%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : LCL158-1 : 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 : n015.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 30.85s 7.33s
% Output : CNFRefutation 30.85s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 15
% Syntax : Number of clauses : 83 ( 83 unt; 0 nHn; 15 RR)
% Number of literals : 83 ( 82 equ; 4 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 : 9 ( 9 usr; 3 con; 0-2 aty)
% Number of variables : 110 ( 6 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(prove_alternative_wajsberg_axiom,negated_conjecture,
'and$ustar'(xor(truth,x),x) != falsehood ).
cnf(wajsberg_1,axiom,
implies(truth,X0) = X0 ).
cnf(wajsberg_2,axiom,
implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2))) = truth ).
cnf(wajsberg_3,axiom,
implies(implies(X0,X1),X1) = implies(implies(X1,X0),X0) ).
cnf(wajsberg_4,axiom,
implies(implies(not(X0),not(X1)),implies(X1,X0)) = truth ).
cnf(or_definition,axiom,
or(X0,X1) = implies(not(X0),X1) ).
cnf(or_commutativity,axiom,
or(X0,X1) = or(X1,X0) ).
cnf(and_definition,axiom,
and(X0,X1) = not(or(not(X0),not(X1))) ).
cnf(and_associativity,axiom,
and(and(X0,X1),X2) = and(X0,and(X1,X2)) ).
cnf(and_commutativity,axiom,
and(X0,X1) = and(X1,X0) ).
cnf(xor_definition,axiom,
xor(X0,X1) = or(and(X0,not(X1)),and(not(X0),X1)) ).
cnf(xor_commutativity,axiom,
xor(X0,X1) = xor(X1,X0) ).
cnf(and_star_definition,axiom,
'and$ustar'(X0,X1) = not(or(not(X0),not(X1))) ).
cnf(and_star_commutativity,axiom,
'and$ustar'(X0,X1) = 'and$ustar'(X1,X0) ).
cnf(false_definition,axiom,
not(truth) = falsehood ).
cnf(c0,plain,
'and$ustar'(xor(truth,x),x) != falsehood,
inference(clausification,[status(esa)],[prove_alternative_wajsberg_axiom]) ).
cnf(c1,plain,
implies(truth,X0) = X0,
inference(clausification,[status(esa)],[wajsberg_1]) ).
cnf(c2,plain,
implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2))) = truth,
inference(clausification,[status(esa)],[wajsberg_2]) ).
cnf(c3,plain,
implies(implies(X0,X1),X1) = implies(implies(X1,X0),X0),
inference(clausification,[status(esa)],[wajsberg_3]) ).
cnf(c4,plain,
implies(implies(not(X0),not(X1)),implies(X1,X0)) = truth,
inference(clausification,[status(esa)],[wajsberg_4]) ).
cnf(c5,plain,
implies(not(X0),X1) = or(X0,X1),
inference(clausification,[status(esa)],[or_definition]) ).
cnf(c7,plain,
or(X0,X1) = or(X1,X0),
inference(clausification,[status(esa)],[or_commutativity]) ).
cnf(c8,plain,
not(or(not(X0),not(X1))) = and(X0,X1),
inference(clausification,[status(esa)],[and_definition]) ).
cnf(c9,plain,
and(X0,and(X1,X2)) = and(and(X0,X1),X2),
inference(clausification,[status(esa)],[and_associativity]) ).
cnf(c10,plain,
and(X0,X1) = and(X1,X0),
inference(clausification,[status(esa)],[and_commutativity]) ).
cnf(c11,plain,
or(and(X0,not(X1)),and(not(X0),X1)) = xor(X0,X1),
inference(clausification,[status(esa)],[xor_definition]) ).
cnf(c12,plain,
xor(X0,X1) = xor(X1,X0),
inference(clausification,[status(esa)],[xor_commutativity]) ).
cnf(c13,plain,
not(or(not(X0),not(X1))) = 'and$ustar'(X0,X1),
inference(clausification,[status(esa)],[and_star_definition]) ).
cnf(c15,plain,
'and$ustar'(X0,X1) = 'and$ustar'(X1,X0),
inference(clausification,[status(esa)],[and_star_commutativity]) ).
cnf(c16,plain,
not(truth) = falsehood,
inference(clausification,[status(esa)],[false_definition]) ).
