%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUM762^1 : 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 : n009.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 08:17:03 AM UTC 2026
% Result : Theorem 0.07s 0.28s
% Output : CNFRefutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 8
% Syntax : Number of formulae : 33 ( 13 unt; 0 typ; 0 def)
% Number of atoms : 74 ( 0 equ; 0 cnn)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 295 ( 36 ~; 31 |; 0 &; 218 @)
% ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 8 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 69 ( 0 ^; 69 !; 0 ?; 69 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_sort1,type,
frac: $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,
moref: frac > frac > $o ).
thf(decl_28,type,
eq: frac > frac > $o ).
thf(decl_29,type,
pf: frac > frac > frac ).
thf(satz44,axiom,
! [X2: frac,X3: frac,X4: frac,X5: frac] :
( ( moref @ X2 @ X3 )
=> ( ( eq @ X2 @ X4 )
=> ( ( eq @ X3 @ X5 )
=> ( moref @ X4 @ X5 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.J00U8LXTVf/E---3.1_3939404.p',satz44) ).
thf(satz56,axiom,
! [X2: frac,X3: frac,X4: frac,X5: frac] :
( ( eq @ X2 @ X3 )
=> ( ( eq @ X4 @ X5 )
=> ( eq @ ( pf @ X2 @ X4 ) @ ( pf @ X3 @ X5 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.J00U8LXTVf/E---3.1_3939404.p',satz56) ).
thf(satz65b,conjecture,
moref @ ( pf @ x @ z ) @ ( pf @ y @ u ),
file('/export/starexec/sandbox/tmp/tmp.J00U8LXTVf/E---3.1_3939404.p',satz65b) ).
thf(satz61,axiom,
! [X2: frac,X3: frac,X4: frac] :
( ( moref @ X2 @ X3 )
=> ( moref @ ( pf @ X2 @ X4 ) @ ( pf @ X3 @ X4 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.J00U8LXTVf/E---3.1_3939404.p',satz61) ).
thf(satz37,axiom,
! [X2: frac] : ( eq @ X2 @ X2 ),
file('/export/starexec/sandbox/tmp/tmp.J00U8LXTVf/E---3.1_3939404.p',satz37) ).
thf(n,axiom,
( ~ ( moref @ z @ u )
=> ( eq @ z @ u ) ),
file('/export/starexec/sandbox/tmp/tmp.J00U8LXTVf/E---3.1_3939404.p',n) ).
thf(satz64,axiom,
! [X2: frac,X3: frac,X4: frac,X5: frac] :
( ( moref @ X2 @ X3 )
=> ( ( moref @ X4 @ X5 )
=> ( moref @ ( pf @ X2 @ X4 ) @ ( pf @ X3 @ X5 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.J00U8LXTVf/E---3.1_3939404.p',satz64) ).
thf(m,axiom,
moref @ x @ y,
file('/export/starexec/sandbox/tmp/tmp.J00U8LXTVf/E---3.1_3939404.p',m) ).
thf(c_0_8,plain,
! [X23: frac,X24: frac,X25: frac,X26: frac] :
( ~ ( moref @ X23 @ X24 )
| ~ ( eq @ X23 @ X25 )
| ~ ( eq @ X24 @ X26 )
| ( moref @ X25 @ X26 ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[satz44])])]) ).
thf(c_0_9,plain,
! [X31: frac,X32: frac,X33: frac,X34: frac] :
( ~ ( eq @ X31 @ X32 )
| ~ ( eq @ X33 @ X34 )
| ( eq @ ( pf @ X31 @ X33 ) @ ( pf @ X32 @ X34 ) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[satz56])])]) ).
thf(c_0_10,negated_conjecture,
~ ( moref @ ( pf @ x @ z ) @ ( pf @ y @ u ) ),
inference(assume_negation,[status(cth)],[satz65b]) ).
