%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP129-1.003 : TPTP v9.3.1. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n016.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 07:27:52 AM UTC 2026
% Result : Unsatisfiable 0.14s 5.62s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 40
% Number of leaves : 11
% Syntax : Number of formulae : 177 ( 19 unt; 0 def)
% Number of atoms : 604 ( 0 equ)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 517 ( 90 ~; 427 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 67 ( 0 sgn 18 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(product_total_function2,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( equalish(VAR_2,VAR_3)
| ~ product(VAR_0,VAR_1,VAR_3)
| ~ product(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',product_total_function2) ).
cnf(c_1,plain,
( equalish(C,D)
| ~ product(A,B,D)
| ~ product(A,B,C) ),
inference(clausify,[status(thm)],[product_total_function2]) ).
fof(e_3_is_not_e_2,axiom,
~ equalish(e_3,e_2),
file('theBenchmark.p',e_3_is_not_e_2) ).
cnf(c_2,plain,
~ equalish(e_3,e_2),
inference(clausify,[status(thm)],[e_3_is_not_e_2]) ).
fof(e_3_is_not_e_1,axiom,
~ equalish(e_3,e_1),
file('theBenchmark.p',e_3_is_not_e_1) ).
cnf(c_3,plain,
~ equalish(e_3,e_1),
inference(clausify,[status(thm)],[e_3_is_not_e_1]) ).
fof(e_2_is_not_e_1,axiom,
~ equalish(e_2,e_1),
file('theBenchmark.p',e_2_is_not_e_1) ).
cnf(c_5,plain,
~ equalish(e_2,e_1),
inference(clausify,[status(thm)],[e_2_is_not_e_1]) ).
fof(product_right_cancellation,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( equalish(VAR_1,VAR_3)
| ~ product(VAR_0,VAR_3,VAR_2)
| ~ product(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',product_right_cancellation) ).
cnf(c_8,plain,
( equalish(B,D)
| ~ product(A,D,C)
| ~ product(A,B,C) ),
inference(clausify,[status(thm)],[product_right_cancellation]) ).
fof(product_left_cancellation,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( equalish(VAR_0,VAR_3)
| ~ product(VAR_3,VAR_1,VAR_2)
| ~ product(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',product_left_cancellation) ).
cnf(c_9,plain,
( equalish(A,D)
| ~ product(D,B,C)
| ~ product(A,B,C) ),
inference(clausify,[status(thm)],[product_left_cancellation]) ).
cnf(c_10,plain,
( ~ product(e_1,A,B)
| ~ product(e_2,A,B) ),
inference(resolve,[status(thm)],[c_9,c_5]) ).
cnf(c_11,plain,
( ~ product(e_1,A,B)
| ~ product(e_3,A,B) ),
inference(resolve,[status(thm)],[c_9,c_3]) ).
cnf(c_12,plain,
( ~ product(e_2,A,B)
| ~ product(e_3,A,B) ),
inference(resolve,[status(thm)],[c_9,c_2]) ).
cnf(c_13,plain,
( ~ product(A,e_1,B)
| ~ product(A,e_2,B) ),
inference(resolve,[status(thm)],[c_8,c_5]) ).
cnf(c_14,plain,
( ~ product(A,e_1,B)
| ~ product(A,e_3,B) ),
inference(resolve,[status(thm)],[c_8,c_3]) ).
cnf(c_15,plain,
( ~ product(A,e_2,B)
| ~ product(A,e_3,B) ),
inference(resolve,[status(thm)],[c_8,c_2]) ).
cnf(c_16,plain,
( ~ product(A,B,e_1)
| ~ product(A,B,e_2) ),
inference(resolve,[status(thm)],[c_1,c_5]) ).
fof(qg3,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( product(VAR_2,VAR_0,VAR_3)
| ~ product(VAR_1,VAR_2,VAR_3)
| ~ product(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',qg3) ).
cnf(c_19,plain,
( product(C,A,D)
| ~ product(B,C,D)
| ~ product(A,B,C) ),
inference(clausify,[status(thm)],[qg3]) ).
fof(product_total_function1,axiom,
! [VAR_0,VAR_1] :
( product(VAR_0,VAR_1,e_3)
| product(VAR_0,VAR_1,e_2)
| product(VAR_0,VAR_1,e_1)
| ~ group_element(VAR_1)
| ~ group_element(VAR_0) ),
file('theBenchmark.p',product_total_function1) ).
cnf(c_20,plain,
( product(A,B,e_3)
| product(A,B,e_2)
| product(A,B,e_1)
| ~ group_element(B)
| ~ group_element(A) ),
inference(clausify,[status(thm)],[product_total_function1]) ).
fof(element_3,axiom,
group_element(e_3),
file('theBenchmark.p',element_3) ).
cnf(c_21,plain,
group_element(e_3),
inference(clausify,[status(thm)],[element_3]) ).
fof(element_2,axiom,
group_element(e_2),
file('theBenchmark.p',element_2) ).
cnf(c_22,plain,
group_element(e_2),
inference(clausify,[status(thm)],[element_2]) ).
