % Result : Theorem 12.49s 2.57s % Output : Proof 16.86s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.13 % Problem : NUM856+1 : TPTP v8.1.2. Released v4.1.0. % 0.07/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.34 % Computer : n009.cluster.edu % 0.13/0.34 % Model : x86_64 x86_64 % 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.34 % Memory : 8042.1875MB % 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.34 % CPULimit : 300 % 0.13/0.34 % WCLimit : 300 % 0.13/0.34 % DateTime : Fri Aug 25 15:56:35 EDT 2023 % 0.13/0.34 % CPUTime : % 0.21/0.62 ________ _____ % 0.21/0.62 ___ __ \_________(_)________________________________ % 0.21/0.62 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.21/0.62 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.21/0.62 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.21/0.62 % 0.21/0.62 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.21/0.62 (2023-06-19) % 0.21/0.62 % 0.21/0.62 (c) Philipp Rümmer, 2009-2023 % 0.21/0.62 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.21/0.62 Amanda Stjerna. % 0.21/0.62 Free software under BSD-3-Clause. % 0.21/0.63 % 0.21/0.63 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.21/0.63 % 0.21/0.63 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.21/0.64 Running up to 7 provers in parallel. % 0.64/0.67 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.64/0.67 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.64/0.67 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.64/0.67 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.64/0.67 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.64/0.67 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.64/0.67 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 2.99/1.22 Prover 4: Preprocessing ... % 2.99/1.23 Prover 1: Preprocessing ... % 2.99/1.25 Prover 5: Preprocessing ... % 2.99/1.25 Prover 3: Preprocessing ... % 2.99/1.25 Prover 2: Preprocessing ... % 2.99/1.25 Prover 6: Preprocessing ... % 2.99/1.27 Prover 0: Preprocessing ... % 8.25/1.98 Prover 1: Warning: ignoring some quantifiers % 9.20/2.03 Prover 5: Proving ... % 9.20/2.05 Prover 4: Warning: ignoring some quantifiers % 9.20/2.06 Prover 6: Proving ... % 9.20/2.06 Prover 3: Warning: ignoring some quantifiers % 9.53/2.07 Prover 1: Constructing countermodel ... % 9.53/2.09 Prover 3: Constructing countermodel ... % 9.53/2.11 Prover 2: Proving ... % 9.53/2.14 Prover 0: Proving ... % 9.53/2.14 Prover 4: Constructing countermodel ... % 12.49/2.56 Prover 5: proved (1904ms) % 12.49/2.57 % 12.49/2.57 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 12.49/2.57 % 12.49/2.57 Prover 3: stopped % 12.49/2.57 Prover 0: stopped % 12.49/2.57 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 12.49/2.57 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 12.49/2.57 Prover 6: stopped % 12.49/2.57 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 12.49/2.58 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 12.49/2.58 Prover 2: stopped % 12.49/2.59 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 13.51/2.68 Prover 7: Preprocessing ... % 13.51/2.69 Prover 11: Preprocessing ... % 13.51/2.69 Prover 10: Preprocessing ... % 13.97/2.70 Prover 13: Preprocessing ... % 13.97/2.70 Prover 8: Preprocessing ... % 15.22/2.88 Prover 8: Warning: ignoring some quantifiers % 15.22/2.89 Prover 13: Warning: ignoring some quantifiers % 15.22/2.89 Prover 10: Warning: ignoring some quantifiers % 15.49/2.90 Prover 8: Constructing countermodel ... % 15.49/2.90 Prover 7: Warning: ignoring some quantifiers % 15.49/2.91 Prover 13: Constructing countermodel ... % 15.49/2.92 Prover 10: Constructing countermodel ... % 15.49/2.92 Prover 1: Found proof (size 168) % 15.49/2.92 Prover 1: proved (2265ms) % 15.49/2.92 Prover 7: Constructing countermodel ... % 15.49/2.93 Prover 10: stopped % 15.49/2.93 Prover 13: stopped % 15.76/2.93 Prover 7: stopped % 15.77/2.93 Prover 4: stopped % 15.77/2.94 Prover 8: stopped % 15.77/2.99 Prover 11: Warning: ignoring some quantifiers % 16.08/3.00 Prover 11: Constructing countermodel ... % 