TSTP Solution File: REL009+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : REL009+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 : n032.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 13:42:46 EDT 2023
% Result : Theorem 10.72s 2.17s
% Output : Proof 11.99s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : REL009+1 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.10 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.12/0.30 % Computer : n032.cluster.edu
% 0.12/0.30 % Model : x86_64 x86_64
% 0.12/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.30 % Memory : 8042.1875MB
% 0.12/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.30 % CPULimit : 300
% 0.12/0.30 % WCLimit : 300
% 0.12/0.30 % DateTime : Fri Aug 25 20:03:43 EDT 2023
% 0.12/0.30 % CPUTime :
% 0.15/0.51 ________ _____
% 0.15/0.51 ___ __ \_________(_)________________________________
% 0.15/0.51 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.15/0.51 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.15/0.51 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.15/0.51
% 0.15/0.51 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.15/0.51 (2023-06-19)
% 0.15/0.51
% 0.15/0.51 (c) Philipp Rümmer, 2009-2023
% 0.15/0.51 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.15/0.51 Amanda Stjerna.
% 0.15/0.51 Free software under BSD-3-Clause.
% 0.15/0.51
% 0.15/0.51 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.15/0.51
% 0.15/0.52 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.15/0.53 Running up to 7 provers in parallel.
% 0.15/0.54 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.15/0.54 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.15/0.54 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.15/0.54 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.15/0.54 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.15/0.54 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.15/0.54 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 1.58/0.89 Prover 4: Preprocessing ...
% 2.13/0.90 Prover 1: Preprocessing ...
% 2.24/0.93 Prover 5: Preprocessing ...
% 2.24/0.93 Prover 0: Preprocessing ...
% 2.24/0.94 Prover 6: Preprocessing ...
% 2.24/0.94 Prover 3: Preprocessing ...
% 2.24/0.94 Prover 2: Preprocessing ...
% 3.52/1.18 Prover 6: Constructing countermodel ...
% 4.22/1.19 Prover 1: Constructing countermodel ...
% 4.37/1.21 Prover 3: Constructing countermodel ...
% 4.40/1.24 Prover 4: Constructing countermodel ...
% 4.40/1.24 Prover 5: Proving ...
% 4.40/1.26 Prover 0: Proving ...
% 5.06/1.37 Prover 2: Proving ...
% 10.72/2.15 Prover 4: Found proof (size 126)
% 10.72/2.15 Prover 4: proved (1615ms)
% 10.72/2.15 Prover 6: stopped
% 10.72/2.15 Prover 1: stopped
% 10.72/2.15 Prover 2: stopped
% 10.72/2.15 Prover 0: stopped
% 10.72/2.15 Prover 5: stopped
% 10.72/2.16 Prover 3: stopped
% 10.72/2.16
% 10.72/2.17 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 10.72/2.17
% 10.72/2.19 % SZS output start Proof for theBenchmark
% 10.72/2.19 Assumptions after simplification:
% 10.72/2.19 ---------------------------------
% 10.72/2.19
% 10.72/2.19 (composition_distributivity)
% 10.72/2.22 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 10.72/2.22 $i] : ( ~ (composition(v1, v2) = v4) | ~ (composition(v0, v2) = v3) | ~
% 10.72/2.22 (join(v3, v4) = v5) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: $i] :
% 10.72/2.22 (composition(v6, v2) = v5 & join(v0, v1) = v6 & $i(v6) & $i(v5))) & ! [v0:
% 10.72/2.22 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 10.72/2.22 (composition(v3, v2) = v4) | ~ (join(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1)
% 10.72/2.22 | ~ $i(v0) | ? [v5: $i] : ? [v6: $i] : (composition(v1, v2) = v6 &
% 10.72/2.22 composition(v0, v2) = v5 & join(v5, v6) = v4 & $i(v6) & $i(v5) & $i(v4)))
% 10.72/2.22
% 10.72/2.22 (converse_additivity)
% 10.72/2.23 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 10.72/2.23 (converse(v1) = v3) | ~ (converse(v0) = v2) | ~ (join(v2, v3) = v4) | ~
% 10.72/2.23 $i(v1) | ~ $i(v0) | ? [v5: $i] : (converse(v5) = v4 & join(v0, v1) = v5 &
% 10.72/2.23 $i(v5) & $i(v4))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 10.72/2.23 (join(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] : ?
% 10.72/2.23 [v5: $i] : (converse(v2) = v3 & converse(v1) = v5 & converse(v0) = v4 &
% 10.72/2.23 join(v4, v5) = v3 & $i(v5) & $i(v4) & $i(v3)))
% 10.72/2.23
% 10.72/2.23 (converse_cancellativity)
% 10.72/2.23 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (composition(v0, v1) = v2) | ~
% 10.72/2.23 $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] :
% 10.72/2.23 (converse(v0) = v3 & composition(v3, v4) = v5 & complement(v2) = v4 &
% 10.72/2.23 complement(v1) = v6 & join(v5, v6) = v6 & $i(v6) & $i(v5) & $i(v4) &
% 10.72/2.23 $i(v3)))
% 10.72/2.23
% 10.72/2.23 (converse_idempotence)
% 10.72/2.23 ! [v0: $i] : ! [v1: $i] : ( ~ (converse(v0) = v1) | ~ $i(v0) | converse(v1)
% 10.72/2.23 = v0)
% 10.72/2.23
% 10.72/2.23 (converse_multiplicativity)
% 10.72/2.23 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 10.72/2.23 (converse(v1) = v2) | ~ (converse(v0) = v3) | ~ (composition(v2, v3) = v4)
% 10.72/2.23 | ~ $i(v1) | ~ $i(v0) | ? [v5: $i] : (converse(v5) = v4 & composition(v0,
% 10.72/2.23 v1) = v5 & $i(v5) & $i(v4))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 10.72/2.23 ( ~ (composition(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4:
% 10.72/2.23 $i] : ? [v5: $i] : (converse(v2) = v3 & converse(v1) = v4 & converse(v0)
% 10.72/2.23 = v5 & composition(v4, v5) = v3 & $i(v5) & $i(v4) & $i(v3)))
% 10.72/2.23
% 10.72/2.23 (goals)
% 10.72/2.23 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5:
% 10.72/2.23 $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : (composition(v2, v1) = v7 &
% 10.72/2.23 composition(v2, v0) = v6 & composition(v1, v2) = v4 & composition(v0, v2) =
% 10.72/2.23 v3 & join(v6, v7) = v8 & join(v3, v4) = v5 & join(v0, v1) = v1 & $i(v8) &
% 10.72/2.24 $i(v7) & $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & ( ~
% 10.72/2.24 (v8 = v7) | ~ (v5 = v4)))
% 10.72/2.24
% 10.72/2.24 (maddux1_join_commutativity)
% 10.72/2.24 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (join(v1, v0) = v2) | ~ $i(v1)
% 10.72/2.24 | ~ $i(v0) | (join(v0, v1) = v2 & $i(v2))) & ! [v0: $i] : ! [v1: $i] : !
