TSTP Solution File: GRP129-2.004 by PyRes---1.3
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : PyRes---1.3
% Problem : GRP129-2.004 : TPTP v8.1.0. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : pyres-fof.py -tifbsVp -nlargest -HPickGiven5 %s
% Computer : n005.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 11:22:01 EDT 2022
% Result : Unsatisfiable 59.24s 59.42s
% Output : Refutation 59.24s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named input)
% Comments :
%------------------------------------------------------------------------------
cnf(e_4_is_not_e_1,axiom,
~ equalish(e_4,e_1),
input ).
cnf(product_right_cancellation,axiom,
( ~ product(X10,X9,X12)
| ~ product(X10,X11,X12)
| equalish(X9,X11) ),
input ).
cnf(e_2_is_not_e_1,axiom,
~ equalish(e_2,e_1),
input ).
cnf(product_left_cancellation,axiom,
( ~ product(X13,X16,X14)
| ~ product(X15,X16,X14)
| equalish(X13,X15) ),
input ).
cnf(e_1_is_not_e_2,axiom,
~ equalish(e_1,e_2),
input ).
cnf(e_2_then_e_3,axiom,
next(e_2,e_3),
input ).
cnf(e_4_greater_e_3,axiom,
greater(e_4,e_3),
input ).
cnf(no_redundancy,axiom,
( ~ product(X2,e_1,X4)
| ~ next(X2,X3)
| ~ greater(X4,X3) ),
input ).
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(X17)
| ~ group_element(X18)
| product(X17,X18,e_1)
| product(X17,X18,e_2)
| product(X17,X18,e_3)
| product(X17,X18,e_4) ),
input ).
cnf(c0,plain,
( ~ group_element(X23)
| product(X23,e_1,e_1)
| product(X23,e_1,e_2)
| product(X23,e_1,e_3)
| product(X23,e_1,e_4) ),
inference(resolution,status(thm),[product_total_function1,element_1]) ).
cnf(c5,plain,
( product(e_2,e_1,e_1)
| product(e_2,e_1,e_2)
| product(e_2,e_1,e_3)
| product(e_2,e_1,e_4) ),
inference(resolution,status(thm),[c0,element_2]) ).
cnf(c55,plain,
( product(e_2,e_1,e_1)
| product(e_2,e_1,e_2)
| product(e_2,e_1,e_3)
| ~ next(e_2,X131)
| ~ greater(e_4,X131) ),
inference(resolution,status(thm),[c5,no_redundancy]) ).
cnf(c671,plain,
( product(e_2,e_1,e_1)
| product(e_2,e_1,e_2)
| product(e_2,e_1,e_3)
| ~ next(e_2,e_3) ),
inference(resolution,status(thm),[c55,e_4_greater_e_3]) ).
cnf(c709,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),[c671,e_2_then_e_3]) ).
cnf(c717,plain,
( product(e_2,e_1,e_2)
| product(e_2,e_1,e_3)
| ~ product(X139,e_1,e_1)
| equalish(X139,e_2) ),
inference(resolution,status(thm),[c709,product_left_cancellation]) ).
cnf(e_1_then_e_2,axiom,
next(e_1,e_2),
input ).
cnf(e_4_greater_e_2,axiom,
greater(e_4,e_2),
input ).
cnf(e_3_greater_e_2,axiom,
greater(e_3,e_2),
input ).
cnf(c4,plain,
( product(e_1,e_1,e_1)
| product(e_1,e_1,e_2)
| product(e_1,e_1,e_3)
| product(e_1,e_1,e_4) ),
inference(resolution,status(thm),[c0,element_1]) ).
cnf(c30,plain,
( product(e_1,e_1,e_1)
| product(e_1,e_1,e_2)
| product(e_1,e_1,e_4)
| ~ next(e_1,X56)
| ~ greater(e_3,X56) ),
inference(resolution,status(thm),[c4,no_redundancy]) ).
cnf(c397,plain,
( product(e_1,e_1,e_1)
| product(e_1,e_1,e_2)
| product(e_1,e_1,e_4)
| ~ next(e_1,e_2) ),
inference(resolution,status(thm),[c30,e_3_greater_e_2]) ).
cnf(c398,plain,
( product(e_1,e_1,e_1)
| product(e_1,e_1,e_2)
| product(e_1,e_1,e_4) ),
inference(resolution,status(thm),[c397,e_1_then_e_2]) ).
cnf(c419,plain,
( product(e_1,e_1,e_1)
| product(e_1,e_1,e_2)
| ~ next(e_1,X60)
| ~ greater(e_4,X60) ),
inference(resolution,status(thm),[c398,no_redundancy]) ).
cnf(c427,plain,
( product(e_1,e_1,e_1)
| product(e_1,e_1,e_2)
| ~ next(e_1,e_2) ),
inference(resolution,status(thm),[c419,e_4_greater_e_2]) ).
cnf(c430,plain,
( product(e_1,e_1,e_1)
| product(e_1,e_1,e_2) ),
inference(resolution,status(thm),[c427,e_1_then_e_2]) ).
cnf(c444,plain,
( product(e_1,e_1,e_1)
| ~ product(e_1,X68,e_2)
| equalish(X68,e_1) ),
inference(resolution,status(thm),[c430,product_right_cancellation]) ).
cnf(qg3,negated_conjecture,
( ~ product(X22,X19,X20)
| ~ product(X19,X20,X21)
| product(X20,X22,X21) ),
input ).
cnf(c445,plain,
( product(e_1,e_1,e_1)
| ~ product(X83,e_1,e_1)
| product(e_1,X83,e_2) ),
inference(resolution,status(thm),[c430,qg3]) ).
cnf(c448,plain,
( product(e_1,e_1,e_1)
| ~ product(X70,e_1,e_2)
| equalish(X70,e_1) ),
inference(resolution,status(thm),[c430,product_left_cancellation]) ).
