%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP129-4.004 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/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 07:28:03 AM UTC 2026
% Result : Unsatisfiable 0.32s 15.54s
% Output : CNFRefutation 0.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 41
% Number of leaves : 14
% Syntax : Number of formulae : 121 ( 25 unt; 0 def)
% Number of atoms : 326 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 292 ( 87 ~; 205 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 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 : 77 ( 1 sgn 22 !; 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_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_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(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]) ).
cnf(c_17,plain,
( ~ product(e_1,A,B)
| ~ product(e_3,A,B) ),
inference(resolve,[status(thm)],[c_15,c_7]) ).
cnf(c_18,plain,
( ~ product(e_2,A,B)
| ~ product(e_3,A,B) ),
inference(resolve,[status(thm)],[c_15,c_6]) ).
cnf(c_19,plain,
( ~ product(e_1,A,B)
| ~ product(e_4,A,B) ),
inference(resolve,[status(thm)],[c_15,c_4]) ).
cnf(c_21,plain,
( ~ product(e_3,A,B)
| ~ product(e_4,A,B) ),
inference(resolve,[status(thm)],[c_15,c_2]) ).
cnf(c_23,plain,
( ~ product(A,e_1,B)
| ~ product(A,e_3,B) ),
inference(resolve,[status(thm)],[c_14,c_7]) ).
cnf(c_24,plain,
( ~ product(A,e_2,B)
| ~ product(A,e_3,B) ),
inference(resolve,[status(thm)],[c_14,c_6]) ).
cnf(c_25,plain,
( ~ product(A,e_1,B)
| ~ product(A,e_4,B) ),
inference(resolve,[status(thm)],[c_14,c_4]) ).
cnf(c_27,plain,
( ~ product(A,e_3,B)
| ~ product(A,e_4,B) ),
inference(resolve,[status(thm)],[c_14,c_2]) ).
cnf(c_29,plain,
( ~ product(A,B,e_1)
| ~ product(A,B,e_3) ),
inference(resolve,[status(thm)],[c_1,c_7]) ).
cnf(c_31,plain,
( ~ product(A,B,e_1)
| ~ product(A,B,e_4) ),
inference(resolve,[status(thm)],[c_1,c_4]) ).
cnf(c_33,plain,
( ~ product(A,B,e_3)
| ~ product(A,B,e_4) ),
inference(resolve,[status(thm)],[c_1,c_2]) ).
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_35,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_36,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_37,plain,
group_element(e_3),
inference(clausify,[status(thm)],[element_3]) ).
fof(element_1,axiom,
group_element(e_1),
file('theBenchmark.p',element_1) ).
cnf(c_39,plain,
group_element(e_1),
inference(clausify,[status(thm)],[element_1]) ).
fof(qg3_1,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( ~ product(VAR_1,VAR_2,VAR_3)
| ~ product(VAR_2,VAR_0,VAR_3)
| product(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',qg3_1) ).
cnf(c_41,plain,
( ~ product(B,C,D)
| ~ product(C,A,D)
| product(A,B,C) ),
inference(clausify,[status(thm)],[qg3_1]) ).
fof(column_surjectivity,axiom,
! [VAR_0,VAR_1] :
( product(VAR_0,e_4,VAR_1)
| product(VAR_0,e_3,VAR_1)
| product(VAR_0,e_2,VAR_1)
| product(VAR_0,e_1,VAR_1)
| ~ group_element(VAR_1)
| ~ group_element(VAR_0) ),
file('theBenchmark.p',column_surjectivity) ).
cnf(c_42,plain,
( product(A,e_4,B)
| product(A,e_3,B)
| product(A,e_2,B)
| product(A,e_1,B)
| ~ group_element(B)
| ~ group_element(A) ),
inference(clausify,[status(thm)],[column_surjectivity]) ).
fof(row_surjectivity,axiom,
! [VAR_0,VAR_1] :
( product(e_4,VAR_0,VAR_1)
| product(e_3,VAR_0,VAR_1)
| product(e_2,VAR_0,VAR_1)
| product(e_1,VAR_0,VAR_1)
| ~ group_element(VAR_1)
| ~ group_element(VAR_0) ),
file('theBenchmark.p',row_surjectivity) ).
cnf(c_43,plain,
( product(e_4,A,B)
| product(e_3,A,B)
| product(e_2,A,B)
| product(e_1,A,B)
| ~ group_element(B)
| ~ group_element(A) ),
inference(clausify,[status(thm)],[row_surjectivity]) ).
