%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : KRS084+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 : n005.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 07:46:00 AM UTC 2026
% Result : Unsatisfiable 0.18s 0.48s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 8
% Syntax : Number of formulae : 47 ( 17 unt; 0 def)
% Number of atoms : 155 ( 9 equ)
% Maximal formula atoms : 23 ( 3 avg)
% Number of connectives : 178 ( 70 ~; 65 |; 35 &)
% ( 4 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 1 con; 0-2 aty)
% Number of variables : 75 ( 0 sgn 43 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(cc_substitution_1,axiom,
! [A,B] :
( ( cc(A)
& A = B )
=> cc(B) ),
file('theBenchmark.p',cc_substitution_1) ).
fof(axiom_2,axiom,
! [X] :
( cUnsatisfiable(X)
<=> ( ~ cc(X)
& ! [Y] :
( rinvR(X,Y)
=> ? [Z] :
( cd(Z)
& rinvF(Y,Z) ) )
& ? [Y] :
( cd(Y)
& rinvF(X,Y) ) ) ),
file('theBenchmark.p',axiom_2) ).
fof(axiom_3,axiom,
! [X] :
( cd(X)
<=> ( cc(X)
& ? [Y] :
( ~ cc(Y)
& rf(X,Y) ) ) ),
file('theBenchmark.p',axiom_3) ).
fof(axiom_4,axiom,
! [X,Y,Z] :
( ( rf(X,Z)
& rf(X,Y) )
=> Y = Z ),
file('theBenchmark.p',axiom_4) ).
fof(axiom_5,axiom,
! [X,Y] :
( rinvF(X,Y)
<=> rf(Y,X) ),
file('theBenchmark.p',axiom_5) ).
fof(axiom_6,axiom,
! [X,Y] :
( rinvR(X,Y)
<=> rr(Y,X) ),
file('theBenchmark.p',axiom_6) ).
fof(axiom_9,axiom,
! [X,Y] :
( rf(X,Y)
=> rr(X,Y) ),
file('theBenchmark.p',axiom_9) ).
cnf(c_26,plain,
( cc(A)
| ~ cc(B)
| A != B ),
inference(clausify,[status(thm)],[cc_substitution_1]) ).
fof(nnf_18,plain,
! [X] :
( ( cc(X)
| ? [Y] :
( ! [Z] :
( ~ cd(Z)
| ~ rinvF(Y,Z) )
& rinvR(X,Y) )
| ! [X3] :
( ~ cd(X3)
| ~ rinvF(X,X3) )
| cUnsatisfiable(X) )
& ( ( ~ cc(X)
& ! [X1] :
( ? [X2] :
( cd(X2)
& rinvF(X1,X2) )
| ~ rinvR(X,X1) )
& ? [X0] :
( cd(X0)
& rinvF(X,X0) ) )
| ~ cUnsatisfiable(X) ) ),
inference(fof_nnf,[status(thm)],[axiom_2]) ).
fof(sk_axiom_2_sk,plain,
! [X] :
( ( cc(X)
| ( ! [Z] :
( ~ cd(Z)
| ~ rinvF(sK3(X),Z) )
& rinvR(X,sK3(X)) )
| ! [X3] :
( ~ cd(X3)
| ~ rinvF(X,X3) )
| cUnsatisfiable(X) )
& ( ( ~ cc(X)
& ! [X1] :
( ( cd(sK1(X,X1))
& rinvF(X1,sK1(X,X1)) )
| ~ rinvR(X,X1) )
& cd(sK0(X))
& rinvF(X,sK0(X)) )
| ~ cUnsatisfiable(X) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK3]),skolemize(X0,sK0(X)),skolemize(X2,sK1(X,X1)),skolemize(Y,sK3(X))],[nnf_18]) ).
fof(sk_axiom_2,plain,
( ! [VAR_0,VAR_1,VAR_2] :
( cc(VAR_0)
| ~ cd(VAR_2)
| ~ rinvF(sK3(VAR_0),VAR_2)
| ~ cd(VAR_1)
| ~ rinvF(VAR_0,VAR_1)
| cUnsatisfiable(VAR_0) )
& ! [VAR_0,VAR_1] :
( cc(VAR_0)
| rinvR(VAR_0,sK3(VAR_0))
| ~ cd(VAR_1)
| ~ rinvF(VAR_0,VAR_1)
| cUnsatisfiable(VAR_0) )
& ! [VAR_0] :
( ~ cc(VAR_0)
| ~ cUnsatisfiable(VAR_0) )
& ! [VAR_0,VAR_1] :
( cd(sK1(VAR_0,VAR_1))
| ~ rinvR(VAR_0,VAR_1)
| ~ cUnsatisfiable(VAR_0) )
& ! [VAR_0,VAR_1] :
( rinvF(VAR_1,sK1(VAR_0,VAR_1))
| ~ rinvR(VAR_0,VAR_1)
| ~ cUnsatisfiable(VAR_0) )
& ! [VAR_0] :
( cd(sK0(VAR_0))
| ~ cUnsatisfiable(VAR_0) )
& ! [VAR_0] :
( rinvF(VAR_0,sK0(VAR_0))
| ~ cUnsatisfiable(VAR_0) ) ),
inference(cnf_transformation,[status(thm)],[sk_axiom_2_sk]) ).
