%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUM765^1 : TPTP v9.3.1. Released v3.7.0.
% 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 08:17:03 AM UTC 2026
% Result : Theorem 0.09s 0.28s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 6
% Syntax : Number of formulae : 33 ( 7 unt; 0 typ; 0 def)
% Number of atoms : 81 ( 0 equ; 0 cnn)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 345 ( 41 ~; 24 |; 3 &; 256 @)
% ( 0 <=>; 21 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 7 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 : 48 ( 0 ^; 48 !; 0 ?; 48 :)
% 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(satz66,conjecture,
( ~ ( moref @ ( pf @ x @ z ) @ ( pf @ y @ u ) )
=> ( eq @ ( pf @ x @ z ) @ ( pf @ y @ u ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.amByMlU33k/E---3.1_714211.p',satz66) ).
thf(satz65b,axiom,
! [X2: frac,X3: frac,X4: frac,X5: frac] :
( ( moref @ X2 @ X3 )
=> ( ( ~ ( moref @ X4 @ X5 )
=> ( eq @ X4 @ X5 ) )
=> ( moref @ ( pf @ X2 @ X4 ) @ ( pf @ X3 @ X5 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.amByMlU33k/E---3.1_714211.p',satz65b) ).
thf(n,axiom,
( ~ ( moref @ z @ u )
=> ( eq @ z @ u ) ),
file('/export/starexec/sandbox2/tmp/tmp.amByMlU33k/E---3.1_714211.p',n) ).
thf(m,axiom,
( ~ ( moref @ x @ y )
=> ( eq @ x @ y ) ),
file('/export/starexec/sandbox2/tmp/tmp.amByMlU33k/E---3.1_714211.p',m) ).
thf(satz65a,axiom,
! [X2: frac,X3: frac,X4: frac,X5: frac] :
( ( ~ ( moref @ X2 @ X3 )
=> ( eq @ X2 @ X3 ) )
=> ( ( moref @ X4 @ X5 )
=> ( moref @ ( pf @ X2 @ X4 ) @ ( pf @ X3 @ X5 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.amByMlU33k/E---3.1_714211.p',satz65a) ).
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/sandbox2/tmp/tmp.amByMlU33k/E---3.1_714211.p',satz56) ).
thf(c_0_6,negated_conjecture,
~ ( ~ ( moref @ ( pf @ x @ z ) @ ( pf @ y @ u ) )
=> ( eq @ ( pf @ x @ z ) @ ( pf @ y @ u ) ) ),
inference(assume_negation,[status(cth)],[satz66]) ).
thf(c_0_7,negated_conjecture,
~ ( ~ ( moref @ ( pf @ x @ z ) @ ( pf @ y @ u ) )
=> ( eq @ ( pf @ x @ z ) @ ( pf @ y @ u ) ) ),
inference(fof_simplification,[status(thm)],[c_0_6]) ).
thf(c_0_8,plain,
! [X2: frac,X3: frac,X4: frac,X5: frac] :
( ( moref @ X2 @ X3 )
=> ( ( ~ ( moref @ X4 @ X5 )
=> ( eq @ X4 @ X5 ) )
=> ( moref @ ( pf @ X2 @ X4 ) @ ( pf @ X3 @ X5 ) ) ) ),
inference(fof_simplification,[status(thm)],[satz65b]) ).
thf(c_0_9,negated_conjecture,
( ~ ( moref @ ( pf @ x @ z ) @ ( pf @ y @ u ) )
& ~ ( eq @ ( pf @ x @ z ) @ ( pf @ y @ u ) ) ),
inference(fof_nnf,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])]) ).
thf(c_0_10,plain,
! [X23: frac,X24: frac,X25: frac,X26: frac] :
( ( ~ ( moref @ X25 @ X26 )
| ( moref @ ( pf @ X23 @ X25 ) @ ( pf @ X24 @ X26 ) )
| ~ ( moref @ X23 @ X24 ) )
& ( ~ ( eq @ X25 @ X26 )
| ( moref @ ( pf @ X23 @ X25 ) @ ( pf @ X24 @ X26 ) )
| ~ ( moref @ X23 @ X24 ) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_8])])])]) ).
