TSTP Solution File: SET741^4 by E---3.1.00
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%------------------------------------------------------------------------------
% File : E---3.1.00
% Problem : SET741^4 : TPTP v8.1.2. Released v3.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n029.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 : Sat May 4 09:20:06 EDT 2024
% Result : Theorem 0.20s 0.54s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 17
% Syntax : Number of formulae : 40 ( 17 unt; 12 typ; 0 def)
% Number of atoms : 73 ( 59 equ; 0 cnn)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 198 ( 15 ~; 11 |; 12 &; 152 @)
% ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 37 ( 37 >; 0 *; 0 +; 0 <<)
% Number of symbols : 14 ( 12 usr; 4 con; 0-3 aty)
% Number of variables : 71 ( 10 ^ 54 !; 7 ?; 71 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_23,type,
fun_composition: ( $i > $i ) > ( $i > $i ) > $i > $i ).
thf(decl_25,type,
fun_injective: ( $i > $i ) > $o ).
thf(decl_26,type,
fun_surjective: ( $i > $i ) > $o ).
thf(decl_27,type,
fun_bijective: ( $i > $i ) > $o ).
thf(decl_30,type,
esk1_0: $i > $i ).
thf(decl_31,type,
esk2_0: $i > $i ).
thf(decl_32,type,
esk3_0: $i > $i ).
thf(decl_33,type,
esk4_1: $i > $i ).
thf(decl_34,type,
esk5_1: $i > $i ).
thf(decl_35,type,
esk6_0: $i ).
thf(decl_36,type,
esk7_0: $i ).
thf(decl_37,type,
esk8_0: $i ).
thf(fun_bijective,axiom,
( fun_bijective
= ( ^ [X1: $i > $i] :
( ( fun_injective @ X1 )
& ( fun_surjective @ X1 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.1cWMzZt6L0/E---3.1_11746.p',fun_bijective) ).
thf(fun_injective,axiom,
( fun_injective
= ( ^ [X1: $i > $i] :
! [X4: $i,X3: $i] :
( ( ( X1 @ X4 )
= ( X1 @ X3 ) )
=> ( X4 = X3 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.1cWMzZt6L0/E---3.1_11746.p',fun_injective) ).
thf(fun_surjective,axiom,
( fun_surjective
= ( ^ [X1: $i > $i] :
! [X3: $i] :
? [X4: $i] :
( X3
= ( X1 @ X4 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.1cWMzZt6L0/E---3.1_11746.p',fun_surjective) ).
thf(thm,conjecture,
! [X1: $i > $i,X5: $i > $i,X8: $i > $i] :
( ( ( fun_injective @ ( fun_composition @ ( fun_composition @ X1 @ X5 ) @ X8 ) )
& ( fun_surjective @ ( fun_composition @ ( fun_composition @ X5 @ X8 ) @ X1 ) )
& ( fun_surjective @ ( fun_composition @ ( fun_composition @ X8 @ X1 ) @ X5 ) ) )
=> ( fun_bijective @ X8 ) ),
file('/export/starexec/sandbox2/tmp/tmp.1cWMzZt6L0/E---3.1_11746.p',thm) ).
thf(fun_composition,axiom,
( fun_composition
= ( ^ [X1: $i > $i,X5: $i > $i,X4: $i] : ( X5 @ ( X1 @ X4 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.1cWMzZt6L0/E---3.1_11746.p',fun_composition) ).
thf(c_0_5,plain,
( fun_bijective
= ( ^ [Z0: $i > $i] :
( ! [X12: $i,X13: $i] :
( ( ( Z0 @ X12 )
= ( Z0 @ X13 ) )
=> ( X12 = X13 ) )
& ! [X14: $i] :
? [X15: $i] :
( X14
= ( Z0 @ X15 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[fun_bijective]) ).
thf(c_0_6,plain,
( fun_injective
= ( ^ [Z0: $i > $i] :
! [X4: $i,X3: $i] :
( ( ( Z0 @ X4 )
= ( Z0 @ X3 ) )
=> ( X4 = X3 ) ) ) ),
inference(fof_simplification,[status(thm)],[fun_injective]) ).
thf(c_0_7,plain,
( fun_surjective
= ( ^ [Z0: $i > $i] :
! [X3: $i] :
? [X4: $i] :
( X3
= ( Z0 @ X4 ) ) ) ),
inference(fof_simplification,[status(thm)],[fun_surjective]) ).
thf(c_0_8,plain,
( fun_bijective
= ( ^ [Z0: $i > $i] :
( ! [X12: $i,X13: $i] :
( ( ( Z0 @ X12 )
= ( Z0 @ X13 ) )
=> ( X12 = X13 ) )
& ! [X14: $i] :
? [X15: $i] :
( X14
= ( Z0 @ X15 ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_5,c_0_6]),c_0_7]) ).
