%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LCL636+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 : n015.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 07:59:14 AM UTC 2026
% Result : Theorem 0.13s 0.37s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 1
% Syntax : Number of formulae : 16 ( 6 unt; 0 def)
% Number of atoms : 396 ( 0 equ)
% Maximal formula atoms : 102 ( 24 avg)
% Number of connectives : 663 ( 283 ~; 239 |; 141 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 32 ( 8 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-1 aty)
% Number of variables : 77 ( 0 sgn 69 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(main,conjecture,
~ ? [X] :
~ ( ~ ( p100(X)
& ~ p101(X)
& ( ~ p101(X)
| p100(X) )
& ( ~ p102(X)
| p101(X) )
& ( ~ p100(X)
| ( ( ~ p1(X)
| ! [Y] :
( ~ p100(Y)
| p1(Y)
| ~ r1(X,Y) ) )
& ( p1(X)
| ! [Y] :
( ~ p100(Y)
| ~ p1(Y)
| ~ r1(X,Y) ) ) ) )
& ( ~ p101(X)
| ( ( ~ p2(X)
| ! [Y] :
( ~ p101(Y)
| p2(Y)
| ~ r1(X,Y) ) )
& ( p2(X)
| ! [Y] :
( ~ p101(Y)
| ~ p2(Y)
| ~ r1(X,Y) ) ) ) )
& ( ~ ( p100(X)
& ~ p101(X) )
| ( ~ ! [Y] :
( ~ ( p101(Y)
& ~ p102(Y)
& p2(Y) )
| ~ r1(X,Y) )
& ~ ! [Y] :
( ~ ( p101(Y)
& ~ p102(Y)
& ~ p2(Y) )
| ~ r1(X,Y) ) ) )
& ! [Y] :
( ( ( ~ p101(Y)
| p100(Y) )
& ( ~ p102(Y)
| p101(Y) )
& ( ~ p100(Y)
| ( ( ~ p1(Y)
| ! [X] :
( ~ p100(X)
| p1(X)
| ~ r1(Y,X) ) )
& ( p1(Y)
| ! [X] :
( ~ p100(X)
| ~ p1(X)
| ~ r1(Y,X) ) ) ) )
& ( ~ p101(Y)
| ( ( ~ p2(Y)
| ! [X] :
( ~ p101(X)
| p2(X)
| ~ r1(Y,X) ) )
& ( p2(Y)
| ! [X] :
( ~ p101(X)
| ~ p2(X)
| ~ r1(Y,X) ) ) ) )
& ( ~ ( p100(Y)
& ~ p101(Y) )
| ( ~ ! [X] :
( ~ ( p101(X)
& ~ p102(X)
& p2(X) )
| ~ r1(Y,X) )
& ~ ! [X] :
( ~ ( p101(X)
& ~ p102(X)
& ~ p2(X) )
| ~ r1(Y,X) ) ) ) )
| ~ r1(X,Y) ) )
| ~ ! [Y] :
( p2(Y)
| ~ r1(X,Y) ) ),
file('theBenchmark.p',main) ).
fof(main_neg,negated_conjecture,
~ ~ ? [X] :
~ ( ~ ( p100(X)
& ~ p101(X)
& ( ~ p101(X)
| p100(X) )
& ( ~ p102(X)
| p101(X) )
& ( ~ p100(X)
| ( ( ~ p1(X)
| ! [Y] :
( ~ p100(Y)
| p1(Y)
| ~ r1(X,Y) ) )
& ( p1(X)
| ! [Y] :
( ~ p100(Y)
| ~ p1(Y)
| ~ r1(X,Y) ) ) ) )
& ( ~ p101(X)
| ( ( ~ p2(X)
| ! [Y] :
( ~ p101(Y)
| p2(Y)
| ~ r1(X,Y) ) )
& ( p2(X)
| ! [Y] :
( ~ p101(Y)
| ~ p2(Y)
| ~ r1(X,Y) ) ) ) )
& ( ~ ( p100(X)
& ~ p101(X) )
| ( ~ ! [Y] :
( ~ ( p101(Y)
& ~ p102(Y)
& p2(Y) )
| ~ r1(X,Y) )
& ~ ! [Y] :
( ~ ( p101(Y)
& ~ p102(Y)
& ~ p2(Y) )
| ~ r1(X,Y) ) ) )
& ! [Y] :
( ( ( ~ p101(Y)
| p100(Y) )
& ( ~ p102(Y)
| p101(Y) )
& ( ~ p100(Y)
| ( ( ~ p1(Y)
| ! [X] :
( ~ p100(X)
| p1(X)
| ~ r1(Y,X) ) )
& ( p1(Y)
| ! [X] :
( ~ p100(X)
| ~ p1(X)
| ~ r1(Y,X) ) ) ) )
& ( ~ p101(Y)
| ( ( ~ p2(Y)
| ! [X] :
( ~ p101(X)
| p2(X)
| ~ r1(Y,X) ) )
& ( p2(Y)
| ! [X] :
( ~ p101(X)
| ~ p2(X)
| ~ r1(Y,X) ) ) ) )
& ( ~ ( p100(Y)
& ~ p101(Y) )
| ( ~ ! [X] :
( ~ ( p101(X)
& ~ p102(X)
& p2(X) )
| ~ r1(Y,X) )
& ~ ! [X] :
( ~ ( p101(X)
& ~ p102(X)
& ~ p2(X) )
| ~ r1(Y,X) ) ) ) )
| ~ r1(X,Y) ) )
| ~ ! [Y] :
( p2(Y)
| ~ r1(X,Y) ) ),
inference(assume_negation,[status(cth)],[main]) ).
