TSTP Solution File: ALG385-1 by E---3.1.00

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : E---3.1.00
% Problem  : ALG385-1 : TPTP v8.2.0. Released v4.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E %s %d THM

% Computer : n021.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Mon May 20 18:06:15 EDT 2024

% Result   : Unsatisfiable 4.61s 1.08s
% Output   : CNFRefutation 4.61s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    5
%            Number of leaves      :   12
% Syntax   : Number of clauses     :   36 (  21 unt;   0 nHn;  20 RR)
%            Number of literals    :   54 (  24 equ;  21 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :    5 (   2 avg)
%            Number of predicates  :    7 (   5 usr;   1 prp; 0-3 aty)
%            Number of functors    :   15 (  15 usr;   7 con; 0-3 aty)
%            Number of variables   :   54 (   5 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(cls_smult__eq__0__iff_2,axiom,
    ( c_Polynomial_Osmult(X2,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X1) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
    | ~ class_Ring__and__Field_Oidom(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_smult__eq__0__iff_2) ).

cnf(cls_add__poly__code_I2_J_0,axiom,
    ( c_HOL_Oplus__class_Oplus(X2,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),tc_Polynomial_Opoly(X1)) = X2
    | ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__poly__code_I2_J_0) ).

cnf(cls_class__semiring_Omul__c_0,axiom,
    ( c_HOL_Otimes__class_Otimes(X2,X3,X1) = c_HOL_Otimes__class_Otimes(X3,X2,X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Omul__c_0) ).

cnf(cls_synthetic__div__unique_0,axiom,
    ( X5 = c_Polynomial_Opoly(X2,X3,X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__0(X1)
    | c_HOL_Oplus__class_Oplus(X2,c_Polynomial_Osmult(X3,X4,X1),tc_Polynomial_Opoly(X1)) != c_Polynomial_OpCons(X5,X4,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_synthetic__div__unique_0) ).

cnf(cls_cs0_0,axiom,
    v_cs____ = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_cs0_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__OrderedGroup_Ocomm__monoid__add,axiom,
    class_OrderedGroup_Ocomm__monoid__add(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Ocomm__monoid__add) ).

cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__1,axiom,
    class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__1) ).

cnf(cls_conjecture_0,negated_conjecture,
    ~ c_lessequals(v_da____,c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_aa____,c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).

cnf(cls_poly__pCons_0,axiom,
    ( 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)
    | ~ class_Ring__and__Field_Ocomm__semiring__0(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_poly__pCons_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_CHAINED_0_01,axiom,
    c_lessequals(v_da____,c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(v_aa____,c_HOL_Otimes__class_Otimes(v_z____,v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CHAINED_0_01) ).

cnf(c_0_12,plain,
    ( c_Polynomial_Osmult(X2,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X1) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
    | ~ class_Ring__and__Field_Oidom(X1) ),
    inference(fof_simplification,[status(thm)],[cls_smult__eq__0__iff_2]) ).

cnf(c_0_13,plain,
    ( c_HOL_Oplus__class_Oplus(X2,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),tc_Polynomial_Opoly(X1)) = X2
    | ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
    inference(fof_simplification,[status(thm)],[cls_add__poly__code_I2_J_0]) ).

cnf(c_0_14,plain,
    ( c_HOL_Otimes__class_Otimes(X2,X3,X1) = c_HOL_Otimes__class_Otimes(X3,X2,X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    inference(fof_simplification,[status(thm)],[cls_class__semiring_Omul__c_0]) ).

cnf(c_0_15,plain,
    ( X5 = c_Polynomial_Opoly(X2,X3,X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__0(X1)
    | c_HOL_Oplus__class_Oplus(X2,c_Polynomial_Osmult(X3,X4,X1),tc_Polynomial_Opoly(X1)) != c_Polynomial_OpCons(X5,X4,X1) ),
    inference(fof_simplification,[status(thm)],[cls_synthetic__div__unique_0]) ).

cnf(c_0_16,plain,
    ( c_Polynomial_Osmult(X2,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X1) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
    | ~ class_Ring__and__Field_Oidom(X1) ),
    c_0_12 ).

cnf(c_0_17,axiom,
    v_cs____ = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
    cls_cs0_0 ).

