%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET839-2 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : 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 02:10:45 PM UTC 2026
% Result : Unsatisfiable 0.11s 0.39s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 6
% Syntax : Number of formulae : 23 ( 7 unt; 0 def)
% Number of atoms : 50 ( 7 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 47 ( 20 ~; 27 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-3 aty)
% Number of variables : 51 ( 51 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,negated_conjecture,
! [V_U] : ~ c_lessequals(v_S,c_insert(V_U,c_emptyset,tc_set(t_a)),tc_set(tc_set(t_a))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,negated_conjecture,
! [V_U,V_V] :
( ~ c_in(V_U,v_S,tc_set(t_a))
| ~ c_in(V_V,v_S,tc_set(t_a))
| c_lessequals(V_U,V_V,tc_set(t_a)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [V_x,V_B,T_a] : c_in(V_x,c_insert(V_x,V_B,T_a),T_a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,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(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_B,T_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,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/sandbox/benchmark/theBenchmark.p') ).
fof(f7,plain,
! [X0] : ~ c_lessequals(v_S,c_insert(X0,c_emptyset,tc_set(t_a)),tc_set(tc_set(t_a))),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f8,plain,
! [V_U] :
( ~ c_in(V_U,v_S,tc_set(t_a))
| ! [V_V] :
( ~ c_in(V_V,v_S,tc_set(t_a))
| c_lessequals(V_U,V_V,tc_set(t_a)) ) ),
inference(miniscoping,[status(thm)],[f2]) ).
fof(f9,plain,
! [X0,X1] :
( ~ c_in(X0,v_S,tc_set(t_a))
| ~ c_in(X1,v_S,tc_set(t_a))
| c_lessequals(X0,X1,tc_set(t_a)) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f10,plain,
! [X0,X1,X2] : c_in(X0,c_insert(X0,X1,X2),X2),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f11,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)],[f4]) ).
fof(f12,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)],[f5]) ).
fof(f13,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)],[f6]) ).
fof(f14,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)],[f13]) ).
fof(f15,plain,
! [X0,X1] :
( ~ c_in(X1,v_S,tc_set(t_a))
| c_lessequals(X1,c_Main_OsubsetI__1(v_S,X0,tc_set(t_a)),tc_set(t_a))
| c_lessequals(v_S,X0,tc_set(tc_set(t_a))) ),
inference(resolution,[status(thm)],[f11,f9]) ).
fof(f16,plain,
! [X0,X1] :
( c_lessequals(v_S,X1,tc_set(tc_set(t_a)))
| c_lessequals(c_Main_OsubsetI__1(v_S,X1,tc_set(t_a)),c_Main_OsubsetI__1(v_S,X0,tc_set(t_a)),tc_set(t_a))
| c_lessequals(v_S,X0,tc_set(tc_set(t_a))) ),
inference(resolution,[status(thm)],[f15,f11]) ).
fof(f17,plain,
! [X0,X1] :
( c_Main_OsubsetI__1(v_S,X1,tc_set(t_a)) = c_Main_OsubsetI__1(v_S,X0,tc_set(t_a))
| ~ c_lessequals(c_Main_OsubsetI__1(v_S,X0,tc_set(t_a)),c_Main_OsubsetI__1(v_S,X1,tc_set(t_a)),tc_set(t_a))
| c_lessequals(v_S,X1,tc_set(tc_set(t_a)))
| c_lessequals(v_S,X0,tc_set(tc_set(t_a))) ),
inference(resolution,[status(thm)],[f16,f14]) ).
fof(f18,plain,
! [X0,X1] :
( c_Main_OsubsetI__1(v_S,X1,tc_set(t_a)) = c_Main_OsubsetI__1(v_S,X0,tc_set(t_a))
| c_lessequals(v_S,X1,tc_set(tc_set(t_a)))
| c_lessequals(v_S,X0,tc_set(tc_set(t_a))) ),
inference(forward_subsumption_resolution,[status(thm)],[f17,f16]) ).
fof(f19,plain,
! [X0,X1] :
( c_Main_OsubsetI__1(v_S,c_insert(X1,c_emptyset,tc_set(t_a)),tc_set(t_a)) = c_Main_OsubsetI__1(v_S,X0,tc_set(t_a))
| c_lessequals(v_S,X0,tc_set(tc_set(t_a))) ),
inference(resolution,[status(thm)],[f18,f7]) ).
fof(f21,plain,
! [X0,X1] : c_Main_OsubsetI__1(v_S,c_insert(X0,c_emptyset,tc_set(t_a)),tc_set(t_a)) = c_Main_OsubsetI__1(v_S,c_insert(X1,c_emptyset,tc_set(t_a)),tc_set(t_a)),
inference(resolution,[status(thm)],[f19,f7]) ).
fof(f32,plain,
! [X0,X1] :
( c_lessequals(v_S,c_insert(X1,c_emptyset,tc_set(t_a)),tc_set(tc_set(t_a)))
| ~ c_in(c_Main_OsubsetI__1(v_S,c_insert(X0,c_emptyset,tc_set(t_a)),tc_set(t_a)),c_insert(X1,c_emptyset,tc_set(t_a)),tc_set(t_a)) ),
inference(paramodulation,[status(thm)],[f21,f12]) ).
fof(f49,plain,
! [X0,X1] : ~ c_in(c_Main_OsubsetI__1(v_S,c_insert(X0,c_emptyset,tc_set(t_a)),tc_set(t_a)),c_insert(X1,c_emptyset,tc_set(t_a)),tc_set(t_a)),
inference(forward_subsumption_resolution,[status(thm)],[f32,f7]) ).
fof(f90,plain,
$false,
inference(resolution,[status(thm)],[f49,f10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET839-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.36 % Computer : n010.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Mon Sep 21 05:41:11 UTC 2026
% 0.11/0.36 % CPUTime :
% 0.11/0.37 % Drodi V4.1.1
% 0.11/0.39 % Refutation found
% 0.11/0.39 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.11/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.42 % Elapsed time: 0.047797 seconds
% 0.14/0.42 % CPU time: 0.140916 seconds
% 0.14/0.42 % Total memory used: 80.092 MB
% 0.14/0.42 % Net memory used: 79.588 MB
%------------------------------------------------------------------------------