%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : ALG406-1 : 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 : n005.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 11:56:03 AM UTC 2026
% Result : Unsatisfiable 3.78s 1.12s
% Output : CNFRefutation 3.78s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 10
% Syntax : Number of clauses : 29 ( 20 unt; 0 nHn; 24 RR)
% Number of literals : 50 ( 2 equ; 25 neg)
% Maximal clause size : 5 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-3 aty)
% Number of variables : 26 ( 1 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_conjecture_0,negated_conjecture,
~ c_lessequals(c_HOL_Otimes__class_Otimes(v_t____,c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),tc_RealDef_Oreal),tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_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/sandbox/benchmark/theBenchmark.p',cls_real__less__def_0) ).
cnf(cls_minus__le__self__iff_0,axiom,
( ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X2,X1),X2,X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1)
| c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__le__self__iff_0) ).
cnf(cls_real__mult__1_0,axiom,
c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),X1,tc_RealDef_Oreal) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__mult__1_0) ).
cnf(cls_mult__left__le__one__le_0,axiom,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(X2,c_HOL_Oone__class_Oone(X1),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_lessequals(c_HOL_Otimes__class_Otimes(X2,X3,X1),X3,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__left__le__one__le_0) ).
cnf(cls_t_I2_J_0,axiom,
c_HOL_Oord__class_Oless(v_t____,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_t_I2_J_0) ).
cnf(cls_complex__mod__minus__le__complex__mod_0,axiom,
c_lessequals(c_HOL_Ouminus__class_Ouminus(c_RealVector_Onorm__class_Onorm(X1,tc_Complex_Ocomplex),tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X1,tc_Complex_Ocomplex),tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_complex__mod__minus__le__complex__mod_0) ).
cnf(clsarity_RealDef__Oreal__OrderedGroup_Olordered__ab__group__add,axiom,
class_OrderedGroup_Olordered__ab__group__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Olordered__ab__group__add) ).
cnf(cls_t_I1_J_0,axiom,
c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),v_t____,tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_t_I1_J_0) ).
cnf(clsarity_RealDef__Oreal__Ring__and__Field_Oordered__idom,axiom,
class_Ring__and__Field_Oordered__idom(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Oordered__idom) ).
cnf(c_0_10,negated_conjecture,
~ c_lessequals(c_HOL_Otimes__class_Otimes(v_t____,c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(fof_simplification,[status(thm)],[cls_conjecture_0]) ).
cnf(c_0_11,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_12,plain,
( ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X2,X1),X2,X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1)
| c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
inference(fof_simplification,[status(thm)],[cls_minus__le__self__iff_0]) ).
cnf(c_0_13,negated_conjecture,
~ c_lessequals(c_HOL_Otimes__class_Otimes(v_t____,c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),tc_RealDef_Oreal),tc_RealDef_Oreal),
c_0_10 ).
cnf(c_0_14,axiom,
c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),X1,tc_RealDef_Oreal) = X1,
cls_real__mult__1_0 ).
cnf(c_0_15,plain,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(X2,c_HOL_Oone__class_Oone(X1),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_lessequals(c_HOL_Otimes__class_Otimes(X2,X3,X1),X3,X1) ),
inference(fof_simplification,[status(thm)],[cls_mult__left__le__one__le_0]) ).
cnf(c_0_16,plain,
( ~ c_HOL_Oord__class_Oless(X1,X2,tc_RealDef_Oreal)
| c_lessequals(X1,X2,tc_RealDef_Oreal) ),
c_0_11 ).
cnf(c_0_17,axiom,
c_HOL_Oord__class_Oless(v_t____,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),
cls_t_I2_J_0 ).
cnf(c_0_18,plain,
( ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X2,X1),X2,X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1)
| c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
c_0_12 ).
cnf(c_0_19,axiom,
c_lessequals(c_HOL_Ouminus__class_Ouminus(c_RealVector_Onorm__class_Onorm(X1,tc_Complex_Ocomplex),tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X1,tc_Complex_Ocomplex),tc_RealDef_Oreal),
cls_complex__mod__minus__le__complex__mod_0 ).
cnf(c_0_20,axiom,
class_OrderedGroup_Olordered__ab__group__add(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__OrderedGroup_Olordered__ab__group__add ).
cnf(c_0_21,axiom,
c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),v_t____,tc_RealDef_Oreal),
cls_t_I1_J_0 ).
