%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : MSC008-2.002 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n018.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 08:04:27 AM UTC 2026
% Result : Unsatisfiable 0.23s 0.53s
% Output : CNFRefutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 9
% Syntax : Number of formulae : 35 ( 5 unt; 0 def)
% Number of atoms : 103 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 97 ( 29 ~; 68 |; 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 : 100 ( 31 sgn 24 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(p1_is_not_p2,axiom,
~ eq(p1,p2),
file('theBenchmark.p',p1_is_not_p2) ).
cnf(c_1,plain,
~ eq(p1,p2),
inference(clausify,[status(thm)],[p1_is_not_p2]) ).
fof(symmetry,axiom,
! [VAR_0,VAR_1] :
( eq(VAR_1,VAR_0)
| ~ eq(VAR_0,VAR_1) ),
file('theBenchmark.p',symmetry) ).
cnf(c_3,plain,
( eq(B,A)
| ~ eq(A,B) ),
inference(clausify,[status(thm)],[symmetry]) ).
fof(latin_element_is_unique,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( eq(VAR_3,VAR_2)
| ~ latin(VAR_0,VAR_1,VAR_3)
| ~ latin(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',latin_element_is_unique) ).
cnf(c_4,plain,
( eq(D,C)
| ~ latin(A,B,D)
| ~ latin(A,B,C) ),
inference(clausify,[status(thm)],[latin_element_is_unique]) ).
fof(greek_element_is_unique,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( eq(VAR_3,VAR_2)
| ~ greek(VAR_0,VAR_1,VAR_3)
| ~ greek(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',greek_element_is_unique) ).
cnf(c_7,plain,
( eq(D,C)
| ~ greek(A,B,D)
| ~ greek(A,B,C) ),
inference(clausify,[status(thm)],[greek_element_is_unique]) ).
fof(latin_column_required,axiom,
! [VAR_0,VAR_1] :
( latin(VAR_0,p2,VAR_1)
| latin(VAR_0,p1,VAR_1) ),
file('theBenchmark.p',latin_column_required) ).
cnf(c_11,plain,
( latin(A,p2,B)
| latin(A,p1,B) ),
inference(clausify,[status(thm)],[latin_column_required]) ).
fof(latin_row_required,axiom,
! [VAR_0,VAR_1] :
( latin(p2,VAR_0,VAR_1)
| latin(p1,VAR_0,VAR_1) ),
file('theBenchmark.p',latin_row_required) ).
cnf(c_12,plain,
( latin(p2,A,B)
| latin(p1,A,B) ),
inference(clausify,[status(thm)],[latin_row_required]) ).
fof(greek_column_required,axiom,
! [VAR_0,VAR_1] :
( greek(VAR_0,p2,VAR_1)
| greek(VAR_0,p1,VAR_1) ),
file('theBenchmark.p',greek_column_required) ).
cnf(c_14,plain,
( greek(A,p2,B)
| greek(A,p1,B) ),
inference(clausify,[status(thm)],[greek_column_required]) ).
fof(greek_row_required,axiom,
! [VAR_0,VAR_1] :
( greek(p2,VAR_0,VAR_1)
| greek(p1,VAR_0,VAR_1) ),
file('theBenchmark.p',greek_row_required) ).
cnf(c_15,plain,
( greek(p2,A,B)
| greek(p1,A,B) ),
inference(clausify,[status(thm)],[greek_row_required]) ).
fof(no_two_same,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4,VAR_5] :
( eq(VAR_4,VAR_0)
| eq(VAR_5,VAR_1)
| ~ latin(VAR_4,VAR_5,VAR_3)
| ~ greek(VAR_4,VAR_5,VAR_2)
| ~ latin(VAR_0,VAR_1,VAR_3)
| ~ greek(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',no_two_same) ).
cnf(c_16,plain,
( eq(E,A)
| eq(F,B)
| ~ latin(E,F,D)
| ~ greek(E,F,C)
| ~ latin(A,B,D)
| ~ greek(A,B,C) ),
inference(clausify,[status(thm)],[no_two_same]) ).
cnf(c_18,plain,
~ eq(p2,p1),
inference(resolve,[status(thm)],[c_3,c_1]) ).
cnf(c_282,plain,
( greek(p1,A,E)
| eq(C,p2)
| eq(D,A)
| ~ latin(C,D,B)
| ~ greek(C,D,E)
| ~ latin(p2,A,B) ),
inference(resolve,[status(thm)],[c_16,c_15]) ).
