TSTP Solution File: SET985+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SET985+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n021.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 15:27:17 EDT 2023
% Result : Theorem 4.92s 1.37s
% Output : Proof 5.64s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SET985+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.14 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.14/0.35 % Computer : n021.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Sat Aug 26 15:45:42 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.21/0.63 ________ _____
% 0.21/0.63 ___ __ \_________(_)________________________________
% 0.21/0.63 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.21/0.63 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.21/0.63 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.21/0.63
% 0.21/0.63 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.21/0.64 (2023-06-19)
% 0.21/0.64
% 0.21/0.64 (c) Philipp Rümmer, 2009-2023
% 0.21/0.64 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.21/0.64 Amanda Stjerna.
% 0.21/0.64 Free software under BSD-3-Clause.
% 0.21/0.64
% 0.21/0.64 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.21/0.64
% 0.21/0.64 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.21/0.65 Running up to 7 provers in parallel.
% 0.21/0.67 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.21/0.67 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.21/0.67 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.21/0.67 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.21/0.67 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.21/0.67 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.21/0.67 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.07/0.99 Prover 1: Preprocessing ...
% 2.07/0.99 Prover 4: Preprocessing ...
% 2.07/1.03 Prover 6: Preprocessing ...
% 2.07/1.03 Prover 5: Preprocessing ...
% 2.07/1.03 Prover 0: Preprocessing ...
% 2.07/1.03 Prover 2: Preprocessing ...
% 2.07/1.03 Prover 3: Preprocessing ...
% 3.25/1.18 Prover 1: Warning: ignoring some quantifiers
% 3.25/1.18 Prover 3: Warning: ignoring some quantifiers
% 3.25/1.19 Prover 3: Constructing countermodel ...
% 3.25/1.19 Prover 5: Proving ...
% 3.25/1.19 Prover 0: Proving ...
% 3.25/1.19 Prover 1: Constructing countermodel ...
% 3.25/1.20 Prover 4: Constructing countermodel ...
% 3.25/1.20 Prover 6: Proving ...
% 4.00/1.24 Prover 2: Proving ...
% 4.92/1.37 Prover 0: proved (716ms)
% 4.92/1.37
% 4.92/1.37 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.92/1.37
% 4.92/1.37 Prover 6: stopped
% 4.92/1.37 Prover 2: stopped
% 4.92/1.38 Prover 3: stopped
% 4.92/1.40 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 4.92/1.40 Prover 5: stopped
% 4.92/1.42 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 4.92/1.42 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 4.92/1.42 Prover 7: Preprocessing ...
% 4.92/1.42 Prover 8: Preprocessing ...
% 4.92/1.42 Prover 10: Preprocessing ...
% 4.92/1.42 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 4.92/1.42 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 4.92/1.42 Prover 4: Found proof (size 47)
% 4.92/1.42 Prover 4: proved (764ms)
% 4.92/1.42 Prover 7: Warning: ignoring some quantifiers
% 4.92/1.43 Prover 1: stopped
% 4.92/1.43 Prover 7: Constructing countermodel ...
% 4.92/1.43 Prover 7: stopped
% 4.92/1.43 Prover 13: Preprocessing ...
% 4.92/1.44 Prover 10: Warning: ignoring some quantifiers
% 4.92/1.44 Prover 11: Preprocessing ...
% 4.92/1.44 Prover 10: Constructing countermodel ...
% 4.92/1.44 Prover 8: Warning: ignoring some quantifiers
% 4.92/1.44 Prover 10: stopped
% 4.92/1.45 Prover 8: Constructing countermodel ...
% 4.92/1.45 Prover 13: stopped
% 4.92/1.45 Prover 11: stopped
% 4.92/1.45 Prover 8: stopped
% 4.92/1.45
% 4.92/1.45 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.92/1.45
% 5.64/1.46 % SZS output start Proof for theBenchmark
% 5.64/1.46 Assumptions after simplification:
% 5.64/1.46 ---------------------------------
% 5.64/1.46
% 5.64/1.46 (fc1_xboole_0)
% 5.64/1.49 empty(empty_set) = 0 & $i(empty_set)
% 5.64/1.49
% 5.64/1.49 (t113_zfmisc_1)
% 5.64/1.49 $i(empty_set) & ! [v0: $i] : ! [v1: $i] : (v1 = empty_set | v0 = empty_set |
% 5.64/1.49 ~ (cartesian_product2(v0, v1) = empty_set) | ~ $i(v1) | ~ $i(v0)) & !
