TSTP Solution File: GRP715+1 by Princess---230619
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : GRP715+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n026.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 01:13:12 EDT 2023
% Result : Theorem 23.73s 3.93s
% Output : Proof 25.69s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP715+1 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.34 % Computer : n026.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 : Mon Aug 28 21:20:20 EDT 2023
% 0.13/0.35 % 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.
% 0.21/0.62
% 0.21/0.62 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.21/0.62
% 0.21/0.62 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.21/0.63 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 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 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 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
% 0.21/0.65 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.12/0.99 Prover 4: Preprocessing ...
% 2.12/0.99 Prover 1: Preprocessing ...
% 2.12/1.03 Prover 6: Preprocessing ...
% 2.12/1.03 Prover 3: Preprocessing ...
% 2.12/1.03 Prover 5: Preprocessing ...
% 2.12/1.03 Prover 2: Preprocessing ...
% 2.12/1.03 Prover 0: Preprocessing ...
% 3.81/1.24 Prover 1: Constructing countermodel ...
% 3.81/1.25 Prover 6: Constructing countermodel ...
% 3.81/1.25 Prover 3: Constructing countermodel ...
% 3.81/1.25 Prover 4: Constructing countermodel ...
% 4.23/1.28 Prover 5: Proving ...
% 4.23/1.28 Prover 0: Proving ...
% 4.88/1.36 Prover 3: gave up
% 4.88/1.37 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 4.88/1.37 Prover 2: Proving ...
% 4.88/1.41 Prover 7: Preprocessing ...
% 4.88/1.46 Prover 6: gave up
% 4.88/1.48 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 4.88/1.49 Prover 8: Preprocessing ...
% 5.56/1.52 Prover 7: Constructing countermodel ...
% 5.56/1.54 Prover 8: Warning: ignoring some quantifiers
% 5.56/1.54 Prover 8: Constructing countermodel ...
% 6.35/1.61 Prover 8: gave up
% 6.73/1.61 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889
% 6.73/1.62 Prover 9: Preprocessing ...
% 7.01/1.70 Prover 9: Constructing countermodel ...
% 7.01/1.74 Prover 1: gave up
% 7.68/1.75 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 7.68/1.76 Prover 10: Preprocessing ...
% 8.06/1.80 Prover 10: Constructing countermodel ...
% 8.06/1.84 Prover 10: gave up
% 8.60/1.86 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 8.60/1.88 Prover 11: Preprocessing ...
% 9.29/1.96 Prover 11: Constructing countermodel ...
% 23.73/3.93 Prover 4: Found proof (size 340)
% 23.73/3.93 Prover 4: proved (3284ms)
% 23.73/3.93 Prover 9: stopped
% 23.73/3.93 Prover 5: stopped
% 23.73/3.93 Prover 2: stopped
% 23.73/3.93 Prover 0: stopped
% 23.73/3.93 Prover 7: stopped
% 23.73/3.93 Prover 11: stopped
% 23.73/3.93
% 23.73/3.93 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 23.73/3.93
% 24.52/4.15 % SZS output start Proof for theBenchmark
% 24.85/4.15 Assumptions after simplification:
% 24.85/4.15 ---------------------------------
% 24.85/4.15
% 24.85/4.15 (f06)
% 24.85/4.18 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 24.85/4.18 $i] : ( ~ (mult(v3, v1) = v4) | ~ (mult(v2, v4) = v5) | ~ (mult(v1, v0) =
% 24.85/4.18 v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: $i] : ? [v7: $i] :
% 24.85/4.18 (mult(v7, v1) = v5 & mult(v6, v0) = v7 & mult(v2, v1) = v6 & $i(v7) & $i(v6)
% 24.85/4.18 & $i(v5))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : !
% 24.85/4.18 [v4: $i] : ( ~ (mult(v3, v0) = v4) | ~ (mult(v2, v1) = v3) | ~ $i(v2) | ~
% 24.85/4.18 $i(v1) | ~ $i(v0) | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : (mult(v6, v1)
% 24.85/4.18 = v7 & mult(v4, v1) = v5 & mult(v2, v7) = v5 & mult(v1, v0) = v6 & $i(v7)
% 24.85/4.18 & $i(v6) & $i(v5)))
% 24.85/4.18
% 24.85/4.18 (f07)
% 24.85/4.18 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (mult(v1, v2) =
% 24.85/4.18 v3) | ~ (mult(v0, v0) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: $i] :
% 24.85/4.18 (mult(v4, v0) = v3 & mult(v1, v0) = v4 & $i(v4) & $i(v3))) & ! [v0: $i] :
% 24.85/4.18 ! [v1: $i] : ! [v2: $i] : ( ~ (mult(v1, v0) = v2) | ~ $i(v1) | ~ $i(v0) |
% 24.85/4.18 ? [v3: $i] : ? [v4: $i] : (mult(v2, v0) = v4 & mult(v1, v3) = v4 & mult(v0,
% 24.85/4.18 v0) = v3 & $i(v4) & $i(v3)))
% 24.85/4.18
% 24.85/4.18 (f08)
% 24.85/4.18 $i(unit) & ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (mult(v0, unit) = v1) |
% 24.85/4.18 ~ $i(v0))
% 24.85/4.18
% 24.85/4.18 (f09)
% 24.85/4.18 $i(unit) & ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (mult(unit, v0) = v1) |
% 24.85/4.18 ~ $i(v0))
% 24.85/4.18
% 24.85/4.18 (f10)
% 24.85/4.19 mult(op_a, op_b) = unit & $i(op_b) & $i(op_a) & $i(unit)
% 24.85/4.19
% 24.85/4.19 (f11)
% 24.85/4.19 mult(op_b, op_a) = unit & $i(op_b) & $i(op_a) & $i(unit)
% 24.85/4.19
% 24.85/4.19 (goals)
% 24.85/4.19 $i(op_b) & $i(op_a) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] :
% 24.85/4.19 ? [v4: $i] : (mult(v3, op_a) = v4 & mult(v1, op_b) = v2 & mult(v0, op_b) = v3
% 24.85/4.19 & mult(v0, op_a) = v1 & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & ( ~ (v4
% 24.85/4.19 = v0) | ~ (v2 = v0)))
% 24.85/4.19
% 24.85/4.19 (function-axioms)
% 24.85/4.19 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 24.85/4.19 (mult(v3, v2) = v1) | ~ (mult(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] :
% 24.85/4.19 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (plus(v3, v2) = v1) | ~ (plus(v3,
% 24.85/4.19 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 24.85/4.19 (minus(v2) = v1) | ~ (minus(v2) = v0))
% 24.85/4.19
% 24.85/4.19 Further assumptions not needed in the proof:
% 24.85/4.19 --------------------------------------------
% 24.85/4.19 f01, f02, f03, f04, f05
% 24.85/4.19
% 24.85/4.19 Those formulas are unsatisfiable:
% 24.85/4.19 ---------------------------------
% 24.85/4.19
% 24.85/4.19 Begin of proof
% 24.85/4.19 |
% 24.85/4.19 | ALPHA: (f06) implies:
% 24.85/4.19 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (
% 24.85/4.19 | ~ (mult(v3, v0) = v4) | ~ (mult(v2, v1) = v3) | ~ $i(v2) | ~
% 24.85/4.19 | $i(v1) | ~ $i(v0) | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] :
% 24.85/4.19 | (mult(v6, v1) = v7 & mult(v4, v1) = v5 & mult(v2, v7) = v5 & mult(v1,
% 24.85/4.19 | v0) = v6 & $i(v7) & $i(v6) & $i(v5)))
% 24.85/4.20 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 24.85/4.20 | ! [v5: $i] : ( ~ (mult(v3, v1) = v4) | ~ (mult(v2, v4) = v5) | ~
% 24.85/4.20 | (mult(v1, v0) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: $i]
% 24.85/4.20 | : ? [v7: $i] : (mult(v7, v1) = v5 & mult(v6, v0) = v7 & mult(v2, v1)
% 24.85/4.20 | = v6 & $i(v7) & $i(v6) & $i(v5)))
% 24.85/4.20 |
% 24.85/4.20 | ALPHA: (f07) implies:
% 24.85/4.20 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (mult(v1, v0) = v2) | ~
% 24.85/4.20 | $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] : (mult(v2, v0) = v4 &
% 24.85/4.20 | mult(v1, v3) = v4 & mult(v0, v0) = v3 & $i(v4) & $i(v3)))
% 24.85/4.20 |
% 24.85/4.20 | ALPHA: (f08) implies:
% 24.85/4.20 | (4) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (mult(v0, unit) = v1) | ~
% 24.85/4.20 | $i(v0))
% 24.85/4.20 |
% 24.85/4.20 | ALPHA: (f09) implies:
% 24.85/4.20 | (5) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (mult(unit, v0) = v1) | ~
% 24.85/4.20 | $i(v0))
% 24.85/4.20 |
% 24.85/4.20 | ALPHA: (f10) implies:
% 24.85/4.20 | (6) mult(op_a, op_b) = unit
% 24.85/4.20 |
% 24.85/4.20 | ALPHA: (f11) implies:
% 24.85/4.20 | (7) mult(op_b, op_a) = unit
% 24.85/4.20 |
% 24.85/4.20 | ALPHA: (goals) implies:
% 24.85/4.20 | (8) $i(op_a)
% 24.85/4.20 | (9) $i(op_b)
% 24.85/4.20 | (10) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 24.85/4.20 | (mult(v3, op_a) = v4 & mult(v1, op_b) = v2 & mult(v0, op_b) = v3 &
% 24.85/4.20 | mult(v0, op_a) = v1 & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & (
% 24.85/4.20 | ~ (v4 = v0) | ~ (v2 = v0)))
% 24.85/4.20 |
% 24.85/4.20 | ALPHA: (function-axioms) implies:
% 24.85/4.20 | (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 24.85/4.20 | (mult(v3, v2) = v1) | ~ (mult(v3, v2) = v0))
% 24.85/4.20 |
% 24.85/4.20 | DELTA: instantiating (10) with fresh symbols all_13_0, all_13_1, all_13_2,
% 24.85/4.20 | all_13_3, all_13_4 gives:
