%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : KRS099+1 : TPTP v9.3.1. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n020.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 0.13s 0.37s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 2
% Syntax : Number of formulae : 17 ( 7 unt; 0 def)
% Number of atoms : 300 ( 101 equ)
% Maximal formula atoms : 203 ( 17 avg)
% Number of connectives : 420 ( 137 ~; 215 |; 64 &)
% ( 1 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 41 ( 7 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 1 con; 0-1 aty)
% Number of variables : 130 ( 0 sgn 110 !; 11 ?)
% Comments :
%------------------------------------------------------------------------------
fof(axiom_2,axiom,
! [X] :
( cUnsatisfiable(X)
<=> ( ! [Y0,Y1] :
( ( rtt(X,Y1)
& rtt(X,Y0) )
=> Y0 = Y1 )
& ! [Y0,Y1] :
( ( rtt(X,Y1)
& rtt(X,Y0) )
=> Y0 = Y1 )
& ! [Y] :
( rtt(X,Y)
=> ca(Y) )
& ? [Y0,Y1,Y2] :
( Y1 != Y2
& Y0 != Y2
& Y0 != Y1
& rtt(X,Y2)
& rtt(X,Y1)
& rtt(X,Y0) ) ) ),
file('theBenchmark.p',axiom_2) ).
fof(nnf_13,plain,
! [X] :
( ( ? [Y0,Y1] :
( Y1 != Y0
& rtt(X,Y1)
& rtt(X,Y0) )
| ? [X10,X11] :
( X11 != X10
& rtt(X,X11)
& rtt(X,X10) )
| ? [Y] :
( ~ ca(Y)
& rtt(X,Y) )
| ! [X8,X9,Y2] :
( Y2 = X9
| Y2 = X8
| X9 = X8
| ~ rtt(X,Y2)
| ~ rtt(X,X9)
| ~ rtt(X,X8) )
| cUnsatisfiable(X) )
& ( ( ! [X6,X7] :
( X7 = X6
| ~ rtt(X,X7)
| ~ rtt(X,X6) )
& ! [X4,X5] :
( X5 = X4
| ~ rtt(X,X5)
| ~ rtt(X,X4) )
& ! [X3] :
( ca(X3)
| ~ rtt(X,X3) )
& ? [X0,X1,X2] :
( X2 != X1
& X2 != X0
& X1 != X0
& rtt(X,X2)
& rtt(X,X1)
& rtt(X,X0) ) )
| ~ cUnsatisfiable(X) ) ),
inference(fof_nnf,[status(thm)],[axiom_2]) ).
fof(sk_axiom_2_sk,plain,
! [X] :
( ( ( sK7(X) != sK6(X)
& rtt(X,sK7(X))
& rtt(X,sK6(X)) )
| ( sK5(X) != sK4(X)
& rtt(X,sK5(X))
& rtt(X,sK4(X)) )
| ( ~ ca(sK3(X))
& rtt(X,sK3(X)) )
| ! [X8,X9,Y2] :
( Y2 = X9
| Y2 = X8
| X9 = X8
| ~ rtt(X,Y2)
| ~ rtt(X,X9)
| ~ rtt(X,X8) )
| cUnsatisfiable(X) )
& ( ( ! [X6,X7] :
( X7 = X6
| ~ rtt(X,X7)
| ~ rtt(X,X6) )
& ! [X4,X5] :
( X5 = X4
| ~ rtt(X,X5)
| ~ rtt(X,X4) )
& ! [X3] :
( ca(X3)
| ~ rtt(X,X3) )
& sK1(X) != sK2(X)
& sK1(X) != sK0(X)
& sK2(X) != sK0(X)
& rtt(X,sK1(X))
& rtt(X,sK2(X))
& rtt(X,sK0(X)) )
| ~ cUnsatisfiable(X) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK2,sK1,sK3,sK4,sK5,sK6,sK7]),skolemize(X0,sK0(X)),skolemize(X1,sK2(X)),skolemize(X2,sK1(X)),skolemize(Y,sK3(X)),skolemize(X10,sK4(X)),skolemize(X11,sK5(X)),skolemize(Y0,sK6(X)),skolemize(Y1,sK7(X))],[nnf_13]) ).