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,
    ( c_HOL_Oplus__class_Oplus(X2,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),tc_Polynomial_Opoly(X1)) = X2
    | ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
    c_0_13 ).

cnf(c_0_20,axiom,
    class_OrderedGroup_Ocomm__monoid__add(tc_Complex_Ocomplex),
    clsarity_Complex__Ocomplex__OrderedGroup_Ocomm__monoid__add ).

cnf(c_0_21,plain,
    ( c_HOL_Otimes__class_Otimes(X2,X3,X1) = c_HOL_Otimes__class_Otimes(X3,X2,X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    c_0_14 ).

cnf(c_0_22,axiom,
    class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex),
    clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__1 ).

cnf(c_0_23,negated_conjecture,
    ~ c_lessequals(v_da____,c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_aa____,c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal),
    inference(fof_simplification,[status(thm)],[cls_conjecture_0]) ).

cnf(c_0_24,plain,
    ( 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)
    | ~ class_Ring__and__Field_Ocomm__semiring__0(X1) ),
    inference(fof_simplification,[status(thm)],[cls_poly__pCons_0]) ).

cnf(c_0_25,plain,
    ( X5 = c_Polynomial_Opoly(X2,X3,X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__0(X1)
    | c_HOL_Oplus__class_Oplus(X2,c_Polynomial_Osmult(X3,X4,X1),tc_Polynomial_Opoly(X1)) != c_Polynomial_OpCons(X5,X4,X1) ),
    c_0_15 ).

cnf(c_0_26,plain,
    c_Polynomial_Osmult(X1,v_cs____,tc_Complex_Ocomplex) = v_cs____,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_17]),c_0_18])]) ).

cnf(c_0_27,plain,
    c_HOL_Oplus__class_Oplus(X1,v_cs____,tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = X1,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_17]) ).

cnf(c_0_28,axiom,
    class_Ring__and__Field_Ocomm__semiring__0(tc_Complex_Ocomplex),
    clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__0 ).

cnf(c_0_29,axiom,
    c_lessequals(v_da____,c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(v_aa____,c_HOL_Otimes__class_Otimes(v_z____,v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal),
    cls_CHAINED_0_01 ).

cnf(c_0_30,plain,
    c_HOL_Otimes__class_Otimes(X1,X2,tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(X2,X1,tc_Complex_Ocomplex),
    inference(spm,[status(thm)],[c_0_21,c_0_22]) ).

cnf(c_0_31,negated_conjecture,
    ~ c_lessequals(v_da____,c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_aa____,c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal),
    c_0_23 ).

cnf(c_0_32,plain,
    ( 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)
    | ~ class_Ring__and__Field_Ocomm__semiring__0(X1) ),
    c_0_24 ).

cnf(c_0_33,plain,
    c_Polynomial_Opoly(c_Polynomial_OpCons(X1,v_cs____,tc_Complex_Ocomplex),X2,tc_Complex_Ocomplex) = X1,
    inference(er,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_27]),c_0_28])])]) ).

cnf(c_0_34,plain,
    c_lessequals(v_da____,c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(v_aa____,c_HOL_Otimes__class_Otimes(v_c____,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal),
    inference(spm,[status(thm)],[c_0_29,c_0_30]) ).

