%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SET015-4 : 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 : n019.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 08:31:35 AM UTC 2026
% Result : Unsatisfiable 25.29s 12.04s
% Output : CNFRefutation 25.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 13
% Syntax : Number of clauses : 61 ( 14 unt; 21 nHn; 45 RR)
% Number of literals : 146 ( 26 equ; 73 neg)
% Maximal clause size : 5 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 84 ( 8 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(extensionality1,axiom,
( X0 = X1
| 'little$uset'(f1(X0,X1)) ) ).
cnf(extensionality2,axiom,
( X0 = X1
| member(f1(X0,X1),X1)
| member(f1(X0,X1),X0) ) ).
cnf(extensionality3,axiom,
( X0 = X1
| ~ member(f1(X0,X1),X1)
| ~ member(f1(X0,X1),X0) ) ).
cnf(intersection1,axiom,
( member(X0,X1)
| ~ member(X0,intersection(X1,X2)) ) ).
cnf(intersection2,axiom,
( member(X0,X2)
| ~ member(X0,intersection(X1,X2)) ) ).
cnf(intersection3,axiom,
( ~ member(X0,X2)
| ~ member(X0,X1)
| member(X0,intersection(X1,X2)) ) ).
cnf(complement1,axiom,
( ~ member(X0,X1)
| ~ member(X0,complement(X1)) ) ).
cnf(complement2,axiom,
( member(X0,X1)
| ~ 'little$uset'(X0)
| member(X0,complement(X1)) ) ).
cnf(union,axiom,
union(X0,X1) = complement(intersection(complement(X0),complement(X1))) ).
cnf(empty_set,axiom,
~ member(X0,'empty$uset') ).
cnf(a_union_b_is_c,hypothesis,
union(as,bs) = cs ).
cnf(b_union_a_is_d,hypothesis,
union(bs,as) = ds ).
cnf(prove_c_equals_d,negated_conjecture,
cs != ds ).
cnf(c1,plain,
( X1 = X0
| 'little$uset'(f1(X0,X1)) ),
inference(clausification,[status(esa)],[extensionality1]) ).
cnf(c2,plain,
( X1 = X0
| member(f1(X0,X1),X0)
| member(f1(X0,X1),X1) ),
inference(clausification,[status(esa)],[extensionality2]) ).
cnf(c3,plain,
( X1 = X0
| ~ member(f1(X0,X1),X0)
| ~ member(f1(X0,X1),X1) ),
inference(clausification,[status(esa)],[extensionality3]) ).
cnf(c4,plain,
( member(X0,X1)
| ~ member(X0,intersection(X1,X2)) ),
inference(clausification,[status(esa)],[intersection1]) ).
cnf(c5,plain,
( member(X0,X2)
| ~ member(X0,intersection(X1,X2)) ),
inference(clausification,[status(esa)],[intersection2]) ).
cnf(c6,plain,
( ~ member(X0,X2)
| member(X0,intersection(X1,X2))
| ~ member(X0,X1) ),
inference(clausification,[status(esa)],[intersection3]) ).
cnf(c7,plain,
( ~ member(X0,X1)
| ~ member(X0,complement(X1)) ),
inference(clausification,[status(esa)],[complement1]) ).
cnf(c8,plain,
( member(X0,X1)
| member(X0,complement(X1))
| ~ 'little$uset'(X0) ),
inference(clausification,[status(esa)],[complement2]) ).
cnf(c9,plain,
complement(intersection(complement(X0),complement(X1))) = union(X0,X1),
inference(clausification,[status(esa)],[union]) ).
cnf(c10,plain,
~ member(X0,'empty$uset'),
inference(clausification,[status(esa)],[empty_set]) ).
cnf(c12,plain,
union(as,bs) = cs,
inference(clausification,[status(esa)],[a_union_b_is_c]) ).
cnf(c13,plain,
union(bs,as) = ds,
inference(clausification,[status(esa)],[b_union_a_is_d]) ).
cnf(c14,plain,
ds != cs,
inference(clausification,[status(esa)],[prove_c_equals_d]) ).
