TSTP Solution File: SEU126+2 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SEU126+2 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n016.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 17:42:38 EDT 2023
% Result : Theorem 9.11s 1.94s
% Output : Proof 10.51s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU126+2 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.12/0.34 % Computer : n016.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Thu Aug 24 00:37:08 EDT 2023
% 0.12/0.35 % CPUTime :
% 0.20/0.58 ________ _____
% 0.20/0.58 ___ __ \_________(_)________________________________
% 0.20/0.58 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.20/0.58 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.20/0.58 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.20/0.58
% 0.20/0.58 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.20/0.58 (2023-06-19)
% 0.20/0.58
% 0.20/0.58 (c) Philipp Rümmer, 2009-2023
% 0.20/0.58 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.20/0.58 Amanda Stjerna.
% 0.20/0.58 Free software under BSD-3-Clause.
% 0.20/0.58
% 0.20/0.58 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.20/0.58
% 0.20/0.58 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.20/0.60 Running up to 7 provers in parallel.
% 0.20/0.61 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.20/0.61 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.20/0.61 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.20/0.61 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.20/0.61 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.20/0.61 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.20/0.61 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.58/1.02 Prover 1: Preprocessing ...
% 2.58/1.02 Prover 4: Preprocessing ...
% 2.80/1.06 Prover 2: Preprocessing ...
% 2.80/1.06 Prover 6: Preprocessing ...
% 2.80/1.07 Prover 3: Preprocessing ...
% 2.80/1.07 Prover 0: Preprocessing ...
% 2.80/1.07 Prover 5: Preprocessing ...
% 5.20/1.47 Prover 1: Warning: ignoring some quantifiers
% 5.20/1.49 Prover 5: Proving ...
% 5.20/1.52 Prover 1: Constructing countermodel ...
% 5.20/1.53 Prover 6: Proving ...
% 5.20/1.53 Prover 3: Warning: ignoring some quantifiers
% 5.20/1.54 Prover 2: Proving ...
% 5.20/1.54 Prover 3: Constructing countermodel ...
% 6.39/1.56 Prover 4: Warning: ignoring some quantifiers
% 6.39/1.59 Prover 4: Constructing countermodel ...
% 7.25/1.67 Prover 0: Proving ...
% 9.11/1.94 Prover 0: proved (1331ms)
% 9.11/1.94
% 9.11/1.94 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 9.11/1.94
% 9.11/1.94 Prover 5: stopped
% 9.11/1.94 Prover 2: stopped
% 9.11/1.94 Prover 3: stopped
% 9.11/1.95 Prover 6: stopped
% 9.11/1.96 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 9.11/1.96 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 9.11/1.96 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 9.11/1.96 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 9.11/1.96 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 9.47/2.00 Prover 10: Preprocessing ...
% 9.47/2.01 Prover 7: Preprocessing ...
% 9.47/2.02 Prover 11: Preprocessing ...
% 9.47/2.02 Prover 13: Preprocessing ...
% 9.47/2.02 Prover 4: Found proof (size 40)
% 9.47/2.02 Prover 4: proved (1413ms)
% 9.47/2.02 Prover 8: Preprocessing ...
% 9.47/2.02 Prover 1: stopped
% 9.47/2.03 Prover 7: stopped
% 9.47/2.03 Prover 10: stopped
% 10.11/2.05 Prover 13: stopped
% 10.11/2.06 Prover 11: stopped
% 10.11/2.12 Prover 8: Warning: ignoring some quantifiers
% 10.11/2.13 Prover 8: Constructing countermodel ...
% 10.11/2.14 Prover 8: stopped
% 10.11/2.14
% 10.11/2.14 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 10.11/2.14
% 10.11/2.14 % SZS output start Proof for theBenchmark
% 10.11/2.14 Assumptions after simplification:
% 10.11/2.14 ---------------------------------
% 10.11/2.14
% 10.11/2.15 (commutativity_k2_xboole_0)
% 10.11/2.17 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (set_union2(v1, v0) = v2) | ~
% 10.11/2.17 $i(v1) | ~ $i(v0) | (set_union2(v0, v1) = v2 & $i(v2))) & ! [v0: $i] : !