% 24.85/4.20 | (12) mult(all_13_1, op_a) = all_13_0 & mult(all_13_3, op_b) = all_13_2 &
% 24.85/4.20 | mult(all_13_4, op_b) = all_13_1 & mult(all_13_4, op_a) = all_13_3 &
% 24.85/4.20 | $i(all_13_0) & $i(all_13_1) & $i(all_13_2) & $i(all_13_3) &
% 24.85/4.20 | $i(all_13_4) & ( ~ (all_13_0 = all_13_4) | ~ (all_13_2 = all_13_4))
% 24.85/4.20 |
% 24.85/4.20 | ALPHA: (12) implies:
% 24.85/4.20 | (13) $i(all_13_4)
% 24.85/4.20 | (14) $i(all_13_3)
% 24.85/4.20 | (15) $i(all_13_2)
% 24.85/4.20 | (16) $i(all_13_1)
% 24.85/4.20 | (17) $i(all_13_0)
% 24.85/4.20 | (18) mult(all_13_4, op_a) = all_13_3
% 24.85/4.20 | (19) mult(all_13_4, op_b) = all_13_1
% 24.85/4.20 | (20) mult(all_13_3, op_b) = all_13_2
% 24.85/4.21 | (21) mult(all_13_1, op_a) = all_13_0
% 24.85/4.21 | (22) ~ (all_13_0 = all_13_4) | ~ (all_13_2 = all_13_4)
% 24.85/4.21 |
% 24.85/4.21 | GROUND_INST: instantiating (3) with op_b, op_a, unit, simplifying with (6),
% 24.85/4.21 | (8), (9) gives:
% 24.85/4.21 | (23) ? [v0: $i] : ? [v1: $i] : (mult(op_b, op_b) = v0 & mult(op_a, v0) =
% 24.85/4.21 | v1 & mult(unit, op_b) = v1 & $i(v1) & $i(v0))
% 24.85/4.21 |
% 24.85/4.21 | GROUND_INST: instantiating (3) with op_a, op_b, unit, simplifying with (7),
% 24.85/4.21 | (8), (9) gives:
% 24.85/4.21 | (24) ? [v0: $i] : ? [v1: $i] : (mult(op_b, v0) = v1 & mult(op_a, op_a) =
% 24.85/4.21 | v0 & mult(unit, op_a) = v1 & $i(v1) & $i(v0))
% 24.85/4.21 |
% 24.85/4.21 | GROUND_INST: instantiating (3) with op_a, all_13_4, all_13_3, simplifying with
% 24.85/4.21 | (8), (13), (18) gives:
% 24.85/4.21 | (25) ? [v0: $i] : ? [v1: $i] : (mult(all_13_3, op_a) = v1 &
% 24.85/4.21 | mult(all_13_4, v0) = v1 & mult(op_a, op_a) = v0 & $i(v1) & $i(v0))
% 24.85/4.21 |
% 24.85/4.21 | GROUND_INST: instantiating (3) with op_b, all_13_4, all_13_1, simplifying with
% 24.85/4.21 | (9), (13), (19) gives:
% 24.85/4.21 | (26) ? [v0: $i] : ? [v1: $i] : (mult(all_13_1, op_b) = v1 &
% 24.85/4.21 | mult(all_13_4, v0) = v1 & mult(op_b, op_b) = v0 & $i(v1) & $i(v0))
% 24.85/4.21 |
% 24.85/4.21 | GROUND_INST: instantiating (1) with op_b, op_a, all_13_4, all_13_3, all_13_2,
% 24.85/4.21 | simplifying with (8), (9), (13), (18), (20) gives:
% 24.85/4.21 | (27) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (mult(v1, op_a) = v2 &
% 24.85/4.21 | mult(all_13_2, op_a) = v0 & mult(all_13_4, v2) = v0 & mult(op_a,
% 24.85/4.21 | op_b) = v1 & $i(v2) & $i(v1) & $i(v0))
% 24.85/4.21 |
% 24.85/4.21 | GROUND_INST: instantiating (3) with op_b, all_13_3, all_13_2, simplifying with
% 24.85/4.21 | (9), (14), (20) gives:
% 24.85/4.21 | (28) ? [v0: $i] : ? [v1: $i] : (mult(all_13_2, op_b) = v1 &
% 24.85/4.21 | mult(all_13_3, v0) = v1 & mult(op_b, op_b) = v0 & $i(v1) & $i(v0))
% 24.85/4.21 |
% 24.85/4.21 | GROUND_INST: instantiating (1) with op_a, op_b, all_13_4, all_13_1, all_13_0,
% 24.85/4.21 | simplifying with (8), (9), (13), (19), (21) gives:
% 24.85/4.21 | (29) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (mult(v1, op_b) = v2 &
% 24.85/4.21 | mult(all_13_0, op_b) = v0 & mult(all_13_4, v2) = v0 & mult(op_b,
% 24.85/4.21 | op_a) = v1 & $i(v2) & $i(v1) & $i(v0))
% 24.85/4.21 |
% 24.85/4.21 | GROUND_INST: instantiating (3) with op_a, all_13_1, all_13_0, simplifying with
% 24.85/4.21 | (8), (16), (21) gives:
% 24.85/4.21 | (30) ? [v0: $i] : ? [v1: $i] : (mult(all_13_0, op_a) = v1 &
% 24.85/4.21 | mult(all_13_1, v0) = v1 & mult(op_a, op_a) = v0 & $i(v1) & $i(v0))
% 24.85/4.21 |
% 24.85/4.21 | DELTA: instantiating (30) with fresh symbols all_20_0, all_20_1 gives:
% 24.85/4.21 | (31) mult(all_13_0, op_a) = all_20_0 & mult(all_13_1, all_20_1) = all_20_0
% 24.85/4.21 | & mult(op_a, op_a) = all_20_1 & $i(all_20_0) & $i(all_20_1)
% 24.85/4.21 |
% 24.85/4.21 | ALPHA: (31) implies:
% 24.85/4.21 | (32) $i(all_20_0)
% 24.85/4.21 | (33) mult(op_a, op_a) = all_20_1
% 24.85/4.21 | (34) mult(all_13_1, all_20_1) = all_20_0
% 24.85/4.22 | (35) mult(all_13_0, op_a) = all_20_0
% 24.85/4.22 |
% 24.85/4.22 | DELTA: instantiating (28) with fresh symbols all_22_0, all_22_1 gives:
% 24.85/4.22 | (36) mult(all_13_2, op_b) = all_22_0 & mult(all_13_3, all_22_1) = all_22_0
% 24.85/4.22 | & mult(op_b, op_b) = all_22_1 & $i(all_22_0) & $i(all_22_1)
% 24.85/4.22 |
% 24.85/4.22 | ALPHA: (36) implies:
% 24.85/4.22 | (37) $i(all_22_0)
% 24.85/4.22 | (38) mult(op_b, op_b) = all_22_1
% 24.85/4.22 | (39) mult(all_13_3, all_22_1) = all_22_0
% 24.85/4.22 | (40) mult(all_13_2, op_b) = all_22_0
% 24.85/4.22 |
% 24.85/4.22 | DELTA: instantiating (26) with fresh symbols all_24_0, all_24_1 gives:
% 24.85/4.22 | (41) mult(all_13_1, op_b) = all_24_0 & mult(all_13_4, all_24_1) = all_24_0
% 24.85/4.22 | & mult(op_b, op_b) = all_24_1 & $i(all_24_0) & $i(all_24_1)
% 24.85/4.22 |
% 24.85/4.22 | ALPHA: (41) implies:
% 24.85/4.22 | (42) $i(all_24_1)
% 24.85/4.22 | (43) mult(op_b, op_b) = all_24_1
% 24.85/4.22 | (44) mult(all_13_1, op_b) = all_24_0
% 24.85/4.22 |
% 24.85/4.22 | DELTA: instantiating (25) with fresh symbols all_26_0, all_26_1 gives:
% 24.85/4.22 | (45) mult(all_13_3, op_a) = all_26_0 & mult(all_13_4, all_26_1) = all_26_0
% 24.85/4.22 | & mult(op_a, op_a) = all_26_1 & $i(all_26_0) & $i(all_26_1)
% 24.85/4.22 |
% 24.85/4.22 | ALPHA: (45) implies:
% 24.85/4.22 | (46) $i(all_26_1)
% 24.85/4.22 | (47) mult(op_a, op_a) = all_26_1
% 24.85/4.22 | (48) mult(all_13_3, op_a) = all_26_0
% 24.85/4.22 |
% 24.85/4.22 | DELTA: instantiating (24) with fresh symbols all_28_0, all_28_1 gives:
% 24.85/4.22 | (49) mult(op_b, all_28_1) = all_28_0 & mult(op_a, op_a) = all_28_1 &
% 24.85/4.22 | mult(unit, op_a) = all_28_0 & $i(all_28_0) & $i(all_28_1)
% 24.85/4.22 |
% 24.85/4.22 | ALPHA: (49) implies:
% 24.85/4.22 | (50) mult(unit, op_a) = all_28_0
% 24.85/4.22 | (51) mult(op_a, op_a) = all_28_1
% 24.85/4.22 | (52) mult(op_b, all_28_1) = all_28_0
% 24.85/4.22 |
% 24.85/4.22 | DELTA: instantiating (23) with fresh symbols all_30_0, all_30_1 gives:
% 24.85/4.22 | (53) mult(op_b, op_b) = all_30_1 & mult(op_a, all_30_1) = all_30_0 &
% 24.85/4.22 | mult(unit, op_b) = all_30_0 & $i(all_30_0) & $i(all_30_1)
% 24.85/4.22 |
% 24.85/4.22 | ALPHA: (53) implies:
% 24.85/4.22 | (54) mult(unit, op_b) = all_30_0
% 24.85/4.22 | (55) mult(op_a, all_30_1) = all_30_0
% 24.85/4.22 | (56) mult(op_b, op_b) = all_30_1
% 24.85/4.22 |
% 24.85/4.22 | DELTA: instantiating (27) with fresh symbols all_32_0, all_32_1, all_32_2
% 24.85/4.22 | gives:
% 24.85/4.22 | (57) mult(all_32_1, op_a) = all_32_0 & mult(all_13_2, op_a) = all_32_2 &
% 24.85/4.22 | mult(all_13_4, all_32_0) = all_32_2 & mult(op_a, op_b) = all_32_1 &
% 24.85/4.22 | $i(all_32_0) & $i(all_32_1) & $i(all_32_2)
% 24.85/4.22 |
% 24.85/4.22 | ALPHA: (57) implies:
% 24.85/4.22 | (58) $i(all_32_1)
% 24.85/4.22 | (59) $i(all_32_0)
% 24.85/4.22 | (60) mult(op_a, op_b) = all_32_1
% 24.85/4.22 | (61) mult(all_13_4, all_32_0) = all_32_2
% 24.85/4.22 | (62) mult(all_13_2, op_a) = all_32_2
% 24.85/4.22 | (63) mult(all_32_1, op_a) = all_32_0
% 24.85/4.22 |
% 24.85/4.22 | DELTA: instantiating (29) with fresh symbols all_34_0, all_34_1, all_34_2
% 24.85/4.22 | gives:
% 24.85/4.22 | (64) mult(all_34_1, op_b) = all_34_0 & mult(all_13_0, op_b) = all_34_2 &
% 24.85/4.22 | mult(all_13_4, all_34_0) = all_34_2 & mult(op_b, op_a) = all_34_1 &
% 24.85/4.22 | $i(all_34_0) & $i(all_34_1) & $i(all_34_2)
% 24.85/4.22 |
% 24.85/4.22 | ALPHA: (64) implies:
% 24.85/4.22 | (65) $i(all_34_0)
% 24.85/4.22 | (66) mult(op_b, op_a) = all_34_1
% 24.85/4.22 | (67) mult(all_13_4, all_34_0) = all_34_2
% 24.85/4.22 | (68) mult(all_13_0, op_b) = all_34_2
% 24.85/4.22 | (69) mult(all_34_1, op_b) = all_34_0
% 24.85/4.22 |
% 24.85/4.22 | GROUND_INST: instantiating (11) with all_26_1, all_28_1, op_a, op_a,
% 24.85/4.22 | simplifying with (47), (51) gives:
% 24.85/4.22 | (70) all_28_1 = all_26_1
% 24.85/4.22 |
% 24.85/4.22 | GROUND_INST: instantiating (11) with all_20_1, all_28_1, op_a, op_a,
% 24.85/4.22 | simplifying with (33), (51) gives:
% 24.85/4.22 | (71) all_28_1 = all_20_1
% 24.85/4.22 |
% 24.85/4.22 | GROUND_INST: instantiating (11) with unit, all_32_1, op_b, op_a, simplifying
% 24.85/4.22 | with (6), (60) gives:
% 24.85/4.22 | (72) all_32_1 = unit
% 24.85/4.22 |
% 24.85/4.22 | GROUND_INST: instantiating (11) with unit, all_34_1, op_a, op_b, simplifying
% 24.85/4.22 | with (7), (66) gives:
% 24.85/4.22 | (73) all_34_1 = unit
% 24.85/4.22 |
% 24.85/4.22 | GROUND_INST: instantiating (11) with all_24_1, all_30_1, op_b, op_b,
