TSTP Solution File: SEU355+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SEU355+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 : n001.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 17:44:15 EDT 2023
% Result : Theorem 10.27s 2.41s
% Output : Proof 12.13s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEU355+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.12 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.12/0.32 % Computer : n001.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 300
% 0.12/0.32 % DateTime : Wed Aug 23 16:35:54 EDT 2023
% 0.12/0.32 % CPUTime :
% 0.17/0.61 ________ _____
% 0.17/0.61 ___ __ \_________(_)________________________________
% 0.17/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.17/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.17/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.17/0.61
% 0.17/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.17/0.61 (2023-06-19)
% 0.17/0.61
% 0.17/0.61 (c) Philipp Rümmer, 2009-2023
% 0.17/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.17/0.61 Amanda Stjerna.
% 0.17/0.61 Free software under BSD-3-Clause.
% 0.17/0.61
% 0.17/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.17/0.61
% 0.17/0.61 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.17/0.63 Running up to 7 provers in parallel.
% 0.17/0.65 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.17/0.65 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.17/0.66 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.17/0.66 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.17/0.66 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.17/0.66 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.17/0.66 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.13/1.11 Prover 1: Preprocessing ...
% 2.13/1.12 Prover 4: Preprocessing ...
% 2.84/1.18 Prover 3: Preprocessing ...
% 2.84/1.18 Prover 2: Preprocessing ...
% 2.84/1.18 Prover 5: Preprocessing ...
% 2.84/1.18 Prover 6: Preprocessing ...
% 2.84/1.18 Prover 0: Preprocessing ...
% 4.70/1.53 Prover 2: Proving ...
% 4.70/1.57 Prover 5: Proving ...
% 4.70/1.61 Prover 1: Warning: ignoring some quantifiers
% 5.13/1.66 Prover 1: Constructing countermodel ...
% 6.46/1.73 Prover 3: Warning: ignoring some quantifiers
% 6.66/1.75 Prover 6: Proving ...
% 6.66/1.77 Prover 3: Constructing countermodel ...
% 7.27/1.87 Prover 4: Warning: ignoring some quantifiers
% 7.71/1.91 Prover 4: Constructing countermodel ...
% 7.71/1.93 Prover 0: Proving ...
% 10.27/2.38 Prover 1: Found proof (size 68)
% 10.27/2.39 Prover 1: proved (1745ms)
% 10.27/2.39 Prover 6: stopped
% 10.27/2.39 Prover 5: stopped
% 10.27/2.39 Prover 2: stopped
% 10.27/2.39 Prover 4: stopped
% 10.27/2.39 Prover 3: stopped
% 10.27/2.41 Prover 0: stopped
% 10.27/2.41
% 10.27/2.41 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 10.27/2.41
% 11.44/2.43 % SZS output start Proof for theBenchmark
% 11.44/2.44 Assumptions after simplification:
% 11.44/2.44 ---------------------------------
% 11.44/2.44
% 11.44/2.44 (d8_lattice3)
% 11.51/2.49 ! [v0: $i] : ( ~ (rel_str(v0) = 0) | ~ $i(v0) | ? [v1: $i] :
% 11.51/2.49 (the_carrier(v0) = v1 & $i(v1) & ! [v2: $i] : ! [v3: $i] : ! [v4: any] :
% 11.51/2.49 ( ~ (relstr_element_smaller(v0, v2, v3) = v4) | ~ $i(v3) | ~ $i(v2) | ?
% 11.51/2.49 [v5: int] : ( ~ (v5 = 0) & element(v3, v1) = v5) | (( ~ (v4 = 0) | !
% 11.51/2.49 [v5: $i] : ( ~ (element(v5, v1) = 0) | ~ $i(v5) | ? [v6: any] : ?
% 11.51/2.49 [v7: any] : (related(v0, v3, v5) = v7 & in(v5, v2) = v6 & ( ~ (v6
% 11.51/2.49 = 0) | v7 = 0)))) & (v4 = 0 | ? [v5: $i] : ? [v6: int] : (
% 11.51/2.49 ~ (v6 = 0) & element(v5, v1) = 0 & related(v0, v3, v5) = v6 &
% 11.51/2.49 in(v5, v2) = 0 & $i(v5)))))))
% 11.51/2.49
% 11.51/2.49 (d9_lattice3)
% 11.51/2.49 ! [v0: $i] : ( ~ (rel_str(v0) = 0) | ~ $i(v0) | ? [v1: $i] :
% 11.51/2.49 (the_carrier(v0) = v1 & $i(v1) & ! [v2: $i] : ! [v3: $i] : ! [v4: any] :
% 11.51/2.49 ( ~ (relstr_set_smaller(v0, v2, v3) = v4) | ~ $i(v3) | ~ $i(v2) | ?
% 11.51/2.49 [v5: int] : ( ~ (v5 = 0) & element(v3, v1) = v5) | (( ~ (v4 = 0) | !