fof(nnf_1,plain,
? [X] :
( p100(X)
& ~ p101(X)
& ( ~ p101(X)
| p100(X) )
& ( ~ p102(X)
| p101(X) )
& ( ~ p100(X)
| ( ( ~ p1(X)
| ! [Y] :
( ~ p100(Y)
| p1(Y)
| ~ r1(X,Y) ) )
& ( p1(X)
| ! [X12] :
( ~ p100(X12)
| ~ p1(X12)
| ~ r1(X,X12) ) ) ) )
& ( ~ p101(X)
| ( ( ~ p2(X)
| ! [X11] :
( ~ p101(X11)
| p2(X11)
| ~ r1(X,X11) ) )
& ( p2(X)
| ! [X10] :
( ~ p101(X10)
| ~ p2(X10)
| ~ r1(X,X10) ) ) ) )
& ( ~ p100(X)
| p101(X)
| ( ? [X9] :
( p101(X9)
& ~ p102(X9)
& p2(X9)
& r1(X,X9) )
& ? [X8] :
( p101(X8)
& ~ p102(X8)
& ~ p2(X8)
& r1(X,X8) ) ) )
& ! [X1] :
( ( ( ~ p101(X1)
| p100(X1) )
& ( ~ p102(X1)
| p101(X1) )
& ( ~ p100(X1)
| ( ( ~ p1(X1)
| ! [X7] :
( ~ p100(X7)
| p1(X7)
| ~ r1(X1,X7) ) )
& ( p1(X1)
| ! [X6] :
( ~ p100(X6)
| ~ p1(X6)
| ~ r1(X1,X6) ) ) ) )
& ( ~ p101(X1)
| ( ( ~ p2(X1)
| ! [X5] :
( ~ p101(X5)
| p2(X5)
| ~ r1(X1,X5) ) )
& ( p2(X1)
| ! [X4] :
( ~ p101(X4)
| ~ p2(X4)
| ~ r1(X1,X4) ) ) ) )
& ( ~ p100(X1)
| p101(X1)
| ( ? [X3] :
( p101(X3)
& ~ p102(X3)
& p2(X3)
& r1(X1,X3) )
& ? [X2] :
( p101(X2)
& ~ p102(X2)
& ~ p2(X2)
& r1(X1,X2) ) ) ) )
| ~ r1(X,X1) )
& ! [X0] :
( p2(X0)
| ~ r1(X,X0) ) ),
inference(fof_nnf,[status(thm)],[main_neg]) ).
