%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : GEO504+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 : n009.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 42.97s 6.52s
% Output : CNFRefutation 42.97s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 13
% Syntax : Number of formulae : 52 ( 21 unt; 0 def)
% Number of atoms : 100 ( 25 equ)
% Maximal formula atoms : 7 ( 1 avg)
% Number of connectives : 85 ( 37 ~; 44 |; 4 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-4 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-4 aty)
% Number of variables : 124 ( 2 sgn 48 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(aSatz2_2,axiom,
! [X0,X1,X2,X3] :
( 's$ue'(X2,X3,X0,X1)
| ~ 's$ue'(X0,X1,X2,X3) ) ).
fof(aSatz2_4,axiom,
! [X0,X1,X2,X3] :
( 's$ue'(X1,X0,X2,X3)
| ~ 's$ue'(X0,X1,X2,X3) ) ).
fof(aSatz2_12,axiom,
! [X0,X1,X2,X3,X4] :
( X2 = ext(X0,X1,X3,X4)
| ~ 's$ue'(X1,X2,X3,X4)
| ~ 's$ut'(X0,X1,X2)
| X0 = X1 ) ).
fof(aSatz2_13,axiom,
! [X0,X1,X2] :
( X0 = X1
| ~ 's$ue'(X0,X1,X2,X2) ) ).
fof(aSatz7_4a,axiom,
! [X0,X1] : 's$um'(X0,X1,s(X1,X0)) ).
fof(aSatz7_6,axiom,
! [X0,X1,X2] :
( X2 = s(X1,X0)
| ~ 's$um'(X0,X1,X2) ) ).
fof(aSatz7_7,axiom,
! [X0,X1] : s(X0,s(X0,X1)) = X1 ).
fof(aSatz7_13,axiom,
! [X0,X1,X2] : 's$ue'(X0,X1,s(X2,X0),s(X2,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$um'(X0,X1,X2) ) ) ).
fof(d_Defn8_1,axiom,
! [X0,X1,X2] :
( ( ~ 's$ue'(X0,X2,X0,s(X1,X2))
| 's$ur'(X0,X1,X2) )
& ( 's$ue'(X0,X2,X0,s(X1,X2))
| ~ 's$ur'(X0,X1,X2) ) ) ).
fof(aA2,axiom,
! [X0,X1,X2,X3,X4,X5] :
( 's$ue'(X2,X3,X4,X5)
| ~ 's$ue'(X0,X1,X4,X5)
| ~ 's$ue'(X0,X1,X2,X3) ) ).
fof(aA4,axiom,
! [X0,X1,X2,X3] :
( 's$ue'(X1,ext(X0,X1,X2,X3),X2,X3)
& 's$ut'(X0,X1,ext(X0,X1,X2,X3)) ) ).
fof(aSatz8_2,conjecture,
! [X0,X1,X2] :
( 's$ur'(X2,X1,X0)
| ~ 's$ur'(X0,X1,X2) ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0,X1,X2] :
( 's$ur'(X2,X1,X0)
| ~ 's$ur'(X0,X1,X2) ),
inference(negate_conjecture,[status(cth)],[aSatz8_2]) ).
cnf(c1,plain,
( 's$ue'(X2,X3,X0,X1)
| ~ 's$ue'(X0,X1,X2,X3) ),
inference(clausification,[status(esa)],[aSatz2_2]) ).
cnf(c3,plain,
( 's$ue'(X1,X0,X2,X3)
| ~ 's$ue'(X0,X1,X2,X3) ),
inference(clausification,[status(esa)],[aSatz2_4]) ).
cnf(c7,plain,
( X2 = ext(X0,X1,X3,X4)
| ~ 's$ue'(X1,X2,X3,X4)
| ~ 's$ut'(X0,X1,X2)
| X0 = X1 ),
inference(clausification,[status(esa)],[aSatz2_12]) ).
cnf(c8,plain,
( X0 = X1
| ~ 's$ue'(X0,X1,X2,X2) ),
inference(clausification,[status(esa)],[aSatz2_13]) ).
cnf(c97,plain,
's$um'(X0,X1,s(X1,X0)),
inference(clausification,[status(esa)],[aSatz7_4a]) ).
cnf(c99,plain,
( X2 = s(X1,X0)
| ~ 's$um'(X0,X1,X2) ),
inference(clausification,[status(esa)],[aSatz7_6]) ).
cnf(c100,plain,
s(X0,s(X0,X1)) = X1,
inference(clausification,[status(esa)],[aSatz7_7]) ).
cnf(c105,plain,
's$ue'(X0,X1,s(X2,X0),s(X2,X1)),
inference(clausification,[status(esa)],[aSatz7_13]) ).
cnf(c155,plain,
( 's$ut'(X0,X1,X2)
| ~ 's$um'(X0,X1,X2) ),
inference(clausification,[status(esa)],[d_Defn7_1]) ).
cnf(c156,plain,
( 's$ue'(X1,X0,X1,X2)
| ~ 's$um'(X0,X1,X2) ),
inference(clausification,[status(esa)],[d_Defn7_1]) ).
