%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : MSC008-2.002 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n015.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 08:04:08 AM UTC 2026
% Result : Unsatisfiable 23.99s 4.30s
% Output : CNFRefutation 23.99s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 12
% Syntax : Number of clauses : 72 ( 9 unt; 51 nHn; 45 RR)
% Number of literals : 209 ( 0 equ; 57 neg)
% Maximal clause size : 6 ( 2 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 : 126 ( 5 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(p1_is_not_p2,axiom,
~ eq(p1,p2) ).
cnf(symmetry,axiom,
( eq(X1,X0)
| ~ eq(X0,X1) ) ).
cnf(latin_element_is_unique,axiom,
( eq(X3,X2)
| ~ latin(X0,X1,X3)
| ~ latin(X0,X1,X2) ) ).
cnf(latin_column_is_unique,axiom,
( eq(X3,X1)
| ~ latin(X0,X3,X2)
| ~ latin(X0,X1,X2) ) ).
cnf(latin_row_is_unique,axiom,
( eq(X3,X0)
| ~ latin(X3,X1,X2)
| ~ latin(X0,X1,X2) ) ).
cnf(greek_row_is_unique,axiom,
( eq(X3,X0)
| ~ greek(X3,X1,X2)
| ~ greek(X0,X1,X2) ) ).
cnf(latin_cell_element,axiom,
( latin(X0,X1,p2)
| latin(X0,X1,p1) ) ).
cnf(latin_column_required,axiom,
( latin(X0,p2,X1)
| latin(X0,p1,X1) ) ).
cnf(latin_row_required,axiom,
( latin(p2,X0,X1)
| latin(p1,X0,X1) ) ).
cnf(greek_cell_element,axiom,
( greek(X0,X1,p2)
| greek(X0,X1,p1) ) ).
cnf(greek_column_required,axiom,
( greek(X0,p2,X1)
| greek(X0,p1,X1) ) ).
cnf(no_two_same,negated_conjecture,
( eq(X4,X0)
| eq(X5,X1)
| ~ latin(X4,X5,X3)
| ~ greek(X4,X5,X2)
| ~ latin(X0,X1,X3)
| ~ greek(X0,X1,X2) ) ).
cnf(c0,plain,
~ eq(p1,p2),
inference(clausification,[status(esa)],[p1_is_not_p2]) ).
cnf(c2,plain,
( eq(X1,X0)
| ~ eq(X0,X1) ),
inference(clausification,[status(esa)],[symmetry]) ).
cnf(c3,plain,
( eq(X2,X3)
| ~ latin(X0,X1,X3)
| ~ latin(X0,X1,X2) ),
inference(clausification,[status(esa)],[latin_element_is_unique]) ).
cnf(c4,plain,
( eq(X1,X3)
| ~ latin(X0,X3,X2)
| ~ latin(X0,X1,X2) ),
inference(clausification,[status(esa)],[latin_column_is_unique]) ).
cnf(c5,plain,
( eq(X0,X3)
| ~ latin(X3,X1,X2)
| ~ latin(X0,X1,X2) ),
inference(clausification,[status(esa)],[latin_row_is_unique]) ).
cnf(c8,plain,
( eq(X0,X3)
| ~ greek(X3,X1,X2)
| ~ greek(X0,X1,X2) ),
inference(clausification,[status(esa)],[greek_row_is_unique]) ).
cnf(c9,plain,
( latin(X0,X1,p2)
| latin(X0,X1,p1) ),
inference(clausification,[status(esa)],[latin_cell_element]) ).
cnf(c10,plain,
( latin(X0,p2,X1)
| latin(X0,p1,X1) ),
inference(clausification,[status(esa)],[latin_column_required]) ).
cnf(c11,plain,
( latin(p2,X0,X1)
| latin(p1,X0,X1) ),
inference(clausification,[status(esa)],[latin_row_required]) ).
cnf(c12,plain,
( greek(X0,X1,p2)
| greek(X0,X1,p1) ),
inference(clausification,[status(esa)],[greek_cell_element]) ).
cnf(c13,plain,
( greek(X0,p2,X1)
| greek(X0,p1,X1) ),
inference(clausification,[status(esa)],[greek_column_required]) ).
cnf(c15,plain,
( ~ latin(X0,X1,X5)
| ~ greek(X3,X4,X2)
| ~ latin(X3,X4,X5)
| eq(X1,X4)
| eq(X0,X3)
| ~ greek(X0,X1,X2) ),
inference(clausification,[status(esa)],[no_two_same]) ).
cnf(d0,plain,
( ~ latin(X0,X2,p1)
| eq(X1,X2)
| latin(X0,X1,p2) ),
inference(resolution,[status(thm)],[c9,c4]) ).
cnf(d1,plain,
( latin(p2,X1,p1)
| latin(p1,X0,p2)
| eq(X0,X1) ),
inference(resolution,[status(thm)],[d0,c11]) ).
