%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SEU098+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n026.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 08:40:52 AM UTC 2026
% Result : Theorem 15.97s 4.40s
% Output : CNFRefutation 15.97s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 12
% Syntax : Number of formulae : 53 ( 17 unt; 0 def)
% Number of atoms : 123 ( 12 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 114 ( 44 ~; 44 |; 13 &)
% ( 3 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 1 con; 0-4 aty)
% Number of variables : 65 ( 6 sgn 24 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(dt_k7_funct_3,axiom,
! [X0,X1] :
( function('first$uprojection'(X0,X1))
& relation('first$uprojection'(X0,X1)) ) ).
fof(dt_k9_funct_3,axiom,
! [X0,X1] :
( 'relation$uof2$uas$usubset'('first$uprojection$uas$ufunc$uof'(X0,X1),'cartesian$uproduct2'(X0,X1),X0)
& 'quasi$utotal'('first$uprojection$uas$ufunc$uof'(X0,X1),'cartesian$uproduct2'(X0,X1),X0)
& function('first$uprojection$uas$ufunc$uof'(X0,X1)) ) ).
fof(fc13_finset_1,axiom,
! [X0,X1] :
( ( finite(X1)
& function(X0)
& relation(X0) )
=> finite('relation$uimage'(X0,X1)) ) ).
fof(fc14_finset_1,axiom,
! [X0,X1] :
( ( finite(X1)
& finite(X0) )
=> finite('cartesian$uproduct2'(X0,X1)) ) ).
fof(redefinition_k2_funct_2,axiom,
! [X0,X1,X2,X3] :
( ( 'relation$uof2'(X2,X0,X1)
& 'quasi$utotal'(X2,X0,X1)
& function(X2) )
=> 'function$uimage'(X0,X1,X2,X3) = 'relation$uimage'(X2,X3) ) ).
fof(redefinition_k9_funct_3,axiom,
! [X0,X1] : 'first$uprojection$uas$ufunc$uof'(X0,X1) = 'first$uprojection'(X0,X1) ).
fof(redefinition_m2_relset_1,axiom,
! [X0,X1,X2] :
( 'relation$uof2$uas$usubset'(X2,X0,X1)
<=> 'relation$uof2'(X2,X0,X1) ) ).
fof(t100_funct_3,axiom,
! [X0] :
( ( function(X0)
& relation(X0) )
=> 'function$uimage'('cartesian$uproduct2'('relation$udom'(X0),'relation$urng'(X0)),'relation$udom'(X0),'first$uprojection$uas$ufunc$uof'('relation$udom'(X0),'relation$urng'(X0)),X0) = 'relation$udom'(X0) ) ).
fof(t13_finset_1,axiom,
! [X0,X1] :
( ( finite(X1)
& subset(X0,X1) )
=> finite(X0) ) ).
fof(t21_relat_1,axiom,
! [X0] :
( relation(X0)
=> subset(X0,'cartesian$uproduct2'('relation$udom'(X0),'relation$urng'(X0))) ) ).
fof(t26_finset_1,axiom,
! [X0] :
( ( function(X0)
& relation(X0) )
=> ( finite('relation$udom'(X0))
=> finite('relation$urng'(X0)) ) ) ).
fof(t29_finset_1,conjecture,
! [X0] :
( ( function(X0)
& relation(X0) )
=> ( finite('relation$udom'(X0))
<=> finite(X0) ) ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0] :
( ( function(X0)
& relation(X0) )
=> ( finite('relation$udom'(X0))
<=> finite(X0) ) ),
inference(negate_conjecture,[status(cth)],[t29_finset_1]) ).
cnf(c27,plain,
relation('first$uprojection'(X0,X1)),
inference(clausification,[status(esa)],[dt_k7_funct_3]) ).
cnf(c29,plain,
function('first$uprojection$uas$ufunc$uof'(X0,X1)),
inference(clausification,[status(esa)],[dt_k9_funct_3]) ).
cnf(c30,plain,
'quasi$utotal'('first$uprojection$uas$ufunc$uof'(X0,X1),'cartesian$uproduct2'(X0,X1),X0),
inference(clausification,[status(esa)],[dt_k9_funct_3]) ).
