%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SYN944+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 : 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 09:43:25 AM UTC 2026
% Result : Theorem 0.15s 0.43s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 1
% Syntax : Number of formulae : 13 ( 6 unt; 0 def)
% Number of atoms : 48 ( 0 equ)
% Maximal formula atoms : 9 ( 3 avg)
% Number of connectives : 49 ( 14 ~; 9 |; 20 &)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 35 ( 2 sgn 22 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_this,conjecture,
! [A,B,C] :
( ( ! [X,Y] :
( r(X,Y)
=> q(X,Y) )
& ! [X] :
( s(X)
=> p(X) )
& r(B,C)
& s(B)
& s(A) )
=> ? [X,Y] :
( q(X,Y)
& p(X) ) ),
file('theBenchmark.p',prove_this) ).
fof(prove_this_neg,negated_conjecture,
~ ! [A,B,C] :
( ( ! [X,Y] :
( r(X,Y)
=> q(X,Y) )
& ! [X] :
( s(X)
=> p(X) )
& r(B,C)
& s(B)
& s(A) )
=> ? [X,Y] :
( q(X,Y)
& p(X) ) ),
inference(assume_negation,[status(cth)],[prove_this]) ).
fof(nnf_1,plain,
? [A,B,C] :
( ! [X,Y] :
( ~ q(X,Y)
| ~ p(X) )
& ! [X1,X2] :
( q(X1,X2)
| ~ r(X1,X2) )
& ! [X0] :
( p(X0)
| ~ s(X0) )
& r(B,C)
& s(B)
& s(A) ),
inference(fof_nnf,[status(thm)],[prove_this_neg]) ).
fof(sk_prove_this_neg,plain,
( ! [X,Y] :
( ~ q(X,Y)
| ~ p(X) )
& ! [X1,X2] :
( q(X1,X2)
| ~ r(X1,X2) )
& ! [X0] :
( p(X0)
| ~ s(X0) )
& r(sK0,sK1)
& s(sK0)
& s(sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK0,sK1]),skolemize(A,sK2),skolemize(B,sK0),skolemize(C,sK1)],[nnf_1]) ).
cnf(c_2,negated_conjecture,
( p(A)
| ~ s(A) ),
inference(split_conjunct,[status(thm)],[sk_prove_this_neg]) ).
cnf(c_3,negated_conjecture,
s(sK0),
inference(split_conjunct,[status(thm)],[sk_prove_this_neg]) ).
cnf(c_5,negated_conjecture,
r(sK0,sK1),
inference(split_conjunct,[status(thm)],[sk_prove_this_neg]) ).
cnf(c_6,negated_conjecture,
( q(A,B)
| ~ r(A,B) ),
inference(split_conjunct,[status(thm)],[sk_prove_this_neg]) ).
cnf(c_7,negated_conjecture,
p(sK0),
inference(resolve,[status(thm)],[c_2,c_3]) ).
cnf(c_8,negated_conjecture,
( ~ q(A,B)
| ~ p(A) ),
inference(split_conjunct,[status(thm)],[sk_prove_this_neg]) ).
cnf(c_10,negated_conjecture,
q(sK0,sK1),
inference(resolve,[status(thm)],[c_5,c_6]) ).
cnf(c_11,negated_conjecture,
~ q(sK0,A),
inference(resolve,[status(thm)],[c_7,c_8]) ).
cnf(c_13,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_10,c_11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN944+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.05 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.15/0.41 % Computer : n008.cluster.edu
% 0.15/0.41 % Model : x86_64 x86_64
% 0.15/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.41 % Memory : 8046.5625MB
% 0.15/0.41 % OS : Linux 6.8.0-71-generic
% 0.15/0.41 % CPULimit : 300
% 0.15/0.41 % WCLimit : 300
% 0.15/0.41 % DateTime : Sat Sep 26 18:51:54 UTC 2026
% 0.15/0.41 % CPUTime :
% 0.15/0.42 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.15/0.42 % Process 134477 was started by sandbox2 on n008,
% 0.15/0.42 % Sat Sep 26 18:51:54 2026
% 0.15/0.42 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.15/0.42
% 0.15/0.42 % From the command line: assign(max_seconds, 300).
% 0.15/0.43
% 0.15/0.43 % SZS status Theorem for theBenchmark
% 0.15/0.43
% 0.15/0.43 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.15/0.43 % Length of proof is 10.
% 0.15/0.43 % Level of proof is 4.
% 0.15/0.43 % Maximum clause weight is 0.000.
% 0.15/0.43 % Given clauses 0.
% 0.15/0.43
% 0.15/0.43 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------