%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : LCL109-3 : 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 : n026.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 07:53:46 AM UTC 2026
% Result : Unsatisfiable 121.41s 18.41s
% Output : CNFRefutation 121.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 12
% Syntax : Number of clauses : 66 ( 56 unt; 0 nHn; 17 RR)
% Number of literals : 76 ( 75 equ; 16 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 111 ( 16 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(lemma_1,axiom,
implies(X0,X0) = truth ).
cnf(lemma_2,axiom,
( X0 = X1
| implies(X0,X1) != implies(X1,X0) ) ).
cnf(lemma_3,axiom,
implies(X0,truth) = truth ).
cnf(lemma_4,axiom,
implies(X0,implies(X1,X0)) = truth ).
cnf(lemma_5,axiom,
( implies(X0,X2) = truth
| implies(X0,X1) != implies(X1,X2) ) ).
cnf(lemma_6,axiom,
implies(implies(X0,X1),implies(implies(X2,X0),implies(X2,X1))) = truth ).
cnf(lemma_7,axiom,
implies(X0,implies(X1,X2)) = implies(X1,implies(X0,X2)) ).
cnf(lemma_9,axiom,
not(not(X0)) = X0 ).
cnf(lemma_10,axiom,
implies(not(X0),not(X1)) = implies(X1,X0) ).
cnf(prove_wajsberg_mv_4,negated_conjecture,
implies(implies(implies(a,b),implies(b,a)),implies(b,a)) != truth ).
cnf(wajsberg_1,axiom,
implies(truth,X0) = X0 ).
cnf(wajsberg_3,axiom,
implies(implies(X0,X1),X1) = implies(implies(X1,X0),X0) ).
cnf(c0,plain,
implies(X0,X0) = truth,
inference(clausification,[status(esa)],[lemma_1]) ).
cnf(c1,plain,
( X0 = X1
| implies(X0,X1) != implies(X1,X0) ),
inference(clausification,[status(esa)],[lemma_2]) ).
cnf(c2,plain,
implies(X0,truth) = truth,
inference(clausification,[status(esa)],[lemma_3]) ).
cnf(c3,plain,
implies(X0,implies(X1,X0)) = truth,
inference(clausification,[status(esa)],[lemma_4]) ).
cnf(c4,plain,
( implies(X0,X2) = truth
| implies(X0,X1) != implies(X1,X2) ),
inference(clausification,[status(esa)],[lemma_5]) ).
cnf(c5,plain,
implies(implies(X0,X1),implies(implies(X2,X0),implies(X2,X1))) = truth,
inference(clausification,[status(esa)],[lemma_6]) ).
cnf(c6,plain,
implies(X0,implies(X1,X2)) = implies(X1,implies(X0,X2)),
inference(clausification,[status(esa)],[lemma_7]) ).
cnf(c8,plain,
not(not(X0)) = X0,
inference(clausification,[status(esa)],[lemma_9]) ).
cnf(c9,plain,
implies(not(X0),not(X1)) = implies(X1,X0),
inference(clausification,[status(esa)],[lemma_10]) ).
cnf(c10,plain,
implies(implies(implies(a,b),implies(b,a)),implies(b,a)) != truth,
inference(clausification,[status(esa)],[prove_wajsberg_mv_4]) ).
cnf(c11,plain,
implies(truth,X0) = X0,
inference(clausification,[status(esa)],[wajsberg_1]) ).
cnf(c13,plain,
implies(implies(X0,X1),X1) = implies(implies(X1,X0),X0),
inference(clausification,[status(esa)],[wajsberg_3]) ).
cnf(d0,plain,
truth = implies(X0,X0),
inference(superposition,[status(thm)],[c0,c9]) ).
cnf(d1,plain,
truth = implies(X0,implies(implies(X0,X1),X1)),
inference(superposition,[status(thm)],[c6,d0]) ).
cnf(d2,plain,
implies(truth,implies(X1,X0)) = implies(implies(implies(X1,X0),X0),X0),
inference(superposition,[status(thm)],[c3,c13]) ).
cnf(d3,plain,
implies(X0,X1) = implies(implies(implies(X0,X1),X1),X1),
inference(demodulation,[status(thm)],[d2,c11]) ).
cnf(d4,plain,
implies(not(X1),implies(X1,X0)) = truth,
inference(superposition,[status(thm)],[c9,c3]) ).
cnf(d5,plain,
implies(implies(implies(X0,X1),X2),implies(truth,implies(not(X0),X2))) = truth,
inference(superposition,[status(thm)],[d4,c5]) ).
cnf(d6,plain,
implies(truth,implies(implies(implies(X0,X1),X2),implies(not(X0),X2))) = truth,
inference(demodulation,[status(thm)],[d5,c6]) ).
cnf(d7,plain,
implies(implies(implies(X0,X1),X2),implies(not(X0),X2)) = truth,
inference(demodulation,[status(thm)],[d6,c11]) ).
cnf(d8,plain,
implies(not(X0),implies(implies(implies(X0,X1),X2),X2)) = truth,
inference(demodulation,[status(thm)],[d7,c6]) ).
cnf(d9,plain,
implies(not(X1),X0) = implies(not(X0),X1),
inference(superposition,[status(thm)],[c8,c9]) ).