cnf(c729,plain,
( product(e_2,e_1,e_1)
| product(e_2,e_1,e_3)
| product(e_1,e_1,e_1)
| equalish(e_2,e_1) ),
inference(resolution,status(thm),[c709,c448]) ).
cnf(c1561,plain,
( product(e_2,e_1,e_1)
| product(e_2,e_1,e_3)
| product(e_1,e_1,e_1) ),
inference(resolution,status(thm),[c729,e_2_is_not_e_1]) ).
cnf(c1580,plain,
( product(e_2,e_1,e_3)
| product(e_1,e_1,e_1)
| product(e_1,e_2,e_2) ),
inference(resolution,status(thm),[c1561,c445]) ).
cnf(c1657,plain,
( product(e_2,e_1,e_3)
| product(e_1,e_1,e_1)
| equalish(e_2,e_1) ),
inference(resolution,status(thm),[c1580,c444]) ).
cnf(c1708,plain,
( product(e_2,e_1,e_3)
| product(e_1,e_1,e_1) ),
inference(resolution,status(thm),[c1657,e_2_is_not_e_1]) ).
cnf(c1728,plain,
( product(e_2,e_1,e_3)
| product(e_2,e_1,e_2)
| equalish(e_1,e_2) ),
inference(resolution,status(thm),[c1708,c717]) ).
cnf(c1859,plain,
( product(e_2,e_1,e_3)
| product(e_2,e_1,e_2) ),
inference(resolution,status(thm),[c1728,e_1_is_not_e_2]) ).
cnf(c1900,plain,
( product(e_2,e_1,e_3)
| ~ product(e_2,X301,e_2)
| equalish(X301,e_1) ),
inference(resolution,status(thm),[c1859,product_right_cancellation]) ).
cnf(c1,plain,
( ~ group_element(X24)
| product(X24,e_2,e_1)
| product(X24,e_2,e_2)
| product(X24,e_2,e_3)
| product(X24,e_2,e_4) ),
inference(resolution,status(thm),[product_total_function1,element_2]) ).
cnf(c8,plain,
( product(e_1,e_2,e_1)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_3)
| product(e_1,e_2,e_4) ),
inference(resolution,status(thm),[c1,element_1]) ).
cnf(c100,plain,
( product(e_1,e_2,e_2)
| product(e_1,e_2,e_3)
| product(e_1,e_2,e_4)
| ~ product(e_1,X246,e_1)
| equalish(X246,e_2) ),
inference(resolution,status(thm),[c8,product_right_cancellation]) ).
cnf(c101,plain,
( product(e_1,e_2,e_2)
| product(e_1,e_2,e_3)
| product(e_1,e_2,e_4)
| ~ product(X248,e_1,e_2)
| product(e_2,X248,e_1) ),
inference(resolution,status(thm),[c8,qg3]) ).
cnf(c433,plain,
( product(e_1,e_1,e_2)
| ~ product(e_1,X64,e_1)
| equalish(X64,e_1) ),
inference(resolution,status(thm),[c430,product_right_cancellation]) ).
cnf(c454,plain,
( product(e_1,e_1,e_2)
| equalish(e_2,e_1)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_3)
| product(e_1,e_2,e_4) ),
inference(resolution,status(thm),[c433,c8]) ).
cnf(c6907,plain,
( product(e_1,e_1,e_2)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_3)
| product(e_1,e_2,e_4) ),
inference(resolution,status(thm),[c454,e_2_is_not_e_1]) ).
cnf(c6966,plain,
( product(e_1,e_2,e_2)
| product(e_1,e_2,e_3)
| product(e_1,e_2,e_4)
| product(e_2,e_1,e_1) ),
inference(resolution,status(thm),[c6907,c101]) ).
cnf(c7115,plain,
( product(e_1,e_2,e_2)
| product(e_1,e_2,e_3)
| product(e_1,e_2,e_4)
| product(e_1,e_1,e_1) ),
inference(resolution,status(thm),[c6966,c445]) ).
cnf(c7196,plain,
( product(e_1,e_2,e_2)
| product(e_1,e_2,e_3)
| product(e_1,e_2,e_4)
| equalish(e_1,e_2) ),
inference(resolution,status(thm),[c7115,c100]) ).
cnf(c7607,plain,
( product(e_1,e_2,e_2)
| product(e_1,e_2,e_3)
| product(e_1,e_2,e_4) ),
inference(resolution,status(thm),[c7196,e_1_is_not_e_2]) ).
cnf(c7692,plain,
( product(e_1,e_2,e_3)
| product(e_1,e_2,e_4)
| ~ product(X1011,e_1,e_2)
| product(e_2,X1011,e_2) ),
inference(resolution,status(thm),[c7607,qg3]) ).
cnf(c8674,plain,
( product(e_1,e_2,e_3)
| product(e_1,e_2,e_4)
| product(e_2,e_2,e_2)
| product(e_2,e_1,e_3) ),
inference(resolution,status(thm),[c7692,c1859]) ).
cnf(c24914,plain,
( product(e_1,e_2,e_3)
| product(e_1,e_2,e_4)
| product(e_2,e_1,e_3)
| equalish(e_2,e_1) ),
inference(resolution,status(thm),[c8674,c1900]) ).
cnf(c25028,plain,
( product(e_1,e_2,e_3)
| product(e_1,e_2,e_4)
| product(e_2,e_1,e_3) ),
inference(resolution,status(thm),[c24914,e_2_is_not_e_1]) ).
cnf(c25029,plain,
( product(e_1,e_2,e_4)
| product(e_2,e_1,e_3)
| ~ product(X1373,e_2,e_3)
| equalish(X1373,e_1) ),
inference(resolution,status(thm),[c25028,product_left_cancellation]) ).
cnf(c25039,plain,
( product(e_1,e_2,e_4)
| product(e_2,e_1,e_3)
| ~ product(X1382,e_1,e_2)
| product(e_2,X1382,e_3) ),
inference(resolution,status(thm),[c25028,qg3]) ).
