TSTP Solution File: GRP130-3.003 by PyRes---1.3

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : PyRes---1.3
% Problem  : GRP130-3.003 : TPTP v8.1.0. Released v1.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : pyres-fof.py -tifbsVp -nlargest -HPickGiven5 %s

% Computer : n007.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 11:22:04 EDT 2022

% Result   : Unsatisfiable 6.53s 6.70s
% Output   : Refutation 6.53s
% Verified : 
% SZS Type : ERROR: Analysing output (Could not find formula named input)

% Comments : 
%------------------------------------------------------------------------------
cnf(e_1_is_not_e_3,axiom,
    ~ equalish(e_1,e_3),
    input ).

cnf(product_right_cancellation,axiom,
    ( ~ product(X14,X11,X12)
    | ~ product(X14,X13,X12)
    | equalish(X11,X13) ),
    input ).

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

cnf(e_2_is_not_e_3,axiom,
    ~ equalish(e_2,e_3),
    input ).

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

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

cnf(cycle2,axiom,
    ( ~ group_element(X10)
    | cycle(X10,e_0)
    | cycle(X10,e_1)
    | cycle(X10,e_2) ),
    input ).

cnf(c2,plain,
    ( cycle(e_1,e_0)
    | cycle(e_1,e_1)
    | cycle(e_1,e_2) ),
    inference(resolution,status(thm),[cycle2,element_1]) ).

cnf(e_1_then_e_2,axiom,
    next(e_1,e_2),
    input ).

cnf(e_1_greater_e_0,axiom,
    greater(e_1,e_0),
    input ).

cnf(cycle4,axiom,
    ( ~ cycle(X27,X25)
    | ~ cycle(X28,X29)
    | ~ next(X27,X28)
    | ~ greater(X25,e_0)
    | ~ next(X29,X26)
    | equalish(X25,X26) ),
    input ).

cnf(c10,plain,
    ( ~ cycle(X63,X64)
    | ~ cycle(X62,e_1)
    | ~ next(X63,X62)
    | ~ greater(X64,e_0)
    | equalish(X64,e_2) ),
    inference(resolution,status(thm),[cycle4,e_1_then_e_2]) ).

cnf(c125,plain,
    ( ~ cycle(X96,e_1)
    | ~ cycle(X95,e_1)
    | ~ next(X96,X95)
    | equalish(e_1,e_2) ),
    inference(resolution,status(thm),[c10,e_1_greater_e_0]) ).

cnf(c268,plain,
    ( ~ cycle(e_1,e_1)
    | ~ cycle(e_2,e_1)
    | equalish(e_1,e_2) ),
    inference(resolution,status(thm),[c125,e_1_then_e_2]) ).

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

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

cnf(c3,plain,
    ( cycle(e_2,e_0)
    | cycle(e_2,e_1)
    | cycle(e_2,e_2) ),
    inference(resolution,status(thm),[cycle2,element_2]) ).

cnf(cycle3,axiom,
    cycle(e_3,e_0),
    input ).

cnf(e_2_then_e_3,axiom,
    next(e_2,e_3),
    input ).

cnf(e_2_greater_e_0,axiom,
    greater(e_2,e_0),
    input ).

cnf(e_0_then_e_1,axiom,
    next(e_0,e_1),
    input ).

cnf(c9,plain,
    ( ~ cycle(X58,X59)
    | ~ cycle(X57,e_0)
    | ~ next(X58,X57)
    | ~ greater(X59,e_0)
    | equalish(X59,e_1) ),
    inference(resolution,status(thm),[cycle4,e_0_then_e_1]) ).

cnf(c114,plain,
    ( ~ cycle(X66,e_2)
    | ~ cycle(X65,e_0)
    | ~ next(X66,X65)
    | equalish(e_2,e_1) ),
    inference(resolution,status(thm),[c9,e_2_greater_e_0]) ).

