%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP131-1.002 : 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 07:28:04 AM UTC 2026
% Result : Unsatisfiable 0.07s 0.37s
% Output : CNFRefutation 0.07s
% 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_2,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_4,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_5,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_6,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_7,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_8,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_7,c_2]) ).
cnf(c_9,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_6,c_2]) ).
cnf(c_10,plain,
( ~ product(e_1,A,B)
| ~ product(e_2,A,B) ),
inference(resolve,[status(thm)],[c_5,c_2]) ).
cnf(c_11,plain,
( ~ product(A,e_1,B)
| ~ product(A,e_2,B) ),
inference(resolve,[status(thm)],[c_4,c_2]) ).
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_13,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_14,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_15,plain,
group_element(e_1),
inference(clausify,[status(thm)],[element_1]) ).
cnf(c_16,plain,
( ~ product(A,e_1,B)
| ~ product(B,e_1,A)
| ~ product(A,e_2,A) ),
inference(factor,[status(thm)],[c_8]) ).
cnf(c_20,plain,
( product(A,A,e_2)
| product(A,A,e_1)
| ~ group_element(A) ),
inference(factor,[status(thm)],[c_13]) ).
cnf(c_21,plain,
( product(A,e_2,e_2)
| product(A,e_2,e_1)
| ~ group_element(A) ),
inference(resolve,[status(thm)],[c_14,c_13]) ).
cnf(c_22,plain,
( product(e_2,A,e_2)
| product(e_2,A,e_1)
| ~ group_element(A) ),
inference(resolve,[status(thm)],[c_14,c_13]) ).
cnf(c_25,plain,
( product(e_1,e_1,e_2)
| product(e_1,e_1,e_1) ),
inference(resolve,[status(thm)],[c_20,c_15]) ).
cnf(c_26,plain,
( product(e_2,e_2,e_2)
| product(e_2,e_2,e_1) ),
inference(resolve,[status(thm)],[c_20,c_14]) ).
cnf(c_27,plain,
( product(e_1,e_2,e_2)
| product(e_1,e_2,e_1) ),
inference(resolve,[status(thm)],[c_21,c_15]) ).
cnf(c_30,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_25,c_9]) ).
cnf(c_34,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_30]) ).
cnf(c_39,plain,
( ~ product(e_1,e_2,e_2)
| product(e_2,e_2,e_1) ),
inference(resolve,[status(thm)],[c_26,c_10]) ).
cnf(c_46,plain,
( ~ product(e_1,e_1,e_2)
| product(e_1,e_2,e_1) ),
inference(resolve,[status(thm)],[c_27,c_11]) ).
cnf(c_47,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_27,c_9]) ).
cnf(c_51,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_47]) ).
cnf(c_53,plain,
( product(e_2,e_1,e_2)
| product(e_2,e_1,e_1) ),
inference(resolve,[status(thm)],[c_22,c_15]) ).
cnf(c_54,plain,
( product(e_1,e_2,e_1)
| product(e_2,e_2,e_1) ),
inference(resolve,[status(thm)],[c_39,c_27]) ).
cnf(c_55,plain,
( product(e_1,e_1,e_1)
| product(e_1,e_2,e_1) ),
inference(resolve,[status(thm)],[c_46,c_25]) ).
cnf(c_58,plain,
( ~ product(e_1,e_1,e_2)
| product(e_2,e_1,e_1) ),
inference(resolve,[status(thm)],[c_53,c_10]) ).
cnf(c_83,plain,
( product(e_1,e_1,e_1)
| product(e_2,e_1,e_1) ),
inference(resolve,[status(thm)],[c_58,c_25]) ).
cnf(c_111,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_34,c_83]) ).
cnf(c_90,plain,
( ~ product(e_1,A,e_1)
| product(e_1,e_1,e_1) ),
inference(copy,[status(thm)],[c_111]) ).
cnf(c_112,plain,
( product(e_1,e_1,e_1)
| product(e_1,e_1,e_1) ),
inference(resolve,[status(thm)],[c_90,c_55]) ).
cnf(c_92,plain,
product(e_1,e_1,e_1),
inference(copy,[status(thm)],[c_112]) ).
cnf(c_113,plain,
( ~ product(e_1,e_1,e_1)
| ~ product(e_1,e_2,e_1) ),
inference(resolve,[status(thm)],[c_92,c_16]) ).
cnf(c_94,plain,
~ product(e_1,e_2,e_1),
inference(resolve,[status(thm)],[c_92,c_113]) ).
cnf(c_107,plain,
product(e_2,e_2,e_1),
inference(resolve,[status(thm)],[c_94,c_54]) ).
cnf(c_114,plain,
( ~ product(e_1,A,e_1)
| ~ product(e_2,e_2,e_1) ),
inference(resolve,[status(thm)],[c_94,c_51]) ).
cnf(c_109,plain,
~ product(e_1,A,e_1),
inference(resolve,[status(thm)],[c_107,c_114]) ).
cnf(c_110,plain,
$false,
inference(resolve,[status(thm)],[c_109,c_92]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP131-1.002 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.33 % Computer : n001.cluster.edu
% 0.07/0.33 % Model : x86_64 x86_64
% 0.07/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.33 % Memory : 8046.5625MB
% 0.07/0.33 % OS : Linux 6.8.0-71-generic
% 0.07/0.34 % CPULimit : 300
% 0.07/0.34 % WCLimit : 300
% 0.07/0.34 % DateTime : Fri Sep 25 14:35:40 UTC 2026
% 0.07/0.34 % CPUTime :
% 0.07/0.34 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.07/0.34 % Process 3525813 was started by sandbox2 on n001,
% 0.07/0.34 % Fri Sep 25 14:35:40 2026
% 0.07/0.34 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.07/0.35
% 0.07/0.35 % From the command line: assign(max_seconds, 300).
% 0.07/0.37
% 0.07/0.37 % SZS status Unsatisfiable for theBenchmark
% 0.07/0.37
% 0.07/0.37 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.07/0.37 % Length of proof is 36.
% 0.07/0.37 % Level of proof is 10.
% 0.07/0.37 % Maximum clause weight is 16.000.
% 0.07/0.37 % Given clauses 35.
% 0.07/0.37
% 0.07/0.37 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------