cnf(c_0_35,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_31,c_0_32]),c_0_33]),c_0_30]),c_0_34]),c_0_28])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem    : ALG385-1 : TPTP v8.2.0. Released v4.1.0.
% 0.11/0.13  % Command    : run_E %s %d THM
% 0.14/0.34  % Computer : n021.cluster.edu
% 0.14/0.34  % Model    : x86_64 x86_64
% 0.14/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34  % Memory   : 8042.1875MB
% 0.14/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34  % CPULimit   : 300
% 0.14/0.34  % WCLimit    : 300
% 0.14/0.34  % DateTime   : Sat May 18 22:36:37 EDT 2024
% 0.14/0.34  % CPUTime    : 
% 0.20/0.47  Running first-order theorem proving
% 0.20/0.47  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
% 4.61/1.08  # Version: 3.1.0
% 4.61/1.08  # Preprocessing class: FMLMSMSSSSSNFFN.
% 4.61/1.08  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 4.61/1.08  # Starting G-E--_008_C45_F1_PI_AE_Q4_CS_SP_S4c with 1500s (5) cores
% 4.61/1.08  # Starting new_bool_3 with 300s (1) cores
% 4.61/1.08  # Starting new_bool_1 with 300s (1) cores
% 4.61/1.08  # Starting sh5l with 300s (1) cores
% 4.61/1.08  # G-E--_008_C45_F1_PI_AE_Q4_CS_SP_S4c with pid 9239 completed with status 0
% 4.61/1.08  # Result found by G-E--_008_C45_F1_PI_AE_Q4_CS_SP_S4c
% 4.61/1.08  # Preprocessing class: FMLMSMSSSSSNFFN.
% 4.61/1.08  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 4.61/1.08  # Starting G-E--_008_C45_F1_PI_AE_Q4_CS_SP_S4c with 1500s (5) cores
% 4.61/1.08  # No SInE strategy applied
% 4.61/1.08  # Search class: FGHSM-SSLM32-MFFFFFNN
% 4.61/1.08  # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 4.61/1.08  # Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI with 811s (1) cores
% 4.61/1.08  # Starting G-E--_008_C45_F1_PI_AE_Q4_CS_SP_S4c with 151s (1) cores
% 4.61/1.08  # Starting G-E--_208_C12_02_nc_F1_SE_CS_SP_PS_S5PRR_RG_S070I with 136s (1) cores
% 4.61/1.08  # Starting G-E--_208_C47_F1_SE_CS_SP_PS_S0Y with 136s (1) cores
% 4.61/1.08  # Starting SAT001_MinMin_p005000_rr_RG with 136s (1) cores
% 4.61/1.08  # SAT001_MinMin_p005000_rr_RG with pid 9249 completed with status 0
% 4.61/1.08  # Result found by SAT001_MinMin_p005000_rr_RG
% 4.61/1.08  # Preprocessing class: FMLMSMSSSSSNFFN.
% 4.61/1.08  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 4.61/1.08  # Starting G-E--_008_C45_F1_PI_AE_Q4_CS_SP_S4c with 1500s (5) cores
% 4.61/1.08  # No SInE strategy applied
% 4.61/1.08  # Search class: FGHSM-SSLM32-MFFFFFNN
% 4.61/1.08  # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 4.61/1.08  # Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI with 811s (1) cores
% 4.61/1.08  # Starting G-E--_008_C45_F1_PI_AE_Q4_CS_SP_S4c with 151s (1) cores
% 4.61/1.08  # Starting G-E--_208_C12_02_nc_F1_SE_CS_SP_PS_S5PRR_RG_S070I with 136s (1) cores
% 4.61/1.08  # Starting G-E--_208_C47_F1_SE_CS_SP_PS_S0Y with 136s (1) cores
% 4.61/1.08  # Starting SAT001_MinMin_p005000_rr_RG with 136s (1) cores
% 4.61/1.08  # Preprocessing time       : 0.008 s
% 4.61/1.08  # Presaturation interreduction done
% 4.61/1.08  
% 4.61/1.08  # Proof found!
% 4.61/1.08  # SZS status Unsatisfiable
% 4.61/1.08  # SZS output start CNFRefutation
% See solution above
% 4.61/1.08  # Parsed axioms                        : 1034
% 4.61/1.08  # Removed by relevancy pruning/SinE    : 0
% 4.61/1.08  # Initial clauses                      : 1034
% 4.61/1.08  # Removed in clause preprocessing      : 0
% 4.61/1.08  # Initial clauses in saturation        : 1034
% 4.61/1.08  # Processed clauses                    : 6529