cnf(c_44,plain,
( product(A,A,e_4)
| product(A,A,e_3)
| product(A,A,e_2)
| product(A,A,e_1)
| ~ group_element(A) ),
inference(factor,[status(thm)],[c_35]) ).
cnf(c_45,plain,
( ~ product(A,A,B)
| product(A,A,A) ),
inference(factor,[status(thm)],[c_41]) ).
cnf(c_58,plain,
( product(e_3,e_4,A)
| product(e_3,e_3,A)
| product(e_3,e_2,A)
| product(e_3,e_1,A)
| ~ group_element(A) ),
inference(resolve,[status(thm)],[c_42,c_37]) ).
cnf(c_59,plain,
( product(e_4,e_4,A)
| product(e_4,e_3,A)
| product(e_4,e_2,A)
| product(e_4,e_1,A)
| ~ group_element(A) ),
inference(resolve,[status(thm)],[c_42,c_36]) ).
cnf(c_66,plain,
( product(e_4,e_3,A)
| product(e_3,e_3,A)
| product(e_2,e_3,A)
| product(e_1,e_3,A)
| ~ group_element(A) ),
inference(resolve,[status(thm)],[c_43,c_37]) ).
cnf(c_67,plain,
( product(e_4,e_4,A)
| product(e_3,e_4,A)
| product(e_2,e_4,A)
| product(e_1,e_4,A)
| ~ group_element(A) ),
inference(resolve,[status(thm)],[c_43,c_36]) ).
cnf(c_72,plain,
( product(e_1,e_1,e_4)
| 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_44,c_39]) ).
cnf(c_1057,plain,
( product(e_1,e_1,e_1)
| 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_72,c_45]) ).
cnf(c_87,plain,
( product(e_1,e_1,e_3)
| product(e_1,e_1,e_2)
| product(e_1,e_1,e_1) ),
inference(copy,[status(thm)],[c_1057]) ).
cnf(c_1058,plain,
( 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_87,c_45]) ).
cnf(c_88,plain,
( product(e_1,e_1,e_2)
| product(e_1,e_1,e_1) ),
inference(copy,[status(thm)],[c_1058]) ).
cnf(c_1059,plain,
( product(e_1,e_1,e_1)
| product(e_1,e_1,e_1) ),
inference(resolve,[status(thm)],[c_88,c_45]) ).
cnf(c_89,plain,
product(e_1,e_1,e_1),
inference(copy,[status(thm)],[c_1059]) ).
cnf(c_95,plain,
~ product(e_1,e_4,e_1),
inference(resolve,[status(thm)],[c_25,c_89]) ).
cnf(c_96,plain,
~ product(e_1,e_3,e_1),
inference(resolve,[status(thm)],[c_23,c_89]) ).
cnf(c_98,plain,
~ product(e_4,e_1,e_1),
inference(resolve,[status(thm)],[c_19,c_89]) ).
cnf(c_99,plain,
~ product(e_3,e_1,e_1),
inference(resolve,[status(thm)],[c_17,c_89]) ).
cnf(c_1060,plain,
( product(e_3,e_4,e_1)
| product(e_3,e_3,e_1)
| product(e_3,e_2,e_1)
| product(e_3,e_1,e_1) ),
inference(resolve,[status(thm)],[c_58,c_39]) ).
cnf(c_216,plain,
( product(e_3,e_4,e_1)
| product(e_3,e_3,e_1)
| product(e_3,e_2,e_1) ),
inference(resolve,[status(thm)],[c_99,c_1060]) ).
cnf(c_225,plain,
( ~ product(e_2,e_4,e_1)
| product(e_3,e_3,e_1)
| product(e_3,e_2,e_1) ),
inference(resolve,[status(thm)],[c_216,c_18]) ).
cnf(c_1061,plain,
( product(e_4,e_4,e_1)
| product(e_4,e_3,e_1)
| product(e_4,e_2,e_1)
| product(e_4,e_1,e_1) ),
inference(resolve,[status(thm)],[c_59,c_39]) ).
cnf(c_236,plain,
( product(e_4,e_4,e_1)
| product(e_4,e_3,e_1)
| product(e_4,e_2,e_1) ),
inference(resolve,[status(thm)],[c_98,c_1061]) ).
cnf(c_239,plain,
( product(e_4,e_4,e_4)
| product(e_4,e_3,e_1)
| product(e_4,e_2,e_1) ),
inference(resolve,[status(thm)],[c_236,c_45]) ).
cnf(c_254,plain,
( ~ product(e_4,e_4,e_1)
| product(e_4,e_3,e_1)
| product(e_4,e_2,e_1) ),
inference(resolve,[status(thm)],[c_239,c_31]) ).