cnf(c_44,plain,
( rinvF(A,sK0(A))
| ~ cUnsatisfiable(A) ),
inference(split_conjunct,[status(thm)],[sk_axiom_2]) ).
cnf(c_45,plain,
( cd(sK0(A))
| ~ cUnsatisfiable(A) ),
inference(split_conjunct,[status(thm)],[sk_axiom_2]) ).
cnf(c_46,plain,
( rinvF(B,sK1(A,B))
| ~ rinvR(A,B)
| ~ cUnsatisfiable(A) ),
inference(split_conjunct,[status(thm)],[sk_axiom_2]) ).
cnf(c_47,plain,
( cd(sK1(A,B))
| ~ rinvR(A,B)
| ~ cUnsatisfiable(A) ),
inference(split_conjunct,[status(thm)],[sk_axiom_2]) ).
fof(nnf_19,plain,
! [X] :
( ( ~ cc(X)
| ! [Y] :
( cc(Y)
| ~ rf(X,Y) )
| cd(X) )
& ( ( cc(X)
& ? [X3] :
( ~ cc(X3)
& rf(X,X3) ) )
| ~ cd(X) ) ),
inference(fof_nnf,[status(thm)],[axiom_3]) ).
fof(sk_axiom_3_sk,plain,
! [X] :
( ( ~ cc(X)
| ! [Y] :
( cc(Y)
| ~ rf(X,Y) )
| cd(X) )
& ( ( cc(X)
& ~ cc(sK2(X))
& rf(X,sK2(X)) )
| ~ cd(X) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(X3,sK2(X))],[nnf_19]) ).
fof(sk_axiom_3,plain,
( ! [VAR_0,VAR_1] :
( ~ cc(VAR_0)
| cc(VAR_1)
| ~ rf(VAR_0,VAR_1)
| cd(VAR_0) )
& ! [VAR_0] :
( cc(VAR_0)
| ~ cd(VAR_0) )
& ! [VAR_0] :
( ~ cc(sK2(VAR_0))
| ~ cd(VAR_0) )
& ! [VAR_0] :
( rf(VAR_0,sK2(VAR_0))
| ~ cd(VAR_0) ) ),
inference(cnf_transformation,[status(thm)],[sk_axiom_3_sk]) ).
cnf(c_51,plain,
( rf(A,sK2(A))
| ~ cd(A) ),
inference(split_conjunct,[status(thm)],[sk_axiom_3]) ).
cnf(c_52,plain,
( ~ cc(sK2(A))
| ~ cd(A) ),
inference(split_conjunct,[status(thm)],[sk_axiom_3]) ).
cnf(c_53,plain,
( cc(A)
| ~ cd(A) ),
inference(split_conjunct,[status(thm)],[sk_axiom_3]) ).
cnf(c_55,plain,
( C = B
| ~ rf(A,C)
| ~ rf(A,B) ),
inference(clausify,[status(thm)],[axiom_4]) ).
cnf(c_56,plain,
( rf(B,A)
| ~ rinvF(A,B) ),
inference(clausify,[status(thm)],[axiom_5]) ).
cnf(c_59,plain,
( ~ rr(B,A)
| rinvR(A,B) ),
inference(clausify,[status(thm)],[axiom_6]) ).
fof(axiom_8,axiom,
cUnsatisfiable(i2003_11_14_17_19_35232),
file('theBenchmark.p',axiom_8) ).
cnf(c_61,plain,
cUnsatisfiable(i2003_11_14_17_19_35232),
inference(clausify,[status(thm)],[axiom_8]) ).
cnf(c_62,plain,
( rr(A,B)
| ~ rf(A,B) ),
inference(clausify,[status(thm)],[axiom_9]) ).
cnf(c_66,plain,
( cd(sK1(i2003_11_14_17_19_35232,A))
| ~ rinvR(i2003_11_14_17_19_35232,A) ),
inference(resolve,[status(thm)],[c_61,c_47]) ).
cnf(c_67,plain,
( rinvF(A,sK1(i2003_11_14_17_19_35232,A))
| ~ rinvR(i2003_11_14_17_19_35232,A) ),
inference(resolve,[status(thm)],[c_61,c_46]) ).
cnf(c_68,plain,
cd(sK0(i2003_11_14_17_19_35232)),
inference(resolve,[status(thm)],[c_61,c_45]) ).
cnf(c_69,plain,
rinvF(i2003_11_14_17_19_35232,sK0(i2003_11_14_17_19_35232)),
inference(resolve,[status(thm)],[c_61,c_44]) ).
