%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : PUZ056-2.005 : TPTP v9.3.1. Released v3.5.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n007.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 08:22:12 AM UTC 2026
% Result : Unsatisfiable 18.58s 4.61s
% Output : CNFRefutation 18.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 77
% Number of leaves : 13
% Syntax : Number of clauses : 102 ( 48 unt; 0 nHn; 84 RR)
% Number of literals : 254 ( 0 equ; 154 neg)
% Maximal clause size : 10 ( 2 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-5 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 120 ( 20 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(rule1,axiom,
( p(X5,X1,X2,X3,X4)
| ~ p(X0,X1,X2,X3,X4) ) ).
cnf(rule2,axiom,
( p(X0,X5,X2,X3,X4)
| ~ neq(X0,X5)
| ~ neq(X0,X1)
| ~ p(X0,X1,X2,X3,X4) ) ).
cnf(rule3,axiom,
( p(X0,X1,X5,X3,X4)
| ~ neq(X1,X5)
| ~ neq(X1,X2)
| ~ neq(X0,X5)
| ~ neq(X0,X2)
| ~ p(X0,X1,X2,X3,X4) ) ).
cnf(rule4,axiom,
( p(X0,X1,X2,X5,X4)
| ~ neq(X2,X5)
| ~ neq(X2,X3)
| ~ neq(X1,X5)
| ~ neq(X1,X3)
| ~ neq(X0,X5)
| ~ neq(X0,X3)
| ~ p(X0,X1,X2,X3,X4) ) ).
cnf(rule5,axiom,
( p(X0,X1,X2,X3,X5)
| ~ neq(X3,X5)
| ~ neq(X3,X4)
| ~ neq(X2,X5)
| ~ neq(X2,X4)
| ~ neq(X1,X5)
| ~ neq(X1,X4)
| ~ neq(X0,X5)
| ~ neq(X0,X4)
| ~ p(X0,X1,X2,X3,X4) ) ).
cnf(neq2,axiom,
neq(s0,s1) ).
cnf(neq3,axiom,
neq(s0,s2) ).
cnf(neq4,axiom,
neq(s1,s0) ).
cnf(neq6,axiom,
neq(s1,s2) ).
cnf(neq7,axiom,
neq(s2,s0) ).
cnf(neq8,axiom,
neq(s2,s1) ).
cnf(init,axiom,
p(s0,s0,s0,s0,s0) ).
cnf(goal,negated_conjecture,
~ p(s2,s2,s2,s2,s2) ).
cnf(c0,plain,
( p(X5,X1,X2,X3,X4)
| ~ p(X0,X1,X2,X3,X4) ),
inference(clausification,[status(esa)],[rule1]) ).
cnf(c1,plain,
( p(X0,X1,X3,X4,X5)
| ~ neq(X0,X2)
| ~ p(X0,X2,X3,X4,X5)
| ~ neq(X0,X1) ),
inference(clausification,[status(esa)],[rule2]) ).
cnf(c2,plain,
( ~ neq(X0,X3)
| ~ neq(X2,X1)
| p(X0,X2,X1,X4,X5)
| ~ neq(X2,X3)
| ~ p(X0,X2,X3,X4,X5)
| ~ neq(X0,X1) ),
inference(clausification,[status(esa)],[rule3]) ).
cnf(c3,plain,
( ~ neq(X0,X5)
| ~ neq(X2,X3)
| ~ p(X0,X1,X2,X5,X4)
| ~ neq(X1,X3)
| ~ neq(X1,X5)
| ~ neq(X0,X3)
| ~ neq(X2,X5)
| p(X0,X1,X2,X3,X4) ),
inference(clausification,[status(esa)],[rule4]) ).
cnf(c4,plain,
( ~ neq(X4,X1)
| ~ neq(X4,X5)
| ~ neq(X3,X5)
| ~ neq(X2,X5)
| ~ p(X2,X3,X4,X0,X5)
| ~ neq(X0,X5)
| ~ neq(X3,X1)
| ~ neq(X2,X1)
| p(X2,X3,X4,X0,X1)
| ~ neq(X0,X1) ),
inference(clausification,[status(esa)],[rule5]) ).
