%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : PUZ040-1 : TPTP v9.3.1. Bugfixed v2.6.0.
% 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 08:22:10 AM UTC 2026
% Result : Unsatisfiable 37.04s 8.73s
% Output : CNFRefutation 37.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 14
% Syntax : Number of clauses : 48 ( 24 unt; 0 nHn; 48 RR)
% Number of literals : 72 ( 0 equ; 26 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-12 aty)
% Number of functors : 14 ( 14 usr; 1 con; 0-2 aty)
% Number of variables : 310 ( 22 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(initial_state,hypothesis,
state(bb(o,s(o)),v1(o,o),v2(o,s(s(s(o)))),v3(s(s(o)),o),v4(s(s(o)),s(s(s(o)))),h(s(s(o)),s(o)),s1(s(s(s(o))),s(o)),s2(s(s(s(o))),s(s(o))),s3(s(s(s(s(o)))),s(o)),s4(s(s(s(s(o)))),s(s(o))),e1(s(s(s(s(o)))),o),e2(s(s(s(s(o)))),s(s(s(o))))) ).
cnf(goal_state,negated_conjecture,
~ state(bb(o,o),X0,X1,X2,X3,X4,X5,X6,X7,X8,X9,X10) ).
cnf(s1_left,axiom,
( state(X0,X1,X2,X3,X4,X5,s1(X6,X7),X8,X9,X10,e1(X6,s(X7)),X11)
| ~ state(X0,X1,X2,X3,X4,X5,s1(X6,s(X7)),X8,X9,X10,e1(X6,X7),X11) ) ).
cnf(s1_down,axiom,
( state(X0,X1,X2,X3,X4,X5,s1(s(X6),X7),X8,X9,X10,e1(X6,X7),X11)
| ~ state(X0,X1,X2,X3,X4,X5,s1(X6,X7),X8,X9,X10,e1(s(X6),X7),X11) ) ).
cnf(s1_up,axiom,
( state(X0,X1,X2,X3,X4,X5,s1(X6,X7),X8,X9,X10,e1(s(X6),X7),X11)
| ~ state(X0,X1,X2,X3,X4,X5,s1(s(X6),X7),X8,X9,X10,e1(X6,X7),X11) ) ).
cnf(s3_up,axiom,
( state(X0,X1,X2,X3,X4,X5,X6,X7,s3(X8,X9),X10,e1(s(X8),X9),X11)
| ~ state(X0,X1,X2,X3,X4,X5,X6,X7,s3(s(X8),X9),X10,e1(X8,X9),X11) ) ).
cnf(v1_down,axiom,
( state(X0,v1(s(X1),X2),X3,X4,X5,X6,X7,X8,X9,X10,e1(X1,X2),X11)
| ~ state(X0,v1(X1,X2),X3,X4,X5,X6,X7,X8,X9,X10,e1(s(s(X1)),X2),X11) ) ).
cnf(v1_up,axiom,
( state(X0,v1(X1,X2),X3,X4,X5,X6,X7,X8,X9,X10,e1(s(s(X1)),X2),X11)
| ~ state(X0,v1(s(X1),X2),X3,X4,X5,X6,X7,X8,X9,X10,e1(X1,X2),X11) ) ).
cnf(v3_right,axiom,
( state(X0,X1,X2,v3(X3,s(X4)),X5,X6,X7,X8,X9,X10,e1(X3,X4),e2(s(X3),X4))
| ~ state(X0,X1,X2,v3(X3,X4),X5,X6,X7,X8,X9,X10,e1(X3,s(X4)),e2(s(X3),s(X4))) ) ).
cnf(v3_down,axiom,
( state(X0,X1,X2,v3(s(X3),X4),X5,X6,X7,X8,X9,X10,e1(X3,X4),X11)
| ~ state(X0,X1,X2,v3(X3,X4),X5,X6,X7,X8,X9,X10,e1(s(s(X3)),X4),X11) ) ).
cnf(v4_down,axiom,
( state(X0,X1,X2,X3,v4(s(X4),X5),X6,X7,X8,X9,X10,e1(X4,X5),X11)
| ~ state(X0,X1,X2,X3,v4(X4,X5),X6,X7,X8,X9,X10,e1(s(s(X4)),X5),X11) ) ).
cnf(h_right,axiom,
( state(X0,X1,X2,X3,X4,h(X5,s(X6)),X7,X8,X9,X10,e1(X5,X6),X11)
| ~ state(X0,X1,X2,X3,X4,h(X5,X6),X7,X8,X9,X10,e1(X5,s(s(X6))),X11) ) ).