thf(c_0_11,plain,
( ~ ( moref @ z @ u )
=> ( eq @ z @ u ) ),
inference(fof_simplification,[status(thm)],[n]) ).
thf(c_0_12,plain,
( ~ ( moref @ x @ y )
=> ( eq @ x @ y ) ),
inference(fof_simplification,[status(thm)],[m]) ).
thf(c_0_13,negated_conjecture,
~ ( moref @ ( pf @ x @ z ) @ ( pf @ y @ u ) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
thf(c_0_14,plain,
! [X2: frac,X3: frac,X4: frac,X5: frac] :
( ( moref @ ( pf @ X4 @ X2 ) @ ( pf @ X5 @ X3 ) )
| ~ ( eq @ X2 @ X3 )
| ~ ( moref @ X4 @ X5 ) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
thf(c_0_15,plain,
( ( moref @ z @ u )
| ( eq @ z @ u ) ),
inference(fof_nnf,[status(thm)],[c_0_11]) ).
thf(c_0_16,plain,
! [X2: frac,X3: frac,X4: frac,X5: frac] :
( ( moref @ ( pf @ X4 @ X2 ) @ ( pf @ X5 @ X3 ) )
| ~ ( moref @ X2 @ X3 )
| ~ ( moref @ X4 @ X5 ) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
thf(c_0_17,plain,
! [X2: frac,X3: frac,X4: frac,X5: frac] :
( ( ~ ( moref @ X2 @ X3 )
=> ( eq @ X2 @ X3 ) )
=> ( ( moref @ X4 @ X5 )
=> ( moref @ ( pf @ X2 @ X4 ) @ ( pf @ X3 @ X5 ) ) ) ),
inference(fof_simplification,[status(thm)],[satz65a]) ).
thf(c_0_18,plain,
( ( moref @ x @ y )
| ( eq @ x @ y ) ),
inference(fof_nnf,[status(thm)],[c_0_12]) ).
thf(c_0_19,negated_conjecture,
( ~ ( moref @ x @ y )
| ~ ( eq @ z @ u ) ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
thf(c_0_20,plain,
( ( moref @ z @ u )
| ( eq @ z @ u ) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
thf(c_0_21,negated_conjecture,
( ~ ( moref @ x @ y )
| ~ ( moref @ z @ u ) ),
inference(spm,[status(thm)],[c_0_13,c_0_16]) ).
thf(c_0_22,plain,
! [X27: frac,X28: frac,X29: frac,X30: frac] :
( ( ~ ( moref @ X27 @ X28 )
| ~ ( moref @ X29 @ X30 )
| ( moref @ ( pf @ X27 @ X29 ) @ ( pf @ X28 @ X30 ) ) )
& ( ~ ( eq @ X27 @ X28 )
| ~ ( moref @ X29 @ X30 )
| ( moref @ ( pf @ X27 @ X29 ) @ ( pf @ X28 @ X30 ) ) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_17])])])]) ).
thf(c_0_23,plain,
( ( moref @ x @ y )
| ( eq @ x @ y ) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
thf(c_0_24,negated_conjecture,
~ ( moref @ x @ y ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_21]) ).
thf(c_0_25,plain,
! [X2: frac,X3: frac,X4: frac,X5: frac] :
( ( moref @ ( pf @ X2 @ X4 ) @ ( pf @ X3 @ X5 ) )
| ~ ( eq @ X2 @ X3 )
| ~ ( moref @ X4 @ X5 ) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
thf(c_0_26,plain,
eq @ x @ y,
inference(sr,[status(thm)],[c_0_23,c_0_24]) ).
