%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : ALG368-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n010.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 11:55:59 AM UTC 2026
% Result : Unsatisfiable 1.39s 0.67s
% Output : CNFRefutation 1.39s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 8
% Syntax : Number of clauses : 26 ( 12 unt; 0 nHn; 19 RR)
% Number of literals : 40 ( 11 equ; 20 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 5 con; 0-3 aty)
% Number of variables : 22 ( 5 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_eq__iff__diff__eq__0_0,axiom,
( ~ class_OrderedGroup_Oab__group__add(X1)
| c_HOL_Ominus__class_Ominus(X2,X2,X1) = c_HOL_Ozero__class_Ozero(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__iff__diff__eq__0_0) ).
cnf(cls_conjecture_2,negated_conjecture,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X1,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_HOL_Ominus__class_Ominus(hAPP(v_x,X1),v_z,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_HOL_Ominus__class_Ominus(v_z,v_z,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_e,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).
cnf(clsarity_Complex__Ocomplex__OrderedGroup_Oab__group__add,axiom,
class_OrderedGroup_Oab__group__add(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Oab__group__add) ).
cnf(cls_order__root_1,axiom,
( ~ class_Ring__and__Field_Oidom(X1)
| c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X2,X1) = c_HOL_Ozero__class_Ozero(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__root_1) ).
cnf(cls_norm__zero_0,axiom,
( ~ class_RealVector_Oreal__normed__vector(X1)
| c_RealVector_Onorm__class_Onorm(c_HOL_Ozero__class_Ozero(X1),X1) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_norm__zero_0) ).
cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Oidom,axiom,
class_Ring__and__Field_Oidom(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Oidom) ).
cnf(clsarity_Complex__Ocomplex__RealVector_Oreal__normed__vector,axiom,
class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__RealVector_Oreal__normed__vector) ).
cnf(cls_ep_0,axiom,
c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),v_e,tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ep_0) ).
cnf(c_0_8,plain,
( ~ class_OrderedGroup_Oab__group__add(X1)
| c_HOL_Ominus__class_Ominus(X2,X2,X1) = c_HOL_Ozero__class_Ozero(X1) ),
inference(fof_simplification,[status(thm)],[cls_eq__iff__diff__eq__0_0]) ).
cnf(c_0_9,negated_conjecture,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X1,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_HOL_Ominus__class_Ominus(hAPP(v_x,X1),v_z,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_HOL_Ominus__class_Ominus(v_z,v_z,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_e,tc_RealDef_Oreal) ),
inference(fof_simplification,[status(thm)],[cls_conjecture_2]) ).
cnf(c_0_10,plain,
( ~ class_OrderedGroup_Oab__group__add(X1)
| c_HOL_Ominus__class_Ominus(X2,X2,X1) = c_HOL_Ozero__class_Ozero(X1) ),
c_0_8 ).
cnf(c_0_11,axiom,
class_OrderedGroup_Oab__group__add(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__OrderedGroup_Oab__group__add ).
cnf(c_0_12,negated_conjecture,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X1,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_HOL_Ominus__class_Ominus(hAPP(v_x,X1),v_z,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_HOL_Ominus__class_Ominus(v_z,v_z,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_e,tc_RealDef_Oreal) ),
c_0_9 ).
cnf(c_0_13,plain,
c_HOL_Ominus__class_Ominus(X1,X1,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_14,plain,
( ~ class_Ring__and__Field_Oidom(X1)
| c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X2,X1) = c_HOL_Ozero__class_Ozero(X1) ),
inference(fof_simplification,[status(thm)],[cls_order__root_1]) ).
cnf(c_0_15,plain,
( ~ class_RealVector_Oreal__normed__vector(X1)
| c_RealVector_Onorm__class_Onorm(c_HOL_Ozero__class_Ozero(X1),X1) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(fof_simplification,[status(thm)],[cls_norm__zero_0]) ).
