%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWW342+1 : TPTP v9.3.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/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 09:14:07 AM UTC 2026
% Result : Theorem 2.82s 1.00s
% Output : CNFRefutation 2.82s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 2
% Syntax : Number of formulae : 12 ( 6 unt; 0 def)
% Number of atoms : 22 ( 3 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 16 ( 6 ~; 1 |; 4 &)
% ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-4 aty)
% Number of functors : 5 ( 5 usr; 5 con; 0-0 aty)
% Number of variables : 15 ( 1 sgn 9 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(fact_evaln__elim__cases_I1_J,axiom,
! [V_t,V_n,V_s] :
( c_Natural_Oevaln(c_Com_Ocom_OSKIP,V_s,V_n,V_t)
=> V_t = V_s ),
file('theBenchmark.p',fact_evaln__elim__cases_I1_J) ).
fof(conj_1,conjecture,
! [B_Z,B_s] :
( v_P(B_Z,B_s)
=> ! [B_s_H] :
( c_Natural_Oevaln(c_Com_Ocom_OSKIP,B_s,v_n,B_s_H)
=> v_P(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] :
( c_Natural_Oevaln(c_Com_Ocom_OSKIP,B_s,v_n,B_s_H)
=> v_P(B_Z,B_s_H) ) ),
inference(assume_negation,[status(cth)],[conj_1]) ).
cnf(c_3098,plain,
( C = A
| ~ c_Natural_Oevaln(c_Com_Ocom_OSKIP,A,B,C) ),
inference(clausify,[status(thm)],[fact_evaln__elim__cases_I1_J]) ).
fof(nnf_1345,plain,
? [B_Z,B_s] :
( ? [B_s_H] :
( ~ v_P(B_Z,B_s_H)
& c_Natural_Oevaln(c_Com_Ocom_OSKIP,B_s,v_n,B_s_H) )
& v_P(B_Z,B_s) ),
inference(fof_nnf,[status(thm)],[conj_1_neg]) ).
fof(sk_conj_1_neg,plain,
( ~ v_P(sK0,sK2)
& c_Natural_Oevaln(c_Com_Ocom_OSKIP,sK1,v_n,sK2)
& v_P(sK0,sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(B_Z,sK0),skolemize(B_s,sK1),skolemize(B_s_H,sK2)],[nnf_1345]) ).
cnf(c_3657,negated_conjecture,
v_P(sK0,sK1),
inference(split_conjunct,[status(thm)],[sk_conj_1_neg]) ).
cnf(c_3658,negated_conjecture,
c_Natural_Oevaln(c_Com_Ocom_OSKIP,sK1,v_n,sK2),
inference(split_conjunct,[status(thm)],[sk_conj_1_neg]) ).
cnf(c_3659,negated_conjecture,
~ v_P(sK0,sK2),
inference(split_conjunct,[status(thm)],[sk_conj_1_neg]) ).
cnf(c_3817,plain,
sK2 = sK1,
inference(resolve,[status(thm)],[c_3098,c_3658]) ).
cnf(c_3819,negated_conjecture,
~ v_P(sK0,sK1),
inference(paramod,[status(thm)],[c_3817,c_3659]) ).
cnf(c_3818,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_3657,c_3819]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWW342+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.37 % Computer : n026.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Sat Sep 26 15:44:26 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.38 % Process 1392000 was started by sandbox2 on n026,
% 0.09/0.38 % Sat Sep 26 15:44:26 2026
% 0.09/0.38 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 2.82/1.00
% 2.82/1.00 % SInE (scan): 1095 to sos (tol 1.5x), 303 to usable (tol 2.0x), 3807 zapped, of 5205 axioms (depth 3).
% 2.82/1.00
% 2.82/1.00 % From the command line: assign(max_seconds, 300).
% 2.82/1.00
% 2.82/1.00 % SZS status Theorem for theBenchmark
% 2.82/1.00
% 2.82/1.00 % Proof 1 at 0.31 (+ 0.12) seconds.
% 2.82/1.00 % Length of proof is 8.
% 2.82/1.00 % Level of proof is 3.
% 2.82/1.00 % Maximum clause weight is 13.000.
% 2.82/1.00 % Given clauses 9.
% 2.82/1.00
% 2.82/1.00 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------