TSTP Solution File: SEU030+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SEU030+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 : n029.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 17.40s 3.15s
% Output : Proof 18.65s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU030+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.12 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.12/0.33 % Computer : n029.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Wed Aug 23 13:33:07 EDT 2023
% 0.12/0.33 % CPUTime :
% 0.18/0.61 ________ _____
% 0.18/0.61 ___ __ \_________(_)________________________________
% 0.18/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.18/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.18/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.18/0.61
% 0.18/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.18/0.61 (2023-06-19)
% 0.18/0.61
% 0.18/0.61 (c) Philipp Rümmer, 2009-2023
% 0.18/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.18/0.61 Amanda Stjerna.
% 0.18/0.61 Free software under BSD-3-Clause.
% 0.18/0.61
% 0.18/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.18/0.61
% 0.18/0.61 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.18/0.62 Running up to 7 provers in parallel.
% 0.18/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.18/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.18/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.18/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.18/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.18/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.18/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 3.15/1.10 Prover 4: Preprocessing ...
% 3.15/1.10 Prover 1: Preprocessing ...
% 3.15/1.14 Prover 0: Preprocessing ...
% 3.15/1.14 Prover 5: Preprocessing ...
% 3.15/1.14 Prover 2: Preprocessing ...
% 3.15/1.14 Prover 3: Preprocessing ...
% 3.15/1.14 Prover 6: Preprocessing ...
% 6.26/1.61 Prover 1: Warning: ignoring some quantifiers
% 6.26/1.64 Prover 3: Warning: ignoring some quantifiers
% 7.15/1.66 Prover 5: Proving ...
% 7.15/1.67 Prover 1: Constructing countermodel ...
% 7.15/1.67 Prover 3: Constructing countermodel ...
% 7.15/1.67 Prover 6: Proving ...
% 7.15/1.68 Prover 2: Proving ...
% 9.75/2.02 Prover 4: Warning: ignoring some quantifiers
% 10.12/2.07 Prover 4: Constructing countermodel ...
% 10.12/2.14 Prover 0: Proving ...
% 11.60/2.39 Prover 3: gave up
% 11.60/2.40 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 11.86/2.44 Prover 7: Preprocessing ...
% 13.84/2.55 Prover 7: Warning: ignoring some quantifiers
% 13.84/2.57 Prover 7: Constructing countermodel ...
% 17.40/3.14 Prover 7: Found proof (size 97)
% 17.40/3.14 Prover 7: proved (747ms)
% 17.40/3.14 Prover 1: stopped
% 17.40/3.14 Prover 5: stopped
% 17.40/3.14 Prover 0: stopped
% 17.40/3.15 Prover 6: stopped
% 17.40/3.15 Prover 4: stopped
% 17.40/3.15 Prover 2: stopped
% 17.40/3.15
% 17.40/3.15 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 17.40/3.15
% 17.40/3.17 % SZS output start Proof for theBenchmark
% 17.40/3.17 Assumptions after simplification:
% 17.40/3.17 ---------------------------------
% 17.40/3.17
% 17.40/3.17 (dt_k2_funct_1)
% 18.59/3.20 ! [v0: $i] : ! [v1: $i] : ( ~ (function_inverse(v0) = v1) | ~ $i(v0) | ~
% 18.59/3.20 relation(v0) | ~ function(v0) | relation(v1)) & ! [v0: $i] : ! [v1: $i] :
% 18.59/3.20 ( ~ (function_inverse(v0) = v1) | ~ $i(v0) | ~ relation(v0) | ~
% 18.59/3.20 function(v0) | function(v1))
% 18.59/3.20
% 18.59/3.20 (l72_funct_1)
% 18.65/3.20 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 18.65/3.20 $i] : ! [v6: $i] : (v5 = v1 | ~ (relation_rng(v1) = v0) | ~
% 18.65/3.20 (relation_dom(v5) = v6) | ~ (identity_relation(v0) = v2) | ~
% 18.65/3.20 (relation_composition(v1, v3) = v4) | ~ $i(v5) | ~ $i(v3) | ~ $i(v1) | ~
% 18.65/3.20 $i(v0) | ~ relation(v5) | ~ relation(v3) | ~ relation(v1) | ~
% 18.65/3.20 function(v5) | ~ function(v3) | ~ function(v1) | ? [v7: $i] : ? [v8: $i]
% 18.65/3.21 : (( ~ (v8 = v2) & relation_composition(v3, v5) = v8 & $i(v8)) | ( ~ (v7 =
% 18.65/3.21 v4) & identity_relation(v6) = v7 & $i(v7)))) & ! [v0: $i] : ! [v1:
% 18.65/3.21 $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v5 = v1 | ~
% 18.65/3.21 (relation_rng(v1) = v0) | ~ (identity_relation(v0) = v2) | ~
% 18.65/3.21 (relation_composition(v3, v5) = v2) | ~ (relation_composition(v1, v3) = v4)
% 18.65/3.21 | ~ $i(v5) | ~ $i(v3) | ~ $i(v1) | ~ $i(v0) | ~ relation(v5) | ~
% 18.65/3.21 relation(v3) | ~ relation(v1) | ~ function(v5) | ~ function(v3) | ~
% 18.65/3.21 function(v1) | ? [v6: $i] : ? [v7: $i] : ( ~ (v7 = v4) & relation_dom(v5)
% 18.65/3.21 = v6 & identity_relation(v6) = v7 & $i(v7) & $i(v6)))
% 18.65/3.21
% 18.65/3.21 (t55_funct_1)
% 18.65/3.21 ! [v0: $i] : ! [v1: $i] : ( ~ (relation_rng(v0) = v1) | ~ $i(v0) | ~
% 18.65/3.21 one_to_one(v0) | ~ relation(v0) | ~ function(v0) | ? [v2: $i] : ? [v3:
% 18.65/3.21 $i] : (relation_rng(v2) = v3 & relation_dom(v2) = v1 & relation_dom(v0) =
% 18.65/3.21 v3 & function_inverse(v0) = v2 & $i(v3) & $i(v2) & $i(v1))) & ! [v0: $i]
% 18.65/3.21 : ! [v1: $i] : ( ~ (relation_dom(v0) = v1) | ~ $i(v0) | ~ one_to_one(v0) |
% 18.65/3.21 ~ relation(v0) | ~ function(v0) | ? [v2: $i] : ? [v3: $i] :
% 18.65/3.21 (relation_rng(v3) = v1 & relation_rng(v0) = v2 & relation_dom(v3) = v2 &
% 18.65/3.21 function_inverse(v0) = v3 & $i(v3) & $i(v2) & $i(v1))) & ! [v0: $i] : !