% 10.72/2.24 [v2: $i] : ( ~ (join(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | (join(v1, v0) =
% 10.72/2.24 v2 & $i(v2)))
% 10.72/2.24
% 10.72/2.24 (function-axioms)
% 10.72/2.24 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 10.72/2.24 (composition(v3, v2) = v1) | ~ (composition(v3, v2) = v0)) & ! [v0: $i] :
% 10.72/2.24 ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (meet(v3, v2) = v1) |
% 10.72/2.24 ~ (meet(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 10.72/2.24 $i] : (v1 = v0 | ~ (join(v3, v2) = v1) | ~ (join(v3, v2) = v0)) & ! [v0:
% 10.72/2.24 $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (converse(v2) = v1) | ~
% 10.72/2.24 (converse(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 |
% 10.72/2.24 ~ (complement(v2) = v1) | ~ (complement(v2) = v0))
% 10.72/2.24
% 10.72/2.24 Further assumptions not needed in the proof:
% 10.72/2.24 --------------------------------------------
% 10.72/2.24 composition_associativity, composition_identity, def_top, def_zero,
% 10.72/2.24 maddux2_join_associativity, maddux3_a_kind_of_de_Morgan,
% 10.72/2.24 maddux4_definiton_of_meet
% 10.72/2.24
% 10.72/2.24 Those formulas are unsatisfiable:
% 10.72/2.24 ---------------------------------
% 10.72/2.24
% 10.72/2.24 Begin of proof
% 10.72/2.24 |
% 10.72/2.24 | ALPHA: (maddux1_join_commutativity) implies:
% 10.72/2.24 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (join(v1, v0) = v2) | ~
% 10.72/2.24 | $i(v1) | ~ $i(v0) | (join(v0, v1) = v2 & $i(v2)))
% 10.72/2.24 |
% 10.72/2.24 | ALPHA: (composition_distributivity) implies:
% 10.72/2.24 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (
% 10.72/2.24 | ~ (composition(v3, v2) = v4) | ~ (join(v0, v1) = v3) | ~ $i(v2) |
% 10.72/2.24 | ~ $i(v1) | ~ $i(v0) | ? [v5: $i] : ? [v6: $i] : (composition(v1,
% 10.72/2.24 | v2) = v6 & composition(v0, v2) = v5 & join(v5, v6) = v4 & $i(v6)
% 10.72/2.24 | & $i(v5) & $i(v4)))
% 10.72/2.24 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 10.72/2.24 | ! [v5: $i] : ( ~ (composition(v1, v2) = v4) | ~ (composition(v0, v2) =
% 10.72/2.24 | v3) | ~ (join(v3, v4) = v5) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 10.72/2.24 | ? [v6: $i] : (composition(v6, v2) = v5 & join(v0, v1) = v6 & $i(v6) &
% 10.72/2.24 | $i(v5)))
% 10.72/2.25 |
% 10.72/2.25 | ALPHA: (converse_additivity) implies:
% 10.72/2.25 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (join(v0, v1) = v2) | ~
% 10.72/2.25 | $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] : ? [v5: $i] :
% 10.72/2.25 | (converse(v2) = v3 & converse(v1) = v5 & converse(v0) = v4 & join(v4,
% 10.72/2.25 | v5) = v3 & $i(v5) & $i(v4) & $i(v3)))
% 10.72/2.25 |
% 10.72/2.25 | ALPHA: (converse_multiplicativity) implies:
% 10.72/2.25 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (composition(v0, v1) =
% 10.72/2.25 | v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] : ? [v5:
% 10.72/2.25 | $i] : (converse(v2) = v3 & converse(v1) = v4 & converse(v0) = v5 &
% 10.72/2.25 | composition(v4, v5) = v3 & $i(v5) & $i(v4) & $i(v3)))
% 10.72/2.25 |
% 10.72/2.25 | ALPHA: (function-axioms) implies:
% 10.72/2.25 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (converse(v2) =
% 10.72/2.25 | v1) | ~ (converse(v2) = v0))
% 10.72/2.25 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 10.72/2.25 | (join(v3, v2) = v1) | ~ (join(v3, v2) = v0))
% 10.72/2.25 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 10.72/2.25 | (composition(v3, v2) = v1) | ~ (composition(v3, v2) = v0))
% 10.72/2.25 |
% 10.72/2.25 | DELTA: instantiating (goals) with fresh symbols all_17_0, all_17_1, all_17_2,
% 10.72/2.25 | all_17_3, all_17_4, all_17_5, all_17_6, all_17_7, all_17_8 gives:
% 10.72/2.25 | (9) composition(all_17_6, all_17_7) = all_17_1 & composition(all_17_6,
% 10.72/2.25 | all_17_8) = all_17_2 & composition(all_17_7, all_17_6) = all_17_4 &
% 10.72/2.25 | composition(all_17_8, all_17_6) = all_17_5 & join(all_17_2, all_17_1) =
% 10.72/2.25 | all_17_0 & join(all_17_5, all_17_4) = all_17_3 & join(all_17_8,
% 10.72/2.25 | all_17_7) = all_17_7 & $i(all_17_0) & $i(all_17_1) & $i(all_17_2) &
% 10.72/2.25 | $i(all_17_3) & $i(all_17_4) & $i(all_17_5) & $i(all_17_6) &
