TSTP Solution File: SEU247+1 by Princess---230619
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SEU247+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 : n007.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 17:43:37 EDT 2023
% Result : Theorem 4.45s 1.41s
% Output : Proof 6.91s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14 % Problem : SEU247+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.15 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.14/0.37 % Computer : n007.cluster.edu
% 0.14/0.37 % Model : x86_64 x86_64
% 0.14/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.37 % Memory : 8042.1875MB
% 0.14/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.37 % CPULimit : 300
% 0.14/0.37 % WCLimit : 300
% 0.14/0.37 % DateTime : Wed Aug 23 17:44:39 EDT 2023
% 0.14/0.37 % CPUTime :
% 0.23/0.64 ________ _____
% 0.23/0.64 ___ __ \_________(_)________________________________
% 0.23/0.64 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.23/0.64 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.23/0.64 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.23/0.64
% 0.23/0.64 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.23/0.64 (2023-06-19)
% 0.23/0.64
% 0.23/0.64 (c) Philipp Rümmer, 2009-2023
% 0.23/0.64 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.23/0.64 Amanda Stjerna.
% 0.23/0.64 Free software under BSD-3-Clause.
% 0.23/0.64
% 0.23/0.64 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.23/0.64
% 0.23/0.64 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.23/0.65 Running up to 7 provers in parallel.
% 0.23/0.66 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.23/0.66 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.23/0.66 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.23/0.66 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.23/0.66 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.23/0.66 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.23/0.66 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.22/1.02 Prover 1: Preprocessing ...
% 2.22/1.02 Prover 4: Preprocessing ...
% 2.34/1.08 Prover 0: Preprocessing ...
% 2.34/1.08 Prover 3: Preprocessing ...
% 2.34/1.08 Prover 6: Preprocessing ...
% 2.34/1.08 Prover 2: Preprocessing ...
% 2.34/1.08 Prover 5: Preprocessing ...
% 3.45/1.21 Prover 1: Warning: ignoring some quantifiers
% 3.45/1.22 Prover 3: Warning: ignoring some quantifiers
% 3.45/1.24 Prover 1: Constructing countermodel ...
% 3.45/1.24 Prover 3: Constructing countermodel ...
% 4.01/1.27 Prover 6: Proving ...
% 4.10/1.28 Prover 4: Constructing countermodel ...
% 4.10/1.29 Prover 0: Proving ...
% 4.10/1.29 Prover 5: Proving ...
% 4.45/1.34 Prover 2: Proving ...
% 4.45/1.41 Prover 5: proved (741ms)
% 4.45/1.41 Prover 0: proved (748ms)
% 4.45/1.41
% 4.45/1.41 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.45/1.41
% 4.45/1.41
% 4.45/1.41 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.45/1.41
% 4.45/1.41 Prover 6: stopped
% 4.45/1.41 Prover 2: stopped
% 4.45/1.41 Prover 3: stopped
% 5.11/1.42 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 5.11/1.42 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 5.11/1.42 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 5.11/1.42 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 5.11/1.43 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 5.11/1.43 Prover 8: Preprocessing ...
% 5.11/1.44 Prover 10: Preprocessing ...
% 5.11/1.44 Prover 11: Preprocessing ...
% 5.11/1.46 Prover 7: Preprocessing ...
% 5.11/1.46 Prover 13: Preprocessing ...
% 5.11/1.50 Prover 10: Constructing countermodel ...
% 5.11/1.52 Prover 8: Warning: ignoring some quantifiers
% 5.11/1.53 Prover 8: Constructing countermodel ...
% 5.11/1.54 Prover 7: Constructing countermodel ...
% 5.11/1.56 Prover 13: Warning: ignoring some quantifiers
% 5.11/1.57 Prover 11: Constructing countermodel ...
% 5.11/1.58 Prover 13: Constructing countermodel ...
