TSTP Solution File: SEU353+1 by Princess---230619
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SEU353+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n028.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 17:44:15 EDT 2023
% Result : Theorem 13.26s 2.69s
% Output : Proof 19.82s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU353+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.33 % Computer : n028.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Thu Aug 24 01:17:19 EDT 2023
% 0.13/0.33 % CPUTime :
% 0.19/0.60 ________ _____
% 0.19/0.60 ___ __ \_________(_)________________________________
% 0.19/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.19/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.19/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.19/0.60
% 0.19/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.19/0.60 (2023-06-19)
% 0.19/0.60
% 0.19/0.60 (c) Philipp Rümmer, 2009-2023
% 0.19/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.19/0.60 Amanda Stjerna.
% 0.19/0.60 Free software under BSD-3-Clause.
% 0.19/0.60
% 0.19/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.19/0.60
% 0.19/0.60 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.19/0.61 Running up to 7 provers in parallel.
% 0.19/0.62 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.19/0.62 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.19/0.62 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.19/0.62 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.19/0.62 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.19/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 0.19/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 3.02/1.20 Prover 4: Preprocessing ...
% 3.02/1.20 Prover 1: Preprocessing ...
% 3.46/1.24 Prover 5: Preprocessing ...
% 3.46/1.24 Prover 0: Preprocessing ...
% 3.46/1.24 Prover 3: Preprocessing ...
% 3.46/1.24 Prover 6: Preprocessing ...
% 3.46/1.25 Prover 2: Preprocessing ...
% 8.13/1.89 Prover 1: Warning: ignoring some quantifiers
% 8.13/1.93 Prover 2: Proving ...
% 8.13/1.94 Prover 5: Proving ...
% 8.13/1.94 Prover 3: Warning: ignoring some quantifiers
% 8.64/1.97 Prover 3: Constructing countermodel ...
% 8.64/2.00 Prover 1: Constructing countermodel ...
% 8.64/2.02 Prover 6: Proving ...
% 8.64/2.02 Prover 4: Warning: ignoring some quantifiers
% 8.64/2.10 Prover 4: Constructing countermodel ...
% 10.31/2.21 Prover 0: Proving ...
% 13.26/2.68 Prover 2: proved (2061ms)
% 13.26/2.68
% 13.26/2.69 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 13.26/2.69
% 13.26/2.69 Prover 3: stopped
% 13.94/2.70 Prover 0: stopped
% 13.94/2.70 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 13.94/2.70 Prover 6: stopped
% 13.94/2.71 Prover 5: proved (2066ms)
% 13.94/2.71
% 13.94/2.71 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 13.94/2.71
% 13.94/2.73 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 13.94/2.73 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 13.94/2.73 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 13.94/2.73 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 14.65/2.80 Prover 8: Preprocessing ...
% 14.65/2.81 Prover 7: Preprocessing ...
% 14.65/2.86 Prover 11: Preprocessing ...
% 14.65/2.88 Prover 13: Preprocessing ...
% 14.65/2.88 Prover 10: Preprocessing ...
% 16.26/3.02 Prover 7: Warning: ignoring some quantifiers
% 16.26/3.04 Prover 10: Warning: ignoring some quantifiers
% 16.26/3.05 Prover 7: Constructing countermodel ...
% 16.26/3.08 Prover 10: Constructing countermodel ...
% 16.26/3.11 Prover 13: Warning: ignoring some quantifiers
% 17.02/3.11 Prover 8: Warning: ignoring some quantifiers
% 17.02/3.14 Prover 8: Constructing countermodel ...
% 17.02/3.17 Prover 13: Constructing countermodel ...
% 18.58/3.41 Prover 11: Warning: ignoring some quantifiers
% 18.58/3.46 Prover 11: Constructing countermodel ...
