%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : KRS114+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 07:46:04 AM UTC 2026
% Result : Unsatisfiable 0.03s 0.38s
% Output : CNFRefutation 0.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 8
% Syntax : Number of formulae : 48 ( 17 unt; 0 def)
% Number of atoms : 163 ( 12 equ)
% Maximal formula atoms : 20 ( 3 avg)
% Number of connectives : 185 ( 70 ~; 69 |; 37 &)
% ( 7 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 13 ( 11 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 1 con; 0-1 aty)
% Number of variables : 80 ( 1 sgn 50 !; 11 ?)
% Comments :
%------------------------------------------------------------------------------
fof(axiom_2,axiom,
! [X] :
( cUnsatisfiable(X)
<=> ( ? [Y] :
( ca_Ax3(Y)
& rs(X,Y) )
& ? [Y] :
( ca_Ax4(Y)
& rr(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_7,axiom,
! [X] :
( ca_Ax3(X)
<=> ( cpxcomp(X)
& cqxcomp(X) ) ),
file('theBenchmark.p',axiom_7) ).
fof(axiom_8,axiom,
! [X] :
( ca_Ax4(X)
<=> ( ? [Y] :
( ca_Vx5(Y)
& rinvR(X,Y) )
& ! [Y0,Y1] :
( ( rinvR(X,Y1)
& rinvR(X,Y0) )
=> Y0 = Y1 ) ) ),
file('theBenchmark.p',axiom_8) ).
fof(axiom_9,axiom,
! [X] :
( ca_Vx5(X)
<=> ! [Y] :
( rs(X,Y)
=> cp(Y) ) ),
file('theBenchmark.p',axiom_9) ).
fof(axiom_10,axiom,
! [X,Y] :
( rinvR(X,Y)
<=> rr(Y,X) ),
file('theBenchmark.p',axiom_10) ).
fof(nnf_25,plain,
! [X] :
( ( ! [Y] :
( ~ ca_Ax3(Y)
| ~ rs(X,Y) )
| ! [X2] :
( ~ ca_Ax4(X2)
| ~ rr(X,X2) )
| cUnsatisfiable(X) )
& ( ( ? [X1] :
( ca_Ax3(X1)
& rs(X,X1) )
& ? [X0] :
( ca_Ax4(X0)
& rr(X,X0) ) )
| ~ cUnsatisfiable(X) ) ),
inference(fof_nnf,[status(thm)],[axiom_2]) ).
fof(sk_axiom_2_sk,plain,
! [X] :
( ( ! [Y] :
( ~ ca_Ax3(Y)
| ~ rs(X,Y) )
| ! [X2] :
( ~ ca_Ax4(X2)
| ~ rr(X,X2) )
| cUnsatisfiable(X) )
& ( ( ca_Ax3(sK1(X))
& rs(X,sK1(X))
& ca_Ax4(sK0(X))
& rr(X,sK0(X)) )
| ~ cUnsatisfiable(X) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0(X)),skolemize(X1,sK1(X))],[nnf_25]) ).
fof(sk_axiom_2,plain,
( ! [VAR_0,VAR_1,VAR_2] :
( ~ ca_Ax3(VAR_2)
| ~ rs(VAR_0,VAR_2)
| ~ ca_Ax4(VAR_1)
| ~ rr(VAR_0,VAR_1)
| cUnsatisfiable(VAR_0) )
& ! [VAR_0] :
( ca_Ax3(sK1(VAR_0))
| ~ cUnsatisfiable(VAR_0) )
& ! [VAR_0] :
( rs(VAR_0,sK1(VAR_0))
| ~ cUnsatisfiable(VAR_0) )
& ! [VAR_0] :
( ca_Ax4(sK0(VAR_0))
| ~ cUnsatisfiable(VAR_0) )
& ! [VAR_0] :
( rr(VAR_0,sK0(VAR_0))
| ~ cUnsatisfiable(VAR_0) ) ),
inference(cnf_transformation,[status(thm)],[sk_axiom_2_sk]) ).
cnf(c_60,plain,
( rr(A,sK0(A))
| ~ cUnsatisfiable(A) ),
inference(split_conjunct,[status(thm)],[sk_axiom_2]) ).
cnf(c_61,plain,
( ca_Ax4(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,
( ca_Ax3(sK1(A))
| ~ cUnsatisfiable(A) ),
inference(split_conjunct,[status(thm)],[sk_axiom_2]) ).
cnf(c_65,plain,
( ~ ra_Px1(A,B)
| ~ cp(A) ),
inference(clausify,[status(thm)],[axiom_3]) ).
fof(nnf_27,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_27]) ).