cnf(d0,plain,
'and$ustar'(X0,X1) = and(X0,X1),
inference(demodulation,[status(thm)],[c8,c13]) ).
cnf(d1,plain,
implies(or(X0,not(X1)),implies(X1,X0)) = truth,
inference(demodulation,[status(thm)],[c4,c5]) ).
cnf(d2,plain,
implies(or(X0,not(truth)),X0) = truth,
inference(superposition,[status(thm)],[c1,d1]) ).
cnf(d3,plain,
implies(or(X0,falsehood),X0) = truth,
inference(demodulation,[status(thm)],[d2,c16]) ).
cnf(d4,plain,
implies(or(falsehood,X0),X0) = truth,
inference(superposition,[status(thm)],[c7,d3]) ).
cnf(d5,plain,
implies(X0,implies(implies(X0,X1),implies(truth,X1))) = truth,
inference(superposition,[status(thm)],[c1,c2]) ).
cnf(d6,plain,
implies(X1,implies(implies(X1,X0),X0)) = truth,
inference(demodulation,[status(thm)],[d5,c1]) ).
cnf(d7,plain,
truth = implies(implies(truth,X0),X0),
inference(superposition,[status(thm)],[d6,c1]) ).
cnf(d8,plain,
truth = implies(X0,X0),
inference(demodulation,[status(thm)],[d7,c1]) ).
cnf(d9,plain,
truth = or(X0,not(X0)),
inference(superposition,[status(thm)],[d8,c5]) ).
cnf(d10,plain,
implies(truth,not(falsehood)) = truth,
inference(superposition,[status(thm)],[d9,d4]) ).
cnf(d11,plain,
not(falsehood) = truth,
inference(demodulation,[status(thm)],[d10,c1]) ).
cnf(d12,plain,
implies(truth,X0) = or(falsehood,X0),
inference(superposition,[status(thm)],[d11,c5]) ).
cnf(d13,plain,
X0 = or(falsehood,X0),
inference(demodulation,[status(thm)],[d12,c1]) ).
cnf(d14,plain,
implies(implies(X0,truth),truth) = implies(X0,X0),
inference(superposition,[status(thm)],[c1,c3]) ).
cnf(d15,plain,
implies(X0,implies(X0,X0)) = truth,
inference(superposition,[status(thm)],[d14,d6]) ).
cnf(d16,plain,
implies(X0,truth) = truth,
inference(demodulation,[status(thm)],[d15,d8]) ).
cnf(d17,plain,
truth = or(X0,truth),
inference(superposition,[status(thm)],[d16,c5]) ).
cnf(d18,plain,
or(truth,X0) = truth,
inference(superposition,[status(thm)],[d17,c7]) ).
cnf(d19,plain,
not(or(truth,not(X0))) = 'and$ustar'(falsehood,X0),
inference(superposition,[status(thm)],[d11,c13]) ).
cnf(d20,plain,
not(truth) = 'and$ustar'(falsehood,X0),
inference(demodulation,[status(thm)],[d19,d18]) ).
cnf(d21,plain,
falsehood = 'and$ustar'(falsehood,X0),
inference(demodulation,[status(thm)],[d20,c16]) ).
cnf(d22,plain,
'and$ustar'(X0,falsehood) = falsehood,
inference(superposition,[status(thm)],[d21,c15]) ).
cnf(d23,plain,
or(and(X0,falsehood),and(not(X0),truth)) = xor(X0,truth),
inference(superposition,[status(thm)],[c16,c11]) ).
cnf(d24,plain,
or('and$ustar'(X0,falsehood),and(not(X0),truth)) = xor(X0,truth),
inference(demodulation,[status(thm)],[d23,d0]) ).
cnf(d25,plain,
or(falsehood,and(not(X0),truth)) = xor(X0,truth),
inference(demodulation,[status(thm)],[d24,d22]) ).
cnf(d26,plain,
and(not(X0),truth) = xor(X0,truth),
inference(demodulation,[status(thm)],[d25,d13]) ).
cnf(d27,plain,
'and$ustar'(not(X0),truth) = xor(X0,truth),
inference(demodulation,[status(thm)],[d26,d0]) ).
cnf(d28,plain,
'and$ustar'(truth,not(X0)) = xor(X0,truth),
inference(demodulation,[status(thm)],[d27,c15]) ).