% 18.65/3.21 [v1: $i] : ( ~ (function_inverse(v0) = v1) | ~ $i(v0) | ~ one_to_one(v0) |
% 18.65/3.21 ~ relation(v0) | ~ function(v0) | ? [v2: $i] : ? [v3: $i] :
% 18.65/3.21 (relation_rng(v1) = v3 & relation_rng(v0) = v2 & relation_dom(v1) = v2 &
% 18.65/3.21 relation_dom(v0) = v3 & $i(v3) & $i(v2)))
% 18.65/3.21
% 18.65/3.21 (t61_funct_1)
% 18.65/3.22 ! [v0: $i] : ! [v1: $i] : ( ~ (relation_rng(v0) = v1) | ~ $i(v0) | ~
% 18.65/3.22 one_to_one(v0) | ~ relation(v0) | ~ function(v0) | ? [v2: $i] : ? [v3:
% 18.65/3.22 $i] : ? [v4: $i] : ? [v5: $i] : (relation_dom(v0) = v4 &
% 18.65/3.22 identity_relation(v4) = v3 & identity_relation(v1) = v5 &
% 18.65/3.22 relation_composition(v2, v0) = v5 & relation_composition(v0, v2) = v3 &
% 18.65/3.22 function_inverse(v0) = v2 & $i(v5) & $i(v4) & $i(v3) & $i(v2))) & ! [v0:
% 18.65/3.22 $i] : ! [v1: $i] : ( ~ (relation_dom(v0) = v1) | ~ $i(v0) | ~
% 18.65/3.22 one_to_one(v0) | ~ relation(v0) | ~ function(v0) | ? [v2: $i] : ? [v3:
% 18.65/3.22 $i] : ? [v4: $i] : ? [v5: $i] : (relation_rng(v0) = v5 &
% 18.65/3.22 identity_relation(v5) = v4 & identity_relation(v1) = v3 &
% 18.65/3.22 relation_composition(v2, v0) = v4 & relation_composition(v0, v2) = v3 &
% 18.65/3.22 function_inverse(v0) = v2 & $i(v5) & $i(v4) & $i(v3) & $i(v2))) & ! [v0:
% 18.65/3.22 $i] : ! [v1: $i] : ( ~ (function_inverse(v0) = v1) | ~ $i(v0) | ~
% 18.65/3.22 one_to_one(v0) | ~ relation(v0) | ~ function(v0) | ? [v2: $i] : ? [v3:
% 18.65/3.22 $i] : ? [v4: $i] : ? [v5: $i] : (relation_rng(v0) = v5 &
% 18.65/3.22 relation_dom(v0) = v3 & identity_relation(v5) = v4 & identity_relation(v3)
% 18.65/3.22 = v2 & relation_composition(v1, v0) = v4 & relation_composition(v0, v1) =
% 18.65/3.22 v2 & $i(v5) & $i(v4) & $i(v3) & $i(v2)))
% 18.65/3.22
% 18.65/3.22 (t63_funct_1)
% 18.65/3.22 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5:
% 18.65/3.22 $i] : ( ~ (v5 = v4) & relation_rng(v0) = v1 & relation_dom(v5) = v1 &
% 18.65/3.22 relation_dom(v0) = v2 & identity_relation(v2) = v3 &
% 18.65/3.22 relation_composition(v0, v5) = v3 & function_inverse(v0) = v4 & $i(v5) &
% 18.65/3.22 $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & one_to_one(v0) & relation(v5) &
% 18.65/3.22 relation(v0) & function(v5) & function(v0))
% 18.65/3.22
% 18.65/3.22 (function-axioms)
% 18.65/3.22 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 18.65/3.22 (relation_composition(v3, v2) = v1) | ~ (relation_composition(v3, v2) =
% 18.65/3.22 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 18.65/3.22 (relation_rng(v2) = v1) | ~ (relation_rng(v2) = v0)) & ! [v0: $i] : !
% 18.65/3.22 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (relation_dom(v2) = v1) | ~
% 18.65/3.22 (relation_dom(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 =
% 18.65/3.22 v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) = v0)) & ! [v0: $i] : !
