TSTP Solution File: SEU056+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SEU056+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 : n006.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 17:42:25 EDT 2023
% Result : Theorem 8.33s 1.86s
% Output : Proof 10.96s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU056+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.12 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.33 % Computer : n006.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 : Wed Aug 23 18:26:23 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.18/0.59 ________ _____
% 0.18/0.59 ___ __ \_________(_)________________________________
% 0.18/0.59 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.18/0.59 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.18/0.59 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.18/0.59
% 0.18/0.59 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.18/0.59 (2023-06-19)
% 0.18/0.59
% 0.18/0.59 (c) Philipp Rümmer, 2009-2023
% 0.18/0.59 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.18/0.59 Amanda Stjerna.
% 0.18/0.59 Free software under BSD-3-Clause.
% 0.18/0.59
% 0.18/0.59 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.18/0.59
% 0.18/0.59 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.18/0.61 Running up to 7 provers in parallel.
% 0.18/0.62 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.18/0.62 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.18/0.62 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.18/0.62 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.18/0.62 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.18/0.62 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.18/0.62 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.52/1.04 Prover 1: Preprocessing ...
% 2.52/1.04 Prover 4: Preprocessing ...
% 2.77/1.08 Prover 3: Preprocessing ...
% 2.77/1.08 Prover 6: Preprocessing ...
% 2.77/1.08 Prover 2: Preprocessing ...
% 2.77/1.08 Prover 5: Preprocessing ...
% 2.77/1.08 Prover 0: Preprocessing ...
% 5.43/1.49 Prover 1: Warning: ignoring some quantifiers
% 5.43/1.53 Prover 2: Proving ...
% 6.07/1.54 Prover 5: Proving ...
% 6.07/1.54 Prover 1: Constructing countermodel ...
% 6.07/1.54 Prover 6: Proving ...
% 6.07/1.55 Prover 3: Warning: ignoring some quantifiers
% 6.07/1.57 Prover 3: Constructing countermodel ...
% 6.45/1.59 Prover 4: Warning: ignoring some quantifiers
% 6.45/1.62 Prover 4: Constructing countermodel ...
% 6.91/1.66 Prover 0: Proving ...
% 8.33/1.85 Prover 3: proved (1237ms)
% 8.33/1.85
% 8.33/1.86 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 8.33/1.86
% 8.33/1.86 Prover 0: stopped
% 8.33/1.86 Prover 2: stopped
% 8.33/1.86 Prover 5: stopped
% 8.33/1.87 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 8.33/1.87 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 8.33/1.87 Prover 6: stopped
% 8.72/1.88 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 8.72/1.88 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 8.72/1.88 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 8.72/1.90 Prover 7: Preprocessing ...
% 8.72/1.91 Prover 8: Preprocessing ...
% 8.72/1.91 Prover 11: Preprocessing ...
% 8.72/1.92 Prover 10: Preprocessing ...
% 9.21/1.95 Prover 13: Preprocessing ...
% 9.21/2.05 Prover 7: Warning: ignoring some quantifiers
% 9.21/2.06 Prover 10: Warning: ignoring some quantifiers
% 9.74/2.06 Prover 7: Constructing countermodel ...
% 9.74/2.07 Prover 10: Constructing countermodel ...
% 9.74/2.09 Prover 13: Warning: ignoring some quantifiers
% 9.74/2.09 Prover 1: Found proof (size 47)
% 9.74/2.09 Prover 1: proved (1480ms)
% 9.74/2.09 Prover 13: Constructing countermodel ...
% 9.74/2.10 Prover 10: stopped
% 9.74/2.10 Prover 4: stopped
% 9.74/2.10 Prover 13: stopped
% 9.74/2.10 Prover 7: stopped
% 10.33/2.12 Prover 8: Warning: ignoring some quantifiers
% 10.33/2.13 Prover 8: Constructing countermodel ...