% 11.51/2.49 [v5: $i] : ( ~ (element(v5, v1) = 0) | ~ $i(v5) | ? [v6: any] : ?
% 11.51/2.49 [v7: any] : (related(v0, v5, v3) = v7 & in(v5, v2) = v6 & ( ~ (v6
% 11.51/2.49 = 0) | v7 = 0)))) & (v4 = 0 | ? [v5: $i] : ? [v6: int] : (
% 11.51/2.50 ~ (v6 = 0) & element(v5, v1) = 0 & related(v0, v5, v3) = v6 &
% 11.51/2.50 in(v5, v2) = 0 & $i(v5)))))))
% 11.51/2.50
% 11.51/2.50 (rc1_xboole_0)
% 11.51/2.50 ? [v0: $i] : (empty(v0) = 0 & $i(v0))
% 11.51/2.50
% 11.51/2.50 (t6_boole)
% 11.51/2.50 $i(empty_set) & ! [v0: $i] : (v0 = empty_set | ~ (empty(v0) = 0) | ~
% 11.51/2.50 $i(v0))
% 11.51/2.50
% 11.51/2.50 (t6_yellow_0)
% 11.51/2.50 $i(empty_set) & ? [v0: $i] : ? [v1: $i] : (rel_str(v0) = 0 & the_carrier(v0)
% 11.51/2.50 = v1 & $i(v1) & $i(v0) & ? [v2: $i] : ? [v3: any] : ? [v4: any] :
% 11.51/2.50 (relstr_set_smaller(v0, empty_set, v2) = v3 & relstr_element_smaller(v0,
% 11.51/2.50 empty_set, v2) = v4 & element(v2, v1) = 0 & $i(v2) & ( ~ (v4 = 0) | ~
% 11.51/2.50 (v3 = 0))))
% 11.51/2.50
% 11.51/2.50 (t7_boole)
% 11.51/2.50 ! [v0: $i] : ! [v1: $i] : ( ~ (in(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ?
% 11.51/2.50 [v2: int] : ( ~ (v2 = 0) & empty(v1) = v2))
% 11.51/2.50
% 11.51/2.50 (function-axioms)
% 11.86/2.51 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 11.86/2.51 [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (relstr_set_smaller(v4, v3, v2) = v1) |
% 11.86/2.51 ~ (relstr_set_smaller(v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : !
% 11.86/2.51 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 |
% 11.86/2.51 ~ (relstr_element_smaller(v4, v3, v2) = v1) | ~
% 11.86/2.51 (relstr_element_smaller(v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : !
% 11.86/2.51 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 |
% 11.86/2.51 ~ (related(v4, v3, v2) = v1) | ~ (related(v4, v3, v2) = v0)) & ! [v0:
% 11.86/2.51 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 11.86/2.51 : (v1 = v0 | ~ (element(v3, v2) = v1) | ~ (element(v3, v2) = v0)) & ! [v0:
% 11.86/2.51 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 11.86/2.51 : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) & ! [v0:
% 11.86/2.51 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 |
% 11.86/2.51 ~ (one_sorted_str(v2) = v1) | ~ (one_sorted_str(v2) = v0)) & ! [v0:
% 11.86/2.51 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 |
% 11.86/2.51 ~ (rel_str(v2) = v1) | ~ (rel_str(v2) = v0)) & ! [v0: $i] : ! [v1: $i] :
% 11.86/2.51 ! [v2: $i] : (v1 = v0 | ~ (the_carrier(v2) = v1) | ~ (the_carrier(v2) = v0))
% 11.86/2.51 & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1
% 11.86/2.51 = v0 | ~ (finite(v2) = v1) | ~ (finite(v2) = v0)) & ! [v0:
% 11.86/2.51 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 |
% 11.86/2.51 ~ (empty(v2) = v1) | ~ (empty(v2) = v0))
% 11.86/2.51
% 11.86/2.51 Further assumptions not needed in the proof:
% 11.86/2.51 --------------------------------------------
% 11.86/2.51 antisymmetry_r2_hidden, cc1_finset_1, dt_k1_xboole_0, dt_l1_orders_2,
% 11.86/2.51 dt_l1_struct_0, dt_m1_subset_1, dt_u1_struct_0, existence_l1_orders_2,
% 11.86/2.51 existence_l1_struct_0, existence_m1_subset_1, fc1_xboole_0, rc1_finset_1,
% 11.86/2.52 rc2_xboole_0, t1_subset, t2_subset, t8_boole
% 11.86/2.52
% 11.86/2.52 Those formulas are unsatisfiable:
% 11.86/2.52 ---------------------------------
% 11.86/2.52
% 11.86/2.52 Begin of proof
% 11.86/2.52 |
