TSTP Solution File: GRP128-2.004 by PyRes---1.3
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : PyRes---1.3
% Problem : GRP128-2.004 : TPTP v8.1.0. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : pyres-fof.py -tifbsVp -nlargest -HPickGiven5 %s
% Computer : n029.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 11:21:59 EDT 2022
% Result : Satisfiable 81.96s 82.17s
% Output : Saturation 81.96s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named input)
% Comments :
%------------------------------------------------------------------------------
cnf(product_left_cancellation,axiom,
( ~ product(X13,X15,X16)
| ~ product(X14,X15,X16)
| equalish(X13,X14) ),
input ).
cnf(e_4_is_not_e_2,axiom,
~ equalish(e_4,e_2),
input ).
cnf(product_right_cancellation,axiom,
( ~ product(X9,X12,X11)
| ~ product(X9,X10,X11)
| equalish(X12,X10) ),
input ).
cnf(qg3,negated_conjecture,
( ~ product(X19,X20,X21)
| ~ product(X21,X20,X22)
| product(X19,X21,X22) ),
input ).
cnf(e_2_is_not_e_1,axiom,
~ equalish(e_2,e_1),
input ).
cnf(product_total_function2,axiom,
( ~ product(X5,X7,X8)
| ~ product(X5,X7,X6)
| equalish(X8,X6) ),
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(c3,plain,
( ~ group_element(X26)
| product(X26,e_1,e_1)
| product(X26,e_1,e_2)
| product(X26,e_1,e_3)
| product(X26,e_1,e_4) ),
inference(resolution,status(thm),[product_total_function1,element_1]) ).
cnf(c16,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),[c3,element_2]) ).
cnf(c227,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,X32)
| ~ greater(e_4,X32) ),
inference(resolution,status(thm),[c16,no_redundancy]) ).
cnf(c333,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),[c227,e_4_greater_e_3]) ).
cnf(c336,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),[c333,e_2_then_e_3]) ).
cnf(c344,plain,
( product(e_2,e_1,e_1)
| product(e_2,e_1,e_3)
| ~ product(e_2,X77,e_2)
| equalish(X77,e_1) ),
inference(resolution,status(thm),[c336,product_right_cancellation]) ).
cnf(c346,plain,
( product(e_2,e_1,e_1)
| product(e_2,e_1,e_3)
| ~ product(X140,e_1,e_2)
| product(X140,e_2,e_2) ),
inference(resolution,status(thm),[c336,qg3]) ).
cnf(c776,plain,
( product(e_2,e_1,e_1)
| product(e_2,e_1,e_3)
| product(e_2,e_2,e_2) ),
inference(resolution,status(thm),[c346,c336]) ).
cnf(c805,plain,
( product(e_2,e_1,e_1)
| product(e_2,e_1,e_3)
| equalish(e_2,e_1) ),
inference(resolution,status(thm),[c776,c344]) ).
cnf(c846,plain,
( product(e_2,e_1,e_1)
| product(e_2,e_1,e_3) ),
inference(resolution,status(thm),[c805,e_2_is_not_e_1]) ).
cnf(c847,plain,
( product(e_2,e_1,e_3)
| ~ product(e_2,e_1,X144)
| equalish(X144,e_1) ),
inference(resolution,status(thm),[c846,product_total_function2]) ).
cnf(e_1_is_not_e_2,axiom,
~ equalish(e_1,e_2),
input ).
cnf(c859,plain,
( product(e_2,e_1,e_3)
| ~ product(X148,e_1,e_1)
| equalish(X148,e_2) ),
inference(resolution,status(thm),[c846,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(c19,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),[c3,element_1]) ).
cnf(c282,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,X651)
| ~ greater(e_3,X651) ),
inference(resolution,status(thm),[c19,no_redundancy]) ).
cnf(c6624,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),[c282,e_3_greater_e_2]) ).
cnf(c8632,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),[c6624,e_1_then_e_2]) ).
cnf(c8692,plain,
( product(e_1,e_1,e_1)
| product(e_1,e_1,e_2)
| ~ next(e_1,X726)
| ~ greater(e_4,X726) ),
inference(resolution,status(thm),[c8632,no_redundancy]) ).
cnf(c8698,plain,
( product(e_1,e_1,e_1)
| product(e_1,e_1,e_2)
| ~ next(e_1,e_2) ),
inference(resolution,status(thm),[c8692,e_4_greater_e_2]) ).
cnf(c8699,plain,
( product(e_1,e_1,e_1)
| product(e_1,e_1,e_2) ),
inference(resolution,status(thm),[c8698,e_1_then_e_2]) ).
cnf(c8701,plain,
( product(e_1,e_1,e_2)
| product(e_2,e_1,e_3)
| equalish(e_1,e_2) ),
inference(resolution,status(thm),[c8699,c859]) ).
cnf(c8820,plain,
( product(e_1,e_1,e_2)
| product(e_2,e_1,e_3) ),
inference(resolution,status(thm),[c8701,e_1_is_not_e_2]) ).
cnf(c8830,plain,
( product(e_2,e_1,e_3)
| ~ product(X752,e_1,e_1)
| product(X752,e_1,e_2) ),
inference(resolution,status(thm),[c8820,qg3]) ).
cnf(c9945,plain,
( product(e_2,e_1,e_3)
| product(e_2,e_1,e_2) ),
inference(resolution,status(thm),[c8830,c846]) ).
cnf(c10008,plain,
( product(e_2,e_1,e_3)
| equalish(e_2,e_1) ),
inference(resolution,status(thm),[c9945,c847]) ).
cnf(c10059,plain,
product(e_2,e_1,e_3),
inference(resolution,status(thm),[c10008,e_2_is_not_e_1]) ).
cnf(c10076,plain,
( ~ product(X757,e_1,e_2)
| product(X757,e_2,e_3) ),
inference(resolution,status(thm),[c10059,qg3]) ).
cnf(e_4_is_not_e_1,axiom,
~ equalish(e_4,e_1),
input ).
cnf(e_2_is_not_e_4,axiom,
~ equalish(e_2,e_4),
input ).
cnf(e_3_is_not_e_2,axiom,
~ equalish(e_3,e_2),
input ).
cnf(e_3_is_not_e_1,axiom,
~ equalish(e_3,e_1),
input ).
cnf(e_4_is_not_e_3,axiom,
~ equalish(e_4,e_3),
input ).
cnf(c10069,plain,
( ~ product(e_2,e_1,X754)
| equalish(X754,e_3) ),
inference(resolution,status(thm),[c10059,product_total_function2]) ).
cnf(c10122,plain,
( product(e_1,e_2,e_3)
| product(e_1,e_1,e_1) ),
inference(resolution,status(thm),[c10076,c8699]) ).
cnf(c10139,plain,
( product(e_1,e_1,e_1)
| ~ product(e_1,X773,e_3)
| equalish(X773,e_2) ),
inference(resolution,status(thm),[c10122,product_right_cancellation]) ).
cnf(e_1_is_not_e_3,axiom,
~ equalish(e_1,e_3),
input ).
cnf(element_3,axiom,
group_element(e_3),
input ).
cnf(c1,plain,
( ~ group_element(X24)
| product(X24,e_3,e_1)
| product(X24,e_3,e_2)
| product(X24,e_3,e_3)
| product(X24,e_3,e_4) ),
inference(resolution,status(thm),[product_total_function1,element_3]) ).
cnf(c11,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),[c1,element_1]) ).
cnf(c132,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,X305,e_1)
| equalish(X305,e_3) ),
inference(resolution,status(thm),[c11,product_right_cancellation]) ).
cnf(c134,plain,
( product(e_1,e_3,e_2)
| product(e_1,e_3,e_3)
| product(e_1,e_3,e_4)
| ~ product(X309,e_3,e_1)
| product(X309,e_1,e_1) ),
inference(resolution,status(thm),[c11,qg3]) ).
cnf(c2962,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,e_1,e_1) ),
inference(resolution,status(thm),[c134,c11]) ).
cnf(c4793,plain,
( product(e_1,e_3,e_2)
| product(e_1,e_3,e_3)
| product(e_1,e_3,e_4)
| equalish(e_1,e_3) ),
inference(resolution,status(thm),[c2962,c132]) ).
cnf(c4860,plain,
( 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),[c4793,e_1_is_not_e_3]) ).
cnf(c4878,plain,
( product(e_1,e_3,e_3)
| product(e_1,e_3,e_4)
| ~ product(e_1,X506,e_2)
| equalish(X506,e_3) ),
inference(resolution,status(thm),[c4860,product_right_cancellation]) ).
