%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : KRS073+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 : n009.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 07:45:58 AM UTC 2026
% Result : Unsatisfiable 0.12s 0.39s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 7
% Syntax : Number of formulae : 34 ( 12 unt; 0 def)
% Number of atoms : 129 ( 8 equ)
% Maximal formula atoms : 35 ( 3 avg)
% Number of connectives : 153 ( 58 ~; 59 |; 28 &)
% ( 3 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 1 con; 0-2 aty)
% Number of variables : 70 ( 0 sgn 43 !; 6 ?)
% 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)
<=> ( ~ cp(X)
& ? [Y] :
( ! [Z] :
( rinvF(Y,Z)
=> ? [W] :
( cp(W)
& rs(Z,W) ) )
& ! [Z] :
( rinvS(Y,Z)
=> cp(Z) )
& 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_5,axiom,
! [X,Y] :
( rinvF(X,Y)
<=> rf(Y,X) ),
file('theBenchmark.p',axiom_5) ).
fof(axiom_7,axiom,
! [X,Y] :
( rinvS(X,Y)
<=> rs(Y,X) ),
file('theBenchmark.p',axiom_7) ).
fof(axiom_11,axiom,
! [X,Y] :
( rs(X,Y)
=> rf(X,Y) ),
file('theBenchmark.p',axiom_11) ).
cnf(c_45,plain,
( rs(C,A)
| ~ rs(C,B)
| A != B ),
inference(clausify,[status(thm)],[rs_substitution_2]) ).
fof(nnf_21,plain,
! [X] :
( ( cp(X)
| ! [Y] :
( ? [Z] :
( ! [W] :
( ~ cp(W)
| ~ rs(Z,W) )
& rinvF(Y,Z) )
| ? [X4] :
( ~ cp(X4)
& rinvS(Y,X4) )
| ~ rf(X,Y) )
| cUnsatisfiable(X) )
& ( ( ~ cp(X)
& ? [X0] :
( ! [X2] :
( ? [X3] :
( cp(X3)
& rs(X2,X3) )
| ~ rinvF(X0,X2) )
& ! [X1] :
( cp(X1)
| ~ rinvS(X0,X1) )
& rf(X,X0) ) )
| ~ cUnsatisfiable(X) ) ),
inference(fof_nnf,[status(thm)],[axiom_2]) ).
fof(sk_axiom_2_sk,plain,
! [X] :
( ( cp(X)
| ! [Y] :
( ( ! [W] :
( ~ cp(W)
| ~ rs(sK3(X,Y),W) )
& rinvF(Y,sK3(X,Y)) )
| ( ~ cp(sK2(X,Y))
& rinvS(Y,sK2(X,Y)) )
| ~ rf(X,Y) )
| cUnsatisfiable(X) )
& ( ( ~ cp(X)
& ! [X2] :
( ( cp(sK1(X,X2))
& rs(X2,sK1(X,X2)) )
| ~ rinvF(sK0(X),X2) )
& ! [X1] :
( cp(X1)
| ~ rinvS(sK0(X),X1) )
& rf(X,sK0(X)) )
| ~ cUnsatisfiable(X) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X0,sK0(X)),skolemize(X3,sK1(X,X2)),skolemize(X4,sK2(X,Y)),skolemize(Z,sK3(X,Y))],[nnf_21]) ).
fof(sk_axiom_2,plain,
( ! [VAR_0,VAR_1,VAR_2] :
( cp(VAR_0)
| ~ cp(VAR_2)
| ~ rs(sK3(VAR_0,VAR_1),VAR_2)
| ~ cp(sK2(VAR_0,VAR_1))
| ~ rf(VAR_0,VAR_1)
| cUnsatisfiable(VAR_0) )
& ! [VAR_0,VAR_1] :
( cp(VAR_0)
| rinvF(VAR_1,sK3(VAR_0,VAR_1))
| ~ cp(sK2(VAR_0,VAR_1))
| ~ rf(VAR_0,VAR_1)
| cUnsatisfiable(VAR_0) )
& ! [VAR_0,VAR_1,VAR_2] :
( cp(VAR_0)
| ~ cp(VAR_2)
| ~ rs(sK3(VAR_0,VAR_1),VAR_2)
| rinvS(VAR_1,sK2(VAR_0,VAR_1))
| ~ rf(VAR_0,VAR_1)
| cUnsatisfiable(VAR_0) )
& ! [VAR_0,VAR_1] :
( cp(VAR_0)
| rinvF(VAR_1,sK3(VAR_0,VAR_1))
| rinvS(VAR_1,sK2(VAR_0,VAR_1))
| ~ rf(VAR_0,VAR_1)
| cUnsatisfiable(VAR_0) )
& ! [VAR_0] :
( ~ cp(VAR_0)
| ~ cUnsatisfiable(VAR_0) )
& ! [VAR_0,VAR_1] :
( cp(sK1(VAR_0,VAR_1))
| ~ rinvF(sK0(VAR_0),VAR_1)
| ~ cUnsatisfiable(VAR_0) )
& ! [VAR_0,VAR_1] :
( rs(VAR_1,sK1(VAR_0,VAR_1))
| ~ rinvF(sK0(VAR_0),VAR_1)
| ~ cUnsatisfiable(VAR_0) )
& ! [VAR_0,VAR_1] :
( cp(VAR_1)
| ~ rinvS(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_52,plain,
( rf(A,sK0(A))
| ~ cUnsatisfiable(A) ),
inference(split_conjunct,[status(thm)],[sk_axiom_2]) ).
