%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : GEO531+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 : n017.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 154.76s 34.73s
% Output : CNFRefutation 154.76s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 16
% Syntax : Number of formulae : 64 ( 25 unt; 0 def)
% Number of atoms : 142 ( 35 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 152 ( 74 ~; 75 |; 3 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-6 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 170 ( 5 sgn 58 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(aSatz2_1,axiom,
! [X0,X1] : 's$ue'(X0,X1,X0,X1) ).
fof(aSatz2_2,axiom,
! [X0,X1,X2,X3] :
( 's$ue'(X2,X3,X0,X1)
| ~ 's$ue'(X0,X1,X2,X3) ) ).
fof(aSatz2_5,axiom,
! [X0,X1,X2,X3] :
( 's$ue'(X0,X1,X3,X2)
| ~ 's$ue'(X0,X1,X2,X3) ) ).
fof(aSatz2_13,axiom,
! [X0,X1,X2] :
( X0 = X1
| ~ 's$ue'(X0,X1,X2,X2) ) ).
fof(aSatz3_1,axiom,
! [X0,X1] : 's$ut'(X0,X1,X1) ).
fof(aNarbouxLemma1,axiom,
! [X0,X1,X2] :
( X2 = X1
| ~ 's$ue'(X0,X2,X0,X1)
| ~ 's$ut'(X0,X1,X2) ) ).
fof(aSatz6_5,axiom,
! [X0,X1] :
( sameside(X0,X1,X0)
| X0 = X1 ) ).
fof(aSatz7_4a,axiom,
! [X0,X1] : 's$um'(X0,X1,s(X1,X0)) ).
fof(aSatz7_6,axiom,
! [X0,X1,X2] :
( X2 = s(X1,X0)
| ~ 's$um'(X0,X1,X2) ) ).
fof(aSatz7_7,axiom,
! [X0,X1] : s(X0,s(X0,X1)) = X1 ).
fof(aSatz7_10b,axiom,
! [X0,X1] :
( X1 != X0
| s(X0,X1) = X1 ) ).
fof(aSatz7_13,axiom,
! [X0,X1,X2] : 's$ue'(X0,X1,s(X2,X0),s(X2,X1)) ).
fof(aSideReflect,axiom,
! [X0,X1,X2,X3] :
( sameside(s(X3,X0),s(X3,X1),s(X3,X2))
| ~ sameside(X0,X1,X2) ) ).
fof(aSatz11_3d,axiom,
! [X0,X1,X2,X3,X4,X5,X6,X7,X8,X9] :
( congruent(X2,X1,X4,X7,X6,X9)
| ~ 's$ue3'(X0,X1,X3,X5,X6,X8)
| ~ sameside(X8,X6,X9)
| ~ sameside(X5,X6,X7)
| ~ sameside(X3,X1,X4)
| ~ sameside(X0,X1,X2) ) ).
fof(d_Defn4_4,axiom,
! [X0,X1,X2,X3,X4,X5] :
( ( 's$ue3'(X0,X1,X2,X3,X4,X5)
| ~ 's$ue'(X1,X2,X4,X5)
| ~ 's$ue'(X0,X2,X3,X5)
| ~ 's$ue'(X0,X1,X3,X4) )
& ( 's$ue'(X1,X2,X4,X5)
| ~ 's$ue3'(X0,X1,X2,X3,X4,X5) )
& ( 's$ue'(X0,X2,X3,X5)
| ~ 's$ue3'(X0,X1,X2,X3,X4,X5) )
& ( 's$ue'(X0,X1,X3,X4)
| ~ 's$ue3'(X0,X1,X2,X3,X4,X5) ) ) ).
fof(aSatz11_6,conjecture,
! [X0,X1,X2] :
( congruent(X0,X1,X2,X0,X1,X2)
| X2 = X1
| X0 = X1 ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0,X1,X2] :
( congruent(X0,X1,X2,X0,X1,X2)
| X2 = X1
| X0 = X1 ),
inference(negate_conjecture,[status(cth)],[aSatz11_6]) ).
cnf(c0,plain,
's$ue'(X0,X1,X0,X1),
inference(clausification,[status(esa)],[aSatz2_1]) ).