cnf(d0,plain,
( ~ 'little$uset'(X2)
| member(X2,intersection(complement(X0),complement(X1)))
| member(X2,union(X0,X1)) ),
inference(superposition,[status(thm)],[c9,c8]) ).
cnf(d1,plain,
( member(f1('empty$uset',X0),X0)
| X0 = 'empty$uset' ),
inference(resolution,[status(thm)],[c2,c10]) ).
cnf(d2,plain,
( member(f1('empty$uset',intersection(X0,X1)),X1)
| intersection(X0,X1) = 'empty$uset' ),
inference(resolution,[status(thm)],[d1,c5]) ).
cnf(d3,plain,
( member(f1('empty$uset',intersection(X0,X1)),X0)
| intersection(X0,X1) = 'empty$uset' ),
inference(resolution,[status(thm)],[d1,c4]) ).
cnf(d4,plain,
( ~ member(f1('empty$uset',intersection(complement(X0),X1)),X0)
| intersection(complement(X0),X1) = 'empty$uset' ),
inference(resolution,[status(thm)],[d3,c7]) ).
cnf(d5,plain,
( intersection(complement(X0),X0) = 'empty$uset'
| intersection(complement(X0),X0) = 'empty$uset' ),
inference(resolution,[status(thm)],[d4,d2]) ).
cnf(d6,plain,
intersection(union(X0,X1),intersection(complement(X0),complement(X1))) = 'empty$uset',
inference(superposition,[status(thm)],[c9,d5]) ).
cnf(d7,plain,
intersection(ds,intersection(complement(bs),complement(as))) = 'empty$uset',
inference(superposition,[status(thm)],[c13,d6]) ).
cnf(d8,plain,
( ~ member(X0,ds)
| ~ member(X0,intersection(complement(bs),complement(as)))
| member(X0,'empty$uset') ),
inference(superposition,[status(thm)],[d7,c6]) ).
cnf(d9,plain,
( ~ member(X0,ds)
| ~ member(X0,intersection(complement(bs),complement(as))) ),
inference(resolution,[status(thm)],[c10,d8]) ).
cnf(d10,plain,
( ~ 'little$uset'(X0)
| member(X0,union(bs,as))
| ~ member(X0,ds) ),
inference(resolution,[status(thm)],[d9,d0]) ).
cnf(d11,plain,
( ~ 'little$uset'(X0)
| ~ member(X0,ds)
| member(X0,ds) ),
inference(demodulation,[status(thm)],[d10,c13]) ).
cnf(d12,plain,
( member(X0,complement(X2))
| ~ 'little$uset'(X0)
| member(X0,union(X1,X2)) ),
inference(resolution,[status(thm)],[d0,c5]) ).
cnf(d13,plain,
( ~ 'little$uset'(X0)
| member(X0,complement(as))
| member(X0,ds) ),
inference(superposition,[status(thm)],[c13,d12]) ).
cnf(d14,plain,
( member(X0,complement(X1))
| ~ 'little$uset'(X0)
| member(X0,union(X1,X2)) ),
inference(resolution,[status(thm)],[d0,c4]) ).
cnf(d15,plain,
( ~ 'little$uset'(X0)
| member(X0,complement(bs))
| member(X0,ds) ),
inference(superposition,[status(thm)],[c13,d14]) ).
cnf(d16,plain,
( ~ member(X2,intersection(complement(X0),complement(X1)))
| ~ member(X2,union(X0,X1)) ),
inference(superposition,[status(thm)],[c9,c7]) ).
cnf(d17,plain,
( ~ member(X0,complement(X1))
| ~ member(X0,complement(X2))
| ~ member(X0,union(X1,X2)) ),
inference(resolution,[status(thm)],[d16,c6]) ).
cnf(d18,plain,
( ~ member(X0,complement(as))
| ~ member(X0,complement(bs))
| ~ member(X0,cs) ),
inference(superposition,[status(thm)],[c12,d17]) ).
