%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : GEO443+1 : TPTP v9.3.1. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n016.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 : Thu Sep 24 12:28:17 PM UTC 2026
% Result : Theorem 4.07s 1.80s
% Output : CNFRefutation 4.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 3
% Syntax : Number of formulae : 12 ( 12 unt; 0 def)
% Number of atoms : 12 ( 11 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 4 ( 4 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 12 ( 3 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 8 con; 0-2 aty)
% Number of variables : 24 ( 0 sgn 18 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(aDISTu_SYM,conjecture,
! [X1049,X1,X8] : s(real,i(s(fun(prod(cart(real,X1049),cart(real,X1049)),real),distance),s(prod(cart(real,X1049),cart(real,X1049)),i(s(fun(cart(real,X1049),prod(cart(real,X1049),cart(real,X1049))),i(s(fun(cart(real,X1049),fun(cart(real,X1049),prod(cart(real,X1049),cart(real,X1049)))),c_),s(cart(real,X1049),X1))),s(cart(real,X1049),X8))))) = s(real,i(s(fun(prod(cart(real,X1049),cart(real,X1049)),real),distance),s(prod(cart(real,X1049),cart(real,X1049)),i(s(fun(cart(real,X1049),prod(cart(real,X1049),cart(real,X1049))),i(s(fun(cart(real,X1049),fun(cart(real,X1049),prod(cart(real,X1049),cart(real,X1049)))),c_),s(cart(real,X1049),X8))),s(cart(real,X1049),X1))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aDISTu_SYM) ).
fof(adist,axiom,
! [X1012,X1,X8] : s(real,i(s(fun(prod(cart(real,X1012),cart(real,X1012)),real),distance),s(prod(cart(real,X1012),cart(real,X1012)),i(s(fun(cart(real,X1012),prod(cart(real,X1012),cart(real,X1012))),i(s(fun(cart(real,X1012),fun(cart(real,X1012),prod(cart(real,X1012),cart(real,X1012)))),c_),s(cart(real,X1012),X1))),s(cart(real,X1012),X8))))) = s(real,i(s(fun(cart(real,X1012),real),vectoru_norm),s(cart(real,X1012),i(s(fun(cart(real,X1012),cart(real,X1012)),i(s(fun(cart(real,X1012),fun(cart(real,X1012),cart(real,X1012))),vectoru_sub),s(cart(real,X1012),X1))),s(cart(real,X1012),X8))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',adist) ).
fof(aNORMu_SUB,axiom,
! [X1018,X1,X8] : s(real,i(s(fun(cart(real,X1018),real),vectoru_norm),s(cart(real,X1018),i(s(fun(cart(real,X1018),cart(real,X1018)),i(s(fun(cart(real,X1018),fun(cart(real,X1018),cart(real,X1018))),vectoru_sub),s(cart(real,X1018),X1))),s(cart(real,X1018),X8))))) = s(real,i(s(fun(cart(real,X1018),real),vectoru_norm),s(cart(real,X1018),i(s(fun(cart(real,X1018),cart(real,X1018)),i(s(fun(cart(real,X1018),fun(cart(real,X1018),cart(real,X1018))),vectoru_sub),s(cart(real,X1018),X8))),s(cart(real,X1018),X1))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aNORMu_SUB) ).
fof(c_0_3,negated_conjecture,
~ ! [X1049,X1,X8] : s(real,i(s(fun(prod(cart(real,X1049),cart(real,X1049)),real),distance),s(prod(cart(real,X1049),cart(real,X1049)),i(s(fun(cart(real,X1049),prod(cart(real,X1049),cart(real,X1049))),i(s(fun(cart(real,X1049),fun(cart(real,X1049),prod(cart(real,X1049),cart(real,X1049)))),c_),s(cart(real,X1049),X1))),s(cart(real,X1049),X8))))) = s(real,i(s(fun(prod(cart(real,X1049),cart(real,X1049)),real),distance),s(prod(cart(real,X1049),cart(real,X1049)),i(s(fun(cart(real,X1049),prod(cart(real,X1049),cart(real,X1049))),i(s(fun(cart(real,X1049),fun(cart(real,X1049),prod(cart(real,X1049),cart(real,X1049)))),c_),s(cart(real,X1049),X8))),s(cart(real,X1049),X1))))),
inference(assume_negation,[status(cth)],[aDISTu_SYM]) ).