cnf(c_0_16,negated_conjecture,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X1,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_HOL_Ominus__class_Ominus(hAPP(v_x,X1),v_z,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_e,tc_RealDef_Oreal) ),
inference(rw,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_17,plain,
( ~ class_Ring__and__Field_Oidom(X1)
| c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X2,X1) = c_HOL_Ozero__class_Ozero(X1) ),
c_0_14 ).
cnf(c_0_18,axiom,
class_Ring__and__Field_Oidom(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__Ring__and__Field_Oidom ).
cnf(c_0_19,plain,
( ~ class_RealVector_Oreal__normed__vector(X1)
| c_RealVector_Onorm__class_Onorm(c_HOL_Ozero__class_Ozero(X1),X1) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ),
c_0_15 ).
cnf(c_0_20,axiom,
class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__RealVector_Oreal__normed__vector ).
cnf(c_0_21,negated_conjecture,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X1,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_e,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_22,plain,
c_RealVector_Onorm__class_Onorm(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_23,axiom,
c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),v_e,tc_RealDef_Oreal),
cls_ep_0 ).
cnf(c_0_24,negated_conjecture,
~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X1,tc_RealDef_Oreal),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_17]),c_0_13]),c_0_22]),c_0_23]),c_0_18])]) ).
cnf(c_0_25,plain,
$false,
inference(sr,[status(thm)],[c_0_23,c_0_24]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG368-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.36 % Computer : n010.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 13:18:11 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.14/0.41 Running first-order theorem proving
% 0.14/0.41 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
% 1.39/0.67 % Version: 3.5.1
% 1.39/0.67 % Preprocessing class: FMLMSMSMSSSNFFN.
% 1.39/0.67 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.39/0.67 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 1.39/0.67 % Starting new_bool_3 with 300s (1) cores
% 1.39/0.67 % Starting new_bool_1 with 300s (1) cores
% 1.39/0.67 % Starting sh5l with 300s (1) cores
% 1.39/0.67 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 952070 completed with status 0
% 1.39/0.67 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 1.39/0.67 % Preprocessing class: FMLMSMSMSSSNFFN.
% 1.39/0.67 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.39/0.67 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 1.39/0.67 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 1.39/0.67 % No SInE strategy applied
% 1.39/0.67 % Search class: FGHSM-SSLM32-MFFFFFNN
% 1.39/0.67 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 1.39/0.67 % Starting SubtermCWHack with 136s (1) cores
% 1.39/0.67 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 1.39/0.67 % Starting G-E--_208_C12_11_nc_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 1.39/0.67 % Starting G-E--_208_C12_02_nc_F1_SE_CS_SP_PS_S5PRR_RG_S070I with 136s (1) cores
% 1.39/0.67 % Starting G-E--_208_C47_F1_SE_CS_SP_PS_S0Y with 136s (1) cores
% 1.39/0.67 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 952082 completed with status 0
% 1.39/0.67 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 1.39/0.67 % Preprocessing class: FMLMSMSMSSSNFFN.
% 1.39/0.67 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.39/0.67 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 1.39/0.67 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 1.39/0.67 % No SInE strategy applied
% 1.39/0.67 % Search class: FGHSM-SSLM32-MFFFFFNN
% 1.39/0.67 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 1.39/0.67 % Starting SubtermCWHack with 136s (1) cores
% 1.39/0.67 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 1.39/0.67 % Preprocessing time : 0.014 s
% 1.39/0.67 % Presaturation interreduction done
% 1.39/0.67
% 1.39/0.67 % Proof found!
