%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SET747^4 : 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 : n012.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 0.08s 0.14s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 4
% Syntax : Number of formulae : 19 ( 13 unt; 0 typ; 0 def)
% Number of atoms : 33 ( 8 equ; 0 cnn)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 163 ( 10 ~; 4 |; 6 &; 133 @)
% ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 32 ( 32 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 8 usr; 3 con; 0-3 aty)
% Number of variables : 51 ( 11 ^; 40 !; 0 ?; 51 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_24,type,
fun_composition: ( $i > $i ) > ( $i > $i ) > $i > $i ).
thf(decl_29,type,
fun_decreasing: ( $i > $i ) > ( $i > $i > $o ) > $o ).
thf(decl_30,type,
fun_increasing: ( $i > $i ) > ( $i > $i > $o ) > $o ).
thf(decl_31,type,
esk1_0: $i > $i ).
thf(decl_32,type,
esk2_0: $i > $i ).
thf(decl_33,type,
epred1_0: $i > $i > $o ).
thf(decl_34,type,
esk3_0: $i ).
thf(decl_35,type,
esk4_0: $i ).
thf(thm,conjecture,
! [X1: $i > $i,X5: $i > $i,X8: $i > $i > $o] :
( ( ( fun_increasing @ X1 @ X8 )
& ( fun_decreasing @ X5 @ X8 ) )
=> ( fun_decreasing @ ( fun_composition @ X1 @ X5 ) @ X8 ) ),
file('/export/starexec/sandbox/tmp/tmp.ftgKyAW7qp/E---3.1_116942.p',thm) ).
thf(fun_decreasing,axiom,
( fun_decreasing
= ( ^ [X1: $i > $i,X7: $i > $i > $o] :
! [X4: $i,X3: $i] :
( ( X7 @ X4 @ X3 )
=> ( X7 @ ( X1 @ X3 ) @ ( X1 @ X4 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.ftgKyAW7qp/E---3.1_116942.p',fun_decreasing) ).
thf(fun_increasing,axiom,
( fun_increasing
= ( ^ [X1: $i > $i,X7: $i > $i > $o] :
! [X4: $i,X3: $i] :
( ( X7 @ X4 @ X3 )
=> ( X7 @ ( X1 @ X4 ) @ ( X1 @ X3 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.ftgKyAW7qp/E---3.1_116942.p',fun_increasing) ).
thf(fun_composition,axiom,
( fun_composition
= ( ^ [X1: $i > $i,X5: $i > $i,X4: $i] : ( X5 @ ( X1 @ X4 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.ftgKyAW7qp/E---3.1_116942.p',fun_composition) ).
thf(c_0_4,negated_conjecture,
~ ! [X1: $i > $i,X5: $i > $i,X8: $i > $i > $o] :
( ( ( fun_increasing @ X1 @ X8 )
& ( fun_decreasing @ X5 @ X8 ) )
=> ( fun_decreasing @ ( fun_composition @ X1 @ X5 ) @ X8 ) ),
inference(assume_negation,[status(cth)],[thm]) ).
thf(c_0_5,plain,
( fun_decreasing
= ( ^ [Z0: $i > $i,Z1: $i > $i > $o] :
! [X4: $i,X3: $i] :
( ( Z1 @ X4 @ X3 )
=> ( Z1 @ ( Z0 @ X3 ) @ ( Z0 @ X4 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[fun_decreasing]) ).
thf(c_0_6,plain,
( fun_increasing
= ( ^ [Z0: $i > $i,Z1: $i > $i > $o] :
! [X4: $i,X3: $i] :
( ( Z1 @ X4 @ X3 )
=> ( Z1 @ ( Z0 @ X4 ) @ ( Z0 @ X3 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[fun_increasing]) ).
thf(c_0_7,negated_conjecture,
~ ! [X1: $i > $i,X5: $i > $i,X8: $i > $i > $o] :
( ( ! [X16: $i,X17: $i] :
( ( X8 @ X16 @ X17 )
=> ( X8 @ ( X1 @ X16 ) @ ( X1 @ X17 ) ) )
& ! [X18: $i,X19: $i] :
( ( X8 @ X18 @ X19 )
=> ( X8 @ ( X5 @ X19 ) @ ( X5 @ X18 ) ) ) )
=> ! [X20: $i,X21: $i] :
( ( X8 @ X20 @ X21 )
=> ( X8 @ ( fun_composition @ X1 @ X5 @ X21 ) @ ( fun_composition @ X1 @ X5 @ X20 ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_4,c_0_5]),c_0_6]) ).
thf(c_0_8,plain,
! [X22: $i > $i,X23: $i > $i,X24: $i] :
( ( fun_composition @ X22 @ X23 @ X24 )
= ( X23 @ ( X22 @ X24 ) ) ),
inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[fun_composition])]) ).
