%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : KRS111+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 : n008.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 0.13s 0.38s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 9
% Syntax : Number of formulae : 45 ( 16 unt; 0 def)
% Number of atoms : 132 ( 11 equ)
% Maximal formula atoms : 19 ( 2 avg)
% Number of connectives : 143 ( 56 ~; 50 |; 29 &)
% ( 3 <=>; 5 =>; 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 : 73 ( 2 sgn 40 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(cpxcomp_substitution_1,axiom,
! [A,B] :
( ( cpxcomp(A)
& A = B )
=> cpxcomp(B) ),
file('theBenchmark.p',cpxcomp_substitution_1) ).
fof(axiom_2,axiom,
! [X] :
( cUnsatisfiable(X)
<=> ( ? [Y] :
( cp(Y)
& rf(X,Y) )
& ? [Y] :
( cowlThing(Y)
& rs(X,Y) )
& ? [Y] :
( cpxcomp(Y)
& rf1(X,Y) ) ) ),
file('theBenchmark.p',axiom_2) ).
fof(axiom_3,axiom,
! [X] :
( cp(X)
<=> ~ ? [Y] : ra_Px1(X,Y) ),
file('theBenchmark.p',axiom_3) ).
fof(axiom_4,axiom,
! [X] :
( cpxcomp(X)
<=> ? [Y0] : ra_Px1(X,Y0) ),
file('theBenchmark.p',axiom_4) ).
fof(axiom_5,axiom,
! [X,Y,Z] :
( ( rf(X,Z)
& rf(X,Y) )
=> Y = Z ),
file('theBenchmark.p',axiom_5) ).
fof(axiom_6,axiom,
! [X,Y,Z] :
( ( rf1(X,Z)
& rf1(X,Y) )
=> Y = Z ),
file('theBenchmark.p',axiom_6) ).
fof(axiom_12,axiom,
! [X,Y] :
( rs(X,Y)
=> rf(X,Y) ),
file('theBenchmark.p',axiom_12) ).
fof(axiom_13,axiom,
! [X,Y] :
( rs(X,Y)
=> rf1(X,Y) ),
file('theBenchmark.p',axiom_13) ).
cnf(c_39,plain,
( cpxcomp(A)
| ~ cpxcomp(B)
| A != B ),
inference(clausify,[status(thm)],[cpxcomp_substitution_1]) ).
fof(nnf_24,plain,
! [X] :
( ( ! [Y] :
( ~ cp(Y)
| ~ rf(X,Y) )
| ! [X4] :
( ~ cowlThing(X4)
| ~ rs(X,X4) )
| ! [X3] :
( ~ cpxcomp(X3)
| ~ rf1(X,X3) )
| cUnsatisfiable(X) )
& ( ( ? [X2] :
( cp(X2)
& rf(X,X2) )
& ? [X1] :
( cowlThing(X1)
& rs(X,X1) )
& ? [X0] :
( cpxcomp(X0)
& rf1(X,X0) ) )
| ~ cUnsatisfiable(X) ) ),
inference(fof_nnf,[status(thm)],[axiom_2]) ).
fof(sk_axiom_2_sk,plain,
! [X] :
( ( ! [Y] :
( ~ cp(Y)
| ~ rf(X,Y) )
| ! [X4] :
( ~ cowlThing(X4)
| ~ rs(X,X4) )
| ! [X3] :
( ~ cpxcomp(X3)
| ~ rf1(X,X3) )
| cUnsatisfiable(X) )
& ( ( cp(sK2(X))
& rf(X,sK2(X))
& cowlThing(sK1(X))
& rs(X,sK1(X))
& cpxcomp(sK0(X))
& rf1(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_24]) ).
