%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : ALG371-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n001.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 12:02:02 PM UTC 2026
% Result : Unsatisfiable 0.10s 0.44s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 8
% Syntax : Number of clauses : 26 ( 12 unt; 0 nHn; 23 RR)
% Number of literals : 47 ( 5 equ; 24 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 33 ( 3 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_real__le__trans_0,axiom,
( ~ c_lessequals(X1,X3,tc_RealDef_Oreal)
| ~ c_lessequals(X3,X2,tc_RealDef_Oreal)
| c_lessequals(X1,X2,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__le__trans_0) ).
cnf(cls_real__le__antisym_0,axiom,
( ~ c_lessequals(X1,X2,tc_RealDef_Oreal)
| ~ c_lessequals(X2,X1,tc_RealDef_Oreal)
| X1 = X2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__le__antisym_0) ).
cnf(cls_real__less__def_0,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,tc_RealDef_Oreal)
| c_lessequals(X1,X2,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__less__def_0) ).
cnf(cls_conjecture_1,negated_conjecture,
c_lessequals(c_RealVector_Onorm__class_Onorm(v_x,tc_Complex_Ocomplex),v_r,tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
cnf(cls_norm__ge__zero_0,axiom,
( ~ class_RealVector_Oreal__normed__vector(X1)
| c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X2,X1),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_norm__ge__zero_0) ).
cnf(clsarity_Complex__Ocomplex__RealVector_Oreal__normed__vector,axiom,
class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__RealVector_Oreal__normed__vector) ).
cnf(cls_conjecture_0,negated_conjecture,
c_HOL_Oord__class_Oless(v_r,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
cnf(cls_real__less__def_1,axiom,
~ c_HOL_Oord__class_Oless(X1,X1,tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__less__def_1) ).
cnf(c_0_8,plain,
( ~ c_lessequals(X1,X3,tc_RealDef_Oreal)
| ~ c_lessequals(X3,X2,tc_RealDef_Oreal)
| c_lessequals(X1,X2,tc_RealDef_Oreal) ),
inference(fof_simplification,[status(thm)],[cls_real__le__trans_0]) ).
cnf(c_0_9,plain,
( ~ c_lessequals(X1,X2,tc_RealDef_Oreal)
| ~ c_lessequals(X2,X1,tc_RealDef_Oreal)
| X1 = X2 ),
inference(fof_simplification,[status(thm)],[cls_real__le__antisym_0]) ).
cnf(c_0_10,plain,
( ~ c_HOL_Oord__class_Oless(X1,X2,tc_RealDef_Oreal)
| c_lessequals(X1,X2,tc_RealDef_Oreal) ),
inference(fof_simplification,[status(thm)],[cls_real__less__def_0]) ).
cnf(c_0_11,plain,
( ~ c_lessequals(X1,X3,tc_RealDef_Oreal)
| ~ c_lessequals(X3,X2,tc_RealDef_Oreal)
| c_lessequals(X1,X2,tc_RealDef_Oreal) ),
c_0_8 ).
cnf(c_0_12,negated_conjecture,
c_lessequals(c_RealVector_Onorm__class_Onorm(v_x,tc_Complex_Ocomplex),v_r,tc_RealDef_Oreal),
cls_conjecture_1 ).
cnf(c_0_13,plain,
( ~ class_RealVector_Oreal__normed__vector(X1)
| c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X2,X1),tc_RealDef_Oreal) ),
inference(fof_simplification,[status(thm)],[cls_norm__ge__zero_0]) ).
cnf(c_0_14,plain,
( ~ c_lessequals(X1,X2,tc_RealDef_Oreal)
| ~ c_lessequals(X2,X1,tc_RealDef_Oreal)
| X1 = X2 ),
c_0_9 ).
cnf(c_0_15,plain,
( ~ c_HOL_Oord__class_Oless(X1,X2,tc_RealDef_Oreal)
| c_lessequals(X1,X2,tc_RealDef_Oreal) ),
c_0_10 ).
