TSTP Solution File: SEU153+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SEU153+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 : n004.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 17:42:49 EDT 2023
% Result : Theorem 6.36s 1.62s
% Output : Proof 7.69s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU153+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 : n004.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 12:36:38 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.20/0.60 ________ _____
% 0.20/0.60 ___ __ \_________(_)________________________________
% 0.20/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.20/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.20/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.20/0.60
% 0.20/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.20/0.60 (2023-06-19)
% 0.20/0.60
% 0.20/0.60 (c) Philipp Rümmer, 2009-2023
% 0.20/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.20/0.60 Amanda Stjerna.
% 0.20/0.60 Free software under BSD-3-Clause.
% 0.20/0.60
% 0.20/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.20/0.60
% 0.20/0.60 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.20/0.61 Running up to 7 provers in parallel.
% 0.20/0.62 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.20/0.62 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.20/0.62 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.20/0.62 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.20/0.62 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.20/0.62 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.20/0.62 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.11/1.02 Prover 1: Preprocessing ...
% 2.11/1.02 Prover 4: Preprocessing ...
% 2.11/1.06 Prover 2: Preprocessing ...
% 2.11/1.06 Prover 0: Preprocessing ...
% 2.11/1.06 Prover 3: Preprocessing ...
% 2.11/1.06 Prover 6: Preprocessing ...
% 2.11/1.06 Prover 5: Preprocessing ...
% 4.20/1.36 Prover 1: Warning: ignoring some quantifiers
% 4.20/1.38 Prover 3: Warning: ignoring some quantifiers
% 4.20/1.39 Prover 4: Warning: ignoring some quantifiers
% 4.20/1.40 Prover 6: Proving ...
% 4.20/1.40 Prover 3: Constructing countermodel ...
% 4.20/1.40 Prover 5: Proving ...
% 4.20/1.40 Prover 2: Proving ...
% 4.20/1.40 Prover 4: Constructing countermodel ...
% 4.20/1.41 Prover 1: Constructing countermodel ...
% 4.20/1.42 Prover 0: Proving ...
% 6.36/1.62 Prover 3: proved (1001ms)
% 6.36/1.62
% 6.36/1.62 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.36/1.62
% 6.36/1.62 Prover 5: stopped
% 6.36/1.62 Prover 6: stopped
% 6.36/1.63 Prover 0: stopped
% 6.36/1.63 Prover 2: stopped
% 6.36/1.63 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 6.36/1.63 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 6.36/1.63 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 6.36/1.63 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 6.36/1.64 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 6.36/1.66 Prover 7: Preprocessing ...
% 6.36/1.66 Prover 8: Preprocessing ...
% 6.36/1.66 Prover 11: Preprocessing ...
% 6.36/1.66 Prover 13: Preprocessing ...
% 6.36/1.67 Prover 10: Preprocessing ...
% 6.90/1.70 Prover 1: Found proof (size 35)
% 6.90/1.70 Prover 1: proved (1085ms)
% 6.90/1.70 Prover 4: stopped
% 6.90/1.71 Prover 13: stopped
% 6.90/1.71 Prover 11: stopped
% 6.90/1.71 Prover 10: stopped
% 6.90/1.72 Prover 7: Warning: ignoring some quantifiers
% 6.90/1.73 Prover 7: Constructing countermodel ...
% 6.90/1.73 Prover 7: stopped
% 6.90/1.75 Prover 8: Warning: ignoring some quantifiers
% 6.90/1.76 Prover 8: Constructing countermodel ...
% 6.90/1.76 Prover 8: stopped
% 6.90/1.77
% 6.90/1.77 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.90/1.77
% 6.90/1.77 % SZS output start Proof for theBenchmark
% 7.48/1.78 Assumptions after simplification:
% 7.48/1.78 ---------------------------------
% 7.48/1.78
% 7.48/1.78 (commutativity_k3_xboole_0)
% 7.56/1.80 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (set_intersection2(v0, v1) = v2)
% 7.56/1.80 | ~ $i(v1) | ~ $i(v0) | (set_intersection2(v1, v0) = v2 & $i(v2)))
% 7.56/1.80
% 7.56/1.80 (d1_tarski)
% 7.56/1.81 ? [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v0 | ~ (singleton(v1) = v2) |
% 7.56/1.81 ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: any] : (in(v3, v0) = v4 &
% 7.56/1.81 $i(v3) & ( ~ (v4 = 0) | ~ (v3 = v1)) & (v4 = 0 | v3 = v1))) & ! [v0: $i]
% 7.56/1.81 : ! [v1: $i] : ( ~ (singleton(v0) = v1) | ~ $i(v1) | ~ $i(v0) | ( ! [v2:
% 7.56/1.81 $i] : (v2 = v0 | ~ (in(v2, v1) = 0) | ~ $i(v2)) & ! [v2: int] : (v2 =
% 7.56/1.81 0 | ~ (in(v0, v1) = v2))))
% 7.56/1.81
% 7.56/1.81 (d1_xboole_0)
% 7.56/1.81 $i(empty_set) & ! [v0: $i] : ( ~ (in(v0, empty_set) = 0) | ~ $i(v0)) & ?