fof(sk_axiom_2,plain,
( ! [VAR_0,VAR_1,VAR_2,VAR_3] :
( sK7(VAR_0) != sK6(VAR_0)
| sK5(VAR_0) != sK4(VAR_0)
| ~ ca(sK3(VAR_0))
| VAR_3 = VAR_2
| VAR_3 = VAR_1
| VAR_2 = VAR_1
| ~ rtt(VAR_0,VAR_3)
| ~ rtt(VAR_0,VAR_2)
| ~ rtt(VAR_0,VAR_1)
| cUnsatisfiable(VAR_0) )
& ! [VAR_0,VAR_1,VAR_2,VAR_3] :
( rtt(VAR_0,sK7(VAR_0))
| sK5(VAR_0) != sK4(VAR_0)
| ~ ca(sK3(VAR_0))
| VAR_3 = VAR_2
| VAR_3 = VAR_1
| VAR_2 = VAR_1
| ~ rtt(VAR_0,VAR_3)
| ~ rtt(VAR_0,VAR_2)
| ~ rtt(VAR_0,VAR_1)
| cUnsatisfiable(VAR_0) )
& ! [VAR_0,VAR_1,VAR_2,VAR_3] :
( rtt(VAR_0,sK6(VAR_0))
| sK5(VAR_0) != sK4(VAR_0)
| ~ ca(sK3(VAR_0))
| VAR_3 = VAR_2
| VAR_3 = VAR_1
| VAR_2 = VAR_1
| ~ rtt(VAR_0,VAR_3)
| ~ rtt(VAR_0,VAR_2)
| ~ rtt(VAR_0,VAR_1)
| cUnsatisfiable(VAR_0) )
& ! [VAR_0,VAR_1,VAR_2,VAR_3] :
( sK7(VAR_0) != sK6(VAR_0)
| rtt(VAR_0,sK5(VAR_0))
| ~ ca(sK3(VAR_0))
| VAR_3 = VAR_2
| VAR_3 = VAR_1
| VAR_2 = VAR_1
| ~ rtt(VAR_0,VAR_3)
| ~ rtt(VAR_0,VAR_2)
| ~ rtt(VAR_0,VAR_1)
| cUnsatisfiable(VAR_0) )
& ! [VAR_0,VAR_1,VAR_2,VAR_3] :
( rtt(VAR_0,sK7(VAR_0))
| rtt(VAR_0,sK5(VAR_0))
| ~ ca(sK3(VAR_0))
| VAR_3 = VAR_2
| VAR_3 = VAR_1
| VAR_2 = VAR_1
| ~ rtt(VAR_0,VAR_3)
| ~ rtt(VAR_0,VAR_2)
| ~ rtt(VAR_0,VAR_1)
| cUnsatisfiable(VAR_0) )
& ! [VAR_0,VAR_1,VAR_2,VAR_3] :
( rtt(VAR_0,sK6(VAR_0))
| rtt(VAR_0,sK5(VAR_0))
| ~ ca(sK3(VAR_0))
| VAR_3 = VAR_2
| VAR_3 = VAR_1
| VAR_2 = VAR_1
| ~ rtt(VAR_0,VAR_3)
| ~ rtt(VAR_0,VAR_2)
| ~ rtt(VAR_0,VAR_1)
| cUnsatisfiable(VAR_0) )
& ! [VAR_0,VAR_1,VAR_2,VAR_3] :
( sK7(VAR_0) != sK6(VAR_0)
| rtt(VAR_0,sK4(VAR_0))
| ~ ca(sK3(VAR_0))
| VAR_3 = VAR_2
| VAR_3 = VAR_1
| VAR_2 = VAR_1
| ~ rtt(VAR_0,VAR_3)
| ~ rtt(VAR_0,VAR_2)
| ~ rtt(VAR_0,VAR_1)
| cUnsatisfiable(VAR_0) )
& ! [VAR_0,VAR_1,VAR_2,VAR_3] :
( rtt(VAR_0,sK7(VAR_0))
| rtt(VAR_0,sK4(VAR_0))
| ~ ca(sK3(VAR_0))
| VAR_3 = VAR_2
| VAR_3 = VAR_1
| VAR_2 = VAR_1
| ~ rtt(VAR_0,VAR_3)
| ~ rtt(VAR_0,VAR_2)
| ~ rtt(VAR_0,VAR_1)
| cUnsatisfiable(VAR_0) )
& ! [VAR_0,VAR_1,VAR_2,VAR_3] :
( rtt(VAR_0,sK6(VAR_0))
| rtt(VAR_0,sK4(VAR_0))
| ~ ca(sK3(VAR_0))
| VAR_3 = VAR_2
| VAR_3 = VAR_1
| VAR_2 = VAR_1
| ~ rtt(VAR_0,VAR_3)
| ~ rtt(VAR_0,VAR_2)
| ~ rtt(VAR_0,VAR_1)
| cUnsatisfiable(VAR_0) )
& ! [VAR_0,VAR_1,VAR_2,VAR_3] :
( sK7(VAR_0) != sK6(VAR_0)
| sK5(VAR_0) != sK4(VAR_0)
| rtt(VAR_0,sK3(VAR_0))
| VAR_3 = VAR_2
| VAR_3 = VAR_1
| VAR_2 = VAR_1
| ~ rtt(VAR_0,VAR_3)
| ~ rtt(VAR_0,VAR_2)
| ~ rtt(VAR_0,VAR_1)
| cUnsatisfiable(VAR_0) )
& ! [VAR_0,VAR_1,VAR_2,VAR_3] :
( rtt(VAR_0,sK7(VAR_0))
| sK5(VAR_0) != sK4(VAR_0)
| rtt(VAR_0,sK3(VAR_0))
