TSTP Solution File: FLD049-3 by E---3.1

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : E---3.1
% Problem  : FLD049-3 : TPTP v8.1.2. Bugfixed v2.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E %s %d THM

% Computer : n017.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 17:30:08 EDT 2023

% Result   : Unsatisfiable 0.17s 0.45s
% Output   : CNFRefutation 0.17s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   16
%            Number of leaves      :   16
% Syntax   : Number of clauses     :   58 (  28 unt;   4 nHn;  58 RR)
%            Number of literals    :  114 (   0 equ;  58 neg)
%            Maximal clause size   :    5 (   1 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    4 (   3 usr;   1 prp; 0-3 aty)
%            Number of functors    :    8 (   8 usr;   6 con; 0-2 aty)
%            Number of variables   :   68 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(existence_of_identity_multiplication,axiom,
    ( product(multiplicative_identity,X1,X1)
    | ~ defined(X1) ),
    file('/export/starexec/sandbox/tmp/tmp.Pgicp2DRaq/E---3.1_19898.p',existence_of_identity_multiplication) ).

cnf(b_is_defined,hypothesis,
    defined(b),
    file('/export/starexec/sandbox/tmp/tmp.Pgicp2DRaq/E---3.1_19898.p',b_is_defined) ).

cnf(associativity_multiplication_2,axiom,
    ( product(X1,X2,X3)
    | ~ product(X4,X5,X1)
    | ~ product(X5,X2,X6)
    | ~ product(X4,X6,X3) ),
    file('/export/starexec/sandbox/tmp/tmp.Pgicp2DRaq/E---3.1_19898.p',associativity_multiplication_2) ).

cnf(existence_of_inverse_multiplication,axiom,
    ( product(multiplicative_inverse(X1),X1,multiplicative_identity)
    | sum(additive_identity,X1,additive_identity)
    | ~ defined(X1) ),
    file('/export/starexec/sandbox/tmp/tmp.Pgicp2DRaq/E---3.1_19898.p',existence_of_inverse_multiplication) ).

cnf(not_sum_5,negated_conjecture,
    ~ sum(additive_identity,b,additive_identity),
    file('/export/starexec/sandbox/tmp/tmp.Pgicp2DRaq/E---3.1_19898.p',not_sum_5) ).

cnf(commutativity_multiplication,axiom,
    ( product(X1,X2,X3)
    | ~ product(X2,X1,X3) ),
    file('/export/starexec/sandbox/tmp/tmp.Pgicp2DRaq/E---3.1_19898.p',commutativity_multiplication) ).

cnf(well_definedness_of_multiplicative_inverse,axiom,
    ( defined(multiplicative_inverse(X1))
    | sum(additive_identity,X1,additive_identity)
    | ~ defined(X1) ),
    file('/export/starexec/sandbox/tmp/tmp.Pgicp2DRaq/E---3.1_19898.p',well_definedness_of_multiplicative_inverse) ).

cnf(d_is_defined,hypothesis,
    defined(d),
    file('/export/starexec/sandbox/tmp/tmp.Pgicp2DRaq/E---3.1_19898.p',d_is_defined) ).

cnf(associativity_multiplication_1,axiom,
    ( product(X1,X2,X3)
    | ~ product(X1,X4,X5)
    | ~ product(X4,X6,X2)
    | ~ product(X5,X6,X3) ),
    file('/export/starexec/sandbox/tmp/tmp.Pgicp2DRaq/E---3.1_19898.p',associativity_multiplication_1) ).

cnf(product_7,negated_conjecture,
    product(a,multiplicative_inverse(b),multiply(c,multiplicative_inverse(d))),
    file('/export/starexec/sandbox/tmp/tmp.Pgicp2DRaq/E---3.1_19898.p',product_7) ).

cnf(not_sum_6,negated_conjecture,
    ~ sum(additive_identity,d,additive_identity),
    file('/export/starexec/sandbox/tmp/tmp.Pgicp2DRaq/E---3.1_19898.p',not_sum_6) ).