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_67,plain,
( ra_Px1(A,sK2(A))
| ~ cpxcomp(A) ),
inference(split_conjunct,[status(thm)],[sk_axiom_4]) ).
cnf(c_74,plain,
( cpxcomp(A)
| ~ ca_Ax3(A) ),
inference(clausify,[status(thm)],[axiom_7]) ).
fof(nnf_31,plain,
! [X] :
( ( ! [Y] :
( ~ ca_Vx5(Y)
| ~ rinvR(X,Y) )
| ? [Y0,Y1] :
( Y1 != Y0
& rinvR(X,Y1)
& rinvR(X,Y0) )
| ca_Ax4(X) )
& ( ( ? [X2] :
( ca_Vx5(X2)
& rinvR(X,X2) )
& ! [X1,X0] :
( X0 = X1
| ~ rinvR(X,X0)
| ~ rinvR(X,X1) ) )
| ~ ca_Ax4(X) ) ),
inference(fof_nnf,[status(thm)],[axiom_8]) ).
fof(sk_axiom_8_sk,plain,
! [X] :
( ( ! [Y] :
( ~ ca_Vx5(Y)
| ~ rinvR(X,Y) )
| ( sK6(X) != sK5(X)
& rinvR(X,sK6(X))
& rinvR(X,sK5(X)) )
| ca_Ax4(X) )
& ( ( ca_Vx5(sK3(X))
& rinvR(X,sK3(X))
& ! [X1,X0] :
( X0 = X1
| ~ rinvR(X,X0)
| ~ rinvR(X,X1) ) )
| ~ ca_Ax4(X) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK5,sK6]),skolemize(X2,sK3(X)),skolemize(Y0,sK5(X)),skolemize(Y1,sK6(X))],[nnf_31]) ).
fof(sk_axiom_8,plain,
( ! [VAR_0,VAR_1] :
( ~ ca_Vx5(VAR_1)
| ~ rinvR(VAR_0,VAR_1)
| sK6(VAR_0) != sK5(VAR_0)
| ca_Ax4(VAR_0) )
& ! [VAR_0,VAR_1] :
( ~ ca_Vx5(VAR_1)
| ~ rinvR(VAR_0,VAR_1)
| rinvR(VAR_0,sK6(VAR_0))
| ca_Ax4(VAR_0) )
& ! [VAR_0,VAR_1] :
( ~ ca_Vx5(VAR_1)
| ~ rinvR(VAR_0,VAR_1)
| rinvR(VAR_0,sK5(VAR_0))
| ca_Ax4(VAR_0) )
& ! [VAR_0] :
( ca_Vx5(sK3(VAR_0))
| ~ ca_Ax4(VAR_0) )
& ! [VAR_0] :
( rinvR(VAR_0,sK3(VAR_0))
| ~ ca_Ax4(VAR_0) )
& ! [VAR_0,VAR_1,VAR_2] :
( VAR_2 = VAR_1
| ~ rinvR(VAR_0,VAR_2)
| ~ rinvR(VAR_0,VAR_1)
| ~ ca_Ax4(VAR_0) ) ),
inference(cnf_transformation,[status(thm)],[sk_axiom_8_sk]) ).
cnf(c_76,plain,
( C = B
| ~ rinvR(A,C)
| ~ rinvR(A,B)
| ~ ca_Ax4(A) ),
inference(split_conjunct,[status(thm)],[sk_axiom_8]) ).
cnf(c_77,plain,
( rinvR(A,sK3(A))
| ~ ca_Ax4(A) ),
inference(split_conjunct,[status(thm)],[sk_axiom_8]) ).
cnf(c_78,plain,
( ca_Vx5(sK3(A))
| ~ ca_Ax4(A) ),
inference(split_conjunct,[status(thm)],[sk_axiom_8]) ).
cnf(c_82,plain,
( cp(B)
| ~ rs(A,B)
| ~ ca_Vx5(A) ),
inference(clausify,[status(thm)],[axiom_9]) ).
cnf(c_86,plain,
( ~ rr(B,A)
| rinvR(A,B) ),
inference(clausify,[status(thm)],[axiom_10]) ).
fof(axiom_11,axiom,
cUnsatisfiable(i2003_11_14_17_21_262),
file('theBenchmark.p',axiom_11) ).
