%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUM753^1 : 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 : 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 08:17:01 AM UTC 2026
% Result : Theorem 0.23s 0.29s
% Output : CNFRefutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 7
% Syntax : Number of formulae : 26 ( 13 unt; 0 typ; 0 def)
% Number of atoms : 57 ( 0 equ; 0 cnn)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 232 ( 29 ~; 25 |; 0 &; 172 @)
% ( 0 <=>; 6 =>; 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 : 57 ( 0 ^; 57 !; 0 ?; 57 :)
% 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,
eq: frac > frac > $o ).
thf(decl_28,type,
moref: frac > frac > $o ).
thf(decl_29,type,
pf: frac > frac > frac ).
thf(satz44,axiom,
! [X1: frac,X2: frac,X3: frac,X4: frac] :
( ( moref @ X1 @ X2 )
=> ( ( eq @ X1 @ X3 )
=> ( ( eq @ X2 @ X4 )
=> ( moref @ X3 @ X4 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.qYyxsXZpM0/E---3.1_1232032.p',satz44) ).
thf(satz56,axiom,
! [X1: frac,X2: frac,X3: frac,X4: frac] :
( ( eq @ X1 @ X2 )
=> ( ( eq @ X3 @ X4 )
=> ( eq @ ( pf @ X1 @ X3 ) @ ( pf @ X2 @ X4 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.qYyxsXZpM0/E---3.1_1232032.p',satz56) ).
thf(satz62d,axiom,
! [X1: frac,X2: frac,X3: frac] :
( ( moref @ X1 @ X2 )
=> ( moref @ ( pf @ X3 @ X1 ) @ ( pf @ X3 @ X2 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.qYyxsXZpM0/E---3.1_1232032.p',satz62d) ).
thf(satz62g,conjecture,
moref @ ( pf @ x @ z ) @ ( pf @ y @ u ),
file('/export/starexec/sandbox2/tmp/tmp.qYyxsXZpM0/E---3.1_1232032.p',satz62g) ).
thf(satz37,axiom,
! [X1: frac] : ( eq @ X1 @ X1 ),
file('/export/starexec/sandbox2/tmp/tmp.qYyxsXZpM0/E---3.1_1232032.p',satz37) ).
thf(e,axiom,
eq @ x @ y,
file('/export/starexec/sandbox2/tmp/tmp.qYyxsXZpM0/E---3.1_1232032.p',e) ).
thf(m,axiom,
moref @ z @ u,
file('/export/starexec/sandbox2/tmp/tmp.qYyxsXZpM0/E---3.1_1232032.p',m) ).
thf(c_0_7,plain,
! [X17: frac,X18: frac,X19: frac,X20: frac] :
( ~ ( moref @ X17 @ X18 )
| ~ ( eq @ X17 @ X19 )
| ~ ( eq @ X18 @ X20 )
| ( moref @ X19 @ X20 ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[satz44])])]) ).
thf(c_0_8,plain,
! [X25: frac,X26: frac,X27: frac,X28: frac] :
( ~ ( eq @ X25 @ X26 )
| ~ ( eq @ X27 @ X28 )
| ( eq @ ( pf @ X25 @ X27 ) @ ( pf @ X26 @ X28 ) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[satz56])])]) ).
thf(c_0_9,plain,
! [X1: frac,X2: frac,X3: frac,X4: frac] :
( ( moref @ X3 @ X4 )
| ~ ( moref @ X1 @ X2 )
| ~ ( eq @ X1 @ X3 )
| ~ ( eq @ X2 @ X4 ) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
thf(c_0_10,plain,
! [X1: frac,X2: frac,X3: frac,X4: frac] :
( ( eq @ ( pf @ X1 @ X3 ) @ ( pf @ X2 @ X4 ) )
| ~ ( eq @ X1 @ X2 )
| ~ ( eq @ X3 @ X4 ) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
thf(c_0_11,plain,
! [X21: frac,X22: frac,X23: frac] :
( ~ ( moref @ X21 @ X22 )
| ( moref @ ( pf @ X23 @ X21 ) @ ( pf @ X23 @ X22 ) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[satz62d])])]) ).
thf(c_0_12,negated_conjecture,
~ ( moref @ ( pf @ x @ z ) @ ( pf @ y @ u ) ),
inference(assume_negation,[status(cth)],[satz62g]) ).
thf(c_0_13,plain,
! [X1: frac,X4: frac,X6: frac,X5: frac,X3: frac,X2: frac] :
( ( moref @ X1 @ ( pf @ X2 @ X3 ) )
| ~ ( moref @ X4 @ ( pf @ X5 @ X6 ) )
| ~ ( eq @ X4 @ X1 )
| ~ ( eq @ X6 @ X3 )
| ~ ( eq @ X5 @ X2 ) ),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
thf(c_0_14,plain,
! [X1: frac,X3: frac,X2: frac] :
( ( moref @ ( pf @ X3 @ X1 ) @ ( pf @ X3 @ X2 ) )
| ~ ( moref @ X1 @ X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
thf(c_0_15,plain,
! [X24: frac] : ( eq @ X24 @ X24 ),
inference(variable_rename,[status(thm)],[satz37]) ).
