TSTP Solution File: SEU795^2 by E---3.1.00
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : E---3.1.00
% Problem : SEU795^2 : TPTP v8.2.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n023.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 03:30:18 EDT 2024
% Result : Theorem 0.18s 0.47s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 17
% Syntax : Number of formulae : 44 ( 8 unt; 12 typ; 0 def)
% Number of atoms : 116 ( 40 equ; 0 cnn)
% Maximal formula atoms : 20 ( 3 avg)
% Number of connectives : 336 ( 29 ~; 30 |; 18 &; 227 @)
% ( 19 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 36 ( 36 >; 0 *; 0 +; 0 <<)
% Number of symbols : 14 ( 12 usr; 7 con; 0-3 aty)
% Number of variables : 99 ( 17 ^ 70 !; 12 ?; 99 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_22,type,
in: $i > $i > $o ).
thf(decl_23,type,
exu: ( $i > $o ) > $o ).
thf(decl_24,type,
descr: ( $i > $o ) > $i ).
thf(decl_25,type,
descrp: $o ).
thf(decl_26,type,
in__Cong: $o ).
thf(decl_27,type,
image1Ex1: $o ).
thf(decl_28,type,
image1: $i > ( $i > $i ) > $i ).
thf(decl_29,type,
esk1_0: $i ).
thf(decl_30,type,
esk2_0: $i > $i ).
thf(decl_31,type,
esk3_0: $i ).
thf(decl_32,type,
esk4_0: $i ).
thf(decl_33,type,
esk5_3: $i > ( $i > $i ) > $i > $i ).
thf(image1Ex1,axiom,
( image1Ex1
<=> ! [X4: $i,X6: $i > $i] :
( exu
@ ^ [X5: $i] :
! [X2: $i] :
( ( in @ X2 @ X5 )
<=> ? [X3: $i] :
( ( in @ X3 @ X4 )
& ( X2
= ( X6 @ X3 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',image1Ex1) ).
thf(descrp,axiom,
( descrp
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ( X1
@ ( descr
@ ^ [X2: $i] : ( X1 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',descrp) ).
thf(image1Equiv,conjecture,
( descrp
=> ( in__Cong
=> ( image1Ex1
=> ! [X4: $i,X6: $i > $i,X2: $i] :
( ( in @ X2
@ ( image1 @ X4
@ ^ [X3: $i] : ( X6 @ X3 ) ) )
<=> ? [X3: $i] :
( ( in @ X3 @ X4 )
& ( X2
= ( X6 @ X3 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',image1Equiv) ).
thf(in__Cong,axiom,
( in__Cong
<=> ! [X4: $i,X5: $i] :
( ( X4 = X5 )
=> ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( in @ X2 @ X4 )
<=> ( in @ X3 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',in__Cong) ).
thf(image1,axiom,
( image1
= ( ^ [X4: $i,X6: $i > $i] :
( descr
@ ^ [X5: $i] :
! [X2: $i] :
( ( in @ X2 @ X5 )
<=> ? [X3: $i] :
( ( in @ X3 @ X4 )
& ( X2
= ( X6 @ X3 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',image1) ).
thf(c_0_5,plain,
( image1Ex1
<=> ! [X4: $i,X6: $i > $i] :
( exu
@ ^ [Z0: $i] :
! [X2: $i] :
( ( in @ X2 @ Z0 )
<=> ? [X3: $i] :
( ( in @ X3 @ X4 )
& ( X2
= ( X6 @ X3 ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[image1Ex1]) ).
thf(c_0_6,plain,
( descrp
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
=> ( X1
@ ( descr
@ ^ [Z0: $i] : ( X1 @ Z0 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[descrp]) ).
