%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : ALG413-1 : 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 : 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 11:56:04 AM UTC 2026
% Result : Unsatisfiable 5.66s 1.64s
% Output : CNFRefutation 5.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 8
% Syntax : Number of clauses : 25 ( 16 unt; 0 nHn; 18 RR)
% Number of literals : 37 ( 21 equ; 16 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 4 con; 0-3 aty)
% Number of variables : 28 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_poly__pCons_0,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__0(X1)
| c_Polynomial_Opoly(c_Polynomial_OpCons(X2,X3,X1),X4,X1) = c_HOL_Oplus__class_Oplus(X2,c_HOL_Otimes__class_Otimes(X4,c_Polynomial_Opoly(X3,X4,X1),X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_poly__pCons_0) ).
cnf(cls_minus__unique_0,axiom,
( c_HOL_Oplus__class_Oplus(X2,X3,X1) != c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Ogroup__add(X1)
| c_HOL_Ouminus__class_Ouminus(X2,X1) = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__unique_0) ).
cnf(cls_CHAINED_0,axiom,
c_Polynomial_Opoly(c_Polynomial_OpCons(v_d____,v_ds____,tc_Complex_Ocomplex),c_RealVector_Oof__real(v_x____,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CHAINED_0) ).
cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__0,axiom,
class_Ring__and__Field_Ocomm__semiring__0(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__0) ).
cnf(cls_conjecture_0,negated_conjecture,
c_RealVector_Onorm__class_Onorm(c_HOL_Otimes__class_Otimes(c_RealVector_Oof__real(v_x____,tc_Complex_Ocomplex),c_Polynomial_Opoly(v_ds____,c_RealVector_Oof__real(v_x____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) != c_RealVector_Onorm__class_Onorm(v_d____,tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
cnf(clsarity_Complex__Ocomplex__OrderedGroup_Ogroup__add,axiom,
class_OrderedGroup_Ogroup__add(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Ogroup__add) ).
cnf(cls_norm__minus__cancel_0,axiom,
( ~ class_RealVector_Oreal__normed__vector(X1)
| c_RealVector_Onorm__class_Onorm(c_HOL_Ouminus__class_Ouminus(X2,X1),X1) = c_RealVector_Onorm__class_Onorm(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_norm__minus__cancel_0) ).
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(c_0_8,plain,
( ~ class_Ring__and__Field_Ocomm__semiring__0(X1)
| c_Polynomial_Opoly(c_Polynomial_OpCons(X2,X3,X1),X4,X1) = c_HOL_Oplus__class_Oplus(X2,c_HOL_Otimes__class_Otimes(X4,c_Polynomial_Opoly(X3,X4,X1),X1),X1) ),
inference(fof_simplification,[status(thm)],[cls_poly__pCons_0]) ).
cnf(c_0_9,plain,
( c_HOL_Oplus__class_Oplus(X2,X3,X1) != c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Ogroup__add(X1)
| c_HOL_Ouminus__class_Ouminus(X2,X1) = X3 ),
inference(fof_simplification,[status(thm)],[cls_minus__unique_0]) ).
cnf(c_0_10,axiom,
c_Polynomial_Opoly(c_Polynomial_OpCons(v_d____,v_ds____,tc_Complex_Ocomplex),c_RealVector_Oof__real(v_x____,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),
cls_CHAINED_0 ).
cnf(c_0_11,plain,
( ~ class_Ring__and__Field_Ocomm__semiring__0(X1)
| c_Polynomial_Opoly(c_Polynomial_OpCons(X2,X3,X1),X4,X1) = c_HOL_Oplus__class_Oplus(X2,c_HOL_Otimes__class_Otimes(X4,c_Polynomial_Opoly(X3,X4,X1),X1),X1) ),
c_0_8 ).
cnf(c_0_12,axiom,
class_Ring__and__Field_Ocomm__semiring__0(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__0 ).
cnf(c_0_13,negated_conjecture,
c_RealVector_Onorm__class_Onorm(c_HOL_Otimes__class_Otimes(c_RealVector_Oof__real(v_x____,tc_Complex_Ocomplex),c_Polynomial_Opoly(v_ds____,c_RealVector_Oof__real(v_x____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) != c_RealVector_Onorm__class_Onorm(v_d____,tc_Complex_Ocomplex),
inference(fof_simplification,[status(thm)],[cls_conjecture_0]) ).
cnf(c_0_14,plain,
( c_HOL_Oplus__class_Oplus(X2,X3,X1) != c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Ogroup__add(X1)
| c_HOL_Ouminus__class_Ouminus(X2,X1) = X3 ),
c_0_9 ).
cnf(c_0_15,plain,
c_HOL_Oplus__class_Oplus(v_d____,c_HOL_Otimes__class_Otimes(c_RealVector_Oof__real(v_x____,tc_Complex_Ocomplex),c_Polynomial_Opoly(v_ds____,c_RealVector_Oof__real(v_x____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_11]),c_0_12])]) ).
cnf(c_0_16,axiom,
class_OrderedGroup_Ogroup__add(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__OrderedGroup_Ogroup__add ).
