%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SEU267+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n003.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 08:41:30 AM UTC 2026
% Result : Theorem 35.84s 19.76s
% Output : CNFRefutation 35.84s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 3
% Syntax : Number of formulae : 15 ( 4 unt; 0 def)
% Number of atoms : 36 ( 35 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 37 ( 16 ~; 13 |; 2 &)
% ( 2 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 46 ( 12 sgn 12 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d1_mcart_1,axiom,
! [X0] :
( ? [X1,X2] : X0 = 'ordered$upair'(X1,X2)
=> ! [X1] :
( X1 = 'pair$ufirst'(X0)
<=> ! [X2,X3] :
( X0 = 'ordered$upair'(X2,X3)
=> X1 = X2 ) ) ) ).
fof(d2_mcart_1,axiom,
! [X0] :
( ? [X1,X2] : X0 = 'ordered$upair'(X1,X2)
=> ! [X1] :
( X1 = 'pair$usecond'(X0)
<=> ! [X2,X3] :
( X0 = 'ordered$upair'(X2,X3)
=> X1 = X3 ) ) ) ).
fof(t7_mcart_1,conjecture,
! [X0,X1] :
( 'pair$usecond'('ordered$upair'(X0,X1)) = X1
& 'pair$ufirst'('ordered$upair'(X0,X1)) = X0 ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0,X1] :
( 'pair$usecond'('ordered$upair'(X0,X1)) = X1
& 'pair$ufirst'('ordered$upair'(X0,X1)) = X0 ),
inference(negate_conjecture,[status(cth)],[t7_mcart_1]) ).
cnf(c121,plain,
( X3 = X4
| X0 != 'ordered$upair'(X4,X5)
| X3 != 'pair$ufirst'(X0)
| X0 != 'ordered$upair'(X1,X2) ),
inference(clausification,[status(esa)],[d1_mcart_1]) ).
cnf(c171,plain,
( X3 = X5
| X0 != 'ordered$upair'(X4,X5)
| X3 != 'pair$usecond'(X0)
| X0 != 'ordered$upair'(X1,X2) ),
inference(clausification,[status(esa)],[d2_mcart_1]) ).
cnf(c836,plain,
( 'pair$usecond'('ordered$upair'(sK896,sK897)) != sK897
| 'pair$ufirst'('ordered$upair'(sK896,sK897)) != sK896 ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( X2 != 'ordered$upair'(X1,X3)
| X0 != 'pair$ufirst'(X2)
| X0 = X1 ),
inference(factoring,[status(thm)],[c121]) ).
cnf(d1,plain,
( X0 != 'pair$ufirst'('ordered$upair'(X1,X2))
| X0 = X1 ),
inference(equality_resolution,[status(thm)],[d0]) ).
cnf(d2,plain,
'pair$ufirst'('ordered$upair'(X0,X1)) = X0,
inference(equality_resolution,[status(thm)],[d1]) ).
cnf(d3,plain,
'pair$usecond'('ordered$upair'(sK896,sK897)) != sK897,
inference(resolution,[status(thm)],[d2,c836]) ).
cnf(d4,plain,
( X2 != 'ordered$upair'(X3,X1)
| X0 != 'pair$usecond'(X2)
| X0 = X1 ),
inference(factoring,[status(thm)],[c171]) ).
cnf(d5,plain,
( X0 != 'pair$usecond'('ordered$upair'(X2,X1))
| X0 = X1 ),
inference(equality_resolution,[status(thm)],[d4]) ).
cnf(d6,plain,
'pair$usecond'('ordered$upair'(X0,X1)) = X1,
inference(equality_resolution,[status(thm)],[d5]) ).
cnf(d7,plain,
$false,
inference(resolution,[status(thm)],[d6,d3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU267+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n003.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sat Sep 26 09:03:55 UTC 2026
% 0.14/0.36 % CPUTime :
% 0.14/0.36 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 35.84/19.76 % SZS status Theorem for theBenchmark.p
% 35.84/19.76 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------