%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUM756^1 : 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 : n006.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 08:17:02 AM UTC 2026
% Result : Theorem 0.08s 0.24s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 6
% Syntax : Number of formulae : 27 ( 10 unt; 0 typ; 0 def)
% Number of atoms : 60 ( 0 equ; 0 cnn)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 233 ( 42 ~; 15 |; 2 &; 158 @)
% ( 0 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 7 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 42 ( 0 ^; 42 !; 0 ?; 42 :)
% 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,
eq: frac > frac > $o ).
thf(decl_27,type,
pf: frac > frac > frac ).
thf(decl_28,type,
lessf: frac > frac > $o ).
thf(decl_29,type,
moref: frac > frac > $o ).
thf(satz41b,axiom,
! [X2: frac,X3: frac] :
~ ( ( ( eq @ X2 @ X3 )
=> ~ ( moref @ X2 @ X3 ) )
=> ~ ~ ( ( ( moref @ X2 @ X3 )
=> ~ ( lessf @ X2 @ X3 ) )
=> ~ ( ( lessf @ X2 @ X3 )
=> ~ ( eq @ X2 @ X3 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.nPSj8Kd8rO/E---3.1_667046.p',satz41b) ).
thf(satz62a,axiom,
! [X2: frac,X3: frac,X4: frac] :
( ( moref @ X2 @ X3 )
=> ( moref @ ( pf @ X2 @ X4 ) @ ( pf @ X3 @ X4 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.nPSj8Kd8rO/E---3.1_667046.p',satz62a) ).
thf(satz62c,axiom,
! [X2: frac,X3: frac,X4: frac] :
( ( lessf @ X2 @ X3 )
=> ( lessf @ ( pf @ X2 @ X4 ) @ ( pf @ X3 @ X4 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.nPSj8Kd8rO/E---3.1_667046.p',satz62c) ).
thf(satz63b,conjecture,
eq @ x @ y,
file('/export/starexec/sandbox2/tmp/tmp.nPSj8Kd8rO/E---3.1_667046.p',satz63b) ).
thf(satz41a,axiom,
! [X2: frac,X3: frac] :
( ~ ( eq @ X2 @ X3 )
=> ( ~ ( moref @ X2 @ X3 )
=> ( lessf @ X2 @ X3 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.nPSj8Kd8rO/E---3.1_667046.p',satz41a) ).
thf(e,axiom,
eq @ ( pf @ x @ z ) @ ( pf @ y @ z ),
file('/export/starexec/sandbox2/tmp/tmp.nPSj8Kd8rO/E---3.1_667046.p',e) ).
thf(c_0_6,plain,
! [X2: frac,X3: frac] :
~ ( ( ( eq @ X2 @ X3 )
=> ~ ( moref @ X2 @ X3 ) )
=> ~ ~ ( ( ( moref @ X2 @ X3 )
=> ~ ( lessf @ X2 @ X3 ) )
=> ~ ( ( lessf @ X2 @ X3 )
=> ~ ( eq @ X2 @ X3 ) ) ) ),
inference(fof_simplification,[status(thm)],[satz41b]) ).
thf(c_0_7,plain,
! [X16: frac,X17: frac] :
( ( ~ ( eq @ X16 @ X17 )
| ~ ( moref @ X16 @ X17 ) )
& ( ~ ( moref @ X16 @ X17 )
| ~ ( lessf @ X16 @ X17 ) )
& ( ~ ( lessf @ X16 @ X17 )
| ~ ( eq @ X16 @ X17 ) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])]) ).
thf(c_0_8,plain,
! [X23: frac,X24: frac,X25: frac] :
( ~ ( moref @ X23 @ X24 )
| ( moref @ ( pf @ X23 @ X25 ) @ ( pf @ X24 @ X25 ) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[satz62a])])]) ).
thf(c_0_9,plain,
! [X18: frac,X19: frac,X20: frac] :
( ~ ( lessf @ X18 @ X19 )
| ( lessf @ ( pf @ X18 @ X20 ) @ ( pf @ X19 @ X20 ) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[satz62c])])]) ).
thf(c_0_10,negated_conjecture,
~ ( eq @ x @ y ),
inference(assume_negation,[status(cth)],[satz63b]) ).
thf(c_0_11,plain,
! [X2: frac,X3: frac] :
( ~ ( eq @ X2 @ X3 )
| ~ ( moref @ X2 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
thf(c_0_12,plain,
! [X2: frac,X4: frac,X3: frac] :
( ( moref @ ( pf @ X2 @ X4 ) @ ( pf @ X3 @ X4 ) )
| ~ ( moref @ X2 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
thf(c_0_13,plain,
! [X2: frac,X3: frac] :
( ~ ( eq @ X2 @ X3 )
=> ( ~ ( moref @ X2 @ X3 )
=> ( lessf @ X2 @ X3 ) ) ),
inference(fof_simplification,[status(thm)],[satz41a]) ).
