%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : KRS112+1 : TPTP v9.3.1. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/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 : 14
% Number of leaves : 13
% Syntax : Number of formulae : 64 ( 22 unt; 0 def)
% Number of atoms : 167 ( 18 equ)
% Maximal formula atoms : 13 ( 2 avg)
% Number of connectives : 173 ( 70 ~; 60 |; 30 &)
% ( 6 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 13 ( 11 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 1 con; 0-1 aty)
% Number of variables : 93 ( 2 sgn 51 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(ca_Ax2_substitution_1,axiom,
! [A,B] :
( ( ca_Ax2(A)
& A = B )
=> ca_Ax2(B) ),
file('theBenchmark.p',ca_Ax2_substitution_1) ).
fof(rf1_substitution_2,axiom,
! [A,B,C] :
( ( rf1(C,A)
& A = B )
=> rf1(C,B) ),
file('theBenchmark.p',rf1_substitution_2) ).
fof(axiom_2,axiom,
! [X] :
( cUnsatisfiable(X)
<=> ( ? [Y] :
( cp(Y)
& rf(X,Y) )
& ? [Y] :
( ca_Ax2(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] :
( ca_Ax2(X)
<=> ( ! [Y] :
( rinvF1(X,Y)
=> ca_Vx3(Y) )
& cpxcomp(X) ) ),
file('theBenchmark.p',axiom_5) ).
fof(axiom_6,axiom,
! [X] :
( ca_Vx3(X)
<=> ? [Y] :
( cowlThing(Y)
& rs(X,Y) ) ),
file('theBenchmark.p',axiom_6) ).
fof(axiom_7,axiom,
! [X,Y,Z] :
( ( rf(X,Z)
& rf(X,Y) )
=> Y = Z ),
file('theBenchmark.p',axiom_7) ).
fof(axiom_8,axiom,
! [X,Y,Z] :
( ( rf1(X,Z)
& rf1(X,Y) )
=> Y = Z ),
file('theBenchmark.p',axiom_8) ).
fof(axiom_10,axiom,
! [X,Y] :
( rinvF1(X,Y)
<=> rf1(Y,X) ),
file('theBenchmark.p',axiom_10) ).
fof(axiom_14,axiom,
! [X,Y] :
( rs(X,Y)
=> rf(X,Y) ),
file('theBenchmark.p',axiom_14) ).
fof(axiom_15,axiom,
! [X,Y] :
( rs(X,Y)
=> rf1(X,Y) ),
file('theBenchmark.p',axiom_15) ).
cnf(c_40,plain,
( ca_Ax2(A)
| ~ ca_Ax2(B)
| A != B ),
inference(clausify,[status(thm)],[ca_Ax2_substitution_1]) ).
cnf(c_51,plain,
( rf1(C,A)
| ~ rf1(C,B)
| A != B ),
inference(clausify,[status(thm)],[rf1_substitution_2]) ).
fof(nnf_26,plain,
! [X] :
( ( ! [Y] :
( ~ cp(Y)
| ~ rf(X,Y) )
| ! [X2] :
( ~ ca_Ax2(X2)
| ~ rf1(X,X2) )
| cUnsatisfiable(X) )
& ( ( ? [X1] :
( cp(X1)
& rf(X,X1) )
& ? [X0] :
( ca_Ax2(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) )
| ! [X2] :
( ~ ca_Ax2(X2)
| ~ rf1(X,X2) )
| cUnsatisfiable(X) )
& ( ( cp(sK1(X))
& rf(X,sK1(X))
& ca_Ax2(sK0(X))
& rf1(X,sK0(X)) )
| ~ cUnsatisfiable(X) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0(X)),skolemize(X1,sK1(X))],[nnf_26]) ).
fof(sk_axiom_2,plain,
( ! [VAR_0,VAR_1,VAR_2] :
( ~ cp(VAR_2)
| ~ rf(VAR_0,VAR_2)
| ~ ca_Ax2(VAR_1)
| ~ rf1(VAR_0,VAR_1)
| cUnsatisfiable(VAR_0) )
& ! [VAR_0] :
( cp(sK1(VAR_0))
| ~ cUnsatisfiable(VAR_0) )
& ! [VAR_0] :
( rf(VAR_0,sK1(VAR_0))
| ~ cUnsatisfiable(VAR_0) )
& ! [VAR_0] :
( ca_Ax2(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_66,plain,
( rf1(A,sK0(A))
| ~ cUnsatisfiable(A) ),
inference(split_conjunct,[status(thm)],[sk_axiom_2]) ).
cnf(c_67,plain,
( ca_Ax2(sK0(A))
| ~ cUnsatisfiable(A) ),
inference(split_conjunct,[status(thm)],[sk_axiom_2]) ).
