TSTP Solution File: SEU188+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SEU188+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 : n020.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 17:43:08 EDT 2023
% Result : Theorem 10.94s 2.41s
% Output : Proof 14.24s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEU188+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.12 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.11/0.33 % Computer : n020.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Wed Aug 23 13:53:31 EDT 2023
% 0.11/0.33 % CPUTime :
% 0.18/0.62 ________ _____
% 0.18/0.62 ___ __ \_________(_)________________________________
% 0.18/0.62 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.18/0.62 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.18/0.62 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.18/0.62
% 0.18/0.62 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.18/0.62 (2023-06-19)
% 0.18/0.62
% 0.18/0.62 (c) Philipp Rümmer, 2009-2023
% 0.18/0.62 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.18/0.62 Amanda Stjerna.
% 0.18/0.62 Free software under BSD-3-Clause.
% 0.18/0.62
% 0.18/0.62 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.18/0.62
% 0.18/0.62 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.18/0.63 Running up to 7 provers in parallel.
% 0.18/0.65 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.18/0.65 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.18/0.65 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.18/0.65 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.18/0.65 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.18/0.65 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.18/0.65 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.87/1.18 Prover 4: Preprocessing ...
% 2.87/1.18 Prover 1: Preprocessing ...
% 2.87/1.23 Prover 2: Preprocessing ...
% 2.87/1.23 Prover 5: Preprocessing ...
% 2.87/1.23 Prover 3: Preprocessing ...
% 2.87/1.23 Prover 6: Preprocessing ...
% 2.87/1.24 Prover 0: Preprocessing ...
% 6.93/1.81 Prover 1: Warning: ignoring some quantifiers
% 6.93/1.81 Prover 3: Warning: ignoring some quantifiers
% 7.47/1.85 Prover 4: Warning: ignoring some quantifiers
% 7.72/1.89 Prover 1: Constructing countermodel ...
% 7.72/1.89 Prover 4: Constructing countermodel ...
% 7.72/1.90 Prover 6: Proving ...
% 7.72/1.90 Prover 2: Proving ...
% 7.72/1.90 Prover 3: Constructing countermodel ...
% 7.72/1.91 Prover 5: Proving ...
% 8.13/1.95 Prover 0: Proving ...
% 10.94/2.41 Prover 6: proved (1756ms)
% 10.94/2.41
% 10.94/2.41 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 10.94/2.41
% 10.94/2.41 Prover 3: stopped
% 10.94/2.41 Prover 2: stopped
% 10.94/2.42 Prover 0: stopped
% 10.94/2.42 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 10.94/2.42 Prover 5: stopped
% 10.94/2.42 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 10.94/2.42 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 10.94/2.42 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 10.94/2.42 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 11.62/2.48 Prover 10: Preprocessing ...
% 11.62/2.49 Prover 7: Preprocessing ...
% 12.11/2.52 Prover 8: Preprocessing ...
% 12.11/2.54 Prover 11: Preprocessing ...
% 12.11/2.56 Prover 13: Preprocessing ...
% 12.56/2.62 Prover 10: Warning: ignoring some quantifiers
% 12.56/2.65 Prover 10: Constructing countermodel ...
% 13.41/2.71 Prover 7: Warning: ignoring some quantifiers
% 13.68/2.73 Prover 7: Constructing countermodel ...
% 13.68/2.79 Prover 1: Found proof (size 80)
% 13.68/2.79 Prover 1: proved (2142ms)
% 13.68/2.79 Prover 7: stopped
% 13.68/2.79 Prover 10: stopped
% 13.68/2.79 Prover 4: stopped
% 13.68/2.79 Prover 8: Warning: ignoring some quantifiers
% 14.24/2.81 Prover 11: Warning: ignoring some quantifiers
% 14.24/2.81 Prover 8: Constructing countermodel ...
% 14.24/2.81 Prover 13: Warning: ignoring some quantifiers
% 14.24/2.82 Prover 8: stopped
% 14.24/2.83 Prover 13: Constructing countermodel ...
% 14.24/2.83 Prover 11: Constructing countermodel ...
