%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUM737^1 : 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 : n004.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 08:16:58 AM UTC 2026
% Result : Theorem 6.20s 1.22s
% Output : CNFRefutation 6.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 8
% Syntax : Number of formulae : 40 ( 28 unt; 0 typ; 0 def)
% Number of atoms : 52 ( 14 equ; 0 cnn)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 414 ( 14 ~; 10 |; 0 &; 388 @)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 6 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 62 ( 0 ^; 62 !; 0 ?; 62 :)
% 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,
u: frac ).
thf(decl_27,type,
more: nat > nat > $o ).
thf(decl_28,type,
ts: nat > nat > nat ).
thf(decl_29,type,
num: frac > nat ).
thf(decl_30,type,
den: frac > nat ).
thf(satz32d,axiom,
! [X1: nat,X2: nat,X3: nat] :
( ( more @ X1 @ X2 )
=> ( more @ ( ts @ X3 @ X1 ) @ ( ts @ X3 @ X2 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.Jp4TLCY8zu/E---3.1_1228303.p',satz32d) ).
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.Jp4TLCY8zu/E---3.1_1228303.p',satz31) ).
thf(satz33a,axiom,
! [X1: nat,X2: nat,X3: nat] :
( ( more @ ( ts @ X1 @ X3 ) @ ( ts @ X2 @ X3 ) )
=> ( more @ X1 @ X2 ) ),
file('/export/starexec/sandbox/tmp/tmp.Jp4TLCY8zu/E---3.1_1228303.p',satz33a) ).
thf(m,axiom,
more @ ( ts @ ( num @ x ) @ ( den @ y ) ) @ ( ts @ ( num @ y ) @ ( den @ x ) ),
file('/export/starexec/sandbox/tmp/tmp.Jp4TLCY8zu/E---3.1_1228303.p',m) ).
thf(satz29,axiom,
! [X1: nat,X2: nat] :
( ( ts @ X1 @ X2 )
= ( ts @ X2 @ X1 ) ),
file('/export/starexec/sandbox/tmp/tmp.Jp4TLCY8zu/E---3.1_1228303.p',satz29) ).
thf(f,axiom,
( ( ts @ ( num @ y ) @ ( den @ u ) )
= ( ts @ ( num @ u ) @ ( den @ y ) ) ),
file('/export/starexec/sandbox/tmp/tmp.Jp4TLCY8zu/E---3.1_1228303.p',f) ).
thf(e,axiom,
( ( ts @ ( num @ x ) @ ( den @ z ) )
= ( ts @ ( num @ z ) @ ( den @ x ) ) ),
file('/export/starexec/sandbox/tmp/tmp.Jp4TLCY8zu/E---3.1_1228303.p',e) ).
thf(satz44,conjecture,
more @ ( ts @ ( num @ z ) @ ( den @ u ) ) @ ( ts @ ( num @ u ) @ ( den @ z ) ),
file('/export/starexec/sandbox/tmp/tmp.Jp4TLCY8zu/E---3.1_1228303.p',satz44) ).
thf(c_0_8,plain,
! [X22: nat,X23: nat,X24: nat] :
( ~ ( more @ X22 @ X23 )
| ( more @ ( ts @ X24 @ X22 ) @ ( ts @ X24 @ X23 ) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[satz32d])])]) ).
thf(c_0_9,plain,
! [X27: nat,X28: nat,X29: nat] :
( ( ts @ ( ts @ X27 @ X28 ) @ X29 )
= ( ts @ X27 @ ( ts @ X28 @ X29 ) ) ),
inference(variable_rename,[status(thm)],[satz31]) ).
thf(c_0_10,plain,
! [X19: nat,X20: nat,X21: nat] :
( ~ ( more @ ( ts @ X19 @ X21 ) @ ( ts @ X20 @ X21 ) )
| ( more @ X19 @ X20 ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[satz33a])])]) ).
thf(c_0_11,plain,
! [X1: nat,X3: nat,X2: nat] :
( ( more @ ( ts @ X3 @ X1 ) @ ( ts @ X3 @ X2 ) )
| ~ ( more @ X1 @ X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
thf(c_0_12,plain,
more @ ( ts @ ( num @ x ) @ ( den @ y ) ) @ ( ts @ ( num @ y ) @ ( den @ x ) ),
inference(split_conjunct,[status(thm)],[m]) ).
thf(c_0_13,plain,
! [X25: nat,X26: nat] :
( ( ts @ X25 @ X26 )
= ( ts @ X26 @ X25 ) ),
inference(variable_rename,[status(thm)],[satz29]) ).