fof(element_1,axiom,
group_element(e_1),
file('theBenchmark.p',element_1) ).
cnf(c_23,plain,
group_element(e_1),
inference(clausify,[status(thm)],[element_1]) ).
cnf(c_24,plain,
( product(A,A,e_3)
| product(A,A,e_2)
| product(A,A,e_1)
| ~ group_element(A) ),
inference(factor,[status(thm)],[c_20]) ).
cnf(c_25,plain,
( product(A,e_3,e_3)
| product(A,e_3,e_2)
| product(A,e_3,e_1)
| ~ group_element(A) ),
inference(resolve,[status(thm)],[c_21,c_20]) ).
cnf(c_26,plain,
( product(e_3,A,e_3)
| product(e_3,A,e_2)
| product(e_3,A,e_1)
| ~ group_element(A) ),
inference(resolve,[status(thm)],[c_21,c_20]) ).
cnf(c_27,plain,
( product(A,e_2,e_3)
| product(A,e_2,e_2)
| product(A,e_2,e_1)
| ~ group_element(A) ),
inference(resolve,[status(thm)],[c_22,c_20]) ).
cnf(c_28,plain,
( product(e_2,A,e_3)
| product(e_2,A,e_2)
| product(e_2,A,e_1)
| ~ group_element(A) ),
inference(resolve,[status(thm)],[c_22,c_20]) ).
cnf(c_31,plain,
( product(e_1,e_1,e_3)
| product(e_1,e_1,e_2)
| product(e_1,e_1,e_1) ),
inference(resolve,[status(thm)],[c_24,c_23]) ).
cnf(c_32,plain,
( product(e_2,e_2,e_3)
| product(e_2,e_2,e_2)
| product(e_2,e_2,e_1) ),
inference(resolve,[status(thm)],[c_24,c_22]) ).
cnf(c_33,plain,
( product(e_3,e_3,e_3)
| product(e_3,e_3,e_2)
| product(e_3,e_3,e_1) ),
inference(resolve,[status(thm)],[c_24,c_21]) ).
cnf(c_34,plain,
( product(e_1,e_3,e_3)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_1) ),
inference(resolve,[status(thm)],[c_25,c_23]) ).
cnf(c_35,plain,
( product(e_2,e_3,e_3)
| product(e_2,e_3,e_2)
| product(e_2,e_3,e_1) ),
inference(resolve,[status(thm)],[c_25,c_22]) ).
cnf(c_37,plain,
( product(e_3,e_1,A)
| ~ product(e_1,e_3,A)
| product(e_1,e_1,e_2)
| product(e_1,e_1,e_1) ),
inference(resolve,[status(thm)],[c_31,c_19]) ).
cnf(c_38,plain,
( ~ product(e_1,e_3,e_3)
| product(e_1,e_1,e_2)
| product(e_1,e_1,e_1) ),
inference(resolve,[status(thm)],[c_31,c_14]) ).
cnf(c_39,plain,
( ~ product(e_1,e_2,e_3)
| product(e_1,e_1,e_2)
| product(e_1,e_1,e_1) ),
inference(resolve,[status(thm)],[c_31,c_13]) ).
cnf(c_41,plain,
( ~ product(e_2,e_1,e_3)
| product(e_1,e_1,e_2)
| product(e_1,e_1,e_1) ),
inference(resolve,[status(thm)],[c_31,c_10]) ).
cnf(c_43,plain,
( product(e_3,e_2,A)
| ~ product(e_2,e_3,A)
| product(e_2,e_2,e_2)
| product(e_2,e_2,e_1) ),
inference(resolve,[status(thm)],[c_32,c_19]) ).
cnf(c_44,plain,
( ~ product(e_2,e_3,e_3)
| product(e_2,e_2,e_2)
| product(e_2,e_2,e_1) ),
inference(resolve,[status(thm)],[c_32,c_15]) ).
cnf(c_51,plain,
( ~ product(e_2,e_3,e_3)
| product(e_3,e_3,e_2)
| product(e_3,e_3,e_1) ),
inference(resolve,[status(thm)],[c_33,c_12]) ).
cnf(c_52,plain,
( ~ product(e_1,e_3,e_3)
| product(e_3,e_3,e_2)
| product(e_3,e_3,e_1) ),
inference(resolve,[status(thm)],[c_33,c_11]) ).
cnf(c_53,plain,
( product(e_3,A,e_3)
| ~ product(A,e_1,e_3)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_1) ),
inference(resolve,[status(thm)],[c_34,c_19]) ).
cnf(c_54,plain,
( product(e_3,e_1,A)
| ~ product(e_3,e_3,A)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_1) ),
inference(resolve,[status(thm)],[c_34,c_19]) ).
cnf(c_60,plain,
( product(e_3,e_2,A)
| ~ product(e_3,e_3,A)
| product(e_2,e_3,e_2)
| product(e_2,e_3,e_1) ),
inference(resolve,[status(thm)],[c_35,c_19]) ).
