%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SET980+1 : TPTP v9.3.1. Bugfixed v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n010.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 08:33:40 AM UTC 2026
% Result : Theorem 12.23s 6.99s
% Output : CNFRefutation 12.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 4
% Syntax : Number of formulae : 51 ( 9 unt; 0 def)
% Number of atoms : 119 ( 46 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 108 ( 40 ~; 59 |; 3 &)
% ( 3 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 60 ( 16 sgn 17 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d1_xboole_0,axiom,
! [X0] :
( X0 = 'empty$uset'
<=> ! [X1] : ~ in(X1,X0) ) ).
fof(l55_zfmisc_1,axiom,
! [X0,X1,X2,X3] :
( in('ordered$upair'(X0,X1),'cartesian$uproduct2'(X2,X3))
<=> ( in(X1,X3)
& in(X0,X2) ) ) ).
fof(t2_tarski,axiom,
! [X0,X1] :
( ! [X2] :
( in(X2,X0)
<=> in(X2,X1) )
=> X0 = X1 ) ).
fof(t134_zfmisc_1,conjecture,
! [X0,X1,X2,X3] :
( 'cartesian$uproduct2'(X0,X1) = 'cartesian$uproduct2'(X2,X3)
=> ( ( X1 = X3
& X0 = X2 )
| X1 = 'empty$uset'
| X0 = 'empty$uset' ) ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0,X1,X2,X3] :
( 'cartesian$uproduct2'(X0,X1) = 'cartesian$uproduct2'(X2,X3)
=> ( ( X1 = X3
& X0 = X2 )
| X1 = 'empty$uset'
| X0 = 'empty$uset' ) ),
inference(negate_conjecture,[status(cth)],[t134_zfmisc_1]) ).
cnf(c3,plain,
( in(sK6(X0),X0)
| X0 = 'empty$uset' ),
inference(clausification,[status(esa)],[d1_xboole_0]) ).
cnf(c7,plain,
( in(X0,X2)
| ~ in('ordered$upair'(X0,X1),'cartesian$uproduct2'(X2,X3)) ),
inference(clausification,[status(esa)],[l55_zfmisc_1]) ).
cnf(c8,plain,
( in(X1,X3)
| ~ in('ordered$upair'(X0,X1),'cartesian$uproduct2'(X2,X3)) ),
inference(clausification,[status(esa)],[l55_zfmisc_1]) ).
cnf(c9,plain,
( ~ in(X1,X3)
| ~ in(X0,X2)
| in('ordered$upair'(X0,X1),'cartesian$uproduct2'(X2,X3)) ),
inference(clausification,[status(esa)],[l55_zfmisc_1]) ).
cnf(c16,plain,
( X0 = X1
| in(sK21(X0,X1),X1)
| in(sK21(X0,X1),X0) ),
inference(clausification,[status(esa)],[t2_tarski]) ).
cnf(c17,plain,
( X0 = X1
| ~ in(sK21(X0,X1),X0)
| ~ in(sK21(X0,X1),X1) ),
inference(clausification,[status(esa)],[t2_tarski]) ).
cnf(c19,plain,
'cartesian$uproduct2'(sK22,sK23) = 'cartesian$uproduct2'(sK24,sK25),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c20,plain,
sK22 != 'empty$uset',
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c21,plain,
sK23 != 'empty$uset',
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c22,plain,
( sK23 != sK25
| sK22 != sK24 ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( in(X1,sK25)
| ~ in('ordered$upair'(X0,X1),'cartesian$uproduct2'(sK22,sK23)) ),
inference(superposition,[status(thm)],[c19,c8]) ).
cnf(d1,plain,
( in(X1,sK25)
| ~ in(X1,sK23)
| ~ in(X0,sK22) ),
inference(resolution,[status(thm)],[c9,d0]) ).
cnf(d2,plain,
( sK22 = 'empty$uset'
| in(X0,sK25)
| ~ in(X0,sK23) ),
inference(resolution,[status(thm)],[d1,c3]) ).
cnf(d3,plain,
( in(X0,sK25)
| ~ in(X0,sK23) ),
inference(resolution,[status(thm)],[c20,d2]) ).
cnf(d4,plain,
( in(sK21(X0,sK23),sK25)
| in(sK21(X0,sK23),X0)
| X0 = sK23 ),
inference(resolution,[status(thm)],[c16,d3]) ).
cnf(d5,plain,
( in(sK21(sK25,sK23),sK25)
| sK25 = sK23 ),
inference(factoring,[status(thm)],[d4]) ).
cnf(d6,plain,
( ~ in(sK21(sK25,sK23),sK23)
| sK25 = sK23
| sK25 = sK23 ),
inference(resolution,[status(thm)],[d5,c17]) ).
cnf(d7,plain,
( in(X0,sK24)
| ~ in('ordered$upair'(X0,X1),'cartesian$uproduct2'(sK22,sK23)) ),
inference(superposition,[status(thm)],[c19,c7]) ).
cnf(d8,plain,
( in(X0,sK24)
| ~ in(X1,sK23)
| ~ in(X0,sK22) ),
inference(resolution,[status(thm)],[c9,d7]) ).
cnf(d9,plain,
( sK22 = 'empty$uset'
| in(sK6(sK22),sK24)
| ~ in(X0,sK23) ),
inference(resolution,[status(thm)],[d8,c3]) ).