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_9]) ).
thf(c_0_15,plain,
( ( ts @ ( num @ y ) @ ( den @ u ) )
= ( ts @ ( num @ u ) @ ( den @ y ) ) ),
inference(split_conjunct,[status(thm)],[f]) ).
thf(c_0_16,plain,
! [X1: nat,X3: nat,X2: nat] :
( ( more @ X1 @ X3 )
| ~ ( more @ ( ts @ X1 @ X2 ) @ ( ts @ X3 @ X2 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
thf(c_0_17,plain,
! [X1: nat] : ( more @ ( ts @ X1 @ ( ts @ ( num @ x ) @ ( den @ y ) ) ) @ ( ts @ X1 @ ( ts @ ( num @ y ) @ ( den @ x ) ) ) ),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
thf(c_0_18,plain,
! [X2: nat,X1: nat] :
( ( ts @ X1 @ X2 )
= ( ts @ X2 @ X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
thf(c_0_19,plain,
! [X1: nat] :
( ( ts @ ( num @ y ) @ ( ts @ ( den @ u ) @ X1 ) )
= ( ts @ ( num @ u ) @ ( ts @ ( den @ y ) @ X1 ) ) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_15]),c_0_14]) ).
thf(c_0_20,plain,
! [X1: nat,X2: nat,X3: nat,X6: nat] :
( ( more @ ( ts @ X1 @ X2 ) @ X3 )
| ~ ( more @ ( ts @ X1 @ ( ts @ X2 @ X6 ) ) @ ( ts @ X3 @ X6 ) ) ),
inference(spm,[status(thm)],[c_0_16,c_0_14]) ).
thf(c_0_21,plain,
! [X1: nat] : ( more @ ( ts @ X1 @ ( ts @ ( num @ x ) @ ( den @ y ) ) ) @ ( ts @ ( num @ y ) @ ( ts @ ( den @ x ) @ X1 ) ) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_14]) ).
thf(c_0_22,plain,
! [X1: nat] :
( ( ts @ ( num @ y ) @ ( ts @ X1 @ ( den @ u ) ) )
= ( ts @ ( num @ u ) @ ( ts @ ( den @ y ) @ X1 ) ) ),
inference(spm,[status(thm)],[c_0_19,c_0_18]) ).
thf(c_0_23,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_18]),c_0_14]) ).
thf(c_0_24,plain,
! [X1: nat,X2: nat,X3: nat] :
( ( more @ X1 @ X2 )
| ~ ( more @ ( ts @ X3 @ X1 ) @ ( ts @ X2 @ X3 ) ) ),
inference(spm,[status(thm)],[c_0_16,c_0_18]) ).
thf(c_0_25,plain,
( ( ts @ ( num @ x ) @ ( den @ z ) )
= ( ts @ ( num @ z ) @ ( den @ x ) ) ),
inference(split_conjunct,[status(thm)],[e]) ).
thf(c_0_26,plain,
! [X1: nat,X2: nat,X3: nat,X6: nat,X7: nat] :
( ( more @ ( ts @ X1 @ X2 ) @ ( ts @ X3 @ X6 ) )
| ~ ( more @ ( ts @ X1 @ ( ts @ X2 @ X7 ) ) @ ( ts @ X3 @ ( ts @ X6 @ X7 ) ) ) ),
inference(spm,[status(thm)],[c_0_20,c_0_14]) ).
thf(c_0_27,plain,
more @ ( ts @ ( num @ x ) @ ( ts @ ( den @ u ) @ ( den @ y ) ) ) @ ( ts @ ( num @ u ) @ ( ts @ ( den @ x ) @ ( den @ y ) ) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_18]),c_0_23]) ).
thf(c_0_28,negated_conjecture,
~ ( more @ ( ts @ ( num @ z ) @ ( den @ u ) ) @ ( ts @ ( num @ u ) @ ( den @ z ) ) ),
inference(assume_negation,[status(cth)],[satz44]) ).
thf(c_0_29,plain,
! [X1: nat,X3: nat,X2: nat] :
( ( more @ X1 @ X2 )
| ~ ( more @ ( ts @ X3 @ X1 ) @ ( ts @ X3 @ X2 ) ) ),
inference(spm,[status(thm)],[c_0_24,c_0_18]) ).
thf(c_0_30,plain,
! [X1: nat] :
( ( ts @ ( num @ x ) @ ( ts @ ( den @ z ) @ X1 ) )
= ( ts @ ( num @ z ) @ ( ts @ ( den @ x ) @ X1 ) ) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_25]),c_0_14]) ).
thf(c_0_31,plain,
more @ ( ts @ ( num @ x ) @ ( den @ u ) ) @ ( ts @ ( num @ u ) @ ( den @ x ) ),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
thf(c_0_32,negated_conjecture,
~ ( more @ ( ts @ ( num @ z ) @ ( den @ u ) ) @ ( ts @ ( num @ u ) @ ( den @ z ) ) ),
inference(fof_simplification,[status(thm)],[c_0_28]) ).
