%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : GEO085+1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n005.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 07:14:08 AM UTC 2026
% Result : Theorem 13.02s 3.37s
% Output : CNFRefutation 13.02s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 4
% Syntax : Number of formulae : 29 ( 8 unt; 0 def)
% Number of atoms : 58 ( 17 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 55 ( 26 ~; 19 |; 5 &)
% ( 2 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 1 con; 0-2 aty)
% Number of variables : 27 ( 1 sgn 6 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(closed_defn,axiom,
! [X0] :
( closed(X0)
<=> ~ ? [X1] : 'end$upoint'(X1,X0) ) ).
fof(open_defn,axiom,
! [X0] :
( open(X0)
<=> ? [X1] : 'end$upoint'(X1,X0) ) ).
fof(c6,axiom,
! [X0,X1] :
( 'end$upoint'(X1,X0)
=> ? [X2] :
( X1 != X2
& 'end$upoint'(X2,X0) ) ) ).
fof(theorem_2_7_1,conjecture,
! [X0] :
( open(X0)
=> ? [X1,X2] :
( 'end$upoint'(X2,X0)
& 'end$upoint'(X1,X0)
& X1 != X2 ) ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0] :
( open(X0)
=> ? [X1,X2] :
( 'end$upoint'(X2,X0)
& 'end$upoint'(X1,X0)
& X1 != X2 ) ),
inference(negate_conjecture,[status(cth)],[theorem_2_7_1]) ).
cnf(c_36,plain,
( ~ 'end$upoint'(X1,X0)
| ~ closed(X0) ),
inference(clausification,[status(esa)],[closed_defn]) ).
cnf(c_37,plain,
( 'end$upoint'(sK27(X0),X0)
| closed(X0) ),
inference(clausification,[status(esa)],[closed_defn]) ).
cnf(c_38,plain,
( 'end$upoint'(sK29(X0),X0)
| ~ open(X0) ),
inference(clausification,[status(esa)],[open_defn]) ).
cnf(c_46,plain,
( 'end$upoint'(sK50(X1,X0),X1)
| ~ 'end$upoint'(X0,X1) ),
inference(clausification,[status(esa)],[c6]) ).
cnf(c_47,plain,
( X0 != sK50(X1,X0)
| ~ 'end$upoint'(X0,X1) ),
inference(clausification,[status(esa)],[c6]) ).
cnf(c_54,plain,
open(sK63),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c_55,plain,
( ~ 'end$upoint'(X1,sK63)
| ~ 'end$upoint'(X0,sK63)
| X0 = X1 ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( ~ 'end$upoint'(X0,sK63)
| sK27(sK63) = X0
| closed(sK63) ),
inference(resolution,[status(thm)],[c_37,c_55]) ).
cnf(d1,plain,
( closed(sK63)
| sK27(sK63) = sK29(sK63)
| ~ open(sK63) ),
inference(resolution,[status(thm)],[c_38,d0]) ).
cnf(d2,plain,
( closed(sK63)
| sK27(sK63) = sK29(sK63) ),
inference(resolution,[status(thm)],[c_54,d1]) ).
cnf(d3,plain,
( ~ closed(X0)
| ~ open(X0) ),
inference(resolution,[status(thm)],[c_38,c_36]) ).
cnf(d4,plain,
~ closed(sK63),
inference(resolution,[status(thm)],[d3,c_54]) ).
cnf(d5,plain,
sK27(sK63) = sK29(sK63),
inference(resolution,[status(thm)],[d4,d2]) ).
cnf(d6,plain,
( ~ open(sK63)
| 'end$upoint'(sK27(sK63),sK63) ),
inference(superposition,[status(thm)],[d5,c_38]) ).
cnf(d7,plain,
'end$upoint'(sK27(sK63),sK63),
inference(resolution,[status(thm)],[c_54,d6]) ).
cnf(d8,plain,
( ~ 'end$upoint'(X0,sK63)
| sK27(sK63) = X0 ),
inference(resolution,[status(thm)],[d4,d0]) ).
cnf(d9,plain,
( sK27(sK63) = sK50(sK63,X0)
| ~ 'end$upoint'(X0,sK63) ),
inference(resolution,[status(thm)],[c_46,d8]) ).
cnf(d10,plain,
sK27(sK63) = sK50(sK63,sK27(sK63)),
inference(resolution,[status(thm)],[d9,d7]) ).
cnf(d11,plain,
( ~ 'end$upoint'(sK27(sK63),sK63)
| sK27(sK63) != sK27(sK63) ),
inference(superposition,[status(thm)],[d10,c_47]) ).
cnf(d12,plain,
sK27(sK63) != sK27(sK63),
inference(resolution,[status(thm)],[d7,d11]) ).
cnf(d13,plain,
( ~ open(sK63)
| sK27(sK63) = sK29(sK63) ),
inference(resolution,[status(thm)],[d8,c_38]) ).
cnf(d14,plain,
( ~ open(sK63)
| sK27(sK63) = sK27(sK63) ),
inference(demodulation,[status(thm)],[d13,d5]) ).
cnf(d15,plain,
sK27(sK63) = sK27(sK63),
inference(resolution,[status(thm)],[c_54,d14]) ).
cnf(d16,plain,
$false,
inference(resolution,[status(thm)],[d15,d12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : GEO085+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.06 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.41 % Computer : n005.cluster.edu
% 0.08/0.41 % Model : x86_64 x86_64
% 0.08/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.41 % Memory : 8046.5625MB
% 0.08/0.41 % OS : Linux 6.8.0-71-generic
% 0.08/0.41 % CPULimit : 300
% 0.08/0.41 % WCLimit : 300
% 0.08/0.41 % DateTime : Fri Sep 25 12:41:04 UTC 2026
% 0.08/0.41 % CPUTime :
% 0.08/0.41 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 13.02/3.37 % SZS status Theorem for theBenchmark.p
% 13.02/3.37 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------