%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LCL686+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 : n012.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 07:59:32 AM UTC 2026
% Result : Theorem 0.11s 0.36s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 2
% Syntax : Number of formulae : 24 ( 6 unt; 0 def)
% Number of atoms : 153 ( 0 equ)
% Maximal formula atoms : 27 ( 6 avg)
% Number of connectives : 234 ( 105 ~; 85 |; 44 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-1 aty)
% Number of variables : 58 ( 0 sgn 31 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(reflexivity,axiom,
! [X] : r1(X,X),
file('theBenchmark.p',reflexivity) ).
fof(main,conjecture,
~ ? [X] :
~ ( ! [Y] :
( ~ ! [X] :
( ~ ( ! [Y] :
( ( p1(Y)
& p2(Y) )
| ( ~ p2(Y)
& ~ p1(Y) )
| ~ r1(X,Y) )
| ! [Y] :
( p3(Y)
| ~ r1(X,Y) )
| ~ ! [Y] :
( ~ ( ( p1(Y)
& ~ p2(Y) )
| ( ~ p1(Y)
& p2(Y) ) )
| ~ r1(X,Y) )
| ! [Y] : ~ r1(X,Y) )
| ~ r1(Y,X) )
| ~ r1(X,Y) )
| ! [Y] :
( ! [X] :
( ~ p1(X)
| ~ r1(Y,X) )
| ~ p3(Y)
| ~ r1(X,Y) ) ),
file('theBenchmark.p',main) ).
fof(main_neg,negated_conjecture,
~ ~ ? [X] :
~ ( ! [Y] :
( ~ ! [X] :
( ~ ( ! [Y] :
( ( p1(Y)
& p2(Y) )
| ( ~ p2(Y)
& ~ p1(Y) )
| ~ r1(X,Y) )
| ! [Y] :
( p3(Y)
| ~ r1(X,Y) )
| ~ ! [Y] :
( ~ ( ( p1(Y)
& ~ p2(Y) )
| ( ~ p1(Y)
& p2(Y) ) )
| ~ r1(X,Y) )
| ! [Y] : ~ r1(X,Y) )
| ~ r1(Y,X) )
| ~ r1(X,Y) )
| ! [Y] :
( ! [X] :
( ~ p1(X)
| ~ r1(Y,X) )
| ~ p3(Y)
| ~ r1(X,Y) ) ),
inference(assume_negation,[status(cth)],[main]) ).
fof(nnf_3,plain,
? [X] :
( ? [Y] :
( ! [X2] :
( ( ? [X6] :
( ( ~ p1(X6)
| ~ p2(X6) )
& ( p2(X6)
| p1(X6) )
& r1(X2,X6) )
& ? [X5] :
( ~ p3(X5)
& r1(X2,X5) )
& ! [X4] :
( ( ( ~ p1(X4)
| p2(X4) )
& ( p1(X4)
| ~ p2(X4) ) )
| ~ r1(X2,X4) )
& ? [X3] : r1(X2,X3) )
| ~ r1(Y,X2) )
& r1(X,Y) )
& ? [X0] :
( ? [X1] :
( p1(X1)
& r1(X0,X1) )
& p3(X0)
& r1(X,X0) ) ),
inference(fof_nnf,[status(thm)],[main_neg]) ).
fof(sk_main_neg_sk,plain,
( ! [X2] :
( ( ( ~ p1(sK1(X2))
| ~ p2(sK1(X2)) )
& ( p2(sK1(X2))
| p1(sK1(X2)) )
& r1(X2,sK1(X2))
& ~ p3(sK6(X2))
& r1(X2,sK6(X2))
& ! [X4] :
( ( ( ~ p1(X4)
| p2(X4) )
& ( p1(X4)
| ~ p2(X4) ) )
| ~ r1(X2,X4) )
& r1(X2,sK5(X2)) )
| ~ r1(sK0,X2) )
& r1(sK2,sK0)
& p1(sK4)
& r1(sK3,sK4)
& p3(sK3)
& r1(sK2,sK3) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3,sK4,sK0,sK5,sK6,sK1]),skolemize(X,sK2),skolemize(X0,sK3),skolemize(X1,sK4),skolemize(Y,sK0),skolemize(X3,sK5(X2)),skolemize(X5,sK6(X2)),skolemize(X6,sK1(X2))],[nnf_3]) ).
fof(sk_main_neg,plain,
( ! [VAR_0] :
( ~ p1(sK1(VAR_0))
| ~ p2(sK1(VAR_0))
| ~ r1(sK0,VAR_0) )
& ! [VAR_0] :
( p2(sK1(VAR_0))
| p1(sK1(VAR_0))
| ~ r1(sK0,VAR_0) )
& ! [VAR_0] :
( r1(VAR_0,sK1(VAR_0))
| ~ r1(sK0,VAR_0) )
& ! [VAR_0] :
( ~ p3(sK6(VAR_0))
| ~ r1(sK0,VAR_0) )
& ! [VAR_0] :
( r1(VAR_0,sK6(VAR_0))
| ~ r1(sK0,VAR_0) )
& ! [VAR_0,VAR_1] :
( ~ p1(VAR_1)
| p2(VAR_1)
| ~ r1(VAR_0,VAR_1)
| ~ r1(sK0,VAR_0) )
& ! [VAR_0,VAR_1] :
( p1(VAR_1)
| ~ p2(VAR_1)
| ~ r1(VAR_0,VAR_1)
| ~ r1(sK0,VAR_0) )
& ! [VAR_0] :
( r1(VAR_0,sK5(VAR_0))
| ~ r1(sK0,VAR_0) )
& r1(sK2,sK0)
& p1(sK4)
& r1(sK3,sK4)
& p3(sK3)
& r1(sK2,sK3) ),
inference(cnf_transformation,[status(thm)],[sk_main_neg_sk]) ).