thf(c_0_27,plain,
! [X19: frac,X20: frac,X21: frac,X22: frac] :
( ~ ( eq @ X19 @ X20 )
| ~ ( eq @ X21 @ X22 )
| ( eq @ ( pf @ X19 @ X21 ) @ ( pf @ X20 @ X22 ) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[satz56])])]) ).
thf(c_0_28,negated_conjecture,
~ ( moref @ z @ u ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_25]),c_0_26])]) ).
thf(c_0_29,negated_conjecture,
~ ( eq @ ( pf @ x @ z ) @ ( pf @ y @ u ) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
thf(c_0_30,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_27]) ).
thf(c_0_31,plain,
eq @ z @ u,
inference(sr,[status(thm)],[c_0_20,c_0_28]) ).
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_29,c_0_30]),c_0_31]),c_0_26])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM765^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.20 % Computer : n019.cluster.edu
% 0.09/0.20 % Model : x86_64 x86_64
% 0.09/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.20 % Memory : 8046.5625MB
% 0.09/0.20 % OS : Linux 6.8.0-71-generic
% 0.09/0.20 % CPULimit : 300
% 0.09/0.20 % WCLimit : 300
% 0.09/0.20 % DateTime : Tue Sep 29 12:53:48 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.25 Running higher-order theorem proving
% 0.09/0.26 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.amByMlU33k/E---3.1_714211.p
% 0.09/0.28 % Version: 3.5.1-ho
% 0.09/0.28 % Preprocessing class: HSMSSMSSSSSNFFN.
% 0.09/0.28 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.09/0.28 % Starting new_ho_10 with 1500s (5) cores
% 0.09/0.28 % Starting new_bool_1 with 300s (1) cores
% 0.09/0.28 % Starting full_lambda_5 with 300s (1) cores
% 0.09/0.28 % Starting new_ho_10_unif with 300s (1) cores
% 0.09/0.28 % full_lambda_5 with pid 714226 completed with status 0
% 0.09/0.28 % Result found by full_lambda_5
% 0.09/0.28 % Preprocessing class: HSMSSMSSSSSNFFN.
% 0.09/0.28 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.09/0.28 % Starting new_ho_10 with 1500s (5) cores
% 0.09/0.28 % Starting new_bool_1 with 300s (1) cores
% 0.09/0.28 % Starting full_lambda_5 with 300s (1) cores
% 0.09/0.28 % (lift_lambdas = 1, lambda_to_forall = 0,unroll_only_formulas = 1, sine = Auto)
% 0.09/0.28 % No SInE strategy applied
% 0.09/0.28 % Search class: HGUNF-FFSF22-SFFFFFNN
% 0.09/0.28 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.09/0.28 % Starting SubtermCWHack with 28s (1) cores
% 0.09/0.28 % SubtermCWHack with pid 714230 completed with status 0
% 0.09/0.28 % Result found by SubtermCWHack
% 0.09/0.28 % Preprocessing class: HSMSSMSSSSSNFFN.
% 0.09/0.28 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.09/0.28 % Starting new_ho_10 with 1500s (5) cores
% 0.09/0.28 % Starting new_bool_1 with 300s (1) cores
% 0.09/0.28 % Starting full_lambda_5 with 300s (1) cores
% 0.09/0.28 % (lift_lambdas = 1, lambda_to_forall = 0,unroll_only_formulas = 1, sine = Auto)
% 0.09/0.28 % No SInE strategy applied
% 0.09/0.28 % Search class: HGUNF-FFSF22-SFFFFFNN
% 0.09/0.28 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.09/0.28 % Starting SubtermCWHack with 28s (1) cores
% 0.09/0.28 % Preprocessing time : 0.001 s
% 0.09/0.28
% 0.09/0.28 % Proof found!
