TSTP Solution File: FLD041-3 by E-SAT---3.1

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : E-SAT---3.1
% Problem  : FLD041-3 : TPTP v8.1.2. Bugfixed v2.1.0.
% 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 17:30:38 EDT 2023

% Result   : Unsatisfiable 1.63s 0.77s
% Output   : CNFRefutation 1.63s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :   18
% Syntax   : Number of clauses     :   58 (  23 unt;   7 nHn;  58 RR)
%            Number of literals    :  135 (   0 equ;  74 neg)
%            Maximal clause size   :    5 (   2 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    5 (   4 usr;   1 prp; 0-3 aty)
%            Number of functors    :    6 (   6 usr;   4 con; 0-1 aty)
%            Number of variables   :  106 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(totality_of_order_relation,axiom,
    ( less_or_equal(X1,X2)
    | less_or_equal(X2,X1)
    | ~ defined(X1)
    | ~ defined(X2) ),
    file('/export/starexec/sandbox2/tmp/tmp.noYGsGvRZQ/E---3.1_17612.p',totality_of_order_relation) ).

cnf(well_definedness_of_multiplicative_identity,axiom,
    defined(multiplicative_identity),
    file('/export/starexec/sandbox2/tmp/tmp.noYGsGvRZQ/E---3.1_17612.p',well_definedness_of_multiplicative_identity) ).

cnf(existence_of_inverse_multiplication,axiom,
    ( product(multiplicative_inverse(X1),X1,multiplicative_identity)
    | sum(additive_identity,X1,additive_identity)
    | ~ defined(X1) ),
    file('/export/starexec/sandbox2/tmp/tmp.noYGsGvRZQ/E---3.1_17612.p',existence_of_inverse_multiplication) ).

cnf(a_is_defined,hypothesis,
    defined(a),
    file('/export/starexec/sandbox2/tmp/tmp.noYGsGvRZQ/E---3.1_17612.p',a_is_defined) ).

cnf(not_sum_3,negated_conjecture,
    ~ sum(additive_identity,a,additive_identity),
    file('/export/starexec/sandbox2/tmp/tmp.noYGsGvRZQ/E---3.1_17612.p',not_sum_3) ).

cnf(b_is_defined,hypothesis,
    defined(b),
    file('/export/starexec/sandbox2/tmp/tmp.noYGsGvRZQ/E---3.1_17612.p',b_is_defined) ).

cnf(not_sum_4,negated_conjecture,
    ~ sum(additive_identity,b,additive_identity),
    file('/export/starexec/sandbox2/tmp/tmp.noYGsGvRZQ/E---3.1_17612.p',not_sum_4) ).

cnf(associativity_multiplication_1,axiom,
    ( product(X1,X2,X3)
    | ~ product(X1,X4,X5)
    | ~ product(X4,X6,X2)
    | ~ product(X5,X6,X3) ),
    file('/export/starexec/sandbox2/tmp/tmp.noYGsGvRZQ/E---3.1_17612.p',associativity_multiplication_1) ).

cnf(existence_of_identity_multiplication,axiom,
    ( product(multiplicative_identity,X1,X1)
    | ~ defined(X1) ),
    file('/export/starexec/sandbox2/tmp/tmp.noYGsGvRZQ/E---3.1_17612.p',existence_of_identity_multiplication) ).

cnf(commutativity_multiplication,axiom,
    ( product(X1,X2,X3)
    | ~ product(X2,X1,X3) ),
    file('/export/starexec/sandbox2/tmp/tmp.noYGsGvRZQ/E---3.1_17612.p',commutativity_multiplication) ).

cnf(distributivity_1,axiom,
    ( sum(X1,X2,X3)
    | ~ sum(X4,X5,X6)
    | ~ product(X6,X7,X3)
    | ~ product(X4,X7,X1)
    | ~ product(X5,X7,X2) ),
    file('/export/starexec/sandbox2/tmp/tmp.noYGsGvRZQ/E---3.1_17612.p',distributivity_1) ).

cnf(antisymmetry_of_order_relation,axiom,
    ( sum(additive_identity,X1,X2)
    | ~ less_or_equal(X1,X2)
    | ~ less_or_equal(X2,X1) ),
    file('/export/starexec/sandbox2/tmp/tmp.noYGsGvRZQ/E---3.1_17612.p',antisymmetry_of_order_relation) ).

