%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : GEO507+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 : 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 07:15:18 AM UTC 2026
% Result : Theorem 32.11s 10.73s
% Output : CNFRefutation 32.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 8
% Syntax : Number of formulae : 34 ( 16 unt; 0 def)
% Number of atoms : 104 ( 17 equ)
% Maximal formula atoms : 30 ( 3 avg)
% Number of connectives : 127 ( 57 ~; 54 |; 16 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-5 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-5 aty)
% Number of variables : 87 ( 11 sgn 37 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(aSatz4_11a,axiom,
! [X0,X1,X2] :
( 's$ucol'(X1,X2,X0)
| ~ 's$ucol'(X0,X1,X2) ) ).
fof(aSatz4_12b,axiom,
! [X0,X1] : 's$ucol'(X0,X1,X0) ).
fof(aSatz8_8,axiom,
! [X0,X1] :
( X0 = X1
| ~ 's$ur'(X0,X1,X0) ) ).
fof(aSatz8_12a,axiom,
! [X0,X1,X2,X3,X4] :
( perpAt(X3,X4,X2,X0,X1)
| ~ perpAt(X0,X1,X2,X3,X4) ) ).
fof(aSatz8_13a,axiom,
! [X0,X1,X2,X3,X4] :
( ( 's$ur'(f813(X0,X1,X3,X4,X2),X2,g813(X0,X1,X3,X4,X2))
| ~ perpAt(X0,X1,X2,X3,X4) )
& ( X2 != g813(X0,X1,X3,X4,X2)
| ~ perpAt(X0,X1,X2,X3,X4) )
& ( X2 != f813(X0,X1,X3,X4,X2)
| ~ perpAt(X0,X1,X2,X3,X4) )
& ( 's$ucol'(X3,X4,g813(X0,X1,X3,X4,X2))
| ~ perpAt(X0,X1,X2,X3,X4) )
& ( 's$ucol'(X0,X1,f813(X0,X1,X3,X4,X2))
| ~ perpAt(X0,X1,X2,X3,X4) )
& ( 's$ucol'(X0,X1,X2)
| ~ perpAt(X0,X1,X2,X3,X4) )
& ( 's$ucol'(X3,X4,X2)
| ~ perpAt(X0,X1,X2,X3,X4) )
& ( X3 != X4
| ~ perpAt(X0,X1,X2,X3,X4) )
& ( X0 != X1
| ~ perpAt(X0,X1,X2,X3,X4) ) ) ).
fof(d_Defn8_11a,axiom,
! [X0,X1,X2,X3,X4,X5,X6] :
( ( ~ 's$ur'(f811(X0,X1,X3,X4,X2),X2,g811(X0,X1,X3,X4,X2))
| ~ 's$ucol'(X3,X4,X2)
| ~ 's$ucol'(X0,X1,X2)
| X3 = X4
| X0 = X1
| perpAt(X0,X1,X2,X3,X4) )
& ( 's$ucol'(X3,X4,g811(X0,X1,X3,X4,X2))
| ~ 's$ucol'(X3,X4,X2)
| ~ 's$ucol'(X0,X1,X2)
| X3 = X4
| X0 = X1
| perpAt(X0,X1,X2,X3,X4) )
& ( 's$ucol'(X0,X1,f811(X0,X1,X3,X4,X2))
| ~ 's$ucol'(X3,X4,X2)
| ~ 's$ucol'(X0,X1,X2)
| X3 = X4
| X0 = X1
| perpAt(X0,X1,X2,X3,X4) )
& ( 's$ur'(X5,X2,X6)
| ~ 's$ucol'(X3,X4,X6)
| ~ 's$ucol'(X0,X1,X5)
| ~ perpAt(X0,X1,X2,X3,X4) )
& ( X3 != X4
| ~ perpAt(X0,X1,X2,X3,X4) )
& ( X0 != X1
| ~ perpAt(X0,X1,X2,X3,X4) )
& ( 's$ucol'(X3,X4,X2)
| ~ perpAt(X0,X1,X2,X3,X4) )
& ( 's$ucol'(X0,X1,X2)
| ~ perpAt(X0,X1,X2,X3,X4) ) ) ).
fof(d_Defn8_11b,axiom,
! [X0,X1,X2,X3,X4] :
( ( ~ perpAt(X0,X1,X4,X2,X3)
| perp(X0,X1,X2,X3) )
& ( perpAt(X0,X1,il(X0,X1,X2,X3),X2,X3)
| ~ perp(X0,X1,X2,X3) ) ) ).