cnf(c8723,plain,
( product(e_1,e_1,e_1)
| product(e_1,e_3,e_3)
| product(e_1,e_3,e_4)
| equalish(e_1,e_3) ),
inference(resolution,status(thm),[c8699,c4878]) ).
cnf(c14886,plain,
( product(e_1,e_1,e_1)
| product(e_1,e_3,e_3)
| product(e_1,e_3,e_4) ),
inference(resolution,status(thm),[c8723,e_1_is_not_e_3]) ).
cnf(c14907,plain,
( product(e_1,e_1,e_1)
| product(e_1,e_3,e_4)
| equalish(e_3,e_2) ),
inference(resolution,status(thm),[c14886,c10139]) ).
cnf(c14987,plain,
( product(e_1,e_1,e_1)
| product(e_1,e_3,e_4) ),
inference(resolution,status(thm),[c14907,e_3_is_not_e_2]) ).
cnf(c15016,plain,
( product(e_1,e_1,e_1)
| ~ product(X888,e_3,e_1)
| product(X888,e_1,e_4) ),
inference(resolution,status(thm),[c14987,qg3]) ).
cnf(e_2_is_not_e_3,axiom,
~ equalish(e_2,e_3),
input ).
cnf(c8,plain,
( product(e_2,e_3,e_1)
| product(e_2,e_3,e_2)
| product(e_2,e_3,e_3)
| product(e_2,e_3,e_4) ),
inference(resolution,status(thm),[c1,element_2]) ).
cnf(c88,plain,
( product(e_2,e_3,e_1)
| product(e_2,e_3,e_3)
| product(e_2,e_3,e_4)
| ~ product(e_2,X218,e_2)
| equalish(X218,e_3) ),
inference(resolution,status(thm),[c8,product_right_cancellation]) ).
cnf(c90,plain,
( product(e_2,e_3,e_1)
| product(e_2,e_3,e_3)
| product(e_2,e_3,e_4)
| ~ product(X221,e_3,e_2)
| product(X221,e_2,e_2) ),
inference(resolution,status(thm),[c8,qg3]) ).
cnf(c1721,plain,
( product(e_2,e_3,e_1)
| product(e_2,e_3,e_3)
| product(e_2,e_3,e_4)
| product(e_2,e_2,e_2) ),
inference(resolution,status(thm),[c90,c8]) ).
cnf(c3844,plain,
( product(e_2,e_3,e_1)
| product(e_2,e_3,e_3)
| product(e_2,e_3,e_4)
| equalish(e_2,e_3) ),
inference(resolution,status(thm),[c1721,c88]) ).
cnf(c3921,plain,
( product(e_2,e_3,e_1)
| product(e_2,e_3,e_3)
| product(e_2,e_3,e_4) ),
inference(resolution,status(thm),[c3844,e_2_is_not_e_3]) ).
cnf(c3954,plain,
( product(e_2,e_3,e_1)
| product(e_2,e_3,e_4)
| ~ product(e_2,X398,e_3)
| equalish(X398,e_3) ),
inference(resolution,status(thm),[c3921,product_right_cancellation]) ).
cnf(c10079,plain,
( product(e_2,e_3,e_1)
| product(e_2,e_3,e_4)
| equalish(e_1,e_3) ),
inference(resolution,status(thm),[c10059,c3954]) ).
cnf(c11281,plain,
( product(e_2,e_3,e_1)
| product(e_2,e_3,e_4) ),
inference(resolution,status(thm),[c10079,e_1_is_not_e_3]) ).
cnf(c11328,plain,
( product(e_2,e_3,e_1)
| ~ product(X800,e_3,e_4)
| equalish(X800,e_2) ),
inference(resolution,status(thm),[c11281,product_left_cancellation]) ).
cnf(c15025,plain,
( product(e_1,e_1,e_1)
| product(e_2,e_3,e_1)
| equalish(e_1,e_2) ),
inference(resolution,status(thm),[c14987,c11328]) ).
cnf(c15331,plain,
( product(e_1,e_1,e_1)
| product(e_2,e_3,e_1) ),
inference(resolution,status(thm),[c15025,e_1_is_not_e_2]) ).
cnf(c15377,plain,
( product(e_1,e_1,e_1)
| product(e_2,e_1,e_4) ),
inference(resolution,status(thm),[c15331,c15016]) ).
cnf(c15405,plain,
( product(e_1,e_1,e_1)
| equalish(e_4,e_3) ),
inference(resolution,status(thm),[c15377,c10069]) ).
cnf(c15443,plain,
product(e_1,e_1,e_1),
inference(resolution,status(thm),[c15405,e_4_is_not_e_3]) ).
cnf(c15461,plain,
( ~ product(X892,e_1,e_1)
| equalish(X892,e_1) ),
inference(resolution,status(thm),[c15443,product_left_cancellation]) ).
cnf(c17,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),[c3,element_3]) ).
cnf(c246,plain,
( product(e_3,e_1,e_1)
| product(e_3,e_1,e_2)
| product(e_3,e_1,e_4)
| ~ product(X557,e_1,e_3)
| equalish(X557,e_3) ),
inference(resolution,status(thm),[c17,product_left_cancellation]) ).
cnf(c10060,plain,
( product(e_3,e_1,e_1)
| product(e_3,e_1,e_2)
| product(e_3,e_1,e_4)
| equalish(e_2,e_3) ),
inference(resolution,status(thm),[c10059,c246]) ).
cnf(c17843,plain,
( product(e_3,e_1,e_1)
| product(e_3,e_1,e_2)
| product(e_3,e_1,e_4) ),
inference(resolution,status(thm),[c10060,e_2_is_not_e_3]) ).
cnf(c17854,plain,
( product(e_3,e_1,e_2)
| product(e_3,e_1,e_4)
| equalish(e_3,e_1) ),
inference(resolution,status(thm),[c17843,c15461]) ).
cnf(c17925,plain,
( product(e_3,e_1,e_2)
| product(e_3,e_1,e_4) ),
inference(resolution,status(thm),[c17854,e_3_is_not_e_1]) ).
cnf(c17930,plain,
( product(e_3,e_1,e_4)
| product(e_3,e_2,e_3) ),
inference(resolution,status(thm),[c17925,c10076]) ).
cnf(c17983,plain,
( product(e_3,e_1,e_4)
| ~ product(e_3,X970,e_3)
| equalish(X970,e_2) ),
inference(resolution,status(thm),[c17930,product_right_cancellation]) ).
cnf(c17982,plain,
( product(e_3,e_1,e_4)
| ~ product(X995,e_2,e_3)
| product(X995,e_3,e_3) ),
inference(resolution,status(thm),[c17930,qg3]) ).
cnf(c19661,plain,
( product(e_3,e_1,e_4)
| product(e_3,e_3,e_3) ),
inference(resolution,status(thm),[c17982,c17930]) ).
cnf(c19718,plain,
( product(e_3,e_1,e_4)
| equalish(e_3,e_2) ),
inference(resolution,status(thm),[c19661,c17983]) ).
cnf(c19751,plain,
product(e_3,e_1,e_4),
inference(resolution,status(thm),[c19718,e_3_is_not_e_2]) ).
cnf(c19755,plain,
( ~ product(e_3,e_1,X997)
| equalish(X997,e_4) ),
inference(resolution,status(thm),[c19751,product_total_function2]) ).
cnf(c0,plain,
( ~ group_element(X23)
| product(X23,e_2,e_1)
| product(X23,e_2,e_2)
| product(X23,e_2,e_3)
| product(X23,e_2,e_4) ),
inference(resolution,status(thm),[product_total_function1,element_2]) ).
cnf(c5,plain,
( product(e_3,e_2,e_1)
| product(e_3,e_2,e_2)
| product(e_3,e_2,e_3)
| product(e_3,e_2,e_4) ),
inference(resolution,status(thm),[c0,element_3]) ).
cnf(c44,plain,
( product(e_3,e_2,e_1)
| product(e_3,e_2,e_2)
| product(e_3,e_2,e_4)
| ~ product(e_3,X107,e_3)
| equalish(X107,e_2) ),
inference(resolution,status(thm),[c5,product_right_cancellation]) ).
cnf(c46,plain,
( product(e_3,e_2,e_1)
| product(e_3,e_2,e_2)
| product(e_3,e_2,e_4)
| ~ product(X114,e_2,e_3)
| product(X114,e_3,e_3) ),
inference(resolution,status(thm),[c5,qg3]) ).