cnf(c31,plain,
'relation$uof2$uas$usubset'('first$uprojection$uas$ufunc$uof'(X0,X1),'cartesian$uproduct2'(X0,X1),X0),
inference(clausification,[status(esa)],[dt_k9_funct_3]) ).
cnf(c39,plain,
( finite('relation$uimage'(X0,X1))
| ~ finite(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(clausification,[status(esa)],[fc13_finset_1]) ).
cnf(c40,plain,
( finite('cartesian$uproduct2'(X0,X1))
| ~ finite(X1)
| ~ finite(X0) ),
inference(clausification,[status(esa)],[fc14_finset_1]) ).
cnf(c153,plain,
( 'function$uimage'(X1,X2,X0,X3) = 'relation$uimage'(X0,X3)
| ~ 'relation$uof2'(X0,X1,X2)
| ~ 'quasi$utotal'(X0,X1,X2)
| ~ function(X0) ),
inference(clausification,[status(esa)],[redefinition_k2_funct_2]) ).
cnf(c154,plain,
'first$uprojection$uas$ufunc$uof'(X0,X1) = 'first$uprojection'(X0,X1),
inference(clausification,[status(esa)],[redefinition_k9_funct_3]) ).
cnf(c155,plain,
( 'relation$uof2'(X0,X1,X2)
| ~ 'relation$uof2$uas$usubset'(X0,X1,X2) ),
inference(clausification,[status(esa)],[redefinition_m2_relset_1]) ).
cnf(c158,plain,
( 'function$uimage'('cartesian$uproduct2'('relation$udom'(X0),'relation$urng'(X0)),'relation$udom'(X0),'first$uprojection$uas$ufunc$uof'('relation$udom'(X0),'relation$urng'(X0)),X0) = 'relation$udom'(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(clausification,[status(esa)],[t100_funct_3]) ).
cnf(c159,plain,
( finite(X0)
| ~ finite(X1)
| ~ subset(X0,X1) ),
inference(clausification,[status(esa)],[t13_finset_1]) ).
cnf(c163,plain,
( subset(X0,'cartesian$uproduct2'('relation$udom'(X0),'relation$urng'(X0)))
| ~ relation(X0) ),
inference(clausification,[status(esa)],[t21_relat_1]) ).
cnf(c164,plain,
( finite('relation$urng'(X0))
| ~ finite('relation$udom'(X0))
| ~ function(X0)
| ~ relation(X0) ),
inference(clausification,[status(esa)],[t26_finset_1]) ).
cnf(c173,plain,
relation(sK118),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c174,plain,
function(sK118),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c176,plain,
( finite(sK118)
| finite('relation$udom'(sK118)) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c177,plain,
( ~ finite('relation$udom'(sK118))
| ~ finite(sK118) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( finite(sK118)
| ~ relation(sK118)
| ~ function(sK118)
| finite('relation$urng'(sK118)) ),
inference(resolution,[status(thm)],[c164,c176]) ).
cnf(d1,plain,
( ~ function(sK118)
| finite(sK118)
| finite('relation$urng'(sK118)) ),
inference(resolution,[status(thm)],[c173,d0]) ).
cnf(d2,plain,
( finite(sK118)
| finite('relation$urng'(sK118)) ),
inference(resolution,[status(thm)],[c174,d1]) ).
cnf(d3,plain,
'relation$uof2'('first$uprojection$uas$ufunc$uof'(X0,X1),'cartesian$uproduct2'(X0,X1),X0),
inference(resolution,[status(thm)],[c155,c31]) ).
cnf(d4,plain,
( ~ 'quasi$utotal'('first$uprojection$uas$ufunc$uof'(X0,X1),'cartesian$uproduct2'(X0,X1),X0)
| ~ function('first$uprojection$uas$ufunc$uof'(X0,X1))
| 'function$uimage'('cartesian$uproduct2'(X0,X1),X0,'first$uprojection$uas$ufunc$uof'(X0,X1),X2) = 'relation$uimage'('first$uprojection$uas$ufunc$uof'(X0,X1),X2) ),
inference(resolution,[status(thm)],[d3,c153]) ).
cnf(d5,plain,
( ~ 'quasi$utotal'('first$uprojection$uas$ufunc$uof'(X0,X1),'cartesian$uproduct2'(X0,X1),X0)
| 'function$uimage'('cartesian$uproduct2'(X0,X1),X0,'first$uprojection$uas$ufunc$uof'(X0,X1),X2) = 'relation$uimage'('first$uprojection$uas$ufunc$uof'(X0,X1),X2) ),
inference(resolution,[status(thm)],[c29,d4]) ).
