%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : GEO450+1 : TPTP v9.3.1. Released v7.0.0.
% 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 : Thu Sep 24 12:30:12 PM UTC 2026
% Result : Theorem 24.37s 20.45s
% Output : CNFRefutation 24.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 4
% Syntax : Number of formulae : 16 ( 16 unt; 0 def)
% Number of atoms : 16 ( 15 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 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 10 con; 0-2 aty)
% Number of variables : 33 ( 0 sgn 22 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(aMATRIXu_SUBu_LZERO,conjecture,
! [X733,X738,X16] : s(cart(cart(real,X733),X738),i(s(fun(cart(cart(real,X733),X738),cart(cart(real,X733),X738)),i(s(fun(cart(cart(real,X733),X738),fun(cart(cart(real,X733),X738),cart(cart(real,X733),X738))),matrixu_sub),s(cart(cart(real,X733),X738),i(s(fun(num,cart(cart(real,X733),X738)),mat),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(cart(cart(real,X733),X738),X16))) = s(cart(cart(real,X733),X738),i(s(fun(cart(cart(real,X733),X738),cart(cart(real,X733),X738)),matrixu_neg),s(cart(cart(real,X733),X738),X16))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aMATRIXu_SUBu_LZERO) ).
fof(aNUMERAL,axiom,
! [X84] : s(num,i(s(fun(num,num),numeral),s(num,X84))) = s(num,X84),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO010+0.ax',aNUMERAL) ).
fof(aMATRIXu_SUBu_RZERO,axiom,
! [X733,X738,X16] : s(cart(cart(real,X733),X738),i(s(fun(cart(cart(real,X733),X738),cart(cart(real,X733),X738)),i(s(fun(cart(cart(real,X733),X738),fun(cart(cart(real,X733),X738),cart(cart(real,X733),X738))),matrixu_sub),s(cart(cart(real,X733),X738),X16))),s(cart(cart(real,X733),X738),i(s(fun(num,cart(cart(real,X733),X738)),mat),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))) = s(cart(cart(real,X733),X738),X16),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aMATRIXu_SUBu_RZERO) ).
fof(aMATRIXu_NEGu_SUB,axiom,
! [X733,X738,X16,X20] : s(cart(cart(real,X733),X738),i(s(fun(cart(cart(real,X733),X738),cart(cart(real,X733),X738)),matrixu_neg),s(cart(cart(real,X733),X738),i(s(fun(cart(cart(real,X733),X738),cart(cart(real,X733),X738)),i(s(fun(cart(cart(real,X733),X738),fun(cart(cart(real,X733),X738),cart(cart(real,X733),X738))),matrixu_sub),s(cart(cart(real,X733),X738),X16))),s(cart(cart(real,X733),X738),X20))))) = s(cart(cart(real,X733),X738),i(s(fun(cart(cart(real,X733),X738),cart(cart(real,X733),X738)),i(s(fun(cart(cart(real,X733),X738),fun(cart(cart(real,X733),X738),cart(cart(real,X733),X738))),matrixu_sub),s(cart(cart(real,X733),X738),X20))),s(cart(cart(real,X733),X738),X16))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aMATRIXu_NEGu_SUB) ).
fof(c_0_4,negated_conjecture,
~ ! [X733,X738,X16] : s(cart(cart(real,X733),X738),i(s(fun(cart(cart(real,X733),X738),cart(cart(real,X733),X738)),i(s(fun(cart(cart(real,X733),X738),fun(cart(cart(real,X733),X738),cart(cart(real,X733),X738))),matrixu_sub),s(cart(cart(real,X733),X738),i(s(fun(num,cart(cart(real,X733),X738)),mat),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(cart(cart(real,X733),X738),X16))) = s(cart(cart(real,X733),X738),i(s(fun(cart(cart(real,X733),X738),cart(cart(real,X733),X738)),matrixu_neg),s(cart(cart(real,X733),X738),X16))),
inference(assume_negation,[status(cth)],[aMATRIXu_SUBu_LZERO]) ).
fof(c_0_5,negated_conjecture,
s(cart(cart(real,esk3735_0),esk3736_0),i(s(fun(cart(cart(real,esk3735_0),esk3736_0),cart(cart(real,esk3735_0),esk3736_0)),i(s(fun(cart(cart(real,esk3735_0),esk3736_0),fun(cart(cart(real,esk3735_0),esk3736_0),cart(cart(real,esk3735_0),esk3736_0))),matrixu_sub),s(cart(cart(real,esk3735_0),esk3736_0),i(s(fun(num,cart(cart(real,esk3735_0),esk3736_0)),mat),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(cart(cart(real,esk3735_0),esk3736_0),esk3737_0))) != s(cart(cart(real,esk3735_0),esk3736_0),i(s(fun(cart(cart(real,esk3735_0),esk3736_0),cart(cart(real,esk3735_0),esk3736_0)),matrixu_neg),s(cart(cart(real,esk3735_0),esk3736_0),esk3737_0))),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])])])]) ).
