%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP131-2.002 : 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 : 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 07:28:04 AM UTC 2026
% Result : Unsatisfiable 0.09s 5.41s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 8
% Syntax : Number of formulae : 48 ( 11 unt; 0 def)
% Number of atoms : 120 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 141 ( 69 ~; 72 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 2 ( 2 usr; 2 con; 0-0 aty)
% Number of variables : 71 ( 6 sgn 22 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(e_2_is_not_e_1,axiom,
~ equalish(e_2,e_1),
file('theBenchmark.p',e_2_is_not_e_1) ).
cnf(c_6,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]) ).
fof(qg1_1,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4,VAR_5] :
( equalish(VAR_0,VAR_3)
| ~ product(VAR_5,VAR_4,VAR_3)
| ~ product(VAR_5,VAR_1,VAR_0)
| ~ product(VAR_3,VAR_4,VAR_2)
| ~ product(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',qg1_1) ).
cnf(c_10,plain,
( equalish(A,D)
| ~ product(F,E,D)
| ~ product(F,B,A)
| ~ product(D,E,C)
| ~ product(A,B,C) ),
inference(clausify,[status(thm)],[qg1_1]) ).
fof(qg1_2,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4,VAR_5] :
( equalish(VAR_1,VAR_4)
| ~ product(VAR_5,VAR_4,VAR_3)
| ~ product(VAR_5,VAR_1,VAR_0)
| ~ product(VAR_3,VAR_4,VAR_2)
| ~ product(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',qg1_2) ).
cnf(c_11,plain,
( equalish(B,E)
| ~ product(F,E,D)
| ~ product(F,B,A)
| ~ product(D,E,C)
| ~ product(A,B,C) ),
inference(clausify,[status(thm)],[qg1_2]) ).
cnf(c_12,plain,
( ~ product(D,e_1,C)
| ~ product(D,e_2,A)
| ~ product(C,e_1,B)
| ~ product(A,e_2,B) ),
inference(resolve,[status(thm)],[c_11,c_6]) ).
cnf(c_13,plain,
( ~ product(D,C,e_1)
| ~ product(D,A,e_2)
| ~ product(e_1,C,B)
| ~ product(e_2,A,B) ),
inference(resolve,[status(thm)],[c_10,c_6]) ).
cnf(c_14,plain,
( ~ product(e_1,A,B)
| ~ product(e_2,A,B) ),
inference(resolve,[status(thm)],[c_9,c_6]) ).
cnf(c_15,plain,
( ~ product(A,e_1,B)
| ~ product(A,e_2,B) ),
inference(resolve,[status(thm)],[c_8,c_6]) ).
fof(product_total_function1,axiom,
! [VAR_0,VAR_1] :
( 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_17,plain,
( 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_2,axiom,
group_element(e_2),
file('theBenchmark.p',element_2) ).
cnf(c_18,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_19,plain,
group_element(e_1),
inference(clausify,[status(thm)],[element_1]) ).
cnf(c_20,plain,
( ~ product(A,e_1,B)
| ~ product(B,e_1,A)
| ~ product(A,e_2,A) ),
inference(factor,[status(thm)],[c_12]) ).
cnf(c_24,plain,
( product(A,A,e_2)
| product(A,A,e_1)
| ~ group_element(A) ),
inference(factor,[status(thm)],[c_17]) ).
cnf(c_25,plain,
( product(A,e_2,e_2)
| product(A,e_2,e_1)
| ~ group_element(A) ),
inference(resolve,[status(thm)],[c_18,c_17]) ).
cnf(c_26,plain,
( product(e_2,A,e_2)
| product(e_2,A,e_1)
| ~ group_element(A) ),
inference(resolve,[status(thm)],[c_18,c_17]) ).
cnf(c_29,plain,
( product(e_1,e_1,e_2)
| product(e_1,e_1,e_1) ),
inference(resolve,[status(thm)],[c_24,c_19]) ).
cnf(c_30,plain,
( product(e_2,e_2,e_2)
| product(e_2,e_2,e_1) ),
inference(resolve,[status(thm)],[c_24,c_18]) ).
cnf(c_31,plain,
( product(e_1,e_2,e_2)
| product(e_1,e_2,e_1) ),
inference(resolve,[status(thm)],[c_25,c_19]) ).
cnf(c_34,plain,
( ~ product(e_1,B,e_1)
| ~ product(e_1,B,A)
| ~ product(e_2,e_1,A)
| product(e_1,e_1,e_1) ),
inference(resolve,[status(thm)],[c_29,c_13]) ).
cnf(c_38,plain,
( ~ product(e_1,A,e_1)
| ~ product(e_2,e_1,e_1)
| product(e_1,e_1,e_1) ),
inference(factor,[status(thm)],[c_34]) ).