fof(sk_main_neg_sk,plain,
( p100(sK0)
& ~ p101(sK0)
& ( ~ p101(sK0)
| p100(sK0) )
& ( ~ p102(sK0)
| p101(sK0) )
& ( ~ p100(sK0)
| ( ( ~ p1(sK0)
| ! [Y] :
( ~ p100(Y)
| p1(Y)
| ~ r1(sK0,Y) ) )
& ( p1(sK0)
| ! [X12] :
( ~ p100(X12)
| ~ p1(X12)
| ~ r1(sK0,X12) ) ) ) )
& ( ~ p101(sK0)
| ( ( ~ p2(sK0)
| ! [X11] :
( ~ p101(X11)
| p2(X11)
| ~ r1(sK0,X11) ) )
& ( p2(sK0)
| ! [X10] :
( ~ p101(X10)
| ~ p2(X10)
| ~ r1(sK0,X10) ) ) ) )
& ( ~ p100(sK0)
| p101(sK0)
| ( p101(sK4)
& ~ p102(sK4)
& p2(sK4)
& r1(sK0,sK4)
& p101(sK1)
& ~ p102(sK1)
& ~ p2(sK1)
& r1(sK0,sK1) ) )
& ! [X1] :
( ( ( ~ p101(X1)
| p100(X1) )
& ( ~ p102(X1)
| p101(X1) )
& ( ~ p100(X1)
| ( ( ~ p1(X1)
| ! [X7] :
( ~ p100(X7)
| p1(X7)
| ~ r1(X1,X7) ) )
& ( p1(X1)
| ! [X6] :
( ~ p100(X6)
| ~ p1(X6)
| ~ r1(X1,X6) ) ) ) )
& ( ~ p101(X1)
| ( ( ~ p2(X1)
| ! [X5] :
( ~ p101(X5)
| p2(X5)
| ~ r1(X1,X5) ) )
& ( p2(X1)
| ! [X4] :
( ~ p101(X4)
| ~ p2(X4)
| ~ r1(X1,X4) ) ) ) )
& ( ~ p100(X1)
| p101(X1)
| ( p101(sK3(X1))
& ~ p102(sK3(X1))
& p2(sK3(X1))
& r1(X1,sK3(X1))
& p101(sK2(X1))
& ~ p102(sK2(X1))
& ~ p2(sK2(X1))
& r1(X1,sK2(X1)) ) ) )
| ~ r1(sK0,X1) )
& ! [X0] :
( p2(X0)
| ~ r1(sK0,X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK2,sK3,sK1,sK4]),skolemize(X,sK0),skolemize(X2,sK2(X1)),skolemize(X3,sK3(X1)),skolemize(X8,sK1),skolemize(X9,sK4)],[nnf_1]) ).
fof(sk_main_neg,plain,
( p100(sK0)
& ~ p101(sK0)
& ( ~ p102(sK0)
| p101(sK0) )
& ! [VAR_0] :
( ~ p100(sK0)
| ~ p1(sK0)
| ~ p100(VAR_0)
| p1(VAR_0)
| ~ r1(sK0,VAR_0) )
& ! [VAR_0] :
( ~ p100(sK0)
| p1(sK0)
| ~ p100(VAR_0)
| ~ p1(VAR_0)
| ~ r1(sK0,VAR_0) )
& ( ~ p100(sK0)
| p101(sK0)
| p101(sK4) )
& ( ~ p100(sK0)
| p101(sK0)
| ~ p102(sK4) )
& ( ~ p100(sK0)
| p101(sK0)
| p2(sK4) )
& ( ~ p100(sK0)
| p101(sK0)
| r1(sK0,sK4) )
& ( ~ p100(sK0)
| p101(sK0)
| p101(sK1) )
& ( ~ p100(sK0)
| p101(sK0)
| ~ p102(sK1) )
& ( ~ p100(sK0)
| p101(sK0)
| ~ p2(sK1) )
& ( ~ p100(sK0)
| p101(sK0)
| r1(sK0,sK1) )
& ! [VAR_0] :
( ~ p101(VAR_0)
| p100(VAR_0)
| ~ r1(sK0,VAR_0) )
& ! [VAR_0] :
( ~ p102(VAR_0)
| p101(VAR_0)
| ~ r1(sK0,VAR_0) )
& ! [VAR_0,VAR_1] :
( ~ p100(VAR_0)
| ~ p1(VAR_0)
| ~ p100(VAR_1)
| p1(VAR_1)
| ~ r1(VAR_0,VAR_1)
| ~ r1(sK0,VAR_0) )
& ! [VAR_0,VAR_1] :
( ~ p100(VAR_0)
| p1(VAR_0)
| ~ p100(VAR_1)
| ~ p1(VAR_1)
| ~ r1(VAR_0,VAR_1)
| ~ r1(sK0,VAR_0) )
& ! [VAR_0,VAR_1] :
( ~ p101(VAR_0)
| ~ p2(VAR_0)
| ~ p101(VAR_1)
| p2(VAR_1)
| ~ r1(VAR_0,VAR_1)
| ~ r1(sK0,VAR_0) )
& ! [VAR_0,VAR_1] :
( ~ p101(VAR_0)
| p2(VAR_0)
| ~ p101(VAR_1)
| ~ p2(VAR_1)
| ~ r1(VAR_0,VAR_1)
| ~ r1(sK0,VAR_0) )
& ! [VAR_0] :
( ~ p100(VAR_0)
| p101(VAR_0)
| p101(sK3(VAR_0))
| ~ r1(sK0,VAR_0) )
& ! [VAR_0] :
( ~ p100(VAR_0)
| p101(VAR_0)
| ~ p102(sK3(VAR_0))