fof(c_0_6,plain,
! [X2341] : s(num,i(s(fun(num,num),numeral),s(num,X2341))) = s(num,X2341),
inference(variable_rename,[status(thm)],[aNUMERAL]) ).
fof(c_0_7,plain,
! [X16132,X16133,X16134] : s(cart(cart(real,X16132),X16133),i(s(fun(cart(cart(real,X16132),X16133),cart(cart(real,X16132),X16133)),i(s(fun(cart(cart(real,X16132),X16133),fun(cart(cart(real,X16132),X16133),cart(cart(real,X16132),X16133))),matrixu_sub),s(cart(cart(real,X16132),X16133),X16134))),s(cart(cart(real,X16132),X16133),i(s(fun(num,cart(cart(real,X16132),X16133)),mat),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))) = s(cart(cart(real,X16132),X16133),X16134),
inference(variable_rename,[status(thm)],[aMATRIXu_SUBu_RZERO]) ).
cnf(c_0_8,negated_conjecture,
s(cart(cart(real,esk3735_0),esk3736_0),i(s(fun(cart(cart(real,esk3735_0),esk3736_0),cart(cart(real,esk3735_0),esk3736_0)),i(s(fun(cart(cart(real,esk3735_0),esk3736_0),fun(cart(cart(real,esk3735_0),esk3736_0),cart(cart(real,esk3735_0),esk3736_0))),matrixu_sub),s(cart(cart(real,esk3735_0),esk3736_0),i(s(fun(num,cart(cart(real,esk3735_0),esk3736_0)),mat),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(cart(cart(real,esk3735_0),esk3736_0),esk3737_0))) != s(cart(cart(real,esk3735_0),esk3736_0),i(s(fun(cart(cart(real,esk3735_0),esk3736_0),cart(cart(real,esk3735_0),esk3736_0)),matrixu_neg),s(cart(cart(real,esk3735_0),esk3736_0),esk3737_0))),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_9,plain,
s(num,i(s(fun(num,num),numeral),s(num,X1))) = s(num,X1),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
fof(c_0_10,plain,
! [X16126,X16127,X16128,X16129] : s(cart(cart(real,X16126),X16127),i(s(fun(cart(cart(real,X16126),X16127),cart(cart(real,X16126),X16127)),matrixu_neg),s(cart(cart(real,X16126),X16127),i(s(fun(cart(cart(real,X16126),X16127),cart(cart(real,X16126),X16127)),i(s(fun(cart(cart(real,X16126),X16127),fun(cart(cart(real,X16126),X16127),cart(cart(real,X16126),X16127))),matrixu_sub),s(cart(cart(real,X16126),X16127),X16128))),s(cart(cart(real,X16126),X16127),X16129))))) = s(cart(cart(real,X16126),X16127),i(s(fun(cart(cart(real,X16126),X16127),cart(cart(real,X16126),X16127)),i(s(fun(cart(cart(real,X16126),X16127),fun(cart(cart(real,X16126),X16127),cart(cart(real,X16126),X16127))),matrixu_sub),s(cart(cart(real,X16126),X16127),X16129))),s(cart(cart(real,X16126),X16127),X16128))),
inference(variable_rename,[status(thm)],[aMATRIXu_NEGu_SUB]) ).
cnf(c_0_11,plain,
s(cart(cart(real,X1),X2),i(s(fun(cart(cart(real,X1),X2),cart(cart(real,X1),X2)),i(s(fun(cart(cart(real,X1),X2),fun(cart(cart(real,X1),X2),cart(cart(real,X1),X2))),matrixu_sub),s(cart(cart(real,X1),X2),X3))),s(cart(cart(real,X1),X2),i(s(fun(num,cart(cart(real,X1),X2)),mat),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))) = s(cart(cart(real,X1),X2),X3),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_12,negated_conjecture,
s(cart(cart(real,esk3735_0),esk3736_0),i(s(fun(cart(cart(real,esk3735_0),esk3736_0),cart(cart(real,esk3735_0),esk3736_0)),i(s(fun(cart(cart(real,esk3735_0),esk3736_0),fun(cart(cart(real,esk3735_0),esk3736_0),cart(cart(real,esk3735_0),esk3736_0))),matrixu_sub),s(cart(cart(real,esk3735_0),esk3736_0),i(s(fun(num,cart(cart(real,esk3735_0),esk3736_0)),mat),s(num,u_0))))),s(cart(cart(real,esk3735_0),esk3736_0),esk3737_0))) != s(cart(cart(real,esk3735_0),esk3736_0),i(s(fun(cart(cart(real,esk3735_0),esk3736_0),cart(cart(real,esk3735_0),esk3736_0)),matrixu_neg),s(cart(cart(real,esk3735_0),esk3736_0),esk3737_0))),
inference(rw,[status(thm)],[c_0_8,c_0_9]) ).
