%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWV261-2 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n010.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 02:47:04 PM UTC 2026
% Result : Unsatisfiable 0.19s 0.54s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 14
% Syntax : Number of formulae : 52 ( 10 unt; 4 def)
% Number of atoms : 104 ( 8 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 97 ( 45 ~; 48 |; 0 &)
% ( 4 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 5 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-3 aty)
% Number of variables : 83 ( 83 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,negated_conjecture,
c_in(v_X,v_G,tc_Message_Omsg),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,negated_conjecture,
~ c_lessequals(c_Message_Oparts(c_insert(v_X,v_H,tc_Message_Omsg)),c_union(c_Message_Oparts(v_G),c_Message_Oparts(v_H),tc_Message_Omsg),tc_set(tc_Message_Omsg)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [V_G,V_H] : c_lessequals(c_Message_Oparts(c_union(V_G,V_H,tc_Message_Omsg)),c_union(c_Message_Oparts(V_G),c_Message_Oparts(V_H),tc_Message_Omsg),tc_set(tc_Message_Omsg)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [V_G,V_H] :
( c_lessequals(c_Message_Oparts(V_G),c_Message_Oparts(V_H),tc_set(tc_Message_Omsg))
| ~ c_lessequals(V_G,V_H,tc_set(tc_Message_Omsg)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [V_c,V_B,T_a,V_A] :
( c_in(V_c,c_union(V_A,V_B,T_a),T_a)
| ~ c_in(V_c,V_B,T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [V_c,V_A,T_a,V_B] :
( c_in(V_c,c_union(V_A,V_B,T_a),T_a)
| ~ c_in(V_c,V_A,T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [V_a,V_b,V_A,T_a] :
( V_a = V_b
| c_in(V_a,V_A,T_a)
| ~ c_in(V_a,c_insert(V_b,V_A,T_a),T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [V_A,V_B,T_a] :
( c_lessequals(V_A,V_B,tc_set(T_a))
| c_in(c_Main_OsubsetI__1(V_A,V_B,T_a),V_A,T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [V_A,V_B,T_a] :
( c_lessequals(V_A,V_B,tc_set(T_a))
| ~ c_in(c_Main_OsubsetI__1(V_A,V_B,T_a),V_B,T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [V_B,V_C,T_a,V_A] :
( c_lessequals(V_A,V_C,tc_set(T_a))
| ~ c_lessequals(V_A,V_B,tc_set(T_a))
| ~ c_lessequals(V_B,V_C,tc_set(T_a)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,plain,
c_in(v_X,v_G,tc_Message_Omsg),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f12,plain,
~ c_lessequals(c_Message_Oparts(c_insert(v_X,v_H,tc_Message_Omsg)),c_union(c_Message_Oparts(v_G),c_Message_Oparts(v_H),tc_Message_Omsg),tc_set(tc_Message_Omsg)),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f13,plain,
! [X0,X1] : c_lessequals(c_Message_Oparts(c_union(X0,X1,tc_Message_Omsg)),c_union(c_Message_Oparts(X0),c_Message_Oparts(X1),tc_Message_Omsg),tc_set(tc_Message_Omsg)),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f14,plain,
! [X0,X1] :
( c_lessequals(c_Message_Oparts(X0),c_Message_Oparts(X1),tc_set(tc_Message_Omsg))
| ~ c_lessequals(X0,X1,tc_set(tc_Message_Omsg)) ),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f15,plain,
! [V_c,V_B,T_a] :
( ! [V_A] : c_in(V_c,c_union(V_A,V_B,T_a),T_a)
| ~ c_in(V_c,V_B,T_a) ),
inference(miniscoping,[status(thm)],[f5]) ).
fof(f16,plain,
! [X0,X1,X2,X3] :
( c_in(X0,c_union(X3,X1,X2),X2)
| ~ c_in(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f17,plain,
! [V_c,V_A,T_a] :
( ! [V_B] : c_in(V_c,c_union(V_A,V_B,T_a),T_a)
| ~ c_in(V_c,V_A,T_a) ),
inference(miniscoping,[status(thm)],[f6]) ).
fof(f18,plain,
! [X0,X1,X2,X3] :
( c_in(X0,c_union(X1,X3,X2),X2)
| ~ c_in(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f19,plain,
! [V_a,V_b] :
( V_a = V_b
| ! [V_A,T_a] :
( c_in(V_a,V_A,T_a)
| ~ c_in(V_a,c_insert(V_b,V_A,T_a),T_a) ) ),
inference(miniscoping,[status(thm)],[f7]) ).