% 10.33/2.14 Prover 8: stopped
% 10.54/2.15 Prover 11: Warning: ignoring some quantifiers
% 10.54/2.16 Prover 11: Constructing countermodel ...
% 10.54/2.17 Prover 11: stopped
% 10.54/2.17
% 10.54/2.17 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 10.54/2.17
% 10.54/2.18 % SZS output start Proof for theBenchmark
% 10.54/2.18 Assumptions after simplification:
% 10.54/2.18 ---------------------------------
% 10.54/2.19
% 10.54/2.19 (cc2_funct_1)
% 10.54/2.21 ! [v0: $i] : ! [v1: any] : ( ~ (one_to_one(v0) = v1) | ~ $i(v0) | ? [v2:
% 10.54/2.21 any] : ? [v3: any] : ? [v4: any] : (relation(v0) = v2 & function(v0) =
% 10.54/2.21 v4 & empty(v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | ~ (v2 = 0) | v1 = 0)))
% 10.54/2.21
% 10.54/2.21 (d7_xboole_0)
% 10.54/2.21 $i(empty_set) & ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~
% 10.54/2.21 (disjoint(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ( ~ (v3 =
% 10.54/2.21 empty_set) & set_intersection2(v0, v1) = v3 & $i(v3))) & ! [v0: $i] :
% 10.54/2.21 ! [v1: $i] : ( ~ (disjoint(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) |
% 10.54/2.21 set_intersection2(v0, v1) = empty_set)
% 10.54/2.21
% 10.54/2.21 (t121_funct_1)
% 10.54/2.21 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 10.54/2.21 $i] : ( ~ (relation_image(v2, v1) = v4) | ~ (relation_image(v2, v0) = v3) |
% 10.54/2.21 ~ (set_intersection2(v3, v4) = v5) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ?
% 10.54/2.21 [v6: any] : ? [v7: any] : ? [v8: any] : ? [v9: $i] : ? [v10: $i] :
% 10.54/2.22 (relation_image(v2, v9) = v10 & set_intersection2(v0, v1) = v9 &
% 10.54/2.22 one_to_one(v2) = v8 & relation(v2) = v6 & function(v2) = v7 & $i(v10) &
% 10.54/2.22 $i(v9) & ( ~ (v8 = 0) | ~ (v7 = 0) | ~ (v6 = 0) | v10 = v5)))
% 10.54/2.22
% 10.54/2.22 (t125_funct_1)
% 10.54/2.22 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5:
% 10.54/2.22 int] : ( ~ (v5 = 0) & relation_image(v2, v1) = v4 & relation_image(v2, v0) =
% 10.54/2.22 v3 & disjoint(v3, v4) = v5 & disjoint(v0, v1) = 0 & one_to_one(v2) = 0 &
% 10.54/2.22 relation(v2) = 0 & function(v2) = 0 & $i(v4) & $i(v3) & $i(v2) & $i(v1) &
% 10.54/2.22 $i(v0))
% 10.54/2.22
% 10.54/2.22 (t149_relat_1)
% 10.54/2.22 $i(empty_set) & ! [v0: $i] : ! [v1: $i] : (v1 = empty_set | ~
% 10.54/2.22 (relation_image(v0, empty_set) = v1) | ~ $i(v0) | ? [v2: int] : ( ~ (v2 =
% 10.54/2.22 0) & relation(v0) = v2))
% 10.54/2.22
% 10.54/2.22 (function-axioms)
% 10.54/2.23 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 10.54/2.23 (relation_image(v3, v2) = v1) | ~ (relation_image(v3, v2) = v0)) & ! [v0:
% 10.54/2.23 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 10.54/2.23 : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) & ! [v0:
% 10.54/2.23 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 10.54/2.23 : (v1 = v0 | ~ (element(v3, v2) = v1) | ~ (element(v3, v2) = v0)) & ! [v0:
% 10.54/2.23 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 10.54/2.23 : (v1 = v0 | ~ (disjoint(v3, v2) = v1) | ~ (disjoint(v3, v2) = v0)) & !
