%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : LCL163-1 : 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 : 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 07:53:53 AM UTC 2026
% Result : Unsatisfiable 4.18s 15.09s
% Output : CNFRefutation 4.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 9
% Syntax : Number of clauses : 62 ( 62 unt; 0 nHn; 5 RR)
% Number of literals : 62 ( 61 equ; 2 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 112 ( 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(false_definition,axiom,
not(truth) = falsehood ).
cnf(implies_definition,axiom,
implies(X0,X1) = xor(truth,'and$ustar'(X0,xor(truth,X1))) ).
cnf(prove_wajsberg_axiom,negated_conjecture,
implies(implies(x,y),y) != implies(implies(y,x),x) ).
cnf(axiom_1,axiom,
not(X0) = xor(X0,truth) ).
cnf(axiom_2,axiom,
xor(X0,falsehood) = X0 ).
cnf(axiom_7,axiom,
xor(X0,xor(truth,X1)) = xor(xor(X0,truth),X1) ).
cnf(axiom_8,axiom,
'and$ustar'(xor('and$ustar'(xor(truth,X0),X1),truth),X1) = 'and$ustar'(xor('and$ustar'(xor(truth,X1),X0),truth),X0) ).
cnf(c0,plain,
xor(X0,X1) = xor(X1,X0),
inference(clausification,[status(esa)],[xor_commutativity]) ).
cnf(c2,plain,
'and$ustar'(X0,X1) = 'and$ustar'(X1,X0),
inference(clausification,[status(esa)],[and_star_commutativity]) ).
cnf(c3,plain,
not(truth) = falsehood,
inference(clausification,[status(esa)],[false_definition]) ).
cnf(c4,plain,
xor(truth,'and$ustar'(X0,xor(truth,X1))) = implies(X0,X1),
inference(clausification,[status(esa)],[implies_definition]) ).
cnf(c5,plain,
implies(implies(y,x),x) != implies(implies(x,y),y),
inference(clausification,[status(esa)],[prove_wajsberg_axiom]) ).
cnf(c6,plain,
xor(X0,truth) = not(X0),
inference(clausification,[status(esa)],[axiom_1]) ).
cnf(c7,plain,
xor(X0,falsehood) = X0,
inference(clausification,[status(esa)],[axiom_2]) ).
cnf(c12,plain,
xor(xor(X0,truth),X1) = xor(X0,xor(truth,X1)),
inference(clausification,[status(esa)],[axiom_7]) ).
cnf(c13,plain,
'and$ustar'(xor('and$ustar'(xor(truth,X0),X1),truth),X1) = 'and$ustar'(xor('and$ustar'(xor(truth,X1),X0),truth),X0),
inference(clausification,[status(esa)],[axiom_8]) ).
cnf(d0,plain,
xor(truth,X0) = not(X0),
inference(superposition,[status(thm)],[c6,c0]) ).
cnf(d1,plain,
xor(truth,'and$ustar'(xor(truth,X1),X0)) = implies(X0,X1),
inference(superposition,[status(thm)],[c2,c4]) ).
cnf(d2,plain,
not('and$ustar'(xor(truth,X0),X1)) = implies(X1,X0),
inference(demodulation,[status(thm)],[d1,d0]) ).
cnf(d3,plain,
not('and$ustar'(not(X0),X1)) = implies(X1,X0),
inference(demodulation,[status(thm)],[d2,d0]) ).
cnf(d4,plain,
xor(truth,'and$ustar'(X2,implies(X0,X1))) = implies(X2,'and$ustar'(X0,xor(truth,X1))),
inference(superposition,[status(thm)],[c4,c4]) ).
cnf(d5,plain,
xor(truth,'and$ustar'(X2,implies(X0,X1))) = implies(X2,'and$ustar'(xor(truth,X1),X0)),
inference(superposition,[status(thm)],[c2,d4]) ).
cnf(d6,plain,
not('and$ustar'(X0,implies(X1,X2))) = implies(X0,'and$ustar'(xor(truth,X2),X1)),
inference(demodulation,[status(thm)],[d5,d0]) ).