cnf(c729,plain,
( product(e_3,e_2,e_1)
| product(e_3,e_2,e_2)
| product(e_3,e_2,e_4)
| product(e_3,e_3,e_3) ),
inference(resolution,status(thm),[c46,c5]) ).
cnf(c2588,plain,
( product(e_3,e_2,e_1)
| product(e_3,e_2,e_2)
| product(e_3,e_2,e_4)
| equalish(e_3,e_2) ),
inference(resolution,status(thm),[c729,c44]) ).
cnf(c2651,plain,
( product(e_3,e_2,e_1)
| product(e_3,e_2,e_2)
| product(e_3,e_2,e_4) ),
inference(resolution,status(thm),[c2588,e_3_is_not_e_2]) ).
cnf(c2703,plain,
( product(e_3,e_2,e_1)
| product(e_3,e_2,e_2)
| ~ product(e_3,X296,e_4)
| equalish(X296,e_2) ),
inference(resolution,status(thm),[c2651,product_right_cancellation]) ).
cnf(c19757,plain,
( product(e_3,e_2,e_1)
| product(e_3,e_2,e_2)
| equalish(e_1,e_2) ),
inference(resolution,status(thm),[c19751,c2703]) ).
cnf(c21214,plain,
( product(e_3,e_2,e_1)
| product(e_3,e_2,e_2) ),
inference(resolution,status(thm),[c19757,e_1_is_not_e_2]) ).
cnf(c21247,plain,
( product(e_3,e_2,e_1)
| ~ product(X1042,e_2,e_2)
| equalish(X1042,e_3) ),
inference(resolution,status(thm),[c21214,product_left_cancellation]) ).
cnf(e_3_is_not_e_4,axiom,
~ equalish(e_3,e_4),
input ).
cnf(c7,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),[c0,element_1]) ).
cnf(c68,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,X176,e_1)
| equalish(X176,e_2) ),
inference(resolution,status(thm),[c7,product_right_cancellation]) ).
cnf(c70,plain,
( product(e_1,e_2,e_2)
| product(e_1,e_2,e_3)
| product(e_1,e_2,e_4)
| ~ product(X184,e_2,e_1)
| product(X184,e_1,e_1) ),
inference(resolution,status(thm),[c7,qg3]) ).
cnf(c957,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),[c70,c7]) ).
cnf(c3607,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),[c957,c68]) ).
cnf(c3657,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),[c3607,e_1_is_not_e_2]) ).
cnf(c3687,plain,
( product(e_1,e_2,e_2)
| product(e_1,e_2,e_4)
| ~ product(e_1,X369,e_3)
| equalish(X369,e_2) ),
inference(resolution,status(thm),[c3657,product_right_cancellation]) ).
cnf(c853,plain,
( product(e_2,e_1,e_3)
| ~ product(e_2,X146,e_1)
| equalish(X146,e_1) ),
inference(resolution,status(thm),[c846,product_right_cancellation]) ).
cnf(c3928,plain,
( product(e_2,e_3,e_3)
| product(e_2,e_3,e_4)
| product(e_2,e_1,e_3)
| equalish(e_3,e_1) ),
inference(resolution,status(thm),[c3921,c853]) ).
cnf(c4076,plain,
( product(e_2,e_3,e_3)
| product(e_2,e_3,e_4)
| product(e_2,e_1,e_3) ),
inference(resolution,status(thm),[c3928,e_3_is_not_e_1]) ).
cnf(c4091,plain,
( product(e_2,e_3,e_4)
| product(e_2,e_1,e_3)
| ~ product(e_2,X410,e_3)
| equalish(X410,e_3) ),
inference(resolution,status(thm),[c4076,product_right_cancellation]) ).
cnf(element_4,axiom,
group_element(e_4),
input ).
cnf(c2,plain,
( ~ group_element(X25)
| product(X25,e_4,e_1)
| product(X25,e_4,e_2)
| product(X25,e_4,e_3)
| product(X25,e_4,e_4) ),
inference(resolution,status(thm),[product_total_function1,element_4]) ).
cnf(c12,plain,
( product(e_2,e_4,e_1)
| product(e_2,e_4,e_2)
| product(e_2,e_4,e_3)
| product(e_2,e_4,e_4) ),
inference(resolution,status(thm),[c2,element_2]) ).
cnf(c152,plain,
( product(e_2,e_4,e_1)
| product(e_2,e_4,e_3)
| product(e_2,e_4,e_4)
| ~ product(e_2,X348,e_2)
| equalish(X348,e_4) ),
inference(resolution,status(thm),[c12,product_right_cancellation]) ).
cnf(c154,plain,
( product(e_2,e_4,e_1)
| product(e_2,e_4,e_3)
| product(e_2,e_4,e_4)
| ~ product(X351,e_4,e_2)
| product(X351,e_2,e_2) ),
inference(resolution,status(thm),[c12,qg3]) ).
cnf(c3513,plain,
( product(e_2,e_4,e_1)
| product(e_2,e_4,e_3)
| product(e_2,e_4,e_4)
| product(e_2,e_2,e_2) ),
inference(resolution,status(thm),[c154,c12]) ).
cnf(c5048,plain,
( product(e_2,e_4,e_1)
| product(e_2,e_4,e_3)
| product(e_2,e_4,e_4)
| equalish(e_2,e_4) ),
inference(resolution,status(thm),[c3513,c152]) ).
cnf(c5121,plain,
( product(e_2,e_4,e_1)
| product(e_2,e_4,e_3)
| product(e_2,e_4,e_4) ),
inference(resolution,status(thm),[c5048,e_2_is_not_e_4]) ).
cnf(c5130,plain,
( product(e_2,e_4,e_3)
| product(e_2,e_4,e_4)
| product(e_2,e_1,e_3)
| equalish(e_4,e_1) ),
inference(resolution,status(thm),[c5121,c853]) ).
cnf(c5296,plain,
( product(e_2,e_4,e_3)
| product(e_2,e_4,e_4)
| product(e_2,e_1,e_3) ),
inference(resolution,status(thm),[c5130,e_4_is_not_e_1]) ).
cnf(c5304,plain,
( product(e_2,e_4,e_4)
| product(e_2,e_1,e_3)
| product(e_2,e_3,e_4)
| equalish(e_4,e_3) ),
inference(resolution,status(thm),[c5296,c4091]) ).
cnf(c5748,plain,
( product(e_2,e_4,e_4)
| product(e_2,e_1,e_3)
| product(e_2,e_3,e_4) ),
inference(resolution,status(thm),[c5304,e_4_is_not_e_3]) ).
cnf(c5776,plain,
( product(e_2,e_4,e_4)
| product(e_2,e_3,e_4)
| ~ product(e_2,e_1,X581)
| equalish(X581,e_3) ),
inference(resolution,status(thm),[c5748,product_total_function2]) ).
cnf(c865,plain,
( product(e_2,e_1,e_1)
| ~ product(e_2,X151,e_3)
| equalish(X151,e_1) ),
inference(resolution,status(thm),[c846,product_right_cancellation]) ).
cnf(c3944,plain,
( product(e_2,e_3,e_1)
| product(e_2,e_3,e_4)
| product(e_2,e_1,e_1)
| equalish(e_3,e_1) ),
inference(resolution,status(thm),[c3921,c865]) ).
cnf(c4247,plain,
( product(e_2,e_3,e_1)
| product(e_2,e_3,e_4)
| product(e_2,e_1,e_1) ),
inference(resolution,status(thm),[c3944,e_3_is_not_e_1]) ).
cnf(c4271,plain,
( product(e_2,e_3,e_4)
| product(e_2,e_1,e_1)
| ~ product(e_2,X425,e_1)
| equalish(X425,e_3) ),
inference(resolution,status(thm),[c4247,product_right_cancellation]) ).
cnf(c5145,plain,
( product(e_2,e_4,e_1)
| product(e_2,e_4,e_4)
| product(e_2,e_1,e_1)
| equalish(e_4,e_1) ),
inference(resolution,status(thm),[c5121,c865]) ).
cnf(c5493,plain,
( product(e_2,e_4,e_1)
| product(e_2,e_4,e_4)
| product(e_2,e_1,e_1) ),
inference(resolution,status(thm),[c5145,e_4_is_not_e_1]) ).
cnf(c5500,plain,
( product(e_2,e_4,e_4)
| product(e_2,e_1,e_1)
| product(e_2,e_3,e_4)
| equalish(e_4,e_3) ),
inference(resolution,status(thm),[c5493,c4271]) ).
