%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWW345+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 : n007.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 09:14:07 AM UTC 2026
% Result : Theorem 4.50s 1.19s
% Output : CNFRefutation 4.50s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 6
% Syntax : Number of formulae : 18 ( 12 unt; 0 def)
% Number of atoms : 28 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 18 ( 8 ~; 6 |; 0 &)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-4 aty)
% Number of functors : 7 ( 7 usr; 7 con; 0-0 aty)
% Number of variables : 14 ( 0 sgn 6 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(conj_1,axiom,
! [B_Z,B_s] :
( v_P(B_Z,B_s)
=> ! [B_s_H] :
( c_Natural_Oevaln(v_c,B_s,v_n,B_s_H)
=> v_Q(B_Z,B_s_H) ) ),
file('theBenchmark.p',conj_1) ).
fof(conj_2,axiom,
! [B_Z,B_s] :
( v_Q(B_Z,B_s)
=> ! [B_s_H] :
( c_Natural_Oevaln(v_d,B_s,v_n,B_s_H)
=> v_R(B_Z,B_s_H) ) ),
file('theBenchmark.p',conj_2) ).
fof(conj_6,conjecture,
v_R(v_Z,v_s_H),
file('theBenchmark.p',conj_6) ).
fof(conj_6_neg,negated_conjecture,
~ v_R(v_Z,v_s_H),
inference(assume_negation,[status(cth)],[conj_6]) ).
cnf(c_3547,plain,
( v_Q(A,C)
| ~ c_Natural_Oevaln(v_c,B,v_n,C)
| ~ v_P(A,B) ),
inference(clausify,[status(thm)],[conj_1]) ).
cnf(c_3548,plain,
( v_R(A,C)
| ~ c_Natural_Oevaln(v_d,B,v_n,C)
| ~ v_Q(A,B) ),
inference(clausify,[status(thm)],[conj_2]) ).
fof(conj_3,axiom,
v_P(v_Z,v_s),
file('theBenchmark.p',conj_3) ).
cnf(c_3549,plain,
v_P(v_Z,v_s),
inference(clausify,[status(thm)],[conj_3]) ).
fof(conj_4,axiom,
c_Natural_Oevaln(v_c,v_s,v_n,v_s1),
file('theBenchmark.p',conj_4) ).
cnf(c_3550,plain,
c_Natural_Oevaln(v_c,v_s,v_n,v_s1),
inference(clausify,[status(thm)],[conj_4]) ).
fof(conj_5,axiom,
c_Natural_Oevaln(v_d,v_s1,v_n,v_s_H),
file('theBenchmark.p',conj_5) ).
cnf(c_3551,plain,
c_Natural_Oevaln(v_d,v_s1,v_n,v_s_H),
inference(clausify,[status(thm)],[conj_5]) ).
cnf(c_3552,negated_conjecture,
~ v_R(v_Z,v_s_H),
inference(clausify,[status(thm)],[conj_6_neg]) ).
cnf(c_3733,plain,
( v_Q(A,v_s1)
| ~ v_P(A,v_s) ),
inference(resolve,[status(thm)],[c_3547,c_3550]) ).
cnf(c_3817,plain,
v_Q(v_Z,v_s1),
inference(resolve,[status(thm)],[c_3733,c_3549]) ).
cnf(c_3824,plain,
( v_R(A,v_s_H)
| ~ v_Q(A,v_s1) ),
inference(resolve,[status(thm)],[c_3548,c_3551]) ).
cnf(c_3831,plain,
v_R(v_Z,v_s_H),
inference(resolve,[status(thm)],[c_3824,c_3817]) ).
cnf(c_3830,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_3552,c_3831]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWW345+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.40 % Computer : n007.cluster.edu
% 0.11/0.40 % Model : x86_64 x86_64
% 0.11/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.40 % Memory : 8046.5625MB
% 0.11/0.40 % OS : Linux 6.8.0-71-generic
% 0.11/0.40 % CPULimit : 300
% 0.11/0.40 % WCLimit : 300
% 0.11/0.40 % DateTime : Sat Sep 26 15:40:24 UTC 2026
% 0.11/0.40 % CPUTime :
% 0.11/0.40 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/0.40 % Process 4091275 was started by sandbox on n007,
% 0.11/0.40 % Sat Sep 26 15:40:24 2026
% 0.11/0.40 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 4.50/1.19
% 4.50/1.19 % SInE (scan): 1056 to sos (tol 1.5x), 317 to usable (tol 2.0x), 3837 zapped, of 5210 axioms (depth 3).
% 4.50/1.19
% 4.50/1.19 % From the command line: assign(max_seconds, 300).
% 4.50/1.19
% 4.50/1.19 % SZS status Theorem for theBenchmark
% 4.50/1.19
% 4.50/1.19 % Proof 1 at 0.41 (+ 0.13) seconds.
% 4.50/1.19 % Length of proof is 13.
% 4.50/1.19 % Level of proof is 4.
% 4.50/1.19 % Maximum clause weight is 16.000.
% 4.50/1.19 % Given clauses 24.
% 4.50/1.19
% 4.50/1.19 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------