% 14.24/2.84 Prover 13: stopped
% 14.24/2.84 Prover 11: stopped
% 14.24/2.84
% 14.24/2.84 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 14.24/2.84
% 14.24/2.87 % SZS output start Proof for theBenchmark
% 14.24/2.87 Assumptions after simplification:
% 14.24/2.87 ---------------------------------
% 14.24/2.87
% 14.24/2.87 (fc5_relat_1)
% 14.24/2.91 ! [v0: $i] : ! [v1: $i] : ( ~ (relation_dom(v0) = v1) | ~ $i(v0) | ? [v2:
% 14.24/2.91 any] : ? [v3: any] : ? [v4: any] : (relation(v0) = v3 & empty(v1) = v4 &
% 14.24/2.91 empty(v0) = v2 & ( ~ (v4 = 0) | ~ (v3 = 0) | v2 = 0)))
% 14.24/2.91
% 14.24/2.91 (fc6_relat_1)
% 14.24/2.92 ! [v0: $i] : ! [v1: $i] : ( ~ (relation_rng(v0) = v1) | ~ $i(v0) | ? [v2:
% 14.24/2.92 any] : ? [v3: any] : ? [v4: any] : (relation(v0) = v3 & empty(v1) = v4 &
% 14.24/2.92 empty(v0) = v2 & ( ~ (v4 = 0) | ~ (v3 = 0) | v2 = 0)))
% 14.24/2.92
% 14.24/2.92 (fc7_relat_1)
% 14.24/2.92 ! [v0: $i] : ! [v1: $i] : ( ~ (relation_dom(v0) = v1) | ~ $i(v0) | ? [v2:
% 14.24/2.92 any] : ? [v3: any] : ? [v4: any] : (relation(v1) = v4 & empty(v1) = v3 &
% 14.24/2.92 empty(v0) = v2 & ( ~ (v2 = 0) | (v4 = 0 & v3 = 0))))
% 14.24/2.92
% 14.24/2.92 (fc8_relat_1)
% 14.24/2.92 ! [v0: $i] : ! [v1: $i] : ( ~ (relation_rng(v0) = v1) | ~ $i(v0) | ? [v2:
% 14.24/2.92 any] : ? [v3: any] : ? [v4: any] : (relation(v1) = v4 & empty(v1) = v3 &
% 14.24/2.92 empty(v0) = v2 & ( ~ (v2 = 0) | (v4 = 0 & v3 = 0))))
% 14.24/2.92
% 14.24/2.92 (rc1_relat_1)
% 14.24/2.93 ? [v0: $i] : (relation(v0) = 0 & empty(v0) = 0 & $i(v0))
% 14.24/2.93
% 14.24/2.93 (rc1_xboole_0)
% 14.24/2.93 ? [v0: $i] : (empty(v0) = 0 & $i(v0))
% 14.24/2.93
% 14.24/2.93 (t56_relat_1)
% 14.24/2.93 $i(empty_set) & ! [v0: $i] : (v0 = empty_set | ~ (relation(v0) = 0) | ~
% 14.24/2.93 $i(v0) | ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : (ordered_pair(v1, v2) =
% 14.24/2.93 v3 & in(v3, v0) = 0 & $i(v3) & $i(v2) & $i(v1)))
% 14.24/2.93
% 14.24/2.93 (t64_relat_1)
% 14.24/2.93 $i(empty_set) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ( ~ (v0 = empty_set)
% 14.24/2.93 & relation_rng(v0) = v2 & relation_dom(v0) = v1 & relation(v0) = 0 & $i(v2)
% 14.24/2.93 & $i(v1) & $i(v0) & (v2 = empty_set | v1 = empty_set))
% 14.24/2.93
% 14.24/2.93 (t6_boole)
% 14.24/2.93 $i(empty_set) & ! [v0: $i] : (v0 = empty_set | ~ (empty(v0) = 0) | ~
% 14.24/2.93 $i(v0))
% 14.24/2.93
% 14.24/2.93 (t7_boole)
% 14.24/2.94 ! [v0: $i] : ! [v1: $i] : ( ~ (in(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ?