cnf(totality_of_multiplication,axiom,
    ( product(X1,X2,multiply(X1,X2))
    | ~ defined(X1)
    | ~ defined(X2) ),
    file('/export/starexec/sandbox/tmp/tmp.Pgicp2DRaq/E---3.1_19898.p',totality_of_multiplication) ).

cnf(a_is_defined,hypothesis,
    defined(a),
    file('/export/starexec/sandbox/tmp/tmp.Pgicp2DRaq/E---3.1_19898.p',a_is_defined) ).

cnf(c_is_defined,hypothesis,
    defined(c),
    file('/export/starexec/sandbox/tmp/tmp.Pgicp2DRaq/E---3.1_19898.p',c_is_defined) ).

cnf(well_definedness_of_multiplication,axiom,
    ( defined(multiply(X1,X2))
    | ~ defined(X1)
    | ~ defined(X2) ),
    file('/export/starexec/sandbox/tmp/tmp.Pgicp2DRaq/E---3.1_19898.p',well_definedness_of_multiplication) ).

cnf(not_product_8,negated_conjecture,
    ~ product(a,d,multiply(b,c)),
    file('/export/starexec/sandbox/tmp/tmp.Pgicp2DRaq/E---3.1_19898.p',not_product_8) ).

cnf(c_0_16,axiom,
    ( product(multiplicative_identity,X1,X1)
    | ~ defined(X1) ),
    existence_of_identity_multiplication ).

cnf(c_0_17,hypothesis,
    defined(b),
    b_is_defined ).

cnf(c_0_18,axiom,
    ( product(X1,X2,X3)
    | ~ product(X4,X5,X1)
    | ~ product(X5,X2,X6)
    | ~ product(X4,X6,X3) ),
    associativity_multiplication_2 ).

cnf(c_0_19,hypothesis,
    product(multiplicative_identity,b,b),
    inference(spm,[status(thm)],[c_0_16,c_0_17]) ).

cnf(c_0_20,hypothesis,
    ( product(X1,b,X2)
    | ~ product(X3,b,X2)
    | ~ product(X3,multiplicative_identity,X1) ),
    inference(spm,[status(thm)],[c_0_18,c_0_19]) ).

cnf(c_0_21,axiom,
    ( product(multiplicative_inverse(X1),X1,multiplicative_identity)
    | sum(additive_identity,X1,additive_identity)
    | ~ defined(X1) ),
    existence_of_inverse_multiplication ).

cnf(c_0_22,negated_conjecture,
    ~ sum(additive_identity,b,additive_identity),
    not_sum_5 ).

cnf(c_0_23,axiom,
    ( product(X1,X2,X3)
    | ~ product(X2,X1,X3) ),
    commutativity_multiplication ).

cnf(c_0_24,hypothesis,
    ( product(X1,b,multiplicative_identity)
    | ~ product(multiplicative_inverse(b),multiplicative_identity,X1) ),
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_17])]),c_0_22]) ).

cnf(c_0_25,plain,
    ( product(X1,multiplicative_identity,X1)
    | ~ defined(X1) ),
    inference(spm,[status(thm)],[c_0_23,c_0_16]) ).

cnf(c_0_26,hypothesis,
    ( product(multiplicative_inverse(b),b,multiplicative_identity)
    | ~ defined(multiplicative_inverse(b)) ),
    inference(spm,[status(thm)],[c_0_24,c_0_25]) ).

cnf(c_0_27,axiom,
    ( defined(multiplicative_inverse(X1))
    | sum(additive_identity,X1,additive_identity)
    | ~ defined(X1) ),
    well_definedness_of_multiplicative_inverse ).

cnf(c_0_28,hypothesis,
    defined(d),
    d_is_defined ).

cnf(c_0_29,axiom,
    ( product(X1,X2,X3)
    | ~ product(X1,X4,X5)
    | ~ product(X4,X6,X2)
    | ~ product(X5,X6,X3) ),
    associativity_multiplication_1 ).

cnf(c_0_30,hypothesis,
    product(multiplicative_inverse(b),b,multiplicative_identity),
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_17])]),c_0_22]) ).

