%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LCL682+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 : n010.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 07:59:30 AM UTC 2026
% Result : Theorem 0.13s 0.39s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 1
% Syntax : Number of formulae : 12 ( 5 unt; 0 def)
% Number of atoms : 118 ( 0 equ)
% Maximal formula atoms : 24 ( 9 avg)
% Number of connectives : 185 ( 79 ~; 61 |; 45 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 7 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 8 ( 7 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 9 con; 0-0 aty)
% Number of variables : 58 ( 0 sgn 44 !; 11 ?)
% Comments :
%------------------------------------------------------------------------------
fof(main,conjecture,
~ ? [X] :
~ ( ! [Y] :
( ! [X] :
( p11(X)
| ~ r1(Y,X) )
| ~ r1(X,Y) )
| ! [Y] :
( ! [X] :
( p12(X)
| ~ r1(Y,X) )
| ~ r1(X,Y) )
| ! [Y] :
( ! [X] :
( p13(X)
| ~ r1(Y,X) )
| ~ r1(X,Y) )
| ! [Y] :
( ! [X] :
( p15(X)
| ~ r1(Y,X) )
| ~ r1(X,Y) )
| ~ ! [Y] :
( ~ ( ~ ! [X] :
( p12(X)
| ~ r1(Y,X) )
| ~ ! [X] :
( p14(X)
| ~ r1(Y,X) )
| ~ ! [X] :
( p12(X)
| ~ r1(Y,X) )
| ~ ! [X] :
( p16(X)
| ~ r1(Y,X) ) )
| ~ r1(X,Y) ) ),
file('theBenchmark.p',main) ).
fof(main_neg,negated_conjecture,
~ ~ ? [X] :
~ ( ! [Y] :
( ! [X] :
( p11(X)
| ~ r1(Y,X) )
| ~ r1(X,Y) )
| ! [Y] :
( ! [X] :
( p12(X)
| ~ r1(Y,X) )
| ~ r1(X,Y) )
| ! [Y] :
( ! [X] :
( p13(X)
| ~ r1(Y,X) )
| ~ r1(X,Y) )
| ! [Y] :
( ! [X] :
( p15(X)
| ~ r1(Y,X) )
| ~ r1(X,Y) )
| ~ ! [Y] :
( ~ ( ~ ! [X] :
( p12(X)
| ~ r1(Y,X) )
| ~ ! [X] :
( p14(X)
| ~ r1(Y,X) )
| ~ ! [X] :
( p12(X)
| ~ r1(Y,X) )
| ~ ! [X] :
( p16(X)
| ~ r1(Y,X) ) )
| ~ r1(X,Y) ) ),
inference(assume_negation,[status(cth)],[main]) ).
fof(nnf_3,plain,
? [X] :
( ? [Y] :
( ? [X11] :
( ~ p11(X11)
& r1(Y,X11) )
& r1(X,Y) )
& ? [X9] :
( ? [X10] :
( ~ p12(X10)
& r1(X9,X10) )
& r1(X,X9) )
& ? [X7] :
( ? [X8] :
( ~ p13(X8)
& r1(X7,X8) )
& r1(X,X7) )
& ? [X5] :
( ? [X6] :
( ~ p15(X6)
& r1(X5,X6) )
& r1(X,X5) )
& ! [X0] :
( ( ! [X4] :
( p12(X4)
| ~ r1(X0,X4) )
& ! [X3] :
( p14(X3)
| ~ r1(X0,X3) )
& ! [X2] :
( p12(X2)
| ~ r1(X0,X2) )
& ! [X1] :
( p16(X1)
| ~ r1(X0,X1) ) )
| ~ r1(X,X0) ) ),
inference(fof_nnf,[status(thm)],[main_neg]) ).