cnf(d2,plain,
( latin(p2,p2,p1)
| latin(p1,p1,p2) ),
inference(resolution,[status(thm)],[d1,c0]) ).
cnf(d3,plain,
( ~ latin(X0,p1,p2)
| eq(p1,X0)
| latin(p2,p2,p1) ),
inference(resolution,[status(thm)],[d2,c5]) ).
cnf(d4,plain,
( ~ latin(X0,p1,X2)
| eq(X1,X2)
| latin(X0,p2,X1) ),
inference(resolution,[status(thm)],[c10,c3]) ).
cnf(d5,plain,
( latin(p2,p1,X1)
| latin(p1,p2,X0)
| eq(X0,X1) ),
inference(resolution,[status(thm)],[d4,c11]) ).
cnf(d6,plain,
( latin(p2,p1,p2)
| latin(p1,p2,p1) ),
inference(resolution,[status(thm)],[d5,c0]) ).
cnf(d7,plain,
( ~ greek(X1,X0,X2)
| ~ greek(p1,p2,X2)
| ~ latin(X1,X0,p1)
| eq(X1,p1)
| eq(X0,p2)
| latin(p2,p1,p2) ),
inference(resolution,[status(thm)],[d6,c15]) ).
cnf(d8,plain,
( latin(X0,X1,p2)
| ~ greek(p1,p2,X2)
| ~ greek(X0,X1,X2)
| latin(p2,p1,p2)
| eq(X1,p2)
| eq(X0,p1) ),
inference(resolution,[status(thm)],[d7,c9]) ).
cnf(d9,plain,
( greek(X0,p2,X2)
| ~ greek(X1,p1,X2)
| eq(X0,X1) ),
inference(resolution,[status(thm)],[c8,c13]) ).
cnf(d10,plain,
( greek(X1,p1,p2)
| greek(X0,p2,p1)
| eq(X0,X1) ),
inference(resolution,[status(thm)],[d9,c12]) ).
cnf(d11,plain,
( greek(p1,p2,p1)
| greek(p2,p1,p2) ),
inference(resolution,[status(thm)],[d10,c0]) ).
cnf(d12,plain,
( latin(X2,p2,X3)
| ~ greek(X1,X0,X4)
| ~ greek(X2,p1,X4)
| ~ latin(X1,X0,X3)
| eq(X1,X2)
| eq(X0,p1) ),
inference(resolution,[status(thm)],[c15,c10]) ).
cnf(d13,plain,
( latin(p2,X1,X2)
| ~ greek(p1,X1,X3)
| ~ greek(X0,p1,X3)
| latin(X0,p2,X2)
| eq(X1,p1)
| eq(p1,X0) ),
inference(resolution,[status(thm)],[d12,c11]) ).
cnf(d14,plain,
( greek(X1,p1,p2)
| ~ greek(p1,X0,p1)
| latin(p2,X0,X2)
| latin(X1,p2,X2)
| eq(p1,X1)
| eq(X0,p1) ),
inference(resolution,[status(thm)],[d13,c12]) ).
cnf(d15,plain,
( greek(p2,p1,p2)
| greek(X0,p1,p2)
| latin(p2,p2,X1)
| latin(X0,p2,X1)
| eq(p1,X0)
| eq(p2,p1) ),
inference(resolution,[status(thm)],[d14,d11]) ).
cnf(d16,plain,
( greek(p2,p1,p2)
| greek(p2,p1,p2)
| latin(p2,p2,X0)
| latin(p2,p2,X0)
| eq(p2,p1) ),
inference(resolution,[status(thm)],[d15,c0]) ).
cnf(d17,plain,
( eq(p1,p2)
| greek(p2,p1,p2)
| latin(p2,p2,X0) ),
inference(resolution,[status(thm)],[d16,c2]) ).
cnf(d18,plain,
( greek(p2,p1,p2)
| latin(p2,p2,X0) ),
inference(resolution,[status(thm)],[c0,d17]) ).
cnf(d19,plain,
( ~ latin(p2,p2,X1)
| eq(X0,X1)
| greek(p2,p1,p2) ),
inference(resolution,[status(thm)],[d18,c3]) ).
cnf(d20,plain,
( greek(p2,p1,p2)
| greek(p2,p1,p2)
| eq(X0,X1) ),
inference(resolution,[status(thm)],[d19,d18]) ).
cnf(d21,plain,
greek(p2,p1,p2),
inference(resolution,[status(thm)],[d20,c0]) ).
cnf(d22,plain,
( ~ greek(p1,p2,p2)
| latin(p2,p1,p2)
| latin(p2,p1,p2)
| eq(p2,p1)
| eq(p1,p2) ),
inference(resolution,[status(thm)],[d21,d8]) ).
