%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SYO691-1.001 : TPTP v9.3.1. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n011.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 09:48:06 AM UTC 2026
% Result : Unsatisfiable 22.27s 5.63s
% Output : CNFRefutation 22.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 7
% Syntax : Number of clauses : 31 ( 9 unt; 0 nHn; 22 RR)
% Number of literals : 84 ( 0 equ; 70 neg)
% Maximal clause size : 6 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 103 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(rule_1,axiom,
top(f(f(f(X0,a),X1),f(X2,a)),f(f(X2,f(f(X1,a),a)),X0)) ).
cnf(prove,negated_conjecture,
~ seq(succ(succ(succ(succ(succ(zero))))),X0,X0) ).
cnf(rewrite_top,axiom,
( step(X0,X1)
| ~ top(X0,X1) ) ).
cnf(rewrite_left,axiom,
( step(f(X0,X2),f(X1,X2))
| ~ step(X0,X1) ) ).
cnf(rewrite_right,axiom,
( step(f(X2,X0),f(X2,X1))
| ~ step(X0,X1) ) ).
cnf(rewrite_sequence_zero,axiom,
seq(zero,X0,X0) ).
cnf(rewrite_sequence_succ,axiom,
( seq(succ(X0),X1,X3)
| ~ step(X2,X3)
| ~ seq(X0,X1,X2) ) ).
cnf(c0,plain,
top(f(f(f(X0,a),X1),f(X2,a)),f(f(X2,f(f(X1,a),a)),X0)),
inference(clausification,[status(esa)],[rule_1]) ).
cnf(c1,plain,
~ seq(succ(succ(succ(succ(succ(zero))))),X0,X0),
inference(clausification,[status(esa)],[prove]) ).
cnf(c2,plain,
( step(X0,X1)
| ~ top(X0,X1) ),
inference(clausification,[status(esa)],[rewrite_top]) ).
cnf(c3,plain,
( step(f(X0,X2),f(X1,X2))
| ~ step(X0,X1) ),
inference(clausification,[status(esa)],[rewrite_left]) ).
cnf(c4,plain,
( step(f(X2,X0),f(X2,X1))
| ~ step(X0,X1) ),
inference(clausification,[status(esa)],[rewrite_right]) ).
cnf(c5,plain,
seq(zero,X0,X0),
inference(clausification,[status(esa)],[rewrite_sequence_zero]) ).
cnf(c6,plain,
( seq(succ(X0),X1,X3)
| ~ step(X2,X3)
| ~ seq(X0,X1,X2) ),
inference(clausification,[status(esa)],[rewrite_sequence_succ]) ).
cnf(d0,plain,
step(f(f(f(X0,a),X1),f(X2,a)),f(f(X2,f(f(X1,a),a)),X0)),
inference(resolution,[status(thm)],[c2,c0]) ).
cnf(d1,plain,
( ~ step(X1,X0)
| ~ seq(succ(succ(succ(succ(zero)))),X0,X1) ),
inference(resolution,[status(thm)],[c6,c1]) ).
cnf(d2,plain,
( ~ step(X2,X0)
| ~ seq(succ(succ(succ(zero))),X1,X2)
| ~ step(X0,X1) ),
inference(resolution,[status(thm)],[d1,c6]) ).
cnf(d3,plain,
( ~ step(X3,X0)
| ~ seq(succ(succ(zero)),X2,X3)
| ~ step(X1,X2)
| ~ step(X0,X1) ),
inference(resolution,[status(thm)],[d2,c6]) ).
cnf(d4,plain,
( ~ step(X4,X0)
| ~ seq(succ(zero),X3,X4)
| ~ step(X1,X2)
| ~ step(X2,X3)
| ~ step(X0,X1) ),
inference(resolution,[status(thm)],[d3,c6]) ).
cnf(d5,plain,
( ~ step(X5,X0)
| ~ seq(zero,X3,X5)
| ~ step(X1,X4)
| ~ step(X4,X2)
| ~ step(X2,X3)
| ~ step(X0,X1) ),
inference(resolution,[status(thm)],[d4,c6]) ).
cnf(d6,plain,
( ~ step(X1,X4)
| ~ step(X4,X2)
| ~ step(X3,X0)
| ~ step(X2,X3)
| ~ step(X0,X1) ),
inference(resolution,[status(thm)],[d5,c5]) ).
cnf(d7,plain,
( ~ step(X4,X5)
| ~ step(f(X3,X5),X0)
| ~ step(X1,X2)
| ~ step(X2,f(X3,X4))
| ~ step(X0,X1) ),
inference(resolution,[status(thm)],[d6,c4]) ).
cnf(d8,plain,
( ~ step(X1,X5)
| ~ step(f(X3,X5),X4)
| ~ step(X4,X2)
| ~ step(X2,f(X3,X0))
| ~ step(X0,X1) ),
inference(resolution,[status(thm)],[d7,c4]) ).
cnf(d9,plain,
( ~ step(X3,X0)
| ~ step(X4,X5)
| ~ step(X5,X1)
| ~ step(X2,f(X3,X4))
| ~ step(f(X0,X1),X2) ),
inference(resolution,[status(thm)],[d8,c3]) ).
cnf(d10,plain,
( ~ step(X4,X5)
| ~ step(f(X5,X1),f(X3,X2))
| ~ step(X3,X4)
| ~ step(X2,X0)
| ~ step(X0,X1) ),
inference(resolution,[status(thm)],[d9,c3]) ).
cnf(d11,plain,
( ~ step(X4,f(X3,a))
| ~ step(X1,X4)
| ~ step(f(X3,f(f(X2,a),a)),X0)
| ~ step(X0,f(f(X1,a),X2)) ),
inference(resolution,[status(thm)],[d10,d0]) ).
cnf(d12,plain,
( ~ step(f(f(f(X4,a),f(f(X2,a),a)),X1),f(f(X3,a),X4))
| ~ step(X3,X0)
| ~ step(X0,f(f(f(X1,a),X2),a)) ),
inference(resolution,[status(thm)],[d11,d0]) ).
cnf(d13,plain,
( ~ step(f(f(X2,a),f(f(X3,a),a)),f(X0,a))
| ~ step(X1,f(f(f(X2,a),X3),a))
| ~ step(X0,X1) ),
inference(resolution,[status(thm)],[d12,c3]) ).
cnf(d14,plain,
( ~ step(f(f(X1,a),f(f(a,a),a)),X0)
| ~ step(X0,f(f(f(f(a,a),a),X1),a)) ),
inference(resolution,[status(thm)],[d13,d0]) ).
cnf(d15,plain,
~ step(f(f(f(a,a),f(f(a,a),a)),X0),f(f(f(f(a,a),a),f(X0,a)),a)),
inference(resolution,[status(thm)],[d14,d0]) ).
cnf(d16,plain,
$false,
inference(resolution,[status(thm)],[d15,d0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SYO691-1.001 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.07 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.44 % Computer : n011.cluster.edu
% 0.18/0.44 % Model : x86_64 x86_64
% 0.18/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.44 % Memory : 8046.5625MB
% 0.18/0.44 % OS : Linux 6.8.0-71-generic
% 0.18/0.44 % CPULimit : 300
% 0.18/0.44 % WCLimit : 300
% 0.18/0.44 % DateTime : Sat Sep 26 19:46:59 UTC 2026
% 0.18/0.45 % CPUTime :
% 0.18/0.45 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 22.27/5.63 % SZS status Unsatisfiable for theBenchmark.p
% 22.27/5.63 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------