thf(c_0_7,negated_conjecture,
~ ( ! [X18: $i > $o] :
( ( exu @ X18 )
=> ( X18
@ ( descr
@ ^ [Z0: $i] : ( X18 @ Z0 ) ) ) )
=> ( ! [X19: $i,X20: $i] :
( ( X19 = X20 )
=> ! [X21: $i,X22: $i] :
( ( X21 = X22 )
=> ( ( in @ X21 @ X19 )
<=> ( in @ X22 @ X20 ) ) ) )
=> ( ! [X23: $i,X24: $i > $i] :
( exu
@ ^ [Z0: $i] :
! [X25: $i] :
( ( in @ X25 @ Z0 )
<=> ? [X26: $i] :
( ( in @ X26 @ X23 )
& ( X25
= ( X24 @ X26 ) ) ) ) )
=> ! [X4: $i,X6: $i > $i,X2: $i] :
( ( in @ X2 @ ( image1 @ X4 @ X6 ) )
<=> ? [X3: $i] :
( ( in @ X3 @ X4 )
& ( X2
= ( X6 @ X3 ) ) ) ) ) ) ),
inference(fool_unroll,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[image1Equiv])]),c_0_5]),c_0_6]),in__Cong])]) ).
thf(c_0_8,plain,
! [X27: $i,X28: $i > $i] :
( ( image1 @ X27 @ X28 )
= ( descr
@ ^ [Z0: $i] :
! [X2: $i] :
( ( in @ X2 @ Z0 )
<=> ? [X3: $i] :
( ( in @ X3 @ X27 )
& ( X2
= ( X28 @ X3 ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[image1])]) ).
thf(c_0_9,negated_conjecture,
! [X29: $i > $o,X30: $i,X31: $i,X32: $i,X33: $i,X34: $i,X35: $i > $i,X39: $i] :
( ( ~ ( exu @ X29 )
| ( X29 @ ( descr @ X29 ) ) )
& ( ~ ( in @ X32 @ X30 )
| ( in @ X33 @ X31 )
| ( X32 != X33 )
| ( X30 != X31 ) )
& ( ~ ( in @ X33 @ X31 )
| ( in @ X32 @ X30 )
| ( X32 != X33 )
| ( X30 != X31 ) )
& ( exu
@ ^ [Z0: $i] :
! [X25: $i] :
( ( in @ X25 @ Z0 )
<=> ? [X26: $i] :
( ( in @ X26 @ X34 )
& ( X25
= ( X35 @ X26 ) ) ) ) )
& ( ~ ( in @ esk3_0 @ ( image1 @ esk1_0 @ esk2_0 ) )
| ~ ( in @ X39 @ esk1_0 )
| ( esk3_0
!= ( esk2_0 @ X39 ) ) )
& ( ( in @ esk4_0 @ esk1_0 )
| ( in @ esk3_0 @ ( image1 @ esk1_0 @ esk2_0 ) ) )
& ( ( esk3_0
= ( esk2_0 @ esk4_0 ) )
| ( in @ esk3_0 @ ( image1 @ esk1_0 @ esk2_0 ) ) ) ),
inference(distribute,[status(thm)],[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_7])])])])])]) ).
thf(c_0_10,plain,
! [X41: $i,X42: $i > $i] :
( ( image1 @ X41 @ X42 )
= ( descr
@ ^ [Z0: $i] :
! [X2: $i] :
( ( in @ X2 @ Z0 )
<=> ? [X3: $i] :
( ( in @ X3 @ X41 )
& ( X2
= ( X42 @ X3 ) ) ) ) ) ),
inference(variable_rename,[status(thm)],[c_0_8]) ).
thf(c_0_11,negated_conjecture,
! [X1: $i > $o] :
( ( X1 @ ( descr @ X1 ) )
| ~ ( exu @ X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
thf(c_0_12,plain,
! [X2: $i,X6: $i > $i] :
( ( image1 @ X2 @ X6 )
= ( descr
@ ^ [Z0: $i] :
! [X53: $i] :
( ( in @ X53 @ Z0 )
<=> ? [X54: $i] :
( ( in @ X54 @ X2 )
& ( X53
= ( X6 @ X54 ) ) ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
thf(c_0_13,negated_conjecture,
! [X4: $i,X6: $i > $i] :
( exu
@ ^ [Z0: $i] :
! [X55: $i] :
( ( in @ X55 @ Z0 )
<=> ? [X56: $i] :
( ( in @ X56 @ X4 )
& ( X55
= ( X6 @ X56 ) ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
thf(c_0_14,negated_conjecture,
! [X2: $i] :
( ~ ( in @ esk3_0 @ ( image1 @ esk1_0 @ esk2_0 ) )
| ~ ( in @ X2 @ esk1_0 )
| ( esk3_0
!= ( esk2_0 @ X2 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
thf(c_0_15,negated_conjecture,
( ( esk3_0
= ( esk2_0 @ esk4_0 ) )
| ( in @ esk3_0 @ ( image1 @ esk1_0 @ esk2_0 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
thf(c_0_16,negated_conjecture,
! [X2: $i,X6: $i > $i,X57: $i] :
( ( in @ X57 @ ( image1 @ X2 @ X6 ) )
<=> ? [X58: $i] :
( ( in @ X58 @ X2 )
& ( X57
= ( X6 @ X58 ) ) ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_12]),c_0_13])]) ).