% 24.85/4.22 | simplifying with (43), (56) gives:
% 24.85/4.22 | (74) all_30_1 = all_24_1
% 24.85/4.22 |
% 24.85/4.22 | GROUND_INST: instantiating (11) with all_22_1, all_30_1, op_b, op_b,
% 24.85/4.22 | simplifying with (38), (56) gives:
% 24.85/4.22 | (75) all_30_1 = all_22_1
% 24.85/4.22 |
% 24.85/4.23 | COMBINE_EQS: (74), (75) imply:
% 24.85/4.23 | (76) all_24_1 = all_22_1
% 24.85/4.23 |
% 24.85/4.23 | COMBINE_EQS: (70), (71) imply:
% 24.85/4.23 | (77) all_26_1 = all_20_1
% 24.85/4.23 |
% 24.85/4.23 | SIMP: (77) implies:
% 24.85/4.23 | (78) all_26_1 = all_20_1
% 24.85/4.23 |
% 24.85/4.23 | REDUCE: (69), (73) imply:
% 24.85/4.23 | (79) mult(unit, op_b) = all_34_0
% 24.85/4.23 |
% 24.85/4.23 | REDUCE: (63), (72) imply:
% 24.85/4.23 | (80) mult(unit, op_a) = all_32_0
% 24.85/4.23 |
% 24.85/4.23 | REDUCE: (52), (71) imply:
% 24.85/4.23 | (81) mult(op_b, all_20_1) = all_28_0
% 25.43/4.23 |
% 25.43/4.23 | REDUCE: (55), (75) imply:
% 25.43/4.23 | (82) mult(op_a, all_22_1) = all_30_0
% 25.43/4.23 |
% 25.43/4.23 | REDUCE: (58), (72) imply:
% 25.43/4.23 | (83) $i(unit)
% 25.43/4.23 |
% 25.43/4.23 | REDUCE: (46), (78) imply:
% 25.43/4.23 | (84) $i(all_20_1)
% 25.43/4.23 |
% 25.43/4.23 | REDUCE: (42), (76) imply:
% 25.43/4.23 | (85) $i(all_22_1)
% 25.43/4.23 |
% 25.43/4.23 | GROUND_INST: instantiating (11) with all_28_0, all_32_0, op_a, unit,
% 25.43/4.23 | simplifying with (50), (80) gives:
% 25.43/4.23 | (86) all_32_0 = all_28_0
% 25.43/4.23 |
% 25.43/4.23 | GROUND_INST: instantiating (11) with all_30_0, all_34_0, op_b, unit,
% 25.43/4.23 | simplifying with (54), (79) gives:
% 25.43/4.23 | (87) all_34_0 = all_30_0
% 25.43/4.23 |
% 25.43/4.23 | REDUCE: (67), (87) imply:
% 25.43/4.23 | (88) mult(all_13_4, all_30_0) = all_34_2
% 25.43/4.23 |
% 25.43/4.23 | REDUCE: (61), (86) imply:
% 25.43/4.23 | (89) mult(all_13_4, all_28_0) = all_32_2
% 25.43/4.23 |
% 25.43/4.23 | REDUCE: (65), (87) imply:
% 25.43/4.23 | (90) $i(all_30_0)
% 25.43/4.23 |
% 25.43/4.23 | REDUCE: (59), (86) imply:
% 25.43/4.23 | (91) $i(all_28_0)
% 25.43/4.23 |
% 25.43/4.23 | GROUND_INST: instantiating (1) with op_a, op_a, op_b, unit, all_28_0,
% 25.43/4.23 | simplifying with (7), (8), (9), (50) gives:
% 25.43/4.23 | (92) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (mult(v1, op_a) = v2 &
% 25.43/4.23 | mult(all_28_0, op_a) = v0 & mult(op_b, v2) = v0 & mult(op_a, op_a) =
% 25.43/4.23 | v1 & $i(v2) & $i(v1) & $i(v0))
% 25.43/4.23 |
% 25.43/4.23 | GROUND_INST: instantiating (1) with op_a, op_b, op_a, unit, all_28_0,
% 25.43/4.23 | simplifying with (6), (8), (9), (50) gives:
% 25.43/4.23 | (93) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (mult(v1, op_b) = v2 &
% 25.43/4.23 | mult(all_28_0, op_b) = v0 & mult(op_b, op_a) = v1 & mult(op_a, v2) =
% 25.43/4.23 | v0 & $i(v2) & $i(v1) & $i(v0))
% 25.43/4.23 |
% 25.43/4.23 | GROUND_INST: instantiating (5) with op_a, all_28_0, simplifying with (8), (50)
% 25.43/4.23 | gives:
% 25.43/4.23 | (94) all_28_0 = op_a
% 25.43/4.23 |
% 25.43/4.23 | GROUND_INST: instantiating (3) with op_a, unit, all_28_0, simplifying with
% 25.43/4.23 | (8), (50), (83) gives:
% 25.43/4.23 | (95) ? [v0: $i] : ? [v1: $i] : (mult(all_28_0, op_a) = v1 & mult(op_a,
% 25.43/4.23 | op_a) = v0 & mult(unit, v0) = v1 & $i(v1) & $i(v0))
% 25.43/4.23 |
% 25.43/4.23 | GROUND_INST: instantiating (1) with op_b, op_a, op_b, unit, all_30_0,
% 25.43/4.23 | simplifying with (7), (8), (9), (54) gives:
% 25.43/4.23 | (96) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (mult(v1, op_a) = v2 &
% 25.43/4.23 | mult(all_30_0, op_a) = v0 & mult(op_b, v2) = v0 & mult(op_a, op_b) =
% 25.43/4.23 | v1 & $i(v2) & $i(v1) & $i(v0))
% 25.43/4.23 |
% 25.43/4.23 | GROUND_INST: instantiating (1) with op_b, op_b, op_a, unit, all_30_0,
% 25.43/4.23 | simplifying with (6), (8), (9), (54) gives:
% 25.43/4.23 | (97) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (mult(v1, op_b) = v2 &
% 25.43/4.23 | mult(all_30_0, op_b) = v0 & mult(op_b, op_b) = v1 & mult(op_a, v2) =
% 25.43/4.23 | v0 & $i(v2) & $i(v1) & $i(v0))
% 25.43/4.23 |
% 25.43/4.23 | GROUND_INST: instantiating (5) with op_b, all_30_0, simplifying with (9), (54)
% 25.43/4.23 | gives:
% 25.43/4.24 | (98) all_30_0 = op_b
% 25.43/4.24 |
% 25.43/4.24 | GROUND_INST: instantiating (3) with op_b, unit, all_30_0, simplifying with
% 25.43/4.24 | (9), (54), (83) gives:
% 25.43/4.24 | (99) ? [v0: $i] : ? [v1: $i] : (mult(all_30_0, op_b) = v1 & mult(op_b,
% 25.43/4.24 | op_b) = v0 & mult(unit, v0) = v1 & $i(v1) & $i(v0))
% 25.43/4.24 |
% 25.43/4.24 | GROUND_INST: instantiating (3) with op_a, op_a, all_20_1, simplifying with
% 25.43/4.24 | (8), (33) gives:
% 25.43/4.24 | (100) ? [v0: $i] : ? [v1: $i] : (mult(all_20_1, op_a) = v1 & mult(op_a,
% 25.43/4.24 | v0) = v1 & mult(op_a, op_a) = v0 & $i(v1) & $i(v0))
% 25.43/4.24 |
% 25.43/4.24 | GROUND_INST: instantiating (3) with op_b, op_b, all_22_1, simplifying with
% 25.43/4.24 | (9), (38) gives:
% 25.43/4.24 | (101) ? [v0: $i] : ? [v1: $i] : (mult(all_22_1, op_b) = v1 & mult(op_b,
% 25.43/4.24 | v0) = v1 & mult(op_b, op_b) = v0 & $i(v1) & $i(v0))
% 25.43/4.24 |
% 25.43/4.24 | GROUND_INST: instantiating (3) with all_28_0, all_13_4, all_32_2, simplifying
% 25.43/4.24 | with (13), (89), (91) gives:
% 25.43/4.24 | (102) ? [v0: $i] : ? [v1: $i] : (mult(all_32_2, all_28_0) = v1 &
% 25.43/4.24 | mult(all_28_0, all_28_0) = v0 & mult(all_13_4, v0) = v1 & $i(v1) &
% 25.43/4.24 | $i(v0))
% 25.43/4.24 |
% 25.43/4.24 | GROUND_INST: instantiating (3) with all_30_0, all_13_4, all_34_2, simplifying
% 25.43/4.24 | with (13), (88), (90) gives:
% 25.43/4.24 | (103) ? [v0: $i] : ? [v1: $i] : (mult(all_34_2, all_30_0) = v1 &
% 25.43/4.24 | mult(all_30_0, all_30_0) = v0 & mult(all_13_4, v0) = v1 & $i(v1) &
% 25.43/4.24 | $i(v0))
% 25.43/4.24 |
% 25.43/4.24 | GROUND_INST: instantiating (1) with op_a, op_a, all_13_4, all_13_3, all_26_0,
% 25.43/4.24 | simplifying with (8), (13), (18), (48) gives:
% 25.43/4.24 | (104) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (mult(v1, op_a) = v2 &
% 25.43/4.24 | mult(all_26_0, op_a) = v0 & mult(all_13_4, v2) = v0 & mult(op_a,
% 25.43/4.24 | op_a) = v1 & $i(v2) & $i(v1) & $i(v0))
% 25.43/4.24 |
% 25.43/4.24 | GROUND_INST: instantiating (3) with op_a, all_13_3, all_26_0, simplifying with
% 25.43/4.24 | (8), (14), (48) gives:
% 25.43/4.24 | (105) ? [v0: $i] : ? [v1: $i] : (mult(all_26_0, op_a) = v1 &
% 25.43/4.24 | mult(all_13_3, v0) = v1 & mult(op_a, op_a) = v0 & $i(v1) & $i(v0))
% 25.43/4.24 |
% 25.43/4.24 | GROUND_INST: instantiating (1) with all_22_1, op_a, all_13_4, all_13_3,
% 25.43/4.24 | all_22_0, simplifying with (8), (13), (18), (39), (85) gives:
% 25.43/4.24 | (106) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (mult(v1, op_a) = v2 &
% 25.43/4.24 | mult(all_22_0, op_a) = v0 & mult(all_13_4, v2) = v0 & mult(op_a,
% 25.43/4.24 | all_22_1) = v1 & $i(v2) & $i(v1) & $i(v0))
% 25.43/4.24 |
% 25.43/4.24 | GROUND_INST: instantiating (1) with op_a, op_b, all_13_3, all_13_2, all_32_2,
% 25.43/4.24 | simplifying with (8), (9), (14), (20), (62) gives:
% 25.43/4.24 | (107) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (mult(v1, op_b) = v2 &
% 25.43/4.24 | mult(all_32_2, op_b) = v0 & mult(all_13_3, v2) = v0 & mult(op_b,
% 25.43/4.24 | op_a) = v1 & $i(v2) & $i(v1) & $i(v0))
% 25.43/4.24 |
% 25.43/4.24 | GROUND_INST: instantiating (3) with op_a, all_13_2, all_32_2, simplifying with
% 25.43/4.24 | (8), (15), (62) gives:
% 25.43/4.24 | (108) ? [v0: $i] : ? [v1: $i] : (mult(all_32_2, op_a) = v1 &
% 25.43/4.24 | mult(all_13_2, v0) = v1 & mult(op_a, op_a) = v0 & $i(v1) & $i(v0))
% 25.43/4.24 |
% 25.43/4.24 | GROUND_INST: instantiating (1) with op_b, op_b, all_13_3, all_13_2, all_22_0,
% 25.43/4.24 | simplifying with (9), (14), (20), (40) gives:
% 25.43/4.24 | (109) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (mult(v1, op_b) = v2 &
% 25.43/4.24 | mult(all_22_0, op_b) = v0 & mult(all_13_3, v2) = v0 & mult(op_b,
% 25.43/4.24 | op_b) = v1 & $i(v2) & $i(v1) & $i(v0))
% 25.43/4.24 |
% 25.43/4.24 | GROUND_INST: instantiating (3) with op_b, all_13_2, all_22_0, simplifying with
% 25.43/4.25 | (9), (15), (40) gives:
% 25.43/4.25 | (110) ? [v0: $i] : ? [v1: $i] : (mult(all_22_0, op_b) = v1 &
% 25.43/4.25 | mult(all_13_2, v0) = v1 & mult(op_b, op_b) = v0 & $i(v1) & $i(v0))
% 25.43/4.25 |
% 25.43/4.25 | GROUND_INST: instantiating (1) with op_b, op_b, all_13_4, all_13_1, all_24_0,
