%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : KRS070+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 : n012.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 0.03s 0.31s
% Output : CNFRefutation 0.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 6
% Syntax : Number of formulae : 33 ( 12 unt; 0 def)
% Number of atoms : 123 ( 7 equ)
% Maximal formula atoms : 30 ( 3 avg)
% Number of connectives : 151 ( 61 ~; 56 |; 29 &)
% ( 1 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 1 con; 0-1 aty)
% Number of variables : 56 ( 0 sgn 33 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(cc2_substitution_1,axiom,
! [A,B] :
( ( cc2(A)
& A = B )
=> cc2(B) ),
file('theBenchmark.p',cc2_substitution_1) ).
fof(axiom_2,axiom,
! [X] :
( cUnsatisfiable(X)
<=> ( ? [Y] :
( cc1(Y)
& rrx3(X,Y) )
& ~ ? [Y] :
( cc1(Y)
& cc2(Y)
& rrx3(X,Y) )
& ? [Y] :
( cc2(Y)
& rrx4(X,Y) ) ) ),
file('theBenchmark.p',axiom_2) ).
fof(axiom_3,axiom,
! [X,Y,Z] :
( ( rrx(X,Z)
& rrx(X,Y) )
=> Y = Z ),
file('theBenchmark.p',axiom_3) ).
fof(axiom_9,axiom,
! [X,Y] :
( rrx3(X,Y)
=> rrx(X,Y) ),
file('theBenchmark.p',axiom_9) ).
fof(axiom_16,axiom,
! [X,Y] :
( rrx4(X,Y)
=> rrx(X,Y) ),
file('theBenchmark.p',axiom_16) ).
cnf(c_46,plain,
( cc2(A)
| ~ cc2(B)
| A != B ),
inference(clausify,[status(thm)],[cc2_substitution_1]) ).
fof(nnf_30,plain,
! [X] :
( ( ! [Y] :
( ~ cc1(Y)
| ~ rrx3(X,Y) )
| ? [X4] :
( cc1(X4)
& cc2(X4)
& rrx3(X,X4) )
| ! [X3] :
( ~ cc2(X3)
| ~ rrx4(X,X3) )
| cUnsatisfiable(X) )
& ( ( ? [X2] :
( cc1(X2)
& rrx3(X,X2) )
& ! [X1] :
( ~ cc1(X1)
| ~ cc2(X1)
| ~ rrx3(X,X1) )
& ? [X0] :
( cc2(X0)
& rrx4(X,X0) ) )
| ~ cUnsatisfiable(X) ) ),
inference(fof_nnf,[status(thm)],[axiom_2]) ).
fof(sk_axiom_2_sk,plain,
! [X] :
( ( ! [Y] :
( ~ cc1(Y)
| ~ rrx3(X,Y) )
| ( cc1(sK2(X))
& cc2(sK2(X))
& rrx3(X,sK2(X)) )
| ! [X3] :
( ~ cc2(X3)
| ~ rrx4(X,X3) )
| cUnsatisfiable(X) )
& ( ( cc1(sK1(X))
& rrx3(X,sK1(X))
& ! [X1] :
( ~ cc1(X1)
| ~ cc2(X1)
| ~ rrx3(X,X1) )
& cc2(sK0(X))
& rrx4(X,sK0(X)) )
| ~ cUnsatisfiable(X) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0(X)),skolemize(X2,sK1(X)),skolemize(X4,sK2(X))],[nnf_30]) ).
fof(sk_axiom_2,plain,
( ! [VAR_0,VAR_1,VAR_2] :
( ~ cc1(VAR_2)
| ~ rrx3(VAR_0,VAR_2)
| cc1(sK2(VAR_0))
| ~ cc2(VAR_1)
| ~ rrx4(VAR_0,VAR_1)
| cUnsatisfiable(VAR_0) )
& ! [VAR_0,VAR_1,VAR_2] :
( ~ cc1(VAR_2)
| ~ rrx3(VAR_0,VAR_2)
| cc2(sK2(VAR_0))
| ~ cc2(VAR_1)
| ~ rrx4(VAR_0,VAR_1)
| cUnsatisfiable(VAR_0) )
& ! [VAR_0,VAR_1,VAR_2] :
( ~ cc1(VAR_2)
| ~ rrx3(VAR_0,VAR_2)
| rrx3(VAR_0,sK2(VAR_0))
| ~ cc2(VAR_1)
| ~ rrx4(VAR_0,VAR_1)
| cUnsatisfiable(VAR_0) )
& ! [VAR_0] :
( cc1(sK1(VAR_0))
| ~ cUnsatisfiable(VAR_0) )
& ! [VAR_0] :
( rrx3(VAR_0,sK1(VAR_0))
| ~ cUnsatisfiable(VAR_0) )
& ! [VAR_0,VAR_1] :
( ~ cc1(VAR_1)
| ~ cc2(VAR_1)
| ~ rrx3(VAR_0,VAR_1)
| ~ cUnsatisfiable(VAR_0) )
& ! [VAR_0] :
( cc2(sK0(VAR_0))
| ~ cUnsatisfiable(VAR_0) )
& ! [VAR_0] :
( rrx4(VAR_0,sK0(VAR_0))
| ~ cUnsatisfiable(VAR_0) ) ),
inference(cnf_transformation,[status(thm)],[sk_axiom_2_sk]) ).
cnf(c_75,plain,
( rrx4(A,sK0(A))
| ~ cUnsatisfiable(A) ),
inference(split_conjunct,[status(thm)],[sk_axiom_2]) ).
