%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SYO245^5 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n007.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 08:42:38 AM UTC 2026
% Result : Theorem 0.07s 0.24s
% Output : CNFRefutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 1
% Syntax : Number of formulae : 12 ( 6 unt; 0 typ; 0 def)
% Number of atoms : 29 ( 19 equ; 0 cnn)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 107 ( 20 ~; 5 |; 8 &; 65 @)
% ( 1 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 35 ( 35 >; 0 *; 0 +; 0 <<)
% Number of symbols : 5 ( 2 usr; 2 con; 0-2 aty)
% Number of variables : 40 ( 7 ^; 22 !; 11 ?; 40 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_23,type,
esk1_0: ( $i > $o ) > $i ).
thf(decl_24,type,
esk1_2: $i > $i > $o ).
thf(cTHM193A,conjecture,
( ! [X1: ( $i > $o ) > $i] :
( ? [X2: $i > $o] :
( ~ ( X2 @ ( X1 @ X2 ) )
& ( ( X1
@ ^ [X3: $i] :
? [X4: $i > $o] :
( ~ ( X4 @ ( X1 @ X4 ) )
& ( X3
= ( X1 @ X4 ) ) ) )
= ( X1 @ X2 ) ) )
=> ? [X2: $i > $o] :
( ~ ( X2 @ ( X1 @ X2 ) )
& ( ( X1
@ ^ [X3: $i] :
? [X4: $i > $o] :
( ~ ( X4 @ ( X1 @ X4 ) )
& ( X3
= ( X1 @ X4 ) ) ) )
= ( X1 @ X2 ) ) ) )
=> ~ ? [X1: ( $i > $o ) > $i] :
! [X5: $i > $o,X6: $i > $o] :
( ( ( X1 @ X5 )
= ( X1 @ X6 ) )
=> ( X5 = X6 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.kiAdtKPMfX/E---3.1_3617643.p',cTHM193A) ).
thf(c_0_1,negated_conjecture,
~ ( ! [X1: ( $i > $o ) > $i] :
( ? [X2: $i > $o] :
( ~ ( X2 @ ( X1 @ X2 ) )
& ( ( X1
@ ^ [X3: $i] :
? [X4: $i > $o] :
( ~ ( X4 @ ( X1 @ X4 ) )
& ( X3
= ( X1 @ X4 ) ) ) )
= ( X1 @ X2 ) ) )
=> ? [X2: $i > $o] :
( ~ ( X2 @ ( X1 @ X2 ) )
& ( ( X1
@ ^ [X3: $i] :
? [X4: $i > $o] :
( ~ ( X4 @ ( X1 @ X4 ) )
& ( X3
= ( X1 @ X4 ) ) ) )
= ( X1 @ X2 ) ) ) )
=> ~ ? [X1: ( $i > $o ) > $i] :
! [X5: $i > $o,X6: $i > $o] :
( ( ( X1 @ X5 )
= ( X1 @ X6 ) )
=> ( X5 = X6 ) ) ),
inference(assume_negation,[status(cth)],[cTHM193A]) ).
thf(c_0_2,negated_conjecture,
~ ( ! [X1: ( $i > $o ) > $i] : $true
=> ~ ? [X1: ( $i > $o ) > $i] :
! [X5: $i > $o,X6: $i > $o] :
( ( ( X1 @ X5 )
= ( X1 @ X6 ) )
=> ( X5 = X6 ) ) ),
inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[c_0_1])]) ).
thf(c_0_3,negated_conjecture,
! [X14: $i > $o,X15: $i > $o] :
( ( ( esk1_0 @ X14 )
!= ( esk1_0 @ X15 ) )
| ( X14 = X15 ) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[c_0_2])])])])]) ).
thf(c_0_4,negated_conjecture,
! [X2: $i > $o,X4: $i > $o] :
( ( X2 = X4 )
| ( ( esk1_0 @ X2 )
!= ( esk1_0 @ X4 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
thf(c_0_5,negated_conjecture,
! [X2: $i > $o] :
( ( esk1_2 @ ( esk1_0 @ X2 ) )
= X2 ),
inference(recognize_injectivity,[status(thm)],[c_0_4]) ).
thf(c_0_6,negated_conjecture,
! [X2: $i > $o,X17: $i] :
( ( esk1_2 @ ( esk1_0 @ X2 ) @ X17 )
<=> ( X2 @ X17 ) ),
inference(arg_cong,[status(thm)],[c_0_5]) ).
thf(c_0_7,negated_conjecture,
! [X2: $i > $o,X3: $i] :
( ( esk1_2 @ ( esk1_0 @ X2 ) @ X3 )
| ~ ( X2 @ X3 ) ),
inference(dynamic_cnf,[status(thm)],[c_0_6]) ).
