%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWV255-1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : 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 02:47:02 PM UTC 2026
% Result : Unsatisfiable 27.84s 4.09s
% Output : CNFRefutation 27.84s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 18
% Syntax : Number of formulae : 65 ( 17 unt; 2 def)
% Number of atoms : 155 ( 27 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 175 ( 85 ~; 88 |; 0 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 3 prp; 0-3 aty)
% Number of functors : 17 ( 17 usr; 9 con; 0-3 aty)
% Number of variables : 114 ( 114 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f29,axiom,
! [V_A,T_a,V_a] :
( c_in(c_insert(V_a,V_A,T_a),c_Finite__Set_OFinites,tc_set(T_a))
| ~ c_in(V_A,c_Finite__Set_OFinites,tc_set(T_a)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f68,axiom,
! [T_a,V_x] :
( c_lessequals(V_x,V_x,T_a)
| ~ class_Orderings_Oorder(T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f95,axiom,
! [V_k] : c_in(c_SetInterval_OlessThan(V_k,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f243,axiom,
class_Orderings_Olinorder(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f249,axiom,
! [T_1] : class_Orderings_Oorder(tc_set(T_1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f1259,axiom,
! [T_a,V_U,V_A,V_x] :
( V_A = c_emptyset
| c_lessequals(V_U,V_x,T_a)
| ~ c_lessequals(c_Finite__Set_OMax(V_A,T_a),V_x,T_a)
| ~ c_in(V_A,c_Finite__Set_OFinites,tc_set(T_a))
| ~ c_in(V_U,V_A,T_a)
| ~ class_Orderings_Olinorder(T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f1276,axiom,
! [V_A,T_a] :
( V_A = c_emptyset
| c_Finite__Set_Ocard(V_A,T_a) != c_0
| ~ c_in(V_A,c_Finite__Set_OFinites,tc_set(T_a)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f1279,axiom,
! [V_A,T_a] :
( c_Finite__Set_Ocard(V_A,T_a) = c_0
| c_in(V_A,c_Finite__Set_OFinites,tc_set(T_a)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2673,axiom,
! [V_a,V_A,T_a] : c_emptyset != c_insert(V_a,V_A,T_a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2684,axiom,
! [V_x,V_A,T_a] : c_in(V_x,c_insert(V_x,V_A,T_a),T_a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2688,axiom,
! [V_x,V_A,T_a,V_B] :
( c_in(V_x,V_B,T_a)
| ~ c_lessequals(c_insert(V_x,V_A,T_a),V_B,tc_set(T_a)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2689,axiom,
! [V_x,V_A,T_a,V_B] :
( c_lessequals(V_A,V_B,tc_set(T_a))
| ~ c_lessequals(c_insert(V_x,V_A,T_a),V_B,tc_set(T_a)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2788,negated_conjecture,
! [V_U] : c_lessequals(V_U,v_xb(V_U),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2789,negated_conjecture,
! [V_U] :
( ~ c_lessequals(v_x,V_U,tc_nat)
| ~ c_in(c_Message_Omsg_ONonce(V_U),c_Message_Oparts(c_insert(v_msg1,c_emptyset,tc_Message_Omsg)),tc_Message_Omsg) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2790,negated_conjecture,
! [V_U] :
( ~ c_lessequals(v_xa,V_U,tc_nat)
| ~ c_in(c_Message_Omsg_ONonce(V_U),c_Message_Oparts(c_insert(v_msg2,c_emptyset,tc_Message_Omsg)),tc_Message_Omsg) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2791,negated_conjecture,
! [V_U] :
( c_in(c_Message_Omsg_ONonce(v_xb(V_U)),c_Message_Oparts(c_insert(v_msg1,c_emptyset,tc_Message_Omsg)),tc_Message_Omsg)
| c_in(c_Message_Omsg_ONonce(v_xb(V_U)),c_Message_Oparts(c_insert(v_msg2,c_emptyset,tc_Message_Omsg)),tc_Message_Omsg) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2834,plain,
! [V_A,T_a] :
( ! [V_a] : c_in(c_insert(V_a,V_A,T_a),c_Finite__Set_OFinites,tc_set(T_a))
| ~ c_in(V_A,c_Finite__Set_OFinites,tc_set(T_a)) ),
inference(miniscoping,[status(thm)],[f29]) ).
fof(f2835,plain,
! [X0,X1,X2] :
( c_in(c_insert(X2,X0,X1),c_Finite__Set_OFinites,tc_set(X1))
| ~ c_in(X0,c_Finite__Set_OFinites,tc_set(X1)) ),
inference(cnf_transformation,[status(thm)],[f2834]) ).
