TSTP Solution File: SEU472^1 by E---3.1.00
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- Process Solution
%------------------------------------------------------------------------------
% File : E---3.1.00
% Problem : SEU472^1 : TPTP v8.2.0. Released v3.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n013.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 : Tue May 21 03:27:31 EDT 2024
% Result : Theorem 0.17s 0.44s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 20
% Syntax : Number of formulae : 36 ( 20 unt; 12 typ; 0 def)
% Number of atoms : 68 ( 25 equ; 0 cnn)
% Maximal formula atoms : 15 ( 2 avg)
% Number of connectives : 278 ( 13 ~; 20 |; 27 &; 186 @)
% ( 0 <=>; 32 =>; 0 <=; 0 <~>)
% Maximal formula depth : 23 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 114 ( 114 >; 0 *; 0 +; 0 <<)
% Number of symbols : 14 ( 12 usr; 3 con; 0-3 aty)
% Number of variables : 118 ( 37 ^ 81 !; 0 ?; 118 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_22,type,
subrel: ( $i > $i > $o ) > ( $i > $i > $o ) > $o ).
thf(decl_25,type,
infl: ( ( $i > $i > $o ) > $i > $i > $o ) > $o ).
thf(decl_29,type,
rc: ( $i > $i > $o ) > $i > $i > $o ).
thf(decl_33,type,
sc: ( $i > $i > $o ) > $i > $i > $o ).
thf(decl_34,type,
trans: ( $i > $i > $o ) > $o ).
thf(decl_35,type,
tc: ( $i > $i > $o ) > $i > $i > $o ).
thf(decl_37,type,
trsc: ( $i > $i > $o ) > $i > $i > $o ).
thf(decl_51,type,
epred1_0: $i > $i > $o ).
thf(decl_52,type,
esk1_0: $i ).
thf(decl_53,type,
esk2_0: $i ).
thf(decl_54,type,
epred2_0: $i > $i > $o ).
thf(decl_55,type,
epred3_0: $i > $i > $o ).
thf(transitive_closure,axiom,
( tc
= ( ^ [X1: $i > $i > $o,X3: $i,X4: $i] :
! [X2: $i > $i > $o] :
( ( ( trans @ X2 )
& ( subrel @ X1 @ X2 ) )
=> ( X2 @ X3 @ X4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET009^0.ax',transitive_closure) ).
thf(subrel,axiom,
( subrel
= ( ^ [X1: $i > $i > $o,X2: $i > $i > $o] :
! [X3: $i,X4: $i] :
( ( X1 @ X3 @ X4 )
=> ( X2 @ X3 @ X4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET009^0.ax',subrel) ).
thf(transitive,axiom,
( trans
= ( ^ [X1: $i > $i > $o] :
! [X3: $i,X4: $i,X6: $i] :
( ( ( X1 @ X3 @ X4 )
& ( X1 @ X4 @ X6 ) )
=> ( X1 @ X3 @ X6 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET009^0.ax',transitive) ).
thf(inflationary,axiom,
( infl
= ( ^ [X5: ( $i > $i > $o ) > $i > $i > $o] :
! [X1: $i > $i > $o] : ( subrel @ X1 @ ( X5 @ X1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET009^0.ax',inflationary) ).
thf(transitive_reflexive_symmetric_closure,axiom,
( trsc
= ( ^ [X1: $i > $i > $o] : ( sc @ ( rc @ ( tc @ X1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET009^0.ax',transitive_reflexive_symmetric_closure) ).
thf(reflexive_closure,axiom,
( rc
= ( ^ [X1: $i > $i > $o,X3: $i,X4: $i] :
( ( X3 = X4 )
| ( X1 @ X3 @ X4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET009^0.ax',reflexive_closure) ).
thf(symmetric_closure,axiom,
( sc
= ( ^ [X1: $i > $i > $o,X3: $i,X4: $i] :
( ( X1 @ X4 @ X3 )
| ( X1 @ X3 @ X4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET009^0.ax',symmetric_closure) ).
