%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : NUM842+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 : n013.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 11:50:20 EDT 2023 % Result : Theorem 10.48s 2.16s % Output : Proof 13.33s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : NUM842+2 : TPTP v8.1.2. Released v4.1.0. % 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.34 % Computer : n013.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 16:54:32 EDT 2023 % 0.13/0.34 % CPUTime : % 0.21/0.61 ________ _____ % 0.21/0.61 ___ __ \_________(_)________________________________ % 0.21/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.21/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.21/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.21/0.61 % 0.21/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.21/0.61 (2023-06-19) % 0.21/0.61 % 0.21/0.61 (c) Philipp Rümmer, 2009-2023 % 0.21/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.21/0.61 Amanda Stjerna. % 0.21/0.61 Free software under BSD-3-Clause. % 0.21/0.61 % 0.21/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.21/0.61 % 0.21/0.61 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.21/0.62 Running up to 7 provers in parallel. % 0.21/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.21/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.21/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.21/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.21/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.21/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.21/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 2.88/1.10 Prover 1: Preprocessing ... % 2.88/1.10 Prover 4: Preprocessing ... % 3.21/1.14 Prover 3: Preprocessing ... % 3.21/1.14 Prover 2: Preprocessing ... % 3.21/1.14 Prover 6: Preprocessing ... % 3.21/1.14 Prover 5: Preprocessing ... % 3.21/1.14 Prover 0: Preprocessing ... % 6.31/1.62 Prover 1: Warning: ignoring some quantifiers % 6.31/1.63 Prover 6: Proving ... % 7.02/1.63 Prover 3: Warning: ignoring some quantifiers % 7.02/1.64 Prover 5: Proving ... % 7.02/1.65 Prover 2: Proving ... % 7.02/1.66 Prover 1: Constructing countermodel ... % 7.02/1.66 Prover 3: Constructing countermodel ... % 7.02/1.66 Prover 4: Warning: ignoring some quantifiers % 7.44/1.70 Prover 4: Constructing countermodel ... % 7.95/1.77 Prover 0: Proving ... % 10.48/2.15 Prover 6: proved (1516ms) % 10.48/2.16 % 10.48/2.16 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 10.48/2.16 % 10.87/2.16 Prover 3: stopped % 10.87/2.16 Prover 2: stopped % 10.87/2.16 Prover 0: stopped % 10.87/2.18 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 10.87/2.18 Prover 5: stopped % 10.87/2.18 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 10.87/2.18 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 10.87/2.18 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 10.87/2.18 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 11.20/2.23 Prover 8: Preprocessing ... % 11.20/2.24 Prover 7: Preprocessing ... % 11.48/2.25 Prover 11: Preprocessing ... % 11.48/2.25 Prover 13: Preprocessing ... % 11.48/2.25 Prover 10: Preprocessing ... % 11.48/2.32 Prover 7: Warning: ignoring some quantifiers % 12.18/2.34 Prover 10: Warning: ignoring some quantifiers % 12.18/2.34 Prover 7: Constructing countermodel ... % 12.18/2.35 Prover 8: Warning: ignoring some quantifiers % 12.18/2.36 Prover 10: Constructing countermodel ... % 12.18/2.36 Prover 8: Constructing countermodel ... % 12.18/2.37 Prover 13: Warning: ignoring some quantifiers % 12.18/2.38 Prover 13: Constructing countermodel ... % 12.18/2.38 Prover 1: Found proof (size 200) % 12.18/2.38 Prover 1: proved (1748ms) % 12.18/2.38 Prover 10: stopped % 12.18/2.38 Prover 7: stopped % 12.18/2.38 Prover 4: stopped % 12.18/2.38 Prover 13: stopped % 12.18/2.38 Prover 8: stopped % 12.59/2.42 Prover 11: Warning: ignoring some quantifiers % 12.59/2.44 Prover 11: Constructing countermodel ... % 12.59/2.45 Prover 11: stopped % 12.59/2.45 % 12.59/2.45 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 12.59/2.45 % 12.93/2.46 % SZS output start Proof for theBenchmark % 12.93/2.47 Assumptions after