TSTP Solution File: SEU198+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SEU198+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 : n014.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 17:43:12 EDT 2023
% Result : Theorem 6.68s 1.68s
% Output : Proof 8.75s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU198+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.34 % Computer : n014.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Wed Aug 23 18:42:19 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.20/0.61 ________ _____
% 0.20/0.61 ___ __ \_________(_)________________________________
% 0.20/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.20/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.20/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.20/0.61
% 0.20/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.20/0.61 (2023-06-19)
% 0.20/0.61
% 0.20/0.61 (c) Philipp Rümmer, 2009-2023
% 0.20/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.20/0.61 Amanda Stjerna.
% 0.20/0.61 Free software under BSD-3-Clause.
% 0.20/0.61
% 0.20/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.20/0.61
% 0.20/0.61 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.20/0.62 Running up to 7 provers in parallel.
% 0.20/0.65 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.20/0.65 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.20/0.65 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.20/0.65 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.20/0.65 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.20/0.65 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.20/0.65 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.55/1.08 Prover 4: Preprocessing ...
% 2.55/1.08 Prover 1: Preprocessing ...
% 2.70/1.12 Prover 2: Preprocessing ...
% 2.70/1.12 Prover 6: Preprocessing ...
% 2.70/1.12 Prover 3: Preprocessing ...
% 2.70/1.12 Prover 5: Preprocessing ...
% 2.88/1.12 Prover 0: Preprocessing ...
% 4.72/1.44 Prover 1: Warning: ignoring some quantifiers
% 4.72/1.48 Prover 3: Warning: ignoring some quantifiers
% 4.72/1.48 Prover 4: Warning: ignoring some quantifiers
% 4.72/1.49 Prover 5: Proving ...
% 4.72/1.49 Prover 2: Proving ...
% 4.72/1.49 Prover 1: Constructing countermodel ...
% 4.72/1.49 Prover 3: Constructing countermodel ...
% 4.72/1.50 Prover 6: Proving ...
% 4.72/1.50 Prover 4: Constructing countermodel ...
% 5.81/1.58 Prover 0: Proving ...
% 6.68/1.68 Prover 3: proved (1036ms)
% 6.68/1.68
% 6.68/1.68 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.68/1.68
% 6.68/1.68 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 6.68/1.69 Prover 0: stopped
% 6.68/1.69 Prover 5: stopped
% 6.68/1.69 Prover 2: stopped
% 6.68/1.70 Prover 6: stopped
% 6.68/1.70 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 6.68/1.70 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 6.68/1.70 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 6.68/1.70 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 6.68/1.74 Prover 7: Preprocessing ...
% 6.68/1.74 Prover 13: Preprocessing ...
% 6.68/1.74 Prover 8: Preprocessing ...
% 6.68/1.75 Prover 11: Preprocessing ...
% 6.68/1.75 Prover 10: Preprocessing ...
% 7.63/1.81 Prover 7: Warning: ignoring some quantifiers
% 7.63/1.82 Prover 7: Constructing countermodel ...
% 7.63/1.83 Prover 10: Warning: ignoring some quantifiers
% 7.96/1.83 Prover 8: Warning: ignoring some quantifiers
% 7.99/1.84 Prover 13: Warning: ignoring some quantifiers
% 7.99/1.85 Prover 10: Constructing countermodel ...
% 7.99/1.86 Prover 8: Constructing countermodel ...
% 7.99/1.86 Prover 13: Constructing countermodel ...
% 7.99/1.90 Prover 1: Found proof (size 28)
% 7.99/1.90 Prover 1: proved (1268ms)
% 8.46/1.90 Prover 13: stopped
% 8.46/1.90 Prover 8: stopped
% 8.46/1.90 Prover 7: stopped
% 8.46/1.91 Prover 10: stopped
% 8.46/1.91 Prover 4: stopped
% 8.46/1.92 Prover 11: Warning: ignoring some quantifiers
% 8.46/1.93 Prover 11: Constructing countermodel ...
