%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : SWX204+1 : TPTP v9.3.1. Released v9.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n026.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 : Tue Sep 29 01:45:33 PM UTC 2026
% Result : Theorem 0.06s 0.26s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 7
% Syntax : Number of formulae : 59 ( 59 unt; 0 def)
% Number of atoms : 59 ( 58 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 4 ( 4 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 1 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 : 46 ( 3 sgn 0 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(c1,axiom,
z != s(X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_002) ).
cnf(c2,axiom,
x2(s(N),Y) = s(x2(N,Y)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_004) ).
cnf(c3,plain,
x2(s(s(z)),X2) = s(x2(s(z),X2)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c4,plain,
x2(s(z),X2) = s(x2(z,X2)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c5,axiom,
x2(z,Y2) = Y2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_003) ).
cnf(c6,plain,
x2(z,X2) = X2,
inference(substitution,[status(thm)],[c5]) ).
cnf(c7,plain,
s(x2(z,X2)) = s(X2),
inference(congruence,[status(thm)],[c6]) ).
cnf(c8,plain,
x2(s(z),X2) = s(X2),
inference(transitivity,[status(thm)],[c4,c7]) ).
cnf(c9,plain,
s(x2(s(z),X2)) = s(s(X2)),
inference(congruence,[status(thm)],[c8]) ).
cnf(c10,plain,
x2(s(s(z)),X2) = s(s(X2)),
inference(transitivity,[status(thm)],[c3,c9]) ).
cnf(c11,plain,
s(s(X2)) = x2(s(s(z)),X2),
inference(symmetry,[status(thm)],[c10]) ).
cnf(c12,plain,
x2(s(X2),X3) = s(x2(X2,X3)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c13,plain,
proj1S(x2(s(X3),X2)) = proj1S(s(x2(X3,X2))),
inference(congruence,[status(thm)],[c12]) ).
cnf(c14,axiom,
proj1S(s(X2)) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_001) ).
cnf(c15,plain,
proj1S(s(x2(X3,X2))) = x2(X3,X2),
inference(substitution,[status(thm)],[c14]) ).
cnf(c16,plain,
proj1S(x2(s(X3),X2)) = x2(X3,X2),
inference(transitivity,[status(thm)],[c13,c15]) ).
cnf(c17,plain,
proj1S(x2(s(s(s(z))),X2)) = x2(s(s(z)),X2),
inference(substitution,[status(thm)],[c16]) ).
cnf(c18,plain,
x2(s(s(z)),X2) = proj1S(x2(s(s(s(z))),X2)),
inference(symmetry,[status(thm)],[c17]) ).
cnf(c19,plain,
proj1S(s(s(s(s(z))))) = s(s(s(z))),
inference(substitution,[status(thm)],[c14]) ).
cnf(c20,plain,
s(s(s(z))) = proj1S(s(s(s(s(z))))),
inference(symmetry,[status(thm)],[c19]) ).
cnf(c21,plain,
x2(s(s(z)),s(s(z))) = s(s(s(s(z)))),
inference(substitution,[status(thm)],[c10]) ).
cnf(c22,plain,
s(s(s(s(z)))) = x2(s(s(z)),s(s(z))),
inference(symmetry,[status(thm)],[c21]) ).
cnf(c23,plain,
x2(s(s(z)),z) = s(s(z)),
inference(substitution,[status(thm)],[c10]) ).
cnf(c24,plain,
s(s(z)) = x2(s(s(z)),z),
inference(symmetry,[status(thm)],[c23]) ).
cnf(c25,plain,
x2(s(s(z)),s(s(z))) = x2(s(s(z)),x2(s(s(z)),z)),
inference(congruence,[status(thm)],[c24]) ).
cnf(c26,axiom,
x22(s(N2),Y2) = x2(Y2,x22(N2,Y2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_006) ).
cnf(c27,plain,
x22(s(z),X2) = x2(X2,x22(z,X2)),
inference(substitution,[status(thm)],[c26]) ).
cnf(c28,axiom,
x22(z,Y2) = z,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_005) ).
cnf(c29,plain,
x22(z,X2) = z,
inference(substitution,[status(thm)],[c28]) ).
cnf(c30,plain,
x2(X2,x22(z,X2)) = x2(X2,z),
inference(congruence,[status(thm)],[c29]) ).
cnf(c31,plain,
x22(s(z),X2) = x2(X2,z),
inference(transitivity,[status(thm)],[c27,c30]) ).
cnf(c32,plain,
x2(X2,z) = x22(s(z),X2),
inference(symmetry,[status(thm)],[c31]) ).
cnf(c33,plain,
x2(X2,x2(X2,z)) = x2(X2,x22(s(z),X2)),
inference(congruence,[status(thm)],[c32]) ).