cnf(c6,plain,
neq(s0,s1),
inference(clausification,[status(esa)],[neq2]) ).
cnf(c7,plain,
neq(s0,s2),
inference(clausification,[status(esa)],[neq3]) ).
cnf(c8,plain,
neq(s1,s0),
inference(clausification,[status(esa)],[neq4]) ).
cnf(c10,plain,
neq(s1,s2),
inference(clausification,[status(esa)],[neq6]) ).
cnf(c11,plain,
neq(s2,s0),
inference(clausification,[status(esa)],[neq7]) ).
cnf(c12,plain,
neq(s2,s1),
inference(clausification,[status(esa)],[neq8]) ).
cnf(c14,plain,
p(s0,s0,s0,s0,s0),
inference(clausification,[status(esa)],[init]) ).
cnf(c15,plain,
~ p(s2,s2,s2,s2,s2),
inference(clausification,[status(esa)],[goal]) ).
cnf(d0,plain,
p(X0,s0,s0,s0,s0),
inference(resolution,[status(thm)],[c14,c0]) ).
cnf(d1,plain,
( ~ neq(X0,X1)
| ~ neq(X0,s0)
| p(X0,X1,s0,s0,s0) ),
inference(resolution,[status(thm)],[d0,c1]) ).
cnf(d2,plain,
( ~ neq(s2,s0)
| p(s2,s1,s0,s0,s0) ),
inference(resolution,[status(thm)],[d1,c12]) ).
cnf(d3,plain,
p(s2,s1,s0,s0,s0),
inference(resolution,[status(thm)],[c11,d2]) ).
cnf(d4,plain,
p(X0,s1,s0,s0,s0),
inference(resolution,[status(thm)],[d3,c0]) ).
cnf(d5,plain,
( ~ neq(s1,X1)
| ~ neq(s1,s0)
| ~ neq(X0,X1)
| ~ neq(X0,s0)
| p(X0,s1,X1,s0,s0) ),
inference(resolution,[status(thm)],[d4,c2]) ).
cnf(d6,plain,
( ~ neq(s1,X1)
| ~ neq(X0,s0)
| ~ neq(X0,X1)
| p(X0,s1,X1,s0,s0) ),
inference(resolution,[status(thm)],[c8,d5]) ).
cnf(d7,plain,
( ~ neq(s1,s2)
| ~ neq(s1,s0)
| p(s1,s1,s2,s0,s0) ),
inference(resolution,[status(thm)],[d6,c10]) ).
cnf(d8,plain,
( ~ neq(s1,s2)
| p(s1,s1,s2,s0,s0) ),
inference(resolution,[status(thm)],[c8,d7]) ).
cnf(d9,plain,
p(s1,s1,s2,s0,s0),
inference(resolution,[status(thm)],[c10,d8]) ).
cnf(d10,plain,
p(X0,s1,s2,s0,s0),
inference(resolution,[status(thm)],[d9,c0]) ).
cnf(d11,plain,
( ~ neq(X0,X1)
| ~ neq(X0,s1)
| p(X0,X1,s2,s0,s0) ),
inference(resolution,[status(thm)],[d10,c1]) ).
cnf(d12,plain,
( ~ neq(s0,s1)
| p(s0,s2,s2,s0,s0) ),
inference(resolution,[status(thm)],[d11,c7]) ).
cnf(d13,plain,
p(s0,s2,s2,s0,s0),
inference(resolution,[status(thm)],[c6,d12]) ).
cnf(d14,plain,
p(X0,s2,s2,s0,s0),
inference(resolution,[status(thm)],[d13,c0]) ).
cnf(d15,plain,
( ~ neq(X0,X1)
| ~ neq(X0,s0)
| ~ neq(s2,X1)
| ~ neq(s2,s0)
| ~ neq(s2,X1)
| ~ neq(s2,s0)
| p(X0,s2,s2,X1,s0) ),
inference(resolution,[status(thm)],[d14,c3]) ).
