TSTP Solution File: KLE151+1 by E-SAT---3.1

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : E-SAT---3.1
% Problem  : KLE151+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E %s %d THM

% Computer : n001.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 18:05:18 EDT 2023

% Result   : Theorem 84.53s 11.20s
% Output   : CNFRefutation 84.53s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :   12
% Syntax   : Number of formulae    :   51 (  42 unt;   0 def)
%            Number of atoms       :   62 (  43 equ)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :   22 (  11   ~;   8   |;   1   &)
%                                         (   1 <=>;   1  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   2 avg)
%            Maximal term depth    :    7 (   2 avg)
%            Number of predicates  :    3 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   3 con; 0-2 aty)
%            Number of variables   :  107 (   0 sgn;  50   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(infty_unfold1,axiom,
    ! [X1] : strong_iteration(X1) = addition(multiplication(X1,strong_iteration(X1)),one),
    file('/export/starexec/sandbox/tmp/tmp.ZM0SnZjvGd/E---3.1_26734.p',infty_unfold1) ).

fof(additive_commutativity,axiom,
    ! [X1,X2] : addition(X1,X2) = addition(X2,X1),
    file('/export/starexec/sandbox/tmp/tmp.ZM0SnZjvGd/E---3.1_26734.p',additive_commutativity) ).

fof(infty_coinduction,axiom,
    ! [X1,X2,X3] :
      ( leq(X3,addition(multiplication(X1,X3),X2))
     => leq(X3,multiplication(strong_iteration(X1),X2)) ),
    file('/export/starexec/sandbox/tmp/tmp.ZM0SnZjvGd/E---3.1_26734.p',infty_coinduction) ).

fof(multiplicative_associativity,axiom,
    ! [X1,X2,X3] : multiplication(X1,multiplication(X2,X3)) = multiplication(multiplication(X1,X2),X3),
    file('/export/starexec/sandbox/tmp/tmp.ZM0SnZjvGd/E---3.1_26734.p',multiplicative_associativity) ).

fof(distributivity2,axiom,
    ! [X1,X2,X3] : multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
    file('/export/starexec/sandbox/tmp/tmp.ZM0SnZjvGd/E---3.1_26734.p',distributivity2) ).

fof(multiplicative_left_identity,axiom,
    ! [X1] : multiplication(one,X1) = X1,
    file('/export/starexec/sandbox/tmp/tmp.ZM0SnZjvGd/E---3.1_26734.p',multiplicative_left_identity) ).

fof(order,axiom,
    ! [X1,X2] :
      ( leq(X1,X2)
    <=> addition(X1,X2) = X2 ),
    file('/export/starexec/sandbox/tmp/tmp.ZM0SnZjvGd/E---3.1_26734.p',order) ).

fof(additive_associativity,axiom,
    ! [X3,X2,X1] : addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
    file('/export/starexec/sandbox/tmp/tmp.ZM0SnZjvGd/E---3.1_26734.p',additive_associativity) ).

fof(distributivity1,axiom,
    ! [X1,X2,X3] : multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
    file('/export/starexec/sandbox/tmp/tmp.ZM0SnZjvGd/E---3.1_26734.p',distributivity1) ).

fof(idempotence,axiom,
    ! [X1] : addition(X1,X1) = X1,
    file('/export/starexec/sandbox/tmp/tmp.ZM0SnZjvGd/E---3.1_26734.p',idempotence) ).

fof(goals,conjecture,
    ! [X4,X5] : leq(multiplication(X4,strong_iteration(multiplication(X5,X4))),multiplication(strong_iteration(multiplication(X4,X5)),X4)),
    file('/export/starexec/sandbox/tmp/tmp.ZM0SnZjvGd/E---3.1_26734.p',goals) ).

fof(multiplicative_right_identity,axiom,
    ! [X1] : multiplication(X1,one) = X1,
    file('/export/starexec/sandbox/tmp/tmp.ZM0SnZjvGd/E---3.1_26734.p',multiplicative_right_identity) ).