cnf(b_left,axiom,
( state(bb(X0,X1),X2,X3,X4,X5,X6,X7,X8,X9,X10,e1(X0,s(s(X1))),e2(s(X0),s(s(X1))))
| ~ state(bb(X0,s(X1)),X2,X3,X4,X5,X6,X7,X8,X9,X10,e1(X0,X1),e2(s(X0),X1)) ) ).
cnf(swap_blanks,axiom,
( state(X0,X1,X2,X3,X4,X5,X6,X7,X8,X9,e1(X12,X13),e2(X10,X11))
| ~ state(X0,X1,X2,X3,X4,X5,X6,X7,X8,X9,e1(X10,X11),e2(X12,X13)) ) ).
cnf(c0,plain,
state(bb(o,s(o)),v1(o,o),v2(o,s(s(s(o)))),v3(s(s(o)),o),v4(s(s(o)),s(s(s(o)))),h(s(s(o)),s(o)),s1(s(s(s(o))),s(o)),s2(s(s(s(o))),s(s(o))),s3(s(s(s(s(o)))),s(o)),s4(s(s(s(s(o)))),s(s(o))),e1(s(s(s(s(o)))),o),e2(s(s(s(s(o)))),s(s(s(o))))),
inference(clausification,[status(esa)],[initial_state]) ).
cnf(c1,plain,
~ state(bb(o,o),X0,X1,X2,X3,X4,X5,X6,X7,X8,X9,X10),
inference(clausification,[status(esa)],[goal_state]) ).
cnf(c3,plain,
( state(X0,X1,X2,X3,X4,X5,s1(X6,X7),X8,X9,X10,e1(X6,s(X7)),X11)
| ~ state(X0,X1,X2,X3,X4,X5,s1(X6,s(X7)),X8,X9,X10,e1(X6,X7),X11) ),
inference(clausification,[status(esa)],[s1_left]) ).
cnf(c4,plain,
( state(X0,X1,X2,X3,X4,X5,s1(s(X6),X7),X8,X9,X10,e1(X6,X7),X11)
| ~ state(X0,X1,X2,X3,X4,X5,s1(X6,X7),X8,X9,X10,e1(s(X6),X7),X11) ),
inference(clausification,[status(esa)],[s1_down]) ).
cnf(c5,plain,
( state(X0,X1,X2,X3,X4,X5,s1(X6,X7),X8,X9,X10,e1(s(X6),X7),X11)
| ~ state(X0,X1,X2,X3,X4,X5,s1(s(X6),X7),X8,X9,X10,e1(X6,X7),X11) ),
inference(clausification,[status(esa)],[s1_up]) ).
cnf(c13,plain,
( state(X0,X1,X2,X3,X4,X5,X6,X7,s3(X8,X9),X10,e1(s(X8),X9),X11)
| ~ state(X0,X1,X2,X3,X4,X5,X6,X7,s3(s(X8),X9),X10,e1(X8,X9),X11) ),
inference(clausification,[status(esa)],[s3_up]) ).
cnf(c20,plain,
( state(X0,v1(s(X1),X2),X3,X4,X5,X6,X7,X8,X9,X10,e1(X1,X2),X11)
| ~ state(X0,v1(X1,X2),X3,X4,X5,X6,X7,X8,X9,X10,e1(s(s(X1)),X2),X11) ),
inference(clausification,[status(esa)],[v1_down]) ).
cnf(c21,plain,
( state(X0,v1(X1,X2),X3,X4,X5,X6,X7,X8,X9,X10,e1(s(s(X1)),X2),X11)
| ~ state(X0,v1(s(X1),X2),X3,X4,X5,X6,X7,X8,X9,X10,e1(X1,X2),X11) ),
inference(clausification,[status(esa)],[v1_up]) ).
cnf(c26,plain,
( state(X0,X1,X2,v3(X3,s(X4)),X5,X6,X7,X8,X9,X10,e1(X3,X4),e2(s(X3),X4))
| ~ state(X0,X1,X2,v3(X3,X4),X5,X6,X7,X8,X9,X10,e1(X3,s(X4)),e2(s(X3),s(X4))) ),
inference(clausification,[status(esa)],[v3_right]) ).