% 10.11/2.17 [v1: $i] : ! [v2: $i] : ( ~ (set_union2(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0)
% 10.11/2.17 | (set_union2(v1, v0) = v2 & $i(v2)))
% 10.11/2.17
% 10.11/2.17 (d10_xboole_0)
% 10.11/2.18 ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (subset(v1, v0) = 0) | ~ $i(v1) |
% 10.11/2.18 ~ $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & subset(v0, v1) = v2)) & ! [v0: $i]
% 10.11/2.18 : ! [v1: $i] : (v1 = v0 | ~ (subset(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) |
% 10.11/2.18 ? [v2: int] : ( ~ (v2 = 0) & subset(v1, v0) = v2)) & ! [v0: $i] : ! [v1:
% 10.11/2.18 int] : (v1 = 0 | ~ (subset(v0, v0) = v1) | ~ $i(v0))
% 10.11/2.18
% 10.11/2.18 (t12_xboole_1)
% 10.11/2.18 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ( ~ (v2 = v1) & subset(v0, v1) = 0 &
% 10.11/2.18 set_union2(v0, v1) = v2 & $i(v2) & $i(v1) & $i(v0))
% 10.11/2.18
% 10.11/2.18 (t7_xboole_1)
% 10.11/2.18 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (set_union2(v0, v1) = v2) | ~
% 10.11/2.18 $i(v1) | ~ $i(v0) | subset(v0, v2) = 0)
% 10.11/2.18
% 10.11/2.18 (t8_xboole_1)
% 10.11/2.18 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0
% 10.11/2.18 | ~ (subset(v3, v1) = v4) | ~ (set_union2(v0, v2) = v3) | ~ $i(v2) | ~
% 10.11/2.18 $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : (subset(v2, v1) = v6 &
% 10.11/2.18 subset(v0, v1) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0))))
% 10.11/2.18
% 10.11/2.18 (function-axioms)
% 10.11/2.19 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 10.11/2.19 [v3: $i] : (v1 = v0 | ~ (disjoint(v3, v2) = v1) | ~ (disjoint(v3, v2) = v0))
% 10.11/2.19 & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 10.11/2.19 [v3: $i] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) &
% 10.11/2.19 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 10.11/2.19 (set_intersection2(v3, v2) = v1) | ~ (set_intersection2(v3, v2) = v0)) & !
% 10.11/2.19 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 10.11/2.19 (set_union2(v3, v2) = v1) | ~ (set_union2(v3, v2) = v0)) & ! [v0:
% 10.11/2.19 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 10.11/2.19 : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) & ! [v0:
% 10.11/2.19 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 |
% 10.11/2.19 ~ (empty(v2) = v1) | ~ (empty(v2) = v0))
% 10.11/2.19
% 10.11/2.19 Further assumptions not needed in the proof:
% 10.11/2.19 --------------------------------------------
% 10.11/2.19 antisymmetry_r2_hidden, commutativity_k3_xboole_0, d1_xboole_0, d2_xboole_0,
% 10.11/2.19 d3_tarski, d3_xboole_0, d7_xboole_0, dt_k1_xboole_0, dt_k2_xboole_0,
% 10.11/2.19 dt_k3_xboole_0, fc1_xboole_0, fc2_xboole_0, fc3_xboole_0,
% 10.11/2.19 idempotence_k2_xboole_0, idempotence_k3_xboole_0, rc1_xboole_0, rc2_xboole_0,
% 10.11/2.19 reflexivity_r1_tarski, symmetry_r1_xboole_0, t1_boole, t1_xboole_1, t2_xboole_1,