fof(sk_main_neg_sk,plain,
( ~ p11(sK8)
& r1(sK7,sK8)
& r1(sK0,sK7)
& ~ p12(sK1)
& r1(sK2,sK1)
& r1(sK0,sK2)
& ~ p13(sK6)
& r1(sK5,sK6)
& r1(sK0,sK5)
& ~ p15(sK4)
& r1(sK3,sK4)
& r1(sK0,sK3)
& ! [X0] :
( ( ! [X4] :
( p12(X4)
| ~ r1(X0,X4) )
& ! [X3] :
( p14(X3)
| ~ r1(X0,X3) )
& ! [X2] :
( p12(X2)
| ~ r1(X0,X2) )
& ! [X1] :
( p16(X1)
| ~ r1(X0,X1) ) )
| ~ r1(sK0,X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK3,sK4,sK5,sK6,sK2,sK1,sK7,sK8]),skolemize(X,sK0),skolemize(X5,sK3),skolemize(X6,sK4),skolemize(X7,sK5),skolemize(X8,sK6),skolemize(X9,sK2),skolemize(X10,sK1),skolemize(Y,sK7),skolemize(X11,sK8)],[nnf_3]) ).
fof(sk_main_neg,plain,
( ~ p11(sK8)
& r1(sK7,sK8)
& r1(sK0,sK7)
& ~ p12(sK1)
& r1(sK2,sK1)
& r1(sK0,sK2)
& ~ p13(sK6)
& r1(sK5,sK6)
& r1(sK0,sK5)
& ~ p15(sK4)
& r1(sK3,sK4)
& r1(sK0,sK3)
& ! [VAR_0,VAR_1] :
( p12(VAR_1)
| ~ r1(VAR_0,VAR_1)
| ~ r1(sK0,VAR_0) )
& ! [VAR_0,VAR_1] :
( p14(VAR_1)
| ~ r1(VAR_0,VAR_1)
| ~ r1(sK0,VAR_0) )
& ! [VAR_0,VAR_1] :
( p12(VAR_1)
| ~ r1(VAR_0,VAR_1)
| ~ r1(sK0,VAR_0) )
& ! [VAR_0,VAR_1] :
( p16(VAR_1)
| ~ r1(VAR_0,VAR_1)
| ~ r1(sK0,VAR_0) ) ),
inference(cnf_transformation,[status(thm)],[sk_main_neg_sk]) ).
cnf(c_4,negated_conjecture,
( p12(B)
| ~ r1(A,B)
| ~ r1(sK0,A) ),
inference(split_conjunct,[status(thm)],[sk_main_neg]) ).
cnf(c_5,negated_conjecture,
~ p12(sK1),
inference(split_conjunct,[status(thm)],[sk_main_neg]) ).
cnf(c_7,negated_conjecture,
( ~ r1(A,sK1)
| ~ r1(sK0,A) ),
inference(resolve,[status(thm)],[c_4,c_5]) ).
cnf(c_14,negated_conjecture,
r1(sK0,sK2),
inference(split_conjunct,[status(thm)],[sk_main_neg]) ).
cnf(c_15,negated_conjecture,
r1(sK2,sK1),
inference(split_conjunct,[status(thm)],[sk_main_neg]) ).
cnf(c_25,negated_conjecture,
~ r1(sK2,sK1),
inference(resolve,[status(thm)],[c_14,c_7]) ).
cnf(c_24,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_15,c_25]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL682+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
% 0.09/0.37 % Computer : n010.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 23:19:29 UTC 2026
% 0.13/0.37 % CPUTime :
% 0.13/0.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.13/0.38 % Process 1917682 was started by sandbox2 on n010,
% 0.13/0.38 % Fri Sep 25 23:19:29 2026
% 0.13/0.38 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.13/0.38
% 0.13/0.38 % From the command line: assign(max_seconds, 300).
% 0.13/0.39
% 0.13/0.39 % SZS status Theorem for theBenchmark
% 0.13/0.39
% 0.13/0.39 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.13/0.39 % Length of proof is 7.
% 0.13/0.39 % Level of proof is 3.
% 0.13/0.39 % Maximum clause weight is 6.000.
% 0.13/0.39 % Given clauses 8.
% 0.13/0.39
% 0.13/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------