TSTP Solution File: HAL003+3 by Princess---230619
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : HAL003+3 : TPTP v8.1.2. Released v2.6.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n022.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 01:53:48 EDT 2023
% Result : Theorem 14.06s 2.83s
% Output : Proof 19.31s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : HAL003+3 : TPTP v8.1.2. Released v2.6.0.
% 0.00/0.11 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.11/0.32 % Computer : n022.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Mon Aug 28 02:32:09 EDT 2023
% 0.11/0.32 % CPUTime :
% 0.17/0.60 ________ _____
% 0.17/0.60 ___ __ \_________(_)________________________________
% 0.17/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.17/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.17/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.17/0.60
% 0.17/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.17/0.60 (2023-06-19)
% 0.17/0.60
% 0.17/0.60 (c) Philipp Rümmer, 2009-2023
% 0.17/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.17/0.60 Amanda Stjerna.
% 0.17/0.60 Free software under BSD-3-Clause.
% 0.17/0.60
% 0.17/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.17/0.60
% 0.17/0.60 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.17/0.61 Running up to 7 provers in parallel.
% 0.17/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.17/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.17/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.17/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.17/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.17/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.17/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 3.21/1.20 Prover 4: Preprocessing ...
% 3.21/1.20 Prover 1: Preprocessing ...
% 3.71/1.25 Prover 6: Preprocessing ...
% 3.71/1.25 Prover 5: Preprocessing ...
% 3.71/1.25 Prover 3: Preprocessing ...
% 3.71/1.25 Prover 2: Preprocessing ...
% 3.71/1.25 Prover 0: Preprocessing ...
% 8.92/2.03 Prover 3: Constructing countermodel ...
% 8.92/2.04 Prover 5: Proving ...
% 8.92/2.06 Prover 2: Proving ...
% 8.92/2.07 Prover 6: Proving ...
% 8.92/2.09 Prover 1: Constructing countermodel ...
% 10.99/2.40 Prover 4: Constructing countermodel ...
% 12.41/2.54 Prover 0: Proving ...
% 14.06/2.83 Prover 3: proved (2204ms)
% 14.06/2.83
% 14.06/2.83 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 14.06/2.83
% 14.06/2.83 Prover 2: stopped
% 14.06/2.83 Prover 0: stopped
% 14.06/2.84 Prover 6: stopped
% 14.06/2.84 Prover 5: stopped
% 14.06/2.85 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 14.06/2.85 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 14.06/2.85 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 14.06/2.85 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 14.06/2.85 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 14.06/2.93 Prover 11: Preprocessing ...
% 14.06/2.94 Prover 8: Preprocessing ...
% 14.06/2.95 Prover 13: Preprocessing ...
% 14.06/2.97 Prover 10: Preprocessing ...
% 14.06/2.99 Prover 7: Preprocessing ...
% 16.48/3.12 Prover 13: Warning: ignoring some quantifiers
% 16.48/3.12 Prover 7: Constructing countermodel ...
% 16.48/3.14 Prover 13: Constructing countermodel ...
% 16.79/3.16 Prover 10: Constructing countermodel ...
% 16.79/3.21 Prover 8: Warning: ignoring some quantifiers
% 16.79/3.22 Prover 8: Constructing countermodel ...
% 18.27/3.38 Prover 1: Found proof (size 45)
% 18.27/3.38 Prover 1: proved (2764ms)
% 18.27/3.38 Prover 13: stopped
% 18.27/3.38 Prover 10: stopped
% 18.27/3.39 Prover 8: stopped
% 18.27/3.39 Prover 4: stopped
% 18.27/3.39 Prover 7: stopped
% 18.66/3.42 Prover 11: Constructing countermodel ...