% 14.24/2.94 [v2: int] : ( ~ (v2 = 0) & empty(v1) = v2))
% 14.24/2.94
% 14.24/2.94 (t8_boole)
% 14.24/2.94 ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (empty(v1) = 0) | ~ (empty(v0) = 0)
% 14.24/2.94 | ~ $i(v1) | ~ $i(v0))
% 14.24/2.94
% 14.24/2.94 (function-axioms)
% 14.24/2.95 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 14.24/2.95 [v3: $i] : (v1 = v0 | ~ (element(v3, v2) = v1) | ~ (element(v3, v2) = v0)) &
% 14.24/2.95 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 14.24/2.95 (ordered_pair(v3, v2) = v1) | ~ (ordered_pair(v3, v2) = v0)) & ! [v0: $i]
% 14.24/2.95 : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (unordered_pair(v3,
% 14.24/2.95 v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) & ! [v0:
% 14.24/2.95 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 14.24/2.95 : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) & ! [v0: $i] : !
% 14.24/2.95 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (singleton(v2) = v1) | ~
% 14.24/2.95 (singleton(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 |
% 14.24/2.95 ~ (relation_rng(v2) = v1) | ~ (relation_rng(v2) = v0)) & ! [v0: $i] : !
% 14.24/2.95 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (relation_dom(v2) = v1) | ~
% 14.24/2.95 (relation_dom(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 14.24/2.95 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (relation(v2) = v1) | ~
% 14.24/2.95 (relation(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 14.24/2.95 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (empty(v2) = v1) | ~
% 14.24/2.95 (empty(v2) = v0))
% 14.24/2.95
% 14.24/2.95 Further assumptions not needed in the proof:
% 14.24/2.95 --------------------------------------------
% 14.24/2.95 antisymmetry_r2_hidden, cc1_relat_1, commutativity_k2_tarski, d4_relat_1,
% 14.24/2.95 d5_relat_1, d5_tarski, dt_k1_relat_1, dt_k1_tarski, dt_k1_xboole_0,
% 14.24/2.95 dt_k2_relat_1, dt_k2_tarski, dt_k4_tarski, dt_m1_subset_1,
% 14.24/2.95 existence_m1_subset_1, fc1_xboole_0, fc1_zfmisc_1, fc2_subset_1, fc3_subset_1,
% 14.24/2.95 fc4_relat_1, rc2_relat_1, rc2_xboole_0, t1_subset, t2_subset
% 14.24/2.95
% 14.24/2.95 Those formulas are unsatisfiable:
% 14.24/2.95 ---------------------------------
% 14.24/2.95
% 14.24/2.95 Begin of proof
% 14.24/2.95 |
% 14.24/2.95 | ALPHA: (t56_relat_1) implies:
% 14.24/2.95 | (1) ! [v0: $i] : (v0 = empty_set | ~ (relation(v0) = 0) | ~ $i(v0) | ?
% 14.24/2.95 | [v1: $i] : ? [v2: $i] : ? [v3: $i] : (ordered_pair(v1, v2) = v3 &
% 14.24/2.95 | in(v3, v0) = 0 & $i(v3) & $i(v2) & $i(v1)))
% 14.24/2.95 |
% 14.24/2.95 | ALPHA: (t6_boole) implies:
% 14.24/2.95 | (2) ! [v0: $i] : (v0 = empty_set | ~ (empty(v0) = 0) | ~ $i(v0))
% 14.24/2.95 |
% 14.24/2.95 | ALPHA: (t64_relat_1) implies:
% 14.24/2.96 | (3) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ( ~ (v0 = empty_set) &
% 14.24/2.96 | relation_rng(v0) = v2 & relation_dom(v0) = v1 & relation(v0) = 0 &
% 14.24/2.96 | $i(v2) & $i(v1) & $i(v0) & (v2 = empty_set | v1 = empty_set))
% 14.24/2.96 |
% 14.24/2.96 | ALPHA: (function-axioms) implies:
% 14.24/2.96 | (4) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 14.24/2.96 | (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0))
% 14.24/2.96 | (5) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 14.24/2.96 | (v1 = v0 | ~ (relation(v2) = v1) | ~ (relation(v2) = v0))
% 14.24/2.96 |
% 14.24/2.96 | DELTA: instantiating (rc1_xboole_0) with fresh symbol all_23_0 gives:
% 14.24/2.96 | (6) empty(all_23_0) = 0 & $i(all_23_0)
% 14.24/2.96 |
% 14.24/2.96 | ALPHA: (6) implies:
% 14.24/2.96 | (7) $i(all_23_0)
% 14.24/2.96 | (8) empty(all_23_0) = 0
% 14.24/2.96 |
% 14.24/2.96 | DELTA: instantiating (rc1_relat_1) with fresh symbol all_28_0 gives:
% 14.24/2.96 | (9) relation(all_28_0) = 0 & empty(all_28_0) = 0 & $i(all_28_0)
% 14.24/2.96 |
% 14.24/2.96 | ALPHA: (9) implies:
% 14.24/2.96 | (10) $i(all_28_0)
% 14.24/2.96 | (11) empty(all_28_0) = 0
% 14.24/2.96 |
% 14.24/2.96 | DELTA: instantiating (3) with fresh symbols all_32_0, all_32_1, all_32_2
% 14.24/2.96 | gives:
% 14.24/2.96 | (12) ~ (all_32_2 = empty_set) & relation_rng(all_32_2) = all_32_0 &
% 14.24/2.96 | relation_dom(all_32_2) = all_32_1 & relation(all_32_2) = 0 &
% 14.24/2.96 | $i(all_32_0) & $i(all_32_1) & $i(all_32_2) & (all_32_0 = empty_set |
% 14.24/2.96 | all_32_1 = empty_set)
% 14.24/2.96 |
% 14.24/2.96 | ALPHA: (12) implies:
% 14.24/2.96 | (13) ~ (all_32_2 = empty_set)
% 14.24/2.96 | (14) $i(all_32_2)
% 14.24/2.96 | (15) relation(all_32_2) = 0
% 14.24/2.97 | (16) relation_dom(all_32_2) = all_32_1
% 14.24/2.97 | (17) relation_rng(all_32_2) = all_32_0
% 14.24/2.97 | (18) all_32_0 = empty_set | all_32_1 = empty_set
% 14.24/2.97 |
% 14.24/2.97 | GROUND_INST: instantiating (t8_boole) with all_23_0, all_28_0, simplifying
% 14.24/2.97 | with (7), (8), (10), (11) gives:
% 14.24/2.97 | (19) all_28_0 = all_23_0
% 14.24/2.97 |
% 14.24/2.97 | GROUND_INST: instantiating (2) with all_28_0, simplifying with (10), (11)
% 14.24/2.97 | gives:
% 14.24/2.97 | (20) all_28_0 = empty_set
% 14.24/2.97 |
% 14.24/2.97 | GROUND_INST: instantiating (1) with all_32_2, simplifying with (14), (15)
% 14.24/2.97 | gives:
% 14.24/2.97 | (21) all_32_2 = empty_set | ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 14.24/2.97 | (ordered_pair(v0, v1) = v2 & in(v2, all_32_2) = 0 & $i(v2) & $i(v1) &
% 14.24/2.97 | $i(v0))
% 14.24/2.97 |
% 14.24/2.97 | GROUND_INST: instantiating (fc7_relat_1) with all_32_2, all_32_1, simplifying
% 14.24/2.97 | with (14), (16) gives:
% 14.24/2.97 | (22) ? [v0: any] : ? [v1: any] : ? [v2: any] : (relation(all_32_1) = v2
% 14.24/2.97 | & empty(all_32_1) = v1 & empty(all_32_2) = v0 & ( ~ (v0 = 0) | (v2 =
% 14.24/2.97 | 0 & v1 = 0)))
% 14.24/2.97 |
% 14.24/2.97 | GROUND_INST: instantiating (fc5_relat_1) with all_32_2, all_32_1, simplifying
% 14.24/2.97 | with (14), (16) gives:
% 14.24/2.97 | (23) ? [v0: any] : ? [v1: any] : ? [v2: any] : (relation(all_32_2) = v1
% 14.24/2.97 | & empty(all_32_1) = v2 & empty(all_32_2) = v0 & ( ~ (v2 = 0) | ~
% 14.24/2.97 | (v1 = 0) | v0 = 0))
% 14.24/2.97 |
% 14.24/2.97 | GROUND_INST: instantiating (fc8_relat_1) with all_32_2, all_32_0, simplifying
% 14.24/2.97 | with (14), (17) gives:
% 14.24/2.97 | (24) ? [v0: any] : ? [v1: any] : ? [v2: any] : (relation(all_32_0) = v2