fof(c_0_4,negated_conjecture,
s(real,i(s(fun(prod(cart(real,esk1_0),cart(real,esk1_0)),real),distance),s(prod(cart(real,esk1_0),cart(real,esk1_0)),i(s(fun(cart(real,esk1_0),prod(cart(real,esk1_0),cart(real,esk1_0))),i(s(fun(cart(real,esk1_0),fun(cart(real,esk1_0),prod(cart(real,esk1_0),cart(real,esk1_0)))),c_),s(cart(real,esk1_0),esk2_0))),s(cart(real,esk1_0),esk3_0))))) != s(real,i(s(fun(prod(cart(real,esk1_0),cart(real,esk1_0)),real),distance),s(prod(cart(real,esk1_0),cart(real,esk1_0)),i(s(fun(cart(real,esk1_0),prod(cart(real,esk1_0),cart(real,esk1_0))),i(s(fun(cart(real,esk1_0),fun(cart(real,esk1_0),prod(cart(real,esk1_0),cart(real,esk1_0)))),c_),s(cart(real,esk1_0),esk3_0))),s(cart(real,esk1_0),esk2_0))))),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_3])])])]) ).
fof(c_0_5,plain,
! [X1285,X1286,X1287] : s(real,i(s(fun(prod(cart(real,X1285),cart(real,X1285)),real),distance),s(prod(cart(real,X1285),cart(real,X1285)),i(s(fun(cart(real,X1285),prod(cart(real,X1285),cart(real,X1285))),i(s(fun(cart(real,X1285),fun(cart(real,X1285),prod(cart(real,X1285),cart(real,X1285)))),c_),s(cart(real,X1285),X1286))),s(cart(real,X1285),X1287))))) = s(real,i(s(fun(cart(real,X1285),real),vectoru_norm),s(cart(real,X1285),i(s(fun(cart(real,X1285),cart(real,X1285)),i(s(fun(cart(real,X1285),fun(cart(real,X1285),cart(real,X1285))),vectoru_sub),s(cart(real,X1285),X1286))),s(cart(real,X1285),X1287))))),
inference(variable_rename,[status(thm)],[adist]) ).
cnf(c_0_6,negated_conjecture,
s(real,i(s(fun(prod(cart(real,esk1_0),cart(real,esk1_0)),real),distance),s(prod(cart(real,esk1_0),cart(real,esk1_0)),i(s(fun(cart(real,esk1_0),prod(cart(real,esk1_0),cart(real,esk1_0))),i(s(fun(cart(real,esk1_0),fun(cart(real,esk1_0),prod(cart(real,esk1_0),cart(real,esk1_0)))),c_),s(cart(real,esk1_0),esk2_0))),s(cart(real,esk1_0),esk3_0))))) != s(real,i(s(fun(prod(cart(real,esk1_0),cart(real,esk1_0)),real),distance),s(prod(cart(real,esk1_0),cart(real,esk1_0)),i(s(fun(cart(real,esk1_0),prod(cart(real,esk1_0),cart(real,esk1_0))),i(s(fun(cart(real,esk1_0),fun(cart(real,esk1_0),prod(cart(real,esk1_0),cart(real,esk1_0)))),c_),s(cart(real,esk1_0),esk3_0))),s(cart(real,esk1_0),esk2_0))))),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_7,plain,
s(real,i(s(fun(prod(cart(real,X1),cart(real,X1)),real),distance),s(prod(cart(real,X1),cart(real,X1)),i(s(fun(cart(real,X1),prod(cart(real,X1),cart(real,X1))),i(s(fun(cart(real,X1),fun(cart(real,X1),prod(cart(real,X1),cart(real,X1)))),c_),s(cart(real,X1),X2))),s(cart(real,X1),X3))))) = s(real,i(s(fun(cart(real,X1),real),vectoru_norm),s(cart(real,X1),i(s(fun(cart(real,X1),cart(real,X1)),i(s(fun(cart(real,X1),fun(cart(real,X1),cart(real,X1))),vectoru_sub),s(cart(real,X1),X2))),s(cart(real,X1),X3))))),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
fof(c_0_8,plain,
! [X2401,X2402,X2403] : s(real,i(s(fun(cart(real,X2401),real),vectoru_norm),s(cart(real,X2401),i(s(fun(cart(real,X2401),cart(real,X2401)),i(s(fun(cart(real,X2401),fun(cart(real,X2401),cart(real,X2401))),vectoru_sub),s(cart(real,X2401),X2402))),s(cart(real,X2401),X2403))))) = s(real,i(s(fun(cart(real,X2401),real),vectoru_norm),s(cart(real,X2401),i(s(fun(cart(real,X2401),cart(real,X2401)),i(s(fun(cart(real,X2401),fun(cart(real,X2401),cart(real,X2401))),vectoru_sub),s(cart(real,X2401),X2403))),s(cart(real,X2401),X2402))))),
inference(variable_rename,[status(thm)],[aNORMu_SUB]) ).