cnf(c131,plain,
    ( ~ cycle(e_2,e_2)
    | ~ cycle(e_3,e_0)
    | equalish(e_2,e_1) ),
    inference(resolution,status(thm),[c114,e_2_then_e_3]) ).

cnf(c134,plain,
    ( ~ cycle(e_2,e_2)
    | equalish(e_2,e_1) ),
    inference(resolution,status(thm),[c131,cycle3]) ).

cnf(c135,plain,
    ( equalish(e_2,e_1)
    | cycle(e_2,e_0)
    | cycle(e_2,e_1) ),
    inference(resolution,status(thm),[c134,c3]) ).

cnf(c144,plain,
    ( cycle(e_2,e_0)
    | cycle(e_2,e_1) ),
    inference(resolution,status(thm),[c135,e_2_is_not_e_1]) ).

cnf(e_2_greater_e_1,axiom,
    greater(e_2,e_1),
    input ).

cnf(cycle5,axiom,
    ( ~ cycle(X35,X33)
    | ~ cycle(X32,e_0)
    | ~ cycle(X36,X34)
    | ~ next(X32,X36)
    | ~ greater(X32,X35)
    | ~ greater(X33,X34) ),
    input ).

cnf(c20,plain,
    ( ~ cycle(X70,e_2)
    | ~ cycle(X72,e_0)
    | ~ cycle(X71,e_0)
    | ~ next(X72,X71)
    | ~ greater(X72,X70) ),
    inference(resolution,status(thm),[cycle5,e_2_greater_e_0]) ).

cnf(c182,plain,
    ( ~ cycle(e_1,e_2)
    | ~ cycle(e_2,e_0)
    | ~ cycle(X111,e_0)
    | ~ next(e_2,X111) ),
    inference(resolution,status(thm),[c20,e_2_greater_e_1]) ).

cnf(c291,plain,
    ( ~ cycle(e_1,e_2)
    | ~ cycle(e_2,e_0)
    | ~ cycle(e_3,e_0) ),
    inference(resolution,status(thm),[c182,e_2_then_e_3]) ).

cnf(c292,plain,
    ( ~ cycle(e_1,e_2)
    | ~ cycle(e_2,e_0) ),
    inference(resolution,status(thm),[c291,cycle3]) ).

cnf(c294,plain,
    ( ~ cycle(e_1,e_2)
    | cycle(e_2,e_1) ),
    inference(resolution,status(thm),[c292,c144]) ).

cnf(c296,plain,
    ( cycle(e_2,e_1)
    | cycle(e_1,e_0)
    | cycle(e_1,e_1) ),
    inference(resolution,status(thm),[c294,c2]) ).

cnf(c22,plain,
    ( ~ cycle(X77,e_1)
    | ~ cycle(X79,e_0)
    | ~ cycle(X78,e_0)
    | ~ next(X79,X78)
    | ~ greater(X79,X77) ),
    inference(resolution,status(thm),[cycle5,e_1_greater_e_0]) ).

cnf(c218,plain,
    ( ~ cycle(e_1,e_1)
    | ~ cycle(e_2,e_0)
    | ~ cycle(X124,e_0)
    | ~ next(e_2,X124) ),
    inference(resolution,status(thm),[c22,e_2_greater_e_1]) ).

cnf(c340,plain,
    ( ~ cycle(e_1,e_1)
    | ~ cycle(e_2,e_0)
    | ~ cycle(e_3,e_0) ),
    inference(resolution,status(thm),[c218,e_2_then_e_3]) ).

cnf(c341,plain,
    ( ~ cycle(e_1,e_1)
    | ~ cycle(e_2,e_0) ),
    inference(resolution,status(thm),[c340,cycle3]) ).

cnf(c342,plain,
    ( ~ cycle(e_1,e_1)
    | cycle(e_2,e_1) ),
    inference(resolution,status(thm),[c341,c144]) ).