thf(c_0_9,negated_conjecture,
~ ! [X1: $i > $i,X5: $i > $i,X8: $i > $i] :
( ( ! [X16: $i,X17: $i] :
( ( ( fun_composition @ ( fun_composition @ X1 @ X5 ) @ X8 @ X16 )
= ( fun_composition @ ( fun_composition @ X1 @ X5 ) @ X8 @ X17 ) )
=> ( X16 = X17 ) )
& ! [X18: $i] :
? [X19: $i] :
( X18
= ( fun_composition @ ( fun_composition @ X5 @ X8 ) @ X1 @ X19 ) )
& ! [X20: $i] :
? [X21: $i] :
( X20
= ( fun_composition @ ( fun_composition @ X8 @ X1 ) @ X5 @ X21 ) ) )
=> ( ! [X22: $i,X23: $i] :
( ( ( X8 @ X22 )
= ( X8 @ X23 ) )
=> ( X22 = X23 ) )
& ! [X24: $i] :
? [X25: $i] :
( X24
= ( X8 @ X25 ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(assume_negation,[status(cth)],[thm]),c_0_6]),c_0_7]),c_0_8]) ).
thf(c_0_10,plain,
! [X26: $i > $i,X27: $i > $i,X28: $i] :
( ( fun_composition @ X26 @ X27 @ X28 )
= ( X27 @ ( X26 @ X28 ) ) ),
inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[fun_composition])]) ).
thf(c_0_11,negated_conjecture,
! [X35: $i,X36: $i,X37: $i,X39: $i,X44: $i] :
( ( ( ( fun_composition @ ( fun_composition @ esk1_0 @ esk2_0 ) @ esk3_0 @ X35 )
!= ( fun_composition @ ( fun_composition @ esk1_0 @ esk2_0 ) @ esk3_0 @ X36 ) )
| ( X35 = X36 ) )
& ( X37
= ( fun_composition @ ( fun_composition @ esk2_0 @ esk3_0 ) @ esk1_0 @ ( esk4_1 @ X37 ) ) )
& ( X39
= ( fun_composition @ ( fun_composition @ esk3_0 @ esk1_0 ) @ esk2_0 @ ( esk5_1 @ X39 ) ) )
& ( ( ( esk3_0 @ esk6_0 )
= ( esk3_0 @ esk7_0 ) )
| ( esk8_0
!= ( esk3_0 @ X44 ) ) )
& ( ( esk6_0 != esk7_0 )
| ( esk8_0
!= ( esk3_0 @ X44 ) ) ) ),
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_9])])])])])]) ).
thf(c_0_12,plain,
! [X29: $i > $i,X30: $i > $i,X31: $i] :
( ( fun_composition @ X29 @ X30 @ X31 )
= ( X30 @ ( X29 @ X31 ) ) ),
inference(variable_rename,[status(thm)],[c_0_10]) ).
thf(c_0_13,negated_conjecture,
! [X3: $i,X4: $i] :
( ( X3 = X4 )
| ( ( fun_composition @ ( fun_composition @ esk1_0 @ esk2_0 ) @ esk3_0 @ X3 )
!= ( fun_composition @ ( fun_composition @ esk1_0 @ esk2_0 ) @ esk3_0 @ X4 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
thf(c_0_14,plain,
! [X1: $i > $i,X5: $i > $i,X3: $i] :
( ( fun_composition @ X1 @ X5 @ X3 )
= ( X5 @ ( X1 @ X3 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
thf(c_0_15,negated_conjecture,
! [X3: $i] :
( X3
= ( fun_composition @ ( fun_composition @ esk3_0 @ esk1_0 ) @ esk2_0 @ ( esk5_1 @ X3 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
thf(c_0_16,negated_conjecture,
! [X3: $i,X4: $i] :
( ( X3 = X4 )
| ( ( esk3_0 @ ( esk2_0 @ ( esk1_0 @ X3 ) ) )
!= ( esk3_0 @ ( esk2_0 @ ( esk1_0 @ X4 ) ) ) ) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_13,c_0_14]),c_0_14]),c_0_14]),c_0_14]) ).
thf(c_0_17,negated_conjecture,
! [X3: $i] :
( ( esk2_0 @ ( esk1_0 @ ( esk3_0 @ ( esk5_1 @ X3 ) ) ) )
= X3 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_15,c_0_14]),c_0_14]) ).
