%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : KRS106+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 07:46:03 AM UTC 2026
% Result : Unsatisfiable 0.15s 0.39s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 10
% Syntax : Number of formulae : 49 ( 17 unt; 0 def)
% Number of atoms : 141 ( 15 equ)
% Maximal formula atoms : 19 ( 2 avg)
% Number of connectives : 154 ( 62 ~; 53 |; 30 &)
% ( 3 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 1 con; 0-1 aty)
% Number of variables : 80 ( 2 sgn 43 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(cp1xcomp_substitution_1,axiom,
! [A,B] :
( ( cp1xcomp(A)
& A = B )
=> cp1xcomp(B) ),
file('theBenchmark.p',cp1xcomp_substitution_1) ).
fof(rf2_substitution_2,axiom,
! [A,B,C] :
( ( rf2(C,A)
& A = B )
=> rf2(C,B) ),
file('theBenchmark.p',rf2_substitution_2) ).
fof(axiom_2,axiom,
! [X] :
( cUnsatisfiable(X)
<=> ( ? [Y] :
( cp1xcomp(Y)
& rf2(X,Y) )
& ? [Y] :
( cp1(Y)
& rf1(X,Y) )
& ? [Y] :
( cp2(Y)
& rf3(X,Y) ) ) ),
file('theBenchmark.p',axiom_2) ).
fof(axiom_3,axiom,
! [X] :
( cp1(X)
<=> ~ ? [Y] : ra_Px1(X,Y) ),
file('theBenchmark.p',axiom_3) ).
fof(axiom_4,axiom,
! [X] :
( cp1xcomp(X)
<=> ? [Y0] : ra_Px1(X,Y0) ),
file('theBenchmark.p',axiom_4) ).
fof(axiom_5,axiom,
! [X,Y,Z] :
( ( rf1(X,Z)
& rf1(X,Y) )
=> Y = Z ),
file('theBenchmark.p',axiom_5) ).
fof(axiom_6,axiom,
! [X,Y,Z] :
( ( rf2(X,Z)
& rf2(X,Y) )
=> Y = Z ),
file('theBenchmark.p',axiom_6) ).
fof(axiom_9,axiom,
! [X,Y] :
( rf3(X,Y)
=> rf1(X,Y) ),
file('theBenchmark.p',axiom_9) ).
fof(axiom_10,axiom,
! [X,Y] :
( rf3(X,Y)
=> rf2(X,Y) ),
file('theBenchmark.p',axiom_10) ).
cnf(c_31,plain,
( cp1xcomp(A)
| ~ cp1xcomp(B)
| A != B ),
inference(clausify,[status(thm)],[cp1xcomp_substitution_1]) ).
cnf(c_38,plain,
( rf2(C,A)
| ~ rf2(C,B)
| A != B ),
inference(clausify,[status(thm)],[rf2_substitution_2]) ).
fof(nnf_19,plain,
! [X] :
( ( ! [Y] :
( ~ cp1xcomp(Y)
| ~ rf2(X,Y) )
| ! [X4] :
( ~ cp1(X4)
| ~ rf1(X,X4) )
| ! [X3] :
( ~ cp2(X3)
| ~ rf3(X,X3) )
| cUnsatisfiable(X) )
& ( ( ? [X2] :
( cp1xcomp(X2)
& rf2(X,X2) )
& ? [X1] :
( cp1(X1)
& rf1(X,X1) )
& ? [X0] :
( cp2(X0)
& rf3(X,X0) ) )
| ~ cUnsatisfiable(X) ) ),
inference(fof_nnf,[status(thm)],[axiom_2]) ).
fof(sk_axiom_2_sk,plain,
! [X] :
( ( ! [Y] :
( ~ cp1xcomp(Y)
| ~ rf2(X,Y) )
| ! [X4] :
( ~ cp1(X4)
| ~ rf1(X,X4) )
| ! [X3] :
( ~ cp2(X3)
| ~ rf3(X,X3) )
| cUnsatisfiable(X) )
& ( ( cp1xcomp(sK2(X))
& rf2(X,sK2(X))
& cp1(sK1(X))
& rf1(X,sK1(X))
& cp2(sK0(X))
& rf3(X,sK0(X)) )
| ~ cUnsatisfiable(X) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0(X)),skolemize(X1,sK1(X)),skolemize(X2,sK2(X))],[nnf_19]) ).