fof(sk_axiom_2,plain,
( ! [VAR_0,VAR_1,VAR_2,VAR_3] :
( ~ cp(VAR_3)
| ~ rf(VAR_0,VAR_3)
| ~ cowlThing(VAR_2)
| ~ rs(VAR_0,VAR_2)
| ~ cpxcomp(VAR_1)
| ~ rf1(VAR_0,VAR_1)
| cUnsatisfiable(VAR_0) )
& ! [VAR_0] :
( cp(sK2(VAR_0))
| ~ cUnsatisfiable(VAR_0) )
& ! [VAR_0] :
( rf(VAR_0,sK2(VAR_0))
| ~ cUnsatisfiable(VAR_0) )
& ! [VAR_0] :
( cowlThing(sK1(VAR_0))
| ~ cUnsatisfiable(VAR_0) )
& ! [VAR_0] :
( rs(VAR_0,sK1(VAR_0))
| ~ cUnsatisfiable(VAR_0) )
& ! [VAR_0] :
( cpxcomp(sK0(VAR_0))
| ~ cUnsatisfiable(VAR_0) )
& ! [VAR_0] :
( rf1(VAR_0,sK0(VAR_0))
| ~ cUnsatisfiable(VAR_0) ) ),
inference(cnf_transformation,[status(thm)],[sk_axiom_2_sk]) ).
cnf(c_60,plain,
( rf1(A,sK0(A))
| ~ cUnsatisfiable(A) ),
inference(split_conjunct,[status(thm)],[sk_axiom_2]) ).
cnf(c_61,plain,
( cpxcomp(sK0(A))
| ~ cUnsatisfiable(A) ),
inference(split_conjunct,[status(thm)],[sk_axiom_2]) ).
cnf(c_62,plain,
( rs(A,sK1(A))
| ~ cUnsatisfiable(A) ),
inference(split_conjunct,[status(thm)],[sk_axiom_2]) ).
cnf(c_63,plain,
( rf(A,sK2(A))
| ~ cUnsatisfiable(A) ),
inference(split_conjunct,[status(thm)],[sk_axiom_2]) ).
cnf(c_64,plain,
( cp(sK2(A))
| ~ cUnsatisfiable(A) ),
inference(split_conjunct,[status(thm)],[sk_axiom_2]) ).
cnf(c_67,plain,
( ~ ra_Px1(A,B)
| ~ cp(A) ),
inference(clausify,[status(thm)],[axiom_3]) ).
fof(nnf_26,plain,
! [X] :
( ( ! [Y0] : ~ ra_Px1(X,Y0)
| cpxcomp(X) )
& ( ? [X4] : ra_Px1(X,X4)
| ~ cpxcomp(X) ) ),
inference(fof_nnf,[status(thm)],[axiom_4]) ).
fof(sk_axiom_4_sk,plain,
! [X] :
( ( ! [Y0] : ~ ra_Px1(X,Y0)
| cpxcomp(X) )
& ( ra_Px1(X,sK3(X))
| ~ cpxcomp(X) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(X4,sK3(X))],[nnf_26]) ).
fof(sk_axiom_4,plain,
( ! [VAR_0,VAR_1] :
( ~ ra_Px1(VAR_0,VAR_1)
| cpxcomp(VAR_0) )
& ! [VAR_0] :
( ra_Px1(VAR_0,sK3(VAR_0))
| ~ cpxcomp(VAR_0) ) ),
inference(cnf_transformation,[status(thm)],[sk_axiom_4_sk]) ).
cnf(c_69,plain,
( ra_Px1(A,sK3(A))
| ~ cpxcomp(A) ),
inference(split_conjunct,[status(thm)],[sk_axiom_4]) ).
cnf(c_71,plain,
( C = B
| ~ rf(A,C)
| ~ rf(A,B) ),
inference(clausify,[status(thm)],[axiom_5]) ).
cnf(c_72,plain,
( C = B
| ~ rf1(A,C)
| ~ rf1(A,B) ),
inference(clausify,[status(thm)],[axiom_6]) ).
fof(axiom_11,axiom,
cUnsatisfiable(i2003_11_14_17_21_15425),
file('theBenchmark.p',axiom_11) ).
cnf(c_80,plain,
cUnsatisfiable(i2003_11_14_17_21_15425),
inference(clausify,[status(thm)],[axiom_11]) ).