cnf(c_0_31,hypothesis,
    product(multiplicative_identity,d,d),
    inference(spm,[status(thm)],[c_0_16,c_0_28]) ).

cnf(c_0_32,plain,
    ( product(X1,X2,X3)
    | ~ product(X1,X4,multiplicative_identity)
    | ~ product(X4,X3,X2)
    | ~ defined(X3) ),
    inference(spm,[status(thm)],[c_0_29,c_0_16]) ).

cnf(c_0_33,hypothesis,
    product(b,multiplicative_inverse(b),multiplicative_identity),
    inference(spm,[status(thm)],[c_0_23,c_0_30]) ).

cnf(c_0_34,negated_conjecture,
    product(a,multiplicative_inverse(b),multiply(c,multiplicative_inverse(d))),
    product_7 ).

cnf(c_0_35,hypothesis,
    ( product(X1,d,X2)
    | ~ product(X3,d,X2)
    | ~ product(X3,multiplicative_identity,X1) ),
    inference(spm,[status(thm)],[c_0_18,c_0_31]) ).

cnf(c_0_36,negated_conjecture,
    ~ sum(additive_identity,d,additive_identity),
    not_sum_6 ).

cnf(c_0_37,axiom,
    ( product(X1,X2,multiply(X1,X2))
    | ~ defined(X1)
    | ~ defined(X2) ),
    totality_of_multiplication ).

cnf(c_0_38,hypothesis,
    ( product(b,X1,X2)
    | ~ product(multiplicative_inverse(b),X2,X1)
    | ~ defined(X2) ),
    inference(spm,[status(thm)],[c_0_32,c_0_33]) ).

cnf(c_0_39,negated_conjecture,
    product(multiplicative_inverse(b),a,multiply(c,multiplicative_inverse(d))),
    inference(spm,[status(thm)],[c_0_23,c_0_34]) ).

cnf(c_0_40,hypothesis,
    defined(a),
    a_is_defined ).

cnf(c_0_41,hypothesis,
    ( product(X1,d,multiplicative_identity)
    | ~ product(multiplicative_inverse(d),multiplicative_identity,X1) ),
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_21]),c_0_28])]),c_0_36]) ).

cnf(c_0_42,plain,
    ( product(X1,X2,X3)
    | ~ product(X4,multiply(X5,X2),X3)
    | ~ product(X4,X5,X1)
    | ~ defined(X2)
    | ~ defined(X5) ),
    inference(spm,[status(thm)],[c_0_18,c_0_37]) ).

cnf(c_0_43,negated_conjecture,
    product(b,multiply(c,multiplicative_inverse(d)),a),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39]),c_0_40])]) ).

cnf(c_0_44,hypothesis,
    defined(c),
    c_is_defined ).

cnf(c_0_45,hypothesis,
    ( product(multiplicative_inverse(d),d,multiplicative_identity)
    | ~ defined(multiplicative_inverse(d)) ),
    inference(spm,[status(thm)],[c_0_41,c_0_25]) ).

cnf(c_0_46,negated_conjecture,
    ( product(X1,multiplicative_inverse(d),a)
    | ~ product(b,c,X1)
    | ~ defined(multiplicative_inverse(d)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_43]),c_0_44])]) ).

cnf(c_0_47,hypothesis,
    product(multiplicative_inverse(d),d,multiplicative_identity),
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_27]),c_0_28])]),c_0_36]) ).

cnf(c_0_48,negated_conjecture,
    ( product(X1,multiplicative_inverse(d),a)
    | ~ product(b,c,X1) ),
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_27]),c_0_28])]),c_0_36]) ).

cnf(c_0_49,hypothesis,
    product(d,multiplicative_inverse(d),multiplicative_identity),
    inference(spm,[status(thm)],[c_0_23,c_0_47]) ).

cnf(c_0_50,negated_conjecture,
    product(multiply(b,c),multiplicative_inverse(d),a),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_37]),c_0_44]),c_0_17])]) ).

