%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : NUM841+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 : n008.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 11:50:19 EDT 2023 % Result : Theorem 8.35s 1.86s % Output : Proof 9.98s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.13 % Problem : NUM841+2 : TPTP v8.1.2. Released v4.1.0. % 0.00/0.14 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.35 % Computer : n008.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 15:50:32 EDT 2023 % 0.13/0.36 % CPUTime : % 0.22/0.63 ________ _____ % 0.22/0.63 ___ __ \_________(_)________________________________ % 0.22/0.63 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.22/0.63 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.22/0.63 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.22/0.63 % 0.22/0.63 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.22/0.63 (2023-06-19) % 0.22/0.63 % 0.22/0.63 (c) Philipp Rümmer, 2009-2023 % 0.22/0.63 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.22/0.63 Amanda Stjerna. % 0.22/0.63 Free software under BSD-3-Clause. % 0.22/0.63 % 0.22/0.63 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.22/0.63 % 0.22/0.63 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.22/0.64 Running up to 7 provers in parallel. % 0.22/0.66 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.22/0.66 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.22/0.66 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.22/0.66 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.22/0.66 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.22/0.66 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.22/0.66 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 2.54/1.06 Prover 4: Preprocessing ... % 2.54/1.06 Prover 1: Preprocessing ... % 2.95/1.10 Prover 0: Preprocessing ... % 2.95/1.10 Prover 5: Preprocessing ... % 2.95/1.10 Prover 3: Preprocessing ... % 2.95/1.10 Prover 6: Preprocessing ... % 2.95/1.10 Prover 2: Preprocessing ... % 5.05/1.47 Prover 1: Warning: ignoring some quantifiers % 5.05/1.49 Prover 3: Warning: ignoring some quantifiers % 5.05/1.50 Prover 4: Constructing countermodel ... % 5.05/1.50 Prover 3: Constructing countermodel ... % 5.05/1.52 Prover 1: Constructing countermodel ... % 5.05/1.52 Prover 6: Proving ... % 5.05/1.52 Prover 5: Proving ... % 5.05/1.53 Prover 0: Proving ... % 6.37/1.60 Prover 2: Proving ... % 7.80/1.86 Prover 3: proved (1208ms) % 7.80/1.86 % 8.35/1.86 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 8.35/1.86 % 8.35/1.86 Prover 2: stopped % 8.35/1.86 Prover 0: stopped % 8.35/1.86 Prover 5: stopped % 8.35/1.87 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 8.35/1.87 Prover 6: stopped % 8.35/1.87 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 8.35/1.87 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 8.35/1.87 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 8.35/1.88 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 8.50/1.91 Prover 10: Preprocessing ... % 8.84/1.93 Prover 8: Preprocessing ... % 8.84/1.94 Prover 7: Preprocessing ... % 8.84/1.94 Prover 13: Preprocessing ... % 8.84/1.95 Prover 11: Preprocessing ... % 9.43/2.01 Prover 10: Warning: ignoring some quantifiers % 9.43/2.02 Prover 10: Constructing countermodel ... % 9.43/2.04 Prover 13: Warning: ignoring some quantifiers % 9.43/2.05 Prover 13: Constructing countermodel ... % 9.43/2.06 Prover 1: Found proof (size 45) % 9.43/2.06 Prover 1: proved (1409ms) % 9.43/2.06 Prover 10: stopped % 9.43/2.06 Prover 4: stopped % 9.43/2.06 Prover 13: stopped % 9.43/2.07 Prover 8: Warning: ignoring some quantifiers % 9.43/2.08 Prover 7: Warning: ignoring some quantifiers % 9.43/2.08 Prover 8: Constructing countermodel ... % 9.43/2.08 Prover 7: Constructing countermodel ... % 9.43/2.09 Prover 8: stopped % 9.43/2.09 Prover 7: stopped % 9.43/2.09 Prover 11: Constructing countermodel ... % 9.43/2.11 Prover 11: stopped % 9.43/2.11 % 9.43/2.11 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 9.43/2.11 % 9.43/2.12 % SZS output start Proof for theBenchmark % 9.43/2.12 Assumptions after simplification: % 9.43/2.12 --------------------------------- % 9.43/2.12 % 9.43/2.12 (ass(cond(33, 0), 0)) % 9.43/2.15 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 9.43/2.15 (vplus(v3, v2) = v4) | ~ (vplus(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ % 9.43/2.15 $i(v0) | ? [v5: $i] : (vplus(v1, v2) = v5 & vplus(v0, v5) = v4 & $i(v5) & % 9.43/2.15 $i(v4))) % 9.43/2.15 % 9.43/2.15 (ass(cond(61, 0), 0)) % 9.43/2.15 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (vplus(v0, v1) = v2) | ~ $i(v1) % 9.43/2.15 | ~ $i(v0) | (vplus(v1, v0) = v2 & $i(v2))) % 9.43/2.15 % 9.43/2.15 (def(cond(conseq(axiom(3)), 11), 1)) % 9.43/2.16 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (greater(v1, v0) = v2) % 9.43/2.16 | ~ $i(v1) | ~ $i(v0) | ! [v3: $i] : ( ~ (vplus(v0, v3) = v1) | ~ % 9.43/2.16 $i(v3))) & ! [v0: $i] : ! [v1: $i] : ( ~ (greater(v1, v0) = 0) | ~ % 9.43/2.16 $i(v1) | ~ $i(v0) | ? [v2: $i] : (vplus(v0, v2) = v1 & $i(v2))) % 9.43/2.16 % 9.43/2.16 (holds(212, 350, 0)) % 9.43/2.16 $i(vd345) & $i(vd347) & $i(vd344) & ? [v0: $i] : ? [v1: $i] : (greater(v0, % 9.43/2.16 v1) = 0 & vplus(vd345, vd347) = v1 & vplus(vd344, vd347) = v0 & $i(v1) & % 9.43/2.16 $i(v0)) % 9.43/2.16 % 9.43/2.16 (holds(213, 351, 0)) % 9.43/2.16 $i(vd345) & $i(vd347) & ? [v0: $i] : (vplus(vd345, vd347) = v0 & vplus(vd347, % 