% 10.11/2.19 t3_xboole_0, t3_xboole_1, t4_xboole_0, t6_boole, t7_boole, t8_boole
% 10.11/2.19
% 10.11/2.19 Those formulas are unsatisfiable:
% 10.11/2.19 ---------------------------------
% 10.11/2.19
% 10.11/2.19 Begin of proof
% 10.11/2.19 |
% 10.11/2.19 | ALPHA: (commutativity_k2_xboole_0) implies:
% 10.11/2.19 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (set_union2(v1, v0) = v2)
% 10.11/2.19 | | ~ $i(v1) | ~ $i(v0) | (set_union2(v0, v1) = v2 & $i(v2)))
% 10.11/2.19 |
% 10.11/2.19 | ALPHA: (d10_xboole_0) implies:
% 10.11/2.19 | (2) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (subset(v0, v0) = v1) | ~
% 10.11/2.19 | $i(v0))
% 10.11/2.19 | (3) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (subset(v1, v0) = 0) | ~
% 10.11/2.19 | $i(v1) | ~ $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & subset(v0, v1) =
% 10.11/2.19 | v2))
% 10.11/2.19 |
% 10.11/2.19 | ALPHA: (function-axioms) implies:
% 10.11/2.19 | (4) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 10.11/2.19 | ! [v3: $i] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2)
% 10.11/2.19 | = v0))
% 10.11/2.19 |
% 10.11/2.19 | DELTA: instantiating (t12_xboole_1) with fresh symbols all_35_0, all_35_1,
% 10.11/2.19 | all_35_2 gives:
% 10.11/2.19 | (5) ~ (all_35_0 = all_35_1) & subset(all_35_2, all_35_1) = 0 &
% 10.11/2.19 | set_union2(all_35_2, all_35_1) = all_35_0 & $i(all_35_0) & $i(all_35_1)
% 10.11/2.19 | & $i(all_35_2)
% 10.11/2.19 |
% 10.11/2.19 | ALPHA: (5) implies:
% 10.11/2.19 | (6) ~ (all_35_0 = all_35_1)
% 10.11/2.19 | (7) $i(all_35_2)
% 10.11/2.19 | (8) $i(all_35_1)
% 10.11/2.19 | (9) set_union2(all_35_2, all_35_1) = all_35_0
% 10.11/2.19 | (10) subset(all_35_2, all_35_1) = 0
% 10.11/2.19 |
% 10.11/2.20 | GROUND_INST: instantiating (1) with all_35_1, all_35_2, all_35_0, simplifying
% 10.11/2.20 | with (7), (8), (9) gives:
% 10.11/2.20 | (11) set_union2(all_35_1, all_35_2) = all_35_0 & $i(all_35_0)
% 10.11/2.20 |
% 10.11/2.20 | ALPHA: (11) implies:
% 10.11/2.20 | (12) $i(all_35_0)
% 10.11/2.20 | (13) set_union2(all_35_1, all_35_2) = all_35_0
% 10.11/2.20 |
% 10.11/2.20 | GROUND_INST: instantiating (t7_xboole_1) with all_35_1, all_35_2, all_35_0,
% 10.11/2.20 | simplifying with (7), (8), (13) gives:
% 10.11/2.20 | (14) subset(all_35_1, all_35_0) = 0
% 10.11/2.20 |
% 10.11/2.20 | GROUND_INST: instantiating (3) with all_35_0, all_35_1, simplifying with (8),
% 10.11/2.20 | (12), (14) gives:
% 10.11/2.20 | (15) all_35_0 = all_35_1 | ? [v0: int] : ( ~ (v0 = 0) & subset(all_35_0,
% 10.11/2.20 | all_35_1) = v0)
% 10.11/2.20 |
% 10.11/2.20 | BETA: splitting (15) gives:
% 10.11/2.20 |
% 10.11/2.20 | Case 1:
% 10.11/2.20 | |
% 10.11/2.20 | | (16) all_35_0 = all_35_1
% 10.11/2.20 | |
% 10.11/2.20 | | REDUCE: (6), (16) imply:
% 10.11/2.20 | | (17) $false
% 10.11/2.20 | |
% 10.11/2.20 | | CLOSE: (17) is inconsistent.