% 18.58/3.48 Prover 7: Found proof (size 51)
% 18.58/3.49 Prover 7: proved (796ms)
% 18.58/3.49 Prover 10: stopped
% 18.58/3.49 Prover 4: stopped
% 18.58/3.49 Prover 13: stopped
% 18.58/3.49 Prover 1: stopped
% 18.58/3.49 Prover 8: stopped
% 18.58/3.50 Prover 11: stopped
% 18.58/3.50
% 18.58/3.50 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 18.58/3.50
% 18.58/3.51 % SZS output start Proof for theBenchmark
% 18.58/3.52 Assumptions after simplification:
% 18.58/3.52 ---------------------------------
% 18.58/3.52
% 18.58/3.52 (d11_grcat_1)
% 19.82/3.55 ! [v0: $i] : ! [v1: $i] : ( ~ (the_carrier(v0) = v1) | ~ $i(v0) | ~
% 19.82/3.55 one_sorted_str(v0) | ? [v2: $i] : (identity_on_carrier(v0) = v2 &
% 19.82/3.55 identity_as_relation_of(v1) = v2 & $i(v2))) & ! [v0: $i] : ! [v1: $i] :
% 19.82/3.55 ( ~ (identity_on_carrier(v0) = v1) | ~ $i(v0) | ~ one_sorted_str(v0) | ?
% 19.82/3.55 [v2: $i] : (the_carrier(v0) = v2 & identity_as_relation_of(v2) = v1 & $i(v2)
% 19.82/3.55 & $i(v1)))
% 19.82/3.55
% 19.82/3.55 (dt_k7_grcat_1)
% 19.82/3.55 ! [v0: $i] : ! [v1: $i] : ( ~ (the_carrier(v0) = v1) | ~ $i(v0) | ~
% 19.82/3.55 one_sorted_str(v0) | ? [v2: $i] : (identity_on_carrier(v0) = v2 & $i(v2) &
% 19.82/3.55 relation_of2_as_subset(v2, v1, v1) & quasi_total(v2, v1, v1) &
% 19.82/3.55 function(v2))) & ! [v0: $i] : ! [v1: $i] : ( ~ (identity_on_carrier(v0)
% 19.82/3.55 = v1) | ~ $i(v0) | ~ one_sorted_str(v0) | function(v1)) & ! [v0: $i] :
% 19.82/3.55 ! [v1: $i] : ( ~ (identity_on_carrier(v0) = v1) | ~ $i(v0) | ~
% 19.82/3.55 one_sorted_str(v0) | ? [v2: $i] : (the_carrier(v0) = v2 & $i(v2) &
% 19.82/3.55 relation_of2_as_subset(v1, v2, v2) & quasi_total(v1, v2, v2)))
% 19.82/3.55
% 19.82/3.55 (fc1_struct_0)
% 19.82/3.55 ! [v0: $i] : ! [v1: $i] : ( ~ (the_carrier(v0) = v1) | ~ $i(v0) | ~
% 19.82/3.55 one_sorted_str(v0) | ~ empty(v1) | empty_carrier(v0))
% 19.82/3.55
% 19.82/3.55 (redefinition_k6_partfun1)
% 19.82/3.55 ! [v0: $i] : ! [v1: $i] : ( ~ (identity_relation(v0) = v1) | ~ $i(v0) |
% 19.82/3.55 (identity_as_relation_of(v0) = v1 & $i(v1))) & ! [v0: $i] : ! [v1: $i] : (
% 19.82/3.55 ~ (identity_as_relation_of(v0) = v1) | ~ $i(v0) | (identity_relation(v0) =
% 19.82/3.56 v1 & $i(v1)))
% 19.82/3.56
% 19.82/3.56 (redefinition_k8_funct_2)
% 19.82/3.56 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 19.82/3.56 (apply_as_element(v0, v1, v2, v3) = v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1)
% 19.82/3.56 | ~ $i(v0) | ~ element(v3, v0) | ~ quasi_total(v2, v0, v1) | ~
% 19.82/3.56 function(v2) | ~ relation_of2(v2, v0, v1) | empty(v0) | (apply(v2, v3) = v4
% 19.82/3.56 & $i(v4)))
% 19.82/3.56
% 19.82/3.56 (redefinition_m2_relset_1)
% 19.82/3.56 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 19.82/3.56 ~ relation_of2_as_subset(v2, v0, v1) | relation_of2(v2, v0, v1)) & ! [v0:
% 19.82/3.56 $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~
% 19.82/3.56 relation_of2(v2, v0, v1) | relation_of2_as_subset(v2, v0, v1))
% 19.82/3.56
% 19.82/3.56 (t2_subset)
% 19.82/3.56 ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ element(v0, v1) |
% 19.82/3.56 empty(v1) | in(v0, v1))
% 19.82/3.56
% 19.82/3.56 (t35_funct_1)
% 19.82/3.56 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v1 | ~
% 19.82/3.56 (apply(v2, v1) = v3) | ~ (identity_relation(v0) = v2) | ~ $i(v1) | ~
% 19.82/3.56 $i(v0) | ~ in(v1, v0))
% 19.82/3.56
% 19.82/3.56 (t91_tmap_1)
% 19.82/3.56 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ( ~ (v4
% 19.82/3.56 = v3) & apply_as_element(v1, v1, v2, v3) = v4 & the_carrier(v0) = v1 &
% 19.82/3.56 identity_on_carrier(v0) = v2 & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) &
% 19.82/3.56 one_sorted_str(v0) & element(v3, v1) & ~ empty_carrier(v0))
% 19.82/3.56
% 19.82/3.56 (function-axioms)
% 19.82/3.56 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 19.82/3.56 $i] : (v1 = v0 | ~ (apply_as_element(v5, v4, v3, v2) = v1) | ~
% 19.82/3.56 (apply_as_element(v5, v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 19.82/3.56 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (apply(v3, v2) = v1) | ~ (apply(v3,
% 19.82/3.56 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1
% 19.82/3.56 = v0 | ~ (cartesian_product2(v3, v2) = v1) | ~ (cartesian_product2(v3, v2)
% 19.82/3.56 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 19.82/3.56 (identity_relation(v2) = v1) | ~ (identity_relation(v2) = v0)) & ! [v0:
% 19.82/3.56 $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (the_carrier(v2) = v1) | ~
% 19.82/3.56 (the_carrier(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0
% 19.82/3.56 | ~ (identity_on_carrier(v2) = v1) | ~ (identity_on_carrier(v2) = v0)) &
% 19.82/3.56 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 19.82/3.56 (identity_as_relation_of(v2) = v1) | ~ (identity_as_relation_of(v2) = v0))
% 19.82/3.57 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (powerset(v2) = v1)
% 19.82/3.57 | ~ (powerset(v2) = v0))
% 19.82/3.57
% 19.82/3.57 Further assumptions not needed in the proof:
% 19.82/3.57 --------------------------------------------
% 19.82/3.57 antisymmetry_r2_hidden, cc1_funct_2, cc1_partfun1, cc1_relset_1, cc2_funct_2,
% 19.82/3.57 cc3_funct_2, cc4_funct_2, cc5_funct_2, cc6_funct_2, dt_k1_funct_1,
% 19.82/3.57 dt_k1_xboole_0, dt_k1_zfmisc_1, dt_k2_zfmisc_1, dt_k6_partfun1, dt_k6_relat_1,
% 19.82/3.57 dt_k8_funct_2, dt_l1_struct_0, dt_m1_relset_1, dt_m1_subset_1, dt_m2_relset_1,
% 19.82/3.57 dt_u1_struct_0, existence_l1_struct_0, existence_m1_relset_1,