9.43/2.16 vd345) = v0 & $i(v0)) % 9.43/2.16 % 9.43/2.16 (holds(213, 351, 1)) % 9.43/2.16 $i(vd348) & $i(vd345) & $i(vd347) & ? [v0: $i] : ? [v1: $i] : (greater(v0, % 9.43/2.16 v1) = 0 & vplus(vd348, vd345) = v1 & vplus(vd347, vd345) = v0 & $i(v1) & % 9.43/2.16 $i(v0)) % 9.43/2.16 % 9.43/2.16 (holds(213, 351, 2)) % 9.43/2.16 $i(vd348) & $i(vd345) & ? [v0: $i] : (vplus(vd348, vd345) = v0 & vplus(vd345, % 9.43/2.16 vd348) = v0 & $i(v0)) % 9.43/2.16 % 9.43/2.16 (holds(214, 352, 0)) % 9.43/2.16 $i(vd348) & $i(vd345) & $i(vd347) & $i(vd344) & ? [v0: $i] : ? [v1: $i] : ? % 9.43/2.16 [v2: int] : ( ~ (v2 = 0) & greater(v0, v1) = v2 & vplus(vd345, vd348) = v1 & % 9.43/2.16 vplus(vd344, vd347) = v0 & $i(v1) & $i(v0)) % 9.43/2.16 % 9.43/2.16 (function-axioms) % 9.43/2.17 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 9.43/2.17 [v3: $i] : (v1 = v0 | ~ (less(v3, v2) = v1) | ~ (less(v3, v2) = v0)) & ! % 9.43/2.17 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 9.43/2.17 $i] : (v1 = v0 | ~ (greater(v3, v2) = v1) | ~ (greater(v3, v2) = v0)) & ! % 9.43/2.17 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (vplus(v3, % 9.43/2.17 v2) = v1) | ~ (vplus(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 9.43/2.17 [v2: $i] : (v1 = v0 | ~ (vskolem2(v2) = v1) | ~ (vskolem2(v2) = v0)) & ! % 9.43/2.17 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (vsucc(v2) = v1) | ~ % 9.43/2.17 (vsucc(v2) = v0)) % 9.43/2.17 % 9.43/2.17 Further assumptions not needed in the proof: % 9.43/2.17 -------------------------------------------- % 9.43/2.17 ass(cond(140, 0), 0), ass(cond(147, 0), 0), ass(cond(189, 0), 0), ass(cond(20, % 9.43/2.17 0), 0), ass(cond(43, 0), 0), ass(cond(52, 0), 0), ass(cond(goal(130), 0), % 9.43/2.17 0), ass(cond(goal(130), 0), 2), ass(cond(goal(193), 0), 0), % 9.43/2.17 ass(cond(goal(193), 0), 1), ass(cond(goal(193), 0), 2), ass(cond(goal(202), 0), % 9.43/2.17 0), ass(cond(goal(202), 0), 1), ass(cond(goal(202), 0), 2), ass(cond(goal(88), % 9.43/2.17 0), 3), holds(conjunct1(211), 346, 0), holds(conjunct2(211), 349, 0), % 9.43/2.17 qu(cond(conseq(axiom(3)), 3), and(holds(definiens(29), 45, 0), % 9.43/2.17 holds(definiens(29), 44, 0))) % 9.43/2.17 % 9.43/2.17 Those formulas are unsatisfiable: % 9.43/2.17 --------------------------------- % 9.43/2.17 % 9.43/2.17 Begin of proof % 9.43/2.17 | % 9.43/2.17 | ALPHA: (holds(213, 351, 2)) implies: % 9.43/2.17 | (1) ? [v0: $i] : (vplus(vd348, vd345) = v0 & vplus(vd345, vd348) = v0 & % 9.43/2.17 | $i(v0)) % 9.43/2.17 | % 9.43/2.17 | ALPHA: (holds(213, 351, 1)) implies: % 9.43/2.17 | (2) ? [v0: $i] : ? [v1: $i] : (greater(v0, v1) = 0 & vplus(vd348, vd345) % 9.43/2.17 | = v1 & vplus(vd347, vd345) = v0 & $i(v1) & $i(v0)) % 9.43/2.17 | % 9.43/2.17 | ALPHA: (holds(213, 351, 0)) implies: % 9.43/2.17 | (3) ? [v0: $i] : (vplus(vd345, vd347) = v0 & vplus(vd347, vd345) = v0 & % 9.43/2.17 | $i(v0)) % 9.43/2.17 | % 9.43/2.17 | ALPHA: (holds(212, 350, 0)) implies: % 9.43/2.18 | (4) ? [v0: $i] : ? [v1: $i] : (greater(v0, v1) = 0 & vplus(vd345, vd347) % 9.43/2.18 | = v1 & vplus(vd344, vd347) = v0 & $i(v1) & $i(v0)) % 9.43/2.18 | % 9.43/2.18 | ALPHA: (def(cond(conseq(axiom(3)), 11), 1)) implies: % 9.43/2.18 | (5) ! [v0: $i] : ! [v1: $i] : ( ~ (greater(v1, v0) = 0) | ~ $i(v1) | ~ % 9.43/2.18 | $i(v0) | ? [v2: $i] : (vplus(v0, v2) = v1 & $i(v2))) % 9.43/2.18 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (greater(v1, % 9.43/2.18 | v0) = v2) | ~ $i(v1) | ~ $i(v0) | ! [v3: $i] : ( ~ (vplus(v0, % 9.43/2.18 | v3) = v1) | ~ $i(v3))) % 9.43/2.18 | % 9.43/2.18 | ALPHA: (holds(214, 352, 0)) implies: % 9.43/2.18 | (7) $i(vd344) % 9.43/2.18 | (8) $i(vd347) % 9.43/2.18 | (9) ? [v0: $i] : ? [v1: $i] : ? [v2: int] : ( ~ (v2 = 0) & greater(v0, % 9.43/2.18 | v1) = v2 & vplus(vd345, vd348) = v1 & vplus(vd344, vd347) = v0 & % 9.43/2.18 | $i(v1) & $i(v0)) % 9.43/2.18 | % 9.43/2.18 | ALPHA: (function-axioms) implies: % 9.43/2.18 | (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 9.43/2.18 | (vplus(v3, v2) = v1) | ~ (vplus(v3, v2) = v0)) % 9.43/2.18 | % 9.43/2.18 | DELTA: instantiating (3) with fresh symbol all_21_0 gives: % 9.43/2.18 | (11) vplus(vd345, vd347) = all_21_0 & vplus(vd347, vd345) = all_21_0 & % 9.43/2.18 | $i(all_21_0) % 9.43/2.18 | % 9.43/2.18 | ALPHA: (11) implies: % 9.43/2.18 | (12) vplus(vd347, vd345) = all_21_0 % 9.43/2.18 | (13) vplus(vd345, vd347) = all_21_0 % 9.43/2.18 | % 9.43/2.18 | DELTA: instantiating (1) with fresh symbol all_24_0 gives: % 9.43/2.18 | (14) vplus(vd348, vd345) = all_24_0 & vplus(vd345, vd348) = all_24_0 & % 9.43/2.18 | $i(all_24_0) % 9.43/2.18 | % 9.43/2.18 | ALPHA: (14) implies: % 9.43/2.18 | (15) vplus(vd345, vd348) = all_24_0 % 9.43/2.18 | (16) vplus(vd348, vd345) = all_24_0 % 9.43/2.18 | % 9.43/2.18 | DELTA: instantiating (2) with fresh symbols all_28_0, all_28_1 gives: % 9.43/2.19 | (17) greater(all_28_1, all_28_0) = 0 & vplus(vd348, vd345) = all_28_0 & % 9.43/2.19 | vplus(vd347, vd345) = all_28_1 & $i(all_28_0) & $i(all_28_1) % 9.43/2.19 | % 9.43/2.19 | ALPHA: (17) implies: % 9.43/2.19 | (18) $i(all_28_1) % 9.43/2.19 | (19) $i(all_28_0) % 9.43/2.19 | (20) vplus(vd347, vd345) = all_28_1 % 9.43/2.19 | (21) vplus(vd348, vd345) = all_28_0 % 9.43/2.19 | (22) greater(all_28_1, all_28_0) = 0 % 9.43/2.19 | % 9.43/2.19 | DELTA: instantiating (4) with fresh symbols all_30_0, all_30_1 gives: % 9.43/2.19 | (23) greater(all_30_1, all_30_0) = 0 & vplus(vd345, vd347) = all_30_0 & % 9.43/2.19 | vplus(vd344, vd347) = all_30_1 & $i(all_30_0) & $i(all_30_1) % 9.43/2.19 | % 9.43/2.19 | ALPHA: (23) implies: % 9.98/2.19 | (24) vplus(vd344, vd347) = all_30_1 % 9.98/2.19 | (25) vplus(vd345, vd347) = all_30_0 % 9.98/2.19 | (26) greater(all_30_1, all_30_0) = 0 % 9.98/2.19 | % 9.98/2.19 | DELTA: instantiating (9) with fresh symbols all_32_0, all_32_1, all_32_2 % 9.98/2.19 | gives: % 9.98/2.19 | (27) ~ (all_32_0 = 0) & greater(all_32_2, all_32_1) = all_32_0 & % 9.98/2.19 | vplus(vd345, vd348) = all_32_1 & vplus(vd344, vd347) = all_32_2 & % 9.98/2.19 | $i(all_32_1) & $i(all_32_2) % 9.98/2.19 | % 9.98/2.19 | ALPHA: (27) implies: % 9.98/2.19 | (28) ~ (all_32_0 = 0) % 9.98/2.19 | (29) vplus(vd344, vd347) = all_32_2 % 9.98/2.19 | (30) vplus(vd345, vd348) = all_32_1 % 9.98/2.19 | (31) greater(all_32_2, all_32_1) = all_32_0 % 9.98/2.19 | % 9.98/2.19 | GROUND_INST: instantiating (10) with all_30_1, all_32_2, vd347, vd344, % 9.98/2.19 | simplifying with (24), (29) gives: % 9.98/2.19 | (32) all_32_2 = all_30_1 % 9.98/2.19 | % 9.98/2.19 | GROUND_INST: instantiating (10) with all_21_0, all_28_1, vd345, vd347, % 9.98/2.19 | simplifying with (12), (20) gives: % 9.98/2.19 | (33) all_28_1 = all_21_0 % 9.98/2.19 | % 9.98/2.19 | GROUND_INST: instantiating (10) with all_21_0, all_30_0, vd347, vd345, % 9.98/2.19 | simplifying with (13), (25) gives: % 9.98/2.19 | (34) all_30_0 = all_21_0 % 9.98/2.19 | % 9.98/2.19 | GROUND_INST: instantiating (10) with all_24_0, all_32_1, vd348, vd345, % 9.98/2.19 | simplifying with (15), (30) gives: % 9.98/2.19 | (35) all_32_1 = all_24_0 % 9.98/2.19 | % 9.98/2.19 | GROUND_INST: instantiating (10) with all_24_0, all_28_0, vd345, vd348, % 9.98/2.19 | simplifying with (16), (21) gives: % 9.98/2.19 | (36) all_28_0 = all_24_0 % 9.98/2.19 | % 9.98/2.19 | REDUCE: (31), (32), (35) imply: % 9.98/2.19 | (37) greater(all_30_1, all_24_0) = all_32_0 % 9.98/2.19 | % 9.98/2.19 | REDUCE: (26), (34) imply: % 9.98/2.19 | (38) greater(all_30_1, all_21_0) = 0 % 9.98/2.19 | % 9.98/2.19 | REDUCE: (22), (33), (36) imply: % 9.98/2.19 | (39) greater(all_21_0, all_24_0) = 0 % 9.98/2.19 | % 9.98/2.19 | REDUCE: (19), (36) imply: % 9.98/2.19 | (40) $i(all_24_0) % 9.98/2.19 | % 9.98/2.19 | REDUCE: (18), (33) imply: % 9.98/2.19 | (41) $i(all_21_0) % 9.98/2.19 | % 9.98/2.20 | GROUND_INST: instantiating (ass(cond(61, 0), 0)) with vd344, vd347, all_30_1, % 9.98/2.20 | simplifying with (7), (8), (24) gives: % 9.98/2.20 | (42) vplus(vd347, vd344) = all_30_1 & $i(all_30_1) % 9.98/2.20 | % 9.98/2.20 | ALPHA: (42) implies: % 9.98/2.20 | (43) $i(all_30_1) % 9.98/2.20 | % 9.98/2.20 | GROUND_INST: instantiating (5) with all_24_0, all_21_0, simplifying with (39), % 9.98/2.20 | (40), (41) gives: % 9.98/2.20 | (44) ? [v0: $i] : (vplus(all_24_0, v0) = all_21_0 & $i(v0)) % 9.98/2.20 | % 9.98/2.20 | GROUND_INST: instantiating (5) with all_21_0, all_30_1, simplifying with (38), % 9.98/2.20 | (41), (43) gives: % 9.98/2.20 | (45) ? [v0: $i] : (vplus(all_21_0, v0) = all_30_1 & $i(v0)) % 9.98/2.20 | % 9.98/2.20 | GROUND_INST: instantiating (6) with all_24_0, all_30_1, all_32_0, simplifying % 9.98/2.20 | with (37), (40), (43) gives: % 9.98/2.20 | (46) all_32_0 = 0 | ! [v0: $i] : ( ~ (vplus(all_24_0, v0) = all_30_1) | ~ % 9.98/2.20 | $i(v0)) % 9.98/2.20 | % 9.98/2.20 | DELTA: instantiating (45) with fresh symbol all_44_0 gives: % 9.98/2.20 | (47) vplus(all_21_0, all_44_0) = all_30_1 & $i(all_44_0) % 9.98/2.20 | % 9.98/2.20 | ALPHA: (47) implies: % 9.98/2.20 | (48) $i(all_44_0) % 9.98/2.20 | (49) vplus(all_21_0, all_44_0) = all_30_1 % 9.98/2.20 | % 9.98/2.20 | DELTA: instantiating (44) with fresh symbol all_46_0 gives: % 9.98/2.20 | (50) vplus(all_24_0, all_46_0) = all_21_0 & $i(all_46_0) % 9.98/2.20 | % 9.98/2.20 | ALPHA: (50) implies: % 9.98/2.20 | (51) $i(all_46_0) % 9.98/2.20 | (52) vplus(all_24_0, all_46_0) = all_21_0 % 9.98/2.20 | % 9.98/2.20 | BETA: splitting (46) gives: % 9.98/2.20 | % 9.98/2.20 | Case 1: % 9.98/2.20 | | % 9.98/2.20 | | (53) all_32_0 = 0 % 9.98/2.20 | | % 9.98/2.20 | | REDUCE: (28), (53) imply: % 9.98/2.20 | | (54) $false % 9.98/2.20 | | % 9.98/2.20 | | CLOSE: (54) is inconsistent. % 9.98/2.20 | | % 9.98/2.20 | Case 2: % 9.98/2.20 | | % 9.98/2.20 | | (55) ! [v0: $i] : ( ~ (vplus(all_24_0, v0) = all_30_1) | ~ $i(v0)) % 9.98/2.20 | | % 9.98/2.20 | | GROUND_INST: instantiating (ass(cond(33, 0), 0)) with all_24_0, all_46_0, % 9.98/2.20 | | all_44_0, all_21_0, all_30_1, simplifying with (40), (48), % 9.98/2.20 | | (49), (51), (52) gives: % 9.98/2.20 | | (56) ? [v0: $i] : (vplus(all_46_0, all_44_0) = v0 & vplus(all_24_0, v0) % 9.98/2.20 | | = all_30_1 & $i(v0) & $i(all_30_1)) % 9.98/2.20 | | % 9.98/2.20 | | DELTA: instantiating (56) with fresh symbol all_71_0 gives: % 9.98/2.20 | | (57) vplus(all_46_0, all_44_0) = all_71_0 & vplus(all_24_0, all_71_0) = % 9.98/2.20 | | all_30_1 & $i(all_71_0) & $i(all_30_1) % 9.98/2.20 | | % 9.98/2.20 | | ALPHA: (57) implies: % 9.98/2.20 | | (58) $i(all_71_0) % 9.98/2.20 | | (59) vplus(all_24_0, all_71_0) = all_30_1 % 9.98/2.20 | | % 9.98/2.20 | | GROUND_INST: instantiating (55) with all_71_0, simplifying with (58), (59) % 9.98/2.20 | | gives: % 9.98/2.20 | | (60) $false % 9.98/2.20 | | % 9.98/2.20 | | CLOSE: (60) is inconsistent. % 9.98/2.20 | | % 9.98/2.20 | End of split % 9.98/2.20 | % 9.98/2.20 End of proof % 9.98/2.21 % SZS output end Proof for theBenchmark % 9.98/2.21 % 9.98/2.21 1576ms %------------------------------------------------------------------------------