%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SET020+1 : TPTP v9.3.1. Bugfixed v5.4.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n012.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 08:31:37 AM UTC 2026
% Result : Theorem 12.32s 3.50s
% Output : CNFRefutation 12.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 2
% Syntax : Number of formulae : 17 ( 9 unt; 0 def)
% Number of atoms : 35 ( 20 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 28 ( 10 ~; 7 |; 8 &)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 14 ( 0 sgn 8 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(first_second,axiom,
! [X0,X1] :
( ( member(X1,'universal$uclass')
& member(X0,'universal$uclass') )
=> ( second('ordered$upair'(X0,X1)) = X1
& first('ordered$upair'(X0,X1)) = X0 ) ) ).
fof(unique_1st_and_2nd_in_pair_of_sets1,conjecture,
! [X0,X1,X2] :
( ( X2 = 'ordered$upair'(X0,X1)
& member(X1,'universal$uclass')
& member(X0,'universal$uclass') )
=> ( second(X2) = X1
& first(X2) = X0 ) ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0,X1,X2] :
( ( X2 = 'ordered$upair'(X0,X1)
& member(X1,'universal$uclass')
& member(X0,'universal$uclass') )
=> ( second(X2) = X1
& first(X2) = X0 ) ),
inference(negate_conjecture,[status(cth)],[unique_1st_and_2nd_in_pair_of_sets1]) ).
cnf(c17,plain,
( first('ordered$upair'(X0,X1)) = X0
| ~ member(X1,'universal$uclass')
| ~ member(X0,'universal$uclass') ),
inference(clausification,[status(esa)],[first_second]) ).
cnf(c18,plain,
( second('ordered$upair'(X0,X1)) = X1
| ~ member(X1,'universal$uclass')
| ~ member(X0,'universal$uclass') ),
inference(clausification,[status(esa)],[first_second]) ).
cnf(c89,plain,
member(sK90,'universal$uclass'),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c90,plain,
member(sK91,'universal$uclass'),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c91,plain,
sK92 = 'ordered$upair'(sK90,sK91),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c92,plain,
( second(sK92) != sK91
| first(sK92) != sK90 ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( ~ member(X0,'universal$uclass')
| second('ordered$upair'(X0,sK91)) = sK91 ),
inference(resolution,[status(thm)],[c18,c90]) ).
cnf(d1,plain,
second('ordered$upair'(sK90,sK91)) = sK91,
inference(resolution,[status(thm)],[d0,c89]) ).
cnf(d2,plain,
second(sK92) = sK91,
inference(demodulation,[status(thm)],[d1,c91]) ).
cnf(d3,plain,
( ~ member(X0,'universal$uclass')
| first('ordered$upair'(X0,sK91)) = X0 ),
inference(resolution,[status(thm)],[c17,c90]) ).
cnf(d4,plain,
first('ordered$upair'(sK90,sK91)) = sK90,
inference(resolution,[status(thm)],[d3,c89]) ).
cnf(d5,plain,
first(sK92) = sK90,
inference(demodulation,[status(thm)],[d4,c91]) ).
cnf(d6,plain,
second(sK92) != sK91,
inference(resolution,[status(thm)],[d5,c92]) ).
cnf(d7,plain,
$false,
inference(resolution,[status(thm)],[d6,d2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET020+1 : TPTP v9.3.1. Bugfixed v5.4.0.
% 0.00/0.03 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n012.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 06:52:20 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.35 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 12.32/3.50 % SZS status Theorem for theBenchmark.p
% 12.32/3.50 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------