thf(transitive_reflexive_symmetric_closure_op_is_inflationary,conjecture,
infl @ trsc,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',transitive_reflexive_symmetric_closure_op_is_inflationary) ).
thf(c_0_8,plain,
( tc
= ( ^ [Z0: $i > $i > $o,Z1: $i,Z2: $i] :
! [X2: $i > $i > $o] :
( ( ! [X15: $i,X16: $i,X17: $i] :
( ( ( X2 @ X15 @ X16 )
& ( X2 @ X16 @ X17 ) )
=> ( X2 @ X15 @ X17 ) )
& ! [X18: $i,X19: $i] :
( ( Z0 @ X18 @ X19 )
=> ( X2 @ X18 @ X19 ) ) )
=> ( X2 @ Z1 @ Z2 ) ) ) ),
inference(fof_simplification,[status(thm)],[transitive_closure]) ).
thf(c_0_9,plain,
( subrel
= ( ^ [Z0: $i > $i > $o,Z1: $i > $i > $o] :
! [X3: $i,X4: $i] :
( ( Z0 @ X3 @ X4 )
=> ( Z1 @ X3 @ X4 ) ) ) ),
inference(fof_simplification,[status(thm)],[subrel]) ).
thf(c_0_10,plain,
( trans
= ( ^ [Z0: $i > $i > $o] :
! [X3: $i,X4: $i,X6: $i] :
( ( ( Z0 @ X3 @ X4 )
& ( Z0 @ X4 @ X6 ) )
=> ( Z0 @ X3 @ X6 ) ) ) ),
inference(fof_simplification,[status(thm)],[transitive]) ).
thf(c_0_11,plain,
( infl
= ( ^ [Z0: ( $i > $i > $o ) > $i > $i > $o] :
! [X1: $i > $i > $o,X9: $i,X10: $i] :
( ( X1 @ X9 @ X10 )
=> ( Z0 @ X1 @ X9 @ X10 ) ) ) ),
inference(fof_simplification,[status(thm)],[inflationary]) ).
thf(c_0_12,plain,
( trsc
= ( ^ [Z0: $i > $i > $o,Z1: $i,Z2: $i] :
( Z2
| ! [X26: $i > $i > $o] :
( ( ! [X27: $i,X28: $i,X29: $i] :
( ( ( X26 @ X27 @ X28 )
& ( X26 @ X28 @ X29 ) )
=> ( X26 @ X27 @ X29 ) )
& ! [X30: $i,X31: $i] :
( ( Z0 @ X30 @ X31 )
=> ( X26 @ X30 @ X31 ) ) )
=> ( X26 @ Z2 @ Z1 ) )
| ( Z1 = Z2 )
| ! [X26: $i > $i > $o] :
( ( ! [X27: $i,X28: $i,X29: $i] :
( ( ( X26 @ X27 @ X28 )
& ( X26 @ X28 @ X29 ) )
=> ( X26 @ X27 @ X29 ) )
& ! [X30: $i,X31: $i] :
( ( Z0 @ X30 @ X31 )
=> ( X26 @ X30 @ X31 ) ) )
=> ( X26 @ Z1 @ Z2 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[transitive_reflexive_symmetric_closure]) ).
thf(c_0_13,plain,
( rc
= ( ^ [Z0: $i > $i > $o,Z1: $i,Z2: $i] :
( ( Z1 = Z2 )
| ( Z0 @ Z1 @ Z2 ) ) ) ),
inference(fof_simplification,[status(thm)],[reflexive_closure]) ).
thf(c_0_14,plain,
( sc
= ( ^ [Z0: $i > $i > $o,Z1: $i,Z2: $i] :
( ( Z0 @ Z2 @ Z1 )
| ( Z0 @ Z1 @ Z2 ) ) ) ),
inference(fof_simplification,[status(thm)],[symmetric_closure]) ).
thf(c_0_15,plain,
( tc
= ( ^ [Z0: $i > $i > $o,Z1: $i,Z2: $i] :
! [X2: $i > $i > $o] :
( ( ! [X15: $i,X16: $i,X17: $i] :
( ( ( X2 @ X15 @ X16 )
& ( X2 @ X16 @ X17 ) )
=> ( X2 @ X15 @ X17 ) )
& ! [X18: $i,X19: $i] :
( ( Z0 @ X18 @ X19 )
=> ( X2 @ X18 @ X19 ) ) )
=> ( X2 @ Z1 @ Z2 ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_8,c_0_9]),c_0_10]) ).
