%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : GEO523+1 : TPTP v9.3.1. Released v7.0.0.
% 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 07:15:19 AM UTC 2026
% Result : Theorem 66.10s 17.81s
% Output : CNFRefutation 66.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 9
% Syntax : Number of formulae : 41 ( 18 unt; 0 def)
% Number of atoms : 83 ( 43 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 68 ( 26 ~; 40 |; 2 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-4 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-3 aty)
% Number of variables : 72 ( 0 sgn 33 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(aSatz7_2,axiom,
! [X0,X1,X2] :
( 's$um'(X2,X1,X0)
| ~ 's$um'(X0,X1,X2) ) ).
fof(aSatz7_4a,axiom,
! [X0,X1] : 's$um'(X0,X1,s(X1,X0)) ).
fof(aSatz7_6,axiom,
! [X0,X1,X2] :
( X2 = s(X1,X0)
| ~ 's$um'(X0,X1,X2) ) ).
fof(aSatz7_17,axiom,
! [X0,X1,X2,X3] :
( X1 = X3
| ~ 's$um'(X0,X3,X2)
| ~ 's$um'(X0,X1,X2) ) ).
fof(aSatz8_22,axiom,
! [X0,X1] : 's$um'(X0,midpoint(X0,X1),X1) ).
fof(aExtPerp4,axiom,
! [X0,X1,X2,X3] :
( perp(X0,X1,X3,X2)
| ~ perp(X0,X1,X2,X3) ) ).
fof(aSatz10_2a,axiom,
! [X0,X1,X2] :
( ( perp(X0,X1,X2,reflect(X0,X1,X2))
| X2 = reflect(X0,X1,X2)
| X0 = X1 )
& ( 's$ucol'(X0,X1,midpoint(X2,reflect(X0,X1,X2)))
| X0 = X1 ) ) ).
fof(aSatz10_2b,axiom,
! [X0,X1,X2,X3] :
( ( X3 = reflect(X0,X1,X2)
| X2 != X3
| ~ 's$ucol'(X0,X1,midpoint(X2,X3))
| X0 = X1 )
& ( X3 = reflect(X0,X1,X2)
| ~ perp(X0,X1,X2,X3)
| ~ 's$ucol'(X0,X1,midpoint(X2,X3))
| X0 = X1 ) ) ).
fof(aSatz10_4,conjecture,
! [X0,X1,X2,X3] :
( reflect(X0,X1,X3) = X2
| reflect(X0,X1,X2) != X3
| X0 = X1 ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0,X1,X2,X3] :
( reflect(X0,X1,X3) = X2
| reflect(X0,X1,X2) != X3
| X0 = X1 ),
inference(negate_conjecture,[status(cth)],[aSatz10_4]) ).
cnf(c94,plain,
( 's$um'(X2,X1,X0)
| ~ 's$um'(X0,X1,X2) ),
inference(clausification,[status(esa)],[aSatz7_2]) ).
cnf(c97,plain,
's$um'(X0,X1,s(X1,X0)),
inference(clausification,[status(esa)],[aSatz7_4a]) ).
cnf(c99,plain,
( s(X1,X0) = X2
| ~ 's$um'(X0,X1,X2) ),
inference(clausification,[status(esa)],[aSatz7_6]) ).
cnf(c110,plain,
( ~ 's$um'(X0,X3,X2)
| X3 = X1
| ~ 's$um'(X0,X1,X2) ),
inference(clausification,[status(esa)],[aSatz7_17]) ).
cnf(c161,plain,
's$um'(X0,midpoint(X0,X1),X1),
inference(clausification,[status(esa)],[aSatz8_22]) ).
cnf(c169,plain,
( perp(X0,X1,X3,X2)
| ~ perp(X0,X1,X2,X3) ),
inference(clausification,[status(esa)],[aExtPerp4]) ).
cnf(c200,plain,
( 's$ucol'(X1,X0,midpoint(X2,reflect(X1,X0,X2)))
| X0 = X1 ),
inference(clausification,[status(esa)],[aSatz10_2a]) ).
