TSTP Solution File: SEU028+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SEU028+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n002.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 17:42:20 EDT 2023
% Result : Theorem 17.32s 3.20s
% Output : Proof 18.05s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SEU028+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.14 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.35 % Computer : n002.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Wed Aug 23 23:42:46 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.21/0.64 ________ _____
% 0.21/0.64 ___ __ \_________(_)________________________________
% 0.21/0.64 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.21/0.64 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.21/0.64 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.21/0.64
% 0.21/0.64 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.21/0.64 (2023-06-19)
% 0.21/0.64
% 0.21/0.64 (c) Philipp Rümmer, 2009-2023
% 0.21/0.64 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.21/0.64 Amanda Stjerna.
% 0.21/0.64 Free software under BSD-3-Clause.
% 0.21/0.64
% 0.21/0.64 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.21/0.64
% 0.21/0.64 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.21/0.66 Running up to 7 provers in parallel.
% 0.21/0.68 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.21/0.68 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.21/0.68 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.21/0.68 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.21/0.68 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.21/0.68 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 0.21/0.68 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 2.95/1.19 Prover 4: Preprocessing ...
% 2.95/1.19 Prover 1: Preprocessing ...
% 2.95/1.22 Prover 2: Preprocessing ...
% 2.95/1.22 Prover 0: Preprocessing ...
% 2.95/1.22 Prover 5: Preprocessing ...
% 2.95/1.22 Prover 3: Preprocessing ...
% 2.95/1.22 Prover 6: Preprocessing ...
% 6.81/1.76 Prover 1: Warning: ignoring some quantifiers
% 7.28/1.80 Prover 1: Constructing countermodel ...
% 7.28/1.82 Prover 3: Warning: ignoring some quantifiers
% 7.28/1.84 Prover 5: Proving ...
% 7.28/1.85 Prover 2: Proving ...
% 7.28/1.85 Prover 3: Constructing countermodel ...
% 7.72/1.87 Prover 6: Proving ...
% 7.72/1.91 Prover 4: Warning: ignoring some quantifiers
% 8.41/1.96 Prover 4: Constructing countermodel ...
% 9.19/2.13 Prover 0: Proving ...
% 12.39/2.52 Prover 3: gave up
% 12.39/2.52 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 12.79/2.56 Prover 7: Preprocessing ...
% 12.79/2.72 Prover 7: Warning: ignoring some quantifiers
% 12.79/2.76 Prover 7: Constructing countermodel ...
% 17.32/3.20 Prover 7: Found proof (size 78)
% 17.32/3.20 Prover 7: proved (682ms)
% 17.32/3.20 Prover 5: stopped
% 17.32/3.20 Prover 0: stopped
% 17.32/3.20 Prover 1: stopped
% 17.32/3.20 Prover 2: stopped
% 17.32/3.20 Prover 6: stopped
% 17.32/3.20 Prover 4: stopped
% 17.32/3.20
% 17.32/3.20 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 17.32/3.20
% 17.32/3.21 % SZS output start Proof for theBenchmark
% 17.32/3.22 Assumptions after simplification:
% 17.32/3.22 ---------------------------------
% 17.32/3.22
% 17.32/3.22 (dt_k2_funct_1)
% 17.32/3.24 ! [v0: $i] : ! [v1: $i] : ( ~ (function_inverse(v0) = v1) | ~ $i(v0) | ~
% 17.32/3.24 relation(v0) | ~ function(v0) | relation(v1)) & ! [v0: $i] : ! [v1: $i] :
% 17.32/3.24 ( ~ (function_inverse(v0) = v1) | ~ $i(v0) | ~ relation(v0) | ~
% 17.32/3.24 function(v0) | function(v1))
% 17.32/3.24
% 17.32/3.24 (dt_k5_relat_1)
% 17.86/3.24 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (relation_composition(v0, v1) =
% 17.86/3.24 v2) | ~ $i(v1) | ~ $i(v0) | ~ relation(v1) | ~ relation(v0) |
% 17.86/3.24 relation(v2))
% 17.86/3.24
% 17.86/3.25 (fc1_funct_1)
% 17.86/3.25 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (relation_composition(v0, v1) =
% 17.86/3.25 v2) | ~ $i(v1) | ~ $i(v0) | ~ relation(v1) | ~ relation(v0) | ~
% 17.86/3.25 function(v1) | ~ function(v0) | relation(v2)) & ! [v0: $i] : ! [v1: $i] :
% 17.86/3.25 ! [v2: $i] : ( ~ (relation_composition(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0)
% 17.86/3.25 | ~ relation(v1) | ~ relation(v0) | ~ function(v1) | ~ function(v0) |
% 17.86/3.25 function(v2))
% 17.86/3.25
% 17.86/3.25 (t34_funct_1)
% 17.86/3.25 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v4 = v3
% 17.86/3.25 | ~ (apply(v1, v3) = v4) | ~ (relation_dom(v1) = v2) | ~
% 17.86/3.25 (identity_relation(v0) = v1) | ~ $i(v3) | ~ $i(v1) | ~ $i(v0) | ~
% 17.86/3.25 relation(v1) | ~ function(v1) | ~ in(v3, v0)) & ! [v0: $i] : ! [v1: $i]
% 17.86/3.25 : ! [v2: $i] : (v2 = v1 | ~ (relation_dom(v1) = v0) | ~
% 17.86/3.25 (identity_relation(v0) = v2) | ~ $i(v1) | ~ $i(v0) | ~ relation(v1) | ~
% 17.86/3.25 function(v1) | ? [v3: $i] : ? [v4: $i] : ( ~ (v4 = v3) & apply(v1, v3) =