cnf(c_68,plain,
( rf(A,sK1(A))
| ~ cUnsatisfiable(A) ),
inference(split_conjunct,[status(thm)],[sk_axiom_2]) ).
cnf(c_69,plain,
( cp(sK1(A))
| ~ cUnsatisfiable(A) ),
inference(split_conjunct,[status(thm)],[sk_axiom_2]) ).
cnf(c_71,plain,
( ~ ra_Px1(A,B)
| ~ cp(A) ),
inference(clausify,[status(thm)],[axiom_3]) ).
fof(nnf_28,plain,
! [X] :
( ( ! [Y0] : ~ ra_Px1(X,Y0)
| cpxcomp(X) )
& ( ? [X2] : ra_Px1(X,X2)
| ~ 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,sK2(X))
| ~ cpxcomp(X) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(X2,sK2(X))],[nnf_28]) ).
fof(sk_axiom_4,plain,
( ! [VAR_0,VAR_1] :
( ~ ra_Px1(VAR_0,VAR_1)
| cpxcomp(VAR_0) )
& ! [VAR_0] :
( ra_Px1(VAR_0,sK2(VAR_0))
| ~ cpxcomp(VAR_0) ) ),
inference(cnf_transformation,[status(thm)],[sk_axiom_4_sk]) ).
cnf(c_73,plain,
( ra_Px1(A,sK2(A))
| ~ cpxcomp(A) ),
inference(split_conjunct,[status(thm)],[sk_axiom_4]) ).
cnf(c_75,plain,
( cpxcomp(A)
| ~ ca_Ax2(A) ),
inference(clausify,[status(thm)],[axiom_5]) ).
cnf(c_76,plain,
( ca_Vx3(B)
| ~ rinvF1(A,B)
| ~ ca_Ax2(A) ),
inference(clausify,[status(thm)],[axiom_5]) ).
fof(nnf_30,plain,
! [X] :
( ( ! [Y] :
( ~ cowlThing(Y)
| ~ rs(X,Y) )
| ca_Vx3(X) )
& ( ? [X2] :
( cowlThing(X2)
& rs(X,X2) )
| ~ ca_Vx3(X) ) ),
inference(fof_nnf,[status(thm)],[axiom_6]) ).
fof(sk_axiom_6_sk,plain,
! [X] :
( ( ! [Y] :
( ~ cowlThing(Y)
| ~ rs(X,Y) )
| ca_Vx3(X) )
& ( ( cowlThing(sK3(X))
& rs(X,sK3(X)) )
| ~ ca_Vx3(X) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(X2,sK3(X))],[nnf_30]) ).
fof(sk_axiom_6,plain,
( ! [VAR_0,VAR_1] :
( ~ cowlThing(VAR_1)
| ~ rs(VAR_0,VAR_1)
| ca_Vx3(VAR_0) )
& ! [VAR_0] :
( cowlThing(sK3(VAR_0))
| ~ ca_Vx3(VAR_0) )
& ! [VAR_0] :
( rs(VAR_0,sK3(VAR_0))
| ~ ca_Vx3(VAR_0) ) ),
inference(cnf_transformation,[status(thm)],[sk_axiom_6_sk]) ).
cnf(c_79,plain,
( rs(A,sK3(A))
| ~ ca_Vx3(A) ),
inference(split_conjunct,[status(thm)],[sk_axiom_6]) ).
cnf(c_82,plain,
( C = B
| ~ rf(A,C)
| ~ rf(A,B) ),
inference(clausify,[status(thm)],[axiom_7]) ).
cnf(c_83,plain,
( C = B
| ~ rf1(A,C)
| ~ rf1(A,B) ),
inference(clausify,[status(thm)],[axiom_8]) ).
cnf(c_87,plain,
( ~ rf1(B,A)
| rinvF1(A,B) ),
inference(clausify,[status(thm)],[axiom_10]) ).
fof(axiom_13,axiom,
cUnsatisfiable(i2003_11_14_17_21_19256),
file('theBenchmark.p',axiom_13) ).
cnf(c_91,plain,
cUnsatisfiable(i2003_11_14_17_21_19256),
inference(clausify,[status(thm)],[axiom_13]) ).
cnf(c_92,plain,
( rf(A,B)
| ~ rs(A,B) ),
inference(clausify,[status(thm)],[axiom_14]) ).
cnf(c_93,plain,
( rf1(A,B)
| ~ rs(A,B) ),
inference(clausify,[status(thm)],[axiom_15]) ).
cnf(c_100,plain,
cp(sK1(i2003_11_14_17_21_19256)),
inference(resolve,[status(thm)],[c_91,c_69]) ).
cnf(c_101,plain,
rf(i2003_11_14_17_21_19256,sK1(i2003_11_14_17_21_19256)),
inference(resolve,[status(thm)],[c_91,c_68]) ).