thf(c_0_9,negated_conjecture,
! [X31: $i,X32: $i,X33: $i,X34: $i] :
( ( ~ ( epred1_0 @ X31 @ X32 )
| ( epred1_0 @ ( esk1_0 @ X31 ) @ ( esk1_0 @ X32 ) ) )
& ( ~ ( epred1_0 @ X33 @ X34 )
| ( epred1_0 @ ( esk2_0 @ X34 ) @ ( esk2_0 @ X33 ) ) )
& ( epred1_0 @ esk3_0 @ esk4_0 )
& ~ ( epred1_0 @ ( fun_composition @ esk1_0 @ esk2_0 @ esk4_0 ) @ ( fun_composition @ esk1_0 @ 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_7])])])])]) ).
thf(c_0_10,plain,
! [X25: $i > $i,X26: $i > $i,X27: $i] :
( ( fun_composition @ X25 @ X26 @ X27 )
= ( X26 @ ( X25 @ X27 ) ) ),
inference(variable_rename,[status(thm)],[c_0_8]) ).
thf(c_0_11,negated_conjecture,
~ ( epred1_0 @ ( fun_composition @ esk1_0 @ esk2_0 @ esk4_0 ) @ ( fun_composition @ esk1_0 @ esk2_0 @ esk3_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
thf(c_0_12,plain,
! [X1: $i > $i,X5: $i > $i,X3: $i] :
( ( fun_composition @ X1 @ X5 @ X3 )
= ( X5 @ ( X1 @ X3 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
thf(c_0_13,negated_conjecture,
~ ( epred1_0 @ ( esk2_0 @ ( esk1_0 @ esk4_0 ) ) @ ( esk2_0 @ ( esk1_0 @ esk3_0 ) ) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_11,c_0_12]),c_0_12]) ).
thf(c_0_14,negated_conjecture,
! [X3: $i,X4: $i] :
( ( epred1_0 @ ( esk2_0 @ X4 ) @ ( esk2_0 @ X3 ) )
| ~ ( epred1_0 @ X3 @ X4 ) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
thf(c_0_15,negated_conjecture,
~ ( epred1_0 @ ( esk1_0 @ esk3_0 ) @ ( esk1_0 @ esk4_0 ) ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
thf(c_0_16,negated_conjecture,
! [X3: $i,X4: $i] :
( ( epred1_0 @ ( esk1_0 @ X3 ) @ ( esk1_0 @ X4 ) )
| ~ ( epred1_0 @ X3 @ X4 ) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
thf(c_0_17,negated_conjecture,
epred1_0 @ esk3_0 @ esk4_0,
inference(split_conjunct,[status(thm)],[c_0_9]) ).
thf(c_0_18,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_16]),c_0_17])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SET747^4 : TPTP v9.3.1. Released v3.6.0.
% 0.00/0.02 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.00/0.10 % Computer : n012.cluster.edu
% 0.00/0.10 % Model : x86_64 x86_64
% 0.00/0.10 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.00/0.10 % Memory : 8046.5625MB
% 0.00/0.10 % OS : Linux 6.8.0-71-generic
% 0.00/0.10 % CPULimit : 300
% 0.00/0.10 % WCLimit : 300
% 0.00/0.10 % DateTime : Tue Sep 29 13:40:33 UTC 2026
% 0.00/0.10 % CPUTime :
% 0.00/0.10 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.12 Running higher-order theorem proving
% 0.08/0.13 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.ftgKyAW7qp/E---3.1_116942.p
% 0.08/0.14 % Version: 3.5.1-ho
% 0.08/0.14 % Preprocessing class: HSSSSMSSMLSNHSN.
% 0.08/0.14 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.08/0.14 % Starting new_ho_9 with 1500s (5) cores
% 0.08/0.14 % Starting post_as_ho1 with 300s (1) cores
% 0.08/0.14 % Starting sh1l with 300s (1) cores
% 0.08/0.14 % Starting post_as_ho10 with 300s (1) cores
% 0.08/0.14 % post_as_ho1 with pid 116977 completed with status 0
% 0.08/0.14 % Result found by post_as_ho1
% 0.08/0.14 % Preprocessing class: HSSSSMSSMLSNHSN.
% 0.08/0.14 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.08/0.14 % Starting new_ho_9 with 1500s (5) cores
% 0.08/0.14 % Starting post_as_ho1 with 300s (1) cores
% 0.08/0.14 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.08/0.14 % No SInE strategy applied
% 0.08/0.14 % Search class: HHUSF-FFSF33-SHSSMSNN
% 0.08/0.14 % partial match(3): HHUSF-FFSF32-SHSFMSBN
% 0.08/0.14 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.08/0.14 % Starting SubtermCWHack with 28s (1) cores
% 0.08/0.14 % SubtermCWHack with pid 116983 completed with status 0
% 0.08/0.14 % Result found by SubtermCWHack
% 0.08/0.14 % Preprocessing class: HSSSSMSSMLSNHSN.