cnf(c345,plain,
    ( cycle(e_2,e_1)
    | cycle(e_1,e_0) ),
    inference(resolution,status(thm),[c342,c296]) ).

cnf(c347,plain,
    ( cycle(e_1,e_0)
    | ~ cycle(e_1,e_1)
    | equalish(e_1,e_2) ),
    inference(resolution,status(thm),[c345,c268]) ).

cnf(c377,plain,
    ( cycle(e_1,e_0)
    | equalish(e_1,e_2)
    | cycle(e_1,e_2) ),
    inference(resolution,status(thm),[c347,c2]) ).

cnf(c391,plain,
    ( cycle(e_1,e_0)
    | cycle(e_1,e_2) ),
    inference(resolution,status(thm),[c377,e_1_is_not_e_2]) ).

cnf(e_3_greater_e_1,axiom,
    greater(e_3,e_1),
    input ).

cnf(cycle6,axiom,
    ( ~ cycle(X20,e_0)
    | ~ product(X20,e_1,X19)
    | ~ greater(X19,X20) ),
    input ).

cnf(product_total_function1,axiom,
    ( ~ group_element(X47)
    | ~ group_element(X46)
    | product(X47,X46,e_1)
    | product(X47,X46,e_2)
    | product(X47,X46,e_3) ),
    input ).

cnf(c77,plain,
    ( ~ group_element(X154)
    | product(X154,e_1,e_1)
    | product(X154,e_1,e_2)
    | product(X154,e_1,e_3) ),
    inference(resolution,status(thm),[product_total_function1,element_1]) ).

cnf(c472,plain,
    ( product(e_1,e_1,e_1)
    | product(e_1,e_1,e_2)
    | product(e_1,e_1,e_3) ),
    inference(resolution,status(thm),[c77,element_1]) ).

cnf(c498,plain,
    ( product(e_1,e_1,e_1)
    | product(e_1,e_1,e_2)
    | ~ cycle(e_1,e_0)
    | ~ greater(e_3,e_1) ),
    inference(resolution,status(thm),[c472,cycle6]) ).

cnf(c879,plain,
    ( product(e_1,e_1,e_1)
    | product(e_1,e_1,e_2)
    | ~ cycle(e_1,e_0) ),
    inference(resolution,status(thm),[c498,e_3_greater_e_1]) ).

cnf(c924,plain,
    ( product(e_1,e_1,e_1)
    | product(e_1,e_1,e_2)
    | cycle(e_1,e_2) ),
    inference(resolution,status(thm),[c879,c391]) ).

cnf(product_total_function2,axiom,
    ( ~ product(X9,X7,X6)
    | ~ product(X9,X7,X8)
    | equalish(X6,X8) ),
    input ).

cnf(c492,plain,
    ( product(e_1,e_1,e_1)
    | product(e_1,e_1,e_3)
    | ~ cycle(e_1,e_0)
    | ~ greater(e_2,e_1) ),
    inference(resolution,status(thm),[c472,cycle6]) ).

cnf(c688,plain,
    ( product(e_1,e_1,e_1)
    | product(e_1,e_1,e_3)
    | ~ cycle(e_1,e_0) ),
    inference(resolution,status(thm),[c492,e_2_greater_e_1]) ).

cnf(c689,plain,
    ( product(e_1,e_1,e_1)
    | product(e_1,e_1,e_3)
    | cycle(e_1,e_2) ),
    inference(resolution,status(thm),[c688,c391]) ).

cnf(c713,plain,
    ( product(e_1,e_1,e_1)
    | cycle(e_1,e_2)
    | ~ product(e_1,e_1,X229)
    | equalish(X229,e_3) ),
    inference(resolution,status(thm),[c689,product_total_function2]) ).

cnf(c1217,plain,
    ( product(e_1,e_1,e_1)
    | cycle(e_1,e_2)
    | equalish(e_2,e_3) ),
    inference(resolution,status(thm),[c713,c924]) ).

cnf(c1273,plain,
    ( product(e_1,e_1,e_1)
    | cycle(e_1,e_2) ),
    inference(resolution,status(thm),[c1217,e_2_is_not_e_3]) ).

cnf(c1275,plain,
    ( cycle(e_1,e_2)
    | ~ product(e_1,X231,e_1)
    | equalish(X231,e_1) ),
    inference(resolution,status(thm),[c1273,product_right_cancellation]) ).