% 18.66/3.44 Prover 11: stopped
% 18.66/3.44
% 18.66/3.44 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 18.66/3.44
% 18.66/3.45 % SZS output start Proof for theBenchmark
% 18.89/3.46 Assumptions after simplification:
% 18.89/3.46 ---------------------------------
% 18.89/3.46
% 18.89/3.46 (g_morphism)
% 18.89/3.49 morphism(g, b, e) = 0 & $i(g) & $i(e) & $i(b)
% 18.89/3.49
% 18.89/3.49 (g_surjection)
% 18.89/3.50 $i(g) & ? [v0: int] : ( ~ (v0 = 0) & surjection(g) = v0)
% 18.89/3.50
% 18.89/3.50 (lemma12)
% 18.89/3.50 $i(g) & $i(e) & $i(b) & ! [v0: $i] : ( ~ (element(v0, e) = 0) | ~ $i(v0) |
% 18.89/3.50 ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : (subtract(b, v1, v2) = v3 &
% 18.89/3.50 apply(g, v3) = v0 & element(v2, b) = 0 & element(v1, b) = 0 & $i(v3) &
% 18.89/3.50 $i(v2) & $i(v1)))
% 18.89/3.50
% 18.89/3.50 (lemma8)
% 18.89/3.51 $i(g) & $i(f) & $i(e) & $i(gamma) & $i(b) & $i(a) & $i(alpha) & ! [v0: $i] :
% 18.89/3.51 ( ~ (element(v0, e) = 0) | ~ $i(v0) | ? [v1: $i] : ? [v2: $i] : ? [v3: $i]
% 18.89/3.51 : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : (subtract(e, v4, v0) = v2 &
% 18.89/3.51 apply(g, v6) = v2 & apply(g, v1) = v4 & apply(f, v3) = v5 & apply(gamma,
% 18.89/3.51 v5) = v2 & apply(alpha, v3) = v6 & element(v3, a) = 0 & element(v2, e) =
% 18.89/3.51 0 & element(v1, b) = 0 & $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) &
% 18.89/3.51 $i(v1)))
% 18.89/3.51
% 18.89/3.51 (properties_for_surjection)
% 18.89/3.51 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (morphism(v0, v1, v2) = 0) | ~
% 18.89/3.51 $i(v2) | ~ $i(v1) | ~ $i(v0) | surjection(v0) = 0 | ? [v3: $i] :
% 18.89/3.51 (element(v3, v2) = 0 & $i(v3) & ! [v4: $i] : ( ~ (element(v4, v1) = 0) | ~
% 18.89/3.51 $i(v4) | ? [v5: $i] : ( ~ (v5 = v3) & apply(v0, v4) = v5 & $i(v5)))))
% 18.89/3.51
% 18.89/3.51 (subtract_distribution)
% 18.89/3.52 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (morphism(v0, v1, v2) = 0) | ~
% 18.89/3.52 $i(v2) | ~ $i(v1) | ~ $i(v0) | ! [v3: $i] : ! [v4: $i] : ! [v5: $i] :
% 18.89/3.52 ! [v6: $i] : ! [v7: $i] : ( ~ (subtract(v2, v5, v6) = v7) | ~ (apply(v0,
% 18.89/3.52 v4) = v6) | ~ (apply(v0, v3) = v5) | ~ $i(v4) | ~ $i(v3) | ? [v8:
% 18.89/3.52 any] : ? [v9: any] : ? [v10: $i] : ? [v11: $i] : (subtract(v1, v3,
% 18.89/3.52 v4) = v10 & apply(v0, v10) = v11 & element(v4, v1) = v9 & element(v3,
% 18.89/3.52 v1) = v8 & $i(v11) & $i(v10) & ( ~ (v9 = 0) | ~ (v8 = 0) | v11 =
% 18.89/3.52 v7))))
% 18.89/3.52
% 18.89/3.52 (subtract_in_domain)
% 18.89/3.52 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0
% 18.89/3.52 | ~ (subtract(v0, v1, v2) = v3) | ~ (element(v3, v0) = v4) | ~ $i(v2) |
% 18.89/3.52 ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : (element(v2, v0) = v6 &
% 18.89/3.52 element(v1, v0) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0))))
% 18.89/3.52
% 18.89/3.52 (function-axioms)
% 18.89/3.53 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 18.89/3.53 [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v1 = v0 | ~ (commute(v5, v4, v3, v2)
% 18.89/3.53 = v1) | ~ (commute(v5, v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] :
% 18.89/3.53 ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (subtract(v4, v3, v2) =
% 18.89/3.53 v1) | ~ (subtract(v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : !
% 18.89/3.53 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 |
% 18.89/3.53 ~ (morphism(v4, v3, v2) = v1) | ~ (morphism(v4, v3, v2) = v0)) & ! [v0:
% 18.89/3.53 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 18.89/3.53 : (v1 = v0 | ~ (exact(v3, v2) = v1) | ~ (exact(v3, v2) = v0)) & ! [v0: $i]
% 18.89/3.53 : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (apply(v3, v2) = v1)
% 18.89/3.53 | ~ (apply(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 18.89/3.53 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (element(v3,
% 18.89/3.53 v2) = v1) | ~ (element(v3, v2) = v0)) & ! [v0: MultipleValueBool] : !
% 18.89/3.53 [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (surjection(v2) = v1) |
% 18.89/3.53 ~ (surjection(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 18.89/3.53 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (injection(v2) = v1) | ~
% 18.89/3.53 (injection(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 |
% 18.89/3.53 ~ (zero(v2) = v1) | ~ (zero(v2) = v0))
% 18.89/3.53
% 18.89/3.53 Further assumptions not needed in the proof:
% 18.89/3.53 --------------------------------------------
% 18.89/3.53 alpha_beta_exact, alpha_g_f_gamma_commute, alpha_injection, alpha_morphism,
% 18.89/3.53 beta_h_g_delta_commute, beta_morphism, beta_surjection, commute_properties,
% 18.89/3.53 delta_morphism, delta_surjection, exact_properties, f_morphism, f_surjection,
% 18.89/3.53 gamma_delta_exact, gamma_injection, gamma_morphism, h_morphism, h_surjection,
% 18.89/3.53 injection_properties, lemma3, morphism, properties_for_commute,
% 18.89/3.53 properties_for_exact, properties_for_injection, subtract_cancellation,
% 18.89/3.53 subtract_to_0, surjection_properties
% 18.89/3.53
% 18.89/3.53 Those formulas are unsatisfiable:
% 18.89/3.53 ---------------------------------
% 18.89/3.53
% 18.89/3.53 Begin of proof
% 18.89/3.54 |
% 18.89/3.54 | ALPHA: (g_morphism) implies:
% 18.89/3.54 | (1) morphism(g, b, e) = 0
% 18.89/3.54 |
% 18.89/3.54 | ALPHA: (lemma8) implies:
% 18.89/3.54 | (2) ! [v0: $i] : ( ~ (element(v0, e) = 0) | ~ $i(v0) | ? [v1: $i] : ?
% 18.89/3.54 | [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] :
% 18.89/3.54 | (subtract(e, v4, v0) = v2 & apply(g, v6) = v2 & apply(g, v1) = v4 &
% 18.89/3.54 | apply(f, v3) = v5 & apply(gamma, v5) = v2 & apply(alpha, v3) = v6 &
% 18.89/3.54 | element(v3, a) = 0 & element(v2, e) = 0 & element(v1, b) = 0 &
% 18.89/3.54 | $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1)))
% 18.89/3.54 |
% 18.89/3.54 | ALPHA: (lemma12) implies:
% 18.89/3.54 | (3) $i(b)
% 18.89/3.54 | (4) $i(e)
% 19.31/3.54 | (5) ! [v0: $i] : ( ~ (element(v0, e) = 0) | ~ $i(v0) | ? [v1: $i] : ?