cnf(d7,plain,
not('and$ustar'(X1,implies(X2,X0))) = implies(X1,'and$ustar'(not(X0),X2)),
inference(demodulation,[status(thm)],[d6,d0]) ).
cnf(d8,plain,
xor(truth,'and$ustar'(X1,xor(X0,truth))) = implies(X1,X0),
inference(superposition,[status(thm)],[c0,c4]) ).
cnf(d9,plain,
not('and$ustar'(X0,xor(X1,truth))) = implies(X0,X1),
inference(demodulation,[status(thm)],[d8,d0]) ).
cnf(d10,plain,
not('and$ustar'(X1,not(X0))) = implies(X1,X0),
inference(demodulation,[status(thm)],[d9,c6]) ).
cnf(d11,plain,
implies(not(X0),X1) = implies(not(X1),X0),
inference(superposition,[status(thm)],[d10,d3]) ).
cnf(d12,plain,
xor(falsehood,X0) = X0,
inference(superposition,[status(thm)],[c7,c0]) ).
cnf(d13,plain,
xor(not(X0),X1) = xor(X0,xor(truth,X1)),
inference(demodulation,[status(thm)],[c12,c6]) ).
cnf(d14,plain,
xor(truth,'and$ustar'(X1,xor(not(truth),X0))) = implies(X1,xor(truth,X0)),
inference(superposition,[status(thm)],[d13,c4]) ).
cnf(d15,plain,
not('and$ustar'(X0,xor(not(truth),X1))) = implies(X0,xor(truth,X1)),
inference(demodulation,[status(thm)],[d14,d0]) ).
cnf(d16,plain,
not('and$ustar'(X0,xor(falsehood,X1))) = implies(X0,xor(truth,X1)),
inference(demodulation,[status(thm)],[d15,c3]) ).
cnf(d17,plain,
not('and$ustar'(X1,X0)) = implies(X1,xor(truth,X0)),
inference(demodulation,[status(thm)],[d16,d12]) ).
cnf(d18,plain,
not('and$ustar'(X1,X0)) = implies(X1,not(X0)),
inference(demodulation,[status(thm)],[d17,d0]) ).
cnf(d19,plain,
xor(not(X1),X0) = xor(X1,xor(X0,truth)),
inference(superposition,[status(thm)],[c0,d13]) ).
cnf(d20,plain,
xor(not(X1),X0) = xor(X1,not(X0)),
inference(demodulation,[status(thm)],[d19,c6]) ).
cnf(d21,plain,
'and$ustar'(X1,xor('and$ustar'(xor(truth,X0),X1),truth)) = 'and$ustar'(xor('and$ustar'(xor(truth,X1),X0),truth),X0),
inference(demodulation,[status(thm)],[c13,c2]) ).
cnf(d22,plain,
'and$ustar'(X1,not('and$ustar'(xor(truth,X0),X1))) = 'and$ustar'(xor('and$ustar'(xor(truth,X1),X0),truth),X0),
inference(demodulation,[status(thm)],[d21,c6]) ).
cnf(d23,plain,
'and$ustar'(X0,not('and$ustar'(xor(truth,X1),X0))) = 'and$ustar'(X1,xor('and$ustar'(xor(truth,X0),X1),truth)),
inference(demodulation,[status(thm)],[d22,c2]) ).
cnf(d24,plain,
'and$ustar'(X0,not('and$ustar'(xor(truth,X1),X0))) = 'and$ustar'(X1,not('and$ustar'(xor(truth,X0),X1))),
inference(demodulation,[status(thm)],[d23,c6]) ).
cnf(d25,plain,
'and$ustar'(X1,not('and$ustar'(xor(not(truth),X0),X1))) = 'and$ustar'(xor(truth,X0),not('and$ustar'(xor(truth,X1),xor(truth,X0)))),
inference(superposition,[status(thm)],[d13,d24]) ).
cnf(d26,plain,
'and$ustar'(X1,not('and$ustar'(xor(truth,not(X0)),X1))) = 'and$ustar'(xor(truth,X0),not('and$ustar'(xor(truth,X1),xor(truth,X0)))),
inference(demodulation,[status(thm)],[d25,d20]) ).