% 10.54/2.23 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 10.54/2.23 (set_intersection2(v3, v2) = v1) | ~ (set_intersection2(v3, v2) = v0)) & !
% 10.54/2.23 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 10.54/2.23 $i] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) & ! [v0: $i]
% 10.54/2.23 : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (powerset(v2) = v1) | ~
% 10.54/2.23 (powerset(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 10.54/2.23 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~
% 10.54/2.23 (relation_empty_yielding(v2) = v1) | ~ (relation_empty_yielding(v2) = v0))
% 10.54/2.23 & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1
% 10.54/2.23 = v0 | ~ (one_to_one(v2) = v1) | ~ (one_to_one(v2) = v0)) & ! [v0:
% 10.54/2.23 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 |
% 10.54/2.23 ~ (relation(v2) = v1) | ~ (relation(v2) = v0)) & ! [v0: MultipleValueBool]
% 10.54/2.23 : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (function(v2) = v1)
% 10.54/2.23 | ~ (function(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 10.54/2.23 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (empty(v2) = v1) | ~
% 10.54/2.23 (empty(v2) = v0))
% 10.54/2.23
% 10.54/2.23 Further assumptions not needed in the proof:
% 10.54/2.23 --------------------------------------------
% 10.54/2.23 antisymmetry_r2_hidden, cc1_funct_1, cc1_relat_1, commutativity_k3_xboole_0,
% 10.54/2.23 existence_m1_subset_1, fc12_relat_1, fc1_relat_1, fc1_subset_1, fc1_xboole_0,
% 10.54/2.23 fc4_relat_1, idempotence_k3_xboole_0, rc1_funct_1, rc1_relat_1, rc1_subset_1,
% 10.54/2.23 rc1_xboole_0, rc2_funct_1, rc2_relat_1, rc2_subset_1, rc2_xboole_0, rc3_funct_1,
% 10.54/2.23 rc3_relat_1, reflexivity_r1_tarski, symmetry_r1_xboole_0, t1_subset, t2_boole,
% 10.54/2.23 t2_subset, t3_subset, t4_subset, t5_subset, t6_boole, t7_boole, t8_boole
% 10.54/2.23
% 10.54/2.23 Those formulas are unsatisfiable:
% 10.54/2.23 ---------------------------------
% 10.54/2.23
% 10.54/2.23 Begin of proof
% 10.54/2.23 |
% 10.54/2.23 | ALPHA: (d7_xboole_0) implies:
% 10.54/2.23 | (1) ! [v0: $i] : ! [v1: $i] : ( ~ (disjoint(v0, v1) = 0) | ~ $i(v1) | ~
% 10.54/2.23 | $i(v0) | set_intersection2(v0, v1) = empty_set)
% 10.54/2.23 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (disjoint(v0,
% 10.54/2.23 | v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ( ~ (v3 =
% 10.54/2.23 | empty_set) & set_intersection2(v0, v1) = v3 & $i(v3)))
% 10.54/2.23 |
% 10.54/2.23 | ALPHA: (t149_relat_1) implies:
% 10.54/2.23 | (3) ! [v0: $i] : ! [v1: $i] : (v1 = empty_set | ~ (relation_image(v0,
% 10.54/2.23 | empty_set) = v1) | ~ $i(v0) | ? [v2: int] : ( ~ (v2 = 0) &
% 10.54/2.23 | relation(v0) = v2))
% 10.54/2.23 |
% 10.54/2.23 | ALPHA: (function-axioms) implies:
% 10.54/2.23 | (4) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 10.54/2.23 | (v1 = v0 | ~ (function(v2) = v1) | ~ (function(v2) = v0))
% 10.54/2.23 | (5) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 10.54/2.23 | (v1 = v0 | ~ (relation(v2) = v1) | ~ (relation(v2) = v0))
