%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SET580+3 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/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 08:32:48 AM UTC 2026
% Result : Theorem 10.55s 1.99s
% Output : CNFRefutation 10.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 4
% Syntax : Number of formulae : 35 ( 6 unt; 0 def)
% Number of atoms : 89 ( 2 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 90 ( 36 ~; 47 |; 1 &)
% ( 6 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 49 ( 4 sgn 14 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(union_defn,axiom,
! [X0,X1,X2] :
( member(X2,union(X0,X1))
<=> ( member(X2,X1)
| member(X2,X0) ) ) ).
fof(difference_defn,axiom,
! [X0,X1,X2] :
( member(X2,difference(X0,X1))
<=> ( ~ member(X2,X1)
& member(X2,X0) ) ) ).
fof(symmetric_difference_defn,axiom,
! [X0,X1] : 'symmetric$udifference'(X0,X1) = union(difference(X0,X1),difference(X1,X0)) ).
fof(prove_th23,conjecture,
! [X0,X1,X2] :
( member(X0,'symmetric$udifference'(X1,X2))
<=> ~ ( member(X0,X1)
<=> member(X0,X2) ) ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0,X1,X2] :
( member(X0,'symmetric$udifference'(X1,X2))
<=> ~ ( member(X0,X1)
<=> member(X0,X2) ) ),
inference(negate_conjecture,[status(cth)],[prove_th23]) ).
cnf(c0,plain,
( member(X0,X2)
| member(X0,X1)
| ~ member(X0,union(X1,X2)) ),
inference(clausification,[status(esa)],[union_defn]) ).
cnf(c1,plain,
( ~ member(X0,X1)
| member(X0,union(X1,X2)) ),
inference(clausification,[status(esa)],[union_defn]) ).
cnf(c2,plain,
( ~ member(X0,X2)
| member(X0,union(X1,X2)) ),
inference(clausification,[status(esa)],[union_defn]) ).
cnf(c3,plain,
( member(X0,X1)
| ~ member(X0,difference(X1,X2)) ),
inference(clausification,[status(esa)],[difference_defn]) ).
cnf(c4,plain,
( ~ member(X0,X2)
| ~ member(X0,difference(X1,X2)) ),
inference(clausification,[status(esa)],[difference_defn]) ).
cnf(c5,plain,
( member(X0,X2)
| ~ member(X0,X1)
| member(X0,difference(X1,X2)) ),
inference(clausification,[status(esa)],[difference_defn]) ).
cnf(c6,plain,
'symmetric$udifference'(X0,X1) = union(difference(X0,X1),difference(X1,X0)),
inference(clausification,[status(esa)],[symmetric_difference_defn]) ).
cnf(c17,plain,
( member(sK16,sK18)
| member(sK16,sK17)
| member(sK16,'symmetric$udifference'(sK17,sK18)) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c18,plain,
( ~ member(sK16,sK17)
| ~ member(sK16,sK18)
| member(sK16,'symmetric$udifference'(sK17,sK18)) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c20,plain,
( ~ member(sK16,'symmetric$udifference'(sK17,sK18))
| member(sK16,sK18)
| ~ member(sK16,sK17) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c25,plain,
( ~ member(sK16,'symmetric$udifference'(sK17,sK18))
| ~ member(sK16,sK18)
| member(sK16,sK17) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( member(X2,difference(X0,X1))
| member(X2,difference(X1,X0))
| ~ member(X2,'symmetric$udifference'(X0,X1)) ),
inference(superposition,[status(thm)],[c6,c0]) ).
cnf(d1,plain,
( member(sK16,sK18)
| member(sK16,sK17)
| member(sK16,difference(sK17,sK18))
| member(sK16,difference(sK18,sK17)) ),
inference(resolution,[status(thm)],[d0,c17]) ).
cnf(d2,plain,
( member(sK16,sK18)
| member(sK16,sK18)
| member(sK16,sK17)
| member(sK16,difference(sK17,sK18)) ),
inference(resolution,[status(thm)],[d1,c3]) ).
cnf(d3,plain,
( member(sK16,sK17)
| member(sK16,sK18)
| member(sK16,sK17) ),
inference(resolution,[status(thm)],[d2,c3]) ).
cnf(d4,plain,
( ~ member(X2,difference(X1,X0))
| member(X2,'symmetric$udifference'(X0,X1)) ),
inference(superposition,[status(thm)],[c6,c2]) ).
cnf(d5,plain,
( ~ member(X0,X2)
| member(X0,X1)
| member(X0,'symmetric$udifference'(X1,X2)) ),
inference(resolution,[status(thm)],[d4,c5]) ).
cnf(d6,plain,
( ~ member(sK16,sK18)
| member(sK16,sK17)
| member(sK16,sK17)
| ~ member(sK16,sK18) ),
inference(resolution,[status(thm)],[d5,c25]) ).
cnf(d7,plain,
( member(sK16,sK17)
| member(sK16,sK17) ),
inference(resolution,[status(thm)],[d6,d3]) ).
cnf(d8,plain,
( member(sK16,sK18)
| ~ member(sK16,'symmetric$udifference'(sK17,sK18)) ),
inference(resolution,[status(thm)],[d7,c20]) ).
cnf(d9,plain,
( ~ member(sK16,sK18)
| ~ member(sK16,sK17)
| member(sK16,difference(sK17,sK18))
| member(sK16,difference(sK18,sK17)) ),
inference(resolution,[status(thm)],[d0,c18]) ).
cnf(d10,plain,
( ~ member(sK16,sK17)
| ~ member(sK16,sK18)
| ~ member(sK16,sK17)
| member(sK16,difference(sK17,sK18)) ),
inference(resolution,[status(thm)],[d9,c4]) ).
cnf(d11,plain,
( ~ member(sK16,sK18)
| ~ member(sK16,sK18)
| ~ member(sK16,sK17) ),
inference(resolution,[status(thm)],[d10,c4]) ).
cnf(d12,plain,
~ member(sK16,sK18),
inference(resolution,[status(thm)],[d7,d11]) ).
cnf(d13,plain,
~ member(sK16,'symmetric$udifference'(sK17,sK18)),
inference(resolution,[status(thm)],[d12,d8]) ).
cnf(d14,plain,
( ~ member(X2,difference(X0,X1))
| member(X2,'symmetric$udifference'(X0,X1)) ),
inference(superposition,[status(thm)],[c6,c1]) ).
cnf(d15,plain,
( ~ member(X0,X1)
| member(X0,X2)
| member(X0,'symmetric$udifference'(X1,X2)) ),
inference(resolution,[status(thm)],[d14,c5]) ).
cnf(d16,plain,
( ~ member(sK16,sK17)
| member(sK16,sK18) ),
inference(resolution,[status(thm)],[d15,d13]) ).
cnf(d17,plain,
member(sK16,sK18),
inference(resolution,[status(thm)],[d7,d16]) ).
cnf(d18,plain,
$false,
inference(resolution,[status(thm)],[d12,d17]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET580+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.55 % Computer : n005.cluster.edu
% 0.10/0.55 % Model : x86_64 x86_64
% 0.10/0.55 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.55 % Memory : 8046.5625MB
% 0.10/0.55 % OS : Linux 6.8.0-71-generic
% 0.10/0.55 % CPULimit : 300
% 0.10/0.55 % WCLimit : 300
% 0.10/0.55 % DateTime : Sat Sep 26 07:57:02 UTC 2026
% 0.10/0.56 % CPUTime :
% 0.10/0.56 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 10.55/1.99 % SZS status Theorem for theBenchmark.p
% 10.55/1.99 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------