% 19.82/3.57 existence_m1_subset_1, existence_m2_relset_1, fc1_subset_1, fc1_xboole_0,
% 19.82/3.57 fc2_partfun1, fc4_subset_1, rc1_funct_2, rc1_partfun1, rc1_subset_1,
% 19.82/3.57 rc1_xboole_0, rc2_funct_2, rc2_partfun1, rc2_subset_1, rc2_xboole_0,
% 19.82/3.57 rc3_partfun1, rc3_struct_0, rc5_struct_0, reflexivity_r1_tarski, t1_subset,
% 19.82/3.57 t3_subset, t4_subset, t5_subset, t6_boole, t7_boole, t8_boole
% 19.82/3.57
% 19.82/3.57 Those formulas are unsatisfiable:
% 19.82/3.57 ---------------------------------
% 19.82/3.57
% 19.82/3.57 Begin of proof
% 19.82/3.57 |
% 19.82/3.57 | ALPHA: (d11_grcat_1) implies:
% 19.82/3.57 | (1) ! [v0: $i] : ! [v1: $i] : ( ~ (identity_on_carrier(v0) = v1) | ~
% 19.82/3.57 | $i(v0) | ~ one_sorted_str(v0) | ? [v2: $i] : (the_carrier(v0) = v2
% 19.82/3.57 | & identity_as_relation_of(v2) = v1 & $i(v2) & $i(v1)))
% 19.82/3.57 | (2) ! [v0: $i] : ! [v1: $i] : ( ~ (the_carrier(v0) = v1) | ~ $i(v0) | ~
% 19.82/3.57 | one_sorted_str(v0) | ? [v2: $i] : (identity_on_carrier(v0) = v2 &
% 19.82/3.57 | identity_as_relation_of(v1) = v2 & $i(v2)))
% 19.82/3.57 |
% 19.82/3.57 | ALPHA: (dt_k7_grcat_1) implies:
% 19.82/3.57 | (3) ! [v0: $i] : ! [v1: $i] : ( ~ (identity_on_carrier(v0) = v1) | ~
% 19.82/3.57 | $i(v0) | ~ one_sorted_str(v0) | ? [v2: $i] : (the_carrier(v0) = v2
% 19.82/3.57 | & $i(v2) & relation_of2_as_subset(v1, v2, v2) & quasi_total(v1, v2,
% 19.82/3.57 | v2)))
% 19.82/3.57 | (4) ! [v0: $i] : ! [v1: $i] : ( ~ (the_carrier(v0) = v1) | ~ $i(v0) | ~
% 19.82/3.57 | one_sorted_str(v0) | ? [v2: $i] : (identity_on_carrier(v0) = v2 &
% 19.82/3.57 | $i(v2) & relation_of2_as_subset(v2, v1, v1) & quasi_total(v2, v1,
% 19.82/3.57 | v1) & function(v2)))
% 19.82/3.57 |
% 19.82/3.57 | ALPHA: (redefinition_k6_partfun1) implies:
% 19.82/3.57 | (5) ! [v0: $i] : ! [v1: $i] : ( ~ (identity_as_relation_of(v0) = v1) | ~
% 19.82/3.57 | $i(v0) | (identity_relation(v0) = v1 & $i(v1)))
% 19.82/3.57 |
% 19.82/3.57 | ALPHA: (redefinition_m2_relset_1) implies:
% 19.82/3.57 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~
% 19.82/3.57 | $i(v0) | ~ relation_of2_as_subset(v2, v0, v1) | relation_of2(v2, v0,
% 19.82/3.57 | v1))
% 19.82/3.57 |
% 19.82/3.57 | ALPHA: (function-axioms) implies:
% 19.82/3.57 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 19.82/3.57 | (identity_on_carrier(v2) = v1) | ~ (identity_on_carrier(v2) = v0))
% 19.82/3.57 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 19.82/3.57 | (the_carrier(v2) = v1) | ~ (the_carrier(v2) = v0))
% 19.82/3.57 |
% 19.82/3.57 | DELTA: instantiating (t91_tmap_1) with fresh symbols all_56_0, all_56_1,
% 19.82/3.57 | all_56_2, all_56_3, all_56_4 gives:
% 19.82/3.58 | (9) ~ (all_56_0 = all_56_1) & apply_as_element(all_56_3, all_56_3,
% 19.82/3.58 | all_56_2, all_56_1) = all_56_0 & the_carrier(all_56_4) = all_56_3 &
