%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : NUM726^4 : TPTP v9.3.1. Released v7.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/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 08:17:33 AM UTC 2026
% Result : Theorem 0.61s 0.43s
% Output : CNFRefutation 0.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 10
% Syntax : Number of formulae : 36 ( 32 unt; 0 typ; 0 def)
% Number of atoms : 72 ( 41 equ; 0 cnn)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 174 ( 4 ~; 0 |; 3 &; 159 @)
% ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 8 ( 8 >; 0 *; 0 +; 0 <<)
% Number of symbols : 20 ( 18 usr; 7 con; 0-3 aty)
% Number of variables : 59 ( 50 ^; 9 !; 0 ?; 59 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_23,type,
is_of: $i > ( $i > $o ) > $o ).
thf(decl_24,type,
all_of: ( $i > $o ) > ( $i > $o ) > $o ).
thf(decl_26,type,
in: $i > $i > $o ).
thf(decl_59,type,
ap: $i > $i > $i ).
thf(decl_78,type,
e_is: $i > $i > $i > $o ).
thf(decl_124,type,
nat: $i ).
thf(decl_125,type,
n_is: $i > $i > $o ).
thf(decl_163,type,
n_ts: $i > $i > $i ).
thf(decl_174,type,
n_1t: $i ).
thf(decl_175,type,
n_2t: $i ).
thf(decl_179,type,
first1: $i > $i > $i ).
thf(decl_180,type,
second1: $i > $i > $i ).
thf(decl_190,type,
frac: $i ).
thf(decl_192,type,
num: $i > $i ).
thf(decl_193,type,
den: $i > $i ).
thf(decl_194,type,
n_eq: $i > $i > $o ).
thf(decl_328,type,
esk130_0: $i ).
thf(decl_329,type,
esk131_0: $i ).
thf(def_e_is,axiom,
( e_is
= ( ^ [X1: $i,X101: $i,X102: $i] : ( X101 = X102 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.hdSMHQZtAg/E---3.1_701796.p',def_e_is) ).
thf(def_all_of,axiom,
( all_of
= ( ^ [X3: $i > $o,X2: $i > $o] :
! [X4: $i] :
( ( is_of @ X4 @ X3 )
=> ( X2 @ X4 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.hdSMHQZtAg/E---3.1_701796.p',def_all_of) ).
thf(def_is_of,axiom,
( is_of
= ( ^ [X1: $i,X2: $i > $o] : ( X2 @ X1 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.hdSMHQZtAg/E---3.1_701796.p',def_is_of) ).
thf(def_n_eq,axiom,
( n_eq
= ( ^ [X1: $i,X436: $i] : ( n_is @ ( n_ts @ ( num @ X1 ) @ ( den @ X436 ) ) @ ( n_ts @ ( num @ X436 ) @ ( den @ X1 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.hdSMHQZtAg/E---3.1_701796.p',def_n_eq) ).
thf(def_n_is,axiom,
( n_is
= ( ^ [Z0: $i,Z1: $i] : ( Z0 = Z1 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.hdSMHQZtAg/E---3.1_701796.p',def_n_is) ).
thf(def_first1,axiom,
( first1
= ( ^ [X1: $i,X427: $i] : ( ap @ X427 @ n_1t ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.hdSMHQZtAg/E---3.1_701796.p',def_first1) ).
thf(def_second1,axiom,
( second1
= ( ^ [X1: $i,X428: $i] : ( ap @ X428 @ n_2t ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.hdSMHQZtAg/E---3.1_701796.p',def_second1) ).
thf(satz38,conjecture,
( all_of
@ ^ [X1: $i] : ( in @ X1 @ frac )
@ ^ [X1: $i] :
( all_of
@ ^ [X437: $i] : ( in @ X437 @ frac )
@ ^ [X438: $i] :
( ( n_eq @ X1 @ X438 )
=> ( n_eq @ X438 @ X1 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.hdSMHQZtAg/E---3.1_701796.p',satz38) ).
thf(def_num,axiom,
( num
= ( first1 @ nat ) ),
file('/export/starexec/sandbox2/tmp/tmp.hdSMHQZtAg/E---3.1_701796.p',def_num) ).
thf(def_den,axiom,
( den
= ( second1 @ nat ) ),
file('/export/starexec/sandbox2/tmp/tmp.hdSMHQZtAg/E---3.1_701796.p',def_den) ).
thf(c_0_10,plain,
( e_is
= ( ^ [Z0: $i,Z1: $i,Z2: $i] : ( Z1 = Z2 ) ) ),
inference(fof_simplification,[status(thm)],[def_e_is]) ).
