TSTP Solution File: SEU444+1 by Princess---230619
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SEU444+1 : TPTP v8.1.2. Released v3.4.0.
% 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 17:44:52 EDT 2023
% Result : Theorem 7.97s 2.00s
% Output : Proof 10.06s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SEU444+1 : TPTP v8.1.2. Released v3.4.0.
% 0.00/0.14 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.15/0.35 % Computer : n006.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Thu Aug 24 00:15:38 EDT 2023
% 0.15/0.35 % CPUTime :
% 0.22/0.63 ________ _____
% 0.22/0.63 ___ __ \_________(_)________________________________
% 0.22/0.63 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.22/0.63 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.22/0.63 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.22/0.63
% 0.22/0.63 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.22/0.63 (2023-06-19)
% 0.22/0.63
% 0.22/0.63 (c) Philipp Rümmer, 2009-2023
% 0.22/0.63 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.22/0.63 Amanda Stjerna.
% 0.22/0.63 Free software under BSD-3-Clause.
% 0.22/0.63
% 0.22/0.63 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.22/0.63
% 0.22/0.63 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.22/0.64 Running up to 7 provers in parallel.
% 0.22/0.67 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.22/0.67 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.22/0.67 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.22/0.67 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.22/0.67 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.22/0.67 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 0.22/0.67 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 2.61/1.16 Prover 4: Preprocessing ...
% 2.61/1.16 Prover 1: Preprocessing ...
% 3.03/1.22 Prover 2: Preprocessing ...
% 3.03/1.22 Prover 6: Preprocessing ...
% 3.03/1.22 Prover 3: Preprocessing ...
% 3.03/1.22 Prover 0: Preprocessing ...
% 3.03/1.22 Prover 5: Preprocessing ...
% 6.09/1.69 Prover 1: Warning: ignoring some quantifiers
% 6.37/1.74 Prover 5: Proving ...
% 6.37/1.75 Prover 3: Warning: ignoring some quantifiers
% 6.37/1.76 Prover 1: Constructing countermodel ...
% 6.37/1.76 Prover 2: Proving ...
% 6.37/1.77 Prover 6: Proving ...
% 6.37/1.77 Prover 3: Constructing countermodel ...
% 6.37/1.79 Prover 4: Warning: ignoring some quantifiers
% 6.99/1.84 Prover 4: Constructing countermodel ...
% 6.99/1.88 Prover 0: Proving ...
% 7.97/2.00 Prover 3: proved (1341ms)
% 7.97/2.00
% 7.97/2.00 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 7.97/2.00
% 7.97/2.00 Prover 6: stopped
% 7.97/2.01 Prover 5: proved (1345ms)
% 7.97/2.01
% 7.97/2.01 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 7.97/2.01
% 7.97/2.01 Prover 0: stopped
% 7.97/2.01 Prover 2: stopped
% 7.97/2.01 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 7.97/2.01 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 7.97/2.01 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 7.97/2.02 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 7.97/2.02 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 8.14/2.11 Prover 13: Preprocessing ...
% 8.84/2.13 Prover 11: Preprocessing ...
% 8.84/2.14 Prover 7: Preprocessing ...
% 8.84/2.14 Prover 10: Preprocessing ...
% 8.84/2.14 Prover 8: Preprocessing ...
% 8.97/2.17 Prover 1: Found proof (size 25)
% 8.97/2.17 Prover 1: proved (1503ms)
% 8.97/2.17 Prover 4: stopped
% 8.97/2.20 Prover 10: stopped
% 8.97/2.21 Prover 7: stopped
% 8.97/2.21 Prover 13: stopped
% 8.97/2.21 Prover 11: stopped
% 9.42/2.26 Prover 8: Warning: ignoring some quantifiers
% 9.67/2.27 Prover 8: Constructing countermodel ...