simplification: % 12.93/2.47 --------------------------------- % 12.93/2.47 % 12.93/2.47 (ass(cond(209, 0), 0)) % 12.93/2.49 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 12.93/2.49 $i] : ! [v6: int] : (v6 = 0 | ~ (vplus(v1, v3) = v5) | ~ (vplus(v0, v2) = % 12.93/2.49 v4) | ~ (greater(v4, v5) = v6) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ % 12.93/2.49 $i(v0) | ? [v7: any] : ? [v8: any] : (greater(v2, v3) = v7 & greater(v0, % 12.93/2.49 v1) = v8 & ( ~ (v8 = 0) | ~ (v7 = 0)))) % 12.93/2.49 % 12.93/2.49 (ass(cond(61, 0), 0)) % 12.93/2.49 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (vplus(v0, v1) = v2) | ~ $i(v1) % 12.93/2.49 | ~ $i(v0) | (vplus(v1, v0) = v2 & $i(v2))) % 12.93/2.49 % 12.93/2.49 (ass(cond(goal(193), 0), 2)) % 12.93/2.49 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 12.93/2.49 int] : (v5 = 0 | ~ (vplus(v1, v2) = v4) | ~ (vplus(v0, v2) = v3) | ~ % 12.93/2.49 (greater(v3, v4) = v5) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: int] : % 12.93/2.49 ( ~ (v6 = 0) & greater(v0, v1) = v6)) % 12.93/2.50 % 12.93/2.50 (def(cond(conseq(axiom(3)), 16), 1)) % 12.93/2.50 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (geq(v1, v0) = v2) | % 12.93/2.50 ~ $i(v1) | ~ $i(v0) | ( ~ (v1 = v0) & ? [v3: int] : ( ~ (v3 = 0) & % 12.93/2.50 greater(v1, v0) = v3))) & ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ % 12.93/2.50 (geq(v1, v0) = 0) | ~ $i(v1) | ~ $i(v0) | greater(v1, v0) = 0) % 12.93/2.50 % 12.93/2.50 (dis(antec(218))) % 12.93/2.50 $i(vd356) & $i(vd354) & $i(vd355) & $i(vd353) & ? [v0: any] : ? [v1: any] : % 12.93/2.50 ? [v2: any] : ? [v3: any] : (geq(vd355, vd356) = v2 & geq(vd353, vd354) = v1 % 12.93/2.50 & greater(vd355, vd356) = v0 & greater(vd353, vd354) = v3 & ((v3 = 0 & v2 = % 12.93/2.50 0) | (v1 = 0 & v0 = 0))) % 12.93/2.50 % 12.93/2.50 (holds(conseq(218), 361, 0)) % 12.93/2.50 $i(vd356) & $i(vd354) & $i(vd355) & $i(vd353) & ? [v0: $i] : ? [v1: $i] : ? % 12.93/2.50 [v2: int] : ( ~ (v2 = 0) & vplus(vd354, vd356) = v1 & vplus(vd353, vd355) = v0 % 12.93/2.50 & greater(v0, v1) = v2 & $i(v1) & $i(v0)) % 12.93/2.50 % 12.93/2.50 (function-axioms) % 13.15/2.50 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 13.15/2.50 [v3: $i] : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = v0)) & ! [v0: % 13.15/2.50 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 13.15/2.50 : (v1 = v0 | ~ (less(v3, v2) = v1) | ~ (less(v3, v2) = v0)) & ! [v0: $i] : % 13.15/2.50 ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (vplus(v3, v2) = v1) | % 13.15/2.50 ~ (vplus(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 13.15/2.50 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (geq(v3, v2) % 13.15/2.50 = v1) | ~ (geq(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 13.15/2.50 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (greater(v3, % 13.15/2.50 v2) = v1) | ~ (greater(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 13.15/2.50 [v2: $i] : (v1 = v0 | ~ (vskolem2(v2) = v1) | ~ (vskolem2(v2) = v0)) & ! % 13.15/2.50 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (vsucc(v2) = v1) | ~ % 13.15/2.51 (vsucc(v2) = v0)) % 13.15/2.51 % 13.15/2.51 Further assumptions not needed in the proof: % 13.15/2.51 -------------------------------------------- % 13.15/2.51 ass(cond(12, 0), 0), ass(cond(140, 0), 0), ass(cond(147, 0), 0), ass(cond(158, % 13.15/2.51 0), 0), ass(cond(163, 0), 0), ass(cond(168, 0), 0), ass(cond(184, 0), 0), % 13.15/2.51 ass(cond(189, 0), 0), ass(cond(20, 0), 0), ass(cond(33, 0), 0), ass(cond(43, 0), % 13.15/2.51 0), ass(cond(52, 0), 0), ass(cond(6, 0), 0), ass(cond(73, 0), 0), ass(cond(81, % 13.15/2.51 0), 0), ass(cond(goal(130), 0), 0), ass(cond(goal(130), 0), 1), % 13.15/2.51 ass(cond(goal(130), 0), 2), ass(cond(goal(130), 0), 3), ass(cond(goal(177), 0), % 13.15/2.51 0), ass(cond(goal(193), 0), 0), ass(cond(goal(193), 0), 1), % 13.15/2.51 ass(cond(goal(202), 0), 0), ass(cond(goal(202), 0), 1), ass(cond(goal(202), 0), % 13.15/2.51 2), ass(cond(goal(88), 0), 0), ass(cond(goal(88), 0), 1), ass(cond(goal(88), % 13.15/2.51 0), 2), ass(cond(goal(88), 0), 3), def(cond(conseq(axiom(3)), 11), 1), % 13.15/2.51 def(cond(conseq(axiom(3)), 12), 