% 11.86/2.52 | ALPHA: (t6_boole) implies:
% 11.86/2.52 | (1) ! [v0: $i] : (v0 = empty_set | ~ (empty(v0) = 0) | ~ $i(v0))
% 11.86/2.52 |
% 11.86/2.52 | ALPHA: (t6_yellow_0) implies:
% 11.86/2.52 | (2) $i(empty_set)
% 11.86/2.52 | (3) ? [v0: $i] : ? [v1: $i] : (rel_str(v0) = 0 & the_carrier(v0) = v1 &
% 11.86/2.52 | $i(v1) & $i(v0) & ? [v2: $i] : ? [v3: any] : ? [v4: any] :
% 11.86/2.52 | (relstr_set_smaller(v0, empty_set, v2) = v3 &
% 11.86/2.52 | relstr_element_smaller(v0, empty_set, v2) = v4 & element(v2, v1) =
% 11.86/2.52 | 0 & $i(v2) & ( ~ (v4 = 0) | ~ (v3 = 0))))
% 11.86/2.52 |
% 11.86/2.52 | ALPHA: (function-axioms) implies:
% 11.86/2.52 | (4) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 11.86/2.52 | (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0))
% 11.86/2.52 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 11.86/2.52 | (the_carrier(v2) = v1) | ~ (the_carrier(v2) = v0))
% 11.86/2.53 | (6) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 11.86/2.53 | ! [v3: $i] : (v1 = v0 | ~ (element(v3, v2) = v1) | ~ (element(v3,
% 11.86/2.53 | v2) = v0))
% 11.86/2.53 |
% 11.86/2.53 | DELTA: instantiating (rc1_xboole_0) with fresh symbol all_16_0 gives:
% 11.86/2.53 | (7) empty(all_16_0) = 0 & $i(all_16_0)
% 11.86/2.53 |
% 11.86/2.53 | ALPHA: (7) implies:
% 11.86/2.53 | (8) $i(all_16_0)
% 11.86/2.53 | (9) empty(all_16_0) = 0
% 11.86/2.53 |
% 11.86/2.53 | DELTA: instantiating (3) with fresh symbols all_25_0, all_25_1 gives:
% 11.86/2.53 | (10) rel_str(all_25_1) = 0 & the_carrier(all_25_1) = all_25_0 &
% 11.86/2.53 | $i(all_25_0) & $i(all_25_1) & ? [v0: $i] : ? [v1: any] : ? [v2:
% 11.86/2.53 | any] : (relstr_set_smaller(all_25_1, empty_set, v0) = v1 &
% 11.86/2.53 | relstr_element_smaller(all_25_1, empty_set, v0) = v2 & element(v0,
% 11.86/2.53 | all_25_0) = 0 & $i(v0) & ( ~ (v2 = 0) | ~ (v1 = 0)))
% 11.86/2.53 |
% 11.86/2.53 | ALPHA: (10) implies:
% 11.86/2.53 | (11) $i(all_25_1)
% 11.86/2.53 | (12) the_carrier(all_25_1) = all_25_0
% 11.86/2.53 | (13) rel_str(all_25_1) = 0
% 11.86/2.53 | (14) ? [v0: $i] : ? [v1: any] : ? [v2: any] :
% 11.86/2.53 | (relstr_set_smaller(all_25_1, empty_set, v0) = v1 &
% 11.86/2.53 | relstr_element_smaller(all_25_1, empty_set, v0) = v2 & element(v0,
% 11.86/2.53 | all_25_0) = 0 & $i(v0) & ( ~ (v2 = 0) | ~ (v1 = 0)))
% 11.86/2.53 |
% 11.86/2.53 | DELTA: instantiating (14) with fresh symbols all_27_0, all_27_1, all_27_2
% 11.86/2.53 | gives:
% 11.86/2.53 | (15) relstr_set_smaller(all_25_1, empty_set, all_27_2) = all_27_1 &
% 11.86/2.53 | relstr_element_smaller(all_25_1, empty_set, all_27_2) = all_27_0 &
% 11.86/2.53 | element(all_27_2, all_25_0) = 0 & $i(all_27_2) & ( ~ (all_27_0 = 0) |
% 11.86/2.54 | ~ (all_27_1 = 0))
% 11.86/2.54 |
% 11.86/2.54 | ALPHA: (15) implies:
% 11.86/2.54 | (16) $i(all_27_2)
% 11.86/2.54 | (17) element(all_27_2, all_25_0) = 0
% 11.86/2.54 | (18) relstr_element_smaller(all_25_1, empty_set, all_27_2) = all_27_0
% 11.86/2.54 | (19) relstr_set_smaller(all_25_1, empty_set, all_27_2) = all_27_1
% 11.86/2.54 | (20) ~ (all_27_0 = 0) | ~ (all_27_1 = 0)
% 11.86/2.54 |
% 11.86/2.54 | GROUND_INST: instantiating (1) with all_16_0, simplifying with (8), (9) gives:
% 11.86/2.54 | (21) all_16_0 = empty_set
% 11.86/2.54 |
% 11.86/2.54 | GROUND_INST: instantiating (d9_lattice3) with all_25_1, simplifying with (11),
% 11.86/2.54 | (13) gives:
% 11.86/2.54 | (22) ? [v0: $i] : (the_carrier(all_25_1) = v0 & $i(v0) & ! [v1: $i] : !