% 9.67/2.28 Prover 8: stopped
% 9.67/2.28
% 9.67/2.28 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 9.67/2.28
% 9.67/2.29 % SZS output start Proof for theBenchmark
% 9.67/2.29 Assumptions after simplification:
% 9.67/2.29 ---------------------------------
% 9.67/2.29
% 9.67/2.29 (t51_relset_2)
% 9.67/2.32 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 9.67/2.32 (k10_relset_1(v0, v1, v3, v0) = v4) | ~ (k6_relset_1(v1, v0, v2) = v3) | ~
% 9.67/2.32 $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: $i] : ? [v7: $i] :
% 9.67/2.32 ? [v8: $i] : (k1_funct_5(v2) = v6 & k2_funct_5(v2) = v7 & k10_relset_1(v1,
% 9.67/2.32 v0, v2, v1) = v8 & m2_relset_1(v2, v1, v0) = v5 & $i(v8) & $i(v7) &
% 9.67/2.32 $i(v6) & ( ~ (v5 = 0) | (v8 = v7 & v6 = v4))))
% 9.67/2.32
% 9.67/2.32 (t56_relset_2)
% 9.67/2.32 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5:
% 9.67/2.32 $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] :
% 9.67/2.32 (k1_funct_5(v2) = v3 & k2_funct_5(v2) = v8 & k10_relset_1(v1, v0, v2, v1) = v6
% 9.67/2.32 & k10_relset_1(v0, v1, v4, v8) = v9 & k10_relset_1(v0, v1, v4, v6) = v7 &
% 9.67/2.32 k10_relset_1(v0, v1, v4, v0) = v5 & m2_relset_1(v2, v1, v0) = 0 &
% 9.67/2.32 k6_relset_1(v1, v0, v2) = v4 & $i(v9) & $i(v8) & $i(v7) & $i(v6) & $i(v5) &
% 9.67/2.32 $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & ( ~ (v9 = v7) | ~ (v5 = v3)))
% 9.67/2.32
% 9.67/2.32 (function-axioms)
% 9.67/2.33 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 9.67/2.33 $i] : (v1 = v0 | ~ (k10_relset_1(v5, v4, v3, v2) = v1) | ~
% 9.67/2.33 (k10_relset_1(v5, v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 9.67/2.33 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~
% 9.67/2.33 (m2_relset_1(v4, v3, v2) = v1) | ~ (m2_relset_1(v4, v3, v2) = v0)) & !
% 9.67/2.33 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 |
% 9.67/2.33 ~ (k6_relset_1(v4, v3, v2) = v1) | ~ (k6_relset_1(v4, v3, v2) = v0)) & !
% 9.67/2.33 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 9.67/2.33 $i] : ! [v4: $i] : (v1 = v0 | ~ (m1_relset_1(v4, v3, v2) = v1) | ~
% 9.67/2.33 (m1_relset_1(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 9.67/2.33 ! [v3: $i] : (v1 = v0 | ~ (k9_relat_1(v3, v2) = v1) | ~ (k9_relat_1(v3, v2)
% 9.67/2.33 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0
% 9.67/2.33 | ~ (k2_zfmisc_1(v3, v2) = v1) | ~ (k2_zfmisc_1(v3, v2) = v0)) & ! [v0:
% 9.67/2.33 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 9.67/2.33 : (v1 = v0 | ~ (r1_tarski(v3, v2) = v1) | ~ (r1_tarski(v3, v2) = v0)) & !
% 9.67/2.33 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 9.67/2.33 $i] : (v1 = v0 | ~ (m1_subset_1(v3, v2) = v1) | ~ (m1_subset_1(v3, v2) =
% 9.67/2.33 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 9.67/2.33 $i] : ! [v3: $i] : (v1 = v0 | ~ (r2_hidden(v3, v2) = v1) | ~
% 9.67/2.33 (r2_hidden(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 =
% 9.67/2.33 v0 | ~ (k1_funct_5(v2) = v1) | ~ (k1_funct_5(v2) = v0)) & ! [v0: $i] : !
% 9.67/2.33 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (k2_funct_5(v2) = v1) | ~
% 9.67/2.33 (k2_funct_5(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0
% 9.67/2.33 | ~ (k4_relat_1(v2) = v1) | ~ (k4_relat_1(v2) = v0)) & ! [v0: $i] : !
