%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : MSC008-1.002 : 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 : n009.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 24.77s 4.49s
% Output : CNFRefutation 24.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 33
% Number of leaves : 15
% Syntax : Number of clauses : 92 ( 10 unt; 63 nHn; 51 RR)
% Number of literals : 263 ( 0 equ; 71 neg)
% Maximal clause size : 5 ( 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 : 171 ( 6 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(p_1_is_not_p_2,axiom,
~ eq('p$u1','p$u2') ).
cnf(symmetry,axiom,
( eq(X1,X0)
| ~ eq(X0,X1) ) ).
cnf(latin_element_is_unique,axiom,
( eq(X2,X3)
| ~ latin(X0,X1,X3)
| ~ latin(X0,X1,X2) ) ).
cnf(latin_column_is_unique,axiom,
( eq(X1,X3)
| ~ latin(X0,X3,X2)
| ~ latin(X0,X1,X2) ) ).
cnf(latin_row_is_unique,axiom,
( eq(X0,X3)
| ~ latin(X3,X1,X2)
| ~ latin(X0,X1,X2) ) ).
cnf(greek_element_is_unique,axiom,
( eq(X2,X3)
| ~ greek(X0,X1,X3)
| ~ greek(X0,X1,X2) ) ).
cnf(greek_row_is_unique,axiom,
( eq(X0,X3)
| ~ greek(X3,X1,X2)
| ~ greek(X0,X1,X2) ) ).
cnf(latin_cell_element,axiom,
( latin(X0,X1,'p$u2')
| latin(X0,X1,'p$u1') ) ).
cnf(latin_column_required,axiom,
( latin(X0,'p$u2',X1)
| latin(X0,'p$u1',X1) ) ).
cnf(latin_row_required,axiom,
( latin('p$u2',X0,X1)
| latin('p$u1',X0,X1) ) ).
cnf(greek_cell_element,axiom,
( greek(X0,X1,'p$u2')
| greek(X0,X1,'p$u1') ) ).
cnf(greek_column_required,axiom,
( greek(X0,'p$u2',X1)
| greek(X0,'p$u1',X1) ) ).
cnf(greek_row_required,axiom,
( greek('p$u2',X0,X1)
| greek('p$u1',X0,X1) ) ).
cnf(no_two_same1,negated_conjecture,
( eq(X1,X5)
| ~ latin(X4,X5,X3)
| ~ greek(X4,X5,X2)
| ~ latin(X0,X1,X3)
| ~ greek(X0,X1,X2) ) ).
cnf(no_two_same2,negated_conjecture,
( eq(X0,X4)
| ~ latin(X4,X5,X3)
| ~ greek(X4,X5,X2)
| ~ latin(X0,X1,X3)
| ~ greek(X0,X1,X2) ) ).
cnf(c0,plain,
~ eq('p$u1','p$u2'),
inference(clausification,[status(esa)],[p_1_is_not_p_2]) ).
cnf(c2,plain,
( eq(X1,X0)
| ~ eq(X0,X1) ),
inference(clausification,[status(esa)],[symmetry]) ).
cnf(c3,plain,
( eq(X3,X2)
| ~ latin(X0,X1,X3)
| ~ latin(X0,X1,X2) ),
inference(clausification,[status(esa)],[latin_element_is_unique]) ).
cnf(c4,plain,
( eq(X3,X1)
| ~ latin(X0,X3,X2)
| ~ latin(X0,X1,X2) ),
inference(clausification,[status(esa)],[latin_column_is_unique]) ).
cnf(c5,plain,
( eq(X3,X0)
| ~ latin(X3,X1,X2)
| ~ latin(X0,X1,X2) ),
inference(clausification,[status(esa)],[latin_row_is_unique]) ).
cnf(c6,plain,
( eq(X3,X2)
| ~ greek(X0,X1,X3)
| ~ greek(X0,X1,X2) ),
inference(clausification,[status(esa)],[greek_element_is_unique]) ).
