%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : LCL155-1 : 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 : n010.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 07:53:52 AM UTC 2026
% Result : Unsatisfiable 41.47s 8.95s
% Output : CNFRefutation 41.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 10
% Syntax : Number of clauses : 64 ( 64 unt; 0 nHn; 7 RR)
% Number of literals : 64 ( 63 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 : 8 ( 8 usr; 3 con; 0-2 aty)
% Number of variables : 82 ( 3 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(prove_alternative_wajsberg_axiom,negated_conjecture,
xor(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(xor_definition,axiom,
xor(X0,X1) = or(and(X0,not(X1)),and(not(X0),X1)) ).
cnf(false_definition,axiom,
not(truth) = falsehood ).
cnf(c0,plain,
xor(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,
or(X0,X1) = implies(not(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,
and(X0,X1) = not(or(not(X0),not(X1))),
inference(clausification,[status(esa)],[and_definition]) ).
cnf(c11,plain,
xor(X0,X1) = or(and(X0,not(X1)),and(not(X0),X1)),
inference(clausification,[status(esa)],[xor_definition]) ).
cnf(c16,plain,
not(truth) = falsehood,
inference(clausification,[status(esa)],[false_definition]) ).
cnf(d0,plain,
implies(X0,implies(implies(X0,X1),implies(truth,X1))) = truth,
inference(superposition,[status(thm)],[c1,c2]) ).
cnf(d1,plain,
implies(X1,implies(implies(X1,X0),X0)) = truth,
inference(demodulation,[status(thm)],[d0,c1]) ).
cnf(d2,plain,
truth = implies(implies(truth,X0),X0),
inference(superposition,[status(thm)],[d1,c1]) ).
cnf(d3,plain,
truth = implies(X0,X0),
inference(demodulation,[status(thm)],[d2,c1]) ).
cnf(d4,plain,
implies(or(X0,not(X1)),implies(X1,X0)) = truth,
inference(demodulation,[status(thm)],[c4,c5]) ).
cnf(d5,plain,
implies(or(X0,not(truth)),X0) = truth,
inference(superposition,[status(thm)],[c1,d4]) ).
cnf(d6,plain,
implies(or(X0,falsehood),X0) = truth,
inference(demodulation,[status(thm)],[d5,c16]) ).
cnf(d7,plain,
implies(or(falsehood,X0),X0) = truth,
inference(superposition,[status(thm)],[c7,d6]) ).
cnf(d8,plain,
or(X0,not(X0)) = truth,
inference(superposition,[status(thm)],[d3,c5]) ).
cnf(d9,plain,
implies(truth,not(falsehood)) = truth,
inference(superposition,[status(thm)],[d8,d7]) ).
cnf(d10,plain,
not(falsehood) = truth,
inference(demodulation,[status(thm)],[d9,c1]) ).
cnf(d11,plain,
or(falsehood,X0) = implies(truth,X0),
inference(superposition,[status(thm)],[d10,c5]) ).
cnf(d12,plain,
or(falsehood,X0) = X0,
inference(demodulation,[status(thm)],[d11,c1]) ).
cnf(d13,plain,
or(X0,falsehood) = X0,
inference(superposition,[status(thm)],[d12,c7]) ).
cnf(d14,plain,
implies(X0,X0) = implies(implies(X0,truth),truth),
inference(superposition,[status(thm)],[c1,c3]) ).
cnf(d15,plain,
implies(X0,implies(X0,X0)) = truth,
inference(superposition,[status(thm)],[d14,d1]) ).
cnf(d16,plain,
implies(X0,truth) = truth,
inference(demodulation,[status(thm)],[d15,d3]) ).
cnf(d17,plain,
or(X0,truth) = truth,
inference(superposition,[status(thm)],[d16,c5]) ).
cnf(d18,plain,
or(truth,X0) = implies(falsehood,X0),
inference(superposition,[status(thm)],[c16,c5]) ).
cnf(d19,plain,
or(X0,truth) = implies(falsehood,X0),
inference(superposition,[status(thm)],[d18,c7]) ).
cnf(d20,plain,
truth = implies(falsehood,X0),
inference(demodulation,[status(thm)],[d19,d17]) ).
cnf(d21,plain,
implies(implies(X0,falsehood),falsehood) = implies(truth,X0),
inference(superposition,[status(thm)],[d20,c3]) ).
cnf(d22,plain,
implies(implies(X0,falsehood),falsehood) = X0,
inference(demodulation,[status(thm)],[d21,c1]) ).
cnf(d23,plain,
implies(or(X0,falsehood),falsehood) = not(X0),
inference(superposition,[status(thm)],[c5,d22]) ).
cnf(d24,plain,
implies(X0,falsehood) = not(X0),
inference(demodulation,[status(thm)],[d23,d13]) ).
cnf(d25,plain,
not(implies(X0,falsehood)) = X0,
inference(demodulation,[status(thm)],[d22,d24]) ).
cnf(d26,plain,
not(not(X0)) = X0,
inference(demodulation,[status(thm)],[d25,d24]) ).
cnf(d27,plain,
and(truth,X0) = not(or(falsehood,not(X0))),
inference(superposition,[status(thm)],[c16,c8]) ).
cnf(d28,plain,
and(truth,X0) = not(not(X0)),
inference(demodulation,[status(thm)],[d27,d12]) ).
cnf(d29,plain,
and(truth,X0) = X0,
inference(demodulation,[status(thm)],[d28,d26]) ).
cnf(d30,plain,
or(not(X0),X1) = implies(X0,X1),
inference(superposition,[status(thm)],[d26,c5]) ).
cnf(d31,plain,
and(X0,X1) = not(or(not(X1),not(X0))),
inference(superposition,[status(thm)],[c7,c8]) ).
cnf(d32,plain,
and(or(falsehood,not(X0)),X1) = not(or(not(X1),and(truth,X0))),
inference(superposition,[status(thm)],[d27,d31]) ).
cnf(d33,plain,
and(not(X0),X1) = not(or(not(X1),and(truth,X0))),
inference(demodulation,[status(thm)],[d32,d12]) ).
cnf(d34,plain,
and(not(X1),X0) = not(implies(X0,and(truth,X1))),
inference(demodulation,[status(thm)],[d33,d30]) ).
cnf(d35,plain,
and(not(X0),X1) = not(implies(X1,X0)),
inference(demodulation,[status(thm)],[d34,d29]) ).
cnf(d36,plain,
and(X0,not(X0)) = not(truth),
inference(superposition,[status(thm)],[d8,c8]) ).
cnf(d37,plain,
and(X0,not(X0)) = falsehood,
inference(demodulation,[status(thm)],[d36,c16]) ).
cnf(d38,plain,
xor(X0,X0) = or(falsehood,and(not(X0),X0)),
inference(superposition,[status(thm)],[d37,c11]) ).
cnf(d39,plain,
xor(X0,X0) = and(not(X0),X0),
inference(demodulation,[status(thm)],[d38,d12]) ).
cnf(d40,plain,
xor(X0,X0) = not(implies(X0,X0)),
inference(demodulation,[status(thm)],[d39,d35]) ).
cnf(d41,plain,
xor(X0,X0) = not(truth),
inference(demodulation,[status(thm)],[d40,d3]) ).
cnf(d42,plain,
xor(X0,X0) = falsehood,
inference(demodulation,[status(thm)],[d41,c16]) ).
cnf(d43,plain,
$false,
inference(resolution,[status(thm)],[d42,c0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL155-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n010.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Fri Sep 25 21:56:14 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.35 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 41.47/8.95 % SZS status Unsatisfiable for theBenchmark.p
% 41.47/8.95 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------