% 10.54/2.23 | (6) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 10.54/2.23 | (v1 = v0 | ~ (one_to_one(v2) = v1) | ~ (one_to_one(v2) = v0))
% 10.96/2.23 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 10.96/2.23 | (set_intersection2(v3, v2) = v1) | ~ (set_intersection2(v3, v2) =
% 10.96/2.23 | v0))
% 10.96/2.23 |
% 10.96/2.23 | DELTA: instantiating (t125_funct_1) with fresh symbols all_47_0, all_47_1,
% 10.96/2.23 | all_47_2, all_47_3, all_47_4, all_47_5 gives:
% 10.96/2.24 | (8) ~ (all_47_0 = 0) & relation_image(all_47_3, all_47_4) = all_47_1 &
% 10.96/2.24 | relation_image(all_47_3, all_47_5) = all_47_2 & disjoint(all_47_2,
% 10.96/2.24 | all_47_1) = all_47_0 & disjoint(all_47_5, all_47_4) = 0 &
% 10.96/2.24 | one_to_one(all_47_3) = 0 & relation(all_47_3) = 0 & function(all_47_3)
% 10.96/2.24 | = 0 & $i(all_47_1) & $i(all_47_2) & $i(all_47_3) & $i(all_47_4) &
% 10.96/2.24 | $i(all_47_5)
% 10.96/2.24 |
% 10.96/2.24 | ALPHA: (8) implies:
% 10.96/2.24 | (9) ~ (all_47_0 = 0)
% 10.96/2.24 | (10) $i(all_47_5)
% 10.96/2.24 | (11) $i(all_47_4)
% 10.96/2.24 | (12) $i(all_47_3)
% 10.96/2.24 | (13) $i(all_47_2)
% 10.96/2.24 | (14) $i(all_47_1)
% 10.96/2.24 | (15) function(all_47_3) = 0
% 10.96/2.24 | (16) relation(all_47_3) = 0
% 10.96/2.24 | (17) one_to_one(all_47_3) = 0
% 10.96/2.24 | (18) disjoint(all_47_5, all_47_4) = 0
% 10.96/2.24 | (19) disjoint(all_47_2, all_47_1) = all_47_0
% 10.96/2.24 | (20) relation_image(all_47_3, all_47_5) = all_47_2
% 10.96/2.24 | (21) relation_image(all_47_3, all_47_4) = all_47_1
% 10.96/2.24 |
% 10.96/2.24 | GROUND_INST: instantiating (cc2_funct_1) with all_47_3, 0, simplifying with
% 10.96/2.24 | (12), (17) gives:
% 10.96/2.24 | (22) ? [v0: MultipleValueBool] : ? [v1: MultipleValueBool] : ? [v2:
% 10.96/2.24 | MultipleValueBool] : (relation(all_47_3) = v0 & function(all_47_3) =
% 10.96/2.24 | v2 & empty(all_47_3) = v1)
% 10.96/2.24 |
% 10.96/2.24 | GROUND_INST: instantiating (1) with all_47_5, all_47_4, simplifying with (10),
% 10.96/2.24 | (11), (18) gives:
% 10.96/2.24 | (23) set_intersection2(all_47_5, all_47_4) = empty_set
% 10.96/2.24 |
% 10.96/2.24 | GROUND_INST: instantiating (2) with all_47_2, all_47_1, all_47_0, simplifying
% 10.96/2.24 | with (13), (14), (19) gives:
% 10.96/2.24 | (24) all_47_0 = 0 | ? [v0: $i] : ( ~ (v0 = empty_set) &
% 10.96/2.24 | set_intersection2(all_47_2, all_47_1) = v0 & $i(v0))
% 10.96/2.24 |
% 10.96/2.24 | DELTA: instantiating (22) with fresh symbols all_55_0, all_55_1, all_55_2
% 10.96/2.24 | gives:
% 10.96/2.24 | (25) relation(all_47_3) = all_55_2 & function(all_47_3) = all_55_0 &
% 10.96/2.24 | empty(all_47_3) = all_55_1
% 10.96/2.24 |
% 10.96/2.24 | ALPHA: (25) implies:
% 10.96/2.24 | (26) function(all_47_3) = all_55_0
% 10.96/2.24 | (27) relation(all_47_3) = all_55_2
% 10.96/2.24 |
% 10.96/2.24 | BETA: splitting (24) gives:
% 10.96/2.24 |
% 10.96/2.24 | Case 1:
% 10.96/2.24 | |
% 10.96/2.24 | | (28) all_47_0 = 0
% 10.96/2.24 | |
% 10.96/2.24 | | REDUCE: (9), (28) imply:
% 10.96/2.24 | | (29) $false
% 10.96/2.24 | |
% 10.96/2.24 | | CLOSE: (29) is inconsistent.