% 0.09/0.28 % SZS status Theorem
% 0.09/0.28 % SZS output start CNFRefutation
% See solution above
% 0.09/0.29 % Parsed axioms : 15
% 0.09/0.29 % Removed by relevancy pruning/SinE : 0
% 0.09/0.29 % Initial clauses : 18
% 0.09/0.29 % Removed in clause preprocessing : 9
% 0.09/0.29 % Initial clauses in saturation : 9
% 0.09/0.29 % Processed clauses : 15
% 0.09/0.29 % ...of these trivial : 0
% 0.09/0.29 % ...subsumed : 1
% 0.09/0.29 % ...remaining for further processing : 14
% 0.09/0.29 % Other redundant clauses eliminated : 0
% 0.09/0.29 % Clauses deleted for lack of memory : 0
% 0.09/0.29 % Backward-subsumed : 2
% 0.09/0.29 % Backward-rewritten : 0
% 0.09/0.29 % Generated clauses : 7
% 0.09/0.29 % ...of the previous two non-redundant : 6
% 0.09/0.29 % ...aggressively subsumed : 0
% 0.09/0.29 % Contextual simplify-reflections : 1
% 0.09/0.29 % Paramodulations : 5
% 0.09/0.29 % Factorizations : 0
% 0.09/0.29 % NegExts : 0
% 0.09/0.29 % Equation resolutions : 0
% 0.09/0.29 % Disequality decompositions : 0
% 0.09/0.29 % Total rewrite steps : 3
% 0.09/0.29 % ...of those cached : 1
% 0.09/0.29 % Propositional unsat checks : 0
% 0.09/0.29 % Propositional check models : 0
% 0.09/0.29 % Propositional check unsatisfiable : 0
% 0.09/0.29 % Propositional clauses : 0
% 0.09/0.29 % Propositional clauses after purity: 0
% 0.09/0.29 % Propositional unsat core size : 0
% 0.09/0.29 % Propositional preprocessing time : 0.000
% 0.09/0.29 % Propositional encoding time : 0.000
% 0.09/0.29 % Propositional solver time : 0.000
% 0.09/0.29 % Success case prop preproc time : 0.000
% 0.09/0.29 % Success case prop encoding time : 0.000
% 0.09/0.29 % Success case prop solver time : 0.000
% 0.09/0.29 % Current number of processed clauses : 10
% 0.09/0.29 % Positive orientable unit clauses : 2
% 0.09/0.29 % Positive unorientable unit clauses: 0
% 0.09/0.29 % Negative unit clauses : 4
% 0.09/0.29 % Non-unit-clauses : 4
% 0.09/0.29 % Current number of unprocessed clauses: 0
% 0.09/0.29 % ...number of literals in the above : 0
% 0.09/0.29 % Current number of archived formulas : 0
% 0.09/0.29 % Current number of archived clauses : 4
% 0.09/0.29 % Clause-clause subsumption calls (NU) : 4
% 0.09/0.29 % Rec. Clause-clause subsumption calls : 4
% 0.09/0.29 % Non-unit clause-clause subsumptions : 2
% 0.09/0.29 % Unit Clause-clause subsumption calls : 4
% 0.09/0.29 % Rewrite failures with RHS unbound : 0
% 0.09/0.29 % BW rewrite match attempts : 0
% 0.09/0.29 % BW rewrite match successes : 0
% 0.09/0.29 % Condensation attempts : 0
% 0.09/0.29 % Condensation successes : 0
% 0.09/0.29 % Termbank termtop insertions : 1061
% 0.09/0.29 % Search garbage collected termcells : 168
% 0.09/0.29
% 0.09/0.29 % -------------------------------------------------
% 0.09/0.29 % User time : 0.006 s
% 0.09/0.29 % System time : 0.001 s
% 0.09/0.29 % Total time : 0.007 s
% 0.09/0.29 % Maximum resident set size: 3640 pages
% 0.09/0.29
% 0.09/0.29 % -------------------------------------------------
% 0.09/0.29 % User time : 0.008 s
% 0.09/0.29 % System time : 0.005 s
% 0.09/0.29 % Total time : 0.013 s
% 0.09/0.29 % Maximum resident set size: 4864 pages
% 0.09/0.29 % E exiting
%------------------------------------------------------------------------------