%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUM748^1 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n003.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 08:17:00 AM UTC 2026
% Result : Theorem 0.09s 0.26s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 4
% Syntax : Number of formulae : 15 ( 15 unt; 0 typ; 0 def)
% Number of atoms : 15 ( 6 equ; 0 cnn)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 204 ( 4 ~; 0 |; 0 &; 200 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 8 usr; 3 con; 0-2 aty)
% Number of variables : 15 ( 0 ^; 15 !; 0 ?; 15 :)
% 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,
pl: nat > nat > nat ).
thf(decl_28,type,
ts: nat > nat > nat ).
thf(decl_29,type,
num: frac > nat ).
thf(decl_30,type,
den: frac > nat ).
thf(satz58,conjecture,
eq @ ( fr @ ( pl @ ( ts @ ( num @ x ) @ ( den @ y ) ) @ ( ts @ ( num @ y ) @ ( den @ x ) ) ) @ ( ts @ ( den @ x ) @ ( den @ y ) ) ) @ ( fr @ ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ ( ts @ ( num @ x ) @ ( den @ y ) ) ) @ ( ts @ ( den @ y ) @ ( den @ x ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.fE7dZwCIyW/E---3.1_2457561.p',satz58) ).
thf(satz29,axiom,
! [X2: nat,X3: nat] :
( ( ts @ X2 @ X3 )
= ( ts @ X3 @ X2 ) ),
file('/export/starexec/sandbox2/tmp/tmp.fE7dZwCIyW/E---3.1_2457561.p',satz29) ).
thf(satz6,axiom,
! [X4: nat,X3: nat] :
( ( pl @ X4 @ X3 )
= ( pl @ X3 @ X4 ) ),
file('/export/starexec/sandbox2/tmp/tmp.fE7dZwCIyW/E---3.1_2457561.p',satz6) ).
thf(satz37,axiom,
! [X1: frac] : ( eq @ X1 @ X1 ),
file('/export/starexec/sandbox2/tmp/tmp.fE7dZwCIyW/E---3.1_2457561.p',satz37) ).
thf(c_0_4,negated_conjecture,
~ ( eq @ ( fr @ ( pl @ ( ts @ ( num @ x ) @ ( den @ y ) ) @ ( ts @ ( num @ y ) @ ( den @ x ) ) ) @ ( ts @ ( den @ x ) @ ( den @ y ) ) ) @ ( fr @ ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ ( ts @ ( num @ x ) @ ( den @ y ) ) ) @ ( ts @ ( den @ y ) @ ( den @ x ) ) ) ),
inference(assume_negation,[status(cth)],[satz58]) ).
thf(c_0_5,negated_conjecture,
~ ( eq @ ( fr @ ( pl @ ( ts @ ( num @ x ) @ ( den @ y ) ) @ ( ts @ ( num @ y ) @ ( den @ x ) ) ) @ ( ts @ ( den @ x ) @ ( den @ y ) ) ) @ ( fr @ ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ ( ts @ ( num @ x ) @ ( den @ y ) ) ) @ ( ts @ ( den @ y ) @ ( den @ x ) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_4]) ).
thf(c_0_6,negated_conjecture,
~ ( eq @ ( fr @ ( pl @ ( ts @ ( num @ x ) @ ( den @ y ) ) @ ( ts @ ( num @ y ) @ ( den @ x ) ) ) @ ( ts @ ( den @ x ) @ ( den @ y ) ) ) @ ( fr @ ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ ( ts @ ( num @ x ) @ ( den @ y ) ) ) @ ( ts @ ( den @ y ) @ ( den @ x ) ) ) ),
inference(fof_nnf,[status(thm)],[c_0_5]) ).
thf(c_0_7,plain,
! [X11: nat,X12: nat] :
( ( ts @ X11 @ X12 )
= ( ts @ X12 @ X11 ) ),
inference(variable_rename,[status(thm)],[satz29]) ).
thf(c_0_8,plain,
! [X13: nat,X14: nat] :
( ( pl @ X13 @ X14 )
= ( pl @ X14 @ X13 ) ),
inference(variable_rename,[status(thm)],[satz6]) ).
thf(c_0_9,plain,
! [X10: frac] : ( eq @ X10 @ X10 ),
inference(variable_rename,[status(thm)],[satz37]) ).
thf(c_0_10,negated_conjecture,
~ ( eq @ ( fr @ ( pl @ ( ts @ ( num @ x ) @ ( den @ y ) ) @ ( ts @ ( num @ y ) @ ( den @ x ) ) ) @ ( ts @ ( den @ x ) @ ( den @ y ) ) ) @ ( fr @ ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ ( ts @ ( num @ x ) @ ( den @ y ) ) ) @ ( ts @ ( den @ y ) @ ( den @ x ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
thf(c_0_11,plain,
! [X3: nat,X2: nat] :
( ( ts @ X2 @ X3 )
= ( ts @ X3 @ X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
thf(c_0_12,plain,
! [X3: nat,X2: nat] :
( ( pl @ X2 @ X3 )
= ( pl @ X3 @ X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
thf(c_0_13,plain,
! [X1: frac] : ( eq @ X1 @ X1 ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
thf(c_0_14,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_10,c_0_11]),c_0_11]),c_0_12]),c_0_11]),c_0_11]),c_0_11]),c_0_13])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM748^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.18 % Computer : n003.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 12:51:28 UTC 2026
% 0.09/0.18 % CPUTime :
% 0.09/0.18 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.23 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.fE7dZwCIyW/E---3.1_2457561.p
% 0.09/0.26 % Version: 3.5.1-ho
% 0.09/0.26 % Preprocessing class: HSSSSMSSSSSNFFN.