thf(c_0_16,plain,
( infl
= ( ^ [Z0: ( $i > $i > $o ) > $i > $i > $o] :
! [X1: $i > $i > $o,X9: $i,X10: $i] :
( ( X1 @ X9 @ X10 )
=> ( Z0 @ X1 @ X9 @ X10 ) ) ) ),
inference(apply_def,[status(thm)],[c_0_11,c_0_9]) ).
thf(c_0_17,plain,
( trsc
= ( ^ [Z0: $i > $i > $o,Z1: $i,Z2: $i] :
( Z2
| ! [X26: $i > $i > $o] :
( ( ! [X27: $i,X28: $i,X29: $i] :
( ( ( X26 @ X27 @ X28 )
& ( X26 @ X28 @ X29 ) )
=> ( X26 @ X27 @ X29 ) )
& ! [X30: $i,X31: $i] :
( ( Z0 @ X30 @ X31 )
=> ( X26 @ X30 @ X31 ) ) )
=> ( X26 @ Z2 @ Z1 ) )
| ( Z1 = Z2 )
| ! [X26: $i > $i > $o] :
( ( ! [X27: $i,X28: $i,X29: $i] :
( ( ( X26 @ X27 @ X28 )
& ( X26 @ X28 @ X29 ) )
=> ( X26 @ X27 @ X29 ) )
& ! [X30: $i,X31: $i] :
( ( Z0 @ X30 @ X31 )
=> ( X26 @ X30 @ X31 ) ) )
=> ( X26 @ Z1 @ Z2 ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_12,c_0_13]),c_0_14]),c_0_15]) ).
thf(c_0_18,negated_conjecture,
~ ! [X169: $i > $i > $o,X170: $i,X171: $i] :
( ( X169 @ X170 @ X171 )
=> ( ( X171 = X170 )
| ! [X157: $i > $i > $o] :
( ( ! [X158: $i,X159: $i,X160: $i] :
( ( ( X157 @ X158 @ X159 )
& ( X157 @ X159 @ X160 ) )
=> ( X157 @ X158 @ X160 ) )
& ! [X161: $i,X162: $i] :
( ( X169 @ X161 @ X162 )
=> ( X157 @ X161 @ X162 ) ) )
=> ( X157 @ X171 @ X170 ) )
| ( X170 = X171 )
| ! [X163: $i > $i > $o] :
( ( ! [X164: $i,X165: $i,X166: $i] :
( ( ( X163 @ X164 @ X165 )
& ( X163 @ X165 @ X166 ) )
=> ( X163 @ X164 @ X166 ) )
& ! [X167: $i,X168: $i] :
( ( X169 @ X167 @ X168 )
=> ( X163 @ X167 @ X168 ) ) )
=> ( X163 @ X170 @ X171 ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(assume_negation,[status(cth)],[transitive_reflexive_symmetric_closure_op_is_inflationary]),c_0_16]),c_0_17]) ).
thf(c_0_19,negated_conjecture,
! [X176: $i,X177: $i,X178: $i,X179: $i,X180: $i,X182: $i,X183: $i,X184: $i,X185: $i,X186: $i] :
( ( epred1_0 @ esk1_0 @ esk2_0 )
& ( esk2_0 != esk1_0 )
& ( ~ ( epred2_0 @ X176 @ X177 )
| ~ ( epred2_0 @ X177 @ X178 )
| ( epred2_0 @ X176 @ X178 ) )
& ( ~ ( epred1_0 @ X179 @ X180 )
| ( epred2_0 @ X179 @ X180 ) )
& ~ ( epred2_0 @ esk2_0 @ esk1_0 )
& ( esk1_0 != esk2_0 )
& ( ~ ( epred3_0 @ X182 @ X183 )
| ~ ( epred3_0 @ X183 @ X184 )
| ( epred3_0 @ X182 @ X184 ) )
& ( ~ ( epred1_0 @ X185 @ X186 )
| ( epred3_0 @ X185 @ X186 ) )
& ~ ( epred3_0 @ esk1_0 @ esk2_0 ) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_18])])])])]) ).