cnf(c28,plain,
( state(X0,X1,X2,v3(s(X3),X4),X5,X6,X7,X8,X9,X10,e1(X3,X4),X11)
| ~ state(X0,X1,X2,v3(X3,X4),X5,X6,X7,X8,X9,X10,e1(s(s(X3)),X4),X11) ),
inference(clausification,[status(esa)],[v3_down]) ).
cnf(c32,plain,
( state(X0,X1,X2,X3,v4(s(X4),X5),X6,X7,X8,X9,X10,e1(X4,X5),X11)
| ~ state(X0,X1,X2,X3,v4(X4,X5),X6,X7,X8,X9,X10,e1(s(s(X4)),X5),X11) ),
inference(clausification,[status(esa)],[v4_down]) ).
cnf(c34,plain,
( state(X0,X1,X2,X3,X4,h(X5,s(X6)),X7,X8,X9,X10,e1(X5,X6),X11)
| ~ state(X0,X1,X2,X3,X4,h(X5,X6),X7,X8,X9,X10,e1(X5,s(s(X6))),X11) ),
inference(clausification,[status(esa)],[h_right]) ).
cnf(c39,plain,
( state(bb(X0,X1),X2,X3,X4,X5,X6,X7,X8,X9,X10,e1(X0,s(s(X1))),e2(s(X0),s(s(X1))))
| ~ state(bb(X0,s(X1)),X2,X3,X4,X5,X6,X7,X8,X9,X10,e1(X0,X1),e2(s(X0),X1)) ),
inference(clausification,[status(esa)],[b_left]) ).
cnf(c42,plain,
( state(X0,X1,X2,X3,X4,X5,X6,X7,X8,X9,e1(X12,X13),e2(X10,X11))
| ~ state(X0,X1,X2,X3,X4,X5,X6,X7,X8,X9,e1(X10,X11),e2(X12,X13)) ),
inference(clausification,[status(esa)],[swap_blanks]) ).
cnf(d0,plain,
state(bb(o,s(o)),v1(o,o),v2(o,s(s(s(o)))),v3(s(s(s(o))),o),v4(s(s(o)),s(s(s(o)))),h(s(s(o)),s(o)),s1(s(s(s(o))),s(o)),s2(s(s(s(o))),s(s(o))),s3(s(s(s(s(o)))),s(o)),s4(s(s(s(s(o)))),s(s(o))),e1(s(s(o)),o),e2(s(s(s(s(o)))),s(s(s(o))))),
inference(resolution,[status(thm)],[c28,c0]) ).
cnf(d1,plain,
state(bb(o,s(o)),v1(s(o),o),v2(o,s(s(s(o)))),v3(s(s(s(o))),o),v4(s(s(o)),s(s(s(o)))),h(s(s(o)),s(o)),s1(s(s(s(o))),s(o)),s2(s(s(s(o))),s(s(o))),s3(s(s(s(s(o)))),s(o)),s4(s(s(s(s(o)))),s(s(o))),e1(o,o),e2(s(s(s(s(o)))),s(s(s(o))))),
inference(resolution,[status(thm)],[d0,c20]) ).
cnf(d2,plain,
state(bb(o,s(o)),v1(s(o),o),v2(o,s(s(s(o)))),v3(s(s(s(o))),o),v4(s(s(o)),s(s(s(o)))),h(s(s(o)),s(o)),s1(s(s(s(o))),s(o)),s2(s(s(s(o))),s(s(o))),s3(s(s(s(s(o)))),s(o)),s4(s(s(s(s(o)))),s(s(o))),e1(s(s(s(s(o)))),s(s(s(o)))),e2(o,o)),
inference(resolution,[status(thm)],[d1,c42]) ).
cnf(d3,plain,
state(bb(o,s(o)),v1(s(o),o),v2(o,s(s(s(o)))),v3(s(s(s(o))),o),v4(s(s(s(o))),s(s(s(o)))),h(s(s(o)),s(o)),s1(s(s(s(o))),s(o)),s2(s(s(s(o))),s(s(o))),s3(s(s(s(s(o)))),s(o)),s4(s(s(s(s(o)))),s(s(o))),e1(s(s(o)),s(s(s(o)))),e2(o,o)),
inference(resolution,[status(thm)],[d2,c32]) ).
cnf(d4,plain,
state(bb(o,s(o)),v1(s(o),o),v2(o,s(s(s(o)))),v3(s(s(s(o))),o),v4(s(s(s(o))),s(s(s(o)))),h(s(s(o)),s(s(o))),s1(s(s(s(o))),s(o)),s2(s(s(s(o))),s(s(o))),s3(s(s(s(s(o)))),s(o)),s4(s(s(s(s(o)))),s(s(o))),e1(s(s(o)),s(o)),e2(o,o)),
inference(resolution,[status(thm)],[d3,c34]) ).
