%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : KRS101+1 : TPTP v9.3.1. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n019.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 07:46:02 AM UTC 2026
% Result : Unsatisfiable 0.12s 0.38s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 3
% Syntax : Number of formulae : 27 ( 10 unt; 0 def)
% Number of atoms : 194 ( 30 equ)
% Maximal formula atoms : 87 ( 7 avg)
% Number of connectives : 269 ( 102 ~; 119 |; 43 &)
% ( 1 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 27 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 1 con; 0-1 aty)
% Number of variables : 96 ( 0 sgn 72 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(axiom_2,axiom,
! [X] :
( cUnsatisfiable(X)
<=> ( ? [Y] :
( ~ ! [Z0,Z1] :
( ( rs(Y,Z1)
& rs(Y,Z0) )
=> Z0 = Z1 )
& rr(X,Y) )
& ! [Y] :
( rr(X,Y)
=> ( cc(Y)
| ~ ? [Z0,Z1] :
( Z0 != Z1
& rs(Y,Z1)
& rs(Y,Z0) ) ) )
& ! [Y] :
( rr(X,Y)
=> cd(Y) ) ) ),
file('theBenchmark.p',axiom_2) ).
fof(axiom_3,axiom,
! [X] :
( cc(X)
=> ~ cd(X) ),
file('theBenchmark.p',axiom_3) ).
fof(nnf_14,plain,
! [X] :
( ( ! [Y] :
( ! [Z0,Z1] :
( Z1 = Z0
| ~ rs(Y,Z1)
| ~ rs(Y,Z0) )
| ~ rr(X,Y) )
| ? [X8] :
( ~ cc(X8)
& ? [X9,X10] :
( X10 != X9
& rs(X8,X10)
& rs(X8,X9) )
& rr(X,X8) )
| ? [X7] :
( ~ cd(X7)
& rr(X,X7) )
| cUnsatisfiable(X) )
& ( ( ? [X4] :
( ? [X5,X6] :
( X6 != X5
& rs(X4,X6)
& rs(X4,X5) )
& rr(X,X4) )
& ! [X1] :
( cc(X1)
| ! [X2,X3] :
( X3 = X2
| ~ rs(X1,X3)
| ~ rs(X1,X2) )
| ~ rr(X,X1) )
& ! [X0] :
( cd(X0)
| ~ rr(X,X0) ) )
| ~ cUnsatisfiable(X) ) ),
inference(fof_nnf,[status(thm)],[axiom_2]) ).
fof(sk_axiom_2_sk,plain,
! [X] :
( ( ! [Y] :
( ! [Z0,Z1] :
( Z1 = Z0
| ~ rs(Y,Z1)
| ~ rs(Y,Z0) )
| ~ rr(X,Y) )
| ( ~ cc(sK4(X))
& sK6(X) != sK5(X)
& rs(sK4(X),sK6(X))
& rs(sK4(X),sK5(X))
& rr(X,sK4(X)) )
| ( ~ cd(sK3(X))
& rr(X,sK3(X)) )
| cUnsatisfiable(X) )
& ( ( sK2(X) != sK1(X)
& rs(sK0(X),sK2(X))
& rs(sK0(X),sK1(X))
& rr(X,sK0(X))
& ! [X1] :
( cc(X1)
| ! [X2,X3] :
( X3 = X2
| ~ rs(X1,X3)
| ~ rs(X1,X2) )
| ~ rr(X,X1) )
& ! [X0] :
( cd(X0)
| ~ rr(X,X0) ) )
| ~ cUnsatisfiable(X) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5,sK6]),skolemize(X4,sK0(X)),skolemize(X5,sK1(X)),skolemize(X6,sK2(X)),skolemize(X7,sK3(X)),skolemize(X8,sK4(X)),skolemize(X9,sK5(X)),skolemize(X10,sK6(X))],[nnf_14]) ).