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

cnf(c79,plain,
    ( ~ group_element(X156)
    | product(X156,e_3,e_1)
    | product(X156,e_3,e_2)
    | product(X156,e_3,e_3) ),
    inference(resolution,status(thm),[product_total_function1,element_3]) ).

cnf(c478,plain,
    ( product(e_1,e_3,e_1)
    | product(e_1,e_3,e_2)
    | product(e_1,e_3,e_3) ),
    inference(resolution,status(thm),[c79,element_1]) ).

cnf(qg3,negated_conjecture,
    ( ~ product(X24,X21,X22)
    | ~ product(X24,X22,X23)
    | product(X23,X21,X24) ),
    input ).

cnf(c580,plain,
    ( product(e_1,e_3,e_1)
    | product(e_1,e_3,e_2)
    | ~ product(e_1,X354,e_3)
    | product(e_3,X354,e_1) ),
    inference(resolution,status(thm),[c478,qg3]) ).

cnf(c2355,plain,
    ( product(e_1,e_3,e_1)
    | product(e_1,e_3,e_2)
    | product(e_3,e_3,e_1) ),
    inference(resolution,status(thm),[c580,c478]) ).

cnf(c2372,plain,
    ( product(e_1,e_3,e_2)
    | product(e_3,e_3,e_1)
    | cycle(e_1,e_2)
    | equalish(e_3,e_1) ),
    inference(resolution,status(thm),[c2355,c1275]) ).

cnf(c6349,plain,
    ( product(e_1,e_3,e_2)
    | product(e_3,e_3,e_1)
    | cycle(e_1,e_2) ),
    inference(resolution,status(thm),[c2372,e_3_is_not_e_1]) ).

cnf(c6368,plain,
    ( product(e_3,e_3,e_1)
    | cycle(e_1,e_2)
    | ~ product(e_1,X724,e_2)
    | equalish(X724,e_3) ),
    inference(resolution,status(thm),[c6349,product_right_cancellation]) ).

cnf(c78,plain,
    ( ~ group_element(X155)
    | product(X155,e_2,e_1)
    | product(X155,e_2,e_2)
    | product(X155,e_2,e_3) ),
    inference(resolution,status(thm),[product_total_function1,element_2]) ).

cnf(c475,plain,
    ( product(e_1,e_2,e_1)
    | product(e_1,e_2,e_2)
    | product(e_1,e_2,e_3) ),
    inference(resolution,status(thm),[c78,element_1]) ).

cnf(c537,plain,
    ( product(e_1,e_2,e_2)
    | product(e_1,e_2,e_3)
    | ~ product(e_1,X272,e_1)
    | equalish(X272,e_2) ),
    inference(resolution,status(thm),[c475,product_right_cancellation]) ).

cnf(c536,plain,
    ( product(e_1,e_2,e_2)
    | product(e_1,e_2,e_3)
    | ~ product(e_1,X270,e_2)
    | product(e_1,X270,e_1) ),
    inference(resolution,status(thm),[c475,qg3]) ).

cnf(e_3_is_not_e_2,axiom,
    ~ equalish(e_3,e_2),
    input ).

cnf(cycle7,axiom,
    ( ~ cycle(X42,X39)
    | ~ product(X42,e_1,X40)
    | ~ greater(X39,e_0)
    | ~ next(X42,X41)
    | equalish(X40,X41) ),
    input ).

