%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SYN066+1 : TPTP v9.3.1. Bugfixed v3.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n008.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 09:36:56 AM UTC 2026
% Result : Theorem 0.09s 5.60s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 4
% Syntax : Number of formulae : 20 ( 8 unt; 0 def)
% Number of atoms : 41 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 34 ( 13 ~; 11 |; 6 &)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 1 con; 0-2 aty)
% Number of variables : 48 ( 9 sgn 17 !; 13 ?)
% Comments :
%------------------------------------------------------------------------------
fof(pel37_1,axiom,
! [Z] :
? [W] :
! [X] :
? [Y] :
( ( big_p(Y,W)
=> ? [U] : big_q(U,W) )
& big_p(Y,Z)
& ( big_p(X,Z)
=> big_p(Y,W) ) ),
file('theBenchmark.p',pel37_1) ).
fof(pel37_2,axiom,
! [X,Z] :
( ~ big_p(X,Z)
=> ? [Y] : big_q(Y,Z) ),
file('theBenchmark.p',pel37_2) ).
fof(pel37_3,axiom,
( ? [X,Y] : big_q(X,Y)
=> ! [Z] : big_r(Z,Z) ),
file('theBenchmark.p',pel37_3) ).
fof(pel37,conjecture,
! [X] :
? [Y] : big_r(X,Y),
file('theBenchmark.p',pel37) ).
fof(pel37_neg,negated_conjecture,
~ ! [X] :
? [Y] : big_r(X,Y),
inference(assume_negation,[status(cth)],[pel37]) ).
cnf(c_5,plain,
( big_r(C,C)
| ~ big_q(A,B) ),
inference(clausify,[status(thm)],[pel37_3]) ).
fof(nnf_2,plain,
! [X,Z] :
( ? [Y] : big_q(Y,Z)
| big_p(X,Z) ),
inference(fof_nnf,[status(thm)],[pel37_2]) ).
fof(sk_pel37_2,plain,
! [X,Z] :
( big_q(sK0(X,Z),Z)
| big_p(X,Z) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(Y,sK0(X,Z))],[nnf_2]) ).
cnf(c_6,plain,
( big_q(sK0(A,B),B)
| big_p(A,B) ),
inference(split_conjunct,[status(thm)],[sk_pel37_2]) ).
fof(nnf_1,plain,
! [Z] :
? [W] :
! [X] :
? [Y] :
( ( ? [U] : big_q(U,W)
| ~ big_p(Y,W) )
& big_p(Y,Z)
& ( big_p(Y,W)
| ~ big_p(X,Z) ) ),
inference(fof_nnf,[status(thm)],[pel37_1]) ).
fof(sk_pel37_1,plain,
! [Z,X] :
( ( big_q(sK3(Z,X),sK2(Z))
| ~ big_p(sK1(Z,X),sK2(Z)) )
& big_p(sK1(Z,X),Z)
& ( big_p(sK1(Z,X),sK2(Z))
| ~ big_p(X,Z) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2,sK3]),skolemize(W,sK2(Z)),skolemize(Y,sK1(Z,X)),skolemize(U,sK3(Z,X))],[nnf_1]) ).
cnf(c_7,plain,
( big_q(sK3(A,B),sK2(A))
| ~ big_p(sK1(A,B),sK2(A)) ),
inference(split_conjunct,[status(thm)],[sk_pel37_1]) ).
fof(nnf_4,plain,
? [X] :
! [Y] : ~ big_r(X,Y),
inference(fof_nnf,[status(thm)],[pel37_neg]) ).
fof(sk_pel37_neg,plain,
! [Y] : ~ big_r(sK4,Y),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(X,sK4)],[nnf_4]) ).
cnf(c_8,negated_conjecture,
~ big_r(sK4,A),
inference(split_conjunct,[status(thm)],[sk_pel37_neg]) ).
cnf(c_9,plain,
( big_p(B,C)
| big_r(A,A) ),
inference(resolve,[status(thm)],[c_5,c_6]) ).
cnf(c_10,plain,
( ~ big_p(sK1(B,C),sK2(B))
| big_r(A,A) ),
inference(resolve,[status(thm)],[c_5,c_7]) ).
cnf(c_11,negated_conjecture,
~ big_p(sK1(A,B),sK2(A)),
inference(resolve,[status(thm)],[c_8,c_10]) ).
cnf(c_12,negated_conjecture,
big_p(A,B),
inference(resolve,[status(thm)],[c_8,c_9]) ).
cnf(c_13,plain,
$false,
inference(resolve,[status(thm)],[c_12,c_11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN066+1 : TPTP v9.3.1. Bugfixed v3.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/5.57 % Computer : n008.cluster.edu
% 0.09/5.57 % Model : x86_64 x86_64
% 0.09/5.57 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.57 % Memory : 8046.5625MB
% 0.09/5.57 % OS : Linux 6.8.0-71-generic
% 0.09/5.58 % CPULimit : 300
% 0.09/5.58 % WCLimit : 300
% 0.09/5.58 % DateTime : Sat Sep 26 17:09:31 UTC 2026
% 0.09/5.58 % CPUTime :
% 0.09/5.58 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/5.58 % Process 4119107 was started by sandbox2 on n008,
% 0.09/5.58 % Sat Sep 26 17:09:31 2026
% 0.09/5.58 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.09/5.58
% 0.09/5.58 % From the command line: assign(max_seconds, 300).
% 0.09/5.60
% 0.09/5.60 % SZS status Theorem for theBenchmark
% 0.09/5.60
% 0.09/5.60 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.09/5.60 % Length of proof is 13.
% 0.09/5.60 % Level of proof is 4.
% 0.09/5.60 % Maximum clause weight is 6.000.
% 0.09/5.60 % Given clauses 0.
% 0.09/5.60
% 0.09/5.60 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------