% 18.65/3.22 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (identity_relation(v2) = v1) | ~
% 18.65/3.22 (identity_relation(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 18.65/3.22 (v1 = v0 | ~ (function_inverse(v2) = v1) | ~ (function_inverse(v2) = v0))
% 18.65/3.22
% 18.65/3.22 Further assumptions not needed in the proof:
% 18.65/3.22 --------------------------------------------
% 18.65/3.22 antisymmetry_r2_hidden, cc1_funct_1, cc1_relat_1, cc2_funct_1, dt_k5_relat_1,
% 18.65/3.22 dt_k6_relat_1, existence_m1_subset_1, fc10_relat_1, fc12_relat_1, fc1_funct_1,
% 18.65/3.22 fc1_subset_1, fc1_xboole_0, fc2_funct_1, fc4_relat_1, fc5_relat_1, fc6_relat_1,
% 18.65/3.22 fc7_relat_1, fc8_relat_1, fc9_relat_1, rc1_funct_1, rc1_relat_1, rc1_subset_1,
% 18.65/3.22 rc1_xboole_0, rc2_funct_1, rc2_relat_1, rc2_subset_1, rc2_xboole_0, rc3_funct_1,
% 18.65/3.22 rc3_relat_1, reflexivity_r1_tarski, t1_subset, t2_subset, t3_subset, t4_subset,
% 18.65/3.22 t5_subset, t6_boole, t7_boole, t8_boole
% 18.65/3.22
% 18.65/3.22 Those formulas are unsatisfiable:
% 18.65/3.22 ---------------------------------
% 18.65/3.22
% 18.65/3.22 Begin of proof
% 18.65/3.22 |
% 18.65/3.22 | ALPHA: (dt_k2_funct_1) implies:
% 18.65/3.22 | (1) ! [v0: $i] : ! [v1: $i] : ( ~ (function_inverse(v0) = v1) | ~ $i(v0)
% 18.65/3.22 | | ~ relation(v0) | ~ function(v0) | function(v1))
% 18.65/3.22 | (2) ! [v0: $i] : ! [v1: $i] : ( ~ (function_inverse(v0) = v1) | ~ $i(v0)
% 18.65/3.22 | | ~ relation(v0) | ~ function(v0) | relation(v1))
% 18.65/3.22 |
% 18.65/3.22 | ALPHA: (l72_funct_1) implies:
% 18.65/3.22 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 18.65/3.22 | ! [v5: $i] : ! [v6: $i] : (v5 = v1 | ~ (relation_rng(v1) = v0) | ~
% 18.65/3.22 | (relation_dom(v5) = v6) | ~ (identity_relation(v0) = v2) | ~
% 18.65/3.23 | (relation_composition(v1, v3) = v4) | ~ $i(v5) | ~ $i(v3) | ~
% 18.65/3.23 | $i(v1) | ~ $i(v0) | ~ relation(v5) | ~ relation(v3) | ~
% 18.65/3.23 | relation(v1) | ~ function(v5) | ~ function(v3) | ~ function(v1) |
% 18.65/3.23 | ? [v7: $i] : ? [v8: $i] : (( ~ (v8 = v2) & relation_composition(v3,
% 18.65/3.23 | v5) = v8 & $i(v8)) | ( ~ (v7 = v4) & identity_relation(v6) = v7
% 18.65/3.23 | & $i(v7))))
% 18.65/3.23 |
% 18.65/3.23 | ALPHA: (t55_funct_1) implies:
% 18.65/3.23 | (4) ! [v0: $i] : ! [v1: $i] : ( ~ (function_inverse(v0) = v1) | ~ $i(v0)
% 18.65/3.23 | | ~ one_to_one(v0) | ~ relation(v0) | ~ function(v0) | ? [v2: $i]
% 18.65/3.23 | : ? [v3: $i] : (relation_rng(v1) = v3 & relation_rng(v0) = v2 &
% 18.65/3.23 | relation_dom(v1) = v2 & relation_dom(v0) = v3 & $i(v3) & $i(v2)))
% 18.65/3.23 | (5) ! [v0: $i] : ! [v1: $i] : ( ~ (relation_dom(v0) = v1) | ~ $i(v0) |
% 18.65/3.23 | ~ one_to_one(v0) | ~ relation(v0) | ~ function(v0) | ? [v2: $i] :
% 18.65/3.23 | ? [v3: $i] : (relation_rng(v3) = v1 & relation_rng(v0) = v2 &
% 18.65/3.23 | relation_dom(v3) = v2 & function_inverse(v0) = v3 & $i(v3) & $i(v2)
% 18.65/3.23 | & $i(v1)))
% 18.65/3.23 | (6) ! [v0: $i] : ! [v1: $i] : ( ~ (relation_rng(v0) = v1) | ~ $i(v0) |
% 18.65/3.23 | ~ one_to_one(v0) | ~ relation(v0) | ~ function(v0) | ? [v2: $i] :
% 18.65/3.23 | ? [v3: $i] : (relation_rng(v2) = v3 & relation_dom(v2) = v1 &
% 18.65/3.23 | relation_dom(v0) = v3 & function_inverse(v0) = v2 & $i(v3) & $i(v2)
% 18.65/3.23 | & $i(v1)))
% 18.65/3.23 |
% 18.65/3.23 | ALPHA: (t61_funct_1) implies:
% 18.65/3.23 | (7) ! [v0: $i] : ! [v1: $i] : ( ~ (function_inverse(v0) = v1) | ~ $i(v0)
% 18.65/3.23 | | ~ one_to_one(v0) | ~ relation(v0) | ~ function(v0) | ? [v2: $i]
% 18.65/3.23 | : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : (relation_rng(v0) = v5 &
% 18.65/3.23 | relation_dom(v0) = v3 & identity_relation(v5) = v4 &
% 18.65/3.23 | identity_relation(v3) = v2 & relation_composition(v1, v0) = v4 &
% 18.65/3.23 | relation_composition(v0, v1) = v2 & $i(v5) & $i(v4) & $i(v3) &
% 18.65/3.23 | $i(v2)))
% 18.65/3.23 | (8) ! [v0: $i] : ! [v1: $i] : ( ~ (relation_dom(v0) = v1) | ~ $i(v0) |
% 18.65/3.23 | ~ one_to_one(v0) | ~ relation(v0) | ~ function(v0) | ? [v2: $i] :