% 19.31/3.54 | [v2: $i] : ? [v3: $i] : (subtract(b, v1, v2) = v3 & apply(g, v3) =
% 19.31/3.54 | v0 & element(v2, b) = 0 & element(v1, b) = 0 & $i(v3) & $i(v2) &
% 19.31/3.54 | $i(v1)))
% 19.31/3.54 |
% 19.31/3.54 | ALPHA: (g_surjection) implies:
% 19.31/3.54 | (6) $i(g)
% 19.31/3.55 | (7) ? [v0: int] : ( ~ (v0 = 0) & surjection(g) = v0)
% 19.31/3.55 |
% 19.31/3.55 | ALPHA: (function-axioms) implies:
% 19.31/3.55 | (8) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 19.31/3.55 | (v1 = v0 | ~ (surjection(v2) = v1) | ~ (surjection(v2) = v0))
% 19.31/3.55 | (9) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 19.31/3.55 | ! [v3: $i] : (v1 = v0 | ~ (element(v3, v2) = v1) | ~ (element(v3,
% 19.31/3.55 | v2) = v0))
% 19.31/3.55 | (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 19.31/3.55 | (apply(v3, v2) = v1) | ~ (apply(v3, v2) = v0))
% 19.31/3.55 |
% 19.31/3.55 | DELTA: instantiating (7) with fresh symbol all_20_0 gives:
% 19.31/3.55 | (11) ~ (all_20_0 = 0) & surjection(g) = all_20_0
% 19.31/3.55 |
% 19.31/3.55 | ALPHA: (11) implies:
% 19.31/3.55 | (12) ~ (all_20_0 = 0)
% 19.31/3.55 | (13) surjection(g) = all_20_0
% 19.31/3.55 |
% 19.31/3.55 | GROUND_INST: instantiating (properties_for_surjection) with g, b, e,
% 19.31/3.55 | simplifying with (1), (3), (4), (6) gives:
% 19.31/3.55 | (14) surjection(g) = 0 | ? [v0: $i] : (element(v0, e) = 0 & $i(v0) & !
% 19.31/3.55 | [v1: $i] : ( ~ (element(v1, b) = 0) | ~ $i(v1) | ? [v2: $i] : ( ~
% 19.31/3.55 | (v2 = v0) & apply(g, v1) = v2 & $i(v2))))
% 19.31/3.55 |
% 19.31/3.55 | GROUND_INST: instantiating (subtract_distribution) with g, b, e, simplifying
% 19.31/3.55 | with (1), (3), (4), (6) gives:
% 19.31/3.56 | (15) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 19.31/3.56 | ( ~ (subtract(e, v2, v3) = v4) | ~ (apply(g, v1) = v3) | ~ (apply(g,
% 19.31/3.56 | v0) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any]
% 19.31/3.56 | : ? [v7: $i] : ? [v8: $i] : (subtract(b, v0, v1) = v7 & apply(g,
% 19.31/3.56 | v7) = v8 & element(v1, b) = v6 & element(v0, b) = v5 & $i(v8) &
% 19.31/3.56 | $i(v7) & ( ~ (v6 = 0) | ~ (v5 = 0) | v8 = v4)))
% 19.31/3.56 |
% 19.31/3.56 | BETA: splitting (14) gives:
% 19.31/3.56 |
% 19.31/3.56 | Case 1:
% 19.31/3.56 | |
% 19.31/3.56 | | (16) surjection(g) = 0
% 19.31/3.56 | |
% 19.31/3.56 | | GROUND_INST: instantiating (8) with all_20_0, 0, g, simplifying with (13),
% 19.31/3.56 | | (16) gives:
% 19.31/3.56 | | (17) all_20_0 = 0
% 19.31/3.56 | |
% 19.31/3.56 | | REDUCE: (12), (17) imply:
% 19.31/3.56 | | (18) $false
% 19.31/3.56 | |
% 19.31/3.56 | | CLOSE: (18) is inconsistent.