cnf(c_0_9,negated_conjecture,
s(real,i(s(fun(cart(real,esk1_0),real),vectoru_norm),s(cart(real,esk1_0),i(s(fun(cart(real,esk1_0),cart(real,esk1_0)),i(s(fun(cart(real,esk1_0),fun(cart(real,esk1_0),cart(real,esk1_0))),vectoru_sub),s(cart(real,esk1_0),esk2_0))),s(cart(real,esk1_0),esk3_0))))) != s(real,i(s(fun(cart(real,esk1_0),real),vectoru_norm),s(cart(real,esk1_0),i(s(fun(cart(real,esk1_0),cart(real,esk1_0)),i(s(fun(cart(real,esk1_0),fun(cart(real,esk1_0),cart(real,esk1_0))),vectoru_sub),s(cart(real,esk1_0),esk3_0))),s(cart(real,esk1_0),esk2_0))))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6,c_0_7]),c_0_7]) ).
cnf(c_0_10,plain,
s(real,i(s(fun(cart(real,X1),real),vectoru_norm),s(cart(real,X1),i(s(fun(cart(real,X1),cart(real,X1)),i(s(fun(cart(real,X1),fun(cart(real,X1),cart(real,X1))),vectoru_sub),s(cart(real,X1),X2))),s(cart(real,X1),X3))))) = s(real,i(s(fun(cart(real,X1),real),vectoru_norm),s(cart(real,X1),i(s(fun(cart(real,X1),cart(real,X1)),i(s(fun(cart(real,X1),fun(cart(real,X1),cart(real,X1))),vectoru_sub),s(cart(real,X1),X3))),s(cart(real,X1),X2))))),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_11,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_9,c_0_10])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO443+1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.36 % Computer : n016.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Sun Sep 20 16:19:36 UTC 2026
% 0.11/0.36 % CPUTime :
% 0.11/0.36 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.41 Running: /export/starexec/sandbox/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.07/1.80 % Version: 3.5.1
% 4.07/1.80 % Preprocessing class: FMLMSMSLSSSNFFN.
% 4.07/1.80 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 4.07/1.80 % Starting G-E--_208_C18C--_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 900s (3) cores
% 4.07/1.80 % Starting new_bool_3 with 600s (2) cores
% 4.07/1.80 % Starting new_bool_1 with 600s (2) cores
% 4.07/1.80 % Starting sh5l with 300s (1) cores
% 4.07/1.80 % new_bool_3 with pid 389896 completed with status 0
% 4.07/1.80 % Result found by new_bool_3
% 4.07/1.80 % Preprocessing class: FMLMSMSLSSSNFFN.
% 4.07/1.80 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 4.07/1.80 % Starting G-E--_208_C18C--_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 900s (3) cores
% 4.07/1.80 % Starting new_bool_3 with 600s (2) cores
% 4.07/1.80 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 4.07/1.80 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 4.07/1.80 % Search class: FGHSM-SMLM33-DFFFFFNN
% 4.07/1.80 % Scheduled 7 strats onto 2 cores with 600 seconds (600 total)
% 4.07/1.80 % Starting SubtermCWHack with 55s (1) cores
% 4.07/1.80 % Starting new_bool_3 with 61s (1) cores
% 4.07/1.80 % new_bool_3 with pid 389900 completed with status 0
% 4.07/1.80 % Result found by new_bool_3
% 4.07/1.80 % Preprocessing class: FMLMSMSLSSSNFFN.
% 4.07/1.80 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 4.07/1.80 % Starting G-E--_208_C18C--_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 900s (3) cores
% 4.07/1.80 % Starting new_bool_3 with 600s (2) cores
% 4.07/1.80 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 4.07/1.80 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 4.07/1.80 % Search class: FGHSM-SMLM33-DFFFFFNN
% 4.07/1.80 % Scheduled 7 strats onto 2 cores with 600 seconds (600 total)
% 4.07/1.80 % Starting SubtermCWHack with 55s (1) cores
% 4.07/1.80 % Starting new_bool_3 with 61s (1) cores
% 4.07/1.80 % Preprocessing time : 0.194 s
% 4.07/1.80 % Presaturation interreduction done
% 4.07/1.80
% 4.07/1.80 % Proof found!