cnf(c25315,plain,
( product(e_1,e_2,e_4)
| product(e_2,e_1,e_3)
| product(e_2,e_2,e_3) ),
inference(resolution,status(thm),[c25039,c1859]) ).
cnf(c25420,plain,
( product(e_1,e_2,e_4)
| product(e_2,e_1,e_3)
| equalish(e_2,e_1) ),
inference(resolution,status(thm),[c25315,c25029]) ).
cnf(c25481,plain,
( product(e_1,e_2,e_4)
| product(e_2,e_1,e_3) ),
inference(resolution,status(thm),[c25420,e_2_is_not_e_1]) ).
cnf(c25483,plain,
( product(e_2,e_1,e_3)
| ~ product(X1384,e_2,e_4)
| equalish(X1384,e_1) ),
inference(resolution,status(thm),[c25481,product_left_cancellation]) ).
cnf(c25494,plain,
( product(e_2,e_1,e_3)
| ~ product(X1390,e_1,e_2)
| product(e_2,X1390,e_4) ),
inference(resolution,status(thm),[c25481,qg3]) ).
cnf(c25829,plain,
( product(e_2,e_1,e_3)
| product(e_2,e_2,e_4) ),
inference(resolution,status(thm),[c25494,c1859]) ).
cnf(c26025,plain,
( product(e_2,e_1,e_3)
| equalish(e_2,e_1) ),
inference(resolution,status(thm),[c25829,c25483]) ).
cnf(c26065,plain,
product(e_2,e_1,e_3),
inference(resolution,status(thm),[c26025,e_2_is_not_e_1]) ).
cnf(c26091,plain,
( ~ product(e_2,X1394,e_3)
| equalish(X1394,e_1) ),
inference(resolution,status(thm),[c26065,product_right_cancellation]) ).
cnf(e_1_is_not_e_3,axiom,
~ equalish(e_1,e_3),
input ).
cnf(e_2_is_not_e_3,axiom,
~ equalish(e_2,e_3),
input ).
cnf(product_total_function2,axiom,
( ~ product(X6,X8,X5)
| ~ product(X6,X8,X7)
| equalish(X5,X7) ),
input ).
cnf(c26081,plain,
( ~ product(e_2,e_1,X1393)
| equalish(X1393,e_3) ),
inference(resolution,status(thm),[c26065,product_total_function2]) ).
cnf(element_3,axiom,
group_element(e_3),
input ).
cnf(c2,plain,
( ~ group_element(X25)
| product(X25,e_3,e_1)
| product(X25,e_3,e_2)
| product(X25,e_3,e_3)
| product(X25,e_3,e_4) ),
inference(resolution,status(thm),[product_total_function1,element_3]) ).
cnf(c12,plain,
( product(e_1,e_3,e_1)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_3)
| product(e_1,e_3,e_4) ),
inference(resolution,status(thm),[c2,element_1]) ).
cnf(c164,plain,
( product(e_1,e_3,e_2)
| product(e_1,e_3,e_3)
| product(e_1,e_3,e_4)
| ~ product(e_1,X408,e_1)
| equalish(X408,e_3) ),
inference(resolution,status(thm),[c12,product_right_cancellation]) ).
cnf(c1710,plain,
( product(e_1,e_1,e_1)
| ~ product(X289,e_2,e_1)
| product(e_1,X289,e_3) ),
inference(resolution,status(thm),[c1708,qg3]) ).
cnf(e_3_is_not_e_2,axiom,
~ equalish(e_3,e_2),
input ).
cnf(e_4_is_not_e_3,axiom,
~ equalish(e_4,e_3),
input ).
cnf(c1725,plain,
( product(e_1,e_1,e_1)
| ~ product(e_2,e_1,X282)
| equalish(X282,e_3) ),
inference(resolution,status(thm),[c1708,product_total_function2]) ).
cnf(c7122,plain,
( product(e_1,e_2,e_3)
| product(e_1,e_2,e_4)
| product(e_1,e_1,e_1)
| equalish(e_2,e_1) ),
inference(resolution,status(thm),[c7115,c444]) ).
cnf(c7256,plain,
( product(e_1,e_2,e_3)
| product(e_1,e_2,e_4)
| product(e_1,e_1,e_1) ),
inference(resolution,status(thm),[c7122,e_2_is_not_e_1]) ).
cnf(c7278,plain,
( product(e_1,e_2,e_3)
| product(e_1,e_1,e_1)
| ~ product(X980,e_1,e_2)
| product(e_2,X980,e_4) ),
inference(resolution,status(thm),[c7256,qg3]) ).
cnf(c7945,plain,
( product(e_1,e_2,e_3)
| product(e_1,e_1,e_1)
| product(e_2,e_1,e_4) ),
inference(resolution,status(thm),[c7278,c430]) ).
cnf(c7994,plain,
( product(e_1,e_2,e_3)
| product(e_1,e_1,e_1)
| equalish(e_4,e_3) ),
inference(resolution,status(thm),[c7945,c1725]) ).
cnf(c8052,plain,
( product(e_1,e_2,e_3)
| product(e_1,e_1,e_1) ),
inference(resolution,status(thm),[c7994,e_4_is_not_e_3]) ).
cnf(c8066,plain,
( product(e_1,e_1,e_1)
| ~ product(e_1,X983,e_3)
| equalish(X983,e_2) ),
inference(resolution,status(thm),[c8052,product_right_cancellation]) ).
cnf(e_3_is_not_e_1,axiom,
~ equalish(e_3,e_1),
input ).
cnf(c467,plain,
( product(e_1,e_1,e_1)
| equalish(e_3,e_1)
| product(e_1,e_3,e_1)
| product(e_1,e_3,e_3)
| product(e_1,e_3,e_4) ),
inference(resolution,status(thm),[c444,c12]) ).
