%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWV821-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/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 09:09:10 AM UTC 2026
% Result : Unsatisfiable 11.69s 1.99s
% Output : CNFRefutation 11.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 3
% Syntax : Number of formulae : 9 ( 6 unt; 0 def)
% Number of atoms : 12 ( 6 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 8 ( 5 ~; 3 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-4 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-4 aty)
% Number of variables : 14 ( 1 sgn 5 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(cls_conjecture_1,axiom,
c_Natural_Oevaln(c_Com_Ocom_OBODY(v_pn),v_xa,c_HOL_Ozero__class_Ozero(tc_nat),v_xb),
file('theBenchmark.p',cls_conjecture_1) ).
cnf(c_610,plain,
c_Natural_Oevaln(c_Com_Ocom_OBODY(v_pn),v_xa,c_HOL_Ozero__class_Ozero(tc_nat),v_xb),
inference(clausify,[status(thm)],[cls_conjecture_1]) ).
fof(cls_evaln__elim__cases_I6_J_0,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( ~ c_Natural_Oevaln(c_Com_Ocom_OBODY(VAR_1),VAR_2,VAR_0,VAR_3)
| VAR_0 = c_Suc(c_Natural_Osko__Natural__Xevaln__elim__cases__6__1(VAR_1,VAR_0,VAR_2,VAR_3)) ),
file('theBenchmark.p',cls_evaln__elim__cases_I6_J_0) ).
cnf(c_621,plain,
( ~ c_Natural_Oevaln(c_Com_Ocom_OBODY(B),C,A,D)
| A = c_Suc(c_Natural_Osko__Natural__Xevaln__elim__cases__6__1(B,A,C,D)) ),
inference(clausify,[status(thm)],[cls_evaln__elim__cases_I6_J_0]) ).
cnf(c_622,plain,
( ~ c_Natural_Oevaln(c_Com_Ocom_OBODY(A),C,B,D)
| c_Suc(c_Natural_Osko__Natural__Xevaln__elim__cases__6__1(A,B,C,D)) = B ),
inference(copy,[status(thm)],[c_621]) ).
fof(cls_nat_Osimps_I2_J_0,axiom,
! [VAR_0] : c_HOL_Ozero__class_Ozero(tc_nat) != c_Suc(VAR_0),
file('theBenchmark.p',cls_nat_Osimps_I2_J_0) ).
cnf(c_654,plain,
c_HOL_Ozero__class_Ozero(tc_nat) != c_Suc(A),
inference(clausify,[status(thm)],[cls_nat_Osimps_I2_J_0]) ).
cnf(c_1552,plain,
c_Suc(c_Natural_Osko__Natural__Xevaln__elim__cases__6__1(v_pn,c_HOL_Ozero__class_Ozero(tc_nat),v_xa,v_xb)) = c_HOL_Ozero__class_Ozero(tc_nat),
inference(resolve,[status(thm)],[c_622,c_610]) ).
cnf(c_1551,plain,
$false,
inference(resolve,[status(thm)],[c_654,c_1552]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWV821-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/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 15:03:09 UTC 2026
% 0.07/0.35 % CPUTime :
% 0.07/0.35 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.07/0.35 % Process 3152202 was started by sandbox on n003,
% 0.07/0.35 % Sat Sep 26 15:03:09 2026
% 0.07/0.35 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.12/0.37
% 0.12/0.37 % From the command line: assign(max_seconds, 300).
% 11.69/1.99
% 11.69/1.99 % SZS status Unsatisfiable for theBenchmark
% 11.69/1.99
% 11.69/1.99 % Proof 1 at 1.39 (+ 0.02) seconds.
% 11.69/1.99 % Length of proof is 5.
% 11.69/1.99 % Level of proof is 2.
% 11.69/1.99 % Maximum clause weight is 29.000.
% 11.69/1.99 % Given clauses 109.
% 11.69/1.99
% 11.69/1.99 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------