%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : GRP682-10 : TPTP v9.3.1. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n004.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 07:24:28 AM UTC 2026
% Result : Unsatisfiable 25.77s 4.50s
% Output : CNFRefutation 25.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 7
% Syntax : Number of clauses : 28 ( 28 unt; 0 nHn; 3 RR)
% Number of literals : 28 ( 27 equ; 2 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 50 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(f01,axiom,
ld(X0,mult(X0,X0)) = X0 ).
cnf(f02,axiom,
rd(mult(X0,X0),X0) = X0 ).
cnf(f03,axiom,
mult(X0,ld(X0,X1)) = ld(X0,mult(X0,X1)) ).
cnf(f04,axiom,
mult(rd(X0,X1),X1) = rd(mult(X0,X1),X1) ).
cnf(f05,axiom,
ld(ld(X0,X1),mult(ld(X0,X1),mult(X2,X3))) = mult(ld(X0,mult(X0,X2)),X3) ).
cnf(f07,axiom,
ld(X0,mult(X0,ld(X1,X1))) = rd(mult(rd(X0,X0),X1),X1) ).
cnf(goal,negated_conjecture,
ld(ld(x0,x1),mult(ld(x0,x1),x2)) != ld(x0,mult(x0,x2)) ).
cnf(c0,plain,
ld(X0,mult(X0,X0)) = X0,
inference(clausification,[status(esa)],[f01]) ).
cnf(c1,plain,
rd(mult(X0,X0),X0) = X0,
inference(clausification,[status(esa)],[f02]) ).
cnf(c2,plain,
mult(X0,ld(X0,X1)) = ld(X0,mult(X0,X1)),
inference(clausification,[status(esa)],[f03]) ).
cnf(c3,plain,
mult(rd(X0,X1),X1) = rd(mult(X0,X1),X1),
inference(clausification,[status(esa)],[f04]) ).
cnf(c4,plain,
ld(ld(X0,X1),mult(ld(X0,X1),mult(X2,X3))) = mult(ld(X0,mult(X0,X2)),X3),
inference(clausification,[status(esa)],[f05]) ).
cnf(c6,plain,
ld(X0,mult(X0,ld(X1,X1))) = rd(mult(rd(X0,X0),X1),X1),
inference(clausification,[status(esa)],[f07]) ).
cnf(c7,plain,
ld(ld(x0,x1),mult(ld(x0,x1),x2)) != ld(x0,mult(x0,x2)),
inference(clausification,[status(esa)],[goal]) ).
cnf(d0,plain,
ld(X0,mult(X0,ld(X1,X1))) = mult(rd(rd(X0,X0),X1),X1),
inference(demodulation,[status(thm)],[c6,c3]) ).
cnf(d1,plain,
mult(rd(X0,X0),X0) = X0,
inference(demodulation,[status(thm)],[c1,c3]) ).
cnf(d2,plain,
mult(rd(rd(X0,X0),X0),X0) = rd(X0,X0),
inference(superposition,[status(thm)],[d1,c3]) ).
cnf(d3,plain,
ld(X0,mult(X0,ld(X0,X0))) = rd(X0,X0),
inference(demodulation,[status(thm)],[d2,d0]) ).
cnf(d4,plain,
ld(X0,ld(X0,mult(X0,X0))) = rd(X0,X0),
inference(demodulation,[status(thm)],[d3,c2]) ).
cnf(d5,plain,
ld(X0,X0) = rd(X0,X0),
inference(demodulation,[status(thm)],[d4,c0]) ).
cnf(d6,plain,
mult(ld(X0,X0),X0) = X0,
inference(demodulation,[status(thm)],[d1,d5]) ).
cnf(d7,plain,
ld(X0,mult(ld(X0,mult(X0,X0)),mult(X1,X2))) = mult(ld(X0,mult(X0,X1)),X2),
inference(superposition,[status(thm)],[c0,c4]) ).
cnf(d8,plain,
ld(X0,mult(X0,mult(X1,X2))) = mult(ld(X0,mult(X0,X1)),X2),
inference(demodulation,[status(thm)],[d7,c0]) ).
cnf(d9,plain,
ld(ld(X1,X2),mult(ld(X1,X2),X0)) = mult(ld(X1,mult(X1,rd(X0,X0))),X0),
inference(superposition,[status(thm)],[d1,c4]) ).
cnf(d10,plain,
ld(ld(X0,X2),mult(ld(X0,X2),X1)) = ld(X0,mult(X0,mult(rd(X1,X1),X1))),
inference(demodulation,[status(thm)],[d9,d8]) ).
cnf(d11,plain,
ld(ld(X1,X2),mult(ld(X1,X2),X0)) = ld(X1,mult(X1,mult(ld(X0,X0),X0))),
inference(demodulation,[status(thm)],[d10,d5]) ).
cnf(d12,plain,
ld(ld(X1,X2),mult(ld(X1,X2),X0)) = ld(X1,mult(X1,X0)),
inference(demodulation,[status(thm)],[d11,d6]) ).
cnf(d13,plain,
$false,
inference(resolution,[status(thm)],[d12,c7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : GRP682-10 : TPTP v9.3.1. Released v8.1.0.
% 0.00/0.06 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.15/0.63 % Computer : n004.cluster.edu
% 0.15/0.63 % Model : x86_64 x86_64
% 0.15/0.63 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.63 % Memory : 8046.5625MB
% 0.15/0.63 % OS : Linux 6.8.0-71-generic
% 0.15/0.63 % CPULimit : 300
% 0.15/0.63 % WCLimit : 300
% 0.15/0.63 % DateTime : Fri Sep 25 15:35:52 UTC 2026
% 0.15/0.63 % CPUTime :
% 0.15/0.63 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 25.77/4.50 % SZS status Unsatisfiable for theBenchmark.p
% 25.77/4.50 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------