cnf(c7869,plain,
( product(e_1,e_1,e_1)
| product(e_1,e_3,e_1)
| product(e_1,e_3,e_3)
| product(e_1,e_3,e_4) ),
inference(resolution,status(thm),[c467,e_3_is_not_e_1]) ).
cnf(c9145,plain,
( product(e_1,e_1,e_1)
| product(e_1,e_3,e_1)
| product(e_1,e_3,e_4)
| equalish(e_3,e_2) ),
inference(resolution,status(thm),[c7869,c8066]) ).
cnf(c9229,plain,
( product(e_1,e_1,e_1)
| product(e_1,e_3,e_1)
| product(e_1,e_3,e_4) ),
inference(resolution,status(thm),[c9145,e_3_is_not_e_2]) ).
cnf(c9255,plain,
( product(e_1,e_1,e_1)
| product(e_1,e_3,e_4)
| ~ product(X1031,e_1,e_3)
| product(e_3,X1031,e_1) ),
inference(resolution,status(thm),[c9229,qg3]) ).
cnf(c9400,plain,
( product(e_1,e_1,e_1)
| product(e_1,e_3,e_4)
| product(e_3,e_2,e_1) ),
inference(resolution,status(thm),[c9255,c1708]) ).
cnf(c9472,plain,
( product(e_1,e_1,e_1)
| product(e_1,e_3,e_4)
| product(e_1,e_3,e_3) ),
inference(resolution,status(thm),[c9400,c1710]) ).
cnf(c9493,plain,
( product(e_1,e_3,e_4)
| product(e_1,e_3,e_3)
| product(e_1,e_3,e_2)
| equalish(e_1,e_3) ),
inference(resolution,status(thm),[c9472,c164]) ).
cnf(c11363,plain,
( product(e_1,e_3,e_4)
| product(e_1,e_3,e_3)
| product(e_1,e_3,e_2) ),
inference(resolution,status(thm),[c9493,e_1_is_not_e_3]) ).
cnf(c11408,plain,
( product(e_1,e_3,e_4)
| product(e_1,e_3,e_3)
| ~ product(X1101,e_1,e_3)
| product(e_3,X1101,e_2) ),
inference(resolution,status(thm),[c11363,qg3]) ).
cnf(c26086,plain,
( product(e_1,e_3,e_4)
| product(e_1,e_3,e_3)
| product(e_3,e_2,e_2) ),
inference(resolution,status(thm),[c26065,c11408]) ).
cnf(c27768,plain,
( product(e_1,e_3,e_4)
| product(e_1,e_3,e_3)
| ~ product(X1629,e_3,e_2)
| product(e_2,X1629,e_2) ),
inference(resolution,status(thm),[c26086,qg3]) ).
cnf(c33809,plain,
( product(e_1,e_3,e_4)
| product(e_1,e_3,e_3)
| product(e_2,e_1,e_2) ),
inference(resolution,status(thm),[c27768,c11363]) ).
cnf(c33917,plain,
( product(e_1,e_3,e_4)
| product(e_1,e_3,e_3)
| equalish(e_2,e_3) ),
inference(resolution,status(thm),[c33809,c26081]) ).
cnf(c34014,plain,
( product(e_1,e_3,e_4)
| product(e_1,e_3,e_3) ),
inference(resolution,status(thm),[c33917,e_2_is_not_e_3]) ).
cnf(c34041,plain,
( product(e_1,e_3,e_3)
| ~ product(X1636,e_1,e_3)
| product(e_3,X1636,e_4) ),
inference(resolution,status(thm),[c34014,qg3]) ).
cnf(c34371,plain,
( product(e_1,e_3,e_3)
| product(e_3,e_2,e_4) ),
inference(resolution,status(thm),[c34041,c26065]) ).
cnf(c34408,plain,
( product(e_3,e_2,e_4)
| ~ product(X1664,e_1,e_3)
| product(e_3,X1664,e_3) ),
inference(resolution,status(thm),[c34371,qg3]) ).
cnf(c35443,plain,
( product(e_3,e_2,e_4)
| product(e_3,e_2,e_3) ),
inference(resolution,status(thm),[c34408,c26065]) ).
cnf(c35464,plain,
( product(e_3,e_2,e_3)
| ~ product(X1665,e_2,e_4)
| equalish(X1665,e_3) ),
inference(resolution,status(thm),[c35443,product_left_cancellation]) ).
cnf(e_4_is_not_e_2,axiom,
~ equalish(e_4,e_2),
input ).
cnf(c1873,plain,
( product(e_2,e_1,e_2)
| ~ product(X295,e_1,e_3)
| equalish(X295,e_2) ),
inference(resolution,status(thm),[c1859,product_left_cancellation]) ).
cnf(c6,plain,
( product(e_3,e_1,e_1)
| product(e_3,e_1,e_2)
| product(e_3,e_1,e_3)
| product(e_3,e_1,e_4) ),
inference(resolution,status(thm),[c0,element_3]) ).
cnf(c63,plain,
( product(e_3,e_1,e_2)
| product(e_3,e_1,e_3)
| product(e_3,e_1,e_4)
| ~ product(X155,e_1,e_1)
| equalish(X155,e_3) ),
inference(resolution,status(thm),[c6,product_left_cancellation]) ).
cnf(c9273,plain,
( product(e_1,e_1,e_1)
| product(e_1,e_3,e_4)
| ~ product(e_1,e_3,X1024)
| equalish(X1024,e_1) ),
inference(resolution,status(thm),[c9229,product_total_function2]) ).
cnf(c9546,plain,
( product(e_1,e_1,e_1)
| product(e_1,e_3,e_4)
| equalish(e_3,e_1) ),
inference(resolution,status(thm),[c9472,c9273]) ).
cnf(c9600,plain,
( product(e_1,e_1,e_1)
| product(e_1,e_3,e_4) ),
inference(resolution,status(thm),[c9546,e_3_is_not_e_1]) ).