% 0.08/0.14 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.08/0.14 % Starting new_ho_9 with 1500s (5) cores
% 0.08/0.14 % Starting post_as_ho1 with 300s (1) cores
% 0.08/0.14 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.08/0.14 % No SInE strategy applied
% 0.08/0.14 % Search class: HHUSF-FFSF33-SHSSMSNN
% 0.08/0.14 % partial match(3): HHUSF-FFSF32-SHSFMSBN
% 0.08/0.14 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.08/0.14 % Starting SubtermCWHack with 28s (1) cores
% 0.08/0.14 % Preprocessing time : 0.001 s
% 0.08/0.14
% 0.08/0.14 % Proof found!
% 0.08/0.14 % SZS status Theorem
% 0.08/0.14 % SZS output start CNFRefutation
% See solution above
% 0.08/0.14 % Parsed axioms : 17
% 0.08/0.14 % Removed by relevancy pruning/SinE : 0
% 0.08/0.14 % Initial clauses : 13
% 0.08/0.14 % Removed in clause preprocessing : 8
% 0.08/0.14 % Initial clauses in saturation : 5
% 0.08/0.14 % Processed clauses : 6
% 0.08/0.14 % ...of these trivial : 0
% 0.08/0.14 % ...subsumed : 0
% 0.08/0.14 % ...remaining for further processing : 6
% 0.08/0.14 % Other redundant clauses eliminated : 0
% 0.08/0.14 % Clauses deleted for lack of memory : 0
% 0.08/0.14 % Backward-subsumed : 0
% 0.08/0.14 % Backward-rewritten : 0
% 0.08/0.14 % Generated clauses : 2
% 0.08/0.14 % ...of the previous two non-redundant : 1
% 0.08/0.14 % ...aggressively subsumed : 0
% 0.08/0.14 % Contextual simplify-reflections : 0
% 0.08/0.14 % Paramodulations : 2
% 0.08/0.14 % Factorizations : 0
% 0.08/0.14 % NegExts : 0
% 0.08/0.14 % Equation resolutions : 0
% 0.08/0.14 % Disequality decompositions : 0
% 0.08/0.14 % Total rewrite steps : 3
% 0.08/0.14 % ...of those cached : 0
% 0.08/0.14 % Propositional unsat checks : 0
% 0.08/0.14 % Propositional check models : 0
% 0.08/0.14 % Propositional check unsatisfiable : 0
% 0.08/0.14 % Propositional clauses : 0
% 0.08/0.14 % Propositional clauses after purity: 0
% 0.08/0.14 % Propositional unsat core size : 0
% 0.08/0.14 % Propositional preprocessing time : 0.000
% 0.08/0.14 % Propositional encoding time : 0.000
% 0.08/0.14 % Propositional solver time : 0.000
% 0.08/0.14 % Success case prop preproc time : 0.000
% 0.08/0.14 % Success case prop encoding time : 0.000
% 0.08/0.14 % Success case prop solver time : 0.000
% 0.08/0.14 % Current number of processed clauses : 6
% 0.08/0.14 % Positive orientable unit clauses : 2
% 0.08/0.14 % Positive unorientable unit clauses: 0
% 0.08/0.14 % Negative unit clauses : 2
% 0.08/0.14 % Non-unit-clauses : 2
% 0.08/0.14 % Current number of unprocessed clauses: 0
% 0.08/0.14 % ...number of literals in the above : 0
% 0.08/0.14 % Current number of archived formulas : 0
% 0.08/0.14 % Current number of archived clauses : 0
% 0.08/0.14 % Clause-clause subsumption calls (NU) : 0
% 0.08/0.14 % Rec. Clause-clause subsumption calls : 0
% 0.08/0.14 % Non-unit clause-clause subsumptions : 0
% 0.08/0.14 % Unit Clause-clause subsumption calls : 1
% 0.08/0.14 % Rewrite failures with RHS unbound : 0
% 0.08/0.14 % BW rewrite match attempts : 0
% 0.08/0.14 % BW rewrite match successes : 0
% 0.08/0.14 % Condensation attempts : 0
% 0.08/0.14 % Condensation successes : 0
% 0.08/0.14 % Termbank termtop insertions : 951
% 0.08/0.14 % Search garbage collected termcells : 252
% 0.08/0.14
% 0.08/0.14 % -------------------------------------------------
% 0.08/0.14 % User time : 0.002 s
% 0.08/0.14 % System time : 0.001 s
% 0.08/0.14 % Total time : 0.003 s
% 0.08/0.14 % Maximum resident set size: 3648 pages
% 0.08/0.14
% 0.08/0.14 % -------------------------------------------------
% 0.08/0.14 % User time : 0.003 s
% 0.08/0.14 % System time : 0.004 s
% 0.08/0.14 % Total time : 0.007 s
% 0.08/0.14 % Maximum resident set size: 4864 pages
% 0.08/0.14 % E exiting
%------------------------------------------------------------------------------