% 10.96/2.24 | |
% 10.96/2.24 | Case 2:
% 10.96/2.24 | |
% 10.96/2.24 | | (30) ? [v0: $i] : ( ~ (v0 = empty_set) & set_intersection2(all_47_2,
% 10.96/2.24 | | all_47_1) = v0 & $i(v0))
% 10.96/2.24 | |
% 10.96/2.24 | | DELTA: instantiating (30) with fresh symbol all_63_0 gives:
% 10.96/2.24 | | (31) ~ (all_63_0 = empty_set) & set_intersection2(all_47_2, all_47_1) =
% 10.96/2.24 | | all_63_0 & $i(all_63_0)
% 10.96/2.24 | |
% 10.96/2.24 | | ALPHA: (31) implies:
% 10.96/2.24 | | (32) ~ (all_63_0 = empty_set)
% 10.96/2.25 | | (33) set_intersection2(all_47_2, all_47_1) = all_63_0
% 10.96/2.25 | |
% 10.96/2.25 | | GROUND_INST: instantiating (4) with 0, all_55_0, all_47_3, simplifying with
% 10.96/2.25 | | (15), (26) gives:
% 10.96/2.25 | | (34) all_55_0 = 0
% 10.96/2.25 | |
% 10.96/2.25 | | GROUND_INST: instantiating (5) with 0, all_55_2, all_47_3, simplifying with
% 10.96/2.25 | | (16), (27) gives:
% 10.96/2.25 | | (35) all_55_2 = 0
% 10.96/2.25 | |
% 10.96/2.25 | | GROUND_INST: instantiating (t121_funct_1) with all_47_5, all_47_4, all_47_3,
% 10.96/2.25 | | all_47_2, all_47_1, all_63_0, simplifying with (10), (11),
% 10.96/2.25 | | (12), (20), (21), (33) gives:
% 10.96/2.25 | | (36) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: $i] : ? [v4:
% 10.96/2.25 | | $i] : (relation_image(all_47_3, v3) = v4 &
% 10.96/2.25 | | set_intersection2(all_47_5, all_47_4) = v3 & one_to_one(all_47_3)
% 10.96/2.25 | | = v2 & relation(all_47_3) = v0 & function(all_47_3) = v1 & $i(v4)
% 10.96/2.25 | | & $i(v3) & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0) | v4 =
% 10.96/2.25 | | all_63_0))
% 10.96/2.25 | |
% 10.96/2.25 | | DELTA: instantiating (36) with fresh symbols all_79_0, all_79_1, all_79_2,
% 10.96/2.25 | | all_79_3, all_79_4 gives:
% 10.96/2.25 | | (37) relation_image(all_47_3, all_79_1) = all_79_0 &
% 10.96/2.25 | | set_intersection2(all_47_5, all_47_4) = all_79_1 &
% 10.96/2.25 | | one_to_one(all_47_3) = all_79_2 & relation(all_47_3) = all_79_4 &
% 10.96/2.25 | | function(all_47_3) = all_79_3 & $i(all_79_0) & $i(all_79_1) & ( ~
% 10.96/2.25 | | (all_79_2 = 0) | ~ (all_79_3 = 0) | ~ (all_79_4 = 0) | all_79_0
% 10.96/2.25 | | = all_63_0)
% 10.96/2.25 | |
% 10.96/2.25 | | ALPHA: (37) implies:
% 10.96/2.25 | | (38) function(all_47_3) = all_79_3
% 10.96/2.25 | | (39) relation(all_47_3) = all_79_4
% 10.96/2.25 | | (40) one_to_one(all_47_3) = all_79_2