cnf(c8,plain,
( eq(X3,X0)
| ~ greek(X3,X1,X2)
| ~ greek(X0,X1,X2) ),
inference(clausification,[status(esa)],[greek_row_is_unique]) ).
cnf(c9,plain,
( latin(X0,X1,'p$u2')
| latin(X0,X1,'p$u1') ),
inference(clausification,[status(esa)],[latin_cell_element]) ).
cnf(c10,plain,
( latin(X0,'p$u2',X1)
| latin(X0,'p$u1',X1) ),
inference(clausification,[status(esa)],[latin_column_required]) ).
cnf(c11,plain,
( latin('p$u2',X0,X1)
| latin('p$u1',X0,X1) ),
inference(clausification,[status(esa)],[latin_row_required]) ).
cnf(c12,plain,
( greek(X0,X1,'p$u2')
| greek(X0,X1,'p$u1') ),
inference(clausification,[status(esa)],[greek_cell_element]) ).
cnf(c13,plain,
( greek(X0,'p$u2',X1)
| greek(X0,'p$u1',X1) ),
inference(clausification,[status(esa)],[greek_column_required]) ).
cnf(c14,plain,
( greek('p$u2',X0,X1)
| greek('p$u1',X0,X1) ),
inference(clausification,[status(esa)],[greek_row_required]) ).
cnf(c15,plain,
( ~ greek(X5,X3,X4)
| ~ latin(X5,X3,X2)
| ~ greek(X0,X1,X4)
| eq(X3,X1)
| ~ latin(X0,X1,X2) ),
inference(clausification,[status(esa)],[no_two_same1]) ).
cnf(c16,plain,
( ~ greek(X0,X1,X5)
| ~ greek(X3,X4,X5)
| ~ latin(X3,X4,X2)
| eq(X3,X0)
| ~ latin(X0,X1,X2) ),
inference(clausification,[status(esa)],[no_two_same2]) ).
cnf(d0,plain,
( greek(X2,'p$u2',X0)
| ~ greek(X2,'p$u1',X1)
| eq(X0,X1) ),
inference(resolution,[status(thm)],[c6,c13]) ).
cnf(d1,plain,
( ~ latin('p$u1',X2,X1)
| eq(X2,X0)
| latin('p$u2',X0,X1) ),
inference(resolution,[status(thm)],[c11,c4]) ).
cnf(d2,plain,
( latin('p$u1',X0,'p$u2')
| latin('p$u2',X1,'p$u1')
| eq(X0,X1) ),
inference(resolution,[status(thm)],[d1,c9]) ).
cnf(d3,plain,
( latin('p$u2','p$u2','p$u1')
| latin('p$u1','p$u1','p$u2') ),
inference(resolution,[status(thm)],[d2,c0]) ).
cnf(d4,plain,
( ~ latin(X0,'p$u1','p$u2')
| eq(X0,'p$u1')
| latin('p$u2','p$u2','p$u1') ),
inference(resolution,[status(thm)],[d3,c5]) ).
cnf(d5,plain,
( greek('p$u2','p$u1',X1)
| greek('p$u1','p$u2',X0)
| eq(X0,X1) ),
inference(resolution,[status(thm)],[d0,c14]) ).
cnf(d6,plain,
( greek('p$u2','p$u1','p$u2')
| greek('p$u1','p$u2','p$u1') ),
inference(resolution,[status(thm)],[d5,c0]) ).
cnf(d7,plain,
( ~ latin('p$u1',X0,X2)
| eq(X2,X1)
| latin('p$u2',X0,X1) ),
inference(resolution,[status(thm)],[c11,c3]) ).
cnf(d8,plain,
( latin('p$u1','p$u2',X0)
| latin('p$u2','p$u1',X1)
| eq(X0,X1) ),
inference(resolution,[status(thm)],[d7,c10]) ).
cnf(d9,plain,
( latin('p$u2','p$u1','p$u2')
| latin('p$u1','p$u2','p$u1') ),
inference(resolution,[status(thm)],[d8,c0]) ).
