%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUM771^1 : TPTP v9.3.1. Released v3.7.0.
% 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 08:17:05 AM UTC 2026
% Result : Theorem 0.09s 0.14s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 3
% Syntax : Number of formulae : 12 ( 12 unt; 0 typ; 0 def)
% Number of atoms : 12 ( 3 equ; 0 cnn)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 132 ( 4 ~; 0 |; 0 &; 128 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 6 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 9 ( 0 ^; 9 !; 0 ?; 9 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_sort1,type,
frac: $tType ).
thf(decl_sort2,type,
nat: $tType ).
thf(decl_23,type,
x: frac ).
thf(decl_24,type,
y: frac ).
thf(decl_25,type,
eq: frac > frac > $o ).
thf(decl_26,type,
fr: nat > nat > frac ).
thf(decl_27,type,
ts: nat > nat > nat ).
thf(decl_28,type,
num: frac > nat ).
thf(decl_29,type,
den: frac > nat ).
thf(satz69,conjecture,
eq @ ( fr @ ( ts @ ( num @ x ) @ ( num @ y ) ) @ ( ts @ ( den @ x ) @ ( den @ y ) ) ) @ ( fr @ ( ts @ ( num @ y ) @ ( num @ x ) ) @ ( ts @ ( den @ y ) @ ( den @ x ) ) ),
file('/export/starexec/sandbox/tmp/tmp.rUha5ahi4Z/E---3.1_64875.p',satz69) ).
thf(satz29,axiom,
! [X2: nat,X3: nat] :
( ( ts @ X2 @ X3 )
= ( ts @ X3 @ X2 ) ),
file('/export/starexec/sandbox/tmp/tmp.rUha5ahi4Z/E---3.1_64875.p',satz29) ).
thf(satz37,axiom,
! [X1: frac] : ( eq @ X1 @ X1 ),
file('/export/starexec/sandbox/tmp/tmp.rUha5ahi4Z/E---3.1_64875.p',satz37) ).
thf(c_0_3,negated_conjecture,
~ ( eq @ ( fr @ ( ts @ ( num @ x ) @ ( num @ y ) ) @ ( ts @ ( den @ x ) @ ( den @ y ) ) ) @ ( fr @ ( ts @ ( num @ y ) @ ( num @ x ) ) @ ( ts @ ( den @ y ) @ ( den @ x ) ) ) ),
inference(assume_negation,[status(cth)],[satz69]) ).
thf(c_0_4,negated_conjecture,
~ ( eq @ ( fr @ ( ts @ ( num @ x ) @ ( num @ y ) ) @ ( ts @ ( den @ x ) @ ( den @ y ) ) ) @ ( fr @ ( ts @ ( num @ y ) @ ( num @ x ) ) @ ( ts @ ( den @ y ) @ ( den @ x ) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_3]) ).
thf(c_0_5,negated_conjecture,
~ ( eq @ ( fr @ ( ts @ ( num @ x ) @ ( num @ y ) ) @ ( ts @ ( den @ x ) @ ( den @ y ) ) ) @ ( fr @ ( ts @ ( num @ y ) @ ( num @ x ) ) @ ( ts @ ( den @ y ) @ ( den @ x ) ) ) ),
inference(fof_nnf,[status(thm)],[c_0_4]) ).
thf(c_0_6,plain,
! [X8: nat,X9: nat] :
( ( ts @ X8 @ X9 )
= ( ts @ X9 @ X8 ) ),
inference(variable_rename,[status(thm)],[satz29]) ).
thf(c_0_7,plain,
! [X7: frac] : ( eq @ X7 @ X7 ),
inference(variable_rename,[status(thm)],[satz37]) ).
thf(c_0_8,negated_conjecture,
~ ( eq @ ( fr @ ( ts @ ( num @ x ) @ ( num @ y ) ) @ ( ts @ ( den @ x ) @ ( den @ y ) ) ) @ ( fr @ ( ts @ ( num @ y ) @ ( num @ x ) ) @ ( ts @ ( den @ y ) @ ( den @ x ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
thf(c_0_9,plain,
! [X3: nat,X2: nat] :
( ( ts @ X2 @ X3 )
= ( ts @ X3 @ X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
thf(c_0_10,plain,
! [X1: frac] : ( eq @ X1 @ X1 ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
thf(c_0_11,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_8,c_0_9]),c_0_9]),c_0_10])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : NUM771^1 : TPTP v9.3.1. Released v3.7.0.
% 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 12:54:33 UTC 2026
% 0.00/0.10 % CPUTime :
% 0.00/0.10 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.12 Running higher-order theorem proving
% 0.09/0.13 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.rUha5ahi4Z/E---3.1_64875.p
% 0.09/0.14 % Version: 3.5.1-ho
% 0.09/0.14 % Preprocessing class: HSSSSMSSSSSNFFN.
% 0.09/0.14 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.09/0.14 % Starting new_ho_10 with 1500s (5) cores
% 0.09/0.14 % Starting ho_unfolding_6 with 300s (1) cores
% 0.09/0.14 % Starting sh4l with 300s (1) cores
% 0.09/0.14 % Starting ehoh_best_nonlift_rwall with 300s (1) cores
% 0.09/0.14 % ho_unfolding_6 with pid 64889 completed with status 0
% 0.09/0.14 % Result found by ho_unfolding_6
% 0.09/0.14 % Preprocessing class: HSSSSMSSSSSNFFN.
