%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : GEO528+1 : TPTP v9.3.1. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n007.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 07:15:20 AM UTC 2026
% Result : Theorem 137.40s 34.29s
% Output : CNFRefutation 137.40s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 8
% Syntax : Number of formulae : 37 ( 13 unt; 0 def)
% Number of atoms : 101 ( 36 equ)
% Maximal formula atoms : 14 ( 2 avg)
% Number of connectives : 104 ( 40 ~; 57 |; 7 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-4 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-4 aty)
% Number of variables : 58 ( 0 sgn 30 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(aSatz8_22,axiom,
! [X0,X1] : 's$um'(X0,midpoint(X0,X1),X1) ).
fof(aSatz10_2a,axiom,
! [X0,X1,X2] :
( ( perp(X0,X1,X2,reflect(X0,X1,X2))
| X2 = reflect(X0,X1,X2)
| X0 = X1 )
& ( 's$ucol'(X0,X1,midpoint(X2,reflect(X0,X1,X2)))
| X0 = X1 ) ) ).
fof(aSatz10_5,axiom,
! [X0,X1,X2] :
( reflect(X0,X1,reflect(X0,X1,X2)) = X2
| X0 = X1 ) ).
fof(aSatz10_8a,axiom,
! [X0,X1,X2] :
( 's$ucol'(X0,X1,X2)
| reflect(X0,X1,X2) != X2
| X0 = X1 ) ).
fof(aSatz10_8b,axiom,
! [X0,X1,X2] :
( reflect(X0,X1,X2) = X2
| ~ 's$ucol'(X0,X1,X2)
| X0 = X1 ) ).
fof(d_Defn7_1,axiom,
! [X0,X1,X2] :
( ( 's$um'(X0,X1,X2)
| ~ 's$ue'(X1,X0,X1,X2)
| ~ 's$ut'(X0,X1,X2) )
& ( 's$ue'(X1,X0,X1,X2)
| ~ 's$um'(X0,X1,X2) )
& ( 's$ut'(X0,X1,X2)
| ~ 's$um'(X0,X1,X2) ) ) ).
fof(d_Defn9_1,axiom,
! [X0,X1,X2,X3,X4] :
( ( 's$ucol'(X0,X1,il(X2,X3,X0,X1))
| ~ opposite(X2,X0,X1,X3) )
& ( 's$ut'(X2,il(X2,X3,X0,X1),X3)
| ~ opposite(X2,X0,X1,X3) )
& ( ~ 's$ucol'(X0,X1,X3)
| ~ opposite(X2,X0,X1,X3) )
& ( ~ 's$ucol'(X0,X1,X2)
| ~ opposite(X2,X0,X1,X3) )
& ( opposite(X2,X0,X1,X3)
| ~ 's$ucol'(X0,X1,X4)
| ~ 's$ut'(X2,X4,X3)
| 's$ucol'(X0,X1,X3)
| 's$ucol'(X0,X1,X2)
| X0 = X1 ) ) ).
fof(aSatz10_14,conjecture,
! [X0,X1,X2,X3] :
( opposite(X2,X0,X1,X3)
| 's$ucol'(X0,X1,X2)
| reflect(X0,X1,X2) != X3
| X0 = X1 ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0,X1,X2,X3] :
( opposite(X2,X0,X1,X3)
| 's$ucol'(X0,X1,X2)
| reflect(X0,X1,X2) != X3
| X0 = X1 ),
inference(negate_conjecture,[status(cth)],[aSatz10_14]) ).
cnf(c161,plain,
's$um'(X0,midpoint(X0,X1),X1),
inference(clausification,[status(esa)],[aSatz8_22]) ).
cnf(c200,plain,
( 's$ucol'(X0,X1,midpoint(X2,reflect(X0,X1,X2)))
| X0 = X1 ),
inference(clausification,[status(esa)],[aSatz10_2a]) ).
cnf(c205,plain,
( reflect(X0,X1,reflect(X0,X1,X2)) = X2
| X0 = X1 ),
inference(clausification,[status(esa)],[aSatz10_5]) ).
cnf(c208,plain,
( 's$ucol'(X0,X1,X2)
| reflect(X0,X1,X2) != X2
| X0 = X1 ),
inference(clausification,[status(esa)],[aSatz10_8a]) ).
cnf(c209,plain,
( reflect(X0,X1,X2) = X2
| ~ 's$ucol'(X0,X1,X2)
| X0 = X1 ),
inference(clausification,[status(esa)],[aSatz10_8b]) ).
