%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : LCL153-1 : 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 : n006.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 30.20s 5.15s
% Output : CNFRefutation 30.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 13
% Syntax : Number of clauses : 107 ( 107 unt; 0 nHn; 10 RR)
% Number of literals : 107 ( 106 equ; 3 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 5 ( 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 : 142 ( 5 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(prove_alternative_wajsberg_axiom,negated_conjecture,
not(x) != xor(x,truth) ).
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_associativity,axiom,
or(or(X0,X1),X2) = or(X0,or(X1,X2)) ).
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(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(false_definition,axiom,
not(truth) = falsehood ).
cnf(c0,plain,
xor(x,truth) != not(x),
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(c6,plain,
or(X0,or(X1,X2)) = or(or(X0,X1),X2),
inference(clausification,[status(esa)],[or_associativity]) ).
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(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(c16,plain,
not(truth) = falsehood,
inference(clausification,[status(esa)],[false_definition]) ).
cnf(d0,plain,
implies(or(X0,not(X1)),implies(X1,X0)) = truth,
inference(demodulation,[status(thm)],[c4,c5]) ).
cnf(d1,plain,
implies(or(X0,not(truth)),X0) = truth,
inference(superposition,[status(thm)],[c1,d0]) ).
cnf(d2,plain,
implies(or(X0,falsehood),X0) = truth,
inference(demodulation,[status(thm)],[d1,c16]) ).
cnf(d3,plain,
implies(or(falsehood,X0),X0) = truth,
inference(superposition,[status(thm)],[c7,d2]) ).
cnf(d4,plain,
implies(X0,implies(implies(X0,X1),implies(truth,X1))) = truth,
inference(superposition,[status(thm)],[c1,c2]) ).
cnf(d5,plain,
implies(X1,implies(implies(X1,X0),X0)) = truth,
inference(demodulation,[status(thm)],[d4,c1]) ).
cnf(d6,plain,
truth = implies(implies(truth,X0),X0),
inference(superposition,[status(thm)],[d5,c1]) ).
cnf(d7,plain,
truth = implies(X0,X0),
inference(demodulation,[status(thm)],[d6,c1]) ).
cnf(d8,plain,
truth = or(X0,not(X0)),
inference(superposition,[status(thm)],[d7,c5]) ).
cnf(d9,plain,
implies(truth,not(falsehood)) = truth,
inference(superposition,[status(thm)],[d8,d3]) ).
cnf(d10,plain,
not(falsehood) = truth,
inference(demodulation,[status(thm)],[d9,c1]) ).
cnf(d11,plain,
implies(truth,X0) = or(falsehood,X0),
inference(superposition,[status(thm)],[d10,c5]) ).
cnf(d12,plain,
X0 = or(falsehood,X0),
inference(demodulation,[status(thm)],[d11,c1]) ).
cnf(d13,plain,
or(X0,falsehood) = X0,
inference(superposition,[status(thm)],[d12,c7]) ).
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,d5]) ).
cnf(d16,plain,
implies(X0,truth) = truth,
inference(demodulation,[status(thm)],[d15,d7]) ).
cnf(d17,plain,
truth = or(X0,truth),
inference(superposition,[status(thm)],[d16,c5]) ).
cnf(d18,plain,
implies(falsehood,X0) = or(truth,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,
not(or(falsehood,not(X0))) = and(truth,X0),
inference(superposition,[status(thm)],[c16,c8]) ).
cnf(d28,plain,
not(not(X0)) = and(truth,X0),
inference(demodulation,[status(thm)],[d27,d12]) ).
cnf(d29,plain,
implies(and(truth,X0),X1) = or(or(falsehood,not(X0)),X1),
inference(superposition,[status(thm)],[d27,c5]) ).
cnf(d30,plain,
implies(not(not(X0)),X1) = or(or(falsehood,not(X0)),X1),
inference(demodulation,[status(thm)],[d29,d28]) ).
cnf(d31,plain,
or(not(X0),X1) = or(or(falsehood,not(X0)),X1),
inference(demodulation,[status(thm)],[d30,c5]) ).
cnf(d32,plain,
or(not(X0),X1) = or(falsehood,or(not(X0),X1)),
inference(demodulation,[status(thm)],[d31,c6]) ).