thf(c_0_14,plain,
! [X2: frac,X3: frac] :
( ~ ( lessf @ X2 @ X3 )
| ~ ( eq @ X2 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
thf(c_0_15,plain,
! [X2: frac,X4: frac,X3: frac] :
( ( lessf @ ( pf @ X2 @ X4 ) @ ( pf @ X3 @ X4 ) )
| ~ ( lessf @ X2 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
thf(c_0_16,negated_conjecture,
~ ( eq @ x @ y ),
inference(fof_simplification,[status(thm)],[c_0_10]) ).
thf(c_0_17,plain,
! [X2: frac,X3: frac,X4: frac] :
( ~ ( eq @ ( pf @ X2 @ X3 ) @ ( pf @ X4 @ X3 ) )
| ~ ( moref @ X2 @ X4 ) ),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
thf(c_0_18,plain,
eq @ ( pf @ x @ z ) @ ( pf @ y @ z ),
inference(split_conjunct,[status(thm)],[e]) ).
thf(c_0_19,plain,
! [X21: frac,X22: frac] :
( ( eq @ X21 @ X22 )
| ( moref @ X21 @ X22 )
| ( lessf @ X21 @ X22 ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_13])]) ).
thf(c_0_20,plain,
! [X2: frac,X3: frac,X4: frac] :
( ~ ( eq @ ( pf @ X2 @ X3 ) @ ( pf @ X4 @ X3 ) )
| ~ ( lessf @ X2 @ X4 ) ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
thf(c_0_21,negated_conjecture,
~ ( eq @ x @ y ),
inference(fof_nnf,[status(thm)],[c_0_16]) ).
thf(c_0_22,plain,
~ ( moref @ x @ y ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
thf(c_0_23,plain,
! [X2: frac,X3: frac] :
( ( eq @ X2 @ X3 )
| ( moref @ X2 @ X3 )
| ( lessf @ X2 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
thf(c_0_24,plain,
~ ( lessf @ x @ y ),
inference(spm,[status(thm)],[c_0_20,c_0_18]) ).
thf(c_0_25,negated_conjecture,
~ ( eq @ x @ y ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
thf(c_0_26,plain,
$false,
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_24]),c_0_25]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM756^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.17 % Computer : n006.cluster.edu
% 0.08/0.17 % Model : x86_64 x86_64
% 0.08/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.17 % Memory : 8046.5625MB
% 0.08/0.17 % OS : Linux 6.8.0-71-generic
% 0.08/0.17 % CPULimit : 300
% 0.08/0.17 % WCLimit : 300
% 0.08/0.17 % DateTime : Tue Sep 29 12:52:08 UTC 2026
% 0.08/0.17 % CPUTime :
% 0.08/0.17 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.21 Running higher-order theorem proving
% 0.08/0.22 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.nPSj8Kd8rO/E---3.1_667046.p
% 0.08/0.24 % Version: 3.5.1-ho
% 0.08/0.24 % Preprocessing class: HSMSSMSSSSSNFFN.
% 0.08/0.24 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.08/0.24 % Starting new_ho_10 with 1500s (5) cores
% 0.08/0.24 % Starting new_bool_1 with 300s (1) cores
% 0.08/0.24 % Starting full_lambda_5 with 300s (1) cores
% 0.08/0.24 % Starting new_ho_10_unif with 300s (1) cores
% 0.08/0.24 % full_lambda_5 with pid 667076 completed with status 0
% 0.08/0.24 % Result found by full_lambda_5
% 0.08/0.24 % Preprocessing class: HSMSSMSSSSSNFFN.
% 0.08/0.24 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.08/0.24 % Starting new_ho_10 with 1500s (5) cores
% 0.08/0.24 % Starting new_bool_1 with 300s (1) cores
% 0.08/0.24 % Starting full_lambda_5 with 300s (1) cores
% 0.08/0.24 % (lift_lambdas = 1, lambda_to_forall = 0,unroll_only_formulas = 1, sine = Auto)
% 0.08/0.24 % No SInE strategy applied
% 0.08/0.24 % Search class: HGHNF-FFSF22-SFFFFFNN
% 0.08/0.24 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.08/0.24 % Starting SubtermCWHack with 28s (1) cores
% 0.08/0.24 % SubtermCWHack with pid 667082 completed with status 0
% 0.08/0.24 % Result found by SubtermCWHack
% 0.08/0.24 % Preprocessing class: HSMSSMSSSSSNFFN.