thf(c_0_11,plain,
! [X2: frac,X3: frac,X4: frac,X5: frac] :
( ( moref @ X4 @ X5 )
| ~ ( moref @ X2 @ X3 )
| ~ ( eq @ X2 @ X4 )
| ~ ( eq @ X3 @ X5 ) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
thf(c_0_12,plain,
! [X2: frac,X3: frac,X4: frac,X5: frac] :
( ( eq @ ( pf @ X2 @ X4 ) @ ( pf @ X3 @ X5 ) )
| ~ ( eq @ X2 @ X3 )
| ~ ( eq @ X4 @ X5 ) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
thf(c_0_13,plain,
! [X27: frac,X28: frac,X29: frac] :
( ~ ( moref @ X27 @ X28 )
| ( moref @ ( pf @ X27 @ X29 ) @ ( pf @ X28 @ X29 ) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[satz61])])]) ).
thf(c_0_14,negated_conjecture,
~ ( moref @ ( pf @ x @ z ) @ ( pf @ y @ u ) ),
inference(fof_simplification,[status(thm)],[c_0_10]) ).
thf(c_0_15,plain,
! [X2: frac,X5: frac,X8: frac,X7: frac,X4: frac,X3: frac] :
( ( moref @ X2 @ ( pf @ X3 @ X4 ) )
| ~ ( moref @ X5 @ ( pf @ X7 @ X8 ) )
| ~ ( eq @ X5 @ X2 )
| ~ ( eq @ X8 @ X4 )
| ~ ( eq @ X7 @ X3 ) ),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
thf(c_0_16,plain,
! [X2: frac,X4: frac,X3: frac] :
( ( moref @ ( pf @ X2 @ X4 ) @ ( pf @ X3 @ X4 ) )
| ~ ( moref @ X2 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
thf(c_0_17,plain,
! [X30: frac] : ( eq @ X30 @ X30 ),
inference(variable_rename,[status(thm)],[satz37]) ).
thf(c_0_18,plain,
( ~ ( moref @ z @ u )
=> ( eq @ z @ u ) ),
inference(fof_simplification,[status(thm)],[n]) ).
thf(c_0_19,negated_conjecture,
~ ( moref @ ( pf @ x @ z ) @ ( pf @ y @ u ) ),
inference(fof_nnf,[status(thm)],[c_0_14]) ).
thf(c_0_20,plain,
! [X35: frac,X36: frac,X37: frac,X38: frac] :
( ~ ( moref @ X35 @ X36 )
| ~ ( moref @ X37 @ X38 )
| ( moref @ ( pf @ X35 @ X37 ) @ ( pf @ X36 @ X38 ) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[satz64])])]) ).
thf(c_0_21,plain,
! [X2: frac,X4: frac,X3: frac,X5: frac,X7: frac,X8: frac] :
( ( moref @ X2 @ ( pf @ X3 @ X4 ) )
| ~ ( eq @ ( pf @ X5 @ X7 ) @ X2 )
| ~ ( eq @ X7 @ X4 )
| ~ ( eq @ X8 @ X3 )
| ~ ( moref @ X5 @ X8 ) ),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
thf(c_0_22,plain,
! [X2: frac] : ( eq @ X2 @ X2 ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
thf(c_0_23,plain,
( ( moref @ z @ u )
| ( eq @ z @ u ) ),
inference(fof_nnf,[status(thm)],[c_0_18]) ).
thf(c_0_24,negated_conjecture,
~ ( moref @ ( pf @ x @ z ) @ ( pf @ y @ u ) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
thf(c_0_25,plain,
! [X2: frac,X3: frac,X4: frac,X5: frac] :
( ( moref @ ( pf @ X2 @ X4 ) @ ( pf @ X3 @ X5 ) )
| ~ ( moref @ X2 @ X3 )
| ~ ( moref @ X4 @ X5 ) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
thf(c_0_26,plain,
moref @ x @ y,
inference(split_conjunct,[status(thm)],[m]) ).
thf(c_0_27,plain,
! [X2: frac,X4: frac,X5: frac,X3: frac,X7: frac] :
( ( moref @ ( pf @ X2 @ X3 ) @ ( pf @ X4 @ X5 ) )
| ~ ( eq @ X3 @ X5 )
| ~ ( eq @ X7 @ X4 )
| ~ ( moref @ X2 @ X7 ) ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
thf(c_0_28,plain,
( ( moref @ z @ u )
| ( eq @ z @ u ) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
thf(c_0_29,negated_conjecture,
~ ( moref @ z @ u ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_26])]) ).