% 25.43/4.25 | simplifying with (9), (13), (19), (44) gives:
% 25.43/4.25 | (111) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (mult(v1, op_b) = v2 &
% 25.43/4.25 | mult(all_24_0, op_b) = v0 & mult(all_13_4, v2) = v0 & mult(op_b,
% 25.43/4.25 | op_b) = v1 & $i(v2) & $i(v1) & $i(v0))
% 25.43/4.25 |
% 25.43/4.25 | GROUND_INST: instantiating (3) with op_b, all_13_1, all_24_0, simplifying with
% 25.43/4.25 | (9), (16), (44) gives:
% 25.43/4.25 | (112) ? [v0: $i] : ? [v1: $i] : (mult(all_24_0, op_b) = v1 &
% 25.43/4.25 | mult(all_13_1, v0) = v1 & mult(op_b, op_b) = v0 & $i(v1) & $i(v0))
% 25.43/4.25 |
% 25.43/4.25 | GROUND_INST: instantiating (1) with all_20_1, op_b, all_13_4, all_13_1,
% 25.43/4.25 | all_20_0, simplifying with (9), (13), (19), (34), (84) gives:
% 25.43/4.25 | (113) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (mult(v1, op_b) = v2 &
% 25.43/4.25 | mult(all_20_0, op_b) = v0 & mult(all_13_4, v2) = v0 & mult(op_b,
% 25.43/4.25 | all_20_1) = v1 & $i(v2) & $i(v1) & $i(v0))
% 25.43/4.25 |
% 25.43/4.25 | GROUND_INST: instantiating (1) with op_a, op_a, all_13_1, all_13_0, all_20_0,
% 25.43/4.25 | simplifying with (8), (16), (21), (35) gives:
% 25.43/4.25 | (114) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (mult(v1, op_a) = v2 &
% 25.43/4.25 | mult(all_20_0, op_a) = v0 & mult(all_13_1, v2) = v0 & mult(op_a,
% 25.43/4.25 | op_a) = v1 & $i(v2) & $i(v1) & $i(v0))
% 25.43/4.25 |
% 25.43/4.25 | GROUND_INST: instantiating (3) with op_a, all_13_0, all_20_0, simplifying with
% 25.43/4.25 | (8), (17), (35) gives:
% 25.43/4.25 | (115) ? [v0: $i] : ? [v1: $i] : (mult(all_20_0, op_a) = v1 &
% 25.43/4.25 | mult(all_13_0, v0) = v1 & mult(op_a, op_a) = v0 & $i(v1) & $i(v0))
% 25.43/4.25 |
% 25.43/4.25 | GROUND_INST: instantiating (1) with op_b, op_a, all_13_1, all_13_0, all_34_2,
% 25.43/4.25 | simplifying with (8), (9), (16), (21), (68) gives:
% 25.43/4.25 | (116) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (mult(v1, op_a) = v2 &
% 25.43/4.25 | mult(all_34_2, op_a) = v0 & mult(all_13_1, v2) = v0 & mult(op_a,
% 25.43/4.25 | op_b) = v1 & $i(v2) & $i(v1) & $i(v0))
% 25.43/4.25 |
% 25.43/4.25 | GROUND_INST: instantiating (3) with op_b, all_13_0, all_34_2, simplifying with
% 25.43/4.25 | (9), (17), (68) gives:
% 25.43/4.25 | (117) ? [v0: $i] : ? [v1: $i] : (mult(all_34_2, op_b) = v1 &
% 25.43/4.25 | mult(all_13_0, v0) = v1 & mult(op_b, op_b) = v0 & $i(v1) & $i(v0))
% 25.43/4.25 |
% 25.43/4.25 | DELTA: instantiating (115) with fresh symbols all_50_0, all_50_1 gives:
% 25.43/4.25 | (118) mult(all_20_0, op_a) = all_50_0 & mult(all_13_0, all_50_1) = all_50_0
% 25.43/4.25 | & mult(op_a, op_a) = all_50_1 & $i(all_50_0) & $i(all_50_1)
% 25.43/4.25 |
% 25.43/4.25 | ALPHA: (118) implies:
% 25.43/4.25 | (119) $i(all_50_1)
% 25.43/4.25 | (120) mult(op_a, op_a) = all_50_1
% 25.43/4.25 |
% 25.43/4.25 | DELTA: instantiating (112) with fresh symbols all_52_0, all_52_1 gives:
% 25.43/4.25 | (121) mult(all_24_0, op_b) = all_52_0 & mult(all_13_1, all_52_1) = all_52_0
% 25.43/4.25 | & mult(op_b, op_b) = all_52_1 & $i(all_52_0) & $i(all_52_1)
% 25.43/4.25 |
% 25.43/4.25 | ALPHA: (121) implies:
% 25.43/4.25 | (122) $i(all_52_1)
% 25.43/4.25 | (123) mult(op_b, op_b) = all_52_1
% 25.43/4.25 |
% 25.43/4.25 | DELTA: instantiating (110) with fresh symbols all_54_0, all_54_1 gives:
% 25.43/4.25 | (124) mult(all_22_0, op_b) = all_54_0 & mult(all_13_2, all_54_1) = all_54_0
% 25.43/4.25 | & mult(op_b, op_b) = all_54_1 & $i(all_54_0) & $i(all_54_1)
% 25.43/4.25 |
% 25.43/4.25 | ALPHA: (124) implies:
% 25.43/4.25 | (125) mult(op_b, op_b) = all_54_1
% 25.43/4.25 |
% 25.43/4.25 | DELTA: instantiating (117) with fresh symbols all_58_0, all_58_1 gives:
% 25.43/4.25 | (126) mult(all_34_2, op_b) = all_58_0 & mult(all_13_0, all_58_1) = all_58_0
% 25.43/4.25 | & mult(op_b, op_b) = all_58_1 & $i(all_58_0) & $i(all_58_1)
% 25.43/4.25 |
% 25.43/4.25 | ALPHA: (126) implies:
% 25.43/4.25 | (127) mult(op_b, op_b) = all_58_1
% 25.43/4.25 |
% 25.43/4.25 | DELTA: instantiating (102) with fresh symbols all_60_0, all_60_1 gives:
% 25.43/4.25 | (128) mult(all_32_2, all_28_0) = all_60_0 & mult(all_28_0, all_28_0) =
% 25.43/4.26 | all_60_1 & mult(all_13_4, all_60_1) = all_60_0 & $i(all_60_0) &
% 25.43/4.26 | $i(all_60_1)
% 25.43/4.26 |
% 25.43/4.26 | ALPHA: (128) implies:
% 25.43/4.26 | (129) mult(all_28_0, all_28_0) = all_60_1
% 25.43/4.26 |
% 25.43/4.26 | DELTA: instantiating (108) with fresh symbols all_64_0, all_64_1 gives:
% 25.43/4.26 | (130) mult(all_32_2, op_a) = all_64_0 & mult(all_13_2, all_64_1) = all_64_0
% 25.43/4.26 | & mult(op_a, op_a) = all_64_1 & $i(all_64_0) & $i(all_64_1)
% 25.43/4.26 |
% 25.43/4.26 | ALPHA: (130) implies:
% 25.43/4.26 | (131) mult(op_a, op_a) = all_64_1
% 25.43/4.26 |
% 25.43/4.26 | DELTA: instantiating (105) with fresh symbols all_66_0, all_66_1 gives:
% 25.43/4.26 | (132) mult(all_26_0, op_a) = all_66_0 & mult(all_13_3, all_66_1) = all_66_0
% 25.43/4.26 | & mult(op_a, op_a) = all_66_1 & $i(all_66_0) & $i(all_66_1)
% 25.43/4.26 |
% 25.43/4.26 | ALPHA: (132) implies:
% 25.43/4.26 | (133) mult(op_a, op_a) = all_66_1
% 25.43/4.26 |
% 25.43/4.26 | DELTA: instantiating (103) with fresh symbols all_70_0, all_70_1 gives:
% 25.43/4.26 | (134) mult(all_34_2, all_30_0) = all_70_0 & mult(all_30_0, all_30_0) =
% 25.43/4.26 | all_70_1 & mult(all_13_4, all_70_1) = all_70_0 & $i(all_70_0) &
% 25.43/4.26 | $i(all_70_1)
% 25.43/4.26 |
% 25.43/4.26 | ALPHA: (134) implies:
% 25.43/4.26 | (135) mult(all_30_0, all_30_0) = all_70_1
% 25.43/4.26 |
% 25.43/4.26 | DELTA: instantiating (101) with fresh symbols all_72_0, all_72_1 gives:
% 25.43/4.26 | (136) mult(all_22_1, op_b) = all_72_0 & mult(op_b, all_72_1) = all_72_0 &
% 25.43/4.26 | mult(op_b, op_b) = all_72_1 & $i(all_72_0) & $i(all_72_1)
% 25.43/4.26 |
% 25.43/4.26 | ALPHA: (136) implies:
% 25.43/4.26 | (137) mult(op_b, op_b) = all_72_1
% 25.43/4.26 |
% 25.43/4.26 | DELTA: instantiating (100) with fresh symbols all_74_0, all_74_1 gives:
% 25.43/4.26 | (138) mult(all_20_1, op_a) = all_74_0 & mult(op_a, all_74_1) = all_74_0 &
% 25.43/4.26 | mult(op_a, op_a) = all_74_1 & $i(all_74_0) & $i(all_74_1)
% 25.43/4.26 |
% 25.43/4.26 | ALPHA: (138) implies:
% 25.43/4.26 | (139) mult(op_a, op_a) = all_74_1
% 25.43/4.26 |
% 25.43/4.26 | DELTA: instantiating (99) with fresh symbols all_76_0, all_76_1 gives:
% 25.43/4.26 | (140) mult(all_30_0, op_b) = all_76_0 & mult(op_b, op_b) = all_76_1 &
% 25.43/4.26 | mult(unit, all_76_1) = all_76_0 & $i(all_76_0) & $i(all_76_1)
% 25.43/4.26 |
% 25.43/4.26 | ALPHA: (140) implies:
% 25.43/4.26 | (141) mult(op_b, op_b) = all_76_1
% 25.43/4.26 | (142) mult(all_30_0, op_b) = all_76_0
% 25.43/4.26 |
% 25.43/4.26 | DELTA: instantiating (95) with fresh symbols all_82_0, all_82_1 gives:
% 25.43/4.26 | (143) mult(all_28_0, op_a) = all_82_0 & mult(op_a, op_a) = all_82_1 &
% 25.43/4.26 | mult(unit, all_82_1) = all_82_0 & $i(all_82_0) & $i(all_82_1)
% 25.43/4.26 |
% 25.43/4.26 | ALPHA: (143) implies:
% 25.43/4.26 | (144) mult(op_a, op_a) = all_82_1
% 25.43/4.26 | (145) mult(all_28_0, op_a) = all_82_0
% 25.43/4.26 |
% 25.43/4.26 | DELTA: instantiating (114) with fresh symbols all_86_0, all_86_1, all_86_2
% 25.43/4.26 | gives:
% 25.43/4.26 | (146) mult(all_86_1, op_a) = all_86_0 & mult(all_20_0, op_a) = all_86_2 &
% 25.43/4.26 | mult(all_13_1, all_86_0) = all_86_2 & mult(op_a, op_a) = all_86_1 &
% 25.43/4.26 | $i(all_86_0) & $i(all_86_1) & $i(all_86_2)
% 25.43/4.26 |
% 25.43/4.26 | ALPHA: (146) implies:
% 25.43/4.26 | (147) mult(op_a, op_a) = all_86_1
% 25.43/4.26 |
% 25.43/4.26 | DELTA: instantiating (97) with fresh symbols all_88_0, all_88_1, all_88_2
% 25.43/4.26 | gives:
% 25.43/4.26 | (148) mult(all_88_1, op_b) = all_88_0 & mult(all_30_0, op_b) = all_88_2 &
% 25.43/4.26 | mult(op_b, op_b) = all_88_1 & mult(op_a, all_88_0) = all_88_2 &
% 25.43/4.26 | $i(all_88_0) & $i(all_88_1) & $i(all_88_2)
% 25.43/4.26 |
% 25.43/4.26 | ALPHA: (148) implies:
% 25.43/4.26 | (149) mult(op_b, op_b) = all_88_1
% 25.43/4.26 | (150) mult(all_30_0, op_b) = all_88_2
% 25.43/4.26 |
% 25.43/4.26 | DELTA: instantiating (93) with fresh symbols all_90_0, all_90_1, all_90_2
% 25.43/4.26 | gives:
% 25.43/4.26 | (151) mult(all_90_1, op_b) = all_90_0 & mult(all_28_0, op_b) = all_90_2 &
% 25.43/4.26 | mult(op_b, op_a) = all_90_1 & mult(op_a, all_90_0) = all_90_2 &
