%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SET684^3 : TPTP v9.3.1. Released v3.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n008.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 08:22:18 AM UTC 2026
% Result : Theorem 0.28s 0.27s
% Output : CNFRefutation 0.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 2
% Syntax : Number of formulae : 17 ( 7 unt; 0 typ; 0 def)
% Number of atoms : 41 ( 2 equ; 0 cnn)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 148 ( 16 ~; 19 |; 10 &; 100 @)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 20 ( 20 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 7 usr; 5 con; 0-4 aty)
% Number of variables : 33 ( 8 ^; 19 !; 6 ?; 33 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_44,type,
rel_composition: ( $i > $i > $o ) > ( $i > $i > $o ) > $i > $i > $o ).
thf(decl_58,type,
epred1_0: $i > $i > $o ).
thf(decl_59,type,
epred2_0: $i > $i > $o ).
thf(decl_60,type,
esk1_0: $i ).
thf(decl_61,type,
esk2_0: $i ).
thf(decl_62,type,
esk3_0: $i ).
thf(decl_63,type,
esk4_0: $i ).
thf(thm,conjecture,
! [X36: $i > $i > $o,X28: $i > $i > $o,X1: $i,X31: $i] :
( ( rel_composition @ X36 @ X28 @ X1 @ X31 )
<=> ? [X3: $i] :
( ( X36 @ X1 @ X3 )
& ( X28 @ X3 @ X31 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.AZFPUjcLnx/E---3.1_3168997.p',thm) ).
thf(rel_composition,axiom,
( rel_composition
= ( ^ [X26: $i > $i > $o,X27: $i > $i > $o,X1: $i,X31: $i] :
? [X3: $i] :
( ( X26 @ X1 @ X3 )
& ( X27 @ X3 @ X31 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.AZFPUjcLnx/E---3.1_3168997.p',rel_composition) ).
thf(c_0_2,negated_conjecture,
~ ! [X36: $i > $i > $o,X28: $i > $i > $o,X1: $i,X31: $i] :
( ( rel_composition @ X36 @ X28 @ X1 @ X31 )
<=> ? [X3: $i] :
( ( X36 @ X1 @ X3 )
& ( X28 @ X3 @ X31 ) ) ),
inference(assume_negation,[status(cth)],[thm]) ).
thf(c_0_3,plain,
( rel_composition
= ( ^ [Z0: $i > $i > $o,Z1: $i > $i > $o,Z2: $i,Z3: $i] :
? [X3: $i] :
( ( Z0 @ Z2 @ X3 )
& ( Z1 @ X3 @ Z3 ) ) ) ),
inference(fof_simplification,[status(thm)],[rel_composition]) ).
thf(c_0_4,negated_conjecture,
~ ! [X36: $i > $i > $o,X28: $i > $i > $o,X1: $i,X31: $i] :
( ? [X42: $i] :
( ( X36 @ X1 @ X42 )
& ( X28 @ X42 @ X31 ) )
<=> ? [X3: $i] :
( ( X36 @ X1 @ X3 )
& ( X28 @ X3 @ X31 ) ) ),
inference(apply_def,[status(thm)],[c_0_2,c_0_3]) ).
thf(c_0_5,negated_conjecture,
! [X47: $i,X48: $i] :
( ( ~ ( epred1_0 @ esk1_0 @ X47 )
| ~ ( epred2_0 @ X47 @ esk2_0 )
| ~ ( epred1_0 @ esk1_0 @ X48 )
| ~ ( epred2_0 @ X48 @ esk2_0 ) )
& ( ( epred1_0 @ esk1_0 @ esk4_0 )
| ( epred1_0 @ esk1_0 @ esk3_0 ) )
& ( ( epred2_0 @ esk4_0 @ esk2_0 )
| ( epred1_0 @ esk1_0 @ esk3_0 ) )
& ( ( epred1_0 @ esk1_0 @ esk4_0 )
| ( epred2_0 @ esk3_0 @ esk2_0 ) )
& ( ( epred2_0 @ esk4_0 @ esk2_0 )
| ( epred2_0 @ esk3_0 @ esk2_0 ) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])])])])]) ).
