%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : KRS077+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 : n011.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 07:45:59 AM UTC 2026
% Result : Unsatisfiable 0.09s 0.38s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 5
% Syntax : Number of formulae : 31 ( 12 unt; 0 def)
% Number of atoms : 155 ( 16 equ)
% Maximal formula atoms : 57 ( 5 avg)
% Number of connectives : 202 ( 78 ~; 82 |; 36 &)
% ( 2 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 1 con; 0-2 aty)
% Number of variables : 75 ( 0 sgn 50 !; 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] :
( cp(Y)
& rs(X,Y) )
& ~ cp(X)
& ? [Y] :
( ! [Z] :
( rinvS(Y,Z)
=> cp(Z) )
& rr(X,Y) )
& ! [Y0,Y1] :
( ( rr(X,Y1)
& rr(X,Y0) )
=> Y0 = Y1 ) ) ),
file('theBenchmark.p',axiom_2) ).
fof(axiom_3,axiom,
! [X,Y] :
( rinvS(X,Y)
<=> rs(Y,X) ),
file('theBenchmark.p',axiom_3) ).
fof(axiom_5,axiom,
! [X,Y] :
( rs(X,Y)
=> rr(X,Y) ),
file('theBenchmark.p',axiom_5) ).
cnf(c_27,plain,
( rs(C,A)
| ~ rs(C,B)
| A != B ),
inference(clausify,[status(thm)],[rs_substitution_2]) ).
fof(nnf_15,plain,
! [X] :
( ( ! [Y] :
( ~ cp(Y)
| ~ rs(X,Y) )
| cp(X)
| ! [X5] :
( ? [Z] :
( ~ cp(Z)
& rinvS(X5,Z) )
| ~ rr(X,X5) )
| ? [Y0,Y1] :
( Y1 != Y0
& rr(X,Y1)
& rr(X,Y0) )
| cUnsatisfiable(X) )
& ( ( ? [X4] :
( cp(X4)
& rs(X,X4) )
& ~ cp(X)
& ? [X2] :
( ! [X3] :
( cp(X3)
| ~ rinvS(X2,X3) )
& rr(X,X2) )
& ! [X0,X1] :
( X1 = X0
| ~ rr(X,X1)
| ~ rr(X,X0) ) )
| ~ cUnsatisfiable(X) ) ),
inference(fof_nnf,[status(thm)],[axiom_2]) ).
fof(sk_axiom_2_sk,plain,
! [X] :
( ( ! [Y] :
( ~ cp(Y)
| ~ rs(X,Y) )
| cp(X)
| ! [X5] :
( ( ~ cp(sK4(X,X5))
& rinvS(X5,sK4(X,X5)) )
| ~ rr(X,X5) )
| ( sK3(X) != sK2(X)
& rr(X,sK3(X))
& rr(X,sK2(X)) )
| cUnsatisfiable(X) )
& ( ( cp(sK1(X))
& rs(X,sK1(X))
& ~ cp(X)
& ! [X3] :
( cp(X3)
| ~ rinvS(sK0(X),X3) )
& rr(X,sK0(X))
& ! [X0,X1] :
( X1 = X0
| ~ rr(X,X1)
| ~ rr(X,X0) ) )
| ~ cUnsatisfiable(X) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4]),skolemize(X2,sK0(X)),skolemize(X4,sK1(X)),skolemize(Y0,sK2(X)),skolemize(Y1,sK3(X)),skolemize(Z,sK4(X,X5))],[nnf_15]) ).