cnf(c_1062,plain,
( product(e_4,e_3,e_1)
| product(e_4,e_2,e_1)
| product(e_4,e_3,e_1)
| product(e_4,e_2,e_1) ),
inference(resolve,[status(thm)],[c_254,c_236]) ).
cnf(c_1063,plain,
( product(e_4,e_3,e_1)
| product(e_4,e_3,e_1)
| product(e_4,e_2,e_1) ),
inference(copy,[status(thm)],[c_1062]) ).
cnf(c_261,plain,
( product(e_4,e_3,e_1)
| product(e_4,e_2,e_1) ),
inference(copy,[status(thm)],[c_1063]) ).
cnf(c_262,plain,
( ~ product(e_3,A,e_1)
| product(A,e_4,e_3)
| product(e_4,e_2,e_1) ),
inference(resolve,[status(thm)],[c_261,c_41]) ).
cnf(c_263,plain,
( ~ product(A,e_4,e_1)
| product(e_3,A,e_4)
| product(e_4,e_2,e_1) ),
inference(resolve,[status(thm)],[c_261,c_41]) ).
cnf(c_268,plain,
( ~ product(e_3,e_3,e_1)
| product(e_4,e_2,e_1) ),
inference(resolve,[status(thm)],[c_261,c_21]) ).
cnf(c_1064,plain,
( product(e_4,e_3,e_1)
| product(e_3,e_3,e_1)
| product(e_2,e_3,e_1)
| product(e_1,e_3,e_1) ),
inference(resolve,[status(thm)],[c_66,c_39]) ).
cnf(c_329,plain,
( product(e_4,e_3,e_1)
| product(e_3,e_3,e_1)
| product(e_2,e_3,e_1) ),
inference(resolve,[status(thm)],[c_96,c_1064]) ).
cnf(c_1065,plain,
( product(e_4,e_4,e_1)
| product(e_3,e_4,e_1)
| product(e_2,e_4,e_1)
| product(e_1,e_4,e_1) ),
inference(resolve,[status(thm)],[c_67,c_39]) ).
cnf(c_334,plain,
( product(e_4,e_4,e_1)
| product(e_3,e_4,e_1)
| product(e_2,e_4,e_1) ),
inference(resolve,[status(thm)],[c_95,c_1065]) ).
cnf(c_343,plain,
( ~ product(e_4,e_2,e_1)
| product(e_3,e_3,e_1)
| product(e_2,e_3,e_1) ),
inference(resolve,[status(thm)],[c_329,c_24]) ).
cnf(c_346,plain,
( product(e_4,e_4,e_4)
| product(e_3,e_4,e_1)
| product(e_2,e_4,e_1) ),
inference(resolve,[status(thm)],[c_334,c_45]) ).
cnf(c_363,plain,
( ~ product(e_4,e_4,e_1)
| product(e_3,e_4,e_1)
| product(e_2,e_4,e_1) ),
inference(resolve,[status(thm)],[c_346,c_31]) ).
cnf(c_1066,plain,
( product(e_3,e_4,e_1)
| product(e_2,e_4,e_1)
| product(e_3,e_4,e_1)
| product(e_2,e_4,e_1) ),
inference(resolve,[status(thm)],[c_363,c_334]) ).
cnf(c_1067,plain,
( product(e_3,e_4,e_1)
| product(e_3,e_4,e_1)
| product(e_2,e_4,e_1) ),
inference(copy,[status(thm)],[c_1066]) ).
cnf(c_373,plain,
( product(e_3,e_4,e_1)
| product(e_2,e_4,e_1) ),
inference(copy,[status(thm)],[c_1067]) ).
cnf(c_375,plain,
( product(e_4,e_4,e_3)
| product(e_4,e_2,e_1)
| product(e_2,e_4,e_1) ),
inference(resolve,[status(thm)],[c_373,c_262]) ).
cnf(c_376,plain,
( ~ product(e_4,A,e_1)
| product(A,e_3,e_4)
| product(e_2,e_4,e_1) ),
inference(resolve,[status(thm)],[c_373,c_41]) ).
cnf(c_382,plain,
( ~ product(e_3,e_3,e_1)
| product(e_2,e_4,e_1) ),
inference(resolve,[status(thm)],[c_373,c_27]) ).
cnf(c_394,plain,
( product(e_4,e_4,e_4)
| product(e_4,e_2,e_1)
| product(e_2,e_4,e_1) ),
inference(resolve,[status(thm)],[c_375,c_45]) ).