% 17.86/3.25 v4 & $i(v4) & $i(v3) & in(v3, v0))) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 17.86/3.25 $i] : (v2 = v0 | ~ (relation_dom(v1) = v2) | ~ (identity_relation(v0) =
% 17.86/3.25 v1) | ~ $i(v1) | ~ $i(v0) | ~ relation(v1) | ~ function(v1))
% 17.86/3.25
% 17.86/3.25 (t56_funct_1)
% 17.86/3.26 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 17.86/3.26 (apply(v3, v0) = v4) | ~ (relation_composition(v1, v2) = v3) | ~
% 17.86/3.26 (function_inverse(v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ one_to_one(v1) | ~
% 17.86/3.26 relation(v1) | ~ function(v1) | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] :
% 17.86/3.26 ((v7 = v0 & v4 = v0 & apply(v2, v6) = v0 & apply(v1, v0) = v6 & $i(v6)) |
% 17.86/3.26 (relation_dom(v1) = v5 & $i(v5) & ~ in(v0, v5)))) & ! [v0: $i] : ! [v1:
% 17.86/3.26 $i] : ! [v2: $i] : ( ~ (apply(v1, v0) = v2) | ~ $i(v1) | ~ $i(v0) | ~
% 17.86/3.26 one_to_one(v1) | ~ relation(v1) | ~ function(v1) | ? [v3: $i] : ? [v4:
% 17.86/3.26 $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ((v7 = v0 & v5 = v0 &
% 17.86/3.26 apply(v6, v0) = v0 & apply(v4, v2) = v0 & relation_composition(v1, v4) =
% 17.86/3.26 v6 & function_inverse(v1) = v4 & $i(v6) & $i(v4)) | (relation_dom(v1) =
% 17.86/3.26 v3 & $i(v3) & ~ in(v0, v3))))
% 17.86/3.26
% 17.86/3.26 (t57_funct_1)
% 17.86/3.26 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 17.86/3.26 (apply(v3, v0) = v4) | ~ (relation_composition(v2, v1) = v3) | ~
% 17.86/3.26 (function_inverse(v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ one_to_one(v1) | ~
% 17.86/3.26 relation(v1) | ~ function(v1) | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] :
% 17.86/3.26 ((v7 = v0 & v4 = v0 & apply(v2, v0) = v6 & apply(v1, v6) = v0 & $i(v6)) |
% 17.86/3.26 (relation_rng(v1) = v5 & $i(v5) & ~ in(v0, v5)))) & ! [v0: $i] : ! [v1:
% 17.86/3.26 $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (apply(v2, v0) = v3) | ~
% 17.86/3.26 (function_inverse(v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ one_to_one(v1) | ~
% 17.86/3.26 relation(v1) | ~ function(v1) | ? [v4: $i] : ? [v5: $i] : ? [v6: $i] :
% 17.86/3.26 ? [v7: $i] : ((v7 = v0 & v5 = v0 & apply(v6, v0) = v0 & apply(v1, v3) = v0 &
% 17.86/3.26 relation_composition(v2, v1) = v6 & $i(v6)) | (relation_rng(v1) = v4 &
% 17.86/3.26 $i(v4) & ~ in(v0, v4))))
% 17.86/3.26
% 17.86/3.26 (t58_funct_1)
% 17.86/3.26 ! [v0: $i] : ! [v1: $i] : ( ~ (relation_dom(v0) = v1) | ~ $i(v0) | ~
% 17.86/3.26 one_to_one(v0) | ~ relation(v0) | ~ function(v0) | ? [v2: $i] : ? [v3:
% 17.86/3.26 $i] : (relation_rng(v3) = v1 & relation_dom(v3) = v1 &
% 17.86/3.26 relation_composition(v0, v2) = v3 & function_inverse(v0) = v2 & $i(v3) &
% 17.86/3.26 $i(v2) & $i(v1))) & ! [v0: $i] : ! [v1: $i] : ( ~ (function_inverse(v0)
% 17.86/3.26 = v1) | ~ $i(v0) | ~ one_to_one(v0) | ~ relation(v0) | ~ function(v0)
% 17.86/3.26 | ? [v2: $i] : ? [v3: $i] : (relation_rng(v2) = v3 & relation_dom(v2) = v3
% 17.86/3.26 & relation_dom(v0) = v3 & relation_composition(v0, v1) = v2 & $i(v3) &
% 17.86/3.26 $i(v2)))
% 17.86/3.26
% 17.86/3.26 (t59_funct_1)
% 17.86/3.26 ! [v0: $i] : ! [v1: $i] : ( ~ (relation_rng(v0) = v1) | ~ $i(v0) | ~
% 17.86/3.26 one_to_one(v0) | ~ relation(v0) | ~ function(v0) | ? [v2: $i] : ? [v3:
% 17.86/3.26 $i] : (relation_rng(v3) = v1 & relation_dom(v3) = v1 &
% 17.86/3.26 relation_composition(v2, v0) = v3 & function_inverse(v0) = v2 & $i(v3) &
% 17.86/3.26 $i(v2) & $i(v1))) & ! [v0: $i] : ! [v1: $i] : ( ~ (function_inverse(v0)
% 17.86/3.26 = v1) | ~ $i(v0) | ~ one_to_one(v0) | ~ relation(v0) | ~ function(v0)
% 17.86/3.26 | ? [v2: $i] : ? [v3: $i] : (relation_rng(v2) = v3 & relation_rng(v0) = v3
% 17.86/3.26 & relation_dom(v2) = v3 & relation_composition(v1, v0) = v2 & $i(v3) &
% 17.86/3.26 $i(v2)))
% 17.86/3.26
% 17.86/3.26 (t61_funct_1)
% 17.86/3.26 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5:
% 17.86/3.26 $i] : ? [v6: $i] : ? [v7: $i] : (function_inverse(v0) = v1 & $i(v1) &
% 17.86/3.26 $i(v0) & one_to_one(v0) & relation(v0) & function(v0) & (( ~ (v7 = v5) &
% 17.86/3.26 relation_rng(v0) = v6 & identity_relation(v6) = v7 &
% 17.86/3.26 relation_composition(v1, v0) = v5 & $i(v7) & $i(v6) & $i(v5)) | ( ~ (v4
% 17.86/3.26 = v2) & relation_dom(v0) = v3 & identity_relation(v3) = v4 &
% 17.86/3.26 relation_composition(v0, v1) = v2 & $i(v4) & $i(v3) & $i(v2))))
% 17.86/3.26
% 17.86/3.26 (function-axioms)
% 17.86/3.27 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 17.86/3.27 (apply(v3, v2) = v1) | ~ (apply(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i]
% 17.86/3.27 : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (relation_composition(v3, v2) =
% 17.86/3.27 v1) | ~ (relation_composition(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i]
% 17.86/3.27 : ! [v2: $i] : (v1 = v0 | ~ (relation_rng(v2) = v1) | ~ (relation_rng(v2) =
% 17.86/3.27 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 17.86/3.27 (relation_dom(v2) = v1) | ~ (relation_dom(v2) = v0)) & ! [v0: $i] : !