cnf(c_0_16,negated_conjecture,
( ~ c_lessequals(X1,c_RealVector_Onorm__class_Onorm(v_x,tc_Complex_Ocomplex),tc_RealDef_Oreal)
| c_lessequals(X1,v_r,tc_RealDef_Oreal) ),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_17,plain,
( ~ class_RealVector_Oreal__normed__vector(X1)
| c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X2,X1),tc_RealDef_Oreal) ),
c_0_13 ).
cnf(c_0_18,axiom,
class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__RealVector_Oreal__normed__vector ).
cnf(c_0_19,plain,
( ~ c_HOL_Oord__class_Oless(X2,X1,tc_RealDef_Oreal)
| ~ c_lessequals(X1,X2,tc_RealDef_Oreal)
| X1 = X2 ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_20,negated_conjecture,
c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),v_r,tc_RealDef_Oreal),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_17]),c_0_18])]) ).
cnf(c_0_21,negated_conjecture,
c_HOL_Oord__class_Oless(v_r,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),
cls_conjecture_0 ).
cnf(c_0_22,plain,
~ c_HOL_Oord__class_Oless(X1,X1,tc_RealDef_Oreal),
inference(fof_simplification,[status(thm)],[cls_real__less__def_1]) ).
cnf(c_0_23,negated_conjecture,
c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = v_r,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_21])]) ).
cnf(c_0_24,plain,
~ c_HOL_Oord__class_Oless(X1,X1,tc_RealDef_Oreal),
c_0_22 ).
cnf(c_0_25,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_21,c_0_23]),c_0_24]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG371-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.36 % Computer : n001.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Mon Sep 21 13:23:30 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.40 Running first-order theorem proving
% 0.10/0.40 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
% 0.10/0.44 % Version: 3.5.1
% 0.10/0.44 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.10/0.44 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.10/0.44 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.10/0.44 % Starting new_bool_3 with 300s (1) cores
% 0.10/0.44 % Starting new_bool_1 with 300s (1) cores
% 0.10/0.44 % Starting sh5l with 300s (1) cores
% 0.10/0.44 % new_bool_1 with pid 3216266 completed with status 0
% 0.10/0.44 % Result found by new_bool_1
% 0.10/0.44 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.10/0.44 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.10/0.44 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.10/0.44 % Starting new_bool_3 with 300s (1) cores
% 0.10/0.44 % Starting new_bool_1 with 300s (1) cores
% 0.10/0.44 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.10/0.44 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.10/0.44 % Search class: FGHSM-FSLM32-MFFFFFNN
% 0.10/0.44 % Scheduled 12 strats onto 1 cores with 300 seconds (300 total)
% 0.10/0.44 % Starting SubtermCWHack with 28s (1) cores
% 0.10/0.44 % SubtermCWHack with pid 3216269 completed with status 0
% 0.10/0.44 % Result found by SubtermCWHack
% 0.10/0.44 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.10/0.44 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.10/0.44 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.10/0.44 % Starting new_bool_3 with 300s (1) cores
% 0.10/0.44 % Starting new_bool_1 with 300s (1) cores
% 0.10/0.44 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.10/0.44 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.10/0.44 % Search class: FGHSM-FSLM32-MFFFFFNN
% 0.10/0.44 % Scheduled 12 strats onto 1 cores with 300 seconds (300 total)
% 0.10/0.44 % Starting SubtermCWHack with 28s (1) cores
% 0.10/0.44 % Preprocessing time : 0.002 s
% 0.10/0.44
% 0.10/0.44 % Proof found!