% 19.82/3.58 | identity_on_carrier(all_56_4) = all_56_2 & $i(all_56_0) & $i(all_56_1)
% 19.82/3.58 | & $i(all_56_2) & $i(all_56_3) & $i(all_56_4) & one_sorted_str(all_56_4)
% 19.82/3.58 | & element(all_56_1, all_56_3) & ~ empty_carrier(all_56_4)
% 19.82/3.58 |
% 19.82/3.58 | ALPHA: (9) implies:
% 19.82/3.58 | (10) ~ (all_56_0 = all_56_1)
% 19.82/3.58 | (11) ~ empty_carrier(all_56_4)
% 19.82/3.58 | (12) element(all_56_1, all_56_3)
% 19.82/3.58 | (13) one_sorted_str(all_56_4)
% 19.82/3.58 | (14) $i(all_56_4)
% 19.82/3.58 | (15) $i(all_56_3)
% 19.82/3.58 | (16) $i(all_56_1)
% 19.82/3.58 | (17) identity_on_carrier(all_56_4) = all_56_2
% 19.82/3.58 | (18) the_carrier(all_56_4) = all_56_3
% 19.82/3.58 | (19) apply_as_element(all_56_3, all_56_3, all_56_2, all_56_1) = all_56_0
% 19.82/3.58 |
% 19.82/3.58 | GROUND_INST: instantiating (t2_subset) with all_56_1, all_56_3, simplifying
% 19.82/3.58 | with (12), (15), (16) gives:
% 19.82/3.58 | (20) empty(all_56_3) | in(all_56_1, all_56_3)
% 19.82/3.58 |
% 19.82/3.58 | GROUND_INST: instantiating (1) with all_56_4, all_56_2, simplifying with (13),
% 19.82/3.58 | (14), (17) gives:
% 19.82/3.58 | (21) ? [v0: $i] : (the_carrier(all_56_4) = v0 &
% 19.82/3.58 | identity_as_relation_of(v0) = all_56_2 & $i(v0) & $i(all_56_2))
% 19.82/3.58 |
% 19.82/3.58 | GROUND_INST: instantiating (3) with all_56_4, all_56_2, simplifying with (13),
% 19.82/3.58 | (14), (17) gives:
% 19.82/3.58 | (22) ? [v0: $i] : (the_carrier(all_56_4) = v0 & $i(v0) &
% 19.82/3.58 | relation_of2_as_subset(all_56_2, v0, v0) & quasi_total(all_56_2, v0,
% 19.82/3.58 | v0))
% 19.82/3.58 |
% 19.82/3.58 | GROUND_INST: instantiating (2) with all_56_4, all_56_3, simplifying with (13),
% 19.82/3.58 | (14), (18) gives:
% 19.82/3.58 | (23) ? [v0: $i] : (identity_on_carrier(all_56_4) = v0 &
% 19.82/3.58 | identity_as_relation_of(all_56_3) = v0 & $i(v0))
% 19.82/3.58 |
% 19.82/3.58 | GROUND_INST: instantiating (4) with all_56_4, all_56_3, simplifying with (13),
% 19.82/3.58 | (14), (18) gives:
% 19.82/3.58 | (24) ? [v0: $i] : (identity_on_carrier(all_56_4) = v0 & $i(v0) &
% 19.82/3.58 | relation_of2_as_subset(v0, all_56_3, all_56_3) & quasi_total(v0,
% 19.82/3.58 | all_56_3, all_56_3) & function(v0))
% 19.82/3.58 |
% 19.82/3.58 | DELTA: instantiating (23) with fresh symbol all_68_0 gives:
% 19.82/3.58 | (25) identity_on_carrier(all_56_4) = all_68_0 &
% 19.82/3.58 | identity_as_relation_of(all_56_3) = all_68_0 & $i(all_68_0)
% 19.82/3.58 |
% 19.82/3.58 | ALPHA: (25) implies:
% 19.82/3.58 | (26) $i(all_68_0)
% 19.82/3.58 | (27) identity_as_relation_of(all_56_3) = all_68_0
% 19.82/3.58 | (28) identity_on_carrier(all_56_4) = all_68_0
% 19.82/3.58 |
% 19.82/3.58 | DELTA: instantiating (22) with fresh symbol all_70_0 gives:
% 19.82/3.58 | (29) the_carrier(all_56_4) = all_70_0 & $i(all_70_0) &
% 19.82/3.58 | relation_of2_as_subset(all_56_2, all_70_0, all_70_0) &
% 19.82/3.58 | quasi_total(all_56_2, all_70_0, all_70_0)
% 19.82/3.58 |
% 19.82/3.58 | ALPHA: (29) implies:
% 19.82/3.58 | (30) quasi_total(all_56_2, all_70_0, all_70_0)
% 19.82/3.58 | (31) relation_of2_as_subset(all_56_2, all_70_0, all_70_0)
% 19.82/3.58 | (32) $i(all_70_0)
% 19.82/3.58 | (33) the_carrier(all_56_4) = all_70_0
% 19.82/3.58 |
% 19.82/3.58 | DELTA: instantiating (21) with fresh symbol all_72_0 gives:
% 19.82/3.58 | (34) the_carrier(all_56_4) = all_72_0 & identity_as_relation_of(all_72_0) =
% 19.82/3.58 | all_56_2 & $i(all_72_0) & $i(all_56_2)
% 19.82/3.58 |
% 19.82/3.58 | ALPHA: (34) implies:
% 19.82/3.58 | (35) the_carrier(all_56_4) = all_72_0
% 19.82/3.58 |
% 19.82/3.58 | DELTA: instantiating (24) with fresh symbol all_74_0 gives:
% 19.82/3.59 | (36) identity_on_carrier(all_56_4) = all_74_0 & $i(all_74_0) &
% 19.82/3.59 | relation_of2_as_subset(all_74_0, all_56_3, all_56_3) &
% 19.82/3.59 | quasi_total(all_74_0, all_56_3, all_56_3) & function(all_74_0)
% 19.82/3.59 |
% 19.82/3.59 | ALPHA: (36) implies:
% 19.82/3.59 | (37) function(all_74_0)
% 19.82/3.59 | (38) identity_on_carrier(all_56_4) = all_74_0
% 19.82/3.59 |
% 19.82/3.59 | GROUND_INST: instantiating (7) with all_56_2, all_74_0, all_56_4, simplifying
% 19.82/3.59 | with (17), (38) gives:
% 19.82/3.59 | (39) all_74_0 = all_56_2
% 19.82/3.59 |
% 19.82/3.59 | GROUND_INST: instantiating (7) with all_68_0, all_74_0, all_56_4, simplifying
% 19.82/3.59 | with (28), (38) gives:
% 19.82/3.59 | (40) all_74_0 = all_68_0
% 19.82/3.59 |
% 19.82/3.59 | GROUND_INST: instantiating (8) with all_56_3, all_72_0, all_56_4, simplifying
% 19.82/3.59 | with (18), (35) gives:
% 19.82/3.59 | (41) all_72_0 = all_56_3
% 19.82/3.59 |
% 19.82/3.59 | GROUND_INST: instantiating (8) with all_70_0, all_72_0, all_56_4, simplifying
% 19.82/3.59 | with (33), (35) gives:
% 19.82/3.59 | (42) all_72_0 = all_70_0
% 19.82/3.59 |
% 19.82/3.59 | COMBINE_EQS: (39), (40) imply:
% 19.82/3.59 | (43) all_68_0 = all_56_2
% 19.82/3.59 |
% 19.82/3.59 | COMBINE_EQS: (41), (42) imply:
% 19.82/3.59 | (44) all_70_0 = all_56_3
% 19.82/3.59 |
% 19.82/3.59 | REDUCE: (27), (43) imply:
% 19.82/3.59 | (45) identity_as_relation_of(all_56_3) = all_56_2
% 19.82/3.59 |
% 19.82/3.59 | REDUCE: (26), (43) imply:
% 19.82/3.59 | (46) $i(all_56_2)
% 19.82/3.59 |
% 19.82/3.59 | REDUCE: (31), (44) imply:
% 19.82/3.59 | (47) relation_of2_as_subset(all_56_2, all_56_3, all_56_3)
% 19.82/3.59 |
% 19.82/3.59 | REDUCE: (30), (44) imply:
% 19.82/3.59 | (48) quasi_total(all_56_2, all_56_3, all_56_3)
% 19.82/3.59 |
% 19.82/3.59 | REDUCE: (37), (39) imply:
% 19.82/3.59 | (49) function(all_56_2)
% 19.82/3.59 |