cnf(c9634,plain,
( product(e_1,e_1,e_1)
| ~ product(X1041,e_1,e_3)
| product(e_3,X1041,e_4) ),
inference(resolution,status(thm),[c9600,qg3]) ).
cnf(c10090,plain,
( product(e_1,e_1,e_1)
| product(e_3,e_2,e_4) ),
inference(resolution,status(thm),[c9634,c1708]) ).
cnf(c10140,plain,
( product(e_1,e_1,e_1)
| ~ product(e_3,X1047,e_4)
| equalish(X1047,e_2) ),
inference(resolution,status(thm),[c10090,product_right_cancellation]) ).
cnf(c1714,plain,
( product(e_1,e_1,e_1)
| ~ product(X279,e_1,e_3)
| equalish(X279,e_2) ),
inference(resolution,status(thm),[c1708,product_left_cancellation]) ).
cnf(c473,plain,
( product(e_1,e_1,e_1)
| equalish(e_3,e_1)
| product(e_3,e_1,e_1)
| product(e_3,e_1,e_3)
| product(e_3,e_1,e_4) ),
inference(resolution,status(thm),[c448,c6]) ).
cnf(c8296,plain,
( product(e_1,e_1,e_1)
| product(e_3,e_1,e_1)
| product(e_3,e_1,e_3)
| product(e_3,e_1,e_4) ),
inference(resolution,status(thm),[c473,e_3_is_not_e_1]) ).
cnf(c12809,plain,
( product(e_1,e_1,e_1)
| product(e_3,e_1,e_1)
| product(e_3,e_1,e_4)
| equalish(e_3,e_2) ),
inference(resolution,status(thm),[c8296,c1714]) ).
cnf(c12922,plain,
( product(e_1,e_1,e_1)
| product(e_3,e_1,e_1)
| product(e_3,e_1,e_4) ),
inference(resolution,status(thm),[c12809,e_3_is_not_e_2]) ).
cnf(c12991,plain,
( product(e_1,e_1,e_1)
| product(e_3,e_1,e_1)
| equalish(e_1,e_2) ),
inference(resolution,status(thm),[c12922,c10140]) ).
cnf(c13070,plain,
( product(e_1,e_1,e_1)
| product(e_3,e_1,e_1) ),
inference(resolution,status(thm),[c12991,e_1_is_not_e_2]) ).
cnf(c13131,plain,
( product(e_1,e_1,e_1)
| product(e_1,e_3,e_2) ),
inference(resolution,status(thm),[c13070,c445]) ).
cnf(c13171,plain,
( product(e_1,e_1,e_1)
| equalish(e_3,e_1) ),
inference(resolution,status(thm),[c13131,c444]) ).
cnf(c13225,plain,
product(e_1,e_1,e_1),
inference(resolution,status(thm),[c13171,e_3_is_not_e_1]) ).
cnf(c13242,plain,
( product(e_3,e_1,e_2)
| product(e_3,e_1,e_3)
| product(e_3,e_1,e_4)
| equalish(e_1,e_3) ),
inference(resolution,status(thm),[c13225,c63]) ).
cnf(c15345,plain,
( product(e_3,e_1,e_2)
| product(e_3,e_1,e_3)
| product(e_3,e_1,e_4) ),
inference(resolution,status(thm),[c13242,e_1_is_not_e_3]) ).
cnf(c15367,plain,
( product(e_3,e_1,e_2)
| product(e_3,e_1,e_4)
| product(e_2,e_1,e_2)
| equalish(e_3,e_2) ),
inference(resolution,status(thm),[c15345,c1873]) ).
cnf(c17431,plain,
( product(e_3,e_1,e_2)
| product(e_3,e_1,e_4)
| product(e_2,e_1,e_2) ),
inference(resolution,status(thm),[c15367,e_3_is_not_e_2]) ).
cnf(c17487,plain,
( product(e_3,e_1,e_2)
| product(e_3,e_1,e_4)
| ~ product(e_2,e_1,X1274)
| equalish(X1274,e_2) ),
inference(resolution,status(thm),[c17431,product_total_function2]) ).
cnf(c26089,plain,
( product(e_3,e_1,e_2)
| product(e_3,e_1,e_4)
| equalish(e_3,e_2) ),
inference(resolution,status(thm),[c26065,c17487]) ).
cnf(c26609,plain,
( product(e_3,e_1,e_2)
| product(e_3,e_1,e_4) ),
inference(resolution,status(thm),[c26089,e_3_is_not_e_2]) ).
cnf(c26657,plain,
( product(e_3,e_1,e_2)
| ~ product(e_3,X1429,e_4)
| equalish(X1429,e_1) ),
inference(resolution,status(thm),[c26609,product_right_cancellation]) ).
cnf(c11369,plain,
( product(e_1,e_3,e_3)
| product(e_1,e_3,e_2)
| ~ product(X1099,e_1,e_3)
| product(e_3,X1099,e_4) ),
inference(resolution,status(thm),[c11363,qg3]) ).
cnf(c26079,plain,
( product(e_1,e_3,e_3)
| product(e_1,e_3,e_2)
| product(e_3,e_2,e_4) ),
inference(resolution,status(thm),[c26065,c11369]) ).
cnf(c27712,plain,
( product(e_1,e_3,e_3)
| product(e_1,e_3,e_2)
| product(e_3,e_1,e_2)
| equalish(e_2,e_1) ),
inference(resolution,status(thm),[c26079,c26657]) ).
cnf(c32625,plain,
( product(e_1,e_3,e_3)
| product(e_1,e_3,e_2)
| product(e_3,e_1,e_2) ),
inference(resolution,status(thm),[c27712,e_2_is_not_e_1]) ).
cnf(c32687,plain,
( product(e_1,e_3,e_3)
| product(e_3,e_1,e_2)
| ~ product(e_1,e_3,X1612)
| equalish(X1612,e_2) ),
inference(resolution,status(thm),[c32625,product_total_function2]) ).
