%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : KRS107+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 : n009.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 0.09s 0.37s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 10
% Syntax : Number of formulae : 49 ( 17 unt; 0 def)
% Number of atoms : 133 ( 8 equ)
% Maximal formula atoms : 16 ( 2 avg)
% Number of connectives : 142 ( 58 ~; 49 |; 26 &)
% ( 5 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 12 ( 10 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 1 con; 0-1 aty)
% Number of variables : 65 ( 1 sgn 35 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(cc2_substitution_1,axiom,
! [A,B] :
( ( cc2(A)
& A = B )
=> cc2(B) ),
file('theBenchmark.p',cc2_substitution_1) ).
fof(axiom_2,axiom,
! [X] :
( cUnsatisfiable(X)
<=> ( ca_Cx1(X)
& ? [Y] :
( cc2(Y)
& rrx4(X,Y) )
& ? [Y] :
( cc1(Y)
& rrx3(X,Y) ) ) ),
file('theBenchmark.p',axiom_2) ).
fof(axiom_3,axiom,
! [X] :
( ca_Ax2(X)
<=> ( cc1(X)
& cc2(X) ) ),
file('theBenchmark.p',axiom_3) ).
fof(axiom_4,axiom,
! [X] :
( ca_Cx1(X)
<=> ? [Y0] : ra_Px1(X,Y0) ),
file('theBenchmark.p',axiom_4) ).
fof(axiom_5,axiom,
! [X] :
( ca_Cx1xcomp(X)
<=> ? [Y] :
( ca_Ax2(Y)
& rrx3(X,Y) ) ),
file('theBenchmark.p',axiom_5) ).
fof(axiom_6,axiom,
! [X] :
( ca_Cx1xcomp(X)
<=> ~ ? [Y] : ra_Px1(X,Y) ),
file('theBenchmark.p',axiom_6) ).
fof(axiom_7,axiom,
! [X,Y,Z] :
( ( rrx(X,Z)
& rrx(X,Y) )
=> Y = Z ),
file('theBenchmark.p',axiom_7) ).
fof(axiom_17,axiom,
! [X,Y] :
( rrx4(X,Y)
=> rrx(X,Y) ),
file('theBenchmark.p',axiom_17) ).
fof(axiom_20,axiom,
! [X,Y] :
( rrx3(X,Y)
=> rrx(X,Y) ),
file('theBenchmark.p',axiom_20) ).
cnf(c_58,plain,
( cc2(A)
| ~ cc2(B)
| A != B ),
inference(clausify,[status(thm)],[cc2_substitution_1]) ).
fof(nnf_35,plain,
! [X] :
( ( ~ ca_Cx1(X)
| ! [Y] :
( ~ cc2(Y)
| ~ rrx4(X,Y) )
| ! [X2] :
( ~ cc1(X2)
| ~ rrx3(X,X2) )
| cUnsatisfiable(X) )
& ( ( ca_Cx1(X)
& ? [X1] :
( cc2(X1)
& rrx4(X,X1) )
& ? [X0] :
( cc1(X0)
& rrx3(X,X0) ) )
| ~ cUnsatisfiable(X) ) ),
inference(fof_nnf,[status(thm)],[axiom_2]) ).
fof(sk_axiom_2_sk,plain,
! [X] :
( ( ~ ca_Cx1(X)
| ! [Y] :
( ~ cc2(Y)
| ~ rrx4(X,Y) )
| ! [X2] :
( ~ cc1(X2)
| ~ rrx3(X,X2) )
| cUnsatisfiable(X) )
& ( ( ca_Cx1(X)
& cc2(sK1(X))
& rrx4(X,sK1(X))
& cc1(sK0(X))
& rrx3(X,sK0(X)) )
| ~ cUnsatisfiable(X) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0(X)),skolemize(X1,sK1(X))],[nnf_35]) ).
fof(sk_axiom_2,plain,
( ! [VAR_0,VAR_1,VAR_2] :
( ~ ca_Cx1(VAR_0)
| ~ cc2(VAR_2)
| ~ rrx4(VAR_0,VAR_2)
| ~ cc1(VAR_1)
| ~ rrx3(VAR_0,VAR_1)
| cUnsatisfiable(VAR_0) )
& ! [VAR_0] :
( ca_Cx1(VAR_0)
| ~ cUnsatisfiable(VAR_0) )
& ! [VAR_0] :
( cc2(sK1(VAR_0))
| ~ cUnsatisfiable(VAR_0) )
& ! [VAR_0] :
( rrx4(VAR_0,sK1(VAR_0))
| ~ cUnsatisfiable(VAR_0) )
& ! [VAR_0] :
( cc1(sK0(VAR_0))
| ~ cUnsatisfiable(VAR_0) )
& ! [VAR_0] :
( rrx3(VAR_0,sK0(VAR_0))
| ~ cUnsatisfiable(VAR_0) ) ),
inference(cnf_transformation,[status(thm)],[sk_axiom_2_sk]) ).