cnf(c494,plain,
    ( product(e_1,e_1,e_1)
    | product(e_1,e_1,e_2)
    | ~ cycle(e_1,X187)
    | ~ greater(X187,e_0)
    | ~ next(e_1,X186)
    | equalish(e_3,X186) ),
    inference(resolution,status(thm),[c472,cycle7]) ).

cnf(c769,plain,
    ( product(e_1,e_1,e_1)
    | product(e_1,e_1,e_2)
    | ~ cycle(e_1,X585)
    | ~ greater(X585,e_0)
    | equalish(e_3,e_2) ),
    inference(resolution,status(thm),[c494,e_1_then_e_2]) ).

cnf(c3786,plain,
    ( product(e_1,e_1,e_1)
    | product(e_1,e_1,e_2)
    | ~ cycle(e_1,e_2)
    | equalish(e_3,e_2) ),
    inference(resolution,status(thm),[c769,e_2_greater_e_0]) ).

cnf(c6811,plain,
    ( product(e_1,e_1,e_1)
    | product(e_1,e_1,e_2)
    | equalish(e_3,e_2) ),
    inference(resolution,status(thm),[c3786,c1273]) ).

cnf(c6875,plain,
    ( product(e_1,e_1,e_1)
    | product(e_1,e_1,e_2) ),
    inference(resolution,status(thm),[c6811,e_3_is_not_e_2]) ).

cnf(c6910,plain,
    ( product(e_1,e_1,e_1)
    | product(e_1,e_2,e_2)
    | product(e_1,e_2,e_3) ),
    inference(resolution,status(thm),[c6875,c536]) ).

cnf(c7171,plain,
    ( product(e_1,e_2,e_2)
    | product(e_1,e_2,e_3)
    | equalish(e_1,e_2) ),
    inference(resolution,status(thm),[c6910,c537]) ).

cnf(c7302,plain,
    ( product(e_1,e_2,e_2)
    | product(e_1,e_2,e_3) ),
    inference(resolution,status(thm),[c7171,e_1_is_not_e_2]) ).

cnf(c7347,plain,
    ( product(e_1,e_2,e_2)
    | ~ product(e_1,X793,e_2)
    | product(e_3,X793,e_1) ),
    inference(resolution,status(thm),[c7302,qg3]) ).

cnf(c8219,plain,
    ( product(e_1,e_2,e_2)
    | product(e_3,e_3,e_1)
    | cycle(e_1,e_2) ),
    inference(resolution,status(thm),[c7347,c6349]) ).

cnf(c8959,plain,
    ( product(e_3,e_3,e_1)
    | cycle(e_1,e_2)
    | equalish(e_2,e_3) ),
    inference(resolution,status(thm),[c8219,c6368]) ).

cnf(c9050,plain,
    ( product(e_3,e_3,e_1)
    | cycle(e_1,e_2) ),
    inference(resolution,status(thm),[c8959,e_2_is_not_e_3]) ).

cnf(c6923,plain,
    ( product(e_1,e_1,e_1)
    | ~ product(e_1,X765,e_2)
    | equalish(X765,e_1) ),
    inference(resolution,status(thm),[c6875,product_right_cancellation]) ).

cnf(c7193,plain,
    ( product(e_1,e_1,e_1)
    | product(e_1,e_2,e_3)
    | equalish(e_2,e_1) ),
    inference(resolution,status(thm),[c6910,c6923]) ).

cnf(c7465,plain,
    ( product(e_1,e_1,e_1)
    | product(e_1,e_2,e_3) ),
    inference(resolution,status(thm),[c7193,e_2_is_not_e_1]) ).

cnf(c7508,plain,
    ( product(e_1,e_1,e_1)
    | ~ product(e_1,X784,e_3)
    | equalish(X784,e_2) ),
    inference(resolution,status(thm),[c7465,product_right_cancellation]) ).