thf(c_0_6,negated_conjecture,
! [X1: $i,X3: $i] :
( ~ ( epred1_0 @ esk1_0 @ X1 )
| ~ ( epred2_0 @ X1 @ esk2_0 )
| ~ ( epred1_0 @ esk1_0 @ X3 )
| ~ ( epred2_0 @ X3 @ esk2_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
thf(c_0_7,negated_conjecture,
( ( epred2_0 @ esk4_0 @ esk2_0 )
| ( epred2_0 @ esk3_0 @ esk2_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
thf(c_0_8,negated_conjecture,
( ( epred1_0 @ esk1_0 @ esk4_0 )
| ( epred2_0 @ esk3_0 @ esk2_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
thf(c_0_9,negated_conjecture,
( ( epred2_0 @ esk4_0 @ esk2_0 )
| ( epred1_0 @ esk1_0 @ esk3_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
thf(c_0_10,negated_conjecture,
( ( epred1_0 @ esk1_0 @ esk4_0 )
| ( epred1_0 @ esk1_0 @ esk3_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
thf(c_0_11,negated_conjecture,
! [X1: $i] :
( ( epred2_0 @ esk3_0 @ esk2_0 )
| ~ ( epred2_0 @ X1 @ esk2_0 )
| ~ ( epred1_0 @ esk1_0 @ X1 ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_6,c_0_7]),c_0_8]) ).
thf(c_0_12,negated_conjecture,
! [X1: $i] :
( ( epred1_0 @ esk1_0 @ esk3_0 )
| ~ ( epred2_0 @ X1 @ esk2_0 )
| ~ ( epred1_0 @ esk1_0 @ X1 ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_6,c_0_9]),c_0_10]) ).
thf(c_0_13,negated_conjecture,
epred2_0 @ esk3_0 @ esk2_0,
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_7]),c_0_8]) ).
thf(c_0_14,negated_conjecture,
epred1_0 @ esk1_0 @ esk3_0,
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_9]),c_0_10]) ).
thf(c_0_15,negated_conjecture,
! [X1: $i] :
( ~ ( epred2_0 @ X1 @ esk2_0 )
| ~ ( epred1_0 @ esk1_0 @ X1 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_6,c_0_13]),c_0_14])]) ).
thf(c_0_16,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_13]),c_0_14])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET684^3 : TPTP v9.3.1. Released v3.6.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.18 % Computer : n008.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Tue Sep 29 13:41:24 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.23 Running higher-order theorem proving
% 0.08/0.24 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/tmp/tmp.AZFPUjcLnx/E---3.1_3168997.p
% 0.28/0.27 % Version: 3.5.1-ho
% 0.28/0.27 % Preprocessing class: HSMSSMSSMLSNHSA.
% 0.28/0.27 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.28/0.27 % Starting new_ho_10 with 1500s (5) cores
% 0.28/0.27 % Starting sh5l with 300s (1) cores
% 0.28/0.27 % Starting new_bool_1 with 300s (1) cores
% 0.28/0.27 % Starting new_bool_2 with 300s (1) cores
% 0.28/0.27 % new_bool_2 with pid 3169037 completed with status 0
% 0.28/0.27 % Result found by new_bool_2
% 0.28/0.27 % Preprocessing class: HSMSSMSSMLSNHSA.
% 0.28/0.27 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.28/0.27 % Starting new_ho_10 with 1500s (5) cores
% 0.28/0.27 % Starting sh5l with 300s (1) cores
% 0.28/0.27 % Starting new_bool_1 with 300s (1) cores
% 0.28/0.27 % Starting new_bool_2 with 300s (1) cores
% 0.28/0.27 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.28/0.27 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.28/0.27 % Search class: HGHNF-FFSS00-SHSSMFNN
% 0.28/0.27 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.28/0.27 % Starting SubtermCWHack with 28s (1) cores
% 0.28/0.27 % SubtermCWHack with pid 3169038 completed with status 0
% 0.28/0.27 % Result found by SubtermCWHack
% 0.28/0.27 % Preprocessing class: HSMSSMSSMLSNHSA.
% 0.28/0.27 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.28/0.27 % Starting new_ho_10 with 1500s (5) cores
% 0.28/0.27 % Starting sh5l with 300s (1) cores
% 0.28/0.27 % Starting new_bool_1 with 300s (1) cores
% 0.28/0.27 % Starting new_bool_2 with 300s (1) cores
% 0.28/0.27 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.28/0.27 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.28/0.27 % Search class: HGHNF-FFSS00-SHSSMFNN
% 0.28/0.27 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.28/0.27 % Starting SubtermCWHack with 28s (1) cores
% 0.28/0.27 % Preprocessing time : 0.001 s
% 0.28/0.27
% 0.28/0.27 % Proof found!