fof(c_0_12,plain,
    ! [X33] : strong_iteration(X33) = addition(multiplication(X33,strong_iteration(X33)),one),
    inference(variable_rename,[status(thm)],[infty_unfold1]) ).

fof(c_0_13,plain,
    ! [X6,X7] : addition(X6,X7) = addition(X7,X6),
    inference(variable_rename,[status(thm)],[additive_commutativity]) ).

fof(c_0_14,plain,
    ! [X34,X35,X36] :
      ( ~ leq(X36,addition(multiplication(X34,X36),X35))
      | leq(X36,multiplication(strong_iteration(X34),X35)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[infty_coinduction])]) ).

fof(c_0_15,plain,
    ! [X13,X14,X15] : multiplication(X13,multiplication(X14,X15)) = multiplication(multiplication(X13,X14),X15),
    inference(variable_rename,[status(thm)],[multiplicative_associativity]) ).

fof(c_0_16,plain,
    ! [X21,X22,X23] : multiplication(addition(X21,X22),X23) = addition(multiplication(X21,X23),multiplication(X22,X23)),
    inference(variable_rename,[status(thm)],[distributivity2]) ).

fof(c_0_17,plain,
    ! [X17] : multiplication(one,X17) = X17,
    inference(variable_rename,[status(thm)],[multiplicative_left_identity]) ).

cnf(c_0_18,plain,
    strong_iteration(X1) = addition(multiplication(X1,strong_iteration(X1)),one),
    inference(split_conjunct,[status(thm)],[c_0_12]) ).

cnf(c_0_19,plain,
    addition(X1,X2) = addition(X2,X1),
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

cnf(c_0_20,plain,
    ( leq(X1,multiplication(strong_iteration(X2),X3))
    | ~ leq(X1,addition(multiplication(X2,X1),X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_14]) ).

cnf(c_0_21,plain,
    multiplication(X1,multiplication(X2,X3)) = multiplication(multiplication(X1,X2),X3),
    inference(split_conjunct,[status(thm)],[c_0_15]) ).

fof(c_0_22,plain,
    ! [X38,X39] :
      ( ( ~ leq(X38,X39)
        | addition(X38,X39) = X39 )
      & ( addition(X38,X39) != X39
        | leq(X38,X39) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[order])]) ).

fof(c_0_23,plain,
    ! [X8,X9,X10] : addition(X10,addition(X9,X8)) = addition(addition(X10,X9),X8),
    inference(variable_rename,[status(thm)],[additive_associativity]) ).

fof(c_0_24,plain,
    ! [X18,X19,X20] : multiplication(X18,addition(X19,X20)) = addition(multiplication(X18,X19),multiplication(X18,X20)),
    inference(variable_rename,[status(thm)],[distributivity1]) ).

cnf(c_0_25,plain,
    multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
    inference(split_conjunct,[status(thm)],[c_0_16]) ).

cnf(c_0_26,plain,
    multiplication(one,X1) = X1,
    inference(split_conjunct,[status(thm)],[c_0_17]) ).

cnf(c_0_27,plain,
    addition(one,multiplication(X1,strong_iteration(X1))) = strong_iteration(X1),
    inference(rw,[status(thm)],[c_0_18,c_0_19]) ).

fof(c_0_28,plain,
    ! [X12] : addition(X12,X12) = X12,
    inference(variable_rename,[status(thm)],[idempotence]) ).

fof(c_0_29,negated_conjecture,
    ~ ! [X4,X5] : leq(multiplication(X4,strong_iteration(multiplication(X5,X4))),multiplication(strong_iteration(multiplication(X4,X5)),X4)),
    inference(assume_negation,[status(cth)],[goals]) ).

cnf(c_0_30,plain,
    ( leq(X1,multiplication(strong_iteration(multiplication(X2,X3)),X4))
    | ~ leq(X1,addition(multiplication(X2,multiplication(X3,X1)),X4)) ),
    inference(spm,[status(thm)],[c_0_20,c_0_21]) ).

