%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : KRS109+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 : n014.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 0.45s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 11
% Syntax : Number of formulae : 53 ( 17 unt; 0 def)
% Number of atoms : 140 ( 9 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 145 ( 58 ~; 51 |; 24 &)
% ( 7 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 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 : 76 ( 1 sgn 43 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(rs_substitution_2,axiom,
! [A,B,C] :
( ( rs(C,A)
& A = B )
=> rs(C,B) ),
file('theBenchmark.p',rs_substitution_2) ).
fof(axiom_2,axiom,
! [X] :
( cUnsatisfiable(X)
<=> ( ? [Y] :
( ca_Ax2(Y)
& rf(X,Y) )
& cpxcomp(X) ) ),
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] :
( rinvF(X,Y)
=> ca_Vx3(Y) )
& ! [Y] :
( rinvS(X,Y)
=> cp(Y) ) ) ),
file('theBenchmark.p',axiom_5) ).
fof(axiom_6,axiom,
! [X] :
( ca_Vx3(X)
<=> ? [Y] :
( cp(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_9,axiom,
! [X,Y] :
( rinvF(X,Y)
<=> rf(Y,X) ),
file('theBenchmark.p',axiom_9) ).
fof(axiom_11,axiom,
! [X,Y] :
( rinvS(X,Y)
<=> rs(Y,X) ),
file('theBenchmark.p',axiom_11) ).
fof(axiom_14,axiom,
! [X,Y] :
( rs(X,Y)
=> rf(X,Y) ),
file('theBenchmark.p',axiom_14) ).
cnf(c_59,plain,
( rs(C,A)
| ~ rs(C,B)
| A != B ),
inference(clausify,[status(thm)],[rs_substitution_2]) ).
fof(nnf_26,plain,
! [X] :
( ( ! [Y] :
( ~ ca_Ax2(Y)
| ~ rf(X,Y) )
| ~ cpxcomp(X)
| cUnsatisfiable(X) )
& ( ( ? [X0] :
( ca_Ax2(X0)
& rf(X,X0) )
& cpxcomp(X) )
| ~ cUnsatisfiable(X) ) ),
inference(fof_nnf,[status(thm)],[axiom_2]) ).
fof(sk_axiom_2_sk,plain,
! [X] :
( ( ! [Y] :
( ~ ca_Ax2(Y)
| ~ rf(X,Y) )
| ~ cpxcomp(X)
| cUnsatisfiable(X) )
& ( ( ca_Ax2(sK0(X))
& rf(X,sK0(X))
& cpxcomp(X) )
| ~ cUnsatisfiable(X) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0(X))],[nnf_26]) ).
fof(sk_axiom_2,plain,
( ! [VAR_0,VAR_1] :
( ~ ca_Ax2(VAR_1)
| ~ rf(VAR_0,VAR_1)
| ~ cpxcomp(VAR_0)
| cUnsatisfiable(VAR_0) )
& ! [VAR_0] :
( ca_Ax2(sK0(VAR_0))
| ~ cUnsatisfiable(VAR_0) )
& ! [VAR_0] :
( rf(VAR_0,sK0(VAR_0))
| ~ cUnsatisfiable(VAR_0) )
& ! [VAR_0] :
( cpxcomp(VAR_0)
| ~ cUnsatisfiable(VAR_0) ) ),
inference(cnf_transformation,[status(thm)],[sk_axiom_2_sk]) ).
cnf(c_66,plain,
( cpxcomp(A)
| ~ cUnsatisfiable(A) ),
inference(split_conjunct,[status(thm)],[sk_axiom_2]) ).
cnf(c_67,plain,
( rf(A,sK0(A))
| ~ cUnsatisfiable(A) ),
inference(split_conjunct,[status(thm)],[sk_axiom_2]) ).
cnf(c_68,plain,
( ca_Ax2(sK0(A))
| ~ cUnsatisfiable(A) ),
inference(split_conjunct,[status(thm)],[sk_axiom_2]) ).