% 8.46/1.94 Prover 11: stopped
% 8.46/1.94
% 8.46/1.94 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 8.46/1.94
% 8.46/1.95 % SZS output start Proof for theBenchmark
% 8.46/1.96 Assumptions after simplification:
% 8.46/1.96 ---------------------------------
% 8.46/1.96
% 8.46/1.96 (d3_tarski)
% 8.75/1.99 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) = v2)
% 8.75/1.99 | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) & in(v3,
% 8.75/1.99 v1) = v4 & in(v3, v0) = 0 & $i(v3))) & ! [v0: $i] : ! [v1: $i] : ( ~
% 8.75/1.99 (subset(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ! [v2: $i] : ( ~ (in(v2, v0)
% 8.75/1.99 = 0) | ~ $i(v2) | in(v2, v1) = 0))
% 8.75/1.99
% 8.75/1.99 (dt_k8_relat_1)
% 8.75/1.99 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (relation_rng_restriction(v0,
% 8.75/1.99 v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] :
% 8.75/1.99 (relation(v2) = v4 & relation(v1) = v3 & ( ~ (v3 = 0) | v4 = 0)))
% 8.75/1.99
% 8.75/1.99 (t115_relat_1)
% 8.75/2.00 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 8.75/2.00 any] : ( ~ (relation_rng(v3) = v4) | ~ (relation_rng_restriction(v1, v2) =
% 8.75/2.00 v3) | ~ (in(v0, v4) = v5) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6:
% 8.75/2.00 any] : ? [v7: any] : ? [v8: $i] : ? [v9: any] : (relation_rng(v2) = v8
% 8.75/2.00 & relation(v2) = v6 & in(v0, v8) = v9 & in(v0, v1) = v7 & $i(v8) & ( ~ (v6
% 8.75/2.00 = 0) | (( ~ (v9 = 0) | ~ (v7 = 0) | v5 = 0) & ( ~ (v5 = 0) | (v9 = 0
% 8.75/2.00 & v7 = 0))))))
% 8.75/2.00
% 8.75/2.00 (t116_relat_1)
% 8.75/2.00 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: int] : ( ~ (v4
% 8.75/2.00 = 0) & relation_rng(v2) = v3 & relation_rng_restriction(v0, v1) = v2 &
% 8.75/2.00 subset(v3, v0) = v4 & relation(v1) = 0 & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 8.75/2.00
% 8.75/2.00 (function-axioms)
% 8.75/2.01 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 8.75/2.01 [v3: $i] : (v1 = v0 | ~ (element(v3, v2) = v1) | ~ (element(v3, v2) = v0)) &
% 8.75/2.01 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 8.75/2.01 (relation_rng_restriction(v3, v2) = v1) | ~ (relation_rng_restriction(v3,
% 8.75/2.01 v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] :
% 8.75/2.01 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~
% 8.75/2.01 (subset(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 8.75/2.01 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (in(v3, v2) =
% 8.75/2.01 v1) | ~ (in(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 8.75/2.01 (v1 = v0 | ~ (relation_rng(v2) = v1) | ~ (relation_rng(v2) = v0)) & ! [v0:
% 8.75/2.01 $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (powerset(v2) = v1) | ~
% 8.75/2.01 (powerset(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 8.75/2.01 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (relation(v2) = v1) | ~
% 8.75/2.01 (relation(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 8.75/2.01 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (empty(v2) = v1) | ~
% 8.75/2.01 (empty(v2) = v0))
% 8.75/2.01
% 8.75/2.01 Further assumptions not needed in the proof:
% 8.75/2.01 --------------------------------------------