% 10.72/2.25 | $i(all_17_7) & $i(all_17_8) & ( ~ (all_17_0 = all_17_1) | ~ (all_17_3
% 10.72/2.25 | = all_17_4))
% 10.72/2.25 |
% 10.72/2.25 | ALPHA: (9) implies:
% 10.72/2.25 | (10) $i(all_17_8)
% 10.72/2.25 | (11) $i(all_17_7)
% 10.72/2.25 | (12) $i(all_17_6)
% 10.72/2.25 | (13) $i(all_17_2)
% 10.72/2.25 | (14) $i(all_17_1)
% 10.72/2.25 | (15) join(all_17_8, all_17_7) = all_17_7
% 10.72/2.25 | (16) join(all_17_5, all_17_4) = all_17_3
% 10.72/2.25 | (17) join(all_17_2, all_17_1) = all_17_0
% 10.72/2.25 | (18) composition(all_17_8, all_17_6) = all_17_5
% 10.72/2.25 | (19) composition(all_17_7, all_17_6) = all_17_4
% 10.72/2.25 | (20) composition(all_17_6, all_17_8) = all_17_2
% 10.72/2.25 | (21) composition(all_17_6, all_17_7) = all_17_1
% 10.72/2.25 | (22) ~ (all_17_0 = all_17_1) | ~ (all_17_3 = all_17_4)
% 10.72/2.25 |
% 10.72/2.25 | GROUND_INST: instantiating (4) with all_17_8, all_17_7, all_17_7, simplifying
% 10.72/2.25 | with (10), (11), (15) gives:
% 10.72/2.25 | (23) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (converse(all_17_7) = v2 &
% 10.72/2.25 | converse(all_17_7) = v0 & converse(all_17_8) = v1 & join(v1, v2) =
% 10.72/2.25 | v0 & $i(v2) & $i(v1) & $i(v0))
% 10.72/2.25 |
% 10.72/2.26 | GROUND_INST: instantiating (1) with all_17_1, all_17_2, all_17_0, simplifying
% 10.72/2.26 | with (13), (14), (17) gives:
% 10.72/2.26 | (24) join(all_17_1, all_17_2) = all_17_0 & $i(all_17_0)
% 10.72/2.26 |
% 10.72/2.26 | ALPHA: (24) implies:
% 10.72/2.26 | (25) $i(all_17_0)
% 10.72/2.26 |
% 10.72/2.26 | GROUND_INST: instantiating (4) with all_17_2, all_17_1, all_17_0, simplifying
% 10.72/2.26 | with (13), (14), (17) gives:
% 10.72/2.26 | (26) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (converse(all_17_0) = v0 &
% 10.72/2.26 | converse(all_17_1) = v2 & converse(all_17_2) = v1 & join(v1, v2) =
% 10.72/2.26 | v0 & $i(v2) & $i(v1) & $i(v0))
% 10.72/2.26 |
% 10.72/2.26 | GROUND_INST: instantiating (converse_cancellativity) with all_17_8, all_17_6,
% 10.72/2.26 | all_17_5, simplifying with (10), (12), (18) gives:
% 10.72/2.26 | (27) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] :
% 10.72/2.26 | (converse(all_17_8) = v0 & composition(v0, v1) = v2 &
% 10.72/2.26 | complement(all_17_5) = v1 & complement(all_17_6) = v3 & join(v2, v3)
% 10.72/2.26 | = v3 & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 10.72/2.26 |
% 10.72/2.26 | GROUND_INST: instantiating (5) with all_17_8, all_17_6, all_17_5, simplifying
% 10.72/2.26 | with (10), (12), (18) gives:
% 10.72/2.26 | (28) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (converse(all_17_5) = v0 &
% 10.72/2.26 | converse(all_17_6) = v1 & converse(all_17_8) = v2 & composition(v1,
% 10.72/2.26 | v2) = v0 & $i(v2) & $i(v1) & $i(v0))
% 10.72/2.26 |
% 10.72/2.26 | GROUND_INST: instantiating (3) with all_17_8, all_17_7, all_17_6, all_17_5,
% 10.72/2.26 | all_17_4, all_17_3, simplifying with (10), (11), (12), (16),
% 10.72/2.26 | (18), (19) gives:
% 10.72/2.26 | (29) ? [v0: $i] : (composition(v0, all_17_6) = all_17_3 & join(all_17_8,
% 10.72/2.26 | all_17_7) = v0 & $i(v0) & $i(all_17_3))
% 10.72/2.26 |
% 10.72/2.26 | GROUND_INST: instantiating (2) with all_17_8, all_17_7, all_17_6, all_17_7,
% 10.72/2.26 | all_17_4, simplifying with (10), (11), (12), (15), (19) gives:
% 10.72/2.26 | (30) ? [v0: $i] : ? [v1: $i] : (composition(all_17_7, all_17_6) = v1 &
% 10.72/2.26 | composition(all_17_8, all_17_6) = v0 & join(v0, v1) = all_17_4 &
% 10.72/2.26 | $i(v1) & $i(v0) & $i(all_17_4))
% 10.72/2.26 |
% 10.72/2.26 | GROUND_INST: instantiating (converse_cancellativity) with all_17_7, all_17_6,
% 10.72/2.26 | all_17_4, simplifying with (11), (12), (19) gives:
% 10.72/2.26 | (31) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] :
% 10.72/2.26 | (converse(all_17_7) = v0 & composition(v0, v1) = v2 &
% 10.72/2.26 | complement(all_17_4) = v1 & complement(all_17_6) = v3 & join(v2, v3)
% 10.72/2.26 | = v3 & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 10.72/2.26 |
% 10.72/2.26 | GROUND_INST: instantiating (5) with all_17_7, all_17_6, all_17_4, simplifying
% 10.72/2.26 | with (11), (12), (19) gives:
% 10.72/2.26 | (32) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (converse(all_17_4) = v0 &
