%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP134-1.003 : 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 : n007.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 1.32s 0.57s
% Output : CNFRefutation 1.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 39
% Number of leaves : 11
% Syntax : Number of formulae : 140 ( 23 unt; 0 def)
% Number of atoms : 427 ( 0 equ)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 373 ( 86 ~; 287 |; 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 : 66 ( 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]) ).
cnf(c_17,plain,
( ~ product(A,B,e_1)
| ~ product(A,B,e_3) ),
inference(resolve,[status(thm)],[c_1,c_3]) ).
cnf(c_18,plain,
( ~ product(A,B,e_2)
| ~ product(A,B,e_3) ),
inference(resolve,[status(thm)],[c_1,c_2]) ).
fof(qg4,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( product(VAR_2,VAR_3,VAR_1)
| ~ product(VAR_1,VAR_0,VAR_3)
| ~ product(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',qg4) ).
cnf(c_19,plain,
( product(C,D,B)
| ~ product(B,A,D)
| ~ product(A,B,C) ),
inference(clausify,[status(thm)],[qg4]) ).
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_25,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_26,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_27,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_28,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_29,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_32,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_25,c_23]) ).
cnf(c_33,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_25,c_22]) ).
cnf(c_34,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_25,c_21]) ).
cnf(c_35,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_26,c_23]) ).
cnf(c_36,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_26,c_22]) ).
cnf(c_37,plain,
( product(e_3,e_3,e_1)
| product(e_1,e_1,e_2)
| product(e_1,e_1,e_1) ),
inference(resolve,[status(thm)],[c_32,c_24]) ).
cnf(c_40,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_33,c_24]) ).
cnf(c_48,plain,
( ~ product(e_3,e_1,e_3)
| product(e_3,e_3,e_2)
| product(e_3,e_3,e_1) ),
inference(resolve,[status(thm)],[c_34,c_14]) ).
cnf(c_50,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_34,c_11]) ).
cnf(c_54,plain,
( ~ product(e_1,e_1,e_3)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_1) ),
inference(resolve,[status(thm)],[c_35,c_14]) ).
cnf(c_56,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_27,c_23]) ).
cnf(c_57,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_27,c_22]) ).
cnf(c_60,plain,
( ~ product(e_2,e_2,e_3)
| product(e_2,e_3,e_2)
| product(e_2,e_3,e_1) ),
inference(resolve,[status(thm)],[c_36,c_15]) ).
cnf(c_69,plain,
( ~ 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_37,c_11]) ).
cnf(c_73,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_40,c_15]) ).
cnf(c_75,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_40,c_12]) ).
cnf(c_77,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_28,c_23]) ).
cnf(c_79,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_29,c_23]) ).
cnf(c_80,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_50,c_35]) ).
cnf(c_81,plain,
( product(e_1,e_1,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_54,c_32]) ).
cnf(c_82,plain,
( product(e_3,e_3,e_2)
| product(e_3,e_3,e_1)
| product(e_3,e_1,e_2)
| product(e_3,e_1,e_1) ),
inference(resolve,[status(thm)],[c_56,c_48]) ).
cnf(c_92,plain,
( ~ product(e_2,e_2,e_3)
| product(e_3,e_2,e_2)
| product(e_3,e_2,e_1) ),
inference(resolve,[status(thm)],[c_57,c_12]) ).
cnf(c_95,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_60,c_33]) ).
cnf(c_100,plain,
( product(A,e_3,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_77,c_19]) ).
cnf(c_102,plain,
( ~ product(e_1,e_1,e_3)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_1) ),
inference(resolve,[status(thm)],[c_77,c_13]) ).
cnf(c_107,plain,
( ~ product(e_1,e_1,e_3)
| product(e_2,e_1,e_2)
| product(e_2,e_1,e_1) ),
inference(resolve,[status(thm)],[c_79,c_10]) ).
cnf(c_111,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_92,c_33]) ).
cnf(c_113,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_102,c_32]) ).
cnf(c_114,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_107,c_32]) ).
cnf(c_124,plain,
( product(e_2,e_2,e_3)
| 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_80,c_24]) ).
cnf(c_132,plain,
( ~ product(e_1,e_2,e_2)
| product(e_1,e_1,e_2)
| product(e_1,e_1,e_1)
| product(e_1,e_3,e_1) ),
inference(resolve,[status(thm)],[c_81,c_15]) ).
