%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LCL638+1.001 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n013.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 07:59:15 AM UTC 2026
% Result : Theorem 0.07s 0.41s
% Output : CNFRefutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 1
% Syntax : Number of formulae : 30 ( 9 unt; 0 def)
% Number of atoms : 233 ( 0 equ)
% Maximal formula atoms : 54 ( 7 avg)
% Number of connectives : 400 ( 197 ~; 158 |; 45 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 2 con; 0-3 aty)
% Number of variables : 122 ( 0 sgn 96 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(main,conjecture,
~ ? [X] :
~ ( ! [Y] :
( ~ ! [X] :
( p1(X)
| ~ r1(Y,X) )
| p1(Y)
| ~ r1(X,Y) )
| ~ ! [Y] :
( ~ ! [X] : ~ r1(Y,X)
| ~ r1(X,Y) )
| ~ ! [Y] :
( ~ ( ! [X] :
( p1(X)
| ~ r1(Y,X) )
& ~ ! [X] :
( ! [Y] :
( p1(Y)
| ~ r1(X,Y) )
| ~ r1(Y,X) ) )
| ~ r1(X,Y) )
| ~ ! [Y] :
( ~ ( ! [X] :
( ~ ! [Y] :
( ~ p1(Y)
| ~ r1(X,Y) )
| ~ r1(Y,X) )
& ~ ! [X] :
( ! [Y] :
( ~ ! [X] :
( ~ p1(X)
| ~ r1(Y,X) )
| ~ r1(X,Y) )
| ~ r1(Y,X) ) )
| ~ r1(X,Y) )
| ~ ! [Y] :
( ~ ( p1(Y)
& ~ ! [X] :
( ~ ! [Y] :
( ~ p1(Y)
| ~ r1(X,Y) )
| ~ r1(Y,X) ) )
| ~ r1(X,Y) )
| ~ ! [Y] :
( ~ ( ~ p1(Y)
& ~ ! [X] :
( ~ ! [Y] :
( p1(Y)
| ~ r1(X,Y) )
| ~ r1(Y,X) ) )
| ~ r1(X,Y) ) ),
file('theBenchmark.p',main) ).
fof(main_neg,negated_conjecture,
~ ~ ? [X] :
~ ( ! [Y] :
( ~ ! [X] :
( p1(X)
| ~ r1(Y,X) )
| p1(Y)
| ~ r1(X,Y) )
| ~ ! [Y] :
( ~ ! [X] : ~ r1(Y,X)
| ~ r1(X,Y) )
| ~ ! [Y] :
( ~ ( ! [X] :
( p1(X)
| ~ r1(Y,X) )
& ~ ! [X] :
( ! [Y] :
( p1(Y)
| ~ r1(X,Y) )
| ~ r1(Y,X) ) )
| ~ r1(X,Y) )
| ~ ! [Y] :
( ~ ( ! [X] :
( ~ ! [Y] :
( ~ p1(Y)
| ~ r1(X,Y) )
| ~ r1(Y,X) )
& ~ ! [X] :
( ! [Y] :
( ~ ! [X] :
( ~ p1(X)
| ~ r1(Y,X) )
| ~ r1(X,Y) )
| ~ r1(Y,X) ) )
| ~ r1(X,Y) )
| ~ ! [Y] :
( ~ ( p1(Y)
& ~ ! [X] :
( ~ ! [Y] :
( ~ p1(Y)
| ~ r1(X,Y) )
| ~ r1(Y,X) ) )
| ~ r1(X,Y) )
| ~ ! [Y] :
( ~ ( ~ p1(Y)
& ~ ! [X] :
( ~ ! [Y] :
( p1(Y)
| ~ r1(X,Y) )
| ~ r1(Y,X) ) )
| ~ r1(X,Y) ) ),
inference(assume_negation,[status(cth)],[main]) ).
