%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SYO526^1 : TPTP v9.3.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n015.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:43:21 AM UTC 2026
% Result : Theorem 0.07s 0.25s
% Output : CNFRefutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 4
% Syntax : Number of formulae : 26 ( 10 unt; 0 typ; 0 def)
% Number of atoms : 58 ( 5 equ; 0 cnn)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 60 ( 19 ~; 15 |; 3 &; 19 @)
% ( 4 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 11 ( 3 ^; 8 !; 0 ?; 11 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_23,type,
a: $o ).
thf(decl_24,type,
b: $o ).
thf(decl_25,type,
f: $i > $o ).
thf(decl_26,type,
g: $i > $o ).
thf(decl_27,type,
esk1_0: $i ).
thf(gb,conjecture,
( g
= ( ^ [X1: $i] : b ) ),
file('/export/starexec/sandbox2/tmp/tmp.9wcV6fptuw/E---3.1_3831069.p',gb) ).
thf(fg,axiom,
f = g,
file('/export/starexec/sandbox2/tmp/tmp.9wcV6fptuw/E---3.1_3831069.p',fg) ).
thf(fa,axiom,
( f
= ( ^ [X1: $i] : a ) ),
file('/export/starexec/sandbox2/tmp/tmp.9wcV6fptuw/E---3.1_3831069.p',fa) ).
thf(ab,axiom,
( a
<=> b ),
file('/export/starexec/sandbox2/tmp/tmp.9wcV6fptuw/E---3.1_3831069.p',ab) ).
thf(c_0_4,negated_conjecture,
( g
!= ( ^ [X1: $i] : b ) ),
inference(assume_negation,[status(cth)],[gb]) ).
thf(c_0_5,negated_conjecture,
~ ! [X3: $i] :
( ( g @ X3 )
<=> b ),
inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[c_0_4])]) ).
thf(c_0_6,plain,
f = g,
inference(split_conjunct,[status(thm)],[fg]) ).
thf(c_0_7,negated_conjecture,
( ( ~ ( g @ esk1_0 )
| ~ b )
& ( ( g @ esk1_0 )
| b ) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])])])]) ).
thf(c_0_8,plain,
! [X6: $i] :
( ( g @ X6 )
<=> ( f @ X6 ) ),
inference(arg_cong,[status(thm)],[c_0_6]) ).
thf(c_0_9,plain,
! [X2: $i] :
( ( f @ X2 )
<=> a ),
inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[fa])]) ).
thf(c_0_10,negated_conjecture,
( ~ ( g @ esk1_0 )
| ~ b ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
thf(c_0_11,plain,
! [X1: $i] :
( ( g @ X1 )
| ~ ( f @ X1 ) ),
inference(dynamic_cnf,[status(thm)],[c_0_8]) ).
thf(c_0_12,plain,
! [X4: $i] :
( ( ~ ( f @ X4 )
| a )
& ( ~ a
| ( f @ X4 ) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_9])])]) ).
thf(c_0_13,plain,
( ( ~ a
| b )
& ( ~ b
| a ) ),
inference(fof_nnf,[status(thm)],[inference(fof_nnf,[status(thm)],[ab])]) ).
thf(c_0_14,negated_conjecture,
( ~ ( f @ esk1_0 )
| ~ b ),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
thf(c_0_15,plain,
! [X1: $i] :
( ( f @ X1 )
| ~ a ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
thf(c_0_16,plain,
( a
| ~ b ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
thf(c_0_17,negated_conjecture,
( ( g @ esk1_0 )
| b ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
thf(c_0_18,negated_conjecture,
~ b,
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_15]),c_0_16]) ).
thf(c_0_19,plain,
! [X1: $i] :
( ( f @ X1 )
| ~ ( g @ X1 ) ),
inference(dynamic_cnf,[status(thm)],[c_0_8]) ).
thf(c_0_20,negated_conjecture,
g @ esk1_0,
inference(sr,[status(thm)],[c_0_17,c_0_18]) ).
thf(c_0_21,plain,
! [X1: $i] :
( a
| ~ ( f @ X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
thf(c_0_22,negated_conjecture,
f @ esk1_0,
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
thf(c_0_23,plain,
( b
| ~ a ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
thf(c_0_24,negated_conjecture,
a,
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
thf(c_0_25,plain,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_23,c_0_24])]),c_0_18]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO526^1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.17 % Computer : n015.cluster.edu
% 0.07/0.17 % Model : x86_64 x86_64
% 0.07/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.17 % Memory : 8046.5625MB
% 0.07/0.17 % OS : Linux 6.8.0-71-generic
% 0.07/0.17 % CPULimit : 300
% 0.07/0.18 % WCLimit : 300
% 0.07/0.18 % DateTime : Tue Sep 29 17:16:03 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.22 Running higher-order theorem proving
% 0.07/0.23 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.9wcV6fptuw/E---3.1_3831069.p
% 0.07/0.25 % Version: 3.5.1-ho
% 0.07/0.25 % partial match(1): HSSSSMSSSSSNSSN
% 0.07/0.25 % Preprocessing class: HSSSSLSSSSSNSSN.
% 0.07/0.25 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.07/0.25 % Starting ehoh_best_nonlift_nonlambdatoforall with 1500s (5) cores
% 0.07/0.25 % Starting post_as_ho10 with 300s (1) cores
% 0.07/0.25 % Starting new_bool_9 with 300s (1) cores
% 0.07/0.25 % Starting sh5l with 300s (1) cores
% 0.07/0.25 % post_as_ho10 with pid 3831083 completed with status 0
% 0.07/0.25 % Result found by post_as_ho10
% 0.07/0.25 % partial match(1): HSSSSMSSSSSNSSN
% 0.07/0.25 % Preprocessing class: HSSSSLSSSSSNSSN.