fof(sk_axiom_2,plain,
( ! [VAR_0,VAR_1,VAR_2,VAR_3] :
( VAR_3 = VAR_2
| ~ rs(VAR_1,VAR_3)
| ~ rs(VAR_1,VAR_2)
| ~ rr(VAR_0,VAR_1)
| ~ cc(sK4(VAR_0))
| ~ cd(sK3(VAR_0))
| cUnsatisfiable(VAR_0) )
& ! [VAR_0,VAR_1,VAR_2,VAR_3] :
( VAR_3 = VAR_2
| ~ rs(VAR_1,VAR_3)
| ~ rs(VAR_1,VAR_2)
| ~ rr(VAR_0,VAR_1)
| sK6(VAR_0) != sK5(VAR_0)
| ~ cd(sK3(VAR_0))
| cUnsatisfiable(VAR_0) )
& ! [VAR_0,VAR_1,VAR_2,VAR_3] :
( VAR_3 = VAR_2
| ~ rs(VAR_1,VAR_3)
| ~ rs(VAR_1,VAR_2)
| ~ rr(VAR_0,VAR_1)
| rs(sK4(VAR_0),sK6(VAR_0))
| ~ cd(sK3(VAR_0))
| cUnsatisfiable(VAR_0) )
& ! [VAR_0,VAR_1,VAR_2,VAR_3] :
( VAR_3 = VAR_2
| ~ rs(VAR_1,VAR_3)
| ~ rs(VAR_1,VAR_2)
| ~ rr(VAR_0,VAR_1)
| rs(sK4(VAR_0),sK5(VAR_0))
| ~ cd(sK3(VAR_0))
| cUnsatisfiable(VAR_0) )
& ! [VAR_0,VAR_1,VAR_2,VAR_3] :
( VAR_3 = VAR_2
| ~ rs(VAR_1,VAR_3)
| ~ rs(VAR_1,VAR_2)
| ~ rr(VAR_0,VAR_1)
| rr(VAR_0,sK4(VAR_0))
| ~ cd(sK3(VAR_0))
| cUnsatisfiable(VAR_0) )
& ! [VAR_0,VAR_1,VAR_2,VAR_3] :
( VAR_3 = VAR_2
| ~ rs(VAR_1,VAR_3)
| ~ rs(VAR_1,VAR_2)
| ~ rr(VAR_0,VAR_1)
| ~ cc(sK4(VAR_0))
| rr(VAR_0,sK3(VAR_0))
| cUnsatisfiable(VAR_0) )
& ! [VAR_0,VAR_1,VAR_2,VAR_3] :
( VAR_3 = VAR_2
| ~ rs(VAR_1,VAR_3)
| ~ rs(VAR_1,VAR_2)
| ~ rr(VAR_0,VAR_1)
| sK6(VAR_0) != sK5(VAR_0)
| rr(VAR_0,sK3(VAR_0))
| cUnsatisfiable(VAR_0) )
& ! [VAR_0,VAR_1,VAR_2,VAR_3] :
( VAR_3 = VAR_2
| ~ rs(VAR_1,VAR_3)
| ~ rs(VAR_1,VAR_2)
| ~ rr(VAR_0,VAR_1)
| rs(sK4(VAR_0),sK6(VAR_0))
| rr(VAR_0,sK3(VAR_0))
| cUnsatisfiable(VAR_0) )
& ! [VAR_0,VAR_1,VAR_2,VAR_3] :
( VAR_3 = VAR_2
| ~ rs(VAR_1,VAR_3)
| ~ rs(VAR_1,VAR_2)
| ~ rr(VAR_0,VAR_1)
| rs(sK4(VAR_0),sK5(VAR_0))
| rr(VAR_0,sK3(VAR_0))
| cUnsatisfiable(VAR_0) )
& ! [VAR_0,VAR_1,VAR_2,VAR_3] :
( VAR_3 = VAR_2
| ~ rs(VAR_1,VAR_3)
| ~ rs(VAR_1,VAR_2)
| ~ rr(VAR_0,VAR_1)
| rr(VAR_0,sK4(VAR_0))
| rr(VAR_0,sK3(VAR_0))
| cUnsatisfiable(VAR_0) )
& ! [VAR_0] :
( sK2(VAR_0) != sK1(VAR_0)
| ~ cUnsatisfiable(VAR_0) )
& ! [VAR_0] :
( rs(sK0(VAR_0),sK2(VAR_0))
| ~ cUnsatisfiable(VAR_0) )
& ! [VAR_0] :
( rs(sK0(VAR_0),sK1(VAR_0))
| ~ cUnsatisfiable(VAR_0) )
& ! [VAR_0] :
( rr(VAR_0,sK0(VAR_0))
| ~ cUnsatisfiable(VAR_0) )
& ! [VAR_0,VAR_1,VAR_2,VAR_3] :
( cc(VAR_1)
| VAR_3 = VAR_2
| ~ rs(VAR_1,VAR_3)
| ~ rs(VAR_1,VAR_2)
| ~ rr(VAR_0,VAR_1)
| ~ cUnsatisfiable(VAR_0) )
& ! [VAR_0,VAR_1] :
( cd(VAR_1)
| ~ rr(VAR_0,VAR_1)
| ~ cUnsatisfiable(VAR_0) ) ),
inference(cnf_transformation,[status(thm)],[sk_axiom_2_sk]) ).
cnf(c_31,plain,
( cd(B)
| ~ rr(A,B)
| ~ cUnsatisfiable(A) ),
inference(split_conjunct,[status(thm)],[sk_axiom_2]) ).
cnf(c_32,plain,
( cc(B)
| D = C
| ~ rs(B,D)
| ~ rs(B,C)
| ~ rr(A,B)
| ~ cUnsatisfiable(A) ),
inference(split_conjunct,[status(thm)],[sk_axiom_2]) ).