% 0.09/0.26 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.09/0.26 % Starting new_ho_10 with 1500s (5) cores
% 0.09/0.26 % Starting ho_unfolding_6 with 300s (1) cores
% 0.09/0.26 % Starting sh4l with 300s (1) cores
% 0.09/0.26 % Starting ehoh_best_nonlift_rwall with 300s (1) cores
% 0.09/0.26 % ho_unfolding_6 with pid 2457575 completed with status 0
% 0.09/0.26 % Result found by ho_unfolding_6
% 0.09/0.26 % Preprocessing class: HSSSSMSSSSSNFFN.
% 0.09/0.26 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.09/0.26 % Starting new_ho_10 with 1500s (5) cores
% 0.09/0.26 % Starting ho_unfolding_6 with 300s (1) cores
% 0.09/0.26 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 1, sine = Auto)
% 0.09/0.26 % No SInE strategy applied
% 0.09/0.26 % Search class: HUUSS-FFSF21-MFFFFFNN
% 0.09/0.26 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.09/0.26 % Starting SubtermCWHack with 28s (1) cores
% 0.09/0.26 % SubtermCWHack with pid 2457580 completed with status 0
% 0.09/0.26 % Result found by SubtermCWHack
% 0.09/0.26 % Preprocessing class: HSSSSMSSSSSNFFN.
% 0.09/0.26 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.09/0.26 % Starting new_ho_10 with 1500s (5) cores
% 0.09/0.26 % Starting ho_unfolding_6 with 300s (1) cores
% 0.09/0.26 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 1, sine = Auto)
% 0.09/0.26 % No SInE strategy applied
% 0.09/0.26 % Search class: HUUSS-FFSF21-MFFFFFNN
% 0.09/0.26 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.09/0.26 % Starting SubtermCWHack with 28s (1) cores
% 0.09/0.26 % Preprocessing time : 0.001 s
% 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 : 14
% 0.09/0.26 % Removed by relevancy pruning/SinE : 0
% 0.09/0.26 % Initial clauses : 14
% 0.09/0.26 % Removed in clause preprocessing : 10
% 0.09/0.26 % Initial clauses in saturation : 4
% 0.09/0.26 % Processed clauses : 4
% 0.09/0.26 % ...of these trivial : 0
% 0.09/0.26 % ...subsumed : 0
% 0.09/0.26 % ...remaining for further processing : 3
% 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 : 0
% 0.09/0.26 % Generated clauses : 0
% 0.09/0.26 % ...of the previous two non-redundant : 0
% 0.09/0.26 % ...aggressively subsumed : 0
% 0.09/0.26 % Contextual simplify-reflections : 0
% 0.09/0.26 % Paramodulations : 0
% 0.09/0.26 % Factorizations : 0
% 0.09/0.26 % NegExts : 0
% 0.09/0.26 % Equation resolutions : 0
% 0.09/0.26 % Disequality decompositions : 0
% 0.09/0.26 % Total rewrite steps : 7
% 0.09/0.26 % ...of those cached : 2
% 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 : 3
% 0.09/0.26 % Positive orientable unit clauses : 1
% 0.09/0.26 % Positive unorientable unit clauses: 2
% 0.09/0.26 % Negative unit clauses : 0
% 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 : 0
% 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 : 0
% 0.09/0.26 % Rewrite failures with RHS unbound : 0
% 0.09/0.26 % BW rewrite match attempts : 0
% 0.09/0.26 % BW rewrite match successes : 0
% 0.09/0.26 % Condensation attempts : 0
% 0.09/0.26 % Condensation successes : 0
% 0.09/0.26 % Termbank termtop insertions : 493
% 0.09/0.26 % Search garbage collected termcells : 19
% 0.09/0.26
% 0.09/0.26 % -------------------------------------------------
% 0.09/0.26 % User time : 0.002 s
% 0.09/0.26 % System time : 0.001 s
% 0.09/0.26 % Total time : 0.004 s
% 0.09/0.26 % Maximum resident set size: 3636 pages
% 0.09/0.26
% 0.09/0.26 % -------------------------------------------------
% 0.09/0.26 % User time : 0.003 s
% 0.09/0.26 % System time : 0.006 s
% 0.09/0.26 % Total time : 0.009 s
% 0.09/0.26 % Maximum resident set size: 4864 pages
% 0.09/0.26 % E exiting
%------------------------------------------------------------------------------