%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : KRS088+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 : n013.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 0.09s 0.39s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 5
% Syntax : Number of formulae : 29 ( 10 unt; 0 def)
% Number of atoms : 95 ( 8 equ)
% Maximal formula atoms : 19 ( 3 avg)
% Number of connectives : 112 ( 46 ~; 41 |; 20 &)
% ( 2 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 1 con; 0-2 aty)
% Number of variables : 49 ( 0 sgn 28 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(cp1_substitution_1,axiom,
! [A,B] :
( ( cp1(A)
& A = B )
=> cp1(B) ),
file('theBenchmark.p',cp1_substitution_1) ).
fof(axiom_2,axiom,
! [X] :
( cUnsatisfiable(X)
<=> ? [Y] :
( cp1(Y)
& ! [Z] :
( rinvF(Y,Z)
=> ? [W] :
( ~ cp1(W)
& rf(Z,W) ) )
& rf(X,Y) ) ),
file('theBenchmark.p',axiom_2) ).
fof(axiom_3,axiom,
! [X,Y,Z] :
( ( rf(X,Z)
& rf(X,Y) )
=> Y = Z ),
file('theBenchmark.p',axiom_3) ).
fof(axiom_4,axiom,
! [X,Y] :
( rinvF(X,Y)
<=> rf(Y,X) ),
file('theBenchmark.p',axiom_4) ).
cnf(c_25,plain,
( cp1(A)
| ~ cp1(B)
| A != B ),
inference(clausify,[status(thm)],[cp1_substitution_1]) ).
fof(nnf_17,plain,
! [X] :
( ( ! [Y] :
( ~ cp1(Y)
| ? [Z] :
( ! [W] :
( cp1(W)
| ~ rf(Z,W) )
& rinvF(Y,Z) )
| ~ rf(X,Y) )
| cUnsatisfiable(X) )
& ( ? [X0] :
( cp1(X0)
& ! [X1] :
( ? [X2] :
( ~ cp1(X2)
& rf(X1,X2) )
| ~ rinvF(X0,X1) )
& rf(X,X0) )
| ~ cUnsatisfiable(X) ) ),
inference(fof_nnf,[status(thm)],[axiom_2]) ).
fof(sk_axiom_2_sk,plain,
! [X] :
( ( ! [Y] :
( ~ cp1(Y)
| ( ! [W] :
( cp1(W)
| ~ rf(sK2(X,Y),W) )
& rinvF(Y,sK2(X,Y)) )
| ~ rf(X,Y) )
| cUnsatisfiable(X) )
& ( ( cp1(sK0(X))
& ! [X1] :
( ( ~ cp1(sK1(X,X1))
& rf(X1,sK1(X,X1)) )
| ~ rinvF(sK0(X),X1) )
& rf(X,sK0(X)) )
| ~ cUnsatisfiable(X) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0(X)),skolemize(X2,sK1(X,X1)),skolemize(Z,sK2(X,Y))],[nnf_17]) ).
fof(sk_axiom_2,plain,
( ! [VAR_0,VAR_1,VAR_2] :
( ~ cp1(VAR_1)
| cp1(VAR_2)
| ~ rf(sK2(VAR_0,VAR_1),VAR_2)
| ~ rf(VAR_0,VAR_1)
| cUnsatisfiable(VAR_0) )
& ! [VAR_0,VAR_1] :
( ~ cp1(VAR_1)
| rinvF(VAR_1,sK2(VAR_0,VAR_1))
| ~ rf(VAR_0,VAR_1)
| cUnsatisfiable(VAR_0) )
& ! [VAR_0] :
( cp1(sK0(VAR_0))
| ~ cUnsatisfiable(VAR_0) )
& ! [VAR_0,VAR_1] :
( ~ cp1(sK1(VAR_0,VAR_1))
| ~ rinvF(sK0(VAR_0),VAR_1)
| ~ cUnsatisfiable(VAR_0) )
& ! [VAR_0,VAR_1] :
( rf(VAR_1,sK1(VAR_0,VAR_1))
| ~ rinvF(sK0(VAR_0),VAR_1)
| ~ cUnsatisfiable(VAR_0) )
& ! [VAR_0] :
( rf(VAR_0,sK0(VAR_0))
| ~ cUnsatisfiable(VAR_0) ) ),
inference(cnf_transformation,[status(thm)],[sk_axiom_2_sk]) ).
cnf(c_40,plain,
( rf(A,sK0(A))
| ~ cUnsatisfiable(A) ),
inference(split_conjunct,[status(thm)],[sk_axiom_2]) ).