cnf(commutativity_addition,axiom,
    ( sum(X1,X2,X3)
    | ~ sum(X2,X1,X3) ),
    file('/export/starexec/sandbox2/tmp/tmp.noYGsGvRZQ/E---3.1_17612.p',commutativity_addition) ).

cnf(existence_of_inverse_addition,axiom,
    ( sum(additive_inverse(X1),X1,additive_identity)
    | ~ defined(X1) ),
    file('/export/starexec/sandbox2/tmp/tmp.noYGsGvRZQ/E---3.1_17612.p',existence_of_inverse_addition) ).

cnf(associativity_multiplication_2,axiom,
    ( product(X1,X2,X3)
    | ~ product(X4,X5,X1)
    | ~ product(X5,X2,X6)
    | ~ product(X4,X6,X3) ),
    file('/export/starexec/sandbox2/tmp/tmp.noYGsGvRZQ/E---3.1_17612.p',associativity_multiplication_2) ).

cnf(associativity_addition_1,axiom,
    ( sum(X1,X2,X3)
    | ~ sum(X1,X4,X5)
    | ~ sum(X4,X6,X2)
    | ~ sum(X5,X6,X3) ),
    file('/export/starexec/sandbox2/tmp/tmp.noYGsGvRZQ/E---3.1_17612.p',associativity_addition_1) ).

cnf(well_definedness_of_multiplicative_inverse,axiom,
    ( defined(multiplicative_inverse(X1))
    | sum(additive_identity,X1,additive_identity)
    | ~ defined(X1) ),
    file('/export/starexec/sandbox2/tmp/tmp.noYGsGvRZQ/E---3.1_17612.p',well_definedness_of_multiplicative_inverse) ).

cnf(product_5,negated_conjecture,
    product(a,b,additive_identity),
    file('/export/starexec/sandbox2/tmp/tmp.noYGsGvRZQ/E---3.1_17612.p',product_5) ).

cnf(c_0_18,axiom,
    ( less_or_equal(X1,X2)
    | less_or_equal(X2,X1)
    | ~ defined(X1)
    | ~ defined(X2) ),
    totality_of_order_relation ).

cnf(c_0_19,axiom,
    defined(multiplicative_identity),
    well_definedness_of_multiplicative_identity ).

cnf(c_0_20,axiom,
    ( product(multiplicative_inverse(X1),X1,multiplicative_identity)
    | sum(additive_identity,X1,additive_identity)
    | ~ defined(X1) ),
    existence_of_inverse_multiplication ).

cnf(c_0_21,hypothesis,
    defined(a),
    a_is_defined ).

cnf(c_0_22,negated_conjecture,
    ~ sum(additive_identity,a,additive_identity),
    not_sum_3 ).

cnf(c_0_23,plain,
    ( less_or_equal(X1,multiplicative_identity)
    | less_or_equal(multiplicative_identity,X1)
    | ~ defined(X1) ),
    inference(spm,[status(thm)],[c_0_18,c_0_19]) ).

cnf(c_0_24,hypothesis,
    defined(b),
    b_is_defined ).

cnf(c_0_25,negated_conjecture,
    ~ sum(additive_identity,b,additive_identity),
    not_sum_4 ).

cnf(c_0_26,axiom,
    ( product(X1,X2,X3)
    | ~ product(X1,X4,X5)
    | ~ product(X4,X6,X2)
    | ~ product(X5,X6,X3) ),
    associativity_multiplication_1 ).

cnf(c_0_27,axiom,
    ( product(multiplicative_identity,X1,X1)
    | ~ defined(X1) ),
    existence_of_identity_multiplication ).

cnf(c_0_28,axiom,
    ( product(X1,X2,X3)
    | ~ product(X2,X1,X3) ),
    commutativity_multiplication ).

cnf(c_0_29,hypothesis,
    product(multiplicative_inverse(a),a,multiplicative_identity),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_22]) ).

cnf(c_0_30,axiom,
    ( sum(X1,X2,X3)
    | ~ sum(X4,X5,X6)
    | ~ product(X6,X7,X3)
    | ~ product(X4,X7,X1)
    | ~ product(X5,X7,X2) ),
    distributivity_1 ).

