TSTP Solution File: KLE040+1 by E---3.1

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : E---3.1
% Problem  : KLE040+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E %s %d THM

% Computer : n004.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 : 2400s
% WCLimit  : 300s
% DateTime : Tue Oct 10 18:03:59 EDT 2023

% Result   : Timeout 4.39s 300.18s
% Output   : None 
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   18
%            Number of leaves      :   11
% Syntax   : Number of formulae    :   61 (  39 unt;   0 def)
%            Number of atoms       :   85 (  44 equ)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :   47 (  23   ~;  20   |;   1   &)
%                                         (   1 <=>;   2  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   2 avg)
%            Maximal term depth    :    5 (   2 avg)
%            Number of predicates  :    3 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   2 con; 0-2 aty)
%            Number of variables   :  101 (   0 sgn;  42   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(additive_associativity,axiom,
    ! [X3,X2,X1] : addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
    file('/export/starexec/sandbox/tmp/tmp.QLRnZWL4DE/E---3.1_31930.p',additive_associativity) ).

fof(additive_idempotence,axiom,
    ! [X1] : addition(X1,X1) = X1,
    file('/export/starexec/sandbox/tmp/tmp.QLRnZWL4DE/E---3.1_31930.p',additive_idempotence) ).

fof(star_induction_right,axiom,
    ! [X1,X2,X3] :
      ( leq(addition(multiplication(X1,X2),X3),X1)
     => leq(multiplication(X3,star(X2)),X1) ),
    file('/export/starexec/sandbox/tmp/tmp.QLRnZWL4DE/E---3.1_31930.p',star_induction_right) ).

fof(multiplicative_right_identity,axiom,
    ! [X1] : multiplication(X1,one) = X1,
    file('/export/starexec/sandbox/tmp/tmp.QLRnZWL4DE/E---3.1_31930.p',multiplicative_right_identity) ).

fof(additive_commutativity,axiom,
    ! [X1,X2] : addition(X1,X2) = addition(X2,X1),
    file('/export/starexec/sandbox/tmp/tmp.QLRnZWL4DE/E---3.1_31930.p',additive_commutativity) ).

fof(order,axiom,
    ! [X1,X2] :
      ( leq(X1,X2)
    <=> addition(X1,X2) = X2 ),
    file('/export/starexec/sandbox/tmp/tmp.QLRnZWL4DE/E---3.1_31930.p',order) ).

fof(multiplicative_left_identity,axiom,
    ! [X1] : multiplication(one,X1) = X1,
    file('/export/starexec/sandbox/tmp/tmp.QLRnZWL4DE/E---3.1_31930.p',multiplicative_left_identity) ).

fof(star_unfold_right,axiom,
    ! [X1] : leq(addition(one,multiplication(X1,star(X1))),star(X1)),
    file('/export/starexec/sandbox/tmp/tmp.QLRnZWL4DE/E---3.1_31930.p',star_unfold_right) ).

fof(star_induction_left,axiom,
    ! [X1,X2,X3] :
      ( leq(addition(multiplication(X1,X2),X3),X2)
     => leq(multiplication(star(X1),X3),X2) ),
    file('/export/starexec/sandbox/tmp/tmp.QLRnZWL4DE/E---3.1_31930.p',star_induction_left) ).

fof(right_distributivity,axiom,
    ! [X1,X2,X3] : multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
    file('/export/starexec/sandbox/tmp/tmp.QLRnZWL4DE/E---3.1_31930.p',right_distributivity) ).

fof(goals,conjecture,
    ! [X4] : multiplication(star(X4),star(X4)) = star(X4),
    file('/export/starexec/sandbox/tmp/tmp.QLRnZWL4DE/E---3.1_31930.p',goals) ).

fof(c_0_11,plain,
    ! [X31,X32,X33] : addition(X33,addition(X32,X31)) = addition(addition(X33,X32),X31),
    inference(variable_rename,[status(thm)],[additive_associativity]) ).

fof(c_0_12,plain,
    ! [X35] : addition(X35,X35) = X35,
    inference(variable_rename,[status(thm)],[additive_idempotence]) ).