% 8.75/2.01 antisymmetry_r2_hidden, cc1_relat_1, dt_k1_xboole_0, dt_k1_zfmisc_1,
% 8.75/2.01 dt_k2_relat_1, dt_m1_subset_1, existence_m1_subset_1, fc1_subset_1,
% 8.75/2.01 fc1_xboole_0, fc4_relat_1, fc6_relat_1, fc8_relat_1, rc1_relat_1, rc1_subset_1,
% 8.75/2.01 rc1_xboole_0, rc2_relat_1, rc2_subset_1, rc2_xboole_0, reflexivity_r1_tarski,
% 8.75/2.01 t1_subset, t2_subset, t3_subset, t4_subset, t5_subset, t6_boole, t7_boole,
% 8.75/2.01 t8_boole
% 8.75/2.01
% 8.75/2.01 Those formulas are unsatisfiable:
% 8.75/2.01 ---------------------------------
% 8.75/2.01
% 8.75/2.01 Begin of proof
% 8.75/2.01 |
% 8.75/2.01 | ALPHA: (d3_tarski) implies:
% 8.75/2.01 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1)
% 8.75/2.01 | = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~
% 8.75/2.01 | (v4 = 0) & in(v3, v1) = v4 & in(v3, v0) = 0 & $i(v3)))
% 8.75/2.01 |
% 8.75/2.01 | ALPHA: (function-axioms) implies:
% 8.75/2.02 | (2) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 8.75/2.02 | (v1 = v0 | ~ (relation(v2) = v1) | ~ (relation(v2) = v0))
% 8.75/2.02 | (3) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 8.75/2.02 | ! [v3: $i] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0))
% 8.75/2.02 |
% 8.75/2.02 | DELTA: instantiating (t116_relat_1) with fresh symbols all_33_0, all_33_1,
% 8.75/2.02 | all_33_2, all_33_3, all_33_4 gives:
% 8.75/2.02 | (4) ~ (all_33_0 = 0) & relation_rng(all_33_2) = all_33_1 &
% 8.75/2.02 | relation_rng_restriction(all_33_4, all_33_3) = all_33_2 &
% 8.75/2.02 | subset(all_33_1, all_33_4) = all_33_0 & relation(all_33_3) = 0 &
% 8.75/2.02 | $i(all_33_1) & $i(all_33_2) & $i(all_33_3) & $i(all_33_4)
% 8.75/2.02 |
% 8.75/2.02 | ALPHA: (4) implies:
% 8.75/2.02 | (5) ~ (all_33_0 = 0)
% 8.75/2.02 | (6) $i(all_33_4)
% 8.75/2.02 | (7) $i(all_33_3)
% 8.75/2.02 | (8) $i(all_33_1)
% 8.75/2.02 | (9) relation(all_33_3) = 0
% 8.75/2.02 | (10) subset(all_33_1, all_33_4) = all_33_0
% 8.75/2.02 | (11) relation_rng_restriction(all_33_4, all_33_3) = all_33_2
% 8.75/2.02 | (12) relation_rng(all_33_2) = all_33_1
% 8.75/2.02 |
% 8.75/2.02 | GROUND_INST: instantiating (1) with all_33_1, all_33_4, all_33_0, simplifying
% 8.75/2.02 | with (6), (8), (10) gives:
% 8.75/2.02 | (13) all_33_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & in(v0,
% 8.75/2.02 | all_33_1) = 0 & in(v0, all_33_4) = v1 & $i(v0))
% 8.75/2.02 |
% 8.75/2.02 | GROUND_INST: instantiating (dt_k8_relat_1) with all_33_4, all_33_3, all_33_2,
% 8.75/2.02 | simplifying with (6), (7), (11) gives:
% 8.75/2.02 | (14) ? [v0: any] : ? [v1: any] : (relation(all_33_2) = v1 &
% 8.75/2.02 | relation(all_33_3) = v0 & ( ~ (v0 = 0) | v1 = 0))
% 8.75/2.02 |
% 8.75/2.03 | DELTA: instantiating (14) with fresh symbols all_41_0, all_41_1 gives:
% 8.75/2.03 | (15) relation(all_33_2) = all_41_0 & relation(all_33_3) = all_41_1 & ( ~
% 8.75/2.03 | (all_41_1 = 0) | all_41_0 = 0)
% 8.75/2.03 |
% 8.75/2.03 | ALPHA: (15) implies:
% 8.75/2.03 | (16) relation(all_33_3) = all_41_1
% 8.75/2.03 |
% 8.75/2.03 | BETA: splitting (13) gives:
% 8.75/2.03 |
% 8.75/2.03 | Case 1:
% 8.75/2.03 | |
% 8.75/2.03 | | (17) all_33_0 = 0
% 8.75/2.03 | |
% 8.75/2.03 | | REDUCE: (5), (17) imply:
% 8.75/2.03 | | (18) $false
% 8.75/2.03 | |
% 8.75/2.03 | | CLOSE: (18) is inconsistent.
