%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LCL664+1.001 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n004.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 07:59:24 AM UTC 2026
% Result : Theorem 0.09s 0.38s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 1
% Syntax : Number of formulae : 9 ( 4 unt; 0 def)
% Number of atoms : 70 ( 0 equ)
% Maximal formula atoms : 16 ( 7 avg)
% Number of connectives : 108 ( 47 ~; 39 |; 22 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 7 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 8 ( 7 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 5 con; 0-0 aty)
% Number of variables : 32 ( 0 sgn 24 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(main,conjecture,
~ ? [X] :
~ ( ! [Y] :
( p11(Y)
| ~ r1(X,Y) )
| ! [Y] :
( p12(Y)
| ~ r1(X,Y) )
| ! [Y] :
( p13(Y)
| ~ r1(X,Y) )
| ! [Y] :
( p15(Y)
| ~ r1(X,Y) )
| ~ ! [Y] :
( p12(Y)
| ~ r1(X,Y) )
| ~ ! [Y] :
( p14(Y)
| ~ r1(X,Y) )
| ~ ! [Y] :
( p12(Y)
| ~ r1(X,Y) )
| ~ ! [Y] :
( p16(Y)
| ~ r1(X,Y) ) ),
file('theBenchmark.p',main) ).
fof(main_neg,negated_conjecture,
~ ~ ? [X] :
~ ( ! [Y] :
( p11(Y)
| ~ r1(X,Y) )
| ! [Y] :
( p12(Y)
| ~ r1(X,Y) )
| ! [Y] :
( p13(Y)
| ~ r1(X,Y) )
| ! [Y] :
( p15(Y)
| ~ r1(X,Y) )
| ~ ! [Y] :
( p12(Y)
| ~ r1(X,Y) )
| ~ ! [Y] :
( p14(Y)
| ~ r1(X,Y) )
| ~ ! [Y] :
( p12(Y)
| ~ r1(X,Y) )
| ~ ! [Y] :
( p16(Y)
| ~ r1(X,Y) ) ),
inference(assume_negation,[status(cth)],[main]) ).
fof(nnf_2,plain,
? [X] :
( ? [Y] :
( ~ p11(Y)
& r1(X,Y) )
& ? [X6] :
( ~ p12(X6)
& r1(X,X6) )
& ? [X5] :
( ~ p13(X5)
& r1(X,X5) )
& ? [X4] :
( ~ p15(X4)
& r1(X,X4) )
& ! [X3] :
( p12(X3)
| ~ r1(X,X3) )
& ! [X2] :
( p14(X2)
| ~ r1(X,X2) )
& ! [X1] :
( p12(X1)
| ~ r1(X,X1) )
& ! [X0] :
( p16(X0)
| ~ r1(X,X0) ) ),
inference(fof_nnf,[status(thm)],[main_neg]) ).
fof(sk_main_neg,plain,
( ~ p11(sK4)
& r1(sK0,sK4)
& ~ p12(sK1)
& r1(sK0,sK1)
& ~ p13(sK3)
& r1(sK0,sK3)
& ~ p15(sK2)
& r1(sK0,sK2)
& ! [X3] :
( p12(X3)
| ~ r1(sK0,X3) )
& ! [X2] :
( p14(X2)
| ~ r1(sK0,X2) )
& ! [X1] :
( p12(X1)
| ~ r1(sK0,X1) )
& ! [X0] :
( p16(X0)
| ~ r1(sK0,X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK2,sK3,sK1,sK4]),skolemize(X,sK0),skolemize(X4,sK2),skolemize(X5,sK3),skolemize(X6,sK1),skolemize(Y,sK4)],[nnf_2]) ).
cnf(c_7,negated_conjecture,
( p12(A)
| ~ r1(sK0,A) ),
inference(split_conjunct,[status(thm)],[sk_main_neg]) ).
cnf(c_10,negated_conjecture,
r1(sK0,sK1),
inference(split_conjunct,[status(thm)],[sk_main_neg]) ).
cnf(c_13,negated_conjecture,
~ p12(sK1),
inference(split_conjunct,[status(thm)],[sk_main_neg]) ).
cnf(c_16,negated_conjecture,
p12(sK1),
inference(resolve,[status(thm)],[c_10,c_7]) ).
cnf(c_18,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_16,c_13]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL664+1.001 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n004.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 23:06:36 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 224204 was started by sandbox on n004,
% 0.09/0.36 % Fri Sep 25 23:06:36 2026
% 0.09/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.09/0.36
% 0.09/0.36 % From the command line: assign(max_seconds, 300).
% 0.09/0.38
% 0.09/0.38 % SZS status Theorem for theBenchmark
% 0.09/0.38
% 0.09/0.38 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.09/0.38 % Length of proof is 6.
% 0.09/0.38 % Level of proof is 3.
% 0.09/0.38 % Maximum clause weight is 0.000.
% 0.09/0.38 % Given clauses 0.
% 0.09/0.38
% 0.09/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------