%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU460^1 : 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 : n006.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 08:23:52 AM UTC 2026
% Result : Theorem 0.07s 0.26s
% Output : CNFRefutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 4
% Syntax : Number of formulae : 18 ( 12 unt; 0 typ; 0 def)
% Number of atoms : 35 ( 7 equ; 0 cnn)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 117 ( 10 ~; 8 |; 3 &; 84 @)
% ( 0 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 43 ( 43 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 7 usr; 3 con; 0-3 aty)
% Number of variables : 41 ( 13 ^; 28 !; 0 ?; 41 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_23,type,
subrel: ( $i > $i > $o ) > ( $i > $i > $o ) > $o ).
thf(decl_27,type,
mono: ( ( $i > $i > $o ) > $i > $i > $o ) > $o ).
thf(decl_34,type,
sc: ( $i > $i > $o ) > $i > $i > $o ).
thf(decl_52,type,
epred1_0: $i > $i > $o ).
thf(decl_53,type,
epred2_0: $i > $i > $o ).
thf(decl_54,type,
esk1_0: $i ).
thf(decl_55,type,
esk2_0: $i ).
thf(monotonic,axiom,
( mono
= ( ^ [X5: ( $i > $i > $o ) > $i > $i > $o] :
! [X1: $i > $i > $o,X2: $i > $i > $o] :
( ( subrel @ X1 @ X2 )
=> ( subrel @ ( X5 @ X1 ) @ ( X5 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.SmQVQNe8PZ/E---3.1_731043.p',monotonic) ).
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/tmp/tmp.SmQVQNe8PZ/E---3.1_731043.p',subrel) ).
thf(symmetric_closure_op_is_monotonic,conjecture,
mono @ sc,
file('/export/starexec/sandbox/tmp/tmp.SmQVQNe8PZ/E---3.1_731043.p',symmetric_closure_op_is_monotonic) ).
thf(symmetric_closure,axiom,
( sc
= ( ^ [X1: $i > $i > $o,X3: $i,X4: $i] :
( ( X1 @ X4 @ X3 )
| ( X1 @ X3 @ X4 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.SmQVQNe8PZ/E---3.1_731043.p',symmetric_closure) ).
thf(c_0_4,plain,
( mono
= ( ^ [Z0: ( $i > $i > $o ) > $i > $i > $o] :
! [X1: $i > $i > $o,X2: $i > $i > $o] :
( ! [X9: $i,X10: $i] :
( ( X1 @ X9 @ X10 )
=> ( X2 @ X9 @ X10 ) )
=> ! [X11: $i,X12: $i] :
( ( Z0 @ X1 @ X11 @ X12 )
=> ( Z0 @ X2 @ X11 @ X12 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[monotonic]) ).
thf(c_0_5,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_6,negated_conjecture,
~ ( mono @ sc ),
inference(assume_negation,[status(cth)],[symmetric_closure_op_is_monotonic]) ).
thf(c_0_7,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_8,plain,
( mono
= ( ^ [Z0: ( $i > $i > $o ) > $i > $i > $o] :
! [X1: $i > $i > $o,X2: $i > $i > $o] :
( ! [X9: $i,X10: $i] :
( ( X1 @ X9 @ X10 )
=> ( X2 @ X9 @ X10 ) )
=> ! [X11: $i,X12: $i] :
( ( Z0 @ X1 @ X11 @ X12 )
=> ( Z0 @ X2 @ X11 @ X12 ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_4,c_0_5]) ).
thf(c_0_9,negated_conjecture,
~ ! [X81: $i > $i > $o,X82: $i > $i > $o] :
( ! [X83: $i,X84: $i] :
( ( X81 @ X83 @ X84 )
=> ( X82 @ X83 @ X84 ) )
=> ! [X85: $i,X86: $i] :
( ( ( X81 @ X86 @ X85 )
| ( X81 @ X85 @ X86 ) )
=> ( ( X82 @ X86 @ X85 )
| ( X82 @ X85 @ X86 ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_6,c_0_7]),c_0_8]) ).
thf(c_0_10,negated_conjecture,
! [X89: $i,X90: $i] :
( ( ~ ( epred1_0 @ X89 @ X90 )
| ( epred2_0 @ X89 @ X90 ) )
& ( ( epred1_0 @ esk2_0 @ esk1_0 )
| ( epred1_0 @ esk1_0 @ esk2_0 ) )
& ~ ( epred2_0 @ esk2_0 @ esk1_0 )
& ~ ( epred2_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_9])])])])]) ).