cnf(c34049,plain,
( product(e_1,e_3,e_3)
| product(e_3,e_1,e_2)
| equalish(e_4,e_2) ),
inference(resolution,status(thm),[c34014,c32687]) ).
cnf(c34658,plain,
( product(e_1,e_3,e_3)
| product(e_3,e_1,e_2) ),
inference(resolution,status(thm),[c34049,e_4_is_not_e_2]) ).
cnf(c34675,plain,
( product(e_3,e_1,e_2)
| ~ product(X1672,e_1,e_3)
| product(e_3,X1672,e_3) ),
inference(resolution,status(thm),[c34658,qg3]) ).
cnf(c35897,plain,
( product(e_3,e_1,e_2)
| product(e_3,e_2,e_3) ),
inference(resolution,status(thm),[c34675,c26065]) ).
cnf(c35939,plain,
( product(e_3,e_1,e_2)
| ~ product(X1677,e_2,e_3)
| equalish(X1677,e_3) ),
inference(resolution,status(thm),[c35897,product_left_cancellation]) ).
cnf(c7695,plain,
( product(e_1,e_2,e_3)
| product(e_1,e_2,e_4)
| ~ product(X970,e_2,e_2)
| equalish(X970,e_1) ),
inference(resolution,status(thm),[c7607,product_left_cancellation]) ).
cnf(c26082,plain,
( ~ product(X1396,e_2,e_1)
| product(e_1,X1396,e_3) ),
inference(resolution,status(thm),[c26065,qg3]) ).
cnf(c9,plain,
( product(e_2,e_2,e_1)
| product(e_2,e_2,e_2)
| product(e_2,e_2,e_3)
| product(e_2,e_2,e_4) ),
inference(resolution,status(thm),[c1,element_2]) ).
cnf(c124,plain,
( product(e_2,e_2,e_1)
| product(e_2,e_2,e_2)
| product(e_2,e_2,e_4)
| ~ product(e_2,X302,e_3)
| equalish(X302,e_2) ),
inference(resolution,status(thm),[c9,product_right_cancellation]) ).
cnf(c26008,plain,
( product(e_2,e_2,e_4)
| product(e_2,e_2,e_1)
| product(e_2,e_2,e_2)
| equalish(e_1,e_2) ),
inference(resolution,status(thm),[c25829,c124]) ).
cnf(c30043,plain,
( product(e_2,e_2,e_4)
| product(e_2,e_2,e_1)
| product(e_2,e_2,e_2) ),
inference(resolution,status(thm),[c26008,e_1_is_not_e_2]) ).
cnf(c30067,plain,
( product(e_2,e_2,e_4)
| product(e_2,e_2,e_2)
| product(e_1,e_2,e_3) ),
inference(resolution,status(thm),[c30043,c26082]) ).
cnf(c30110,plain,
( product(e_2,e_2,e_2)
| product(e_1,e_2,e_3)
| ~ product(e_2,X1537,e_4)
| equalish(X1537,e_2) ),
inference(resolution,status(thm),[c30067,product_right_cancellation]) ).
cnf(c30104,plain,
( product(e_2,e_2,e_2)
| product(e_1,e_2,e_3)
| ~ product(X1745,e_2,e_2)
| product(e_2,X1745,e_4) ),
inference(resolution,status(thm),[c30067,qg3]) ).
cnf(c7737,plain,
( product(e_1,e_2,e_2)
| product(e_1,e_2,e_3)
| ~ product(X976,e_2,e_4)
| equalish(X976,e_1) ),
inference(resolution,status(thm),[c7607,product_left_cancellation]) ).
cnf(c30105,plain,
( product(e_2,e_2,e_2)
| product(e_1,e_2,e_3)
| product(e_1,e_2,e_2)
| equalish(e_2,e_1) ),
inference(resolution,status(thm),[c30067,c7737]) ).
cnf(c38654,plain,
( product(e_2,e_2,e_2)
| product(e_1,e_2,e_3)
| product(e_1,e_2,e_2) ),
inference(resolution,status(thm),[c30105,e_2_is_not_e_1]) ).
cnf(c38706,plain,
( product(e_2,e_2,e_2)
| product(e_1,e_2,e_3)
| product(e_2,e_1,e_4) ),
inference(resolution,status(thm),[c38654,c30104]) ).
cnf(c38770,plain,
( product(e_2,e_2,e_2)
| product(e_1,e_2,e_3)
| equalish(e_1,e_2) ),
inference(resolution,status(thm),[c38706,c30110]) ).
cnf(c38830,plain,
( product(e_2,e_2,e_2)
| product(e_1,e_2,e_3) ),
inference(resolution,status(thm),[c38770,e_1_is_not_e_2]) ).
cnf(c38848,plain,
( product(e_1,e_2,e_3)
| product(e_1,e_2,e_4)
| equalish(e_2,e_1) ),
inference(resolution,status(thm),[c38830,c7695]) ).
cnf(c39208,plain,
( product(e_1,e_2,e_3)
| product(e_1,e_2,e_4) ),
inference(resolution,status(thm),[c38848,e_2_is_not_e_1]) ).
cnf(c39211,plain,
( product(e_1,e_2,e_4)
| product(e_3,e_1,e_2)
| equalish(e_1,e_3) ),
inference(resolution,status(thm),[c39208,c35939]) ).
cnf(c39925,plain,
( product(e_1,e_2,e_4)
| product(e_3,e_1,e_2) ),
inference(resolution,status(thm),[c39211,e_1_is_not_e_3]) ).
cnf(c39220,plain,
( product(e_1,e_2,e_4)
| ~ product(X1788,e_1,e_2)
| product(e_2,X1788,e_3) ),
inference(resolution,status(thm),[c39208,qg3]) ).
cnf(c40130,plain,
( product(e_1,e_2,e_4)
| product(e_2,e_3,e_3) ),
inference(resolution,status(thm),[c39220,c39925]) ).