fof(nnf_1,plain,
? [X] :
( ? [Y] :
( ! [X18] :
( p1(X18)
| ~ r1(Y,X18) )
& ~ p1(Y)
& r1(X,Y) )
& ! [X16] :
( ? [X17] : r1(X16,X17)
| ~ r1(X,X16) )
& ! [X12] :
( ? [X15] :
( ~ p1(X15)
& r1(X12,X15) )
| ! [X13] :
( ! [X14] :
( p1(X14)
| ~ r1(X13,X14) )
| ~ r1(X12,X13) )
| ~ r1(X,X12) )
& ! [X6] :
( ? [X10] :
( ! [X11] :
( ~ p1(X11)
| ~ r1(X10,X11) )
& r1(X6,X10) )
| ! [X7] :
( ! [X8] :
( ? [X9] :
( p1(X9)
& r1(X8,X9) )
| ~ r1(X7,X8) )
| ~ r1(X6,X7) )
| ~ r1(X,X6) )
& ! [X3] :
( ~ p1(X3)
| ! [X4] :
( ? [X5] :
( p1(X5)
& r1(X4,X5) )
| ~ r1(X3,X4) )
| ~ r1(X,X3) )
& ! [X0] :
( p1(X0)
| ! [X1] :
( ? [X2] :
( ~ p1(X2)
& r1(X1,X2) )
| ~ r1(X0,X1) )
| ~ r1(X,X0) ) ),
inference(fof_nnf,[status(thm)],[main_neg]) ).
fof(sk_main_neg_sk,plain,
( ! [X18] :
( p1(X18)
| ~ r1(sK4,X18) )
& ~ p1(sK4)
& r1(sK0,sK4)
& ! [X16] :
( r1(X16,sK3(X16))
| ~ r1(sK0,X16) )
& ! [X12] :
( ( ~ p1(sK2(X12))
& r1(X12,sK2(X12)) )
| ! [X13] :
( ! [X14] :
( p1(X14)
| ~ r1(X13,X14) )
| ~ r1(X12,X13) )
| ~ r1(sK0,X12) )
& ! [X6] :
( ( ! [X11] :
( ~ p1(X11)
| ~ r1(sK7(X6),X11) )
& r1(X6,sK7(X6)) )
| ! [X7] :
( ! [X8] :
( ( p1(sK6(X6,X7,X8))
& r1(X8,sK6(X6,X7,X8)) )
| ~ r1(X7,X8) )
| ~ r1(X6,X7) )
| ~ r1(sK0,X6) )
& ! [X3] :
( ~ p1(X3)
| ! [X4] :
( ( p1(sK5(X3,X4))
& r1(X4,sK5(X3,X4)) )
| ~ r1(X3,X4) )
| ~ r1(sK0,X3) )
& ! [X0] :
( p1(X0)
| ! [X1] :
( ( ~ p1(sK1(X0,X1))
& r1(X1,sK1(X0,X1)) )
| ~ r1(X0,X1) )
| ~ r1(sK0,X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK5,sK6,sK7,sK2,sK3,sK4]),skolemize(X,sK0),skolemize(X2,sK1(X0,X1)),skolemize(X5,sK5(X3,X4)),skolemize(X9,sK6(X6,X7,X8)),skolemize(X10,sK7(X6)),skolemize(X15,sK2(X12)),skolemize(X17,sK3(X16)),skolemize(Y,sK4)],[nnf_1]) ).