fof(sk_axiom_2,plain,
( ! [VAR_0,VAR_1,VAR_2,VAR_3] :
( ~ cp1xcomp(VAR_3)
| ~ rf2(VAR_0,VAR_3)
| ~ cp1(VAR_2)
| ~ rf1(VAR_0,VAR_2)
| ~ cp2(VAR_1)
| ~ rf3(VAR_0,VAR_1)
| cUnsatisfiable(VAR_0) )
& ! [VAR_0] :
( cp1xcomp(sK2(VAR_0))
| ~ cUnsatisfiable(VAR_0) )
& ! [VAR_0] :
( rf2(VAR_0,sK2(VAR_0))
| ~ cUnsatisfiable(VAR_0) )
& ! [VAR_0] :
( cp1(sK1(VAR_0))
| ~ cUnsatisfiable(VAR_0) )
& ! [VAR_0] :
( rf1(VAR_0,sK1(VAR_0))
| ~ cUnsatisfiable(VAR_0) )
& ! [VAR_0] :
( cp2(sK0(VAR_0))
| ~ cUnsatisfiable(VAR_0) )
& ! [VAR_0] :
( rf3(VAR_0,sK0(VAR_0))
| ~ cUnsatisfiable(VAR_0) ) ),
inference(cnf_transformation,[status(thm)],[sk_axiom_2_sk]) ).
cnf(c_47,plain,
( rf3(A,sK0(A))
| ~ cUnsatisfiable(A) ),
inference(split_conjunct,[status(thm)],[sk_axiom_2]) ).
cnf(c_49,plain,
( rf1(A,sK1(A))
| ~ cUnsatisfiable(A) ),
inference(split_conjunct,[status(thm)],[sk_axiom_2]) ).
cnf(c_50,plain,
( cp1(sK1(A))
| ~ cUnsatisfiable(A) ),
inference(split_conjunct,[status(thm)],[sk_axiom_2]) ).
cnf(c_51,plain,
( rf2(A,sK2(A))
| ~ cUnsatisfiable(A) ),
inference(split_conjunct,[status(thm)],[sk_axiom_2]) ).
cnf(c_52,plain,
( cp1xcomp(sK2(A))
| ~ cUnsatisfiable(A) ),
inference(split_conjunct,[status(thm)],[sk_axiom_2]) ).
cnf(c_54,plain,
( ~ ra_Px1(A,B)
| ~ cp1(A) ),
inference(clausify,[status(thm)],[axiom_3]) ).
fof(nnf_21,plain,
! [X] :
( ( ! [Y0] : ~ ra_Px1(X,Y0)
| cp1xcomp(X) )
& ( ? [X4] : ra_Px1(X,X4)
| ~ cp1xcomp(X) ) ),
inference(fof_nnf,[status(thm)],[axiom_4]) ).
fof(sk_axiom_4_sk,plain,
! [X] :
( ( ! [Y0] : ~ ra_Px1(X,Y0)
| cp1xcomp(X) )
& ( ra_Px1(X,sK3(X))
| ~ cp1xcomp(X) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(X4,sK3(X))],[nnf_21]) ).
fof(sk_axiom_4,plain,
( ! [VAR_0,VAR_1] :
( ~ ra_Px1(VAR_0,VAR_1)
| cp1xcomp(VAR_0) )
& ! [VAR_0] :
( ra_Px1(VAR_0,sK3(VAR_0))
| ~ cp1xcomp(VAR_0) ) ),
inference(cnf_transformation,[status(thm)],[sk_axiom_4_sk]) ).
cnf(c_56,plain,
( ra_Px1(A,sK3(A))
| ~ cp1xcomp(A) ),
inference(split_conjunct,[status(thm)],[sk_axiom_4]) ).
cnf(c_58,plain,
( C = B
| ~ rf1(A,C)
| ~ rf1(A,B) ),
inference(clausify,[status(thm)],[axiom_5]) ).
cnf(c_59,plain,
( C = B
| ~ rf2(A,C)
| ~ rf2(A,B) ),
inference(clausify,[status(thm)],[axiom_6]) ).
fof(axiom_8,axiom,
cUnsatisfiable(i2003_11_14_17_20_57644),
file('theBenchmark.p',axiom_8) ).
cnf(c_61,plain,
cUnsatisfiable(i2003_11_14_17_20_57644),
inference(clausify,[status(thm)],[axiom_8]) ).
cnf(c_62,plain,
( rf1(A,B)
| ~ rf3(A,B) ),
inference(clausify,[status(thm)],[axiom_9]) ).
cnf(c_63,plain,
( rf2(A,B)
| ~ rf3(A,B) ),
inference(clausify,[status(thm)],[axiom_10]) ).