thf(c_0_30,plain,
! [X3: frac,X2: frac,X5: frac,X4: frac] :
( ( moref @ ( pf @ X2 @ X3 ) @ ( pf @ X4 @ X5 ) )
| ~ ( eq @ X3 @ X5 )
| ~ ( moref @ X2 @ X4 ) ),
inference(spm,[status(thm)],[c_0_27,c_0_22]) ).
thf(c_0_31,plain,
eq @ z @ u,
inference(sr,[status(thm)],[c_0_28,c_0_29]) ).
thf(c_0_32,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_30]),c_0_31]),c_0_26])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM762^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.19 % Computer : n009.cluster.edu
% 0.07/0.19 % Model : x86_64 x86_64
% 0.07/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.19 % Memory : 8046.5625MB
% 0.07/0.19 % OS : Linux 6.8.0-71-generic
% 0.07/0.19 % CPULimit : 300
% 0.07/0.19 % WCLimit : 300
% 0.07/0.19 % DateTime : Tue Sep 29 12:53:15 UTC 2026
% 0.07/0.19 % CPUTime :
% 0.07/0.19 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.23 Running higher-order theorem proving
% 0.07/0.25 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.J00U8LXTVf/E---3.1_3939404.p
% 0.07/0.28 % Version: 3.5.1-ho
% 0.07/0.28 % Preprocessing class: HSMSSMSSSSSNFFN.
% 0.07/0.28 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.07/0.28 % Starting new_ho_10 with 1500s (5) cores
% 0.07/0.28 % Starting new_bool_1 with 300s (1) cores
% 0.07/0.28 % Starting full_lambda_5 with 300s (1) cores
% 0.07/0.28 % Starting new_ho_10_unif with 300s (1) cores
% 0.07/0.28 % new_ho_10_unif with pid 3939420 completed with status 0
% 0.07/0.28 % Result found by new_ho_10_unif
% 0.07/0.28 % Preprocessing class: HSMSSMSSSSSNFFN.
% 0.07/0.28 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.07/0.28 % Starting new_ho_10 with 1500s (5) cores
% 0.07/0.28 % Starting new_bool_1 with 300s (1) cores
% 0.07/0.28 % Starting full_lambda_5 with 300s (1) cores
% 0.07/0.28 % Starting new_ho_10_unif with 300s (1) cores
% 0.07/0.28 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.07/0.28 % No SInE strategy applied
% 0.07/0.28 % Search class: HGUNF-FFSF22-SFFFFFNN
% 0.07/0.28 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.07/0.28 % Starting SubtermCWHack with 28s (1) cores
% 0.07/0.28 % SubtermCWHack with pid 3939421 completed with status 0
% 0.07/0.28 % Result found by SubtermCWHack
% 0.07/0.28 % Preprocessing class: HSMSSMSSSSSNFFN.
% 0.07/0.28 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.07/0.28 % Starting new_ho_10 with 1500s (5) cores
% 0.07/0.28 % Starting new_bool_1 with 300s (1) cores
% 0.07/0.28 % Starting full_lambda_5 with 300s (1) cores
% 0.07/0.28 % Starting new_ho_10_unif with 300s (1) cores
% 0.07/0.28 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.07/0.28 % No SInE strategy applied
% 0.07/0.28 % Search class: HGUNF-FFSF22-SFFFFFNN
% 0.07/0.28 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.07/0.28 % Starting SubtermCWHack with 28s (1) cores
% 0.07/0.28 % Preprocessing time : 0.001 s
% 0.07/0.28
% 0.07/0.28 % Proof found!