cnf(c_0_31,plain,
    ( leq(X1,X2)
    | addition(X1,X2) != X2 ),
    inference(split_conjunct,[status(thm)],[c_0_22]) ).

cnf(c_0_32,plain,
    addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
    inference(split_conjunct,[status(thm)],[c_0_23]) ).

cnf(c_0_33,plain,
    multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
    inference(split_conjunct,[status(thm)],[c_0_24]) ).

cnf(c_0_34,plain,
    addition(X1,multiplication(X2,X1)) = multiplication(addition(X2,one),X1),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_19]) ).

cnf(c_0_35,plain,
    addition(one,multiplication(X1,multiplication(X2,strong_iteration(multiplication(X1,X2))))) = strong_iteration(multiplication(X1,X2)),
    inference(spm,[status(thm)],[c_0_27,c_0_21]) ).

fof(c_0_36,plain,
    ! [X16] : multiplication(X16,one) = X16,
    inference(variable_rename,[status(thm)],[multiplicative_right_identity]) ).

cnf(c_0_37,plain,
    addition(X1,X1) = X1,
    inference(split_conjunct,[status(thm)],[c_0_28]) ).

fof(c_0_38,negated_conjecture,
    ~ leq(multiplication(esk1_0,strong_iteration(multiplication(esk2_0,esk1_0))),multiplication(strong_iteration(multiplication(esk1_0,esk2_0)),esk1_0)),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_29])])]) ).

cnf(c_0_39,plain,
    ( leq(X1,multiplication(strong_iteration(multiplication(X2,X3)),X4))
    | addition(X1,addition(multiplication(X2,multiplication(X3,X1)),X4)) != addition(multiplication(X2,multiplication(X3,X1)),X4) ),
    inference(spm,[status(thm)],[c_0_30,c_0_31]) ).

cnf(c_0_40,plain,
    addition(multiplication(X1,X2),addition(multiplication(X1,X3),X4)) = addition(multiplication(X1,addition(X2,X3)),X4),
    inference(spm,[status(thm)],[c_0_32,c_0_33]) ).

cnf(c_0_41,plain,
    addition(X1,multiplication(X2,multiplication(X3,X1))) = multiplication(addition(one,multiplication(X2,X3)),X1),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_21]),c_0_19]) ).

cnf(c_0_42,plain,
    addition(one,addition(multiplication(X1,multiplication(X2,strong_iteration(multiplication(X1,X2)))),X3)) = addition(strong_iteration(multiplication(X1,X2)),X3),
    inference(spm,[status(thm)],[c_0_32,c_0_35]) ).

cnf(c_0_43,plain,
    multiplication(X1,one) = X1,
    inference(split_conjunct,[status(thm)],[c_0_36]) ).

cnf(c_0_44,plain,
    addition(X1,addition(X1,X2)) = addition(X1,X2),
    inference(spm,[status(thm)],[c_0_32,c_0_37]) ).

cnf(c_0_45,negated_conjecture,
    ~ leq(multiplication(esk1_0,strong_iteration(multiplication(esk2_0,esk1_0))),multiplication(strong_iteration(multiplication(esk1_0,esk2_0)),esk1_0)),
    inference(split_conjunct,[status(thm)],[c_0_38]) ).

cnf(c_0_46,plain,
    ( leq(multiplication(X1,X2),multiplication(strong_iteration(multiplication(X1,X3)),X4))
    | addition(multiplication(X1,multiplication(addition(one,multiplication(X3,X1)),X2)),X4) != addition(multiplication(X1,multiplication(X3,multiplication(X1,X2))),X4) ),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_40]),c_0_41]) ).

cnf(c_0_47,plain,
    multiplication(addition(one,multiplication(X1,X2)),strong_iteration(multiplication(X1,X2))) = strong_iteration(multiplication(X1,X2)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_37]),c_0_35]),c_0_41]) ).

cnf(c_0_48,plain,
    addition(X1,multiplication(X1,X2)) = multiplication(X1,addition(X2,one)),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_43]),c_0_19]) ).

