%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUM727^1 : 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 : 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 08:16:57 AM UTC 2026
% Result : Theorem 0.22s 0.31s
% Output : CNFRefutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 6
% Syntax : Number of formulae : 26 ( 20 unt; 0 typ; 0 def)
% Number of atoms : 32 ( 31 equ; 0 cnn)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 203 ( 9 ~; 5 |; 0 &; 188 @)
% ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Number of types : 2 ( 2 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 36 ( 0 ^; 36 !; 0 ?; 36 :)
% 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,
ts: nat > nat > nat ).
thf(decl_27,type,
num: frac > nat ).
thf(decl_28,type,
den: frac > nat ).
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.YOpvyT3e6H/E---3.1_2453611.p',satz31) ).
thf(satz33b,axiom,
! [X1: nat,X2: nat,X3: nat] :
( ( ( ts @ X1 @ X3 )
= ( ts @ X2 @ X3 ) )
=> ( X1 = X2 ) ),
file('/export/starexec/sandbox/tmp/tmp.YOpvyT3e6H/E---3.1_2453611.p',satz33b) ).
thf(satz29,axiom,
! [X1: nat,X2: nat] :
( ( ts @ X1 @ X2 )
= ( ts @ X2 @ X1 ) ),
file('/export/starexec/sandbox/tmp/tmp.YOpvyT3e6H/E---3.1_2453611.p',satz29) ).
thf(e,axiom,
( ( ts @ ( num @ x ) @ ( den @ y ) )
= ( ts @ ( num @ y ) @ ( den @ x ) ) ),
file('/export/starexec/sandbox/tmp/tmp.YOpvyT3e6H/E---3.1_2453611.p',e) ).
thf(satz39,conjecture,
( ( ts @ ( num @ x ) @ ( den @ z ) )
= ( ts @ ( num @ z ) @ ( den @ x ) ) ),
file('/export/starexec/sandbox/tmp/tmp.YOpvyT3e6H/E---3.1_2453611.p',satz39) ).
thf(f,axiom,
( ( ts @ ( num @ y ) @ ( den @ z ) )
= ( ts @ ( num @ z ) @ ( den @ y ) ) ),
file('/export/starexec/sandbox/tmp/tmp.YOpvyT3e6H/E---3.1_2453611.p',f) ).
thf(c_0_6,plain,
! [X17: nat,X18: nat,X19: nat] :
( ( ts @ ( ts @ X17 @ X18 ) @ X19 )
= ( ts @ X17 @ ( ts @ X18 @ X19 ) ) ),
inference(variable_rename,[status(thm)],[satz31]) ).
thf(c_0_7,plain,
! [X12: nat,X13: nat,X14: nat] :
( ( ( ts @ X12 @ X14 )
!= ( ts @ X13 @ X14 ) )
| ( X12 = X13 ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[satz33b])])]) ).
thf(c_0_8,plain,
! [X15: nat,X16: nat] :
( ( ts @ X15 @ X16 )
= ( ts @ X16 @ X15 ) ),
inference(variable_rename,[status(thm)],[satz29]) ).
thf(c_0_9,plain,
! [X1: nat,X2: nat,X3: nat] :
( ( ts @ ( ts @ X1 @ X2 ) @ X3 )
= ( ts @ X1 @ ( ts @ X2 @ X3 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
thf(c_0_10,plain,
( ( ts @ ( num @ x ) @ ( den @ y ) )
= ( ts @ ( num @ y ) @ ( den @ x ) ) ),
inference(split_conjunct,[status(thm)],[e]) ).
thf(c_0_11,plain,
! [X1: nat,X3: nat,X2: nat] :
( ( X1 = X3 )
| ( ( ts @ X1 @ X2 )
!= ( ts @ X3 @ X2 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
thf(c_0_12,plain,
! [X2: nat,X1: nat] :
( ( ts @ X1 @ X2 )
= ( ts @ X2 @ X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
thf(c_0_13,plain,
! [X1: nat] :
( ( ts @ ( num @ x ) @ ( ts @ ( den @ y ) @ X1 ) )
= ( ts @ ( num @ y ) @ ( ts @ ( den @ x ) @ X1 ) ) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_10]),c_0_9]) ).
thf(c_0_14,negated_conjecture,
( ( ts @ ( num @ x ) @ ( den @ z ) )
!= ( ts @ ( num @ z ) @ ( den @ x ) ) ),
inference(assume_negation,[status(cth)],[satz39]) ).
thf(c_0_15,plain,
! [X1: nat,X2: nat,X3: nat] :
( ( X1 = X2 )
| ( ( ts @ X3 @ X1 )
!= ( ts @ X2 @ X3 ) ) ),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
thf(c_0_16,plain,
! [X1: nat] :
( ( ts @ ( num @ x ) @ ( ts @ X1 @ ( den @ y ) ) )
= ( ts @ ( num @ y ) @ ( ts @ ( den @ x ) @ X1 ) ) ),
inference(spm,[status(thm)],[c_0_13,c_0_12]) ).