fof(sk_main_neg,plain,
( ! [VAR_0] :
( p1(VAR_0)
| ~ r1(sK4,VAR_0) )
& ~ p1(sK4)
& r1(sK0,sK4)
& ! [VAR_0] :
( r1(VAR_0,sK3(VAR_0))
| ~ r1(sK0,VAR_0) )
& ! [VAR_0,VAR_1,VAR_2] :
( ~ p1(sK2(VAR_0))
| p1(VAR_2)
| ~ r1(VAR_1,VAR_2)
| ~ r1(VAR_0,VAR_1)
| ~ r1(sK0,VAR_0) )
& ! [VAR_0,VAR_1,VAR_2] :
( r1(VAR_0,sK2(VAR_0))
| p1(VAR_2)
| ~ r1(VAR_1,VAR_2)
| ~ r1(VAR_0,VAR_1)
| ~ r1(sK0,VAR_0) )
& ! [VAR_0,VAR_1,VAR_2,VAR_3] :
( ~ p1(VAR_3)
| ~ r1(sK7(VAR_0),VAR_3)
| p1(sK6(VAR_0,VAR_1,VAR_2))
| ~ r1(VAR_1,VAR_2)
| ~ r1(VAR_0,VAR_1)
| ~ r1(sK0,VAR_0) )
& ! [VAR_0,VAR_1,VAR_2] :
( r1(VAR_0,sK7(VAR_0))
| p1(sK6(VAR_0,VAR_1,VAR_2))
| ~ r1(VAR_1,VAR_2)
| ~ r1(VAR_0,VAR_1)
| ~ r1(sK0,VAR_0) )
& ! [VAR_0,VAR_1,VAR_2,VAR_3] :
( ~ p1(VAR_3)
| ~ r1(sK7(VAR_0),VAR_3)
| r1(VAR_2,sK6(VAR_0,VAR_1,VAR_2))
| ~ r1(VAR_1,VAR_2)
| ~ r1(VAR_0,VAR_1)
| ~ r1(sK0,VAR_0) )
& ! [VAR_0,VAR_1,VAR_2] :
( r1(VAR_0,sK7(VAR_0))
| r1(VAR_2,sK6(VAR_0,VAR_1,VAR_2))
| ~ r1(VAR_1,VAR_2)
| ~ r1(VAR_0,VAR_1)
| ~ r1(sK0,VAR_0) )
& ! [VAR_0,VAR_1] :
( ~ p1(VAR_0)
| p1(sK5(VAR_0,VAR_1))
| ~ r1(VAR_0,VAR_1)
| ~ r1(sK0,VAR_0) )
& ! [VAR_0,VAR_1] :
( ~ p1(VAR_0)
| r1(VAR_1,sK5(VAR_0,VAR_1))
| ~ r1(VAR_0,VAR_1)
| ~ r1(sK0,VAR_0) )
& ! [VAR_0,VAR_1] :
( p1(VAR_0)
| ~ p1(sK1(VAR_0,VAR_1))
| ~ r1(VAR_0,VAR_1)
| ~ r1(sK0,VAR_0) )
& ! [VAR_0,VAR_1] :
( p1(VAR_0)
| r1(VAR_1,sK1(VAR_0,VAR_1))
| ~ r1(VAR_0,VAR_1)
| ~ r1(sK0,VAR_0) ) ),
inference(cnf_transformation,[status(thm)],[sk_main_neg_sk]) ).
cnf(c_2,negated_conjecture,
( p1(A)
| r1(B,sK1(A,B))
| ~ r1(A,B)
| ~ r1(sK0,A) ),
inference(split_conjunct,[status(thm)],[sk_main_neg]) ).
cnf(c_3,negated_conjecture,
( p1(A)
| ~ p1(sK1(A,B))
| ~ r1(A,B)
| ~ r1(sK0,A) ),
inference(split_conjunct,[status(thm)],[sk_main_neg]) ).
cnf(c_10,negated_conjecture,
( r1(A,sK2(A))
| p1(C)
| ~ r1(B,C)
| ~ r1(A,B)
| ~ r1(sK0,A) ),
inference(split_conjunct,[status(thm)],[sk_main_neg]) ).
cnf(c_11,negated_conjecture,
( ~ p1(sK2(A))
| p1(C)
| ~ r1(B,C)
| ~ r1(A,B)
| ~ r1(sK0,A) ),
inference(split_conjunct,[status(thm)],[sk_main_neg]) ).
cnf(c_12,negated_conjecture,
( r1(A,sK3(A))
| ~ r1(sK0,A) ),
inference(split_conjunct,[status(thm)],[sk_main_neg]) ).
cnf(c_13,negated_conjecture,
r1(sK0,sK4),
inference(split_conjunct,[status(thm)],[sk_main_neg]) ).
cnf(c_14,negated_conjecture,
~ p1(sK4),
inference(split_conjunct,[status(thm)],[sk_main_neg]) ).
cnf(c_15,negated_conjecture,
( p1(A)
| ~ r1(sK4,A) ),
inference(split_conjunct,[status(thm)],[sk_main_neg]) ).
cnf(c_46,plain,
r1(sK4,sK3(sK4)),
inference(resolve,[status(thm)],[c_13,c_12]) ).
cnf(c_113,negated_conjecture,
( p1(sK4)
| ~ p1(sK1(sK4,sK3(sK4)))
| ~ r1(sK0,sK4) ),
inference(resolve,[status(thm)],[c_46,c_3]) ).