cnf(c_73,plain,
cc(sK0(i2003_11_14_17_19_35232)),
inference(resolve,[status(thm)],[c_68,c_53]) ).
cnf(c_164,plain,
( cc(A)
| A != sK0(i2003_11_14_17_19_35232) ),
inference(resolve,[status(thm)],[c_73,c_26]) ).
cnf(c_82,plain,
( cc(A)
| sK0(i2003_11_14_17_19_35232) != A ),
inference(copy,[status(thm)],[c_164]) ).
cnf(c_83,plain,
rf(sK0(i2003_11_14_17_19_35232),i2003_11_14_17_19_35232),
inference(resolve,[status(thm)],[c_69,c_56]) ).
cnf(c_88,plain,
rr(sK0(i2003_11_14_17_19_35232),i2003_11_14_17_19_35232),
inference(resolve,[status(thm)],[c_83,c_62]) ).
cnf(c_95,plain,
rinvR(i2003_11_14_17_19_35232,sK0(i2003_11_14_17_19_35232)),
inference(resolve,[status(thm)],[c_88,c_59]) ).
cnf(c_98,plain,
rinvF(sK0(i2003_11_14_17_19_35232),sK1(i2003_11_14_17_19_35232,sK0(i2003_11_14_17_19_35232))),
inference(resolve,[status(thm)],[c_95,c_67]) ).
cnf(c_99,plain,
cd(sK1(i2003_11_14_17_19_35232,sK0(i2003_11_14_17_19_35232))),
inference(resolve,[status(thm)],[c_95,c_66]) ).
cnf(c_113,plain,
~ cc(sK2(sK1(i2003_11_14_17_19_35232,sK0(i2003_11_14_17_19_35232)))),
inference(resolve,[status(thm)],[c_99,c_52]) ).
cnf(c_114,plain,
rf(sK1(i2003_11_14_17_19_35232,sK0(i2003_11_14_17_19_35232)),sK2(sK1(i2003_11_14_17_19_35232,sK0(i2003_11_14_17_19_35232)))),
inference(resolve,[status(thm)],[c_99,c_51]) ).
cnf(c_120,plain,
rf(sK1(i2003_11_14_17_19_35232,sK0(i2003_11_14_17_19_35232)),sK0(i2003_11_14_17_19_35232)),
inference(resolve,[status(thm)],[c_98,c_56]) ).
cnf(c_165,plain,
sK0(i2003_11_14_17_19_35232) != sK2(sK1(i2003_11_14_17_19_35232,sK0(i2003_11_14_17_19_35232))),
inference(resolve,[status(thm)],[c_82,c_113]) ).
cnf(c_146,plain,
sK2(sK1(i2003_11_14_17_19_35232,sK0(i2003_11_14_17_19_35232))) != sK0(i2003_11_14_17_19_35232),
inference(copy,[status(thm)],[c_165]) ).
cnf(c_166,plain,
( sK2(sK1(i2003_11_14_17_19_35232,sK0(i2003_11_14_17_19_35232))) = A
| ~ rf(sK1(i2003_11_14_17_19_35232,sK0(i2003_11_14_17_19_35232)),A) ),
inference(resolve,[status(thm)],[c_55,c_114]) ).
cnf(c_167,plain,
~ rf(sK1(i2003_11_14_17_19_35232,sK0(i2003_11_14_17_19_35232)),sK0(i2003_11_14_17_19_35232)),
inference(resolve,[status(thm)],[c_166,c_146]) ).
cnf(c_163,plain,
$false,
inference(resolve,[status(thm)],[c_120,c_167]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : KRS084+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.44 % Computer : n005.cluster.edu
% 0.18/0.44 % Model : x86_64 x86_64
% 0.18/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.44 % Memory : 8046.5625MB
% 0.18/0.44 % OS : Linux 6.8.0-71-generic
% 0.18/0.44 % CPULimit : 300
% 0.18/0.44 % WCLimit : 300
% 0.18/0.44 % DateTime : Fri Sep 25 19:38:32 UTC 2026
% 0.18/0.44 % CPUTime :
% 0.18/0.44 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.18/0.44 % Process 835 was started by sandbox2 on n005,
% 0.18/0.44 % Fri Sep 25 19:38:32 2026
% 0.18/0.44 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.18/0.46
% 0.18/0.46 % From the command line: assign(max_seconds, 300).
% 0.18/0.48
% 0.18/0.48 % SZS status Unsatisfiable for theBenchmark
% 0.18/0.48
% 0.18/0.48 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.18/0.48 % Length of proof is 36.
% 0.18/0.48 % Level of proof is 9.
% 0.18/0.48 % Maximum clause weight is 30.000.
% 0.18/0.48 % Given clauses 107.
% 0.18/0.48
% 0.18/0.48 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------