thf(c_0_11,plain,
( all_of
= ( ^ [Z0: $i > $o,Z1: $i > $o] :
! [X4: $i] :
( ( Z0 @ X4 )
=> ( Z1 @ X4 ) ) ) ),
inference(fof_simplification,[status(thm)],[def_all_of]) ).
thf(c_0_12,plain,
( is_of
= ( ^ [Z0: $i,Z1: $i > $o] : ( Z1 @ Z0 ) ) ),
inference(fof_simplification,[status(thm)],[def_is_of]) ).
thf(c_0_13,plain,
( n_eq
= ( ^ [Z0: $i,Z1: $i] :
( ( n_ts @ ( num @ Z0 ) @ ( den @ Z1 ) )
= ( n_ts @ ( num @ Z1 ) @ ( den @ Z0 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[def_n_eq]) ).
thf(c_0_14,axiom,
( n_is
= ( ^ [Z0: $i,Z1: $i] : ( Z0 = Z1 ) ) ),
inference(apply_def,[status(thm)],[def_n_is,c_0_10]) ).
thf(c_0_15,plain,
( first1
= ( ^ [Z0: $i,Z1: $i] : ( ap @ Z1 @ n_1t ) ) ),
inference(fof_simplification,[status(thm)],[def_first1]) ).
thf(c_0_16,plain,
( second1
= ( ^ [Z0: $i,Z1: $i] : ( ap @ Z1 @ n_2t ) ) ),
inference(fof_simplification,[status(thm)],[def_second1]) ).
thf(c_0_17,negated_conjecture,
~ ( all_of
@ ^ [X1: $i] : ( in @ X1 @ frac )
@ ^ [X1: $i] :
( all_of
@ ^ [X437: $i] : ( in @ X437 @ frac )
@ ^ [X438: $i] :
( ( n_eq @ X1 @ X438 )
=> ( n_eq @ X438 @ X1 ) ) ) ),
inference(assume_negation,[status(cth)],[satz38]) ).
thf(c_0_18,plain,
( all_of
= ( ^ [Z0: $i > $o,Z1: $i > $o] :
! [X4: $i] :
( ( Z0 @ X4 )
=> ( Z1 @ X4 ) ) ) ),
inference(apply_def,[status(thm)],[c_0_11,c_0_12]) ).
thf(c_0_19,plain,
( n_eq
= ( ^ [Z0: $i,Z1: $i] :
( ( n_ts @ ( num @ Z0 ) @ ( den @ Z1 ) )
= ( n_ts @ ( num @ Z1 ) @ ( den @ Z0 ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_13,c_0_14]) ).
thf(c_0_20,plain,
( first1
= ( ^ [Z0: $i,Z1: $i] : ( ap @ Z1 @ n_1t ) ) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
thf(c_0_21,plain,
( second1
= ( ^ [Z0: $i,Z1: $i] : ( ap @ Z1 @ n_2t ) ) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
thf(c_0_22,negated_conjecture,
~ ! [X1253: $i] :
( ( in @ X1253 @ frac )
=> ! [X1252: $i] :
( ( in @ X1252 @ frac )
=> ( ( ( n_ts @ ( num @ X1253 ) @ ( den @ X1252 ) )
= ( n_ts @ ( num @ X1252 ) @ ( den @ X1253 ) ) )
=> ( ( n_ts @ ( num @ X1252 ) @ ( den @ X1253 ) )
= ( n_ts @ ( num @ X1253 ) @ ( den @ X1252 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[c_0_17]),c_0_18]),c_0_19]) ).
thf(c_0_23,plain,
( num
= ( first1 @ nat ) ),
inference(split_conjunct,[status(thm)],[def_num]) ).
thf(c_0_24,plain,
! [X1: $i] :
( ( first1 @ X1 )
= ( ^ [Z0: $i] : ( ap @ Z0 @ n_1t ) ) ),
inference(arg_cong,[status(thm)],[c_0_20]) ).
thf(c_0_25,plain,
( den
= ( second1 @ nat ) ),
inference(split_conjunct,[status(thm)],[def_den]) ).
thf(c_0_26,plain,
! [X1: $i] :
( ( second1 @ X1 )
= ( ^ [Z0: $i] : ( ap @ Z0 @ n_2t ) ) ),
inference(arg_cong,[status(thm)],[c_0_21]) ).
thf(c_0_27,negated_conjecture,
( ( in @ esk130_0 @ frac )
& ( in @ esk131_0 @ frac )
& ( ( n_ts @ ( num @ esk130_0 ) @ ( den @ esk131_0 ) )
= ( n_ts @ ( num @ esk131_0 ) @ ( den @ esk130_0 ) ) )
& ( ( n_ts @ ( num @ esk131_0 ) @ ( den @ esk130_0 ) )
!= ( n_ts @ ( num @ esk130_0 ) @ ( den @ esk131_0 ) ) ) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_22])])])]) ).
