%------------------------------------------------------------------------------
% File     : PyRes---1.3
% Problem  : GRP123-3.003 : TPTP v8.1.0. Released v1.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : pyres-fof.py -tifbsVp -nlargest -HPickGiven5 %s

% Computer : n018.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  : 600s
% DateTime : Sat Jul 16 11:21:44 EDT 2022

% Result   : Unsatisfiable 0.91s 1.10s
% Output   : Refutation 0.91s
% Verified : 
% SZS Type : ERROR: Analysing output (Could not find formula named input)

% Comments : 
%------------------------------------------------------------------------------
cnf(e_3_is_not_e_2,axiom,
    ~ equalish(e_3,e_2),
    input ).

cnf(product_left_cancellation,axiom,
    ( ~ product(X30,X28,X29)
    | ~ product(X27,X28,X29)
    | equalish(X30,X27) ),
    input ).

cnf(e_1_is_not_e_2,axiom,
    ~ equalish(e_1,e_2),
    input ).

cnf(product_idempotence,axiom,
    product(X2,X2,X2),
    input ).

cnf(product_right_cancellation,axiom,
    ( ~ product(X17,X18,X16)
    | ~ product(X17,X15,X16)
    | equalish(X18,X15) ),
    input ).

cnf(c7,plain,
    ( ~ product(X19,X20,X19)
    | equalish(X20,X19) ),
    inference(resolution,status(thm),[product_right_cancellation,product_idempotence]) ).

cnf(e_2_is_not_e_1,axiom,
    ~ equalish(e_2,e_1),
    input ).

cnf(c12,plain,
    ( ~ product(X31,X32,X32)
    | equalish(X31,X32) ),
    inference(resolution,status(thm),[product_left_cancellation,product_idempotence]) ).

cnf(element_2,axiom,
    group_element(e_2),
    input ).

cnf(element_1,axiom,
    group_element(e_1),
    input ).

cnf(product_total_function1,axiom,
    ( ~ group_element(X50)
    | ~ group_element(X49)
    | product(X50,X49,e_1)
    | product(X50,X49,e_2)
    | product(X50,X49,e_3) ),
    input ).

cnf(c37,plain,
    ( ~ group_element(X138)
    | product(X138,e_1,e_1)
    | product(X138,e_1,e_2)
    | product(X138,e_1,e_3) ),
    inference(resolution,status(thm),[product_total_function1,element_1]) ).

cnf(c152,plain,
    ( product(e_2,e_1,e_1)
    | product(e_2,e_1,e_2)
    | product(e_2,e_1,e_3) ),
    inference(resolution,status(thm),[c37,element_2]) ).

cnf(c190,plain,
    ( product(e_2,e_1,e_2)
    | product(e_2,e_1,e_3)
    | equalish(e_2,e_1) ),
    inference(resolution,status(thm),[c152,c12]) ).

cnf(c236,plain,
    ( product(e_2,e_1,e_2)
    | product(e_2,e_1,e_3) ),
    inference(resolution,status(thm),[c190,e_2_is_not_e_1]) ).

cnf(c244,plain,
    ( product(e_2,e_1,e_3)
    | equalish(e_1,e_2) ),
    inference(resolution,status(thm),[c236,c7]) ).

cnf(c294,plain,
    product(e_2,e_1,e_3),
    inference(resolution,status(thm),[c244,e_1_is_not_e_2]) ).

cnf(c296,plain,
    ( ~ product(X175,e_1,e_3)
    | equalish(X175,e_2) ),
    inference(resolution,status(thm),[c294,product_left_cancellation]) ).

cnf(qg1_2,negated_conjecture,
    ( ~ product(X64,X60,X65)
    | ~ product(X63,X61,X65)
    | ~ product(X62,X60,X64)
    | ~ product(X62,X61,X63)
    | equalish(X60,X61) ),
    input ).

cnf(c58,plain,
    ( ~ product(X76,X77,X78)
    | ~ product(X79,X79,X78)
    | ~ product(X79,X77,X76)
    | equalish(X77,X79) ),
    inference(resolution,status(thm),[qg1_2,product_idempotence]) ).

cnf(c289,plain,
    ( equalish(e_1,e_2)
    | ~ product(e_3,e_1,X187)
    | ~ product(e_2,e_2,X187) ),
    inference(resolution,status(thm),[c244,c58]) ).

cnf(c411,plain,
    ( equalish(e_1,e_2)
    | ~ product(e_3,e_1,e_2) ),
    inference(resolution,status(thm),[c289,product_idempotence]) ).

cnf(e_3_is_not_e_1,axiom,
    ~ equalish(e_3,e_1),
    input ).

cnf(element_3,axiom,
    group_element(e_3),
    input ).

cnf(c153,plain,
    ( product(e_3,e_1,e_1)
    | product(e_3,e_1,e_2)
    | product(e_3,e_1,e_3) ),
    inference(resolution,status(thm),[c37,element_3]) ).

cnf(c258,plain,
    ( product(e_3,e_1,e_2)
    | product(e_3,e_1,e_3)
    | equalish(e_3,e_1) ),
    inference(resolution,status(thm),[c153,c12]) ).

cnf(c438,plain,
    ( product(e_3,e_1,e_2)
    | product(e_3,e_1,e_3) ),
    inference(resolution,status(thm),[c258,e_3_is_not_e_1]) ).

cnf(c443,plain,
    ( product(e_3,e_1,e_3)
    | equalish(e_1,e_2) ),
    inference(resolution,status(thm),[c438,c411]) ).

cnf(c472,plain,
    product(e_3,e_1,e_3),
    inference(resolution,status(thm),[c443,e_1_is_not_e_2]) ).

cnf(c477,plain,
    equalish(e_3,e_2),
    inference(resolution,status(thm),[c472,c296]) ).

cnf(c484,plain,
    $false,
    inference(resolution,status(thm),[c477,e_3_is_not_e_2]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.09  % Problem  : GRP123-3.003 : TPTP v8.1.0. Released v1.2.0.
% 0.04/0.09  % Command  : pyres-fof.py -tifbsVp -nlargest -HPickGiven5 %s
% 0.09/0.29  % Computer : n018.cluster.edu
% 0.09/0.29  % Model    : x86_64 x86_64
% 0.09/0.29  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.29  % Memory   : 8042.1875MB
% 0.09/0.29  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.09/0.29  % CPULimit : 300
% 0.09/0.29  % WCLimit  : 600
% 0.09/0.29  % DateTime : Mon Jun 13 16:45:42 EDT 2022
% 0.09/0.29  % CPUTime  : 
% 0.91/1.10  # Version:  1.3
% 0.91/1.10  # SZS status Unsatisfiable
% 0.91/1.10  # SZS output start CNFRefutation
% See solution above
% 0.91/1.10  
% 0.91/1.10  # Initial clauses    : 32
% 0.91/1.10  # Processed clauses  : 194
% 0.91/1.10  # Factors computed   : 0
% 0.91/1.10  # Resolvents computed: 485
% 0.91/1.10  # Tautologies deleted: 0
% 0.91/1.10  # Forward subsumed   : 76
% 0.91/1.10  # Backward subsumed  : 92
% 0.91/1.10  # -------- CPU Time ---------
% 0.91/1.10  # User time          : 0.788 s
% 0.91/1.10  # System time        : 0.015 s
% 0.91/1.10  # Total time         : 0.803 s
%------------------------------------------------------------------------------