%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : COL030-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/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 06:56:42 AM UTC 2026
% Result : Unsatisfiable 3.31s 18.32s
% Output : CNFRefutation 3.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 3
% Syntax : Number of clauses : 13 ( 13 unt; 0 nHn; 5 RR)
% Number of literals : 13 ( 12 equ; 4 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 25 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(s_definition,axiom,
apply(apply(apply(s,X0),X1),X2) = apply(apply(X0,X2),apply(X1,X2)) ).
cnf(l_definition,axiom,
apply(apply(l,X0),X1) = apply(X0,apply(X1,X1)) ).
cnf(prove_fixed_point,negated_conjecture,
apply(X0,f(X0)) != apply(f(X0),apply(X0,f(X0))) ).
cnf(c0,plain,
apply(apply(X0,X1),apply(X2,X1)) = apply(apply(apply(s,X0),X2),X1),
inference(clausification,[status(esa)],[s_definition]) ).
cnf(c1,plain,
apply(X0,apply(X1,X1)) = apply(apply(l,X0),X1),
inference(clausification,[status(esa)],[l_definition]) ).
cnf(c2,plain,
apply(f(X0),apply(X0,f(X0))) != apply(X0,f(X0)),
inference(clausification,[status(esa)],[prove_fixed_point]) ).
cnf(d0,plain,
apply(X2,apply(apply(apply(s,X0),X0),X1)) = apply(apply(l,X2),apply(X0,X1)),
inference(superposition,[status(thm)],[c0,c1]) ).
cnf(d1,plain,
apply(X2,apply(apply(X0,X1),apply(X0,X1))) = apply(apply(l,X2),apply(X0,X1)),
inference(superposition,[status(thm)],[c0,d0]) ).
cnf(d2,plain,
apply(apply(l,X0),apply(X1,X2)) = apply(apply(l,X0),apply(X1,X2)),
inference(demodulation,[status(thm)],[d1,c1]) ).
cnf(d3,plain,
apply(apply(apply(s,l),X1),X0) = apply(apply(l,X0),apply(X1,X0)),
inference(superposition,[status(thm)],[c0,d2]) ).
cnf(d4,plain,
apply(apply(l,f(apply(apply(s,X0),X0))),apply(X0,f(apply(apply(s,X0),X0)))) != apply(apply(apply(s,X0),X0),f(apply(apply(s,X0),X0))),
inference(superposition,[status(thm)],[d0,c2]) ).
cnf(d5,plain,
apply(apply(apply(s,l),X0),f(apply(apply(s,X0),X0))) != apply(apply(apply(s,X0),X0),f(apply(apply(s,X0),X0))),
inference(demodulation,[status(thm)],[d4,d3]) ).
cnf(d6,plain,
$false,
inference(equality_resolution,[status(thm)],[d5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : COL030-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.06 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.16/0.42 % Computer : n011.cluster.edu
% 0.16/0.42 % Model : x86_64 x86_64
% 0.16/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.42 % Memory : 8046.5625MB
% 0.16/0.42 % OS : Linux 6.8.0-71-generic
% 0.16/0.42 % CPULimit : 300
% 0.16/0.42 % WCLimit : 300
% 0.16/0.42 % DateTime : Sat Sep 26 23:06:44 UTC 2026
% 0.16/0.42 % CPUTime :
% 0.16/0.42 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.31/18.32 % SZS status Unsatisfiable for theBenchmark.p
% 3.31/18.32 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------