% 14.24/2.97 | & empty(all_32_0) = v1 & empty(all_32_2) = v0 & ( ~ (v0 = 0) | (v2 =
% 14.24/2.97 | 0 & v1 = 0)))
% 14.24/2.98 |
% 14.24/2.98 | GROUND_INST: instantiating (fc6_relat_1) with all_32_2, all_32_0, simplifying
% 14.24/2.98 | with (14), (17) gives:
% 14.24/2.98 | (25) ? [v0: any] : ? [v1: any] : ? [v2: any] : (relation(all_32_2) = v1
% 14.24/2.98 | & empty(all_32_0) = v2 & empty(all_32_2) = v0 & ( ~ (v2 = 0) | ~
% 14.24/2.98 | (v1 = 0) | v0 = 0))
% 14.24/2.98 |
% 14.24/2.98 | COMBINE_EQS: (19), (20) imply:
% 14.24/2.98 | (26) all_23_0 = empty_set
% 14.24/2.98 |
% 14.24/2.98 | SIMP: (26) implies:
% 14.24/2.98 | (27) all_23_0 = empty_set
% 14.24/2.98 |
% 14.24/2.98 | DELTA: instantiating (25) with fresh symbols all_40_0, all_40_1, all_40_2
% 14.24/2.98 | gives:
% 14.24/2.98 | (28) relation(all_32_2) = all_40_1 & empty(all_32_0) = all_40_0 &
% 14.24/2.98 | empty(all_32_2) = all_40_2 & ( ~ (all_40_0 = 0) | ~ (all_40_1 = 0) |
% 14.24/2.98 | all_40_2 = 0)
% 14.24/2.98 |
% 14.24/2.98 | ALPHA: (28) implies:
% 14.24/2.98 | (29) empty(all_32_2) = all_40_2
% 14.24/2.98 | (30) empty(all_32_0) = all_40_0
% 14.24/2.98 | (31) relation(all_32_2) = all_40_1
% 14.24/2.98 | (32) ~ (all_40_0 = 0) | ~ (all_40_1 = 0) | all_40_2 = 0
% 14.24/2.98 |
% 14.24/2.98 | DELTA: instantiating (24) with fresh symbols all_42_0, all_42_1, all_42_2
% 14.24/2.98 | gives:
% 14.24/2.98 | (33) relation(all_32_0) = all_42_0 & empty(all_32_0) = all_42_1 &
% 14.24/2.98 | empty(all_32_2) = all_42_2 & ( ~ (all_42_2 = 0) | (all_42_0 = 0 &
% 14.24/2.98 | all_42_1 = 0))
% 14.24/2.98 |
% 14.24/2.98 | ALPHA: (33) implies:
% 14.24/2.98 | (34) empty(all_32_2) = all_42_2
% 14.24/2.98 | (35) empty(all_32_0) = all_42_1
% 14.24/2.98 |
% 14.24/2.98 | DELTA: instantiating (23) with fresh symbols all_44_0, all_44_1, all_44_2
% 14.24/2.98 | gives:
% 14.24/2.98 | (36) relation(all_32_2) = all_44_1 & empty(all_32_1) = all_44_0 &
% 14.24/2.98 | empty(all_32_2) = all_44_2 & ( ~ (all_44_0 = 0) | ~ (all_44_1 = 0) |
% 14.24/2.98 | all_44_2 = 0)
% 14.24/2.98 |
% 14.24/2.98 | ALPHA: (36) implies:
% 14.24/2.98 | (37) empty(all_32_2) = all_44_2
% 14.24/2.98 | (38) empty(all_32_1) = all_44_0
% 14.24/2.98 | (39) relation(all_32_2) = all_44_1
% 14.24/2.98 | (40) ~ (all_44_0 = 0) | ~ (all_44_1 = 0) | all_44_2 = 0
% 14.24/2.98 |
% 14.24/2.98 | DELTA: instantiating (22) with fresh symbols all_46_0, all_46_1, all_46_2
% 14.24/2.98 | gives:
% 14.24/2.99 | (41) relation(all_32_1) = all_46_0 & empty(all_32_1) = all_46_1 &
% 14.24/2.99 | empty(all_32_2) = all_46_2 & ( ~ (all_46_2 = 0) | (all_46_0 = 0 &
% 14.24/2.99 | all_46_1 = 0))
% 14.24/2.99 |
% 14.24/2.99 | ALPHA: (41) implies:
% 14.24/2.99 | (42) empty(all_32_2) = all_46_2
% 14.24/2.99 | (43) empty(all_32_1) = all_46_1
% 14.24/2.99 |
% 14.24/2.99 | REDUCE: (8), (27) imply:
% 14.24/2.99 | (44) empty(empty_set) = 0
% 14.24/2.99 |
% 14.24/2.99 | BETA: splitting (21) gives:
% 14.24/2.99 |
% 14.24/2.99 | Case 1:
% 14.24/2.99 | |
% 14.24/2.99 | | (45) all_32_2 = empty_set
% 14.24/2.99 | |
% 14.24/2.99 | | REDUCE: (13), (45) imply:
% 14.24/2.99 | | (46) $false
% 14.24/2.99 | |
% 14.24/2.99 | | CLOSE: (46) is inconsistent.