% 1.39/0.67 % SZS status Unsatisfiable
% 1.39/0.67 % SZS output start CNFRefutation
% See solution above
% 1.39/0.67 % Parsed axioms : 1044
% 1.39/0.67 % Removed by relevancy pruning/SinE : 0
% 1.39/0.67 % Initial clauses : 1044
% 1.39/0.67 % Removed in clause preprocessing : 0
% 1.39/0.67 % Initial clauses in saturation : 1044
% 1.39/0.67 % Processed clauses : 1709
% 1.39/0.67 % ...of these trivial : 20
% 1.39/0.67 % ...subsumed : 217
% 1.39/0.67 % ...remaining for further processing : 1472
% 1.39/0.67 % Other redundant clauses eliminated : 9
% 1.39/0.67 % Clauses deleted for lack of memory : 0
% 1.39/0.67 % Backward-subsumed : 16
% 1.39/0.67 % Backward-rewritten : 3
% 1.39/0.67 % Generated clauses : 1479
% 1.39/0.67 % ...of the previous two non-redundant : 1172
% 1.39/0.67 % ...aggressively subsumed : 0
% 1.39/0.67 % Contextual simplify-reflections : 0
% 1.39/0.67 % Paramodulations : 1450
% 1.39/0.67 % Factorizations : 2
% 1.39/0.67 % NegExts : 0
% 1.39/0.67 % Equation resolutions : 15
% 1.39/0.67 % Disequality decompositions : 0
% 1.39/0.67 % Total rewrite steps : 954
% 1.39/0.67 % ...of those cached : 827
% 1.39/0.67 % Propositional unsat checks : 0
% 1.39/0.67 % Propositional check models : 0
% 1.39/0.67 % Propositional check unsatisfiable : 0
% 1.39/0.67 % Propositional clauses : 0
% 1.39/0.67 % Propositional clauses after purity: 0
% 1.39/0.67 % Propositional unsat core size : 0
% 1.39/0.67 % Propositional preprocessing time : 0.000
% 1.39/0.67 % Propositional encoding time : 0.000
% 1.39/0.67 % Propositional solver time : 0.000
% 1.39/0.67 % Success case prop preproc time : 0.000
% 1.39/0.67 % Success case prop encoding time : 0.000
% 1.39/0.67 % Success case prop solver time : 0.000
% 1.39/0.67 % Current number of processed clauses : 491
% 1.39/0.67 % Positive orientable unit clauses : 223
% 1.39/0.67 % Positive unorientable unit clauses: 2
% 1.39/0.67 % Negative unit clauses : 24
% 1.39/0.67 % Non-unit-clauses : 242
% 1.39/0.67 % Current number of unprocessed clauses: 1455
% 1.39/0.67 % ...number of literals in the above : 3321
% 1.39/0.67 % Current number of archived formulas : 0
% 1.39/0.67 % Current number of archived clauses : 981
% 1.39/0.67 % Clause-clause subsumption calls (NU) : 109483
% 1.39/0.67 % Rec. Clause-clause subsumption calls : 60005
% 1.39/0.67 % Non-unit clause-clause subsumptions : 97
% 1.39/0.67 % Unit Clause-clause subsumption calls : 442
% 1.39/0.67 % Rewrite failures with RHS unbound : 0
% 1.39/0.67 % BW rewrite match attempts : 90
% 1.39/0.67 % BW rewrite match successes : 41
% 1.39/0.67 % Condensation attempts : 0
% 1.39/0.67 % Condensation successes : 0
% 1.39/0.67 % Termbank termtop insertions : 65962
% 1.39/0.67 % Search garbage collected termcells : 1910
% 1.39/0.67
% 1.39/0.67 % -------------------------------------------------
% 1.39/0.67 % User time : 0.181 s
% 1.39/0.67 % System time : 0.010 s
% 1.39/0.67 % Total time : 0.191 s
% 1.39/0.67 % Maximum resident set size: 5648 pages
% 1.39/0.67
% 1.39/0.67 % -------------------------------------------------
% 1.39/0.67 % User time : 0.812 s
% 1.39/0.67 % System time : 0.064 s
% 1.39/0.67 % Total time : 0.877 s
% 1.39/0.67 % Maximum resident set size: 5376 pages
% 1.39/0.67 % E exiting
%------------------------------------------------------------------------------