%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUM741^1 : 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 : n019.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 08:16:59 AM UTC 2026
% Result : Theorem 0.32s 0.45s
% Output : CNFRefutation 0.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 7
% Syntax : Number of formulae : 32 ( 20 unt; 0 typ; 0 def)
% Number of atoms : 47 ( 8 equ; 0 cnn)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 337 ( 16 ~; 12 |; 0 &; 306 @)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 7 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 63 ( 0 ^; 63 !; 0 ?; 63 :)
% 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,
z: frac ).
thf(decl_26,type,
less: nat > nat > $o ).
thf(decl_27,type,
ts: nat > nat > nat ).
thf(decl_28,type,
num: frac > nat ).
thf(decl_29,type,
den: frac > nat ).
thf(satz33c,axiom,
! [X1: nat,X2: nat,X3: nat] :
( ( less @ ( ts @ X1 @ X3 ) @ ( ts @ X2 @ X3 ) )
=> ( less @ X1 @ X2 ) ),
file('/export/starexec/sandbox/tmp/tmp.c3awk21A4P/E---3.1_705986.p',satz33c) ).
thf(satz29,axiom,
! [X1: nat,X2: nat] :
( ( ts @ X1 @ X2 )
= ( ts @ X2 @ X1 ) ),
file('/export/starexec/sandbox/tmp/tmp.c3awk21A4P/E---3.1_705986.p',satz29) ).
thf(satz31,axiom,
! [X1: nat,X2: nat,X3: nat] :
( ( ts @ ( ts @ X1 @ X2 ) @ X3 )
= ( ts @ X1 @ ( ts @ X2 @ X3 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.c3awk21A4P/E---3.1_705986.p',satz31) ).
thf(satz34a,axiom,
! [X1: nat,X2: nat,X3: nat,X4: nat] :
( ( less @ X1 @ X2 )
=> ( ( less @ X3 @ X4 )
=> ( less @ ( ts @ X1 @ X3 ) @ ( ts @ X2 @ X4 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.c3awk21A4P/E---3.1_705986.p',satz34a) ).
thf(l,axiom,
less @ ( ts @ ( num @ x ) @ ( den @ y ) ) @ ( ts @ ( num @ y ) @ ( den @ x ) ),
file('/export/starexec/sandbox/tmp/tmp.c3awk21A4P/E---3.1_705986.p',l) ).
thf(satz50,conjecture,
less @ ( ts @ ( num @ x ) @ ( den @ z ) ) @ ( ts @ ( num @ z ) @ ( den @ x ) ),
file('/export/starexec/sandbox/tmp/tmp.c3awk21A4P/E---3.1_705986.p',satz50) ).
thf(k,axiom,
less @ ( ts @ ( num @ y ) @ ( den @ z ) ) @ ( ts @ ( num @ z ) @ ( den @ y ) ),
file('/export/starexec/sandbox/tmp/tmp.c3awk21A4P/E---3.1_705986.p',k) ).
thf(c_0_7,plain,
! [X17: nat,X18: nat,X19: nat] :
( ~ ( less @ ( ts @ X17 @ X19 ) @ ( ts @ X18 @ X19 ) )
| ( less @ X17 @ X18 ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[satz33c])])]) ).
thf(c_0_8,plain,
! [X24: nat,X25: nat] :
( ( ts @ X24 @ X25 )
= ( ts @ X25 @ X24 ) ),
inference(variable_rename,[status(thm)],[satz29]) ).
thf(c_0_9,plain,
! [X1: nat,X3: nat,X2: nat] :
( ( less @ X1 @ X3 )
| ~ ( less @ ( ts @ X1 @ X2 ) @ ( ts @ X3 @ X2 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
thf(c_0_10,plain,
! [X2: nat,X1: nat] :
( ( ts @ X1 @ X2 )
= ( ts @ X2 @ X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
thf(c_0_11,plain,
! [X26: nat,X27: nat,X28: nat] :
( ( ts @ ( ts @ X26 @ X27 ) @ X28 )
= ( ts @ X26 @ ( ts @ X27 @ X28 ) ) ),
inference(variable_rename,[status(thm)],[satz31]) ).
thf(c_0_12,plain,
! [X20: nat,X21: nat,X22: nat,X23: nat] :
( ~ ( less @ X20 @ X21 )
| ~ ( less @ X22 @ X23 )
| ( less @ ( ts @ X20 @ X22 ) @ ( ts @ X21 @ X23 ) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[satz34a])])]) ).