cnf(c1,plain,
( 's$ue'(X2,X3,X0,X1)
| ~ 's$ue'(X0,X1,X2,X3) ),
inference(clausification,[status(esa)],[aSatz2_2]) ).
cnf(c4,plain,
( 's$ue'(X0,X1,X3,X2)
| ~ 's$ue'(X0,X1,X2,X3) ),
inference(clausification,[status(esa)],[aSatz2_5]) ).
cnf(c8,plain,
( X0 = X1
| ~ 's$ue'(X0,X1,X2,X2) ),
inference(clausification,[status(esa)],[aSatz2_13]) ).
cnf(c11,plain,
's$ut'(X0,X1,X1),
inference(clausification,[status(esa)],[aSatz3_1]) ).
cnf(c61,plain,
( X2 = X1
| ~ 's$ue'(X0,X2,X0,X1)
| ~ 's$ut'(X0,X1,X2) ),
inference(clausification,[status(esa)],[aNarbouxLemma1]) ).
cnf(c74,plain,
( sameside(X0,X1,X0)
| X0 = X1 ),
inference(clausification,[status(esa)],[aSatz6_5]) ).
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(c104,plain,
( X1 != X0
| s(X0,X1) = X1 ),
inference(clausification,[status(esa)],[aSatz7_10b]) ).
cnf(c105,plain,
's$ue'(X0,X1,s(X2,X0),s(X2,X1)),
inference(clausification,[status(esa)],[aSatz7_13]) ).
cnf(c177,plain,
( sameside(s(X3,X0),s(X3,X1),s(X3,X2))
| ~ sameside(X0,X1,X2) ),
inference(clausification,[status(esa)],[aSideReflect]) ).
cnf(c227,plain,
( ~ sameside(X3,X4,X9)
| ~ sameside(X0,X1,X8)
| congruent(X8,X1,X7,X9,X4,X6)
| ~ sameside(X2,X1,X7)
| ~ sameside(X5,X4,X6)
| ~ 's$ue3'(X0,X1,X2,X3,X4,X5) ),
inference(clausification,[status(esa)],[aSatz11_3d]) ).
cnf(c255,plain,
( 's$ue3'(X0,X1,X4,X2,X3,X5)
| ~ 's$ue'(X1,X4,X3,X5)
| ~ 's$ue'(X0,X4,X2,X5)
| ~ 's$ue'(X0,X1,X2,X3) ),
inference(clausification,[status(esa)],[d_Defn4_4]) ).
cnf(c324,plain,
sK964 != sK965,
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c325,plain,
sK966 != sK965,
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c326,plain,
~ congruent(sK964,sK965,sK966,sK964,sK965,sK966),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
s(X0,X0) = X0,
inference(equality_resolution,[status(thm)],[c104]) ).
cnf(d1,plain,
( ~ 's$um'(X0,X0,X1)
| X1 = X0 ),
inference(superposition,[status(thm)],[c99,d0]) ).
cnf(d2,plain,
's$um'(s(X0,X1),X0,X1),
inference(superposition,[status(thm)],[c100,c97]) ).
cnf(d3,plain,
( ~ sameside(X0,X1,X2)
| sameside(X0,s(X0,X1),s(X0,X2)) ),
inference(superposition,[status(thm)],[d0,c177]) ).
cnf(d4,plain,
's$ue'(X0,X1,X0,s(X0,X1)),
inference(superposition,[status(thm)],[d0,c105]) ).
cnf(d5,plain,
's$ue'(X0,s(X0,X1),X0,X1),
inference(resolution,[status(thm)],[d4,c1]) ).
cnf(d6,plain,
X0 = s(X0,X0),
inference(resolution,[status(thm)],[d5,c8]) ).
cnf(d7,plain,
( ~ sameside(X0,X1,X0)
| sameside(X0,s(X0,X1),X0) ),
inference(superposition,[status(thm)],[d6,d3]) ).
cnf(d8,plain,
's$ue'(X2,s(X0,X1),s(X0,X2),X1),
inference(superposition,[status(thm)],[c100,c105]) ).
cnf(d9,plain,
X0 = s(X1,s(X1,X0)),
inference(resolution,[status(thm)],[d8,c8]) ).
cnf(d10,plain,
( ~ sameside(X0,s(X0,X1),X0)
| sameside(X0,X1,X0) ),
inference(superposition,[status(thm)],[d9,d7]) ).
