%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SET579+3 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n016.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 08:32:47 AM UTC 2026
% Result : Theorem 20.97s 4.52s
% Output : CNFRefutation 20.97s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 4
% Syntax : Number of formulae : 34 ( 5 unt; 0 def)
% Number of atoms : 78 ( 8 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 66 ( 22 ~; 32 |; 4 &)
% ( 5 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 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 : 58 ( 2 sgn 16 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(difference_defn,axiom,
! [X0,X1,X2] :
( member(X2,difference(X0,X1))
<=> ( ~ member(X2,X1)
& member(X2,X0) ) ) ).
fof(equal_defn,axiom,
! [X0,X1] :
( X0 = X1
<=> ( subset(X1,X0)
& subset(X0,X1) ) ) ).
fof(subset_defn,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X0)
=> member(X2,X1) ) ) ).
fof(prove_th20,conjecture,
! [X0,X1,X2] :
( ! [X3] :
( member(X3,X0)
<=> ( ~ member(X3,X2)
& member(X3,X1) ) )
=> X0 = difference(X1,X2) ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0,X1,X2] :
( ! [X3] :
( member(X3,X0)
<=> ( ~ member(X3,X2)
& member(X3,X1) ) )
=> X0 = difference(X1,X2) ),
inference(negate_conjecture,[status(cth)],[prove_th20]) ).
cnf(c0,plain,
( member(X0,X1)
| ~ member(X0,difference(X1,X2)) ),
inference(clausification,[status(esa)],[difference_defn]) ).
cnf(c1,plain,
( ~ member(X0,X2)
| ~ member(X0,difference(X1,X2)) ),
inference(clausification,[status(esa)],[difference_defn]) ).
cnf(c2,plain,
( member(X0,X2)
| ~ member(X0,X1)
| member(X0,difference(X1,X2)) ),
inference(clausification,[status(esa)],[difference_defn]) ).
cnf(c5,plain,
( ~ subset(X1,X0)
| ~ subset(X0,X1)
| X0 = X1 ),
inference(clausification,[status(esa)],[equal_defn]) ).
cnf(c7,plain,
( member(sK8(X0,X1),X0)
| subset(X0,X1) ),
inference(clausification,[status(esa)],[subset_defn]) ).
cnf(c8,plain,
( ~ member(sK8(X0,X1),X1)
| subset(X0,X1) ),
inference(clausification,[status(esa)],[subset_defn]) ).
cnf(c10,plain,
( member(X0,sK11)
| ~ member(X0,sK10) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c11,plain,
( ~ member(X0,sK12)
| ~ member(X0,sK10) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c12,plain,
( member(X0,sK12)
| ~ member(X0,sK11)
| member(X0,sK10) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c13,plain,
sK10 != difference(sK11,sK12),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( ~ member(sK8(difference(X0,X1),X2),X1)
| subset(difference(X0,X1),X2) ),
inference(resolution,[status(thm)],[c7,c1]) ).
cnf(d1,plain,
( member(sK8(difference(X0,X1),X2),X0)
| subset(difference(X0,X1),X2) ),
inference(resolution,[status(thm)],[c7,c0]) ).
cnf(d2,plain,
( member(sK8(difference(sK11,X0),X1),sK12)
| member(sK8(difference(sK11,X0),X1),sK10)
| subset(difference(sK11,X0),X1) ),
inference(resolution,[status(thm)],[d1,c12]) ).
cnf(d3,plain,
( subset(difference(sK11,sK12),X0)
| subset(difference(sK11,sK12),X0)
| member(sK8(difference(sK11,sK12),X0),sK10) ),
inference(resolution,[status(thm)],[d2,d0]) ).
cnf(d4,plain,
( subset(difference(sK11,sK12),sK10)
| subset(difference(sK11,sK12),sK10) ),
inference(resolution,[status(thm)],[d3,c8]) ).
cnf(d5,plain,
( ~ subset(sK10,difference(sK11,sK12))
| sK10 = difference(sK11,sK12) ),
inference(resolution,[status(thm)],[d4,c5]) ).
cnf(d6,plain,
~ subset(sK10,difference(sK11,sK12)),
inference(resolution,[status(thm)],[c13,d5]) ).
cnf(d7,plain,
( ~ member(sK8(X0,difference(X1,X2)),X1)
| member(sK8(X0,difference(X1,X2)),X2)
| subset(X0,difference(X1,X2)) ),
inference(resolution,[status(thm)],[c8,c2]) ).
cnf(d8,plain,
( member(sK8(difference(sK10,X0),X1),sK11)
| subset(difference(sK10,X0),X1) ),
inference(resolution,[status(thm)],[d1,c10]) ).
cnf(d9,plain,
( subset(difference(sK10,X0),difference(sK11,X1))
| member(sK8(difference(sK10,X0),difference(sK11,X1)),X1)
| subset(difference(sK10,X0),difference(sK11,X1)) ),
inference(resolution,[status(thm)],[d8,d7]) ).
cnf(d10,plain,
( subset(difference(sK10,X0),difference(sK11,X0))
| subset(difference(sK10,X0),difference(sK11,X0)) ),
inference(resolution,[status(thm)],[d9,d0]) ).
cnf(d11,plain,
( subset(difference(X0,X1),X0)
| subset(difference(X0,X1),X0) ),
inference(resolution,[status(thm)],[d1,c8]) ).
cnf(d12,plain,
( ~ subset(X0,difference(X0,X1))
| X0 = difference(X0,X1) ),
inference(resolution,[status(thm)],[d11,c5]) ).
cnf(d13,plain,
( subset(X0,difference(X0,X1))
| subset(X0,difference(X0,X1))
| member(sK8(X0,difference(X0,X1)),X1) ),
inference(resolution,[status(thm)],[d7,c7]) ).
cnf(d14,plain,
( ~ member(sK8(X0,difference(X0,sK12)),sK10)
| subset(X0,difference(X0,sK12)) ),
inference(resolution,[status(thm)],[d13,c11]) ).
cnf(d15,plain,
( subset(sK10,difference(sK10,sK12))
| subset(sK10,difference(sK10,sK12)) ),
inference(resolution,[status(thm)],[d14,c7]) ).
cnf(d16,plain,
sK10 = difference(sK10,sK12),
inference(resolution,[status(thm)],[d15,d12]) ).
cnf(d17,plain,
subset(sK10,difference(sK11,sK12)),
inference(superposition,[status(thm)],[d16,d10]) ).
cnf(d18,plain,
$false,
inference(resolution,[status(thm)],[d17,d6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET579+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n016.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sat Sep 26 08:02:00 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.35 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 20.97/4.52 % SZS status Theorem for theBenchmark.p
% 20.97/4.52 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------