% 10.11/2.20 | |
% 10.11/2.20 | Case 2:
% 10.11/2.20 | |
% 10.11/2.20 | | (18) ? [v0: int] : ( ~ (v0 = 0) & subset(all_35_0, all_35_1) = v0)
% 10.11/2.20 | |
% 10.11/2.20 | | DELTA: instantiating (18) with fresh symbol all_80_0 gives:
% 10.11/2.20 | | (19) ~ (all_80_0 = 0) & subset(all_35_0, all_35_1) = all_80_0
% 10.11/2.20 | |
% 10.11/2.20 | | ALPHA: (19) implies:
% 10.11/2.20 | | (20) ~ (all_80_0 = 0)
% 10.11/2.20 | | (21) subset(all_35_0, all_35_1) = all_80_0
% 10.11/2.20 | |
% 10.11/2.20 | | GROUND_INST: instantiating (t8_xboole_1) with all_35_1, all_35_1, all_35_2,
% 10.11/2.20 | | all_35_0, all_80_0, simplifying with (7), (8), (13), (21)
% 10.11/2.20 | | gives:
% 10.11/2.20 | | (22) all_80_0 = 0 | ? [v0: any] : ? [v1: any] : (subset(all_35_1,
% 10.11/2.20 | | all_35_1) = v0 & subset(all_35_2, all_35_1) = v1 & ( ~ (v1 = 0)
% 10.11/2.20 | | | ~ (v0 = 0)))
% 10.11/2.20 | |
% 10.11/2.20 | | GROUND_INST: instantiating (t8_xboole_1) with all_35_2, all_35_1, all_35_1,
% 10.11/2.20 | | all_35_0, all_80_0, simplifying with (7), (8), (9), (21) gives:
% 10.51/2.20 | | (23) all_80_0 = 0 | ? [v0: any] : ? [v1: any] : (subset(all_35_1,
% 10.51/2.20 | | all_35_1) = v1 & subset(all_35_2, all_35_1) = v0 & ( ~ (v1 = 0)
% 10.51/2.20 | | | ~ (v0 = 0)))
% 10.51/2.20 | |
% 10.51/2.20 | | BETA: splitting (23) gives:
% 10.51/2.20 | |
% 10.51/2.20 | | Case 1:
% 10.51/2.20 | | |
% 10.51/2.20 | | | (24) all_80_0 = 0
% 10.51/2.20 | | |
% 10.51/2.20 | | | REDUCE: (20), (24) imply:
% 10.51/2.20 | | | (25) $false
% 10.51/2.20 | | |
% 10.51/2.20 | | | CLOSE: (25) is inconsistent.
% 10.51/2.20 | | |
% 10.51/2.20 | | Case 2:
% 10.51/2.20 | | |
% 10.51/2.21 | | | (26) ? [v0: any] : ? [v1: any] : (subset(all_35_1, all_35_1) = v1 &
% 10.51/2.21 | | | subset(all_35_2, all_35_1) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 10.51/2.21 | | |
% 10.51/2.21 | | | DELTA: instantiating (26) with fresh symbols all_98_0, all_98_1 gives:
% 10.51/2.21 | | | (27) subset(all_35_1, all_35_1) = all_98_0 & subset(all_35_2, all_35_1)
% 10.51/2.21 | | | = all_98_1 & ( ~ (all_98_0 = 0) | ~ (all_98_1 = 0))
% 10.51/2.21 | | |
% 10.51/2.21 | | | ALPHA: (27) implies:
% 10.51/2.21 | | | (28) subset(all_35_2, all_35_1) = all_98_1
% 10.51/2.21 | | | (29) subset(all_35_1, all_35_1) = all_98_0
% 10.51/2.21 | | | (30) ~ (all_98_0 = 0) | ~ (all_98_1 = 0)
% 10.51/2.21 | | |
% 10.51/2.21 | | | BETA: splitting (22) gives:
% 10.51/2.21 | | |
% 10.51/2.21 | | | Case 1:
% 10.51/2.21 | | | |
% 10.51/2.21 | | | | (31) all_80_0 = 0
% 10.51/2.21 | | | |
% 10.51/2.21 | | | | REDUCE: (20), (31) imply:
% 10.51/2.21 | | | | (32) $false
% 10.51/2.21 | | | |
% 10.51/2.21 | | | | CLOSE: (32) is inconsistent.