cnf(d27,plain,
'and$ustar'(X1,not('and$ustar'(not(not(X0)),X1))) = 'and$ustar'(xor(truth,X0),not('and$ustar'(xor(truth,X1),xor(truth,X0)))),
inference(demodulation,[status(thm)],[d26,d0]) ).
cnf(d28,plain,
'and$ustar'(X1,implies(X1,not(X0))) = 'and$ustar'(xor(truth,X0),not('and$ustar'(xor(truth,X1),xor(truth,X0)))),
inference(demodulation,[status(thm)],[d27,d3]) ).
cnf(d29,plain,
'and$ustar'(X0,not('and$ustar'(X0,X1))) = 'and$ustar'(xor(truth,X1),not('and$ustar'(xor(truth,X0),xor(truth,X1)))),
inference(demodulation,[status(thm)],[d28,d18]) ).
cnf(d30,plain,
'and$ustar'(X1,not('and$ustar'(X1,X0))) = 'and$ustar'(not(X0),not('and$ustar'(xor(truth,X1),xor(truth,X0)))),
inference(demodulation,[status(thm)],[d29,d0]) ).
cnf(d31,plain,
'and$ustar'(X0,not('and$ustar'(X0,X1))) = 'and$ustar'(not(X1),not('and$ustar'(not(X0),xor(truth,X1)))),
inference(demodulation,[status(thm)],[d30,d0]) ).
cnf(d32,plain,
'and$ustar'(X0,not('and$ustar'(X0,X1))) = 'and$ustar'(not(X1),implies(xor(truth,X1),X0)),
inference(demodulation,[status(thm)],[d31,d3]) ).
cnf(d33,plain,
'and$ustar'(X1,not('and$ustar'(X1,X0))) = 'and$ustar'(not(X0),implies(not(X0),X1)),
inference(demodulation,[status(thm)],[d32,d0]) ).
cnf(d34,plain,
not('and$ustar'(not(X1),implies(not(X1),not(X0)))) = implies(not('and$ustar'(not(X0),X1)),X0),
inference(superposition,[status(thm)],[d33,d3]) ).
cnf(d35,plain,
implies(implies(not(X0),not(X1)),X0) = implies(not('and$ustar'(not(X1),X0)),X1),
inference(demodulation,[status(thm)],[d34,d3]) ).
cnf(d36,plain,
implies(not('and$ustar'(not(X0),X1)),X0) = implies(not('and$ustar'(not(X1),X0)),X1),
inference(demodulation,[status(thm)],[d35,d18]) ).
cnf(d37,plain,
implies(not(X0),'and$ustar'(not(X0),X1)) = implies(not('and$ustar'(not(X1),X0)),X1),
inference(demodulation,[status(thm)],[d36,d11]) ).
cnf(d38,plain,
not('and$ustar'(not(X0),implies(X1,X0))) = implies(not('and$ustar'(not(X1),X0)),X1),
inference(demodulation,[status(thm)],[d37,d7]) ).
cnf(d39,plain,
implies(implies(X1,X0),X0) = implies(not('and$ustar'(not(X1),X0)),X1),
inference(demodulation,[status(thm)],[d38,d3]) ).
cnf(d40,plain,
implies(implies(X0,X1),X1) = implies(not(X0),'and$ustar'(not(X0),X1)),
inference(demodulation,[status(thm)],[d39,d11]) ).
cnf(d41,plain,
implies(implies(X0,X1),X1) = not('and$ustar'(not(X0),implies(X1,X0))),
inference(demodulation,[status(thm)],[d40,d7]) ).
cnf(d42,plain,
implies(implies(X0,X1),X1) = implies(implies(X1,X0),X0),
inference(demodulation,[status(thm)],[d41,d3]) ).
cnf(d43,plain,
$false,
inference(resolution,[status(thm)],[d42,c5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL163-1 : 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 : n004.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 21:56:36 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.18/15.09 % SZS status Unsatisfiable for theBenchmark.p
% 4.18/15.09 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------