cnf(d5,plain,
state(bb(o,s(o)),v1(s(o),o),v2(o,s(s(s(o)))),v3(s(s(s(o))),o),v4(s(s(s(o))),s(s(s(o)))),h(s(s(o)),s(s(o))),s1(s(s(o)),s(o)),s2(s(s(s(o))),s(s(o))),s3(s(s(s(s(o)))),s(o)),s4(s(s(s(s(o)))),s(s(o))),e1(s(s(s(o))),s(o)),e2(o,o)),
inference(resolution,[status(thm)],[d4,c5]) ).
cnf(d6,plain,
state(bb(o,s(o)),v1(s(o),o),v2(o,s(s(s(o)))),v3(s(s(s(o))),o),v4(s(s(s(o))),s(s(s(o)))),h(s(s(o)),s(s(o))),s1(s(s(o)),s(o)),s2(s(s(s(o))),s(s(o))),s3(s(s(s(o))),s(o)),s4(s(s(s(s(o)))),s(s(o))),e1(s(s(s(s(o)))),s(o)),e2(o,o)),
inference(resolution,[status(thm)],[d5,c13]) ).
cnf(d7,plain,
state(bb(o,s(o)),v1(s(o),o),v2(o,s(s(s(o)))),v3(s(s(s(o))),o),v4(s(s(s(o))),s(s(s(o)))),h(s(s(o)),s(s(o))),s1(s(s(o)),s(o)),s2(s(s(s(o))),s(s(o))),s3(s(s(s(o))),s(o)),s4(s(s(s(s(o)))),s(s(o))),e1(o,o),e2(s(s(s(s(o)))),s(o))),
inference(resolution,[status(thm)],[d6,c42]) ).
cnf(d8,plain,
state(bb(o,s(o)),v1(o,o),v2(o,s(s(s(o)))),v3(s(s(s(o))),o),v4(s(s(s(o))),s(s(s(o)))),h(s(s(o)),s(s(o))),s1(s(s(o)),s(o)),s2(s(s(s(o))),s(s(o))),s3(s(s(s(o))),s(o)),s4(s(s(s(s(o)))),s(s(o))),e1(s(s(o)),o),e2(s(s(s(s(o)))),s(o))),
inference(resolution,[status(thm)],[d7,c21]) ).
cnf(d9,plain,
state(bb(o,s(o)),v1(o,o),v2(o,s(s(s(o)))),v3(s(s(s(o))),o),v4(s(s(s(o))),s(s(s(o)))),h(s(s(o)),s(s(o))),s1(s(s(o)),o),s2(s(s(s(o))),s(s(o))),s3(s(s(s(o))),s(o)),s4(s(s(s(s(o)))),s(s(o))),e1(s(s(o)),s(o)),e2(s(s(s(s(o)))),s(o))),
inference(resolution,[status(thm)],[d8,c3]) ).
cnf(d10,plain,
state(bb(o,s(o)),v1(o,o),v2(o,s(s(s(o)))),v3(s(s(s(o))),o),v4(s(s(s(o))),s(s(s(o)))),h(s(s(o)),s(s(o))),s1(s(s(o)),o),s2(s(s(s(o))),s(s(o))),s3(s(s(o)),s(o)),s4(s(s(s(s(o)))),s(s(o))),e1(s(s(s(o))),s(o)),e2(s(s(s(s(o)))),s(o))),
inference(resolution,[status(thm)],[d9,c13]) ).
cnf(d11,plain,
state(bb(o,s(o)),v1(o,o),v2(o,s(s(s(o)))),v3(s(s(s(o))),s(o)),v4(s(s(s(o))),s(s(s(o)))),h(s(s(o)),s(s(o))),s1(s(s(o)),o),s2(s(s(s(o))),s(s(o))),s3(s(s(o)),s(o)),s4(s(s(s(s(o)))),s(s(o))),e1(s(s(s(o))),o),e2(s(s(s(s(o)))),o)),
inference(resolution,[status(thm)],[d10,c26]) ).