% 9.67/2.33 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (k1_zfmisc_1(v2) = v1) | ~
% 9.67/2.33 (k1_zfmisc_1(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 9.67/2.33 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (v1_xboole_0(v2) = v1) | ~
% 9.67/2.33 (v1_xboole_0(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 9.67/2.33 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (v1_relat_1(v2) = v1) | ~
% 9.67/2.33 (v1_relat_1(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 9.67/2.33 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (v3_relat_1(v2) = v1) | ~
% 9.67/2.33 (v3_relat_1(v2) = v0))
% 9.67/2.33
% 9.67/2.33 Further assumptions not needed in the proof:
% 9.67/2.33 --------------------------------------------
% 9.67/2.33 antisymmetry_r2_hidden, cc1_relat_1, cc1_relset_1, dt_k10_relset_1,
% 9.67/2.33 dt_k1_funct_5, dt_k1_xboole_0, dt_k1_zfmisc_1, dt_k2_funct_5, dt_k2_zfmisc_1,
% 9.67/2.33 dt_k4_relat_1, dt_k6_relset_1, dt_k9_relat_1, dt_m1_relset_1, dt_m1_subset_1,
% 9.67/2.33 dt_m2_relset_1, existence_m1_relset_1, existence_m1_subset_1,
% 9.67/2.33 existence_m2_relset_1, fc11_relat_1, fc12_relat_1, fc1_subset_1, fc1_sysrel,
% 9.67/2.33 fc4_relat_1, fc4_subset_1, involutiveness_k4_relat_1,
% 9.67/2.33 involutiveness_k6_relset_1, rc1_relat_1, rc1_subset_1, rc2_relat_1,
% 9.67/2.33 rc2_subset_1, rc3_relat_1, redefinition_k10_relset_1, redefinition_k6_relset_1,
% 9.67/2.33 redefinition_m2_relset_1, reflexivity_r1_tarski, t1_subset, t2_subset,
% 9.67/2.33 t3_subset, t4_subset, t5_subset, t6_boole, t7_boole, t8_boole
% 9.67/2.33
% 9.67/2.33 Those formulas are unsatisfiable:
% 9.67/2.33 ---------------------------------
% 9.67/2.33
% 9.67/2.33 Begin of proof
% 9.67/2.33 |
% 9.67/2.33 | ALPHA: (function-axioms) implies:
% 9.67/2.33 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (k2_funct_5(v2)
% 9.67/2.34 | = v1) | ~ (k2_funct_5(v2) = v0))
% 9.67/2.34 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (k1_funct_5(v2)
% 9.67/2.34 | = v1) | ~ (k1_funct_5(v2) = v0))
% 9.67/2.34 | (3) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 9.67/2.34 | ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (m2_relset_1(v4, v3, v2) =
% 9.67/2.34 | v1) | ~ (m2_relset_1(v4, v3, v2) = v0))
% 9.67/2.34 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 9.67/2.34 | ! [v5: $i] : (v1 = v0 | ~ (k10_relset_1(v5, v4, v3, v2) = v1) | ~
% 9.67/2.34 | (k10_relset_1(v5, v4, v3, v2) = v0))
% 9.67/2.34 |
% 9.67/2.34 | DELTA: instantiating (t56_relset_2) with fresh symbols all_42_0, all_42_1,
% 9.67/2.34 | all_42_2, all_42_3, all_42_4, all_42_5, all_42_6, all_42_7, all_42_8,
% 9.67/2.34 | all_42_9 gives:
% 9.67/2.34 | (5) k1_funct_5(all_42_7) = all_42_6 & k2_funct_5(all_42_7) = all_42_1 &
% 9.67/2.34 | k10_relset_1(all_42_8, all_42_9, all_42_7, all_42_8) = all_42_3 &
% 9.67/2.34 | k10_relset_1(all_42_9, all_42_8, all_42_5, all_42_1) = all_42_0 &
% 9.67/2.34 | k10_relset_1(all_42_9, all_42_8, all_42_5, all_42_3) = all_42_2 &
% 9.67/2.34 | k10_relset_1(all_42_9, all_42_8, all_42_5, all_42_9) = all_42_4 &
% 9.67/2.34 | m2_relset_1(all_42_7, all_42_8, all_42_9) = 0 & k6_relset_1(all_42_8,
% 9.67/2.34 | all_42_9, all_42_7) = all_42_5 & $i(all_42_0) & $i(all_42_1) &
% 9.67/2.34 | $i(all_42_2) & $i(all_42_3) & $i(all_42_4) & $i(all_42_5) &
% 9.67/2.34 | $i(all_42_6) & $i(all_42_7) & $i(all_42_8) & $i(all_42_9) & ( ~