thf(c_0_17,negated_conjecture,
! [X2: $i] :
( ( ( esk2_0 @ esk4_0 )
= esk3_0 )
| ( ( esk2_0 @ X2 )
!= esk3_0 )
| ~ ( in @ X2 @ esk1_0 ) ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
thf(c_0_18,negated_conjecture,
! [X2: $i,X3: $i,X6: $i > $i] :
( ( in @ ( esk5_3 @ X2 @ X6 @ X3 ) @ X2 )
| ~ ( in @ X3 @ ( image1 @ X2 @ X6 ) ) ),
inference(dynamic_cnf,[status(thm)],[c_0_16]) ).
thf(c_0_19,negated_conjecture,
! [X2: $i,X3: $i,X6: $i > $i] :
( ( ( X6 @ ( esk5_3 @ X2 @ X6 @ X3 ) )
= X3 )
| ~ ( in @ X3 @ ( image1 @ X2 @ X6 ) ) ),
inference(dynamic_cnf,[status(thm)],[c_0_16]) ).
thf(c_0_20,negated_conjecture,
! [X2: $i,X6: $i > $i] :
( ( ( esk2_0 @ esk4_0 )
= esk3_0 )
| ( ( esk2_0 @ ( esk5_3 @ esk1_0 @ X6 @ X2 ) )
!= esk3_0 )
| ~ ( in @ X2 @ ( image1 @ esk1_0 @ X6 ) ) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
thf(c_0_21,negated_conjecture,
( ( ( esk2_0 @ ( esk5_3 @ esk1_0 @ esk2_0 @ esk3_0 ) )
= esk3_0 )
| ( ( esk2_0 @ esk4_0 )
= esk3_0 ) ),
inference(spm,[status(thm)],[c_0_19,c_0_15]) ).
thf(c_0_22,negated_conjecture,
! [X2: $i,X6: $i > $i,X3: $i] :
( ( in @ ( X6 @ X2 ) @ ( image1 @ X3 @ X6 ) )
| ~ ( in @ X2 @ X3 ) ),
inference(er,[status(thm)],[inference(dynamic_cnf,[status(thm)],[c_0_16])]) ).
thf(c_0_23,negated_conjecture,
( ( esk2_0 @ esk4_0 )
= esk3_0 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_15]),c_0_21]) ).
thf(c_0_24,negated_conjecture,
( ( in @ esk4_0 @ esk1_0 )
| ( in @ esk3_0 @ ( image1 @ esk1_0 @ esk2_0 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
thf(c_0_25,negated_conjecture,
! [X2: $i] :
( ( in @ esk3_0 @ ( image1 @ X2 @ esk2_0 ) )
| ~ ( in @ esk4_0 @ X2 ) ),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
thf(c_0_26,negated_conjecture,
! [X2: $i] :
( ( in @ esk4_0 @ esk1_0 )
| ( ( esk2_0 @ X2 )
!= esk3_0 )
| ~ ( in @ X2 @ esk1_0 ) ),
inference(spm,[status(thm)],[c_0_14,c_0_24]) ).
thf(c_0_27,negated_conjecture,
! [X2: $i] :
( ( ( esk2_0 @ X2 )
!= esk3_0 )
| ~ ( in @ X2 @ esk1_0 ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_25]),c_0_26]) ).