cnf(c_65,plain,
( product(e_1,e_3,e_2)
| product(e_1,e_3,e_1)
| product(e_1,e_1,e_2)
| product(e_1,e_1,e_1) ),
inference(resolve,[status(thm)],[c_38,c_34]) ).
cnf(c_66,plain,
( product(e_3,e_1,e_3)
| product(e_3,e_1,e_2)
| product(e_3,e_1,e_1) ),
inference(resolve,[status(thm)],[c_26,c_23]) ).
cnf(c_68,plain,
( product(e_2,e_3,e_2)
| product(e_2,e_3,e_1)
| product(e_2,e_2,e_2)
| product(e_2,e_2,e_1) ),
inference(resolve,[status(thm)],[c_44,c_35]) ).
cnf(c_69,plain,
( product(e_1,e_2,e_3)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_1) ),
inference(resolve,[status(thm)],[c_27,c_23]) ).
cnf(c_70,plain,
( product(e_2,e_3,e_2)
| product(e_2,e_3,e_1)
| product(e_3,e_3,e_2)
| product(e_3,e_3,e_1) ),
inference(resolve,[status(thm)],[c_51,c_35]) ).
cnf(c_71,plain,
( product(e_1,e_3,e_2)
| product(e_1,e_3,e_1)
| product(e_3,e_3,e_2)
| product(e_3,e_3,e_1) ),
inference(resolve,[status(thm)],[c_52,c_34]) ).
cnf(c_72,plain,
( product(e_2,e_1,e_3)
| product(e_2,e_1,e_2)
| product(e_2,e_1,e_1) ),
inference(resolve,[status(thm)],[c_28,c_23]) ).
cnf(c_78,plain,
( ~ product(e_3,e_3,e_3)
| product(e_3,e_1,e_2)
| product(e_3,e_1,e_1) ),
inference(resolve,[status(thm)],[c_66,c_14]) ).
cnf(c_80,plain,
( ~ product(e_2,e_1,e_3)
| product(e_3,e_1,e_2)
| product(e_3,e_1,e_1) ),
inference(resolve,[status(thm)],[c_66,c_12]) ).
cnf(c_92,plain,
( product(e_1,e_1,e_2)
| product(e_1,e_1,e_1)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_1) ),
inference(resolve,[status(thm)],[c_69,c_39]) ).
cnf(c_94,plain,
( product(e_3,e_1,A)
| ~ product(e_2,e_3,A)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_1) ),
inference(resolve,[status(thm)],[c_69,c_19]) ).
cnf(c_101,plain,
( product(e_1,e_1,e_2)
| product(e_1,e_1,e_1)
| product(e_2,e_1,e_2)
| product(e_2,e_1,e_1) ),
inference(resolve,[status(thm)],[c_72,c_41]) ).
cnf(c_109,plain,
( product(e_2,e_1,e_2)
| product(e_2,e_1,e_1)
| product(e_3,e_1,e_2)
| product(e_3,e_1,e_1) ),
inference(resolve,[status(thm)],[c_80,c_72]) ).
cnf(c_112,plain,
( product(e_3,e_1,e_2)
| product(e_3,e_1,e_1)
| product(e_3,e_3,e_3)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_1) ),
inference(resolve,[status(thm)],[c_53,c_66]) ).
cnf(c_118,plain,
( ~ product(e_1,e_2,e_2)
| product(e_1,e_3,e_1)
| product(e_1,e_1,e_2)
| product(e_1,e_1,e_1) ),
inference(resolve,[status(thm)],[c_65,c_15]) ).
cnf(c_630,plain,
( product(e_3,e_2,e_2)
| product(e_2,e_2,e_2)
| product(e_2,e_2,e_1)
| product(e_2,e_3,e_1)
| product(e_2,e_2,e_2)
| product(e_2,e_2,e_1) ),
inference(resolve,[status(thm)],[c_68,c_43]) ).
cnf(c_631,plain,
( product(e_3,e_2,e_2)
| product(e_2,e_2,e_2)
| product(e_2,e_3,e_1)
| product(e_2,e_2,e_2)
| product(e_2,e_2,e_1) ),
inference(copy,[status(thm)],[c_630]) ).
cnf(c_121,plain,
( product(e_3,e_2,e_2)
| product(e_2,e_3,e_1)
| product(e_2,e_2,e_2)
| product(e_2,e_2,e_1) ),
inference(copy,[status(thm)],[c_631]) ).
cnf(c_123,plain,
( product(e_2,e_2,A)
| ~ product(e_3,e_2,A)
| product(e_2,e_3,e_1)
| product(e_2,e_2,e_2)
| product(e_2,e_2,e_1) ),
inference(resolve,[status(thm)],[c_68,c_19]) ).
cnf(c_128,plain,
( ~ product(e_3,e_2,e_2)
| product(e_2,e_3,e_1)
| product(e_2,e_2,e_2)
| product(e_2,e_2,e_1) ),
inference(factor,[status(thm)],[c_123]) ).
cnf(c_632,plain,
( product(e_3,e_2,e_2)
| product(e_2,e_3,e_2)
| product(e_2,e_3,e_1)
| product(e_2,e_3,e_2)
| product(e_2,e_3,e_1)
| product(e_3,e_3,e_1) ),
inference(resolve,[status(thm)],[c_70,c_60]) ).
