%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SET121-7 : TPTP v9.3.1. Bugfixed v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n016.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 08:32:07 AM UTC 2026
% Result : Unsatisfiable 33.86s 24.28s
% Output : CNFRefutation 33.86s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 5
% Syntax : Number of clauses : 14 ( 6 unt; 6 nHn; 7 RR)
% Number of literals : 23 ( 12 equ; 6 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 16 ( 6 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(corollary_2_to_cartesian_product,axiom,
( member(X1,'universal$uclass')
| ~ member('ordered$upair'(X0,X1),'cross$uproduct'(X2,X3)) ) ).
cnf(existence_of_1st_and_2nd_2,axiom,
( first(X0) = X0
| member('ordered$upair'(first(X0),second(X0)),'cross$uproduct'('universal$uclass','universal$uclass')) ) ).
cnf(existence_of_1st_and_2nd_4,axiom,
( first(X0) = X0
| 'ordered$upair'(first(X0),second(X0)) = X0 ) ).
cnf(prove_corollary_1_to_OP_determines_components2_1,negated_conjecture,
~ member(y,'universal$uclass') ).
cnf(prove_corollary_1_to_OP_determines_components2_2,negated_conjecture,
first('ordered$upair'(x,y)) != 'ordered$upair'(x,y) ).
cnf(c3,plain,
( member(X1,'universal$uclass')
| ~ member('ordered$upair'(X0,X1),'cross$uproduct'(X2,X3)) ),
inference(clausification,[status(esa)],[corollary_2_to_cartesian_product]) ).
cnf(c62,plain,
( first(X0) = X0
| member('ordered$upair'(first(X0),second(X0)),'cross$uproduct'('universal$uclass','universal$uclass')) ),
inference(clausification,[status(esa)],[existence_of_1st_and_2nd_2]) ).
cnf(c64,plain,
( first(X0) = X0
| 'ordered$upair'(first(X0),second(X0)) = X0 ),
inference(clausification,[status(esa)],[existence_of_1st_and_2nd_4]) ).
cnf(c76,plain,
~ member(y,'universal$uclass'),
inference(clausification,[status(esa)],[prove_corollary_1_to_OP_determines_components2_1]) ).
cnf(c77,plain,
first('ordered$upair'(x,y)) != 'ordered$upair'(x,y),
inference(clausification,[status(esa)],[prove_corollary_1_to_OP_determines_components2_2]) ).
cnf(d0,plain,
( first(X0) = X0
| first(X0) = X0
| member(X0,'cross$uproduct'('universal$uclass','universal$uclass')) ),
inference(superposition,[status(thm)],[c64,c62]) ).
cnf(d1,plain,
( member(X1,'universal$uclass')
| first('ordered$upair'(X0,X1)) = 'ordered$upair'(X0,X1) ),
inference(resolution,[status(thm)],[d0,c3]) ).
cnf(d2,plain,
first('ordered$upair'(X0,y)) = 'ordered$upair'(X0,y),
inference(resolution,[status(thm)],[d1,c76]) ).
cnf(d3,plain,
$false,
inference(resolution,[status(thm)],[d2,c77]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SET121-7 : TPTP v9.3.1. Bugfixed v7.3.0.
% 0.00/0.02 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/5.38 % Computer : n016.cluster.edu
% 0.09/5.38 % Model : x86_64 x86_64
% 0.09/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.38 % Memory : 8046.5625MB
% 0.09/5.38 % OS : Linux 6.8.0-71-generic
% 0.03/15.38 % CPULimit : 300
% 0.03/15.38 % WCLimit : 300
% 0.03/15.38 % DateTime : Sat Sep 26 07:10:50 UTC 2026
% 0.03/15.38 % CPUTime :
% 0.03/15.38 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 33.86/24.28 % SZS status Unsatisfiable for theBenchmark.p
% 33.86/24.28 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------