%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : KRS092+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 : n006.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 0.09s 0.37s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 3
% Syntax : Number of formulae : 18 ( 5 unt; 0 def)
% Number of atoms : 78 ( 0 equ)
% Maximal formula atoms : 19 ( 4 avg)
% Number of connectives : 105 ( 45 ~; 39 |; 18 &)
% ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 1 con; 0-1 aty)
% Number of variables : 38 ( 2 sgn 19 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(axiom_2,axiom,
! [X] :
( cUnsatisfiable(X)
<=> ( ! [Y] :
( rr(X,Y)
=> ( cc(Y)
& cd(Y) ) )
& ? [Y] :
( cowlThing(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,
( ~ cd(A)
| ~ cc(A) ),
inference(clausify,[status(thm)],[axiom_3]) ).
fof(nnf_3,plain,
! [X] :
( ( ? [Y] :
( ( ~ cc(Y)
| ~ cd(Y) )
& rr(X,Y) )
| ! [X2] :
( ~ cowlThing(X2)
| ~ rr(X,X2) )
| cUnsatisfiable(X) )
& ( ( ! [X1] :
( ( cc(X1)
& cd(X1) )
| ~ rr(X,X1) )
& ? [X0] :
( cowlThing(X0)
& rr(X,X0) ) )
| ~ cUnsatisfiable(X) ) ),
inference(fof_nnf,[status(thm)],[axiom_2]) ).
fof(sk_axiom_2_sk,plain,
! [X] :
( ( ( ( ~ cc(sK1(X))
| ~ cd(sK1(X)) )
& rr(X,sK1(X)) )
| ! [X2] :
( ~ cowlThing(X2)
| ~ rr(X,X2) )
| cUnsatisfiable(X) )
& ( ( ! [X1] :
( ( cc(X1)
& cd(X1) )
| ~ rr(X,X1) )
& cowlThing(sK0(X))
& rr(X,sK0(X)) )
| ~ cUnsatisfiable(X) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0(X)),skolemize(Y,sK1(X))],[nnf_3]) ).
fof(sk_axiom_2,plain,
( ! [VAR_0,VAR_1] :
( ~ cc(sK1(VAR_0))
| ~ cd(sK1(VAR_0))
| ~ cowlThing(VAR_1)
| ~ rr(VAR_0,VAR_1)
| cUnsatisfiable(VAR_0) )
& ! [VAR_0,VAR_1] :
( rr(VAR_0,sK1(VAR_0))
| ~ cowlThing(VAR_1)
| ~ rr(VAR_0,VAR_1)
| cUnsatisfiable(VAR_0) )
& ! [VAR_0,VAR_1] :
( cc(VAR_1)
| ~ rr(VAR_0,VAR_1)
| ~ cUnsatisfiable(VAR_0) )
& ! [VAR_0,VAR_1] :
( cd(VAR_1)
| ~ rr(VAR_0,VAR_1)
| ~ cUnsatisfiable(VAR_0) )
& ! [VAR_0] :
( cowlThing(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_17,plain,
( cd(B)
| ~ rr(A,B)
| ~ cUnsatisfiable(A) ),
inference(split_conjunct,[status(thm)],[sk_axiom_2]) ).
cnf(c_18,plain,
( cc(B)
| ~ rr(A,B)
| ~ cUnsatisfiable(A) ),
inference(split_conjunct,[status(thm)],[sk_axiom_2]) ).
cnf(c_20,plain,
( ~ cc(B)
| ~ rr(A,B)
| ~ cUnsatisfiable(A) ),
inference(resolve,[status(thm)],[c_17,c_15]) ).
cnf(c_22,plain,
( rr(A,sK0(A))
| ~ cUnsatisfiable(A) ),
inference(split_conjunct,[status(thm)],[sk_axiom_2]) ).
fof(axiom_8,axiom,
cUnsatisfiable(i2003_11_14_17_20_04172),
file('theBenchmark.p',axiom_8) ).
cnf(c_23,plain,
cUnsatisfiable(i2003_11_14_17_20_04172),
inference(clausify,[status(thm)],[axiom_8]) ).
cnf(c_26,plain,
( ~ rr(C,B)
| ~ cUnsatisfiable(C)
| ~ rr(A,B)
| ~ cUnsatisfiable(A) ),
inference(resolve,[status(thm)],[c_18,c_20]) ).
cnf(c_31,plain,
( ~ rr(A,B)
| ~ rr(A,B)
| ~ cUnsatisfiable(A) ),
inference(factor,[status(thm)],[c_26]) ).
cnf(c_27,plain,
( ~ rr(A,B)
| ~ cUnsatisfiable(A) ),
inference(copy,[status(thm)],[c_31]) ).
cnf(c_28,plain,
rr(i2003_11_14_17_20_04172,sK0(i2003_11_14_17_20_04172)),
inference(resolve,[status(thm)],[c_23,c_22]) ).
cnf(c_29,plain,
~ rr(i2003_11_14_17_20_04172,A),
inference(resolve,[status(thm)],[c_27,c_23]) ).
cnf(c_30,plain,
$false,
inference(resolve,[status(thm)],[c_29,c_28]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KRS092+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n006.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 19:38:41 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.36 % Process 3571497 was started by sandbox2 on n006,
% 0.09/0.36 % Fri Sep 25 19:38:41 2026
% 0.09/0.36 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.09/0.36
% 0.09/0.36 % From the command line: assign(max_seconds, 300).
% 0.09/0.37
% 0.09/0.37 % SZS status Unsatisfiable for theBenchmark
% 0.09/0.37
% 0.09/0.37 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.09/0.37 % Length of proof is 13.
% 0.09/0.37 % Level of proof is 6.
% 0.09/0.37 % Maximum clause weight is 10.000.
% 0.09/0.37 % Given clauses 4.
% 0.09/0.37
% 0.09/0.37 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------