cnf(c_6,negated_conjecture,
( p2(sK1(A))
| p1(sK1(A))
| ~ r1(sK0,A) ),
inference(split_conjunct,[status(thm)],[sk_main_neg]) ).
cnf(c_7,negated_conjecture,
( ~ p1(sK1(A))
| ~ p2(sK1(A))
| ~ r1(sK0,A) ),
inference(split_conjunct,[status(thm)],[sk_main_neg]) ).
cnf(c_8,negated_conjecture,
( ~ p1(B)
| p2(B)
| ~ r1(A,B)
| ~ r1(sK0,A) ),
inference(split_conjunct,[status(thm)],[sk_main_neg]) ).
cnf(c_9,negated_conjecture,
( p1(B)
| ~ p2(B)
| ~ r1(A,B)
| ~ r1(sK0,A) ),
inference(split_conjunct,[status(thm)],[sk_main_neg]) ).
cnf(c_12,negated_conjecture,
( ~ p2(sK1(B))
| ~ r1(sK0,B)
| ~ p2(sK1(B))
| ~ r1(A,sK1(B))
| ~ r1(sK0,A) ),
inference(resolve,[status(thm)],[c_9,c_7]) ).
cnf(c_13,negated_conjecture,
( ~ r1(sK0,B)
| ~ p2(sK1(B))
| ~ r1(A,sK1(B))
| ~ r1(sK0,A) ),
inference(copy,[status(thm)],[c_12]) ).
cnf(c_14,negated_conjecture,
( p2(sK1(B))
| ~ r1(sK0,B)
| p2(sK1(B))
| ~ r1(A,sK1(B))
| ~ r1(sK0,A) ),
inference(resolve,[status(thm)],[c_8,c_6]) ).
cnf(c_15,negated_conjecture,
( ~ r1(sK0,B)
| p2(sK1(B))
| ~ r1(A,sK1(B))
| ~ r1(sK0,A) ),
inference(copy,[status(thm)],[c_14]) ).
cnf(c_16,plain,
r1(A,A),
inference(clausify,[status(thm)],[reflexivity]) ).
cnf(c_23,negated_conjecture,
( r1(A,sK1(A))
| ~ r1(sK0,A) ),
inference(split_conjunct,[status(thm)],[sk_main_neg]) ).
cnf(c_24,plain,
( ~ p2(sK1(A))
| ~ r1(A,sK1(A))
| ~ r1(sK0,A) ),
inference(factor,[status(thm)],[c_13]) ).
cnf(c_25,plain,
( p2(sK1(A))
| ~ r1(A,sK1(A))
| ~ r1(sK0,A) ),
inference(factor,[status(thm)],[c_15]) ).
cnf(c_40,plain,
r1(sK0,sK1(sK0)),
inference(resolve,[status(thm)],[c_23,c_16]) ).
cnf(c_44,plain,
( ~ p2(sK1(sK0))
| ~ r1(sK0,sK1(sK0)) ),
inference(resolve,[status(thm)],[c_24,c_16]) ).
cnf(c_41,plain,
~ p2(sK1(sK0)),
inference(resolve,[status(thm)],[c_40,c_44]) ).
cnf(c_45,plain,
( p2(sK1(sK0))
| ~ r1(sK0,sK1(sK0)) ),
inference(resolve,[status(thm)],[c_25,c_16]) ).
cnf(c_46,plain,
p2(sK1(sK0)),
inference(resolve,[status(thm)],[c_40,c_45]) ).
cnf(c_43,plain,
$false,
inference(resolve,[status(thm)],[c_41,c_46]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL686+1.001 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.34 % Computer : n012.cluster.edu
% 0.07/0.34 % Model : x86_64 x86_64
% 0.07/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.34 % Memory : 8046.5625MB
% 0.07/0.34 % OS : Linux 6.8.0-71-generic
% 0.07/0.34 % CPULimit : 300
% 0.07/0.34 % WCLimit : 300
% 0.07/0.34 % DateTime : Fri Sep 25 23:22:37 UTC 2026
% 0.07/0.35 % CPUTime :
% 0.07/0.35 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.07/0.35 % Process 3303447 was started by sandbox on n012,
% 0.07/0.35 % Fri Sep 25 23:22:37 2026
% 0.07/0.35 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.07/0.35
% 0.07/0.35 % From the command line: assign(max_seconds, 300).
% 0.11/0.36
% 0.11/0.36 % SZS status Theorem for theBenchmark
% 0.11/0.36
% 0.11/0.36 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.11/0.36 % Length of proof is 17.
% 0.11/0.36 % Level of proof is 6.
% 0.11/0.36 % Maximum clause weight is 13.000.
% 0.11/0.36 % Given clauses 13.
% 0.11/0.36
% 0.11/0.36 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------