%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : KRS097+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 : n012.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 07:46:01 AM UTC 2026
% Result : Unsatisfiable 0.11s 0.36s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 4
% Syntax : Number of formulae : 26 ( 10 unt; 0 def)
% Number of atoms : 119 ( 14 equ)
% Maximal formula atoms : 35 ( 4 avg)
% Number of connectives : 156 ( 63 ~; 58 |; 33 &)
% ( 1 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 1 con; 0-1 aty)
% Number of variables : 58 ( 0 sgn 36 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(cd_substitution_1,axiom,
! [A,B] :
( ( cd(A)
& A = B )
=> cd(B) ),
file('theBenchmark.p',cd_substitution_1) ).
fof(axiom_2,axiom,
! [X] :
( cUnsatisfiable(X)
<=> ( ? [Y] :
( cc(Y)
& rr(X,Y) )
& ~ ? [Y0,Y1] :
( Y0 != Y1
& rr(X,Y1)
& rr(X,Y0) )
& ? [Y] :
( cd(Y)
& rr(X,Y) )
& ? [Y0] : rr(X,Y0) ) ),
file('theBenchmark.p',axiom_2) ).
fof(axiom_6,axiom,
! [X] :
~ ( cc(X)
& cd(X) ),
file('theBenchmark.p',axiom_6) ).
cnf(c_42,plain,
( cd(A)
| ~ cd(B)
| A != B ),
inference(clausify,[status(thm)],[cd_substitution_1]) ).
fof(nnf_28,plain,
! [X] :
( ( ! [Y] :
( ~ cc(Y)
| ~ rr(X,Y) )
| ? [Y0,Y1] :
( Y1 != Y0
& rr(X,Y1)
& rr(X,Y0) )
| ! [X6] :
( ~ cd(X6)
| ~ rr(X,X6) )
| ! [X5] : ~ rr(X,X5)
| cUnsatisfiable(X) )
& ( ( ? [X4] :
( cc(X4)
& rr(X,X4) )
& ! [X2,X3] :
( X3 = X2
| ~ rr(X,X3)
| ~ rr(X,X2) )
& ? [X1] :
( cd(X1)
& rr(X,X1) )
& ? [X0] : rr(X,X0) )
| ~ cUnsatisfiable(X) ) ),
inference(fof_nnf,[status(thm)],[axiom_2]) ).
fof(sk_axiom_2_sk,plain,
! [X] :
( ( ! [Y] :
( ~ cc(Y)
| ~ rr(X,Y) )
| ( sK4(X) != sK3(X)
& rr(X,sK4(X))
& rr(X,sK3(X)) )
| ! [X6] :
( ~ cd(X6)
| ~ rr(X,X6) )
| ! [X5] : ~ rr(X,X5)
| cUnsatisfiable(X) )
& ( ( cc(sK1(X))
& rr(X,sK1(X))
& ! [X2,X3] :
( X3 = X2
| ~ rr(X,X3)
| ~ rr(X,X2) )
& cd(sK0(X))
& rr(X,sK0(X))
& rr(X,sK2(X)) )
| ~ cUnsatisfiable(X) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK0,sK1,sK3,sK4]),skolemize(X0,sK2(X)),skolemize(X1,sK0(X)),skolemize(X4,sK1(X)),skolemize(Y0,sK3(X)),skolemize(Y1,sK4(X))],[nnf_28]) ).
fof(sk_axiom_2,plain,
( ! [VAR_0,VAR_1,VAR_2,VAR_3] :
( ~ cc(VAR_3)
| ~ rr(VAR_0,VAR_3)
| sK4(VAR_0) != sK3(VAR_0)
| ~ cd(VAR_2)
| ~ rr(VAR_0,VAR_2)
| ~ rr(VAR_0,VAR_1)
| cUnsatisfiable(VAR_0) )
& ! [VAR_0,VAR_1,VAR_2,VAR_3] :
( ~ cc(VAR_3)
| ~ rr(VAR_0,VAR_3)
| rr(VAR_0,sK4(VAR_0))
| ~ cd(VAR_2)
| ~ rr(VAR_0,VAR_2)
| ~ rr(VAR_0,VAR_1)
| cUnsatisfiable(VAR_0) )
& ! [VAR_0,VAR_1,VAR_2,VAR_3] :
( ~ cc(VAR_3)
| ~ rr(VAR_0,VAR_3)
| rr(VAR_0,sK3(VAR_0))
| ~ cd(VAR_2)
| ~ rr(VAR_0,VAR_2)
| ~ rr(VAR_0,VAR_1)
| cUnsatisfiable(VAR_0) )
& ! [VAR_0] :
( cc(sK1(VAR_0))
| ~ cUnsatisfiable(VAR_0) )
& ! [VAR_0] :
( rr(VAR_0,sK1(VAR_0))
| ~ cUnsatisfiable(VAR_0) )
& ! [VAR_0,VAR_1,VAR_2] :
( VAR_2 = VAR_1
| ~ rr(VAR_0,VAR_2)
| ~ rr(VAR_0,VAR_1)
| ~ cUnsatisfiable(VAR_0) )
& ! [VAR_0] :
( cd(sK0(VAR_0))
| ~ cUnsatisfiable(VAR_0) )
& ! [VAR_0] :
( rr(VAR_0,sK0(VAR_0))
| ~ cUnsatisfiable(VAR_0) )
& ! [VAR_0] :
( rr(VAR_0,sK2(VAR_0))
| ~ cUnsatisfiable(VAR_0) ) ),
inference(cnf_transformation,[status(thm)],[sk_axiom_2_sk]) ).
