%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : KRS071+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 : n014.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 07:45:58 AM UTC 2026
% Result : Unsatisfiable 0.10s 0.40s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 6
% Syntax : Number of formulae : 44 ( 16 unt; 0 def)
% Number of atoms : 220 ( 46 equ)
% Maximal formula atoms : 67 ( 5 avg)
% Number of connectives : 291 ( 115 ~; 124 |; 46 &)
% ( 1 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 25 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 1 con; 0-1 aty)
% Number of variables : 92 ( 0 sgn 58 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(cp1_substitution_1,axiom,
! [A,B] :
( ( cp1(A)
& A = B )
=> cp1(B) ),
file('theBenchmark.p',cp1_substitution_1) ).
fof(cp2_substitution_1,axiom,
! [A,B] :
( ( cp2(A)
& A = B )
=> cp2(B) ),
file('theBenchmark.p',cp2_substitution_1) ).
fof(axiom_2,axiom,
! [X] :
( cUnsatisfiable(X)
<=> ( ! [Y0,Y1,Y2] :
( ( rr(X,Y2)
& rr(X,Y1)
& rr(X,Y0) )
=> ( Y1 = Y2
| Y0 = Y2
| Y0 = Y1 ) )
& ? [Y] :
( cp3(Y)
& rr(X,Y) )
& ? [Y] :
( cp2(Y)
& rr(X,Y) )
& ? [Y] :
( cp1(Y)
& rr(X,Y) ) ) ),
file('theBenchmark.p',axiom_2) ).
fof(axiom_3,axiom,
! [X] :
( cp1(X)
=> ~ ( cp5(X)
| cp3(X)
| cp2(X)
| cp4(X) ) ),
file('theBenchmark.p',axiom_3) ).
fof(axiom_4,axiom,
! [X] :
( cp2(X)
=> ~ ( cp5(X)
| cp3(X)
| cp4(X) ) ),
file('theBenchmark.p',axiom_4) ).
cnf(c_26,plain,
( cp1(A)
| ~ cp1(B)
| A != B ),
inference(clausify,[status(thm)],[cp1_substitution_1]) ).
cnf(c_27,plain,
( cp2(A)
| ~ cp2(B)
| A != B ),
inference(clausify,[status(thm)],[cp2_substitution_1]) ).
fof(nnf_17,plain,
! [X] :
( ( ? [Y0,Y1,Y2] :
( Y2 != Y1
& Y2 != Y0
& Y1 != Y0
& rr(X,Y2)
& rr(X,Y1)
& rr(X,Y0) )
| ! [Y] :
( ~ cp3(Y)
| ~ rr(X,Y) )
| ! [X7] :
( ~ cp2(X7)
| ~ rr(X,X7) )
| ! [X6] :
( ~ cp1(X6)
| ~ rr(X,X6) )
| cUnsatisfiable(X) )
& ( ( ! [X3,X4,X5] :
( X5 = X4
| X5 = X3
| X4 = X3
| ~ rr(X,X5)
| ~ rr(X,X4)
| ~ rr(X,X3) )
& ? [X2] :
( cp3(X2)
& rr(X,X2) )
& ? [X1] :
( cp2(X1)
& rr(X,X1) )
& ? [X0] :
( cp1(X0)
& rr(X,X0) ) )
| ~ cUnsatisfiable(X) ) ),
inference(fof_nnf,[status(thm)],[axiom_2]) ).
fof(sk_axiom_2_sk,plain,
! [X] :
( ( ( sK5(X) != sK4(X)
& sK5(X) != sK3(X)
& sK4(X) != sK3(X)
& rr(X,sK5(X))
& rr(X,sK4(X))
& rr(X,sK3(X)) )
| ! [Y] :
( ~ cp3(Y)
| ~ rr(X,Y) )
| ! [X7] :
( ~ cp2(X7)
| ~ rr(X,X7) )
| ! [X6] :
( ~ cp1(X6)
| ~ rr(X,X6) )
| cUnsatisfiable(X) )
& ( ( ! [X3,X4,X5] :
( X5 = X4
| X5 = X3
| X4 = X3
| ~ rr(X,X5)
| ~ rr(X,X4)
| ~ rr(X,X3) )
& cp3(sK2(X))
& rr(X,sK2(X))
& cp2(sK1(X))
& rr(X,sK1(X))
& cp1(sK0(X))
& rr(X,sK0(X)) )
| ~ cUnsatisfiable(X) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5]),skolemize(X0,sK0(X)),skolemize(X1,sK1(X)),skolemize(X2,sK2(X)),skolemize(Y0,sK3(X)),skolemize(Y1,sK4(X)),skolemize(Y2,sK5(X))],[nnf_17]) ).