% 11.86/2.54 | [v2: $i] : ! [v3: any] : ( ~ (relstr_set_smaller(all_25_1, v1, v2)
% 11.86/2.54 | = v3) | ~ $i(v2) | ~ $i(v1) | ? [v4: int] : ( ~ (v4 = 0) &
% 11.86/2.54 | element(v2, v0) = v4) | (( ~ (v3 = 0) | ! [v4: $i] : ( ~
% 11.86/2.54 | (element(v4, v0) = 0) | ~ $i(v4) | ? [v5: any] : ? [v6:
% 11.86/2.54 | any] : (related(all_25_1, v4, v2) = v6 & in(v4, v1) = v5 &
% 11.86/2.54 | ( ~ (v5 = 0) | v6 = 0)))) & (v3 = 0 | ? [v4: $i] : ?
% 11.86/2.54 | [v5: int] : ( ~ (v5 = 0) & element(v4, v0) = 0 &
% 11.86/2.54 | related(all_25_1, v4, v2) = v5 & in(v4, v1) = 0 &
% 11.86/2.54 | $i(v4))))))
% 11.86/2.54 |
% 11.86/2.54 | GROUND_INST: instantiating (d8_lattice3) with all_25_1, simplifying with (11),
% 11.86/2.54 | (13) gives:
% 11.86/2.55 | (23) ? [v0: $i] : (the_carrier(all_25_1) = v0 & $i(v0) & ! [v1: $i] : !
% 11.86/2.55 | [v2: $i] : ! [v3: any] : ( ~ (relstr_element_smaller(all_25_1, v1,
% 11.86/2.55 | v2) = v3) | ~ $i(v2) | ~ $i(v1) | ? [v4: int] : ( ~ (v4 =
% 11.86/2.55 | 0) & element(v2, v0) = v4) | (( ~ (v3 = 0) | ! [v4: $i] : ( ~
% 11.86/2.55 | (element(v4, v0) = 0) | ~ $i(v4) | ? [v5: any] : ? [v6:
% 11.86/2.55 | any] : (related(all_25_1, v2, v4) = v6 & in(v4, v1) = v5 &
% 11.86/2.55 | ( ~ (v5 = 0) | v6 = 0)))) & (v3 = 0 | ? [v4: $i] : ?
% 11.86/2.55 | [v5: int] : ( ~ (v5 = 0) & element(v4, v0) = 0 &
% 11.86/2.55 | related(all_25_1, v2, v4) = v5 & in(v4, v1) = 0 &
% 11.86/2.55 | $i(v4))))))
% 11.86/2.55 |
% 11.86/2.55 | DELTA: instantiating (23) with fresh symbol all_35_0 gives:
% 11.86/2.55 | (24) the_carrier(all_25_1) = all_35_0 & $i(all_35_0) & ! [v0: $i] : !
% 11.86/2.55 | [v1: $i] : ! [v2: any] : ( ~ (relstr_element_smaller(all_25_1, v0,
% 11.86/2.55 | v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ( ~ (v3 = 0)
% 11.86/2.55 | & element(v1, all_35_0) = v3) | (( ~ (v2 = 0) | ! [v3: $i] : ( ~
% 11.86/2.55 | (element(v3, all_35_0) = 0) | ~ $i(v3) | ? [v4: any] : ?
% 11.86/2.55 | [v5: any] : (related(all_25_1, v1, v3) = v5 & in(v3, v0) = v4
% 11.86/2.55 | & ( ~ (v4 = 0) | v5 = 0)))) & (v2 = 0 | ? [v3: $i] : ?