16.08/3.02 Prover 11: stopped % 16.08/3.02 % 16.08/3.02 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 16.08/3.02 % 16.08/3.03 % SZS output start Proof for theBenchmark % 16.08/3.04 Assumptions after simplification: % 16.08/3.04 --------------------------------- % 16.08/3.04 % 16.08/3.04 (ass(cond(270, 0), 0)) % 16.38/3.07 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (vmul(v0, v1) = v2) | ~ $i(v1) % 16.38/3.07 | ~ $i(v0) | (vmul(v1, v0) = v2 & $i(v2))) % 16.38/3.07 % 16.38/3.07 (ass(cond(299, 0), 2)) % 16.38/3.08 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 16.38/3.08 int] : (v5 = 0 | ~ (vmul(v2, v0) = v4) | ~ (vmul(v1, v0) = v3) | ~ % 16.38/3.08 (greater(v3, v4) = v5) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: int] : % 16.38/3.08 ( ~ (v6 = 0) & greater(v1, v2) = v6)) % 16.38/3.08 % 16.38/3.08 (ass(cond(312, 0), 0)) % 16.38/3.08 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 16.38/3.08 $i] : ! [v6: int] : (v6 = 0 | ~ (vmul(v1, v3) = v5) | ~ (vmul(v0, v2) = % 16.38/3.08 v4) | ~ (greater(v4, v5) = v6) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ % 16.38/3.08 $i(v0) | ? [v7: any] : ? [v8: any] : (greater(v2, v3) = v7 & greater(v0, % 16.38/3.08 v1) = v8 & ( ~ (v8 = 0) | ~ (v7 = 0)))) % 16.38/3.08 % 16.38/3.08 (def(cond(conseq(axiom(3)), 16), 1)) % 16.38/3.09 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (geq(v1, v0) = v2) | % 16.38/3.09 ~ $i(v1) | ~ $i(v0) | ( ~ (v1 = v0) & ? [v3: int] : ( ~ (v3 = 0) & % 16.38/3.09 greater(v1, v0) = v3))) & ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ % 16.38/3.09 (geq(v1, v0) = 0) | ~ $i(v1) | ~ $i(v0) | greater(v1, v0) = 0) % 16.38/3.09 % 16.38/3.09 (dis(antec(scope(318)))) % 16.38/3.09 $i(vd520) & $i(vd518) & $i(vd519) & $i(vd517) & ? [v0: any] : ? [v1: any] : % 16.38/3.09 ? [v2: any] : ? [v3: any] : (geq(vd519, vd520) = v2 & geq(vd517, vd518) = v1 % 16.38/3.09 & greater(vd519, vd520) = v0 & greater(vd517, vd518) = v3 & ((v3 = 0 & v2 = % 16.38/3.09 0) | (v1 = 0 & v0 = 0))) % 16.38/3.09 % 16.38/3.09 (holds(conseq(scope(318)), 525, 0)) % 16.38/3.09 $i(vd520) & $i(vd518) & $i(vd519) & $i(vd517) & ? [v0: $i] : ? [v1: $i] : ? % 16.38/3.09 [v2: int] : ( ~ (v2 = 0) & vmul(vd518, vd520) = v1 & vmul(vd517, vd519) = v0 & % 16.38/3.09 greater(v0, v1) = v2 & $i(v1) & $i(v0)) % 16.38/3.09 % 16.38/3.09 (function-axioms) % 16.38/3.10 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 16.38/3.10 [v3: $i] : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = v0)) & ! [v0: % 16.38/3.10 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (vplus(v3, v2) % 16.38/3.10 = v1) | ~ (vplus(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 16.38/3.10 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (less(v3, v2) % 16.38/3.10 = v1) | ~ (less(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] % 16.38/3.10 : ! [v3: $i] : (v1 = v0 | ~ (vmul(v3, v2) = v1) | ~ (vmul(v3, v2) = v0)) & % 16.38/3.10 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 16.38/3.10 $i] : (v1 = v0 | ~ (geq(v3, v2) = v1) | ~ (geq(v3, v2) = v0)) & ! [v0: % 16.38/3.10 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 16.38/3.10 : (v1 = v0 | ~ (greater(v3, v2) = v1) | ~ (greater(v3, v2) = v0)) & ! [v0: % 16.38/3.10 $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (vskolem2(v2) = v1) | ~ % 16.38/3.10 (vskolem2(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | % 16.38/3.10 ~ (vsucc(v2) = v1) | ~ (vsucc(v2) = v0)) % 16.38/3.10 % 16.38/3.10 Further assumptions not needed in the proof: % 16.38/3.10 -------------------------------------------- % 16.38/3.10 ass(cond(12, 0), 0), ass(cond(140, 0), 0), ass(cond(147, 0), 0), ass(cond(158, % 16.38/3.10 0), 0), ass(cond(163, 0), 0), ass(cond(168, 0), 0), ass(cond(184, 0), 0), % 16.38/3.10 ass(cond(189, 0), 0), ass(cond(20, 0), 0), ass(cond(209, 0), 0), ass(cond(223, % 16.38/3.10 0), 0), ass(cond(228, 0), 0), ass(cond(234, 0), 0), ass(cond(241, 0), 0), % 16.38/3.10 ass(cond(253, 0), 0), ass(cond(261, 0), 0), ass(cond(281, 0), 0), ass(cond(290, % 16.38/3.10 0), 0), ass(cond(299, 0), 0), ass(cond(299, 0), 1), ass(cond(33, 0), 