cnf(c_89,plain,
( rrx3(A,sK0(A))
| ~ cUnsatisfiable(A) ),
inference(split_conjunct,[status(thm)],[sk_axiom_2]) ).
cnf(c_90,plain,
( cc1(sK0(A))
| ~ cUnsatisfiable(A) ),
inference(split_conjunct,[status(thm)],[sk_axiom_2]) ).
cnf(c_91,plain,
( rrx4(A,sK1(A))
| ~ cUnsatisfiable(A) ),
inference(split_conjunct,[status(thm)],[sk_axiom_2]) ).
cnf(c_92,plain,
( cc2(sK1(A))
| ~ cUnsatisfiable(A) ),
inference(split_conjunct,[status(thm)],[sk_axiom_2]) ).
cnf(c_93,plain,
( ca_Cx1(A)
| ~ cUnsatisfiable(A) ),
inference(split_conjunct,[status(thm)],[sk_axiom_2]) ).
cnf(c_97,plain,
( ~ cc1(A)
| ~ cc2(A)
| ca_Ax2(A) ),
inference(clausify,[status(thm)],[axiom_3]) ).
fof(nnf_37,plain,
! [X] :
( ( ! [Y0] : ~ ra_Px1(X,Y0)
| ca_Cx1(X) )
& ( ? [X2] : ra_Px1(X,X2)
| ~ ca_Cx1(X) ) ),
inference(fof_nnf,[status(thm)],[axiom_4]) ).
fof(sk_axiom_4_sk,plain,
! [X] :
( ( ! [Y0] : ~ ra_Px1(X,Y0)
| ca_Cx1(X) )
& ( ra_Px1(X,sK2(X))
| ~ ca_Cx1(X) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(X2,sK2(X))],[nnf_37]) ).
fof(sk_axiom_4,plain,
( ! [VAR_0,VAR_1] :
( ~ ra_Px1(VAR_0,VAR_1)
| ca_Cx1(VAR_0) )
& ! [VAR_0] :
( ra_Px1(VAR_0,sK2(VAR_0))
| ~ ca_Cx1(VAR_0) ) ),
inference(cnf_transformation,[status(thm)],[sk_axiom_4_sk]) ).
cnf(c_98,plain,
( ra_Px1(A,sK2(A))
| ~ ca_Cx1(A) ),
inference(split_conjunct,[status(thm)],[sk_axiom_4]) ).
cnf(c_102,plain,
( ~ ca_Ax2(B)
| ~ rrx3(A,B)
| ca_Cx1xcomp(A) ),
inference(clausify,[status(thm)],[axiom_5]) ).
cnf(c_103,plain,
( ~ ra_Px1(A,B)
| ~ ca_Cx1xcomp(A) ),
inference(clausify,[status(thm)],[axiom_6]) ).
cnf(c_105,plain,
( C = B
| ~ rrx(A,C)
| ~ rrx(A,B) ),
inference(clausify,[status(thm)],[axiom_7]) ).
fof(axiom_12,axiom,
cUnsatisfiable(i2003_11_14_17_21_01226),
file('theBenchmark.p',axiom_12) ).
cnf(c_110,plain,
cUnsatisfiable(i2003_11_14_17_21_01226),
inference(clausify,[status(thm)],[axiom_12]) ).
cnf(c_115,plain,
( rrx(A,B)
| ~ rrx4(A,B) ),
inference(clausify,[status(thm)],[axiom_17]) ).
cnf(c_118,plain,
( rrx(A,B)
| ~ rrx3(A,B) ),
inference(clausify,[status(thm)],[axiom_20]) ).
cnf(c_123,plain,
ca_Cx1(i2003_11_14_17_21_01226),
inference(resolve,[status(thm)],[c_110,c_93]) ).
cnf(c_124,plain,
cc2(sK1(i2003_11_14_17_21_01226)),
inference(resolve,[status(thm)],[c_110,c_92]) ).