fof(f2882,plain,
! [T_a] :
( ! [V_x] : c_lessequals(V_x,V_x,T_a)
| ~ class_Orderings_Oorder(T_a) ),
inference(miniscoping,[status(thm)],[f68]) ).
fof(f2883,plain,
! [X0,X1] :
( c_lessequals(X1,X1,X0)
| ~ class_Orderings_Oorder(X0) ),
inference(cnf_transformation,[status(thm)],[f2882]) ).
fof(f2914,plain,
! [X0] : c_in(c_SetInterval_OlessThan(X0,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)),
inference(cnf_transformation,[status(thm)],[f95]) ).
fof(f3074,plain,
class_Orderings_Olinorder(tc_nat),
inference(cnf_transformation,[status(thm)],[f243]) ).
fof(f3081,plain,
! [X0] : class_Orderings_Oorder(tc_set(X0)),
inference(cnf_transformation,[status(thm)],[f249]) ).
fof(f4114,plain,
! [V_A] :
( V_A = c_emptyset
| ! [T_a,V_U,V_x] :
( c_lessequals(V_U,V_x,T_a)
| ~ c_lessequals(c_Finite__Set_OMax(V_A,T_a),V_x,T_a)
| ~ c_in(V_A,c_Finite__Set_OFinites,tc_set(T_a))
| ~ c_in(V_U,V_A,T_a)
| ~ class_Orderings_Olinorder(T_a) ) ),
inference(miniscoping,[status(thm)],[f1259]) ).
fof(f4115,plain,
! [X0,X1,X2,X3] :
( X2 = c_emptyset
| c_lessequals(X1,X3,X0)
| ~ c_lessequals(c_Finite__Set_OMax(X2,X0),X3,X0)
| ~ c_in(X2,c_Finite__Set_OFinites,tc_set(X0))
| ~ c_in(X1,X2,X0)
| ~ class_Orderings_Olinorder(X0) ),
inference(cnf_transformation,[status(thm)],[f4114]) ).
fof(f4148,plain,
! [V_A] :
( V_A = c_emptyset
| ! [T_a] :
( c_Finite__Set_Ocard(V_A,T_a) != c_0
| ~ c_in(V_A,c_Finite__Set_OFinites,tc_set(T_a)) ) ),
inference(miniscoping,[status(thm)],[f1276]) ).
fof(f4149,plain,
! [X0,X1] :
( X0 = c_emptyset
| c_Finite__Set_Ocard(X0,X1) != c_0
| ~ c_in(X0,c_Finite__Set_OFinites,tc_set(X1)) ),
inference(cnf_transformation,[status(thm)],[f4148]) ).
fof(f4152,plain,
! [X0,X1] :
( c_Finite__Set_Ocard(X0,X1) = c_0
| c_in(X0,c_Finite__Set_OFinites,tc_set(X1)) ),
inference(cnf_transformation,[status(thm)],[f1279]) ).
fof(f6059,plain,
! [X0,X1,X2] : c_emptyset != c_insert(X0,X1,X2),
inference(cnf_transformation,[status(thm)],[f2673]) ).
fof(f6076,plain,
! [X0,X1,X2] : c_in(X0,c_insert(X0,X1,X2),X2),
inference(cnf_transformation,[status(thm)],[f2684]) ).
fof(f6081,plain,
! [V_x,T_a,V_B] :
( c_in(V_x,V_B,T_a)
| ! [V_A] : ~ c_lessequals(c_insert(V_x,V_A,T_a),V_B,tc_set(T_a)) ),
inference(miniscoping,[status(thm)],[f2688]) ).
fof(f6082,plain,
! [X0,X1,X2,X3] :
( c_in(X0,X3,X2)
| ~ c_lessequals(c_insert(X0,X1,X2),X3,tc_set(X2)) ),
inference(cnf_transformation,[status(thm)],[f6081]) ).
fof(f6083,plain,
! [V_A,T_a,V_B] :
( c_lessequals(V_A,V_B,tc_set(T_a))
| ! [V_x] : ~ c_lessequals(c_insert(V_x,V_A,T_a),V_B,tc_set(T_a)) ),
inference(miniscoping,[status(thm)],[f2689]) ).
fof(f6084,plain,
! [X0,X1,X2,X3] :
( c_lessequals(X1,X3,tc_set(X2))
| ~ c_lessequals(c_insert(X0,X1,X2),X3,tc_set(X2)) ),
inference(cnf_transformation,[status(thm)],[f6083]) ).
fof(f6203,plain,
! [X0] : c_lessequals(X0,v_xb(X0),tc_nat),
inference(cnf_transformation,[status(thm)],[f2788]) ).