% 5.11/1.58 Prover 4: Found proof (size 44)
% 5.11/1.58 Prover 4: proved (922ms)
% 5.11/1.59 Prover 1: stopped
% 5.11/1.59 Prover 10: stopped
% 5.11/1.59 Prover 7: stopped
% 5.11/1.59 Prover 13: stopped
% 5.11/1.59 Prover 8: stopped
% 5.11/1.59 Prover 11: stopped
% 5.11/1.59
% 5.11/1.59 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.11/1.59
% 6.07/1.61 % SZS output start Proof for theBenchmark
% 6.07/1.61 Assumptions after simplification:
% 6.07/1.61 ---------------------------------
% 6.07/1.61
% 6.07/1.61 (dt_k2_wellord1)
% 6.07/1.64 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (relation_restriction(v0, v1) =
% 6.07/1.64 v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : (relation(v2)
% 6.07/1.64 = v4 & relation(v0) = v3 & ( ~ (v3 = 0) | v4 = 0)))
% 6.07/1.64
% 6.07/1.64 (dt_k7_relat_1)
% 6.07/1.65 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (relation_dom_restriction(v0,
% 6.07/1.65 v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] :
% 6.07/1.65 (relation(v2) = v4 & relation(v0) = v3 & ( ~ (v3 = 0) | v4 = 0)))
% 6.07/1.65
% 6.07/1.65 (t140_relat_1)
% 6.07/1.65 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 6.07/1.65 (relation_rng_restriction(v0, v3) = v4) | ~ (relation_dom_restriction(v2,
% 6.07/1.65 v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6:
% 6.07/1.65 $i] : ? [v7: $i] : (relation_rng_restriction(v0, v2) = v6 &
% 6.07/1.65 relation_dom_restriction(v6, v1) = v7 & relation(v2) = v5 & $i(v7) &
% 6.07/1.65 $i(v6) & ( ~ (v5 = 0) | v7 = v4))) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 6.07/1.65 $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (relation_rng_restriction(v0, v2) =
% 6.07/1.65 v3) | ~ (relation_dom_restriction(v3, v1) = v4) | ~ $i(v2) | ~ $i(v1) |
% 6.07/1.65 ~ $i(v0) | ? [v5: any] : ? [v6: $i] : ? [v7: $i] :
% 6.07/1.65 (relation_rng_restriction(v0, v6) = v7 & relation_dom_restriction(v2, v1) =
% 6.07/1.65 v6 & relation(v2) = v5 & $i(v7) & $i(v6) & ( ~ (v5 = 0) | v7 = v4)))
% 6.07/1.65
% 6.07/1.65 (t17_wellord1)
% 6.07/1.66 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (relation_rng_restriction(v0,
% 6.07/1.66 v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: $i] : ? [v5:
% 6.07/1.66 $i] : (relation_dom_restriction(v2, v0) = v5 & relation(v1) = v3 &
% 6.07/1.66 relation_restriction(v1, v0) = v4 & $i(v5) & $i(v4) & ( ~ (v3 = 0) | v5 =
% 6.07/1.66 v4))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 6.07/1.66 (relation_restriction(v1, v0) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] :
% 6.07/1.66 ? [v4: $i] : ? [v5: $i] : (relation_rng_restriction(v0, v1) = v4 &
% 6.07/1.66 relation_dom_restriction(v4, v0) = v5 & relation(v1) = v3 & $i(v5) &
% 6.07/1.66 $i(v4) & ( ~ (v3 = 0) | v5 = v2)))
% 6.07/1.66
% 6.07/1.66 (t18_wellord1)