% 17.86/3.27 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2)
% 17.86/3.27 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 17.86/3.27 (identity_relation(v2) = v1) | ~ (identity_relation(v2) = v0)) & ! [v0:
% 17.86/3.27 $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (function_inverse(v2) = v1)
% 17.86/3.27 | ~ (function_inverse(v2) = v0))
% 17.86/3.27
% 17.86/3.27 Further assumptions not needed in the proof:
% 17.86/3.27 --------------------------------------------
% 17.86/3.27 antisymmetry_r2_hidden, cc1_funct_1, cc1_relat_1, cc2_funct_1, dt_k6_relat_1,
% 17.86/3.27 existence_m1_subset_1, fc10_relat_1, fc12_relat_1, fc1_subset_1, fc1_xboole_0,
% 17.86/3.27 fc2_funct_1, fc4_relat_1, fc5_relat_1, fc6_relat_1, fc7_relat_1, fc8_relat_1,
% 17.86/3.27 fc9_relat_1, rc1_funct_1, rc1_relat_1, rc1_subset_1, rc1_xboole_0, rc2_funct_1,
% 17.86/3.27 rc2_relat_1, rc2_subset_1, rc2_xboole_0, rc3_funct_1, rc3_relat_1,
% 17.86/3.27 reflexivity_r1_tarski, t1_subset, t2_subset, t3_subset, t4_subset, t5_subset,
% 17.86/3.27 t6_boole, t7_boole, t8_boole
% 17.86/3.27
% 17.86/3.27 Those formulas are unsatisfiable:
% 17.86/3.27 ---------------------------------
% 17.86/3.27
% 17.86/3.27 Begin of proof
% 17.86/3.27 |
% 17.86/3.27 | ALPHA: (dt_k2_funct_1) implies:
% 17.86/3.27 | (1) ! [v0: $i] : ! [v1: $i] : ( ~ (function_inverse(v0) = v1) | ~ $i(v0)
% 17.86/3.27 | | ~ relation(v0) | ~ function(v0) | function(v1))
% 17.86/3.27 | (2) ! [v0: $i] : ! [v1: $i] : ( ~ (function_inverse(v0) = v1) | ~ $i(v0)
% 17.86/3.27 | | ~ relation(v0) | ~ function(v0) | relation(v1))
% 17.86/3.27 |
% 17.86/3.27 | ALPHA: (fc1_funct_1) implies:
% 17.86/3.27 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (relation_composition(v0,
% 17.86/3.27 | v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ relation(v1) | ~
% 17.86/3.27 | relation(v0) | ~ function(v1) | ~ function(v0) | function(v2))
% 17.86/3.27 |
% 17.86/3.27 | ALPHA: (t34_funct_1) implies:
% 17.86/3.27 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v1 | ~
% 17.86/3.27 | (relation_dom(v1) = v0) | ~ (identity_relation(v0) = v2) | ~ $i(v1)
% 17.86/3.27 | | ~ $i(v0) | ~ relation(v1) | ~ function(v1) | ? [v3: $i] : ?
% 17.86/3.27 | [v4: $i] : ( ~ (v4 = v3) & apply(v1, v3) = v4 & $i(v4) & $i(v3) &
% 17.86/3.27 | in(v3, v0)))
% 17.86/3.27 |
% 17.86/3.27 | ALPHA: (t56_funct_1) implies:
% 17.86/3.27 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (
% 17.86/3.27 | ~ (apply(v3, v0) = v4) | ~ (relation_composition(v1, v2) = v3) | ~
% 17.86/3.27 | (function_inverse(v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~
% 17.86/3.27 | one_to_one(v1) | ~ relation(v1) | ~ function(v1) | ? [v5: $i] : ?
% 17.86/3.27 | [v6: $i] : ? [v7: $i] : ((v7 = v0 & v4 = v0 & apply(v2, v6) = v0 &
% 17.86/3.27 | apply(v1, v0) = v6 & $i(v6)) | (relation_dom(v1) = v5 & $i(v5) &
% 17.86/3.27 | ~ in(v0, v5))))
% 17.86/3.27 |
% 17.86/3.27 | ALPHA: (t57_funct_1) implies:
% 17.86/3.28 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (
% 17.86/3.28 | ~ (apply(v3, v0) = v4) | ~ (relation_composition(v2, v1) = v3) | ~
% 17.86/3.28 | (function_inverse(v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~
% 17.86/3.28 | one_to_one(v1) | ~ relation(v1) | ~ function(v1) | ? [v5: $i] : ?