% 25.43/4.26 | $i(all_90_0) & $i(all_90_1) & $i(all_90_2)
% 25.43/4.26 |
% 25.43/4.26 | ALPHA: (151) implies:
% 25.43/4.26 | (152) $i(all_90_0)
% 25.43/4.26 | (153) mult(op_b, op_a) = all_90_1
% 25.43/4.26 | (154) mult(all_28_0, op_b) = all_90_2
% 25.43/4.26 | (155) mult(all_90_1, op_b) = all_90_0
% 25.43/4.26 |
% 25.43/4.26 | DELTA: instantiating (92) with fresh symbols all_92_0, all_92_1, all_92_2
% 25.43/4.26 | gives:
% 25.43/4.26 | (156) mult(all_92_1, op_a) = all_92_0 & mult(all_28_0, op_a) = all_92_2 &
% 25.43/4.26 | mult(op_b, all_92_0) = all_92_2 & mult(op_a, op_a) = all_92_1 &
% 25.43/4.26 | $i(all_92_0) & $i(all_92_1) & $i(all_92_2)
% 25.43/4.26 |
% 25.43/4.26 | ALPHA: (156) implies:
% 25.43/4.26 | (157) mult(op_a, op_a) = all_92_1
% 25.43/4.26 | (158) mult(all_28_0, op_a) = all_92_2
% 25.43/4.26 |
% 25.43/4.26 | DELTA: instantiating (96) with fresh symbols all_94_0, all_94_1, all_94_2
% 25.43/4.26 | gives:
% 25.43/4.26 | (159) mult(all_94_1, op_a) = all_94_0 & mult(all_30_0, op_a) = all_94_2 &
% 25.43/4.26 | mult(op_b, all_94_0) = all_94_2 & mult(op_a, op_b) = all_94_1 &
% 25.43/4.26 | $i(all_94_0) & $i(all_94_1) & $i(all_94_2)
% 25.43/4.26 |
% 25.43/4.26 | ALPHA: (159) implies:
% 25.43/4.26 | (160) $i(all_94_0)
% 25.43/4.26 | (161) mult(op_a, op_b) = all_94_1
% 25.43/4.26 | (162) mult(all_30_0, op_a) = all_94_2
% 25.43/4.26 | (163) mult(all_94_1, op_a) = all_94_0
% 25.43/4.26 |
% 25.43/4.26 | DELTA: instantiating (116) with fresh symbols all_96_0, all_96_1, all_96_2
% 25.43/4.26 | gives:
% 25.43/4.26 | (164) mult(all_96_1, op_a) = all_96_0 & mult(all_34_2, op_a) = all_96_2 &
% 25.43/4.26 | mult(all_13_1, all_96_0) = all_96_2 & mult(op_a, op_b) = all_96_1 &
% 25.43/4.26 | $i(all_96_0) & $i(all_96_1) & $i(all_96_2)
% 25.43/4.26 |
% 25.43/4.26 | ALPHA: (164) implies:
% 25.43/4.26 | (165) $i(all_96_2)
% 25.43/4.26 | (166) mult(op_a, op_b) = all_96_1
% 25.43/4.26 | (167) mult(all_34_2, op_a) = all_96_2
% 25.43/4.26 | (168) mult(all_96_1, op_a) = all_96_0
% 25.43/4.26 |
% 25.43/4.26 | DELTA: instantiating (111) with fresh symbols all_98_0, all_98_1, all_98_2
% 25.43/4.26 | gives:
% 25.43/4.26 | (169) mult(all_98_1, op_b) = all_98_0 & mult(all_24_0, op_b) = all_98_2 &
% 25.43/4.26 | mult(all_13_4, all_98_0) = all_98_2 & mult(op_b, op_b) = all_98_1 &
% 25.43/4.26 | $i(all_98_0) & $i(all_98_1) & $i(all_98_2)
% 25.43/4.26 |
% 25.43/4.26 | ALPHA: (169) implies:
% 25.43/4.26 | (170) mult(op_b, op_b) = all_98_1
% 25.43/4.26 |
% 25.43/4.26 | DELTA: instantiating (104) with fresh symbols all_100_0, all_100_1, all_100_2
% 25.43/4.26 | gives:
% 25.43/4.26 | (171) mult(all_100_1, op_a) = all_100_0 & mult(all_26_0, op_a) = all_100_2
% 25.43/4.26 | & mult(all_13_4, all_100_0) = all_100_2 & mult(op_a, op_a) =
% 25.43/4.26 | all_100_1 & $i(all_100_0) & $i(all_100_1) & $i(all_100_2)
% 25.43/4.26 |
% 25.43/4.26 | ALPHA: (171) implies:
% 25.43/4.26 | (172) mult(op_a, op_a) = all_100_1
% 25.43/4.26 |
% 25.43/4.26 | DELTA: instantiating (109) with fresh symbols all_102_0, all_102_1, all_102_2
% 25.43/4.26 | gives:
% 25.43/4.27 | (173) mult(all_102_1, op_b) = all_102_0 & mult(all_22_0, op_b) = all_102_2
% 25.43/4.27 | & mult(all_13_3, all_102_0) = all_102_2 & mult(op_b, op_b) =
% 25.43/4.27 | all_102_1 & $i(all_102_0) & $i(all_102_1) & $i(all_102_2)
% 25.43/4.27 |
% 25.43/4.27 | ALPHA: (173) implies:
% 25.43/4.27 | (174) mult(op_b, op_b) = all_102_1
% 25.43/4.27 |
% 25.43/4.27 | DELTA: instantiating (107) with fresh symbols all_104_0, all_104_1, all_104_2
% 25.43/4.27 | gives:
% 25.43/4.27 | (175) mult(all_104_1, op_b) = all_104_0 & mult(all_32_2, op_b) = all_104_2
% 25.43/4.27 | & mult(all_13_3, all_104_0) = all_104_2 & mult(op_b, op_a) =
% 25.43/4.27 | all_104_1 & $i(all_104_0) & $i(all_104_1) & $i(all_104_2)
% 25.43/4.27 |
% 25.43/4.27 | ALPHA: (175) implies:
% 25.43/4.27 | (176) $i(all_104_2)
% 25.43/4.27 | (177) mult(op_b, op_a) = all_104_1
% 25.43/4.27 | (178) mult(all_32_2, op_b) = all_104_2
% 25.43/4.27 | (179) mult(all_104_1, op_b) = all_104_0
% 25.43/4.27 |
% 25.43/4.27 | DELTA: instantiating (106) with fresh symbols all_106_0, all_106_1, all_106_2
% 25.43/4.27 | gives:
% 25.43/4.27 | (180) mult(all_106_1, op_a) = all_106_0 & mult(all_22_0, op_a) = all_106_2
% 25.43/4.27 | & mult(all_13_4, all_106_0) = all_106_2 & mult(op_a, all_22_1) =
% 25.43/4.27 | all_106_1 & $i(all_106_0) & $i(all_106_1) & $i(all_106_2)
% 25.43/4.27 |
% 25.43/4.27 | ALPHA: (180) implies:
% 25.43/4.27 | (181) mult(op_a, all_22_1) = all_106_1
% 25.43/4.27 | (182) mult(all_13_4, all_106_0) = all_106_2
% 25.43/4.27 | (183) mult(all_22_0, op_a) = all_106_2
% 25.43/4.27 | (184) mult(all_106_1, op_a) = all_106_0
% 25.43/4.27 |
% 25.43/4.27 | DELTA: instantiating (113) with fresh symbols all_108_0, all_108_1, all_108_2
% 25.43/4.27 | gives:
% 25.43/4.27 | (185) mult(all_108_1, op_b) = all_108_0 & mult(all_20_0, op_b) = all_108_2
% 25.43/4.27 | & mult(all_13_4, all_108_0) = all_108_2 & mult(op_b, all_20_1) =
% 25.43/4.27 | all_108_1 & $i(all_108_0) & $i(all_108_1) & $i(all_108_2)
% 25.43/4.27 |
% 25.43/4.27 | ALPHA: (185) implies:
% 25.43/4.27 | (186) mult(op_b, all_20_1) = all_108_1
% 25.43/4.27 | (187) mult(all_13_4, all_108_0) = all_108_2
% 25.43/4.27 | (188) mult(all_20_0, op_b) = all_108_2
% 25.43/4.27 | (189) mult(all_108_1, op_b) = all_108_0
% 25.43/4.27 |
% 25.43/4.27 | REDUCE: (98), (135) imply:
% 25.43/4.27 | (190) mult(op_b, op_b) = all_70_1
% 25.43/4.27 |
% 25.43/4.27 | REDUCE: (98), (150) imply:
% 25.43/4.27 | (191) mult(op_b, op_b) = all_88_2
% 25.43/4.27 |
% 25.43/4.27 | REDUCE: (98), (142) imply:
% 25.43/4.27 | (192) mult(op_b, op_b) = all_76_0
% 25.43/4.27 |
% 25.43/4.27 | REDUCE: (98), (162) imply:
% 25.43/4.27 | (193) mult(op_b, op_a) = all_94_2
% 25.43/4.27 |
% 25.43/4.27 | REDUCE: (94), (129) imply:
% 25.43/4.27 | (194) mult(op_a, op_a) = all_60_1
% 25.43/4.27 |
% 25.43/4.27 | REDUCE: (94), (154) imply:
% 25.43/4.27 | (195) mult(op_a, op_b) = all_90_2
% 25.43/4.27 |
% 25.43/4.27 | REDUCE: (94), (158) imply:
% 25.43/4.27 | (196) mult(op_a, op_a) = all_92_2
% 25.43/4.27 |
% 25.43/4.27 | REDUCE: (94), (145) imply:
% 25.43/4.27 | (197) mult(op_a, op_a) = all_82_0
% 25.43/4.27 |
% 25.43/4.27 | REDUCE: (88), (98) imply:
% 25.43/4.27 | (198) mult(all_13_4, op_b) = all_34_2
% 25.43/4.27 |
% 25.43/4.27 | REDUCE: (89), (94) imply:
% 25.43/4.27 | (199) mult(all_13_4, op_a) = all_32_2
% 25.43/4.27 |
% 25.43/4.27 | REDUCE: (81), (94) imply:
% 25.43/4.27 | (200) mult(op_b, all_20_1) = op_a
% 25.43/4.27 |
% 25.43/4.27 | REDUCE: (82), (98) imply:
% 25.43/4.27 | (201) mult(op_a, all_22_1) = op_b
% 25.43/4.27 |
% 25.43/4.27 | REDUCE: (54), (98) imply:
% 25.43/4.27 | (202) mult(unit, op_b) = op_b
% 25.43/4.27 |
% 25.43/4.27 | REDUCE: (50), (94) imply:
% 25.43/4.27 | (203) mult(unit, op_a) = op_a
% 25.43/4.27 |
% 25.43/4.27 | GROUND_INST: instantiating (11) with all_20_1, all_74_1, op_a, op_a,
% 25.43/4.27 | simplifying with (33), (139) gives:
% 25.43/4.27 | (204) all_74_1 = all_20_1
% 25.43/4.27 |
% 25.43/4.27 | GROUND_INST: instantiating (11) with all_60_1, all_74_1, op_a, op_a,
% 25.43/4.27 | simplifying with (139), (194) gives:
% 25.43/4.27 | (205) all_74_1 = all_60_1
% 25.43/4.27 |
% 25.43/4.27 | GROUND_INST: instantiating (11) with all_82_0, all_86_1, op_a, op_a,
% 25.43/4.27 | simplifying with (147), (197) gives:
% 25.43/4.27 | (206) all_86_1 = all_82_0
% 25.43/4.27 |
% 25.43/4.27 | GROUND_INST: instantiating (11) with all_74_1, all_86_1, op_a, op_a,
% 25.43/4.27 | simplifying with (139), (147) gives:
% 25.43/4.27 | (207) all_86_1 = all_74_1
% 25.43/4.27 |
% 25.43/4.27 | GROUND_INST: instantiating (11) with all_64_1, all_86_1, op_a, op_a,
% 25.43/4.27 | simplifying with (131), (147) gives:
% 25.43/4.27 | (208) all_86_1 = all_64_1
% 25.43/4.27 |
% 25.43/4.27 | GROUND_INST: instantiating (11) with all_82_1, all_92_2, op_a, op_a,
% 25.43/4.27 | simplifying with (144), (196) gives:
% 25.43/4.27 | (209) all_92_2 = all_82_1
% 25.43/4.27 |
% 25.43/4.27 | GROUND_INST: instantiating (11) with all_74_1, all_92_2, op_a, op_a,
% 25.43/4.27 | simplifying with (139), (196) gives:
% 25.43/4.27 | (210) all_92_2 = all_74_1
% 25.43/4.27 |
% 25.43/4.27 | GROUND_INST: instantiating (11) with all_82_1, all_92_1, op_a, op_a,
% 25.43/4.27 | simplifying with (144), (157) gives:
% 25.43/4.27 | (211) all_92_1 = all_82_1
% 25.43/4.27 |
% 25.43/4.27 | GROUND_INST: instantiating (11) with all_50_1, all_92_1, op_a, op_a,