% 7.56/1.81 [v0: $i] : (v0 = empty_set | ~ $i(v0) | ? [v1: $i] : (in(v1, v0) = 0 &
% 7.56/1.81 $i(v1)))
% 7.56/1.81
% 7.56/1.81 (d3_xboole_0)
% 7.56/1.81 ? [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v0 | ~
% 7.56/1.81 (set_intersection2(v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ?
% 7.56/1.81 [v4: $i] : ? [v5: any] : ? [v6: any] : ? [v7: any] : (in(v4, v2) = v7 &
% 7.56/1.81 in(v4, v1) = v6 & in(v4, v0) = v5 & $i(v4) & ( ~ (v7 = 0) | ~ (v6 = 0) |
% 7.56/1.81 ~ (v5 = 0)) & (v5 = 0 | (v7 = 0 & v6 = 0)))) & ! [v0: $i] : ! [v1: $i]
% 7.56/1.81 : ! [v2: $i] : ( ~ (set_intersection2(v0, v1) = v2) | ~ $i(v2) | ~ $i(v1) |
% 7.56/1.81 ~ $i(v0) | ( ! [v3: $i] : ! [v4: any] : ( ~ (in(v3, v0) = v4) | ~ $i(v3)
% 7.56/1.81 | ? [v5: any] : ? [v6: any] : (in(v3, v2) = v5 & in(v3, v1) = v6 & ( ~
% 7.56/1.81 (v5 = 0) | (v6 = 0 & v4 = 0)))) & ! [v3: $i] : ( ~ (in(v3, v0) = 0)
% 7.56/1.81 | ~ $i(v3) | ? [v4: any] : ? [v5: any] : (in(v3, v2) = v5 & in(v3,
% 7.56/1.81 v1) = v4 & ( ~ (v4 = 0) | v5 = 0)))))
% 7.56/1.81
% 7.56/1.81 (d7_xboole_0)
% 7.67/1.82 $i(empty_set) & ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~
% 7.67/1.82 (disjoint(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ( ~ (v3 =
% 7.67/1.82 empty_set) & set_intersection2(v0, v1) = v3 & $i(v3))) & ! [v0: $i] :
% 7.67/1.82 ! [v1: $i] : ( ~ (disjoint(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) |
% 7.67/1.82 set_intersection2(v0, v1) = empty_set)
% 7.67/1.82
% 7.67/1.82 (l25_zfmisc_1)
% 7.67/1.82 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (disjoint(v2, v1) = 0 &
% 7.67/1.82 singleton(v0) = v2 & in(v0, v1) = 0 & $i(v2) & $i(v1) & $i(v0))
% 7.67/1.82
% 7.67/1.82 (symmetry_r1_xboole_0)
% 7.67/1.82 ! [v0: $i] : ! [v1: $i] : ( ~ (disjoint(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0)
% 7.69/1.82 | disjoint(v1, v0) = 0)
% 7.69/1.82
% 7.69/1.82 (function-axioms)
% 7.69/1.82 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 7.69/1.82 [v3: $i] : (v1 = v0 | ~ (disjoint(v3, v2) = v1) | ~ (disjoint(v3, v2) = v0))
% 7.69/1.82 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 7.69/1.82 (set_intersection2(v3, v2) = v1) | ~ (set_intersection2(v3, v2) = v0)) & !
