%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : GEO083+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 07:14:07 AM UTC 2026
% Result : Theorem 26.00s 5.64s
% Output : CNFRefutation 26.00s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 3
% Syntax : Number of formulae : 26 ( 3 unt; 0 def)
% Number of atoms : 64 ( 4 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 57 ( 19 ~; 28 |; 4 &)
% ( 3 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 62 ( 5 sgn 15 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(part_of_defn,axiom,
! [X0,X1] :
( 'part$uof'(X1,X0)
<=> ! [X2] :
( 'incident$uc'(X2,X1)
=> 'incident$uc'(X2,X0) ) ) ).
fof(sum_defn,axiom,
! [X0,X1,X2] :
( X0 = sum(X1,X2)
<=> ! [X3] :
( 'incident$uc'(X3,X0)
<=> ( 'incident$uc'(X3,X2)
| 'incident$uc'(X3,X1) ) ) ) ).
fof(corollary_2_6_1,conjecture,
! [X0,X1,X2,X3] :
( ( meet(X3,X0,X2)
& meet(X3,X0,X1)
& 'part$uof'(X1,X2) )
=> 'part$uof'(sum(X0,X1),sum(X0,X2)) ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0,X1,X2,X3] :
( ( meet(X3,X0,X2)
& meet(X3,X0,X1)
& 'part$uof'(X1,X2) )
=> 'part$uof'(sum(X0,X1),sum(X0,X2)) ),
inference(negate_conjecture,[status(cth)],[corollary_2_6_1]) ).
cnf(c_0,plain,
( 'incident$uc'(X2,X1)
| ~ 'incident$uc'(X2,X0)
| ~ 'part$uof'(X0,X1) ),
inference(clausification,[status(esa)],[part_of_defn]) ).
cnf(c_1,plain,
( 'incident$uc'(sK3(X1,X0),X0)
| 'part$uof'(X0,X1) ),
inference(clausification,[status(esa)],[part_of_defn]) ).
cnf(c_2,plain,
( ~ 'incident$uc'(sK3(X1,X0),X1)
| 'part$uof'(X0,X1) ),
inference(clausification,[status(esa)],[part_of_defn]) ).
cnf(c_3,plain,
( 'incident$uc'(X3,X0)
| 'incident$uc'(X3,X1)
| ~ 'incident$uc'(X3,X2)
| sum(X0,X1) != X2 ),
inference(clausification,[status(esa)],[sum_defn]) ).
cnf(c_4,plain,
( ~ 'incident$uc'(X3,X0)
| 'incident$uc'(X3,X2)
| sum(X0,X1) != X2 ),
inference(clausification,[status(esa)],[sum_defn]) ).
cnf(c_5,plain,
( ~ 'incident$uc'(X3,X1)
| 'incident$uc'(X3,X2)
| sum(X0,X1) != X2 ),
inference(clausification,[status(esa)],[sum_defn]) ).
cnf(c_50,plain,
'part$uof'(sK63,sK64),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c_51,plain,
~ 'part$uof'(sum(sK62,sK63),sum(sK62,sK64)),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( ~ 'incident$uc'(X0,X1)
| 'incident$uc'(X0,sum(X1,X2)) ),
inference(equality_resolution,[status(thm)],[c_4]) ).
cnf(d1,plain,
( 'part$uof'(X2,sum(X0,X1))
| ~ 'incident$uc'(sK3(sum(X0,X1),X2),X0) ),
inference(resolution,[status(thm)],[d0,c_2]) ).
cnf(d2,plain,
( ~ 'incident$uc'(X0,sum(X2,X1))
| 'incident$uc'(X0,X2)
| 'incident$uc'(X0,X1) ),
inference(equality_resolution,[status(thm)],[c_3]) ).
cnf(d3,plain,
( 'part$uof'(sum(X1,X2),X0)
| 'incident$uc'(sK3(X0,sum(X1,X2)),X2)
| 'incident$uc'(sK3(X0,sum(X1,X2)),X1) ),
inference(resolution,[status(thm)],[d2,c_1]) ).
cnf(d4,plain,
( ~ 'incident$uc'(X0,sK63)
| 'incident$uc'(X0,sK64) ),
inference(resolution,[status(thm)],[c_0,c_50]) ).
cnf(d5,plain,
( 'incident$uc'(sK3(X0,sK63),sK64)
| 'part$uof'(sK63,X0) ),
inference(resolution,[status(thm)],[c_1,d4]) ).
cnf(d6,plain,
( ~ 'incident$uc'(X0,X2)
| 'incident$uc'(X0,sum(X1,X2)) ),
inference(equality_resolution,[status(thm)],[c_5]) ).
cnf(d7,plain,
( 'part$uof'(X2,sum(X0,X1))
| ~ 'incident$uc'(sK3(sum(X0,X1),X2),X1) ),
inference(resolution,[status(thm)],[d6,c_2]) ).
cnf(d8,plain,
( 'part$uof'(sK63,sum(X0,sK64))
| 'part$uof'(sK63,sum(X0,sK64)) ),
inference(resolution,[status(thm)],[d7,d5]) ).
cnf(d9,plain,
( ~ 'incident$uc'(X0,sK63)
| 'incident$uc'(X0,sum(X1,sK64)) ),
inference(resolution,[status(thm)],[d8,c_0]) ).
cnf(d10,plain,
( 'part$uof'(X1,sum(X0,sK64))
| ~ 'incident$uc'(sK3(sum(X0,sK64),X1),sK63) ),
inference(resolution,[status(thm)],[d9,c_2]) ).
cnf(d11,plain,
( 'part$uof'(sum(X0,sK63),sum(X1,sK64))
| 'incident$uc'(sK3(sum(X1,sK64),sum(X0,sK63)),X0)
| 'part$uof'(sum(X0,sK63),sum(X1,sK64)) ),
inference(resolution,[status(thm)],[d10,d3]) ).
cnf(d12,plain,
( 'part$uof'(sum(X0,sK63),sum(X0,sK64))
| 'part$uof'(sum(X0,sK63),sum(X0,sK64)) ),
inference(resolution,[status(thm)],[d11,d1]) ).
cnf(d13,plain,
$false,
inference(resolution,[status(thm)],[d12,c_51]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO083+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.37 % Computer : n005.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Fri Sep 25 12:40:03 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 26.00/5.64 % SZS status Theorem for theBenchmark.p
% 26.00/5.64 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------