%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET839-1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n009.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 22.65s 3.48s
% Output : CNFRefutation 11.73s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 12
% Syntax : Number of formulae : 51 ( 17 unt; 2 def)
% Number of atoms : 103 ( 16 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 97 ( 45 ~; 50 |; 0 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 3 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-3 aty)
% Number of variables : 86 ( 86 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f163,axiom,
! [V_X,V_C,T_a,V_A] :
( c_in(V_A,V_X,T_a)
| ~ c_in(V_A,c_Inter(V_C,T_a),T_a)
| ~ c_in(V_X,V_C,tc_set(T_a)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f174,axiom,
! [V_a,T_a] : ~ c_in(V_a,c_emptyset,T_a),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p') ).
fof(f226,axiom,
! [T_a] : c_in(c_emptyset,c_Finite__Set_OFinites,tc_set(T_a)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f299,axiom,
! [V_A,T_a] : c_lessequals(c_emptyset,V_A,tc_set(T_a)),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p') ).
fof(f1358,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(f1359,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(f1581,plain,
! [V_X,T_a,V_A] :
( c_in(V_A,V_X,T_a)
| ! [V_C] :
( ~ c_in(V_A,c_Inter(V_C,T_a),T_a)
| ~ c_in(V_X,V_C,tc_set(T_a)) ) ),
inference(miniscoping,[status(thm)],[f163]) ).
fof(f1582,plain,
! [X0,X1,X2,X3] :
( c_in(X3,X0,X2)
| ~ c_in(X3,c_Inter(X1,X2),X2)
| ~ c_in(X0,X1,tc_set(X2)) ),
inference(cnf_transformation,[status(thm)],[f1581]) ).
fof(f1599,plain,
! [X0,X1] : ~ c_in(X0,c_emptyset,X1),
inference(cnf_transformation,[status(thm)],[f174]) ).
fof(f1602,plain,
! [X0,X1,X2] : c_in(X0,c_insert(X0,X1,X2),X2),
inference(cnf_transformation,[status(thm)],[f176]) ).
fof(f1675,plain,
! [X0] : c_in(c_emptyset,c_Finite__Set_OFinites,tc_set(X0)),
inference(cnf_transformation,[status(thm)],[f226]) ).
fof(f1762,plain,
! [X0,X1] : c_lessequals(c_emptyset,X0,tc_set(X1)),
inference(cnf_transformation,[status(thm)],[f299]) ).
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_a)),tc_set(tc_set(t_a))),
inference(cnf_transformation,[status(thm)],[f1358]) ).
fof(f2836,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)],[f1359]) ).
fof(f2837,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)],[f2836]) ).
fof(f2891,plain,
! [X0,X1] :
( X0 = c_emptyset
| ~ c_lessequals(X0,c_emptyset,tc_set(X1)) ),
inference(resolution,[status(thm)],[f1777,f1762]) ).
fof(f6810,plain,
! [X0,X1] :
( c_in(X0,c_emptyset,X1)
| ~ c_in(X0,c_Inter(c_Finite__Set_OFinites,X1),X1) ),
inference(resolution,[status(thm)],[f1582,f1675]) ).
fof(f6849,plain,
! [X0,X1] : ~ c_in(X0,c_Inter(c_Finite__Set_OFinites,X1),X1),
inference(forward_subsumption_resolution,[status(thm)],[f6810,f1599]) ).
fof(f17414,plain,
! [X0,X1] : c_lessequals(c_Inter(c_Finite__Set_OFinites,X0),X1,tc_set(X0)),
inference(resolution,[status(thm)],[f1774,f6849]) ).
fof(f17457,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)],[f1774,f2837]) ).
fof(f17842,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)],[f17457,f1774]) ).
fof(f17891,plain,
! [X0] : c_Inter(c_Finite__Set_OFinites,X0) = c_emptyset,
inference(resolution,[status(thm)],[f17414,f2891]) ).
fof(f18343,plain,
! [X0,X1] :
( c_Main_OsubsetI__1(v_S,X0,tc_set(t_a)) = c_Main_OsubsetI__1(v_S,X1,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)],[f17842,f1777]) ).
fof(f18350,plain,
! [X0,X1] :
( c_Main_OsubsetI__1(v_S,X0,tc_set(t_a)) = c_Main_OsubsetI__1(v_S,X1,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)],[f18343,f17842]) ).
fof(f18511,plain,
! [X0] :
( v_S = c_emptyset
| c_Main_OsubsetI__1(v_S,c_emptyset,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)],[f18350,f2891]) ).
fof(f18553,definition,
( sQ120_spl
<=> v_S = c_emptyset ),
introduced(definition,[new_symbols(definition,[sQ120_spl])],[split_symbol_definition]) ).