cnf(c_102,plain,
ca_Ax2(sK0(i2003_11_14_17_21_19256)),
inference(resolve,[status(thm)],[c_91,c_67]) ).
cnf(c_103,plain,
rf1(i2003_11_14_17_21_19256,sK0(i2003_11_14_17_21_19256)),
inference(resolve,[status(thm)],[c_91,c_66]) ).
cnf(c_111,plain,
~ ra_Px1(sK1(i2003_11_14_17_21_19256),A),
inference(resolve,[status(thm)],[c_71,c_100]) ).
cnf(c_115,plain,
( sK1(i2003_11_14_17_21_19256) = A
| ~ rf(i2003_11_14_17_21_19256,A) ),
inference(resolve,[status(thm)],[c_101,c_82]) ).
cnf(c_118,plain,
~ cpxcomp(sK1(i2003_11_14_17_21_19256)),
inference(resolve,[status(thm)],[c_73,c_111]) ).
cnf(c_119,plain,
~ ca_Ax2(sK1(i2003_11_14_17_21_19256)),
inference(resolve,[status(thm)],[c_75,c_118]) ).
cnf(c_169,plain,
( ca_Ax2(A)
| A != sK0(i2003_11_14_17_21_19256) ),
inference(resolve,[status(thm)],[c_40,c_102]) ).
cnf(c_120,plain,
sK1(i2003_11_14_17_21_19256) != sK0(i2003_11_14_17_21_19256),
inference(resolve,[status(thm)],[c_169,c_119]) ).
cnf(c_124,plain,
rinvF1(sK0(i2003_11_14_17_21_19256),i2003_11_14_17_21_19256),
inference(resolve,[status(thm)],[c_103,c_87]) ).
cnf(c_170,plain,
( sK0(i2003_11_14_17_21_19256) = A
| ~ rf1(i2003_11_14_17_21_19256,A) ),
inference(resolve,[status(thm)],[c_83,c_103]) ).
cnf(c_171,plain,
sK0(i2003_11_14_17_21_19256) != sK1(i2003_11_14_17_21_19256),
inference(copy,[status(thm)],[c_120]) ).
cnf(c_128,plain,
~ rf1(i2003_11_14_17_21_19256,sK1(i2003_11_14_17_21_19256)),
inference(resolve,[status(thm)],[c_170,c_171]) ).
cnf(c_172,plain,
( ca_Vx3(i2003_11_14_17_21_19256)
| ~ ca_Ax2(sK0(i2003_11_14_17_21_19256)) ),
inference(resolve,[status(thm)],[c_124,c_76]) ).
cnf(c_131,plain,
ca_Vx3(i2003_11_14_17_21_19256),
inference(resolve,[status(thm)],[c_102,c_172]) ).
cnf(c_134,plain,
rs(i2003_11_14_17_21_19256,sK3(i2003_11_14_17_21_19256)),
inference(resolve,[status(thm)],[c_131,c_79]) ).
cnf(c_149,plain,
rf1(i2003_11_14_17_21_19256,sK3(i2003_11_14_17_21_19256)),
inference(resolve,[status(thm)],[c_134,c_93]) ).
cnf(c_150,plain,
rf(i2003_11_14_17_21_19256,sK3(i2003_11_14_17_21_19256)),
inference(resolve,[status(thm)],[c_134,c_92]) ).
cnf(c_173,plain,
( rf1(i2003_11_14_17_21_19256,A)
| A != sK3(i2003_11_14_17_21_19256) ),
inference(resolve,[status(thm)],[c_51,c_149]) ).
cnf(c_174,plain,
sK1(i2003_11_14_17_21_19256) != sK3(i2003_11_14_17_21_19256),
inference(resolve,[status(thm)],[c_173,c_128]) ).
cnf(c_160,plain,
sK3(i2003_11_14_17_21_19256) != sK1(i2003_11_14_17_21_19256),
inference(copy,[status(thm)],[c_174]) ).
cnf(c_175,plain,
sK1(i2003_11_14_17_21_19256) = sK3(i2003_11_14_17_21_19256),
inference(resolve,[status(thm)],[c_115,c_150]) ).
cnf(c_176,plain,
sK3(i2003_11_14_17_21_19256) = sK1(i2003_11_14_17_21_19256),
inference(copy,[status(thm)],[c_175]) ).
cnf(c_168,plain,
$false,
inference(resolve,[status(thm)],[c_160,c_176]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : KRS112+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox/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 1703766 was started by sandbox on n008,
% 0.09/0.35 % Fri Sep 25 19:40:39 2026
% 0.09/0.35 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.13/0.36
% 0.13/0.36 % 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 46.
% 0.13/0.38 % Level of proof is 9.
% 0.13/0.38 % Maximum clause weight is 17.000.
% 0.13/0.38 % Given clauses 90.
% 0.13/0.38
% 0.13/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------