cnf(c_87,plain,
cUnsatisfiable(i2003_11_14_17_21_262),
inference(clausify,[status(thm)],[axiom_11]) ).
cnf(c_98,plain,
ca_Ax3(sK1(i2003_11_14_17_21_262)),
inference(resolve,[status(thm)],[c_87,c_63]) ).
cnf(c_99,plain,
rs(i2003_11_14_17_21_262,sK1(i2003_11_14_17_21_262)),
inference(resolve,[status(thm)],[c_87,c_62]) ).
cnf(c_100,plain,
ca_Ax4(sK0(i2003_11_14_17_21_262)),
inference(resolve,[status(thm)],[c_87,c_61]) ).
cnf(c_101,plain,
rr(i2003_11_14_17_21_262,sK0(i2003_11_14_17_21_262)),
inference(resolve,[status(thm)],[c_87,c_60]) ).
cnf(c_107,plain,
cpxcomp(sK1(i2003_11_14_17_21_262)),
inference(resolve,[status(thm)],[c_98,c_74]) ).
cnf(c_110,plain,
ca_Vx5(sK3(sK0(i2003_11_14_17_21_262))),
inference(resolve,[status(thm)],[c_100,c_78]) ).
cnf(c_111,plain,
rinvR(sK0(i2003_11_14_17_21_262),sK3(sK0(i2003_11_14_17_21_262))),
inference(resolve,[status(thm)],[c_100,c_77]) ).
cnf(c_113,plain,
ra_Px1(sK1(i2003_11_14_17_21_262),sK2(sK1(i2003_11_14_17_21_262))),
inference(resolve,[status(thm)],[c_107,c_67]) ).
cnf(c_117,plain,
( cp(sK1(i2003_11_14_17_21_262))
| ~ ca_Vx5(i2003_11_14_17_21_262) ),
inference(resolve,[status(thm)],[c_99,c_82]) ).
cnf(c_120,plain,
rinvR(sK0(i2003_11_14_17_21_262),i2003_11_14_17_21_262),
inference(resolve,[status(thm)],[c_101,c_86]) ).
cnf(c_137,plain,
( i2003_11_14_17_21_262 = A
| ~ rinvR(sK0(i2003_11_14_17_21_262),A)
| ~ ca_Ax4(sK0(i2003_11_14_17_21_262)) ),
inference(resolve,[status(thm)],[c_120,c_76]) ).
cnf(c_124,plain,
( i2003_11_14_17_21_262 = A
| ~ rinvR(sK0(i2003_11_14_17_21_262),A) ),
inference(resolve,[status(thm)],[c_100,c_137]) ).
cnf(c_138,plain,
i2003_11_14_17_21_262 = sK3(sK0(i2003_11_14_17_21_262)),
inference(resolve,[status(thm)],[c_111,c_124]) ).
cnf(c_132,plain,
sK3(sK0(i2003_11_14_17_21_262)) = i2003_11_14_17_21_262,
inference(copy,[status(thm)],[c_138]) ).
cnf(c_134,plain,
ca_Vx5(i2003_11_14_17_21_262),
inference(paramod,[status(thm)],[c_132,c_110]) ).
cnf(c_135,plain,
cp(sK1(i2003_11_14_17_21_262)),
inference(resolve,[status(thm)],[c_134,c_117]) ).
cnf(c_139,plain,
~ cp(sK1(i2003_11_14_17_21_262)),
inference(resolve,[status(thm)],[c_113,c_65]) ).
cnf(c_136,plain,
$false,
inference(resolve,[status(thm)],[c_135,c_139]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : KRS114+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n008.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Fri Sep 25 19:41:09 UTC 2026
% 0.03/0.36 % CPUTime :
% 0.03/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.03/0.36 % Process 1705565 was started by sandbox2 on n008,
% 0.03/0.36 % Fri Sep 25 19:41:09 2026
% 0.03/0.36 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.03/0.37
% 0.03/0.37 % From the command line: assign(max_seconds, 300).
% 0.03/0.38
% 0.03/0.38 % SZS status Unsatisfiable for theBenchmark
% 0.03/0.38
% 0.03/0.38 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.03/0.38 % Length of proof is 35.
% 0.03/0.38 % Level of proof is 8.
% 0.03/0.38 % Maximum clause weight is 21.000.
% 0.03/0.38 % Given clauses 96.
% 0.03/0.38
% 0.03/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------