fof(f20,plain,
! [X0,X1,X2,X3] :
( X0 = X1
| c_in(X0,X2,X3)
| ~ c_in(X0,c_insert(X1,X2,X3),X3) ),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f21,plain,
! [X0,X1,X2] :
( c_lessequals(X0,X1,tc_set(X2))
| c_in(c_Main_OsubsetI__1(X0,X1,X2),X0,X2) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f22,plain,
! [X0,X1,X2] :
( c_lessequals(X0,X1,tc_set(X2))
| ~ c_in(c_Main_OsubsetI__1(X0,X1,X2),X1,X2) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f23,plain,
! [V_C,T_a,V_A] :
( c_lessequals(V_A,V_C,tc_set(T_a))
| ! [V_B] :
( ~ c_lessequals(V_A,V_B,tc_set(T_a))
| ~ c_lessequals(V_B,V_C,tc_set(T_a)) ) ),
inference(miniscoping,[status(thm)],[f10]) ).
fof(f24,plain,
! [X0,X1,X2,X3] :
( c_lessequals(X3,X1,tc_set(X2))
| ~ c_lessequals(X3,X0,tc_set(X2))
| ~ c_lessequals(X0,X1,tc_set(X2)) ),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f25,plain,
! [X0] :
( ~ c_lessequals(c_Message_Oparts(c_insert(v_X,v_H,tc_Message_Omsg)),X0,tc_set(tc_Message_Omsg))
| ~ c_lessequals(X0,c_union(c_Message_Oparts(v_G),c_Message_Oparts(v_H),tc_Message_Omsg),tc_set(tc_Message_Omsg)) ),
inference(resolution,[status(thm)],[f24,f12]) ).
fof(f26,plain,
! [X0] :
( ~ c_lessequals(c_insert(v_X,v_H,tc_Message_Omsg),X0,tc_set(tc_Message_Omsg))
| ~ c_lessequals(c_Message_Oparts(X0),c_union(c_Message_Oparts(v_G),c_Message_Oparts(v_H),tc_Message_Omsg),tc_set(tc_Message_Omsg)) ),
inference(resolution,[status(thm)],[f25,f14]) ).
fof(f32,plain,
! [X0,X1,X2,X3] :
( c_Main_OsubsetI__1(c_insert(X0,X1,X2),X3,X2) = X0
| c_in(c_Main_OsubsetI__1(c_insert(X0,X1,X2),X3,X2),X1,X2)
| c_lessequals(c_insert(X0,X1,X2),X3,tc_set(X2)) ),
inference(resolution,[status(thm)],[f21,f20]) ).
fof(f34,plain,
! [X0,X1,X2,X3] :
( ~ c_in(c_Main_OsubsetI__1(X0,c_union(X1,X2,X3),X3),X1,X3)
| c_lessequals(X0,c_union(X1,X2,X3),tc_set(X3)) ),
inference(resolution,[status(thm)],[f22,f18]) ).
fof(f35,plain,
! [X0,X1,X2,X3] :
( ~ c_in(c_Main_OsubsetI__1(X0,c_union(X1,X2,X3),X3),X2,X3)
| c_lessequals(X0,c_union(X1,X2,X3),tc_set(X3)) ),
inference(resolution,[status(thm)],[f22,f16]) ).
fof(f66,plain,
! [X0] :
( ~ c_lessequals(c_Message_Oparts(X0),c_union(c_Message_Oparts(v_G),c_Message_Oparts(v_H),tc_Message_Omsg),tc_set(tc_Message_Omsg))
| c_Main_OsubsetI__1(c_insert(v_X,v_H,tc_Message_Omsg),X0,tc_Message_Omsg) = v_X
| c_in(c_Main_OsubsetI__1(c_insert(v_X,v_H,tc_Message_Omsg),X0,tc_Message_Omsg),v_H,tc_Message_Omsg) ),
inference(resolution,[status(thm)],[f32,f26]) ).
fof(f166,plain,
( c_Main_OsubsetI__1(c_insert(v_X,v_H,tc_Message_Omsg),c_union(v_G,v_H,tc_Message_Omsg),tc_Message_Omsg) = v_X
| c_in(c_Main_OsubsetI__1(c_insert(v_X,v_H,tc_Message_Omsg),c_union(v_G,v_H,tc_Message_Omsg),tc_Message_Omsg),v_H,tc_Message_Omsg) ),
inference(resolution,[status(thm)],[f66,f13]) ).
fof(f170,definition,
( sQ2_spl
<=> c_in(c_Main_OsubsetI__1(c_insert(v_X,v_H,tc_Message_Omsg),c_union(v_G,v_H,tc_Message_Omsg),tc_Message_Omsg),v_H,tc_Message_Omsg) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f171,plain,
( ~ sQ2_spl
| c_in(c_Main_OsubsetI__1(c_insert(v_X,v_H,tc_Message_Omsg),c_union(v_G,v_H,tc_Message_Omsg),tc_Message_Omsg),v_H,tc_Message_Omsg) ),
inference(component_clause,[status(thm)],[f170]) ).
