%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWV898-1 : 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 : 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 09:09:18 AM UTC 2026
% Result : Unsatisfiable 0.15s 5.63s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 3
% Syntax : Number of formulae : 8 ( 6 unt; 0 def)
% Number of atoms : 10 ( 0 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 6 ( 4 ~; 2 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 5 con; 0-5 aty)
% Number of variables : 10 ( 2 sgn 4 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(cls_conjecture_3,axiom,
~ c_Finite__Set_Ofinite(c_Set_Oimage(c_COMBB(c_Hoare__Mirabelle_OMGT,c_COMBB(c_Option_Othe(tc_Com_Ocom),c_Com_Obody,tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),tc_Com_Ocom,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_Com_Opname),c_Map_Odom(c_Com_Obody,tc_Com_Opname,tc_Com_Ocom),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),
file('theBenchmark.p',cls_conjecture_3) ).
cnf(c_204,plain,
~ c_Finite__Set_Ofinite(c_Set_Oimage(c_COMBB(c_Hoare__Mirabelle_OMGT,c_COMBB(c_Option_Othe(tc_Com_Ocom),c_Com_Obody,tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),tc_Com_Ocom,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_Com_Opname),c_Map_Odom(c_Com_Obody,tc_Com_Opname,tc_Com_Ocom),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),
inference(clausify,[status(thm)],[cls_conjecture_3]) ).
fof(cls_finite__imageI_0,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( ~ c_Finite__Set_Ofinite(VAR_1,VAR_2)
| c_Finite__Set_Ofinite(c_Set_Oimage(VAR_0,VAR_1,VAR_2,VAR_3),VAR_3) ),
file('theBenchmark.p',cls_finite__imageI_0) ).
cnf(c_213,plain,
( ~ c_Finite__Set_Ofinite(B,C)
| c_Finite__Set_Ofinite(c_Set_Oimage(A,B,C,D),D) ),
inference(clausify,[status(thm)],[cls_finite__imageI_0]) ).
fof(cls_finite__dom__body_0,axiom,
c_Finite__Set_Ofinite(c_Map_Odom(c_Com_Obody,tc_Com_Opname,tc_Com_Ocom),tc_Com_Opname),
file('theBenchmark.p',cls_finite__dom__body_0) ).
cnf(c_225,plain,
c_Finite__Set_Ofinite(c_Map_Odom(c_Com_Obody,tc_Com_Opname,tc_Com_Ocom),tc_Com_Opname),
inference(clausify,[status(thm)],[cls_finite__dom__body_0]) ).
cnf(c_981,plain,
c_Finite__Set_Ofinite(c_Set_Oimage(A,c_Map_Odom(c_Com_Obody,tc_Com_Opname,tc_Com_Ocom),tc_Com_Opname,B),B),
inference(resolve,[status(thm)],[c_225,c_213]) ).
cnf(c_982,plain,
$false,
inference(resolve,[status(thm)],[c_981,c_204]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWV898-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/5.38 % Computer : n026.cluster.edu
% 0.10/5.38 % Model : x86_64 x86_64
% 0.10/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.38 % Memory : 8046.5625MB
% 0.10/5.38 % OS : Linux 6.8.0-71-generic
% 0.10/5.38 % CPULimit : 300
% 0.10/5.38 % WCLimit : 300
% 0.10/5.38 % DateTime : Sat Sep 26 15:10:46 UTC 2026
% 0.10/5.38 % CPUTime :
% 0.10/5.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/5.38 % Process 1316645 was started by sandbox2 on n026,
% 0.10/5.38 % Sat Sep 26 15:10:46 2026
% 0.10/5.38 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.15/5.41
% 0.15/5.41 % From the command line: assign(max_seconds, 300).
% 0.15/5.63
% 0.15/5.63 % SZS status Unsatisfiable for theBenchmark
% 0.15/5.63
% 0.15/5.63 % Proof 1 at 0.18 (+ 0.02) seconds.
% 0.15/5.63 % Length of proof is 5.
% 0.15/5.63 % Level of proof is 2.
% 0.15/5.63 % Maximum clause weight is 50.000.
% 0.15/5.63 % Given clauses 130.
% 0.15/5.63
% 0.15/5.63 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------