% 5.64/1.49 [v0: $i] : ! [v1: $i] : (v1 = empty_set | ~ (cartesian_product2(v0,
% 5.64/1.49 empty_set) = v1) | ~ $i(v0)) & ! [v0: $i] : ! [v1: $i] : (v1 =
% 5.64/1.49 empty_set | ~ (cartesian_product2(empty_set, v0) = v1) | ~ $i(v0))
% 5.64/1.49
% 5.64/1.49 (t138_zfmisc_1)
% 5.64/1.50 $i(empty_set) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : !
% 5.64/1.50 [v4: $i] : ! [v5: $i] : (v4 = empty_set | ~ (cartesian_product2(v2, v3) =
% 5.64/1.50 v5) | ~ (cartesian_product2(v0, v1) = v4) | ~ (subset(v4, v5) = 0) | ~
% 5.64/1.50 $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | (subset(v1, v3) = 0 &
% 5.64/1.50 subset(v0, v2) = 0))
% 5.64/1.50
% 5.64/1.50 (t139_zfmisc_1)
% 5.64/1.50 ? [v0: $i] : ? [v1: int] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5:
% 5.64/1.50 $i] : ? [v6: $i] : ? [v7: any] : ? [v8: $i] : ? [v9: $i] : ? [v10: any]
% 5.64/1.50 : ? [v11: int] : ( ~ (v11 = 0) & ~ (v1 = 0) & cartesian_product2(v4, v3) =
% 5.64/1.50 v9 & cartesian_product2(v3, v4) = v6 & cartesian_product2(v2, v0) = v8 &
% 5.64/1.50 cartesian_product2(v0, v2) = v5 & subset(v8, v9) = v10 & subset(v5, v6) = v7
% 5.64/1.50 & subset(v2, v4) = v11 & empty(v0) = v1 & $i(v9) & $i(v8) & $i(v6) & $i(v5)
% 5.64/1.50 & $i(v4) & $i(v3) & $i(v2) & $i(v0) & (v10 = 0 | v7 = 0))
% 5.64/1.50
% 5.64/1.50 (t2_xboole_1)
% 5.64/1.50 $i(empty_set) & ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (subset(empty_set,
% 5.64/1.50 v0) = v1) | ~ $i(v0))
% 5.64/1.50
% 5.64/1.50 (function-axioms)
% 5.64/1.51 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 5.64/1.51 (cartesian_product2(v3, v2) = v1) | ~ (cartesian_product2(v3, v2) = v0)) &
% 5.64/1.51 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 5.64/1.51 $i] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) & !
% 5.64/1.51 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0
% 5.64/1.51 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0))
% 5.64/1.51
% 5.64/1.51 Further assumptions not needed in the proof:
% 5.64/1.51 --------------------------------------------
% 5.64/1.51 rc1_xboole_0, rc2_xboole_0, reflexivity_r1_tarski
% 5.64/1.51
% 5.64/1.51 Those formulas are unsatisfiable:
% 5.64/1.51 ---------------------------------
% 5.64/1.51
% 5.64/1.51 Begin of proof
% 5.64/1.51 |
% 5.64/1.51 | ALPHA: (fc1_xboole_0) implies:
% 5.64/1.51 | (1) empty(empty_set) = 0
% 5.64/1.51 |
% 5.64/1.51 | ALPHA: (t113_zfmisc_1) implies:
% 5.64/1.51 | (2) ! [v0: $i] : ! [v1: $i] : (v1 = empty_set | v0 = empty_set | ~
% 5.64/1.51 | (cartesian_product2(v0, v1) = empty_set) | ~ $i(v1) | ~ $i(v0))
% 5.64/1.51 |
% 5.64/1.51 | ALPHA: (t138_zfmisc_1) implies:
% 5.64/1.51 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 5.64/1.51 | ! [v5: $i] : (v4 = empty_set | ~ (cartesian_product2(v2, v3) = v5) |
