%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : KRS087+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 : n019.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 0.13s 0.38s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 4
% Syntax : Number of formulae : 23 ( 9 unt; 0 def)
% Number of atoms : 90 ( 0 equ)
% Maximal formula atoms : 23 ( 3 avg)
% Number of connectives : 112 ( 45 ~; 40 |; 23 &)
% ( 2 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 1 con; 0-3 aty)
% Number of variables : 44 ( 0 sgn 27 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(axiom_2,axiom,
! [X] :
( cUnsatisfiable(X)
<=> ( ? [Y] :
( ? [Z] :
( cp1(Z)
& ! [W] :
( rinvR(Z,W)
=> ~ cp1(W) )
& rr(Y,Z) )
& rr(X,Y) )
& cp1(X) ) ),
file('theBenchmark.p',axiom_2) ).
fof(axiom_5,axiom,
! [X,Y] :
( rinvR(X,Y)
<=> rr(Y,X) ),
file('theBenchmark.p',axiom_5) ).
fof(axiom_6,axiom,
! [X,Y,Z] :
( ( rr(Y,Z)
& rr(X,Y) )
=> rr(X,Z) ),
file('theBenchmark.p',axiom_6) ).
fof(nnf_17,plain,
! [X] :
( ( ! [Y] :
( ! [Z] :
( ~ cp1(Z)
| ? [W] :
( cp1(W)
& rinvR(Z,W) )
| ~ rr(Y,Z) )
| ~ rr(X,Y) )
| ~ cp1(X)
| cUnsatisfiable(X) )
& ( ( ? [X0] :
( ? [X1] :
( cp1(X1)
& ! [X2] :
( ~ cp1(X2)
| ~ rinvR(X1,X2) )
& rr(X0,X1) )
& rr(X,X0) )
& cp1(X) )
| ~ cUnsatisfiable(X) ) ),
inference(fof_nnf,[status(thm)],[axiom_2]) ).
fof(sk_axiom_2_sk,plain,
! [X] :
( ( ! [Y] :
( ! [Z] :
( ~ cp1(Z)
| ( cp1(sK2(X,Y,Z))
& rinvR(Z,sK2(X,Y,Z)) )
| ~ rr(Y,Z) )
| ~ rr(X,Y) )
| ~ cp1(X)
| cUnsatisfiable(X) )
& ( ( cp1(sK1(X))
& ! [X2] :
( ~ cp1(X2)
| ~ rinvR(sK1(X),X2) )
& rr(sK0(X),sK1(X))
& rr(X,sK0(X))
& cp1(X) )
| ~ cUnsatisfiable(X) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0(X)),skolemize(X1,sK1(X)),skolemize(W,sK2(X,Y,Z))],[nnf_17]) ).
fof(sk_axiom_2,plain,
( ! [VAR_0,VAR_1,VAR_2] :
( ~ cp1(VAR_2)
| cp1(sK2(VAR_0,VAR_1,VAR_2))
| ~ rr(VAR_1,VAR_2)
| ~ rr(VAR_0,VAR_1)
| ~ cp1(VAR_0)
| cUnsatisfiable(VAR_0) )
& ! [VAR_0,VAR_1,VAR_2] :
( ~ cp1(VAR_2)
| rinvR(VAR_2,sK2(VAR_0,VAR_1,VAR_2))
| ~ rr(VAR_1,VAR_2)
| ~ rr(VAR_0,VAR_1)
| ~ cp1(VAR_0)
| cUnsatisfiable(VAR_0) )
& ! [VAR_0] :
( cp1(sK1(VAR_0))
| ~ cUnsatisfiable(VAR_0) )
& ! [VAR_0,VAR_1] :
( ~ cp1(VAR_1)
| ~ rinvR(sK1(VAR_0),VAR_1)
| ~ cUnsatisfiable(VAR_0) )
& ! [VAR_0] :
( rr(sK0(VAR_0),sK1(VAR_0))
| ~ cUnsatisfiable(VAR_0) )
& ! [VAR_0] :
( rr(VAR_0,sK0(VAR_0))
| ~ cUnsatisfiable(VAR_0) )
& ! [VAR_0] :
( cp1(VAR_0)
| ~ cUnsatisfiable(VAR_0) ) ),
inference(cnf_transformation,[status(thm)],[sk_axiom_2_sk]) ).