% 10.96/2.25 | | (41) set_intersection2(all_47_5, all_47_4) = all_79_1
% 10.96/2.25 | | (42) relation_image(all_47_3, all_79_1) = all_79_0
% 10.96/2.25 | | (43) ~ (all_79_2 = 0) | ~ (all_79_3 = 0) | ~ (all_79_4 = 0) | all_79_0
% 10.96/2.25 | | = all_63_0
% 10.96/2.25 | |
% 10.96/2.25 | | GROUND_INST: instantiating (4) with 0, all_79_3, all_47_3, simplifying with
% 10.96/2.25 | | (15), (38) gives:
% 10.96/2.25 | | (44) all_79_3 = 0
% 10.96/2.25 | |
% 10.96/2.25 | | GROUND_INST: instantiating (5) with 0, all_79_4, all_47_3, simplifying with
% 10.96/2.25 | | (16), (39) gives:
% 10.96/2.25 | | (45) all_79_4 = 0
% 10.96/2.25 | |
% 10.96/2.25 | | GROUND_INST: instantiating (6) with 0, all_79_2, all_47_3, simplifying with
% 10.96/2.25 | | (17), (40) gives:
% 10.96/2.25 | | (46) all_79_2 = 0
% 10.96/2.25 | |
% 10.96/2.25 | | GROUND_INST: instantiating (7) with empty_set, all_79_1, all_47_4, all_47_5,
% 10.96/2.25 | | simplifying with (23), (41) gives:
% 10.96/2.25 | | (47) all_79_1 = empty_set
% 10.96/2.25 | |
% 10.96/2.25 | | REDUCE: (42), (47) imply:
% 10.96/2.25 | | (48) relation_image(all_47_3, empty_set) = all_79_0
% 10.96/2.25 | |
% 10.96/2.25 | | BETA: splitting (43) gives:
% 10.96/2.25 | |
% 10.96/2.25 | | Case 1:
% 10.96/2.25 | | |
% 10.96/2.25 | | | (49) ~ (all_79_2 = 0)
% 10.96/2.25 | | |
% 10.96/2.25 | | | REDUCE: (46), (49) imply:
% 10.96/2.25 | | | (50) $false
% 10.96/2.25 | | |
% 10.96/2.25 | | | CLOSE: (50) is inconsistent.
% 10.96/2.25 | | |
% 10.96/2.25 | | Case 2:
% 10.96/2.25 | | |
% 10.96/2.25 | | | (51) ~ (all_79_3 = 0) | ~ (all_79_4 = 0) | all_79_0 = all_63_0
% 10.96/2.25 | | |
% 10.96/2.25 | | | BETA: splitting (51) gives:
% 10.96/2.25 | | |
% 10.96/2.25 | | | Case 1:
% 10.96/2.25 | | | |
% 10.96/2.25 | | | | (52) ~ (all_79_3 = 0)
% 10.96/2.25 | | | |
% 10.96/2.25 | | | | REDUCE: (44), (52) imply:
% 10.96/2.25 | | | | (53) $false
% 10.96/2.25 | | | |
% 10.96/2.25 | | | | CLOSE: (53) is inconsistent.
% 10.96/2.25 | | | |
% 10.96/2.25 | | | Case 2:
% 10.96/2.25 | | | |
% 10.96/2.25 | | | | (54) ~ (all_79_4 = 0) | all_79_0 = all_63_0
% 10.96/2.25 | | | |
% 10.96/2.25 | | | | BETA: splitting (54) gives:
% 10.96/2.25 | | | |
% 10.96/2.25 | | | | Case 1:
% 10.96/2.25 | | | | |
% 10.96/2.25 | | | | | (55) ~ (all_79_4 = 0)
% 10.96/2.25 | | | | |
% 10.96/2.25 | | | | | REDUCE: (45), (55) imply:
% 10.96/2.25 | | | | | (56) $false
% 10.96/2.25 | | | | |
% 10.96/2.25 | | | | | CLOSE: (56) is inconsistent.