cnf(c_33,plain,
( rr(A,sK0(A))
| ~ cUnsatisfiable(A) ),
inference(split_conjunct,[status(thm)],[sk_axiom_2]) ).
cnf(c_34,plain,
( rs(sK0(A),sK1(A))
| ~ cUnsatisfiable(A) ),
inference(split_conjunct,[status(thm)],[sk_axiom_2]) ).
cnf(c_35,plain,
( rs(sK0(A),sK2(A))
| ~ cUnsatisfiable(A) ),
inference(split_conjunct,[status(thm)],[sk_axiom_2]) ).
cnf(c_36,plain,
( sK2(A) != sK1(A)
| ~ cUnsatisfiable(A) ),
inference(split_conjunct,[status(thm)],[sk_axiom_2]) ).
cnf(c_47,plain,
( ~ cd(A)
| ~ cc(A) ),
inference(clausify,[status(thm)],[axiom_3]) ).
fof(axiom_4,axiom,
cUnsatisfiable(i2003_11_14_17_20_36582),
file('theBenchmark.p',axiom_4) ).
cnf(c_48,plain,
cUnsatisfiable(i2003_11_14_17_20_36582),
inference(clausify,[status(thm)],[axiom_4]) ).
cnf(c_50,plain,
sK2(i2003_11_14_17_20_36582) != sK1(i2003_11_14_17_20_36582),
inference(resolve,[status(thm)],[c_48,c_36]) ).
cnf(c_51,plain,
rs(sK0(i2003_11_14_17_20_36582),sK2(i2003_11_14_17_20_36582)),
inference(resolve,[status(thm)],[c_48,c_35]) ).
cnf(c_52,plain,
rs(sK0(i2003_11_14_17_20_36582),sK1(i2003_11_14_17_20_36582)),
inference(resolve,[status(thm)],[c_48,c_34]) ).
cnf(c_53,plain,
rr(i2003_11_14_17_20_36582,sK0(i2003_11_14_17_20_36582)),
inference(resolve,[status(thm)],[c_48,c_33]) ).
cnf(c_67,plain,
( cd(sK0(i2003_11_14_17_20_36582))
| ~ cUnsatisfiable(i2003_11_14_17_20_36582) ),
inference(resolve,[status(thm)],[c_53,c_31]) ).
cnf(c_56,plain,
cd(sK0(i2003_11_14_17_20_36582)),
inference(resolve,[status(thm)],[c_48,c_67]) ).
cnf(c_60,plain,
~ cc(sK0(i2003_11_14_17_20_36582)),
inference(resolve,[status(thm)],[c_47,c_56]) ).
cnf(c_68,plain,
( cc(sK0(i2003_11_14_17_20_36582))
| B = A
| ~ rs(sK0(i2003_11_14_17_20_36582),B)
| ~ rs(sK0(i2003_11_14_17_20_36582),A)
| ~ cUnsatisfiable(i2003_11_14_17_20_36582) ),
inference(resolve,[status(thm)],[c_32,c_53]) ).
cnf(c_69,plain,
( cc(sK0(i2003_11_14_17_20_36582))
| A = sK1(i2003_11_14_17_20_36582)
| ~ rs(sK0(i2003_11_14_17_20_36582),A)
| ~ cUnsatisfiable(i2003_11_14_17_20_36582) ),
inference(resolve,[status(thm)],[c_68,c_52]) ).
cnf(c_70,plain,
( cc(sK0(i2003_11_14_17_20_36582))
| sK2(i2003_11_14_17_20_36582) = sK1(i2003_11_14_17_20_36582)
| ~ cUnsatisfiable(i2003_11_14_17_20_36582) ),
inference(resolve,[status(thm)],[c_69,c_51]) ).
cnf(c_71,plain,
( cc(sK0(i2003_11_14_17_20_36582))
| ~ cUnsatisfiable(i2003_11_14_17_20_36582) ),
inference(resolve,[status(thm)],[c_70,c_50]) ).
cnf(c_72,plain,
~ cUnsatisfiable(i2003_11_14_17_20_36582),
inference(resolve,[status(thm)],[c_71,c_60]) ).
cnf(c_66,plain,
$false,
inference(resolve,[status(thm)],[c_48,c_72]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KRS101+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n019.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Fri Sep 25 19:39:33 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.35 % Process 3493540 was started by sandbox on n019,
% 0.08/0.35 % Fri Sep 25 19:39:33 2026
% 0.08/0.35 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.08/0.36
% 0.08/0.36 % From the command line: assign(max_seconds, 300).
% 0.12/0.38
% 0.12/0.38 % SZS status Unsatisfiable for theBenchmark
% 0.12/0.38
% 0.12/0.38 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.12/0.38 % Length of proof is 17.
% 0.12/0.38 % Level of proof is 5.
% 0.12/0.38 % Maximum clause weight is 16.000.
% 0.12/0.38 % Given clauses 39.
% 0.12/0.38
% 0.12/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------