cnf(c6319,plain,
( product(e_2,e_4,e_4)
| product(e_2,e_1,e_1)
| product(e_2,e_3,e_4) ),
inference(resolution,status(thm),[c5500,e_4_is_not_e_3]) ).
cnf(c6373,plain,
( product(e_2,e_4,e_4)
| product(e_2,e_3,e_4)
| equalish(e_1,e_3) ),
inference(resolution,status(thm),[c6319,c5776]) ).
cnf(c6472,plain,
( product(e_2,e_4,e_4)
| product(e_2,e_3,e_4) ),
inference(resolution,status(thm),[c6373,e_1_is_not_e_3]) ).
cnf(c6511,plain,
( product(e_2,e_4,e_4)
| ~ product(X625,e_3,e_2)
| product(X625,e_2,e_4) ),
inference(resolution,status(thm),[c6472,qg3]) ).
cnf(c4908,plain,
( product(e_1,e_3,e_2)
| product(e_1,e_3,e_3)
| ~ product(X513,e_3,e_4)
| equalish(X513,e_1) ),
inference(resolution,status(thm),[c4860,product_left_cancellation]) ).
cnf(c6513,plain,
( product(e_2,e_4,e_4)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_3)
| equalish(e_2,e_1) ),
inference(resolution,status(thm),[c6472,c4908]) ).
cnf(c8060,plain,
( product(e_2,e_4,e_4)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_3) ),
inference(resolution,status(thm),[c6513,e_2_is_not_e_1]) ).
cnf(c8100,plain,
( product(e_2,e_4,e_4)
| product(e_1,e_3,e_3)
| product(e_1,e_2,e_4) ),
inference(resolution,status(thm),[c8060,c6511]) ).
cnf(c8177,plain,
( product(e_2,e_4,e_4)
| product(e_1,e_2,e_4)
| product(e_1,e_2,e_2)
| equalish(e_3,e_2) ),
inference(resolution,status(thm),[c8100,c3687]) ).
cnf(c14437,plain,
( product(e_2,e_4,e_4)
| product(e_1,e_2,e_4)
| product(e_1,e_2,e_2) ),
inference(resolution,status(thm),[c8177,e_3_is_not_e_2]) ).
cnf(c14458,plain,
( product(e_1,e_2,e_4)
| product(e_1,e_2,e_2)
| ~ product(e_2,X860,e_4)
| equalish(X860,e_4) ),
inference(resolution,status(thm),[c14437,product_right_cancellation]) ).
cnf(c17944,plain,
( product(e_3,e_1,e_2)
| ~ product(X980,e_1,e_3)
| product(X980,e_3,e_4) ),
inference(resolution,status(thm),[c17925,qg3]) ).
cnf(c18755,plain,
( product(e_3,e_1,e_2)
| product(e_2,e_3,e_4) ),
inference(resolution,status(thm),[c17944,c10059]) ).
cnf(c18761,plain,
( product(e_2,e_3,e_4)
| ~ product(e_3,e_1,X982)
| equalish(X982,e_2) ),
inference(resolution,status(thm),[c18755,product_total_function2]) ).
cnf(c19754,plain,
( product(e_2,e_3,e_4)
| equalish(e_4,e_2) ),
inference(resolution,status(thm),[c19751,c18761]) ).
cnf(c20077,plain,
product(e_2,e_3,e_4),
inference(resolution,status(thm),[c19754,e_4_is_not_e_2]) ).
cnf(c20094,plain,
( product(e_1,e_2,e_4)
| product(e_1,e_2,e_2)
| equalish(e_3,e_4) ),
inference(resolution,status(thm),[c20077,c14458]) ).
cnf(c22081,plain,
( product(e_1,e_2,e_4)
| product(e_1,e_2,e_2) ),
inference(resolution,status(thm),[c20094,e_3_is_not_e_4]) ).
cnf(c22106,plain,
( product(e_1,e_2,e_4)
| product(e_3,e_2,e_1)
| equalish(e_1,e_3) ),
inference(resolution,status(thm),[c22081,c21247]) ).
cnf(c22677,plain,
( product(e_1,e_2,e_4)
| product(e_3,e_2,e_1) ),
inference(resolution,status(thm),[c22106,e_1_is_not_e_3]) ).
cnf(c22111,plain,
( product(e_1,e_2,e_4)
| ~ product(X1080,e_2,e_1)
| product(X1080,e_1,e_2) ),
inference(resolution,status(thm),[c22081,qg3]) ).
cnf(c22987,plain,
( product(e_1,e_2,e_4)
| product(e_3,e_1,e_2) ),
inference(resolution,status(thm),[c22111,c22677]) ).
cnf(c23062,plain,
( product(e_1,e_2,e_4)
| equalish(e_2,e_4) ),
inference(resolution,status(thm),[c22987,c19755]) ).
cnf(c23082,plain,
product(e_1,e_2,e_4),
inference(resolution,status(thm),[c23062,e_2_is_not_e_4]) ).
cnf(c23098,plain,
( ~ product(X1083,e_2,e_4)
| equalish(X1083,e_1) ),
inference(resolution,status(thm),[c23082,product_left_cancellation]) ).
cnf(c20090,plain,
( ~ product(X1007,e_3,e_2)
| product(X1007,e_2,e_4) ),
inference(resolution,status(thm),[c20077,qg3]) ).
cnf(c10083,plain,
( ~ product(e_2,X755,e_3)
| equalish(X755,e_1) ),
inference(resolution,status(thm),[c10059,product_right_cancellation]) ).
cnf(c10,plain,
( product(e_4,e_3,e_1)
| product(e_4,e_3,e_2)
| product(e_4,e_3,e_3)
| product(e_4,e_3,e_4) ),
inference(resolution,status(thm),[c1,element_4]) ).
cnf(c128,plain,
( product(e_4,e_3,e_1)
| product(e_4,e_3,e_2)
| product(e_4,e_3,e_3)
| ~ product(e_4,X298,e_4)
| equalish(X298,e_3) ),
inference(resolution,status(thm),[c10,product_right_cancellation]) ).
cnf(c130,plain,
( product(e_4,e_3,e_1)
| product(e_4,e_3,e_2)
| product(e_4,e_3,e_3)
| ~ product(X302,e_3,e_4)
| product(X302,e_4,e_4) ),
inference(resolution,status(thm),[c10,qg3]) ).
cnf(c2917,plain,
( product(e_4,e_3,e_1)
| product(e_4,e_3,e_2)
| product(e_4,e_3,e_3)
| product(e_4,e_4,e_4) ),
inference(resolution,status(thm),[c130,c10]) ).
cnf(c4552,plain,
( product(e_4,e_3,e_1)
| product(e_4,e_3,e_2)
| product(e_4,e_3,e_3)
| equalish(e_4,e_3) ),
inference(resolution,status(thm),[c2917,c128]) ).
cnf(c4626,plain,
( product(e_4,e_3,e_1)
| product(e_4,e_3,e_2)
| product(e_4,e_3,e_3) ),
inference(resolution,status(thm),[c4552,e_4_is_not_e_3]) ).
cnf(c4670,plain,
( product(e_4,e_3,e_1)
| product(e_4,e_3,e_2)
| ~ product(X499,e_3,e_4)
| product(X499,e_4,e_3) ),
inference(resolution,status(thm),[c4626,qg3]) ).
cnf(c20092,plain,
( product(e_4,e_3,e_1)
| product(e_4,e_3,e_2)
| product(e_2,e_4,e_3) ),
inference(resolution,status(thm),[c20077,c4670]) ).
cnf(c23270,plain,
( product(e_4,e_3,e_1)
| product(e_4,e_3,e_2)
| equalish(e_4,e_1) ),
inference(resolution,status(thm),[c20092,c10083]) ).
cnf(c23309,plain,
( product(e_4,e_3,e_1)
| product(e_4,e_3,e_2) ),
inference(resolution,status(thm),[c23270,e_4_is_not_e_1]) ).
cnf(c23325,plain,
( product(e_4,e_3,e_1)
| product(e_4,e_2,e_4) ),
inference(resolution,status(thm),[c23309,c20090]) ).
cnf(c23362,plain,
( product(e_4,e_3,e_1)
| equalish(e_4,e_1) ),
inference(resolution,status(thm),[c23325,c23098]) ).
cnf(c23380,plain,
product(e_4,e_3,e_1),
inference(resolution,status(thm),[c23362,e_4_is_not_e_1]) ).