cnf(c_43,plain,
( ~ product(e_1,e_2,e_2)
| product(e_2,e_2,e_1) ),
inference(resolve,[status(thm)],[c_30,c_14]) ).
cnf(c_50,plain,
( ~ product(e_1,e_1,e_2)
| product(e_1,e_2,e_1) ),
inference(resolve,[status(thm)],[c_31,c_15]) ).
cnf(c_51,plain,
( ~ product(e_1,B,e_1)
| ~ product(e_1,B,A)
| ~ product(e_2,e_2,A)
| product(e_1,e_2,e_1) ),
inference(resolve,[status(thm)],[c_31,c_13]) ).
cnf(c_55,plain,
( ~ product(e_1,A,e_1)
| ~ product(e_2,e_2,e_1)
| product(e_1,e_2,e_1) ),
inference(factor,[status(thm)],[c_51]) ).
cnf(c_57,plain,
( product(e_2,e_1,e_2)
| product(e_2,e_1,e_1) ),
inference(resolve,[status(thm)],[c_26,c_19]) ).
cnf(c_58,plain,
( product(e_1,e_2,e_1)
| product(e_2,e_2,e_1) ),
inference(resolve,[status(thm)],[c_43,c_31]) ).
cnf(c_59,plain,
( product(e_1,e_1,e_1)
| product(e_1,e_2,e_1) ),
inference(resolve,[status(thm)],[c_50,c_29]) ).
cnf(c_62,plain,
( ~ product(e_1,e_1,e_2)
| product(e_2,e_1,e_1) ),
inference(resolve,[status(thm)],[c_57,c_14]) ).
cnf(c_87,plain,
( product(e_1,e_1,e_1)
| product(e_2,e_1,e_1) ),
inference(resolve,[status(thm)],[c_62,c_29]) ).
cnf(c_115,plain,
( product(e_1,e_1,e_1)
| ~ product(e_1,A,e_1)
| product(e_1,e_1,e_1) ),
inference(resolve,[status(thm)],[c_38,c_87]) ).
cnf(c_94,plain,
( ~ product(e_1,A,e_1)
| product(e_1,e_1,e_1) ),
inference(copy,[status(thm)],[c_115]) ).
cnf(c_116,plain,
( product(e_1,e_1,e_1)
| product(e_1,e_1,e_1) ),
inference(resolve,[status(thm)],[c_94,c_59]) ).
cnf(c_96,plain,
product(e_1,e_1,e_1),
inference(copy,[status(thm)],[c_116]) ).
cnf(c_117,plain,
( ~ product(e_1,e_1,e_1)
| ~ product(e_1,e_2,e_1) ),
inference(resolve,[status(thm)],[c_96,c_20]) ).
cnf(c_98,plain,
~ product(e_1,e_2,e_1),
inference(resolve,[status(thm)],[c_96,c_117]) ).
cnf(c_111,plain,
product(e_2,e_2,e_1),
inference(resolve,[status(thm)],[c_98,c_58]) ).
cnf(c_118,plain,
( ~ product(e_1,A,e_1)
| ~ product(e_2,e_2,e_1) ),
inference(resolve,[status(thm)],[c_98,c_55]) ).
cnf(c_113,plain,
~ product(e_1,A,e_1),
inference(resolve,[status(thm)],[c_111,c_118]) ).
cnf(c_114,plain,
$false,
inference(resolve,[status(thm)],[c_113,c_96]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP131-2.002 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/5.37 % Computer : n016.cluster.edu
% 0.07/5.37 % Model : x86_64 x86_64
% 0.07/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/5.37 % Memory : 8046.5625MB
% 0.07/5.37 % OS : Linux 6.8.0-71-generic
% 0.07/5.37 % CPULimit : 300
% 0.07/5.37 % WCLimit : 300
% 0.07/5.37 % DateTime : Fri Sep 25 14:34:35 UTC 2026
% 0.07/5.37 % CPUTime :
% 0.07/5.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.07/5.37 % Process 2605134 was started by sandbox on n016,
% 0.07/5.37 % Fri Sep 25 14:34:35 2026
% 0.07/5.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.07/5.37
% 0.07/5.37 % From the command line: assign(max_seconds, 300).
% 0.09/5.41
% 0.09/5.41 % SZS status Unsatisfiable for theBenchmark
% 0.09/5.41
% 0.09/5.41 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.09/5.41 % Length of proof is 36.
% 0.09/5.41 % Level of proof is 10.
% 0.09/5.41 % Maximum clause weight is 16.000.
% 0.09/5.41 % Given clauses 35.
% 0.09/5.41
% 0.09/5.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------