% 11.86/2.55 | [v4: int] : ( ~ (v4 = 0) & element(v3, all_35_0) = 0 &
% 11.86/2.55 | related(all_25_1, v1, v3) = v4 & in(v3, v0) = 0 & $i(v3)))))
% 11.86/2.55 |
% 11.86/2.55 | ALPHA: (24) implies:
% 11.86/2.55 | (25) the_carrier(all_25_1) = all_35_0
% 11.86/2.56 | (26) ! [v0: $i] : ! [v1: $i] : ! [v2: any] : ( ~
% 11.86/2.56 | (relstr_element_smaller(all_25_1, v0, v1) = v2) | ~ $i(v1) | ~
% 11.86/2.56 | $i(v0) | ? [v3: int] : ( ~ (v3 = 0) & element(v1, all_35_0) = v3) |
% 11.86/2.56 | (( ~ (v2 = 0) | ! [v3: $i] : ( ~ (element(v3, all_35_0) = 0) | ~
% 11.86/2.56 | $i(v3) | ? [v4: any] : ? [v5: any] : (related(all_25_1, v1,
% 11.86/2.56 | v3) = v5 & in(v3, v0) = v4 & ( ~ (v4 = 0) | v5 = 0)))) &
% 11.86/2.56 | (v2 = 0 | ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) & element(v3,
% 11.86/2.56 | all_35_0) = 0 & related(all_25_1, v1, v3) = v4 & in(v3, v0)
% 11.86/2.56 | = 0 & $i(v3)))))
% 11.86/2.56 |
% 11.86/2.56 | GROUND_INST: instantiating (26) with empty_set, all_27_2, all_27_0,
% 11.86/2.56 | simplifying with (2), (16), (18) gives:
% 11.86/2.56 | (27) ? [v0: int] : ( ~ (v0 = 0) & element(all_27_2, all_35_0) = v0) | (( ~
% 11.86/2.56 | (all_27_0 = 0) | ! [v0: $i] : ( ~ (element(v0, all_35_0) = 0) |
% 11.86/2.56 | ~ $i(v0) | ? [v1: any] : ? [v2: any] : (related(all_25_1,
% 11.86/2.56 | all_27_2, v0) = v2 & in(v0, empty_set) = v1 & ( ~ (v1 = 0) |
% 11.86/2.56 | v2 = 0)))) & (all_27_0 = 0 | ? [v0: $i] : ? [v1: int] : (
% 11.86/2.56 | ~ (v1 = 0) & element(v0, all_35_0) = 0 & related(all_25_1,
% 11.86/2.56 | all_27_2, v0) = v1 & in(v0, empty_set) = 0 & $i(v0))))
% 11.86/2.56 |
% 11.86/2.56 | DELTA: instantiating (22) with fresh symbol all_38_0 gives:
% 11.86/2.57 | (28) the_carrier(all_25_1) = all_38_0 & $i(all_38_0) & ! [v0: $i] : !
% 11.86/2.57 | [v1: $i] : ! [v2: any] : ( ~ (relstr_set_smaller(all_25_1, v0, v1) =
% 11.86/2.57 | v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ( ~ (v3 = 0) &
% 11.86/2.57 | element(v1, all_38_0) = v3) | (( ~ (v2 = 0) | ! [v3: $i] : ( ~
% 11.86/2.57 | (element(v3, all_38_0) = 0) | ~ $i(v3) | ? [v4: any] : ?
% 11.86/2.57 | [v5: any] : (related(all_25_1, v3, v1) = v5 & in(v3, v0) = v4
% 11.86/2.57 | & ( ~ (v4 = 0) | v5 = 0)))) & (v2 = 0 | ? [v3: $i] : ?
% 11.86/2.57 | [v4: int] : ( ~ (v4 = 0) & element(v3, all_38_0) = 0 &
% 11.86/2.57 | related(all_25_1, v3, v1) = v4 & in(v3, v0) = 0 & $i(v3)))))
% 11.86/2.57 |
% 11.86/2.57 | ALPHA: (28) implies:
% 11.86/2.57 | (29) the_carrier(all_25_1) = all_38_0
% 12.13/2.57 | (30) ! [v0: $i] : ! [v1: $i] : ! [v2: any] : ( ~
% 12.13/2.57 | (relstr_set_smaller(all_25_1, v0, v1) = v2) | ~ $i(v1) | ~ $i(v0)
% 12.13/2.57 | | ? [v3: int] : ( ~ (v3 = 0) & element(v1, all_38_0) = v3) | (( ~
% 12.13/2.57 | (v2 = 0) | ! [v3: $i] : ( ~ (element(v3, all_38_0) = 0) | ~
% 12.13/2.57 | $i(v3) | ? [v4: any] : ? [v5: any] : (related(all_25_1, v3,
% 12.13/2.57 | v1) = v5 & in(v3, v0) = v4 & ( ~ (v4 = 0) | v5 = 0)))) &
% 12.13/2.57 | (v2 = 0 | ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) & element(v3,
% 12.13/2.57 | all_38_0) = 0 & related(all_25_1, v3, v1) = v4 & in(v3, v0)
% 12.13/2.57 | = 0 & $i(v3)))))
% 12.13/2.57 |
% 12.13/2.57 | GROUND_INST: instantiating (30) with empty_set, all_27_2, all_27_1,
% 12.13/2.57 | simplifying with (2), (16), (19) gives:
% 12.13/2.57 | (31) ? [v0: int] : ( ~ (v0 = 0) & element(all_27_2, all_38_0) = v0) | (( ~