% 19.31/3.56 | |
% 19.31/3.56 | Case 2:
% 19.31/3.56 | |
% 19.31/3.56 | | (19) ? [v0: $i] : (element(v0, e) = 0 & $i(v0) & ! [v1: $i] : ( ~
% 19.31/3.56 | | (element(v1, b) = 0) | ~ $i(v1) | ? [v2: $i] : ( ~ (v2 = v0) &
% 19.31/3.56 | | apply(g, v1) = v2 & $i(v2))))
% 19.31/3.56 | |
% 19.31/3.56 | | DELTA: instantiating (19) with fresh symbol all_53_0 gives:
% 19.31/3.56 | | (20) element(all_53_0, e) = 0 & $i(all_53_0) & ! [v0: $i] : ( ~
% 19.31/3.56 | | (element(v0, b) = 0) | ~ $i(v0) | ? [v1: any] : ( ~ (v1 =
% 19.31/3.56 | | all_53_0) & apply(g, v0) = v1 & $i(v1)))
% 19.31/3.56 | |
% 19.31/3.56 | | ALPHA: (20) implies:
% 19.31/3.56 | | (21) $i(all_53_0)
% 19.31/3.56 | | (22) element(all_53_0, e) = 0
% 19.31/3.56 | | (23) ! [v0: $i] : ( ~ (element(v0, b) = 0) | ~ $i(v0) | ? [v1: any] :
% 19.31/3.56 | | ( ~ (v1 = all_53_0) & apply(g, v0) = v1 & $i(v1)))
% 19.31/3.56 | |
% 19.31/3.56 | | GROUND_INST: instantiating (2) with all_53_0, simplifying with (21), (22)
% 19.31/3.56 | | gives:
% 19.31/3.57 | | (24) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i]
% 19.31/3.57 | | : ? [v5: $i] : (subtract(e, v3, all_53_0) = v1 & apply(g, v5) = v1
% 19.31/3.57 | | & apply(g, v0) = v3 & apply(f, v2) = v4 & apply(gamma, v4) = v1 &
% 19.31/3.57 | | apply(alpha, v2) = v5 & element(v2, a) = 0 & element(v1, e) = 0 &
% 19.31/3.57 | | element(v0, b) = 0 & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) &
% 19.31/3.57 | | $i(v0))
% 19.31/3.57 | |
% 19.31/3.57 | | GROUND_INST: instantiating (5) with all_53_0, simplifying with (21), (22)
% 19.31/3.57 | | gives:
% 19.31/3.57 | | (25) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (subtract(b, v0, v1) = v2
% 19.31/3.57 | | & apply(g, v2) = all_53_0 & element(v1, b) = 0 & element(v0, b) =
% 19.31/3.57 | | 0 & $i(v2) & $i(v1) & $i(v0))
% 19.31/3.57 | |
% 19.31/3.57 | | DELTA: instantiating (25) with fresh symbols all_61_0, all_61_1, all_61_2
% 19.31/3.57 | | gives:
% 19.31/3.57 | | (26) subtract(b, all_61_2, all_61_1) = all_61_0 & apply(g, all_61_0) =
% 19.31/3.57 | | all_53_0 & element(all_61_1, b) = 0 & element(all_61_2, b) = 0 &
% 19.31/3.57 | | $i(all_61_0) & $i(all_61_1) & $i(all_61_2)
% 19.31/3.57 | |
% 19.31/3.57 | | ALPHA: (26) implies:
% 19.31/3.57 | | (27) $i(all_61_2)
% 19.31/3.57 | | (28) $i(all_61_1)
% 19.31/3.57 | | (29) $i(all_61_0)
% 19.31/3.57 | | (30) element(all_61_2, b) = 0
% 19.31/3.57 | | (31) element(all_61_1, b) = 0
% 19.31/3.57 | | (32) apply(g, all_61_0) = all_53_0
% 19.31/3.57 | | (33) subtract(b, all_61_2, all_61_1) = all_61_0
% 19.31/3.57 | |
% 19.31/3.57 | | DELTA: instantiating (24) with fresh symbols all_63_0, all_63_1, all_63_2,
% 19.31/3.57 | | all_63_3, all_63_4, all_63_5 gives:
% 19.31/3.57 | | (34) subtract(e, all_63_2, all_53_0) = all_63_4 & apply(g, all_63_0) =
% 19.31/3.57 | | all_63_4 & apply(g, all_63_5) = all_63_2 & apply(f, all_63_3) =
% 19.31/3.57 | | all_63_1 & apply(gamma, all_63_1) = all_63_4 & apply(alpha,
% 19.31/3.57 | | all_63_3) = all_63_0 & element(all_63_3, a) = 0 &
% 19.31/3.57 | | element(all_63_4, e) = 0 & element(all_63_5, b) = 0 & $i(all_63_0) &