% 0.10/0.44 % SZS status Unsatisfiable
% 0.10/0.44 % SZS output start CNFRefutation
% See solution above
% 0.10/0.44 % Parsed axioms : 504
% 0.10/0.44 % Removed by relevancy pruning/SinE : 293
% 0.10/0.44 % Initial clauses : 211
% 0.10/0.44 % Removed in clause preprocessing : 0
% 0.10/0.44 % Initial clauses in saturation : 211
% 0.10/0.44 % Processed clauses : 105
% 0.10/0.44 % ...of these trivial : 1
% 0.10/0.44 % ...subsumed : 32
% 0.10/0.44 % ...remaining for further processing : 72
% 0.10/0.44 % Other redundant clauses eliminated : 0
% 0.10/0.44 % Clauses deleted for lack of memory : 0
% 0.10/0.44 % Backward-subsumed : 0
% 0.10/0.44 % Backward-rewritten : 21
% 0.10/0.44 % Generated clauses : 114
% 0.10/0.44 % ...of the previous two non-redundant : 90
% 0.10/0.44 % ...aggressively subsumed : 0
% 0.10/0.44 % Contextual simplify-reflections : 0
% 0.10/0.44 % Paramodulations : 110
% 0.10/0.44 % Factorizations : 4
% 0.10/0.44 % NegExts : 0
% 0.10/0.44 % Equation resolutions : 0
% 0.10/0.44 % Disequality decompositions : 0
% 0.10/0.44 % Total rewrite steps : 73
% 0.10/0.44 % ...of those cached : 52
% 0.10/0.44 % Propositional unsat checks : 0
% 0.10/0.44 % Propositional check models : 0
% 0.10/0.44 % Propositional check unsatisfiable : 0
% 0.10/0.44 % Propositional clauses : 0
% 0.10/0.44 % Propositional clauses after purity: 0
% 0.10/0.44 % Propositional unsat core size : 0
% 0.10/0.44 % Propositional preprocessing time : 0.000
% 0.10/0.44 % Propositional encoding time : 0.000
% 0.10/0.44 % Propositional solver time : 0.000
% 0.10/0.44 % Success case prop preproc time : 0.000
% 0.10/0.44 % Success case prop encoding time : 0.000
% 0.10/0.44 % Success case prop solver time : 0.000
% 0.10/0.44 % Current number of processed clauses : 51
% 0.10/0.45 % Positive orientable unit clauses : 20
% 0.10/0.45 % Positive unorientable unit clauses: 2
% 0.10/0.45 % Negative unit clauses : 1
% 0.10/0.45 % Non-unit-clauses : 28
% 0.10/0.45 % Current number of unprocessed clauses: 180
% 0.10/0.45 % ...number of literals in the above : 716
% 0.10/0.45 % Current number of archived formulas : 0
% 0.10/0.45 % Current number of archived clauses : 21
% 0.10/0.45 % Clause-clause subsumption calls (NU) : 99
% 0.10/0.45 % Rec. Clause-clause subsumption calls : 97
% 0.10/0.45 % Non-unit clause-clause subsumptions : 25
% 0.10/0.45 % Unit Clause-clause subsumption calls : 17
% 0.10/0.45 % Rewrite failures with RHS unbound : 0
% 0.10/0.45 % BW rewrite match attempts : 21
% 0.10/0.45 % BW rewrite match successes : 5
% 0.10/0.45 % Condensation attempts : 0
% 0.10/0.45 % Condensation successes : 0
% 0.10/0.45 % Termbank termtop insertions : 13742
% 0.10/0.45 % Search garbage collected termcells : 1417
% 0.10/0.45
% 0.10/0.45 % -------------------------------------------------
% 0.10/0.45 % User time : 0.008 s
% 0.10/0.45 % System time : 0.005 s
% 0.10/0.45 % Total time : 0.013 s
% 0.10/0.45 % Maximum resident set size: 4244 pages
% 0.10/0.45
% 0.10/0.45 % -------------------------------------------------
% 0.10/0.45 % User time : 0.023 s
% 0.10/0.45 % System time : 0.009 s
% 0.10/0.45 % Total time : 0.031 s
% 0.10/0.45 % Maximum resident set size: 5120 pages
% 0.10/0.45 % E exiting
%------------------------------------------------------------------------------