% 10.72/2.26 | converse(all_17_6) = v1 & converse(all_17_7) = v2 & composition(v1,
% 10.72/2.26 | v2) = v0 & $i(v2) & $i(v1) & $i(v0))
% 10.72/2.26 |
% 10.72/2.26 | GROUND_INST: instantiating (converse_cancellativity) with all_17_6, all_17_8,
% 10.72/2.26 | all_17_2, simplifying with (10), (12), (20) gives:
% 10.72/2.26 | (33) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] :
% 10.72/2.26 | (converse(all_17_6) = v0 & composition(v0, v1) = v2 &
% 10.72/2.26 | complement(all_17_2) = v1 & complement(all_17_8) = v3 & join(v2, v3)
% 10.72/2.26 | = v3 & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 10.72/2.26 |
% 10.72/2.26 | GROUND_INST: instantiating (5) with all_17_6, all_17_8, all_17_2, simplifying
% 10.72/2.26 | with (10), (12), (20) gives:
% 10.72/2.26 | (34) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (converse(all_17_2) = v0 &
% 10.72/2.26 | converse(all_17_6) = v2 & converse(all_17_8) = v1 & composition(v1,
% 10.72/2.26 | v2) = v0 & $i(v2) & $i(v1) & $i(v0))
% 10.72/2.26 |
% 10.72/2.26 | GROUND_INST: instantiating (converse_cancellativity) with all_17_6, all_17_7,
% 10.72/2.26 | all_17_1, simplifying with (11), (12), (21) gives:
% 10.72/2.27 | (35) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] :
% 10.72/2.27 | (converse(all_17_6) = v0 & composition(v0, v1) = v2 &
% 10.72/2.27 | complement(all_17_1) = v1 & complement(all_17_7) = v3 & join(v2, v3)
% 10.72/2.27 | = v3 & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 10.72/2.27 |
% 10.72/2.27 | GROUND_INST: instantiating (5) with all_17_6, all_17_7, all_17_1, simplifying
% 10.72/2.27 | with (11), (12), (21) gives:
% 10.72/2.27 | (36) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (converse(all_17_1) = v0 &
% 10.72/2.27 | converse(all_17_6) = v2 & converse(all_17_7) = v1 & composition(v1,
% 10.72/2.27 | v2) = v0 & $i(v2) & $i(v1) & $i(v0))
% 10.72/2.27 |
% 10.72/2.27 | DELTA: instantiating (29) with fresh symbol all_27_0 gives:
% 10.72/2.27 | (37) composition(all_27_0, all_17_6) = all_17_3 & join(all_17_8, all_17_7)
% 10.72/2.27 | = all_27_0 & $i(all_27_0) & $i(all_17_3)
% 10.72/2.27 |
% 10.72/2.27 | ALPHA: (37) implies:
% 10.72/2.27 | (38) join(all_17_8, all_17_7) = all_27_0
% 10.72/2.27 | (39) composition(all_27_0, all_17_6) = all_17_3
% 10.72/2.27 |
% 10.72/2.27 | DELTA: instantiating (30) with fresh symbols all_29_0, all_29_1 gives:
% 10.72/2.27 | (40) composition(all_17_7, all_17_6) = all_29_0 & composition(all_17_8,
% 10.72/2.27 | all_17_6) = all_29_1 & join(all_29_1, all_29_0) = all_17_4 &
% 10.72/2.27 | $i(all_29_0) & $i(all_29_1) & $i(all_17_4)
% 10.72/2.27 |
% 10.72/2.27 | ALPHA: (40) implies:
% 10.72/2.27 | (41) composition(all_17_7, all_17_6) = all_29_0
% 10.72/2.27 |
% 10.72/2.27 | DELTA: instantiating (28) with fresh symbols all_31_0, all_31_1, all_31_2
% 10.72/2.27 | gives:
% 10.72/2.27 | (42) converse(all_17_5) = all_31_2 & converse(all_17_6) = all_31_1 &
% 10.72/2.27 | converse(all_17_8) = all_31_0 & composition(all_31_1, all_31_0) =
% 10.72/2.27 | all_31_2 & $i(all_31_0) & $i(all_31_1) & $i(all_31_2)
% 10.72/2.27 |
% 10.72/2.27 | ALPHA: (42) implies:
% 10.72/2.27 | (43) converse(all_17_8) = all_31_0
% 10.72/2.27 | (44) converse(all_17_6) = all_31_1
% 10.72/2.27 |
% 10.72/2.27 | DELTA: instantiating (34) with fresh symbols all_33_0, all_33_1, all_33_2
% 10.72/2.27 | gives:
% 10.72/2.27 | (45) converse(all_17_2) = all_33_2 & converse(all_17_6) = all_33_0 &
% 10.72/2.27 | converse(all_17_8) = all_33_1 & composition(all_33_1, all_33_0) =
% 10.72/2.27 | all_33_2 & $i(all_33_0) & $i(all_33_1) & $i(all_33_2)
% 10.72/2.27 |
% 10.72/2.27 | ALPHA: (45) implies:
% 10.72/2.27 | (46) $i(all_33_1)
% 10.72/2.27 | (47) $i(all_33_0)
% 10.72/2.27 | (48) composition(all_33_1, all_33_0) = all_33_2
% 10.72/2.27 | (49) converse(all_17_8) = all_33_1
% 10.72/2.27 | (50) converse(all_17_6) = all_33_0
% 10.72/2.27 | (51) converse(all_17_2) = all_33_2
% 10.72/2.27 |
% 10.72/2.27 | DELTA: instantiating (32) with fresh symbols all_35_0, all_35_1, all_35_2
% 10.72/2.27 | gives:
% 10.72/2.27 | (52) converse(all_17_4) = all_35_2 & converse(all_17_6) = all_35_1 &
% 10.72/2.27 | converse(all_17_7) = all_35_0 & composition(all_35_1, all_35_0) =
% 10.72/2.27 | all_35_2 & $i(all_35_0) & $i(all_35_1) & $i(all_35_2)