% 19.31/3.57 | | $i(all_63_1) & $i(all_63_2) & $i(all_63_3) & $i(all_63_4) &
% 19.31/3.57 | | $i(all_63_5)
% 19.31/3.57 | |
% 19.31/3.57 | | ALPHA: (34) implies:
% 19.31/3.57 | | (35) $i(all_63_5)
% 19.31/3.57 | | (36) apply(g, all_63_5) = all_63_2
% 19.31/3.57 | | (37) subtract(e, all_63_2, all_53_0) = all_63_4
% 19.31/3.57 | |
% 19.31/3.57 | | GROUND_INST: instantiating (15) with all_63_5, all_61_0, all_63_2, all_53_0,
% 19.31/3.57 | | all_63_4, simplifying with (29), (32), (35), (36), (37) gives:
% 19.31/3.57 | | (38) ? [v0: any] : ? [v1: any] : ? [v2: $i] : ? [v3: $i] :
% 19.31/3.58 | | (subtract(b, all_63_5, all_61_0) = v2 & apply(g, v2) = v3 &
% 19.31/3.58 | | element(all_63_5, b) = v0 & element(all_61_0, b) = v1 & $i(v3) &
% 19.31/3.58 | | $i(v2) & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = all_63_4))
% 19.31/3.58 | |
% 19.31/3.58 | | DELTA: instantiating (38) with fresh symbols all_78_0, all_78_1, all_78_2,
% 19.31/3.58 | | all_78_3 gives:
% 19.31/3.58 | | (39) subtract(b, all_63_5, all_61_0) = all_78_1 & apply(g, all_78_1) =
% 19.31/3.58 | | all_78_0 & element(all_63_5, b) = all_78_3 & element(all_61_0, b) =
% 19.31/3.58 | | all_78_2 & $i(all_78_0) & $i(all_78_1) & ( ~ (all_78_2 = 0) | ~
% 19.31/3.58 | | (all_78_3 = 0) | all_78_0 = all_63_4)
% 19.31/3.58 | |
% 19.31/3.58 | | ALPHA: (39) implies:
% 19.31/3.58 | | (40) element(all_61_0, b) = all_78_2
% 19.31/3.58 | |
% 19.31/3.58 | | GROUND_INST: instantiating (subtract_in_domain) with b, all_61_2, all_61_1,
% 19.31/3.58 | | all_61_0, all_78_2, simplifying with (3), (27), (28), (33),
% 19.31/3.58 | | (40) gives:
% 19.31/3.58 | | (41) all_78_2 = 0 | ? [v0: any] : ? [v1: any] : (element(all_61_1, b) =
% 19.31/3.58 | | v1 & element(all_61_2, b) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 19.31/3.58 | |
% 19.31/3.58 | | BETA: splitting (41) gives:
% 19.31/3.58 | |
% 19.31/3.58 | | Case 1:
% 19.31/3.58 | | |
% 19.31/3.58 | | | (42) all_78_2 = 0
% 19.31/3.58 | | |
% 19.31/3.58 | | | REDUCE: (40), (42) imply:
% 19.31/3.58 | | | (43) element(all_61_0, b) = 0
% 19.31/3.58 | | |
% 19.31/3.58 | | | GROUND_INST: instantiating (23) with all_61_0, simplifying with (29), (43)
% 19.31/3.58 | | | gives:
% 19.31/3.58 | | | (44) ? [v0: any] : ( ~ (v0 = all_53_0) & apply(g, all_61_0) = v0 &
% 19.31/3.58 | | | $i(v0))
% 19.31/3.58 | | |
% 19.31/3.58 | | | DELTA: instantiating (44) with fresh symbol all_130_0 gives:
% 19.31/3.58 | | | (45) ~ (all_130_0 = all_53_0) & apply(g, all_61_0) = all_130_0 &
% 19.31/3.58 | | | $i(all_130_0)
% 19.31/3.58 | | |
% 19.31/3.58 | | | ALPHA: (45) implies:
% 19.31/3.58 | | | (46) ~ (all_130_0 = all_53_0)
% 19.31/3.58 | | | (47) apply(g, all_61_0) = all_130_0
% 19.31/3.58 | | |
% 19.31/3.58 | | | GROUND_INST: instantiating (10) with all_53_0, all_130_0, all_61_0, g,
% 19.31/3.58 | | | simplifying with (32), (47) gives:
% 19.31/3.58 | | | (48) all_130_0 = all_53_0
% 19.31/3.58 | | |
% 19.31/3.58 | | | REDUCE: (46), (48) imply:
% 19.31/3.58 | | | (49) $false
% 19.31/3.58 | | |
% 19.31/3.58 | | | CLOSE: (49) is inconsistent.