thf(c_0_28,negated_conjecture,
! [X2: $i,X6: $i > $i] :
( ( ( esk2_0 @ ( esk5_3 @ esk1_0 @ X6 @ X2 ) )
!= esk3_0 )
| ~ ( in @ X2 @ ( image1 @ esk1_0 @ X6 ) ) ),
inference(spm,[status(thm)],[c_0_27,c_0_18]) ).
thf(c_0_29,negated_conjecture,
( ( ( esk2_0 @ ( esk5_3 @ esk1_0 @ esk2_0 @ esk3_0 ) )
= esk3_0 )
| ( in @ esk4_0 @ esk1_0 ) ),
inference(spm,[status(thm)],[c_0_19,c_0_24]) ).
thf(c_0_30,negated_conjecture,
in @ esk4_0 @ esk1_0,
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_24]),c_0_29]) ).
thf(c_0_31,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_30]),c_0_23])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SEU795^2 : TPTP v8.2.0. Released v3.7.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n023.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Sun May 19 15:37:52 EDT 2024
% 0.12/0.33 % CPUTime :
% 0.18/0.45 Running higher-order theorem proving
% 0.18/0.45 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
% 0.18/0.47 # Version: 3.1.0-ho
% 0.18/0.47 # Preprocessing class: HSSSSLSSSLMCHSA.
% 0.18/0.47 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.18/0.47 # Starting pre_casc_6 with 1500s (5) cores
% 0.18/0.47 # Starting new_bool_12 with 300s (1) cores
% 0.18/0.47 # Starting new_bool_6 with 300s (1) cores
% 0.18/0.47 # Starting pre_casc_9 with 300s (1) cores
% 0.18/0.47 # pre_casc_9 with pid 31759 completed with status 0
% 0.18/0.47 # Result found by pre_casc_9
% 0.18/0.47 # Preprocessing class: HSSSSLSSSLMCHSA.
% 0.18/0.47 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.18/0.47 # Starting pre_casc_6 with 1500s (5) cores
% 0.18/0.47 # Starting new_bool_12 with 300s (1) cores
% 0.18/0.47 # Starting new_bool_6 with 300s (1) cores
% 0.18/0.47 # Starting pre_casc_9 with 300s (1) cores
% 0.18/0.47 # SinE strategy is GSinE(CountFormulas,hypos,1,,1,20000,1.5,true)
% 0.18/0.47 # Search class: HGHSS-FFSF21-DHSFMSBN
% 0.18/0.47 # partial match(3): HGHSF-FFSF21-SHSFMMBN
% 0.18/0.47 # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.18/0.47 # Starting new_ho_10 with 163s (1) cores
% 0.18/0.47 # new_ho_10 with pid 31760 completed with status 0
% 0.18/0.47 # Result found by new_ho_10
% 0.18/0.47 # Preprocessing class: HSSSSLSSSLMCHSA.
% 0.18/0.47 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.18/0.47 # Starting pre_casc_6 with 1500s (5) cores
% 0.18/0.47 # Starting new_bool_12 with 300s (1) cores
% 0.18/0.47 # Starting new_bool_6 with 300s (1) cores
% 0.18/0.47 # Starting pre_casc_9 with 300s (1) cores
% 0.18/0.47 # SinE strategy is GSinE(CountFormulas,hypos,1,,1,20000,1.5,true)
% 0.18/0.47 # Search class: HGHSS-FFSF21-DHSFMSBN
% 0.18/0.47 # partial match(3): HGHSF-FFSF21-SHSFMMBN
% 0.18/0.47 # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.18/0.47 # Starting new_ho_10 with 163s (1) cores
% 0.18/0.47 # Preprocessing time : 0.001 s
% 0.18/0.47 # Presaturation interreduction done
% 0.18/0.47
% 0.18/0.47 # Proof found!