fof(c_0_13,plain,
    ! [X11,X12,X13] :
      ( ~ leq(addition(multiplication(X11,X12),X13),X11)
      | leq(multiplication(X13,star(X12)),X11) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[star_induction_right])]) ).

fof(c_0_14,plain,
    ! [X17] : multiplication(X17,one) = X17,
    inference(variable_rename,[status(thm)],[multiplicative_right_identity]) ).

cnf(c_0_15,plain,
    addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

cnf(c_0_16,plain,
    addition(X1,X1) = X1,
    inference(split_conjunct,[status(thm)],[c_0_12]) ).

fof(c_0_17,plain,
    ! [X29,X30] : addition(X29,X30) = addition(X30,X29),
    inference(variable_rename,[status(thm)],[additive_commutativity]) ).

cnf(c_0_18,plain,
    ( leq(multiplication(X3,star(X2)),X1)
    | ~ leq(addition(multiplication(X1,X2),X3),X1) ),
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

cnf(c_0_19,plain,
    multiplication(X1,one) = X1,
    inference(split_conjunct,[status(thm)],[c_0_14]) ).

fof(c_0_20,plain,
    ! [X27,X28] :
      ( ( ~ leq(X27,X28)
        | addition(X27,X28) = X28 )
      & ( addition(X27,X28) != X28
        | leq(X27,X28) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[order])]) ).

cnf(c_0_21,plain,
    addition(X1,addition(X1,X2)) = addition(X1,X2),
    inference(spm,[status(thm)],[c_0_15,c_0_16]) ).

cnf(c_0_22,plain,
    addition(X1,X2) = addition(X2,X1),
    inference(split_conjunct,[status(thm)],[c_0_17]) ).

cnf(c_0_23,plain,
    ( leq(multiplication(X1,star(one)),X2)
    | ~ leq(addition(X2,X1),X2) ),
    inference(spm,[status(thm)],[c_0_18,c_0_19]) ).

cnf(c_0_24,plain,
    ( leq(X1,X2)
    | addition(X1,X2) != X2 ),
    inference(split_conjunct,[status(thm)],[c_0_20]) ).

cnf(c_0_25,plain,
    addition(X1,addition(X2,X1)) = addition(X2,X1),
    inference(spm,[status(thm)],[c_0_21,c_0_22]) ).

fof(c_0_26,plain,
    ! [X18] : multiplication(one,X18) = X18,
    inference(variable_rename,[status(thm)],[multiplicative_left_identity]) ).

fof(c_0_27,plain,
    ! [X6] : leq(addition(one,multiplication(X6,star(X6))),star(X6)),
    inference(variable_rename,[status(thm)],[star_unfold_right]) ).

cnf(c_0_28,plain,
    ( leq(multiplication(X1,star(one)),X2)
    | addition(X1,X2) != X2 ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_15]),c_0_25]) ).

cnf(c_0_29,plain,
    multiplication(one,X1) = X1,
    inference(split_conjunct,[status(thm)],[c_0_26]) ).

cnf(c_0_30,plain,
    leq(addition(one,multiplication(X1,star(X1))),star(X1)),
    inference(split_conjunct,[status(thm)],[c_0_27]) ).

cnf(c_0_31,plain,
    ( addition(X1,X2) = X2
    | ~ leq(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_20]) ).

cnf(c_0_32,plain,
    ( leq(star(one),X1)
    | addition(one,X1) != X1 ),
    inference(spm,[status(thm)],[c_0_28,c_0_29]) ).

cnf(c_0_33,plain,
    leq(addition(one,star(one)),star(one)),
    inference(spm,[status(thm)],[c_0_30,c_0_29]) ).

cnf(c_0_34,plain,
    ( addition(star(one),X1) = X1
    | addition(one,X1) != X1 ),
    inference(spm,[status(thm)],[c_0_31,c_0_32]) ).

cnf(c_0_35,plain,
    addition(one,star(one)) = star(one),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_33]),c_0_15]),c_0_16]) ).