thf(c_0_20,negated_conjecture,
! [X3: $i,X4: $i] :
( ( epred3_0 @ X3 @ X4 )
| ~ ( epred1_0 @ X3 @ X4 ) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
thf(c_0_21,negated_conjecture,
epred1_0 @ esk1_0 @ esk2_0,
inference(split_conjunct,[status(thm)],[c_0_19]) ).
thf(c_0_22,negated_conjecture,
~ ( epred3_0 @ esk1_0 @ esk2_0 ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
thf(c_0_23,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_22]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.10 % Problem : SEU472^1 : TPTP v8.2.0. Released v3.6.0.
% 0.02/0.11 % Command : run_E %s %d THM
% 0.11/0.31 % Computer : n013.cluster.edu
% 0.11/0.31 % Model : x86_64 x86_64
% 0.11/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.31 % Memory : 8042.1875MB
% 0.11/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.31 % CPULimit : 300
% 0.11/0.31 % WCLimit : 300
% 0.11/0.31 % DateTime : Sun May 19 18:10:23 EDT 2024
% 0.11/0.31 % CPUTime :
% 0.17/0.42 Running higher-order theorem proving
% 0.17/0.42 Running: /export/starexec/sandbox/solver/bin/eprover-ho --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/0.44 # Version: 3.1.0-ho
% 0.17/0.44 # Preprocessing class: HSSSSMSSMLSNHHN.
% 0.17/0.44 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.17/0.44 # Starting new_ho_10 with 1500s (5) cores
% 0.17/0.44 # Starting pre_casc_5 with 300s (1) cores
% 0.17/0.44 # Starting post_as_ho11 with 300s (1) cores
% 0.17/0.44 # Starting ho_unfolding_1 with 300s (1) cores
% 0.17/0.44 # post_as_ho11 with pid 14001 completed with status 0
% 0.17/0.44 # Result found by post_as_ho11
% 0.17/0.44 # Preprocessing class: HSSSSMSSMLSNHHN.
% 0.17/0.44 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.17/0.44 # Starting new_ho_10 with 1500s (5) cores
% 0.17/0.44 # Starting pre_casc_5 with 300s (1) cores
% 0.17/0.44 # Starting post_as_ho11 with 300s (1) cores
% 0.17/0.44 # No SInE strategy applied
% 0.17/0.44 # Search class: HHUSF-FFSF00-SHHSMFNN
% 0.17/0.44 # partial match(1): HHUNF-FFSF00-SHHSMFNN
% 0.17/0.44 # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.17/0.44 # Starting new_ho_10 with 163s (1) cores
% 0.17/0.44 # new_ho_10 with pid 14005 completed with status 0
% 0.17/0.44 # Result found by new_ho_10
% 0.17/0.44 # Preprocessing class: HSSSSMSSMLSNHHN.
% 0.17/0.44 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.17/0.44 # Starting new_ho_10 with 1500s (5) cores
% 0.17/0.44 # Starting pre_casc_5 with 300s (1) cores
% 0.17/0.44 # Starting post_as_ho11 with 300s (1) cores
% 0.17/0.44 # No SInE strategy applied
% 0.17/0.44 # Search class: HHUSF-FFSF00-SHHSMFNN
% 0.17/0.44 # partial match(1): HHUNF-FFSF00-SHHSMFNN
% 0.17/0.44 # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.17/0.44 # Starting new_ho_10 with 163s (1) cores
% 0.17/0.44 # Preprocessing time : 0.001 s
% 0.17/0.44 # Presaturation interreduction done
% 0.17/0.44
% 0.17/0.44 # Proof found!