cnf(c_114,negated_conjecture,
( p1(sK4)
| ~ p1(sK1(sK4,sK3(sK4))) ),
inference(resolve,[status(thm)],[c_13,c_113]) ).
cnf(c_91,negated_conjecture,
~ p1(sK1(sK4,sK3(sK4))),
inference(resolve,[status(thm)],[c_14,c_114]) ).
cnf(c_115,negated_conjecture,
( p1(sK4)
| r1(sK3(sK4),sK1(sK4,sK3(sK4)))
| ~ r1(sK0,sK4) ),
inference(resolve,[status(thm)],[c_46,c_2]) ).
cnf(c_116,negated_conjecture,
( p1(sK4)
| r1(sK3(sK4),sK1(sK4,sK3(sK4))) ),
inference(resolve,[status(thm)],[c_13,c_115]) ).
cnf(c_92,negated_conjecture,
r1(sK3(sK4),sK1(sK4,sK3(sK4))),
inference(resolve,[status(thm)],[c_14,c_116]) ).
cnf(c_117,negated_conjecture,
( ~ p1(sK2(sK4))
| p1(B)
| ~ r1(A,B)
| ~ r1(sK4,A) ),
inference(resolve,[status(thm)],[c_11,c_13]) ).
cnf(c_118,negated_conjecture,
( ~ p1(sK2(sK4))
| p1(A)
| ~ r1(sK3(sK4),A) ),
inference(resolve,[status(thm)],[c_117,c_46]) ).
cnf(c_119,negated_conjecture,
( ~ p1(sK2(sK4))
| p1(sK1(sK4,sK3(sK4))) ),
inference(resolve,[status(thm)],[c_118,c_92]) ).
cnf(c_108,negated_conjecture,
~ p1(sK2(sK4)),
inference(resolve,[status(thm)],[c_119,c_91]) ).
cnf(c_109,negated_conjecture,
~ r1(sK4,sK2(sK4)),
inference(resolve,[status(thm)],[c_15,c_108]) ).
cnf(c_120,negated_conjecture,
( r1(sK4,sK2(sK4))
| p1(A)
| ~ r1(sK3(sK4),A)
| ~ r1(sK0,sK4) ),
inference(resolve,[status(thm)],[c_10,c_46]) ).
cnf(c_121,negated_conjecture,
( r1(sK4,sK2(sK4))
| p1(sK1(sK4,sK3(sK4)))
| ~ r1(sK0,sK4) ),
inference(resolve,[status(thm)],[c_120,c_92]) ).
cnf(c_122,negated_conjecture,
( r1(sK4,sK2(sK4))
| ~ r1(sK0,sK4) ),
inference(resolve,[status(thm)],[c_121,c_91]) ).
cnf(c_123,negated_conjecture,
~ r1(sK0,sK4),
inference(resolve,[status(thm)],[c_122,c_109]) ).
cnf(c_112,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_13,c_123]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL638+1.001 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.38 % Computer : n013.cluster.edu
% 0.07/0.38 % Model : x86_64 x86_64
% 0.07/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.38 % Memory : 8046.5625MB
% 0.07/0.38 % OS : Linux 6.8.0-71-generic
% 0.07/0.38 % CPULimit : 300
% 0.07/0.38 % WCLimit : 300
% 0.07/0.38 % DateTime : Fri Sep 25 22:48:54 UTC 2026
% 0.07/0.38 % CPUTime :
% 0.07/0.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.07/0.38 % Process 1417965 was started by sandbox2 on n013,
% 0.07/0.38 % Fri Sep 25 22:48:54 2026
% 0.07/0.38 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.07/0.39
% 0.07/0.39 % From the command line: assign(max_seconds, 300).
% 0.07/0.41
% 0.07/0.41 % SZS status Theorem for theBenchmark
% 0.07/0.41
% 0.07/0.41 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.07/0.41 % Length of proof is 15.
% 0.07/0.41 % Level of proof is 6.
% 0.07/0.41 % Maximum clause weight is 15.000.
% 0.07/0.41 % Given clauses 50.
% 0.07/0.41
% 0.07/0.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------