% 10.96/2.25 | | | | |
% 10.96/2.25 | | | | Case 2:
% 10.96/2.25 | | | | |
% 10.96/2.25 | | | | | (57) all_79_0 = all_63_0
% 10.96/2.25 | | | | |
% 10.96/2.25 | | | | | REDUCE: (48), (57) imply:
% 10.96/2.25 | | | | | (58) relation_image(all_47_3, empty_set) = all_63_0
% 10.96/2.25 | | | | |
% 10.96/2.25 | | | | | GROUND_INST: instantiating (3) with all_47_3, all_63_0, simplifying
% 10.96/2.25 | | | | | with (12), (58) gives:
% 10.96/2.26 | | | | | (59) all_63_0 = empty_set | ? [v0: int] : ( ~ (v0 = 0) &
% 10.96/2.26 | | | | | relation(all_47_3) = v0)
% 10.96/2.26 | | | | |
% 10.96/2.26 | | | | | BETA: splitting (59) gives:
% 10.96/2.26 | | | | |
% 10.96/2.26 | | | | | Case 1:
% 10.96/2.26 | | | | | |
% 10.96/2.26 | | | | | | (60) all_63_0 = empty_set
% 10.96/2.26 | | | | | |
% 10.96/2.26 | | | | | | REDUCE: (32), (60) imply:
% 10.96/2.26 | | | | | | (61) $false
% 10.96/2.26 | | | | | |
% 10.96/2.26 | | | | | | CLOSE: (61) is inconsistent.
% 10.96/2.26 | | | | | |
% 10.96/2.26 | | | | | Case 2:
% 10.96/2.26 | | | | | |
% 10.96/2.26 | | | | | | (62) ? [v0: int] : ( ~ (v0 = 0) & relation(all_47_3) = v0)
% 10.96/2.26 | | | | | |
% 10.96/2.26 | | | | | | DELTA: instantiating (62) with fresh symbol all_110_0 gives:
% 10.96/2.26 | | | | | | (63) ~ (all_110_0 = 0) & relation(all_47_3) = all_110_0
% 10.96/2.26 | | | | | |
% 10.96/2.26 | | | | | | ALPHA: (63) implies:
% 10.96/2.26 | | | | | | (64) ~ (all_110_0 = 0)
% 10.96/2.26 | | | | | | (65) relation(all_47_3) = all_110_0
% 10.96/2.26 | | | | | |
% 10.96/2.26 | | | | | | GROUND_INST: instantiating (5) with 0, all_110_0, all_47_3,
% 10.96/2.26 | | | | | | simplifying with (16), (65) gives:
% 10.96/2.26 | | | | | | (66) all_110_0 = 0
% 10.96/2.26 | | | | | |
% 10.96/2.26 | | | | | | REDUCE: (64), (66) imply:
% 10.96/2.26 | | | | | | (67) $false
% 10.96/2.26 | | | | | |
% 10.96/2.26 | | | | | | CLOSE: (67) is inconsistent.
% 10.96/2.26 | | | | | |
% 10.96/2.26 | | | | | End of split
% 10.96/2.26 | | | | |
% 10.96/2.26 | | | | End of split
% 10.96/2.26 | | | |
% 10.96/2.26 | | | End of split
% 10.96/2.26 | | |
% 10.96/2.26 | | End of split
% 10.96/2.26 | |
% 10.96/2.26 | End of split
% 10.96/2.26 |
% 10.96/2.26 End of proof
% 10.96/2.26 % SZS output end Proof for theBenchmark
% 10.96/2.26
% 10.96/2.26 1664ms
%------------------------------------------------------------------------------