cnf(c_125,plain,
rrx4(i2003_11_14_17_21_01226,sK1(i2003_11_14_17_21_01226)),
inference(resolve,[status(thm)],[c_110,c_91]) ).
cnf(c_126,plain,
cc1(sK0(i2003_11_14_17_21_01226)),
inference(resolve,[status(thm)],[c_110,c_90]) ).
cnf(c_127,plain,
rrx3(i2003_11_14_17_21_01226,sK0(i2003_11_14_17_21_01226)),
inference(resolve,[status(thm)],[c_110,c_89]) ).
cnf(c_129,plain,
ra_Px1(i2003_11_14_17_21_01226,sK2(i2003_11_14_17_21_01226)),
inference(resolve,[status(thm)],[c_123,c_98]) ).
cnf(c_137,plain,
rrx(i2003_11_14_17_21_01226,sK1(i2003_11_14_17_21_01226)),
inference(resolve,[status(thm)],[c_125,c_115]) ).
cnf(c_142,plain,
rrx(i2003_11_14_17_21_01226,sK0(i2003_11_14_17_21_01226)),
inference(resolve,[status(thm)],[c_127,c_118]) ).
cnf(c_145,plain,
( ~ ca_Ax2(sK0(i2003_11_14_17_21_01226))
| ca_Cx1xcomp(i2003_11_14_17_21_01226) ),
inference(resolve,[status(thm)],[c_127,c_102]) ).
cnf(c_148,plain,
~ ca_Cx1xcomp(i2003_11_14_17_21_01226),
inference(resolve,[status(thm)],[c_129,c_103]) ).
cnf(c_151,plain,
~ ca_Ax2(sK0(i2003_11_14_17_21_01226)),
inference(resolve,[status(thm)],[c_148,c_145]) ).
cnf(c_160,plain,
( ~ cc1(sK0(i2003_11_14_17_21_01226))
| ~ cc2(sK0(i2003_11_14_17_21_01226)) ),
inference(resolve,[status(thm)],[c_97,c_151]) ).
cnf(c_155,plain,
~ cc2(sK0(i2003_11_14_17_21_01226)),
inference(resolve,[status(thm)],[c_160,c_126]) ).
cnf(c_161,plain,
( cc2(A)
| A != sK1(i2003_11_14_17_21_01226) ),
inference(resolve,[status(thm)],[c_58,c_124]) ).
cnf(c_162,plain,
sK0(i2003_11_14_17_21_01226) != sK1(i2003_11_14_17_21_01226),
inference(resolve,[status(thm)],[c_161,c_155]) ).
cnf(c_156,plain,
sK1(i2003_11_14_17_21_01226) != sK0(i2003_11_14_17_21_01226),
inference(copy,[status(thm)],[c_162]) ).
cnf(c_163,plain,
( sK1(i2003_11_14_17_21_01226) = A
| ~ rrx(i2003_11_14_17_21_01226,A) ),
inference(resolve,[status(thm)],[c_105,c_137]) ).
cnf(c_164,plain,
~ rrx(i2003_11_14_17_21_01226,sK0(i2003_11_14_17_21_01226)),
inference(resolve,[status(thm)],[c_163,c_156]) ).
cnf(c_159,plain,
$false,
inference(resolve,[status(thm)],[c_142,c_164]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KRS107+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.34 % Computer : n009.cluster.edu
% 0.09/0.34 % Model : x86_64 x86_64
% 0.09/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.34 % Memory : 8046.5625MB
% 0.09/0.34 % OS : Linux 6.8.0-71-generic
% 0.09/0.34 % CPULimit : 300
% 0.09/0.34 % WCLimit : 300
% 0.09/0.34 % DateTime : Fri Sep 25 19:39:44 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.35 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.35 % Process 2369200 was started by sandbox2 on n009,
% 0.09/0.35 % Fri Sep 25 19:39:44 2026
% 0.09/0.35 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.09/0.36
% 0.09/0.36 % From the command line: assign(max_seconds, 300).
% 0.09/0.37
% 0.09/0.37 % SZS status Unsatisfiable for theBenchmark
% 0.09/0.37
% 0.09/0.37 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.09/0.37 % Length of proof is 37.
% 0.09/0.37 % Level of proof is 8.
% 0.09/0.37 % Maximum clause weight is 9.000.
% 0.09/0.37 % Given clauses 79.
% 0.09/0.37
% 0.09/0.37 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------