cnf(c7504,plain,
    ( product(e_1,e_1,e_1)
    | ~ product(e_1,X795,e_2)
    | product(e_3,X795,e_1) ),
    inference(resolution,status(thm),[c7465,qg3]) ).

cnf(c8349,plain,
    ( product(e_1,e_1,e_1)
    | product(e_3,e_1,e_1) ),
    inference(resolution,status(thm),[c7504,c6875]) ).

cnf(c8393,plain,
    ( product(e_1,e_1,e_1)
    | ~ product(e_3,X821,e_1)
    | product(e_1,X821,e_3) ),
    inference(resolution,status(thm),[c8349,qg3]) ).

cnf(c9135,plain,
    ( product(e_1,e_1,e_1)
    | product(e_1,e_1,e_3) ),
    inference(resolution,status(thm),[c8393,c8349]) ).

cnf(c9177,plain,
    ( product(e_1,e_1,e_1)
    | equalish(e_1,e_2) ),
    inference(resolution,status(thm),[c9135,c7508]) ).

cnf(c9224,plain,
    product(e_1,e_1,e_1),
    inference(resolution,status(thm),[c9177,e_1_is_not_e_2]) ).

cnf(c9233,plain,
    ( ~ cycle(e_1,X837)
    | ~ greater(X837,e_0)
    | ~ next(e_1,X836)
    | equalish(e_1,X836) ),
    inference(resolution,status(thm),[c9224,cycle7]) ).

cnf(c9271,plain,
    ( ~ cycle(e_1,X838)
    | ~ greater(X838,e_0)
    | equalish(e_1,e_2) ),
    inference(resolution,status(thm),[c9233,e_1_then_e_2]) ).

cnf(c9272,plain,
    ( ~ cycle(e_1,e_2)
    | equalish(e_1,e_2) ),
    inference(resolution,status(thm),[c9271,e_2_greater_e_0]) ).

cnf(c9275,plain,
    ( equalish(e_1,e_2)
    | product(e_3,e_3,e_1) ),
    inference(resolution,status(thm),[c9272,c9050]) ).

cnf(c9307,plain,
    product(e_3,e_3,e_1),
    inference(resolution,status(thm),[c9275,e_1_is_not_e_2]) ).

cnf(c9247,plain,
    ( ~ product(e_1,e_1,X824)
    | equalish(X824,e_1) ),
    inference(resolution,status(thm),[c9224,product_total_function2]) ).

cnf(c474,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),[c77,element_3]) ).

cnf(c519,plain,
    ( product(e_3,e_1,e_2)
    | product(e_3,e_1,e_3)
    | ~ product(e_3,X243,e_1)
    | product(e_1,X243,e_3) ),
    inference(resolution,status(thm),[c474,qg3]) ).

cnf(c1389,plain,
    ( product(e_3,e_1,e_2)
    | product(e_3,e_1,e_3)
    | product(e_1,e_1,e_3) ),
    inference(resolution,status(thm),[c519,c474]) ).

cnf(c9454,plain,
    ( ~ product(e_3,X843,e_3)
    | product(e_1,X843,e_3) ),
    inference(resolution,status(thm),[c9307,qg3]) ).

cnf(c9480,plain,
    ( product(e_1,e_1,e_3)
    | product(e_3,e_1,e_2) ),
    inference(resolution,status(thm),[c9454,c1389]) ).

cnf(c9593,plain,
    ( product(e_3,e_1,e_2)
    | equalish(e_3,e_1) ),
    inference(resolution,status(thm),[c9480,c9247]) ).

cnf(c9656,plain,
    product(e_3,e_1,e_2),
    inference(resolution,status(thm),[c9593,e_3_is_not_e_1]) ).

cnf(c9672,plain,
    ( ~ product(e_3,X848,e_1)
    | product(e_2,X848,e_3) ),
    inference(resolution,status(thm),[c9656,qg3]) ).