cnf(c_0_36,plain,
    ( addition(X1,star(one)) = X1
    | addition(one,X1) != X1 ),
    inference(spm,[status(thm)],[c_0_22,c_0_34]) ).

cnf(c_0_37,plain,
    ( leq(multiplication(X1,star(X2)),X3)
    | ~ leq(addition(X1,multiplication(X3,X2)),X3) ),
    inference(spm,[status(thm)],[c_0_18,c_0_22]) ).

cnf(c_0_38,plain,
    star(one) = one,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_16])]) ).

cnf(c_0_39,plain,
    ( leq(X1,X2)
    | ~ leq(addition(X1,X2),X2) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_19]),c_0_38]),c_0_19]) ).

cnf(c_0_40,plain,
    ( leq(addition(X1,X2),X3)
    | ~ leq(addition(X1,addition(X2,X3)),X3) ),
    inference(spm,[status(thm)],[c_0_39,c_0_15]) ).

fof(c_0_41,plain,
    ! [X8,X9,X10] :
      ( ~ leq(addition(multiplication(X8,X9),X10),X9)
      | leq(multiplication(star(X8),X10),X9) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[star_induction_left])]) ).

cnf(c_0_42,plain,
    ( leq(addition(X1,X2),X1)
    | ~ leq(addition(X2,X1),X1) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_16]),c_0_15]),c_0_25]) ).

cnf(c_0_43,plain,
    ( leq(multiplication(star(X1),X3),X2)
    | ~ leq(addition(multiplication(X1,X2),X3),X2) ),
    inference(split_conjunct,[status(thm)],[c_0_41]) ).

cnf(c_0_44,plain,
    addition(one,addition(star(X1),multiplication(X1,star(X1)))) = star(X1),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_30]),c_0_15]),c_0_22]) ).

cnf(c_0_45,plain,
    ( leq(multiplication(X1,star(one)),X2)
    | ~ leq(addition(X1,X2),X2) ),
    inference(spm,[status(thm)],[c_0_23,c_0_22]) ).

cnf(c_0_46,plain,
    ( leq(addition(X1,X2),X1)
    | addition(X2,X1) != X1 ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_24]),c_0_15]),c_0_16]) ).

cnf(c_0_47,plain,
    ( leq(multiplication(star(X1),X2),X3)
    | ~ leq(addition(X2,multiplication(X1,X3)),X3) ),
    inference(spm,[status(thm)],[c_0_43,c_0_22]) ).

cnf(c_0_48,plain,
    addition(star(X1),multiplication(X1,star(X1))) = star(X1),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_44]),c_0_15]),c_0_22]),c_0_21]) ).

cnf(c_0_49,plain,
    leq(X1,X1),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_46]),c_0_38]),c_0_19]),c_0_16])]) ).

fof(c_0_50,plain,
    ! [X19,X20,X21] : multiplication(X19,addition(X20,X21)) = addition(multiplication(X19,X20),multiplication(X19,X21)),
    inference(variable_rename,[status(thm)],[right_distributivity]) ).

fof(c_0_51,negated_conjecture,
    ~ ! [X4] : multiplication(star(X4),star(X4)) = star(X4),
    inference(assume_negation,[status(cth)],[goals]) ).

cnf(c_0_52,plain,
    leq(multiplication(star(X1),star(X1)),star(X1)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_48]),c_0_49])]) ).

cnf(c_0_53,plain,
    multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
    inference(split_conjunct,[status(thm)],[c_0_50]) ).

fof(c_0_54,negated_conjecture,
    multiplication(star(esk1_0),star(esk1_0)) != star(esk1_0),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_51])])]) ).

cnf(c_0_55,plain,
    addition(star(X1),multiplication(star(X1),star(X1))) = star(X1),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_52]),c_0_22]) ).

cnf(c_0_56,plain,
    addition(X1,multiplication(X1,X2)) = multiplication(X1,addition(X2,one)),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_19]),c_0_22]) ).

cnf(c_0_57,plain,
    addition(one,star(X1)) = star(X1),
    inference(spm,[status(thm)],[c_0_21,c_0_44]) ).