| ~ r1(sK0,VAR_0) )
& ! [VAR_0] :
( ~ p100(VAR_0)
| p101(VAR_0)
| p2(sK3(VAR_0))
| ~ r1(sK0,VAR_0) )
& ! [VAR_0] :
( ~ p100(VAR_0)
| p101(VAR_0)
| r1(VAR_0,sK3(VAR_0))
| ~ r1(sK0,VAR_0) )
& ! [VAR_0] :
( ~ p100(VAR_0)
| p101(VAR_0)
| p101(sK2(VAR_0))
| ~ r1(sK0,VAR_0) )
& ! [VAR_0] :
( ~ p100(VAR_0)
| p101(VAR_0)
| ~ p102(sK2(VAR_0))
| ~ r1(sK0,VAR_0) )
& ! [VAR_0] :
( ~ p100(VAR_0)
| p101(VAR_0)
| ~ p2(sK2(VAR_0))
| ~ r1(sK0,VAR_0) )
& ! [VAR_0] :
( ~ p100(VAR_0)
| p101(VAR_0)
| r1(VAR_0,sK2(VAR_0))
| ~ r1(sK0,VAR_0) )
& ! [VAR_0] :
( p2(VAR_0)
| ~ r1(sK0,VAR_0) ) ),
inference(cnf_transformation,[status(thm)],[sk_main_neg_sk]) ).
cnf(c_2,negated_conjecture,
p100(sK0),
inference(split_conjunct,[status(thm)],[sk_main_neg]) ).
cnf(c_3,negated_conjecture,
~ p101(sK0),
inference(split_conjunct,[status(thm)],[sk_main_neg]) ).
cnf(c_16,negated_conjecture,
( ~ p100(sK0)
| p101(sK0)
| ~ p2(sK1) ),
inference(split_conjunct,[status(thm)],[sk_main_neg]) ).
cnf(c_49,negated_conjecture,
( ~ p100(sK0)
| ~ p2(sK1) ),
inference(resolve,[status(thm)],[c_3,c_16]) ).
cnf(c_17,negated_conjecture,
~ p2(sK1),
inference(resolve,[status(thm)],[c_2,c_49]) ).
cnf(c_18,negated_conjecture,
( ~ p100(sK0)
| p101(sK0)
| r1(sK0,sK1) ),
inference(split_conjunct,[status(thm)],[sk_main_neg]) ).
cnf(c_50,negated_conjecture,
( ~ p100(sK0)
| r1(sK0,sK1) ),
inference(resolve,[status(thm)],[c_3,c_18]) ).
cnf(c_19,negated_conjecture,
r1(sK0,sK1),
inference(resolve,[status(thm)],[c_2,c_50]) ).
cnf(c_31,negated_conjecture,
( p2(A)
| ~ r1(sK0,A) ),
inference(split_conjunct,[status(thm)],[sk_main_neg]) ).
cnf(c_51,negated_conjecture,
p2(sK1),
inference(resolve,[status(thm)],[c_31,c_19]) ).
cnf(c_48,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_17,c_51]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL636+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
% 0.08/0.35 % Computer : n015.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Fri Sep 25 22:52:13 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.13/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.13/0.36 % Process 2481583 was started by sandbox on n015,
% 0.13/0.36 % Fri Sep 25 22:52:13 2026
% 0.13/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.13/0.36
% 0.13/0.36 % From the command line: assign(max_seconds, 300).
% 0.13/0.37
% 0.13/0.37 % SZS status Theorem for theBenchmark
% 0.13/0.37
% 0.13/0.37 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.13/0.37 % Length of proof is 9.
% 0.13/0.37 % Level of proof is 3.
% 0.13/0.37 % Maximum clause weight is 5.000.
% 0.13/0.37 % Given clauses 21.
% 0.13/0.37
% 0.13/0.37 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------