cnf(c40172,plain,
( product(e_1,e_2,e_4)
| equalish(e_3,e_1) ),
inference(resolution,status(thm),[c40130,c26091]) ).
cnf(c40204,plain,
product(e_1,e_2,e_4),
inference(resolution,status(thm),[c40172,e_3_is_not_e_1]) ).
cnf(c40208,plain,
( product(e_3,e_2,e_3)
| equalish(e_1,e_3) ),
inference(resolution,status(thm),[c40204,c35464]) ).
cnf(c40366,plain,
product(e_3,e_2,e_3),
inference(resolution,status(thm),[c40208,e_1_is_not_e_3]) ).
cnf(c40379,plain,
( ~ product(X1800,e_3,e_2)
| product(e_2,X1800,e_3) ),
inference(resolution,status(thm),[c40366,qg3]) ).
cnf(c34048,plain,
( product(e_1,e_3,e_3)
| ~ product(e_1,X1632,e_4)
| equalish(X1632,e_3) ),
inference(resolution,status(thm),[c34014,product_right_cancellation]) ).
cnf(c40207,plain,
( product(e_1,e_3,e_3)
| equalish(e_2,e_3) ),
inference(resolution,status(thm),[c40204,c34048]) ).
cnf(c40290,plain,
product(e_1,e_3,e_3),
inference(resolution,status(thm),[c40207,e_2_is_not_e_3]) ).
cnf(c40311,plain,
( ~ product(e_1,X1794,e_3)
| equalish(X1794,e_3) ),
inference(resolution,status(thm),[c40290,product_right_cancellation]) ).
cnf(e_2_is_not_e_4,axiom,
~ equalish(e_2,e_4),
input ).
cnf(e_1_is_not_e_4,axiom,
~ equalish(e_1,e_4),
input ).
cnf(element_4,axiom,
group_element(e_4),
input ).
cnf(c3,plain,
( ~ group_element(X26)
| product(X26,e_4,e_1)
| product(X26,e_4,e_2)
| product(X26,e_4,e_3)
| product(X26,e_4,e_4) ),
inference(resolution,status(thm),[product_total_function1,element_4]) ).
cnf(c16,plain,
( product(e_1,e_4,e_1)
| product(e_1,e_4,e_2)
| product(e_1,e_4,e_3)
| product(e_1,e_4,e_4) ),
inference(resolution,status(thm),[c3,element_1]) ).
cnf(c228,plain,
( product(e_1,e_4,e_2)
| product(e_1,e_4,e_3)
| product(e_1,e_4,e_4)
| ~ product(e_1,X515,e_1)
| equalish(X515,e_4) ),
inference(resolution,status(thm),[c16,product_right_cancellation]) ).
cnf(c13244,plain,
( product(e_1,e_4,e_2)
| product(e_1,e_4,e_3)
| product(e_1,e_4,e_4)
| equalish(e_1,e_4) ),
inference(resolution,status(thm),[c13225,c228]) ).
cnf(c15664,plain,
( product(e_1,e_4,e_2)
| product(e_1,e_4,e_3)
| product(e_1,e_4,e_4) ),
inference(resolution,status(thm),[c13244,e_1_is_not_e_4]) ).
cnf(c15817,plain,
( product(e_1,e_4,e_2)
| product(e_1,e_4,e_3)
| ~ product(e_1,X1221,e_4)
| equalish(X1221,e_4) ),
inference(resolution,status(thm),[c15664,product_right_cancellation]) ).
cnf(c40215,plain,
( product(e_1,e_4,e_2)
| product(e_1,e_4,e_3)
| equalish(e_2,e_4) ),
inference(resolution,status(thm),[c40204,c15817]) ).
cnf(c43683,plain,
( product(e_1,e_4,e_2)
| product(e_1,e_4,e_3) ),
inference(resolution,status(thm),[c40215,e_2_is_not_e_4]) ).
cnf(c43706,plain,
( product(e_1,e_4,e_2)
| equalish(e_4,e_3) ),
inference(resolution,status(thm),[c43683,c40311]) ).
cnf(c43727,plain,
product(e_1,e_4,e_2),
inference(resolution,status(thm),[c43706,e_4_is_not_e_3]) ).
cnf(c43734,plain,
( ~ product(X1880,e_1,e_4)
| product(e_4,X1880,e_2) ),
inference(resolution,status(thm),[c43727,qg3]) ).
cnf(c43731,plain,
( ~ product(X1877,e_4,e_2)
| equalish(X1877,e_1) ),
inference(resolution,status(thm),[c43727,product_left_cancellation]) ).
cnf(e_3_is_not_e_4,axiom,
~ equalish(e_3,e_4),
input ).
cnf(c1893,plain,
( product(e_2,e_1,e_3)
| ~ product(X299,e_1,e_2)
| equalish(X299,e_2) ),
inference(resolution,status(thm),[c1859,product_left_cancellation]) ).
cnf(c7,plain,
( product(e_4,e_1,e_1)
| product(e_4,e_1,e_2)
| product(e_4,e_1,e_3)
| product(e_4,e_1,e_4) ),
inference(resolution,status(thm),[c0,element_4]) ).
cnf(c83,plain,
( product(e_4,e_1,e_2)
| product(e_4,e_1,e_3)
| product(e_4,e_1,e_4)
| ~ product(X216,e_1,e_1)
| equalish(X216,e_4) ),
inference(resolution,status(thm),[c7,product_left_cancellation]) ).
cnf(c13229,plain,
( product(e_4,e_1,e_2)
| product(e_4,e_1,e_3)
| product(e_4,e_1,e_4)
| equalish(e_1,e_4) ),
inference(resolution,status(thm),[c13225,c83]) ).
cnf(c15114,plain,
( product(e_4,e_1,e_2)
| product(e_4,e_1,e_3)
| product(e_4,e_1,e_4) ),
inference(resolution,status(thm),[c13229,e_1_is_not_e_4]) ).