cnf(d16,plain,
( ~ neq(s2,X1)
| ~ neq(X0,s0)
| ~ neq(X0,X1)
| p(X0,s2,s2,X1,s0) ),
inference(resolution,[status(thm)],[c11,d15]) ).
cnf(d17,plain,
( ~ neq(s2,s1)
| ~ neq(s2,s0)
| p(s2,s2,s2,s1,s0) ),
inference(resolution,[status(thm)],[d16,c12]) ).
cnf(d18,plain,
( ~ neq(s2,s1)
| p(s2,s2,s2,s1,s0) ),
inference(resolution,[status(thm)],[c11,d17]) ).
cnf(d19,plain,
p(s2,s2,s2,s1,s0),
inference(resolution,[status(thm)],[c12,d18]) ).
cnf(d20,plain,
p(X0,s2,s2,s1,s0),
inference(resolution,[status(thm)],[d19,c0]) ).
cnf(d21,plain,
( ~ neq(X0,X1)
| ~ neq(X0,s2)
| p(X0,X1,s2,s1,s0) ),
inference(resolution,[status(thm)],[d20,c1]) ).
cnf(d22,plain,
( ~ neq(s1,s2)
| p(s1,s0,s2,s1,s0) ),
inference(resolution,[status(thm)],[d21,c8]) ).
cnf(d23,plain,
p(s1,s0,s2,s1,s0),
inference(resolution,[status(thm)],[c10,d22]) ).
cnf(d24,plain,
p(X0,s0,s2,s1,s0),
inference(resolution,[status(thm)],[d23,c0]) ).
cnf(d25,plain,
( ~ neq(s0,X1)
| ~ neq(s0,s2)
| ~ neq(X0,X1)
| ~ neq(X0,s2)
| p(X0,s0,X1,s1,s0) ),
inference(resolution,[status(thm)],[d24,c2]) ).
cnf(d26,plain,
( ~ neq(s0,X1)
| ~ neq(X0,s2)
| ~ neq(X0,X1)
| p(X0,s0,X1,s1,s0) ),
inference(resolution,[status(thm)],[c7,d25]) ).
cnf(d27,plain,
( ~ neq(s0,s1)
| ~ neq(s0,s2)
| p(s0,s0,s1,s1,s0) ),
inference(resolution,[status(thm)],[d26,c6]) ).
cnf(d28,plain,
( ~ neq(s0,s2)
| p(s0,s0,s1,s1,s0) ),
inference(resolution,[status(thm)],[c6,d27]) ).
cnf(d29,plain,
p(s0,s0,s1,s1,s0),
inference(resolution,[status(thm)],[c7,d28]) ).
cnf(d30,plain,
p(X0,s0,s1,s1,s0),
inference(resolution,[status(thm)],[d29,c0]) ).
cnf(d31,plain,
( ~ neq(X0,X1)
| ~ neq(X0,s0)
| p(X0,X1,s1,s1,s0) ),
inference(resolution,[status(thm)],[d30,c1]) ).
cnf(d32,plain,
( ~ neq(s2,s0)
| p(s2,s1,s1,s1,s0) ),
inference(resolution,[status(thm)],[d31,c12]) ).
cnf(d33,plain,
p(s2,s1,s1,s1,s0),
inference(resolution,[status(thm)],[c11,d32]) ).
cnf(d34,plain,
p(X0,s1,s1,s1,s0),
inference(resolution,[status(thm)],[d33,c0]) ).
cnf(d35,plain,
( ~ neq(X0,X1)
| ~ neq(X0,s0)
| ~ neq(s1,X1)
| ~ neq(s1,s0)
| ~ neq(s1,X1)
| ~ neq(s1,s0)
| ~ neq(s1,X1)
| ~ neq(s1,s0)
| p(X0,s1,s1,s1,X1) ),
inference(resolution,[status(thm)],[d34,c4]) ).