cnf(d10,plain,
( latin(X1,'p$u2',X3)
| ~ greek(X0,X2,X4)
| ~ greek(X1,'p$u1',X4)
| ~ latin(X0,X2,X3)
| eq(X0,X1) ),
inference(resolution,[status(thm)],[c16,c10]) ).
cnf(d11,plain,
( latin('p$u2','p$u1','p$u2')
| ~ greek('p$u1','p$u2',X1)
| ~ greek(X0,'p$u1',X1)
| latin(X0,'p$u2','p$u1')
| eq('p$u1',X0) ),
inference(resolution,[status(thm)],[d10,d9]) ).
cnf(d12,plain,
( greek(X0,'p$u1','p$u2')
| ~ greek('p$u1','p$u2','p$u1')
| latin('p$u2','p$u1','p$u2')
| latin(X0,'p$u2','p$u1')
| eq('p$u1',X0) ),
inference(resolution,[status(thm)],[d11,c12]) ).
cnf(d13,plain,
( greek('p$u2','p$u1','p$u2')
| greek(X0,'p$u1','p$u2')
| latin('p$u2','p$u1','p$u2')
| latin(X0,'p$u2','p$u1')
| eq('p$u1',X0) ),
inference(resolution,[status(thm)],[d12,d6]) ).
cnf(d14,plain,
( greek('p$u2','p$u1','p$u2')
| greek('p$u2','p$u1','p$u2')
| latin('p$u2','p$u1','p$u2')
| latin('p$u2','p$u2','p$u1') ),
inference(resolution,[status(thm)],[d13,c0]) ).
cnf(d15,plain,
( latin('p$u2','p$u2','p$u1')
| eq('p$u2','p$u1')
| greek('p$u2','p$u1','p$u2')
| latin('p$u2','p$u2','p$u1') ),
inference(resolution,[status(thm)],[d14,d4]) ).
cnf(d16,plain,
( eq('p$u1','p$u2')
| greek('p$u2','p$u1','p$u2')
| latin('p$u2','p$u2','p$u1') ),
inference(resolution,[status(thm)],[d15,c2]) ).
cnf(d17,plain,
( greek('p$u2','p$u1','p$u2')
| latin('p$u2','p$u2','p$u1') ),
inference(resolution,[status(thm)],[c0,d16]) ).
cnf(d18,plain,
( ~ latin('p$u2','p$u2',X0)
| eq(X0,'p$u1')
| greek('p$u2','p$u1','p$u2') ),
inference(resolution,[status(thm)],[d17,c3]) ).
cnf(d19,plain,
( latin('p$u2',X1,X3)
| ~ greek(X2,X0,X4)
| ~ greek('p$u1',X1,X4)
| ~ latin(X2,X0,X3)
| eq(X0,X1) ),
inference(resolution,[status(thm)],[c15,c11]) ).
cnf(d20,plain,
( latin(X2,'p$u2',X1)
| ~ greek('p$u1',X0,X3)
| ~ greek(X2,'p$u1',X3)
| latin('p$u2',X0,X1)
| eq('p$u1',X0) ),
inference(resolution,[status(thm)],[d19,c10]) ).
cnf(d21,plain,
( greek(X1,'p$u1','p$u2')
| ~ greek('p$u1',X0,'p$u1')
| latin('p$u2',X0,X2)
| latin(X1,'p$u2',X2)
| eq('p$u1',X0) ),
inference(resolution,[status(thm)],[d20,c12]) ).
cnf(d22,plain,
( greek('p$u2','p$u1','p$u2')
| greek(X0,'p$u1','p$u2')
| latin('p$u2','p$u2',X1)
| latin(X0,'p$u2',X1)
| eq('p$u1','p$u2') ),
inference(resolution,[status(thm)],[d21,d6]) ).
cnf(d23,plain,
( greek('p$u2','p$u1','p$u2')
| greek(X0,'p$u1','p$u2')
| latin('p$u2','p$u2',X1)
| latin(X0,'p$u2',X1) ),
inference(resolution,[status(thm)],[c0,d22]) ).