% 0.28/0.27 % SZS status Theorem
% 0.28/0.27 % SZS output start CNFRefutation
% See solution above
% 0.28/0.27 % Parsed axioms : 71
% 0.28/0.27 % Removed by relevancy pruning/SinE : 69
% 0.28/0.27 % Initial clauses : 5
% 0.28/0.27 % Removed in clause preprocessing : 0
% 0.28/0.27 % Initial clauses in saturation : 5
% 0.28/0.27 % Processed clauses : 10
% 0.28/0.27 % ...of these trivial : 0
% 0.28/0.27 % ...subsumed : 0
% 0.28/0.27 % ...remaining for further processing : 10
% 0.28/0.27 % Other redundant clauses eliminated : 0
% 0.28/0.27 % Clauses deleted for lack of memory : 0
% 0.28/0.27 % Backward-subsumed : 2
% 0.28/0.27 % Backward-rewritten : 5
% 0.28/0.27 % Generated clauses : 10
% 0.28/0.27 % ...of the previous two non-redundant : 8
% 0.28/0.27 % ...aggressively subsumed : 0
% 0.28/0.27 % Contextual simplify-reflections : 4
% 0.28/0.27 % Paramodulations : 10
% 0.28/0.27 % Factorizations : 0
% 0.28/0.27 % NegExts : 0
% 0.28/0.27 % Equation resolutions : 0
% 0.28/0.27 % Disequality decompositions : 0
% 0.28/0.27 % Total rewrite steps : 8
% 0.28/0.27 % ...of those cached : 6
% 0.28/0.27 % Propositional unsat checks : 0
% 0.28/0.27 % Propositional check models : 0
% 0.28/0.27 % Propositional check unsatisfiable : 0
% 0.28/0.27 % Propositional clauses : 0
% 0.28/0.27 % Propositional clauses after purity: 0
% 0.28/0.27 % Propositional unsat core size : 0
% 0.28/0.27 % Propositional preprocessing time : 0.000
% 0.28/0.27 % Propositional encoding time : 0.000
% 0.28/0.27 % Propositional solver time : 0.000
% 0.28/0.27 % Success case prop preproc time : 0.000
% 0.28/0.27 % Success case prop encoding time : 0.000
% 0.28/0.27 % Success case prop solver time : 0.000
% 0.28/0.27 % Current number of processed clauses : 3
% 0.28/0.27 % Positive orientable unit clauses : 2
% 0.28/0.27 % Positive unorientable unit clauses: 0
% 0.28/0.27 % Negative unit clauses : 0
% 0.28/0.27 % Non-unit-clauses : 1
% 0.28/0.27 % Current number of unprocessed clauses: 1
% 0.28/0.27 % ...number of literals in the above : 4
% 0.28/0.27 % Current number of archived formulas : 0
% 0.28/0.27 % Current number of archived clauses : 7
% 0.28/0.27 % Clause-clause subsumption calls (NU) : 7
% 0.28/0.27 % Rec. Clause-clause subsumption calls : 7
% 0.28/0.27 % Non-unit clause-clause subsumptions : 5
% 0.28/0.27 % Unit Clause-clause subsumption calls : 2
% 0.28/0.27 % Rewrite failures with RHS unbound : 0
% 0.28/0.27 % BW rewrite match attempts : 2
% 0.28/0.27 % BW rewrite match successes : 2
% 0.28/0.27 % Condensation attempts : 0
% 0.28/0.27 % Condensation successes : 0
% 0.28/0.27 % Termbank termtop insertions : 986
% 0.28/0.27 % Search garbage collected termcells : 446
% 0.28/0.27
% 0.28/0.27 % -------------------------------------------------
% 0.28/0.27 % User time : 0.001 s
% 0.28/0.27 % System time : 0.004 s
% 0.28/0.27 % Total time : 0.005 s
% 0.28/0.27 % Maximum resident set size: 3708 pages
% 0.28/0.27
% 0.28/0.27 % -------------------------------------------------
% 0.28/0.27 % User time : 0.003 s
% 0.28/0.27 % System time : 0.010 s
% 0.28/0.27 % Total time : 0.013 s
% 0.28/0.27 % Maximum resident set size: 4608 pages
% 0.28/0.27 % E exiting
%------------------------------------------------------------------------------