% 10.72/2.27 |
% 10.72/2.27 | ALPHA: (52) implies:
% 10.72/2.27 | (53) converse(all_17_7) = all_35_0
% 10.72/2.27 | (54) converse(all_17_6) = all_35_1
% 10.72/2.27 |
% 10.72/2.27 | DELTA: instantiating (36) with fresh symbols all_37_0, all_37_1, all_37_2
% 10.72/2.27 | gives:
% 10.72/2.27 | (55) converse(all_17_1) = all_37_2 & converse(all_17_6) = all_37_0 &
% 10.72/2.27 | converse(all_17_7) = all_37_1 & composition(all_37_1, all_37_0) =
% 10.72/2.27 | all_37_2 & $i(all_37_0) & $i(all_37_1) & $i(all_37_2)
% 10.72/2.27 |
% 10.72/2.27 | ALPHA: (55) implies:
% 10.72/2.27 | (56) $i(all_37_1)
% 10.72/2.27 | (57) composition(all_37_1, all_37_0) = all_37_2
% 10.72/2.27 | (58) converse(all_17_7) = all_37_1
% 10.72/2.27 | (59) converse(all_17_6) = all_37_0
% 10.72/2.27 | (60) converse(all_17_1) = all_37_2
% 10.72/2.27 |
% 10.72/2.27 | DELTA: instantiating (26) with fresh symbols all_39_0, all_39_1, all_39_2
% 10.72/2.27 | gives:
% 10.72/2.27 | (61) converse(all_17_0) = all_39_2 & converse(all_17_1) = all_39_0 &
% 10.72/2.27 | converse(all_17_2) = all_39_1 & join(all_39_1, all_39_0) = all_39_2 &
% 10.72/2.27 | $i(all_39_0) & $i(all_39_1) & $i(all_39_2)
% 10.72/2.27 |
% 10.72/2.27 | ALPHA: (61) implies:
% 10.72/2.27 | (62) $i(all_39_1)
% 10.72/2.27 | (63) $i(all_39_0)
% 10.72/2.27 | (64) join(all_39_1, all_39_0) = all_39_2
% 10.72/2.27 | (65) converse(all_17_2) = all_39_1
% 10.72/2.27 | (66) converse(all_17_1) = all_39_0
% 10.72/2.27 | (67) converse(all_17_0) = all_39_2
% 10.72/2.27 |
% 10.72/2.27 | DELTA: instantiating (23) with fresh symbols all_41_0, all_41_1, all_41_2
% 10.72/2.27 | gives:
% 10.72/2.27 | (68) converse(all_17_7) = all_41_0 & converse(all_17_7) = all_41_2 &
% 10.72/2.27 | converse(all_17_8) = all_41_1 & join(all_41_1, all_41_0) = all_41_2 &
% 10.72/2.27 | $i(all_41_0) & $i(all_41_1) & $i(all_41_2)
% 10.72/2.27 |
% 10.72/2.27 | ALPHA: (68) implies:
% 10.72/2.27 | (69) join(all_41_1, all_41_0) = all_41_2
% 10.72/2.28 | (70) converse(all_17_8) = all_41_1
% 10.72/2.28 | (71) converse(all_17_7) = all_41_2
% 10.72/2.28 | (72) converse(all_17_7) = all_41_0
% 10.72/2.28 |
% 10.72/2.28 | DELTA: instantiating (27) with fresh symbols all_45_0, all_45_1, all_45_2,
% 10.72/2.28 | all_45_3 gives:
% 10.72/2.28 | (73) converse(all_17_8) = all_45_3 & composition(all_45_3, all_45_2) =
% 10.72/2.28 | all_45_1 & complement(all_17_5) = all_45_2 & complement(all_17_6) =
% 10.72/2.28 | all_45_0 & join(all_45_1, all_45_0) = all_45_0 & $i(all_45_0) &
% 10.72/2.28 | $i(all_45_1) & $i(all_45_2) & $i(all_45_3)
% 10.72/2.28 |
% 10.72/2.28 | ALPHA: (73) implies:
% 10.72/2.28 | (74) converse(all_17_8) = all_45_3
% 10.72/2.28 |
% 10.72/2.28 | DELTA: instantiating (31) with fresh symbols all_47_0, all_47_1, all_47_2,
% 10.72/2.28 | all_47_3 gives:
% 10.72/2.28 | (75) converse(all_17_7) = all_47_3 & composition(all_47_3, all_47_2) =
% 10.72/2.28 | all_47_1 & complement(all_17_4) = all_47_2 & complement(all_17_6) =
% 10.72/2.28 | all_47_0 & join(all_47_1, all_47_0) = all_47_0 & $i(all_47_0) &
% 10.72/2.28 | $i(all_47_1) & $i(all_47_2) & $i(all_47_3)
% 10.72/2.28 |
% 10.72/2.28 | ALPHA: (75) implies:
% 10.72/2.28 | (76) converse(all_17_7) = all_47_3
% 10.72/2.28 |
% 10.72/2.28 | DELTA: instantiating (35) with fresh symbols all_49_0, all_49_1, all_49_2,
% 10.72/2.28 | all_49_3 gives:
% 11.99/2.28 | (77) converse(all_17_6) = all_49_3 & composition(all_49_3, all_49_2) =
% 11.99/2.28 | all_49_1 & complement(all_17_1) = all_49_2 & complement(all_17_7) =
% 11.99/2.28 | all_49_0 & join(all_49_1, all_49_0) = all_49_0 & $i(all_49_0) &
% 11.99/2.28 | $i(all_49_1) & $i(all_49_2) & $i(all_49_3)
% 11.99/2.28 |
% 11.99/2.28 | ALPHA: (77) implies:
% 11.99/2.28 | (78) converse(all_17_6) = all_49_3
% 11.99/2.28 |
% 11.99/2.28 | DELTA: instantiating (33) with fresh symbols all_51_0, all_51_1, all_51_2,
% 11.99/2.28 | all_51_3 gives:
% 11.99/2.28 | (79) converse(all_17_6) = all_51_3 & composition(all_51_3, all_51_2) =
% 11.99/2.28 | all_51_1 & complement(all_17_2) = all_51_2 & complement(all_17_8) =
% 11.99/2.28 | all_51_0 & join(all_51_1, all_51_0) = all_51_0 & $i(all_51_0) &
% 11.99/2.28 | $i(all_51_1) & $i(all_51_2) & $i(all_51_3)
% 11.99/2.28 |
% 11.99/2.28 | ALPHA: (79) implies:
% 11.99/2.28 | (80) converse(all_17_6) = all_51_3
% 11.99/2.28 |
% 11.99/2.28 | GROUND_INST: instantiating (7) with all_17_7, all_27_0, all_17_7, all_17_8,
% 11.99/2.28 | simplifying with (15), (38) gives:
% 11.99/2.28 | (81) all_27_0 = all_17_7
% 11.99/2.28 |
% 11.99/2.28 | GROUND_INST: instantiating (8) with all_17_4, all_29_0, all_17_6, all_17_7,
% 11.99/2.28 | simplifying with (19), (41) gives:
% 11.99/2.28 | (82) all_29_0 = all_17_4
% 11.99/2.28 |
% 11.99/2.28 | GROUND_INST: instantiating (6) with all_33_1, all_41_1, all_17_8, simplifying
% 11.99/2.28 | with (49), (70) gives:
% 11.99/2.28 | (83) all_41_1 = all_33_1
% 11.99/2.28 |
% 11.99/2.28 | GROUND_INST: instantiating (6) with all_41_1, all_45_3, all_17_8, simplifying
% 11.99/2.28 | with (70), (74) gives:
% 11.99/2.28 | (84) all_45_3 = all_41_1
% 11.99/2.28 |
% 11.99/2.28 | GROUND_INST: instantiating (6) with all_31_0, all_45_3, all_17_8, simplifying
% 11.99/2.28 | with (43), (74) gives:
% 11.99/2.28 | (85) all_45_3 = all_31_0
% 11.99/2.28 |
% 11.99/2.28 | GROUND_INST: instantiating (6) with all_37_1, all_41_2, all_17_7, simplifying
% 11.99/2.28 | with (58), (71) gives:
% 11.99/2.28 | (86) all_41_2 = all_37_1
% 11.99/2.28 |
% 11.99/2.28 | GROUND_INST: instantiating (6) with all_41_2, all_41_0, all_17_7, simplifying
% 11.99/2.28 | with (71), (72) gives:
% 11.99/2.28 | (87) all_41_0 = all_41_2
% 11.99/2.28 |
% 11.99/2.28 | GROUND_INST: instantiating (6) with all_41_0, all_47_3, all_17_7, simplifying
% 11.99/2.28 | with (72), (76) gives:
% 11.99/2.28 | (88) all_47_3 = all_41_0
% 11.99/2.28 |
% 11.99/2.28 | GROUND_INST: instantiating (6) with all_35_0, all_47_3, all_17_7, simplifying
% 11.99/2.28 | with (53), (76) gives:
% 11.99/2.28 | (89) all_47_3 = all_35_0
% 11.99/2.28 |
% 11.99/2.28 | GROUND_INST: instantiating (6) with all_37_0, all_49_3, all_17_6, simplifying
% 11.99/2.28 | with (59), (78) gives:
% 11.99/2.28 | (90) all_49_3 = all_37_0
% 11.99/2.28 |
% 11.99/2.28 | GROUND_INST: instantiating (6) with all_35_1, all_49_3, all_17_6, simplifying
% 11.99/2.28 | with (54), (78) gives:
% 11.99/2.28 | (91) all_49_3 = all_35_1
% 11.99/2.28 |
% 11.99/2.28 | GROUND_INST: instantiating (6) with all_31_1, all_49_3, all_17_6, simplifying
% 11.99/2.28 | with (44), (78) gives:
% 11.99/2.28 | (92) all_49_3 = all_31_1
% 11.99/2.28 |
% 11.99/2.28 | GROUND_INST: instantiating (6) with all_37_0, all_51_3, all_17_6, simplifying
% 11.99/2.28 | with (59), (80) gives:
% 11.99/2.28 | (93) all_51_3 = all_37_0
% 11.99/2.28 |
% 11.99/2.28 | GROUND_INST: instantiating (6) with all_33_0, all_51_3, all_17_6, simplifying
% 11.99/2.28 | with (50), (80) gives:
% 11.99/2.29 | (94) all_51_3 = all_33_0
% 11.99/2.29 |
% 11.99/2.29 | GROUND_INST: instantiating (6) with all_33_2, all_39_1, all_17_2, simplifying
% 11.99/2.29 | with (51), (65) gives:
% 11.99/2.29 | (95) all_39_1 = all_33_2
% 11.99/2.29 |
% 11.99/2.29 | GROUND_INST: instantiating (6) with all_37_2, all_39_0, all_17_1, simplifying
% 11.99/2.29 | with (60), (66) gives:
% 11.99/2.29 | (96) all_39_0 = all_37_2
% 11.99/2.29 |
% 11.99/2.29 | COMBINE_EQS: (93), (94) imply:
% 11.99/2.29 | (97) all_37_0 = all_33_0
% 11.99/2.29 |
% 11.99/2.29 | SIMP: (97) implies:
% 11.99/2.29 | (98) all_37_0 = all_33_0
% 11.99/2.29 |
% 11.99/2.29 | COMBINE_EQS: (90), (91) imply:
% 11.99/2.29 | (99) all_37_0 = all_35_1
% 11.99/2.29 |
% 11.99/2.29 | SIMP: (99) implies:
% 11.99/2.29 | (100) all_37_0 = all_35_1
% 11.99/2.29 |
% 11.99/2.29 | COMBINE_EQS: (91), (92) imply:
% 11.99/2.29 | (101) all_35_1 = all_31_1
% 11.99/2.29 |
% 11.99/2.29 | COMBINE_EQS: (88), (89) imply:
% 11.99/2.29 | (102) all_41_0 = all_35_0
% 11.99/2.29 |
% 11.99/2.29 | SIMP: (102) implies:
% 11.99/2.29 | (103) all_41_0 = all_35_0
% 11.99/2.29 |
% 11.99/2.29 | COMBINE_EQS: (84), (85) imply:
% 11.99/2.29 | (104) all_41_1 = all_31_0
% 11.99/2.29 |
% 11.99/2.29 | SIMP: (104) implies:
% 11.99/2.29 | (105) all_41_1 = all_31_0
% 11.99/2.29 |
% 11.99/2.29 | COMBINE_EQS: (87), (103) imply:
% 11.99/2.29 | (106) all_41_2 = all_35_0
% 11.99/2.29 |
% 11.99/2.29 | SIMP: (106) implies:
% 11.99/2.29 | (107) all_41_2 = all_35_0
% 11.99/2.29 |
% 11.99/2.29 | COMBINE_EQS: (83), (105) imply:
% 11.99/2.29 | (108) all_33_1 = all_31_0