fof(sk_axiom_2,plain,
( ! [VAR_0,VAR_1,VAR_2,VAR_3] :
( sK5(VAR_0) != sK4(VAR_0)
| ~ cp3(VAR_3)
| ~ rr(VAR_0,VAR_3)
| ~ cp2(VAR_2)
| ~ rr(VAR_0,VAR_2)
| ~ cp1(VAR_1)
| ~ rr(VAR_0,VAR_1)
| cUnsatisfiable(VAR_0) )
& ! [VAR_0,VAR_1,VAR_2,VAR_3] :
( sK5(VAR_0) != sK3(VAR_0)
| ~ cp3(VAR_3)
| ~ rr(VAR_0,VAR_3)
| ~ cp2(VAR_2)
| ~ rr(VAR_0,VAR_2)
| ~ cp1(VAR_1)
| ~ rr(VAR_0,VAR_1)
| cUnsatisfiable(VAR_0) )
& ! [VAR_0,VAR_1,VAR_2,VAR_3] :
( sK4(VAR_0) != sK3(VAR_0)
| ~ cp3(VAR_3)
| ~ rr(VAR_0,VAR_3)
| ~ cp2(VAR_2)
| ~ rr(VAR_0,VAR_2)
| ~ cp1(VAR_1)
| ~ rr(VAR_0,VAR_1)
| cUnsatisfiable(VAR_0) )
& ! [VAR_0,VAR_1,VAR_2,VAR_3] :
( rr(VAR_0,sK5(VAR_0))
| ~ cp3(VAR_3)
| ~ rr(VAR_0,VAR_3)
| ~ cp2(VAR_2)
| ~ rr(VAR_0,VAR_2)
| ~ cp1(VAR_1)
| ~ rr(VAR_0,VAR_1)
| cUnsatisfiable(VAR_0) )
& ! [VAR_0,VAR_1,VAR_2,VAR_3] :
( rr(VAR_0,sK4(VAR_0))
| ~ cp3(VAR_3)
| ~ rr(VAR_0,VAR_3)
| ~ cp2(VAR_2)
| ~ rr(VAR_0,VAR_2)
| ~ cp1(VAR_1)
| ~ rr(VAR_0,VAR_1)
| cUnsatisfiable(VAR_0) )
& ! [VAR_0,VAR_1,VAR_2,VAR_3] :
( rr(VAR_0,sK3(VAR_0))
| ~ cp3(VAR_3)
| ~ rr(VAR_0,VAR_3)
| ~ cp2(VAR_2)
| ~ rr(VAR_0,VAR_2)
| ~ cp1(VAR_1)
| ~ rr(VAR_0,VAR_1)
| cUnsatisfiable(VAR_0) )
& ! [VAR_0,VAR_1,VAR_2,VAR_3] :
( VAR_3 = VAR_2
| VAR_3 = VAR_1
| VAR_2 = VAR_1
| ~ rr(VAR_0,VAR_3)
| ~ rr(VAR_0,VAR_2)
| ~ rr(VAR_0,VAR_1)
| ~ cUnsatisfiable(VAR_0) )
& ! [VAR_0] :
( cp3(sK2(VAR_0))
| ~ cUnsatisfiable(VAR_0) )
& ! [VAR_0] :
( rr(VAR_0,sK2(VAR_0))
| ~ cUnsatisfiable(VAR_0) )
& ! [VAR_0] :
( cp2(sK1(VAR_0))
| ~ cUnsatisfiable(VAR_0) )
& ! [VAR_0] :
( rr(VAR_0,sK1(VAR_0))
| ~ cUnsatisfiable(VAR_0) )
& ! [VAR_0] :
( cp1(sK0(VAR_0))
| ~ cUnsatisfiable(VAR_0) )
& ! [VAR_0] :
( rr(VAR_0,sK0(VAR_0))
| ~ cUnsatisfiable(VAR_0) ) ),
inference(cnf_transformation,[status(thm)],[sk_axiom_2_sk]) ).