cnf(d33,plain,
or(not(X0),X1) = or(not(X0),X1),
inference(demodulation,[status(thm)],[d32,d12]) ).
cnf(d34,plain,
X0 = or(X0,falsehood),
inference(superposition,[status(thm)],[d12,c7]) ).
cnf(d35,plain,
not(X0) = or(not(X0),falsehood),
inference(superposition,[status(thm)],[d34,d33]) ).
cnf(d36,plain,
not(X0) = not(X0),
inference(demodulation,[status(thm)],[d35,d13]) ).
cnf(d37,plain,
not(or(not(X0),truth)) = and(X0,falsehood),
inference(superposition,[status(thm)],[d10,c8]) ).
cnf(d38,plain,
not(truth) = and(X0,falsehood),
inference(demodulation,[status(thm)],[d37,d17]) ).
cnf(d39,plain,
falsehood = and(X0,falsehood),
inference(demodulation,[status(thm)],[d38,c16]) ).
cnf(d40,plain,
not(or(not(X0),falsehood)) = and(X0,truth),
inference(superposition,[status(thm)],[c16,c8]) ).
cnf(d41,plain,
not(or(falsehood,not(X0))) = and(X0,truth),
inference(demodulation,[status(thm)],[d40,c7]) ).
cnf(d42,plain,
not(not(X0)) = and(X0,truth),
inference(demodulation,[status(thm)],[d41,d12]) ).
cnf(d43,plain,
not(or(falsehood,falsehood)) = and(truth,truth),
inference(superposition,[status(thm)],[c16,d27]) ).
cnf(d44,plain,
or(and(X0,and(truth,truth)),and(not(X0),or(falsehood,falsehood))) = xor(X0,or(falsehood,falsehood)),
inference(superposition,[status(thm)],[d43,c11]) ).
cnf(d45,plain,
or(and(X0,not(not(truth))),and(not(X0),or(falsehood,falsehood))) = xor(X0,or(falsehood,falsehood)),
inference(demodulation,[status(thm)],[d44,d28]) ).
cnf(d46,plain,
or(and(X0,not(falsehood)),and(not(X0),or(falsehood,falsehood))) = xor(X0,or(falsehood,falsehood)),
inference(demodulation,[status(thm)],[d45,c16]) ).
cnf(d47,plain,
or(and(X0,truth),and(not(X0),or(falsehood,falsehood))) = xor(X0,or(falsehood,falsehood)),
inference(demodulation,[status(thm)],[d46,d10]) ).
cnf(d48,plain,
or(not(not(X0)),and(not(X0),or(falsehood,falsehood))) = xor(X0,or(falsehood,falsehood)),
inference(demodulation,[status(thm)],[d47,d42]) ).
cnf(d49,plain,
or(not(not(X0)),and(not(X0),falsehood)) = xor(X0,or(falsehood,falsehood)),
inference(demodulation,[status(thm)],[d48,d12]) ).
cnf(d50,plain,
or(not(not(X0)),falsehood) = xor(X0,or(falsehood,falsehood)),
inference(demodulation,[status(thm)],[d49,d39]) ).
cnf(d51,plain,
not(not(X0)) = xor(X0,or(falsehood,falsehood)),
inference(demodulation,[status(thm)],[d50,d13]) ).
cnf(d52,plain,
not(not(X0)) = xor(X0,falsehood),
inference(demodulation,[status(thm)],[d51,d12]) ).
cnf(d53,plain,
xor(X0,falsehood) = not(not(X0)),
inference(superposition,[status(thm)],[d52,d36]) ).
cnf(d54,plain,
xor(X0,falsehood) = X0,
inference(demodulation,[status(thm)],[d53,d26]) ).
cnf(d55,plain,
xor(X0,falsehood) = and(X0,truth),
inference(demodulation,[status(thm)],[d42,d52]) ).
cnf(d56,plain,
or(and(X1,and(X0,truth)),and(not(X1),or(falsehood,not(X0)))) = xor(X1,or(falsehood,not(X0))),
inference(superposition,[status(thm)],[d41,c11]) ).
cnf(d57,plain,
or(and(X1,xor(X0,falsehood)),and(not(X1),or(falsehood,not(X0)))) = xor(X1,or(falsehood,not(X0))),
inference(demodulation,[status(thm)],[d56,d55]) ).