% 7.69/1.82 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 7.69/1.82 $i] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) & ! [v0:
% 7.69/1.82 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 |
% 7.69/1.82 ~ (empty(v2) = v1) | ~ (empty(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 7.69/1.82 [v2: $i] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0))
% 7.69/1.82
% 7.69/1.82 Further assumptions not needed in the proof:
% 7.69/1.82 --------------------------------------------
% 7.69/1.82 antisymmetry_r2_hidden, dt_k1_tarski, dt_k1_xboole_0, dt_k3_xboole_0,
% 7.69/1.82 fc1_xboole_0, idempotence_k3_xboole_0, rc1_xboole_0, rc2_xboole_0
% 7.69/1.82
% 7.69/1.82 Those formulas are unsatisfiable:
% 7.69/1.82 ---------------------------------
% 7.69/1.82
% 7.69/1.82 Begin of proof
% 7.69/1.82 |
% 7.69/1.82 | ALPHA: (d1_tarski) implies:
% 7.69/1.82 | (1) ! [v0: $i] : ! [v1: $i] : ( ~ (singleton(v0) = v1) | ~ $i(v1) | ~
% 7.69/1.82 | $i(v0) | ( ! [v2: $i] : (v2 = v0 | ~ (in(v2, v1) = 0) | ~ $i(v2)) &
% 7.69/1.82 | ! [v2: int] : (v2 = 0 | ~ (in(v0, v1) = v2))))
% 7.69/1.82 |
% 7.69/1.82 | ALPHA: (d1_xboole_0) implies:
% 7.69/1.83 | (2) ! [v0: $i] : ( ~ (in(v0, empty_set) = 0) | ~ $i(v0))
% 7.69/1.83 |
% 7.69/1.83 | ALPHA: (d3_xboole_0) implies:
% 7.69/1.83 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (set_intersection2(v0,
% 7.69/1.83 | v1) = v2) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ( ! [v3: $i] : !
% 7.69/1.83 | [v4: any] : ( ~ (in(v3, v0) = v4) | ~ $i(v3) | ? [v5: any] : ?
% 7.69/1.83 | [v6: any] : (in(v3, v2) = v5 & in(v3, v1) = v6 & ( ~ (v5 = 0) |
% 7.69/1.83 | (v6 = 0 & v4 = 0)))) & ! [v3: $i] : ( ~ (in(v3, v0) = 0) |
% 7.69/1.83 | ~ $i(v3) | ? [v4: any] : ? [v5: any] : (in(v3, v2) = v5 &
% 7.69/1.83 | in(v3, v1) = v4 & ( ~ (v4 = 0) | v5 = 0)))))
% 7.69/1.83 |
% 7.69/1.83 | ALPHA: (d7_xboole_0) implies:
% 7.69/1.83 | (4) ! [v0: $i] : ! [v1: $i] : ( ~ (disjoint(v0, v1) = 0) | ~ $i(v1) | ~
% 7.69/1.83 | $i(v0) | set_intersection2(v0, v1) = empty_set)
% 7.69/1.83 |
% 7.69/1.83 | ALPHA: (function-axioms) implies:
% 7.69/1.83 | (5) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 7.69/1.83 | ! [v3: $i] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0))
% 7.69/1.83 |
% 7.69/1.83 | DELTA: instantiating (l25_zfmisc_1) with fresh symbols all_18_0, all_18_1,
% 7.69/1.83 | all_18_2 gives:
% 7.69/1.83 | (6) disjoint(all_18_0, all_18_1) = 0 & singleton(all_18_2) = all_18_0 &
% 7.69/1.83 | in(all_18_2, all_18_1) = 0 & $i(all_18_0) & $i(all_18_1) & $i(all_18_2)
% 7.69/1.83 |
% 7.69/1.83 | ALPHA: (6) implies:
% 7.69/1.83 | (7) $i(all_18_2)
% 7.69/1.83 | (8) $i(all_18_1)
% 7.69/1.83 | (9) $i(all_18_0)
% 7.69/1.83 | (10) in(all_18_2, all_18_1) = 0
% 7.69/1.83 | (11) singleton(all_18_2) = all_18_0