cnf(c_81,plain,
( rf(A,B)
| ~ rs(A,B) ),
inference(clausify,[status(thm)],[axiom_12]) ).
cnf(c_82,plain,
( rf1(A,B)
| ~ rs(A,B) ),
inference(clausify,[status(thm)],[axiom_13]) ).
cnf(c_87,plain,
cp(sK2(i2003_11_14_17_21_15425)),
inference(resolve,[status(thm)],[c_80,c_64]) ).
cnf(c_88,plain,
rf(i2003_11_14_17_21_15425,sK2(i2003_11_14_17_21_15425)),
inference(resolve,[status(thm)],[c_80,c_63]) ).
cnf(c_89,plain,
rs(i2003_11_14_17_21_15425,sK1(i2003_11_14_17_21_15425)),
inference(resolve,[status(thm)],[c_80,c_62]) ).
cnf(c_90,plain,
cpxcomp(sK0(i2003_11_14_17_21_15425)),
inference(resolve,[status(thm)],[c_80,c_61]) ).
cnf(c_91,plain,
rf1(i2003_11_14_17_21_15425,sK0(i2003_11_14_17_21_15425)),
inference(resolve,[status(thm)],[c_80,c_60]) ).
cnf(c_95,plain,
~ ra_Px1(sK2(i2003_11_14_17_21_15425),A),
inference(resolve,[status(thm)],[c_67,c_87]) ).
cnf(c_102,plain,
~ cpxcomp(sK2(i2003_11_14_17_21_15425)),
inference(resolve,[status(thm)],[c_69,c_95]) ).
cnf(c_130,plain,
( cpxcomp(A)
| A != sK0(i2003_11_14_17_21_15425) ),
inference(resolve,[status(thm)],[c_39,c_90]) ).
cnf(c_103,plain,
sK2(i2003_11_14_17_21_15425) != sK0(i2003_11_14_17_21_15425),
inference(resolve,[status(thm)],[c_130,c_102]) ).
cnf(c_131,plain,
( sK2(i2003_11_14_17_21_15425) = A
| ~ rf(i2003_11_14_17_21_15425,A) ),
inference(resolve,[status(thm)],[c_71,c_88]) ).
cnf(c_104,plain,
~ rf(i2003_11_14_17_21_15425,sK0(i2003_11_14_17_21_15425)),
inference(resolve,[status(thm)],[c_131,c_103]) ).
cnf(c_107,plain,
rf1(i2003_11_14_17_21_15425,sK1(i2003_11_14_17_21_15425)),
inference(resolve,[status(thm)],[c_89,c_82]) ).
cnf(c_108,plain,
rf(i2003_11_14_17_21_15425,sK1(i2003_11_14_17_21_15425)),
inference(resolve,[status(thm)],[c_89,c_81]) ).
cnf(c_132,plain,
( A = sK0(i2003_11_14_17_21_15425)
| ~ rf1(i2003_11_14_17_21_15425,A) ),
inference(resolve,[status(thm)],[c_72,c_91]) ).
cnf(c_124,plain,
sK1(i2003_11_14_17_21_15425) = sK0(i2003_11_14_17_21_15425),
inference(resolve,[status(thm)],[c_132,c_107]) ).
cnf(c_133,plain,
rf(i2003_11_14_17_21_15425,sK0(i2003_11_14_17_21_15425)),
inference(paramod,[status(thm)],[c_124,c_108]) ).
cnf(c_129,plain,
$false,
inference(resolve,[status(thm)],[c_104,c_133]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : KRS111+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n008.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Fri Sep 25 19:40:39 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 1703778 was started by sandbox2 on n008,
% 0.09/0.35 % Fri Sep 25 19:40:39 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).
% 0.13/0.38
% 0.13/0.38 % SZS status Unsatisfiable for theBenchmark
% 0.13/0.38
% 0.13/0.38 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.13/0.38 % Length of proof is 34.
% 0.13/0.38 % Level of proof is 7.
% 0.13/0.38 % Maximum clause weight is 16.000.
% 0.13/0.38 % Given clauses 61.
% 0.13/0.38
% 0.13/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------