cnf(c_133,plain,
( product(e_2,e_2,e_3)
| product(e_3,e_3,e_1)
| product(e_3,e_1,e_2)
| product(e_3,e_1,e_1) ),
inference(resolve,[status(thm)],[c_82,c_24]) ).
cnf(c_581,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_95,c_75]) ).
cnf(c_582,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_581]) ).
cnf(c_144,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_582]) ).
cnf(c_146,plain,
( product(e_1,A,e_3)
| ~ product(e_3,e_2,A)
| product(e_2,e_2,e_2)
| product(e_2,e_2,e_1) ),
inference(resolve,[status(thm)],[c_144,c_19]) ).
cnf(c_167,plain,
( product(e_2,e_1,e_2)
| product(e_2,e_1,e_1)
| product(e_3,e_3,e_1)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_1) ),
inference(resolve,[status(thm)],[c_100,c_79]) ).
cnf(c_583,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_111,c_73]) ).
cnf(c_584,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_583]) ).
cnf(c_192,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_584]) ).
cnf(c_206,plain,
( product(e_2,A,e_1)
| ~ product(e_1,e_2,A)
| 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_114,c_19]) ).
cnf(c_207,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_206]) ).
cnf(c_221,plain,
( product(e_1,e_1,e_3)
| product(e_2,e_2,e_3)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_1) ),
inference(resolve,[status(thm)],[c_124,c_24]) ).
cnf(c_585,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_1,e_2)
| product(e_1,e_1,e_1)
| product(e_1,e_3,e_1) ),
inference(resolve,[status(thm)],[c_132,c_113]) ).
cnf(c_586,plain,
( 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)
| product(e_1,e_3,e_1) ),
inference(copy,[status(thm)],[c_585]) ).
cnf(c_237,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_3,e_1) ),
inference(copy,[status(thm)],[c_586]) ).
cnf(c_246,plain,
( product(e_1,e_1,e_3)
| product(e_2,e_2,e_3)
| product(e_3,e_1,e_2)
| product(e_3,e_1,e_1) ),
inference(resolve,[status(thm)],[c_133,c_24]) ).
cnf(c_587,plain,
( product(e_2,e_2,e_2)
| product(e_2,e_2,e_1)
| product(e_1,e_1,e_3)
| product(e_2,e_2,e_2)
| product(e_2,e_2,e_1) ),
inference(resolve,[status(thm)],[c_146,c_192]) ).
cnf(c_588,plain,
( product(e_2,e_2,e_2)
| product(e_1,e_1,e_3)
| product(e_2,e_2,e_2)
| product(e_2,e_2,e_1) ),
inference(copy,[status(thm)],[c_587]) ).
cnf(c_275,plain,
( product(e_1,e_1,e_3)
| product(e_2,e_2,e_2)
| product(e_2,e_2,e_1) ),
inference(copy,[status(thm)],[c_588]) ).
cnf(c_278,plain,
( ~ product(e_2,e_1,e_2)
| product(e_1,e_1,e_3)
| product(e_2,e_2,e_1) ),
inference(resolve,[status(thm)],[c_275,c_13]) ).
cnf(c_308,plain,
( ~ product(e_2,e_2,e_2)
| product(e_1,e_1,e_3)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_1) ),
inference(resolve,[status(thm)],[c_221,c_18]) ).
cnf(c_309,plain,
( ~ product(e_2,e_2,e_1)
| product(e_1,e_1,e_3)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_1) ),
inference(resolve,[status(thm)],[c_221,c_17]) ).
cnf(c_589,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_1,e_2)
| product(e_1,e_1,e_1) ),
inference(resolve,[status(thm)],[c_237,c_69]) ).
cnf(c_590,plain,
( 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_589]) ).
cnf(c_316,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_590]) ).
cnf(c_591,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_316,c_207]) ).
cnf(c_592,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_591]) ).
cnf(c_317,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_592]) ).
cnf(c_318,plain,
( product(A,e_1,e_1)
| ~ 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_316,c_19]) ).
cnf(c_320,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_318]) ).
cnf(c_593,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_320,c_317]) ).