cnf(c165,plain,
( 's$ue'(X0,X2,X0,s(X1,X2))
| ~ 's$ur'(X0,X1,X2) ),
inference(clausification,[status(esa)],[d_Defn8_1]) ).
cnf(c166,plain,
( ~ 's$ue'(X0,X2,X0,s(X1,X2))
| 's$ur'(X0,X1,X2) ),
inference(clausification,[status(esa)],[d_Defn8_1]) ).
cnf(c178,plain,
( 's$ue'(X2,X3,X4,X5)
| ~ 's$ue'(X0,X1,X4,X5)
| ~ 's$ue'(X0,X1,X2,X3) ),
inference(clausification,[status(esa)],[aA2]) ).
cnf(c181,plain,
's$ue'(X0,ext(X1,X0,X2,X3),X2,X3),
inference(clausification,[status(esa)],[aA4]) ).
cnf(c189,plain,
's$ur'(sK513,sK514,sK515),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c190,plain,
~ 's$ur'(sK515,sK514,sK513),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( 's$ue'(X0,X1,X1,X2)
| ~ 's$um'(X0,X1,X2) ),
inference(resolution,[status(thm)],[c156,c3]) ).
cnf(d1,plain,
( X0 = X1
| ~ 's$um'(X0,X1,X1) ),
inference(resolution,[status(thm)],[d0,c8]) ).
cnf(d2,plain,
's$ue'(X0,X1,s(X2,X1),s(X2,X0)),
inference(resolution,[status(thm)],[c105,c3]) ).
cnf(d3,plain,
's$um'(s(X0,X1),X0,X1),
inference(superposition,[status(thm)],[c100,c97]) ).
cnf(d4,plain,
X0 = s(X1,s(X1,X0)),
inference(resolution,[status(thm)],[c99,d3]) ).
cnf(d5,plain,
's$ue'(X2,s(X0,X1),X1,s(X0,X2)),
inference(superposition,[status(thm)],[d4,d2]) ).
cnf(d6,plain,
's$ue'(X0,X1,X2,ext(X3,X2,X0,X1)),
inference(resolution,[status(thm)],[c181,c1]) ).
cnf(d7,plain,
's$ut'(s(X0,X1),X0,X1),
inference(resolution,[status(thm)],[c155,d3]) ).
cnf(d8,plain,
( ~ 's$ut'(X3,X0,X2)
| X2 = ext(X3,X0,X0,s(X1,X2))
| X3 = X0
| ~ 's$ur'(X0,X1,X2) ),
inference(resolution,[status(thm)],[c165,c7]) ).
cnf(d9,plain,
( ~ 's$ut'(X0,sK513,sK515)
| sK515 = ext(X0,sK513,sK513,s(sK514,sK515))
| X0 = sK513 ),
inference(resolution,[status(thm)],[d8,c189]) ).
cnf(d10,plain,
( sK515 = ext(s(sK513,sK515),sK513,sK513,s(sK514,sK515))
| s(sK513,sK515) = sK513 ),
inference(resolution,[status(thm)],[d9,d7]) ).
cnf(d11,plain,
( s(sK513,sK515) = sK513
| 's$ue'(sK513,s(sK514,sK515),sK513,sK515) ),
inference(superposition,[status(thm)],[d10,d6]) ).
cnf(d12,plain,
( ~ 's$ue'(sK513,s(sK514,sK515),X0,X1)
| 's$ue'(sK513,sK515,X0,X1)
| s(sK513,sK515) = sK513 ),
inference(resolution,[status(thm)],[d11,c178]) ).
cnf(d13,plain,
( 's$ue'(sK513,sK515,sK515,s(sK514,sK513))
| s(sK513,sK515) = sK513 ),
inference(resolution,[status(thm)],[d12,d5]) ).
cnf(d14,plain,
( 's$ue'(sK515,sK513,sK515,s(sK514,sK513))
| s(sK513,sK515) = sK513 ),
inference(resolution,[status(thm)],[d13,c3]) ).
cnf(d15,plain,
( 's$ur'(sK515,sK514,sK513)
| s(sK513,sK515) = sK513 ),
inference(resolution,[status(thm)],[d14,c166]) ).
cnf(d16,plain,
s(sK513,sK515) = sK513,
inference(resolution,[status(thm)],[c190,d15]) ).
cnf(d17,plain,
's$um'(sK515,sK513,sK513),
inference(superposition,[status(thm)],[d16,c97]) ).
cnf(d18,plain,
sK515 = sK513,
inference(resolution,[status(thm)],[d17,d1]) ).
cnf(d19,plain,
's$ur'(sK513,sK514,sK513),
inference(demodulation,[status(thm)],[c189,d18]) ).
cnf(d20,plain,
~ 's$ur'(sK513,sK514,sK513),
inference(demodulation,[status(thm)],[c190,d18]) ).
cnf(d21,plain,
$false,
inference(resolution,[status(thm)],[d20,d19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO504+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
% 0.09/0.36 % Computer : n009.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Fri Sep 25 13:36:59 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 42.97/6.52 % SZS status Theorem for theBenchmark.p
% 42.97/6.52 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------