fof(f6204,plain,
! [X0] :
( ~ c_lessequals(v_x,X0,tc_nat)
| ~ c_in(c_Message_Omsg_ONonce(X0),c_Message_Oparts(c_insert(v_msg1,c_emptyset,tc_Message_Omsg)),tc_Message_Omsg) ),
inference(cnf_transformation,[status(thm)],[f2789]) ).
fof(f6205,plain,
! [X0] :
( ~ c_lessequals(v_xa,X0,tc_nat)
| ~ c_in(c_Message_Omsg_ONonce(X0),c_Message_Oparts(c_insert(v_msg2,c_emptyset,tc_Message_Omsg)),tc_Message_Omsg) ),
inference(cnf_transformation,[status(thm)],[f2790]) ).
fof(f6206,plain,
! [X0] :
( c_in(c_Message_Omsg_ONonce(v_xb(X0)),c_Message_Oparts(c_insert(v_msg1,c_emptyset,tc_Message_Omsg)),tc_Message_Omsg)
| c_in(c_Message_Omsg_ONonce(v_xb(X0)),c_Message_Oparts(c_insert(v_msg2,c_emptyset,tc_Message_Omsg)),tc_Message_Omsg) ),
inference(cnf_transformation,[status(thm)],[f2791]) ).
fof(f6216,plain,
! [X0] :
( ~ c_lessequals(v_x,v_xb(X0),tc_nat)
| c_in(c_Message_Omsg_ONonce(v_xb(X0)),c_Message_Oparts(c_insert(v_msg2,c_emptyset,tc_Message_Omsg)),tc_Message_Omsg) ),
inference(resolution,[status(thm)],[f6206,f6204]) ).
fof(f6217,plain,
! [X0] :
( ~ c_lessequals(v_xa,v_xb(X0),tc_nat)
| ~ c_lessequals(v_x,v_xb(X0),tc_nat) ),
inference(resolution,[status(thm)],[f6216,f6205]) ).
fof(f9896,plain,
! [X0,X1,X2] :
( c_lessequals(X1,c_insert(X2,X1,X0),tc_set(X0))
| ~ class_Orderings_Oorder(tc_set(X0)) ),
inference(resolution,[status(thm)],[f2883,f6084]) ).
fof(f9917,plain,
! [X0,X1,X2] : c_lessequals(X0,c_insert(X1,X0,X2),tc_set(X2)),
inference(forward_subsumption_resolution,[status(thm)],[f9896,f3081]) ).
fof(f9956,plain,
! [X0,X1,X2,X3] : c_in(X0,c_insert(X1,c_insert(X0,X2,X3),X3),X3),
inference(resolution,[status(thm)],[f9917,f6082]) ).
fof(f23668,definition,
( sQ198_spl
<=> class_Orderings_Olinorder(tc_nat) ),
introduced(definition,[new_symbols(definition,[sQ198_spl])],[split_symbol_definition]) ).
fof(f23670,plain,
( sQ198_spl
| ~ class_Orderings_Olinorder(tc_nat) ),
inference(component_clause,[status(thm)],[f23668]) ).
fof(f26412,plain,
! [X0,X1] :
( X1 = c_emptyset
| c_lessequals(X0,v_xb(c_Finite__Set_OMax(X1,tc_nat)),tc_nat)
| ~ c_in(X1,c_Finite__Set_OFinites,tc_set(tc_nat))
| ~ c_in(X0,X1,tc_nat)
| ~ class_Orderings_Olinorder(tc_nat) ),
inference(resolution,[status(thm)],[f4115,f6203]) ).
fof(f26448,definition,
! [X0,X1] :
( sQ292_spl
<=> ( X1 = c_emptyset
| c_lessequals(X0,v_xb(c_Finite__Set_OMax(X1,tc_nat)),tc_nat)
| ~ c_in(X1,c_Finite__Set_OFinites,tc_set(tc_nat))
| ~ c_in(X0,X1,tc_nat) ) ),
introduced(definition,[new_symbols(definition,[sQ292_spl])],[split_symbol_definition]) ).
fof(f26449,plain,
! [X0,X1] :
( ~ sQ292_spl
| X1 = c_emptyset
| c_lessequals(X0,v_xb(c_Finite__Set_OMax(X1,tc_nat)),tc_nat)
| ~ c_in(X1,c_Finite__Set_OFinites,tc_set(tc_nat))
| ~ c_in(X0,X1,tc_nat) ),
inference(component_clause,[status(thm)],[f26448]) ).
fof(f26451,plain,
( sQ292_spl
| ~ sQ198_spl ),
inference(split_clause,[status(thm)],[f26412,f23668,f26448]) ).
fof(f26457,plain,
( sQ198_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f23670,f3074]) ).
fof(f26458,plain,
sQ198_spl,
inference(contradiction_clause,[status(thm)],[f26457]) ).