cnf(c_0_31,axiom,
    ( sum(additive_identity,X1,X2)
    | ~ less_or_equal(X1,X2)
    | ~ less_or_equal(X2,X1) ),
    antisymmetry_of_order_relation ).

cnf(c_0_32,plain,
    less_or_equal(multiplicative_identity,multiplicative_identity),
    inference(spm,[status(thm)],[c_0_23,c_0_19]) ).

cnf(c_0_33,hypothesis,
    product(multiplicative_inverse(b),b,multiplicative_identity),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_24]),c_0_25]) ).

cnf(c_0_34,plain,
    ( product(X1,X2,X3)
    | ~ product(X1,X4,multiplicative_identity)
    | ~ product(X4,X3,X2)
    | ~ defined(X3) ),
    inference(spm,[status(thm)],[c_0_26,c_0_27]) ).

cnf(c_0_35,hypothesis,
    product(a,multiplicative_inverse(a),multiplicative_identity),
    inference(spm,[status(thm)],[c_0_28,c_0_29]) ).

cnf(c_0_36,axiom,
    ( sum(X1,X2,X3)
    | ~ sum(X2,X1,X3) ),
    commutativity_addition ).

cnf(c_0_37,axiom,
    ( sum(additive_inverse(X1),X1,additive_identity)
    | ~ defined(X1) ),
    existence_of_inverse_addition ).

cnf(c_0_38,plain,
    ( sum(X1,X2,X3)
    | ~ product(X4,X3,X2)
    | ~ product(X5,X3,X1)
    | ~ defined(X3)
    | ~ sum(X5,X4,multiplicative_identity) ),
    inference(spm,[status(thm)],[c_0_30,c_0_27]) ).

cnf(c_0_39,plain,
    sum(additive_identity,multiplicative_identity,multiplicative_identity),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_32])]) ).

cnf(c_0_40,axiom,
    ( product(X1,X2,X3)
    | ~ product(X4,X5,X1)
    | ~ product(X5,X2,X6)
    | ~ product(X4,X6,X3) ),
    associativity_multiplication_2 ).

cnf(c_0_41,hypothesis,
    product(b,multiplicative_inverse(b),multiplicative_identity),
    inference(spm,[status(thm)],[c_0_28,c_0_33]) ).

cnf(c_0_42,hypothesis,
    ( product(a,X1,X2)
    | ~ product(multiplicative_inverse(a),X2,X1)
    | ~ defined(X2) ),
    inference(spm,[status(thm)],[c_0_34,c_0_35]) ).

cnf(c_0_43,axiom,
    ( sum(X1,X2,X3)
    | ~ sum(X1,X4,X5)
    | ~ sum(X4,X6,X2)
    | ~ sum(X5,X6,X3) ),
    associativity_addition_1 ).

cnf(c_0_44,plain,
    ( sum(X1,additive_inverse(X1),additive_identity)
    | ~ defined(X1) ),
    inference(spm,[status(thm)],[c_0_36,c_0_37]) ).

cnf(c_0_45,plain,
    ( sum(X1,X2,X3)
    | ~ product(multiplicative_identity,X3,X2)
    | ~ product(additive_identity,X3,X1)
    | ~ defined(X3) ),
    inference(spm,[status(thm)],[c_0_38,c_0_39]) ).

cnf(c_0_46,hypothesis,
    ( product(X1,multiplicative_inverse(b),X2)
    | ~ product(X3,multiplicative_identity,X2)
    | ~ product(X3,b,X1) ),
    inference(spm,[status(thm)],[c_0_40,c_0_41]) ).

cnf(c_0_47,hypothesis,
    product(a,multiplicative_identity,a),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_29]),c_0_21])]) ).

cnf(c_0_48,axiom,
    ( defined(multiplicative_inverse(X1))
    | sum(additive_identity,X1,additive_identity)
    | ~ defined(X1) ),
    well_definedness_of_multiplicative_inverse ).

cnf(c_0_49,plain,
    ( sum(X1,X2,additive_identity)
    | ~ defined(X3)
    | ~ sum(X4,additive_inverse(X3),X2)
    | ~ sum(X1,X4,X3) ),
    inference(spm,[status(thm)],[c_0_43,c_0_44]) ).

