%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : KRS012-1 : TPTP v9.3.1. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/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 07:45:53 AM UTC 2026
% Result : Unsatisfiable 0.12s 0.37s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 6
% Syntax : Number of formulae : 20 ( 9 unt; 0 def)
% Number of atoms : 38 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 38 ( 20 ~; 18 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 2 ( 2 usr; 1 con; 0-1 aty)
% Number of variables : 14 ( 0 sgn 6 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(clause_3,axiom,
! [VAR_0,VAR_1] :
( ~ d(VAR_0)
| ~ r(VAR_1,VAR_0)
| ~ c(VAR_1)
| e(VAR_0) ),
file('theBenchmark.p',clause_3) ).
cnf(c_1,plain,
( ~ d(A)
| ~ r(B,A)
| ~ c(B)
| e(A) ),
inference(clausify,[status(thm)],[clause_3]) ).
fof(clause_1,axiom,
c(exists),
file('theBenchmark.p',clause_1) ).
cnf(c_2,plain,
c(exists),
inference(clausify,[status(thm)],[clause_1]) ).
fof(clause_4,axiom,
! [VAR_0,VAR_1] :
( ~ r(VAR_1,VAR_0)
| ~ c(VAR_1)
| d(VAR_0) ),
file('theBenchmark.p',clause_4) ).
cnf(c_3,plain,
( ~ r(B,A)
| ~ c(B)
| d(A) ),
inference(clausify,[status(thm)],[clause_4]) ).
fof(clause_12,axiom,
! [VAR_0] :
( ~ e(u1r1(VAR_0))
| f(VAR_0) ),
file('theBenchmark.p',clause_12) ).
cnf(c_11,plain,
( ~ e(u1r1(A))
| f(A) ),
inference(clausify,[status(thm)],[clause_12]) ).
fof(clause_13,axiom,
! [VAR_0] :
( r(VAR_0,u1r1(VAR_0))
| f(VAR_0) ),
file('theBenchmark.p',clause_13) ).
cnf(c_12,plain,
( r(A,u1r1(A))
| f(A) ),
inference(clausify,[status(thm)],[clause_13]) ).
fof(clause_2,axiom,
~ f(exists),
file('theBenchmark.p',clause_2) ).
cnf(c_13,plain,
~ f(exists),
inference(clausify,[status(thm)],[clause_2]) ).
cnf(c_14,plain,
r(exists,u1r1(exists)),
inference(resolve,[status(thm)],[c_13,c_12]) ).
cnf(c_15,plain,
~ e(u1r1(exists)),
inference(resolve,[status(thm)],[c_13,c_11]) ).
cnf(c_18,plain,
( ~ d(A)
| ~ r(exists,A)
| e(A) ),
inference(resolve,[status(thm)],[c_1,c_2]) ).
cnf(c_19,plain,
( ~ r(exists,A)
| d(A) ),
inference(resolve,[status(thm)],[c_3,c_2]) ).
cnf(c_39,plain,
( ~ d(u1r1(exists))
| e(u1r1(exists)) ),
inference(resolve,[status(thm)],[c_18,c_14]) ).
cnf(c_37,plain,
~ d(u1r1(exists)),
inference(resolve,[status(thm)],[c_15,c_39]) ).
cnf(c_40,plain,
d(u1r1(exists)),
inference(resolve,[status(thm)],[c_19,c_14]) ).
cnf(c_38,plain,
$false,
inference(resolve,[status(thm)],[c_37,c_40]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : KRS012-1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.34 % Computer : n006.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % 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 19:32:40 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.35 % Process 3556501 was started by sandbox on n006,
% 0.08/0.35 % Fri Sep 25 19:32:40 2026
% 0.08/0.35 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.08/0.35
% 0.08/0.35 % 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 12.
% 0.12/0.37 % Level of proof is 3.
% 0.12/0.37 % Maximum clause weight is 7.000.
% 0.12/0.37 % Given clauses 6.
% 0.12/0.37
% 0.12/0.37 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------