cnf(c_53,plain,
( cp(B)
| ~ rinvS(sK0(A),B)
| ~ cUnsatisfiable(A) ),
inference(split_conjunct,[status(thm)],[sk_axiom_2]) ).
cnf(c_54,plain,
( rs(B,sK1(A,B))
| ~ rinvF(sK0(A),B)
| ~ cUnsatisfiable(A) ),
inference(split_conjunct,[status(thm)],[sk_axiom_2]) ).
cnf(c_56,plain,
( ~ cp(A)
| ~ cUnsatisfiable(A) ),
inference(split_conjunct,[status(thm)],[sk_axiom_2]) ).
cnf(c_61,plain,
( C = B
| ~ rf(A,C)
| ~ rf(A,B) ),
inference(clausify,[status(thm)],[axiom_3]) ).
cnf(c_64,plain,
( ~ rf(B,A)
| rinvF(A,B) ),
inference(clausify,[status(thm)],[axiom_5]) ).
cnf(c_68,plain,
( ~ rs(B,A)
| rinvS(A,B) ),
inference(clausify,[status(thm)],[axiom_7]) ).
fof(axiom_9,axiom,
cUnsatisfiable(i2003_11_14_17_18_54369),
file('theBenchmark.p',axiom_9) ).
cnf(c_70,plain,
cUnsatisfiable(i2003_11_14_17_18_54369),
inference(clausify,[status(thm)],[axiom_9]) ).
cnf(c_72,plain,
( rf(A,B)
| ~ rs(A,B) ),
inference(clausify,[status(thm)],[axiom_11]) ).
cnf(c_75,plain,
~ cp(i2003_11_14_17_18_54369),
inference(resolve,[status(thm)],[c_70,c_56]) ).
cnf(c_76,plain,
rf(i2003_11_14_17_18_54369,sK0(i2003_11_14_17_18_54369)),
inference(resolve,[status(thm)],[c_70,c_52]) ).
cnf(c_100,plain,
( cp(A)
| ~ rinvS(sK0(i2003_11_14_17_18_54369),A) ),
inference(resolve,[status(thm)],[c_53,c_70]) ).
cnf(c_78,plain,
~ rinvS(sK0(i2003_11_14_17_18_54369),i2003_11_14_17_18_54369),
inference(resolve,[status(thm)],[c_100,c_75]) ).
cnf(c_79,plain,
~ rs(i2003_11_14_17_18_54369,sK0(i2003_11_14_17_18_54369)),
inference(resolve,[status(thm)],[c_68,c_78]) ).
cnf(c_80,plain,
rinvF(sK0(i2003_11_14_17_18_54369),i2003_11_14_17_18_54369),
inference(resolve,[status(thm)],[c_76,c_64]) ).
cnf(c_81,plain,
( sK0(i2003_11_14_17_18_54369) = A
| ~ rf(i2003_11_14_17_18_54369,A) ),
inference(resolve,[status(thm)],[c_76,c_61]) ).
cnf(c_101,plain,
( rs(i2003_11_14_17_18_54369,sK1(i2003_11_14_17_18_54369,i2003_11_14_17_18_54369))
| ~ cUnsatisfiable(i2003_11_14_17_18_54369) ),
inference(resolve,[status(thm)],[c_80,c_54]) ).
cnf(c_85,plain,
rs(i2003_11_14_17_18_54369,sK1(i2003_11_14_17_18_54369,i2003_11_14_17_18_54369)),
inference(resolve,[status(thm)],[c_70,c_101]) ).
cnf(c_91,plain,
rf(i2003_11_14_17_18_54369,sK1(i2003_11_14_17_18_54369,i2003_11_14_17_18_54369)),
inference(resolve,[status(thm)],[c_85,c_72]) ).
cnf(c_102,plain,
( rs(i2003_11_14_17_18_54369,A)
| A != sK1(i2003_11_14_17_18_54369,i2003_11_14_17_18_54369) ),
inference(resolve,[status(thm)],[c_45,c_85]) ).
cnf(c_98,plain,
sK0(i2003_11_14_17_18_54369) != sK1(i2003_11_14_17_18_54369,i2003_11_14_17_18_54369),
inference(resolve,[status(thm)],[c_102,c_79]) ).
cnf(c_103,plain,
sK0(i2003_11_14_17_18_54369) = sK1(i2003_11_14_17_18_54369,i2003_11_14_17_18_54369),
inference(resolve,[status(thm)],[c_91,c_81]) ).
cnf(c_99,plain,
$false,
inference(resolve,[status(thm)],[c_98,c_103]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : KRS073+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n009.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 19:38:30 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 2365316 was started by sandbox2 on n009,
% 0.08/0.36 % Fri Sep 25 19:38:30 2026
% 0.08/0.36 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.12/0.37
% 0.12/0.37 % From the command line: assign(max_seconds, 300).
% 0.12/0.39
% 0.12/0.39 % SZS status Unsatisfiable for theBenchmark
% 0.12/0.39
% 0.12/0.39 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.12/0.39 % Length of proof is 26.
% 0.12/0.39 % Level of proof is 6.
% 0.12/0.39 % Maximum clause weight is 11.000.
% 0.12/0.39 % Given clauses 55.
% 0.12/0.39
% 0.12/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------