% 18.65/3.23 | ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : (relation_rng(v0) = v5 &
% 18.65/3.23 | identity_relation(v5) = v4 & identity_relation(v1) = v3 &
% 18.65/3.23 | relation_composition(v2, v0) = v4 & relation_composition(v0, v2) =
% 18.65/3.23 | v3 & function_inverse(v0) = v2 & $i(v5) & $i(v4) & $i(v3) &
% 18.65/3.23 | $i(v2)))
% 18.65/3.23 | (9) ! [v0: $i] : ! [v1: $i] : ( ~ (relation_rng(v0) = v1) | ~ $i(v0) |
% 18.65/3.23 | ~ one_to_one(v0) | ~ relation(v0) | ~ function(v0) | ? [v2: $i] :
% 18.65/3.23 | ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : (relation_dom(v0) = v4 &
% 18.65/3.23 | identity_relation(v4) = v3 & identity_relation(v1) = v5 &
% 18.65/3.23 | relation_composition(v2, v0) = v5 & relation_composition(v0, v2) =
% 18.65/3.23 | v3 & function_inverse(v0) = v2 & $i(v5) & $i(v4) & $i(v3) &
% 18.65/3.23 | $i(v2)))
% 18.65/3.23 |
% 18.65/3.23 | ALPHA: (function-axioms) implies:
% 18.65/3.23 | (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 18.65/3.23 | (function_inverse(v2) = v1) | ~ (function_inverse(v2) = v0))
% 18.65/3.23 | (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 18.65/3.23 | (identity_relation(v2) = v1) | ~ (identity_relation(v2) = v0))
% 18.65/3.23 | (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 18.65/3.23 | (relation_dom(v2) = v1) | ~ (relation_dom(v2) = v0))
% 18.65/3.23 | (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 18.65/3.23 | (relation_rng(v2) = v1) | ~ (relation_rng(v2) = v0))
% 18.65/3.23 | (14) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 18.65/3.23 | (relation_composition(v3, v2) = v1) | ~ (relation_composition(v3,
% 18.65/3.23 | v2) = v0))
% 18.65/3.23 |
% 18.65/3.23 | DELTA: instantiating (t63_funct_1) with fresh symbols all_51_0, all_51_1,
% 18.65/3.23 | all_51_2, all_51_3, all_51_4, all_51_5 gives:
% 18.65/3.23 | (15) ~ (all_51_0 = all_51_1) & relation_rng(all_51_5) = all_51_4 &
% 18.65/3.23 | relation_dom(all_51_0) = all_51_4 & relation_dom(all_51_5) = all_51_3
% 18.65/3.23 | & identity_relation(all_51_3) = all_51_2 &
% 18.65/3.23 | relation_composition(all_51_5, all_51_0) = all_51_2 &
% 18.65/3.23 | function_inverse(all_51_5) = all_51_1 & $i(all_51_0) & $i(all_51_1) &
% 18.65/3.23 | $i(all_51_2) & $i(all_51_3) & $i(all_51_4) & $i(all_51_5) &
% 18.65/3.23 | one_to_one(all_51_5) & relation(all_51_0) & relation(all_51_5) &
% 18.65/3.23 | function(all_51_0) & function(all_51_5)
% 18.65/3.23 |
% 18.65/3.23 | ALPHA: (15) implies:
% 18.65/3.24 | (16) ~ (all_51_0 = all_51_1)
% 18.65/3.24 | (17) function(all_51_5)
% 18.65/3.24 | (18) function(all_51_0)
% 18.65/3.24 | (19) relation(all_51_5)
% 18.65/3.24 | (20) relation(all_51_0)
% 18.65/3.24 | (21) one_to_one(all_51_5)
% 18.65/3.24 | (22) $i(all_51_5)
% 18.65/3.24 | (23) $i(all_51_0)
% 18.65/3.24 | (24) function_inverse(all_51_5) = all_51_1
% 18.65/3.24 | (25) relation_composition(all_51_5, all_51_0) = all_51_2
% 18.65/3.24 | (26) identity_relation(all_51_3) = all_51_2
% 18.65/3.24 | (27) relation_dom(all_51_5) = all_51_3
% 18.65/3.24 | (28) relation_dom(all_51_0) = all_51_4
% 18.65/3.24 | (29) relation_rng(all_51_5) = all_51_4
% 18.65/3.24 |
% 18.65/3.24 | GROUND_INST: instantiating (7) with all_51_5, all_51_1, simplifying with (17),
% 18.65/3.24 | (19), (21), (22), (24) gives:
% 18.65/3.24 | (30) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] :
% 18.65/3.24 | (relation_rng(all_51_5) = v3 & relation_dom(all_51_5) = v1 &
% 18.65/3.24 | identity_relation(v3) = v2 & identity_relation(v1) = v0 &
% 18.65/3.24 | relation_composition(all_51_1, all_51_5) = v2 &
% 18.65/3.24 | relation_composition(all_51_5, all_51_1) = v0 & $i(v3) & $i(v2) &
% 18.65/3.24 | $i(v1) & $i(v0))
% 18.65/3.24 |
% 18.65/3.24 | GROUND_INST: instantiating (4) with all_51_5, all_51_1, simplifying with (17),
% 18.65/3.24 | (19), (21), (22), (24) gives:
% 18.65/3.25 | (31) ? [v0: $i] : ? [v1: $i] : (relation_rng(all_51_1) = v1 &
% 18.65/3.25 | relation_rng(all_51_5) = v0 & relation_dom(all_51_1) = v0 &
% 18.65/3.25 | relation_dom(all_51_5) = v1 & $i(v1) & $i(v0))
% 18.65/3.25 |
% 18.65/3.25 | GROUND_INST: instantiating (2) with all_51_5, all_51_1, simplifying with (17),