cnf(c_442,plain,
( ~ product(e_4,e_4,e_3)
| product(e_4,e_2,e_1)
| product(e_2,e_4,e_1) ),
inference(resolve,[status(thm)],[c_394,c_33]) ).
cnf(c_1068,plain,
( product(e_4,e_2,e_1)
| product(e_2,e_4,e_1)
| product(e_4,e_2,e_1)
| product(e_2,e_4,e_1) ),
inference(resolve,[status(thm)],[c_442,c_375]) ).
cnf(c_1069,plain,
( product(e_4,e_2,e_1)
| product(e_4,e_2,e_1)
| product(e_2,e_4,e_1) ),
inference(copy,[status(thm)],[c_1068]) ).
cnf(c_512,plain,
( product(e_4,e_2,e_1)
| product(e_2,e_4,e_1) ),
inference(copy,[status(thm)],[c_1069]) ).
cnf(c_1070,plain,
( product(e_2,e_3,e_4)
| product(e_2,e_4,e_1)
| product(e_2,e_4,e_1) ),
inference(resolve,[status(thm)],[c_512,c_376]) ).
cnf(c_513,plain,
( product(e_2,e_3,e_4)
| product(e_2,e_4,e_1) ),
inference(copy,[status(thm)],[c_1070]) ).
cnf(c_514,plain,
( product(e_3,e_3,e_1)
| product(e_2,e_3,e_1)
| product(e_2,e_4,e_1) ),
inference(resolve,[status(thm)],[c_512,c_343]) ).
cnf(c_533,plain,
( product(e_3,e_2,e_4)
| product(e_4,e_2,e_1)
| product(e_2,e_3,e_4) ),
inference(resolve,[status(thm)],[c_513,c_263]) ).
cnf(c_534,plain,
( product(e_3,e_3,e_1)
| product(e_3,e_2,e_1)
| product(e_2,e_3,e_4) ),
inference(resolve,[status(thm)],[c_513,c_225]) ).
cnf(c_1071,plain,
( product(e_2,e_4,e_1)
| product(e_2,e_3,e_1)
| product(e_2,e_4,e_1) ),
inference(resolve,[status(thm)],[c_514,c_382]) ).
cnf(c_565,plain,
( product(e_2,e_3,e_1)
| product(e_2,e_4,e_1) ),
inference(copy,[status(thm)],[c_1071]) ).
cnf(c_566,plain,
( product(e_3,e_2,e_4)
| product(e_4,e_2,e_1)
| product(e_2,e_3,e_1) ),
inference(resolve,[status(thm)],[c_565,c_263]) ).
cnf(c_567,plain,
( product(e_3,e_3,e_1)
| product(e_3,e_2,e_1)
| product(e_2,e_3,e_1) ),
inference(resolve,[status(thm)],[c_565,c_225]) ).
cnf(c_568,plain,
( ~ product(e_4,A,e_1)
| product(A,e_2,e_4)
| product(e_2,e_3,e_1) ),
inference(resolve,[status(thm)],[c_565,c_41]) ).
cnf(c_607,plain,
( ~ product(e_3,e_2,e_1)
| product(e_3,e_2,e_4)
| product(e_2,e_3,e_4) ),
inference(resolve,[status(thm)],[c_533,c_21]) ).
cnf(c_610,plain,
( product(e_3,e_3,e_3)
| product(e_3,e_2,e_1)
| product(e_2,e_3,e_4) ),
inference(resolve,[status(thm)],[c_534,c_45]) ).
cnf(c_646,plain,
( product(e_4,e_2,e_1)
| product(e_3,e_2,e_1)
| product(e_2,e_3,e_1) ),
inference(resolve,[status(thm)],[c_567,c_268]) ).
cnf(c_1072,plain,
( product(e_3,e_2,e_4)
| product(e_2,e_3,e_1)
| product(e_2,e_2,e_4)
| product(e_2,e_3,e_1) ),
inference(resolve,[status(thm)],[c_568,c_566]) ).
cnf(c_661,plain,
( product(e_3,e_2,e_4)
| product(e_2,e_2,e_4)
| product(e_2,e_3,e_1) ),
inference(copy,[status(thm)],[c_1072]) ).
cnf(c_714,plain,
( ~ product(e_3,e_3,e_1)
| product(e_3,e_2,e_1)
| product(e_2,e_3,e_4) ),
inference(resolve,[status(thm)],[c_610,c_29]) ).