cnf(c_0_22,negated_conjecture,
~ c_lessequals(c_HOL_Otimes__class_Otimes(v_t____,c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),tc_RealDef_Oreal),
inference(rw,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_23,plain,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(X2,c_HOL_Oone__class_Oone(X1),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_lessequals(c_HOL_Otimes__class_Otimes(X2,X3,X1),X3,X1) ),
c_0_15 ).
cnf(c_0_24,axiom,
class_Ring__and__Field_Oordered__idom(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__Ring__and__Field_Oordered__idom ).
cnf(c_0_25,plain,
c_lessequals(v_t____,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_26,plain,
c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X1,tc_Complex_Ocomplex),tc_RealDef_Oreal),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_20])]) ).
cnf(c_0_27,plain,
c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),v_t____,tc_RealDef_Oreal),
inference(spm,[status(thm)],[c_0_16,c_0_21]) ).
cnf(c_0_28,negated_conjecture,
$false,
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_22,c_0_23]),c_0_24]),c_0_25]),c_0_26]),c_0_27])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : ALG406-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.07 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.17/0.43 % Computer : n005.cluster.edu
% 0.17/0.43 % Model : x86_64 x86_64
% 0.17/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.43 % Memory : 8046.5625MB
% 0.17/0.43 % OS : Linux 6.8.0-71-generic
% 0.17/0.43 % CPULimit : 300
% 0.17/0.43 % WCLimit : 300
% 0.17/0.43 % DateTime : Mon Sep 21 13:19:20 UTC 2026
% 0.17/0.43 % CPUTime :
% 0.17/0.43 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.17/0.49 Running first-order theorem proving
% 0.17/0.49 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
% 3.78/1.12 % Version: 3.5.1
% 3.78/1.12 % Preprocessing class: FSLSSMSSSSSNFFN.
% 3.78/1.12 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 3.78/1.12 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 3.78/1.12 % Starting new_bool_3 with 300s (1) cores
% 3.78/1.12 % Starting new_bool_1 with 300s (1) cores
% 3.78/1.12 % Starting sh5l with 300s (1) cores
% 3.78/1.12 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 3569631 completed with status 0
% 3.78/1.12 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 3.78/1.12 % Preprocessing class: FSLSSMSSSSSNFFN.
% 3.78/1.12 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 3.78/1.12 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 3.78/1.12 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 3.78/1.12 % No SInE strategy applied
% 3.78/1.12 % Search class: FGHSM-FSLM31-MFFFFFNN
% 3.78/1.12 % Scheduled 8 strats onto 5 cores with 1500 seconds (1500 total)
% 3.78/1.12 % Starting SubtermCWHack with 136s (1) cores
% 3.78/1.12 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 3.78/1.12 % Starting G-E--_208_C12_11_nc_F1_SE_CS_SP_PS_S5PRR_S04BN with 136s (1) cores
% 3.78/1.12 % Starting G-E--_207_B07_F1_AE_CS_SP_PI_PS_S0Y with 136s (1) cores
% 3.78/1.12 % Starting U----_116Y_C05_02_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 3.78/1.12 % U----_116Y_C05_02_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with pid 3569642 completed with status 0
% 3.78/1.12 % Result found by U----_116Y_C05_02_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN
% 3.78/1.12 % Preprocessing class: FSLSSMSSSSSNFFN.
% 3.78/1.12 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 3.78/1.12 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 3.78/1.12 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 3.78/1.12 % No SInE strategy applied
% 3.78/1.12 % Search class: FGHSM-FSLM31-MFFFFFNN
% 3.78/1.12 % Scheduled 8 strats onto 5 cores with 1500 seconds (1500 total)
% 3.78/1.12 % Starting SubtermCWHack with 136s (1) cores
% 3.78/1.12 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 3.78/1.12 % Starting G-E--_208_C12_11_nc_F1_SE_CS_SP_PS_S5PRR_S04BN with 136s (1) cores
% 3.78/1.12 % Starting G-E--_207_B07_F1_AE_CS_SP_PI_PS_S0Y with 136s (1) cores
% 3.78/1.12 % Starting U----_116Y_C05_02_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 3.78/1.12 % Preprocessing time : 0.012 s
% 3.78/1.12 % Presaturation interreduction done
% 3.78/1.12
% 3.78/1.12 % Proof found!
