%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP124-1.004 : TPTP v9.3.1. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n009.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 07:27:37 AM UTC 2026
% Result : Unsatisfiable 0.40s 0.63s
% Output : CNFRefutation 0.40s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 16
% Syntax : Number of formulae : 130 ( 45 unt; 0 def)
% Number of atoms : 298 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 306 ( 138 ~; 168 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 100 ( 0 sgn 23 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(e_4_is_not_e_3,axiom,
~ equalish(e_4,e_3),
file('theBenchmark.p',e_4_is_not_e_3) ).
cnf(c_2,plain,
~ equalish(e_4,e_3),
inference(clausify,[status(thm)],[e_4_is_not_e_3]) ).
fof(e_4_is_not_e_2,axiom,
~ equalish(e_4,e_2),
file('theBenchmark.p',e_4_is_not_e_2) ).
cnf(c_3,plain,
~ equalish(e_4,e_2),
inference(clausify,[status(thm)],[e_4_is_not_e_2]) ).
fof(e_4_is_not_e_1,axiom,
~ equalish(e_4,e_1),
file('theBenchmark.p',e_4_is_not_e_1) ).
cnf(c_4,plain,
~ equalish(e_4,e_1),
inference(clausify,[status(thm)],[e_4_is_not_e_1]) ).
fof(e_3_is_not_e_2,axiom,
~ equalish(e_3,e_2),
file('theBenchmark.p',e_3_is_not_e_2) ).
cnf(c_6,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_7,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_10,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_14,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_15,plain,
( equalish(A,D)
| ~ product(D,B,C)
| ~ product(A,B,C) ),
inference(clausify,[status(thm)],[product_left_cancellation]) ).
fof(qg2_1,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4,VAR_5] :
( equalish(VAR_0,VAR_3)
| ~ product(VAR_5,VAR_3,VAR_4)
| ~ product(VAR_5,VAR_0,VAR_1)
| ~ product(VAR_3,VAR_4,VAR_2)
| ~ product(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',qg2_1) ).
cnf(c_16,plain,
( equalish(A,D)
| ~ product(F,D,E)
| ~ product(F,A,B)
| ~ product(D,E,C)
| ~ product(A,B,C) ),
inference(clausify,[status(thm)],[qg2_1]) ).
fof(qg2_2,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4,VAR_5] :
( equalish(VAR_1,VAR_4)
| ~ product(VAR_5,VAR_3,VAR_4)
| ~ product(VAR_5,VAR_0,VAR_1)
| ~ product(VAR_3,VAR_4,VAR_2)
| ~ product(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',qg2_2) ).
cnf(c_17,plain,
( equalish(B,E)
| ~ product(F,D,E)
| ~ product(F,A,B)
| ~ product(D,E,C)
| ~ product(A,B,C) ),
inference(clausify,[status(thm)],[qg2_2]) ).
cnf(c_18,plain,
( ~ product(D,C,e_1)
| ~ product(D,A,e_2)
| ~ product(C,e_1,B)
| ~ product(A,e_2,B) ),
inference(resolve,[status(thm)],[c_17,c_10]) ).
cnf(c_20,plain,
( ~ product(D,C,e_2)
| ~ product(D,A,e_3)
| ~ product(C,e_2,B)
| ~ product(A,e_3,B) ),
inference(resolve,[status(thm)],[c_17,c_6]) ).
cnf(c_23,plain,
( ~ product(D,C,e_3)
| ~ product(D,A,e_4)
| ~ product(C,e_3,B)
| ~ product(A,e_4,B) ),
inference(resolve,[status(thm)],[c_17,c_2]) ).
cnf(c_26,plain,
( ~ product(D,e_2,C)
| ~ product(D,e_3,A)
| ~ product(e_2,C,B)
| ~ product(e_3,A,B) ),
inference(resolve,[status(thm)],[c_16,c_6]) ).
