%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET851-2 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n012.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 02:10:49 PM UTC 2026
% Result : Unsatisfiable 0.03s 0.32s
% Output : CNFRefutation 0.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 11
% Syntax : Number of formulae : 34 ( 13 unt; 4 def)
% Number of atoms : 61 ( 5 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 52 ( 25 ~; 23 |; 0 &)
% ( 4 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 5 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-3 aty)
% Number of variables : 18 ( 18 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [V_A,T_a] : c_lessequals(V_A,V_A,tc_set(T_a)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [V_x,V_y,T_a,V_S] :
( c_lessequals(V_x,c_Zorn_Osucc(V_S,V_y,T_a),tc_set(tc_set(T_a)))
| ~ c_lessequals(V_x,V_y,tc_set(tc_set(T_a))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,negated_conjecture,
c_in(v_x,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,negated_conjecture,
~ c_lessequals(c_Zorn_Osucc(v_S,v_x,t_a),v_m,tc_set(tc_set(t_a))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,negated_conjecture,
~ c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),c_Zorn_Osucc(v_S,v_x,t_a),tc_set(tc_set(t_a))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,negated_conjecture,
( c_lessequals(v_x,v_m,tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),v_x,tc_set(tc_set(t_a))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,negated_conjecture,
! [V_U] :
( ~ c_in(V_U,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| ~ c_lessequals(V_U,v_m,tc_set(tc_set(t_a)))
| V_U = v_m
| c_lessequals(c_Zorn_Osucc(v_S,V_U,t_a),v_m,tc_set(tc_set(t_a))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,plain,
! [X0,X1] : c_lessequals(X0,X0,tc_set(X1)),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f9,plain,
! [V_x,V_y,T_a] :
( ! [V_S] : c_lessequals(V_x,c_Zorn_Osucc(V_S,V_y,T_a),tc_set(tc_set(T_a)))
| ~ c_lessequals(V_x,V_y,tc_set(tc_set(T_a))) ),
inference(miniscoping,[status(thm)],[f2]) ).
fof(f10,plain,
! [X0,X1,X2,X3] :
( c_lessequals(X0,c_Zorn_Osucc(X3,X1,X2),tc_set(tc_set(X2)))
| ~ c_lessequals(X0,X1,tc_set(tc_set(X2))) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f11,plain,
c_in(v_x,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f12,plain,
~ c_lessequals(c_Zorn_Osucc(v_S,v_x,t_a),v_m,tc_set(tc_set(t_a))),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f13,plain,
~ c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),c_Zorn_Osucc(v_S,v_x,t_a),tc_set(tc_set(t_a))),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f14,plain,
( c_lessequals(v_x,v_m,tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),v_x,tc_set(tc_set(t_a))) ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f15,plain,
! [X0] :
( ~ c_in(X0,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| ~ c_lessequals(X0,v_m,tc_set(tc_set(t_a)))
| X0 = v_m
| c_lessequals(c_Zorn_Osucc(v_S,X0,t_a),v_m,tc_set(tc_set(t_a))) ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f16,definition,
( sQ0_spl
<=> c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),v_x,tc_set(tc_set(t_a))) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f17,plain,
( ~ sQ0_spl
| c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),v_x,tc_set(tc_set(t_a))) ),
inference(component_clause,[status(thm)],[f16]) ).
fof(f19,definition,
( sQ1_spl
<=> c_lessequals(v_x,v_m,tc_set(tc_set(t_a))) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f22,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f14,f16,f19]) ).
fof(f23,plain,
~ c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),v_x,tc_set(tc_set(t_a))),
inference(resolution,[status(thm)],[f10,f13]) ).
fof(f24,plain,
( ~ sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f23,f17]) ).
fof(f25,plain,
~ sQ0_spl,
inference(contradiction_clause,[status(thm)],[f24]) ).
fof(f26,plain,
( ~ c_in(v_x,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| ~ c_lessequals(v_x,v_m,tc_set(tc_set(t_a)))
| v_x = v_m ),
inference(resolution,[status(thm)],[f15,f12]) ).
fof(f27,definition,
( sQ2_spl
<=> v_x = v_m ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f28,plain,
( ~ sQ2_spl
| v_x = v_m ),
inference(component_clause,[status(thm)],[f27]) ).
fof(f30,definition,
( sQ3_spl
<=> c_in(v_x,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f32,plain,
( sQ3_spl
| ~ c_in(v_x,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))) ),
inference(component_clause,[status(thm)],[f30]) ).
fof(f33,plain,
( ~ sQ3_spl
| ~ sQ1_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f26,f27,f19,f30]) ).
fof(f36,plain,
( ~ sQ2_spl
| ~ c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),c_Zorn_Osucc(v_S,v_m,t_a),tc_set(tc_set(t_a))) ),
inference(backward_demodulation,[status(thm)],[f28,f13]) ).
fof(f39,plain,
( ~ sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f36,f8]) ).
fof(f40,plain,
~ sQ2_spl,
inference(contradiction_clause,[status(thm)],[f39]) ).
fof(f41,plain,
( sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f11,f32]) ).
fof(f42,plain,
sQ3_spl,
inference(contradiction_clause,[status(thm)],[f41]) ).
fof(f43,plain,
$false,
inference(sat_refutation,[status(thm)],[f22,f25,f33,f40,f42]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SET851-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.02 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.03/0.29 % Computer : n012.cluster.edu
% 0.03/0.29 % Model : x86_64 x86_64
% 0.03/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/0.29 % Memory : 8046.5625MB
% 0.03/0.29 % OS : Linux 6.8.0-71-generic
% 0.03/0.29 % CPULimit : 300
% 0.03/0.29 % WCLimit : 300
% 0.03/0.29 % DateTime : Mon Sep 21 05:41:21 UTC 2026
% 0.03/0.29 % CPUTime :
% 0.03/0.30 % Drodi V4.1.1
% 0.03/0.32 % Refutation found
% 0.03/0.32 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.03/0.32 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.07/0.34 % Elapsed time: 0.040052 seconds
% 0.07/0.34 % CPU time: 0.087407 seconds
% 0.07/0.34 % Total memory used: 79.951 MB
% 0.07/0.34 % Net memory used: 79.466 MB
%------------------------------------------------------------------------------