cnf(c201,plain,
( reflect(X1,X0,X2) = X2
| perp(X1,X0,X2,reflect(X1,X0,X2))
| X0 = X1 ),
inference(clausification,[status(esa)],[aSatz10_2a]) ).
cnf(c202,plain,
( ~ 's$ucol'(X1,X0,midpoint(X2,X3))
| reflect(X1,X0,X2) = X3
| ~ perp(X1,X0,X2,X3)
| X0 = X1 ),
inference(clausification,[status(esa)],[aSatz10_2b]) ).
cnf(c291,plain,
sK848 != sK847,
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c292,plain,
reflect(sK847,sK848,sK850) != sK849,
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c293,plain,
reflect(sK847,sK848,sK849) = sK850,
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( reflect(sK847,sK848,sK849) = sK849
| sK848 = sK847
| perp(sK847,sK848,sK849,sK850) ),
inference(superposition,[status(thm)],[c293,c201]) ).
cnf(d1,plain,
( perp(sK847,sK848,sK849,sK850)
| sK848 = sK847
| sK850 = sK849 ),
inference(demodulation,[status(thm)],[d0,c293]) ).
cnf(d2,plain,
( perp(sK847,sK848,sK849,sK850)
| sK850 = sK849 ),
inference(resolution,[status(thm)],[c291,d1]) ).
cnf(d3,plain,
( perp(sK847,sK848,sK850,sK849)
| sK850 = sK849 ),
inference(resolution,[status(thm)],[d2,c169]) ).
cnf(d4,plain,
's$um'(X0,midpoint(X1,X0),X1),
inference(resolution,[status(thm)],[c94,c161]) ).
cnf(d5,plain,
( ~ 's$um'(X2,X1,s(X0,X2))
| X0 = X1 ),
inference(resolution,[status(thm)],[c110,c97]) ).
cnf(d6,plain,
X0 = midpoint(s(X0,X1),X1),
inference(resolution,[status(thm)],[d5,d4]) ).
cnf(d7,plain,
s(midpoint(X0,X1),X0) = X1,
inference(resolution,[status(thm)],[c99,c161]) ).
cnf(d8,plain,
midpoint(X0,X1) = midpoint(X1,X0),
inference(superposition,[status(thm)],[d7,d6]) ).
cnf(d9,plain,
( sK848 = sK847
| 's$ucol'(sK847,sK848,midpoint(sK849,sK850)) ),
inference(superposition,[status(thm)],[c293,c200]) ).
cnf(d10,plain,
's$ucol'(sK847,sK848,midpoint(sK849,sK850)),
inference(resolution,[status(thm)],[c291,d9]) ).
cnf(d11,plain,
's$ucol'(sK847,sK848,midpoint(sK850,sK849)),
inference(demodulation,[status(thm)],[d10,d8]) ).
cnf(d12,plain,
( ~ perp(sK847,sK848,sK850,sK849)
| reflect(sK847,sK848,sK850) = sK849
| sK848 = sK847 ),
inference(resolution,[status(thm)],[d11,c202]) ).
cnf(d13,plain,
( ~ perp(sK847,sK848,sK850,sK849)
| reflect(sK847,sK848,sK850) = sK849 ),
inference(resolution,[status(thm)],[c291,d12]) ).
cnf(d14,plain,
~ perp(sK847,sK848,sK850,sK849),
inference(resolution,[status(thm)],[c292,d13]) ).
cnf(d15,plain,
sK850 = sK849,
inference(resolution,[status(thm)],[d14,d3]) ).
cnf(d16,plain,
reflect(sK847,sK848,sK850) = sK850,
inference(demodulation,[status(thm)],[c293,d15]) ).
cnf(d17,plain,
reflect(sK847,sK848,sK850) != sK850,
inference(demodulation,[status(thm)],[c292,d15]) ).
cnf(d18,plain,
$false,
inference(resolution,[status(thm)],[d17,d16]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO523+1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n020.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Fri Sep 25 13:39:33 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 66.10/17.81 % SZS status Theorem for theBenchmark.p
% 66.10/17.81 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------