cnf(c10092,plain,
( ~ product(X756,e_1,e_3)
| equalish(X756,e_2) ),
inference(resolution,status(thm),[c10059,product_left_cancellation]) ).
cnf(c8086,plain,
( product(e_1,e_3,e_2)
| product(e_1,e_3,e_3)
| ~ product(e_2,X707,e_4)
| equalish(X707,e_4) ),
inference(resolution,status(thm),[c8060,product_right_cancellation]) ).
cnf(c20082,plain,
( product(e_1,e_3,e_2)
| product(e_1,e_3,e_3)
| equalish(e_3,e_4) ),
inference(resolution,status(thm),[c20077,c8086]) ).
cnf(c21708,plain,
( product(e_1,e_3,e_2)
| product(e_1,e_3,e_3) ),
inference(resolution,status(thm),[c20082,e_3_is_not_e_4]) ).
cnf(c21742,plain,
( product(e_1,e_3,e_2)
| ~ product(X1068,e_3,e_1)
| product(X1068,e_1,e_3) ),
inference(resolution,status(thm),[c21708,qg3]) ).
cnf(c23384,plain,
( product(e_1,e_3,e_2)
| product(e_4,e_1,e_3) ),
inference(resolution,status(thm),[c23380,c21742]) ).
cnf(c23475,plain,
( product(e_1,e_3,e_2)
| equalish(e_4,e_2) ),
inference(resolution,status(thm),[c23384,c10092]) ).
cnf(c23500,plain,
product(e_1,e_3,e_2),
inference(resolution,status(thm),[c23475,e_4_is_not_e_2]) ).
cnf(c23506,plain,
( ~ product(X1115,e_3,e_1)
| product(X1115,e_1,e_2) ),
inference(resolution,status(thm),[c23500,qg3]) ).
cnf(c23528,plain,
product(e_4,e_1,e_2),
inference(resolution,status(thm),[c23506,c23380]) ).
cnf(c23533,plain,
product(e_4,e_2,e_3),
inference(resolution,status(thm),[c23528,c10076]) ).
cnf(c23550,plain,
( ~ product(e_4,X1122,e_3)
| equalish(X1122,e_2) ),
inference(resolution,status(thm),[c23533,product_right_cancellation]) ).
cnf(c23535,plain,
( ~ product(X1124,e_1,e_4)
| product(X1124,e_4,e_2) ),
inference(resolution,status(thm),[c23528,qg3]) ).
cnf(c23614,plain,
product(e_3,e_4,e_2),
inference(resolution,status(thm),[c23535,c19751]) ).
cnf(c23626,plain,
( ~ product(X1127,e_4,e_2)
| equalish(X1127,e_3) ),
inference(resolution,status(thm),[c23614,product_left_cancellation]) ).
cnf(c14,plain,
( product(e_4,e_4,e_1)
| product(e_4,e_4,e_2)
| product(e_4,e_4,e_3)
| product(e_4,e_4,e_4) ),
inference(resolution,status(thm),[c2,element_4]) ).
cnf(c183,plain,
( product(e_4,e_4,e_2)
| product(e_4,e_4,e_3)
| product(e_4,e_4,e_4)
| ~ product(X420,e_4,e_1)
| equalish(X420,e_4) ),
inference(resolution,status(thm),[c14,product_left_cancellation]) ).
cnf(c4289,plain,
( product(e_2,e_3,e_1)
| product(e_2,e_1,e_1)
| ~ product(e_2,X429,e_4)
| equalish(X429,e_3) ),
inference(resolution,status(thm),[c4247,product_right_cancellation]) ).
cnf(c5536,plain,
( product(e_2,e_4,e_1)
| product(e_2,e_1,e_1)
| product(e_2,e_3,e_1)
| equalish(e_4,e_3) ),
inference(resolution,status(thm),[c5493,c4289]) ).
cnf(c6718,plain,
( product(e_2,e_4,e_1)
| product(e_2,e_1,e_1)
| product(e_2,e_3,e_1) ),
inference(resolution,status(thm),[c5536,e_4_is_not_e_3]) ).
cnf(c6755,plain,
( product(e_2,e_4,e_1)
| product(e_2,e_3,e_1)
| ~ product(e_2,e_1,X660)
| equalish(X660,e_1) ),
inference(resolution,status(thm),[c6718,product_total_function2]) ).
cnf(c10063,plain,
( product(e_2,e_4,e_1)
| product(e_2,e_3,e_1)
| equalish(e_3,e_1) ),
inference(resolution,status(thm),[c10059,c6755]) ).
cnf(c10751,plain,
( product(e_2,e_4,e_1)
| product(e_2,e_3,e_1) ),
inference(resolution,status(thm),[c10063,e_3_is_not_e_1]) ).
cnf(c10790,plain,
( product(e_2,e_4,e_1)
| ~ product(e_2,e_3,X786)
| equalish(X786,e_1) ),
inference(resolution,status(thm),[c10751,product_total_function2]) ).
cnf(c20089,plain,
( product(e_2,e_4,e_1)
| equalish(e_4,e_1) ),
inference(resolution,status(thm),[c20077,c10790]) ).
cnf(c20350,plain,
product(e_2,e_4,e_1),
inference(resolution,status(thm),[c20089,e_4_is_not_e_1]) ).
cnf(c20361,plain,
( product(e_4,e_4,e_2)
| product(e_4,e_4,e_3)
| product(e_4,e_4,e_4)
| equalish(e_2,e_4) ),
inference(resolution,status(thm),[c20350,c183]) ).
cnf(c24038,plain,
( product(e_4,e_4,e_2)
| product(e_4,e_4,e_3)
| product(e_4,e_4,e_4) ),
inference(resolution,status(thm),[c20361,e_2_is_not_e_4]) ).
cnf(c24045,plain,
( product(e_4,e_4,e_3)
| product(e_4,e_4,e_4)
| equalish(e_4,e_3) ),
inference(resolution,status(thm),[c24038,c23626]) ).
cnf(c24097,plain,
( product(e_4,e_4,e_3)
| product(e_4,e_4,e_4) ),
inference(resolution,status(thm),[c24045,e_4_is_not_e_3]) ).
cnf(c24100,plain,
( product(e_4,e_4,e_4)
| equalish(e_4,e_2) ),
inference(resolution,status(thm),[c24097,c23550]) ).
cnf(c24127,plain,
product(e_4,e_4,e_4),
inference(resolution,status(thm),[c24100,e_4_is_not_e_2]) ).
cnf(c24134,plain,
( ~ product(X1324,e_4,e_4)
| equalish(X1324,e_4) ),
inference(resolution,status(thm),[c24127,product_left_cancellation]) ).
cnf(c24133,plain,
( ~ product(e_4,X1323,e_4)
| equalish(X1323,e_4) ),
inference(resolution,status(thm),[c24127,product_right_cancellation]) ).
cnf(c24129,plain,
( ~ product(e_4,e_4,X1322)
| equalish(X1322,e_4) ),
inference(resolution,status(thm),[c24127,product_total_function2]) ).
cnf(c23625,plain,
( ~ product(e_3,X1126,e_2)
| equalish(X1126,e_4) ),
inference(resolution,status(thm),[c23614,product_right_cancellation]) ).
cnf(c23392,plain,
( ~ product(X1110,e_3,e_1)
| equalish(X1110,e_4) ),
inference(resolution,status(thm),[c23380,product_left_cancellation]) ).
cnf(c9,plain,
( product(e_3,e_3,e_1)
| product(e_3,e_3,e_2)
| product(e_3,e_3,e_3)
| product(e_3,e_3,e_4) ),
inference(resolution,status(thm),[c1,element_3]) ).
cnf(c112,plain,
( product(e_3,e_3,e_1)
| product(e_3,e_3,e_2)
| product(e_3,e_3,e_3)
| ~ product(e_3,X267,e_4)
| equalish(X267,e_3) ),
inference(resolution,status(thm),[c9,product_right_cancellation]) ).
cnf(c19702,plain,
( product(e_3,e_3,e_3)
| product(e_3,e_3,e_1)
| product(e_3,e_3,e_2)
| equalish(e_1,e_3) ),
inference(resolution,status(thm),[c19661,c112]) ).
cnf(c23917,plain,
( product(e_3,e_3,e_3)
| product(e_3,e_3,e_1)
| product(e_3,e_3,e_2) ),
inference(resolution,status(thm),[c19702,e_1_is_not_e_3]) ).