thf(c_0_28,plain,
( num
= ( ^ [Z0: $i] : ( ap @ Z0 @ n_1t ) ) ),
inference(rw,[status(thm)],[c_0_23,c_0_24]) ).
thf(c_0_29,plain,
( den
= ( ^ [Z0: $i] : ( ap @ Z0 @ n_2t ) ) ),
inference(rw,[status(thm)],[c_0_25,c_0_26]) ).
thf(c_0_30,negated_conjecture,
( ( n_ts @ ( num @ esk130_0 ) @ ( den @ esk131_0 ) )
= ( n_ts @ ( num @ esk131_0 ) @ ( den @ esk130_0 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
thf(c_0_31,plain,
! [X1: $i] :
( ( num @ X1 )
= ( ap @ X1 @ n_1t ) ),
inference(arg_cong,[status(thm)],[c_0_28]) ).
thf(c_0_32,plain,
! [X1: $i] :
( ( den @ X1 )
= ( ap @ X1 @ n_2t ) ),
inference(arg_cong,[status(thm)],[c_0_29]) ).
thf(c_0_33,negated_conjecture,
( ( n_ts @ ( num @ esk131_0 ) @ ( den @ esk130_0 ) )
!= ( n_ts @ ( num @ esk130_0 ) @ ( den @ esk131_0 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
thf(c_0_34,negated_conjecture,
( ( n_ts @ ( ap @ esk131_0 @ n_1t ) @ ( ap @ esk130_0 @ n_2t ) )
= ( n_ts @ ( ap @ esk130_0 @ n_1t ) @ ( ap @ esk131_0 @ n_2t ) ) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_30,c_0_31]),c_0_32]),c_0_31]),c_0_32]) ).
thf(c_0_35,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)],[c_0_33,c_0_31]),c_0_32]),c_0_34]),c_0_31]),c_0_32])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM726^4 : TPTP v9.3.1. Released v7.1.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.18 % Computer : n019.cluster.edu
% 0.11/0.18 % Model : x86_64 x86_64
% 0.11/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.18 % Memory : 8046.5625MB
% 0.11/0.18 % OS : Linux 6.8.0-71-generic
% 0.11/0.18 % CPULimit : 300
% 0.11/0.18 % WCLimit : 300
% 0.11/0.18 % DateTime : Tue Sep 29 12:45:32 UTC 2026
% 0.11/0.18 % CPUTime :
% 0.11/0.18 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.22 Running higher-order theorem proving
% 0.11/0.28 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.hdSMHQZtAg/E---3.1_701796.p
% 0.61/0.43 % Version: 3.5.1-ho
% 0.61/0.43 % Preprocessing class: HSLMSMSMLMLCHSA.
% 0.61/0.43 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.61/0.43 % Starting new_ho_10 with 1500s (5) cores
% 0.61/0.43 % Starting ho_unfolding_6 with 300s (1) cores
% 0.61/0.43 % Starting sh4l with 300s (1) cores
% 0.61/0.43 % Starting ehoh_best_nonlift_nonlambdatoforall with 300s (1) cores
% 0.61/0.43 % sh4l with pid 701830 completed with status 0
% 0.61/0.43 % Result found by sh4l
% 0.61/0.43 % Preprocessing class: HSLMSMSMLMLCHSA.
% 0.61/0.43 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.61/0.43 % Starting new_ho_10 with 1500s (5) cores
% 0.61/0.43 % Starting ho_unfolding_6 with 300s (1) cores
% 0.61/0.43 % Starting sh4l with 300s (1) cores
% 0.61/0.43 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 1, sine = Auto)
% 0.61/0.43 % No SInE strategy applied
% 0.61/0.43 % Search class: HGHSM-FSLM32-DHSMSSBN
% 0.61/0.43 % partial match(1): HGHSM-FSLM32-MHSMSSBN
% 0.61/0.43 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.61/0.43 % Starting SubtermCWHack with 31s (1) cores
% 0.61/0.43 % SubtermCWHack with pid 701838 completed with status 0
% 0.61/0.43 % Result found by SubtermCWHack
% 0.61/0.43 % Preprocessing class: HSLMSMSMLMLCHSA.