% 18.65/3.25 | (19), (22), (24) gives:
% 18.65/3.25 | (32) relation(all_51_1)
% 18.65/3.25 |
% 18.65/3.25 | GROUND_INST: instantiating (1) with all_51_5, all_51_1, simplifying with (17),
% 18.65/3.25 | (19), (22), (24) gives:
% 18.65/3.25 | (33) function(all_51_1)
% 18.65/3.25 |
% 18.65/3.25 | GROUND_INST: instantiating (8) with all_51_5, all_51_3, simplifying with (17),
% 18.65/3.25 | (19), (21), (22), (27) gives:
% 18.65/3.25 | (34) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] :
% 18.65/3.25 | (relation_rng(all_51_5) = v3 & identity_relation(v3) = v2 &
% 18.65/3.25 | identity_relation(all_51_3) = v1 & relation_composition(v0,
% 18.65/3.25 | all_51_5) = v2 & relation_composition(all_51_5, v0) = v1 &
% 18.65/3.25 | function_inverse(all_51_5) = v0 & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 18.65/3.25 |
% 18.65/3.25 | GROUND_INST: instantiating (5) with all_51_5, all_51_3, simplifying with (17),
% 18.65/3.25 | (19), (21), (22), (27) gives:
% 18.65/3.25 | (35) ? [v0: $i] : ? [v1: $i] : (relation_rng(v1) = all_51_3 &
% 18.65/3.25 | relation_rng(all_51_5) = v0 & relation_dom(v1) = v0 &
% 18.65/3.25 | function_inverse(all_51_5) = v1 & $i(v1) & $i(v0) & $i(all_51_3))
% 18.65/3.25 |
% 18.65/3.25 | GROUND_INST: instantiating (9) with all_51_5, all_51_4, simplifying with (17),
% 18.65/3.25 | (19), (21), (22), (29) gives:
% 18.65/3.25 | (36) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] :
% 18.65/3.25 | (relation_dom(all_51_5) = v2 & identity_relation(v2) = v1 &
% 18.65/3.25 | identity_relation(all_51_4) = v3 & relation_composition(v0,
% 18.65/3.25 | all_51_5) = v3 & relation_composition(all_51_5, v0) = v1 &
% 18.65/3.25 | function_inverse(all_51_5) = v0 & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 18.65/3.25 |
% 18.65/3.25 | GROUND_INST: instantiating (6) with all_51_5, all_51_4, simplifying with (17),
% 18.65/3.25 | (19), (21), (22), (29) gives:
% 18.65/3.25 | (37) ? [v0: $i] : ? [v1: $i] : (relation_rng(v0) = v1 & relation_dom(v0)
% 18.65/3.25 | = all_51_4 & relation_dom(all_51_5) = v1 &
% 18.65/3.25 | function_inverse(all_51_5) = v0 & $i(v1) & $i(v0) & $i(all_51_4))
% 18.65/3.25 |
% 18.65/3.25 | DELTA: instantiating (31) with fresh symbols all_63_0, all_63_1 gives:
% 18.65/3.25 | (38) relation_rng(all_51_1) = all_63_0 & relation_rng(all_51_5) = all_63_1
% 18.65/3.25 | & relation_dom(all_51_1) = all_63_1 & relation_dom(all_51_5) =
% 18.65/3.25 | all_63_0 & $i(all_63_0) & $i(all_63_1)
% 18.65/3.25 |
% 18.65/3.25 | ALPHA: (38) implies:
% 18.65/3.25 | (39) $i(all_63_0)
% 18.65/3.25 | (40) relation_dom(all_51_5) = all_63_0
% 18.65/3.25 | (41) relation_rng(all_51_5) = all_63_1
% 18.65/3.25 | (42) relation_rng(all_51_1) = all_63_0
% 18.65/3.25 |
% 18.65/3.25 | DELTA: instantiating (35) with fresh symbols all_65_0, all_65_1 gives:
% 18.65/3.25 | (43) relation_rng(all_65_0) = all_51_3 & relation_rng(all_51_5) = all_65_1
% 18.65/3.25 | & relation_dom(all_65_0) = all_65_1 & function_inverse(all_51_5) =
% 18.65/3.25 | all_65_0 & $i(all_65_0) & $i(all_65_1) & $i(all_51_3)
% 18.65/3.25 |
% 18.65/3.25 | ALPHA: (43) implies:
% 18.65/3.25 | (44) $i(all_65_0)
% 18.65/3.25 | (45) function_inverse(all_51_5) = all_65_0
% 18.65/3.25 | (46) relation_rng(all_51_5) = all_65_1
% 18.65/3.25 |
% 18.65/3.25 | DELTA: instantiating (37) with fresh symbols all_67_0, all_67_1 gives:
% 18.65/3.25 | (47) relation_rng(all_67_1) = all_67_0 & relation_dom(all_67_1) = all_51_4
% 18.65/3.25 | & relation_dom(all_51_5) = all_67_0 & function_inverse(all_51_5) =
% 18.65/3.25 | all_67_1 & $i(all_67_0) & $i(all_67_1) & $i(all_51_4)
% 18.65/3.25 |
% 18.65/3.25 | ALPHA: (47) implies:
% 18.65/3.26 | (48) function_inverse(all_51_5) = all_67_1
% 18.65/3.26 | (49) relation_dom(all_51_5) = all_67_0
% 18.65/3.26 |
% 18.65/3.26 | DELTA: instantiating (34) with fresh symbols all_69_0, all_69_1, all_69_2,
% 18.65/3.26 | all_69_3 gives:
% 18.65/3.26 | (50) relation_rng(all_51_5) = all_69_0 & identity_relation(all_69_0) =
% 18.65/3.26 | all_69_1 & identity_relation(all_51_3) = all_69_2 &
% 18.65/3.26 | relation_composition(all_69_3, all_51_5) = all_69_1 &
