%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SYO612-1 : TPTP v9.3.1. Released v7.1.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n020.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 09:46:47 AM UTC 2026
% Result : Unsatisfiable 11.25s 2.00s
% Output : CNFRefutation 11.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 3
% Syntax : Number of clauses : 19 ( 6 unt; 0 nHn; 15 RR)
% Number of literals : 109 ( 0 equ; 104 neg)
% Maximal clause size : 13 ( 5 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 1 con; 0-1 aty)
% Number of variables : 87 ( 20 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(sos_01,axiom,
le(X0,X0) ).
cnf(sos_04,axiom,
eq(f(X0),a0) ).
cnf(sos_05,axiom,
( ~ le(s(X5),X6)
| ~ le(s(X4),X5)
| ~ le(s(X3),X4)
| ~ le(s(X2),X3)
| ~ le(s(X1),X2)
| ~ le(s(X0),X1)
| ~ eq(f(X6),a0)
| ~ eq(f(X5),a0)
| ~ eq(f(X4),a0)
| ~ eq(f(X3),a0)
| ~ eq(f(X2),a0)
| ~ eq(f(X1),a0)
| ~ eq(f(X0),a0) ) ).
cnf(c0,plain,
le(X0,X0),
inference(clausification,[status(esa)],[sos_01]) ).
cnf(c3,plain,
eq(f(X0),a0),
inference(clausification,[status(esa)],[sos_04]) ).
cnf(c4,plain,
( ~ le(s(X2),X6)
| ~ le(s(X3),X4)
| ~ le(s(X1),X3)
| ~ le(s(X4),X0)
| ~ le(s(X6),X5)
| ~ eq(f(X6),a0)
| ~ le(s(X0),X2)
| ~ eq(f(X5),a0)
| ~ eq(f(X4),a0)
| ~ eq(f(X3),a0)
| ~ eq(f(X2),a0)
| ~ eq(f(X1),a0)
| ~ eq(f(X0),a0) ),
inference(clausification,[status(esa)],[sos_05]) ).
cnf(d0,plain,
( ~ eq(f(X6),a0)
| ~ eq(f(X3),a0)
| ~ eq(f(X1),a0)
| ~ eq(f(X4),a0)
| ~ eq(f(X2),a0)
| ~ eq(f(X0),a0)
| ~ le(s(X6),X2)
| ~ le(s(X3),X0)
| ~ le(s(X1),X4)
| ~ le(s(X4),X5)
| ~ le(s(X2),X3)
| ~ le(s(X0),X1) ),
inference(resolution,[status(thm)],[c3,c4]) ).
cnf(d1,plain,
( ~ eq(f(X6),a0)
| ~ eq(f(X1),a0)
| ~ eq(f(X4),a0)
| ~ eq(f(X2),a0)
| ~ eq(f(X0),a0)
| ~ le(s(X5),X6)
| ~ le(s(X6),X2)
| ~ le(s(X1),X4)
| ~ le(s(X4),X5)
| ~ le(s(X2),X3)
| ~ le(s(X0),X1) ),
inference(resolution,[status(thm)],[d0,c3]) ).
cnf(d2,plain,
( ~ eq(f(X6),a0)
| ~ eq(f(X5),a0)
| ~ eq(f(X1),a0)
| ~ eq(f(X3),a0)
| ~ le(s(X6),X5)
| ~ le(s(X5),X3)
| ~ le(s(X1),X4)
| ~ le(s(X3),X2)
| ~ le(s(X2),X0)
| ~ le(s(X0),X1) ),
inference(resolution,[status(thm)],[c3,d1]) ).
cnf(d3,plain,
( ~ eq(f(X2),a0)
| ~ eq(f(X1),a0)
| ~ eq(f(X0),a0)
| ~ le(s(X4),X5)
| ~ le(s(X5),X6)
| ~ le(s(X3),X4)
| ~ le(s(X2),X3)
| ~ le(s(X1),X2)
| ~ le(s(X0),X1) ),
inference(resolution,[status(thm)],[d2,c3]) ).
cnf(d4,plain,
( ~ eq(f(X6),a0)
| ~ eq(f(X5),a0)
| ~ le(s(X6),X5)
| ~ le(s(X5),X4)
| ~ le(s(X4),X3)
| ~ le(s(X3),X2)
| ~ le(s(X2),X0)
| ~ le(s(X0),X1) ),
inference(resolution,[status(thm)],[c3,d3]) ).
cnf(d5,plain,
( ~ eq(f(X0),a0)
| ~ le(s(X5),X6)
| ~ le(s(X4),X5)
| ~ le(s(X3),X4)
| ~ le(s(X2),X3)
| ~ le(s(X1),X2)
| ~ le(s(X0),X1) ),
inference(resolution,[status(thm)],[d4,c3]) ).
cnf(d6,plain,
( ~ le(s(X6),X5)
| ~ le(s(X5),X4)
| ~ le(s(X4),X3)
| ~ le(s(X3),X2)
| ~ le(s(X2),X0)
| ~ le(s(X0),X1) ),
inference(resolution,[status(thm)],[c3,d5]) ).
cnf(d7,plain,
( ~ le(s(X4),X5)
| ~ le(s(X3),X4)
| ~ le(s(X2),X3)
| ~ le(s(X1),X2)
| ~ le(s(X0),X1) ),
inference(resolution,[status(thm)],[d6,c0]) ).
cnf(d8,plain,
( ~ le(s(s(X4)),X3)
| ~ le(s(X3),X2)
| ~ le(s(X2),X0)
| ~ le(s(X0),X1) ),
inference(resolution,[status(thm)],[d7,c0]) ).
cnf(d9,plain,
( ~ le(s(X2),X3)
| ~ le(s(X1),X2)
| ~ le(s(s(s(X0))),X1) ),
inference(resolution,[status(thm)],[d8,c0]) ).
cnf(d10,plain,
( ~ le(s(s(s(s(X2)))),X0)
| ~ le(s(X0),X1) ),
inference(resolution,[status(thm)],[d9,c0]) ).
cnf(d11,plain,
~ le(s(s(s(s(s(X0))))),X1),
inference(resolution,[status(thm)],[d10,c0]) ).
cnf(d12,plain,
$false,
inference(resolution,[status(thm)],[d11,c0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO612-1 : TPTP v9.3.1. Released v7.1.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n020.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Sat Sep 26 19:39:18 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 11.25/2.00 % SZS status Unsatisfiable for theBenchmark.p
% 11.25/2.00 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------