% 5.64/1.51 | ~ (cartesian_product2(v0, v1) = v4) | ~ (subset(v4, v5) = 0) | ~
% 5.64/1.51 | $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | (subset(v1, v3) = 0 &
% 5.64/1.51 | subset(v0, v2) = 0))
% 5.64/1.51 |
% 5.64/1.51 | ALPHA: (t2_xboole_1) implies:
% 5.64/1.52 | (4) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (subset(empty_set, v0) = v1)
% 5.64/1.52 | | ~ $i(v0))
% 5.64/1.52 |
% 5.64/1.52 | ALPHA: (function-axioms) implies:
% 5.64/1.52 | (5) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 5.64/1.52 | (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0))
% 5.64/1.52 | (6) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 5.64/1.52 | ! [v3: $i] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2)
% 5.64/1.52 | = v0))
% 5.64/1.52 |
% 5.64/1.52 | DELTA: instantiating (t139_zfmisc_1) with fresh symbols all_12_0, all_12_1,
% 5.64/1.52 | all_12_2, all_12_3, all_12_4, all_12_5, all_12_6, all_12_7, all_12_8,
% 5.64/1.52 | all_12_9, all_12_10, all_12_11 gives:
% 5.64/1.52 | (7) ~ (all_12_0 = 0) & ~ (all_12_10 = 0) & cartesian_product2(all_12_7,
% 5.64/1.52 | all_12_8) = all_12_2 & cartesian_product2(all_12_8, all_12_7) =
% 5.64/1.52 | all_12_5 & cartesian_product2(all_12_9, all_12_11) = all_12_3 &
% 5.64/1.52 | cartesian_product2(all_12_11, all_12_9) = all_12_6 & subset(all_12_3,
% 5.64/1.52 | all_12_2) = all_12_1 & subset(all_12_6, all_12_5) = all_12_4 &
% 5.64/1.52 | subset(all_12_9, all_12_7) = all_12_0 & empty(all_12_11) = all_12_10 &
% 5.64/1.52 | $i(all_12_2) & $i(all_12_3) & $i(all_12_5) & $i(all_12_6) &
% 5.64/1.52 | $i(all_12_7) & $i(all_12_8) & $i(all_12_9) & $i(all_12_11) & (all_12_1
% 5.64/1.52 | = 0 | all_12_4 = 0)
% 5.64/1.52 |
% 5.64/1.52 | ALPHA: (7) implies:
% 5.64/1.52 | (8) ~ (all_12_10 = 0)
% 5.64/1.52 | (9) ~ (all_12_0 = 0)
% 5.64/1.52 | (10) $i(all_12_11)
% 5.64/1.52 | (11) $i(all_12_9)
% 5.64/1.52 | (12) $i(all_12_8)
% 5.64/1.52 | (13) $i(all_12_7)
% 5.64/1.52 | (14) empty(all_12_11) = all_12_10
% 5.64/1.52 | (15) subset(all_12_9, all_12_7) = all_12_0
% 5.64/1.52 | (16) subset(all_12_6, all_12_5) = all_12_4
% 5.64/1.52 | (17) subset(all_12_3, all_12_2) = all_12_1
% 5.64/1.53 | (18) cartesian_product2(all_12_11, all_12_9) = all_12_6
% 5.64/1.53 | (19) cartesian_product2(all_12_9, all_12_11) = all_12_3
% 5.64/1.53 | (20) cartesian_product2(all_12_8, all_12_7) = all_12_5
% 5.64/1.53 | (21) cartesian_product2(all_12_7, all_12_8) = all_12_2
% 5.64/1.53 | (22) all_12_1 = 0 | all_12_4 = 0
% 5.64/1.53 |
% 5.64/1.53 | BETA: splitting (22) gives:
% 5.64/1.53 |
% 5.64/1.53 | Case 1:
% 5.64/1.53 | |
% 5.64/1.53 | | (23) all_12_1 = 0
% 5.64/1.53 | |
% 5.64/1.53 | | REDUCE: (17), (23) imply:
% 5.64/1.53 | | (24) subset(all_12_3, all_12_2) = 0
% 5.64/1.53 | |
