%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET842-2 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n005.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 02:10:46 PM UTC 2026
% Result : Unsatisfiable 0.18s 0.50s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 8
% Syntax : Number of formulae : 27 ( 5 unt; 1 def)
% Number of atoms : 54 ( 0 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 48 ( 21 ~; 26 |; 0 &)
% ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 4 ( 3 usr; 2 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-3 aty)
% Number of variables : 46 ( 46 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,negated_conjecture,
~ c_lessequals(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(tc_set(t_a))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,negated_conjecture,
! [V_U] :
( ~ c_in(V_U,v_Y,tc_set(tc_set(t_a)))
| c_lessequals(V_U,v_m,tc_set(tc_set(t_a))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [V_A,V_C,T_a] :
( c_in(c_Main_OUnionE__1(V_A,V_C,T_a),V_C,tc_set(T_a))
| ~ c_in(V_A,c_Union(V_C,T_a),T_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [V_A,V_C,T_a] :
( c_in(V_A,c_Main_OUnionE__1(V_A,V_C,T_a),T_a)
| ~ c_in(V_A,c_Union(V_C,T_a),T_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [V_c,V_A,T_a,V_B] :
( c_in(V_c,V_B,T_a)
| ~ c_lessequals(V_A,V_B,tc_set(T_a))
| ~ c_in(V_c,V_A,T_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,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/sandbox/benchmark/theBenchmark.p') ).
fof(f7,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/sandbox/benchmark/theBenchmark.p') ).
fof(f8,plain,
~ c_lessequals(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(tc_set(t_a))),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f9,plain,
! [X0] :
( ~ c_in(X0,v_Y,tc_set(tc_set(t_a)))
| c_lessequals(X0,v_m,tc_set(tc_set(t_a))) ),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f10,plain,
! [X0,X1,X2] :
( c_in(c_Main_OUnionE__1(X0,X1,X2),X1,tc_set(X2))
| ~ c_in(X0,c_Union(X1,X2),X2) ),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f11,plain,
! [X0,X1,X2] :
( c_in(X0,c_Main_OUnionE__1(X0,X1,X2),X2)
| ~ c_in(X0,c_Union(X1,X2),X2) ),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f12,plain,
! [V_c,T_a,V_B] :
( c_in(V_c,V_B,T_a)
| ! [V_A] :
( ~ c_lessequals(V_A,V_B,tc_set(T_a))
| ~ c_in(V_c,V_A,T_a) ) ),
inference(miniscoping,[status(thm)],[f5]) ).
fof(f13,plain,
! [X0,X1,X2,X3] :
( c_in(X0,X3,X2)
| ~ c_lessequals(X1,X3,tc_set(X2))
| ~ c_in(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f14,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)],[f6]) ).
fof(f15,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)],[f7]) ).
fof(f16,plain,
! [X0,X1,X2] :
( c_in(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(X0,X1),X2,X1),X0,X1),X0,tc_set(X1))
| c_lessequals(c_Union(X0,X1),X2,tc_set(X1)) ),
inference(resolution,[status(thm)],[f14,f10]) ).
fof(f27,plain,
! [X0] :
( c_lessequals(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_Y,tc_set(t_a)),X0,tc_set(t_a)),v_Y,tc_set(t_a)),v_m,tc_set(tc_set(t_a)))
| c_lessequals(c_Union(v_Y,tc_set(t_a)),X0,tc_set(tc_set(t_a))) ),
inference(resolution,[status(thm)],[f16,f9]) ).
fof(f28,plain,
! [X0,X1] :
( c_in(X1,v_m,tc_set(t_a))
| ~ c_in(X1,c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_Y,tc_set(t_a)),X0,tc_set(t_a)),v_Y,tc_set(t_a)),tc_set(t_a))
| c_lessequals(c_Union(v_Y,tc_set(t_a)),X0,tc_set(tc_set(t_a))) ),
inference(resolution,[status(thm)],[f27,f13]) ).
fof(f33,plain,
! [X0] :
( ~ c_in(c_Main_OsubsetI__1(c_Union(v_Y,tc_set(t_a)),X0,tc_set(t_a)),c_Union(v_Y,tc_set(t_a)),tc_set(t_a))
| c_in(c_Main_OsubsetI__1(c_Union(v_Y,tc_set(t_a)),X0,tc_set(t_a)),v_m,tc_set(t_a))
| c_lessequals(c_Union(v_Y,tc_set(t_a)),X0,tc_set(tc_set(t_a))) ),
inference(resolution,[status(thm)],[f28,f11]) ).
fof(f34,plain,
! [X0] :
( c_in(c_Main_OsubsetI__1(c_Union(v_Y,tc_set(t_a)),X0,tc_set(t_a)),v_m,tc_set(t_a))
| c_lessequals(c_Union(v_Y,tc_set(t_a)),X0,tc_set(tc_set(t_a))) ),
inference(forward_subsumption_resolution,[status(thm)],[f33,f14]) ).
fof(f35,plain,
( c_lessequals(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(tc_set(t_a)))
| c_lessequals(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(tc_set(t_a))) ),
inference(resolution,[status(thm)],[f34,f15]) ).
fof(f36,definition,
( sQ0_spl
<=> c_lessequals(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(tc_set(t_a))) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f37,plain,
( ~ sQ0_spl
| c_lessequals(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(tc_set(t_a))) ),
inference(component_clause,[status(thm)],[f36]) ).
fof(f39,plain,
sQ0_spl,
inference(split_clause,[status(thm)],[f35,f36]) ).
fof(f40,plain,
( ~ sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f37,f8]) ).
fof(f41,plain,
~ sQ0_spl,
inference(contradiction_clause,[status(thm)],[f40]) ).
fof(f42,plain,
$false,
inference(sat_refutation,[status(thm)],[f39,f41]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SET842-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.07 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.47 % Computer : n005.cluster.edu
% 0.18/0.47 % Model : x86_64 x86_64
% 0.18/0.47 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.47 % Memory : 8046.5625MB
% 0.18/0.47 % OS : Linux 6.8.0-71-generic
% 0.18/0.47 % CPULimit : 300
% 0.18/0.47 % WCLimit : 300
% 0.18/0.47 % DateTime : Mon Sep 21 05:40:47 UTC 2026
% 0.18/0.47 % CPUTime :
% 0.18/0.48 % Drodi V4.1.1
% 0.18/0.50 % Refutation found
% 0.18/0.50 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.18/0.50 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.21/0.55 % Elapsed time: 0.065959 seconds
% 0.21/0.55 % CPU time: 0.081862 seconds
% 0.21/0.55 % Total memory used: 2.830 MB
% 0.21/0.55 % Net memory used: 2.822 MB
%------------------------------------------------------------------------------