cnf(d10,plain,
( in(sK6(sK22),sK24)
| ~ in(X0,sK23) ),
inference(resolution,[status(thm)],[c20,d9]) ).
cnf(d11,plain,
( sK23 = 'empty$uset'
| in(sK6(sK22),sK24) ),
inference(resolution,[status(thm)],[d10,c3]) ).
cnf(d12,plain,
in(sK6(sK22),sK24),
inference(resolution,[status(thm)],[c21,d11]) ).
cnf(d13,plain,
( sK23 = 'empty$uset'
| in(sK6(sK23),sK25) ),
inference(resolution,[status(thm)],[d3,c3]) ).
cnf(d14,plain,
in(sK6(sK23),sK25),
inference(resolution,[status(thm)],[c21,d13]) ).
cnf(d15,plain,
( ~ in(X1,sK25)
| ~ in(X0,sK24)
| in('ordered$upair'(X0,X1),'cartesian$uproduct2'(sK22,sK23)) ),
inference(superposition,[status(thm)],[c19,c9]) ).
cnf(d16,plain,
( in(X1,sK22)
| ~ in(X1,sK24)
| ~ in(X0,sK25) ),
inference(resolution,[status(thm)],[d15,c7]) ).
cnf(d17,plain,
( ~ in(X0,sK24)
| in(X0,sK22) ),
inference(resolution,[status(thm)],[d16,d14]) ).
cnf(d18,plain,
in(sK6(sK22),sK22),
inference(resolution,[status(thm)],[d17,d12]) ).
cnf(d19,plain,
( in(X0,sK23)
| ~ in(X1,sK24)
| ~ in(X0,sK25) ),
inference(resolution,[status(thm)],[d15,c8]) ).
cnf(d20,plain,
( in(sK6(sK23),sK23)
| ~ in(X0,sK24) ),
inference(resolution,[status(thm)],[d19,d14]) ).
cnf(d21,plain,
in(sK6(sK23),sK23),
inference(resolution,[status(thm)],[d20,d12]) ).
cnf(d22,plain,
( in(sK21(X0,sK22),sK24)
| ~ in(X1,sK23)
| in(sK21(X0,sK22),X0)
| X0 = sK22 ),
inference(resolution,[status(thm)],[c16,d8]) ).
cnf(d23,plain,
( in(sK21(X0,sK22),sK24)
| in(sK21(X0,sK22),X0)
| X0 = sK22 ),
inference(resolution,[status(thm)],[d22,d21]) ).
cnf(d24,plain,
( in(sK21(sK24,sK22),sK24)
| sK24 = sK22 ),
inference(factoring,[status(thm)],[d23]) ).
cnf(d25,plain,
( ~ in(sK21(sK24,sK22),sK22)
| sK24 = sK22
| sK24 = sK22 ),
inference(resolution,[status(thm)],[d24,c17]) ).
cnf(d26,plain,
( in(sK21(sK24,sK22),sK22)
| sK24 = sK22 ),
inference(resolution,[status(thm)],[d24,d17]) ).
cnf(d27,plain,
( sK24 = sK22
| sK24 = sK22 ),
inference(resolution,[status(thm)],[d26,d25]) ).
cnf(d28,plain,
( in(sK21(sK25,sK23),sK23)
| ~ in(X0,sK24)
| sK25 = sK23 ),
inference(resolution,[status(thm)],[d5,d19]) ).
cnf(d29,plain,
( in(sK21(sK25,sK23),sK23)
| ~ in(X0,sK22)
| sK25 = sK23 ),
inference(demodulation,[status(thm)],[d28,d27]) ).
cnf(d30,plain,
( in(sK21(sK25,sK23),sK23)
| sK25 = sK23 ),
inference(resolution,[status(thm)],[d29,d18]) ).
cnf(d31,plain,
( sK25 = sK23
| sK25 = sK23 ),
inference(resolution,[status(thm)],[d30,d6]) ).
cnf(d32,plain,
( sK23 != sK25
| sK22 != sK22 ),
inference(demodulation,[status(thm)],[c22,d27]) ).
cnf(d33,plain,
( sK23 != sK23
| sK22 != sK22 ),
inference(demodulation,[status(thm)],[d32,d31]) ).
cnf(d34,plain,
sK22 != sK22,
inference(equality_resolution,[status(thm)],[d33]) ).
cnf(d35,plain,
$false,
inference(equality_resolution,[status(thm)],[d34]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET980+1 : TPTP v9.3.1. Bugfixed v4.0.0.
% 0.00/0.03 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.05/5.34 % Computer : n010.cluster.edu
% 0.05/5.34 % Model : x86_64 x86_64
% 0.05/5.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.05/5.34 % Memory : 8046.5625MB
% 0.05/5.34 % OS : Linux 6.8.0-71-generic
% 0.05/5.34 % CPULimit : 300
% 0.05/5.34 % WCLimit : 300
% 0.05/5.34 % DateTime : Sat Sep 26 08:29:20 UTC 2026
% 0.05/5.34 % CPUTime :
% 0.05/5.34 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 12.23/6.99 % SZS status Theorem for theBenchmark.p
% 12.23/6.99 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------