% 17.86/3.28 | [v6: $i] : ? [v7: $i] : ((v7 = v0 & v4 = v0 & apply(v2, v0) = v6 &
% 17.86/3.28 | apply(v1, v6) = v0 & $i(v6)) | (relation_rng(v1) = v5 & $i(v5) &
% 17.86/3.28 | ~ in(v0, v5))))
% 17.86/3.28 |
% 17.86/3.28 | ALPHA: (t58_funct_1) implies:
% 17.86/3.28 | (7) ! [v0: $i] : ! [v1: $i] : ( ~ (function_inverse(v0) = v1) | ~ $i(v0)
% 17.86/3.28 | | ~ one_to_one(v0) | ~ relation(v0) | ~ function(v0) | ? [v2: $i]
% 17.86/3.28 | : ? [v3: $i] : (relation_rng(v2) = v3 & relation_dom(v2) = v3 &
% 17.86/3.28 | relation_dom(v0) = v3 & relation_composition(v0, v1) = v2 & $i(v3)
% 17.86/3.28 | & $i(v2)))
% 17.86/3.28 |
% 17.86/3.28 | ALPHA: (t59_funct_1) implies:
% 17.86/3.28 | (8) ! [v0: $i] : ! [v1: $i] : ( ~ (function_inverse(v0) = v1) | ~ $i(v0)
% 17.86/3.28 | | ~ one_to_one(v0) | ~ relation(v0) | ~ function(v0) | ? [v2: $i]
% 17.86/3.28 | : ? [v3: $i] : (relation_rng(v2) = v3 & relation_rng(v0) = v3 &
% 17.86/3.28 | relation_dom(v2) = v3 & relation_composition(v1, v0) = v2 & $i(v3)
% 17.86/3.28 | & $i(v2)))
% 17.86/3.28 |
% 17.86/3.28 | ALPHA: (function-axioms) implies:
% 17.86/3.28 | (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 17.86/3.28 | (relation_dom(v2) = v1) | ~ (relation_dom(v2) = v0))
% 17.86/3.28 | (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 17.86/3.28 | (relation_rng(v2) = v1) | ~ (relation_rng(v2) = v0))
% 17.86/3.28 | (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 17.86/3.28 | (relation_composition(v3, v2) = v1) | ~ (relation_composition(v3,
% 17.86/3.28 | v2) = v0))
% 17.86/3.28 |
% 17.86/3.28 | DELTA: instantiating (t61_funct_1) with fresh symbols all_53_0, all_53_1,
% 17.86/3.28 | all_53_2, all_53_3, all_53_4, all_53_5, all_53_6, all_53_7 gives:
% 17.86/3.28 | (12) function_inverse(all_53_7) = all_53_6 & $i(all_53_6) & $i(all_53_7) &
% 17.86/3.28 | one_to_one(all_53_7) & relation(all_53_7) & function(all_53_7) & (( ~
% 17.86/3.28 | (all_53_0 = all_53_2) & relation_rng(all_53_7) = all_53_1 &
% 17.86/3.28 | identity_relation(all_53_1) = all_53_0 &
% 17.86/3.28 | relation_composition(all_53_6, all_53_7) = all_53_2 & $i(all_53_0)
% 17.86/3.28 | & $i(all_53_1) & $i(all_53_2)) | ( ~ (all_53_3 = all_53_5) &
% 17.86/3.28 | relation_dom(all_53_7) = all_53_4 & identity_relation(all_53_4) =
% 17.86/3.28 | all_53_3 & relation_composition(all_53_7, all_53_6) = all_53_5 &
% 17.86/3.28 | $i(all_53_3) & $i(all_53_4) & $i(all_53_5)))
% 17.86/3.28 |
% 17.86/3.28 | ALPHA: (12) implies:
% 17.86/3.28 | (13) function(all_53_7)
% 17.86/3.28 | (14) relation(all_53_7)
% 17.86/3.28 | (15) one_to_one(all_53_7)
% 17.86/3.28 | (16) $i(all_53_7)
% 17.86/3.28 | (17) $i(all_53_6)
% 17.86/3.28 | (18) function_inverse(all_53_7) = all_53_6
% 17.86/3.28 | (19) ( ~ (all_53_0 = all_53_2) & relation_rng(all_53_7) = all_53_1 &
% 17.86/3.28 | identity_relation(all_53_1) = all_53_0 &
% 17.86/3.28 | relation_composition(all_53_6, all_53_7) = all_53_2 & $i(all_53_0) &
% 17.86/3.28 | $i(all_53_1) & $i(all_53_2)) | ( ~ (all_53_3 = all_53_5) &
% 17.86/3.28 | relation_dom(all_53_7) = all_53_4 & identity_relation(all_53_4) =
% 18.05/3.28 | all_53_3 & relation_composition(all_53_7, all_53_6) = all_53_5 &
% 18.05/3.28 | $i(all_53_3) & $i(all_53_4) & $i(all_53_5))
% 18.05/3.28 |
% 18.05/3.28 | GROUND_INST: instantiating (8) with all_53_7, all_53_6, simplifying with (13),
% 18.05/3.28 | (14), (15), (16), (18) gives:
% 18.05/3.29 | (20) ? [v0: $i] : ? [v1: $i] : (relation_rng(v0) = v1 &
% 18.05/3.29 | relation_rng(all_53_7) = v1 & relation_dom(v0) = v1 &
% 18.05/3.29 | relation_composition(all_53_6, all_53_7) = v0 & $i(v1) & $i(v0))
% 18.05/3.29 |
% 18.05/3.29 | GROUND_INST: instantiating (7) with all_53_7, all_53_6, simplifying with (13),