% 9.67/2.34 | (all_42_0 = all_42_2) | ~ (all_42_4 = all_42_6))
% 9.67/2.34 |
% 9.67/2.34 | ALPHA: (5) implies:
% 9.67/2.34 | (6) $i(all_42_9)
% 9.67/2.34 | (7) $i(all_42_8)
% 9.67/2.34 | (8) $i(all_42_7)
% 9.67/2.34 | (9) k6_relset_1(all_42_8, all_42_9, all_42_7) = all_42_5
% 9.67/2.34 | (10) m2_relset_1(all_42_7, all_42_8, all_42_9) = 0
% 9.67/2.34 | (11) k10_relset_1(all_42_9, all_42_8, all_42_5, all_42_9) = all_42_4
% 9.67/2.34 | (12) k10_relset_1(all_42_9, all_42_8, all_42_5, all_42_3) = all_42_2
% 9.67/2.34 | (13) k10_relset_1(all_42_9, all_42_8, all_42_5, all_42_1) = all_42_0
% 9.67/2.34 | (14) k10_relset_1(all_42_8, all_42_9, all_42_7, all_42_8) = all_42_3
% 9.67/2.34 | (15) k2_funct_5(all_42_7) = all_42_1
% 9.67/2.34 | (16) k1_funct_5(all_42_7) = all_42_6
% 9.67/2.34 | (17) ~ (all_42_0 = all_42_2) | ~ (all_42_4 = all_42_6)
% 9.67/2.34 |
% 9.67/2.34 | GROUND_INST: instantiating (t51_relset_2) with all_42_9, all_42_8, all_42_7,
% 9.67/2.34 | all_42_5, all_42_4, simplifying with (6), (7), (8), (9), (11)
% 9.67/2.34 | gives:
% 9.67/2.34 | (18) ? [v0: any] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] :
% 9.67/2.34 | (k1_funct_5(all_42_7) = v1 & k2_funct_5(all_42_7) = v2 &
% 9.67/2.34 | k10_relset_1(all_42_8, all_42_9, all_42_7, all_42_8) = v3 &
% 9.67/2.34 | m2_relset_1(all_42_7, all_42_8, all_42_9) = v0 & $i(v3) & $i(v2) &
% 9.67/2.34 | $i(v1) & ( ~ (v0 = 0) | (v3 = v2 & v1 = all_42_4)))
% 9.67/2.34 |
% 9.67/2.34 | DELTA: instantiating (18) with fresh symbols all_50_0, all_50_1, all_50_2,
% 9.67/2.34 | all_50_3 gives:
% 10.06/2.35 | (19) k1_funct_5(all_42_7) = all_50_2 & k2_funct_5(all_42_7) = all_50_1 &
% 10.06/2.35 | k10_relset_1(all_42_8, all_42_9, all_42_7, all_42_8) = all_50_0 &
% 10.06/2.35 | m2_relset_1(all_42_7, all_42_8, all_42_9) = all_50_3 & $i(all_50_0) &
% 10.06/2.35 | $i(all_50_1) & $i(all_50_2) & ( ~ (all_50_3 = 0) | (all_50_0 =
% 10.06/2.35 | all_50_1 & all_50_2 = all_42_4))
% 10.06/2.35 |
% 10.06/2.35 | ALPHA: (19) implies:
% 10.06/2.35 | (20) m2_relset_1(all_42_7, all_42_8, all_42_9) = all_50_3
% 10.06/2.35 | (21) k10_relset_1(all_42_8, all_42_9, all_42_7, all_42_8) = all_50_0
% 10.06/2.35 | (22) k2_funct_5(all_42_7) = all_50_1
% 10.06/2.35 | (23) k1_funct_5(all_42_7) = all_50_2
% 10.06/2.35 | (24) ~ (all_50_3 = 0) | (all_50_0 = all_50_1 & all_50_2 = all_42_4)
% 10.06/2.35 |
% 10.06/2.35 | GROUND_INST: instantiating (3) with 0, all_50_3, all_42_9, all_42_8, all_42_7,
% 10.06/2.35 | simplifying with (10), (20) gives:
% 10.06/2.35 | (25) all_50_3 = 0
% 10.06/2.35 |
% 10.06/2.35 | GROUND_INST: instantiating (4) with all_42_3, all_50_0, all_42_8, all_42_7,
% 10.06/2.35 | all_42_9, all_42_8, simplifying with (14), (21) gives:
% 10.06/2.35 | (26) all_50_0 = all_42_3
% 10.06/2.35 |
% 10.06/2.35 | GROUND_INST: instantiating (1) with all_42_1, all_50_1, all_42_7, simplifying
% 10.06/2.35 | with (15), (22) gives:
% 10.06/2.35 | (27) all_50_1 = all_42_1
% 10.06/2.35 |
% 10.06/2.35 | GROUND_INST: instantiating (2) with all_42_6, all_50_2, all_42_7, simplifying
% 10.06/2.35 | with (16), (23) gives:
% 10.06/2.35 | (28) all_50_2 = all_42_6
% 10.06/2.35 |
% 10.06/2.35 | BETA: splitting (24) gives:
% 10.06/2.35 |
% 10.06/2.35 | Case 1:
% 10.06/2.35 | |
% 10.06/2.35 | | (29) ~ (all_50_3 = 0)
% 10.06/2.35 | |
% 10.06/2.35 | | REDUCE: (25), (29) imply:
% 10.06/2.35 | | (30) $false
% 10.06/2.35 | |
% 10.06/2.35 | | CLOSE: (30) is inconsistent.