cnf(c_0_58,negated_conjecture,
    multiplication(star(esk1_0),star(esk1_0)) != star(esk1_0),
    inference(split_conjunct,[status(thm)],[c_0_54]) ).

cnf(c_0_59,plain,
    multiplication(star(X1),star(X1)) = star(X1),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_55,c_0_56]),c_0_22]),c_0_57]) ).

cnf(c_0_60,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_58,c_0_59])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11  % Problem    : KLE040+1 : TPTP v8.1.2. Released v4.0.0.
% 0.06/0.12  % Command    : run_E %s %d THM
% 0.12/0.32  % Computer : n004.cluster.edu
% 0.12/0.32  % Model    : x86_64 x86_64
% 0.12/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32  % Memory   : 8042.1875MB
% 0.12/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32  % CPULimit   : 2400
% 0.12/0.32  % WCLimit    : 300
% 0.12/0.32  % DateTime   : Tue Oct  3 04:48:59 EDT 2023
% 0.12/0.32  % CPUTime    : 
% 0.17/0.44  Running first-order theorem proving
% 0.17/0.44  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/tmp/tmp.QLRnZWL4DE/E---3.1_31930.p
% 4.39/300.18  # Version: 3.1pre001
% 4.39/300.18  # Preprocessing class: FSMSSMSSSSSNFFN.
% 4.39/300.18  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 4.39/300.18  # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 4.39/300.18  # Starting new_bool_3 with 300s (1) cores
% 4.39/300.18  # Starting new_bool_1 with 300s (1) cores
% 4.39/300.18  # Starting sh5l with 300s (1) cores
% 4.39/300.18  # sh5l with pid 32011 completed with status 0
% 4.39/300.18  # Result found by sh5l
% 4.39/300.18  # Preprocessing class: FSMSSMSSSSSNFFN.
% 4.39/300.18  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 4.39/300.18  # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 4.39/300.18  # Starting new_bool_3 with 300s (1) cores
% 4.39/300.18  # Starting new_bool_1 with 300s (1) cores
% 4.39/300.18  # Starting sh5l with 300s (1) cores
% 4.39/300.18  # SinE strategy is gf500_gu_R04_F100_L20000
% 4.39/300.18  # Search class: FHUSM-FFSF21-MFFFFFNN
% 4.39/300.18  # Scheduled 11 strats onto 1 cores with 300 seconds (300 total)
% 4.39/300.18  # Starting G-E--_208_C12_11_nc_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 28s (1) cores
% 4.39/300.18  # G-E--_208_C12_11_nc_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with pid 32018 completed with status 0
% 4.39/300.18  # Result found by G-E--_208_C12_11_nc_F1_SE_CS_SP_PS_S5PRR_RG_S04AN
% 4.39/300.18  # Preprocessing class: FSMSSMSSSSSNFFN.
% 4.39/300.18  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 4.39/300.18  # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 4.39/300.18  # Starting new_bool_3 with 300s (1) cores
% 4.39/300.18  # Starting new_bool_1 with 300s (1) cores
% 4.39/300.18  # Starting sh5l with 300s (1) cores
% 4.39/300.18  # SinE strategy is gf500_gu_R04_F100_L20000
% 4.39/300.18  # Search class: FHUSM-FFSF21-MFFFFFNN
% 4.39/300.18  # Scheduled 11 strats onto 1 cores with 300 seconds (300 total)
% 4.39/300.18  # Starting G-E--_208_C12_11_nc_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 28s (1) cores
% 4.39/300.18  # Preprocessing time       : 0.001 s
% 4.39/300.18  # Presaturation interreduction done
% 4.39/300.18  
% 4.39/300.18  # Proof found!
% 4.39/300.18  # SZS status Theorem
% 4.39/300.18  # SZS output start CNFRefutation
% See solution above
% 4.39/300.18  # Parsed axioms                        : 17
% 4.39/300.18  # Removed by relevancy pruning/SinE    : 0
% 4.39/300.18  # Initial clauses                      : 18
% 4.39/300.18  # Removed in clause preprocessing      : 0
% 4.39/300.18  # Initial clauses in saturation        : 18