% 25.43/4.27 | simplifying with (120), (157) gives:
% 25.43/4.27 | (212) all_92_1 = all_50_1
% 25.43/4.27 |
% 25.43/4.27 | GROUND_INST: instantiating (11) with all_92_2, all_100_1, op_a, op_a,
% 25.43/4.27 | simplifying with (172), (196) gives:
% 25.43/4.27 | (213) all_100_1 = all_92_2
% 25.43/4.27 |
% 25.43/4.27 | GROUND_INST: instantiating (11) with all_66_1, all_100_1, op_a, op_a,
% 25.43/4.27 | simplifying with (133), (172) gives:
% 25.43/4.27 | (214) all_100_1 = all_66_1
% 25.43/4.27 |
% 25.43/4.27 | GROUND_INST: instantiating (11) with unit, all_94_1, op_b, op_a, simplifying
% 25.43/4.27 | with (6), (161) gives:
% 25.43/4.27 | (215) all_94_1 = unit
% 25.43/4.27 |
% 25.43/4.27 | GROUND_INST: instantiating (11) with all_94_1, all_96_1, op_b, op_a,
% 25.43/4.27 | simplifying with (161), (166) gives:
% 25.43/4.27 | (216) all_96_1 = all_94_1
% 25.43/4.27 |
% 25.43/4.27 | GROUND_INST: instantiating (11) with all_90_2, all_96_1, op_b, op_a,
% 25.43/4.27 | simplifying with (166), (195) gives:
% 25.43/4.27 | (217) all_96_1 = all_90_2
% 25.43/4.27 |
% 25.43/4.27 | GROUND_INST: instantiating (11) with op_b, all_106_1, all_22_1, op_a,
% 25.43/4.27 | simplifying with (181), (201) gives:
% 25.43/4.27 | (218) all_106_1 = op_b
% 25.43/4.27 |
% 25.43/4.27 | GROUND_INST: instantiating (11) with unit, all_104_1, op_a, op_b, simplifying
% 25.43/4.27 | with (7), (177) gives:
% 25.43/4.27 | (219) all_104_1 = unit
% 25.43/4.27 |
% 25.43/4.28 | GROUND_INST: instantiating (11) with all_94_2, all_104_1, op_a, op_b,
% 25.43/4.28 | simplifying with (177), (193) gives:
% 25.43/4.28 | (220) all_104_1 = all_94_2
% 25.43/4.28 |
% 25.43/4.28 | GROUND_INST: instantiating (11) with all_90_1, all_104_1, op_a, op_b,
% 25.43/4.28 | simplifying with (153), (177) gives:
% 25.43/4.28 | (221) all_104_1 = all_90_1
% 25.43/4.28 |
% 25.43/4.28 | GROUND_INST: instantiating (11) with all_58_1, all_70_1, op_b, op_b,
% 25.43/4.28 | simplifying with (127), (190) gives:
% 25.43/4.28 | (222) all_70_1 = all_58_1
% 25.43/4.28 |
% 25.43/4.28 | GROUND_INST: instantiating (11) with all_22_1, all_72_1, op_b, op_b,
% 25.43/4.28 | simplifying with (38), (137) gives:
% 25.43/4.28 | (223) all_72_1 = all_22_1
% 25.43/4.28 |
% 25.43/4.28 | GROUND_INST: instantiating (11) with all_70_1, all_72_1, op_b, op_b,
% 25.43/4.28 | simplifying with (137), (190) gives:
% 25.43/4.28 | (224) all_72_1 = all_70_1
% 25.43/4.28 |
% 25.43/4.28 | GROUND_INST: instantiating (11) with all_72_1, all_76_1, op_b, op_b,
% 25.43/4.28 | simplifying with (137), (141) gives:
% 25.43/4.28 | (225) all_76_1 = all_72_1
% 25.43/4.28 |
% 25.43/4.28 | GROUND_INST: instantiating (11) with all_76_1, all_76_0, op_b, op_b,
% 25.43/4.28 | simplifying with (141), (192) gives:
% 25.43/4.28 | (226) all_76_0 = all_76_1
% 25.43/4.28 |
% 25.43/4.28 | GROUND_INST: instantiating (11) with all_70_1, all_88_2, op_b, op_b,
% 25.43/4.28 | simplifying with (190), (191) gives:
% 25.43/4.28 | (227) all_88_2 = all_70_1
% 25.43/4.28 |
% 25.43/4.28 | GROUND_INST: instantiating (11) with all_52_1, all_88_2, op_b, op_b,
% 25.43/4.28 | simplifying with (123), (191) gives:
% 25.43/4.28 | (228) all_88_2 = all_52_1
% 25.43/4.28 |
% 25.43/4.28 | GROUND_INST: instantiating (11) with all_76_0, all_88_1, op_b, op_b,
% 25.43/4.28 | simplifying with (149), (192) gives:
% 25.43/4.28 | (229) all_88_1 = all_76_0
% 25.43/4.28 |
% 25.43/4.28 | GROUND_INST: instantiating (11) with all_88_1, all_98_1, op_b, op_b,
% 25.43/4.28 | simplifying with (149), (170) gives:
% 25.43/4.28 | (230) all_98_1 = all_88_1
% 25.43/4.28 |
% 25.43/4.28 | GROUND_INST: instantiating (11) with all_98_1, all_102_1, op_b, op_b,
% 25.43/4.28 | simplifying with (170), (174) gives:
% 25.43/4.28 | (231) all_102_1 = all_98_1
% 25.43/4.28 |
% 25.43/4.28 | GROUND_INST: instantiating (11) with all_54_1, all_102_1, op_b, op_b,
% 25.43/4.28 | simplifying with (125), (174) gives:
% 25.43/4.28 | (232) all_102_1 = all_54_1
% 25.43/4.28 |
% 25.43/4.28 | GROUND_INST: instantiating (11) with op_a, all_108_1, all_20_1, op_b,
% 25.43/4.28 | simplifying with (186), (200) gives:
% 25.43/4.28 | (233) all_108_1 = op_a
% 25.43/4.28 |
% 25.43/4.28 | GROUND_INST: instantiating (11) with all_13_3, all_32_2, op_a, all_13_4,
% 25.43/4.28 | simplifying with (18), (199) gives:
% 25.43/4.28 | (234) all_32_2 = all_13_3
% 25.43/4.28 |
% 25.43/4.28 | GROUND_INST: instantiating (11) with all_13_1, all_34_2, op_b, all_13_4,
% 25.43/4.28 | simplifying with (19), (198) gives:
% 25.43/4.28 | (235) all_34_2 = all_13_1
% 25.43/4.28 |
% 25.43/4.28 | COMBINE_EQS: (220), (221) imply:
% 25.43/4.28 | (236) all_94_2 = all_90_1
% 25.43/4.28 |
% 25.43/4.28 | COMBINE_EQS: (219), (220) imply:
% 25.43/4.28 | (237) all_94_2 = unit
% 25.43/4.28 |
% 25.43/4.28 | COMBINE_EQS: (231), (232) imply:
% 25.43/4.28 | (238) all_98_1 = all_54_1
% 25.43/4.28 |
% 25.43/4.28 | SIMP: (238) implies:
% 25.43/4.28 | (239) all_98_1 = all_54_1
% 25.43/4.28 |
% 25.43/4.28 | COMBINE_EQS: (213), (214) imply:
% 25.43/4.28 | (240) all_92_2 = all_66_1
% 25.69/4.28 |
% 25.69/4.28 | SIMP: (240) implies:
% 25.69/4.28 | (241) all_92_2 = all_66_1
% 25.69/4.28 |
% 25.69/4.28 | COMBINE_EQS: (230), (239) imply:
% 25.69/4.28 | (242) all_88_1 = all_54_1
% 25.69/4.28 |
% 25.69/4.28 | SIMP: (242) implies:
% 25.69/4.28 | (243) all_88_1 = all_54_1
% 25.69/4.28 |
% 25.69/4.28 | COMBINE_EQS: (216), (217) imply:
% 25.69/4.28 | (244) all_94_1 = all_90_2
% 25.69/4.28 |
% 25.69/4.28 | SIMP: (244) implies:
% 25.69/4.28 | (245) all_94_1 = all_90_2
% 25.69/4.28 |
% 25.69/4.28 | COMBINE_EQS: (215), (245) imply:
% 25.69/4.28 | (246) all_90_2 = unit
% 25.69/4.28 |
% 25.69/4.28 | COMBINE_EQS: (236), (237) imply:
% 25.69/4.28 | (247) all_90_1 = unit
% 25.69/4.28 |
% 25.69/4.28 | SIMP: (247) implies:
% 25.69/4.28 | (248) all_90_1 = unit
% 25.69/4.28 |
% 25.69/4.28 | COMBINE_EQS: (211), (212) imply:
% 25.69/4.28 | (249) all_82_1 = all_50_1
% 25.69/4.28 |
% 25.69/4.28 | SIMP: (249) implies:
% 25.69/4.28 | (250) all_82_1 = all_50_1
% 25.69/4.28 |
% 25.69/4.28 | COMBINE_EQS: (210), (241) imply:
% 25.69/4.28 | (251) all_74_1 = all_66_1
% 25.69/4.28 |
% 25.69/4.28 | SIMP: (251) implies:
% 25.69/4.28 | (252) all_74_1 = all_66_1
% 25.69/4.28 |
% 25.69/4.28 | COMBINE_EQS: (209), (241) imply:
% 25.69/4.28 | (253) all_82_1 = all_66_1
% 25.69/4.28 |
% 25.69/4.28 | SIMP: (253) implies:
% 25.69/4.28 | (254) all_82_1 = all_66_1
% 25.69/4.28 |
% 25.69/4.28 | COMBINE_EQS: (229), (243) imply:
% 25.69/4.28 | (255) all_76_0 = all_54_1
% 25.69/4.28 |
% 25.69/4.28 | SIMP: (255) implies:
% 25.69/4.28 | (256) all_76_0 = all_54_1
% 25.69/4.28 |
% 25.69/4.28 | COMBINE_EQS: (227), (228) imply:
% 25.69/4.28 | (257) all_70_1 = all_52_1
% 25.69/4.28 |
% 25.69/4.28 | SIMP: (257) implies:
% 25.69/4.28 | (258) all_70_1 = all_52_1
% 25.69/4.28 |
% 25.69/4.28 | COMBINE_EQS: (206), (208) imply:
% 25.69/4.28 | (259) all_82_0 = all_64_1
% 25.69/4.28 |
% 25.69/4.28 | COMBINE_EQS: (206), (207) imply:
% 25.69/4.28 | (260) all_82_0 = all_74_1
% 25.69/4.28 |
% 25.69/4.28 | COMBINE_EQS: (259), (260) imply:
% 25.69/4.28 | (261) all_74_1 = all_64_1
% 25.69/4.28 |
% 25.69/4.28 | SIMP: (261) implies:
% 25.69/4.28 | (262) all_74_1 = all_64_1
% 25.69/4.28 |
% 25.69/4.28 | COMBINE_EQS: (250), (254) imply:
% 25.69/4.28 | (263) all_66_1 = all_50_1
% 25.69/4.28 |
% 25.69/4.28 | SIMP: (263) implies:
% 25.69/4.28 | (264) all_66_1 = all_50_1
% 25.69/4.28 |
% 25.69/4.28 | COMBINE_EQS: (226), (256) imply:
% 25.69/4.28 | (265) all_76_1 = all_54_1
% 25.69/4.28 |
% 25.69/4.28 | SIMP: (265) implies:
% 25.69/4.28 | (266) all_76_1 = all_54_1
% 25.69/4.28 |
% 25.69/4.28 | COMBINE_EQS: (225), (266) imply:
% 25.69/4.28 | (267) all_72_1 = all_54_1
% 25.69/4.28 |
% 25.69/4.28 | SIMP: (267) implies:
% 25.69/4.28 | (268) all_72_1 = all_54_1
% 25.69/4.28 |
% 25.69/4.28 | COMBINE_EQS: (204), (262) imply:
% 25.69/4.28 | (269) all_64_1 = all_20_1
% 25.69/4.28 |
% 25.69/4.28 | COMBINE_EQS: (205), (262) imply:
% 25.69/4.28 | (270) all_64_1 = all_60_1
% 25.69/4.28 |
% 25.69/4.28 | COMBINE_EQS: (252), (262) imply:
% 25.69/4.28 | (271) all_66_1 = all_64_1
% 25.69/4.28 |
% 25.69/4.28 | SIMP: (271) implies:
% 25.69/4.28 | (272) all_66_1 = all_64_1
% 25.69/4.28 |
% 25.69/4.28 | COMBINE_EQS: (223), (268) imply:
% 25.69/4.28 | (273) all_54_1 = all_22_1
% 25.69/4.28 |
% 25.69/4.28 | COMBINE_EQS: (224), (268) imply:
% 25.69/4.28 | (274) all_70_1 = all_54_1