cnf(c_0_50,plain,
    ( sum(X1,X2,X2)
    | ~ product(additive_identity,X2,X1)
    | ~ defined(X2) ),
    inference(spm,[status(thm)],[c_0_45,c_0_27]) ).

cnf(c_0_51,hypothesis,
    ( product(X1,multiplicative_inverse(b),a)
    | ~ product(a,b,X1) ),
    inference(spm,[status(thm)],[c_0_46,c_0_47]) ).

cnf(c_0_52,hypothesis,
    defined(multiplicative_inverse(b)),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_24]),c_0_25]) ).

cnf(c_0_53,negated_conjecture,
    product(a,b,additive_identity),
    product_5 ).

cnf(c_0_54,plain,
    ( sum(X1,additive_identity,additive_identity)
    | ~ defined(X2)
    | ~ sum(X1,X2,X2) ),
    inference(spm,[status(thm)],[c_0_49,c_0_44]) ).

cnf(c_0_55,hypothesis,
    sum(a,multiplicative_inverse(b),multiplicative_inverse(b)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_51]),c_0_52]),c_0_53])]) ).

cnf(c_0_56,hypothesis,
    sum(a,additive_identity,additive_identity),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_55]),c_0_52])]) ).

cnf(c_0_57,hypothesis,
    $false,
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_56]),c_0_22]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.14  % Problem    : FLD041-3 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.14/0.15  % Command    : run_E %s %d THM
% 0.15/0.37  % Computer : n004.cluster.edu
% 0.15/0.37  % Model    : x86_64 x86_64
% 0.15/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37  % Memory   : 8042.1875MB
% 0.15/0.37  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37  % CPULimit   : 2400
% 0.15/0.37  % WCLimit    : 300
% 0.15/0.37  % DateTime   : Mon Oct  2 23:13:30 EDT 2023
% 0.15/0.37  % CPUTime    : 
% 0.22/0.52  Running first-order model finding
% 0.22/0.52  Running: /export/starexec/sandbox2/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/sandbox2/tmp/tmp.noYGsGvRZQ/E---3.1_17612.p
% 1.63/0.77  # Version: 3.1pre001
% 1.63/0.77  # Preprocessing class: FSMSSMSSSSSNFFN.
% 1.63/0.77  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.63/0.77  # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 1.63/0.77  # Starting new_bool_3 with 300s (1) cores
% 1.63/0.77  # Starting new_bool_1 with 300s (1) cores
% 1.63/0.77  # Starting sh5l with 300s (1) cores
% 1.63/0.77  # G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 17699 completed with status 0
% 1.63/0.77  # Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 1.63/0.77  # Preprocessing class: FSMSSMSSSSSNFFN.
% 1.63/0.77  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.63/0.77  # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 1.63/0.77  # No SInE strategy applied
% 1.63/0.77  # Search class: FGUNF-FFMS21-SFFFFFNN
% 1.63/0.77  # Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 1.63/0.77  # Starting G-E--_208_C12_11_nc_F1_SE_CS_SP_PS_S5PRR_S04BN with 675s (1) cores
% 1.63/0.77  # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 1.63/0.77  # Starting U----_206e_02_C07_23_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 1.63/0.77  # Starting G-E--_208_C02CMA_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 1.63/0.77  # Starting G-E--_207_C18_F1_AE_CS_SP_PI_PS_S0S with 136s (1) cores
% 1.63/0.77  # G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 17706 completed with status 0
% 1.63/0.77  # Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 1.63/0.77  # Preprocessing class: FSMSSMSSSSSNFFN.
% 1.63/0.77  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.63/0.77  # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 1.63/0.77  # No SInE strategy applied
% 1.63/0.77  # Search class: FGUNF-FFMS21-SFFFFFNN
% 1.63/0.77  # Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 1.63/0.77  # Starting G-E--_208_C12_11_nc_F1_SE_CS_SP_PS_S5PRR_S04BN with 675s (1) cores
% 1.63/0.77  # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 1.63/0.77  # Preprocessing time       : 0.001 s
% 1.63/0.77  # Presaturation interreduction done