cnf(c_41,plain,
( rr(A,sK0(A))
| ~ cUnsatisfiable(A) ),
inference(split_conjunct,[status(thm)],[sk_axiom_2]) ).
cnf(c_42,plain,
( cp1(sK0(A))
| ~ cUnsatisfiable(A) ),
inference(split_conjunct,[status(thm)],[sk_axiom_2]) ).
cnf(c_43,plain,
( rr(A,sK1(A))
| ~ cUnsatisfiable(A) ),
inference(split_conjunct,[status(thm)],[sk_axiom_2]) ).
cnf(c_44,plain,
( cp2(sK1(A))
| ~ cUnsatisfiable(A) ),
inference(split_conjunct,[status(thm)],[sk_axiom_2]) ).
cnf(c_45,plain,
( rr(A,sK2(A))
| ~ cUnsatisfiable(A) ),
inference(split_conjunct,[status(thm)],[sk_axiom_2]) ).
cnf(c_46,plain,
( cp3(sK2(A))
| ~ cUnsatisfiable(A) ),
inference(split_conjunct,[status(thm)],[sk_axiom_2]) ).
cnf(c_47,plain,
( D = C
| D = B
| C = B
| ~ rr(A,D)
| ~ rr(A,C)
| ~ rr(A,B)
| ~ cUnsatisfiable(A) ),
inference(split_conjunct,[status(thm)],[sk_axiom_2]) ).
cnf(c_55,plain,
( ~ cp2(A)
| ~ cp1(A) ),
inference(clausify,[status(thm)],[axiom_3]) ).
cnf(c_56,plain,
( ~ cp3(A)
| ~ cp1(A) ),
inference(clausify,[status(thm)],[axiom_3]) ).
cnf(c_59,plain,
( ~ cp3(A)
| ~ cp2(A) ),
inference(clausify,[status(thm)],[axiom_4]) ).
fof(axiom_8,axiom,
cUnsatisfiable(i2003_11_14_17_18_39380),
file('theBenchmark.p',axiom_8) ).
cnf(c_66,plain,
cUnsatisfiable(i2003_11_14_17_18_39380),
inference(clausify,[status(thm)],[axiom_8]) ).
cnf(c_68,plain,
cp3(sK2(i2003_11_14_17_18_39380)),
inference(resolve,[status(thm)],[c_66,c_46]) ).
cnf(c_69,plain,
rr(i2003_11_14_17_18_39380,sK2(i2003_11_14_17_18_39380)),
inference(resolve,[status(thm)],[c_66,c_45]) ).
cnf(c_70,plain,
cp2(sK1(i2003_11_14_17_18_39380)),
inference(resolve,[status(thm)],[c_66,c_44]) ).
cnf(c_71,plain,
rr(i2003_11_14_17_18_39380,sK1(i2003_11_14_17_18_39380)),
inference(resolve,[status(thm)],[c_66,c_43]) ).
cnf(c_72,plain,
cp1(sK0(i2003_11_14_17_18_39380)),
inference(resolve,[status(thm)],[c_66,c_42]) ).
cnf(c_73,plain,
rr(i2003_11_14_17_18_39380,sK0(i2003_11_14_17_18_39380)),
inference(resolve,[status(thm)],[c_66,c_41]) ).
cnf(c_75,plain,
~ cp2(sK2(i2003_11_14_17_18_39380)),
inference(resolve,[status(thm)],[c_68,c_59]) ).
cnf(c_76,plain,
~ cp1(sK2(i2003_11_14_17_18_39380)),
inference(resolve,[status(thm)],[c_68,c_56]) ).
cnf(c_80,plain,
~ cp1(sK1(i2003_11_14_17_18_39380)),
inference(resolve,[status(thm)],[c_70,c_55]) ).
