%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWW302+1 : TPTP v9.3.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n026.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 09:14:04 AM UTC 2026
% Result : Theorem 0.13s 0.43s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 2
% Syntax : Number of formulae : 12 ( 4 unt; 0 def)
% Number of atoms : 28 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 26 ( 10 ~; 5 |; 4 &)
% ( 0 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 19 ( 0 sgn 12 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(conj_0,axiom,
! [B_Z,B_s] :
( v_Q_H(B_Z,B_s)
=> v_Q(B_Z,B_s) ),
file('theBenchmark.p',conj_0) ).
fof(conj_1,conjecture,
! [B_Z,B_s] :
( v_P(B_Z,B_s)
=> ! [B_s_H] :
( ! [B_Z_H] :
( v_P(B_Z_H,B_s)
=> v_Q_H(B_Z_H,B_s_H) )
=> v_Q(B_Z,B_s_H) ) ),
file('theBenchmark.p',conj_1) ).
fof(conj_1_neg,negated_conjecture,
~ ! [B_Z,B_s] :
( v_P(B_Z,B_s)
=> ! [B_s_H] :
( ! [B_Z_H] :
( v_P(B_Z_H,B_s)
=> v_Q_H(B_Z_H,B_s_H) )
=> v_Q(B_Z,B_s_H) ) ),
inference(assume_negation,[status(cth)],[conj_1]) ).
fof(nnf_2,plain,
? [B_Z,B_s] :
( ? [B_s_H] :
( ~ v_Q(B_Z,B_s_H)
& ! [B_Z_H] :
( v_Q_H(B_Z_H,B_s_H)
| ~ v_P(B_Z_H,B_s) ) )
& v_P(B_Z,B_s) ),
inference(fof_nnf,[status(thm)],[conj_1_neg]) ).
fof(sk_conj_1_neg,plain,
( ~ v_Q(sK2,sK1)
& ! [B_Z_H] :
( v_Q_H(B_Z_H,sK1)
| ~ v_P(B_Z_H,sK0) )
& v_P(sK2,sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK0,sK1]),skolemize(B_Z,sK2),skolemize(B_s,sK0),skolemize(B_s_H,sK1)],[nnf_2]) ).
cnf(c_3,negated_conjecture,
( v_Q_H(A,sK1)
| ~ v_P(A,sK0) ),
inference(split_conjunct,[status(thm)],[sk_conj_1_neg]) ).
cnf(c_4,plain,
( v_Q(A,B)
| ~ v_Q_H(A,B) ),
inference(clausify,[status(thm)],[conj_0]) ).
cnf(c_5,negated_conjecture,
~ v_Q(sK2,sK1),
inference(split_conjunct,[status(thm)],[sk_conj_1_neg]) ).
cnf(c_6,negated_conjecture,
( v_Q(A,sK1)
| ~ v_P(A,sK0) ),
inference(resolve,[status(thm)],[c_3,c_4]) ).
cnf(c_7,negated_conjecture,
v_P(sK2,sK0),
inference(split_conjunct,[status(thm)],[sk_conj_1_neg]) ).
cnf(c_8,negated_conjecture,
~ v_P(sK2,sK0),
inference(resolve,[status(thm)],[c_5,c_6]) ).
cnf(c_9,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_7,c_8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWW302+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n026.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sat Sep 26 15:39:40 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.36 % Process 1381552 was started by sandbox on n026,
% 0.09/0.36 % Sat Sep 26 15:39:40 2026
% 0.09/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.13/0.43
% 0.13/0.43 % SInE (scan): 1 to sos (tol 1.5x), 0 to usable (tol 2.0x), 5240 zapped, of 5241 axioms (depth 3).
% 0.13/0.43
% 0.13/0.43 % From the command line: assign(max_seconds, 300).
% 0.13/0.43
% 0.13/0.43 % SZS status Theorem for theBenchmark
% 0.13/0.43
% 0.13/0.43 % Proof 1 at 0.01 (+ 0.01) seconds.
% 0.13/0.43 % Length of proof is 9.
% 0.13/0.43 % Level of proof is 4.
% 0.13/0.43 % Maximum clause weight is 0.000.
% 0.13/0.43 % Given clauses 0.
% 0.13/0.43
% 0.13/0.43 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------