%------------------------------------------------------------------------------
% 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 : n005.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 : Theorem 15.98s 2.84s
% Output : CNFRefutation 15.98s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 7
% Syntax : Number of formulae : 29 ( 29 unt; 0 def)
% Number of atoms : 29 ( 28 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 5 ( 5 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 1 con; 0-2 aty)
% Number of variables : 26 ( 2 sgn 8 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(axiom_001,axiom,
! [X0] : proj1S(s(X0)) = X0 ).
fof(axiom_002,axiom,
! [X0] : z != s(X0) ).
fof(axiom_003,axiom,
! [X0] : x2(z,X0) = X0 ).
fof(axiom_004,axiom,
! [X0,X1] : x2(s(X1),X0) = s(x2(X1,X0)) ).
fof(axiom_005,axiom,
! [X0] : x22(z,X0) = z ).
fof(axiom_006,axiom,
! [X0,X1] : x22(s(X1),X0) = x2(X0,x22(X1,X0)) ).
fof(goal_007,conjecture,
? [X0] : x22(X0,X0) != X0 ).
fof(negated_conjecture,negated_conjecture,
~ ? [X0] : x22(X0,X0) != X0,
inference(negate_conjecture,[status(cth)],[goal_007]) ).
cnf(c0,plain,
proj1S(s(X0)) = X0,
inference(clausification,[status(esa)],[axiom_001]) ).
cnf(c1,plain,
z != s(X0),
inference(clausification,[status(esa)],[axiom_002]) ).
cnf(c2,plain,
x2(z,X0) = X0,
inference(clausification,[status(esa)],[axiom_003]) ).
cnf(c3,plain,
x2(s(X0),X1) = s(x2(X0,X1)),
inference(clausification,[status(esa)],[axiom_004]) ).
cnf(c4,plain,
x22(z,X0) = z,
inference(clausification,[status(esa)],[axiom_005]) ).
cnf(c5,plain,
x22(s(X0),X1) = x2(X1,x22(X0,X1)),
inference(clausification,[status(esa)],[axiom_006]) ).
cnf(c6,plain,
x22(X0,X0) = X0,
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
x22(s(X1),s(X0)) = s(x2(X0,x22(X1,s(X0)))),
inference(superposition,[status(thm)],[c5,c3]) ).
cnf(d1,plain,
proj1S(x22(s(X1),s(X0))) = x2(X0,x22(X1,s(X0))),
inference(superposition,[status(thm)],[d0,c0]) ).
cnf(d2,plain,
proj1S(s(X0)) = x2(X0,x22(X0,s(X0))),
inference(superposition,[status(thm)],[c6,d1]) ).
cnf(d3,plain,
X0 = x2(X0,x22(X0,s(X0))),
inference(demodulation,[status(thm)],[d2,c0]) ).
cnf(d4,plain,
x22(s(z),X0) = x2(X0,z),
inference(superposition,[status(thm)],[c4,c5]) ).
cnf(d5,plain,
s(z) = x2(s(z),x2(s(s(z)),z)),
inference(superposition,[status(thm)],[d4,d3]) ).
cnf(d6,plain,
s(z) = s(x2(z,x2(s(s(z)),z))),
inference(demodulation,[status(thm)],[d5,c3]) ).
cnf(d7,plain,
s(z) = s(x2(s(s(z)),z)),
inference(demodulation,[status(thm)],[d6,c2]) ).
cnf(d8,plain,
s(z) = s(s(x2(s(z),z))),
inference(demodulation,[status(thm)],[d7,c3]) ).
cnf(d9,plain,
s(z) = s(s(s(x2(z,z)))),
inference(demodulation,[status(thm)],[d8,c3]) ).
cnf(d10,plain,
s(z) = s(s(s(z))),
inference(demodulation,[status(thm)],[d9,c2]) ).
cnf(d11,plain,
proj1S(s(z)) = s(s(z)),
inference(superposition,[status(thm)],[d10,c0]) ).
cnf(d12,plain,
z = s(s(z)),
inference(demodulation,[status(thm)],[d11,c0]) ).
cnf(d13,plain,
$false,
inference(resolution,[status(thm)],[c1,d12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SWX204+1 : TPTP v9.3.1. Released v9.3.0.
% 0.00/0.06 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/0.44 % Computer : n005.cluster.edu
% 0.17/0.44 % Model : x86_64 x86_64
% 0.17/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.44 % Memory : 8046.5625MB
% 0.17/0.44 % OS : Linux 6.8.0-71-generic
% 0.17/0.44 % CPULimit : 300
% 0.17/0.44 % WCLimit : 300
% 0.17/0.44 % DateTime : Sat Sep 26 16:55:31 UTC 2026
% 0.17/0.45 % CPUTime :
% 0.17/0.45 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 15.98/2.84 % SZS status Theorem for theBenchmark.p
% 15.98/2.84 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------