cnf(c23930,plain,
( product(e_3,e_3,e_3)
| product(e_3,e_3,e_2)
| equalish(e_3,e_4) ),
inference(resolution,status(thm),[c23917,c23392]) ).
cnf(c23972,plain,
( product(e_3,e_3,e_3)
| equalish(e_3,e_4) ),
inference(resolution,status(thm),[c23930,c23625]) ).
cnf(c23988,plain,
product(e_3,e_3,e_3),
inference(resolution,status(thm),[c23972,e_3_is_not_e_4]) ).
cnf(c23993,plain,
( ~ product(X1298,e_3,e_3)
| equalish(X1298,e_3) ),
inference(resolution,status(thm),[c23988,product_left_cancellation]) ).
cnf(c23991,plain,
( ~ product(e_3,X1296,e_3)
| equalish(X1296,e_3) ),
inference(resolution,status(thm),[c23988,product_right_cancellation]) ).
cnf(c23989,plain,
( ~ product(e_3,e_3,X1295)
| equalish(X1295,e_3) ),
inference(resolution,status(thm),[c23988,product_total_function2]) ).
cnf(c20095,plain,
( ~ product(e_2,X1001,e_4)
| equalish(X1001,e_3) ),
inference(resolution,status(thm),[c20077,product_right_cancellation]) ).
cnf(c20365,plain,
( ~ product(e_2,X1005,e_1)
| equalish(X1005,e_4) ),
inference(resolution,status(thm),[c20350,product_right_cancellation]) ).
cnf(c4,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),[c0,element_2]) ).
cnf(c28,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,X57,e_3)
| equalish(X57,e_2) ),
inference(resolution,status(thm),[c4,product_right_cancellation]) ).
cnf(c10078,plain,
( product(e_2,e_2,e_1)
| product(e_2,e_2,e_2)
| product(e_2,e_2,e_4)
| equalish(e_1,e_2) ),
inference(resolution,status(thm),[c10059,c28]) ).
cnf(c23776,plain,
( product(e_2,e_2,e_1)
| product(e_2,e_2,e_2)
| product(e_2,e_2,e_4) ),
inference(resolution,status(thm),[c10078,e_1_is_not_e_2]) ).
cnf(c23777,plain,
( product(e_2,e_2,e_2)
| product(e_2,e_2,e_4)
| equalish(e_2,e_4) ),
inference(resolution,status(thm),[c23776,c20365]) ).
cnf(c23835,plain,
( product(e_2,e_2,e_2)
| product(e_2,e_2,e_4) ),
inference(resolution,status(thm),[c23777,e_2_is_not_e_4]) ).
cnf(c23845,plain,
( product(e_2,e_2,e_2)
| equalish(e_2,e_3) ),
inference(resolution,status(thm),[c23835,c20095]) ).
cnf(c23865,plain,
product(e_2,e_2,e_2),
inference(resolution,status(thm),[c23845,e_2_is_not_e_3]) ).
cnf(c23872,plain,
( ~ product(X1252,e_2,e_2)
| equalish(X1252,e_2) ),
inference(resolution,status(thm),[c23865,product_left_cancellation]) ).
cnf(c23871,plain,
( ~ product(e_2,X1251,e_2)
| equalish(X1251,e_2) ),
inference(resolution,status(thm),[c23865,product_right_cancellation]) ).
cnf(c23867,plain,
( ~ product(e_2,e_2,X1250)
| equalish(X1250,e_2) ),
inference(resolution,status(thm),[c23865,product_total_function2]) ).
cnf(c23549,plain,
( ~ product(X1131,e_2,e_4)
| product(X1131,e_4,e_3) ),
inference(resolution,status(thm),[c23533,qg3]) ).
cnf(c23685,plain,
product(e_1,e_4,e_3),
inference(resolution,status(thm),[c23549,c23082]) ).
cnf(c23705,plain,
( ~ product(X1137,e_4,e_1)
| product(X1137,e_1,e_3) ),
inference(resolution,status(thm),[c23685,qg3]) ).
cnf(c20362,plain,
( ~ product(X1008,e_4,e_2)
| product(X1008,e_2,e_1) ),
inference(resolution,status(thm),[c20350,qg3]) ).
cnf(c23621,plain,
product(e_3,e_2,e_1),
inference(resolution,status(thm),[c23614,c20362]) ).
cnf(c23632,plain,
( ~ product(X1136,e_2,e_3)
| product(X1136,e_3,e_1) ),
inference(resolution,status(thm),[c23621,qg3]) ).
cnf(c23622,plain,
( ~ product(X1135,e_4,e_3)
| product(X1135,e_3,e_2) ),
inference(resolution,status(thm),[c23614,qg3]) ).
cnf(c23708,plain,
( ~ product(X1134,e_4,e_3)
| equalish(X1134,e_1) ),
inference(resolution,status(thm),[c23685,product_left_cancellation]) ).
cnf(c23706,plain,
( ~ product(e_1,X1133,e_3)
| equalish(X1133,e_4) ),
inference(resolution,status(thm),[c23685,product_right_cancellation]) ).
cnf(c23702,plain,
( ~ product(e_1,e_4,X1132)
| equalish(X1132,e_3) ),
inference(resolution,status(thm),[c23685,product_total_function2]) ).
cnf(c23635,plain,
( ~ product(X1130,e_2,e_1)
| equalish(X1130,e_3) ),
inference(resolution,status(thm),[c23621,product_left_cancellation]) ).
cnf(c23633,plain,
( ~ product(e_3,X1129,e_1)
| equalish(X1129,e_2) ),
inference(resolution,status(thm),[c23621,product_right_cancellation]) ).
cnf(c23630,plain,
( ~ product(e_3,e_2,X1128)
| equalish(X1128,e_1) ),
inference(resolution,status(thm),[c23621,product_total_function2]) ).
cnf(c23618,plain,
( ~ product(e_3,e_4,X1125)
| equalish(X1125,e_2) ),
inference(resolution,status(thm),[c23614,product_total_function2]) ).
cnf(c23552,plain,
( ~ product(X1123,e_2,e_3)
| equalish(X1123,e_4) ),
inference(resolution,status(thm),[c23533,product_left_cancellation]) ).
cnf(c23543,plain,
( ~ product(e_4,e_2,X1121)
| equalish(X1121,e_3) ),
inference(resolution,status(thm),[c23533,product_total_function2]) ).
cnf(c23540,plain,
( ~ product(X1120,e_1,e_2)
| equalish(X1120,e_4) ),
inference(resolution,status(thm),[c23528,product_left_cancellation]) ).
cnf(c23538,plain,
( ~ product(e_4,X1119,e_2)
| equalish(X1119,e_1) ),
inference(resolution,status(thm),[c23528,product_right_cancellation]) ).
cnf(c23531,plain,
( ~ product(e_4,e_1,X1117)
| equalish(X1117,e_2) ),
inference(resolution,status(thm),[c23528,product_total_function2]) ).
cnf(e_2_greater_e_1,axiom,
greater(e_2,e_1),
input ).
cnf(c23539,plain,
( ~ next(e_4,X1116)
| ~ greater(e_2,X1116) ),
inference(resolution,status(thm),[c23528,no_redundancy]) ).
cnf(c23553,plain,
~ next(e_4,e_1),
inference(resolution,status(thm),[c23539,e_2_greater_e_1]) ).
cnf(c23508,plain,
( ~ product(X1114,e_3,e_2)
| equalish(X1114,e_1) ),
inference(resolution,status(thm),[c23500,product_left_cancellation]) ).
cnf(c23507,plain,
( ~ product(e_1,X1113,e_2)
| equalish(X1113,e_3) ),
inference(resolution,status(thm),[c23500,product_right_cancellation]) ).
cnf(c23504,plain,
( ~ product(e_1,e_3,X1112)
| equalish(X1112,e_2) ),
inference(resolution,status(thm),[c23500,product_total_function2]) ).
cnf(c23388,plain,
( ~ product(X1111,e_3,e_4)
| product(X1111,e_4,e_1) ),
inference(resolution,status(thm),[c23380,qg3]) ).
cnf(c23390,plain,
( ~ product(e_4,X1109,e_1)
| equalish(X1109,e_3) ),
inference(resolution,status(thm),[c23380,product_right_cancellation]) ).
cnf(c23385,plain,
( ~ product(e_4,e_3,X1108)
| equalish(X1108,e_1) ),
inference(resolution,status(thm),[c23380,product_total_function2]) ).
cnf(c23089,plain,
( ~ product(X1085,e_2,e_1)
| product(X1085,e_1,e_4) ),
inference(resolution,status(thm),[c23082,qg3]) ).