cnf(c_40,plain,
( cp1(A)
| ~ cUnsatisfiable(A) ),
inference(split_conjunct,[status(thm)],[sk_axiom_2]) ).
cnf(c_41,plain,
( rr(A,sK0(A))
| ~ cUnsatisfiable(A) ),
inference(split_conjunct,[status(thm)],[sk_axiom_2]) ).
cnf(c_42,plain,
( rr(sK0(A),sK1(A))
| ~ cUnsatisfiable(A) ),
inference(split_conjunct,[status(thm)],[sk_axiom_2]) ).
cnf(c_43,plain,
( ~ cp1(B)
| ~ rinvR(sK1(A),B)
| ~ cUnsatisfiable(A) ),
inference(split_conjunct,[status(thm)],[sk_axiom_2]) ).
cnf(c_51,plain,
( ~ rr(B,A)
| rinvR(A,B) ),
inference(clausify,[status(thm)],[axiom_5]) ).
cnf(c_52,plain,
( rr(A,C)
| ~ rr(B,C)
| ~ rr(A,B) ),
inference(clausify,[status(thm)],[axiom_6]) ).
fof(axiom_7,axiom,
cUnsatisfiable(i2003_11_14_17_19_46763),
file('theBenchmark.p',axiom_7) ).
cnf(c_53,plain,
cUnsatisfiable(i2003_11_14_17_19_46763),
inference(clausify,[status(thm)],[axiom_7]) ).
cnf(c_60,plain,
rr(sK0(i2003_11_14_17_19_46763),sK1(i2003_11_14_17_19_46763)),
inference(resolve,[status(thm)],[c_53,c_42]) ).
cnf(c_61,plain,
rr(i2003_11_14_17_19_46763,sK0(i2003_11_14_17_19_46763)),
inference(resolve,[status(thm)],[c_53,c_41]) ).
cnf(c_62,plain,
cp1(i2003_11_14_17_19_46763),
inference(resolve,[status(thm)],[c_53,c_40]) ).
cnf(c_95,plain,
( ~ cp1(A)
| ~ rinvR(sK1(i2003_11_14_17_19_46763),A) ),
inference(resolve,[status(thm)],[c_43,c_53]) ).
cnf(c_65,plain,
~ rinvR(sK1(i2003_11_14_17_19_46763),i2003_11_14_17_19_46763),
inference(resolve,[status(thm)],[c_95,c_62]) ).
cnf(c_92,plain,
~ rr(i2003_11_14_17_19_46763,sK1(i2003_11_14_17_19_46763)),
inference(resolve,[status(thm)],[c_51,c_65]) ).
cnf(c_96,plain,
( rr(A,sK1(i2003_11_14_17_19_46763))
| ~ rr(A,sK0(i2003_11_14_17_19_46763)) ),
inference(resolve,[status(thm)],[c_52,c_60]) ).
cnf(c_97,plain,
~ rr(i2003_11_14_17_19_46763,sK0(i2003_11_14_17_19_46763)),
inference(resolve,[status(thm)],[c_96,c_92]) ).
cnf(c_94,plain,
$false,
inference(resolve,[status(thm)],[c_61,c_97]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : KRS087+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n019.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Fri Sep 25 19:39:04 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.36 % Process 3491749 was started by sandbox on n019,
% 0.08/0.36 % Fri Sep 25 19:39:04 2026
% 0.08/0.36 % 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 16.
% 0.13/0.38 % Level of proof is 5.
% 0.13/0.38 % Maximum clause weight is 9.000.
% 0.13/0.38 % Given clauses 42.
% 0.13/0.38
% 0.13/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------