% 5.64/1.53 | | GROUND_INST: instantiating (3) with all_12_9, all_12_11, all_12_7, all_12_8,
% 5.64/1.53 | | all_12_3, all_12_2, simplifying with (10), (11), (12), (13),
% 5.64/1.53 | | (19), (21), (24) gives:
% 5.64/1.53 | | (25) all_12_3 = empty_set | (subset(all_12_9, all_12_7) = 0 &
% 5.64/1.53 | | subset(all_12_11, all_12_8) = 0)
% 5.64/1.53 | |
% 5.64/1.53 | | BETA: splitting (25) gives:
% 5.64/1.53 | |
% 5.64/1.53 | | Case 1:
% 5.64/1.53 | | |
% 5.64/1.53 | | | (26) all_12_3 = empty_set
% 5.64/1.53 | | |
% 5.64/1.53 | | | REDUCE: (19), (26) imply:
% 5.64/1.53 | | | (27) cartesian_product2(all_12_9, all_12_11) = empty_set
% 5.64/1.53 | | |
% 5.64/1.53 | | | GROUND_INST: instantiating (2) with all_12_9, all_12_11, simplifying with
% 5.64/1.53 | | | (10), (11), (27) gives:
% 5.64/1.53 | | | (28) all_12_9 = empty_set | all_12_11 = empty_set
% 5.64/1.53 | | |
% 5.64/1.53 | | | BETA: splitting (28) gives:
% 5.64/1.53 | | |
% 5.64/1.53 | | | Case 1:
% 5.64/1.53 | | | |
% 5.64/1.53 | | | | (29) all_12_9 = empty_set
% 5.64/1.53 | | | |
% 5.64/1.53 | | | | REDUCE: (15), (29) imply:
% 5.64/1.53 | | | | (30) subset(empty_set, all_12_7) = all_12_0
% 5.64/1.53 | | | |
% 5.64/1.53 | | | | GROUND_INST: instantiating (4) with all_12_7, all_12_0, simplifying with
% 5.64/1.53 | | | | (13), (30) gives:
% 5.64/1.53 | | | | (31) all_12_0 = 0
% 5.64/1.53 | | | |
% 5.64/1.53 | | | | REDUCE: (9), (31) imply:
% 5.64/1.53 | | | | (32) $false
% 5.64/1.53 | | | |
% 5.64/1.53 | | | | CLOSE: (32) is inconsistent.
% 5.64/1.53 | | | |
% 5.64/1.53 | | | Case 2:
% 5.64/1.53 | | | |
% 5.64/1.53 | | | | (33) all_12_11 = empty_set
% 5.64/1.53 | | | |
% 5.64/1.53 | | | | REDUCE: (14), (33) imply:
% 5.64/1.53 | | | | (34) empty(empty_set) = all_12_10
% 5.64/1.53 | | | |
% 5.64/1.53 | | | | GROUND_INST: instantiating (5) with 0, all_12_10, empty_set, simplifying
% 5.64/1.53 | | | | with (1), (34) gives:
% 5.64/1.53 | | | | (35) all_12_10 = 0
% 5.64/1.53 | | | |
% 5.64/1.53 | | | | REDUCE: (8), (35) imply:
% 5.64/1.53 | | | | (36) $false
% 5.64/1.53 | | | |
% 5.64/1.53 | | | | CLOSE: (36) is inconsistent.
% 5.64/1.53 | | | |
% 5.64/1.53 | | | End of split
% 5.64/1.53 | | |
% 5.64/1.53 | | Case 2:
% 5.64/1.53 | | |
% 5.64/1.54 | | | (37) subset(all_12_9, all_12_7) = 0 & subset(all_12_11, all_12_8) = 0
% 5.64/1.54 | | |
% 5.64/1.54 | | | ALPHA: (37) implies:
% 5.64/1.54 | | | (38) subset(all_12_9, all_12_7) = 0
% 5.64/1.54 | | |
% 5.64/1.54 | | | GROUND_INST: instantiating (6) with all_12_0, 0, all_12_7, all_12_9,
% 5.64/1.54 | | | simplifying with (15), (38) gives:
% 5.64/1.54 | | | (39) all_12_0 = 0
% 5.64/1.54 | | |
% 5.64/1.54 | | | REDUCE: (9), (39) imply:
% 5.64/1.54 | | | (40) $false
% 5.64/1.54 | | |
% 5.64/1.54 | | | CLOSE: (40) is inconsistent.