cnf(d10,plain,
implies(X2,implies(not(X1),X0)) = implies(not(X0),implies(X2,X1)),
inference(superposition,[status(thm)],[d9,c6]) ).
cnf(d11,plain,
implies(X0,implies(not(X0),X1)) = truth,
inference(superposition,[status(thm)],[c8,d4]) ).
cnf(d12,plain,
implies(truth,implies(not(X0),X1)) = implies(implies(implies(not(X0),X1),X0),X0),
inference(superposition,[status(thm)],[d11,c13]) ).
cnf(d13,plain,
implies(not(X0),X1) = implies(implies(implies(not(X0),X1),X0),X0),
inference(demodulation,[status(thm)],[d12,c11]) ).
cnf(d14,plain,
implies(X2,implies(X1,X0)) = implies(not(X0),implies(X2,not(X1))),
inference(superposition,[status(thm)],[c9,c6]) ).
cnf(d15,plain,
implies(implies(implies(X0,X1),not(X2)),implies(X2,X0)) = truth,
inference(superposition,[status(thm)],[d14,d8]) ).
cnf(d16,plain,
implies(X2,implies(implies(implies(X0,X1),not(X2)),X0)) = truth,
inference(demodulation,[status(thm)],[d15,c6]) ).
cnf(d17,plain,
( implies(X2,not(X1)) = truth
| implies(X2,not(X0)) != implies(X1,X0) ),
inference(superposition,[status(thm)],[c9,c4]) ).
cnf(d18,plain,
( implies(implies(X0,not(X1)),not(X2)) = truth
| implies(implies(not(X1),X0),X0) != implies(X2,X1) ),
inference(superposition,[status(thm)],[c13,d17]) ).
cnf(d19,plain,
implies(implies(X0,not(X0)),not(implies(not(X0),X0))) = truth,
inference(equality_resolution,[status(thm)],[d18]) ).
cnf(d20,plain,
implies(implies(not(X0),X0),implies(truth,X0)) = truth,
inference(superposition,[status(thm)],[d19,d16]) ).
cnf(d21,plain,
implies(truth,implies(implies(not(X0),X0),X0)) = truth,
inference(demodulation,[status(thm)],[d20,c6]) ).
cnf(d22,plain,
implies(implies(not(X0),X0),X0) = truth,
inference(demodulation,[status(thm)],[d21,c11]) ).
cnf(d23,plain,
implies(not(X0),X0) = implies(truth,X0),
inference(superposition,[status(thm)],[d22,d13]) ).
cnf(d24,plain,
implies(not(X0),X0) = X0,
inference(demodulation,[status(thm)],[d23,c11]) ).
cnf(d25,plain,
implies(X1,X0) = implies(not(X0),implies(X1,X0)),
inference(superposition,[status(thm)],[d24,d10]) ).
cnf(d26,plain,
implies(implies(implies(X0,X1),X0),X0) = truth,
inference(superposition,[status(thm)],[d25,d8]) ).
cnf(d27,plain,
implies(implies(X0,X1),X0) = implies(truth,X0),
inference(superposition,[status(thm)],[d26,d3]) ).
cnf(d28,plain,
implies(implies(X0,X1),X0) = X0,
inference(demodulation,[status(thm)],[d27,c11]) ).
cnf(d29,plain,
implies(b,implies(implies(implies(a,b),implies(b,a)),a)) != truth,
inference(demodulation,[status(thm)],[c10,c6]) ).
cnf(d30,plain,
implies(b,implies(implies(b,implies(implies(a,b),a)),a)) != truth,
inference(demodulation,[status(thm)],[d29,c6]) ).
cnf(d31,plain,
implies(b,implies(implies(b,a),a)) != truth,
inference(demodulation,[status(thm)],[d30,d28]) ).
cnf(d32,plain,
truth != truth,
inference(demodulation,[status(thm)],[d31,d1]) ).
cnf(d33,plain,
( X1 = implies(X0,X1)
| implies(X1,implies(X0,X1)) != implies(implies(X1,X0),X0) ),
inference(superposition,[status(thm)],[c13,c1]) ).
cnf(d34,plain,
( truth != implies(implies(X0,X1),X1)
| X0 = implies(X1,X0) ),
inference(demodulation,[status(thm)],[d33,c3]) ).
cnf(d35,plain,
truth = implies(X0,truth),
inference(superposition,[status(thm)],[c3,c11]) ).
cnf(d36,plain,
( X0 = implies(truth,X0)
| truth != truth ),
inference(superposition,[status(thm)],[d35,d34]) ).
cnf(d37,plain,
( truth != truth
| X0 = X0 ),
inference(demodulation,[status(thm)],[d36,c11]) ).
cnf(d38,plain,
implies(truth,truth) = truth,
inference(superposition,[status(thm)],[c2,c3]) ).
cnf(d39,plain,
truth = truth,
inference(demodulation,[status(thm)],[d38,c11]) ).
cnf(d40,plain,
X0 = X0,
inference(resolution,[status(thm)],[d39,d37]) ).
cnf(d41,plain,
$false,
inference(resolution,[status(thm)],[d40,d32]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL109-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n026.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Fri Sep 25 21:54:24 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 121.41/18.41 % SZS status Unsatisfiable for theBenchmark.p
% 121.41/18.41 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------