thf(c_0_13,plain,
! [X1: nat,X2: nat,X3: nat] :
( ( less @ X1 @ X2 )
| ~ ( less @ ( ts @ X3 @ X1 ) @ ( ts @ X2 @ X3 ) ) ),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
thf(c_0_14,plain,
! [X1: nat,X2: nat,X3: nat] :
( ( ts @ ( ts @ X1 @ X2 ) @ X3 )
= ( ts @ X1 @ ( ts @ X2 @ X3 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
thf(c_0_15,plain,
! [X1: nat,X2: nat,X3: nat,X4: nat] :
( ( less @ ( ts @ X1 @ X3 ) @ ( ts @ X2 @ X4 ) )
| ~ ( less @ X1 @ X2 )
| ~ ( less @ X3 @ X4 ) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
thf(c_0_16,plain,
less @ ( ts @ ( num @ x ) @ ( den @ y ) ) @ ( ts @ ( num @ y ) @ ( den @ x ) ),
inference(split_conjunct,[status(thm)],[l]) ).
thf(c_0_17,negated_conjecture,
~ ( less @ ( ts @ ( num @ x ) @ ( den @ z ) ) @ ( ts @ ( num @ z ) @ ( den @ x ) ) ),
inference(assume_negation,[status(cth)],[satz50]) ).
thf(c_0_18,plain,
! [X1: nat,X3: nat,X2: nat] :
( ( less @ X1 @ X2 )
| ~ ( less @ ( ts @ X3 @ X1 ) @ ( ts @ X3 @ X2 ) ) ),
inference(spm,[status(thm)],[c_0_13,c_0_10]) ).
thf(c_0_19,plain,
! [X1: nat,X3: nat,X2: nat] :
( ( ts @ X1 @ ( ts @ X2 @ X3 ) )
= ( ts @ X3 @ ( ts @ X1 @ X2 ) ) ),
inference(spm,[status(thm)],[c_0_10,c_0_14]) ).
thf(c_0_20,plain,
! [X1: nat,X2: nat] :
( ( less @ ( ts @ X1 @ ( ts @ ( num @ x ) @ ( den @ y ) ) ) @ ( ts @ X2 @ ( ts @ ( num @ y ) @ ( den @ x ) ) ) )
| ~ ( less @ X1 @ X2 ) ),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
thf(c_0_21,plain,
less @ ( ts @ ( num @ y ) @ ( den @ z ) ) @ ( ts @ ( num @ z ) @ ( den @ y ) ),
inference(split_conjunct,[status(thm)],[k]) ).
thf(c_0_22,plain,
! [X1: nat,X2: nat,X3: nat] :
( ( ts @ X1 @ ( ts @ X2 @ X3 ) )
= ( ts @ X2 @ ( ts @ X1 @ X3 ) ) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_10]),c_0_14]) ).
thf(c_0_23,negated_conjecture,
~ ( less @ ( ts @ ( num @ x ) @ ( den @ z ) ) @ ( ts @ ( num @ z ) @ ( den @ x ) ) ),
inference(fof_simplification,[status(thm)],[c_0_17]) ).
thf(c_0_24,plain,
! [X1: nat,X2: nat,X3: nat,X4: nat] :
( ( less @ X1 @ ( ts @ X2 @ X3 ) )
| ~ ( less @ ( ts @ X4 @ X1 ) @ ( ts @ X2 @ ( ts @ X3 @ X4 ) ) ) ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
thf(c_0_25,plain,
! [X2: nat,X1: nat,X4: nat,X3: nat] :
( ( less @ ( ts @ X1 @ X2 ) @ X3 )
| ~ ( less @ ( ts @ X2 @ ( ts @ X4 @ X1 ) ) @ ( ts @ X4 @ X3 ) ) ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
thf(c_0_26,plain,
less @ ( ts @ ( num @ x ) @ ( ts @ ( num @ y ) @ ( ts @ ( den @ y ) @ ( den @ z ) ) ) ) @ ( ts @ ( num @ y ) @ ( ts @ ( num @ z ) @ ( ts @ ( den @ x ) @ ( den @ y ) ) ) ),
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)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_14]),c_0_14]),c_0_22]),c_0_10]),c_0_22]),c_0_22]),c_0_10]),c_0_22]) ).
thf(c_0_27,negated_conjecture,
~ ( less @ ( ts @ ( num @ x ) @ ( den @ z ) ) @ ( ts @ ( num @ z ) @ ( den @ x ) ) ),
inference(fof_nnf,[status(thm)],[c_0_23]) ).