thf(c_0_33,plain,
! [X1: nat,X2: nat] :
( ( more @ X1 @ ( ts @ ( den @ z ) @ X2 ) )
| ~ ( more @ ( ts @ ( num @ x ) @ X1 ) @ ( ts @ ( num @ z ) @ ( ts @ ( den @ x ) @ X2 ) ) ) ),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
thf(c_0_34,plain,
! [X1: nat] : ( more @ ( ts @ X1 @ ( ts @ ( num @ x ) @ ( den @ u ) ) ) @ ( ts @ X1 @ ( ts @ ( num @ u ) @ ( den @ x ) ) ) ),
inference(spm,[status(thm)],[c_0_11,c_0_31]) ).
thf(c_0_35,negated_conjecture,
~ ( more @ ( ts @ ( num @ z ) @ ( den @ u ) ) @ ( ts @ ( num @ u ) @ ( den @ z ) ) ),
inference(fof_nnf,[status(thm)],[c_0_32]) ).
thf(c_0_36,plain,
! [X1: nat,X2: nat] :
( ( more @ X1 @ ( ts @ ( den @ z ) @ X2 ) )
| ~ ( more @ ( ts @ ( num @ x ) @ X1 ) @ ( ts @ ( num @ z ) @ ( ts @ X2 @ ( den @ x ) ) ) ) ),
inference(spm,[status(thm)],[c_0_33,c_0_18]) ).
thf(c_0_37,plain,
! [X1: nat] : ( more @ ( ts @ ( num @ x ) @ ( ts @ X1 @ ( den @ u ) ) ) @ ( ts @ X1 @ ( ts @ ( num @ u ) @ ( den @ x ) ) ) ),
inference(spm,[status(thm)],[c_0_34,c_0_23]) ).
thf(c_0_38,negated_conjecture,
~ ( more @ ( ts @ ( num @ z ) @ ( den @ u ) ) @ ( ts @ ( num @ u ) @ ( den @ z ) ) ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
thf(c_0_39,plain,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_18]),c_0_38]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM737^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.19 % Computer : n004.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Tue Sep 29 12:46:36 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.23 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.Jp4TLCY8zu/E---3.1_1228303.p
% 6.20/1.22 % Version: 3.5.1-ho
% 6.20/1.22 % Preprocessing class: HSMSSMSSSSSNFFN.
% 6.20/1.22 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 6.20/1.22 % Starting new_ho_10 with 1500s (5) cores
% 6.20/1.22 % Starting new_bool_1 with 300s (1) cores
% 6.20/1.22 % Starting full_lambda_5 with 300s (1) cores
% 6.20/1.22 % Starting new_ho_10_unif with 300s (1) cores
% 6.20/1.22 % new_ho_10 with pid 1228316 completed with status 0
% 6.20/1.22 % Result found by new_ho_10
% 6.20/1.22 % Preprocessing class: HSMSSMSSSSSNFFN.
% 6.20/1.22 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 6.20/1.22 % Starting new_ho_10 with 1500s (5) cores
% 6.20/1.22 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 6.20/1.22 % No SInE strategy applied
% 6.20/1.22 % Search class: HHUSS-FFSS21-SFFFFFNN
% 6.20/1.22 % partial match(1): FHUSS-FFSS21-SFFFFFNN
% 6.20/1.22 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 6.20/1.22 % Starting SubtermCWHack with 136s (1) cores
% 6.20/1.22 % Starting new_ho_10 with 151s (1) cores
% 6.20/1.22 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S0Y with 136s (1) cores
% 6.20/1.22 % Starting new_bool_3 with 136s (1) cores
% 6.20/1.22 % Starting new_bool_1 with 136s (1) cores
% 6.20/1.22 % new_bool_1 with pid 1228327 completed with status 0
% 6.20/1.22 % Result found by new_bool_1
% 6.20/1.22 % Preprocessing class: HSMSSMSSSSSNFFN.
% 6.20/1.22 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 6.20/1.22 % Starting new_ho_10 with 1500s (5) cores
% 6.20/1.22 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 6.20/1.22 % No SInE strategy applied
% 6.20/1.22 % Search class: HHUSS-FFSS21-SFFFFFNN
% 6.20/1.22 % partial match(1): FHUSS-FFSS21-SFFFFFNN
% 6.20/1.22 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 6.20/1.22 % Starting SubtermCWHack with 136s (1) cores
% 6.20/1.22 % Starting new_ho_10 with 151s (1) cores
% 6.20/1.22 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S0Y with 136s (1) cores
% 6.20/1.22 % Starting new_bool_3 with 136s (1) cores
% 6.20/1.22 % Starting new_bool_1 with 136s (1) cores
% 6.20/1.22 % Preprocessing time : 0.001 s
% 6.20/1.22 % Presaturation interreduction done
% 6.20/1.22
% 6.20/1.22 % Proof found!