% 6.07/1.66 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ( ~ (v4
% 6.07/1.66 = v2) & relation_rng_restriction(v0, v3) = v4 &
% 6.07/1.66 relation_dom_restriction(v1, v0) = v3 & relation(v1) = 0 &
% 6.07/1.66 relation_restriction(v1, v0) = v2 & $i(v4) & $i(v3) & $i(v2) & $i(v1) &
% 6.07/1.66 $i(v0))
% 6.07/1.66
% 6.07/1.66 (function-axioms)
% 6.07/1.67 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 6.07/1.67 (relation_rng_restriction(v3, v2) = v1) | ~ (relation_rng_restriction(v3,
% 6.07/1.67 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1
% 6.07/1.67 = v0 | ~ (relation_dom_restriction(v3, v2) = v1) | ~
% 6.07/1.67 (relation_dom_restriction(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 6.07/1.67 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (relation_restriction(v3, v2) = v1) |
% 6.07/1.67 ~ (relation_restriction(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 6.07/1.67 $i] : ! [v3: $i] : (v1 = v0 | ~ (cartesian_product2(v3, v2) = v1) | ~
% 6.07/1.67 (cartesian_product2(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i]
% 6.07/1.67 : ! [v3: $i] : (v1 = v0 | ~ (set_intersection2(v3, v2) = v1) | ~
% 6.07/1.67 (set_intersection2(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 6.07/1.67 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (relation(v2) = v1) | ~
% 6.07/1.67 (relation(v2) = v0))
% 6.07/1.67
% 6.07/1.67 Further assumptions not needed in the proof:
% 6.07/1.67 --------------------------------------------
% 6.07/1.67 commutativity_k3_xboole_0, d6_wellord1, dt_k2_zfmisc_1, dt_k3_xboole_0,
% 6.07/1.67 dt_k8_relat_1, idempotence_k3_xboole_0
% 6.07/1.67
% 6.07/1.67 Those formulas are unsatisfiable:
% 6.07/1.67 ---------------------------------
% 6.07/1.67
% 6.07/1.67 Begin of proof
% 6.07/1.67 |
% 6.07/1.67 | ALPHA: (t140_relat_1) implies:
% 6.07/1.68 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (
% 6.07/1.68 | ~ (relation_rng_restriction(v0, v3) = v4) | ~
% 6.07/1.68 | (relation_dom_restriction(v2, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~
% 6.07/1.68 | $i(v0) | ? [v5: any] : ? [v6: $i] : ? [v7: $i] :
% 6.07/1.68 | (relation_rng_restriction(v0, v2) = v6 & relation_dom_restriction(v6,
% 6.07/1.68 | v1) = v7 & relation(v2) = v5 & $i(v7) & $i(v6) & ( ~ (v5 = 0) |
% 6.07/1.68 | v7 = v4)))
% 6.07/1.68 |
% 6.07/1.68 | ALPHA: (t17_wellord1) implies:
% 6.07/1.68 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (relation_restriction(v1,
% 6.07/1.68 | v0) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: $i] :
% 6.07/1.68 | ? [v5: $i] : (relation_rng_restriction(v0, v1) = v4 &
% 6.07/1.68 | relation_dom_restriction(v4, v0) = v5 & relation(v1) = v3 & $i(v5)
% 6.07/1.68 | & $i(v4) & ( ~ (v3 = 0) | v5 = v2)))
% 6.07/1.68 |
