%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SYN980+1 : TPTP v9.3.1. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/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 09:43:30 AM UTC 2026
% Result : Theorem 0.16s 0.44s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 1
% Syntax : Number of formulae : 14 ( 3 unt; 0 def)
% Number of atoms : 47 ( 0 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 51 ( 18 ~; 14 |; 11 &)
% ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 2 ( 2 usr; 1 con; 0-1 aty)
% Number of variables : 30 ( 4 sgn 16 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_this,conjecture,
! [B] :
( ! [Y] :
( ( r(B)
=> r(Y) )
=> p(f(Y),Y) )
=> ? [X,Y] :
( ( q(f(B),B)
=> q(X,Y) )
& p(X,Y) ) ),
file('theBenchmark.p',prove_this) ).
fof(prove_this_neg,negated_conjecture,
~ ! [B] :
( ! [Y] :
( ( r(B)
=> r(Y) )
=> p(f(Y),Y) )
=> ? [X,Y] :
( ( q(f(B),B)
=> q(X,Y) )
& p(X,Y) ) ),
inference(assume_negation,[status(cth)],[prove_this]) ).
fof(nnf_1,plain,
? [B] :
( ! [X,Y] :
( ( ~ q(X,Y)
& q(f(B),B) )
| ~ p(X,Y) )
& ! [X0] :
( p(f(X0),X0)
| ( ~ r(X0)
& r(B) ) ) ),
inference(fof_nnf,[status(thm)],[prove_this_neg]) ).
fof(sk_prove_this_neg_sk,plain,
( ! [X,Y] :
( ( ~ q(X,Y)
& q(f(sK0),sK0) )
| ~ p(X,Y) )
& ! [X0] :
( p(f(X0),X0)
| ( ~ r(X0)
& r(sK0) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(B,sK0)],[nnf_1]) ).
fof(sk_prove_this_neg,plain,
( ! [VAR_0,VAR_1] :
( ~ q(VAR_0,VAR_1)
| ~ p(VAR_0,VAR_1) )
& ! [VAR_0,VAR_1] :
( q(f(sK0),sK0)
| ~ p(VAR_0,VAR_1) )
& ! [VAR_0] :
( p(f(VAR_0),VAR_0)
| ~ r(VAR_0) )
& ! [VAR_0] :
( p(f(VAR_0),VAR_0)
| r(sK0) ) ),
inference(cnf_transformation,[status(thm)],[sk_prove_this_neg_sk]) ).
cnf(c_2,negated_conjecture,
( p(f(A),A)
| ~ r(A) ),
inference(split_conjunct,[status(thm)],[sk_prove_this_neg]) ).
cnf(c_3,negated_conjecture,
( p(f(A),A)
| r(sK0) ),
inference(split_conjunct,[status(thm)],[sk_prove_this_neg]) ).
cnf(c_4,negated_conjecture,
( q(f(sK0),sK0)
| ~ p(A,B) ),
inference(split_conjunct,[status(thm)],[sk_prove_this_neg]) ).
cnf(c_5,negated_conjecture,
( ~ q(A,B)
| ~ p(A,B) ),
inference(split_conjunct,[status(thm)],[sk_prove_this_neg]) ).
cnf(c_6,negated_conjecture,
( ~ p(f(sK0),sK0)
| ~ p(A,B) ),
inference(resolve,[status(thm)],[c_4,c_5]) ).
cnf(c_7,negated_conjecture,
( p(f(A),A)
| p(f(sK0),sK0) ),
inference(resolve,[status(thm)],[c_2,c_3]) ).
cnf(c_8,plain,
~ p(f(sK0),sK0),
inference(factor,[status(thm)],[c_6]) ).
cnf(c_10,plain,
p(f(sK0),sK0),
inference(factor,[status(thm)],[c_7]) ).
cnf(c_9,plain,
$false,
inference(resolve,[status(thm)],[c_8,c_10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN980+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/0.42 % Computer : n015.cluster.edu
% 0.16/0.42 % Model : x86_64 x86_64
% 0.16/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.42 % Memory : 8046.5625MB
% 0.16/0.42 % OS : Linux 6.8.0-71-generic
% 0.16/0.42 % CPULimit : 300
% 0.16/0.42 % WCLimit : 300
% 0.16/0.42 % DateTime : Sat Sep 26 18:56:00 UTC 2026
% 0.16/0.42 % CPUTime :
% 0.16/0.42 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.16/0.42 % Process 529635 was started by sandbox2 on n015,
% 0.16/0.42 % Sat Sep 26 18:56:00 2026
% 0.16/0.42 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.16/0.43
% 0.16/0.43 % From the command line: assign(max_seconds, 300).
% 0.16/0.44
% 0.16/0.44 % SZS status Theorem for theBenchmark
% 0.16/0.44
% 0.16/0.44 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.16/0.44 % Length of proof is 9.
% 0.16/0.44 % Level of proof is 4.
% 0.16/0.44 % Maximum clause weight is 8.000.
% 0.16/0.44 % Given clauses 0.
% 0.16/0.44
% 0.16/0.44 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------