%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SET912+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n019.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 08:33:33 AM UTC 2026
% Result : Theorem 12.70s 2.04s
% Output : CNFRefutation 12.70s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 5
% Syntax : Number of formulae : 21 ( 12 unt; 0 def)
% Number of atoms : 35 ( 16 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 : 29 ( 0 sgn 15 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(commutativity_k2_tarski,axiom,
! [X0,X1] : 'unordered$upair'(X0,X1) = 'unordered$upair'(X1,X0) ).
fof(commutativity_k3_xboole_0,axiom,
! [X0,X1] : 'set$uintersection2'(X0,X1) = 'set$uintersection2'(X1,X0) ).
fof(t28_xboole_1,axiom,
! [X0,X1] :
( subset(X0,X1)
=> 'set$uintersection2'(X0,X1) = X0 ) ).
fof(t38_zfmisc_1,axiom,
! [X0,X1,X2] :
( subset('unordered$upair'(X0,X1),X2)
<=> ( in(X1,X2)
& in(X0,X2) ) ) ).
fof(t53_zfmisc_1,conjecture,
! [X0,X1,X2] :
( ( in(X2,X1)
& in(X0,X1) )
=> 'set$uintersection2'('unordered$upair'(X0,X2),X1) = 'unordered$upair'(X0,X2) ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0,X1,X2] :
( ( in(X2,X1)
& in(X0,X1) )
=> 'set$uintersection2'('unordered$upair'(X0,X2),X1) = 'unordered$upair'(X0,X2) ),
inference(negate_conjecture,[status(cth)],[t53_zfmisc_1]) ).
cnf(c1,plain,
'unordered$upair'(X0,X1) = 'unordered$upair'(X1,X0),
inference(clausification,[status(esa)],[commutativity_k2_tarski]) ).
cnf(c2,plain,
'set$uintersection2'(X0,X1) = 'set$uintersection2'(X1,X0),
inference(clausification,[status(esa)],[commutativity_k3_xboole_0]) ).
cnf(c7,plain,
( 'set$uintersection2'(X0,X1) = X0
| ~ subset(X0,X1) ),
inference(clausification,[status(esa)],[t28_xboole_1]) ).
cnf(c10,plain,
( ~ in(X1,X2)
| ~ in(X0,X2)
| subset('unordered$upair'(X0,X1),X2) ),
inference(clausification,[status(esa)],[t38_zfmisc_1]) ).
cnf(c11,plain,
in(sK17,sK18),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c12,plain,
in(sK19,sK18),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c13,plain,
'set$uintersection2'('unordered$upair'(sK17,sK19),sK18) != 'unordered$upair'(sK17,sK19),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( 'set$uintersection2'('unordered$upair'(X2,X0),X1) = 'unordered$upair'(X2,X0)
| ~ in(X2,X1)
| ~ in(X0,X1) ),
inference(resolution,[status(thm)],[c10,c7]) ).
cnf(d1,plain,
( ~ in(X0,sK18)
| 'set$uintersection2'('unordered$upair'(X0,sK17),sK18) = 'unordered$upair'(X0,sK17) ),
inference(resolution,[status(thm)],[d0,c11]) ).
cnf(d2,plain,
( ~ in(X0,sK18)
| 'set$uintersection2'(sK18,'unordered$upair'(X0,sK17)) = 'unordered$upair'(X0,sK17) ),
inference(demodulation,[status(thm)],[d1,c2]) ).
cnf(d3,plain,
'set$uintersection2'(sK18,'unordered$upair'(sK19,sK17)) = 'unordered$upair'(sK19,sK17),
inference(resolution,[status(thm)],[d2,c12]) ).
cnf(d4,plain,
'set$uintersection2'(sK18,'unordered$upair'(sK17,sK19)) = 'unordered$upair'(sK19,sK17),
inference(demodulation,[status(thm)],[d3,c1]) ).
cnf(d5,plain,
'set$uintersection2'(sK18,'unordered$upair'(sK17,sK19)) = 'unordered$upair'(sK17,sK19),
inference(demodulation,[status(thm)],[d4,c1]) ).
cnf(d6,plain,
'set$uintersection2'(sK18,'unordered$upair'(sK17,sK19)) != 'unordered$upair'(sK17,sK19),
inference(demodulation,[status(thm)],[c13,c2]) ).
cnf(d7,plain,
$false,
inference(resolution,[status(thm)],[d6,d5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET912+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.37 % Computer : n019.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 08:25:34 UTC 2026
% 0.09/0.38 % CPUTime :
% 0.09/0.38 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 12.70/2.04 % SZS status Theorem for theBenchmark.p
% 12.70/2.04 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------