cnf(c_0_49,plain,
    addition(one,strong_iteration(X1)) = strong_iteration(X1),
    inference(spm,[status(thm)],[c_0_44,c_0_27]) ).

cnf(c_0_50,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[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_47]),c_0_19]),c_0_48]),c_0_19]),c_0_49]),c_0_19]),c_0_48]),c_0_19]),c_0_35])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem    : KLE151+1 : TPTP v8.1.2. Released v4.0.0.
% 0.07/0.13  % Command    : run_E %s %d THM
% 0.14/0.34  % Computer : n001.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
% 0.14/0.35  % CPULimit   : 2400
% 0.14/0.35  % WCLimit    : 300
% 0.14/0.35  % DateTime   : Tue Oct  3 05:16:37 EDT 2023
% 0.14/0.35  % CPUTime    : 
% 0.20/0.48  Running first-order model finding
% 0.20/0.48  Running: /export/starexec/sandbox/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --satauto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/tmp/tmp.ZM0SnZjvGd/E---3.1_26734.p
% 84.53/11.20  # Version: 3.1pre001
% 84.53/11.20  # Preprocessing class: FSMSSMSSSSSNFFN.
% 84.53/11.20  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 84.53/11.20  # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 84.53/11.20  # Starting new_bool_3 with 300s (1) cores
% 84.53/11.20  # Starting new_bool_1 with 300s (1) cores
% 84.53/11.20  # Starting sh5l with 300s (1) cores
% 84.53/11.20  # G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 26811 completed with status 0
% 84.53/11.20  # Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 84.53/11.20  # Preprocessing class: FSMSSMSSSSSNFFN.
% 84.53/11.20  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 84.53/11.20  # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 84.53/11.20  # No SInE strategy applied
% 84.53/11.20  # Search class: FHUSM-FFSF21-MFFFFFNN
% 84.53/11.20  # Scheduled 11 strats onto 5 cores with 1500 seconds (1500 total)
% 84.53/11.20  # Starting G-E--_208_C12_11_nc_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 84.53/11.20  # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 84.53/11.20  # Starting G-E--_092_C01_F1_AE_CS_SP_PS_CO_S0Y with 136s (1) cores
% 84.53/11.20  # Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S4d with 136s (1) cores
% 84.53/11.20  # Starting G-E--_207_C18_F1_AE_CS_SP_PI_PS_S2U with 136s (1) cores
% 84.53/11.20  # G-E--_207_C18_F1_AE_CS_SP_PI_PS_S2U with pid 26821 completed with status 0
% 84.53/11.20  # Result found by G-E--_207_C18_F1_AE_CS_SP_PI_PS_S2U
% 84.53/11.20  # Preprocessing class: FSMSSMSSSSSNFFN.
% 84.53/11.20  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 84.53/11.20  # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 84.53/11.20  # No SInE strategy applied
% 84.53/11.20  # Search class: FHUSM-FFSF21-MFFFFFNN
% 84.53/11.20  # Scheduled 11 strats onto 5 cores with 1500 seconds (1500 total)
% 84.53/11.20  # Starting G-E--_208_C12_11_nc_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 84.53/11.20  # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 84.53/11.20  # Starting G-E--_092_C01_F1_AE_CS_SP_PS_CO_S0Y with 136s (1) cores
% 84.53/11.20  # Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S4d with 136s (1) cores
% 84.53/11.20  # Starting G-E--_207_C18_F1_AE_CS_SP_PI_PS_S2U with 136s (1) cores
% 84.53/11.20  # Preprocessing time       : 0.001 s
% 84.53/11.20  # Presaturation interreduction done
% 84.53/11.20  
% 84.53/11.20  # Proof found!
% 84.53/11.20  # SZS status Theorem
% 84.53/11.20  # SZS output start CNFRefutation
% See solution above
% 84.53/11.20  # Parsed axioms                        : 19
% 84.53/11.20  # Removed by relevancy pruning/SinE    : 0
% 84.53/11.20  # Initial clauses                      : 20