0), % 16.38/3.10 ass(cond(43, 0), 0), ass(cond(52, 0), 0), ass(cond(6, 0), 0), ass(cond(61, 0), % 16.38/3.10 0), ass(cond(73, 0), 0), ass(cond(81, 0), 0), ass(cond(conjunct1(307), 0), 0), % 16.38/3.10 ass(cond(conjunct1(conjunct2(307)), 0), 0), ass(cond(conjunct2(conjunct2(307)), % 16.38/3.10 0), 0), ass(cond(goal(130), 0), 0), ass(cond(goal(130), 0), 1), % 16.38/3.10 ass(cond(goal(130), 0), 2), ass(cond(goal(130), 0), 3), ass(cond(goal(177), 0), % 16.38/3.10 0), ass(cond(goal(193), 0), 0), ass(cond(goal(193), 0), 1), % 16.38/3.10 ass(cond(goal(193), 0), 2), ass(cond(goal(202), 0), 0), ass(cond(goal(202), 0), % 16.38/3.10 1), ass(cond(goal(202), 0), 2), ass(cond(goal(216), 0), 0), ass(cond(goal(88), % 16.38/3.10 0), 0), ass(cond(goal(88), 0), 1), ass(cond(goal(88), 0), 2), % 16.38/3.10 ass(cond(goal(88), 0), 3), def(cond(conseq(axiom(3)), 11), 1), % 16.38/3.10 def(cond(conseq(axiom(3)), 12), 1), def(cond(conseq(axiom(3)), 17), 1), % 16.38/3.10 qu(antec(axiom(3)), imp(antec(axiom(3)))), qu(cond(conseq(axiom(3)), 3), % 16.38/3.10 and(holds(definiens(29), 45, 0), holds(definiens(29), 44, 0))), % 16.38/3.10 qu(cond(conseq(axiom(3)), 32), and(holds(definiens(249), 399, 0), % 16.38/3.10 holds(definiens(249), 398, 0))), qu(restrictor(axiom(1)), % 16.38/3.10 holds(scope(axiom(1)), 2, 0)) % 16.38/3.10 % 16.38/3.10 Those formulas are unsatisfiable: % 16.38/3.10 --------------------------------- % 16.38/3.10 % 16.38/3.10 Begin of proof % 16.38/3.10 | % 16.38/3.10 | ALPHA: (dis(antec(scope(318)))) implies: % 16.38/3.10 | (1) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] : (geq(vd519, % 16.38/3.10 | vd520) = v2 & geq(vd517, vd518) = v1 & greater(vd519, vd520) = v0 & % 16.38/3.10 | greater(vd517, vd518) = v3 & ((v3 = 0 & v2 = 0) | (v1 = 0 & v0 = 0))) % 16.38/3.10 | % 16.38/3.10 | ALPHA: (def(cond(conseq(axiom(3)), 16), 1)) implies: % 16.38/3.10 | (2) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (geq(v1, v0) = 0) | ~ $i(v1) % 16.38/3.10 | | ~ $i(v0) | greater(v1, v0) = 0) % 16.38/3.10 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (geq(v1, v0) = % 16.38/3.10 | v2) | ~ $i(v1) | ~ $i(v0) | ( ~ (v1 = v0) & ? [v3: int] : ( ~ % 16.38/3.10 | (v3 = 0) & greater(v1, v0) = v3))) % 16.38/3.10 | % 16.38/3.10 | ALPHA: (holds(conseq(scope(318)), 525, 0)) implies: % 16.38/3.10 | (4) $i(vd517) % 16.38/3.10 | (5) $i(vd519) % 16.38/3.10 | (6) $i(vd518) % 16.38/3.10 | (7) $i(vd520) % 16.38/3.11 | (8) ? [v0: $i] : ? [v1: $i] : ? [v2: int] : ( ~ (v2 = 0) & vmul(vd518, % 16.38/3.11 | vd520) = v1 & vmul(vd517, vd519) = v0 & greater(v0, v1) = v2 & % 16.38/3.11 | $i(v1) & $i(v0)) % 16.38/3.11 | % 16.38/3.11 | ALPHA: (function-axioms) implies: % 16.38/3.11 | (9) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 16.38/3.11 | ! [v3: $i] : (v1 = v0 | ~ (greater(v3, v2) = v1) | ~ (greater(v3, % 16.38/3.11 | v2) = v0)) % 16.38/3.11 | % 16.38/3.11 | DELTA: instantiating (8) with fresh symbols all_60_0, all_60_1, all_60_2 % 16.38/3.11 | gives: % 16.38/3.11 | (10) ~ (all_60_0 = 0) & vmul(vd518, vd520) = all_60_1 & vmul(vd517, vd519) % 16.38/3.11 | = all_60_2 & greater(all_60_2, all_60_1) = all_60_0 & $i(all_60_1) & % 16.38/3.11 | $i(all_60_2) % 16.38/3.11 | % 16.38/3.11 | ALPHA: (10) implies: % 16.38/3.11 | (11) ~ (all_60_0 = 0) % 16.38/3.11 | (12) greater(all_60_2, all_60_1) = all_60_0 % 16.38/3.11 | (13) vmul(vd517, vd519) = all_60_2 % 16.38/3.11 | (14) vmul(vd518, vd520) = all_60_1 % 16.38/3.11 | % 16.38/3.11 | DELTA: instantiating (1) with fresh symbols all_64_0, all_64_1, all_64_2, % 16.38/3.11 | all_64_3 gives: % 16.38/3.11 | (15) geq(vd519, vd520) = all_64_1 & geq(vd517, vd518) = all_64_2 & % 16.38/3.11 | greater(vd519, vd520) = all_64_3 & greater(vd517, vd518) = all_64_0 & % 16.38/3.11 | ((all_64_0 = 0 & all_64_1 = 0) | (all_64_2 = 0 & all_64_3 = 0)) % 16.38/3.11 | % 16.38/3.11 | ALPHA: (15) implies: % 16.38/3.11 | (16) greater(vd517, vd518) = all_64_0 % 16.38/3.11 | (17) greater(vd519, vd520) = all_64_3 % 16.38/3.11 | (18) geq(vd517, vd518) = all_64_2 % 16.38/3.11 | (19) geq(vd519, vd520) = all_64_1 % 16.38/3.11 | (20) (all_64_0 = 0 & all_64_1 = 0) | (all_64_2 = 0 & all_64_3 = 0) % 16.38/3.11 | % 16.38/3.11 | GROUND_INST: instantiating (3) with vd518, vd517, all_64_2, simplifying with % 16.38/3.11 | (4), (6), (18) gives: % 16.38/3.11 | (21) all_64_2 = 0 | ( ~ (vd518 = vd517) & ? [v0: int] : ( ~ (v0 = 0) & % 16.38/3.11 | greater(vd517, vd518) = v0)) % 16.38/3.11 | % 16.38/3.11 | GROUND_INST: instantiating (ass(cond(270, 0), 0)) with vd517, vd519, all_60_2, % 16.38/3.11 | simplifying with (4), (5), (13) gives: % 16.38/3.12 | (22) vmul(vd519, vd517) = all_60_2 & $i(all_60_2) % 16.38/3.12 | % 16.38/3.12 | ALPHA: (22) implies: % 16.38/3.12 | (23) vmul(vd519, vd517) = all_60_2 % 16.38/3.12 | % 16.38/3.12 | GROUND_INST: instantiating (ass(cond(312, 0), 0)) with vd517, vd518, vd519, % 16.38/3.12 | vd520, all_60_2, all_60_1, all_60_0, simplifying with (4), (5), % 16.38/3.12 | (6), (7), (12), (13), (14) gives: % 16.38/3.12 | (24) all_60_0 = 0 | ? [v0: any] : ? [v1: any] : (greater(vd519, vd520) = % 16.38/3.12 | v0 & greater(vd517, vd518) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 16.38/3.12 | % 16.38/3.12 | GROUND_INST: instantiating (ass(cond(270, 0), 0)) with vd518, vd520, all_60_1, % 16.38/3.12 | simplifying with (6), (7), (14) gives: % 16.38/3.12 | (25) vmul(vd520, vd518) = all_60_1 & $i(all_60_1) % 16.38/3.12 | % 16.38/3.12 | ALPHA: (25) implies: % 16.38/3.12 | (26) vmul(vd520, vd518) = all_60_1 % 16.38/3.12 | % 16.38/3.12 | GROUND_INST: instantiating (ass(cond(312, 0), 0)) with vd519, vd520, vd517, % 16.38/3.12 | vd518, all_60_2, all_60_1, all_60_0, simplifying with (4), (5), % 16.38/3.12 | (6), (7), (12), (23), (26) gives: % 16.38/3.12 | (27) all_60_0 = 0 | ? [v0: any] : ? [v1: any] : (greater(vd519, vd520) = % 16.38/3.12 | v1 & greater(vd517, vd518) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 16.38/3.12 | % 16.38/3.12 | BETA: splitting (20) gives: % 16.38/3.12 | % 16.38/3.12 | Case 1: % 16.38/3.12 | | % 16.38/3.12 | | (28) all_64_0 = 0 & all_64_1 = 0 % 16.38/3.12 | | % 16.38/3.12 | | ALPHA: (28) implies: % 16.38/3.12 | | (29) all_64_1 = 0 % 16.38/3.12 | | (30) all_64_0 = 0 % 16.38/3.12 | | % 16.38/3.12 | | REDUCE: (19), (29) imply: % 16.38/3.12 | | (31) geq(vd519, vd520) = 0 % 16.38/3.12 | | % 16.38/3.12 | | REDUCE: (16), (30) imply: % 16.38/3.12 | | (32) greater(vd517, vd518) = 0 % 16.38/3.12 | | % 16.38/3.12 | | BETA: splitting (27) gives: % 16.38/3.12 | | % 16.38/3.12 | | Case 1: % 16.38/3.12 | | | % 16.38/3.12 | | | (33) all_60_0 = 0 % 16.38/3.12 | | | % 16.38/3.12 | | | REDUCE: (11), (33) imply: % 16.38/3.12 | | | (34) $false % 16.38/3.12 | | | % 16.38/3.12 | | | CLOSE: (34) is inconsistent. % 16.38/3.12 | | | % 16.38/3.12 | | Case 2: % 16.38/3.12 | | | % 16.38/3.12 | | | (35) ? [v0: any] : ? [v1: any] : (greater(vd519, vd520) = v1 & % 16.38/3.12 | | | greater(vd517, vd518) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 16.38/3.12 | | | % 16.38/3.12 | | | DELTA: instantiating (35) with fresh symbols all_133_0, all_133_1 gives: % 16.38/3.13 | | | (36) greater(vd519, vd520) = all_133_0 & greater(vd517, vd518) = % 16.38/3.13 | | | all_133_1 & ( ~ (all_133_0 = 0) | ~ (all_133_1 = 0)) % 16.38/3.13 | | | % 16.38/3.13 | | | ALPHA: (36) implies: % 16.38/3.13 | | | (37) greater(vd517, vd518) = all_133_1 % 16.38/3.13 | | | % 16.38/3.13 | | | BETA: splitting (24) gives: % 16.38/3.13 | | | % 16.38/3.13 | | | Case 1: % 16.38/3.13 | | | | % 16.38/3.13 | | | | (38) all_60_0 = 0 % 16.38/3.13 | | | | % 16.38/3.13 | | | | REDUCE: (11), (38) imply: % 16.38/3.13 | | | | (39) $false % 16.38/3.13 | | | | % 16.38/3.13 | | | | CLOSE: (39) is inconsistent. % 16.38/3.13 | | | | % 16.38/3.13 | | | Case 2: % 16.38/3.13 | | | | % 16.38/3.13 | | | | (40) ? [v0: any] : ? [v1: any] : (greater(vd519, vd520) = v0 & % 16.38/3.13 | | | | greater(vd517, vd518) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 16.38/3.13 | | | | % 16.38/3.13 | | | | DELTA: instantiating (40) with fresh symbols all_139_0, all_139_1 gives: % 16.38/3.13 | | | | (41) greater(vd519, vd520) = all_139_1 & greater(vd517, vd518) = % 16.38/3.13 | | | | all_139_0 & ( ~ (all_139_0 = 0) | ~ (all_139_1 = 0)) % 16.38/3.13 | | | | % 16.38/3.13 | | | | ALPHA: (41) implies: % 16.38/3.13 | | | | (42) greater(vd517, vd518) = all_139_0 % 16.38/3.13 | | | | % 16.38/3.13 | | | | BETA: splitting (21) gives: % 16.38/3.13 | | | | % 16.38/3.13 | | | | Case 1: % 16.38/3.13 | | | | | % 16.38/3.13 | | | | | (43) all_64_2 = 0 % 16.38/3.13 | | | | | % 16.38/3.13 | | | | | REDUCE: (18), (43) imply: % 16.38/3.13 | | | | | (44) geq(vd517, vd518) = 0 % 16.38/3.13 | | | | | % 16.38/3.13 | | | | | GROUND_INST: instantiating (9) with all_133_1, all_139_0, vd518, % 16.38/3.13 | | | | | vd517, simplifying with (37), (42) gives: % 16.38/3.13 | | | | | (45) all_139_0 = all_133_1 % 16.38/3.13 | | | | | % 16.38/3.13 | | | | | GROUND_INST: instantiating (9) with 0, all_139_0, vd518, vd517, % 16.38/3.13 | | | | | simplifying with (32), (42) gives: % 16.38/3.13 | | | | | (46) all_139_0 = 0 % 16.38/3.13 | | | | | % 16.38/3.13 | | | | | COMBINE_EQS: (45), (46) imply: % 16.38/3.13 | | | | | (47) all_133_1 = 0 % 16.38/3.13 | | | | | % 16.38/3.13 | | | | | SIMP: (47) implies: % 16.38/3.13 | | | | | (48) all_133_1 = 0 % 16.38/3.13 | | | | | % 16.38/3.13 | | | | | GROUND_INST: instantiating (2) with vd520, vd519, simplifying with % 16.38/3.13 | | | | | (5), (7), (31) gives: % 16.38/3.13 | | | | | (49) vd520 = vd519 | greater(vd519, vd520) = 0 % 16.38/3.13 | | | | | % 16.38/3.13 | | | | | BETA: splitting (49) gives: % 16.38/3.13 | | | | | % 16.38/3.13 | | | | | Case 1: % 16.38/3.13 | | | | | | % 16.38/3.13 | | | | | | (50) greater(vd519, vd520) = 0 % 16.38/3.13 | | | | | | % 16.38/3.13 | | | | | | REF_CLOSE: (2), (4), (5), (6), (7), (9), (11), (12), (16), (23), % 16.38/3.13 | | | | | | (24), (26), (27), (44), (50), (ass(cond(299, 0), 2)) are % 16.38/3.13 | | | | | | inconsistent by sub-proof #2. % 16.38/3.13 | | | | | | % 16.38/3.13 | | | | | Case 2: % 16.38/3.13 | | | | | | % 16.38/3.13 | | | | | | (51) vd520 = vd519 % 16.38/3.13 | | | | | | % 16.38/3.13 | | | | | | REDUCE: (14), (51) imply: % 16.38/3.13 | | | | | | (52) vmul(vd518, vd519) = all_60_1 % 16.38/3.14 | | | | | | % 16.38/3.14 | | | | | | GROUND_INST: instantiating (ass(cond(299, 0), 2)) with vd519, vd517, % 16.38/3.14 | | | | | | vd518, all_60_2, all_60_1, all_60_0, simplifying with % 16.38/3.14 | | | | | | (4), (5), (6), (12), (13), (52) gives: % 16.38/3.14 | | | | | | (53) all_60_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & greater(vd517, % 16.38/3.14 | | | | | | vd518) = v0) % 16.38/3.14 | | | | | | % 16.38/3.14 | | | | | | BETA: splitting (53) gives: % 16.38/3.14 | | | | | | % 16.38/3.14 | | | | | | Case 1: % 16.38/3.14 | | | | | | | % 16.38/3.14 | | | | | | | (54) all_60_0 = 0 % 16.38/3.14 | | | | | | | % 16.38/3.14 | | | | | | | REDUCE: (11), (54) imply: % 16.38/3.14 | | | | | | | (55) $false % 16.38/3.14 | | | | | | | % 16.38/3.14 | | | | | | | CLOSE: (55) is inconsistent. % 16.38/3.14 | | | | | | | % 16.38/3.14 | | | | | | Case 2: % 16.38/3.14 | | | | | | | % 16.38/3.14 | | | | | | | (56) ? [v0: int] : ( ~ (v0 = 0) & greater(vd517, vd518) = v0) % 16.38/3.14 | | | | | | | % 16.38/3.14 | | | | | | | DELTA: instantiating (56) with fresh symbol all_179_0 gives: % 16.38/3.14 | | | | | | | (57) ~ (all_179_0 = 0) & greater(vd517, vd518) = all_179_0 % 16.38/3.14 | | | | | | | % 16.38/3.14 | | | | | | | REF_CLOSE: (9), (32), (57) are inconsistent by sub-proof #1. % 16.38/3.14 | | | | | | | % 16.38/3.14 | | | | | | End of split % 16.38/3.14 | | | | | | % 16.38/3.14 | | | | | End of split % 16.38/3.14 | | | | | % 16.38/3.14 | | | | Case 2: % 16.38/3.14 | | | | | % 16.38/3.14 | | | | | (58) ~ (vd518 = vd517) & ? [v0: int] : ( ~ (v0 = 0) & % 16.38/3.14 | | | | | greater(vd517, vd518) = v0) % 16.38/3.14 | | | | | % 16.38/3.14 | | | | | ALPHA: (58) implies: % 16.38/3.14 | | | | | (59) ? [v0: int] : ( ~ (v0 = 0) & greater(vd517, vd518) = v0) % 16.38/3.14 | | | | | % 16.38/3.14 | | | | | DELTA: instantiating (59) with fresh symbol all_179_0 gives: % 16.38/3.14 | | | | | (60) ~ (all_179_0 = 0) & greater(vd517, vd518) = all_179_0 % 16.38/3.14 | | | | | % 16.38/3.14 | | | | | REF_CLOSE: (9), (32), (60) are inconsistent by sub-proof #1. % 16.38/3.14 | | | | | % 16.38/3.14 | | | | End of split % 16.38/3.14 | | | | % 16.38/3.14 | | | End of split % 16.38/3.14 | | | % 16.38/3.14 | | End of split % 16.38/3.14 | | % 16.38/3.14 | Case 2: % 16.38/3.14 | | % 16.38/3.14 | | (61) all_64_2 = 0 & all_64_3 = 0 % 16.38/3.14 | | % 16.38/3.14 | | ALPHA: (61) implies: % 16.38/3.14 | | (62) all_64_3 = 0 % 16.38/3.14 | | (63) all_64_2 = 0 % 16.38/3.14 | | % 16.38/3.14 | | REDUCE: (18), (63) imply: % 16.38/3.14 | | (64) geq(vd517, vd518) = 0 % 16.38/3.14 | | % 16.38/3.14 | | REDUCE: (17), (62) imply: % 16.38/3.14 | | (65) greater(vd519, vd520) = 0 % 16.38/3.14 | | % 16.38/3.14 | | REF_CLOSE: (2), (4), (5), (6), (7), (9), (11), (12), (16), (23), (24), (26), % 16.38/3.14 | | (27), (64), (65), (ass(cond(299, 0), 2)) are inconsistent by % 16.38/3.14 | | sub-proof #2. % 16.38/3.14 | | % 16.38/3.14 | End of split % 16.38/3.14 | % 16.38/3.14 End of proof % 16.38/3.15 % 16.38/3.15 Sub-proof #1 shows that the following formulas are inconsistent: % 16.38/3.15 ---------------------------------------------------------------- % 16.38/3.15 (1) ~ (all_179_0 = 0) & greater(vd517, vd518) = all_179_0 % 16.38/3.15 (2) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 16.38/3.15 ! [v3: $i] : (v1 = v0 | ~ (greater(v3, v2) = v1) | ~ (greater(v3, v2) = % 16.38/3.15 v0)) % 16.38/3.15 (3) greater(vd517, vd518) = 0 % 16.38/3.15 % 16.38/3.15 Begin of proof % 16.38/3.15 | % 16.38/3.15 | ALPHA: (1) implies: % 16.38/3.15 | (4) ~ (all_179_0 = 0) % 16.38/3.15 | (5) greater(vd517, vd518) = all_179_0 % 16.38/3.15 | % 16.38/3.15 | GROUND_INST: instantiating (2) with 0, all_179_0, vd518, vd517, simplifying % 16.38/3.15 | with (3), (5) gives: % 16.38/3.15 | (6) all_179_0 = 0 % 16.38/3.15 | % 16.38/3.15 | REDUCE: (4), (6) imply: % 16.38/3.15 | (7) $false % 16.38/3.15 | % 16.38/3.15 | CLOSE: (7) is inconsistent. % 16.38/3.15 | % 16.38/3.15 End of proof % 16.38/3.15 % 16.38/3.15 Sub-proof #2 shows that the following formulas are inconsistent: % 16.38/3.15 ---------------------------------------------------------------- % 16.38/3.15 (1) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 16.38/3.15 ! [v3: $i] : (v1 = v0 | ~ (greater(v3, v2) = v1) | ~ (greater(v3, v2) = % 16.38/3.15 v0)) % 16.38/3.15 (2) $i(vd517) % 16.38/3.15 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! % 16.38/3.15 [v5: int] : (v5 = 0 | ~ (vmul(v2, v0) = v4) | ~ (vmul(v1, v0) = v3) | % 16.38/3.15 ~ (greater(v3, v4) = v5) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: % 16.38/3.15 int] : ( ~ (v6 = 0) & greater(v1, v2) = v6)) % 16.38/3.15 (4) greater(vd519, vd520) = 0 % 16.38/3.15 (5) all_60_0 = 0 | ? [v0: any] : ? [v1: any] : (greater(vd519, vd520) = v0 % 16.38/3.15 & greater(vd517, vd518) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 16.38/3.15 (6) $i(vd520) % 16.38/3.15 (7) greater(vd517, vd518) = all_64_0 % 16.38/3.15 (8) vmul(vd520, vd518) = all_60_1 % 16.38/3.15 (9) geq(vd517, vd518) = 0 % 16.38/3.15 (10) $i(vd519) % 16.38/3.15 (11) greater(all_60_2, all_60_1) = all_60_0 % 16.38/3.15 (12) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (geq(v1, v0) = 0) | ~ $i(v1) % 16.38/3.15 | ~ $i(v0) | greater(v1, v0) = 0) % 16.38/3.15 (13) all_60_0 = 0 | ? [v0: any] : ? [v1: any] : (greater(vd519, vd520) = v1 % 16.38/3.15 & greater(vd517, vd518) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 16.38/3.15 (14) $i(vd518) % 16.38/3.15 (15) vmul(vd519, vd517) = all_60_2 % 16.38/3.15 (16) ~ (all_60_0 = 0) % 16.38/3.15 % 16.38/3.15 Begin of proof % 16.38/3.15 | % 16.38/3.15 | BETA: splitting (13) gives: % 16.38/3.15 | % 16.38/3.15 | Case 1: % 16.38/3.15 | | % 16.38/3.15 | | (17) all_60_0 = 0 % 16.38/3.15 | | % 16.38/3.15 | | REDUCE: (16), (17) imply: % 16.38/3.15 | | (18) $false % 16.38/3.15 | | % 16.38/3.15 | | CLOSE: (18) is inconsistent. % 16.38/3.15 | | % 16.38/3.15 | Case 2: % 16.38/3.15 | | % 16.38/3.16 | | (19) ? [v0: any] : ? [v1: any] : (greater(vd519, vd520) = v1 & % 16.38/3.16 | | greater(vd517, vd518) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 16.38/3.16 | | % 