% 8.75/2.03 | |
% 8.75/2.03 | Case 2:
% 8.75/2.03 | |
% 8.75/2.03 | | (19) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & in(v0, all_33_1) = 0 &
% 8.75/2.03 | | in(v0, all_33_4) = v1 & $i(v0))
% 8.75/2.03 | |
% 8.75/2.03 | | DELTA: instantiating (19) with fresh symbols all_51_0, all_51_1 gives:
% 8.75/2.03 | | (20) ~ (all_51_0 = 0) & in(all_51_1, all_33_1) = 0 & in(all_51_1,
% 8.75/2.03 | | all_33_4) = all_51_0 & $i(all_51_1)
% 8.75/2.03 | |
% 8.75/2.03 | | ALPHA: (20) implies:
% 8.75/2.03 | | (21) ~ (all_51_0 = 0)
% 8.75/2.03 | | (22) $i(all_51_1)
% 8.75/2.03 | | (23) in(all_51_1, all_33_4) = all_51_0
% 8.75/2.03 | | (24) in(all_51_1, all_33_1) = 0
% 8.75/2.03 | |
% 8.75/2.03 | | GROUND_INST: instantiating (2) with 0, all_41_1, all_33_3, simplifying with
% 8.75/2.03 | | (9), (16) gives:
% 8.75/2.03 | | (25) all_41_1 = 0
% 8.75/2.03 | |
% 8.75/2.03 | | GROUND_INST: instantiating (t115_relat_1) with all_51_1, all_33_4, all_33_3,
% 8.75/2.03 | | all_33_2, all_33_1, 0, simplifying with (6), (7), (11), (12),
% 8.75/2.03 | | (22), (24) gives:
% 8.75/2.03 | | (26) ? [v0: any] : ? [v1: any] : ? [v2: $i] : ? [v3: any] :
% 8.75/2.03 | | (relation_rng(all_33_3) = v2 & relation(all_33_3) = v0 &
% 8.75/2.03 | | in(all_51_1, v2) = v3 & in(all_51_1, all_33_4) = v1 & $i(v2) & ( ~
% 8.75/2.03 | | (v0 = 0) | (v3 = 0 & v1 = 0)))
% 8.75/2.03 | |
% 8.75/2.03 | | DELTA: instantiating (26) with fresh symbols all_70_0, all_70_1, all_70_2,
% 8.75/2.03 | | all_70_3 gives:
% 8.75/2.04 | | (27) relation_rng(all_33_3) = all_70_1 & relation(all_33_3) = all_70_3 &
% 8.75/2.04 | | in(all_51_1, all_70_1) = all_70_0 & in(all_51_1, all_33_4) =
% 8.75/2.04 | | all_70_2 & $i(all_70_1) & ( ~ (all_70_3 = 0) | (all_70_0 = 0 &
% 8.75/2.04 | | all_70_2 = 0))
% 8.75/2.04 | |
% 8.75/2.04 | | ALPHA: (27) implies:
% 8.75/2.04 | | (28) in(all_51_1, all_33_4) = all_70_2
% 8.75/2.04 | | (29) relation(all_33_3) = all_70_3
% 8.75/2.04 | | (30) ~ (all_70_3 = 0) | (all_70_0 = 0 & all_70_2 = 0)
% 8.75/2.04 | |
% 8.75/2.04 | | GROUND_INST: instantiating (3) with all_51_0, all_70_2, all_33_4, all_51_1,
% 8.75/2.04 | | simplifying with (23), (28) gives:
% 8.75/2.04 | | (31) all_70_2 = all_51_0
% 8.75/2.04 | |
% 8.75/2.04 | | GROUND_INST: instantiating (2) with 0, all_70_3, all_33_3, simplifying with
% 8.75/2.04 | | (9), (29) gives:
% 8.75/2.04 | | (32) all_70_3 = 0
% 8.75/2.04 | |
% 8.75/2.04 | | BETA: splitting (30) gives:
% 8.75/2.04 | |
% 8.75/2.04 | | Case 1:
% 8.75/2.04 | | |
% 8.75/2.04 | | | (33) ~ (all_70_3 = 0)
% 8.75/2.04 | | |
% 8.75/2.04 | | | REDUCE: (32), (33) imply:
% 8.75/2.04 | | | (34) $false
% 8.75/2.04 | | |
% 8.75/2.04 | | | CLOSE: (34) is inconsistent.
% 8.75/2.04 | | |
% 8.75/2.04 | | Case 2:
% 8.75/2.04 | | |
% 8.75/2.04 | | | (35) all_70_0 = 0 & all_70_2 = 0
% 8.75/2.04 | | |
% 8.75/2.04 | | | ALPHA: (35) implies:
% 8.75/2.04 | | | (36) all_70_2 = 0
% 8.75/2.04 | | |
% 8.75/2.04 | | | COMBINE_EQS: (31), (36) imply:
% 8.75/2.04 | | | (37) all_51_0 = 0
% 8.75/2.04 | | |
% 8.75/2.04 | | | REDUCE: (21), (37) imply:
% 8.75/2.04 | | | (38) $false
% 8.75/2.04 | | |
% 8.75/2.04 | | | CLOSE: (38) is inconsistent.
% 8.75/2.04 | | |
% 8.75/2.04 | | End of split
% 8.75/2.04 | |
% 8.75/2.04 | End of split
% 8.75/2.04 |
% 8.75/2.04 End of proof
% 8.75/2.04 % SZS output end Proof for theBenchmark
% 8.75/2.04
% 8.75/2.04 1427ms
%------------------------------------------------------------------------------