%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : LCL161-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n014.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 07:53:53 AM UTC 2026
% Result : Unsatisfiable 20.48s 5.92s
% Output : CNFRefutation 20.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 9
% Syntax : Number of clauses : 30 ( 30 unt; 0 nHn; 3 RR)
% Number of literals : 30 ( 29 equ; 2 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 38 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(xor_commutativity,axiom,
xor(X0,X1) = xor(X1,X0) ).
cnf(and_star_commutativity,axiom,
'and$ustar'(X0,X1) = 'and$ustar'(X1,X0) ).
cnf(implies_definition,axiom,
implies(X0,X1) = xor(truth,'and$ustar'(X0,xor(truth,X1))) ).
cnf(prove_wajsberg_axiom,negated_conjecture,
implies(truth,x) != x ).
cnf(axiom_1,axiom,
not(X0) = xor(X0,truth) ).
cnf(axiom_2,axiom,
xor(X0,falsehood) = X0 ).
cnf(axiom_3,axiom,
xor(X0,X0) = falsehood ).
cnf(axiom_4,axiom,
'and$ustar'(X0,truth) = X0 ).
cnf(axiom_7,axiom,
xor(X0,xor(truth,X1)) = xor(xor(X0,truth),X1) ).
cnf(c0,plain,
xor(X0,X1) = xor(X1,X0),
inference(clausification,[status(esa)],[xor_commutativity]) ).
cnf(c2,plain,
'and$ustar'(X0,X1) = 'and$ustar'(X1,X0),
inference(clausification,[status(esa)],[and_star_commutativity]) ).
cnf(c4,plain,
implies(X0,X1) = xor(truth,'and$ustar'(X0,xor(truth,X1))),
inference(clausification,[status(esa)],[implies_definition]) ).
cnf(c5,plain,
implies(truth,x) != x,
inference(clausification,[status(esa)],[prove_wajsberg_axiom]) ).
cnf(c6,plain,
not(X0) = xor(X0,truth),
inference(clausification,[status(esa)],[axiom_1]) ).
cnf(c7,plain,
xor(X0,falsehood) = X0,
inference(clausification,[status(esa)],[axiom_2]) ).
cnf(c8,plain,
xor(X0,X0) = falsehood,
inference(clausification,[status(esa)],[axiom_3]) ).
cnf(c9,plain,
'and$ustar'(X0,truth) = X0,
inference(clausification,[status(esa)],[axiom_4]) ).
cnf(c12,plain,
xor(X0,xor(truth,X1)) = xor(xor(X0,truth),X1),
inference(clausification,[status(esa)],[axiom_7]) ).
cnf(d0,plain,
xor(X0,xor(truth,X1)) = xor(not(X0),X1),
inference(demodulation,[status(thm)],[c12,c6]) ).
cnf(d1,plain,
xor(X0,falsehood) = xor(not(X0),truth),
inference(superposition,[status(thm)],[c8,d0]) ).
cnf(d2,plain,
X0 = xor(not(X0),truth),
inference(demodulation,[status(thm)],[d1,c7]) ).
cnf(d3,plain,
X0 = not(not(X0)),
inference(demodulation,[status(thm)],[d2,c6]) ).
cnf(d4,plain,
xor(truth,X0) = not(X0),
inference(superposition,[status(thm)],[c6,c0]) ).
cnf(d5,plain,
implies(X1,X0) = xor(truth,'and$ustar'(X1,xor(X0,truth))),
inference(superposition,[status(thm)],[c0,c4]) ).
cnf(d6,plain,
implies(X1,X0) = xor(truth,'and$ustar'(X1,not(X0))),
inference(demodulation,[status(thm)],[d5,c6]) ).
cnf(d7,plain,
'and$ustar'(truth,X0) = X0,
inference(superposition,[status(thm)],[c9,c2]) ).
cnf(d8,plain,
implies(truth,X0) = xor(truth,not(X0)),
inference(superposition,[status(thm)],[d7,d6]) ).
cnf(d9,plain,
implies(truth,X0) = not(not(X0)),
inference(demodulation,[status(thm)],[d8,d4]) ).
cnf(d10,plain,
implies(truth,X0) = X0,
inference(demodulation,[status(thm)],[d9,d3]) ).
cnf(d11,plain,
$false,
inference(resolution,[status(thm)],[d10,c5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL161-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n014.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Fri Sep 25 21:56:18 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 20.48/5.92 % SZS status Unsatisfiable for theBenchmark.p
% 20.48/5.92 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------