cnf(d24,plain,
( greek('p$u2','p$u1','p$u2')
| greek('p$u2','p$u1','p$u2')
| latin('p$u2','p$u2',X0)
| greek('p$u2','p$u1','p$u2')
| eq(X0,'p$u1') ),
inference(resolution,[status(thm)],[d18,d23]) ).
cnf(d25,plain,
( eq('p$u1',X0)
| greek('p$u2','p$u1','p$u2')
| latin('p$u2','p$u2',X0) ),
inference(resolution,[status(thm)],[d24,c2]) ).
cnf(d26,plain,
( greek('p$u2','p$u1','p$u2')
| latin('p$u2','p$u2','p$u2') ),
inference(resolution,[status(thm)],[d25,c0]) ).
cnf(d27,plain,
( greek('p$u2','p$u1','p$u2')
| eq('p$u2','p$u1')
| greek('p$u2','p$u1','p$u2') ),
inference(resolution,[status(thm)],[d26,d18]) ).
cnf(d28,plain,
( eq('p$u1','p$u2')
| greek('p$u2','p$u1','p$u2') ),
inference(resolution,[status(thm)],[d27,c2]) ).
cnf(d29,plain,
greek('p$u2','p$u1','p$u2'),
inference(resolution,[status(thm)],[c0,d28]) ).
cnf(d30,plain,
( greek('p$u2','p$u2',X0)
| eq(X0,'p$u2') ),
inference(resolution,[status(thm)],[d29,d0]) ).
cnf(d31,plain,
greek('p$u2','p$u2','p$u1'),
inference(resolution,[status(thm)],[d30,c0]) ).
cnf(d32,plain,
( ~ greek('p$u2','p$u2',X0)
| eq('p$u1',X0) ),
inference(resolution,[status(thm)],[d31,c6]) ).
cnf(d33,plain,
( latin(X3,X1,'p$u2')
| ~ greek(X2,X0,X4)
| ~ greek(X3,X1,X4)
| ~ latin(X2,X0,'p$u1')
| eq(X0,X1) ),
inference(resolution,[status(thm)],[c15,c9]) ).
cnf(d34,plain,
( ~ greek('p$u1','p$u2',X2)
| ~ greek(X1,X0,X2)
| latin(X1,X0,'p$u2')
| eq('p$u2',X0)
| latin('p$u2','p$u1','p$u2') ),
inference(resolution,[status(thm)],[d9,d33]) ).
cnf(d35,plain,
( ~ greek('p$u1','p$u2','p$u2')
| latin('p$u2','p$u1','p$u2')
| latin('p$u2','p$u1','p$u2')
| eq('p$u2','p$u1') ),
inference(resolution,[status(thm)],[d29,d34]) ).
cnf(d36,plain,
( greek(X1,'p$u2',X2)
| ~ greek(X0,'p$u1',X2)
| eq(X0,X1) ),
inference(resolution,[status(thm)],[c8,c13]) ).
cnf(d37,plain,
( greek(X0,'p$u2','p$u2')
| eq('p$u2',X0) ),
inference(resolution,[status(thm)],[d29,d36]) ).
cnf(d38,plain,
( eq(X0,'p$u2')
| greek(X0,'p$u2','p$u2') ),
inference(resolution,[status(thm)],[d37,c2]) ).
cnf(d39,plain,
greek('p$u1','p$u2','p$u2'),
inference(resolution,[status(thm)],[d38,c0]) ).
cnf(d40,plain,
( latin('p$u2','p$u1','p$u2')
| eq('p$u2','p$u1') ),
inference(resolution,[status(thm)],[d39,d35]) ).
cnf(d41,plain,
( eq('p$u1','p$u2')
| latin('p$u2','p$u1','p$u2') ),
inference(resolution,[status(thm)],[d40,c2]) ).
cnf(d42,plain,
latin('p$u2','p$u1','p$u2'),
inference(resolution,[status(thm)],[c0,d41]) ).
cnf(d43,plain,
( latin('p$u2','p$u2','p$u1')
| eq('p$u2','p$u1') ),
inference(resolution,[status(thm)],[d42,d4]) ).