% 18.65/3.26 | relation_composition(all_51_5, all_69_3) = all_69_2 &
% 18.65/3.26 | function_inverse(all_51_5) = all_69_3 & $i(all_69_0) & $i(all_69_1) &
% 18.65/3.26 | $i(all_69_2) & $i(all_69_3)
% 18.65/3.26 |
% 18.65/3.26 | ALPHA: (50) implies:
% 18.65/3.26 | (51) function_inverse(all_51_5) = all_69_3
% 18.65/3.26 | (52) identity_relation(all_51_3) = all_69_2
% 18.65/3.26 | (53) identity_relation(all_69_0) = all_69_1
% 18.65/3.26 | (54) relation_rng(all_51_5) = all_69_0
% 18.65/3.26 |
% 18.65/3.26 | DELTA: instantiating (36) with fresh symbols all_71_0, all_71_1, all_71_2,
% 18.65/3.26 | all_71_3 gives:
% 18.65/3.26 | (55) relation_dom(all_51_5) = all_71_1 & identity_relation(all_71_1) =
% 18.65/3.26 | all_71_2 & identity_relation(all_51_4) = all_71_0 &
% 18.65/3.26 | relation_composition(all_71_3, all_51_5) = all_71_0 &
% 18.65/3.26 | relation_composition(all_51_5, all_71_3) = all_71_2 &
% 18.65/3.26 | function_inverse(all_51_5) = all_71_3 & $i(all_71_0) & $i(all_71_1) &
% 18.65/3.26 | $i(all_71_2) & $i(all_71_3)
% 18.65/3.26 |
% 18.65/3.26 | ALPHA: (55) implies:
% 18.65/3.26 | (56) function_inverse(all_51_5) = all_71_3
% 18.65/3.26 | (57) relation_composition(all_71_3, all_51_5) = all_71_0
% 18.65/3.26 | (58) identity_relation(all_51_4) = all_71_0
% 18.65/3.26 | (59) relation_dom(all_51_5) = all_71_1
% 18.65/3.26 |
% 18.65/3.26 | DELTA: instantiating (30) with fresh symbols all_73_0, all_73_1, all_73_2,
% 18.65/3.26 | all_73_3 gives:
% 18.65/3.26 | (60) relation_rng(all_51_5) = all_73_0 & relation_dom(all_51_5) = all_73_2
% 18.65/3.26 | & identity_relation(all_73_0) = all_73_1 & identity_relation(all_73_2)
% 18.65/3.26 | = all_73_3 & relation_composition(all_51_1, all_51_5) = all_73_1 &
% 18.65/3.26 | relation_composition(all_51_5, all_51_1) = all_73_3 & $i(all_73_0) &
% 18.65/3.26 | $i(all_73_1) & $i(all_73_2) & $i(all_73_3)
% 18.65/3.26 |
% 18.65/3.26 | ALPHA: (60) implies:
% 18.65/3.26 | (61) identity_relation(all_73_0) = all_73_1
% 18.65/3.26 | (62) relation_dom(all_51_5) = all_73_2
% 18.65/3.26 | (63) relation_rng(all_51_5) = all_73_0
% 18.65/3.26 |
% 18.65/3.26 | GROUND_INST: instantiating (10) with all_51_1, all_69_3, all_51_5, simplifying
% 18.65/3.26 | with (24), (51) gives:
% 18.65/3.26 | (64) all_69_3 = all_51_1
% 18.65/3.26 |
% 18.65/3.26 | GROUND_INST: instantiating (10) with all_67_1, all_69_3, all_51_5, simplifying
% 18.65/3.26 | with (48), (51) gives:
% 18.65/3.26 | (65) all_69_3 = all_67_1
% 18.65/3.26 |
% 18.65/3.26 | GROUND_INST: instantiating (10) with all_67_1, all_71_3, all_51_5, simplifying
% 18.65/3.26 | with (48), (56) gives:
% 18.65/3.26 | (66) all_71_3 = all_67_1
% 18.65/3.26 |
% 18.65/3.26 | GROUND_INST: instantiating (10) with all_65_0, all_71_3, all_51_5, simplifying
% 18.65/3.26 | with (45), (56) gives:
% 18.65/3.26 | (67) all_71_3 = all_65_0
% 18.65/3.26 |
% 18.65/3.26 | GROUND_INST: instantiating (11) with all_51_2, all_69_2, all_51_3, simplifying
% 18.65/3.26 | with (26), (52) gives:
% 18.65/3.26 | (68) all_69_2 = all_51_2
% 18.65/3.26 |
% 18.65/3.26 | GROUND_INST: instantiating (11) with all_69_1, all_73_1, all_69_0, simplifying
% 18.65/3.26 | with (53) gives:
% 18.65/3.26 | (69) all_73_1 = all_69_1 | ~ (identity_relation(all_69_0) = all_73_1)
% 18.65/3.26 |
% 18.65/3.26 | GROUND_INST: instantiating (11) with all_71_0, all_73_1, all_51_4, simplifying
% 18.65/3.26 | with (58) gives:
% 18.65/3.26 | (70) all_73_1 = all_71_0 | ~ (identity_relation(all_51_4) = all_73_1)
% 18.65/3.26 |
% 18.65/3.26 | GROUND_INST: instantiating (12) with all_51_3, all_71_1, all_51_5, simplifying
% 18.65/3.26 | with (27), (59) gives:
% 18.65/3.26 | (71) all_71_1 = all_51_3
% 18.65/3.26 |
% 18.65/3.26 | GROUND_INST: instantiating (12) with all_67_0, all_71_1, all_51_5, simplifying
% 18.65/3.26 | with (49), (59) gives:
% 18.65/3.26 | (72) all_71_1 = all_67_0
% 18.65/3.26 |
% 18.65/3.26 | GROUND_INST: instantiating (12) with all_67_0, all_73_2, all_51_5, simplifying
% 18.65/3.26 | with (49), (62) gives:
% 18.65/3.26 | (73) all_73_2 = all_67_0
% 18.65/3.26 |