cnf(d36,plain,
( ~ neq(s1,X1)
| ~ neq(X0,s0)
| ~ neq(X0,X1)
| p(X0,s1,s1,s1,X1) ),
inference(resolution,[status(thm)],[c8,d35]) ).
cnf(d37,plain,
( ~ neq(s1,s2)
| ~ neq(s1,s0)
| p(s1,s1,s1,s1,s2) ),
inference(resolution,[status(thm)],[d36,c10]) ).
cnf(d38,plain,
( ~ neq(s1,s2)
| p(s1,s1,s1,s1,s2) ),
inference(resolution,[status(thm)],[c8,d37]) ).
cnf(d39,plain,
p(s1,s1,s1,s1,s2),
inference(resolution,[status(thm)],[c10,d38]) ).
cnf(d40,plain,
p(X0,s1,s1,s1,s2),
inference(resolution,[status(thm)],[d39,c0]) ).
cnf(d41,plain,
( ~ neq(X0,X1)
| ~ neq(X0,s1)
| p(X0,X1,s1,s1,s2) ),
inference(resolution,[status(thm)],[d40,c1]) ).
cnf(d42,plain,
( ~ neq(s0,s1)
| p(s0,s2,s1,s1,s2) ),
inference(resolution,[status(thm)],[d41,c7]) ).
cnf(d43,plain,
p(s0,s2,s1,s1,s2),
inference(resolution,[status(thm)],[c6,d42]) ).
cnf(d44,plain,
p(X0,s2,s1,s1,s2),
inference(resolution,[status(thm)],[d43,c0]) ).
cnf(d45,plain,
( ~ neq(s2,X1)
| ~ neq(s2,s1)
| ~ neq(X0,X1)
| ~ neq(X0,s1)
| p(X0,s2,X1,s1,s2) ),
inference(resolution,[status(thm)],[d44,c2]) ).
cnf(d46,plain,
( ~ neq(s2,X1)
| ~ neq(X0,s1)
| ~ neq(X0,X1)
| p(X0,s2,X1,s1,s2) ),
inference(resolution,[status(thm)],[c12,d45]) ).
cnf(d47,plain,
( ~ neq(s2,s0)
| ~ neq(s2,s1)
| p(s2,s2,s0,s1,s2) ),
inference(resolution,[status(thm)],[d46,c11]) ).
cnf(d48,plain,
( ~ neq(s2,s1)
| p(s2,s2,s0,s1,s2) ),
inference(resolution,[status(thm)],[c11,d47]) ).
cnf(d49,plain,
p(s2,s2,s0,s1,s2),
inference(resolution,[status(thm)],[c12,d48]) ).
cnf(d50,plain,
p(X0,s2,s0,s1,s2),
inference(resolution,[status(thm)],[d49,c0]) ).
cnf(d51,plain,
( ~ neq(X0,X1)
| ~ neq(X0,s2)
| p(X0,X1,s0,s1,s2) ),
inference(resolution,[status(thm)],[d50,c1]) ).
cnf(d52,plain,
( ~ neq(s1,s2)
| p(s1,s0,s0,s1,s2) ),
inference(resolution,[status(thm)],[d51,c8]) ).
cnf(d53,plain,
p(s1,s0,s0,s1,s2),
inference(resolution,[status(thm)],[c10,d52]) ).
cnf(d54,plain,
p(X0,s0,s0,s1,s2),
inference(resolution,[status(thm)],[d53,c0]) ).
cnf(d55,plain,
( ~ neq(X0,X1)
| ~ neq(X0,s1)
| ~ neq(s0,X1)
| ~ neq(s0,s1)
| ~ neq(s0,X1)
| ~ neq(s0,s1)
| p(X0,s0,s0,X1,s2) ),
inference(resolution,[status(thm)],[d54,c3]) ).
cnf(d56,plain,
( ~ neq(s0,X1)
| ~ neq(X0,s1)
| ~ neq(X0,X1)
| p(X0,s0,s0,X1,s2) ),
inference(resolution,[status(thm)],[c6,d55]) ).
