%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWV860-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n003.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 09:09:14 AM UTC 2026
% Result : Unsatisfiable 0.85s 0.53s
% Output : CNFRefutation 0.85s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 4
% Syntax : Number of formulae : 11 ( 9 unt; 0 def)
% Number of atoms : 13 ( 3 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 7 ( 5 ~; 2 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-4 aty)
% Number of functors : 7 ( 7 usr; 6 con; 0-2 aty)
% Number of variables : 6 ( 1 sgn 3 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(cls_conjecture_2,axiom,
~ hBOOL(hAPP(hAPP(v_P,v_x),v_xb)),
file('theBenchmark.p',cls_conjecture_2) ).
cnf(c_163,plain,
~ hBOOL(hAPP(hAPP(v_P,v_x),v_xb)),
inference(clausify,[status(thm)],[cls_conjecture_2]) ).
fof(cls_conjecture_1,axiom,
c_Natural_Oevaln(c_Com_Ocom_OSKIP,v_xa,v_n,v_xb),
file('theBenchmark.p',cls_conjecture_1) ).
cnf(c_164,plain,
c_Natural_Oevaln(c_Com_Ocom_OSKIP,v_xa,v_n,v_xb),
inference(clausify,[status(thm)],[cls_conjecture_1]) ).
fof(cls_conjecture_0,axiom,
hBOOL(hAPP(hAPP(v_P,v_x),v_xa)),
file('theBenchmark.p',cls_conjecture_0) ).
cnf(c_165,plain,
hBOOL(hAPP(hAPP(v_P,v_x),v_xa)),
inference(clausify,[status(thm)],[cls_conjecture_0]) ).
fof(cls_evaln__elim__cases_I1_J_0,axiom,
! [VAR_0,VAR_1,VAR_2] :
( ~ c_Natural_Oevaln(c_Com_Ocom_OSKIP,VAR_1,VAR_2,VAR_0)
| VAR_0 = VAR_1 ),
file('theBenchmark.p',cls_evaln__elim__cases_I1_J_0) ).
cnf(c_166,plain,
( ~ c_Natural_Oevaln(c_Com_Ocom_OSKIP,B,C,A)
| A = B ),
inference(clausify,[status(thm)],[cls_evaln__elim__cases_I1_J_0]) ).
cnf(c_906,plain,
v_xb = v_xa,
inference(resolve,[status(thm)],[c_166,c_164]) ).
cnf(c_908,plain,
~ hBOOL(hAPP(hAPP(v_P,v_x),v_xa)),
inference(paramod,[status(thm)],[c_906,c_163]) ).
cnf(c_907,plain,
$false,
inference(resolve,[status(thm)],[c_165,c_908]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV860-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.34 % Computer : n003.cluster.edu
% 0.07/0.34 % Model : x86_64 x86_64
% 0.07/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.34 % Memory : 8046.5625MB
% 0.07/0.34 % OS : Linux 6.8.0-71-generic
% 0.07/0.34 % CPULimit : 300
% 0.07/0.34 % WCLimit : 300
% 0.07/0.34 % DateTime : Sat Sep 26 15:06:24 UTC 2026
% 0.07/0.34 % CPUTime :
% 0.07/0.34 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.07/0.34 % Process 3160166 was started by sandbox2 on n003,
% 0.07/0.34 % Sat Sep 26 15:06:24 2026
% 0.07/0.34 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.07/0.36
% 0.07/0.36 % From the command line: assign(max_seconds, 300).
% 0.85/0.53
% 0.85/0.53 % SZS status Unsatisfiable for theBenchmark
% 0.85/0.53
% 0.85/0.53 % Proof 1 at 0.09 (+ 0.01) seconds.
% 0.85/0.53 % Length of proof is 6.
% 0.85/0.53 % Level of proof is 2.
% 0.85/0.53 % Maximum clause weight is 23.000.
% 0.85/0.53 % Given clauses 120.
% 0.85/0.53
% 0.85/0.53 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------