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) ),
inference(copy,[status(thm)],[c_593]) ).
cnf(c_324,plain,
( product(e_1,e_1,e_2)
| product(e_1,e_1,e_1) ),
inference(copy,[status(thm)],[c_594]) ).
cnf(c_327,plain,
( product(e_2,e_2,e_1)
| product(e_1,e_1,e_1) ),
inference(resolve,[status(thm)],[c_324,c_24]) ).
cnf(c_344,plain,
( ~ product(e_1,e_1,e_2)
| product(e_1,e_1,e_3)
| product(e_2,e_2,e_3)
| product(e_3,e_1,e_1) ),
inference(resolve,[status(thm)],[c_246,c_11]) ).
cnf(c_595,plain,
( product(e_1,e_1,e_3)
| product(e_2,e_2,e_1)
| product(e_1,e_1,e_3)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_1) ),
inference(resolve,[status(thm)],[c_308,c_275]) ).
cnf(c_400,plain,
( product(e_2,e_2,e_1)
| product(e_1,e_1,e_3)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_1) ),
inference(copy,[status(thm)],[c_595]) ).
cnf(c_426,plain,
( product(e_1,e_1,e_1)
| product(e_1,e_1,e_3)
| product(e_2,e_2,e_3)
| product(e_3,e_1,e_1) ),
inference(resolve,[status(thm)],[c_344,c_324]) ).
cnf(c_427,plain,
( product(e_1,e_1,e_3)
| 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) ),
inference(resolve,[status(thm)],[c_167,c_24]) ).
cnf(c_596,plain,
( product(e_1,e_1,e_3)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_1)
| product(e_1,e_1,e_3)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_1) ),
inference(resolve,[status(thm)],[c_400,c_309]) ).
cnf(c_597,plain,
( product(e_1,e_1,e_3)
| product(e_1,e_3,e_2)
| product(e_1,e_1,e_3)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_1) ),
inference(copy,[status(thm)],[c_596]) ).
cnf(c_598,plain,
( product(e_1,e_1,e_3)
| product(e_1,e_1,e_3)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_1) ),
inference(copy,[status(thm)],[c_597]) ).
cnf(c_465,plain,
( product(e_1,e_1,e_3)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_1) ),
inference(copy,[status(thm)],[c_598]) ).
cnf(c_476,plain,
( ~ product(e_1,e_2,e_2)
| product(e_1,e_1,e_3)
| product(e_1,e_3,e_1) ),
inference(resolve,[status(thm)],[c_465,c_15]) ).
cnf(c_477,plain,
( ~ product(e_1,e_1,e_2)
| product(e_1,e_1,e_3)
| product(e_1,e_3,e_1) ),
inference(resolve,[status(thm)],[c_465,c_14]) ).
cnf(c_478,plain,
( product(e_1,e_1,e_1)
| product(e_1,e_1,e_3)
| product(e_1,e_3,e_1) ),
inference(resolve,[status(thm)],[c_477,c_324]) ).
cnf(c_480,plain,
( product(A,e_1,e_1)
| ~ product(e_3,e_1,A)
| product(e_1,e_1,e_1)
| product(e_1,e_1,e_3) ),
inference(resolve,[status(thm)],[c_478,c_19]) ).
cnf(c_482,plain,
( ~ product(e_3,e_1,e_1)
| product(e_1,e_1,e_1)
| product(e_1,e_1,e_3) ),
inference(factor,[status(thm)],[c_480]) ).
cnf(c_599,plain,
( product(e_1,e_1,e_1)
| product(e_1,e_1,e_3)
| product(e_1,e_1,e_1)
| product(e_1,e_1,e_3)
| product(e_2,e_2,e_3) ),
inference(resolve,[status(thm)],[c_426,c_482]) ).
cnf(c_600,plain,
( product(e_1,e_1,e_1)
| product(e_1,e_1,e_1)
| product(e_1,e_1,e_3)
| product(e_2,e_2,e_3) ),
inference(copy,[status(thm)],[c_599]) ).
cnf(c_485,plain,
( product(e_1,e_1,e_1)
| product(e_1,e_1,e_3)
| product(e_2,e_2,e_3) ),
inference(copy,[status(thm)],[c_600]) ).
cnf(c_494,plain,
( ~ product(e_2,e_2,e_1)
| product(e_1,e_1,e_1)
| product(e_1,e_1,e_3) ),
inference(resolve,[status(thm)],[c_485,c_17]) ).
cnf(c_601,plain,
( product(e_1,e_1,e_1)
| product(e_1,e_1,e_1)
| product(e_1,e_1,e_3) ),
inference(resolve,[status(thm)],[c_494,c_327]) ).