cnf(c_283,plain,
( latin(p1,E,D)
| greek(p1,E,C)
| eq(A,p2)
| eq(B,E)
| ~ latin(A,B,D)
| ~ greek(A,B,C) ),
inference(resolve,[status(thm)],[c_282,c_12]) ).
cnf(c_284,plain,
( greek(A,p1,D)
| latin(p1,C,B)
| greek(p1,C,D)
| eq(A,p2)
| eq(p2,C)
| ~ latin(A,p2,B) ),
inference(resolve,[status(thm)],[c_283,c_14]) ).
cnf(c_109,plain,
( latin(B,p1,D)
| greek(B,p1,C)
| latin(p1,A,D)
| greek(p1,A,C)
| eq(B,p2)
| eq(p2,A) ),
inference(resolve,[status(thm)],[c_284,c_11]) ).
cnf(c_285,plain,
( latin(p1,p1,B)
| latin(p1,p1,B)
| greek(p1,p1,A)
| eq(p1,p2)
| eq(p2,p1) ),
inference(factor,[status(thm)],[c_109]) ).
cnf(c_286,plain,
( latin(p1,p1,B)
| greek(p1,p1,A)
| eq(p1,p2)
| eq(p2,p1) ),
inference(copy,[status(thm)],[c_285]) ).
cnf(c_287,plain,
( latin(p1,p1,B)
| greek(p1,p1,A)
| eq(p1,p2) ),
inference(resolve,[status(thm)],[c_18,c_286]) ).
cnf(c_150,plain,
( latin(p1,p1,B)
| greek(p1,p1,A) ),
inference(resolve,[status(thm)],[c_1,c_287]) ).
cnf(c_288,plain,
( greek(p1,p1,C)
| eq(A,B)
| ~ latin(p1,p1,A) ),
inference(resolve,[status(thm)],[c_4,c_150]) ).
cnf(c_208,plain,
( greek(p1,p1,D)
| greek(p1,p1,C)
| eq(A,B) ),
inference(resolve,[status(thm)],[c_288,c_150]) ).
cnf(c_217,plain,
( greek(p1,p1,C)
| eq(A,B) ),
inference(factor,[status(thm)],[c_208]) ).
cnf(c_289,plain,
( eq(C,D)
| eq(A,B)
| ~ greek(p1,p1,A) ),
inference(resolve,[status(thm)],[c_7,c_217]) ).
cnf(c_252,plain,
( eq(E,F)
| eq(C,D)
| eq(A,B) ),
inference(resolve,[status(thm)],[c_289,c_217]) ).
cnf(c_279,plain,
( eq(C,D)
| eq(A,B) ),
inference(factor,[status(thm)],[c_252]) ).
cnf(c_280,plain,
eq(A,B),
inference(factor,[status(thm)],[c_279]) ).
cnf(c_281,plain,
$false,
inference(resolve,[status(thm)],[c_280,c_18]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : MSC008-2.002 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.44 % Computer : n018.cluster.edu
% 0.19/0.44 % Model : x86_64 x86_64
% 0.19/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.44 % Memory : 8046.5625MB
% 0.19/0.44 % OS : Linux 6.8.0-71-generic
% 0.19/0.44 % CPULimit : 300
% 0.19/0.44 % WCLimit : 300
% 0.19/0.44 % DateTime : Sat Sep 26 00:17:22 UTC 2026
% 0.19/0.45 % CPUTime :
% 0.19/0.45 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.19/0.45 % Process 3198182 was started by sandbox2 on n018,
% 0.19/0.45 % Sat Sep 26 00:17:22 2026
% 0.19/0.45 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.19/0.46
% 0.19/0.46 % From the command line: assign(max_seconds, 300).
% 0.23/0.53
% 0.23/0.53 % SZS status Unsatisfiable for theBenchmark
% 0.23/0.53
% 0.23/0.53 % Proof 1 at 0.05 (+ 0.02) seconds.
% 0.23/0.53 % Length of proof is 18.
% 0.23/0.53 % Level of proof is 8.
% 0.23/0.53 % Maximum clause weight is 27.000.
% 0.23/0.53 % Given clauses 20.
% 0.23/0.53
% 0.23/0.53 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------