% 0.07/0.25 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.07/0.25 % Starting ehoh_best_nonlift_nonlambdatoforall with 1500s (5) cores
% 0.07/0.25 % Starting post_as_ho10 with 300s (1) cores
% 0.07/0.25 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.07/0.25 % No SInE strategy applied
% 0.07/0.25 % Search class: HGHSF-FFSF00-SSSFFFNN
% 0.07/0.25 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.07/0.25 % Starting SubtermCWHack with 28s (1) cores
% 0.07/0.25 % SubtermCWHack with pid 3831092 completed with status 0
% 0.07/0.25 % Result found by SubtermCWHack
% 0.07/0.25 % partial match(1): HSSSSMSSSSSNSSN
% 0.07/0.25 % Preprocessing class: HSSSSLSSSSSNSSN.
% 0.07/0.25 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.07/0.25 % Starting ehoh_best_nonlift_nonlambdatoforall with 1500s (5) cores
% 0.07/0.25 % Starting post_as_ho10 with 300s (1) cores
% 0.07/0.25 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.07/0.25 % No SInE strategy applied
% 0.07/0.25 % Search class: HGHSF-FFSF00-SSSFFFNN
% 0.07/0.25 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.07/0.25 % Starting SubtermCWHack with 28s (1) cores
% 0.07/0.25 % Preprocessing time : 0.001 s
% 0.07/0.25
% 0.07/0.25 % Proof found!
% 0.07/0.25 % SZS status Theorem
% 0.07/0.25 % SZS output start CNFRefutation
% See solution above
% 0.07/0.25 % Parsed axioms : 8
% 0.07/0.25 % Removed by relevancy pruning/SinE : 0
% 0.07/0.25 % Initial clauses : 11
% 0.07/0.25 % Removed in clause preprocessing : 4
% 0.07/0.25 % Initial clauses in saturation : 7
% 0.07/0.25 % Processed clauses : 15
% 0.07/0.25 % ...of these trivial : 0
% 0.07/0.25 % ...subsumed : 0
% 0.07/0.25 % ...remaining for further processing : 15
% 0.07/0.25 % Other redundant clauses eliminated : 0
% 0.07/0.25 % Clauses deleted for lack of memory : 0
% 0.07/0.25 % Backward-subsumed : 3
% 0.07/0.25 % Backward-rewritten : 3
% 0.07/0.25 % Generated clauses : 13
% 0.07/0.25 % ...of the previous two non-redundant : 9
% 0.07/0.25 % ...aggressively subsumed : 0
% 0.07/0.25 % Contextual simplify-reflections : 1
% 0.07/0.25 % Paramodulations : 9
% 0.07/0.25 % Factorizations : 0
% 0.07/0.25 % NegExts : 0
% 0.07/0.25 % Equation resolutions : 0
% 0.07/0.25 % Disequality decompositions : 0
% 0.07/0.25 % Total rewrite steps : 1
% 0.07/0.25 % ...of those cached : 0
% 0.07/0.25 % Propositional unsat checks : 0
% 0.07/0.25 % Propositional check models : 0
% 0.07/0.25 % Propositional check unsatisfiable : 0
% 0.07/0.25 % Propositional clauses : 0
% 0.07/0.25 % Propositional clauses after purity: 0
% 0.07/0.25 % Propositional unsat core size : 0
% 0.07/0.25 % Propositional preprocessing time : 0.000
% 0.07/0.25 % Propositional encoding time : 0.000
% 0.07/0.25 % Propositional solver time : 0.000
% 0.07/0.25 % Success case prop preproc time : 0.000
% 0.07/0.25 % Success case prop encoding time : 0.000
% 0.07/0.25 % Success case prop solver time : 0.000
% 0.07/0.25 % Current number of processed clauses : 7
% 0.07/0.25 % Positive orientable unit clauses : 4
% 0.07/0.25 % Positive unorientable unit clauses: 0
% 0.07/0.25 % Negative unit clauses : 1
% 0.07/0.25 % Non-unit-clauses : 2
% 0.07/0.25 % Current number of unprocessed clauses: 1
% 0.07/0.25 % ...number of literals in the above : 2
% 0.07/0.25 % Current number of archived formulas : 0
% 0.07/0.25 % Current number of archived clauses : 8
% 0.07/0.25 % Clause-clause subsumption calls (NU) : 1
% 0.07/0.25 % Rec. Clause-clause subsumption calls : 1
% 0.07/0.25 % Non-unit clause-clause subsumptions : 1
% 0.07/0.25 % Unit Clause-clause subsumption calls : 3
% 0.07/0.25 % Rewrite failures with RHS unbound : 0
% 0.07/0.25 % BW rewrite match attempts : 1
% 0.07/0.25 % BW rewrite match successes : 1
% 0.07/0.25 % Condensation attempts : 0
% 0.07/0.25 % Condensation successes : 0
% 0.07/0.25 % Termbank termtop insertions : 535
% 0.07/0.25 % Search garbage collected termcells : 64
% 0.07/0.25
% 0.07/0.25 % -------------------------------------------------
% 0.07/0.25 % User time : 0.005 s
% 0.07/0.25 % System time : 0.002 s
% 0.07/0.25 % Total time : 0.006 s
% 0.07/0.25 % Maximum resident set size: 3628 pages
% 0.07/0.25
% 0.07/0.25 % -------------------------------------------------
% 0.07/0.25 % User time : 0.007 s
% 0.07/0.25 % System time : 0.005 s
% 0.07/0.25 % Total time : 0.012 s
% 0.07/0.25 % Maximum resident set size: 4864 pages
% 0.07/0.25 % E exiting
%------------------------------------------------------------------------------