% 25.69/4.28 |
% 25.69/4.28 | SIMP: (274) implies:
% 25.69/4.28 | (275) all_70_1 = all_54_1
% 25.69/4.28 |
% 25.69/4.28 | COMBINE_EQS: (222), (258) imply:
% 25.69/4.28 | (276) all_58_1 = all_52_1
% 25.69/4.28 |
% 25.69/4.28 | COMBINE_EQS: (222), (275) imply:
% 25.69/4.28 | (277) all_58_1 = all_54_1
% 25.69/4.28 |
% 25.69/4.28 | COMBINE_EQS: (264), (272) imply:
% 25.69/4.28 | (278) all_64_1 = all_50_1
% 25.69/4.28 |
% 25.69/4.28 | SIMP: (278) implies:
% 25.69/4.28 | (279) all_64_1 = all_50_1
% 25.69/4.28 |
% 25.69/4.28 | COMBINE_EQS: (269), (270) imply:
% 25.69/4.28 | (280) all_60_1 = all_20_1
% 25.69/4.28 |
% 25.69/4.28 | COMBINE_EQS: (270), (279) imply:
% 25.69/4.28 | (281) all_60_1 = all_50_1
% 25.69/4.28 |
% 25.69/4.28 | COMBINE_EQS: (280), (281) imply:
% 25.69/4.28 | (282) all_50_1 = all_20_1
% 25.69/4.28 |
% 25.69/4.28 | COMBINE_EQS: (276), (277) imply:
% 25.69/4.28 | (283) all_54_1 = all_52_1
% 25.69/4.28 |
% 25.69/4.28 | SIMP: (283) implies:
% 25.69/4.28 | (284) all_54_1 = all_52_1
% 25.69/4.28 |
% 25.69/4.28 | COMBINE_EQS: (273), (284) imply:
% 25.69/4.28 | (285) all_52_1 = all_22_1
% 25.69/4.28 |
% 25.69/4.28 | COMBINE_EQS: (217), (246) imply:
% 25.69/4.28 | (286) all_96_1 = unit
% 25.69/4.28 |
% 25.69/4.28 | REDUCE: (189), (233) imply:
% 25.69/4.28 | (287) mult(op_a, op_b) = all_108_0
% 25.69/4.28 |
% 25.69/4.28 | REDUCE: (184), (218) imply:
% 25.69/4.28 | (288) mult(op_b, op_a) = all_106_0
% 25.69/4.28 |
% 25.69/4.28 | REDUCE: (179), (219) imply:
% 25.69/4.28 | (289) mult(unit, op_b) = all_104_0
% 25.69/4.28 |
% 25.69/4.28 | REDUCE: (168), (286) imply:
% 25.69/4.28 | (290) mult(unit, op_a) = all_96_0
% 25.69/4.28 |
% 25.69/4.28 | REDUCE: (163), (215) imply:
% 25.69/4.28 | (291) mult(unit, op_a) = all_94_0
% 25.69/4.29 |
% 25.69/4.29 | REDUCE: (155), (248) imply:
% 25.69/4.29 | (292) mult(unit, op_b) = all_90_0
% 25.69/4.29 |
% 25.69/4.29 | REDUCE: (167), (235) imply:
% 25.69/4.29 | (293) mult(all_13_1, op_a) = all_96_2
% 25.69/4.29 |
% 25.69/4.29 | REDUCE: (178), (234) imply:
% 25.69/4.29 | (294) mult(all_13_3, op_b) = all_104_2
% 25.69/4.29 |
% 25.69/4.29 | REDUCE: (68), (235) imply:
% 25.69/4.29 | (295) mult(all_13_0, op_b) = all_13_1
% 25.69/4.29 |
% 25.69/4.29 | REDUCE: (62), (234) imply:
% 25.69/4.29 | (296) mult(all_13_2, op_a) = all_13_3
% 25.69/4.29 |
% 25.69/4.29 | GROUND_INST: instantiating (11) with op_a, all_96_0, op_a, unit, simplifying
% 25.69/4.29 | with (203), (290) gives:
% 25.69/4.29 | (297) all_96_0 = op_a
% 25.69/4.29 |
% 25.69/4.29 | GROUND_INST: instantiating (11) with all_94_0, all_96_0, op_a, unit,
% 25.69/4.29 | simplifying with (290), (291) gives:
% 25.69/4.29 | (298) all_96_0 = all_94_0
% 25.69/4.29 |
% 25.69/4.29 | GROUND_INST: instantiating (11) with op_b, all_104_0, op_b, unit, simplifying
% 25.69/4.29 | with (202), (289) gives:
% 25.69/4.29 | (299) all_104_0 = op_b
% 25.69/4.29 |
% 25.69/4.29 | GROUND_INST: instantiating (11) with all_90_0, all_104_0, op_b, unit,
% 25.69/4.29 | simplifying with (289), (292) gives:
% 25.69/4.29 | (300) all_104_0 = all_90_0
% 25.69/4.29 |
% 25.69/4.29 | GROUND_INST: instantiating (11) with unit, all_108_0, op_b, op_a, simplifying
% 25.69/4.29 | with (6), (287) gives:
% 25.69/4.29 | (301) all_108_0 = unit
% 25.69/4.29 |
% 25.69/4.29 | GROUND_INST: instantiating (11) with unit, all_106_0, op_a, op_b, simplifying
% 25.69/4.29 | with (7), (288) gives:
% 25.69/4.29 | (302) all_106_0 = unit
% 25.69/4.29 |
% 25.69/4.29 | GROUND_INST: instantiating (11) with all_13_2, all_104_2, op_b, all_13_3,
% 25.69/4.29 | simplifying with (20), (294) gives:
% 25.69/4.29 | (303) all_104_2 = all_13_2
% 25.69/4.29 |
% 25.69/4.29 | GROUND_INST: instantiating (11) with all_13_0, all_96_2, op_a, all_13_1,
% 25.69/4.29 | simplifying with (21), (293) gives:
% 25.69/4.29 | (304) all_96_2 = all_13_0
% 25.69/4.29 |
% 25.69/4.29 | COMBINE_EQS: (299), (300) imply:
% 25.69/4.29 | (305) all_90_0 = op_b
% 25.69/4.29 |
% 25.69/4.29 | SIMP: (305) implies:
% 25.69/4.29 | (306) all_90_0 = op_b
% 25.69/4.29 |
% 25.69/4.29 | COMBINE_EQS: (297), (298) imply:
% 25.69/4.29 | (307) all_94_0 = op_a
% 25.69/4.29 |
% 25.69/4.29 | REDUCE: (187), (301) imply:
% 25.69/4.29 | (308) mult(all_13_4, unit) = all_108_2
% 25.69/4.29 |
% 25.69/4.29 | REDUCE: (182), (302) imply:
% 25.69/4.29 | (309) mult(all_13_4, unit) = all_106_2
% 25.69/4.29 |
% 25.69/4.29 | GROUND_INST: instantiating (11) with all_106_2, all_108_2, unit, all_13_4,
% 25.69/4.29 | simplifying with (308), (309) gives:
% 25.69/4.29 | (310) all_108_2 = all_106_2
% 25.69/4.29 |
% 25.69/4.29 | REDUCE: (188), (310) imply:
% 25.69/4.29 | (311) mult(all_20_0, op_b) = all_106_2
% 25.69/4.29 |
% 25.69/4.29 | GROUND_INST: instantiating (4) with all_13_4, all_106_2, simplifying with
% 25.69/4.29 | (13), (309) gives:
% 25.69/4.29 | (312) all_106_2 = all_13_4
% 25.69/4.29 |
% 25.69/4.29 | GROUND_INST: instantiating (1) with all_22_1, op_a, all_13_2, all_13_3,
% 25.69/4.29 | all_22_0, simplifying with (8), (15), (39), (85), (296) gives:
% 25.69/4.29 | (313) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (mult(v1, op_a) = v2 &
% 25.69/4.29 | mult(all_22_0, op_a) = v0 & mult(all_13_2, v2) = v0 & mult(op_a,
% 25.69/4.29 | all_22_1) = v1 & $i(v2) & $i(v1) & $i(v0))
% 25.69/4.29 |
% 25.69/4.29 | GROUND_INST: instantiating (1) with all_20_1, op_b, all_13_0, all_13_1,
% 25.69/4.29 | all_20_0, simplifying with (9), (17), (34), (84), (295) gives:
% 25.69/4.29 | (314) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (mult(v1, op_b) = v2 &
% 25.69/4.29 | mult(all_20_0, op_b) = v0 & mult(all_13_0, v2) = v0 & mult(op_b,
% 25.69/4.29 | all_20_1) = v1 & $i(v2) & $i(v1) & $i(v0))
% 25.69/4.29 |
% 25.69/4.29 | GROUND_INST: instantiating (1) with op_b, op_a, all_13_0, all_20_0, all_106_2,
% 25.69/4.29 | simplifying with (8), (9), (17), (35), (311) gives:
% 25.69/4.29 | (315) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (mult(v1, op_a) = v2 &
% 25.69/4.29 | mult(all_106_2, op_a) = v0 & mult(all_13_0, v2) = v0 & mult(op_a,
% 25.69/4.29 | op_b) = v1 & $i(v2) & $i(v1) & $i(v0))
% 25.69/4.29 |
% 25.69/4.29 | GROUND_INST: instantiating (2) with op_a, op_b, all_20_0, unit, op_b,
% 25.69/4.29 | all_106_2, simplifying with (7), (8), (9), (32), (202), (311)
% 25.69/4.29 | gives:
% 25.69/4.29 | (316) ? [v0: $i] : ? [v1: $i] : (mult(v1, op_b) = all_106_2 & mult(v0,
% 25.69/4.29 | op_a) = v1 & mult(all_20_0, op_b) = v0 & $i(v1) & $i(v0) &
% 25.69/4.29 | $i(all_106_2))
% 25.69/4.29 |
% 25.69/4.29 | GROUND_INST: instantiating (3) with op_b, all_20_0, all_106_2, simplifying
% 25.69/4.29 | with (9), (32), (311) gives:
% 25.69/4.29 | (317) ? [v0: $i] : ? [v1: $i] : (mult(all_106_2, op_b) = v1 &
% 25.69/4.29 | mult(all_20_0, v0) = v1 & mult(op_b, op_b) = v0 & $i(v1) & $i(v0))
% 25.69/4.29 |
% 25.69/4.29 | GROUND_INST: instantiating (1) with op_a, op_b, all_13_2, all_22_0, all_106_2,
% 25.69/4.29 | simplifying with (8), (9), (15), (40), (183) gives:
% 25.69/4.29 | (318) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (mult(v1, op_b) = v2 &
% 25.69/4.29 | mult(all_106_2, op_b) = v0 & mult(all_13_2, v2) = v0 & mult(op_b,
% 25.69/4.29 | op_a) = v1 & $i(v2) & $i(v1) & $i(v0))
% 25.69/4.29 |
% 25.69/4.29 | GROUND_INST: instantiating (2) with op_b, op_a, all_22_0, unit, op_a,
% 25.69/4.29 | all_106_2, simplifying with (6), (8), (9), (37), (183), (203)
% 25.69/4.29 | gives:
% 25.69/4.29 | (319) ? [v0: $i] : ? [v1: $i] : (mult(v1, op_a) = all_106_2 & mult(v0,
% 25.69/4.29 | op_b) = v1 & mult(all_22_0, op_a) = v0 & $i(v1) & $i(v0) &
% 25.69/4.29 | $i(all_106_2))
% 25.69/4.29 |
% 25.69/4.29 | GROUND_INST: instantiating (3) with op_a, all_22_0, all_106_2, simplifying
% 25.69/4.29 | with (8), (37), (183) gives:
% 25.69/4.29 | (320) ? [v0: $i] : ? [v1: $i] : (mult(all_106_2, op_a) = v1 &
% 25.69/4.29 | mult(all_22_0, v0) = v1 & mult(op_a, op_a) = v0 & $i(v1) & $i(v0))
% 25.69/4.29 |
% 25.69/4.29 | DELTA: instantiating (317) with fresh symbols all_140_0, all_140_1 gives:
% 25.69/4.29 | (321) mult(all_106_2, op_b) = all_140_0 & mult(all_20_0, all_140_1) =
% 25.69/4.29 | all_140_0 & mult(op_b, op_b) = all_140_1 & $i(all_140_0) &
% 25.69/4.29 | $i(all_140_1)
% 25.69/4.29 |
% 25.69/4.29 | ALPHA: (321) implies:
% 25.69/4.29 | (322) mult(all_106_2, op_b) = all_140_0
% 25.69/4.29 |
% 25.69/4.29 | DELTA: instantiating (320) with fresh symbols all_148_0, all_148_1 gives:
