%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET840-1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n002.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 16.52s 2.66s
% Output : CNFRefutation 16.52s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 7
% Syntax : Number of formulae : 26 ( 6 unt; 0 def)
% Number of atoms : 56 ( 6 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 57 ( 27 ~; 30 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-3 aty)
% Number of variables : 59 ( 59 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f173,axiom,
! [V_A,V_X,T_a,V_C] :
( c_in(V_A,c_Union(V_C,T_a),T_a)
| ~ c_in(V_X,V_C,tc_set(T_a))
| ~ c_in(V_A,V_X,T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f176,axiom,
! [V_x,V_B,T_a] : c_in(V_x,c_insert(V_x,V_B,T_a),T_a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f307,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(f308,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(f309,axiom,
! [V_B,V_A,T_a] :
( V_A = V_B
| ~ c_lessequals(V_A,V_B,tc_set(T_a))
| ~ c_lessequals(V_B,V_A,tc_set(T_a)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f1358,negated_conjecture,
! [V_U] : ~ c_lessequals(v_S,c_insert(V_U,c_emptyset,tc_set(t_b)),tc_set(tc_set(t_b))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f1359,negated_conjecture,
! [V_U] :
( ~ c_in(V_U,v_S,tc_set(t_b))
| c_lessequals(c_Union(v_S,t_b),V_U,tc_set(t_b)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f1597,plain,
! [V_A,T_a,V_C] :
( c_in(V_A,c_Union(V_C,T_a),T_a)
| ! [V_X] :
( ~ c_in(V_X,V_C,tc_set(T_a))
| ~ c_in(V_A,V_X,T_a) ) ),
inference(miniscoping,[status(thm)],[f173]) ).
fof(f1598,plain,
! [X0,X1,X2,X3] :
( c_in(X0,c_Union(X3,X2),X2)
| ~ c_in(X1,X3,tc_set(X2))
| ~ c_in(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f1597]) ).
fof(f1602,plain,
! [X0,X1,X2] : c_in(X0,c_insert(X0,X1,X2),X2),
inference(cnf_transformation,[status(thm)],[f176]) ).
fof(f1774,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)],[f307]) ).
fof(f1775,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)],[f308]) ).
fof(f1776,plain,
! [V_B,V_A] :
( V_A = V_B
| ! [T_a] :
( ~ c_lessequals(V_A,V_B,tc_set(T_a))
| ~ c_lessequals(V_B,V_A,tc_set(T_a)) ) ),
inference(miniscoping,[status(thm)],[f309]) ).
fof(f1777,plain,
! [X0,X1,X2] :
( X1 = X0
| ~ c_lessequals(X1,X0,tc_set(X2))
| ~ c_lessequals(X0,X1,tc_set(X2)) ),
inference(cnf_transformation,[status(thm)],[f1776]) ).
fof(f2835,plain,
! [X0] : ~ c_lessequals(v_S,c_insert(X0,c_emptyset,tc_set(t_b)),tc_set(tc_set(t_b))),
inference(cnf_transformation,[status(thm)],[f1358]) ).
fof(f2836,plain,
! [X0] :
( ~ c_in(X0,v_S,tc_set(t_b))
| c_lessequals(c_Union(v_S,t_b),X0,tc_set(t_b)) ),
inference(cnf_transformation,[status(thm)],[f1359]) ).
fof(f2843,plain,
! [X0] :
( ~ c_in(X0,v_S,tc_set(t_b))
| c_Union(v_S,t_b) = X0
| ~ c_lessequals(X0,c_Union(v_S,t_b),tc_set(t_b)) ),
inference(resolution,[status(thm)],[f1777,f2836]) ).
fof(f8570,plain,
! [X0,X1,X2,X3] :
( ~ c_in(X3,X1,tc_set(X2))
| ~ c_in(c_Main_OsubsetI__1(X0,c_Union(X1,X2),X2),X3,X2)
| c_lessequals(X0,c_Union(X1,X2),tc_set(X2)) ),
inference(resolution,[status(thm)],[f1775,f1598]) ).
fof(f10496,plain,
! [X0,X1,X2] :
( c_lessequals(X0,c_Union(X1,X2),tc_set(X2))
| ~ c_in(X0,X1,tc_set(X2))
| c_lessequals(X0,c_Union(X1,X2),tc_set(X2)) ),
inference(resolution,[status(thm)],[f8570,f1774]) ).
fof(f10536,plain,
! [X0,X1,X2] :
( ~ c_in(X0,X1,tc_set(X2))
| c_lessequals(X0,c_Union(X1,X2),tc_set(X2)) ),
inference(duplicate_literals_removal,[status(thm)],[f10496]) ).
fof(f10539,plain,
! [X0] :
( ~ c_in(X0,v_S,tc_set(t_b))
| c_Union(v_S,t_b) = X0 ),
inference(backward_subsumption_resolution,[status(thm)],[f2843,f10536]) ).
fof(f10686,plain,
! [X0] :
( c_lessequals(v_S,X0,tc_set(tc_set(t_b)))
| c_Union(v_S,t_b) = c_Main_OsubsetI__1(v_S,X0,tc_set(t_b)) ),
inference(resolution,[status(thm)],[f10539,f1774]) ).
fof(f11478,plain,
! [X0] :
( c_lessequals(v_S,X0,tc_set(tc_set(t_b)))
| c_lessequals(v_S,X0,tc_set(tc_set(t_b)))
| ~ c_in(c_Union(v_S,t_b),X0,tc_set(t_b)) ),
inference(paramodulation,[status(thm)],[f10686,f1775]) ).
fof(f11483,plain,
! [X0] :
( c_lessequals(v_S,X0,tc_set(tc_set(t_b)))
| ~ c_in(c_Union(v_S,t_b),X0,tc_set(t_b)) ),
inference(duplicate_literals_removal,[status(thm)],[f11478]) ).
fof(f11518,plain,
! [X0] : c_lessequals(v_S,c_insert(c_Union(v_S,t_b),X0,tc_set(t_b)),tc_set(tc_set(t_b))),
inference(resolution,[status(thm)],[f11483,f1602]) ).
fof(f11529,plain,
$false,
inference(resolution,[status(thm)],[f11518,f2835]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET840-1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.14/0.41 % Computer : n002.cluster.edu
% 0.14/0.41 % Model : x86_64 x86_64
% 0.14/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.41 % Memory : 8046.5625MB
% 0.14/0.41 % OS : Linux 6.8.0-71-generic
% 0.14/0.41 % CPULimit : 300
% 0.14/0.41 % WCLimit : 300
% 0.14/0.41 % DateTime : Mon Sep 21 05:43:33 UTC 2026
% 0.14/0.42 % CPUTime :
% 0.18/0.53 % Drodi V4.1.1
% 16.52/2.66 % Refutation found
% 16.52/2.66 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 16.52/2.66 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.82/2.74 % Elapsed time: 2.304077 seconds
% 0.82/2.74 % CPU time: 17.094759 seconds
% 0.82/2.74 % Total memory used: 300.893 MB
% 0.82/2.74 % Net memory used: 285.131 MB
%------------------------------------------------------------------------------