% 14.24/2.99 | |
% 14.24/2.99 | Case 2:
% 14.24/2.99 | |
% 14.24/2.99 | | (47) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (ordered_pair(v0, v1) = v2
% 14.24/2.99 | | & in(v2, all_32_2) = 0 & $i(v2) & $i(v1) & $i(v0))
% 14.24/2.99 | |
% 14.24/2.99 | | DELTA: instantiating (47) with fresh symbols all_52_0, all_52_1, all_52_2
% 14.24/2.99 | | gives:
% 14.24/2.99 | | (48) ordered_pair(all_52_2, all_52_1) = all_52_0 & in(all_52_0, all_32_2)
% 14.24/2.99 | | = 0 & $i(all_52_0) & $i(all_52_1) & $i(all_52_2)
% 14.24/2.99 | |
% 14.24/2.99 | | ALPHA: (48) implies:
% 14.24/2.99 | | (49) $i(all_52_0)
% 14.24/2.99 | | (50) in(all_52_0, all_32_2) = 0
% 14.24/2.99 | |
% 14.24/2.99 | | GROUND_INST: instantiating (4) with all_42_2, all_44_2, all_32_2,
% 14.24/2.99 | | simplifying with (34), (37) gives:
% 14.24/2.99 | | (51) all_44_2 = all_42_2
% 14.24/2.99 | |
% 14.24/2.99 | | GROUND_INST: instantiating (4) with all_44_2, all_46_2, all_32_2,
% 14.24/2.99 | | simplifying with (37), (42) gives:
% 14.24/2.99 | | (52) all_46_2 = all_44_2
% 14.24/2.99 | |
% 14.24/2.99 | | GROUND_INST: instantiating (4) with all_40_2, all_46_2, all_32_2,
% 14.24/2.99 | | simplifying with (29), (42) gives:
% 14.24/2.99 | | (53) all_46_2 = all_40_2
% 14.24/2.99 | |
% 14.24/2.99 | | GROUND_INST: instantiating (4) with all_44_0, all_46_1, all_32_1,
% 14.24/2.99 | | simplifying with (38), (43) gives:
% 14.24/2.99 | | (54) all_46_1 = all_44_0
% 14.24/2.99 | |
% 14.24/3.00 | | GROUND_INST: instantiating (4) with all_40_0, all_42_1, all_32_0,
% 14.24/3.00 | | simplifying with (30), (35) gives:
% 14.24/3.00 | | (55) all_42_1 = all_40_0
% 14.24/3.00 | |
% 14.24/3.00 | | GROUND_INST: instantiating (5) with 0, all_44_1, all_32_2, simplifying with
% 14.24/3.00 | | (15), (39) gives:
% 14.24/3.00 | | (56) all_44_1 = 0
% 14.24/3.00 | |
% 14.24/3.00 | | GROUND_INST: instantiating (5) with all_40_1, all_44_1, all_32_2,
% 14.24/3.00 | | simplifying with (31), (39) gives:
% 14.24/3.00 | | (57) all_44_1 = all_40_1
% 14.24/3.00 | |
% 14.24/3.00 | | COMBINE_EQS: (52), (53) imply:
% 14.24/3.00 | | (58) all_44_2 = all_40_2
% 14.24/3.00 | |
% 14.24/3.00 | | SIMP: (58) implies:
% 14.24/3.00 | | (59) all_44_2 = all_40_2
% 14.24/3.00 | |