1), def(cond(conseq(axiom(3)), 17), 1), % 13.15/2.51 qu(antec(axiom(3)), imp(antec(axiom(3)))), qu(cond(conseq(axiom(3)), 3), % 13.15/2.51 and(holds(definiens(29), 45, 0), holds(definiens(29), 44, 0))), % 13.15/2.51 qu(restrictor(axiom(1)), holds(scope(axiom(1)), 2, 0)) % 13.15/2.51 % 13.15/2.51 Those formulas are unsatisfiable: % 13.15/2.51 --------------------------------- % 13.15/2.51 % 13.15/2.51 Begin of proof % 13.15/2.51 | % 13.15/2.51 | ALPHA: (dis(antec(218))) implies: % 13.15/2.51 | (1) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] : (geq(vd355, % 13.15/2.51 | vd356) = v2 & geq(vd353, vd354) = v1 & greater(vd355, vd356) = v0 & % 13.15/2.51 | greater(vd353, vd354) = v3 & ((v3 = 0 & v2 = 0) | (v1 = 0 & v0 = 0))) % 13.15/2.51 | % 13.15/2.51 | ALPHA: (def(cond(conseq(axiom(3)), 16), 1)) implies: % 13.15/2.51 | (2) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (geq(v1, v0) = 0) | ~ $i(v1) % 13.15/2.51 | | ~ $i(v0) | greater(v1, v0) = 0) % 13.15/2.51 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (geq(v1, v0) = % 13.15/2.51 | v2) | ~ $i(v1) | ~ $i(v0) | ( ~ (v1 = v0) & ? [v3: int] : ( ~ % 13.15/2.51 | (v3 = 0) & greater(v1, v0) = v3))) % 13.15/2.51 | % 13.15/2.51 | ALPHA: (holds(conseq(218), 361, 0)) implies: % 13.15/2.51 | (4) $i(vd353) % 13.15/2.51 | (5) $i(vd355) % 13.15/2.51 | (6) $i(vd354) % 13.15/2.51 | (7) $i(vd356) % 13.15/2.51 | (8) ? [v0: $i] : ? [v1: $i] : ? [v2: int] : ( ~ (v2 = 0) & vplus(vd354, % 13.15/2.51 | vd356) = v1 & vplus(vd353, vd355) = v0 & greater(v0, v1) = v2 & % 13.15/2.51 | $i(v1) & $i(v0)) % 13.15/2.51 | % 13.15/2.51 | ALPHA: (function-axioms) implies: % 13.15/2.51 | (9) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 13.15/2.51 | ! [v3: $i] : (v1 = v0 | ~ (greater(v3, v2) = v1) | ~ (greater(v3, % 13.15/2.51 | v2) = v0)) % 13.15/2.51 | % 13.15/2.51 | DELTA: instantiating (8) with fresh symbols all_42_0, all_42_1, all_42_2 % 13.15/2.51 | gives: % 13.15/2.52 | (10) ~ (all_42_0 = 0) & vplus(vd354, vd356) = all_42_1 & vplus(vd353, % 13.15/2.52 | vd355) = all_42_2 & greater(all_42_2, all_42_1) = all_42_0 & % 13.15/2.52 | $i(all_42_1) & $i(all_42_2) % 13.15/2.52 | % 13.15/2.52 | ALPHA: (10) implies: % 13.15/2.52 | (11) ~ (all_42_0 = 0) % 13.15/2.52 | (12) greater(all_42_2, all_42_1) = all_42_0 % 13.15/2.52 | (13) vplus(vd353, vd355) = all_42_2 % 13.15/2.52 | (14) vplus(vd354, vd356) = all_42_1 % 13.15/2.52 | % 13.15/2.52 | DELTA: instantiating (1) with fresh symbols all_46_0, all_46_1, all_46_2, % 13.15/2.52 | all_46_3 gives: % 13.15/2.52 | (15) geq(vd355, vd356) = all_46_1 & geq(vd353, vd354) = all_46_2 & % 13.15/2.52 | greater(vd355, vd356) = all_46_3 & greater(vd353, vd354) = all_46_0 & % 13.15/2.52 | ((all_46_0 = 0 & all_46_1 = 0) | (all_46_2 = 0 & all_46_3 = 0)) % 13.15/2.52 | % 13.15/2.52 | ALPHA: (15) implies: % 13.15/2.52 | (16) greater(vd353, vd354) = all_46_0 % 13.15/2.52 | (17) greater(vd355, vd356) = all_46_3 % 13.15/2.52 | (18) geq(vd353, vd354) = all_46_2 % 13.15/2.52 | (19) geq(vd355, vd356) = all_46_1 % 13.15/2.52 | (20) (all_46_0 = 0 & all_46_1 = 0) | (all_46_2 = 0 & all_46_3 = 0) % 13.15/2.52 | % 13.15/2.52 | GROUND_INST: instantiating (3) with vd354, vd353, all_46_2, simplifying with % 13.15/2.52 | (4), (6), (18) gives: % 13.15/2.52 | (21) all_46_2 = 0 | ( ~ (vd354 = vd353) & ? [v0: int] : ( ~ (v0 = 0) & % 13.15/2.52 | greater(vd353, vd354) = v0)) % 13.15/2.52 | % 13.15/2.52 | GROUND_INST: instantiating (ass(cond(61, 0), 0)) with vd353, vd355, all_42_2, % 13.15/2.52 | simplifying with (4), (5), (13) gives: % 13.15/2.52 | (22) vplus(vd355, vd353) = all_42_2 & $i(all_42_2) % 13.15/2.52 | % 13.15/2.52 | ALPHA: (22) implies: % 13.15/2.52 | (23) vplus(vd355, vd353) = all_42_2 % 13.15/2.52 | % 13.15/2.52 | GROUND_INST: instantiating (ass(cond(209, 0), 0)) with vd353, vd354, vd355, % 13.15/2.52 | vd356, all_42_2, all_42_1, all_42_0, simplifying with (4), (5), % 13.15/2.52 | (6), (7), (12), (13), (14) gives: % 13.15/2.52 | (24) all_42_0 = 0 | ? [v0: any] : ? [v1: any] : (greater(vd355, vd356) = % 13.15/2.52 | v0 & greater(vd353, vd354) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 13.15/2.52 | % 13.15/2.52 | GROUND_INST: instantiating (ass(cond(61, 0), 0)) with