%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SET724^4 : TPTP v9.3.1. Released v3.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/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 08:22:18 AM UTC 2026
% Result : Theorem 0.09s 0.26s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 3
% Syntax : Number of formulae : 17 ( 13 unt; 0 typ; 0 def)
% Number of atoms : 29 ( 24 equ; 0 cnn)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 67 ( 5 ~; 0 |; 5 &; 54 @)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 19 ( 19 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 7 usr; 2 con; 0-3 aty)
% Number of variables : 33 ( 5 ^; 25 !; 3 ?; 33 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_24,type,
fun_composition: ( $i > $i ) > ( $i > $i ) > $i > $i ).
thf(decl_27,type,
fun_surjective: ( $i > $i ) > $o ).
thf(decl_31,type,
esk1_0: $i > $i ).
thf(decl_32,type,
esk2_0: $i > $i ).
thf(decl_33,type,
esk3_0: $i > $i ).
thf(decl_34,type,
esk4_1: $i > $i ).
thf(decl_35,type,
esk4_0: $i ).
thf(thm,conjecture,
! [X1: $i > $i,X5: $i > $i,X8: $i > $i] :
( ( ( ( fun_composition @ X1 @ X5 )
= ( fun_composition @ X1 @ X8 ) )
& ( fun_surjective @ X1 ) )
=> ( X5 = X8 ) ),
file('/export/starexec/sandbox2/tmp/tmp.3xQ37thv4D/E---3.1_727646.p',thm) ).
thf(fun_surjective,axiom,
( fun_surjective
= ( ^ [X1: $i > $i] :
! [X3: $i] :
? [X4: $i] :
( X3
= ( X1 @ X4 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.3xQ37thv4D/E---3.1_727646.p',fun_surjective) ).
thf(fun_composition,axiom,
( fun_composition
= ( ^ [X1: $i > $i,X5: $i > $i,X4: $i] : ( X5 @ ( X1 @ X4 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.3xQ37thv4D/E---3.1_727646.p',fun_composition) ).
thf(c_0_3,negated_conjecture,
~ ! [X1: $i > $i,X5: $i > $i,X8: $i > $i] :
( ( ( ( fun_composition @ X1 @ X5 )
= ( fun_composition @ X1 @ X8 ) )
& ( fun_surjective @ X1 ) )
=> ( X5 = X8 ) ),
inference(assume_negation,[status(cth)],[thm]) ).
thf(c_0_4,plain,
( fun_surjective
= ( ^ [Z0: $i > $i] :
! [X3: $i] :
? [X4: $i] :
( X3
= ( Z0 @ X4 ) ) ) ),
inference(fof_simplification,[status(thm)],[fun_surjective]) ).
thf(c_0_5,negated_conjecture,
~ ! [X1: $i > $i,X5: $i > $i,X8: $i > $i] :
( ( ( ( fun_composition @ X1 @ X5 )
= ( fun_composition @ X1 @ X8 ) )
& ! [X16: $i] :
? [X17: $i] :
( X16
= ( X1 @ X17 ) ) )
=> ( X5 = X8 ) ),
inference(apply_def,[status(thm)],[c_0_3,c_0_4]) ).
thf(c_0_6,plain,
! [X18: $i > $i,X19: $i > $i,X20: $i] :
( ( fun_composition @ X18 @ X19 @ X20 )
= ( X19 @ ( X18 @ X20 ) ) ),
inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[fun_composition])]) ).
thf(c_0_7,negated_conjecture,
! [X27: $i] :
( ( ( fun_composition @ esk1_0 @ esk2_0 )
= ( fun_composition @ esk1_0 @ esk3_0 ) )
& ( X27
= ( esk1_0 @ ( esk4_1 @ X27 ) ) )
& ( esk2_0 != esk3_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_5])])])])]) ).
thf(c_0_8,plain,
! [X21: $i > $i,X22: $i > $i,X23: $i] :
( ( fun_composition @ X21 @ X22 @ X23 )
= ( X22 @ ( X21 @ X23 ) ) ),
inference(variable_rename,[status(thm)],[c_0_6]) ).