cnf(d23,plain,
( ~ greek(p1,p2,p2)
| latin(p2,p1,p2)
| eq(p2,p1) ),
inference(resolution,[status(thm)],[c0,d22]) ).
cnf(d24,plain,
( greek(X0,p2,p2)
| eq(X0,p2) ),
inference(resolution,[status(thm)],[d21,d9]) ).
cnf(d25,plain,
greek(p1,p2,p2),
inference(resolution,[status(thm)],[d24,c0]) ).
cnf(d26,plain,
( latin(p2,p1,p2)
| eq(p2,p1) ),
inference(resolution,[status(thm)],[d25,d23]) ).
cnf(d27,plain,
( eq(p1,p2)
| latin(p2,p1,p2) ),
inference(resolution,[status(thm)],[d26,c2]) ).
cnf(d28,plain,
latin(p2,p1,p2),
inference(resolution,[status(thm)],[c0,d27]) ).
cnf(d29,plain,
( latin(p2,p2,p1)
| eq(p1,p2) ),
inference(resolution,[status(thm)],[d28,d3]) ).
cnf(d30,plain,
latin(p2,p2,p1),
inference(resolution,[status(thm)],[c0,d29]) ).
cnf(d31,plain,
( ~ latin(p2,p2,X0)
| eq(p1,X0) ),
inference(resolution,[status(thm)],[d30,c3]) ).
cnf(d32,plain,
( ~ latin(p2,p1,X0)
| eq(p2,X0) ),
inference(resolution,[status(thm)],[d28,c3]) ).
cnf(d33,plain,
( ~ latin(p1,X0,X2)
| eq(X1,X2)
| latin(p2,X0,X1) ),
inference(resolution,[status(thm)],[c11,c3]) ).
cnf(d34,plain,
( latin(p1,p2,X1)
| latin(p2,p1,X0)
| eq(X0,X1) ),
inference(resolution,[status(thm)],[d33,c10]) ).
cnf(d35,plain,
( latin(p2,p1,p1)
| latin(p1,p2,p2) ),
inference(resolution,[status(thm)],[d34,c0]) ).
cnf(d36,plain,
( ~ greek(X1,X0,X2)
| ~ greek(p1,p2,X2)
| ~ latin(X1,X0,p2)
| eq(X1,p1)
| eq(X0,p2)
| latin(p2,p1,p1) ),
inference(resolution,[status(thm)],[d35,c15]) ).
cnf(d37,plain,
( latin(X0,p2,p2)
| ~ greek(p1,p2,X1)
| ~ greek(X0,p1,X1)
| latin(p2,p1,p1)
| eq(p1,p2)
| eq(X0,p1) ),
inference(resolution,[status(thm)],[d36,c10]) ).
cnf(d38,plain,
( ~ greek(p1,p2,X1)
| ~ greek(X0,p1,X1)
| latin(p2,p1,p1)
| latin(X0,p2,p2)
| eq(X0,p1) ),
inference(resolution,[status(thm)],[c0,d37]) ).
cnf(d39,plain,
( ~ greek(p1,p2,p2)
| latin(p2,p1,p1)
| latin(p2,p2,p2)
| eq(p2,p1) ),
inference(resolution,[status(thm)],[d21,d38]) ).
cnf(d40,plain,
( latin(p2,p2,p2)
| latin(p2,p1,p1)
| eq(p2,p1) ),
inference(resolution,[status(thm)],[d25,d39]) ).
cnf(d41,plain,
( eq(p1,p2)
| latin(p2,p2,p2)
| latin(p2,p1,p1) ),
inference(resolution,[status(thm)],[d40,c2]) ).
cnf(d42,plain,
( latin(p2,p2,p2)
| latin(p2,p1,p1) ),
inference(resolution,[status(thm)],[c0,d41]) ).
cnf(d43,plain,
( eq(p2,p1)
| latin(p2,p2,p2) ),
inference(resolution,[status(thm)],[d42,d32]) ).
cnf(d44,plain,
( eq(p1,p2)
| latin(p2,p2,p2) ),
inference(resolution,[status(thm)],[d43,c2]) ).
cnf(d45,plain,
latin(p2,p2,p2),
inference(resolution,[status(thm)],[c0,d44]) ).
cnf(d46,plain,
eq(p1,p2),
inference(resolution,[status(thm)],[d45,d31]) ).
cnf(d47,plain,
$false,
inference(resolution,[status(thm)],[c0,d46]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : MSC008-2.002 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.34 % Computer : n015.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.08/0.34 % CPULimit : 300
% 0.08/0.34 % WCLimit : 300
% 0.08/0.34 % DateTime : Sat Sep 26 00:18:28 UTC 2026
% 0.08/0.34 % CPUTime :
% 0.08/0.34 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 23.99/4.30 % SZS status Unsatisfiable for theBenchmark.p
% 23.99/4.30 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------