cnf(c_633,plain,
( product(e_3,e_2,e_2)
| product(e_2,e_3,e_2)
| product(e_2,e_3,e_2)
| product(e_2,e_3,e_1)
| product(e_3,e_3,e_1) ),
inference(copy,[status(thm)],[c_632]) ).
cnf(c_129,plain,
( product(e_3,e_2,e_2)
| product(e_2,e_3,e_2)
| product(e_2,e_3,e_1)
| product(e_3,e_3,e_1) ),
inference(copy,[status(thm)],[c_633]) ).
cnf(c_132,plain,
( ~ product(e_3,e_2,e_2)
| product(e_2,e_3,e_2)
| product(e_2,e_3,e_1)
| product(e_3,e_3,e_1) ),
inference(resolve,[status(thm)],[c_70,c_15]) ).
cnf(c_634,plain,
( product(e_3,e_1,e_2)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_1)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_1)
| product(e_3,e_3,e_1) ),
inference(resolve,[status(thm)],[c_71,c_54]) ).
cnf(c_635,plain,
( product(e_3,e_1,e_2)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_1)
| product(e_3,e_3,e_1) ),
inference(copy,[status(thm)],[c_634]) ).
cnf(c_136,plain,
( product(e_3,e_1,e_2)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_1)
| product(e_3,e_3,e_1) ),
inference(copy,[status(thm)],[c_635]) ).
cnf(c_140,plain,
( ~ product(e_3,e_1,e_2)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_1)
| product(e_3,e_3,e_1) ),
inference(resolve,[status(thm)],[c_71,c_14]) ).
cnf(c_203,plain,
( product(e_1,A,e_2)
| ~ product(A,e_2,e_1)
| product(e_1,e_1,e_2)
| product(e_1,e_1,e_1)
| product(e_2,e_1,e_1) ),
inference(resolve,[status(thm)],[c_101,c_19]) ).
cnf(c_208,plain,
( ~ product(e_1,e_2,e_1)
| product(e_1,e_1,e_2)
| product(e_1,e_1,e_1)
| product(e_2,e_1,e_1) ),
inference(factor,[status(thm)],[c_203]) ).
cnf(c_220,plain,
( ~ product(e_1,e_1,e_2)
| product(e_2,e_1,e_2)
| product(e_2,e_1,e_1)
| product(e_3,e_1,e_1) ),
inference(resolve,[status(thm)],[c_109,c_11]) ).
cnf(c_636,plain,
( product(e_1,e_1,e_2)
| product(e_1,e_1,e_1)
| product(e_1,e_2,e_1)
| product(e_1,e_3,e_1)
| product(e_1,e_1,e_2)
| product(e_1,e_1,e_1) ),
inference(resolve,[status(thm)],[c_118,c_92]) ).
cnf(c_637,plain,
( product(e_1,e_1,e_2)
| product(e_1,e_2,e_1)
| product(e_1,e_3,e_1)
| product(e_1,e_1,e_2)
| product(e_1,e_1,e_1) ),
inference(copy,[status(thm)],[c_636]) ).
cnf(c_231,plain,
( product(e_1,e_2,e_1)
| product(e_1,e_3,e_1)
| product(e_1,e_1,e_2)
| product(e_1,e_1,e_1) ),
inference(copy,[status(thm)],[c_637]) ).
cnf(c_638,plain,
( product(e_2,e_3,e_1)
| product(e_2,e_2,e_2)
| product(e_2,e_2,e_1)
| product(e_2,e_3,e_1)
| product(e_2,e_2,e_2)
| product(e_2,e_2,e_1) ),
inference(resolve,[status(thm)],[c_128,c_121]) ).
cnf(c_639,plain,
( product(e_2,e_3,e_1)
| product(e_2,e_2,e_2)
| product(e_2,e_3,e_1)
| product(e_2,e_2,e_2)
| product(e_2,e_2,e_1) ),
inference(copy,[status(thm)],[c_638]) ).
cnf(c_640,plain,
( product(e_2,e_3,e_1)
| product(e_2,e_3,e_1)
| product(e_2,e_2,e_2)
| product(e_2,e_2,e_1) ),
inference(copy,[status(thm)],[c_639]) ).
cnf(c_248,plain,
( product(e_2,e_3,e_1)
| product(e_2,e_2,e_2)
| product(e_2,e_2,e_1) ),
inference(copy,[status(thm)],[c_640]) ).
cnf(c_256,plain,
( ~ product(e_1,e_3,e_1)
| product(e_2,e_2,e_2)
| product(e_2,e_2,e_1) ),
inference(resolve,[status(thm)],[c_248,c_10]) ).
cnf(c_641,plain,
( product(e_3,e_1,e_2)
| product(e_3,e_1,e_1)
| product(e_3,e_1,e_2)
| product(e_3,e_1,e_1)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_1) ),
inference(resolve,[status(thm)],[c_112,c_78]) ).
