%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LCL646+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 : n003.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 07:59:18 AM UTC 2026
% Result : Theorem 0.09s 5.39s
% 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] :
( p1(Y)
| ~ r1(X,Y) )
| ! [Y] :
( p2(Y)
| ~ r1(X,Y) )
| ! [Y] :
( p3(Y)
| ~ r1(X,Y) )
| ! [Y] :
( p5(Y)
| ~ r1(X,Y) )
| ~ ! [Y] :
( p2(Y)
| ~ r1(X,Y) )
| ~ ! [Y] :
( p4(Y)
| ~ r1(X,Y) )
| ~ ! [Y] :
( p2(Y)
| ~ r1(X,Y) )
| ~ ! [Y] :
( p6(Y)
| ~ r1(X,Y) ) ),
file('theBenchmark.p',main) ).
fof(main_neg,negated_conjecture,
~ ~ ? [X] :
~ ( ! [Y] :
( p1(Y)
| ~ r1(X,Y) )
| ! [Y] :
( p2(Y)
| ~ r1(X,Y) )
| ! [Y] :
( p3(Y)
| ~ r1(X,Y) )
| ! [Y] :
( p5(Y)
| ~ r1(X,Y) )
| ~ ! [Y] :
( p2(Y)
| ~ r1(X,Y) )
| ~ ! [Y] :
( p4(Y)
| ~ r1(X,Y) )
| ~ ! [Y] :
( p2(Y)
| ~ r1(X,Y) )
| ~ ! [Y] :
( p6(Y)
| ~ r1(X,Y) ) ),
inference(assume_negation,[status(cth)],[main]) ).
fof(nnf_1,plain,
? [X] :
( ? [Y] :
( ~ p1(Y)
& r1(X,Y) )
& ? [X6] :
( ~ p2(X6)
& r1(X,X6) )
& ? [X5] :
( ~ p3(X5)
& r1(X,X5) )
& ? [X4] :
( ~ p5(X4)
& r1(X,X4) )
& ! [X3] :
( p2(X3)
| ~ r1(X,X3) )
& ! [X2] :
( p4(X2)
| ~ r1(X,X2) )
& ! [X1] :
( p2(X1)
| ~ r1(X,X1) )
& ! [X0] :
( p6(X0)
| ~ r1(X,X0) ) ),
inference(fof_nnf,[status(thm)],[main_neg]) ).
fof(sk_main_neg,plain,
( ~ p1(sK4)
& r1(sK0,sK4)
& ~ p2(sK1)
& r1(sK0,sK1)
& ~ p3(sK3)
& r1(sK0,sK3)
& ~ p5(sK2)
& r1(sK0,sK2)
& ! [X3] :
( p2(X3)
| ~ r1(sK0,X3) )
& ! [X2] :
( p4(X2)
| ~ r1(sK0,X2) )
& ! [X1] :
( p2(X1)
| ~ r1(sK0,X1) )
& ! [X0] :
( p6(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_1]) ).
cnf(c_3,negated_conjecture,
( p2(A)
| ~ r1(sK0,A) ),
inference(split_conjunct,[status(thm)],[sk_main_neg]) ).
cnf(c_8,negated_conjecture,
r1(sK0,sK1),
inference(split_conjunct,[status(thm)],[sk_main_neg]) ).
cnf(c_11,negated_conjecture,
~ p2(sK1),
inference(split_conjunct,[status(thm)],[sk_main_neg]) ).
cnf(c_13,negated_conjecture,
p2(sK1),
inference(resolve,[status(thm)],[c_8,c_3]) ).
cnf(c_15,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_13,c_11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL646+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
% 0.09/5.37 % Computer : n003.cluster.edu
% 0.09/5.37 % Model : x86_64 x86_64
% 0.09/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.37 % Memory : 8046.5625MB
% 0.09/5.37 % OS : Linux 6.8.0-71-generic
% 0.09/5.37 % CPULimit : 300
% 0.09/5.37 % WCLimit : 300
% 0.09/5.37 % DateTime : Fri Sep 25 22:56:58 UTC 2026
% 0.09/5.38 % CPUTime :
% 0.09/5.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/5.38 % Process 1343642 was started by sandbox on n003,
% 0.09/5.38 % Fri Sep 25 22:56:58 2026
% 0.09/5.38 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.09/5.38
% 0.09/5.38 % From the command line: assign(max_seconds, 300).
% 0.09/5.39
% 0.09/5.39 % SZS status Theorem for theBenchmark
% 0.09/5.39
% 0.09/5.39 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.09/5.39 % Length of proof is 6.
% 0.09/5.39 % Level of proof is 3.
% 0.09/5.39 % Maximum clause weight is 0.000.
% 0.09/5.39 % Given clauses 0.
% 0.09/5.39
% 0.09/5.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------