% 14.24/3.00 | | COMBINE_EQS: (56), (57) imply:
% 14.24/3.00 | | (60) all_40_1 = 0
% 14.24/3.00 | |
% 14.24/3.00 | | SIMP: (60) implies:
% 14.24/3.00 | | (61) all_40_1 = 0
% 14.24/3.00 | |
% 14.24/3.00 | | COMBINE_EQS: (51), (59) imply:
% 14.24/3.00 | | (62) all_42_2 = all_40_2
% 14.24/3.00 | |
% 14.24/3.00 | | SIMP: (62) implies:
% 14.24/3.00 | | (63) all_42_2 = all_40_2
% 14.24/3.00 | |
% 14.24/3.00 | | GROUND_INST: instantiating (t7_boole) with all_52_0, all_32_2, simplifying
% 14.24/3.00 | | with (14), (49), (50) gives:
% 14.24/3.00 | | (64) ? [v0: int] : ( ~ (v0 = 0) & empty(all_32_2) = v0)
% 14.24/3.00 | |
% 14.24/3.00 | | DELTA: instantiating (64) with fresh symbol all_81_0 gives:
% 14.24/3.00 | | (65) ~ (all_81_0 = 0) & empty(all_32_2) = all_81_0
% 14.24/3.00 | |
% 14.24/3.00 | | ALPHA: (65) implies:
% 14.24/3.00 | | (66) ~ (all_81_0 = 0)
% 14.24/3.00 | | (67) empty(all_32_2) = all_81_0
% 14.24/3.00 | |
% 14.24/3.00 | | GROUND_INST: instantiating (4) with all_40_2, all_81_0, all_32_2,
% 14.24/3.00 | | simplifying with (29), (67) gives:
% 14.24/3.00 | | (68) all_81_0 = all_40_2
% 14.24/3.00 | |
% 14.24/3.00 | | REDUCE: (66), (68) imply:
% 14.24/3.00 | | (69) ~ (all_40_2 = 0)
% 14.24/3.00 | |
% 14.24/3.00 | | BETA: splitting (32) gives:
% 14.24/3.00 | |
% 14.24/3.00 | | Case 1:
% 14.24/3.00 | | |
% 14.24/3.00 | | | (70) ~ (all_40_0 = 0)
% 14.24/3.00 | | |
% 14.24/3.00 | | | BETA: splitting (40) gives:
% 14.24/3.00 | | |
% 14.24/3.00 | | | Case 1:
% 14.24/3.00 | | | |
% 14.24/3.00 | | | | (71) ~ (all_44_0 = 0)
% 14.24/3.00 | | | |
% 14.24/3.00 | | | | BETA: splitting (18) gives:
% 14.24/3.00 | | | |
% 14.24/3.00 | | | | Case 1:
% 14.24/3.00 | | | | |
% 14.24/3.00 | | | | | (72) all_32_0 = empty_set
% 14.24/3.00 | | | | |
% 14.24/3.00 | | | | | REDUCE: (30), (72) imply:
% 14.24/3.00 | | | | | (73) empty(empty_set) = all_40_0
% 14.24/3.00 | | | | |
% 14.24/3.00 | | | | | GROUND_INST: instantiating (4) with 0, all_40_0, empty_set,
% 14.24/3.00 | | | | | simplifying with (44), (73) gives:
% 14.24/3.00 | | | | | (74) all_40_0 = 0
% 14.24/3.00 | | | | |
% 14.24/3.00 | | | | | REDUCE: (70), (74) imply:
% 14.24/3.00 | | | | | (75) $false
% 14.24/3.00 | | | | |
% 14.24/3.00 | | | | | CLOSE: (75) is inconsistent.