cnf(c34,plain,
x22(s(s(z)),X2) = x2(X2,x22(s(z),X2)),
inference(substitution,[status(thm)],[c26]) ).
cnf(c35,plain,
x2(X2,x22(s(z),X2)) = x22(s(s(z)),X2),
inference(symmetry,[status(thm)],[c34]) ).
cnf(c36,plain,
x2(X2,x2(X2,z)) = x22(s(s(z)),X2),
inference(transitivity,[status(thm)],[c33,c35]) ).
cnf(c37,plain,
x2(s(s(z)),x2(s(s(z)),z)) = x22(s(s(z)),s(s(z))),
inference(substitution,[status(thm)],[c36]) ).
fof(c38,conjecture,
? [X2] : x22(X2,X2) != X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goal_007) ).
fof(c39,negated_conjecture,
~ ? [X2] : x22(X2,X2) != X2,
inference(negate_conjecture,[status(cth)],[c38]) ).
cnf(c40,plain,
x22(X2,X2) = X2,
inference(clausify,[status(esa)],[c39]) ).
cnf(c41,plain,
x22(s(s(z)),s(s(z))) = s(s(z)),
inference(substitution,[status(thm)],[c40]) ).
cnf(c42,plain,
x2(s(s(z)),x2(s(s(z)),z)) = s(s(z)),
inference(transitivity,[status(thm)],[c37,c41]) ).
cnf(c43,plain,
x2(s(s(z)),s(s(z))) = s(s(z)),
inference(transitivity,[status(thm)],[c25,c42]) ).
cnf(c44,plain,
s(s(s(s(z)))) = s(s(z)),
inference(transitivity,[status(thm)],[c22,c43]) ).
cnf(c45,plain,
proj1S(s(s(s(s(z))))) = proj1S(s(s(z))),
inference(congruence,[status(thm)],[c44]) ).
cnf(c46,plain,
proj1S(s(s(z))) = s(z),
inference(substitution,[status(thm)],[c14]) ).
cnf(c47,plain,
proj1S(s(s(s(s(z))))) = s(z),
inference(transitivity,[status(thm)],[c45,c46]) ).
cnf(c48,plain,
s(s(s(z))) = s(z),
inference(transitivity,[status(thm)],[c20,c47]) ).
cnf(c49,plain,
x2(s(s(s(z))),X2) = x2(s(z),X2),
inference(congruence,[status(thm)],[c48]) ).
cnf(c50,plain,
proj1S(x2(s(s(s(z))),X2)) = proj1S(x2(s(z),X2)),
inference(congruence,[status(thm)],[c49]) ).
cnf(c51,plain,
proj1S(x2(s(z),X2)) = x2(z,X2),
inference(substitution,[status(thm)],[c16]) ).
cnf(c52,plain,
x2(z,X2) = X2,
inference(substitution,[status(thm)],[c5]) ).
cnf(c53,plain,
proj1S(x2(s(z),X2)) = X2,
inference(transitivity,[status(thm)],[c51,c52]) ).
cnf(c54,plain,
proj1S(x2(s(s(s(z))),X2)) = X2,
inference(transitivity,[status(thm)],[c50,c53]) ).
cnf(c55,plain,
x2(s(s(z)),X2) = X2,
inference(transitivity,[status(thm)],[c18,c54]) ).
cnf(c56,plain,
s(s(X2)) = X2,
inference(transitivity,[status(thm)],[c11,c55]) ).
cnf(c57,plain,
s(s(z)) = z,
inference(substitution,[status(thm)],[c56]) ).
cnf(c58,plain,
z = s(s(z)),
inference(symmetry,[status(thm)],[c57]) ).
cnf(c59,plain,
$false,
inference(resolution,[status(thm)],[c1,c58]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWX204+1 : TPTP v9.3.1. Released v9.3.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.06/0.18 % Computer : n026.cluster.edu
% 0.06/0.18 % Model : x86_64 x86_64
% 0.06/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.18 % Memory : 8046.5625MB
% 0.06/0.18 % OS : Linux 6.8.0-71-generic
% 0.06/0.18 % CPULimit : 300
% 0.06/0.18 % WCLimit : 300
% 0.06/0.18 % DateTime : Mon Sep 28 15:12:40 UTC 2026
% 0.06/0.18 % CPUTime :
% 0.06/0.18 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.06/0.26 Command-line arguments: --lhs-weight 9 --flip-ordering --complete-subsets --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 0.06/0.26
% 0.06/0.26 % SZS status Theorem
% 0.06/0.26
% 0.06/0.27 % SZS output start CNFRefutation
% See solution above
% 0.21/0.29
% 0.21/0.29 RESULT: Theorem (the conjecture is true).
%------------------------------------------------------------------------------