% 4.61/1.08  # ...of these trivial                  : 114
% 4.61/1.08  # ...subsumed                          : 3768
% 4.61/1.08  # ...remaining for further processing  : 2647
% 4.61/1.08  # Other redundant clauses eliminated   : 229
% 4.61/1.08  # Clauses deleted for lack of memory   : 0
% 4.61/1.08  # Backward-subsumed                    : 38
% 4.61/1.08  # Backward-rewritten                   : 29
% 4.61/1.08  # Generated clauses                    : 23452
% 4.61/1.08  # ...of the previous two non-redundant : 19477
% 4.61/1.08  # ...aggressively subsumed             : 0
% 4.61/1.08  # Contextual simplify-reflections      : 1
% 4.61/1.08  # Paramodulations                      : 23208
% 4.61/1.08  # Factorizations                       : 2
% 4.61/1.08  # NegExts                              : 0
% 4.61/1.08  # Equation resolutions                 : 242
% 4.61/1.08  # Disequality decompositions           : 0
% 4.61/1.08  # Total rewrite steps                  : 16281
% 4.61/1.08  # ...of those cached                   : 15604
% 4.61/1.08  # Propositional unsat checks           : 0
% 4.61/1.08  #    Propositional check models        : 0
% 4.61/1.08  #    Propositional check unsatisfiable : 0
% 4.61/1.08  #    Propositional clauses             : 0
% 4.61/1.08  #    Propositional clauses after purity: 0
% 4.61/1.08  #    Propositional unsat core size     : 0
% 4.61/1.08  #    Propositional preprocessing time  : 0.000
% 4.61/1.08  #    Propositional encoding time       : 0.000
% 4.61/1.08  #    Propositional solver time         : 0.000
% 4.61/1.08  #    Success case prop preproc time    : 0.000
% 4.61/1.08  #    Success case prop encoding time   : 0.000
% 4.61/1.08  #    Success case prop solver time     : 0.000
% 4.61/1.08  # Current number of processed clauses  : 1657
% 4.61/1.08  #    Positive orientable unit clauses  : 334
% 4.61/1.08  #    Positive unorientable unit clauses: 5
% 4.61/1.08  #    Negative unit clauses             : 218
% 4.61/1.08  #    Non-unit-clauses                  : 1100
% 4.61/1.08  # Current number of unprocessed clauses: 14808
% 4.61/1.08  # ...number of literals in the above   : 39090
% 4.61/1.08  # Current number of archived formulas  : 0
% 4.61/1.08  # Current number of archived clauses   : 990
% 4.61/1.08  # Clause-clause subsumption calls (NU) : 214769
% 4.61/1.08  # Rec. Clause-clause subsumption calls : 122218
% 4.61/1.08  # Non-unit clause-clause subsumptions  : 1755
% 4.61/1.08  # Unit Clause-clause subsumption calls : 22590
% 4.61/1.08  # Rewrite failures with RHS unbound    : 0
% 4.61/1.08  # BW rewrite match attempts            : 562
% 4.61/1.08  # BW rewrite match successes           : 66
% 4.61/1.08  # Condensation attempts                : 0
% 4.61/1.08  # Condensation successes               : 0
% 4.61/1.08  # Termbank termtop insertions          : 362141
% 4.61/1.08  # Search garbage collected termcells   : 1983
% 4.61/1.08  
% 4.61/1.08  # -------------------------------------------------
% 4.61/1.08  # User time                : 0.533 s
% 4.61/1.08  # System time              : 0.019 s
% 4.61/1.08  # Total time               : 0.552 s
% 4.61/1.08  # Maximum resident set size: 3764 pages
% 4.61/1.08  
% 4.61/1.08  # -------------------------------------------------
% 4.61/1.08  # User time                : 2.595 s
% 4.61/1.08  # System time              : 0.089 s
% 4.61/1.08  # Total time               : 2.684 s
% 4.61/1.08  # Maximum resident set size: 2404 pages
% 4.61/1.08  % E---3.1 exiting
% 4.61/1.08  % E exiting
%------------------------------------------------------------------------------