% 10.51/2.21 | | | |
% 10.51/2.21 | | | Case 2:
% 10.51/2.21 | | | |
% 10.51/2.21 | | | | (33) ? [v0: any] : ? [v1: any] : (subset(all_35_1, all_35_1) = v0 &
% 10.51/2.21 | | | | subset(all_35_2, all_35_1) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 10.51/2.21 | | | |
% 10.51/2.21 | | | | DELTA: instantiating (33) with fresh symbols all_108_0, all_108_1 gives:
% 10.51/2.21 | | | | (34) subset(all_35_1, all_35_1) = all_108_1 & subset(all_35_2,
% 10.51/2.21 | | | | all_35_1) = all_108_0 & ( ~ (all_108_0 = 0) | ~ (all_108_1 =
% 10.51/2.21 | | | | 0))
% 10.51/2.21 | | | |
% 10.51/2.21 | | | | ALPHA: (34) implies:
% 10.51/2.21 | | | | (35) subset(all_35_2, all_35_1) = all_108_0
% 10.51/2.21 | | | | (36) subset(all_35_1, all_35_1) = all_108_1
% 10.51/2.21 | | | |
% 10.51/2.21 | | | | GROUND_INST: instantiating (4) with 0, all_108_0, all_35_1, all_35_2,
% 10.51/2.21 | | | | simplifying with (10), (35) gives:
% 10.51/2.21 | | | | (37) all_108_0 = 0
% 10.51/2.21 | | | |
% 10.51/2.21 | | | | GROUND_INST: instantiating (4) with all_98_1, all_108_0, all_35_1,
% 10.51/2.21 | | | | all_35_2, simplifying with (28), (35) gives:
% 10.51/2.21 | | | | (38) all_108_0 = all_98_1
% 10.51/2.21 | | | |
% 10.51/2.21 | | | | GROUND_INST: instantiating (4) with all_98_0, all_108_1, all_35_1,
% 10.51/2.21 | | | | all_35_1, simplifying with (29), (36) gives:
% 10.51/2.21 | | | | (39) all_108_1 = all_98_0
% 10.51/2.21 | | | |
% 10.51/2.21 | | | | COMBINE_EQS: (37), (38) imply:
% 10.51/2.21 | | | | (40) all_98_1 = 0
% 10.51/2.21 | | | |
% 10.51/2.21 | | | | BETA: splitting (30) gives:
% 10.51/2.21 | | | |
% 10.51/2.21 | | | | Case 1:
% 10.51/2.21 | | | | |
% 10.51/2.21 | | | | | (41) ~ (all_98_0 = 0)
% 10.51/2.21 | | | | |
% 10.51/2.21 | | | | | GROUND_INST: instantiating (2) with all_35_1, all_98_0, simplifying
% 10.51/2.21 | | | | | with (8), (29) gives:
% 10.51/2.21 | | | | | (42) all_98_0 = 0
% 10.51/2.21 | | | | |
% 10.51/2.21 | | | | | REDUCE: (41), (42) imply:
% 10.51/2.21 | | | | | (43) $false
% 10.51/2.21 | | | | |
% 10.51/2.21 | | | | | CLOSE: (43) is inconsistent.
% 10.51/2.21 | | | | |
% 10.51/2.21 | | | | Case 2:
% 10.51/2.21 | | | | |
% 10.51/2.21 | | | | | (44) ~ (all_98_1 = 0)
% 10.51/2.21 | | | | |
% 10.51/2.21 | | | | | REDUCE: (40), (44) imply:
% 10.51/2.21 | | | | | (45) $false
% 10.51/2.21 | | | | |
% 10.51/2.21 | | | | | CLOSE: (45) is inconsistent.
% 10.51/2.21 | | | | |
% 10.51/2.21 | | | | End of split
% 10.51/2.21 | | | |
% 10.51/2.21 | | | End of split
% 10.51/2.21 | | |
% 10.51/2.21 | | End of split
% 10.51/2.21 | |
% 10.51/2.21 | End of split
% 10.51/2.21 |
% 10.51/2.21 End of proof
% 10.51/2.21 % SZS output end Proof for theBenchmark
% 10.51/2.21
% 10.51/2.21 1628ms
%------------------------------------------------------------------------------