16.38/3.16 | | DELTA: instantiating (19) with fresh symbols all_133_0, all_133_1 gives: % 16.38/3.16 | | (20) greater(vd519, vd520) = all_133_0 & greater(vd517, vd518) = % 16.38/3.16 | | all_133_1 & ( ~ (all_133_0 = 0) | ~ (all_133_1 = 0)) % 16.38/3.16 | | % 16.38/3.16 | | ALPHA: (20) implies: % 16.38/3.16 | | (21) greater(vd517, vd518) = all_133_1 % 16.38/3.16 | | (22) greater(vd519, vd520) = all_133_0 % 16.38/3.16 | | (23) ~ (all_133_0 = 0) | ~ (all_133_1 = 0) % 16.38/3.16 | | % 16.38/3.16 | | BETA: splitting (5) gives: % 16.38/3.16 | | % 16.38/3.16 | | Case 1: % 16.38/3.16 | | | % 16.38/3.16 | | | (24) all_60_0 = 0 % 16.38/3.16 | | | % 16.38/3.16 | | | REDUCE: (16), (24) imply: % 16.38/3.16 | | | (25) $false % 16.38/3.16 | | | % 16.38/3.16 | | | CLOSE: (25) is inconsistent. % 16.38/3.16 | | | % 16.38/3.16 | | Case 2: % 16.38/3.16 | | | % 16.38/3.16 | | | (26) ? [v0: any] : ? [v1: any] : (greater(vd519, vd520) = v0 & % 16.38/3.16 | | | greater(vd517, vd518) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 16.38/3.16 | | | % 16.38/3.16 | | | DELTA: instantiating (26) with fresh symbols all_143_0, all_143_1 gives: % 16.38/3.16 | | | (27) greater(vd519, vd520) = all_143_1 & greater(vd517, vd518) = % 16.38/3.16 | | | all_143_0 & ( ~ (all_143_0 = 0) | ~ (all_143_1 = 0)) % 16.38/3.16 | | | % 16.38/3.16 | | | ALPHA: (27) implies: % 16.86/3.16 | | | (28) greater(vd517, vd518) = all_143_0 % 16.86/3.16 | | | (29) greater(vd519, vd520) = all_143_1 % 16.86/3.16 | | | % 16.86/3.16 | | | GROUND_INST: instantiating (1) with all_64_0, all_143_0, vd518, vd517, % 16.86/3.16 | | | simplifying with (7), (28) gives: % 16.86/3.16 | | | (30) all_143_0 = all_64_0 % 16.86/3.16 | | | % 16.86/3.16 | | | GROUND_INST: instantiating (1) with all_133_1, all_143_0, vd518, vd517, % 16.86/3.16 | | | simplifying with (21), (28) gives: % 16.86/3.16 | | | (31) all_143_0 = all_133_1 % 16.86/3.16 | | | % 16.86/3.16 | | | GROUND_INST: instantiating (1) with all_133_0, all_143_1, vd520, vd519, % 16.86/3.16 | | | simplifying with (22), (29) gives: % 16.86/3.16 | | | (32) all_143_1 = all_133_0 % 16.86/3.16 | | | % 16.86/3.16 | | | GROUND_INST: instantiating (1) with 0, all_143_1, vd520, vd519, % 16.86/3.16 | | | simplifying with (4), (29) gives: % 16.86/3.16 | | | (33) all_143_1 = 0 % 16.86/3.16 | | | % 16.86/3.16 | | | COMBINE_EQS: (30), (31) imply: % 16.86/3.16 | | | (34) all_133_1 = all_64_0 % 16.86/3.16 | | | % 16.86/3.16 | | | COMBINE_EQS: (32), (33) imply: % 16.86/3.16 | | | (35) all_133_0 = 0 % 16.86/3.16 | | | % 16.86/3.16 | | | SIMP: (35) implies: % 16.86/3.16 | | | (36) all_133_0 = 0 % 16.86/3.16 | | | % 16.86/3.16 | | | BETA: splitting (23) gives: % 16.86/3.16 | | | % 16.86/3.16 | | | Case 1: % 16.86/3.16 | | | | % 16.86/3.16 | | | | (37) ~ (all_133_0 = 0) % 16.86/3.16 | | | | % 16.86/3.16 | | | | REDUCE: (36), (37) imply: % 16.86/3.17 | | | | (38) $false % 16.86/3.17 | | | | % 16.86/3.17 | | | | CLOSE: (38) is inconsistent. % 16.86/3.17 | | | | % 16.86/3.17 | | | Case 2: % 16.86/3.17 | | | | % 16.86/3.17 | | | | (39) ~ (all_133_1 = 0) % 16.86/3.17 | | | | % 16.86/3.17 | | | | REDUCE: (34), (39) imply: % 16.86/3.17 | | | | (40) ~ (all_64_0 = 0) % 16.86/3.17 | | | | % 16.86/3.17 | | | | GROUND_INST: instantiating (12) with vd518, vd517, simplifying with (2), % 16.86/3.17 | | | | (9), (14) gives: % 16.86/3.17 | | | | (41) vd518 = vd517 | greater(vd517, vd518) = 0 % 16.86/3.17 | | | | % 16.86/3.17 | | | | BETA: splitting (41) gives: % 16.86/3.17 | | | | % 16.86/3.17 | | | | Case 1: % 16.86/3.17 | | | | | % 16.86/3.17 | | | | | (42) greater(vd517, vd518) = 0 % 16.86/3.17 | | | | | % 16.86/3.17 | | | | | GROUND_INST: instantiating (1) with all_64_0, 0, vd518, vd517, % 16.86/3.17 | | | | | simplifying with (7), (42) gives: % 16.86/3.17 | | | | | (43) all_64_0 = 0 % 16.86/3.17 | | | | | % 16.86/3.17 | | | | | REDUCE: (40), (43) imply: % 16.86/3.17 | | | | | (44) $false % 16.86/3.17 | | | | | % 16.86/3.17 | | | | | CLOSE: (44) is inconsistent. % 16.86/3.17 | | | | | % 16.86/3.17 | | | | Case 2: % 16.86/3.17 | | | | | % 16.86/3.17 | | | | | (45) vd518 = vd517 % 