%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : LCL445-2 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /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 : Thu Sep 24 01:07:45 PM UTC 2026
% Result : Unsatisfiable 0.13s 0.40s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 8
% Syntax : Number of formulae : 28 ( 14 unt; 2 def)
% Number of atoms : 45 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 34 ( 17 ~; 15 |; 0 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 3 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-3 aty)
% Number of variables : 32 ( 32 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,negated_conjecture,
c_in(v_q,c_PropLog_Othms(c_insert(v_p,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,negated_conjecture,
c_in(v_q,c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(v_p,c_PropLog_Opl_Ofalse,t_a),v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,negated_conjecture,
~ c_in(v_q,c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [V_q,V_p,V_H,T_a] :
( c_in(c_PropLog_Opl_Oop_A_N_62(V_p,V_q,T_a),c_PropLog_Othms(V_H,T_a),tc_PropLog_Opl(T_a))
| ~ c_in(V_q,c_PropLog_Othms(c_insert(V_p,V_H,tc_PropLog_Opl(T_a)),T_a),tc_PropLog_Opl(T_a)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [V_p,V_H,T_a,V_q] :
( c_in(V_q,c_PropLog_Othms(V_H,T_a),tc_PropLog_Opl(T_a))
| ~ c_in(c_PropLog_Opl_Oop_A_N_62(V_p,V_q,T_a),c_PropLog_Othms(V_H,T_a),tc_PropLog_Opl(T_a))
| ~ c_in(V_p,c_PropLog_Othms(V_H,T_a),tc_PropLog_Opl(T_a)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [V_p,V_q,T_a,V_H] : c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(V_p,V_q,T_a),c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(V_p,c_PropLog_Opl_Ofalse,T_a),V_q,T_a),V_q,T_a),T_a),c_PropLog_Othms(V_H,T_a),tc_PropLog_Opl(T_a)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,plain,
c_in(v_q,c_PropLog_Othms(c_insert(v_p,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f8,plain,
c_in(v_q,c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(v_p,c_PropLog_Opl_Ofalse,t_a),v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f9,plain,
~ c_in(v_q,c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f10,plain,
! [X0,X1,X2,X3] :
( c_in(c_PropLog_Opl_Oop_A_N_62(X1,X0,X3),c_PropLog_Othms(X2,X3),tc_PropLog_Opl(X3))
| ~ c_in(X0,c_PropLog_Othms(c_insert(X1,X2,tc_PropLog_Opl(X3)),X3),tc_PropLog_Opl(X3)) ),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f11,plain,
! [V_H,T_a,V_q] :
( c_in(V_q,c_PropLog_Othms(V_H,T_a),tc_PropLog_Opl(T_a))
| ! [V_p] :
( ~ c_in(c_PropLog_Opl_Oop_A_N_62(V_p,V_q,T_a),c_PropLog_Othms(V_H,T_a),tc_PropLog_Opl(T_a))
| ~ c_in(V_p,c_PropLog_Othms(V_H,T_a),tc_PropLog_Opl(T_a)) ) ),
inference(miniscoping,[status(thm)],[f5]) ).
fof(f12,plain,
! [X0,X1,X2,X3] :
( c_in(X3,c_PropLog_Othms(X1,X2),tc_PropLog_Opl(X2))
| ~ c_in(c_PropLog_Opl_Oop_A_N_62(X0,X3,X2),c_PropLog_Othms(X1,X2),tc_PropLog_Opl(X2))
| ~ c_in(X0,c_PropLog_Othms(X1,X2),tc_PropLog_Opl(X2)) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f13,plain,
! [X0,X1,X2,X3] : c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(X0,X1,X2),c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(X0,c_PropLog_Opl_Ofalse,X2),X1,X2),X1,X2),X2),c_PropLog_Othms(X3,X2),tc_PropLog_Opl(X2)),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f14,plain,
c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(v_p,c_PropLog_Opl_Ofalse,t_a),v_q,t_a),c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)),
inference(resolution,[status(thm)],[f10,f8]) ).
fof(f15,plain,
c_in(c_PropLog_Opl_Oop_A_N_62(v_p,v_q,t_a),c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)),
inference(resolution,[status(thm)],[f10,f7]) ).
fof(f18,plain,
! [X0,X1,X2,X3] :
( c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(X0,c_PropLog_Opl_Ofalse,X2),X1,X2),X1,X2),c_PropLog_Othms(X3,X2),tc_PropLog_Opl(X2))
| ~ c_in(c_PropLog_Opl_Oop_A_N_62(X0,X1,X2),c_PropLog_Othms(X3,X2),tc_PropLog_Opl(X2)) ),
inference(resolution,[status(thm)],[f12,f13]) ).
fof(f23,definition,
( sQ1_spl
<=> c_in(v_q,c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f24,plain,
( ~ sQ1_spl
| c_in(v_q,c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)) ),
inference(component_clause,[status(thm)],[f23]) ).
fof(f31,plain,
( ~ sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f24,f9]) ).
fof(f32,plain,
~ sQ1_spl,
inference(contradiction_clause,[status(thm)],[f31]) ).
fof(f37,plain,
c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(v_p,c_PropLog_Opl_Ofalse,t_a),v_q,t_a),v_q,t_a),c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)),
inference(resolution,[status(thm)],[f18,f15]) ).
fof(f40,plain,
( c_in(v_q,c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a))
| ~ c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(v_p,c_PropLog_Opl_Ofalse,t_a),v_q,t_a),c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)) ),
inference(resolution,[status(thm)],[f37,f12]) ).
fof(f41,definition,
( sQ3_spl
<=> c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(v_p,c_PropLog_Opl_Ofalse,t_a),v_q,t_a),c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f43,plain,
( sQ3_spl
| ~ c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(v_p,c_PropLog_Opl_Ofalse,t_a),v_q,t_a),c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)) ),
inference(component_clause,[status(thm)],[f41]) ).
fof(f44,plain,
( sQ1_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f40,f41,f23]) ).
fof(f45,plain,
( sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f43,f14]) ).
fof(f46,plain,
sQ3_spl,
inference(contradiction_clause,[status(thm)],[f45]) ).
fof(f47,plain,
$false,
inference(sat_refutation,[status(thm)],[f32,f44,f46]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL445-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n003.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Mon Sep 21 00:34:15 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.37 % Drodi V4.1.1
% 0.13/0.40 % Refutation found
% 0.13/0.40 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.13/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.44 % Elapsed time: 0.072856 seconds
% 0.13/0.44 % CPU time: 0.198584 seconds
% 0.13/0.44 % Total memory used: 55.881 MB
% 0.13/0.44 % Net memory used: 55.381 MB
%------------------------------------------------------------------------------