%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP133-1.003 : 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 : n001.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 07:28:05 AM UTC 2026
% Result : Unsatisfiable 0.21s 0.61s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 34
% Number of leaves : 11
% Syntax : Number of formulae : 126 ( 20 unt; 0 def)
% Number of atoms : 406 ( 0 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 354 ( 74 ~; 280 |; 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 : 62 ( 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_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_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]) ).
cnf(c_17,plain,
( ~ product(A,B,e_1)
| ~ product(A,B,e_3) ),
inference(resolve,[status(thm)],[c_1,c_3]) ).
fof(qg3,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( product(VAR_2,VAR_3,VAR_0)
| ~ product(VAR_1,VAR_0,VAR_3)
| ~ product(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',qg3) ).
cnf(c_19,plain,
( product(C,D,A)
| ~ product(B,A,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(B,B,A)
| ~ product(A,A,B) ),
inference(factor,[status(thm)],[c_19]) ).
cnf(c_564,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_20,c_22]) ).
cnf(c_31,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_564,c_22]) ).
cnf(c_565,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_20,c_21]) ).
cnf(c_32,plain,
( product(e_3,e_2,e_3)
| product(e_3,e_2,e_2)
| product(e_3,e_2,e_1) ),
inference(resolve,[status(thm)],[c_565,c_22]) ).
cnf(c_566,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_20,c_22]) ).
cnf(c_33,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_566,c_21]) ).
cnf(c_567,plain,
( product(e_1,A,e_3)
| product(e_1,A,e_2)
| product(e_1,A,e_1)
| ~ group_element(A) ),
inference(resolve,[status(thm)],[c_20,c_23]) ).
cnf(c_36,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_567,c_23]) ).
cnf(c_568,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_20,c_22]) ).
cnf(c_37,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_568,c_23]) ).
cnf(c_569,plain,
( product(e_1,A,e_3)
| product(e_1,A,e_2)
| product(e_1,A,e_1)
| ~ group_element(A) ),
inference(resolve,[status(thm)],[c_20,c_23]) ).
cnf(c_39,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_569,c_22]) ).
cnf(c_47,plain,
( product(e_3,e_3,e_2)
| product(e_2,e_2,e_2)
| product(e_2,e_2,e_1) ),
inference(resolve,[status(thm)],[c_31,c_24]) ).
cnf(c_570,plain,
( product(e_3,e_2,e_2)
| product(e_3,e_2,e_1)
| ~ product(e_2,e_2,e_3) ),
inference(resolve,[status(thm)],[c_12,c_32]) ).
cnf(c_58,plain,
( product(e_2,e_2,e_2)
| product(e_2,e_2,e_1)
| product(e_3,e_2,e_2)
| product(e_3,e_2,e_1) ),
inference(resolve,[status(thm)],[c_570,c_31]) ).
cnf(c_571,plain,
( product(e_2,e_3,e_2)
| product(e_2,e_3,e_1)
| ~ product(e_2,e_2,e_3) ),
inference(resolve,[status(thm)],[c_15,c_33]) ).
cnf(c_66,plain,
( product(e_2,e_2,e_2)
| product(e_2,e_2,e_1)
| product(e_2,e_3,e_2)
| product(e_2,e_3,e_1) ),
inference(resolve,[status(thm)],[c_571,c_31]) ).
cnf(c_572,plain,
( product(e_2,e_1,e_2)
| product(e_2,e_1,e_1)
| ~ product(e_1,e_1,e_3) ),
inference(resolve,[status(thm)],[c_10,c_37]) ).
cnf(c_76,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_572,c_36]) ).
cnf(c_86,plain,
( product(e_3,A,e_1)
| ~ product(e_2,e_1,A)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_1) ),
inference(resolve,[status(thm)],[c_39,c_19]) ).
cnf(c_573,plain,
( product(e_2,e_1,e_2)
| product(e_2,e_1,e_1)
| product(e_3,A,e_2)
| ~ product(e_1,e_2,A) ),
inference(resolve,[status(thm)],[c_19,c_37]) ).