cnf(d57,plain,
( ~ neq(s0,s2)
| ~ neq(s0,s1)
| p(s0,s0,s0,s2,s2) ),
inference(resolution,[status(thm)],[d56,c7]) ).
cnf(d58,plain,
( ~ neq(s0,s2)
| p(s0,s0,s0,s2,s2) ),
inference(resolution,[status(thm)],[c6,d57]) ).
cnf(d59,plain,
p(s0,s0,s0,s2,s2),
inference(resolution,[status(thm)],[c7,d58]) ).
cnf(d60,plain,
p(X0,s0,s0,s2,s2),
inference(resolution,[status(thm)],[d59,c0]) ).
cnf(d61,plain,
( ~ neq(X0,X1)
| ~ neq(X0,s0)
| p(X0,X1,s0,s2,s2) ),
inference(resolution,[status(thm)],[d60,c1]) ).
cnf(d62,plain,
( ~ neq(s2,s0)
| p(s2,s1,s0,s2,s2) ),
inference(resolution,[status(thm)],[d61,c12]) ).
cnf(d63,plain,
p(s2,s1,s0,s2,s2),
inference(resolution,[status(thm)],[c11,d62]) ).
cnf(d64,plain,
p(X0,s1,s0,s2,s2),
inference(resolution,[status(thm)],[d63,c0]) ).
cnf(d65,plain,
( ~ neq(s1,X1)
| ~ neq(s1,s0)
| ~ neq(X0,X1)
| ~ neq(X0,s0)
| p(X0,s1,X1,s2,s2) ),
inference(resolution,[status(thm)],[d64,c2]) ).
cnf(d66,plain,
( ~ neq(s1,X1)
| ~ neq(X0,s0)
| ~ neq(X0,X1)
| p(X0,s1,X1,s2,s2) ),
inference(resolution,[status(thm)],[c8,d65]) ).
cnf(d67,plain,
( ~ neq(s1,s2)
| ~ neq(s1,s0)
| p(s1,s1,s2,s2,s2) ),
inference(resolution,[status(thm)],[d66,c10]) ).
cnf(d68,plain,
( ~ neq(s1,s2)
| p(s1,s1,s2,s2,s2) ),
inference(resolution,[status(thm)],[c8,d67]) ).
cnf(d69,plain,
p(s1,s1,s2,s2,s2),
inference(resolution,[status(thm)],[c10,d68]) ).
cnf(d70,plain,
p(X0,s1,s2,s2,s2),
inference(resolution,[status(thm)],[d69,c0]) ).
cnf(d71,plain,
( ~ neq(X0,X1)
| ~ neq(X0,s1)
| p(X0,X1,s2,s2,s2) ),
inference(resolution,[status(thm)],[d70,c1]) ).
cnf(d72,plain,
( ~ neq(s0,s1)
| p(s0,s2,s2,s2,s2) ),
inference(resolution,[status(thm)],[d71,c7]) ).
cnf(d73,plain,
p(s0,s2,s2,s2,s2),
inference(resolution,[status(thm)],[c6,d72]) ).
cnf(d74,plain,
p(X0,s2,s2,s2,s2),
inference(resolution,[status(thm)],[d73,c0]) ).
cnf(d75,plain,
$false,
inference(resolution,[status(thm)],[d74,c15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : PUZ056-2.005 : TPTP v9.3.1. Released v3.5.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.58 % Computer : n007.cluster.edu
% 0.12/0.58 % Model : x86_64 x86_64
% 0.12/0.58 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.58 % Memory : 8046.5625MB
% 0.12/0.58 % OS : Linux 6.8.0-71-generic
% 0.12/0.58 % CPULimit : 300
% 0.12/0.58 % WCLimit : 300
% 0.12/0.58 % DateTime : Sat Sep 26 05:06:55 UTC 2026
% 0.12/0.59 % CPUTime :
% 0.12/0.59 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 18.58/4.61 % SZS status Unsatisfiable for theBenchmark.p
% 18.58/4.61 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------