cnf(c_0_17,plain,
( ~ class_RealVector_Oreal__normed__vector(X1)
| c_RealVector_Onorm__class_Onorm(c_HOL_Ouminus__class_Ouminus(X2,X1),X1) = c_RealVector_Onorm__class_Onorm(X2,X1) ),
inference(fof_simplification,[status(thm)],[cls_norm__minus__cancel_0]) ).
cnf(c_0_18,negated_conjecture,
c_RealVector_Onorm__class_Onorm(c_HOL_Otimes__class_Otimes(c_RealVector_Oof__real(v_x____,tc_Complex_Ocomplex),c_Polynomial_Opoly(v_ds____,c_RealVector_Oof__real(v_x____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) != c_RealVector_Onorm__class_Onorm(v_d____,tc_Complex_Ocomplex),
c_0_13 ).
cnf(c_0_19,plain,
c_HOL_Otimes__class_Otimes(c_RealVector_Oof__real(v_x____,tc_Complex_Ocomplex),c_Polynomial_Opoly(v_ds____,c_RealVector_Oof__real(v_x____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ouminus__class_Ouminus(v_d____,tc_Complex_Ocomplex),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_15]),c_0_16])]) ).
cnf(c_0_20,plain,
( ~ class_RealVector_Oreal__normed__vector(X1)
| c_RealVector_Onorm__class_Onorm(c_HOL_Ouminus__class_Ouminus(X2,X1),X1) = c_RealVector_Onorm__class_Onorm(X2,X1) ),
c_0_17 ).
cnf(c_0_21,axiom,
class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__RealVector_Oreal__normed__vector ).
cnf(c_0_22,negated_conjecture,
c_RealVector_Onorm__class_Onorm(c_HOL_Ouminus__class_Ouminus(v_d____,tc_Complex_Ocomplex),tc_Complex_Ocomplex) != c_RealVector_Onorm__class_Onorm(v_d____,tc_Complex_Ocomplex),
inference(rw,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_23,plain,
c_RealVector_Onorm__class_Onorm(c_HOL_Ouminus__class_Ouminus(X1,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_RealVector_Onorm__class_Onorm(X1,tc_Complex_Ocomplex),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_24,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_22,c_0_23])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : ALG413-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.08 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.17/0.48 % Computer : n004.cluster.edu
% 0.17/0.48 % Model : x86_64 x86_64
% 0.17/0.48 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.48 % Memory : 8046.5625MB
% 0.17/0.48 % OS : Linux 6.8.0-71-generic
% 0.17/0.48 % CPULimit : 300
% 0.17/0.48 % WCLimit : 300
% 0.17/0.48 % DateTime : Mon Sep 21 13:20:05 UTC 2026
% 0.17/0.48 % CPUTime :
% 0.17/0.48 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.22/0.56 Running first-order theorem proving
% 0.22/0.56 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
% 5.66/1.64 % Version: 3.5.1
% 5.66/1.64 % Preprocessing class: FMLMSMSSSSSNFFN.
% 5.66/1.64 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 5.66/1.64 % Starting G-E--_008_C45_F1_PI_AE_Q4_CS_SP_S4c with 1500s (5) cores
% 5.66/1.64 % Starting new_bool_3 with 300s (1) cores
% 5.66/1.64 % Starting new_bool_1 with 300s (1) cores
% 5.66/1.64 % Starting sh5l with 300s (1) cores
% 5.66/1.64 % G-E--_008_C45_F1_PI_AE_Q4_CS_SP_S4c with pid 3224388 completed with status 0
% 5.66/1.64 % Result found by G-E--_008_C45_F1_PI_AE_Q4_CS_SP_S4c
% 5.66/1.64 % Preprocessing class: FMLMSMSSSSSNFFN.
% 5.66/1.64 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 5.66/1.64 % Starting G-E--_008_C45_F1_PI_AE_Q4_CS_SP_S4c with 1500s (5) cores
% 5.66/1.64 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 5.66/1.64 % No SInE strategy applied
% 5.66/1.64 % Search class: FGHSM-SSLM32-MFFFFFNN
% 5.66/1.64 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 5.66/1.64 % Starting SubtermCWHack with 136s (1) cores
% 5.66/1.64 % Starting G-E--_008_C45_F1_PI_AE_Q4_CS_SP_S4c with 151s (1) cores
% 5.66/1.64 % Starting G-E--_208_C12_11_nc_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 5.66/1.64 % Starting G-E--_208_C12_02_nc_F1_SE_CS_SP_PS_S5PRR_RG_S070I with 136s (1) cores
% 5.66/1.64 % Starting G-E--_208_C47_F1_SE_CS_SP_PS_S0Y with 136s (1) cores
% 5.66/1.64 % G-E--_008_C45_F1_PI_AE_Q4_CS_SP_S4c with pid 3224396 completed with status 0
% 5.66/1.64 % Result found by G-E--_008_C45_F1_PI_AE_Q4_CS_SP_S4c
% 5.66/1.64 % Preprocessing class: FMLMSMSSSSSNFFN.