thf(c_0_18,negated_conjecture,
! [X3: $i,X4: $i] :
( ( X3
= ( esk3_0 @ ( esk5_1 @ X4 ) ) )
| ( ( esk3_0 @ ( esk2_0 @ ( esk1_0 @ X3 ) ) )
!= ( esk3_0 @ X4 ) ) ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
thf(c_0_19,negated_conjecture,
! [X3: $i] :
( ( ( esk3_0 @ esk6_0 )
= ( esk3_0 @ esk7_0 ) )
| ( esk8_0
!= ( esk3_0 @ X3 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
thf(c_0_20,negated_conjecture,
! [X3: $i] :
( ( esk3_0 @ ( esk5_1 @ ( esk2_0 @ ( esk1_0 @ X3 ) ) ) )
= X3 ),
inference(er,[status(thm)],[c_0_18]) ).
thf(c_0_21,negated_conjecture,
! [X3: $i,X4: $i] :
( ( ( esk3_0 @ ( esk5_1 @ X3 ) )
= ( esk3_0 @ ( esk5_1 @ X4 ) ) )
| ( ( esk3_0 @ X3 )
!= ( esk3_0 @ X4 ) ) ),
inference(spm,[status(thm)],[c_0_18,c_0_17]) ).
thf(c_0_22,negated_conjecture,
( ( esk3_0 @ esk6_0 )
= ( esk3_0 @ esk7_0 ) ),
inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20])]) ).
thf(c_0_23,negated_conjecture,
! [X3: $i] :
( ( ( esk3_0 @ ( esk5_1 @ X3 ) )
= ( esk3_0 @ ( esk5_1 @ esk6_0 ) ) )
| ( ( esk3_0 @ X3 )
!= ( esk3_0 @ esk7_0 ) ) ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
thf(c_0_24,negated_conjecture,
! [X3: $i] :
( ( esk6_0 != esk7_0 )
| ( esk8_0
!= ( esk3_0 @ X3 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
thf(c_0_25,negated_conjecture,
! [X3: $i] :
( ( X3 = esk6_0 )
| ( ( esk3_0 @ X3 )
!= ( esk3_0 @ esk7_0 ) ) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_23]),c_0_17]) ).
thf(c_0_26,negated_conjecture,
esk6_0 != esk7_0,
inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_20])]) ).
thf(c_0_27,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(er,[status(thm)],[c_0_25]),c_0_26]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : SET741^4 : TPTP v8.1.2. Released v3.6.0.
% 0.12/0.14 % Command : run_E %s %d THM
% 0.14/0.35 % Computer : n029.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Fri May 3 10:34:22 EDT 2024
% 0.14/0.35 % CPUTime :
% 0.20/0.52 Running higher-order theorem proving
% 0.20/0.52 Running: /export/starexec/sandbox2/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/sandbox2/tmp/tmp.1cWMzZt6L0/E---3.1_11746.p
% 0.20/0.54 # Version: 3.1.0-ho
% 0.20/0.54 # Preprocessing class: HSSSSMSSMLSNHSN.
% 0.20/0.54 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.20/0.54 # Starting new_ho_9 with 1500s (5) cores
% 0.20/0.54 # Starting post_as_ho1 with 300s (1) cores
% 0.20/0.54 # Starting sh1l with 300s (1) cores
% 0.20/0.54 # Starting post_as_ho10 with 300s (1) cores
% 0.20/0.54 # post_as_ho1 with pid 11869 completed with status 0
% 0.20/0.54 # Result found by post_as_ho1
% 0.20/0.54 # Preprocessing class: HSSSSMSSMLSNHSN.
% 0.20/0.54 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.20/0.54 # Starting new_ho_9 with 1500s (5) cores
% 0.20/0.54 # Starting post_as_ho1 with 300s (1) cores
% 0.20/0.54 # No SInE strategy applied
% 0.20/0.54 # Search class: HHHPS-FFSF31-SHSSMSNN
% 0.20/0.54 # partial match(3): HHHNS-FFSF11-SHSSMFNN
% 0.20/0.54 # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.20/0.54 # Starting new_ho_10 with 163s (1) cores
% 0.20/0.54 # new_ho_10 with pid 11875 completed with status 0
% 0.20/0.54 # Result found by new_ho_10
% 0.20/0.54 # Preprocessing class: HSSSSMSSMLSNHSN.
% 0.20/0.54 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.20/0.54 # Starting new_ho_9 with 1500s (5) cores
% 0.20/0.54 # Starting post_as_ho1 with 300s (1) cores
% 0.20/0.54 # No SInE strategy applied
% 0.20/0.54 # Search class: HHHPS-FFSF31-SHSSMSNN
% 0.20/0.54 # partial match(3): HHHNS-FFSF11-SHSSMFNN
% 0.20/0.54 # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.20/0.54 # Starting new_ho_10 with 163s (1) cores
% 0.20/0.54 # Preprocessing time : 0.001 s
% 0.20/0.54 # Presaturation interreduction done
% 0.20/0.54
% 0.20/0.54 # Proof found!