cnf(c_76,plain,
( cc2(sK0(A))
| ~ cUnsatisfiable(A) ),
inference(split_conjunct,[status(thm)],[sk_axiom_2]) ).
cnf(c_77,plain,
( ~ cc1(B)
| ~ cc2(B)
| ~ rrx3(A,B)
| ~ cUnsatisfiable(A) ),
inference(split_conjunct,[status(thm)],[sk_axiom_2]) ).
cnf(c_78,plain,
( rrx3(A,sK1(A))
| ~ cUnsatisfiable(A) ),
inference(split_conjunct,[status(thm)],[sk_axiom_2]) ).
cnf(c_79,plain,
( cc1(sK1(A))
| ~ cUnsatisfiable(A) ),
inference(split_conjunct,[status(thm)],[sk_axiom_2]) ).
cnf(c_83,plain,
( C = B
| ~ rrx(A,C)
| ~ rrx(A,B) ),
inference(clausify,[status(thm)],[axiom_3]) ).
fof(axiom_8,axiom,
cUnsatisfiable(i2003_11_14_17_18_32242),
file('theBenchmark.p',axiom_8) ).
cnf(c_88,plain,
cUnsatisfiable(i2003_11_14_17_18_32242),
inference(clausify,[status(thm)],[axiom_8]) ).
cnf(c_89,plain,
( rrx(A,B)
| ~ rrx3(A,B) ),
inference(clausify,[status(thm)],[axiom_9]) ).
cnf(c_96,plain,
( rrx(A,B)
| ~ rrx4(A,B) ),
inference(clausify,[status(thm)],[axiom_16]) ).
cnf(c_98,plain,
cc1(sK1(i2003_11_14_17_18_32242)),
inference(resolve,[status(thm)],[c_88,c_79]) ).
cnf(c_99,plain,
rrx3(i2003_11_14_17_18_32242,sK1(i2003_11_14_17_18_32242)),
inference(resolve,[status(thm)],[c_88,c_78]) ).
cnf(c_100,plain,
cc2(sK0(i2003_11_14_17_18_32242)),
inference(resolve,[status(thm)],[c_88,c_76]) ).
cnf(c_101,plain,
rrx4(i2003_11_14_17_18_32242,sK0(i2003_11_14_17_18_32242)),
inference(resolve,[status(thm)],[c_88,c_75]) ).
cnf(c_106,plain,
rrx(i2003_11_14_17_18_32242,sK1(i2003_11_14_17_18_32242)),
inference(resolve,[status(thm)],[c_99,c_89]) ).
cnf(c_125,plain,
( ~ cc1(sK1(i2003_11_14_17_18_32242))
| ~ cc2(sK1(i2003_11_14_17_18_32242))
| ~ cUnsatisfiable(i2003_11_14_17_18_32242) ),
inference(resolve,[status(thm)],[c_99,c_77]) ).
cnf(c_126,plain,
( ~ cc1(sK1(i2003_11_14_17_18_32242))
| ~ cc2(sK1(i2003_11_14_17_18_32242)) ),
inference(resolve,[status(thm)],[c_88,c_125]) ).
cnf(c_108,plain,
~ cc2(sK1(i2003_11_14_17_18_32242)),
inference(resolve,[status(thm)],[c_98,c_126]) ).
cnf(c_111,plain,
rrx(i2003_11_14_17_18_32242,sK0(i2003_11_14_17_18_32242)),
inference(resolve,[status(thm)],[c_101,c_96]) ).
cnf(c_127,plain,
( cc2(A)
| A != sK0(i2003_11_14_17_18_32242) ),
inference(resolve,[status(thm)],[c_46,c_100]) ).
cnf(c_116,plain,
sK1(i2003_11_14_17_18_32242) != sK0(i2003_11_14_17_18_32242),
inference(resolve,[status(thm)],[c_127,c_108]) ).
cnf(c_128,plain,
( sK1(i2003_11_14_17_18_32242) = A
| ~ rrx(i2003_11_14_17_18_32242,A) ),
inference(resolve,[status(thm)],[c_83,c_106]) ).
cnf(c_129,plain,
~ rrx(i2003_11_14_17_18_32242,sK0(i2003_11_14_17_18_32242)),
inference(resolve,[status(thm)],[c_128,c_116]) ).
cnf(c_124,plain,
$false,
inference(resolve,[status(thm)],[c_111,c_129]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : KRS070+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.02 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.03/0.29 % Computer : n012.cluster.edu
% 0.03/0.29 % Model : x86_64 x86_64
% 0.03/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/0.29 % Memory : 8046.5625MB
% 0.03/0.29 % OS : Linux 6.8.0-71-generic
% 0.03/0.29 % CPULimit : 300
% 0.03/0.29 % WCLimit : 300
% 0.03/0.29 % DateTime : Fri Sep 25 19:37:50 UTC 2026
% 0.03/0.29 % CPUTime :
% 0.03/0.29 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.03/0.29 % Process 2810708 was started by sandbox on n012,
% 0.03/0.29 % Fri Sep 25 19:37:50 2026
% 0.03/0.29 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.03/0.30
% 0.03/0.30 % From the command line: assign(max_seconds, 300).
% 0.03/0.31
% 0.03/0.31 % SZS status Unsatisfiable for theBenchmark
% 0.03/0.31
% 0.03/0.31 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.03/0.31 % Length of proof is 24.
% 0.03/0.31 % Level of proof is 5.
% 0.03/0.31 % Maximum clause weight is 9.000.
% 0.03/0.31 % Given clauses 63.
% 0.03/0.31
% 0.03/0.31 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------