thf(c_0_17,plain,
( ( ts @ ( num @ y ) @ ( den @ z ) )
= ( ts @ ( num @ z ) @ ( den @ y ) ) ),
inference(split_conjunct,[status(thm)],[f]) ).
thf(c_0_18,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_9,c_0_12]),c_0_9]) ).
thf(c_0_19,negated_conjecture,
( ( ts @ ( num @ x ) @ ( den @ z ) )
!= ( ts @ ( num @ z ) @ ( den @ x ) ) ),
inference(fof_simplification,[status(thm)],[c_0_14]) ).
thf(c_0_20,plain,
! [X1: nat,X3: nat,X2: nat] :
( ( X1 = X2 )
| ( ( ts @ X3 @ X1 )
!= ( ts @ X3 @ X2 ) ) ),
inference(spm,[status(thm)],[c_0_15,c_0_12]) ).
thf(c_0_21,plain,
( ( ts @ ( num @ y ) @ ( ts @ ( num @ z ) @ ( den @ x ) ) )
= ( ts @ ( num @ y ) @ ( ts @ ( num @ x ) @ ( den @ z ) ) ) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_17]),c_0_18]),c_0_12]) ).
thf(c_0_22,negated_conjecture,
( ( ts @ ( num @ x ) @ ( den @ z ) )
!= ( ts @ ( num @ z ) @ ( den @ x ) ) ),
inference(fof_nnf,[status(thm)],[c_0_19]) ).
thf(c_0_23,plain,
! [X1: nat] :
( ( X1
= ( ts @ ( num @ z ) @ ( den @ x ) ) )
| ( ( ts @ ( num @ y ) @ X1 )
!= ( ts @ ( num @ y ) @ ( ts @ ( num @ x ) @ ( den @ z ) ) ) ) ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
thf(c_0_24,negated_conjecture,
( ( ts @ ( num @ x ) @ ( den @ z ) )
!= ( ts @ ( num @ z ) @ ( den @ x ) ) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
thf(c_0_25,plain,
$false,
inference(sr,[status(thm)],[inference(er,[status(thm)],[c_0_23]),c_0_24]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM727^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.18 % Computer : n003.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Tue Sep 29 12:47:13 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.22 Running higher-order theorem proving
% 0.08/0.24 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.YOpvyT3e6H/E---3.1_2453611.p
% 0.22/0.31 % Version: 3.5.1-ho
% 0.22/0.31 % Preprocessing class: HSSSSMSSSSSNFFN.
% 0.22/0.31 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/0.31 % Starting new_ho_10 with 1500s (5) cores
% 0.22/0.31 % Starting ho_unfolding_6 with 300s (1) cores
% 0.22/0.31 % Starting sh4l with 300s (1) cores
% 0.22/0.31 % Starting ehoh_best_nonlift_rwall with 300s (1) cores
% 0.22/0.31 % new_ho_10 with pid 2453624 completed with status 0
% 0.22/0.31 % Result found by new_ho_10
% 0.22/0.31 % Preprocessing class: HSSSSMSSSSSNFFN.
% 0.22/0.31 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/0.31 % Starting new_ho_10 with 1500s (5) cores
% 0.22/0.31 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.22/0.31 % No SInE strategy applied
% 0.22/0.31 % Search class: HHUPS-FFSF21-SFFFFFNN
% 0.22/0.31 % partial match(1): HUUPS-FFSF21-SFFFFFNN
% 0.22/0.31 % Scheduled 5 strats onto 5 cores with 1500 seconds (1500 total)
% 0.22/0.31 % Starting SubtermCWHack with 151s (1) cores
% 0.22/0.31 % Starting new_ho_10 with 901s (1) cores
% 0.22/0.31 % Starting sh5l with 151s (1) cores
% 0.22/0.31 % Starting new_bool_1 with 151s (1) cores
% 0.22/0.31 % Starting new_bool_2 with 146s (1) cores
% 0.22/0.31 % sh5l with pid 2453632 completed with status 0
% 0.22/0.31 % Result found by sh5l
% 0.22/0.31 % Preprocessing class: HSSSSMSSSSSNFFN.