thf(c_0_28,plain,
! [X2: nat,X1: nat,X3: nat,X4: nat,X5: nat] :
( ( less @ ( ts @ X1 @ X2 ) @ ( ts @ X3 @ X4 ) )
| ~ ( less @ ( ts @ X2 @ ( ts @ X5 @ X1 ) ) @ ( ts @ X3 @ ( ts @ X4 @ X5 ) ) ) ),
inference(spm,[status(thm)],[c_0_24,c_0_19]) ).
thf(c_0_29,plain,
less @ ( ts @ ( num @ x ) @ ( ts @ ( den @ y ) @ ( den @ z ) ) ) @ ( ts @ ( num @ z ) @ ( ts @ ( den @ x ) @ ( den @ y ) ) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_14]),c_0_10]),c_0_22]) ).
thf(c_0_30,negated_conjecture,
~ ( less @ ( ts @ ( num @ x ) @ ( den @ z ) ) @ ( ts @ ( num @ z ) @ ( den @ x ) ) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
thf(c_0_31,plain,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_10]),c_0_30]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : NUM741^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.07 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.23/0.27 % Computer : n019.cluster.edu
% 0.23/0.27 % Model : x86_64 x86_64
% 0.23/0.27 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.23/0.27 % Memory : 8046.5625MB
% 0.23/0.27 % OS : Linux 6.8.0-71-generic
% 0.23/0.27 % CPULimit : 300
% 0.23/0.27 % WCLimit : 300
% 0.23/0.27 % DateTime : Tue Sep 29 12:47:17 UTC 2026
% 0.23/0.28 % CPUTime :
% 0.23/0.28 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.23/0.33 Running higher-order theorem proving
% 0.23/0.35 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.c3awk21A4P/E---3.1_705986.p
% 0.32/0.45 % Version: 3.5.1-ho
% 0.32/0.45 % Preprocessing class: HSMSSMSSSSSNFFN.
% 0.32/0.45 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.32/0.45 % Starting new_ho_10 with 1500s (5) cores
% 0.32/0.45 % Starting new_bool_1 with 300s (1) cores
% 0.32/0.45 % Starting full_lambda_5 with 300s (1) cores
% 0.32/0.45 % Starting new_ho_10_unif with 300s (1) cores
% 0.32/0.45 % new_ho_10 with pid 705999 completed with status 0
% 0.32/0.45 % Result found by new_ho_10
% 0.32/0.45 % Preprocessing class: HSMSSMSSSSSNFFN.
% 0.32/0.45 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.32/0.45 % Starting new_ho_10 with 1500s (5) cores
% 0.32/0.45 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.32/0.45 % No SInE strategy applied
% 0.32/0.45 % Search class: HHUSS-FFSF21-SFFFFFNN
% 0.32/0.45 % partial match(1): FHUSS-FFSF21-SFFFFFNN
% 0.32/0.45 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.32/0.45 % Starting SubtermCWHack with 136s (1) cores
% 0.32/0.45 % Starting new_ho_10 with 151s (1) cores
% 0.32/0.45 % Starting G-E--_208_B00_00_F1_SE_CS_SP_PS_S064A with 136s (1) cores
% 0.32/0.45 % Starting new_bool_3 with 136s (1) cores
% 0.32/0.45 % Starting new_bool_1 with 136s (1) cores
% 0.32/0.45 % new_bool_1 with pid 706010 completed with status 0
% 0.32/0.45 % Result found by new_bool_1
% 0.32/0.45 % Preprocessing class: HSMSSMSSSSSNFFN.
% 0.32/0.45 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.32/0.45 % Starting new_ho_10 with 1500s (5) cores
% 0.32/0.45 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.32/0.45 % No SInE strategy applied
% 0.32/0.45 % Search class: HHUSS-FFSF21-SFFFFFNN
% 0.32/0.45 % partial match(1): FHUSS-FFSF21-SFFFFFNN
% 0.32/0.45 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.32/0.45 % Starting SubtermCWHack with 136s (1) cores
% 0.32/0.45 % Starting new_ho_10 with 151s (1) cores
% 0.32/0.45 % Starting G-E--_208_B00_00_F1_SE_CS_SP_PS_S064A with 136s (1) cores
% 0.32/0.45 % Starting new_bool_3 with 136s (1) cores
% 0.32/0.45 % Starting new_bool_1 with 136s (1) cores
% 0.32/0.45 % Preprocessing time : 0.001 s
% 0.32/0.45 % Presaturation interreduction done
% 0.32/0.45
% 0.32/0.45 % Proof found!