cnf(c15121,plain,
( product(e_4,e_1,e_3)
| product(e_4,e_1,e_4)
| product(e_2,e_1,e_3)
| equalish(e_4,e_2) ),
inference(resolution,status(thm),[c15114,c1893]) ).
cnf(c16039,plain,
( product(e_4,e_1,e_3)
| product(e_4,e_1,e_4)
| product(e_2,e_1,e_3) ),
inference(resolution,status(thm),[c15121,e_4_is_not_e_2]) ).
cnf(c16040,plain,
( product(e_4,e_1,e_4)
| product(e_2,e_1,e_3)
| ~ product(X1227,e_1,e_3)
| equalish(X1227,e_4) ),
inference(resolution,status(thm),[c16039,product_left_cancellation]) ).
cnf(c15352,plain,
( product(e_3,e_1,e_3)
| product(e_3,e_1,e_4)
| product(e_2,e_1,e_3)
| equalish(e_3,e_2) ),
inference(resolution,status(thm),[c15345,c1893]) ).
cnf(c17076,plain,
( product(e_3,e_1,e_3)
| product(e_3,e_1,e_4)
| product(e_2,e_1,e_3) ),
inference(resolution,status(thm),[c15352,e_3_is_not_e_2]) ).
cnf(c17093,plain,
( product(e_3,e_1,e_4)
| product(e_2,e_1,e_3)
| product(e_4,e_1,e_4)
| equalish(e_3,e_4) ),
inference(resolution,status(thm),[c17076,c16040]) ).
cnf(c17877,plain,
( product(e_3,e_1,e_4)
| product(e_2,e_1,e_3)
| product(e_4,e_1,e_4) ),
inference(resolution,status(thm),[c17093,e_3_is_not_e_4]) ).
cnf(c17917,plain,
( product(e_3,e_1,e_4)
| product(e_4,e_1,e_4)
| ~ product(e_2,e_1,X1294)
| equalish(X1294,e_3) ),
inference(resolution,status(thm),[c17877,product_total_function2]) ).
cnf(c15138,plain,
( product(e_4,e_1,e_2)
| product(e_4,e_1,e_4)
| product(e_2,e_1,e_2)
| equalish(e_4,e_2) ),
inference(resolution,status(thm),[c15114,c1873]) ).
cnf(c16687,plain,
( product(e_4,e_1,e_2)
| product(e_4,e_1,e_4)
| product(e_2,e_1,e_2) ),
inference(resolution,status(thm),[c15138,e_4_is_not_e_2]) ).
cnf(c16688,plain,
( product(e_4,e_1,e_4)
| product(e_2,e_1,e_2)
| ~ product(X1240,e_1,e_2)
| equalish(X1240,e_4) ),
inference(resolution,status(thm),[c16687,product_left_cancellation]) ).
cnf(c17439,plain,
( product(e_3,e_1,e_4)
| product(e_2,e_1,e_2)
| product(e_4,e_1,e_4)
| equalish(e_3,e_4) ),
inference(resolution,status(thm),[c17431,c16688]) ).
cnf(c19738,plain,
( product(e_3,e_1,e_4)
| product(e_2,e_1,e_2)
| product(e_4,e_1,e_4) ),
inference(resolution,status(thm),[c17439,e_3_is_not_e_4]) ).
cnf(c19771,plain,
( product(e_3,e_1,e_4)
| product(e_4,e_1,e_4)
| equalish(e_2,e_3) ),
inference(resolution,status(thm),[c19738,c17917]) ).
cnf(c19896,plain,
( product(e_3,e_1,e_4)
| product(e_4,e_1,e_4) ),
inference(resolution,status(thm),[c19771,e_2_is_not_e_3]) ).
cnf(c43769,plain,
( product(e_4,e_4,e_2)
| product(e_3,e_1,e_4) ),
inference(resolution,status(thm),[c43734,c19896]) ).
cnf(c43790,plain,
( product(e_3,e_1,e_4)
| equalish(e_4,e_1) ),
inference(resolution,status(thm),[c43769,c43731]) ).
cnf(c43848,plain,
product(e_3,e_1,e_4),
inference(resolution,status(thm),[c43790,e_4_is_not_e_1]) ).
cnf(c43857,plain,
product(e_4,e_3,e_2),
inference(resolution,status(thm),[c43848,c43734]) ).
cnf(c43872,plain,
product(e_2,e_4,e_3),
inference(resolution,status(thm),[c43857,c40379]) ).
cnf(c43888,plain,
equalish(e_4,e_1),
inference(resolution,status(thm),[c43872,c26091]) ).
cnf(c43897,plain,
$false,
inference(resolution,status(thm),[c43888,e_4_is_not_e_1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP129-2.004 : TPTP v8.1.0. Released v1.2.0.
% 0.07/0.13 % Command : pyres-fof.py -tifbsVp -nlargest -HPickGiven5 %s
% 0.12/0.33 % Computer : n005.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 : Tue Jun 14 08:35:09 EDT 2022
% 0.12/0.34 % CPUTime :
% 59.24/59.42 # Version: 1.3
% 59.24/59.42 # SZS status Unsatisfiable
% 59.24/59.42 # SZS output start CNFRefutation
% See solution above
% 59.24/59.43
% 59.24/59.43 # Initial clauses : 31
% 59.24/59.43 # Processed clauses : 1616
% 59.24/59.43 # Factors computed : 0
% 59.24/59.43 # Resolvents computed: 43898
% 59.24/59.43 # Tautologies deleted: 0
% 59.24/59.43 # Forward subsumed : 5038
% 59.24/59.43 # Backward subsumed : 1333
% 59.24/59.43 # -------- CPU Time ---------
% 59.24/59.43 # User time : 58.907 s
% 59.24/59.43 # System time : 0.184 s
% 59.24/59.43 # Total time : 59.091 s
%------------------------------------------------------------------------------