% 18.05/3.29 | (14), (15), (16), (18) gives:
% 18.05/3.29 | (21) ? [v0: $i] : ? [v1: $i] : (relation_rng(v0) = v1 & relation_dom(v0)
% 18.05/3.29 | = v1 & relation_dom(all_53_7) = v1 & relation_composition(all_53_7,
% 18.05/3.29 | all_53_6) = v0 & $i(v1) & $i(v0))
% 18.05/3.29 |
% 18.05/3.29 | GROUND_INST: instantiating (2) with all_53_7, all_53_6, simplifying with (13),
% 18.05/3.29 | (14), (16), (18) gives:
% 18.05/3.29 | (22) relation(all_53_6)
% 18.05/3.29 |
% 18.05/3.29 | GROUND_INST: instantiating (1) with all_53_7, all_53_6, simplifying with (13),
% 18.05/3.29 | (14), (16), (18) gives:
% 18.05/3.29 | (23) function(all_53_6)
% 18.05/3.29 |
% 18.05/3.29 | DELTA: instantiating (20) with fresh symbols all_65_0, all_65_1 gives:
% 18.05/3.29 | (24) relation_rng(all_65_1) = all_65_0 & relation_rng(all_53_7) = all_65_0
% 18.05/3.29 | & relation_dom(all_65_1) = all_65_0 & relation_composition(all_53_6,
% 18.05/3.29 | all_53_7) = all_65_1 & $i(all_65_0) & $i(all_65_1)
% 18.05/3.29 |
% 18.05/3.29 | ALPHA: (24) implies:
% 18.05/3.29 | (25) $i(all_65_1)
% 18.05/3.29 | (26) $i(all_65_0)
% 18.05/3.29 | (27) relation_composition(all_53_6, all_53_7) = all_65_1
% 18.05/3.29 | (28) relation_dom(all_65_1) = all_65_0
% 18.05/3.29 | (29) relation_rng(all_53_7) = all_65_0
% 18.05/3.29 |
% 18.05/3.29 | DELTA: instantiating (21) with fresh symbols all_67_0, all_67_1 gives:
% 18.05/3.29 | (30) relation_rng(all_67_1) = all_67_0 & relation_dom(all_67_1) = all_67_0
% 18.05/3.29 | & relation_dom(all_53_7) = all_67_0 & relation_composition(all_53_7,
% 18.05/3.29 | all_53_6) = all_67_1 & $i(all_67_0) & $i(all_67_1)
% 18.05/3.29 |
% 18.05/3.29 | ALPHA: (30) implies:
% 18.05/3.29 | (31) $i(all_67_1)
% 18.05/3.29 | (32) $i(all_67_0)
% 18.05/3.29 | (33) relation_composition(all_53_7, all_53_6) = all_67_1
% 18.05/3.29 | (34) relation_dom(all_53_7) = all_67_0
% 18.05/3.29 | (35) relation_dom(all_67_1) = all_67_0
% 18.05/3.29 |
% 18.05/3.29 | GROUND_INST: instantiating (3) with all_53_7, all_53_6, all_67_1, simplifying
% 18.05/3.29 | with (13), (14), (16), (17), (22), (23), (33) gives:
% 18.05/3.29 | (36) function(all_67_1)
% 18.05/3.29 |
% 18.05/3.29 | GROUND_INST: instantiating (dt_k5_relat_1) with all_53_7, all_53_6, all_67_1,
% 18.05/3.29 | simplifying with (14), (16), (17), (22), (33) gives:
% 18.05/3.29 | (37) relation(all_67_1)
% 18.05/3.29 |
% 18.05/3.29 | GROUND_INST: instantiating (3) with all_53_6, all_53_7, all_65_1, simplifying
% 18.05/3.29 | with (13), (14), (16), (17), (22), (23), (27) gives:
% 18.05/3.29 | (38) function(all_65_1)
% 18.05/3.29 |
% 18.05/3.29 | GROUND_INST: instantiating (dt_k5_relat_1) with all_53_6, all_53_7, all_65_1,
% 18.05/3.29 | simplifying with (14), (16), (17), (22), (27) gives:
% 18.05/3.29 | (39) relation(all_65_1)
% 18.05/3.29 |
% 18.05/3.29 | BETA: splitting (19) gives:
% 18.05/3.29 |
% 18.05/3.29 | Case 1:
% 18.05/3.29 | |
% 18.05/3.30 | | (40) ~ (all_53_0 = all_53_2) & relation_rng(all_53_7) = all_53_1 &
% 18.05/3.30 | | identity_relation(all_53_1) = all_53_0 &
% 18.05/3.30 | | relation_composition(all_53_6, all_53_7) = all_53_2 & $i(all_53_0) &
% 18.05/3.30 | | $i(all_53_1) & $i(all_53_2)
% 18.05/3.30 | |
% 18.05/3.30 | | ALPHA: (40) implies:
% 18.05/3.30 | | (41) ~ (all_53_0 = all_53_2)
% 18.05/3.30 | | (42) relation_composition(all_53_6, all_53_7) = all_53_2
% 18.05/3.30 | | (43) identity_relation(all_53_1) = all_53_0
% 18.05/3.30 | | (44) relation_rng(all_53_7) = all_53_1
% 18.05/3.30 | |
% 18.05/3.30 | | GROUND_INST: instantiating (11) with all_65_1, all_53_2, all_53_7, all_53_6,
% 18.05/3.30 | | simplifying with (27), (42) gives:
% 18.05/3.30 | | (45) all_65_1 = all_53_2
% 18.05/3.30 | |