cnf(c_518,plain,
( product(e_1,e_1,e_1)
| product(e_1,e_1,e_3) ),
inference(copy,[status(thm)],[c_601]) ).
cnf(c_528,plain,
( ~ product(e_1,e_1,e_2)
| product(e_1,e_1,e_1) ),
inference(resolve,[status(thm)],[c_518,c_18]) ).
cnf(c_602,plain,
( product(e_1,e_1,e_1)
| product(e_1,e_1,e_1) ),
inference(resolve,[status(thm)],[c_528,c_324]) ).
cnf(c_541,plain,
product(e_1,e_1,e_1),
inference(copy,[status(thm)],[c_602]) ).
cnf(c_544,plain,
~ product(e_1,e_1,e_3),
inference(resolve,[status(thm)],[c_17,c_541]) ).
cnf(c_545,plain,
~ product(e_1,e_1,e_2),
inference(resolve,[status(thm)],[c_16,c_541]) ).
cnf(c_546,plain,
~ product(e_1,e_3,e_1),
inference(resolve,[status(thm)],[c_14,c_541]) ).
cnf(c_547,plain,
~ product(e_1,e_2,e_1),
inference(resolve,[status(thm)],[c_13,c_541]) ).
cnf(c_549,plain,
~ product(e_2,e_1,e_1),
inference(resolve,[status(thm)],[c_10,c_541]) ).
cnf(c_603,plain,
( ~ product(e_1,e_2,e_2)
| product(e_1,e_1,e_3) ),
inference(resolve,[status(thm)],[c_546,c_476]) ).
cnf(c_550,plain,
~ product(e_1,e_2,e_2),
inference(resolve,[status(thm)],[c_544,c_603]) ).
cnf(c_604,plain,
( product(e_1,e_1,e_3)
| product(e_2,e_1,e_2)
| product(e_2,e_1,e_1)
| product(e_1,e_2,e_2) ),
inference(resolve,[status(thm)],[c_547,c_427]) ).
cnf(c_605,plain,
( product(e_1,e_1,e_3)
| product(e_2,e_1,e_2)
| product(e_2,e_1,e_1) ),
inference(resolve,[status(thm)],[c_550,c_604]) ).
cnf(c_606,plain,
( product(e_1,e_1,e_3)
| product(e_2,e_1,e_2) ),
inference(resolve,[status(thm)],[c_549,c_605]) ).
cnf(c_565,plain,
product(e_2,e_1,e_2),
inference(resolve,[status(thm)],[c_544,c_606]) ).
cnf(c_607,plain,
( ~ product(e_2,e_1,e_2)
| product(e_2,e_2,e_1) ),
inference(resolve,[status(thm)],[c_544,c_278]) ).
cnf(c_567,plain,
product(e_2,e_2,e_1),
inference(resolve,[status(thm)],[c_565,c_607]) ).
cnf(c_608,plain,
~ product(e_2,e_2,e_1),
inference(resolve,[status(thm)],[c_24,c_545]) ).
cnf(c_580,plain,
$false,
inference(resolve,[status(thm)],[c_567,c_608]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP134-1.003 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.37 % Computer : n007.cluster.edu
% 0.08/0.37 % Model : x86_64 x86_64
% 0.08/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.37 % Memory : 8046.5625MB
% 0.08/0.37 % OS : Linux 6.8.0-71-generic
% 0.08/0.37 % CPULimit : 300
% 0.08/0.37 % WCLimit : 300
% 0.08/0.37 % DateTime : Fri Sep 25 14:28:24 UTC 2026
% 0.08/0.38 % CPUTime :
% 0.08/0.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.38 % Process 1205999 was started by sandbox2 on n007,
% 0.08/0.38 % Fri Sep 25 14:28:24 2026
% 0.08/0.38 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.08/0.39
% 0.08/0.39 % From the command line: assign(max_seconds, 300).
% 1.32/0.57
% 1.32/0.57 % SZS status Unsatisfiable for theBenchmark
% 1.32/0.57
% 1.32/0.57 % Proof 1 at 0.12 (+ 0.05) seconds.
% 1.32/0.57 % Length of proof is 101.
% 1.32/0.57 % Level of proof is 23.
% 1.32/0.57 % Maximum clause weight is 20.000.
% 1.32/0.57 % Given clauses 274.
% 1.32/0.57
% 1.32/0.57 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------