%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : KRS096+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 : n020.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 07:46:01 AM UTC 2026
% Result : Unsatisfiable 0.12s 0.37s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 4
% Syntax : Number of formulae : 26 ( 10 unt; 0 def)
% Number of atoms : 109 ( 14 equ)
% Maximal formula atoms : 30 ( 4 avg)
% Number of connectives : 138 ( 55 ~; 52 |; 27 &)
% ( 1 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 1 con; 0-1 aty)
% Number of variables : 50 ( 0 sgn 32 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(cc_substitution_1,axiom,
! [A,B] :
( ( cc(A)
& A = B )
=> cc(B) ),
file('theBenchmark.p',cc_substitution_1) ).
fof(axiom_2,axiom,
! [X] :
( cUnsatisfiable(X)
<=> ( ! [Y0,Y1] :
( ( rr(X,Y1)
& rr(X,Y0) )
=> Y0 = Y1 )
& ? [Y] :
( cd(Y)
& rr(X,Y) )
& ? [Y] :
( cc(Y)
& rr(X,Y) ) ) ),
file('theBenchmark.p',axiom_2) ).
fof(axiom_3,axiom,
! [X] :
( cc(X)
=> ~ cd(X) ),
file('theBenchmark.p',axiom_3) ).
cnf(c_15,plain,
( cc(A)
| ~ cc(B)
| A != B ),
inference(clausify,[status(thm)],[cc_substitution_1]) ).
fof(nnf_12,plain,
! [X] :
( ( ? [Y0,Y1] :
( Y1 != Y0
& rr(X,Y1)
& rr(X,Y0) )
| ! [Y] :
( ~ cd(Y)
| ~ rr(X,Y) )
| ! [X4] :
( ~ cc(X4)
| ~ rr(X,X4) )
| cUnsatisfiable(X) )
& ( ( ! [X2,X3] :
( X3 = X2
| ~ rr(X,X3)
| ~ rr(X,X2) )
& ? [X1] :
( cd(X1)
& rr(X,X1) )
& ? [X0] :
( cc(X0)
& rr(X,X0) ) )
| ~ cUnsatisfiable(X) ) ),
inference(fof_nnf,[status(thm)],[axiom_2]) ).
fof(sk_axiom_2_sk,plain,
! [X] :
( ( ( sK3(X) != sK2(X)
& rr(X,sK3(X))
& rr(X,sK2(X)) )
| ! [Y] :
( ~ cd(Y)
| ~ rr(X,Y) )
| ! [X4] :
( ~ cc(X4)
| ~ rr(X,X4) )
| cUnsatisfiable(X) )
& ( ( ! [X2,X3] :
( X3 = X2
| ~ rr(X,X3)
| ~ rr(X,X2) )
& cd(sK1(X))
& rr(X,sK1(X))
& cc(sK0(X))
& rr(X,sK0(X)) )
| ~ cUnsatisfiable(X) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X0,sK0(X)),skolemize(X1,sK1(X)),skolemize(Y0,sK2(X)),skolemize(Y1,sK3(X))],[nnf_12]) ).
fof(sk_axiom_2,plain,
( ! [VAR_0,VAR_1,VAR_2] :
( sK3(VAR_0) != sK2(VAR_0)
| ~ cd(VAR_2)
| ~ rr(VAR_0,VAR_2)
| ~ cc(VAR_1)
| ~ rr(VAR_0,VAR_1)
| cUnsatisfiable(VAR_0) )
& ! [VAR_0,VAR_1,VAR_2] :
( rr(VAR_0,sK3(VAR_0))
| ~ cd(VAR_2)
| ~ rr(VAR_0,VAR_2)
| ~ cc(VAR_1)
| ~ rr(VAR_0,VAR_1)
| cUnsatisfiable(VAR_0) )
& ! [VAR_0,VAR_1,VAR_2] :
( rr(VAR_0,sK2(VAR_0))
| ~ cd(VAR_2)
| ~ rr(VAR_0,VAR_2)
| ~ cc(VAR_1)
| ~ rr(VAR_0,VAR_1)
| 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) )
& ! [VAR_0] :
( cd(sK1(VAR_0))
| ~ cUnsatisfiable(VAR_0) )
& ! [VAR_0] :
( rr(VAR_0,sK1(VAR_0))
| ~ cUnsatisfiable(VAR_0) )
& ! [VAR_0] :
( cc(sK0(VAR_0))
| ~ cUnsatisfiable(VAR_0) )
& ! [VAR_0] :
( rr(VAR_0,sK0(VAR_0))
| ~ cUnsatisfiable(VAR_0) ) ),
inference(cnf_transformation,[status(thm)],[sk_axiom_2_sk]) ).