% 18.05/3.30 | | GROUND_INST: instantiating (10) with all_65_0, all_53_1, all_53_7,
% 18.05/3.30 | | simplifying with (29), (44) gives:
% 18.05/3.30 | | (46) all_65_0 = all_53_1
% 18.05/3.30 | |
% 18.05/3.30 | | REDUCE: (28), (45), (46) imply:
% 18.05/3.30 | | (47) relation_dom(all_53_2) = all_53_1
% 18.05/3.30 | |
% 18.05/3.30 | | REDUCE: (26), (46) imply:
% 18.05/3.30 | | (48) $i(all_53_1)
% 18.05/3.30 | |
% 18.05/3.30 | | REDUCE: (25), (45) imply:
% 18.05/3.30 | | (49) $i(all_53_2)
% 18.05/3.30 | |
% 18.05/3.30 | | REDUCE: (39), (45) imply:
% 18.05/3.30 | | (50) relation(all_53_2)
% 18.05/3.30 | |
% 18.05/3.30 | | REDUCE: (38), (45) imply:
% 18.05/3.30 | | (51) function(all_53_2)
% 18.05/3.30 | |
% 18.05/3.30 | | GROUND_INST: instantiating (4) with all_53_1, all_53_2, all_53_0,
% 18.05/3.30 | | simplifying with (43), (47), (48), (49), (50), (51) gives:
% 18.05/3.30 | | (52) all_53_0 = all_53_2 | ? [v0: $i] : ? [v1: $i] : ( ~ (v1 = v0) &
% 18.05/3.30 | | apply(all_53_2, v0) = v1 & $i(v1) & $i(v0) & in(v0, all_53_1))
% 18.05/3.30 | |
% 18.05/3.30 | | BETA: splitting (52) gives:
% 18.05/3.30 | |
% 18.05/3.30 | | Case 1:
% 18.05/3.30 | | |
% 18.05/3.30 | | | (53) all_53_0 = all_53_2
% 18.05/3.30 | | |
% 18.05/3.30 | | | REDUCE: (41), (53) imply:
% 18.05/3.30 | | | (54) $false
% 18.05/3.30 | | |
% 18.05/3.30 | | | CLOSE: (54) is inconsistent.
% 18.05/3.30 | | |
% 18.05/3.30 | | Case 2:
% 18.05/3.30 | | |
% 18.05/3.30 | | | (55) ? [v0: $i] : ? [v1: $i] : ( ~ (v1 = v0) & apply(all_53_2, v0) =
% 18.05/3.30 | | | v1 & $i(v1) & $i(v0) & in(v0, all_53_1))
% 18.05/3.30 | | |
% 18.05/3.30 | | | DELTA: instantiating (55) with fresh symbols all_118_0, all_118_1 gives:
% 18.05/3.30 | | | (56) ~ (all_118_0 = all_118_1) & apply(all_53_2, all_118_1) =
% 18.05/3.30 | | | all_118_0 & $i(all_118_0) & $i(all_118_1) & in(all_118_1,
% 18.05/3.30 | | | all_53_1)
% 18.05/3.30 | | |
% 18.05/3.30 | | | ALPHA: (56) implies:
% 18.05/3.30 | | | (57) ~ (all_118_0 = all_118_1)
% 18.05/3.30 | | | (58) in(all_118_1, all_53_1)
% 18.05/3.30 | | | (59) $i(all_118_1)
% 18.05/3.30 | | | (60) apply(all_53_2, all_118_1) = all_118_0
% 18.05/3.30 | | |
% 18.05/3.31 | | | GROUND_INST: instantiating (6) with all_118_1, all_53_7, all_53_6,
% 18.05/3.31 | | | all_53_2, all_118_0, simplifying with (13), (14), (15), (16),
% 18.05/3.31 | | | (18), (42), (59), (60) gives:
% 18.05/3.31 | | | (61) ? [v0: $i] : ? [v1: $i] : ? [v2: int] : ((v2 = all_118_1 &
% 18.05/3.31 | | | all_118_0 = all_118_1 & apply(all_53_6, all_118_1) = v1 &
% 18.05/3.31 | | | apply(all_53_7, v1) = all_118_1 & $i(v1)) |
% 18.05/3.31 | | | (relation_rng(all_53_7) = v0 & $i(v0) & ~ in(all_118_1, v0)))
% 18.05/3.31 | | |
% 18.05/3.31 | | | DELTA: instantiating (61) with fresh symbols all_130_0, all_130_1,
% 18.05/3.31 | | | all_130_2 gives:
% 18.05/3.31 | | | (62) (all_130_0 = all_118_1 & all_118_0 = all_118_1 & apply(all_53_6,
% 18.05/3.31 | | | all_118_1) = all_130_1 & apply(all_53_7, all_130_1) =
% 18.05/3.31 | | | all_118_1 & $i(all_130_1)) | (relation_rng(all_53_7) = all_130_2
% 18.05/3.31 | | | & $i(all_130_2) & ~ in(all_118_1, all_130_2))
% 18.05/3.31 | | |
% 18.05/3.31 | | | BETA: splitting (62) gives:
% 18.05/3.31 | | |
% 18.05/3.31 | | | Case 1:
% 18.05/3.31 | | | |
% 18.05/3.31 | | | | (63) all_130_0 = all_118_1 & all_118_0 = all_118_1 & apply(all_53_6,
% 18.05/3.31 | | | | all_118_1) = all_130_1 & apply(all_53_7, all_130_1) =
% 18.05/3.31 | | | | all_118_1 & $i(all_130_1)
% 18.05/3.31 | | | |
% 18.05/3.31 | | | | ALPHA: (63) implies:
% 18.05/3.31 | | | | (64) all_118_0 = all_118_1
% 18.05/3.31 | | | |
% 18.05/3.31 | | | | REDUCE: (57), (64) imply:
% 18.05/3.31 | | | | (65) $false
% 18.05/3.31 | | | |
% 18.05/3.31 | | | | CLOSE: (65) is inconsistent.