cnf(c_88,plain,
( product(e_1,e_2,e_2)
| product(e_1,e_2,e_1)
| product(e_2,e_1,e_2)
| product(e_2,e_1,e_1)
| product(e_3,e_3,e_2) ),
inference(resolve,[status(thm)],[c_573,c_39]) ).
cnf(c_574,plain,
( product(e_1,e_2,e_2)
| product(e_1,e_2,e_1)
| product(e_3,A,e_1)
| ~ product(e_2,e_1,A) ),
inference(resolve,[status(thm)],[c_19,c_39]) ).
cnf(c_89,plain,
( product(e_2,e_1,e_2)
| product(e_2,e_1,e_1)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_1)
| product(e_3,e_3,e_1) ),
inference(resolve,[status(thm)],[c_574,c_37]) ).
cnf(c_575,plain,
( product(e_1,e_2,e_2)
| product(e_1,e_2,e_1)
| ~ product(e_1,e_1,e_3) ),
inference(resolve,[status(thm)],[c_13,c_39]) ).
cnf(c_90,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_575,c_36]) ).
cnf(c_576,plain,
( product(e_2,e_2,e_2)
| product(e_2,e_2,e_1)
| ~ product(e_1,e_2,e_3) ),
inference(resolve,[status(thm)],[c_10,c_31]) ).
cnf(c_92,plain,
( product(e_1,e_2,e_2)
| product(e_1,e_2,e_1)
| product(e_2,e_2,e_2)
| product(e_2,e_2,e_1) ),
inference(resolve,[status(thm)],[c_576,c_39]) ).
cnf(c_106,plain,
( ~ product(e_3,e_2,e_2)
| product(e_2,e_2,e_2)
| product(e_2,e_2,e_1) ),
inference(resolve,[status(thm)],[c_47,c_15]) ).
cnf(c_108,plain,
( ~ product(e_2,e_3,e_2)
| product(e_2,e_2,e_2)
| product(e_2,e_2,e_1) ),
inference(resolve,[status(thm)],[c_47,c_12]) ).
cnf(c_577,plain,
( product(e_2,e_2,e_2)
| product(e_2,e_2,e_1)
| product(e_2,e_2,e_2)
| product(e_2,e_2,e_1)
| product(e_3,e_2,e_1) ),
inference(resolve,[status(thm)],[c_58,c_106]) ).
cnf(c_578,plain,
( product(e_2,e_2,e_2)
| product(e_2,e_2,e_2)
| product(e_2,e_2,e_1)
| product(e_3,e_2,e_1) ),
inference(copy,[status(thm)],[c_577]) ).
cnf(c_125,plain,
( product(e_2,e_2,e_2)
| product(e_2,e_2,e_1)
| product(e_3,e_2,e_1) ),
inference(copy,[status(thm)],[c_578]) ).
cnf(c_579,plain,
( product(e_2,e_2,e_2)
| product(e_2,e_2,e_1)
| product(e_2,e_2,e_2)
| product(e_2,e_2,e_1)
| product(e_2,e_3,e_1) ),
inference(resolve,[status(thm)],[c_66,c_108]) ).
cnf(c_580,plain,
( product(e_2,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) ),
inference(copy,[status(thm)],[c_579]) ).
cnf(c_130,plain,
( product(e_2,e_2,e_2)
| product(e_2,e_2,e_1)
| product(e_2,e_3,e_1) ),
inference(copy,[status(thm)],[c_580]) ).
cnf(c_581,plain,
( product(e_2,e_2,e_2)
| product(e_2,e_2,e_1)
| product(e_1,A,e_3)
| ~ product(e_2,e_3,A) ),
inference(resolve,[status(thm)],[c_19,c_125]) ).
cnf(c_582,plain,
( product(e_2,e_2,e_2)
| product(e_2,e_2,e_1)
| product(e_2,e_2,e_2)
| product(e_2,e_2,e_1)
| product(e_1,e_1,e_3) ),
inference(resolve,[status(thm)],[c_581,c_130]) ).
cnf(c_583,plain,
( product(e_2,e_2,e_2)
| product(e_2,e_2,e_2)
| product(e_2,e_2,e_1)
| product(e_1,e_1,e_3) ),
inference(copy,[status(thm)],[c_582]) ).