% 0.32/0.45 % SZS status Theorem
% 0.32/0.45 % SZS output start CNFRefutation
% See solution above
% 0.32/0.45 % Parsed axioms : 16
% 0.32/0.45 % Removed by relevancy pruning/SinE : 0
% 0.32/0.45 % Initial clauses : 16
% 0.32/0.45 % Removed in clause preprocessing : 9
% 0.32/0.45 % Initial clauses in saturation : 7
% 0.32/0.45 % Processed clauses : 589
% 0.32/0.45 % ...of these trivial : 12
% 0.32/0.45 % ...subsumed : 488
% 0.32/0.45 % ...remaining for further processing : 89
% 0.32/0.45 % Other redundant clauses eliminated : 0
% 0.32/0.45 % Clauses deleted for lack of memory : 0
% 0.32/0.45 % Backward-subsumed : 0
% 0.32/0.45 % Backward-rewritten : 0
% 0.32/0.45 % Generated clauses : 2498
% 0.32/0.45 % ...of the previous two non-redundant : 2478
% 0.32/0.45 % ...aggressively subsumed : 0
% 0.32/0.45 % Contextual simplify-reflections : 0
% 0.32/0.45 % Paramodulations : 2498
% 0.32/0.45 % Factorizations : 0
% 0.32/0.45 % NegExts : 0
% 0.32/0.45 % Equation resolutions : 0
% 0.32/0.45 % Disequality decompositions : 0
% 0.32/0.45 % Total rewrite steps : 1124
% 0.32/0.45 % ...of those cached : 914
% 0.32/0.45 % Propositional unsat checks : 0
% 0.32/0.45 % Propositional check models : 0
% 0.32/0.45 % Propositional check unsatisfiable : 0
% 0.32/0.45 % Propositional clauses : 0
% 0.32/0.45 % Propositional clauses after purity: 0
% 0.32/0.45 % Propositional unsat core size : 0
% 0.32/0.45 % Propositional preprocessing time : 0.000
% 0.32/0.45 % Propositional encoding time : 0.000
% 0.32/0.45 % Propositional solver time : 0.000
% 0.32/0.45 % Success case prop preproc time : 0.000
% 0.32/0.45 % Success case prop encoding time : 0.000
% 0.32/0.45 % Success case prop solver time : 0.000
% 0.32/0.45 % Current number of processed clauses : 82
% 0.32/0.45 % Positive orientable unit clauses : 7
% 0.32/0.45 % Positive unorientable unit clauses: 4
% 0.32/0.45 % Negative unit clauses : 1
% 0.32/0.45 % Non-unit-clauses : 70
% 0.32/0.45 % Current number of unprocessed clauses: 1867
% 0.32/0.45 % ...number of literals in the above : 3676
% 0.32/0.45 % Current number of archived formulas : 0
% 0.32/0.45 % Current number of archived clauses : 7
% 0.32/0.45 % Clause-clause subsumption calls (NU) : 6880
% 0.32/0.45 % Rec. Clause-clause subsumption calls : 6880
% 0.32/0.45 % Non-unit clause-clause subsumptions : 451
% 0.32/0.45 % Unit Clause-clause subsumption calls : 10
% 0.32/0.45 % Rewrite failures with RHS unbound : 0
% 0.32/0.45 % BW rewrite match attempts : 94
% 0.32/0.45 % BW rewrite match successes : 82
% 0.32/0.45 % Condensation attempts : 0
% 0.32/0.45 % Condensation successes : 0
% 0.32/0.45 % Termbank termtop insertions : 62526
% 0.32/0.45 % Search garbage collected termcells : 76
% 0.32/0.45
% 0.32/0.45 % -------------------------------------------------
% 0.32/0.45 % User time : 0.057 s
% 0.32/0.45 % System time : 0.006 s
% 0.32/0.45 % Total time : 0.063 s
% 0.32/0.45 % Maximum resident set size: 3636 pages
% 0.32/0.45
% 0.32/0.45 % -------------------------------------------------
% 0.32/0.45 % User time : 0.318 s
% 0.32/0.45 % System time : 0.023 s
% 0.32/0.45 % Total time : 0.341 s
% 0.32/0.45 % Maximum resident set size: 4864 pages
% 0.32/0.45 % E exiting
%------------------------------------------------------------------------------