16.86/3.17 | | | | | % 16.86/3.17 | | | | | REDUCE: (8), (45) imply: % 16.86/3.17 | | | | | (46) vmul(vd520, vd517) = all_60_1 % 16.86/3.17 | | | | | % 16.86/3.17 | | | | | GROUND_INST: instantiating (3) with vd517, vd519, vd520, all_60_2, % 16.86/3.17 | | | | | all_60_1, all_60_0, simplifying with (2), (6), (10), % 16.86/3.17 | | | | | (11), (15), (46) gives: % 16.86/3.17 | | | | | (47) all_60_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & greater(vd519, % 16.86/3.17 | | | | | vd520) = v0) % 16.86/3.17 | | | | | % 16.86/3.17 | | | | | BETA: splitting (47) gives: % 16.86/3.17 | | | | | % 16.86/3.17 | | | | | Case 1: % 16.86/3.17 | | | | | | % 16.86/3.17 | | | | | | (48) all_60_0 = 0 % 16.86/3.17 | | | | | | % 16.86/3.17 | | | | | | REDUCE: (16), (48) imply: % 16.86/3.17 | | | | | | (49) $false % 16.86/3.17 | | | | | | % 16.86/3.17 | | | | | | CLOSE: (49) is inconsistent. % 16.86/3.17 | | | | | | % 16.86/3.17 | | | | | Case 2: % 16.86/3.17 | | | | | | % 16.86/3.17 | | | | | | (50) ? [v0: int] : ( ~ (v0 = 0) & greater(vd519, vd520) = v0) % 16.86/3.17 | | | | | | % 16.86/3.17 | | | | | | DELTA: instantiating (50) with fresh symbol all_139_0 gives: % 16.86/3.17 | | | | | | (51) ~ (all_139_0 = 0) & greater(vd519, vd520) = all_139_0 % 16.86/3.17 | | | | | | % 16.86/3.17 | | | | | | ALPHA: (51) implies: % 16.86/3.17 | | | | | | (52) ~ (all_139_0 = 0) % 16.86/3.17 | | | | | | (53) greater(vd519, vd520) = all_139_0 % 16.86/3.17 | | | | | | % 16.86/3.17 | | | | | | BETA: splitting (5) gives: % 16.86/3.17 | | | | | | % 16.86/3.17 | | | | | | Case 1: % 16.86/3.17 | | | | | | | % 16.86/3.17 | | | | | | | (54) all_60_0 = 0 % 16.86/3.17 | | | | | | | % 16.86/3.17 | | | | | | | REDUCE: (16), (54) imply: % 16.86/3.17 | | | | | | | (55) $false % 16.86/3.17 | | | | | | | % 16.86/3.17 | | | | | | | CLOSE: (55) is inconsistent. % 16.86/3.17 | | | | | | | % 16.86/3.17 | | | | | | Case 2: % 16.86/3.17 | | | | | | | % 16.86/3.17 | | | | | | | % 16.86/3.17 | | | | | | | DELTA: instantiating (26) with fresh symbols all_145_0, all_145_1 % 16.86/3.17 | | | | | | | gives: % 16.86/3.17 | | | | | | | (56) greater(vd519, vd520) = all_145_1 & greater(vd517, vd518) % 16.86/3.17 | | | | | | | = all_145_0 & ( ~ (all_145_0 = 0) | ~ (all_145_1 = 0)) % 16.86/3.17 | | | | | | | % 16.86/3.17 | | | | | | | ALPHA: (56) implies: % 16.86/3.17 | | | | | | | (57) greater(vd519, vd520) = all_145_1 % 16.86/3.17 | | | | | | | % 16.86/3.17 | | | | | | | GROUND_INST: instantiating (1) with all_133_0, all_139_0, vd520, % 16.86/3.17 | | | | | | | vd519, simplifying with (22), (53) gives: % 16.86/3.17 | | | | | | | (58) all_139_0 = all_133_0 % 16.86/3.17 | | | | | | | % 16.86/3.18 | | | | | | | GROUND_INST: instantiating (1) with all_139_0, all_145_1, vd520, % 16.86/3.18 | | | | | | | vd519, simplifying with (53), (57) gives: % 16.86/3.18 | | | | | | | (59) all_145_1 = all_139_0 % 16.86/3.18 | | | | | | | % 16.86/3.18 | | | | | | | GROUND_INST: instantiating (1) with 0, all_145_1, vd520, vd519, % 16.86/3.18 | | | | | | | simplifying with (4), (57) gives: % 16.86/3.18 | | | | | | | (60) all_145_1 = 0 % 16.86/3.18 | | | | | | | % 16.86/3.18 | | | | | | | COMBINE_EQS: (59), (60) imply: % 16.86/3.18 | | | | | | | (61) all_139_0 = 0 % 16.86/3.18 | | | | | | | % 16.86/3.18 | | | | | | | SIMP: (61) implies: % 16.86/3.18 | | | | | | | (62) all_139_0 = 0 % 16.86/3.18 | | | | | | | % 16.86/3.18 | | | | | | | REDUCE: (52), (62) imply: % 16.86/3.18 | | | | | | | (63) $false % 16.86/3.18 | | | | | | | % 16.86/3.18 | | | | | | | CLOSE: (63) is inconsistent. % 16.86/3.18 | | | | | | | % 16.86/3.18 | | | | | | End of split % 16.86/3.18 | | | | | | % 16.86/3.18 | | | | | End of split % 16.86/3.18 | | | | | % 16.86/3.18 | | | | End of split % 16.86/3.18 | | | | % 16.86/3.18 | | | End of split % 16.86/3.18 | | | % 16.86/3.18 | | End of split % 16.86/3.18 | | % 16.86/3.18 | End of split % 16.86/3.18 | % 16.86/3.18 End of proof % 16.86/3.18 % SZS output end Proof for theBenchmark % 16.86/3.18 % 16.86/3.18 2551ms %------------------------------------------------------------------------------