cnf(d19,plain,
( ~ 'little$uset'(X0)
| member(X0,ds)
| ~ member(X0,cs)
| ~ member(X0,complement(as)) ),
inference(resolution,[status(thm)],[d18,d15]) ).
cnf(d20,plain,
( ~ 'little$uset'(X0)
| member(X0,ds)
| ~ 'little$uset'(X0)
| member(X0,ds)
| ~ member(X0,cs) ),
inference(resolution,[status(thm)],[d19,d13]) ).
cnf(d21,plain,
( member(f1(cs,X0),X0)
| X0 = cs
| ~ 'little$uset'(f1(cs,X0))
| member(f1(cs,X0),ds) ),
inference(resolution,[status(thm)],[d20,c2]) ).
cnf(d22,plain,
( ~ 'little$uset'(f1(cs,ds))
| member(f1(cs,ds),ds)
| ~ 'little$uset'(f1(cs,ds))
| member(f1(cs,ds),ds)
| ds = cs ),
inference(resolution,[status(thm)],[d21,d11]) ).
cnf(d23,plain,
( ~ 'little$uset'(f1(cs,ds))
| member(f1(cs,ds),ds) ),
inference(resolution,[status(thm)],[c14,d22]) ).
cnf(d24,plain,
( ~ 'little$uset'(X0)
| member(X0,complement(as))
| member(X0,cs) ),
inference(superposition,[status(thm)],[c12,d14]) ).
cnf(d25,plain,
( ~ 'little$uset'(X0)
| member(X0,complement(bs))
| member(X0,cs) ),
inference(superposition,[status(thm)],[c12,d12]) ).
cnf(d26,plain,
( ~ member(X0,complement(bs))
| ~ member(X0,complement(as))
| ~ member(X0,ds) ),
inference(superposition,[status(thm)],[c13,d17]) ).
cnf(d27,plain,
( ~ 'little$uset'(X0)
| member(X0,cs)
| ~ member(X0,ds)
| ~ member(X0,complement(as)) ),
inference(resolution,[status(thm)],[d26,d25]) ).
cnf(d28,plain,
( ~ 'little$uset'(X0)
| member(X0,cs)
| ~ 'little$uset'(X0)
| ~ member(X0,ds)
| member(X0,cs) ),
inference(resolution,[status(thm)],[d27,d24]) ).
cnf(d29,plain,
( ~ 'little$uset'(f1(cs,ds))
| member(f1(cs,ds),cs)
| ~ 'little$uset'(f1(cs,ds)) ),
inference(resolution,[status(thm)],[d23,d28]) ).
cnf(d30,plain,
( ~ member(f1(cs,ds),ds)
| ds = cs
| ~ 'little$uset'(f1(cs,ds)) ),
inference(resolution,[status(thm)],[d29,c3]) ).
cnf(d31,plain,
( ~ 'little$uset'(f1(cs,ds))
| ~ member(f1(cs,ds),ds) ),
inference(resolution,[status(thm)],[c14,d30]) ).
cnf(d32,plain,
( ~ 'little$uset'(f1(cs,ds))
| ~ 'little$uset'(f1(cs,ds)) ),
inference(resolution,[status(thm)],[d31,d23]) ).
cnf(d33,plain,
ds = cs,
inference(resolution,[status(thm)],[d32,c1]) ).
cnf(d34,plain,
$false,
inference(resolution,[status(thm)],[c14,d33]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SET015-4 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.06 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.44 % Computer : n019.cluster.edu
% 0.17/0.44 % Model : x86_64 x86_64
% 0.17/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.44 % Memory : 8046.5625MB
% 0.17/0.44 % OS : Linux 6.8.0-71-generic
% 0.17/0.44 % CPULimit : 300
% 0.17/0.44 % WCLimit : 300
% 0.17/0.44 % DateTime : Sat Sep 26 06:51:06 UTC 2026
% 0.17/0.44 % CPUTime :
% 0.17/0.44 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 25.29/12.04 % SZS status Unsatisfiable for theBenchmark.p
% 25.29/12.04 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------