fof(sk_axiom_2,plain,
( ! [VAR_0,VAR_1,VAR_2] :
( ~ cp(VAR_2)
| ~ rs(VAR_0,VAR_2)
| cp(VAR_0)
| ~ cp(sK4(VAR_0,VAR_1))
| ~ rr(VAR_0,VAR_1)
| sK3(VAR_0) != sK2(VAR_0)
| cUnsatisfiable(VAR_0) )
& ! [VAR_0,VAR_1,VAR_2] :
( ~ cp(VAR_2)
| ~ rs(VAR_0,VAR_2)
| cp(VAR_0)
| rinvS(VAR_1,sK4(VAR_0,VAR_1))
| ~ rr(VAR_0,VAR_1)
| sK3(VAR_0) != sK2(VAR_0)
| cUnsatisfiable(VAR_0) )
& ! [VAR_0,VAR_1,VAR_2] :
( ~ cp(VAR_2)
| ~ rs(VAR_0,VAR_2)
| cp(VAR_0)
| ~ cp(sK4(VAR_0,VAR_1))
| ~ rr(VAR_0,VAR_1)
| rr(VAR_0,sK3(VAR_0))
| cUnsatisfiable(VAR_0) )
& ! [VAR_0,VAR_1,VAR_2] :
( ~ cp(VAR_2)
| ~ rs(VAR_0,VAR_2)
| cp(VAR_0)
| rinvS(VAR_1,sK4(VAR_0,VAR_1))
| ~ rr(VAR_0,VAR_1)
| rr(VAR_0,sK3(VAR_0))
| cUnsatisfiable(VAR_0) )
& ! [VAR_0,VAR_1,VAR_2] :
( ~ cp(VAR_2)
| ~ rs(VAR_0,VAR_2)
| cp(VAR_0)
| ~ cp(sK4(VAR_0,VAR_1))
| ~ rr(VAR_0,VAR_1)
| rr(VAR_0,sK2(VAR_0))
| cUnsatisfiable(VAR_0) )
& ! [VAR_0,VAR_1,VAR_2] :
( ~ cp(VAR_2)
| ~ rs(VAR_0,VAR_2)
| cp(VAR_0)
| rinvS(VAR_1,sK4(VAR_0,VAR_1))
| ~ rr(VAR_0,VAR_1)
| rr(VAR_0,sK2(VAR_0))
| cUnsatisfiable(VAR_0) )
& ! [VAR_0] :
( cp(sK1(VAR_0))
| ~ cUnsatisfiable(VAR_0) )
& ! [VAR_0] :
( rs(VAR_0,sK1(VAR_0))
| ~ cUnsatisfiable(VAR_0) )
& ! [VAR_0] :
( ~ cp(VAR_0)
| ~ cUnsatisfiable(VAR_0) )
& ! [VAR_0,VAR_1] :
( cp(VAR_1)
| ~ rinvS(sK0(VAR_0),VAR_1)
| ~ cUnsatisfiable(VAR_0) )
& ! [VAR_0] :
( rr(VAR_0,sK0(VAR_0))
| ~ cUnsatisfiable(VAR_0) )
& ! [VAR_0,VAR_1,VAR_2] :
( VAR_2 = VAR_1
| ~ rr(VAR_0,VAR_2)
| ~ rr(VAR_0,VAR_1)
| ~ cUnsatisfiable(VAR_0) ) ),
inference(cnf_transformation,[status(thm)],[sk_axiom_2_sk]) ).
cnf(c_34,plain,
( C = B
| ~ rr(A,C)
| ~ rr(A,B)
| ~ cUnsatisfiable(A) ),
inference(split_conjunct,[status(thm)],[sk_axiom_2]) ).
cnf(c_35,plain,
( rr(A,sK0(A))
| ~ cUnsatisfiable(A) ),
inference(split_conjunct,[status(thm)],[sk_axiom_2]) ).
cnf(c_36,plain,
( cp(B)
| ~ rinvS(sK0(A),B)
| ~ cUnsatisfiable(A) ),
inference(split_conjunct,[status(thm)],[sk_axiom_2]) ).
cnf(c_37,plain,
( ~ cp(A)
| ~ cUnsatisfiable(A) ),
inference(split_conjunct,[status(thm)],[sk_axiom_2]) ).
cnf(c_38,plain,
( rs(A,sK1(A))
| ~ cUnsatisfiable(A) ),
inference(split_conjunct,[status(thm)],[sk_axiom_2]) ).