% 4.39/300.18  # Processed clauses                    : 381
% 4.39/300.18  # ...of these trivial                  : 35
% 4.39/300.18  # ...subsumed                          : 167
% 4.39/300.18  # ...remaining for further processing  : 179
% 4.39/300.18  # Other redundant clauses eliminated   : 13
% 4.39/300.18  # Clauses deleted for lack of memory   : 0
% 4.39/300.18  # Backward-subsumed                    : 16
% 4.39/300.18  # Backward-rewritten                   : 43
% 4.39/300.18  # Generated clauses                    : 2283
% 4.39/300.18  # ...of the previous two non-redundant : 1284
% 4.39/300.18  # ...aggressively subsumed             : 0
% 4.39/300.18  # Contextual simplify-reflections      : 1
% 4.39/300.18  # Paramodulations                      : 2270
% 4.39/300.18  # Factorizations                       : 0
% 4.39/300.18  # NegExts                              : 0
% 4.39/300.18  # Equation resolutions                 : 13
% 4.39/300.18  # Total rewrite steps                  : 3272
% 4.39/300.18  # Propositional unsat checks           : 0
% 4.39/300.18  #    Propositional check models        : 0
% 4.39/300.18  #    Propositional check unsatisfiable : 0
% 4.39/300.18  #    Propositional clauses             : 0
% 4.39/300.18  #    Propositional clauses after purity: 0
% 4.39/300.18  #    Propositional unsat core size     : 0
% 4.39/300.18  #    Propositional preprocessing time  : 0.000
% 4.39/300.18  #    Propositional encoding time       : 0.000
% 4.39/300.18  #    Propositional solver time         : 0.000
% 4.39/300.18  #    Success case prop preproc time    : 0.000
% 4.39/300.18  #    Success case prop encoding time   : 0.000
% 4.39/300.18  #    Success case prop solver time     : 0.000
% 4.39/300.18  # Current number of processed clauses  : 102
% 4.39/300.18  #    Positive orientable unit clauses  : 43
% 4.39/300.18  #    Positive unorientable unit clauses: 4
% 4.39/300.18  #    Negative unit clauses             : 6
% 4.39/300.18  #    Non-unit-clauses                  : 49
% 4.39/300.18  # Current number of unprocessed clauses: 889
% 4.39/300.18  # ...number of literals in the above   : 1596
% 4.39/300.18  # Current number of archived formulas  : 0
% 4.39/300.18  # Current number of archived clauses   : 77
% 4.39/300.18  # Clause-clause subsumption calls (NU) : 813
% 4.39/300.18  # Rec. Clause-clause subsumption calls : 797
% 4.39/300.18  # Non-unit clause-clause subsumptions  : 150
% 4.39/300.18  # Unit Clause-clause subsumption calls : 127
% 4.39/300.18  # Rewrite failures with RHS unbound    : 0
% 4.39/300.18  # BW rewrite match attempts            : 199
% 4.39/300.18  # BW rewrite match successes           : 58
% 4.39/300.18  # Condensation attempts                : 0
% 4.39/300.18  # Condensation successes               : 0
% 4.39/300.18  # Termbank termtop insertions          : 23844
% 4.39/300.18  
% 4.39/300.18  # -------------------------------------------------
% 4.39/300.18  # User time                : 0.029 s
% 4.39/300.18  # System time              : 0.002 s
% 4.39/300.18  # Total time               : 0.031 s
% 4.39/300.18  # Maximum resident set size: 1740 pages
% 4.39/300.18  
% 4.39/300.18  # -------------------------------------------------
% 4.39/300.18  # User time                : 0.029 s
% 4.39/300.18  # System time              : 0.004 s
% 4.39/300.18  # Total time               : 0.034 s
% 4.39/300.18  # Maximum resident set size: 1688 pages
% 4.39/300.18  % E---3.1 exiting
% 4.39/300.18  % E---3.1 exiting
%------------------------------------------------------------------------------