% 0.17/0.44 # SZS status Theorem
% 0.17/0.44 # SZS output start CNFRefutation
% See solution above
% 0.17/0.44 # Parsed axioms : 59
% 0.17/0.44 # Removed by relevancy pruning/SinE : 0
% 0.17/0.44 # Initial clauses : 38
% 0.17/0.44 # Removed in clause preprocessing : 29
% 0.17/0.44 # Initial clauses in saturation : 9
% 0.17/0.44 # Processed clauses : 15
% 0.17/0.44 # ...of these trivial : 0
% 0.17/0.44 # ...subsumed : 1
% 0.17/0.44 # ...remaining for further processing : 14
% 0.17/0.44 # Other redundant clauses eliminated : 0
% 0.17/0.44 # Clauses deleted for lack of memory : 0
% 0.17/0.44 # Backward-subsumed : 0
% 0.17/0.44 # Backward-rewritten : 0
% 0.17/0.44 # Generated clauses : 2
% 0.17/0.44 # ...of the previous two non-redundant : 1
% 0.17/0.44 # ...aggressively subsumed : 0
% 0.17/0.44 # Contextual simplify-reflections : 0
% 0.17/0.44 # Paramodulations : 2
% 0.17/0.44 # Factorizations : 0
% 0.17/0.44 # NegExts : 0
% 0.17/0.44 # Equation resolutions : 0
% 0.17/0.44 # Disequality decompositions : 0
% 0.17/0.44 # Total rewrite steps : 0
% 0.17/0.44 # ...of those cached : 0
% 0.17/0.44 # Propositional unsat checks : 0
% 0.17/0.44 # Propositional check models : 0
% 0.17/0.44 # Propositional check unsatisfiable : 0
% 0.17/0.44 # Propositional clauses : 0
% 0.17/0.44 # Propositional clauses after purity: 0
% 0.17/0.44 # Propositional unsat core size : 0
% 0.17/0.44 # Propositional preprocessing time : 0.000
% 0.17/0.44 # Propositional encoding time : 0.000
% 0.17/0.44 # Propositional solver time : 0.000
% 0.17/0.44 # Success case prop preproc time : 0.000
% 0.17/0.44 # Success case prop encoding time : 0.000
% 0.17/0.44 # Success case prop solver time : 0.000
% 0.17/0.44 # Current number of processed clauses : 6
% 0.17/0.44 # Positive orientable unit clauses : 1
% 0.17/0.44 # Positive unorientable unit clauses: 0
% 0.17/0.44 # Negative unit clauses : 3
% 0.17/0.44 # Non-unit-clauses : 2
% 0.17/0.44 # Current number of unprocessed clauses: 3
% 0.17/0.44 # ...number of literals in the above : 7
% 0.17/0.44 # Current number of archived formulas : 0
% 0.17/0.44 # Current number of archived clauses : 8
% 0.17/0.44 # Clause-clause subsumption calls (NU) : 2
% 0.17/0.44 # Rec. Clause-clause subsumption calls : 2
% 0.17/0.44 # Non-unit clause-clause subsumptions : 0
% 0.17/0.44 # Unit Clause-clause subsumption calls : 0
% 0.17/0.44 # Rewrite failures with RHS unbound : 0
% 0.17/0.44 # BW rewrite match attempts : 0
% 0.17/0.44 # BW rewrite match successes : 0
% 0.17/0.44 # Condensation attempts : 15
% 0.17/0.44 # Condensation successes : 0
% 0.17/0.44 # Termbank termtop insertions : 3447
% 0.17/0.44 # Search garbage collected termcells : 993
% 0.17/0.44
% 0.17/0.44 # -------------------------------------------------
% 0.17/0.44 # User time : 0.002 s
% 0.17/0.44 # System time : 0.004 s
% 0.17/0.44 # Total time : 0.006 s
% 0.17/0.44 # Maximum resident set size: 2156 pages
% 0.17/0.44
% 0.17/0.44 # -------------------------------------------------
% 0.17/0.44 # User time : 0.005 s
% 0.17/0.44 # System time : 0.005 s
% 0.17/0.44 # Total time : 0.010 s
% 0.17/0.44 # Maximum resident set size: 1788 pages
% 0.17/0.44 % E---3.1 exiting
% 0.17/0.44 % E exiting
%------------------------------------------------------------------------------