cnf(c_1073,plain,
( product(e_2,e_2,e_4)
| product(e_2,e_3,e_1)
| product(e_3,e_2,e_1)
| product(e_2,e_3,e_1) ),
inference(resolve,[status(thm)],[c_646,c_568]) ).
cnf(c_788,plain,
( product(e_2,e_2,e_4)
| product(e_3,e_2,e_1)
| product(e_2,e_3,e_1) ),
inference(copy,[status(thm)],[c_1073]) ).
cnf(c_814,plain,
( ~ product(e_3,e_2,e_1)
| product(e_2,e_2,e_4)
| product(e_2,e_3,e_1) ),
inference(resolve,[status(thm)],[c_661,c_31]) ).
cnf(c_1074,plain,
( product(e_3,e_2,e_1)
| product(e_2,e_3,e_4)
| product(e_3,e_2,e_1)
| product(e_2,e_3,e_4) ),
inference(resolve,[status(thm)],[c_714,c_534]) ).
cnf(c_1075,plain,
( product(e_3,e_2,e_1)
| product(e_3,e_2,e_1)
| product(e_2,e_3,e_4) ),
inference(copy,[status(thm)],[c_1074]) ).
cnf(c_896,plain,
( product(e_3,e_2,e_1)
| product(e_2,e_3,e_4) ),
inference(copy,[status(thm)],[c_1075]) ).
cnf(c_1076,plain,
( product(e_3,e_2,e_4)
| product(e_2,e_3,e_4)
| product(e_2,e_3,e_4) ),
inference(resolve,[status(thm)],[c_896,c_607]) ).
cnf(c_898,plain,
( product(e_3,e_2,e_4)
| product(e_2,e_3,e_4) ),
inference(copy,[status(thm)],[c_1076]) ).
cnf(c_920,plain,
( ~ product(e_3,e_2,e_1)
| product(e_2,e_3,e_4) ),
inference(resolve,[status(thm)],[c_898,c_31]) ).
cnf(c_1077,plain,
( product(e_2,e_3,e_4)
| product(e_2,e_3,e_4) ),
inference(resolve,[status(thm)],[c_920,c_896]) ).
cnf(c_965,plain,
product(e_2,e_3,e_4),
inference(copy,[status(thm)],[c_1077]) ).
cnf(c_976,plain,
~ product(e_2,e_3,e_1),
inference(resolve,[status(thm)],[c_965,c_31]) ).
cnf(c_977,plain,
~ product(e_2,e_2,e_4),
inference(resolve,[status(thm)],[c_965,c_24]) ).
cnf(c_1078,plain,
( ~ product(e_3,e_2,e_1)
| product(e_2,e_2,e_4) ),
inference(resolve,[status(thm)],[c_976,c_814]) ).
cnf(c_1033,plain,
~ product(e_3,e_2,e_1),
inference(resolve,[status(thm)],[c_977,c_1078]) ).
cnf(c_1079,plain,
( product(e_2,e_2,e_4)
| product(e_3,e_2,e_1) ),
inference(resolve,[status(thm)],[c_976,c_788]) ).
cnf(c_1080,plain,
product(e_2,e_2,e_4),
inference(resolve,[status(thm)],[c_1033,c_1079]) ).
cnf(c_1056,plain,
$false,
inference(resolve,[status(thm)],[c_977,c_1080]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP129-4.004 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/5.38 % Computer : n016.cluster.edu
% 0.09/5.38 % Model : x86_64 x86_64
% 0.09/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.38 % Memory : 8046.5625MB
% 0.09/5.38 % OS : Linux 6.8.0-71-generic
% 0.06/15.42 % CPULimit : 300
% 0.06/15.42 % WCLimit : 300
% 0.06/15.42 % DateTime : Fri Sep 25 14:28:27 UTC 2026
% 0.06/15.42 % CPUTime :
% 0.06/15.42 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.06/15.42 % Process 3104031 was started by sandbox on n006,
% 0.06/15.42 % Fri Sep 25 14:28:27 2026
% 0.06/15.42 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.06/15.43
% 0.06/15.43 % From the command line: assign(max_seconds, 300).
% 0.32/15.54
% 0.32/15.54 % SZS status Unsatisfiable for theBenchmark
% 0.32/15.54
% 0.32/15.54 % Proof 1 at 0.08 (+ 0.03) seconds.
% 0.32/15.54 % Length of proof is 83.
% 0.32/15.54 % Level of proof is 26.
% 0.32/15.54 % Maximum clause weight is 20.000.
% 0.32/15.54 % Given clauses 279.
% 0.32/15.54
% 0.32/15.54 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------