% 18.65/3.26 | GROUND_INST: instantiating (12) with all_63_0, all_73_2, all_51_5, simplifying
% 18.65/3.26 | with (40), (62) gives:
% 18.65/3.26 | (74) all_73_2 = all_63_0
% 18.65/3.26 |
% 18.65/3.26 | GROUND_INST: instantiating (13) with all_51_4, all_69_0, all_51_5, simplifying
% 18.65/3.26 | with (29), (54) gives:
% 18.65/3.26 | (75) all_69_0 = all_51_4
% 18.65/3.26 |
% 18.65/3.26 | GROUND_INST: instantiating (13) with all_65_1, all_69_0, all_51_5, simplifying
% 18.65/3.26 | with (46), (54) gives:
% 18.65/3.26 | (76) all_69_0 = all_65_1
% 18.65/3.26 |
% 18.65/3.26 | GROUND_INST: instantiating (13) with all_69_0, all_73_0, all_51_5, simplifying
% 18.65/3.26 | with (54), (63) gives:
% 18.65/3.26 | (77) all_73_0 = all_69_0
% 18.65/3.26 |
% 18.65/3.27 | GROUND_INST: instantiating (13) with all_63_1, all_73_0, all_51_5, simplifying
% 18.65/3.27 | with (41), (63) gives:
% 18.65/3.27 | (78) all_73_0 = all_63_1
% 18.65/3.27 |
% 18.65/3.27 | COMBINE_EQS: (77), (78) imply:
% 18.65/3.27 | (79) all_69_0 = all_63_1
% 18.65/3.27 |
% 18.65/3.27 | SIMP: (79) implies:
% 18.65/3.27 | (80) all_69_0 = all_63_1
% 18.65/3.27 |
% 18.65/3.27 | COMBINE_EQS: (73), (74) imply:
% 18.65/3.27 | (81) all_67_0 = all_63_0
% 18.65/3.27 |
% 18.65/3.27 | SIMP: (81) implies:
% 18.65/3.27 | (82) all_67_0 = all_63_0
% 18.65/3.27 |
% 18.65/3.27 | COMBINE_EQS: (71), (72) imply:
% 18.65/3.27 | (83) all_67_0 = all_51_3
% 18.65/3.27 |
% 18.65/3.27 | SIMP: (83) implies:
% 18.65/3.27 | (84) all_67_0 = all_51_3
% 18.65/3.27 |
% 18.65/3.27 | COMBINE_EQS: (66), (67) imply:
% 18.65/3.27 | (85) all_67_1 = all_65_0
% 18.65/3.27 |
% 18.65/3.27 | SIMP: (85) implies:
% 18.65/3.27 | (86) all_67_1 = all_65_0
% 18.65/3.27 |
% 18.65/3.27 | COMBINE_EQS: (76), (80) imply:
% 18.65/3.27 | (87) all_65_1 = all_63_1
% 18.65/3.27 |
% 18.65/3.27 | COMBINE_EQS: (75), (76) imply:
% 18.65/3.27 | (88) all_65_1 = all_51_4
% 18.65/3.27 |
% 18.65/3.27 | COMBINE_EQS: (64), (65) imply:
% 18.65/3.27 | (89) all_67_1 = all_51_1
% 18.65/3.27 |
% 18.65/3.27 | SIMP: (89) implies:
% 18.65/3.27 | (90) all_67_1 = all_51_1
% 18.65/3.27 |
% 18.65/3.27 | COMBINE_EQS: (82), (84) imply:
% 18.65/3.27 | (91) all_63_0 = all_51_3
% 18.65/3.27 |
% 18.65/3.27 | SIMP: (91) implies:
% 18.65/3.27 | (92) all_63_0 = all_51_3
% 18.65/3.27 |
% 18.65/3.27 | COMBINE_EQS: (86), (90) imply:
% 18.65/3.27 | (93) all_65_0 = all_51_1
% 18.65/3.27 |
% 18.65/3.27 | COMBINE_EQS: (87), (88) imply:
% 18.65/3.27 | (94) all_63_1 = all_51_4
% 18.65/3.27 |
% 18.65/3.27 | COMBINE_EQS: (67), (93) imply:
% 18.65/3.27 | (95) all_71_3 = all_51_1
% 18.65/3.27 |
% 18.65/3.27 | COMBINE_EQS: (78), (94) imply:
% 18.65/3.27 | (96) all_73_0 = all_51_4
% 18.65/3.27 |
% 18.65/3.27 | REDUCE: (42), (92) imply:
% 18.65/3.27 | (97) relation_rng(all_51_1) = all_51_3
% 18.65/3.27 |
% 18.65/3.27 | REDUCE: (61), (96) imply:
% 18.65/3.27 | (98) identity_relation(all_51_4) = all_73_1
% 18.65/3.27 |
% 18.65/3.27 | REDUCE: (57), (95) imply:
% 18.65/3.27 | (99) relation_composition(all_51_1, all_51_5) = all_71_0
% 18.65/3.27 |
% 18.65/3.27 | REDUCE: (44), (93) imply:
% 18.65/3.27 | (100) $i(all_51_1)
% 18.65/3.27 |
% 18.65/3.27 | REDUCE: (39), (92) imply:
% 18.65/3.27 | (101) $i(all_51_3)
% 18.65/3.27 |
% 18.65/3.27 | BETA: splitting (69) gives:
% 18.65/3.27 |
% 18.65/3.27 | Case 1:
% 18.65/3.27 | |
% 18.65/3.27 | | (102) ~ (identity_relation(all_69_0) = all_73_1)
% 18.65/3.27 | |
% 18.65/3.27 | | REDUCE: (75), (102) imply:
% 18.65/3.27 | | (103) ~ (identity_relation(all_51_4) = all_73_1)
% 18.65/3.27 | |
% 18.65/3.27 | | PRED_UNIFY: (98), (103) imply:
% 18.65/3.27 | | (104) $false
% 18.65/3.27 | |
% 18.65/3.27 | | CLOSE: (104) is inconsistent.
% 18.65/3.27 | |
% 18.65/3.27 | Case 2:
% 18.65/3.27 | |
% 18.65/3.27 | | (105) all_73_1 = all_69_1
% 18.65/3.27 | |
% 18.65/3.27 | | BETA: splitting (70) gives:
% 18.65/3.27 | |
% 18.65/3.27 | | Case 1:
% 18.65/3.27 | | |
% 18.65/3.27 | | | (106) ~ (identity_relation(all_51_4) = all_73_1)
% 18.65/3.27 | | |
% 18.65/3.27 | | | PRED_UNIFY: (98), (106) imply:
% 18.65/3.27 | | | (107) $false
% 18.65/3.27 | | |
% 18.65/3.27 | | | CLOSE: (107) is inconsistent.
