%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SET012-4 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n005.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 08:31:33 AM UTC 2026
% Result : Unsatisfiable 12.22s 2.08s
% Output : CNFRefutation 12.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 8
% Syntax : Number of clauses : 34 ( 8 unt; 15 nHn; 28 RR)
% Number of literals : 82 ( 21 equ; 34 neg)
% Maximal clause size : 4 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 30 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(extensionality1,axiom,
( X0 = X1
| 'little$uset'(f1(X0,X1)) ) ).
cnf(extensionality2,axiom,
( X0 = X1
| member(f1(X0,X1),X1)
| member(f1(X0,X1),X0) ) ).
cnf(extensionality3,axiom,
( X0 = X1
| ~ member(f1(X0,X1),X1)
| ~ member(f1(X0,X1),X0) ) ).
cnf(complement1,axiom,
( ~ member(X0,X1)
| ~ member(X0,complement(X1)) ) ).
cnf(complement2,axiom,
( member(X0,X1)
| ~ 'little$uset'(X0)
| member(X0,complement(X1)) ) ).
cnf(complement_of_a_is_b,hypothesis,
complement(as) = bs ).
cnf(complement_of_b_is_c,hypothesis,
complement(bs) = cs ).
cnf(prove_a_equals_c,negated_conjecture,
as != cs ).
cnf(c1,plain,
( X0 = X1
| 'little$uset'(f1(X0,X1)) ),
inference(clausification,[status(esa)],[extensionality1]) ).
cnf(c2,plain,
( X0 = X1
| member(f1(X0,X1),X1)
| member(f1(X0,X1),X0) ),
inference(clausification,[status(esa)],[extensionality2]) ).
cnf(c3,plain,
( X0 = X1
| ~ member(f1(X0,X1),X1)
| ~ member(f1(X0,X1),X0) ),
inference(clausification,[status(esa)],[extensionality3]) ).
cnf(c4,plain,
( ~ member(X0,X1)
| ~ member(X0,complement(X1)) ),
inference(clausification,[status(esa)],[complement1]) ).
cnf(c5,plain,
( member(X0,X1)
| ~ 'little$uset'(X0)
| member(X0,complement(X1)) ),
inference(clausification,[status(esa)],[complement2]) ).
cnf(c8,plain,
complement(as) = bs,
inference(clausification,[status(esa)],[complement_of_a_is_b]) ).
cnf(c9,plain,
complement(bs) = cs,
inference(clausification,[status(esa)],[complement_of_b_is_c]) ).
cnf(c10,plain,
as != cs,
inference(clausification,[status(esa)],[prove_a_equals_c]) ).
cnf(d0,plain,
( ~ 'little$uset'(X0)
| member(X0,as)
| member(X0,bs) ),
inference(superposition,[status(thm)],[c8,c5]) ).
cnf(d1,plain,
( member(f1(X0,complement(X1)),X0)
| X0 = complement(X1)
| ~ member(f1(X0,complement(X1)),X1) ),
inference(resolution,[status(thm)],[c4,c2]) ).
cnf(d2,plain,
( ~ 'little$uset'(f1(X0,complement(bs)))
| member(f1(X0,complement(bs)),as)
| member(f1(X0,complement(bs)),X0)
| X0 = complement(bs) ),
inference(resolution,[status(thm)],[d1,d0]) ).
cnf(d3,plain,
( ~ 'little$uset'(f1(X0,complement(bs)))
| member(f1(X0,complement(bs)),as)
| member(f1(X0,complement(bs)),X0)
| X0 = cs ),
inference(demodulation,[status(thm)],[d2,c9]) ).
cnf(d4,plain,
( ~ 'little$uset'(f1(X0,complement(bs)))
| member(f1(X0,complement(bs)),as)
| member(f1(X0,cs),X0)
| X0 = cs ),
inference(demodulation,[status(thm)],[d3,c9]) ).
cnf(d5,plain,
( ~ 'little$uset'(f1(X0,complement(bs)))
| member(f1(X0,cs),as)
| member(f1(X0,cs),X0)
| X0 = cs ),
inference(demodulation,[status(thm)],[d4,c9]) ).
cnf(d6,plain,
( ~ 'little$uset'(f1(X0,cs))
| member(f1(X0,cs),as)
| member(f1(X0,cs),X0)
| X0 = cs ),
inference(demodulation,[status(thm)],[d5,c9]) ).
cnf(d7,plain,
( ~ 'little$uset'(f1(as,cs))
| member(f1(as,cs),as)
| as = cs ),
inference(factoring,[status(thm)],[d6]) ).
cnf(d8,plain,
( ~ 'little$uset'(f1(as,cs))
| member(f1(as,cs),as) ),
inference(resolution,[status(thm)],[c10,d7]) ).
cnf(d9,plain,
( ~ member(X0,as)
| ~ member(X0,bs) ),
inference(superposition,[status(thm)],[c8,c4]) ).
cnf(d10,plain,
( ~ 'little$uset'(X0)
| member(X0,bs)
| member(X0,cs) ),
inference(superposition,[status(thm)],[c9,c5]) ).
cnf(d11,plain,
( ~ member(f1(as,cs),cs)
| as = cs
| ~ 'little$uset'(f1(as,cs)) ),
inference(resolution,[status(thm)],[d8,c3]) ).
cnf(d12,plain,
( ~ 'little$uset'(f1(as,cs))
| ~ member(f1(as,cs),cs) ),
inference(resolution,[status(thm)],[c10,d11]) ).
cnf(d13,plain,
( ~ 'little$uset'(f1(as,cs))
| member(f1(as,cs),bs)
| ~ 'little$uset'(f1(as,cs)) ),
inference(resolution,[status(thm)],[d12,d10]) ).
cnf(d14,plain,
( ~ member(f1(as,cs),as)
| ~ 'little$uset'(f1(as,cs)) ),
inference(resolution,[status(thm)],[d13,d9]) ).
cnf(d15,plain,
( ~ 'little$uset'(f1(as,cs))
| ~ 'little$uset'(f1(as,cs)) ),
inference(resolution,[status(thm)],[d14,d8]) ).
cnf(d16,plain,
as = cs,
inference(resolution,[status(thm)],[d15,c1]) ).
cnf(d17,plain,
$false,
inference(resolution,[status(thm)],[c10,d16]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET012-4 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.37 % Computer : n005.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sat Sep 26 06:49:32 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 12.22/2.08 % SZS status Unsatisfiable for theBenchmark.p
% 12.22/2.08 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------