cnf(c_31,plain,
( ~ product(e_1,A,B)
| ~ product(e_3,A,B) ),
inference(resolve,[status(thm)],[c_15,c_7]) ).
cnf(c_32,plain,
( ~ product(e_2,A,B)
| ~ product(e_3,A,B) ),
inference(resolve,[status(thm)],[c_15,c_6]) ).
cnf(c_33,plain,
( ~ product(e_1,A,B)
| ~ product(e_4,A,B) ),
inference(resolve,[status(thm)],[c_15,c_4]) ).
cnf(c_34,plain,
( ~ product(e_2,A,B)
| ~ product(e_4,A,B) ),
inference(resolve,[status(thm)],[c_15,c_3]) ).
cnf(c_35,plain,
( ~ product(e_3,A,B)
| ~ product(e_4,A,B) ),
inference(resolve,[status(thm)],[c_15,c_2]) ).
cnf(c_36,plain,
( ~ product(A,e_1,B)
| ~ product(A,e_2,B) ),
inference(resolve,[status(thm)],[c_14,c_10]) ).
cnf(c_37,plain,
( ~ product(A,e_1,B)
| ~ product(A,e_3,B) ),
inference(resolve,[status(thm)],[c_14,c_7]) ).
cnf(c_38,plain,
( ~ product(A,e_2,B)
| ~ product(A,e_3,B) ),
inference(resolve,[status(thm)],[c_14,c_6]) ).
cnf(c_39,plain,
( ~ product(A,e_1,B)
| ~ product(A,e_4,B) ),
inference(resolve,[status(thm)],[c_14,c_4]) ).
cnf(c_40,plain,
( ~ product(A,e_2,B)
| ~ product(A,e_4,B) ),
inference(resolve,[status(thm)],[c_14,c_3]) ).
cnf(c_41,plain,
( ~ product(A,e_3,B)
| ~ product(A,e_4,B) ),
inference(resolve,[status(thm)],[c_14,c_2]) ).
fof(product_idempotence,axiom,
! [VAR_0] : product(VAR_0,VAR_0,VAR_0),
file('theBenchmark.p',product_idempotence) ).
cnf(c_48,plain,
product(A,A,A),
inference(clausify,[status(thm)],[product_idempotence]) ).
fof(product_total_function1,axiom,
! [VAR_0,VAR_1] :
( product(VAR_0,VAR_1,e_4)
| 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_49,plain,
( product(A,B,e_4)
| 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_4,axiom,
group_element(e_4),
file('theBenchmark.p',element_4) ).
cnf(c_50,plain,
group_element(e_4),
inference(clausify,[status(thm)],[element_4]) ).
fof(element_3,axiom,
group_element(e_3),
file('theBenchmark.p',element_3) ).
cnf(c_51,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_52,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_53,plain,
group_element(e_1),
inference(clausify,[status(thm)],[element_1]) ).
cnf(c_109,plain,
~ product(e_4,e_3,e_4),
inference(resolve,[status(thm)],[c_48,c_41]) ).
cnf(c_110,plain,
~ product(e_4,e_2,e_4),
inference(resolve,[status(thm)],[c_48,c_40]) ).
cnf(c_111,plain,
~ product(e_4,e_1,e_4),
inference(resolve,[status(thm)],[c_48,c_39]) ).
cnf(c_112,plain,
~ product(e_3,e_2,e_3),
inference(resolve,[status(thm)],[c_48,c_38]) ).
cnf(c_113,plain,
~ product(e_3,e_1,e_3),
inference(resolve,[status(thm)],[c_48,c_37]) ).
cnf(c_115,plain,
~ product(e_3,e_4,e_4),
inference(resolve,[status(thm)],[c_48,c_35]) ).
cnf(c_116,plain,
~ product(e_2,e_4,e_4),
inference(resolve,[status(thm)],[c_48,c_34]) ).