vd354, vd356, all_42_1, % 13.15/2.52 | simplifying with (6), (7), (14) gives: % 13.15/2.52 | (25) vplus(vd356, vd354) = all_42_1 & $i(all_42_1) % 13.15/2.52 | % 13.15/2.52 | ALPHA: (25) implies: % 13.15/2.52 | (26) vplus(vd356, vd354) = all_42_1 % 13.15/2.52 | % 13.15/2.52 | GROUND_INST: instantiating (ass(cond(209, 0), 0)) with vd355, vd356, vd353, % 13.15/2.52 | vd354, all_42_2, all_42_1, all_42_0, simplifying with (4), (5), % 13.15/2.52 | (6), (7), (12), (23), (26) gives: % 13.15/2.52 | (27) all_42_0 = 0 | ? [v0: any] : ? [v1: any] : (greater(vd355, vd356) = % 13.15/2.52 | v1 & greater(vd353, vd354) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 13.15/2.52 | % 13.15/2.52 | BETA: splitting (20) gives: % 13.15/2.52 | % 13.15/2.52 | Case 1: % 13.15/2.52 | | % 13.15/2.52 | | (28) all_46_0 = 0 & all_46_1 = 0 % 13.15/2.52 | | % 13.15/2.52 | | ALPHA: (28) implies: % 13.15/2.52 | | (29) all_46_1 = 0 % 13.15/2.52 | | (30) all_46_0 = 0 % 13.15/2.52 | | % 13.15/2.52 | | REDUCE: (19), (29) imply: % 13.15/2.52 | | (31) geq(vd355, vd356) = 0 % 13.15/2.52 | | % 13.15/2.52 | | REDUCE: (16), (30) imply: % 13.15/2.52 | | (32) greater(vd353, vd354) = 0 % 13.15/2.52 | | % 13.15/2.52 | | BETA: splitting (21) gives: % 13.15/2.52 | | % 13.15/2.52 | | Case 1: % 13.15/2.52 | | | % 13.15/2.52 | | | (33) all_46_2 = 0 % 13.15/2.52 | | | % 13.15/2.53 | | | REDUCE: (18), (33) imply: % 13.15/2.53 | | | (34) geq(vd353, vd354) = 0 % 13.15/2.53 | | | % 13.15/2.53 | | | GROUND_INST: instantiating (2) with vd356, vd355, simplifying with (5), % 13.15/2.53 | | | (7), (31) gives: % 13.15/2.53 | | | (35) vd356 = vd355 | greater(vd355, vd356) = 0 % 13.15/2.53 | | | % 13.15/2.53 | | | BETA: splitting (35) gives: % 13.15/2.53 | | | % 13.15/2.53 | | | Case 1: % 13.15/2.53 | | | | % 13.15/2.53 | | | | (36) greater(vd355, vd356) = 0 % 13.15/2.53 | | | | % 13.15/2.53 | | | | REF_CLOSE: (2), (4), (5), (6), (7), (9), (11), (12), (16), (23), (24), % 13.15/2.53 | | | | (26), (27), (34), (36), (ass(cond(goal(193), 0), 2)) are % 13.15/2.53 | | | | inconsistent by sub-proof #2. % 13.15/2.53 | | | | % 13.15/2.53 | | | Case 2: % 13.15/2.53 | | | | % 13.15/2.53 | | | | (37) vd356 = vd355 % 13.15/2.53 | | | | % 13.15/2.53 | | | | REDUCE: (14), (37) imply: % 13.15/2.53 | | | | (38) vplus(vd354, vd355) = all_42_1 % 13.15/2.53 | | | | % 13.15/2.53 | | | | GROUND_INST: instantiating (ass(cond(goal(193), 0), 2)) with vd353, % 13.15/2.53 | | | | vd354, vd355, all_42_2, all_42_1, all_42_0, simplifying % 13.15/2.53 | | | | with (4), (5), (6), (12), (13), (38) gives: % 13.15/2.53 | | | | (39) all_42_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & greater(vd353, % 13.15/2.53 | | | | vd354) = v0) % 13.15/2.53 | | | | % 13.15/2.53 | | | | BETA: splitting (39) gives: % 13.15/2.53 | | | | % 13.15/2.53 | | | | Case 1: % 13.15/2.53 | | | | | % 13.15/2.53 | | | | | (40) all_42_0 = 0 % 13.15/2.53 | | | | | % 13.15/2.53 | | | | | REDUCE: (11), (40) imply: % 13.15/2.53 | | | | | (41) $false % 13.15/2.53 | | | | | % 13.15/2.53 | | | | | CLOSE: (41) is inconsistent. % 13.15/2.53 | | | | | % 13.15/2.53 | | | | Case 2: % 13.15/2.53 | | | | | % 13.15/2.53 | | | | | (42) ? [v0: int] : ( ~ (v0 = 0) & greater(vd353, vd354) = v0) % 13.15/2.53 | | | | | % 13.15/2.53 | | | | | REF_CLOSE: (9), (11), (24), (27), (32), (42) are inconsistent by % 13.15/2.53 | | | | | sub-proof #1. % 13.15/2.53 | | | | | % 13.15/2.53 | | | | End of split % 13.15/2.53 | | | | % 13.15/2.53 | | | End of split % 13.15/2.53 | | | % 13.15/2.53 | | Case 2: % 13.15/2.53 | | | % 13.15/2.53 | | | (43) ~ (vd354 = vd353) & ? [v0: int] : ( ~ (v0 = 0) & greater(vd353, % 13.15/2.53 | | | vd354) = v0) % 13.15/2.53 | | | % 13.15/2.53 | | | ALPHA: (43) implies: % 13.15/2.53 | | | (44) ? [v0: int] : ( ~ (v0 = 0) & greater(vd353, vd354) = v0) % 13.15/2.53 | | | % 13.15/2.53 | | | REF_CLOSE: (9), (11), (24), (27), (32), (44) are inconsistent by sub-proof % 13.15/2.53 | | | #1. % 13.15/2.53 | | | % 13.15/2.53 | | End of split % 13.15/2.53 | | % 13.15/2.53 | Case 2: % 13.15/2.53 | | % 13.15/2.53 | | (45) all_46_2 = 0 & all_46_3 = 0 % 13.15/2.53 | | % 13.15/2.53 | | ALPHA: (45) implies: % 13.15/2.53 | | (46) all_46_3 = 0 % 13.15/2.53 | | (47) all_46_2 = 0 % 13.15/2.53 | | % 13.15/2.53 | | REDUCE: (18), (47) imply: % 13.15/2.53 | | (48) geq(vd353, vd354) = 0 % 13.15/2.53 | | % 13.15/2.53 | | REDUCE: (17), (46) imply: % 13.15/2.53 | | (49) greater(vd355, vd356) = 0 % 13.15/2.53 | | % 13.15/2.54 | | REF_CLOSE: (2), (4), (5), (6), (7), (9), (11), (12), (16), (23), (24), (26), % 13.15/2.54 | | (27), (48), (49), (ass(cond(goal(193), 0), 2)) are inconsistent % 13.15/2.54 | | by sub-proof #2. % 13.15/2.54 | | % 13.15/2.54 | End of split % 13.15/2.54 | % 13.15/2.54 End of proof % 13.15/2.54 % 13.15/2.54 Sub-proof #1 shows that the following formulas are inconsistent: % 13.15/2.54 ---------------------------------------------------------------- % 13.15/2.54 (1) all_42_0 = 0 | ? [v0: any] : ? [v1: any] : (greater(vd355, vd356) = v1 % 13.15/2.54 & greater(vd353, vd354) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 13.15/2.54 (2) all_42_0 = 0 | ? [v0: any] : ? [v1: any] : (greater(vd355, vd356) = v0 % 13.15/2.54 & greater(vd353, vd354) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 13.15/2.54 (3) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 13.15/2.54 ! [v3: $i] : (v1 = v0 | ~ (greater(v3, v2) = v1) | ~ (greater(v3, v2) = % 13.15/2.54 v0)) % 13.15/2.54 (4) greater(vd353, vd354) = 0 % 13.15/2.54 (5) ~ (all_42_0 = 0) % 13.15/2.54 (6) ? [v0: int] : ( ~ (v0 = 0) & greater(vd353, vd354) = v0) % 13.15/2.54 % 13.15/2.54 Begin of proof % 13.15/2.54 | % 13.15/2.54 | DELTA: instantiating (6) with fresh symbol all_121_0 gives: % 13.15/2.54 | (7) ~ (all_121_0 = 0) & greater(vd353, vd354) = all_121_0 % 13.15/2.54 | % 13.15/2.54 | ALPHA: (7) implies: % 13.15/2.54 | (8) ~ (all_121_0 = 0) % 13.15/2.54 | (9) greater(vd353, vd354) = all_121_0 % 13.15/2.54 | % 13.15/2.54 | BETA: splitting (2) gives: % 13.15/2.54 | % 13.15/2.54 | Case 1: % 13.15/2.54 | | % 13.15/2.54 | | (10) all_42_0 = 0 % 13.15/2.54 | | % 13.15/2.54 | | REDUCE: (5), (10) imply: % 13.15/2.54 | | (11) $false % 13.15/2.54 | | % 13.15/2.54 | | CLOSE: (11) is inconsistent. % 13.15/2.54 | | % 13.15/2.54 | Case 2: % 13.15/2.54 | | % 13.15/2.54 | | (12) ? [v0: any] : ? [v1: any] : (greater(vd355, vd356) = v0 & % 13.15/2.54 | | greater(vd353, vd354) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 13.15/2.54 | | % 13.15/2.54 | | DELTA: instantiating (12) with fresh symbols all_127_0, all_127_1 gives: % 13.15/2.54 | | (13) greater(vd355, vd356) = all_127_1 & greater(vd353, vd354) = % 13.15/2.54 | | all_127_0 & ( ~ (all_127_0 = 0) | ~ (all_127_1 = 0)) % 13.15/2.54 | | % 13.15/2.54 | | ALPHA: (13) implies: % 13.33/2.54 | | (14) greater(vd353, vd354) = all_127_0 % 13.33/2.54 | | % 13.33/2.54 | | BETA: splitting (1) gives: % 13.33/2.54 | | % 13.33/2.54 | | Case 1: % 13.33/2.54 | | | % 13.33/2.54 | | | (15) all_42_0 = 0 % 13.33/2.54 | | | % 13.33/2.54 | | | REDUCE: (5), (15) imply: % 13.33/2.54 | | | (16) $false % 13.33/2.54 | | | % 13.33/2.54 | | | CLOSE: (16) is inconsistent. % 13.33/2.54 | | | % 13.33/2.54 | | Case 2: % 13.33/2.54 | | | % 13.33/2.54 | | | (17) ? [v0: any] : ? [v1: any] : (greater(vd355, vd356) = v1 & % 13.33/2.54 | | | greater(vd353, vd354) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 13.33/2.54 | | | % 13.33/2.54 | | | DELTA: instantiating (17) with fresh symbols all_133_0, all_133_1 gives: % 13.33/2.54 | | | (18) greater(vd355, vd356) = all_133_0 & greater(vd353, vd354) = % 13.33/2.54 | | | all_133_1 & ( ~ (all_133_0 = 0) | ~ (all_133_1 = 0)) % 13.33/2.54 | | | % 13.33/2.54 | | | ALPHA: (18) implies: % 13.33/2.54 | | | (19) greater(vd353, vd354) = all_133_1 % 13.33/2.54 | | | % 13.33/2.54 | | | GROUND_INST: instantiating (3) with 0, all_127_0, vd354, vd353, % 13.33/2.54 | | | simplifying with (4), (14) gives: % 13.33/2.54 | | | (20) all_127_0 = 0 % 13.33/2.54 | | | % 13.33/2.54 | | | GROUND_INST: instantiating (3) with all_127_0, all_133_1, vd354, vd353, % 13.33/2.54 | | | simplifying with (14), (19) gives: % 13.33/2.54 | | | (21) all_133_1 = all_127_0 % 13.33/2.54 | | | % 13.33/2.54 | | | GROUND_INST: instantiating (3) with all_121_0, all_133_1, vd354, vd353, % 13.33/2.54 | | | simplifying with (9), (19) gives: % 13.33/2.54 | | | (22) all_133_1 = all_121_0 % 13.33/2.54 | | | % 13.33/2.54 | | | COMBINE_EQS: (21), (22) imply: % 13.33/2.54 | | | (23) all_127_0 = all_121_0 % 13.33/2.54 | | | % 13.33/2.54 | | | SIMP: (23) implies: % 13.33/2.54 | | | (24) all_127_0 = all_121_0 % 13.33/2.54 | | | % 13.33/2.54 | | | COMBINE_EQS: (20), (24) imply: % 13.33/2.54 | | | (25) all_121_0 = 0 % 13.33/2.54 | | | % 13.33/2.54 | | | SIMP: (25) implies: % 13.33/2.54 | | | (26) all_121_0 = 0 % 13.33/2.54 | | | % 13.33/2.54 | | | REDUCE: (8), (26) imply: % 13.33/2.54 | | | (27) $false % 13.33/2.54 | | | % 13.33/2.54 | | | CLOSE: (27) is inconsistent. % 13.33/2.54 | | | % 13.33/2.54 | | End of split % 13.33/2.54 | | % 13.33/2.54 | End of split % 13.33/2.54 | % 13.33/2.54 End of proof % 13.33/2.54 % 13.33/2.54 Sub-proof #2 shows that the following formulas are inconsistent: % 13.33/2.54 ---------------------------------------------------------------- % 13.33/2.54 (1) greater(vd353, vd354) = all_46_0 % 13.33/2.55 (2) greater(vd355, vd356) = 0 % 13.33/2.55 (3) all_42_0 = 0 | ? [v0: any] : ? [v1: any] : (greater(vd355, vd356) = v1 % 13.33/2.55 & greater(vd353, vd354) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 13.33/2.55 (4) geq(vd353, vd354) = 0 % 13.33/2.55 (5) all_42_0 = 0 | ? [v0: any] : ? [v1: any] : (greater(vd355, vd356) = v0 % 13.33/2.55 & greater(vd353, vd354) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 13.33/2.55 (6) $i(vd354) % 13.33/2.55 (7) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 13.33/2.55 ! [v3: $i] : (v1 = v0 | ~ (greater(v3, v2) = v1) | ~ (greater(v3, v2) = % 13.33/2.55 v0)) % 13.33/2.55 (8) $i(vd353) % 13.33/2.55 (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! % 13.33/2.55 [v5: int] : (v5 = 0 | ~ (vplus(v1, v2) = v4) | ~ (vplus(v0, v2) = v3) | % 13.33/2.55 ~ (greater(v3, v4) = v5) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: % 13.33/2.55 int] : ( ~ (v6 = 0) & greater(v0, v1) = v6)) % 13.33/2.55 (10) vplus(vd355, vd353) = all_42_2 % 13.33/2.55 (11) greater(all_42_2, all_42_1) = all_42_0 % 13.33/2.55 (12) ~ (all_42_0 = 0) % 13.33/2.55 (13) $i(vd355) % 13.33/2.55 (14) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (geq(v1, v0) = 0) | ~ $i(v1) % 13.33/2.55 | ~ $i(v0) | greater(v1, v0) = 0) % 13.33/2.55 (15) $i(vd356) % 13.33/2.55 (16) vplus(vd356, vd354) = all_42_1 % 13.33/2.55 % 13.33/2.55 Begin of proof % 13.33/2.55 | % 13.33/2.55 | BETA: splitting (5) gives: % 13.33/2.55 | % 13.33/2.55 | Case 1: % 13.33/2.55 | | % 13.33/2.55 | | (17) all_42_0 = 0 % 13.33/2.55 | | % 13.33/2.55 | | REDUCE: (12), (17) imply: % 13.33/2.55 | | (18) $false % 13.33/2.55 | | % 13.33/2.55 | | CLOSE: (18) is inconsistent. % 13.33/2.55 | | % 13.33/2.55 | Case 2: % 13.33/2.55 | | % 13.33/2.55 | | (19) ? [v0: any] : ? [v1: any] : (greater(vd355, vd356) = v0 & % 13.33/2.55 | | greater(vd353, vd354) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 13.33/2.55 | | % 13.33/2.55 | | DELTA: instantiating (19) with fresh symbols all_125_0, all_125_1 gives: % 13.33/2.55 | | (20) greater(vd355, vd356) = all_125_1 & greater(vd353, vd354) = % 13.33/2.55 | | all_125_0 & ( ~ (all_125_0 = 0) | ~ (all_125_1 = 0)) % 13.33/2.55 | | % 13.33/2.55 | | ALPHA: (20) implies: % 13.33/2.55 | | (21) greater(vd353, vd354) = all_125_0 % 13.33/2.55 | | (22) greater(vd355, vd356) = all_125_1 % 13.33/2.55 | | % 13.33/2.55 | | BETA: splitting (3) gives: % 13.33/2.55 | | % 13.33/2.55 | | Case 1: % 13.33/2.55 | | | % 13.33/2.55 | | | (23) all_42_0 = 0 % 13.33/2.55 | | | % 13.33/2.55 | | | REDUCE: (12), (23) imply: % 13.33/2.55 | | | (24) $false % 13.33/2.55 | | | % 13.33/2.55 | | | CLOSE: (24) is inconsistent. % 13.33/2.55 | | | % 13.33/2.55 | | Case 2: % 13.33/2.55 | | | % 13.33/2.55 | | | (25) ? [v0: any] : ? [v1: any] : (greater(vd355, vd356) = v1 & % 13.33/2.55 | | | greater(vd353, vd354) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 13.33/2.55 | | | % 13.33/2.55 | | | DELTA: instantiating (25) with fresh symbols all_131_0, all_131_1 gives: % 13.33/2.55 | | | (26) greater(vd355, vd356) = all_131_0 & greater(vd353, vd354) = % 13.33/2.55 | | | all_131_1 & ( ~ (all_131_0 = 0) | ~ (all_131_1 = 0)) % 13.33/2.55 | | | % 13.33/2.55 | | | ALPHA: (26) implies: % 13.33/2.55 | | | (27) greater(vd353, vd354) = all_131_1 % 13.33/2.55 | | | (28) greater(vd355, vd356) = all_131_0 % 13.33/2.55 | | | (29) ~ (all_131_0 = 0) | ~ (all_131_1 = 0) % 13.33/2.55 | | | % 13.33/2.55 | | | GROUND_INST: instantiating (7) with all_46_0, all_131_1, vd354, vd353, % 13.33/2.55 | | | simplifying with (1), (27) gives: % 13.33/2.55 | | | (30) all_131_1 = all_46_0 % 13.33/2.55 | | | % 13.33/2.55 | | | GROUND_INST: instantiating (7) with all_125_0, all_131_1, vd354, vd353, % 13.33/2.55 | | | simplifying with (21), (27) gives: % 13.33/2.55 | | | (31) all_131_1 = all_125_0 % 13.33/2.55 | | | % 13.33/2.55 | | | GROUND_INST: instantiating (7) with all_125_1, all_131_0, vd356, vd355, % 13.33/2.55 | | | simplifying with (22), (28) gives: % 13.33/2.55 | | | (32) all_131_0 = all_125_1 % 13.33/2.55 | | | % 13.33/2.55 | | | GROUND_INST: instantiating (7) with 0, all_131_0, vd356, vd355, % 13.33/2.55 | | | simplifying with (2), (28) gives: % 13.33/2.55 | | | (33) all_131_0 = 0 % 13.33/2.55 | | | % 13.33/2.56 | | | COMBINE_EQS: (32), (33) imply: % 13.33/2.56 | | | (34) all_125_1 = 0 % 13.33/2.56 | | | % 13.33/2.56 | | | SIMP: (34) implies: % 13.33/2.56 | | | (35) all_125_1 = 0 % 13.33/2.56 | | | % 13.33/2.56 | | | COMBINE_EQS: (30), (31) imply: % 13.33/2.56 | | | (36) all_125_0 = all_46_0 % 13.33/2.56 | | | % 13.33/2.56 | | | SIMP: (36) implies: % 13.33/2.56 | | | (37) all_125_0 = all_46_0 % 13.33/2.56 | | | % 13.33/2.56 | | | BETA: splitting (29) gives: % 13.33/2.56 | | | % 13.33/2.56 | | | Case 1: % 13.33/2.56 | | | | % 13.33/2.56 | | | | (38) ~ (all_131_0 = 0) % 13.33/2.56 | | | | % 13.33/2.56 | | | | REDUCE: (33), (38) imply: % 13.33/2.56 | | | | (39) $false % 13.33/2.56 | | | | % 13.33/2.56 | | | | CLOSE: (39) is inconsistent. % 13.33/2.56 | | | | % 13.33/2.56 | | | Case 2: % 13.33/2.56 | | | | % 13.33/2.56 | | | | (40) ~ (all_131_1 = 0) % 13.33/2.56 | | | | % 13.33/2.56 | | | | REDUCE: (30), (40) imply: % 13.33/2.56 | | | | (41) ~ (all_46_0 = 0) % 13.33/2.56 | | | | % 13.33/2.56 | | | | GROUND_INST: instantiating (14) with vd354, vd353, simplifying with (4), % 13.33/2.56 | | | | (6), (8) gives: % 13.33/2.56 | | | | (42) vd354 = vd353 | greater(vd353, vd354) = 0 % 13.33/2.56 | | | | % 13.33/2.56 | | | | BETA: splitting (42) gives: % 13.33/2.56 | | | | % 13.33/2.56 | | | | Case 1: % 13.33/2.56 | | | | | % 13.33/2.56 | | | | | (43) greater(vd353, vd354) = 0 % 13.33/2.56 | | | | | % 13.33/2.56 | | | | | GROUND_INST: instantiating (7) with all_46_0, 0, vd354, vd353, % 13.33/2.56 | | | | | simplifying with (1), (43) gives: % 13.33/2.56 | | | | | (44) all_46_0 = 0 % 13.33/2.56 | | | | | % 13.33/2.56 | | | | | REDUCE: (41), (44) imply: % 13.33/2.56 | | | | | (45) $false % 13.33/2.56 | | | | | % 13.33/2.56 | | | | | CLOSE: (45) is inconsistent. % 13.33/2.56 | | | | | % 13.33/2.56 | | | | Case 2: % 13.33/2.56 | | | | | % 13.33/2.56 | | | | | (46) vd354 = vd353 % 13.33/2.56 | | | | | % 13.33/2.56 | | | | | REDUCE: (16), (46) imply: % 13.33/2.56 | | | | | (47) vplus(vd356, vd353) = all_42_1 % 13.33/2.56 | | | | | % 13.33/2.56 | | | | | GROUND_INST: instantiating (9) with vd355, vd356, vd353, all_42_2, % 13.33/2.56 | | | | | all_42_1, all_42_0, simplifying with (8), (10), (11), % 13.33/2.56 | | | | | (13), (15), (47) gives: % 13.33/2.56 | | | | | (48) all_42_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & greater(vd355, % 13.33/2.56 | | | | | vd356) = v0) % 13.33/2.56 | | | | | % 13.33/2.56 | | | | | BETA: splitting (48) gives: % 13.33/2.56 | | | | | % 13.33/2.56 | | | | | Case 1: % 13.33/2.56 | | | | | | % 13.33/2.56 | | | | | | (49) all_42_0 = 0 % 13.33/2.56 | | | | | | % 13.33/2.56 | | | | | | REDUCE: (12), (49) imply: % 13.33/2.56 | | | | | | (50) $false % 13.33/2.56 | | | | | | % 13.33/2.56 | | | | | | CLOSE: (50) is inconsistent. % 13.33/2.56 | | | | | | % 13.33/2.56 | | | | | Case 2: % 13.33/2.56 | | | | | | % 13.33/2.56 | | | | | | (51) ? [v0: int] : ( ~ (v0 = 0) & greater(vd355, vd356) = v0) % 13.33/2.56 | | | | | | % 13.33/2.56 | | | | | | DELTA: instantiating (51) with fresh symbol all_121_0 gives: % 13.33/2.56 | | | | | | (52) ~ (all_121_0 = 0) & greater(vd355, vd356) = all_121_0 % 13.33/2.56 | | | | | | % 13.33/2.56 | | | | | | ALPHA: (52) implies: % 13.33/2.56 | | | | | | (53) ~ (all_121_0 = 0) % 13.33/2.56 | | | | | | (54) greater(vd355, vd356) = all_121_0 % 13.33/2.56 | | | | | | % 13.33/2.56 | | | | | | BETA: splitting (5) gives: % 13.33/2.56 | | | | | | % 13.33/2.56 | | | | | | Case 1: % 13.33/2.56 | | | | | | | % 13.33/2.56 | | | | | | | (55) all_42_0 = 0 % 13.33/2.56 | | | | | | | % 13.33/2.56 | | | | | | | REDUCE: (12), (55) imply: % 13.33/2.56 | | | | | | | (56) $false % 13.33/2.56 | | | | | | | % 13.33/2.56 | | | | | | | CLOSE: (56) is inconsistent. % 13.33/2.56 | | | | | | | % 13.33/2.56 | | | | | | Case 2: % 13.33/2.56 | | | | | | | % 13.33/2.56 | | | | | | | % 13.33/2.56 | | | | | | | DELTA: instantiating (19) with fresh symbols all_127_0, all_127_1 % 13.33/2.56 | | | | | | | gives: % 13.33/2.56 | | | | | | | (57) greater(vd355, vd356) = all_127_1 & greater(vd353, vd354) % 13.33/2.56 | | | | | | | = all_127_0 & ( ~ (all_127_0 = 0) | ~ (all_127_1 = 0)) % 13.33/2.56 | | | | | | | % 13.33/2.56 | | | | | | | ALPHA: (57) implies: % 13.33/2.56 | | | | | | | (58) greater(vd355, vd356) = all_127_1 % 13.33/2.56 | | | | | | | % 13.33/2.56 | | | | | | | BETA: splitting (3) gives: % 13.33/2.56 | | | | | | | % 13.33/2.56 | | | | | | | Case 1: % 13.33/2.56 | | | | | | | | % 13.33/2.56 | | | | | | | | (59) all_42_0 = 0 % 13.33/2.56 | | | | | | | | % 13.33/2.56 | | | | | | | | REDUCE: (12), (59) imply: % 13.33/2.56 | | | | | | | | (60) $false % 13.33/2.56 | | | | | | | | % 13.33/2.56 | | | | | | | | CLOSE: (60) is inconsistent. % 13.33/2.56 | | | | | | | | % 13.33/2.56 | | | | | | | Case 2: % 13.33/2.56 | | | | | | | | % 13.33/2.56 | | | | | | | | % 13.33/2.56 | | | | | | | | DELTA: instantiating (25) with fresh symbols all_138_0, % 13.33/2.56 | | | | | | | | all_138_1 gives: % 13.33/2.56 | | | | | | | | (61) greater(vd355, vd356) = all_138_0 & greater(vd353, % 13.33/2.56 | | | | | | | | vd354) = all_138_1 & ( ~ (all_138_0 = 0) | ~ % 13.33/2.56 | | | | | | | | (all_138_1 = 0)) % 13.33/2.56 | | | | | | | | % 13.33/2.56 | | | | | | | | ALPHA: (61) implies: % 13.33/2.56 | | | | | | | | (62) greater(vd355, vd356) = all_138_0 % 13.33/2.56 | | | | | | | | % 13.33/2.56 | | | | | | | | GROUND_INST: instantiating (7) with all_121_0, all_127_1, vd356, % 13.33/2.56 | | | | | | | | vd355, simplifying with (54), (58) gives: % 13.33/2.56 | | | | | | | | (63) all_127_1 = all_121_0 % 13.33/2.56 | | | | | | | | % 13.33/2.56 | | | | | | | | GROUND_INST: instantiating (7) with all_127_1, all_138_0, vd356, % 13.33/2.56 | | | | | | | | vd355, simplifying with (58), (62) gives: % 13.33/2.56 | | | | | | | | (64) all_138_0 = all_127_1 % 13.33/2.56 | | | | | | | | % 13.33/2.56 | | | | | | | | GROUND_INST: instantiating (7) with 0, all_138_0, vd356, vd355, % 13.33/2.56 | | | | | | | | simplifying with (2), (62) gives: % 13.33/2.56 | | | | | | | | (65) all_138_0 = 0 % 13.33/2.56 | | | | | | | | % 13.33/2.56 | | | | | | | | COMBINE_EQS: (64), (65) imply: % 13.33/2.56 | | | | | | | | (66) all_127_1 = 0 % 13.33/2.56 | | | | | | | | % 13.33/2.56 | | | | | | | | SIMP: (66) implies: % 13.33/2.56 | | | | | | | | (67) all_127_1 = 0 % 13.33/2.56 | | | | | | | | % 13.33/2.56 | | | | | | | | COMBINE_EQS: (63), (67) imply: % 13.33/2.57 | | | | | | | | (68) all_121_0 = 0 % 13.33/2.57 | | | | | | | | % 13.33/2.57 | | | | | | | | SIMP: (68) implies: % 13.33/2.57 | | | | | | | | (69) all_121_0 = 0 % 13.33/2.57 | | | | | | | | % 13.33/2.57 | | | | | | | | REDUCE: (53), (69) imply: % 13.33/2.57 | | | | | | | | (70) $false % 13.33/2.57 | | | | | | | | % 13.33/2.57 | | | | | | | | CLOSE: (70) is inconsistent. % 13.33/2.57 | | | | | | | | % 13.33/2.57 | | | | | | | End of split % 13.33/2.57 | | | | | | | % 13.33/2.57 | | | | | | End of split % 13.33/2.57 | | | | | | % 13.33/2.57 | | | | | End of split % 13.33/2.57 | | | | | % 13.33/2.57 | | | | End of split % 13.33/2.57 | | | | % 13.33/2.57 | | | End of split % 13.33/2.57 | | | % 13.33/2.57 | | End of split % 13.33/2.57 | | % 13.33/2.57 | End of split % 13.33/2.57 | % 13.33/2.57 End of proof % 13.33/2.57 % SZS output end Proof for theBenchmark % 13.33/2.57 % 13.33/2.57 1954ms %------------------------------------------------------------------------------