%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SEU219+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 : n020.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 08:41:19 AM UTC 2026
% Result : Theorem 42.54s 9.73s
% Output : CNFRefutation 42.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 10
% Syntax : Number of formulae : 45 ( 27 unt; 0 def)
% Number of atoms : 75 ( 45 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 52 ( 22 ~; 15 |; 6 &)
% ( 0 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 1 con; 0-2 aty)
% Number of variables : 40 ( 4 sgn 18 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(commutativity_k2_xboole_0,axiom,
! [X0,X1] : 'set$uunion2'(X0,X1) = 'set$uunion2'(X1,X0) ).
fof(commutativity_k3_xboole_0,axiom,
! [X0,X1] : 'set$uintersection2'(X0,X1) = 'set$uintersection2'(X1,X0) ).
fof(d9_funct_1,axiom,
! [X0] :
( ( function(X0)
& relation(X0) )
=> ( 'one$uto$uone'(X0)
=> 'function$uinverse'(X0) = 'relation$uinverse'(X0) ) ) ).
fof(idempotence_k2_xboole_0,axiom,
! [X0,X1] : 'set$uunion2'(X0,X0) = X0 ).
fof(idempotence_k3_xboole_0,axiom,
! [X0,X1] : 'set$uintersection2'(X0,X0) = X0 ).
fof(t119_relat_1,lemma,
! [X0,X1] :
( relation(X1)
=> 'relation$urng'('relation$urng$urestriction'(X0,X1)) = 'set$uintersection2'('relation$urng'(X1),X0) ) ).
fof(t12_xboole_1,lemma,
! [X0,X1] :
( subset(X0,X1)
=> 'set$uunion2'(X0,X1) = X1 ) ).
fof(t17_xboole_1,lemma,
! [X0,X1] : subset('set$uintersection2'(X0,X1),X0) ).
fof(t37_relat_1,lemma,
! [X0] :
( relation(X0)
=> ( 'relation$udom'(X0) = 'relation$urng'('relation$uinverse'(X0))
& 'relation$urng'(X0) = 'relation$udom'('relation$uinverse'(X0)) ) ) ).
fof(t55_funct_1,conjecture,
! [X0] :
( ( function(X0)
& relation(X0) )
=> ( 'one$uto$uone'(X0)
=> ( 'relation$udom'(X0) = 'relation$urng'('function$uinverse'(X0))
& 'relation$urng'(X0) = 'relation$udom'('function$uinverse'(X0)) ) ) ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0] :
( ( function(X0)
& relation(X0) )
=> ( 'one$uto$uone'(X0)
=> ( 'relation$udom'(X0) = 'relation$urng'('function$uinverse'(X0))
& 'relation$urng'(X0) = 'relation$udom'('function$uinverse'(X0)) ) ) ),
inference(negate_conjecture,[status(cth)],[t55_funct_1]) ).
cnf(c8,plain,
'set$uunion2'(X0,X1) = 'set$uunion2'(X1,X0),
inference(clausification,[status(esa)],[commutativity_k2_xboole_0]) ).
cnf(c9,plain,
'set$uintersection2'(X0,X1) = 'set$uintersection2'(X1,X0),
inference(clausification,[status(esa)],[commutativity_k3_xboole_0]) ).
cnf(c234,plain,
( 'function$uinverse'(X0) = 'relation$uinverse'(X0)
| ~ 'one$uto$uone'(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(clausification,[status(esa)],[d9_funct_1]) ).
cnf(c282,plain,
'set$uunion2'(X0,X0) = X0,
inference(clausification,[status(esa)],[idempotence_k2_xboole_0]) ).
cnf(c283,plain,
'set$uintersection2'(X0,X0) = X0,
inference(clausification,[status(esa)],[idempotence_k3_xboole_0]) ).
cnf(c344,plain,
( 'relation$urng'('relation$urng$urestriction'(X1,X0)) = 'set$uintersection2'('relation$urng'(X0),X1)
| ~ relation(X0) ),
inference(clausification,[status(esa)],[t119_relat_1]) ).
cnf(c346,plain,
( 'set$uunion2'(X0,X1) = X1
| ~ subset(X0,X1) ),
inference(clausification,[status(esa)],[t12_xboole_1]) ).
cnf(c367,plain,
subset('set$uintersection2'(X0,X1),X0),
inference(clausification,[status(esa)],[t17_xboole_1]) ).
cnf(c403,plain,
( 'relation$urng'(X0) = 'relation$udom'('relation$uinverse'(X0))
| ~ relation(X0) ),
inference(clausification,[status(esa)],[t37_relat_1]) ).
cnf(c404,plain,
( 'relation$udom'(X0) = 'relation$urng'('relation$uinverse'(X0))
| ~ relation(X0) ),
inference(clausification,[status(esa)],[t37_relat_1]) ).