% 10.06/2.35 | |
% 10.06/2.35 | Case 2:
% 10.06/2.35 | |
% 10.06/2.35 | | (31) all_50_0 = all_50_1 & all_50_2 = all_42_4
% 10.06/2.35 | |
% 10.06/2.35 | | ALPHA: (31) implies:
% 10.06/2.35 | | (32) all_50_2 = all_42_4
% 10.06/2.35 | | (33) all_50_0 = all_50_1
% 10.06/2.35 | |
% 10.06/2.35 | | COMBINE_EQS: (26), (33) imply:
% 10.06/2.35 | | (34) all_50_1 = all_42_3
% 10.06/2.35 | |
% 10.06/2.35 | | SIMP: (34) implies:
% 10.06/2.35 | | (35) all_50_1 = all_42_3
% 10.06/2.35 | |
% 10.06/2.35 | | COMBINE_EQS: (27), (35) imply:
% 10.06/2.35 | | (36) all_42_1 = all_42_3
% 10.06/2.35 | |
% 10.06/2.35 | | COMBINE_EQS: (28), (32) imply:
% 10.06/2.35 | | (37) all_42_4 = all_42_6
% 10.06/2.35 | |
% 10.06/2.35 | | REDUCE: (13), (36) imply:
% 10.06/2.35 | | (38) k10_relset_1(all_42_9, all_42_8, all_42_5, all_42_3) = all_42_0
% 10.06/2.35 | |
% 10.06/2.35 | | BETA: splitting (17) gives:
% 10.06/2.35 | |
% 10.06/2.35 | | Case 1:
% 10.06/2.35 | | |
% 10.06/2.35 | | | (39) ~ (all_42_0 = all_42_2)
% 10.06/2.35 | | |
% 10.06/2.35 | | | GROUND_INST: instantiating (4) with all_42_2, all_42_0, all_42_3,
% 10.06/2.35 | | | all_42_5, all_42_8, all_42_9, simplifying with (12), (38)
% 10.06/2.35 | | | gives:
% 10.06/2.35 | | | (40) all_42_0 = all_42_2
% 10.06/2.35 | | |
% 10.06/2.36 | | | REDUCE: (39), (40) imply:
% 10.06/2.36 | | | (41) $false
% 10.06/2.36 | | |
% 10.06/2.36 | | | CLOSE: (41) is inconsistent.
% 10.06/2.36 | | |
% 10.06/2.36 | | Case 2:
% 10.06/2.36 | | |
% 10.06/2.36 | | | (42) ~ (all_42_4 = all_42_6)
% 10.06/2.36 | | |
% 10.06/2.36 | | | REDUCE: (37), (42) imply:
% 10.06/2.36 | | | (43) $false
% 10.06/2.36 | | |
% 10.06/2.36 | | | CLOSE: (43) is inconsistent.
% 10.06/2.36 | | |
% 10.06/2.36 | | End of split
% 10.06/2.36 | |
% 10.06/2.36 | End of split
% 10.06/2.36 |
% 10.06/2.36 End of proof
% 10.06/2.36 % SZS output end Proof for theBenchmark
% 10.06/2.36
% 10.06/2.36 1727ms
%------------------------------------------------------------------------------