thf(c_0_9,negated_conjecture,
( ( fun_composition @ esk1_0 @ esk2_0 )
= ( fun_composition @ esk1_0 @ esk3_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
thf(c_0_10,plain,
! [X1: $i > $i,X5: $i > $i,X3: $i] :
( ( fun_composition @ X1 @ X5 @ X3 )
= ( X5 @ ( X1 @ X3 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
thf(c_0_11,negated_conjecture,
esk2_0 != esk3_0,
inference(split_conjunct,[status(thm)],[c_0_7]) ).
thf(c_0_12,negated_conjecture,
! [X3: $i] :
( ( esk2_0 @ ( esk1_0 @ X3 ) )
= ( esk3_0 @ ( esk1_0 @ X3 ) ) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(arg_cong,[status(thm)],[c_0_9]),c_0_10]),c_0_10]) ).
thf(c_0_13,negated_conjecture,
! [X3: $i] :
( X3
= ( esk1_0 @ ( esk4_1 @ X3 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
thf(c_0_14,negated_conjecture,
( ( esk2_0 @ esk4_0 )
!= ( esk3_0 @ esk4_0 ) ),
inference(neg_ext,[status(thm)],[c_0_11]) ).
thf(c_0_15,negated_conjecture,
! [X3: $i] :
( ( esk2_0 @ X3 )
= ( esk3_0 @ X3 ) ),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
thf(c_0_16,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_14,c_0_15])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET724^4 : TPTP v9.3.1. Released v3.6.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.18 % Computer : n006.cluster.edu
% 0.09/0.18 % Model : x86_64 x86_64
% 0.09/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.18 % Memory : 8046.5625MB
% 0.09/0.18 % OS : Linux 6.8.0-71-generic
% 0.09/0.18 % CPULimit : 300
% 0.09/0.18 % WCLimit : 300
% 0.09/0.18 % DateTime : Tue Sep 29 13:40:39 UTC 2026
% 0.09/0.18 % CPUTime :
% 0.09/0.18 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.22 Running higher-order theorem proving
% 0.09/0.24 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.3xQ37thv4D/E---3.1_727646.p
% 0.09/0.26 % Version: 3.5.1-ho
% 0.09/0.26 % Preprocessing class: HSSSSMSSMLSNHSN.
% 0.09/0.26 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.09/0.26 % Starting new_ho_9 with 1500s (5) cores
% 0.09/0.26 % Starting post_as_ho1 with 300s (1) cores
% 0.09/0.26 % Starting sh1l with 300s (1) cores
% 0.09/0.26 % Starting post_as_ho10 with 300s (1) cores
% 0.09/0.26 % new_ho_9 with pid 727659 completed with status 0
% 0.09/0.26 % Result found by new_ho_9
% 0.09/0.26 % Preprocessing class: HSSSSMSSMLSNHSN.
% 0.09/0.26 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.09/0.26 % Starting new_ho_9 with 1500s (5) cores
% 0.09/0.26 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.09/0.26 % No SInE strategy applied
% 0.09/0.26 % Search class: HUUPS-FFSF32-SHSSMSNN
% 0.09/0.26 % partial match(4): HUUPS-FFSF11-SHSFMFNN
% 0.09/0.26 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.09/0.26 % Starting SubtermCWHack with 136s (1) cores
% 0.09/0.26 % Starting new_ho_9 with 151s (1) cores
% 0.09/0.26 % Starting sh5l with 136s (1) cores
% 0.09/0.26 % Starting new_bool_1 with 136s (1) cores
% 0.09/0.26 % Starting new_bool_2 with 136s (1) cores
% 0.09/0.26 % SubtermCWHack with pid 727663 completed with status 10
% 0.09/0.26 % Starting new_bool_9 with 136s (1) cores
% 0.09/0.26 % new_ho_9 with pid 727665 completed with status 0
% 0.09/0.26 % Result found by new_ho_9
% 0.09/0.26 % Preprocessing class: HSSSSMSSMLSNHSN.
% 0.09/0.26 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.09/0.26 % Starting new_ho_9 with 1500s (5) cores
% 0.09/0.26 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.09/0.26 % No SInE strategy applied
% 0.09/0.26 % Search class: HUUPS-FFSF32-SHSSMSNN
% 0.09/0.26 % partial match(4): HUUPS-FFSF11-SHSFMFNN
% 0.09/0.26 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.09/0.26 % Starting SubtermCWHack with 136s (1) cores
% 0.09/0.26 % Starting new_ho_9 with 151s (1) cores
% 0.09/0.26 % Preprocessing time : 0.001 s
% 0.09/0.26 % Presaturation interreduction done
% 0.09/0.26
% 0.09/0.26 % Proof found!