cnf(c_0_51,hypothesis,
    ( product(d,X1,X2)
    | ~ product(multiplicative_inverse(d),X2,X1)
    | ~ defined(X2) ),
    inference(spm,[status(thm)],[c_0_32,c_0_49]) ).

cnf(c_0_52,negated_conjecture,
    product(multiplicative_inverse(d),multiply(b,c),a),
    inference(spm,[status(thm)],[c_0_23,c_0_50]) ).

cnf(c_0_53,hypothesis,
    ( product(d,a,multiply(b,c))
    | ~ defined(multiply(b,c)) ),
    inference(spm,[status(thm)],[c_0_51,c_0_52]) ).

cnf(c_0_54,axiom,
    ( defined(multiply(X1,X2))
    | ~ defined(X1)
    | ~ defined(X2) ),
    well_definedness_of_multiplication ).

cnf(c_0_55,hypothesis,
    product(d,a,multiply(b,c)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_54]),c_0_44]),c_0_17])]) ).

cnf(c_0_56,negated_conjecture,
    ~ product(a,d,multiply(b,c)),
    not_product_8 ).

cnf(c_0_57,hypothesis,
    $false,
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_55]),c_0_56]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.10  % Problem    : FLD049-3 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.02/0.11  % Command    : run_E %s %d THM
% 0.11/0.31  % Computer : n017.cluster.edu
% 0.11/0.31  % Model    : x86_64 x86_64
% 0.11/0.31  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.31  % Memory   : 8042.1875MB
% 0.11/0.31  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.31  % CPULimit   : 2400
% 0.11/0.31  % WCLimit    : 300
% 0.11/0.31  % DateTime   : Mon Oct  2 22:46:41 EDT 2023
% 0.11/0.31  % CPUTime    : 
% 0.17/0.42  Running first-order theorem proving
% 0.17/0.42  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.Pgicp2DRaq/E---3.1_19898.p
% 0.17/0.45  # Version: 3.1pre001
% 0.17/0.45  # Preprocessing class: FSMSSMSSSSSNFFN.
% 0.17/0.45  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.17/0.45  # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.17/0.45  # Starting new_bool_3 with 300s (1) cores
% 0.17/0.45  # Starting new_bool_1 with 300s (1) cores
% 0.17/0.45  # Starting sh5l with 300s (1) cores
% 0.17/0.45  # new_bool_3 with pid 19977 completed with status 0
% 0.17/0.45  # Result found by new_bool_3
% 0.17/0.45  # Preprocessing class: FSMSSMSSSSSNFFN.
% 0.17/0.45  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.17/0.45  # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.17/0.45  # Starting new_bool_3 with 300s (1) cores
% 0.17/0.45  # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.17/0.45  # Search class: FGUNF-FFMM21-SFFFFFNN
% 0.17/0.45  # Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.17/0.45  # Starting G-E--_006_C18_F1_PI_AE_Q4_CS_SP_S2S with 131s (1) cores
% 0.17/0.45  # G-E--_006_C18_F1_PI_AE_Q4_CS_SP_S2S with pid 19980 completed with status 0
% 0.17/0.45  # Result found by G-E--_006_C18_F1_PI_AE_Q4_CS_SP_S2S
% 0.17/0.45  # Preprocessing class: FSMSSMSSSSSNFFN.
% 0.17/0.45  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.17/0.45  # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.17/0.45  # Starting new_bool_3 with 300s (1) cores
% 0.17/0.45  # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.17/0.45  # Search class: FGUNF-FFMM21-SFFFFFNN
% 0.17/0.45  # Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.17/0.45  # Starting G-E--_006_C18_F1_PI_AE_Q4_CS_SP_S2S with 131s (1) cores
% 0.17/0.45  # Preprocessing time       : 0.001 s
% 0.17/0.45  
% 0.17/0.45  # Proof found!
% 0.17/0.45  # SZS status Unsatisfiable
% 0.17/0.45  # SZS output start CNFRefutation
% See solution above
% 0.17/0.45  # Parsed axioms                        : 34
% 0.17/0.45  # Removed by relevancy pruning/SinE    : 9
% 0.17/0.45  # Initial clauses                      : 25