% 19.82/3.59 | GROUND_INST: instantiating (6) with all_56_3, all_56_3, all_56_2, simplifying
% 19.82/3.59 | with (15), (46), (47) gives:
% 19.82/3.59 | (50) relation_of2(all_56_2, all_56_3, all_56_3)
% 19.82/3.59 |
% 19.82/3.59 | GROUND_INST: instantiating (5) with all_56_3, all_56_2, simplifying with (15),
% 19.82/3.59 | (45) gives:
% 19.82/3.59 | (51) identity_relation(all_56_3) = all_56_2 & $i(all_56_2)
% 19.82/3.59 |
% 19.82/3.59 | ALPHA: (51) implies:
% 19.82/3.59 | (52) identity_relation(all_56_3) = all_56_2
% 19.82/3.59 |
% 19.82/3.59 | GROUND_INST: instantiating (redefinition_k8_funct_2) with all_56_3, all_56_3,
% 19.82/3.59 | all_56_2, all_56_1, all_56_0, simplifying with (12), (15), (16),
% 19.82/3.59 | (19), (46), (48), (49), (50) gives:
% 19.82/3.59 | (53) empty(all_56_3) | (apply(all_56_2, all_56_1) = all_56_0 &
% 19.82/3.59 | $i(all_56_0))
% 19.82/3.59 |
% 19.82/3.59 | GROUND_INST: instantiating (fc1_struct_0) with all_56_4, all_56_3, simplifying
% 19.82/3.59 | with (11), (13), (14), (18) gives:
% 19.82/3.59 | (54) ~ empty(all_56_3)
% 19.82/3.59 |
% 19.82/3.59 | BETA: splitting (53) gives:
% 19.82/3.59 |
% 19.82/3.59 | Case 1:
% 19.82/3.59 | |
% 19.82/3.59 | | (55) empty(all_56_3)
% 19.82/3.59 | |
% 19.82/3.59 | | PRED_UNIFY: (54), (55) imply:
% 19.82/3.59 | | (56) $false
% 19.82/3.59 | |
% 19.82/3.59 | | CLOSE: (56) is inconsistent.
% 19.82/3.59 | |
% 19.82/3.59 | Case 2:
% 19.82/3.59 | |
% 19.82/3.59 | | (57) apply(all_56_2, all_56_1) = all_56_0 & $i(all_56_0)
% 19.82/3.59 | |
% 19.82/3.59 | | ALPHA: (57) implies:
% 19.82/3.59 | | (58) apply(all_56_2, all_56_1) = all_56_0
% 19.82/3.59 | |
% 19.82/3.59 | | BETA: splitting (20) gives:
% 19.82/3.59 | |
% 19.82/3.59 | | Case 1:
% 19.82/3.59 | | |
% 19.82/3.59 | | | (59) empty(all_56_3)
% 19.82/3.59 | | |
% 19.82/3.59 | | | PRED_UNIFY: (54), (59) imply:
% 19.82/3.59 | | | (60) $false
% 19.82/3.59 | | |
% 19.82/3.59 | | | CLOSE: (60) is inconsistent.
% 19.82/3.59 | | |
% 19.82/3.59 | | Case 2:
% 19.82/3.59 | | |
% 19.82/3.60 | | | (61) in(all_56_1, all_56_3)
% 19.82/3.60 | | |
% 19.82/3.60 | | | GROUND_INST: instantiating (t35_funct_1) with all_56_3, all_56_1,
% 19.82/3.60 | | | all_56_2, all_56_0, simplifying with (15), (16), (52), (58),
% 19.82/3.60 | | | (61) gives:
% 19.82/3.60 | | | (62) all_56_0 = all_56_1
% 19.82/3.60 | | |
% 19.82/3.60 | | | REDUCE: (10), (62) imply:
% 19.82/3.60 | | | (63) $false
% 19.82/3.60 | | |
% 19.82/3.60 | | | CLOSE: (63) is inconsistent.
% 19.82/3.60 | | |
% 19.82/3.60 | | End of split
% 19.82/3.60 | |
% 19.82/3.60 | End of split
% 19.82/3.60 |
% 19.82/3.60 End of proof
% 19.82/3.60 % SZS output end Proof for theBenchmark
% 19.82/3.60
% 19.82/3.60 2995ms
%------------------------------------------------------------------------------