cnf(c_118,plain,
~ product(e_2,e_3,e_3),
inference(resolve,[status(thm)],[c_48,c_32]) ).
cnf(c_119,plain,
~ product(e_1,e_3,e_3),
inference(resolve,[status(thm)],[c_48,c_31]) ).
cnf(c_135,plain,
( ~ product(B,e_2,e_2)
| ~ product(B,e_3,A)
| ~ product(e_3,A,e_2) ),
inference(resolve,[status(thm)],[c_48,c_26]) ).
cnf(c_148,plain,
( ~ product(B,A,e_3)
| ~ product(B,e_4,e_4)
| ~ product(A,e_3,e_4) ),
inference(resolve,[status(thm)],[c_48,c_23]) ).
cnf(c_157,plain,
( ~ product(e_2,A,e_3)
| ~ product(e_2,e_2,B)
| ~ product(A,e_3,B) ),
inference(resolve,[status(thm)],[c_48,c_20]) ).
cnf(c_165,plain,
( ~ product(e_1,A,e_2)
| ~ product(e_1,e_1,B)
| ~ product(A,e_2,B) ),
inference(resolve,[status(thm)],[c_48,c_18]) ).
cnf(c_168,plain,
( ~ product(B,A,e_1)
| ~ product(B,e_2,e_2)
| ~ product(A,e_1,e_2) ),
inference(resolve,[status(thm)],[c_48,c_18]) ).
cnf(c_175,plain,
~ product(e_3,e_4,e_3),
inference(resolve,[status(thm)],[c_41,c_48]) ).
cnf(c_176,plain,
~ product(e_2,e_4,e_2),
inference(resolve,[status(thm)],[c_40,c_48]) ).
cnf(c_178,plain,
~ product(e_2,e_3,e_2),
inference(resolve,[status(thm)],[c_38,c_48]) ).
cnf(c_179,plain,
~ product(e_1,e_3,e_1),
inference(resolve,[status(thm)],[c_37,c_48]) ).
cnf(c_181,plain,
~ product(e_4,e_3,e_3),
inference(resolve,[status(thm)],[c_35,c_48]) ).
cnf(c_182,plain,
~ product(e_4,e_2,e_2),
inference(resolve,[status(thm)],[c_34,c_48]) ).
cnf(c_183,plain,
~ product(e_4,e_1,e_1),
inference(resolve,[status(thm)],[c_33,c_48]) ).
cnf(c_184,plain,
~ product(e_3,e_2,e_2),
inference(resolve,[status(thm)],[c_32,c_48]) ).
cnf(c_185,plain,
~ product(e_3,e_1,e_1),
inference(resolve,[status(thm)],[c_31,c_48]) ).
cnf(c_187,plain,
( product(A,e_4,e_4)
| product(A,e_4,e_3)
| product(A,e_4,e_2)
| product(A,e_4,e_1)
| ~ group_element(A) ),
inference(resolve,[status(thm)],[c_50,c_49]) ).
cnf(c_188,plain,
( product(e_4,A,e_4)
| product(e_4,A,e_3)
| product(e_4,A,e_2)
| product(e_4,A,e_1)
| ~ group_element(A) ),
inference(resolve,[status(thm)],[c_50,c_49]) ).
cnf(c_189,plain,
( product(A,e_3,e_4)
| 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_51,c_49]) ).
cnf(c_190,plain,
( product(e_3,A,e_4)
| 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_51,c_49]) ).
cnf(c_931,plain,
( product(e_2,e_4,e_4)
| product(e_2,e_4,e_3)
| product(e_2,e_4,e_2)
| product(e_2,e_4,e_1) ),
inference(resolve,[status(thm)],[c_187,c_52]) ).
cnf(c_932,plain,
( product(e_2,e_4,e_4)
| product(e_2,e_4,e_3)
| product(e_2,e_4,e_1) ),
inference(resolve,[status(thm)],[c_176,c_931]) ).