% 7.69/1.83 | (12) disjoint(all_18_0, all_18_1) = 0
% 7.69/1.83 |
% 7.69/1.83 | GROUND_INST: instantiating (1) with all_18_2, all_18_0, simplifying with (7),
% 7.69/1.83 | (9), (11) gives:
% 7.69/1.83 | (13) ! [v0: any] : (v0 = all_18_2 | ~ (in(v0, all_18_0) = 0) | ~ $i(v0))
% 7.69/1.83 | & ! [v0: int] : (v0 = 0 | ~ (in(all_18_2, all_18_0) = v0))
% 7.69/1.83 |
% 7.69/1.83 | ALPHA: (13) implies:
% 7.69/1.84 | (14) ! [v0: int] : (v0 = 0 | ~ (in(all_18_2, all_18_0) = v0))
% 7.69/1.84 |
% 7.69/1.84 | GROUND_INST: instantiating (symmetry_r1_xboole_0) with all_18_0, all_18_1,
% 7.69/1.84 | simplifying with (8), (9), (12) gives:
% 7.69/1.84 | (15) disjoint(all_18_1, all_18_0) = 0
% 7.69/1.84 |
% 7.69/1.84 | GROUND_INST: instantiating (4) with all_18_0, all_18_1, simplifying with (8),
% 7.69/1.84 | (9), (12) gives:
% 7.69/1.84 | (16) set_intersection2(all_18_0, all_18_1) = empty_set
% 7.69/1.84 |
% 7.69/1.84 | GROUND_INST: instantiating (commutativity_k3_xboole_0) with all_18_0,
% 7.69/1.84 | all_18_1, empty_set, simplifying with (8), (9), (16) gives:
% 7.69/1.84 | (17) set_intersection2(all_18_1, all_18_0) = empty_set & $i(empty_set)
% 7.69/1.84 |
% 7.69/1.84 | ALPHA: (17) implies:
% 7.69/1.84 | (18) $i(empty_set)
% 7.69/1.84 |
% 7.69/1.84 | GROUND_INST: instantiating (4) with all_18_1, all_18_0, simplifying with (8),
% 7.69/1.84 | (9), (15) gives:
% 7.69/1.84 | (19) set_intersection2(all_18_1, all_18_0) = empty_set
% 7.69/1.84 |
% 7.69/1.84 | GROUND_INST: instantiating (3) with all_18_1, all_18_0, empty_set, simplifying
% 7.69/1.84 | with (8), (9), (18), (19) gives:
% 7.69/1.84 | (20) ! [v0: $i] : ! [v1: any] : ( ~ (in(v0, all_18_1) = v1) | ~ $i(v0) |
% 7.69/1.84 | ? [v2: any] : ? [v3: any] : (in(v0, all_18_0) = v3 & in(v0,
% 7.69/1.84 | empty_set) = v2 & ( ~ (v2 = 0) | (v3 = 0 & v1 = 0)))) & ! [v0:
% 7.69/1.84 | $i] : ( ~ (in(v0, all_18_1) = 0) | ~ $i(v0) | ? [v1: any] : ?
% 7.69/1.84 | [v2: any] : (in(v0, all_18_0) = v1 & in(v0, empty_set) = v2 & ( ~
% 7.69/1.84 | (v1 = 0) | v2 = 0)))
% 7.69/1.84 |
% 7.69/1.84 | ALPHA: (20) implies:
% 7.69/1.84 | (21) ! [v0: $i] : ( ~ (in(v0, all_18_1) = 0) | ~ $i(v0) | ? [v1: any] :
% 7.69/1.84 | ? [v2: any] : (in(v0, all_18_0) = v1 & in(v0, empty_set) = v2 & ( ~
% 7.69/1.84 | (v1 = 0) | v2 = 0)))
% 7.69/1.84 | (22) ! [v0: $i] : ! [v1: any] : ( ~ (in(v0, all_18_1) = v1) | ~ $i(v0) |
% 7.69/1.84 | ? [v2: any] : ? [v3: any] : (in(v0, all_18_0) = v3 & in(v0,
% 7.69/1.84 | empty_set) = v2 & ( ~ (v2 = 0) | (v3 = 0 & v1 = 0))))
% 7.69/1.84 |
% 7.69/1.84 | GROUND_INST: instantiating (21) with all_18_2, simplifying with (7), (10)
% 7.69/1.84 | gives:
% 7.69/1.84 | (23) ? [v0: any] : ? [v1: any] : (in(all_18_2, all_18_0) = v0 &
% 7.69/1.84 | in(all_18_2, empty_set) = v1 & ( ~ (v0 = 0) | v1 = 0))