thf(c_0_11,negated_conjecture,
~ ( epred2_0 @ esk2_0 @ esk1_0 ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
thf(c_0_12,negated_conjecture,
! [X3: $i,X4: $i] :
( ( epred2_0 @ X3 @ X4 )
| ~ ( epred1_0 @ X3 @ X4 ) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
thf(c_0_13,negated_conjecture,
~ ( epred2_0 @ esk1_0 @ esk2_0 ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
thf(c_0_14,negated_conjecture,
( ( epred1_0 @ esk2_0 @ esk1_0 )
| ( epred1_0 @ esk1_0 @ esk2_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
thf(c_0_15,negated_conjecture,
~ ( epred1_0 @ esk2_0 @ esk1_0 ),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
thf(c_0_16,negated_conjecture,
~ ( epred1_0 @ esk1_0 @ esk2_0 ),
inference(spm,[status(thm)],[c_0_13,c_0_12]) ).
thf(c_0_17,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(sr,[status(thm)],[c_0_14,c_0_15]),c_0_16]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU460^1 : TPTP v9.3.1. Released v3.6.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.19 % Computer : n006.cluster.edu
% 0.07/0.19 % Model : x86_64 x86_64
% 0.07/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.19 % Memory : 8046.5625MB
% 0.07/0.19 % OS : Linux 6.8.0-71-generic
% 0.07/0.19 % CPULimit : 300
% 0.07/0.19 % WCLimit : 300
% 0.07/0.19 % DateTime : Tue Sep 29 13:41:39 UTC 2026
% 0.07/0.19 % CPUTime :
% 0.07/0.19 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.23 Running higher-order theorem proving
% 0.07/0.24 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.SmQVQNe8PZ/E---3.1_731043.p
% 0.07/0.26 % Version: 3.5.1-ho
% 0.07/0.26 % Preprocessing class: HSSSSMSSMLSNHHN.
% 0.07/0.26 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.07/0.26 % Starting new_ho_10 with 1500s (5) cores
% 0.07/0.26 % Starting pre_casc_5 with 300s (1) cores
% 0.07/0.26 % Starting post_as_ho11 with 300s (1) cores
% 0.07/0.26 % Starting ho_unfolding_1 with 300s (1) cores
% 0.07/0.26 % pre_casc_5 with pid 731074 completed with status 0
% 0.07/0.26 % Result found by pre_casc_5
% 0.07/0.26 % Preprocessing class: HSSSSMSSMLSNHHN.
% 0.07/0.26 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.07/0.26 % Starting new_ho_10 with 1500s (5) cores
% 0.07/0.26 % Starting pre_casc_5 with 300s (1) cores
% 0.07/0.26 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,3,,5,20000,1.0,true))
% 0.07/0.26 % SinE strategy is GSinE(CountFormulas,hypos,3,,5,20000,1.0,true)
% 0.07/0.26 % Search class: HGUNF-FFSF00-SHHSMFNN
% 0.07/0.26 % partial match(1): HGUNF-FFSF00-SHSSMFNN
% 0.07/0.26 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.07/0.26 % Starting SubtermCWHack with 28s (1) cores
% 0.07/0.26 % SubtermCWHack with pid 731078 completed with status 0
% 0.07/0.26 % Result found by SubtermCWHack
% 0.07/0.26 % Preprocessing class: HSSSSMSSMLSNHHN.
% 0.07/0.26 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.07/0.26 % Starting new_ho_10 with 1500s (5) cores
% 0.07/0.26 % Starting pre_casc_5 with 300s (1) cores
% 0.07/0.26 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,3,,5,20000,1.0,true))
% 0.07/0.26 % SinE strategy is GSinE(CountFormulas,hypos,3,,5,20000,1.0,true)
% 0.07/0.26 % Search class: HGUNF-FFSF00-SHHSMFNN
% 0.07/0.26 % partial match(1): HGUNF-FFSF00-SHSSMFNN
% 0.07/0.26 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.07/0.26 % Starting SubtermCWHack with 28s (1) cores
% 0.07/0.26 % Preprocessing time : 0.001 s
% 0.07/0.26
% 0.07/0.26 % Proof found!