cnf(c_196,plain,
( product(e_2,e_4,e_3)
| product(e_2,e_4,e_1) ),
inference(resolve,[status(thm)],[c_116,c_932]) ).
cnf(c_933,plain,
( product(e_3,e_4,e_4)
| product(e_3,e_4,e_3)
| product(e_3,e_4,e_2)
| product(e_3,e_4,e_1) ),
inference(resolve,[status(thm)],[c_187,c_51]) ).
cnf(c_934,plain,
( product(e_3,e_4,e_4)
| product(e_3,e_4,e_2)
| product(e_3,e_4,e_1) ),
inference(resolve,[status(thm)],[c_175,c_933]) ).
cnf(c_197,plain,
( product(e_3,e_4,e_2)
| product(e_3,e_4,e_1) ),
inference(resolve,[status(thm)],[c_115,c_934]) ).
cnf(c_262,plain,
( product(e_3,e_4,e_1)
| ~ product(A,e_2,e_2)
| ~ product(A,e_3,e_4) ),
inference(resolve,[status(thm)],[c_135,c_197]) ).
cnf(c_268,plain,
( product(e_2,e_4,e_1)
| ~ product(e_2,e_2,A)
| ~ product(e_4,e_3,A) ),
inference(resolve,[status(thm)],[c_157,c_196]) ).
cnf(c_935,plain,
( product(e_4,e_1,e_4)
| product(e_4,e_1,e_3)
| product(e_4,e_1,e_2)
| product(e_4,e_1,e_1) ),
inference(resolve,[status(thm)],[c_188,c_53]) ).
cnf(c_936,plain,
( product(e_4,e_1,e_4)
| product(e_4,e_1,e_3)
| product(e_4,e_1,e_2) ),
inference(resolve,[status(thm)],[c_183,c_935]) ).
cnf(c_271,plain,
( product(e_4,e_1,e_3)
| product(e_4,e_1,e_2) ),
inference(resolve,[status(thm)],[c_111,c_936]) ).
cnf(c_937,plain,
( product(e_4,e_2,e_4)
| product(e_4,e_2,e_3)
| product(e_4,e_2,e_2)
| product(e_4,e_2,e_1) ),
inference(resolve,[status(thm)],[c_188,c_52]) ).
cnf(c_938,plain,
( product(e_4,e_2,e_4)
| product(e_4,e_2,e_3)
| product(e_4,e_2,e_1) ),
inference(resolve,[status(thm)],[c_182,c_937]) ).
cnf(c_272,plain,
( product(e_4,e_2,e_3)
| product(e_4,e_2,e_1) ),
inference(resolve,[status(thm)],[c_110,c_938]) ).
cnf(c_939,plain,
( product(e_4,e_3,e_4)
| product(e_4,e_3,e_3)
| product(e_4,e_3,e_2)
| product(e_4,e_3,e_1) ),
inference(resolve,[status(thm)],[c_188,c_51]) ).
cnf(c_940,plain,
( product(e_4,e_3,e_4)
| product(e_4,e_3,e_2)
| product(e_4,e_3,e_1) ),
inference(resolve,[status(thm)],[c_181,c_939]) ).
cnf(c_273,plain,
( product(e_4,e_3,e_2)
| product(e_4,e_3,e_1) ),
inference(resolve,[status(thm)],[c_109,c_940]) ).
cnf(c_941,plain,
( product(e_1,e_3,e_4)
| 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_189,c_53]) ).
cnf(c_942,plain,
( product(e_1,e_3,e_4)
| product(e_1,e_3,e_3)
| product(e_1,e_3,e_2) ),
inference(resolve,[status(thm)],[c_179,c_941]) ).
cnf(c_274,plain,
( product(e_1,e_3,e_4)
| product(e_1,e_3,e_2) ),
inference(resolve,[status(thm)],[c_119,c_942]) ).
cnf(c_943,plain,
( product(e_2,e_3,e_4)
| 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_189,c_52]) ).
