%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : LCL109-5 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n003.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 07:53:47 AM UTC 2026
% Result : Unsatisfiable 14.30s 7.29s
% Output : CNFRefutation 14.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 9
% Syntax : Number of clauses : 41 ( 27 unt; 0 nHn; 12 RR)
% Number of literals : 55 ( 24 equ; 16 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 70 ( 9 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(lemma_1,axiom,
( ordered(implies(X0,X2),implies(X1,X2))
| ~ ordered(X0,X1) ) ).
cnf(lemma_3_1,axiom,
( ordered(X1,implies(X0,X2))
| ~ ordered(X0,implies(X1,X2)) ) ).
cnf(prove_mv_4,negated_conjecture,
'big$uV'(implies(x,y),implies(y,x)) != truth ).
cnf(wajsberg_1,axiom,
implies(truth,X0) = X0 ).
cnf(wajsberg_2,axiom,
implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2))) = truth ).
cnf(wajsberg_3,axiom,
implies(implies(X0,X1),X1) = implies(implies(X1,X0),X0) ).
cnf(big_V_definition,axiom,
'big$uV'(X0,X1) = implies(implies(X0,X1),X1) ).
cnf(partial_order_definition1,axiom,
( implies(X0,X1) = truth
| ~ ordered(X0,X1) ) ).
cnf(partial_order_definition2,axiom,
( ordered(X0,X1)
| implies(X0,X1) != truth ) ).
cnf(c0,plain,
( ordered(implies(X0,X2),implies(X1,X2))
| ~ ordered(X0,X1) ),
inference(clausification,[status(esa)],[lemma_1]) ).
cnf(c2,plain,
( ordered(X1,implies(X0,X2))
| ~ ordered(X0,implies(X1,X2)) ),
inference(clausification,[status(esa)],[lemma_3_1]) ).
cnf(c8,plain,
'big$uV'(implies(x,y),implies(y,x)) != truth,
inference(clausification,[status(esa)],[prove_mv_4]) ).
cnf(c9,plain,
implies(truth,X0) = X0,
inference(clausification,[status(esa)],[wajsberg_1]) ).
cnf(c10,plain,
implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2))) = truth,
inference(clausification,[status(esa)],[wajsberg_2]) ).
cnf(c11,plain,
implies(implies(X0,X1),X1) = implies(implies(X1,X0),X0),
inference(clausification,[status(esa)],[wajsberg_3]) ).
cnf(c13,plain,
'big$uV'(X0,X1) = implies(implies(X0,X1),X1),
inference(clausification,[status(esa)],[big_V_definition]) ).
cnf(c15,plain,
( implies(X0,X1) = truth
| ~ ordered(X0,X1) ),
inference(clausification,[status(esa)],[partial_order_definition1]) ).
cnf(c16,plain,
( ordered(X0,X1)
| implies(X0,X1) != truth ),
inference(clausification,[status(esa)],[partial_order_definition2]) ).
cnf(d0,plain,
( ~ ordered(truth,X1)
| ordered(X0,implies(X1,X0)) ),
inference(superposition,[status(thm)],[c9,c0]) ).
cnf(d1,plain,
( ~ ordered(truth,truth)
| ordered(X0,X0) ),
inference(superposition,[status(thm)],[c9,d0]) ).
cnf(d2,plain,
( ordered(truth,X0)
| X0 != truth ),
inference(superposition,[status(thm)],[c9,c16]) ).
cnf(d3,plain,
ordered(truth,truth),
inference(equality_resolution,[status(thm)],[d2]) ).
cnf(d4,plain,
ordered(X0,X0),
inference(resolution,[status(thm)],[d3,d1]) ).
cnf(d5,plain,
ordered(X0,implies(implies(X0,X1),X1)),
inference(resolution,[status(thm)],[d4,c2]) ).
cnf(d6,plain,
ordered(X0,implies(implies(X1,X0),X0)),
inference(superposition,[status(thm)],[c11,d5]) ).
cnf(d7,plain,
ordered(X1,'big$uV'(X0,X1)),
inference(demodulation,[status(thm)],[d6,c13]) ).
cnf(d8,plain,
( ~ ordered(X1,X0)
| ordered(X0,implies(implies(X1,X2),X2)) ),
inference(resolution,[status(thm)],[c2,c0]) ).
cnf(d9,plain,
( ordered(X2,'big$uV'(X0,X1))
| ~ ordered(X0,X2) ),
inference(demodulation,[status(thm)],[d8,c13]) ).
cnf(d10,plain,
implies(X0,X0) = truth,
inference(resolution,[status(thm)],[d4,c15]) ).
cnf(d11,plain,
'big$uV'(X0,X0) = implies(truth,X0),
inference(superposition,[status(thm)],[d10,c13]) ).
cnf(d12,plain,
'big$uV'(X0,X0) = X0,
inference(demodulation,[status(thm)],[d11,c9]) ).
cnf(d13,plain,
( ~ ordered(X0,X1)
| ordered(X1,X0) ),
inference(superposition,[status(thm)],[d12,d9]) ).
cnf(d14,plain,
ordered('big$uV'(X0,X1),X1),
inference(resolution,[status(thm)],[d13,d7]) ).
cnf(d15,plain,
implies(X0,implies(implies(X0,X1),implies(truth,X1))) = truth,
inference(superposition,[status(thm)],[c9,c10]) ).
cnf(d16,plain,
implies(X1,implies(implies(X1,X0),X0)) = truth,
inference(demodulation,[status(thm)],[d15,c9]) ).
cnf(d17,plain,
implies(X0,'big$uV'(X0,X1)) = truth,
inference(demodulation,[status(thm)],[d16,c13]) ).
cnf(d18,plain,
truth = 'big$uV'(truth,X0),
inference(superposition,[status(thm)],[d17,c9]) ).
cnf(d19,plain,
ordered(truth,X0),
inference(superposition,[status(thm)],[d18,d14]) ).
cnf(d20,plain,
implies(truth,X0) = truth,
inference(resolution,[status(thm)],[d19,c15]) ).
cnf(d21,plain,
X0 = truth,
inference(superposition,[status(thm)],[c9,d20]) ).
cnf(d22,plain,
$false,
inference(resolution,[status(thm)],[d21,c8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL109-5 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/5.38 % Computer : n003.cluster.edu
% 0.10/5.38 % Model : x86_64 x86_64
% 0.10/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.38 % Memory : 8046.5625MB
% 0.10/5.38 % OS : Linux 6.8.0-71-generic
% 0.10/5.38 % CPULimit : 300
% 0.10/5.38 % WCLimit : 300
% 0.10/5.38 % DateTime : Fri Sep 25 21:53:44 UTC 2026
% 0.10/5.38 % CPUTime :
% 0.10/5.38 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 14.30/7.29 % SZS status Unsatisfiable for theBenchmark.p
% 14.30/7.29 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------