fof(f27063,plain,
! [X0] :
( ~ sQ292_spl
| ~ c_lessequals(v_xa,v_xb(c_Finite__Set_OMax(X0,tc_nat)),tc_nat)
| X0 = c_emptyset
| ~ c_in(X0,c_Finite__Set_OFinites,tc_set(tc_nat))
| ~ c_in(v_x,X0,tc_nat) ),
inference(resolution,[status(thm)],[f26449,f6217]) ).
fof(f27425,plain,
! [X0] :
( ~ sQ292_spl
| X0 = c_emptyset
| ~ c_in(X0,c_Finite__Set_OFinites,tc_set(tc_nat))
| ~ c_in(v_xa,X0,tc_nat)
| X0 = c_emptyset
| ~ c_in(X0,c_Finite__Set_OFinites,tc_set(tc_nat))
| ~ c_in(v_x,X0,tc_nat) ),
inference(resolution,[status(thm)],[f27063,f26449]) ).
fof(f27426,plain,
! [X0] :
( ~ sQ292_spl
| ~ c_in(v_xa,X0,tc_nat)
| X0 = c_emptyset
| ~ c_in(X0,c_Finite__Set_OFinites,tc_set(tc_nat))
| ~ c_in(v_x,X0,tc_nat) ),
inference(duplicate_literals_removal,[status(thm)],[f27425]) ).
fof(f27888,plain,
! [X0] :
( ~ sQ292_spl
| ~ c_in(v_xa,X0,tc_nat)
| X0 = c_emptyset
| ~ c_in(v_x,X0,tc_nat)
| c_Finite__Set_Ocard(X0,tc_nat) = c_0 ),
inference(resolution,[status(thm)],[f4152,f27426]) ).
fof(f27926,plain,
! [X0] :
( ~ sQ292_spl
| ~ c_in(v_xa,c_insert(v_x,X0,tc_nat),tc_nat)
| c_insert(v_x,X0,tc_nat) = c_emptyset
| c_Finite__Set_Ocard(c_insert(v_x,X0,tc_nat),tc_nat) = c_0 ),
inference(resolution,[status(thm)],[f27888,f6076]) ).
fof(f27974,plain,
! [X0] :
( ~ sQ292_spl
| ~ c_in(v_xa,c_insert(v_x,X0,tc_nat),tc_nat)
| c_Finite__Set_Ocard(c_insert(v_x,X0,tc_nat),tc_nat) = c_0 ),
inference(forward_subsumption_resolution,[status(thm)],[f27926,f6059]) ).
fof(f28205,plain,
! [X0] :
( ~ sQ292_spl
| c_Finite__Set_Ocard(c_insert(v_x,c_insert(v_xa,X0,tc_nat),tc_nat),tc_nat) = c_0 ),
inference(resolution,[status(thm)],[f27974,f9956]) ).
fof(f28220,plain,
! [X0] :
( ~ sQ292_spl
| c_insert(v_x,c_insert(v_xa,X0,tc_nat),tc_nat) = c_emptyset
| ~ c_in(c_insert(v_x,c_insert(v_xa,X0,tc_nat),tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)) ),
inference(resolution,[status(thm)],[f28205,f4149]) ).
fof(f28225,plain,
! [X0] :
( ~ sQ292_spl
| ~ c_in(c_insert(v_x,c_insert(v_xa,X0,tc_nat),tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)) ),
inference(forward_subsumption_resolution,[status(thm)],[f28220,f6059]) ).
fof(f28243,plain,
! [X0] :
( ~ sQ292_spl
| ~ c_in(c_insert(v_xa,X0,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)) ),
inference(resolution,[status(thm)],[f28225,f2835]) ).
fof(f28248,plain,
! [X0] :
( ~ sQ292_spl
| ~ c_in(X0,c_Finite__Set_OFinites,tc_set(tc_nat)) ),
inference(resolution,[status(thm)],[f28243,f2835]) ).
fof(f28289,plain,
( ~ sQ292_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f2914,f28248]) ).
fof(f28313,plain,
~ sQ292_spl,
inference(contradiction_clause,[status(thm)],[f28289]) ).
fof(f28314,plain,
$false,
inference(sat_refutation,[status(thm)],[f26451,f26458,f28313]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV255-1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.36 % Computer : n008.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 08:37:10 UTC 2026
% 0.11/0.36 % CPUTime :
% 0.14/0.49 % Drodi V4.1.1
% 27.84/4.09 % Refutation found
% 27.84/4.09 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 27.84/4.09 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 28.50/4.20 % Elapsed time: 3.815940 seconds
% 28.50/4.20 % CPU time: 29.057401 seconds
% 28.50/4.20 % Total memory used: 649.898 MB
% 28.50/4.20 % Net memory used: 628.718 MB
%------------------------------------------------------------------------------