% 0.07/0.28 % SZS status Theorem
% 0.07/0.28 % SZS output start CNFRefutation
% See solution above
% 0.07/0.28 % Parsed axioms : 17
% 0.07/0.28 % Removed by relevancy pruning/SinE : 0
% 0.07/0.28 % Initial clauses : 17
% 0.07/0.28 % Removed in clause preprocessing : 9
% 0.07/0.28 % Initial clauses in saturation : 8
% 0.07/0.28 % Processed clauses : 34
% 0.07/0.28 % ...of these trivial : 0
% 0.07/0.28 % ...subsumed : 3
% 0.07/0.28 % ...remaining for further processing : 31
% 0.07/0.28 % Other redundant clauses eliminated : 0
% 0.07/0.28 % Clauses deleted for lack of memory : 0
% 0.07/0.28 % Backward-subsumed : 4
% 0.07/0.28 % Backward-rewritten : 0
% 0.07/0.28 % Generated clauses : 43
% 0.07/0.28 % ...of the previous two non-redundant : 41
% 0.07/0.28 % ...aggressively subsumed : 0
% 0.07/0.28 % Contextual simplify-reflections : 0
% 0.07/0.28 % Paramodulations : 42
% 0.07/0.28 % Factorizations : 0
% 0.07/0.28 % NegExts : 0
% 0.07/0.28 % Equation resolutions : 0
% 0.07/0.28 % Disequality decompositions : 0
% 0.07/0.28 % Total rewrite steps : 4
% 0.07/0.28 % ...of those cached : 2
% 0.07/0.28 % Propositional unsat checks : 0
% 0.07/0.28 % Propositional check models : 0
% 0.07/0.28 % Propositional check unsatisfiable : 0
% 0.07/0.28 % Propositional clauses : 0
% 0.07/0.28 % Propositional clauses after purity: 0
% 0.07/0.28 % Propositional unsat core size : 0
% 0.07/0.28 % Propositional preprocessing time : 0.000
% 0.07/0.28 % Propositional encoding time : 0.000
% 0.07/0.28 % Propositional solver time : 0.000
% 0.07/0.28 % Success case prop preproc time : 0.000
% 0.07/0.28 % Success case prop encoding time : 0.000
% 0.07/0.28 % Success case prop solver time : 0.000
% 0.07/0.28 % Current number of processed clauses : 26
% 0.07/0.28 % Positive orientable unit clauses : 3
% 0.07/0.28 % Positive unorientable unit clauses: 0
% 0.07/0.28 % Negative unit clauses : 4
% 0.07/0.28 % Non-unit-clauses : 19
% 0.07/0.28 % Current number of unprocessed clauses: 13
% 0.07/0.28 % ...number of literals in the above : 71
% 0.07/0.28 % Current number of archived formulas : 0
% 0.07/0.28 % Current number of archived clauses : 5
% 0.07/0.28 % Clause-clause subsumption calls (NU) : 158
% 0.07/0.28 % Rec. Clause-clause subsumption calls : 129
% 0.07/0.28 % Non-unit clause-clause subsumptions : 5
% 0.07/0.28 % Unit Clause-clause subsumption calls : 8
% 0.07/0.28 % Rewrite failures with RHS unbound : 0
% 0.07/0.28 % BW rewrite match attempts : 0
% 0.07/0.28 % BW rewrite match successes : 0
% 0.07/0.28 % Condensation attempts : 0
% 0.07/0.28 % Condensation successes : 0
% 0.07/0.28 % Termbank termtop insertions : 1685
% 0.07/0.28 % Search garbage collected termcells : 155
% 0.07/0.28
% 0.07/0.28 % -------------------------------------------------
% 0.07/0.28 % User time : 0.005 s
% 0.07/0.28 % System time : 0.003 s
% 0.07/0.28 % Total time : 0.008 s
% 0.07/0.28 % Maximum resident set size: 3640 pages
% 0.07/0.28
% 0.07/0.28 % -------------------------------------------------
% 0.07/0.28 % User time : 0.008 s
% 0.07/0.28 % System time : 0.006 s
% 0.07/0.28 % Total time : 0.014 s
% 0.07/0.28 % Maximum resident set size: 4864 pages
% 0.07/0.28 % E exiting
%------------------------------------------------------------------------------