% 4.07/1.80 % SZS status Theorem
% 4.07/1.80 % SZS output start CNFRefutation
% See solution above
% 4.07/1.81 % Parsed axioms : 2891
% 4.07/1.81 % Removed by relevancy pruning/SinE : 1859
% 4.07/1.81 % Initial clauses : 3037
% 4.07/1.81 % Removed in clause preprocessing : 172
% 4.07/1.81 % Initial clauses in saturation : 2865
% 4.07/1.81 % Processed clauses : 1059
% 4.07/1.81 % ...of these trivial : 47
% 4.07/1.81 % ...subsumed : 84
% 4.07/1.81 % ...remaining for further processing : 928
% 4.07/1.81 % Other redundant clauses eliminated : 0
% 4.07/1.81 % Clauses deleted for lack of memory : 0
% 4.07/1.81 % Backward-subsumed : 4
% 4.07/1.81 % Backward-rewritten : 28
% 4.07/1.81 % Generated clauses : 0
% 4.07/1.81 % ...of the previous two non-redundant : 13
% 4.07/1.81 % ...aggressively subsumed : 0
% 4.07/1.81 % Contextual simplify-reflections : 1
% 4.07/1.81 % Paramodulations : 0
% 4.07/1.81 % Factorizations : 0
% 4.07/1.81 % NegExts : 0
% 4.07/1.81 % Equation resolutions : 0
% 4.07/1.81 % Disequality decompositions : 0
% 4.07/1.81 % Total rewrite steps : 711
% 4.07/1.81 % ...of those cached : 546
% 4.07/1.81 % Propositional unsat checks : 0
% 4.07/1.81 % Propositional check models : 0
% 4.07/1.81 % Propositional check unsatisfiable : 0
% 4.07/1.81 % Propositional clauses : 0
% 4.07/1.81 % Propositional clauses after purity: 0
% 4.07/1.81 % Propositional unsat core size : 0
% 4.07/1.81 % Propositional preprocessing time : 0.000
% 4.07/1.81 % Propositional encoding time : 0.000
% 4.07/1.81 % Propositional solver time : 0.000
% 4.07/1.81 % Success case prop preproc time : 0.000
% 4.07/1.81 % Success case prop encoding time : 0.000
% 4.07/1.81 % Success case prop solver time : 0.000
% 4.07/1.81 % Current number of processed clauses : 896
% 4.07/1.81 % Positive orientable unit clauses : 229
% 4.07/1.81 % Positive unorientable unit clauses: 14
% 4.07/1.81 % Negative unit clauses : 7
% 4.07/1.81 % Non-unit-clauses : 646
% 4.07/1.81 % Current number of unprocessed clauses: 1819
% 4.07/1.81 % ...number of literals in the above : 13297
% 4.07/1.81 % Current number of archived formulas : 0
% 4.07/1.81 % Current number of archived clauses : 32
% 4.07/1.81 % Clause-clause subsumption calls (NU) : 62962
% 4.07/1.81 % Rec. Clause-clause subsumption calls : 35744
% 4.07/1.81 % Non-unit clause-clause subsumptions : 88
% 4.07/1.81 % Unit Clause-clause subsumption calls : 31
% 4.07/1.81 % Rewrite failures with RHS unbound : 8
% 4.07/1.81 % BW rewrite match attempts : 42391
% 4.07/1.81 % BW rewrite match successes : 80
% 4.07/1.81 % Condensation attempts : 0
% 4.07/1.81 % Condensation successes : 0
% 4.07/1.81 % Termbank termtop insertions : 1802322
% 4.07/1.81 % Search garbage collected termcells : 94627
% 4.07/1.81
% 4.07/1.81 % -------------------------------------------------
% 4.07/1.81 % User time : 0.874 s
% 4.07/1.81 % System time : 0.056 s
% 4.07/1.81 % Total time : 0.930 s
% 4.07/1.81 % Maximum resident set size: 23092 pages
% 4.07/1.81
% 4.07/1.81 % -------------------------------------------------
% 4.07/1.81 % User time : 1.588 s
% 4.07/1.81 % System time : 0.107 s
% 4.07/1.81 % Total time : 1.695 s
% 4.07/1.81 % Maximum resident set size: 13312 pages
% 4.07/1.81 % E exiting
%------------------------------------------------------------------------------