| VAR_3 = VAR_2
| VAR_3 = VAR_1
| VAR_2 = VAR_1
| ~ rtt(VAR_0,VAR_3)
| ~ rtt(VAR_0,VAR_2)
| ~ rtt(VAR_0,VAR_1)
| cUnsatisfiable(VAR_0) )
& ! [VAR_0,VAR_1,VAR_2,VAR_3] :
( rtt(VAR_0,sK6(VAR_0))
| sK5(VAR_0) != sK4(VAR_0)
| rtt(VAR_0,sK3(VAR_0))
| VAR_3 = VAR_2
| VAR_3 = VAR_1
| VAR_2 = VAR_1
| ~ rtt(VAR_0,VAR_3)
| ~ rtt(VAR_0,VAR_2)
| ~ rtt(VAR_0,VAR_1)
| cUnsatisfiable(VAR_0) )
& ! [VAR_0,VAR_1,VAR_2,VAR_3] :
( sK7(VAR_0) != sK6(VAR_0)
| rtt(VAR_0,sK5(VAR_0))
| rtt(VAR_0,sK3(VAR_0))
| VAR_3 = VAR_2
| VAR_3 = VAR_1
| VAR_2 = VAR_1
| ~ rtt(VAR_0,VAR_3)
| ~ rtt(VAR_0,VAR_2)
| ~ rtt(VAR_0,VAR_1)
| cUnsatisfiable(VAR_0) )
& ! [VAR_0,VAR_1,VAR_2,VAR_3] :
( rtt(VAR_0,sK7(VAR_0))
| rtt(VAR_0,sK5(VAR_0))
| rtt(VAR_0,sK3(VAR_0))
| VAR_3 = VAR_2
| VAR_3 = VAR_1
| VAR_2 = VAR_1
| ~ rtt(VAR_0,VAR_3)
| ~ rtt(VAR_0,VAR_2)
| ~ rtt(VAR_0,VAR_1)
| cUnsatisfiable(VAR_0) )
& ! [VAR_0,VAR_1,VAR_2,VAR_3] :
( rtt(VAR_0,sK6(VAR_0))
| rtt(VAR_0,sK5(VAR_0))
| rtt(VAR_0,sK3(VAR_0))
| VAR_3 = VAR_2
| VAR_3 = VAR_1
| VAR_2 = VAR_1
| ~ rtt(VAR_0,VAR_3)
| ~ rtt(VAR_0,VAR_2)
| ~ rtt(VAR_0,VAR_1)
| cUnsatisfiable(VAR_0) )
& ! [VAR_0,VAR_1,VAR_2,VAR_3] :
( sK7(VAR_0) != sK6(VAR_0)
| rtt(VAR_0,sK4(VAR_0))
| rtt(VAR_0,sK3(VAR_0))
| VAR_3 = VAR_2
| VAR_3 = VAR_1
| VAR_2 = VAR_1
| ~ rtt(VAR_0,VAR_3)
| ~ rtt(VAR_0,VAR_2)
| ~ rtt(VAR_0,VAR_1)
| cUnsatisfiable(VAR_0) )
& ! [VAR_0,VAR_1,VAR_2,VAR_3] :
( rtt(VAR_0,sK7(VAR_0))
| rtt(VAR_0,sK4(VAR_0))
| rtt(VAR_0,sK3(VAR_0))
| VAR_3 = VAR_2
| VAR_3 = VAR_1
| VAR_2 = VAR_1
| ~ rtt(VAR_0,VAR_3)
| ~ rtt(VAR_0,VAR_2)
| ~ rtt(VAR_0,VAR_1)
| cUnsatisfiable(VAR_0) )
& ! [VAR_0,VAR_1,VAR_2,VAR_3] :
( rtt(VAR_0,sK6(VAR_0))
| rtt(VAR_0,sK4(VAR_0))
| rtt(VAR_0,sK3(VAR_0))
| VAR_3 = VAR_2
| VAR_3 = VAR_1
| VAR_2 = VAR_1
| ~ rtt(VAR_0,VAR_3)
| ~ rtt(VAR_0,VAR_2)
| ~ rtt(VAR_0,VAR_1)
| cUnsatisfiable(VAR_0) )
& ! [VAR_0,VAR_1,VAR_2] :
( VAR_2 = VAR_1
| ~ rtt(VAR_0,VAR_2)
| ~ rtt(VAR_0,VAR_1)
| ~ cUnsatisfiable(VAR_0) )
& ! [VAR_0,VAR_1,VAR_2] :
( VAR_2 = VAR_1
| ~ rtt(VAR_0,VAR_2)
| ~ rtt(VAR_0,VAR_1)
| ~ cUnsatisfiable(VAR_0) )
& ! [VAR_0,VAR_1] :
( ca(VAR_1)
| ~ rtt(VAR_0,VAR_1)
| ~ cUnsatisfiable(VAR_0) )
& ! [VAR_0] :
( sK1(VAR_0) != sK2(VAR_0)
| ~ cUnsatisfiable(VAR_0) )
& ! [VAR_0] :
( sK1(VAR_0) != sK0(VAR_0)
| ~ cUnsatisfiable(VAR_0) )
& ! [VAR_0] :
( sK2(VAR_0) != sK0(VAR_0)
| ~ cUnsatisfiable(VAR_0) )
& ! [VAR_0] :
( rtt(VAR_0,sK1(VAR_0))
| ~ cUnsatisfiable(VAR_0) )
& ! [VAR_0] :
( rtt(VAR_0,sK2(VAR_0))
| ~ cUnsatisfiable(VAR_0) )
& ! [VAR_0] :
( rtt(VAR_0,sK0(VAR_0))
