%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET830-2 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n008.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 02:10:43 PM UTC 2026
% Result : Unsatisfiable 0.09s 0.38s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 12
% Syntax : Number of formulae : 44 ( 11 unt; 2 def)
% Number of atoms : 88 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 82 ( 38 ~; 42 |; 0 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 3 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-3 aty)
% Number of variables : 84 ( 84 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [V_c,V_A,V_B,T_a] :
( c_in(V_c,V_B,T_a)
| ~ c_in(V_c,c_inter(V_A,V_B,T_a),T_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [V_c,V_A,V_B,T_a] :
( c_in(V_c,V_A,T_a)
| ~ c_in(V_c,c_inter(V_A,V_B,T_a),T_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [V_c,V_B,T_a,V_A] :
( c_in(V_c,c_inter(V_A,V_B,T_a),T_a)
| ~ c_in(V_c,V_A,T_a)
| ~ c_in(V_c,V_B,T_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,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(f5,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(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_B,T_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,negated_conjecture,
c_in(v_x,v_Y,t_a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,negated_conjecture,
c_in(v_x,v_Z,t_a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,negated_conjecture,
~ c_in(v_x,v_X,t_a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,negated_conjecture,
! [V_U] :
( ~ c_lessequals(V_U,v_Y,tc_set(t_a))
| ~ c_lessequals(V_U,v_Z,tc_set(t_a))
| c_lessequals(V_U,v_X,tc_set(t_a)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,plain,
! [V_c,V_B,T_a] :
( c_in(V_c,V_B,T_a)
| ! [V_A] : ~ c_in(V_c,c_inter(V_A,V_B,T_a),T_a) ),
inference(miniscoping,[status(thm)],[f1]) ).
fof(f12,plain,
! [X0,X1,X2,X3] :
( c_in(X0,X2,X3)
| ~ c_in(X0,c_inter(X1,X2,X3),X3) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f13,plain,
! [V_c,V_A,T_a] :
( c_in(V_c,V_A,T_a)
| ! [V_B] : ~ c_in(V_c,c_inter(V_A,V_B,T_a),T_a) ),
inference(miniscoping,[status(thm)],[f2]) ).
fof(f14,plain,
! [X0,X1,X2,X3] :
( c_in(X0,X1,X3)
| ~ c_in(X0,c_inter(X1,X2,X3),X3) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f15,plain,
! [X0,X1,X2,X3] :
( c_in(X0,c_inter(X3,X1,X2),X2)
| ~ c_in(X0,X3,X2)
| ~ c_in(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f16,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)],[f4]) ).
fof(f17,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)],[f16]) ).
fof(f18,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)],[f5]) ).
fof(f19,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)],[f6]) ).
fof(f20,plain,
c_in(v_x,v_Y,t_a),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f21,plain,
c_in(v_x,v_Z,t_a),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f22,plain,
~ c_in(v_x,v_X,t_a),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f23,plain,
! [X0] :
( ~ c_lessequals(X0,v_Y,tc_set(t_a))
| ~ c_lessequals(X0,v_Z,tc_set(t_a))
| c_lessequals(X0,v_X,tc_set(t_a)) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f24,plain,
! [X0,X1] :
( ~ c_lessequals(X1,v_Y,tc_set(t_a))
| ~ c_lessequals(X1,v_Z,tc_set(t_a))
| c_in(X0,v_X,t_a)
| ~ c_in(X0,X1,t_a) ),
inference(resolution,[status(thm)],[f17,f23]) ).
fof(f25,plain,
! [X0,X1,X2,X3] :
( c_in(c_Main_OsubsetI__1(c_inter(X0,X1,X2),X3,X2),X0,X2)
| c_lessequals(c_inter(X0,X1,X2),X3,tc_set(X2)) ),
inference(resolution,[status(thm)],[f18,f14]) ).