% 18.65/3.27 | | |
% 18.65/3.27 | | Case 2:
% 18.65/3.27 | | |
% 18.65/3.27 | | | (108) all_73_1 = all_71_0
% 18.65/3.27 | | |
% 18.65/3.27 | | | COMBINE_EQS: (105), (108) imply:
% 18.65/3.27 | | | (109) all_71_0 = all_69_1
% 18.65/3.27 | | |
% 18.65/3.27 | | | SIMP: (109) implies:
% 18.65/3.27 | | | (110) all_71_0 = all_69_1
% 18.65/3.27 | | |
% 18.65/3.27 | | | REDUCE: (58), (110) imply:
% 18.65/3.27 | | | (111) identity_relation(all_51_4) = all_69_1
% 18.65/3.27 | | |
% 18.65/3.27 | | | REDUCE: (99), (110) imply:
% 18.65/3.27 | | | (112) relation_composition(all_51_1, all_51_5) = all_69_1
% 18.65/3.27 | | |
% 18.65/3.27 | | | GROUND_INST: instantiating (3) with all_51_3, all_51_1, all_51_2,
% 18.65/3.27 | | | all_51_5, all_69_1, all_51_0, all_51_4, simplifying with
% 18.65/3.27 | | | (17), (18), (19), (20), (22), (23), (26), (28), (32), (33),
% 18.65/3.27 | | | (97), (100), (101), (112) gives:
% 18.65/3.28 | | | (113) all_51_0 = all_51_1 | ? [v0: any] : ? [v1: any] : (( ~ (v1 =
% 18.65/3.28 | | | all_51_2) & relation_composition(all_51_5, all_51_0) = v1 &
% 18.65/3.28 | | | $i(v1)) | ( ~ (v0 = all_69_1) & identity_relation(all_51_4) =
% 18.65/3.28 | | | v0 & $i(v0)))
% 18.65/3.28 | | |
% 18.65/3.28 | | | BETA: splitting (113) gives:
% 18.65/3.28 | | |
% 18.65/3.28 | | | Case 1:
% 18.65/3.28 | | | |
% 18.65/3.28 | | | | (114) all_51_0 = all_51_1
% 18.65/3.28 | | | |
% 18.65/3.28 | | | | REDUCE: (16), (114) imply:
% 18.65/3.28 | | | | (115) $false
% 18.65/3.28 | | | |
% 18.65/3.28 | | | | CLOSE: (115) is inconsistent.
% 18.65/3.28 | | | |
% 18.65/3.28 | | | Case 2:
% 18.65/3.28 | | | |
% 18.65/3.28 | | | | (116) ? [v0: any] : ? [v1: any] : (( ~ (v1 = all_51_2) &
% 18.65/3.28 | | | | relation_composition(all_51_5, all_51_0) = v1 & $i(v1)) | (
% 18.65/3.28 | | | | ~ (v0 = all_69_1) & identity_relation(all_51_4) = v0 &
% 18.65/3.28 | | | | $i(v0)))
% 18.65/3.28 | | | |
% 18.65/3.28 | | | | DELTA: instantiating (116) with fresh symbols all_111_0, all_111_1
% 18.65/3.28 | | | | gives:
% 18.65/3.28 | | | | (117) ( ~ (all_111_0 = all_51_2) & relation_composition(all_51_5,
% 18.65/3.28 | | | | all_51_0) = all_111_0 & $i(all_111_0)) | ( ~ (all_111_1 =
% 18.65/3.28 | | | | all_69_1) & identity_relation(all_51_4) = all_111_1 &
% 18.65/3.28 | | | | $i(all_111_1))
% 18.65/3.28 | | | |
% 18.65/3.28 | | | | BETA: splitting (117) gives:
% 18.65/3.28 | | | |
% 18.65/3.28 | | | | Case 1:
% 18.65/3.28 | | | | |
% 18.65/3.28 | | | | | (118) ~ (all_111_0 = all_51_2) & relation_composition(all_51_5,
% 18.65/3.28 | | | | | all_51_0) = all_111_0 & $i(all_111_0)
% 18.65/3.28 | | | | |
% 18.65/3.28 | | | | | ALPHA: (118) implies:
% 18.65/3.28 | | | | | (119) ~ (all_111_0 = all_51_2)
% 18.65/3.28 | | | | | (120) relation_composition(all_51_5, all_51_0) = all_111_0
% 18.65/3.28 | | | | |
% 18.65/3.28 | | | | | GROUND_INST: instantiating (14) with all_51_2, all_111_0, all_51_0,
% 18.65/3.28 | | | | | all_51_5, simplifying with (25), (120) gives:
% 18.65/3.28 | | | | | (121) all_111_0 = all_51_2
% 18.65/3.28 | | | | |
% 18.65/3.28 | | | | | REDUCE: (119), (121) imply:
% 18.65/3.28 | | | | | (122) $false
% 18.65/3.28 | | | | |
% 18.65/3.28 | | | | | CLOSE: (122) is inconsistent.
% 18.65/3.28 | | | | |
% 18.65/3.28 | | | | Case 2:
% 18.65/3.28 | | | | |
% 18.65/3.28 | | | | | (123) ~ (all_111_1 = all_69_1) & identity_relation(all_51_4) =
% 18.65/3.28 | | | | | all_111_1 & $i(all_111_1)
% 18.65/3.28 | | | | |
% 18.65/3.28 | | | | | ALPHA: (123) implies:
% 18.65/3.28 | | | | | (124) ~ (all_111_1 = all_69_1)
% 18.65/3.28 | | | | | (125) identity_relation(all_51_4) = all_111_1
% 18.65/3.28 | | | | |
% 18.65/3.28 | | | | | GROUND_INST: instantiating (11) with all_69_1, all_111_1, all_51_4,
% 18.65/3.28 | | | | | simplifying with (111), (125) gives:
% 18.65/3.28 | | | | | (126) all_111_1 = all_69_1
% 18.65/3.28 | | | | |
% 18.65/3.28 | | | | | REDUCE: (124), (126) imply:
% 18.65/3.28 | | | | | (127) $false
% 18.65/3.28 | | | | |
% 18.65/3.28 | | | | | CLOSE: (127) is inconsistent.
% 18.65/3.28 | | | | |
% 18.65/3.28 | | | | End of split
% 18.65/3.28 | | | |
% 18.65/3.28 | | | End of split
% 18.65/3.28 | | |
% 18.65/3.28 | | End of split
% 18.65/3.28 | |
% 18.65/3.28 | End of split
% 18.65/3.28 |
% 18.65/3.28 End of proof
% 18.65/3.28 % SZS output end Proof for theBenchmark
% 18.65/3.28
% 18.65/3.28 2667ms
%------------------------------------------------------------------------------