cnf(d6,plain,
'function$uimage'('cartesian$uproduct2'(X0,X1),X0,'first$uprojection$uas$ufunc$uof'(X0,X1),X2) = 'relation$uimage'('first$uprojection$uas$ufunc$uof'(X0,X1),X2),
inference(resolution,[status(thm)],[c30,d5]) ).
cnf(d7,plain,
( ~ function(sK118)
| 'function$uimage'('cartesian$uproduct2'('relation$udom'(sK118),'relation$urng'(sK118)),'relation$udom'(sK118),'first$uprojection$uas$ufunc$uof'('relation$udom'(sK118),'relation$urng'(sK118)),sK118) = 'relation$udom'(sK118) ),
inference(resolution,[status(thm)],[c158,c173]) ).
cnf(d8,plain,
'function$uimage'('cartesian$uproduct2'('relation$udom'(sK118),'relation$urng'(sK118)),'relation$udom'(sK118),'first$uprojection$uas$ufunc$uof'('relation$udom'(sK118),'relation$urng'(sK118)),sK118) = 'relation$udom'(sK118),
inference(resolution,[status(thm)],[c174,d7]) ).
cnf(d9,plain,
'relation$uimage'('first$uprojection$uas$ufunc$uof'('relation$udom'(sK118),'relation$urng'(sK118)),sK118) = 'relation$udom'(sK118),
inference(demodulation,[status(thm)],[d8,d6]) ).
cnf(d10,plain,
( ~ relation('first$uprojection$uas$ufunc$uof'('relation$udom'(sK118),'relation$urng'(sK118)))
| ~ function('first$uprojection$uas$ufunc$uof'('relation$udom'(sK118),'relation$urng'(sK118)))
| ~ finite(sK118)
| finite('relation$udom'(sK118)) ),
inference(superposition,[status(thm)],[d9,c39]) ).
cnf(d11,plain,
( ~ relation('first$uprojection$uas$ufunc$uof'('relation$udom'(sK118),'relation$urng'(sK118)))
| ~ finite(sK118)
| finite('relation$udom'(sK118)) ),
inference(resolution,[status(thm)],[c29,d10]) ).
cnf(d12,plain,
relation('first$uprojection$uas$ufunc$uof'(X0,X1)),
inference(demodulation,[status(thm)],[c27,c154]) ).
cnf(d13,plain,
( ~ finite(sK118)
| finite('relation$udom'(sK118)) ),
inference(resolution,[status(thm)],[d12,d11]) ).
cnf(d14,plain,
( ~ finite(sK118)
| ~ finite(sK118) ),
inference(resolution,[status(thm)],[d13,c177]) ).
cnf(d15,plain,
finite('relation$urng'(sK118)),
inference(resolution,[status(thm)],[d14,d2]) ).
cnf(d16,plain,
( ~ finite('cartesian$uproduct2'('relation$udom'(X0),'relation$urng'(X0)))
| finite(X0)
| ~ relation(X0) ),
inference(resolution,[status(thm)],[c163,c159]) ).
cnf(d17,plain,
( ~ finite('relation$udom'(X0))
| ~ finite('relation$urng'(X0))
| ~ relation(X0)
| finite(X0) ),
inference(resolution,[status(thm)],[d16,c40]) ).
cnf(d18,plain,
( ~ relation(sK118)
| ~ finite('relation$udom'(sK118))
| finite(sK118) ),
inference(resolution,[status(thm)],[d17,d15]) ).
cnf(d19,plain,
( finite(sK118)
| ~ finite('relation$udom'(sK118)) ),
inference(resolution,[status(thm)],[c173,d18]) ).
cnf(d20,plain,
~ finite('relation$udom'(sK118)),
inference(resolution,[status(thm)],[d14,d19]) ).
cnf(d21,plain,
finite('relation$udom'(sK118)),
inference(resolution,[status(thm)],[d14,c176]) ).
cnf(d22,plain,
$false,
inference(resolution,[status(thm)],[d21,d20]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU098+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n026.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 08:39:10 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 15.97/4.40 % SZS status Theorem for theBenchmark.p
% 15.97/4.40 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------