cnf(c_0_13,plain,
s(cart(cart(real,X1),X2),i(s(fun(cart(cart(real,X1),X2),cart(cart(real,X1),X2)),matrixu_neg),s(cart(cart(real,X1),X2),i(s(fun(cart(cart(real,X1),X2),cart(cart(real,X1),X2)),i(s(fun(cart(cart(real,X1),X2),fun(cart(cart(real,X1),X2),cart(cart(real,X1),X2))),matrixu_sub),s(cart(cart(real,X1),X2),X3))),s(cart(cart(real,X1),X2),X4))))) = s(cart(cart(real,X1),X2),i(s(fun(cart(cart(real,X1),X2),cart(cart(real,X1),X2)),i(s(fun(cart(cart(real,X1),X2),fun(cart(cart(real,X1),X2),cart(cart(real,X1),X2))),matrixu_sub),s(cart(cart(real,X1),X2),X4))),s(cart(cart(real,X1),X2),X3))),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_14,plain,
s(cart(cart(real,X1),X2),i(s(fun(cart(cart(real,X1),X2),cart(cart(real,X1),X2)),i(s(fun(cart(cart(real,X1),X2),fun(cart(cart(real,X1),X2),cart(cart(real,X1),X2))),matrixu_sub),s(cart(cart(real,X1),X2),X3))),s(cart(cart(real,X1),X2),i(s(fun(num,cart(cart(real,X1),X2)),mat),s(num,u_0))))) = s(cart(cart(real,X1),X2),X3),
inference(rw,[status(thm)],[c_0_11,c_0_9]) ).
cnf(c_0_15,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_12,c_0_13]),c_0_14])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO450+1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/15.40 % Computer : n004.cluster.edu
% 0.12/15.40 % Model : x86_64 x86_64
% 0.12/15.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/15.40 % Memory : 8046.5625MB
% 0.12/15.40 % OS : Linux 6.8.0-71-generic
% 0.15/15.40 % CPULimit : 300
% 0.15/15.40 % WCLimit : 300
% 0.15/15.40 % DateTime : Sun Sep 20 16:22:36 UTC 2026
% 0.15/15.40 % CPUTime :
% 0.15/15.40 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.15/15.44 Running first-order theorem proving
% 0.15/15.44 Running: /export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p
% 24.37/20.45 % Version: 3.5.1
% 24.37/20.45 % Preprocessing class: FMLMSMSLSSSNFFN.
% 24.37/20.45 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 24.37/20.45 % Starting G-E--_208_C18C--_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 900s (3) cores
% 24.37/20.45 % Starting new_bool_3 with 600s (2) cores
% 24.37/20.45 % Starting new_bool_1 with 600s (2) cores
% 24.37/20.45 % Starting sh5l with 300s (1) cores
% 24.37/20.45 % G-E--_208_C18C--_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with pid 1085426 completed with status 0
% 24.37/20.45 % Result found by G-E--_208_C18C--_F1_SE_CS_SP_PS_S5PRR_RG_S04AN
% 24.37/20.45 % Preprocessing class: FMLMSMSLSSSNFFN.
% 24.37/20.45 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 24.37/20.45 % Starting G-E--_208_C18C--_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 900s (3) cores
% 24.37/20.45 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 24.37/20.45 % No SInE strategy applied
% 24.37/20.45 % Search class: FGHSM-SMLM33-DFFFFFNN
% 24.37/20.45 % Scheduled 7 strats onto 3 cores with 898 seconds (898 total)
% 24.37/20.45 % Starting SubtermCWHack with 81s (1) cores
% 24.37/20.45 % Starting G-E--_208_C18C--_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 90s (1) cores
% 24.37/20.45 % Starting U----_206e_00_B11_00_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 81s (1) cores
% 24.37/20.45 % U----_206e_00_B11_00_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with pid 1085437 completed with status 0
% 24.37/20.45 % Result found by U----_206e_00_B11_00_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN
% 24.37/20.45 % Preprocessing class: FMLMSMSLSSSNFFN.