cnf(c_70,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) )
& ( ? [X0] : ra_Px1(X,X0)
| ~ 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,sK1(X))
| ~ cpxcomp(X) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X0,sK1(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,sK1(VAR_0))
| ~ cpxcomp(VAR_0) ) ),
inference(cnf_transformation,[status(thm)],[sk_axiom_4_sk]) ).
cnf(c_72,plain,
( ra_Px1(A,sK1(A))
| ~ cpxcomp(A) ),
inference(split_conjunct,[status(thm)],[sk_axiom_4]) ).
cnf(c_74,plain,
( cp(B)
| ~ rinvS(A,B)
| ~ ca_Ax2(A) ),
inference(clausify,[status(thm)],[axiom_5]) ).
cnf(c_75,plain,
( ca_Vx3(B)
| ~ rinvF(A,B)
| ~ ca_Ax2(A) ),
inference(clausify,[status(thm)],[axiom_5]) ).
fof(nnf_30,plain,
! [X] :
( ( ! [Y] :
( ~ cp(Y)
| ~ rs(X,Y) )
| ca_Vx3(X) )
& ( ? [X0] :
( cp(X0)
& rs(X,X0) )
| ~ ca_Vx3(X) ) ),
inference(fof_nnf,[status(thm)],[axiom_6]) ).
fof(sk_axiom_6_sk,plain,
! [X] :
( ( ! [Y] :
( ~ cp(Y)
| ~ rs(X,Y) )
| ca_Vx3(X) )
& ( ( cp(sK2(X))
& rs(X,sK2(X)) )
| ~ ca_Vx3(X) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(X0,sK2(X))],[nnf_30]) ).
fof(sk_axiom_6,plain,
( ! [VAR_0,VAR_1] :
( ~ cp(VAR_1)
| ~ rs(VAR_0,VAR_1)
| ca_Vx3(VAR_0) )
& ! [VAR_0] :
( cp(sK2(VAR_0))
| ~ ca_Vx3(VAR_0) )
& ! [VAR_0] :
( rs(VAR_0,sK2(VAR_0))
| ~ ca_Vx3(VAR_0) ) ),
inference(cnf_transformation,[status(thm)],[sk_axiom_6_sk]) ).
cnf(c_80,plain,
( rs(A,sK2(A))
| ~ ca_Vx3(A) ),
inference(split_conjunct,[status(thm)],[sk_axiom_6]) ).
cnf(c_83,plain,
( C = B
| ~ rf(A,C)
| ~ rf(A,B) ),
inference(clausify,[status(thm)],[axiom_7]) ).
cnf(c_86,plain,
( ~ rf(B,A)
| rinvF(A,B) ),
inference(clausify,[status(thm)],[axiom_9]) ).
cnf(c_90,plain,
( ~ rs(B,A)
| rinvS(A,B) ),
inference(clausify,[status(thm)],[axiom_11]) ).
fof(axiom_13,axiom,
cUnsatisfiable(i2003_11_14_17_21_08508),
file('theBenchmark.p',axiom_13) ).
cnf(c_92,plain,
cUnsatisfiable(i2003_11_14_17_21_08508),
inference(clausify,[status(thm)],[axiom_13]) ).
cnf(c_93,plain,
( rf(A,B)
| ~ rs(A,B) ),
inference(clausify,[status(thm)],[axiom_14]) ).
cnf(c_102,plain,
ca_Ax2(sK0(i2003_11_14_17_21_08508)),
inference(resolve,[status(thm)],[c_92,c_68]) ).
cnf(c_103,plain,
rf(i2003_11_14_17_21_08508,sK0(i2003_11_14_17_21_08508)),
inference(resolve,[status(thm)],[c_92,c_67]) ).
cnf(c_104,plain,
cpxcomp(i2003_11_14_17_21_08508),
inference(resolve,[status(thm)],[c_92,c_66]) ).
cnf(c_106,plain,
ra_Px1(i2003_11_14_17_21_08508,sK1(i2003_11_14_17_21_08508)),
inference(resolve,[status(thm)],[c_104,c_72]) ).
cnf(c_111,plain,
rinvF(sK0(i2003_11_14_17_21_08508),i2003_11_14_17_21_08508),
inference(resolve,[status(thm)],[c_103,c_86]) ).