% 6.07/1.68 | ALPHA: (function-axioms) implies:
% 6.07/1.68 | (3) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 6.07/1.68 | (v1 = v0 | ~ (relation(v2) = v1) | ~ (relation(v2) = v0))
% 6.07/1.68 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 6.07/1.68 | (relation_dom_restriction(v3, v2) = v1) | ~
% 6.07/1.68 | (relation_dom_restriction(v3, v2) = v0))
% 6.07/1.68 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 6.07/1.68 | (relation_rng_restriction(v3, v2) = v1) | ~
% 6.07/1.68 | (relation_rng_restriction(v3, v2) = v0))
% 6.07/1.68 |
% 6.07/1.68 | DELTA: instantiating (t18_wellord1) with fresh symbols all_11_0, all_11_1,
% 6.07/1.68 | all_11_2, all_11_3, all_11_4 gives:
% 6.07/1.68 | (6) ~ (all_11_0 = all_11_2) & relation_rng_restriction(all_11_4, all_11_1)
% 6.07/1.68 | = all_11_0 & relation_dom_restriction(all_11_3, all_11_4) = all_11_1 &
% 6.07/1.68 | relation(all_11_3) = 0 & relation_restriction(all_11_3, all_11_4) =
% 6.07/1.68 | all_11_2 & $i(all_11_0) & $i(all_11_1) & $i(all_11_2) & $i(all_11_3) &
% 6.07/1.68 | $i(all_11_4)
% 6.07/1.68 |
% 6.07/1.68 | ALPHA: (6) implies:
% 6.07/1.68 | (7) ~ (all_11_0 = all_11_2)
% 6.07/1.68 | (8) $i(all_11_4)
% 6.07/1.69 | (9) $i(all_11_3)
% 6.07/1.69 | (10) relation_restriction(all_11_3, all_11_4) = all_11_2
% 6.07/1.69 | (11) relation(all_11_3) = 0
% 6.07/1.69 | (12) relation_dom_restriction(all_11_3, all_11_4) = all_11_1
% 6.07/1.69 | (13) relation_rng_restriction(all_11_4, all_11_1) = all_11_0
% 6.07/1.69 |
% 6.07/1.69 | GROUND_INST: instantiating (2) with all_11_4, all_11_3, all_11_2, simplifying
% 6.07/1.69 | with (8), (9), (10) gives:
% 6.07/1.69 | (14) ? [v0: any] : ? [v1: $i] : ? [v2: $i] :
% 6.07/1.69 | (relation_rng_restriction(all_11_4, all_11_3) = v1 &
% 6.07/1.69 | relation_dom_restriction(v1, all_11_4) = v2 & relation(all_11_3) =
% 6.07/1.69 | v0 & $i(v2) & $i(v1) & ( ~ (v0 = 0) | v2 = all_11_2))
% 6.07/1.69 |
% 6.07/1.69 | GROUND_INST: instantiating (dt_k2_wellord1) with all_11_3, all_11_4, all_11_2,
% 6.07/1.69 | simplifying with (8), (9), (10) gives:
% 6.07/1.69 | (15) ? [v0: any] : ? [v1: any] : (relation(all_11_2) = v1 &
% 6.07/1.69 | relation(all_11_3) = v0 & ( ~ (v0 = 0) | v1 = 0))
% 6.07/1.69 |
% 6.07/1.69 | GROUND_INST: instantiating (dt_k7_relat_1) with all_11_3, all_11_4, all_11_1,
% 6.07/1.69 | simplifying with (8), (9), (12) gives:
% 6.07/1.69 | (16) ? [v0: any] : ? [v1: any] : (relation(all_11_1) = v1 &
% 6.07/1.69 | relation(all_11_3) = v0 & ( ~ (v0 = 0) | v1 = 0))
% 6.07/1.69 |
% 6.07/1.69 | GROUND_INST: instantiating (1) with all_11_4, all_11_4, all_11_3, all_11_1,
% 6.07/1.69 | all_11_0, simplifying with (8), (9), (12), (13) gives:
% 6.83/1.69 | (17) ? [v0: any] : ? [v1: $i] : ? [v2: $i] :
% 6.83/1.69 | (relation_rng_restriction(all_11_4, all_11_3) = v1 &