cnf(c23091,plain,
( ~ product(e_1,X1082,e_4)
| equalish(X1082,e_2) ),
inference(resolution,status(thm),[c23082,product_right_cancellation]) ).
cnf(c23085,plain,
( ~ product(e_1,e_2,X1081)
| equalish(X1081,e_4) ),
inference(resolution,status(thm),[c23082,product_total_function2]) ).
cnf(c20369,plain,
( ~ product(X1006,e_4,e_1)
| equalish(X1006,e_2) ),
inference(resolution,status(thm),[c20350,product_left_cancellation]) ).
cnf(c20358,plain,
( ~ product(e_2,e_4,X1004)
| equalish(X1004,e_1) ),
inference(resolution,status(thm),[c20350,product_total_function2]) ).
cnf(c19760,plain,
( ~ product(X1003,e_1,e_3)
| product(X1003,e_3,e_4) ),
inference(resolution,status(thm),[c19751,qg3]) ).
cnf(c20099,plain,
( ~ product(X1002,e_3,e_4)
| equalish(X1002,e_2) ),
inference(resolution,status(thm),[c20077,product_left_cancellation]) ).
cnf(c20084,plain,
( ~ product(e_2,e_3,X1000)
| equalish(X1000,e_4) ),
inference(resolution,status(thm),[c20077,product_total_function2]) ).
cnf(c19771,plain,
( ~ product(X999,e_1,e_4)
| equalish(X999,e_3) ),
inference(resolution,status(thm),[c19751,product_left_cancellation]) ).
cnf(c19766,plain,
( ~ product(e_3,X998,e_4)
| equalish(X998,e_1) ),
inference(resolution,status(thm),[c19751,product_right_cancellation]) ).
cnf(c19768,plain,
( ~ next(e_3,X996)
| ~ greater(e_4,X996) ),
inference(resolution,status(thm),[c19751,no_redundancy]) ).
cnf(c19777,plain,
~ next(e_3,e_2),
inference(resolution,status(thm),[c19768,e_4_greater_e_2]) ).
cnf(e_4_greater_e_1,axiom,
greater(e_4,e_1),
input ).
cnf(c19776,plain,
~ next(e_3,e_1),
inference(resolution,status(thm),[c19768,e_4_greater_e_1]) ).
cnf(c19775,plain,
~ next(e_3,e_3),
inference(resolution,status(thm),[c19768,e_4_greater_e_3]) ).
cnf(c15457,plain,
( ~ product(e_1,X891,e_1)
| equalish(X891,e_1) ),
inference(resolution,status(thm),[c15443,product_right_cancellation]) ).
cnf(c15446,plain,
( ~ product(e_1,e_1,X890)
| equalish(X890,e_1) ),
inference(resolution,status(thm),[c15443,product_total_function2]) ).
cnf(c15460,plain,
( ~ next(e_1,X889)
| ~ greater(e_1,X889) ),
inference(resolution,status(thm),[c15443,no_redundancy]) ).
cnf(e_3_greater_e_1,axiom,
greater(e_3,e_1),
input ).
cnf(c10089,plain,
( ~ next(e_2,X753)
| ~ greater(e_3,X753) ),
inference(resolution,status(thm),[c10059,no_redundancy]) ).
cnf(c10096,plain,
~ next(e_2,e_1),
inference(resolution,status(thm),[c10089,e_3_greater_e_1]) ).
cnf(c10095,plain,
~ next(e_2,e_2),
inference(resolution,status(thm),[c10089,e_3_greater_e_2]) ).
cnf(c6,plain,
( product(e_4,e_2,e_1)
| product(e_4,e_2,e_2)
| product(e_4,e_2,e_3)
| product(e_4,e_2,e_4) ),
inference(resolution,status(thm),[c0,element_4]) ).
cnf(c64,plain,
( product(e_4,e_2,e_1)
| product(e_4,e_2,e_2)
| product(e_4,e_2,e_3)
| ~ product(e_4,X159,e_4)
| equalish(X159,e_2) ),
inference(resolution,status(thm),[c6,product_right_cancellation]) ).
cnf(c66,plain,
( product(e_4,e_2,e_1)
| product(e_4,e_2,e_2)
| product(e_4,e_2,e_3)
| ~ product(X168,e_2,e_4)
| product(X168,e_4,e_4) ),
inference(resolution,status(thm),[c6,qg3]) ).
cnf(c941,plain,
( product(e_4,e_2,e_1)
| product(e_4,e_2,e_2)
| product(e_4,e_2,e_3)
| product(e_4,e_4,e_4) ),
inference(resolution,status(thm),[c66,c6]) ).
cnf(c3209,plain,
( product(e_4,e_2,e_1)
| product(e_4,e_2,e_2)
| product(e_4,e_2,e_3)
| equalish(e_4,e_2) ),
inference(resolution,status(thm),[c941,c64]) ).
cnf(c3267,plain,
( product(e_4,e_2,e_1)
| product(e_4,e_2,e_2)
| product(e_4,e_2,e_3) ),
inference(resolution,status(thm),[c3209,e_4_is_not_e_2]) ).
cnf(c3276,plain,
( product(e_4,e_2,e_2)
| product(e_4,e_2,e_3)
| ~ product(X319,e_2,e_1)
| equalish(X319,e_4) ),
inference(resolution,status(thm),[c3267,product_left_cancellation]) ).
cnf(c3346,plain,
( product(e_4,e_2,e_2)
| product(e_4,e_2,e_3)
| equalish(e_4,e_4) ),
inference(resolution,status(thm),[c3276,c3267]) ).
cnf(c3357,plain,
( product(e_4,e_2,e_3)
| equalish(e_4,e_4)
| ~ product(X322,e_2,e_2)
| equalish(X322,e_4) ),
inference(resolution,status(thm),[c3346,product_left_cancellation]) ).
cnf(c3410,plain,
( product(e_4,e_2,e_3)
| equalish(e_4,e_4) ),
inference(resolution,status(thm),[c3357,c3346]) ).
cnf(c3421,plain,
( equalish(e_4,e_4)
| ~ product(X325,e_2,e_3)
| equalish(X325,e_4) ),
inference(resolution,status(thm),[c3410,product_left_cancellation]) ).
cnf(c3443,plain,
equalish(e_4,e_4),
inference(resolution,status(thm),[c3421,c3410]) ).
cnf(c51,plain,
( product(e_3,e_2,e_1)
| product(e_3,e_2,e_2)
| product(e_3,e_2,e_3)
| ~ product(X131,e_2,e_4)
| equalish(X131,e_3) ),
inference(resolution,status(thm),[c5,product_left_cancellation]) ).
cnf(c747,plain,
( product(e_3,e_2,e_1)
| product(e_3,e_2,e_2)
| product(e_3,e_2,e_3)
| equalish(e_3,e_3) ),
inference(resolution,status(thm),[c51,c5]) ).
cnf(c350,plain,
( product(e_2,e_1,e_1)
| product(e_2,e_1,e_2)
| ~ product(e_2,e_1,X83)
| equalish(X83,e_3) ),
inference(resolution,status(thm),[c336,product_total_function2]) ).
cnf(c538,plain,
( product(e_2,e_1,e_1)
| product(e_2,e_1,e_2)
| equalish(e_3,e_3) ),
inference(resolution,status(thm),[c350,c336]) ).
cnf(c559,plain,
( product(e_2,e_1,e_1)
| equalish(e_3,e_3)
| ~ product(e_2,X92,e_2)
| equalish(X92,e_1) ),
inference(resolution,status(thm),[c538,product_right_cancellation]) ).
cnf(c555,plain,
( product(e_2,e_1,e_1)
| equalish(e_3,e_3)
| ~ product(X106,e_1,e_2)
| product(X106,e_2,e_2) ),
inference(resolution,status(thm),[c538,qg3]) ).
cnf(c638,plain,
( product(e_2,e_1,e_1)
| equalish(e_3,e_3)
| product(e_2,e_2,e_2) ),
inference(resolution,status(thm),[c555,c538]) ).
cnf(c668,plain,
( product(e_2,e_1,e_1)
| equalish(e_3,e_3)
| equalish(e_2,e_1) ),
inference(resolution,status(thm),[c638,c559]) ).
cnf(c690,plain,
( product(e_2,e_1,e_1)
| equalish(e_3,e_3) ),
inference(resolution,status(thm),[c668,e_2_is_not_e_1]) ).
