%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : COL032-1 : 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 : n012.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 06:56:43 AM UTC 2026
% Result : Unsatisfiable 10.97s 16.75s
% Output : CNFRefutation 10.97s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 3
% Syntax : Number of clauses : 11 ( 11 unt; 0 nHn; 6 RR)
% Number of literals : 11 ( 10 equ; 5 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 7 ( 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 : 17 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(m_definition,axiom,
apply(m,X0) = apply(X0,X0) ).
cnf(q_definition,axiom,
apply(apply(apply(q,X0),X1),X2) = apply(X1,apply(X0,X2)) ).
cnf(prove_fixed_point,negated_conjecture,
apply(X0,f(X0)) != apply(f(X0),apply(X0,f(X0))) ).
cnf(c0,plain,
apply(X0,X0) = apply(m,X0),
inference(clausification,[status(esa)],[m_definition]) ).
cnf(c1,plain,
apply(X0,apply(X1,X2)) = apply(apply(apply(q,X1),X0),X2),
inference(clausification,[status(esa)],[q_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(f(apply(apply(q,X0),X1)),apply(X1,apply(X0,f(apply(apply(q,X0),X1))))) != apply(apply(apply(q,X0),X1),f(apply(apply(q,X0),X1))),
inference(superposition,[status(thm)],[c1,c2]) ).
cnf(d1,plain,
apply(f(apply(apply(q,X0),X1)),apply(X1,apply(X0,f(apply(apply(q,X0),X1))))) != apply(X1,apply(X0,f(apply(apply(q,X0),X1)))),
inference(demodulation,[status(thm)],[d0,c1]) ).
cnf(d2,plain,
apply(X1,apply(X0,apply(apply(q,X0),X1))) = apply(m,apply(apply(q,X0),X1)),
inference(superposition,[status(thm)],[c1,c0]) ).
cnf(d3,plain,
apply(m,apply(apply(q,X0),f(apply(apply(q,apply(q,X0)),X0)))) != apply(X0,apply(apply(q,X0),f(apply(apply(q,apply(q,X0)),X0)))),
inference(superposition,[status(thm)],[d2,d1]) ).
cnf(d4,plain,
$false,
inference(equality_resolution,[status(thm)],[d3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : COL032-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.02 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.04/15.31 % Computer : n012.cluster.edu
% 0.04/15.31 % Model : x86_64 x86_64
% 0.04/15.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.04/15.31 % Memory : 8046.5625MB
% 0.04/15.31 % OS : Linux 6.8.0-71-generic
% 0.04/15.31 % CPULimit : 300
% 0.04/15.31 % WCLimit : 300
% 0.04/15.31 % DateTime : Sat Sep 26 23:06:40 UTC 2026
% 0.04/15.31 % CPUTime :
% 0.04/15.31 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 10.97/16.75 % SZS status Unsatisfiable for theBenchmark.p
% 10.97/16.75 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------