cnf(c_115,plain,
~ cp(i2003_11_14_17_21_08508),
inference(resolve,[status(thm)],[c_106,c_70]) ).
cnf(c_145,plain,
( ca_Vx3(i2003_11_14_17_21_08508)
| ~ ca_Ax2(sK0(i2003_11_14_17_21_08508)) ),
inference(resolve,[status(thm)],[c_111,c_75]) ).
cnf(c_118,plain,
ca_Vx3(i2003_11_14_17_21_08508),
inference(resolve,[status(thm)],[c_102,c_145]) ).
cnf(c_122,plain,
rs(i2003_11_14_17_21_08508,sK2(i2003_11_14_17_21_08508)),
inference(resolve,[status(thm)],[c_118,c_80]) ).
cnf(c_146,plain,
( cp(A)
| ~ rinvS(sK0(i2003_11_14_17_21_08508),A) ),
inference(resolve,[status(thm)],[c_74,c_102]) ).
cnf(c_124,plain,
~ rinvS(sK0(i2003_11_14_17_21_08508),i2003_11_14_17_21_08508),
inference(resolve,[status(thm)],[c_146,c_115]) ).
cnf(c_125,plain,
~ rs(i2003_11_14_17_21_08508,sK0(i2003_11_14_17_21_08508)),
inference(resolve,[status(thm)],[c_90,c_124]) ).
cnf(c_130,plain,
rf(i2003_11_14_17_21_08508,sK2(i2003_11_14_17_21_08508)),
inference(resolve,[status(thm)],[c_122,c_93]) ).
cnf(c_147,plain,
( rs(i2003_11_14_17_21_08508,A)
| A != sK2(i2003_11_14_17_21_08508) ),
inference(resolve,[status(thm)],[c_59,c_122]) ).
cnf(c_148,plain,
sK0(i2003_11_14_17_21_08508) != sK2(i2003_11_14_17_21_08508),
inference(resolve,[status(thm)],[c_147,c_125]) ).
cnf(c_135,plain,
sK2(i2003_11_14_17_21_08508) != sK0(i2003_11_14_17_21_08508),
inference(copy,[status(thm)],[c_148]) ).
cnf(c_149,plain,
( A = sK0(i2003_11_14_17_21_08508)
| ~ rf(i2003_11_14_17_21_08508,A) ),
inference(resolve,[status(thm)],[c_83,c_103]) ).
cnf(c_150,plain,
sK2(i2003_11_14_17_21_08508) = sK0(i2003_11_14_17_21_08508),
inference(resolve,[status(thm)],[c_149,c_130]) ).
cnf(c_144,plain,
$false,
inference(resolve,[status(thm)],[c_135,c_150]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : KRS109+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.15/0.41 % Computer : n014.cluster.edu
% 0.15/0.41 % Model : x86_64 x86_64
% 0.15/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.41 % Memory : 8046.5625MB
% 0.15/0.41 % OS : Linux 6.8.0-71-generic
% 0.15/0.41 % CPULimit : 300
% 0.15/0.41 % WCLimit : 300
% 0.15/0.41 % DateTime : Fri Sep 25 19:39:47 UTC 2026
% 0.15/0.42 % CPUTime :
% 0.15/0.42 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.15/0.42 % Process 929530 was started by sandbox2 on n014,
% 0.15/0.42 % Fri Sep 25 19:39:47 2026
% 0.15/0.42 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.15/0.44
% 0.15/0.44 % From the command line: assign(max_seconds, 300).
% 0.15/0.45
% 0.15/0.45 % SZS status Unsatisfiable for theBenchmark
% 0.15/0.45
% 0.15/0.45 % Proof 1 at 0.00 (+ 0.01) seconds.
% 0.15/0.45 % Length of proof is 37.
% 0.15/0.45 % Level of proof is 8.
% 0.15/0.45 % Maximum clause weight is 16.000.
% 0.15/0.45 % Given clauses 75.
% 0.15/0.45
% 0.15/0.45 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------