fof(f26,plain,
! [X0,X1,X2,X3] :
( c_in(c_Main_OsubsetI__1(c_inter(X0,X1,X2),X3,X2),X1,X2)
| c_lessequals(c_inter(X0,X1,X2),X3,tc_set(X2)) ),
inference(resolution,[status(thm)],[f18,f12]) ).
fof(f32,plain,
! [X0,X1,X2] :
( c_lessequals(c_inter(X0,X1,X2),X0,tc_set(X2))
| c_lessequals(c_inter(X0,X1,X2),X0,tc_set(X2)) ),
inference(resolution,[status(thm)],[f25,f19]) ).
fof(f35,plain,
! [X0,X1,X2] : c_lessequals(c_inter(X0,X1,X2),X0,tc_set(X2)),
inference(duplicate_literals_removal,[status(thm)],[f32]) ).
fof(f45,plain,
! [X0,X1] :
( ~ c_lessequals(c_inter(v_Z,X1,t_a),v_Y,tc_set(t_a))
| c_in(X0,v_X,t_a)
| ~ c_in(X0,c_inter(v_Z,X1,t_a),t_a) ),
inference(resolution,[status(thm)],[f35,f24]) ).
fof(f51,plain,
! [X0,X1,X2] :
( c_lessequals(c_inter(X0,X1,X2),X1,tc_set(X2))
| c_lessequals(c_inter(X0,X1,X2),X1,tc_set(X2)) ),
inference(resolution,[status(thm)],[f26,f19]) ).
fof(f54,plain,
! [X0,X1,X2] : c_lessequals(c_inter(X0,X1,X2),X1,tc_set(X2)),
inference(duplicate_literals_removal,[status(thm)],[f51]) ).
fof(f91,plain,
! [X0] :
( c_in(X0,v_X,t_a)
| ~ c_in(X0,c_inter(v_Z,v_Y,t_a),t_a) ),
inference(resolution,[status(thm)],[f45,f54]) ).
fof(f98,plain,
! [X0] :
( ~ c_in(X0,v_Z,t_a)
| ~ c_in(X0,v_Y,t_a)
| c_in(X0,v_X,t_a) ),
inference(resolution,[status(thm)],[f91,f15]) ).
fof(f101,plain,
( ~ c_in(v_x,v_Z,t_a)
| ~ c_in(v_x,v_Y,t_a) ),
inference(resolution,[status(thm)],[f98,f22]) ).
fof(f102,definition,
( sQ2_spl
<=> c_in(v_x,v_Y,t_a) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f104,plain,
( sQ2_spl
| ~ c_in(v_x,v_Y,t_a) ),
inference(component_clause,[status(thm)],[f102]) ).
fof(f105,definition,
( sQ3_spl
<=> c_in(v_x,v_Z,t_a) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f107,plain,
( sQ3_spl
| ~ c_in(v_x,v_Z,t_a) ),
inference(component_clause,[status(thm)],[f105]) ).
fof(f108,plain,
( ~ sQ3_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f101,f102,f105]) ).
fof(f109,plain,
( sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f104,f20]) ).
fof(f110,plain,
sQ2_spl,
inference(contradiction_clause,[status(thm)],[f109]) ).
fof(f111,plain,
( sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f107,f21]) ).
fof(f112,plain,
sQ3_spl,
inference(contradiction_clause,[status(thm)],[f111]) ).
fof(f113,plain,
$false,
inference(sat_refutation,[status(thm)],[f108,f110,f112]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET830-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n008.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Mon Sep 21 05:41:09 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 % Drodi V4.1.1
% 0.09/0.38 % Refutation found
% 0.09/0.38 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.09/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.09/0.41 % Elapsed time: 0.042092 seconds
% 0.09/0.41 % CPU time: 0.112894 seconds
% 0.09/0.41 % Total memory used: 16.873 MB
% 0.09/0.41 % Net memory used: 16.372 MB
%------------------------------------------------------------------------------