% 7.69/1.84 |
% 7.69/1.84 | GROUND_INST: instantiating (22) with all_18_2, 0, simplifying with (7), (10)
% 7.69/1.84 | gives:
% 7.69/1.84 | (24) ? [v0: any] : ? [v1: any] : (in(all_18_2, all_18_0) = v1 &
% 7.69/1.84 | in(all_18_2, empty_set) = v0 & ( ~ (v0 = 0) | v1 = 0))
% 7.69/1.84 |
% 7.69/1.84 | DELTA: instantiating (24) with fresh symbols all_46_0, all_46_1 gives:
% 7.69/1.84 | (25) in(all_18_2, all_18_0) = all_46_0 & in(all_18_2, empty_set) = all_46_1
% 7.69/1.84 | & ( ~ (all_46_1 = 0) | all_46_0 = 0)
% 7.69/1.84 |
% 7.69/1.84 | ALPHA: (25) implies:
% 7.69/1.84 | (26) in(all_18_2, empty_set) = all_46_1
% 7.69/1.85 | (27) in(all_18_2, all_18_0) = all_46_0
% 7.69/1.85 |
% 7.69/1.85 | DELTA: instantiating (23) with fresh symbols all_48_0, all_48_1 gives:
% 7.69/1.85 | (28) in(all_18_2, all_18_0) = all_48_1 & in(all_18_2, empty_set) = all_48_0
% 7.69/1.85 | & ( ~ (all_48_1 = 0) | all_48_0 = 0)
% 7.69/1.85 |
% 7.69/1.85 | ALPHA: (28) implies:
% 7.69/1.85 | (29) in(all_18_2, empty_set) = all_48_0
% 7.69/1.85 | (30) in(all_18_2, all_18_0) = all_48_1
% 7.69/1.85 | (31) ~ (all_48_1 = 0) | all_48_0 = 0
% 7.69/1.85 |
% 7.69/1.85 | GROUND_INST: instantiating (5) with all_46_1, all_48_0, empty_set, all_18_2,
% 7.69/1.85 | simplifying with (26), (29) gives:
% 7.69/1.85 | (32) all_48_0 = all_46_1
% 7.69/1.85 |
% 7.69/1.85 | GROUND_INST: instantiating (5) with all_46_0, all_48_1, all_18_0, all_18_2,
% 7.69/1.85 | simplifying with (27), (30) gives:
% 7.69/1.85 | (33) all_48_1 = all_46_0
% 7.69/1.85 |
% 7.69/1.85 | GROUND_INST: instantiating (14) with all_48_1, simplifying with (30) gives:
% 7.69/1.85 | (34) all_48_1 = 0
% 7.69/1.85 |
% 7.69/1.85 | COMBINE_EQS: (33), (34) imply:
% 7.69/1.85 | (35) all_46_0 = 0
% 7.69/1.85 |
% 7.69/1.85 | BETA: splitting (31) gives:
% 7.69/1.85 |
% 7.69/1.85 | Case 1:
% 7.69/1.85 | |
% 7.69/1.85 | | (36) ~ (all_48_1 = 0)
% 7.69/1.85 | |
% 7.69/1.85 | | REDUCE: (34), (36) imply:
% 7.69/1.85 | | (37) $false
% 7.69/1.85 | |
% 7.69/1.85 | | CLOSE: (37) is inconsistent.
% 7.69/1.85 | |
% 7.69/1.85 | Case 2:
% 7.69/1.85 | |
% 7.69/1.85 | | (38) all_48_0 = 0
% 7.69/1.85 | |
% 7.69/1.85 | | COMBINE_EQS: (32), (38) imply:
% 7.69/1.85 | | (39) all_46_1 = 0
% 7.69/1.85 | |
% 7.69/1.85 | | REDUCE: (26), (39) imply:
% 7.69/1.85 | | (40) in(all_18_2, empty_set) = 0
% 7.69/1.85 | |
% 7.69/1.85 | | GROUND_INST: instantiating (2) with all_18_2, simplifying with (7), (40)
% 7.69/1.85 | | gives:
% 7.69/1.85 | | (41) $false
% 7.69/1.85 | |
% 7.69/1.85 | | CLOSE: (41) is inconsistent.
% 7.69/1.85 | |
% 7.69/1.85 | End of split
% 7.69/1.85 |
% 7.69/1.85 End of proof
% 7.69/1.85 % SZS output end Proof for theBenchmark
% 7.69/1.85
% 7.69/1.85 1254ms
%------------------------------------------------------------------------------