%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LCL678+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 07:59:29 AM UTC 2026
% Result : Theorem 0.09s 0.39s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 2
% Syntax : Number of formulae : 15 ( 4 unt; 0 def)
% Number of atoms : 52 ( 0 equ)
% Maximal formula atoms : 9 ( 3 avg)
% Number of connectives : 82 ( 45 ~; 28 |; 9 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 1 con; 0-1 aty)
% Number of variables : 33 ( 1 sgn 18 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(reflexivity,axiom,
! [X] : r1(X,X),
file('theBenchmark.p',reflexivity) ).
fof(main,conjecture,
~ ? [X] :
~ ~ ! [Y] :
( ~ ! [X] :
( ~ ! [Y] :
( p1(Y)
| ~ r1(X,Y) )
| ! [Y] :
( p1(Y)
| ~ r1(X,Y) )
| ~ r1(Y,X) )
| ~ r1(X,Y) ),
file('theBenchmark.p',main) ).
fof(main_neg,negated_conjecture,
~ ~ ? [X] :
~ ~ ! [Y] :
( ~ ! [X] :
( ~ ! [Y] :
( p1(Y)
| ~ r1(X,Y) )
| ! [Y] :
( p1(Y)
| ~ r1(X,Y) )
| ~ r1(Y,X) )
| ~ r1(X,Y) ),
inference(assume_negation,[status(cth)],[main]) ).
fof(nnf_3,plain,
? [X] :
! [Y] :
( ? [X0] :
( ! [X2] :
( p1(X2)
| ~ r1(X0,X2) )
& ? [X1] :
( ~ p1(X1)
& r1(X0,X1) )
& r1(Y,X0) )
| ~ r1(X,Y) ),
inference(fof_nnf,[status(thm)],[main_neg]) ).
fof(sk_main_neg_sk,plain,
! [Y] :
( ( ! [X2] :
( p1(X2)
| ~ r1(sK1(Y),X2) )
& ~ p1(sK2(Y))
& r1(sK1(Y),sK2(Y))
& r1(Y,sK1(Y)) )
| ~ r1(sK0,Y) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X,sK0),skolemize(X0,sK1(Y)),skolemize(X1,sK2(Y))],[nnf_3]) ).
fof(sk_main_neg,plain,
( ! [VAR_0,VAR_1] :
( p1(VAR_1)
| ~ r1(sK1(VAR_0),VAR_1)
| ~ r1(sK0,VAR_0) )
& ! [VAR_0] :
( ~ p1(sK2(VAR_0))
| ~ r1(sK0,VAR_0) )
& ! [VAR_0] :
( r1(sK1(VAR_0),sK2(VAR_0))
| ~ r1(sK0,VAR_0) )
& ! [VAR_0] :
( r1(VAR_0,sK1(VAR_0))
| ~ r1(sK0,VAR_0) ) ),
inference(cnf_transformation,[status(thm)],[sk_main_neg_sk]) ).
cnf(c_4,negated_conjecture,
( p1(B)
| ~ r1(sK1(A),B)
| ~ r1(sK0,A) ),
inference(split_conjunct,[status(thm)],[sk_main_neg]) ).
cnf(c_5,negated_conjecture,
( ~ p1(sK2(A))
| ~ r1(sK0,A) ),
inference(split_conjunct,[status(thm)],[sk_main_neg]) ).
cnf(c_6,negated_conjecture,
( ~ r1(sK0,B)
| ~ r1(sK1(A),sK2(B))
| ~ r1(sK0,A) ),
inference(resolve,[status(thm)],[c_4,c_5]) ).
cnf(c_7,negated_conjecture,
( r1(sK1(A),sK2(A))
| ~ r1(sK0,A) ),
inference(split_conjunct,[status(thm)],[sk_main_neg]) ).
cnf(c_10,plain,
r1(A,A),
inference(clausify,[status(thm)],[reflexivity]) ).
cnf(c_13,negated_conjecture,
( ~ r1(sK0,A)
| ~ r1(sK0,A)
| ~ r1(sK0,A) ),
inference(resolve,[status(thm)],[c_7,c_6]) ).
cnf(c_14,negated_conjecture,
( ~ r1(sK0,A)
| ~ r1(sK0,A) ),
inference(copy,[status(thm)],[c_13]) ).
cnf(c_11,negated_conjecture,
~ r1(sK0,A),
inference(copy,[status(thm)],[c_14]) ).
cnf(c_12,plain,
$false,
inference(resolve,[status(thm)],[c_11,c_10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL678+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
% 0.09/0.37 % Computer : n003.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Fri Sep 25 23:18:38 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.37 % Process 1386810 was started by sandbox on n003,
% 0.09/0.37 % Fri Sep 25 23:18:38 2026
% 0.09/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.09/0.38
% 0.09/0.38 % From the command line: assign(max_seconds, 300).
% 0.09/0.39
% 0.09/0.39 % SZS status Theorem for theBenchmark
% 0.09/0.39
% 0.09/0.39 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.09/0.39 % Length of proof is 9.
% 0.09/0.39 % Level of proof is 4.
% 0.09/0.39 % Maximum clause weight is 11.000.
% 0.09/0.39 % Given clauses 2.
% 0.09/0.39
% 0.09/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------