cnf(c252,plain,
( 's$ut'(X0,X1,X2)
| ~ 's$um'(X0,X1,X2) ),
inference(clausification,[status(esa)],[d_Defn7_1]) ).
cnf(c274,plain,
( opposite(X3,X0,X1,X2)
| ~ 's$ucol'(X0,X1,X4)
| X0 = X1
| ~ 's$ut'(X3,X4,X2)
| 's$ucol'(X0,X1,X3)
| 's$ucol'(X0,X1,X2) ),
inference(clausification,[status(esa)],[d_Defn9_1]) ).
cnf(c303,plain,
sK896 != sK897,
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c304,plain,
reflect(sK896,sK897,sK898) = sK899,
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c305,plain,
~ 's$ucol'(sK896,sK897,sK898),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c306,plain,
~ opposite(sK898,sK896,sK897,sK899),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( sK896 = sK897
| 's$ucol'(sK896,sK897,midpoint(sK898,sK899)) ),
inference(superposition,[status(thm)],[c304,c200]) ).
cnf(d1,plain,
's$ucol'(sK896,sK897,midpoint(sK898,sK899)),
inference(resolution,[status(thm)],[c303,d0]) ).
cnf(d2,plain,
( 's$ucol'(sK896,sK897,sK898)
| ~ 's$ucol'(sK896,sK897,X0)
| 's$ucol'(sK896,sK897,sK899)
| ~ 's$ut'(sK898,X0,sK899)
| sK896 = sK897 ),
inference(resolution,[status(thm)],[c274,c306]) ).
cnf(d3,plain,
( 's$ucol'(sK896,sK897,sK899)
| 's$ucol'(sK896,sK897,sK898)
| ~ 's$ucol'(sK896,sK897,X0)
| ~ 's$ut'(sK898,X0,sK899) ),
inference(resolution,[status(thm)],[c303,d2]) ).
cnf(d4,plain,
( 's$ucol'(sK896,sK897,sK899)
| ~ 's$ucol'(sK896,sK897,X0)
| ~ 's$ut'(sK898,X0,sK899) ),
inference(resolution,[status(thm)],[c305,d3]) ).
cnf(d5,plain,
( sK896 = sK897
| reflect(sK896,sK897,sK899) = sK898 ),
inference(superposition,[status(thm)],[c304,c205]) ).
cnf(d6,plain,
reflect(sK896,sK897,sK899) = sK898,
inference(resolution,[status(thm)],[c303,d5]) ).
cnf(d7,plain,
( ~ 's$ucol'(sK896,sK897,sK899)
| sK896 = sK897
| sK899 = sK898 ),
inference(superposition,[status(thm)],[c209,d6]) ).
cnf(d8,plain,
( ~ 's$ucol'(sK896,sK897,sK899)
| sK899 = sK898 ),
inference(resolution,[status(thm)],[c303,d7]) ).
cnf(d9,plain,
( 's$ucol'(sK896,sK897,sK898)
| sK896 = sK897
| sK899 != sK898 ),
inference(superposition,[status(thm)],[c304,c208]) ).
cnf(d10,plain,
( 's$ucol'(sK896,sK897,sK898)
| sK899 != sK898 ),
inference(resolution,[status(thm)],[c303,d9]) ).
cnf(d11,plain,
sK899 != sK898,
inference(resolution,[status(thm)],[c305,d10]) ).
cnf(d12,plain,
~ 's$ucol'(sK896,sK897,sK899),
inference(resolution,[status(thm)],[d11,d8]) ).
cnf(d13,plain,
( ~ 's$ucol'(sK896,sK897,X0)
| ~ 's$ut'(sK898,X0,sK899) ),
inference(resolution,[status(thm)],[d12,d4]) ).
cnf(d14,plain,
~ 's$ut'(sK898,midpoint(sK898,sK899),sK899),
inference(resolution,[status(thm)],[d13,d1]) ).
cnf(d15,plain,
's$ut'(X0,midpoint(X0,X1),X1),
inference(resolution,[status(thm)],[c252,c161]) ).
cnf(d16,plain,
$false,
inference(resolution,[status(thm)],[d15,d14]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO528+1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.03 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.34 % Computer : n007.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.08/0.34 % CPULimit : 300
% 0.08/0.34 % WCLimit : 300
% 0.08/0.34 % DateTime : Fri Sep 25 13:37:08 UTC 2026
% 0.08/0.34 % CPUTime :
% 0.08/0.34 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 137.40/34.29 % SZS status Theorem for theBenchmark.p
% 137.40/34.29 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------