% 18.05/3.31 | | | |
% 18.05/3.31 | | | Case 2:
% 18.05/3.31 | | | |
% 18.05/3.31 | | | | (66) relation_rng(all_53_7) = all_130_2 & $i(all_130_2) & ~
% 18.05/3.31 | | | | in(all_118_1, all_130_2)
% 18.05/3.31 | | | |
% 18.05/3.31 | | | | ALPHA: (66) implies:
% 18.05/3.31 | | | | (67) ~ in(all_118_1, all_130_2)
% 18.05/3.31 | | | | (68) relation_rng(all_53_7) = all_130_2
% 18.05/3.31 | | | |
% 18.05/3.31 | | | | GROUND_INST: instantiating (10) with all_53_1, all_130_2, all_53_7,
% 18.05/3.31 | | | | simplifying with (44), (68) gives:
% 18.05/3.31 | | | | (69) all_130_2 = all_53_1
% 18.05/3.31 | | | |
% 18.05/3.31 | | | | PRED_UNIFY: (58), (67) imply:
% 18.05/3.31 | | | | (70) ~ (all_130_2 = all_53_1)
% 18.05/3.31 | | | |
% 18.05/3.31 | | | | REDUCE: (69), (70) imply:
% 18.05/3.31 | | | | (71) $false
% 18.05/3.31 | | | |
% 18.05/3.31 | | | | CLOSE: (71) is inconsistent.
% 18.05/3.31 | | | |
% 18.05/3.31 | | | End of split
% 18.05/3.31 | | |
% 18.05/3.31 | | End of split
% 18.05/3.31 | |
% 18.05/3.31 | Case 2:
% 18.05/3.31 | |
% 18.05/3.31 | | (72) ~ (all_53_3 = all_53_5) & relation_dom(all_53_7) = all_53_4 &
% 18.05/3.31 | | identity_relation(all_53_4) = all_53_3 &
% 18.05/3.31 | | relation_composition(all_53_7, all_53_6) = all_53_5 & $i(all_53_3) &
% 18.05/3.31 | | $i(all_53_4) & $i(all_53_5)
% 18.05/3.31 | |
% 18.05/3.31 | | ALPHA: (72) implies:
% 18.05/3.31 | | (73) ~ (all_53_3 = all_53_5)
% 18.05/3.31 | | (74) relation_composition(all_53_7, all_53_6) = all_53_5
% 18.05/3.31 | | (75) identity_relation(all_53_4) = all_53_3
% 18.05/3.31 | | (76) relation_dom(all_53_7) = all_53_4
% 18.05/3.31 | |
% 18.05/3.31 | | GROUND_INST: instantiating (11) with all_67_1, all_53_5, all_53_6, all_53_7,
% 18.05/3.31 | | simplifying with (33), (74) gives:
% 18.05/3.31 | | (77) all_67_1 = all_53_5
% 18.05/3.31 | |
% 18.05/3.31 | | GROUND_INST: instantiating (9) with all_67_0, all_53_4, all_53_7,
% 18.05/3.31 | | simplifying with (34), (76) gives:
% 18.05/3.31 | | (78) all_67_0 = all_53_4
% 18.05/3.31 | |
% 18.05/3.31 | | REDUCE: (35), (77), (78) imply:
% 18.05/3.31 | | (79) relation_dom(all_53_5) = all_53_4
% 18.05/3.31 | |
% 18.05/3.31 | | REDUCE: (32), (78) imply:
% 18.05/3.31 | | (80) $i(all_53_4)
% 18.05/3.31 | |
% 18.05/3.31 | | REDUCE: (31), (77) imply:
% 18.05/3.31 | | (81) $i(all_53_5)
% 18.05/3.31 | |
% 18.05/3.31 | | REDUCE: (37), (77) imply:
% 18.05/3.31 | | (82) relation(all_53_5)
% 18.05/3.31 | |
% 18.05/3.31 | | REDUCE: (36), (77) imply:
% 18.05/3.31 | | (83) function(all_53_5)
% 18.05/3.31 | |
% 18.05/3.31 | | GROUND_INST: instantiating (4) with all_53_4, all_53_5, all_53_3,
% 18.05/3.31 | | simplifying with (75), (79), (80), (81), (82), (83) gives:
% 18.05/3.31 | | (84) all_53_3 = all_53_5 | ? [v0: $i] : ? [v1: $i] : ( ~ (v1 = v0) &
% 18.05/3.31 | | apply(all_53_5, v0) = v1 & $i(v1) & $i(v0) & in(v0, all_53_4))
% 18.05/3.31 | |
% 18.05/3.31 | | BETA: splitting (84) gives:
% 18.05/3.31 | |
% 18.05/3.31 | | Case 1:
% 18.05/3.31 | | |
% 18.05/3.31 | | | (85) all_53_3 = all_53_5
% 18.05/3.31 | | |
% 18.05/3.31 | | | REDUCE: (73), (85) imply:
% 18.05/3.31 | | | (86) $false
% 18.05/3.31 | | |
% 18.05/3.31 | | | CLOSE: (86) is inconsistent.