cnf(c_47,plain,
( ~ rs(B,A)
| rinvS(A,B) ),
inference(clausify,[status(thm)],[axiom_3]) ).
fof(axiom_4,axiom,
cUnsatisfiable(i2003_11_14_17_19_09372),
file('theBenchmark.p',axiom_4) ).
cnf(c_48,plain,
cUnsatisfiable(i2003_11_14_17_19_09372),
inference(clausify,[status(thm)],[axiom_4]) ).
cnf(c_49,plain,
( rr(A,B)
| ~ rs(A,B) ),
inference(clausify,[status(thm)],[axiom_5]) ).
cnf(c_55,plain,
rs(i2003_11_14_17_19_09372,sK1(i2003_11_14_17_19_09372)),
inference(resolve,[status(thm)],[c_48,c_38]) ).
cnf(c_56,plain,
~ cp(i2003_11_14_17_19_09372),
inference(resolve,[status(thm)],[c_48,c_37]) ).
cnf(c_57,plain,
rr(i2003_11_14_17_19_09372,sK0(i2003_11_14_17_19_09372)),
inference(resolve,[status(thm)],[c_48,c_35]) ).
cnf(c_82,plain,
( cp(A)
| ~ rinvS(sK0(i2003_11_14_17_19_09372),A) ),
inference(resolve,[status(thm)],[c_36,c_48]) ).
cnf(c_59,plain,
~ rinvS(sK0(i2003_11_14_17_19_09372),i2003_11_14_17_19_09372),
inference(resolve,[status(thm)],[c_82,c_56]) ).
cnf(c_60,plain,
~ rs(i2003_11_14_17_19_09372,sK0(i2003_11_14_17_19_09372)),
inference(resolve,[status(thm)],[c_47,c_59]) ).
cnf(c_64,plain,
rr(i2003_11_14_17_19_09372,sK1(i2003_11_14_17_19_09372)),
inference(resolve,[status(thm)],[c_55,c_49]) ).
cnf(c_83,plain,
( rs(i2003_11_14_17_19_09372,A)
| A != sK1(i2003_11_14_17_19_09372) ),
inference(resolve,[status(thm)],[c_27,c_55]) ).
cnf(c_84,plain,
sK0(i2003_11_14_17_19_09372) != sK1(i2003_11_14_17_19_09372),
inference(resolve,[status(thm)],[c_83,c_60]) ).
cnf(c_68,plain,
sK1(i2003_11_14_17_19_09372) != sK0(i2003_11_14_17_19_09372),
inference(copy,[status(thm)],[c_84]) ).
cnf(c_85,plain,
( A = sK0(i2003_11_14_17_19_09372)
| ~ rr(i2003_11_14_17_19_09372,A)
| ~ cUnsatisfiable(i2003_11_14_17_19_09372) ),
inference(resolve,[status(thm)],[c_34,c_57]) ).
cnf(c_86,plain,
( sK1(i2003_11_14_17_19_09372) = sK0(i2003_11_14_17_19_09372)
| ~ cUnsatisfiable(i2003_11_14_17_19_09372) ),
inference(resolve,[status(thm)],[c_85,c_64]) ).
cnf(c_87,plain,
~ cUnsatisfiable(i2003_11_14_17_19_09372),
inference(resolve,[status(thm)],[c_86,c_68]) ).
cnf(c_81,plain,
$false,
inference(resolve,[status(thm)],[c_48,c_87]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KRS077+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 : n011.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 19:38:44 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.36 % Process 2708686 was started by sandbox on n011,
% 0.09/0.36 % Fri Sep 25 19:38:44 2026
% 0.09/0.36 % 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).
% 0.09/0.38
% 0.09/0.38 % SZS status Unsatisfiable for theBenchmark
% 0.09/0.38
% 0.09/0.38 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.09/0.38 % Length of proof is 21.
% 0.09/0.38 % Level of proof is 6.
% 0.09/0.38 % Maximum clause weight is 11.000.
% 0.09/0.38 % Given clauses 51.
% 0.09/0.38
% 0.09/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------