% 6.20/1.22 % SZS status Theorem
% 6.20/1.22 % SZS output start CNFRefutation
% See solution above
% 6.20/1.22 % Parsed axioms : 19
% 6.20/1.22 % Removed by relevancy pruning/SinE : 0
% 6.20/1.22 % Initial clauses : 19
% 6.20/1.22 % Removed in clause preprocessing : 11
% 6.20/1.22 % Initial clauses in saturation : 8
% 6.20/1.22 % Processed clauses : 3556
% 6.20/1.22 % ...of these trivial : 284
% 6.20/1.22 % ...subsumed : 2662
% 6.20/1.22 % ...remaining for further processing : 609
% 6.20/1.22 % Other redundant clauses eliminated : 0
% 6.20/1.22 % Clauses deleted for lack of memory : 0
% 6.20/1.22 % Backward-subsumed : 14
% 6.20/1.22 % Backward-rewritten : 3
% 6.20/1.22 % Generated clauses : 32132
% 6.20/1.22 % ...of the previous two non-redundant : 31833
% 6.20/1.22 % ...aggressively subsumed : 0
% 6.20/1.22 % Contextual simplify-reflections : 0
% 6.20/1.22 % Paramodulations : 32132
% 6.20/1.22 % Factorizations : 0
% 6.20/1.22 % NegExts : 0
% 6.20/1.22 % Equation resolutions : 0
% 6.20/1.22 % Disequality decompositions : 0
% 6.20/1.22 % Total rewrite steps : 22371
% 6.20/1.22 % ...of those cached : 19686
% 6.20/1.22 % Propositional unsat checks : 0
% 6.20/1.22 % Propositional check models : 0
% 6.20/1.22 % Propositional check unsatisfiable : 0
% 6.20/1.22 % Propositional clauses : 0
% 6.20/1.22 % Propositional clauses after purity: 0
% 6.20/1.22 % Propositional unsat core size : 0
% 6.20/1.22 % Propositional preprocessing time : 0.000
% 6.20/1.22 % Propositional encoding time : 0.000
% 6.20/1.22 % Propositional solver time : 0.000
% 6.20/1.22 % Success case prop preproc time : 0.000
% 6.20/1.22 % Success case prop encoding time : 0.000
% 6.20/1.22 % Success case prop solver time : 0.000
% 6.20/1.22 % Current number of processed clauses : 584
% 6.20/1.22 % Positive orientable unit clauses : 37
% 6.20/1.22 % Positive unorientable unit clauses: 4
% 6.20/1.22 % Negative unit clauses : 1
% 6.20/1.22 % Non-unit-clauses : 542
% 6.20/1.22 % Current number of unprocessed clauses: 28278
% 6.20/1.22 % ...number of literals in the above : 56117
% 6.20/1.22 % Current number of archived formulas : 0
% 6.20/1.22 % Current number of archived clauses : 25
% 6.20/1.22 % Clause-clause subsumption calls (NU) : 136839
% 6.20/1.22 % Rec. Clause-clause subsumption calls : 136839
% 6.20/1.22 % Non-unit clause-clause subsumptions : 2639
% 6.20/1.22 % Unit Clause-clause subsumption calls : 22
% 6.20/1.22 % Rewrite failures with RHS unbound : 0
% 6.20/1.22 % BW rewrite match attempts : 1112
% 6.20/1.22 % BW rewrite match successes : 83
% 6.20/1.22 % Condensation attempts : 0
% 6.20/1.22 % Condensation successes : 0
% 6.20/1.22 % Termbank termtop insertions : 966355
% 6.20/1.22 % Search garbage collected termcells : 85
% 6.20/1.22
% 6.20/1.22 % -------------------------------------------------
% 6.20/1.22 % User time : 0.660 s
% 6.20/1.22 % System time : 0.027 s
% 6.20/1.22 % Total time : 0.687 s
% 6.20/1.22 % Maximum resident set size: 3900 pages
% 6.20/1.22
% 6.20/1.22 % -------------------------------------------------
% 6.20/1.22 % User time : 3.997 s
% 6.20/1.22 % System time : 0.155 s
% 6.20/1.22 % Total time : 4.152 s
% 6.20/1.22 % Maximum resident set size: 4608 pages
% 6.20/1.22 % E exiting
%------------------------------------------------------------------------------