cnf(c_41,plain,
( rf(B,sK1(A,B))
| ~ rinvF(sK0(A),B)
| ~ cUnsatisfiable(A) ),
inference(split_conjunct,[status(thm)],[sk_axiom_2]) ).
cnf(c_42,plain,
( ~ cp1(sK1(A,B))
| ~ rinvF(sK0(A),B)
| ~ cUnsatisfiable(A) ),
inference(split_conjunct,[status(thm)],[sk_axiom_2]) ).
cnf(c_43,plain,
( cp1(sK0(A))
| ~ cUnsatisfiable(A) ),
inference(split_conjunct,[status(thm)],[sk_axiom_2]) ).
cnf(c_46,plain,
( C = B
| ~ rf(A,C)
| ~ rf(A,B) ),
inference(clausify,[status(thm)],[axiom_3]) ).
cnf(c_48,plain,
( ~ rf(B,A)
| rinvF(A,B) ),
inference(clausify,[status(thm)],[axiom_4]) ).
fof(axiom_7,axiom,
cUnsatisfiable(i2003_11_14_17_19_49673),
file('theBenchmark.p',axiom_7) ).
cnf(c_52,plain,
cUnsatisfiable(i2003_11_14_17_19_49673),
inference(clausify,[status(thm)],[axiom_7]) ).
cnf(c_54,plain,
cp1(sK0(i2003_11_14_17_19_49673)),
inference(resolve,[status(thm)],[c_52,c_43]) ).
cnf(c_55,plain,
rf(i2003_11_14_17_19_49673,sK0(i2003_11_14_17_19_49673)),
inference(resolve,[status(thm)],[c_52,c_40]) ).
cnf(c_68,plain,
( cp1(A)
| A != sK0(i2003_11_14_17_19_49673) ),
inference(resolve,[status(thm)],[c_54,c_25]) ).
cnf(c_57,plain,
( cp1(A)
| sK0(i2003_11_14_17_19_49673) != A ),
inference(copy,[status(thm)],[c_68]) ).
cnf(c_58,plain,
rinvF(sK0(i2003_11_14_17_19_49673),i2003_11_14_17_19_49673),
inference(resolve,[status(thm)],[c_55,c_48]) ).
cnf(c_69,plain,
( ~ cp1(sK1(i2003_11_14_17_19_49673,i2003_11_14_17_19_49673))
| ~ cUnsatisfiable(i2003_11_14_17_19_49673) ),
inference(resolve,[status(thm)],[c_58,c_42]) ).
cnf(c_62,plain,
~ cp1(sK1(i2003_11_14_17_19_49673,i2003_11_14_17_19_49673)),
inference(resolve,[status(thm)],[c_52,c_69]) ).
cnf(c_70,plain,
( rf(i2003_11_14_17_19_49673,sK1(i2003_11_14_17_19_49673,i2003_11_14_17_19_49673))
| ~ cUnsatisfiable(i2003_11_14_17_19_49673) ),
inference(resolve,[status(thm)],[c_58,c_41]) ).
cnf(c_63,plain,
rf(i2003_11_14_17_19_49673,sK1(i2003_11_14_17_19_49673,i2003_11_14_17_19_49673)),
inference(resolve,[status(thm)],[c_52,c_70]) ).
cnf(c_66,plain,
sK0(i2003_11_14_17_19_49673) != sK1(i2003_11_14_17_19_49673,i2003_11_14_17_19_49673),
inference(resolve,[status(thm)],[c_57,c_62]) ).
cnf(c_71,plain,
( sK0(i2003_11_14_17_19_49673) = A
| ~ rf(i2003_11_14_17_19_49673,A) ),
inference(resolve,[status(thm)],[c_46,c_55]) ).
cnf(c_72,plain,
~ rf(i2003_11_14_17_19_49673,sK1(i2003_11_14_17_19_49673,i2003_11_14_17_19_49673)),
inference(resolve,[status(thm)],[c_71,c_66]) ).
cnf(c_67,plain,
$false,
inference(resolve,[status(thm)],[c_63,c_72]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KRS088+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n013.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Fri Sep 25 19:38:21 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.37 % Process 1027322 was started by sandbox on n013,
% 0.09/0.37 % Fri Sep 25 19:38:21 2026
% 0.09/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.09/0.37
% 0.09/0.37 % From the command line: assign(max_seconds, 300).
% 0.09/0.39
% 0.09/0.39 % SZS status Unsatisfiable for theBenchmark
% 0.09/0.39
% 0.09/0.39 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.09/0.39 % Length of proof is 20.
% 0.09/0.39 % Level of proof is 6.
% 0.09/0.39 % Maximum clause weight is 11.000.
% 0.09/0.39 % Given clauses 37.
% 0.09/0.39
% 0.09/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------