% 0.09/0.26 % SZS status Theorem
% 0.09/0.26 % SZS output start CNFRefutation
% See solution above
% 0.09/0.26 % Parsed axioms : 17
% 0.09/0.26 % Removed by relevancy pruning/SinE : 0
% 0.09/0.26 % Initial clauses : 12
% 0.09/0.26 % Removed in clause preprocessing : 8
% 0.09/0.26 % Initial clauses in saturation : 4
% 0.09/0.26 % Processed clauses : 11
% 0.09/0.26 % ...of these trivial : 0
% 0.09/0.26 % ...subsumed : 0
% 0.09/0.26 % ...remaining for further processing : 11
% 0.09/0.26 % Other redundant clauses eliminated : 0
% 0.09/0.26 % Clauses deleted for lack of memory : 0
% 0.09/0.26 % Backward-subsumed : 0
% 0.09/0.26 % Backward-rewritten : 2
% 0.09/0.26 % Generated clauses : 4
% 0.09/0.26 % ...of the previous two non-redundant : 3
% 0.09/0.26 % ...aggressively subsumed : 0
% 0.09/0.26 % Contextual simplify-reflections : 0
% 0.09/0.26 % Paramodulations : 1
% 0.09/0.26 % Factorizations : 0
% 0.09/0.26 % NegExts : 1
% 0.09/0.26 % Equation resolutions : 0
% 0.09/0.26 % Disequality decompositions : 0
% 0.09/0.26 % Total rewrite steps : 4
% 0.09/0.26 % ...of those cached : 0
% 0.09/0.26 % Propositional unsat checks : 0
% 0.09/0.26 % Propositional check models : 0
% 0.09/0.26 % Propositional check unsatisfiable : 0
% 0.09/0.26 % Propositional clauses : 0
% 0.09/0.26 % Propositional clauses after purity: 0
% 0.09/0.26 % Propositional unsat core size : 0
% 0.09/0.26 % Propositional preprocessing time : 0.000
% 0.09/0.26 % Propositional encoding time : 0.000
% 0.09/0.26 % Propositional solver time : 0.000
% 0.09/0.26 % Success case prop preproc time : 0.000
% 0.09/0.26 % Success case prop encoding time : 0.000
% 0.09/0.26 % Success case prop solver time : 0.000
% 0.09/0.26 % Current number of processed clauses : 5
% 0.09/0.26 % Positive orientable unit clauses : 4
% 0.09/0.26 % Positive unorientable unit clauses: 0
% 0.09/0.26 % Negative unit clauses : 1
% 0.09/0.26 % Non-unit-clauses : 0
% 0.09/0.26 % Current number of unprocessed clauses: 0
% 0.09/0.26 % ...number of literals in the above : 0
% 0.09/0.26 % Current number of archived formulas : 0
% 0.09/0.26 % Current number of archived clauses : 6
% 0.09/0.26 % Clause-clause subsumption calls (NU) : 0
% 0.09/0.26 % Rec. Clause-clause subsumption calls : 0
% 0.09/0.26 % Non-unit clause-clause subsumptions : 0
% 0.09/0.26 % Unit Clause-clause subsumption calls : 1
% 0.09/0.26 % Rewrite failures with RHS unbound : 0
% 0.09/0.26 % BW rewrite match attempts : 7
% 0.09/0.26 % BW rewrite match successes : 2
% 0.09/0.26 % Condensation attempts : 11
% 0.09/0.26 % Condensation successes : 0
% 0.09/0.26 % Termbank termtop insertions : 684
% 0.09/0.26 % Search garbage collected termcells : 99
% 0.09/0.26
% 0.09/0.26 % -------------------------------------------------
% 0.09/0.26 % User time : 0.002 s
% 0.09/0.26 % System time : 0.007 s
% 0.09/0.26 % Total time : 0.009 s
% 0.09/0.26 % Maximum resident set size: 3648 pages
% 0.09/0.26
% 0.09/0.26 % -------------------------------------------------
% 0.09/0.26 % User time : 0.007 s
% 0.09/0.26 % System time : 0.014 s
% 0.09/0.26 % Total time : 0.020 s
% 0.09/0.26 % Maximum resident set size: 4864 pages
% 0.09/0.26 % E exiting
%------------------------------------------------------------------------------