% 0.18/0.47 # SZS status Theorem
% 0.18/0.47 # SZS output start CNFRefutation
% See solution above
% 0.18/0.47 # Parsed axioms : 13
% 0.18/0.47 # Removed by relevancy pruning/SinE : 8
% 0.18/0.47 # Initial clauses : 8
% 0.18/0.47 # Removed in clause preprocessing : 2
% 0.18/0.47 # Initial clauses in saturation : 6
% 0.18/0.47 # Processed clauses : 34
% 0.18/0.47 # ...of these trivial : 0
% 0.18/0.47 # ...subsumed : 0
% 0.18/0.47 # ...remaining for further processing : 34
% 0.18/0.47 # Other redundant clauses eliminated : 1
% 0.18/0.47 # Clauses deleted for lack of memory : 0
% 0.18/0.47 # Backward-subsumed : 2
% 0.18/0.47 # Backward-rewritten : 7
% 0.18/0.47 # Generated clauses : 74
% 0.18/0.47 # ...of the previous two non-redundant : 69
% 0.18/0.47 # ...aggressively subsumed : 0
% 0.18/0.47 # Contextual simplify-reflections : 4
% 0.18/0.47 # Paramodulations : 70
% 0.18/0.47 # Factorizations : 0
% 0.18/0.47 # NegExts : 0
% 0.18/0.47 # Equation resolutions : 1
% 0.18/0.47 # Disequality decompositions : 0
% 0.18/0.47 # Total rewrite steps : 9
% 0.18/0.47 # ...of those cached : 6
% 0.18/0.47 # Propositional unsat checks : 0
% 0.18/0.47 # Propositional check models : 0
% 0.18/0.47 # Propositional check unsatisfiable : 0
% 0.18/0.47 # Propositional clauses : 0
% 0.18/0.47 # Propositional clauses after purity: 0
% 0.18/0.47 # Propositional unsat core size : 0
% 0.18/0.47 # Propositional preprocessing time : 0.000
% 0.18/0.47 # Propositional encoding time : 0.000
% 0.18/0.47 # Propositional solver time : 0.000
% 0.18/0.47 # Success case prop preproc time : 0.000
% 0.18/0.47 # Success case prop encoding time : 0.000
% 0.18/0.47 # Success case prop solver time : 0.000
% 0.18/0.47 # Current number of processed clauses : 18
% 0.18/0.47 # Positive orientable unit clauses : 4
% 0.18/0.47 # Positive unorientable unit clauses: 0
% 0.18/0.47 # Negative unit clauses : 0
% 0.18/0.47 # Non-unit-clauses : 14
% 0.18/0.47 # Current number of unprocessed clauses: 42
% 0.18/0.47 # ...number of literals in the above : 131
% 0.18/0.47 # Current number of archived formulas : 0
% 0.18/0.47 # Current number of archived clauses : 16
% 0.18/0.47 # Clause-clause subsumption calls (NU) : 110
% 0.18/0.47 # Rec. Clause-clause subsumption calls : 101
% 0.18/0.47 # Non-unit clause-clause subsumptions : 6
% 0.18/0.47 # Unit Clause-clause subsumption calls : 2
% 0.18/0.47 # Rewrite failures with RHS unbound : 0
% 0.18/0.47 # BW rewrite match attempts : 2
% 0.18/0.47 # BW rewrite match successes : 2
% 0.18/0.47 # Condensation attempts : 34
% 0.18/0.47 # Condensation successes : 0
% 0.18/0.47 # Termbank termtop insertions : 3364
% 0.18/0.47 # Search garbage collected termcells : 408
% 0.18/0.47
% 0.18/0.47 # -------------------------------------------------
% 0.18/0.47 # User time : 0.006 s
% 0.18/0.47 # System time : 0.002 s
% 0.18/0.47 # Total time : 0.008 s
% 0.18/0.47 # Maximum resident set size: 1924 pages
% 0.18/0.47
% 0.18/0.47 # -------------------------------------------------
% 0.18/0.47 # User time : 0.007 s
% 0.18/0.47 # System time : 0.004 s
% 0.18/0.47 # Total time : 0.011 s
% 0.18/0.47 # Maximum resident set size: 1740 pages
% 0.18/0.47 % E---3.1 exiting
% 0.18/0.47 % E exiting
%------------------------------------------------------------------------------