% 6.83/1.69 | relation_dom_restriction(v1, all_11_4) = v2 & relation(all_11_3) =
% 6.83/1.69 | v0 & $i(v2) & $i(v1) & ( ~ (v0 = 0) | v2 = all_11_0))
% 6.83/1.69 |
% 6.83/1.69 | DELTA: instantiating (16) with fresh symbols all_20_0, all_20_1 gives:
% 6.83/1.69 | (18) relation(all_11_1) = all_20_0 & relation(all_11_3) = all_20_1 & ( ~
% 6.83/1.69 | (all_20_1 = 0) | all_20_0 = 0)
% 6.83/1.69 |
% 6.83/1.69 | ALPHA: (18) implies:
% 6.83/1.69 | (19) relation(all_11_3) = all_20_1
% 6.83/1.69 |
% 6.83/1.69 | DELTA: instantiating (15) with fresh symbols all_24_0, all_24_1 gives:
% 6.83/1.69 | (20) relation(all_11_2) = all_24_0 & relation(all_11_3) = all_24_1 & ( ~
% 6.83/1.69 | (all_24_1 = 0) | all_24_0 = 0)
% 6.83/1.69 |
% 6.83/1.69 | ALPHA: (20) implies:
% 6.83/1.69 | (21) relation(all_11_3) = all_24_1
% 6.83/1.69 |
% 6.83/1.69 | DELTA: instantiating (14) with fresh symbols all_28_0, all_28_1, all_28_2
% 6.83/1.69 | gives:
% 6.83/1.70 | (22) relation_rng_restriction(all_11_4, all_11_3) = all_28_1 &
% 6.83/1.70 | relation_dom_restriction(all_28_1, all_11_4) = all_28_0 &
% 6.83/1.70 | relation(all_11_3) = all_28_2 & $i(all_28_0) & $i(all_28_1) & ( ~
% 6.83/1.70 | (all_28_2 = 0) | all_28_0 = all_11_2)
% 6.83/1.70 |
% 6.83/1.70 | ALPHA: (22) implies:
% 6.83/1.70 | (23) relation(all_11_3) = all_28_2
% 6.83/1.70 | (24) relation_dom_restriction(all_28_1, all_11_4) = all_28_0
% 6.83/1.70 | (25) relation_rng_restriction(all_11_4, all_11_3) = all_28_1
% 6.83/1.70 | (26) ~ (all_28_2 = 0) | all_28_0 = all_11_2
% 6.83/1.70 |
% 6.83/1.70 | DELTA: instantiating (17) with fresh symbols all_30_0, all_30_1, all_30_2
% 6.83/1.70 | gives:
% 6.83/1.70 | (27) relation_rng_restriction(all_11_4, all_11_3) = all_30_1 &
% 6.83/1.70 | relation_dom_restriction(all_30_1, all_11_4) = all_30_0 &
% 6.83/1.70 | relation(all_11_3) = all_30_2 & $i(all_30_0) & $i(all_30_1) & ( ~
% 6.83/1.70 | (all_30_2 = 0) | all_30_0 = all_11_0)
% 6.83/1.70 |
% 6.83/1.70 | ALPHA: (27) implies:
% 6.83/1.70 | (28) relation(all_11_3) = all_30_2
% 6.83/1.70 | (29) relation_dom_restriction(all_30_1, all_11_4) = all_30_0
% 6.83/1.70 | (30) relation_rng_restriction(all_11_4, all_11_3) = all_30_1
% 6.83/1.70 | (31) ~ (all_30_2 = 0) | all_30_0 = all_11_0
% 6.83/1.70 |
% 6.83/1.70 | GROUND_INST: instantiating (3) with 0, all_28_2, all_11_3, simplifying with
% 6.83/1.70 | (11), (23) gives:
% 6.83/1.70 | (32) all_28_2 = 0
% 6.83/1.70 |
% 6.83/1.70 | GROUND_INST: instantiating (3) with all_24_1, all_28_2, all_11_3, simplifying
% 6.83/1.70 | with (21), (23) gives:
% 6.83/1.70 | (33) all_28_2 = all_24_1
% 6.83/1.70 |
% 6.83/1.70 | GROUND_INST: instantiating (3) with all_28_2, all_30_2, all_11_3, simplifying
% 6.83/1.70 | with (23), (28) gives:
% 6.83/1.70 | (34) all_30_2 = all_28_2
% 6.83/1.70 |