cnf(d44,plain,
( eq('p$u1','p$u2')
| latin('p$u2','p$u2','p$u1') ),
inference(resolution,[status(thm)],[d43,c2]) ).
cnf(d45,plain,
latin('p$u2','p$u2','p$u1'),
inference(resolution,[status(thm)],[c0,d44]) ).
cnf(d46,plain,
( ~ latin('p$u2','p$u2',X0)
| eq(X0,'p$u1') ),
inference(resolution,[status(thm)],[d45,c3]) ).
cnf(d47,plain,
( ~ latin('p$u2','p$u1',X0)
| eq(X0,'p$u2') ),
inference(resolution,[status(thm)],[d42,c3]) ).
cnf(d48,plain,
( ~ latin(X0,X2,'p$u1')
| eq(X2,X1)
| latin(X0,X1,'p$u2') ),
inference(resolution,[status(thm)],[c9,c4]) ).
cnf(d49,plain,
( latin('p$u2',X0,'p$u1')
| latin('p$u1',X1,'p$u2')
| eq(X0,X1) ),
inference(resolution,[status(thm)],[d48,c11]) ).
cnf(d50,plain,
( latin('p$u2','p$u1','p$u1')
| latin('p$u1','p$u2','p$u2') ),
inference(resolution,[status(thm)],[d49,c0]) ).
cnf(d51,plain,
( ~ greek('p$u1','p$u2',X1)
| ~ greek(X0,'p$u1',X1)
| latin(X0,'p$u2','p$u2')
| eq('p$u1',X0)
| latin('p$u2','p$u1','p$u1') ),
inference(resolution,[status(thm)],[d50,d10]) ).
cnf(d52,plain,
( greek(X0,'p$u2',X1)
| ~ greek('p$u1','p$u2',X1)
| latin('p$u2','p$u1','p$u1')
| latin(X0,'p$u2','p$u2')
| eq('p$u1',X0) ),
inference(resolution,[status(thm)],[d51,c13]) ).
cnf(d53,plain,
( greek('p$u2','p$u2',X1)
| greek(X0,'p$u2',X1)
| latin('p$u2','p$u1','p$u1')
| latin(X0,'p$u2','p$u2')
| eq('p$u1',X0) ),
inference(resolution,[status(thm)],[d52,c14]) ).
cnf(d54,plain,
( greek('p$u2','p$u2',X0)
| greek('p$u2','p$u2',X0)
| latin('p$u2','p$u1','p$u1')
| latin('p$u2','p$u2','p$u2') ),
inference(resolution,[status(thm)],[d53,c0]) ).
cnf(d55,plain,
( eq('p$u1','p$u2')
| greek('p$u2','p$u2',X0)
| latin('p$u2','p$u2','p$u2') ),
inference(resolution,[status(thm)],[d54,d47]) ).
cnf(d56,plain,
( greek('p$u2','p$u2',X0)
| latin('p$u2','p$u2','p$u2') ),
inference(resolution,[status(thm)],[c0,d55]) ).
cnf(d57,plain,
( eq('p$u2','p$u1')
| greek('p$u2','p$u2',X0) ),
inference(resolution,[status(thm)],[d56,d46]) ).
cnf(d58,plain,
( eq('p$u1','p$u2')
| greek('p$u2','p$u2',X0) ),
inference(resolution,[status(thm)],[d57,c2]) ).
cnf(d59,plain,
greek('p$u2','p$u2',X0),
inference(resolution,[status(thm)],[c0,d58]) ).
cnf(d60,plain,
eq('p$u1',X0),
inference(resolution,[status(thm)],[d59,d32]) ).
cnf(d61,plain,
$false,
inference(resolution,[status(thm)],[d60,c0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : MSC008-1.002 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n009.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sat Sep 26 00:15:00 UTC 2026
% 0.14/0.36 % CPUTime :
% 0.14/0.36 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 24.77/4.49 % SZS status Unsatisfiable for theBenchmark.p
% 24.77/4.49 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------