%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SYN979+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 : n002.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 0.17s 0.42s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 1
% Syntax : Number of formulae : 9 ( 4 unt; 0 def)
% Number of atoms : 54 ( 0 equ)
% Maximal formula atoms : 12 ( 6 avg)
% Number of connectives : 57 ( 12 ~; 7 |; 30 &)
% ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 7 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 2 ( 2 usr; 2 con; 0-0 aty)
% Number of variables : 16 ( 2 sgn 8 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_this,conjecture,
! [A,B] :
? [X,Y] :
( ( s(A)
& ( s(A)
=> p(X,Y) )
& r(B)
& r(A)
& ( r(Y)
=> p(B,Y) )
& q(B)
& q(A)
& ( q(X)
=> p(X,A) ) )
=> p(A,B) ),
file('theBenchmark.p',prove_this) ).
fof(prove_this_neg,negated_conjecture,
~ ! [A,B] :
? [X,Y] :
( ( s(A)
& ( s(A)
=> p(X,Y) )
& r(B)
& r(A)
& ( r(Y)
=> p(B,Y) )
& q(B)
& q(A)
& ( q(X)
=> p(X,A) ) )
=> p(A,B) ),
inference(assume_negation,[status(cth)],[prove_this]) ).
fof(nnf_1,plain,
? [A,B] :
! [X,Y] :
( ~ p(A,B)
& s(A)
& ( p(X,Y)
| ~ s(A) )
& r(B)
& r(A)
& ( p(B,Y)
| ~ r(Y) )
& q(B)
& q(A)
& ( p(X,A)
| ~ q(X) ) ),
inference(fof_nnf,[status(thm)],[prove_this_neg]) ).
fof(sk_prove_this_neg,plain,
! [X,Y] :
( ~ p(sK0,sK1)
& s(sK0)
& ( p(X,Y)
| ~ s(sK0) )
& r(sK1)
& r(sK0)
& ( p(sK1,Y)
| ~ r(Y) )
& q(sK1)
& q(sK0)
& ( p(X,sK0)
| ~ q(X) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(A,sK0),skolemize(B,sK1)],[nnf_1]) ).
cnf(c_5,negated_conjecture,
~ p(sK0,sK1),
inference(split_conjunct,[status(thm)],[sk_prove_this_neg]) ).
cnf(c_8,negated_conjecture,
( p(A,B)
| ~ s(sK0) ),
inference(split_conjunct,[status(thm)],[sk_prove_this_neg]) ).
cnf(c_10,negated_conjecture,
~ s(sK0),
inference(resolve,[status(thm)],[c_8,c_5]) ).
cnf(c_11,negated_conjecture,
s(sK0),
inference(split_conjunct,[status(thm)],[sk_prove_this_neg]) ).
cnf(c_12,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_10,c_11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SYN979+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.05 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/0.40 % Computer : n002.cluster.edu
% 0.16/0.40 % Model : x86_64 x86_64
% 0.16/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.40 % Memory : 8046.5625MB
% 0.16/0.40 % OS : Linux 6.8.0-71-generic
% 0.16/0.40 % CPULimit : 300
% 0.16/0.40 % WCLimit : 300
% 0.17/0.40 % DateTime : Sat Sep 26 18:55:21 UTC 2026
% 0.17/0.41 % CPUTime :
% 0.17/0.41 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.17/0.41 % Process 2440224 was started by sandbox2 on n002,
% 0.17/0.41 % Sat Sep 26 18:55:21 2026
% 0.17/0.41 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.17/0.41
% 0.17/0.41 % From the command line: assign(max_seconds, 300).
% 0.17/0.42
% 0.17/0.42 % SZS status Theorem for theBenchmark
% 0.17/0.42
% 0.17/0.42 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.17/0.42 % Length of proof is 6.
% 0.17/0.42 % Level of proof is 3.
% 0.17/0.42 % Maximum clause weight is 0.000.
% 0.17/0.42 % Given clauses 0.
% 0.17/0.42
% 0.17/0.42 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------