% 18.05/3.31 | | |
% 18.05/3.31 | | Case 2:
% 18.05/3.31 | | |
% 18.05/3.32 | | | (87) ? [v0: $i] : ? [v1: $i] : ( ~ (v1 = v0) & apply(all_53_5, v0) =
% 18.05/3.32 | | | v1 & $i(v1) & $i(v0) & in(v0, all_53_4))
% 18.05/3.32 | | |
% 18.05/3.32 | | | DELTA: instantiating (87) with fresh symbols all_118_0, all_118_1 gives:
% 18.05/3.32 | | | (88) ~ (all_118_0 = all_118_1) & apply(all_53_5, all_118_1) =
% 18.05/3.32 | | | all_118_0 & $i(all_118_0) & $i(all_118_1) & in(all_118_1,
% 18.05/3.32 | | | all_53_4)
% 18.05/3.32 | | |
% 18.05/3.32 | | | ALPHA: (88) implies:
% 18.05/3.32 | | | (89) ~ (all_118_0 = all_118_1)
% 18.05/3.32 | | | (90) in(all_118_1, all_53_4)
% 18.05/3.32 | | | (91) $i(all_118_1)
% 18.05/3.32 | | | (92) apply(all_53_5, all_118_1) = all_118_0
% 18.05/3.32 | | |
% 18.05/3.32 | | | GROUND_INST: instantiating (5) with all_118_1, all_53_7, all_53_6,
% 18.05/3.32 | | | all_53_5, all_118_0, simplifying with (13), (14), (15), (16),
% 18.05/3.32 | | | (18), (74), (91), (92) gives:
% 18.05/3.32 | | | (93) ? [v0: $i] : ? [v1: $i] : ? [v2: int] : ((v2 = all_118_1 &
% 18.05/3.32 | | | all_118_0 = all_118_1 & apply(all_53_6, v1) = all_118_1 &
% 18.05/3.32 | | | apply(all_53_7, all_118_1) = v1 & $i(v1)) |
% 18.05/3.32 | | | (relation_dom(all_53_7) = v0 & $i(v0) & ~ in(all_118_1, v0)))
% 18.05/3.32 | | |
% 18.05/3.32 | | | DELTA: instantiating (93) with fresh symbols all_130_0, all_130_1,
% 18.05/3.32 | | | all_130_2 gives:
% 18.05/3.32 | | | (94) (all_130_0 = all_118_1 & all_118_0 = all_118_1 & apply(all_53_6,
% 18.05/3.32 | | | all_130_1) = all_118_1 & apply(all_53_7, all_118_1) =
% 18.05/3.32 | | | all_130_1 & $i(all_130_1)) | (relation_dom(all_53_7) = all_130_2
% 18.05/3.32 | | | & $i(all_130_2) & ~ in(all_118_1, all_130_2))
% 18.05/3.32 | | |
% 18.05/3.32 | | | BETA: splitting (94) gives:
% 18.05/3.32 | | |
% 18.05/3.32 | | | Case 1:
% 18.05/3.32 | | | |
% 18.05/3.32 | | | | (95) all_130_0 = all_118_1 & all_118_0 = all_118_1 & apply(all_53_6,
% 18.05/3.32 | | | | all_130_1) = all_118_1 & apply(all_53_7, all_118_1) =
% 18.05/3.32 | | | | all_130_1 & $i(all_130_1)
% 18.05/3.32 | | | |
% 18.05/3.32 | | | | ALPHA: (95) implies:
% 18.05/3.32 | | | | (96) all_118_0 = all_118_1
% 18.05/3.32 | | | |
% 18.05/3.32 | | | | REDUCE: (89), (96) imply:
% 18.05/3.32 | | | | (97) $false
% 18.05/3.32 | | | |
% 18.05/3.32 | | | | CLOSE: (97) is inconsistent.
% 18.05/3.32 | | | |
% 18.05/3.32 | | | Case 2:
% 18.05/3.32 | | | |
% 18.05/3.32 | | | | (98) relation_dom(all_53_7) = all_130_2 & $i(all_130_2) & ~
% 18.05/3.32 | | | | in(all_118_1, all_130_2)
% 18.05/3.32 | | | |
% 18.05/3.32 | | | | ALPHA: (98) implies:
% 18.05/3.32 | | | | (99) ~ in(all_118_1, all_130_2)
% 18.05/3.32 | | | | (100) relation_dom(all_53_7) = all_130_2
% 18.05/3.32 | | | |
% 18.05/3.32 | | | | GROUND_INST: instantiating (9) with all_53_4, all_130_2, all_53_7,
% 18.05/3.32 | | | | simplifying with (76), (100) gives:
% 18.05/3.32 | | | | (101) all_130_2 = all_53_4
% 18.05/3.32 | | | |
% 18.05/3.32 | | | | PRED_UNIFY: (90), (99) imply:
% 18.05/3.32 | | | | (102) ~ (all_130_2 = all_53_4)
% 18.05/3.32 | | | |
% 18.05/3.32 | | | | REDUCE: (101), (102) imply:
% 18.05/3.32 | | | | (103) $false
% 18.05/3.32 | | | |
% 18.05/3.32 | | | | CLOSE: (103) is inconsistent.
% 18.05/3.32 | | | |
% 18.05/3.32 | | | End of split
% 18.05/3.32 | | |
% 18.05/3.32 | | End of split
% 18.05/3.32 | |
% 18.05/3.32 | End of split
% 18.05/3.32 |
% 18.05/3.32 End of proof
% 18.05/3.32 % SZS output end Proof for theBenchmark
% 18.05/3.32
% 18.05/3.32 2675ms
%------------------------------------------------------------------------------