cnf(c_135,plain,
( product(e_2,e_2,e_2)
| product(e_2,e_2,e_1)
| product(e_1,e_1,e_3) ),
inference(copy,[status(thm)],[c_583]) ).
cnf(c_584,plain,
( product(e_2,e_2,e_2)
| product(e_2,e_2,e_1)
| product(e_1,A,e_2)
| ~ product(e_3,e_2,A) ),
inference(resolve,[status(thm)],[c_19,c_130]) ).
cnf(c_585,plain,
( product(e_2,e_2,e_2)
| product(e_2,e_2,e_1)
| product(e_2,e_2,e_2)
| product(e_2,e_2,e_1)
| product(e_1,e_1,e_2) ),
inference(resolve,[status(thm)],[c_584,c_125]) ).
cnf(c_586,plain,
( product(e_2,e_2,e_2)
| product(e_2,e_2,e_2)
| product(e_2,e_2,e_1)
| product(e_1,e_1,e_2) ),
inference(copy,[status(thm)],[c_585]) ).
cnf(c_136,plain,
( product(e_2,e_2,e_2)
| product(e_2,e_2,e_1)
| product(e_1,e_1,e_2) ),
inference(copy,[status(thm)],[c_586]) ).
cnf(c_140,plain,
( ~ product(e_1,e_2,e_2)
| product(e_2,e_2,e_1)
| product(e_1,e_1,e_3) ),
inference(resolve,[status(thm)],[c_135,c_10]) ).
cnf(c_143,plain,
( ~ product(e_2,e_1,e_2)
| product(e_2,e_2,e_1)
| product(e_1,e_1,e_2) ),
inference(resolve,[status(thm)],[c_136,c_13]) ).
cnf(c_144,plain,
( ~ product(e_1,e_2,e_2)
| product(e_2,e_2,e_1)
| product(e_1,e_1,e_2) ),
inference(resolve,[status(thm)],[c_136,c_10]) ).
cnf(c_587,plain,
( product(e_2,e_2,e_1)
| product(e_1,e_1,e_2)
| 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_76,c_143]) ).
cnf(c_174,plain,
( product(e_2,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(copy,[status(thm)],[c_587]) ).
cnf(c_588,plain,
( product(e_2,e_2,e_1)
| product(e_1,e_1,e_2)
| product(e_1,e_1,e_2)
| product(e_1,e_1,e_1)
| product(e_1,e_2,e_1) ),
inference(resolve,[status(thm)],[c_90,c_144]) ).
cnf(c_210,plain,
( product(e_2,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) ),
inference(copy,[status(thm)],[c_588]) ).
cnf(c_225,plain,
( ~ product(e_2,e_1,e_2)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_1)
| product(e_2,e_2,e_1) ),
inference(resolve,[status(thm)],[c_92,c_13]) ).
cnf(c_589,plain,
( product(e_1,e_2,e_2)
| product(e_1,e_2,e_1)
| product(e_2,e_1,e_2)
| product(e_2,e_1,e_1)
| ~ product(e_3,e_3,e_1) ),
inference(resolve,[status(thm)],[c_16,c_88]) ).
cnf(c_590,plain,
( product(e_2,e_1,e_2)
| product(e_2,e_1,e_1)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_1)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_1)
| product(e_2,e_1,e_2)
| product(e_2,e_1,e_1) ),
inference(resolve,[status(thm)],[c_589,c_89]) ).
cnf(c_591,plain,
( product(e_2,e_1,e_2)
| product(e_2,e_1,e_1)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_1)
| product(e_2,e_1,e_2)
| product(e_2,e_1,e_1) ),
inference(copy,[status(thm)],[c_590]) ).
cnf(c_592,plain,
( product(e_2,e_1,e_2)
| product(e_2,e_1,e_1)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_1)
| product(e_2,e_1,e_2)
| product(e_2,e_1,e_1) ),
inference(copy,[status(thm)],[c_591]) ).
cnf(c_593,plain,
( product(e_2,e_1,e_2)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_1)
| product(e_2,e_1,e_2)
| product(e_2,e_1,e_1) ),
inference(copy,[status(thm)],[c_592]) ).