% 19.31/3.58 | | |
% 19.31/3.58 | | Case 2:
% 19.31/3.58 | | |
% 19.31/3.58 | | | (50) ? [v0: any] : ? [v1: any] : (element(all_61_1, b) = v1 &
% 19.31/3.58 | | | element(all_61_2, b) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 19.31/3.58 | | |
% 19.31/3.58 | | | DELTA: instantiating (50) with fresh symbols all_109_0, all_109_1 gives:
% 19.31/3.58 | | | (51) element(all_61_1, b) = all_109_0 & element(all_61_2, b) =
% 19.31/3.58 | | | all_109_1 & ( ~ (all_109_0 = 0) | ~ (all_109_1 = 0))
% 19.31/3.58 | | |
% 19.31/3.58 | | | ALPHA: (51) implies:
% 19.31/3.58 | | | (52) element(all_61_2, b) = all_109_1
% 19.31/3.59 | | | (53) element(all_61_1, b) = all_109_0
% 19.31/3.59 | | | (54) ~ (all_109_0 = 0) | ~ (all_109_1 = 0)
% 19.31/3.59 | | |
% 19.31/3.59 | | | GROUND_INST: instantiating (9) with 0, all_109_1, b, all_61_2, simplifying
% 19.31/3.59 | | | with (30), (52) gives:
% 19.31/3.59 | | | (55) all_109_1 = 0
% 19.31/3.59 | | |
% 19.31/3.59 | | | GROUND_INST: instantiating (9) with 0, all_109_0, b, all_61_1, simplifying
% 19.31/3.59 | | | with (31), (53) gives:
% 19.31/3.59 | | | (56) all_109_0 = 0
% 19.31/3.59 | | |
% 19.31/3.59 | | | BETA: splitting (54) gives:
% 19.31/3.59 | | |
% 19.31/3.59 | | | Case 1:
% 19.31/3.59 | | | |
% 19.31/3.59 | | | | (57) ~ (all_109_0 = 0)
% 19.31/3.59 | | | |
% 19.31/3.59 | | | | REDUCE: (56), (57) imply:
% 19.31/3.59 | | | | (58) $false
% 19.31/3.59 | | | |
% 19.31/3.59 | | | | CLOSE: (58) is inconsistent.
% 19.31/3.59 | | | |
% 19.31/3.59 | | | Case 2:
% 19.31/3.59 | | | |
% 19.31/3.59 | | | | (59) ~ (all_109_1 = 0)
% 19.31/3.59 | | | |
% 19.31/3.59 | | | | REDUCE: (55), (59) imply:
% 19.31/3.59 | | | | (60) $false
% 19.31/3.59 | | | |
% 19.31/3.59 | | | | CLOSE: (60) is inconsistent.
% 19.31/3.59 | | | |
% 19.31/3.59 | | | End of split
% 19.31/3.59 | | |
% 19.31/3.59 | | End of split
% 19.31/3.59 | |
% 19.31/3.59 | End of split
% 19.31/3.59 |
% 19.31/3.59 End of proof
% 19.31/3.59 % SZS output end Proof for theBenchmark
% 19.31/3.59
% 19.31/3.59 2992ms
%------------------------------------------------------------------------------