cnf(c_642,plain,
( product(e_3,e_1,e_2)
| product(e_3,e_1,e_2)
| product(e_3,e_1,e_1)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_1) ),
inference(copy,[status(thm)],[c_641]) ).
cnf(c_257,plain,
( product(e_3,e_1,e_2)
| product(e_3,e_1,e_1)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_1) ),
inference(copy,[status(thm)],[c_642]) ).
cnf(c_643,plain,
( product(e_3,e_2,e_1)
| product(e_2,e_3,e_2)
| product(e_2,e_3,e_1)
| product(e_3,e_2,e_2)
| product(e_2,e_3,e_2)
| product(e_2,e_3,e_1) ),
inference(resolve,[status(thm)],[c_129,c_60]) ).
cnf(c_644,plain,
( product(e_3,e_2,e_1)
| product(e_2,e_3,e_2)
| product(e_3,e_2,e_2)
| product(e_2,e_3,e_2)
| product(e_2,e_3,e_1) ),
inference(copy,[status(thm)],[c_643]) ).
cnf(c_268,plain,
( product(e_3,e_2,e_1)
| product(e_3,e_2,e_2)
| product(e_2,e_3,e_2)
| product(e_2,e_3,e_1) ),
inference(copy,[status(thm)],[c_644]) ).
cnf(c_271,plain,
( ~ product(e_3,e_2,e_1)
| product(e_3,e_2,e_2)
| product(e_2,e_3,e_2)
| product(e_2,e_3,e_1) ),
inference(resolve,[status(thm)],[c_129,c_15]) ).
cnf(c_282,plain,
( ~ product(e_3,e_1,e_1)
| product(e_3,e_1,e_2)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_1) ),
inference(resolve,[status(thm)],[c_136,c_14]) ).
cnf(c_645,plain,
( product(e_3,e_1,e_1)
| product(e_1,e_1,e_2)
| product(e_1,e_1,e_1)
| product(e_1,e_2,e_1)
| product(e_1,e_1,e_2)
| product(e_1,e_1,e_1) ),
inference(resolve,[status(thm)],[c_231,c_37]) ).
cnf(c_646,plain,
( product(e_3,e_1,e_1)
| product(e_1,e_1,e_2)
| product(e_1,e_2,e_1)
| product(e_1,e_1,e_2)
| product(e_1,e_1,e_1) ),
inference(copy,[status(thm)],[c_645]) ).
cnf(c_312,plain,
( product(e_3,e_1,e_1)
| product(e_1,e_2,e_1)
| product(e_1,e_1,e_2)
| product(e_1,e_1,e_1) ),
inference(copy,[status(thm)],[c_646]) ).
cnf(c_314,plain,
( product(e_1,e_1,A)
| ~ product(e_3,e_1,A)
| product(e_1,e_2,e_1)
| product(e_1,e_1,e_2)
| product(e_1,e_1,e_1) ),
inference(resolve,[status(thm)],[c_231,c_19]) ).
cnf(c_317,plain,
( ~ product(e_3,e_1,e_1)
| product(e_1,e_2,e_1)
| product(e_1,e_1,e_2)
| product(e_1,e_1,e_1) ),
inference(factor,[status(thm)],[c_314]) ).
cnf(c_647,plain,
( product(e_1,e_3,e_2)
| product(e_1,e_3,e_1)
| product(e_3,e_3,e_1)
| product(e_3,e_1,e_1)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_1) ),
inference(resolve,[status(thm)],[c_257,c_140]) ).
cnf(c_648,plain,
( product(e_1,e_3,e_2)
| product(e_3,e_3,e_1)
| product(e_3,e_1,e_1)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_1) ),
inference(copy,[status(thm)],[c_647]) ).
cnf(c_323,plain,
( product(e_3,e_3,e_1)
| product(e_3,e_1,e_1)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_1) ),
inference(copy,[status(thm)],[c_648]) ).
cnf(c_649,plain,
( product(e_2,e_3,e_2)
| product(e_2,e_3,e_1)
| product(e_3,e_3,e_1)
| product(e_3,e_2,e_1)
| product(e_2,e_3,e_2)
| product(e_2,e_3,e_1) ),
inference(resolve,[status(thm)],[c_268,c_132]) ).
cnf(c_650,plain,
( product(e_2,e_3,e_2)
| product(e_3,e_3,e_1)
| product(e_3,e_2,e_1)
| product(e_2,e_3,e_2)
| product(e_2,e_3,e_1) ),
inference(copy,[status(thm)],[c_649]) ).
cnf(c_335,plain,
( product(e_3,e_3,e_1)
| product(e_3,e_2,e_1)
| product(e_2,e_3,e_2)
| product(e_2,e_3,e_1) ),
inference(copy,[status(thm)],[c_650]) ).
cnf(c_651,plain,
( product(e_1,e_2,e_1)
| product(e_1,e_1,e_2)
| product(e_1,e_1,e_1)
| product(e_1,e_2,e_1)
| product(e_1,e_1,e_2)
| product(e_1,e_1,e_1) ),
inference(resolve,[status(thm)],[c_317,c_312]) ).