cnf(d29,plain,
and(X0,and(X1,X2)) = and(X2,and(X0,X1)),
inference(superposition,[status(thm)],[c9,c10]) ).
cnf(d30,plain,
'and$ustar'(X0,and(X1,X2)) = and(X2,and(X0,X1)),
inference(demodulation,[status(thm)],[d29,d0]) ).
cnf(d31,plain,
'and$ustar'(X2,'and$ustar'(X0,X1)) = and(X1,and(X2,X0)),
inference(demodulation,[status(thm)],[d30,d0]) ).
cnf(d32,plain,
'and$ustar'(X1,'and$ustar'(X2,X0)) = 'and$ustar'(X0,and(X1,X2)),
inference(demodulation,[status(thm)],[d31,d0]) ).
cnf(d33,plain,
'and$ustar'(X0,'and$ustar'(X1,X2)) = 'and$ustar'(X2,'and$ustar'(X0,X1)),
inference(demodulation,[status(thm)],[d32,d0]) ).
cnf(d34,plain,
not(truth) = 'and$ustar'(X0,not(X0)),
inference(superposition,[status(thm)],[d9,c13]) ).
cnf(d35,plain,
falsehood = 'and$ustar'(X0,not(X0)),
inference(demodulation,[status(thm)],[d34,c16]) ).
cnf(d36,plain,
not(or(falsehood,not(X0))) = and(truth,X0),
inference(superposition,[status(thm)],[c16,c8]) ).
cnf(d37,plain,
not(or(falsehood,not(X0))) = 'and$ustar'(truth,X0),
inference(demodulation,[status(thm)],[d36,d0]) ).
cnf(d38,plain,
not(not(X0)) = 'and$ustar'(truth,X0),
inference(demodulation,[status(thm)],[d37,d13]) ).
cnf(d39,plain,
falsehood = 'and$ustar'(not(X0),'and$ustar'(truth,X0)),
inference(superposition,[status(thm)],[d38,d35]) ).
cnf(d40,plain,
falsehood = 'and$ustar'(X0,'and$ustar'(not(X0),truth)),
inference(demodulation,[status(thm)],[d39,d33]) ).
cnf(d41,plain,
falsehood = 'and$ustar'(X0,'and$ustar'(truth,not(X0))),
inference(demodulation,[status(thm)],[d40,c15]) ).
cnf(d42,plain,
falsehood = 'and$ustar'(X0,xor(X0,truth)),
inference(demodulation,[status(thm)],[d41,d28]) ).
cnf(d43,plain,
falsehood = 'and$ustar'(X0,xor(truth,X0)),
inference(superposition,[status(thm)],[c12,d42]) ).
cnf(d44,plain,
'and$ustar'(x,xor(truth,x)) != falsehood,
inference(demodulation,[status(thm)],[c0,c15]) ).
cnf(d45,plain,
falsehood != falsehood,
inference(demodulation,[status(thm)],[d44,d43]) ).
cnf(d46,plain,
not(or(falsehood,falsehood)) = 'and$ustar'(truth,truth),
inference(superposition,[status(thm)],[c16,d37]) ).
cnf(d47,plain,
not(falsehood) = 'and$ustar'(truth,truth),
inference(demodulation,[status(thm)],[d46,d13]) ).
cnf(d48,plain,
truth = 'and$ustar'(truth,truth),
inference(demodulation,[status(thm)],[d47,d11]) ).
cnf(d49,plain,
falsehood = 'and$ustar'(not(truth),truth),
inference(superposition,[status(thm)],[d48,d39]) ).
cnf(d50,plain,
falsehood = 'and$ustar'(truth,not(truth)),
inference(demodulation,[status(thm)],[d49,c15]) ).
cnf(d51,plain,
falsehood = falsehood,
inference(demodulation,[status(thm)],[d50,d35]) ).
cnf(d52,plain,
$false,
inference(resolution,[status(thm)],[d51,d45]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : LCL158-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.06 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.44 % Computer : n015.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 : Fri Sep 25 21:59:28 UTC 2026
% 0.17/0.44 % CPUTime :
% 0.17/0.44 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 30.85/7.33 % SZS status Unsatisfiable for theBenchmark.p
% 30.85/7.33 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------