cnf(c9697,plain,
    product(e_2,e_3,e_3),
    inference(resolution,status(thm),[c9672,c9307]) ).

cnf(c9709,plain,
    ( ~ product(e_2,X850,e_3)
    | equalish(X850,e_3) ),
    inference(resolution,status(thm),[c9697,product_right_cancellation]) ).

cnf(c473,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),[c77,element_2]) ).

cnf(c501,plain,
    ( product(e_2,e_1,e_2)
    | product(e_2,e_1,e_3)
    | ~ product(e_2,X203,e_1)
    | product(e_1,X203,e_2) ),
    inference(resolution,status(thm),[c473,qg3]) ).

cnf(c981,plain,
    ( product(e_2,e_1,e_2)
    | product(e_2,e_1,e_3)
    | product(e_1,e_1,e_2) ),
    inference(resolution,status(thm),[c501,c473]) ).

cnf(c1040,plain,
    ( product(e_2,e_1,e_2)
    | product(e_2,e_1,e_3)
    | ~ cycle(e_1,e_0)
    | ~ greater(e_2,e_1) ),
    inference(resolution,status(thm),[c981,cycle6]) ).

cnf(c3861,plain,
    ( product(e_2,e_1,e_2)
    | product(e_2,e_1,e_3)
    | ~ cycle(e_1,e_0) ),
    inference(resolution,status(thm),[c1040,e_2_greater_e_1]) ).

cnf(c9277,plain,
    ( equalish(e_1,e_2)
    | cycle(e_1,e_0) ),
    inference(resolution,status(thm),[c9272,c391]) ).

cnf(c9280,plain,
    cycle(e_1,e_0),
    inference(resolution,status(thm),[c9277,e_1_is_not_e_2]) ).

cnf(c9296,plain,
    ( product(e_2,e_1,e_2)
    | product(e_2,e_1,e_3) ),
    inference(resolution,status(thm),[c9280,c3861]) ).

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

cnf(c9664,plain,
    ( ~ product(X845,e_1,e_2)
    | equalish(X845,e_3) ),
    inference(resolution,status(thm),[c9656,product_left_cancellation]) ).

cnf(c9680,plain,
    ( equalish(e_2,e_3)
    | product(e_2,e_1,e_3) ),
    inference(resolution,status(thm),[c9664,c9296]) ).

cnf(c9732,plain,
    product(e_2,e_1,e_3),
    inference(resolution,status(thm),[c9680,e_2_is_not_e_3]) ).

cnf(c9762,plain,
    equalish(e_1,e_3),
    inference(resolution,status(thm),[c9732,c9709]) ).

cnf(c9772,plain,
    $false,
    inference(resolution,status(thm),[c9762,e_1_is_not_e_3]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem  : GRP130-3.003 : TPTP v8.1.0. Released v1.2.0.
% 0.06/0.12  % Command  : pyres-fof.py -tifbsVp -nlargest -HPickGiven5 %s
% 0.12/0.33  % Computer : n007.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 600
% 0.12/0.33  % DateTime : Mon Jun 13 17:56:09 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 6.53/6.70  # Version:  1.3
% 6.53/6.70  # SZS status Unsatisfiable
% 6.53/6.70  # SZS output start CNFRefutation
% See solution above
% 6.53/6.70  
% 6.53/6.70  # Initial clauses    : 30
% 6.53/6.70  # Processed clauses  : 788
% 6.53/6.70  # Factors computed   : 0
% 6.53/6.70  # Resolvents computed: 9773
% 6.53/6.70  # Tautologies deleted: 29
% 6.53/6.70  # Forward subsumed   : 1927
% 6.53/6.70  # Backward subsumed  : 579
% 6.53/6.70  # -------- CPU Time ---------
% 6.53/6.70  # User time          : 6.338 s
% 6.53/6.70  # System time        : 0.025 s
% 6.53/6.70  # Total time         : 6.363 s
%------------------------------------------------------------------------------