%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SYN941+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 : n006.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 09:43:25 AM UTC 2026
% Result : Theorem 0.14s 5.43s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 1
% Syntax : Number of formulae : 16 ( 5 unt; 0 def)
% Number of atoms : 59 ( 0 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 73 ( 30 ~; 22 |; 15 &)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-1 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-1 aty)
% Number of variables : 27 ( 6 sgn 13 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_this,conjecture,
! [B,C] :
( q(f(B))
=> ? [X,Y] :
( q(X)
& ( p(f(Y))
=> ( ( r(Y)
=> ( r(C)
& r(B) ) )
& p(X) ) ) ) ),
file('theBenchmark.p',prove_this) ).
fof(prove_this_neg,negated_conjecture,
~ ! [B,C] :
( q(f(B))
=> ? [X,Y] :
( q(X)
& ( p(f(Y))
=> ( ( r(Y)
=> ( r(C)
& r(B) ) )
& p(X) ) ) ) ),
inference(assume_negation,[status(cth)],[prove_this]) ).
fof(nnf_1,plain,
? [B,C] :
( ! [X,Y] :
( ~ q(X)
| ( ( ( ( ~ r(C)
| ~ r(B) )
& r(Y) )
| ~ p(X) )
& p(f(Y)) ) )
& q(f(B)) ),
inference(fof_nnf,[status(thm)],[prove_this_neg]) ).
fof(sk_prove_this_neg_sk,plain,
( ! [X,Y] :
( ~ q(X)
| ( ( ( ( ~ r(sK1)
| ~ r(sK0) )
& r(Y) )
| ~ p(X) )
& p(f(Y)) ) )
& q(f(sK0)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(B,sK0),skolemize(C,sK1)],[nnf_1]) ).
fof(sk_prove_this_neg,plain,
( ! [VAR_0] :
( ~ q(VAR_0)
| ~ r(sK1)
| ~ r(sK0)
| ~ p(VAR_0) )
& ! [VAR_0,VAR_1] :
( ~ q(VAR_0)
| r(VAR_1)
| ~ p(VAR_0) )
& ! [VAR_0,VAR_1] :
( ~ q(VAR_1)
| p(f(VAR_0)) )
& q(f(sK0)) ),
inference(cnf_transformation,[status(thm)],[sk_prove_this_neg_sk]) ).
cnf(c_2,negated_conjecture,
( ~ q(B)
| p(f(A)) ),
inference(split_conjunct,[status(thm)],[sk_prove_this_neg]) ).
cnf(c_3,negated_conjecture,
q(f(sK0)),
inference(split_conjunct,[status(thm)],[sk_prove_this_neg]) ).
cnf(c_4,negated_conjecture,
( ~ q(A)
| r(B)
| ~ p(A) ),
inference(split_conjunct,[status(thm)],[sk_prove_this_neg]) ).
cnf(c_5,negated_conjecture,
( ~ q(A)
| ~ r(sK1)
| ~ r(sK0)
| ~ p(A) ),
inference(split_conjunct,[status(thm)],[sk_prove_this_neg]) ).
cnf(c_6,negated_conjecture,
p(f(A)),
inference(resolve,[status(thm)],[c_2,c_3]) ).
cnf(c_7,negated_conjecture,
( r(A)
| ~ p(f(sK0)) ),
inference(resolve,[status(thm)],[c_4,c_3]) ).
cnf(c_8,negated_conjecture,
( ~ r(sK1)
| ~ r(sK0)
| ~ p(f(sK0)) ),
inference(resolve,[status(thm)],[c_5,c_3]) ).
cnf(c_9,negated_conjecture,
( ~ r(sK1)
| ~ r(sK0) ),
inference(resolve,[status(thm)],[c_6,c_8]) ).
cnf(c_10,negated_conjecture,
r(A),
inference(resolve,[status(thm)],[c_6,c_7]) ).
cnf(c_12,negated_conjecture,
~ r(sK1),
inference(resolve,[status(thm)],[c_10,c_9]) ).
cnf(c_11,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_10,c_12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SYN941+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.14/5.41 % Computer : n006.cluster.edu
% 0.14/5.41 % Model : x86_64 x86_64
% 0.14/5.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/5.41 % Memory : 8046.5625MB
% 0.14/5.41 % OS : Linux 6.8.0-71-generic
% 0.14/5.41 % CPULimit : 300
% 0.14/5.41 % WCLimit : 300
% 0.14/5.41 % DateTime : Sat Sep 26 18:50:46 UTC 2026
% 0.14/5.41 % CPUTime :
% 0.14/5.41 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.14/5.41 % Process 1894247 was started by sandbox2 on n006,
% 0.14/5.41 % Sat Sep 26 18:50:46 2026
% 0.14/5.41 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.14/5.42
% 0.14/5.42 % From the command line: assign(max_seconds, 300).
% 0.14/5.43
% 0.14/5.43 % SZS status Theorem for theBenchmark
% 0.14/5.43
% 0.14/5.43 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.14/5.43 % Length of proof is 11.
% 0.14/5.43 % Level of proof is 4.
% 0.14/5.43 % Maximum clause weight is 4.000.
% 0.14/5.43 % Given clauses 0.
% 0.14/5.43
% 0.14/5.43 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------