cnf(c_27,plain,
( rr(A,sK0(A))
| ~ cUnsatisfiable(A) ),
inference(split_conjunct,[status(thm)],[sk_axiom_2]) ).
cnf(c_28,plain,
( cc(sK0(A))
| ~ cUnsatisfiable(A) ),
inference(split_conjunct,[status(thm)],[sk_axiom_2]) ).
cnf(c_29,plain,
( rr(A,sK1(A))
| ~ cUnsatisfiable(A) ),
inference(split_conjunct,[status(thm)],[sk_axiom_2]) ).
cnf(c_30,plain,
( cd(sK1(A))
| ~ cUnsatisfiable(A) ),
inference(split_conjunct,[status(thm)],[sk_axiom_2]) ).
cnf(c_31,plain,
( C = B
| ~ rr(A,C)
| ~ rr(A,B)
| ~ cUnsatisfiable(A) ),
inference(split_conjunct,[status(thm)],[sk_axiom_2]) ).
cnf(c_35,plain,
( ~ cd(A)
| ~ cc(A) ),
inference(clausify,[status(thm)],[axiom_3]) ).
fof(axiom_4,axiom,
cUnsatisfiable(i2003_11_14_17_20_18265),
file('theBenchmark.p',axiom_4) ).
cnf(c_36,plain,
cUnsatisfiable(i2003_11_14_17_20_18265),
inference(clausify,[status(thm)],[axiom_4]) ).
cnf(c_38,plain,
cd(sK1(i2003_11_14_17_20_18265)),
inference(resolve,[status(thm)],[c_36,c_30]) ).
cnf(c_39,plain,
rr(i2003_11_14_17_20_18265,sK1(i2003_11_14_17_20_18265)),
inference(resolve,[status(thm)],[c_36,c_29]) ).
cnf(c_40,plain,
cc(sK0(i2003_11_14_17_20_18265)),
inference(resolve,[status(thm)],[c_36,c_28]) ).
cnf(c_41,plain,
rr(i2003_11_14_17_20_18265,sK0(i2003_11_14_17_20_18265)),
inference(resolve,[status(thm)],[c_36,c_27]) ).
cnf(c_43,plain,
~ cc(sK1(i2003_11_14_17_20_18265)),
inference(resolve,[status(thm)],[c_38,c_35]) ).
cnf(c_55,plain,
( cc(A)
| A != sK0(i2003_11_14_17_20_18265) ),
inference(resolve,[status(thm)],[c_15,c_40]) ).
cnf(c_53,plain,
sK1(i2003_11_14_17_20_18265) != sK0(i2003_11_14_17_20_18265),
inference(resolve,[status(thm)],[c_55,c_43]) ).
cnf(c_56,plain,
( A = sK0(i2003_11_14_17_20_18265)
| ~ rr(i2003_11_14_17_20_18265,A)
| ~ cUnsatisfiable(i2003_11_14_17_20_18265) ),
inference(resolve,[status(thm)],[c_31,c_41]) ).
cnf(c_57,plain,
( sK1(i2003_11_14_17_20_18265) = sK0(i2003_11_14_17_20_18265)
| ~ cUnsatisfiable(i2003_11_14_17_20_18265) ),
inference(resolve,[status(thm)],[c_56,c_39]) ).
cnf(c_58,plain,
~ cUnsatisfiable(i2003_11_14_17_20_18265),
inference(resolve,[status(thm)],[c_57,c_53]) ).
cnf(c_54,plain,
$false,
inference(resolve,[status(thm)],[c_36,c_58]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KRS096+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n020.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Fri Sep 25 19:40:04 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.12/0.35 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.12/0.35 % Process 3598854 was started by sandbox on n020,
% 0.12/0.35 % Fri Sep 25 19:40:04 2026
% 0.12/0.35 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.12/0.36
% 0.12/0.36 % From the command line: assign(max_seconds, 300).
% 0.12/0.37
% 0.12/0.37 % SZS status Unsatisfiable for theBenchmark
% 0.12/0.37
% 0.12/0.37 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.12/0.37 % Length of proof is 18.
% 0.12/0.37 % Level of proof is 5.
% 0.12/0.37 % Maximum clause weight is 11.000.
% 0.12/0.37 % Given clauses 30.
% 0.12/0.37
% 0.12/0.37 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------