% 6.83/1.70 | GROUND_INST: instantiating (3) with all_20_1, all_30_2, all_11_3, simplifying
% 6.83/1.70 | with (19), (28) gives:
% 6.83/1.70 | (35) all_30_2 = all_20_1
% 6.83/1.70 |
% 6.83/1.70 | GROUND_INST: instantiating (5) with all_28_1, all_30_1, all_11_3, all_11_4,
% 6.83/1.70 | simplifying with (25), (30) gives:
% 6.83/1.70 | (36) all_30_1 = all_28_1
% 6.83/1.70 |
% 6.83/1.70 | COMBINE_EQS: (34), (35) imply:
% 6.83/1.70 | (37) all_28_2 = all_20_1
% 6.83/1.70 |
% 6.83/1.70 | SIMP: (37) implies:
% 6.83/1.70 | (38) all_28_2 = all_20_1
% 6.83/1.70 |
% 6.83/1.70 | COMBINE_EQS: (32), (33) imply:
% 6.83/1.70 | (39) all_24_1 = 0
% 6.83/1.70 |
% 6.83/1.70 | COMBINE_EQS: (33), (38) imply:
% 6.83/1.70 | (40) all_24_1 = all_20_1
% 6.83/1.70 |
% 6.83/1.70 | COMBINE_EQS: (39), (40) imply:
% 6.83/1.70 | (41) all_20_1 = 0
% 6.83/1.70 |
% 6.83/1.70 | COMBINE_EQS: (35), (41) imply:
% 6.83/1.70 | (42) all_30_2 = 0
% 6.83/1.70 |
% 6.83/1.70 | REDUCE: (29), (36) imply:
% 6.83/1.70 | (43) relation_dom_restriction(all_28_1, all_11_4) = all_30_0
% 6.83/1.70 |
% 6.83/1.70 | BETA: splitting (31) gives:
% 6.83/1.70 |
% 6.83/1.70 | Case 1:
% 6.83/1.70 | |
% 6.83/1.70 | | (44) ~ (all_30_2 = 0)
% 6.83/1.70 | |
% 6.83/1.70 | | REDUCE: (42), (44) imply:
% 6.89/1.70 | | (45) $false
% 6.89/1.71 | |
% 6.89/1.71 | | CLOSE: (45) is inconsistent.
% 6.89/1.71 | |
% 6.89/1.71 | Case 2:
% 6.89/1.71 | |
% 6.89/1.71 | | (46) all_30_0 = all_11_0
% 6.89/1.71 | |
% 6.89/1.71 | | REDUCE: (43), (46) imply:
% 6.89/1.71 | | (47) relation_dom_restriction(all_28_1, all_11_4) = all_11_0
% 6.89/1.71 | |
% 6.89/1.71 | | BETA: splitting (26) gives:
% 6.89/1.71 | |
% 6.89/1.71 | | Case 1:
% 6.89/1.71 | | |
% 6.89/1.71 | | | (48) ~ (all_28_2 = 0)
% 6.89/1.71 | | |
% 6.89/1.71 | | | REDUCE: (32), (48) imply:
% 6.89/1.71 | | | (49) $false
% 6.89/1.71 | | |
% 6.89/1.71 | | | CLOSE: (49) is inconsistent.
% 6.89/1.71 | | |
% 6.89/1.71 | | Case 2:
% 6.89/1.71 | | |
% 6.89/1.71 | | | (50) all_28_0 = all_11_2
% 6.89/1.71 | | |
% 6.89/1.71 | | | REDUCE: (24), (50) imply:
% 6.89/1.71 | | | (51) relation_dom_restriction(all_28_1, all_11_4) = all_11_2
% 6.89/1.71 | | |
% 6.89/1.71 | | | GROUND_INST: instantiating (4) with all_11_2, all_11_0, all_11_4,
% 6.89/1.71 | | | all_28_1, simplifying with (47), (51) gives:
% 6.89/1.71 | | | (52) all_11_0 = all_11_2
% 6.89/1.71 | | |
% 6.89/1.71 | | | REDUCE: (7), (52) imply:
% 6.89/1.71 | | | (53) $false
% 6.89/1.71 | | |
% 6.89/1.71 | | | CLOSE: (53) is inconsistent.
% 6.89/1.71 | | |
% 6.89/1.71 | | End of split
% 6.89/1.71 | |
% 6.89/1.71 | End of split
% 6.89/1.71 |
% 6.89/1.71 End of proof
% 6.91/1.71 % SZS output end Proof for theBenchmark
% 6.91/1.71
% 6.91/1.71 1070ms
%------------------------------------------------------------------------------