thf(c_0_16,negated_conjecture,
~ ( moref @ ( pf @ x @ z ) @ ( pf @ y @ u ) ),
inference(fof_simplification,[status(thm)],[c_0_12]) ).
thf(c_0_17,plain,
! [X1: frac,X2: frac,X4: frac,X3: frac,X5: frac,X6: frac] :
( ( moref @ X1 @ ( pf @ X2 @ X3 ) )
| ~ ( eq @ ( pf @ X4 @ X5 ) @ X1 )
| ~ ( eq @ X6 @ X3 )
| ~ ( eq @ X4 @ X2 )
| ~ ( moref @ X5 @ X6 ) ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
thf(c_0_18,plain,
! [X1: frac] : ( eq @ X1 @ X1 ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
thf(c_0_19,negated_conjecture,
~ ( moref @ ( pf @ x @ z ) @ ( pf @ y @ u ) ),
inference(fof_nnf,[status(thm)],[c_0_16]) ).
thf(c_0_20,plain,
! [X1: frac,X2: frac,X4: frac,X3: frac,X5: frac] :
( ( moref @ ( pf @ X1 @ X2 ) @ ( pf @ X3 @ X4 ) )
| ~ ( eq @ X5 @ X4 )
| ~ ( eq @ X1 @ X3 )
| ~ ( moref @ X2 @ X5 ) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
thf(c_0_21,negated_conjecture,
~ ( moref @ ( pf @ x @ z ) @ ( pf @ y @ u ) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
thf(c_0_22,plain,
! [X1: frac,X2: frac,X3: frac,X4: frac] :
( ( moref @ ( pf @ X1 @ X2 ) @ ( pf @ X3 @ X4 ) )
| ~ ( eq @ X1 @ X3 )
| ~ ( moref @ X2 @ X4 ) ),
inference(spm,[status(thm)],[c_0_20,c_0_18]) ).
thf(c_0_23,plain,
eq @ x @ y,
inference(split_conjunct,[status(thm)],[e]) ).
thf(c_0_24,plain,
moref @ z @ u,
inference(split_conjunct,[status(thm)],[m]) ).
thf(c_0_25,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_23]),c_0_24])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM753^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.20 % Computer : n004.cluster.edu
% 0.08/0.20 % Model : x86_64 x86_64
% 0.08/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.20 % Memory : 8046.5625MB
% 0.08/0.20 % OS : Linux 6.8.0-71-generic
% 0.08/0.20 % CPULimit : 300
% 0.08/0.20 % WCLimit : 300
% 0.08/0.20 % DateTime : Tue Sep 29 12:50:37 UTC 2026
% 0.08/0.21 % CPUTime :
% 0.08/0.21 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.25 Running higher-order theorem proving
% 0.23/0.27 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.qYyxsXZpM0/E---3.1_1232032.p
% 0.23/0.29 % Version: 3.5.1-ho
% 0.23/0.29 % Preprocessing class: HSMSSMSSSSSNFFN.
% 0.23/0.29 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.23/0.29 % Starting new_ho_10 with 1500s (5) cores
% 0.23/0.29 % Starting new_bool_1 with 300s (1) cores
% 0.23/0.29 % Starting full_lambda_5 with 300s (1) cores
% 0.23/0.29 % Starting new_ho_10_unif with 300s (1) cores
% 0.23/0.29 % new_ho_10 with pid 1232045 completed with status 0
% 0.23/0.29 % Result found by new_ho_10
% 0.23/0.29 % Preprocessing class: HSMSSMSSSSSNFFN.
% 0.23/0.29 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.23/0.29 % Starting new_ho_10 with 1500s (5) cores
% 0.23/0.29 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.23/0.29 % No SInE strategy applied
% 0.23/0.29 % Search class: HHUNF-FFSF22-SFFFFFNN
% 0.23/0.29 % Scheduled 5 strats onto 5 cores with 1500 seconds (1500 total)
% 0.23/0.29 % Starting SubtermCWHack with 151s (1) cores
% 0.23/0.29 % Starting new_ho_10 with 901s (1) cores
% 0.23/0.29 % Starting sh5l with 151s (1) cores
% 0.23/0.29 % Starting ehoh_best_sine_rwall with 151s (1) cores
% 0.23/0.29 % Starting lpo1_def_fix with 146s (1) cores
% 0.23/0.29 % SubtermCWHack with pid 1232050 completed with status 0
% 0.23/0.29 % Result found by SubtermCWHack
% 0.23/0.29 % Preprocessing class: HSMSSMSSSSSNFFN.