fof(aSatz8_14a,conjecture,
! [X0,X1,X2,X3] :
( ~ 's$ucol'(X0,X1,X3)
| ~ 's$ucol'(X0,X1,X2)
| ~ perp(X0,X1,X2,X3) ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0,X1,X2,X3] :
( ~ 's$ucol'(X0,X1,X3)
| ~ 's$ucol'(X0,X1,X2)
| ~ perp(X0,X1,X2,X3) ),
inference(negate_conjecture,[status(cth)],[aSatz8_14a]) ).
cnf(c33,plain,
( 's$ucol'(X1,X2,X0)
| ~ 's$ucol'(X0,X1,X2) ),
inference(clausification,[status(esa)],[aSatz4_11a]) ).
cnf(c39,plain,
's$ucol'(X0,X1,X0),
inference(clausification,[status(esa)],[aSatz4_12b]) ).
cnf(c125,plain,
( X1 = X0
| ~ 's$ur'(X0,X1,X0) ),
inference(clausification,[status(esa)],[aSatz8_8]) ).
cnf(c128,plain,
( perpAt(X3,X4,X2,X0,X1)
| ~ perpAt(X0,X1,X2,X3,X4) ),
inference(clausification,[status(esa)],[aSatz8_12a]) ).
cnf(c130,plain,
( X1 != X0
| ~ perpAt(X0,X1,X2,X3,X4) ),
inference(clausification,[status(esa)],[aSatz8_13a]) ).
cnf(c190,plain,
( ~ 's$ucol'(X0,X1,X6)
| 's$ur'(X6,X2,X5)
| ~ 's$ucol'(X3,X4,X5)
| ~ perpAt(X0,X1,X2,X3,X4) ),
inference(clausification,[status(esa)],[d_Defn8_11a]) ).
cnf(c196,plain,
( perpAt(X0,X1,il(X0,X1,X2,X3),X2,X3)
| ~ perp(X0,X1,X2,X3) ),
inference(clausification,[status(esa)],[d_Defn8_11b]) ).
cnf(c210,plain,
perp(sK564,sK565,sK566,sK567),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c211,plain,
's$ucol'(sK564,sK565,sK567),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c212,plain,
's$ucol'(sK564,sK565,sK566),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
perpAt(sK564,sK565,il(sK564,sK565,sK566,sK567),sK566,sK567),
inference(resolution,[status(thm)],[c196,c210]) ).
cnf(d1,plain,
( ~ perpAt(X0,X1,X3,X4,X5)
| 's$ur'(X2,X3,X4)
| ~ 's$ucol'(X0,X1,X2) ),
inference(resolution,[status(thm)],[c190,c39]) ).
cnf(d2,plain,
( ~ perpAt(sK564,sK565,X0,X1,X2)
| 's$ur'(sK566,X0,X1) ),
inference(resolution,[status(thm)],[d1,c212]) ).
cnf(d3,plain,
's$ur'(sK566,il(sK564,sK565,sK566,sK567),sK566),
inference(resolution,[status(thm)],[d2,d0]) ).
cnf(d4,plain,
il(sK564,sK565,sK566,sK567) = sK566,
inference(resolution,[status(thm)],[d3,c125]) ).
cnf(d5,plain,
perpAt(sK566,sK567,il(sK564,sK565,sK566,sK567),sK564,sK565),
inference(resolution,[status(thm)],[d0,c128]) ).
cnf(d6,plain,
perpAt(sK566,sK567,sK566,sK564,sK565),
inference(demodulation,[status(thm)],[d5,d4]) ).
cnf(d7,plain,
's$ucol'(X0,X1,X1),
inference(resolution,[status(thm)],[c33,c39]) ).
cnf(d8,plain,
( ~ perpAt(X0,X1,X3,sK564,sK565)
| 's$ur'(X2,X3,sK567)
| ~ 's$ucol'(X0,X1,X2) ),
inference(resolution,[status(thm)],[c190,c211]) ).
cnf(d9,plain,
( ~ perpAt(X2,X0,X1,sK564,sK565)
| 's$ur'(X0,X1,sK567) ),
inference(resolution,[status(thm)],[d8,d7]) ).
cnf(d10,plain,
's$ur'(sK567,sK566,sK567),
inference(resolution,[status(thm)],[d9,d6]) ).
cnf(d11,plain,
sK566 = sK567,
inference(resolution,[status(thm)],[d10,c125]) ).
cnf(d12,plain,
perpAt(sK566,sK566,sK566,sK564,sK565),
inference(demodulation,[status(thm)],[d6,d11]) ).
cnf(d13,plain,
~ perpAt(X0,X0,X1,X2,X3),
inference(equality_resolution,[status(thm)],[c130]) ).
cnf(d14,plain,
$false,
inference(resolution,[status(thm)],[d13,d12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO507+1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.37 % Computer : n026.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Fri Sep 25 13:39:40 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 32.11/10.73 % SZS status Theorem for theBenchmark.p
% 32.11/10.73 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------