cnf(c_944,plain,
( product(e_2,e_3,e_4)
| product(e_2,e_3,e_3)
| product(e_2,e_3,e_1) ),
inference(resolve,[status(thm)],[c_178,c_943]) ).
cnf(c_275,plain,
( product(e_2,e_3,e_4)
| product(e_2,e_3,e_1) ),
inference(resolve,[status(thm)],[c_118,c_944]) ).
cnf(c_945,plain,
( product(e_3,e_1,e_4)
| 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_190,c_53]) ).
cnf(c_946,plain,
( product(e_3,e_1,e_4)
| product(e_3,e_1,e_3)
| product(e_3,e_1,e_2) ),
inference(resolve,[status(thm)],[c_185,c_945]) ).
cnf(c_276,plain,
( product(e_3,e_1,e_4)
| product(e_3,e_1,e_2) ),
inference(resolve,[status(thm)],[c_113,c_946]) ).
cnf(c_947,plain,
( product(e_3,e_2,e_4)
| 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_190,c_52]) ).
cnf(c_948,plain,
( product(e_3,e_2,e_4)
| product(e_3,e_2,e_3)
| product(e_3,e_2,e_1) ),
inference(resolve,[status(thm)],[c_184,c_947]) ).
cnf(c_277,plain,
( product(e_3,e_2,e_4)
| product(e_3,e_2,e_1) ),
inference(resolve,[status(thm)],[c_112,c_948]) ).
cnf(c_949,plain,
( ~ product(e_4,e_4,e_4)
| ~ product(e_1,e_3,e_4)
| product(e_4,e_1,e_2) ),
inference(resolve,[status(thm)],[c_271,c_148]) ).
cnf(c_282,plain,
( ~ product(e_1,e_3,e_4)
| product(e_4,e_1,e_2) ),
inference(resolve,[status(thm)],[c_48,c_949]) ).
cnf(c_950,plain,
( ~ product(e_4,e_4,e_4)
| ~ product(e_2,e_3,e_4)
| product(e_4,e_2,e_1) ),
inference(resolve,[status(thm)],[c_272,c_148]) ).
cnf(c_301,plain,
( ~ product(e_2,e_3,e_4)
| product(e_4,e_2,e_1) ),
inference(resolve,[status(thm)],[c_48,c_950]) ).
cnf(c_951,plain,
( product(e_2,e_4,e_1)
| ~ product(e_2,e_2,e_2)
| product(e_4,e_3,e_1) ),
inference(resolve,[status(thm)],[c_273,c_268]) ).
cnf(c_317,plain,
( product(e_2,e_4,e_1)
| product(e_4,e_3,e_1) ),
inference(resolve,[status(thm)],[c_48,c_951]) ).
cnf(c_328,plain,
( ~ product(e_4,e_1,e_2)
| product(e_4,e_3,e_1) ),
inference(resolve,[status(thm)],[c_273,c_37]) ).
cnf(c_952,plain,
( product(e_3,e_4,e_1)
| ~ product(e_2,e_2,e_2)
| product(e_2,e_3,e_1) ),
inference(resolve,[status(thm)],[c_275,c_262]) ).
cnf(c_360,plain,
( product(e_3,e_4,e_1)
| product(e_2,e_3,e_1) ),
inference(resolve,[status(thm)],[c_48,c_952]) ).
cnf(c_405,plain,
( ~ product(e_3,e_1,e_4)
| product(e_3,e_2,e_1) ),
inference(resolve,[status(thm)],[c_277,c_36]) ).
cnf(c_419,plain,
( product(e_1,e_3,e_2)
| product(e_4,e_1,e_2) ),
inference(resolve,[status(thm)],[c_282,c_274]) ).
cnf(c_438,plain,
( product(e_2,e_3,e_1)
| product(e_4,e_2,e_1) ),
inference(resolve,[status(thm)],[c_301,c_275]) ).