% 3.78/1.12 % SZS status Unsatisfiable
% 3.78/1.12 % SZS output start CNFRefutation
% See solution above
% 3.78/1.12 % Parsed axioms : 678
% 3.78/1.12 % Removed by relevancy pruning/SinE : 0
% 3.78/1.12 % Initial clauses : 678
% 3.78/1.12 % Removed in clause preprocessing : 0
% 3.78/1.12 % Initial clauses in saturation : 678
% 3.78/1.12 % Processed clauses : 1470
% 3.78/1.12 % ...of these trivial : 44
% 3.78/1.12 % ...subsumed : 179
% 3.78/1.12 % ...remaining for further processing : 1247
% 3.78/1.12 % Other redundant clauses eliminated : 106
% 3.78/1.12 % Clauses deleted for lack of memory : 0
% 3.78/1.12 % Backward-subsumed : 1
% 3.78/1.12 % Backward-rewritten : 1
% 3.78/1.12 % Generated clauses : 18066
% 3.78/1.12 % ...of the previous two non-redundant : 16202
% 3.78/1.12 % ...aggressively subsumed : 0
% 3.78/1.12 % Contextual simplify-reflections : 0
% 3.78/1.12 % Paramodulations : 17944
% 3.78/1.12 % Factorizations : 4
% 3.78/1.12 % NegExts : 0
% 3.78/1.12 % Equation resolutions : 118
% 3.78/1.12 % Disequality decompositions : 0
% 3.78/1.12 % Total rewrite steps : 6376
% 3.78/1.12 % ...of those cached : 6089
% 3.78/1.12 % Propositional unsat checks : 0
% 3.78/1.12 % Propositional check models : 0
% 3.78/1.12 % Propositional check unsatisfiable : 0
% 3.78/1.12 % Propositional clauses : 0
% 3.78/1.12 % Propositional clauses after purity: 0
% 3.78/1.12 % Propositional unsat core size : 0
% 3.78/1.12 % Propositional preprocessing time : 0.000
% 3.78/1.12 % Propositional encoding time : 0.000
% 3.78/1.12 % Propositional solver time : 0.000
% 3.78/1.12 % Success case prop preproc time : 0.000
% 3.78/1.12 % Success case prop encoding time : 0.000
% 3.78/1.12 % Success case prop solver time : 0.000
% 3.78/1.12 % Current number of processed clauses : 637
% 3.78/1.12 % Positive orientable unit clauses : 173
% 3.78/1.12 % Positive unorientable unit clauses: 1
% 3.78/1.12 % Negative unit clauses : 14
% 3.78/1.12 % Non-unit-clauses : 449
% 3.78/1.12 % Current number of unprocessed clauses: 16001
% 3.78/1.12 % ...number of literals in the above : 59232
% 3.78/1.12 % Current number of archived formulas : 0
% 3.78/1.12 % Current number of archived clauses : 610
% 3.78/1.12 % Clause-clause subsumption calls (NU) : 44578
% 3.78/1.12 % Rec. Clause-clause subsumption calls : 26423
% 3.78/1.12 % Non-unit clause-clause subsumptions : 93
% 3.78/1.12 % Unit Clause-clause subsumption calls : 478
% 3.78/1.12 % Rewrite failures with RHS unbound : 0
% 3.78/1.12 % BW rewrite match attempts : 132
% 3.78/1.12 % BW rewrite match successes : 15
% 3.78/1.12 % Condensation attempts : 0
% 3.78/1.12 % Condensation successes : 0
% 3.78/1.12 % Termbank termtop insertions : 273983
% 3.78/1.12 % Search garbage collected termcells : 1264
% 3.78/1.12
% 3.78/1.12 % -------------------------------------------------
% 3.78/1.12 % User time : 0.512 s
% 3.78/1.12 % System time : 0.029 s
% 3.78/1.12 % Total time : 0.541 s
% 3.78/1.12 % Maximum resident set size: 4596 pages
% 3.78/1.12
% 3.78/1.12 % -------------------------------------------------
% 3.78/1.12 % User time : 2.372 s
% 3.78/1.12 % System time : 0.120 s
% 3.78/1.12 % Total time : 2.492 s
% 3.78/1.12 % Maximum resident set size: 5120 pages
% 3.78/1.12 % E exiting
%------------------------------------------------------------------------------