cnf(d11,plain,
( X0 = s(X0,X1)
| sameside(X0,X1,X0) ),
inference(resolution,[status(thm)],[d10,c74]) ).
cnf(d12,plain,
( sameside(X0,X1,X0)
| 's$um'(X0,X0,X1) ),
inference(superposition,[status(thm)],[d11,d2]) ).
cnf(d13,plain,
( X1 = X0
| sameside(X0,X1,X0) ),
inference(resolution,[status(thm)],[d12,d1]) ).
cnf(d14,plain,
( congruent(X8,X0,X6,X9,X2,X7)
| ~ sameside(X5,X2,X9)
| ~ sameside(X4,X0,X8)
| ~ sameside(X3,X2,X7)
| ~ sameside(X1,X0,X6)
| ~ 's$ue'(X4,X0,X5,X2)
| ~ 's$ue'(X4,X1,X5,X3)
| ~ 's$ue'(X0,X1,X2,X3) ),
inference(resolution,[status(thm)],[c255,c227]) ).
cnf(d15,plain,
( ~ sameside(X1,sK965,sK966)
| ~ sameside(X3,sK965,sK966)
| ~ sameside(X0,sK965,sK964)
| ~ sameside(X2,sK965,sK964)
| ~ 's$ue'(sK965,X1,sK965,X3)
| ~ 's$ue'(X0,sK965,X2,sK965)
| ~ 's$ue'(X0,X1,X2,X3) ),
inference(resolution,[status(thm)],[d14,c326]) ).
cnf(d16,plain,
( ~ sameside(X0,sK965,sK964)
| ~ sameside(X1,sK965,sK966)
| ~ sameside(X2,sK965,sK964)
| ~ sameside(X1,sK965,sK966)
| ~ 's$ue'(X0,sK965,X2,sK965)
| ~ 's$ue'(X0,X1,X2,X1) ),
inference(resolution,[status(thm)],[d15,c0]) ).
cnf(d17,plain,
( ~ sameside(X0,sK965,sK964)
| ~ sameside(X1,sK965,sK966)
| ~ sameside(X0,sK965,sK964)
| ~ 's$ue'(X0,X1,X0,X1) ),
inference(resolution,[status(thm)],[d16,c0]) ).
cnf(d18,plain,
( ~ sameside(X1,sK965,sK964)
| ~ sameside(X0,sK965,sK966) ),
inference(resolution,[status(thm)],[c0,d17]) ).
cnf(d19,plain,
( sK965 = sK966
| ~ sameside(X0,sK965,sK964) ),
inference(resolution,[status(thm)],[d18,d13]) ).
cnf(d20,plain,
( sK964 = sK965
| sK965 = sK966 ),
inference(resolution,[status(thm)],[d19,c74]) ).
cnf(d21,plain,
sK965 = sK966,
inference(resolution,[status(thm)],[c324,d20]) ).
cnf(d22,plain,
sK965 != sK965,
inference(demodulation,[status(thm)],[c325,d21]) ).
cnf(d23,plain,
's$ue'(X0,X1,s(X2,X1),s(X2,X0)),
inference(resolution,[status(thm)],[c105,c4]) ).
cnf(d24,plain,
( ~ 's$ut'(s(X1,X0),s(X1,s(X1,X0)),X0)
| X0 = s(X1,s(X1,X0)) ),
inference(resolution,[status(thm)],[c61,d23]) ).
cnf(d25,plain,
( ~ 's$ut'(s(X0,X1),s(X0,s(X0,X1)),X1)
| X1 = X1 ),
inference(demodulation,[status(thm)],[d24,c100]) ).
cnf(d26,plain,
( ~ 's$ut'(s(X0,X1),X1,X1)
| X1 = X1 ),
inference(demodulation,[status(thm)],[d25,c100]) ).
cnf(d27,plain,
X0 = X0,
inference(resolution,[status(thm)],[c11,d26]) ).
cnf(d28,plain,
$false,
inference(resolution,[status(thm)],[d27,d22]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO531+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
% 0.11/0.37 % Computer : n017.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 13:34:47 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 154.76/34.73 % SZS status Theorem for theBenchmark.p
% 154.76/34.73 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------