% 14.24/3.00 | | | | |
% 14.24/3.00 | | | | Case 2:
% 14.24/3.00 | | | | |
% 14.24/3.00 | | | | | (76) all_32_1 = empty_set
% 14.24/3.00 | | | | |
% 14.24/3.00 | | | | | REDUCE: (38), (76) imply:
% 14.24/3.01 | | | | | (77) empty(empty_set) = all_44_0
% 14.24/3.01 | | | | |
% 14.24/3.01 | | | | | GROUND_INST: instantiating (4) with 0, all_44_0, empty_set,
% 14.24/3.01 | | | | | simplifying with (44), (77) gives:
% 14.24/3.01 | | | | | (78) all_44_0 = 0
% 14.24/3.01 | | | | |
% 14.24/3.01 | | | | | REDUCE: (71), (78) imply:
% 14.24/3.01 | | | | | (79) $false
% 14.24/3.01 | | | | |
% 14.24/3.01 | | | | | CLOSE: (79) is inconsistent.
% 14.24/3.01 | | | | |
% 14.24/3.01 | | | | End of split
% 14.24/3.01 | | | |
% 14.24/3.01 | | | Case 2:
% 14.24/3.01 | | | |
% 14.24/3.01 | | | | (80) ~ (all_44_1 = 0) | all_44_2 = 0
% 14.24/3.01 | | | |
% 14.24/3.01 | | | | BETA: splitting (80) gives:
% 14.24/3.01 | | | |
% 14.24/3.01 | | | | Case 1:
% 14.24/3.01 | | | | |
% 14.24/3.01 | | | | | (81) ~ (all_44_1 = 0)
% 14.24/3.01 | | | | |
% 14.24/3.01 | | | | | REDUCE: (56), (81) imply:
% 14.24/3.01 | | | | | (82) $false
% 14.24/3.01 | | | | |
% 14.24/3.01 | | | | | CLOSE: (82) is inconsistent.
% 14.24/3.01 | | | | |
% 14.24/3.01 | | | | Case 2:
% 14.24/3.01 | | | | |
% 14.24/3.01 | | | | | (83) all_44_2 = 0
% 14.24/3.01 | | | | |
% 14.24/3.01 | | | | | COMBINE_EQS: (59), (83) imply:
% 14.24/3.01 | | | | | (84) all_40_2 = 0
% 14.24/3.01 | | | | |
% 14.24/3.01 | | | | | SIMP: (84) implies:
% 14.24/3.01 | | | | | (85) all_40_2 = 0
% 14.24/3.01 | | | | |
% 14.24/3.01 | | | | | REDUCE: (69), (85) imply:
% 14.24/3.01 | | | | | (86) $false
% 14.24/3.01 | | | | |
% 14.24/3.01 | | | | | CLOSE: (86) is inconsistent.
% 14.24/3.01 | | | | |
% 14.24/3.01 | | | | End of split
% 14.24/3.01 | | | |
% 14.24/3.01 | | | End of split
% 14.24/3.01 | | |
% 14.24/3.01 | | Case 2:
% 14.24/3.01 | | |
% 14.24/3.01 | | | (87) ~ (all_40_1 = 0) | all_40_2 = 0
% 14.24/3.01 | | |
% 14.24/3.01 | | | BETA: splitting (87) gives:
% 14.24/3.01 | | |
% 14.24/3.01 | | | Case 1:
% 14.24/3.01 | | | |
% 14.24/3.01 | | | | (88) ~ (all_40_1 = 0)
% 14.24/3.01 | | | |
% 14.24/3.01 | | | | REDUCE: (61), (88) imply:
% 14.24/3.01 | | | | (89) $false
% 14.24/3.01 | | | |
% 14.24/3.01 | | | | CLOSE: (89) is inconsistent.
% 14.24/3.01 | | | |
% 14.24/3.01 | | | Case 2:
% 14.24/3.01 | | | |
% 14.24/3.01 | | | | (90) all_40_2 = 0
% 14.24/3.01 | | | |
% 14.24/3.01 | | | | REDUCE: (69), (90) imply:
% 14.24/3.01 | | | | (91) $false
% 14.24/3.01 | | | |
% 14.24/3.01 | | | | CLOSE: (91) is inconsistent.
% 14.24/3.01 | | | |
% 14.24/3.01 | | | End of split
% 14.24/3.01 | | |
% 14.24/3.01 | | End of split
% 14.24/3.01 | |
% 14.24/3.01 | End of split
% 14.24/3.01 |
% 14.24/3.01 End of proof
% 14.24/3.01 % SZS output end Proof for theBenchmark
% 14.24/3.01
% 14.24/3.01 2393ms
%------------------------------------------------------------------------------