% 11.99/2.29 |
% 11.99/2.29 | COMBINE_EQS: (86), (107) imply:
% 11.99/2.29 | (109) all_37_1 = all_35_0
% 11.99/2.29 |
% 11.99/2.29 | COMBINE_EQS: (98), (100) imply:
% 11.99/2.29 | (110) all_35_1 = all_33_0
% 11.99/2.29 |
% 11.99/2.29 | SIMP: (110) implies:
% 11.99/2.29 | (111) all_35_1 = all_33_0
% 11.99/2.29 |
% 11.99/2.29 | COMBINE_EQS: (101), (111) imply:
% 11.99/2.29 | (112) all_33_0 = all_31_1
% 11.99/2.29 |
% 11.99/2.29 | COMBINE_EQS: (98), (112) imply:
% 11.99/2.29 | (113) all_37_0 = all_31_1
% 11.99/2.29 |
% 11.99/2.29 | REDUCE: (57), (109), (113) imply:
% 11.99/2.29 | (114) composition(all_35_0, all_31_1) = all_37_2
% 11.99/2.29 |
% 11.99/2.29 | REDUCE: (48), (108), (112) imply:
% 11.99/2.29 | (115) composition(all_31_0, all_31_1) = all_33_2
% 11.99/2.29 |
% 11.99/2.29 | REDUCE: (39), (81) imply:
% 11.99/2.29 | (116) composition(all_17_7, all_17_6) = all_17_3
% 11.99/2.29 |
% 11.99/2.29 | REDUCE: (69), (103), (105), (107) imply:
% 11.99/2.29 | (117) join(all_31_0, all_35_0) = all_35_0
% 11.99/2.29 |
% 11.99/2.29 | REDUCE: (64), (95), (96) imply:
% 11.99/2.29 | (118) join(all_33_2, all_37_2) = all_39_2
% 11.99/2.29 |
% 11.99/2.29 | REDUCE: (63), (96) imply:
% 11.99/2.29 | (119) $i(all_37_2)
% 11.99/2.29 |
% 11.99/2.29 | REDUCE: (62), (95) imply:
% 11.99/2.29 | (120) $i(all_33_2)
% 11.99/2.29 |
% 11.99/2.29 | REDUCE: (56), (109) imply:
% 11.99/2.29 | (121) $i(all_35_0)
% 11.99/2.29 |
% 11.99/2.29 | REDUCE: (47), (112) imply:
% 11.99/2.29 | (122) $i(all_31_1)
% 11.99/2.29 |
% 11.99/2.29 | REDUCE: (46), (108) imply:
% 11.99/2.29 | (123) $i(all_31_0)
% 11.99/2.29 |
% 11.99/2.29 | GROUND_INST: instantiating (8) with all_17_4, all_17_3, all_17_6, all_17_7,
% 11.99/2.29 | simplifying with (19), (116) gives:
% 11.99/2.29 | (124) all_17_3 = all_17_4
% 11.99/2.29 |
% 11.99/2.29 | BETA: splitting (22) gives:
% 11.99/2.29 |
% 11.99/2.29 | Case 1:
% 11.99/2.29 | |
% 11.99/2.29 | | (125) ~ (all_17_0 = all_17_1)
% 11.99/2.29 | |
% 11.99/2.29 | | GROUND_INST: instantiating (4) with all_33_2, all_37_2, all_39_2,
% 11.99/2.29 | | simplifying with (118), (119), (120) gives:
% 11.99/2.30 | | (126) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (converse(all_39_2) = v0
% 11.99/2.30 | | & converse(all_37_2) = v2 & converse(all_33_2) = v1 & join(v1,
% 11.99/2.30 | | v2) = v0 & $i(v2) & $i(v1) & $i(v0))
% 11.99/2.30 | |
% 11.99/2.30 | | GROUND_INST: instantiating (3) with all_31_0, all_35_0, all_31_1, all_33_2,
% 11.99/2.30 | | all_37_2, all_39_2, simplifying with (114), (115), (118),
% 11.99/2.30 | | (121), (122), (123) gives:
% 11.99/2.30 | | (127) ? [v0: $i] : (composition(v0, all_31_1) = all_39_2 &
% 11.99/2.30 | | join(all_31_0, all_35_0) = v0 & $i(v0) & $i(all_39_2))
% 11.99/2.30 | |
% 11.99/2.30 | | GROUND_INST: instantiating (2) with all_31_0, all_35_0, all_31_1, all_35_0,
% 11.99/2.30 | | all_37_2, simplifying with (114), (117), (121), (122), (123)
% 11.99/2.30 | | gives:
% 11.99/2.30 | | (128) ? [v0: $i] : ? [v1: $i] : (composition(all_35_0, all_31_1) = v1 &
% 11.99/2.30 | | composition(all_31_0, all_31_1) = v0 & join(v0, v1) = all_37_2 &
% 11.99/2.30 | | $i(v1) & $i(v0) & $i(all_37_2))
% 11.99/2.30 | |
% 11.99/2.30 | | GROUND_INST: instantiating (5) with all_35_0, all_31_1, all_37_2,
% 11.99/2.30 | | simplifying with (114), (121), (122) gives:
% 11.99/2.30 | | (129) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (converse(all_37_2) = v0
% 11.99/2.30 | | & converse(all_35_0) = v2 & converse(all_31_1) = v1 &
% 11.99/2.30 | | composition(v1, v2) = v0 & $i(v2) & $i(v1) & $i(v0))
% 11.99/2.30 | |
% 11.99/2.30 | | GROUND_INST: instantiating (converse_idempotence) with all_17_1, all_37_2,
% 11.99/2.30 | | simplifying with (14), (60) gives:
% 11.99/2.30 | | (130) converse(all_37_2) = all_17_1
% 11.99/2.30 | |
% 11.99/2.30 | | GROUND_INST: instantiating (converse_idempotence) with all_17_0, all_39_2,
% 11.99/2.30 | | simplifying with (25), (67) gives:
% 11.99/2.30 | | (131) converse(all_39_2) = all_17_0
% 11.99/2.30 | |
% 11.99/2.30 | | DELTA: instantiating (127) with fresh symbol all_103_0 gives:
% 11.99/2.30 | | (132) composition(all_103_0, all_31_1) = all_39_2 & join(all_31_0,
% 11.99/2.30 | | all_35_0) = all_103_0 & $i(all_103_0) & $i(all_39_2)