% 0.07/0.26 % SZS status Theorem
% 0.07/0.26 % SZS output start CNFRefutation
% See solution above
% 0.07/0.26 % Parsed axioms : 59
% 0.07/0.26 % Removed by relevancy pruning/SinE : 45
% 0.07/0.26 % Initial clauses : 4
% 0.07/0.26 % Removed in clause preprocessing : 0
% 0.07/0.26 % Initial clauses in saturation : 4
% 0.07/0.26 % Processed clauses : 7
% 0.07/0.26 % ...of these trivial : 0
% 0.07/0.26 % ...subsumed : 0
% 0.07/0.26 % ...remaining for further processing : 6
% 0.07/0.26 % Other redundant clauses eliminated : 0
% 0.07/0.26 % Clauses deleted for lack of memory : 0
% 0.07/0.26 % Backward-subsumed : 0
% 0.07/0.26 % Backward-rewritten : 0
% 0.07/0.26 % Generated clauses : 3
% 0.07/0.26 % ...of the previous two non-redundant : 3
% 0.07/0.26 % ...aggressively subsumed : 0
% 0.07/0.26 % Contextual simplify-reflections : 0
% 0.07/0.26 % Paramodulations : 2
% 0.07/0.26 % Factorizations : 0
% 0.07/0.26 % NegExts : 0
% 0.07/0.26 % Equation resolutions : 0
% 0.07/0.26 % Disequality decompositions : 0
% 0.07/0.26 % Total rewrite steps : 0
% 0.07/0.26 % ...of those cached : 0
% 0.07/0.26 % Propositional unsat checks : 0
% 0.07/0.26 % Propositional check models : 0
% 0.07/0.26 % Propositional check unsatisfiable : 0
% 0.07/0.26 % Propositional clauses : 0
% 0.07/0.26 % Propositional clauses after purity: 0
% 0.07/0.26 % Propositional unsat core size : 0
% 0.07/0.26 % Propositional preprocessing time : 0.000
% 0.07/0.26 % Propositional encoding time : 0.000
% 0.07/0.26 % Propositional solver time : 0.000
% 0.07/0.26 % Success case prop preproc time : 0.000
% 0.07/0.26 % Success case prop encoding time : 0.000
% 0.07/0.26 % Success case prop solver time : 0.000
% 0.07/0.26 % Current number of processed clauses : 5
% 0.07/0.26 % Positive orientable unit clauses : 0
% 0.07/0.26 % Positive unorientable unit clauses: 0
% 0.07/0.26 % Negative unit clauses : 4
% 0.07/0.26 % Non-unit-clauses : 1
% 0.07/0.26 % Current number of unprocessed clauses: 0
% 0.07/0.26 % ...number of literals in the above : 0
% 0.07/0.26 % Current number of archived formulas : 0
% 0.07/0.26 % Current number of archived clauses : 1
% 0.07/0.26 % Clause-clause subsumption calls (NU) : 0
% 0.07/0.26 % Rec. Clause-clause subsumption calls : 0
% 0.07/0.26 % Non-unit clause-clause subsumptions : 0
% 0.07/0.26 % Unit Clause-clause subsumption calls : 2
% 0.07/0.26 % Rewrite failures with RHS unbound : 0
% 0.07/0.26 % BW rewrite match attempts : 0
% 0.07/0.26 % BW rewrite match successes : 0
% 0.07/0.26 % Condensation attempts : 0
% 0.07/0.26 % Condensation successes : 0
% 0.07/0.26 % Termbank termtop insertions : 1690
% 0.07/0.26 % Search garbage collected termcells : 584
% 0.07/0.26
% 0.07/0.26 % -------------------------------------------------
% 0.07/0.26 % User time : 0.005 s
% 0.07/0.26 % System time : 0.002 s
% 0.07/0.26 % Total time : 0.006 s
% 0.07/0.26 % Maximum resident set size: 3940 pages
% 0.07/0.26
% 0.07/0.26 % -------------------------------------------------
% 0.07/0.26 % User time : 0.006 s
% 0.07/0.26 % System time : 0.007 s
% 0.07/0.26 % Total time : 0.013 s
% 0.07/0.26 % Maximum resident set size: 4864 pages
% 0.07/0.26 % E exiting
%------------------------------------------------------------------------------