% 0.17/0.45  # Removed in clause preprocessing      : 0
% 0.17/0.45  # Initial clauses in saturation        : 25
% 0.17/0.45  # Processed clauses                    : 247
% 0.17/0.45  # ...of these trivial                  : 5
% 0.17/0.45  # ...subsumed                          : 27
% 0.17/0.45  # ...remaining for further processing  : 215
% 0.17/0.45  # Other redundant clauses eliminated   : 0
% 0.17/0.45  # Clauses deleted for lack of memory   : 0
% 0.17/0.45  # Backward-subsumed                    : 1
% 0.17/0.45  # Backward-rewritten                   : 3
% 0.17/0.45  # Generated clauses                    : 843
% 0.17/0.45  # ...of the previous two non-redundant : 681
% 0.17/0.45  # ...aggressively subsumed             : 0
% 0.17/0.45  # Contextual simplify-reflections      : 0
% 0.17/0.45  # Paramodulations                      : 843
% 0.17/0.45  # Factorizations                       : 0
% 0.17/0.45  # NegExts                              : 0
% 0.17/0.45  # Equation resolutions                 : 0
% 0.17/0.45  # Total rewrite steps                  : 392
% 0.17/0.45  # Propositional unsat checks           : 0
% 0.17/0.45  #    Propositional check models        : 0
% 0.17/0.45  #    Propositional check unsatisfiable : 0
% 0.17/0.45  #    Propositional clauses             : 0
% 0.17/0.45  #    Propositional clauses after purity: 0
% 0.17/0.45  #    Propositional unsat core size     : 0
% 0.17/0.45  #    Propositional preprocessing time  : 0.000
% 0.17/0.45  #    Propositional encoding time       : 0.000
% 0.17/0.45  #    Propositional solver time         : 0.000
% 0.17/0.45  #    Success case prop preproc time    : 0.000
% 0.17/0.45  #    Success case prop encoding time   : 0.000
% 0.17/0.45  #    Success case prop solver time     : 0.000
% 0.17/0.45  # Current number of processed clauses  : 211
% 0.17/0.45  #    Positive orientable unit clauses  : 61
% 0.17/0.45  #    Positive unorientable unit clauses: 0
% 0.17/0.45  #    Negative unit clauses             : 4
% 0.17/0.45  #    Non-unit-clauses                  : 146
% 0.17/0.45  # Current number of unprocessed clauses: 459
% 0.17/0.45  # ...number of literals in the above   : 1584
% 0.17/0.45  # Current number of archived formulas  : 0
% 0.17/0.45  # Current number of archived clauses   : 4
% 0.17/0.45  # Clause-clause subsumption calls (NU) : 2542
% 0.17/0.45  # Rec. Clause-clause subsumption calls : 1843
% 0.17/0.45  # Non-unit clause-clause subsumptions  : 28
% 0.17/0.45  # Unit Clause-clause subsumption calls : 12
% 0.17/0.45  # Rewrite failures with RHS unbound    : 0
% 0.17/0.45  # BW rewrite match attempts            : 4
% 0.17/0.45  # BW rewrite match successes           : 3
% 0.17/0.45  # Condensation attempts                : 0
% 0.17/0.45  # Condensation successes               : 0
% 0.17/0.45  # Termbank termtop insertions          : 13204
% 0.17/0.45  
% 0.17/0.45  # -------------------------------------------------
% 0.17/0.45  # User time                : 0.016 s
% 0.17/0.45  # System time              : 0.003 s
% 0.17/0.45  # Total time               : 0.019 s
% 0.17/0.45  # Maximum resident set size: 1616 pages
% 0.17/0.45  
% 0.17/0.45  # -------------------------------------------------
% 0.17/0.45  # User time                : 0.018 s
% 0.17/0.45  # System time              : 0.004 s
% 0.17/0.45  # Total time               : 0.022 s
% 0.17/0.45  # Maximum resident set size: 1704 pages
% 0.17/0.45  % E---3.1 exiting
% 0.17/0.45  % E---3.1 exiting
%------------------------------------------------------------------------------