% 0.09/0.14 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.09/0.14 % Starting new_ho_10 with 1500s (5) cores
% 0.09/0.14 % Starting ho_unfolding_6 with 300s (1) cores
% 0.09/0.14 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 1, sine = Auto)
% 0.09/0.14 % No SInE strategy applied
% 0.09/0.14 % Search class: HUUSS-FFSF21-MFFFFFNN
% 0.09/0.14 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.09/0.14 % Starting SubtermCWHack with 28s (1) cores
% 0.09/0.14 % SubtermCWHack with pid 64893 completed with status 0
% 0.09/0.14 % Result found by SubtermCWHack
% 0.09/0.14 % Preprocessing class: HSSSSMSSSSSNFFN.
% 0.09/0.14 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.09/0.14 % Starting new_ho_10 with 1500s (5) cores
% 0.09/0.14 % Starting ho_unfolding_6 with 300s (1) cores
% 0.09/0.14 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 1, sine = Auto)
% 0.09/0.14 % No SInE strategy applied
% 0.09/0.14 % Search class: HUUSS-FFSF21-MFFFFFNN
% 0.09/0.14 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.09/0.14 % Starting SubtermCWHack with 28s (1) cores
% 0.09/0.14 % Preprocessing time : 0.001 s
% 0.09/0.14
% 0.09/0.14 % Proof found!
% 0.09/0.14 % SZS status Theorem
% 0.09/0.14 % SZS output start CNFRefutation
% See solution above
% 0.09/0.14 % Parsed axioms : 12
% 0.09/0.14 % Removed by relevancy pruning/SinE : 0
% 0.09/0.14 % Initial clauses : 12
% 0.09/0.14 % Removed in clause preprocessing : 9
% 0.09/0.14 % Initial clauses in saturation : 3
% 0.09/0.14 % Processed clauses : 3
% 0.09/0.14 % ...of these trivial : 0
% 0.09/0.14 % ...subsumed : 0
% 0.09/0.14 % ...remaining for further processing : 2
% 0.09/0.14 % Other redundant clauses eliminated : 0
% 0.09/0.14 % Clauses deleted for lack of memory : 0
% 0.09/0.14 % Backward-subsumed : 0
% 0.09/0.14 % Backward-rewritten : 0
% 0.09/0.14 % Generated clauses : 0
% 0.09/0.14 % ...of the previous two non-redundant : 0
% 0.09/0.14 % ...aggressively subsumed : 0
% 0.09/0.14 % Contextual simplify-reflections : 0
% 0.09/0.14 % Paramodulations : 0
% 0.09/0.14 % Factorizations : 0
% 0.09/0.14 % NegExts : 0
% 0.09/0.14 % Equation resolutions : 0
% 0.09/0.14 % Disequality decompositions : 0
% 0.09/0.14 % Total rewrite steps : 3
% 0.09/0.14 % ...of those cached : 0
% 0.09/0.14 % Propositional unsat checks : 0
% 0.09/0.14 % Propositional check models : 0
% 0.09/0.14 % Propositional check unsatisfiable : 0
% 0.09/0.14 % Propositional clauses : 0
% 0.09/0.14 % Propositional clauses after purity: 0
% 0.09/0.14 % Propositional unsat core size : 0
% 0.09/0.14 % Propositional preprocessing time : 0.000
% 0.09/0.14 % Propositional encoding time : 0.000
% 0.09/0.14 % Propositional solver time : 0.000
% 0.09/0.14 % Success case prop preproc time : 0.000
% 0.09/0.14 % Success case prop encoding time : 0.000
% 0.09/0.14 % Success case prop solver time : 0.000
% 0.09/0.14 % Current number of processed clauses : 2
% 0.09/0.14 % Positive orientable unit clauses : 1
% 0.09/0.14 % Positive unorientable unit clauses: 1
% 0.09/0.14 % Negative unit clauses : 0
% 0.09/0.14 % Non-unit-clauses : 0
% 0.09/0.14 % Current number of unprocessed clauses: 0
% 0.09/0.14 % ...number of literals in the above : 0
% 0.09/0.14 % Current number of archived formulas : 0
% 0.09/0.14 % Current number of archived clauses : 0
% 0.09/0.14 % Clause-clause subsumption calls (NU) : 0
% 0.09/0.14 % Rec. Clause-clause subsumption calls : 0
% 0.09/0.14 % Non-unit clause-clause subsumptions : 0
% 0.09/0.14 % Unit Clause-clause subsumption calls : 0
% 0.09/0.14 % Rewrite failures with RHS unbound : 0
% 0.09/0.14 % BW rewrite match attempts : 0
% 0.09/0.14 % BW rewrite match successes : 0
% 0.09/0.14 % Condensation attempts : 0
% 0.09/0.14 % Condensation successes : 0
% 0.09/0.14 % Termbank termtop insertions : 346
% 0.09/0.14 % Search garbage collected termcells : 13
% 0.09/0.14
% 0.09/0.14 % -------------------------------------------------
% 0.09/0.14 % User time : 0.002 s
% 0.09/0.14 % System time : 0.000 s
% 0.09/0.14 % Total time : 0.002 s
% 0.09/0.14 % Maximum resident set size: 3632 pages
% 0.09/0.14
% 0.09/0.14 % -------------------------------------------------
% 0.09/0.14 % User time : 0.002 s
% 0.09/0.14 % System time : 0.003 s
% 0.09/0.14 % Total time : 0.006 s
% 0.09/0.14 % Maximum resident set size: 4864 pages
% 0.09/0.14 % E exiting
%------------------------------------------------------------------------------