fof(f18554,plain,
( ~ sQ120_spl
| v_S = c_emptyset ),
inference(component_clause,[status(thm)],[f18553]) ).
fof(f18557,definition,
! [X0] :
( sQ121_spl
<=> ( c_Main_OsubsetI__1(v_S,c_emptyset,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))) ) ),
introduced(definition,[new_symbols(definition,[sQ121_spl])],[split_symbol_definition]) ).
fof(f18558,plain,
! [X0] :
( ~ sQ121_spl
| c_Main_OsubsetI__1(v_S,c_emptyset,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(component_clause,[status(thm)],[f18557]) ).
fof(f18560,plain,
( sQ120_spl
| sQ121_spl ),
inference(split_clause,[status(thm)],[f18511,f18557,f18553]) ).
fof(f18665,plain,
! [X0] :
( ~ sQ120_spl
| c_Inter(c_Finite__Set_OFinites,X0) = v_S ),
inference(backward_demodulation,[status(thm)],[f18554,f17891]) ).
fof(f18936,plain,
! [X0] :
( ~ sQ120_spl
| ~ c_lessequals(v_S,c_insert(X0,v_S,tc_set(t_a)),tc_set(tc_set(t_a))) ),
inference(backward_demodulation,[status(thm)],[f18554,f2835]) ).
fof(f19337,plain,
! [X0,X1] : c_lessequals(c_emptyset,X0,tc_set(X1)),
inference(resolution,[status(thm)],[f1599,f1774]) ).
fof(f19404,plain,
! [X0] :
( ~ sQ121_spl
| c_Main_OsubsetI__1(v_S,c_emptyset,tc_set(t_a)) = c_Main_OsubsetI__1(v_S,c_insert(X0,c_emptyset,tc_set(t_a)),tc_set(t_a)) ),
inference(resolution,[status(thm)],[f18558,f2835]) ).
fof(f19440,plain,
( ~ sQ120_spl
| c_emptyset = v_S ),
inference(forward_demodulation,[status(thm)],[f17891,f18665]) ).
fof(f19544,plain,
! [X0,X1] :
( ~ sQ120_spl
| c_lessequals(v_S,X0,tc_set(X1)) ),
inference(forward_demodulation,[status(thm)],[f19440,f19337]) ).
fof(f19578,plain,
( ~ sQ120_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f18936,f19544]) ).
fof(f19579,plain,
~ sQ120_spl,
inference(contradiction_clause,[status(thm)],[f19578]) ).
fof(f19669,plain,
! [X0] :
( ~ sQ121_spl
| c_lessequals(v_S,c_insert(X0,c_emptyset,tc_set(t_a)),tc_set(tc_set(t_a)))
| ~ c_in(c_Main_OsubsetI__1(v_S,c_emptyset,tc_set(t_a)),c_insert(X0,c_emptyset,tc_set(t_a)),tc_set(t_a)) ),
inference(paramodulation,[status(thm)],[f19404,f1775]) ).
fof(f19671,plain,
! [X0] :
( ~ sQ121_spl
| ~ c_in(c_Main_OsubsetI__1(v_S,c_emptyset,tc_set(t_a)),c_insert(X0,c_emptyset,tc_set(t_a)),tc_set(t_a)) ),
inference(forward_subsumption_resolution,[status(thm)],[f19669,f2835]) ).
fof(f19806,plain,
( ~ sQ121_spl
| $false ),
inference(resolution,[status(thm)],[f19671,f1602]) ).
fof(f19807,plain,
~ sQ121_spl,
inference(contradiction_clause,[status(thm)],[f19806]) ).
fof(f19808,plain,
$false,
inference(sat_refutation,[status(thm)],[f18560,f19579,f19807]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET839-1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.55 % Computer : n009.cluster.edu
% 0.10/0.55 % Model : x86_64 x86_64
% 0.10/0.55 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.55 % Memory : 8046.5625MB
% 0.10/0.55 % OS : Linux 6.8.0-71-generic
% 0.10/0.55 % CPULimit : 300
% 0.10/0.55 % WCLimit : 300
% 0.10/0.55 % DateTime : Mon Sep 21 05:40:58 UTC 2026
% 0.10/0.56 % CPUTime :
% 0.14/0.58 % Drodi V4.1.1
% 22.65/3.48 % Refutation found
% 22.65/3.48 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 22.65/3.48 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 2.08/3.97 % Elapsed time: 3.400111 seconds
% 2.08/3.97 % CPU time: 23.587018 seconds
% 2.08/3.97 % Total memory used: 423.687 MB
% 2.08/3.97 % Net memory used: 388.147 MB
%------------------------------------------------------------------------------