% 5.66/1.64 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 5.66/1.64 % Starting G-E--_008_C45_F1_PI_AE_Q4_CS_SP_S4c with 1500s (5) cores
% 5.66/1.64 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 5.66/1.64 % No SInE strategy applied
% 5.66/1.64 % Search class: FGHSM-SSLM32-MFFFFFNN
% 5.66/1.64 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 5.66/1.64 % Starting SubtermCWHack with 136s (1) cores
% 5.66/1.64 % Starting G-E--_008_C45_F1_PI_AE_Q4_CS_SP_S4c with 151s (1) cores
% 5.66/1.64 % Preprocessing time : 0.020 s
% 5.66/1.64
% 5.66/1.64 % Proof found!
% 5.66/1.64 % SZS status Unsatisfiable
% 5.66/1.64 % SZS output start CNFRefutation
% See solution above
% 5.66/1.64 % Parsed axioms : 1051
% 5.66/1.64 % Removed by relevancy pruning/SinE : 0
% 5.66/1.64 % Initial clauses : 1051
% 5.66/1.64 % Removed in clause preprocessing : 1
% 5.66/1.64 % Initial clauses in saturation : 1050
% 5.66/1.64 % Processed clauses : 1097
% 5.66/1.64 % ...of these trivial : 20
% 5.66/1.64 % ...subsumed : 106
% 5.66/1.64 % ...remaining for further processing : 971
% 5.66/1.64 % Other redundant clauses eliminated : 4
% 5.66/1.64 % Clauses deleted for lack of memory : 0
% 5.66/1.64 % Backward-subsumed : 0
% 5.66/1.64 % Backward-rewritten : 4
% 5.66/1.64 % Generated clauses : 27070
% 5.66/1.64 % ...of the previous two non-redundant : 26342
% 5.66/1.64 % ...aggressively subsumed : 0
% 5.66/1.64 % Contextual simplify-reflections : 0
% 5.66/1.64 % Paramodulations : 27027
% 5.66/1.64 % Factorizations : 8
% 5.66/1.64 % NegExts : 0
% 5.66/1.64 % Equation resolutions : 35
% 5.66/1.64 % Disequality decompositions : 0
% 5.66/1.64 % Total rewrite steps : 4607
% 5.66/1.64 % ...of those cached : 4350
% 5.66/1.64 % Propositional unsat checks : 0
% 5.66/1.64 % Propositional check models : 0
% 5.66/1.64 % Propositional check unsatisfiable : 0
% 5.66/1.64 % Propositional clauses : 0
% 5.66/1.64 % Propositional clauses after purity: 0
% 5.66/1.64 % Propositional unsat core size : 0
% 5.66/1.64 % Propositional preprocessing time : 0.000
% 5.66/1.64 % Propositional encoding time : 0.000
% 5.66/1.64 % Propositional solver time : 0.000
% 5.66/1.64 % Success case prop preproc time : 0.000
% 5.66/1.64 % Success case prop encoding time : 0.000
% 5.66/1.64 % Success case prop solver time : 0.000
% 5.66/1.64 % Current number of processed clauses : 967
% 5.66/1.64 % Positive orientable unit clauses : 183
% 5.66/1.64 % Positive unorientable unit clauses: 3
% 5.66/1.64 % Negative unit clauses : 4
% 5.66/1.64 % Non-unit-clauses : 777
% 5.66/1.64 % Current number of unprocessed clauses: 26293
% 5.66/1.64 % ...number of literals in the above : 100064
% 5.66/1.64 % Current number of archived formulas : 0
% 5.66/1.64 % Current number of archived clauses : 5
% 5.66/1.64 % Clause-clause subsumption calls (NU) : 122016
% 5.66/1.64 % Rec. Clause-clause subsumption calls : 45850
% 5.66/1.64 % Non-unit clause-clause subsumptions : 105
% 5.66/1.64 % Unit Clause-clause subsumption calls : 30
% 5.66/1.64 % Rewrite failures with RHS unbound : 0
% 5.66/1.64 % BW rewrite match attempts : 10
% 5.66/1.64 % BW rewrite match successes : 5
% 5.66/1.64 % Condensation attempts : 0
% 5.66/1.64 % Condensation successes : 0
% 5.66/1.64 % Termbank termtop insertions : 411736
% 5.66/1.64 % Search garbage collected termcells : 1997
% 5.66/1.64
% 5.66/1.64 % -------------------------------------------------
% 5.66/1.64 % User time : 0.863 s
% 5.66/1.64 % System time : 0.043 s
% 5.66/1.64 % Total time : 0.906 s
% 5.66/1.64 % Maximum resident set size: 5384 pages
% 5.66/1.64
% 5.66/1.64 % -------------------------------------------------
% 5.66/1.64 % User time : 3.807 s
% 5.66/1.64 % System time : 0.182 s
% 5.66/1.64 % Total time : 3.989 s
% 5.66/1.64 % Maximum resident set size: 5120 pages
% 5.66/1.64 % E exiting
%------------------------------------------------------------------------------