cnf(c_114,plain,
( sK2(i2003_11_14_17_18_39380) = B
| sK2(i2003_11_14_17_18_39380) = A
| B = A
| ~ rr(i2003_11_14_17_18_39380,B)
| ~ rr(i2003_11_14_17_18_39380,A)
| ~ cUnsatisfiable(i2003_11_14_17_18_39380) ),
inference(resolve,[status(thm)],[c_69,c_47]) ).
cnf(c_91,plain,
( sK2(i2003_11_14_17_18_39380) = B
| sK2(i2003_11_14_17_18_39380) = A
| B = A
| ~ rr(i2003_11_14_17_18_39380,B)
| ~ rr(i2003_11_14_17_18_39380,A) ),
inference(resolve,[status(thm)],[c_66,c_114]) ).
cnf(c_115,plain,
( cp2(A)
| A != sK1(i2003_11_14_17_18_39380) ),
inference(resolve,[status(thm)],[c_27,c_70]) ).
cnf(c_98,plain,
sK2(i2003_11_14_17_18_39380) != sK1(i2003_11_14_17_18_39380),
inference(resolve,[status(thm)],[c_115,c_75]) ).
cnf(c_116,plain,
( cp1(A)
| A != sK0(i2003_11_14_17_18_39380) ),
inference(resolve,[status(thm)],[c_26,c_72]) ).
cnf(c_99,plain,
sK2(i2003_11_14_17_18_39380) != sK0(i2003_11_14_17_18_39380),
inference(resolve,[status(thm)],[c_116,c_76]) ).
cnf(c_117,plain,
( cp1(A)
| A != sK0(i2003_11_14_17_18_39380) ),
inference(resolve,[status(thm)],[c_26,c_72]) ).
cnf(c_110,plain,
sK1(i2003_11_14_17_18_39380) != sK0(i2003_11_14_17_18_39380),
inference(resolve,[status(thm)],[c_117,c_80]) ).
cnf(c_118,plain,
( sK2(i2003_11_14_17_18_39380) = sK1(i2003_11_14_17_18_39380)
| sK2(i2003_11_14_17_18_39380) = A
| sK1(i2003_11_14_17_18_39380) = A
| ~ rr(i2003_11_14_17_18_39380,A) ),
inference(resolve,[status(thm)],[c_91,c_71]) ).
cnf(c_119,plain,
( sK2(i2003_11_14_17_18_39380) = sK1(i2003_11_14_17_18_39380)
| sK2(i2003_11_14_17_18_39380) = sK0(i2003_11_14_17_18_39380)
| ~ rr(i2003_11_14_17_18_39380,sK0(i2003_11_14_17_18_39380)) ),
inference(resolve,[status(thm)],[c_118,c_110]) ).
cnf(c_120,plain,
( sK2(i2003_11_14_17_18_39380) = sK1(i2003_11_14_17_18_39380)
| ~ rr(i2003_11_14_17_18_39380,sK0(i2003_11_14_17_18_39380)) ),
inference(resolve,[status(thm)],[c_119,c_99]) ).
cnf(c_121,plain,
~ rr(i2003_11_14_17_18_39380,sK0(i2003_11_14_17_18_39380)),
inference(resolve,[status(thm)],[c_120,c_98]) ).
cnf(c_113,plain,
$false,
inference(resolve,[status(thm)],[c_73,c_121]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KRS071+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n014.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Fri Sep 25 19:37:48 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.37 % Process 924520 was started by sandbox2 on n014,
% 0.10/0.37 % Fri Sep 25 19:37:48 2026
% 0.10/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.10/0.38
% 0.10/0.38 % From the command line: assign(max_seconds, 300).
% 0.10/0.40
% 0.10/0.40 % SZS status Unsatisfiable for theBenchmark
% 0.10/0.40
% 0.10/0.40 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.10/0.40 % Length of proof is 32.
% 0.10/0.40 % Level of proof is 5.
% 0.10/0.40 % Maximum clause weight is 20.000.
% 0.10/0.40 % Given clauses 77.
% 0.10/0.40
% 0.10/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------