% 1.63/0.77  
% 1.63/0.77  # Proof found!
% 1.63/0.77  # SZS status Unsatisfiable
% 1.63/0.77  # SZS output start CNFRefutation
% See solution above
% 1.63/0.77  # Parsed axioms                        : 31
% 1.63/0.77  # Removed by relevancy pruning/SinE    : 0
% 1.63/0.77  # Initial clauses                      : 31
% 1.63/0.77  # Removed in clause preprocessing      : 0
% 1.63/0.77  # Initial clauses in saturation        : 31
% 1.63/0.77  # Processed clauses                    : 2455
% 1.63/0.77  # ...of these trivial                  : 21
% 1.63/0.77  # ...subsumed                          : 963
% 1.63/0.77  # ...remaining for further processing  : 1471
% 1.63/0.77  # Other redundant clauses eliminated   : 0
% 1.63/0.77  # Clauses deleted for lack of memory   : 0
% 1.63/0.77  # Backward-subsumed                    : 110
% 1.63/0.77  # Backward-rewritten                   : 19
% 1.63/0.77  # Generated clauses                    : 10215
% 1.63/0.77  # ...of the previous two non-redundant : 9020
% 1.63/0.77  # ...aggressively subsumed             : 0
% 1.63/0.77  # Contextual simplify-reflections      : 1
% 1.63/0.77  # Paramodulations                      : 10215
% 1.63/0.77  # Factorizations                       : 0
% 1.63/0.77  # NegExts                              : 0
% 1.63/0.77  # Equation resolutions                 : 0
% 1.63/0.77  # Total rewrite steps                  : 3273
% 1.63/0.77  # Propositional unsat checks           : 0
% 1.63/0.77  #    Propositional check models        : 0
% 1.63/0.77  #    Propositional check unsatisfiable : 0
% 1.63/0.77  #    Propositional clauses             : 0
% 1.63/0.77  #    Propositional clauses after purity: 0
% 1.63/0.77  #    Propositional unsat core size     : 0
% 1.63/0.77  #    Propositional preprocessing time  : 0.000
% 1.63/0.77  #    Propositional encoding time       : 0.000
% 1.63/0.77  #    Propositional solver time         : 0.000
% 1.63/0.77  #    Success case prop preproc time    : 0.000
% 1.63/0.77  #    Success case prop encoding time   : 0.000
% 1.63/0.77  #    Success case prop solver time     : 0.000
% 1.63/0.77  # Current number of processed clauses  : 1311
% 1.63/0.77  #    Positive orientable unit clauses  : 150
% 1.63/0.77  #    Positive unorientable unit clauses: 0
% 1.63/0.77  #    Negative unit clauses             : 34
% 1.63/0.77  #    Non-unit-clauses                  : 1127
% 1.63/0.77  # Current number of unprocessed clauses: 6562
% 1.63/0.77  # ...number of literals in the above   : 23713
% 1.63/0.77  # Current number of archived formulas  : 0
% 1.63/0.77  # Current number of archived clauses   : 160
% 1.63/0.77  # Clause-clause subsumption calls (NU) : 184353
% 1.63/0.77  # Rec. Clause-clause subsumption calls : 148900
% 1.63/0.77  # Non-unit clause-clause subsumptions  : 971
% 1.63/0.77  # Unit Clause-clause subsumption calls : 10231
% 1.63/0.77  # Rewrite failures with RHS unbound    : 0
% 1.63/0.77  # BW rewrite match attempts            : 42
% 1.63/0.77  # BW rewrite match successes           : 4
% 1.63/0.77  # Condensation attempts                : 0
% 1.63/0.77  # Condensation successes               : 0
% 1.63/0.77  # Termbank termtop insertions          : 147887
% 1.63/0.77  
% 1.63/0.77  # -------------------------------------------------
% 1.63/0.77  # User time                : 0.229 s
% 1.63/0.77  # System time              : 0.010 s
% 1.63/0.77  # Total time               : 0.240 s
% 1.63/0.77  # Maximum resident set size: 1660 pages
% 1.63/0.77  
% 1.63/0.77  # -------------------------------------------------
% 1.63/0.77  # User time                : 1.022 s
% 1.63/0.77  # System time              : 0.068 s
% 1.63/0.77  # Total time               : 1.091 s
% 1.63/0.77  # Maximum resident set size: 1700 pages
% 1.63/0.77  % E---3.1 exiting
%------------------------------------------------------------------------------