thf(c_0_8,negated_conjecture,
! [X2: $i > $o,X3: $i] :
( ( esk1_2
@ ( esk1_0
@ ^ [Z0: $i] :
~ ( X2 @ Z0 ) )
@ X3 )
| ( X2 @ X3 ) ),
inference(primitive_enumeration,[status(thm)],[inference(cn,[status(thm)],[]),c_0_7]) ).
thf(c_0_9,negated_conjecture,
! [X2: $i > $o,X3: $i] :
( ( X2 @ X3 )
| ~ ( esk1_2 @ ( esk1_0 @ X2 ) @ X3 ) ),
inference(dynamic_cnf,[status(thm)],[c_0_6]) ).
thf(c_0_10,negated_conjecture,
( esk1_2
@ ( esk1_0
@ ^ [Z0: $i] :
~ ( esk1_2 @ Z0 @ Z0 ) )
@ ( esk1_0
@ ^ [Z0: $i] :
~ ( esk1_2 @ Z0 @ Z0 ) ) ),
inference(ef,[status(thm)],[c_0_8]) ).
thf(c_0_11,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_10])]),c_0_10])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYO245^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.16 % Computer : n007.cluster.edu
% 0.07/0.16 % Model : x86_64 x86_64
% 0.07/0.16 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.16 % Memory : 8046.5625MB
% 0.07/0.16 % OS : Linux 6.8.0-71-generic
% 0.07/0.17 % CPULimit : 300
% 0.07/0.17 % WCLimit : 300
% 0.07/0.17 % DateTime : Tue Sep 29 16:38:56 UTC 2026
% 0.07/0.17 % CPUTime :
% 0.07/0.17 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.21 Running higher-order theorem proving
% 0.07/0.22 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.kiAdtKPMfX/E---3.1_3617643.p
% 0.07/0.24 % Version: 3.5.1-ho
% 0.07/0.24 % Preprocessing class: HSSSSMSSSSMNHHA.
% 0.07/0.24 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.07/0.24 % Starting post_as_ho5 with 1500s (5) cores
% 0.07/0.24 % Starting sh2lt with 300s (1) cores
% 0.07/0.24 % Starting ehoh_best8_lambda with 300s (1) cores
% 0.07/0.24 % Starting post_as_ho10 with 300s (1) cores
% 0.07/0.24 % post_as_ho5 with pid 3617677 completed with status 0
% 0.07/0.24 % Result found by post_as_ho5
% 0.07/0.24 % Preprocessing class: HSSSSMSSSSMNHHA.
% 0.07/0.24 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.07/0.24 % Starting post_as_ho5 with 1500s (5) cores
% 0.07/0.24 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = GSinE(CountFormulas,,true,1.0,0,2,20000,1.0,true))
% 0.07/0.24 % SinE strategy is GSinE(CountFormulas,,true,1.0,0,2,20000,1.0,true)
% 0.07/0.24 % Search class: HHUPF-FFSF00-SHHFFFBN
% 0.07/0.24 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.07/0.24 % Starting SubtermCWHack with 136s (1) cores
% 0.07/0.24 % Starting post_as_ho5 with 151s (1) cores
% 0.07/0.24 % Starting lpo8_s with 136s (1) cores
% 0.07/0.24 % Starting sh5l with 136s (1) cores
% 0.07/0.24 % Starting sh2lt with 136s (1) cores
% 0.07/0.24 % lpo8_s with pid 3617684 completed with status 10
% 0.07/0.24 % Starting new_bool_1 with 136s (1) cores
% 0.07/0.24 % SubtermCWHack with pid 3617682 completed with status 10
% 0.07/0.24 % post_as_ho5 with pid 3617683 completed with status 10
% 0.07/0.24 % Starting post_as_ho10 with 669s (1) cores
% 0.07/0.24 % sh5l with pid 3617685 completed with status 10
% 0.07/0.24 % sh2lt with pid 3617686 completed with status 10
% 0.07/0.24 % post_as_ho10 with pid 3617693 completed with status 0
% 0.07/0.24 % Result found by post_as_ho10
% 0.07/0.24 % Preprocessing class: HSSSSMSSSSMNHHA.
% 0.07/0.24 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.07/0.24 % Starting post_as_ho5 with 1500s (5) cores
% 0.07/0.24 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = GSinE(CountFormulas,,true,1.0,0,2,20000,1.0,true))
% 0.07/0.24 % SinE strategy is GSinE(CountFormulas,,true,1.0,0,2,20000,1.0,true)
% 0.07/0.24 % Search class: HHUPF-FFSF00-SHHFFFBN
% 0.07/0.24 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.07/0.24 % Starting SubtermCWHack with 136s (1) cores
% 0.07/0.24 % Starting post_as_ho5 with 151s (1) cores
% 0.07/0.24 % Starting lpo8_s with 136s (1) cores
% 0.07/0.24 % Starting sh5l with 136s (1) cores
% 0.07/0.24 % Starting sh2lt with 136s (1) cores
% 0.07/0.24 % lpo8_s with pid 3617684 completed with status 10
% 0.07/0.24 % Starting new_bool_1 with 136s (1) cores
% 0.07/0.24 % SubtermCWHack with pid 3617682 completed with status 10
% 0.07/0.24 % post_as_ho5 with pid 3617683 completed with status 10
% 0.07/0.24 % Starting post_as_ho10 with 669s (1) cores
% 0.07/0.24 % Preprocessing time : 0.001 s
% 0.07/0.24 % Presaturation interreduction done
% 0.07/0.24
% 0.07/0.24 % Proof found!