% 0.22/0.31 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/0.31 % Starting new_ho_10 with 1500s (5) cores
% 0.22/0.31 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.22/0.31 % No SInE strategy applied
% 0.22/0.31 % Search class: HHUPS-FFSF21-SFFFFFNN
% 0.22/0.31 % partial match(1): HUUPS-FFSF21-SFFFFFNN
% 0.22/0.31 % Scheduled 5 strats onto 5 cores with 1500 seconds (1500 total)
% 0.22/0.31 % Starting SubtermCWHack with 151s (1) cores
% 0.22/0.31 % Starting new_ho_10 with 901s (1) cores
% 0.22/0.31 % Starting sh5l with 151s (1) cores
% 0.22/0.31 % Preprocessing time : 0.001 s
% 0.22/0.31 % Presaturation interreduction done
% 0.22/0.31
% 0.22/0.31 % Proof found!
% 0.22/0.31 % SZS status Theorem
% 0.22/0.31 % SZS output start CNFRefutation
% See solution above
% 0.22/0.31 % Parsed axioms : 14
% 0.22/0.31 % Removed by relevancy pruning/SinE : 0
% 0.22/0.31 % Initial clauses : 14
% 0.22/0.31 % Removed in clause preprocessing : 8
% 0.22/0.31 % Initial clauses in saturation : 6
% 0.22/0.31 % Processed clauses : 91
% 0.22/0.31 % ...of these trivial : 1
% 0.22/0.31 % ...subsumed : 48
% 0.22/0.31 % ...remaining for further processing : 42
% 0.22/0.31 % Other redundant clauses eliminated : 0
% 0.22/0.31 % Clauses deleted for lack of memory : 0
% 0.22/0.31 % Backward-subsumed : 0
% 0.22/0.31 % Backward-rewritten : 0
% 0.22/0.31 % Generated clauses : 682
% 0.22/0.31 % ...of the previous two non-redundant : 653
% 0.22/0.31 % ...aggressively subsumed : 0
% 0.22/0.31 % Contextual simplify-reflections : 0
% 0.22/0.31 % Paramodulations : 671
% 0.22/0.31 % Factorizations : 0
% 0.22/0.31 % NegExts : 0
% 0.22/0.31 % Equation resolutions : 11
% 0.22/0.31 % Disequality decompositions : 0
% 0.22/0.31 % Total rewrite steps : 266
% 0.22/0.31 % ...of those cached : 163
% 0.22/0.31 % Propositional unsat checks : 0
% 0.22/0.31 % Propositional check models : 0
% 0.22/0.31 % Propositional check unsatisfiable : 0
% 0.22/0.31 % Propositional clauses : 0
% 0.22/0.31 % Propositional clauses after purity: 0
% 0.22/0.31 % Propositional unsat core size : 0
% 0.22/0.31 % Propositional preprocessing time : 0.000
% 0.22/0.31 % Propositional encoding time : 0.000
% 0.22/0.31 % Propositional solver time : 0.000
% 0.22/0.31 % Success case prop preproc time : 0.000
% 0.22/0.31 % Success case prop encoding time : 0.000
% 0.22/0.31 % Success case prop solver time : 0.000
% 0.22/0.31 % Current number of processed clauses : 36
% 0.22/0.31 % Positive orientable unit clauses : 8
% 0.22/0.31 % Positive unorientable unit clauses: 3
% 0.22/0.31 % Negative unit clauses : 1
% 0.22/0.31 % Non-unit-clauses : 24
% 0.22/0.31 % Current number of unprocessed clauses: 574
% 0.22/0.31 % ...number of literals in the above : 1050
% 0.22/0.31 % Current number of archived formulas : 0
% 0.22/0.31 % Current number of archived clauses : 6
% 0.22/0.31 % Clause-clause subsumption calls (NU) : 339
% 0.22/0.31 % Rec. Clause-clause subsumption calls : 339
% 0.22/0.31 % Non-unit clause-clause subsumptions : 46
% 0.22/0.31 % Unit Clause-clause subsumption calls : 7
% 0.22/0.31 % Rewrite failures with RHS unbound : 0
% 0.22/0.31 % BW rewrite match attempts : 62
% 0.22/0.31 % BW rewrite match successes : 62
% 0.22/0.31 % Condensation attempts : 91
% 0.22/0.31 % Condensation successes : 0
% 0.22/0.31 % Termbank termtop insertions : 30841
% 0.22/0.31 % Search garbage collected termcells : 37
% 0.22/0.31
% 0.22/0.31 % -------------------------------------------------
% 0.22/0.31 % User time : 0.025 s
% 0.22/0.31 % System time : 0.004 s
% 0.22/0.31 % Total time : 0.029 s
% 0.22/0.31 % Maximum resident set size: 3632 pages
% 0.22/0.31
% 0.22/0.31 % -------------------------------------------------
% 0.22/0.31 % User time : 0.210 s
% 0.22/0.31 % System time : 0.017 s
% 0.22/0.31 % Total time : 0.227 s
% 0.22/0.31 % Maximum resident set size: 4864 pages
% 0.22/0.31 % E exiting
%------------------------------------------------------------------------------