%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SEU010+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 : n018.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 08:40:45 AM UTC 2026
% Result : Theorem 12.40s 3.50s
% Output : CNFRefutation 12.40s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 4
% Syntax : Number of formulae : 16 ( 7 unt; 0 def)
% Number of atoms : 33 ( 15 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 27 ( 10 ~; 7 |; 4 &)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 1 con; 0-2 aty)
% Number of variables : 15 ( 1 sgn 8 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(reflexivity_r1_tarski,axiom,
! [X0,X1] : subset(X0,X0) ).
fof(t77_relat_1,axiom,
! [X0,X1] :
( relation(X1)
=> ( subset('relation$udom'(X1),X0)
=> 'relation$ucomposition'('identity$urelation'(X0),X1) = X1 ) ) ).
fof(t79_relat_1,axiom,
! [X0,X1] :
( relation(X1)
=> ( subset('relation$urng'(X1),X0)
=> 'relation$ucomposition'(X1,'identity$urelation'(X0)) = X1 ) ) ).
fof(t42_funct_1,conjecture,
! [X0] :
( ( function(X0)
& relation(X0) )
=> ( 'relation$ucomposition'(X0,'identity$urelation'('relation$urng'(X0))) = X0
& 'relation$ucomposition'('identity$urelation'('relation$udom'(X0)),X0) = X0 ) ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0] :
( ( function(X0)
& relation(X0) )
=> ( 'relation$ucomposition'(X0,'identity$urelation'('relation$urng'(X0))) = X0
& 'relation$ucomposition'('identity$urelation'('relation$udom'(X0)),X0) = X0 ) ),
inference(negate_conjecture,[status(cth)],[t42_funct_1]) ).
cnf(c28,plain,
subset(X0,X0),
inference(clausification,[status(esa)],[reflexivity_r1_tarski]) ).
cnf(c51,plain,
( 'relation$ucomposition'('identity$urelation'(X1),X0) = X0
| ~ subset('relation$udom'(X0),X1)
| ~ relation(X0) ),
inference(clausification,[status(esa)],[t77_relat_1]) ).
cnf(c52,plain,
( 'relation$ucomposition'(X0,'identity$urelation'(X1)) = X0
| ~ subset('relation$urng'(X0),X1)
| ~ relation(X0) ),
inference(clausification,[status(esa)],[t79_relat_1]) ).
cnf(c53,plain,
relation(sK54),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c55,plain,
( 'relation$ucomposition'(sK54,'identity$urelation'('relation$urng'(sK54))) != sK54
| 'relation$ucomposition'('identity$urelation'('relation$udom'(sK54)),sK54) != sK54 ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( ~ relation(X0)
| 'relation$ucomposition'(X0,'identity$urelation'('relation$urng'(X0))) = X0 ),
inference(resolution,[status(thm)],[c52,c28]) ).
cnf(d1,plain,
'relation$ucomposition'(sK54,'identity$urelation'('relation$urng'(sK54))) = sK54,
inference(resolution,[status(thm)],[d0,c53]) ).
cnf(d2,plain,
( ~ relation(X0)
| 'relation$ucomposition'('identity$urelation'('relation$udom'(X0)),X0) = X0 ),
inference(resolution,[status(thm)],[c51,c28]) ).
cnf(d3,plain,
'relation$ucomposition'('identity$urelation'('relation$udom'(sK54)),sK54) = sK54,
inference(resolution,[status(thm)],[d2,c53]) ).
cnf(d4,plain,
'relation$ucomposition'(sK54,'identity$urelation'('relation$urng'(sK54))) != sK54,
inference(resolution,[status(thm)],[d3,c55]) ).
cnf(d5,plain,
$false,
inference(resolution,[status(thm)],[d4,d1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU010+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.03 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.42 % Computer : n018.cluster.edu
% 0.07/0.42 % Model : x86_64 x86_64
% 0.07/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.42 % Memory : 8046.5625MB
% 0.07/0.42 % OS : Linux 6.8.0-71-generic
% 0.07/0.42 % CPULimit : 300
% 0.07/0.42 % WCLimit : 300
% 0.07/0.42 % DateTime : Sat Sep 26 08:32:37 UTC 2026
% 0.07/0.42 % CPUTime :
% 0.07/0.42 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 12.40/3.50 % SZS status Theorem for theBenchmark.p
% 12.40/3.50 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------