cnf(c_242,plain,
( product(e_1,e_2,e_2)
| product(e_1,e_2,e_1)
| product(e_2,e_1,e_2)
| product(e_2,e_1,e_1) ),
inference(copy,[status(thm)],[c_593]) ).
cnf(c_594,plain,
( product(e_1,e_1,e_2)
| 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_174,c_24]) ).
cnf(c_306,plain,
( product(e_1,e_1,e_2)
| product(e_1,e_1,e_1)
| product(e_2,e_1,e_1) ),
inference(copy,[status(thm)],[c_594]) ).
cnf(c_307,plain,
( product(A,e_1,e_1)
| ~ product(e_1,e_2,A)
| product(e_1,e_1,e_2)
| product(e_1,e_1,e_1) ),
inference(resolve,[status(thm)],[c_306,c_19]) ).
cnf(c_309,plain,
( ~ 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_307]) ).
cnf(c_595,plain,
( product(e_1,e_1,e_2)
| product(e_1,e_1,e_2)
| product(e_1,e_1,e_1)
| product(e_1,e_2,e_1) ),
inference(resolve,[status(thm)],[c_210,c_24]) ).
cnf(c_321,plain,
( product(e_1,e_1,e_2)
| product(e_1,e_1,e_1)
| product(e_1,e_2,e_1) ),
inference(copy,[status(thm)],[c_595]) ).
cnf(c_596,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_321,c_309]) ).
cnf(c_597,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_596]) ).
cnf(c_322,plain,
( product(e_1,e_1,e_2)
| product(e_1,e_1,e_1) ),
inference(copy,[status(thm)],[c_597]) ).
cnf(c_324,plain,
( product(e_2,e_2,e_1)
| product(e_1,e_1,e_1) ),
inference(resolve,[status(thm)],[c_322,c_24]) ).
cnf(c_330,plain,
( ~ product(e_2,e_1,e_1)
| product(e_1,e_1,e_1) ),
inference(resolve,[status(thm)],[c_324,c_13]) ).
cnf(c_331,plain,
( ~ product(e_1,e_2,e_1)
| product(e_1,e_1,e_1) ),
inference(resolve,[status(thm)],[c_324,c_10]) ).
cnf(c_598,plain,
( product(e_1,e_2,e_2)
| product(e_1,e_2,e_1)
| product(e_2,e_2,e_1)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_1)
| product(e_2,e_1,e_1) ),
inference(resolve,[status(thm)],[c_242,c_225]) ).
cnf(c_599,plain,
( product(e_1,e_2,e_2)
| product(e_2,e_2,e_1)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_1)
| product(e_2,e_1,e_1) ),
inference(copy,[status(thm)],[c_598]) ).
cnf(c_344,plain,
( product(e_2,e_2,e_1)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_1)
| product(e_2,e_1,e_1) ),
inference(copy,[status(thm)],[c_599]) ).
cnf(c_600,plain,
( product(e_3,e_2,e_1)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_1)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_1)
| product(e_2,e_1,e_1) ),
inference(resolve,[status(thm)],[c_242,c_86]) ).
cnf(c_601,plain,
( product(e_3,e_2,e_1)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_1)
| product(e_2,e_1,e_1) ),
inference(copy,[status(thm)],[c_600]) ).
cnf(c_345,plain,
( product(e_3,e_2,e_1)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_1)
| product(e_2,e_1,e_1) ),
inference(copy,[status(thm)],[c_601]) ).
cnf(c_602,plain,
( product(e_1,e_2,e_2)
| product(e_1,e_2,e_1)
| product(e_2,e_1,e_1)
| ~ product(e_2,e_2,e_1) ),
inference(resolve,[status(thm)],[c_12,c_345]) ).
cnf(c_603,plain,
( product(e_1,e_2,e_2)
| product(e_1,e_2,e_1)
| product(e_2,e_1,e_1)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_1)
| product(e_2,e_1,e_1) ),
inference(resolve,[status(thm)],[c_602,c_344]) ).
cnf(c_604,plain,
( product(e_1,e_2,e_2)
| product(e_1,e_2,e_1)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_1)
| product(e_2,e_1,e_1) ),
inference(copy,[status(thm)],[c_603]) ).