% 0.08/0.24 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.08/0.24 % Starting new_ho_10 with 1500s (5) cores
% 0.08/0.24 % Starting new_bool_1 with 300s (1) cores
% 0.08/0.24 % Starting full_lambda_5 with 300s (1) cores
% 0.08/0.24 % (lift_lambdas = 1, lambda_to_forall = 0,unroll_only_formulas = 1, sine = Auto)
% 0.08/0.24 % No SInE strategy applied
% 0.08/0.24 % Search class: HGHNF-FFSF22-SFFFFFNN
% 0.08/0.24 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.08/0.24 % Starting SubtermCWHack with 28s (1) cores
% 0.08/0.24 % Preprocessing time : 0.001 s
% 0.08/0.24
% 0.08/0.24 % Proof found!
% 0.08/0.24 % SZS status Theorem
% 0.08/0.24 % SZS output start CNFRefutation
% See solution above
% 0.08/0.24 % Parsed axioms : 15
% 0.08/0.24 % Removed by relevancy pruning/SinE : 0
% 0.08/0.24 % Initial clauses : 17
% 0.08/0.24 % Removed in clause preprocessing : 9
% 0.08/0.24 % Initial clauses in saturation : 8
% 0.08/0.24 % Processed clauses : 12
% 0.08/0.24 % ...of these trivial : 0
% 0.08/0.24 % ...subsumed : 0
% 0.08/0.24 % ...remaining for further processing : 12
% 0.08/0.24 % Other redundant clauses eliminated : 0
% 0.08/0.24 % Clauses deleted for lack of memory : 0
% 0.08/0.24 % Backward-subsumed : 0
% 0.08/0.24 % Backward-rewritten : 0
% 0.08/0.24 % Generated clauses : 8
% 0.08/0.24 % ...of the previous two non-redundant : 5
% 0.08/0.24 % ...aggressively subsumed : 0
% 0.08/0.24 % Contextual simplify-reflections : 0
% 0.08/0.24 % Paramodulations : 8
% 0.08/0.24 % Factorizations : 0
% 0.08/0.24 % NegExts : 0
% 0.08/0.24 % Equation resolutions : 0
% 0.08/0.24 % Disequality decompositions : 0
% 0.08/0.24 % Total rewrite steps : 0
% 0.08/0.24 % ...of those cached : 0
% 0.08/0.24 % Propositional unsat checks : 0
% 0.08/0.24 % Propositional check models : 0
% 0.08/0.24 % Propositional check unsatisfiable : 0
% 0.08/0.24 % Propositional clauses : 0
% 0.08/0.24 % Propositional clauses after purity: 0
% 0.08/0.24 % Propositional unsat core size : 0
% 0.08/0.24 % Propositional preprocessing time : 0.000
% 0.08/0.24 % Propositional encoding time : 0.000
% 0.08/0.24 % Propositional solver time : 0.000
% 0.08/0.24 % Success case prop preproc time : 0.000
% 0.08/0.24 % Success case prop encoding time : 0.000
% 0.08/0.24 % Success case prop solver time : 0.000
% 0.08/0.24 % Current number of processed clauses : 12
% 0.08/0.24 % Positive orientable unit clauses : 1
% 0.08/0.24 % Positive unorientable unit clauses: 0
% 0.08/0.24 % Negative unit clauses : 3
% 0.08/0.24 % Non-unit-clauses : 8
% 0.08/0.24 % Current number of unprocessed clauses: 1
% 0.08/0.24 % ...number of literals in the above : 2
% 0.08/0.24 % Current number of archived formulas : 0
% 0.08/0.24 % Current number of archived clauses : 0
% 0.08/0.24 % Clause-clause subsumption calls (NU) : 4
% 0.08/0.24 % Rec. Clause-clause subsumption calls : 2
% 0.08/0.24 % Non-unit clause-clause subsumptions : 0
% 0.08/0.24 % Unit Clause-clause subsumption calls : 0
% 0.08/0.24 % Rewrite failures with RHS unbound : 0
% 0.08/0.24 % BW rewrite match attempts : 0
% 0.08/0.24 % BW rewrite match successes : 0
% 0.08/0.24 % Condensation attempts : 0
% 0.08/0.24 % Condensation successes : 0
% 0.08/0.24 % Termbank termtop insertions : 943
% 0.08/0.24 % Search garbage collected termcells : 145
% 0.08/0.24
% 0.08/0.24 % -------------------------------------------------
% 0.08/0.24 % User time : 0.002 s
% 0.08/0.24 % System time : 0.003 s
% 0.08/0.24 % Total time : 0.005 s
% 0.08/0.24 % Maximum resident set size: 3640 pages
% 0.08/0.24
% 0.08/0.24 % -------------------------------------------------
% 0.08/0.24 % User time : 0.002 s
% 0.08/0.24 % System time : 0.008 s
% 0.08/0.24 % Total time : 0.010 s
% 0.08/0.24 % Maximum resident set size: 4864 pages
% 0.08/0.24 % E exiting
%------------------------------------------------------------------------------