% 0.07/0.24 % SZS status Theorem
% 0.07/0.24 % SZS output start CNFRefutation
% See solution above
% 0.07/0.24 % Parsed axioms : 1
% 0.07/0.24 % Removed by relevancy pruning/SinE : 0
% 0.07/0.24 % Initial clauses : 1
% 0.07/0.24 % Removed in clause preprocessing : 0
% 0.07/0.24 % Initial clauses in saturation : 1
% 0.07/0.24 % Processed clauses : 39
% 0.07/0.24 % ...of these trivial : 1
% 0.07/0.24 % ...subsumed : 11
% 0.07/0.24 % ...remaining for further processing : 27
% 0.07/0.24 % Other redundant clauses eliminated : 3
% 0.07/0.24 % Clauses deleted for lack of memory : 0
% 0.07/0.24 % Backward-subsumed : 0
% 0.07/0.24 % Backward-rewritten : 0
% 0.07/0.24 % Generated clauses : 81
% 0.07/0.24 % ...of the previous two non-redundant : 51
% 0.07/0.24 % ...aggressively subsumed : 0
% 0.07/0.24 % Contextual simplify-reflections : 0
% 0.07/0.24 % Paramodulations : 30
% 0.07/0.24 % Factorizations : 2
% 0.07/0.24 % NegExts : 0
% 0.07/0.24 % Equation resolutions : 12
% 0.07/0.24 % Disequality decompositions : 0
% 0.07/0.24 % Total rewrite steps : 8
% 0.07/0.24 % ...of those cached : 4
% 0.07/0.24 % Propositional unsat checks : 0
% 0.07/0.24 % Propositional check models : 0
% 0.07/0.24 % Propositional check unsatisfiable : 0
% 0.07/0.24 % Propositional clauses : 0
% 0.07/0.24 % Propositional clauses after purity: 0
% 0.07/0.24 % Propositional unsat core size : 0
% 0.07/0.24 % Propositional preprocessing time : 0.000
% 0.07/0.24 % Propositional encoding time : 0.000
% 0.07/0.24 % Propositional solver time : 0.000
% 0.07/0.24 % Success case prop preproc time : 0.000
% 0.07/0.24 % Success case prop encoding time : 0.000
% 0.07/0.24 % Success case prop solver time : 0.000
% 0.07/0.24 % Current number of processed clauses : 24
% 0.07/0.24 % Positive orientable unit clauses : 7
% 0.07/0.24 % Positive unorientable unit clauses: 0
% 0.07/0.24 % Negative unit clauses : 2
% 0.07/0.24 % Non-unit-clauses : 15
% 0.07/0.24 % Current number of unprocessed clauses: 13
% 0.07/0.24 % ...number of literals in the above : 24
% 0.07/0.24 % Current number of archived formulas : 0
% 0.07/0.24 % Current number of archived clauses : 3
% 0.07/0.24 % Clause-clause subsumption calls (NU) : 126
% 0.07/0.24 % Rec. Clause-clause subsumption calls : 110
% 0.07/0.24 % Non-unit clause-clause subsumptions : 8
% 0.07/0.24 % Unit Clause-clause subsumption calls : 12
% 0.07/0.24 % Rewrite failures with RHS unbound : 0
% 0.07/0.24 % BW rewrite match attempts : 22
% 0.07/0.24 % BW rewrite match successes : 2
% 0.07/0.24 % Condensation attempts : 0
% 0.07/0.24 % Condensation successes : 0
% 0.07/0.24 % Termbank termtop insertions : 3941
% 0.07/0.24 % Search garbage collected termcells : 86
% 0.07/0.24
% 0.07/0.24 % -------------------------------------------------
% 0.07/0.24 % User time : 0.007 s
% 0.07/0.24 % System time : 0.010 s
% 0.07/0.24 % Total time : 0.017 s
% 0.07/0.24 % Maximum resident set size: 3632 pages
% 0.07/0.24
% 0.07/0.24 % -------------------------------------------------
% 0.07/0.24 % User time : 0.009 s
% 0.07/0.24 % System time : 0.018 s
% 0.07/0.24 % Total time : 0.027 s
% 0.07/0.24 % Maximum resident set size: 4608 pages
% 0.07/0.24 % E exiting
%------------------------------------------------------------------------------