% 12.13/2.57 | (all_27_1 = 0) | ! [v0: $i] : ( ~ (element(v0, all_38_0) = 0) |
% 12.13/2.57 | ~ $i(v0) | ? [v1: any] : ? [v2: any] : (related(all_25_1, v0,
% 12.13/2.57 | all_27_2) = v2 & in(v0, empty_set) = v1 & ( ~ (v1 = 0) | v2
% 12.13/2.57 | = 0)))) & (all_27_1 = 0 | ? [v0: $i] : ? [v1: int] : ( ~
% 12.13/2.57 | (v1 = 0) & element(v0, all_38_0) = 0 & related(all_25_1, v0,
% 12.13/2.57 | all_27_2) = v1 & in(v0, empty_set) = 0 & $i(v0))))
% 12.13/2.57 |
% 12.13/2.58 | REDUCE: (9), (21) imply:
% 12.13/2.58 | (32) empty(empty_set) = 0
% 12.13/2.58 |
% 12.13/2.58 | GROUND_INST: instantiating (5) with all_25_0, all_38_0, all_25_1, simplifying
% 12.13/2.58 | with (12), (29) gives:
% 12.13/2.58 | (33) all_38_0 = all_25_0
% 12.13/2.58 |
% 12.13/2.58 | GROUND_INST: instantiating (5) with all_35_0, all_38_0, all_25_1, simplifying
% 12.13/2.58 | with (25), (29) gives:
% 12.13/2.58 | (34) all_38_0 = all_35_0
% 12.13/2.58 |
% 12.13/2.58 | COMBINE_EQS: (33), (34) imply:
% 12.13/2.58 | (35) all_35_0 = all_25_0
% 12.13/2.58 |
% 12.13/2.58 | BETA: splitting (20) gives:
% 12.13/2.58 |
% 12.13/2.58 | Case 1:
% 12.13/2.58 | |
% 12.13/2.58 | | (36) ~ (all_27_0 = 0)
% 12.13/2.58 | |
% 12.13/2.58 | | BETA: splitting (27) gives:
% 12.13/2.58 | |
% 12.13/2.58 | | Case 1:
% 12.13/2.58 | | |
% 12.13/2.58 | | | (37) ? [v0: int] : ( ~ (v0 = 0) & element(all_27_2, all_35_0) = v0)
% 12.13/2.58 | | |
% 12.13/2.58 | | | DELTA: instantiating (37) with fresh symbol all_70_0 gives:
% 12.13/2.58 | | | (38) ~ (all_70_0 = 0) & element(all_27_2, all_35_0) = all_70_0
% 12.13/2.58 | | |
% 12.13/2.58 | | | ALPHA: (38) implies:
% 12.13/2.58 | | | (39) ~ (all_70_0 = 0)
% 12.13/2.58 | | | (40) element(all_27_2, all_35_0) = all_70_0
% 12.13/2.58 | | |
% 12.13/2.58 | | | REDUCE: (35), (40) imply:
% 12.13/2.58 | | | (41) element(all_27_2, all_25_0) = all_70_0
% 12.13/2.58 | | |
% 12.13/2.58 | | | GROUND_INST: instantiating (6) with 0, all_70_0, all_25_0, all_27_2,
% 12.13/2.58 | | | simplifying with (17), (41) gives:
% 12.13/2.58 | | | (42) all_70_0 = 0
% 12.13/2.58 | | |
% 12.13/2.58 | | | REDUCE: (39), (42) imply:
% 12.13/2.58 | | | (43) $false
% 12.13/2.59 | | |
% 12.13/2.59 | | | CLOSE: (43) is inconsistent.
% 12.13/2.59 | | |
% 12.13/2.59 | | Case 2:
% 12.13/2.59 | | |
% 12.13/2.59 | | | (44) ( ~ (all_27_0 = 0) | ! [v0: $i] : ( ~ (element(v0, all_35_0) = 0)
% 12.13/2.59 | | | | ~ $i(v0) | ? [v1: any] : ? [v2: any] : (related(all_25_1,
% 12.13/2.59 | | | all_27_2, v0) = v2 & in(v0, empty_set) = v1 & ( ~ (v1 = 0)
% 12.13/2.59 | | | | v2 = 0)))) & (all_27_0 = 0 | ? [v0: $i] : ? [v1: int]
% 12.13/2.59 | | | : ( ~ (v1 = 0) & element(v0, all_35_0) = 0 & related(all_25_1,
% 12.13/2.59 | | | all_27_2, v0) = v1 & in(v0, empty_set) = 0 & $i(v0)))
% 12.13/2.59 | | |
% 12.13/2.59 | | | ALPHA: (44) implies:
% 12.13/2.59 | | | (45) all_27_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) &
% 12.13/2.59 | | | element(v0, all_35_0) = 0 & related(all_25_1, all_27_2, v0) = v1
% 12.13/2.59 | | | & in(v0, empty_set) = 0 & $i(v0))
% 12.13/2.59 | | |
% 12.13/2.59 | | | BETA: splitting (45) gives:
% 12.13/2.59 | | |
% 12.13/2.59 | | | Case 1:
% 12.13/2.59 | | | |
% 12.13/2.59 | | | | (46) all_27_0 = 0
% 12.13/2.59 | | | |
% 12.13/2.59 | | | | REDUCE: (36), (46) imply:
% 12.13/2.59 | | | | (47) $false
% 12.13/2.59 | | | |
% 12.13/2.59 | | | | CLOSE: (47) is inconsistent.