cnf(c_652,plain,
( product(e_1,e_2,e_1)
| product(e_1,e_1,e_2)
| product(e_1,e_2,e_1)
| product(e_1,e_1,e_2)
| product(e_1,e_1,e_1) ),
inference(copy,[status(thm)],[c_651]) ).
cnf(c_653,plain,
( product(e_1,e_2,e_1)
| product(e_1,e_2,e_1)
| product(e_1,e_1,e_2)
| product(e_1,e_1,e_1) ),
inference(copy,[status(thm)],[c_652]) ).
cnf(c_401,plain,
( product(e_1,e_2,e_1)
| product(e_1,e_1,e_2)
| product(e_1,e_1,e_1) ),
inference(copy,[status(thm)],[c_653]) ).
cnf(c_654,plain,
( product(e_1,e_1,e_2)
| product(e_1,e_1,e_1)
| product(e_2,e_1,e_1)
| product(e_1,e_1,e_2)
| product(e_1,e_1,e_1) ),
inference(resolve,[status(thm)],[c_401,c_208]) ).
cnf(c_655,plain,
( product(e_1,e_1,e_2)
| product(e_2,e_1,e_1)
| product(e_1,e_1,e_2)
| product(e_1,e_1,e_1) ),
inference(copy,[status(thm)],[c_654]) ).
cnf(c_403,plain,
( product(e_2,e_1,e_1)
| product(e_1,e_1,e_2)
| product(e_1,e_1,e_1) ),
inference(copy,[status(thm)],[c_655]) ).
cnf(c_406,plain,
( product(e_1,e_1,A)
| ~ product(e_2,e_1,A)
| product(e_1,e_1,e_2)
| product(e_1,e_1,e_1) ),
inference(resolve,[status(thm)],[c_401,c_19]) ).
cnf(c_411,plain,
( ~ product(e_2,e_1,e_1)
| product(e_1,e_1,e_2)
| product(e_1,e_1,e_1) ),
inference(factor,[status(thm)],[c_406]) ).
cnf(c_656,plain,
( product(e_1,e_1,e_2)
| product(e_1,e_1,e_1)
| product(e_1,e_1,e_2)
| product(e_1,e_1,e_1) ),
inference(resolve,[status(thm)],[c_411,c_403]) ).
cnf(c_657,plain,
( product(e_1,e_1,e_2)
| product(e_1,e_1,e_2)
| product(e_1,e_1,e_1) ),
inference(copy,[status(thm)],[c_656]) ).
cnf(c_419,plain,
( product(e_1,e_1,e_2)
| product(e_1,e_1,e_1) ),
inference(copy,[status(thm)],[c_657]) ).
cnf(c_425,plain,
( product(e_2,e_1,e_2)
| product(e_2,e_1,e_1)
| product(e_3,e_1,e_1)
| product(e_1,e_1,e_1) ),
inference(resolve,[status(thm)],[c_419,c_220]) ).
cnf(c_428,plain,
( product(e_1,A,e_2)
| ~ product(A,e_1,e_1)
| product(e_1,e_1,e_1) ),
inference(resolve,[status(thm)],[c_419,c_19]) ).
cnf(c_431,plain,
( ~ product(e_1,e_3,e_2)
| product(e_1,e_1,e_1) ),
inference(resolve,[status(thm)],[c_419,c_14]) ).
cnf(c_434,plain,
( ~ product(e_2,e_1,e_2)
| product(e_1,e_1,e_1) ),
inference(resolve,[status(thm)],[c_419,c_10]) ).
cnf(c_658,plain,
( product(e_3,e_1,e_1)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_1)
| product(e_3,e_1,e_1)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_1) ),
inference(resolve,[status(thm)],[c_323,c_54]) ).
cnf(c_659,plain,
( product(e_3,e_1,e_1)
| product(e_1,e_3,e_2)
| product(e_3,e_1,e_1)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_1) ),
inference(copy,[status(thm)],[c_658]) ).
cnf(c_660,plain,
( product(e_3,e_1,e_1)
| product(e_3,e_1,e_1)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_1) ),
inference(copy,[status(thm)],[c_659]) ).
cnf(c_439,plain,
( product(e_3,e_1,e_1)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_1) ),
inference(copy,[status(thm)],[c_660]) ).
cnf(c_661,plain,
( product(e_1,e_3,e_2)
| product(e_1,e_1,e_1)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_1) ),
inference(resolve,[status(thm)],[c_439,c_428]) ).
cnf(c_440,plain,
( product(e_1,e_1,e_1)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_1) ),
inference(copy,[status(thm)],[c_661]) ).
cnf(c_662,plain,
( product(e_3,e_1,e_2)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_1)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_1) ),
inference(resolve,[status(thm)],[c_439,c_282]) ).
cnf(c_663,plain,
( product(e_3,e_1,e_2)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_1) ),
inference(copy,[status(thm)],[c_662]) ).
cnf(c_442,plain,
( product(e_3,e_1,e_2)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_1) ),
inference(copy,[status(thm)],[c_663]) ).