cnf(c_70,plain,
cp1xcomp(sK2(i2003_11_14_17_20_57644)),
inference(resolve,[status(thm)],[c_61,c_52]) ).
cnf(c_71,plain,
rf2(i2003_11_14_17_20_57644,sK2(i2003_11_14_17_20_57644)),
inference(resolve,[status(thm)],[c_61,c_51]) ).
cnf(c_72,plain,
cp1(sK1(i2003_11_14_17_20_57644)),
inference(resolve,[status(thm)],[c_61,c_50]) ).
cnf(c_73,plain,
rf1(i2003_11_14_17_20_57644,sK1(i2003_11_14_17_20_57644)),
inference(resolve,[status(thm)],[c_61,c_49]) ).
cnf(c_75,plain,
rf3(i2003_11_14_17_20_57644,sK0(i2003_11_14_17_20_57644)),
inference(resolve,[status(thm)],[c_61,c_47]) ).
cnf(c_83,plain,
~ ra_Px1(sK1(i2003_11_14_17_20_57644),A),
inference(resolve,[status(thm)],[c_54,c_72]) ).
cnf(c_87,plain,
~ cp1xcomp(sK1(i2003_11_14_17_20_57644)),
inference(resolve,[status(thm)],[c_56,c_83]) ).
cnf(c_115,plain,
( cp1xcomp(A)
| A != sK2(i2003_11_14_17_20_57644) ),
inference(resolve,[status(thm)],[c_31,c_70]) ).
cnf(c_116,plain,
sK1(i2003_11_14_17_20_57644) != sK2(i2003_11_14_17_20_57644),
inference(resolve,[status(thm)],[c_115,c_87]) ).
cnf(c_88,plain,
sK2(i2003_11_14_17_20_57644) != sK1(i2003_11_14_17_20_57644),
inference(copy,[status(thm)],[c_116]) ).
cnf(c_117,plain,
( sK2(i2003_11_14_17_20_57644) = A
| ~ rf2(i2003_11_14_17_20_57644,A) ),
inference(resolve,[status(thm)],[c_59,c_71]) ).
cnf(c_89,plain,
~ rf2(i2003_11_14_17_20_57644,sK1(i2003_11_14_17_20_57644)),
inference(resolve,[status(thm)],[c_117,c_88]) ).
cnf(c_96,plain,
rf2(i2003_11_14_17_20_57644,sK0(i2003_11_14_17_20_57644)),
inference(resolve,[status(thm)],[c_75,c_63]) ).
cnf(c_97,plain,
rf1(i2003_11_14_17_20_57644,sK0(i2003_11_14_17_20_57644)),
inference(resolve,[status(thm)],[c_75,c_62]) ).
cnf(c_118,plain,
( rf2(i2003_11_14_17_20_57644,A)
| A != sK0(i2003_11_14_17_20_57644) ),
inference(resolve,[status(thm)],[c_38,c_96]) ).
cnf(c_104,plain,
sK1(i2003_11_14_17_20_57644) != sK0(i2003_11_14_17_20_57644),
inference(resolve,[status(thm)],[c_118,c_89]) ).
cnf(c_119,plain,
( sK1(i2003_11_14_17_20_57644) = A
| ~ rf1(i2003_11_14_17_20_57644,A) ),
inference(resolve,[status(thm)],[c_58,c_73]) ).
cnf(c_120,plain,
~ rf1(i2003_11_14_17_20_57644,sK0(i2003_11_14_17_20_57644)),
inference(resolve,[status(thm)],[c_119,c_104]) ).
cnf(c_114,plain,
$false,
inference(resolve,[status(thm)],[c_97,c_120]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KRS106+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.36 % Computer : n020.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Fri Sep 25 19:40:33 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/0.37 % Process 3600226 was started by sandbox2 on n020,
% 0.11/0.37 % Fri Sep 25 19:40:33 2026
% 0.11/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.15/0.38
% 0.15/0.38 % From the command line: assign(max_seconds, 300).
% 0.15/0.39
% 0.15/0.39 % SZS status Unsatisfiable for theBenchmark
% 0.15/0.39
% 0.15/0.39 % Proof 1 at 0.00 (+ 0.01) seconds.
% 0.15/0.39 % Length of proof is 36.
% 0.15/0.39 % Level of proof is 8.
% 0.15/0.39 % Maximum clause weight is 16.000.
% 0.15/0.39 % Given clauses 63.
% 0.15/0.39
% 0.15/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------