% 12.13/2.59 | | | |
% 12.13/2.59 | | | Case 2:
% 12.13/2.59 | | | |
% 12.13/2.59 | | | | (48) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & element(v0,
% 12.13/2.59 | | | | all_35_0) = 0 & related(all_25_1, all_27_2, v0) = v1 &
% 12.13/2.59 | | | | in(v0, empty_set) = 0 & $i(v0))
% 12.13/2.59 | | | |
% 12.13/2.59 | | | | DELTA: instantiating (48) with fresh symbols all_73_0, all_73_1 gives:
% 12.13/2.59 | | | | (49) ~ (all_73_0 = 0) & element(all_73_1, all_35_0) = 0 &
% 12.13/2.59 | | | | related(all_25_1, all_27_2, all_73_1) = all_73_0 & in(all_73_1,
% 12.13/2.59 | | | | empty_set) = 0 & $i(all_73_1)
% 12.13/2.59 | | | |
% 12.13/2.59 | | | | ALPHA: (49) implies:
% 12.13/2.60 | | | | (50) $i(all_73_1)
% 12.13/2.60 | | | | (51) in(all_73_1, empty_set) = 0
% 12.13/2.60 | | | |
% 12.13/2.60 | | | | GROUND_INST: instantiating (t7_boole) with all_73_1, empty_set,
% 12.13/2.60 | | | | simplifying with (2), (50), (51) gives:
% 12.13/2.60 | | | | (52) ? [v0: int] : ( ~ (v0 = 0) & empty(empty_set) = v0)
% 12.13/2.60 | | | |
% 12.13/2.60 | | | | DELTA: instantiating (52) with fresh symbol all_83_0 gives:
% 12.13/2.60 | | | | (53) ~ (all_83_0 = 0) & empty(empty_set) = all_83_0
% 12.13/2.60 | | | |
% 12.13/2.60 | | | | ALPHA: (53) implies:
% 12.13/2.60 | | | | (54) ~ (all_83_0 = 0)
% 12.13/2.60 | | | | (55) empty(empty_set) = all_83_0
% 12.13/2.60 | | | |
% 12.13/2.60 | | | | GROUND_INST: instantiating (4) with 0, all_83_0, empty_set, simplifying
% 12.13/2.60 | | | | with (32), (55) gives:
% 12.13/2.60 | | | | (56) all_83_0 = 0
% 12.13/2.60 | | | |
% 12.13/2.60 | | | | REDUCE: (54), (56) imply:
% 12.13/2.60 | | | | (57) $false
% 12.13/2.60 | | | |
% 12.13/2.60 | | | | CLOSE: (57) is inconsistent.
% 12.13/2.60 | | | |
% 12.13/2.60 | | | End of split
% 12.13/2.60 | | |
% 12.13/2.60 | | End of split
% 12.13/2.60 | |
% 12.13/2.60 | Case 2:
% 12.13/2.60 | |
% 12.13/2.60 | | (58) ~ (all_27_1 = 0)
% 12.13/2.60 | |
% 12.13/2.60 | | BETA: splitting (31) gives:
% 12.13/2.60 | |
% 12.13/2.60 | | Case 1:
% 12.13/2.60 | | |
% 12.13/2.60 | | | (59) ? [v0: int] : ( ~ (v0 = 0) & element(all_27_2, all_38_0) = v0)
% 12.13/2.60 | | |
% 12.13/2.60 | | | DELTA: instantiating (59) with fresh symbol all_71_0 gives:
% 12.13/2.60 | | | (60) ~ (all_71_0 = 0) & element(all_27_2, all_38_0) = all_71_0
% 12.13/2.60 | | |
% 12.13/2.60 | | | ALPHA: (60) implies:
% 12.13/2.60 | | | (61) ~ (all_71_0 = 0)
% 12.13/2.60 | | | (62) element(all_27_2, all_38_0) = all_71_0
% 12.13/2.60 | | |
% 12.13/2.60 | | | REDUCE: (33), (62) imply:
% 12.13/2.60 | | | (63) element(all_27_2, all_25_0) = all_71_0
% 12.13/2.60 | | |
% 12.13/2.60 | | | GROUND_INST: instantiating (6) with 0, all_71_0, all_25_0, all_27_2,
% 12.13/2.60 | | | simplifying with (17), (63) gives:
% 12.13/2.60 | | | (64) all_71_0 = 0
% 12.13/2.60 | | |
% 12.13/2.60 | | | REDUCE: (61), (64) imply:
% 12.13/2.60 | | | (65) $false
% 12.13/2.60 | | |
% 12.13/2.60 | | | CLOSE: (65) is inconsistent.