% 0.20/0.54 # SZS status Theorem
% 0.20/0.54 # SZS output start CNFRefutation
% See solution above
% 0.20/0.54 # Parsed axioms : 17
% 0.20/0.54 # Removed by relevancy pruning/SinE : 0
% 0.20/0.54 # Initial clauses : 14
% 0.20/0.54 # Removed in clause preprocessing : 8
% 0.20/0.54 # Initial clauses in saturation : 6
% 0.20/0.54 # Processed clauses : 35
% 0.20/0.54 # ...of these trivial : 1
% 0.20/0.54 # ...subsumed : 7
% 0.20/0.54 # ...remaining for further processing : 27
% 0.20/0.54 # Other redundant clauses eliminated : 12
% 0.20/0.54 # Clauses deleted for lack of memory : 0
% 0.20/0.54 # Backward-subsumed : 1
% 0.20/0.54 # Backward-rewritten : 5
% 0.20/0.54 # Generated clauses : 71
% 0.20/0.54 # ...of the previous two non-redundant : 52
% 0.20/0.54 # ...aggressively subsumed : 0
% 0.20/0.54 # Contextual simplify-reflections : 0
% 0.20/0.54 # Paramodulations : 52
% 0.20/0.54 # Factorizations : 0
% 0.20/0.54 # NegExts : 0
% 0.20/0.54 # Equation resolutions : 19
% 0.20/0.54 # Disequality decompositions : 0
% 0.20/0.54 # Total rewrite steps : 24
% 0.20/0.54 # ...of those cached : 5
% 0.20/0.54 # Propositional unsat checks : 0
% 0.20/0.54 # Propositional check models : 0
% 0.20/0.54 # Propositional check unsatisfiable : 0
% 0.20/0.54 # Propositional clauses : 0
% 0.20/0.54 # Propositional clauses after purity: 0
% 0.20/0.54 # Propositional unsat core size : 0
% 0.20/0.54 # Propositional preprocessing time : 0.000
% 0.20/0.54 # Propositional encoding time : 0.000
% 0.20/0.54 # Propositional solver time : 0.000
% 0.20/0.54 # Success case prop preproc time : 0.000
% 0.20/0.54 # Success case prop encoding time : 0.000
% 0.20/0.54 # Success case prop solver time : 0.000
% 0.20/0.54 # Current number of processed clauses : 15
% 0.20/0.54 # Positive orientable unit clauses : 6
% 0.20/0.54 # Positive unorientable unit clauses: 0
% 0.20/0.54 # Negative unit clauses : 1
% 0.20/0.54 # Non-unit-clauses : 8
% 0.20/0.54 # Current number of unprocessed clauses: 27
% 0.20/0.54 # ...number of literals in the above : 54
% 0.20/0.54 # Current number of archived formulas : 0
% 0.20/0.54 # Current number of archived clauses : 12
% 0.20/0.54 # Clause-clause subsumption calls (NU) : 10
% 0.20/0.54 # Rec. Clause-clause subsumption calls : 10
% 0.20/0.54 # Non-unit clause-clause subsumptions : 7
% 0.20/0.54 # Unit Clause-clause subsumption calls : 1
% 0.20/0.54 # Rewrite failures with RHS unbound : 0
% 0.20/0.54 # BW rewrite match attempts : 11
% 0.20/0.54 # BW rewrite match successes : 6
% 0.20/0.54 # Condensation attempts : 35
% 0.20/0.54 # Condensation successes : 0
% 0.20/0.54 # Termbank termtop insertions : 1851
% 0.20/0.54 # Search garbage collected termcells : 266
% 0.20/0.54
% 0.20/0.54 # -------------------------------------------------
% 0.20/0.54 # User time : 0.008 s
% 0.20/0.54 # System time : 0.001 s
% 0.20/0.54 # Total time : 0.009 s
% 0.20/0.54 # Maximum resident set size: 1728 pages
% 0.20/0.54
% 0.20/0.54 # -------------------------------------------------
% 0.20/0.54 # User time : 0.010 s
% 0.20/0.54 # System time : 0.004 s
% 0.20/0.54 # Total time : 0.014 s
% 0.20/0.54 # Maximum resident set size: 1736 pages
% 0.20/0.54 % E---3.1 exiting
% 0.20/0.54 % E exiting
%------------------------------------------------------------------------------