% 5.64/1.54 | | |
% 5.64/1.54 | | End of split
% 5.64/1.54 | |
% 5.64/1.54 | Case 2:
% 5.64/1.54 | |
% 5.64/1.54 | | (41) all_12_4 = 0
% 5.64/1.54 | |
% 5.64/1.54 | | REDUCE: (16), (41) imply:
% 5.64/1.54 | | (42) subset(all_12_6, all_12_5) = 0
% 5.64/1.54 | |
% 5.64/1.54 | | GROUND_INST: instantiating (3) with all_12_11, all_12_9, all_12_8, all_12_7,
% 5.64/1.54 | | all_12_6, all_12_5, simplifying with (10), (11), (12), (13),
% 5.64/1.54 | | (18), (20), (42) gives:
% 5.64/1.54 | | (43) all_12_6 = empty_set | (subset(all_12_9, all_12_7) = 0 &
% 5.64/1.54 | | subset(all_12_11, all_12_8) = 0)
% 5.64/1.54 | |
% 5.64/1.54 | | BETA: splitting (43) gives:
% 5.64/1.54 | |
% 5.64/1.54 | | Case 1:
% 5.64/1.54 | | |
% 5.64/1.54 | | | (44) all_12_6 = empty_set
% 5.64/1.54 | | |
% 5.64/1.54 | | | REDUCE: (18), (44) imply:
% 5.64/1.54 | | | (45) cartesian_product2(all_12_11, all_12_9) = empty_set
% 5.64/1.54 | | |
% 5.64/1.54 | | | GROUND_INST: instantiating (2) with all_12_11, all_12_9, simplifying with
% 5.64/1.54 | | | (10), (11), (45) gives:
% 5.64/1.54 | | | (46) all_12_9 = empty_set | all_12_11 = empty_set
% 5.64/1.54 | | |
% 5.64/1.54 | | | BETA: splitting (46) gives:
% 5.64/1.54 | | |
% 5.64/1.54 | | | Case 1:
% 5.64/1.54 | | | |
% 5.64/1.54 | | | | (47) all_12_9 = empty_set
% 5.64/1.54 | | | |
% 5.64/1.54 | | | | REDUCE: (15), (47) imply:
% 5.64/1.54 | | | | (48) subset(empty_set, all_12_7) = all_12_0
% 5.64/1.54 | | | |
% 5.64/1.54 | | | | GROUND_INST: instantiating (4) with all_12_7, all_12_0, simplifying with
% 5.64/1.54 | | | | (13), (48) gives:
% 5.64/1.54 | | | | (49) all_12_0 = 0
% 5.64/1.54 | | | |
% 5.64/1.54 | | | | REDUCE: (9), (49) imply:
% 5.64/1.54 | | | | (50) $false
% 5.64/1.54 | | | |
% 5.64/1.54 | | | | CLOSE: (50) is inconsistent.
% 5.64/1.54 | | | |
% 5.64/1.54 | | | Case 2:
% 5.64/1.54 | | | |
% 5.64/1.54 | | | | (51) all_12_11 = empty_set
% 5.64/1.54 | | | |
% 5.64/1.54 | | | | REDUCE: (14), (51) imply:
% 5.64/1.54 | | | | (52) empty(empty_set) = all_12_10
% 5.64/1.54 | | | |
% 5.64/1.54 | | | | GROUND_INST: instantiating (5) with 0, all_12_10, empty_set, simplifying
% 5.64/1.54 | | | | with (1), (52) gives:
% 5.64/1.54 | | | | (53) all_12_10 = 0
% 5.64/1.54 | | | |
% 5.64/1.54 | | | | REDUCE: (8), (53) imply:
% 5.64/1.54 | | | | (54) $false
% 5.64/1.54 | | | |
% 5.64/1.54 | | | | CLOSE: (54) is inconsistent.
% 5.64/1.54 | | | |
% 5.64/1.54 | | | End of split
% 5.64/1.54 | | |
% 5.64/1.54 | | Case 2:
% 5.64/1.54 | | |
% 5.64/1.54 | | | (55) subset(all_12_9, all_12_7) = 0 & subset(all_12_11, all_12_8) = 0
% 5.64/1.54 | | |
% 5.64/1.54 | | | ALPHA: (55) implies:
% 5.64/1.54 | | | (56) subset(all_12_9, all_12_7) = 0
% 5.64/1.54 | | |
% 5.64/1.54 | | | GROUND_INST: instantiating (6) with all_12_0, 0, all_12_7, all_12_9,
% 5.64/1.54 | | | simplifying with (15), (56) gives:
% 5.64/1.54 | | | (57) all_12_0 = 0
% 5.64/1.54 | | |
% 5.64/1.54 | | | REDUCE: (9), (57) imply:
% 5.64/1.54 | | | (58) $false
% 5.64/1.54 | | |
% 5.64/1.54 | | | CLOSE: (58) is inconsistent.
% 5.64/1.54 | | |
% 5.64/1.54 | | End of split
% 5.64/1.54 | |
% 5.64/1.54 | End of split
% 5.64/1.54 |
% 5.64/1.54 End of proof
% 5.64/1.55 % SZS output end Proof for theBenchmark
% 5.64/1.55
% 5.64/1.55 908ms
%------------------------------------------------------------------------------