cnf(c_605,plain,
( product(e_1,e_2,e_2)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_1)
| product(e_2,e_1,e_1) ),
inference(copy,[status(thm)],[c_604]) ).
cnf(c_453,plain,
( product(e_1,e_2,e_2)
| product(e_1,e_2,e_1)
| product(e_2,e_1,e_1) ),
inference(copy,[status(thm)],[c_605]) ).
cnf(c_454,plain,
( 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_453,c_330]) ).
cnf(c_459,plain,
( ~ 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_453,c_10]) ).
cnf(c_606,plain,
( product(e_1,e_1,e_1)
| product(e_1,e_2,e_1)
| ~ product(e_1,e_1,e_2) ),
inference(resolve,[status(thm)],[c_13,c_454]) ).
cnf(c_607,plain,
( product(e_1,e_1,e_1)
| product(e_1,e_1,e_1)
| product(e_1,e_2,e_1) ),
inference(resolve,[status(thm)],[c_606,c_322]) ).
cnf(c_467,plain,
( product(e_1,e_1,e_1)
| product(e_1,e_2,e_1) ),
inference(copy,[status(thm)],[c_607]) ).
cnf(c_608,plain,
( product(e_1,e_1,e_1)
| product(e_1,e_1,e_1) ),
inference(resolve,[status(thm)],[c_467,c_331]) ).
cnf(c_468,plain,
product(e_1,e_1,e_1),
inference(copy,[status(thm)],[c_608]) ).
cnf(c_469,plain,
( product(e_1,e_2,e_2)
| product(e_1,e_2,e_1) ),
inference(resolve,[status(thm)],[c_468,c_459]) ).
cnf(c_472,plain,
~ product(e_1,e_1,e_3),
inference(resolve,[status(thm)],[c_17,c_468]) ).
cnf(c_473,plain,
~ product(e_1,e_1,e_2),
inference(resolve,[status(thm)],[c_16,c_468]) ).
cnf(c_475,plain,
~ product(e_1,e_2,e_1),
inference(resolve,[status(thm)],[c_13,c_468]) ).
cnf(c_501,plain,
( ~ product(e_1,e_2,e_2)
| product(e_2,e_2,e_1) ),
inference(resolve,[status(thm)],[c_472,c_140]) ).
cnf(c_517,plain,
product(e_1,e_2,e_2),
inference(resolve,[status(thm)],[c_475,c_469]) ).
cnf(c_546,plain,
product(e_2,e_2,e_1),
inference(resolve,[status(thm)],[c_517,c_501]) ).
cnf(c_609,plain,
~ product(e_2,e_2,e_1),
inference(resolve,[status(thm)],[c_24,c_473]) ).
cnf(c_563,plain,
$false,
inference(resolve,[status(thm)],[c_546,c_609]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GRP133-1.003 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/0.44 % Computer : n001.cluster.edu
% 0.16/0.44 % Model : x86_64 x86_64
% 0.16/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.44 % Memory : 8046.5625MB
% 0.16/0.44 % OS : Linux 6.8.0-71-generic
% 0.16/0.44 % CPULimit : 300
% 0.16/0.44 % WCLimit : 300
% 0.16/0.44 % DateTime : Fri Sep 25 14:35:55 UTC 2026
% 0.16/0.44 % CPUTime :
% 0.16/0.45 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.16/0.45 % Process 3526211 was started by sandbox2 on n001,
% 0.16/0.45 % Fri Sep 25 14:35:55 2026
% 0.16/0.45 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.16/0.45
% 0.16/0.45 % From the command line: assign(max_seconds, 300).
% 0.21/0.61
% 0.21/0.61 % SZS status Unsatisfiable for theBenchmark
% 0.21/0.61
% 0.21/0.61 % Proof 1 at 0.12 (+ 0.03) seconds.
% 0.21/0.61 % Length of proof is 69.
% 0.21/0.61 % Level of proof is 20.
% 0.21/0.61 % Maximum clause weight is 25.000.
% 0.21/0.61 % Given clauses 221.
% 0.21/0.61
% 0.21/0.61 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------