cnf(d58,plain,
or(and(X1,xor(X0,falsehood)),and(not(X1),not(X0))) = xor(X1,or(falsehood,not(X0))),
inference(demodulation,[status(thm)],[d57,d12]) ).
cnf(d59,plain,
or(and(X1,xor(X0,falsehood)),and(not(X1),not(X0))) = xor(X1,not(X0)),
inference(demodulation,[status(thm)],[d58,d12]) ).
cnf(d60,plain,
xor(X0,falsehood) = and(truth,X0),
inference(demodulation,[status(thm)],[d28,d52]) ).
cnf(d61,plain,
or(and(or(falsehood,not(X0)),not(X1)),and(and(X0,truth),X1)) = xor(or(falsehood,not(X0)),X1),
inference(superposition,[status(thm)],[d41,c11]) ).
cnf(d62,plain,
or(and(and(X0,truth),X1),and(or(falsehood,not(X0)),not(X1))) = xor(or(falsehood,not(X0)),X1),
inference(demodulation,[status(thm)],[d61,c7]) ).
cnf(d63,plain,
or(and(X0,and(truth,X1)),and(or(falsehood,not(X0)),not(X1))) = xor(or(falsehood,not(X0)),X1),
inference(demodulation,[status(thm)],[d62,c9]) ).
cnf(d64,plain,
or(and(X1,xor(X0,falsehood)),and(or(falsehood,not(X1)),not(X0))) = xor(or(falsehood,not(X1)),X0),
inference(demodulation,[status(thm)],[d63,d60]) ).
cnf(d65,plain,
or(and(X0,xor(X1,falsehood)),and(not(X0),not(X1))) = xor(or(falsehood,not(X0)),X1),
inference(demodulation,[status(thm)],[d64,d12]) ).
cnf(d66,plain,
xor(X0,not(X1)) = xor(or(falsehood,not(X0)),X1),
inference(demodulation,[status(thm)],[d65,d59]) ).
cnf(d67,plain,
xor(X0,not(X1)) = xor(not(X0),X1),
inference(demodulation,[status(thm)],[d66,d12]) ).
cnf(d68,plain,
truth = not(falsehood),
inference(superposition,[status(thm)],[d12,d8]) ).
cnf(d69,plain,
xor(falsehood,not(X0)) = xor(truth,X0),
inference(superposition,[status(thm)],[d68,d67]) ).
cnf(d70,plain,
not(or(falsehood,and(X0,truth))) = and(or(falsehood,not(X0)),truth),
inference(superposition,[status(thm)],[d41,d41]) ).
cnf(d71,plain,
not(and(X0,truth)) = and(or(falsehood,not(X0)),truth),
inference(demodulation,[status(thm)],[d70,d12]) ).
cnf(d72,plain,
not(xor(X0,falsehood)) = and(or(falsehood,not(X0)),truth),
inference(demodulation,[status(thm)],[d71,d55]) ).
cnf(d73,plain,
not(xor(X0,falsehood)) = xor(or(falsehood,not(X0)),falsehood),
inference(demodulation,[status(thm)],[d72,d55]) ).
cnf(d74,plain,
not(xor(X0,falsehood)) = xor(falsehood,or(falsehood,not(X0))),
inference(demodulation,[status(thm)],[d73,c12]) ).
cnf(d75,plain,
not(xor(X0,falsehood)) = xor(falsehood,not(X0)),
inference(demodulation,[status(thm)],[d74,d12]) ).
cnf(d76,plain,
not(xor(X0,falsehood)) = xor(truth,X0),
inference(demodulation,[status(thm)],[d75,d69]) ).
cnf(d77,plain,
not(X0) = xor(truth,X0),
inference(demodulation,[status(thm)],[d76,d54]) ).
cnf(d78,plain,
not(X0) = xor(X0,truth),
inference(superposition,[status(thm)],[d77,c12]) ).
cnf(d79,plain,
not(x) != not(x),
inference(demodulation,[status(thm)],[c0,d78]) ).
cnf(d80,plain,
$false,
inference(resolution,[status(thm)],[d36,d79]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL153-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.36 % Computer : n006.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Fri Sep 25 21:55:57 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 30.20/5.15 % SZS status Unsatisfiable for theBenchmark.p
% 30.20/5.15 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------