%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SET907+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n015.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 08:33:32 AM UTC 2026
% Result : Theorem 10.50s 2.76s
% Output : CNFRefutation 10.50s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 4
% Syntax : Number of formulae : 17 ( 8 unt; 0 def)
% Number of atoms : 31 ( 12 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 24 ( 10 ~; 7 |; 3 &)
% ( 1 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 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 : 25 ( 0 sgn 13 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(commutativity_k2_xboole_0,axiom,
! [X0,X1] : 'set$uunion2'(X0,X1) = 'set$uunion2'(X1,X0) ).
fof(t12_xboole_1,axiom,
! [X0,X1] :
( subset(X0,X1)
=> 'set$uunion2'(X0,X1) = X1 ) ).
fof(t38_zfmisc_1,axiom,
! [X0,X1,X2] :
( subset('unordered$upair'(X0,X1),X2)
<=> ( in(X1,X2)
& in(X0,X2) ) ) ).
fof(t48_zfmisc_1,conjecture,
! [X0,X1,X2] :
( ( in(X2,X1)
& in(X0,X1) )
=> 'set$uunion2'('unordered$upair'(X0,X2),X1) = X1 ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0,X1,X2] :
( ( in(X2,X1)
& in(X0,X1) )
=> 'set$uunion2'('unordered$upair'(X0,X2),X1) = X1 ),
inference(negate_conjecture,[status(cth)],[t48_zfmisc_1]) ).
cnf(c2,plain,
'set$uunion2'(X0,X1) = 'set$uunion2'(X1,X0),
inference(clausification,[status(esa)],[commutativity_k2_xboole_0]) ).
cnf(c9,plain,
( 'set$uunion2'(X0,X1) = X1
| ~ subset(X0,X1) ),
inference(clausification,[status(esa)],[t12_xboole_1]) ).
cnf(c12,plain,
( ~ in(X1,X2)
| ~ in(X0,X2)
| subset('unordered$upair'(X0,X1),X2) ),
inference(clausification,[status(esa)],[t38_zfmisc_1]) ).
cnf(c13,plain,
in(sK21,sK22),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c14,plain,
in(sK23,sK22),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c15,plain,
'set$uunion2'('unordered$upair'(sK21,sK23),sK22) != sK22,
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( 'set$uunion2'('unordered$upair'(X0,X2),X1) = X1
| ~ in(X2,X1)
| ~ in(X0,X1) ),
inference(resolution,[status(thm)],[c12,c9]) ).
cnf(d1,plain,
( ~ in(X0,sK22)
| 'set$uunion2'('unordered$upair'(sK21,X0),sK22) = sK22 ),
inference(resolution,[status(thm)],[d0,c13]) ).
cnf(d2,plain,
( ~ in(X0,sK22)
| 'set$uunion2'(sK22,'unordered$upair'(sK21,X0)) = sK22 ),
inference(demodulation,[status(thm)],[d1,c2]) ).
cnf(d3,plain,
'set$uunion2'(sK22,'unordered$upair'(sK21,sK23)) = sK22,
inference(resolution,[status(thm)],[d2,c14]) ).
cnf(d4,plain,
'set$uunion2'(sK22,'unordered$upair'(sK21,sK23)) != sK22,
inference(demodulation,[status(thm)],[c15,c2]) ).
cnf(d5,plain,
$false,
inference(resolution,[status(thm)],[d4,d3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET907+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.37 % Computer : n015.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Sat Sep 26 08:28:29 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 10.50/2.76 % SZS status Theorem for theBenchmark.p
% 10.50/2.76 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------