%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP130-4.003 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n011.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 0.14s 10.42s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 11
% Syntax : Number of formulae : 48 ( 20 unt; 0 def)
% Number of atoms : 104 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 99 ( 43 ~; 56 |; 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 : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 46 ( 1 sgn 16 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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_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]) ).
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]) ).
fof(qg3_2,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( ~ product(VAR_0,VAR_3,VAR_1)
| ~ product(VAR_2,VAR_3,VAR_0)
| product(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',qg3_2) ).
cnf(c_24,plain,
( ~ product(A,D,B)
| ~ product(C,D,A)
| product(A,B,C) ),
inference(clausify,[status(thm)],[qg3_2]) ).
fof(qg3_1,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( ~ product(VAR_0,VAR_2,VAR_3)
| ~ product(VAR_3,VAR_1,VAR_0)
| product(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',qg3_1) ).
cnf(c_25,plain,
( ~ product(A,C,D)
| ~ product(D,B,A)
| product(A,B,C) ),
inference(clausify,[status(thm)],[qg3_1]) ).
fof(column_surjectivity,axiom,
! [VAR_0,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_26,plain,
( 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]) ).
cnf(c_30,plain,
( ~ product(A,B,A)
| product(A,A,A) ),
inference(factor,[status(thm)],[c_24]) ).
cnf(c_31,plain,
( ~ product(A,B,A)
| product(A,B,B) ),
inference(factor,[status(thm)],[c_25]) ).
cnf(c_32,plain,
( product(A,e_3,A)
| product(A,e_2,A)
| product(A,e_1,A)
| ~ group_element(A) ),
inference(factor,[status(thm)],[c_26]) ).
cnf(c_35,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_37,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_55,plain,
( product(e_1,e_3,e_1)
| product(e_1,e_2,e_1)
| product(e_1,e_1,e_1) ),
inference(resolve,[status(thm)],[c_32,c_23]) ).
cnf(c_128,plain,
( product(e_1,e_1,e_1)
| product(e_1,e_2,e_1)
| product(e_1,e_1,e_1) ),
inference(resolve,[status(thm)],[c_55,c_30]) ).
cnf(c_83,plain,
( product(e_1,e_2,e_1)
| product(e_1,e_1,e_1) ),
inference(copy,[status(thm)],[c_128]) ).
cnf(c_84,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_35,c_23]) ).
cnf(c_129,plain,
( product(e_1,e_1,e_1)
| product(e_1,e_1,e_1) ),
inference(resolve,[status(thm)],[c_83,c_30]) ).
cnf(c_87,plain,
product(e_1,e_1,e_1),
inference(copy,[status(thm)],[c_129]) ).
cnf(c_95,plain,
~ product(e_3,e_1,e_1),
inference(resolve,[status(thm)],[c_11,c_87]) ).
cnf(c_96,plain,
~ product(e_2,e_1,e_1),
inference(resolve,[status(thm)],[c_10,c_87]) ).
cnf(c_98,plain,
( product(e_3,e_1,e_3)
| product(e_3,e_1,e_2) ),
inference(resolve,[status(thm)],[c_95,c_84]) ).
cnf(c_130,plain,
( product(e_3,e_1,e_1)
| product(e_3,e_1,e_2) ),
inference(resolve,[status(thm)],[c_98,c_31]) ).
cnf(c_109,plain,
product(e_3,e_1,e_2),
inference(resolve,[status(thm)],[c_95,c_130]) ).
cnf(c_116,plain,
~ product(e_2,e_1,e_2),
inference(resolve,[status(thm)],[c_109,c_12]) ).
cnf(c_131,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_37,c_23]) ).
cnf(c_132,plain,
( product(e_2,e_1,e_3)
| product(e_2,e_1,e_2) ),
inference(resolve,[status(thm)],[c_96,c_131]) ).
cnf(c_125,plain,
product(e_2,e_1,e_3),
inference(resolve,[status(thm)],[c_116,c_132]) ).
cnf(c_133,plain,
( ~ product(e_3,e_1,A)
| ~ product(A,e_1,e_3) ),
inference(resolve,[status(thm)],[c_25,c_95]) ).
cnf(c_134,plain,
~ product(e_2,e_1,e_3),
inference(resolve,[status(thm)],[c_133,c_109]) ).
cnf(c_127,plain,
$false,
inference(resolve,[status(thm)],[c_125,c_134]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP130-4.003 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/10.39 % Computer : n011.cluster.edu
% 0.11/10.39 % Model : x86_64 x86_64
% 0.11/10.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/10.39 % Memory : 8046.5625MB
% 0.11/10.39 % OS : Linux 6.8.0-71-generic
% 0.11/10.39 % CPULimit : 300
% 0.11/10.39 % WCLimit : 300
% 0.11/10.39 % DateTime : Fri Sep 25 14:29:39 UTC 2026
% 0.11/10.40 % CPUTime :
% 0.14/10.40 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.14/10.40 % Process 2220205 was started by sandbox2 on n011,
% 0.14/10.40 % Fri Sep 25 14:29:39 2026
% 0.14/10.40 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.14/10.40
% 0.14/10.40 % From the command line: assign(max_seconds, 300).
% 0.14/10.42
% 0.14/10.42 % SZS status Unsatisfiable for theBenchmark
% 0.14/10.42
% 0.14/10.42 % Proof 1 at 0.01 (+ 0.01) seconds.
% 0.14/10.42 % Length of proof is 30.
% 0.14/10.42 % Level of proof is 10.
% 0.14/10.42 % Maximum clause weight is 16.000.
% 0.14/10.42 % Given clauses 45.
% 0.14/10.42
% 0.14/10.42 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------