%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SWX204-1 : TPTP v9.3.1. Released v9.3.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n019.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 09:15:38 AM UTC 2026
% Result : Unsatisfiable 30.35s 4.35s
% Output : CNFRefutation 30.35s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 10
% Syntax : Number of clauses : 46 ( 46 unt; 0 nHn; 23 RR)
% Number of literals : 46 ( 45 equ; 4 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 : 9 ( 9 usr; 3 con; 0-2 aty)
% Number of variables : 33 ( 6 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(axiom,axiom,
x2(z,X0) = X0 ).
cnf(axiom_001,axiom,
x2(s(X0),X1) = s(x2(X0,X1)) ).
cnf(axiom_002,axiom,
x22(z,X0) = z ).
cnf(axiom_003,axiom,
x22(s(X0),X1) = x2(X1,x22(X0,X1)) ).
cnf(axiom_004,axiom,
'mul$uidem'(X0) = eq(x22(X0,X0),X0) ).
cnf(axiom_007,axiom,
eq(s(X0),s(X1)) = eq(X0,X1) ).
cnf(axiom_009,axiom,
eq(s(X0),z) = bfalse ).
cnf(axiom_010,axiom,
eq(X0,X0) = btrue ).
cnf(axiom_011,axiom,
eq2(X0,X0) = btrue ).
cnf(goal,negated_conjecture,
eq2('mul$uidem'(X0),bfalse) != btrue ).
cnf(c0,plain,
x2(z,X0) = X0,
inference(clausification,[status(esa)],[axiom]) ).
cnf(c1,plain,
x2(s(X0),X1) = s(x2(X0,X1)),
inference(clausification,[status(esa)],[axiom_001]) ).
cnf(c2,plain,
x22(z,X0) = z,
inference(clausification,[status(esa)],[axiom_002]) ).
cnf(c3,plain,
x22(s(X0),X1) = x2(X1,x22(X0,X1)),
inference(clausification,[status(esa)],[axiom_003]) ).
cnf(c4,plain,
'mul$uidem'(X0) = eq(x22(X0,X0),X0),
inference(clausification,[status(esa)],[axiom_004]) ).
cnf(c7,plain,
eq(s(X0),s(X1)) = eq(X0,X1),
inference(clausification,[status(esa)],[axiom_007]) ).
cnf(c9,plain,
eq(s(X0),z) = bfalse,
inference(clausification,[status(esa)],[axiom_009]) ).
cnf(c10,plain,
eq(X0,X0) = btrue,
inference(clausification,[status(esa)],[axiom_010]) ).
cnf(c11,plain,
eq2(X0,X0) = btrue,
inference(clausification,[status(esa)],[axiom_011]) ).
cnf(c12,plain,
eq2('mul$uidem'(X0),bfalse) != btrue,
inference(clausification,[status(esa)],[goal]) ).
cnf(d0,plain,
x22(s(X1),s(X0)) = s(x2(X0,x22(X1,s(X0)))),
inference(superposition,[status(thm)],[c3,c1]) ).
cnf(d1,plain,
x22(s(X1),s(s(X0))) = s(s(x2(X0,x22(X1,s(s(X0)))))),
inference(superposition,[status(thm)],[c1,d0]) ).
cnf(d2,plain,
x22(s(X0),s(s(z))) = s(s(x22(X0,s(s(z))))),
inference(superposition,[status(thm)],[c0,d1]) ).
cnf(d3,plain,
x22(s(z),X0) = x2(X0,z),
inference(superposition,[status(thm)],[c2,c3]) ).
cnf(d4,plain,
x22(s(s(z)),s(s(z))) = s(s(x2(s(s(z)),z))),
inference(superposition,[status(thm)],[d3,d2]) ).
cnf(d5,plain,
x22(s(s(z)),s(s(z))) = s(s(s(x2(s(z),z)))),
inference(demodulation,[status(thm)],[d4,c1]) ).
cnf(d6,plain,
x22(s(s(z)),s(s(z))) = s(s(s(s(x2(z,z))))),
inference(demodulation,[status(thm)],[d5,c1]) ).
cnf(d7,plain,
x22(s(s(z)),s(s(z))) = s(s(s(s(z)))),
inference(demodulation,[status(thm)],[d6,c0]) ).
cnf(d8,plain,
'mul$uidem'(s(s(z))) = eq(s(s(s(s(z)))),s(s(z))),
inference(superposition,[status(thm)],[d7,c4]) ).
cnf(d9,plain,
'mul$uidem'(s(s(z))) = eq(s(s(s(z))),s(z)),
inference(demodulation,[status(thm)],[d8,c7]) ).
cnf(d10,plain,
'mul$uidem'(s(s(z))) = eq(s(s(z)),z),
inference(demodulation,[status(thm)],[d9,c7]) ).
cnf(d11,plain,
'mul$uidem'(s(s(z))) = bfalse,
inference(demodulation,[status(thm)],[d10,c9]) ).
cnf(d12,plain,
eq2(bfalse,bfalse) != btrue,
inference(superposition,[status(thm)],[d11,c12]) ).
cnf(d13,plain,
btrue != btrue,
inference(demodulation,[status(thm)],[d12,c11]) ).
cnf(d14,plain,
'mul$uidem'(s(z)) = eq(x2(s(z),z),s(z)),
inference(superposition,[status(thm)],[d3,c4]) ).
cnf(d15,plain,
'mul$uidem'(s(z)) = eq(s(x2(z,z)),s(z)),
inference(demodulation,[status(thm)],[d14,c1]) ).
cnf(d16,plain,
'mul$uidem'(s(z)) = eq(x2(z,z),z),
inference(demodulation,[status(thm)],[d15,c7]) ).
cnf(d17,plain,
'mul$uidem'(s(z)) = eq(z,z),
inference(demodulation,[status(thm)],[d16,c0]) ).
cnf(d18,plain,
'mul$uidem'(s(z)) = btrue,
inference(demodulation,[status(thm)],[d17,c10]) ).
cnf(d19,plain,
x22(s(X0),s(z)) = s(x22(X0,s(z))),
inference(superposition,[status(thm)],[c0,d0]) ).
cnf(d20,plain,
'mul$uidem'(s(z)) = eq(s(x22(z,s(z))),s(z)),
inference(superposition,[status(thm)],[d19,c4]) ).
cnf(d21,plain,
btrue = eq(s(x22(z,s(z))),s(z)),
inference(demodulation,[status(thm)],[d20,d18]) ).
cnf(d22,plain,
btrue = eq(x22(z,s(z)),z),
inference(demodulation,[status(thm)],[d21,c7]) ).
cnf(d23,plain,
btrue = eq(z,z),
inference(demodulation,[status(thm)],[d22,c2]) ).
cnf(d24,plain,
btrue = btrue,
inference(demodulation,[status(thm)],[d23,c10]) ).
cnf(d25,plain,
$false,
inference(resolution,[status(thm)],[d24,d13]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWX204-1 : TPTP v9.3.1. Released v9.3.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n019.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Sat Sep 26 16:55:48 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 30.35/4.35 % SZS status Unsatisfiable for theBenchmark.p
% 30.35/4.35 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------