cnf(c_69,plain,
( rr(A,sK0(A))
| ~ cUnsatisfiable(A) ),
inference(split_conjunct,[status(thm)],[sk_axiom_2]) ).
cnf(c_70,plain,
( cd(sK0(A))
| ~ cUnsatisfiable(A) ),
inference(split_conjunct,[status(thm)],[sk_axiom_2]) ).
cnf(c_71,plain,
( C = B
| ~ rr(A,C)
| ~ rr(A,B)
| ~ cUnsatisfiable(A) ),
inference(split_conjunct,[status(thm)],[sk_axiom_2]) ).
cnf(c_72,plain,
( rr(A,sK1(A))
| ~ cUnsatisfiable(A) ),
inference(split_conjunct,[status(thm)],[sk_axiom_2]) ).
cnf(c_73,plain,
( cc(sK1(A))
| ~ cUnsatisfiable(A) ),
inference(split_conjunct,[status(thm)],[sk_axiom_2]) ).
fof(axiom_4,axiom,
cUnsatisfiable(i2003_11_14_17_20_21603),
file('theBenchmark.p',axiom_4) ).
cnf(c_80,plain,
cUnsatisfiable(i2003_11_14_17_20_21603),
inference(clausify,[status(thm)],[axiom_4]) ).
cnf(c_82,plain,
( ~ cc(A)
| ~ cd(A) ),
inference(clausify,[status(thm)],[axiom_6]) ).
cnf(c_94,plain,
cc(sK1(i2003_11_14_17_20_21603)),
inference(resolve,[status(thm)],[c_80,c_73]) ).
cnf(c_95,plain,
rr(i2003_11_14_17_20_21603,sK1(i2003_11_14_17_20_21603)),
inference(resolve,[status(thm)],[c_80,c_72]) ).
cnf(c_96,plain,
cd(sK0(i2003_11_14_17_20_21603)),
inference(resolve,[status(thm)],[c_80,c_70]) ).
cnf(c_97,plain,
rr(i2003_11_14_17_20_21603,sK0(i2003_11_14_17_20_21603)),
inference(resolve,[status(thm)],[c_80,c_69]) ).
cnf(c_103,plain,
~ cd(sK1(i2003_11_14_17_20_21603)),
inference(resolve,[status(thm)],[c_82,c_94]) ).
cnf(c_121,plain,
( cd(A)
| A != sK0(i2003_11_14_17_20_21603) ),
inference(resolve,[status(thm)],[c_42,c_96]) ).
cnf(c_113,plain,
sK1(i2003_11_14_17_20_21603) != sK0(i2003_11_14_17_20_21603),
inference(resolve,[status(thm)],[c_121,c_103]) ).
cnf(c_122,plain,
( A = sK0(i2003_11_14_17_20_21603)
| ~ rr(i2003_11_14_17_20_21603,A)
| ~ cUnsatisfiable(i2003_11_14_17_20_21603) ),
inference(resolve,[status(thm)],[c_71,c_97]) ).
cnf(c_123,plain,
( sK1(i2003_11_14_17_20_21603) = sK0(i2003_11_14_17_20_21603)
| ~ cUnsatisfiable(i2003_11_14_17_20_21603) ),
inference(resolve,[status(thm)],[c_122,c_95]) ).
cnf(c_124,plain,
~ cUnsatisfiable(i2003_11_14_17_20_21603),
inference(resolve,[status(thm)],[c_123,c_113]) ).
cnf(c_120,plain,
$false,
inference(resolve,[status(thm)],[c_80,c_124]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : KRS097+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.34 % Computer : n012.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
% 0.08/0.34 % CPULimit : 300
% 0.08/0.34 % WCLimit : 300
% 0.08/0.34 % DateTime : Fri Sep 25 19:39:05 UTC 2026
% 0.08/0.34 % CPUTime :
% 0.08/0.34 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.34 % Process 2814379 was started by sandbox2 on n012,
% 0.08/0.34 % Fri Sep 25 19:39:05 2026
% 0.08/0.34 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.08/0.35
% 0.08/0.35 % From the command line: assign(max_seconds, 300).
% 0.11/0.36
% 0.11/0.36 % SZS status Unsatisfiable for theBenchmark
% 0.11/0.36
% 0.11/0.36 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.11/0.36 % Length of proof is 18.
% 0.11/0.36 % Level of proof is 5.
% 0.11/0.36 % Maximum clause weight is 11.000.
% 0.11/0.36 % Given clauses 65.
% 0.11/0.36
% 0.11/0.36 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------