cnf(c_447,plain,
( ~ product(e_3,e_1,e_2)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_1) ),
inference(resolve,[status(thm)],[c_439,c_16]) ).
cnf(c_664,plain,
( product(e_1,e_1,e_1)
| product(e_1,e_1,e_1)
| product(e_1,e_3,e_1) ),
inference(resolve,[status(thm)],[c_440,c_431]) ).
cnf(c_453,plain,
( product(e_1,e_1,e_1)
| product(e_1,e_3,e_1) ),
inference(copy,[status(thm)],[c_664]) ).
cnf(c_456,plain,
( product(e_2,e_2,e_2)
| product(e_2,e_2,e_1)
| product(e_1,e_1,e_1) ),
inference(resolve,[status(thm)],[c_453,c_256]) ).
cnf(c_461,plain,
( product(e_1,e_1,A)
| ~ product(e_3,e_1,A)
| product(e_1,e_1,e_1) ),
inference(resolve,[status(thm)],[c_453,c_19]) ).
cnf(c_465,plain,
( ~ product(e_2,e_3,e_1)
| product(e_1,e_1,e_1) ),
inference(resolve,[status(thm)],[c_453,c_10]) ).
cnf(c_466,plain,
( ~ product(e_3,e_1,e_1)
| product(e_1,e_1,e_1) ),
inference(factor,[status(thm)],[c_461]) ).
cnf(c_665,plain,
( product(e_1,e_3,e_2)
| product(e_1,e_3,e_1)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_1) ),
inference(resolve,[status(thm)],[c_447,c_442]) ).
cnf(c_666,plain,
( product(e_1,e_3,e_2)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_1) ),
inference(copy,[status(thm)],[c_665]) ).
cnf(c_479,plain,
( product(e_1,e_3,e_2)
| product(e_1,e_3,e_1) ),
inference(copy,[status(thm)],[c_666]) ).
cnf(c_491,plain,
( ~ product(e_1,e_2,e_2)
| product(e_1,e_3,e_1) ),
inference(resolve,[status(thm)],[c_479,c_15]) ).
cnf(c_494,plain,
( ~ product(e_2,e_3,e_2)
| product(e_1,e_3,e_1) ),
inference(resolve,[status(thm)],[c_479,c_10]) ).
cnf(c_497,plain,
( ~ product(e_2,e_3,e_2)
| product(e_2,e_2,e_1)
| product(e_1,e_1,e_1) ),
inference(resolve,[status(thm)],[c_456,c_15]) ).
cnf(c_667,plain,
( product(e_3,e_2,e_1)
| product(e_2,e_3,e_2)
| product(e_2,e_3,e_1)
| product(e_3,e_2,e_1)
| product(e_2,e_3,e_2)
| product(e_2,e_3,e_1) ),
inference(resolve,[status(thm)],[c_335,c_60]) ).
cnf(c_668,plain,
( product(e_3,e_2,e_1)
| product(e_2,e_3,e_2)
| product(e_3,e_2,e_1)
| product(e_2,e_3,e_2)
| product(e_2,e_3,e_1) ),
inference(copy,[status(thm)],[c_667]) ).
cnf(c_669,plain,
( product(e_3,e_2,e_1)
| product(e_3,e_2,e_1)
| product(e_2,e_3,e_2)
| product(e_2,e_3,e_1) ),
inference(copy,[status(thm)],[c_668]) ).
cnf(c_515,plain,
( product(e_3,e_2,e_1)
| product(e_2,e_3,e_2)
| product(e_2,e_3,e_1) ),
inference(copy,[status(thm)],[c_669]) ).
cnf(c_670,plain,
( product(e_3,e_2,e_2)
| product(e_2,e_3,e_2)
| product(e_2,e_3,e_1)
| product(e_2,e_3,e_2)
| product(e_2,e_3,e_1) ),
inference(resolve,[status(thm)],[c_515,c_271]) ).
cnf(c_671,plain,
( product(e_3,e_2,e_2)
| product(e_2,e_3,e_2)
| product(e_2,e_3,e_2)
| product(e_2,e_3,e_1) ),
inference(copy,[status(thm)],[c_670]) ).
cnf(c_517,plain,
( product(e_3,e_2,e_2)
| product(e_2,e_3,e_2)
| product(e_2,e_3,e_1) ),
inference(copy,[status(thm)],[c_671]) ).
cnf(c_523,plain,
( ~ product(e_3,e_2,e_2)
| product(e_2,e_3,e_2)
| product(e_2,e_3,e_1) ),
inference(resolve,[status(thm)],[c_515,c_16]) ).
cnf(c_672,plain,
( product(e_2,e_3,e_2)
| product(e_2,e_3,e_1)
| product(e_2,e_3,e_2)
| product(e_2,e_3,e_1) ),
inference(resolve,[status(thm)],[c_523,c_517]) ).
cnf(c_673,plain,
( product(e_2,e_3,e_2)
| product(e_2,e_3,e_2)
| product(e_2,e_3,e_1) ),
inference(copy,[status(thm)],[c_672]) ).