fof(f173,definition,
( sQ3_spl
<=> c_Main_OsubsetI__1(c_insert(v_X,v_H,tc_Message_Omsg),c_union(v_G,v_H,tc_Message_Omsg),tc_Message_Omsg) = v_X ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f174,plain,
( ~ sQ3_spl
| c_Main_OsubsetI__1(c_insert(v_X,v_H,tc_Message_Omsg),c_union(v_G,v_H,tc_Message_Omsg),tc_Message_Omsg) = v_X ),
inference(component_clause,[status(thm)],[f173]) ).
fof(f176,plain,
( sQ3_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f166,f170,f173]) ).
fof(f239,plain,
( ~ sQ2_spl
| c_lessequals(c_insert(v_X,v_H,tc_Message_Omsg),c_union(v_G,v_H,tc_Message_Omsg),tc_set(tc_Message_Omsg)) ),
inference(resolution,[status(thm)],[f171,f35]) ).
fof(f242,plain,
( ~ sQ2_spl
| ~ c_lessequals(c_Message_Oparts(c_union(v_G,v_H,tc_Message_Omsg)),c_union(c_Message_Oparts(v_G),c_Message_Oparts(v_H),tc_Message_Omsg),tc_set(tc_Message_Omsg)) ),
inference(resolution,[status(thm)],[f239,f26]) ).
fof(f243,plain,
( ~ sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f242,f13]) ).
fof(f244,plain,
~ sQ2_spl,
inference(contradiction_clause,[status(thm)],[f243]) ).
fof(f246,plain,
( ~ sQ3_spl
| ~ c_in(v_X,v_G,tc_Message_Omsg)
| c_lessequals(c_insert(v_X,v_H,tc_Message_Omsg),c_union(v_G,v_H,tc_Message_Omsg),tc_set(tc_Message_Omsg)) ),
inference(paramodulation,[status(thm)],[f174,f34]) ).
fof(f249,definition,
( sQ10_spl
<=> c_lessequals(c_insert(v_X,v_H,tc_Message_Omsg),c_union(v_G,v_H,tc_Message_Omsg),tc_set(tc_Message_Omsg)) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f250,plain,
( ~ sQ10_spl
| c_lessequals(c_insert(v_X,v_H,tc_Message_Omsg),c_union(v_G,v_H,tc_Message_Omsg),tc_set(tc_Message_Omsg)) ),
inference(component_clause,[status(thm)],[f249]) ).
fof(f253,definition,
( sQ11_spl
<=> c_in(v_X,v_G,tc_Message_Omsg) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f255,plain,
( sQ11_spl
| ~ c_in(v_X,v_G,tc_Message_Omsg) ),
inference(component_clause,[status(thm)],[f253]) ).
fof(f256,plain,
( ~ sQ3_spl
| ~ sQ11_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f246,f249,f253,f173]) ).
fof(f276,plain,
( ~ sQ10_spl
| ~ c_lessequals(c_Message_Oparts(c_union(v_G,v_H,tc_Message_Omsg)),c_union(c_Message_Oparts(v_G),c_Message_Oparts(v_H),tc_Message_Omsg),tc_set(tc_Message_Omsg)) ),
inference(resolution,[status(thm)],[f250,f26]) ).
fof(f277,plain,
( ~ sQ10_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f276,f13]) ).
fof(f278,plain,
~ sQ10_spl,
inference(contradiction_clause,[status(thm)],[f277]) ).
fof(f279,plain,
( sQ11_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f255,f11]) ).
fof(f280,plain,
sQ11_spl,
inference(contradiction_clause,[status(thm)],[f279]) ).
fof(f281,plain,
$false,
inference(sat_refutation,[status(thm)],[f176,f244,f256,f278,f280]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SWV261-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.07 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.48 % Computer : n010.cluster.edu
% 0.19/0.48 % Model : x86_64 x86_64
% 0.19/0.48 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.48 % Memory : 8046.5625MB
% 0.19/0.48 % OS : Linux 6.8.0-71-generic
% 0.19/0.48 % CPULimit : 300
% 0.19/0.48 % WCLimit : 300
% 0.19/0.49 % DateTime : Mon Sep 21 08:37:10 UTC 2026
% 0.19/0.49 % CPUTime :
% 0.19/0.52 % Drodi V4.1.1
% 0.19/0.54 % Refutation found
% 0.19/0.54 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.19/0.54 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.24/0.61 % Elapsed time: 0.100882 seconds
% 0.24/0.61 % CPU time: 0.147339 seconds
% 0.24/0.61 % Total memory used: 16.168 MB
% 0.24/0.61 % Net memory used: 16.097 MB
%------------------------------------------------------------------------------