% 84.53/11.20  # Removed in clause preprocessing      : 0
% 84.53/11.20  # Initial clauses in saturation        : 20
% 84.53/11.20  # Processed clauses                    : 26923
% 84.53/11.20  # ...of these trivial                  : 438
% 84.53/11.20  # ...subsumed                          : 24063
% 84.53/11.20  # ...remaining for further processing  : 2422
% 84.53/11.20  # Other redundant clauses eliminated   : 52
% 84.53/11.20  # Clauses deleted for lack of memory   : 0
% 84.53/11.20  # Backward-subsumed                    : 244
% 84.53/11.20  # Backward-rewritten                   : 107
% 84.53/11.20  # Generated clauses                    : 561759
% 84.53/11.20  # ...of the previous two non-redundant : 492711
% 84.53/11.20  # ...aggressively subsumed             : 0
% 84.53/11.20  # Contextual simplify-reflections      : 15
% 84.53/11.20  # Paramodulations                      : 561497
% 84.53/11.20  # Factorizations                       : 0
% 84.53/11.20  # NegExts                              : 0
% 84.53/11.20  # Equation resolutions                 : 262
% 84.53/11.20  # Total rewrite steps                  : 860075
% 84.53/11.20  # Propositional unsat checks           : 0
% 84.53/11.20  #    Propositional check models        : 0
% 84.53/11.20  #    Propositional check unsatisfiable : 0
% 84.53/11.20  #    Propositional clauses             : 0
% 84.53/11.20  #    Propositional clauses after purity: 0
% 84.53/11.20  #    Propositional unsat core size     : 0
% 84.53/11.20  #    Propositional preprocessing time  : 0.000
% 84.53/11.20  #    Propositional encoding time       : 0.000
% 84.53/11.20  #    Propositional solver time         : 0.000
% 84.53/11.20  #    Success case prop preproc time    : 0.000
% 84.53/11.20  #    Success case prop encoding time   : 0.000
% 84.53/11.20  #    Success case prop solver time     : 0.000
% 84.53/11.20  # Current number of processed clauses  : 2051
% 84.53/11.20  #    Positive orientable unit clauses  : 218
% 84.53/11.20  #    Positive unorientable unit clauses: 18
% 84.53/11.20  #    Negative unit clauses             : 117
% 84.53/11.20  #    Non-unit-clauses                  : 1698
% 84.53/11.20  # Current number of unprocessed clauses: 463470
% 84.53/11.20  # ...number of literals in the above   : 1184262
% 84.53/11.20  # Current number of archived formulas  : 0
% 84.53/11.20  # Current number of archived clauses   : 371
% 84.53/11.20  # Clause-clause subsumption calls (NU) : 347748
% 84.53/11.20  # Rec. Clause-clause subsumption calls : 286109
% 84.53/11.20  # Non-unit clause-clause subsumptions  : 5881
% 84.53/11.20  # Unit Clause-clause subsumption calls : 7835
% 84.53/11.20  # Rewrite failures with RHS unbound    : 0
% 84.53/11.20  # BW rewrite match attempts            : 1913
% 84.53/11.20  # BW rewrite match successes           : 365
% 84.53/11.20  # Condensation attempts                : 0
% 84.53/11.20  # Condensation successes               : 0
% 84.53/11.20  # Termbank termtop insertions          : 11526935
% 84.53/11.20  
% 84.53/11.20  # -------------------------------------------------
% 84.53/11.20  # User time                : 10.135 s
% 84.53/11.20  # System time              : 0.316 s
% 84.53/11.20  # Total time               : 10.451 s
% 84.53/11.20  # Maximum resident set size: 1752 pages
% 84.53/11.20  
% 84.53/11.20  # -------------------------------------------------
% 84.53/11.20  # User time                : 50.904 s
% 84.53/11.20  # System time              : 1.757 s
% 84.53/11.20  # Total time               : 52.660 s
% 84.53/11.20  # Maximum resident set size: 1688 pages
% 84.53/11.20  % E---3.1 exiting
%------------------------------------------------------------------------------