cnf(d12,plain,
state(bb(o,s(o)),v1(o,o),v2(o,s(s(s(o)))),v3(s(s(s(o))),s(o)),v4(s(s(s(o))),s(s(s(o)))),h(s(s(o)),s(s(o))),s1(s(s(s(o))),o),s2(s(s(s(o))),s(s(o))),s3(s(s(o)),s(o)),s4(s(s(s(s(o)))),s(s(o))),e1(s(s(o)),o),e2(s(s(s(s(o)))),o)),
inference(resolution,[status(thm)],[d11,c4]) ).
cnf(d13,plain,
state(bb(o,s(o)),v1(s(o),o),v2(o,s(s(s(o)))),v3(s(s(s(o))),s(o)),v4(s(s(s(o))),s(s(s(o)))),h(s(s(o)),s(s(o))),s1(s(s(s(o))),o),s2(s(s(s(o))),s(s(o))),s3(s(s(o)),s(o)),s4(s(s(s(s(o)))),s(s(o))),e1(o,o),e2(s(s(s(s(o)))),o)),
inference(resolution,[status(thm)],[d12,c20]) ).
cnf(d14,plain,
state(bb(o,s(o)),v1(s(o),o),v2(o,s(s(s(o)))),v3(s(s(s(o))),s(o)),v4(s(s(s(o))),s(s(s(o)))),h(s(s(o)),s(s(o))),s1(s(s(s(o))),o),s2(s(s(s(o))),s(s(o))),s3(s(s(o)),s(o)),s4(s(s(s(s(o)))),s(s(o))),e1(s(s(s(s(o)))),o),e2(o,o)),
inference(resolution,[status(thm)],[d13,c42]) ).
cnf(d15,plain,
state(bb(o,s(o)),v1(s(o),o),v2(o,s(s(s(o)))),v3(s(s(s(o))),s(o)),v4(s(s(s(o))),s(s(s(o)))),h(s(s(o)),s(s(o))),s1(s(s(s(s(o)))),o),s2(s(s(s(o))),s(s(o))),s3(s(s(o)),s(o)),s4(s(s(s(s(o)))),s(s(o))),e1(s(s(s(o))),o),e2(o,o)),
inference(resolution,[status(thm)],[d14,c4]) ).
cnf(d16,plain,
state(bb(o,s(o)),v1(s(s(o)),o),v2(o,s(s(s(o)))),v3(s(s(s(o))),s(o)),v4(s(s(s(o))),s(s(s(o)))),h(s(s(o)),s(s(o))),s1(s(s(s(s(o)))),o),s2(s(s(s(o))),s(s(o))),s3(s(s(o)),s(o)),s4(s(s(s(s(o)))),s(s(o))),e1(s(o),o),e2(o,o)),
inference(resolution,[status(thm)],[d15,c20]) ).
cnf(d17,plain,
state(bb(o,s(o)),v1(s(s(o)),o),v2(o,s(s(s(o)))),v3(s(s(s(o))),s(o)),v4(s(s(s(o))),s(s(s(o)))),h(s(s(o)),s(s(o))),s1(s(s(s(s(o)))),o),s2(s(s(s(o))),s(s(o))),s3(s(s(o)),s(o)),s4(s(s(s(s(o)))),s(s(o))),e1(o,o),e2(s(o),o)),
inference(resolution,[status(thm)],[d16,c42]) ).
cnf(d18,plain,
state(bb(o,o),v1(s(s(o)),o),v2(o,s(s(s(o)))),v3(s(s(s(o))),s(o)),v4(s(s(s(o))),s(s(s(o)))),h(s(s(o)),s(s(o))),s1(s(s(s(s(o)))),o),s2(s(s(s(o))),s(s(o))),s3(s(s(o)),s(o)),s4(s(s(s(s(o)))),s(s(o))),e1(o,s(s(o))),e2(s(o),s(s(o)))),
inference(resolution,[status(thm)],[d17,c39]) ).
cnf(d19,plain,
$false,
inference(resolution,[status(thm)],[c1,d18]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : PUZ040-1 : TPTP v9.3.1. Bugfixed v2.6.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.37 % Computer : n015.cluster.edu
% 0.08/0.37 % Model : x86_64 x86_64
% 0.08/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.37 % Memory : 8046.5625MB
% 0.08/0.37 % OS : Linux 6.8.0-71-generic
% 0.08/0.37 % CPULimit : 300
% 0.08/0.37 % WCLimit : 300
% 0.08/0.37 % DateTime : Sat Sep 26 05:10:29 UTC 2026
% 0.08/0.38 % CPUTime :
% 0.08/0.38 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 37.04/8.73 % SZS status Unsatisfiable for theBenchmark.p
% 37.04/8.73 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------