% 11.99/2.30 | |
% 11.99/2.30 | | ALPHA: (132) implies:
% 11.99/2.30 | | (133) join(all_31_0, all_35_0) = all_103_0
% 11.99/2.30 | | (134) composition(all_103_0, all_31_1) = all_39_2
% 11.99/2.30 | |
% 11.99/2.30 | | DELTA: instantiating (128) with fresh symbols all_109_0, all_109_1 gives:
% 11.99/2.30 | | (135) composition(all_35_0, all_31_1) = all_109_0 & composition(all_31_0,
% 11.99/2.30 | | all_31_1) = all_109_1 & join(all_109_1, all_109_0) = all_37_2 &
% 11.99/2.30 | | $i(all_109_0) & $i(all_109_1) & $i(all_37_2)
% 11.99/2.30 | |
% 11.99/2.30 | | ALPHA: (135) implies:
% 11.99/2.30 | | (136) composition(all_35_0, all_31_1) = all_109_0
% 11.99/2.30 | |
% 11.99/2.30 | | DELTA: instantiating (129) with fresh symbols all_111_0, all_111_1,
% 11.99/2.30 | | all_111_2 gives:
% 11.99/2.30 | | (137) converse(all_37_2) = all_111_2 & converse(all_35_0) = all_111_0 &
% 11.99/2.30 | | converse(all_31_1) = all_111_1 & composition(all_111_1, all_111_0)
% 11.99/2.30 | | = all_111_2 & $i(all_111_0) & $i(all_111_1) & $i(all_111_2)
% 11.99/2.30 | |
% 11.99/2.30 | | ALPHA: (137) implies:
% 11.99/2.30 | | (138) converse(all_37_2) = all_111_2
% 11.99/2.30 | |
% 11.99/2.30 | | DELTA: instantiating (126) with fresh symbols all_125_0, all_125_1,
% 11.99/2.30 | | all_125_2 gives:
% 11.99/2.30 | | (139) converse(all_39_2) = all_125_2 & converse(all_37_2) = all_125_0 &
% 11.99/2.30 | | converse(all_33_2) = all_125_1 & join(all_125_1, all_125_0) =
% 11.99/2.30 | | all_125_2 & $i(all_125_0) & $i(all_125_1) & $i(all_125_2)
% 11.99/2.30 | |
% 11.99/2.30 | | ALPHA: (139) implies:
% 11.99/2.30 | | (140) converse(all_37_2) = all_125_0
% 11.99/2.30 | | (141) converse(all_39_2) = all_125_2
% 11.99/2.30 | |
% 11.99/2.30 | | GROUND_INST: instantiating (7) with all_35_0, all_103_0, all_35_0, all_31_0,
% 11.99/2.30 | | simplifying with (117), (133) gives:
% 11.99/2.30 | | (142) all_103_0 = all_35_0
% 11.99/2.30 | |
% 11.99/2.30 | | GROUND_INST: instantiating (8) with all_37_2, all_109_0, all_31_1, all_35_0,
% 11.99/2.30 | | simplifying with (114), (136) gives:
% 11.99/2.30 | | (143) all_109_0 = all_37_2
% 11.99/2.30 | |
% 11.99/2.30 | | GROUND_INST: instantiating (6) with all_111_2, all_125_0, all_37_2,
% 11.99/2.30 | | simplifying with (138), (140) gives:
% 11.99/2.30 | | (144) all_125_0 = all_111_2
% 11.99/2.30 | |
% 11.99/2.30 | | GROUND_INST: instantiating (6) with all_17_1, all_125_0, all_37_2,
% 11.99/2.30 | | simplifying with (130), (140) gives:
% 11.99/2.30 | | (145) all_125_0 = all_17_1
% 11.99/2.30 | |
% 11.99/2.30 | | GROUND_INST: instantiating (6) with all_17_0, all_125_2, all_39_2,
% 11.99/2.30 | | simplifying with (131), (141) gives:
% 11.99/2.30 | | (146) all_125_2 = all_17_0
% 11.99/2.30 | |
% 11.99/2.30 | | COMBINE_EQS: (144), (145) imply:
% 11.99/2.30 | | (147) all_111_2 = all_17_1
% 11.99/2.30 | |
% 11.99/2.30 | | SIMP: (147) implies:
% 11.99/2.30 | | (148) all_111_2 = all_17_1
% 11.99/2.30 | |
% 11.99/2.30 | | REDUCE: (134), (142) imply:
% 11.99/2.30 | | (149) composition(all_35_0, all_31_1) = all_39_2
% 11.99/2.30 | |
% 11.99/2.30 | | GROUND_INST: instantiating (8) with all_37_2, all_39_2, all_31_1, all_35_0,
% 11.99/2.30 | | simplifying with (114), (149) gives:
% 11.99/2.31 | | (150) all_39_2 = all_37_2
% 11.99/2.31 | |
% 11.99/2.31 | | REDUCE: (131), (150) imply:
% 11.99/2.31 | | (151) converse(all_37_2) = all_17_0
% 11.99/2.31 | |
% 11.99/2.31 | | GROUND_INST: instantiating (6) with all_17_1, all_17_0, all_37_2,
% 11.99/2.31 | | simplifying with (130), (151) gives:
% 11.99/2.31 | | (152) all_17_0 = all_17_1
% 11.99/2.31 | |
% 11.99/2.31 | | REDUCE: (125), (152) imply:
% 11.99/2.31 | | (153) $false
% 11.99/2.31 | |
% 11.99/2.31 | | CLOSE: (153) is inconsistent.
% 11.99/2.31 | |
% 11.99/2.31 | Case 2:
% 11.99/2.31 | |
% 11.99/2.31 | | (154) ~ (all_17_3 = all_17_4)
% 11.99/2.31 | |
% 11.99/2.31 | | REDUCE: (124), (154) imply:
% 11.99/2.31 | | (155) $false
% 11.99/2.31 | |
% 11.99/2.31 | | CLOSE: (155) is inconsistent.
% 11.99/2.31 | |
% 11.99/2.31 | End of split
% 11.99/2.31 |
% 11.99/2.31 End of proof
% 11.99/2.31 % SZS output end Proof for theBenchmark
% 11.99/2.31
% 11.99/2.31 1793ms
%------------------------------------------------------------------------------