cnf(c695,plain,
( equalish(e_3,e_3)
| ~ product(e_2,X111,e_1)
| equalish(X111,e_1) ),
inference(resolution,status(thm),[c690,product_right_cancellation]) ).
cnf(c29,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,e_2,X60)
| equalish(X60,e_3) ),
inference(resolution,status(thm),[c4,product_total_function2]) ).
cnf(c458,plain,
( product(e_2,e_2,e_1)
| product(e_2,e_2,e_2)
| product(e_2,e_2,e_4)
| equalish(e_3,e_3) ),
inference(resolution,status(thm),[c29,c4]) ).
cnf(c976,plain,
( product(e_2,e_2,e_2)
| product(e_2,e_2,e_4)
| equalish(e_3,e_3)
| equalish(e_2,e_1) ),
inference(resolution,status(thm),[c458,c695]) ).
cnf(c1049,plain,
( product(e_2,e_2,e_2)
| product(e_2,e_2,e_4)
| equalish(e_3,e_3) ),
inference(resolution,status(thm),[c976,e_2_is_not_e_1]) ).
cnf(c1079,plain,
( product(e_2,e_2,e_2)
| equalish(e_3,e_3)
| ~ product(X202,e_2,e_4)
| equalish(X202,e_2) ),
inference(resolution,status(thm),[c1049,product_left_cancellation]) ).
cnf(c1072,plain,
( product(e_2,e_2,e_2)
| equalish(e_3,e_3)
| ~ product(X207,e_2,e_2)
| product(X207,e_2,e_4) ),
inference(resolution,status(thm),[c1049,qg3]) ).
cnf(c39,plain,
( product(e_3,e_2,e_2)
| product(e_3,e_2,e_3)
| product(e_3,e_2,e_4)
| ~ product(X96,e_2,e_1)
| equalish(X96,e_3) ),
inference(resolution,status(thm),[c5,product_left_cancellation]) ).
cnf(c613,plain,
( product(e_3,e_2,e_2)
| product(e_3,e_2,e_3)
| product(e_3,e_2,e_4)
| equalish(e_3,e_3) ),
inference(resolution,status(thm),[c39,c5]) ).
cnf(c1271,plain,
( product(e_3,e_2,e_3)
| product(e_3,e_2,e_4)
| equalish(e_3,e_3)
| product(e_2,e_2,e_2) ),
inference(resolution,status(thm),[c613,c1072]) ).
cnf(c1977,plain,
( product(e_3,e_2,e_3)
| equalish(e_3,e_3)
| product(e_2,e_2,e_2)
| equalish(e_3,e_2) ),
inference(resolution,status(thm),[c1271,c1079]) ).
cnf(c2052,plain,
( product(e_3,e_2,e_3)
| equalish(e_3,e_3)
| product(e_2,e_2,e_2) ),
inference(resolution,status(thm),[c1977,e_3_is_not_e_2]) ).
cnf(c2053,plain,
( equalish(e_3,e_3)
| product(e_2,e_2,e_2)
| ~ product(e_3,e_2,X225)
| equalish(X225,e_3) ),
inference(resolution,status(thm),[c2052,product_total_function2]) ).
cnf(c2114,plain,
( equalish(e_3,e_3)
| product(e_2,e_2,e_2) ),
inference(resolution,status(thm),[c2053,c2052]) ).
cnf(c2129,plain,
( equalish(e_3,e_3)
| ~ product(X229,e_2,e_2)
| equalish(X229,e_2) ),
inference(resolution,status(thm),[c2114,product_left_cancellation]) ).
cnf(c2155,plain,
( equalish(e_3,e_3)
| equalish(e_3,e_2)
| product(e_3,e_2,e_1)
| product(e_3,e_2,e_3) ),
inference(resolution,status(thm),[c2129,c747]) ).
cnf(c2190,plain,
( equalish(e_3,e_3)
| product(e_3,e_2,e_1)
| product(e_3,e_2,e_3) ),
inference(resolution,status(thm),[c2155,e_3_is_not_e_2]) ).
cnf(c2233,plain,
( equalish(e_3,e_3)
| product(e_3,e_2,e_3)
| ~ product(X245,e_2,e_1)
| equalish(X245,e_3) ),
inference(resolution,status(thm),[c2190,product_left_cancellation]) ).
cnf(c2284,plain,
( equalish(e_3,e_3)
| product(e_3,e_2,e_3) ),
inference(resolution,status(thm),[c2233,c2190]) ).
cnf(c2295,plain,
( equalish(e_3,e_3)
| ~ product(e_3,e_2,X246)
| equalish(X246,e_3) ),
inference(resolution,status(thm),[c2284,product_total_function2]) ).
cnf(c2318,plain,
equalish(e_3,e_3),
inference(resolution,status(thm),[c2295,c2284]) ).
cnf(c341,plain,
( product(e_2,e_1,e_2)
| product(e_2,e_1,e_3)
| ~ product(X58,e_1,e_1)
| equalish(X58,e_2) ),
inference(resolution,status(thm),[c336,product_left_cancellation]) ).
cnf(c434,plain,
( product(e_2,e_1,e_2)
| product(e_2,e_1,e_3)
| equalish(e_2,e_2) ),
inference(resolution,status(thm),[c341,c336]) ).
cnf(c440,plain,
( product(e_2,e_1,e_3)
| equalish(e_2,e_2)
| ~ product(e_2,e_1,X64)
| equalish(X64,e_2) ),
inference(resolution,status(thm),[c434,product_total_function2]) ).
cnf(c475,plain,
( product(e_2,e_1,e_3)
| equalish(e_2,e_2) ),
inference(resolution,status(thm),[c440,c434]) ).
cnf(c484,plain,
( equalish(e_2,e_2)
| ~ product(X69,e_1,e_3)
| equalish(X69,e_2) ),
inference(resolution,status(thm),[c475,product_left_cancellation]) ).
cnf(c505,plain,
equalish(e_2,e_2),
inference(resolution,status(thm),[c484,c475]) ).
cnf(c338,plain,
( product(e_2,e_1,e_2)
| product(e_2,e_1,e_3)
| ~ product(e_2,X38,e_1)
| equalish(X38,e_1) ),
inference(resolution,status(thm),[c336,product_right_cancellation]) ).
cnf(c369,plain,
( product(e_2,e_1,e_2)
| product(e_2,e_1,e_3)
| equalish(e_1,e_1) ),
inference(resolution,status(thm),[c338,c336]) ).
cnf(c371,plain,
( product(e_2,e_1,e_3)
| equalish(e_1,e_1)
| ~ product(e_2,X42,e_2)
| equalish(X42,e_1) ),
inference(resolution,status(thm),[c369,product_right_cancellation]) ).
cnf(c390,plain,
( product(e_2,e_1,e_3)
| equalish(e_1,e_1) ),
inference(resolution,status(thm),[c371,c369]) ).
cnf(c398,plain,
( equalish(e_1,e_1)
| ~ product(e_2,X45,e_3)
| equalish(X45,e_1) ),
inference(resolution,status(thm),[c390,product_right_cancellation]) ).
cnf(c415,plain,
equalish(e_1,e_1),
inference(resolution,status(thm),[c398,c390]) ).
cnf(e_1_is_not_e_4,axiom,
~ equalish(e_1,e_4),
input ).
cnf(e_3_then_e_4,axiom,
next(e_3,e_4),
input ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP128-2.004 : TPTP v8.1.0. Released v1.2.0.
% 0.07/0.12 % Command : pyres-fof.py -tifbsVp -nlargest -HPickGiven5 %s
% 0.13/0.33 % Computer : n029.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Mon Jun 13 15:43:25 EDT 2022
% 0.13/0.34 % CPUTime :
% 81.96/82.17 # Version: 1.3
% 81.96/82.17 # SZS status Satisfiable
% 81.96/82.17 # SZS output start Saturation
% See solution above
% 81.96/82.17
% 81.96/82.17 # Initial clauses : 31
% 81.96/82.17 # Processed clauses : 1144
% 81.96/82.17 # Factors computed : 0
% 81.96/82.17 # Resolvents computed: 24138
% 81.96/82.17 # Tautologies deleted: 99
% 81.96/82.17 # Forward subsumed : 22926
% 81.96/82.17 # Backward subsumed : 1019
% 81.96/82.17 # -------- CPU Time ---------
% 81.96/82.17 # User time : 81.669 s
% 81.96/82.17 # System time : 0.135 s
% 81.96/82.17 # Total time : 81.804 s
%------------------------------------------------------------------------------