cnf(c_446,plain,
( ~ product(e_4,e_2,e_1)
| product(e_2,e_4,e_1) ),
inference(resolve,[status(thm)],[c_317,c_38]) ).
cnf(c_470,plain,
( ~ product(e_2,e_4,e_1)
| product(e_2,e_3,e_1) ),
inference(resolve,[status(thm)],[c_360,c_32]) ).
cnf(c_567,plain,
( product(e_3,e_1,e_2)
| product(e_3,e_2,e_1) ),
inference(resolve,[status(thm)],[c_405,c_276]) ).
cnf(c_569,plain,
( product(e_4,e_3,e_1)
| product(e_1,e_3,e_2) ),
inference(resolve,[status(thm)],[c_419,c_328]) ).
cnf(c_626,plain,
( product(e_2,e_3,e_1)
| product(e_2,e_4,e_1) ),
inference(resolve,[status(thm)],[c_446,c_438]) ).
cnf(c_953,plain,
( ~ product(e_1,e_3,e_2)
| ~ product(e_1,e_1,e_1)
| product(e_3,e_1,e_2) ),
inference(resolve,[status(thm)],[c_567,c_165]) ).
cnf(c_799,plain,
( ~ product(e_1,e_3,e_2)
| product(e_3,e_1,e_2) ),
inference(resolve,[status(thm)],[c_48,c_953]) ).
cnf(c_834,plain,
( ~ product(e_2,e_3,e_1)
| product(e_1,e_3,e_2) ),
inference(resolve,[status(thm)],[c_569,c_34]) ).
cnf(c_954,plain,
( product(e_2,e_3,e_1)
| product(e_2,e_3,e_1) ),
inference(resolve,[status(thm)],[c_626,c_470]) ).
cnf(c_918,plain,
product(e_2,e_3,e_1),
inference(copy,[status(thm)],[c_954]) ).
cnf(c_919,plain,
product(e_1,e_3,e_2),
inference(resolve,[status(thm)],[c_918,c_834]) ).
cnf(c_924,plain,
product(e_3,e_1,e_2),
inference(resolve,[status(thm)],[c_919,c_799]) ).
cnf(c_955,plain,
( ~ product(e_2,e_2,e_2)
| ~ product(e_3,e_1,e_2) ),
inference(resolve,[status(thm)],[c_918,c_168]) ).
cnf(c_956,plain,
~ product(e_2,e_2,e_2),
inference(resolve,[status(thm)],[c_924,c_955]) ).
cnf(c_930,plain,
$false,
inference(resolve,[status(thm)],[c_48,c_956]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP124-1.004 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.39 % Computer : n009.cluster.edu
% 0.10/0.39 % Model : x86_64 x86_64
% 0.10/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.39 % Memory : 8046.5625MB
% 0.10/0.39 % OS : Linux 6.8.0-71-generic
% 0.10/0.39 % CPULimit : 300
% 0.10/0.39 % WCLimit : 300
% 0.10/0.39 % DateTime : Fri Sep 25 14:24:44 UTC 2026
% 0.10/0.39 % CPUTime :
% 0.10/0.39 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.39 % Process 1800582 was started by sandbox on n009,
% 0.10/0.39 % Fri Sep 25 14:24:44 2026
% 0.10/0.39 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.10/0.40
% 0.10/0.40 % From the command line: assign(max_seconds, 300).
% 0.40/0.63
% 0.40/0.63 % SZS status Unsatisfiable for theBenchmark
% 0.40/0.63
% 0.40/0.63 % Proof 1 at 0.07 (+ 0.02) seconds.
% 0.40/0.63 % Length of proof is 88.
% 0.40/0.63 % Level of proof is 11.
% 0.40/0.63 % Maximum clause weight is 25.000.
% 0.40/0.63 % Given clauses 305.
% 0.40/0.63
% 0.40/0.63 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------