% 12.13/2.60 | | |
% 12.13/2.60 | | Case 2:
% 12.13/2.60 | | |
% 12.13/2.61 | | | (66) ( ~ (all_27_1 = 0) | ! [v0: $i] : ( ~ (element(v0, all_38_0) = 0)
% 12.13/2.61 | | | | ~ $i(v0) | ? [v1: any] : ? [v2: any] : (related(all_25_1,
% 12.13/2.61 | | | v0, all_27_2) = v2 & in(v0, empty_set) = v1 & ( ~ (v1 = 0)
% 12.13/2.61 | | | | v2 = 0)))) & (all_27_1 = 0 | ? [v0: $i] : ? [v1: int]
% 12.13/2.61 | | | : ( ~ (v1 = 0) & element(v0, all_38_0) = 0 & related(all_25_1,
% 12.13/2.61 | | | v0, all_27_2) = v1 & in(v0, empty_set) = 0 & $i(v0)))
% 12.13/2.61 | | |
% 12.13/2.61 | | | ALPHA: (66) implies:
% 12.13/2.61 | | | (67) all_27_1 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) &
% 12.13/2.61 | | | element(v0, all_38_0) = 0 & related(all_25_1, v0, all_27_2) = v1
% 12.13/2.61 | | | & in(v0, empty_set) = 0 & $i(v0))
% 12.13/2.61 | | |
% 12.13/2.61 | | | BETA: splitting (67) gives:
% 12.13/2.61 | | |
% 12.13/2.61 | | | Case 1:
% 12.13/2.61 | | | |
% 12.13/2.61 | | | | (68) all_27_1 = 0
% 12.13/2.61 | | | |
% 12.13/2.61 | | | | REDUCE: (58), (68) imply:
% 12.13/2.61 | | | | (69) $false
% 12.13/2.61 | | | |
% 12.13/2.61 | | | | CLOSE: (69) is inconsistent.
% 12.13/2.61 | | | |
% 12.13/2.61 | | | Case 2:
% 12.13/2.61 | | | |
% 12.13/2.61 | | | | (70) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & element(v0,
% 12.13/2.61 | | | | all_38_0) = 0 & related(all_25_1, v0, all_27_2) = v1 &
% 12.13/2.61 | | | | in(v0, empty_set) = 0 & $i(v0))
% 12.13/2.61 | | | |
% 12.13/2.61 | | | | DELTA: instantiating (70) with fresh symbols all_78_0, all_78_1 gives:
% 12.13/2.61 | | | | (71) ~ (all_78_0 = 0) & element(all_78_1, all_38_0) = 0 &
% 12.13/2.61 | | | | related(all_25_1, all_78_1, all_27_2) = all_78_0 & in(all_78_1,
% 12.13/2.61 | | | | empty_set) = 0 & $i(all_78_1)
% 12.13/2.61 | | | |
% 12.13/2.61 | | | | ALPHA: (71) implies:
% 12.13/2.61 | | | | (72) $i(all_78_1)
% 12.13/2.61 | | | | (73) in(all_78_1, empty_set) = 0
% 12.13/2.61 | | | |
% 12.13/2.61 | | | | GROUND_INST: instantiating (t7_boole) with all_78_1, empty_set,
% 12.13/2.61 | | | | simplifying with (2), (72), (73) gives:
% 12.13/2.61 | | | | (74) ? [v0: int] : ( ~ (v0 = 0) & empty(empty_set) = v0)
% 12.13/2.61 | | | |
% 12.13/2.61 | | | | DELTA: instantiating (74) with fresh symbol all_88_0 gives:
% 12.13/2.61 | | | | (75) ~ (all_88_0 = 0) & empty(empty_set) = all_88_0
% 12.13/2.61 | | | |
% 12.13/2.61 | | | | ALPHA: (75) implies:
% 12.13/2.61 | | | | (76) ~ (all_88_0 = 0)
% 12.13/2.62 | | | | (77) empty(empty_set) = all_88_0
% 12.13/2.62 | | | |
% 12.13/2.62 | | | | GROUND_INST: instantiating (4) with 0, all_88_0, empty_set, simplifying
% 12.13/2.62 | | | | with (32), (77) gives:
% 12.13/2.62 | | | | (78) all_88_0 = 0
% 12.13/2.62 | | | |
% 12.13/2.62 | | | | REDUCE: (76), (78) imply:
% 12.13/2.62 | | | | (79) $false
% 12.13/2.62 | | | |
% 12.13/2.62 | | | | CLOSE: (79) is inconsistent.
% 12.13/2.62 | | | |
% 12.13/2.62 | | | End of split
% 12.13/2.62 | | |
% 12.13/2.62 | | End of split
% 12.13/2.62 | |
% 12.13/2.62 | End of split
% 12.13/2.62 |
% 12.13/2.62 End of proof
% 12.13/2.62 % SZS output end Proof for theBenchmark
% 12.13/2.62
% 12.13/2.62 2004ms
%------------------------------------------------------------------------------