cnf(c_545,plain,
( product(e_2,e_3,e_2)
| product(e_2,e_3,e_1) ),
inference(copy,[status(thm)],[c_673]) ).
cnf(c_546,plain,
( product(e_2,e_2,e_1)
| product(e_1,e_1,e_1)
| product(e_2,e_3,e_1) ),
inference(resolve,[status(thm)],[c_545,c_497]) ).
cnf(c_547,plain,
( product(e_1,e_3,e_1)
| product(e_2,e_3,e_1) ),
inference(resolve,[status(thm)],[c_545,c_494]) ).
cnf(c_562,plain,
( product(e_3,e_1,e_1)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_1)
| product(e_1,e_3,e_1) ),
inference(resolve,[status(thm)],[c_547,c_94]) ).
cnf(c_674,plain,
( product(e_1,e_1,e_1)
| product(e_2,e_2,e_1)
| product(e_1,e_1,e_1) ),
inference(resolve,[status(thm)],[c_546,c_465]) ).
cnf(c_572,plain,
( product(e_2,e_2,e_1)
| product(e_1,e_1,e_1) ),
inference(copy,[status(thm)],[c_674]) ).
cnf(c_578,plain,
( ~ product(e_2,e_1,e_1)
| product(e_1,e_1,e_1) ),
inference(resolve,[status(thm)],[c_572,c_13]) ).
cnf(c_675,plain,
( product(e_1,e_1,e_1)
| product(e_2,e_1,e_2)
| product(e_2,e_1,e_1)
| product(e_1,e_1,e_1) ),
inference(resolve,[status(thm)],[c_425,c_466]) ).
cnf(c_602,plain,
( product(e_2,e_1,e_2)
| product(e_2,e_1,e_1)
| product(e_1,e_1,e_1) ),
inference(copy,[status(thm)],[c_675]) ).
cnf(c_676,plain,
( product(e_1,e_1,e_1)
| product(e_2,e_1,e_1)
| product(e_1,e_1,e_1) ),
inference(resolve,[status(thm)],[c_602,c_434]) ).
cnf(c_605,plain,
( product(e_2,e_1,e_1)
| product(e_1,e_1,e_1) ),
inference(copy,[status(thm)],[c_676]) ).
cnf(c_677,plain,
( product(e_1,e_1,e_1)
| product(e_1,e_1,e_1) ),
inference(resolve,[status(thm)],[c_605,c_578]) ).
cnf(c_606,plain,
product(e_1,e_1,e_1),
inference(copy,[status(thm)],[c_677]) ).
cnf(c_611,plain,
~ product(e_1,e_3,e_1),
inference(resolve,[status(thm)],[c_606,c_14]) ).
cnf(c_612,plain,
~ product(e_1,e_2,e_1),
inference(resolve,[status(thm)],[c_606,c_13]) ).
cnf(c_613,plain,
~ product(e_3,e_1,e_1),
inference(resolve,[status(thm)],[c_606,c_11]) ).
cnf(c_678,plain,
( product(e_3,e_1,e_1)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_1) ),
inference(resolve,[status(thm)],[c_611,c_562]) ).
cnf(c_679,plain,
( product(e_3,e_1,e_1)
| product(e_1,e_2,e_2) ),
inference(resolve,[status(thm)],[c_612,c_678]) ).
cnf(c_624,plain,
product(e_1,e_2,e_2),
inference(resolve,[status(thm)],[c_613,c_679]) ).
cnf(c_680,plain,
~ product(e_1,e_2,e_2),
inference(resolve,[status(thm)],[c_611,c_491]) ).
cnf(c_629,plain,
$false,
inference(resolve,[status(thm)],[c_624,c_680]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP129-1.003 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/5.54 % Computer : n016.cluster.edu
% 0.09/5.54 % Model : x86_64 x86_64
% 0.09/5.54 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.54 % Memory : 8046.5625MB
% 0.09/5.54 % OS : Linux 6.8.0-71-generic
% 0.09/5.55 % CPULimit : 300
% 0.09/5.55 % WCLimit : 300
% 0.09/5.55 % DateTime : Fri Sep 25 14:32:53 UTC 2026
% 0.09/5.55 % CPUTime :
% 0.09/5.55 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/5.55 % Process 2598398 was started by sandbox2 on n016,
% 0.09/5.55 % Fri Sep 25 14:32:53 2026
% 0.09/5.55 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.09/5.55
% 0.09/5.55 % From the command line: assign(max_seconds, 300).
% 0.14/5.62
% 0.14/5.62 % SZS status Unsatisfiable for theBenchmark
% 0.14/5.62
% 0.14/5.62 % Proof 1 at 0.05 (+ 0.01) seconds.
% 0.14/5.62 % Length of proof is 115.
% 0.14/5.62 % Level of proof is 24.
% 0.14/5.62 % Maximum clause weight is 25.000.
% 0.14/5.62 % Given clauses 314.
% 0.14/5.62
% 0.14/5.62 % SZS output start CNFRefutation for theBenchmark
% See solution above
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