| ~ cUnsatisfiable(VAR_0) ) ),
inference(cnf_transformation,[status(thm)],[sk_axiom_2_sk]) ).
cnf(c_30,plain,
( rtt(A,sK0(A))
| ~ cUnsatisfiable(A) ),
inference(split_conjunct,[status(thm)],[sk_axiom_2]) ).
cnf(c_32,plain,
( rtt(A,sK1(A))
| ~ cUnsatisfiable(A) ),
inference(split_conjunct,[status(thm)],[sk_axiom_2]) ).
cnf(c_34,plain,
( sK1(A) != sK0(A)
| ~ cUnsatisfiable(A) ),
inference(split_conjunct,[status(thm)],[sk_axiom_2]) ).
cnf(c_37,plain,
( C = B
| ~ rtt(A,C)
| ~ rtt(A,B)
| ~ cUnsatisfiable(A) ),
inference(split_conjunct,[status(thm)],[sk_axiom_2]) ).
fof(axiom_5,axiom,
cUnsatisfiable(i2003_11_14_17_20_29215),
file('theBenchmark.p',axiom_5) ).
cnf(c_58,plain,
cUnsatisfiable(i2003_11_14_17_20_29215),
inference(clausify,[status(thm)],[axiom_5]) ).
cnf(c_62,plain,
sK1(i2003_11_14_17_20_29215) != sK0(i2003_11_14_17_20_29215),
inference(resolve,[status(thm)],[c_58,c_34]) ).
cnf(c_64,plain,
rtt(i2003_11_14_17_20_29215,sK1(i2003_11_14_17_20_29215)),
inference(resolve,[status(thm)],[c_58,c_32]) ).
cnf(c_66,plain,
rtt(i2003_11_14_17_20_29215,sK0(i2003_11_14_17_20_29215)),
inference(resolve,[status(thm)],[c_58,c_30]) ).
cnf(c_73,plain,
( B = A
| ~ rtt(i2003_11_14_17_20_29215,B)
| ~ rtt(i2003_11_14_17_20_29215,A) ),
inference(resolve,[status(thm)],[c_37,c_58]) ).
cnf(c_74,plain,
( sK1(i2003_11_14_17_20_29215) = A
| ~ rtt(i2003_11_14_17_20_29215,A) ),
inference(resolve,[status(thm)],[c_73,c_64]) ).
cnf(c_75,plain,
~ rtt(i2003_11_14_17_20_29215,sK0(i2003_11_14_17_20_29215)),
inference(resolve,[status(thm)],[c_74,c_62]) ).
cnf(c_72,plain,
$false,
inference(resolve,[status(thm)],[c_66,c_75]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KRS099+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.34 % Computer : n020.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
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Fri Sep 25 19:40:18 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 3599454 was started by sandbox2 on n020,
% 0.08/0.35 % Fri Sep 25 19:40:18 2026
% 0.08/0.35 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.13/0.36
% 0.13/0.36 % From the command line: assign(max_seconds, 300).
% 0.13/0.37
% 0.13/0.37 % SZS status Unsatisfiable for theBenchmark
% 0.13/0.37
% 0.13/0.37 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.13/0.37 % Length of proof is 10.
% 0.13/0.37 % Level of proof is 3.
% 0.13/0.37 % Maximum clause weight is 17.000.
% 0.13/0.37 % Given clauses 48.
% 0.13/0.37
% 0.13/0.37 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------