% 25.69/4.29 | (323) mult(all_106_2, op_a) = all_148_0 & mult(all_22_0, all_148_1) =
% 25.69/4.29 | all_148_0 & mult(op_a, op_a) = all_148_1 & $i(all_148_0) &
% 25.69/4.29 | $i(all_148_1)
% 25.69/4.29 |
% 25.69/4.29 | ALPHA: (323) implies:
% 25.69/4.29 | (324) mult(all_106_2, op_a) = all_148_0
% 25.69/4.29 |
% 25.69/4.29 | DELTA: instantiating (319) with fresh symbols all_216_0, all_216_1 gives:
% 25.69/4.29 | (325) mult(all_216_0, op_a) = all_106_2 & mult(all_216_1, op_b) = all_216_0
% 25.69/4.29 | & mult(all_22_0, op_a) = all_216_1 & $i(all_216_0) & $i(all_216_1) &
% 25.69/4.29 | $i(all_106_2)
% 25.69/4.29 |
% 25.69/4.29 | ALPHA: (325) implies:
% 25.69/4.29 | (326) mult(all_22_0, op_a) = all_216_1
% 25.69/4.29 | (327) mult(all_216_1, op_b) = all_216_0
% 25.69/4.29 | (328) mult(all_216_0, op_a) = all_106_2
% 25.69/4.29 |
% 25.69/4.29 | DELTA: instantiating (316) with fresh symbols all_238_0, all_238_1 gives:
% 25.69/4.29 | (329) mult(all_238_0, op_b) = all_106_2 & mult(all_238_1, op_a) = all_238_0
% 25.69/4.29 | & mult(all_20_0, op_b) = all_238_1 & $i(all_238_0) & $i(all_238_1) &
% 25.69/4.29 | $i(all_106_2)
% 25.69/4.29 |
% 25.69/4.29 | ALPHA: (329) implies:
% 25.69/4.29 | (330) mult(all_20_0, op_b) = all_238_1
% 25.69/4.29 | (331) mult(all_238_1, op_a) = all_238_0
% 25.69/4.29 | (332) mult(all_238_0, op_b) = all_106_2
% 25.69/4.29 |
% 25.69/4.29 | DELTA: instantiating (314) with fresh symbols all_292_0, all_292_1, all_292_2
% 25.69/4.29 | gives:
% 25.69/4.29 | (333) mult(all_292_1, op_b) = all_292_0 & mult(all_20_0, op_b) = all_292_2
% 25.69/4.29 | & mult(all_13_0, all_292_0) = all_292_2 & mult(op_b, all_20_1) =
% 25.69/4.29 | all_292_1 & $i(all_292_0) & $i(all_292_1) & $i(all_292_2)
% 25.69/4.29 |
% 25.69/4.29 | ALPHA: (333) implies:
% 25.69/4.29 | (334) mult(all_20_0, op_b) = all_292_2
% 25.69/4.29 |
% 25.69/4.29 | DELTA: instantiating (318) with fresh symbols all_306_0, all_306_1, all_306_2
% 25.69/4.29 | gives:
% 25.69/4.30 | (335) mult(all_306_1, op_b) = all_306_0 & mult(all_106_2, op_b) = all_306_2
% 25.69/4.30 | & mult(all_13_2, all_306_0) = all_306_2 & mult(op_b, op_a) =
% 25.69/4.30 | all_306_1 & $i(all_306_0) & $i(all_306_1) & $i(all_306_2)
% 25.69/4.30 |
% 25.69/4.30 | ALPHA: (335) implies:
% 25.69/4.30 | (336) mult(all_106_2, op_b) = all_306_2
% 25.69/4.30 |
% 25.69/4.30 | DELTA: instantiating (315) with fresh symbols all_334_0, all_334_1, all_334_2
% 25.69/4.30 | gives:
% 25.69/4.30 | (337) mult(all_334_1, op_a) = all_334_0 & mult(all_106_2, op_a) = all_334_2
% 25.69/4.30 | & mult(all_13_0, all_334_0) = all_334_2 & mult(op_a, op_b) =
% 25.69/4.30 | all_334_1 & $i(all_334_0) & $i(all_334_1) & $i(all_334_2)
% 25.69/4.30 |
% 25.69/4.30 | ALPHA: (337) implies:
% 25.69/4.30 | (338) mult(all_106_2, op_a) = all_334_2
% 25.69/4.30 |
% 25.69/4.30 | DELTA: instantiating (313) with fresh symbols all_366_0, all_366_1, all_366_2
% 25.69/4.30 | gives:
% 25.69/4.30 | (339) mult(all_366_1, op_a) = all_366_0 & mult(all_22_0, op_a) = all_366_2
% 25.69/4.30 | & mult(all_13_2, all_366_0) = all_366_2 & mult(op_a, all_22_1) =
% 25.69/4.30 | all_366_1 & $i(all_366_0) & $i(all_366_1) & $i(all_366_2)
% 25.69/4.30 |
% 25.69/4.30 | ALPHA: (339) implies:
% 25.69/4.30 | (340) mult(all_22_0, op_a) = all_366_2
% 25.69/4.30 |
% 25.69/4.30 | REDUCE: (312), (332) imply:
% 25.69/4.30 | (341) mult(all_238_0, op_b) = all_13_4
% 25.69/4.30 |
% 25.69/4.30 | REDUCE: (312), (328) imply:
% 25.69/4.30 | (342) mult(all_216_0, op_a) = all_13_4
% 25.69/4.30 |
% 25.69/4.30 | REDUCE: (312), (336) imply:
% 25.69/4.30 | (343) mult(all_13_4, op_b) = all_306_2
% 25.69/4.30 |
% 25.69/4.30 | REDUCE: (312), (322) imply:
% 25.69/4.30 | (344) mult(all_13_4, op_b) = all_140_0
% 25.69/4.30 |
% 25.69/4.30 | REDUCE: (312), (338) imply:
% 25.69/4.30 | (345) mult(all_13_4, op_a) = all_334_2
% 25.69/4.30 |
% 25.69/4.30 | REDUCE: (312), (324) imply:
% 25.69/4.30 | (346) mult(all_13_4, op_a) = all_148_0
% 25.69/4.30 |
% 25.69/4.30 | REDUCE: (183), (312) imply:
% 25.69/4.30 | (347) mult(all_22_0, op_a) = all_13_4
% 25.69/4.30 |
% 25.69/4.30 | REDUCE: (311), (312) imply:
% 25.69/4.30 | (348) mult(all_20_0, op_b) = all_13_4
% 25.69/4.30 |
% 25.69/4.30 | GROUND_INST: instantiating (11) with all_13_3, all_334_2, op_a, all_13_4,
% 25.69/4.30 | simplifying with (18), (345) gives:
% 25.69/4.30 | (349) all_334_2 = all_13_3
% 25.69/4.30 |
% 25.69/4.30 | GROUND_INST: instantiating (11) with all_148_0, all_334_2, op_a, all_13_4,
% 25.69/4.30 | simplifying with (345), (346) gives:
% 25.69/4.30 | (350) all_334_2 = all_148_0
% 25.69/4.30 |
% 25.69/4.30 | GROUND_INST: instantiating (11) with all_13_1, all_306_2, op_b, all_13_4,
% 25.69/4.30 | simplifying with (19), (343) gives:
% 25.69/4.30 | (351) all_306_2 = all_13_1
% 25.69/4.30 |
% 25.69/4.30 | GROUND_INST: instantiating (11) with all_140_0, all_306_2, op_b, all_13_4,
% 25.69/4.30 | simplifying with (343), (344) gives:
% 25.69/4.30 | (352) all_306_2 = all_140_0
% 25.69/4.30 |
% 25.69/4.30 | GROUND_INST: instantiating (11) with all_238_1, all_292_2, op_b, all_20_0,
% 25.69/4.30 | simplifying with (330), (334) gives:
% 25.69/4.30 | (353) all_292_2 = all_238_1
% 25.69/4.30 |
% 25.69/4.30 | GROUND_INST: instantiating (11) with all_13_4, all_292_2, op_b, all_20_0,
% 25.69/4.30 | simplifying with (334), (348) gives:
% 25.69/4.30 | (354) all_292_2 = all_13_4
% 25.69/4.30 |
% 25.69/4.30 | GROUND_INST: instantiating (11) with all_216_1, all_366_2, op_a, all_22_0,
% 25.69/4.30 | simplifying with (326), (340) gives:
% 25.69/4.30 | (355) all_366_2 = all_216_1
% 25.69/4.30 |
% 25.69/4.30 | GROUND_INST: instantiating (11) with all_13_4, all_366_2, op_a, all_22_0,
% 25.69/4.30 | simplifying with (340), (347) gives:
% 25.69/4.30 | (356) all_366_2 = all_13_4
% 25.69/4.30 |
% 25.69/4.30 | COMBINE_EQS: (355), (356) imply:
% 25.69/4.30 | (357) all_216_1 = all_13_4
% 25.69/4.30 |
% 25.69/4.30 | SIMP: (357) implies:
% 25.69/4.30 | (358) all_216_1 = all_13_4
% 25.69/4.30 |
% 25.69/4.30 | COMBINE_EQS: (349), (350) imply:
% 25.69/4.30 | (359) all_148_0 = all_13_3
% 25.69/4.30 |
% 25.69/4.30 | COMBINE_EQS: (351), (352) imply:
% 25.69/4.30 | (360) all_140_0 = all_13_1
% 25.69/4.30 |
% 25.69/4.30 | SIMP: (360) implies:
% 25.69/4.30 | (361) all_140_0 = all_13_1
% 25.69/4.30 |
% 25.69/4.30 | COMBINE_EQS: (353), (354) imply:
% 25.69/4.30 | (362) all_238_1 = all_13_4
% 25.69/4.30 |
% 25.69/4.30 | REDUCE: (331), (362) imply:
% 25.69/4.30 | (363) mult(all_13_4, op_a) = all_238_0
% 25.69/4.30 |
% 25.69/4.30 | REDUCE: (327), (358) imply:
% 25.69/4.30 | (364) mult(all_13_4, op_b) = all_216_0
% 25.69/4.30 |
% 25.69/4.30 | GROUND_INST: instantiating (11) with all_13_3, all_238_0, op_a, all_13_4,
% 25.69/4.30 | simplifying with (18), (363) gives:
% 25.69/4.30 | (365) all_238_0 = all_13_3
% 25.69/4.30 |
% 25.69/4.30 | GROUND_INST: instantiating (11) with all_13_1, all_216_0, op_b, all_13_4,
% 25.69/4.30 | simplifying with (19), (364) gives:
% 25.69/4.30 | (366) all_216_0 = all_13_1
% 25.69/4.30 |
% 25.69/4.30 | REDUCE: (341), (365) imply:
% 25.69/4.30 | (367) mult(all_13_3, op_b) = all_13_4
% 25.69/4.30 |
% 25.69/4.30 | REDUCE: (342), (366) imply:
% 25.69/4.30 | (368) mult(all_13_1, op_a) = all_13_4
% 25.69/4.30 |
% 25.69/4.30 | GROUND_INST: instantiating (11) with all_13_2, all_13_4, op_b, all_13_3,
% 25.69/4.30 | simplifying with (20), (367) gives:
% 25.69/4.30 | (369) all_13_2 = all_13_4
% 25.69/4.30 |
% 25.69/4.30 | GROUND_INST: instantiating (11) with all_13_0, all_13_4, op_a, all_13_1,
% 25.69/4.30 | simplifying with (21), (368) gives:
% 25.69/4.30 | (370) all_13_0 = all_13_4
% 25.69/4.30 |
% 25.69/4.30 | BETA: splitting (22) gives:
% 25.69/4.30 |
% 25.69/4.30 | Case 1:
% 25.69/4.30 | |
% 25.69/4.30 | | (371) ~ (all_13_0 = all_13_4)
% 25.69/4.30 | |
% 25.69/4.30 | | REDUCE: (370), (371) imply:
% 25.69/4.30 | | (372) $false
% 25.69/4.30 | |
% 25.69/4.30 | | CLOSE: (372) is inconsistent.
% 25.69/4.30 | |
% 25.69/4.30 | Case 2:
% 25.69/4.30 | |
% 25.69/4.30 | | (373) ~ (all_13_2 = all_13_4)
% 25.69/4.30 | |
% 25.69/4.30 | | REDUCE: (369), (373) imply:
% 25.69/4.30 | | (374) $false
% 25.69/4.30 | |
% 25.69/4.30 | | CLOSE: (374) is inconsistent.
% 25.69/4.30 | |
% 25.69/4.30 | End of split
% 25.69/4.30 |
% 25.69/4.30 End of proof
% 25.69/4.30 % SZS output end Proof for theBenchmark
% 25.69/4.30
% 25.69/4.30 3685ms
%------------------------------------------------------------------------------