%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWV865-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n020.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 : Thu Sep 24 02:49:41 PM UTC 2026
% Result : Unsatisfiable 0.13s 0.38s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 10
% Syntax : Number of formulae : 37 ( 7 unt; 4 def)
% Number of atoms : 77 ( 31 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 71 ( 31 ~; 36 |; 0 &)
% ( 4 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 6 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-1 aty)
% Number of variables : 31 ( 31 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f15,axiom,
! [V_u,V_t,V_c,V_s] :
( ~ c_Natural_Oevalc(V_c,V_s,V_t)
| ~ c_Natural_Oevalc(V_c,V_s,V_u)
| V_u = V_t ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f19,axiom,
! [V_t] :
( ~ c_Hoare__Mirabelle_Ostate__not__singleton
| v_sko__Hoare__Mirabelle__Xsingle__stateE__1(V_t) != V_t ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f26,negated_conjecture,
c_Hoare__Mirabelle_Ostate__not__singleton,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f27,negated_conjecture,
~ c_Natural_Oevalc(v_c,v_Z,v_s_H),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f29,negated_conjecture,
! [V_Z_Ha] :
( c_Natural_Oevalc(v_c,v_Z,v_Z_H(V_Z_Ha))
| V_Z_Ha = v_s_H ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f30,negated_conjecture,
! [V_Z_Ha] :
( V_Z_Ha = v_s_H
| V_Z_Ha != v_Z_H(V_Z_Ha) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f49,plain,
! [V_t,V_c,V_s] :
( ~ c_Natural_Oevalc(V_c,V_s,V_t)
| ! [V_u] :
( ~ c_Natural_Oevalc(V_c,V_s,V_u)
| V_u = V_t ) ),
inference(miniscoping,[status(thm)],[f15]) ).
fof(f50,plain,
! [X0,X1,X2,X3] :
( ~ c_Natural_Oevalc(X2,X3,X1)
| ~ c_Natural_Oevalc(X2,X3,X0)
| X0 = X1 ),
inference(cnf_transformation,[status(thm)],[f49]) ).
fof(f55,plain,
( ~ c_Hoare__Mirabelle_Ostate__not__singleton
| ! [V_t] : v_sko__Hoare__Mirabelle__Xsingle__stateE__1(V_t) != V_t ),
inference(miniscoping,[status(thm)],[f19]) ).
fof(f56,plain,
! [X0] :
( ~ c_Hoare__Mirabelle_Ostate__not__singleton
| v_sko__Hoare__Mirabelle__Xsingle__stateE__1(X0) != X0 ),
inference(cnf_transformation,[status(thm)],[f55]) ).
fof(f66,plain,
c_Hoare__Mirabelle_Ostate__not__singleton,
inference(cnf_transformation,[status(thm)],[f26]) ).
fof(f67,plain,
~ c_Natural_Oevalc(v_c,v_Z,v_s_H),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f69,plain,
! [X0] :
( c_Natural_Oevalc(v_c,v_Z,v_Z_H(X0))
| X0 = v_s_H ),
inference(cnf_transformation,[status(thm)],[f29]) ).
fof(f70,plain,
! [X0] :
( X0 = v_s_H
| X0 != v_Z_H(X0) ),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f74,definition,
( sQ1_spl
<=> c_Hoare__Mirabelle_Ostate__not__singleton ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f76,plain,
( sQ1_spl
| ~ c_Hoare__Mirabelle_Ostate__not__singleton ),
inference(component_clause,[status(thm)],[f74]) ).
fof(f82,definition,
! [X0] :
( sQ3_spl
<=> v_sko__Hoare__Mirabelle__Xsingle__stateE__1(X0) != X0 ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f83,plain,
! [X0] :
( ~ sQ3_spl
| v_sko__Hoare__Mirabelle__Xsingle__stateE__1(X0) != X0 ),
inference(component_clause,[status(thm)],[f82]) ).
fof(f85,plain,
( ~ sQ1_spl
| sQ3_spl ),
inference(split_clause,[status(thm)],[f56,f82,f74]) ).
fof(f116,plain,
( sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f76,f66]) ).
fof(f117,plain,
sQ1_spl,
inference(contradiction_clause,[status(thm)],[f116]) ).
fof(f119,plain,
! [X0,X1] :
( X1 = v_s_H
| ~ c_Natural_Oevalc(v_c,v_Z,X0)
| X0 = v_Z_H(X1) ),
inference(resolution,[status(thm)],[f50,f69]) ).
fof(f120,plain,
! [X0,X1] :
( X0 = v_s_H
| X1 = v_s_H
| v_Z_H(X0) = v_Z_H(X1) ),
inference(resolution,[status(thm)],[f119,f69]) ).
fof(f121,plain,
! [X0] :
( v_Z_H(X0) = v_s_H
| X0 = v_s_H
| v_Z_H(X0) = v_s_H ),
inference(resolution,[status(thm)],[f120,f70]) ).
fof(f131,plain,
! [X0] :
( X0 = v_s_H
| v_Z_H(X0) = v_s_H ),
inference(duplicate_literals_removal,[status(thm)],[f121]) ).
fof(f136,definition,
! [X2] :
( sQ6_spl
<=> ( X2 = v_s_H
| X2 = v_s_H ) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f137,plain,
! [X0] :
( ~ sQ6_spl
| X0 = v_s_H
| X0 = v_s_H ),
inference(component_clause,[status(thm)],[f136]) ).
fof(f152,plain,
! [X0] :
( ~ sQ6_spl
| X0 = v_s_H ),
inference(duplicate_literals_removal,[status(thm)],[f137]) ).
fof(f153,plain,
( ~ sQ3_spl
| ~ sQ6_spl
| $false ),
inference(resolution,[status(thm)],[f152,f83]) ).
fof(f157,plain,
( ~ sQ3_spl
| ~ sQ6_spl ),
inference(contradiction_clause,[status(thm)],[f153]) ).
fof(f164,plain,
! [X0] :
( X0 = v_s_H
| c_Natural_Oevalc(v_c,v_Z,v_s_H)
| X0 = v_s_H ),
inference(paramodulation,[status(thm)],[f131,f69]) ).
fof(f169,definition,
( sQ9_spl
<=> c_Natural_Oevalc(v_c,v_Z,v_s_H) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f170,plain,
( ~ sQ9_spl
| c_Natural_Oevalc(v_c,v_Z,v_s_H) ),
inference(component_clause,[status(thm)],[f169]) ).
fof(f172,plain,
( sQ9_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f164,f136,f169]) ).
fof(f173,plain,
( ~ sQ9_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f170,f67]) ).
fof(f174,plain,
~ sQ9_spl,
inference(contradiction_clause,[status(thm)],[f173]) ).
fof(f175,plain,
$false,
inference(sat_refutation,[status(thm)],[f85,f117,f157,f172,f174]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV865-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n020.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Mon Sep 21 09:30:02 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.36 % Drodi V4.1.1
% 0.13/0.38 % Refutation found
% 0.13/0.38 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.13/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.41 % Elapsed time: 0.045071 seconds
% 0.13/0.41 % CPU time: 0.140021 seconds
% 0.13/0.41 % Total memory used: 102.076 MB
% 0.13/0.41 % Net memory used: 101.839 MB
%------------------------------------------------------------------------------