% 24.37/20.45 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 24.37/20.45 % Starting G-E--_208_C18C--_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 900s (3) cores
% 24.37/20.45 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 24.37/20.45 % No SInE strategy applied
% 24.37/20.45 % Search class: FGHSM-SMLM33-DFFFFFNN
% 24.37/20.45 % Scheduled 7 strats onto 3 cores with 898 seconds (898 total)
% 24.37/20.45 % Starting SubtermCWHack with 81s (1) cores
% 24.37/20.45 % Starting G-E--_208_C18C--_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 90s (1) cores
% 24.37/20.45 % Starting U----_206e_00_B11_00_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 81s (1) cores
% 24.37/20.45 % Preprocessing time : 0.754 s
% 24.37/20.45 % Presaturation interreduction done
% 24.37/20.45
% 24.37/20.45 % Proof found!
% 24.37/20.45 % SZS status Theorem
% 24.37/20.45 % SZS output start CNFRefutation
% See solution above
% 24.37/20.45 % Parsed axioms : 3135
% 24.37/20.45 % Removed by relevancy pruning/SinE : 0
% 24.37/20.45 % Initial clauses : 8979
% 24.37/20.45 % Removed in clause preprocessing : 322
% 24.37/20.45 % Initial clauses in saturation : 8657
% 24.37/20.45 % Processed clauses : 2333
% 24.37/20.45 % ...of these trivial : 93
% 24.37/20.45 % ...subsumed : 161
% 24.37/20.45 % ...remaining for further processing : 2079
% 24.37/20.45 % Other redundant clauses eliminated : 0
% 24.37/20.45 % Clauses deleted for lack of memory : 0
% 24.37/20.45 % Backward-subsumed : 9
% 24.37/20.45 % Backward-rewritten : 317
% 24.37/20.45 % Generated clauses : 0
% 24.37/20.45 % ...of the previous two non-redundant : 259
% 24.37/20.45 % ...aggressively subsumed : 0
% 24.37/20.45 % Contextual simplify-reflections : 5
% 24.37/20.45 % Paramodulations : 0
% 24.37/20.45 % Factorizations : 0
% 24.37/20.45 % NegExts : 0
% 24.37/20.45 % Equation resolutions : 0
% 24.37/20.45 % Disequality decompositions : 0
% 24.37/20.45 % Total rewrite steps : 2344
% 24.37/20.45 % ...of those cached : 1618
% 24.37/20.45 % Propositional unsat checks : 0
% 24.37/20.45 % Propositional check models : 0
% 24.37/20.45 % Propositional check unsatisfiable : 0
% 24.37/20.45 % Propositional clauses : 0
% 24.37/20.45 % Propositional clauses after purity: 0
% 24.37/20.45 % Propositional unsat core size : 0
% 24.37/20.45 % Propositional preprocessing time : 0.000
% 24.37/20.45 % Propositional encoding time : 0.000
% 24.37/20.45 % Propositional solver time : 0.000
% 24.37/20.45 % Success case prop preproc time : 0.000
% 24.37/20.45 % Success case prop encoding time : 0.000
% 24.37/20.45 % Success case prop solver time : 0.000
% 24.37/20.45 % Current number of processed clauses : 1753
% 24.37/20.45 % Positive orientable unit clauses : 456
% 24.37/20.45 % Positive unorientable unit clauses: 51
% 24.37/20.45 % Negative unit clauses : 17
% 24.37/20.45 % Non-unit-clauses : 1229
% 24.37/20.45 % Current number of unprocessed clauses: 6583
% 24.37/20.45 % ...number of literals in the above : 43370
% 24.37/20.45 % Current number of archived formulas : 0
% 24.37/20.45 % Current number of archived clauses : 326
% 24.37/20.45 % Clause-clause subsumption calls (NU) : 146617
% 24.37/20.45 % Rec. Clause-clause subsumption calls : 104505
% 24.37/20.45 % Non-unit clause-clause subsumptions : 154
% 24.37/20.45 % Unit Clause-clause subsumption calls : 263
% 24.37/20.45 % Rewrite failures with RHS unbound : 0
% 24.37/20.45 % BW rewrite match attempts : 190801
% 24.37/20.45 % BW rewrite match successes : 2485
% 24.37/20.45 % Condensation attempts : 0
% 24.37/20.45 % Condensation successes : 0
% 24.37/20.45 % Termbank termtop insertions : 5707078
% 24.37/20.45 % Search garbage collected termcells : 172229
% 24.37/20.45
% 24.37/20.45 % -------------------------------------------------
% 24.37/20.45 % User time : 3.599 s
% 24.37/20.45 % System time : 0.171 s
% 24.37/20.45 % Total time : 3.770 s
% 24.37/20.45 % Maximum resident set size: 66484 pages
% 24.37/20.45
% 24.37/20.45 % -------------------------------------------------
% 24.37/20.45 % User time : 6.921 s
% 24.37/20.45 % System time : 0.384 s
% 24.37/20.45 % Total time : 7.305 s
% 24.37/20.45 % Maximum resident set size: 14336 pages
% 24.37/20.45 % E exiting
%------------------------------------------------------------------------------