% 0.61/0.43 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.61/0.43 % Starting new_ho_10 with 1500s (5) cores
% 0.61/0.43 % Starting ho_unfolding_6 with 300s (1) cores
% 0.61/0.43 % Starting sh4l with 300s (1) cores
% 0.61/0.43 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 1, sine = Auto)
% 0.61/0.43 % No SInE strategy applied
% 0.61/0.43 % Search class: HGHSM-FSLM32-DHSMSSBN
% 0.61/0.43 % partial match(1): HGHSM-FSLM32-MHSMSSBN
% 0.61/0.43 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.61/0.43 % Starting SubtermCWHack with 31s (1) cores
% 0.61/0.43 % Preprocessing time : 0.010 s
% 0.61/0.43
% 0.61/0.43 % Proof found!
% 0.61/0.43 % SZS status Theorem
% 0.61/0.43 % SZS output start CNFRefutation
% See solution above
% 0.61/0.43 % Parsed axioms : 531
% 0.61/0.43 % Removed by relevancy pruning/SinE : 0
% 0.61/0.43 % Initial clauses : 1633
% 0.61/0.43 % Removed in clause preprocessing : 1100
% 0.61/0.43 % Initial clauses in saturation : 533
% 0.61/0.43 % Processed clauses : 385
% 0.61/0.43 % ...of these trivial : 48
% 0.61/0.43 % ...subsumed : 70
% 0.61/0.43 % ...remaining for further processing : 266
% 0.61/0.43 % Other redundant clauses eliminated : 13
% 0.61/0.43 % Clauses deleted for lack of memory : 0
% 0.61/0.43 % Backward-subsumed : 1
% 0.61/0.43 % Backward-rewritten : 5
% 0.61/0.43 % Generated clauses : 579
% 0.61/0.43 % ...of the previous two non-redundant : 547
% 0.61/0.43 % ...aggressively subsumed : 0
% 0.61/0.43 % Contextual simplify-reflections : 0
% 0.61/0.43 % Paramodulations : 411
% 0.61/0.43 % Factorizations : 0
% 0.61/0.43 % NegExts : 0
% 0.61/0.43 % Equation resolutions : 14
% 0.61/0.43 % Disequality decompositions : 0
% 0.61/0.43 % Total rewrite steps : 104
% 0.61/0.43 % ...of those cached : 38
% 0.61/0.43 % Propositional unsat checks : 0
% 0.61/0.43 % Propositional check models : 0
% 0.61/0.43 % Propositional check unsatisfiable : 0
% 0.61/0.43 % Propositional clauses : 0
% 0.61/0.43 % Propositional clauses after purity: 0
% 0.61/0.43 % Propositional unsat core size : 0
% 0.61/0.43 % Propositional preprocessing time : 0.000
% 0.61/0.43 % Propositional encoding time : 0.000
% 0.61/0.43 % Propositional solver time : 0.000
% 0.61/0.43 % Success case prop preproc time : 0.000
% 0.61/0.43 % Success case prop encoding time : 0.000
% 0.61/0.43 % Success case prop solver time : 0.000
% 0.61/0.43 % Current number of processed clauses : 260
% 0.61/0.43 % Positive orientable unit clauses : 135
% 0.61/0.43 % Positive unorientable unit clauses: 2
% 0.61/0.43 % Negative unit clauses : 13
% 0.61/0.43 % Non-unit-clauses : 110
% 0.61/0.43 % Current number of unprocessed clauses: 695
% 0.61/0.43 % ...number of literals in the above : 3097
% 0.61/0.43 % Current number of archived formulas : 0
% 0.61/0.43 % Current number of archived clauses : 6
% 0.61/0.43 % Clause-clause subsumption calls (NU) : 2336
% 0.61/0.43 % Rec. Clause-clause subsumption calls : 2175
% 0.61/0.43 % Non-unit clause-clause subsumptions : 50
% 0.61/0.43 % Unit Clause-clause subsumption calls : 1017
% 0.61/0.43 % Rewrite failures with RHS unbound : 0
% 0.61/0.43 % BW rewrite match attempts : 142
% 0.61/0.43 % BW rewrite match successes : 7
% 0.61/0.43 % Condensation attempts : 0
% 0.61/0.43 % Condensation successes : 0
% 0.61/0.43 % Termbank termtop insertions : 183459
% 0.61/0.43 % Search garbage collected termcells : 69266
% 0.61/0.43
% 0.61/0.43 % -------------------------------------------------
% 0.61/0.43 % User time : 0.096 s
% 0.61/0.43 % System time : 0.020 s
% 0.61/0.43 % Total time : 0.116 s
% 0.61/0.43 % Maximum resident set size: 12728 pages
% 0.61/0.43
% 0.61/0.43 % -------------------------------------------------
% 0.61/0.43 % User time : 0.113 s
% 0.61/0.43 % System time : 0.026 s
% 0.61/0.43 % Total time : 0.139 s
% 0.61/0.43 % Maximum resident set size: 5632 pages
% 0.61/0.43 % E exiting
%------------------------------------------------------------------------------