%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SET616+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 : n009.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 08:32:54 AM UTC 2026
% Result : Theorem 16.03s 2.52s
% Output : CNFRefutation 16.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 3
% Syntax : Number of formulae : 21 ( 4 unt; 0 def)
% Number of atoms : 48 ( 17 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 44 ( 17 ~; 21 |; 1 &)
% ( 2 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 25 ( 1 sgn 10 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(member_equal,axiom,
! [X0,X1] :
( ! [X2] :
( member(X2,X0)
<=> member(X2,X1) )
=> X0 = X1 ) ).
fof(difference_defn,axiom,
! [X0,X1,X2] :
( member(X2,difference(X0,X1))
<=> ( ~ member(X2,X1)
& member(X2,X0) ) ) ).
fof(prove_th90,conjecture,
! [X0,X1] :
( difference(X0,X1) = difference(X1,X0)
=> X0 = X1 ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0,X1] :
( difference(X0,X1) = difference(X1,X0)
=> X0 = X1 ),
inference(negate_conjecture,[status(cth)],[prove_th90]) ).
cnf(c1,plain,
( X0 = X1
| member(sK2(X0,X1),X1)
| member(sK2(X0,X1),X0) ),
inference(clausification,[status(esa)],[member_equal]) ).
cnf(c2,plain,
( X0 = X1
| ~ member(sK2(X0,X1),X0)
| ~ member(sK2(X0,X1),X1) ),
inference(clausification,[status(esa)],[member_equal]) ).
cnf(c5,plain,
( ~ member(X0,X2)
| ~ member(X0,difference(X1,X2)) ),
inference(clausification,[status(esa)],[difference_defn]) ).
cnf(c6,plain,
( member(X0,X2)
| ~ member(X0,X1)
| member(X0,difference(X1,X2)) ),
inference(clausification,[status(esa)],[difference_defn]) ).
cnf(c20,plain,
difference(sK17,sK18) = difference(sK18,sK17),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c21,plain,
sK17 != sK18,
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( ~ member(X0,sK17)
| ~ member(X0,difference(sK17,sK18)) ),
inference(superposition,[status(thm)],[c20,c5]) ).
cnf(d1,plain,
( ~ member(X0,sK17)
| ~ member(X0,sK17)
| member(X0,sK18) ),
inference(resolution,[status(thm)],[c6,d0]) ).
cnf(d2,plain,
( member(sK2(X0,sK17),X0)
| X0 = sK17
| member(sK2(X0,sK17),sK18) ),
inference(resolution,[status(thm)],[d1,c1]) ).
cnf(d3,plain,
( member(sK2(sK18,sK17),sK18)
| sK18 = sK17 ),
inference(factoring,[status(thm)],[d2]) ).
cnf(d4,plain,
( ~ member(sK2(sK18,sK17),sK17)
| sK18 = sK17
| sK18 = sK17 ),
inference(resolution,[status(thm)],[d3,c2]) ).
cnf(d5,plain,
( ~ member(X0,sK18)
| member(X0,sK17)
| member(X0,difference(sK17,sK18)) ),
inference(superposition,[status(thm)],[c20,c6]) ).
cnf(d6,plain,
( ~ member(X0,sK18)
| ~ member(X0,sK18)
| member(X0,sK17) ),
inference(resolution,[status(thm)],[d5,c5]) ).
cnf(d7,plain,
( member(sK2(sK18,sK17),sK17)
| sK18 = sK17 ),
inference(resolution,[status(thm)],[d3,d6]) ).
cnf(d8,plain,
( sK18 = sK17
| sK18 = sK17 ),
inference(resolution,[status(thm)],[d7,d4]) ).
cnf(d9,plain,
sK17 != sK17,
inference(demodulation,[status(thm)],[c21,d8]) ).
cnf(d10,plain,
$false,
inference(equality_resolution,[status(thm)],[d9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SET616+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.06 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/0.43 % Computer : n009.cluster.edu
% 0.17/0.43 % Model : x86_64 x86_64
% 0.17/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.43 % Memory : 8046.5625MB
% 0.17/0.43 % OS : Linux 6.8.0-71-generic
% 0.17/0.43 % CPULimit : 300
% 0.17/0.43 % WCLimit : 300
% 0.17/0.43 % DateTime : Sat Sep 26 08:00:29 UTC 2026
% 0.17/0.44 % CPUTime :
% 0.17/0.44 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 16.03/2.52 % SZS status Theorem for theBenchmark.p
% 16.03/2.52 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------