cnf(c501,plain,
relation(sK568),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c502,plain,
function(sK568),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c503,plain,
'one$uto$uone'(sK568),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c504,plain,
( 'relation$udom'(sK568) != 'relation$urng'('function$uinverse'(sK568))
| 'relation$urng'(sK568) != 'relation$udom'('function$uinverse'(sK568)) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
'relation$urng'(sK568) = 'relation$udom'('relation$uinverse'(sK568)),
inference(resolution,[status(thm)],[c403,c501]) ).
cnf(d1,plain,
'relation$udom'(sK568) = 'relation$urng'('relation$uinverse'(sK568)),
inference(resolution,[status(thm)],[c404,c501]) ).
cnf(d2,plain,
( ~ relation(sK568)
| ~ function(sK568)
| 'function$uinverse'(sK568) = 'relation$uinverse'(sK568) ),
inference(resolution,[status(thm)],[c234,c503]) ).
cnf(d3,plain,
( ~ function(sK568)
| 'function$uinverse'(sK568) = 'relation$uinverse'(sK568) ),
inference(resolution,[status(thm)],[c501,d2]) ).
cnf(d4,plain,
'function$uinverse'(sK568) = 'relation$uinverse'(sK568),
inference(resolution,[status(thm)],[c502,d3]) ).
cnf(d5,plain,
( 'relation$urng'(sK568) != 'relation$udom'('function$uinverse'(sK568))
| 'relation$udom'(sK568) != 'relation$urng'('relation$uinverse'(sK568)) ),
inference(demodulation,[status(thm)],[c504,d4]) ).
cnf(d6,plain,
( 'relation$urng'(sK568) != 'relation$udom'('relation$uinverse'(sK568))
| 'relation$udom'(sK568) != 'relation$urng'('relation$uinverse'(sK568)) ),
inference(demodulation,[status(thm)],[d5,d4]) ).
cnf(d7,plain,
( 'relation$urng'(sK568) != 'relation$udom'('relation$uinverse'(sK568))
| 'relation$udom'(sK568) != 'relation$udom'(sK568) ),
inference(demodulation,[status(thm)],[d6,d1]) ).
cnf(d8,plain,
( 'relation$urng'(sK568) != 'relation$urng'(sK568)
| 'relation$udom'(sK568) != 'relation$udom'(sK568) ),
inference(demodulation,[status(thm)],[d7,d0]) ).
cnf(d9,plain,
subset('set$uintersection2'(X1,X0),X0),
inference(superposition,[status(thm)],[c9,c367]) ).
cnf(d10,plain,
'relation$urng'('relation$urng$urestriction'(X0,sK568)) = 'set$uintersection2'('relation$urng'(sK568),X0),
inference(resolution,[status(thm)],[c344,c501]) ).
cnf(d11,plain,
subset('relation$urng'('relation$urng$urestriction'(X0,sK568)),X0),
inference(superposition,[status(thm)],[d10,d9]) ).
cnf(d12,plain,
'set$uunion2'('relation$urng'('relation$urng$urestriction'(X0,sK568)),X0) = X0,
inference(resolution,[status(thm)],[c346,d11]) ).
cnf(d13,plain,
'set$uunion2'(X0,'relation$urng'('relation$urng$urestriction'(X0,sK568))) = X0,
inference(demodulation,[status(thm)],[d12,c8]) ).
cnf(d14,plain,
X0 = 'set$uintersection2'(X0,X0),
inference(superposition,[status(thm)],[c283,c9]) ).
cnf(d15,plain,
'relation$urng'(sK568) = 'relation$urng'('relation$urng$urestriction'('relation$urng'(sK568),sK568)),
inference(superposition,[status(thm)],[d10,d14]) ).
cnf(d16,plain,
'set$uunion2'('relation$urng'(sK568),'relation$urng'(sK568)) = 'relation$urng'(sK568),
inference(superposition,[status(thm)],[d15,d13]) ).
cnf(d17,plain,
'relation$urng'(sK568) = 'relation$urng'(sK568),
inference(demodulation,[status(thm)],[d16,c282]) ).
cnf(d18,plain,
'relation$udom'(sK568) != 'relation$udom'(sK568),
inference(resolution,[status(thm)],[d17,d8]) ).
cnf(d19,plain,
$false,
inference(equality_resolution,[status(thm)],[d18]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SEU219+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.44 % Computer : n020.cluster.edu
% 0.19/0.44 % Model : x86_64 x86_64
% 0.19/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.44 % Memory : 8046.5625MB
% 0.19/0.44 % OS : Linux 6.8.0-71-generic
% 0.19/0.44 % CPULimit : 300
% 0.19/0.44 % WCLimit : 300
% 0.19/0.44 % DateTime : Sat Sep 26 08:53:04 UTC 2026
% 0.19/0.44 % CPUTime :
% 0.19/0.44 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 42.54/9.73 % SZS status Theorem for theBenchmark.p
% 42.54/9.73 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------