% 0.23/0.29 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.23/0.29 % Starting new_ho_10 with 1500s (5) cores
% 0.23/0.29 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.23/0.29 % No SInE strategy applied
% 0.23/0.29 % Search class: HHUNF-FFSF22-SFFFFFNN
% 0.23/0.29 % Scheduled 5 strats onto 5 cores with 1500 seconds (1500 total)
% 0.23/0.29 % Starting SubtermCWHack with 151s (1) cores
% 0.23/0.29 % Preprocessing time : 0.001 s
% 0.23/0.29
% 0.23/0.29 % Proof found!
% 0.23/0.29 % SZS status Theorem
% 0.23/0.29 % SZS output start CNFRefutation
% See solution above
% 0.23/0.29 % Parsed axioms : 15
% 0.23/0.29 % Removed by relevancy pruning/SinE : 0
% 0.23/0.29 % Initial clauses : 15
% 0.23/0.29 % Removed in clause preprocessing : 8
% 0.23/0.29 % Initial clauses in saturation : 7
% 0.23/0.29 % Processed clauses : 34
% 0.23/0.29 % ...of these trivial : 0
% 0.23/0.29 % ...subsumed : 3
% 0.23/0.29 % ...remaining for further processing : 31
% 0.23/0.29 % Other redundant clauses eliminated : 0
% 0.23/0.29 % Clauses deleted for lack of memory : 0
% 0.23/0.29 % Backward-subsumed : 0
% 0.23/0.29 % Backward-rewritten : 0
% 0.23/0.29 % Generated clauses : 60
% 0.23/0.29 % ...of the previous two non-redundant : 58
% 0.23/0.29 % ...aggressively subsumed : 0
% 0.23/0.29 % Contextual simplify-reflections : 0
% 0.23/0.29 % Paramodulations : 60
% 0.23/0.29 % Factorizations : 0
% 0.23/0.29 % NegExts : 0
% 0.23/0.29 % Equation resolutions : 0
% 0.23/0.29 % Disequality decompositions : 0
% 0.23/0.29 % Total rewrite steps : 3
% 0.23/0.29 % ...of those cached : 1
% 0.23/0.29 % Propositional unsat checks : 0
% 0.23/0.29 % Propositional check models : 0
% 0.23/0.29 % Propositional check unsatisfiable : 0
% 0.23/0.29 % Propositional clauses : 0
% 0.23/0.29 % Propositional clauses after purity: 0
% 0.23/0.29 % Propositional unsat core size : 0
% 0.23/0.29 % Propositional preprocessing time : 0.000
% 0.23/0.29 % Propositional encoding time : 0.000
% 0.23/0.29 % Propositional solver time : 0.000
% 0.23/0.29 % Success case prop preproc time : 0.000
% 0.23/0.29 % Success case prop encoding time : 0.000
% 0.23/0.29 % Success case prop solver time : 0.000
% 0.23/0.29 % Current number of processed clauses : 31
% 0.23/0.29 % Positive orientable unit clauses : 3
% 0.23/0.29 % Positive unorientable unit clauses: 0
% 0.23/0.29 % Negative unit clauses : 2
% 0.23/0.29 % Non-unit-clauses : 26
% 0.23/0.29 % Current number of unprocessed clauses: 28
% 0.23/0.29 % ...number of literals in the above : 164
% 0.23/0.29 % Current number of archived formulas : 0
% 0.23/0.29 % Current number of archived clauses : 0
% 0.23/0.29 % Clause-clause subsumption calls (NU) : 330
% 0.23/0.29 % Rec. Clause-clause subsumption calls : 253
% 0.23/0.29 % Non-unit clause-clause subsumptions : 2
% 0.23/0.29 % Unit Clause-clause subsumption calls : 1
% 0.23/0.29 % Rewrite failures with RHS unbound : 0
% 0.23/0.29 % BW rewrite match attempts : 1
% 0.23/0.29 % BW rewrite match successes : 0
% 0.23/0.29 % Condensation attempts : 0
% 0.23/0.29 % Condensation successes : 0
% 0.23/0.29 % Termbank termtop insertions : 1898
% 0.23/0.29 % Search garbage collected termcells : 109
% 0.23/0.29
% 0.23/0.29 % -------------------------------------------------
% 0.23/0.29 % User time : 0.007 s
% 0.23/0.29 % System time : 0.001 s
% 0.23/0.29 % Total time : 0.008 s
% 0.23/0.29 % Maximum resident set size: 3636 pages
% 0.23/0.29
% 0.23/0.29 % -------------------------------------------------
% 0.23/0.29 % User time : 0.016 s
% 0.23/0.29 % System time : 0.013 s
% 0.23/0.29 % Total time : 0.029 s
% 0.23/0.29 % Maximum resident set size: 4864 pages
% 0.23/0.29 % E exiting
%------------------------------------------------------------------------------